premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
If someone is either not rich or generous then fred is happy and vice versa. If someone is not happy then lucy is either tall or not generous and vice versa. Everyone who is kind or wise is generous and vice versa. If someone is not strong then lucy is either not old or not curious and vice versa. Everyone who is both curious and kind is curious or patient and vice versa. Everyone who is humble or creative is both strong and brave. If alice is wise then someone is not rich or not humble and vice versa. If lucy is both not calm and rich then someone is either kind or rich. Everyone who is strong is either not curious or old. Everyone who is creative is either not curious or not old and vice versa. Everyone who is tall or brave is either tall or rich and vice versa. Everyone who is both not old and not humble is brave and vice versa. If fred is both happy and strong then susan is not curious. Fred is not patient or not strong. Someone is both not tall and not calm. Someone is not calm. Someone is either not old or not tall. Paul is not funny or wise. Someone is not humble. | Fred is not strong. | contradiction | ((?[X]:((~rich(X)<~>generous(X))))<=>(happy(fred)))&
((?[X]:(~happy(X)))<=>((tall(lucy)<~>~generous(lucy))))&
(![X]:((kind(X)|wise(X))<=>generous(X)))&
((?[X]:(~strong(X)))<=>((~old(lucy)<~>~curious(lucy))))&
(![X]:((curious(X)&kind(X))<=>(curious(X)|patient(X))))&
(![X]:((humble(X)|creative(X))=>(strong(X)&brave(X))))&
((wise(alice))<=>(?[X]:((~rich(X)|~humble(X)))))&
(((~calm(lucy)&rich(lucy)))=>(?[X]:((kind(X)<~>rich(X)))))&
(![X]:(strong(X)=>(~curious(X)<~>old(X))))&
(![X]:(creative(X)<=>(~curious(X)<~>~old(X))))&
(![X]:((tall(X)|brave(X))<=>(tall(X)<~>rich(X))))&
(![X]:((~old(X)&~humble(X))<=>brave(X)))&
(((happy(fred)&strong(fred)))=>(~curious(susan)))&
((~patient(fred)|~strong(fred)))&
(?[X]:((~tall(X)&~calm(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~old(X)<~>~tall(X))))&
((~funny(paul)|wise(paul)))&
(?[X]:(~humble(X))) | ~strong(fred) | [
"p3",
"p5",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5229130893228259057876240
% SZS output start Proof for 5229130893228259057876240
4. ? [X0] : ~strong(X0) <=> (~old(lucy) <~> ~curious(lucy)) [input p3]
6. ! [X0] : ((creative(X0) | humble(X0)) => (brave(X0) & strong(X0))) [input p5]
9. ! [X0] : (strong(X0) => (~curious(X0) <~> old(X0))) [input p8]
10. ! [X0] : (creative(X0) <=> (~curious(X0) <~> ~old(X0))) [input p9]
20. ~strong(fred) [input hypothesis]
21. ! [X0] : ((~curious(X0) <~> ~old(X0)) => creative(X0)) [unused predicate definition removal 10]
23. ! [X0] : ((brave(X0) & strong(X0)) | (~creative(X0) & ~humble(X0))) [ennf transformation 6]
26. ! [X0] : ((~curious(X0) <~> old(X0)) | ~strong(X0)) [ennf transformation 9]
27. ! [X0] : (creative(X0) | (~curious(X0) <=> ~old(X0))) [ennf transformation 21]
40. (? [X0] : ~strong(X0) | ((~old(lucy) | curious(lucy)) & (~curious(lucy) | old(lucy)))) & (((curious(lucy) | old(lucy)) & (~curious(lucy) | ~old(lucy))) | ! [X0] : strong(X0)) [nnf transformation 4]
41. (? [X0] : ~strong(X0) | ((~old(lucy) | curious(lucy)) & (~curious(lucy) | old(lucy)))) & (((curious(lucy) | old(lucy)) & (~curious(lucy) | ~old(lucy))) | ! [X1] : strong(X1)) [rectify 40]
42. ? [X0] : ~strong(X0) => ~strong(sK2) [choice axiom]
43. (~strong(sK2) | ((~old(lucy) | curious(lucy)) & (~curious(lucy) | old(lucy)))) & (((curious(lucy) | old(lucy)) & (~curious(lucy) | ~old(lucy))) | ! [X1] : strong(X1)) [skolemisation 41,42]
53. ! [X0] : (((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | ~strong(X0)) [nnf transformation 26]
54. ! [X0] : (creative(X0) | ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0)))) [nnf transformation 27]
79. ~curious(lucy) | ~old(lucy) | strong(X1) [cnf transformation 43]
80. curious(lucy) | old(lucy) | strong(X1) [cnf transformation 43]
89. ~creative(X0) | strong(X0) [cnf transformation 23]
97. ~curious(X0) | old(X0) | ~strong(X0) [cnf transformation 53]
98. ~old(X0) | curious(X0) | ~strong(X0) [cnf transformation 53]
99. ~old(X0) | creative(X0) | curious(X0) [cnf transformation 54]
100. ~curious(X0) | creative(X0) | old(X0) [cnf transformation 54]
118. ~strong(fred) [cnf transformation 20]
163. 10 <=> curious(lucy) [avatar definition]
164. ~curious(lucy) <- (~10) [avatar component clause 163]
165. curious(lucy) <- (10) [avatar component clause 163]
167. 11 <=> old(lucy) [avatar definition]
168. old(lucy) <- (11) [avatar component clause 167]
169. ~old(lucy) <- (~11) [avatar component clause 167]
177. 13 <=> ! [X1] : strong(X1) [avatar definition]
178. strong(X1) <- (13) [avatar component clause 177]
179. 13 | 11 | 10 [avatar split clause 80,163,167,177]
180. 13 | ~11 | ~10 [avatar split clause 79,163,167,177]
223. 23 <=> strong(fred) [avatar definition]
225. ~strong(fred) <- (~23) [avatar component clause 223]
246. ~23 [avatar split clause 118,223]
261. old(lucy) | ~strong(lucy) <- (10) [resolution 97,165]
262. ~strong(lucy) <- (10, ~11) [subsumption resolution 261,169]
280. creative(lucy) | old(lucy) <- (10) [resolution 100,165]
281. creative(lucy) <- (10, ~11) [subsumption resolution 280,169]
284. strong(lucy) <- (10, ~11) [resolution 281,89]
285. $false <- (10, ~11) [subsumption resolution 284,262]
286. ~10 | 11 [avatar contradiction clause 285]
296. creative(lucy) | curious(lucy) <- (11) [resolution 168,99]
297. curious(lucy) | ~strong(lucy) <- (11) [resolution 168,98]
298. creative(lucy) <- (~10, 11) [subsumption resolution 296,164]
299. ~strong(lucy) <- (~10, 11) [subsumption resolution 297,164]
303. strong(lucy) <- (~10, 11) [resolution 298,89]
304. $false <- (~10, 11) [subsumption resolution 303,299]
305. 10 | ~11 [avatar contradiction clause 304]
319. $false <- (13, ~23) [resolution 178,225]
324. ~13 | 23 [avatar contradiction clause 319]
325. $false [avatar sat refutation 179,180,246,286,305,324]
% SZS output end Proof for 5229130893228259057876240
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is either not generous or wise is not tall or rich.
Everyone who is either not wise or not funny is old and vice versa.
If mary is either not strong or not tall then someone is either not calm or not strong and vice versa.
Everyone who is strong is either not old or humble.
Everyone who is not creative or not humble is both not old and not tall.
If someone is not brave or not strong then fred is patient or tall.
Everyone who is either wise or strong is not calm and vice versa.
Everyone who is either strong or not strong is both not creative and curious and vice versa.
If paul is not generous or tall then paul is not happy or not quiet and vice versa.
Everyone who is funny is not funny or not calm and vice versa.
Everyone who is not brave is creative or tall and vice versa.
Everyone who is funny is both happy and not quiet and vice versa.
Everyone who is both not rich and creative is either humble or not funny and vice versa.
If paul is not wise then someone is both not humble and not tall.
Everyone who is both generous and brave is both not calm and rich and vice versa.
If someone is rich then someone is both happy and funny and vice versa.
Someone is both not calm and not strong.
Susan is not tall.
Lucy is either rich or not humble. | Fred is strong. | contradiction | (![X]:((~generous(X)<~>wise(X))=>(~tall(X)|rich(X))))&
(![X]:((~wise(X)<~>~funny(X))<=>old(X)))&
(((~strong(mary)<~>~tall(mary)))<=>(?[X]:((~calm(X)<~>~strong(X)))))&
(![X]:(strong(X)=>(~old(X)<~>humble(X))))&
(![X]:((~creative(X)|~humble(X))=>(~old(X)&~tall(X))))&
((?[X]:((~brave(X)|~strong(X))))=>((patient(fred)|tall(fred))))&
(![X]:((wise(X)<~>strong(X))<=>~calm(X)))&
(![X]:((strong(X)<~>~strong(X))<=>(~creative(X)&curious(X))))&
(((~generous(paul)|tall(paul)))<=>((~happy(paul)|~quiet(paul))))&
(![X]:(funny(X)<=>(~funny(X)|~calm(X))))&
(![X]:(~brave(X)<=>(creative(X)|tall(X))))&
(![X]:(funny(X)<=>(happy(X)&~quiet(X))))&
(![X]:((~rich(X)&creative(X))<=>(humble(X)<~>~funny(X))))&
((~wise(paul))=>(?[X]:((~humble(X)&~tall(X)))))&
(![X]:((generous(X)&brave(X))<=>(~calm(X)&rich(X))))&
((?[X]:(rich(X)))<=>(?[X]:((happy(X)&funny(X)))))&
(?[X]:((~calm(X)&~strong(X))))&
(~tall(susan))&
((rich(lucy)<~>~humble(lucy))) | strong(fred) | [
"p1",
"p4",
"p6",
"p7",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7530058520186854492587662
% SZS output start Proof for 7530058520186854492587662
2. ! [X0] : ((~wise(X0) <~> ~funny(X0)) <=> old(X0)) [input p1]
5. ! [X0] : ((~humble(X0) | ~creative(X0)) => (~tall(X0) & ~old(X0))) [input p4]
7. ! [X0] : ((wise(X0) <~> strong(X0)) <=> ~calm(X0)) [input p6]
8. ! [X0] : ((strong(X0) <~> ~strong(X0)) <=> (curious(X0) & ~creative(X0))) [input p7]
10. ! [X0] : (funny(X0) <=> (~calm(X0) | ~funny(X0))) [input p9]
13. ! [X0] : ((creative(X0) & ~rich(X0)) <=> (humble(X0) <~> ~funny(X0))) [input p12]
20. strong(fred) [input hypothesis]
26. ! [X0] : ((~tall(X0) & ~old(X0)) | (humble(X0) & creative(X0))) [ennf transformation 5]
29. ! [X0] : ((((funny(X0) | wise(X0)) & (~funny(X0) | ~wise(X0))) | ~old(X0)) & (old(X0) | ((~wise(X0) | funny(X0)) & (~funny(X0) | wise(X0))))) [nnf transformation 2]
35. ! [X0] : ((((~strong(X0) | ~wise(X0)) & (strong(X0) | wise(X0))) | calm(X0)) & (~calm(X0) | ((wise(X0) | ~strong(X0)) & (strong(X0) | ~wise(X0))))) [nnf transformation 7]
36. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | (~curious(X0) | creative(X0))) & ((curious(X0) & ~creative(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [nnf transformation 8]
37. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ~curious(X0) | creative(X0)) & ((curious(X0) & ~creative(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [flattening 36]
40. ! [X0] : ((funny(X0) | (calm(X0) & funny(X0))) & ((~calm(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 10]
41. ! [X0] : ((funny(X0) | (calm(X0) & funny(X0))) & (~calm(X0) | ~funny(X0) | ~funny(X0))) [flattening 40]
46. ! [X0] : (((creative(X0) & ~rich(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0)))) & (((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | (~creative(X0) | rich(X0)))) [nnf transformation 13]
47. ! [X0] : (((creative(X0) & ~rich(X0)) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0)))) & (((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | ~creative(X0) | rich(X0))) [flattening 46]
62. ~funny(X0) | old(X0) | wise(X0) [cnf transformation 29]
77. ~old(X0) | humble(X0) [cnf transformation 26]
83. ~strong(X0) | ~wise(X0) | calm(X0) [cnf transformation 35]
84. ~creative(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 37]
85. ~creative(X0) | strong(X0) | strong(X0) [cnf transformation 37]
94. ~calm(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 41]
95. funny(X0) | funny(X0) [cnf transformation 41]
107. creative(X0) | ~funny(X0) | ~humble(X0) [cnf transformation 47]
123. strong(fred) [cnf transformation 20]
124. ~calm(X0) | ~funny(X0) [duplicate literal removal 94]
125. funny(X0) [duplicate literal removal 95]
126. ~creative(X0) | ~strong(X0) [duplicate literal removal 84]
127. ~creative(X0) | strong(X0) [duplicate literal removal 85]
161. ~creative(X0) [subsumption resolution 126,127]
182. ~calm(X0) [subsumption resolution 124,125]
186. ~funny(X0) | ~humble(X0) [subsumption resolution 107,161]
187. ~humble(X0) [subsumption resolution 186,125]
219. old(X0) | wise(X0) [resolution 62,125]
220. wise(X0) | humble(X0) [resolution 219,77]
222. wise(X0) [subsumption resolution 220,187]
237. ~wise(fred) | calm(fred) [resolution 83,123]
240. calm(fred) [subsumption resolution 237,222]
241. $false [subsumption resolution 240,182]
% SZS output end Proof for 7530058520186854492587662
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not wise is not rich.
Everyone who is old is not rich and vice versa.
If fred is patient then lucy is not curious or happy.
Everyone who is both not patient and rich is both creative and not humble and vice versa.
Everyone who is not old or rich is generous or not kind and vice versa.
Everyone who is either not brave or creative is not quiet or quiet and vice versa.
Everyone who is not happy is either generous or not generous.
If john is quiet then someone is either old or kind.
If alice is not kind then alice is either not happy or not generous.
Everyone who is funny is either not calm or not old and vice versa.
If mary is not calm or not brave then someone is both kind and creative and vice versa.
If someone is not generous or creative then john is happy or kind.
Everyone who is either not kind or not tall is either not kind or not generous.
Everyone who is either not rich or wise is calm.
If paul is either generous or kind then alice is either not calm or not tall.
Everyone who is both kind and wise is either generous or not funny and vice versa.
Someone is either not wise or humble.
Someone is funny.
Fred is either not calm or not brave.
Someone is either calm or rich.
Someone is rich.
Someone is not humble or not strong. | Paul is wise. | entailment | (![X]:((strong(X)|~wise(X))=>~rich(X)))&
(![X]:(old(X)<=>~rich(X)))&
((patient(fred))=>((~curious(lucy)|happy(lucy))))&
(![X]:((~patient(X)&rich(X))<=>(creative(X)&~humble(X))))&
(![X]:((~old(X)|rich(X))<=>(generous(X)|~kind(X))))&
(![X]:((~brave(X)<~>creative(X))<=>(~quiet(X)|quiet(X))))&
(![X]:(~happy(X)=>(generous(X)<~>~generous(X))))&
((quiet(john))=>(?[X]:((old(X)<~>kind(X)))))&
((~kind(alice))=>((~happy(alice)<~>~generous(alice))))&
(![X]:(funny(X)<=>(~calm(X)<~>~old(X))))&
(((~calm(mary)|~brave(mary)))<=>(?[X]:((kind(X)&creative(X)))))&
((?[X]:((~generous(X)|creative(X))))=>((happy(john)|kind(john))))&
(![X]:((~kind(X)<~>~tall(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((~rich(X)<~>wise(X))=>calm(X)))&
(((generous(paul)<~>kind(paul)))=>((~calm(alice)<~>~tall(alice))))&
(![X]:((kind(X)&wise(X))<=>(generous(X)<~>~funny(X))))&
(?[X]:((~wise(X)<~>humble(X))))&
(?[X]:(funny(X)))&
((~calm(fred)<~>~brave(fred)))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:(rich(X)))&
(?[X]:((~humble(X)|~strong(X)))) | wise(paul) | [
"p0",
"p1",
"p4",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5704008893365730771964567
% SZS output start Proof for 5704008893365730771964567
1. ! [X0] : ((~wise(X0) | strong(X0)) => ~rich(X0)) [input p0]
2. ! [X0] : (old(X0) <=> ~rich(X0)) [input p1]
5. ! [X0] : ((rich(X0) | ~old(X0)) <=> (~kind(X0) | generous(X0))) [input p4]
10. ! [X0] : (funny(X0) <=> (~calm(X0) <~> ~old(X0))) [input p9]
14. ! [X0] : ((~rich(X0) <~> wise(X0)) => calm(X0)) [input p13]
16. ! [X0] : ((wise(X0) & kind(X0)) <=> (generous(X0) <~> ~funny(X0))) [input p15]
23. ~wise(paul) [input hypothesis]
25. ! [X0] : (~wise(X0) => ~rich(X0)) [pure predicate removal 1]
27. ! [X0] : (~rich(X0) | wise(X0)) [ennf transformation 25]
34. ! [X0] : (calm(X0) | (~rich(X0) <=> wise(X0))) [ennf transformation 14]
36. ! [X0] : ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))) [nnf transformation 2]
39. ! [X0] : (((rich(X0) | ~old(X0)) | (kind(X0) & ~generous(X0))) & ((~kind(X0) | generous(X0)) | (~rich(X0) & old(X0)))) [nnf transformation 5]
40. ! [X0] : ((rich(X0) | ~old(X0) | (kind(X0) & ~generous(X0))) & (~kind(X0) | generous(X0) | (~rich(X0) & old(X0)))) [flattening 39]
48. ! [X0] : ((funny(X0) | ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0)))) & (((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | ~funny(X0))) [nnf transformation 10]
55. ! [X0] : (calm(X0) | ((~rich(X0) | ~wise(X0)) & (wise(X0) | rich(X0)))) [nnf transformation 34]
57. ! [X0] : (((wise(X0) & kind(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0)))) & (((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | (~wise(X0) | ~kind(X0)))) [nnf transformation 16]
58. ! [X0] : (((wise(X0) & kind(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0)))) & (((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | ~wise(X0) | ~kind(X0))) [flattening 57]
70. ~rich(X0) | wise(X0) [cnf transformation 27]
71. ~old(X0) | ~rich(X0) [cnf transformation 36]
72. old(X0) | rich(X0) [cnf transformation 36]
79. rich(X0) | ~old(X0) | ~generous(X0) [cnf transformation 40]
93. ~calm(X0) | ~old(X0) | ~funny(X0) [cnf transformation 48]
108. calm(X0) | wise(X0) | rich(X0) [cnf transformation 55]
109. calm(X0) | ~rich(X0) | ~wise(X0) [cnf transformation 55]
119. funny(X0) | generous(X0) | wise(X0) [cnf transformation 58]
128. ~wise(paul) [cnf transformation 23]
132. ~generous(X0) | ~old(X0) [subsumption resolution 79,71]
205. ~rich(X0) | calm(X0) [subsumption resolution 109,70]
206. calm(X0) | wise(X0) [subsumption resolution 108,205]
360. ~funny(X0) | ~old(X0) | wise(X0) [resolution 93,206]
594. ~old(X0) | wise(X0) | generous(X0) | wise(X0) [resolution 360,119]
599. ~old(X0) | wise(X0) | generous(X0) [duplicate literal removal 594]
600. ~old(X0) | wise(X0) [subsumption resolution 599,132]
802. wise(X0) | rich(X0) [resolution 600,72]
807. wise(X0) [subsumption resolution 802,70]
812. $false [resolution 807,128]
% SZS output end Proof for 5704008893365730771964567
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or calm is either not tall or not old.
Everyone who is curious or not wise is either calm or not quiet and vice versa.
If someone is humble then fred is both calm and rich.
Everyone who is rich or strong is either patient or quiet.
If someone is happy or calm then someone is both not wise and not calm.
Everyone who is not calm or not happy is not kind.
If someone is wise then john is both not generous and not creative.
Everyone who is not generous is happy.
Everyone who is either not humble or wise is humble.
If someone is either not calm or patient then john is not strong or not happy and vice versa.
If someone is either not quiet or not funny then someone is not brave or not quiet and vice versa.
Everyone who is both tall and kind is both not generous and not patient and vice versa.
If someone is both wise and not curious then someone is both wise and strong and vice versa.
Everyone who is patient or not funny is both not wise and generous.
If someone is not old or not humble then alice is kind or creative.
If someone is happy then alice is either not old or not creative.
Someone is both funny and not quiet.
Someone is either not wise or not tall.
Alice is funny or not creative.
Fred is old.
Someone is rich or creative.
Someone is not strong.
Someone is both not calm and tall.
Paul is curious or not patient. | Fred is not humble. | neutral | (![X]:((funny(X)|calm(X))=>(~tall(X)<~>~old(X))))&
(![X]:((curious(X)|~wise(X))<=>(calm(X)<~>~quiet(X))))&
((?[X]:(humble(X)))=>((calm(fred)&rich(fred))))&
(![X]:((rich(X)|strong(X))=>(patient(X)<~>quiet(X))))&
((?[X]:((happy(X)|calm(X))))=>(?[X]:((~wise(X)&~calm(X)))))&
(![X]:((~calm(X)|~happy(X))=>~kind(X)))&
((?[X]:(wise(X)))=>((~generous(john)&~creative(john))))&
(![X]:(~generous(X)=>happy(X)))&
(![X]:((~humble(X)<~>wise(X))=>humble(X)))&
((?[X]:((~calm(X)<~>patient(X))))<=>((~strong(john)|~happy(john))))&
((?[X]:((~quiet(X)<~>~funny(X))))<=>(?[X]:((~brave(X)|~quiet(X)))))&
(![X]:((tall(X)&kind(X))<=>(~generous(X)&~patient(X))))&
((?[X]:((wise(X)&~curious(X))))<=>(?[X]:((wise(X)&strong(X)))))&
(![X]:((patient(X)|~funny(X))=>(~wise(X)&generous(X))))&
((?[X]:((~old(X)|~humble(X))))=>((kind(alice)|creative(alice))))&
((?[X]:(happy(X)))=>((~old(alice)<~>~creative(alice))))&
(?[X]:((funny(X)&~quiet(X))))&
(?[X]:((~wise(X)<~>~tall(X))))&
((funny(alice)|~creative(alice)))&
(old(fred))&
(?[X]:((rich(X)|creative(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~calm(X)&tall(X))))&
((curious(paul)|~patient(paul))) | ~humble(fred) | [] | null | 0 |
If someone is both not strong and strong then someone is both not generous and kind and vice versa.
Everyone who is kind or not curious is strong or curious and vice versa.
Everyone who is either old or not tall is not quiet or not strong and vice versa.
If someone is brave then fred is quiet or not generous and vice versa.
Everyone who is both not wise and not creative is not old or brave.
If someone is both not generous and strong then someone is both not humble and funny and vice versa.
If someone is both not tall and humble then lucy is happy or creative and vice versa.
If mary is either calm or not old then paul is both calm and not tall and vice versa.
If someone is tall then someone is both rich and old and vice versa.
If someone is not happy or not wise then someone is both not kind and tall.
If john is not brave or kind then susan is both not quiet and rich.
If susan is both not wise and rich then john is quiet and vice versa.
If susan is either quiet or not old then alice is either curious or wise.
If someone is both generous and strong then someone is either not calm or not rich.
If paul is rich or funny then someone is strong or not strong and vice versa.
If someone is either humble or not patient then fred is both creative and not funny.
Someone is not old or patient.
Someone is both creative and not kind.
Alice is not funny.
Lucy is not kind or not calm.
Fred is both not calm and not old.
Someone is strong or calm.
Lucy is not funny or not kind.
Someone is strong or generous. | Alice is not creative. | neutral | ((?[X]:((~strong(X)&strong(X))))<=>(?[X]:((~generous(X)&kind(X)))))&
(![X]:((kind(X)|~curious(X))<=>(strong(X)|curious(X))))&
(![X]:((old(X)<~>~tall(X))<=>(~quiet(X)|~strong(X))))&
((?[X]:(brave(X)))<=>((quiet(fred)|~generous(fred))))&
(![X]:((~wise(X)&~creative(X))=>(~old(X)|brave(X))))&
((?[X]:((~generous(X)&strong(X))))<=>(?[X]:((~humble(X)&funny(X)))))&
((?[X]:((~tall(X)&humble(X))))<=>((happy(lucy)|creative(lucy))))&
(((calm(mary)<~>~old(mary)))<=>((calm(paul)&~tall(paul))))&
((?[X]:(tall(X)))<=>(?[X]:((rich(X)&old(X)))))&
((?[X]:((~happy(X)|~wise(X))))=>(?[X]:((~kind(X)&tall(X)))))&
(((~brave(john)|kind(john)))=>((~quiet(susan)&rich(susan))))&
(((~wise(susan)&rich(susan)))<=>(quiet(john)))&
(((quiet(susan)<~>~old(susan)))=>((curious(alice)<~>wise(alice))))&
((?[X]:((generous(X)&strong(X))))=>(?[X]:((~calm(X)<~>~rich(X)))))&
(((rich(paul)|funny(paul)))<=>(?[X]:((strong(X)|~strong(X)))))&
((?[X]:((humble(X)<~>~patient(X))))=>((creative(fred)&~funny(fred))))&
(?[X]:((~old(X)|patient(X))))&
(?[X]:((creative(X)&~kind(X))))&
(~funny(alice))&
((~kind(lucy)|~calm(lucy)))&
((~calm(fred)&~old(fred)))&
(?[X]:((strong(X)|calm(X))))&
((~funny(lucy)|~kind(lucy)))&
(?[X]:((strong(X)|generous(X)))) | ~creative(alice) | [] | null | 0 |
Everyone who is wise or generous is humble or curious.
If mary is both wise and not happy then someone is not old.
Everyone who is both not creative and happy is either humble or creative and vice versa.
If someone is either not rich or not quiet then someone is not rich and vice versa.
Everyone who is curious or not patient is both not generous and not happy and vice versa.
If paul is both not rich and rich then alice is either kind or not quiet and vice versa.
If someone is rich then susan is either generous or not quiet and vice versa.
Everyone who is quiet or happy is both not brave and kind and vice versa.
Everyone who is both not old and not rich is calm or tall.
If someone is not calm or rich then alice is both happy and rich and vice versa.
If someone is both curious and brave then alice is both not quiet and not strong.
If susan is both wise and not curious then lucy is either not patient or quiet and vice versa.
Everyone who is tall or not calm is patient and vice versa.
Everyone who is not brave is happy.
Everyone who is rich or not strong is either old or quiet.
If mary is not creative then fred is brave or patient and vice versa.
Alice is curious or kind.
Lucy is either wise or not humble.
Susan is quiet or not happy.
John is both not humble and patient.
Fred is not old or not kind.
Alice is either not rich or not generous.
Someone is quiet. | Paul is creative. | neutral | (![X]:((wise(X)|generous(X))=>(humble(X)|curious(X))))&
(((wise(mary)&~happy(mary)))=>(?[X]:(~old(X))))&
(![X]:((~creative(X)&happy(X))<=>(humble(X)<~>creative(X))))&
((?[X]:((~rich(X)<~>~quiet(X))))<=>(?[X]:(~rich(X))))&
(![X]:((curious(X)|~patient(X))<=>(~generous(X)&~happy(X))))&
(((~rich(paul)&rich(paul)))<=>((kind(alice)<~>~quiet(alice))))&
((?[X]:(rich(X)))<=>((generous(susan)<~>~quiet(susan))))&
(![X]:((quiet(X)|happy(X))<=>(~brave(X)&kind(X))))&
(![X]:((~old(X)&~rich(X))=>(calm(X)|tall(X))))&
((?[X]:((~calm(X)|rich(X))))<=>((happy(alice)&rich(alice))))&
((?[X]:((curious(X)&brave(X))))=>((~quiet(alice)&~strong(alice))))&
(((wise(susan)&~curious(susan)))<=>((~patient(lucy)<~>quiet(lucy))))&
(![X]:((tall(X)|~calm(X))<=>patient(X)))&
(![X]:(~brave(X)=>happy(X)))&
(![X]:((rich(X)|~strong(X))=>(old(X)<~>quiet(X))))&
((~creative(mary))<=>((brave(fred)|patient(fred))))&
((curious(alice)|kind(alice)))&
((wise(lucy)<~>~humble(lucy)))&
((quiet(susan)|~happy(susan)))&
((~humble(john)&patient(john)))&
((~old(fred)|~kind(fred)))&
((~rich(alice)<~>~generous(alice)))&
(?[X]:(quiet(X))) | creative(paul) | [] | null | 0 |
Everyone who is not humble or brave is not quiet or not humble.
If paul is both not generous and rich then john is either not kind or calm.
Everyone who is not calm is wise or creative and vice versa.
If someone is either not patient or not kind then fred is tall.
Everyone who is both humble and kind is both not funny and tall and vice versa.
Everyone who is both old and not old is both rich and funny and vice versa.
If someone is either not wise or not funny then mary is both not humble and not happy.
If someone is kind or tall then susan is either not patient or not happy and vice versa.
Everyone who is brave is both kind and not kind and vice versa.
Everyone who is both generous and not creative is quiet or not happy and vice versa.
If susan is not creative then mary is both not strong and patient and vice versa.
If mary is not strong or kind then paul is not tall and vice versa.
Everyone who is either not generous or patient is not brave and vice versa.
Everyone who is both not rich and not patient is either calm or not old and vice versa.
Everyone who is not happy or rich is not patient or rich and vice versa.
Everyone who is happy or not strong is either not curious or not patient.
Lucy is kind or brave.
Someone is not brave.
Someone is both not happy and old.
Alice is either not creative or not curious.
John is either not kind or not patient.
Susan is either not brave or not strong.
John is either old or not humble. | Lucy is humble. | neutral | (![X]:((~humble(X)|brave(X))=>(~quiet(X)|~humble(X))))&
(((~generous(paul)&rich(paul)))=>((~kind(john)<~>calm(john))))&
(![X]:(~calm(X)<=>(wise(X)|creative(X))))&
((?[X]:((~patient(X)<~>~kind(X))))=>(tall(fred)))&
(![X]:((humble(X)&kind(X))<=>(~funny(X)&tall(X))))&
(![X]:((old(X)&~old(X))<=>(rich(X)&funny(X))))&
((?[X]:((~wise(X)<~>~funny(X))))=>((~humble(mary)&~happy(mary))))&
((?[X]:((kind(X)|tall(X))))<=>((~patient(susan)<~>~happy(susan))))&
(![X]:(brave(X)<=>(kind(X)&~kind(X))))&
(![X]:((generous(X)&~creative(X))<=>(quiet(X)|~happy(X))))&
((~creative(susan))<=>((~strong(mary)&patient(mary))))&
(((~strong(mary)|kind(mary)))<=>(~tall(paul)))&
(![X]:((~generous(X)<~>patient(X))<=>~brave(X)))&
(![X]:((~rich(X)&~patient(X))<=>(calm(X)<~>~old(X))))&
(![X]:((~happy(X)|rich(X))<=>(~patient(X)|rich(X))))&
(![X]:((happy(X)|~strong(X))=>(~curious(X)<~>~patient(X))))&
((kind(lucy)|brave(lucy)))&
(?[X]:(~brave(X)))&
(?[X]:((~happy(X)&old(X))))&
((~creative(alice)<~>~curious(alice)))&
((~kind(john)<~>~patient(john)))&
((~brave(susan)<~>~strong(susan)))&
((old(john)<~>~humble(john))) | humble(lucy) | [] | null | 0 |
If lucy is either not kind or brave then someone is not wise or quiet and vice versa. If john is both happy and rich then someone is not humble or funny and vice versa. If paul is not funny or creative then alice is both not curious and not strong and vice versa. Everyone who is both patient and not tall is rich or not patient and vice versa. Everyone who is quiet or wise is not quiet or not funny. If john is kind then susan is calm or not humble and vice versa. Everyone who is either funny or strong is tall. If someone is not wise then paul is both brave and creative and vice versa. Everyone who is either not old or funny is either not quiet or creative and vice versa. If john is both patient and tall then someone is brave and vice versa. If someone is both strong and curious then someone is both curious and not patient and vice versa. If john is old then someone is either brave or rich. If alice is either not creative or not curious then someone is both calm and brave and vice versa. If alice is both not curious and not funny then susan is either not calm or wise and vice versa. Everyone who is both not old and not wise is curious and vice versa. Everyone who is not patient or not funny is both not calm and not brave. Alice is not tall. Someone is not tall or wise. Mary is either generous or not funny. Someone is either not generous or not funny. Someone is wise. Someone is not quiet. | John is happy. | entailment | (((~kind(lucy)<~>brave(lucy)))<=>(?[X]:((~wise(X)|quiet(X)))))&
(((happy(john)&rich(john)))<=>(?[X]:((~humble(X)|funny(X)))))&
(((~funny(paul)|creative(paul)))<=>((~curious(alice)&~strong(alice))))&
(![X]:((patient(X)&~tall(X))<=>(rich(X)|~patient(X))))&
(![X]:((quiet(X)|wise(X))=>(~quiet(X)|~funny(X))))&
((kind(john))<=>((calm(susan)|~humble(susan))))&
(![X]:((funny(X)<~>strong(X))=>tall(X)))&
((?[X]:(~wise(X)))<=>((brave(paul)&creative(paul))))&
(![X]:((~old(X)<~>funny(X))<=>(~quiet(X)<~>creative(X))))&
(((patient(john)&tall(john)))<=>(?[X]:(brave(X))))&
((?[X]:((strong(X)&curious(X))))<=>(?[X]:((curious(X)&~patient(X)))))&
((old(john))=>(?[X]:((brave(X)<~>rich(X)))))&
(((~creative(alice)<~>~curious(alice)))<=>(?[X]:((calm(X)&brave(X)))))&
(((~curious(alice)&~funny(alice)))<=>((~calm(susan)<~>wise(susan))))&
(![X]:((~old(X)&~wise(X))<=>curious(X)))&
(![X]:((~patient(X)|~funny(X))=>(~calm(X)&~brave(X))))&
(~tall(alice))&
(?[X]:((~tall(X)|wise(X))))&
((generous(mary)<~>~funny(mary)))&
(?[X]:((~generous(X)<~>~funny(X))))&
(?[X]:(wise(X)))&
(?[X]:(~quiet(X))) | happy(john) | [
"p1",
"p2",
"p7",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1633598479257122831135696
% SZS output start Proof for 1633598479257122831135696
2. (rich(john) & happy(john)) <=> ? [X0] : (funny(X0) | ~humble(X0)) [input p1]
3. (creative(paul) | ~funny(paul)) <=> (~strong(alice) & ~curious(alice)) [input p2]
8. ? [X0] : ~wise(X0) <=> (creative(paul) & brave(paul)) [input p7]
14. (~funny(alice) & ~curious(alice)) <=> (~calm(susan) <~> wise(susan)) [input p13]
16. ! [X0] : ((~funny(X0) | ~patient(X0)) => (~brave(X0) & ~calm(X0))) [input p15]
23. ~happy(john) [input hypothesis]
29. ! [X0] : ((~brave(X0) & ~calm(X0)) | (funny(X0) & patient(X0))) [ennf transformation 16]
34. ((rich(john) & happy(john)) | ! [X0] : (~funny(X0) & humble(X0))) & (? [X0] : (funny(X0) | ~humble(X0)) | (~rich(john) | ~happy(john))) [nnf transformation 2]
35. ((rich(john) & happy(john)) | ! [X0] : (~funny(X0) & humble(X0))) & (? [X0] : (funny(X0) | ~humble(X0)) | ~rich(john) | ~happy(john)) [flattening 34]
36. ((rich(john) & happy(john)) | ! [X0] : (~funny(X0) & humble(X0))) & (? [X1] : (funny(X1) | ~humble(X1)) | ~rich(john) | ~happy(john)) [rectify 35]
37. ? [X1] : (funny(X1) | ~humble(X1)) => (funny(sK1) | ~humble(sK1)) [choice axiom]
38. ((rich(john) & happy(john)) | ! [X0] : (~funny(X0) & humble(X0))) & ((funny(sK1) | ~humble(sK1)) | ~rich(john) | ~happy(john)) [skolemisation 36,37]
39. ((creative(paul) | ~funny(paul)) | (strong(alice) | curious(alice))) & ((~strong(alice) & ~curious(alice)) | (~creative(paul) & funny(paul))) [nnf transformation 3]
40. (creative(paul) | ~funny(paul) | strong(alice) | curious(alice)) & ((~strong(alice) & ~curious(alice)) | (~creative(paul) & funny(paul))) [flattening 39]
46. (? [X0] : ~wise(X0) | (~creative(paul) | ~brave(paul))) & ((creative(paul) & brave(paul)) | ! [X0] : wise(X0)) [nnf transformation 8]
47. (? [X0] : ~wise(X0) | ~creative(paul) | ~brave(paul)) & ((creative(paul) & brave(paul)) | ! [X0] : wise(X0)) [flattening 46]
48. (? [X0] : ~wise(X0) | ~creative(paul) | ~brave(paul)) & ((creative(paul) & brave(paul)) | ! [X1] : wise(X1)) [rectify 47]
49. ? [X0] : ~wise(X0) => ~wise(sK2) [choice axiom]
50. (~wise(sK2) | ~creative(paul) | ~brave(paul)) & ((creative(paul) & brave(paul)) | ! [X1] : wise(X1)) [skolemisation 48,49]
69. ((~funny(alice) & ~curious(alice)) | ((~calm(susan) | ~wise(susan)) & (wise(susan) | calm(susan)))) & (((~wise(susan) | calm(susan)) & (wise(susan) | ~calm(susan))) | (funny(alice) | curious(alice))) [nnf transformation 14]
70. ((~funny(alice) & ~curious(alice)) | ((~calm(susan) | ~wise(susan)) & (wise(susan) | calm(susan)))) & (((~wise(susan) | calm(susan)) & (wise(susan) | ~calm(susan))) | funny(alice) | curious(alice)) [flattening 69]
91. happy(john) | ~funny(X0) [cnf transformation 38]
94. ~curious(alice) | funny(paul) [cnf transformation 40]
111. brave(paul) | wise(X1) [cnf transformation 50]
138. ~wise(susan) | calm(susan) | funny(alice) | curious(alice) [cnf transformation 70]
147. ~calm(X0) | funny(X0) [cnf transformation 29]
149. ~brave(X0) | funny(X0) [cnf transformation 29]
158. ~happy(john) [cnf transformation 23]
175. 4 <=> ! [X0] : wise(X0) [avatar definition]
176. wise(X0) <- (4) [avatar component clause 175]
191. 7 <=> ! [X0] : ~funny(X0) [avatar definition]
192. ~funny(X0) <- (7) [avatar component clause 191]
203. 10 <=> happy(john) [avatar definition]
206. 7 | 10 [avatar split clause 91,203,191]
218. 13 <=> curious(alice) [avatar definition]
226. 15 <=> funny(paul) [avatar definition]
227. funny(paul) <- (15) [avatar component clause 226]
228. ~funny(paul) <- (~15) [avatar component clause 226]
237. 15 | ~13 [avatar split clause 94,218,226]
249. 19 <=> calm(susan) [avatar definition]
250. calm(susan) <- (19) [avatar component clause 249]
255. 20 <=> brave(paul) [avatar definition]
256. brave(paul) <- (20) [avatar component clause 255]
264. 4 | 20 [avatar split clause 111,255,175]
320. 32 <=> wise(susan) [avatar definition]
322. ~wise(susan) <- (~32) [avatar component clause 320]
324. 33 <=> funny(alice) [avatar definition]
325. funny(alice) <- (33) [avatar component clause 324]
331. 13 | 33 | 19 | ~32 [avatar split clause 138,320,249,324,218]
362. ~10 [avatar split clause 158,203]
365. $false <- (4, ~32) [resolution 322,176]
366. ~4 | 32 [avatar contradiction clause 365]
372. funny(paul) <- (20) [resolution 149,256]
374. $false <- (~15, 20) [subsumption resolution 372,228]
375. 15 | ~20 [avatar contradiction clause 374]
380. funny(susan) <- (19) [resolution 250,147]
381. $false <- (7, 19) [subsumption resolution 380,192]
382. ~7 | ~19 [avatar contradiction clause 381]
385. $false <- (7, 15) [subsumption resolution 227,192]
386. ~7 | ~15 [avatar contradiction clause 385]
387. $false <- (7, 33) [subsumption resolution 325,192]
388. ~7 | ~33 [avatar contradiction clause 387]
389. $false [avatar sat refutation 206,237,264,331,362,366,375,382,386,388]
% SZS output end Proof for 1633598479257122831135696
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious or patient then someone is not creative and vice versa. Everyone who is not old or not funny is either not strong or patient. If mary is both not happy and happy then paul is both brave and quiet. Everyone who is both tall and curious is not calm or not humble and vice versa. Everyone who is either wise or not quiet is not creative or not brave and vice versa. Everyone who is strong or not humble is humble. Everyone who is calm is curious or not funny and vice versa. Everyone who is rich or funny is both strong and tall. If someone is both not rich and not calm then someone is both quiet and not strong and vice versa. If lucy is generous or not generous then lucy is both not old and humble and vice versa. Everyone who is kind is generous and vice versa. If susan is not quiet or tall then paul is not patient and vice versa. If mary is not quiet then someone is either tall or not funny and vice versa. If someone is not wise or not tall then someone is strong or creative. If someone is not strong then someone is curious or patient. Someone is not kind. Fred is either not generous or generous. Someone is not old or not wise. Alice is not patient or not creative. Lucy is both curious and not quiet. Susan is not tall or curious. | Paul is rich. | neutral | ((?[X]:((curious(X)|patient(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~old(X)|~funny(X))=>(~strong(X)<~>patient(X))))&
(((~happy(mary)&happy(mary)))=>((brave(paul)&quiet(paul))))&
(![X]:((tall(X)&curious(X))<=>(~calm(X)|~humble(X))))&
(![X]:((wise(X)<~>~quiet(X))<=>(~creative(X)|~brave(X))))&
(![X]:((strong(X)|~humble(X))=>humble(X)))&
(![X]:(calm(X)<=>(curious(X)|~funny(X))))&
(![X]:((rich(X)|funny(X))=>(strong(X)&tall(X))))&
((?[X]:((~rich(X)&~calm(X))))<=>(?[X]:((quiet(X)&~strong(X)))))&
(((generous(lucy)|~generous(lucy)))<=>((~old(lucy)&humble(lucy))))&
(![X]:(kind(X)<=>generous(X)))&
(((~quiet(susan)|tall(susan)))<=>(~patient(paul)))&
((~quiet(mary))<=>(?[X]:((tall(X)<~>~funny(X)))))&
((?[X]:((~wise(X)|~tall(X))))=>(?[X]:((strong(X)|creative(X)))))&
((?[X]:(~strong(X)))=>(?[X]:((curious(X)|patient(X)))))&
(?[X]:(~kind(X)))&
((~generous(fred)<~>generous(fred)))&
(?[X]:((~old(X)|~wise(X))))&
((~patient(alice)|~creative(alice)))&
((curious(lucy)&~quiet(lucy)))&
((~tall(susan)|curious(susan))) | rich(paul) | [] | null | 0 |
Everyone who is either not creative or patient is generous or rich and vice versa.
Everyone who is both not generous and generous is quiet and vice versa.
If someone is both kind and not kind then john is not calm or patient.
Everyone who is brave is either rich or curious.
If susan is either wise or not strong then john is either not quiet or kind and vice versa.
Everyone who is both not wise and not brave is not humble and vice versa.
Everyone who is either not wise or curious is both not strong and strong and vice versa.
Everyone who is kind or brave is kind and vice versa.
If someone is generous then someone is both not happy and generous and vice versa.
If lucy is curious then fred is quiet or not brave and vice versa.
Everyone who is either not curious or quiet is both humble and not calm.
Everyone who is not wise is not happy.
Everyone who is not humble is both not calm and kind and vice versa.
Everyone who is either brave or quiet is either curious or not wise and vice versa.
If someone is either brave or generous then someone is either not happy or rich.
Someone is both not curious and funny.
Someone is curious.
Someone is not generous or not funny.
Someone is not patient or not calm.
Alice is not curious or generous.
John is old or not old.
Someone is both not brave and not tall.
Someone is rich or kind. | Alice is not brave. | entailment | (![X]:((~creative(X)<~>patient(X))<=>(generous(X)|rich(X))))&
(![X]:((~generous(X)&generous(X))<=>quiet(X)))&
((?[X]:((kind(X)&~kind(X))))=>((~calm(john)|patient(john))))&
(![X]:(brave(X)=>(rich(X)<~>curious(X))))&
(((wise(susan)<~>~strong(susan)))<=>((~quiet(john)<~>kind(john))))&
(![X]:((~wise(X)&~brave(X))<=>~humble(X)))&
(![X]:((~wise(X)<~>curious(X))<=>(~strong(X)&strong(X))))&
(![X]:((kind(X)|brave(X))<=>kind(X)))&
((?[X]:(generous(X)))<=>(?[X]:((~happy(X)&generous(X)))))&
((curious(lucy))<=>((quiet(fred)|~brave(fred))))&
(![X]:((~curious(X)<~>quiet(X))=>(humble(X)&~calm(X))))&
(![X]:(~wise(X)=>~happy(X)))&
(![X]:(~humble(X)<=>(~calm(X)&kind(X))))&
(![X]:((brave(X)<~>quiet(X))<=>(curious(X)<~>~wise(X))))&
((?[X]:((brave(X)<~>generous(X))))=>(?[X]:((~happy(X)<~>rich(X)))))&
(?[X]:((~curious(X)&funny(X))))&
(?[X]:(curious(X)))&
(?[X]:((~generous(X)|~funny(X))))&
(?[X]:((~patient(X)|~calm(X))))&
((~curious(alice)|generous(alice)))&
((old(john)|~old(john)))&
(?[X]:((~brave(X)&~tall(X))))&
(?[X]:((rich(X)|kind(X)))) | ~brave(alice) | [
"p1",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3133896248528467097196307
% SZS output start Proof for 3133896248528467097196307
2. ! [X0] : ((generous(X0) & ~generous(X0)) <=> quiet(X0)) [input p1]
7. ! [X0] : ((~wise(X0) <~> curious(X0)) <=> (strong(X0) & ~strong(X0))) [input p6]
14. ! [X0] : ((brave(X0) <~> quiet(X0)) <=> (curious(X0) <~> ~wise(X0))) [input p13]
24. brave(alice) [input hypothesis]
36. ! [X0] : (((generous(X0) & ~generous(X0)) | ~quiet(X0)) & (quiet(X0) | (~generous(X0) | generous(X0)))) [nnf transformation 2]
37. ! [X0] : (((generous(X0) & ~generous(X0)) | ~quiet(X0)) & (quiet(X0) | ~generous(X0) | generous(X0))) [flattening 36]
42. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [nnf transformation 7]
43. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [flattening 42]
56. ! [X0] : ((((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0)))) & (((wise(X0) | ~curious(X0)) & (~wise(X0) | curious(X0))) | ((brave(X0) | ~quiet(X0)) & (quiet(X0) | ~brave(X0))))) [nnf transformation 14]
80. ~generous(X0) | ~quiet(X0) [cnf transformation 37]
81. generous(X0) | ~quiet(X0) [cnf transformation 37]
96. ~strong(X0) | curious(X0) | wise(X0) [cnf transformation 43]
97. ~strong(X0) | ~wise(X0) | ~curious(X0) [cnf transformation 43]
98. strong(X0) | curious(X0) | wise(X0) [cnf transformation 43]
99. strong(X0) | ~wise(X0) | ~curious(X0) [cnf transformation 43]
119. ~wise(X0) | curious(X0) | quiet(X0) | ~brave(X0) [cnf transformation 56]
121. wise(X0) | ~curious(X0) | quiet(X0) | ~brave(X0) [cnf transformation 56]
140. brave(alice) [cnf transformation 24]
141. ~quiet(X0) [subsumption resolution 80,81]
162. ~wise(X0) | ~curious(X0) [subsumption resolution 97,99]
163. curious(X0) | wise(X0) [subsumption resolution 96,98]
198. wise(X0) | ~curious(X0) | ~brave(X0) [subsumption resolution 121,141]
199. ~curious(X0) | ~brave(X0) [subsumption resolution 198,162]
200. ~wise(X0) | curious(X0) | ~brave(X0) [subsumption resolution 119,141]
201. curious(X0) | ~brave(X0) [subsumption resolution 200,163]
202. ~brave(X0) [subsumption resolution 201,199]
251. $false [subsumption resolution 140,202]
% SZS output end Proof for 3133896248528467097196307
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not strong or not generous then susan is not creative.
If alice is either tall or not humble then susan is patient and vice versa.
Everyone who is not creative is quiet.
If fred is not calm or not curious then john is not generous or patient.
Everyone who is not patient or not curious is not kind or not humble.
Everyone who is either not humble or not generous is both not creative and wise and vice versa.
Everyone who is not old or not strong is either creative or old.
Everyone who is not strong or not quiet is not humble and vice versa.
Everyone who is not generous or not happy is not old.
If someone is either not humble or quiet then paul is not generous.
Everyone who is quiet is either strong or not funny.
Everyone who is wise or rich is humble or funny.
If john is calm then someone is either not humble or not strong.
Everyone who is either not funny or strong is not happy or humble and vice versa.
Lucy is both not funny and not brave.
Fred is wise.
Alice is kind.
Someone is either not calm or quiet.
Someone is not humble.
Someone is both not calm and not happy.
Someone is both not rich and kind. | Fred is not creative. | contradiction | (((~strong(paul)|~generous(paul)))=>(~creative(susan)))&
(((tall(alice)<~>~humble(alice)))<=>(patient(susan)))&
(![X]:(~creative(X)=>quiet(X)))&
(((~calm(fred)|~curious(fred)))=>((~generous(john)|patient(john))))&
(![X]:((~patient(X)|~curious(X))=>(~kind(X)|~humble(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>(~creative(X)&wise(X))))&
(![X]:((~old(X)|~strong(X))=>(creative(X)<~>old(X))))&
(![X]:((~strong(X)|~quiet(X))<=>~humble(X)))&
(![X]:((~generous(X)|~happy(X))=>~old(X)))&
((?[X]:((~humble(X)<~>quiet(X))))=>(~generous(paul)))&
(![X]:(quiet(X)=>(strong(X)<~>~funny(X))))&
(![X]:((wise(X)|rich(X))=>(humble(X)|funny(X))))&
((calm(john))=>(?[X]:((~humble(X)<~>~strong(X)))))&
(![X]:((~funny(X)<~>strong(X))<=>(~happy(X)|humble(X))))&
((~funny(lucy)&~brave(lucy)))&
(wise(fred))&
(kind(alice))&
(?[X]:((~calm(X)<~>quiet(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~calm(X)&~happy(X))))&
(?[X]:((~rich(X)&kind(X)))) | ~creative(fred) | [
"p2",
"p5",
"p6",
"p7",
"p8",
"p10",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7779199151593935492484041
% SZS output start Proof for 7779199151593935492484041
3. ! [X0] : (~creative(X0) => quiet(X0)) [input p2]
6. ! [X0] : ((~humble(X0) <~> ~generous(X0)) <=> (wise(X0) & ~creative(X0))) [input p5]
7. ! [X0] : ((~strong(X0) | ~old(X0)) => (creative(X0) <~> old(X0))) [input p6]
8. ! [X0] : ((~quiet(X0) | ~strong(X0)) <=> ~humble(X0)) [input p7]
9. ! [X0] : ((~happy(X0) | ~generous(X0)) => ~old(X0)) [input p8]
11. ! [X0] : (quiet(X0) => (strong(X0) <~> ~funny(X0))) [input p10]
12. ! [X0] : ((rich(X0) | wise(X0)) => (funny(X0) | humble(X0))) [input p11]
14. ! [X0] : ((~funny(X0) <~> strong(X0)) <=> (humble(X0) | ~happy(X0))) [input p13]
16. wise(fred) [input p15]
22. ~creative(fred) [input hypothesis]
25. ! [X0] : (wise(X0) => (funny(X0) | humble(X0))) [pure predicate removal 12]
29. ! [X0] : (quiet(X0) | creative(X0)) [ennf transformation 3]
34. ! [X0] : ((creative(X0) <~> old(X0)) | (strong(X0) & old(X0))) [ennf transformation 7]
35. ! [X0] : (~old(X0) | (happy(X0) & generous(X0))) [ennf transformation 9]
37. ! [X0] : ((strong(X0) <~> ~funny(X0)) | ~quiet(X0)) [ennf transformation 11]
38. ! [X0] : ((funny(X0) | humble(X0)) | ~wise(X0)) [ennf transformation 25]
39. ! [X0] : (funny(X0) | humble(X0) | ~wise(X0)) [flattening 38]
42. ! [X0] : ((((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | (~wise(X0) | creative(X0))) & ((wise(X0) & ~creative(X0)) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0))))) [nnf transformation 6]
43. ! [X0] : ((((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | ~wise(X0) | creative(X0)) & ((wise(X0) & ~creative(X0)) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0))))) [flattening 42]
44. ! [X0] : (((~old(X0) | ~creative(X0)) & (old(X0) | creative(X0))) | (strong(X0) & old(X0))) [nnf transformation 34]
45. ! [X0] : (((~quiet(X0) | ~strong(X0)) | humble(X0)) & (~humble(X0) | (quiet(X0) & strong(X0)))) [nnf transformation 8]
46. ! [X0] : ((~quiet(X0) | ~strong(X0) | humble(X0)) & (~humble(X0) | (quiet(X0) & strong(X0)))) [flattening 45]
48. ! [X0] : (((funny(X0) | ~strong(X0)) & (~funny(X0) | strong(X0))) | ~quiet(X0)) [nnf transformation 37]
52. ! [X0] : ((((~strong(X0) | funny(X0)) & (strong(X0) | ~funny(X0))) | (~humble(X0) & happy(X0))) & ((humble(X0) | ~happy(X0)) | ((~funny(X0) | ~strong(X0)) & (strong(X0) | funny(X0))))) [nnf transformation 14]
53. ! [X0] : ((((~strong(X0) | funny(X0)) & (strong(X0) | ~funny(X0))) | (~humble(X0) & happy(X0))) & (humble(X0) | ~happy(X0) | ((~funny(X0) | ~strong(X0)) & (strong(X0) | funny(X0))))) [flattening 52]
69. quiet(X0) | creative(X0) [cnf transformation 29]
76. ~wise(X0) | ~humble(X0) | ~generous(X0) | creative(X0) [cnf transformation 43]
78. old(X0) | creative(X0) | old(X0) [cnf transformation 44]
82. ~humble(X0) | strong(X0) [cnf transformation 46]
85. ~old(X0) | generous(X0) [cnf transformation 35]
86. ~old(X0) | happy(X0) [cnf transformation 35]
89. ~funny(X0) | strong(X0) | ~quiet(X0) [cnf transformation 48]
91. ~wise(X0) | humble(X0) | funny(X0) [cnf transformation 39]
95. ~funny(X0) | ~happy(X0) | humble(X0) | ~strong(X0) [cnf transformation 53]
99. ~strong(X0) | funny(X0) | ~humble(X0) [cnf transformation 53]
101. wise(fred) [cnf transformation 16]
109. ~creative(fred) [cnf transformation 22]
110. old(X0) | creative(X0) [duplicate literal removal 78]
180. ~humble(X0) | funny(X0) [subsumption resolution 99,82]
193. happy(X0) | creative(X0) [resolution 110,86]
194. creative(X1) | generous(X1) [resolution 110,85]
229. generous(fred) [resolution 194,109]
257. humble(fred) | funny(fred) [resolution 91,101]
268. funny(fred) [subsumption resolution 257,180]
270. strong(fred) | ~quiet(fred) [resolution 268,89]
272. 25 <=> happy(fred) [avatar definition]
273. ~happy(fred) <- (~25) [avatar component clause 272]
276. 26 <=> strong(fred) [avatar definition]
286. ~humble(fred) | ~generous(fred) | creative(fred) [resolution 76,101]
287. ~humble(fred) | creative(fred) [subsumption resolution 286,229]
288. ~humble(fred) [subsumption resolution 287,109]
297. ~happy(fred) | humble(fred) | ~strong(fred) [resolution 95,268]
301. ~happy(fred) | ~strong(fred) [subsumption resolution 297,288]
316. creative(fred) <- (~25) [resolution 273,193]
317. $false <- (~25) [subsumption resolution 316,109]
318. 25 [avatar contradiction clause 317]
320. 29 <=> quiet(fred) [avatar definition]
322. ~quiet(fred) <- (~29) [avatar component clause 320]
323. ~29 | 26 [avatar split clause 270,276,320]
324. ~26 | ~25 [avatar split clause 301,272,276]
326. creative(fred) <- (~29) [resolution 322,69]
327. $false <- (~29) [subsumption resolution 326,109]
328. 29 [avatar contradiction clause 327]
329. $false [avatar sat refutation 318,323,324,328]
% SZS output end Proof for 7779199151593935492484041
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or calm is creative.
Everyone who is not old or not strong is not humble and vice versa.
If john is both wise and not strong then someone is strong and vice versa.
Everyone who is not humble is either not wise or not calm.
Everyone who is not humble is either tall or not funny and vice versa.
Everyone who is both not generous and not rich is not quiet and vice versa.
If someone is funny or patient then someone is both not strong and not generous and vice versa.
If alice is either not creative or not strong then fred is either not kind or not tall and vice versa.
If mary is either not quiet or not wise then john is either not funny or quiet.
Everyone who is rich is brave or creative.
Everyone who is kind or quiet is not quiet or curious.
Everyone who is both kind and patient is wise or not patient.
Everyone who is not humble is either happy or humble.
If susan is either strong or not happy then fred is both not happy and generous.
Everyone who is funny is not funny or not strong and vice versa.
If someone is both curious and quiet then someone is not calm or not old and vice versa.
Paul is either not tall or not generous.
Someone is either not creative or not kind.
Someone is curious.
Someone is either not curious or wise.
Someone is quiet or not tall.
Susan is both wise and quiet. | Paul is happy. | entailment | (![X]:((humble(X)|calm(X))=>creative(X)))&
(![X]:((~old(X)|~strong(X))<=>~humble(X)))&
(((wise(john)&~strong(john)))<=>(?[X]:(strong(X))))&
(![X]:(~humble(X)=>(~wise(X)<~>~calm(X))))&
(![X]:(~humble(X)<=>(tall(X)<~>~funny(X))))&
(![X]:((~generous(X)&~rich(X))<=>~quiet(X)))&
((?[X]:((funny(X)|patient(X))))<=>(?[X]:((~strong(X)&~generous(X)))))&
(((~creative(alice)<~>~strong(alice)))<=>((~kind(fred)<~>~tall(fred))))&
(((~quiet(mary)<~>~wise(mary)))=>((~funny(john)<~>quiet(john))))&
(![X]:(rich(X)=>(brave(X)|creative(X))))&
(![X]:((kind(X)|quiet(X))=>(~quiet(X)|curious(X))))&
(![X]:((kind(X)&patient(X))=>(wise(X)|~patient(X))))&
(![X]:(~humble(X)=>(happy(X)<~>humble(X))))&
(((strong(susan)<~>~happy(susan)))=>((~happy(fred)&generous(fred))))&
(![X]:(funny(X)<=>(~funny(X)|~strong(X))))&
((?[X]:((curious(X)&quiet(X))))<=>(?[X]:((~calm(X)|~old(X)))))&
((~tall(paul)<~>~generous(paul)))&
(?[X]:((~creative(X)<~>~kind(X))))&
(?[X]:(curious(X)))&
(?[X]:((~curious(X)<~>wise(X))))&
(?[X]:((quiet(X)|~tall(X))))&
((wise(susan)&quiet(susan))) | happy(paul) | [
"p1",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4871597481137635470583132
% SZS output start Proof for 4871597481137635470583132
2. ! [X0] : ((~strong(X0) | ~old(X0)) <=> ~humble(X0)) [input p1]
13. ! [X0] : (~humble(X0) => (happy(X0) <~> humble(X0))) [input p12]
15. ! [X0] : (funny(X0) <=> (~strong(X0) | ~funny(X0))) [input p14]
23. ~happy(paul) [input hypothesis]
34. ! [X0] : ((happy(X0) <~> humble(X0)) | humble(X0)) [ennf transformation 13]
36. ! [X0] : (((~strong(X0) | ~old(X0)) | humble(X0)) & (~humble(X0) | (strong(X0) & old(X0)))) [nnf transformation 2]
37. ! [X0] : ((~strong(X0) | ~old(X0) | humble(X0)) & (~humble(X0) | (strong(X0) & old(X0)))) [flattening 36]
54. ! [X0] : (((~humble(X0) | ~happy(X0)) & (humble(X0) | happy(X0))) | humble(X0)) [nnf transformation 34]
56. ! [X0] : ((funny(X0) | (strong(X0) & funny(X0))) & ((~strong(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 15]
57. ! [X0] : ((funny(X0) | (strong(X0) & funny(X0))) & (~strong(X0) | ~funny(X0) | ~funny(X0))) [flattening 56]
77. ~humble(X0) | strong(X0) [cnf transformation 37]
111. humble(X0) | happy(X0) | humble(X0) [cnf transformation 54]
117. ~strong(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 57]
118. funny(X0) | funny(X0) [cnf transformation 57]
135. ~happy(paul) [cnf transformation 23]
136. ~strong(X0) | ~funny(X0) [duplicate literal removal 117]
137. funny(X0) [duplicate literal removal 118]
138. happy(X0) | humble(X0) [duplicate literal removal 111]
142. 1 <=> ! [X0] : ~strong(X0) [avatar definition]
143. ~strong(X0) <- (1) [avatar component clause 142]
253. ~strong(X0) [subsumption resolution 136,137]
254. 1 [avatar split clause 253,142]
330. humble(paul) [resolution 138,135]
333. strong(paul) [resolution 330,77]
336. $false <- (1) [subsumption resolution 333,143]
337. ~1 [avatar contradiction clause 336]
338. $false [avatar sat refutation 254,337]
% SZS output end Proof for 4871597481137635470583132
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is both not kind and humble and vice versa. If alice is either not funny or curious then someone is either not quiet or quiet and vice versa. Everyone who is either strong or not wise is either not quiet or patient. Everyone who is either not curious or not happy is not rich. If someone is both happy and not tall then susan is both funny and not strong. If susan is both not happy and not calm then susan is either not brave or not happy. If someone is creative or not patient then mary is either wise or strong. Everyone who is not brave or not happy is calm or not calm and vice versa. If someone is either not strong or not rich then someone is not old. Everyone who is tall or curious is both tall and brave. Everyone who is patient is either happy or not generous. Everyone who is both rich and patient is generous or not curious and vice versa. If someone is not funny then lucy is not wise or quiet and vice versa. Everyone who is old or curious is either not curious or strong and vice versa. Everyone who is not patient or not calm is either not humble or not old. Everyone who is either not old or tall is either not wise or calm and vice versa. Fred is humble or not happy. Someone is not curious or not patient. Lucy is either brave or generous. Someone is not curious or not calm. Someone is both brave and not old. Someone is either not wise or happy. Someone is brave or quiet. | Mary is not wise. | neutral | (![X]:(~happy(X)<=>(~kind(X)&humble(X))))&
(((~funny(alice)<~>curious(alice)))<=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:((strong(X)<~>~wise(X))=>(~quiet(X)<~>patient(X))))&
(![X]:((~curious(X)<~>~happy(X))=>~rich(X)))&
((?[X]:((happy(X)&~tall(X))))=>((funny(susan)&~strong(susan))))&
(((~happy(susan)&~calm(susan)))=>((~brave(susan)<~>~happy(susan))))&
((?[X]:((creative(X)|~patient(X))))=>((wise(mary)<~>strong(mary))))&
(![X]:((~brave(X)|~happy(X))<=>(calm(X)|~calm(X))))&
((?[X]:((~strong(X)<~>~rich(X))))=>(?[X]:(~old(X))))&
(![X]:((tall(X)|curious(X))=>(tall(X)&brave(X))))&
(![X]:(patient(X)=>(happy(X)<~>~generous(X))))&
(![X]:((rich(X)&patient(X))<=>(generous(X)|~curious(X))))&
((?[X]:(~funny(X)))<=>((~wise(lucy)|quiet(lucy))))&
(![X]:((old(X)|curious(X))<=>(~curious(X)<~>strong(X))))&
(![X]:((~patient(X)|~calm(X))=>(~humble(X)<~>~old(X))))&
(![X]:((~old(X)<~>tall(X))<=>(~wise(X)<~>calm(X))))&
((humble(fred)|~happy(fred)))&
(?[X]:((~curious(X)|~patient(X))))&
((brave(lucy)<~>generous(lucy)))&
(?[X]:((~curious(X)|~calm(X))))&
(?[X]:((brave(X)&~old(X))))&
(?[X]:((~wise(X)<~>happy(X))))&
(?[X]:((brave(X)|quiet(X)))) | ~wise(mary) | [] | null | 0 |
If someone is funny or brave then someone is either not strong or not happy.
