premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If someone is both not strong and curious then someone is either old or creative and vice versa.
Everyone who is happy is not humble or curious.
If someone is both not creative and not strong then paul is wise and vice versa.
If someone is either not tall or old then someone is either not happy or old and vice versa.
Everyone who is either brave or calm is rich or generous and vice versa.
If alice is either generous or not generous then alice is both brave and not kind.
Everyone who is not tall or wise is both not rich and quiet and vice versa.
Everyone who is both not tall and not patient is either calm or quiet.
Everyone who is not quiet or not humble is humble or old.
If alice is not brave or not happy then someone is patient or not happy.
Everyone who is patient or happy is either not happy or old and vice versa.
If someone is both not patient and not quiet then someone is either not tall or rich and vice versa.
If someone is not strong or humble then someone is not rich and vice versa.
If mary is both not generous and not curious then alice is both not curious and strong.
Everyone who is both not wise and not quiet is not rich and vice versa.
Someone is not humble or not funny.
Someone is not wise.
John is either not brave or happy.
John is both not happy and not humble.
Lucy is either old or not quiet.
Alice is not strong.
Someone is creative or calm.
Alice is not quiet or kind. | John is not tall. | contradiction | ((?[X]:((~strong(X)&curious(X))))<=>(?[X]:((old(X)<~>creative(X)))))&
(![X]:(happy(X)=>(~humble(X)|curious(X))))&
((?[X]:((~creative(X)&~strong(X))))<=>(wise(paul)))&
((?[X]:((~tall(X)<~>old(X))))<=>(?[X]:((~happy(X)<~>old(X)))))&
(![X]:((brave(X)<~>calm(X))<=>(rich(X)|generous(X))))&
(((generous(alice)<~>~generous(alice)))=>((brave(alice)&~kind(alice))))&
(![X]:((~tall(X)|wise(X))<=>(~rich(X)&quiet(X))))&
(![X]:((~tall(X)&~patient(X))=>(calm(X)<~>quiet(X))))&
(![X]:((~quiet(X)|~humble(X))=>(humble(X)|old(X))))&
(((~brave(alice)|~happy(alice)))=>(?[X]:((patient(X)|~happy(X)))))&
(![X]:((patient(X)|happy(X))<=>(~happy(X)<~>old(X))))&
((?[X]:((~patient(X)&~quiet(X))))<=>(?[X]:((~tall(X)<~>rich(X)))))&
((?[X]:((~strong(X)|humble(X))))<=>(?[X]:(~rich(X))))&
(((~generous(mary)&~curious(mary)))=>((~curious(alice)&strong(alice))))&
(![X]:((~wise(X)&~quiet(X))<=>~rich(X)))&
(?[X]:((~humble(X)|~funny(X))))&
(?[X]:(~wise(X)))&
((~brave(john)<~>happy(john)))&
((~happy(john)&~humble(john)))&
((old(lucy)<~>~quiet(lucy)))&
(~strong(alice))&
(?[X]:((creative(X)|calm(X))))&
((~quiet(alice)|kind(alice))) | ~tall(john) | [
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5244251420792625517232596
% SZS output start Proof for 5244251420792625517232596
7. ! [X0] : ((wise(X0) | ~tall(X0)) <=> (quiet(X0) & ~rich(X0))) [input p6]
15. ! [X0] : ((~quiet(X0) & ~wise(X0)) <=> ~rich(X0)) [input p14]
24. ~tall(john) [input hypothesis]
57. ! [X0] : (((wise(X0) | ~tall(X0)) | (~quiet(X0) | rich(X0))) & ((quiet(X0) & ~rich(X0)) | (~wise(X0) & tall(X0)))) [nnf transformation 7]
58. ! [X0] : ((wise(X0) | ~tall(X0) | ~quiet(X0) | rich(X0)) & ((quiet(X0) & ~rich(X0)) | (~wise(X0) & tall(X0)))) [flattening 57]
74. ! [X0] : (((~quiet(X0) & ~wise(X0)) | rich(X0)) & (~rich(X0) | (quiet(X0) | wise(X0)))) [nnf transformation 15]
75. ! [X0] : (((~quiet(X0) & ~wise(X0)) | rich(X0)) & (~rich(X0) | quiet(X0) | wise(X0))) [flattening 74]
110. ~rich(X0) | tall(X0) [cnf transformation 58]
112. quiet(X0) | tall(X0) [cnf transformation 58]
140. ~quiet(X0) | rich(X0) [cnf transformation 75]
151. ~tall(john) [cnf transformation 24]
286. 28 <=> ! [X1] : tall(X1) [avatar definition]
287. tall(X1) <- (28) [avatar component clause 286]
394. rich(X0) | tall(X0) [resolution 140,112]
395. tall(X0) [subsumption resolution 394,110]
396. 28 [avatar split clause 395,286]
397. $false <- (28) [resolution 287,151]
402. ~28 [avatar contradiction clause 397]
403. $false [avatar sat refutation 396,402]
% SZS output end Proof for 5244251420792625517232596
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or happy is both curious and not funny.
If john is both creative and tall then lucy is not rich or rich and vice versa.
Everyone who is both strong and patient is either quiet or not quiet and vice versa.
If someone is quiet then fred is not humble or not happy.
If fred is not generous or not curious then fred is not strong or old.
If someone is humble then alice is calm or funny.
Everyone who is humble or calm is rich and vice versa.
If someone is either humble or not funny then someone is not generous or not wise and vice versa.
Everyone who is not generous or old is rich or wise.
If someone is brave or not old then someone is not curious.
Everyone who is either quiet or not generous is generous.
If someone is either not generous or not old then someone is calm and vice versa.
Everyone who is either humble or not curious is kind or calm.
If someone is either not happy or not wise then someone is either not happy or not calm.
Everyone who is calm or not humble is not kind and vice versa.
Everyone who is not calm is quiet or not quiet and vice versa.
Someone is either not old or quiet.
Fred is humble.
Someone is not rich.
Mary is not old or quiet.
Susan is strong.
Someone is not calm.
Alice is either strong or quiet.
Someone is not tall. | Alice is not happy. | entailment | (![X]:((~tall(X)|happy(X))=>(curious(X)&~funny(X))))&
(((creative(john)&tall(john)))<=>((~rich(lucy)|rich(lucy))))&
(![X]:((strong(X)&patient(X))<=>(quiet(X)<~>~quiet(X))))&
((?[X]:(quiet(X)))=>((~humble(fred)|~happy(fred))))&
(((~generous(fred)|~curious(fred)))=>((~strong(fred)|old(fred))))&
((?[X]:(humble(X)))=>((calm(alice)|funny(alice))))&
(![X]:((humble(X)|calm(X))<=>rich(X)))&
((?[X]:((humble(X)<~>~funny(X))))<=>(?[X]:((~generous(X)|~wise(X)))))&
(![X]:((~generous(X)|old(X))=>(rich(X)|wise(X))))&
((?[X]:((brave(X)|~old(X))))=>(?[X]:(~curious(X))))&
(![X]:((quiet(X)<~>~generous(X))=>generous(X)))&
((?[X]:((~generous(X)<~>~old(X))))<=>(?[X]:(calm(X))))&
(![X]:((humble(X)<~>~curious(X))=>(kind(X)|calm(X))))&
((?[X]:((~happy(X)<~>~wise(X))))=>(?[X]:((~happy(X)<~>~calm(X)))))&
(![X]:((calm(X)|~humble(X))<=>~kind(X)))&
(![X]:(~calm(X)<=>(quiet(X)|~quiet(X))))&
(?[X]:((~old(X)<~>quiet(X))))&
(humble(fred))&
(?[X]:(~rich(X)))&
((~old(mary)|quiet(mary)))&
(strong(susan))&
(?[X]:(~calm(X)))&
((strong(alice)<~>quiet(alice)))&
(?[X]:(~tall(X))) | ~happy(alice) | [
"p0",
"p5",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4915249063253763739216867
% SZS output start Proof for 4915249063253763739216867
1. ! [X0] : ((happy(X0) | ~tall(X0)) => (~funny(X0) & curious(X0))) [input p0]
6. ? [X0] : humble(X0) => (funny(alice) | calm(alice)) [input p5]
16. ! [X0] : (~calm(X0) <=> (~quiet(X0) | quiet(X0))) [input p15]
18. humble(fred) [input p17]
25. happy(alice) [input hypothesis]
32. ! [X0] : ((~funny(X0) & curious(X0)) | (~happy(X0) & tall(X0))) [ennf transformation 1]
37. (funny(alice) | calm(alice)) | ! [X0] : ~humble(X0) [ennf transformation 6]
38. funny(alice) | calm(alice) | ! [X0] : ~humble(X0) [flattening 37]
72. ! [X0] : ((~calm(X0) | (quiet(X0) & ~quiet(X0))) & ((~quiet(X0) | quiet(X0)) | calm(X0))) [nnf transformation 16]
73. ! [X0] : ((~calm(X0) | (quiet(X0) & ~quiet(X0))) & (~quiet(X0) | quiet(X0) | calm(X0))) [flattening 72]
87. ~funny(X0) | ~happy(X0) [cnf transformation 32]
102. funny(alice) | calm(alice) | ~humble(X0) [cnf transformation 38]
130. ~calm(X0) | ~quiet(X0) [cnf transformation 73]
131. ~calm(X0) | quiet(X0) [cnf transformation 73]
134. humble(fred) [cnf transformation 18]
142. happy(alice) [cnf transformation 25]
170. 5 <=> humble(fred) [avatar definition]
171. humble(fred) <- (5) [avatar component clause 170]
195. 10 <=> ! [X0] : ~humble(X0) [avatar definition]
196. ~humble(X0) <- (10) [avatar component clause 195]
198. 11 <=> calm(alice) [avatar definition]
200. calm(alice) <- (11) [avatar component clause 198]
202. 12 <=> funny(alice) [avatar definition]
204. funny(alice) <- (12) [avatar component clause 202]
205. 10 | 11 | 12 [avatar split clause 102,202,198,195]
249. 23 <=> ! [X1] : ~calm(X1) [avatar definition]
250. ~calm(X1) <- (23) [avatar component clause 249]
291. ~calm(X0) [subsumption resolution 130,131]
292. 23 [avatar split clause 291,249]
303. 5 [avatar split clause 134,170]
314. $false <- (5, 10) [subsumption resolution 171,196]
315. ~5 | ~10 [avatar contradiction clause 314]
316. $false <- (11, 23) [subsumption resolution 200,250]
317. ~11 | ~23 [avatar contradiction clause 316]
324. ~happy(alice) <- (12) [resolution 87,204]
325. $false <- (12) [subsumption resolution 324,142]
326. ~12 [avatar contradiction clause 325]
327. $false [avatar sat refutation 205,292,303,315,317,326]
% SZS output end Proof for 4915249063253763739216867
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or not humble is both generous and not patient.
If someone is not creative or not humble then paul is either rich or not tall.
Everyone who is both wise and not happy is either not calm or humble.
Everyone who is creative is both patient and old.
If someone is kind or calm then someone is not wise or brave.
Everyone who is not funny is either not wise or not patient.
Everyone who is both not curious and creative is either brave or not old.
Everyone who is either not old or not happy is both patient and not tall and vice versa.
If mary is quiet then paul is not rich.
Everyone who is not old or curious is not tall.
Everyone who is either brave or not happy is funny or old and vice versa.
Everyone who is not patient or creative is both not tall and not creative and vice versa.
Everyone who is not brave or happy is not patient and vice versa.
If someone is either not happy or not old then fred is kind.
Everyone who is either tall or strong is both not calm and not strong and vice versa.
Paul is either not wise or kind.
Fred is quiet.
Someone is kind or brave.
Fred is either wise or not creative. | Paul is rich. | contradiction | (![X]:((~generous(X)|~humble(X))=>(generous(X)&~patient(X))))&
((?[X]:((~creative(X)|~humble(X))))=>((rich(paul)<~>~tall(paul))))&
(![X]:((wise(X)&~happy(X))=>(~calm(X)<~>humble(X))))&
(![X]:(creative(X)=>(patient(X)&old(X))))&
((?[X]:((kind(X)|calm(X))))=>(?[X]:((~wise(X)|brave(X)))))&
(![X]:(~funny(X)=>(~wise(X)<~>~patient(X))))&
(![X]:((~curious(X)&creative(X))=>(brave(X)<~>~old(X))))&
(![X]:((~old(X)<~>~happy(X))<=>(patient(X)&~tall(X))))&
((quiet(mary))=>(~rich(paul)))&
(![X]:((~old(X)|curious(X))=>~tall(X)))&
(![X]:((brave(X)<~>~happy(X))<=>(funny(X)|old(X))))&
(![X]:((~patient(X)|creative(X))<=>(~tall(X)&~creative(X))))&
(![X]:((~brave(X)|happy(X))<=>~patient(X)))&
((?[X]:((~happy(X)<~>~old(X))))=>(kind(fred)))&
(![X]:((tall(X)<~>strong(X))<=>(~calm(X)&~strong(X))))&
((~wise(paul)<~>kind(paul)))&
(quiet(fred))&
(?[X]:((kind(X)|brave(X))))&
((wise(fred)<~>~creative(fred))) | rich(paul) | [
"p1",
"p7",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5073466281341841288670883
% SZS output start Proof for 5073466281341841288670883
2. ? [X0] : (~humble(X0) | ~creative(X0)) => (rich(paul) <~> ~tall(paul)) [input p1]
8. ! [X0] : ((~old(X0) <~> ~happy(X0)) <=> (~tall(X0) & patient(X0))) [input p7]
10. ! [X0] : ((curious(X0) | ~old(X0)) => ~tall(X0)) [input p9]
12. ! [X0] : ((creative(X0) | ~patient(X0)) <=> (~creative(X0) & ~tall(X0))) [input p11]
13. ! [X0] : ((happy(X0) | ~brave(X0)) <=> ~patient(X0)) [input p12]
20. rich(paul) [input hypothesis]
24. (rich(paul) <~> ~tall(paul)) | ! [X0] : (humble(X0) & creative(X0)) [ennf transformation 2]
33. ! [X0] : (~tall(X0) | (~curious(X0) & old(X0))) [ennf transformation 10]
35. ((tall(paul) | ~rich(paul)) & (~tall(paul) | rich(paul))) | ! [X0] : (humble(X0) & creative(X0)) [nnf transformation 24]
42. ! [X0] : ((((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | (tall(X0) | ~patient(X0))) & ((~tall(X0) & patient(X0)) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0))))) [nnf transformation 8]
43. ! [X0] : ((((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | tall(X0) | ~patient(X0)) & ((~tall(X0) & patient(X0)) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0))))) [flattening 42]
46. ! [X0] : (((creative(X0) | ~patient(X0)) | (creative(X0) | tall(X0))) & ((~creative(X0) & ~tall(X0)) | (~creative(X0) & patient(X0)))) [nnf transformation 12]
47. ! [X0] : ((creative(X0) | ~patient(X0) | creative(X0) | tall(X0)) & ((~creative(X0) & ~tall(X0)) | (~creative(X0) & patient(X0)))) [flattening 46]
48. ! [X0] : (((happy(X0) | ~brave(X0)) | patient(X0)) & (~patient(X0) | (~happy(X0) & brave(X0)))) [nnf transformation 13]
49. ! [X0] : ((happy(X0) | ~brave(X0) | patient(X0)) & (~patient(X0) | (~happy(X0) & brave(X0)))) [flattening 48]
60. tall(paul) | ~rich(paul) | creative(X0) [cnf transformation 35]
75. ~old(X0) | ~tall(X0) | happy(X0) [cnf transformation 43]
79. ~tall(X0) | old(X0) [cnf transformation 33]
87. ~tall(X0) | patient(X0) [cnf transformation 47]
90. ~creative(X0) | ~creative(X0) [cnf transformation 47]
93. ~happy(X0) | ~patient(X0) [cnf transformation 49]
109. rich(paul) [cnf transformation 20]
112. ~creative(X0) [duplicate literal removal 90]
118. 2 <=> rich(paul) [avatar definition]
122. 3 <=> tall(paul) [avatar definition]
124. tall(paul) <- (3) [avatar component clause 122]
127. 4 <=> ! [X0] : creative(X0) [avatar definition]
128. creative(X0) <- (4) [avatar component clause 127]
129. 4 | ~2 | 3 [avatar split clause 60,122,118,127]
186. 2 [avatar split clause 109,118]
187. old(paul) <- (3) [resolution 79,124]
188. patient(paul) <- (3) [resolution 87,124]
192. ~tall(paul) | happy(paul) <- (3) [resolution 75,187]
193. happy(paul) <- (3) [subsumption resolution 192,124]
196. ~patient(paul) <- (3) [resolution 193,93]
197. $false <- (3) [subsumption resolution 196,188]
198. ~3 [avatar contradiction clause 197]
199. $false <- (4) [subsumption resolution 128,112]
200. ~4 [avatar contradiction clause 199]
201. $false [avatar sat refutation 129,186,198,200]
% SZS output end Proof for 5073466281341841288670883
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not old then someone is not kind or not curious.
If someone is both not quiet and not patient then mary is not strong and vice versa.
If someone is not patient or old then mary is kind and vice versa.
If alice is not strong or not old then someone is not wise and vice versa.
If someone is not tall then someone is happy or not wise and vice versa.
If someone is not funny then someone is both tall and not quiet.
Everyone who is either not quiet or not creative is both brave and not creative.
Everyone who is tall or quiet is not strong.
If mary is not funny or not kind then paul is either wise or strong.
Everyone who is both funny and not kind is not calm or not old.
If someone is wise or curious then someone is both brave and not old and vice versa.
Everyone who is strong or not funny is both not humble and not quiet and vice versa.
Everyone who is both not kind and tall is both calm and not wise.
Everyone who is not patient or not funny is both patient and not rich and vice versa.
Everyone who is brave is creative or patient and vice versa.
If fred is tall then someone is not funny or not calm and vice versa.
Someone is not tall or calm.
Someone is both funny and not kind.
Alice is patient.
Susan is not strong.
Alice is not kind.
Someone is either tall or not brave.
Paul is either creative or not rich. | Mary is patient. | entailment | ((~old(alice))=>(?[X]:((~kind(X)|~curious(X)))))&
((?[X]:((~quiet(X)&~patient(X))))<=>(~strong(mary)))&
((?[X]:((~patient(X)|old(X))))<=>(kind(mary)))&
(((~strong(alice)|~old(alice)))<=>(?[X]:(~wise(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((happy(X)|~wise(X)))))&
((?[X]:(~funny(X)))=>(?[X]:((tall(X)&~quiet(X)))))&
(![X]:((~quiet(X)<~>~creative(X))=>(brave(X)&~creative(X))))&
(![X]:((tall(X)|quiet(X))=>~strong(X)))&
(((~funny(mary)|~kind(mary)))=>((wise(paul)<~>strong(paul))))&
(![X]:((funny(X)&~kind(X))=>(~calm(X)|~old(X))))&
((?[X]:((wise(X)|curious(X))))<=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((strong(X)|~funny(X))<=>(~humble(X)&~quiet(X))))&
(![X]:((~kind(X)&tall(X))=>(calm(X)&~wise(X))))&
(![X]:((~patient(X)|~funny(X))<=>(patient(X)&~rich(X))))&
(![X]:(brave(X)<=>(creative(X)|patient(X))))&
((tall(fred))<=>(?[X]:((~funny(X)|~calm(X)))))&
(?[X]:((~tall(X)|calm(X))))&
(?[X]:((funny(X)&~kind(X))))&
(patient(alice))&
(~strong(susan))&
(~kind(alice))&
(?[X]:((tall(X)<~>~brave(X))))&
((creative(paul)<~>~rich(paul))) | patient(mary) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1755666736740770036780605
% SZS output start Proof for 1755666736740770036780605
14. ! [X0] : ((~funny(X0) | ~patient(X0)) <=> (~rich(X0) & patient(X0))) [input p13]
24. ~patient(mary) [input hypothesis]
69. ! [X0] : (((~funny(X0) | ~patient(X0)) | (rich(X0) | ~patient(X0))) & ((~rich(X0) & patient(X0)) | (funny(X0) & patient(X0)))) [nnf transformation 14]
70. ! [X0] : ((~funny(X0) | ~patient(X0) | rich(X0) | ~patient(X0)) & ((~rich(X0) & patient(X0)) | (funny(X0) & patient(X0)))) [flattening 69]
123. patient(X0) | patient(X0) [cnf transformation 70]
144. ~patient(mary) [cnf transformation 24]
145. patient(X0) [duplicate literal removal 123]
197. 12 <=> ! [X1] : patient(X1) [avatar definition]
198. patient(X1) <- (12) [avatar component clause 197]
294. 12 [avatar split clause 145,197]
348. $false <- (12) [resolution 198,144]
349. ~12 [avatar contradiction clause 348]
350. $false [avatar sat refutation 294,349]
% SZS output end Proof for 1755666736740770036780605
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and not tall is either not creative or not patient. Everyone who is both not creative and not curious is funny and vice versa. Everyone who is generous or not quiet is rich. Everyone who is not old is both not creative and strong and vice versa. Everyone who is not quiet is funny or not humble and vice versa. Everyone who is either funny or not tall is both not tall and not old and vice versa. If john is brave or strong then someone is both curious and not brave. If susan is not funny then alice is tall. If someone is both old and curious then someone is either not curious or brave and vice versa. If lucy is humble or calm then someone is either curious or rich and vice versa. Everyone who is not creative is either kind or not kind. Everyone who is both curious and rich is both not humble and humble and vice versa. Everyone who is both not strong and brave is patient or funny and vice versa. Everyone who is either not funny or old is both rich and not happy. If paul is either not quiet or patient then fred is both not rich and not wise and vice versa. Everyone who is curious or strong is both not kind and calm and vice versa. Someone is old. Paul is not wise. Fred is kind or not calm. Fred is either not quiet or not tall. Mary is not wise or not strong. Someone is either not calm or creative. Fred is both not kind and not generous. John is not brave. | Alice is not brave. | neutral | (![X]:((funny(X)&~tall(X))=>(~creative(X)<~>~patient(X))))&
(![X]:((~creative(X)&~curious(X))<=>funny(X)))&
(![X]:((generous(X)|~quiet(X))=>rich(X)))&
(![X]:(~old(X)<=>(~creative(X)&strong(X))))&
(![X]:(~quiet(X)<=>(funny(X)|~humble(X))))&
(![X]:((funny(X)<~>~tall(X))<=>(~tall(X)&~old(X))))&
(((brave(john)|strong(john)))=>(?[X]:((curious(X)&~brave(X)))))&
((~funny(susan))=>(tall(alice)))&
((?[X]:((old(X)&curious(X))))<=>(?[X]:((~curious(X)<~>brave(X)))))&
(((humble(lucy)|calm(lucy)))<=>(?[X]:((curious(X)<~>rich(X)))))&
(![X]:(~creative(X)=>(kind(X)<~>~kind(X))))&
(![X]:((curious(X)&rich(X))<=>(~humble(X)&humble(X))))&
(![X]:((~strong(X)&brave(X))<=>(patient(X)|funny(X))))&
(![X]:((~funny(X)<~>old(X))=>(rich(X)&~happy(X))))&
(((~quiet(paul)<~>patient(paul)))<=>((~rich(fred)&~wise(fred))))&
(![X]:((curious(X)|strong(X))<=>(~kind(X)&calm(X))))&
(?[X]:(old(X)))&
(~wise(paul))&
((kind(fred)|~calm(fred)))&
((~quiet(fred)<~>~tall(fred)))&
((~wise(mary)|~strong(mary)))&
(?[X]:((~calm(X)<~>creative(X))))&
((~kind(fred)&~generous(fred)))&
(~brave(john)) | ~brave(alice) | [] | null | 0 |
Everyone who is both rich and not creative is either patient or not tall and vice versa. If someone is either not rich or creative then fred is either wise or calm and vice versa. Everyone who is both not rich and not curious is old or funny and vice versa. Everyone who is not wise is kind and vice versa. If fred is happy or creative then someone is not strong or not quiet. If susan is not funny then someone is either funny or not calm. If alice is either not kind or rich then someone is either not funny or not generous and vice versa. If lucy is not strong then someone is calm and vice versa. Everyone who is not strong or not humble is both not generous and generous. Everyone who is not calm is not happy or wise. Everyone who is both brave and not wise is either humble or not creative and vice versa. Everyone who is either wise or not rich is either not tall or not humble and vice versa. Everyone who is either not creative or not curious is not patient or old. If alice is funny then susan is either not strong or not quiet. If alice is brave then mary is both not humble and not quiet and vice versa. If lucy is both old and patient then someone is generous or not strong. Susan is either not kind or not quiet. Alice is either quiet or calm. Someone is either curious or not tall. Someone is both generous and wise. Mary is both not rich and happy. Someone is not curious or not happy. Someone is not curious or not kind. | Mary is not funny. | neutral | (![X]:((rich(X)&~creative(X))<=>(patient(X)<~>~tall(X))))&
((?[X]:((~rich(X)<~>creative(X))))<=>((wise(fred)<~>calm(fred))))&
(![X]:((~rich(X)&~curious(X))<=>(old(X)|funny(X))))&
(![X]:(~wise(X)<=>kind(X)))&
(((happy(fred)|creative(fred)))=>(?[X]:((~strong(X)|~quiet(X)))))&
((~funny(susan))=>(?[X]:((funny(X)<~>~calm(X)))))&
(((~kind(alice)<~>rich(alice)))<=>(?[X]:((~funny(X)<~>~generous(X)))))&
((~strong(lucy))<=>(?[X]:(calm(X))))&
(![X]:((~strong(X)|~humble(X))=>(~generous(X)&generous(X))))&
(![X]:(~calm(X)=>(~happy(X)|wise(X))))&
(![X]:((brave(X)&~wise(X))<=>(humble(X)<~>~creative(X))))&
(![X]:((wise(X)<~>~rich(X))<=>(~tall(X)<~>~humble(X))))&
(![X]:((~creative(X)<~>~curious(X))=>(~patient(X)|old(X))))&
((funny(alice))=>((~strong(susan)<~>~quiet(susan))))&
((brave(alice))<=>((~humble(mary)&~quiet(mary))))&
(((old(lucy)&patient(lucy)))=>(?[X]:((generous(X)|~strong(X)))))&
((~kind(susan)<~>~quiet(susan)))&
((quiet(alice)<~>calm(alice)))&
(?[X]:((curious(X)<~>~tall(X))))&
(?[X]:((generous(X)&wise(X))))&
((~rich(mary)&happy(mary)))&
(?[X]:((~curious(X)|~happy(X))))&
(?[X]:((~curious(X)|~kind(X)))) | ~funny(mary) | [] | null | 0 |
Everyone who is both quiet and not old is not tall or not humble and vice versa. If mary is not funny or not rich then someone is patient and vice versa. Everyone who is not funny is calm or not tall. Everyone who is both not strong and not rich is not kind and vice versa. If someone is funny or not wise then fred is patient. If fred is not tall or old then fred is tall. If someone is both brave and not wise then lucy is both not quiet and quiet and vice versa. Everyone who is either not strong or not generous is not humble. Everyone who is both humble and not calm is calm and vice versa. Everyone who is either strong or not rich is both not rich and curious. If lucy is humble then fred is either not generous or not calm and vice versa. Everyone who is strong is both not patient and not kind and vice versa. Everyone who is not generous or not tall is not curious or patient. If lucy is old then someone is old and vice versa. Everyone who is both not rich and creative is not funny or not strong. Paul is not curious. Lucy is old or curious. Someone is creative. Someone is either not rich or not wise. Someone is rich or funny. Someone is either not quiet or not humble. Paul is both creative and not generous. Someone is kind or rich. | Mary is not funny. | neutral | (![X]:((quiet(X)&~old(X))<=>(~tall(X)|~humble(X))))&
(((~funny(mary)|~rich(mary)))<=>(?[X]:(patient(X))))&
(![X]:(~funny(X)=>(calm(X)|~tall(X))))&
(![X]:((~strong(X)&~rich(X))<=>~kind(X)))&
((?[X]:((funny(X)|~wise(X))))=>(patient(fred)))&
(((~tall(fred)|old(fred)))=>(tall(fred)))&
((?[X]:((brave(X)&~wise(X))))<=>((~quiet(lucy)&quiet(lucy))))&
(![X]:((~strong(X)<~>~generous(X))=>~humble(X)))&
(![X]:((humble(X)&~calm(X))<=>calm(X)))&
(![X]:((strong(X)<~>~rich(X))=>(~rich(X)&curious(X))))&
((humble(lucy))<=>((~generous(fred)<~>~calm(fred))))&
(![X]:(strong(X)<=>(~patient(X)&~kind(X))))&
(![X]:((~generous(X)|~tall(X))=>(~curious(X)|patient(X))))&
((old(lucy))<=>(?[X]:(old(X))))&
(![X]:((~rich(X)&creative(X))=>(~funny(X)|~strong(X))))&
(~curious(paul))&
((old(lucy)|curious(lucy)))&
(?[X]:(creative(X)))&
(?[X]:((~rich(X)<~>~wise(X))))&
(?[X]:((rich(X)|funny(X))))&
(?[X]:((~quiet(X)<~>~humble(X))))&
((creative(paul)&~generous(paul)))&
(?[X]:((kind(X)|rich(X)))) | ~funny(mary) | [] | null | 0 |
If paul is either not patient or not rich then paul is either tall or not calm.
If lucy is creative or strong then susan is calm or not humble and vice versa.
If someone is both tall and patient then someone is not strong or not old.
Everyone who is not wise or patient is either not strong or calm and vice versa.
Everyone who is not rich or not tall is happy or not tall.
If susan is brave or not quiet then lucy is wise and vice versa.
Everyone who is not funny or wise is not brave or not wise and vice versa.
If mary is both funny and not creative then someone is either patient or wise.
If someone is both calm and old then lucy is both calm and rich and vice versa.
Everyone who is happy is not brave and vice versa.
Everyone who is happy or not tall is funny or not quiet.
If someone is either kind or quiet then paul is both not strong and not brave.
Everyone who is happy is old.
If alice is humble or funny then someone is both calm and wise.
Everyone who is not humble or generous is both not generous and tall and vice versa.
If someone is either not generous or not humble then paul is both not old and generous and vice versa.
Someone is either calm or rich.
Lucy is rich.
Someone is either not generous or old.
Someone is both not strong and not funny.
Someone is not rich.
Someone is both old and curious.
Someone is either generous or kind. | Alice is humble. | contradiction | (((~patient(paul)<~>~rich(paul)))=>((tall(paul)<~>~calm(paul))))&
(((creative(lucy)|strong(lucy)))<=>((calm(susan)|~humble(susan))))&
((?[X]:((tall(X)&patient(X))))=>(?[X]:((~strong(X)|~old(X)))))&
(![X]:((~wise(X)|patient(X))<=>(~strong(X)<~>calm(X))))&
(![X]:((~rich(X)|~tall(X))=>(happy(X)|~tall(X))))&
(((brave(susan)|~quiet(susan)))<=>(wise(lucy)))&
(![X]:((~funny(X)|wise(X))<=>(~brave(X)|~wise(X))))&
(((funny(mary)&~creative(mary)))=>(?[X]:((patient(X)<~>wise(X)))))&
((?[X]:((calm(X)&old(X))))<=>((calm(lucy)&rich(lucy))))&
(![X]:(happy(X)<=>~brave(X)))&
(![X]:((happy(X)|~tall(X))=>(funny(X)|~quiet(X))))&
((?[X]:((kind(X)<~>quiet(X))))=>((~strong(paul)&~brave(paul))))&
(![X]:(happy(X)=>old(X)))&
(((humble(alice)|funny(alice)))=>(?[X]:((calm(X)&wise(X)))))&
(![X]:((~humble(X)|generous(X))<=>(~generous(X)&tall(X))))&
((?[X]:((~generous(X)<~>~humble(X))))<=>((~old(paul)&generous(paul))))&
(?[X]:((calm(X)<~>rich(X))))&
(rich(lucy))&
(?[X]:((~generous(X)<~>old(X))))&
(?[X]:((~strong(X)&~funny(X))))&
(?[X]:(~rich(X)))&
(?[X]:((old(X)&curious(X))))&
(?[X]:((generous(X)<~>kind(X)))) | humble(alice) | [
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2407353220923960152846603
% SZS output start Proof for 2407353220923960152846603
15. ! [X0] : ((generous(X0) | ~humble(X0)) <=> (tall(X0) & ~generous(X0))) [input p14]
16. ? [X0] : (~generous(X0) <~> ~humble(X0)) <=> (generous(paul) & ~old(paul)) [input p15]
24. humble(alice) [input hypothesis]
62. ! [X0] : (((generous(X0) | ~humble(X0)) | (~tall(X0) | generous(X0))) & ((tall(X0) & ~generous(X0)) | (~generous(X0) & humble(X0)))) [nnf transformation 15]
63. ! [X0] : ((generous(X0) | ~humble(X0) | ~tall(X0) | generous(X0)) & ((tall(X0) & ~generous(X0)) | (~generous(X0) & humble(X0)))) [flattening 62]
64. (? [X0] : ((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | (~generous(paul) | old(paul))) & ((generous(paul) & ~old(paul)) | ! [X0] : ((~generous(X0) | humble(X0)) & (~humble(X0) | generous(X0)))) [nnf transformation 16]
65. (? [X0] : ((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | ~generous(paul) | old(paul)) & ((generous(paul) & ~old(paul)) | ! [X0] : ((~generous(X0) | humble(X0)) & (~humble(X0) | generous(X0)))) [flattening 64]
66. (? [X0] : ((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | ~generous(paul) | old(paul)) & ((generous(paul) & ~old(paul)) | ! [X1] : ((~generous(X1) | humble(X1)) & (~humble(X1) | generous(X1)))) [rectify 65]
67. ? [X0] : ((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) => ((humble(sK4) | generous(sK4)) & (~humble(sK4) | ~generous(sK4))) [choice axiom]
68. (((humble(sK4) | generous(sK4)) & (~humble(sK4) | ~generous(sK4))) | ~generous(paul) | old(paul)) & ((generous(paul) & ~old(paul)) | ! [X1] : ((~generous(X1) | humble(X1)) & (~humble(X1) | generous(X1)))) [skolemisation 66,67]
128. ~generous(X0) | ~generous(X0) [cnf transformation 63]
134. generous(paul) | ~humble(X1) | generous(X1) [cnf transformation 68]
149. humble(alice) [cnf transformation 24]
150. ~generous(X0) [duplicate literal removal 128]
300. ~humble(X1) | generous(X1) [subsumption resolution 134,150]
301. ~humble(X1) [subsumption resolution 300,150]
315. $false [subsumption resolution 149,301]
% SZS output end Proof for 2407353220923960152846603
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and not old is either not funny or not humble and vice versa.
Everyone who is either not creative or not funny is either kind or strong.
If someone is not kind then mary is rich and vice versa.
Everyone who is happy is strong and vice versa.
If fred is creative or not old then someone is both strong and not rich.
Everyone who is not funny or curious is both curious and not quiet and vice versa.
Everyone who is both curious and not calm is wise.
If someone is either not rich or kind then someone is both not rich and wise and vice versa.
If someone is both calm and brave then someone is both quiet and not patient.
Everyone who is humble or quiet is quiet or not creative.
If someone is both calm and not generous then susan is not generous and vice versa.
Everyone who is creative is not tall or not strong and vice versa.
Everyone who is both not creative and patient is both happy and strong.
If john is funny or not curious then someone is tall or wise and vice versa.
Everyone who is calm or not rich is not old or not generous.
If lucy is not funny then someone is either quiet or happy.
Someone is either old or not tall.
Alice is creative or not rich.
Lucy is either not happy or creative.
Someone is wise.
Fred is not old.
Susan is not wise or not quiet.
Someone is not curious.
Fred is rich. | Lucy is not happy. | contradiction | (![X]:((~brave(X)&~old(X))<=>(~funny(X)<~>~humble(X))))&
(![X]:((~creative(X)<~>~funny(X))=>(kind(X)<~>strong(X))))&
((?[X]:(~kind(X)))<=>(rich(mary)))&
(![X]:(happy(X)<=>strong(X)))&
(((creative(fred)|~old(fred)))=>(?[X]:((strong(X)&~rich(X)))))&
(![X]:((~funny(X)|curious(X))<=>(curious(X)&~quiet(X))))&
(![X]:((curious(X)&~calm(X))=>wise(X)))&
((?[X]:((~rich(X)<~>kind(X))))<=>(?[X]:((~rich(X)&wise(X)))))&
((?[X]:((calm(X)&brave(X))))=>(?[X]:((quiet(X)&~patient(X)))))&
(![X]:((humble(X)|quiet(X))=>(quiet(X)|~creative(X))))&
((?[X]:((calm(X)&~generous(X))))<=>(~generous(susan)))&
(![X]:(creative(X)<=>(~tall(X)|~strong(X))))&
(![X]:((~creative(X)&patient(X))=>(happy(X)&strong(X))))&
(((funny(john)|~curious(john)))<=>(?[X]:((tall(X)|wise(X)))))&
(![X]:((calm(X)|~rich(X))=>(~old(X)|~generous(X))))&
((~funny(lucy))=>(?[X]:((quiet(X)<~>happy(X)))))&
(?[X]:((old(X)<~>~tall(X))))&
((creative(alice)|~rich(alice)))&
((~happy(lucy)<~>creative(lucy)))&
(?[X]:(wise(X)))&
(~old(fred))&
((~wise(susan)|~quiet(susan)))&
(?[X]:(~curious(X)))&
(rich(fred)) | ~happy(lucy) | [
"p3",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3185128719328693132801882
% SZS output start Proof for 3185128719328693132801882
4. ! [X0] : (happy(X0) <=> strong(X0)) [input p3]
12. ! [X0] : (creative(X0) <=> (~strong(X0) | ~tall(X0))) [input p11]
19. ~happy(lucy) <~> creative(lucy) [input p18]
25. ~happy(lucy) [input hypothesis]
47. ! [X0] : ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0))) [nnf transformation 4]
64. ! [X0] : ((creative(X0) | (strong(X0) & tall(X0))) & ((~strong(X0) | ~tall(X0)) | ~creative(X0))) [nnf transformation 12]
65. ! [X0] : ((creative(X0) | (strong(X0) & tall(X0))) & (~strong(X0) | ~tall(X0) | ~creative(X0))) [flattening 64]
77. (~creative(lucy) | happy(lucy)) & (creative(lucy) | ~happy(lucy)) [nnf transformation 19]
95. ~strong(X0) | happy(X0) [cnf transformation 47]
120. strong(X0) | creative(X0) [cnf transformation 65]
133. ~creative(lucy) | happy(lucy) [cnf transformation 77]
139. ~happy(lucy) [cnf transformation 25]
292. 34 <=> happy(lucy) [avatar definition]
293. ~happy(lucy) <- (~34) [avatar component clause 292]
296. 35 <=> creative(lucy) [avatar definition]
298. ~creative(lucy) <- (~35) [avatar component clause 296]
299. 34 | ~35 [avatar split clause 133,296,292]
311. ~34 [avatar split clause 139,292]
329. happy(X0) | creative(X0) [resolution 120,95]
464. creative(lucy) <- (~34) [resolution 329,293]
466. $false <- (~34, ~35) [subsumption resolution 464,298]
467. 34 | 35 [avatar contradiction clause 466]
468. $false [avatar sat refutation 299,311,467]
% SZS output end Proof for 3185128719328693132801882
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not quiet then someone is both not calm and not tall.
If someone is not wise then fred is curious.
If someone is not patient then someone is both strong and not rich.
If someone is brave then fred is wise and vice versa.
If alice is humble or not tall then someone is not tall or happy and vice versa.
If someone is both not calm and kind then someone is both rich and not rich.
Everyone who is wise is either generous or not creative and vice versa.
Everyone who is both patient and not curious is brave or old and vice versa.
Everyone who is either not calm or not wise is both not old and rich.
If someone is either funny or not quiet then someone is both old and not wise.
Everyone who is both not kind and brave is not calm or rich.
Everyone who is not calm or not wise is both not brave and brave.
Everyone who is rich is calm or patient.
Everyone who is both not generous and old is wise or calm.
If john is either not old or kind then lucy is not happy and vice versa.
Everyone who is not old or wise is strong or not brave.
Paul is either rich or funny.
Someone is not kind or old.
John is either rich or not humble.
Mary is either not strong or humble.
Someone is not brave.
Alice is curious.
Someone is not generous.
Someone is wise. | Fred is quiet. | entailment | ((?[X]:(~quiet(X)))=>(?[X]:((~calm(X)&~tall(X)))))&
((?[X]:(~wise(X)))=>(curious(fred)))&
((?[X]:(~patient(X)))=>(?[X]:((strong(X)&~rich(X)))))&
((?[X]:(brave(X)))<=>(wise(fred)))&
(((humble(alice)|~tall(alice)))<=>(?[X]:((~tall(X)|happy(X)))))&
((?[X]:((~calm(X)&kind(X))))=>(?[X]:((rich(X)&~rich(X)))))&
(![X]:(wise(X)<=>(generous(X)<~>~creative(X))))&
(![X]:((patient(X)&~curious(X))<=>(brave(X)|old(X))))&
(![X]:((~calm(X)<~>~wise(X))=>(~old(X)&rich(X))))&
((?[X]:((funny(X)<~>~quiet(X))))=>(?[X]:((old(X)&~wise(X)))))&
(![X]:((~kind(X)&brave(X))=>(~calm(X)|rich(X))))&
(![X]:((~calm(X)|~wise(X))=>(~brave(X)&brave(X))))&
(![X]:(rich(X)=>(calm(X)|patient(X))))&
(![X]:((~generous(X)&old(X))=>(wise(X)|calm(X))))&
(((~old(john)<~>kind(john)))<=>(~happy(lucy)))&
(![X]:((~old(X)|wise(X))=>(strong(X)|~brave(X))))&
((rich(paul)<~>funny(paul)))&
(?[X]:((~kind(X)|old(X))))&
((rich(john)<~>~humble(john)))&
((~strong(mary)<~>humble(mary)))&
(?[X]:(~brave(X)))&
(curious(alice))&
(?[X]:(~generous(X)))&
(?[X]:(wise(X))) | quiet(fred) | [
"p0",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 9204933076722637528530160
% SZS output start Proof for 9204933076722637528530160
1. ? [X0] : ~quiet(X0) => ? [X0] : (~tall(X0) & ~calm(X0)) [input p0]
12. ! [X0] : ((~wise(X0) | ~calm(X0)) => (brave(X0) & ~brave(X0))) [input p11]
25. ~quiet(fred) [input hypothesis]
26. ? [X0] : ~quiet(X0) => ? [X1] : (~tall(X1) & ~calm(X1)) [rectify 1]
30. ? [X1] : (~tall(X1) & ~calm(X1)) | ! [X0] : quiet(X0) [ennf transformation 26]
38. ! [X0] : ((brave(X0) & ~brave(X0)) | (wise(X0) & calm(X0))) [ennf transformation 12]
45. ? [X0] : (~tall(X0) & ~calm(X0)) | ! [X1] : quiet(X1) [rectify 30]
46. ? [X0] : (~tall(X0) & ~calm(X0)) => (~tall(sK0) & ~calm(sK0)) [choice axiom]
47. (~tall(sK0) & ~calm(sK0)) | ! [X1] : quiet(X1) [skolemisation 45,46]
83. ~calm(sK0) | quiet(X1) [cnf transformation 47]
114. ~brave(X0) | calm(X0) [cnf transformation 38]
116. brave(X0) | calm(X0) [cnf transformation 38]
137. ~quiet(fred) [cnf transformation 25]
139. 1 <=> ! [X1] : quiet(X1) [avatar definition]
140. quiet(X1) <- (1) [avatar component clause 139]
147. 3 <=> calm(sK0) [avatar definition]
149. ~calm(sK0) <- (~3) [avatar component clause 147]
150. 1 | ~3 [avatar split clause 83,147,139]
240. calm(X0) [subsumption resolution 114,116]
296. $false <- (~3) [subsumption resolution 149,240]
297. 3 [avatar contradiction clause 296]
298. $false <- (1) [resolution 140,137]
299. ~1 [avatar contradiction clause 298]
300. $false [avatar sat refutation 150,297,299]
% SZS output end Proof for 9204933076722637528530160
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either happy or not funny is both humble and quiet and vice versa. Everyone who is both kind and quiet is curious and vice versa. If john is both brave and not tall then john is both not patient and quiet and vice versa. If alice is both not tall and not patient then someone is both not creative and calm. If paul is wise then john is both not strong and not old and vice versa. Everyone who is strong is humble and vice versa. If someone is either not calm or patient then someone is not strong or not happy and vice versa. Everyone who is old is kind or not generous and vice versa. If someone is either generous or not strong then someone is not tall and vice versa. Everyone who is both curious and generous is either not curious or not rich. If lucy is either not generous or tall then mary is either not humble or generous. If john is not tall or wise then john is both not quiet and not generous. If someone is both curious and strong then mary is creative and vice versa. If paul is either wise or not brave then someone is either old or creative. Everyone who is not happy or strong is not happy and vice versa. Everyone who is both strong and creative is rich or not rich and vice versa. Paul is not happy or not quiet. Someone is creative. Alice is not kind. Someone is not patient. Lucy is not strong or quiet. Paul is either not calm or not rich. Someone is either old or not calm. | John is old. | neutral | (![X]:((happy(X)<~>~funny(X))<=>(humble(X)&quiet(X))))&
(![X]:((kind(X)&quiet(X))<=>curious(X)))&
(((brave(john)&~tall(john)))<=>((~patient(john)&quiet(john))))&
(((~tall(alice)&~patient(alice)))=>(?[X]:((~creative(X)&calm(X)))))&
((wise(paul))<=>((~strong(john)&~old(john))))&
(![X]:(strong(X)<=>humble(X)))&
((?[X]:((~calm(X)<~>patient(X))))<=>(?[X]:((~strong(X)|~happy(X)))))&
(![X]:(old(X)<=>(kind(X)|~generous(X))))&
((?[X]:((generous(X)<~>~strong(X))))<=>(?[X]:(~tall(X))))&
(![X]:((curious(X)&generous(X))=>(~curious(X)<~>~rich(X))))&
(((~generous(lucy)<~>tall(lucy)))=>((~humble(mary)<~>generous(mary))))&
(((~tall(john)|wise(john)))=>((~quiet(john)&~generous(john))))&
((?[X]:((curious(X)&strong(X))))<=>(creative(mary)))&
(((wise(paul)<~>~brave(paul)))=>(?[X]:((old(X)<~>creative(X)))))&
(![X]:((~happy(X)|strong(X))<=>~happy(X)))&
(![X]:((strong(X)&creative(X))<=>(rich(X)|~rich(X))))&
((~happy(paul)|~quiet(paul)))&
(?[X]:(creative(X)))&
(~kind(alice))&
(?[X]:(~patient(X)))&
((~strong(lucy)|quiet(lucy)))&
((~calm(paul)<~>~rich(paul)))&
(?[X]:((old(X)<~>~calm(X)))) | old(john) | [] | null | 0 |
Everyone who is both brave and not curious is not humble or not creative.
If lucy is both creative and patient then someone is patient or not tall and vice versa.
If someone is both not funny and creative then someone is brave.
If someone is both not kind and not strong then fred is not generous and vice versa.
If john is either wise or creative then john is either wise or funny.
Everyone who is not wise or not old is not brave and vice versa.
Everyone who is either not kind or wise is not calm or old and vice versa.
Everyone who is both not creative and not curious is not happy or kind and vice versa.
If john is both curious and not funny then alice is wise and vice versa.
If someone is humble then someone is not quiet.
If someone is either not creative or not curious then alice is not quiet or calm.
Everyone who is not creative or generous is creative.
If someone is either not calm or not brave then fred is either not patient or not humble and vice versa.
Everyone who is generous is not funny or generous.
If someone is either quiet or not patient then someone is not happy and vice versa.
Everyone who is wise or not funny is generous or happy.
Someone is patient or kind.
Mary is not strong.
Someone is not strong.
Someone is either funny or not wise.
Someone is either not tall or not creative.
Someone is not curious. | Mary is funny. | entailment | (![X]:((brave(X)&~curious(X))=>(~humble(X)|~creative(X))))&
(((creative(lucy)&patient(lucy)))<=>(?[X]:((patient(X)|~tall(X)))))&
((?[X]:((~funny(X)&creative(X))))=>(?[X]:(brave(X))))&
((?[X]:((~kind(X)&~strong(X))))<=>(~generous(fred)))&
(((wise(john)<~>creative(john)))=>((wise(john)<~>funny(john))))&
(![X]:((~wise(X)|~old(X))<=>~brave(X)))&
(![X]:((~kind(X)<~>wise(X))<=>(~calm(X)|old(X))))&
(![X]:((~creative(X)&~curious(X))<=>(~happy(X)|kind(X))))&
(((curious(john)&~funny(john)))<=>(wise(alice)))&
((?[X]:(humble(X)))=>(?[X]:(~quiet(X))))&
((?[X]:((~creative(X)<~>~curious(X))))=>((~quiet(alice)|calm(alice))))&
(![X]:((~creative(X)|generous(X))=>creative(X)))&
((?[X]:((~calm(X)<~>~brave(X))))<=>((~patient(fred)<~>~humble(fred))))&
(![X]:(generous(X)=>(~funny(X)|generous(X))))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(?[X]:(~happy(X))))&
(![X]:((wise(X)|~funny(X))=>(generous(X)|happy(X))))&
(?[X]:((patient(X)|kind(X))))&
(~strong(mary))&
(?[X]:(~strong(X)))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:((~tall(X)<~>~creative(X))))&
(?[X]:(~curious(X))) | funny(mary) | [
"p2",
"p5",
"p6",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7846187681640562870480334
% SZS output start Proof for 7846187681640562870480334
3. ? [X0] : (creative(X0) & ~funny(X0)) => ? [X0] : brave(X0) [input p2]
6. ! [X0] : ((~old(X0) | ~wise(X0)) <=> ~brave(X0)) [input p5]
7. ! [X0] : ((~kind(X0) <~> wise(X0)) <=> (old(X0) | ~calm(X0))) [input p6]
8. ! [X0] : ((~curious(X0) & ~creative(X0)) <=> (kind(X0) | ~happy(X0))) [input p7]
12. ! [X0] : ((generous(X0) | ~creative(X0)) => creative(X0)) [input p11]
23. ~funny(mary) [input hypothesis]
24. ? [X0] : (creative(X0) & ~funny(X0)) => ? [X1] : brave(X1) [rectify 3]
29. ? [X1] : brave(X1) | ! [X0] : (~creative(X0) | funny(X0)) [ennf transformation 24]
34. ! [X0] : (creative(X0) | (~generous(X0) & creative(X0))) [ennf transformation 12]
44. ? [X0] : brave(X0) | ! [X1] : (~creative(X1) | funny(X1)) [rectify 29]
45. ? [X0] : brave(X0) => brave(sK1) [choice axiom]
46. brave(sK1) | ! [X1] : (~creative(X1) | funny(X1)) [skolemisation 44,45]
52. ! [X0] : (((~old(X0) | ~wise(X0)) | brave(X0)) & (~brave(X0) | (old(X0) & wise(X0)))) [nnf transformation 6]
53. ! [X0] : ((~old(X0) | ~wise(X0) | brave(X0)) & (~brave(X0) | (old(X0) & wise(X0)))) [flattening 52]
54. ! [X0] : ((((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) | (~old(X0) & calm(X0))) & ((old(X0) | ~calm(X0)) | ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0))))) [nnf transformation 7]
55. ! [X0] : ((((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) | (~old(X0) & calm(X0))) & (old(X0) | ~calm(X0) | ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0))))) [flattening 54]
56. ! [X0] : (((~curious(X0) & ~creative(X0)) | (~kind(X0) & happy(X0))) & ((kind(X0) | ~happy(X0)) | (curious(X0) | creative(X0)))) [nnf transformation 8]
57. ! [X0] : (((~curious(X0) & ~creative(X0)) | (~kind(X0) & happy(X0))) & (kind(X0) | ~happy(X0) | curious(X0) | creative(X0))) [flattening 56]
91. brave(sK1) | ~creative(X1) | funny(X1) [cnf transformation 46]
99. ~brave(X0) | wise(X0) [cnf transformation 53]
100. ~brave(X0) | old(X0) [cnf transformation 53]
107. ~old(X0) | kind(X0) | ~wise(X0) [cnf transformation 55]
110. ~kind(X0) | ~creative(X0) [cnf transformation 57]
119. creative(X0) | creative(X0) [cnf transformation 34]
144. ~funny(mary) [cnf transformation 23]
145. creative(X0) [duplicate literal removal 119]
176. 7 <=> ! [X1] : (~creative(X1) | funny(X1)) [avatar definition]
177. ~creative(X1) | funny(X1) <- (7) [avatar component clause 176]
179. 8 <=> brave(sK1) [avatar definition]
181. brave(sK1) <- (8) [avatar component clause 179]
182. 7 | 8 [avatar split clause 91,179,176]
327. funny(X1) <- (7) [subsumption resolution 177,145]
328. $false <- (7) [resolution 327,144]
333. ~7 [avatar contradiction clause 328]
334. wise(sK1) <- (8) [resolution 99,181]
335. old(sK1) <- (8) [resolution 100,181]
365. 43 <=> kind(sK1) [avatar definition]
367. kind(sK1) <- (43) [avatar component clause 365]
369. kind(sK1) | ~wise(sK1) <- (8) [resolution 107,335]
370. kind(sK1) <- (8) [subsumption resolution 369,334]
371. 43 | ~8 [avatar split clause 370,179,365]
376. ~creative(sK1) <- (43) [resolution 367,110]
377. $false <- (43) [subsumption resolution 376,145]
378. ~43 [avatar contradiction clause 377]
379. $false [avatar sat refutation 182,333,371,378]
% SZS output end Proof for 7846187681640562870480334
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not wise or brave is not tall or not patient.
Everyone who is both happy and humble is quiet or not humble.
If fred is not kind then someone is either wise or creative.
Everyone who is not old is either not wise or not calm.
Everyone who is not strong is curious or not calm and vice versa.
If john is not tall then someone is not tall.
Everyone who is not rich or happy is not tall.
Everyone who is both not humble and not old is old and vice versa.
Everyone who is not old or brave is either generous or not creative and vice versa.
Everyone who is both generous and not brave is either funny or kind and vice versa.
Everyone who is either curious or rich is strong.
Everyone who is not funny or funny is curious or not humble.
Everyone who is kind is both not humble and funny.
If someone is both quiet and curious then someone is either happy or brave and vice versa.
If someone is brave or curious then paul is either not curious or not generous.
Someone is both not calm and not funny.
Someone is either not wise or not patient.
Someone is either funny or humble.
Paul is both rich and not funny.
John is not funny.
Mary is not generous or calm.
John is both quiet and tall. | Paul is brave. | neutral | (![X]:((~wise(X)<~>brave(X))=>(~tall(X)|~patient(X))))&
(![X]:((happy(X)&humble(X))=>(quiet(X)|~humble(X))))&
((~kind(fred))=>(?[X]:((wise(X)<~>creative(X)))))&
(![X]:(~old(X)=>(~wise(X)<~>~calm(X))))&
(![X]:(~strong(X)<=>(curious(X)|~calm(X))))&
((~tall(john))=>(?[X]:(~tall(X))))&
(![X]:((~rich(X)|happy(X))=>~tall(X)))&
(![X]:((~humble(X)&~old(X))<=>old(X)))&
(![X]:((~old(X)|brave(X))<=>(generous(X)<~>~creative(X))))&
(![X]:((generous(X)&~brave(X))<=>(funny(X)<~>kind(X))))&
(![X]:((curious(X)<~>rich(X))=>strong(X)))&
(![X]:((~funny(X)|funny(X))=>(curious(X)|~humble(X))))&
(![X]:(kind(X)=>(~humble(X)&funny(X))))&
((?[X]:((quiet(X)&curious(X))))<=>(?[X]:((happy(X)<~>brave(X)))))&
((?[X]:((brave(X)|curious(X))))=>((~curious(paul)<~>~generous(paul))))&
(?[X]:((~calm(X)&~funny(X))))&
(?[X]:((~wise(X)<~>~patient(X))))&
(?[X]:((funny(X)<~>humble(X))))&
((rich(paul)&~funny(paul)))&
(~funny(john))&
((~generous(mary)|calm(mary)))&
((quiet(john)&tall(john))) | brave(paul) | [] | null | 0 |
Everyone who is not patient is both happy and quiet and vice versa.
Everyone who is funny or not quiet is either creative or not generous and vice versa.
Everyone who is creative is both kind and patient.
If paul is either not calm or wise then someone is creative or wise and vice versa.
If alice is happy or not patient then someone is humble.
If susan is not creative or wise then someone is either brave or tall.
Everyone who is not calm or not funny is humble or not tall.
Everyone who is both not calm and strong is not patient and vice versa.
Everyone who is both not brave and kind is not strong and vice versa.
If someone is both patient and not generous then alice is patient.
Everyone who is not wise or not quiet is both patient and happy and vice versa.
Everyone who is either not creative or not rich is both not creative and not old and vice versa.
If someone is either not patient or curious then fred is not funny and vice versa.
If someone is not wise or old then someone is either kind or not calm.
Everyone who is not calm is brave or not happy and vice versa.
If someone is either not old or patient then susan is both creative and strong and vice versa.
Someone is both not kind and brave.
Someone is both not creative and not rich.
Susan is tall.
Someone is either not strong or patient.
Someone is calm or not humble.
Paul is either quiet or rich.
