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 quiet and not happy then someone is either brave or not old and vice versa. Everyone who is both quiet and not wise is happy or not curious. Everyone who is not rich is either not quiet or brave and vice versa. If someone is not patient then someone is both brave and patient. Everyone who is quiet is not generous or happy and vice versa. If someone is wise then someone is either tall or not brave and vice versa. Everyone who is both strong and rich is patient or not funny and vice versa. If susan is funny then someone is quiet. Everyone who is both not generous and rich is either not creative or not humble. If someone is both happy and not humble then mary is both patient and not old and vice versa. If someone is funny then lucy is either not creative or not rich and vice versa. Everyone who is either not calm or old is tall. Everyone who is either not creative or tall is either quiet or not wise and vice versa. If someone is both quiet and patient then alice is both not calm and not brave and vice versa. Everyone who is both not quiet and not rich is both not quiet and brave and vice versa. If john is both old and creative then john is patient or not happy. Someone is rich. Paul is either quiet or not tall. Lucy is not kind. John is not happy or tall. Paul is both wise and happy. Mary is either not creative or not generous. Fred is both not generous and not funny. | Mary is patient. | entailment | ((?[X]:((~quiet(X)&~happy(X))))<=>(?[X]:((brave(X)<~>~old(X)))))&
(![X]:((quiet(X)&~wise(X))=>(happy(X)|~curious(X))))&
(![X]:(~rich(X)<=>(~quiet(X)<~>brave(X))))&
((?[X]:(~patient(X)))=>(?[X]:((brave(X)&patient(X)))))&
(![X]:(quiet(X)<=>(~generous(X)|happy(X))))&
((?[X]:(wise(X)))<=>(?[X]:((tall(X)<~>~brave(X)))))&
(![X]:((strong(X)&rich(X))<=>(patient(X)|~funny(X))))&
((funny(susan))=>(?[X]:(quiet(X))))&
(![X]:((~generous(X)&rich(X))=>(~creative(X)<~>~humble(X))))&
((?[X]:((happy(X)&~humble(X))))<=>((patient(mary)&~old(mary))))&
((?[X]:(funny(X)))<=>((~creative(lucy)<~>~rich(lucy))))&
(![X]:((~calm(X)<~>old(X))=>tall(X)))&
(![X]:((~creative(X)<~>tall(X))<=>(quiet(X)<~>~wise(X))))&
((?[X]:((quiet(X)&patient(X))))<=>((~calm(alice)&~brave(alice))))&
(![X]:((~quiet(X)&~rich(X))<=>(~quiet(X)&brave(X))))&
(((old(john)&creative(john)))=>((patient(john)|~happy(john))))&
(?[X]:(rich(X)))&
((quiet(paul)<~>~tall(paul)))&
(~kind(lucy))&
((~happy(john)|tall(john)))&
((wise(paul)&happy(paul)))&
((~creative(mary)<~>~generous(mary)))&
((~generous(fred)&~funny(fred))) | patient(mary) | [
"p2",
"p3",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8165733090422207897910140
% SZS output start Proof for 8165733090422207897910140
3. ! [X0] : (~rich(X0) <=> (~quiet(X0) <~> brave(X0))) [input p2]
4. ? [X0] : ~patient(X0) => ? [X0] : (patient(X0) & brave(X0)) [input p3]
7. ! [X0] : ((rich(X0) & strong(X0)) <=> (~funny(X0) | patient(X0))) [input p6]
15. ! [X0] : ((~rich(X0) & ~quiet(X0)) <=> (brave(X0) & ~quiet(X0))) [input p14]
24. ~patient(mary) [input hypothesis]
26. ? [X0] : ~patient(X0) => ? [X1] : (patient(X1) & brave(X1)) [rectify 4]
30. ? [X1] : (patient(X1) & brave(X1)) | ! [X0] : patient(X0) [ennf transformation 26]
42. ! [X0] : ((~rich(X0) | ((~quiet(X0) | ~brave(X0)) & (brave(X0) | quiet(X0)))) & (((~brave(X0) | quiet(X0)) & (brave(X0) | ~quiet(X0))) | rich(X0))) [nnf transformation 3]
43. ? [X0] : (patient(X0) & brave(X0)) | ! [X1] : patient(X1) [rectify 30]
44. ? [X0] : (patient(X0) & brave(X0)) => (patient(sK2) & brave(sK2)) [choice axiom]
45. (patient(sK2) & brave(sK2)) | ! [X1] : patient(X1) [skolemisation 43,44]
53. ! [X0] : (((rich(X0) & strong(X0)) | (funny(X0) & ~patient(X0))) & ((~funny(X0) | patient(X0)) | (~rich(X0) | ~strong(X0)))) [nnf transformation 7]
54. ! [X0] : (((rich(X0) & strong(X0)) | (funny(X0) & ~patient(X0))) & (~funny(X0) | patient(X0) | ~rich(X0) | ~strong(X0))) [flattening 53]
74. ! [X0] : (((~rich(X0) & ~quiet(X0)) | (~brave(X0) | quiet(X0))) & ((brave(X0) & ~quiet(X0)) | (rich(X0) | quiet(X0)))) [nnf transformation 15]
75. ! [X0] : (((~rich(X0) & ~quiet(X0)) | ~brave(X0) | quiet(X0)) & ((brave(X0) & ~quiet(X0)) | rich(X0) | quiet(X0))) [flattening 74]
89. ~rich(X0) | ~quiet(X0) | ~brave(X0) [cnf transformation 42]
90. brave(sK2) | patient(X1) [cnf transformation 45]
91. patient(sK2) | patient(X1) [cnf transformation 45]
102. ~patient(X0) | rich(X0) [cnf transformation 54]
132. ~rich(X0) | ~brave(X0) | quiet(X0) [cnf transformation 75]
144. ~patient(mary) [cnf transformation 24]
177. 8 <=> ! [X1] : patient(X1) [avatar definition]
178. patient(X1) <- (8) [avatar component clause 177]
180. 9 <=> patient(sK2) [avatar definition]
182. patient(sK2) <- (9) [avatar component clause 180]
183. 8 | 9 [avatar split clause 91,180,177]
185. 10 <=> brave(sK2) [avatar definition]
187. brave(sK2) <- (10) [avatar component clause 185]
188. 8 | 10 [avatar split clause 90,185,177]
224. 19 <=> patient(mary) [avatar definition]
226. ~patient(mary) <- (~19) [avatar component clause 224]
288. ~rich(X0) | ~brave(X0) [subsumption resolution 132,89]
332. ~19 [avatar split clause 144,224]
333. $false <- (8, ~19) [resolution 226,178]
334. ~8 | 19 [avatar contradiction clause 333]
345. rich(sK2) <- (9) [resolution 102,182]
352. ~brave(sK2) <- (9) [resolution 288,345]
353. $false <- (9, 10) [subsumption resolution 352,187]
354. ~9 | ~10 [avatar contradiction clause 353]
355. $false [avatar sat refutation 183,188,332,334,354]
% SZS output end Proof for 8165733090422207897910140
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not rich or curious then someone is either creative or not funny and vice versa.