Everyone who is both patient and not strong is not creative or not strong.
If someone is not humble or not tall then susan is either not kind or not tall.
Everyone who is both not old and funny is generous and vice versa.
Everyone who is brave or creative is not old or curious.
If someone is either not generous or happy then mary is both not brave and tall and vice versa.
Everyone who is both old and not patient is generous or not funny.
If lucy is not rich or not curious then alice is brave or funny and vice versa.
Everyone who is either not strong or not humble is tall or generous and vice versa.
Everyone who is either not generous or generous is either tall or not brave.
If paul is both not old and not tall then someone is either not rich or not wise.
Everyone who is either not wise or quiet is creative.
Everyone who is either not humble or patient is both kind and not happy.
Everyone who is curious or creative is both happy and not wise and vice versa.
Everyone who is either not tall or generous is not brave or kind.
Everyone who is both not tall and humble is not humble or quiet and vice versa.
Someone is funny or strong.
Fred is tall.
Mary is creative.
Someone is both not kind and not quiet.
Alice is both curious and strong.
Fred is not strong.
Someone is not quiet. | Lucy is not generous. | entailment | ((?[X]:((funny(X)|brave(X))))=>(?[X]:((~strong(X)<~>~happy(X)))))&
(![X]:((patient(X)&~strong(X))=>(~creative(X)|~strong(X))))&
((?[X]:((~humble(X)|~tall(X))))=>((~kind(susan)<~>~tall(susan))))&
(![X]:((~old(X)&funny(X))<=>generous(X)))&
(![X]:((brave(X)|creative(X))=>(~old(X)|curious(X))))&
((?[X]:((~generous(X)<~>happy(X))))<=>((~brave(mary)&tall(mary))))&
(![X]:((old(X)&~patient(X))=>(generous(X)|~funny(X))))&
(((~rich(lucy)|~curious(lucy)))<=>((brave(alice)|funny(alice))))&
(![X]:((~strong(X)<~>~humble(X))<=>(tall(X)|generous(X))))&
(![X]:((~generous(X)<~>generous(X))=>(tall(X)<~>~brave(X))))&
(((~old(paul)&~tall(paul)))=>(?[X]:((~rich(X)<~>~wise(X)))))&
(![X]:((~wise(X)<~>quiet(X))=>creative(X)))&
(![X]:((~humble(X)<~>patient(X))=>(kind(X)&~happy(X))))&
(![X]:((curious(X)|creative(X))<=>(happy(X)&~wise(X))))&
(![X]:((~tall(X)<~>generous(X))=>(~brave(X)|kind(X))))&
(![X]:((~tall(X)&humble(X))<=>(~humble(X)|quiet(X))))&
(?[X]:((funny(X)|strong(X))))&
(tall(fred))&
(creative(mary))&
(?[X]:((~kind(X)&~quiet(X))))&
((curious(alice)&strong(alice)))&
(~strong(fred))&
(?[X]:(~quiet(X))) | ~generous(lucy) | [
"p3",
"p5",
"p6",
"p7",
"p8",
"p9",
"p12",
"p13",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2792584386226083078750086
% SZS output start Proof for 2792584386226083078750086
4. ! [X0] : ((funny(X0) & ~old(X0)) <=> generous(X0)) [input p3]
6. ? [X0] : (~generous(X0) <~> happy(X0)) <=> (tall(mary) & ~brave(mary)) [input p5]
7. ! [X0] : ((~patient(X0) & old(X0)) => (~funny(X0) | generous(X0))) [input p6]
8. (~curious(lucy) | ~rich(lucy)) <=> (funny(alice) | brave(alice)) [input p7]
9. ! [X0] : ((~strong(X0) <~> ~humble(X0)) <=> (generous(X0) | tall(X0))) [input p8]
10. ! [X0] : ((~generous(X0) <~> generous(X0)) => (tall(X0) <~> ~brave(X0))) [input p9]
13. ! [X0] : ((~humble(X0) <~> patient(X0)) => (~happy(X0) & kind(X0))) [input p12]
14. ! [X0] : ((creative(X0) | curious(X0)) <=> (~wise(X0) & happy(X0))) [input p13]
16. ! [X0] : ((humble(X0) & ~tall(X0)) <=> (quiet(X0) | ~humble(X0))) [input p15]
21. strong(alice) & curious(alice) [input p20]
24. generous(lucy) [input hypothesis]
32. ! [X0] : ((~funny(X0) | generous(X0)) | (patient(X0) | ~old(X0))) [ennf transformation 7]
33. ! [X0] : (~funny(X0) | generous(X0) | patient(X0) | ~old(X0)) [flattening 32]
34. ! [X0] : ((tall(X0) <~> ~brave(X0)) | (~generous(X0) <=> generous(X0))) [ennf transformation 10]
38. ! [X0] : ((~happy(X0) & kind(X0)) | (~humble(X0) <=> patient(X0))) [ennf transformation 13]
46. ! [X0] : (((funny(X0) & ~old(X0)) | ~generous(X0)) & (generous(X0) | (~funny(X0) | old(X0)))) [nnf transformation 4]
47. ! [X0] : (((funny(X0) & ~old(X0)) | ~generous(X0)) & (generous(X0) | ~funny(X0) | old(X0))) [flattening 46]
48. (? [X0] : ((~happy(X0) | generous(X0)) & (happy(X0) | ~generous(X0))) | (~tall(mary) | brave(mary))) & ((tall(mary) & ~brave(mary)) | ! [X0] : ((~generous(X0) | ~happy(X0)) & (happy(X0) | generous(X0)))) [nnf transformation 6]
49. (? [X0] : ((~happy(X0) | generous(X0)) & (happy(X0) | ~generous(X0))) | ~tall(mary) | brave(mary)) & ((tall(mary) & ~brave(mary)) | ! [X0] : ((~generous(X0) | ~happy(X0)) & (happy(X0) | generous(X0)))) [flattening 48]
50. (? [X0] : ((~happy(X0) | generous(X0)) & (happy(X0) | ~generous(X0))) | ~tall(mary) | brave(mary)) & ((tall(mary) & ~brave(mary)) | ! [X1] : ((~generous(X1) | ~happy(X1)) & (happy(X1) | generous(X1)))) [rectify 49]
51. ? [X0] : ((~happy(X0) | generous(X0)) & (happy(X0) | ~generous(X0))) => ((~happy(sK1) | generous(sK1)) & (happy(sK1) | ~generous(sK1))) [choice axiom]
52. (((~happy(sK1) | generous(sK1)) & (happy(sK1) | ~generous(sK1))) | ~tall(mary) | brave(mary)) & ((tall(mary) & ~brave(mary)) | ! [X1] : ((~generous(X1) | ~happy(X1)) & (happy(X1) | generous(X1)))) [skolemisation 50,51]
53. ((~curious(lucy) | ~rich(lucy)) | (~funny(alice) & ~brave(alice))) & ((funny(alice) | brave(alice)) | (curious(lucy) & rich(lucy))) [nnf transformation 8]
54. (~curious(lucy) | ~rich(lucy) | (~funny(alice) & ~brave(alice))) & (funny(alice) | brave(alice) | (curious(lucy) & rich(lucy))) [flattening 53]
55. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | (~generous(X0) & ~tall(X0))) & ((generous(X0) | tall(X0)) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [nnf transformation 9]
56. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | (~generous(X0) & ~tall(X0))) & (generous(X0) | tall(X0) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [flattening 55]
57. ! [X0] : (((brave(X0) | ~tall(X0)) & (~brave(X0) | tall(X0))) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) [nnf transformation 34]
62. ! [X0] : ((~happy(X0) & kind(X0)) | ((~humble(X0) | ~patient(X0)) & (patient(X0) | humble(X0)))) [nnf transformation 38]
63. ! [X0] : (((creative(X0) | curious(X0)) | (wise(X0) | ~happy(X0))) & ((~wise(X0) & happy(X0)) | (~creative(X0) & ~curious(X0)))) [nnf transformation 14]
64. ! [X0] : ((creative(X0) | curious(X0) | wise(X0) | ~happy(X0)) & ((~wise(X0) & happy(X0)) | (~creative(X0) & ~curious(X0)))) [flattening 63]
66. ! [X0] : (((humble(X0) & ~tall(X0)) | (~quiet(X0) & humble(X0))) & ((quiet(X0) | ~humble(X0)) | (~humble(X0) | tall(X0)))) [nnf transformation 16]
67. ! [X0] : (((humble(X0) & ~tall(X0)) | (~quiet(X0) & humble(X0))) & (quiet(X0) | ~humble(X0) | ~humble(X0) | tall(X0))) [flattening 66]
83. ~funny(X0) | generous(X0) | old(X0) [cnf transformation 47]
89. ~brave(mary) | ~generous(X1) | ~happy(X1) [cnf transformation 52]
91. tall(mary) | ~generous(X1) | ~happy(X1) [cnf transformation 52]
94. ~funny(X0) | generous(X0) | patient(X0) | ~old(X0) [cnf transformation 33]
96. funny(alice) | brave(alice) | curious(lucy) [cnf transformation 54]
101. ~tall(X0) | ~strong(X0) | ~humble(X0) [cnf transformation 56]
102. ~generous(X0) | ~strong(X0) | ~humble(X0) [cnf transformation 56]
105. ~brave(X0) | tall(X0) | generous(X0) | generous(X0) [cnf transformation 57]
106. ~brave(X0) | tall(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 57]
107. brave(X0) | ~tall(X0) | generous(X0) | generous(X0) [cnf transformation 57]
108. brave(X0) | ~tall(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 57]
116. ~humble(X0) | ~happy(X0) | ~patient(X0) [cnf transformation 62]
117. ~curious(X0) | happy(X0) [cnf transformation 64]
127. humble(X0) | humble(X0) [cnf transformation 67]
134. curious(alice) [cnf transformation 21]
135. strong(alice) [cnf transformation 21]
138. generous(lucy) [cnf transformation 24]
140. humble(X0) [duplicate literal removal 127]
141. ~brave(X0) | tall(X0) | generous(X0) [duplicate literal removal 105]
142. ~generous(X0) | tall(X0) | ~brave(X0) [duplicate literal removal 106]
143. brave(X0) | ~tall(X0) | generous(X0) [duplicate literal removal 107]
144. ~generous(X0) | ~tall(X0) | brave(X0) [duplicate literal removal 108]
176. 8 <=> ! [X0] : humble(X0) [avatar definition]
177. humble(X0) <- (8) [avatar component clause 176]
182. 9 <=> brave(mary) [avatar definition]
183. ~brave(mary) <- (~9) [avatar component clause 182]
186. 10 <=> tall(mary) [avatar definition]
187. tall(mary) <- (10) [avatar component clause 186]
200. 13 <=> ! [X1] : (~generous(X1) | ~happy(X1)) [avatar definition]
201. ~generous(X1) | ~happy(X1) <- (13) [avatar component clause 200]
202. 13 | 10 [avatar split clause 91,186,200]
207. 13 | ~9 [avatar split clause 89,182,200]
209. ~funny(X0) | generous(X0) | patient(X0) [subsumption resolution 94,83]
211. 15 <=> funny(alice) [avatar definition]
212. funny(alice) <- (15) [avatar component clause 211]
219. 17 <=> curious(lucy) [avatar definition]
220. curious(lucy) <- (17) [avatar component clause 219]
224. 18 <=> brave(alice) [avatar definition]
225. brave(alice) <- (18) [avatar component clause 224]
228. 17 | 18 | 15 [avatar split clause 96,211,224,219]
230. ~tall(X0) | brave(X0) [subsumption resolution 143,144]
231. ~brave(X0) | tall(X0) [subsumption resolution 141,142]
251. 8 [avatar split clause 140,176]
263. happy(alice) [resolution 117,134]
270. brave(mary) <- (10) [resolution 230,187]
280. 26 <=> generous(alice) [avatar definition]
282. generous(alice) <- (26) [avatar component clause 280]
295. $false <- (~9, 10) [subsumption resolution 270,183]
296. 9 | ~10 [avatar contradiction clause 295]
297. happy(lucy) <- (17) [resolution 220,117]
298. ~happy(lucy) <- (13) [resolution 201,138]
299. $false <- (13, 17) [subsumption resolution 298,297]
300. ~13 | ~17 [avatar contradiction clause 299]
301. tall(alice) <- (18) [resolution 225,231]
331. ~strong(alice) | ~humble(alice) <- (18) [resolution 101,301]
332. ~humble(alice) <- (18) [subsumption resolution 331,135]
333. $false <- (8, 18) [subsumption resolution 332,177]
334. ~8 | ~18 [avatar contradiction clause 333]
380. ~patient(X0) | ~happy(X0) <- (8) [resolution 116,177]
404. generous(alice) | patient(alice) <- (15) [resolution 209,212]
408. 38 <=> patient(alice) [avatar definition]
410. patient(alice) <- (38) [avatar component clause 408]
411. 38 | 26 | ~15 [avatar split clause 404,211,280,408]
514. ~happy(alice) <- (8, 38) [resolution 380,410]
515. $false <- (8, 38) [subsumption resolution 514,263]
516. ~8 | ~38 [avatar contradiction clause 515]
519. ~strong(alice) | ~humble(alice) <- (26) [resolution 282,102]
527. ~humble(alice) <- (26) [subsumption resolution 519,135]
528. $false <- (8, 26) [subsumption resolution 527,177]
529. ~8 | ~26 [avatar contradiction clause 528]
541. $false [avatar sat refutation 202,207,228,251,296,300,334,411,516,529]
% SZS output end Proof for 2792584386226083078750086
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is wise.
If someone is not kind then paul is either not brave or not happy and vice versa.
If someone is either quiet or not curious then someone is either quiet or not tall.
Everyone who is not kind is both not kind and not curious.
Everyone who is either not old or not strong is happy.
Everyone who is either not happy or generous is either not brave or funny.
If susan is both not kind and happy then paul is either not funny or brave and vice versa.
Everyone who is both not happy and quiet is either not curious or curious and vice versa.
Everyone who is funny or not kind is either not rich or not humble.
If someone is both not kind and not rich then susan is either happy or funny and vice versa.
If someone is not old or not funny then alice is not tall or not strong and vice versa.
If fred is tall then someone is not happy and vice versa.
If someone is kind or humble then fred is generous.
If someone is strong or old then lucy is both not patient and not tall.
If fred is humble then alice is patient or not humble.
Everyone who is not generous or brave is not strong and vice versa.
Lucy is both not kind and not patient.
Mary is either quiet or not kind.
Paul is not old.
Someone is not kind or not rich.
Someone is either strong or not kind.
Someone is rich. | Lucy is not generous. | neutral | (![X]:(generous(X)=>wise(X)))&
((?[X]:(~kind(X)))<=>((~brave(paul)<~>~happy(paul))))&
((?[X]:((quiet(X)<~>~curious(X))))=>(?[X]:((quiet(X)<~>~tall(X)))))&
(![X]:(~kind(X)=>(~kind(X)&~curious(X))))&
(![X]:((~old(X)<~>~strong(X))=>happy(X)))&
(![X]:((~happy(X)<~>generous(X))=>(~brave(X)<~>funny(X))))&
(((~kind(susan)&happy(susan)))<=>((~funny(paul)<~>brave(paul))))&
(![X]:((~happy(X)&quiet(X))<=>(~curious(X)<~>curious(X))))&
(![X]:((funny(X)|~kind(X))=>(~rich(X)<~>~humble(X))))&
((?[X]:((~kind(X)&~rich(X))))<=>((happy(susan)<~>funny(susan))))&
((?[X]:((~old(X)|~funny(X))))<=>((~tall(alice)|~strong(alice))))&
((tall(fred))<=>(?[X]:(~happy(X))))&
((?[X]:((kind(X)|humble(X))))=>(generous(fred)))&
((?[X]:((strong(X)|old(X))))=>((~patient(lucy)&~tall(lucy))))&
((humble(fred))=>((patient(alice)|~humble(alice))))&
(![X]:((~generous(X)|brave(X))<=>~strong(X)))&
((~kind(lucy)&~patient(lucy)))&
((quiet(mary)<~>~kind(mary)))&
(~old(paul))&
(?[X]:((~kind(X)|~rich(X))))&
(?[X]:((strong(X)<~>~kind(X))))&
(?[X]:(rich(X))) | ~generous(lucy) | [] | null | 0 |
If someone is either old or curious then lucy is either rich or not quiet and vice versa.
Everyone who is either not generous or not calm is not tall or patient.
Everyone who is not brave is both strong and quiet and vice versa.
Everyone who is not creative is brave and vice versa.
If someone is either generous or quiet then someone is either not calm or not brave.
Everyone who is both not tall and strong is not tall.
If lucy is not brave then someone is not wise or not happy.
If someone is either humble or creative then john is not kind or not curious.
Everyone who is not creative or not curious is both not humble and not funny.
Everyone who is old or tall is not curious or generous and vice versa.
If someone is not happy then mary is not creative or not kind and vice versa.
Everyone who is not calm or strong is either not rich or patient.
Everyone who is either creative or calm is either not tall or not funny.
Everyone who is either not quiet or quiet is rich or not calm and vice versa.
Everyone who is kind or not generous is either not happy or tall.
Everyone who is either brave or funny is both calm and not wise and vice versa.
John is not rich or not tall.
Someone is quiet.
Alice is both not calm and not humble.
Someone is not humble or not patient.
Someone is patient or not kind.
Someone is not humble.
Someone is rich.
Someone is brave or curious. | Lucy is generous. | neutral | ((?[X]:((old(X)<~>curious(X))))<=>((rich(lucy)<~>~quiet(lucy))))&
(![X]:((~generous(X)<~>~calm(X))=>(~tall(X)|patient(X))))&
(![X]:(~brave(X)<=>(strong(X)&quiet(X))))&
(![X]:(~creative(X)<=>brave(X)))&
((?[X]:((generous(X)<~>quiet(X))))=>(?[X]:((~calm(X)<~>~brave(X)))))&
(![X]:((~tall(X)&strong(X))=>~tall(X)))&
((~brave(lucy))=>(?[X]:((~wise(X)|~happy(X)))))&
((?[X]:((humble(X)<~>creative(X))))=>((~kind(john)|~curious(john))))&
(![X]:((~creative(X)|~curious(X))=>(~humble(X)&~funny(X))))&
(![X]:((old(X)|tall(X))<=>(~curious(X)|generous(X))))&
((?[X]:(~happy(X)))<=>((~creative(mary)|~kind(mary))))&
(![X]:((~calm(X)|strong(X))=>(~rich(X)<~>patient(X))))&
(![X]:((creative(X)<~>calm(X))=>(~tall(X)<~>~funny(X))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(rich(X)|~calm(X))))&
(![X]:((kind(X)|~generous(X))=>(~happy(X)<~>tall(X))))&
(![X]:((brave(X)<~>funny(X))<=>(calm(X)&~wise(X))))&
((~rich(john)|~tall(john)))&
(?[X]:(quiet(X)))&
((~calm(alice)&~humble(alice)))&
(?[X]:((~humble(X)|~patient(X))))&
(?[X]:((patient(X)|~kind(X))))&
(?[X]:(~humble(X)))&
(?[X]:(rich(X)))&
(?[X]:((brave(X)|curious(X)))) | generous(lucy) | [] | null | 0 |
If someone is either not rich or not funny then paul is patient or not wise. Everyone who is both not rich and curious is humble or quiet and vice versa. If fred is not patient or old then someone is old and vice versa. Everyone who is not quiet is either not curious or not patient and vice versa. If someone is both old and not curious then someone is not old and vice versa. Everyone who is not strong is wise or not patient and vice versa. Everyone who is both kind and not strong is not generous and vice versa. Everyone who is not kind or kind is both kind and strong and vice versa. Everyone who is both not rich and kind is funny or creative. If someone is curious or calm then alice is either kind or brave. Everyone who is both not brave and not strong is not quiet and vice versa. If someone is creative then lucy is either calm or quiet and vice versa. Everyone who is not quiet is humble or not curious and vice versa. If someone is happy or not happy then mary is creative. If lucy is not strong then fred is both humble and quiet and vice versa. If someone is either brave or not tall then someone is either not creative or not humble and vice versa. Someone is not patient or old. Fred is creative or not creative. Someone is funny or not happy. Susan is not tall or not creative. Someone is not rich or generous. Someone is either not brave or not curious. John is patient. | Lucy is not patient. | contradiction | ((?[X]:((~rich(X)<~>~funny(X))))=>((patient(paul)|~wise(paul))))&
(![X]:((~rich(X)&curious(X))<=>(humble(X)|quiet(X))))&
(((~patient(fred)|old(fred)))<=>(?[X]:(old(X))))&
(![X]:(~quiet(X)<=>(~curious(X)<~>~patient(X))))&
((?[X]:((old(X)&~curious(X))))<=>(?[X]:(~old(X))))&
(![X]:(~strong(X)<=>(wise(X)|~patient(X))))&
(![X]:((kind(X)&~strong(X))<=>~generous(X)))&
(![X]:((~kind(X)|kind(X))<=>(kind(X)&strong(X))))&
(![X]:((~rich(X)&kind(X))=>(funny(X)|creative(X))))&
((?[X]:((curious(X)|calm(X))))=>((kind(alice)<~>brave(alice))))&
(![X]:((~brave(X)&~strong(X))<=>~quiet(X)))&
((?[X]:(creative(X)))<=>((calm(lucy)<~>quiet(lucy))))&
(![X]:(~quiet(X)<=>(humble(X)|~curious(X))))&
((?[X]:((happy(X)|~happy(X))))=>(creative(mary)))&
((~strong(lucy))<=>((humble(fred)&quiet(fred))))&
((?[X]:((brave(X)<~>~tall(X))))<=>(?[X]:((~creative(X)<~>~humble(X)))))&
(?[X]:((~patient(X)|old(X))))&
((creative(fred)|~creative(fred)))&
(?[X]:((funny(X)|~happy(X))))&
((~tall(susan)|~creative(susan)))&
(?[X]:((~rich(X)|generous(X))))&
(?[X]:((~brave(X)<~>~curious(X))))&
(patient(john)) | ~patient(lucy) | [
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6850286640394348192320715
% SZS output start Proof for 6850286640394348192320715
6. ! [X0] : (~strong(X0) <=> (~patient(X0) | wise(X0))) [input p5]
8. ! [X0] : ((kind(X0) | ~kind(X0)) <=> (strong(X0) & kind(X0))) [input p7]
24. ~patient(lucy) [input hypothesis]
50. ! [X0] : ((~strong(X0) | (patient(X0) & ~wise(X0))) & ((~patient(X0) | wise(X0)) | strong(X0))) [nnf transformation 6]
51. ! [X0] : ((~strong(X0) | (patient(X0) & ~wise(X0))) & (~patient(X0) | wise(X0) | strong(X0))) [flattening 50]
52. ! [X0] : (((kind(X0) | ~kind(X0)) | (~strong(X0) | ~kind(X0))) & ((strong(X0) & kind(X0)) | (~kind(X0) & kind(X0)))) [nnf transformation 8]
53. ! [X0] : ((kind(X0) | ~kind(X0) | ~strong(X0) | ~kind(X0)) & ((strong(X0) & kind(X0)) | (~kind(X0) & kind(X0)))) [flattening 52]
98. ~strong(X0) | patient(X0) [cnf transformation 51]
102. strong(X0) | kind(X0) [cnf transformation 53]
103. ~kind(X0) | strong(X0) [cnf transformation 53]
141. ~patient(lucy) [cnf transformation 24]
201. strong(X0) [subsumption resolution 102,103]
331. patient(X0) [resolution 98,201]
333. $false [resolution 331,141]
% SZS output end Proof for 6850286640394348192320715
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or quiet is either patient or generous.
Everyone who is both brave and humble is funny or happy.
If susan is brave or not brave then susan is either calm or brave and vice versa.
Everyone who is calm is not old and vice versa.
If paul is creative or funny then alice is either curious or not kind.
If someone is both not strong and brave then someone is curious.
If lucy is patient or wise then someone is strong and vice versa.
If lucy is either creative or generous then alice is not calm and vice versa.
Everyone who is either not creative or funny is both not brave and tall and vice versa.
Everyone who is either kind or not generous is both kind and not curious and vice versa.
Everyone who is funny is either not wise or not brave.
If someone is either brave or curious then john is not humble.
Everyone who is patient or generous is both quiet and curious.
If someone is rich or not old then someone is rich or not rich.
Everyone who is not curious or creative is either not calm or not humble.
If paul is not wise then alice is both not generous and funny.
Someone is funny or creative.
Mary is either not generous or not patient.
Someone is not rich or calm.
John is rich or not kind.
Someone is not patient or patient.
Alice is brave.
Paul is not rich or creative. | John is kind. | neutral | (![X]:((~happy(X)|quiet(X))=>(patient(X)<~>generous(X))))&
(![X]:((brave(X)&humble(X))=>(funny(X)|happy(X))))&
(((brave(susan)|~brave(susan)))<=>((calm(susan)<~>brave(susan))))&
(![X]:(calm(X)<=>~old(X)))&
(((creative(paul)|funny(paul)))=>((curious(alice)<~>~kind(alice))))&
((?[X]:((~strong(X)&brave(X))))=>(?[X]:(curious(X))))&
(((patient(lucy)|wise(lucy)))<=>(?[X]:(strong(X))))&
(((creative(lucy)<~>generous(lucy)))<=>(~calm(alice)))&
(![X]:((~creative(X)<~>funny(X))<=>(~brave(X)&tall(X))))&
(![X]:((kind(X)<~>~generous(X))<=>(kind(X)&~curious(X))))&
(![X]:(funny(X)=>(~wise(X)<~>~brave(X))))&
((?[X]:((brave(X)<~>curious(X))))=>(~humble(john)))&
(![X]:((patient(X)|generous(X))=>(quiet(X)&curious(X))))&
((?[X]:((rich(X)|~old(X))))=>(?[X]:((rich(X)|~rich(X)))))&
(![X]:((~curious(X)|creative(X))=>(~calm(X)<~>~humble(X))))&
((~wise(paul))=>((~generous(alice)&funny(alice))))&
(?[X]:((funny(X)|creative(X))))&
((~generous(mary)<~>~patient(mary)))&
(?[X]:((~rich(X)|calm(X))))&
((rich(john)|~kind(john)))&
(?[X]:((~patient(X)|patient(X))))&
(brave(alice))&
((~rich(paul)|creative(paul))) | kind(john) | [] | null | 0 |
If mary is both curious and not curious then mary is not creative.
Everyone who is both calm and kind is either not quiet or old.
If alice is both not humble and not patient then someone is patient or not strong and vice versa.
If someone is both strong and not funny then lucy is both not humble and kind.
If someone is funny or not curious then mary is both old and curious.
If mary is either quiet or not funny then fred is calm.
If paul is both curious and not funny then paul is funny and vice versa.
If someone is both not wise and tall then paul is not funny and vice versa.
If someone is either not wise or quiet then someone is kind or patient.
If alice is both not curious and not strong then someone is either not old or patient and vice versa.
If susan is not generous then someone is either patient or not humble and vice versa.
If paul is not humble or curious then someone is not generous or happy.
Everyone who is not happy or not old is both not wise and not calm and vice versa.
Everyone who is brave is funny and vice versa.
Everyone who is both not calm and old is not calm or humble and vice versa.
Everyone who is curious or not tall is both not brave and not strong and vice versa.
Fred is both creative and old.
Alice is calm.
Someone is quiet or not humble.
Mary is not happy.
Lucy is generous.
Alice is not kind.
Someone is either brave or old.
Fred is both funny and not kind. | Mary is funny. | contradiction | (((curious(mary)&~curious(mary)))=>(~creative(mary)))&
(![X]:((calm(X)&kind(X))=>(~quiet(X)<~>old(X))))&
(((~humble(alice)&~patient(alice)))<=>(?[X]:((patient(X)|~strong(X)))))&
((?[X]:((strong(X)&~funny(X))))=>((~humble(lucy)&kind(lucy))))&
((?[X]:((funny(X)|~curious(X))))=>((old(mary)&curious(mary))))&
(((quiet(mary)<~>~funny(mary)))=>(calm(fred)))&
(((curious(paul)&~funny(paul)))<=>(funny(paul)))&
((?[X]:((~wise(X)&tall(X))))<=>(~funny(paul)))&
((?[X]:((~wise(X)<~>quiet(X))))=>(?[X]:((kind(X)|patient(X)))))&
(((~curious(alice)&~strong(alice)))<=>(?[X]:((~old(X)<~>patient(X)))))&
((~generous(susan))<=>(?[X]:((patient(X)<~>~humble(X)))))&
(((~humble(paul)|curious(paul)))=>(?[X]:((~generous(X)|happy(X)))))&
(![X]:((~happy(X)|~old(X))<=>(~wise(X)&~calm(X))))&
(![X]:(brave(X)<=>funny(X)))&
(![X]:((~calm(X)&old(X))<=>(~calm(X)|humble(X))))&
(![X]:((curious(X)|~tall(X))<=>(~brave(X)&~strong(X))))&
((creative(fred)&old(fred)))&
(calm(alice))&
(?[X]:((quiet(X)|~humble(X))))&
(~happy(mary))&
(generous(lucy))&
(~kind(alice))&
(?[X]:((brave(X)<~>old(X))))&
((funny(fred)&~kind(fred))) | funny(mary) | [
"p4",
"p13",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3975544302921137225236263
% SZS output start Proof for 3975544302921137225236263
5. ? [X0] : (~curious(X0) | funny(X0)) => (curious(mary) & old(mary)) [input p4]
14. ! [X0] : (brave(X0) <=> funny(X0)) [input p13]
16. ! [X0] : ((~tall(X0) | curious(X0)) <=> (~strong(X0) & ~brave(X0))) [input p15]
24. ~kind(fred) & funny(fred) [input p23]
25. funny(mary) [input hypothesis]
32. (curious(mary) & old(mary)) | ! [X0] : (curious(X0) & ~funny(X0)) [ennf transformation 5]
66. ! [X0] : ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0))) [nnf transformation 14]
69. ! [X0] : (((~tall(X0) | curious(X0)) | (strong(X0) | brave(X0))) & ((~strong(X0) & ~brave(X0)) | (tall(X0) & ~curious(X0)))) [nnf transformation 16]
70. ! [X0] : ((~tall(X0) | curious(X0) | strong(X0) | brave(X0)) & ((~strong(X0) & ~brave(X0)) | (tall(X0) & ~curious(X0)))) [flattening 69]
88. curious(mary) | ~funny(X0) [cnf transformation 32]
118. ~funny(X0) | brave(X0) [cnf transformation 66]
124. ~brave(X0) | ~curious(X0) [cnf transformation 70]
138. funny(fred) [cnf transformation 24]
140. funny(mary) [cnf transformation 25]
187. 11 <=> curious(mary) [avatar definition]
189. curious(mary) <- (11) [avatar component clause 187]
192. 12 <=> ! [X0] : ~funny(X0) [avatar definition]
193. ~funny(X0) <- (12) [avatar component clause 192]
194. 12 | 11 [avatar split clause 88,187,192]
202. 14 <=> funny(mary) [avatar definition]
204. funny(mary) <- (14) [avatar component clause 202]
308. 14 [avatar split clause 140,202]
316. $false <- (12) [resolution 193,138]
317. ~12 [avatar contradiction clause 316]
323. brave(mary) <- (14) [resolution 118,204]
327. ~curious(mary) <- (14) [resolution 124,323]
328. $false <- (11, 14) [subsumption resolution 327,189]
329. ~11 | ~14 [avatar contradiction clause 328]
330. $false [avatar sat refutation 194,308,317,329]
% SZS output end Proof for 3975544302921137225236263
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or not funny is both happy and not curious and vice versa.
If susan is not curious then someone is either not tall or kind.
If someone is tall then lucy is either not rich or curious.
If someone is both creative and not tall then someone is both not funny and curious.
Everyone who is strong is not funny or not wise and vice versa.
If someone is either funny or brave then alice is not tall or wise.
If someone is not creative then john is either not humble or not rich and vice versa.
Everyone who is either not happy or creative is both funny and not patient and vice versa.
If alice is not creative then someone is either not creative or not calm and vice versa.
Everyone who is either not humble or old is both not kind and creative.
If susan is tall or not strong then someone is not old.
Everyone who is both creative and not strong is either brave or not rich and vice versa.
Everyone who is both tall and not curious is either tall or not funny.
If susan is both curious and not happy then someone is not old and vice versa.
Everyone who is not kind is old or not patient.
Everyone who is not happy or not humble is not generous and vice versa.
Someone is brave or not patient.
Someone is either not curious or humble.
Someone is not kind.
Someone is not wise.
Someone is not generous.
Susan is funny.
Alice is not creative.
Lucy is strong or not wise. | Susan is not humble. | neutral | (![X]:((~old(X)|~funny(X))<=>(happy(X)&~curious(X))))&
((~curious(susan))=>(?[X]:((~tall(X)<~>kind(X)))))&
((?[X]:(tall(X)))=>((~rich(lucy)<~>curious(lucy))))&
((?[X]:((creative(X)&~tall(X))))=>(?[X]:((~funny(X)&curious(X)))))&
(![X]:(strong(X)<=>(~funny(X)|~wise(X))))&
((?[X]:((funny(X)<~>brave(X))))=>((~tall(alice)|wise(alice))))&
((?[X]:(~creative(X)))<=>((~humble(john)<~>~rich(john))))&
(![X]:((~happy(X)<~>creative(X))<=>(funny(X)&~patient(X))))&
((~creative(alice))<=>(?[X]:((~creative(X)<~>~calm(X)))))&
(![X]:((~humble(X)<~>old(X))=>(~kind(X)&creative(X))))&
(((tall(susan)|~strong(susan)))=>(?[X]:(~old(X))))&
(![X]:((creative(X)&~strong(X))<=>(brave(X)<~>~rich(X))))&
(![X]:((tall(X)&~curious(X))=>(tall(X)<~>~funny(X))))&
(((curious(susan)&~happy(susan)))<=>(?[X]:(~old(X))))&
(![X]:(~kind(X)=>(old(X)|~patient(X))))&
(![X]:((~happy(X)|~humble(X))<=>~generous(X)))&
(?[X]:((brave(X)|~patient(X))))&
(?[X]:((~curious(X)<~>humble(X))))&
(?[X]:(~kind(X)))&
(?[X]:(~wise(X)))&
(?[X]:(~generous(X)))&
(funny(susan))&
(~creative(alice))&
((strong(lucy)|~wise(lucy))) | ~humble(susan) | [] | null | 0 |
Everyone who is both not creative and curious is not humble. Everyone who is either not creative or generous is either not patient or old. Everyone who is either not generous or quiet is not patient and vice versa. Everyone who is both not tall and not happy is either quiet or humble and vice versa. Everyone who is curious is either old or not patient and vice versa. Everyone who is funny is not funny or not creative and vice versa. If alice is either not curious or humble then lucy is either creative or not wise. If someone is either not brave or not curious then mary is curious or calm and vice versa. Everyone who is both happy and not happy is calm or quiet and vice versa. If someone is rich or patient then someone is kind. Everyone who is tall is creative or rich. If someone is not creative or tall then someone is funny or happy and vice versa. Everyone who is either not old or not brave is both not calm and not tall. Everyone who is either calm or creative is generous or rich and vice versa. Fred is either not patient or not strong. Someone is both funny and not generous. Someone is either humble or not patient. | Mary is not happy. | contradiction | (![X]:((~creative(X)&curious(X))=>~humble(X)))&
(![X]:((~creative(X)<~>generous(X))=>(~patient(X)<~>old(X))))&
(![X]:((~generous(X)<~>quiet(X))<=>~patient(X)))&
(![X]:((~tall(X)&~happy(X))<=>(quiet(X)<~>humble(X))))&
(![X]:(curious(X)<=>(old(X)<~>~patient(X))))&
(![X]:(funny(X)<=>(~funny(X)|~creative(X))))&
(((~curious(alice)<~>humble(alice)))=>((creative(lucy)<~>~wise(lucy))))&
((?[X]:((~brave(X)<~>~curious(X))))<=>((curious(mary)|calm(mary))))&
(![X]:((happy(X)&~happy(X))<=>(calm(X)|quiet(X))))&
((?[X]:((rich(X)|patient(X))))=>(?[X]:(kind(X))))&
(![X]:(tall(X)=>(creative(X)|rich(X))))&
((?[X]:((~creative(X)|tall(X))))<=>(?[X]:((funny(X)|happy(X)))))&
(![X]:((~old(X)<~>~brave(X))=>(~calm(X)&~tall(X))))&
(![X]:((calm(X)<~>creative(X))<=>(generous(X)|rich(X))))&
((~patient(fred)<~>~strong(fred)))&
(?[X]:((funny(X)&~generous(X))))&
(?[X]:((humble(X)<~>~patient(X)))) | ~happy(mary) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p5",
"p8",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8163693285902679295828115
% SZS output start Proof for 8163693285902679295828115
1. ! [X0] : ((curious(X0) & ~creative(X0)) => ~humble(X0)) [input p0]
2. ! [X0] : ((~creative(X0) <~> generous(X0)) => (~patient(X0) <~> old(X0))) [input p1]
3. ! [X0] : ((~generous(X0) <~> quiet(X0)) <=> ~patient(X0)) [input p2]
4. ! [X0] : ((~happy(X0) & ~tall(X0)) <=> (quiet(X0) <~> humble(X0))) [input p3]
5. ! [X0] : (curious(X0) <=> (old(X0) <~> ~patient(X0))) [input p4]
6. ! [X0] : (funny(X0) <=> (~creative(X0) | ~funny(X0))) [input p5]
9. ! [X0] : ((~happy(X0) & happy(X0)) <=> (quiet(X0) | calm(X0))) [input p8]
11. ! [X0] : (tall(X0) => (rich(X0) | creative(X0))) [input p10]
14. ! [X0] : ((calm(X0) <~> creative(X0)) <=> (rich(X0) | generous(X0))) [input p13]
18. ~happy(mary) [input hypothesis]
22. ! [X0] : (~humble(X0) | (~curious(X0) | creative(X0))) [ennf transformation 1]
23. ! [X0] : (~humble(X0) | ~curious(X0) | creative(X0)) [flattening 22]
24. ! [X0] : ((~patient(X0) <~> old(X0)) | (~creative(X0) <=> generous(X0))) [ennf transformation 2]
26. ! [X0] : ((rich(X0) | creative(X0)) | ~tall(X0)) [ennf transformation 11]
27. ! [X0] : (rich(X0) | creative(X0) | ~tall(X0)) [flattening 26]
29. ! [X0] : (((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0)))) [nnf transformation 24]
30. ! [X0] : ((((~quiet(X0) | generous(X0)) & (quiet(X0) | ~generous(X0))) | patient(X0)) & (~patient(X0) | ((~generous(X0) | ~quiet(X0)) & (quiet(X0) | generous(X0))))) [nnf transformation 3]
31. ! [X0] : (((~happy(X0) & ~tall(X0)) | ((quiet(X0) | ~humble(X0)) & (humble(X0) | ~quiet(X0)))) & (((~humble(X0) | ~quiet(X0)) & (humble(X0) | quiet(X0))) | (happy(X0) | tall(X0)))) [nnf transformation 4]
32. ! [X0] : (((~happy(X0) & ~tall(X0)) | ((quiet(X0) | ~humble(X0)) & (humble(X0) | ~quiet(X0)))) & (((~humble(X0) | ~quiet(X0)) & (humble(X0) | quiet(X0))) | happy(X0) | tall(X0))) [flattening 31]
33. ! [X0] : ((curious(X0) | ((old(X0) | patient(X0)) & (~patient(X0) | ~old(X0)))) & (((patient(X0) | ~old(X0)) & (~patient(X0) | old(X0))) | ~curious(X0))) [nnf transformation 5]
34. ! [X0] : ((funny(X0) | (creative(X0) & funny(X0))) & ((~creative(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 6]
35. ! [X0] : ((funny(X0) | (creative(X0) & funny(X0))) & (~creative(X0) | ~funny(X0) | ~funny(X0))) [flattening 34]
42. ! [X0] : (((~happy(X0) & happy(X0)) | (~quiet(X0) & ~calm(X0))) & ((quiet(X0) | calm(X0)) | (happy(X0) | ~happy(X0)))) [nnf transformation 9]
43. ! [X0] : (((~happy(X0) & happy(X0)) | (~quiet(X0) & ~calm(X0))) & (quiet(X0) | calm(X0) | happy(X0) | ~happy(X0))) [flattening 42]
50. ! [X0] : ((((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | (~rich(X0) & ~generous(X0))) & ((rich(X0) | generous(X0)) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0))))) [nnf transformation 14]
51. ! [X0] : ((((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | (~rich(X0) & ~generous(X0))) & (rich(X0) | generous(X0) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0))))) [flattening 50]
58. ~humble(X0) | ~curious(X0) | creative(X0) [cnf transformation 23]
61. ~old(X0) | patient(X0) | generous(X0) | creative(X0) [cnf transformation 29]
63. ~patient(X0) | quiet(X0) | generous(X0) [cnf transformation 30]
67. happy(X0) | quiet(X0) | humble(X0) | tall(X0) [cnf transformation 32]
76. old(X0) | curious(X0) | patient(X0) [cnf transformation 33]
77. ~creative(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 35]
78. funny(X0) | funny(X0) [cnf transformation 35]
91. happy(X0) | ~calm(X0) [cnf transformation 43]
92. happy(X0) | ~quiet(X0) [cnf transformation 43]
93. ~calm(X0) | ~happy(X0) [cnf transformation 43]
94. ~happy(X0) | ~quiet(X0) [cnf transformation 43]
95. rich(X0) | creative(X0) | ~tall(X0) [cnf transformation 27]
106. creative(X0) | calm(X0) | ~generous(X0) [cnf transformation 51]
107. creative(X0) | calm(X0) | ~rich(X0) [cnf transformation 51]
116. ~happy(mary) [cnf transformation 18]
117. ~creative(X0) | ~funny(X0) [duplicate literal removal 77]
118. funny(X0) [duplicate literal removal 78]
119. ~creative(X0) [subsumption resolution 117,118]
164. ~quiet(X0) [subsumption resolution 92,94]
165. ~calm(X0) [subsumption resolution 91,93]
166. ~tall(X0) | rich(X0) [subsumption resolution 95,119]
167. calm(X0) | ~rich(X0) [subsumption resolution 107,119]
168. ~rich(X0) [subsumption resolution 167,165]
169. calm(X0) | ~generous(X0) [subsumption resolution 106,119]
170. ~generous(X0) [subsumption resolution 169,165]
211. patient(X0) | generous(X0) | creative(X0) | curious(X0) | patient(X0) [resolution 61,76]
212. patient(X0) | generous(X0) | creative(X0) | curious(X0) [duplicate literal removal 211]
213. patient(X0) | creative(X0) | curious(X0) [subsumption resolution 212,170]
214. patient(X0) | curious(X0) [subsumption resolution 213,119]
219. curious(X3) | quiet(X3) | generous(X3) [resolution 214,63]
223. curious(X3) | generous(X3) [subsumption resolution 219,164]
224. curious(X3) [subsumption resolution 223,170]
227. quiet(mary) | humble(mary) | tall(mary) [resolution 67,116]
233. humble(mary) | tall(mary) [subsumption resolution 227,164]
235. 16 <=> tall(mary) [avatar definition]
237. tall(mary) <- (16) [avatar component clause 235]
239. 17 <=> humble(mary) [avatar definition]
241. humble(mary) <- (17) [avatar component clause 239]
242. 16 | 17 [avatar split clause 233,239,235]
246. rich(mary) <- (16) [resolution 237,166]
258. $false <- (16) [subsumption resolution 246,168]
259. ~16 [avatar contradiction clause 258]
260. ~curious(mary) | creative(mary) <- (17) [resolution 241,58]
264. creative(mary) <- (17) [subsumption resolution 260,224]
265. $false <- (17) [subsumption resolution 264,119]
266. ~17 [avatar contradiction clause 265]
270. $false [avatar sat refutation 242,259,266]
% SZS output end Proof for 8163693285902679295828115
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is wise then someone is not quiet and vice versa.
Everyone who is either creative or not wise is not funny and vice versa.
Everyone who is both calm and quiet is not quiet.
If alice is old then someone is not wise or not kind and vice versa.
Everyone who is not happy is not rich.
If someone is not patient then someone is not funny or generous.
Everyone who is not generous is generous or happy and vice versa.
Everyone who is both rich and not humble is both funny and quiet.
If someone is both funny and not calm then someone is both not patient and old.
If someone is not tall or generous then alice is not humble or kind and vice versa.
Everyone who is both not quiet and not kind is brave or quiet and vice versa.
If paul is humble then someone is happy or not humble.
If paul is not rich then someone is not tall or calm and vice versa.
If someone is both tall and creative then someone is either not rich or not funny.
Everyone who is both old and happy is both rich and brave and vice versa.
If mary is both calm and not happy then someone is either not humble or generous and vice versa.
Someone is old.
Lucy is not calm or not wise.
Paul is both happy and not creative.
John is both humble and not strong.
Paul is not patient or happy.
Mary is either generous or creative.
Paul is either patient or kind. | John is tall. | entailment | ((?[X]:(wise(X)))<=>(?[X]:(~quiet(X))))&
(![X]:((creative(X)<~>~wise(X))<=>~funny(X)))&
(![X]:((calm(X)&quiet(X))=>~quiet(X)))&
((old(alice))<=>(?[X]:((~wise(X)|~kind(X)))))&
(![X]:(~happy(X)=>~rich(X)))&
((?[X]:(~patient(X)))=>(?[X]:((~funny(X)|generous(X)))))&
(![X]:(~generous(X)<=>(generous(X)|happy(X))))&
(![X]:((rich(X)&~humble(X))=>(funny(X)&quiet(X))))&
((?[X]:((funny(X)&~calm(X))))=>(?[X]:((~patient(X)&old(X)))))&
((?[X]:((~tall(X)|generous(X))))<=>((~humble(alice)|kind(alice))))&
(![X]:((~quiet(X)&~kind(X))<=>(brave(X)|quiet(X))))&
((humble(paul))=>(?[X]:((happy(X)|~humble(X)))))&
((~rich(paul))<=>(?[X]:((~tall(X)|calm(X)))))&
((?[X]:((tall(X)&creative(X))))=>(?[X]:((~rich(X)<~>~funny(X)))))&
(![X]:((old(X)&happy(X))<=>(rich(X)&brave(X))))&
(((calm(mary)&~happy(mary)))<=>(?[X]:((~humble(X)<~>generous(X)))))&
(?[X]:(old(X)))&
((~calm(lucy)|~wise(lucy)))&
((happy(paul)&~creative(paul)))&
((humble(john)&~strong(john)))&
((~patient(paul)|happy(paul)))&
((generous(mary)<~>creative(mary)))&
((patient(paul)<~>kind(paul))) | tall(john) | [
"p3",
"p6",
"p9",
"p10",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 626221511061730336623514
% SZS output start Proof for 626221511061730336623514
4. old(alice) <=> ? [X0] : (~kind(X0) | ~wise(X0)) [input p3]
7. ! [X0] : (~generous(X0) <=> (happy(X0) | generous(X0))) [input p6]
10. ? [X0] : (generous(X0) | ~tall(X0)) <=> (kind(alice) | ~humble(alice)) [input p9]
11. ! [X0] : ((~kind(X0) & ~quiet(X0)) <=> (quiet(X0) | brave(X0))) [input p10]
15. ! [X0] : ((happy(X0) & old(X0)) <=> (brave(X0) & rich(X0))) [input p14]
16. (~happy(mary) & calm(mary)) <=> ? [X0] : (~humble(X0) <~> generous(X0)) [input p15]
17. ? [X0] : old(X0) [input p16]
24. ~tall(john) [input hypothesis]
45. (old(alice) | ! [X0] : (kind(X0) & wise(X0))) & (? [X0] : (~kind(X0) | ~wise(X0)) | ~old(alice)) [nnf transformation 4]
46. (old(alice) | ! [X0] : (kind(X0) & wise(X0))) & (? [X1] : (~kind(X1) | ~wise(X1)) | ~old(alice)) [rectify 45]
47. ? [X1] : (~kind(X1) | ~wise(X1)) => (~kind(sK2) | ~wise(sK2)) [choice axiom]
48. (old(alice) | ! [X0] : (kind(X0) & wise(X0))) & ((~kind(sK2) | ~wise(sK2)) | ~old(alice)) [skolemisation 46,47]
52. ! [X0] : ((~generous(X0) | (~happy(X0) & ~generous(X0))) & ((happy(X0) | generous(X0)) | generous(X0))) [nnf transformation 7]
53. ! [X0] : ((~generous(X0) | (~happy(X0) & ~generous(X0))) & (happy(X0) | generous(X0) | generous(X0))) [flattening 52]
57. (? [X0] : (generous(X0) | ~tall(X0)) | (~kind(alice) & humble(alice))) & ((kind(alice) | ~humble(alice)) | ! [X0] : (~generous(X0) & tall(X0))) [nnf transformation 10]
58. (? [X0] : (generous(X0) | ~tall(X0)) | (~kind(alice) & humble(alice))) & (kind(alice) | ~humble(alice) | ! [X0] : (~generous(X0) & tall(X0))) [flattening 57]
59. (? [X0] : (generous(X0) | ~tall(X0)) | (~kind(alice) & humble(alice))) & (kind(alice) | ~humble(alice) | ! [X1] : (~generous(X1) & tall(X1))) [rectify 58]
60. ? [X0] : (generous(X0) | ~tall(X0)) => (generous(sK5) | ~tall(sK5)) [choice axiom]
61. ((generous(sK5) | ~tall(sK5)) | (~kind(alice) & humble(alice))) & (kind(alice) | ~humble(alice) | ! [X1] : (~generous(X1) & tall(X1))) [skolemisation 59,60]
62. ! [X0] : (((~kind(X0) & ~quiet(X0)) | (~quiet(X0) & ~brave(X0))) & ((quiet(X0) | brave(X0)) | (kind(X0) | quiet(X0)))) [nnf transformation 11]
63. ! [X0] : (((~kind(X0) & ~quiet(X0)) | (~quiet(X0) & ~brave(X0))) & (quiet(X0) | brave(X0) | kind(X0) | quiet(X0))) [flattening 62]
74. ! [X0] : (((happy(X0) & old(X0)) | (~brave(X0) | ~rich(X0))) & ((brave(X0) & rich(X0)) | (~happy(X0) | ~old(X0)))) [nnf transformation 15]
75. ! [X0] : (((happy(X0) & old(X0)) | ~brave(X0) | ~rich(X0)) & ((brave(X0) & rich(X0)) | ~happy(X0) | ~old(X0))) [flattening 74]
76. ((~happy(mary) & calm(mary)) | ! [X0] : ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0)))) & (? [X0] : ((~generous(X0) | humble(X0)) & (generous(X0) | ~humble(X0))) | (happy(mary) | ~calm(mary))) [nnf transformation 16]
77. ((~happy(mary) & calm(mary)) | ! [X0] : ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0)))) & (? [X0] : ((~generous(X0) | humble(X0)) & (generous(X0) | ~humble(X0))) | happy(mary) | ~calm(mary)) [flattening 76]
78. ((~happy(mary) & calm(mary)) | ! [X0] : ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0)))) & (? [X1] : ((~generous(X1) | humble(X1)) & (generous(X1) | ~humble(X1))) | happy(mary) | ~calm(mary)) [rectify 77]
79. ? [X1] : ((~generous(X1) | humble(X1)) & (generous(X1) | ~humble(X1))) => ((~generous(sK9) | humble(sK9)) & (generous(sK9) | ~humble(sK9))) [choice axiom]
80. ((~happy(mary) & calm(mary)) | ! [X0] : ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0)))) & (((~generous(sK9) | humble(sK9)) & (generous(sK9) | ~humble(sK9))) | happy(mary) | ~calm(mary)) [skolemisation 78,79]
81. ? [X0] : old(X0) => old(sK10) [choice axiom]
82. old(sK10) [skolemisation 17,81]
94. old(alice) | kind(X0) [cnf transformation 48]
97. happy(X0) | generous(X0) | generous(X0) [cnf transformation 53]
98. ~generous(X0) | ~generous(X0) [cnf transformation 53]
104. kind(alice) | ~humble(alice) | tall(X1) [cnf transformation 61]
111. ~brave(X0) | ~kind(X0) [cnf transformation 63]
120. brave(X0) | ~happy(X0) | ~old(X0) [cnf transformation 75]
127. ~happy(mary) | generous(X0) | humble(X0) [cnf transformation 80]
129. old(sK10) [cnf transformation 82]
139. ~tall(john) [cnf transformation 24]
142. happy(X0) | generous(X0) [duplicate literal removal 97]
143. ~generous(X0) [duplicate literal removal 98]
162. 5 <=> ! [X0] : kind(X0) [avatar definition]
163. kind(X0) <- (5) [avatar component clause 162]
165. 6 <=> old(alice) [avatar definition]
167. old(alice) <- (6) [avatar component clause 165]
168. 5 | 6 [avatar split clause 94,165,162]
194. happy(X0) [subsumption resolution 142,143]
210. 16 <=> kind(alice) [avatar definition]
211. kind(alice) <- (16) [avatar component clause 210]
220. 18 <=> humble(alice) [avatar definition]
221. ~humble(alice) <- (~18) [avatar component clause 220]
225. 19 <=> ! [X1] : tall(X1) [avatar definition]
226. tall(X1) <- (19) [avatar component clause 225]
227. 19 | ~18 | 16 [avatar split clause 104,210,220,225]
260. ~old(X0) | brave(X0) [subsumption resolution 120,194]
262. generous(X0) | humble(X0) [subsumption resolution 127,194]
263. humble(X0) [subsumption resolution 262,143]
284. $false <- (~18) [subsumption resolution 221,263]
285. 18 [avatar contradiction clause 284]
288. brave(sK10) [resolution 260,129]
289. brave(alice) <- (6) [resolution 260,167]
290. ~kind(sK10) [resolution 288,111]
293. ~kind(alice) <- (6) [resolution 289,111]
294. $false <- (6, 16) [subsumption resolution 293,211]
295. ~6 | ~16 [avatar contradiction clause 294]
306. $false <- (19) [resolution 226,139]
311. ~19 [avatar contradiction clause 306]
316. $false <- (5) [resolution 290,163]
317. ~5 [avatar contradiction clause 316]
318. $false [avatar sat refutation 168,227,285,295,311,317]
% SZS output end Proof for 626221511061730336623514
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is not strong.
Everyone who is either brave or not strong is either not funny or not tall and vice versa.
Everyone who is not calm or wise is both happy and not patient and vice versa.
Everyone who is both not brave and not tall is both quiet and strong.
Everyone who is patient is either brave or not wise and vice versa.
If john is happy or calm then someone is either quiet or not tall and vice versa.
If someone is not patient then someone is both not strong and happy and vice versa.
If alice is not calm or wise then mary is both not curious and not generous and vice versa.
Everyone who is quiet or not wise is not kind or kind.
If someone is both old and calm then someone is both not happy and old and vice versa.
If paul is not curious then someone is patient or not brave and vice versa.
If someone is either not brave or funny then someone is calm and vice versa.
Everyone who is either not strong or kind is either not patient or not funny.
Everyone who is both not old and not funny is wise or funny and vice versa.
Everyone who is wise or not strong is tall or not creative and vice versa.
Everyone who is both rich and not kind is tall or not curious and vice versa.
Alice is wise.
Mary is both calm and rich.
Lucy is not happy or not strong.
Someone is both rich and generous.