Someone is both not creative and not patient. | Alice is rich. | entailment | (![X]:(~patient(X)<=>(happy(X)&quiet(X))))&
(![X]:((funny(X)|~quiet(X))<=>(creative(X)<~>~generous(X))))&
(![X]:(creative(X)=>(kind(X)&patient(X))))&
(((~calm(paul)<~>wise(paul)))<=>(?[X]:((creative(X)|wise(X)))))&
(((happy(alice)|~patient(alice)))=>(?[X]:(humble(X))))&
(((~creative(susan)|wise(susan)))=>(?[X]:((brave(X)<~>tall(X)))))&
(![X]:((~calm(X)|~funny(X))=>(humble(X)|~tall(X))))&
(![X]:((~calm(X)&strong(X))<=>~patient(X)))&
(![X]:((~brave(X)&kind(X))<=>~strong(X)))&
((?[X]:((patient(X)&~generous(X))))=>(patient(alice)))&
(![X]:((~wise(X)|~quiet(X))<=>(patient(X)&happy(X))))&
(![X]:((~creative(X)<~>~rich(X))<=>(~creative(X)&~old(X))))&
((?[X]:((~patient(X)<~>curious(X))))<=>(~funny(fred)))&
((?[X]:((~wise(X)|old(X))))=>(?[X]:((kind(X)<~>~calm(X)))))&
(![X]:(~calm(X)<=>(brave(X)|~happy(X))))&
((?[X]:((~old(X)<~>patient(X))))<=>((creative(susan)&strong(susan))))&
(?[X]:((~kind(X)&brave(X))))&
(?[X]:((~creative(X)&~rich(X))))&
(tall(susan))&
(?[X]:((~strong(X)<~>patient(X))))&
(?[X]:((calm(X)|~humble(X))))&
((quiet(paul)<~>rich(paul)))&
(?[X]:((~creative(X)&~patient(X)))) | rich(alice) | [
"p0",
"p1",
"p2",
"p7",
"p8",
"p9",
"p11",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5263530813471669758454095
% SZS output start Proof for 5263530813471669758454095
1. ! [X0] : (~patient(X0) <=> (quiet(X0) & happy(X0))) [input p0]
2. ! [X0] : ((~quiet(X0) | funny(X0)) <=> (creative(X0) <~> ~generous(X0))) [input p1]
3. ! [X0] : (creative(X0) => (patient(X0) & kind(X0))) [input p2]
8. ! [X0] : ((strong(X0) & ~calm(X0)) <=> ~patient(X0)) [input p7]
9. ! [X0] : ((kind(X0) & ~brave(X0)) <=> ~strong(X0)) [input p8]
10. ? [X0] : (~generous(X0) & patient(X0)) => patient(alice) [input p9]
12. ! [X0] : ((~creative(X0) <~> ~rich(X0)) <=> (~old(X0) & ~creative(X0))) [input p11]
15. ! [X0] : (~calm(X0) <=> (~happy(X0) | brave(X0))) [input p14]
16. ? [X0] : (~old(X0) <~> patient(X0)) <=> (strong(susan) & creative(susan)) [input p15]
20. ? [X0] : (~strong(X0) <~> patient(X0)) [input p19]
24. ~rich(alice) [input hypothesis]
26. ! [X0] : ((patient(X0) & kind(X0)) | ~creative(X0)) [ennf transformation 3]
31. patient(alice) | ! [X0] : (generous(X0) | ~patient(X0)) [ennf transformation 10]
33. ! [X0] : ((~patient(X0) | (~quiet(X0) | ~happy(X0))) & ((quiet(X0) & happy(X0)) | patient(X0))) [nnf transformation 1]
34. ! [X0] : ((~patient(X0) | ~quiet(X0) | ~happy(X0)) & ((quiet(X0) & happy(X0)) | patient(X0))) [flattening 33]
35. ! [X0] : (((~quiet(X0) | funny(X0)) | ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0)))) & (((generous(X0) | ~creative(X0)) & (~generous(X0) | creative(X0))) | (quiet(X0) & ~funny(X0)))) [nnf transformation 2]
36. ! [X0] : ((~quiet(X0) | funny(X0) | ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0)))) & (((generous(X0) | ~creative(X0)) & (~generous(X0) | creative(X0))) | (quiet(X0) & ~funny(X0)))) [flattening 35]
46. ! [X0] : (((strong(X0) & ~calm(X0)) | patient(X0)) & (~patient(X0) | (~strong(X0) | calm(X0)))) [nnf transformation 8]
47. ! [X0] : (((strong(X0) & ~calm(X0)) | patient(X0)) & (~patient(X0) | ~strong(X0) | calm(X0))) [flattening 46]
48. ! [X0] : (((kind(X0) & ~brave(X0)) | strong(X0)) & (~strong(X0) | (~kind(X0) | brave(X0)))) [nnf transformation 9]
49. ! [X0] : (((kind(X0) & ~brave(X0)) | strong(X0)) & (~strong(X0) | ~kind(X0) | brave(X0))) [flattening 48]
52. ! [X0] : ((((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | (old(X0) | creative(X0))) & ((~old(X0) & ~creative(X0)) | ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0))))) [nnf transformation 12]
53. ! [X0] : ((((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | old(X0) | creative(X0)) & ((~old(X0) & ~creative(X0)) | ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0))))) [flattening 52]
62. ! [X0] : ((~calm(X0) | (happy(X0) & ~brave(X0))) & ((~happy(X0) | brave(X0)) | calm(X0))) [nnf transformation 15]
63. ! [X0] : ((~calm(X0) | (happy(X0) & ~brave(X0))) & (~happy(X0) | brave(X0) | calm(X0))) [flattening 62]
64. (? [X0] : ((~patient(X0) | old(X0)) & (patient(X0) | ~old(X0))) | (~strong(susan) | ~creative(susan))) & ((strong(susan) & creative(susan)) | ! [X0] : ((~old(X0) | ~patient(X0)) & (patient(X0) | old(X0)))) [nnf transformation 16]
65. (? [X0] : ((~patient(X0) | old(X0)) & (patient(X0) | ~old(X0))) | ~strong(susan) | ~creative(susan)) & ((strong(susan) & creative(susan)) | ! [X0] : ((~old(X0) | ~patient(X0)) & (patient(X0) | old(X0)))) [flattening 64]
66. (? [X0] : ((~patient(X0) | old(X0)) & (patient(X0) | ~old(X0))) | ~strong(susan) | ~creative(susan)) & ((strong(susan) & creative(susan)) | ! [X1] : ((~old(X1) | ~patient(X1)) & (patient(X1) | old(X1)))) [rectify 65]
67. ? [X0] : ((~patient(X0) | old(X0)) & (patient(X0) | ~old(X0))) => ((~patient(sK5) | old(sK5)) & (patient(sK5) | ~old(sK5))) [choice axiom]
68. (((~patient(sK5) | old(sK5)) & (patient(sK5) | ~old(sK5))) | ~strong(susan) | ~creative(susan)) & ((strong(susan) & creative(susan)) | ! [X1] : ((~old(X1) | ~patient(X1)) & (patient(X1) | old(X1)))) [skolemisation 66,67]
73. ? [X0] : ((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) [nnf transformation 20]
74. ? [X0] : ((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) => ((~patient(sK8) | strong(sK8)) & (patient(sK8) | ~strong(sK8))) [choice axiom]
75. (~patient(sK8) | strong(sK8)) & (patient(sK8) | ~strong(sK8)) [skolemisation 73,74]
83. ~quiet(X0) | ~patient(X0) | ~happy(X0) [cnf transformation 34]
85. ~generous(X0) | creative(X0) | quiet(X0) [cnf transformation 36]
90. ~creative(X0) | kind(X0) [cnf transformation 26]
91. ~creative(X0) | patient(X0) [cnf transformation 26]
106. ~strong(X0) | ~patient(X0) | calm(X0) [cnf transformation 47]
108. strong(X0) | patient(X0) [cnf transformation 47]
109. ~strong(X0) | ~kind(X0) | brave(X0) [cnf transformation 49]
112. patient(alice) | generous(X0) | ~patient(X0) [cnf transformation 31]
119. ~creative(X0) | ~creative(X0) | rich(X0) [cnf transformation 53]
123. rich(X0) | creative(X0) | old(X0) | creative(X0) [cnf transformation 53]
133. ~brave(X0) | ~calm(X0) [cnf transformation 63]
134. ~calm(X0) | happy(X0) [cnf transformation 63]
136. creative(susan) | ~old(X1) | ~patient(X1) [cnf transformation 68]
138. strong(susan) | ~old(X1) | ~patient(X1) [cnf transformation 68]
146. patient(sK8) | ~strong(sK8) [cnf transformation 75]
147. ~patient(sK8) | strong(sK8) [cnf transformation 75]
153. ~rich(alice) [cnf transformation 24]
154. ~creative(X0) | rich(X0) [duplicate literal removal 119]
155. old(X0) | creative(X0) | rich(X0) [duplicate literal removal 123]
185. 7 <=> patient(alice) [avatar definition]
187. patient(alice) <- (7) [avatar component clause 185]
212. 13 <=> creative(susan) [avatar definition]
214. creative(susan) <- (13) [avatar component clause 212]
219. 14 <=> ! [X0] : (generous(X0) | ~patient(X0)) [avatar definition]
220. ~patient(X0) | generous(X0) <- (14) [avatar component clause 219]
221. 14 | 7 [avatar split clause 112,185,219]
263. 24 <=> strong(susan) [avatar definition]
264. strong(susan) <- (24) [avatar component clause 263]
277. 27 <=> ! [X1] : (~old(X1) | ~patient(X1)) [avatar definition]
278. ~old(X1) | ~patient(X1) <- (27) [avatar component clause 277]
279. 27 | 24 [avatar split clause 138,263,277]
284. 27 | 13 [avatar split clause 136,212,277]
286. strong(sK8) [subsumption resolution 147,108]
287. patient(sK8) [subsumption resolution 146,286]
309. kind(susan) <- (13) [resolution 90,214]
311. patient(susan) <- (13) [resolution 91,214]
362. 39 <=> calm(susan) [avatar definition]
363. ~calm(susan) <- (~39) [avatar component clause 362]
364. calm(susan) <- (39) [avatar component clause 362]
378. ~patient(sK8) | calm(sK8) [resolution 106,286]
380. calm(sK8) [subsumption resolution 378,287]
385. ~kind(susan) | brave(susan) <- (24) [resolution 109,264]
387. ~kind(sK8) | brave(sK8) [resolution 109,286]
388. brave(susan) <- (13, 24) [subsumption resolution 385,309]
390. 41 <=> brave(sK8) [avatar definition]
392. brave(sK8) <- (41) [avatar component clause 390]
394. 42 <=> kind(sK8) [avatar definition]
397. 41 | ~42 [avatar split clause 387,394,390]
419. happy(sK8) [resolution 380,134]
422. ~calm(susan) <- (13, 24) [resolution 388,133]
424. $false <- (13, 24, 39) [subsumption resolution 422,364]
425. ~13 | ~24 | ~39 [avatar contradiction clause 424]
428. ~patient(X0) | creative(X0) | rich(X0) <- (27) [resolution 278,155]
429. ~patient(X0) | rich(X0) <- (27) [subsumption resolution 428,154]
456. rich(alice) <- (7, 27) [resolution 429,187]
460. $false <- (7, 27) [subsumption resolution 456,153]
461. ~7 | ~27 [avatar contradiction clause 460]
476. generous(sK8) <- (14) [resolution 220,287]
493. creative(sK8) | quiet(sK8) <- (14) [resolution 476,85]
496. 47 <=> creative(sK8) [avatar definition]
497. creative(sK8) <- (47) [avatar component clause 496]
500. 48 <=> quiet(sK8) [avatar definition]
501. quiet(sK8) <- (48) [avatar component clause 500]
508. 48 | 47 | ~14 [avatar split clause 493,219,496,500]
551. ~patient(sK8) | ~happy(sK8) <- (48) [resolution 501,83]
552. ~happy(sK8) <- (48) [subsumption resolution 551,287]
553. $false <- (48) [subsumption resolution 552,419]
554. ~48 [avatar contradiction clause 553]
559. kind(sK8) <- (47) [resolution 497,90]
562. 42 | ~47 [avatar split clause 559,496,394]
563. ~calm(sK8) <- (41) [resolution 392,133]
565. $false <- (41) [subsumption resolution 563,380]
566. ~41 [avatar contradiction clause 565]
578. ~patient(susan) | calm(susan) <- (24) [resolution 264,106]
579. calm(susan) <- (13, 24) [subsumption resolution 578,311]
580. $false <- (13, 24, ~39) [subsumption resolution 579,363]
581. ~13 | ~24 | 39 [avatar contradiction clause 580]
582. $false [avatar sat refutation 221,279,284,397,425,461,508,554,562,566,581]
% SZS output end Proof for 5263530813471669758454095
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not wise and not tall then someone is either not wise or humble. Everyone who is not calm or tall is either curious or humble and vice versa. If susan is not generous or generous then mary is both not old and not kind and vice versa. If mary is curious then paul is either not curious or not patient. If someone is either not funny or not generous then mary is not brave and vice versa. Everyone who is either happy or rich is both creative and generous and vice versa. Everyone who is kind or not happy is creative or not calm and vice versa. If someone is not quiet then mary is rich and vice versa. Everyone who is not old is either strong or not brave. Everyone who is rich is calm and vice versa. Everyone who is both wise and not creative is brave and vice versa. Everyone who is both not patient and not funny is either old or patient. Everyone who is either not tall or happy is both creative and not happy and vice versa. Everyone who is both not funny and not generous is both not rich and curious. If someone is not generous or brave then someone is not calm or happy. Everyone who is not calm is not curious and vice versa. Mary is either kind or not generous. Someone is both not creative and not funny. Someone is both quiet and curious. Fred is not calm. Paul is both not generous and curious. John is not quiet. John is not rich. Someone is either humble or generous. | Mary is creative. | contradiction | (((~wise(susan)&~tall(susan)))=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:((~calm(X)|tall(X))<=>(curious(X)<~>humble(X))))&
(((~generous(susan)|generous(susan)))<=>((~old(mary)&~kind(mary))))&
((curious(mary))=>((~curious(paul)<~>~patient(paul))))&
((?[X]:((~funny(X)<~>~generous(X))))<=>(~brave(mary)))&
(![X]:((happy(X)<~>rich(X))<=>(creative(X)&generous(X))))&
(![X]:((kind(X)|~happy(X))<=>(creative(X)|~calm(X))))&
((?[X]:(~quiet(X)))<=>(rich(mary)))&
(![X]:(~old(X)=>(strong(X)<~>~brave(X))))&
(![X]:(rich(X)<=>calm(X)))&
(![X]:((wise(X)&~creative(X))<=>brave(X)))&
(![X]:((~patient(X)&~funny(X))=>(old(X)<~>patient(X))))&
(![X]:((~tall(X)<~>happy(X))<=>(creative(X)&~happy(X))))&
(![X]:((~funny(X)&~generous(X))=>(~rich(X)&curious(X))))&
((?[X]:((~generous(X)|brave(X))))=>(?[X]:((~calm(X)|happy(X)))))&
(![X]:(~calm(X)<=>~curious(X)))&
((kind(mary)<~>~generous(mary)))&
(?[X]:((~creative(X)&~funny(X))))&
(?[X]:((quiet(X)&curious(X))))&
(~calm(fred))&
((~generous(paul)&curious(paul)))&
(~quiet(john))&
(~rich(john))&
(?[X]:((humble(X)<~>generous(X)))) | creative(mary) | [
"p2",
"p5",
"p6",
"p7",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3317658349415921288540394
% SZS output start Proof for 3317658349415921288540394
3. (generous(susan) | ~generous(susan)) <=> (~kind(mary) & ~old(mary)) [input p2]
6. ! [X0] : ((happy(X0) <~> rich(X0)) <=> (generous(X0) & creative(X0))) [input p5]
7. ! [X0] : ((~happy(X0) | kind(X0)) <=> (~calm(X0) | creative(X0))) [input p6]
8. ? [X0] : ~quiet(X0) <=> rich(mary) [input p7]
17. kind(mary) <~> ~generous(mary) [input p16]
22. ~quiet(john) [input p21]
25. creative(mary) [input hypothesis]
41. ((generous(susan) | ~generous(susan)) | (kind(mary) | old(mary))) & ((~kind(mary) & ~old(mary)) | (~generous(susan) & generous(susan))) [nnf transformation 3]
42. (generous(susan) | ~generous(susan) | kind(mary) | old(mary)) & ((~kind(mary) & ~old(mary)) | (~generous(susan) & generous(susan))) [flattening 41]
48. ! [X0] : ((((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | (~generous(X0) | ~creative(X0))) & ((generous(X0) & creative(X0)) | ((happy(X0) | ~rich(X0)) & (rich(X0) | ~happy(X0))))) [nnf transformation 6]
49. ! [X0] : ((((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | ~generous(X0) | ~creative(X0)) & ((generous(X0) & creative(X0)) | ((happy(X0) | ~rich(X0)) & (rich(X0) | ~happy(X0))))) [flattening 48]
50. ! [X0] : (((~happy(X0) | kind(X0)) | (calm(X0) & ~creative(X0))) & ((~calm(X0) | creative(X0)) | (happy(X0) & ~kind(X0)))) [nnf transformation 7]
51. ! [X0] : ((~happy(X0) | kind(X0) | (calm(X0) & ~creative(X0))) & (~calm(X0) | creative(X0) | (happy(X0) & ~kind(X0)))) [flattening 50]
52. (? [X0] : ~quiet(X0) | ~rich(mary)) & (rich(mary) | ! [X0] : quiet(X0)) [nnf transformation 8]
53. (? [X0] : ~quiet(X0) | ~rich(mary)) & (rich(mary) | ! [X1] : quiet(X1)) [rectify 52]
54. ? [X0] : ~quiet(X0) => ~quiet(sK2) [choice axiom]
55. (~quiet(sK2) | ~rich(mary)) & (rich(mary) | ! [X1] : quiet(X1)) [skolemisation 53,54]
67. (generous(mary) | ~kind(mary)) & (~generous(mary) | kind(mary)) [nnf transformation 17]
85. ~kind(mary) | generous(susan) [cnf transformation 42]
86. ~kind(mary) | ~generous(susan) [cnf transformation 42]
97. ~rich(X0) | happy(X0) | generous(X0) [cnf transformation 49]
102. ~creative(X0) | kind(X0) | ~happy(X0) [cnf transformation 51]
104. rich(mary) | quiet(X1) [cnf transformation 55]
127. ~generous(mary) | kind(mary) [cnf transformation 67]
128. generous(mary) | ~kind(mary) [cnf transformation 67]
136. ~quiet(john) [cnf transformation 22]
140. creative(mary) [cnf transformation 25]
163. 5 <=> generous(susan) [avatar definition]
167. 6 <=> kind(mary) [avatar definition]
169. ~kind(mary) <- (~6) [avatar component clause 167]
170. ~5 | ~6 [avatar split clause 86,167,163]
171. 5 | ~6 [avatar split clause 85,167,163]
215. 16 <=> rich(mary) [avatar definition]
216. rich(mary) <- (16) [avatar component clause 215]
224. 18 <=> ! [X1] : quiet(X1) [avatar definition]
225. quiet(X1) <- (18) [avatar component clause 224]
226. 18 | 16 [avatar split clause 104,215,224]
244. 23 <=> generous(mary) [avatar definition]
245. ~generous(mary) <- (~23) [avatar component clause 244]
247. ~6 | 23 [avatar split clause 128,244,167]
248. 6 | ~23 [avatar split clause 127,244,167]
339. happy(mary) | generous(mary) <- (16) [resolution 97,216]
342. happy(mary) <- (16, ~23) [subsumption resolution 339,245]
362. kind(mary) | ~happy(mary) [resolution 102,140]
364. ~happy(mary) <- (~6) [subsumption resolution 362,169]
365. $false <- (~6, 16, ~23) [subsumption resolution 364,342]
366. 6 | ~16 | 23 [avatar contradiction clause 365]
369. $false <- (18) [resolution 225,136]
372. ~18 [avatar contradiction clause 369]
373. $false [avatar sat refutation 170,171,226,247,248,366,372]
% SZS output end Proof for 3317658349415921288540394
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet or not strong is both kind and not funny and vice versa.
Everyone who is either patient or rich is not happy or kind.
Everyone who is not old or tall is happy and vice versa.
Everyone who is both not kind and rich is humble.
Everyone who is generous is wise.
Everyone who is both quiet and humble is quiet or strong and vice versa.
Everyone who is kind or tall is both strong and generous.
Everyone who is either curious or not funny is either not brave or strong and vice versa.
If someone is both not creative and curious then mary is generous or calm and vice versa.
Everyone who is both not calm and strong is either wise or kind and vice versa.
Everyone who is both not calm and rich is not generous.
Everyone who is not generous or not curious is either happy or generous and vice versa.
Everyone who is either creative or tall is either patient or not funny.
Everyone who is not rich or not humble is not patient or not rich.
Everyone who is both not strong and rich is either not kind or wise.
If someone is either not creative or not patient then someone is not humble or not generous and vice versa.
Someone is old.
Mary is curious or old.
Paul is both curious and wise.
Fred is not kind or creative.
Someone is either not quiet or kind.
Someone is both generous and not creative. | Mary is old. | neutral | (![X]:((quiet(X)|~strong(X))<=>(kind(X)&~funny(X))))&
(![X]:((patient(X)<~>rich(X))=>(~happy(X)|kind(X))))&
(![X]:((~old(X)|tall(X))<=>happy(X)))&
(![X]:((~kind(X)&rich(X))=>humble(X)))&
(![X]:(generous(X)=>wise(X)))&
(![X]:((quiet(X)&humble(X))<=>(quiet(X)|strong(X))))&
(![X]:((kind(X)|tall(X))=>(strong(X)&generous(X))))&
(![X]:((curious(X)<~>~funny(X))<=>(~brave(X)<~>strong(X))))&
((?[X]:((~creative(X)&curious(X))))<=>((generous(mary)|calm(mary))))&
(![X]:((~calm(X)&strong(X))<=>(wise(X)<~>kind(X))))&
(![X]:((~calm(X)&rich(X))=>~generous(X)))&
(![X]:((~generous(X)|~curious(X))<=>(happy(X)<~>generous(X))))&
(![X]:((creative(X)<~>tall(X))=>(patient(X)<~>~funny(X))))&
(![X]:((~rich(X)|~humble(X))=>(~patient(X)|~rich(X))))&
(![X]:((~strong(X)&rich(X))=>(~kind(X)<~>wise(X))))&
((?[X]:((~creative(X)<~>~patient(X))))<=>(?[X]:((~humble(X)|~generous(X)))))&
(?[X]:(old(X)))&
((curious(mary)|old(mary)))&
((curious(paul)&wise(paul)))&
((~kind(fred)|creative(fred)))&
(?[X]:((~quiet(X)<~>kind(X))))&
(?[X]:((generous(X)&~creative(X)))) | old(mary) | [] | null | 0 |
If someone is not quiet then john is not humble and vice versa.
Everyone who is humble is creative or not strong.
If mary is humble or funny then someone is either not curious or not patient.
If someone is humble or tall then someone is either funny or humble.
Everyone who is both curious and not wise is happy or humble and vice versa.
If mary is patient then someone is both calm and happy and vice versa.
If alice is both wise and not old then someone is either not calm or creative and vice versa.
If someone is either not brave or not creative then alice is curious.
Everyone who is rich or not generous is both not wise and creative.
Everyone who is not quiet or not patient is not curious and vice versa.
If someone is not quiet then someone is both not happy and old and vice versa.
If alice is patient then someone is quiet and vice versa.
Everyone who is both kind and wise is both not humble and happy and vice versa.
If alice is either not funny or quiet then someone is both not tall and curious.
If someone is both generous and humble then someone is both rich and kind and vice versa.
Everyone who is either brave or not rich is either quiet or not kind and vice versa.
Someone is tall or old.
Someone is either kind or not patient.
Mary is tall or not happy.
Alice is not patient.
Someone is generous or not strong.
Someone is either not strong or not wise.
Someone is either not funny or not brave. | John is humble. | contradiction | ((?[X]:(~quiet(X)))<=>(~humble(john)))&
(![X]:(humble(X)=>(creative(X)|~strong(X))))&
(((humble(mary)|funny(mary)))=>(?[X]:((~curious(X)<~>~patient(X)))))&
((?[X]:((humble(X)|tall(X))))=>(?[X]:((funny(X)<~>humble(X)))))&
(![X]:((curious(X)&~wise(X))<=>(happy(X)|humble(X))))&
((patient(mary))<=>(?[X]:((calm(X)&happy(X)))))&
(((wise(alice)&~old(alice)))<=>(?[X]:((~calm(X)<~>creative(X)))))&
((?[X]:((~brave(X)<~>~creative(X))))=>(curious(alice)))&
(![X]:((rich(X)|~generous(X))=>(~wise(X)&creative(X))))&
(![X]:((~quiet(X)|~patient(X))<=>~curious(X)))&
((?[X]:(~quiet(X)))<=>(?[X]:((~happy(X)&old(X)))))&
((patient(alice))<=>(?[X]:(quiet(X))))&
(![X]:((kind(X)&wise(X))<=>(~humble(X)&happy(X))))&
(((~funny(alice)<~>quiet(alice)))=>(?[X]:((~tall(X)&curious(X)))))&
((?[X]:((generous(X)&humble(X))))<=>(?[X]:((rich(X)&kind(X)))))&
(![X]:((brave(X)<~>~rich(X))<=>(quiet(X)<~>~kind(X))))&
(?[X]:((tall(X)|old(X))))&
(?[X]:((kind(X)<~>~patient(X))))&
((tall(mary)|~happy(mary)))&
(~patient(alice))&
(?[X]:((generous(X)|~strong(X))))&
(?[X]:((~strong(X)<~>~wise(X))))&
(?[X]:((~funny(X)<~>~brave(X)))) | humble(john) | [
"p0",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3752167205879695256985169
% SZS output start Proof for 3752167205879695256985169
1. ? [X0] : ~quiet(X0) <=> ~humble(john) [input p0]
12. patient(alice) <=> ? [X0] : quiet(X0) [input p11]
20. ~patient(alice) [input p19]
24. humble(john) [input hypothesis]
35. (? [X0] : ~quiet(X0) | humble(john)) & (~humble(john) | ! [X0] : quiet(X0)) [nnf transformation 1]
36. (? [X0] : ~quiet(X0) | humble(john)) & (~humble(john) | ! [X1] : quiet(X1)) [rectify 35]
37. ? [X0] : ~quiet(X0) => ~quiet(sK0) [choice axiom]
38. (~quiet(sK0) | humble(john)) & (~humble(john) | ! [X1] : quiet(X1)) [skolemisation 36,37]
65. (patient(alice) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | ~patient(alice)) [nnf transformation 12]
66. (patient(alice) | ! [X0] : ~quiet(X0)) & (? [X1] : quiet(X1) | ~patient(alice)) [rectify 65]
67. ? [X1] : quiet(X1) => quiet(sK7) [choice axiom]
68. (patient(alice) | ! [X0] : ~quiet(X0)) & (quiet(sK7) | ~patient(alice)) [skolemisation 66,67]
93. ~humble(john) | quiet(X1) [cnf transformation 38]
131. patient(alice) | ~quiet(X0) [cnf transformation 68]
156. ~patient(alice) [cnf transformation 20]
162. humble(john) [cnf transformation 24]
164. 1 <=> humble(john) [avatar definition]
173. 3 <=> ! [X1] : quiet(X1) [avatar definition]
174. quiet(X1) <- (3) [avatar component clause 173]
175. 3 | ~1 [avatar split clause 93,164,173]
291. 29 <=> ! [X0] : ~quiet(X0) [avatar definition]
292. ~quiet(X0) <- (29) [avatar component clause 291]
294. 30 <=> patient(alice) [avatar definition]
297. 29 | 30 [avatar split clause 131,294,291]
379. ~30 [avatar split clause 156,294]
409. 1 [avatar split clause 162,164]
410. $false <- (3, 29) [subsumption resolution 174,292]
411. ~3 | ~29 [avatar contradiction clause 410]
412. $false [avatar sat refutation 175,297,379,409,411]
% SZS output end Proof for 3752167205879695256985169
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not rich and calm then alice is either quiet or not kind and vice versa. If john is either not happy or quiet then someone is both curious and happy and vice versa. Everyone who is either happy or tall is both curious and not creative and vice versa. Everyone who is either not wise or not strong is both humble and calm. Everyone who is either not old or not creative is both not humble and quiet. Everyone who is brave is both humble and calm and vice versa. Everyone who is not curious or patient is either funny or not kind. If paul is strong then someone is either not quiet or wise and vice versa. Everyone who is calm is not brave. If someone is old or creative then someone is either not patient or patient and vice versa. If someone is both not brave and not patient then fred is either not rich or wise. Everyone who is either not strong or quiet is either not strong or patient. If alice is either wise or brave then someone is brave. If someone is either not happy or not kind then fred is not creative and vice versa. Everyone who is either not strong or kind is both curious and old. If someone is either not patient or not curious then someone is both not kind and not calm and vice versa. Someone is both calm and not happy. Someone is both not creative and generous. Mary is either not humble or not rich. Someone is quiet. Paul is both kind and humble. Someone is not humble. Someone is either not quiet or tall. Susan is not funny or not creative. | Susan is not brave. | entailment | ((?[X]:((~rich(X)&calm(X))))<=>((quiet(alice)<~>~kind(alice))))&
(((~happy(john)<~>quiet(john)))<=>(?[X]:((curious(X)&happy(X)))))&
(![X]:((happy(X)<~>tall(X))<=>(curious(X)&~creative(X))))&
(![X]:((~wise(X)<~>~strong(X))=>(humble(X)&calm(X))))&
(![X]:((~old(X)<~>~creative(X))=>(~humble(X)&quiet(X))))&
(![X]:(brave(X)<=>(humble(X)&calm(X))))&
(![X]:((~curious(X)|patient(X))=>(funny(X)<~>~kind(X))))&
((strong(paul))<=>(?[X]:((~quiet(X)<~>wise(X)))))&
(![X]:(calm(X)=>~brave(X)))&
((?[X]:((old(X)|creative(X))))<=>(?[X]:((~patient(X)<~>patient(X)))))&
((?[X]:((~brave(X)&~patient(X))))=>((~rich(fred)<~>wise(fred))))&
(![X]:((~strong(X)<~>quiet(X))=>(~strong(X)<~>patient(X))))&
(((wise(alice)<~>brave(alice)))=>(?[X]:(brave(X))))&
((?[X]:((~happy(X)<~>~kind(X))))<=>(~creative(fred)))&
(![X]:((~strong(X)<~>kind(X))=>(curious(X)&old(X))))&
((?[X]:((~patient(X)<~>~curious(X))))<=>(?[X]:((~kind(X)&~calm(X)))))&
(?[X]:((calm(X)&~happy(X))))&
(?[X]:((~creative(X)&generous(X))))&
((~humble(mary)<~>~rich(mary)))&
(?[X]:(quiet(X)))&
((kind(paul)&humble(paul)))&
(?[X]:(~humble(X)))&
(?[X]:((~quiet(X)<~>tall(X))))&
((~funny(susan)|~creative(susan))) | ~brave(susan) | [
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3379596421703698595708266
% SZS output start Proof for 3379596421703698595708266
6. ! [X0] : (brave(X0) <=> (calm(X0) & humble(X0))) [input p5]
9. ! [X0] : (calm(X0) => ~brave(X0)) [input p8]
25. brave(susan) [input hypothesis]
32. ! [X0] : (~brave(X0) | ~calm(X0)) [ennf transformation 9]
49. ! [X0] : ((brave(X0) | (~calm(X0) | ~humble(X0))) & ((calm(X0) & humble(X0)) | ~brave(X0))) [nnf transformation 6]
50. ! [X0] : ((brave(X0) | ~calm(X0) | ~humble(X0)) & ((calm(X0) & humble(X0)) | ~brave(X0))) [flattening 49]
115. calm(X0) | ~brave(X0) [cnf transformation 50]
125. ~brave(X0) | ~calm(X0) [cnf transformation 32]
166. brave(susan) [cnf transformation 25]
243. ~brave(X0) [subsumption resolution 125,115]
356. $false [subsumption resolution 166,243]
% SZS output end Proof for 3379596421703698595708266
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not generous or not rich then susan is not generous or not brave. Everyone who is either not old or generous is either not old or not brave. Everyone who is not kind is not old and vice versa. Everyone who is funny is not calm or not tall and vice versa. If john is either not humble or strong then mary is not creative. Everyone who is brave is not patient. Everyone who is humble is either not calm or not kind. If someone is both not old and not brave then alice is either not old or patient and vice versa. Everyone who is not strong is either wise or not quiet. If lucy is not tall or curious then someone is both not kind and not humble and vice versa. Everyone who is both humble and old is rich or not happy and vice versa. Everyone who is creative is either generous or not old. If lucy is both quiet and not generous then someone is either not creative or not rich. If someone is strong or not happy then someone is happy or calm and vice versa. If someone is not rich then someone is old or curious and vice versa. If fred is either not humble or not quiet then someone is quiet or creative. Susan is not happy. Lucy is not generous or not creative. Paul is both curious and not funny. Paul is quiet. Alice is either not happy or rich. Someone is not curious. Paul is both wise and not generous. Someone is kind. | Paul is happy. | entailment | (((~generous(paul)<~>~rich(paul)))=>((~generous(susan)|~brave(susan))))&
(![X]:((~old(X)<~>generous(X))=>(~old(X)<~>~brave(X))))&
(![X]:(~kind(X)<=>~old(X)))&
(![X]:(funny(X)<=>(~calm(X)|~tall(X))))&
(((~humble(john)<~>strong(john)))=>(~creative(mary)))&
(![X]:(brave(X)=>~patient(X)))&
(![X]:(humble(X)=>(~calm(X)<~>~kind(X))))&
((?[X]:((~old(X)&~brave(X))))<=>((~old(alice)<~>patient(alice))))&
(![X]:(~strong(X)=>(wise(X)<~>~quiet(X))))&
(((~tall(lucy)|curious(lucy)))<=>(?[X]:((~kind(X)&~humble(X)))))&
(![X]:((humble(X)&old(X))<=>(rich(X)|~happy(X))))&
(![X]:(creative(X)=>(generous(X)<~>~old(X))))&
(((quiet(lucy)&~generous(lucy)))=>(?[X]:((~creative(X)<~>~rich(X)))))&
((?[X]:((strong(X)|~happy(X))))<=>(?[X]:((happy(X)|calm(X)))))&
((?[X]:(~rich(X)))<=>(?[X]:((old(X)|curious(X)))))&
(((~humble(fred)<~>~quiet(fred)))=>(?[X]:((quiet(X)|creative(X)))))&
(~happy(susan))&
((~generous(lucy)|~creative(lucy)))&
((curious(paul)&~funny(paul)))&
(quiet(paul))&
((~happy(alice)<~>rich(alice)))&
(?[X]:(~curious(X)))&
((wise(paul)&~generous(paul)))&
(?[X]:(kind(X))) | happy(paul) | [
"p2",
"p3",
"p6",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2508123829589595705669102
% SZS output start Proof for 2508123829589595705669102
3. ! [X0] : (~kind(X0) <=> ~old(X0)) [input p2]
4. ! [X0] : (funny(X0) <=> (~tall(X0) | ~calm(X0))) [input p3]
7. ! [X0] : (humble(X0) => (~calm(X0) <~> ~kind(X0))) [input p6]
11. ! [X0] : ((old(X0) & humble(X0)) <=> (~happy(X0) | rich(X0))) [input p10]
19. ~funny(paul) & curious(paul) [input p18]
25. ~happy(paul) [input hypothesis]
28. ! [X0] : ((~tall(X0) | ~calm(X0)) => funny(X0)) [unused predicate definition removal 4]
32. ! [X0] : (funny(X0) | (tall(X0) & calm(X0))) [ennf transformation 28]
35. ! [X0] : ((~calm(X0) <~> ~kind(X0)) | ~humble(X0)) [ennf transformation 7]
43. ! [X0] : ((~kind(X0) | old(X0)) & (~old(X0) | kind(X0))) [nnf transformation 3]
45. ! [X0] : (((kind(X0) | calm(X0)) & (~kind(X0) | ~calm(X0))) | ~humble(X0)) [nnf transformation 35]
56. ! [X0] : (((old(X0) & humble(X0)) | (happy(X0) & ~rich(X0))) & ((~happy(X0) | rich(X0)) | (~old(X0) | ~humble(X0)))) [nnf transformation 11]
57. ! [X0] : (((old(X0) & humble(X0)) | (happy(X0) & ~rich(X0))) & (~happy(X0) | rich(X0) | ~old(X0) | ~humble(X0))) [flattening 56]
86. ~old(X0) | kind(X0) [cnf transformation 43]
88. calm(X0) | funny(X0) [cnf transformation 32]
93. ~humble(X0) | ~calm(X0) | ~kind(X0) [cnf transformation 45]
110. happy(X0) | humble(X0) [cnf transformation 57]
112. happy(X0) | old(X0) [cnf transformation 57]
129. ~funny(paul) [cnf transformation 19]
137. ~happy(paul) [cnf transformation 25]
340. humble(paul) [resolution 110,137]
344. old(paul) [resolution 112,137]
353. ~calm(paul) | ~kind(paul) [resolution 93,340]
357. 43 <=> kind(paul) [avatar definition]
361. 44 <=> calm(paul) [avatar definition]
363. ~calm(paul) <- (~44) [avatar component clause 361]
364. ~43 | ~44 [avatar split clause 353,361,357]
396. kind(paul) [resolution 344,86]
475. funny(paul) <- (~44) [resolution 363,88]
476. $false <- (~44) [subsumption resolution 475,129]
477. 44 [avatar contradiction clause 476]
478. 43 [avatar split clause 396,357]
479. $false [avatar sat refutation 364,477,478]
% SZS output end Proof for 2508123829589595705669102
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If mary is both not funny and not happy then someone is not generous.
If susan is generous then someone is either not happy or brave.
Everyone who is not kind is both not humble and not old.
If someone is both funny and not strong then someone is quiet or curious.
Everyone who is wise or kind is both not generous and old.
Everyone who is wise is not wise or patient.
If someone is not generous then susan is either not generous or old and vice versa.
If someone is both not strong and not curious then mary is generous or not calm and vice versa.
Everyone who is not generous or humble is both quiet and not kind.
If someone is both strong and curious then alice is not humble or humble.
If someone is quiet then someone is funny and vice versa.
Everyone who is either creative or not kind is either happy or not humble.
Everyone who is not tall or old is either quiet or kind.
Everyone who is either not happy or tall is both old and creative and vice versa.
If susan is both wise and brave then lucy is old or happy and vice versa.
Everyone who is brave or quiet is not creative and vice versa.
Someone is calm.
Someone is either quiet or curious.
Alice is brave.
Fred is wise or not humble.
Someone is not calm.
Someone is either old or not strong. | Alice is wise. | contradiction | (((~funny(mary)&~happy(mary)))=>(?[X]:(~generous(X))))&
((generous(susan))=>(?[X]:((~happy(X)<~>brave(X)))))&
(![X]:(~kind(X)=>(~humble(X)&~old(X))))&
((?[X]:((funny(X)&~strong(X))))=>(?[X]:((quiet(X)|curious(X)))))&
(![X]:((wise(X)|kind(X))=>(~generous(X)&old(X))))&
(![X]:(wise(X)=>(~wise(X)|patient(X))))&
((?[X]:(~generous(X)))<=>((~generous(susan)<~>old(susan))))&
((?[X]:((~strong(X)&~curious(X))))<=>((generous(mary)|~calm(mary))))&
(![X]:((~generous(X)|humble(X))=>(quiet(X)&~kind(X))))&
((?[X]:((strong(X)&curious(X))))=>((~humble(alice)|humble(alice))))&
((?[X]:(quiet(X)))<=>(?[X]:(funny(X))))&
(![X]:((creative(X)<~>~kind(X))=>(happy(X)<~>~humble(X))))&
(![X]:((~tall(X)|old(X))=>(quiet(X)<~>kind(X))))&
(![X]:((~happy(X)<~>tall(X))<=>(old(X)&creative(X))))&
(((wise(susan)&brave(susan)))<=>((old(lucy)|happy(lucy))))&
(![X]:((brave(X)|quiet(X))<=>~creative(X)))&
(?[X]:(calm(X)))&
(?[X]:((quiet(X)<~>curious(X))))&
(brave(alice))&
((wise(fred)|~humble(fred)))&
(?[X]:(~calm(X)))&
(?[X]:((old(X)<~>~strong(X)))) | wise(alice) | [
"p2",
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3712724963323905619611793
% SZS output start Proof for 3712724963323905619611793
3. ! [X0] : (~kind(X0) => (~old(X0) & ~humble(X0))) [input p2]
5. ! [X0] : ((kind(X0) | wise(X0)) => (old(X0) & ~generous(X0))) [input p4]
9. ! [X0] : ((humble(X0) | ~generous(X0)) => (~kind(X0) & quiet(X0))) [input p8]
23. wise(alice) [input hypothesis]
30. ! [X0] : ((~old(X0) & ~humble(X0)) | kind(X0)) [ennf transformation 3]
32. ! [X0] : ((old(X0) & ~generous(X0)) | (~kind(X0) & ~wise(X0))) [ennf transformation 5]
33. ! [X0] : ((~kind(X0) & quiet(X0)) | (~humble(X0) & generous(X0))) [ennf transformation 9]
82. ~old(X0) | kind(X0) [cnf transformation 30]
85. ~kind(X0) | ~generous(X0) [cnf transformation 32]
86. ~wise(X0) | old(X0) [cnf transformation 32]
99. ~kind(X0) | generous(X0) [cnf transformation 33]
134. wise(alice) [cnf transformation 23]
214. ~kind(X0) [subsumption resolution 99,85]
282. old(alice) [resolution 86,134]
283. kind(alice) [resolution 282,82]
284. $false [subsumption resolution 283,214]
% SZS output end Proof for 3712724963323905619611793
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind then paul is either not brave or patient and vice versa. If someone is both not quiet and strong then someone is not wise or humble. Everyone who is either not tall or not calm is either not brave or not creative and vice versa. If someone is not brave or kind then someone is not funny or brave and vice versa. Everyone who is both not funny and brave is creative or not brave and vice versa. Everyone who is either not old or happy is both not happy and creative. If lucy is both patient and not happy then someone is funny. Everyone who is either humble or happy is both strong and not curious and vice versa. Everyone who is both kind and not rich is either brave or wise and vice versa. If fred is either wise or creative then paul is humble or patient. Everyone who is both old and quiet is both not humble and rich and vice versa. Everyone who is not wise or not patient is humble or generous. Everyone who is both patient and funny is not wise or old and vice versa. Everyone who is not old or creative is both not tall and calm. Someone is humble or not strong. Someone is either not funny or patient. Susan is both strong and not kind. Someone is not creative or not rich. Alice is either calm or funny. Someone is patient. Someone is not tall or not patient. | Susan is not creative. | entailment | ((?[X]:(~kind(X)))<=>((~brave(paul)<~>patient(paul))))&
((?[X]:((~quiet(X)&strong(X))))=>(?[X]:((~wise(X)|humble(X)))))&
(![X]:((~tall(X)<~>~calm(X))<=>(~brave(X)<~>~creative(X))))&
((?[X]:((~brave(X)|kind(X))))<=>(?[X]:((~funny(X)|brave(X)))))&
(![X]:((~funny(X)&brave(X))<=>(creative(X)|~brave(X))))&
(![X]:((~old(X)<~>happy(X))=>(~happy(X)&creative(X))))&
(((patient(lucy)&~happy(lucy)))=>(?[X]:(funny(X))))&
(![X]:((humble(X)<~>happy(X))<=>(strong(X)&~curious(X))))&
(![X]:((kind(X)&~rich(X))<=>(brave(X)<~>wise(X))))&
(((wise(fred)<~>creative(fred)))=>((humble(paul)|patient(paul))))&
(![X]:((old(X)&quiet(X))<=>(~humble(X)&rich(X))))&
(![X]:((~wise(X)|~patient(X))=>(humble(X)|generous(X))))&
(![X]:((patient(X)&funny(X))<=>(~wise(X)|old(X))))&
(![X]:((~old(X)|creative(X))=>(~tall(X)&calm(X))))&
(?[X]:((humble(X)|~strong(X))))&
(?[X]:((~funny(X)<~>patient(X))))&
((strong(susan)&~kind(susan)))&
(?[X]:((~creative(X)|~rich(X))))&
((calm(alice)<~>funny(alice)))&
(?[X]:(patient(X)))&
(?[X]:((~tall(X)|~patient(X)))) | ~creative(susan) | [
"p2",
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5971570489681945784299973
% SZS output start Proof for 5971570489681945784299973
3. ! [X0] : ((~tall(X0) <~> ~calm(X0)) <=> (~brave(X0) <~> ~creative(X0))) [input p2]
5. ! [X0] : ((brave(X0) & ~funny(X0)) <=> (~brave(X0) | creative(X0))) [input p4]
14. ! [X0] : ((creative(X0) | ~old(X0)) => (calm(X0) & ~tall(X0))) [input p13]
22. creative(susan) [input hypothesis]
32. ! [X0] : ((calm(X0) & ~tall(X0)) | (~creative(X0) & old(X0))) [ennf transformation 14]
40. ! [X0] : ((((calm(X0) | tall(X0)) & (~calm(X0) | ~tall(X0))) | ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0)))) & (((creative(X0) | brave(X0)) & (~creative(X0) | ~brave(X0))) | ((~tall(X0) | calm(X0)) & (~calm(X0) | tall(X0))))) [nnf transformation 3]
46. ! [X0] : (((brave(X0) & ~funny(X0)) | (brave(X0) & ~creative(X0))) & ((~brave(X0) | creative(X0)) | (~brave(X0) | funny(X0)))) [nnf transformation 5]
47. ! [X0] : (((brave(X0) & ~funny(X0)) | (brave(X0) & ~creative(X0))) & (~brave(X0) | creative(X0) | ~brave(X0) | funny(X0))) [flattening 46]
77. ~creative(X0) | ~brave(X0) | ~calm(X0) | tall(X0) [cnf transformation 40]
93. brave(X0) | brave(X0) [cnf transformation 47]
123. ~creative(X0) | ~tall(X0) [cnf transformation 32]
125. ~creative(X0) | calm(X0) [cnf transformation 32]
136. creative(susan) [cnf transformation 22]
139. brave(X0) [duplicate literal removal 93]
200. 15 <=> ! [X3] : brave(X3) [avatar definition]
201. brave(X3) <- (15) [avatar component clause 200]
203. 15 [avatar split clause 139,200]
294. ~tall(susan) [resolution 123,136]
297. calm(susan) [resolution 125,136]
321. ~brave(susan) | ~calm(susan) | tall(susan) [resolution 77,136]
322. ~calm(susan) | tall(susan) <- (15) [subsumption resolution 321,201]
323. tall(susan) <- (15) [subsumption resolution 322,297]
324. $false <- (15) [subsumption resolution 323,294]
325. ~15 [avatar contradiction clause 324]
326. $false [avatar sat refutation 203,325]
% SZS output end Proof for 5971570489681945784299973
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative then paul is either happy or not rich.
Everyone who is either quiet or not wise is brave.
If alice is either kind or not curious then susan is not creative or calm.
Everyone who is not brave is not old.
If someone is both patient and strong then mary is both not patient and humble.
Everyone who is both not rich and happy is both quiet and not humble and vice versa.
Everyone who is humble is both happy and not happy.
Everyone who is not old is either humble or creative.
If someone is not tall then alice is not quiet or calm.
Everyone who is humble is both not humble and not quiet and vice versa.
If lucy is either quiet or not generous then lucy is not calm or happy and vice versa.
Everyone who is not humble or tall is either wise or not kind.
Everyone who is both kind and humble is not patient or wise.
If john is both generous and brave then someone is both not wise and strong.
If someone is not funny then someone is both not calm and not quiet and vice versa.
If someone is not funny then fred is strong.
Alice is either not brave or not rich.
Someone is both creative and strong.
Fred is both not patient and strong.
Lucy is either tall or creative.
Mary is not humble or funny.
John is either humble or not curious.
Fred is either kind or not tall.
Someone is both not rich and not old. | Fred is funny. | entailment | ((?[X]:(~creative(X)))=>((happy(paul)<~>~rich(paul))))&
(![X]:((quiet(X)<~>~wise(X))=>brave(X)))&
(((kind(alice)<~>~curious(alice)))=>((~creative(susan)|calm(susan))))&
(![X]:(~brave(X)=>~old(X)))&
((?[X]:((patient(X)&strong(X))))=>((~patient(mary)&humble(mary))))&
(![X]:((~rich(X)&happy(X))<=>(quiet(X)&~humble(X))))&
(![X]:(humble(X)=>(happy(X)&~happy(X))))&
(![X]:(~old(X)=>(humble(X)<~>creative(X))))&
((?[X]:(~tall(X)))=>((~quiet(alice)|calm(alice))))&
(![X]:(humble(X)<=>(~humble(X)&~quiet(X))))&
(((quiet(lucy)<~>~generous(lucy)))<=>((~calm(lucy)|happy(lucy))))&
(![X]:((~humble(X)|tall(X))=>(wise(X)<~>~kind(X))))&
(![X]:((kind(X)&humble(X))=>(~patient(X)|wise(X))))&
(((generous(john)&brave(john)))=>(?[X]:((~wise(X)&strong(X)))))&
((?[X]:(~funny(X)))<=>(?[X]:((~calm(X)&~quiet(X)))))&
((?[X]:(~funny(X)))=>(strong(fred)))&
((~brave(alice)<~>~rich(alice)))&
(?[X]:((creative(X)&strong(X))))&
((~patient(fred)&strong(fred)))&
((tall(lucy)<~>creative(lucy)))&
((~humble(mary)|funny(mary)))&
((humble(john)<~>~curious(john)))&
((kind(fred)<~>~tall(fred)))&
(?[X]:((~rich(X)&~old(X)))) | funny(fred) | [
"p6",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8600629460891023282536861
% SZS output start Proof for 8600629460891023282536861
7. ! [X0] : (humble(X0) => (~happy(X0) & happy(X0))) [input p6]
10. ! [X0] : (humble(X0) <=> (~quiet(X0) & ~humble(X0))) [input p9]
15. ? [X0] : ~funny(X0) <=> ? [X0] : (~quiet(X0) & ~calm(X0)) [input p14]
25. ~funny(fred) [input hypothesis]
26. ? [X0] : ~funny(X0) <=> ? [X1] : (~quiet(X1) & ~calm(X1)) [rectify 15]
39. ! [X0] : ((~happy(X0) & happy(X0)) | ~humble(X0)) [ennf transformation 7]
52. ! [X0] : ((humble(X0) | (quiet(X0) | humble(X0))) & ((~quiet(X0) & ~humble(X0)) | ~humble(X0))) [nnf transformation 10]
53. ! [X0] : ((humble(X0) | quiet(X0) | humble(X0)) & ((~quiet(X0) & ~humble(X0)) | ~humble(X0))) [flattening 52]
59. (? [X0] : ~funny(X0) | ! [X1] : (quiet(X1) | calm(X1))) & (? [X1] : (~quiet(X1) & ~calm(X1)) | ! [X0] : funny(X0)) [nnf transformation 26]
60. (? [X0] : ~funny(X0) | ! [X1] : (quiet(X1) | calm(X1))) & (? [X2] : (~quiet(X2) & ~calm(X2)) | ! [X3] : funny(X3)) [rectify 59]
61. ? [X0] : ~funny(X0) => ~funny(sK1) [choice axiom]
62. ? [X2] : (~quiet(X2) & ~calm(X2)) => (~quiet(sK2) & ~calm(sK2)) [choice axiom]
63. (~funny(sK1) | ! [X1] : (quiet(X1) | calm(X1))) & ((~quiet(sK2) & ~calm(sK2)) | ! [X3] : funny(X3)) [skolemisation 60,62,61]
83. happy(X0) | ~humble(X0) [cnf transformation 39]
84. ~happy(X0) | ~humble(X0) [cnf transformation 39]
90. humble(X0) | quiet(X0) | humble(X0) [cnf transformation 53]
103. ~quiet(sK2) | funny(X3) [cnf transformation 63]
117. ~funny(fred) [cnf transformation 25]
119. humble(X0) | quiet(X0) [duplicate literal removal 90]
151. ~humble(X0) [subsumption resolution 83,84]
165. quiet(X0) [subsumption resolution 119,151]
199. funny(X3) [subsumption resolution 103,165]
231. $false [subsumption resolution 117,199]
% SZS output end Proof for 8600629460891023282536861
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or patient is both not humble and old and vice versa.
If fred is either not patient or old then someone is not strong.
If fred is funny or not patient then someone is not curious or patient.
Everyone who is either calm or patient is not quiet or not strong and vice versa.
Everyone who is both quiet and not patient is both not curious and calm and vice versa.
If someone is both not calm and not kind then someone is either funny or not patient and vice versa.
If lucy is happy then someone is not generous or rich.
Everyone who is both quiet and curious is generous or humble and vice versa.
If someone is not rich then someone is both not wise and wise and vice versa.
Everyone who is either strong or not patient is not generous or wise.
Everyone who is both patient and wise is either not happy or generous and vice versa.
If someone is either quiet or tall then someone is either wise or strong.
Everyone who is either not old or not wise is generous or brave and vice versa.
Everyone who is either brave or not old is funny and vice versa.
Everyone who is funny is either not humble or happy and vice versa.
If someone is rich or generous then john is not old or not quiet.
Someone is old.
Lucy is either tall or not patient.
Fred is both generous and wise.
Lucy is not patient.
Susan is curious or creative.
Someone is either not strong or curious.
Fred is either generous or not quiet.
Someone is curious or funny. | Lucy is old. | contradiction | (![X]:((tall(X)<~>patient(X))<=>(~humble(X)&old(X))))&
(((~patient(fred)<~>old(fred)))=>(?[X]:(~strong(X))))&
(((funny(fred)|~patient(fred)))=>(?[X]:((~curious(X)|patient(X)))))&
(![X]:((calm(X)<~>patient(X))<=>(~quiet(X)|~strong(X))))&
(![X]:((quiet(X)&~patient(X))<=>(~curious(X)&calm(X))))&
((?[X]:((~calm(X)&~kind(X))))<=>(?[X]:((funny(X)<~>~patient(X)))))&
((happy(lucy))=>(?[X]:((~generous(X)|rich(X)))))&
(![X]:((quiet(X)&curious(X))<=>(generous(X)|humble(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~wise(X)&wise(X)))))&
(![X]:((strong(X)<~>~patient(X))=>(~generous(X)|wise(X))))&
(![X]:((patient(X)&wise(X))<=>(~happy(X)<~>generous(X))))&
((?[X]:((quiet(X)<~>tall(X))))=>(?[X]:((wise(X)<~>strong(X)))))&
(![X]:((~old(X)<~>~wise(X))<=>(generous(X)|brave(X))))&
(![X]:((brave(X)<~>~old(X))<=>funny(X)))&
(![X]:(funny(X)<=>(~humble(X)<~>happy(X))))&
((?[X]:((rich(X)|generous(X))))=>((~old(john)|~quiet(john))))&
(?[X]:(old(X)))&
((tall(lucy)<~>~patient(lucy)))&
((generous(fred)&wise(fred)))&
(~patient(lucy))&
((curious(susan)|creative(susan)))&
(?[X]:((~strong(X)<~>curious(X))))&
((generous(fred)<~>~quiet(fred)))&
(?[X]:((curious(X)|funny(X)))) | old(lucy) | [
"p0",
"p4",
"p7",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5134669034155106016349054
% SZS output start Proof for 5134669034155106016349054
1. ! [X0] : ((tall(X0) <~> patient(X0)) <=> (old(X0) & ~humble(X0))) [input p0]
5. ! [X0] : ((~patient(X0) & quiet(X0)) <=> (calm(X0) & ~curious(X0))) [input p4]
8. ! [X0] : ((curious(X0) & quiet(X0)) <=> (humble(X0) | generous(X0))) [input p7]
18. tall(lucy) <~> ~patient(lucy) [input p17]
20. ~patient(lucy) [input p19]
25. old(lucy) [input hypothesis]
38. ! [X0] : ((((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) | (~old(X0) | humble(X0))) & ((old(X0) & ~humble(X0)) | ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0))))) [nnf transformation 1]
39. ! [X0] : ((((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) | ~old(X0) | humble(X0)) & ((old(X0) & ~humble(X0)) | ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0))))) [flattening 38]
47. ! [X0] : (((~patient(X0) & quiet(X0)) | (~calm(X0) | curious(X0))) & ((calm(X0) & ~curious(X0)) | (patient(X0) | ~quiet(X0)))) [nnf transformation 5]
48. ! [X0] : (((~patient(X0) & quiet(X0)) | ~calm(X0) | curious(X0)) & ((calm(X0) & ~curious(X0)) | patient(X0) | ~quiet(X0))) [flattening 47]
56. ! [X0] : (((curious(X0) & quiet(X0)) | (~humble(X0) & ~generous(X0))) & ((humble(X0) | generous(X0)) | (~curious(X0) | ~quiet(X0)))) [nnf transformation 8]
57. ! [X0] : (((curious(X0) & quiet(X0)) | (~humble(X0) & ~generous(X0))) & (humble(X0) | generous(X0) | ~curious(X0) | ~quiet(X0))) [flattening 56]
76. (patient(lucy) | ~tall(lucy)) & (~patient(lucy) | tall(lucy)) [nnf transformation 18]
87. ~old(X0) | tall(X0) | patient(X0) | humble(X0) [cnf transformation 39]
99. ~quiet(X0) | patient(X0) | ~curious(X0) [cnf transformation 48]
112. ~humble(X0) | quiet(X0) [cnf transformation 57]
114. ~humble(X0) | curious(X0) [cnf transformation 57]
148. patient(lucy) | ~tall(lucy) [cnf transformation 76]
151. ~patient(lucy) [cnf transformation 20]
157. old(lucy) [cnf transformation 25]
275. 27 <=> tall(lucy) [avatar definition]
277. ~tall(lucy) <- (~27) [avatar component clause 275]
279. 28 <=> patient(lucy) [avatar definition]
280. ~patient(lucy) <- (~28) [avatar component clause 279]
282. ~27 | 28 [avatar split clause 148,279,275]
284. ~28 [avatar split clause 151,279]
479. 51 <=> humble(lucy) [avatar definition]
481. humble(lucy) <- (51) [avatar component clause 479]
508. tall(lucy) | patient(lucy) | humble(lucy) [resolution 87,157]
523. patient(lucy) | humble(lucy) <- (~27) [subsumption resolution 508,277]
524. humble(lucy) <- (~27, ~28) [subsumption resolution 523,280]
533. 51 | 27 | 28 [avatar split clause 524,279,275,479]
539. curious(lucy) <- (51) [resolution 481,114]
540. quiet(lucy) <- (51) [resolution 481,112]
747. patient(lucy) | ~curious(lucy) <- (51) [resolution 540,99]
758. ~curious(lucy) <- (~28, 51) [subsumption resolution 747,280]
759. $false <- (~28, 51) [subsumption resolution 758,539]
760. 28 | ~51 [avatar contradiction clause 759]
761. $false [avatar sat refutation 282,284,533,760]
% SZS output end Proof for 5134669034155106016349054
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or not tall is either brave or not humble.
Everyone who is not quiet is either not tall or brave and vice versa.
Everyone who is either strong or not calm is quiet or not happy.
Everyone who is happy is both not wise and funny and vice versa.
If someone is either generous or not strong then someone is not curious or not wise and vice versa.
If lucy is not brave or old then john is quiet or not strong and vice versa.
If susan is both strong and not quiet then someone is humble.
If someone is either not funny or not happy then lucy is either patient or not funny.
If someone is humble or brave then john is patient or quiet.
Everyone who is not brave is curious or funny.
If someone is not quiet then someone is calm.
Everyone who is not patient is brave.
Everyone who is not kind or creative is not happy.
Everyone who is both not humble and not patient is either not humble or not quiet and vice versa.
If someone is either kind or happy then alice is calm.
Everyone who is both strong and funny is either not humble or funny and vice versa.
Someone is quiet or creative.
Someone is either not happy or not humble.
Someone is patient or old.
Mary is either not funny or not tall.