Everyone who is both not quiet and not humble is quiet.
Everyone who is calm or not generous is either generous or humble.
If someone is both not old and not creative then someone is both brave and curious.
Everyone who is either not calm or humble is not calm and vice versa.
Everyone who is both not calm and funny is not generous and vice versa.
If susan is quiet or not generous then mary is either not happy or not curious and vice versa.
Everyone who is both not generous and brave is both kind and not quiet and vice versa.
If someone is generous or funny then someone is either funny or not curious and vice versa.
Everyone who is not rich or not happy is calm or not kind.
Everyone who is not strong is not rich.
If someone is both not tall and not creative then someone is happy or funny.
Everyone who is brave is creative and vice versa.
Everyone who is brave is both not brave and creative and vice versa.
Everyone who is both not happy and not creative is generous.
Everyone who is not humble or not curious is kind or not happy and vice versa.
Someone is either funny or not patient.
Mary is either not creative or calm.
Fred is not kind.
Someone is not brave.
Paul is either brave or curious.
Someone is both generous and not kind.
John is wise or funny. | Mary is creative. | contradiction | (((~rich(lucy)|curious(lucy)))<=>(?[X]:((creative(X)<~>~funny(X)))))&
(![X]:((~quiet(X)&~humble(X))=>quiet(X)))&
(![X]:((calm(X)|~generous(X))=>(generous(X)<~>humble(X))))&
((?[X]:((~old(X)&~creative(X))))=>(?[X]:((brave(X)&curious(X)))))&
(![X]:((~calm(X)<~>humble(X))<=>~calm(X)))&
(![X]:((~calm(X)&funny(X))<=>~generous(X)))&
(((quiet(susan)|~generous(susan)))<=>((~happy(mary)<~>~curious(mary))))&
(![X]:((~generous(X)&brave(X))<=>(kind(X)&~quiet(X))))&
((?[X]:((generous(X)|funny(X))))<=>(?[X]:((funny(X)<~>~curious(X)))))&
(![X]:((~rich(X)|~happy(X))=>(calm(X)|~kind(X))))&
(![X]:(~strong(X)=>~rich(X)))&
((?[X]:((~tall(X)&~creative(X))))=>(?[X]:((happy(X)|funny(X)))))&
(![X]:(brave(X)<=>creative(X)))&
(![X]:(brave(X)<=>(~brave(X)&creative(X))))&
(![X]:((~happy(X)&~creative(X))=>generous(X)))&
(![X]:((~humble(X)|~curious(X))<=>(kind(X)|~happy(X))))&
(?[X]:((funny(X)<~>~patient(X))))&
((~creative(mary)<~>calm(mary)))&
(~kind(fred))&
(?[X]:(~brave(X)))&
((brave(paul)<~>curious(paul)))&
(?[X]:((generous(X)&~kind(X))))&
((wise(john)|funny(john))) | creative(mary) | [
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7159226293291436130730397
% SZS output start Proof for 7159226293291436130730397
13. ! [X0] : (brave(X0) <=> creative(X0)) [input p12]
14. ! [X0] : (brave(X0) <=> (creative(X0) & ~brave(X0))) [input p13]
24. creative(mary) [input hypothesis]
57. ! [X0] : ((brave(X0) | ~creative(X0)) & (creative(X0) | ~brave(X0))) [nnf transformation 13]
58. ! [X0] : ((brave(X0) | (~creative(X0) | brave(X0))) & ((creative(X0) & ~brave(X0)) | ~brave(X0))) [nnf transformation 14]
59. ! [X0] : ((brave(X0) | ~creative(X0) | brave(X0)) & ((creative(X0) & ~brave(X0)) | ~brave(X0))) [flattening 58]
108. ~creative(X0) | brave(X0) [cnf transformation 57]
109. ~brave(X0) | ~brave(X0) [cnf transformation 59]
127. creative(mary) [cnf transformation 24]
128. ~brave(X0) [duplicate literal removal 109]
215. 17 <=> creative(mary) [avatar definition]
217. creative(mary) <- (17) [avatar component clause 215]
225. 17 [avatar split clause 127,215]
228. brave(mary) <- (17) [resolution 108,217]
229. $false <- (17) [subsumption resolution 228,128]
230. ~17 [avatar contradiction clause 229]
231. $false [avatar sat refutation 225,230]
% SZS output end Proof for 7159226293291436130730397
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or brave is funny. If susan is not curious or not old then someone is either curious or not old and vice versa. If mary is both tall and not happy then fred is strong and vice versa. Everyone who is either brave or curious is both not patient and brave and vice versa. If someone is quiet or brave then fred is not funny or not strong and vice versa. If susan is both not kind and funny then someone is both not funny and humble and vice versa. Everyone who is kind or quiet is not happy or happy. Everyone who is not patient is either brave or not curious. If john is not rich then susan is either not humble or not funny. If someone is old or wise then someone is not rich and vice versa. Everyone who is both generous and tall is both funny and not generous. Everyone who is not patient or not creative is both not rich and creative and vice versa. Everyone who is either not kind or patient is both strong and brave. If susan is not strong then fred is not generous and vice versa. If john is curious or brave then someone is either humble or generous and vice versa. Everyone who is not old or generous is both curious and not calm and vice versa. Someone is old. Someone is strong or patient. Alice is either not patient or not calm. Fred is not calm or not creative. Someone is both not kind and not curious. Someone is not calm. Someone is not generous or not patient. | Fred is creative. | entailment | (![X]:((humble(X)|brave(X))=>funny(X)))&