Someone is not brave or kind. | Alice is quiet. | entailment | (![X]:(brave(X)=>~strong(X)))&
(![X]:((brave(X)<~>~strong(X))<=>(~funny(X)<~>~tall(X))))&
(![X]:((~calm(X)|wise(X))<=>(happy(X)&~patient(X))))&
(![X]:((~brave(X)&~tall(X))=>(quiet(X)&strong(X))))&
(![X]:(patient(X)<=>(brave(X)<~>~wise(X))))&
(((happy(john)|calm(john)))<=>(?[X]:((quiet(X)<~>~tall(X)))))&
((?[X]:(~patient(X)))<=>(?[X]:((~strong(X)&happy(X)))))&
(((~calm(alice)|wise(alice)))<=>((~curious(mary)&~generous(mary))))&
(![X]:((quiet(X)|~wise(X))=>(~kind(X)|kind(X))))&
((?[X]:((old(X)&calm(X))))<=>(?[X]:((~happy(X)&old(X)))))&
((~curious(paul))<=>(?[X]:((patient(X)|~brave(X)))))&
((?[X]:((~brave(X)<~>funny(X))))<=>(?[X]:(calm(X))))&
(![X]:((~strong(X)<~>kind(X))=>(~patient(X)<~>~funny(X))))&
(![X]:((~old(X)&~funny(X))<=>(wise(X)|funny(X))))&
(![X]:((wise(X)|~strong(X))<=>(tall(X)|~creative(X))))&
(![X]:((rich(X)&~kind(X))<=>(tall(X)|~curious(X))))&
(wise(alice))&
((calm(mary)&rich(mary)))&
((~happy(lucy)|~strong(lucy)))&
(?[X]:((rich(X)&generous(X))))&
(?[X]:((~brave(X)|kind(X)))) | quiet(alice) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p12",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4643978344100473149565965
% SZS output start Proof for 4643978344100473149565965
1. ! [X0] : (brave(X0) => ~strong(X0)) [input p0]
2. ! [X0] : ((brave(X0) <~> ~strong(X0)) <=> (~funny(X0) <~> ~tall(X0))) [input p1]
3. ! [X0] : ((wise(X0) | ~calm(X0)) <=> (~patient(X0) & happy(X0))) [input p2]
4. ! [X0] : ((~tall(X0) & ~brave(X0)) => (strong(X0) & quiet(X0))) [input p3]
5. ! [X0] : (patient(X0) <=> (brave(X0) <~> ~wise(X0))) [input p4]
13. ! [X0] : ((~strong(X0) <~> kind(X0)) => (~patient(X0) <~> ~funny(X0))) [input p12]
14. ! [X0] : ((~funny(X0) & ~old(X0)) <=> (funny(X0) | wise(X0))) [input p13]
16. ! [X0] : ((~kind(X0) & rich(X0)) <=> (~curious(X0) | tall(X0))) [input p15]
17. wise(alice) [input p16]
22. ~quiet(alice) [input hypothesis]
26. ! [X0] : (~strong(X0) | ~brave(X0)) [ennf transformation 1]
27. ! [X0] : ((strong(X0) & quiet(X0)) | (tall(X0) | brave(X0))) [ennf transformation 4]
28. ! [X0] : ((strong(X0) & quiet(X0)) | tall(X0) | brave(X0)) [flattening 27]
31. ! [X0] : ((~patient(X0) <~> ~funny(X0)) | (~strong(X0) <=> kind(X0))) [ennf transformation 13]
32. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0)))) & (((tall(X0) | funny(X0)) & (~tall(X0) | ~funny(X0))) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [nnf transformation 2]
33. ! [X0] : (((wise(X0) | ~calm(X0)) | (patient(X0) | ~happy(X0))) & ((~patient(X0) & happy(X0)) | (~wise(X0) & calm(X0)))) [nnf transformation 3]
34. ! [X0] : ((wise(X0) | ~calm(X0) | patient(X0) | ~happy(X0)) & ((~patient(X0) & happy(X0)) | (~wise(X0) & calm(X0)))) [flattening 33]
35. ! [X0] : ((patient(X0) | ((brave(X0) | wise(X0)) & (~wise(X0) | ~brave(X0)))) & (((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | ~patient(X0))) [nnf transformation 5]
62. ! [X0] : (((funny(X0) | patient(X0)) & (~funny(X0) | ~patient(X0))) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0)))) [nnf transformation 31]
63. ! [X0] : (((~funny(X0) & ~old(X0)) | (~funny(X0) & ~wise(X0))) & ((funny(X0) | wise(X0)) | (funny(X0) | old(X0)))) [nnf transformation 14]
64. ! [X0] : (((~funny(X0) & ~old(X0)) | (~funny(X0) & ~wise(X0))) & (funny(X0) | wise(X0) | funny(X0) | old(X0))) [flattening 63]
67. ! [X0] : (((~kind(X0) & rich(X0)) | (curious(X0) & ~tall(X0))) & ((~curious(X0) | tall(X0)) | (kind(X0) | ~rich(X0)))) [nnf transformation 16]
68. ! [X0] : (((~kind(X0) & rich(X0)) | (curious(X0) & ~tall(X0))) & (~curious(X0) | tall(X0) | kind(X0) | ~rich(X0))) [flattening 67]
73. ~strong(X0) | ~brave(X0) [cnf transformation 26]
78. ~strong(X0) | brave(X0) | ~tall(X0) | funny(X0) [cnf transformation 32]
80. strong(X0) | ~brave(X0) | ~tall(X0) | funny(X0) [cnf transformation 32]
85. ~patient(X0) | ~wise(X0) [cnf transformation 34]
87. quiet(X0) | tall(X0) | brave(X0) [cnf transformation 28]
91. patient(X0) | ~wise(X0) | ~brave(X0) [cnf transformation 35]
122. kind(X0) | patient(X0) | funny(X0) | strong(X0) [cnf transformation 62]
128. ~funny(X0) | ~funny(X0) [cnf transformation 64]
136. ~kind(X0) | ~tall(X0) [cnf transformation 68]
138. wise(alice) [cnf transformation 17]
145. ~quiet(alice) [cnf transformation 22]
147. ~funny(X0) [duplicate literal removal 128]
149. ~tall(X0) | ~brave(X0) | funny(X0) [subsumption resolution 80,73]
151. ~tall(X0) | ~strong(X0) | funny(X0) [subsumption resolution 78,149]
152. ~wise(X0) | ~brave(X0) [subsumption resolution 91,85]
208. 13 <=> wise(alice) [avatar definition]
210. wise(alice) <- (13) [avatar component clause 208]
286. 13 [avatar split clause 138,208]
316. ~brave(alice) <- (13) [resolution 152,210]
341. tall(alice) | brave(alice) [resolution 87,145]
343. tall(alice) <- (13) [subsumption resolution 341,316]
387. ~strong(alice) | funny(alice) <- (13) [resolution 151,343]
388. ~strong(alice) <- (13) [subsumption resolution 387,147]
433. patient(X2) | funny(X2) | strong(X2) | ~tall(X2) [resolution 122,136]
435. ~tall(X2) | strong(X2) | patient(X2) [subsumption resolution 433,147]
494. strong(alice) | patient(alice) <- (13) [resolution 435,343]
499. patient(alice) <- (13) [subsumption resolution 494,388]
520. ~wise(alice) <- (13) [resolution 499,85]
522. $false <- (13) [subsumption resolution 520,210]
523. ~13 [avatar contradiction clause 522]
525. $false [avatar sat refutation 286,523]
% SZS output end Proof for 4643978344100473149565965
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or happy is both tall and creative. Everyone who is both not kind and curious is wise or patient. If someone is not brave or rich then alice is not brave or not rich. If someone is tall then someone is creative. If fred is both not generous and not brave then someone is either humble or not creative and vice versa. If paul is either not brave or not rich then alice is not humble or patient. Everyone who is old is both calm and quiet and vice versa. Everyone who is kind or creative is both happy and not rich. Everyone who is either not curious or not humble is both kind and tall and vice versa. Everyone who is not rich or quiet is calm or not curious and vice versa. Everyone who is not wise is both rich and not patient. Everyone who is strong is both curious and old. If fred is both kind and not happy then mary is not kind or calm. Everyone who is either not curious or happy is both not happy and rich and vice versa. Everyone who is patient or not curious is not humble or happy and vice versa. Mary is not creative. Lucy is either not creative or not happy. Someone is both kind and not old. Fred is rich or not patient. Someone is not generous or not kind. Someone is both happy and not calm. | Lucy is not happy. | contradiction | (![X]:((~kind(X)<~>happy(X))=>(tall(X)&creative(X))))&
(![X]:((~kind(X)&curious(X))=>(wise(X)|patient(X))))&
((?[X]:((~brave(X)|rich(X))))=>((~brave(alice)|~rich(alice))))&
((?[X]:(tall(X)))=>(?[X]:(creative(X))))&
(((~generous(fred)&~brave(fred)))<=>(?[X]:((humble(X)<~>~creative(X)))))&
(((~brave(paul)<~>~rich(paul)))=>((~humble(alice)|patient(alice))))&
(![X]:(old(X)<=>(calm(X)&quiet(X))))&
(![X]:((kind(X)|creative(X))=>(happy(X)&~rich(X))))&
(![X]:((~curious(X)<~>~humble(X))<=>(kind(X)&tall(X))))&
(![X]:((~rich(X)|quiet(X))<=>(calm(X)|~curious(X))))&
(![X]:(~wise(X)=>(rich(X)&~patient(X))))&
(![X]:(strong(X)=>(curious(X)&old(X))))&
(((kind(fred)&~happy(fred)))=>((~kind(mary)|calm(mary))))&
(![X]:((~curious(X)<~>happy(X))<=>(~happy(X)&rich(X))))&
(![X]:((patient(X)|~curious(X))<=>(~humble(X)|happy(X))))&
(~creative(mary))&
((~creative(lucy)<~>~happy(lucy)))&
(?[X]:((kind(X)&~old(X))))&
((rich(fred)|~patient(fred)))&
(?[X]:((~generous(X)|~kind(X))))&
(?[X]:((happy(X)&~calm(X)))) | ~happy(lucy) | [
"p7",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3396361154468472066583328
% SZS output start Proof for 3396361154468472066583328
8. ! [X0] : ((creative(X0) | kind(X0)) => (~rich(X0) & happy(X0))) [input p7]
17. ~creative(lucy) <~> ~happy(lucy) [input p16]
22. ~happy(lucy) [input hypothesis]
36. ! [X0] : ((~rich(X0) & happy(X0)) | (~creative(X0) & ~kind(X0))) [ennf transformation 8]
57. (happy(lucy) | creative(lucy)) & (~happy(lucy) | ~creative(lucy)) [nnf transformation 17]
81. happy(X0) | ~creative(X0) [cnf transformation 36]
107. happy(lucy) | creative(lucy) [cnf transformation 57]
114. ~happy(lucy) [cnf transformation 22]
187. happy(lucy) [subsumption resolution 107,81]
207. $false [subsumption resolution 114,187]
% SZS output end Proof for 3396361154468472066583328
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not humble is either generous or not calm.
If someone is either not creative or quiet then alice is either quiet or not kind and vice versa.
Everyone who is kind or not kind is both calm and not patient and vice versa.
If john is both not patient and not creative then fred is wise.
Everyone who is not humble is not creative or curious.
If john is not happy then someone is either not wise or not old and vice versa.
Everyone who is either rich or happy is both happy and funny.
Everyone who is creative or happy is either not brave or not creative.
Everyone who is both curious and not wise is either not wise or not brave and vice versa.
If someone is either not curious or not rich then someone is strong or not old.
If susan is not patient or funny then fred is either wise or not happy and vice versa.
Everyone who is either humble or happy is funny or generous and vice versa.
If someone is either not brave or not creative then lucy is wise or not old.
Everyone who is rich or not patient is both not humble and not curious and vice versa.
Everyone who is both not funny and not creative is both not wise and creative and vice versa.
Everyone who is either wise or tall is both calm and quiet.
Susan is not quiet.
Someone is either not rich or not calm.
Someone is either not rich or calm.
Susan is wise.
Someone is old or not funny.
Fred is quiet or generous.
Someone is not patient or not funny.
Alice is not curious or not quiet. | John is wise. | entailment | (![X]:((patient(X)|~humble(X))=>(generous(X)<~>~calm(X))))&
((?[X]:((~creative(X)<~>quiet(X))))<=>((quiet(alice)<~>~kind(alice))))&
(![X]:((kind(X)|~kind(X))<=>(calm(X)&~patient(X))))&
(((~patient(john)&~creative(john)))=>(wise(fred)))&
(![X]:(~humble(X)=>(~creative(X)|curious(X))))&
((~happy(john))<=>(?[X]:((~wise(X)<~>~old(X)))))&
(![X]:((rich(X)<~>happy(X))=>(happy(X)&funny(X))))&
(![X]:((creative(X)|happy(X))=>(~brave(X)<~>~creative(X))))&
(![X]:((curious(X)&~wise(X))<=>(~wise(X)<~>~brave(X))))&
((?[X]:((~curious(X)<~>~rich(X))))=>(?[X]:((strong(X)|~old(X)))))&
(((~patient(susan)|funny(susan)))<=>((wise(fred)<~>~happy(fred))))&
(![X]:((humble(X)<~>happy(X))<=>(funny(X)|generous(X))))&
((?[X]:((~brave(X)<~>~creative(X))))=>((wise(lucy)|~old(lucy))))&
(![X]:((rich(X)|~patient(X))<=>(~humble(X)&~curious(X))))&
(![X]:((~funny(X)&~creative(X))<=>(~wise(X)&creative(X))))&
(![X]:((wise(X)<~>tall(X))=>(calm(X)&quiet(X))))&
(~quiet(susan))&
(?[X]:((~rich(X)<~>~calm(X))))&
(?[X]:((~rich(X)<~>calm(X))))&
(wise(susan))&
(?[X]:((old(X)|~funny(X))))&
((quiet(fred)|generous(fred)))&
(?[X]:((~patient(X)|~funny(X))))&
((~curious(alice)|~quiet(alice))) | wise(john) | [
"p0",
"p2",
"p7",
"p8",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3016358537267684585905167
% SZS output start Proof for 3016358537267684585905167
1. ! [X0] : ((~humble(X0) | patient(X0)) => (generous(X0) <~> ~calm(X0))) [input p0]
3. ! [X0] : ((~kind(X0) | kind(X0)) <=> (~patient(X0) & calm(X0))) [input p2]
8. ! [X0] : ((happy(X0) | creative(X0)) => (~brave(X0) <~> ~creative(X0))) [input p7]
9. ! [X0] : ((~wise(X0) & curious(X0)) <=> (~wise(X0) <~> ~brave(X0))) [input p8]
12. ! [X0] : ((humble(X0) <~> happy(X0)) <=> (generous(X0) | funny(X0))) [input p11]
14. ! [X0] : ((~patient(X0) | rich(X0)) <=> (~curious(X0) & ~humble(X0))) [input p13]
15. ! [X0] : ((~creative(X0) & ~funny(X0)) <=> (creative(X0) & ~wise(X0))) [input p14]
25. ~wise(john) [input hypothesis]
28. ! [X0] : ((generous(X0) <~> ~calm(X0)) | (humble(X0) & ~patient(X0))) [ennf transformation 1]
34. ! [X0] : ((~brave(X0) <~> ~creative(X0)) | (~happy(X0) & ~creative(X0))) [ennf transformation 8]
38. ! [X0] : (((calm(X0) | ~generous(X0)) & (~calm(X0) | generous(X0))) | (humble(X0) & ~patient(X0))) [nnf transformation 28]
43. ! [X0] : (((~kind(X0) | kind(X0)) | (patient(X0) | ~calm(X0))) & ((~patient(X0) & calm(X0)) | (kind(X0) & ~kind(X0)))) [nnf transformation 3]
44. ! [X0] : ((~kind(X0) | kind(X0) | patient(X0) | ~calm(X0)) & ((~patient(X0) & calm(X0)) | (kind(X0) & ~kind(X0)))) [flattening 43]
50. ! [X0] : (((creative(X0) | brave(X0)) & (~creative(X0) | ~brave(X0))) | (~happy(X0) & ~creative(X0))) [nnf transformation 34]
51. ! [X0] : (((~wise(X0) & curious(X0)) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0)))) & (((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | (wise(X0) | ~curious(X0)))) [nnf transformation 9]
52. ! [X0] : (((~wise(X0) & curious(X0)) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0)))) & (((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | wise(X0) | ~curious(X0))) [flattening 51]
55. ! [X0] : ((((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | (~generous(X0) & ~funny(X0))) & ((generous(X0) | funny(X0)) | ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0))))) [nnf transformation 12]
56. ! [X0] : ((((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | (~generous(X0) & ~funny(X0))) & (generous(X0) | funny(X0) | ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0))))) [flattening 55]
58. ! [X0] : (((~patient(X0) | rich(X0)) | (curious(X0) | humble(X0))) & ((~curious(X0) & ~humble(X0)) | (patient(X0) & ~rich(X0)))) [nnf transformation 14]
59. ! [X0] : ((~patient(X0) | rich(X0) | curious(X0) | humble(X0)) & ((~curious(X0) & ~humble(X0)) | (patient(X0) & ~rich(X0)))) [flattening 58]
60. ! [X0] : (((~creative(X0) & ~funny(X0)) | (~creative(X0) | wise(X0))) & ((creative(X0) & ~wise(X0)) | (creative(X0) | funny(X0)))) [nnf transformation 15]
61. ! [X0] : (((~creative(X0) & ~funny(X0)) | ~creative(X0) | wise(X0)) & ((creative(X0) & ~wise(X0)) | creative(X0) | funny(X0))) [flattening 60]
74. ~calm(X0) | generous(X0) | humble(X0) [cnf transformation 38]
85. calm(X0) | ~kind(X0) [cnf transformation 44]
86. kind(X0) | calm(X0) [cnf transformation 44]
87. ~patient(X0) | ~kind(X0) [cnf transformation 44]
88. ~patient(X0) | kind(X0) [cnf transformation 44]
103. ~happy(X0) | brave(X0) | creative(X0) [cnf transformation 50]
106. ~brave(X0) | curious(X0) | wise(X0) [cnf transformation 52]
119. ~generous(X0) | humble(X0) | happy(X0) [cnf transformation 56]
125. ~humble(X0) | patient(X0) [cnf transformation 59]
127. ~curious(X0) | patient(X0) [cnf transformation 59]
132. ~creative(X0) | ~creative(X0) | wise(X0) [cnf transformation 61]
147. ~wise(john) [cnf transformation 25]
149. ~creative(X0) | wise(X0) [duplicate literal removal 132]
184. ~patient(X0) [subsumption resolution 87,88]
185. calm(X0) [subsumption resolution 85,86]
251. ~curious(X0) [subsumption resolution 127,184]
252. ~humble(X0) [subsumption resolution 125,184]
294. generous(X0) | humble(X0) [resolution 74,185]
295. generous(X0) [subsumption resolution 294,252]
361. humble(X0) | happy(X0) [resolution 119,295]
362. happy(X0) [subsumption resolution 361,252]
364. brave(X0) | creative(X0) [resolution 362,103]
419. creative(X0) | curious(X0) | wise(X0) [resolution 364,106]
422. creative(X0) | wise(X0) [subsumption resolution 419,251]
423. wise(X0) [subsumption resolution 422,149]
427. $false [resolution 423,147]
% SZS output end Proof for 3016358537267684585905167
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or generous is either generous or not generous. Everyone who is both patient and tall is rich or tall and vice versa. Everyone who is not happy or rich is not calm and vice versa. Everyone who is humble or not generous is both rich and not old and vice versa. Everyone who is both not calm and not humble is both not funny and not patient. If someone is creative or not creative then someone is kind or not happy and vice versa. Everyone who is both not humble and not creative is either funny or not calm. Everyone who is humble is either not creative or patient and vice versa. Everyone who is either curious or kind is not patient. If alice is both not kind and kind then john is either creative or not creative. Everyone who is not funny or calm is not happy or not creative and vice versa. Everyone who is humble is either not creative or happy. Everyone who is both quiet and not creative is not tall or not old and vice versa. If someone is creative or not kind then someone is not tall and vice versa. Everyone who is not tall or generous is not old or funny and vice versa. Someone is not creative or not strong. Someone is both patient and calm. Mary is either not kind or not patient. Fred is either not generous or curious. | Fred is not happy. | contradiction | (![X]:((happy(X)<~>generous(X))=>(generous(X)<~>~generous(X))))&
(![X]:((patient(X)&tall(X))<=>(rich(X)|tall(X))))&
(![X]:((~happy(X)|rich(X))<=>~calm(X)))&
(![X]:((humble(X)|~generous(X))<=>(rich(X)&~old(X))))&
(![X]:((~calm(X)&~humble(X))=>(~funny(X)&~patient(X))))&
((?[X]:((creative(X)|~creative(X))))<=>(?[X]:((kind(X)|~happy(X)))))&
(![X]:((~humble(X)&~creative(X))=>(funny(X)<~>~calm(X))))&
(![X]:(humble(X)<=>(~creative(X)<~>patient(X))))&
(![X]:((curious(X)<~>kind(X))=>~patient(X)))&
(((~kind(alice)&kind(alice)))=>((creative(john)<~>~creative(john))))&
(![X]:((~funny(X)|calm(X))<=>(~happy(X)|~creative(X))))&
(![X]:(humble(X)=>(~creative(X)<~>happy(X))))&
(![X]:((quiet(X)&~creative(X))<=>(~tall(X)|~old(X))))&
((?[X]:((creative(X)|~kind(X))))<=>(?[X]:(~tall(X))))&
(![X]:((~tall(X)|generous(X))<=>(~old(X)|funny(X))))&
(?[X]:((~creative(X)|~strong(X))))&
(?[X]:((patient(X)&calm(X))))&
((~kind(mary)<~>~patient(mary)))&
((~generous(fred)<~>curious(fred))) | ~happy(fred) | [
"p1",
"p2",
"p3",
"p4",
"p7",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8153853854635782876554733
% SZS output start Proof for 8153853854635782876554733
2. ! [X0] : ((tall(X0) & patient(X0)) <=> (tall(X0) | rich(X0))) [input p1]
3. ! [X0] : ((rich(X0) | ~happy(X0)) <=> ~calm(X0)) [input p2]
4. ! [X0] : ((~generous(X0) | humble(X0)) <=> (~old(X0) & rich(X0))) [input p3]
5. ! [X0] : ((~humble(X0) & ~calm(X0)) => (~patient(X0) & ~funny(X0))) [input p4]
8. ! [X0] : (humble(X0) <=> (~creative(X0) <~> patient(X0))) [input p7]
12. ! [X0] : (humble(X0) => (~creative(X0) <~> happy(X0))) [input p11]
13. ! [X0] : ((~creative(X0) & quiet(X0)) <=> (~old(X0) | ~tall(X0))) [input p12]
20. ~happy(fred) [input hypothesis]
25. ! [X0] : ((~patient(X0) & ~funny(X0)) | (humble(X0) | calm(X0))) [ennf transformation 5]
26. ! [X0] : ((~patient(X0) & ~funny(X0)) | humble(X0) | calm(X0)) [flattening 25]
32. ! [X0] : ((~creative(X0) <~> happy(X0)) | ~humble(X0)) [ennf transformation 12]
34. ! [X0] : (((tall(X0) & patient(X0)) | (~tall(X0) & ~rich(X0))) & ((tall(X0) | rich(X0)) | (~tall(X0) | ~patient(X0)))) [nnf transformation 2]
35. ! [X0] : (((tall(X0) & patient(X0)) | (~tall(X0) & ~rich(X0))) & (tall(X0) | rich(X0) | ~tall(X0) | ~patient(X0))) [flattening 34]
36. ! [X0] : (((rich(X0) | ~happy(X0)) | calm(X0)) & (~calm(X0) | (~rich(X0) & happy(X0)))) [nnf transformation 3]
37. ! [X0] : ((rich(X0) | ~happy(X0) | calm(X0)) & (~calm(X0) | (~rich(X0) & happy(X0)))) [flattening 36]
38. ! [X0] : (((~generous(X0) | humble(X0)) | (old(X0) | ~rich(X0))) & ((~old(X0) & rich(X0)) | (generous(X0) & ~humble(X0)))) [nnf transformation 4]
39. ! [X0] : ((~generous(X0) | humble(X0) | old(X0) | ~rich(X0)) & ((~old(X0) & rich(X0)) | (generous(X0) & ~humble(X0)))) [flattening 38]
46. ! [X0] : ((humble(X0) | ((~creative(X0) | ~patient(X0)) & (patient(X0) | creative(X0)))) & (((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | ~humble(X0))) [nnf transformation 8]
51. ! [X0] : (((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | ~humble(X0)) [nnf transformation 32]
52. ! [X0] : (((~creative(X0) & quiet(X0)) | (old(X0) & tall(X0))) & ((~old(X0) | ~tall(X0)) | (creative(X0) | ~quiet(X0)))) [nnf transformation 13]
53. ! [X0] : (((~creative(X0) & quiet(X0)) | (old(X0) & tall(X0))) & (~old(X0) | ~tall(X0) | creative(X0) | ~quiet(X0))) [flattening 52]
70. ~rich(X0) | patient(X0) [cnf transformation 35]
71. ~tall(X0) | patient(X0) [cnf transformation 35]
74. ~calm(X0) | happy(X0) [cnf transformation 37]
77. ~humble(X0) | rich(X0) [cnf transformation 39]
83. ~patient(X0) | humble(X0) | calm(X0) [cnf transformation 26]
91. ~humble(X0) | creative(X0) | ~patient(X0) [cnf transformation 46]
92. creative(X0) | patient(X0) | humble(X0) [cnf transformation 46]
102. ~creative(X0) | happy(X0) | ~humble(X0) [cnf transformation 51]
107. ~creative(X0) | tall(X0) [cnf transformation 53]
122. ~happy(fred) [cnf transformation 20]
201. patient(X3) | humble(X3) | tall(X3) [resolution 92,107]
203. humble(X3) | patient(X3) [subsumption resolution 201,71]
207. patient(X1) | rich(X1) [resolution 203,77]
208. patient(X1) [subsumption resolution 207,70]
214. humble(X0) | calm(X0) [resolution 208,83]
216. calm(X0) | creative(X0) | ~patient(X0) [resolution 214,91]
218. creative(X0) | calm(X0) [subsumption resolution 216,208]
228. happy(X0) | ~humble(X0) | calm(X0) [resolution 102,218]
230. happy(X0) | calm(X0) [subsumption resolution 228,214]
231. happy(X0) [subsumption resolution 230,74]
232. $false [resolution 231,122]
% SZS output end Proof for 8153853854635782876554733
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is kind or not creative then fred is either not kind or not generous and vice versa.
Everyone who is not old is patient.
Everyone who is both generous and patient is strong or not quiet and vice versa.
If someone is both humble and patient then someone is both not patient and not brave and vice versa.
If john is both tall and rich then someone is creative.
If susan is not humble then someone is both not humble and not wise.
Everyone who is strong or generous is not happy.
Everyone who is not patient or not old is either not rich or not creative and vice versa.
If alice is strong then mary is brave.
If someone is humble then fred is both not old and not generous and vice versa.
Everyone who is either not quiet or tall is either not curious or kind.
Everyone who is either not humble or wise is funny and vice versa.
Everyone who is not wise or not rich is both not quiet and old and vice versa.
If mary is either not happy or not rich then someone is either funny or not happy.
Everyone who is quiet is both old and not humble.
Everyone who is both creative and funny is brave or calm and vice versa.
Someone is old or kind.
Fred is either not creative or not kind.
Someone is not strong.
Fred is not brave.
Someone is either rich or not tall.
Mary is not creative. | John is kind. | neutral | (((kind(paul)|~creative(paul)))<=>((~kind(fred)<~>~generous(fred))))&
(![X]:(~old(X)=>patient(X)))&
(![X]:((generous(X)&patient(X))<=>(strong(X)|~quiet(X))))&
((?[X]:((humble(X)&patient(X))))<=>(?[X]:((~patient(X)&~brave(X)))))&
(((tall(john)&rich(john)))=>(?[X]:(creative(X))))&
((~humble(susan))=>(?[X]:((~humble(X)&~wise(X)))))&
(![X]:((strong(X)|generous(X))=>~happy(X)))&
(![X]:((~patient(X)|~old(X))<=>(~rich(X)<~>~creative(X))))&
((strong(alice))=>(brave(mary)))&
((?[X]:(humble(X)))<=>((~old(fred)&~generous(fred))))&
(![X]:((~quiet(X)<~>tall(X))=>(~curious(X)<~>kind(X))))&
(![X]:((~humble(X)<~>wise(X))<=>funny(X)))&
(![X]:((~wise(X)|~rich(X))<=>(~quiet(X)&old(X))))&
(((~happy(mary)<~>~rich(mary)))=>(?[X]:((funny(X)<~>~happy(X)))))&
(![X]:(quiet(X)=>(old(X)&~humble(X))))&
(![X]:((creative(X)&funny(X))<=>(brave(X)|calm(X))))&
(?[X]:((old(X)|kind(X))))&
((~creative(fred)<~>~kind(fred)))&
(?[X]:(~strong(X)))&
(~brave(fred))&
(?[X]:((rich(X)<~>~tall(X))))&
(~creative(mary)) | kind(john) | [] | null | 0 |
If fred is both not rich and patient then lucy is old or curious and vice versa.
Everyone who is both generous and not rich is brave.
Everyone who is either kind or not rich is both generous and not humble.
If someone is curious or humble then someone is either curious or funny.
If someone is both curious and not quiet then lucy is not rich or brave and vice versa.
Everyone who is either patient or calm is either generous or not creative.
If paul is strong or not patient then alice is humble.
Everyone who is not happy or not humble is not happy.
If john is calm then someone is both not humble and quiet and vice versa.
If someone is either brave or happy then john is quiet.
If paul is either kind or not rich then john is either not quiet or kind.
If john is both not wise and not tall then alice is either not tall or not creative.
If someone is either strong or wise then mary is either not creative or strong.
If alice is creative then someone is not kind or old and vice versa.
Everyone who is either strong or not happy is not funny and vice versa.
Everyone who is generous is not curious and vice versa.
Fred is not strong.
John is happy.
Susan is creative or humble.
Someone is both not kind and tall.
Someone is either not curious or wise.
Lucy is either not generous or creative.
Someone is both humble and old.
Someone is strong. | Alice is not creative. | contradiction | (((~rich(fred)&patient(fred)))<=>((old(lucy)|curious(lucy))))&
(![X]:((generous(X)&~rich(X))=>brave(X)))&
(![X]:((kind(X)<~>~rich(X))=>(generous(X)&~humble(X))))&
((?[X]:((curious(X)|humble(X))))=>(?[X]:((curious(X)<~>funny(X)))))&
((?[X]:((curious(X)&~quiet(X))))<=>((~rich(lucy)|brave(lucy))))&
(![X]:((patient(X)<~>calm(X))=>(generous(X)<~>~creative(X))))&
(((strong(paul)|~patient(paul)))=>(humble(alice)))&
(![X]:((~happy(X)|~humble(X))=>~happy(X)))&
((calm(john))<=>(?[X]:((~humble(X)&quiet(X)))))&
((?[X]:((brave(X)<~>happy(X))))=>(quiet(john)))&
(((kind(paul)<~>~rich(paul)))=>((~quiet(john)<~>kind(john))))&
(((~wise(john)&~tall(john)))=>((~tall(alice)<~>~creative(alice))))&
((?[X]:((strong(X)<~>wise(X))))=>((~creative(mary)<~>strong(mary))))&
((creative(alice))<=>(?[X]:((~kind(X)|old(X)))))&
(![X]:((strong(X)<~>~happy(X))<=>~funny(X)))&
(![X]:(generous(X)<=>~curious(X)))&
(~strong(fred))&
(happy(john))&
((creative(susan)|humble(susan)))&
(?[X]:((~kind(X)&tall(X))))&
(?[X]:((~curious(X)<~>wise(X))))&
((~generous(lucy)<~>creative(lucy)))&
(?[X]:((humble(X)&old(X))))&
(?[X]:(strong(X))) | ~creative(alice) | [
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4126354066231820082297629
% SZS output start Proof for 4126354066231820082297629
14. creative(alice) <=> ? [X0] : (old(X0) | ~kind(X0)) [input p13]
23. ? [X0] : (old(X0) & humble(X0)) [input p22]
25. ~creative(alice) [input hypothesis]
60. (creative(alice) | ! [X0] : (~old(X0) & kind(X0))) & (? [X0] : (old(X0) | ~kind(X0)) | ~creative(alice)) [nnf transformation 14]
61. (creative(alice) | ! [X0] : (~old(X0) & kind(X0))) & (? [X1] : (old(X1) | ~kind(X1)) | ~creative(alice)) [rectify 60]
62. ? [X1] : (old(X1) | ~kind(X1)) => (old(sK3) | ~kind(sK3)) [choice axiom]
63. (creative(alice) | ! [X0] : (~old(X0) & kind(X0))) & ((old(sK3) | ~kind(sK3)) | ~creative(alice)) [skolemisation 61,62]
72. ? [X0] : (old(X0) & humble(X0)) => (old(sK6) & humble(sK6)) [choice axiom]
73. old(sK6) & humble(sK6) [skolemisation 23,72]
120. creative(alice) | ~old(X0) [cnf transformation 63]
137. old(sK6) [cnf transformation 73]
139. ~creative(alice) [cnf transformation 25]
276. 30 <=> creative(alice) [avatar definition]
300. 35 <=> ! [X0] : ~old(X0) [avatar definition]
301. ~old(X0) <- (35) [avatar component clause 300]
302. 35 | 30 [avatar split clause 120,276,300]
345. ~30 [avatar split clause 139,276]
348. $false <- (35) [resolution 301,137]
349. ~35 [avatar contradiction clause 348]
350. $false [avatar sat refutation 302,345,349]
% SZS output end Proof for 4126354066231820082297629
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not funny or wise is either rich or not tall and vice versa.
Everyone who is both not old and not strong is brave or creative and vice versa.
Everyone who is not rich is strong.
Everyone who is both not rich and brave is not happy or not curious and vice versa.
Everyone who is both not wise and happy is either not tall or brave and vice versa.
If john is either not old or not rich then lucy is both not brave and humble.
Everyone who is not old is not brave and vice versa.
Everyone who is quiet is both creative and not creative.
Everyone who is wise or not happy is both not happy and not calm and vice versa.
If susan is not rich then lucy is creative or happy and vice versa.
Everyone who is either patient or not kind is not rich and vice versa.
If someone is both not funny and not generous then someone is either not tall or happy and vice versa.
If someone is not creative or not tall then someone is not quiet and vice versa.
If someone is not happy or not strong then mary is either tall or not tall.
Someone is either kind or not rich.
Someone is either not curious or strong.
John is either not humble or strong.
Someone is both not strong and calm.
Fred is both not kind and not creative. | Susan is not strong. | contradiction | (![X]:((~funny(X)<~>wise(X))<=>(rich(X)<~>~tall(X))))&
(![X]:((~old(X)&~strong(X))<=>(brave(X)|creative(X))))&
(![X]:(~rich(X)=>strong(X)))&
(![X]:((~rich(X)&brave(X))<=>(~happy(X)|~curious(X))))&
(![X]:((~wise(X)&happy(X))<=>(~tall(X)<~>brave(X))))&
(((~old(john)<~>~rich(john)))=>((~brave(lucy)&humble(lucy))))&
(![X]:(~old(X)<=>~brave(X)))&
(![X]:(quiet(X)=>(creative(X)&~creative(X))))&
(![X]:((wise(X)|~happy(X))<=>(~happy(X)&~calm(X))))&
((~rich(susan))<=>((creative(lucy)|happy(lucy))))&
(![X]:((patient(X)<~>~kind(X))<=>~rich(X)))&
((?[X]:((~funny(X)&~generous(X))))<=>(?[X]:((~tall(X)<~>happy(X)))))&
((?[X]:((~creative(X)|~tall(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:((~happy(X)|~strong(X))))=>((tall(mary)<~>~tall(mary))))&
(?[X]:((kind(X)<~>~rich(X))))&
(?[X]:((~curious(X)<~>strong(X))))&
((~humble(john)<~>strong(john)))&
(?[X]:((~strong(X)&calm(X))))&
((~kind(fred)&~creative(fred))) | ~strong(susan) | [
"p1",
"p2",
"p3",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7514545434350179052322830
% SZS output start Proof for 7514545434350179052322830
2. ! [X0] : ((~strong(X0) & ~old(X0)) <=> (creative(X0) | brave(X0))) [input p1]
3. ! [X0] : (~rich(X0) => strong(X0)) [input p2]
4. ! [X0] : ((brave(X0) & ~rich(X0)) <=> (~curious(X0) | ~happy(X0))) [input p3]
7. ! [X0] : (~old(X0) <=> ~brave(X0)) [input p6]
10. ~rich(susan) <=> (happy(lucy) | creative(lucy)) [input p9]
20. ~strong(susan) [input hypothesis]
23. ! [X0] : (strong(X0) | rich(X0)) [ennf transformation 3]
28. ! [X0] : (((~strong(X0) & ~old(X0)) | (~creative(X0) & ~brave(X0))) & ((creative(X0) | brave(X0)) | (strong(X0) | old(X0)))) [nnf transformation 2]
29. ! [X0] : (((~strong(X0) & ~old(X0)) | (~creative(X0) & ~brave(X0))) & (creative(X0) | brave(X0) | strong(X0) | old(X0))) [flattening 28]
30. ! [X0] : (((brave(X0) & ~rich(X0)) | (curious(X0) & happy(X0))) & ((~curious(X0) | ~happy(X0)) | (~brave(X0) | rich(X0)))) [nnf transformation 4]
31. ! [X0] : (((brave(X0) & ~rich(X0)) | (curious(X0) & happy(X0))) & (~curious(X0) | ~happy(X0) | ~brave(X0) | rich(X0))) [flattening 30]
35. ! [X0] : ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0))) [nnf transformation 7]
38. (~rich(susan) | (~happy(lucy) & ~creative(lucy))) & ((happy(lucy) | creative(lucy)) | rich(susan)) [nnf transformation 10]
39. (~rich(susan) | (~happy(lucy) & ~creative(lucy))) & (happy(lucy) | creative(lucy) | rich(susan)) [flattening 38]
70. ~brave(X0) | ~old(X0) [cnf transformation 29]
74. strong(X0) | rich(X0) [cnf transformation 23]
78. happy(X0) | brave(X0) [cnf transformation 31]
90. ~brave(X0) | old(X0) [cnf transformation 35]
91. ~old(X0) | brave(X0) [cnf transformation 35]
101. ~rich(susan) | ~happy(lucy) [cnf transformation 39]
129. ~strong(susan) [cnf transformation 20]
152. ~old(X0) [subsumption resolution 91,70]
153. ~brave(X0) [subsumption resolution 90,152]
156. 5 <=> happy(lucy) [avatar definition]
158. ~happy(lucy) <- (~5) [avatar component clause 156]
160. 6 <=> rich(susan) [avatar definition]
163. ~5 | ~6 [avatar split clause 101,160,156]
245. rich(susan) [resolution 74,129]
252. 6 [avatar split clause 245,160]
262. brave(lucy) <- (~5) [resolution 78,158]
265. $false <- (~5) [subsumption resolution 262,153]
266. 5 [avatar contradiction clause 265]
267. $false [avatar sat refutation 163,252,266]
% SZS output end Proof for 7514545434350179052322830
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not old is kind or brave and vice versa.
If john is not wise then someone is not funny or not curious and vice versa.
Everyone who is not brave or not curious is not kind and vice versa.
If someone is curious then someone is either not creative or tall.
Everyone who is either not curious or tall is either calm or creative and vice versa.
If someone is happy then fred is both not tall and happy and vice versa.
If someone is either brave or not kind then someone is either not funny or curious and vice versa.
Everyone who is either calm or creative is not kind.
If someone is both not funny and not humble then someone is both not quiet and not happy and vice versa.
Everyone who is both not old and not curious is patient or curious.
If john is both old and not strong then someone is not calm.
If paul is both not funny and curious then someone is not strong and vice versa.
Everyone who is not brave is not happy.
Everyone who is patient is both not quiet and not tall.
Everyone who is funny is rich and vice versa.
Everyone who is both not tall and not wise is strong or brave and vice versa.
Susan is happy or old.
Fred is not old or humble.
Someone is either tall or not brave.
Someone is either creative or not creative.
Paul is rich or not patient.
Someone is funny or not tall.
Someone is both quiet and not happy.
Paul is either funny or not funny. | Susan is happy. | neutral | (![X]:((patient(X)<~>~old(X))<=>(kind(X)|brave(X))))&
((~wise(john))<=>(?[X]:((~funny(X)|~curious(X)))))&
(![X]:((~brave(X)|~curious(X))<=>~kind(X)))&
((?[X]:(curious(X)))=>(?[X]:((~creative(X)<~>tall(X)))))&
(![X]:((~curious(X)<~>tall(X))<=>(calm(X)<~>creative(X))))&
((?[X]:(happy(X)))<=>((~tall(fred)&happy(fred))))&
((?[X]:((brave(X)<~>~kind(X))))<=>(?[X]:((~funny(X)<~>curious(X)))))&
(![X]:((calm(X)<~>creative(X))=>~kind(X)))&
((?[X]:((~funny(X)&~humble(X))))<=>(?[X]:((~quiet(X)&~happy(X)))))&
(![X]:((~old(X)&~curious(X))=>(patient(X)|curious(X))))&
(((old(john)&~strong(john)))=>(?[X]:(~calm(X))))&
(((~funny(paul)&curious(paul)))<=>(?[X]:(~strong(X))))&
(![X]:(~brave(X)=>~happy(X)))&
(![X]:(patient(X)=>(~quiet(X)&~tall(X))))&
(![X]:(funny(X)<=>rich(X)))&
(![X]:((~tall(X)&~wise(X))<=>(strong(X)|brave(X))))&
((happy(susan)|old(susan)))&
((~old(fred)|humble(fred)))&
(?[X]:((tall(X)<~>~brave(X))))&
(?[X]:((creative(X)<~>~creative(X))))&
((rich(paul)|~patient(paul)))&
(?[X]:((funny(X)|~tall(X))))&
(?[X]:((quiet(X)&~happy(X))))&
((funny(paul)<~>~funny(paul))) | happy(susan) | [] | null | 0 |
Everyone who is quiet or not wise is wise or not humble.
If fred is not brave then fred is both curious and wise.
Everyone who is either not happy or not curious is old and vice versa.
If mary is rich then someone is old.
If someone is quiet or not old then someone is either not tall or strong and vice versa.
If lucy is both brave and not patient then fred is generous or not creative.
Everyone who is not calm is curious.
Everyone who is both not brave and generous is not rich or kind.
If fred is both not rich and not brave then someone is not quiet.
Everyone who is kind or patient is not old and vice versa.
If lucy is either not strong or not humble then someone is both not quiet and not funny and vice versa.
Everyone who is creative is not tall or rich.
Everyone who is both not brave and rich is both not patient and not happy and vice versa.
Everyone who is not rich is both not quiet and wise.
If someone is either calm or curious then someone is either kind or happy and vice versa.
If alice is either not strong or funny then someone is both not wise and tall and vice versa.
Someone is calm.
Mary is either humble or tall.
Paul is both not rich and not brave.
Someone is both not strong and not happy.
Alice is either brave or kind.
Fred is funny or not funny.
John is humble or rich.
Mary is both happy and humble. | Paul is not quiet. | entailment | (![X]:((quiet(X)|~wise(X))=>(wise(X)|~humble(X))))&
((~brave(fred))=>((curious(fred)&wise(fred))))&
(![X]:((~happy(X)<~>~curious(X))<=>old(X)))&
((rich(mary))=>(?[X]:(old(X))))&
((?[X]:((quiet(X)|~old(X))))<=>(?[X]:((~tall(X)<~>strong(X)))))&
(((brave(lucy)&~patient(lucy)))=>((generous(fred)|~creative(fred))))&
(![X]:(~calm(X)=>curious(X)))&
(![X]:((~brave(X)&generous(X))=>(~rich(X)|kind(X))))&
(((~rich(fred)&~brave(fred)))=>(?[X]:(~quiet(X))))&
(![X]:((kind(X)|patient(X))<=>~old(X)))&
(((~strong(lucy)<~>~humble(lucy)))<=>(?[X]:((~quiet(X)&~funny(X)))))&
(![X]:(creative(X)=>(~tall(X)|rich(X))))&
(![X]:((~brave(X)&rich(X))<=>(~patient(X)&~happy(X))))&
(![X]:(~rich(X)=>(~quiet(X)&wise(X))))&
((?[X]:((calm(X)<~>curious(X))))<=>(?[X]:((kind(X)<~>happy(X)))))&
(((~strong(alice)<~>funny(alice)))<=>(?[X]:((~wise(X)&tall(X)))))&
(?[X]:(calm(X)))&
((humble(mary)<~>tall(mary)))&
((~rich(paul)&~brave(paul)))&
(?[X]:((~strong(X)&~happy(X))))&
((brave(alice)<~>kind(alice)))&
((funny(fred)|~funny(fred)))&
((humble(john)|rich(john)))&
((happy(mary)&humble(mary))) | ~quiet(paul) | [
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5251158379262929602361435
% SZS output start Proof for 5251158379262929602361435
14. ! [X0] : (~rich(X0) => (wise(X0) & ~quiet(X0))) [input p13]
19. ~brave(paul) & ~rich(paul) [input p18]
25. quiet(paul) [input hypothesis]
38. ! [X0] : ((wise(X0) & ~quiet(X0)) | rich(X0)) [ennf transformation 14]
102. ~quiet(X0) | rich(X0) [cnf transformation 38]
121. ~rich(paul) [cnf transformation 19]
131. quiet(paul) [cnf transformation 25]
320. rich(paul) [resolution 102,131]
321. $false [subsumption resolution 320,121]
% SZS output end Proof for 5251158379262929602361435
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm or calm is both not creative and not brave and vice versa.
Everyone who is not calm or not funny is tall or not humble and vice versa.
If someone is curious or tall then someone is both tall and brave.
If lucy is both curious and not funny then susan is either not humble or brave.
Everyone who is both patient and not tall is either not tall or not humble and vice versa.
Everyone who is strong or calm is kind.
Everyone who is quiet or not rich is both not happy and kind.
If someone is not quiet then someone is either patient or not brave.
If mary is either old or not patient then john is both patient and not rich and vice versa.
Everyone who is not wise is either not old or not humble and vice versa.
Everyone who is either humble or not humble is not happy or not wise and vice versa.
If someone is generous then susan is either quiet or not kind and vice versa.
If mary is creative or old then someone is either not patient or kind and vice versa.
Everyone who is either strong or not creative is kind or not wise and vice versa.
Everyone who is not old is not funny or not humble.
Everyone who is either not old or not calm is either strong or brave and vice versa.
Someone is either funny or creative.
Fred is either not calm or happy.
Paul is both not old and wise.
Someone is both not brave and funny.
Someone is either calm or not old.
Someone is both humble and not brave.
Someone is happy. | Susan is not happy. | neutral | (![X]:((~calm(X)|calm(X))<=>(~creative(X)&~brave(X))))&
(![X]:((~calm(X)|~funny(X))<=>(tall(X)|~humble(X))))&
((?[X]:((curious(X)|tall(X))))=>(?[X]:((tall(X)&brave(X)))))&
(((curious(lucy)&~funny(lucy)))=>((~humble(susan)<~>brave(susan))))&
(![X]:((patient(X)&~tall(X))<=>(~tall(X)<~>~humble(X))))&
(![X]:((strong(X)|calm(X))=>kind(X)))&
(![X]:((quiet(X)|~rich(X))=>(~happy(X)&kind(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((patient(X)<~>~brave(X)))))&
(((old(mary)<~>~patient(mary)))<=>((patient(john)&~rich(john))))&
(![X]:(~wise(X)<=>(~old(X)<~>~humble(X))))&
(![X]:((humble(X)<~>~humble(X))<=>(~happy(X)|~wise(X))))&
((?[X]:(generous(X)))<=>((quiet(susan)<~>~kind(susan))))&
(((creative(mary)|old(mary)))<=>(?[X]:((~patient(X)<~>kind(X)))))&
(![X]:((strong(X)<~>~creative(X))<=>(kind(X)|~wise(X))))&
(![X]:(~old(X)=>(~funny(X)|~humble(X))))&
(![X]:((~old(X)<~>~calm(X))<=>(strong(X)<~>brave(X))))&
(?[X]:((funny(X)<~>creative(X))))&
((~calm(fred)<~>happy(fred)))&
((~old(paul)&wise(paul)))&
(?[X]:((~brave(X)&funny(X))))&
(?[X]:((calm(X)<~>~old(X))))&
(?[X]:((humble(X)&~brave(X))))&
(?[X]:(happy(X))) | ~happy(susan) | [] | null | 0 |
If someone is old or wise then alice is calm. Everyone who is either not kind or not happy is either not quiet or old and vice versa. If someone is not old then susan is not funny. If mary is patient then someone is not calm and vice versa. If john is either not happy or rich then someone is old or not strong and vice versa. Everyone who is not quiet or not happy is both not funny and rich and vice versa. Everyone who is either not quiet or calm is both kind and not brave and vice versa. Everyone who is either old or not strong is both patient and not happy and vice versa. Everyone who is both not curious and rich is not strong. Everyone who is both not calm and not quiet is both calm and not creative. Everyone who is both not calm and curious is not funny or not quiet and vice versa. If someone is not creative or strong then fred is quiet or humble. If mary is either humble or happy then someone is not happy or humble and vice versa. Everyone who is either quiet or tall is either not tall or brave and vice versa. Everyone who is quiet or not rich is both quiet and not wise. Someone is kind or funny. Someone is rich or not kind. Someone is either strong or not tall. Someone is either generous or not quiet. Susan is not rich or old. Mary is not kind or not tall. | Susan is not funny. | entailment | ((?[X]:((old(X)|wise(X))))=>(calm(alice)))&
(![X]:((~kind(X)<~>~happy(X))<=>(~quiet(X)<~>old(X))))&
((?[X]:(~old(X)))=>(~funny(susan)))&
((patient(mary))<=>(?[X]:(~calm(X))))&
(((~happy(john)<~>rich(john)))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((~quiet(X)|~happy(X))<=>(~funny(X)&rich(X))))&
(![X]:((~quiet(X)<~>calm(X))<=>(kind(X)&~brave(X))))&
(![X]:((old(X)<~>~strong(X))<=>(patient(X)&~happy(X))))&
(![X]:((~curious(X)&rich(X))=>~strong(X)))&
(![X]:((~calm(X)&~quiet(X))=>(calm(X)&~creative(X))))&
(![X]:((~calm(X)&curious(X))<=>(~funny(X)|~quiet(X))))&
((?[X]:((~creative(X)|strong(X))))=>((quiet(fred)|humble(fred))))&
(((humble(mary)<~>happy(mary)))<=>(?[X]:((~happy(X)|humble(X)))))&
(![X]:((quiet(X)<~>tall(X))<=>(~tall(X)<~>brave(X))))&
(![X]:((quiet(X)|~rich(X))=>(quiet(X)&~wise(X))))&
(?[X]:((kind(X)|funny(X))))&
(?[X]:((rich(X)|~kind(X))))&
(?[X]:((strong(X)<~>~tall(X))))&
(?[X]:((generous(X)<~>~quiet(X))))&
((~rich(susan)|old(susan)))&
((~kind(mary)|~tall(mary))) | ~funny(susan) | [
"p0",
"p1",
"p2",
"p5",
"p6",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 235360138362132627999536
% SZS output start Proof for 235360138362132627999536
1. ? [X0] : (wise(X0) | old(X0)) => calm(alice) [input p0]
2. ! [X0] : ((~kind(X0) <~> ~happy(X0)) <=> (~quiet(X0) <~> old(X0))) [input p1]
3. ? [X0] : ~old(X0) => ~funny(susan) [input p2]
6. ! [X0] : ((~happy(X0) | ~quiet(X0)) <=> (rich(X0) & ~funny(X0))) [input p5]
7. ! [X0] : ((~quiet(X0) <~> calm(X0)) <=> (~brave(X0) & kind(X0))) [input p6]
10. ! [X0] : ((~quiet(X0) & ~calm(X0)) => (~creative(X0) & calm(X0))) [input p9]
11. ! [X0] : ((curious(X0) & ~calm(X0)) <=> (~quiet(X0) | ~funny(X0))) [input p10]
22. funny(susan) [input hypothesis]
23. ? [X0] : old(X0) => calm(alice) [pure predicate removal 1]
25. calm(alice) | ! [X0] : ~old(X0) [ennf transformation 23]
26. ~funny(susan) | ! [X0] : old(X0) [ennf transformation 3]
29. ! [X0] : ((~creative(X0) & calm(X0)) | (quiet(X0) | calm(X0))) [ennf transformation 10]
30. ! [X0] : ((~creative(X0) & calm(X0)) | quiet(X0) | calm(X0)) [flattening 29]
34. ! [X0] : ((((happy(X0) | kind(X0)) & (~happy(X0) | ~kind(X0))) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | ((~kind(X0) | happy(X0)) & (~happy(X0) | kind(X0))))) [nnf transformation 2]
43. ! [X0] : (((~happy(X0) | ~quiet(X0)) | (~rich(X0) | funny(X0))) & ((rich(X0) & ~funny(X0)) | (happy(X0) & quiet(X0)))) [nnf transformation 6]
44. ! [X0] : ((~happy(X0) | ~quiet(X0) | ~rich(X0) | funny(X0)) & ((rich(X0) & ~funny(X0)) | (happy(X0) & quiet(X0)))) [flattening 43]
45. ! [X0] : ((((~calm(X0) | quiet(X0)) & (calm(X0) | ~quiet(X0))) | (brave(X0) | ~kind(X0))) & ((~brave(X0) & kind(X0)) | ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0))))) [nnf transformation 7]
46. ! [X0] : ((((~calm(X0) | quiet(X0)) & (calm(X0) | ~quiet(X0))) | brave(X0) | ~kind(X0)) & ((~brave(X0) & kind(X0)) | ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0))))) [flattening 45]
49. ! [X0] : (((curious(X0) & ~calm(X0)) | (quiet(X0) & funny(X0))) & ((~quiet(X0) | ~funny(X0)) | (~curious(X0) | calm(X0)))) [nnf transformation 11]
50. ! [X0] : (((curious(X0) & ~calm(X0)) | (quiet(X0) & funny(X0))) & (~quiet(X0) | ~funny(X0) | ~curious(X0) | calm(X0))) [flattening 49]
66. calm(alice) | ~old(X0) [cnf transformation 25]
72. ~quiet(X0) | ~kind(X0) | ~happy(X0) | ~old(X0) [cnf transformation 34]
75. ~funny(susan) | old(X0) [cnf transformation 26]
85. ~funny(X0) | happy(X0) [cnf transformation 44]
90. ~quiet(X0) | kind(X0) | ~calm(X0) [cnf transformation 46]
102. calm(X0) | quiet(X0) | calm(X0) [cnf transformation 30]
105. ~calm(X0) | funny(X0) [cnf transformation 50]
106. ~calm(X0) | quiet(X0) [cnf transformation 50]
135. funny(susan) [cnf transformation 22]
140. quiet(X0) | calm(X0) [duplicate literal removal 102]
142. 1 <=> ! [X0] : ~old(X0) [avatar definition]
143. ~old(X0) <- (1) [avatar component clause 142]
145. 2 <=> calm(alice) [avatar definition]
147. calm(alice) <- (2) [avatar component clause 145]
148. 1 | 2 [avatar split clause 66,145,142]
150. 3 <=> ! [X0] : old(X0) [avatar definition]
151. old(X0) <- (3) [avatar component clause 150]
153. 4 <=> funny(susan) [avatar definition]
156. 3 | ~4 [avatar split clause 75,153,150]
195. quiet(X0) [subsumption resolution 106,140]
275. 4 [avatar split clause 135,153]
296. funny(alice) <- (2) [resolution 147,105]
297. happy(alice) <- (2) [resolution 296,85]
301. ~calm(X2) | kind(X2) [resolution 90,195]
303. kind(alice) <- (2) [resolution 301,147]
332. ~kind(X2) | ~happy(X2) | ~old(X2) [resolution 72,195]
334. ~happy(X2) | ~kind(X2) <- (3) [subsumption resolution 332,151]
344. ~kind(alice) <- (2, 3) [resolution 334,297]
345. $false <- (2, 3) [subsumption resolution 344,303]
346. ~2 | ~3 [avatar contradiction clause 345]
347. $false <- (1, 3) [subsumption resolution 143,151]
348. ~1 | ~3 [avatar contradiction clause 347]
349. $false [avatar sat refutation 148,156,275,346,348]
% SZS output end Proof for 235360138362132627999536
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not wise or not rich then someone is both not rich and not strong and vice versa. Everyone who is not funny or not wise is either not strong or quiet and vice versa. Everyone who is either brave or creative is either strong or happy and vice versa. If john is either not quiet or strong then susan is brave or rich and vice versa. Everyone who is both not calm and not rich is curious and vice versa. If john is wise or not humble then mary is either humble or not funny. If someone is not generous or funny then mary is not creative or generous. Everyone who is either not humble or calm is either not calm or not rich and vice versa. Everyone who is both tall and not kind is both funny and curious. Everyone who is not rich is either humble or creative. If fred is not wise or not curious then someone is both creative and happy. Everyone who is both quiet and not generous is both brave and calm. Everyone who is both funny and wise is strong or happy and vice versa. If someone is curious or not rich then someone is either not old or tall. Everyone who is not strong is not brave and vice versa. If someone is both kind and not tall then someone is wise and vice versa. Lucy is either not quiet or quiet. Alice is either not patient or not tall. Alice is not tall or not generous. Lucy is either rich or quiet. Lucy is either not generous or calm. John is both not quiet and kind. Someone is curious. | Lucy is curious. | contradiction | (((~wise(paul)|~rich(paul)))<=>(?[X]:((~rich(X)&~strong(X)))))&
(![X]:((~funny(X)|~wise(X))<=>(~strong(X)<~>quiet(X))))&
(![X]:((brave(X)<~>creative(X))<=>(strong(X)<~>happy(X))))&
(((~quiet(john)<~>strong(john)))<=>((brave(susan)|rich(susan))))&
(![X]:((~calm(X)&~rich(X))<=>curious(X)))&
(((wise(john)|~humble(john)))=>((humble(mary)<~>~funny(mary))))&
((?[X]:((~generous(X)|funny(X))))=>((~creative(mary)|generous(mary))))&
(![X]:((~humble(X)<~>calm(X))<=>(~calm(X)<~>~rich(X))))&
(![X]:((tall(X)&~kind(X))=>(funny(X)&curious(X))))&
(![X]:(~rich(X)=>(humble(X)<~>creative(X))))&
(((~wise(fred)|~curious(fred)))=>(?[X]:((creative(X)&happy(X)))))&
(![X]:((quiet(X)&~generous(X))=>(brave(X)&calm(X))))&
(![X]:((funny(X)&wise(X))<=>(strong(X)|happy(X))))&
((?[X]:((curious(X)|~rich(X))))=>(?[X]:((~old(X)<~>tall(X)))))&
(![X]:(~strong(X)<=>~brave(X)))&
((?[X]:((kind(X)&~tall(X))))<=>(?[X]:(wise(X))))&
((~quiet(lucy)<~>quiet(lucy)))&
((~patient(alice)<~>~tall(alice)))&
((~tall(alice)|~generous(alice)))&
((rich(lucy)<~>quiet(lucy)))&
((~generous(lucy)<~>calm(lucy)))&
((~quiet(john)&kind(john)))&
(?[X]:(curious(X))) | curious(lucy) | [
"p4",
"p11",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8680312959669057711969005
% SZS output start Proof for 8680312959669057711969005
5. ! [X0] : ((~rich(X0) & ~calm(X0)) <=> curious(X0)) [input p4]
12. ! [X0] : ((~generous(X0) & quiet(X0)) => (calm(X0) & brave(X0))) [input p11]
20. rich(lucy) <~> quiet(lucy) [input p19]
21. ~generous(lucy) <~> calm(lucy) [input p20]
24. curious(lucy) [input hypothesis]
34. ! [X0] : ((calm(X0) & brave(X0)) | (generous(X0) | ~quiet(X0))) [ennf transformation 12]
35. ! [X0] : ((calm(X0) & brave(X0)) | generous(X0) | ~quiet(X0)) [flattening 34]
47. ! [X0] : (((~rich(X0) & ~calm(X0)) | ~curious(X0)) & (curious(X0) | (rich(X0) | calm(X0)))) [nnf transformation 5]
48. ! [X0] : (((~rich(X0) & ~calm(X0)) | ~curious(X0)) & (curious(X0) | rich(X0) | calm(X0))) [flattening 47]
68. (~quiet(lucy) | ~rich(lucy)) & (quiet(lucy) | rich(lucy)) [nnf transformation 20]
69. (~calm(lucy) | generous(lucy)) & (calm(lucy) | ~generous(lucy)) [nnf transformation 21]
98. ~curious(X0) | ~calm(X0) [cnf transformation 48]
99. ~curious(X0) | ~rich(X0) [cnf transformation 48]
123. ~quiet(X0) | generous(X0) | calm(X0) [cnf transformation 35]
143. quiet(lucy) | rich(lucy) [cnf transformation 68]
145. calm(lucy) | ~generous(lucy) [cnf transformation 69]
150. curious(lucy) [cnf transformation 24]
315. 34 <=> rich(lucy) [avatar definition]
319. 35 <=> quiet(lucy) [avatar definition]
320. quiet(lucy) <- (35) [avatar component clause 319]
323. 34 | 35 [avatar split clause 143,319,315]
325. 36 <=> generous(lucy) [avatar definition]
329. 37 <=> calm(lucy) [avatar definition]
333. ~36 | 37 [avatar split clause 145,329,325]
338. ~calm(lucy) [resolution 98,150]
341. ~rich(lucy) [resolution 99,150]
345. ~34 [avatar split clause 341,315]
367. generous(lucy) | calm(lucy) <- (35) [resolution 123,320]
371. 37 | 36 | ~35 [avatar split clause 367,319,325,329]
377. ~37 [avatar split clause 338,329]
378. $false [avatar sat refutation 323,333,345,371,377]
% SZS output end Proof for 8680312959669057711969005
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not strong is not quiet and vice versa.
If someone is either not funny or creative then fred is not curious and vice versa.
If someone is either not rich or not old then someone is either humble or not strong and vice versa.
Everyone who is not calm or not quiet is not quiet and vice versa.
Everyone who is both generous and not funny is either not calm or not brave and vice versa.
Everyone who is rich or not tall is either tall or rich and vice versa.
If fred is either not creative or kind then someone is not curious or wise and vice versa.
If fred is either not kind or happy then mary is either generous or old and vice versa.
If paul is happy or generous then paul is not happy or not wise.
Everyone who is not rich is both old and not wise and vice versa.
If someone is patient then fred is both kind and creative.
Everyone who is not brave is old or patient.
Everyone who is not tall is not kind.
Everyone who is either not rich or not calm is old or not kind.
If someone is either not calm or happy then lucy is either not generous or curious and vice versa.
Everyone who is both not rich and strong is not funny or tall.
Susan is not patient or calm.
Someone is both brave and curious.
Someone is not strong or not humble.
Paul is not quiet.
Susan is patient or old.
Mary is not generous or wise.