Fred is either happy or not brave.
Someone is either generous or old.
Someone is both not strong and patient.
Someone is both not generous and patient. | Mary is not funny. | contradiction | (![X]:((~funny(X)|~tall(X))=>(brave(X)<~>~humble(X))))&
(![X]:(~quiet(X)<=>(~tall(X)<~>brave(X))))&
(![X]:((strong(X)<~>~calm(X))=>(quiet(X)|~happy(X))))&
(![X]:(happy(X)<=>(~wise(X)&funny(X))))&
((?[X]:((generous(X)<~>~strong(X))))<=>(?[X]:((~curious(X)|~wise(X)))))&
(((~brave(lucy)|old(lucy)))<=>((quiet(john)|~strong(john))))&
(((strong(susan)&~quiet(susan)))=>(?[X]:(humble(X))))&
((?[X]:((~funny(X)<~>~happy(X))))=>((patient(lucy)<~>~funny(lucy))))&
((?[X]:((humble(X)|brave(X))))=>((patient(john)|quiet(john))))&
(![X]:(~brave(X)=>(curious(X)|funny(X))))&
((?[X]:(~quiet(X)))=>(?[X]:(calm(X))))&
(![X]:(~patient(X)=>brave(X)))&
(![X]:((~kind(X)|creative(X))=>~happy(X)))&
(![X]:((~humble(X)&~patient(X))<=>(~humble(X)<~>~quiet(X))))&
((?[X]:((kind(X)<~>happy(X))))=>(calm(alice)))&
(![X]:((strong(X)&funny(X))<=>(~humble(X)<~>funny(X))))&
(?[X]:((quiet(X)|creative(X))))&
(?[X]:((~happy(X)<~>~humble(X))))&
(?[X]:((patient(X)|old(X))))&
((~funny(mary)<~>~tall(mary)))&
((happy(fred)<~>~brave(fred)))&
(?[X]:((generous(X)<~>old(X))))&
(?[X]:((~strong(X)&patient(X))))&
(?[X]:((~generous(X)&patient(X)))) | ~funny(mary) | [
"p0",
"p1",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 262006125458209244981711
% SZS output start Proof for 262006125458209244981711
1. ! [X0] : ((~tall(X0) | ~funny(X0)) => (brave(X0) <~> ~humble(X0))) [input p0]
2. ! [X0] : (~quiet(X0) <=> (~tall(X0) <~> brave(X0))) [input p1]
14. ! [X0] : ((~patient(X0) & ~humble(X0)) <=> (~humble(X0) <~> ~quiet(X0))) [input p13]
16. ! [X0] : ((funny(X0) & strong(X0)) <=> (~humble(X0) <~> funny(X0))) [input p15]
20. ~funny(mary) <~> ~tall(mary) [input p19]
25. ~funny(mary) [input hypothesis]
28. ! [X0] : ((brave(X0) <~> ~humble(X0)) | (tall(X0) & funny(X0))) [ennf transformation 1]
42. ! [X0] : (((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) | (tall(X0) & funny(X0))) [nnf transformation 28]
43. ! [X0] : ((~quiet(X0) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0)))) & (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | quiet(X0))) [nnf transformation 2]
60. ! [X0] : (((~patient(X0) & ~humble(X0)) | ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0)))) & (((quiet(X0) | humble(X0)) & (~quiet(X0) | ~humble(X0))) | (patient(X0) | humble(X0)))) [nnf transformation 14]
61. ! [X0] : (((~patient(X0) & ~humble(X0)) | ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0)))) & (((quiet(X0) | humble(X0)) & (~quiet(X0) | ~humble(X0))) | patient(X0) | humble(X0))) [flattening 60]
63. ! [X0] : (((funny(X0) & strong(X0)) | ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0)))) & (((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | (~funny(X0) | ~strong(X0)))) [nnf transformation 16]
64. ! [X0] : (((funny(X0) & strong(X0)) | ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0)))) & (((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | ~funny(X0) | ~strong(X0))) [flattening 63]
72. (tall(mary) | funny(mary)) & (~tall(mary) | ~funny(mary)) [nnf transformation 20]
81. ~humble(X0) | brave(X0) | funny(X0) [cnf transformation 42]
88. ~quiet(X0) | ~tall(X0) | ~brave(X0) [cnf transformation 43]
119. ~humble(X0) | ~humble(X0) | quiet(X0) [cnf transformation 61]
128. funny(X0) | funny(X0) | humble(X0) [cnf transformation 64]
135. tall(mary) | funny(mary) [cnf transformation 72]
144. ~funny(mary) [cnf transformation 25]
146. humble(X0) | funny(X0) [duplicate literal removal 128]
148. ~humble(X0) | quiet(X0) [duplicate literal removal 119]
288. 32 <=> funny(mary) [avatar definition]
289. ~funny(mary) <- (~32) [avatar component clause 288]
292. 33 <=> tall(mary) [avatar definition]
294. tall(mary) <- (33) [avatar component clause 292]
295. 32 | 33 [avatar split clause 135,292,288]
317. ~32 [avatar split clause 144,288]
325. quiet(X0) | funny(X0) [resolution 148,146]
328. brave(X0) | funny(X0) | funny(X0) [resolution 81,146]
329. brave(X0) | funny(X0) [duplicate literal removal 328]
380. 42 <=> quiet(mary) [avatar definition]
381. ~quiet(mary) <- (~42) [avatar component clause 380]
382. quiet(mary) <- (42) [avatar component clause 380]
384. 43 <=> brave(mary) [avatar definition]
385. ~brave(mary) <- (~43) [avatar component clause 384]
401. ~tall(mary) | ~brave(mary) <- (42) [resolution 382,88]
403. ~brave(mary) <- (33, 42) [subsumption resolution 401,294]
404. ~43 | ~33 | ~42 [avatar split clause 403,380,292,384]
442. funny(mary) <- (~43) [resolution 385,329]
443. $false <- (~32, ~43) [subsumption resolution 442,289]
444. 32 | 43 [avatar contradiction clause 443]
571. funny(mary) <- (~42) [resolution 325,381]
579. $false <- (~32, ~42) [subsumption resolution 571,289]
580. 32 | 42 [avatar contradiction clause 579]
581. $false [avatar sat refutation 295,317,404,444,580]
% SZS output end Proof for 262006125458209244981711
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise is both not creative and generous.
Everyone who is not quiet or not wise is either not curious or curious and vice versa.
If someone is both generous and not strong then fred is quiet.
Everyone who is not old or not patient is both not old and not calm and vice versa.
Everyone who is humble or not brave is both not patient and not generous.
If someone is not patient then susan is either not funny or funny.
Everyone who is either not generous or old is either not old or tall.
If mary is rich then someone is rich and vice versa.
If alice is creative then someone is either not funny or not happy.
Everyone who is not rich or not calm is either not creative or wise and vice versa.
If someone is happy then someone is not creative and vice versa.
If someone is either not funny or creative then fred is not quiet or not patient and vice versa.
If someone is old then someone is both not calm and not quiet.
If alice is wise then john is not patient.
Everyone who is not calm or not rich is happy and vice versa.
Everyone who is quiet is not funny.
Alice is tall or not creative.
Alice is not creative or not strong.
Someone is both not strong and tall.
Mary is either not patient or tall.
Paul is not creative or not wise.
John is not wise.
Someone is kind or not generous.
Someone is curious or not wise. | Alice is not creative. | neutral | (![X]:(wise(X)=>(~creative(X)&generous(X))))&
(![X]:((~quiet(X)|~wise(X))<=>(~curious(X)<~>curious(X))))&
((?[X]:((generous(X)&~strong(X))))=>(quiet(fred)))&
(![X]:((~old(X)|~patient(X))<=>(~old(X)&~calm(X))))&
(![X]:((humble(X)|~brave(X))=>(~patient(X)&~generous(X))))&
((?[X]:(~patient(X)))=>((~funny(susan)<~>funny(susan))))&
(![X]:((~generous(X)<~>old(X))=>(~old(X)<~>tall(X))))&
((rich(mary))<=>(?[X]:(rich(X))))&
((creative(alice))=>(?[X]:((~funny(X)<~>~happy(X)))))&
(![X]:((~rich(X)|~calm(X))<=>(~creative(X)<~>wise(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~creative(X))))&
((?[X]:((~funny(X)<~>creative(X))))<=>((~quiet(fred)|~patient(fred))))&
((?[X]:(old(X)))=>(?[X]:((~calm(X)&~quiet(X)))))&
((wise(alice))=>(~patient(john)))&
(![X]:((~calm(X)|~rich(X))<=>happy(X)))&
(![X]:(quiet(X)=>~funny(X)))&
((tall(alice)|~creative(alice)))&
((~creative(alice)|~strong(alice)))&
(?[X]:((~strong(X)&tall(X))))&
((~patient(mary)<~>tall(mary)))&
((~creative(paul)|~wise(paul)))&
(~wise(john))&
(?[X]:((kind(X)|~generous(X))))&
(?[X]:((curious(X)|~wise(X)))) | ~creative(alice) | [] | null | 0 |
If mary is both not kind and not wise then someone is both not strong and not quiet and vice versa.
Everyone who is kind is not creative.
If mary is not happy then someone is not curious.
Everyone who is brave or not generous is not old and vice versa.
If someone is rich or not patient then someone is not funny or not wise.
Everyone who is not curious or patient is both not generous and kind.
If someone is either patient or generous then someone is both funny and kind and vice versa.
Everyone who is humble or not funny is both old and wise.
If alice is not curious or tall then someone is both wise and not humble and vice versa.
If someone is not strong or happy then someone is either calm or not funny.
If someone is generous then someone is old.
If someone is either calm or not wise then someone is both old and not happy.
Everyone who is not generous is humble.
If paul is curious then fred is kind or generous.
Everyone who is either not quiet or happy is not calm or funny and vice versa.
If john is not wise or not tall then someone is generous.
Paul is not patient or strong.
John is wise or not funny.
Someone is rich or calm.
Susan is either rich or happy.
Fred is not curious or brave.
Mary is either not quiet or not humble.
Someone is either curious or not curious. | John is curious. | entailment | (((~kind(mary)&~wise(mary)))<=>(?[X]:((~strong(X)&~quiet(X)))))&
(![X]:(kind(X)=>~creative(X)))&
((~happy(mary))=>(?[X]:(~curious(X))))&
(![X]:((brave(X)|~generous(X))<=>~old(X)))&
((?[X]:((rich(X)|~patient(X))))=>(?[X]:((~funny(X)|~wise(X)))))&
(![X]:((~curious(X)|patient(X))=>(~generous(X)&kind(X))))&
((?[X]:((patient(X)<~>generous(X))))<=>(?[X]:((funny(X)&kind(X)))))&
(![X]:((humble(X)|~funny(X))=>(old(X)&wise(X))))&
(((~curious(alice)|tall(alice)))<=>(?[X]:((wise(X)&~humble(X)))))&
((?[X]:((~strong(X)|happy(X))))=>(?[X]:((calm(X)<~>~funny(X)))))&
((?[X]:(generous(X)))=>(?[X]:(old(X))))&
((?[X]:((calm(X)<~>~wise(X))))=>(?[X]:((old(X)&~happy(X)))))&
(![X]:(~generous(X)=>humble(X)))&
((curious(paul))=>((kind(fred)|generous(fred))))&
(![X]:((~quiet(X)<~>happy(X))<=>(~calm(X)|funny(X))))&
(((~wise(john)|~tall(john)))=>(?[X]:(generous(X))))&
((~patient(paul)|strong(paul)))&
((wise(john)|~funny(john)))&
(?[X]:((rich(X)|calm(X))))&
((rich(susan)<~>happy(susan)))&
((~curious(fred)|brave(fred)))&
((~quiet(mary)<~>~humble(mary)))&
(?[X]:((curious(X)<~>~curious(X)))) | curious(john) | [
"p3",
"p5",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 420230426886097702910878
% SZS output start Proof for 420230426886097702910878
4. ! [X0] : ((~generous(X0) | brave(X0)) <=> ~old(X0)) [input p3]
6. ! [X0] : ((patient(X0) | ~curious(X0)) => (kind(X0) & ~generous(X0))) [input p5]
8. ! [X0] : ((~funny(X0) | humble(X0)) => (wise(X0) & old(X0))) [input p7]
13. ! [X0] : (~generous(X0) => humble(X0)) [input p12]
24. ~curious(john) [input hypothesis]
30. ! [X0] : ((~generous(X0) | brave(X0)) => ~old(X0)) [unused predicate definition removal 4]
33. ! [X0] : (~old(X0) | (generous(X0) & ~brave(X0))) [ennf transformation 30]
35. ! [X0] : ((kind(X0) & ~generous(X0)) | (~patient(X0) & curious(X0))) [ennf transformation 6]
36. ! [X0] : ((wise(X0) & old(X0)) | (funny(X0) & ~humble(X0))) [ennf transformation 8]
40. ! [X0] : (humble(X0) | generous(X0)) [ennf transformation 13]
92. ~old(X0) | generous(X0) [cnf transformation 33]
95. ~generous(X0) | curious(X0) [cnf transformation 35]
105. ~humble(X0) | old(X0) [cnf transformation 36]
123. humble(X0) | generous(X0) [cnf transformation 40]
143. ~curious(john) [cnf transformation 24]
385. generous(X1) | old(X1) [resolution 123,105]
390. generous(X1) [subsumption resolution 385,92]
411. curious(X0) [resolution 390,95]
489. $false [resolution 411,143]
% SZS output end Proof for 420230426886097702910878
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or old is both not humble and not wise. Everyone who is either not patient or not happy is either calm or not rich. If someone is not strong or not rich then john is not curious or not creative. If paul is both wise and happy then someone is either not tall or generous and vice versa. If someone is both strong and not rich then alice is both not strong and not calm and vice versa. Everyone who is either patient or not patient is both quiet and strong. If john is either not creative or not tall then fred is either not funny or not happy and vice versa. If mary is both not quiet and not creative then susan is funny or not curious. Everyone who is both not patient and not funny is not funny or generous and vice versa. If someone is both not funny and not generous then mary is both calm and humble. If paul is tall then someone is not rich. If someone is not humble or not wise then fred is both creative and not curious and vice versa. Everyone who is not generous or kind is both not wise and not calm and vice versa. Everyone who is either not wise or curious is curious or rich and vice versa. If someone is either wise or humble then someone is either not old or not happy and vice versa. Everyone who is either not strong or not happy is not tall and vice versa. Fred is calm. Someone is either old or not happy. Someone is either funny or kind. Alice is either rich or not happy. Someone is either kind or not generous. John is tall. Lucy is rich or not patient. | Paul is not creative. | neutral | (![X]:((rich(X)|old(X))=>(~humble(X)&~wise(X))))&
(![X]:((~patient(X)<~>~happy(X))=>(calm(X)<~>~rich(X))))&
((?[X]:((~strong(X)|~rich(X))))=>((~curious(john)|~creative(john))))&
(((wise(paul)&happy(paul)))<=>(?[X]:((~tall(X)<~>generous(X)))))&
((?[X]:((strong(X)&~rich(X))))<=>((~strong(alice)&~calm(alice))))&
(![X]:((patient(X)<~>~patient(X))=>(quiet(X)&strong(X))))&
(((~creative(john)<~>~tall(john)))<=>((~funny(fred)<~>~happy(fred))))&
(((~quiet(mary)&~creative(mary)))=>((funny(susan)|~curious(susan))))&
(![X]:((~patient(X)&~funny(X))<=>(~funny(X)|generous(X))))&
((?[X]:((~funny(X)&~generous(X))))=>((calm(mary)&humble(mary))))&
((tall(paul))=>(?[X]:(~rich(X))))&
((?[X]:((~humble(X)|~wise(X))))<=>((creative(fred)&~curious(fred))))&
(![X]:((~generous(X)|kind(X))<=>(~wise(X)&~calm(X))))&
(![X]:((~wise(X)<~>curious(X))<=>(curious(X)|rich(X))))&
((?[X]:((wise(X)<~>humble(X))))<=>(?[X]:((~old(X)<~>~happy(X)))))&
(![X]:((~strong(X)<~>~happy(X))<=>~tall(X)))&
(calm(fred))&
(?[X]:((old(X)<~>~happy(X))))&
(?[X]:((funny(X)<~>kind(X))))&
((rich(alice)<~>~happy(alice)))&
(?[X]:((kind(X)<~>~generous(X))))&
(tall(john))&
((rich(lucy)|~patient(lucy))) | ~creative(paul) | [] | null | 0 |
Everyone who is not kind or not curious is kind.
Everyone who is not funny is either not generous or not calm.
If john is both strong and calm then lucy is both brave and wise and vice versa.
If someone is not wise then someone is either curious or wise.
If someone is rich then someone is both not generous and not wise and vice versa.
Everyone who is strong or curious is both strong and not tall and vice versa.
If someone is both patient and funny then lucy is strong and vice versa.
If paul is generous or rich then someone is not curious or not wise.
If lucy is strong or not tall then someone is strong.
If paul is either generous or not happy then someone is not old or not quiet and vice versa.
Everyone who is not wise or kind is either not rich or funny and vice versa.
Everyone who is both not generous and not rich is either not strong or not curious.
Everyone who is both not creative and kind is not generous or not funny and vice versa.
If paul is calm or not rich then someone is not calm or not tall and vice versa.
If susan is either strong or wise then alice is curious and vice versa.
Everyone who is not wise or old is either not funny or creative and vice versa.
Someone is wise or humble.
John is rich.
Susan is patient or not kind.
Someone is strong.
Someone is generous.
Someone is both not generous and brave.
John is not rich or happy.
Paul is curious. | Susan is not patient. | contradiction | (![X]:((~kind(X)|~curious(X))=>kind(X)))&
(![X]:(~funny(X)=>(~generous(X)<~>~calm(X))))&
(((strong(john)&calm(john)))<=>((brave(lucy)&wise(lucy))))&
((?[X]:(~wise(X)))=>(?[X]:((curious(X)<~>wise(X)))))&
((?[X]:(rich(X)))<=>(?[X]:((~generous(X)&~wise(X)))))&
(![X]:((strong(X)|curious(X))<=>(strong(X)&~tall(X))))&
((?[X]:((patient(X)&funny(X))))<=>(strong(lucy)))&
(((generous(paul)|rich(paul)))=>(?[X]:((~curious(X)|~wise(X)))))&
(((strong(lucy)|~tall(lucy)))=>(?[X]:(strong(X))))&
(((generous(paul)<~>~happy(paul)))<=>(?[X]:((~old(X)|~quiet(X)))))&
(![X]:((~wise(X)|kind(X))<=>(~rich(X)<~>funny(X))))&
(![X]:((~generous(X)&~rich(X))=>(~strong(X)<~>~curious(X))))&
(![X]:((~creative(X)&kind(X))<=>(~generous(X)|~funny(X))))&
(((calm(paul)|~rich(paul)))<=>(?[X]:((~calm(X)|~tall(X)))))&
(((strong(susan)<~>wise(susan)))<=>(curious(alice)))&
(![X]:((~wise(X)|old(X))<=>(~funny(X)<~>creative(X))))&
(?[X]:((wise(X)|humble(X))))&
(rich(john))&
((patient(susan)|~kind(susan)))&
(?[X]:(strong(X)))&
(?[X]:(generous(X)))&
(?[X]:((~generous(X)&brave(X))))&
((~rich(john)|happy(john)))&
(curious(paul)) | ~patient(susan) | [
"p0",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3157759302073936718660729
% SZS output start Proof for 3157759302073936718660729
1. ! [X0] : ((~curious(X0) | ~kind(X0)) => kind(X0)) [input p0]
19. ~kind(susan) | patient(susan) [input p18]
25. ~patient(susan) [input hypothesis]
29. ! [X0] : (kind(X0) | (curious(X0) & kind(X0))) [ennf transformation 1]
81. kind(X0) | kind(X0) [cnf transformation 29]
140. ~kind(susan) | patient(susan) [cnf transformation 19]
147. ~patient(susan) [cnf transformation 25]
148. kind(X0) [duplicate literal removal 81]
318. patient(susan) [subsumption resolution 140,148]
320. $false [subsumption resolution 147,318]
% SZS output end Proof for 3157759302073936718660729
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not brave or happy then john is curious or tall and vice versa.
Everyone who is not kind is both humble and not calm.
If paul is strong or wise then someone is wise or quiet.
Everyone who is both not old and not kind is both not calm and tall.
If alice is brave then someone is both not humble and not creative.
Everyone who is humble is both strong and not humble.
If susan is happy or not quiet then paul is not old or happy and vice versa.
If lucy is both brave and funny then lucy is creative or strong and vice versa.
Everyone who is not quiet is not rich or kind and vice versa.
If susan is both not old and quiet then susan is brave.
If someone is wise then someone is either happy or humble.
If alice is not happy then someone is both happy and not wise.
Everyone who is not generous is either happy or not calm.
If someone is humble then john is happy or not kind.
If someone is not tall or not strong then mary is creative or not tall and vice versa.
If susan is either quiet or humble then mary is both quiet and not rich.
Paul is creative.
Someone is not brave or not humble.
Lucy is not happy.
Someone is not humble.
Someone is either not happy or not quiet.
Someone is either calm or not old.
Someone is not curious or curious. | Paul is not kind. | contradiction | (((~brave(mary)<~>happy(mary)))<=>((curious(john)|tall(john))))&
(![X]:(~kind(X)=>(humble(X)&~calm(X))))&
(((strong(paul)|wise(paul)))=>(?[X]:((wise(X)|quiet(X)))))&
(![X]:((~old(X)&~kind(X))=>(~calm(X)&tall(X))))&
((brave(alice))=>(?[X]:((~humble(X)&~creative(X)))))&
(![X]:(humble(X)=>(strong(X)&~humble(X))))&
(((happy(susan)|~quiet(susan)))<=>((~old(paul)|happy(paul))))&
(((brave(lucy)&funny(lucy)))<=>((creative(lucy)|strong(lucy))))&
(![X]:(~quiet(X)<=>(~rich(X)|kind(X))))&
(((~old(susan)&quiet(susan)))=>(brave(susan)))&
((?[X]:(wise(X)))=>(?[X]:((happy(X)<~>humble(X)))))&
((~happy(alice))=>(?[X]:((happy(X)&~wise(X)))))&
(![X]:(~generous(X)=>(happy(X)<~>~calm(X))))&
((?[X]:(humble(X)))=>((happy(john)|~kind(john))))&
((?[X]:((~tall(X)|~strong(X))))<=>((creative(mary)|~tall(mary))))&
(((quiet(susan)<~>humble(susan)))=>((quiet(mary)&~rich(mary))))&
(creative(paul))&
(?[X]:((~brave(X)|~humble(X))))&
(~happy(lucy))&
(?[X]:(~humble(X)))&
(?[X]:((~happy(X)<~>~quiet(X))))&
(?[X]:((calm(X)<~>~old(X))))&
(?[X]:((~curious(X)|curious(X)))) | ~kind(paul) | [
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1043495828520097858127017
% SZS output start Proof for 1043495828520097858127017
2. ! [X0] : (~kind(X0) => (~calm(X0) & humble(X0))) [input p1]
6. ! [X0] : (humble(X0) => (~humble(X0) & strong(X0))) [input p5]
24. ~kind(paul) [input hypothesis]
27. ! [X0] : ((~calm(X0) & humble(X0)) | kind(X0)) [ennf transformation 2]
32. ! [X0] : ((~humble(X0) & strong(X0)) | ~humble(X0)) [ennf transformation 6]
82. humble(X0) | kind(X0) [cnf transformation 27]
91. ~humble(X0) | ~humble(X0) [cnf transformation 32]
127. ~kind(paul) [cnf transformation 24]
128. ~humble(X0) [duplicate literal removal 91]
314. kind(X0) [resolution 82,128]
315. $false [resolution 314,127]
% SZS output end Proof for 1043495828520097858127017
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm or quiet then alice is either not generous or not rich.
If mary is either not brave or funny then someone is happy.
If john is tall then someone is not rich or wise and vice versa.
If someone is either not patient or strong then someone is kind.
Everyone who is either strong or funny is generous or calm and vice versa.
Everyone who is both not creative and not rich is both old and not creative.
Everyone who is not happy is either not quiet or not calm and vice versa.
If paul is both not patient and strong then susan is wise.
Everyone who is both not generous and old is brave or not strong and vice versa.
Everyone who is not kind or not generous is both not generous and not wise and vice versa.
Everyone who is either not curious or patient is old or not quiet.
If someone is either humble or not tall then paul is either not patient or not creative and vice versa.
If john is generous or not tall then someone is both generous and curious.
Everyone who is curious or not humble is either not happy or not curious and vice versa.
Everyone who is either not happy or not rich is both happy and quiet and vice versa.
Everyone who is not quiet or funny is not kind and vice versa.
Someone is both not happy and not funny.
John is either patient or not rich.
Mary is both quiet and calm.
Fred is both brave and not funny.
Someone is not kind or rich.
Someone is humble.
Alice is both not generous and not strong.
Someone is either patient or not curious. | Alice is happy. | entailment | ((?[X]:((~calm(X)|quiet(X))))=>((~generous(alice)<~>~rich(alice))))&
(((~brave(mary)<~>funny(mary)))=>(?[X]:(happy(X))))&
((tall(john))<=>(?[X]:((~rich(X)|wise(X)))))&
((?[X]:((~patient(X)<~>strong(X))))=>(?[X]:(kind(X))))&
(![X]:((strong(X)<~>funny(X))<=>(generous(X)|calm(X))))&
(![X]:((~creative(X)&~rich(X))=>(old(X)&~creative(X))))&
(![X]:(~happy(X)<=>(~quiet(X)<~>~calm(X))))&
(((~patient(paul)&strong(paul)))=>(wise(susan)))&
(![X]:((~generous(X)&old(X))<=>(brave(X)|~strong(X))))&
(![X]:((~kind(X)|~generous(X))<=>(~generous(X)&~wise(X))))&
(![X]:((~curious(X)<~>patient(X))=>(old(X)|~quiet(X))))&
((?[X]:((humble(X)<~>~tall(X))))<=>((~patient(paul)<~>~creative(paul))))&
(((generous(john)|~tall(john)))=>(?[X]:((generous(X)&curious(X)))))&
(![X]:((curious(X)|~humble(X))<=>(~happy(X)<~>~curious(X))))&
(![X]:((~happy(X)<~>~rich(X))<=>(happy(X)&quiet(X))))&
(![X]:((~quiet(X)|funny(X))<=>~kind(X)))&
(?[X]:((~happy(X)&~funny(X))))&
((patient(john)<~>~rich(john)))&
((quiet(mary)&calm(mary)))&
((brave(fred)&~funny(fred)))&
(?[X]:((~kind(X)|rich(X))))&
(?[X]:(humble(X)))&
((~generous(alice)&~strong(alice)))&
(?[X]:((patient(X)<~>~curious(X)))) | happy(alice) | [
"p0",
"p14",
"p18",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4483174572263447562447339
% SZS output start Proof for 4483174572263447562447339
1. ? [X0] : (quiet(X0) | ~calm(X0)) => (~generous(alice) <~> ~rich(alice)) [input p0]
15. ! [X0] : ((~happy(X0) <~> ~rich(X0)) <=> (quiet(X0) & happy(X0))) [input p14]
19. calm(mary) & quiet(mary) [input p18]
23. ~strong(alice) & ~generous(alice) [input p22]
25. ~happy(alice) [input hypothesis]
27. (~generous(alice) <~> ~rich(alice)) | ! [X0] : (~quiet(X0) & calm(X0)) [ennf transformation 1]
37. ((rich(alice) | generous(alice)) & (~rich(alice) | ~generous(alice))) | ! [X0] : (~quiet(X0) & calm(X0)) [nnf transformation 27]
65. ! [X0] : ((((rich(X0) | happy(X0)) & (~rich(X0) | ~happy(X0))) | (~quiet(X0) | ~happy(X0))) & ((quiet(X0) & happy(X0)) | ((~happy(X0) | rich(X0)) & (~rich(X0) | happy(X0))))) [nnf transformation 15]
66. ! [X0] : ((((rich(X0) | happy(X0)) & (~rich(X0) | ~happy(X0))) | ~quiet(X0) | ~happy(X0)) & ((quiet(X0) & happy(X0)) | ((~happy(X0) | rich(X0)) & (~rich(X0) | happy(X0))))) [flattening 65]
82. rich(alice) | generous(alice) | ~quiet(X0) [cnf transformation 37]
133. happy(X0) | ~rich(X0) | happy(X0) [cnf transformation 66]
146. quiet(mary) [cnf transformation 19]
152. ~generous(alice) [cnf transformation 23]
156. ~happy(alice) [cnf transformation 25]
157. ~rich(X0) | happy(X0) [duplicate literal removal 133]
162. 1 <=> ! [X0] : ~quiet(X0) [avatar definition]
163. ~quiet(X0) <- (1) [avatar component clause 162]
165. 2 <=> generous(alice) [avatar definition]
169. 3 <=> rich(alice) [avatar definition]
171. rich(alice) <- (3) [avatar component clause 169]
172. 1 | 2 | 3 [avatar split clause 82,169,165,162]
300. ~2 [avatar split clause 152,165]
315. happy(alice) <- (3) [resolution 157,171]
316. $false <- (3) [subsumption resolution 315,156]
317. ~3 [avatar contradiction clause 316]
318. $false <- (1) [resolution 163,146]
321. ~1 [avatar contradiction clause 318]
322. $false [avatar sat refutation 172,300,317,321]
% SZS output end Proof for 4483174572263447562447339
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not humble is kind.
Everyone who is quiet is both creative and tall.
Everyone who is brave or not patient is either rich or curious and vice versa.
If alice is not curious then fred is not wise or wise.
Everyone who is happy is either not quiet or calm.
If alice is not tall or not generous then someone is rich and vice versa.
Everyone who is not patient or patient is both not tall and not quiet.
Everyone who is rich is either not calm or tall.
If someone is both calm and not generous then fred is creative or happy.
Everyone who is not strong or not creative is not tall or not generous.
Everyone who is not tall is not wise or rich and vice versa.
Everyone who is kind or creative is curious.
If susan is not kind then john is both patient and not strong and vice versa.
If susan is both wise and quiet then someone is both not calm and not generous.
Everyone who is either not curious or generous is not patient.
If lucy is either not quiet or creative then susan is both not creative and wise.
Mary is not creative or kind.
Lucy is both not patient and funny.
Mary is both curious and not wise.
Someone is old or not tall.
Mary is old or patient.
Someone is both wise and not creative.
Someone is funny.
John is not calm. | John is not tall. | entailment | (![X]:((humble(X)<~>~humble(X))=>kind(X)))&
(![X]:(quiet(X)=>(creative(X)&tall(X))))&
(![X]:((brave(X)|~patient(X))<=>(rich(X)<~>curious(X))))&
((~curious(alice))=>((~wise(fred)|wise(fred))))&
(![X]:(happy(X)=>(~quiet(X)<~>calm(X))))&
(((~tall(alice)|~generous(alice)))<=>(?[X]:(rich(X))))&
(![X]:((~patient(X)|patient(X))=>(~tall(X)&~quiet(X))))&
(![X]:(rich(X)=>(~calm(X)<~>tall(X))))&
((?[X]:((calm(X)&~generous(X))))=>((creative(fred)|happy(fred))))&
(![X]:((~strong(X)|~creative(X))=>(~tall(X)|~generous(X))))&
(![X]:(~tall(X)<=>(~wise(X)|rich(X))))&
(![X]:((kind(X)|creative(X))=>curious(X)))&
((~kind(susan))<=>((patient(john)&~strong(john))))&
(((wise(susan)&quiet(susan)))=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:((~curious(X)<~>generous(X))=>~patient(X)))&
(((~quiet(lucy)<~>creative(lucy)))=>((~creative(susan)&wise(susan))))&
((~creative(mary)|kind(mary)))&
((~patient(lucy)&funny(lucy)))&
((curious(mary)&~wise(mary)))&
(?[X]:((old(X)|~tall(X))))&
((old(mary)|patient(mary)))&
(?[X]:((wise(X)&~creative(X))))&
(?[X]:(funny(X)))&
(~calm(john)) | ~tall(john) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 3041763773044296683910238
% SZS output start Proof for 3041763773044296683910238
7. ! [X0] : ((patient(X0) | ~patient(X0)) => (~quiet(X0) & ~tall(X0))) [input p6]
25. tall(john) [input hypothesis]
35. ! [X0] : ((~quiet(X0) & ~tall(X0)) | (~patient(X0) & patient(X0))) [ennf transformation 7]
82. ~tall(X0) | patient(X0) [cnf transformation 35]
83. ~tall(X0) | ~patient(X0) [cnf transformation 35]
114. tall(john) [cnf transformation 25]
137. ~tall(X0) [subsumption resolution 82,83]
180. $false [subsumption resolution 114,137]
% SZS output end Proof for 3041763773044296683910238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or not strong is either brave or generous. Everyone who is not calm or not patient is not kind or wise. Everyone who is not wise or humble is not wise or tall and vice versa. Everyone who is not kind is happy or old and vice versa. If mary is not calm or rich then someone is either not kind or not calm. If alice is either curious or not old then someone is either not rich or not strong. Everyone who is curious or wise is either calm or humble. If someone is both not quiet and not rich then alice is both patient and old and vice versa. Everyone who is not old or creative is both not calm and not tall and vice versa. Everyone who is either not rich or brave is both not brave and not happy and vice versa. If john is not creative or humble then mary is not calm. Everyone who is both rich and humble is both not kind and funny and vice versa. If someone is either strong or tall then john is tall or kind. Everyone who is both not creative and not calm is both happy and not quiet and vice versa. If someone is not old or happy then lucy is either not creative or not wise and vice versa. Everyone who is either funny or tall is strong. Alice is either not curious or brave. John is either not quiet or not creative. Alice is either creative or not wise. Someone is either not calm or not wise. Someone is both not curious and brave. Someone is either kind or not kind. Lucy is brave. | Lucy is creative. | neutral | (![X]:((~curious(X)|~strong(X))=>(brave(X)<~>generous(X))))&
(![X]:((~calm(X)|~patient(X))=>(~kind(X)|wise(X))))&
(![X]:((~wise(X)|humble(X))<=>(~wise(X)|tall(X))))&
(![X]:(~kind(X)<=>(happy(X)|old(X))))&
(((~calm(mary)|rich(mary)))=>(?[X]:((~kind(X)<~>~calm(X)))))&
(((curious(alice)<~>~old(alice)))=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((curious(X)|wise(X))=>(calm(X)<~>humble(X))))&
((?[X]:((~quiet(X)&~rich(X))))<=>((patient(alice)&old(alice))))&
(![X]:((~old(X)|creative(X))<=>(~calm(X)&~tall(X))))&
(![X]:((~rich(X)<~>brave(X))<=>(~brave(X)&~happy(X))))&
(((~creative(john)|humble(john)))=>(~calm(mary)))&
(![X]:((rich(X)&humble(X))<=>(~kind(X)&funny(X))))&
((?[X]:((strong(X)<~>tall(X))))=>((tall(john)|kind(john))))&
(![X]:((~creative(X)&~calm(X))<=>(happy(X)&~quiet(X))))&
((?[X]:((~old(X)|happy(X))))<=>((~creative(lucy)<~>~wise(lucy))))&
(![X]:((funny(X)<~>tall(X))=>strong(X)))&
((~curious(alice)<~>brave(alice)))&
((~quiet(john)<~>~creative(john)))&
((creative(alice)<~>~wise(alice)))&
(?[X]:((~calm(X)<~>~wise(X))))&
(?[X]:((~curious(X)&brave(X))))&
(?[X]:((kind(X)<~>~kind(X))))&
(brave(lucy)) | creative(lucy) | [] | null | 0 |
If someone is not curious or quiet then mary is not quiet. If someone is patient or wise then someone is funny or not happy and vice versa. If lucy is not creative or funny then someone is not wise. Everyone who is either not funny or patient is not quiet or not curious and vice versa. Everyone who is not humble is not tall or not brave and vice versa. If mary is both funny and tall then someone is not tall and vice versa. If john is either old or not quiet then someone is either not strong or humble. If someone is not quiet or not old then susan is both not strong and not calm and vice versa. Everyone who is either humble or not tall is either brave or tall. If alice is not kind then someone is quiet or not curious. Everyone who is not rich or rich is either not rich or patient. Everyone who is not wise or kind is not old or not kind. Everyone who is both quiet and funny is either kind or funny and vice versa. If susan is both brave and kind then john is either calm or not brave and vice versa. If someone is not rich then someone is both not kind and strong. If someone is either not humble or not old then lucy is rich or not happy. Someone is brave. Alice is both not old and tall. Paul is not rich. Paul is either not funny or not quiet. Someone is not patient. Someone is quiet or not rich. Someone is both strong and not funny. Someone is either not old or calm. | Mary is brave. | contradiction | ((?[X]:((~curious(X)|quiet(X))))=>(~quiet(mary)))&
((?[X]:((patient(X)|wise(X))))<=>(?[X]:((funny(X)|~happy(X)))))&
(((~creative(lucy)|funny(lucy)))=>(?[X]:(~wise(X))))&
(![X]:((~funny(X)<~>patient(X))<=>(~quiet(X)|~curious(X))))&
(![X]:(~humble(X)<=>(~tall(X)|~brave(X))))&
(((funny(mary)&tall(mary)))<=>(?[X]:(~tall(X))))&
(((old(john)<~>~quiet(john)))=>(?[X]:((~strong(X)<~>humble(X)))))&
((?[X]:((~quiet(X)|~old(X))))<=>((~strong(susan)&~calm(susan))))&
(![X]:((humble(X)<~>~tall(X))=>(brave(X)<~>tall(X))))&
((~kind(alice))=>(?[X]:((quiet(X)|~curious(X)))))&
(![X]:((~rich(X)|rich(X))=>(~rich(X)<~>patient(X))))&
(![X]:((~wise(X)|kind(X))=>(~old(X)|~kind(X))))&
(![X]:((quiet(X)&funny(X))<=>(kind(X)<~>funny(X))))&
(((brave(susan)&kind(susan)))<=>((calm(john)<~>~brave(john))))&
((?[X]:(~rich(X)))=>(?[X]:((~kind(X)&strong(X)))))&
((?[X]:((~humble(X)<~>~old(X))))=>((rich(lucy)|~happy(lucy))))&
(?[X]:(brave(X)))&
((~old(alice)&tall(alice)))&
(~rich(paul))&
((~funny(paul)<~>~quiet(paul)))&
(?[X]:(~patient(X)))&
(?[X]:((quiet(X)|~rich(X))))&
(?[X]:((strong(X)&~funny(X))))&
(?[X]:((~old(X)<~>calm(X)))) | brave(mary) | [
"p4",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 223150033988215833591254
% SZS output start Proof for 223150033988215833591254
5. ! [X0] : (~humble(X0) <=> (~brave(X0) | ~tall(X0))) [input p4]
6. (tall(mary) & funny(mary)) <=> ? [X0] : ~tall(X0) [input p5]
9. ! [X0] : ((humble(X0) <~> ~tall(X0)) => (brave(X0) <~> tall(X0))) [input p8]
25. brave(mary) [input hypothesis]
32. ! [X0] : ((brave(X0) <~> tall(X0)) | (humble(X0) <=> ~tall(X0))) [ennf transformation 9]
49. ! [X0] : ((~humble(X0) | (brave(X0) & tall(X0))) & ((~brave(X0) | ~tall(X0)) | humble(X0))) [nnf transformation 5]
50. ! [X0] : ((~humble(X0) | (brave(X0) & tall(X0))) & (~brave(X0) | ~tall(X0) | humble(X0))) [flattening 49]
51. ((tall(mary) & funny(mary)) | ! [X0] : tall(X0)) & (? [X0] : ~tall(X0) | (~tall(mary) | ~funny(mary))) [nnf transformation 6]
52. ((tall(mary) & funny(mary)) | ! [X0] : tall(X0)) & (? [X0] : ~tall(X0) | ~tall(mary) | ~funny(mary)) [flattening 51]
53. ((tall(mary) & funny(mary)) | ! [X0] : tall(X0)) & (? [X1] : ~tall(X1) | ~tall(mary) | ~funny(mary)) [rectify 52]
54. ? [X1] : ~tall(X1) => ~tall(sK3) [choice axiom]
55. ((tall(mary) & funny(mary)) | ! [X0] : tall(X0)) & (~tall(sK3) | ~tall(mary) | ~funny(mary)) [skolemisation 53,54]
64. ! [X0] : (((~tall(X0) | ~brave(X0)) & (tall(X0) | brave(X0))) | ((humble(X0) | tall(X0)) & (~tall(X0) | ~humble(X0)))) [nnf transformation 32]
101. ~brave(X0) | ~tall(X0) | humble(X0) [cnf transformation 50]
106. tall(mary) | tall(X0) [cnf transformation 55]
118. ~tall(X0) | ~brave(X0) | ~tall(X0) | ~humble(X0) [cnf transformation 64]
155. brave(mary) [cnf transformation 25]
162. ~tall(X0) | ~brave(X0) | ~humble(X0) [duplicate literal removal 118]
217. 14 <=> ! [X0] : tall(X0) [avatar definition]
218. tall(X0) <- (14) [avatar component clause 217]
220. 15 <=> tall(mary) [avatar definition]
221. ~tall(mary) <- (~15) [avatar component clause 220]
223. 14 | 15 [avatar split clause 106,220,217]
281. ~brave(X0) | ~tall(X0) [subsumption resolution 162,101]
383. ~tall(mary) [resolution 281,155]
387. ~15 [avatar split clause 383,220]
388. $false <- (14, ~15) [resolution 221,218]
389. ~14 | 15 [avatar contradiction clause 388]
390. $false [avatar sat refutation 223,387,389]
% SZS output end Proof for 223150033988215833591254
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is either creative or not wise.
If someone is not happy or wise then lucy is not strong.
Everyone who is both brave and not happy is not humble and vice versa.
Everyone who is either not generous or happy is not tall and vice versa.
If lucy is tall then someone is either not tall or kind and vice versa.
If someone is not wise or not strong then someone is not rich or not happy.
Everyone who is both humble and not kind is not calm or calm and vice versa.
Everyone who is wise is both tall and not kind.
Everyone who is either tall or not brave is not rich and vice versa.
If someone is kind or not happy then lucy is generous and vice versa.
Everyone who is not brave or old is not old.
If alice is not happy then fred is not kind or not wise and vice versa.
If alice is happy then paul is both brave and humble and vice versa.
Everyone who is not humble is not strong.
If someone is both not humble and humble then john is strong and vice versa.
Everyone who is rich is both funny and not creative.
Alice is either patient or tall.
Susan is both not brave and not old.
John is both humble and not strong.
Someone is either not kind or not curious.
Someone is both creative and patient.
Susan is either kind or wise.
Alice is either curious or not rich.
Paul is creative. | Lucy is not brave. | entailment | (![X]:(old(X)=>(creative(X)<~>~wise(X))))&
((?[X]:((~happy(X)|wise(X))))=>(~strong(lucy)))&
(![X]:((brave(X)&~happy(X))<=>~humble(X)))&
(![X]:((~generous(X)<~>happy(X))<=>~tall(X)))&
((tall(lucy))<=>(?[X]:((~tall(X)<~>kind(X)))))&
((?[X]:((~wise(X)|~strong(X))))=>(?[X]:((~rich(X)|~happy(X)))))&
(![X]:((humble(X)&~kind(X))<=>(~calm(X)|calm(X))))&
(![X]:(wise(X)=>(tall(X)&~kind(X))))&
(![X]:((tall(X)<~>~brave(X))<=>~rich(X)))&
((?[X]:((kind(X)|~happy(X))))<=>(generous(lucy)))&
(![X]:((~brave(X)|old(X))=>~old(X)))&
((~happy(alice))<=>((~kind(fred)|~wise(fred))))&
((happy(alice))<=>((brave(paul)&humble(paul))))&
(![X]:(~humble(X)=>~strong(X)))&
((?[X]:((~humble(X)&humble(X))))<=>(strong(john)))&
(![X]:(rich(X)=>(funny(X)&~creative(X))))&
((patient(alice)<~>tall(alice)))&
((~brave(susan)&~old(susan)))&
((humble(john)&~strong(john)))&
(?[X]:((~kind(X)<~>~curious(X))))&
(?[X]:((creative(X)&patient(X))))&
((kind(susan)<~>wise(susan)))&
((curious(alice)<~>~rich(alice)))&
(creative(paul)) | ~brave(lucy) | [
"p2",
"p3",
"p4",
"p6",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6763542842986215632954581
% SZS output start Proof for 6763542842986215632954581
3. ! [X0] : ((~happy(X0) & brave(X0)) <=> ~humble(X0)) [input p2]
4. ! [X0] : ((~generous(X0) <~> happy(X0)) <=> ~tall(X0)) [input p3]
5. tall(lucy) <=> ? [X0] : (~tall(X0) <~> kind(X0)) [input p4]
7. ! [X0] : ((~kind(X0) & humble(X0)) <=> (calm(X0) | ~calm(X0))) [input p6]
10. ? [X0] : (~happy(X0) | kind(X0)) <=> generous(lucy) [input p9]
12. ~happy(alice) <=> (~wise(fred) | ~kind(fred)) [input p11]
25. brave(lucy) [input hypothesis]
36. ! [X0] : (((~happy(X0) & brave(X0)) | humble(X0)) & (~humble(X0) | (happy(X0) | ~brave(X0)))) [nnf transformation 3]
37. ! [X0] : (((~happy(X0) & brave(X0)) | humble(X0)) & (~humble(X0) | happy(X0) | ~brave(X0))) [flattening 36]
38. ! [X0] : ((((~happy(X0) | generous(X0)) & (happy(X0) | ~generous(X0))) | tall(X0)) & (~tall(X0) | ((~generous(X0) | ~happy(X0)) & (happy(X0) | generous(X0))))) [nnf transformation 4]
39. (tall(lucy) | ! [X0] : ((~tall(X0) | ~kind(X0)) & (kind(X0) | tall(X0)))) & (? [X0] : ((~kind(X0) | tall(X0)) & (kind(X0) | ~tall(X0))) | ~tall(lucy)) [nnf transformation 5]
40. (tall(lucy) | ! [X0] : ((~tall(X0) | ~kind(X0)) & (kind(X0) | tall(X0)))) & (? [X1] : ((~kind(X1) | tall(X1)) & (kind(X1) | ~tall(X1))) | ~tall(lucy)) [rectify 39]
41. ? [X1] : ((~kind(X1) | tall(X1)) & (kind(X1) | ~tall(X1))) => ((~kind(sK0) | tall(sK0)) & (kind(sK0) | ~tall(sK0))) [choice axiom]
42. (tall(lucy) | ! [X0] : ((~tall(X0) | ~kind(X0)) & (kind(X0) | tall(X0)))) & (((~kind(sK0) | tall(sK0)) & (kind(sK0) | ~tall(sK0))) | ~tall(lucy)) [skolemisation 40,41]
46. ! [X0] : (((~kind(X0) & humble(X0)) | (~calm(X0) & calm(X0))) & ((calm(X0) | ~calm(X0)) | (kind(X0) | ~humble(X0)))) [nnf transformation 7]
47. ! [X0] : (((~kind(X0) & humble(X0)) | (~calm(X0) & calm(X0))) & (calm(X0) | ~calm(X0) | kind(X0) | ~humble(X0))) [flattening 46]
49. (? [X0] : (~happy(X0) | kind(X0)) | ~generous(lucy)) & (generous(lucy) | ! [X0] : (happy(X0) & ~kind(X0))) [nnf transformation 10]
50. (? [X0] : (~happy(X0) | kind(X0)) | ~generous(lucy)) & (generous(lucy) | ! [X1] : (happy(X1) & ~kind(X1))) [rectify 49]
51. ? [X0] : (~happy(X0) | kind(X0)) => (~happy(sK2) | kind(sK2)) [choice axiom]
52. ((~happy(sK2) | kind(sK2)) | ~generous(lucy)) & (generous(lucy) | ! [X1] : (happy(X1) & ~kind(X1))) [skolemisation 50,51]
53. (~happy(alice) | (wise(fred) & kind(fred))) & ((~wise(fred) | ~kind(fred)) | happy(alice)) [nnf transformation 12]
54. (~happy(alice) | (wise(fred) & kind(fred))) & (~wise(fred) | ~kind(fred) | happy(alice)) [flattening 53]
71. ~humble(X0) | happy(X0) | ~brave(X0) [cnf transformation 37]
75. ~tall(X0) | ~generous(X0) | ~happy(X0) [cnf transformation 38]
80. tall(lucy) | kind(X0) | tall(X0) [cnf transformation 42]
85. humble(X0) | calm(X0) [cnf transformation 47]
86. ~calm(X0) | humble(X0) [cnf transformation 47]
87. ~kind(X0) | calm(X0) [cnf transformation 47]
88. ~calm(X0) | ~kind(X0) [cnf transformation 47]
96. generous(lucy) | happy(X1) [cnf transformation 52]
99. ~happy(alice) | kind(fred) [cnf transformation 54]
123. brave(lucy) [cnf transformation 25]
133. 3 <=> ! [X0] : happy(X0) [avatar definition]
134. happy(X0) <- (3) [avatar component clause 133]
140. 5 <=> tall(lucy) [avatar definition]
141. ~tall(lucy) <- (~5) [avatar component clause 140]
142. tall(lucy) <- (5) [avatar component clause 140]
145. 6 <=> ! [X0] : (kind(X0) | tall(X0)) [avatar definition]
146. kind(X0) | tall(X0) <- (6) [avatar component clause 145]
147. 6 | 5 [avatar split clause 80,140,145]
174. ~kind(X0) [subsumption resolution 87,88]
175. humble(X0) [subsumption resolution 85,86]
178. 13 <=> generous(lucy) [avatar definition]
186. 3 | 13 [avatar split clause 96,178,133]
192. 16 <=> happy(alice) [avatar definition]
194. ~happy(alice) <- (~16) [avatar component clause 192]
196. ~happy(alice) [subsumption resolution 99,174]
197. ~16 [avatar split clause 196,192]
232. ~brave(X1) | happy(X1) [resolution 71,175]
244. ~generous(lucy) | ~happy(lucy) <- (5) [resolution 75,142]
251. happy(lucy) [resolution 232,123]
254. ~generous(lucy) <- (5) [subsumption resolution 244,251]
255. ~13 | ~5 [avatar split clause 254,140,178]
258. $false <- (3, ~16) [resolution 134,194]
261. ~3 | 16 [avatar contradiction clause 258]
262. tall(X0) <- (6) [subsumption resolution 146,174]
263. $false <- (~5, 6) [subsumption resolution 141,262]
264. 5 | ~6 [avatar contradiction clause 263]
265. $false [avatar sat refutation 147,186,197,255,261,264]
% SZS output end Proof for 6763542842986215632954581
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not kind then someone is both generous and tall and vice versa. If john is brave or strong then someone is not quiet. Everyone who is either not quiet or not strong is either happy or not kind and vice versa. If someone is not generous then fred is rich. If someone is both not patient and tall then mary is both not humble and not generous. Everyone who is not calm or rich is both funny and not quiet and vice versa. Everyone who is funny is not quiet and vice versa. If someone is both strong and quiet then someone is not old and vice versa. Everyone who is both not creative and creative is tall and vice versa. If alice is creative or not tall then someone is both old and not humble and vice versa. Everyone who is not strong is both not tall and not humble and vice versa. Everyone who is either not quiet or not happy is rich or happy. Everyone who is not calm or not old is both wise and tall. If someone is both strong and not patient then john is either not quiet or not creative and vice versa. If fred is either funny or not creative then someone is both not calm and funny. If alice is kind or funny then fred is either not curious or not tall. Someone is either not generous or humble. John is either not tall or not brave. Fred is not funny or not brave. Fred is brave. Susan is both humble and generous. Someone is either humble or not wise. | Fred is creative. | entailment | ((?[X]:((wise(X)|~kind(X))))<=>(?[X]:((generous(X)&tall(X)))))&
(((brave(john)|strong(john)))=>(?[X]:(~quiet(X))))&
(![X]:((~quiet(X)<~>~strong(X))<=>(happy(X)<~>~kind(X))))&
((?[X]:(~generous(X)))=>(rich(fred)))&
((?[X]:((~patient(X)&tall(X))))=>((~humble(mary)&~generous(mary))))&
(![X]:((~calm(X)|rich(X))<=>(funny(X)&~quiet(X))))&
(![X]:(funny(X)<=>~quiet(X)))&
((?[X]:((strong(X)&quiet(X))))<=>(?[X]:(~old(X))))&
(![X]:((~creative(X)&creative(X))<=>tall(X)))&
(((creative(alice)|~tall(alice)))<=>(?[X]:((old(X)&~humble(X)))))&
(![X]:(~strong(X)<=>(~tall(X)&~humble(X))))&
(![X]:((~quiet(X)<~>~happy(X))=>(rich(X)|happy(X))))&
(![X]:((~calm(X)|~old(X))=>(wise(X)&tall(X))))&
((?[X]:((strong(X)&~patient(X))))<=>((~quiet(john)<~>~creative(john))))&
(((funny(fred)<~>~creative(fred)))=>(?[X]:((~calm(X)&funny(X)))))&
(((kind(alice)|funny(alice)))=>((~curious(fred)<~>~tall(fred))))&
(?[X]:((~generous(X)<~>humble(X))))&
((~tall(john)<~>~brave(john)))&
((~funny(fred)|~brave(fred)))&
(brave(fred))&
((humble(susan)&generous(susan)))&
(?[X]:((humble(X)<~>~wise(X)))) | creative(fred) | [
"p8",
"p12",
"p14",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4726218027278709102889130
% SZS output start Proof for 4726218027278709102889130
9. ! [X0] : ((creative(X0) & ~creative(X0)) <=> tall(X0)) [input p8]
13. ! [X0] : ((~old(X0) | ~calm(X0)) => (tall(X0) & wise(X0))) [input p12]
15. (funny(fred) <~> ~creative(fred)) => ? [X0] : (funny(X0) & ~calm(X0)) [input p14]
19. ~brave(fred) | ~funny(fred) [input p18]
20. brave(fred) [input p19]
23. ~creative(fred) [input hypothesis]
31. ! [X0] : ((tall(X0) & wise(X0)) | (old(X0) & calm(X0))) [ennf transformation 13]
32. ? [X0] : (funny(X0) & ~calm(X0)) | (funny(fred) <=> ~creative(fred)) [ennf transformation 15]
50. ! [X0] : (((creative(X0) & ~creative(X0)) | ~tall(X0)) & (tall(X0) | (~creative(X0) | creative(X0)))) [nnf transformation 9]
51. ! [X0] : (((creative(X0) & ~creative(X0)) | ~tall(X0)) & (tall(X0) | ~creative(X0) | creative(X0))) [flattening 50]
64. ? [X0] : (funny(X0) & ~calm(X0)) | ((funny(fred) | creative(fred)) & (~creative(fred) | ~funny(fred))) [nnf transformation 32]
65. ? [X0] : (funny(X0) & ~calm(X0)) => (funny(sK7) & ~calm(sK7)) [choice axiom]
66. (funny(sK7) & ~calm(sK7)) | ((funny(fred) | creative(fred)) & (~creative(fred) | ~funny(fred))) [skolemisation 64,65]
104. ~creative(X0) | ~tall(X0) [cnf transformation 51]
105. creative(X0) | ~tall(X0) [cnf transformation 51]
118. tall(X0) | calm(X0) [cnf transformation 31]
127. ~calm(sK7) | funny(fred) | creative(fred) [cnf transformation 66]
138. ~brave(fred) | ~funny(fred) [cnf transformation 19]
139. brave(fred) [cnf transformation 20]
144. ~creative(fred) [cnf transformation 23]
232. ~tall(X0) [subsumption resolution 104,105]
239. calm(X0) [subsumption resolution 118,232]
266. 26 <=> creative(fred) [avatar definition]
270. 27 <=> funny(fred) [avatar definition]
279. funny(fred) | creative(fred) [subsumption resolution 127,239]
280. 26 | 27 [avatar split clause 279,270,266]
312. 34 <=> brave(fred) [avatar definition]
315. ~27 | ~34 [avatar split clause 138,312,270]
316. 34 [avatar split clause 139,312]
327. ~26 [avatar split clause 144,266]
328. $false [avatar sat refutation 280,315,316,327]
% SZS output end Proof for 4726218027278709102889130
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is both not strong and not creative and vice versa.
Everyone who is tall is both not rich and not kind and vice versa.
Everyone who is both strong and old is strong or patient.
If someone is both not funny and not tall then someone is both not calm and quiet.
If susan is both generous and patient then lucy is quiet or funny and vice versa.
Everyone who is either not wise or not funny is either funny or not tall and vice versa.
Everyone who is funny is strong or not quiet and vice versa.
If paul is either creative or rich then susan is both not creative and rich and vice versa.
Everyone who is happy is both rich and happy.
If alice is not wise or old then someone is either patient or not curious and vice versa.
If paul is both rich and not tall then someone is not generous.
Everyone who is not curious or not quiet is both not tall and brave.
If fred is creative then someone is not old or quiet and vice versa.
If alice is strong or kind then fred is either humble or not quiet.
Everyone who is both curious and patient is not tall and vice versa.
Everyone who is both curious and not patient is either not humble or happy.
Someone is old or not happy.
Alice is either tall or wise.
Mary is both not wise and old.
Someone is curious or not curious.
Someone is both not humble and curious.