(((~curious(susan)|~old(susan)))<=>(?[X]:((curious(X)<~>~old(X)))))&
(((tall(mary)&~happy(mary)))<=>(strong(fred)))&
(![X]:((brave(X)<~>curious(X))<=>(~patient(X)&brave(X))))&
((?[X]:((quiet(X)|brave(X))))<=>((~funny(fred)|~strong(fred))))&
(((~kind(susan)&funny(susan)))<=>(?[X]:((~funny(X)&humble(X)))))&
(![X]:((kind(X)|quiet(X))=>(~happy(X)|happy(X))))&
(![X]:(~patient(X)=>(brave(X)<~>~curious(X))))&
((~rich(john))=>((~humble(susan)<~>~funny(susan))))&
((?[X]:((old(X)|wise(X))))<=>(?[X]:(~rich(X))))&
(![X]:((generous(X)&tall(X))=>(funny(X)&~generous(X))))&
(![X]:((~patient(X)|~creative(X))<=>(~rich(X)&creative(X))))&
(![X]:((~kind(X)<~>patient(X))=>(strong(X)&brave(X))))&
((~strong(susan))<=>(~generous(fred)))&
(((curious(john)|brave(john)))<=>(?[X]:((humble(X)<~>generous(X)))))&
(![X]:((~old(X)|generous(X))<=>(curious(X)&~calm(X))))&
(?[X]:(old(X)))&
(?[X]:((strong(X)|patient(X))))&
((~patient(alice)<~>~calm(alice)))&
((~calm(fred)|~creative(fred)))&
(?[X]:((~kind(X)&~curious(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~generous(X)|~patient(X)))) | creative(fred) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8368549647581010535425882
% SZS output start Proof for 8368549647581010535425882
12. ! [X0] : ((~creative(X0) | ~patient(X0)) <=> (creative(X0) & ~rich(X0))) [input p11]
24. ~creative(fred) [input hypothesis]
60. ! [X0] : (((~creative(X0) | ~patient(X0)) | (~creative(X0) | rich(X0))) & ((creative(X0) & ~rich(X0)) | (creative(X0) & patient(X0)))) [nnf transformation 12]
61. ! [X0] : ((~creative(X0) | ~patient(X0) | ~creative(X0) | rich(X0)) & ((creative(X0) & ~rich(X0)) | (creative(X0) & patient(X0)))) [flattening 60]
121. creative(X0) | creative(X0) [cnf transformation 61]
149. ~creative(fred) [cnf transformation 24]
150. creative(X0) [duplicate literal removal 121]
346. $false [subsumption resolution 149,150]
% SZS output end Proof for 8368549647581010535425882
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or not curious is either not brave or happy and vice versa. If john is both happy and not old then paul is not wise or kind and vice versa. If alice is not quiet then someone is both not kind and not strong and vice versa. Everyone who is both not tall and generous is not wise and vice versa. Everyone who is both not brave and calm is brave or generous and vice versa. If mary is either kind or wise then someone is both not wise and curious and vice versa. Everyone who is not patient or kind is both not wise and kind and vice versa. If someone is generous or quiet then someone is humble or wise and vice versa. Everyone who is quiet or tall is both not kind and brave and vice versa. If someone is not old or patient then someone is calm or not generous. Everyone who is either not happy or not curious is both not tall and not calm. If someone is not quiet then paul is either patient or not wise. Everyone who is not calm or wise is happy. Everyone who is either tall or old is both not curious and not kind. Everyone who is either old or not brave is curious or generous and vice versa. Everyone who is tall is not humble or brave. Mary is rich. Someone is both funny and rich. Lucy is not curious. Paul is not generous. Mary is not creative. John is curious or not generous. Someone is not strong or strong. | Mary is calm. | entailment | (![X]:((happy(X)<~>~curious(X))<=>(~brave(X)<~>happy(X))))&
(((happy(john)&~old(john)))<=>((~wise(paul)|kind(paul))))&
((~quiet(alice))<=>(?[X]:((~kind(X)&~strong(X)))))&
(![X]:((~tall(X)&generous(X))<=>~wise(X)))&
(![X]:((~brave(X)&calm(X))<=>(brave(X)|generous(X))))&
(((kind(mary)<~>wise(mary)))<=>(?[X]:((~wise(X)&curious(X)))))&
(![X]:((~patient(X)|kind(X))<=>(~wise(X)&kind(X))))&
((?[X]:((generous(X)|quiet(X))))<=>(?[X]:((humble(X)|wise(X)))))&
(![X]:((quiet(X)|tall(X))<=>(~kind(X)&brave(X))))&
((?[X]:((~old(X)|patient(X))))=>(?[X]:((calm(X)|~generous(X)))))&
(![X]:((~happy(X)<~>~curious(X))=>(~tall(X)&~calm(X))))&
((?[X]:(~quiet(X)))=>((patient(paul)<~>~wise(paul))))&
(![X]:((~calm(X)|wise(X))=>happy(X)))&
(![X]:((tall(X)<~>old(X))=>(~curious(X)&~kind(X))))&
(![X]:((old(X)<~>~brave(X))<=>(curious(X)|generous(X))))&
(![X]:(tall(X)=>(~humble(X)|brave(X))))&
(rich(mary))&
(?[X]:((funny(X)&rich(X))))&
(~curious(lucy))&
(~generous(paul))&
(~creative(mary))&
((curious(john)|~generous(john)))&
(?[X]:((~strong(X)|strong(X)))) | calm(mary) | [