Mary is not calm or not brave. | Fred is strong. | neutral | (![X]:((~brave(X)<~>~strong(X))<=>~quiet(X)))&
((?[X]:((~funny(X)<~>creative(X))))<=>(~curious(fred)))&
((?[X]:((~rich(X)<~>~old(X))))<=>(?[X]:((humble(X)<~>~strong(X)))))&
(![X]:((~calm(X)|~quiet(X))<=>~quiet(X)))&
(![X]:((generous(X)&~funny(X))<=>(~calm(X)<~>~brave(X))))&
(![X]:((rich(X)|~tall(X))<=>(tall(X)<~>rich(X))))&
(((~creative(fred)<~>kind(fred)))<=>(?[X]:((~curious(X)|wise(X)))))&
(((~kind(fred)<~>happy(fred)))<=>((generous(mary)<~>old(mary))))&
(((happy(paul)|generous(paul)))=>((~happy(paul)|~wise(paul))))&
(![X]:(~rich(X)<=>(old(X)&~wise(X))))&
((?[X]:(patient(X)))=>((kind(fred)&creative(fred))))&
(![X]:(~brave(X)=>(old(X)|patient(X))))&
(![X]:(~tall(X)=>~kind(X)))&
(![X]:((~rich(X)<~>~calm(X))=>(old(X)|~kind(X))))&
((?[X]:((~calm(X)<~>happy(X))))<=>((~generous(lucy)<~>curious(lucy))))&
(![X]:((~rich(X)&strong(X))=>(~funny(X)|tall(X))))&
((~patient(susan)|calm(susan)))&
(?[X]:((brave(X)&curious(X))))&
(?[X]:((~strong(X)|~humble(X))))&
(~quiet(paul))&
((patient(susan)|old(susan)))&
((~generous(mary)|wise(mary)))&
((~calm(mary)|~brave(mary))) | strong(fred) | [] | null | 0 |
Everyone who is funny is not curious and vice versa. If paul is patient then john is not quiet and vice versa. If someone is brave or not quiet then alice is not happy. Everyone who is both not kind and not rich is tall and vice versa. Everyone who is humble or kind is both not calm and patient. If someone is both patient and not curious then alice is patient and vice versa. Everyone who is both not old and not generous is not patient. If someone is either not humble or tall then susan is either old or not brave. Everyone who is either not kind or not rich is both not old and funny. Everyone who is either calm or strong is not strong and vice versa. Everyone who is strong is not creative or not funny and vice versa. If someone is not brave then someone is either not happy or not strong. Everyone who is not happy or not funny is both happy and kind and vice versa. If alice is not quiet then someone is either not tall or not brave. If fred is both not curious and patient then john is patient. Alice is either brave or creative. Someone is brave or tall. Alice is wise. Someone is rich or not wise. Someone is either not wise or rich. Fred is either not patient or rich. John is both rich and creative. | Alice is patient. | neutral | (![X]:(funny(X)<=>~curious(X)))&
((patient(paul))<=>(~quiet(john)))&
((?[X]:((brave(X)|~quiet(X))))=>(~happy(alice)))&
(![X]:((~kind(X)&~rich(X))<=>tall(X)))&
(![X]:((humble(X)|kind(X))=>(~calm(X)&patient(X))))&
((?[X]:((patient(X)&~curious(X))))<=>(patient(alice)))&
(![X]:((~old(X)&~generous(X))=>~patient(X)))&
((?[X]:((~humble(X)<~>tall(X))))=>((old(susan)<~>~brave(susan))))&
(![X]:((~kind(X)<~>~rich(X))=>(~old(X)&funny(X))))&
(![X]:((calm(X)<~>strong(X))<=>~strong(X)))&
(![X]:(strong(X)<=>(~creative(X)|~funny(X))))&
((?[X]:(~brave(X)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:((~happy(X)|~funny(X))<=>(happy(X)&kind(X))))&
((~quiet(alice))=>(?[X]:((~tall(X)<~>~brave(X)))))&
(((~curious(fred)&patient(fred)))=>(patient(john)))&
((brave(alice)<~>creative(alice)))&
(?[X]:((brave(X)|tall(X))))&
(wise(alice))&
(?[X]:((rich(X)|~wise(X))))&
(?[X]:((~wise(X)<~>rich(X))))&
((~patient(fred)<~>rich(fred)))&
((rich(john)&creative(john))) | patient(alice) | [] | null | 0 |
If lucy is both not funny and wise then someone is not rich or not wise and vice versa. Everyone who is wise or old is tall or not tall and vice versa. If someone is strong then alice is not curious. If john is calm then alice is funny or not happy. Everyone who is quiet is kind or patient and vice versa. Everyone who is either strong or not patient is not happy and vice versa. Everyone who is either rich or humble is not creative or humble and vice versa. Everyone who is kind or not happy is either strong or happy. If lucy is not funny or not humble then susan is both not humble and not calm and vice versa. If someone is creative or kind then paul is either generous or curious and vice versa. Everyone who is curious is either not wise or not creative and vice versa. If mary is not quiet or tall then mary is not creative or not tall and vice versa. If someone is patient or not curious then paul is not happy and vice versa. Everyone who is generous or not funny is kind or not patient. If someone is either not generous or not funny then lucy is curious. If someone is not funny or not calm then fred is curious. Someone is either not generous or not wise. Someone is generous. Someone is strong or wise. Someone is both rich and not generous. Alice is either brave or not brave. Susan is wise or not patient. | Alice is generous. | neutral | (((~funny(lucy)&wise(lucy)))<=>(?[X]:((~rich(X)|~wise(X)))))&
(![X]:((wise(X)|old(X))<=>(tall(X)|~tall(X))))&
((?[X]:(strong(X)))=>(~curious(alice)))&
((calm(john))=>((funny(alice)|~happy(alice))))&
(![X]:(quiet(X)<=>(kind(X)|patient(X))))&
(![X]:((strong(X)<~>~patient(X))<=>~happy(X)))&
(![X]:((rich(X)<~>humble(X))<=>(~creative(X)|humble(X))))&
(![X]:((kind(X)|~happy(X))=>(strong(X)<~>happy(X))))&
(((~funny(lucy)|~humble(lucy)))<=>((~humble(susan)&~calm(susan))))&
((?[X]:((creative(X)|kind(X))))<=>((generous(paul)<~>curious(paul))))&
(![X]:(curious(X)<=>(~wise(X)<~>~creative(X))))&
(((~quiet(mary)|tall(mary)))<=>((~creative(mary)|~tall(mary))))&
((?[X]:((patient(X)|~curious(X))))<=>(~happy(paul)))&
(![X]:((generous(X)|~funny(X))=>(kind(X)|~patient(X))))&
((?[X]:((~generous(X)<~>~funny(X))))=>(curious(lucy)))&
((?[X]:((~funny(X)|~calm(X))))=>(curious(fred)))&
(?[X]:((~generous(X)<~>~wise(X))))&
(?[X]:(generous(X)))&
(?[X]:((strong(X)|wise(X))))&
(?[X]:((rich(X)&~generous(X))))&
((brave(alice)<~>~brave(alice)))&
((wise(susan)|~patient(susan))) | generous(alice) | [] | null | 0 |
If susan is not quiet or not generous then someone is both patient and not curious.
Everyone who is either not calm or not happy is either not old or not wise and vice versa.
If paul is curious or not creative then paul is both not funny and not old and vice versa.
Everyone who is not brave is brave or not tall.
Everyone who is both not curious and happy is not tall and vice versa.
If someone is both not brave and not wise then someone is both not wise and not tall and vice versa.
If mary is both not rich and patient then someone is not humble.
Everyone who is creative or old is either brave or tall.
Everyone who is generous or happy is not wise and vice versa.
Everyone who is both funny and strong is both not calm and tall and vice versa.
Everyone who is brave is either kind or wise.
If someone is curious then susan is both not tall and not rich and vice versa.
Everyone who is either quiet or strong is either creative or tall.
Everyone who is not brave is both tall and not patient.
Everyone who is both old and not humble is both not happy and not humble and vice versa.
If mary is not wise or funny then fred is both not patient and not tall and vice versa.
Someone is either old or quiet.
Someone is not tall or not rich.
Someone is curious or patient.
Paul is rich.
Lucy is generous or not happy. | Paul is kind. | contradiction | (((~quiet(susan)|~generous(susan)))=>(?[X]:((patient(X)&~curious(X)))))&
(![X]:((~calm(X)<~>~happy(X))<=>(~old(X)<~>~wise(X))))&
(((curious(paul)|~creative(paul)))<=>((~funny(paul)&~old(paul))))&
(![X]:(~brave(X)=>(brave(X)|~tall(X))))&
(![X]:((~curious(X)&happy(X))<=>~tall(X)))&
((?[X]:((~brave(X)&~wise(X))))<=>(?[X]:((~wise(X)&~tall(X)))))&
(((~rich(mary)&patient(mary)))=>(?[X]:(~humble(X))))&
(![X]:((creative(X)|old(X))=>(brave(X)<~>tall(X))))&
(![X]:((generous(X)|happy(X))<=>~wise(X)))&
(![X]:((funny(X)&strong(X))<=>(~calm(X)&tall(X))))&
(![X]:(brave(X)=>(kind(X)<~>wise(X))))&
((?[X]:(curious(X)))<=>((~tall(susan)&~rich(susan))))&
(![X]:((quiet(X)<~>strong(X))=>(creative(X)<~>tall(X))))&
(![X]:(~brave(X)=>(tall(X)&~patient(X))))&
(![X]:((old(X)&~humble(X))<=>(~happy(X)&~humble(X))))&
(((~wise(mary)|funny(mary)))<=>((~patient(fred)&~tall(fred))))&
(?[X]:((old(X)<~>quiet(X))))&
(?[X]:((~tall(X)|~rich(X))))&
(?[X]:((curious(X)|patient(X))))&
(rich(paul))&
((generous(lucy)|~happy(lucy))) | kind(paul) | [
"p1",
"p2",
"p3",
"p4",
"p5",
"p7",
"p8",
"p9",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1745821640192770998287091
% SZS output start Proof for 1745821640192770998287091
2. ! [X0] : ((~calm(X0) <~> ~happy(X0)) <=> (~old(X0) <~> ~wise(X0))) [input p1]
3. (~creative(paul) | curious(paul)) <=> (~old(paul) & ~funny(paul)) [input p2]
4. ! [X0] : (~brave(X0) => (~tall(X0) | brave(X0))) [input p3]
5. ! [X0] : ((happy(X0) & ~curious(X0)) <=> ~tall(X0)) [input p4]
6. ? [X0] : (~wise(X0) & ~brave(X0)) <=> ? [X0] : (~tall(X0) & ~wise(X0)) [input p5]
8. ! [X0] : ((old(X0) | creative(X0)) => (brave(X0) <~> tall(X0))) [input p7]
9. ! [X0] : ((happy(X0) | generous(X0)) <=> ~wise(X0)) [input p8]
10. ! [X0] : ((strong(X0) & funny(X0)) <=> (tall(X0) & ~calm(X0))) [input p9]
11. ! [X0] : (brave(X0) => (kind(X0) <~> wise(X0))) [input p10]
12. ? [X0] : curious(X0) <=> (~rich(susan) & ~tall(susan)) [input p11]
14. ! [X0] : (~brave(X0) => (~patient(X0) & tall(X0))) [input p13]
22. kind(paul) [input hypothesis]
23. ? [X0] : (~wise(X0) & ~brave(X0)) <=> ? [X1] : (~tall(X1) & ~wise(X1)) [rectify 6]
25. ! [X0] : ((~tall(X0) | brave(X0)) | brave(X0)) [ennf transformation 4]
26. ! [X0] : (~tall(X0) | brave(X0) | brave(X0)) [flattening 25]
29. ! [X0] : ((brave(X0) <~> tall(X0)) | (~old(X0) & ~creative(X0))) [ennf transformation 8]
30. ! [X0] : ((kind(X0) <~> wise(X0)) | ~brave(X0)) [ennf transformation 11]
32. ! [X0] : ((~patient(X0) & tall(X0)) | brave(X0)) [ennf transformation 14]
35. ! [X0] : ((((happy(X0) | calm(X0)) & (~happy(X0) | ~calm(X0))) | ((~old(X0) | wise(X0)) & (~wise(X0) | old(X0)))) & (((wise(X0) | old(X0)) & (~wise(X0) | ~old(X0))) | ((~calm(X0) | happy(X0)) & (~happy(X0) | calm(X0))))) [nnf transformation 2]
36. ((~creative(paul) | curious(paul)) | (old(paul) | funny(paul))) & ((~old(paul) & ~funny(paul)) | (creative(paul) & ~curious(paul))) [nnf transformation 3]
37. (~creative(paul) | curious(paul) | old(paul) | funny(paul)) & ((~old(paul) & ~funny(paul)) | (creative(paul) & ~curious(paul))) [flattening 36]
38. ! [X0] : (((happy(X0) & ~curious(X0)) | tall(X0)) & (~tall(X0) | (~happy(X0) | curious(X0)))) [nnf transformation 5]
39. ! [X0] : (((happy(X0) & ~curious(X0)) | tall(X0)) & (~tall(X0) | ~happy(X0) | curious(X0))) [flattening 38]
40. (? [X0] : (~wise(X0) & ~brave(X0)) | ! [X1] : (tall(X1) | wise(X1))) & (? [X1] : (~tall(X1) & ~wise(X1)) | ! [X0] : (wise(X0) | brave(X0))) [nnf transformation 23]
41. (? [X0] : (~wise(X0) & ~brave(X0)) | ! [X1] : (tall(X1) | wise(X1))) & (? [X2] : (~tall(X2) & ~wise(X2)) | ! [X3] : (wise(X3) | brave(X3))) [rectify 40]
42. ? [X0] : (~wise(X0) & ~brave(X0)) => (~wise(sK1) & ~brave(sK1)) [choice axiom]
43. ? [X2] : (~tall(X2) & ~wise(X2)) => (~tall(sK2) & ~wise(sK2)) [choice axiom]
44. ((~wise(sK1) & ~brave(sK1)) | ! [X1] : (tall(X1) | wise(X1))) & ((~tall(sK2) & ~wise(sK2)) | ! [X3] : (wise(X3) | brave(X3))) [skolemisation 41,43,42]
47. ! [X0] : (((~tall(X0) | ~brave(X0)) & (tall(X0) | brave(X0))) | (~old(X0) & ~creative(X0))) [nnf transformation 29]
48. ! [X0] : (((happy(X0) | generous(X0)) | wise(X0)) & (~wise(X0) | (~happy(X0) & ~generous(X0)))) [nnf transformation 9]
49. ! [X0] : ((happy(X0) | generous(X0) | wise(X0)) & (~wise(X0) | (~happy(X0) & ~generous(X0)))) [flattening 48]
50. ! [X0] : (((strong(X0) & funny(X0)) | (~tall(X0) | calm(X0))) & ((tall(X0) & ~calm(X0)) | (~strong(X0) | ~funny(X0)))) [nnf transformation 10]
51. ! [X0] : (((strong(X0) & funny(X0)) | ~tall(X0) | calm(X0)) & ((tall(X0) & ~calm(X0)) | ~strong(X0) | ~funny(X0))) [flattening 50]
52. ! [X0] : (((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) | ~brave(X0)) [nnf transformation 30]
53. (? [X0] : curious(X0) | (rich(susan) | tall(susan))) & ((~rich(susan) & ~tall(susan)) | ! [X0] : ~curious(X0)) [nnf transformation 12]
54. (? [X0] : curious(X0) | rich(susan) | tall(susan)) & ((~rich(susan) & ~tall(susan)) | ! [X0] : ~curious(X0)) [flattening 53]
55. (? [X0] : curious(X0) | rich(susan) | tall(susan)) & ((~rich(susan) & ~tall(susan)) | ! [X1] : ~curious(X1)) [rectify 54]
56. ? [X0] : curious(X0) => curious(sK4) [choice axiom]
57. (curious(sK4) | rich(susan) | tall(susan)) & ((~rich(susan) & ~tall(susan)) | ! [X1] : ~curious(X1)) [skolemisation 55,56]
77. ~calm(X0) | old(X0) | wise(X0) | happy(X0) [cnf transformation 35]
83. ~funny(paul) | creative(paul) [cnf transformation 37]
87. ~tall(X0) | brave(X0) | brave(X0) [cnf transformation 26]
88. ~tall(X0) | ~happy(X0) | curious(X0) [cnf transformation 39]
90. tall(X0) | happy(X0) [cnf transformation 39]
93. ~brave(sK1) | tall(X1) | wise(X1) [cnf transformation 44]
98. ~tall(X0) | ~brave(X0) | ~creative(X0) [cnf transformation 47]
99. ~tall(X0) | ~brave(X0) | ~old(X0) [cnf transformation 47]
101. ~wise(X0) | ~happy(X0) [cnf transformation 49]
105. ~tall(X0) | funny(X0) | calm(X0) [cnf transformation 51]
108. ~kind(X0) | ~wise(X0) | ~brave(X0) [cnf transformation 52]
109. ~tall(susan) | ~curious(X1) [cnf transformation 57]
116. tall(X0) | brave(X0) [cnf transformation 32]
133. kind(paul) [cnf transformation 22]
134. ~tall(X0) | brave(X0) [duplicate literal removal 87]
156. 5 <=> funny(paul) [avatar definition]
157. ~funny(paul) <- (~5) [avatar component clause 156]
160. 6 <=> old(paul) [avatar definition]
162. old(paul) <- (6) [avatar component clause 160]
168. 8 <=> creative(paul) [avatar definition]
169. creative(paul) <- (8) [avatar component clause 168]
174. 8 | ~5 [avatar split clause 83,156,168]
177. 9 <=> ! [X1] : (tall(X1) | wise(X1)) [avatar definition]
178. tall(X1) | wise(X1) <- (9) [avatar component clause 177]
185. 11 <=> brave(sK1) [avatar definition]
187. ~brave(sK1) <- (~11) [avatar component clause 185]
188. 9 | ~11 [avatar split clause 93,185,177]
215. ~tall(X0) | ~old(X0) [subsumption resolution 99,134]
216. ~tall(X0) | ~creative(X0) [subsumption resolution 98,134]
220. 18 <=> tall(susan) [avatar definition]
221. ~tall(susan) <- (~18) [avatar component clause 220]
233. 21 <=> ! [X1] : ~curious(X1) [avatar definition]
234. ~curious(X1) <- (21) [avatar component clause 233]
236. 21 | ~18 [avatar split clause 109,220,233]
237. brave(X0) [subsumption resolution 116,134]
296. $false <- (~11) [subsumption resolution 187,237]
297. 11 [avatar contradiction clause 296]
300. happy(susan) <- (~18) [resolution 90,221]
309. wise(susan) <- (9, ~18) [resolution 178,221]
316. ~old(X0) | wise(X0) <- (9) [resolution 215,178]
321. ~happy(susan) <- (9, ~18) [resolution 309,101]
323. $false <- (9, ~18) [subsumption resolution 321,300]
324. ~9 | 18 [avatar contradiction clause 323]
347. ~creative(X0) | wise(X0) <- (9) [resolution 216,178]
354. ~happy(X0) | curious(X0) | wise(X0) <- (9) [resolution 88,178]
360. ~happy(X0) | wise(X0) <- (9, 21) [subsumption resolution 354,234]
361. ~happy(X0) <- (9, 21) [subsumption resolution 360,101]
369. funny(X1) | calm(X1) | happy(X1) [resolution 105,90]
374. funny(X1) | calm(X1) <- (9, 21) [subsumption resolution 369,361]
383. ~wise(paul) | ~brave(paul) [resolution 108,133]
384. ~wise(paul) [subsumption resolution 383,237]
467. calm(paul) <- (~5, 9, 21) [resolution 374,157]
469. old(paul) | wise(paul) | happy(paul) <- (~5, 9, 21) [resolution 467,77]
474. old(paul) | happy(paul) <- (~5, 9, 21) [subsumption resolution 469,384]
475. old(paul) <- (~5, 9, 21) [subsumption resolution 474,361]
476. 6 | 5 | ~9 | ~21 [avatar split clause 475,233,177,156,160]
480. wise(paul) <- (6, 9) [resolution 162,316]
485. $false <- (6, 9) [subsumption resolution 480,384]
486. ~6 | ~9 [avatar contradiction clause 485]
488. wise(paul) <- (8, 9) [resolution 169,347]
492. $false <- (8, 9) [subsumption resolution 488,384]
493. ~8 | ~9 [avatar contradiction clause 492]
494. $false [avatar sat refutation 174,188,236,297,324,476,486,493]
% SZS output end Proof for 1745821640192770998287091
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.043 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either not old or strong then paul is either old or kind and vice versa. If someone is either patient or not generous then someone is either not calm or not patient and vice versa. Everyone who is not happy or wise is not wise or not calm and vice versa. If someone is either not old or tall then someone is not humble or brave and vice versa. Everyone who is not curious is either generous or kind and vice versa. Everyone who is not calm is both patient and not wise and vice versa. Everyone who is either generous or not tall is curious or not brave and vice versa. If paul is either wise or not brave then someone is tall. Everyone who is not calm or not happy is either not creative or not strong. Everyone who is both wise and creative is not generous. If alice is both not generous and wise then someone is both not happy and not funny and vice versa. If someone is generous or not humble then fred is not brave or not wise and vice versa. Everyone who is rich is both happy and not tall. Everyone who is either generous or not patient is generous. Everyone who is both not creative and not wise is not rich and vice versa. Everyone who is wise or not humble is not happy. Someone is strong or wise. Someone is curious. Paul is humble. Someone is both brave and old. Someone is either not tall or kind. Someone is both not wise and kind. | Fred is kind. | neutral | (((~old(fred)<~>strong(fred)))<=>((old(paul)<~>kind(paul))))&
((?[X]:((patient(X)<~>~generous(X))))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
(![X]:((~happy(X)|wise(X))<=>(~wise(X)|~calm(X))))&
((?[X]:((~old(X)<~>tall(X))))<=>(?[X]:((~humble(X)|brave(X)))))&
(![X]:(~curious(X)<=>(generous(X)<~>kind(X))))&
(![X]:(~calm(X)<=>(patient(X)&~wise(X))))&
(![X]:((generous(X)<~>~tall(X))<=>(curious(X)|~brave(X))))&
(((wise(paul)<~>~brave(paul)))=>(?[X]:(tall(X))))&
(![X]:((~calm(X)|~happy(X))=>(~creative(X)<~>~strong(X))))&
(![X]:((wise(X)&creative(X))=>~generous(X)))&
(((~generous(alice)&wise(alice)))<=>(?[X]:((~happy(X)&~funny(X)))))&
((?[X]:((generous(X)|~humble(X))))<=>((~brave(fred)|~wise(fred))))&
(![X]:(rich(X)=>(happy(X)&~tall(X))))&
(![X]:((generous(X)<~>~patient(X))=>generous(X)))&
(![X]:((~creative(X)&~wise(X))<=>~rich(X)))&
(![X]:((wise(X)|~humble(X))=>~happy(X)))&
(?[X]:((strong(X)|wise(X))))&
(?[X]:(curious(X)))&
(humble(paul))&
(?[X]:((brave(X)&old(X))))&
(?[X]:((~tall(X)<~>kind(X))))&
(?[X]:((~wise(X)&kind(X)))) | kind(fred) | [] | null | 0 |
Everyone who is not generous or creative is either brave or not quiet and vice versa.
If someone is calm then someone is not creative or rich.
Everyone who is both calm and not happy is funny.
Everyone who is happy or not tall is not brave and vice versa.
If someone is both patient and not funny then fred is not funny or humble.
Everyone who is both happy and old is curious.
If paul is not calm then fred is not tall or not patient.
If fred is both quiet and not curious then fred is both wise and rich and vice versa.
Everyone who is humble or funny is either not rich or not brave and vice versa.
Everyone who is either not brave or patient is not creative.
Everyone who is not quiet is either not calm or not brave and vice versa.
Everyone who is either not rich or not humble is both not wise and not calm.
If someone is both not wise and patient then someone is strong and vice versa.
Everyone who is both brave and calm is either brave or not creative and vice versa.
If john is calm or not calm then paul is strong or not strong and vice versa.
If someone is both not old and happy then paul is not humble or not brave.
Mary is both generous and curious.
Susan is both tall and wise.
Someone is creative.
Someone is not curious or humble.
Someone is both not humble and old.
Someone is both creative and wise.
Paul is not wise or happy.
Paul is either not wise or calm. | Susan is not patient. | neutral | (![X]:((~generous(X)|creative(X))<=>(brave(X)<~>~quiet(X))))&
((?[X]:(calm(X)))=>(?[X]:((~creative(X)|rich(X)))))&
(![X]:((calm(X)&~happy(X))=>funny(X)))&
(![X]:((happy(X)|~tall(X))<=>~brave(X)))&
((?[X]:((patient(X)&~funny(X))))=>((~funny(fred)|humble(fred))))&
(![X]:((happy(X)&old(X))=>curious(X)))&
((~calm(paul))=>((~tall(fred)|~patient(fred))))&
(((quiet(fred)&~curious(fred)))<=>((wise(fred)&rich(fred))))&
(![X]:((humble(X)|funny(X))<=>(~rich(X)<~>~brave(X))))&
(![X]:((~brave(X)<~>patient(X))=>~creative(X)))&
(![X]:(~quiet(X)<=>(~calm(X)<~>~brave(X))))&
(![X]:((~rich(X)<~>~humble(X))=>(~wise(X)&~calm(X))))&
((?[X]:((~wise(X)&patient(X))))<=>(?[X]:(strong(X))))&
(![X]:((brave(X)&calm(X))<=>(brave(X)<~>~creative(X))))&
(((calm(john)|~calm(john)))<=>((strong(paul)|~strong(paul))))&
((?[X]:((~old(X)&happy(X))))=>((~humble(paul)|~brave(paul))))&
((generous(mary)&curious(mary)))&
((tall(susan)&wise(susan)))&
(?[X]:(creative(X)))&
(?[X]:((~curious(X)|humble(X))))&
(?[X]:((~humble(X)&old(X))))&
(?[X]:((creative(X)&wise(X))))&
((~wise(paul)|happy(paul)))&
((~wise(paul)<~>calm(paul))) | ~patient(susan) | [] | null | 0 |
Everyone who is generous is not creative or tall and vice versa.
Everyone who is both kind and funny is wise or generous.
If alice is either not generous or tall then paul is both funny and wise.
If someone is either generous or not kind then someone is either not happy or generous and vice versa.
Everyone who is not rich or wise is either patient or not creative.
If someone is both not curious and not strong then someone is not generous.
Everyone who is either not calm or not humble is not brave or brave and vice versa.
Everyone who is either not old or creative is not old.
If susan is old or rich then susan is both humble and not humble and vice versa.
If paul is both not patient and calm then someone is not wise.
Everyone who is not brave is both not humble and not tall.
Everyone who is not wise is funny.
If someone is either not quiet or not tall then someone is both not funny and not quiet and vice versa.
Everyone who is creative is both funny and not patient.
If mary is either kind or not old then lucy is happy or tall.
Everyone who is generous is not curious or patient and vice versa.
Mary is not brave.
Paul is not creative.
Someone is strong.
Someone is generous.
Someone is either not calm or not strong.
Someone is either calm or not patient.
Someone is funny.
Someone is either not patient or patient. | Susan is not curious. | entailment | (![X]:(generous(X)<=>(~creative(X)|tall(X))))&
(![X]:((kind(X)&funny(X))=>(wise(X)|generous(X))))&
(((~generous(alice)<~>tall(alice)))=>((funny(paul)&wise(paul))))&
((?[X]:((generous(X)<~>~kind(X))))<=>(?[X]:((~happy(X)<~>generous(X)))))&
(![X]:((~rich(X)|wise(X))=>(patient(X)<~>~creative(X))))&
((?[X]:((~curious(X)&~strong(X))))=>(?[X]:(~generous(X))))&
(![X]:((~calm(X)<~>~humble(X))<=>(~brave(X)|brave(X))))&
(![X]:((~old(X)<~>creative(X))=>~old(X)))&
(((old(susan)|rich(susan)))<=>((humble(susan)&~humble(susan))))&
(((~patient(paul)&calm(paul)))=>(?[X]:(~wise(X))))&
(![X]:(~brave(X)=>(~humble(X)&~tall(X))))&
(![X]:(~wise(X)=>funny(X)))&
((?[X]:((~quiet(X)<~>~tall(X))))<=>(?[X]:((~funny(X)&~quiet(X)))))&
(![X]:(creative(X)=>(funny(X)&~patient(X))))&
(((kind(mary)<~>~old(mary)))=>((happy(lucy)|tall(lucy))))&
(![X]:(generous(X)<=>(~curious(X)|patient(X))))&
(~brave(mary))&
(~creative(paul))&
(?[X]:(strong(X)))&
(?[X]:(generous(X)))&
(?[X]:((~calm(X)<~>~strong(X))))&
(?[X]:((calm(X)<~>~patient(X))))&
(?[X]:(funny(X)))&
(?[X]:((~patient(X)<~>patient(X)))) | ~curious(susan) | [
"p0",
"p4",
"p8",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7255867335512505473305537
% SZS output start Proof for 7255867335512505473305537
1. ! [X0] : (generous(X0) <=> (tall(X0) | ~creative(X0))) [input p0]
5. ! [X0] : ((wise(X0) | ~rich(X0)) => (patient(X0) <~> ~creative(X0))) [input p4]
9. (rich(susan) | old(susan)) <=> (~humble(susan) & humble(susan)) [input p8]
14. ! [X0] : (creative(X0) => (~patient(X0) & funny(X0))) [input p13]
16. ! [X0] : (generous(X0) <=> (patient(X0) | ~curious(X0))) [input p15]
25. curious(susan) [input hypothesis]
32. ! [X0] : ((patient(X0) <~> ~creative(X0)) | (~wise(X0) & rich(X0))) [ennf transformation 5]
39. ! [X0] : ((~patient(X0) & funny(X0)) | ~creative(X0)) [ennf transformation 14]
42. ! [X0] : ((generous(X0) | (~tall(X0) & creative(X0))) & ((tall(X0) | ~creative(X0)) | ~generous(X0))) [nnf transformation 1]
43. ! [X0] : ((generous(X0) | (~tall(X0) & creative(X0))) & (tall(X0) | ~creative(X0) | ~generous(X0))) [flattening 42]
50. ! [X0] : (((creative(X0) | ~patient(X0)) & (~creative(X0) | patient(X0))) | (~wise(X0) & rich(X0))) [nnf transformation 32]
57. ((rich(susan) | old(susan)) | (humble(susan) | ~humble(susan))) & ((~humble(susan) & humble(susan)) | (~rich(susan) & ~old(susan))) [nnf transformation 9]
58. (rich(susan) | old(susan) | humble(susan) | ~humble(susan)) & ((~humble(susan) & humble(susan)) | (~rich(susan) & ~old(susan))) [flattening 57]
67. ! [X0] : ((generous(X0) | (~patient(X0) & curious(X0))) & ((patient(X0) | ~curious(X0)) | ~generous(X0))) [nnf transformation 16]
68. ! [X0] : ((generous(X0) | (~patient(X0) & curious(X0))) & (patient(X0) | ~curious(X0) | ~generous(X0))) [flattening 67]
85. creative(X0) | generous(X0) [cnf transformation 43]
100. ~creative(X0) | patient(X0) | rich(X0) [cnf transformation 50]
102. ~patient(X0) | creative(X0) | rich(X0) [cnf transformation 50]
114. humble(susan) | ~rich(susan) [cnf transformation 58]
116. ~humble(susan) | ~rich(susan) [cnf transformation 58]
129. ~patient(X0) | ~creative(X0) [cnf transformation 39]
132. ~curious(X0) | patient(X0) | ~generous(X0) [cnf transformation 68]
134. ~patient(X0) | generous(X0) [cnf transformation 68]
146. curious(susan) [cnf transformation 25]
219. 15 <=> rich(susan) [avatar definition]
221. ~rich(susan) <- (~15) [avatar component clause 219]
223. 16 <=> humble(susan) [avatar definition]
226. ~15 | ~16 [avatar split clause 116,223,219]
232. ~15 | 16 [avatar split clause 114,223,219]
327. patient(X0) | rich(X0) | generous(X0) [resolution 100,85]
328. rich(X0) | generous(X0) [subsumption resolution 327,134]
331. generous(susan) <- (~15) [resolution 328,221]
335. patient(susan) | ~generous(susan) [resolution 132,146]
337. patient(susan) <- (~15) [subsumption resolution 335,331]
339. creative(susan) | rich(susan) <- (~15) [resolution 337,102]
341. ~creative(susan) <- (~15) [resolution 337,129]
347. 37 <=> creative(susan) [avatar definition]
351. creative(susan) <- (~15) [subsumption resolution 339,221]
352. 37 | 15 [avatar split clause 351,219,347]
353. ~37 | 15 [avatar split clause 341,219,347]
354. $false [avatar sat refutation 226,232,352,353]
% SZS output end Proof for 7255867335512505473305537
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and kind is not calm. Everyone who is either patient or not happy is both not tall and not kind and vice versa. If lucy is old then someone is brave and vice versa. Everyone who is strong is not quiet. If someone is both not kind and not funny then lucy is not strong. If someone is brave then john is both not old and strong and vice versa. If john is not wise then lucy is calm or not kind and vice versa. Everyone who is either generous or not brave is not wise or not brave and vice versa. If someone is either not rich or not patient then lucy is wise or quiet. If susan is either not generous or strong then someone is either not humble or quiet and vice versa. Everyone who is both not funny and not humble is not brave or creative and vice versa. If susan is both not humble and not happy then fred is either brave or not brave. If susan is not funny then alice is not kind or happy. If someone is not calm then susan is either generous or tall. Everyone who is calm or not generous is both not creative and patient and vice versa. Everyone who is both not old and kind is tall or not old and vice versa. Fred is both quiet and not brave. Someone is not strong or not happy. Paul is humble or kind. Lucy is either not quiet or not patient. Someone is not wise or strong. Someone is quiet or calm. Someone is not rich. Someone is not quiet. | Lucy is patient. | neutral | (![X]:((~calm(X)&kind(X))=>~calm(X)))&
(![X]:((patient(X)<~>~happy(X))<=>(~tall(X)&~kind(X))))&
((old(lucy))<=>(?[X]:(brave(X))))&
(![X]:(strong(X)=>~quiet(X)))&
((?[X]:((~kind(X)&~funny(X))))=>(~strong(lucy)))&
((?[X]:(brave(X)))<=>((~old(john)&strong(john))))&
((~wise(john))<=>((calm(lucy)|~kind(lucy))))&
(![X]:((generous(X)<~>~brave(X))<=>(~wise(X)|~brave(X))))&
((?[X]:((~rich(X)<~>~patient(X))))=>((wise(lucy)|quiet(lucy))))&
(((~generous(susan)<~>strong(susan)))<=>(?[X]:((~humble(X)<~>quiet(X)))))&
(![X]:((~funny(X)&~humble(X))<=>(~brave(X)|creative(X))))&
(((~humble(susan)&~happy(susan)))=>((brave(fred)<~>~brave(fred))))&
((~funny(susan))=>((~kind(alice)|happy(alice))))&
((?[X]:(~calm(X)))=>((generous(susan)<~>tall(susan))))&
(![X]:((calm(X)|~generous(X))<=>(~creative(X)&patient(X))))&
(![X]:((~old(X)&kind(X))<=>(tall(X)|~old(X))))&
((quiet(fred)&~brave(fred)))&
(?[X]:((~strong(X)|~happy(X))))&
((humble(paul)|kind(paul)))&
((~quiet(lucy)<~>~patient(lucy)))&
(?[X]:((~wise(X)|strong(X))))&
(?[X]:((quiet(X)|calm(X))))&
(?[X]:(~rich(X)))&
(?[X]:(~quiet(X))) | patient(lucy) | [] | null | 0 |
Everyone who is either quiet or calm is both not generous and not funny.
Everyone who is either creative or rich is tall.
If susan is funny then someone is funny.
If lucy is both rich and not generous then someone is both not brave and wise and vice versa.
If someone is either funny or happy then susan is curious or not generous.
If mary is either not old or not calm then someone is either not strong or not patient and vice versa.
Everyone who is not humble is both generous and quiet and vice versa.
Everyone who is both not calm and not happy is either not quiet or generous.
Everyone who is generous or not kind is calm and vice versa.
If someone is not old or rich then someone is kind or not happy and vice versa.
If someone is either old or humble then someone is either not funny or patient and vice versa.
Everyone who is curious or not humble is both creative and kind and vice versa.
Everyone who is both not patient and not calm is kind.
If john is not kind then john is generous and vice versa.
If someone is curious or brave then mary is not creative.
Everyone who is both not generous and not kind is both curious and old.
Lucy is both not happy and not wise.
Someone is both brave and generous.
Someone is both old and not funny.
Someone is both calm and not rich.
Someone is tall.
Lucy is not strong or not curious.
Lucy is both generous and calm.
Someone is either strong or not generous. | John is not calm. | entailment | (![X]:((quiet(X)<~>calm(X))=>(~generous(X)&~funny(X))))&
(![X]:((creative(X)<~>rich(X))=>tall(X)))&
((funny(susan))=>(?[X]:(funny(X))))&
(((rich(lucy)&~generous(lucy)))<=>(?[X]:((~brave(X)&wise(X)))))&
((?[X]:((funny(X)<~>happy(X))))=>((curious(susan)|~generous(susan))))&
(((~old(mary)<~>~calm(mary)))<=>(?[X]:((~strong(X)<~>~patient(X)))))&
(![X]:(~humble(X)<=>(generous(X)&quiet(X))))&
(![X]:((~calm(X)&~happy(X))=>(~quiet(X)<~>generous(X))))&
(![X]:((generous(X)|~kind(X))<=>calm(X)))&
((?[X]:((~old(X)|rich(X))))<=>(?[X]:((kind(X)|~happy(X)))))&
((?[X]:((old(X)<~>humble(X))))<=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:((curious(X)|~humble(X))<=>(creative(X)&kind(X))))&
(![X]:((~patient(X)&~calm(X))=>kind(X)))&
((~kind(john))<=>(generous(john)))&
((?[X]:((curious(X)|brave(X))))=>(~creative(mary)))&
(![X]:((~generous(X)&~kind(X))=>(curious(X)&old(X))))&
((~happy(lucy)&~wise(lucy)))&
(?[X]:((brave(X)&generous(X))))&
(?[X]:((old(X)&~funny(X))))&
(?[X]:((calm(X)&~rich(X))))&
(?[X]:(tall(X)))&
((~strong(lucy)|~curious(lucy)))&
((generous(lucy)&calm(lucy)))&
(?[X]:((strong(X)<~>~generous(X)))) | ~calm(john) | [
"p0",
"p6",
"p8",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6055962187700683015284100
% SZS output start Proof for 6055962187700683015284100
1. ! [X0] : ((quiet(X0) <~> calm(X0)) => (~funny(X0) & ~generous(X0))) [input p0]
7. ! [X0] : (~humble(X0) <=> (quiet(X0) & generous(X0))) [input p6]
9. ! [X0] : ((~kind(X0) | generous(X0)) <=> calm(X0)) [input p8]
12. ! [X0] : ((~humble(X0) | curious(X0)) <=> (kind(X0) & creative(X0))) [input p11]
14. ~kind(john) <=> generous(john) [input p13]
16. ! [X0] : ((~kind(X0) & ~generous(X0)) => (old(X0) & curious(X0))) [input p15]
25. calm(john) [input hypothesis]
30. ! [X0] : ((~funny(X0) & ~generous(X0)) | (quiet(X0) <=> calm(X0))) [ennf transformation 1]
39. ! [X0] : ((old(X0) & curious(X0)) | (kind(X0) | generous(X0))) [ennf transformation 16]
40. ! [X0] : ((old(X0) & curious(X0)) | kind(X0) | generous(X0)) [flattening 39]
41. ! [X0] : ((~funny(X0) & ~generous(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0)))) [nnf transformation 30]
54. ! [X0] : ((~humble(X0) | (~quiet(X0) | ~generous(X0))) & ((quiet(X0) & generous(X0)) | humble(X0))) [nnf transformation 7]
55. ! [X0] : ((~humble(X0) | ~quiet(X0) | ~generous(X0)) & ((quiet(X0) & generous(X0)) | humble(X0))) [flattening 54]
57. ! [X0] : (((~kind(X0) | generous(X0)) | ~calm(X0)) & (calm(X0) | (kind(X0) & ~generous(X0)))) [nnf transformation 9]
58. ! [X0] : ((~kind(X0) | generous(X0) | ~calm(X0)) & (calm(X0) | (kind(X0) & ~generous(X0)))) [flattening 57]
69. ! [X0] : (((~humble(X0) | curious(X0)) | (~kind(X0) | ~creative(X0))) & ((kind(X0) & creative(X0)) | (humble(X0) & ~curious(X0)))) [nnf transformation 12]
70. ! [X0] : ((~humble(X0) | curious(X0) | ~kind(X0) | ~creative(X0)) & ((kind(X0) & creative(X0)) | (humble(X0) & ~curious(X0)))) [flattening 69]
71. (~kind(john) | ~generous(john)) & (generous(john) | kind(john)) [nnf transformation 14]
82. ~generous(X0) | quiet(X0) | ~calm(X0) [cnf transformation 41]
102. ~humble(X0) | ~quiet(X0) | ~generous(X0) [cnf transformation 55]
107. ~kind(X0) | generous(X0) | ~calm(X0) [cnf transformation 58]
122. ~curious(X0) | kind(X0) [cnf transformation 70]
123. kind(X0) | humble(X0) [cnf transformation 70]
127. ~kind(john) | ~generous(john) [cnf transformation 71]
130. curious(X0) | kind(X0) | generous(X0) [cnf transformation 40]
145. calm(john) [cnf transformation 25]
295. 34 <=> generous(john) [avatar definition]
296. generous(john) <- (34) [avatar component clause 295]
297. ~generous(john) <- (~34) [avatar component clause 295]
299. 35 <=> kind(john) [avatar definition]
301. ~kind(john) <- (~35) [avatar component clause 299]
302. ~34 | ~35 [avatar split clause 127,299,295]
316. kind(X0) | generous(X0) [subsumption resolution 130,122]
345. humble(john) <- (~35) [resolution 123,301]
352. quiet(john) | ~calm(john) <- (34) [resolution 82,296]
356. quiet(john) <- (34) [subsumption resolution 352,145]
361. ~quiet(john) | ~generous(john) <- (~35) [resolution 102,345]
362. ~generous(john) <- (34, ~35) [subsumption resolution 361,356]
363. $false <- (34, ~35) [subsumption resolution 362,296]
364. ~34 | 35 [avatar contradiction clause 363]
365. generous(X0) | ~calm(X0) | generous(X0) [resolution 107,316]
369. ~calm(X0) | generous(X0) [duplicate literal removal 365]
371. generous(john) [resolution 369,145]
375. $false <- (~34) [subsumption resolution 371,297]
376. 34 [avatar contradiction clause 375]
377. $false [avatar sat refutation 302,364,376]
% SZS output end Proof for 6055962187700683015284100
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not kind is either not old or not wise.
If mary is both not generous and generous then mary is brave or not rich and vice versa.
If mary is tall or generous then someone is not tall.
Everyone who is not creative is both not curious and rich.
Everyone who is not brave or not creative is quiet.
Everyone who is both not generous and creative is both not curious and creative and vice versa.
If someone is not quiet or patient then someone is not rich and vice versa.
Everyone who is both not rich and not creative is both generous and creative and vice versa.
Everyone who is curious or not curious is either calm or not strong.
If someone is either happy or patient then susan is either funny or not humble.
Everyone who is either not brave or wise is either not funny or not curious and vice versa.
If someone is either not calm or not wise then someone is either tall or not tall.
Everyone who is either not quiet or patient is not old or funny and vice versa.
Everyone who is either not tall or not old is both quiet and not generous and vice versa.
If paul is either old or not curious then someone is tall or old and vice versa.
Fred is not humble or wise.
Someone is either calm or quiet.
Someone is rich or not humble.
Someone is not kind.
Someone is either old or not wise.
Someone is either not brave or patient.
Paul is not tall.
Someone is creative. | Fred is not brave. | neutral | (![X]:((generous(X)|~kind(X))=>(~old(X)<~>~wise(X))))&
(((~generous(mary)&generous(mary)))<=>((brave(mary)|~rich(mary))))&
(((tall(mary)|generous(mary)))=>(?[X]:(~tall(X))))&
(![X]:(~creative(X)=>(~curious(X)&rich(X))))&
(![X]:((~brave(X)|~creative(X))=>quiet(X)))&
(![X]:((~generous(X)&creative(X))<=>(~curious(X)&creative(X))))&
((?[X]:((~quiet(X)|patient(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~rich(X)&~creative(X))<=>(generous(X)&creative(X))))&
(![X]:((curious(X)|~curious(X))=>(calm(X)<~>~strong(X))))&
((?[X]:((happy(X)<~>patient(X))))=>((funny(susan)<~>~humble(susan))))&
(![X]:((~brave(X)<~>wise(X))<=>(~funny(X)<~>~curious(X))))&
((?[X]:((~calm(X)<~>~wise(X))))=>(?[X]:((tall(X)<~>~tall(X)))))&
(![X]:((~quiet(X)<~>patient(X))<=>(~old(X)|funny(X))))&
(![X]:((~tall(X)<~>~old(X))<=>(quiet(X)&~generous(X))))&
(((old(paul)<~>~curious(paul)))<=>(?[X]:((tall(X)|old(X)))))&
((~humble(fred)|wise(fred)))&
(?[X]:((calm(X)<~>quiet(X))))&
(?[X]:((rich(X)|~humble(X))))&
(?[X]:(~kind(X)))&
(?[X]:((old(X)<~>~wise(X))))&
(?[X]:((~brave(X)<~>patient(X))))&
(~tall(paul))&
(?[X]:(creative(X))) | ~brave(fred) | [] | null | 0 |
Everyone who is strong is either not humble or not quiet.
Everyone who is both quiet and not humble is kind and vice versa.
Everyone who is either not funny or not creative is both not generous and tall and vice versa.
If mary is curious then someone is quiet and vice versa.
Everyone who is not rich is not humble and vice versa.
If john is patient then lucy is either brave or not rich.
Everyone who is both patient and wise is patient or not patient and vice versa.
Everyone who is curious or happy is wise and vice versa.
Everyone who is both not funny and humble is brave or curious and vice versa.
Everyone who is funny is either not wise or not strong and vice versa.
If paul is strong then someone is not wise or wise.
If fred is not funny then susan is both not wise and curious and vice versa.
Everyone who is wise is not old.
Everyone who is either brave or patient is either old or not kind.
If alice is either curious or brave then someone is both not curious and generous and vice versa.
Everyone who is quiet is either brave or not patient.
Someone is not happy or not wise.
Someone is not funny or brave.
Someone is either curious or rich.
Lucy is happy.
Someone is both tall and brave.
John is not funny.
Someone is not calm or curious. | Susan is not humble. | neutral | (![X]:(strong(X)=>(~humble(X)<~>~quiet(X))))&
(![X]:((quiet(X)&~humble(X))<=>kind(X)))&
(![X]:((~funny(X)<~>~creative(X))<=>(~generous(X)&tall(X))))&
((curious(mary))<=>(?[X]:(quiet(X))))&
(![X]:(~rich(X)<=>~humble(X)))&
((patient(john))=>((brave(lucy)<~>~rich(lucy))))&
(![X]:((patient(X)&wise(X))<=>(patient(X)|~patient(X))))&
(![X]:((curious(X)|happy(X))<=>wise(X)))&
(![X]:((~funny(X)&humble(X))<=>(brave(X)|curious(X))))&
(![X]:(funny(X)<=>(~wise(X)<~>~strong(X))))&
((strong(paul))=>(?[X]:((~wise(X)|wise(X)))))&
((~funny(fred))<=>((~wise(susan)&curious(susan))))&
(![X]:(wise(X)=>~old(X)))&
(![X]:((brave(X)<~>patient(X))=>(old(X)<~>~kind(X))))&
(((curious(alice)<~>brave(alice)))<=>(?[X]:((~curious(X)&generous(X)))))&
(![X]:(quiet(X)=>(brave(X)<~>~patient(X))))&
(?[X]:((~happy(X)|~wise(X))))&
(?[X]:((~funny(X)|brave(X))))&
(?[X]:((curious(X)<~>rich(X))))&
(happy(lucy))&
(?[X]:((tall(X)&brave(X))))&
(~funny(john))&
(?[X]:((~calm(X)|curious(X)))) | ~humble(susan) | [] | null | 0 |
If lucy is not creative then alice is both not tall and humble and vice versa. Everyone who is both patient and not brave is both strong and calm. Everyone who is either not strong or not funny is rich or generous and vice versa. Everyone who is both happy and not rich is either not curious or not rich and vice versa. If alice is not quiet then paul is not kind. If paul is not brave then someone is not rich and vice versa. If mary is patient or not generous then someone is both patient and old. Everyone who is either not happy or not rich is either not happy or kind and vice versa. If someone is either funny or not generous then someone is wise and vice versa. Everyone who is both not happy and not brave is either humble or not brave. Everyone who is patient or calm is funny. Everyone who is either brave or not calm is either not kind or calm. Everyone who is not kind or not old is not funny and vice versa. Everyone who is patient is happy or creative. If someone is creative or not curious then john is either kind or funny and vice versa. If fred is either not tall or not quiet then lucy is curious and vice versa. Someone is either not creative or calm. Lucy is happy or calm. John is not patient. Fred is both happy and old. Susan is not strong or not old. Fred is wise or not brave. Mary is old or not kind. | Mary is creative. | neutral | ((~creative(lucy))<=>((~tall(alice)&humble(alice))))&
(![X]:((patient(X)&~brave(X))=>(strong(X)&calm(X))))&
(![X]:((~strong(X)<~>~funny(X))<=>(rich(X)|generous(X))))&
(![X]:((happy(X)&~rich(X))<=>(~curious(X)<~>~rich(X))))&
((~quiet(alice))=>(~kind(paul)))&
((~brave(paul))<=>(?[X]:(~rich(X))))&
(((patient(mary)|~generous(mary)))=>(?[X]:((patient(X)&old(X)))))&
(![X]:((~happy(X)<~>~rich(X))<=>(~happy(X)<~>kind(X))))&
((?[X]:((funny(X)<~>~generous(X))))<=>(?[X]:(wise(X))))&
(![X]:((~happy(X)&~brave(X))=>(humble(X)<~>~brave(X))))&
(![X]:((patient(X)|calm(X))=>funny(X)))&
(![X]:((brave(X)<~>~calm(X))=>(~kind(X)<~>calm(X))))&
(![X]:((~kind(X)|~old(X))<=>~funny(X)))&
(![X]:(patient(X)=>(happy(X)|creative(X))))&
((?[X]:((creative(X)|~curious(X))))<=>((kind(john)<~>funny(john))))&
(((~tall(fred)<~>~quiet(fred)))<=>(curious(lucy)))&
(?[X]:((~creative(X)<~>calm(X))))&
((happy(lucy)|calm(lucy)))&
(~patient(john))&
((happy(fred)&old(fred)))&
((~strong(susan)|~old(susan)))&
((wise(fred)|~brave(fred)))&
((old(mary)|~kind(mary))) | creative(mary) | [] | null | 0 |
If someone is not wise or not strong then susan is both not curious and not strong.
Everyone who is not generous is either patient or not generous and vice versa.
If someone is not curious then lucy is both not kind and not creative and vice versa.
If someone is both patient and strong then mary is not tall.
If paul is humble then alice is not patient or wise.
If someone is both not happy and wise then alice is strong or not strong.
Everyone who is both not humble and patient is not creative and vice versa.
Everyone who is both not tall and generous is either not curious or not humble and vice versa.
Everyone who is either old or not curious is both not funny and creative and vice versa.
If mary is not humble or patient then fred is tall or old and vice versa.
If fred is kind then someone is both creative and brave and vice versa.
Everyone who is not creative or not calm is either funny or brave.
If someone is either not rich or rich then alice is not calm.
If paul is not funny or rich then susan is old and vice versa.
If fred is patient or creative then alice is strong.
Everyone who is not happy is both funny and not curious.
Paul is kind or brave.
John is both not calm and not quiet.
Someone is either patient or calm.
Someone is either not patient or generous.
Someone is not old.
Paul is not old or brave.
Someone is funny. | John is happy. | entailment | ((?[X]:((~wise(X)|~strong(X))))=>((~curious(susan)&~strong(susan))))&
(![X]:(~generous(X)<=>(patient(X)<~>~generous(X))))&
((?[X]:(~curious(X)))<=>((~kind(lucy)&~creative(lucy))))&
((?[X]:((patient(X)&strong(X))))=>(~tall(mary)))&
((humble(paul))=>((~patient(alice)|wise(alice))))&
((?[X]:((~happy(X)&wise(X))))=>((strong(alice)|~strong(alice))))&
(![X]:((~humble(X)&patient(X))<=>~creative(X)))&
(![X]:((~tall(X)&generous(X))<=>(~curious(X)<~>~humble(X))))&
(![X]:((old(X)<~>~curious(X))<=>(~funny(X)&creative(X))))&
(((~humble(mary)|patient(mary)))<=>((tall(fred)|old(fred))))&
((kind(fred))<=>(?[X]:((creative(X)&brave(X)))))&
(![X]:((~creative(X)|~calm(X))=>(funny(X)<~>brave(X))))&
((?[X]:((~rich(X)<~>rich(X))))=>(~calm(alice)))&
(((~funny(paul)|rich(paul)))<=>(old(susan)))&
(((patient(fred)|creative(fred)))=>(strong(alice)))&
(![X]:(~happy(X)=>(funny(X)&~curious(X))))&
((kind(paul)|brave(paul)))&
((~calm(john)&~quiet(john)))&
(?[X]:((patient(X)<~>calm(X))))&
(?[X]:((~patient(X)<~>generous(X))))&
(?[X]:(~old(X)))&
((~old(paul)|brave(paul)))&
(?[X]:(funny(X))) | happy(john) | [
"p1",
"p2",
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3276780080079661363349102
% SZS output start Proof for 3276780080079661363349102
2. ! [X0] : (~generous(X0) <=> (patient(X0) <~> ~generous(X0))) [input p1]
3. ? [X0] : ~curious(X0) <=> (~creative(lucy) & ~kind(lucy)) [input p2]
7. ! [X0] : ((patient(X0) & ~humble(X0)) <=> ~creative(X0)) [input p6]
16. ! [X0] : (~happy(X0) => (~curious(X0) & funny(X0))) [input p15]
24. ~happy(john) [input hypothesis]
35. ! [X0] : ((~curious(X0) & funny(X0)) | happy(X0)) [ennf transformation 16]
36. ! [X0] : ((~generous(X0) | ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0)))) & (((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | generous(X0))) [nnf transformation 2]
37. (? [X0] : ~curious(X0) | (creative(lucy) | kind(lucy))) & ((~creative(lucy) & ~kind(lucy)) | ! [X0] : curious(X0)) [nnf transformation 3]
38. (? [X0] : ~curious(X0) | creative(lucy) | kind(lucy)) & ((~creative(lucy) & ~kind(lucy)) | ! [X0] : curious(X0)) [flattening 37]
39. (? [X0] : ~curious(X0) | creative(lucy) | kind(lucy)) & ((~creative(lucy) & ~kind(lucy)) | ! [X1] : curious(X1)) [rectify 38]
40. ? [X0] : ~curious(X0) => ~curious(sK0) [choice axiom]
41. (~curious(sK0) | creative(lucy) | kind(lucy)) & ((~creative(lucy) & ~kind(lucy)) | ! [X1] : curious(X1)) [skolemisation 39,40]
42. ! [X0] : (((patient(X0) & ~humble(X0)) | creative(X0)) & (~creative(X0) | (~patient(X0) | humble(X0)))) [nnf transformation 7]
43. ! [X0] : (((patient(X0) & ~humble(X0)) | creative(X0)) & (~creative(X0) | ~patient(X0) | humble(X0))) [flattening 42]
73. generous(X0) | ~patient(X0) | generous(X0) [cnf transformation 36]
74. ~generous(X0) | ~generous(X0) | ~patient(X0) [cnf transformation 36]
77. ~creative(lucy) | curious(X1) [cnf transformation 41]
84. patient(X0) | creative(X0) [cnf transformation 43]
116. ~curious(X0) | happy(X0) [cnf transformation 35]
126. ~happy(john) [cnf transformation 24]
129. generous(X0) | ~patient(X0) [duplicate literal removal 73]
130. ~generous(X0) | ~patient(X0) [duplicate literal removal 74]
149. ~patient(X0) [subsumption resolution 129,130]
155. 6 <=> creative(lucy) [avatar definition]
156. ~creative(lucy) <- (~6) [avatar component clause 155]
164. 8 <=> ! [X1] : curious(X1) [avatar definition]
165. curious(X1) <- (8) [avatar component clause 164]
166. 8 | ~6 [avatar split clause 77,155,164]
168. creative(X0) [subsumption resolution 84,149]
246. $false <- (~6) [subsumption resolution 156,168]
247. 6 [avatar contradiction clause 246]
255. happy(X0) <- (8) [resolution 116,165]
256. $false <- (8) [resolution 255,126]
257. ~8 [avatar contradiction clause 256]
258. $false [avatar sat refutation 166,247,257]
% SZS output end Proof for 3276780080079661363349102
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny then lucy is either humble or rich. Everyone who is not kind is not brave or not happy. Everyone who is not funny or not brave is both generous and humble and vice versa. If someone is both not quiet and not kind then someone is both not kind and kind. If susan is kind or creative then someone is funny. Everyone who is both calm and not kind is either creative or not patient and vice versa. Everyone who is both wise and funny is happy or not funny. Everyone who is not quiet or curious is not generous and vice versa. If someone is both tall and funny then someone is both not funny and not quiet. If someone is not creative or creative then alice is either not kind or quiet and vice versa. If susan is either quiet or not happy then alice is both patient and generous. If john is either funny or happy then paul is both not old and not patient and vice versa. If paul is not brave or rich then someone is not quiet and vice versa. Everyone who is brave or not generous is old or not brave and vice versa. Everyone who is patient is kind and vice versa. If someone is either rich or happy then fred is both not calm and not kind and vice versa. Someone is not wise. Someone is brave. Alice is happy. Paul is both not calm and not wise. Mary is both generous and not happy. Someone is either generous or not happy. John is both old and brave. Someone is generous. | Alice is not patient. | contradiction | ((?[X]:(funny(X)))=>((humble(lucy)<~>rich(lucy))))&
(![X]:(~kind(X)=>(~brave(X)|~happy(X))))&
(![X]:((~funny(X)|~brave(X))<=>(generous(X)&humble(X))))&
((?[X]:((~quiet(X)&~kind(X))))=>(?[X]:((~kind(X)&kind(X)))))&
(((kind(susan)|creative(susan)))=>(?[X]:(funny(X))))&
(![X]:((calm(X)&~kind(X))<=>(creative(X)<~>~patient(X))))&
(![X]:((wise(X)&funny(X))=>(happy(X)|~funny(X))))&
(![X]:((~quiet(X)|curious(X))<=>~generous(X)))&
((?[X]:((tall(X)&funny(X))))=>(?[X]:((~funny(X)&~quiet(X)))))&
((?[X]:((~creative(X)|creative(X))))<=>((~kind(alice)<~>quiet(alice))))&
(((quiet(susan)<~>~happy(susan)))=>((patient(alice)&generous(alice))))&
(((funny(john)<~>happy(john)))<=>((~old(paul)&~patient(paul))))&
(((~brave(paul)|rich(paul)))<=>(?[X]:(~quiet(X))))&
(![X]:((brave(X)|~generous(X))<=>(old(X)|~brave(X))))&
(![X]:(patient(X)<=>kind(X)))&
((?[X]:((rich(X)<~>happy(X))))<=>((~calm(fred)&~kind(fred))))&
(?[X]:(~wise(X)))&
(?[X]:(brave(X)))&
(happy(alice))&
((~calm(paul)&~wise(paul)))&
((generous(mary)&~happy(mary)))&
(?[X]:((generous(X)<~>~happy(X))))&
((old(john)&brave(john)))&
(?[X]:(generous(X))) | ~patient(alice) | [
"p3",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8219283087567795488178520
% SZS output start Proof for 8219283087567795488178520
4. ? [X0] : (~kind(X0) & ~quiet(X0)) => ? [X0] : (kind(X0) & ~kind(X0)) [input p3]
10. ? [X0] : (creative(X0) | ~creative(X0)) <=> (~kind(alice) <~> quiet(alice)) [input p9]
15. ! [X0] : (patient(X0) <=> kind(X0)) [input p14]
25. ~patient(alice) [input hypothesis]
26. ? [X0] : (~kind(X0) & ~quiet(X0)) => ? [X1] : (kind(X1) & ~kind(X1)) [rectify 4]
35. ? [X1] : (kind(X1) & ~kind(X1)) | ! [X0] : (kind(X0) | quiet(X0)) [ennf transformation 26]
41. ? [X0] : (kind(X0) & ~kind(X0)) | ! [X1] : (kind(X1) | quiet(X1)) [rectify 35]
42. ? [X0] : (kind(X0) & ~kind(X0)) => (kind(sK0) & ~kind(sK0)) [choice axiom]
43. (kind(sK0) & ~kind(sK0)) | ! [X1] : (kind(X1) | quiet(X1)) [skolemisation 41,42]
50. (? [X0] : (creative(X0) | ~creative(X0)) | ((~kind(alice) | ~quiet(alice)) & (quiet(alice) | kind(alice)))) & (((~quiet(alice) | kind(alice)) & (quiet(alice) | ~kind(alice))) | ! [X0] : (~creative(X0) & creative(X0))) [nnf transformation 10]
51. (? [X0] : (creative(X0) | ~creative(X0)) | ((~kind(alice) | ~quiet(alice)) & (quiet(alice) | kind(alice)))) & (((~quiet(alice) | kind(alice)) & (quiet(alice) | ~kind(alice))) | ! [X1] : (~creative(X1) & creative(X1))) [rectify 50]
52. ? [X0] : (creative(X0) | ~creative(X0)) => (creative(sK2) | ~creative(sK2)) [choice axiom]
53. ((creative(sK2) | ~creative(sK2)) | ((~kind(alice) | ~quiet(alice)) & (quiet(alice) | kind(alice)))) & (((~quiet(alice) | kind(alice)) & (quiet(alice) | ~kind(alice))) | ! [X1] : (~creative(X1) & creative(X1))) [skolemisation 51,52]
64. ! [X0] : ((patient(X0) | ~kind(X0)) & (kind(X0) | ~patient(X0))) [nnf transformation 15]
85. ~kind(sK0) | kind(X1) | quiet(X1) [cnf transformation 43]
86. kind(sK0) | kind(X1) | quiet(X1) [cnf transformation 43]
100. ~quiet(alice) | kind(alice) | creative(X1) [cnf transformation 53]
101. ~quiet(alice) | kind(alice) | ~creative(X1) [cnf transformation 53]
122. ~kind(X0) | patient(X0) [cnf transformation 64]
139. ~patient(alice) [cnf transformation 25]
156. 4 <=> ! [X1] : (kind(X1) | quiet(X1)) [avatar definition]
157. quiet(X1) | kind(X1) <- (4) [avatar component clause 156]
159. 5 <=> kind(sK0) [avatar definition]
162. 4 | 5 [avatar split clause 86,159,156]
163. 4 | ~5 [avatar split clause 85,159,156]
179. 9 <=> ! [X1] : ~creative(X1) [avatar definition]
180. ~creative(X1) <- (9) [avatar component clause 179]
182. 10 <=> kind(alice) [avatar definition]
183. ~kind(alice) <- (~10) [avatar component clause 182]
184. kind(alice) <- (10) [avatar component clause 182]
186. 11 <=> quiet(alice) [avatar definition]
188. ~quiet(alice) <- (~11) [avatar component clause 186]
189. 9 | 10 | ~11 [avatar split clause 101,186,182,179]
191. 12 <=> ! [X1] : creative(X1) [avatar definition]
192. creative(X1) <- (12) [avatar component clause 191]
193. 12 | 10 | ~11 [avatar split clause 100,186,182,191]
211. 16 <=> patient(alice) [avatar definition]
212. ~patient(alice) <- (~16) [avatar component clause 211]
297. ~16 [avatar split clause 139,211]
312. patient(alice) <- (10) [resolution 122,184]
313. $false <- (10, ~16) [subsumption resolution 312,212]
314. ~10 | 16 [avatar contradiction clause 313]
316. kind(alice) <- (4, ~11) [resolution 157,188]
317. $false <- (4, ~10, ~11) [subsumption resolution 316,183]
318. ~4 | 10 | 11 [avatar contradiction clause 317]
319. $false <- (9, 12) [subsumption resolution 180,192]
320. ~9 | ~12 [avatar contradiction clause 319]
321. $false [avatar sat refutation 162,163,189,193,297,314,318,320]
% SZS output end Proof for 8219283087567795488178520
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not happy then alice is happy. Everyone who is both not old and not funny is brave or not tall. If susan is both not calm and creative then paul is not old and vice versa. If lucy is both rich and happy then john is creative or not funny. Everyone who is humble or happy is both old and not tall and vice versa. Everyone who is not happy is both not kind and kind. If susan is both brave and not quiet then fred is either not creative or calm and vice versa. If someone is not curious then someone is both not humble and generous. Everyone who is generous is both old and funny and vice versa. If someone is funny or not generous then someone is both not tall and not quiet. Everyone who is either rich or creative is not strong. If someone is not happy or not curious then john is not humble. If someone is not rich then someone is either tall or not wise. Everyone who is either happy or curious is creative and vice versa. Everyone who is both not creative and humble is both not old and curious and vice versa. If someone is not happy or not kind then john is both generous and not quiet. Alice is both not brave and not strong. Paul is not curious. Someone is not kind. Someone is either not humble or not old. Susan is calm. Paul is not calm or not humble. Someone is not wise or not quiet. Fred is both not quiet and not patient. | Paul is old. | entailment | ((~happy(alice))=>(happy(alice)))&
(![X]:((~old(X)&~funny(X))=>(brave(X)|~tall(X))))&
(((~calm(susan)&creative(susan)))<=>(~old(paul)))&
(((rich(lucy)&happy(lucy)))=>((creative(john)|~funny(john))))&
(![X]:((humble(X)|happy(X))<=>(old(X)&~tall(X))))&
(![X]:(~happy(X)=>(~kind(X)&kind(X))))&
(((brave(susan)&~quiet(susan)))<=>((~creative(fred)<~>calm(fred))))&
((?[X]:(~curious(X)))=>(?[X]:((~humble(X)&generous(X)))))&
(![X]:(generous(X)<=>(old(X)&funny(X))))&
((?[X]:((funny(X)|~generous(X))))=>(?[X]:((~tall(X)&~quiet(X)))))&
(![X]:((rich(X)<~>creative(X))=>~strong(X)))&
((?[X]:((~happy(X)|~curious(X))))=>(~humble(john)))&
((?[X]:(~rich(X)))=>(?[X]:((tall(X)<~>~wise(X)))))&
(![X]:((happy(X)<~>curious(X))<=>creative(X)))&
(![X]:((~creative(X)&humble(X))<=>(~old(X)&curious(X))))&
((?[X]:((~happy(X)|~kind(X))))=>((generous(john)&~quiet(john))))&
((~brave(alice)&~strong(alice)))&
(~curious(paul))&
(?[X]:(~kind(X)))&
(?[X]:((~humble(X)<~>~old(X))))&
(calm(susan))&
((~calm(paul)|~humble(paul)))&
(?[X]:((~wise(X)|~quiet(X))))&
((~quiet(fred)&~patient(fred))) | old(paul) | [
"p2",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1627876976392467532340287
% SZS output start Proof for 1627876976392467532340287
3. (creative(susan) & ~calm(susan)) <=> ~old(paul) [input p2]
21. calm(susan) [input p20]
25. ~old(paul) [input hypothesis]
45. ((creative(susan) & ~calm(susan)) | old(paul)) & (~old(paul) | (~creative(susan) | calm(susan))) [nnf transformation 3]
46. ((creative(susan) & ~calm(susan)) | old(paul)) & (~old(paul) | ~creative(susan) | calm(susan)) [flattening 45]
74. ~calm(susan) | old(paul) [cnf transformation 46]
119. calm(susan) [cnf transformation 21]
123. ~old(paul) [cnf transformation 25]
126. 1 <=> old(paul) [avatar definition]
135. 3 <=> calm(susan) [avatar definition]
138. 1 | ~3 [avatar split clause 74,135,126]
248. 3 [avatar split clause 119,135]
267. ~1 [avatar split clause 123,126]
268. $false [avatar sat refutation 138,248,267]
% SZS output end Proof for 1627876976392467532340287
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not wise and patient then lucy is either creative or not tall and vice versa.