Susan is tall or not humble. | Alice is not brave. | neutral | (![X]:(kind(X)<=>(~strong(X)&~creative(X))))&
(![X]:(tall(X)<=>(~rich(X)&~kind(X))))&
(![X]:((strong(X)&old(X))=>(strong(X)|patient(X))))&
((?[X]:((~funny(X)&~tall(X))))=>(?[X]:((~calm(X)&quiet(X)))))&
(((generous(susan)&patient(susan)))<=>((quiet(lucy)|funny(lucy))))&
(![X]:((~wise(X)<~>~funny(X))<=>(funny(X)<~>~tall(X))))&
(![X]:(funny(X)<=>(strong(X)|~quiet(X))))&
(((creative(paul)<~>rich(paul)))<=>((~creative(susan)&rich(susan))))&
(![X]:(happy(X)=>(rich(X)&happy(X))))&
(((~wise(alice)|old(alice)))<=>(?[X]:((patient(X)<~>~curious(X)))))&
(((rich(paul)&~tall(paul)))=>(?[X]:(~generous(X))))&
(![X]:((~curious(X)|~quiet(X))=>(~tall(X)&brave(X))))&
((creative(fred))<=>(?[X]:((~old(X)|quiet(X)))))&
(((strong(alice)|kind(alice)))=>((humble(fred)<~>~quiet(fred))))&
(![X]:((curious(X)&patient(X))<=>~tall(X)))&
(![X]:((curious(X)&~patient(X))=>(~humble(X)<~>happy(X))))&
(?[X]:((old(X)|~happy(X))))&
((tall(alice)<~>wise(alice)))&
((~wise(mary)&old(mary)))&
(?[X]:((curious(X)|~curious(X))))&
(?[X]:((~humble(X)&curious(X))))&
((tall(susan)|~humble(susan))) | ~brave(alice) | [] | null | 0 |
Everyone who is creative or brave is either curious or not creative and vice versa. If someone is calm then john is not humble and vice versa. If someone is quiet or old then someone is both not tall and calm. Everyone who is not wise is either strong or not quiet and vice versa. Everyone who is both curious and generous is funny or not strong and vice versa. Everyone who is either not tall or strong is both not curious and funny. If john is not rich or not old then mary is both quiet and not calm and vice versa. Everyone who is both not creative and old is quiet or not humble and vice versa. Everyone who is kind or not wise is both wise and not strong and vice versa. If someone is kind or not creative then someone is both not happy and strong and vice versa. Everyone who is not tall is not strong or calm. If someone is both patient and curious then john is patient. Everyone who is both not strong and not funny is either not funny or brave. Everyone who is not brave is either not old or humble. Everyone who is either old or funny is either creative or wise. If someone is not humble or not generous then someone is happy and vice versa. Paul is funny. Someone is not old or not strong. Someone is either not strong or not wise. Paul is not rich or not generous. Someone is not patient or not quiet. Someone is either not generous or not patient. Paul is creative. | John is tall. | contradiction | (![X]:((creative(X)|brave(X))<=>(curious(X)<~>~creative(X))))&
((?[X]:(calm(X)))<=>(~humble(john)))&
((?[X]:((quiet(X)|old(X))))=>(?[X]:((~tall(X)&calm(X)))))&
(![X]:(~wise(X)<=>(strong(X)<~>~quiet(X))))&
(![X]:((curious(X)&generous(X))<=>(funny(X)|~strong(X))))&
(![X]:((~tall(X)<~>strong(X))=>(~curious(X)&funny(X))))&
(((~rich(john)|~old(john)))<=>((quiet(mary)&~calm(mary))))&
(![X]:((~creative(X)&old(X))<=>(quiet(X)|~humble(X))))&
(![X]:((kind(X)|~wise(X))<=>(wise(X)&~strong(X))))&
((?[X]:((kind(X)|~creative(X))))<=>(?[X]:((~happy(X)&strong(X)))))&
(![X]:(~tall(X)=>(~strong(X)|calm(X))))&
((?[X]:((patient(X)&curious(X))))=>(patient(john)))&
(![X]:((~strong(X)&~funny(X))=>(~funny(X)<~>brave(X))))&
(![X]:(~brave(X)=>(~old(X)<~>humble(X))))&
(![X]:((old(X)<~>funny(X))=>(creative(X)<~>wise(X))))&
((?[X]:((~humble(X)|~generous(X))))<=>(?[X]:(happy(X))))&
(funny(paul))&
(?[X]:((~old(X)|~strong(X))))&
(?[X]:((~strong(X)<~>~wise(X))))&
((~rich(paul)|~generous(paul)))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:((~generous(X)<~>~patient(X))))&
(creative(paul)) | tall(john) | [
"p0",
"p1",
"p4",
"p5",
"p7",
"p8",
"p9",
"p10",
"p12",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5339456914959550115495686
% SZS output start Proof for 5339456914959550115495686
1. ! [X0] : ((brave(X0) | creative(X0)) <=> (curious(X0) <~> ~creative(X0))) [input p0]
2. ? [X0] : calm(X0) <=> ~humble(john) [input p1]
5. ! [X0] : ((generous(X0) & curious(X0)) <=> (~strong(X0) | funny(X0))) [input p4]
6. ! [X0] : ((~tall(X0) <~> strong(X0)) => (funny(X0) & ~curious(X0))) [input p5]
8. ! [X0] : ((old(X0) & ~creative(X0)) <=> (~humble(X0) | quiet(X0))) [input p7]
9. ! [X0] : ((~wise(X0) | kind(X0)) <=> (~strong(X0) & wise(X0))) [input p8]
10. ? [X0] : (~creative(X0) | kind(X0)) <=> ? [X0] : (strong(X0) & ~happy(X0)) [input p9]
11. ! [X0] : (~tall(X0) => (calm(X0) | ~strong(X0))) [input p10]
13. ! [X0] : ((~funny(X0) & ~strong(X0)) => (~funny(X0) <~> brave(X0))) [input p12]
14. ! [X0] : (~brave(X0) => (~old(X0) <~> humble(X0))) [input p13]
19. ? [X0] : (~strong(X0) <~> ~wise(X0)) [input p18]
24. tall(john) [input hypothesis]
26. ? [X0] : (~creative(X0) | kind(X0)) <=> ? [X1] : (strong(X1) & ~happy(X1)) [rectify 10]
29. ! [X0] : ((funny(X0) & ~curious(X0)) | (~tall(X0) <=> strong(X0))) [ennf transformation 6]
30. ! [X0] : ((calm(X0) | ~strong(X0)) | tall(X0)) [ennf transformation 11]
31. ! [X0] : (calm(X0) | ~strong(X0) | tall(X0)) [flattening 30]
33. ! [X0] : ((~funny(X0) <~> brave(X0)) | (funny(X0) | strong(X0))) [ennf transformation 13]
34. ! [X0] : ((~funny(X0) <~> brave(X0)) | funny(X0) | strong(X0)) [flattening 33]
35. ! [X0] : ((~old(X0) <~> humble(X0)) | brave(X0)) [ennf transformation 14]
37. ! [X0] : (((brave(X0) | creative(X0)) | ((curious(X0) | creative(X0)) & (~creative(X0) | ~curious(X0)))) & (((creative(X0) | ~curious(X0)) & (~creative(X0) | curious(X0))) | (~brave(X0) & ~creative(X0)))) [nnf transformation 1]
38. ! [X0] : ((brave(X0) | creative(X0) | ((curious(X0) | creative(X0)) & (~creative(X0) | ~curious(X0)))) & (((creative(X0) | ~curious(X0)) & (~creative(X0) | curious(X0))) | (~brave(X0) & ~creative(X0)))) [flattening 37]
39. (? [X0] : calm(X0) | humble(john)) & (~humble(john) | ! [X0] : ~calm(X0)) [nnf transformation 2]
40. (? [X0] : calm(X0) | humble(john)) & (~humble(john) | ! [X1] : ~calm(X1)) [rectify 39]
41. ? [X0] : calm(X0) => calm(sK0) [choice axiom]
42. (calm(sK0) | humble(john)) & (~humble(john) | ! [X1] : ~calm(X1)) [skolemisation 40,41]
47. ! [X0] : (((generous(X0) & curious(X0)) | (strong(X0) & ~funny(X0))) & ((~strong(X0) | funny(X0)) | (~generous(X0) | ~curious(X0)))) [nnf transformation 5]
48. ! [X0] : (((generous(X0) & curious(X0)) | (strong(X0) & ~funny(X0))) & (~strong(X0) | funny(X0) | ~generous(X0) | ~curious(X0))) [flattening 47]
49. ! [X0] : ((funny(X0) & ~curious(X0)) | ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0)))) [nnf transformation 29]
52. ! [X0] : (((old(X0) & ~creative(X0)) | (humble(X0) & ~quiet(X0))) & ((~humble(X0) | quiet(X0)) | (~old(X0) | creative(X0)))) [nnf transformation 8]
53. ! [X0] : (((old(X0) & ~creative(X0)) | (humble(X0) & ~quiet(X0))) & (~humble(X0) | quiet(X0) | ~old(X0) | creative(X0))) [flattening 52]
54. ! [X0] : (((~wise(X0) | kind(X0)) | (strong(X0) | ~wise(X0))) & ((~strong(X0) & wise(X0)) | (wise(X0) & ~kind(X0)))) [nnf transformation 9]
55. ! [X0] : ((~wise(X0) | kind(X0) | strong(X0) | ~wise(X0)) & ((~strong(X0) & wise(X0)) | (wise(X0) & ~kind(X0)))) [flattening 54]
56. (? [X0] : (~creative(X0) | kind(X0)) | ! [X1] : (~strong(X1) | happy(X1))) & (? [X1] : (strong(X1) & ~happy(X1)) | ! [X0] : (creative(X0) & ~kind(X0))) [nnf transformation 26]
57. (? [X0] : (~creative(X0) | kind(X0)) | ! [X1] : (~strong(X1) | happy(X1))) & (? [X2] : (strong(X2) & ~happy(X2)) | ! [X3] : (creative(X3) & ~kind(X3))) [rectify 56]
58. ? [X0] : (~creative(X0) | kind(X0)) => (~creative(sK2) | kind(sK2)) [choice axiom]
59. ? [X2] : (strong(X2) & ~happy(X2)) => (strong(sK3) & ~happy(sK3)) [choice axiom]
60. ((~creative(sK2) | kind(sK2)) | ! [X1] : (~strong(X1) | happy(X1))) & ((strong(sK3) & ~happy(sK3)) | ! [X3] : (creative(X3) & ~kind(X3))) [skolemisation 57,59,58]
61. ! [X0] : (((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | funny(X0) | strong(X0)) [nnf transformation 34]
62. ! [X0] : (((~humble(X0) | old(X0)) & (humble(X0) | ~old(X0))) | brave(X0)) [nnf transformation 35]
71. ? [X0] : ((wise(X0) | strong(X0)) & (~wise(X0) | ~strong(X0))) [nnf transformation 19]
72. ? [X0] : ((wise(X0) | strong(X0)) & (~wise(X0) | ~strong(X0))) => ((wise(sK7) | strong(sK7)) & (~wise(sK7) | ~strong(sK7))) [choice axiom]
73. (wise(sK7) | strong(sK7)) & (~wise(sK7) | ~strong(sK7)) [skolemisation 71,72]
82. ~curious(X0) | creative(X0) | ~brave(X0) [cnf transformation 38]
85. ~humble(john) | ~calm(X1) [cnf transformation 42]
96. ~funny(X0) | curious(X0) [cnf transformation 48]
97. strong(X0) | curious(X0) [cnf transformation 48]
100. ~curious(X0) | strong(X0) | tall(X0) [cnf transformation 49]
101. ~strong(X0) | ~tall(X0) | ~curious(X0) [cnf transformation 49]
103. ~strong(X0) | ~tall(X0) | funny(X0) [cnf transformation 49]
111. ~creative(X0) | humble(X0) [cnf transformation 53]
113. old(X0) | humble(X0) [cnf transformation 53]
115. wise(X0) | wise(X0) [cnf transformation 55]
118. ~wise(X0) | kind(X0) | strong(X0) | ~wise(X0) [cnf transformation 55]
121. strong(sK3) | ~kind(X3) [cnf transformation 60]
124. calm(X0) | ~strong(X0) | tall(X0) [cnf transformation 31]
127. ~brave(X0) | funny(X0) | funny(X0) | strong(X0) [cnf transformation 61]
128. humble(X0) | ~old(X0) | brave(X0) [cnf transformation 62]
139. ~wise(sK7) | ~strong(sK7) [cnf transformation 73]
146. tall(john) [cnf transformation 24]
147. ~brave(X0) | funny(X0) | strong(X0) [duplicate literal removal 127]
148. wise(X0) [duplicate literal removal 115]
149. ~wise(X0) | kind(X0) | strong(X0) [duplicate literal removal 118]
153. 1 <=> humble(john) [avatar definition]
154. ~humble(john) <- (~1) [avatar component clause 153]
162. 3 <=> ! [X1] : ~calm(X1) [avatar definition]
163. ~calm(X1) <- (3) [avatar component clause 162]
164. 3 | ~1 [avatar split clause 85,153,162]
183. strong(X0) | tall(X0) [subsumption resolution 100,97]
221. 16 <=> strong(sK3) [avatar definition]
223. strong(sK3) <- (16) [avatar component clause 221]
226. 17 <=> ! [X3] : ~kind(X3) [avatar definition]
227. ~kind(X3) <- (17) [avatar component clause 226]
228. 17 | 16 [avatar split clause 121,221,226]
235. tall(X0) | calm(X0) [subsumption resolution 124,183]
245. humble(X0) | brave(X0) [subsumption resolution 128,113]
281. ~strong(sK7) [subsumption resolution 139,148]
327. brave(john) <- (~1) [resolution 245,154]
364. ~tall(sK3) | ~curious(sK3) <- (16) [resolution 101,223]
369. 39 <=> curious(sK3) [avatar definition]
371. ~curious(sK3) <- (~39) [avatar component clause 369]
373. 40 <=> tall(sK3) [avatar definition]
374. tall(sK3) <- (40) [avatar component clause 373]
375. ~tall(sK3) <- (~40) [avatar component clause 373]
376. ~39 | ~40 | ~16 [avatar split clause 364,221,373,369]
391. ~tall(X1) | funny(X1) | curious(X1) [resolution 103,97]
398. ~tall(X1) | curious(X1) [subsumption resolution 391,96]
400. funny(john) | strong(john) <- (~1) [resolution 147,327]
402. 44 <=> strong(john) [avatar definition]
404. strong(john) <- (44) [avatar component clause 402]
406. 45 <=> funny(john) [avatar definition]
408. funny(john) <- (45) [avatar component clause 406]
409. 44 | 45 | 1 [avatar split clause 400,153,406,402]
414. brave(john) <- (~1) [resolution 154,245]
415. kind(X0) | strong(X0) [resolution 149,148]
474. ~tall(john) | funny(john) <- (44) [resolution 404,103]
479. funny(john) <- (44) [subsumption resolution 474,146]
480. 45 | ~44 [avatar split clause 479,402,406]
486. curious(john) <- (45) [resolution 408,96]
488. 53 <=> creative(john) [avatar definition]
489. creative(john) <- (53) [avatar component clause 488]
561. strong(X0) <- (17) [resolution 227,415]
601. curious(sK3) <- (40) [resolution 374,398]
602. $false <- (~39, 40) [subsumption resolution 601,371]
603. 39 | ~40 [avatar contradiction clause 602]
604. calm(sK3) <- (~40) [resolution 375,235]
659. $false <- (17) [resolution 561,281]
662. ~17 [avatar contradiction clause 659]
695. creative(john) | ~brave(john) <- (45) [resolution 486,82]
699. creative(john) <- (~1, 45) [subsumption resolution 695,414]
700. 53 | 1 | ~45 [avatar split clause 699,406,153,488]
708. humble(john) <- (53) [resolution 489,111]
711. 1 | ~53 [avatar split clause 708,488,153]
714. $false <- (3, ~40) [resolution 163,604]
717. ~3 | 40 [avatar contradiction clause 714]
718. $false [avatar sat refutation 164,228,376,409,480,603,662,700,711,717]
% SZS output end Proof for 5339456914959550115495686
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble then susan is either not happy or not brave and vice versa. If alice is both not rich and rich then john is either not quiet or not calm. If someone is either funny or strong then fred is humble and vice versa. If someone is both not happy and not creative then susan is either funny or not humble and vice versa. If someone is both patient and not creative then paul is either quiet or calm and vice versa. If someone is both not quiet and happy then john is either tall or happy. Everyone who is both generous and kind is not curious or kind. Everyone who is happy or not wise is tall or wise. If someone is not quiet then fred is not quiet. Everyone who is calm or wise is not patient. Everyone who is curious or not humble is both not happy and humble. Everyone who is not funny or not calm is not kind and vice versa. If someone is curious then fred is not calm and vice versa. If john is rich or not humble then mary is creative or generous and vice versa. If paul is happy or quiet then mary is either happy or rich. Everyone who is both patient and not brave is either rich or patient and vice versa. Someone is curious or not strong. Someone is strong or funny. Paul is both not calm and not funny. John is both wise and not creative. Lucy is not happy. Lucy is either not rich or not happy. Paul is either not generous or calm. | Mary is not generous. | entailment | ((?[X]:(~humble(X)))<=>((~happy(susan)<~>~brave(susan))))&
(((~rich(alice)&rich(alice)))=>((~quiet(john)<~>~calm(john))))&
((?[X]:((funny(X)<~>strong(X))))<=>(humble(fred)))&
((?[X]:((~happy(X)&~creative(X))))<=>((funny(susan)<~>~humble(susan))))&
((?[X]:((patient(X)&~creative(X))))<=>((quiet(paul)<~>calm(paul))))&
((?[X]:((~quiet(X)&happy(X))))=>((tall(john)<~>happy(john))))&
(![X]:((generous(X)&kind(X))=>(~curious(X)|kind(X))))&
(![X]:((happy(X)|~wise(X))=>(tall(X)|wise(X))))&
((?[X]:(~quiet(X)))=>(~quiet(fred)))&
(![X]:((calm(X)|wise(X))=>~patient(X)))&
(![X]:((curious(X)|~humble(X))=>(~happy(X)&humble(X))))&
(![X]:((~funny(X)|~calm(X))<=>~kind(X)))&
((?[X]:(curious(X)))<=>(~calm(fred)))&
(((rich(john)|~humble(john)))<=>((creative(mary)|generous(mary))))&
(((happy(paul)|quiet(paul)))=>((happy(mary)<~>rich(mary))))&
(![X]:((patient(X)&~brave(X))<=>(rich(X)<~>patient(X))))&
(?[X]:((curious(X)|~strong(X))))&
(?[X]:((strong(X)|funny(X))))&
((~calm(paul)&~funny(paul)))&
((wise(john)&~creative(john)))&
(~happy(lucy))&
((~rich(lucy)<~>~happy(lucy)))&
((~generous(paul)<~>calm(paul))) | ~generous(mary) | [
"p9",
"p10",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8288609333492760399894991
% SZS output start Proof for 8288609333492760399894991
10. ! [X0] : ((wise(X0) | calm(X0)) => ~patient(X0)) [input p9]
11. ! [X0] : ((~humble(X0) | curious(X0)) => (humble(X0) & ~happy(X0))) [input p10]
14. (~humble(john) | rich(john)) <=> (generous(mary) | creative(mary)) [input p13]
16. ! [X0] : ((~brave(X0) & patient(X0)) <=> (rich(X0) <~> patient(X0))) [input p15]
20. ~creative(john) & wise(john) [input p19]
24. generous(mary) [input hypothesis]
33. ! [X0] : (~patient(X0) | (~wise(X0) & ~calm(X0))) [ennf transformation 10]
34. ! [X0] : ((humble(X0) & ~happy(X0)) | (humble(X0) & ~curious(X0))) [ennf transformation 11]
60. ((~humble(john) | rich(john)) | (~generous(mary) & ~creative(mary))) & ((generous(mary) | creative(mary)) | (humble(john) & ~rich(john))) [nnf transformation 14]
61. (~humble(john) | rich(john) | (~generous(mary) & ~creative(mary))) & (generous(mary) | creative(mary) | (humble(john) & ~rich(john))) [flattening 60]
63. ! [X0] : (((~brave(X0) & patient(X0)) | ((rich(X0) | ~patient(X0)) & (patient(X0) | ~rich(X0)))) & (((~patient(X0) | ~rich(X0)) & (patient(X0) | rich(X0))) | (brave(X0) | ~patient(X0)))) [nnf transformation 16]
64. ! [X0] : (((~brave(X0) & patient(X0)) | ((rich(X0) | ~patient(X0)) & (patient(X0) | ~rich(X0)))) & (((~patient(X0) | ~rich(X0)) & (patient(X0) | rich(X0))) | brave(X0) | ~patient(X0))) [flattening 63]
100. ~wise(X0) | ~patient(X0) [cnf transformation 33]
104. humble(X0) | humble(X0) [cnf transformation 34]
113. ~humble(john) | rich(john) | ~generous(mary) [cnf transformation 61]
120. patient(X0) | patient(X0) | ~rich(X0) [cnf transformation 64]
128. wise(john) [cnf transformation 20]
135. generous(mary) [cnf transformation 24]
137. ~rich(X0) | patient(X0) [duplicate literal removal 120]
138. humble(X0) [duplicate literal removal 104]
155. 4 <=> ! [X1] : humble(X1) [avatar definition]
156. humble(X1) <- (4) [avatar component clause 155]
252. 4 [avatar split clause 138,155]
267. 28 <=> generous(mary) [avatar definition]
271. 29 <=> rich(john) [avatar definition]
273. rich(john) <- (29) [avatar component clause 271]
275. 30 <=> humble(john) [avatar definition]
277. ~humble(john) <- (~30) [avatar component clause 275]
278. ~28 | 29 | ~30 [avatar split clause 113,275,271,267]
329. 28 [avatar split clause 135,267]
334. $false <- (4, ~30) [resolution 277,156]
335. ~4 | 30 [avatar contradiction clause 334]
336. ~patient(john) [resolution 100,128]
339. patient(john) <- (29) [resolution 137,273]
341. $false <- (29) [subsumption resolution 339,336]
342. ~29 [avatar contradiction clause 341]
343. $false [avatar sat refutation 252,278,329,335,342]
% SZS output end Proof for 8288609333492760399894991
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If fred is quiet or patient then someone is not curious or wise and vice versa.
If mary is either curious or not creative then someone is either wise or not funny and vice versa.
If someone is not rich then mary is both not rich and not strong and vice versa.
If mary is both not brave and not creative then someone is not rich.
If alice is either not old or not funny then fred is both generous and wise and vice versa.
If paul is either not patient or not generous then mary is both not humble and not rich and vice versa.
Everyone who is both rich and quiet is humble.
If someone is either brave or not funny then someone is both not rich and curious and vice versa.
Everyone who is either happy or curious is not kind or funny and vice versa.
Everyone who is both kind and creative is either not old or creative.
Everyone who is either not brave or patient is old or not calm and vice versa.
If someone is not rich then lucy is both kind and not generous and vice versa.
If mary is not old then paul is either not kind or not funny and vice versa.
Everyone who is wise or rich is generous.
If mary is happy or wise then someone is both calm and not humble.
Everyone who is not calm is not old and vice versa.
Someone is either not brave or kind.
Fred is both not old and happy.
Fred is both creative and not patient.
Someone is not curious or creative.
Paul is both not quiet and funny.
Alice is brave or not old.
Someone is patient.
Someone is not strong or not funny. | Lucy is not kind. | contradiction | (((quiet(fred)|patient(fred)))<=>(?[X]:((~curious(X)|wise(X)))))&
(((curious(mary)<~>~creative(mary)))<=>(?[X]:((wise(X)<~>~funny(X)))))&
((?[X]:(~rich(X)))<=>((~rich(mary)&~strong(mary))))&
(((~brave(mary)&~creative(mary)))=>(?[X]:(~rich(X))))&
(((~old(alice)<~>~funny(alice)))<=>((generous(fred)&wise(fred))))&
(((~patient(paul)<~>~generous(paul)))<=>((~humble(mary)&~rich(mary))))&
(![X]:((rich(X)&quiet(X))=>humble(X)))&
((?[X]:((brave(X)<~>~funny(X))))<=>(?[X]:((~rich(X)&curious(X)))))&
(![X]:((happy(X)<~>curious(X))<=>(~kind(X)|funny(X))))&
(![X]:((kind(X)&creative(X))=>(~old(X)<~>creative(X))))&
(![X]:((~brave(X)<~>patient(X))<=>(old(X)|~calm(X))))&
((?[X]:(~rich(X)))<=>((kind(lucy)&~generous(lucy))))&
((~old(mary))<=>((~kind(paul)<~>~funny(paul))))&
(![X]:((wise(X)|rich(X))=>generous(X)))&
(((happy(mary)|wise(mary)))=>(?[X]:((calm(X)&~humble(X)))))&
(![X]:(~calm(X)<=>~old(X)))&
(?[X]:((~brave(X)<~>kind(X))))&
((~old(fred)&happy(fred)))&
((creative(fred)&~patient(fred)))&
(?[X]:((~curious(X)|creative(X))))&
((~quiet(paul)&funny(paul)))&
((brave(alice)|~old(alice)))&
(?[X]:(patient(X)))&
(?[X]:((~strong(X)|~funny(X)))) | ~kind(lucy) | [
"p5",
"p7",
"p10",
"p11",
"p13",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6838096808499190378314040
% SZS output start Proof for 6838096808499190378314040
6. (~patient(paul) <~> ~generous(paul)) <=> (~rich(mary) & ~humble(mary)) [input p5]
8. ? [X0] : (brave(X0) <~> ~funny(X0)) <=> ? [X0] : (curious(X0) & ~rich(X0)) [input p7]
11. ! [X0] : ((~brave(X0) <~> patient(X0)) <=> (~calm(X0) | old(X0))) [input p10]
12. ? [X0] : ~rich(X0) <=> (~generous(lucy) & kind(lucy)) [input p11]
14. ! [X0] : ((rich(X0) | wise(X0)) => generous(X0)) [input p13]
16. ! [X0] : (~calm(X0) <=> ~old(X0)) [input p15]
21. funny(paul) & ~quiet(paul) [input p20]
25. ~kind(lucy) [input hypothesis]
26. ? [X0] : (brave(X0) <~> ~funny(X0)) <=> ? [X1] : (curious(X1) & ~rich(X1)) [rectify 8]
33. ! [X0] : (generous(X0) | (~rich(X0) & ~wise(X0))) [ennf transformation 14]
53. (((generous(paul) | patient(paul)) & (~generous(paul) | ~patient(paul))) | (rich(mary) | humble(mary))) & ((~rich(mary) & ~humble(mary)) | ((~patient(paul) | generous(paul)) & (~generous(paul) | patient(paul)))) [nnf transformation 6]
54. (((generous(paul) | patient(paul)) & (~generous(paul) | ~patient(paul))) | rich(mary) | humble(mary)) & ((~rich(mary) & ~humble(mary)) | ((~patient(paul) | generous(paul)) & (~generous(paul) | patient(paul)))) [flattening 53]
55. (? [X0] : ((funny(X0) | ~brave(X0)) & (~funny(X0) | brave(X0))) | ! [X1] : (~curious(X1) | rich(X1))) & (? [X1] : (curious(X1) & ~rich(X1)) | ! [X0] : ((brave(X0) | funny(X0)) & (~funny(X0) | ~brave(X0)))) [nnf transformation 26]
56. (? [X0] : ((funny(X0) | ~brave(X0)) & (~funny(X0) | brave(X0))) | ! [X1] : (~curious(X1) | rich(X1))) & (? [X2] : (curious(X2) & ~rich(X2)) | ! [X3] : ((brave(X3) | funny(X3)) & (~funny(X3) | ~brave(X3)))) [rectify 55]
57. ? [X0] : ((funny(X0) | ~brave(X0)) & (~funny(X0) | brave(X0))) => ((funny(sK4) | ~brave(sK4)) & (~funny(sK4) | brave(sK4))) [choice axiom]
58. ? [X2] : (curious(X2) & ~rich(X2)) => (curious(sK5) & ~rich(sK5)) [choice axiom]
59. (((funny(sK4) | ~brave(sK4)) & (~funny(sK4) | brave(sK4))) | ! [X1] : (~curious(X1) | rich(X1))) & ((curious(sK5) & ~rich(sK5)) | ! [X3] : ((brave(X3) | funny(X3)) & (~funny(X3) | ~brave(X3)))) [skolemisation 56,58,57]
63. ! [X0] : ((((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | (calm(X0) & ~old(X0))) & ((~calm(X0) | old(X0)) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0))))) [nnf transformation 11]
64. ! [X0] : ((((~patient(X0) | brave(X0)) & (patient(X0) | ~brave(X0))) | (calm(X0) & ~old(X0))) & (~calm(X0) | old(X0) | ((~brave(X0) | ~patient(X0)) & (patient(X0) | brave(X0))))) [flattening 63]
65. (? [X0] : ~rich(X0) | (generous(lucy) | ~kind(lucy))) & ((~generous(lucy) & kind(lucy)) | ! [X0] : rich(X0)) [nnf transformation 12]
66. (? [X0] : ~rich(X0) | generous(lucy) | ~kind(lucy)) & ((~generous(lucy) & kind(lucy)) | ! [X0] : rich(X0)) [flattening 65]
67. (? [X0] : ~rich(X0) | generous(lucy) | ~kind(lucy)) & ((~generous(lucy) & kind(lucy)) | ! [X1] : rich(X1)) [rectify 66]
68. ? [X0] : ~rich(X0) => ~rich(sK6) [choice axiom]
69. (~rich(sK6) | generous(lucy) | ~kind(lucy)) & ((~generous(lucy) & kind(lucy)) | ! [X1] : rich(X1)) [skolemisation 67,68]
73. ! [X0] : ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0))) [nnf transformation 16]
107. ~rich(mary) | ~generous(paul) | patient(paul) [cnf transformation 54]
112. ~rich(sK5) | ~funny(X3) | ~brave(X3) [cnf transformation 59]
130. ~old(X0) | brave(X0) | ~patient(X0) [cnf transformation 64]
131. ~patient(X0) | brave(X0) | calm(X0) [cnf transformation 64]
132. kind(lucy) | rich(X1) [cnf transformation 69]
140. ~rich(X0) | generous(X0) [cnf transformation 33]
146. ~calm(X0) | old(X0) [cnf transformation 73]
155. funny(paul) [cnf transformation 21]
159. ~kind(lucy) [cnf transformation 25]
218. 13 <=> rich(mary) [avatar definition]
219. ~rich(mary) <- (~13) [avatar component clause 218]
231. 16 <=> ! [X1] : rich(X1) [avatar definition]
232. rich(X1) <- (16) [avatar component clause 231]
271. 24 <=> patient(paul) [avatar definition]
273. patient(paul) <- (24) [avatar component clause 271]
275. 25 <=> generous(paul) [avatar definition]
276. ~generous(paul) <- (~25) [avatar component clause 275]
281. 24 | ~25 | ~13 [avatar split clause 107,218,275,271]
306. 31 <=> ! [X3] : (~funny(X3) | ~brave(X3)) [avatar definition]
307. ~brave(X3) | ~funny(X3) <- (31) [avatar component clause 306]
310. 32 <=> rich(sK5) [avatar definition]
312. ~rich(sK5) <- (~32) [avatar component clause 310]
314. 31 | ~32 [avatar split clause 112,310,306]
316. 33 <=> kind(lucy) [avatar definition]
329. 16 | 33 [avatar split clause 132,316,231]
331. 36 <=> funny(paul) [avatar definition]
333. funny(paul) <- (36) [avatar component clause 331]
386. 36 [avatar split clause 155,331]
401. ~33 [avatar split clause 159,316]
404. $false <- (16, ~32) [resolution 312,232]
405. ~16 | 32 [avatar contradiction clause 404]
406. generous(X0) <- (16) [resolution 140,232]
407. $false <- (16, ~25) [resolution 406,276]
408. ~16 | 25 [avatar contradiction clause 407]
411. $false <- (~13, 16) [subsumption resolution 219,232]
412. 13 | ~16 [avatar contradiction clause 411]
513. brave(paul) | calm(paul) <- (24) [resolution 131,273]
524. 67 <=> calm(paul) [avatar definition]
526. calm(paul) <- (67) [avatar component clause 524]
528. 68 <=> brave(paul) [avatar definition]
529. ~brave(paul) <- (~68) [avatar component clause 528]
530. brave(paul) <- (68) [avatar component clause 528]
531. 67 | 68 | ~24 [avatar split clause 513,271,528,524]
539. 70 <=> old(paul) [avatar definition]
541. old(paul) <- (70) [avatar component clause 539]
561. old(paul) <- (67) [resolution 526,146]
564. 70 | ~67 [avatar split clause 561,524,539]
566. ~funny(paul) <- (31, 68) [resolution 530,307]
567. $false <- (31, 36, 68) [subsumption resolution 566,333]
568. ~31 | ~36 | ~68 [avatar contradiction clause 567]
573. brave(paul) | ~patient(paul) <- (70) [resolution 541,130]
576. ~patient(paul) <- (~68, 70) [subsumption resolution 573,529]
577. $false <- (24, ~68, 70) [subsumption resolution 576,273]
578. ~24 | 68 | ~70 [avatar contradiction clause 577]
579. $false [avatar sat refutation 281,314,329,386,401,405,408,412,531,564,568,578]
% SZS output end Proof for 6838096808499190378314040
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or humble is patient or wise.
If alice is tall or not patient then someone is both quiet and patient and vice versa.
Everyone who is not calm is both not patient and curious and vice versa.
If lucy is both not wise and wise then someone is wise or not quiet and vice versa.
Everyone who is both not humble and not tall is both calm and not funny and vice versa.
Everyone who is either curious or not quiet is either not old or calm and vice versa.
If someone is not strong or not creative then someone is humble and vice versa.
If fred is both calm and old then someone is not old or not humble.
Everyone who is either not humble or patient is not wise.
Everyone who is either not rich or not tall is tall or calm and vice versa.
Everyone who is both not happy and not wise is not calm and vice versa.
If someone is not patient then susan is both rich and not tall and vice versa.
Everyone who is tall is either not rich or quiet.
If someone is either wise or curious then someone is not funny or not curious.
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.
Someone is curious or tall.
Someone is not wise.
Someone is brave or not kind.
Someone is either not funny or curious.
Alice is not strong. | Alice is not happy. | contradiction | (![X]:((~rich(X)|humble(X))=>(patient(X)|wise(X))))&
(((tall(alice)|~patient(alice)))<=>(?[X]:((quiet(X)&patient(X)))))&
(![X]:(~calm(X)<=>(~patient(X)&curious(X))))&
(((~wise(lucy)&wise(lucy)))<=>(?[X]:((wise(X)|~quiet(X)))))&
(![X]:((~humble(X)&~tall(X))<=>(calm(X)&~funny(X))))&
(![X]:((curious(X)<~>~quiet(X))<=>(~old(X)<~>calm(X))))&
((?[X]:((~strong(X)|~creative(X))))<=>(?[X]:(humble(X))))&
(((calm(fred)&old(fred)))=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:((~humble(X)<~>patient(X))=>~wise(X)))&
(![X]:((~rich(X)<~>~tall(X))<=>(tall(X)|calm(X))))&
(![X]:((~happy(X)&~wise(X))<=>~calm(X)))&
((?[X]:(~patient(X)))<=>((rich(susan)&~tall(susan))))&
(![X]:(tall(X)=>(~rich(X)<~>quiet(X))))&
((?[X]:((wise(X)<~>curious(X))))=>(?[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))))&
(?[X]:(~wise(X)))&
(?[X]:((brave(X)|~kind(X))))&
(?[X]:((~funny(X)<~>curious(X))))&
(~strong(alice)) | ~happy(alice) | [
"p0",
"p2",
"p3",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6245380625222426392944080
% SZS output start Proof for 6245380625222426392944080
1. ! [X0] : ((humble(X0) | ~rich(X0)) => (wise(X0) | patient(X0))) [input p0]
3. ! [X0] : (~calm(X0) <=> (curious(X0) & ~patient(X0))) [input p2]
4. (wise(lucy) & ~wise(lucy)) <=> ? [X0] : (~quiet(X0) | wise(X0)) [input p3]
10. ! [X0] : ((~rich(X0) <~> ~tall(X0)) <=> (calm(X0) | tall(X0))) [input p9]
11. ! [X0] : ((~wise(X0) & ~happy(X0)) <=> ~calm(X0)) [input p10]
22. ~happy(alice) [input hypothesis]
27. ! [X0] : ((wise(X0) | patient(X0)) | (~humble(X0) & rich(X0))) [ennf transformation 1]
28. ! [X0] : (wise(X0) | patient(X0) | (~humble(X0) & rich(X0))) [flattening 27]
42. ! [X0] : ((~calm(X0) | (~curious(X0) | patient(X0))) & ((curious(X0) & ~patient(X0)) | calm(X0))) [nnf transformation 3]
43. ! [X0] : ((~calm(X0) | ~curious(X0) | patient(X0)) & ((curious(X0) & ~patient(X0)) | calm(X0))) [flattening 42]
44. ((wise(lucy) & ~wise(lucy)) | ! [X0] : (quiet(X0) & ~wise(X0))) & (? [X0] : (~quiet(X0) | wise(X0)) | (~wise(lucy) | wise(lucy))) [nnf transformation 4]
45. ((wise(lucy) & ~wise(lucy)) | ! [X0] : (quiet(X0) & ~wise(X0))) & (? [X0] : (~quiet(X0) | wise(X0)) | ~wise(lucy) | wise(lucy)) [flattening 44]
46. ((wise(lucy) & ~wise(lucy)) | ! [X0] : (quiet(X0) & ~wise(X0))) & (? [X1] : (~quiet(X1) | wise(X1)) | ~wise(lucy) | wise(lucy)) [rectify 45]
47. ? [X1] : (~quiet(X1) | wise(X1)) => (~quiet(sK1) | wise(sK1)) [choice axiom]
48. ((wise(lucy) & ~wise(lucy)) | ! [X0] : (quiet(X0) & ~wise(X0))) & ((~quiet(sK1) | wise(sK1)) | ~wise(lucy) | wise(lucy)) [skolemisation 46,47]
60. ! [X0] : ((((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | (~calm(X0) & ~tall(X0))) & ((calm(X0) | tall(X0)) | ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0))))) [nnf transformation 10]
61. ! [X0] : ((((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | (~calm(X0) & ~tall(X0))) & (calm(X0) | tall(X0) | ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0))))) [flattening 60]
62. ! [X0] : (((~wise(X0) & ~happy(X0)) | calm(X0)) & (~calm(X0) | (wise(X0) | happy(X0)))) [nnf transformation 11]
63. ! [X0] : (((~wise(X0) & ~happy(X0)) | calm(X0)) & (~calm(X0) | wise(X0) | happy(X0))) [flattening 62]
87. wise(X0) | patient(X0) | rich(X0) [cnf transformation 28]
94. ~patient(X0) | calm(X0) [cnf transformation 43]
98. ~wise(lucy) | ~wise(X0) [cnf transformation 48]
100. wise(lucy) | ~wise(X0) [cnf transformation 48]
121. calm(X0) | tall(X0) | ~rich(X0) | tall(X0) [cnf transformation 61]
122. ~tall(X0) | ~rich(X0) | ~tall(X0) [cnf transformation 61]
126. ~calm(X0) | wise(X0) | happy(X0) [cnf transformation 63]
128. ~wise(X0) | calm(X0) [cnf transformation 63]
145. ~happy(alice) [cnf transformation 22]
146. calm(X0) | tall(X0) | ~rich(X0) [duplicate literal removal 121]
147. ~tall(X0) | ~rich(X0) [duplicate literal removal 122]
176. 7 <=> wise(lucy) [avatar definition]
181. 8 <=> ! [X0] : ~wise(X0) [avatar definition]
182. ~wise(X0) <- (8) [avatar component clause 181]
183. 8 | 7 [avatar split clause 100,176,181]
185. 8 | ~7 [avatar split clause 98,176,181]
231. ~rich(X0) | calm(X0) [subsumption resolution 146,147]
314. patient(X0) | rich(X0) | calm(X0) [resolution 87,128]
325. patient(X0) | calm(X0) [subsumption resolution 314,231]
326. calm(X0) [subsumption resolution 325,94]
370. wise(X1) | happy(X1) [resolution 126,326]
376. happy(X1) <- (8) [subsumption resolution 370,182]
377. $false <- (8) [resolution 376,145]
379. ~8 [avatar contradiction clause 377]
380. $false [avatar sat refutation 183,185,379]
% SZS output end Proof for 6245380625222426392944080
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not creative or not old then mary is both creative and not patient and vice versa.
Everyone who is not generous is not quiet and vice versa.
Everyone who is either strong or not old is both not humble and strong.
If someone is not funny or not kind then someone is not creative and vice versa.
Everyone who is not happy or old is either curious or not creative and vice versa.
If someone is not brave then john is both tall and not funny and vice versa.
If john is not calm or strong then paul is both not tall and not humble and vice versa.
If fred is both not quiet and not wise then lucy is either not rich or patient.
If susan is both strong and not curious then paul is not funny or funny.
Everyone who is not curious is rich.
If paul is either not creative or not strong then someone is old or not generous and vice versa.
Everyone who is not generous or creative is either curious or not brave and vice versa.
Everyone who is kind is curious or wise.
If someone is either not creative or not patient then fred is generous or tall and vice versa.
If someone is not quiet or curious then mary is both not curious and generous.
Everyone who is not creative is both old and not patient and vice versa.
Alice is either kind or generous.
Someone is both not creative and not calm.
Susan is not kind.
Someone is not generous or not old.
Alice is not generous or not kind.
Someone is both not strong and not generous.
Mary is not humble or rich.
Alice is both humble and generous. | John is funny. | contradiction | ((?[X]:((~creative(X)<~>~old(X))))<=>((creative(mary)&~patient(mary))))&
(![X]:(~generous(X)<=>~quiet(X)))&
(![X]:((strong(X)<~>~old(X))=>(~humble(X)&strong(X))))&
((?[X]:((~funny(X)|~kind(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~happy(X)|old(X))<=>(curious(X)<~>~creative(X))))&
((?[X]:(~brave(X)))<=>((tall(john)&~funny(john))))&
(((~calm(john)|strong(john)))<=>((~tall(paul)&~humble(paul))))&
(((~quiet(fred)&~wise(fred)))=>((~rich(lucy)<~>patient(lucy))))&
(((strong(susan)&~curious(susan)))=>((~funny(paul)|funny(paul))))&
(![X]:(~curious(X)=>rich(X)))&
(((~creative(paul)<~>~strong(paul)))<=>(?[X]:((old(X)|~generous(X)))))&
(![X]:((~generous(X)|creative(X))<=>(curious(X)<~>~brave(X))))&
(![X]:(kind(X)=>(curious(X)|wise(X))))&
((?[X]:((~creative(X)<~>~patient(X))))<=>((generous(fred)|tall(fred))))&
((?[X]:((~quiet(X)|curious(X))))=>((~curious(mary)&generous(mary))))&
(![X]:(~creative(X)<=>(old(X)&~patient(X))))&
((kind(alice)<~>generous(alice)))&
(?[X]:((~creative(X)&~calm(X))))&
(~kind(susan))&
(?[X]:((~generous(X)|~old(X))))&
((~generous(alice)|~kind(alice)))&
(?[X]:((~strong(X)&~generous(X))))&
((~humble(mary)|rich(mary)))&
((humble(alice)&generous(alice))) | funny(john) | [
"p0",
"p5",
"p11",
"p14",
"p15",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1361844729041302420802371
% SZS output start Proof for 1361844729041302420802371
1. ? [X0] : (~creative(X0) <~> ~old(X0)) <=> (~patient(mary) & creative(mary)) [input p0]
6. ? [X0] : ~brave(X0) <=> (~funny(john) & tall(john)) [input p5]
12. ! [X0] : ((creative(X0) | ~generous(X0)) <=> (curious(X0) <~> ~brave(X0))) [input p11]
15. ? [X0] : (curious(X0) | ~quiet(X0)) => (generous(mary) & ~curious(mary)) [input p14]
16. ! [X0] : (~creative(X0) <=> (~patient(X0) & old(X0))) [input p15]
18. ? [X0] : (~calm(X0) & ~creative(X0)) [input p17]
22. ? [X0] : (~generous(X0) & ~strong(X0)) [input p21]
25. funny(john) [input hypothesis]
34. (generous(mary) & ~curious(mary)) | ! [X0] : (~curious(X0) & quiet(X0)) [ennf transformation 15]
35. (? [X0] : ((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | (patient(mary) | ~creative(mary))) & ((~patient(mary) & creative(mary)) | ! [X0] : ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0)))) [nnf transformation 1]
36. (? [X0] : ((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | patient(mary) | ~creative(mary)) & ((~patient(mary) & creative(mary)) | ! [X0] : ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0)))) [flattening 35]
37. (? [X0] : ((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | patient(mary) | ~creative(mary)) & ((~patient(mary) & creative(mary)) | ! [X1] : ((~creative(X1) | old(X1)) & (~old(X1) | creative(X1)))) [rectify 36]
38. ? [X0] : ((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) => ((old(sK0) | creative(sK0)) & (~old(sK0) | ~creative(sK0))) [choice axiom]
39. (((old(sK0) | creative(sK0)) & (~old(sK0) | ~creative(sK0))) | patient(mary) | ~creative(mary)) & ((~patient(mary) & creative(mary)) | ! [X1] : ((~creative(X1) | old(X1)) & (~old(X1) | creative(X1)))) [skolemisation 37,38]
49. (? [X0] : ~brave(X0) | (funny(john) | ~tall(john))) & ((~funny(john) & tall(john)) | ! [X0] : brave(X0)) [nnf transformation 6]
50. (? [X0] : ~brave(X0) | funny(john) | ~tall(john)) & ((~funny(john) & tall(john)) | ! [X0] : brave(X0)) [flattening 49]
51. (? [X0] : ~brave(X0) | funny(john) | ~tall(john)) & ((~funny(john) & tall(john)) | ! [X1] : brave(X1)) [rectify 50]
52. ? [X0] : ~brave(X0) => ~brave(sK3) [choice axiom]
53. (~brave(sK3) | funny(john) | ~tall(john)) & ((~funny(john) & tall(john)) | ! [X1] : brave(X1)) [skolemisation 51,52]
60. ! [X0] : (((creative(X0) | ~generous(X0)) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | (~creative(X0) & generous(X0)))) [nnf transformation 12]
61. ! [X0] : ((creative(X0) | ~generous(X0) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | (~creative(X0) & generous(X0)))) [flattening 60]
67. ! [X0] : ((~creative(X0) | (patient(X0) | ~old(X0))) & ((~patient(X0) & old(X0)) | creative(X0))) [nnf transformation 16]
68. ! [X0] : ((~creative(X0) | patient(X0) | ~old(X0)) & ((~patient(X0) & old(X0)) | creative(X0))) [flattening 67]
70. ? [X0] : (~calm(X0) & ~creative(X0)) => (~calm(sK6) & ~creative(sK6)) [choice axiom]
71. ~calm(sK6) & ~creative(sK6) [skolemisation 18,70]
74. ? [X0] : (~generous(X0) & ~strong(X0)) => (~generous(sK8) & ~strong(sK8)) [choice axiom]
75. ~generous(sK8) & ~strong(sK8) [skolemisation 22,74]
76. creative(mary) | ~old(X1) | creative(X1) [cnf transformation 39]
98. ~funny(john) | brave(X1) [cnf transformation 53]
112. ~brave(X0) | curious(X0) | generous(X0) [cnf transformation 61]
113. ~brave(X0) | curious(X0) | ~creative(X0) [cnf transformation 61]
125. ~curious(mary) | ~curious(X0) [cnf transformation 34]
128. old(X0) | creative(X0) [cnf transformation 68]
133. ~creative(sK6) [cnf transformation 71]
139. ~generous(sK8) [cnf transformation 75]
142. funny(john) [cnf transformation 25]
145. 1 <=> creative(mary) [avatar definition]
146. creative(mary) <- (1) [avatar component clause 145]
167. 6 <=> ! [X1] : (~old(X1) | creative(X1)) [avatar definition]
168. ~old(X1) | creative(X1) <- (6) [avatar component clause 167]
171. 6 | 1 [avatar split clause 76,145,167]
173. 7 <=> ! [X1] : creative(X1) [avatar definition]
174. creative(X1) <- (7) [avatar component clause 173]
201. 14 <=> funny(john) [avatar definition]
210. 16 <=> ! [X1] : brave(X1) [avatar definition]
211. brave(X1) <- (16) [avatar component clause 210]
212. 16 | ~14 [avatar split clause 98,201,210]
236. 21 <=> ! [X0] : generous(X0) [avatar definition]
237. generous(X0) <- (21) [avatar component clause 236]
292. 33 <=> ! [X0] : ~curious(X0) [avatar definition]
293. ~curious(X0) <- (33) [avatar component clause 292]
304. 36 <=> curious(mary) [avatar definition]
307. 33 | ~36 [avatar split clause 125,304,292]
331. 14 [avatar split clause 142,201]
332. creative(X1) <- (6) [subsumption resolution 168,128]
333. 7 | ~6 [avatar split clause 332,167,173]
335. $false <- (7) [resolution 174,133]
338. ~7 [avatar contradiction clause 335]
418. curious(X0) | generous(X0) <- (16) [resolution 112,211]
419. ~creative(X0) | curious(X0) <- (16) [resolution 113,211]
446. curious(mary) <- (1, 16) [resolution 419,146]
453. 36 | ~1 | ~16 [avatar split clause 446,210,145,304]
459. generous(X0) <- (16, 33) [resolution 293,418]
460. 21 | ~16 | ~33 [avatar split clause 459,292,210,236]
465. $false <- (21) [resolution 237,139]
466. ~21 [avatar contradiction clause 465]
470. $false [avatar sat refutation 171,212,307,331,333,338,453,460,466]
% SZS output end Proof for 1361844729041302420802371
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong then someone is not rich or not kind.
Everyone who is strong is either not quiet or strong and vice versa.
If someone is either not curious or not happy then someone is patient.
Everyone who is both calm and not happy is both calm and not funny and vice versa.
Everyone who is patient or not generous is generous.
Everyone who is not quiet is old or rich.
If john is not humble or curious then susan is both not wise and not curious.
Everyone who is both not patient and humble is either strong or not quiet.
Everyone who is both not kind and not happy is funny or not kind.
If someone is both not strong and not rich then someone is either calm or quiet and vice versa.
If someone is not happy or old then someone is both not curious and funny and vice versa.
Everyone who is both happy and not quiet is not kind or humble.
Everyone who is both funny and not creative is either calm or patient.
If susan is not calm or not curious then lucy is not generous and vice versa.
Everyone who is either old or not creative is not patient or tall and vice versa.
Someone is quiet or not patient.
Someone is patient or curious.
Fred is either not old or brave.
John is both not creative and not rich.
Mary is both not old and strong.
Paul is either humble or not old.
Someone is both not patient and not brave. | Fred is not funny. | neutral | ((?[X]:(strong(X)))=>(?[X]:((~rich(X)|~kind(X)))))&
(![X]:(strong(X)<=>(~quiet(X)<~>strong(X))))&
((?[X]:((~curious(X)<~>~happy(X))))=>(?[X]:(patient(X))))&
(![X]:((calm(X)&~happy(X))<=>(calm(X)&~funny(X))))&
(![X]:((patient(X)|~generous(X))=>generous(X)))&
(![X]:(~quiet(X)=>(old(X)|rich(X))))&
(((~humble(john)|curious(john)))=>((~wise(susan)&~curious(susan))))&
(![X]:((~patient(X)&humble(X))=>(strong(X)<~>~quiet(X))))&
(![X]:((~kind(X)&~happy(X))=>(funny(X)|~kind(X))))&
((?[X]:((~strong(X)&~rich(X))))<=>(?[X]:((calm(X)<~>quiet(X)))))&
((?[X]:((~happy(X)|old(X))))<=>(?[X]:((~curious(X)&funny(X)))))&
(![X]:((happy(X)&~quiet(X))=>(~kind(X)|humble(X))))&
(![X]:((funny(X)&~creative(X))=>(calm(X)<~>patient(X))))&
(((~calm(susan)|~curious(susan)))<=>(~generous(lucy)))&
(![X]:((old(X)<~>~creative(X))<=>(~patient(X)|tall(X))))&
(?[X]:((quiet(X)|~patient(X))))&
(?[X]:((patient(X)|curious(X))))&
((~old(fred)<~>brave(fred)))&
((~creative(john)&~rich(john)))&
((~old(mary)&strong(mary)))&
((humble(paul)<~>~old(paul)))&
(?[X]:((~patient(X)&~brave(X)))) | ~funny(fred) | [] | null | 0 |
If someone is creative or old then lucy is not brave and vice versa. Everyone who is either curious or not old is not old or strong and vice versa. Everyone who is kind or calm is either not happy or brave and vice versa. If someone is both not brave and quiet then someone is kind or brave and vice versa. Everyone who is both kind and not happy is kind or patient and vice versa. If someone is both not strong and not curious then fred is calm. Everyone who is humble or not wise is both wise and not calm and vice versa. Everyone who is either creative or not patient is either not quiet or not wise and vice versa. If someone is quiet then someone is both calm and brave and vice versa. If someone is both humble and not humble then someone is both not quiet and kind. Everyone who is either rich or not wise is patient or not creative and vice versa. Everyone who is not curious is not quiet or tall and vice versa. Everyone who is either not happy or creative is not happy or kind. Everyone who is funny or creative is either not creative or patient. If susan is both not creative and not old then someone is either kind or happy and vice versa. Everyone who is both not funny and not tall is not generous and vice versa. Mary is tall. John is both humble and not tall. Mary is calm or not brave. Mary is not quiet. Alice is not funny. Mary is either curious or not funny. | Mary is not wise. | contradiction | ((?[X]:((creative(X)|old(X))))<=>(~brave(lucy)))&
(![X]:((curious(X)<~>~old(X))<=>(~old(X)|strong(X))))&
(![X]:((kind(X)|calm(X))<=>(~happy(X)<~>brave(X))))&
((?[X]:((~brave(X)&quiet(X))))<=>(?[X]:((kind(X)|brave(X)))))&
(![X]:((kind(X)&~happy(X))<=>(kind(X)|patient(X))))&
((?[X]:((~strong(X)&~curious(X))))=>(calm(fred)))&
(![X]:((humble(X)|~wise(X))<=>(wise(X)&~calm(X))))&
(![X]:((creative(X)<~>~patient(X))<=>(~quiet(X)<~>~wise(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((calm(X)&brave(X)))))&
((?[X]:((humble(X)&~humble(X))))=>(?[X]:((~quiet(X)&kind(X)))))&
(![X]:((rich(X)<~>~wise(X))<=>(patient(X)|~creative(X))))&
(![X]:(~curious(X)<=>(~quiet(X)|tall(X))))&
(![X]:((~happy(X)<~>creative(X))=>(~happy(X)|kind(X))))&
(![X]:((funny(X)|creative(X))=>(~creative(X)<~>patient(X))))&
(((~creative(susan)&~old(susan)))<=>(?[X]:((kind(X)<~>happy(X)))))&
(![X]:((~funny(X)&~tall(X))<=>~generous(X)))&
(tall(mary))&
((humble(john)&~tall(john)))&
((calm(mary)|~brave(mary)))&
(~quiet(mary))&
(~funny(alice))&
((curious(mary)<~>~funny(mary))) | ~wise(mary) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6693759892162126570771190
% SZS output start Proof for 6693759892162126570771190
7. ! [X0] : ((~wise(X0) | humble(X0)) <=> (~calm(X0) & wise(X0))) [input p6]
23. ~wise(mary) [input hypothesis]
47. ! [X0] : (((~wise(X0) | humble(X0)) | (calm(X0) | ~wise(X0))) & ((~calm(X0) & wise(X0)) | (wise(X0) & ~humble(X0)))) [nnf transformation 7]
48. ! [X0] : ((~wise(X0) | humble(X0) | calm(X0) | ~wise(X0)) & ((~calm(X0) & wise(X0)) | (wise(X0) & ~humble(X0)))) [flattening 47]
97. wise(X0) | wise(X0) [cnf transformation 48]
143. ~wise(mary) [cnf transformation 23]
146. wise(X0) [duplicate literal removal 97]
287. $false [subsumption resolution 143,146]
% SZS output end Proof for 6693759892162126570771190
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not curious then lucy is not strong.
If someone is either not curious or not happy then paul is both not tall and tall and vice versa.
If alice is not funny or not quiet then mary is either happy or brave and vice versa.
If someone is creative then paul is both not old and kind and vice versa.
Everyone who is brave is either not creative or brave and vice versa.
Everyone who is both not brave and not kind is not funny.
Everyone who is either not tall or not brave is strong or not creative.
If alice is quiet or funny then someone is either not quiet or quiet and vice versa.
Everyone who is both creative and funny is calm.
Everyone who is humble or quiet is both not creative and not rich.
If someone is either old or not creative then someone is either strong or not tall and vice versa.
Everyone who is either tall or not quiet is either humble or generous and vice versa.
Everyone who is both not humble and old is both not quiet and curious and vice versa.
Everyone who is not brave is not happy.
Fred is not happy or not wise.
Someone is both not strong and not curious.
Someone is not quiet or rich.
John is both not kind and patient.
Lucy is not creative or tall.
Someone is either kind or not happy.
Someone is either old or not brave.
Paul is either happy or not humble. | Paul is creative. | entailment | ((~curious(paul))=>(~strong(lucy)))&
((?[X]:((~curious(X)<~>~happy(X))))<=>((~tall(paul)&tall(paul))))&
(((~funny(alice)|~quiet(alice)))<=>((happy(mary)<~>brave(mary))))&
((?[X]:(creative(X)))<=>((~old(paul)&kind(paul))))&
(![X]:(brave(X)<=>(~creative(X)<~>brave(X))))&
(![X]:((~brave(X)&~kind(X))=>~funny(X)))&
(![X]:((~tall(X)<~>~brave(X))=>(strong(X)|~creative(X))))&
(((quiet(alice)|funny(alice)))<=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:((creative(X)&funny(X))=>calm(X)))&
(![X]:((humble(X)|quiet(X))=>(~creative(X)&~rich(X))))&
((?[X]:((old(X)<~>~creative(X))))<=>(?[X]:((strong(X)<~>~tall(X)))))&
(![X]:((tall(X)<~>~quiet(X))<=>(humble(X)<~>generous(X))))&
(![X]:((~humble(X)&old(X))<=>(~quiet(X)&curious(X))))&
(![X]:(~brave(X)=>~happy(X)))&
((~happy(fred)|~wise(fred)))&
(?[X]:((~strong(X)&~curious(X))))&
(?[X]:((~quiet(X)|rich(X))))&
((~kind(john)&patient(john)))&
((~creative(lucy)|tall(lucy)))&
(?[X]:((kind(X)<~>~happy(X))))&
(?[X]:((old(X)<~>~brave(X))))&
((happy(paul)<~>~humble(paul))) | creative(paul) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 809648867900940074178435
% SZS output start Proof for 809648867900940074178435
5. ! [X0] : (brave(X0) <=> (~creative(X0) <~> brave(X0))) [input p4]
23. ~creative(paul) [input hypothesis]
47. ! [X0] : ((brave(X0) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | ~brave(X0))) [nnf transformation 5]
90. ~brave(X0) | creative(X0) | ~brave(X0) [cnf transformation 47]
91. brave(X0) | brave(X0) | creative(X0) [cnf transformation 47]
138. ~creative(paul) [cnf transformation 23]
141. ~brave(X0) | creative(X0) [duplicate literal removal 90]
142. brave(X0) | creative(X0) [duplicate literal removal 91]
206. creative(X0) [subsumption resolution 141,142]
278. $false [subsumption resolution 138,206]
% SZS output end Proof for 809648867900940074178435
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is strong or not generous then someone is funny.
If paul is curious then susan is either not happy or funny and vice versa.
Everyone who is either not brave or not kind is quiet.
Everyone who is not patient is both patient and not humble and vice versa.
If john is either quiet or curious then someone is either strong or not happy.
Everyone who is tall or calm is both curious and not generous and vice versa.
If alice is both not quiet and not funny then someone is not generous or patient and vice versa.
If fred is either rich or brave then someone is not rich or kind and vice versa.
Everyone who is not rich or not creative is both brave and not patient and vice versa.