"p0",
"p3",
"p4",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 1250822556387971914956359
% SZS output start Proof for 1250822556387971914956359
1. ! [X0] : ((happy(X0) <~> ~curious(X0)) <=> (~brave(X0) <~> happy(X0))) [input p0]
4. ! [X0] : ((generous(X0) & ~tall(X0)) <=> ~wise(X0)) [input p3]
5. ! [X0] : ((calm(X0) & ~brave(X0)) <=> (generous(X0) | brave(X0))) [input p4]
6. (kind(mary) <~> wise(mary)) <=> ? [X0] : (curious(X0) & ~wise(X0)) [input p5]
7. ! [X0] : ((kind(X0) | ~patient(X0)) <=> (kind(X0) & ~wise(X0))) [input p6]
24. ~calm(mary) [input hypothesis]
38. ! [X0] : ((((curious(X0) | ~happy(X0)) & (~curious(X0) | happy(X0))) | ((~brave(X0) | ~happy(X0)) & (happy(X0) | brave(X0)))) & (((~happy(X0) | brave(X0)) & (happy(X0) | ~brave(X0))) | ((happy(X0) | curious(X0)) & (~curious(X0) | ~happy(X0))))) [nnf transformation 1]
45. ! [X0] : (((generous(X0) & ~tall(X0)) | wise(X0)) & (~wise(X0) | (~generous(X0) | tall(X0)))) [nnf transformation 4]
46. ! [X0] : (((generous(X0) & ~tall(X0)) | wise(X0)) & (~wise(X0) | ~generous(X0) | tall(X0))) [flattening 45]
47. ! [X0] : (((calm(X0) & ~brave(X0)) | (~generous(X0) & ~brave(X0))) & ((generous(X0) | brave(X0)) | (~calm(X0) | brave(X0)))) [nnf transformation 5]
48. ! [X0] : (((calm(X0) & ~brave(X0)) | (~generous(X0) & ~brave(X0))) & (generous(X0) | brave(X0) | ~calm(X0) | brave(X0))) [flattening 47]
49. (((~wise(mary) | ~kind(mary)) & (wise(mary) | kind(mary))) | ! [X0] : (~curious(X0) | wise(X0))) & (? [X0] : (curious(X0) & ~wise(X0)) | ((kind(mary) | ~wise(mary)) & (wise(mary) | ~kind(mary)))) [nnf transformation 6]
50. (((~wise(mary) | ~kind(mary)) & (wise(mary) | kind(mary))) | ! [X0] : (~curious(X0) | wise(X0))) & (? [X1] : (curious(X1) & ~wise(X1)) | ((kind(mary) | ~wise(mary)) & (wise(mary) | ~kind(mary)))) [rectify 49]
51. ? [X1] : (curious(X1) & ~wise(X1)) => (curious(sK1) & ~wise(sK1)) [choice axiom]
52. (((~wise(mary) | ~kind(mary)) & (wise(mary) | kind(mary))) | ! [X0] : (~curious(X0) | wise(X0))) & ((curious(sK1) & ~wise(sK1)) | ((kind(mary) | ~wise(mary)) & (wise(mary) | ~kind(mary)))) [skolemisation 50,51]
53. ! [X0] : (((kind(X0) | ~patient(X0)) | (~kind(X0) | wise(X0))) & ((kind(X0) & ~wise(X0)) | (~kind(X0) & patient(X0)))) [nnf transformation 7]
54. ! [X0] : ((kind(X0) | ~patient(X0) | ~kind(X0) | wise(X0)) & ((kind(X0) & ~wise(X0)) | (~kind(X0) & patient(X0)))) [flattening 53]
74. ~happy(X0) | brave(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 38]
76. ~curious(X0) | happy(X0) | happy(X0) | brave(X0) [cnf transformation 38]
90. generous(X0) | wise(X0) [cnf transformation 46]
92. ~brave(X0) | ~brave(X0) [cnf transformation 48]
95. ~generous(X0) | calm(X0) [cnf transformation 48]
99. curious(sK1) | kind(mary) | ~wise(mary) [cnf transformation 52]
103. ~kind(X0) | ~wise(X0) [cnf transformation 54]
141. ~calm(mary) [cnf transformation 24]
143. ~brave(X0) [duplicate literal removal 92]
145. ~happy(X0) | brave(X0) | ~curious(X0) [duplicate literal removal 74]
146. ~curious(X0) | happy(X0) | brave(X0) [duplicate literal removal 76]
148. ~curious(X0) | brave(X0) [subsumption resolution 145,146]
194. 10 <=> kind(mary) [avatar definition]
195. kind(mary) <- (10) [avatar component clause 194]
198. 11 <=> wise(mary) [avatar definition]
199. wise(mary) <- (11) [avatar component clause 198]
204. 12 <=> curious(sK1) [avatar definition]
206. curious(sK1) <- (12) [avatar component clause 204]
207. ~11 | 10 | 12 [avatar split clause 99,204,194,198]
276. calm(X0) | wise(X0) [resolution 95,90]
310. wise(mary) [resolution 276,141]
317. 11 [avatar split clause 310,198]
319. ~wise(mary) <- (10) [resolution 195,103]
320. $false <- (10, 11) [subsumption resolution 319,199]
321. ~10 | ~11 [avatar contradiction clause 320]
326. brave(sK1) <- (12) [resolution 206,148]
330. $false <- (12) [subsumption resolution 326,143]
331. ~12 [avatar contradiction clause 330]
332. $false [avatar sat refutation 207,317,321,331]
% SZS output end Proof for 1250822556387971914956359
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not brave is not patient and vice versa.
Everyone who is either kind or patient is not brave.
If someone is either rich or happy then someone is either brave or not patient and vice versa.
If someone is not happy then someone is both generous and not brave and vice versa.
If someone is either brave or curious then someone is not tall.
If mary is not brave or wise then paul is both kind and not wise.
If lucy is funny or humble then someone is either strong or not brave and vice versa.
Everyone who is both generous and not calm is both quiet and old.
Everyone who is calm is both not calm and not funny.
Everyone who is either brave or not funny is either not creative or not wise.