Everyone who is both not happy and not tall is wise and vice versa.
Everyone who is not old is quiet.
Everyone who is either not tall or old is funny or rich and vice versa.
Everyone who is creative or calm is strong.
Everyone who is not quiet or patient is not rich or not creative and vice versa.
If mary is not creative or not strong then john is curious or not generous and vice versa.
If someone is not patient then someone is both calm and not humble and vice versa.
If susan is both strong and not kind then mary is both happy and not creative and vice versa.
Everyone who is both not strong and rich is either not generous or curious.
If alice is calm then alice is not rich or not funny.
If someone is not happy then lucy is both kind and tall and vice versa.
Everyone who is patient or quiet is kind.
If someone is either creative or old then paul is both calm and not wise and vice versa.
Everyone who is not brave or old is either humble or curious.
Everyone who is both not old and not funny is both wise and not curious and vice versa.
Someone is either not patient or humble.
Lucy is both generous and strong.
Someone is either not wise or not old.
John is not old.
Lucy is tall or calm.
Someone is both happy and not patient.
Fred is both curious and generous.
Susan is either not curious or old. | Paul is not quiet. | neutral | ((?[X]:((~wise(X)&patient(X))))<=>((creative(lucy)<~>~tall(lucy))))&
(![X]:((~happy(X)&~tall(X))<=>wise(X)))&
(![X]:(~old(X)=>quiet(X)))&
(![X]:((~tall(X)<~>old(X))<=>(funny(X)|rich(X))))&
(![X]:((creative(X)|calm(X))=>strong(X)))&
(![X]:((~quiet(X)|patient(X))<=>(~rich(X)|~creative(X))))&
(((~creative(mary)|~strong(mary)))<=>((curious(john)|~generous(john))))&
((?[X]:(~patient(X)))<=>(?[X]:((calm(X)&~humble(X)))))&
(((strong(susan)&~kind(susan)))<=>((happy(mary)&~creative(mary))))&
(![X]:((~strong(X)&rich(X))=>(~generous(X)<~>curious(X))))&
((calm(alice))=>((~rich(alice)|~funny(alice))))&
((?[X]:(~happy(X)))<=>((kind(lucy)&tall(lucy))))&
(![X]:((patient(X)|quiet(X))=>kind(X)))&
((?[X]:((creative(X)<~>old(X))))<=>((calm(paul)&~wise(paul))))&
(![X]:((~brave(X)|old(X))=>(humble(X)<~>curious(X))))&
(![X]:((~old(X)&~funny(X))<=>(wise(X)&~curious(X))))&
(?[X]:((~patient(X)<~>humble(X))))&
((generous(lucy)&strong(lucy)))&
(?[X]:((~wise(X)<~>~old(X))))&
(~old(john))&
((tall(lucy)|calm(lucy)))&
(?[X]:((happy(X)&~patient(X))))&
((curious(fred)&generous(fred)))&
((~curious(susan)<~>old(susan))) | ~quiet(paul) | [] | null | 0 |
Everyone who is not quiet or not wise is either curious or quiet.
If someone is both old and brave then someone is both tall and brave and vice versa.
If someone is kind then paul is happy and vice versa.
If someone is either strong or wise then john is happy or calm.
Everyone who is wise is curious or not quiet.
Everyone who is either not old or patient is either funny or patient and vice versa.
Everyone who is humble or not creative is not kind and vice versa.
If fred is patient then someone is either quiet or generous and vice versa.
If fred is funny or not humble then someone is not strong or funny and vice versa.
If someone is humble then susan is either tall or quiet and vice versa.
If someone is either not calm or not tall then paul is strong or not curious and vice versa.
If someone is both not creative and not curious then someone is not rich or patient and vice versa.
If someone is both old and not curious then alice is not generous.
Everyone who is not tall is not brave or patient.
Everyone who is not old or old is both brave and not funny and vice versa.
If someone is both not tall and old then someone is not quiet or happy.
Someone is not rich.
Someone is happy.
Susan is both not rich and happy.
Someone is kind or wise.
Alice is not curious or humble.
Paul is both quiet and not tall.
Someone is not happy or patient.
Paul is either calm or rich. | Paul is funny. | contradiction | (![X]:((~quiet(X)|~wise(X))=>(curious(X)<~>quiet(X))))&
((?[X]:((old(X)&brave(X))))<=>(?[X]:((tall(X)&brave(X)))))&
((?[X]:(kind(X)))<=>(happy(paul)))&
((?[X]:((strong(X)<~>wise(X))))=>((happy(john)|calm(john))))&
(![X]:(wise(X)=>(curious(X)|~quiet(X))))&
(![X]:((~old(X)<~>patient(X))<=>(funny(X)<~>patient(X))))&
(![X]:((humble(X)|~creative(X))<=>~kind(X)))&
((patient(fred))<=>(?[X]:((quiet(X)<~>generous(X)))))&
(((funny(fred)|~humble(fred)))<=>(?[X]:((~strong(X)|funny(X)))))&
((?[X]:(humble(X)))<=>((tall(susan)<~>quiet(susan))))&
((?[X]:((~calm(X)<~>~tall(X))))<=>((strong(paul)|~curious(paul))))&
((?[X]:((~creative(X)&~curious(X))))<=>(?[X]:((~rich(X)|patient(X)))))&
((?[X]:((old(X)&~curious(X))))=>(~generous(alice)))&
(![X]:(~tall(X)=>(~brave(X)|patient(X))))&
(![X]:((~old(X)|old(X))<=>(brave(X)&~funny(X))))&
((?[X]:((~tall(X)&old(X))))=>(?[X]:((~quiet(X)|happy(X)))))&
(?[X]:(~rich(X)))&
(?[X]:(happy(X)))&
((~rich(susan)&happy(susan)))&
(?[X]:((kind(X)|wise(X))))&
((~curious(alice)|humble(alice)))&
((quiet(paul)&~tall(paul)))&
(?[X]:((~happy(X)|patient(X))))&
((calm(paul)<~>rich(paul))) | funny(paul) | [
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3157370633582522701969268
% SZS output start Proof for 3157370633582522701969268
6. ! [X0] : ((~old(X0) <~> patient(X0)) <=> (funny(X0) <~> patient(X0))) [input p5]
15. ! [X0] : ((old(X0) | ~old(X0)) <=> (~funny(X0) & brave(X0))) [input p14]
25. funny(paul) [input hypothesis]
49. ! [X0] : ((((~patient(X0) | old(X0)) & (patient(X0) | ~old(X0))) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0)))) & (((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | ((~old(X0) | ~patient(X0)) & (patient(X0) | old(X0))))) [nnf transformation 6]
75. ! [X0] : (((old(X0) | ~old(X0)) | (funny(X0) | ~brave(X0))) & ((~funny(X0) & brave(X0)) | (~old(X0) & old(X0)))) [nnf transformation 15]
76. ! [X0] : ((old(X0) | ~old(X0) | funny(X0) | ~brave(X0)) & ((~funny(X0) & brave(X0)) | (~old(X0) & old(X0)))) [flattening 75]
105. ~patient(X0) | ~funny(X0) | ~old(X0) | ~patient(X0) [cnf transformation 49]
106. patient(X0) | ~old(X0) | patient(X0) | ~funny(X0) [cnf transformation 49]
140. ~funny(X0) | old(X0) [cnf transformation 76]
155. funny(paul) [cnf transformation 25]
157. ~patient(X0) | ~funny(X0) | ~old(X0) [duplicate literal removal 105]
158. patient(X0) | ~old(X0) | ~funny(X0) [duplicate literal removal 106]
217. ~funny(X0) | ~old(X0) [subsumption resolution 157,158]
242. 19 <=> ! [X0] : ~funny(X0) [avatar definition]
243. ~funny(X0) <- (19) [avatar component clause 242]
352. ~funny(X0) [subsumption resolution 140,217]
353. 19 [avatar split clause 352,242]
408. $false <- (19) [resolution 243,155]
409. ~19 [avatar contradiction clause 408]
410. $false [avatar sat refutation 353,409]
% SZS output end Proof for 3157370633582522701969268
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not happy then fred is not quiet and vice versa. Everyone who is either not old or not kind is both not rich and brave and vice versa. If someone is either not creative or quiet then someone is not generous and vice versa. Everyone who is either not quiet or kind is either not strong or brave. If someone is old then paul is both funny and rich. If paul is not brave then someone is not happy or old and vice versa. If someone is not tall or creative then paul is both not brave and strong and vice versa. Everyone who is patient or calm is kind or brave and vice versa. Everyone who is not curious or not tall is both generous and not strong. If someone is both not calm and humble then someone is not happy and vice versa. Everyone who is kind or not brave is not tall. Everyone who is both creative and patient is either old or not old. If someone is both not wise and not humble then someone is both strong and not generous. If mary is not patient or old then someone is brave and vice versa. If someone is both not happy and calm then susan is humble or calm and vice versa. Someone is curious or old. Someone is not wise or old. Someone is not old or not calm. Someone is either not funny or not humble. Someone is not patient or generous. Mary is either not strong or calm. Someone is kind or patient. | Susan is old. | contradiction | ((?[X]:((~creative(X)&~happy(X))))<=>(~quiet(fred)))&
(![X]:((~old(X)<~>~kind(X))<=>(~rich(X)&brave(X))))&
((?[X]:((~creative(X)<~>quiet(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~quiet(X)<~>kind(X))=>(~strong(X)<~>brave(X))))&
((?[X]:(old(X)))=>((funny(paul)&rich(paul))))&
((~brave(paul))<=>(?[X]:((~happy(X)|old(X)))))&
((?[X]:((~tall(X)|creative(X))))<=>((~brave(paul)&strong(paul))))&
(![X]:((patient(X)|calm(X))<=>(kind(X)|brave(X))))&
(![X]:((~curious(X)|~tall(X))=>(generous(X)&~strong(X))))&
((?[X]:((~calm(X)&humble(X))))<=>(?[X]:(~happy(X))))&
(![X]:((kind(X)|~brave(X))=>~tall(X)))&
(![X]:((creative(X)&patient(X))=>(old(X)<~>~old(X))))&
((?[X]:((~wise(X)&~humble(X))))=>(?[X]:((strong(X)&~generous(X)))))&
(((~patient(mary)|old(mary)))<=>(?[X]:(brave(X))))&
((?[X]:((~happy(X)&calm(X))))<=>((humble(susan)|calm(susan))))&
(?[X]:((curious(X)|old(X))))&
(?[X]:((~wise(X)|old(X))))&
(?[X]:((~old(X)|~calm(X))))&
(?[X]:((~funny(X)<~>~humble(X))))&
(?[X]:((~patient(X)|generous(X))))&
((~strong(mary)<~>calm(mary)))&
(?[X]:((kind(X)|patient(X)))) | old(susan) | [
"p5",
"p6",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5753832195119915785160850
% SZS output start Proof for 5753832195119915785160850
6. ~brave(paul) <=> ? [X0] : (old(X0) | ~happy(X0)) [input p5]
7. ? [X0] : (creative(X0) | ~tall(X0)) <=> (strong(paul) & ~brave(paul)) [input p6]
9. ! [X0] : ((~tall(X0) | ~curious(X0)) => (~strong(X0) & generous(X0))) [input p8]
11. ! [X0] : ((~brave(X0) | kind(X0)) => ~tall(X0)) [input p10]
23. old(susan) [input hypothesis]
27. ! [X0] : (~tall(X0) => (~strong(X0) & generous(X0))) [pure predicate removal 9]
31. ! [X0] : ((~strong(X0) & generous(X0)) | tall(X0)) [ennf transformation 27]
32. ! [X0] : (~tall(X0) | (brave(X0) & ~kind(X0))) [ennf transformation 11]
48. (~brave(paul) | ! [X0] : (~old(X0) & happy(X0))) & (? [X0] : (old(X0) | ~happy(X0)) | brave(paul)) [nnf transformation 6]
49. (~brave(paul) | ! [X0] : (~old(X0) & happy(X0))) & (? [X1] : (old(X1) | ~happy(X1)) | brave(paul)) [rectify 48]
50. ? [X1] : (old(X1) | ~happy(X1)) => (old(sK3) | ~happy(sK3)) [choice axiom]
51. (~brave(paul) | ! [X0] : (~old(X0) & happy(X0))) & ((old(sK3) | ~happy(sK3)) | brave(paul)) [skolemisation 49,50]
52. (? [X0] : (creative(X0) | ~tall(X0)) | (~strong(paul) | brave(paul))) & ((strong(paul) & ~brave(paul)) | ! [X0] : (~creative(X0) & tall(X0))) [nnf transformation 7]
53. (? [X0] : (creative(X0) | ~tall(X0)) | ~strong(paul) | brave(paul)) & ((strong(paul) & ~brave(paul)) | ! [X0] : (~creative(X0) & tall(X0))) [flattening 52]
54. (? [X0] : (creative(X0) | ~tall(X0)) | ~strong(paul) | brave(paul)) & ((strong(paul) & ~brave(paul)) | ! [X1] : (~creative(X1) & tall(X1))) [rectify 53]
55. ? [X0] : (creative(X0) | ~tall(X0)) => (creative(sK4) | ~tall(sK4)) [choice axiom]
56. ((creative(sK4) | ~tall(sK4)) | ~strong(paul) | brave(paul)) & ((strong(paul) & ~brave(paul)) | ! [X1] : (~creative(X1) & tall(X1))) [skolemisation 54,55]
111. ~brave(paul) | ~old(X0) [cnf transformation 51]
114. strong(paul) | tall(X1) [cnf transformation 56]
122. ~strong(X0) | tall(X0) [cnf transformation 31]
127. ~tall(X0) | brave(X0) [cnf transformation 32]
148. old(susan) [cnf transformation 23]
193. 11 <=> ! [X0] : ~old(X0) [avatar definition]
194. ~old(X0) <- (11) [avatar component clause 193]
206. 14 <=> brave(paul) [avatar definition]
208. ~brave(paul) <- (~14) [avatar component clause 206]
209. 11 | ~14 [avatar split clause 111,206,193]
224. 18 <=> strong(paul) [avatar definition]
225. strong(paul) <- (18) [avatar component clause 224]
241. 22 <=> ! [X1] : tall(X1) [avatar definition]
242. tall(X1) <- (22) [avatar component clause 241]
243. 22 | 18 [avatar split clause 114,224,241]
377. $false <- (11) [resolution 194,148]
378. ~11 [avatar contradiction clause 377]
398. tall(paul) <- (18) [resolution 225,122]
414. brave(paul) <- (18) [resolution 398,127]
416. $false <- (~14, 18) [subsumption resolution 414,208]
417. 14 | ~18 [avatar contradiction clause 416]
420. brave(X0) <- (22) [resolution 242,127]
422. $false <- (~14, 22) [resolution 420,208]
423. 14 | ~22 [avatar contradiction clause 422]
424. $false [avatar sat refutation 209,243,378,417,423]
% SZS output end Proof for 5753832195119915785160850
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or not generous is not calm. If fred is not curious then fred is wise and vice versa. Everyone who is not quiet is both not calm and generous. If john is not funny or not wise then someone is quiet and vice versa. If someone is either humble or not humble then mary is both not strong and curious. Everyone who is both tall and brave is either not calm or not rich. Everyone who is not generous is either wise or tall and vice versa. Everyone who is either not curious or curious is brave. If someone is generous or wise then someone is not creative. If fred is both calm and not quiet then john is quiet and vice versa. If john is not tall then someone is either curious or not calm and vice versa. If someone is not creative or not tall then fred is both tall and strong and vice versa. If john is happy then someone is either wise or old. Everyone who is humble or kind is not patient or not wise and vice versa. Everyone who is either not curious or humble is both curious and not kind and vice versa. Susan is either not brave or not humble. Someone is wise. Fred is not rich. Someone is either not old or old. Someone is wise or not kind. Someone is strong or not curious. | Susan is not tall. | neutral | (![X]:((~strong(X)|~generous(X))=>~calm(X)))&
((~curious(fred))<=>(wise(fred)))&
(![X]:(~quiet(X)=>(~calm(X)&generous(X))))&
(((~funny(john)|~wise(john)))<=>(?[X]:(quiet(X))))&
((?[X]:((humble(X)<~>~humble(X))))=>((~strong(mary)&curious(mary))))&
(![X]:((tall(X)&brave(X))=>(~calm(X)<~>~rich(X))))&
(![X]:(~generous(X)<=>(wise(X)<~>tall(X))))&
(![X]:((~curious(X)<~>curious(X))=>brave(X)))&
((?[X]:((generous(X)|wise(X))))=>(?[X]:(~creative(X))))&
(((calm(fred)&~quiet(fred)))<=>(quiet(john)))&
((~tall(john))<=>(?[X]:((curious(X)<~>~calm(X)))))&
((?[X]:((~creative(X)|~tall(X))))<=>((tall(fred)&strong(fred))))&
((happy(john))=>(?[X]:((wise(X)<~>old(X)))))&
(![X]:((humble(X)|kind(X))<=>(~patient(X)|~wise(X))))&
(![X]:((~curious(X)<~>humble(X))<=>(curious(X)&~kind(X))))&
((~brave(susan)<~>~humble(susan)))&
(?[X]:(wise(X)))&
(~rich(fred))&
(?[X]:((~old(X)<~>old(X))))&
(?[X]:((wise(X)|~kind(X))))&
(?[X]:((strong(X)|~curious(X)))) | ~tall(susan) | [] | null | 0 |
If fred is not curious or not generous then alice is either not patient or curious. Everyone who is rich is not brave and vice versa. If fred is not tall or not humble then someone is creative or not humble and vice versa. If someone is creative or not creative then alice is both not creative and not wise and vice versa. If susan is curious then paul is strong or not creative and vice versa. Everyone who is strong or not quiet is funny or wise. Everyone who is both curious and not kind is patient and vice versa. Everyone who is both not generous and not brave is not kind. Everyone who is both rich and not patient is both brave and happy and vice versa. Everyone who is either not strong or not patient is not quiet and vice versa. Everyone who is not brave is funny or not funny and vice versa. If fred is either not curious or quiet then someone is either not old or humble and vice versa. If paul is both not humble and not calm then someone is happy or not rich. If susan is either quiet or not kind then susan is either quiet or not funny. If someone is both not generous and not calm then someone is both rich and not kind. Someone is generous or patient. Lucy is either not creative or kind. Susan is either creative or not wise. Alice is either not brave or not funny. Someone is creative or not old. Someone is both not creative and not happy. | Lucy is not brave. | entailment | (((~curious(fred)|~generous(fred)))=>((~patient(alice)<~>curious(alice))))&
(![X]:(rich(X)<=>~brave(X)))&
(((~tall(fred)|~humble(fred)))<=>(?[X]:((creative(X)|~humble(X)))))&
((?[X]:((creative(X)|~creative(X))))<=>((~creative(alice)&~wise(alice))))&
((curious(susan))<=>((strong(paul)|~creative(paul))))&
(![X]:((strong(X)|~quiet(X))=>(funny(X)|wise(X))))&
(![X]:((curious(X)&~kind(X))<=>patient(X)))&
(![X]:((~generous(X)&~brave(X))=>~kind(X)))&
(![X]:((rich(X)&~patient(X))<=>(brave(X)&happy(X))))&
(![X]:((~strong(X)<~>~patient(X))<=>~quiet(X)))&
(![X]:(~brave(X)<=>(funny(X)|~funny(X))))&
(((~curious(fred)<~>quiet(fred)))<=>(?[X]:((~old(X)<~>humble(X)))))&
(((~humble(paul)&~calm(paul)))=>(?[X]:((happy(X)|~rich(X)))))&
(((quiet(susan)<~>~kind(susan)))=>((quiet(susan)<~>~funny(susan))))&
((?[X]:((~generous(X)&~calm(X))))=>(?[X]:((rich(X)&~kind(X)))))&
(?[X]:((generous(X)|patient(X))))&
((~creative(lucy)<~>kind(lucy)))&
((creative(susan)<~>~wise(susan)))&
((~brave(alice)<~>~funny(alice)))&
(?[X]:((creative(X)|~old(X))))&
(?[X]:((~creative(X)&~happy(X)))) | ~brave(lucy) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 126433587048358180643126
% SZS output start Proof for 126433587048358180643126
11. ! [X0] : (~brave(X0) <=> (~funny(X0) | funny(X0))) [input p10]
22. brave(lucy) [input hypothesis]
52. ! [X0] : ((~brave(X0) | (funny(X0) & ~funny(X0))) & ((~funny(X0) | funny(X0)) | brave(X0))) [nnf transformation 11]
53. ! [X0] : ((~brave(X0) | (funny(X0) & ~funny(X0))) & (~funny(X0) | funny(X0) | brave(X0))) [flattening 52]
96. ~brave(X0) | ~funny(X0) [cnf transformation 53]
97. ~brave(X0) | funny(X0) [cnf transformation 53]
119. brave(lucy) [cnf transformation 22]
194. ~brave(X0) [subsumption resolution 96,97]
265. $false [subsumption resolution 119,194]
% SZS output end Proof for 126433587048358180643126
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is brave and vice versa.
If someone is not kind or old then someone is creative.
Everyone who is both not patient and happy is not patient.
Everyone who is not curious is not calm or not humble and vice versa.
Everyone who is either quiet or happy is creative and vice versa.
Everyone who is either strong or kind is quiet or not strong.
Everyone who is either creative or brave is either not quiet or not wise.
Everyone who is either not old or patient is both generous and not brave.
If fred is both not kind and not old then paul is not calm.
If paul is both funny and not strong then mary is kind or not curious.
Everyone who is either quiet or not patient is wise and vice versa.
Everyone who is both humble and curious is not humble or not patient and vice versa.
If someone is both not curious and not old then john is not patient and vice versa.
If someone is both not wise and tall then someone is tall and vice versa.
If lucy is creative or not creative then someone is either calm or not kind and vice versa.
If susan is either not brave or quiet then alice is quiet or not old and vice versa.
John is both funny and not generous.
Alice is not curious.
Mary is either old or rich.
John is not kind or patient.
Someone is both not generous and curious.
Someone is either old or not rich. | John is quiet. | neutral | (![X]:(~funny(X)<=>brave(X)))&
((?[X]:((~kind(X)|old(X))))=>(?[X]:(creative(X))))&
(![X]:((~patient(X)&happy(X))=>~patient(X)))&
(![X]:(~curious(X)<=>(~calm(X)|~humble(X))))&
(![X]:((quiet(X)<~>happy(X))<=>creative(X)))&
(![X]:((strong(X)<~>kind(X))=>(quiet(X)|~strong(X))))&
(![X]:((creative(X)<~>brave(X))=>(~quiet(X)<~>~wise(X))))&
(![X]:((~old(X)<~>patient(X))=>(generous(X)&~brave(X))))&
(((~kind(fred)&~old(fred)))=>(~calm(paul)))&
(((funny(paul)&~strong(paul)))=>((kind(mary)|~curious(mary))))&
(![X]:((quiet(X)<~>~patient(X))<=>wise(X)))&
(![X]:((humble(X)&curious(X))<=>(~humble(X)|~patient(X))))&
((?[X]:((~curious(X)&~old(X))))<=>(~patient(john)))&
((?[X]:((~wise(X)&tall(X))))<=>(?[X]:(tall(X))))&
(((creative(lucy)|~creative(lucy)))<=>(?[X]:((calm(X)<~>~kind(X)))))&
(((~brave(susan)<~>quiet(susan)))<=>((quiet(alice)|~old(alice))))&
((funny(john)&~generous(john)))&
(~curious(alice))&
((old(mary)<~>rich(mary)))&
((~kind(john)|patient(john)))&
(?[X]:((~generous(X)&curious(X))))&
(?[X]:((old(X)<~>~rich(X)))) | quiet(john) | [] | null | 0 |
Everyone who is both not curious and happy is either strong or not rich and vice versa.
Everyone who is not rich or humble is both curious and humble.
If paul is either humble or not funny then someone is both calm and quiet and vice versa.
Everyone who is both curious and not curious is either rich or not wise and vice versa.
Everyone who is not wise or not funny is either creative or not patient and vice versa.
Everyone who is both not calm and not brave is humble or kind and vice versa.
Everyone who is kind or calm is not calm or not creative.
Everyone who is both not funny and not rich is both calm and not old and vice versa.
Everyone who is either not generous or not brave is both humble and happy and vice versa.
Everyone who is not old or rich is curious.
If someone is either humble or not curious then lucy is both not humble and creative.
If alice is not funny or not wise then alice is strong or old and vice versa.
Everyone who is not old is either not brave or not generous and vice versa.
If someone is not rich then mary is not curious or creative.
Everyone who is not brave or brave is not humble or happy and vice versa.
Someone is either humble or not quiet.
Lucy is either old or generous.
Paul is both generous and not quiet.
Someone is not curious or brave.
Mary is either rich or not patient.
Mary is not funny. | Paul is not happy. | neutral | (![X]:((~curious(X)&happy(X))<=>(strong(X)<~>~rich(X))))&
(![X]:((~rich(X)|humble(X))=>(curious(X)&humble(X))))&
(((humble(paul)<~>~funny(paul)))<=>(?[X]:((calm(X)&quiet(X)))))&
(![X]:((curious(X)&~curious(X))<=>(rich(X)<~>~wise(X))))&
(![X]:((~wise(X)|~funny(X))<=>(creative(X)<~>~patient(X))))&
(![X]:((~calm(X)&~brave(X))<=>(humble(X)|kind(X))))&
(![X]:((kind(X)|calm(X))=>(~calm(X)|~creative(X))))&
(![X]:((~funny(X)&~rich(X))<=>(calm(X)&~old(X))))&
(![X]:((~generous(X)<~>~brave(X))<=>(humble(X)&happy(X))))&
(![X]:((~old(X)|rich(X))=>curious(X)))&
((?[X]:((humble(X)<~>~curious(X))))=>((~humble(lucy)&creative(lucy))))&
(((~funny(alice)|~wise(alice)))<=>((strong(alice)|old(alice))))&
(![X]:(~old(X)<=>(~brave(X)<~>~generous(X))))&
((?[X]:(~rich(X)))=>((~curious(mary)|creative(mary))))&
(![X]:((~brave(X)|brave(X))<=>(~humble(X)|happy(X))))&
(?[X]:((humble(X)<~>~quiet(X))))&
((old(lucy)<~>generous(lucy)))&
((generous(paul)&~quiet(paul)))&
(?[X]:((~curious(X)|brave(X))))&
((rich(mary)<~>~patient(mary)))&
(~funny(mary)) | ~happy(paul) | [] | null | 0 |
If mary is happy or not old then fred is either not quiet or kind and vice versa. Everyone who is wise is not generous or not quiet. If someone is either not creative or not quiet then fred is either funny or quiet. If someone is quiet or not kind then paul is not rich or not creative and vice versa. If susan is not funny or brave then someone is tall or quiet and vice versa. If john is either funny or calm then someone is both kind and not funny. If alice is either rich or calm then someone is both not humble and patient. If someone is both patient and strong then paul is not tall or not wise and vice versa. Everyone who is either not old or not humble is not old and vice versa. Everyone who is both patient and not patient is either not curious or not quiet. Everyone who is not creative is both not kind and rich. Everyone who is old is either not creative or not strong. Everyone who is patient or curious is not rich and vice versa. If someone is not humble then someone is not patient or not wise and vice versa. If susan is not brave then john is calm or patient. If alice is either not patient or tall then susan is both not old and not brave. Fred is either not calm or creative. Fred is both humble and strong. John is not calm or patient. John is calm or old. Mary is either not patient or not tall. | Fred is not old. | entailment | (((happy(mary)|~old(mary)))<=>((~quiet(fred)<~>kind(fred))))&
(![X]:(wise(X)=>(~generous(X)|~quiet(X))))&
((?[X]:((~creative(X)<~>~quiet(X))))=>((funny(fred)<~>quiet(fred))))&
((?[X]:((quiet(X)|~kind(X))))<=>((~rich(paul)|~creative(paul))))&
(((~funny(susan)|brave(susan)))<=>(?[X]:((tall(X)|quiet(X)))))&
(((funny(john)<~>calm(john)))=>(?[X]:((kind(X)&~funny(X)))))&
(((rich(alice)<~>calm(alice)))=>(?[X]:((~humble(X)&patient(X)))))&
((?[X]:((patient(X)&strong(X))))<=>((~tall(paul)|~wise(paul))))&
(![X]:((~old(X)<~>~humble(X))<=>~old(X)))&
(![X]:((patient(X)&~patient(X))=>(~curious(X)<~>~quiet(X))))&
(![X]:(~creative(X)=>(~kind(X)&rich(X))))&
(![X]:(old(X)=>(~creative(X)<~>~strong(X))))&
(![X]:((patient(X)|curious(X))<=>~rich(X)))&
((?[X]:(~humble(X)))<=>(?[X]:((~patient(X)|~wise(X)))))&
((~brave(susan))=>((calm(john)|patient(john))))&
(((~patient(alice)<~>tall(alice)))=>((~old(susan)&~brave(susan))))&
((~calm(fred)<~>creative(fred)))&
((humble(fred)&strong(fred)))&
((~calm(john)|patient(john)))&
((calm(john)|old(john)))&
((~patient(mary)<~>~tall(mary))) | ~old(fred) | [
"p8",
"p10",
"p11",
"p12",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 640996754957967609283440
% SZS output start Proof for 640996754957967609283440
9. ! [X0] : ((~old(X0) <~> ~humble(X0)) <=> ~old(X0)) [input p8]
11. ! [X0] : (~creative(X0) => (rich(X0) & ~kind(X0))) [input p10]
12. ! [X0] : (old(X0) => (~creative(X0) <~> ~strong(X0))) [input p11]
13. ! [X0] : ((curious(X0) | patient(X0)) <=> ~rich(X0)) [input p12]
14. ? [X0] : ~humble(X0) <=> ? [X0] : (~wise(X0) | ~patient(X0)) [input p13]
18. strong(fred) & humble(fred) [input p17]
22. old(fred) [input hypothesis]
23. ? [X0] : ~humble(X0) <=> ? [X1] : (~wise(X1) | ~patient(X1)) [rectify 14]
30. ! [X0] : ((rich(X0) & ~kind(X0)) | creative(X0)) [ennf transformation 11]
31. ! [X0] : ((~creative(X0) <~> ~strong(X0)) | ~old(X0)) [ennf transformation 12]
59. ! [X0] : ((((humble(X0) | old(X0)) & (~humble(X0) | ~old(X0))) | old(X0)) & (~old(X0) | ((~old(X0) | humble(X0)) & (~humble(X0) | old(X0))))) [nnf transformation 9]
61. ! [X0] : (((strong(X0) | creative(X0)) & (~strong(X0) | ~creative(X0))) | ~old(X0)) [nnf transformation 31]
62. ! [X0] : (((curious(X0) | patient(X0)) | rich(X0)) & (~rich(X0) | (~curious(X0) & ~patient(X0)))) [nnf transformation 13]
63. ! [X0] : ((curious(X0) | patient(X0) | rich(X0)) & (~rich(X0) | (~curious(X0) & ~patient(X0)))) [flattening 62]
64. (? [X0] : ~humble(X0) | ! [X1] : (wise(X1) & patient(X1))) & (? [X1] : (~wise(X1) | ~patient(X1)) | ! [X0] : humble(X0)) [nnf transformation 23]
65. (? [X0] : ~humble(X0) | ! [X1] : (wise(X1) & patient(X1))) & (? [X2] : (~wise(X2) | ~patient(X2)) | ! [X3] : humble(X3)) [rectify 64]
66. ? [X0] : ~humble(X0) => ~humble(sK5) [choice axiom]
67. ? [X2] : (~wise(X2) | ~patient(X2)) => (~wise(sK6) | ~patient(sK6)) [choice axiom]
68. (~humble(sK5) | ! [X1] : (wise(X1) & patient(X1))) & ((~wise(sK6) | ~patient(sK6)) | ! [X3] : humble(X3)) [skolemisation 65,67,66]
104. ~old(X0) | ~old(X0) | humble(X0) [cnf transformation 59]
106. humble(X0) | old(X0) | old(X0) [cnf transformation 59]
110. rich(X0) | creative(X0) [cnf transformation 30]
111. ~strong(X0) | ~creative(X0) | ~old(X0) [cnf transformation 61]
113. ~patient(X0) | ~rich(X0) [cnf transformation 63]
117. ~humble(sK5) | patient(X1) [cnf transformation 68]
127. strong(fred) [cnf transformation 18]
132. old(fred) [cnf transformation 22]
133. ~old(X0) | humble(X0) [duplicate literal removal 104]
134. humble(X0) | old(X0) [duplicate literal removal 106]
284. humble(X0) [subsumption resolution 133,134]
286. patient(X1) [subsumption resolution 117,284]
325. ~rich(X0) [resolution 113,286]
326. creative(X0) [resolution 325,110]
331. ~creative(fred) | ~old(fred) [resolution 111,127]
333. ~old(fred) [subsumption resolution 331,326]
334. $false [subsumption resolution 333,132]
% SZS output end Proof for 640996754957967609283440
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is happy then fred is both old and rich and vice versa.
Everyone who is not quiet is not kind or not calm.
If someone is quiet then someone is not happy or calm and vice versa.
Everyone who is generous is strong and vice versa.
Everyone who is generous is not strong.
Everyone who is not creative is not wise or not quiet and vice versa.
Everyone who is both creative and wise is not generous and vice versa.
If someone is not strong or not curious then mary is funny and vice versa.
If someone is happy then john is both humble and kind.
If someone is humble then paul is either patient or not humble and vice versa.
Everyone who is patient or not brave is not old or not kind.
Everyone who is both not tall and not quiet is happy.
Everyone who is both wise and not brave is old and vice versa.
Everyone who is either kind or patient is creative or not happy and vice versa.
Everyone who is either strong or not generous is not curious or funny and vice versa.
Everyone who is not brave or not calm is either not old or generous.
Someone is quiet or not humble.
Mary is creative.
Alice is quiet or tall.
John is both creative and tall.
Alice is not happy.
Alice is either not happy or not wise.
Lucy is patient. | Lucy is tall. | neutral | ((happy(paul))<=>((old(fred)&rich(fred))))&
(![X]:(~quiet(X)=>(~kind(X)|~calm(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((~happy(X)|calm(X)))))&
(![X]:(generous(X)<=>strong(X)))&
(![X]:(generous(X)=>~strong(X)))&
(![X]:(~creative(X)<=>(~wise(X)|~quiet(X))))&
(![X]:((creative(X)&wise(X))<=>~generous(X)))&
((?[X]:((~strong(X)|~curious(X))))<=>(funny(mary)))&
((?[X]:(happy(X)))=>((humble(john)&kind(john))))&
((?[X]:(humble(X)))<=>((patient(paul)<~>~humble(paul))))&
(![X]:((patient(X)|~brave(X))=>(~old(X)|~kind(X))))&
(![X]:((~tall(X)&~quiet(X))=>happy(X)))&
(![X]:((wise(X)&~brave(X))<=>old(X)))&
(![X]:((kind(X)<~>patient(X))<=>(creative(X)|~happy(X))))&
(![X]:((strong(X)<~>~generous(X))<=>(~curious(X)|funny(X))))&
(![X]:((~brave(X)|~calm(X))=>(~old(X)<~>generous(X))))&
(?[X]:((quiet(X)|~humble(X))))&
(creative(mary))&
((quiet(alice)|tall(alice)))&
((creative(john)&tall(john)))&
(~happy(alice))&
((~happy(alice)<~>~wise(alice)))&
(patient(lucy)) | tall(lucy) | [] | null | 0 |
Everyone who is not creative or happy is either not humble or not funny and vice versa. Everyone who is both creative and not curious is both not tall and not humble. Everyone who is both creative and not creative is generous and vice versa. If someone is tall then mary is happy. If someone is not patient then someone is calm or rich. If mary is either humble or tall then someone is old or not brave. Everyone who is patient is either not creative or wise and vice versa. Everyone who is not patient or creative is both not old and not strong and vice versa. If someone is both not humble and not patient then susan is either strong or not strong and vice versa. If lucy is not humble then susan is both calm and happy and vice versa. Everyone who is not patient is not rich or tall and vice versa. If someone is not funny or not calm then susan is rich or happy and vice versa. Everyone who is either not creative or funny is not generous. Everyone who is either not creative or brave is either curious or old. Everyone who is both curious and not quiet is both not rich and not humble. If alice is either happy or not curious then someone is either not brave or humble. Someone is both not humble and not tall. Susan is old. Someone is not kind or not tall. Fred is not humble or quiet. Someone is either generous or funny. Mary is both not kind and strong. Someone is humble. John is patient or not rich. | Mary is tall. | contradiction | (![X]:((~creative(X)|happy(X))<=>(~humble(X)<~>~funny(X))))&
(![X]:((creative(X)&~curious(X))=>(~tall(X)&~humble(X))))&
(![X]:((creative(X)&~creative(X))<=>generous(X)))&
((?[X]:(tall(X)))=>(happy(mary)))&
((?[X]:(~patient(X)))=>(?[X]:((calm(X)|rich(X)))))&
(((humble(mary)<~>tall(mary)))=>(?[X]:((old(X)|~brave(X)))))&
(![X]:(patient(X)<=>(~creative(X)<~>wise(X))))&
(![X]:((~patient(X)|creative(X))<=>(~old(X)&~strong(X))))&
((?[X]:((~humble(X)&~patient(X))))<=>((strong(susan)<~>~strong(susan))))&
((~humble(lucy))<=>((calm(susan)&happy(susan))))&
(![X]:(~patient(X)<=>(~rich(X)|tall(X))))&
((?[X]:((~funny(X)|~calm(X))))<=>((rich(susan)|happy(susan))))&
(![X]:((~creative(X)<~>funny(X))=>~generous(X)))&
(![X]:((~creative(X)<~>brave(X))=>(curious(X)<~>old(X))))&
(![X]:((curious(X)&~quiet(X))=>(~rich(X)&~humble(X))))&
(((happy(alice)<~>~curious(alice)))=>(?[X]:((~brave(X)<~>humble(X)))))&
(?[X]:((~humble(X)&~tall(X))))&
(old(susan))&
(?[X]:((~kind(X)|~tall(X))))&
((~humble(fred)|quiet(fred)))&
(?[X]:((generous(X)<~>funny(X))))&
((~kind(mary)&strong(mary)))&
(?[X]:(humble(X)))&
((patient(john)|~rich(john))) | tall(mary) | [
"p7",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 654938223774897071074496
% SZS output start Proof for 654938223774897071074496
8. ! [X0] : ((creative(X0) | ~patient(X0)) <=> (~strong(X0) & ~old(X0))) [input p7]
11. ! [X0] : (~patient(X0) <=> (tall(X0) | ~rich(X0))) [input p10]
22. strong(mary) & ~kind(mary) [input p21]
25. tall(mary) [input hypothesis]
28. strong(mary) [pure predicate removal 22]
50. ! [X0] : (((creative(X0) | ~patient(X0)) | (strong(X0) | old(X0))) & ((~strong(X0) & ~old(X0)) | (~creative(X0) & patient(X0)))) [nnf transformation 8]
51. ! [X0] : ((creative(X0) | ~patient(X0) | strong(X0) | old(X0)) & ((~strong(X0) & ~old(X0)) | (~creative(X0) & patient(X0)))) [flattening 50]
58. ! [X0] : ((~patient(X0) | (~tall(X0) & rich(X0))) & ((tall(X0) | ~rich(X0)) | patient(X0))) [nnf transformation 11]
59. ! [X0] : ((~patient(X0) | (~tall(X0) & rich(X0))) & (tall(X0) | ~rich(X0) | patient(X0))) [flattening 58]
98. ~strong(X0) | patient(X0) [cnf transformation 51]
112. ~patient(X0) | ~tall(X0) [cnf transformation 59]
132. strong(mary) [cnf transformation 28]
135. tall(mary) [cnf transformation 25]
162. 6 <=> tall(mary) [avatar definition]
163. tall(mary) <- (6) [avatar component clause 162]
264. 6 [avatar split clause 135,162]
269. patient(mary) [resolution 98,132]
275. ~tall(mary) [resolution 112,269]
276. $false <- (6) [subsumption resolution 275,163]
277. ~6 [avatar contradiction clause 276]
278. $false [avatar sat refutation 264,277]
% SZS output end Proof for 654938223774897071074496
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or old then someone is creative. Everyone who is not brave is curious or not brave. If someone is creative or brave then alice is both tall and not funny. Everyone who is both brave and old is either not humble or not happy and vice versa. Everyone who is not old is both tall and kind and vice versa. Everyone who is both not calm and creative is either kind or not old and vice versa. Everyone who is either wise or generous is patient. Everyone who is humble or calm is both calm and not quiet. If mary is tall then someone is not tall or not brave and vice versa. If someone is both calm and not old then paul is strong and vice versa. Everyone who is both calm and not old is not curious. If someone is wise then someone is both not calm and not brave and vice versa. Everyone who is generous or rich is calm and vice versa. Everyone who is both not calm and happy is not quiet or happy and vice versa. If lucy is either not quiet or old then john is either not creative or not old and vice versa. Everyone who is both not strong and kind is not patient. Someone is not generous or patient. Mary is both not rich and not quiet. Someone is creative or not tall. Someone is either happy or generous. Someone is both not funny and wise. Lucy is not funny or not kind. Someone is either not tall or patient. | Mary is not generous. | entailment | (((happy(john)|old(john)))=>(?[X]:(creative(X))))&
(![X]:(~brave(X)=>(curious(X)|~brave(X))))&
((?[X]:((creative(X)|brave(X))))=>((tall(alice)&~funny(alice))))&
(![X]:((brave(X)&old(X))<=>(~humble(X)<~>~happy(X))))&
(![X]:(~old(X)<=>(tall(X)&kind(X))))&
(![X]:((~calm(X)&creative(X))<=>(kind(X)<~>~old(X))))&
(![X]:((wise(X)<~>generous(X))=>patient(X)))&
(![X]:((humble(X)|calm(X))=>(calm(X)&~quiet(X))))&
((tall(mary))<=>(?[X]:((~tall(X)|~brave(X)))))&
((?[X]:((calm(X)&~old(X))))<=>(strong(paul)))&
(![X]:((calm(X)&~old(X))=>~curious(X)))&
((?[X]:(wise(X)))<=>(?[X]:((~calm(X)&~brave(X)))))&
(![X]:((generous(X)|rich(X))<=>calm(X)))&
(![X]:((~calm(X)&happy(X))<=>(~quiet(X)|happy(X))))&
(((~quiet(lucy)<~>old(lucy)))<=>((~creative(john)<~>~old(john))))&
(![X]:((~strong(X)&kind(X))=>~patient(X)))&
(?[X]:((~generous(X)|patient(X))))&
((~rich(mary)&~quiet(mary)))&
(?[X]:((creative(X)|~tall(X))))&
(?[X]:((happy(X)<~>generous(X))))&
(?[X]:((~funny(X)&wise(X))))&
((~funny(lucy)|~kind(lucy)))&
(?[X]:((~tall(X)<~>patient(X)))) | ~generous(mary) | [
"p7",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 323883632494835119889504
% SZS output start Proof for 323883632494835119889504
8. ! [X0] : ((calm(X0) | humble(X0)) => (~quiet(X0) & calm(X0))) [input p7]
13. ! [X0] : ((rich(X0) | generous(X0)) <=> calm(X0)) [input p12]
14. ! [X0] : ((happy(X0) & ~calm(X0)) <=> (happy(X0) | ~quiet(X0))) [input p13]
24. generous(mary) [input hypothesis]
34. ! [X0] : ((~quiet(X0) & calm(X0)) | (~calm(X0) & ~humble(X0))) [ennf transformation 8]
61. ! [X0] : (((rich(X0) | generous(X0)) | ~calm(X0)) & (calm(X0) | (~rich(X0) & ~generous(X0)))) [nnf transformation 13]
62. ! [X0] : ((rich(X0) | generous(X0) | ~calm(X0)) & (calm(X0) | (~rich(X0) & ~generous(X0)))) [flattening 61]
63. ! [X0] : (((happy(X0) & ~calm(X0)) | (~happy(X0) & quiet(X0))) & ((happy(X0) | ~quiet(X0)) | (~happy(X0) | calm(X0)))) [nnf transformation 14]
64. ! [X0] : (((happy(X0) & ~calm(X0)) | (~happy(X0) & quiet(X0))) & (happy(X0) | ~quiet(X0) | ~happy(X0) | calm(X0))) [flattening 63]
103. ~quiet(X0) | ~calm(X0) [cnf transformation 34]
114. ~generous(X0) | calm(X0) [cnf transformation 62]
118. ~calm(X0) | quiet(X0) [cnf transformation 64]
140. generous(mary) [cnf transformation 24]
229. ~calm(X0) [subsumption resolution 118,103]
299. calm(mary) [resolution 114,140]
300. $false [subsumption resolution 299,229]
% SZS output end Proof for 323883632494835119889504
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either creative or quiet is old or strong and vice versa. If someone is either not rich or not curious then someone is either tall or not happy and vice versa. Everyone who is not generous or not rich is strong or not old and vice versa. If someone is not happy or not creative then fred is creative or happy and vice versa. If lucy is not generous then someone is either old or quiet and vice versa. Everyone who is creative or not funny is kind. Everyone who is both quiet and not creative is both calm and not kind and vice versa. Everyone who is not curious is either quiet or rich and vice versa. If someone is either brave or not calm then someone is either humble or not old. If someone is either not humble or brave then mary is kind or not humble. Everyone who is either not tall or not generous is tall and vice versa. If someone is quiet or wise then alice is not wise and vice versa. Everyone who is brave or curious is both rich and kind and vice versa. Everyone who is not generous is either not humble or not old. Everyone who is not happy is quiet and vice versa. Everyone who is not calm is both humble and kind and vice versa. Someone is curious or funny. John is both not generous and not wise. Someone is funny or not rich. Mary is brave. Someone is both old and not wise. Someone is either wise or not creative. | Lucy is wise. | neutral | (![X]:((creative(X)<~>quiet(X))<=>(old(X)|strong(X))))&
((?[X]:((~rich(X)<~>~curious(X))))<=>(?[X]:((tall(X)<~>~happy(X)))))&
(![X]:((~generous(X)|~rich(X))<=>(strong(X)|~old(X))))&
((?[X]:((~happy(X)|~creative(X))))<=>((creative(fred)|happy(fred))))&
((~generous(lucy))<=>(?[X]:((old(X)<~>quiet(X)))))&
(![X]:((creative(X)|~funny(X))=>kind(X)))&
(![X]:((quiet(X)&~creative(X))<=>(calm(X)&~kind(X))))&
(![X]:(~curious(X)<=>(quiet(X)<~>rich(X))))&
((?[X]:((brave(X)<~>~calm(X))))=>(?[X]:((humble(X)<~>~old(X)))))&
((?[X]:((~humble(X)<~>brave(X))))=>((kind(mary)|~humble(mary))))&
(![X]:((~tall(X)<~>~generous(X))<=>tall(X)))&
((?[X]:((quiet(X)|wise(X))))<=>(~wise(alice)))&
(![X]:((brave(X)|curious(X))<=>(rich(X)&kind(X))))&
(![X]:(~generous(X)=>(~humble(X)<~>~old(X))))&
(![X]:(~happy(X)<=>quiet(X)))&
(![X]:(~calm(X)<=>(humble(X)&kind(X))))&
(?[X]:((curious(X)|funny(X))))&
((~generous(john)&~wise(john)))&
(?[X]:((funny(X)|~rich(X))))&
(brave(mary))&
(?[X]:((old(X)&~wise(X))))&
(?[X]:((wise(X)<~>~creative(X)))) | wise(lucy) | [] | null | 0 |
Everyone who is either not rich or brave is either quiet or old.
If paul is not rich then fred is not brave or not creative and vice versa.
Everyone who is both humble and brave is quiet and vice versa.
Everyone who is calm or not tall is not strong.
Everyone who is not happy is wise or old.
If someone is either curious or old then someone is both calm and not rich.
Everyone who is either not calm or not rich is both not strong and not old and vice versa.
Everyone who is not old or not quiet is either not humble or patient and vice versa.
Everyone who is either happy or calm is either not happy or not kind.
Everyone who is curious is tall or not wise and vice versa.
Everyone who is either not happy or strong is either wise or strong and vice versa.
If mary is both calm and old then alice is either curious or humble.
If lucy is creative or brave then someone is either patient or not curious and vice versa.
Everyone who is not strong or not curious is both patient and not patient.
If alice is generous or old then mary is not happy.
Mary is not calm.
Susan is both not patient and curious.
Someone is either not old or not rich.
Someone is both not rich and strong.
Lucy is either not quiet or happy. | Alice is not happy. | neutral | (![X]:((~rich(X)<~>brave(X))=>(quiet(X)<~>old(X))))&
((~rich(paul))<=>((~brave(fred)|~creative(fred))))&
(![X]:((humble(X)&brave(X))<=>quiet(X)))&
(![X]:((calm(X)|~tall(X))=>~strong(X)))&
(![X]:(~happy(X)=>(wise(X)|old(X))))&
((?[X]:((curious(X)<~>old(X))))=>(?[X]:((calm(X)&~rich(X)))))&
(![X]:((~calm(X)<~>~rich(X))<=>(~strong(X)&~old(X))))&
(![X]:((~old(X)|~quiet(X))<=>(~humble(X)<~>patient(X))))&
(![X]:((happy(X)<~>calm(X))=>(~happy(X)<~>~kind(X))))&
(![X]:(curious(X)<=>(tall(X)|~wise(X))))&
(![X]:((~happy(X)<~>strong(X))<=>(wise(X)<~>strong(X))))&
(((calm(mary)&old(mary)))=>((curious(alice)<~>humble(alice))))&
(((creative(lucy)|brave(lucy)))<=>(?[X]:((patient(X)<~>~curious(X)))))&
(![X]:((~strong(X)|~curious(X))=>(patient(X)&~patient(X))))&
(((generous(alice)|old(alice)))=>(~happy(mary)))&
(~calm(mary))&
((~patient(susan)&curious(susan)))&
(?[X]:((~old(X)<~>~rich(X))))&
(?[X]:((~rich(X)&strong(X))))&
((~quiet(lucy)<~>happy(lucy))) | ~happy(alice) | [] | null | 0 |
If john is not tall then fred is both not rich and not humble and vice versa. Everyone who is patient or not quiet is both not strong and rich. If mary is not creative then someone is not wise or not old and vice versa. If someone is both not brave and not happy then someone is both generous and not tall. Everyone who is tall or not tall is either patient or not brave. Everyone who is both strong and happy is both not creative and not rich and vice versa. If alice is happy then mary is both patient and not creative. If lucy is funny then paul is both not old and not rich and vice versa. Everyone who is both not kind and happy is calm and vice versa. Everyone who is not tall or humble is both wise and brave and vice versa. Everyone who is either kind or calm is not kind and vice versa. Everyone who is not generous is both creative and humble and vice versa. If someone is both not generous and humble then someone is tall or not strong and vice versa. If someone is not funny or not tall then someone is patient and vice versa. If paul is curious then fred is both not rich and not calm and vice versa. Everyone who is either old or strong is not tall or wise. Someone is both tall and old. Susan is not quiet. Someone is either kind or not humble. Someone is curious or not tall. Someone is funny or wise. Someone is both not strong and calm. Susan is both curious and not wise. Someone is curious. | Lucy is rich. | neutral | ((~tall(john))<=>((~rich(fred)&~humble(fred))))&
(![X]:((patient(X)|~quiet(X))=>(~strong(X)&rich(X))))&
((~creative(mary))<=>(?[X]:((~wise(X)|~old(X)))))&
((?[X]:((~brave(X)&~happy(X))))=>(?[X]:((generous(X)&~tall(X)))))&
(![X]:((tall(X)|~tall(X))=>(patient(X)<~>~brave(X))))&
(![X]:((strong(X)&happy(X))<=>(~creative(X)&~rich(X))))&
((happy(alice))=>((patient(mary)&~creative(mary))))&
((funny(lucy))<=>((~old(paul)&~rich(paul))))&
(![X]:((~kind(X)&happy(X))<=>calm(X)))&
(![X]:((~tall(X)|humble(X))<=>(wise(X)&brave(X))))&
(![X]:((kind(X)<~>calm(X))<=>~kind(X)))&
(![X]:(~generous(X)<=>(creative(X)&humble(X))))&
((?[X]:((~generous(X)&humble(X))))<=>(?[X]:((tall(X)|~strong(X)))))&
((?[X]:((~funny(X)|~tall(X))))<=>(?[X]:(patient(X))))&
((curious(paul))<=>((~rich(fred)&~calm(fred))))&
(![X]:((old(X)<~>strong(X))=>(~tall(X)|wise(X))))&
(?[X]:((tall(X)&old(X))))&
(~quiet(susan))&
(?[X]:((kind(X)<~>~humble(X))))&
(?[X]:((curious(X)|~tall(X))))&
(?[X]:((funny(X)|wise(X))))&
(?[X]:((~strong(X)&calm(X))))&
((curious(susan)&~wise(susan)))&
(?[X]:(curious(X))) | rich(lucy) | [] | null | 0 |
Everyone who is either not curious or funny is both old and not creative. Everyone who is old or humble is creative. If someone is not curious then mary is either creative or not funny and vice versa. Everyone who is rich or old is both curious and not quiet and vice versa. If someone is both old and patient then alice is kind or curious and vice versa. Everyone who is not strong or not happy is both not happy and kind. Everyone who is not kind or generous is calm and vice versa. If john is both not quiet and tall then someone is tall or humble and vice versa. Everyone who is curious or quiet is both funny and rich. Everyone who is not patient is both not old and funny and vice versa. If john is humble then alice is either not rich or not quiet. If john is both creative and funny then susan is either not quiet or brave and vice versa. If mary is kind then paul is creative or curious and vice versa. Everyone who is both not generous and not kind is both not happy and not creative. If fred is both old and not humble then someone is either old or not tall and vice versa. Someone is not quiet or patient. John is creative. Someone is either not kind or tall. Alice is not humble. Someone is not humble or humble. Someone is not brave. | Alice is quiet. | contradiction | (![X]:((~curious(X)<~>funny(X))=>(old(X)&~creative(X))))&
(![X]:((old(X)|humble(X))=>creative(X)))&
((?[X]:(~curious(X)))<=>((creative(mary)<~>~funny(mary))))&
(![X]:((rich(X)|old(X))<=>(curious(X)&~quiet(X))))&
((?[X]:((old(X)&patient(X))))<=>((kind(alice)|curious(alice))))&
(![X]:((~strong(X)|~happy(X))=>(~happy(X)&kind(X))))&
(![X]:((~kind(X)|generous(X))<=>calm(X)))&
(((~quiet(john)&tall(john)))<=>(?[X]:((tall(X)|humble(X)))))&
(![X]:((curious(X)|quiet(X))=>(funny(X)&rich(X))))&
(![X]:(~patient(X)<=>(~old(X)&funny(X))))&
((humble(john))=>((~rich(alice)<~>~quiet(alice))))&
(((creative(john)&funny(john)))<=>((~quiet(susan)<~>brave(susan))))&
((kind(mary))<=>((creative(paul)|curious(paul))))&
(![X]:((~generous(X)&~kind(X))=>(~happy(X)&~creative(X))))&
(((old(fred)&~humble(fred)))<=>(?[X]:((old(X)<~>~tall(X)))))&
(?[X]:((~quiet(X)|patient(X))))&
(creative(john))&
(?[X]:((~kind(X)<~>tall(X))))&
(~humble(alice))&
(?[X]:((~humble(X)|humble(X))))&
(?[X]:(~brave(X))) | quiet(alice) | [
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5986560642264803749540573
% SZS output start Proof for 5986560642264803749540573
4. ! [X0] : ((old(X0) | rich(X0)) <=> (~quiet(X0) & curious(X0))) [input p3]
9. ! [X0] : ((quiet(X0) | curious(X0)) => (rich(X0) & funny(X0))) [input p8]
22. quiet(alice) [input hypothesis]
28. ! [X0] : ((rich(X0) & funny(X0)) | (~quiet(X0) & ~curious(X0))) [ennf transformation 9]
35. ! [X0] : (((old(X0) | rich(X0)) | (quiet(X0) | ~curious(X0))) & ((~quiet(X0) & curious(X0)) | (~old(X0) & ~rich(X0)))) [nnf transformation 4]
36. ! [X0] : ((old(X0) | rich(X0) | quiet(X0) | ~curious(X0)) & ((~quiet(X0) & curious(X0)) | (~old(X0) & ~rich(X0)))) [flattening 35]
80. ~quiet(X0) | ~rich(X0) [cnf transformation 36]
98. rich(X0) | ~quiet(X0) [cnf transformation 28]
126. quiet(alice) [cnf transformation 22]
197. ~quiet(X0) [subsumption resolution 98,80]
280. $false [subsumption resolution 126,197]
% SZS output end Proof for 5986560642264803749540573
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and wise is quiet or happy and vice versa.