Everyone who is both rich and not happy is both wise and tall.
If lucy is both not tall and not wise then alice is both not strong and curious.
If someone is calm or not old then someone is both strong and not humble.
If mary is either rich or funny then alice is both not generous and strong and vice versa.
If someone is either funny or happy then someone is both patient and strong.
Everyone who is not humble is strong and vice versa.
Someone is either not patient or not tall.
Paul is both curious and not generous.
Someone is either kind or not wise.
Someone is either not quiet or wise.
John is both not curious and patient.
Someone is not curious. | Alice is patient. | entailment | (((strong(lucy)|~generous(lucy)))=>(?[X]:(funny(X))))&
((curious(paul))<=>((~happy(susan)<~>funny(susan))))&
(![X]:((~brave(X)<~>~kind(X))=>quiet(X)))&
(![X]:(~patient(X)<=>(patient(X)&~humble(X))))&
(((quiet(john)<~>curious(john)))=>(?[X]:((strong(X)<~>~happy(X)))))&
(![X]:((tall(X)|calm(X))<=>(curious(X)&~generous(X))))&
(((~quiet(alice)&~funny(alice)))<=>(?[X]:((~generous(X)|patient(X)))))&
(((rich(fred)<~>brave(fred)))<=>(?[X]:((~rich(X)|kind(X)))))&
(![X]:((~rich(X)|~creative(X))<=>(brave(X)&~patient(X))))&
(![X]:((rich(X)&~happy(X))=>(wise(X)&tall(X))))&
(((~tall(lucy)&~wise(lucy)))=>((~strong(alice)&curious(alice))))&
((?[X]:((calm(X)|~old(X))))=>(?[X]:((strong(X)&~humble(X)))))&
(((rich(mary)<~>funny(mary)))<=>((~generous(alice)&strong(alice))))&
((?[X]:((funny(X)<~>happy(X))))=>(?[X]:((patient(X)&strong(X)))))&
(![X]:(~humble(X)<=>strong(X)))&
(?[X]:((~patient(X)<~>~tall(X))))&
((curious(paul)&~generous(paul)))&
(?[X]:((kind(X)<~>~wise(X))))&
(?[X]:((~quiet(X)<~>wise(X))))&
((~curious(john)&patient(john)))&
(?[X]:(~curious(X))) | patient(alice) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 1912827734918510748125907
% SZS output start Proof for 1912827734918510748125907
4. ! [X0] : (~patient(X0) <=> (~humble(X0) & patient(X0))) [input p3]
22. ~patient(alice) [input hypothesis]
39. ! [X0] : ((~patient(X0) | (humble(X0) | ~patient(X0))) & ((~humble(X0) & patient(X0)) | patient(X0))) [nnf transformation 4]
40. ! [X0] : ((~patient(X0) | humble(X0) | ~patient(X0)) & ((~humble(X0) & patient(X0)) | patient(X0))) [flattening 39]
86. patient(X0) | patient(X0) [cnf transformation 40]
143. ~patient(alice) [cnf transformation 22]
144. patient(X0) [duplicate literal removal 86]
313. $false [subsumption resolution 143,144]
% SZS output end Proof for 1912827734918510748125907
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both calm and not humble then susan is either calm or patient and vice versa.
Everyone who is not old or not brave is both patient and not happy.
If paul is either calm or not curious then someone is either wise or not generous.
Everyone who is both happy and not rich is both generous and quiet.
Everyone who is either not rich or tall is either not quiet or rich and vice versa.
If paul is either not calm or happy then someone is not quiet and vice versa.
Everyone who is not quiet is both not generous and not tall.
Everyone who is both happy and old is either not humble or not rich.
Everyone who is rich is both calm and not tall and vice versa.
Everyone who is brave is not strong and vice versa.
If someone is brave then someone is both not wise and funny and vice versa.
Everyone who is both patient and kind is both rich and wise and vice versa.
Everyone who is not brave or brave is brave or not creative and vice versa.
Everyone who is not strong or patient is both rich and funny.
Everyone who is both calm and not rich is both not old and wise and vice versa.
If someone is both not old and old then someone is not funny and vice versa.
Susan is patient or not kind.
Someone is not kind.
Someone is both not kind and not strong.
John is both not patient and not humble.
Lucy is either not wise or curious.
Paul is either quiet or brave.
Someone is either not creative or old. | Lucy is generous. | contradiction | (((calm(fred)&~humble(fred)))<=>((calm(susan)<~>patient(susan))))&
(![X]:((~old(X)|~brave(X))=>(patient(X)&~happy(X))))&
(((calm(paul)<~>~curious(paul)))=>(?[X]:((wise(X)<~>~generous(X)))))&
(![X]:((happy(X)&~rich(X))=>(generous(X)&quiet(X))))&
(![X]:((~rich(X)<~>tall(X))<=>(~quiet(X)<~>rich(X))))&
(((~calm(paul)<~>happy(paul)))<=>(?[X]:(~quiet(X))))&
(![X]:(~quiet(X)=>(~generous(X)&~tall(X))))&
(![X]:((happy(X)&old(X))=>(~humble(X)<~>~rich(X))))&
(![X]:(rich(X)<=>(calm(X)&~tall(X))))&
(![X]:(brave(X)<=>~strong(X)))&
((?[X]:(brave(X)))<=>(?[X]:((~wise(X)&funny(X)))))&
(![X]:((patient(X)&kind(X))<=>(rich(X)&wise(X))))&
(![X]:((~brave(X)|brave(X))<=>(brave(X)|~creative(X))))&
(![X]:((~strong(X)|patient(X))=>(rich(X)&funny(X))))&
(![X]:((calm(X)&~rich(X))<=>(~old(X)&wise(X))))&
((?[X]:((~old(X)&old(X))))<=>(?[X]:(~funny(X))))&
((patient(susan)|~kind(susan)))&
(?[X]:(~kind(X)))&
(?[X]:((~kind(X)&~strong(X))))&
((~patient(john)&~humble(john)))&
((~wise(lucy)<~>curious(lucy)))&
((quiet(paul)<~>brave(paul)))&
(?[X]:((~creative(X)<~>old(X)))) | generous(lucy) | [
"p1",
"p4",
"p6",
"p8",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 404668847648307571864581
% SZS output start Proof for 404668847648307571864581
2. ! [X0] : ((~brave(X0) | ~old(X0)) => (~happy(X0) & patient(X0))) [input p1]
5. ! [X0] : ((~rich(X0) <~> tall(X0)) <=> (~quiet(X0) <~> rich(X0))) [input p4]
7. ! [X0] : (~quiet(X0) => (~tall(X0) & ~generous(X0))) [input p6]
9. ! [X0] : (rich(X0) <=> (~tall(X0) & calm(X0))) [input p8]
10. ! [X0] : (brave(X0) <=> ~strong(X0)) [input p9]
14. ! [X0] : ((patient(X0) | ~strong(X0)) => (funny(X0) & rich(X0))) [input p13]
24. generous(lucy) [input hypothesis]
27. ! [X0] : ((~happy(X0) & patient(X0)) | (brave(X0) & old(X0))) [ennf transformation 2]
31. ! [X0] : ((~tall(X0) & ~generous(X0)) | quiet(X0)) [ennf transformation 7]
34. ! [X0] : ((funny(X0) & rich(X0)) | (~patient(X0) & strong(X0))) [ennf transformation 14]
40. ! [X0] : ((((~tall(X0) | rich(X0)) & (tall(X0) | ~rich(X0))) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0)))) & (((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | ((~rich(X0) | ~tall(X0)) & (tall(X0) | rich(X0))))) [nnf transformation 5]
46. ! [X0] : ((rich(X0) | (tall(X0) | ~calm(X0))) & ((~tall(X0) & calm(X0)) | ~rich(X0))) [nnf transformation 9]
47. ! [X0] : ((rich(X0) | tall(X0) | ~calm(X0)) & ((~tall(X0) & calm(X0)) | ~rich(X0))) [flattening 46]
48. ! [X0] : ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))) [nnf transformation 10]
81. brave(X0) | patient(X0) [cnf transformation 27]
90. rich(X0) | ~quiet(X0) | tall(X0) | rich(X0) [cnf transformation 40]
95. tall(X0) | ~rich(X0) | ~quiet(X0) | ~rich(X0) [cnf transformation 40]
102. ~generous(X0) | quiet(X0) [cnf transformation 31]
107. ~tall(X0) | ~rich(X0) [cnf transformation 47]
109. ~strong(X0) | ~brave(X0) [cnf transformation 48]
122. strong(X0) | rich(X0) [cnf transformation 34]
123. ~patient(X0) | rich(X0) [cnf transformation 34]
145. generous(lucy) [cnf transformation 24]
148. rich(X0) | ~quiet(X0) | tall(X0) [duplicate literal removal 90]
150. tall(X0) | ~rich(X0) | ~quiet(X0) [duplicate literal removal 95]
195. ~quiet(X0) | tall(X0) [subsumption resolution 148,150]
287. quiet(lucy) [resolution 102,145]
291. ~brave(X0) | rich(X0) [resolution 122,109]
305. tall(lucy) [resolution 195,287]
314. ~rich(lucy) [resolution 305,107]
317. rich(X0) | patient(X0) [resolution 291,81]
321. rich(X0) [subsumption resolution 317,123]
323. $false [resolution 321,314]
% SZS output end Proof for 404668847648307571864581
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is rich or not humble then alice is happy.
Everyone who is either not patient or not generous is funny or not generous.
If someone is either not creative or not strong then someone is either not creative or patient and vice versa.
If someone is both calm and not brave then lucy is curious or not calm and vice versa.
Everyone who is both not patient and not quiet is old or happy and vice versa.
Everyone who is not calm or generous is either creative or funny and vice versa.
If john is either not creative or strong then someone is not calm and vice versa.
If someone is not kind then lucy is both old and not wise.
If fred is both not quiet and not curious then lucy is humble and vice versa.
Everyone who is not generous or patient is not creative.
Everyone who is both not tall and humble is strong and vice versa.
If fred is both funny and not kind then someone is not humble or calm and vice versa.
If susan is either rich or wise then someone is calm or wise and vice versa.
Everyone who is patient is either generous or not tall and vice versa.
Everyone who is not tall or not rich is calm.
If mary is both humble and not patient then susan is not kind and vice versa.
Someone is either not patient or strong.
Mary is either tall or not calm.
John is both not old and not tall.
Someone is not creative.
Someone is either not calm or not rich.
Someone is not creative or humble.
Someone is either old or not tall.
Fred is both not humble and quiet. | Susan is not creative. | entailment | ((?[X]:((rich(X)|~humble(X))))=>(happy(alice)))&
(![X]:((~patient(X)<~>~generous(X))=>(funny(X)|~generous(X))))&
((?[X]:((~creative(X)<~>~strong(X))))<=>(?[X]:((~creative(X)<~>patient(X)))))&
((?[X]:((calm(X)&~brave(X))))<=>((curious(lucy)|~calm(lucy))))&
(![X]:((~patient(X)&~quiet(X))<=>(old(X)|happy(X))))&
(![X]:((~calm(X)|generous(X))<=>(creative(X)<~>funny(X))))&
(((~creative(john)<~>strong(john)))<=>(?[X]:(~calm(X))))&
((?[X]:(~kind(X)))=>((old(lucy)&~wise(lucy))))&
(((~quiet(fred)&~curious(fred)))<=>(humble(lucy)))&
(![X]:((~generous(X)|patient(X))=>~creative(X)))&
(![X]:((~tall(X)&humble(X))<=>strong(X)))&
(((funny(fred)&~kind(fred)))<=>(?[X]:((~humble(X)|calm(X)))))&
(((rich(susan)<~>wise(susan)))<=>(?[X]:((calm(X)|wise(X)))))&
(![X]:(patient(X)<=>(generous(X)<~>~tall(X))))&
(![X]:((~tall(X)|~rich(X))=>calm(X)))&
(((humble(mary)&~patient(mary)))<=>(~kind(susan)))&
(?[X]:((~patient(X)<~>strong(X))))&
((tall(mary)<~>~calm(mary)))&
((~old(john)&~tall(john)))&
(?[X]:(~creative(X)))&
(?[X]:((~calm(X)<~>~rich(X))))&
(?[X]:((~creative(X)|humble(X))))&
(?[X]:((old(X)<~>~tall(X))))&
((~humble(fred)&quiet(fred))) | ~creative(susan) | [
"p1",
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5633969912634569160345986
% SZS output start Proof for 5633969912634569160345986
2. ! [X0] : ((~patient(X0) <~> ~generous(X0)) => (~generous(X0) | funny(X0))) [input p1]
6. ! [X0] : ((generous(X0) | ~calm(X0)) <=> (creative(X0) <~> funny(X0))) [input p5]
10. ! [X0] : ((patient(X0) | ~generous(X0)) => ~creative(X0)) [input p9]
25. creative(susan) [input hypothesis]
28. ! [X0] : ((~generous(X0) | funny(X0)) | (~patient(X0) <=> ~generous(X0))) [ennf transformation 2]
29. ! [X0] : (~generous(X0) | funny(X0) | (~patient(X0) <=> ~generous(X0))) [flattening 28]
31. ! [X0] : (~creative(X0) | (~patient(X0) & generous(X0))) [ennf transformation 10]
33. ! [X0] : (~generous(X0) | funny(X0) | ((~patient(X0) | generous(X0)) & (~generous(X0) | patient(X0)))) [nnf transformation 29]
46. ! [X0] : (((generous(X0) | ~calm(X0)) | ((creative(X0) | ~funny(X0)) & (funny(X0) | ~creative(X0)))) & (((~funny(X0) | ~creative(X0)) & (funny(X0) | creative(X0))) | (~generous(X0) & calm(X0)))) [nnf transformation 6]
47. ! [X0] : ((generous(X0) | ~calm(X0) | ((creative(X0) | ~funny(X0)) & (funny(X0) | ~creative(X0)))) & (((~funny(X0) | ~creative(X0)) & (funny(X0) | creative(X0))) | (~generous(X0) & calm(X0)))) [flattening 46]
84. ~generous(X0) | funny(X0) | ~generous(X0) | patient(X0) [cnf transformation 33]
107. ~creative(X0) | ~funny(X0) | ~generous(X0) [cnf transformation 47]
119. ~creative(X0) | generous(X0) [cnf transformation 31]
120. ~creative(X0) | ~patient(X0) [cnf transformation 31]
158. creative(susan) [cnf transformation 25]
159. ~generous(X0) | funny(X0) | patient(X0) [duplicate literal removal 84]
173. 4 <=> ! [X1] : (~creative(X1) | ~patient(X1)) [avatar definition]
174. ~creative(X1) | ~patient(X1) <- (4) [avatar component clause 173]
279. 4 [avatar split clause 120,173]
392. generous(susan) [resolution 119,158]
399. ~patient(susan) <- (4) [resolution 174,158]
458. 53 <=> funny(susan) [avatar definition]
474. ~funny(susan) | ~generous(susan) [resolution 107,158]
527. funny(susan) | patient(susan) [resolution 159,392]
657. funny(susan) <- (4) [subsumption resolution 527,399]
658. 53 | ~4 [avatar split clause 657,173,458]
659. ~funny(susan) [subsumption resolution 474,392]
660. ~53 [avatar split clause 659,458]
665. $false [avatar sat refutation 279,658,660]
% SZS output end Proof for 5633969912634569160345986
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is rich then john is both happy and strong.
If someone is not kind then someone is tall and vice versa.
If someone is strong or humble then someone is quiet and vice versa.
Everyone who is both not quiet and not generous is old or generous.
Everyone who is tall or calm is both not patient and not kind and vice versa.
If john is both not quiet and not rich then susan is not curious or not strong.
Everyone who is not strong or wise is not tall.
Everyone who is either not old or rich is not quiet or funny and vice versa.
Everyone who is patient is wise or patient and vice versa.
If someone is both quiet and not generous then fred is not funny or not quiet.
If susan is either generous or not brave then someone is both not creative and happy and vice versa.
Everyone who is either old or not quiet is not strong.
Everyone who is both not tall and patient is creative or strong and vice versa.
If someone is either creative or not happy then someone is either not patient or strong and vice versa.
Everyone who is both humble and happy is both curious and creative and vice versa.
If someone is not old or tall then fred is both not funny and funny and vice versa.
Mary is not calm.
Susan is either not calm or not funny.
Lucy is not creative.
Lucy is wise.
Paul is both not wise and old.
Someone is both not generous and humble.
Someone is rich.
Paul is quiet. | Susan is old. | entailment | ((?[X]:(rich(X)))=>((happy(john)&strong(john))))&
((?[X]:(~kind(X)))<=>(?[X]:(tall(X))))&
((?[X]:((strong(X)|humble(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~quiet(X)&~generous(X))=>(old(X)|generous(X))))&
(![X]:((tall(X)|calm(X))<=>(~patient(X)&~kind(X))))&
(((~quiet(john)&~rich(john)))=>((~curious(susan)|~strong(susan))))&
(![X]:((~strong(X)|wise(X))=>~tall(X)))&
(![X]:((~old(X)<~>rich(X))<=>(~quiet(X)|funny(X))))&
(![X]:(patient(X)<=>(wise(X)|patient(X))))&
((?[X]:((quiet(X)&~generous(X))))=>((~funny(fred)|~quiet(fred))))&
(((generous(susan)<~>~brave(susan)))<=>(?[X]:((~creative(X)&happy(X)))))&
(![X]:((old(X)<~>~quiet(X))=>~strong(X)))&
(![X]:((~tall(X)&patient(X))<=>(creative(X)|strong(X))))&
((?[X]:((creative(X)<~>~happy(X))))<=>(?[X]:((~patient(X)<~>strong(X)))))&
(![X]:((humble(X)&happy(X))<=>(curious(X)&creative(X))))&
((?[X]:((~old(X)|tall(X))))<=>((~funny(fred)&funny(fred))))&
(~calm(mary))&
((~calm(susan)<~>~funny(susan)))&
(~creative(lucy))&
(wise(lucy))&
((~wise(paul)&old(paul)))&
(?[X]:((~generous(X)&humble(X))))&
(?[X]:(rich(X)))&
(quiet(paul)) | old(susan) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6022018582335925440453397
% SZS output start Proof for 6022018582335925440453397
16. ? [X0] : (tall(X0) | ~old(X0)) <=> (funny(fred) & ~funny(fred)) [input p15]
25. ~old(susan) [input hypothesis]
68. (? [X0] : (tall(X0) | ~old(X0)) | (~funny(fred) | funny(fred))) & ((funny(fred) & ~funny(fred)) | ! [X0] : (~tall(X0) & old(X0))) [nnf transformation 16]
69. (? [X0] : (tall(X0) | ~old(X0)) | ~funny(fred) | funny(fred)) & ((funny(fred) & ~funny(fred)) | ! [X0] : (~tall(X0) & old(X0))) [flattening 68]
70. (? [X0] : (tall(X0) | ~old(X0)) | ~funny(fred) | funny(fred)) & ((funny(fred) & ~funny(fred)) | ! [X1] : (~tall(X1) & old(X1))) [rectify 69]
71. ? [X0] : (tall(X0) | ~old(X0)) => (tall(sK7) | ~old(sK7)) [choice axiom]
72. ((tall(sK7) | ~old(sK7)) | ~funny(fred) | funny(fred)) & ((funny(fred) & ~funny(fred)) | ! [X1] : (~tall(X1) & old(X1))) [skolemisation 70,71]
129. ~funny(fred) | old(X1) [cnf transformation 72]
131. funny(fred) | old(X1) [cnf transformation 72]
145. ~old(susan) [cnf transformation 25]
221. 19 <=> funny(fred) [avatar definition]
294. 33 <=> ! [X1] : old(X1) [avatar definition]
295. old(X1) <- (33) [avatar component clause 294]
296. 33 | 19 [avatar split clause 131,221,294]
298. 33 | ~19 [avatar split clause 129,221,294]
309. $false <- (33) [resolution 295,145]
310. ~33 [avatar contradiction clause 309]
311. $false [avatar sat refutation 296,298,310]
% SZS output end Proof for 6022018582335925440453397
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either quiet or calm then someone is either calm or brave and vice versa.
Everyone who is not happy or not strong is either not calm or not brave.
If someone is either kind or not old then lucy is either not old or rich and vice versa.
Everyone who is tall or not calm is not calm or not quiet and vice versa.
If alice is either kind or strong then someone is curious and vice versa.
Everyone who is either not patient or happy is not rich or tall and vice versa.
If someone is creative or not tall then someone is funny and vice versa.
Everyone who is either not creative or calm is both not happy and happy and vice versa.
If john is not wise or not calm then fred is both not creative and not rich and vice versa.
Everyone who is old or not tall is not generous or not brave.
Everyone who is either not tall or not patient is either strong or not strong and vice versa.
If someone is either not kind or not rich then mary is either not generous or tall.
Everyone who is either strong or not curious is both not happy and creative and vice versa.
Everyone who is either not quiet or strong is wise or curious.
Everyone who is happy or not humble is either not curious or not patient.
Everyone who is kind is either not generous or brave and vice versa.
Someone is both not calm and humble.
Alice is both strong and rich.
Mary is either not happy or not wise.
Paul is either not creative or patient.
Fred is either curious or happy.
Alice is not humble.
Someone is either not strong or creative. | Paul is generous. | neutral | (((quiet(fred)<~>calm(fred)))<=>(?[X]:((calm(X)<~>brave(X)))))&
(![X]:((~happy(X)|~strong(X))=>(~calm(X)<~>~brave(X))))&
((?[X]:((kind(X)<~>~old(X))))<=>((~old(lucy)<~>rich(lucy))))&
(![X]:((tall(X)|~calm(X))<=>(~calm(X)|~quiet(X))))&
(((kind(alice)<~>strong(alice)))<=>(?[X]:(curious(X))))&
(![X]:((~patient(X)<~>happy(X))<=>(~rich(X)|tall(X))))&
((?[X]:((creative(X)|~tall(X))))<=>(?[X]:(funny(X))))&
(![X]:((~creative(X)<~>calm(X))<=>(~happy(X)&happy(X))))&
(((~wise(john)|~calm(john)))<=>((~creative(fred)&~rich(fred))))&
(![X]:((old(X)|~tall(X))=>(~generous(X)|~brave(X))))&
(![X]:((~tall(X)<~>~patient(X))<=>(strong(X)<~>~strong(X))))&
((?[X]:((~kind(X)<~>~rich(X))))=>((~generous(mary)<~>tall(mary))))&
(![X]:((strong(X)<~>~curious(X))<=>(~happy(X)&creative(X))))&
(![X]:((~quiet(X)<~>strong(X))=>(wise(X)|curious(X))))&
(![X]:((happy(X)|~humble(X))=>(~curious(X)<~>~patient(X))))&
(![X]:(kind(X)<=>(~generous(X)<~>brave(X))))&
(?[X]:((~calm(X)&humble(X))))&
((strong(alice)&rich(alice)))&
((~happy(mary)<~>~wise(mary)))&
((~creative(paul)<~>patient(paul)))&
((curious(fred)<~>happy(fred)))&
(~humble(alice))&
(?[X]:((~strong(X)<~>creative(X)))) | generous(paul) | [] | null | 0 |
Everyone who is either wise or not humble is both not quiet and not wise. If someone is both kind and not calm then someone is not calm and vice versa. If mary is either not kind or not patient then fred is rich. Everyone who is not calm is either creative or not rich. Everyone who is not humble or not patient is not calm or strong. If lucy is not curious then fred is either funny or not funny. Everyone who is happy is both not quiet and quiet and vice versa. Everyone who is not quiet or not funny is not kind or not happy and vice versa. Everyone who is either funny or not old is either not old or not strong and vice versa. Everyone who is both calm and strong is both not funny and not happy and vice versa. If susan is either not curious or patient then someone is not rich or tall and vice versa. Everyone who is both rich and not funny is either not calm or not happy. If paul is either not curious or not brave then john is not calm. Everyone who is either calm or not calm is either wise or not humble. If paul is patient then alice is both not generous and old. Someone is not wise or not generous. Someone is not strong or humble. Someone is either not quiet or rich. Someone is either not tall or not patient. Someone is rich. Someone is either not curious or not rich. Mary is either happy or rich. Someone is not funny. | John is not creative. | neutral | (![X]:((wise(X)<~>~humble(X))=>(~quiet(X)&~wise(X))))&
((?[X]:((kind(X)&~calm(X))))<=>(?[X]:(~calm(X))))&
(((~kind(mary)<~>~patient(mary)))=>(rich(fred)))&
(![X]:(~calm(X)=>(creative(X)<~>~rich(X))))&
(![X]:((~humble(X)|~patient(X))=>(~calm(X)|strong(X))))&
((~curious(lucy))=>((funny(fred)<~>~funny(fred))))&
(![X]:(happy(X)<=>(~quiet(X)&quiet(X))))&
(![X]:((~quiet(X)|~funny(X))<=>(~kind(X)|~happy(X))))&
(![X]:((funny(X)<~>~old(X))<=>(~old(X)<~>~strong(X))))&
(![X]:((calm(X)&strong(X))<=>(~funny(X)&~happy(X))))&
(((~curious(susan)<~>patient(susan)))<=>(?[X]:((~rich(X)|tall(X)))))&
(![X]:((rich(X)&~funny(X))=>(~calm(X)<~>~happy(X))))&
(((~curious(paul)<~>~brave(paul)))=>(~calm(john)))&
(![X]:((calm(X)<~>~calm(X))=>(wise(X)<~>~humble(X))))&
((patient(paul))=>((~generous(alice)&old(alice))))&
(?[X]:((~wise(X)|~generous(X))))&
(?[X]:((~strong(X)|humble(X))))&
(?[X]:((~quiet(X)<~>rich(X))))&
(?[X]:((~tall(X)<~>~patient(X))))&
(?[X]:(rich(X)))&
(?[X]:((~curious(X)<~>~rich(X))))&
((happy(mary)<~>rich(mary)))&
(?[X]:(~funny(X))) | ~creative(john) | [] | null | 0 |
Everyone who is not rich is either calm or not generous.
Everyone who is either calm or quiet is creative and vice versa.
Everyone who is either rich or not happy is not creative.
If mary is both not happy and not old then someone is humble or tall and vice versa.
Everyone who is either not curious or old is not patient and vice versa.
If john is not brave or not wise then someone is generous and vice versa.
If someone is not wise then john is either not kind or calm.
If someone is strong or tall then someone is either not curious or not quiet and vice versa.
Everyone who is not humble or rich is both funny and not generous.
If someone is either wise or strong then john is funny or not rich.
Everyone who is both not funny and generous is either not quiet or happy and vice versa.
If susan is both creative and not tall then someone is not rich or not kind.
If fred is brave then someone is both not strong and strong.
Everyone who is curious is happy.
If alice is either not rich or creative then fred is brave and vice versa.
If susan is patient or not strong then john is either rich or not funny and vice versa.
Someone is both not strong and not calm.
Someone is either not tall or old.
John is not brave.
Alice is curious or creative.
Someone is kind.
Someone is not happy or strong. | Alice is not tall. | neutral | (![X]:(~rich(X)=>(calm(X)<~>~generous(X))))&
(![X]:((calm(X)<~>quiet(X))<=>creative(X)))&
(![X]:((rich(X)<~>~happy(X))=>~creative(X)))&
(((~happy(mary)&~old(mary)))<=>(?[X]:((humble(X)|tall(X)))))&
(![X]:((~curious(X)<~>old(X))<=>~patient(X)))&
(((~brave(john)|~wise(john)))<=>(?[X]:(generous(X))))&
((?[X]:(~wise(X)))=>((~kind(john)<~>calm(john))))&
((?[X]:((strong(X)|tall(X))))<=>(?[X]:((~curious(X)<~>~quiet(X)))))&
(![X]:((~humble(X)|rich(X))=>(funny(X)&~generous(X))))&
((?[X]:((wise(X)<~>strong(X))))=>((funny(john)|~rich(john))))&
(![X]:((~funny(X)&generous(X))<=>(~quiet(X)<~>happy(X))))&
(((creative(susan)&~tall(susan)))=>(?[X]:((~rich(X)|~kind(X)))))&
((brave(fred))=>(?[X]:((~strong(X)&strong(X)))))&
(![X]:(curious(X)=>happy(X)))&
(((~rich(alice)<~>creative(alice)))<=>(brave(fred)))&
(((patient(susan)|~strong(susan)))<=>((rich(john)<~>~funny(john))))&
(?[X]:((~strong(X)&~calm(X))))&
(?[X]:((~tall(X)<~>old(X))))&
(~brave(john))&
((curious(alice)|creative(alice)))&
(?[X]:(kind(X)))&
(?[X]:((~happy(X)|strong(X)))) | ~tall(alice) | [] | null | 0 |
Everyone who is both not rich and not tall is both not strong and not calm.
If mary is not quiet then someone is not humble.
If mary is both generous and not kind then paul is wise and vice versa.
If alice is not rich then john is not brave.
Everyone who is either not wise or not curious is either not rich or happy and vice versa.
Everyone who is not tall is calm or funny and vice versa.
Everyone who is not rich is either not strong or not brave.
Everyone who is not curious is both tall and not patient and vice versa.
If alice is both creative and funny then someone is both not quiet and curious and vice versa.
Everyone who is not quiet or not wise is either creative or not curious.
Everyone who is both not happy and happy is humble or strong.
Everyone who is either generous or wise is both old and not creative and vice versa.
Everyone who is both not curious and not creative is quiet or rich.
If susan is both not calm and not happy then susan is both not brave and patient and vice versa.
Everyone who is either wise or strong is not old and vice versa.
Everyone who is not happy is not patient and vice versa.
Alice is either funny or not calm.
Someone is either strong or quiet.
Someone is either not funny or tall.
Someone is either quiet or patient.
Someone is both kind and not humble.
Someone is not quiet.
Paul is either tall or not kind.
Fred is either creative or not wise. | Susan is old. | neutral | (![X]:((~rich(X)&~tall(X))=>(~strong(X)&~calm(X))))&
((~quiet(mary))=>(?[X]:(~humble(X))))&
(((generous(mary)&~kind(mary)))<=>(wise(paul)))&
((~rich(alice))=>(~brave(john)))&
(![X]:((~wise(X)<~>~curious(X))<=>(~rich(X)<~>happy(X))))&
(![X]:(~tall(X)<=>(calm(X)|funny(X))))&
(![X]:(~rich(X)=>(~strong(X)<~>~brave(X))))&
(![X]:(~curious(X)<=>(tall(X)&~patient(X))))&
(((creative(alice)&funny(alice)))<=>(?[X]:((~quiet(X)&curious(X)))))&
(![X]:((~quiet(X)|~wise(X))=>(creative(X)<~>~curious(X))))&
(![X]:((~happy(X)&happy(X))=>(humble(X)|strong(X))))&
(![X]:((generous(X)<~>wise(X))<=>(old(X)&~creative(X))))&
(![X]:((~curious(X)&~creative(X))=>(quiet(X)|rich(X))))&
(((~calm(susan)&~happy(susan)))<=>((~brave(susan)&patient(susan))))&
(![X]:((wise(X)<~>strong(X))<=>~old(X)))&
(![X]:(~happy(X)<=>~patient(X)))&
((funny(alice)<~>~calm(alice)))&
(?[X]:((strong(X)<~>quiet(X))))&
(?[X]:((~funny(X)<~>tall(X))))&
(?[X]:((quiet(X)<~>patient(X))))&
(?[X]:((kind(X)&~humble(X))))&
(?[X]:(~quiet(X)))&
((tall(paul)<~>~kind(paul)))&
((creative(fred)<~>~wise(fred))) | old(susan) | [] | null | 0 |
Everyone who is not curious or not funny is not happy and vice versa. If someone is both not humble and wise then mary is tall and vice versa. If someone is either quiet or humble then mary is not humble or wise and vice versa. Everyone who is both not tall and strong is brave or not generous and vice versa. Everyone who is either not calm or not happy is happy or rich. Everyone who is tall or not kind is both humble and not calm. Everyone who is funny or not curious is both not wise and not creative and vice versa. If someone is not curious or not old then lucy is both humble and not rich and vice versa. If susan is either not creative or calm then someone is both not funny and funny. Everyone who is either not calm or not funny is not calm and vice versa. Everyone who is either brave or not curious is either calm or kind. Everyone who is either not old or rich is curious or not tall. If mary is not brave or not calm then mary is both curious and rich. Everyone who is funny is tall or not tall. Everyone who is both brave and not wise is not humble or tall and vice versa. If someone is both strong and not generous then someone is wise. Susan is both not quiet and happy. Someone is not patient. Alice is both not tall and quiet. Someone is not calm. Mary is old. Lucy is not patient. Someone is both not wise and brave. | Susan is generous. | entailment | (![X]:((~curious(X)|~funny(X))<=>~happy(X)))&
((?[X]:((~humble(X)&wise(X))))<=>(tall(mary)))&
((?[X]:((quiet(X)<~>humble(X))))<=>((~humble(mary)|wise(mary))))&
(![X]:((~tall(X)&strong(X))<=>(brave(X)|~generous(X))))&
(![X]:((~calm(X)<~>~happy(X))=>(happy(X)|rich(X))))&
(![X]:((tall(X)|~kind(X))=>(humble(X)&~calm(X))))&
(![X]:((funny(X)|~curious(X))<=>(~wise(X)&~creative(X))))&
((?[X]:((~curious(X)|~old(X))))<=>((humble(lucy)&~rich(lucy))))&
(((~creative(susan)<~>calm(susan)))=>(?[X]:((~funny(X)&funny(X)))))&
(![X]:((~calm(X)<~>~funny(X))<=>~calm(X)))&
(![X]:((brave(X)<~>~curious(X))=>(calm(X)<~>kind(X))))&
(![X]:((~old(X)<~>rich(X))=>(curious(X)|~tall(X))))&
(((~brave(mary)|~calm(mary)))=>((curious(mary)&rich(mary))))&
(![X]:(funny(X)=>(tall(X)|~tall(X))))&
(![X]:((brave(X)&~wise(X))<=>(~humble(X)|tall(X))))&
((?[X]:((strong(X)&~generous(X))))=>(?[X]:(wise(X))))&
((~quiet(susan)&happy(susan)))&
(?[X]:(~patient(X)))&
((~tall(alice)&quiet(alice)))&
(?[X]:(~calm(X)))&
(old(mary))&
(~patient(lucy))&
(?[X]:((~wise(X)&brave(X)))) | generous(susan) | [
"p3",
"p6",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6593516710000188705356269
% SZS output start Proof for 6593516710000188705356269
4. ! [X0] : ((strong(X0) & ~tall(X0)) <=> (~generous(X0) | brave(X0))) [input p3]
7. ! [X0] : ((~curious(X0) | funny(X0)) <=> (~creative(X0) & ~wise(X0))) [input p6]
10. ! [X0] : ((~calm(X0) <~> ~funny(X0)) <=> ~calm(X0)) [input p9]
16. ? [X0] : (~generous(X0) & strong(X0)) => ? [X0] : wise(X0) [input p15]
24. ~generous(susan) [input hypothesis]
25. ? [X0] : (~generous(X0) & strong(X0)) => ? [X1] : wise(X1) [rectify 16]
38. ? [X1] : wise(X1) | ! [X0] : (generous(X0) | ~strong(X0)) [ennf transformation 25]
50. ! [X0] : (((strong(X0) & ~tall(X0)) | (generous(X0) & ~brave(X0))) & ((~generous(X0) | brave(X0)) | (~strong(X0) | tall(X0)))) [nnf transformation 4]
51. ! [X0] : (((strong(X0) & ~tall(X0)) | (generous(X0) & ~brave(X0))) & (~generous(X0) | brave(X0) | ~strong(X0) | tall(X0))) [flattening 50]
53. ! [X0] : (((~curious(X0) | funny(X0)) | (creative(X0) | wise(X0))) & ((~creative(X0) & ~wise(X0)) | (curious(X0) & ~funny(X0)))) [nnf transformation 7]
54. ! [X0] : ((~curious(X0) | funny(X0) | creative(X0) | wise(X0)) & ((~creative(X0) & ~wise(X0)) | (curious(X0) & ~funny(X0)))) [flattening 53]
63. ! [X0] : ((((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) | calm(X0)) & (~calm(X0) | ((~calm(X0) | funny(X0)) & (~funny(X0) | calm(X0))))) [nnf transformation 10]
68. ? [X0] : wise(X0) | ! [X1] : (generous(X1) | ~strong(X1)) [rectify 38]
69. ? [X0] : wise(X0) => wise(sK4) [choice axiom]
70. wise(sK4) | ! [X1] : (generous(X1) | ~strong(X1)) [skolemisation 68,69]
91. generous(X0) | strong(X0) [cnf transformation 51]
98. ~wise(X0) | ~funny(X0) [cnf transformation 54]
113. ~calm(X0) | ~calm(X0) | funny(X0) [cnf transformation 63]
115. funny(X0) | calm(X0) | calm(X0) [cnf transformation 63]
132. wise(sK4) | generous(X1) | ~strong(X1) [cnf transformation 70]
141. ~generous(susan) [cnf transformation 24]
142. ~calm(X0) | funny(X0) [duplicate literal removal 113]
143. funny(X0) | calm(X0) [duplicate literal removal 115]
234. funny(X0) [subsumption resolution 142,143]
262. wise(sK4) | generous(X1) [subsumption resolution 132,91]
264. 24 <=> ! [X1] : generous(X1) [avatar definition]
265. generous(X1) <- (24) [avatar component clause 264]
267. 25 <=> wise(sK4) [avatar definition]
269. wise(sK4) <- (25) [avatar component clause 267]
270. 24 | 25 [avatar split clause 262,267,264]
273. $false <- (24) [resolution 265,141]
274. ~24 [avatar contradiction clause 273]
286. ~funny(sK4) <- (25) [resolution 98,269]
287. $false <- (25) [subsumption resolution 286,234]
288. ~25 [avatar contradiction clause 287]
289. $false [avatar sat refutation 270,274,288]
% SZS output end Proof for 6593516710000188705356269
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not brave is either curious or not old and vice versa. Everyone who is not calm or not creative is not humble or not curious. If someone is not curious or generous then alice is either not curious or tall. Everyone who is not funny or not calm is curious or not old and vice versa. Everyone who is both not brave and curious is not curious and vice versa. Everyone who is not patient or not generous is not creative or wise and vice versa. If john is not rich or rich then someone is kind or not tall. Everyone who is calm is either humble or generous. Everyone who is either not happy or not generous is either strong or rich and vice versa. If someone is wise then someone is both not humble and not kind. If paul is either not brave or not tall then someone is either brave or quiet. Everyone who is rich is not generous or humble and vice versa. Everyone who is both strong and not happy is not happy or not quiet. If fred is curious then someone is kind or patient and vice versa. If susan is old or not quiet then paul is either not tall or not old. If lucy is creative then mary is either not quiet or generous and vice versa. John is calm or strong. Someone is both happy and patient. John is not creative or curious. Paul is either not wise or patient. Paul is either generous or not humble. Lucy is both not quiet and curious. Someone is not wise. | John is calm. | neutral | (![X]:(~brave(X)<=>(curious(X)<~>~old(X))))&
(![X]:((~calm(X)|~creative(X))=>(~humble(X)|~curious(X))))&
((?[X]:((~curious(X)|generous(X))))=>((~curious(alice)<~>tall(alice))))&
(![X]:((~funny(X)|~calm(X))<=>(curious(X)|~old(X))))&
(![X]:((~brave(X)&curious(X))<=>~curious(X)))&
(![X]:((~patient(X)|~generous(X))<=>(~creative(X)|wise(X))))&
(((~rich(john)|rich(john)))=>(?[X]:((kind(X)|~tall(X)))))&
(![X]:(calm(X)=>(humble(X)<~>generous(X))))&
(![X]:((~happy(X)<~>~generous(X))<=>(strong(X)<~>rich(X))))&
((?[X]:(wise(X)))=>(?[X]:((~humble(X)&~kind(X)))))&
(((~brave(paul)<~>~tall(paul)))=>(?[X]:((brave(X)<~>quiet(X)))))&
(![X]:(rich(X)<=>(~generous(X)|humble(X))))&
(![X]:((strong(X)&~happy(X))=>(~happy(X)|~quiet(X))))&
((curious(fred))<=>(?[X]:((kind(X)|patient(X)))))&
(((old(susan)|~quiet(susan)))=>((~tall(paul)<~>~old(paul))))&
((creative(lucy))<=>((~quiet(mary)<~>generous(mary))))&
((calm(john)|strong(john)))&
(?[X]:((happy(X)&patient(X))))&
((~creative(john)|curious(john)))&
((~wise(paul)<~>patient(paul)))&
((generous(paul)<~>~humble(paul)))&
((~quiet(lucy)&curious(lucy)))&
(?[X]:(~wise(X))) | calm(john) | [] | null | 0 |
Everyone who is both not patient and not strong is not humble or not quiet. If someone is either happy or strong then fred is curious or brave and vice versa. Everyone who is not rich is not tall or not wise. Everyone who is calm is both not quiet and calm and vice versa. If someone is both quiet and funny then someone is brave and vice versa. If someone is generous then mary is not curious and vice versa. Everyone who is strong or funny is both quiet and not curious. Everyone who is both not tall and old is both tall and not calm. Everyone who is not happy or not generous is generous or not tall. Everyone who is not generous is both not brave and not creative. Everyone who is not brave or not rich is both happy and calm. Everyone who is both funny and not wise is either not tall or not kind. Everyone who is either generous or not patient is both generous and quiet and vice versa. Everyone who is either wise or not kind is either not old or creative and vice versa. If mary is both wise and not kind then lucy is either wise or not brave. If mary is not tall or not kind then fred is not brave or patient and vice versa. Mary is humble or brave. Someone is both not old and not calm. Fred is wise. Someone is either calm or not patient. Lucy is curious. Someone is either kind or humble. Someone is both kind and wise. | Fred is patient. | neutral | (![X]:((~patient(X)&~strong(X))=>(~humble(X)|~quiet(X))))&
((?[X]:((happy(X)<~>strong(X))))<=>((curious(fred)|brave(fred))))&
(![X]:(~rich(X)=>(~tall(X)|~wise(X))))&
(![X]:(calm(X)<=>(~quiet(X)&calm(X))))&
((?[X]:((quiet(X)&funny(X))))<=>(?[X]:(brave(X))))&
((?[X]:(generous(X)))<=>(~curious(mary)))&
(![X]:((strong(X)|funny(X))=>(quiet(X)&~curious(X))))&
(![X]:((~tall(X)&old(X))=>(tall(X)&~calm(X))))&
(![X]:((~happy(X)|~generous(X))=>(generous(X)|~tall(X))))&
(![X]:(~generous(X)=>(~brave(X)&~creative(X))))&
(![X]:((~brave(X)|~rich(X))=>(happy(X)&calm(X))))&
(![X]:((funny(X)&~wise(X))=>(~tall(X)<~>~kind(X))))&
(![X]:((generous(X)<~>~patient(X))<=>(generous(X)&quiet(X))))&
(![X]:((wise(X)<~>~kind(X))<=>(~old(X)<~>creative(X))))&
(((wise(mary)&~kind(mary)))=>((wise(lucy)<~>~brave(lucy))))&
(((~tall(mary)|~kind(mary)))<=>((~brave(fred)|patient(fred))))&
((humble(mary)|brave(mary)))&
(?[X]:((~old(X)&~calm(X))))&
(wise(fred))&
(?[X]:((calm(X)<~>~patient(X))))&
(curious(lucy))&
(?[X]:((kind(X)<~>humble(X))))&
(?[X]:((kind(X)&wise(X)))) | patient(fred) | [] | null | 0 |
If paul is both kind and not rich then someone is both rich and not tall.
If someone is both creative and tall then susan is tall and vice versa.
Everyone who is both not calm and not old is patient and vice versa.
Everyone who is both patient and not curious is either happy or not quiet and vice versa.
If someone is funny or quiet then someone is both rich and creative and vice versa.
Everyone who is not patient is either not strong or not creative.
If john is either creative or quiet then someone is not creative and vice versa.
Everyone who is strong is not old or not kind and vice versa.
Everyone who is either not humble or rich is both wise and not funny.
Everyone who is generous or old is both not rich and not humble and vice versa.
If fred is both quiet and humble then mary is old or not humble.
Everyone who is creative is not kind and vice versa.
If someone is not humble then paul is either not humble or curious.
If alice is either generous or not kind then paul is either not happy or brave and vice versa.
Everyone who is either not generous or brave is both funny and not curious.
If someone is happy then fred is either not brave or curious and vice versa.
Someone is both happy and not calm.
John is not happy or brave.
Someone is both not creative and rich.
Someone is either not tall or not wise.
Someone is not generous or not calm.
Someone is both not curious and kind. | Alice is generous. | neutral | (((kind(paul)&~rich(paul)))=>(?[X]:((rich(X)&~tall(X)))))&
((?[X]:((creative(X)&tall(X))))<=>(tall(susan)))&
(![X]:((~calm(X)&~old(X))<=>patient(X)))&
(![X]:((patient(X)&~curious(X))<=>(happy(X)<~>~quiet(X))))&
((?[X]:((funny(X)|quiet(X))))<=>(?[X]:((rich(X)&creative(X)))))&
(![X]:(~patient(X)=>(~strong(X)<~>~creative(X))))&
(((creative(john)<~>quiet(john)))<=>(?[X]:(~creative(X))))&
(![X]:(strong(X)<=>(~old(X)|~kind(X))))&
(![X]:((~humble(X)<~>rich(X))=>(wise(X)&~funny(X))))&
(![X]:((generous(X)|old(X))<=>(~rich(X)&~humble(X))))&
(((quiet(fred)&humble(fred)))=>((old(mary)|~humble(mary))))&
(![X]:(creative(X)<=>~kind(X)))&
((?[X]:(~humble(X)))=>((~humble(paul)<~>curious(paul))))&
(((generous(alice)<~>~kind(alice)))<=>((~happy(paul)<~>brave(paul))))&
(![X]:((~generous(X)<~>brave(X))=>(funny(X)&~curious(X))))&
((?[X]:(happy(X)))<=>((~brave(fred)<~>curious(fred))))&
(?[X]:((happy(X)&~calm(X))))&
((~happy(john)|brave(john)))&
(?[X]:((~creative(X)&rich(X))))&
(?[X]:((~tall(X)<~>~wise(X))))&
(?[X]:((~generous(X)|~calm(X))))&
(?[X]:((~curious(X)&kind(X)))) | generous(alice) | [] | null | 0 |
Everyone who is both not old and patient is tall or kind.
Everyone who is both happy and humble is both humble and not kind.
If lucy is not kind then someone is not tall.
If paul is tall or not old then someone is not happy.
Everyone who is kind is either funny or not happy.
If paul is humble then paul is both quiet and not curious and vice versa.
Everyone who is not brave is both not strong and not calm.
If paul is curious or brave then someone is not curious.
Everyone who is both generous and not old is wise or tall.
If paul is both not calm and kind then lucy is not humble.
Everyone who is strong or curious is both not old and generous and vice versa.
Everyone who is kind is not strong or not funny and vice versa.
Everyone who is both curious and quiet is both quiet and rich and vice versa.
Everyone who is both not old and funny is both rich and tall.
Everyone who is both wise and tall is both kind and not brave.
If someone is wise or brave then susan is either funny or happy and vice versa.
Someone is old.
Susan is humble or not humble.
Someone is not creative.
Lucy is not funny.
Someone is either not humble or not curious.
John is both not generous and not quiet.
Paul is not tall. | Susan is not brave. | neutral | (![X]:((~old(X)&patient(X))=>(tall(X)|kind(X))))&
(![X]:((happy(X)&humble(X))=>(humble(X)&~kind(X))))&
((~kind(lucy))=>(?[X]:(~tall(X))))&
(((tall(paul)|~old(paul)))=>(?[X]:(~happy(X))))&
(![X]:(kind(X)=>(funny(X)<~>~happy(X))))&
((humble(paul))<=>((quiet(paul)&~curious(paul))))&
(![X]:(~brave(X)=>(~strong(X)&~calm(X))))&
(((curious(paul)|brave(paul)))=>(?[X]:(~curious(X))))&
(![X]:((generous(X)&~old(X))=>(wise(X)|tall(X))))&
(((~calm(paul)&kind(paul)))=>(~humble(lucy)))&
(![X]:((strong(X)|curious(X))<=>(~old(X)&generous(X))))&
(![X]:(kind(X)<=>(~strong(X)|~funny(X))))&
(![X]:((curious(X)&quiet(X))<=>(quiet(X)&rich(X))))&
(![X]:((~old(X)&funny(X))=>(rich(X)&tall(X))))&
(![X]:((wise(X)&tall(X))=>(kind(X)&~brave(X))))&
((?[X]:((wise(X)|brave(X))))<=>((funny(susan)<~>happy(susan))))&
(?[X]:(old(X)))&
((humble(susan)|~humble(susan)))&
(?[X]:(~creative(X)))&
(~funny(lucy))&
(?[X]:((~humble(X)<~>~curious(X))))&
((~generous(john)&~quiet(john)))&
(~tall(paul)) | ~brave(susan) | [] | null | 0 |
Everyone who is not calm or calm is either not quiet or not strong. Everyone who is not patient or funny is calm or old. If john is not creative then susan is funny. Everyone who is not calm or not brave is not patient or not kind and vice versa. Everyone who is not tall is either not old or not rich. If susan is either not calm or not quiet then someone is strong and vice versa. If fred is either old or not old then paul is brave. Everyone who is either funny or brave is both not patient and not brave and vice versa. If paul is both not generous and rich then someone is either creative or not wise. Everyone who is generous or old is both creative and not strong. If mary is both not tall and rich then fred is both not happy and happy. If john is tall then alice is not kind. If someone is both not tall and kind then susan is either humble or not happy and vice versa. Everyone who is strong or curious is not kind or not tall. If fred is wise or not curious then paul is not funny and vice versa. Everyone who is either curious or patient is strong or not humble and vice versa. John is both strong and not patient. Someone is both creative and rich. Someone is happy. Someone is not brave or generous. Mary is either not kind or not calm. John is not wise. Someone is either not quiet or quiet. Lucy is either not brave or not wise. | Paul is brave. | entailment | (![X]:((~calm(X)|calm(X))=>(~quiet(X)<~>~strong(X))))&
(![X]:((~patient(X)|funny(X))=>(calm(X)|old(X))))&
((~creative(john))=>(funny(susan)))&
(![X]:((~calm(X)|~brave(X))<=>(~patient(X)|~kind(X))))&
(![X]:(~tall(X)=>(~old(X)<~>~rich(X))))&
(((~calm(susan)<~>~quiet(susan)))<=>(?[X]:(strong(X))))&
(((old(fred)<~>~old(fred)))=>(brave(paul)))&
(![X]:((funny(X)<~>brave(X))<=>(~patient(X)&~brave(X))))&
(((~generous(paul)&rich(paul)))=>(?[X]:((creative(X)<~>~wise(X)))))&
(![X]:((generous(X)|old(X))=>(creative(X)&~strong(X))))&
(((~tall(mary)&rich(mary)))=>((~happy(fred)&happy(fred))))&
((tall(john))=>(~kind(alice)))&
((?[X]:((~tall(X)&kind(X))))<=>((humble(susan)<~>~happy(susan))))&
(![X]:((strong(X)|curious(X))=>(~kind(X)|~tall(X))))&
(((wise(fred)|~curious(fred)))<=>(~funny(paul)))&
(![X]:((curious(X)<~>patient(X))<=>(strong(X)|~humble(X))))&
((strong(john)&~patient(john)))&
(?[X]:((creative(X)&rich(X))))&
(?[X]:(happy(X)))&
(?[X]:((~brave(X)|generous(X))))&
((~kind(mary)<~>~calm(mary)))&
(~wise(john))&
(?[X]:((~quiet(X)<~>quiet(X))))&
((~brave(lucy)<~>~wise(lucy))) | brave(paul) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8342814075724607235152754
% SZS output start Proof for 8342814075724607235152754
7. (old(fred) <~> ~old(fred)) => brave(paul) [input p6]
25. ~brave(paul) [input hypothesis]
31. brave(paul) | (old(fred) <=> ~old(fred)) [ennf transformation 7]
48. brave(paul) | ((old(fred) | old(fred)) & (~old(fred) | ~old(fred))) [nnf transformation 31]
90. brave(paul) | ~old(fred) | ~old(fred) [cnf transformation 48]
91. brave(paul) | old(fred) | old(fred) [cnf transformation 48]
137. ~brave(paul) [cnf transformation 25]
140. brave(paul) | ~old(fred) [duplicate literal removal 90]
141. brave(paul) | old(fred) [duplicate literal removal 91]
173. 7 <=> old(fred) [avatar definition]
177. 8 <=> brave(paul) [avatar definition]
180. 7 | 8 [avatar split clause 141,177,173]
181. ~7 | 8 [avatar split clause 140,177,173]
292. ~8 [avatar split clause 137,177]
293. $false [avatar sat refutation 180,181,292]
% SZS output end Proof for 8342814075724607235152754
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not creative then someone is not rich. Everyone who is both strong and creative is not quiet and vice versa. If someone is both not strong and funny then paul is either humble or not tall and vice versa. Everyone who is kind is not funny and vice versa. Everyone who is old is either calm or strong. If someone is not wise then someone is humble. Everyone who is not quiet or not creative is both calm and happy. Everyone who is rich is either tall or strong and vice versa. Everyone who is either old or strong is calm or not wise. Everyone who is both not happy and humble is either strong or curious and vice versa. If alice is either strong or not quiet then someone is either not tall or happy. Everyone who is both generous and not wise is not kind or not rich and vice versa. Everyone who is strong or kind is funny. Everyone who is both rich and not generous is either old or wise and vice versa. Everyone who is either not quiet or not wise is not old or tall and vice versa. Fred is both strong and happy. Someone is kind or not curious. Someone is either strong or humble. Someone is funny. | Alice is not happy. | neutral | ((?[X]:((~quiet(X)|~creative(X))))=>(?[X]:(~rich(X))))&
(![X]:((strong(X)&creative(X))<=>~quiet(X)))&
((?[X]:((~strong(X)&funny(X))))<=>((humble(paul)<~>~tall(paul))))&
(![X]:(kind(X)<=>~funny(X)))&
(![X]:(old(X)=>(calm(X)<~>strong(X))))&
((?[X]:(~wise(X)))=>(?[X]:(humble(X))))&
(![X]:((~quiet(X)|~creative(X))=>(calm(X)&happy(X))))&
(![X]:(rich(X)<=>(tall(X)<~>strong(X))))&
(![X]:((old(X)<~>strong(X))=>(calm(X)|~wise(X))))&
(![X]:((~happy(X)&humble(X))<=>(strong(X)<~>curious(X))))&
(((strong(alice)<~>~quiet(alice)))=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((generous(X)&~wise(X))<=>(~kind(X)|~rich(X))))&
(![X]:((strong(X)|kind(X))=>funny(X)))&
(![X]:((rich(X)&~generous(X))<=>(old(X)<~>wise(X))))&
(![X]:((~quiet(X)<~>~wise(X))<=>(~old(X)|tall(X))))&
((strong(fred)&happy(fred)))&
(?[X]:((kind(X)|~curious(X))))&
(?[X]:((strong(X)<~>humble(X))))&
(?[X]:(funny(X))) | ~happy(alice) | [] | null | 0 |
If someone is tall or kind then alice is both not patient and not strong and vice versa. Everyone who is both not quiet and not curious is kind or curious and vice versa. If someone is old then fred is not humble and vice versa. Everyone who is tall is generous and vice versa. If someone is both curious and funny then someone is either curious or not humble and vice versa. If paul is both not wise and not kind then someone is not rich or not calm and vice versa. Everyone who is either not humble or not old is not generous. If alice is old or not calm then susan is both curious and not tall. Everyone who is old is strong or brave. Everyone who is not old is both patient and rich and vice versa. Everyone who is both not humble and not tall is wise or not tall. If alice is not happy then paul is both funny and calm. If mary is either not rich or patient then someone is both not happy and calm and vice versa. If lucy is not humble then alice is generous or not quiet. If someone is not calm or not quiet then someone is not brave or not strong. Everyone who is both not happy and strong is either happy or not quiet. Mary is quiet. Fred is either not patient or not funny. Someone is both happy and not kind. Paul is both not wise and brave. Someone is calm or not old. | Susan is not happy. | neutral | ((?[X]:((tall(X)|kind(X))))<=>((~patient(alice)&~strong(alice))))&
(![X]:((~quiet(X)&~curious(X))<=>(kind(X)|curious(X))))&
((?[X]:(old(X)))<=>(~humble(fred)))&
(![X]:(tall(X)<=>generous(X)))&
((?[X]:((curious(X)&funny(X))))<=>(?[X]:((curious(X)<~>~humble(X)))))&
(((~wise(paul)&~kind(paul)))<=>(?[X]:((~rich(X)|~calm(X)))))&
(![X]:((~humble(X)<~>~old(X))=>~generous(X)))&
(((old(alice)|~calm(alice)))=>((curious(susan)&~tall(susan))))&
(![X]:(old(X)=>(strong(X)|brave(X))))&
(![X]:(~old(X)<=>(patient(X)&rich(X))))&
(![X]:((~humble(X)&~tall(X))=>(wise(X)|~tall(X))))&
((~happy(alice))=>((funny(paul)&calm(paul))))&
(((~rich(mary)<~>patient(mary)))<=>(?[X]:((~happy(X)&calm(X)))))&
((~humble(lucy))=>((generous(alice)|~quiet(alice))))&
((?[X]:((~calm(X)|~quiet(X))))=>(?[X]:((~brave(X)|~strong(X)))))&
(![X]:((~happy(X)&strong(X))=>(happy(X)<~>~quiet(X))))&
(quiet(mary))&
((~patient(fred)<~>~funny(fred)))&
(?[X]:((happy(X)&~kind(X))))&
((~wise(paul)&brave(paul)))&
(?[X]:((calm(X)|~old(X)))) | ~happy(susan) | [] | null | 0 |
Everyone who is calm or kind is either old or not generous.
Everyone who is either kind or not happy is both not happy and humble and vice versa.
Everyone who is both not happy and not wise is not old and vice versa.
Everyone who is old or not strong is either patient or not creative.
If mary is humble then lucy is not curious and vice versa.
Everyone who is not calm is not wise and vice versa.
If someone is both strong and creative then john is old or tall and vice versa.
Everyone who is not old or happy is either not happy or not kind and vice versa.
Everyone who is rich or not generous is not brave.
If someone is either not curious or not funny then lucy is not calm or not old.
If fred is not humble then someone is either curious or not generous and vice versa.
Everyone who is not humble is both not quiet and not happy and vice versa.
Everyone who is rich or not curious is wise or not creative.
If john is either not old or curious then mary is not happy or not patient.
Everyone who is both happy and kind is not old.
Everyone who is both not creative and humble is patient or tall and vice versa.
Someone is both calm and not funny.
John is not happy or not brave.
Fred is either strong or rich.
Someone is not quiet or funny.