Everyone who is curious or patient is both calm and not wise and vice versa.
Everyone who is either not calm or not generous is not happy or not old.
If lucy is funny or not tall then mary is old and vice versa.
Everyone who is either rich or not patient is patient.
If someone is both humble and rich then paul is both kind and not brave and vice versa.
Everyone who is humble is not creative.
John is patient or humble.
Alice is both not creative and not old.
Lucy is not creative.
Fred is both kind and not funny. | Alice is kind. | neutral | (![X]:((~rich(X)|~brave(X))<=>~patient(X)))&
(![X]:((kind(X)<~>patient(X))=>~brave(X)))&
((?[X]:((rich(X)<~>happy(X))))<=>(?[X]:((brave(X)<~>~patient(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:((generous(X)&~brave(X)))))&
((?[X]:((brave(X)<~>curious(X))))=>(?[X]:(~tall(X))))&
(((~brave(mary)|wise(mary)))=>((kind(paul)&~wise(paul))))&
(((funny(lucy)|humble(lucy)))<=>(?[X]:((strong(X)<~>~brave(X)))))&
(![X]:((generous(X)&~calm(X))=>(quiet(X)&old(X))))&
(![X]:(calm(X)=>(~calm(X)&~funny(X))))&
(![X]:((brave(X)<~>~funny(X))=>(~creative(X)<~>~wise(X))))&
(![X]:((curious(X)|patient(X))<=>(calm(X)&~wise(X))))&
(![X]:((~calm(X)<~>~generous(X))=>(~happy(X)|~old(X))))&
(((funny(lucy)|~tall(lucy)))<=>(old(mary)))&
(![X]:((rich(X)<~>~patient(X))=>patient(X)))&
((?[X]:((humble(X)&rich(X))))<=>((kind(paul)&~brave(paul))))&
(![X]:(humble(X)=>~creative(X)))&
((patient(john)|humble(john)))&
((~creative(alice)&~old(alice)))&
(~creative(lucy))&
((kind(fred)&~funny(fred))) | kind(alice) | [] | null | 0 |
If someone is generous or not brave then someone is either creative or curious.
If mary is not happy or funny then someone is both not rich and not creative.
If john is wise then someone is tall.
Everyone who is curious or funny is either rich or quiet.
If someone is either rich or not happy then john is not patient.
Everyone who is either brave or patient is both quiet and not old.
Everyone who is generous or not strong is either old or strong.
If someone is not curious or not quiet then fred is rich.
Everyone who is not brave or generous is either tall or curious and vice versa.
If fred is not brave or calm then someone is not funny.
Everyone who is funny is either brave or patient.
If susan is either tall or curious then someone is either strong or not funny and vice versa.
If someone is not old or not creative then someone is not quiet or wise.
Everyone who is both not old and tall is not tall.
Everyone who is curious is both not old and not tall and vice versa.
If mary is not funny then mary is either not rich or creative and vice versa.
Someone is not curious.
Paul is either not generous or funny.
Susan is happy.
Someone is not quiet or not generous.
Someone is either not rich or brave.
Someone is creative or not wise.
Someone is both humble and not quiet. | Fred is funny. | contradiction | ((?[X]:((generous(X)|~brave(X))))=>(?[X]:((creative(X)<~>curious(X)))))&
(((~happy(mary)|funny(mary)))=>(?[X]:((~rich(X)&~creative(X)))))&
((wise(john))=>(?[X]:(tall(X))))&
(![X]:((curious(X)|funny(X))=>(rich(X)<~>quiet(X))))&
((?[X]:((rich(X)<~>~happy(X))))=>(~patient(john)))&
(![X]:((brave(X)<~>patient(X))=>(quiet(X)&~old(X))))&
(![X]:((generous(X)|~strong(X))=>(old(X)<~>strong(X))))&
((?[X]:((~curious(X)|~quiet(X))))=>(rich(fred)))&
(![X]:((~brave(X)|generous(X))<=>(tall(X)<~>curious(X))))&
(((~brave(fred)|calm(fred)))=>(?[X]:(~funny(X))))&
(![X]:(funny(X)=>(brave(X)<~>patient(X))))&
(((tall(susan)<~>curious(susan)))<=>(?[X]:((strong(X)<~>~funny(X)))))&
((?[X]:((~old(X)|~creative(X))))=>(?[X]:((~quiet(X)|wise(X)))))&
(![X]:((~old(X)&tall(X))=>~tall(X)))&
(![X]:(curious(X)<=>(~old(X)&~tall(X))))&
((~funny(mary))<=>((~rich(mary)<~>creative(mary))))&
(?[X]:(~curious(X)))&
((~generous(paul)<~>funny(paul)))&
(happy(susan))&
(?[X]:((~quiet(X)|~generous(X))))&
(?[X]:((~rich(X)<~>brave(X))))&
(?[X]:((creative(X)|~wise(X))))&
(?[X]:((humble(X)&~quiet(X)))) | funny(fred) | [
"p3",
"p5",
"p7",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6181656635388733802243547
% SZS output start Proof for 6181656635388733802243547
4. ! [X0] : ((funny(X0) | curious(X0)) => (rich(X0) <~> quiet(X0))) [input p3]
6. ! [X0] : ((brave(X0) <~> patient(X0)) => (~old(X0) & quiet(X0))) [input p5]
8. ? [X0] : (~quiet(X0) | ~curious(X0)) => rich(fred) [input p7]
11. ! [X0] : (funny(X0) => (brave(X0) <~> patient(X0))) [input p10]
17. ? [X0] : ~curious(X0) [input p16]
24. funny(fred) [input hypothesis]
32. ! [X0] : ((rich(X0) <~> quiet(X0)) | (~funny(X0) & ~curious(X0))) [ennf transformation 4]
34. ! [X0] : ((~old(X0) & quiet(X0)) | (brave(X0) <=> patient(X0))) [ennf transformation 6]
36. rich(fred) | ! [X0] : (quiet(X0) & curious(X0)) [ennf transformation 8]
38. ! [X0] : ((brave(X0) <~> patient(X0)) | ~funny(X0)) [ennf transformation 11]
50. ! [X0] : (((~quiet(X0) | ~rich(X0)) & (quiet(X0) | rich(X0))) | (~funny(X0) & ~curious(X0))) [nnf transformation 32]