If someone is kind then someone is not brave.
If john is not happy or tall then someone is not calm or not kind and vice versa.
If someone is either generous or not rich then lucy is both not creative and not patient and vice versa.
Everyone who is both strong and funny is either not funny or not strong and vice versa.
Everyone who is not humble is not happy.
If susan is both brave and rich then someone is happy and vice versa.
Everyone who is not patient is not strong.
If alice is both old and kind then someone is wise or not quiet.
Everyone who is old or not brave is happy.
Everyone who is both funny and not humble is not strong or not brave.
If someone is both brave and not brave then someone is either not wise or old and vice versa.
Everyone who is wise is both calm and brave and vice versa.
Everyone who is funny or brave is not happy and vice versa.
Everyone who is either not curious or not creative is either not calm or old.
Everyone who is either not creative or not generous is calm or not kind.
Fred is calm or quiet.
Someone is either wise or happy.
John is not kind.
Someone is either not wise or not patient.
Someone is calm or not curious. | Lucy is kind. | contradiction | (![X]:((~patient(X)&wise(X))<=>(quiet(X)|happy(X))))&
((?[X]:(kind(X)))=>(?[X]:(~brave(X))))&
(((~happy(john)|tall(john)))<=>(?[X]:((~calm(X)|~kind(X)))))&
((?[X]:((generous(X)<~>~rich(X))))<=>((~creative(lucy)&~patient(lucy))))&
(![X]:((strong(X)&funny(X))<=>(~funny(X)<~>~strong(X))))&
(![X]:(~humble(X)=>~happy(X)))&
(((brave(susan)&rich(susan)))<=>(?[X]:(happy(X))))&
(![X]:(~patient(X)=>~strong(X)))&
(((old(alice)&kind(alice)))=>(?[X]:((wise(X)|~quiet(X)))))&
(![X]:((old(X)|~brave(X))=>happy(X)))&
(![X]:((funny(X)&~humble(X))=>(~strong(X)|~brave(X))))&
((?[X]:((brave(X)&~brave(X))))<=>(?[X]:((~wise(X)<~>old(X)))))&
(![X]:(wise(X)<=>(calm(X)&brave(X))))&
(![X]:((funny(X)|brave(X))<=>~happy(X)))&
(![X]:((~curious(X)<~>~creative(X))=>(~calm(X)<~>old(X))))&
(![X]:((~creative(X)<~>~generous(X))=>(calm(X)|~kind(X))))&
((calm(fred)|quiet(fred)))&
(?[X]:((wise(X)<~>happy(X))))&
(~kind(john))&
(?[X]:((~wise(X)<~>~patient(X))))&
(?[X]:((calm(X)|~curious(X)))) | kind(lucy) | [
"p0",
"p1",
"p6",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7973978989195032342127229
% SZS output start Proof for 7973978989195032342127229
1. ! [X0] : ((wise(X0) & ~patient(X0)) <=> (happy(X0) | quiet(X0))) [input p0]
2. ? [X0] : kind(X0) => ? [X0] : ~brave(X0) [input p1]
7. (rich(susan) & brave(susan)) <=> ? [X0] : happy(X0) [input p6]
10. ! [X0] : ((~brave(X0) | old(X0)) => happy(X0)) [input p9]
13. ! [X0] : (wise(X0) <=> (brave(X0) & calm(X0))) [input p12]
14. ! [X0] : ((brave(X0) | funny(X0)) <=> ~happy(X0)) [input p13]
22. kind(lucy) [input hypothesis]
23. ? [X0] : kind(X0) => ? [X1] : ~brave(X1) [rectify 2]
27. ? [X1] : ~brave(X1) | ! [X0] : ~kind(X0) [ennf transformation 23]
31. ! [X0] : (happy(X0) | (brave(X0) & ~old(X0))) [ennf transformation 10]
35. ! [X0] : (((wise(X0) & ~patient(X0)) | (~happy(X0) & ~quiet(X0))) & ((happy(X0) | quiet(X0)) | (~wise(X0) | patient(X0)))) [nnf transformation 1]
36. ! [X0] : (((wise(X0) & ~patient(X0)) | (~happy(X0) & ~quiet(X0))) & (happy(X0) | quiet(X0) | ~wise(X0) | patient(X0))) [flattening 35]
37. ? [X0] : ~brave(X0) | ! [X1] : ~kind(X1) [rectify 27]
38. ? [X0] : ~brave(X0) => ~brave(sK0) [choice axiom]
39. ~brave(sK0) | ! [X1] : ~kind(X1) [skolemisation 37,38]
52. ((rich(susan) & brave(susan)) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | (~rich(susan) | ~brave(susan))) [nnf transformation 7]
53. ((rich(susan) & brave(susan)) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | ~rich(susan) | ~brave(susan)) [flattening 52]
54. ((rich(susan) & brave(susan)) | ! [X0] : ~happy(X0)) & (? [X1] : happy(X1) | ~rich(susan) | ~brave(susan)) [rectify 53]
55. ? [X1] : happy(X1) => happy(sK3) [choice axiom]
56. ((rich(susan) & brave(susan)) | ! [X0] : ~happy(X0)) & (happy(sK3) | ~rich(susan) | ~brave(susan)) [skolemisation 54,55]
64. ! [X0] : ((wise(X0) | (~brave(X0) | ~calm(X0))) & ((brave(X0) & calm(X0)) | ~wise(X0))) [nnf transformation 13]
65. ! [X0] : ((wise(X0) | ~brave(X0) | ~calm(X0)) & ((brave(X0) & calm(X0)) | ~wise(X0))) [flattening 64]
66. ! [X0] : (((brave(X0) | funny(X0)) | happy(X0)) & (~happy(X0) | (~brave(X0) & ~funny(X0)))) [nnf transformation 14]
67. ! [X0] : ((brave(X0) | funny(X0) | happy(X0)) & (~happy(X0) | (~brave(X0) & ~funny(X0)))) [flattening 66]
82. ~happy(X0) | wise(X0) [cnf transformation 36]
83. ~brave(sK0) | ~kind(X1) [cnf transformation 39]
100. happy(sK3) | ~rich(susan) | ~brave(susan) [cnf transformation 56]
101. brave(susan) | ~happy(X0) [cnf transformation 56]
102. rich(susan) | ~happy(X0) [cnf transformation 56]
106. brave(X0) | happy(X0) [cnf transformation 31]
114. ~wise(X0) | brave(X0) [cnf transformation 65]
117. ~brave(X0) | ~happy(X0) [cnf transformation 67]
132. kind(lucy) [cnf transformation 22]
137. 1 <=> ! [X1] : ~kind(X1) [avatar definition]
138. ~kind(X1) <- (1) [avatar component clause 137]
140. 2 <=> brave(sK0) [avatar definition]
142. ~brave(sK0) <- (~2) [avatar component clause 140]
143. 1 | ~2 [avatar split clause 83,140,137]
200. 15 <=> ! [X0] : ~happy(X0) [avatar definition]
201. ~happy(X0) <- (15) [avatar component clause 200]
203. 16 <=> rich(susan) [avatar definition]
206. 15 | 16 [avatar split clause 102,203,200]
208. 17 <=> brave(susan) [avatar definition]
211. 15 | 17 [avatar split clause 101,208,200]
213. 18 <=> happy(sK3) [avatar definition]
215. happy(sK3) <- (18) [avatar component clause 213]
216. ~17 | ~16 | 18 [avatar split clause 100,213,203,208]
261. happy(sK0) <- (~2) [resolution 106,142]
262. $false <- (~2, 15) [subsumption resolution 261,201]
263. 2 | ~15 [avatar contradiction clause 262]
264. $false <- (1) [resolution 138,132]
265. ~1 [avatar contradiction clause 264]
267. wise(sK3) <- (18) [resolution 215,82]
276. brave(sK3) <- (18) [resolution 114,267]
302. ~happy(sK3) <- (18) [resolution 276,117]
303. $false <- (18) [subsumption resolution 302,215]
304. ~18 [avatar contradiction clause 303]
305. $false [avatar sat refutation 143,206,211,216,263,265,304]
% SZS output end Proof for 7973978989195032342127229
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not brave then someone is humble or not calm.
Everyone who is not generous is not funny.
If someone is funny then mary is either not kind or creative and vice versa.
Everyone who is creative or kind is both not curious and quiet.
Everyone who is strong or not curious is kind and vice versa.
Everyone who is not brave or not creative is not old or quiet and vice versa.
Everyone who is old or brave is both tall and creative.
Everyone who is either not wise or quiet is not rich.
Everyone who is not brave or patient is not quiet or not kind.
Everyone who is not kind or not humble is either not happy or strong.
If someone is generous or not brave then alice is not curious or not creative.
If mary is either not old or not happy then someone is not rich or not curious.
Everyone who is brave or rich is calm or not tall.
If someone is either not quiet or curious then someone is patient and vice versa.
Everyone who is calm or wise is humble or not kind.
Susan is either happy or funny.
Someone is either brave or not calm.
Mary is patient.
Someone is either kind or patient.
Someone is rich. | Alice is not old. | entailment | ((?[X]:((kind(X)|~brave(X))))=>(?[X]:((humble(X)|~calm(X)))))&
(![X]:(~generous(X)=>~funny(X)))&
((?[X]:(funny(X)))<=>((~kind(mary)<~>creative(mary))))&
(![X]:((creative(X)|kind(X))=>(~curious(X)&quiet(X))))&
(![X]:((strong(X)|~curious(X))<=>kind(X)))&
(![X]:((~brave(X)|~creative(X))<=>(~old(X)|quiet(X))))&
(![X]:((old(X)|brave(X))=>(tall(X)&creative(X))))&
(![X]:((~wise(X)<~>quiet(X))=>~rich(X)))&
(![X]:((~brave(X)|patient(X))=>(~quiet(X)|~kind(X))))&
(![X]:((~kind(X)|~humble(X))=>(~happy(X)<~>strong(X))))&
((?[X]:((generous(X)|~brave(X))))=>((~curious(alice)|~creative(alice))))&
(((~old(mary)<~>~happy(mary)))=>(?[X]:((~rich(X)|~curious(X)))))&
(![X]:((brave(X)|rich(X))=>(calm(X)|~tall(X))))&
((?[X]:((~quiet(X)<~>curious(X))))<=>(?[X]:(patient(X))))&
(![X]:((calm(X)|wise(X))=>(humble(X)|~kind(X))))&
((happy(susan)<~>funny(susan)))&
(?[X]:((brave(X)<~>~calm(X))))&
(patient(mary))&
(?[X]:((kind(X)<~>patient(X))))&
(?[X]:(rich(X))) | ~old(alice) | [
"p3",
"p4",
"p5",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 9160327871448057223558477
% SZS output start Proof for 9160327871448057223558477
4. ! [X0] : ((kind(X0) | creative(X0)) => (quiet(X0) & ~curious(X0))) [input p3]
5. ! [X0] : ((~curious(X0) | strong(X0)) <=> kind(X0)) [input p4]
6. ! [X0] : ((~creative(X0) | ~brave(X0)) <=> (quiet(X0) | ~old(X0))) [input p5]
7. ! [X0] : ((brave(X0) | old(X0)) => (creative(X0) & tall(X0))) [input p6]
9. ! [X0] : ((patient(X0) | ~brave(X0)) => (~kind(X0) | ~quiet(X0))) [input p8]
21. old(alice) [input hypothesis]
28. ! [X0] : ((quiet(X0) & ~curious(X0)) | (~kind(X0) & ~creative(X0))) [ennf transformation 4]
29. ! [X0] : ((creative(X0) & tall(X0)) | (~brave(X0) & ~old(X0))) [ennf transformation 7]
31. ! [X0] : ((~kind(X0) | ~quiet(X0)) | (~patient(X0) & brave(X0))) [ennf transformation 9]
32. ! [X0] : (~kind(X0) | ~quiet(X0) | (~patient(X0) & brave(X0))) [flattening 31]
43. ! [X0] : (((~curious(X0) | strong(X0)) | ~kind(X0)) & (kind(X0) | (curious(X0) & ~strong(X0)))) [nnf transformation 5]
44. ! [X0] : ((~curious(X0) | strong(X0) | ~kind(X0)) & (kind(X0) | (curious(X0) & ~strong(X0)))) [flattening 43]
45. ! [X0] : (((~creative(X0) | ~brave(X0)) | (~quiet(X0) & old(X0))) & ((quiet(X0) | ~old(X0)) | (creative(X0) & brave(X0)))) [nnf transformation 6]
46. ! [X0] : ((~creative(X0) | ~brave(X0) | (~quiet(X0) & old(X0))) & (quiet(X0) | ~old(X0) | (creative(X0) & brave(X0)))) [flattening 45]
71. ~curious(X0) | ~creative(X0) [cnf transformation 28]
73. ~creative(X0) | quiet(X0) [cnf transformation 28]
74. ~kind(X0) | quiet(X0) [cnf transformation 28]
76. curious(X0) | kind(X0) [cnf transformation 44]
81. ~creative(X0) | ~brave(X0) | ~quiet(X0) [cnf transformation 46]
84. ~old(X0) | creative(X0) [cnf transformation 29]
85. creative(X0) | ~brave(X0) [cnf transformation 29]
88. ~kind(X0) | ~quiet(X0) | brave(X0) [cnf transformation 32]
110. old(alice) [cnf transformation 21]
130. ~creative(X0) | ~brave(X0) [subsumption resolution 81,73]
132. ~brave(X0) [subsumption resolution 85,130]
134. ~kind(X0) | ~quiet(X0) [subsumption resolution 88,132]
135. ~kind(X0) [subsumption resolution 134,74]
195. kind(X1) | ~creative(X1) [resolution 76,71]
198. ~creative(X1) [subsumption resolution 195,135]
208. creative(alice) [resolution 84,110]
209. $false [subsumption resolution 208,198]
% SZS output end Proof for 9160327871448057223558477
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is both old and not funny then someone is happy and vice versa.
Everyone who is kind or not quiet is both not rich and not curious.
Everyone who is both not calm and not kind is not wise or generous and vice versa.
If someone is not kind or not strong then paul is generous.
Everyone who is either not old or old is generous and vice versa.
Everyone who is calm or not strong is creative and vice versa.
If alice is not kind or generous then someone is brave and vice versa.
Everyone who is both not tall and not funny is either funny or not calm.
Everyone who is either generous or not old is not creative.
If john is both not happy and quiet then lucy is not funny or happy.
If someone is either not funny or patient then fred is not curious and vice versa.
If john is either happy or tall then someone is both not humble and not strong and vice versa.
Everyone who is both not tall and not creative is either rich or strong.
Everyone who is both curious and not old is either not old or strong.
If someone is not humble then someone is not creative.
If someone is either not wise or old then lucy is both not kind and not funny.
Alice is both not wise and not calm.
Someone is both not tall and not kind.
Someone is both not quiet and humble.
Fred is quiet.
Someone is not tall or not rich.
Someone is curious or patient.
Paul is rich. | John is not calm. | entailment | ((?[X]:((old(X)&~funny(X))))<=>(?[X]:(happy(X))))&
(![X]:((kind(X)|~quiet(X))=>(~rich(X)&~curious(X))))&
(![X]:((~calm(X)&~kind(X))<=>(~wise(X)|generous(X))))&
((?[X]:((~kind(X)|~strong(X))))=>(generous(paul)))&
(![X]:((~old(X)<~>old(X))<=>generous(X)))&
(![X]:((calm(X)|~strong(X))<=>creative(X)))&
(((~kind(alice)|generous(alice)))<=>(?[X]:(brave(X))))&
(![X]:((~tall(X)&~funny(X))=>(funny(X)<~>~calm(X))))&
(![X]:((generous(X)<~>~old(X))=>~creative(X)))&
(((~happy(john)&quiet(john)))=>((~funny(lucy)|happy(lucy))))&
((?[X]:((~funny(X)<~>patient(X))))<=>(~curious(fred)))&
(((happy(john)<~>tall(john)))<=>(?[X]:((~humble(X)&~strong(X)))))&
(![X]:((~tall(X)&~creative(X))=>(rich(X)<~>strong(X))))&
(![X]:((curious(X)&~old(X))=>(~old(X)<~>strong(X))))&
((?[X]:(~humble(X)))=>(?[X]:(~creative(X))))&
((?[X]:((~wise(X)<~>old(X))))=>((~kind(lucy)&~funny(lucy))))&
((~wise(alice)&~calm(alice)))&
(?[X]:((~tall(X)&~kind(X))))&
(?[X]:((~quiet(X)&humble(X))))&
(quiet(fred))&
(?[X]:((~tall(X)|~rich(X))))&
(?[X]:((curious(X)|patient(X))))&
(rich(paul)) | ~calm(john) | [
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 1793786186061577364401518
% SZS output start Proof for 1793786186061577364401518
3. ! [X0] : ((~kind(X0) & ~calm(X0)) <=> (generous(X0) | ~wise(X0))) [input p2]
5. ! [X0] : ((~old(X0) <~> old(X0)) <=> generous(X0)) [input p4]
24. calm(john) [input hypothesis]
45. ! [X0] : (((~kind(X0) & ~calm(X0)) | (~generous(X0) & wise(X0))) & ((generous(X0) | ~wise(X0)) | (kind(X0) | calm(X0)))) [nnf transformation 3]
46. ! [X0] : (((~kind(X0) & ~calm(X0)) | (~generous(X0) & wise(X0))) & (generous(X0) | ~wise(X0) | kind(X0) | calm(X0))) [flattening 45]
47. ! [X0] : ((((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | ~generous(X0)) & (generous(X0) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0))))) [nnf transformation 5]
88. ~generous(X0) | ~calm(X0) [cnf transformation 46]
93. generous(X0) | old(X0) | old(X0) [cnf transformation 47]
94. generous(X0) | ~old(X0) | ~old(X0) [cnf transformation 47]
137. calm(john) [cnf transformation 24]
140. generous(X0) | old(X0) [duplicate literal removal 93]
141. generous(X0) | ~old(X0) [duplicate literal removal 94]
175. generous(X0) [subsumption resolution 140,141]
284. ~calm(X0) [resolution 88,175]
285. $false [resolution 284,137]
% SZS output end Proof for 1793786186061577364401518
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both calm and not brave then someone is either humble or not generous and vice versa. If lucy is happy or brave then mary is either not generous or rich. Everyone who is quiet or humble is either old or not wise and vice versa. Everyone who is not curious or not brave is not kind and vice versa. If someone is both curious and tall then paul is rich or not calm. If mary is both rich and quiet then someone is curious. Everyone who is not quiet is not strong or not brave and vice versa. Everyone who is not funny or not brave is not patient or brave and vice versa. If fred is not brave or not strong then someone is wise or not creative. If someone is not quiet then someone is curious and vice versa. If someone is generous or calm then someone is wise and vice versa. If someone is not quiet then someone is not old and vice versa. Everyone who is both not rich and not strong is creative. If fred is either wise or not kind then someone is patient and vice versa. Everyone who is both brave and kind is not tall or not kind and vice versa. Everyone who is not generous is either not calm or happy. Someone is both humble and not strong. Someone is either not brave or strong. Susan is either not funny or happy. Lucy is both curious and humble. Someone is either not humble or funny. Lucy is not quiet. | Fred is not kind. | contradiction | (((calm(fred)&~brave(fred)))<=>(?[X]:((humble(X)<~>~generous(X)))))&
(((happy(lucy)|brave(lucy)))=>((~generous(mary)<~>rich(mary))))&
(![X]:((quiet(X)|humble(X))<=>(old(X)<~>~wise(X))))&
(![X]:((~curious(X)|~brave(X))<=>~kind(X)))&
((?[X]:((curious(X)&tall(X))))=>((rich(paul)|~calm(paul))))&
(((rich(mary)&quiet(mary)))=>(?[X]:(curious(X))))&
(![X]:(~quiet(X)<=>(~strong(X)|~brave(X))))&
(![X]:((~funny(X)|~brave(X))<=>(~patient(X)|brave(X))))&
(((~brave(fred)|~strong(fred)))=>(?[X]:((wise(X)|~creative(X)))))&
((?[X]:(~quiet(X)))<=>(?[X]:(curious(X))))&
((?[X]:((generous(X)|calm(X))))<=>(?[X]:(wise(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:(~old(X))))&
(![X]:((~rich(X)&~strong(X))=>creative(X)))&
(((wise(fred)<~>~kind(fred)))<=>(?[X]:(patient(X))))&
(![X]:((brave(X)&kind(X))<=>(~tall(X)|~kind(X))))&
(![X]:(~generous(X)=>(~calm(X)<~>happy(X))))&
(?[X]:((humble(X)&~strong(X))))&
(?[X]:((~brave(X)<~>strong(X))))&
((~funny(susan)<~>happy(susan)))&
((curious(lucy)&humble(lucy)))&
(?[X]:((~humble(X)<~>funny(X))))&
(~quiet(lucy)) | ~kind(fred) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2539025740223579578672244
% SZS output start Proof for 2539025740223579578672244
15. ! [X0] : ((kind(X0) & brave(X0)) <=> (~kind(X0) | ~tall(X0))) [input p14]
23. ~kind(fred) [input hypothesis]
73. ! [X0] : (((kind(X0) & brave(X0)) | (kind(X0) & tall(X0))) & ((~kind(X0) | ~tall(X0)) | (~kind(X0) | ~brave(X0)))) [nnf transformation 15]
74. ! [X0] : (((kind(X0) & brave(X0)) | (kind(X0) & tall(X0))) & (~kind(X0) | ~tall(X0) | ~kind(X0) | ~brave(X0))) [flattening 73]
131. kind(X0) | kind(X0) [cnf transformation 74]
145. ~kind(fred) [cnf transformation 23]
147. kind(X0) [duplicate literal removal 131]
336. $false [subsumption resolution 145,147]
% SZS output end Proof for 2539025740223579578672244
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If john is not calm then someone is not strong.
Everyone who is old or patient is both quiet and not rich.
Everyone who is both calm and not kind is generous or not happy.
If someone is both happy and curious then someone is both brave and not brave and vice versa.
If john is both not curious and not patient then someone is brave.
If susan is not tall then fred is not humble or quiet.
If john is tall or curious then lucy is both not tall and wise.
Everyone who is both curious and funny is patient or not patient.
If someone is humble then someone is either kind or not quiet.
If susan is both not tall and quiet then alice is either not old or not rich.
Everyone who is kind is both strong and not tall.
Everyone who is quiet is either not happy or brave.
If alice is not rich then mary is both not creative and happy.
Everyone who is creative or brave is both not kind and happy.
If someone is both not funny and tall then fred is either tall or happy and vice versa.
Everyone who is both quiet and humble is wise.
Lucy is humble.
Someone is both patient and wise.
Fred is both not old and not quiet.
Susan is quiet.
Fred is humble or brave.
Lucy is either funny or humble.
Susan is either not old or not patient.
Mary is both not patient and wise. | Fred is patient. | contradiction | ((~calm(john))=>(?[X]:(~strong(X))))&
(![X]:((old(X)|patient(X))=>(quiet(X)&~rich(X))))&
(![X]:((calm(X)&~kind(X))=>(generous(X)|~happy(X))))&
((?[X]:((happy(X)&curious(X))))<=>(?[X]:((brave(X)&~brave(X)))))&
(((~curious(john)&~patient(john)))=>(?[X]:(brave(X))))&
((~tall(susan))=>((~humble(fred)|quiet(fred))))&
(((tall(john)|curious(john)))=>((~tall(lucy)&wise(lucy))))&
(![X]:((curious(X)&funny(X))=>(patient(X)|~patient(X))))&
((?[X]:(humble(X)))=>(?[X]:((kind(X)<~>~quiet(X)))))&
(((~tall(susan)&quiet(susan)))=>((~old(alice)<~>~rich(alice))))&
(![X]:(kind(X)=>(strong(X)&~tall(X))))&
(![X]:(quiet(X)=>(~happy(X)<~>brave(X))))&
((~rich(alice))=>((~creative(mary)&happy(mary))))&
(![X]:((creative(X)|brave(X))=>(~kind(X)&happy(X))))&
((?[X]:((~funny(X)&tall(X))))<=>((tall(fred)<~>happy(fred))))&
(![X]:((quiet(X)&humble(X))=>wise(X)))&
(humble(lucy))&
(?[X]:((patient(X)&wise(X))))&
((~old(fred)&~quiet(fred)))&
(quiet(susan))&
((humble(fred)|brave(fred)))&
((funny(lucy)<~>humble(lucy)))&
((~old(susan)<~>~patient(susan)))&
((~patient(mary)&wise(mary))) | patient(fred) | [
"p1",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8117191243957265119599373
% SZS output start Proof for 8117191243957265119599373
2. ! [X0] : ((patient(X0) | old(X0)) => (~rich(X0) & quiet(X0))) [input p1]
19. ~quiet(fred) & ~old(fred) [input p18]
25. patient(fred) [input hypothesis]
37. ! [X0] : ((~rich(X0) & quiet(X0)) | (~patient(X0) & ~old(X0))) [ennf transformation 2]
74. ~patient(X0) | quiet(X0) [cnf transformation 37]
105. ~quiet(fred) [cnf transformation 19]
113. patient(fred) [cnf transformation 25]
145. 8 <=> quiet(fred) [avatar definition]
146. ~quiet(fred) <- (~8) [avatar component clause 145]
215. ~8 [avatar split clause 105,145]
235. quiet(fred) [resolution 74,113]
237. $false <- (~8) [subsumption resolution 235,146]
238. 8 [avatar contradiction clause 237]
239. $false [avatar sat refutation 215,238]
% SZS output end Proof for 8117191243957265119599373
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or not curious then mary is either wise or funny.
Everyone who is both not calm and calm is both not strong and quiet and vice versa.
If someone is not humble or happy then someone is either brave or wise and vice versa.
Everyone who is either funny or not happy is not kind.
Everyone who is not funny or brave is either strong or not brave and vice versa.
Everyone who is not creative or wise is funny or not generous and vice versa.
Everyone who is both not generous and kind is both patient and humble.
Everyone who is old or funny is either not brave or not quiet.
If someone is kind then fred is strong or not old.
Everyone who is either strong or not tall is either not rich or not strong.
Everyone who is either quiet or not calm is creative.
If someone is rich or not curious then someone is tall or old.
Everyone who is not kind or curious is either not strong or not humble.
Everyone who is not creative or happy is either not patient or calm and vice versa.
If someone is not humble or creative then someone is both not funny and not brave.
Everyone who is not funny or not creative is old or quiet.
Someone is not patient.
Lucy is both rich and not creative.
Susan is old or not humble.
Paul is either not old or creative.
Susan is both calm and funny. | Mary is not funny. | neutral | ((?[X]:((calm(X)|~curious(X))))=>((wise(mary)<~>funny(mary))))&
(![X]:((~calm(X)&calm(X))<=>(~strong(X)&quiet(X))))&
((?[X]:((~humble(X)|happy(X))))<=>(?[X]:((brave(X)<~>wise(X)))))&
(![X]:((funny(X)<~>~happy(X))=>~kind(X)))&
(![X]:((~funny(X)|brave(X))<=>(strong(X)<~>~brave(X))))&
(![X]:((~creative(X)|wise(X))<=>(funny(X)|~generous(X))))&
(![X]:((~generous(X)&kind(X))=>(patient(X)&humble(X))))&
(![X]:((old(X)|funny(X))=>(~brave(X)<~>~quiet(X))))&
((?[X]:(kind(X)))=>((strong(fred)|~old(fred))))&
(![X]:((strong(X)<~>~tall(X))=>(~rich(X)<~>~strong(X))))&
(![X]:((quiet(X)<~>~calm(X))=>creative(X)))&
((?[X]:((rich(X)|~curious(X))))=>(?[X]:((tall(X)|old(X)))))&
(![X]:((~kind(X)|curious(X))=>(~strong(X)<~>~humble(X))))&
(![X]:((~creative(X)|happy(X))<=>(~patient(X)<~>calm(X))))&
((?[X]:((~humble(X)|creative(X))))=>(?[X]:((~funny(X)&~brave(X)))))&
(![X]:((~funny(X)|~creative(X))=>(old(X)|quiet(X))))&
(?[X]:(~patient(X)))&
((rich(lucy)&~creative(lucy)))&
((old(susan)|~humble(susan)))&
((~old(paul)<~>creative(paul)))&
((calm(susan)&funny(susan))) | ~funny(mary) | [] | null | 0 |
If someone is not brave then susan is either not tall or wise.
Everyone who is not curious is either not humble or curious and vice versa.
Everyone who is either not humble or not quiet is rich and vice versa.
Everyone who is not calm or quiet is curious.
If alice is tall then someone is not funny or tall and vice versa.
If alice is not funny or not creative then alice is both not quiet and patient and vice versa.
If lucy is funny then paul is either not rich or not brave and vice versa.
Everyone who is both brave and not brave is either happy or not wise and vice versa.
Everyone who is either not brave or not happy is not rich.
Everyone who is wise is both strong and generous.
If someone is not happy then someone is brave or not calm and vice versa.
Everyone who is both strong and rich is creative.
Everyone who is both kind and happy is both not curious and happy and vice versa.
Everyone who is not quiet or not funny is either not funny or funny.
Everyone who is either humble or not strong is happy or not brave and vice versa.
Everyone who is rich is quiet or patient and vice versa.
Lucy is not strong.
Someone is both old and not happy.
Paul is either not funny or strong.
John is rich.
Mary is both not curious and not strong.
Susan is not curious.
Susan is both not strong and not generous.
Someone is either not humble or strong. | Susan is tall. | neutral | ((?[X]:(~brave(X)))=>((~tall(susan)<~>wise(susan))))&
(![X]:(~curious(X)<=>(~humble(X)<~>curious(X))))&
(![X]:((~humble(X)<~>~quiet(X))<=>rich(X)))&
(![X]:((~calm(X)|quiet(X))=>curious(X)))&
((tall(alice))<=>(?[X]:((~funny(X)|tall(X)))))&
(((~funny(alice)|~creative(alice)))<=>((~quiet(alice)&patient(alice))))&
((funny(lucy))<=>((~rich(paul)<~>~brave(paul))))&
(![X]:((brave(X)&~brave(X))<=>(happy(X)<~>~wise(X))))&
(![X]:((~brave(X)<~>~happy(X))=>~rich(X)))&
(![X]:(wise(X)=>(strong(X)&generous(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((brave(X)|~calm(X)))))&
(![X]:((strong(X)&rich(X))=>creative(X)))&
(![X]:((kind(X)&happy(X))<=>(~curious(X)&happy(X))))&
(![X]:((~quiet(X)|~funny(X))=>(~funny(X)<~>funny(X))))&
(![X]:((humble(X)<~>~strong(X))<=>(happy(X)|~brave(X))))&
(![X]:(rich(X)<=>(quiet(X)|patient(X))))&
(~strong(lucy))&
(?[X]:((old(X)&~happy(X))))&
((~funny(paul)<~>strong(paul)))&
(rich(john))&
((~curious(mary)&~strong(mary)))&
(~curious(susan))&
((~strong(susan)&~generous(susan)))&
(?[X]:((~humble(X)<~>strong(X)))) | tall(susan) | [] | null | 0 |
If lucy is either not calm or wise then mary is strong or wise.
Everyone who is both funny and not creative is not happy or wise and vice versa.
If mary is both tall and not quiet then someone is either curious or not happy.
If john is not tall or tall then someone is kind and vice versa.
If lucy is generous or quiet then someone is both humble and not calm and vice versa.
If alice is both calm and not quiet then someone is kind.
Everyone who is generous or quiet is both not calm and humble and vice versa.
Everyone who is either funny or not tall is not calm or not rich and vice versa.
Everyone who is not rich or tall is both humble and creative and vice versa.
If mary is both not curious and not brave then paul is not strong or rich and vice versa.
Everyone who is not wise or kind is not humble or generous and vice versa.
Everyone who is both humble and wise is both calm and not old.
If mary is not quiet then someone is curious and vice versa.
If john is not funny then someone is both not funny and creative.
If alice is curious or not quiet then lucy is not humble or old and vice versa.
Everyone who is humble is both tall and not patient.
Someone is both not quiet and not brave.
Someone is rich or not calm.
Alice is humble or quiet.
Someone is not rich.
Alice is either quiet or not wise.
Someone is both not happy and not old.
Fred is either not happy or calm. | Paul is curious. | neutral | (((~calm(lucy)<~>wise(lucy)))=>((strong(mary)|wise(mary))))&
(![X]:((funny(X)&~creative(X))<=>(~happy(X)|wise(X))))&
(((tall(mary)&~quiet(mary)))=>(?[X]:((curious(X)<~>~happy(X)))))&
(((~tall(john)|tall(john)))<=>(?[X]:(kind(X))))&
(((generous(lucy)|quiet(lucy)))<=>(?[X]:((humble(X)&~calm(X)))))&
(((calm(alice)&~quiet(alice)))=>(?[X]:(kind(X))))&
(![X]:((generous(X)|quiet(X))<=>(~calm(X)&humble(X))))&
(![X]:((funny(X)<~>~tall(X))<=>(~calm(X)|~rich(X))))&
(![X]:((~rich(X)|tall(X))<=>(humble(X)&creative(X))))&
(((~curious(mary)&~brave(mary)))<=>((~strong(paul)|rich(paul))))&
(![X]:((~wise(X)|kind(X))<=>(~humble(X)|generous(X))))&
(![X]:((humble(X)&wise(X))=>(calm(X)&~old(X))))&
((~quiet(mary))<=>(?[X]:(curious(X))))&
((~funny(john))=>(?[X]:((~funny(X)&creative(X)))))&
(((curious(alice)|~quiet(alice)))<=>((~humble(lucy)|old(lucy))))&
(![X]:(humble(X)=>(tall(X)&~patient(X))))&
(?[X]:((~quiet(X)&~brave(X))))&
(?[X]:((rich(X)|~calm(X))))&
((humble(alice)|quiet(alice)))&
(?[X]:(~rich(X)))&
((quiet(alice)<~>~wise(alice)))&
(?[X]:((~happy(X)&~old(X))))&
((~happy(fred)<~>calm(fred))) | curious(paul) | [] | null | 0 |
Everyone who is either not brave or kind is both brave and not tall.
Everyone who is either generous or happy is rich.
Everyone who is not calm or not funny is rich or strong and vice versa.
If someone is calm or kind then someone is both kind and rich.
Everyone who is both kind and not old is both calm and not curious and vice versa.
Everyone who is not wise is kind.
If fred is either not old or strong then fred is either not funny or not humble and vice versa.
Everyone who is either not patient or not wise is kind or not strong.
If someone is not happy then john is both not happy and funny.
Everyone who is not quiet or not calm is both not creative and not wise.
Everyone who is not brave or old is either not humble or tall and vice versa.
Everyone who is either not brave or not old is both not kind and not old and vice versa.
Everyone who is strong is not creative or not generous and vice versa.
If someone is generous or not quiet then someone is either not old or patient.
Everyone who is either not wise or curious is not old or patient and vice versa.
If lucy is generous or not calm then paul is not rich.
John is either curious or not quiet.
Someone is both not funny and not old.
Someone is quiet or brave.
Lucy is both not wise and kind.
Someone is either brave or not tall.
Lucy is both calm and old.
Paul is either old or calm.
Someone is kind. | Lucy is humble. | contradiction | (![X]:((~brave(X)<~>kind(X))=>(brave(X)&~tall(X))))&
(![X]:((generous(X)<~>happy(X))=>rich(X)))&
(![X]:((~calm(X)|~funny(X))<=>(rich(X)|strong(X))))&
((?[X]:((calm(X)|kind(X))))=>(?[X]:((kind(X)&rich(X)))))&
(![X]:((kind(X)&~old(X))<=>(calm(X)&~curious(X))))&
(![X]:(~wise(X)=>kind(X)))&
(((~old(fred)<~>strong(fred)))<=>((~funny(fred)<~>~humble(fred))))&
(![X]:((~patient(X)<~>~wise(X))=>(kind(X)|~strong(X))))&
((?[X]:(~happy(X)))=>((~happy(john)&funny(john))))&
(![X]:((~quiet(X)|~calm(X))=>(~creative(X)&~wise(X))))&
(![X]:((~brave(X)|old(X))<=>(~humble(X)<~>tall(X))))&
(![X]:((~brave(X)<~>~old(X))<=>(~kind(X)&~old(X))))&
(![X]:(strong(X)<=>(~creative(X)|~generous(X))))&
((?[X]:((generous(X)|~quiet(X))))=>(?[X]:((~old(X)<~>patient(X)))))&
(![X]:((~wise(X)<~>curious(X))<=>(~old(X)|patient(X))))&
(((generous(lucy)|~calm(lucy)))=>(~rich(paul)))&
((curious(john)<~>~quiet(john)))&
(?[X]:((~funny(X)&~old(X))))&
(?[X]:((quiet(X)|brave(X))))&
((~wise(lucy)&kind(lucy)))&
(?[X]:((brave(X)<~>~tall(X))))&
((calm(lucy)&old(lucy)))&
((old(paul)<~>calm(paul)))&
(?[X]:(kind(X))) | humble(lucy) | [
"p0",
"p10",
"p11",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 413066051807451167229630
% SZS output start Proof for 413066051807451167229630
1. ! [X0] : ((~brave(X0) <~> kind(X0)) => (~tall(X0) & brave(X0))) [input p0]
11. ! [X0] : ((old(X0) | ~brave(X0)) <=> (~humble(X0) <~> tall(X0))) [input p10]
12. ! [X0] : ((~brave(X0) <~> ~old(X0)) <=> (~old(X0) & ~kind(X0))) [input p11]
20. kind(lucy) & ~wise(lucy) [input p19]
22. old(lucy) & calm(lucy) [input p21]
25. humble(lucy) [input hypothesis]
28. ! [X0] : ((~tall(X0) & brave(X0)) | (~brave(X0) <=> kind(X0))) [ennf transformation 1]
38. ! [X0] : ((~tall(X0) & brave(X0)) | ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0)))) [nnf transformation 28]
49. ! [X0] : (((old(X0) | ~brave(X0)) | ((~humble(X0) | ~tall(X0)) & (tall(X0) | humble(X0)))) & (((~tall(X0) | humble(X0)) & (tall(X0) | ~humble(X0))) | (~old(X0) & brave(X0)))) [nnf transformation 11]
50. ! [X0] : ((old(X0) | ~brave(X0) | ((~humble(X0) | ~tall(X0)) & (tall(X0) | humble(X0)))) & (((~tall(X0) | humble(X0)) & (tall(X0) | ~humble(X0))) | (~old(X0) & brave(X0)))) [flattening 49]
51. ! [X0] : ((((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | (old(X0) | kind(X0))) & ((~old(X0) & ~kind(X0)) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0))))) [nnf transformation 12]
52. ! [X0] : ((((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | old(X0) | kind(X0)) & ((~old(X0) & ~kind(X0)) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0))))) [flattening 51]
75. ~tall(X0) | ~brave(X0) | ~kind(X0) [cnf transformation 38]
108. ~humble(X0) | tall(X0) | ~old(X0) [cnf transformation 50]
115. ~old(X0) | ~old(X0) | brave(X0) [cnf transformation 52]
140. kind(lucy) [cnf transformation 20]
144. old(lucy) [cnf transformation 22]
148. humble(lucy) [cnf transformation 25]
149. ~old(X0) | brave(X0) [duplicate literal removal 115]
286. brave(lucy) [resolution 149,144]
375. tall(lucy) | ~old(lucy) [resolution 108,148]
376. tall(lucy) [subsumption resolution 375,144]
379. ~brave(lucy) | ~kind(lucy) [resolution 376,75]
381. ~kind(lucy) [subsumption resolution 379,286]
382. $false [subsumption resolution 381,140]
% SZS output end Proof for 413066051807451167229630
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is not curious then someone is funny or not humble.
If fred is not curious or not strong then someone is humble and vice versa.
If mary is funny then alice is patient.
Everyone who is calm is both not wise and old.
Everyone who is either not strong or not wise is either strong or calm and vice versa.
If someone is not rich or not kind then someone is both not happy and not rich and vice versa.
Everyone who is both generous and humble is either not humble or funny.
Everyone who is either not humble or not brave is patient and vice versa.
If someone is both not kind and humble then mary is brave.
If someone is both not generous and tall then someone is either not brave or wise and vice versa.
Everyone who is strong or not quiet is both not quiet and not curious.
If alice is either not curious or strong then susan is curious or quiet.
If someone is either humble or rich then someone is both patient and creative.
If john is either not wise or happy then paul is strong or patient and vice versa.
If paul is both calm and not funny then mary is both not curious and funny.
If someone is wise or funny then john is either not calm or strong.
Someone is generous.
Someone is curious or not rich.
Paul is not kind.
Someone is old.
Paul is either curious or creative.
John is curious.
Mary is either happy or not kind.
Mary is humble or creative. | John is calm. | contradiction | ((?[X]:(~curious(X)))=>(?[X]:((funny(X)|~humble(X)))))&
(((~curious(fred)|~strong(fred)))<=>(?[X]:(humble(X))))&
((funny(mary))=>(patient(alice)))&
(![X]:(calm(X)=>(~wise(X)&old(X))))&
(![X]:((~strong(X)<~>~wise(X))<=>(strong(X)<~>calm(X))))&
((?[X]:((~rich(X)|~kind(X))))<=>(?[X]:((~happy(X)&~rich(X)))))&
(![X]:((generous(X)&humble(X))=>(~humble(X)<~>funny(X))))&
(![X]:((~humble(X)<~>~brave(X))<=>patient(X)))&
((?[X]:((~kind(X)&humble(X))))=>(brave(mary)))&
((?[X]:((~generous(X)&tall(X))))<=>(?[X]:((~brave(X)<~>wise(X)))))&
(![X]:((strong(X)|~quiet(X))=>(~quiet(X)&~curious(X))))&
(((~curious(alice)<~>strong(alice)))=>((curious(susan)|quiet(susan))))&
((?[X]:((humble(X)<~>rich(X))))=>(?[X]:((patient(X)&creative(X)))))&
(((~wise(john)<~>happy(john)))<=>((strong(paul)|patient(paul))))&
(((calm(paul)&~funny(paul)))=>((~curious(mary)&funny(mary))))&
((?[X]:((wise(X)|funny(X))))=>((~calm(john)<~>strong(john))))&
(?[X]:(generous(X)))&
(?[X]:((curious(X)|~rich(X))))&
(~kind(paul))&
(?[X]:(old(X)))&
((curious(paul)<~>creative(paul)))&
(curious(john))&
((happy(mary)<~>~kind(mary)))&
((humble(mary)|creative(mary))) | calm(john) | [
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 711883300118786235061803
% SZS output start Proof for 711883300118786235061803
4. ! [X0] : (calm(X0) => (old(X0) & ~wise(X0))) [input p3]
5. ! [X0] : ((~strong(X0) <~> ~wise(X0)) <=> (strong(X0) <~> calm(X0))) [input p4]
25. calm(john) [input hypothesis]
30. ! [X0] : (calm(X0) => ~wise(X0)) [pure predicate removal 4]
34. ! [X0] : (~wise(X0) | ~calm(X0)) [ennf transformation 30]
53. ! [X0] : ((((wise(X0) | strong(X0)) & (~wise(X0) | ~strong(X0))) | ((strong(X0) | ~calm(X0)) & (calm(X0) | ~strong(X0)))) & (((~calm(X0) | ~strong(X0)) & (calm(X0) | strong(X0))) | ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0))))) [nnf transformation 5]
85. ~wise(X0) | ~calm(X0) [cnf transformation 34]
89. ~calm(X0) | ~strong(X0) | ~strong(X0) | wise(X0) [cnf transformation 53]
90. ~wise(X0) | ~strong(X0) | calm(X0) | ~strong(X0) [cnf transformation 53]
93. wise(X0) | strong(X0) | strong(X0) | ~calm(X0) [cnf transformation 53]
143. calm(john) [cnf transformation 25]
146. ~calm(X0) | ~strong(X0) | wise(X0) [duplicate literal removal 89]
147. ~wise(X0) | ~strong(X0) | calm(X0) [duplicate literal removal 90]
148. wise(X0) | strong(X0) | ~calm(X0) [duplicate literal removal 93]
188. strong(X0) | ~calm(X0) [subsumption resolution 148,85]
189. ~wise(X0) | ~strong(X0) [subsumption resolution 147,85]
190. ~calm(X0) | ~strong(X0) [subsumption resolution 146,189]
191. ~calm(X0) [subsumption resolution 190,188]
353. $false [subsumption resolution 143,191]
% SZS output end Proof for 711883300118786235061803
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or humble is not calm or not generous.
Everyone who is kind or tall is not creative or not calm.
If mary is not wise or not creative then someone is not rich.
Everyone who is both not wise and not rich is funny and vice versa.
Everyone who is either generous or not old is both not humble and old.
If mary is either not strong or not generous then paul is either generous or wise.
If john is not generous or wise then someone is both not quiet and not strong and vice versa.
Everyone who is both kind and not quiet is both not kind and funny.
Everyone who is either old or not curious is strong.
If paul is both not strong and generous then john is not strong or not wise and vice versa.
Everyone who is either calm or not calm is both not tall and curious and vice versa.
If paul is both kind and not quiet then someone is not rich and vice versa.
If fred is either tall or not calm then someone is both old and not tall and vice versa.
Everyone who is both not quiet and strong is both not curious and not brave.
Everyone who is creative is both not calm and not patient and vice versa.
Everyone who is generous is kind or not humble and vice versa.
Fred is not kind.
John is brave or strong.
Someone is either not patient or rich.
Mary is either not quiet or quiet.
John is not patient or not creative.
Paul is both creative and not generous.
Someone is not funny.
Lucy is both patient and not funny. | Paul is strong. | entailment | (![X]:((calm(X)<~>humble(X))=>(~calm(X)|~generous(X))))&
(![X]:((kind(X)|tall(X))=>(~creative(X)|~calm(X))))&
(((~wise(mary)|~creative(mary)))=>(?[X]:(~rich(X))))&
(![X]:((~wise(X)&~rich(X))<=>funny(X)))&
(![X]:((generous(X)<~>~old(X))=>(~humble(X)&old(X))))&
(((~strong(mary)<~>~generous(mary)))=>((generous(paul)<~>wise(paul))))&
(((~generous(john)|wise(john)))<=>(?[X]:((~quiet(X)&~strong(X)))))&
(![X]:((kind(X)&~quiet(X))=>(~kind(X)&funny(X))))&
(![X]:((old(X)<~>~curious(X))=>strong(X)))&
(((~strong(paul)&generous(paul)))<=>((~strong(john)|~wise(john))))&
(![X]:((calm(X)<~>~calm(X))<=>(~tall(X)&curious(X))))&
(((kind(paul)&~quiet(paul)))<=>(?[X]:(~rich(X))))&
(((tall(fred)<~>~calm(fred)))<=>(?[X]:((old(X)&~tall(X)))))&
(![X]:((~quiet(X)&strong(X))=>(~curious(X)&~brave(X))))&
(![X]:(creative(X)<=>(~calm(X)&~patient(X))))&
(![X]:(generous(X)<=>(kind(X)|~humble(X))))&
(~kind(fred))&
((brave(john)|strong(john)))&
(?[X]:((~patient(X)<~>rich(X))))&
((~quiet(mary)<~>quiet(mary)))&
((~patient(john)|~creative(john)))&
((creative(paul)&~generous(paul)))&
(?[X]:(~funny(X)))&
((patient(lucy)&~funny(lucy))) | strong(paul) | [
"p4",
"p8",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 37111945769800284975562
% SZS output start Proof for 37111945769800284975562
5. ! [X0] : ((generous(X0) <~> ~old(X0)) => (old(X0) & ~humble(X0))) [input p4]
9. ! [X0] : ((old(X0) <~> ~curious(X0)) => strong(X0)) [input p8]
11. ! [X0] : ((calm(X0) <~> ~calm(X0)) <=> (curious(X0) & ~tall(X0))) [input p10]
22. ~generous(paul) & creative(paul) [input p21]
25. ~strong(paul) [input hypothesis]
31. ! [X0] : ((old(X0) & ~humble(X0)) | (generous(X0) <=> ~old(X0))) [ennf transformation 5]
35. ! [X0] : (strong(X0) | (old(X0) <=> ~curious(X0))) [ennf transformation 9]
43. ! [X0] : ((old(X0) & ~humble(X0)) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0)))) [nnf transformation 31]
50. ! [X0] : (strong(X0) | ((old(X0) | curious(X0)) & (~curious(X0) | ~old(X0)))) [nnf transformation 35]
53. ! [X0] : ((((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | (~curious(X0) | tall(X0))) & ((curious(X0) & ~tall(X0)) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0))))) [nnf transformation 11]
54. ! [X0] : ((((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | ~curious(X0) | tall(X0)) & ((curious(X0) & ~tall(X0)) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0))))) [flattening 53]
86. old(X0) | generous(X0) | old(X0) [cnf transformation 43]
98. ~curious(X0) | strong(X0) | ~old(X0) [cnf transformation 50]
107. curious(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 54]
108. curious(X0) | calm(X0) | calm(X0) [cnf transformation 54]
136. ~generous(paul) [cnf transformation 22]
140. ~strong(paul) [cnf transformation 25]
143. curious(X0) | ~calm(X0) [duplicate literal removal 107]
144. curious(X0) | calm(X0) [duplicate literal removal 108]
146. old(X0) | generous(X0) [duplicate literal removal 86]
171. 6 <=> generous(paul) [avatar definition]
173. ~generous(paul) <- (~6) [avatar component clause 171]
213. 14 <=> strong(paul) [avatar definition]
215. ~strong(paul) <- (~14) [avatar component clause 213]
219. curious(X0) [subsumption resolution 143,144]
266. ~6 [avatar split clause 136,171]
267. ~14 [avatar split clause 140,213]
309. ~old(X1) | strong(X1) [resolution 98,219]
312. strong(X0) | generous(X0) [resolution 309,146]
320. generous(paul) <- (~14) [resolution 312,215]
324. $false <- (~6, ~14) [subsumption resolution 320,173]
325. 6 | 14 [avatar contradiction clause 324]
326. $false [avatar sat refutation 266,267,325]
% SZS output end Proof for 37111945769800284975562
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble then john is not creative or patient.
Everyone who is patient is calm and vice versa.
If john is patient or humble then john is not patient.
If paul is either humble or not patient then someone is not calm.
If john is either not happy or rich then someone is old or not strong and vice versa.
Everyone who is not quiet or not happy is both not funny and rich and vice versa.
Everyone who is either not quiet or calm is both kind and not brave and vice versa.
Everyone who is either old or not strong is both patient and not happy and vice versa.
Everyone who is both not curious and rich is not strong.
Everyone who is both not calm and not quiet is both calm and not creative.
Everyone who is both not calm and curious is not funny or not quiet and vice versa.
If someone is not creative or strong then fred is quiet or humble.
If mary is either humble or happy then someone is not happy or humble and vice versa.
Everyone who is either quiet or tall is either not tall or brave and vice versa.
Everyone who is quiet or not rich is both quiet and not wise.
Someone is kind or funny.
Someone is rich or not kind.
Susan is not happy.
Someone is either strong or not tall.
Someone is either generous or not quiet.
Susan is not rich or old.
Mary is not kind or not tall. | John is funny. | entailment | ((?[X]:(~humble(X)))=>((~creative(john)|patient(john))))&
(![X]:(patient(X)<=>calm(X)))&
(((patient(john)|humble(john)))=>(~patient(john)))&
(((humble(paul)<~>~patient(paul)))=>(?[X]:(~calm(X))))&
(((~happy(john)<~>rich(john)))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((~quiet(X)|~happy(X))<=>(~funny(X)&rich(X))))&
(![X]:((~quiet(X)<~>calm(X))<=>(kind(X)&~brave(X))))&
(![X]:((old(X)<~>~strong(X))<=>(patient(X)&~happy(X))))&
(![X]:((~curious(X)&rich(X))=>~strong(X)))&
(![X]:((~calm(X)&~quiet(X))=>(calm(X)&~creative(X))))&
(![X]:((~calm(X)&curious(X))<=>(~funny(X)|~quiet(X))))&
((?[X]:((~creative(X)|strong(X))))=>((quiet(fred)|humble(fred))))&
(((humble(mary)<~>happy(mary)))<=>(?[X]:((~happy(X)|humble(X)))))&
(![X]:((quiet(X)<~>tall(X))<=>(~tall(X)<~>brave(X))))&
(![X]:((quiet(X)|~rich(X))=>(quiet(X)&~wise(X))))&
(?[X]:((kind(X)|funny(X))))&
(?[X]:((rich(X)|~kind(X))))&
(~happy(susan))&
(?[X]:((strong(X)<~>~tall(X))))&
(?[X]:((generous(X)<~>~quiet(X))))&
((~rich(susan)|old(susan)))&
((~kind(mary)|~tall(mary))) | funny(john) | [
"p4",
"p5",
"p9",
"p10",
"p17",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4516641789140019808341463
% SZS output start Proof for 4516641789140019808341463
5. (~happy(john) <~> rich(john)) <=> ? [X0] : (~strong(X0) | old(X0)) [input p4]
6. ! [X0] : ((~happy(X0) | ~quiet(X0)) <=> (rich(X0) & ~funny(X0))) [input p5]
10. ! [X0] : ((~quiet(X0) & ~calm(X0)) => (~creative(X0) & calm(X0))) [input p9]
11. ! [X0] : ((curious(X0) & ~calm(X0)) <=> (~quiet(X0) | ~funny(X0))) [input p10]
18. ~happy(susan) [input p17]
21. old(susan) | ~rich(susan) [input p20]
23. ~funny(john) [input hypothesis]
31. ! [X0] : ((~creative(X0) & calm(X0)) | (quiet(X0) | calm(X0))) [ennf transformation 10]
32. ! [X0] : ((~creative(X0) & calm(X0)) | quiet(X0) | calm(X0)) [flattening 31]
40. (((~rich(john) | happy(john)) & (rich(john) | ~happy(john))) | ! [X0] : (strong(X0) & ~old(X0))) & (? [X0] : (~strong(X0) | old(X0)) | ((~happy(john) | ~rich(john)) & (rich(john) | happy(john)))) [nnf transformation 5]
41. (((~rich(john) | happy(john)) & (rich(john) | ~happy(john))) | ! [X0] : (strong(X0) & ~old(X0))) & (? [X1] : (~strong(X1) | old(X1)) | ((~happy(john) | ~rich(john)) & (rich(john) | happy(john)))) [rectify 40]
42. ? [X1] : (~strong(X1) | old(X1)) => (~strong(sK1) | old(sK1)) [choice axiom]
43. (((~rich(john) | happy(john)) & (rich(john) | ~happy(john))) | ! [X0] : (strong(X0) & ~old(X0))) & ((~strong(sK1) | old(sK1)) | ((~happy(john) | ~rich(john)) & (rich(john) | happy(john)))) [skolemisation 41,42]
44. ! [X0] : (((~happy(X0) | ~quiet(X0)) | (~rich(X0) | funny(X0))) & ((rich(X0) & ~funny(X0)) | (happy(X0) & quiet(X0)))) [nnf transformation 6]
45. ! [X0] : ((~happy(X0) | ~quiet(X0) | ~rich(X0) | funny(X0)) & ((rich(X0) & ~funny(X0)) | (happy(X0) & quiet(X0)))) [flattening 44]
50. ! [X0] : (((curious(X0) & ~calm(X0)) | (quiet(X0) & funny(X0))) & ((~quiet(X0) | ~funny(X0)) | (~curious(X0) | calm(X0)))) [nnf transformation 11]
51. ! [X0] : (((curious(X0) & ~calm(X0)) | (quiet(X0) & funny(X0))) & (~quiet(X0) | ~funny(X0) | ~curious(X0) | calm(X0))) [flattening 50]
76. rich(john) | ~happy(john) | ~old(X0) [cnf transformation 43]
78. ~rich(john) | happy(john) | ~old(X0) [cnf transformation 43]
83. rich(X0) | happy(X0) [cnf transformation 45]
84. ~quiet(X0) | ~happy(X0) | ~rich(X0) | funny(X0) [cnf transformation 45]
98. calm(X0) | quiet(X0) | calm(X0) [cnf transformation 32]
101. ~calm(X0) | funny(X0) [cnf transformation 51]
125. ~happy(susan) [cnf transformation 18]
130. old(susan) | ~rich(susan) [cnf transformation 21]
132. ~funny(john) [cnf transformation 23]
137. quiet(X0) | calm(X0) [duplicate literal removal 98]
175. 9 <=> happy(john) [avatar definition]
176. ~happy(john) <- (~9) [avatar component clause 175]
177. happy(john) <- (9) [avatar component clause 175]
179. 10 <=> rich(john) [avatar definition]
180. rich(john) <- (10) [avatar component clause 179]
181. ~rich(john) <- (~10) [avatar component clause 179]
184. 11 <=> ! [X0] : ~old(X0) [avatar definition]
185. ~old(X0) <- (11) [avatar component clause 184]
186. 11 | 9 | ~10 [avatar split clause 78,179,175,184]
188. 11 | ~9 | 10 [avatar split clause 76,179,175,184]
262. 26 <=> rich(susan) [avatar definition]
264. ~rich(susan) <- (~26) [avatar component clause 262]
266. 27 <=> old(susan) [avatar definition]
268. old(susan) <- (27) [avatar component clause 266]
269. ~26 | 27 [avatar split clause 130,266,262]
279. happy(john) <- (~10) [resolution 83,181]
280. happy(susan) <- (~26) [resolution 83,264]
281. $false <- (~9, ~10) [subsumption resolution 279,176]
282. 9 | 10 [avatar contradiction clause 281]
283. $false <- (~26) [subsumption resolution 280,125]
284. 26 [avatar contradiction clause 283]
334. ~happy(X0) | ~rich(X0) | funny(X0) | calm(X0) [resolution 84,137]
337. ~rich(X0) | ~happy(X0) | funny(X0) [subsumption resolution 334,101]
406. ~happy(john) | funny(john) <- (10) [resolution 337,180]
408. funny(john) <- (9, 10) [subsumption resolution 406,177]
409. $false <- (9, 10) [subsumption resolution 408,132]
410. ~9 | ~10 [avatar contradiction clause 409]
426. $false <- (11, 27) [resolution 185,268]
429. ~11 | ~27 [avatar contradiction clause 426]
430. $false [avatar sat refutation 186,188,269,282,284,410,429]
% SZS output end Proof for 4516641789140019808341463
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is both tall and not calm.
If lucy is both not calm and not curious then alice is not old or humble and vice versa.
If fred is either not humble or calm then someone is either not funny or not generous.
Everyone who is quiet or not strong is both not rich and calm.
If fred is both not creative and generous then someone is either not rich or not generous and vice versa.
If lucy is both old and creative then someone is humble or rich.
Everyone who is not brave is not creative and vice versa.
If paul is not tall or not curious then fred is not creative and vice versa.
Everyone who is strong or calm is either not patient or wise and vice versa.
If someone is wise then someone is both happy and quiet and vice versa.
Everyone who is not creative is both brave and humble and vice versa.
Everyone who is either strong or not patient is not rich and vice versa.
If someone is funny or not quiet then someone is wise or not happy.
Everyone who is both not tall and not strong is both happy and not funny.
Everyone who is not creative is either quiet or not humble and vice versa.
If someone is not patient or kind then someone is either calm or curious.
Paul is quiet or not old.
John is tall or strong.
Someone is either not creative or calm.
Someone is both not wise and not generous.