Someone is funny or humble. | John is brave. | neutral | (![X]:((calm(X)|kind(X))=>(old(X)<~>~generous(X))))&
(![X]:((kind(X)<~>~happy(X))<=>(~happy(X)&humble(X))))&
(![X]:((~happy(X)&~wise(X))<=>~old(X)))&
(![X]:((old(X)|~strong(X))=>(patient(X)<~>~creative(X))))&
((humble(mary))<=>(~curious(lucy)))&
(![X]:(~calm(X)<=>~wise(X)))&
((?[X]:((strong(X)&creative(X))))<=>((old(john)|tall(john))))&
(![X]:((~old(X)|happy(X))<=>(~happy(X)<~>~kind(X))))&
(![X]:((rich(X)|~generous(X))=>~brave(X)))&
((?[X]:((~curious(X)<~>~funny(X))))=>((~calm(lucy)|~old(lucy))))&
((~humble(fred))<=>(?[X]:((curious(X)<~>~generous(X)))))&
(![X]:(~humble(X)<=>(~quiet(X)&~happy(X))))&
(![X]:((rich(X)|~curious(X))=>(wise(X)|~creative(X))))&
(((~old(john)<~>curious(john)))=>((~happy(mary)|~patient(mary))))&
(![X]:((happy(X)&kind(X))=>~old(X)))&
(![X]:((~creative(X)&humble(X))<=>(patient(X)|tall(X))))&
(?[X]:((calm(X)&~funny(X))))&
((~happy(john)|~brave(john)))&
((strong(fred)<~>rich(fred)))&
(?[X]:((~quiet(X)|funny(X))))&
(?[X]:((funny(X)|humble(X)))) | brave(john) | [] | null | 0 |
Everyone who is both old and happy is both not happy and humble and vice versa.
If john is not wise or patient then john is not brave.
If alice is not wise then someone is patient or not generous.
If mary is both not funny and not brave then someone is not strong or not patient and vice versa.
Everyone who is rich is not old or not wise.
Everyone who is both not tall and not kind is both not calm and old and vice versa.
Everyone who is not patient is old and vice versa.
Everyone who is either not rich or not creative is rich or brave.
If fred is not rich then someone is both wise and humble and vice versa.
Everyone who is both not rich and funny is not generous or not curious.
Everyone who is both not funny and happy is both not humble and patient and vice versa.
Everyone who is both not rich and not creative is not wise or generous and vice versa.
If john is both kind and humble then someone is strong.
Everyone who is either not rich or not kind is wise.
If someone is both not patient and not calm then someone is both not generous and not strong and vice versa.
If someone is both curious and patient then someone is not curious.
Someone is not funny or rich.
Someone is not old.
Someone is not calm.
Fred is either strong or not tall.
Alice is not rich.
Mary is both funny and not rich.
Someone is funny. | Fred is calm. | neutral | (![X]:((old(X)&happy(X))<=>(~happy(X)&humble(X))))&
(((~wise(john)|patient(john)))=>(~brave(john)))&
((~wise(alice))=>(?[X]:((patient(X)|~generous(X)))))&
(((~funny(mary)&~brave(mary)))<=>(?[X]:((~strong(X)|~patient(X)))))&
(![X]:(rich(X)=>(~old(X)|~wise(X))))&
(![X]:((~tall(X)&~kind(X))<=>(~calm(X)&old(X))))&
(![X]:(~patient(X)<=>old(X)))&
(![X]:((~rich(X)<~>~creative(X))=>(rich(X)|brave(X))))&
((~rich(fred))<=>(?[X]:((wise(X)&humble(X)))))&
(![X]:((~rich(X)&funny(X))=>(~generous(X)|~curious(X))))&
(![X]:((~funny(X)&happy(X))<=>(~humble(X)&patient(X))))&
(![X]:((~rich(X)&~creative(X))<=>(~wise(X)|generous(X))))&
(((kind(john)&humble(john)))=>(?[X]:(strong(X))))&
(![X]:((~rich(X)<~>~kind(X))=>wise(X)))&
((?[X]:((~patient(X)&~calm(X))))<=>(?[X]:((~generous(X)&~strong(X)))))&
((?[X]:((curious(X)&patient(X))))=>(?[X]:(~curious(X))))&
(?[X]:((~funny(X)|rich(X))))&
(?[X]:(~old(X)))&
(?[X]:(~calm(X)))&
((strong(fred)<~>~tall(fred)))&
(~rich(alice))&
((funny(mary)&~rich(mary)))&
(?[X]:(funny(X))) | calm(fred) | [] | null | 0 |
Everyone who is funny or not kind is both creative and not happy. Everyone who is both wise and not calm is not creative or calm. Everyone who is old is funny. Everyone who is creative or old is generous and vice versa. Everyone who is both not rich and tall is both not curious and not wise. If mary is either calm or not wise then someone is either tall or old and vice versa. If someone is not humble then someone is humble or not patient and vice versa. If someone is kind then someone is both not brave and quiet. Everyone who is both not old and curious is old or wise. Everyone who is wise or happy is both not happy and not strong and vice versa. Everyone who is both calm and funny is not kind or not generous. If paul is either not rich or not strong then someone is either not calm or creative and vice versa. If someone is creative or not wise then someone is not calm or humble. Everyone who is both not funny and strong is not kind or not creative. If someone is wise or generous then someone is quiet or strong. If someone is both not funny and not old then paul is both not strong and happy. Someone is strong or tall. Someone is humble. Someone is old. Someone is not old. Lucy is calm. Someone is funny or wise. | Lucy is generous. | entailment | (![X]:((funny(X)|~kind(X))=>(creative(X)&~happy(X))))&
(![X]:((wise(X)&~calm(X))=>(~creative(X)|calm(X))))&
(![X]:(old(X)=>funny(X)))&
(![X]:((creative(X)|old(X))<=>generous(X)))&
(![X]:((~rich(X)&tall(X))=>(~curious(X)&~wise(X))))&
(((calm(mary)<~>~wise(mary)))<=>(?[X]:((tall(X)<~>old(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((humble(X)|~patient(X)))))&
((?[X]:(kind(X)))=>(?[X]:((~brave(X)&quiet(X)))))&
(![X]:((~old(X)&curious(X))=>(old(X)|wise(X))))&
(![X]:((wise(X)|happy(X))<=>(~happy(X)&~strong(X))))&
(![X]:((calm(X)&funny(X))=>(~kind(X)|~generous(X))))&
(((~rich(paul)<~>~strong(paul)))<=>(?[X]:((~calm(X)<~>creative(X)))))&
((?[X]:((creative(X)|~wise(X))))=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((~funny(X)&strong(X))=>(~kind(X)|~creative(X))))&
((?[X]:((wise(X)|generous(X))))=>(?[X]:((quiet(X)|strong(X)))))&
((?[X]:((~funny(X)&~old(X))))=>((~strong(paul)&happy(paul))))&
(?[X]:((strong(X)|tall(X))))&
(?[X]:(humble(X)))&
(?[X]:(old(X)))&
(?[X]:(~old(X)))&
(calm(lucy))&
(?[X]:((funny(X)|wise(X)))) | generous(lucy) | [
"p0",
"p2",
"p3",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5795532787213167192202329
% SZS output start Proof for 5795532787213167192202329
1. ! [X0] : ((~kind(X0) | funny(X0)) => (~happy(X0) & creative(X0))) [input p0]
3. ! [X0] : (old(X0) => funny(X0)) [input p2]
4. ! [X0] : ((old(X0) | creative(X0)) <=> generous(X0)) [input p3]
10. ! [X0] : ((happy(X0) | wise(X0)) <=> (~strong(X0) & ~happy(X0))) [input p9]
16. ? [X0] : (~old(X0) & ~funny(X0)) => (happy(paul) & ~strong(paul)) [input p15]
23. ~generous(lucy) [input hypothesis]
28. ! [X0] : ((old(X0) | creative(X0)) => generous(X0)) [unused predicate definition removal 4]
34. ! [X0] : ((~happy(X0) & creative(X0)) | (kind(X0) & ~funny(X0))) [ennf transformation 1]
37. ! [X0] : (funny(X0) | ~old(X0)) [ennf transformation 3]
38. ! [X0] : (generous(X0) | (~old(X0) & ~creative(X0))) [ennf transformation 28]
46. (happy(paul) & ~strong(paul)) | ! [X0] : (old(X0) | funny(X0)) [ennf transformation 16]
56. ! [X0] : (((happy(X0) | wise(X0)) | (strong(X0) | happy(X0))) & ((~strong(X0) & ~happy(X0)) | (~happy(X0) & ~wise(X0)))) [nnf transformation 10]
57. ! [X0] : ((happy(X0) | wise(X0) | strong(X0) | happy(X0)) & ((~strong(X0) & ~happy(X0)) | (~happy(X0) & ~wise(X0)))) [flattening 56]
75. ~funny(X0) | creative(X0) [cnf transformation 34]
80. ~old(X0) | funny(X0) [cnf transformation 37]
81. ~creative(X0) | generous(X0) [cnf transformation 38]
96. ~happy(X0) | ~happy(X0) [cnf transformation 57]
113. happy(paul) | old(X0) | funny(X0) [cnf transformation 46]
120. ~generous(lucy) [cnf transformation 23]
121. ~happy(X0) [duplicate literal removal 96]
224. old(X0) | funny(X0) [subsumption resolution 113,121]
225. funny(X0) [subsumption resolution 224,80]
235. creative(X0) [resolution 75,225]
243. generous(X1) [resolution 81,235]
244. $false [resolution 243,120]
% SZS output end Proof for 5795532787213167192202329
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both patient and wise then someone is both tall and not curious.
Everyone who is funny is either wise or old and vice versa.
Everyone who is either wise or calm is not creative and vice versa.
If john is either not rich or brave then someone is both not quiet and not generous and vice versa.
If paul is funny then paul is not funny or wise and vice versa.
Everyone who is either quiet or not creative is quiet and vice versa.
If someone is curious then mary is old.
If someone is either quiet or rich then fred is not quiet or not rich.
If susan is both not strong and not humble then mary is either not humble or kind and vice versa.
If someone is quiet then fred is either not tall or not generous.
Everyone who is either calm or funny is both strong and not brave.
If someone is kind then someone is either patient or happy.
If someone is both not happy and funny then mary is brave or not generous and vice versa.
Everyone who is not rich or generous is either humble or not quiet and vice versa.
Everyone who is not quiet or creative is both brave and quiet.
Everyone who is not brave is both not quiet and not patient and vice versa.
Alice is either not tall or not calm.
Susan is either rich or old.
Fred is both happy and wise.
Fred is happy.
Someone is both creative and generous.
Someone is not generous or creative. | Fred is not humble. | contradiction | ((?[X]:((patient(X)&wise(X))))=>(?[X]:((tall(X)&~curious(X)))))&
(![X]:(funny(X)<=>(wise(X)<~>old(X))))&
(![X]:((wise(X)<~>calm(X))<=>~creative(X)))&
(((~rich(john)<~>brave(john)))<=>(?[X]:((~quiet(X)&~generous(X)))))&
((funny(paul))<=>((~funny(paul)|wise(paul))))&
(![X]:((quiet(X)<~>~creative(X))<=>quiet(X)))&
((?[X]:(curious(X)))=>(old(mary)))&
((?[X]:((quiet(X)<~>rich(X))))=>((~quiet(fred)|~rich(fred))))&
(((~strong(susan)&~humble(susan)))<=>((~humble(mary)<~>kind(mary))))&
((?[X]:(quiet(X)))=>((~tall(fred)<~>~generous(fred))))&
(![X]:((calm(X)<~>funny(X))=>(strong(X)&~brave(X))))&
((?[X]:(kind(X)))=>(?[X]:((patient(X)<~>happy(X)))))&
((?[X]:((~happy(X)&funny(X))))<=>((brave(mary)|~generous(mary))))&
(![X]:((~rich(X)|generous(X))<=>(humble(X)<~>~quiet(X))))&
(![X]:((~quiet(X)|creative(X))=>(brave(X)&quiet(X))))&
(![X]:(~brave(X)<=>(~quiet(X)&~patient(X))))&
((~tall(alice)<~>~calm(alice)))&
((rich(susan)<~>old(susan)))&
((happy(fred)&wise(fred)))&
(happy(fred))&
(?[X]:((creative(X)&generous(X))))&
(?[X]:((~generous(X)|creative(X)))) | ~humble(fred) | [
"p3",
"p5",
"p7",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1080906900842374939349304
% SZS output start Proof for 1080906900842374939349304
4. (~rich(john) <~> brave(john)) <=> ? [X0] : (~generous(X0) & ~quiet(X0)) [input p3]
6. ! [X0] : ((quiet(X0) <~> ~creative(X0)) <=> quiet(X0)) [input p5]
8. ? [X0] : (quiet(X0) <~> rich(X0)) => (~rich(fred) | ~quiet(fred)) [input p7]
14. ! [X0] : ((generous(X0) | ~rich(X0)) <=> (humble(X0) <~> ~quiet(X0))) [input p13]
15. ! [X0] : ((creative(X0) | ~quiet(X0)) => (quiet(X0) & brave(X0))) [input p14]
23. ~humble(fred) [input hypothesis]
29. (~rich(fred) | ~quiet(fred)) | ! [X0] : (quiet(X0) <=> rich(X0)) [ennf transformation 8]
30. ~rich(fred) | ~quiet(fred) | ! [X0] : (quiet(X0) <=> rich(X0)) [flattening 29]
34. ! [X0] : ((quiet(X0) & brave(X0)) | (~creative(X0) & quiet(X0))) [ennf transformation 15]
40. (((~brave(john) | rich(john)) & (brave(john) | ~rich(john))) | ! [X0] : (generous(X0) | quiet(X0))) & (? [X0] : (~generous(X0) & ~quiet(X0)) | ((~rich(john) | ~brave(john)) & (brave(john) | rich(john)))) [nnf transformation 4]
41. (((~brave(john) | rich(john)) & (brave(john) | ~rich(john))) | ! [X0] : (generous(X0) | quiet(X0))) & (? [X1] : (~generous(X1) & ~quiet(X1)) | ((~rich(john) | ~brave(john)) & (brave(john) | rich(john)))) [rectify 40]
42. ? [X1] : (~generous(X1) & ~quiet(X1)) => (~generous(sK1) & ~quiet(sK1)) [choice axiom]
43. (((~brave(john) | rich(john)) & (brave(john) | ~rich(john))) | ! [X0] : (generous(X0) | quiet(X0))) & ((~generous(sK1) & ~quiet(sK1)) | ((~rich(john) | ~brave(john)) & (brave(john) | rich(john)))) [skolemisation 41,42]
46. ! [X0] : ((((creative(X0) | ~quiet(X0)) & (~creative(X0) | quiet(X0))) | ~quiet(X0)) & (quiet(X0) | ((quiet(X0) | creative(X0)) & (~creative(X0) | ~quiet(X0))))) [nnf transformation 6]
47. ~rich(fred) | ~quiet(fred) | ! [X0] : ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0))) [nnf transformation 30]
61. ! [X0] : (((generous(X0) | ~rich(X0)) | ((humble(X0) | quiet(X0)) & (~quiet(X0) | ~humble(X0)))) & (((quiet(X0) | ~humble(X0)) & (~quiet(X0) | humble(X0))) | (~generous(X0) & rich(X0)))) [nnf transformation 14]
62. ! [X0] : ((generous(X0) | ~rich(X0) | ((humble(X0) | quiet(X0)) & (~quiet(X0) | ~humble(X0)))) & (((quiet(X0) | ~humble(X0)) & (~quiet(X0) | humble(X0))) | (~generous(X0) & rich(X0)))) [flattening 61]
81. ~quiet(sK1) | ~rich(john) | ~brave(john) [cnf transformation 43]
90. quiet(X0) | quiet(X0) | creative(X0) [cnf transformation 46]
92. creative(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 46]
93. ~rich(fred) | ~quiet(fred) | rich(X0) | ~quiet(X0) [cnf transformation 47]
114. ~quiet(X0) | humble(X0) | rich(X0) [cnf transformation 62]
121. brave(X0) | ~creative(X0) [cnf transformation 34]
123. quiet(X0) | ~creative(X0) [cnf transformation 34]
137. ~humble(fred) [cnf transformation 23]
139. quiet(X0) | creative(X0) [duplicate literal removal 90]
140. ~quiet(X0) | creative(X0) [duplicate literal removal 92]
155. 4 <=> rich(john) [avatar definition]
156. ~rich(john) <- (~4) [avatar component clause 155]
159. 5 <=> brave(john) [avatar definition]
161. ~brave(john) <- (~5) [avatar component clause 159]
171. 7 <=> quiet(sK1) [avatar definition]
173. ~quiet(sK1) <- (~7) [avatar component clause 171]
174. ~5 | ~4 | ~7 [avatar split clause 81,171,155,159]
187. creative(X0) [subsumption resolution 139,140]
192. 11 <=> quiet(fred) [avatar definition]
194. ~quiet(fred) <- (~11) [avatar component clause 192]
196. 12 <=> rich(fred) [avatar definition]
201. 13 <=> ! [X0] : (rich(X0) | ~quiet(X0)) [avatar definition]
202. rich(X0) | ~quiet(X0) <- (13) [avatar component clause 201]
203. 13 | ~11 | ~12 [avatar split clause 93,196,192,201]
276. quiet(X0) [subsumption resolution 123,187]
277. brave(X0) [subsumption resolution 121,187]
300. $false <- (~11) [subsumption resolution 194,276]
301. 11 [avatar contradiction clause 300]
302. $false <- (~7) [subsumption resolution 173,276]
303. 7 [avatar contradiction clause 302]
304. $false <- (~5) [subsumption resolution 161,277]
305. 5 [avatar contradiction clause 304]
371. humble(X0) | rich(X0) [resolution 114,276]
409. rich(fred) [resolution 371,137]
416. 12 [avatar split clause 409,196]
417. rich(X0) <- (13) [subsumption resolution 202,276]
418. $false <- (~4, 13) [resolution 417,156]
420. 4 | ~13 [avatar contradiction clause 418]
421. $false [avatar sat refutation 174,203,301,303,305,416,420]
% SZS output end Proof for 1080906900842374939349304
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and generous then alice is either not curious or not funny and vice versa.
If someone is either not generous or tall then someone is rich and vice versa.
Everyone who is brave is both happy and strong.
Everyone who is both not funny and not curious is not funny or not creative and vice versa.
Everyone who is either funny or not brave is not rich and vice versa.
Everyone who is not creative or tall is not quiet and vice versa.
Everyone who is not funny or curious is not generous or not patient and vice versa.
Everyone who is both not calm and not tall is both kind and not quiet.
Everyone who is either not happy or rich is both not curious and curious.
Everyone who is either not rich or tall is funny or not happy and vice versa.
Everyone who is either not kind or not humble is strong and vice versa.
If someone is not old or not funny then lucy is either calm or not creative and vice versa.
Everyone who is both not wise and generous is either not brave or not humble.
If someone is not humble or not creative then mary is both not brave and not generous and vice versa.
If someone is both not funny and not old then susan is both not generous and not quiet and vice versa.
If someone is either tall or quiet then paul is both happy and not old and vice versa.
Lucy is both old and not strong.
Mary is brave or not tall.
Someone is not generous or wise.
Fred is brave or not patient.
Someone is either not patient or creative.
Fred is either not generous or not quiet.
Someone is either funny or old. | Paul is not funny. | neutral | ((?[X]:((~tall(X)&generous(X))))<=>((~curious(alice)<~>~funny(alice))))&
((?[X]:((~generous(X)<~>tall(X))))<=>(?[X]:(rich(X))))&
(![X]:(brave(X)=>(happy(X)&strong(X))))&
(![X]:((~funny(X)&~curious(X))<=>(~funny(X)|~creative(X))))&
(![X]:((funny(X)<~>~brave(X))<=>~rich(X)))&
(![X]:((~creative(X)|tall(X))<=>~quiet(X)))&
(![X]:((~funny(X)|curious(X))<=>(~generous(X)|~patient(X))))&
(![X]:((~calm(X)&~tall(X))=>(kind(X)&~quiet(X))))&
(![X]:((~happy(X)<~>rich(X))=>(~curious(X)&curious(X))))&
(![X]:((~rich(X)<~>tall(X))<=>(funny(X)|~happy(X))))&
(![X]:((~kind(X)<~>~humble(X))<=>strong(X)))&
((?[X]:((~old(X)|~funny(X))))<=>((calm(lucy)<~>~creative(lucy))))&
(![X]:((~wise(X)&generous(X))=>(~brave(X)<~>~humble(X))))&
((?[X]:((~humble(X)|~creative(X))))<=>((~brave(mary)&~generous(mary))))&
((?[X]:((~funny(X)&~old(X))))<=>((~generous(susan)&~quiet(susan))))&
((?[X]:((tall(X)<~>quiet(X))))<=>((happy(paul)&~old(paul))))&
((old(lucy)&~strong(lucy)))&
((brave(mary)|~tall(mary)))&
(?[X]:((~generous(X)|wise(X))))&
((brave(fred)|~patient(fred)))&
(?[X]:((~patient(X)<~>creative(X))))&
((~generous(fred)<~>~quiet(fred)))&
(?[X]:((funny(X)<~>old(X)))) | ~funny(paul) | [] | null | 0 |
If someone is not kind then someone is either funny or not strong and vice versa.
Everyone who is either rich or not calm is old or not creative.
Everyone who is not humble is either not quiet or wise and vice versa.
If lucy is both generous and not patient then susan is both rich and not rich and vice versa.
If fred is humble or strong then john is quiet or strong.
If someone is either not rich or wise then someone is both quiet and not creative and vice versa.
Everyone who is not wise or kind is both quiet and humble and vice versa.
If john is humble then someone is both not wise and kind.
If alice is both generous and wise then someone is curious or rich.
If someone is kind or not funny then mary is either old or not curious and vice versa.
Everyone who is not tall is curious or tall.
Everyone who is not kind is not happy or creative and vice versa.
Everyone who is both kind and not happy is not old and vice versa.
Everyone who is not curious is both brave and not old.
If someone is curious then someone is both happy and creative and vice versa.
Everyone who is not funny or not strong is both not tall and creative and vice versa.
Someone is strong or funny.
Susan is either not brave or not wise.
Someone is not happy.
Someone is both calm and not strong.
Mary is not happy.
Someone is not quiet or not funny. | Alice is wise. | neutral | ((?[X]:(~kind(X)))<=>(?[X]:((funny(X)<~>~strong(X)))))&
(![X]:((rich(X)<~>~calm(X))=>(old(X)|~creative(X))))&
(![X]:(~humble(X)<=>(~quiet(X)<~>wise(X))))&
(((generous(lucy)&~patient(lucy)))<=>((rich(susan)&~rich(susan))))&
(((humble(fred)|strong(fred)))=>((quiet(john)|strong(john))))&
((?[X]:((~rich(X)<~>wise(X))))<=>(?[X]:((quiet(X)&~creative(X)))))&
(![X]:((~wise(X)|kind(X))<=>(quiet(X)&humble(X))))&
((humble(john))=>(?[X]:((~wise(X)&kind(X)))))&
(((generous(alice)&wise(alice)))=>(?[X]:((curious(X)|rich(X)))))&
((?[X]:((kind(X)|~funny(X))))<=>((old(mary)<~>~curious(mary))))&
(![X]:(~tall(X)=>(curious(X)|tall(X))))&
(![X]:(~kind(X)<=>(~happy(X)|creative(X))))&
(![X]:((kind(X)&~happy(X))<=>~old(X)))&
(![X]:(~curious(X)=>(brave(X)&~old(X))))&
((?[X]:(curious(X)))<=>(?[X]:((happy(X)&creative(X)))))&
(![X]:((~funny(X)|~strong(X))<=>(~tall(X)&creative(X))))&
(?[X]:((strong(X)|funny(X))))&
((~brave(susan)<~>~wise(susan)))&
(?[X]:(~happy(X)))&
(?[X]:((calm(X)&~strong(X))))&
(~happy(mary))&
(?[X]:((~quiet(X)|~funny(X)))) | wise(alice) | [] | null | 0 |
If someone is curious or not old then someone is happy or creative and vice versa.
If someone is generous then john is both quiet and not rich and vice versa.
If lucy is not curious then paul is either humble or old.
Everyone who is tall is both not curious and kind and vice versa.
If lucy is quiet or tall then susan is humble or not patient.
If john is either not calm or not strong then someone is not creative or not humble and vice versa.
If lucy is not curious then fred is both not patient and curious.
Everyone who is either happy or not curious is either not kind or humble and vice versa.
Everyone who is both not quiet and not wise is strong or quiet and vice versa.
If someone is not strong or rich then mary is not curious or not tall.
Everyone who is either not curious or strong is not kind and vice versa.
If paul is either not kind or not strong then mary is not old or brave and vice versa.
Everyone who is either not old or not humble is both rich and not funny and vice versa.
If someone is strong then john is generous or quiet and vice versa.
Everyone who is either patient or not brave is not tall or old.
Everyone who is either not tall or generous is not quiet and vice versa.
Someone is brave.
Someone is kind or patient.
Alice is both not brave and old.
Mary is not strong or rich.
Someone is not curious or not kind.
Fred is both wise and brave.
Lucy is rich.
Alice is quiet or patient. | Susan is strong. | contradiction | ((?[X]:((curious(X)|~old(X))))<=>(?[X]:((happy(X)|creative(X)))))&
((?[X]:(generous(X)))<=>((quiet(john)&~rich(john))))&
((~curious(lucy))=>((humble(paul)<~>old(paul))))&
(![X]:(tall(X)<=>(~curious(X)&kind(X))))&
(((quiet(lucy)|tall(lucy)))=>((humble(susan)|~patient(susan))))&
(((~calm(john)<~>~strong(john)))<=>(?[X]:((~creative(X)|~humble(X)))))&
((~curious(lucy))=>((~patient(fred)&curious(fred))))&
(![X]:((happy(X)<~>~curious(X))<=>(~kind(X)<~>humble(X))))&
(![X]:((~quiet(X)&~wise(X))<=>(strong(X)|quiet(X))))&
((?[X]:((~strong(X)|rich(X))))=>((~curious(mary)|~tall(mary))))&
(![X]:((~curious(X)<~>strong(X))<=>~kind(X)))&
(((~kind(paul)<~>~strong(paul)))<=>((~old(mary)|brave(mary))))&
(![X]:((~old(X)<~>~humble(X))<=>(rich(X)&~funny(X))))&
((?[X]:(strong(X)))<=>((generous(john)|quiet(john))))&
(![X]:((patient(X)<~>~brave(X))=>(~tall(X)|old(X))))&
(![X]:((~tall(X)<~>generous(X))<=>~quiet(X)))&
(?[X]:(brave(X)))&
(?[X]:((kind(X)|patient(X))))&
((~brave(alice)&old(alice)))&
((~strong(mary)|rich(mary)))&
(?[X]:((~curious(X)|~kind(X))))&
((wise(fred)&brave(fred)))&
(rich(lucy))&
((quiet(alice)|patient(alice))) | strong(susan) | [
"p1",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4903463491907353713435440
% SZS output start Proof for 4903463491907353713435440
2. ? [X0] : generous(X0) <=> (~rich(john) & quiet(john)) [input p1]
9. ! [X0] : ((~wise(X0) & ~quiet(X0)) <=> (quiet(X0) | strong(X0))) [input p8]
14. ? [X0] : strong(X0) <=> (quiet(john) | generous(john)) [input p13]
25. strong(susan) [input hypothesis]
40. (? [X0] : generous(X0) | (rich(john) | ~quiet(john))) & ((~rich(john) & quiet(john)) | ! [X0] : ~generous(X0)) [nnf transformation 2]
41. (? [X0] : generous(X0) | rich(john) | ~quiet(john)) & ((~rich(john) & quiet(john)) | ! [X0] : ~generous(X0)) [flattening 40]
42. (? [X0] : generous(X0) | rich(john) | ~quiet(john)) & ((~rich(john) & quiet(john)) | ! [X1] : ~generous(X1)) [rectify 41]
43. ? [X0] : generous(X0) => generous(sK2) [choice axiom]
44. (generous(sK2) | rich(john) | ~quiet(john)) & ((~rich(john) & quiet(john)) | ! [X1] : ~generous(X1)) [skolemisation 42,43]
53. ! [X0] : (((~wise(X0) & ~quiet(X0)) | (~quiet(X0) & ~strong(X0))) & ((quiet(X0) | strong(X0)) | (wise(X0) | quiet(X0)))) [nnf transformation 9]
54. ! [X0] : (((~wise(X0) & ~quiet(X0)) | (~quiet(X0) & ~strong(X0))) & (quiet(X0) | strong(X0) | wise(X0) | quiet(X0))) [flattening 53]
60. (? [X0] : strong(X0) | (~quiet(john) & ~generous(john))) & ((quiet(john) | generous(john)) | ! [X0] : ~strong(X0)) [nnf transformation 14]
61. (? [X0] : strong(X0) | (~quiet(john) & ~generous(john))) & (quiet(john) | generous(john) | ! [X0] : ~strong(X0)) [flattening 60]
62. (? [X0] : strong(X0) | (~quiet(john) & ~generous(john))) & (quiet(john) | generous(john) | ! [X1] : ~strong(X1)) [rectify 61]
63. ? [X0] : strong(X0) => strong(sK4) [choice axiom]
64. (strong(sK4) | (~quiet(john) & ~generous(john))) & (quiet(john) | generous(john) | ! [X1] : ~strong(X1)) [skolemisation 62,63]
77. quiet(john) | ~generous(X1) [cnf transformation 44]
105. ~quiet(X0) | ~quiet(X0) [cnf transformation 54]
126. quiet(john) | generous(john) | ~strong(X1) [cnf transformation 64]
145. strong(susan) [cnf transformation 25]
147. ~quiet(X0) [duplicate literal removal 105]
181. 9 <=> quiet(john) [avatar definition]
182. quiet(john) <- (9) [avatar component clause 181]
194. 12 <=> ! [X1] : ~generous(X1) [avatar definition]
195. ~generous(X1) <- (12) [avatar component clause 194]
197. 12 | 9 [avatar split clause 77,181,194]
292. 32 <=> generous(john) [avatar definition]
293. generous(john) <- (32) [avatar component clause 292]
300. generous(john) | ~strong(X1) [subsumption resolution 126,147]
302. 34 <=> ! [X1] : ~strong(X1) [avatar definition]
303. ~strong(X1) <- (34) [avatar component clause 302]
304. 34 | 32 [avatar split clause 300,292,302]
335. $false <- (9) [subsumption resolution 182,147]
336. ~9 [avatar contradiction clause 335]
339. $false <- (12, 32) [resolution 293,195]
340. ~12 | ~32 [avatar contradiction clause 339]
341. $false <- (34) [resolution 303,145]
344. ~34 [avatar contradiction clause 341]
345. $false [avatar sat refutation 197,304,336,340,344]
% SZS output end Proof for 4903463491907353713435440
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not quiet or not brave then someone is not creative or old and vice versa. If fred is either not funny or not strong then fred is funny and vice versa. Everyone who is both not patient and not tall is either not funny or not strong and vice versa. If mary is both kind and not calm then mary is not generous or old. If someone is both not happy and funny then someone is either wise or rich and vice versa. Everyone who is both creative and old is either not brave or calm and vice versa. If fred is both not quiet and not kind then someone is calm and vice versa. Everyone who is both not curious and not rich is either funny or creative and vice versa. If lucy is both wise and kind then someone is both not tall and brave. If someone is both not humble and not old then mary is strong. Everyone who is either not happy or not creative is not humble or not wise and vice versa. If someone is either not happy or not old then someone is both not happy and not humble. Everyone who is both rich and not kind is not curious and vice versa. If fred is wise or not funny then susan is not generous or not happy and vice versa. Everyone who is not funny is both kind and brave. If susan is both not rich and brave then lucy is both not generous and curious. Someone is both brave and happy. Someone is either tall or patient. John is not old or not tall. Fred is either not tall or funny. Someone is either not tall or rich. Someone is not funny. Fred is creative or rich. Someone is not old. | Fred is creative. | contradiction | (((~quiet(alice)<~>~brave(alice)))<=>(?[X]:((~creative(X)|old(X)))))&
(((~funny(fred)<~>~strong(fred)))<=>(funny(fred)))&
(![X]:((~patient(X)&~tall(X))<=>(~funny(X)<~>~strong(X))))&
(((kind(mary)&~calm(mary)))=>((~generous(mary)|old(mary))))&
((?[X]:((~happy(X)&funny(X))))<=>(?[X]:((wise(X)<~>rich(X)))))&
(![X]:((creative(X)&old(X))<=>(~brave(X)<~>calm(X))))&
(((~quiet(fred)&~kind(fred)))<=>(?[X]:(calm(X))))&
(![X]:((~curious(X)&~rich(X))<=>(funny(X)<~>creative(X))))&
(((wise(lucy)&kind(lucy)))=>(?[X]:((~tall(X)&brave(X)))))&
((?[X]:((~humble(X)&~old(X))))=>(strong(mary)))&
(![X]:((~happy(X)<~>~creative(X))<=>(~humble(X)|~wise(X))))&
((?[X]:((~happy(X)<~>~old(X))))=>(?[X]:((~happy(X)&~humble(X)))))&
(![X]:((rich(X)&~kind(X))<=>~curious(X)))&
(((wise(fred)|~funny(fred)))<=>((~generous(susan)|~happy(susan))))&
(![X]:(~funny(X)=>(kind(X)&brave(X))))&
(((~rich(susan)&brave(susan)))=>((~generous(lucy)&curious(lucy))))&
(?[X]:((brave(X)&happy(X))))&
(?[X]:((tall(X)<~>patient(X))))&
((~old(john)|~tall(john)))&
((~tall(fred)<~>funny(fred)))&
(?[X]:((~tall(X)<~>rich(X))))&
(?[X]:(~funny(X)))&
((creative(fred)|rich(fred)))&
(?[X]:(~old(X))) | creative(fred) | [
"p1",
"p2",
"p7",
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7645303809675996786742514
% SZS output start Proof for 7645303809675996786742514
2. (~funny(fred) <~> ~strong(fred)) <=> funny(fred) [input p1]
3. ! [X0] : ((~tall(X0) & ~patient(X0)) <=> (~funny(X0) <~> ~strong(X0))) [input p2]
8. ! [X0] : ((~rich(X0) & ~curious(X0)) <=> (funny(X0) <~> creative(X0))) [input p7]
13. ! [X0] : ((~kind(X0) & rich(X0)) <=> ~curious(X0)) [input p12]
15. ! [X0] : (~funny(X0) => (brave(X0) & kind(X0))) [input p14]
20. ~tall(fred) <~> funny(fred) [input p19]
25. creative(fred) [input hypothesis]
34. ! [X0] : ((brave(X0) & kind(X0)) | funny(X0)) [ennf transformation 15]
41. (((strong(fred) | funny(fred)) & (~strong(fred) | ~funny(fred))) | ~funny(fred)) & (funny(fred) | ((~funny(fred) | strong(fred)) & (~strong(fred) | funny(fred)))) [nnf transformation 2]
42. ! [X0] : (((~tall(X0) & ~patient(X0)) | ((~funny(X0) | strong(X0)) & (~strong(X0) | funny(X0)))) & (((strong(X0) | funny(X0)) & (~strong(X0) | ~funny(X0))) | (tall(X0) | patient(X0)))) [nnf transformation 3]
43. ! [X0] : (((~tall(X0) & ~patient(X0)) | ((~funny(X0) | strong(X0)) & (~strong(X0) | funny(X0)))) & (((strong(X0) | funny(X0)) & (~strong(X0) | ~funny(X0))) | tall(X0) | patient(X0))) [flattening 42]
56. ! [X0] : (((~rich(X0) & ~curious(X0)) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) & (((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | (rich(X0) | curious(X0)))) [nnf transformation 8]
57. ! [X0] : (((~rich(X0) & ~curious(X0)) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) & (((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | rich(X0) | curious(X0))) [flattening 56]
66. ! [X0] : (((~kind(X0) & rich(X0)) | curious(X0)) & (~curious(X0) | (kind(X0) | ~rich(X0)))) [nnf transformation 13]
67. ! [X0] : (((~kind(X0) & rich(X0)) | curious(X0)) & (~curious(X0) | kind(X0) | ~rich(X0))) [flattening 66]
75. (~funny(fred) | tall(fred)) & (funny(fred) | ~tall(fred)) [nnf transformation 20]
91. ~strong(fred) | ~funny(fred) | ~funny(fred) [cnf transformation 41]
98. ~tall(X0) | ~funny(X0) | strong(X0) [cnf transformation 43]
118. ~curious(X0) | funny(X0) | ~creative(X0) [cnf transformation 57]
136. ~kind(X0) | curious(X0) [cnf transformation 67]
141. kind(X0) | funny(X0) [cnf transformation 34]
151. ~funny(fred) | tall(fred) [cnf transformation 75]
157. creative(fred) [cnf transformation 25]
159. ~strong(fred) | ~funny(fred) [duplicate literal removal 91]
189. 7 <=> funny(fred) [avatar definition]
190. funny(fred) <- (7) [avatar component clause 189]
193. 8 <=> strong(fred) [avatar definition]
195. ~strong(fred) <- (~8) [avatar component clause 193]
196. ~7 | ~8 [avatar split clause 159,193,189]
362. 45 <=> tall(fred) [avatar definition]
364. tall(fred) <- (45) [avatar component clause 362]
365. 45 | ~7 [avatar split clause 151,189,362]
378. 48 <=> creative(fred) [avatar definition]
380. creative(fred) <- (48) [avatar component clause 378]
386. 48 [avatar split clause 157,378]
389. curious(X0) | funny(X0) [resolution 141,136]
436. funny(X0) | ~creative(X0) | funny(X0) [resolution 118,389]
439. ~creative(X0) | funny(X0) [duplicate literal removal 436]
479. funny(fred) <- (48) [resolution 439,380]
485. 7 | ~48 [avatar split clause 479,378,189]
487. ~funny(fred) | strong(fred) <- (45) [resolution 364,98]
489. strong(fred) <- (7, 45) [subsumption resolution 487,190]
490. $false <- (7, ~8, 45) [subsumption resolution 489,195]
491. ~7 | 8 | ~45 [avatar contradiction clause 490]
492. $false [avatar sat refutation 196,365,386,485,491]
% SZS output end Proof for 7645303809675996786742514
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative or not curious then someone is either not patient or calm and vice versa.
Everyone who is not creative or not funny is either not tall or not curious.
Everyone who is humble or tall is both wise and not brave and vice versa.
If lucy is rich then alice is either not kind or quiet and vice versa.
If john is funny then fred is curious and vice versa.
If someone is both not wise and generous then someone is both generous and not humble.
Everyone who is not quiet or curious is both not calm and old.
Everyone who is either not kind or not calm is both humble and old and vice versa.
If paul is not humble or funny then someone is funny or not happy and vice versa.
Everyone who is rich or not tall is calm or humble.
Everyone who is calm or happy is both calm and not funny and vice versa.
Everyone who is old or not tall is not happy.
Everyone who is both not curious and not funny is not rich.
Everyone who is brave is tall or strong.
If alice is happy then fred is either tall or not curious and vice versa.
Paul is not generous or calm.
John is not old or not calm.
Someone is both happy and not patient.
John is curious.
John is not humble.
Alice is both generous and not brave. | Paul is not old. | neutral | ((?[X]:((creative(X)|~curious(X))))<=>(?[X]:((~patient(X)<~>calm(X)))))&
(![X]:((~creative(X)|~funny(X))=>(~tall(X)<~>~curious(X))))&
(![X]:((humble(X)|tall(X))<=>(wise(X)&~brave(X))))&
((rich(lucy))<=>((~kind(alice)<~>quiet(alice))))&
((funny(john))<=>(curious(fred)))&
((?[X]:((~wise(X)&generous(X))))=>(?[X]:((generous(X)&~humble(X)))))&
(![X]:((~quiet(X)|curious(X))=>(~calm(X)&old(X))))&
(![X]:((~kind(X)<~>~calm(X))<=>(humble(X)&old(X))))&
(((~humble(paul)|funny(paul)))<=>(?[X]:((funny(X)|~happy(X)))))&
(![X]:((rich(X)|~tall(X))=>(calm(X)|humble(X))))&
(![X]:((calm(X)|happy(X))<=>(calm(X)&~funny(X))))&
(![X]:((old(X)|~tall(X))=>~happy(X)))&
(![X]:((~curious(X)&~funny(X))=>~rich(X)))&
(![X]:(brave(X)=>(tall(X)|strong(X))))&
((happy(alice))<=>((tall(fred)<~>~curious(fred))))&
((~generous(paul)|calm(paul)))&
((~old(john)|~calm(john)))&
(?[X]:((happy(X)&~patient(X))))&
(curious(john))&
(~humble(john))&
((generous(alice)&~brave(alice))) | ~old(paul) | [] | null | 0 |
Everyone who is either not funny or not old is tall and vice versa.
If john is not tall then someone is either not calm or quiet.
Everyone who is not kind is not funny.
If lucy is either kind or quiet then someone is both generous and not patient.
Everyone who is not rich or not creative is not humble and vice versa.
If someone is both not creative and not generous then mary is not old or not kind and vice versa.
Everyone who is both not humble and brave is both wise and not quiet and vice versa.
Everyone who is either not happy or tall is either not tall or strong and vice versa.
If paul is both not calm and rich then someone is humble and vice versa.
Everyone who is tall is calm or brave.
Everyone who is not quiet or not humble is either generous or not humble and vice versa.
Everyone who is either not happy or not creative is wise or not curious and vice versa.
Everyone who is either rich or not funny is either curious or not curious and vice versa.
Everyone who is not strong or not generous is brave and vice versa.
Everyone who is not happy or tall is not rich or funny.
Everyone who is not funny is not calm and vice versa.
Someone is creative or patient.
Someone is wise or not creative.
Someone is both patient and not funny.
Someone is not wise or not calm.
Someone is not generous or quiet. | John is wise. | entailment | (![X]:((~funny(X)<~>~old(X))<=>tall(X)))&
((~tall(john))=>(?[X]:((~calm(X)<~>quiet(X)))))&
(![X]:(~kind(X)=>~funny(X)))&
(((kind(lucy)<~>quiet(lucy)))=>(?[X]:((generous(X)&~patient(X)))))&
(![X]:((~rich(X)|~creative(X))<=>~humble(X)))&
((?[X]:((~creative(X)&~generous(X))))<=>((~old(mary)|~kind(mary))))&
(![X]:((~humble(X)&brave(X))<=>(wise(X)&~quiet(X))))&
(![X]:((~happy(X)<~>tall(X))<=>(~tall(X)<~>strong(X))))&
(((~calm(paul)&rich(paul)))<=>(?[X]:(humble(X))))&
(![X]:(tall(X)=>(calm(X)|brave(X))))&
(![X]:((~quiet(X)|~humble(X))<=>(generous(X)<~>~humble(X))))&
(![X]:((~happy(X)<~>~creative(X))<=>(wise(X)|~curious(X))))&
(![X]:((rich(X)<~>~funny(X))<=>(curious(X)<~>~curious(X))))&
(![X]:((~strong(X)|~generous(X))<=>brave(X)))&
(![X]:((~happy(X)|tall(X))=>(~rich(X)|funny(X))))&
(![X]:(~funny(X)<=>~calm(X)))&
(?[X]:((creative(X)|patient(X))))&
(?[X]:((wise(X)|~creative(X))))&
(?[X]:((patient(X)&~funny(X))))&
(?[X]:((~wise(X)|~calm(X))))&
(?[X]:((~generous(X)|quiet(X)))) | wise(john) | [
"p6",
"p8",
"p10",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6720018115923620081464110
% SZS output start Proof for 6720018115923620081464110
7. ! [X0] : ((brave(X0) & ~humble(X0)) <=> (~quiet(X0) & wise(X0))) [input p6]
9. (rich(paul) & ~calm(paul)) <=> ? [X0] : humble(X0) [input p8]
11. ! [X0] : ((~humble(X0) | ~quiet(X0)) <=> (generous(X0) <~> ~humble(X0))) [input p10]
13. ! [X0] : ((rich(X0) <~> ~funny(X0)) <=> (curious(X0) <~> ~curious(X0))) [input p12]
14. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> brave(X0)) [input p13]
16. ! [X0] : (~funny(X0) <=> ~calm(X0)) [input p15]
22. ~wise(john) [input hypothesis]
44. ! [X0] : (((brave(X0) & ~humble(X0)) | (quiet(X0) | ~wise(X0))) & ((~quiet(X0) & wise(X0)) | (~brave(X0) | humble(X0)))) [nnf transformation 7]
45. ! [X0] : (((brave(X0) & ~humble(X0)) | quiet(X0) | ~wise(X0)) & ((~quiet(X0) & wise(X0)) | ~brave(X0) | humble(X0))) [flattening 44]
47. ((rich(paul) & ~calm(paul)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | (~rich(paul) | calm(paul))) [nnf transformation 9]
48. ((rich(paul) & ~calm(paul)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | ~rich(paul) | calm(paul)) [flattening 47]
49. ((rich(paul) & ~calm(paul)) | ! [X0] : ~humble(X0)) & (? [X1] : humble(X1) | ~rich(paul) | calm(paul)) [rectify 48]
50. ? [X1] : humble(X1) => humble(sK3) [choice axiom]
51. ((rich(paul) & ~calm(paul)) | ! [X0] : ~humble(X0)) & (humble(sK3) | ~rich(paul) | calm(paul)) [skolemisation 49,50]
52. ! [X0] : (((~humble(X0) | ~quiet(X0)) | ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0)))) & (((humble(X0) | ~generous(X0)) & (~humble(X0) | generous(X0))) | (humble(X0) & quiet(X0)))) [nnf transformation 11]
53. ! [X0] : ((~humble(X0) | ~quiet(X0) | ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0)))) & (((humble(X0) | ~generous(X0)) & (~humble(X0) | generous(X0))) | (humble(X0) & quiet(X0)))) [flattening 52]
56. ! [X0] : ((((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0))))) [nnf transformation 13]
57. ! [X0] : (((~generous(X0) | ~strong(X0)) | ~brave(X0)) & (brave(X0) | (generous(X0) & strong(X0)))) [nnf transformation 14]
58. ! [X0] : ((~generous(X0) | ~strong(X0) | ~brave(X0)) & (brave(X0) | (generous(X0) & strong(X0)))) [flattening 57]
59. ! [X0] : ((~funny(X0) | calm(X0)) & (~calm(X0) | funny(X0))) [nnf transformation 16]
89. ~brave(X0) | wise(X0) | humble(X0) [cnf transformation 45]
102. ~calm(paul) | ~humble(X0) [cnf transformation 51]
103. rich(paul) | ~humble(X0) [cnf transformation 51]
108. humble(X0) | ~generous(X0) | humble(X0) [cnf transformation 53]
123. funny(X0) | ~rich(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 56]
124. funny(X0) | ~rich(X0) | curious(X0) | curious(X0) [cnf transformation 56]
126. brave(X0) | generous(X0) [cnf transformation 58]
131. ~funny(X0) | calm(X0) [cnf transformation 59]
138. ~wise(john) [cnf transformation 22]
141. funny(X0) | ~rich(X0) | ~curious(X0) [duplicate literal removal 123]
142. funny(X0) | ~rich(X0) | curious(X0) [duplicate literal removal 124]
143. ~generous(X0) | humble(X0) [duplicate literal removal 108]
210. 13 <=> ! [X0] : ~humble(X0) [avatar definition]
211. ~humble(X0) <- (13) [avatar component clause 210]
213. 14 <=> rich(paul) [avatar definition]
215. rich(paul) <- (14) [avatar component clause 213]
216. 13 | 14 [avatar split clause 103,213,210]
218. 15 <=> calm(paul) [avatar definition]
220. ~calm(paul) <- (~15) [avatar component clause 218]
221. 13 | ~15 [avatar split clause 102,218,210]
227. ~rich(X0) | funny(X0) [subsumption resolution 141,142]
269. wise(X0) | humble(X0) | generous(X0) [resolution 89,126]
270. wise(X0) | generous(X0) <- (13) [subsumption resolution 269,211]
271. generous(john) <- (13) [resolution 270,138]
274. humble(john) <- (13) [resolution 271,143]
275. $false <- (13) [subsumption resolution 274,211]
276. ~13 [avatar contradiction clause 275]
288. funny(paul) <- (14) [resolution 215,227]
293. calm(paul) <- (14) [resolution 288,131]
304. $false <- (14, ~15) [subsumption resolution 293,220]
305. ~14 | 15 [avatar contradiction clause 304]
306. $false [avatar sat refutation 216,221,276,305]
% SZS output end Proof for 6720018115923620081464110
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and not generous is either creative or not calm. If someone is either rich or not generous then fred is quiet. If paul is quiet or patient then paul is not brave or patient and vice versa. Everyone who is both funny and generous is happy and vice versa. Everyone who is humble or not creative is calm. Everyone who is both wise and not patient is both curious and not curious. Everyone who is both not curious and not strong is creative or not quiet and vice versa. Everyone who is curious or not rich is either happy or not brave. If mary is wise or not curious then susan is both humble and old. Everyone who is kind or happy is both not brave and curious and vice versa. Everyone who is quiet or not humble is not quiet or quiet and vice versa. Everyone who is not kind is either quiet or humble and vice versa. Everyone who is either not funny or patient is either humble or not quiet and vice versa. If someone is rich or not tall then someone is either creative or generous and vice versa. John is either curious or not creative. Someone is either not patient or patient. Lucy is either not happy or not humble. Someone is both rich and wise. Someone is not tall or quiet. Someone is both brave and not generous. Someone is either not patient or curious. Someone is either rich or not old. | Susan is not curious. | neutral | (![X]:((calm(X)&~generous(X))=>(creative(X)<~>~calm(X))))&
((?[X]:((rich(X)<~>~generous(X))))=>(quiet(fred)))&
(((quiet(paul)|patient(paul)))<=>((~brave(paul)|patient(paul))))&
(![X]:((funny(X)&generous(X))<=>happy(X)))&
(![X]:((humble(X)|~creative(X))=>calm(X)))&
(![X]:((wise(X)&~patient(X))=>(curious(X)&~curious(X))))&
(![X]:((~curious(X)&~strong(X))<=>(creative(X)|~quiet(X))))&
(![X]:((curious(X)|~rich(X))=>(happy(X)<~>~brave(X))))&
(((wise(mary)|~curious(mary)))=>((humble(susan)&old(susan))))&
(![X]:((kind(X)|happy(X))<=>(~brave(X)&curious(X))))&
(![X]:((quiet(X)|~humble(X))<=>(~quiet(X)|quiet(X))))&
(![X]:(~kind(X)<=>(quiet(X)<~>humble(X))))&
(![X]:((~funny(X)<~>patient(X))<=>(humble(X)<~>~quiet(X))))&
((?[X]:((rich(X)|~tall(X))))<=>(?[X]:((creative(X)<~>generous(X)))))&
((curious(john)<~>~creative(john)))&
(?[X]:((~patient(X)<~>patient(X))))&
((~happy(lucy)<~>~humble(lucy)))&
(?[X]:((rich(X)&wise(X))))&
(?[X]:((~tall(X)|quiet(X))))&
(?[X]:((brave(X)&~generous(X))))&
(?[X]:((~patient(X)<~>curious(X))))&
(?[X]:((rich(X)<~>~old(X)))) | ~curious(susan) | [] | null | 0 |
Everyone who is not happy or patient is kind.
If someone is not generous then someone is both patient and not funny.
Everyone who is both not wise and not funny is not quiet.
Everyone who is either not old or not strong is both not curious and wise.
If someone is both not old and not wise then lucy is rich or not quiet and vice versa.
If someone is not rich or not tall then mary is both brave and not funny.
Everyone who is not old or happy is either brave or not humble.
Everyone who is both not tall and not patient is not patient or funny.
If someone is both rich and quiet then john is either not curious or not calm.
Everyone who is calm or strong is not creative or not quiet and vice versa.
If mary is brave or creative then paul is calm and vice versa.
Everyone who is both not old and old is happy or creative and vice versa.
If someone is not wise or not tall then lucy is not quiet or not tall and vice versa.
Everyone who is both creative and patient is either not wise or not tall and vice versa.
If paul is both quiet and not generous then someone is either not rich or not humble and vice versa.
Everyone who is either not happy or not quiet is not curious and vice versa.
Fred is not happy.
John is strong or not rich.
Someone is either not old or not kind.
Fred is either patient or humble.
John is calm. | John is not kind. | contradiction | (![X]:((~happy(X)|patient(X))=>kind(X)))&
((?[X]:(~generous(X)))=>(?[X]:((patient(X)&~funny(X)))))&
(![X]:((~wise(X)&~funny(X))=>~quiet(X)))&
(![X]:((~old(X)<~>~strong(X))=>(~curious(X)&wise(X))))&
((?[X]:((~old(X)&~wise(X))))<=>((rich(lucy)|~quiet(lucy))))&
((?[X]:((~rich(X)|~tall(X))))=>((brave(mary)&~funny(mary))))&
(![X]:((~old(X)|happy(X))=>(brave(X)<~>~humble(X))))&
(![X]:((~tall(X)&~patient(X))=>(~patient(X)|funny(X))))&
((?[X]:((rich(X)&quiet(X))))=>((~curious(john)<~>~calm(john))))&
(![X]:((calm(X)|strong(X))<=>(~creative(X)|~quiet(X))))&
(((brave(mary)|creative(mary)))<=>(calm(paul)))&
(![X]:((~old(X)&old(X))<=>(happy(X)|creative(X))))&
((?[X]:((~wise(X)|~tall(X))))<=>((~quiet(lucy)|~tall(lucy))))&
(![X]:((creative(X)&patient(X))<=>(~wise(X)<~>~tall(X))))&
(((quiet(paul)&~generous(paul)))<=>(?[X]:((~rich(X)<~>~humble(X)))))&
(![X]:((~happy(X)<~>~quiet(X))<=>~curious(X)))&
(~happy(fred))&
((strong(john)|~rich(john)))&
(?[X]:((~old(X)<~>~kind(X))))&
((patient(fred)<~>humble(fred)))&
(calm(john)) | ~kind(john) | [
"p0",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 468796819215885038472149
% SZS output start Proof for 468796819215885038472149
1. ! [X0] : ((patient(X0) | ~happy(X0)) => kind(X0)) [input p0]
12. ! [X0] : ((old(X0) & ~old(X0)) <=> (creative(X0) | happy(X0))) [input p11]
22. ~kind(john) [input hypothesis]
24. ! [X0] : (kind(X0) | (~patient(X0) & happy(X0))) [ennf transformation 1]
49. ! [X0] : (((old(X0) & ~old(X0)) | (~creative(X0) & ~happy(X0))) & ((creative(X0) | happy(X0)) | (~old(X0) | old(X0)))) [nnf transformation 12]
50. ! [X0] : (((old(X0) & ~old(X0)) | (~creative(X0) & ~happy(X0))) & (creative(X0) | happy(X0) | ~old(X0) | old(X0))) [flattening 49]
68. kind(X0) | happy(X0) [cnf transformation 24]
101. ~old(X0) | ~happy(X0) [cnf transformation 50]
103. old(X0) | ~happy(X0) [cnf transformation 50]
132. ~kind(john) [cnf transformation 22]
213. ~happy(X0) [subsumption resolution 101,103]
299. happy(john) [resolution 68,132]
301. $false [subsumption resolution 299,213]
% SZS output end Proof for 468796819215885038472149
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is not patient then someone is not brave or not humble and vice versa.
If someone is either not calm or rich then someone is not kind.
Everyone who is not generous is not funny or not creative.
Everyone who is either not creative or not patient is either curious or not calm and vice versa.
Everyone who is either not strong or humble is patient.
If someone is kind or happy then lucy is both funny and not humble.
If paul is funny or quiet then alice is both funny and not generous.
If someone is old or creative then fred is not brave and vice versa.
If someone is not wise then someone is both not patient and not funny.
Everyone who is not generous is either not old or not wise.
If lucy is not brave then lucy is patient and vice versa.
Everyone who is not humble or not rich is not happy or quiet.
Everyone who is either patient or not rich is both not tall and not old.
Everyone who is either rich or not rich is funny or patient and vice versa.
Everyone who is curious is not generous.
Someone is kind or generous.
Alice is not calm or not humble.
Someone is either not creative or not kind.
Someone is both not quiet and not old.
Someone is patient or not wise.