52. ! [X0] : ((~old(X0) & quiet(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) [nnf transformation 34]
58. ! [X0] : (((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | ~funny(X0)) [nnf transformation 38]
69. ? [X0] : ~curious(X0) => ~curious(sK6) [choice axiom]
70. ~curious(sK6) [skolemisation 17,69]
93. ~quiet(X0) | ~rich(X0) | ~funny(X0) [cnf transformation 50]
96. ~brave(X0) | patient(X0) | quiet(X0) [cnf transformation 52]
97. ~patient(X0) | brave(X0) | quiet(X0) [cnf transformation 52]
104. rich(fred) | curious(X0) [cnf transformation 36]
113. ~funny(X0) | brave(X0) | patient(X0) [cnf transformation 58]
114. ~patient(X0) | ~brave(X0) | ~funny(X0) [cnf transformation 58]
133. ~curious(sK6) [cnf transformation 70]
142. funny(fred) [cnf transformation 24]
208. 15 <=> rich(fred) [avatar definition]
213. 16 <=> ! [X0] : curious(X0) [avatar definition]
214. curious(X0) <- (16) [avatar component clause 213]
215. 16 | 15 [avatar split clause 104,208,213]
217. 17 <=> brave(fred) [avatar definition]
218. ~brave(fred) <- (~17) [avatar component clause 217]
219. brave(fred) <- (17) [avatar component clause 217]
365. brave(fred) | patient(fred) [resolution 113,142]
367. 43 <=> patient(fred) [avatar definition]
369. patient(fred) <- (43) [avatar component clause 367]
370. 43 | 17 [avatar split clause 365,217,367]
371. patient(fred) | quiet(fred) <- (17) [resolution 219,96]
373. 44 <=> quiet(fred) [avatar definition]
374. ~quiet(fred) <- (~44) [avatar component clause 373]
375. quiet(fred) <- (44) [avatar component clause 373]
376. 44 | 43 | ~17 [avatar split clause 371,217,367,373]
377. ~brave(fred) | ~funny(fred) <- (43) [resolution 369,114]
379. ~funny(fred) <- (17, 43) [subsumption resolution 377,219]
380. $false <- (17, 43) [subsumption resolution 379,142]
381. ~17 | ~43 [avatar contradiction clause 380]
385. ~rich(fred) | ~funny(fred) <- (44) [resolution 375,93]
396. ~rich(fred) <- (44) [subsumption resolution 385,142]
397. ~15 | ~44 [avatar split clause 396,373,208]
413. $false <- (16) [resolution 214,133]
414. ~16 [avatar contradiction clause 413]
419. brave(fred) | quiet(fred) <- (43) [resolution 369,97]
420. quiet(fred) <- (~17, 43) [subsumption resolution 419,218]
421. $false <- (~17, 43, ~44) [subsumption resolution 420,374]
422. 17 | ~43 | 44 [avatar contradiction clause 421]
423. $false [avatar sat refutation 215,370,376,381,397,414,422]
% SZS output end Proof for 6181656635388733802243547
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is both calm and creative.
Everyone who is brave is not creative or not quiet and vice versa.
Everyone who is not old or not quiet is not patient or not wise.
If fred is either not kind or funny then john is happy or tall.
Everyone who is tall is both humble and old and vice versa.
Everyone who is patient is calm or rich and vice versa.
Everyone who is quiet is either tall or not generous and vice versa.
If lucy is both not humble and not tall then someone is humble or not funny.
Everyone who is quiet is either not calm or not happy.
Everyone who is funny is creative or not creative.
Everyone who is either not creative or tall is either not calm or not wise.
Everyone who is calm is either not strong or humble and vice versa.
Everyone who is not rich or patient is both not happy and not quiet and vice versa.
Everyone who is both not generous and brave is funny or not quiet and vice versa.
If someone is both not humble and not curious then mary is both old and not strong and vice versa.
Everyone who is not calm is not calm or not strong.
Mary is not brave or calm.
Someone is curious.
Fred is tall or brave.
Someone is rich. | Mary is strong. | entailment | (![X]:(~wise(X)=>(calm(X)&creative(X))))&
(![X]:(brave(X)<=>(~creative(X)|~quiet(X))))&
(![X]:((~old(X)|~quiet(X))=>(~patient(X)|~wise(X))))&
(((~kind(fred)<~>funny(fred)))=>((happy(john)|tall(john))))&
(![X]:(tall(X)<=>(humble(X)&old(X))))&
(![X]:(patient(X)<=>(calm(X)|rich(X))))&
(![X]:(quiet(X)<=>(tall(X)<~>~generous(X))))&
(((~humble(lucy)&~tall(lucy)))=>(?[X]:((humble(X)|~funny(X)))))&
(![X]:(quiet(X)=>(~calm(X)<~>~happy(X))))&
(![X]:(funny(X)=>(creative(X)|~creative(X))))&
(![X]:((~creative(X)<~>tall(X))=>(~calm(X)<~>~wise(X))))&
(![X]:(calm(X)<=>(~strong(X)<~>humble(X))))&
(![X]:((~rich(X)|patient(X))<=>(~happy(X)&~quiet(X))))&
(![X]:((~generous(X)&brave(X))<=>(funny(X)|~quiet(X))))&
((?[X]:((~humble(X)&~curious(X))))<=>((old(mary)&~strong(mary))))&
(![X]:(~calm(X)=>(~calm(X)|~strong(X))))&
((~brave(mary)|calm(mary)))&
(?[X]:(curious(X)))&
((tall(fred)|brave(fred)))&
(?[X]:(rich(X))) | strong(mary) | [
"p1",
"p4",
"p5",
"p6",
"p11",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3376255318438852005226784
% SZS output start Proof for 3376255318438852005226784
2. ! [X0] : (brave(X0) <=> (~quiet(X0) | ~creative(X0))) [input p1]
5. ! [X0] : (tall(X0) <=> (old(X0) & humble(X0))) [input p4]