John is both brave and not wise. | Paul is not happy. | entailment | (![X]:(patient(X)=>(tall(X)&~calm(X))))&
(((~calm(lucy)&~curious(lucy)))<=>((~old(alice)|humble(alice))))&
(((~humble(fred)<~>calm(fred)))=>(?[X]:((~funny(X)<~>~generous(X)))))&
(![X]:((quiet(X)|~strong(X))=>(~rich(X)&calm(X))))&
(((~creative(fred)&generous(fred)))<=>(?[X]:((~rich(X)<~>~generous(X)))))&
(((old(lucy)&creative(lucy)))=>(?[X]:((humble(X)|rich(X)))))&
(![X]:(~brave(X)<=>~creative(X)))&
(((~tall(paul)|~curious(paul)))<=>(~creative(fred)))&
(![X]:((strong(X)|calm(X))<=>(~patient(X)<~>wise(X))))&
((?[X]:(wise(X)))<=>(?[X]:((happy(X)&quiet(X)))))&
(![X]:(~creative(X)<=>(brave(X)&humble(X))))&
(![X]:((strong(X)<~>~patient(X))<=>~rich(X)))&
((?[X]:((funny(X)|~quiet(X))))=>(?[X]:((wise(X)|~happy(X)))))&
(![X]:((~tall(X)&~strong(X))=>(happy(X)&~funny(X))))&
(![X]:(~creative(X)<=>(quiet(X)<~>~humble(X))))&
((?[X]:((~patient(X)|kind(X))))=>(?[X]:((calm(X)<~>curious(X)))))&
((quiet(paul)|~old(paul)))&
((tall(john)|strong(john)))&
(?[X]:((~creative(X)<~>calm(X))))&
(?[X]:((~wise(X)&~generous(X))))&
((brave(john)&~wise(john))) | ~happy(paul) | [
"p0",
"p3",
"p6",
"p8",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 643126889639106043738488
% SZS output start Proof for 643126889639106043738488
1. ! [X0] : (patient(X0) => (~calm(X0) & tall(X0))) [input p0]
4. ! [X0] : ((~strong(X0) | quiet(X0)) => (calm(X0) & ~rich(X0))) [input p3]
7. ! [X0] : (~brave(X0) <=> ~creative(X0)) [input p6]
9. ! [X0] : ((calm(X0) | strong(X0)) <=> (~patient(X0) <~> wise(X0))) [input p8]
10. ? [X0] : wise(X0) <=> ? [X0] : (quiet(X0) & happy(X0)) [input p9]
11. ! [X0] : (~creative(X0) <=> (humble(X0) & brave(X0))) [input p10]
15. ! [X0] : (~creative(X0) <=> (quiet(X0) <~> ~humble(X0))) [input p14]
22. happy(paul) [input hypothesis]
23. ? [X0] : wise(X0) <=> ? [X1] : (quiet(X1) & happy(X1)) [rectify 10]
27. ! [X0] : ((~calm(X0) & tall(X0)) | ~patient(X0)) [ennf transformation 1]
29. ! [X0] : ((calm(X0) & ~rich(X0)) | (strong(X0) & ~quiet(X0))) [ennf transformation 4]
48. ! [X0] : ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0))) [nnf transformation 7]
51. ! [X0] : (((calm(X0) | strong(X0)) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) & (((~wise(X0) | patient(X0)) & (wise(X0) | ~patient(X0))) | (~calm(X0) & ~strong(X0)))) [nnf transformation 9]
52. ! [X0] : ((calm(X0) | strong(X0) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) & (((~wise(X0) | patient(X0)) & (wise(X0) | ~patient(X0))) | (~calm(X0) & ~strong(X0)))) [flattening 51]
53. (? [X0] : wise(X0) | ! [X1] : (~quiet(X1) | ~happy(X1))) & (? [X1] : (quiet(X1) & happy(X1)) | ! [X0] : ~wise(X0)) [nnf transformation 23]
54. (? [X0] : wise(X0) | ! [X1] : (~quiet(X1) | ~happy(X1))) & (? [X2] : (quiet(X2) & happy(X2)) | ! [X3] : ~wise(X3)) [rectify 53]
55. ? [X0] : wise(X0) => wise(sK3) [choice axiom]
56. ? [X2] : (quiet(X2) & happy(X2)) => (quiet(sK4) & happy(sK4)) [choice axiom]
57. (wise(sK3) | ! [X1] : (~quiet(X1) | ~happy(X1))) & ((quiet(sK4) & happy(sK4)) | ! [X3] : ~wise(X3)) [skolemisation 54,56,55]
58. ! [X0] : ((~creative(X0) | (~humble(X0) | ~brave(X0))) & ((humble(X0) & brave(X0)) | creative(X0))) [nnf transformation 11]
59. ! [X0] : ((~creative(X0) | ~humble(X0) | ~brave(X0)) & ((humble(X0) & brave(X0)) | creative(X0))) [flattening 58]
64. ! [X0] : ((~creative(X0) | ((quiet(X0) | humble(X0)) & (~humble(X0) | ~quiet(X0)))) & (((humble(X0) | ~quiet(X0)) & (~humble(X0) | quiet(X0))) | creative(X0))) [nnf transformation 15]
75. ~calm(X0) | ~patient(X0) [cnf transformation 27]
87. ~quiet(X0) | calm(X0) [cnf transformation 29]
96. ~creative(X0) | brave(X0) [cnf transformation 48]
97. ~brave(X0) | creative(X0) [cnf transformation 48]
104. ~wise(X0) | patient(X0) | ~calm(X0) [cnf transformation 52]
109. wise(sK3) | ~quiet(X1) | ~happy(X1) [cnf transformation 57]
110. brave(X0) | creative(X0) [cnf transformation 59]
112. ~creative(X0) | ~humble(X0) | ~brave(X0) [cnf transformation 59]
124. ~creative(X0) | quiet(X0) | humble(X0) [cnf transformation 64]
135. happy(paul) [cnf transformation 22]
233. ~wise(X0) | ~calm(X0) [subsumption resolution 104,75]
235. 21 <=> ! [X1] : (~quiet(X1) | ~happy(X1)) [avatar definition]
236. ~happy(X1) | ~quiet(X1) <- (21) [avatar component clause 235]
238. 22 <=> wise(sK3) [avatar definition]
240. wise(sK3) <- (22) [avatar component clause 238]
241. 21 | 22 [avatar split clause 109,238,235]
255. ~creative(X0) | ~humble(X0) [subsumption resolution 112,96]
256. creative(X0) [subsumption resolution 110,97]
275. quiet(X0) | humble(X0) [subsumption resolution 124,256]
290. 33 <=> quiet(paul) [avatar definition]
291. ~quiet(paul) <- (~33) [avatar component clause 290]
324. ~quiet(paul) <- (21) [resolution 236,135]
325. ~33 | ~21 [avatar split clause 324,235,290]
327. ~humble(X1) [resolution 255,256]
328. humble(X0) | calm(X0) [resolution 275,87]
329. humble(paul) <- (~33) [resolution 275,291]
330. calm(X0) [subsumption resolution 328,327]
331. $false <- (~33) [subsumption resolution 329,327]
332. 33 [avatar contradiction clause 331]
335. ~calm(sK3) <- (22) [resolution 240,233]
336. $false <- (22) [subsumption resolution 335,330]
337. ~22 [avatar contradiction clause 336]
338. $false [avatar sat refutation 241,325,332,337]
% SZS output end Proof for 643126889639106043738488
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is either curious or old then alice is either tall or happy.
Everyone who is not curious or not strong is not quiet and vice versa.
Everyone who is both brave and generous is either quiet or not calm and vice versa.
If someone is not happy then someone is both humble and not quiet.
Everyone who is both curious and generous is either calm or generous.
Everyone who is calm or not calm is not tall or curious.
Everyone who is creative or quiet is wise and vice versa.
Everyone who is not wise or creative is curious.
Everyone who is either quiet or not funny is either not generous or not calm.
Everyone who is both patient and not patient is not old.
Everyone who is not happy is both tall and calm and vice versa.
Everyone who is not wise or not kind is either strong or old.
If lucy is both wise and not tall then fred is not rich.
If susan is not strong then someone is not old or funny and vice versa.
Everyone who is not strong is not tall and vice versa.
If someone is rich then someone is tall or quiet.
Paul is either not funny or old.
Alice is both not generous and kind.
Someone is either wise or not kind.
Someone is either calm or old.
Alice is both not strong and happy.
Someone is either quiet or not strong.
Someone is both not tall and generous. | Alice is happy. | entailment | ((?[X]:((curious(X)<~>old(X))))=>((tall(alice)<~>happy(alice))))&
(![X]:((~curious(X)|~strong(X))<=>~quiet(X)))&
(![X]:((brave(X)&generous(X))<=>(quiet(X)<~>~calm(X))))&
((?[X]:(~happy(X)))=>(?[X]:((humble(X)&~quiet(X)))))&
(![X]:((curious(X)&generous(X))=>(calm(X)<~>generous(X))))&
(![X]:((calm(X)|~calm(X))=>(~tall(X)|curious(X))))&
(![X]:((creative(X)|quiet(X))<=>wise(X)))&
(![X]:((~wise(X)|creative(X))=>curious(X)))&
(![X]:((quiet(X)<~>~funny(X))=>(~generous(X)<~>~calm(X))))&
(![X]:((patient(X)&~patient(X))=>~old(X)))&
(![X]:(~happy(X)<=>(tall(X)&calm(X))))&
(![X]:((~wise(X)|~kind(X))=>(strong(X)<~>old(X))))&
(((wise(lucy)&~tall(lucy)))=>(~rich(fred)))&
((~strong(susan))<=>(?[X]:((~old(X)|funny(X)))))&
(![X]:(~strong(X)<=>~tall(X)))&
((?[X]:(rich(X)))=>(?[X]:((tall(X)|quiet(X)))))&
((~funny(paul)<~>old(paul)))&
((~generous(alice)&kind(alice)))&
(?[X]:((wise(X)<~>~kind(X))))&
(?[X]:((calm(X)<~>old(X))))&
((~strong(alice)&happy(alice)))&
(?[X]:((quiet(X)<~>~strong(X))))&
(?[X]:((~tall(X)&generous(X)))) | happy(alice) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4099138995540980564274333
% SZS output start Proof for 4099138995540980564274333
21. happy(alice) & ~strong(alice) [input p20]
24. ~happy(alice) [input hypothesis]
122. happy(alice) [cnf transformation 21]
127. ~happy(alice) [cnf transformation 24]
137. 3 <=> happy(alice) [avatar definition]
209. 3 [avatar split clause 122,137]
219. ~3 [avatar split clause 127,137]
220. $false [avatar sat refutation 209,219]
% SZS output end Proof for 4099138995540980564274333
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or funny is both old and not creative.
Everyone who is both old and patient is both not old and not strong.
Everyone who is not strong or not happy is both not happy and kind.
Everyone who is not kind or generous is calm and vice versa.
If john is both not quiet and tall then someone is tall or humble and vice versa.
Everyone who is curious or quiet is both funny and rich.
Everyone who is not patient is both not old and funny and vice versa.
Everyone who is not curious or calm is both not humble and kind and vice versa.
If john is humble then alice is either not rich or not quiet.
If john is both creative and funny then susan is either not quiet or brave and vice versa.
If mary is kind then paul is creative or curious and vice versa.
Everyone who is both not generous and not kind is both not happy and not creative.
If fred is both old and not humble then someone is either old or not tall and vice versa.
Everyone who is quiet is both humble and not creative and vice versa.
If paul is not creative or not strong then someone is strong and vice versa.
Everyone who is quiet is kind.
Someone is brave or strong.
Alice is wise.
Someone is not strong or not rich.
Someone is happy or not kind.
Mary is rich. | John is not generous. | neutral | (![X]:((~curious(X)<~>funny(X))=>(old(X)&~creative(X))))&
(![X]:((old(X)&patient(X))=>(~old(X)&~strong(X))))&
(![X]:((~strong(X)|~happy(X))=>(~happy(X)&kind(X))))&
(![X]:((~kind(X)|generous(X))<=>calm(X)))&
(((~quiet(john)&tall(john)))<=>(?[X]:((tall(X)|humble(X)))))&
(![X]:((curious(X)|quiet(X))=>(funny(X)&rich(X))))&
(![X]:(~patient(X)<=>(~old(X)&funny(X))))&
(![X]:((~curious(X)|calm(X))<=>(~humble(X)&kind(X))))&
((humble(john))=>((~rich(alice)<~>~quiet(alice))))&
(((creative(john)&funny(john)))<=>((~quiet(susan)<~>brave(susan))))&
((kind(mary))<=>((creative(paul)|curious(paul))))&
(![X]:((~generous(X)&~kind(X))=>(~happy(X)&~creative(X))))&
(((old(fred)&~humble(fred)))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:(quiet(X)<=>(humble(X)&~creative(X))))&
(((~creative(paul)|~strong(paul)))<=>(?[X]:(strong(X))))&
(![X]:(quiet(X)=>kind(X)))&
(?[X]:((brave(X)|strong(X))))&
(wise(alice))&
(?[X]:((~strong(X)|~rich(X))))&
(?[X]:((happy(X)|~kind(X))))&
(rich(mary)) | ~generous(john) | [] | null | 0 |
If someone is not brave or wise then lucy is both not patient and not old.
Everyone who is brave or not funny is not creative.
Everyone who is quiet is not wise or not patient.
Everyone who is both old and curious is wise and vice versa.
If someone is not generous or wise then someone is both not kind and calm and vice versa.
If someone is not funny or patient then mary is both patient and kind and vice versa.
Everyone who is both creative and generous is not creative or not quiet and vice versa.
If someone is humble then lucy is brave.
If alice is not old or rich then mary is wise.
Everyone who is not patient or old is both generous and not wise.
If lucy is both tall and not happy then someone is not old.
Everyone who is both not curious and creative is either not calm or not rich.
If someone is funny or rich then someone is both funny and not patient and vice versa.
If alice is generous then someone is funny or not funny.
Lucy is either strong or calm.
Someone is happy.
Paul is both happy and not wise.
Susan is rich or not curious.
John is kind.
Someone is both not curious and calm. | Lucy is not quiet. | entailment | ((?[X]:((~brave(X)|wise(X))))=>((~patient(lucy)&~old(lucy))))&
(![X]:((brave(X)|~funny(X))=>~creative(X)))&
(![X]:(quiet(X)=>(~wise(X)|~patient(X))))&
(![X]:((old(X)&curious(X))<=>wise(X)))&
((?[X]:((~generous(X)|wise(X))))<=>(?[X]:((~kind(X)&calm(X)))))&
((?[X]:((~funny(X)|patient(X))))<=>((patient(mary)&kind(mary))))&
(![X]:((creative(X)&generous(X))<=>(~creative(X)|~quiet(X))))&
((?[X]:(humble(X)))=>(brave(lucy)))&
(((~old(alice)|rich(alice)))=>(wise(mary)))&
(![X]:((~patient(X)|old(X))=>(generous(X)&~wise(X))))&
(((tall(lucy)&~happy(lucy)))=>(?[X]:(~old(X))))&
(![X]:((~curious(X)&creative(X))=>(~calm(X)<~>~rich(X))))&
((?[X]:((funny(X)|rich(X))))<=>(?[X]:((funny(X)&~patient(X)))))&
((generous(alice))=>(?[X]:((funny(X)|~funny(X)))))&
((strong(lucy)<~>calm(lucy)))&
(?[X]:(happy(X)))&
((happy(paul)&~wise(paul)))&
((rich(susan)|~curious(susan)))&
(kind(john))&
(?[X]:((~curious(X)&calm(X)))) | ~quiet(lucy) | [
"p0",
"p1",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1600366067923004637566961
% SZS output start Proof for 1600366067923004637566961
1. ? [X0] : (wise(X0) | ~brave(X0)) => (~old(lucy) & ~patient(lucy)) [input p0]
2. ! [X0] : ((~funny(X0) | brave(X0)) => ~creative(X0)) [input p1]
7. ! [X0] : ((generous(X0) & creative(X0)) <=> (~quiet(X0) | ~creative(X0))) [input p6]
10. ! [X0] : ((old(X0) | ~patient(X0)) => (~wise(X0) & generous(X0))) [input p9]
21. quiet(lucy) [input hypothesis]
28. (~old(lucy) & ~patient(lucy)) | ! [X0] : (~wise(X0) & brave(X0)) [ennf transformation 1]
29. ! [X0] : (~creative(X0) | (funny(X0) & ~brave(X0))) [ennf transformation 2]
33. ! [X0] : ((~wise(X0) & generous(X0)) | (~old(X0) & patient(X0))) [ennf transformation 10]
49. ! [X0] : (((generous(X0) & creative(X0)) | (quiet(X0) & creative(X0))) & ((~quiet(X0) | ~creative(X0)) | (~generous(X0) | ~creative(X0)))) [nnf transformation 7]
50. ! [X0] : (((generous(X0) & creative(X0)) | (quiet(X0) & creative(X0))) & (~quiet(X0) | ~creative(X0) | ~generous(X0) | ~creative(X0))) [flattening 49]
62. ~patient(lucy) | brave(X0) [cnf transformation 28]
66. ~creative(X0) | ~brave(X0) [cnf transformation 29]
82. ~quiet(X0) | ~creative(X0) | ~generous(X0) | ~creative(X0) [cnf transformation 50]
83. creative(X0) | creative(X0) [cnf transformation 50]
89. generous(X0) | patient(X0) [cnf transformation 33]
108. quiet(lucy) [cnf transformation 21]
109. ~quiet(X0) | ~creative(X0) | ~generous(X0) [duplicate literal removal 82]
110. creative(X0) [duplicate literal removal 83]
120. 3 <=> ! [X0] : brave(X0) [avatar definition]
121. brave(X0) <- (3) [avatar component clause 120]
124. 4 <=> patient(lucy) [avatar definition]
128. 3 | ~4 [avatar split clause 62,124,120]
183. ~generous(X0) | ~quiet(X0) [subsumption resolution 109,110]
253. ~brave(X0) [resolution 66,110]
264. ~quiet(X0) | patient(X0) [resolution 183,89]
278. patient(lucy) [resolution 264,108]
283. 4 [avatar split clause 278,124]
284. $false <- (3) [subsumption resolution 121,253]
285. ~3 [avatar contradiction clause 284]
286. $false [avatar sat refutation 128,283,285]
% SZS output end Proof for 1600366067923004637566961
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is curious and vice versa.
If lucy is not quiet then someone is curious or quiet and vice versa.
Everyone who is either curious or patient is both not happy and creative and vice versa.
If someone is either calm or funny then someone is quiet or not humble and vice versa.
If lucy is calm then paul is wise.
Everyone who is not humble or not rich is not funny or funny.
If paul is quiet then someone is both tall and not happy.
Everyone who is old is both not wise and not quiet.
Everyone who is both not humble and curious is either creative or not creative and vice versa.
If lucy is either calm or not patient then someone is not old or not strong.
Everyone who is both creative and strong is both tall and not strong and vice versa.
Everyone who is either not generous or humble is both kind and not rich.
If someone is not curious or quiet then susan is either not rich or not calm.
Everyone who is not tall or old is both creative and funny.
Everyone who is both not tall and not curious is humble and vice versa.
Someone is both generous and not calm.
Someone is either not funny or not wise.
Someone is either generous or not curious.
Alice is not rich.
Mary is both old and calm.
Someone is both patient and generous.
Fred is not kind. | Alice is tall. | contradiction | (![X]:(old(X)<=>curious(X)))&
((~quiet(lucy))<=>(?[X]:((curious(X)|quiet(X)))))&
(![X]:((curious(X)<~>patient(X))<=>(~happy(X)&creative(X))))&
((?[X]:((calm(X)<~>funny(X))))<=>(?[X]:((quiet(X)|~humble(X)))))&
((calm(lucy))=>(wise(paul)))&
(![X]:((~humble(X)|~rich(X))=>(~funny(X)|funny(X))))&
((quiet(paul))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:(old(X)=>(~wise(X)&~quiet(X))))&
(![X]:((~humble(X)&curious(X))<=>(creative(X)<~>~creative(X))))&
(((calm(lucy)<~>~patient(lucy)))=>(?[X]:((~old(X)|~strong(X)))))&
(![X]:((creative(X)&strong(X))<=>(tall(X)&~strong(X))))&
(![X]:((~generous(X)<~>humble(X))=>(kind(X)&~rich(X))))&
((?[X]:((~curious(X)|quiet(X))))=>((~rich(susan)<~>~calm(susan))))&
(![X]:((~tall(X)|old(X))=>(creative(X)&funny(X))))&
(![X]:((~tall(X)&~curious(X))<=>humble(X)))&
(?[X]:((generous(X)&~calm(X))))&
(?[X]:((~funny(X)<~>~wise(X))))&
(?[X]:((generous(X)<~>~curious(X))))&
(~rich(alice))&
((old(mary)&calm(mary)))&
(?[X]:((patient(X)&generous(X))))&
(~kind(fred)) | tall(alice) | [
"p0",
"p8",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7813785021496265235117663
% SZS output start Proof for 7813785021496265235117663
1. ! [X0] : (old(X0) <=> curious(X0)) [input p0]
9. ! [X0] : ((curious(X0) & ~humble(X0)) <=> (creative(X0) <~> ~creative(X0))) [input p8]
11. ! [X0] : ((strong(X0) & creative(X0)) <=> (~strong(X0) & tall(X0))) [input p10]
14. ! [X0] : ((old(X0) | ~tall(X0)) => (funny(X0) & creative(X0))) [input p13]
23. tall(alice) [input hypothesis]
33. ! [X0] : ((funny(X0) & creative(X0)) | (~old(X0) & tall(X0))) [ennf transformation 14]
34. ! [X0] : ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0))) [nnf transformation 1]
48. ! [X0] : (((curious(X0) & ~humble(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | (~curious(X0) | humble(X0)))) [nnf transformation 9]
49. ! [X0] : (((curious(X0) & ~humble(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | ~curious(X0) | humble(X0))) [flattening 48]
53. ! [X0] : (((strong(X0) & creative(X0)) | (strong(X0) | ~tall(X0))) & ((~strong(X0) & tall(X0)) | (~strong(X0) | ~creative(X0)))) [nnf transformation 11]
54. ! [X0] : (((strong(X0) & creative(X0)) | strong(X0) | ~tall(X0)) & ((~strong(X0) & tall(X0)) | ~strong(X0) | ~creative(X0))) [flattening 53]
70. ~curious(X0) | old(X0) [cnf transformation 34]
97. curious(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 49]
98. curious(X0) | creative(X0) | creative(X0) [cnf transformation 49]
102. ~strong(X0) | ~strong(X0) | ~creative(X0) [cnf transformation 54]
104. strong(X0) | strong(X0) | ~tall(X0) [cnf transformation 54]
114. ~old(X0) | creative(X0) [cnf transformation 33]
132. tall(alice) [cnf transformation 23]
133. ~strong(X0) | ~creative(X0) [duplicate literal removal 102]
134. ~tall(X0) | strong(X0) [duplicate literal removal 104]
137. curious(X0) | ~creative(X0) [duplicate literal removal 97]
138. curious(X0) | creative(X0) [duplicate literal removal 98]
214. curious(X0) [subsumption resolution 137,138]
254. old(X0) [resolution 70,214]
259. creative(X0) [resolution 114,254]
264. strong(alice) [resolution 134,132]
267. ~creative(alice) [resolution 264,133]
268. $false [subsumption resolution 267,259]
% SZS output end Proof for 7813785021496265235117663
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is both wise and generous then mary is calm or curious.
If someone is either wise or not generous then someone is either not wise or not humble.
Everyone who is calm or wise is either calm or not tall and vice versa.
Everyone who is both tall and calm is not happy or not creative.
If someone is both humble and kind then someone is either not creative or not rich.
Everyone who is either not humble or generous is quiet or patient.
If mary is generous then someone is both funny and not happy.
If someone is both happy and not rich then fred is not old or strong and vice versa.
Everyone who is both wise and not old is both not wise and not generous.
If lucy is funny or not creative then someone is old or creative.
Everyone who is funny is not humble or old and vice versa.
Everyone who is not happy is tall or not strong and vice versa.
Everyone who is not tall is not humble or funny.
If paul is both rich and not strong then lucy is both old and tall and vice versa.
If paul is both old and not quiet then someone is either not strong or happy.
Everyone who is curious is both old and curious and vice versa.
Alice is not old or generous.
Someone is generous.
Someone is both not funny and not kind.
Someone is both not rich and not creative.
Alice is strong.
Someone is not strong or calm.
John is not patient or tall.
Lucy is either tall or not curious. | Lucy is not old. | contradiction | (((wise(john)&generous(john)))=>((calm(mary)|curious(mary))))&
((?[X]:((wise(X)<~>~generous(X))))=>(?[X]:((~wise(X)<~>~humble(X)))))&
(![X]:((calm(X)|wise(X))<=>(calm(X)<~>~tall(X))))&
(![X]:((tall(X)&calm(X))=>(~happy(X)|~creative(X))))&
((?[X]:((humble(X)&kind(X))))=>(?[X]:((~creative(X)<~>~rich(X)))))&
(![X]:((~humble(X)<~>generous(X))=>(quiet(X)|patient(X))))&
((generous(mary))=>(?[X]:((funny(X)&~happy(X)))))&
((?[X]:((happy(X)&~rich(X))))<=>((~old(fred)|strong(fred))))&
(![X]:((wise(X)&~old(X))=>(~wise(X)&~generous(X))))&
(((funny(lucy)|~creative(lucy)))=>(?[X]:((old(X)|creative(X)))))&
(![X]:(funny(X)<=>(~humble(X)|old(X))))&
(![X]:(~happy(X)<=>(tall(X)|~strong(X))))&
(![X]:(~tall(X)=>(~humble(X)|funny(X))))&
(((rich(paul)&~strong(paul)))<=>((old(lucy)&tall(lucy))))&
(((old(paul)&~quiet(paul)))=>(?[X]:((~strong(X)<~>happy(X)))))&
(![X]:(curious(X)<=>(old(X)&curious(X))))&
((~old(alice)|generous(alice)))&
(?[X]:(generous(X)))&
(?[X]:((~funny(X)&~kind(X))))&
(?[X]:((~rich(X)&~creative(X))))&
(strong(alice))&
(?[X]:((~strong(X)|calm(X))))&
((~patient(john)|tall(john)))&
((tall(lucy)<~>~curious(lucy))) | ~old(lucy) | [
"p2",
"p8",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7345729113701166036295848
% SZS output start Proof for 7345729113701166036295848
3. ! [X0] : ((wise(X0) | calm(X0)) <=> (calm(X0) <~> ~tall(X0))) [input p2]
9. ! [X0] : ((~old(X0) & wise(X0)) => (~generous(X0) & ~wise(X0))) [input p8]
16. ! [X0] : (curious(X0) <=> (curious(X0) & old(X0))) [input p15]
24. tall(lucy) <~> ~curious(lucy) [input p23]
25. ~old(lucy) [input hypothesis]
39. ! [X0] : ((~generous(X0) & ~wise(X0)) | (old(X0) | ~wise(X0))) [ennf transformation 9]
40. ! [X0] : ((~generous(X0) & ~wise(X0)) | old(X0) | ~wise(X0)) [flattening 39]
48. ! [X0] : (((wise(X0) | calm(X0)) | ((calm(X0) | tall(X0)) & (~tall(X0) | ~calm(X0)))) & (((tall(X0) | ~calm(X0)) & (~tall(X0) | calm(X0))) | (~wise(X0) & ~calm(X0)))) [nnf transformation 3]
49. ! [X0] : ((wise(X0) | calm(X0) | ((calm(X0) | tall(X0)) & (~tall(X0) | ~calm(X0)))) & (((tall(X0) | ~calm(X0)) & (~tall(X0) | calm(X0))) | (~wise(X0) & ~calm(X0)))) [flattening 48]
65. ! [X0] : ((curious(X0) | (~curious(X0) | ~old(X0))) & ((curious(X0) & old(X0)) | ~curious(X0))) [nnf transformation 16]
66. ! [X0] : ((curious(X0) | ~curious(X0) | ~old(X0)) & ((curious(X0) & old(X0)) | ~curious(X0))) [flattening 65]
75. (curious(lucy) | ~tall(lucy)) & (~curious(lucy) | tall(lucy)) [nnf transformation 24]
83. tall(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 49]
86. wise(X0) | calm(X0) | calm(X0) | tall(X0) [cnf transformation 49]
95. ~wise(X0) | old(X0) | ~wise(X0) [cnf transformation 40]
110. ~curious(X0) | old(X0) [cnf transformation 66]
121. curious(lucy) | ~tall(lucy) [cnf transformation 75]
122. ~old(lucy) [cnf transformation 25]
123. ~wise(X0) | old(X0) [duplicate literal removal 95]
124. ~calm(X0) | tall(X0) [duplicate literal removal 83]
125. tall(X0) | calm(X0) | wise(X0) [duplicate literal removal 86]
220. 21 <=> old(lucy) [avatar definition]
222. ~old(lucy) <- (~21) [avatar component clause 220]
224. 22 <=> tall(lucy) [avatar definition]
226. ~tall(lucy) <- (~22) [avatar component clause 224]
258. 29 <=> curious(lucy) [avatar definition]
260. curious(lucy) <- (29) [avatar component clause 258]
261. ~22 | 29 [avatar split clause 121,258,224]
263. ~21 [avatar split clause 122,220]
273. old(lucy) <- (29) [resolution 260,110]
274. $false <- (~21, 29) [subsumption resolution 273,222]
275. 21 | ~29 [avatar contradiction clause 274]
315. calm(lucy) | wise(lucy) <- (~22) [resolution 125,226]
328. 38 <=> wise(lucy) [avatar definition]
330. wise(lucy) <- (38) [avatar component clause 328]
332. 39 <=> calm(lucy) [avatar definition]
334. calm(lucy) <- (39) [avatar component clause 332]
335. 38 | 39 | 22 [avatar split clause 315,224,332,328]
365. old(lucy) <- (38) [resolution 330,123]
366. $false <- (~21, 38) [subsumption resolution 365,222]
367. 21 | ~38 [avatar contradiction clause 366]
369. tall(lucy) <- (39) [resolution 334,124]
370. $false <- (~22, 39) [subsumption resolution 369,226]
371. 22 | ~39 [avatar contradiction clause 370]
372. $false [avatar sat refutation 261,263,275,335,367,371]
% SZS output end Proof for 7345729113701166036295848
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or generous is both tall and wise and vice versa.
Everyone who is either not calm or not quiet is either not calm or patient.
If someone is creative or rich then someone is funny or tall and vice versa.
If someone is not strong then mary is not kind or tall.
If someone is either rich or not wise then paul is strong.
If john is either not old or not happy then lucy is not wise or not patient.
Everyone who is either not strong or not patient is not patient.
Everyone who is rich or curious is not wise and vice versa.
Everyone who is creative or quiet is strong or brave.
Everyone who is both old and rich is quiet or not funny.
Everyone who is funny or quiet is both kind and wise and vice versa.
If someone is both not patient and not tall then paul is either humble or not creative and vice versa.
Everyone who is both kind and wise is either generous or happy.
If alice is kind then someone is humble and vice versa.
Everyone who is not patient is both funny and not humble and vice versa.
Someone is either not strong or quiet.
Paul is not patient.
Someone is either patient or tall.
Mary is either not patient or not curious.
Someone is not brave.
Someone is not old.
Mary is not happy or not quiet. | Paul is happy. | neutral | (![X]:((rich(X)|generous(X))<=>(tall(X)&wise(X))))&
(![X]:((~calm(X)<~>~quiet(X))=>(~calm(X)<~>patient(X))))&
((?[X]:((creative(X)|rich(X))))<=>(?[X]:((funny(X)|tall(X)))))&
((?[X]:(~strong(X)))=>((~kind(mary)|tall(mary))))&
((?[X]:((rich(X)<~>~wise(X))))=>(strong(paul)))&
(((~old(john)<~>~happy(john)))=>((~wise(lucy)|~patient(lucy))))&
(![X]:((~strong(X)<~>~patient(X))=>~patient(X)))&
(![X]:((rich(X)|curious(X))<=>~wise(X)))&
(![X]:((creative(X)|quiet(X))=>(strong(X)|brave(X))))&
(![X]:((old(X)&rich(X))=>(quiet(X)|~funny(X))))&
(![X]:((funny(X)|quiet(X))<=>(kind(X)&wise(X))))&
((?[X]:((~patient(X)&~tall(X))))<=>((humble(paul)<~>~creative(paul))))&
(![X]:((kind(X)&wise(X))=>(generous(X)<~>happy(X))))&
((kind(alice))<=>(?[X]:(humble(X))))&
(![X]:(~patient(X)<=>(funny(X)&~humble(X))))&
(?[X]:((~strong(X)<~>quiet(X))))&
(~patient(paul))&
(?[X]:((patient(X)<~>tall(X))))&
((~patient(mary)<~>~curious(mary)))&
(?[X]:(~brave(X)))&
(?[X]:(~old(X)))&
((~happy(mary)|~quiet(mary))) | happy(paul) | [] | null | 0 |
Everyone who is not generous is both not tall and curious and vice versa. Everyone who is both not quiet and not patient is rich. Everyone who is both humble and not rich is not strong or not funny and vice versa. Everyone who is old is not strong or not patient. Everyone who is both not wise and kind is either rich or not funny and vice versa. Everyone who is either not old or creative is both not generous and generous and vice versa. Everyone who is old or funny is both calm and quiet and vice versa. If someone is both not calm and tall then john is both not calm and wise and vice versa. Everyone who is funny or not wise is curious. If someone is both quiet and kind then someone is not calm or not humble. If someone is both tall and not generous then susan is both quiet and humble. Everyone who is not brave is not patient. Everyone who is not patient is both not tall and not curious and vice versa. If someone is not strong or not creative then lucy is creative and vice versa. If someone is happy then someone is both not calm and creative and vice versa. If fred is not tall then someone is not creative or happy and vice versa. Susan is not funny. John is either brave or not rich. Susan is not strong. Someone is quiet or not generous. Lucy is not generous or kind. Someone is both not strong and not funny. | Susan is brave. | entailment | (![X]:(~generous(X)<=>(~tall(X)&curious(X))))&
(![X]:((~quiet(X)&~patient(X))=>rich(X)))&
(![X]:((humble(X)&~rich(X))<=>(~strong(X)|~funny(X))))&
(![X]:(old(X)=>(~strong(X)|~patient(X))))&
(![X]:((~wise(X)&kind(X))<=>(rich(X)<~>~funny(X))))&
(![X]:((~old(X)<~>creative(X))<=>(~generous(X)&generous(X))))&
(![X]:((old(X)|funny(X))<=>(calm(X)&quiet(X))))&
((?[X]:((~calm(X)&tall(X))))<=>((~calm(john)&wise(john))))&
(![X]:((funny(X)|~wise(X))=>curious(X)))&
((?[X]:((quiet(X)&kind(X))))=>(?[X]:((~calm(X)|~humble(X)))))&
((?[X]:((tall(X)&~generous(X))))=>((quiet(susan)&humble(susan))))&
(![X]:(~brave(X)=>~patient(X)))&
(![X]:(~patient(X)<=>(~tall(X)&~curious(X))))&
((?[X]:((~strong(X)|~creative(X))))<=>(creative(lucy)))&
((?[X]:(happy(X)))<=>(?[X]:((~calm(X)&creative(X)))))&
((~tall(fred))<=>(?[X]:((~creative(X)|happy(X)))))&
(~funny(susan))&
((brave(john)<~>~rich(john)))&
(~strong(susan))&
(?[X]:((quiet(X)|~generous(X))))&
((~generous(lucy)|kind(lucy)))&
(?[X]:((~strong(X)&~funny(X)))) | brave(susan) | [
"p2",
"p4",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5598656537234621173206234
% SZS output start Proof for 5598656537234621173206234
3. ! [X0] : ((~rich(X0) & humble(X0)) <=> (~funny(X0) | ~strong(X0))) [input p2]
5. ! [X0] : ((kind(X0) & ~wise(X0)) <=> (rich(X0) <~> ~funny(X0))) [input p4]
9. ! [X0] : ((~wise(X0) | funny(X0)) => curious(X0)) [input p8]
12. ! [X0] : (~brave(X0) => ~patient(X0)) [input p11]
13. ! [X0] : (~patient(X0) <=> (~curious(X0) & ~tall(X0))) [input p12]
23. ~brave(susan) [input hypothesis]
30. ! [X0] : (curious(X0) | (wise(X0) & ~funny(X0))) [ennf transformation 9]
33. ! [X0] : (~patient(X0) | brave(X0)) [ennf transformation 12]
36. ! [X0] : (((~rich(X0) & humble(X0)) | (funny(X0) & strong(X0))) & ((~funny(X0) | ~strong(X0)) | (rich(X0) | ~humble(X0)))) [nnf transformation 3]
37. ! [X0] : (((~rich(X0) & humble(X0)) | (funny(X0) & strong(X0))) & (~funny(X0) | ~strong(X0) | rich(X0) | ~humble(X0))) [flattening 36]
38. ! [X0] : (((kind(X0) & ~wise(X0)) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0)))) & (((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | (~kind(X0) | wise(X0)))) [nnf transformation 5]
39. ! [X0] : (((kind(X0) & ~wise(X0)) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0)))) & (((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | ~kind(X0) | wise(X0))) [flattening 38]
52. ! [X0] : ((~patient(X0) | (curious(X0) | tall(X0))) & ((~curious(X0) & ~tall(X0)) | patient(X0))) [nnf transformation 13]
53. ! [X0] : ((~patient(X0) | curious(X0) | tall(X0)) & ((~curious(X0) & ~tall(X0)) | patient(X0))) [flattening 52]
80. ~rich(X0) | funny(X0) [cnf transformation 37]
85. ~wise(X0) | rich(X0) | funny(X0) [cnf transformation 39]
103. ~funny(X0) | curious(X0) [cnf transformation 30]
104. wise(X0) | curious(X0) [cnf transformation 30]
108. ~patient(X0) | brave(X0) [cnf transformation 33]
110. ~curious(X0) | patient(X0) [cnf transformation 53]
129. ~brave(susan) [cnf transformation 23]
132. ~wise(X0) | funny(X0) [subsumption resolution 85,80]
269. funny(X0) | curious(X0) [resolution 132,104]
270. curious(X0) [subsumption resolution 269,103]
279. patient(X0) [resolution 270,110]
304. brave(X0) [resolution 279,108]
316. $false [resolution 304,129]
% SZS output end Proof for 5598656537234621173206234
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and not strong is both not humble and not strong.
Everyone who is either not wise or not generous is not rich.
Everyone who is patient is not calm or humble.
Everyone who is both not brave and creative is both funny and humble.
If someone is both not humble and creative then someone is not quiet or patient.
Everyone who is calm is both happy and tall.
Everyone who is either wise or kind is quiet and vice versa.
Everyone who is both not old and rich is either quiet or calm.
Everyone who is either calm or happy is humble or wise 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.
Lucy is either old or not creative.
Someone is humble or not kind.
Someone is generous or patient.
Someone is brave.
Someone is patient or not humble. | Fred is generous. | contradiction | (![X]:((happy(X)&~strong(X))=>(~humble(X)&~strong(X))))&
(![X]:((~wise(X)<~>~generous(X))=>~rich(X)))&
(![X]:(patient(X)=>(~calm(X)|humble(X))))&
(![X]:((~brave(X)&creative(X))=>(funny(X)&humble(X))))&
((?[X]:((~humble(X)&creative(X))))=>(?[X]:((~quiet(X)|patient(X)))))&
(![X]:(calm(X)=>(happy(X)&tall(X))))&
(![X]:((wise(X)<~>kind(X))<=>quiet(X)))&
(![X]:((~old(X)&rich(X))=>(quiet(X)<~>calm(X))))&
(![X]:((calm(X)<~>happy(X))<=>(humble(X)|wise(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(lucy)<~>~creative(lucy)))&
(?[X]:((humble(X)|~kind(X))))&
(?[X]:((generous(X)|patient(X))))&
(?[X]:(brave(X)))&
(?[X]:((patient(X)|~humble(X)))) | generous(fred) | [
"p5",
"p9",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 866718204134082408279712
% SZS output start Proof for 866718204134082408279712
6. ! [X0] : (calm(X0) => (tall(X0) & happy(X0))) [input p5]
10. ! [X0] : ((~generous(X0) <~> ~calm(X0)) <=> (~funny(X0) | ~brave(X0))) [input p9]
11. ! [X0] : ((~curious(X0) | happy(X0)) <=> ~happy(X0)) [input p10]
14. ! [X0] : (happy(X0) <=> (~brave(X0) | ~old(X0))) [input p13]
15. ! [X0] : ((~tall(X0) <~> ~funny(X0)) <=> ~tall(X0)) [input p14]
22. generous(fred) [input hypothesis]
34. ! [X0] : ((tall(X0) & happy(X0)) | ~calm(X0)) [ennf transformation 6]
42. ! [X0] : ((((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | (funny(X0) & brave(X0))) & ((~funny(X0) | ~brave(X0)) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0))))) [nnf transformation 10]
43. ! [X0] : ((((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | (funny(X0) & brave(X0))) & (~funny(X0) | ~brave(X0) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0))))) [flattening 42]
44. ! [X0] : (((~curious(X0) | happy(X0)) | happy(X0)) & (~happy(X0) | (curious(X0) & ~happy(X0)))) [nnf transformation 11]
45. ! [X0] : ((~curious(X0) | happy(X0) | happy(X0)) & (~happy(X0) | (curious(X0) & ~happy(X0)))) [flattening 44]
52. ! [X0] : ((happy(X0) | (brave(X0) & old(X0))) & ((~brave(X0) | ~old(X0)) | ~happy(X0))) [nnf transformation 14]
53. ! [X0] : ((happy(X0) | (brave(X0) & old(X0))) & (~brave(X0) | ~old(X0) | ~happy(X0))) [flattening 52]
54. ! [X0] : ((((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | tall(X0)) & (~tall(X0) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0))))) [nnf transformation 15]
73. ~calm(X0) | happy(X0) [cnf transformation 34]
86. ~funny(X0) | ~brave(X0) | ~generous(X0) | calm(X0) [cnf transformation 43]
91. ~happy(X0) | ~happy(X0) [cnf transformation 45]
102. happy(X0) | brave(X0) [cnf transformation 53]
104. ~tall(X0) | ~tall(X0) | funny(X0) [cnf transformation 54]
106. funny(X0) | tall(X0) | tall(X0) [cnf transformation 54]
114. generous(fred) [cnf transformation 22]
115. ~tall(X0) | funny(X0) [duplicate literal removal 104]
116. tall(X0) | funny(X0) [duplicate literal removal 106]
117. ~happy(X0) [duplicate literal removal 91]
146. 6 <=> ! [X0] : funny(X0) [avatar definition]
147. funny(X0) <- (6) [avatar component clause 146]
171. brave(X0) [subsumption resolution 102,117]
173. funny(X0) [subsumption resolution 115,116]
174. 6 [avatar split clause 173,146]
219. ~brave(X1) | ~generous(X1) | calm(X1) <- (6) [resolution 86,147]
221. ~generous(X1) | calm(X1) <- (6) [subsumption resolution 219,171]
222. calm(fred) <- (6) [resolution 221,114]
225. happy(fred) <- (6) [resolution 222,73]
241. $false <- (6) [subsumption resolution 225,117]
242. ~6 [avatar contradiction clause 241]
245. $false [avatar sat refutation 174,242]
% SZS output end Proof for 866718204134082408279712
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and not rich is either creative or kind.
If susan is tall then someone is both not tall and rich and vice versa.
If lucy is calm then fred is not kind or not curious and vice versa.
If someone is calm then someone is both not funny and curious.
Everyone who is quiet or not creative is not kind or calm.
Everyone who is not old is both generous and calm.
If someone is not curious or not humble then paul is either patient or not quiet.
Everyone who is both not humble and not generous is either not rich or not old and vice versa.
If someone is both not quiet and not brave then someone is both not wise and not quiet and vice versa.
If someone is generous or tall then alice is strong and vice versa.
Everyone who is not happy is brave or humble.
Everyone who is not happy or not funny is both creative and quiet.
If someone is not creative or quiet then someone is both wise and not wise.
Everyone who is not patient is both not kind and happy and vice versa.
If someone is either brave or wise then susan is both brave and not strong and vice versa.
If someone is either kind or happy then someone is both not kind and not creative and vice versa.
Alice is not tall or not old.
Someone is not calm or funny.
Mary is not rich or curious.
Paul is patient or not calm.
Someone is wise or not curious.
Someone is not happy or not generous. | Susan is curious. | entailment | (![X]:((~curious(X)&~rich(X))=>(creative(X)<~>kind(X))))&
((tall(susan))<=>(?[X]:((~tall(X)&rich(X)))))&
((calm(lucy))<=>((~kind(fred)|~curious(fred))))&
((?[X]:(calm(X)))=>(?[X]:((~funny(X)&curious(X)))))&
(![X]:((quiet(X)|~creative(X))=>(~kind(X)|calm(X))))&
(![X]:(~old(X)=>(generous(X)&calm(X))))&
((?[X]:((~curious(X)|~humble(X))))=>((patient(paul)<~>~quiet(paul))))&
(![X]:((~humble(X)&~generous(X))<=>(~rich(X)<~>~old(X))))&
((?[X]:((~quiet(X)&~brave(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
((?[X]:((generous(X)|tall(X))))<=>(strong(alice)))&
(![X]:(~happy(X)=>(brave(X)|humble(X))))&
(![X]:((~happy(X)|~funny(X))=>(creative(X)&quiet(X))))&
((?[X]:((~creative(X)|quiet(X))))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:(~patient(X)<=>(~kind(X)&happy(X))))&
((?[X]:((brave(X)<~>wise(X))))<=>((brave(susan)&~strong(susan))))&
((?[X]:((kind(X)<~>happy(X))))<=>(?[X]:((~kind(X)&~creative(X)))))&
((~tall(alice)|~old(alice)))&
(?[X]:((~calm(X)|funny(X))))&
((~rich(mary)|curious(mary)))&
((patient(paul)|~calm(paul)))&
(?[X]:((wise(X)|~curious(X))))&
(?[X]:((~happy(X)|~generous(X)))) | curious(susan) | [
"p6",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6076739985011534178556313
% SZS output start Proof for 6076739985011534178556313
7. ? [X0] : (~humble(X0) | ~curious(X0)) => (patient(paul) <~> ~quiet(paul)) [input p6]
13. ? [X0] : (quiet(X0) | ~creative(X0)) => ? [X0] : (~wise(X0) & wise(X0)) [input p12]
14. ! [X0] : (~patient(X0) <=> (happy(X0) & ~kind(X0))) [input p13]
16. ? [X0] : (kind(X0) <~> happy(X0)) <=> ? [X0] : (~creative(X0) & ~kind(X0)) [input p15]
23. ~curious(susan) [input hypothesis]
26. ? [X0] : (quiet(X0) | ~creative(X0)) => ? [X1] : (~wise(X1) & wise(X1)) [rectify 13]
27. ? [X0] : (kind(X0) <~> happy(X0)) <=> ? [X1] : (~creative(X1) & ~kind(X1)) [rectify 16]
34. (patient(paul) <~> ~quiet(paul)) | ! [X0] : (humble(X0) & curious(X0)) [ennf transformation 7]
38. ? [X1] : (~wise(X1) & wise(X1)) | ! [X0] : (~quiet(X0) & creative(X0)) [ennf transformation 26]
49. ((quiet(paul) | ~patient(paul)) & (~quiet(paul) | patient(paul))) | ! [X0] : (humble(X0) & curious(X0)) [nnf transformation 34]
61. ? [X0] : (~wise(X0) & wise(X0)) | ! [X1] : (~quiet(X1) & creative(X1)) [rectify 38]
62. ? [X0] : (~wise(X0) & wise(X0)) => (~wise(sK5) & wise(sK5)) [choice axiom]
63. (~wise(sK5) & wise(sK5)) | ! [X1] : (~quiet(X1) & creative(X1)) [skolemisation 61,62]
64. ! [X0] : ((~patient(X0) | (~happy(X0) | kind(X0))) & ((happy(X0) & ~kind(X0)) | patient(X0))) [nnf transformation 14]
65. ! [X0] : ((~patient(X0) | ~happy(X0) | kind(X0)) & ((happy(X0) & ~kind(X0)) | patient(X0))) [flattening 64]
71. (? [X0] : ((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | ! [X1] : (creative(X1) | kind(X1))) & (? [X1] : (~creative(X1) & ~kind(X1)) | ! [X0] : ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) [nnf transformation 27]
72. (? [X0] : ((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | ! [X1] : (creative(X1) | kind(X1))) & (? [X2] : (~creative(X2) & ~kind(X2)) | ! [X3] : ((kind(X3) | ~happy(X3)) & (happy(X3) | ~kind(X3)))) [rectify 71]
73. ? [X0] : ((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) => ((~happy(sK7) | ~kind(sK7)) & (happy(sK7) | kind(sK7))) [choice axiom]
74. ? [X2] : (~creative(X2) & ~kind(X2)) => (~creative(sK8) & ~kind(sK8)) [choice axiom]
75. (((~happy(sK7) | ~kind(sK7)) & (happy(sK7) | kind(sK7))) | ! [X1] : (creative(X1) | kind(X1))) & ((~creative(sK8) & ~kind(sK8)) | ! [X3] : ((kind(X3) | ~happy(X3)) & (happy(X3) | ~kind(X3)))) [skolemisation 72,74,73]
98. quiet(paul) | ~patient(paul) | curious(X0) [cnf transformation 49]
118. wise(sK5) | creative(X1) [cnf transformation 63]
119. wise(sK5) | ~quiet(X1) [cnf transformation 63]
120. ~wise(sK5) | creative(X1) [cnf transformation 63]
121. ~wise(sK5) | ~quiet(X1) [cnf transformation 63]
122. ~kind(X0) | patient(X0) [cnf transformation 65]
123. happy(X0) | patient(X0) [cnf transformation 65]
134. ~creative(sK8) | kind(X3) | ~happy(X3) [cnf transformation 75]
143. ~curious(susan) [cnf transformation 23]
194. 12 <=> patient(paul) [avatar definition]
196. ~patient(paul) <- (~12) [avatar component clause 194]
198. 13 <=> quiet(paul) [avatar definition]
200. quiet(paul) <- (13) [avatar component clause 198]
203. 14 <=> ! [X0] : curious(X0) [avatar definition]
204. curious(X0) <- (14) [avatar component clause 203]
205. 14 | ~12 | 13 [avatar split clause 98,198,194,203]
258. 26 <=> ! [X1] : ~quiet(X1) [avatar definition]
259. ~quiet(X1) <- (26) [avatar component clause 258]
261. 27 <=> wise(sK5) [avatar definition]
264. 26 | ~27 [avatar split clause 121,261,258]
266. 28 <=> ! [X1] : creative(X1) [avatar definition]
267. creative(X1) <- (28) [avatar component clause 266]
268. 28 | ~27 [avatar split clause 120,261,266]
269. 26 | 27 [avatar split clause 119,261,258]
270. 28 | 27 [avatar split clause 118,261,266]
313. 38 <=> ! [X3] : (kind(X3) | ~happy(X3)) [avatar definition]
314. ~happy(X3) | kind(X3) <- (38) [avatar component clause 313]
316. 39 <=> creative(sK8) [avatar definition]
318. ~creative(sK8) <- (~39) [avatar component clause 316]
319. 38 | ~39 [avatar split clause 134,316,313]
380. $false <- (28, ~39) [resolution 318,267]
381. ~28 | 39 [avatar contradiction clause 380]
394. kind(X0) | patient(X0) <- (38) [resolution 314,123]
397. patient(X0) <- (38) [subsumption resolution 394,122]
399. $false <- (~12, 38) [resolution 397,196]
400. 12 | ~38 [avatar contradiction clause 399]
401. $false <- (13, 26) [subsumption resolution 200,259]
402. ~13 | ~26 [avatar contradiction clause 401]
403. $false <- (14) [resolution 204,143]
406. ~14 [avatar contradiction clause 403]
407. $false [avatar sat refutation 205,264,268,269,270,319,381,400,402,406]
% SZS output end Proof for 6076739985011534178556313
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or not happy is both calm and strong and vice versa. If mary is either rich or happy then susan is not happy and vice versa. If someone is either not creative or happy then someone is either funny or not wise. Everyone who is not calm or not funny is either not old or old and vice versa. If john is not quiet or not happy then alice is wise. Everyone who is either happy or not kind is not strong or brave. Everyone who is either not happy or not curious is either not quiet or happy and vice versa. Everyone who is both curious and not curious is both not curious and calm. Everyone who is either creative or humble is not wise or quiet and vice versa. Everyone who is both not strong and not kind is quiet or not quiet and vice versa. Everyone who is curious is either funny or not wise and vice versa. Everyone who is either quiet or not rich is either wise or kind and vice versa. If someone is humble then someone is rich or happy. If susan is either tall or not tall then fred is both old and not calm and vice versa. Everyone who is either not rich or not old is either old or not kind and vice versa. Everyone who is either curious or humble is both happy and calm. Someone is either curious or not strong. Lucy is not calm or creative. Fred is not old or not quiet. Paul is not wise. Lucy is either not calm or not happy. Someone is not brave or not rich. Alice is not strong. | Alice is not funny. | entailment | (![X]:((generous(X)<~>~happy(X))<=>(calm(X)&strong(X))))&
(((rich(mary)<~>happy(mary)))<=>(~happy(susan)))&
((?[X]:((~creative(X)<~>happy(X))))=>(?[X]:((funny(X)<~>~wise(X)))))&
(![X]:((~calm(X)|~funny(X))<=>(~old(X)<~>old(X))))&
(((~quiet(john)|~happy(john)))=>(wise(alice)))&
(![X]:((happy(X)<~>~kind(X))=>(~strong(X)|brave(X))))&
(![X]:((~happy(X)<~>~curious(X))<=>(~quiet(X)<~>happy(X))))&
(![X]:((curious(X)&~curious(X))=>(~curious(X)&calm(X))))&
(![X]:((creative(X)<~>humble(X))<=>(~wise(X)|quiet(X))))&
(![X]:((~strong(X)&~kind(X))<=>(quiet(X)|~quiet(X))))&
(![X]:(curious(X)<=>(funny(X)<~>~wise(X))))&
(![X]:((quiet(X)<~>~rich(X))<=>(wise(X)<~>kind(X))))&
((?[X]:(humble(X)))=>(?[X]:((rich(X)|happy(X)))))&
(((tall(susan)<~>~tall(susan)))<=>((old(fred)&~calm(fred))))&
(![X]:((~rich(X)<~>~old(X))<=>(old(X)<~>~kind(X))))&
(![X]:((curious(X)<~>humble(X))=>(happy(X)&calm(X))))&
(?[X]:((curious(X)<~>~strong(X))))&
((~calm(lucy)|creative(lucy)))&
((~old(fred)|~quiet(fred)))&
(~wise(paul))&
((~calm(lucy)<~>~happy(lucy)))&
(?[X]:((~brave(X)|~rich(X))))&
(~strong(alice)) | ~funny(alice) | [
"p6",
"p9",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3850542580388582428214673
% SZS output start Proof for 3850542580388582428214673
7. ! [X0] : ((~happy(X0) <~> ~curious(X0)) <=> (~quiet(X0) <~> happy(X0))) [input p6]
10. ! [X0] : ((~kind(X0) & ~strong(X0)) <=> (~quiet(X0) | quiet(X0))) [input p9]
11. ! [X0] : (curious(X0) <=> (funny(X0) <~> ~wise(X0))) [input p10]
12. ! [X0] : ((quiet(X0) <~> ~rich(X0)) <=> (wise(X0) <~> kind(X0))) [input p11]
15. ! [X0] : ((~rich(X0) <~> ~old(X0)) <=> (old(X0) <~> ~kind(X0))) [input p14]
24. funny(alice) [input hypothesis]
45. ! [X0] : ((((curious(X0) | happy(X0)) & (~curious(X0) | ~happy(X0))) | ((~quiet(X0) | ~happy(X0)) & (happy(X0) | quiet(X0)))) & (((~happy(X0) | quiet(X0)) & (happy(X0) | ~quiet(X0))) | ((~happy(X0) | curious(X0)) & (~curious(X0) | happy(X0))))) [nnf transformation 7]
48. ! [X0] : (((~kind(X0) & ~strong(X0)) | (quiet(X0) & ~quiet(X0))) & ((~quiet(X0) | quiet(X0)) | (kind(X0) | strong(X0)))) [nnf transformation 10]
49. ! [X0] : (((~kind(X0) & ~strong(X0)) | (quiet(X0) & ~quiet(X0))) & (~quiet(X0) | quiet(X0) | kind(X0) | strong(X0))) [flattening 48]
50. ! [X0] : ((curious(X0) | ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0)))) & (((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | ~curious(X0))) [nnf transformation 11]
51. ! [X0] : ((((rich(X0) | ~quiet(X0)) & (~rich(X0) | quiet(X0))) | ((wise(X0) | ~kind(X0)) & (kind(X0) | ~wise(X0)))) & (((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0))))) [nnf transformation 12]
57. ! [X0] : ((((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0)))) & (((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0))))) [nnf transformation 15]
89. happy(X0) | ~quiet(X0) | ~curious(X0) | happy(X0) [cnf transformation 45]
92. ~happy(X0) | quiet(X0) | ~happy(X0) | curious(X0) [cnf transformation 45]
94. ~curious(X0) | ~happy(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 45]
95. curious(X0) | happy(X0) | happy(X0) | quiet(X0) [cnf transformation 45]
108. ~kind(X0) | ~quiet(X0) [cnf transformation 49]
109. ~kind(X0) | quiet(X0) [cnf transformation 49]
111. ~curious(X0) | ~funny(X0) | wise(X0) [cnf transformation 50]
112. ~wise(X0) | curious(X0) | ~funny(X0) [cnf transformation 50]
114. kind(X0) | wise(X0) | ~rich(X0) | ~quiet(X0) [cnf transformation 51]
118. ~rich(X0) | quiet(X0) | kind(X0) | ~wise(X0) [cnf transformation 51]
131. kind(X0) | ~old(X0) | ~old(X0) | rich(X0) [cnf transformation 57]
136. old(X0) | rich(X0) | old(X0) | kind(X0) [cnf transformation 57]
150. funny(alice) [cnf transformation 24]
152. kind(X0) | ~old(X0) | rich(X0) [duplicate literal removal 131]
154. old(X0) | rich(X0) | kind(X0) [duplicate literal removal 136]
160. happy(X0) | ~quiet(X0) | ~curious(X0) [duplicate literal removal 89]
161. ~happy(X0) | quiet(X0) | curious(X0) [duplicate literal removal 92]
162. ~curious(X0) | ~happy(X0) | ~quiet(X0) [duplicate literal removal 94]
163. curious(X0) | happy(X0) | quiet(X0) [duplicate literal removal 95]
206. 9 <=> wise(alice) [avatar definition]
207. ~wise(alice) <- (~9) [avatar component clause 206]
208. wise(alice) <- (9) [avatar component clause 206]
215. curious(X0) | quiet(X0) [subsumption resolution 161,163]
216. ~curious(X0) | ~quiet(X0) [subsumption resolution 160,162]
217. ~kind(X0) [subsumption resolution 108,109]
220. ~wise(X0) | quiet(X0) | ~rich(X0) [subsumption resolution 118,217]
222. ~quiet(X0) | ~rich(X0) | wise(X0) [subsumption resolution 114,217]
251. old(X0) | rich(X0) [subsumption resolution 154,217]
252. ~old(X0) | rich(X0) [subsumption resolution 152,217]
253. rich(X0) [subsumption resolution 252,251]
325. ~funny(X0) | wise(X0) | quiet(X0) [resolution 111,215]
497. wise(alice) | quiet(alice) [resolution 325,150]
498. quiet(alice) <- (~9) [subsumption resolution 497,207]
499. ~rich(alice) | wise(alice) <- (~9) [resolution 498,222]
502. wise(alice) <- (~9) [subsumption resolution 499,253]
503. $false <- (~9) [subsumption resolution 502,207]
504. 9 [avatar contradiction clause 503]
507. 36 <=> quiet(alice) [avatar definition]
509. quiet(alice) <- (36) [avatar component clause 507]
513. quiet(alice) | ~rich(alice) <- (9) [resolution 208,220]
514. curious(alice) | ~funny(alice) <- (9) [resolution 208,112]
515. quiet(alice) <- (9) [subsumption resolution 513,253]
516. 36 | ~9 [avatar split clause 515,206,507]
517. curious(alice) <- (9) [subsumption resolution 514,150]
523. ~quiet(alice) <- (9) [resolution 517,216]
527. $false <- (9, 36) [subsumption resolution 523,509]
528. ~9 | ~36 [avatar contradiction clause 527]
529. $false [avatar sat refutation 504,516,528]
% SZS output end Proof for 3850542580388582428214673
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or creative is both quiet and curious and vice versa. Everyone who is either creative or calm is both not calm and wise. If someone is either not curious or curious then someone is wise or not tall. Everyone who is brave is both not tall and not generous and vice versa. If someone is both humble and not kind then lucy is either patient or not generous. If someone is both old and not strong then john is either generous or wise. Everyone who is not old is quiet or funny and vice versa. If fred is both not quiet and generous then mary is not humble and vice versa. If someone is either not brave or not creative then someone is either not funny or wise. If someone is either not rich or not humble then someone is either not calm or generous and vice versa. If fred is both not creative and not generous then someone is both not strong and not humble and vice versa. Everyone who is not wise is tall or not creative and vice versa. If someone is either not old or quiet then someone is either not kind or wise. If paul is strong then someone is strong. Everyone who is old or not quiet is both curious and not brave. Paul is either wise or not old. Fred is tall. Someone is either humble or not quiet. Lucy is brave or creative. Someone is wise or funny. Alice is both happy and wise. | Mary is not humble. | contradiction | (![X]:((~wise(X)|creative(X))<=>(quiet(X)&curious(X))))&
(![X]:((creative(X)<~>calm(X))=>(~calm(X)&wise(X))))&
((?[X]:((~curious(X)<~>curious(X))))=>(?[X]:((wise(X)|~tall(X)))))&
(![X]:(brave(X)<=>(~tall(X)&~generous(X))))&
((?[X]:((humble(X)&~kind(X))))=>((patient(lucy)<~>~generous(lucy))))&
((?[X]:((old(X)&~strong(X))))=>((generous(john)<~>wise(john))))&
(![X]:(~old(X)<=>(quiet(X)|funny(X))))&
(((~quiet(fred)&generous(fred)))<=>(~humble(mary)))&
((?[X]:((~brave(X)<~>~creative(X))))=>(?[X]:((~funny(X)<~>wise(X)))))&
((?[X]:((~rich(X)<~>~humble(X))))<=>(?[X]:((~calm(X)<~>generous(X)))))&
(((~creative(fred)&~generous(fred)))<=>(?[X]:((~strong(X)&~humble(X)))))&
(![X]:(~wise(X)<=>(tall(X)|~creative(X))))&
((?[X]:((~old(X)<~>quiet(X))))=>(?[X]:((~kind(X)<~>wise(X)))))&
((strong(paul))=>(?[X]:(strong(X))))&
(![X]:((old(X)|~quiet(X))=>(curious(X)&~brave(X))))&
((wise(paul)<~>~old(paul)))&
(tall(fred))&
(?[X]:((humble(X)<~>~quiet(X))))&
((brave(lucy)|creative(lucy)))&
(?[X]:((wise(X)|funny(X))))&
((happy(alice)&wise(alice))) | ~humble(mary) | [
"p0",
"p7",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8520057658518267661601233
% SZS output start Proof for 8520057658518267661601233
1. ! [X0] : ((creative(X0) | ~wise(X0)) <=> (curious(X0) & quiet(X0))) [input p0]
8. (generous(fred) & ~quiet(fred)) <=> ~humble(mary) [input p7]
12. ! [X0] : (~wise(X0) <=> (~creative(X0) | tall(X0))) [input p11]
17. tall(fred) [input p16]
22. ~humble(mary) [input hypothesis]
36. ! [X0] : (((creative(X0) | ~wise(X0)) | (~curious(X0) | ~quiet(X0))) & ((curious(X0) & quiet(X0)) | (~creative(X0) & wise(X0)))) [nnf transformation 1]
37. ! [X0] : ((creative(X0) | ~wise(X0) | ~curious(X0) | ~quiet(X0)) & ((curious(X0) & quiet(X0)) | (~creative(X0) & wise(X0)))) [flattening 36]
49. ((generous(fred) & ~quiet(fred)) | humble(mary)) & (~humble(mary) | (~generous(fred) | quiet(fred))) [nnf transformation 8]
50. ((generous(fred) & ~quiet(fred)) | humble(mary)) & (~humble(mary) | ~generous(fred) | quiet(fred)) [flattening 49]
65. ! [X0] : ((~wise(X0) | (creative(X0) & ~tall(X0))) & ((~creative(X0) | tall(X0)) | wise(X0))) [nnf transformation 12]
66. ! [X0] : ((~wise(X0) | (creative(X0) & ~tall(X0))) & (~creative(X0) | tall(X0) | wise(X0))) [flattening 65]
79. quiet(X0) | wise(X0) [cnf transformation 37]
101. ~quiet(fred) | humble(mary) [cnf transformation 50]
120. ~tall(X0) | ~wise(X0) [cnf transformation 66]
133. tall(fred) [cnf transformation 17]
139. ~humble(mary) [cnf transformation 22]
186. 11 <=> humble(mary) [avatar definition]
195. 13 <=> quiet(fred) [avatar definition]
197. ~quiet(fred) <- (~13) [avatar component clause 195]
198. 11 | ~13 [avatar split clause 101,195,186]
333. ~11 [avatar split clause 139,186]
334. wise(fred) <- (~13) [resolution 79,197]
338. ~wise(fred) [resolution 120,133]
339. $false <- (~13) [subsumption resolution 338,334]
340. 13 [avatar contradiction clause 339]
341. $false [avatar sat refutation 198,333,340]
% SZS output end Proof for 8520057658518267661601233
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and kind is not old. If john is both not rich and not funny then someone is both not wise and not generous and vice versa. If someone is either not rich or rich then someone is both not wise and not creative. If someone is both creative and calm then john is either tall or wise. If someone is both not brave and creative then mary is either not strong or rich. Everyone who is both not tall and quiet is not humble or not wise and vice versa. If someone is not brave then mary is either tall or strong. If someone is both not creative and not curious then someone is rich or not generous. Everyone who is both brave and not calm is either not generous or happy and vice versa. Everyone who is both not creative and happy is creative and vice versa. If lucy is not generous then someone is both not humble and patient. If lucy is either strong or not strong then someone is quiet and vice versa. Everyone who is curious is either calm or not patient and vice versa. Everyone who is both generous and not funny is not quiet or kind and vice versa. Everyone who is both strong and brave is not strong. Someone is both not old and strong. John is calm. John is both not brave and not curious. Alice is either funny or brave. Lucy is both not creative and not strong. Fred is old. Someone is both not kind and strong. John is old. | Fred is creative. | contradiction | (![X]:((~humble(X)&kind(X))=>~old(X)))&
(((~rich(john)&~funny(john)))<=>(?[X]:((~wise(X)&~generous(X)))))&
((?[X]:((~rich(X)<~>rich(X))))=>(?[X]:((~wise(X)&~creative(X)))))&
((?[X]:((creative(X)&calm(X))))=>((tall(john)<~>wise(john))))&
((?[X]:((~brave(X)&creative(X))))=>((~strong(mary)<~>rich(mary))))&
(![X]:((~tall(X)&quiet(X))<=>(~humble(X)|~wise(X))))&
((?[X]:(~brave(X)))=>((tall(mary)<~>strong(mary))))&
((?[X]:((~creative(X)&~curious(X))))=>(?[X]:((rich(X)|~generous(X)))))&
(![X]:((brave(X)&~calm(X))<=>(~generous(X)<~>happy(X))))&
(![X]:((~creative(X)&happy(X))<=>creative(X)))&
((~generous(lucy))=>(?[X]:((~humble(X)&patient(X)))))&
(((strong(lucy)<~>~strong(lucy)))<=>(?[X]:(quiet(X))))&
(![X]:(curious(X)<=>(calm(X)<~>~patient(X))))&
(![X]:((generous(X)&~funny(X))<=>(~quiet(X)|kind(X))))&
(![X]:((strong(X)&brave(X))=>~strong(X)))&
(?[X]:((~old(X)&strong(X))))&
(calm(john))&
((~brave(john)&~curious(john)))&
((funny(alice)<~>brave(alice)))&
((~creative(lucy)&~strong(lucy)))&
(old(fred))&
(?[X]:((~kind(X)&strong(X))))&
(old(john)) | creative(fred) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 461156270802260629849432
% SZS output start Proof for 461156270802260629849432
10. ! [X0] : ((happy(X0) & ~creative(X0)) <=> creative(X0)) [input p9]
24. creative(fred) [input hypothesis]
56. ! [X0] : (((happy(X0) & ~creative(X0)) | ~creative(X0)) & (creative(X0) | (~happy(X0) | creative(X0)))) [nnf transformation 10]
57. ! [X0] : (((happy(X0) & ~creative(X0)) | ~creative(X0)) & (creative(X0) | ~happy(X0) | creative(X0))) [flattening 56]
100. ~creative(X0) | ~creative(X0) [cnf transformation 57]
131. creative(fred) [cnf transformation 24]
136. ~creative(X0) [duplicate literal removal 100]
265. $false [subsumption resolution 131,136]
% SZS output end Proof for 461156270802260629849432
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not funny is not strong and vice versa. Everyone who is not rich or not creative is both generous and patient and vice versa. Everyone who is either not happy or not brave is both not curious and old. Everyone who is funny is rich and vice versa. Everyone who is not happy is not wise. Everyone who is not happy or not quiet is both brave and not old and vice versa. If someone is not tall then lucy is either not generous or not rich and vice versa. Everyone who is both not strong and not curious is both not calm and not funny and vice versa. If alice is both quiet and strong then someone is both not strong and not funny. If someone is both not calm and generous then someone is both not wise and brave and vice versa. Everyone who is funny or patient is both not strong and curious. If someone is both funny and calm then paul is not humble or calm and vice versa. If susan is old then susan is either strong or not creative. Everyone who is wise is both not patient and not generous. If someone is either generous or funny then lucy is funny. Everyone who is both wise and funny is not humble or quiet and vice versa. Alice is both old and creative. Someone is either not generous or not old. Alice is not patient. Lucy is not patient or strong. Someone is either funny or not calm. | Paul is strong. | contradiction | (![X]:((~humble(X)|~funny(X))<=>~strong(X)))&
(![X]:((~rich(X)|~creative(X))<=>(generous(X)&patient(X))))&
(![X]:((~happy(X)<~>~brave(X))=>(~curious(X)&old(X))))&
(![X]:(funny(X)<=>rich(X)))&
(![X]:(~happy(X)=>~wise(X)))&
(![X]:((~happy(X)|~quiet(X))<=>(brave(X)&~old(X))))&
((?[X]:(~tall(X)))<=>((~generous(lucy)<~>~rich(lucy))))&
(![X]:((~strong(X)&~curious(X))<=>(~calm(X)&~funny(X))))&
(((quiet(alice)&strong(alice)))=>(?[X]:((~strong(X)&~funny(X)))))&
((?[X]:((~calm(X)&generous(X))))<=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:((funny(X)|patient(X))=>(~strong(X)&curious(X))))&
((?[X]:((funny(X)&calm(X))))<=>((~humble(paul)|calm(paul))))&
((old(susan))=>((strong(susan)<~>~creative(susan))))&
(![X]:(wise(X)=>(~patient(X)&~generous(X))))&
((?[X]:((generous(X)<~>funny(X))))=>(funny(lucy)))&
(![X]:((wise(X)&funny(X))<=>(~humble(X)|quiet(X))))&
((old(alice)&creative(alice)))&
(?[X]:((~generous(X)<~>~old(X))))&
(~patient(alice))&
((~patient(lucy)|strong(lucy)))&
(?[X]:((funny(X)<~>~calm(X)))) | strong(paul) | [
"p0",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1435236145814209665518984
% SZS output start Proof for 1435236145814209665518984
1. ! [X0] : ((~funny(X0) | ~humble(X0)) <=> ~strong(X0)) [input p0]
11. ! [X0] : ((patient(X0) | funny(X0)) => (curious(X0) & ~strong(X0))) [input p10]
22. strong(paul) [input hypothesis]
28. ! [X0] : ((curious(X0) & ~strong(X0)) | (~patient(X0) & ~funny(X0))) [ennf transformation 11]
32. ! [X0] : (((~funny(X0) | ~humble(X0)) | strong(X0)) & (~strong(X0) | (funny(X0) & humble(X0)))) [nnf transformation 1]
33. ! [X0] : ((~funny(X0) | ~humble(X0) | strong(X0)) & (~strong(X0) | (funny(X0) & humble(X0)))) [flattening 32]
69. ~strong(X0) | funny(X0) [cnf transformation 33]
102. ~strong(X0) | ~funny(X0) [cnf transformation 28]
130. strong(paul) [cnf transformation 22]
196. ~strong(X0) [subsumption resolution 102,69]
264. $false [subsumption resolution 130,196]
% SZS output end Proof for 1435236145814209665518984
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or funny is both patient and not generous and vice versa.