Someone is wise or happy. | John is patient. | contradiction | ((~patient(john))<=>(?[X]:((~brave(X)|~humble(X)))))&
((?[X]:((~calm(X)<~>rich(X))))=>(?[X]:(~kind(X))))&
(![X]:(~generous(X)=>(~funny(X)|~creative(X))))&
(![X]:((~creative(X)<~>~patient(X))<=>(curious(X)<~>~calm(X))))&
(![X]:((~strong(X)<~>humble(X))=>patient(X)))&
((?[X]:((kind(X)|happy(X))))=>((funny(lucy)&~humble(lucy))))&
(((funny(paul)|quiet(paul)))=>((funny(alice)&~generous(alice))))&
((?[X]:((old(X)|creative(X))))<=>(~brave(fred)))&
((?[X]:(~wise(X)))=>(?[X]:((~patient(X)&~funny(X)))))&
(![X]:(~generous(X)=>(~old(X)<~>~wise(X))))&
((~brave(lucy))<=>(patient(lucy)))&
(![X]:((~humble(X)|~rich(X))=>(~happy(X)|quiet(X))))&
(![X]:((patient(X)<~>~rich(X))=>(~tall(X)&~old(X))))&
(![X]:((rich(X)<~>~rich(X))<=>(funny(X)|patient(X))))&
(![X]:(curious(X)=>~generous(X)))&
(?[X]:((kind(X)|generous(X))))&
((~calm(alice)|~humble(alice)))&
(?[X]:((~creative(X)<~>~kind(X))))&
(?[X]:((~quiet(X)&~old(X))))&
(?[X]:((patient(X)|~wise(X))))&
(?[X]:((wise(X)|happy(X)))) | patient(john) | [
"p0",
"p5",
"p7",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2908317343198777525335372
% SZS output start Proof for 2908317343198777525335372
1. ~patient(john) <=> ? [X0] : (~humble(X0) | ~brave(X0)) [input p0]
6. ? [X0] : (happy(X0) | kind(X0)) => (~humble(lucy) & funny(lucy)) [input p5]
8. ? [X0] : (creative(X0) | old(X0)) <=> ~brave(fred) [input p7]
18. ? [X0] : (~creative(X0) <~> ~kind(X0)) [input p17]
22. patient(john) [input hypothesis]
30. (~humble(lucy) & funny(lucy)) | ! [X0] : (~happy(X0) & ~kind(X0)) [ennf transformation 6]
38. (~patient(john) | ! [X0] : (humble(X0) & brave(X0))) & (? [X0] : (~humble(X0) | ~brave(X0)) | patient(john)) [nnf transformation 1]
39. (~patient(john) | ! [X0] : (humble(X0) & brave(X0))) & (? [X1] : (~humble(X1) | ~brave(X1)) | patient(john)) [rectify 38]
40. ? [X1] : (~humble(X1) | ~brave(X1)) => (~humble(sK0) | ~brave(sK0)) [choice axiom]
41. (~patient(john) | ! [X0] : (humble(X0) & brave(X0))) & ((~humble(sK0) | ~brave(sK0)) | patient(john)) [skolemisation 39,40]
48. (? [X0] : (creative(X0) | old(X0)) | brave(fred)) & (~brave(fred) | ! [X0] : (~creative(X0) & ~old(X0))) [nnf transformation 8]
49. (? [X0] : (creative(X0) | old(X0)) | brave(fred)) & (~brave(fred) | ! [X1] : (~creative(X1) & ~old(X1))) [rectify 48]
50. ? [X0] : (creative(X0) | old(X0)) => (creative(sK2) | old(sK2)) [choice axiom]
51. ((creative(sK2) | old(sK2)) | brave(fred)) & (~brave(fred) | ! [X1] : (~creative(X1) & ~old(X1))) [skolemisation 49,50]
62. ? [X0] : ((kind(X0) | creative(X0)) & (~kind(X0) | ~creative(X0))) [nnf transformation 18]
63. ? [X0] : ((kind(X0) | creative(X0)) & (~kind(X0) | ~creative(X0))) => ((kind(sK5) | creative(sK5)) & (~kind(sK5) | ~creative(sK5))) [choice axiom]
64. (kind(sK5) | creative(sK5)) & (~kind(sK5) | ~creative(sK5)) [skolemisation 62,63]
72. ~patient(john) | brave(X0) [cnf transformation 41]
73. ~patient(john) | humble(X0) [cnf transformation 41]
89. ~humble(lucy) | ~kind(X0) [cnf transformation 30]
96. ~brave(fred) | ~creative(X1) [cnf transformation 51]
118. kind(sK5) | creative(sK5) [cnf transformation 64]
123. patient(john) [cnf transformation 22]
127. 1 <=> ! [X0] : humble(X0) [avatar definition]
128. humble(X0) <- (1) [avatar component clause 127]
130. 2 <=> patient(john) [avatar definition]
133. 1 | ~2 [avatar split clause 73,130,127]
135. 3 <=> ! [X0] : brave(X0) [avatar definition]
136. brave(X0) <- (3) [avatar component clause 135]
137. 3 | ~2 [avatar split clause 72,130,135]
163. 10 <=> humble(lucy) [avatar definition]
165. ~humble(lucy) <- (~10) [avatar component clause 163]
168. 11 <=> ! [X0] : ~kind(X0) [avatar definition]
169. ~kind(X0) <- (11) [avatar component clause 168]
170. 11 | ~10 [avatar split clause 89,163,168]
198. 17 <=> brave(fred) [avatar definition]
199. ~brave(fred) <- (~17) [avatar component clause 198]
211. 20 <=> ! [X1] : ~creative(X1) [avatar definition]
212. ~creative(X1) <- (20) [avatar component clause 211]
213. 20 | ~17 [avatar split clause 96,198,211]
261. 31 <=> creative(sK5) [avatar definition]
263. creative(sK5) <- (31) [avatar component clause 261]
265. 32 <=> kind(sK5) [avatar definition]
267. kind(sK5) <- (32) [avatar component clause 265]
268. 31 | 32 [avatar split clause 118,265,261]
288. 2 [avatar split clause 123,130]
289. $false <- (3, ~17) [resolution 199,136]
290. ~3 | 17 [avatar contradiction clause 289]
297. $false <- (1, ~10) [subsumption resolution 165,128]
298. ~1 | 10 [avatar contradiction clause 297]
299. $false <- (20, 31) [resolution 263,212]
300. ~20 | ~31 [avatar contradiction clause 299]
301. $false <- (11, 32) [subsumption resolution 267,169]
302. ~11 | ~32 [avatar contradiction clause 301]
303. $false [avatar sat refutation 133,137,170,213,268,288,290,298,300,302]
% SZS output end Proof for 2908317343198777525335372
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and not tall is not tall or funny and vice versa.
Everyone who is both not generous and wise is both old and not tall.
Everyone who is either quiet or old is generous.
Everyone who is humble is not kind.
Everyone who is either kind or not wise is either humble or not patient.
Everyone who is either not strong or funny is rich.
If someone is either funny or not brave then someone is not tall or kind.
If someone is not creative or not tall then someone is both happy and not tall and vice versa.
Everyone who is either tall or not creative is not humble or not generous and vice versa.
If someone is quiet then someone is both strong and old and vice versa.
If lucy is not tall or not curious then someone is both creative and not old and vice versa.
If lucy is either not quiet or generous then someone is not funny or not humble and vice versa.
Everyone who is both not creative and happy is not generous.
If someone is not rich then someone is not happy or not brave and vice versa.
If lucy is not brave or not tall then someone is either not rich or curious and vice versa.
Everyone who is both not wise and not tall is both not curious and kind and vice versa.
Someone is happy.
Mary is not funny or strong.
Mary is both generous and kind.
Alice is both humble and not wise.
John is both humble and not generous.
Paul is either kind or brave.
Alice is not happy or not funny.
Alice is either not wise or happy. | Lucy is not curious. | neutral | (![X]:((~strong(X)&~tall(X))<=>(~tall(X)|funny(X))))&
(![X]:((~generous(X)&wise(X))=>(old(X)&~tall(X))))&
(![X]:((quiet(X)<~>old(X))=>generous(X)))&
(![X]:(humble(X)=>~kind(X)))&
(![X]:((kind(X)<~>~wise(X))=>(humble(X)<~>~patient(X))))&
(![X]:((~strong(X)<~>funny(X))=>rich(X)))&
((?[X]:((funny(X)<~>~brave(X))))=>(?[X]:((~tall(X)|kind(X)))))&
((?[X]:((~creative(X)|~tall(X))))<=>(?[X]:((happy(X)&~tall(X)))))&
(![X]:((tall(X)<~>~creative(X))<=>(~humble(X)|~generous(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((strong(X)&old(X)))))&
(((~tall(lucy)|~curious(lucy)))<=>(?[X]:((creative(X)&~old(X)))))&
(((~quiet(lucy)<~>generous(lucy)))<=>(?[X]:((~funny(X)|~humble(X)))))&
(![X]:((~creative(X)&happy(X))=>~generous(X)))&
((?[X]:(~rich(X)))<=>(?[X]:((~happy(X)|~brave(X)))))&
(((~brave(lucy)|~tall(lucy)))<=>(?[X]:((~rich(X)<~>curious(X)))))&
(![X]:((~wise(X)&~tall(X))<=>(~curious(X)&kind(X))))&
(?[X]:(happy(X)))&
((~funny(mary)|strong(mary)))&
((generous(mary)&kind(mary)))&
((humble(alice)&~wise(alice)))&
((humble(john)&~generous(john)))&
((kind(paul)<~>brave(paul)))&
((~happy(alice)|~funny(alice)))&
((~wise(alice)<~>happy(alice))) | ~curious(lucy) | [] | null | 0 |
If paul is both humble and patient then someone is wise.
If lucy is not humble then fred is either not kind or generous.
Everyone who is not calm or not happy is not creative or tall.
Everyone who is not curious is both patient and not strong and vice versa.
If fred is funny then someone is either patient or humble.
If lucy is both happy and not quiet then someone is both happy and calm.
If someone is both rich and old then lucy is either kind or curious.
Everyone who is both rich and not generous is happy.
Everyone who is either not kind or happy is both calm and not kind and vice versa.
Everyone who is not rich or wise is both curious and not tall and vice versa.
Everyone who is both patient and creative is both not rich and wise and vice versa.
Everyone who is either rich or brave is not curious or quiet.
If john is wise then paul is both not rich and funny.
If alice is not old then lucy is both not creative and kind and vice versa.
If someone is humble then susan is either rich or not wise.
Everyone who is both funny and strong is rich or not strong and vice versa.
Lucy is generous.
John is not funny.
Paul is not brave.
Someone is either not strong or kind.
Someone is old or not creative.
Fred is both not patient and not creative. | Alice is not strong. | contradiction | (((humble(paul)&patient(paul)))=>(?[X]:(wise(X))))&
((~humble(lucy))=>((~kind(fred)<~>generous(fred))))&
(![X]:((~calm(X)|~happy(X))=>(~creative(X)|tall(X))))&
(![X]:(~curious(X)<=>(patient(X)&~strong(X))))&
((funny(fred))=>(?[X]:((patient(X)<~>humble(X)))))&
(((happy(lucy)&~quiet(lucy)))=>(?[X]:((happy(X)&calm(X)))))&
((?[X]:((rich(X)&old(X))))=>((kind(lucy)<~>curious(lucy))))&
(![X]:((rich(X)&~generous(X))=>happy(X)))&
(![X]:((~kind(X)<~>happy(X))<=>(calm(X)&~kind(X))))&
(![X]:((~rich(X)|wise(X))<=>(curious(X)&~tall(X))))&
(![X]:((patient(X)&creative(X))<=>(~rich(X)&wise(X))))&
(![X]:((rich(X)<~>brave(X))=>(~curious(X)|quiet(X))))&
((wise(john))=>((~rich(paul)&funny(paul))))&
((~old(alice))<=>((~creative(lucy)&kind(lucy))))&
((?[X]:(humble(X)))=>((rich(susan)<~>~wise(susan))))&
(![X]:((funny(X)&strong(X))<=>(rich(X)|~strong(X))))&
(generous(lucy))&
(~funny(john))&
(~brave(paul))&
(?[X]:((~strong(X)<~>kind(X))))&
(?[X]:((old(X)|~creative(X))))&
((~patient(fred)&~creative(fred))) | ~strong(alice) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3328798092382234085725463
% SZS output start Proof for 3328798092382234085725463
16. ! [X0] : ((strong(X0) & funny(X0)) <=> (~strong(X0) | rich(X0))) [input p15]
23. ~strong(alice) [input hypothesis]
56. ! [X0] : (((strong(X0) & funny(X0)) | (strong(X0) & ~rich(X0))) & ((~strong(X0) | rich(X0)) | (~strong(X0) | ~funny(X0)))) [nnf transformation 16]
57. ! [X0] : (((strong(X0) & funny(X0)) | (strong(X0) & ~rich(X0))) & (~strong(X0) | rich(X0) | ~strong(X0) | ~funny(X0))) [flattening 56]
102. strong(X0) | strong(X0) [cnf transformation 57]
110. ~strong(alice) [cnf transformation 23]
112. strong(X0) [duplicate literal removal 102]
218. $false [subsumption resolution 110,112]
% SZS output end Proof for 3328798092382234085725463
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and brave is both humble and happy.
If someone is either generous or not happy then paul is both wise and not rich and vice versa.
Everyone who is creative or tall is either brave or not strong and vice versa.
Everyone who is calm or not creative is not brave or kind and vice versa.
Everyone who is old or brave is curious.
Everyone who is either patient or humble is not rich.
Everyone who is both calm and not happy is either not curious or not generous and vice versa.
If mary is wise then someone is not brave or not strong and vice versa.
Everyone who is brave is either not old or not curious.
If someone is humble or not old then lucy is either calm or not quiet and vice versa.
If mary is rich or not curious then mary is not curious.
Everyone who is either not patient or not generous is generous and vice versa.
If fred is both not creative and not old then someone is kind.
If fred is either curious or not brave then someone is either not patient or not curious and vice versa.
If mary is kind or generous then fred is either not wise or not funny and vice versa.
Everyone who is funny is both not brave and curious.
Mary is not patient.
Someone is not tall.
Someone is either old or brave.
Mary is either not strong or not wise.
Someone is either rich or generous.
Someone is either wise or quiet.
Someone is both curious and rich.
Someone is both not calm and generous. | Mary is generous. | neutral | (![X]:((generous(X)&brave(X))=>(humble(X)&happy(X))))&
((?[X]:((generous(X)<~>~happy(X))))<=>((wise(paul)&~rich(paul))))&
(![X]:((creative(X)|tall(X))<=>(brave(X)<~>~strong(X))))&
(![X]:((calm(X)|~creative(X))<=>(~brave(X)|kind(X))))&
(![X]:((old(X)|brave(X))=>curious(X)))&
(![X]:((patient(X)<~>humble(X))=>~rich(X)))&
(![X]:((calm(X)&~happy(X))<=>(~curious(X)<~>~generous(X))))&
((wise(mary))<=>(?[X]:((~brave(X)|~strong(X)))))&
(![X]:(brave(X)=>(~old(X)<~>~curious(X))))&
((?[X]:((humble(X)|~old(X))))<=>((calm(lucy)<~>~quiet(lucy))))&
(((rich(mary)|~curious(mary)))=>(~curious(mary)))&
(![X]:((~patient(X)<~>~generous(X))<=>generous(X)))&
(((~creative(fred)&~old(fred)))=>(?[X]:(kind(X))))&
(((curious(fred)<~>~brave(fred)))<=>(?[X]:((~patient(X)<~>~curious(X)))))&
(((kind(mary)|generous(mary)))<=>((~wise(fred)<~>~funny(fred))))&
(![X]:(funny(X)=>(~brave(X)&curious(X))))&
(~patient(mary))&
(?[X]:(~tall(X)))&
(?[X]:((old(X)<~>brave(X))))&
((~strong(mary)<~>~wise(mary)))&
(?[X]:((rich(X)<~>generous(X))))&
(?[X]:((wise(X)<~>quiet(X))))&
(?[X]:((curious(X)&rich(X))))&
(?[X]:((~calm(X)&generous(X)))) | generous(mary) | [] | null | 0 |
If susan is either brave or tall then someone is not rich.
If fred is kind or not curious then fred is both not funny and not rich.
Everyone who is quiet is both not wise and funny and vice versa.
If susan is either funny or old then someone is either not funny or not creative and vice versa.
If someone is either rich or not generous then susan is either not funny or kind.
Everyone who is not old is not wise.
Everyone who is either not brave or not rich is strong or not patient and vice versa.
Everyone who is not creative or not old is both creative and not patient.
Everyone who is funny or creative is not kind or funny and vice versa.
If someone is happy or not creative then john is either humble or rich.
Everyone who is not old is either not patient or not happy and vice versa.
If someone is not old or generous then alice is not generous and vice versa.
Everyone who is both tall and not generous is brave and vice versa.
Everyone who is both not brave and kind is quiet or humble.
If someone is not curious or curious then someone is not rich or not curious.
Everyone who is both generous and patient is not humble and vice versa.
Susan is quiet or not old.
Someone is not happy or not kind.
Someone is not wise or not patient.
Alice is not happy or happy.
Susan is either not wise or not generous.
Someone is both kind and not humble.
Someone is either not creative or not curious. | Fred is not rich. | neutral | (((brave(susan)<~>tall(susan)))=>(?[X]:(~rich(X))))&
(((kind(fred)|~curious(fred)))=>((~funny(fred)&~rich(fred))))&
(![X]:(quiet(X)<=>(~wise(X)&funny(X))))&
(((funny(susan)<~>old(susan)))<=>(?[X]:((~funny(X)<~>~creative(X)))))&
((?[X]:((rich(X)<~>~generous(X))))=>((~funny(susan)<~>kind(susan))))&
(![X]:(~old(X)=>~wise(X)))&
(![X]:((~brave(X)<~>~rich(X))<=>(strong(X)|~patient(X))))&
(![X]:((~creative(X)|~old(X))=>(creative(X)&~patient(X))))&
(![X]:((funny(X)|creative(X))<=>(~kind(X)|funny(X))))&
((?[X]:((happy(X)|~creative(X))))=>((humble(john)<~>rich(john))))&
(![X]:(~old(X)<=>(~patient(X)<~>~happy(X))))&
((?[X]:((~old(X)|generous(X))))<=>(~generous(alice)))&
(![X]:((tall(X)&~generous(X))<=>brave(X)))&
(![X]:((~brave(X)&kind(X))=>(quiet(X)|humble(X))))&
((?[X]:((~curious(X)|curious(X))))=>(?[X]:((~rich(X)|~curious(X)))))&
(![X]:((generous(X)&patient(X))<=>~humble(X)))&
((quiet(susan)|~old(susan)))&
(?[X]:((~happy(X)|~kind(X))))&
(?[X]:((~wise(X)|~patient(X))))&
((~happy(alice)|happy(alice)))&
((~wise(susan)<~>~generous(susan)))&
(?[X]:((kind(X)&~humble(X))))&
(?[X]:((~creative(X)<~>~curious(X)))) | ~rich(fred) | [] | null | 0 |
Everyone who is funny is not calm and vice versa.
Everyone who is strong or not tall is both tall and not kind and vice versa.
If lucy is old or calm then alice is both calm and patient and vice versa.
Everyone who is not kind is not quiet and vice versa.
If someone is both not tall and curious then alice is old or humble.
Everyone who is both creative and not calm is both humble and not old.
If someone is either not creative or not humble then alice is both not humble and not rich and vice versa.
Everyone who is both brave and happy is both calm and not happy and vice versa.
If someone is not rich then someone is not tall.
If fred is curious or calm then someone is patient or happy and vice versa.
If someone is either strong or not kind then someone is both happy and wise and vice versa.
Everyone who is both curious and brave is either not kind or not quiet and vice versa.
Everyone who is generous or not wise is either not tall or not quiet and vice versa.
If susan is both happy and not curious then susan is either not calm or not rich and vice versa.
Everyone who is not brave or creative is tall.
Everyone who is either not calm or not rich is creative or rich.
Someone is either kind or not humble.
Fred is humble.
Someone is tall.
Someone is both kind and not brave.
Alice is not brave.
Alice is either rich or not funny.
Mary is not patient or kind.
Someone is either kind or brave. | Fred is creative. | entailment | (![X]:(funny(X)<=>~calm(X)))&
(![X]:((strong(X)|~tall(X))<=>(tall(X)&~kind(X))))&
(((old(lucy)|calm(lucy)))<=>((calm(alice)&patient(alice))))&
(![X]:(~kind(X)<=>~quiet(X)))&
((?[X]:((~tall(X)&curious(X))))=>((old(alice)|humble(alice))))&
(![X]:((creative(X)&~calm(X))=>(humble(X)&~old(X))))&
((?[X]:((~creative(X)<~>~humble(X))))<=>((~humble(alice)&~rich(alice))))&
(![X]:((brave(X)&happy(X))<=>(calm(X)&~happy(X))))&
((?[X]:(~rich(X)))=>(?[X]:(~tall(X))))&
(((curious(fred)|calm(fred)))<=>(?[X]:((patient(X)|happy(X)))))&
((?[X]:((strong(X)<~>~kind(X))))<=>(?[X]:((happy(X)&wise(X)))))&
(![X]:((curious(X)&brave(X))<=>(~kind(X)<~>~quiet(X))))&
(![X]:((generous(X)|~wise(X))<=>(~tall(X)<~>~quiet(X))))&
(((happy(susan)&~curious(susan)))<=>((~calm(susan)<~>~rich(susan))))&
(![X]:((~brave(X)|creative(X))=>tall(X)))&
(![X]:((~calm(X)<~>~rich(X))=>(creative(X)|rich(X))))&
(?[X]:((kind(X)<~>~humble(X))))&
(humble(fred))&
(?[X]:(tall(X)))&
(?[X]:((kind(X)&~brave(X))))&
(~brave(alice))&
((rich(alice)<~>~funny(alice)))&
((~patient(mary)|kind(mary)))&
(?[X]:((kind(X)<~>brave(X)))) | creative(fred) | [
"p1",
"p6",
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2046015126463109535732256
% SZS output start Proof for 2046015126463109535732256
2. ! [X0] : ((~tall(X0) | strong(X0)) <=> (~kind(X0) & tall(X0))) [input p1]
7. ? [X0] : (~creative(X0) <~> ~humble(X0)) <=> (~rich(alice) & ~humble(alice)) [input p6]
9. ? [X0] : ~rich(X0) => ? [X0] : ~tall(X0) [input p8]
18. humble(fred) [input p17]
25. ~creative(fred) [input hypothesis]
26. ? [X0] : ~rich(X0) => ? [X1] : ~tall(X1) [rectify 9]
32. ? [X1] : ~tall(X1) | ! [X0] : rich(X0) [ennf transformation 26]
37. ! [X0] : (((~tall(X0) | strong(X0)) | (kind(X0) | ~tall(X0))) & ((~kind(X0) & tall(X0)) | (tall(X0) & ~strong(X0)))) [nnf transformation 2]
38. ! [X0] : ((~tall(X0) | strong(X0) | kind(X0) | ~tall(X0)) & ((~kind(X0) & tall(X0)) | (tall(X0) & ~strong(X0)))) [flattening 37]
42. (? [X0] : ((humble(X0) | creative(X0)) & (~humble(X0) | ~creative(X0))) | (rich(alice) | humble(alice))) & ((~rich(alice) & ~humble(alice)) | ! [X0] : ((~creative(X0) | humble(X0)) & (~humble(X0) | creative(X0)))) [nnf transformation 7]
43. (? [X0] : ((humble(X0) | creative(X0)) & (~humble(X0) | ~creative(X0))) | rich(alice) | humble(alice)) & ((~rich(alice) & ~humble(alice)) | ! [X0] : ((~creative(X0) | humble(X0)) & (~humble(X0) | creative(X0)))) [flattening 42]
44. (? [X0] : ((humble(X0) | creative(X0)) & (~humble(X0) | ~creative(X0))) | rich(alice) | humble(alice)) & ((~rich(alice) & ~humble(alice)) | ! [X1] : ((~creative(X1) | humble(X1)) & (~humble(X1) | creative(X1)))) [rectify 43]
45. ? [X0] : ((humble(X0) | creative(X0)) & (~humble(X0) | ~creative(X0))) => ((humble(sK0) | creative(sK0)) & (~humble(sK0) | ~creative(sK0))) [choice axiom]
46. (((humble(sK0) | creative(sK0)) & (~humble(sK0) | ~creative(sK0))) | rich(alice) | humble(alice)) & ((~rich(alice) & ~humble(alice)) | ! [X1] : ((~creative(X1) | humble(X1)) & (~humble(X1) | creative(X1)))) [skolemisation 44,45]
49. ? [X0] : ~tall(X0) | ! [X1] : rich(X1) [rectify 32]
50. ? [X0] : ~tall(X0) => ~tall(sK1) [choice axiom]
51. ~tall(sK1) | ! [X1] : rich(X1) [skolemisation 49,50]
83. tall(X0) | tall(X0) [cnf transformation 38]
99. ~rich(alice) | ~humble(X1) | creative(X1) [cnf transformation 46]
107. ~tall(sK1) | rich(X1) [cnf transformation 51]
142. humble(fred) [cnf transformation 18]
152. ~creative(fred) [cnf transformation 25]
156. tall(X0) [duplicate literal removal 83]
184. 6 <=> rich(alice) [avatar definition]
185. ~rich(alice) <- (~6) [avatar component clause 184]
202. 10 <=> ! [X1] : (~humble(X1) | creative(X1)) [avatar definition]
203. ~humble(X1) | creative(X1) <- (10) [avatar component clause 202]
204. 10 | ~6 [avatar split clause 99,184,202]
207. rich(X1) [subsumption resolution 107,156]
312. $false <- (~6) [subsumption resolution 185,207]
313. 6 [avatar contradiction clause 312]
337. creative(fred) <- (10) [resolution 203,142]
338. $false <- (10) [subsumption resolution 337,152]
339. ~10 [avatar contradiction clause 338]
340. $false [avatar sat refutation 204,313,339]
% SZS output end Proof for 2046015126463109535732256
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not rich is both old and not patient and vice versa. If someone is both quiet and tall then someone is not humble or not strong. If fred is either curious or humble then someone is calm or rich and vice versa. Everyone who is not happy is both rich and brave. Everyone who is both not creative and not wise is quiet or not patient and vice versa. Everyone who is either wise or not wise is rich or not old. Everyone who is both tall and generous is old. If john is not old then someone is either not kind or quiet. If someone is not brave then someone is not humble. Everyone who is both rich and curious is either happy or strong and vice versa. Everyone who is not quiet is not creative or old. Everyone who is rich or not rich is calm and vice versa. Everyone who is not creative or strong is old. If lucy is tall or not kind then paul is not curious or not patient. Everyone who is either not brave or strong is either funny or not funny and vice versa. If john is either not generous or not humble then alice is both strong and not curious and vice versa. Someone is not old or quiet. Someone is strong or not funny. Someone is strong or curious. Someone is rich or not calm. Alice is both funny and curious. Fred is not generous or not calm. | Lucy is old. | entailment | (![X]:((~strong(X)<~>~rich(X))<=>(old(X)&~patient(X))))&
((?[X]:((quiet(X)&tall(X))))=>(?[X]:((~humble(X)|~strong(X)))))&
(((curious(fred)<~>humble(fred)))<=>(?[X]:((calm(X)|rich(X)))))&
(![X]:(~happy(X)=>(rich(X)&brave(X))))&
(![X]:((~creative(X)&~wise(X))<=>(quiet(X)|~patient(X))))&
(![X]:((wise(X)<~>~wise(X))=>(rich(X)|~old(X))))&
(![X]:((tall(X)&generous(X))=>old(X)))&
((~old(john))=>(?[X]:((~kind(X)<~>quiet(X)))))&
((?[X]:(~brave(X)))=>(?[X]:(~humble(X))))&
(![X]:((rich(X)&curious(X))<=>(happy(X)<~>strong(X))))&
(![X]:(~quiet(X)=>(~creative(X)|old(X))))&
(![X]:((rich(X)|~rich(X))<=>calm(X)))&
(![X]:((~creative(X)|strong(X))=>old(X)))&
(((tall(lucy)|~kind(lucy)))=>((~curious(paul)|~patient(paul))))&
(![X]:((~brave(X)<~>strong(X))<=>(funny(X)<~>~funny(X))))&
(((~generous(john)<~>~humble(john)))<=>((strong(alice)&~curious(alice))))&
(?[X]:((~old(X)|quiet(X))))&
(?[X]:((strong(X)|~funny(X))))&
(?[X]:((strong(X)|curious(X))))&
(?[X]:((rich(X)|~calm(X))))&
((funny(alice)&curious(alice)))&
((~generous(fred)|~calm(fred))) | old(lucy) | [
"p4",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6562550479590848958872459
% SZS output start Proof for 6562550479590848958872459
5. ! [X0] : ((~wise(X0) & ~creative(X0)) <=> (~patient(X0) | quiet(X0))) [input p4]
11. ! [X0] : (~quiet(X0) => (old(X0) | ~creative(X0))) [input p10]
13. ! [X0] : ((strong(X0) | ~creative(X0)) => old(X0)) [input p12]
23. ~old(lucy) [input hypothesis]
34. ! [X0] : ((old(X0) | ~creative(X0)) | quiet(X0)) [ennf transformation 11]
35. ! [X0] : (old(X0) | ~creative(X0) | quiet(X0)) [flattening 34]
36. ! [X0] : (old(X0) | (~strong(X0) & creative(X0))) [ennf transformation 13]
45. ! [X0] : (((~wise(X0) & ~creative(X0)) | (patient(X0) & ~quiet(X0))) & ((~patient(X0) | quiet(X0)) | (wise(X0) | creative(X0)))) [nnf transformation 5]
46. ! [X0] : (((~wise(X0) & ~creative(X0)) | (patient(X0) & ~quiet(X0))) & (~patient(X0) | quiet(X0) | wise(X0) | creative(X0))) [flattening 45]
84. ~creative(X0) | ~quiet(X0) [cnf transformation 46]
99. old(X0) | ~creative(X0) | quiet(X0) [cnf transformation 35]
103. old(X0) | creative(X0) [cnf transformation 36]
127. ~old(lucy) [cnf transformation 23]
187. old(X0) | ~creative(X0) [subsumption resolution 99,84]
189. old(X0) [subsumption resolution 103,187]
249. $false [subsumption resolution 127,189]
% SZS output end Proof for 6562550479590848958872459
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is creative or not wise then mary is tall or old.
Everyone who is both not strong and rich is both not generous and not old.
Everyone who is both kind and not rich is either not calm or not happy.
Everyone who is not old is either wise or humble and vice versa.
Everyone who is either not tall or not wise is not wise or not creative and vice versa.
If mary is not curious then someone is not patient or tall.
If someone is either not strong or brave then paul is either patient or not funny.
Everyone who is both old and generous is happy or not kind.
Everyone who is either not funny or not generous is both kind and not rich.
If someone is not quiet or not rich then someone is both generous and not generous and vice versa.
If mary is both not humble and humble then susan is funny and vice versa.
If someone is both not strong and wise then someone is not calm and vice versa.
If someone is not rich then alice is old or not wise.
If someone is not brave or generous then someone is either not creative or not tall and vice versa.
Everyone who is humble or not funny is strong.
Everyone who is either not tall or not curious is both not quiet and not wise and vice versa.
Susan is either creative or not creative.
John is old or not tall.
Susan is either curious or happy.
Susan is wise or rich.
Someone is kind or not wise.
Someone is quiet.
Paul is strong or curious. | Mary is curious. | neutral | (((creative(mary)|~wise(mary)))=>((tall(mary)|old(mary))))&
(![X]:((~strong(X)&rich(X))=>(~generous(X)&~old(X))))&
(![X]:((kind(X)&~rich(X))=>(~calm(X)<~>~happy(X))))&
(![X]:(~old(X)<=>(wise(X)<~>humble(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(~wise(X)|~creative(X))))&
((~curious(mary))=>(?[X]:((~patient(X)|tall(X)))))&
((?[X]:((~strong(X)<~>brave(X))))=>((patient(paul)<~>~funny(paul))))&
(![X]:((old(X)&generous(X))=>(happy(X)|~kind(X))))&
(![X]:((~funny(X)<~>~generous(X))=>(kind(X)&~rich(X))))&
((?[X]:((~quiet(X)|~rich(X))))<=>(?[X]:((generous(X)&~generous(X)))))&
(((~humble(mary)&humble(mary)))<=>(funny(susan)))&
((?[X]:((~strong(X)&wise(X))))<=>(?[X]:(~calm(X))))&
((?[X]:(~rich(X)))=>((old(alice)|~wise(alice))))&
((?[X]:((~brave(X)|generous(X))))<=>(?[X]:((~creative(X)<~>~tall(X)))))&
(![X]:((humble(X)|~funny(X))=>strong(X)))&
(![X]:((~tall(X)<~>~curious(X))<=>(~quiet(X)&~wise(X))))&
((creative(susan)<~>~creative(susan)))&
((old(john)|~tall(john)))&
((curious(susan)<~>happy(susan)))&
((wise(susan)|rich(susan)))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:(quiet(X)))&
((strong(paul)|curious(paul))) | curious(mary) | [] | null | 0 |
If someone is both humble and not calm then paul is either not happy or brave. Everyone who is both rich and brave is both not generous and not calm and vice versa. Everyone who is old is both not strong and creative. If susan is not funny then someone is either humble or not brave. Everyone who is not generous is not creative. If fred is happy or humble then someone is not funny or wise. Everyone who is kind is humble and vice versa. If lucy is both generous and creative then paul is wise or not brave. Everyone who is both not curious and creative is calm or patient and vice versa. If susan is creative then someone is either creative or not tall. Everyone who is not kind is kind or not kind and vice versa. If someone is not patient then someone is both strong and not calm. Everyone who is humble or not tall is not old or not kind and vice versa. Everyone who is brave or quiet is both not calm and generous. If paul is both not old and not curious then someone is both not curious and strong and vice versa. Someone is either tall or not humble. John is either not tall or quiet. Someone is either quiet or not happy. Someone is patient or not patient. Someone is both happy and not rich. Mary is not humble or old. | Lucy is not kind. | entailment | ((?[X]:((humble(X)&~calm(X))))=>((~happy(paul)<~>brave(paul))))&
(![X]:((rich(X)&brave(X))<=>(~generous(X)&~calm(X))))&
(![X]:(old(X)=>(~strong(X)&creative(X))))&
((~funny(susan))=>(?[X]:((humble(X)<~>~brave(X)))))&
(![X]:(~generous(X)=>~creative(X)))&
(((happy(fred)|humble(fred)))=>(?[X]:((~funny(X)|wise(X)))))&
(![X]:(kind(X)<=>humble(X)))&
(((generous(lucy)&creative(lucy)))=>((wise(paul)|~brave(paul))))&
(![X]:((~curious(X)&creative(X))<=>(calm(X)|patient(X))))&
((creative(susan))=>(?[X]:((creative(X)<~>~tall(X)))))&
(![X]:(~kind(X)<=>(kind(X)|~kind(X))))&
((?[X]:(~patient(X)))=>(?[X]:((strong(X)&~calm(X)))))&
(![X]:((humble(X)|~tall(X))<=>(~old(X)|~kind(X))))&
(![X]:((brave(X)|quiet(X))=>(~calm(X)&generous(X))))&
(((~old(paul)&~curious(paul)))<=>(?[X]:((~curious(X)&strong(X)))))&
(?[X]:((tall(X)<~>~humble(X))))&
((~tall(john)<~>quiet(john)))&
(?[X]:((quiet(X)<~>~happy(X))))&
(?[X]:((patient(X)|~patient(X))))&
(?[X]:((happy(X)&~rich(X))))&
((~humble(mary)|old(mary))) | ~kind(lucy) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 503512021841871121928588
% SZS output start Proof for 503512021841871121928588
11. ! [X0] : (~kind(X0) <=> (~kind(X0) | kind(X0))) [input p10]
22. kind(lucy) [input hypothesis]
42. ! [X0] : ((~kind(X0) | (kind(X0) & ~kind(X0))) & ((~kind(X0) | kind(X0)) | kind(X0))) [nnf transformation 11]
43. ! [X0] : ((~kind(X0) | (kind(X0) & ~kind(X0))) & (~kind(X0) | kind(X0) | kind(X0))) [flattening 42]
84. ~kind(X0) | ~kind(X0) [cnf transformation 43]
110. kind(lucy) [cnf transformation 22]
112. ~kind(X0) [duplicate literal removal 84]
215. $false [subsumption resolution 110,112]
% SZS output end Proof for 503512021841871121928588
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old or humble then susan is both humble and kind. If someone is not happy then mary is both not strong and strong and vice versa. Everyone who is both not humble and curious is both not happy and wise and vice versa. Everyone who is not kind is both not kind and calm and vice versa. Everyone who is not generous or curious is funny. If someone is generous then lucy is either not curious or not humble and vice versa. Everyone who is either not wise or not curious is not rich and vice versa. Everyone who is not humble is curious and vice versa. Everyone who is patient is not curious or strong. Everyone who is not strong or curious is rich. If someone is strong then alice is both not wise and generous. Everyone who is either not generous or wise is not calm and vice versa. If someone is either not funny or creative then mary is not creative and vice versa. If paul is either not wise or not old then someone is either funny or not strong and vice versa. If paul is patient then john is either quiet or strong. Everyone who is creative is funny or kind. John is not strong or not old. Someone is either not brave or brave. John is happy or tall. Alice is not brave or calm. John is wise. Someone is not quiet. Someone is not kind. | Alice is happy. | entailment | ((?[X]:((~old(X)|humble(X))))=>((humble(susan)&kind(susan))))&
((?[X]:(~happy(X)))<=>((~strong(mary)&strong(mary))))&
(![X]:((~humble(X)&curious(X))<=>(~happy(X)&wise(X))))&
(![X]:(~kind(X)<=>(~kind(X)&calm(X))))&
(![X]:((~generous(X)|curious(X))=>funny(X)))&
((?[X]:(generous(X)))<=>((~curious(lucy)<~>~humble(lucy))))&
(![X]:((~wise(X)<~>~curious(X))<=>~rich(X)))&
(![X]:(~humble(X)<=>curious(X)))&
(![X]:(patient(X)=>(~curious(X)|strong(X))))&
(![X]:((~strong(X)|curious(X))=>rich(X)))&
((?[X]:(strong(X)))=>((~wise(alice)&generous(alice))))&
(![X]:((~generous(X)<~>wise(X))<=>~calm(X)))&
((?[X]:((~funny(X)<~>creative(X))))<=>(~creative(mary)))&
(((~wise(paul)<~>~old(paul)))<=>(?[X]:((funny(X)<~>~strong(X)))))&
((patient(paul))=>((quiet(john)<~>strong(john))))&
(![X]:(creative(X)=>(funny(X)|kind(X))))&
((~strong(john)|~old(john)))&
(?[X]:((~brave(X)<~>brave(X))))&
((happy(john)|tall(john)))&
((~brave(alice)|calm(alice)))&
(wise(john))&
(?[X]:(~quiet(X)))&
(?[X]:(~kind(X))) | happy(alice) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 3485073467692054227759590
% SZS output start Proof for 3485073467692054227759590
2. ? [X0] : ~happy(X0) <=> (strong(mary) & ~strong(mary)) [input p1]
24. ~happy(alice) [input hypothesis]
37. (? [X0] : ~happy(X0) | (~strong(mary) | strong(mary))) & ((strong(mary) & ~strong(mary)) | ! [X0] : happy(X0)) [nnf transformation 2]
38. (? [X0] : ~happy(X0) | ~strong(mary) | strong(mary)) & ((strong(mary) & ~strong(mary)) | ! [X0] : happy(X0)) [flattening 37]
39. (? [X0] : ~happy(X0) | ~strong(mary) | strong(mary)) & ((strong(mary) & ~strong(mary)) | ! [X1] : happy(X1)) [rectify 38]
40. ? [X0] : ~happy(X0) => ~happy(sK0) [choice axiom]
41. (~happy(sK0) | ~strong(mary) | strong(mary)) & ((strong(mary) & ~strong(mary)) | ! [X1] : happy(X1)) [skolemisation 39,40]
70. ~strong(mary) | happy(X1) [cnf transformation 41]
71. strong(mary) | happy(X1) [cnf transformation 41]
117. ~happy(alice) [cnf transformation 24]
137. 5 <=> ! [X1] : happy(X1) [avatar definition]
138. happy(X1) <- (5) [avatar component clause 137]
140. 6 <=> strong(mary) [avatar definition]
143. 5 | 6 [avatar split clause 71,140,137]
144. 5 | ~6 [avatar split clause 70,140,137]
247. $false <- (5) [resolution 138,117]
248. ~5 [avatar contradiction clause 247]
249. $false [avatar sat refutation 143,144,248]
% SZS output end Proof for 3485073467692054227759590
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or tall is rich and vice versa.
If paul is both creative and tall then someone is brave or tall and vice versa.
Everyone who is both not rich and generous is curious or not patient and vice versa.
Everyone who is either old or not brave is either not strong or wise and vice versa.
Everyone who is both humble and tall is both not generous and not creative.
Everyone who is happy or not rich is not calm.
Everyone who is brave or not tall is brave or strong and vice versa.
Everyone who is quiet is funny or patient.
Everyone who is not happy is either not rich or brave and vice versa.
If someone is either quiet or brave then susan is not patient or not brave.
If someone is both curious and not tall then paul is either not curious or not brave and vice versa.
Everyone who is both not rich and kind is either not funny or creative.
If paul is both not old and quiet then someone is both not quiet and patient.
Everyone who is quiet is creative and vice versa.
Everyone who is not quiet is both not wise and not quiet.
Lucy is not quiet or curious.
Someone is either not brave or humble.
Lucy is not brave or not quiet.
Alice is either wise or not strong.
Someone is either not patient or not old. | Alice is not curious. | entailment | (![X]:((~rich(X)|tall(X))<=>rich(X)))&
(((creative(paul)&tall(paul)))<=>(?[X]:((brave(X)|tall(X)))))&
(![X]:((~rich(X)&generous(X))<=>(curious(X)|~patient(X))))&
(![X]:((old(X)<~>~brave(X))<=>(~strong(X)<~>wise(X))))&
(![X]:((humble(X)&tall(X))=>(~generous(X)&~creative(X))))&
(![X]:((happy(X)|~rich(X))=>~calm(X)))&
(![X]:((brave(X)|~tall(X))<=>(brave(X)|strong(X))))&
(![X]:(quiet(X)=>(funny(X)|patient(X))))&
(![X]:(~happy(X)<=>(~rich(X)<~>brave(X))))&
((?[X]:((quiet(X)<~>brave(X))))=>((~patient(susan)|~brave(susan))))&
((?[X]:((curious(X)&~tall(X))))<=>((~curious(paul)<~>~brave(paul))))&
(![X]:((~rich(X)&kind(X))=>(~funny(X)<~>creative(X))))&
(((~old(paul)&quiet(paul)))=>(?[X]:((~quiet(X)&patient(X)))))&
(![X]:(quiet(X)<=>creative(X)))&
(![X]:(~quiet(X)=>(~wise(X)&~quiet(X))))&
((~quiet(lucy)|curious(lucy)))&
(?[X]:((~brave(X)<~>humble(X))))&
((~brave(lucy)|~quiet(lucy)))&
((wise(alice)<~>~strong(alice)))&
(?[X]:((~patient(X)<~>~old(X)))) | ~curious(alice) | [
"p0",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 7361323173636127529913384
% SZS output start Proof for 7361323173636127529913384
1. ! [X0] : ((tall(X0) | ~rich(X0)) <=> rich(X0)) [input p0]
3. ! [X0] : ((generous(X0) & ~rich(X0)) <=> (~patient(X0) | curious(X0))) [input p2]
21. curious(alice) [input hypothesis]
34. ! [X0] : (((tall(X0) | ~rich(X0)) | ~rich(X0)) & (rich(X0) | (~tall(X0) & rich(X0)))) [nnf transformation 1]
35. ! [X0] : ((tall(X0) | ~rich(X0) | ~rich(X0)) & (rich(X0) | (~tall(X0) & rich(X0)))) [flattening 34]
41. ! [X0] : (((generous(X0) & ~rich(X0)) | (patient(X0) & ~curious(X0))) & ((~patient(X0) | curious(X0)) | (~generous(X0) | rich(X0)))) [nnf transformation 3]
42. ! [X0] : (((generous(X0) & ~rich(X0)) | (patient(X0) & ~curious(X0))) & (~patient(X0) | curious(X0) | ~generous(X0) | rich(X0))) [flattening 41]
61. rich(X0) | rich(X0) [cnf transformation 35]
70. ~rich(X0) | ~curious(X0) [cnf transformation 42]
110. curious(alice) [cnf transformation 21]
111. rich(X0) [duplicate literal removal 61]
141. ~curious(X0) [subsumption resolution 70,111]
204. $false [subsumption resolution 110,141]
% SZS output end Proof for 7361323173636127529913384
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and curious is both wise and tall.
If someone is both generous and not happy then someone is not strong.
If john is both not happy and happy then someone is kind or tall.
If fred is both not patient and brave then someone is both not quiet and wise.
Everyone who is not wise or not curious is not humble or quiet.
If fred is either not strong or not tall then fred is both funny and not brave and vice versa.
If someone is both generous and funny then someone is both not brave and curious.
If someone is either not funny or funny then someone is not patient and vice versa.
Everyone who is calm or not patient is not calm.
Everyone who is either curious or calm is both not funny and not tall.
If someone is calm or not humble then someone is both creative and curious and vice versa.
Everyone who is not humble is strong or rich and vice versa.
If someone is wise or not happy then john is tall or not calm.
If lucy is brave or not strong then fred is old and vice versa.
Everyone who is not patient or happy is not kind and vice versa.
If john is humble or not kind then alice is not old or not strong.
Someone is brave or not happy.
John is not happy.
Someone is either not old or creative.
Paul is both funny and brave.
Someone is either calm or not curious.
Someone is not creative.
Alice is both old and kind.
Paul is not curious. | John is calm. | contradiction | (![X]:((~calm(X)&curious(X))=>(wise(X)&tall(X))))&
((?[X]:((generous(X)&~happy(X))))=>(?[X]:(~strong(X))))&
(((~happy(john)&happy(john)))=>(?[X]:((kind(X)|tall(X)))))&
(((~patient(fred)&brave(fred)))=>(?[X]:((~quiet(X)&wise(X)))))&
(![X]:((~wise(X)|~curious(X))=>(~humble(X)|quiet(X))))&
(((~strong(fred)<~>~tall(fred)))<=>((funny(fred)&~brave(fred))))&
((?[X]:((generous(X)&funny(X))))=>(?[X]:((~brave(X)&curious(X)))))&
((?[X]:((~funny(X)<~>funny(X))))<=>(?[X]:(~patient(X))))&
(![X]:((calm(X)|~patient(X))=>~calm(X)))&
(![X]:((curious(X)<~>calm(X))=>(~funny(X)&~tall(X))))&
((?[X]:((calm(X)|~humble(X))))<=>(?[X]:((creative(X)&curious(X)))))&
(![X]:(~humble(X)<=>(strong(X)|rich(X))))&
((?[X]:((wise(X)|~happy(X))))=>((tall(john)|~calm(john))))&
(((brave(lucy)|~strong(lucy)))<=>(old(fred)))&
(![X]:((~patient(X)|happy(X))<=>~kind(X)))&
(((humble(john)|~kind(john)))=>((~old(alice)|~strong(alice))))&
(?[X]:((brave(X)|~happy(X))))&
(~happy(john))&
(?[X]:((~old(X)<~>creative(X))))&
((funny(paul)&brave(paul)))&
(?[X]:((calm(X)<~>~curious(X))))&
(?[X]:(~creative(X)))&
((old(alice)&kind(alice)))&
(~curious(paul)) | calm(john) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8249271072312016481929998
% SZS output start Proof for 8249271072312016481929998
9. ! [X0] : ((~patient(X0) | calm(X0)) => ~calm(X0)) [input p8]
25. calm(john) [input hypothesis]
41. ! [X0] : (~calm(X0) | (patient(X0) & ~calm(X0))) [ennf transformation 9]
96. ~calm(X0) | ~calm(X0) [cnf transformation 41]
131. calm(john) [cnf transformation 25]
132. ~calm(X0) [duplicate literal removal 96]
261. $false [subsumption resolution 131,132]
% SZS output end Proof for 8249271072312016481929998
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is both not tall and quiet and vice versa. Everyone who is not generous is both not wise and not patient. If someone is not creative or not funny then paul is tall and vice versa. If susan is either old or not quiet then someone is old and vice versa. Everyone who is either not kind or curious is wise or calm. Everyone who is strong or funny is brave. Everyone who is not patient is either humble or not wise. Everyone who is both not creative and creative is patient or not curious and vice versa. Everyone who is either happy or not wise is funny or creative and vice versa. If susan is happy then mary is both not wise and funny and vice versa. Everyone who is not calm or rich is either kind or happy and vice versa. Everyone who is not tall is not rich and vice versa. If someone is both not humble and not kind then fred is not humble and vice versa. Everyone who is either not happy or not funny is both humble and patient. Everyone who is either not patient or not generous is not rich or old. If susan is not kind or not creative then someone is either not happy or not creative and vice versa. Someone is creative. Someone is both curious and not calm. Someone is not generous or not rich. Someone is not quiet or calm. Paul is either kind or not brave. Mary is quiet. Someone is either not old or not curious. | Fred is patient. | contradiction | (![X]:(~curious(X)<=>(~tall(X)&quiet(X))))&
(![X]:(~generous(X)=>(~wise(X)&~patient(X))))&
((?[X]:((~creative(X)|~funny(X))))<=>(tall(paul)))&
(((old(susan)<~>~quiet(susan)))<=>(?[X]:(old(X))))&
(![X]:((~kind(X)<~>curious(X))=>(wise(X)|calm(X))))&
(![X]:((strong(X)|funny(X))=>brave(X)))&
(![X]:(~patient(X)=>(humble(X)<~>~wise(X))))&
(![X]:((~creative(X)&creative(X))<=>(patient(X)|~curious(X))))&
(![X]:((happy(X)<~>~wise(X))<=>(funny(X)|creative(X))))&
((happy(susan))<=>((~wise(mary)&funny(mary))))&
(![X]:((~calm(X)|rich(X))<=>(kind(X)<~>happy(X))))&
(![X]:(~tall(X)<=>~rich(X)))&
((?[X]:((~humble(X)&~kind(X))))<=>(~humble(fred)))&
(![X]:((~happy(X)<~>~funny(X))=>(humble(X)&patient(X))))&
(![X]:((~patient(X)<~>~generous(X))=>(~rich(X)|old(X))))&
(((~kind(susan)|~creative(susan)))<=>(?[X]:((~happy(X)<~>~creative(X)))))&
(?[X]:(creative(X)))&
(?[X]:((curious(X)&~calm(X))))&
(?[X]:((~generous(X)|~rich(X))))&
(?[X]:((~quiet(X)|calm(X))))&
((kind(paul)<~>~brave(paul)))&
(quiet(mary))&
(?[X]:((~old(X)<~>~curious(X)))) | patient(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4495183745178537178146746
% SZS output start Proof for 4495183745178537178146746
8. ! [X0] : ((creative(X0) & ~creative(X0)) <=> (~curious(X0) | patient(X0))) [input p7]
24. patient(fred) [input hypothesis]
46. ! [X0] : (((creative(X0) & ~creative(X0)) | (curious(X0) & ~patient(X0))) & ((~curious(X0) | patient(X0)) | (~creative(X0) | creative(X0)))) [nnf transformation 8]
47. ! [X0] : (((creative(X0) & ~creative(X0)) | (curious(X0) & ~patient(X0))) & (~curious(X0) | patient(X0) | ~creative(X0) | creative(X0))) [flattening 46]
96. ~creative(X0) | ~patient(X0) [cnf transformation 47]
98. creative(X0) | ~patient(X0) [cnf transformation 47]
142. patient(fred) [cnf transformation 24]
184. ~patient(X0) [subsumption resolution 96,98]
278. $false [subsumption resolution 142,184]
% SZS output end Proof for 4495183745178537178146746
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is humble. Everyone who is not generous is not humble. Everyone who is either not tall or not funny is both not strong and old. If lucy is rich then someone is old. If someone is not happy or not brave then someone is both not generous and creative and vice versa. If someone is curious then someone is both not happy and not kind and vice versa. Everyone who is both not happy and not curious is both not funny and not humble and vice versa. If paul is not rich or humble then alice is funny and vice versa. Everyone who is either not funny or not patient is not kind and vice versa. Everyone who is either curious or not humble is both creative and not patient. Everyone who is either brave or calm is not calm and vice versa. Everyone who is not kind is funny. If someone is either kind or not brave then someone is humble. Everyone who is not brave or happy is quiet or happy. If alice is rich or not calm then john is not strong or not kind. If alice is both not happy and not rich then paul is rich or quiet and vice versa. Mary is not kind. Someone is either not calm or funny. Paul is not strong. Fred is either not creative or not calm. Someone is not strong. Alice is both not quiet and not humble. Mary is either not curious or curious. Fred is both not funny and not strong. | Alice is not humble. | entailment | (![X]:(~happy(X)=>humble(X)))&
(![X]:(~generous(X)=>~humble(X)))&
(![X]:((~tall(X)<~>~funny(X))=>(~strong(X)&old(X))))&
((rich(lucy))=>(?[X]:(old(X))))&
((?[X]:((~happy(X)|~brave(X))))<=>(?[X]:((~generous(X)&creative(X)))))&
((?[X]:(curious(X)))<=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:((~happy(X)&~curious(X))<=>(~funny(X)&~humble(X))))&
(((~rich(paul)|humble(paul)))<=>(funny(alice)))&
(![X]:((~funny(X)<~>~patient(X))<=>~kind(X)))&
(![X]:((curious(X)<~>~humble(X))=>(creative(X)&~patient(X))))&
(![X]:((brave(X)<~>calm(X))<=>~calm(X)))&
(![X]:(~kind(X)=>funny(X)))&
((?[X]:((kind(X)<~>~brave(X))))=>(?[X]:(humble(X))))&
(![X]:((~brave(X)|happy(X))=>(quiet(X)|happy(X))))&
(((rich(alice)|~calm(alice)))=>((~strong(john)|~kind(john))))&
(((~happy(alice)&~rich(alice)))<=>((rich(paul)|quiet(paul))))&
(~kind(mary))&
(?[X]:((~calm(X)<~>funny(X))))&
(~strong(paul))&
((~creative(fred)<~>~calm(fred)))&
(?[X]:(~strong(X)))&
((~quiet(alice)&~humble(alice)))&
((~curious(mary)<~>curious(mary)))&
((~funny(fred)&~strong(fred))) | ~humble(alice) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 106771529531211089022151
% SZS output start Proof for 106771529531211089022151
22. ~humble(alice) & ~quiet(alice) [input p21]
25. humble(alice) [input hypothesis]
116. ~humble(alice) [cnf transformation 22]
120. humble(alice) [cnf transformation 25]
242. $false [subsumption resolution 120,116]
% SZS output end Proof for 106771529531211089022151
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and not wise is either curious or happy.
Everyone who is not kind or calm is not funny.
If someone is both tall and brave then someone is funny and vice versa.
If john is tall or quiet then susan is both humble and not generous.
Everyone who is not calm or humble is either not funny or brave and vice versa.
If someone is both not brave and not curious then someone is either calm or not happy.
If someone is either not wise or curious then someone is not calm or not tall.
If susan is creative or not tall then someone is either not old or not rich and vice versa.
Everyone who is kind or not wise is both creative and not brave.
Everyone who is not calm or not wise is creative or not patient and vice versa.
If lucy is either not creative or not quiet then lucy is either old or happy.
Everyone who is either patient or not patient is either not funny or not patient.
If someone is both creative and rich then alice is curious and vice versa.
Everyone who is both not patient and strong is not strong.
Everyone who is both not strong and funny is both not rich and old.
Everyone who is either not quiet or old is both strong and not tall and vice versa.
John is either humble or not curious.
Paul is either calm or tall.
Someone is either not generous or rich.
Someone is rich.
Someone is both patient and rich.
Someone is either funny or not wise.
Someone is both happy and not humble.
John is strong or not quiet. | Susan is funny. | contradiction | (![X]:((~rich(X)&~wise(X))=>(curious(X)<~>happy(X))))&
(![X]:((~kind(X)|calm(X))=>~funny(X)))&
((?[X]:((tall(X)&brave(X))))<=>(?[X]:(funny(X))))&
(((tall(john)|quiet(john)))=>((humble(susan)&~generous(susan))))&
(![X]:((~calm(X)|humble(X))<=>(~funny(X)<~>brave(X))))&
((?[X]:((~brave(X)&~curious(X))))=>(?[X]:((calm(X)<~>~happy(X)))))&
((?[X]:((~wise(X)<~>curious(X))))=>(?[X]:((~calm(X)|~tall(X)))))&
(((creative(susan)|~tall(susan)))<=>(?[X]:((~old(X)<~>~rich(X)))))&
(![X]:((kind(X)|~wise(X))=>(creative(X)&~brave(X))))&
(![X]:((~calm(X)|~wise(X))<=>(creative(X)|~patient(X))))&
(((~creative(lucy)<~>~quiet(lucy)))=>((old(lucy)<~>happy(lucy))))&
(![X]:((patient(X)<~>~patient(X))=>(~funny(X)<~>~patient(X))))&
((?[X]:((creative(X)&rich(X))))<=>(curious(alice)))&
(![X]:((~patient(X)&strong(X))=>~strong(X)))&
(![X]:((~strong(X)&funny(X))=>(~rich(X)&old(X))))&
(![X]:((~quiet(X)<~>old(X))<=>(strong(X)&~tall(X))))&
((humble(john)<~>~curious(john)))&
((calm(paul)<~>tall(paul)))&
(?[X]:((~generous(X)<~>rich(X))))&
(?[X]:(rich(X)))&
(?[X]:((patient(X)&rich(X))))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:((happy(X)&~humble(X))))&
((strong(john)|~quiet(john))) | funny(susan) | [
"p1",
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 965199305149394462491135
% SZS output start Proof for 965199305149394462491135
2. ! [X0] : ((calm(X0) | ~kind(X0)) => ~funny(X0)) [input p1]
5. ! [X0] : ((humble(X0) | ~calm(X0)) <=> (~funny(X0) <~> brave(X0))) [input p4]
9. ! [X0] : ((~wise(X0) | kind(X0)) => (~brave(X0) & creative(X0))) [input p8]
25. funny(susan) [input hypothesis]
31. ! [X0] : (~funny(X0) | (~calm(X0) & kind(X0))) [ennf transformation 2]
35. ! [X0] : ((~brave(X0) & creative(X0)) | (wise(X0) & ~kind(X0))) [ennf transformation 9]
48. ! [X0] : (((humble(X0) | ~calm(X0)) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0)))) & (((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | (~humble(X0) & calm(X0)))) [nnf transformation 5]
49. ! [X0] : ((humble(X0) | ~calm(X0) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0)))) & (((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | (~humble(X0) & calm(X0)))) [flattening 48]
89. ~funny(X0) | kind(X0) [cnf transformation 31]
90. ~funny(X0) | ~calm(X0) [cnf transformation 31]
98. brave(X0) | ~funny(X0) | calm(X0) [cnf transformation 49]
116. ~brave(X0) | ~kind(X0) [cnf transformation 35]
156. funny(susan) [cnf transformation 25]
204. ~funny(X0) | brave(X0) [subsumption resolution 98,90]
345. kind(susan) [resolution 89,156]
361. brave(susan) [resolution 204,156]
368. ~kind(susan) [resolution 361,116]
369. $false [subsumption resolution 368,345]
% SZS output end Proof for 965199305149394462491135
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or quiet is both not tall and humble and vice versa.
Everyone who is both quiet and not brave is either not funny or brave and vice versa.
Everyone who is either funny or rich is happy.
If someone is not funny then someone is either not calm or not patient.
If mary is both happy and funny then someone is both not kind and creative and vice versa.
Everyone who is either calm or old is both not patient and patient and vice versa.
Everyone who is not wise is patient.
If alice is either patient or rich then someone is not curious and vice versa.
Everyone who is both curious and not patient is tall.
Everyone who is both not creative and curious is either not tall or not funny and vice versa.
If someone is rich then someone is both not kind and patient.
Everyone who is not old is both quiet and not wise.
Everyone who is both generous and not quiet is not patient and vice versa.
Everyone who is either tall or not creative is funny or not patient and vice versa.
If someone is either generous or tall then fred is not patient.
If someone is either not patient or curious then someone is both not curious and not calm and vice versa.
Mary is both strong and old.
Lucy is both not quiet and rich.
Susan is either humble or not wise.
Lucy is happy.
Someone is patient or wise.
Someone is creative.
Someone is not kind or strong.