6. ! [X0] : (patient(X0) <=> (rich(X0) | calm(X0))) [input p5]
7. ! [X0] : (quiet(X0) <=> (tall(X0) <~> ~generous(X0))) [input p6]
12. ! [X0] : (calm(X0) <=> (~strong(X0) <~> humble(X0))) [input p11]
13. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (~quiet(X0) & ~happy(X0))) [input p12]
14. ! [X0] : ((brave(X0) & ~generous(X0)) <=> (~quiet(X0) | funny(X0))) [input p13]
17. calm(mary) | ~brave(mary) [input p16]
21. ~strong(mary) [input hypothesis]
35. ! [X0] : ((brave(X0) | (quiet(X0) & creative(X0))) & ((~quiet(X0) | ~creative(X0)) | ~brave(X0))) [nnf transformation 2]
36. ! [X0] : ((brave(X0) | (quiet(X0) & creative(X0))) & (~quiet(X0) | ~creative(X0) | ~brave(X0))) [flattening 35]
38. ! [X0] : ((tall(X0) | (~old(X0) | ~humble(X0))) & ((old(X0) & humble(X0)) | ~tall(X0))) [nnf transformation 5]
39. ! [X0] : ((tall(X0) | ~old(X0) | ~humble(X0)) & ((old(X0) & humble(X0)) | ~tall(X0))) [flattening 38]
40. ! [X0] : ((patient(X0) | (~rich(X0) & ~calm(X0))) & ((rich(X0) | calm(X0)) | ~patient(X0))) [nnf transformation 6]
41. ! [X0] : ((patient(X0) | (~rich(X0) & ~calm(X0))) & (rich(X0) | calm(X0) | ~patient(X0))) [flattening 40]
42. ! [X0] : ((quiet(X0) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0)))) & (((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | ~quiet(X0))) [nnf transformation 7]
47. ! [X0] : ((calm(X0) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0)))) & (((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | ~calm(X0))) [nnf transformation 12]
48. ! [X0] : (((patient(X0) | ~rich(X0)) | (quiet(X0) | happy(X0))) & ((~quiet(X0) & ~happy(X0)) | (~patient(X0) & rich(X0)))) [nnf transformation 13]
49. ! [X0] : ((patient(X0) | ~rich(X0) | quiet(X0) | happy(X0)) & ((~quiet(X0) & ~happy(X0)) | (~patient(X0) & rich(X0)))) [flattening 48]
50. ! [X0] : (((brave(X0) & ~generous(X0)) | (quiet(X0) & ~funny(X0))) & ((~quiet(X0) | funny(X0)) | (~brave(X0) | generous(X0)))) [nnf transformation 14]
51. ! [X0] : (((brave(X0) & ~generous(X0)) | (quiet(X0) & ~funny(X0))) & (~quiet(X0) | funny(X0) | ~brave(X0) | generous(X0))) [flattening 50]
65. quiet(X0) | brave(X0) [cnf transformation 36]
70. ~tall(X0) | humble(X0) [cnf transformation 39]
74. ~calm(X0) | patient(X0) [cnf transformation 41]
75. ~rich(X0) | patient(X0) [cnf transformation 41]
79. generous(X0) | tall(X0) | quiet(X0) [cnf transformation 42]
89. ~humble(X0) | strong(X0) | ~calm(X0) [cnf transformation 47]
94. ~quiet(X0) | rich(X0) [cnf transformation 49]
95. ~patient(X0) | ~quiet(X0) [cnf transformation 49]
99. ~generous(X0) | quiet(X0) [cnf transformation 51]
107. calm(mary) | ~brave(mary) [cnf transformation 17]
111. ~strong(mary) [cnf transformation 21]
150. 9 <=> strong(mary) [avatar definition]
151. ~strong(mary) <- (~9) [avatar component clause 150]
169. 13 <=> brave(mary) [avatar definition]
171. ~brave(mary) <- (~13) [avatar component clause 169]
173. 14 <=> calm(mary) [avatar definition]
175. calm(mary) <- (14) [avatar component clause 173]
176. ~13 | 14 [avatar split clause 107,173,169]
186. ~9 [avatar split clause 111,150]
192. rich(X0) | brave(X0) [resolution 94,65]
197. patient(X0) | brave(X0) [resolution 192,75]
215. brave(X2) | ~quiet(X2) [resolution 197,95]
217. brave(X2) [subsumption resolution 215,65]
221. $false <- (~13) [resolution 217,171]
222. 13 [avatar contradiction clause 221]
223. patient(mary) <- (14) [resolution 175,74]
227. ~quiet(mary) <- (14) [resolution 223,95]
229. 19 <=> quiet(mary) [avatar definition]
230. ~quiet(mary) <- (~19) [avatar component clause 229]
237. ~19 | ~14 [avatar split clause 227,173,229]
252. tall(X2) | quiet(X2) | quiet(X2) [resolution 79,99]
254. tall(X2) | quiet(X2) [duplicate literal removal 252]
259. humble(X2) | quiet(X2) [resolution 254,70]
295. ~calm(X0) | strong(X0) | quiet(X0) [resolution 89,259]
348. strong(mary) | quiet(mary) <- (14) [resolution 295,175]
351. quiet(mary) <- (~9, 14) [subsumption resolution 348,151]
352. $false <- (~9, 14, ~19) [subsumption resolution 351,230]
353. 9 | ~14 | 19 [avatar contradiction clause 352]
354. $false [avatar sat refutation 176,186,222,237,353]
% SZS output end Proof for 3376255318438852005226784
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind and not happy is not creative or not tall and vice versa. Everyone who is either not rich or strong is not brave and vice versa. Everyone who is not calm is both not rich and not wise. If paul is rich or wise then susan is calm or not quiet. If paul is both tall and not curious then paul is strong or not generous. If someone is both not strong and not quiet then someone is both not creative and not quiet. If lucy is not humble then someone is not old or tall and vice versa. If susan is either patient or kind then paul is both curious and funny. If john is not funny then someone is either curious or tall. Everyone who is either not strong or not kind is not funny and vice versa. If someone is either not patient or not funny then lucy is not humble and vice versa. Everyone who is brave is not tall and vice versa. If someone is not funny then someone is brave. Everyone who is not generous is curious or funny. Everyone who is kind is happy. If susan is not patient or not brave then someone is either not old or not humble and vice versa. Someone is either not tall or not creative. Someone is both not happy and not humble. Fred is not creative. Susan is not calm. John is not wise or not funny. Someone is not rich or wise. Mary is either not happy or not humble. | Mary is not happy. | neutral | (![X]:((~kind(X)&~happy(X))<=>(~creative(X)|~tall(X))))&