Everyone who is both quiet and wise is both strong and not curious.
If alice is not happy or strong then john is not rich or wise.
If someone is either not kind or not brave then someone is either not patient or rich.
If someone is either humble or happy then fred is both not strong and kind and vice versa.
If mary is quiet then lucy is old.
Everyone who is either not wise or not tall is not creative or not generous.
Everyone who is either calm or not wise is either not kind or not patient and vice versa.
Everyone who is both not quiet and strong is kind and vice versa.
If someone is brave or not kind then mary is both happy and not happy and vice versa.
If someone is humble or not quiet then someone is not tall or rich.
Everyone who is not calm or not happy is both happy and curious.
If alice is both not happy and kind then lucy is both calm and not brave and vice versa.
Everyone who is both not patient and kind is either kind or creative and vice versa.
If someone is old then susan is generous.
Paul is either rich or not generous.
Someone is not old or calm.
Someone is either not patient or not happy.
Alice is kind.
Lucy is both patient and funny.
Someone is both generous and not creative.
Someone is not calm.
Someone is not old or humble. | Fred is not humble. | contradiction | (![X]:((~curious(X)<~>funny(X))<=>(patient(X)&~generous(X))))&
(![X]:((quiet(X)&wise(X))=>(strong(X)&~curious(X))))&
(((~happy(alice)|strong(alice)))=>((~rich(john)|wise(john))))&
((?[X]:((~kind(X)<~>~brave(X))))=>(?[X]:((~patient(X)<~>rich(X)))))&
((?[X]:((humble(X)<~>happy(X))))<=>((~strong(fred)&kind(fred))))&
((quiet(mary))=>(old(lucy)))&
(![X]:((~wise(X)<~>~tall(X))=>(~creative(X)|~generous(X))))&
(![X]:((calm(X)<~>~wise(X))<=>(~kind(X)<~>~patient(X))))&
(![X]:((~quiet(X)&strong(X))<=>kind(X)))&
((?[X]:((brave(X)|~kind(X))))<=>((happy(mary)&~happy(mary))))&
((?[X]:((humble(X)|~quiet(X))))=>(?[X]:((~tall(X)|rich(X)))))&
(![X]:((~calm(X)|~happy(X))=>(happy(X)&curious(X))))&
(((~happy(alice)&kind(alice)))<=>((calm(lucy)&~brave(lucy))))&
(![X]:((~patient(X)&kind(X))<=>(kind(X)<~>creative(X))))&
((?[X]:(old(X)))=>(generous(susan)))&
((rich(paul)<~>~generous(paul)))&
(?[X]:((~old(X)|calm(X))))&
(?[X]:((~patient(X)<~>~happy(X))))&
(kind(alice))&
((patient(lucy)&funny(lucy)))&
(?[X]:((generous(X)&~creative(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~old(X)|humble(X)))) | ~humble(fred) | [
"p4",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2356670171100963564142238
% SZS output start Proof for 2356670171100963564142238
5. ? [X0] : (humble(X0) <~> happy(X0)) <=> (kind(fred) & ~strong(fred)) [input p4]
9. ! [X0] : ((strong(X0) & ~quiet(X0)) <=> kind(X0)) [input p8]
10. ? [X0] : (~kind(X0) | brave(X0)) <=> (~happy(mary) & happy(mary)) [input p9]
12. ! [X0] : ((~happy(X0) | ~calm(X0)) => (curious(X0) & happy(X0))) [input p11]
24. ~humble(fred) [input hypothesis]
36. ! [X0] : ((curious(X0) & happy(X0)) | (happy(X0) & calm(X0))) [ennf transformation 12]
44. (? [X0] : ((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | (~kind(fred) | strong(fred))) & ((kind(fred) & ~strong(fred)) | ! [X0] : ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0)))) [nnf transformation 5]
45. (? [X0] : ((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | ~kind(fred) | strong(fred)) & ((kind(fred) & ~strong(fred)) | ! [X0] : ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0)))) [flattening 44]
46. (? [X0] : ((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | ~kind(fred) | strong(fred)) & ((kind(fred) & ~strong(fred)) | ! [X1] : ((humble(X1) | ~happy(X1)) & (happy(X1) | ~humble(X1)))) [rectify 45]
47. ? [X0] : ((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) => ((~happy(sK1) | ~humble(sK1)) & (happy(sK1) | humble(sK1))) [choice axiom]
48. (((~happy(sK1) | ~humble(sK1)) & (happy(sK1) | humble(sK1))) | ~kind(fred) | strong(fred)) & ((kind(fred) & ~strong(fred)) | ! [X1] : ((humble(X1) | ~happy(X1)) & (happy(X1) | ~humble(X1)))) [skolemisation 46,47]
51. ! [X0] : (((strong(X0) & ~quiet(X0)) | ~kind(X0)) & (kind(X0) | (~strong(X0) | quiet(X0)))) [nnf transformation 9]
52. ! [X0] : (((strong(X0) & ~quiet(X0)) | ~kind(X0)) & (kind(X0) | ~strong(X0) | quiet(X0))) [flattening 51]
53. (? [X0] : (~kind(X0) | brave(X0)) | (happy(mary) | ~happy(mary))) & ((~happy(mary) & happy(mary)) | ! [X0] : (kind(X0) & ~brave(X0))) [nnf transformation 10]
54. (? [X0] : (~kind(X0) | brave(X0)) | happy(mary) | ~happy(mary)) & ((~happy(mary) & happy(mary)) | ! [X0] : (kind(X0) & ~brave(X0))) [flattening 53]
55. (? [X0] : (~kind(X0) | brave(X0)) | happy(mary) | ~happy(mary)) & ((~happy(mary) & happy(mary)) | ! [X1] : (kind(X1) & ~brave(X1))) [rectify 54]
56. ? [X0] : (~kind(X0) | brave(X0)) => (~kind(sK2) | brave(sK2)) [choice axiom]
57. ((~kind(sK2) | brave(sK2)) | happy(mary) | ~happy(mary)) & ((~happy(mary) & happy(mary)) | ! [X1] : (kind(X1) & ~brave(X1))) [skolemisation 55,56]
92. ~strong(fred) | humble(X1) | ~happy(X1) [cnf transformation 48]
110. ~kind(X0) | strong(X0) [cnf transformation 52]
112. happy(mary) | kind(X1) [cnf transformation 57]
114. ~happy(mary) | kind(X1) [cnf transformation 57]
119. happy(X0) | happy(X0) [cnf transformation 36]
145. ~humble(fred) [cnf transformation 24]
148. happy(X0) [duplicate literal removal 119]
186. 9 <=> strong(fred) [avatar definition]
187. ~strong(fred) <- (~9) [avatar component clause 186]
204. 13 <=> ! [X1] : (humble(X1) | ~happy(X1)) [avatar definition]
205. humble(X1) | ~happy(X1) <- (13) [avatar component clause 204]
211. 13 | ~9 [avatar split clause 92,186,204]
223. 17 <=> ! [X1] : kind(X1) [avatar definition]
224. kind(X1) <- (17) [avatar component clause 223]
226. 18 <=> happy(mary) [avatar definition]
229. 17 | ~18 [avatar split clause 114,226,223]
234. 17 | 18 [avatar split clause 112,226,223]
310. strong(X0) <- (17) [resolution 110,224]
314. $false <- (~9, 17) [resolution 310,187]
315. 9 | ~17 [avatar contradiction clause 314]
316. humble(X1) <- (13) [subsumption resolution 205,148]
317. $false <- (13) [resolution 316,145]
320. ~13 [avatar contradiction clause 317]
321. $false [avatar sat refutation 211,229,234,315,320]
% SZS output end Proof for 2356670171100963564142238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is either creative or calm and vice versa.
If someone is not funny or wise then someone is either not creative or not old and vice versa.
If fred is either rich or not old then mary is not kind.
Everyone who is generous or tall is humble or not funny.
If someone is brave then someone is both not generous and generous and vice versa.
Everyone who is both not humble and funny is either tall or funny.
Everyone who is creative or not tall is either creative or not curious and vice versa.
Everyone who is patient is not patient or not humble.
If alice is not humble then mary is either strong or not patient and vice versa.
If someone is creative or curious then someone is not tall.
If mary is old then mary is both calm and generous and vice versa.
If john is humble then alice is either rich or wise.
Everyone who is generous or not humble is not calm or calm and vice versa.
Everyone who is either not humble or not quiet is either wise or not happy and vice versa.
Everyone who is not brave or strong is both quiet and strong and vice versa.
Everyone who is humble or not curious is brave or funny and vice versa.
Someone is both tall and not wise.
Susan is either happy or not creative.
Fred is not tall.
Lucy is old or tall.
Someone is not happy.
John is not happy or not generous.
John is generous or curious. | John is creative. | neutral | (![X]:(~creative(X)<=>(creative(X)<~>calm(X))))&
((?[X]:((~funny(X)|wise(X))))<=>(?[X]:((~creative(X)<~>~old(X)))))&
(((rich(fred)<~>~old(fred)))=>(~kind(mary)))&
(![X]:((generous(X)|tall(X))=>(humble(X)|~funny(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~generous(X)&generous(X)))))&
(![X]:((~humble(X)&funny(X))=>(tall(X)<~>funny(X))))&
(![X]:((creative(X)|~tall(X))<=>(creative(X)<~>~curious(X))))&
(![X]:(patient(X)=>(~patient(X)|~humble(X))))&
((~humble(alice))<=>((strong(mary)<~>~patient(mary))))&
((?[X]:((creative(X)|curious(X))))=>(?[X]:(~tall(X))))&
((old(mary))<=>((calm(mary)&generous(mary))))&
((humble(john))=>((rich(alice)<~>wise(alice))))&
(![X]:((generous(X)|~humble(X))<=>(~calm(X)|calm(X))))&
(![X]:((~humble(X)<~>~quiet(X))<=>(wise(X)<~>~happy(X))))&
(![X]:((~brave(X)|strong(X))<=>(quiet(X)&strong(X))))&
(![X]:((humble(X)|~curious(X))<=>(brave(X)|funny(X))))&
(?[X]:((tall(X)&~wise(X))))&
((happy(susan)<~>~creative(susan)))&
(~tall(fred))&
((old(lucy)|tall(lucy)))&
(?[X]:(~happy(X)))&
((~happy(john)|~generous(john)))&
((generous(john)|curious(john))) | creative(john) | [] | null | 0 |
Everyone who is creative is not humble and vice versa.
Everyone who is both humble and not calm is not rich and vice versa.
If someone is wise then mary is both generous and curious and vice versa.
Everyone who is both happy and not creative is both not happy and not quiet.
If someone is either not brave or not rich then someone is either brave or old and vice versa.
If fred is either calm or not wise then lucy is quiet or brave.
Everyone who is old or curious is either not quiet or not curious and vice versa.
Everyone who is either not quiet or not tall is both not old and patient.
Everyone who is both not funny and not rich is creative or not wise.
Everyone who is either not tall or not quiet is both not generous and not funny.
If mary is generous then someone is either wise or not wise and vice versa.
Everyone who is rich is both not patient and wise and vice versa.
Everyone who is either curious or not generous is both happy and not rich.
Everyone who is both rich and not calm is not old.
Someone is funny.
Someone is either generous or brave.
Susan is patient or not humble.
Someone is not calm or not tall.
Someone is not patient.
Alice is not happy.
Paul is not happy. | Fred is not humble. | contradiction | (![X]:(creative(X)<=>~humble(X)))&
(![X]:((humble(X)&~calm(X))<=>~rich(X)))&
((?[X]:(wise(X)))<=>((generous(mary)&curious(mary))))&
(![X]:((happy(X)&~creative(X))=>(~happy(X)&~quiet(X))))&
((?[X]:((~brave(X)<~>~rich(X))))<=>(?[X]:((brave(X)<~>old(X)))))&
(((calm(fred)<~>~wise(fred)))=>((quiet(lucy)|brave(lucy))))&
(![X]:((old(X)|curious(X))<=>(~quiet(X)<~>~curious(X))))&
(![X]:((~quiet(X)<~>~tall(X))=>(~old(X)&patient(X))))&
(![X]:((~funny(X)&~rich(X))=>(creative(X)|~wise(X))))&
(![X]:((~tall(X)<~>~quiet(X))=>(~generous(X)&~funny(X))))&
((generous(mary))<=>(?[X]:((wise(X)<~>~wise(X)))))&
(![X]:(rich(X)<=>(~patient(X)&wise(X))))&
(![X]:((curious(X)<~>~generous(X))=>(happy(X)&~rich(X))))&
(![X]:((rich(X)&~calm(X))=>~old(X)))&
(?[X]:(funny(X)))&
(?[X]:((generous(X)<~>brave(X))))&
((patient(susan)|~humble(susan)))&
(?[X]:((~calm(X)|~tall(X))))&
(?[X]:(~patient(X)))&
(~happy(alice))&
(~happy(paul)) | ~humble(fred) | [
"p0",
"p1",
"p2",
"p3",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3321808489541944488732038
% SZS output start Proof for 3321808489541944488732038
1. ! [X0] : (creative(X0) <=> ~humble(X0)) [input p0]
2. ! [X0] : ((~calm(X0) & humble(X0)) <=> ~rich(X0)) [input p1]
3. ? [X0] : wise(X0) <=> (curious(mary) & generous(mary)) [input p2]
4. ! [X0] : ((~creative(X0) & happy(X0)) => (~quiet(X0) & ~happy(X0))) [input p3]
11. generous(mary) <=> ? [X0] : (wise(X0) <~> ~wise(X0)) [input p10]
12. ! [X0] : (rich(X0) <=> (wise(X0) & ~patient(X0))) [input p11]
13. ! [X0] : ((curious(X0) <~> ~generous(X0)) => (~rich(X0) & happy(X0))) [input p12]
22. ~humble(fred) [input hypothesis]
24. ! [X0] : (creative(X0) => ~humble(X0)) [unused predicate definition removal 1]
25. ! [X0] : (~humble(X0) | ~creative(X0)) [ennf transformation 24]
26. ! [X0] : ((~quiet(X0) & ~happy(X0)) | (creative(X0) | ~happy(X0))) [ennf transformation 4]
27. ! [X0] : ((~quiet(X0) & ~happy(X0)) | creative(X0) | ~happy(X0)) [flattening 26]
34. ! [X0] : ((~rich(X0) & happy(X0)) | (curious(X0) <=> ~generous(X0))) [ennf transformation 13]
37. ! [X0] : (((~calm(X0) & humble(X0)) | rich(X0)) & (~rich(X0) | (calm(X0) | ~humble(X0)))) [nnf transformation 2]
38. ! [X0] : (((~calm(X0) & humble(X0)) | rich(X0)) & (~rich(X0) | calm(X0) | ~humble(X0))) [flattening 37]
39. (? [X0] : wise(X0) | (~curious(mary) | ~generous(mary))) & ((curious(mary) & generous(mary)) | ! [X0] : ~wise(X0)) [nnf transformation 3]
40. (? [X0] : wise(X0) | ~curious(mary) | ~generous(mary)) & ((curious(mary) & generous(mary)) | ! [X0] : ~wise(X0)) [flattening 39]
41. (? [X0] : wise(X0) | ~curious(mary) | ~generous(mary)) & ((curious(mary) & generous(mary)) | ! [X1] : ~wise(X1)) [rectify 40]
42. ? [X0] : wise(X0) => wise(sK0) [choice axiom]
43. (wise(sK0) | ~curious(mary) | ~generous(mary)) & ((curious(mary) & generous(mary)) | ! [X1] : ~wise(X1)) [skolemisation 41,42]
54. (generous(mary) | ! [X0] : ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (? [X0] : ((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | ~generous(mary)) [nnf transformation 11]
55. (generous(mary) | ! [X0] : ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (? [X1] : ((wise(X1) | ~wise(X1)) & (~wise(X1) | wise(X1))) | ~generous(mary)) [rectify 54]
56. ? [X1] : ((wise(X1) | ~wise(X1)) & (~wise(X1) | wise(X1))) => ((wise(sK3) | ~wise(sK3)) & (~wise(sK3) | wise(sK3))) [choice axiom]
57. (generous(mary) | ! [X0] : ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(sK3) | ~wise(sK3)) & (~wise(sK3) | wise(sK3))) | ~generous(mary)) [skolemisation 55,56]
58. ! [X0] : ((rich(X0) | (~wise(X0) | patient(X0))) & ((wise(X0) & ~patient(X0)) | ~rich(X0))) [nnf transformation 12]
59. ! [X0] : ((rich(X0) | ~wise(X0) | patient(X0)) & ((wise(X0) & ~patient(X0)) | ~rich(X0))) [flattening 58]
60. ! [X0] : ((~rich(X0) & happy(X0)) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0)))) [nnf transformation 34]
70. ~humble(X0) | ~creative(X0) [cnf transformation 25]
72. rich(X0) | humble(X0) [cnf transformation 38]
75. curious(mary) | ~wise(X1) [cnf transformation 43]
77. ~happy(X0) | creative(X0) | ~happy(X0) [cnf transformation 27]
106. generous(mary) | ~wise(X0) | ~wise(X0) [cnf transformation 57]
109. ~rich(X0) | wise(X0) [cnf transformation 59]
111. ~curious(X0) | ~generous(X0) | happy(X0) [cnf transformation 60]
113. ~curious(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 60]
124. ~humble(fred) [cnf transformation 22]
125. generous(mary) | ~wise(X0) [duplicate literal removal 106]
129. ~happy(X0) | creative(X0) [duplicate literal removal 77]
131. 1 <=> generous(mary) [avatar definition]
132. generous(mary) <- (1) [avatar component clause 131]
135. 2 <=> curious(mary) [avatar definition]
136. curious(mary) <- (2) [avatar component clause 135]
144. 4 <=> ! [X1] : ~wise(X1) [avatar definition]
145. ~wise(X1) <- (4) [avatar component clause 144]
146. 4 | 2 [avatar split clause 75,135,144]
206. 4 | 1 [avatar split clause 125,131,144]
242. wise(X0) | humble(X0) [resolution 109,72]
244. humble(X0) <- (4) [subsumption resolution 242,145]
247. $false <- (4) [resolution 244,124]
251. ~4 [avatar contradiction clause 247]
302. ~generous(mary) | happy(mary) <- (2) [resolution 111,136]
303. happy(mary) <- (1, 2) [subsumption resolution 302,132]
328. ~generous(mary) | ~rich(mary) <- (2) [resolution 113,136]
329. ~rich(mary) <- (1, 2) [subsumption resolution 328,132]
389. creative(mary) <- (1, 2) [resolution 303,129]
390. humble(mary) <- (1, 2) [resolution 329,72]
407. ~creative(mary) <- (1, 2) [resolution 390,70]
408. $false <- (1, 2) [subsumption resolution 407,389]
409. ~1 | ~2 [avatar contradiction clause 408]
410. $false [avatar sat refutation 146,206,251,409]
% SZS output end Proof for 3321808489541944488732038
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not old is both rich and not patient and vice versa.
Everyone who is old or not curious is not curious and vice versa.
If someone is either not calm or not wise then fred is funny or old and vice versa.
Everyone who is rich is not brave or not strong.
Everyone who is not creative or tall is humble and vice versa.
If someone is not humble or generous then someone is both creative and quiet and vice versa.
If paul is either tall or old then john is either happy or kind.
Everyone who is not funny or not strong is not brave.
Everyone who is generous or not old is not curious.
If mary is either brave or quiet then alice is both not creative and not quiet and vice versa.
Everyone who is either not curious or not calm is not humble.
If mary is both happy and humble then alice is strong or not humble.
Everyone who is not tall or brave is either calm or strong and vice versa.
If john is calm then susan is both not kind and old and vice versa.
Everyone who is both not funny and creative is either humble or not calm and vice versa.
If fred is not tall or happy then alice is either curious or not funny and vice versa.
Paul is both quiet and kind.
Susan is either calm or funny.
Someone is happy or not funny.
Paul is not generous.
Paul is both old and strong.
Alice is both not patient and old.
Someone is both strong and humble. | Susan is not brave. | neutral | (![X]:((funny(X)<~>~old(X))<=>(rich(X)&~patient(X))))&
(![X]:((old(X)|~curious(X))<=>~curious(X)))&
((?[X]:((~calm(X)<~>~wise(X))))<=>((funny(fred)|old(fred))))&
(![X]:(rich(X)=>(~brave(X)|~strong(X))))&
(![X]:((~creative(X)|tall(X))<=>humble(X)))&
((?[X]:((~humble(X)|generous(X))))<=>(?[X]:((creative(X)&quiet(X)))))&
(((tall(paul)<~>old(paul)))=>((happy(john)<~>kind(john))))&
(![X]:((~funny(X)|~strong(X))=>~brave(X)))&
(![X]:((generous(X)|~old(X))=>~curious(X)))&
(((brave(mary)<~>quiet(mary)))<=>((~creative(alice)&~quiet(alice))))&
(![X]:((~curious(X)<~>~calm(X))=>~humble(X)))&
(((happy(mary)&humble(mary)))=>((strong(alice)|~humble(alice))))&
(![X]:((~tall(X)|brave(X))<=>(calm(X)<~>strong(X))))&
((calm(john))<=>((~kind(susan)&old(susan))))&
(![X]:((~funny(X)&creative(X))<=>(humble(X)<~>~calm(X))))&
(((~tall(fred)|happy(fred)))<=>((curious(alice)<~>~funny(alice))))&
((quiet(paul)&kind(paul)))&
((calm(susan)<~>funny(susan)))&
(?[X]:((happy(X)|~funny(X))))&
(~generous(paul))&
((old(paul)&strong(paul)))&
((~patient(alice)&old(alice)))&
(?[X]:((strong(X)&humble(X)))) | ~brave(susan) | [] | null | 0 |
Everyone who is either not happy or creative is either not tall or happy.
Everyone who is both not calm and not tall is either not generous or old and vice versa.
Everyone who is both not brave and not wise is either not brave or funny and vice versa.
Everyone who is both calm and not funny is both not creative and not humble and vice versa.
If paul is not tall or not happy then someone is both quiet and not happy and vice versa.
If someone is both not wise and strong then someone is both not wise and quiet.
If fred is not old then someone is both creative and not brave and vice versa.
Everyone who is either strong or rich is either strong or not calm.
Everyone who is not rich is both not rich and quiet.
Everyone who is both not humble and calm is either creative or patient.
Everyone who is tall or not patient is humble.
Everyone who is both not wise and not humble is not tall or not creative and vice versa.
Everyone who is not happy is both wise and kind.
Everyone who is either not brave or not kind is rich or calm and vice versa.
Everyone who is quiet or not old is both funny and brave.
If fred is both not calm and funny then someone is curious and vice versa.
Someone is either not brave or wise.
Fred is either not strong or not creative.
Someone is not quiet. | Fred is not humble. | contradiction | (![X]:((~happy(X)<~>creative(X))=>(~tall(X)<~>happy(X))))&
(![X]:((~calm(X)&~tall(X))<=>(~generous(X)<~>old(X))))&
(![X]:((~brave(X)&~wise(X))<=>(~brave(X)<~>funny(X))))&
(![X]:((calm(X)&~funny(X))<=>(~creative(X)&~humble(X))))&
(((~tall(paul)|~happy(paul)))<=>(?[X]:((quiet(X)&~happy(X)))))&
((?[X]:((~wise(X)&strong(X))))=>(?[X]:((~wise(X)&quiet(X)))))&
((~old(fred))<=>(?[X]:((creative(X)&~brave(X)))))&
(![X]:((strong(X)<~>rich(X))=>(strong(X)<~>~calm(X))))&
(![X]:(~rich(X)=>(~rich(X)&quiet(X))))&
(![X]:((~humble(X)&calm(X))=>(creative(X)<~>patient(X))))&
(![X]:((tall(X)|~patient(X))=>humble(X)))&
(![X]:((~wise(X)&~humble(X))<=>(~tall(X)|~creative(X))))&
(![X]:(~happy(X)=>(wise(X)&kind(X))))&
(![X]:((~brave(X)<~>~kind(X))<=>(rich(X)|calm(X))))&
(![X]:((quiet(X)|~old(X))=>(funny(X)&brave(X))))&
(((~calm(fred)&funny(fred)))<=>(?[X]:(curious(X))))&
(?[X]:((~brave(X)<~>wise(X))))&
((~strong(fred)<~>~creative(fred)))&
(?[X]:(~quiet(X))) | ~humble(fred) | [
"p0",
"p2",
"p5",
"p10",
"p11",
"p12",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3665839511702935158345925
% SZS output start Proof for 3665839511702935158345925
1. ! [X0] : ((~happy(X0) <~> creative(X0)) => (~tall(X0) <~> happy(X0))) [input p0]
3. ! [X0] : ((~wise(X0) & ~brave(X0)) <=> (~brave(X0) <~> funny(X0))) [input p2]
6. ? [X0] : (strong(X0) & ~wise(X0)) => ? [X0] : (quiet(X0) & ~wise(X0)) [input p5]
11. ! [X0] : ((~patient(X0) | tall(X0)) => humble(X0)) [input p10]
12. ! [X0] : ((~humble(X0) & ~wise(X0)) <=> (~creative(X0) | ~tall(X0))) [input p11]
13. ! [X0] : (~happy(X0) => (kind(X0) & wise(X0))) [input p12]
15. ! [X0] : ((~old(X0) | quiet(X0)) => (brave(X0) & funny(X0))) [input p14]
18. ~strong(fred) <~> ~creative(fred) [input p17]
20. ~humble(fred) [input hypothesis]
21. ? [X0] : (strong(X0) & ~wise(X0)) => ? [X1] : (quiet(X1) & ~wise(X1)) [rectify 6]
22. ! [X0] : ((~tall(X0) <~> happy(X0)) | (~happy(X0) <=> creative(X0))) [ennf transformation 1]
23. ? [X1] : (quiet(X1) & ~wise(X1)) | ! [X0] : (~strong(X0) | wise(X0)) [ennf transformation 21]
28. ! [X0] : (humble(X0) | (patient(X0) & ~tall(X0))) [ennf transformation 11]
29. ! [X0] : ((kind(X0) & wise(X0)) | happy(X0)) [ennf transformation 13]
30. ! [X0] : ((brave(X0) & funny(X0)) | (old(X0) & ~quiet(X0))) [ennf transformation 15]
31. ! [X0] : (((~happy(X0) | tall(X0)) & (happy(X0) | ~tall(X0))) | ((~happy(X0) | ~creative(X0)) & (creative(X0) | happy(X0)))) [nnf transformation 22]
34. ! [X0] : (((~wise(X0) & ~brave(X0)) | ((~brave(X0) | ~funny(X0)) & (funny(X0) | brave(X0)))) & (((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | (wise(X0) | brave(X0)))) [nnf transformation 3]
35. ! [X0] : (((~wise(X0) & ~brave(X0)) | ((~brave(X0) | ~funny(X0)) & (funny(X0) | brave(X0)))) & (((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | wise(X0) | brave(X0))) [flattening 34]
43. ? [X0] : (quiet(X0) & ~wise(X0)) | ! [X1] : (~strong(X1) | wise(X1)) [rectify 23]
44. ? [X0] : (quiet(X0) & ~wise(X0)) => (quiet(sK1) & ~wise(sK1)) [choice axiom]
45. (quiet(sK1) & ~wise(sK1)) | ! [X1] : (~strong(X1) | wise(X1)) [skolemisation 43,44]
52. ! [X0] : (((~humble(X0) & ~wise(X0)) | (creative(X0) & tall(X0))) & ((~creative(X0) | ~tall(X0)) | (humble(X0) | wise(X0)))) [nnf transformation 12]
53. ! [X0] : (((~humble(X0) & ~wise(X0)) | (creative(X0) & tall(X0))) & (~creative(X0) | ~tall(X0) | humble(X0) | wise(X0))) [flattening 52]
64. (creative(fred) | strong(fred)) & (~creative(fred) | ~strong(fred)) [nnf transformation 18]
70. ~happy(X0) | tall(X0) | ~happy(X0) | ~creative(X0) [cnf transformation 31]
80. ~brave(X0) | ~brave(X0) | ~funny(X0) [cnf transformation 35]
93. quiet(sK1) | ~strong(X1) | wise(X1) [cnf transformation 45]
105. ~tall(X0) | humble(X0) [cnf transformation 28]
108. ~wise(X0) | tall(X0) [cnf transformation 53]
109. ~wise(X0) | creative(X0) [cnf transformation 53]
112. wise(X0) | happy(X0) [cnf transformation 29]
120. ~quiet(X0) | funny(X0) [cnf transformation 30]
122. ~quiet(X0) | brave(X0) [cnf transformation 30]
130. creative(fred) | strong(fred) [cnf transformation 64]
132. ~humble(fred) [cnf transformation 20]
136. ~funny(X0) | ~brave(X0) [duplicate literal removal 80]
138. ~creative(X0) | tall(X0) | ~happy(X0) [duplicate literal removal 70]
165. 6 <=> ! [X1] : (~strong(X1) | wise(X1)) [avatar definition]
166. ~strong(X1) | wise(X1) <- (6) [avatar component clause 165]
168. 7 <=> quiet(sK1) [avatar definition]
170. quiet(sK1) <- (7) [avatar component clause 168]
171. 6 | 7 [avatar split clause 93,168,165]
225. 19 <=> strong(fred) [avatar definition]
227. strong(fred) <- (19) [avatar component clause 225]
229. 20 <=> creative(fred) [avatar definition]
230. ~creative(fred) <- (~20) [avatar component clause 229]
231. creative(fred) <- (20) [avatar component clause 229]
232. 19 | 20 [avatar split clause 130,229,225]
239. tall(X1) | happy(X1) [resolution 112,108]
250. wise(fred) <- (6, 19) [resolution 166,227]
252. creative(fred) <- (6, 19) [resolution 250,109]
254. $false <- (6, 19, ~20) [subsumption resolution 252,230]
255. ~6 | ~19 | 20 [avatar contradiction clause 254]
279. 24 <=> tall(fred) [avatar definition]
280. tall(fred) <- (24) [avatar component clause 279]
330. tall(fred) | ~happy(fred) <- (20) [resolution 138,231]
336. humble(fred) <- (24) [resolution 280,105]
337. $false <- (24) [subsumption resolution 336,132]
338. ~24 [avatar contradiction clause 337]
339. tall(fred) <- (20) [subsumption resolution 330,239]
340. 24 | ~20 [avatar split clause 339,229,279]
345. brave(sK1) <- (7) [resolution 170,122]
346. funny(sK1) <- (7) [resolution 170,120]
375. ~brave(sK1) <- (7) [resolution 346,136]
379. $false <- (7) [subsumption resolution 375,345]
380. ~7 [avatar contradiction clause 379]
381. $false [avatar sat refutation 171,232,255,338,340,380]
% SZS output end Proof for 3665839511702935158345925
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and not generous then john is either not creative or generous and vice versa.
Everyone who is patient is both not humble and not creative.
Everyone who is quiet or tall is calm.
Everyone who is old or creative is calm or funny.
If fred is rich or not happy then susan is both not calm and funny.
Everyone who is both rich and not strong is both old and not curious.
If someone is both not strong and brave then someone is creative and vice versa.
Everyone who is funny is either not humble or strong and vice versa.
Everyone who is not brave or patient is either not calm or not patient and vice versa.
Everyone who is funny or not creative is not funny.
Everyone who is not kind or patient is creative or funny and vice versa.
If john is both patient and tall then alice is not quiet.
If fred is not rich then lucy is either not creative or not old.
Everyone who is not happy or creative is tall and vice versa.
Everyone who is not rich or quiet is either kind or not calm.
If someone is both rich and not curious then alice is humble and vice versa.
Someone is happy or not funny.
Susan is not brave.
Someone is quiet.
Alice is not generous or not brave.
Someone is strong or tall.
Alice is not tall.
Someone is not creative. | Lucy is not funny. | entailment | ((?[X]:((brave(X)&~generous(X))))<=>((~creative(john)<~>generous(john))))&
(![X]:(patient(X)=>(~humble(X)&~creative(X))))&
(![X]:((quiet(X)|tall(X))=>calm(X)))&
(![X]:((old(X)|creative(X))=>(calm(X)|funny(X))))&
(((rich(fred)|~happy(fred)))=>((~calm(susan)&funny(susan))))&
(![X]:((rich(X)&~strong(X))=>(old(X)&~curious(X))))&
((?[X]:((~strong(X)&brave(X))))<=>(?[X]:(creative(X))))&
(![X]:(funny(X)<=>(~humble(X)<~>strong(X))))&
(![X]:((~brave(X)|patient(X))<=>(~calm(X)<~>~patient(X))))&
(![X]:((funny(X)|~creative(X))=>~funny(X)))&
(![X]:((~kind(X)|patient(X))<=>(creative(X)|funny(X))))&
(((patient(john)&tall(john)))=>(~quiet(alice)))&
((~rich(fred))=>((~creative(lucy)<~>~old(lucy))))&
(![X]:((~happy(X)|creative(X))<=>tall(X)))&
(![X]:((~rich(X)|quiet(X))=>(kind(X)<~>~calm(X))))&
((?[X]:((rich(X)&~curious(X))))<=>(humble(alice)))&
(?[X]:((happy(X)|~funny(X))))&
(~brave(susan))&
(?[X]:(quiet(X)))&
((~generous(alice)|~brave(alice)))&
(?[X]:((strong(X)|tall(X))))&
(~tall(alice))&
(?[X]:(~creative(X))) | ~funny(lucy) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4242437289503702615992588
% SZS output start Proof for 4242437289503702615992588
10. ! [X0] : ((~creative(X0) | funny(X0)) => ~funny(X0)) [input p9]
24. funny(lucy) [input hypothesis]
33. ! [X0] : (~funny(X0) | (creative(X0) & ~funny(X0))) [ennf transformation 10]
99. ~funny(X0) | ~funny(X0) [cnf transformation 33]
125. funny(lucy) [cnf transformation 24]
126. ~funny(X0) [duplicate literal removal 99]
246. $false [subsumption resolution 125,126]
% SZS output end Proof for 4242437289503702615992588
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and not happy is either old or not curious.
Everyone who is not strong or quiet is both funny and humble and vice versa.
If john is happy then someone is both not brave and not old and vice versa.
If lucy is either humble or kind then someone is not kind.
If someone is both not rich and humble then paul is both not calm and not tall.
Everyone who is both funny and wise is both not funny and not curious and vice versa.
If fred is not happy or not generous then mary is not funny and vice versa.
If fred is not old then someone is curious or not happy.
Everyone who is both kind and not curious is both not happy and calm and vice versa.
If alice is generous then someone is brave.
Everyone who is wise is either humble or not creative.
If john is old or wise then john is not curious or not wise and vice versa.
Everyone who is both not rich and generous is tall or not creative.
If someone is both not funny and not curious then paul is wise or not kind.
If susan is either rich or generous then john is strong or not quiet.
If paul is both not creative and kind then fred is not calm or calm and vice versa.
Susan is calm or curious.
Fred is either not patient or quiet.
Someone is either kind or old.
Alice is not calm.
Lucy is either humble or old.
Someone is tall or kind.
Susan is both brave and not humble.
Someone is rich or funny. | Paul is not kind. | contradiction | (![X]:((~calm(X)&~happy(X))=>(old(X)<~>~curious(X))))&
(![X]:((~strong(X)|quiet(X))<=>(funny(X)&humble(X))))&
((happy(john))<=>(?[X]:((~brave(X)&~old(X)))))&
(((humble(lucy)<~>kind(lucy)))=>(?[X]:(~kind(X))))&
((?[X]:((~rich(X)&humble(X))))=>((~calm(paul)&~tall(paul))))&
(![X]:((funny(X)&wise(X))<=>(~funny(X)&~curious(X))))&
(((~happy(fred)|~generous(fred)))<=>(~funny(mary)))&
((~old(fred))=>(?[X]:((curious(X)|~happy(X)))))&
(![X]:((kind(X)&~curious(X))<=>(~happy(X)&calm(X))))&
((generous(alice))=>(?[X]:(brave(X))))&
(![X]:(wise(X)=>(humble(X)<~>~creative(X))))&
(((old(john)|wise(john)))<=>((~curious(john)|~wise(john))))&
(![X]:((~rich(X)&generous(X))=>(tall(X)|~creative(X))))&
((?[X]:((~funny(X)&~curious(X))))=>((wise(paul)|~kind(paul))))&
(((rich(susan)<~>generous(susan)))=>((strong(john)|~quiet(john))))&
(((~creative(paul)&kind(paul)))<=>((~calm(fred)|calm(fred))))&
((calm(susan)|curious(susan)))&
((~patient(fred)<~>quiet(fred)))&
(?[X]:((kind(X)<~>old(X))))&
(~calm(alice))&
((humble(lucy)<~>old(lucy)))&
(?[X]:((tall(X)|kind(X))))&
((brave(susan)&~humble(susan)))&
(?[X]:((rich(X)|funny(X)))) | ~kind(paul) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4245384339415455063103999
% SZS output start Proof for 4245384339415455063103999
16. (kind(paul) & ~creative(paul)) <=> (calm(fred) | ~calm(fred)) [input p15]
25. ~kind(paul) [input hypothesis]
63. ((kind(paul) & ~creative(paul)) | (~calm(fred) & calm(fred))) & ((calm(fred) | ~calm(fred)) | (~kind(paul) | creative(paul))) [nnf transformation 16]
64. ((kind(paul) & ~creative(paul)) | (~calm(fred) & calm(fred))) & (calm(fred) | ~calm(fred) | ~kind(paul) | creative(paul)) [flattening 63]
114. kind(paul) | calm(fred) [cnf transformation 64]
115. kind(paul) | ~calm(fred) [cnf transformation 64]
128. ~kind(paul) [cnf transformation 25]
250. 26 <=> calm(fred) [avatar definition]
254. 27 <=> kind(paul) [avatar definition]
257. ~26 | 27 [avatar split clause 115,254,250]
258. 26 | 27 [avatar split clause 114,254,250]
318. ~27 [avatar split clause 128,254]
319. $false [avatar sat refutation 257,258,318]
% SZS output end Proof for 4245384339415455063103999
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both calm and not wise then john is either strong or not brave and vice versa. If lucy is patient then someone is both not creative and patient. Everyone who is calm or not happy is both patient and happy and vice versa. Everyone who is both not tall and not quiet is both tall and not brave and vice versa. Everyone who is both wise and not strong is rich or not tall and vice versa. If john is both generous and curious then someone is not wise or not brave. If someone is either calm or wise then alice is both wise and not happy and vice versa. If someone is either not creative or happy then fred is either not wise or not curious. Everyone who is either not creative or creative is either not funny or kind and vice versa. Everyone who is rich or creative is not creative and vice versa. Everyone who is quiet is rich or quiet and vice versa. Everyone who is generous or not happy is not strong and vice versa. Everyone who is either not rich or not humble is both not quiet and not wise and vice versa. If fred is not kind or not strong then fred is not tall or quiet and vice versa. Everyone who is happy is patient. Someone is tall or not strong. Fred is not tall or not happy. Mary is either brave or not old. Fred is not kind. | John is not generous. | contradiction | (((calm(alice)&~wise(alice)))<=>((strong(john)<~>~brave(john))))&
((patient(lucy))=>(?[X]:((~creative(X)&patient(X)))))&
(![X]:((calm(X)|~happy(X))<=>(patient(X)&happy(X))))&
(![X]:((~tall(X)&~quiet(X))<=>(tall(X)&~brave(X))))&
(![X]:((wise(X)&~strong(X))<=>(rich(X)|~tall(X))))&
(((generous(john)&curious(john)))=>(?[X]:((~wise(X)|~brave(X)))))&
((?[X]:((calm(X)<~>wise(X))))<=>((wise(alice)&~happy(alice))))&
((?[X]:((~creative(X)<~>happy(X))))=>((~wise(fred)<~>~curious(fred))))&
(![X]:((~creative(X)<~>creative(X))<=>(~funny(X)<~>kind(X))))&
(![X]:((rich(X)|creative(X))<=>~creative(X)))&
(![X]:(quiet(X)<=>(rich(X)|quiet(X))))&
(![X]:((generous(X)|~happy(X))<=>~strong(X)))&
(![X]:((~rich(X)<~>~humble(X))<=>(~quiet(X)&~wise(X))))&
(((~kind(fred)|~strong(fred)))<=>((~tall(fred)|quiet(fred))))&
(![X]:(happy(X)=>patient(X)))&
(?[X]:((tall(X)|~strong(X))))&
((~tall(fred)|~happy(fred)))&
((brave(mary)<~>~old(mary)))&
(~kind(fred)) | ~generous(john) | [
"p2",
"p4",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7391861352171096066126173
% SZS output start Proof for 7391861352171096066126173
3. ! [X0] : ((~happy(X0) | calm(X0)) <=> (happy(X0) & patient(X0))) [input p2]
5. ! [X0] : ((~strong(X0) & wise(X0)) <=> (~tall(X0) | rich(X0))) [input p4]
10. ! [X0] : ((creative(X0) | rich(X0)) <=> ~creative(X0)) [input p9]
12. ! [X0] : ((~happy(X0) | generous(X0)) <=> ~strong(X0)) [input p11]
20. ~generous(john) [input hypothesis]
30. ! [X0] : (((~happy(X0) | calm(X0)) | (~happy(X0) | ~patient(X0))) & ((happy(X0) & patient(X0)) | (happy(X0) & ~calm(X0)))) [nnf transformation 3]
31. ! [X0] : ((~happy(X0) | calm(X0) | ~happy(X0) | ~patient(X0)) & ((happy(X0) & patient(X0)) | (happy(X0) & ~calm(X0)))) [flattening 30]
34. ! [X0] : (((~strong(X0) & wise(X0)) | (tall(X0) & ~rich(X0))) & ((~tall(X0) | rich(X0)) | (strong(X0) | ~wise(X0)))) [nnf transformation 5]
35. ! [X0] : (((~strong(X0) & wise(X0)) | (tall(X0) & ~rich(X0))) & (~tall(X0) | rich(X0) | strong(X0) | ~wise(X0))) [flattening 34]
45. ! [X0] : (((creative(X0) | rich(X0)) | creative(X0)) & (~creative(X0) | (~creative(X0) & ~rich(X0)))) [nnf transformation 10]
46. ! [X0] : ((creative(X0) | rich(X0) | creative(X0)) & (~creative(X0) | (~creative(X0) & ~rich(X0)))) [flattening 45]
49. ! [X0] : (((~happy(X0) | generous(X0)) | strong(X0)) & (~strong(X0) | (happy(X0) & ~generous(X0)))) [nnf transformation 12]
50. ! [X0] : ((~happy(X0) | generous(X0) | strong(X0)) & (~strong(X0) | (happy(X0) & ~generous(X0)))) [flattening 49]
69. happy(X0) | happy(X0) [cnf transformation 31]
78. ~rich(X0) | ~strong(X0) [cnf transformation 35]
100. ~creative(X0) | ~creative(X0) [cnf transformation 46]
101. creative(X0) | rich(X0) | creative(X0) [cnf transformation 46]
107. ~happy(X0) | generous(X0) | strong(X0) [cnf transformation 50]
124. ~generous(john) [cnf transformation 20]
125. ~creative(X0) [duplicate literal removal 100]
126. rich(X0) | creative(X0) [duplicate literal removal 101]
133. happy(X0) [duplicate literal removal 69]
172. 8 <=> generous(john) [avatar definition]
174. ~generous(john) <- (~8) [avatar component clause 172]
192. 12 <=> ! [X0] : ~creative(X0) [avatar definition]
193. ~creative(X0) <- (12) [avatar component clause 192]
207. 12 [avatar split clause 125,192]
208. generous(X0) | strong(X0) [subsumption resolution 107,133]
241. ~8 [avatar split clause 124,172]
249. creative(X2) | ~strong(X2) [resolution 126,78]
252. ~strong(X2) <- (12) [subsumption resolution 249,193]
268. strong(john) <- (~8) [resolution 208,174]
270. $false <- (~8, 12) [subsumption resolution 268,252]
271. 8 | ~12 [avatar contradiction clause 270]
272. $false [avatar sat refutation 207,241,271]
% SZS output end Proof for 7391861352171096066126173
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or not curious is either calm or old and vice versa. Everyone who is either not brave or generous is tall or not rich. Everyone who is both not curious and patient is both patient and curious and vice versa. If paul is not happy or not curious then someone is either not funny or strong. Everyone who is either not creative or not generous is not strong or generous. Everyone who is either brave or not wise is not kind or funny. Everyone who is strong or funny is either not curious or not happy and vice versa. If someone is wise then susan is funny or generous and vice versa. Everyone who is either not creative or humble is not strong or curious. If paul is both not calm and not patient then someone is not rich and vice versa. If someone is either brave or not happy then fred is not funny or not happy and vice versa. Everyone who is not generous or not strong is either not calm or curious. If alice is not generous or quiet then susan is either not rich or not brave and vice versa. If alice is both not patient and kind then someone is both not happy and not quiet and vice versa. Everyone who is both not generous and funny is either not quiet or not humble. If john is both not wise and curious then someone is both not quiet and not happy and vice versa. John is not creative or generous. Someone is both not quiet and tall. Someone is not rich or not patient. Someone is strong or quiet. Someone is not tall. Someone is humble. | Fred is not creative. | neutral | (![X]:((~happy(X)<~>~curious(X))<=>(calm(X)<~>old(X))))&
(![X]:((~brave(X)<~>generous(X))=>(tall(X)|~rich(X))))&
(![X]:((~curious(X)&patient(X))<=>(patient(X)&curious(X))))&
(((~happy(paul)|~curious(paul)))=>(?[X]:((~funny(X)<~>strong(X)))))&
(![X]:((~creative(X)<~>~generous(X))=>(~strong(X)|generous(X))))&
(![X]:((brave(X)<~>~wise(X))=>(~kind(X)|funny(X))))&
(![X]:((strong(X)|funny(X))<=>(~curious(X)<~>~happy(X))))&
((?[X]:(wise(X)))<=>((funny(susan)|generous(susan))))&
(![X]:((~creative(X)<~>humble(X))=>(~strong(X)|curious(X))))&
(((~calm(paul)&~patient(paul)))<=>(?[X]:(~rich(X))))&
((?[X]:((brave(X)<~>~happy(X))))<=>((~funny(fred)|~happy(fred))))&
(![X]:((~generous(X)|~strong(X))=>(~calm(X)<~>curious(X))))&
(((~generous(alice)|quiet(alice)))<=>((~rich(susan)<~>~brave(susan))))&
(((~patient(alice)&kind(alice)))<=>(?[X]:((~happy(X)&~quiet(X)))))&
(![X]:((~generous(X)&funny(X))=>(~quiet(X)<~>~humble(X))))&
(((~wise(john)&curious(john)))<=>(?[X]:((~quiet(X)&~happy(X)))))&
((~creative(john)|generous(john)))&
(?[X]:((~quiet(X)&tall(X))))&
(?[X]:((~rich(X)|~patient(X))))&
(?[X]:((strong(X)|quiet(X))))&
(?[X]:(~tall(X)))&
(?[X]:(humble(X))) | ~creative(fred) | [] | null | 0 |
If someone is either creative or patient then someone is generous or not kind.
Everyone who is not brave is both calm and not calm.
Everyone who is both not humble and not strong is either not wise or not calm.
Everyone who is either creative or quiet is either not rich or humble and vice versa.
Everyone who is either curious or not funny is curious or not wise and vice versa.
Everyone who is happy is not happy or funny.
Everyone who is rich or not creative is either not tall or curious.
If someone is not happy then someone is both old and funny and vice versa.
Everyone who is either not tall or calm is not funny and vice versa.
If someone is either strong or old then someone is not patient and vice versa.
Everyone who is not wise is both kind and not funny and vice versa.
Everyone who is both creative and kind is both not kind and not wise.
Everyone who is both funny and not tall is either not kind or not strong and vice versa.
Everyone who is either happy or kind is not strong or not wise.
Everyone who is either old or funny is both not kind and strong.
Everyone who is not old or strong is either calm or old and vice versa.
Someone is rich.
Someone is either not strong or brave.
Someone is patient or not tall.
Lucy is both not patient and not old.
Someone is not kind or humble.
Susan is either not humble or not creative.
Someone is either not generous or not brave.
Someone is both not old and not curious. | Lucy is not brave. | contradiction | ((?[X]:((creative(X)<~>patient(X))))=>(?[X]:((generous(X)|~kind(X)))))&
(![X]:(~brave(X)=>(calm(X)&~calm(X))))&
(![X]:((~humble(X)&~strong(X))=>(~wise(X)<~>~calm(X))))&
(![X]:((creative(X)<~>quiet(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((curious(X)<~>~funny(X))<=>(curious(X)|~wise(X))))&
(![X]:(happy(X)=>(~happy(X)|funny(X))))&
(![X]:((rich(X)|~creative(X))=>(~tall(X)<~>curious(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((old(X)&funny(X)))))&
(![X]:((~tall(X)<~>calm(X))<=>~funny(X)))&
((?[X]:((strong(X)<~>old(X))))<=>(?[X]:(~patient(X))))&
(![X]:(~wise(X)<=>(kind(X)&~funny(X))))&
(![X]:((creative(X)&kind(X))=>(~kind(X)&~wise(X))))&
(![X]:((funny(X)&~tall(X))<=>(~kind(X)<~>~strong(X))))&
(![X]:((happy(X)<~>kind(X))=>(~strong(X)|~wise(X))))&
(![X]:((old(X)<~>funny(X))=>(~kind(X)&strong(X))))&
(![X]:((~old(X)|strong(X))<=>(calm(X)<~>old(X))))&
(?[X]:(rich(X)))&
(?[X]:((~strong(X)<~>brave(X))))&
(?[X]:((patient(X)|~tall(X))))&
((~patient(lucy)&~old(lucy)))&
(?[X]:((~kind(X)|humble(X))))&
((~humble(susan)<~>~creative(susan)))&
(?[X]:((~generous(X)<~>~brave(X))))&
(?[X]:((~old(X)&~curious(X)))) | ~brave(lucy) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 539175845680537447020524
% SZS output start Proof for 539175845680537447020524
2. ! [X0] : (~brave(X0) => (~calm(X0) & calm(X0))) [input p1]
25. ~brave(lucy) [input hypothesis]
30. ! [X0] : ((~calm(X0) & calm(X0)) | brave(X0)) [ennf transformation 2]
86. calm(X0) | brave(X0) [cnf transformation 30]
87. ~calm(X0) | brave(X0) [cnf transformation 30]
156. ~brave(lucy) [cnf transformation 25]
179. brave(X0) [subsumption resolution 86,87]
258. $false [subsumption resolution 156,179]
% SZS output end Proof for 539175845680537447020524
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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