John is brave. | Fred is not wise. | neutral | (![X]:((wise(X)|quiet(X))<=>(~tall(X)&humble(X))))&
(![X]:((quiet(X)&~brave(X))<=>(~funny(X)<~>brave(X))))&
(![X]:((funny(X)<~>rich(X))=>happy(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~calm(X)<~>~patient(X)))))&
(((happy(mary)&funny(mary)))<=>(?[X]:((~kind(X)&creative(X)))))&
(![X]:((calm(X)<~>old(X))<=>(~patient(X)&patient(X))))&
(![X]:(~wise(X)=>patient(X)))&
(((patient(alice)<~>rich(alice)))<=>(?[X]:(~curious(X))))&
(![X]:((curious(X)&~patient(X))=>tall(X)))&
(![X]:((~creative(X)&curious(X))<=>(~tall(X)<~>~funny(X))))&
((?[X]:(rich(X)))=>(?[X]:((~kind(X)&patient(X)))))&
(![X]:(~old(X)=>(quiet(X)&~wise(X))))&
(![X]:((generous(X)&~quiet(X))<=>~patient(X)))&
(![X]:((tall(X)<~>~creative(X))<=>(funny(X)|~patient(X))))&
((?[X]:((generous(X)<~>tall(X))))=>(~patient(fred)))&
((?[X]:((~patient(X)<~>curious(X))))<=>(?[X]:((~curious(X)&~calm(X)))))&
((strong(mary)&old(mary)))&
((~quiet(lucy)&rich(lucy)))&
((humble(susan)<~>~wise(susan)))&
(happy(lucy))&
(?[X]:((patient(X)|wise(X))))&
(?[X]:(creative(X)))&
(?[X]:((~kind(X)|strong(X))))&
(brave(john)) | ~wise(fred) | [] | null | 0 |
Everyone who is humble or calm is both old and not curious and vice versa. Everyone who is generous or wise is both not happy and funny. Everyone who is generous or patient is not rich. Everyone who is calm or not funny is both wise and humble and vice versa. Everyone who is either creative or not brave is tall or not quiet. If lucy is not strong then someone is brave or funny. If lucy is both not funny and not curious then someone is not strong and vice versa. Everyone who is not wise is both not strong and old and vice versa. Everyone who is not rich is either generous or not humble. Everyone who is creative is old and vice versa. Everyone who is creative or happy is either not funny or curious and vice versa. Everyone who is either patient or kind is tall. If john is not rich or funny then lucy is not brave or not humble and vice versa. Lucy is brave. Someone is wise. Paul is either not funny or not rich. Someone is not humble or old. | John is quiet. | neutral | (![X]:((humble(X)|calm(X))<=>(old(X)&~curious(X))))&
(![X]:((generous(X)|wise(X))=>(~happy(X)&funny(X))))&
(![X]:((generous(X)|patient(X))=>~rich(X)))&
(![X]:((calm(X)|~funny(X))<=>(wise(X)&humble(X))))&
(![X]:((creative(X)<~>~brave(X))=>(tall(X)|~quiet(X))))&
((~strong(lucy))=>(?[X]:((brave(X)|funny(X)))))&
(((~funny(lucy)&~curious(lucy)))<=>(?[X]:(~strong(X))))&
(![X]:(~wise(X)<=>(~strong(X)&old(X))))&
(![X]:(~rich(X)=>(generous(X)<~>~humble(X))))&
(![X]:(creative(X)<=>old(X)))&
(![X]:((creative(X)|happy(X))<=>(~funny(X)<~>curious(X))))&
(![X]:((patient(X)<~>kind(X))=>tall(X)))&
(((~rich(john)|funny(john)))<=>((~brave(lucy)|~humble(lucy))))&
(brave(lucy))&
(?[X]:(wise(X)))&
((~funny(paul)<~>~rich(paul)))&
(?[X]:((~humble(X)|old(X)))) | quiet(john) | [] | null | 0 |
If alice is both happy and not happy then someone is humble and vice versa.
Everyone who is either not funny or not patient is strong and vice versa.
Everyone who is generous is tall.
If someone is both not strong and not happy then someone is curious.
If alice is either not old or not quiet then fred is both not generous and not strong and vice versa.
If someone is not strong or not creative then susan is either curious or not creative.
Everyone who is patient or not patient is both not wise and patient and vice versa.
Everyone who is not old or brave is either not kind or not generous.
Everyone who is either not generous or not curious is both not old and funny.
Everyone who is both quiet and not curious is not wise or brave and vice versa.
Everyone who is not kind is both calm and humble and vice versa.
If paul is both calm and not old then someone is either calm or rich.
If someone is not wise then fred is both not generous and not strong and vice versa.
If someone is either rich or not funny then lucy is not tall.
If mary is not old or patient then someone is happy or not wise.
Someone is strong or not quiet.
John is calm or creative.
Alice is either rich or not curious.
Susan is not wise or strong.
Someone is not tall.
Someone is either kind or not tall. | Lucy is not curious. | entailment | (((happy(alice)&~happy(alice)))<=>(?[X]:(humble(X))))&
(![X]:((~funny(X)<~>~patient(X))<=>strong(X)))&
(![X]:(generous(X)=>tall(X)))&
((?[X]:((~strong(X)&~happy(X))))=>(?[X]:(curious(X))))&
(((~old(alice)<~>~quiet(alice)))<=>((~generous(fred)&~strong(fred))))&
((?[X]:((~strong(X)|~creative(X))))=>((curious(susan)<~>~creative(susan))))&
(![X]:((patient(X)|~patient(X))<=>(~wise(X)&patient(X))))&
(![X]:((~old(X)|brave(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((~generous(X)<~>~curious(X))=>(~old(X)&funny(X))))&
(![X]:((quiet(X)&~curious(X))<=>(~wise(X)|brave(X))))&
(![X]:(~kind(X)<=>(calm(X)&humble(X))))&
(((calm(paul)&~old(paul)))=>(?[X]:((calm(X)<~>rich(X)))))&
((?[X]:(~wise(X)))<=>((~generous(fred)&~strong(fred))))&
((?[X]:((rich(X)<~>~funny(X))))=>(~tall(lucy)))&
(((~old(mary)|patient(mary)))=>(?[X]:((happy(X)|~wise(X)))))&
(?[X]:((strong(X)|~quiet(X))))&
((calm(john)|creative(john)))&
((rich(alice)<~>~curious(alice)))&
((~wise(susan)|strong(susan)))&
(?[X]:(~tall(X)))&
(?[X]:((kind(X)<~>~tall(X)))) | ~curious(lucy) | [
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7696522625532608147358315
% SZS output start Proof for 7696522625532608147358315
7. ! [X0] : ((~patient(X0) | patient(X0)) <=> (patient(X0) & ~wise(X0))) [input p6]
10. ! [X0] : ((~curious(X0) & quiet(X0)) <=> (brave(X0) | ~wise(X0))) [input p9]
22. curious(lucy) [input hypothesis]
45. ! [X0] : (((~patient(X0) | patient(X0)) | (~patient(X0) | wise(X0))) & ((patient(X0) & ~wise(X0)) | (patient(X0) & ~patient(X0)))) [nnf transformation 7]
46. ! [X0] : ((~patient(X0) | patient(X0) | ~patient(X0) | wise(X0)) & ((patient(X0) & ~wise(X0)) | (patient(X0) & ~patient(X0)))) [flattening 45]
49. ! [X0] : (((~curious(X0) & quiet(X0)) | (~brave(X0) & wise(X0))) & ((brave(X0) | ~wise(X0)) | (curious(X0) | ~quiet(X0)))) [nnf transformation 10]
50. ! [X0] : (((~curious(X0) & quiet(X0)) | (~brave(X0) & wise(X0))) & (brave(X0) | ~wise(X0) | curious(X0) | ~quiet(X0))) [flattening 49]
91. ~wise(X0) | ~patient(X0) [cnf transformation 46]
94. patient(X0) | patient(X0) [cnf transformation 46]
107. ~curious(X0) | wise(X0) [cnf transformation 50]
129. curious(lucy) [cnf transformation 22]
130. patient(X0) [duplicate literal removal 94]
189. ~wise(X0) [subsumption resolution 91,130]
190. ~curious(X0) [subsumption resolution 107,189]
247. $false [subsumption resolution 129,190]
% SZS output end Proof for 7696522625532608147358315
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not brave then susan is funny or not calm and vice versa.
Everyone who is not happy or brave is either wise or not creative.
Everyone who is either not creative or strong is funny and vice versa.
If someone is not generous or not strong then someone is either not rich or humble.
Everyone who is not wise or not tall is both not curious and not creative.
Everyone who is both wise and not creative is both not patient and happy and vice versa.
If someone is either tall or not quiet then susan is creative and vice versa.
Everyone who is not patient or creative is not quiet and vice versa.
Everyone who is not kind or tall is quiet.
If someone is funny then someone is creative.
If lucy is both creative and not generous then someone is either rich or happy.
Everyone who is both not patient and not old is not kind or not happy and vice versa.
If john is patient or old then someone is both not tall and not rich and vice versa.
If paul is strong then john is either calm or funny and vice versa.
If paul is either calm or not old then someone is quiet.
Lucy is kind.
John is not old or not creative.
Mary is not creative.
Mary is patient.
Fred is patient or calm. | Susan is not funny. | entailment | ((~brave(mary))<=>((funny(susan)|~calm(susan))))&
(![X]:((~happy(X)|brave(X))=>(wise(X)<~>~creative(X))))&
(![X]:((~creative(X)<~>strong(X))<=>funny(X)))&
((?[X]:((~generous(X)|~strong(X))))=>(?[X]:((~rich(X)<~>humble(X)))))&
(![X]:((~wise(X)|~tall(X))=>(~curious(X)&~creative(X))))&
(![X]:((wise(X)&~creative(X))<=>(~patient(X)&happy(X))))&
((?[X]:((tall(X)<~>~quiet(X))))<=>(creative(susan)))&
(![X]:((~patient(X)|creative(X))<=>~quiet(X)))&
(![X]:((~kind(X)|tall(X))=>quiet(X)))&
((?[X]:(funny(X)))=>(?[X]:(creative(X))))&
(((creative(lucy)&~generous(lucy)))=>(?[X]:((rich(X)<~>happy(X)))))&
(![X]:((~patient(X)&~old(X))<=>(~kind(X)|~happy(X))))&
(((patient(john)|old(john)))<=>(?[X]:((~tall(X)&~rich(X)))))&
((strong(paul))<=>((calm(john)<~>funny(john))))&
(((calm(paul)<~>~old(paul)))=>(?[X]:(quiet(X))))&
(kind(lucy))&
((~old(john)|~creative(john)))&
(~creative(mary))&
(patient(mary))&
((patient(fred)|calm(fred))) | ~funny(susan) | [
"p4",
"p6",
"p7",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7453587858514254206299702
% SZS output start Proof for 7453587858514254206299702
5. ! [X0] : ((~tall(X0) | ~wise(X0)) => (~creative(X0) & ~curious(X0))) [input p4]
7. ? [X0] : (tall(X0) <~> ~quiet(X0)) <=> creative(susan) [input p6]
8. ! [X0] : ((creative(X0) | ~patient(X0)) <=> ~quiet(X0)) [input p7]
9. ! [X0] : ((tall(X0) | ~kind(X0)) => quiet(X0)) [input p8]
10. ? [X0] : funny(X0) => ? [X0] : creative(X0) [input p9]
21. funny(susan) [input hypothesis]
23. ? [X0] : funny(X0) => ? [X1] : creative(X1) [rectify 10]
24. ! [X0] : ((~tall(X0) | ~wise(X0)) => ~creative(X0)) [pure predicate removal 5]
29. ! [X0] : (~creative(X0) | (tall(X0) & wise(X0))) [ennf transformation 24]
30. ! [X0] : (quiet(X0) | (~tall(X0) & kind(X0))) [ennf transformation 9]
31. ? [X1] : creative(X1) | ! [X0] : ~funny(X0) [ennf transformation 23]
43. (? [X0] : ((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) | ~creative(susan)) & (creative(susan) | ! [X0] : ((tall(X0) | quiet(X0)) & (~quiet(X0) | ~tall(X0)))) [nnf transformation 7]
44. (? [X0] : ((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) | ~creative(susan)) & (creative(susan) | ! [X1] : ((tall(X1) | quiet(X1)) & (~quiet(X1) | ~tall(X1)))) [rectify 43]
45. ? [X0] : ((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) => ((quiet(sK1) | ~tall(sK1)) & (~quiet(sK1) | tall(sK1))) [choice axiom]
46. (((quiet(sK1) | ~tall(sK1)) & (~quiet(sK1) | tall(sK1))) | ~creative(susan)) & (creative(susan) | ! [X1] : ((tall(X1) | quiet(X1)) & (~quiet(X1) | ~tall(X1)))) [skolemisation 44,45]
47. ! [X0] : (((creative(X0) | ~patient(X0)) | quiet(X0)) & (~quiet(X0) | (~creative(X0) & patient(X0)))) [nnf transformation 8]
48. ! [X0] : ((creative(X0) | ~patient(X0) | quiet(X0)) & (~quiet(X0) | (~creative(X0) & patient(X0)))) [flattening 47]
49. ? [X0] : creative(X0) | ! [X1] : ~funny(X1) [rectify 31]
50. ? [X0] : creative(X0) => creative(sK2) [choice axiom]
51. creative(sK2) | ! [X1] : ~funny(X1) [skolemisation 49,50]
77. ~creative(X0) | tall(X0) [cnf transformation 29]
82. creative(susan) | ~quiet(X1) | ~tall(X1) [cnf transformation 46]
87. ~quiet(X0) | ~creative(X0) [cnf transformation 48]
90. ~tall(X0) | quiet(X0) [cnf transformation 30]
91. creative(sK2) | ~funny(X1) [cnf transformation 51]
113. funny(susan) [cnf transformation 21]
124. 3 <=> funny(susan) [avatar definition]
125. funny(susan) <- (3) [avatar component clause 124]
143. 7 <=> creative(susan) [avatar definition]
144. creative(susan) <- (7) [avatar component clause 143]
161. 11 <=> ! [X1] : (~quiet(X1) | ~tall(X1)) [avatar definition]
162. ~quiet(X1) | ~tall(X1) <- (11) [avatar component clause 161]
163. 11 | 7 [avatar split clause 82,143,161]
165. 12 <=> ! [X1] : ~funny(X1) [avatar definition]
166. ~funny(X1) <- (12) [avatar component clause 165]
168. 13 <=> creative(sK2) [avatar definition]
170. creative(sK2) <- (13) [avatar component clause 168]
171. 12 | 13 [avatar split clause 91,168,165]
240. 3 [avatar split clause 113,124]
241. $false <- (3, 12) [subsumption resolution 125,166]
242. ~3 | ~12 [avatar contradiction clause 241]
245. tall(susan) <- (7) [resolution 77,144]
246. tall(sK2) <- (13) [resolution 77,170]
247. quiet(susan) <- (7) [resolution 90,245]
263. ~creative(susan) <- (7) [resolution 247,87]
265. $false <- (7) [subsumption resolution 263,144]
266. ~7 [avatar contradiction clause 265]
267. ~tall(X1) <- (11) [subsumption resolution 162,90]
270. $false <- (11, 13) [resolution 267,246]
271. ~11 | ~13 [avatar contradiction clause 270]
272. $false [avatar sat refutation 163,171,240,242,266,271]
% SZS output end Proof for 7453587858514254206299702
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not calm or not generous then paul is either quiet or not quiet.
If fred is both curious and wise then alice is not generous or not funny and vice versa.
Everyone who is both calm and happy is not patient.
Everyone who is brave is humble and vice versa.
Everyone who is not strong or calm is either brave or generous and vice versa.
If someone is tall then fred is either curious or not old.
Everyone who is both not strong and not wise is not funny and vice versa.
Everyone who is happy is both not quiet and strong.
Everyone who is tall or humble is not creative and vice versa.
Everyone who is not happy is either patient or quiet and vice versa.
Everyone who is both not funny and not curious is both not happy and generous and vice versa.
If someone is not funny then john is kind and vice versa.
If mary is funny or not curious then fred is either not rich or quiet and vice versa.
Everyone who is either not creative or curious is not humble or patient and vice versa.
Everyone who is not curious is either wise or funny and vice versa.
If paul is quiet then someone is either not brave or not generous and vice versa.
Paul is either not funny or rich.
Alice is both humble and not quiet.
Susan is rich or not funny.
Fred is not old or not humble.
Susan is creative or not funny.
Susan is either not tall or kind.
John is generous.
Alice is not tall or strong. | John is happy. | entailment | ((?[X]:((~calm(X)<~>~generous(X))))=>((quiet(paul)<~>~quiet(paul))))&
(((curious(fred)&wise(fred)))<=>((~generous(alice)|~funny(alice))))&
(![X]:((calm(X)&happy(X))=>~patient(X)))&
(![X]:(brave(X)<=>humble(X)))&
(![X]:((~strong(X)|calm(X))<=>(brave(X)<~>generous(X))))&
((?[X]:(tall(X)))=>((curious(fred)<~>~old(fred))))&
(![X]:((~strong(X)&~wise(X))<=>~funny(X)))&
(![X]:(happy(X)=>(~quiet(X)&strong(X))))&
(![X]:((tall(X)|humble(X))<=>~creative(X)))&
(![X]:(~happy(X)<=>(patient(X)<~>quiet(X))))&
(![X]:((~funny(X)&~curious(X))<=>(~happy(X)&generous(X))))&
((?[X]:(~funny(X)))<=>(kind(john)))&
(((funny(mary)|~curious(mary)))<=>((~rich(fred)<~>quiet(fred))))&
(![X]:((~creative(X)<~>curious(X))<=>(~humble(X)|patient(X))))&
(![X]:(~curious(X)<=>(wise(X)<~>funny(X))))&
((quiet(paul))<=>(?[X]:((~brave(X)<~>~generous(X)))))&
((~funny(paul)<~>rich(paul)))&
((humble(alice)&~quiet(alice)))&
((rich(susan)|~funny(susan)))&
((~old(fred)|~humble(fred)))&
((creative(susan)|~funny(susan)))&
((~tall(susan)<~>kind(susan)))&
(generous(john))&
((~tall(alice)|strong(alice))) | happy(john) | [
"p6",
"p10",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 269406274786309274505246
% SZS output start Proof for 269406274786309274505246
7. ! [X0] : ((~wise(X0) & ~strong(X0)) <=> ~funny(X0)) [input p6]
11. ! [X0] : ((~curious(X0) & ~funny(X0)) <=> (generous(X0) & ~happy(X0))) [input p10]
15. ! [X0] : (~curious(X0) <=> (wise(X0) <~> funny(X0))) [input p14]
23. generous(john) [input p22]
25. ~happy(john) [input hypothesis]
38. ! [X0] : (((~wise(X0) & ~strong(X0)) | funny(X0)) & (~funny(X0) | (wise(X0) | strong(X0)))) [nnf transformation 7]
39. ! [X0] : (((~wise(X0) & ~strong(X0)) | funny(X0)) & (~funny(X0) | wise(X0) | strong(X0))) [flattening 38]
43. ! [X0] : (((~curious(X0) & ~funny(X0)) | (~generous(X0) | happy(X0))) & ((generous(X0) & ~happy(X0)) | (curious(X0) | funny(X0)))) [nnf transformation 11]
44. ! [X0] : (((~curious(X0) & ~funny(X0)) | ~generous(X0) | happy(X0)) & ((generous(X0) & ~happy(X0)) | curious(X0) | funny(X0))) [flattening 43]
53. ! [X0] : ((~curious(X0) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0)))) & (((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | curious(X0))) [nnf transformation 15]
82. ~wise(X0) | funny(X0) [cnf transformation 39]
94. ~funny(X0) | ~generous(X0) | happy(X0) [cnf transformation 44]
95. ~curious(X0) | ~generous(X0) | happy(X0) [cnf transformation 44]
110. funny(X0) | wise(X0) | curious(X0) [cnf transformation 53]
111. ~funny(X0) | ~wise(X0) | curious(X0) [cnf transformation 53]
127. generous(john) [cnf transformation 23]
129. ~happy(john) [cnf transformation 25]
199. ~wise(X0) | curious(X0) [subsumption resolution 111,82]
200. funny(X0) | curious(X0) [subsumption resolution 110,199]
320. ~generous(X1) | happy(X1) | curious(X1) [resolution 94,200]
331. ~generous(X1) | happy(X1) [subsumption resolution 320,95]
427. happy(john) [resolution 331,127]
428. $false [subsumption resolution 427,129]
% SZS output end Proof for 269406274786309274505246
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or not brave is either happy or curious. Everyone who is not tall is not kind or rich and vice versa. Everyone who is either not old or not calm is funny or happy. Everyone who is either not creative or not rich is creative. If alice is both not kind and not tall then someone is both rich and not tall. Everyone who is either not humble or not happy is brave and vice versa. Everyone who is funny is not funny or strong and vice versa. If someone is not calm or not wise then someone is not generous or humble and vice versa. If someone is both strong and not funny then mary is not patient or curious. If susan is generous then someone is both not strong and not calm and vice versa. Everyone who is creative is either not curious or not wise. If someone is either tall or not old then mary is not quiet or strong and vice versa. If susan is both creative and not calm then fred is not kind or funny. If someone is not wise then someone is brave or not kind. If someone is generous or not creative then someone is not brave and vice versa. If lucy is not strong or brave then fred is happy or not calm and vice versa. Susan is not patient. Paul is not generous. Someone is brave. Lucy is tall. Mary is both not old and rich. Someone is either happy or brave. Fred is either not humble or happy. | Lucy is funny. | entailment | (![X]:((~funny(X)|~brave(X))=>(happy(X)<~>curious(X))))&
(![X]:(~tall(X)<=>(~kind(X)|rich(X))))&
(![X]:((~old(X)<~>~calm(X))=>(funny(X)|happy(X))))&
(![X]:((~creative(X)<~>~rich(X))=>creative(X)))&
(((~kind(alice)&~tall(alice)))=>(?[X]:((rich(X)&~tall(X)))))&
(![X]:((~humble(X)<~>~happy(X))<=>brave(X)))&
(![X]:(funny(X)<=>(~funny(X)|strong(X))))&
((?[X]:((~calm(X)|~wise(X))))<=>(?[X]:((~generous(X)|humble(X)))))&
((?[X]:((strong(X)&~funny(X))))=>((~patient(mary)|curious(mary))))&
((generous(susan))<=>(?[X]:((~strong(X)&~calm(X)))))&
(![X]:(creative(X)=>(~curious(X)<~>~wise(X))))&
((?[X]:((tall(X)<~>~old(X))))<=>((~quiet(mary)|strong(mary))))&
(((creative(susan)&~calm(susan)))=>((~kind(fred)|funny(fred))))&
((?[X]:(~wise(X)))=>(?[X]:((brave(X)|~kind(X)))))&
((?[X]:((generous(X)|~creative(X))))<=>(?[X]:(~brave(X))))&
(((~strong(lucy)|brave(lucy)))<=>((happy(fred)|~calm(fred))))&
(~patient(susan))&
(~generous(paul))&
(?[X]:(brave(X)))&
(tall(lucy))&
((~old(mary)&rich(mary)))&
(?[X]:((happy(X)<~>brave(X))))&
((~humble(fred)<~>happy(fred))) | funny(lucy) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6341145439834845813700289
% SZS output start Proof for 6341145439834845813700289
7. ! [X0] : (funny(X0) <=> (strong(X0) | ~funny(X0))) [input p6]
24. ~funny(lucy) [input hypothesis]
48. ! [X0] : ((funny(X0) | (~strong(X0) & funny(X0))) & ((strong(X0) | ~funny(X0)) | ~funny(X0))) [nnf transformation 7]
49. ! [X0] : ((funny(X0) | (~strong(X0) & funny(X0))) & (strong(X0) | ~funny(X0) | ~funny(X0))) [flattening 48]
99. funny(X0) | funny(X0) [cnf transformation 49]
134. ~funny(lucy) [cnf transformation 24]
136. funny(X0) [duplicate literal removal 99]
282. $false [subsumption resolution 134,136]
% SZS output end Proof for 6341145439834845813700289
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not wise is both not brave and not creative.
If someone is either wise or tall then someone is both not calm and quiet.
Everyone who is both not rich and not humble is either happy or not creative and vice versa.
If fred is both kind and not creative then someone is not patient.
If paul is both not wise and not brave then someone is both strong and not funny.
If someone is creative or not curious then someone is both not rich and not creative.
If susan is happy then someone is brave or not creative.
Everyone who is not funny is funny or brave and vice versa.
If alice is calm or not wise then someone is not strong.
Everyone who is both not curious and tall is generous.
Everyone who is not tall is kind or rich and vice versa.
Everyone who is either quiet or not strong is brave or rich and vice versa.
Everyone who is not calm is both not funny and tall and vice versa.
If someone is not strong then someone is not wise.
If someone is both not kind and brave then fred is either not funny or not patient.
If lucy is both creative and not humble then alice is quiet or creative.
Someone is humble or quiet.
Someone is not curious.
Someone is both curious and not calm.
Alice is wise or brave.
Susan is calm or happy.
Alice is both tall and not humble.
Someone is both strong and tall. | Fred is patient. | entailment | (![X]:(~wise(X)=>(~brave(X)&~creative(X))))&
((?[X]:((wise(X)<~>tall(X))))=>(?[X]:((~calm(X)&quiet(X)))))&
(![X]:((~rich(X)&~humble(X))<=>(happy(X)<~>~creative(X))))&
(((kind(fred)&~creative(fred)))=>(?[X]:(~patient(X))))&
(((~wise(paul)&~brave(paul)))=>(?[X]:((strong(X)&~funny(X)))))&
((?[X]:((creative(X)|~curious(X))))=>(?[X]:((~rich(X)&~creative(X)))))&
((happy(susan))=>(?[X]:((brave(X)|~creative(X)))))&
(![X]:(~funny(X)<=>(funny(X)|brave(X))))&
(((calm(alice)|~wise(alice)))=>(?[X]:(~strong(X))))&
(![X]:((~curious(X)&tall(X))=>generous(X)))&
(![X]:(~tall(X)<=>(kind(X)|rich(X))))&
(![X]:((quiet(X)<~>~strong(X))<=>(brave(X)|rich(X))))&
(![X]:(~calm(X)<=>(~funny(X)&tall(X))))&
((?[X]:(~strong(X)))=>(?[X]:(~wise(X))))&
((?[X]:((~kind(X)&brave(X))))=>((~funny(fred)<~>~patient(fred))))&
(((creative(lucy)&~humble(lucy)))=>((quiet(alice)|creative(alice))))&
(?[X]:((humble(X)|quiet(X))))&
(?[X]:(~curious(X)))&
(?[X]:((curious(X)&~calm(X))))&
((wise(alice)|brave(alice)))&
((calm(susan)|happy(susan)))&
((tall(alice)&~humble(alice)))&
(?[X]:((strong(X)&tall(X)))) | patient(fred) | [
"p7",
"p10",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8256279593876461958887016
% SZS output start Proof for 8256279593876461958887016
8. ! [X0] : (~funny(X0) <=> (brave(X0) | funny(X0))) [input p7]
11. ! [X0] : (~tall(X0) <=> (rich(X0) | kind(X0))) [input p10]
15. ? [X0] : (brave(X0) & ~kind(X0)) => (~funny(fred) <~> ~patient(fred)) [input p14]
22. ~humble(alice) & tall(alice) [input p21]
24. ~patient(fred) [input hypothesis]
39. (~funny(fred) <~> ~patient(fred)) | ! [X0] : (~brave(X0) | kind(X0)) [ennf transformation 15]
57. ! [X0] : ((~funny(X0) | (~brave(X0) & ~funny(X0))) & ((brave(X0) | funny(X0)) | funny(X0))) [nnf transformation 8]
58. ! [X0] : ((~funny(X0) | (~brave(X0) & ~funny(X0))) & (brave(X0) | funny(X0) | funny(X0))) [flattening 57]
61. ! [X0] : ((~tall(X0) | (~rich(X0) & ~kind(X0))) & ((rich(X0) | kind(X0)) | tall(X0))) [nnf transformation 11]
62. ! [X0] : ((~tall(X0) | (~rich(X0) & ~kind(X0))) & (rich(X0) | kind(X0) | tall(X0))) [flattening 61]
70. ((patient(fred) | funny(fred)) & (~patient(fred) | ~funny(fred))) | ! [X0] : (~brave(X0) | kind(X0)) [nnf transformation 39]
99. brave(X0) | funny(X0) | funny(X0) [cnf transformation 58]
100. ~funny(X0) | ~funny(X0) [cnf transformation 58]
105. ~kind(X0) | ~tall(X0) [cnf transformation 62]
118. patient(fred) | funny(fred) | ~brave(X0) | kind(X0) [cnf transformation 70]
126. tall(alice) [cnf transformation 22]
130. ~patient(fred) [cnf transformation 24]
131. brave(X0) | funny(X0) [duplicate literal removal 99]
132. ~funny(X0) [duplicate literal removal 100]
211. brave(X0) [subsumption resolution 131,132]
237. patient(fred) | ~brave(X0) | kind(X0) [subsumption resolution 118,132]
238. patient(fred) | kind(X0) [subsumption resolution 237,211]
240. 23 <=> ! [X0] : kind(X0) [avatar definition]
241. kind(X0) <- (23) [avatar component clause 240]
243. 24 <=> patient(fred) [avatar definition]
246. 23 | 24 [avatar split clause 238,243,240]
278. ~24 [avatar split clause 130,243]
286. ~tall(X0) <- (23) [resolution 105,241]
287. $false <- (23) [resolution 286,126]
290. ~23 [avatar contradiction clause 287]
291. $false [avatar sat refutation 246,278,290]
% SZS output end Proof for 8256279593876461958887016
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not wise or wise then alice is either not creative or not old.
If someone is wise then fred is either not brave or old.
If someone is either not wise or not happy then someone is both not funny and not brave.
If john is kind or not happy then someone is either not rich or brave.
If susan is both quiet and not kind then someone is either happy or not patient and vice versa.
Everyone who is creative is funny or curious.
If john is either not strong or not old then someone is wise.
Everyone who is happy is either not strong or not funny and vice versa.
Everyone who is curious or not old is curious.
Everyone who is not happy or happy is strong.
If someone is not strong or not quiet then someone is both not funny and patient.
Everyone who is not tall or kind is curious and vice versa.
Everyone who is both brave and not quiet is both quiet and not rich and vice versa.
Everyone who is happy is not happy or not kind and vice versa.
If someone is both kind and generous then someone is both wise and not tall and vice versa.
Everyone who is not creative or not rich is wise or not happy.
John is not quiet or patient.
Someone is both brave and old.
Someone is not old.
Someone is both not kind and not humble.
Someone is either old or strong.
Someone is not kind.
Paul is not patient or old. | Mary is funny. | contradiction | (((~wise(mary)|wise(mary)))=>((~creative(alice)<~>~old(alice))))&
((?[X]:(wise(X)))=>((~brave(fred)<~>old(fred))))&
((?[X]:((~wise(X)<~>~happy(X))))=>(?[X]:((~funny(X)&~brave(X)))))&
(((kind(john)|~happy(john)))=>(?[X]:((~rich(X)<~>brave(X)))))&
(((quiet(susan)&~kind(susan)))<=>(?[X]:((happy(X)<~>~patient(X)))))&
(![X]:(creative(X)=>(funny(X)|curious(X))))&
(((~strong(john)<~>~old(john)))=>(?[X]:(wise(X))))&
(![X]:(happy(X)<=>(~strong(X)<~>~funny(X))))&
(![X]:((curious(X)|~old(X))=>curious(X)))&
(![X]:((~happy(X)|happy(X))=>strong(X)))&
((?[X]:((~strong(X)|~quiet(X))))=>(?[X]:((~funny(X)&patient(X)))))&
(![X]:((~tall(X)|kind(X))<=>curious(X)))&
(![X]:((brave(X)&~quiet(X))<=>(quiet(X)&~rich(X))))&
(![X]:(happy(X)<=>(~happy(X)|~kind(X))))&
((?[X]:((kind(X)&generous(X))))<=>(?[X]:((wise(X)&~tall(X)))))&
(![X]:((~creative(X)|~rich(X))=>(wise(X)|~happy(X))))&
((~quiet(john)|patient(john)))&
(?[X]:((brave(X)&old(X))))&
(?[X]:(~old(X)))&
(?[X]:((~kind(X)&~humble(X))))&
(?[X]:((old(X)<~>strong(X))))&
(?[X]:(~kind(X)))&
((~patient(paul)|old(paul))) | funny(mary) | [
"p7",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4811424081916997772935923
% SZS output start Proof for 4811424081916997772935923
8. ! [X0] : (happy(X0) <=> (~strong(X0) <~> ~funny(X0))) [input p7]
10. ! [X0] : ((happy(X0) | ~happy(X0)) => strong(X0)) [input p9]
14. ! [X0] : (happy(X0) <=> (~kind(X0) | ~happy(X0))) [input p13]
24. funny(mary) [input hypothesis]
37. ! [X0] : (strong(X0) | (~happy(X0) & happy(X0))) [ennf transformation 10]
58. ! [X0] : ((happy(X0) | ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0)))) & (((funny(X0) | strong(X0)) & (~funny(X0) | ~strong(X0))) | ~happy(X0))) [nnf transformation 8]
66. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | ~happy(X0))) [nnf transformation 14]
67. ! [X0] : ((happy(X0) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ~happy(X0))) [flattening 66]
107. ~strong(X0) | ~funny(X0) | ~happy(X0) [cnf transformation 58]
113. strong(X0) | happy(X0) [cnf transformation 37]
114. ~happy(X0) | strong(X0) [cnf transformation 37]
127. happy(X0) | happy(X0) [cnf transformation 67]
144. funny(mary) [cnf transformation 24]
146. happy(X0) [duplicate literal removal 127]
258. strong(X0) [subsumption resolution 113,114]
338. ~funny(X0) | ~happy(X0) [resolution 107,258]
339. ~funny(X0) [subsumption resolution 338,146]
340. $false [resolution 339,144]
% SZS output end Proof for 4811424081916997772935923
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not happy is either not happy or brave. Everyone who is not kind is both quiet and not brave and vice versa. Everyone who is both strong and happy is rich or creative. If someone is both not old and not humble then lucy is creative. If someone is either not rich or not kind then someone is happy and vice versa. If someone is not tall or not generous then paul is not brave. Everyone who is either not patient or not humble is not brave. If someone is both not patient and not brave then paul is kind or rich and vice versa. Everyone who is not strong is both not tall and tall and vice versa. Everyone who is not old or kind is both not quiet and brave. Everyone who is generous is tall or not happy and vice versa. Everyone who is both strong and kind is creative. Everyone who is both patient and not humble is strong or curious and vice versa. If someone is tall then mary is not humble or not tall and vice versa. Everyone who is kind is not patient. Everyone who is both creative and quiet is either funny or patient. Someone is both not funny and quiet. Lucy is wise or patient. Someone is both curious and not humble. Mary is wise or not quiet. Someone is either not funny or not generous. | Paul is not creative. | neutral | (![X]:((quiet(X)<~>~happy(X))=>(~happy(X)<~>brave(X))))&
(![X]:(~kind(X)<=>(quiet(X)&~brave(X))))&
(![X]:((strong(X)&happy(X))=>(rich(X)|creative(X))))&
((?[X]:((~old(X)&~humble(X))))=>(creative(lucy)))&
((?[X]:((~rich(X)<~>~kind(X))))<=>(?[X]:(happy(X))))&
((?[X]:((~tall(X)|~generous(X))))=>(~brave(paul)))&
(![X]:((~patient(X)<~>~humble(X))=>~brave(X)))&
((?[X]:((~patient(X)&~brave(X))))<=>((kind(paul)|rich(paul))))&
(![X]:(~strong(X)<=>(~tall(X)&tall(X))))&
(![X]:((~old(X)|kind(X))=>(~quiet(X)&brave(X))))&
(![X]:(generous(X)<=>(tall(X)|~happy(X))))&
(![X]:((strong(X)&kind(X))=>creative(X)))&
(![X]:((patient(X)&~humble(X))<=>(strong(X)|curious(X))))&
((?[X]:(tall(X)))<=>((~humble(mary)|~tall(mary))))&
(![X]:(kind(X)=>~patient(X)))&
(![X]:((creative(X)&quiet(X))=>(funny(X)<~>patient(X))))&
(?[X]:((~funny(X)&quiet(X))))&
((wise(lucy)|patient(lucy)))&
(?[X]:((curious(X)&~humble(X))))&
((wise(mary)|~quiet(mary)))&
(?[X]:((~funny(X)<~>~generous(X)))) | ~creative(paul) | [] | null | 0 |
If someone is not strong or generous then fred is not brave or funny.
If someone is not tall or not generous then mary is both strong and not wise and vice versa.
Everyone who is brave is either quiet or wise and vice versa.
Everyone who is kind is either not calm or curious.
Everyone who is not humble or not quiet is kind and vice versa.
If mary is both wise and happy then alice is generous or not humble and vice versa.
If someone is not patient or not happy then someone is either not kind or humble.
Everyone who is both tall and brave is kind or calm and vice versa.
If susan is both not happy and not funny then someone is both not calm and kind and vice versa.
If fred is both humble and not wise then someone is not funny or patient.
If someone is not creative then mary is either not brave or not tall and vice versa.
Everyone who is either not old or not tall is not wise and vice versa.
Everyone who is not generous is not tall or not brave.
Everyone who is either curious or calm is not patient or calm.
If someone is funny or not quiet then someone is either not funny or curious.
Everyone who is wise or funny is either wise or not kind.
Someone is not quiet or kind.
Susan is not strong.
Alice is not rich.
Someone is not curious.
Fred is either not happy or not wise.
Someone is not tall.
Someone is not wise. | Alice is quiet. | entailment | ((?[X]:((~strong(X)|generous(X))))=>((~brave(fred)|funny(fred))))&
((?[X]:((~tall(X)|~generous(X))))<=>((strong(mary)&~wise(mary))))&
(![X]:(brave(X)<=>(quiet(X)<~>wise(X))))&
(![X]:(kind(X)=>(~calm(X)<~>curious(X))))&
(![X]:((~humble(X)|~quiet(X))<=>kind(X)))&
(((wise(mary)&happy(mary)))<=>((generous(alice)|~humble(alice))))&
((?[X]:((~patient(X)|~happy(X))))=>(?[X]:((~kind(X)<~>humble(X)))))&
(![X]:((tall(X)&brave(X))<=>(kind(X)|calm(X))))&
(((~happy(susan)&~funny(susan)))<=>(?[X]:((~calm(X)&kind(X)))))&
(((humble(fred)&~wise(fred)))=>(?[X]:((~funny(X)|patient(X)))))&
((?[X]:(~creative(X)))<=>((~brave(mary)<~>~tall(mary))))&
(![X]:((~old(X)<~>~tall(X))<=>~wise(X)))&
(![X]:(~generous(X)=>(~tall(X)|~brave(X))))&
(![X]:((curious(X)<~>calm(X))=>(~patient(X)|calm(X))))&
((?[X]:((funny(X)|~quiet(X))))=>(?[X]:((~funny(X)<~>curious(X)))))&
(![X]:((wise(X)|funny(X))=>(wise(X)<~>~kind(X))))&
(?[X]:((~quiet(X)|kind(X))))&
(~strong(susan))&
(~rich(alice))&
(?[X]:(~curious(X)))&
((~happy(fred)<~>~wise(fred)))&
(?[X]:(~tall(X)))&
(?[X]:(~wise(X))) | quiet(alice) | [
"p1",
"p4",
"p5",
"p7",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4741811844301333137361025
% SZS output start Proof for 4741811844301333137361025
2. ? [X0] : (~generous(X0) | ~tall(X0)) <=> (~wise(mary) & strong(mary)) [input p1]
5. ! [X0] : ((~quiet(X0) | ~humble(X0)) <=> kind(X0)) [input p4]
6. (happy(mary) & wise(mary)) <=> (~humble(alice) | generous(alice)) [input p5]
8. ! [X0] : ((brave(X0) & tall(X0)) <=> (calm(X0) | kind(X0))) [input p7]
13. ! [X0] : (~generous(X0) => (~brave(X0) | ~tall(X0))) [input p12]
22. ? [X0] : ~tall(X0) [input p21]
24. ~quiet(alice) [input hypothesis]
34. ! [X0] : ((~brave(X0) | ~tall(X0)) | generous(X0)) [ennf transformation 13]
35. ! [X0] : (~brave(X0) | ~tall(X0) | generous(X0)) [flattening 34]
40. (? [X0] : (~generous(X0) | ~tall(X0)) | (wise(mary) | ~strong(mary))) & ((~wise(mary) & strong(mary)) | ! [X0] : (generous(X0) & tall(X0))) [nnf transformation 2]
41. (? [X0] : (~generous(X0) | ~tall(X0)) | wise(mary) | ~strong(mary)) & ((~wise(mary) & strong(mary)) | ! [X0] : (generous(X0) & tall(X0))) [flattening 40]
42. (? [X0] : (~generous(X0) | ~tall(X0)) | wise(mary) | ~strong(mary)) & ((~wise(mary) & strong(mary)) | ! [X1] : (generous(X1) & tall(X1))) [rectify 41]
43. ? [X0] : (~generous(X0) | ~tall(X0)) => (~generous(sK0) | ~tall(sK0)) [choice axiom]
44. ((~generous(sK0) | ~tall(sK0)) | wise(mary) | ~strong(mary)) & ((~wise(mary) & strong(mary)) | ! [X1] : (generous(X1) & tall(X1))) [skolemisation 42,43]
47. ! [X0] : (((~quiet(X0) | ~humble(X0)) | ~kind(X0)) & (kind(X0) | (quiet(X0) & humble(X0)))) [nnf transformation 5]
48. ! [X0] : ((~quiet(X0) | ~humble(X0) | ~kind(X0)) & (kind(X0) | (quiet(X0) & humble(X0)))) [flattening 47]
49. ((happy(mary) & wise(mary)) | (humble(alice) & ~generous(alice))) & ((~humble(alice) | generous(alice)) | (~happy(mary) | ~wise(mary))) [nnf transformation 6]
50. ((happy(mary) & wise(mary)) | (humble(alice) & ~generous(alice))) & (~humble(alice) | generous(alice) | ~happy(mary) | ~wise(mary)) [flattening 49]
55. ! [X0] : (((brave(X0) & tall(X0)) | (~calm(X0) & ~kind(X0))) & ((calm(X0) | kind(X0)) | (~brave(X0) | ~tall(X0)))) [nnf transformation 8]
56. ! [X0] : (((brave(X0) & tall(X0)) | (~calm(X0) & ~kind(X0))) & (calm(X0) | kind(X0) | ~brave(X0) | ~tall(X0))) [flattening 55]
80. ? [X0] : ~tall(X0) => ~tall(sK8) [choice axiom]
81. ~tall(sK8) [skolemisation 22,80]
88. ~wise(mary) | tall(X1) [cnf transformation 44]
98. kind(X0) | quiet(X0) [cnf transformation 48]
101. wise(mary) | ~generous(alice) [cnf transformation 50]
110. ~kind(X0) | tall(X0) [cnf transformation 56]
112. ~kind(X0) | brave(X0) [cnf transformation 56]
127. ~tall(X0) | ~brave(X0) | generous(X0) [cnf transformation 35]
143. ~tall(sK8) [cnf transformation 81]
145. ~quiet(alice) [cnf transformation 24]
169. 6 <=> wise(mary) [avatar definition]
186. 10 <=> ! [X1] : tall(X1) [avatar definition]
187. tall(X1) <- (10) [avatar component clause 186]
188. 10 | ~6 [avatar split clause 88,169,186]
201. 13 <=> generous(alice) [avatar definition]
206. ~13 | 6 [avatar split clause 101,169,201]
318. quiet(X0) | tall(X0) [resolution 110,98]
321. quiet(X0) | brave(X0) [resolution 112,98]
398. tall(alice) [resolution 318,145]
403. ~brave(alice) | generous(alice) [resolution 398,127]
409. brave(alice) [resolution 321,145]
418. generous(alice) [subsumption resolution 403,409]
419. 13 [avatar split clause 418,201]
437. $false <- (10) [resolution 187,143]
440. ~10 [avatar contradiction clause 437]
442. $false [avatar sat refutation 188,206,419,440]
% SZS output end Proof for 4741811844301333137361025
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or not old is kind or not quiet and vice versa.
Everyone who is both not wise and not curious is kind or tall.
If fred is either not quiet or not generous then john is either creative or tall and vice versa.
Everyone who is both tall and not brave is either kind or not tall.
If mary is both quiet and not patient then someone is not generous or not rich.
If someone is not old or humble then someone is strong or brave and vice versa.
Everyone who is not tall or kind is tall and vice versa.
Everyone who is not happy is both not wise and not happy.
Everyone who is kind or quiet is not funny or not calm and vice versa.
Everyone who is not strong or wise is tall.
Everyone who is not humble or strong is not kind or not generous.
Everyone who is not calm or rich is not quiet or generous and vice versa.
Everyone who is brave is both not quiet and generous.
Everyone who is not strong or rich is creative.
If someone is not calm then someone is not humble.
Everyone who is creative is both not tall and old.
Someone is not kind or not humble.
Someone is either funny or strong.
Susan is both kind and not creative.
Someone is either creative or not happy. | Susan is quiet. | neutral | (![X]:((happy(X)<~>~old(X))<=>(kind(X)|~quiet(X))))&
(![X]:((~wise(X)&~curious(X))=>(kind(X)|tall(X))))&
(((~quiet(fred)<~>~generous(fred)))<=>((creative(john)<~>tall(john))))&
(![X]:((tall(X)&~brave(X))=>(kind(X)<~>~tall(X))))&
(((quiet(mary)&~patient(mary)))=>(?[X]:((~generous(X)|~rich(X)))))&
((?[X]:((~old(X)|humble(X))))<=>(?[X]:((strong(X)|brave(X)))))&
(![X]:((~tall(X)|kind(X))<=>tall(X)))&
(![X]:(~happy(X)=>(~wise(X)&~happy(X))))&
(![X]:((kind(X)|quiet(X))<=>(~funny(X)|~calm(X))))&
(![X]:((~strong(X)|wise(X))=>tall(X)))&
(![X]:((~humble(X)|strong(X))=>(~kind(X)|~generous(X))))&
(![X]:((~calm(X)|rich(X))<=>(~quiet(X)|generous(X))))&
(![X]:(brave(X)=>(~quiet(X)&generous(X))))&
(![X]:((~strong(X)|rich(X))=>creative(X)))&
((?[X]:(~calm(X)))=>(?[X]:(~humble(X))))&
(![X]:(creative(X)=>(~tall(X)&old(X))))&
(?[X]:((~kind(X)|~humble(X))))&
(?[X]:((funny(X)<~>strong(X))))&
((kind(susan)&~creative(susan)))&
(?[X]:((creative(X)<~>~happy(X)))) | quiet(susan) | [] | null | 0 |
Everyone who is old is not funny.
Everyone who is not tall or not quiet is both not quiet and not patient.
If someone is either not quiet or tall then someone is not tall or not brave and vice versa.
If someone is humble or not generous then susan is not creative.
Everyone who is not old or not wise is both kind and not curious and vice versa.
If mary is either not creative or happy then someone is not patient and vice versa.
Everyone who is not wise is generous or curious.
Everyone who is not quiet or creative is either not creative or brave and vice versa.
If someone is both patient and old then lucy is either not humble or not brave and vice versa.
Everyone who is either strong or not generous is calm and vice versa.
If susan is creative then someone is either quiet or funny and vice versa.
If someone is humble then someone is both not calm and quiet and vice versa.
Everyone who is curious is funny or humble and vice versa.
If susan is either patient or not funny then someone is either not generous or not wise.
Everyone who is both funny and patient is either not happy or not funny.
If someone is not creative then fred is creative or funny.
Someone is both rich and quiet.
Someone is not calm.
Susan is either funny or brave.
Susan is strong or quiet.
Fred is calm or not rich.
Someone is curious or old.
Someone is not tall or strong. | Lucy is generous. | entailment | (![X]:(old(X)=>~funny(X)))&
(![X]:((~tall(X)|~quiet(X))=>(~quiet(X)&~patient(X))))&
((?[X]:((~quiet(X)<~>tall(X))))<=>(?[X]:((~tall(X)|~brave(X)))))&
((?[X]:((humble(X)|~generous(X))))=>(~creative(susan)))&
(![X]:((~old(X)|~wise(X))<=>(kind(X)&~curious(X))))&
(((~creative(mary)<~>happy(mary)))<=>(?[X]:(~patient(X))))&
(![X]:(~wise(X)=>(generous(X)|curious(X))))&
(![X]:((~quiet(X)|creative(X))<=>(~creative(X)<~>brave(X))))&
((?[X]:((patient(X)&old(X))))<=>((~humble(lucy)<~>~brave(lucy))))&
(![X]:((strong(X)<~>~generous(X))<=>calm(X)))&
((creative(susan))<=>(?[X]:((quiet(X)<~>funny(X)))))&
((?[X]:(humble(X)))<=>(?[X]:((~calm(X)&quiet(X)))))&
(![X]:(curious(X)<=>(funny(X)|humble(X))))&
(((patient(susan)<~>~funny(susan)))=>(?[X]:((~generous(X)<~>~wise(X)))))&
(![X]:((funny(X)&patient(X))=>(~happy(X)<~>~funny(X))))&
((?[X]:(~creative(X)))=>((creative(fred)|funny(fred))))&
(?[X]:((rich(X)&quiet(X))))&
(?[X]:(~calm(X)))&
((funny(susan)<~>brave(susan)))&
((strong(susan)|quiet(susan)))&
((calm(fred)|~rich(fred)))&
(?[X]:((curious(X)|old(X))))&
(?[X]:((~tall(X)|strong(X)))) | generous(lucy) | [
"p0",
"p3",
"p4",
"p7",
"p10",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4761917887396598317982810
% SZS output start Proof for 4761917887396598317982810
1. ! [X0] : (old(X0) => ~funny(X0)) [input p0]
4. ? [X0] : (~generous(X0) | humble(X0)) => ~creative(susan) [input p3]
5. ! [X0] : ((~wise(X0) | ~old(X0)) <=> (~curious(X0) & kind(X0))) [input p4]
8. ! [X0] : ((creative(X0) | ~quiet(X0)) <=> (~creative(X0) <~> brave(X0))) [input p7]
11. creative(susan) <=> ? [X0] : (quiet(X0) <~> funny(X0)) [input p10]
13. ! [X0] : (curious(X0) <=> (humble(X0) | funny(X0))) [input p12]
19. funny(susan) <~> brave(susan) [input p18]
24. ~generous(lucy) [input hypothesis]
27. ! [X0] : (~funny(X0) | ~old(X0)) [ennf transformation 1]
29. ~creative(susan) | ! [X0] : (generous(X0) & ~humble(X0)) [ennf transformation 4]
42. ! [X0] : (((~wise(X0) | ~old(X0)) | (curious(X0) | ~kind(X0))) & ((~curious(X0) & kind(X0)) | (wise(X0) & old(X0)))) [nnf transformation 5]
43. ! [X0] : ((~wise(X0) | ~old(X0) | curious(X0) | ~kind(X0)) & ((~curious(X0) & kind(X0)) | (wise(X0) & old(X0)))) [flattening 42]
48. ! [X0] : (((creative(X0) | ~quiet(X0)) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | (~creative(X0) & quiet(X0)))) [nnf transformation 8]
49. ! [X0] : ((creative(X0) | ~quiet(X0) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | (~creative(X0) & quiet(X0)))) [flattening 48]
55. (creative(susan) | ! [X0] : ((quiet(X0) | ~funny(X0)) & (funny(X0) | ~quiet(X0)))) & (? [X0] : ((~funny(X0) | ~quiet(X0)) & (funny(X0) | quiet(X0))) | ~creative(susan)) [nnf transformation 11]
56. (creative(susan) | ! [X0] : ((quiet(X0) | ~funny(X0)) & (funny(X0) | ~quiet(X0)))) & (? [X1] : ((~funny(X1) | ~quiet(X1)) & (funny(X1) | quiet(X1))) | ~creative(susan)) [rectify 55]
57. ? [X1] : ((~funny(X1) | ~quiet(X1)) & (funny(X1) | quiet(X1))) => ((~funny(sK4) | ~quiet(sK4)) & (funny(sK4) | quiet(sK4))) [choice axiom]
58. (creative(susan) | ! [X0] : ((quiet(X0) | ~funny(X0)) & (funny(X0) | ~quiet(X0)))) & (((~funny(sK4) | ~quiet(sK4)) & (funny(sK4) | quiet(sK4))) | ~creative(susan)) [skolemisation 56,57]
64. ! [X0] : ((curious(X0) | (~humble(X0) & ~funny(X0))) & ((humble(X0) | funny(X0)) | ~curious(X0))) [nnf transformation 13]
65. ! [X0] : ((curious(X0) | (~humble(X0) & ~funny(X0))) & (humble(X0) | funny(X0) | ~curious(X0))) [flattening 64]
74. (~brave(susan) | ~funny(susan)) & (brave(susan) | funny(susan)) [nnf transformation 19]
79. ~funny(X0) | ~old(X0) [cnf transformation 27]
91. ~creative(susan) | generous(X0) [cnf transformation 29]
94. ~curious(X0) | old(X0) [cnf transformation 43]
104. ~brave(X0) | creative(X0) | quiet(X0) [cnf transformation 49]
120. creative(susan) | funny(X0) | ~quiet(X0) [cnf transformation 58]
126. ~funny(X0) | curious(X0) [cnf transformation 65]
138. brave(susan) | funny(susan) [cnf transformation 74]
144. ~generous(lucy) [cnf transformation 24]
180. 8 <=> ! [X0] : generous(X0) [avatar definition]
181. generous(X0) <- (8) [avatar component clause 180]
183. 9 <=> creative(susan) [avatar definition]
185. ~creative(susan) <- (~9) [avatar component clause 183]
186. 8 | ~9 [avatar split clause 91,183,180]
241. 21 <=> ! [X0] : (funny(X0) | ~quiet(X0)) [avatar definition]
242. ~quiet(X0) | funny(X0) <- (21) [avatar component clause 241]
243. 21 | 9 [avatar split clause 120,183,241]
273. 28 <=> funny(susan) [avatar definition]
274. ~funny(susan) <- (~28) [avatar component clause 273]
275. funny(susan) <- (28) [avatar component clause 273]
303. 35 <=> brave(susan) [avatar definition]
304. brave(susan) <- (35) [avatar component clause 303]
307. 28 | 35 [avatar split clause 138,303,273]
313. 37 <=> quiet(susan) [avatar definition]
315. quiet(susan) <- (37) [avatar component clause 313]
340. $false <- (8) [resolution 181,144]
341. ~8 [avatar contradiction clause 340]
342. ~old(susan) <- (28) [resolution 79,275]
348. curious(susan) <- (28) [resolution 126,275]
350. old(susan) <- (28) [resolution 348,94]
351. $false <- (28) [subsumption resolution 350,342]
352. ~28 [avatar contradiction clause 351]
365. creative(susan) | quiet(susan) <- (35) [resolution 104,304]
369. quiet(susan) <- (~9, 35) [subsumption resolution 365,185]
370. 37 | 9 | ~35 [avatar split clause 369,303,183,313]
381. funny(susan) <- (21, 37) [resolution 315,242]
383. $false <- (21, ~28, 37) [subsumption resolution 381,274]
384. ~21 | 28 | ~37 [avatar contradiction clause 383]
385. $false [avatar sat refutation 186,243,307,341,352,370,384]
% SZS output end Proof for 4761917887396598317982810
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not strong is not humble or not brave and vice versa.
If someone is either not rich or old then alice is not rich or not old and vice versa.
Everyone who is both not patient and humble is both not patient and not curious and vice versa.
If fred is kind or quiet then someone is either curious or humble and vice versa.
Everyone who is strong or funny is quiet and vice versa.
If someone is not strong then someone is both calm and not calm and vice versa.
Everyone who is both not happy and quiet is either generous or not happy and vice versa.
If john is either strong or not humble then john is both brave and not wise.
Everyone who is not funny or not wise is both strong and not wise.
Everyone who is both not curious and tall is both brave and not wise and vice versa.
Everyone who is both not tall and tall is not wise or not calm and vice versa.
Everyone who is rich is not happy or not generous and vice versa.
If fred is either not quiet or quiet then alice is not tall and vice versa.
Everyone who is both not wise and curious is both not quiet and not old.
If susan is both not brave and curious then lucy is both calm and not strong.
Someone is not happy.
Fred is creative.
John is both creative and not generous.
Mary is both brave and funny.
Alice is rich or not curious. | Alice is not funny. | contradiction | (![X]:((~brave(X)<~>~strong(X))<=>(~humble(X)|~brave(X))))&
((?[X]:((~rich(X)<~>old(X))))<=>((~rich(alice)|~old(alice))))&
(![X]:((~patient(X)&humble(X))<=>(~patient(X)&~curious(X))))&
(((kind(fred)|quiet(fred)))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((strong(X)|funny(X))<=>quiet(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((calm(X)&~calm(X)))))&
(![X]:((~happy(X)&quiet(X))<=>(generous(X)<~>~happy(X))))&
(((strong(john)<~>~humble(john)))=>((brave(john)&~wise(john))))&
(![X]:((~funny(X)|~wise(X))=>(strong(X)&~wise(X))))&
(![X]:((~curious(X)&tall(X))<=>(brave(X)&~wise(X))))&
(![X]:((~tall(X)&tall(X))<=>(~wise(X)|~calm(X))))&
(![X]:(rich(X)<=>(~happy(X)|~generous(X))))&
(((~quiet(fred)<~>quiet(fred)))<=>(~tall(alice)))&
(![X]:((~wise(X)&curious(X))=>(~quiet(X)&~old(X))))&
(((~brave(susan)&curious(susan)))=>((calm(lucy)&~strong(lucy))))&
(?[X]:(~happy(X)))&
(creative(fred))&
((creative(john)&~generous(john)))&
((brave(mary)&funny(mary)))&
((rich(alice)|~curious(alice))) | ~funny(alice) | [
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7501795027570148672441481
% SZS output start Proof for 7501795027570148672441481
9. ! [X0] : ((~wise(X0) | ~funny(X0)) => (~wise(X0) & strong(X0))) [input p8]
11. ! [X0] : ((tall(X0) & ~tall(X0)) <=> (~calm(X0) | ~wise(X0))) [input p10]
21. ~funny(alice) [input hypothesis]
26. ! [X0] : ((~wise(X0) & strong(X0)) | (wise(X0) & funny(X0))) [ennf transformation 9]
57. ! [X0] : (((tall(X0) & ~tall(X0)) | (calm(X0) & wise(X0))) & ((~calm(X0) | ~wise(X0)) | (~tall(X0) | tall(X0)))) [nnf transformation 11]
58. ! [X0] : (((tall(X0) & ~tall(X0)) | (calm(X0) & wise(X0))) & (~calm(X0) | ~wise(X0) | ~tall(X0) | tall(X0))) [flattening 57]
104. ~wise(X0) | funny(X0) [cnf transformation 26]
111. ~tall(X0) | wise(X0) [cnf transformation 58]
113. tall(X0) | wise(X0) [cnf transformation 58]
131. ~funny(alice) [cnf transformation 21]
228. wise(X0) [subsumption resolution 111,113]
262. funny(X1) [resolution 104,228]
264. $false [resolution 262,131]
% SZS output end Proof for 7501795027570148672441481
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.