(![X]:((~rich(X)<~>strong(X))<=>~brave(X)))&
(![X]:(~calm(X)=>(~rich(X)&~wise(X))))&
(((rich(paul)|wise(paul)))=>((calm(susan)|~quiet(susan))))&
(((tall(paul)&~curious(paul)))=>((strong(paul)|~generous(paul))))&
((?[X]:((~strong(X)&~quiet(X))))=>(?[X]:((~creative(X)&~quiet(X)))))&
((~humble(lucy))<=>(?[X]:((~old(X)|tall(X)))))&
(((patient(susan)<~>kind(susan)))=>((curious(paul)&funny(paul))))&
((~funny(john))=>(?[X]:((curious(X)<~>tall(X)))))&
(![X]:((~strong(X)<~>~kind(X))<=>~funny(X)))&
((?[X]:((~patient(X)<~>~funny(X))))<=>(~humble(lucy)))&
(![X]:(brave(X)<=>~tall(X)))&
((?[X]:(~funny(X)))=>(?[X]:(brave(X))))&
(![X]:(~generous(X)=>(curious(X)|funny(X))))&
(![X]:(kind(X)=>happy(X)))&
(((~patient(susan)|~brave(susan)))<=>(?[X]:((~old(X)<~>~humble(X)))))&
(?[X]:((~tall(X)<~>~creative(X))))&
(?[X]:((~happy(X)&~humble(X))))&
(~creative(fred))&
(~calm(susan))&
((~wise(john)|~funny(john)))&
(?[X]:((~rich(X)|wise(X))))&
((~happy(mary)<~>~humble(mary))) | ~happy(mary) | [] | null | 0 |
If paul is kind or generous then someone is both not calm and not happy.
If someone is not brave then susan is humble or not rich and vice versa.
If john is not quiet then someone is both not strong and not creative and vice versa.
If someone is not creative or generous then alice is either not strong or patient and vice versa.
If someone is not old then fred is either generous or old and vice versa.
Everyone who is wise is patient or not patient.
Everyone who is humble or not quiet is either brave or calm and vice versa.
Everyone who is not kind or brave is either not humble or not happy.
Everyone who is brave is both brave and not strong.
If someone is both tall and rich then someone is both tall and not generous and vice versa.
If someone is both curious and patient then mary is creative and vice versa.
Everyone who is either rich or not rich is not wise and vice versa.
Everyone who is calm or not wise is either wise or not curious and vice versa.
If someone is generous or patient then mary is not curious or not wise and vice versa.
If someone is generous then john is both curious and not kind.
Everyone who is both not patient and not tall is either not patient or creative.
Someone is kind.
Someone is both not old and not funny.
John is both happy and not brave.
Someone is either strong or not wise.
Someone is either not tall or old.
Someone is either kind or not old.
Susan is either wise or not calm. | Paul is curious. | contradiction | (((kind(paul)|generous(paul)))=>(?[X]:((~calm(X)&~happy(X)))))&
((?[X]:(~brave(X)))<=>((humble(susan)|~rich(susan))))&
((~quiet(john))<=>(?[X]:((~strong(X)&~creative(X)))))&
((?[X]:((~creative(X)|generous(X))))<=>((~strong(alice)<~>patient(alice))))&
((?[X]:(~old(X)))<=>((generous(fred)<~>old(fred))))&
(![X]:(wise(X)=>(patient(X)|~patient(X))))&
(![X]:((humble(X)|~quiet(X))<=>(brave(X)<~>calm(X))))&
(![X]:((~kind(X)|brave(X))=>(~humble(X)<~>~happy(X))))&
(![X]:(brave(X)=>(brave(X)&~strong(X))))&
((?[X]:((tall(X)&rich(X))))<=>(?[X]:((tall(X)&~generous(X)))))&
((?[X]:((curious(X)&patient(X))))<=>(creative(mary)))&
(![X]:((rich(X)<~>~rich(X))<=>~wise(X)))&
(![X]:((calm(X)|~wise(X))<=>(wise(X)<~>~curious(X))))&
((?[X]:((generous(X)|patient(X))))<=>((~curious(mary)|~wise(mary))))&
((?[X]:(generous(X)))=>((curious(john)&~kind(john))))&
(![X]:((~patient(X)&~tall(X))=>(~patient(X)<~>creative(X))))&
(?[X]:(kind(X)))&
(?[X]:((~old(X)&~funny(X))))&
((happy(john)&~brave(john)))&
(?[X]:((strong(X)<~>~wise(X))))&
(?[X]:((~tall(X)<~>old(X))))&
(?[X]:((kind(X)<~>~old(X))))&
((wise(susan)<~>~calm(susan))) | curious(paul) | [
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 9150646423556628838619446
% SZS output start Proof for 9150646423556628838619446
12. ! [X0] : ((rich(X0) <~> ~rich(X0)) <=> ~wise(X0)) [input p11]
13. ! [X0] : ((~wise(X0) | calm(X0)) <=> (wise(X0) <~> ~curious(X0))) [input p12]
24. curious(paul) [input hypothesis]
66. ! [X0] : ((((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | wise(X0)) & (~wise(X0) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0))))) [nnf transformation 12]
67. ! [X0] : (((~wise(X0) | calm(X0)) | ((wise(X0) | curious(X0)) & (~curious(X0) | ~wise(X0)))) & (((curious(X0) | ~wise(X0)) & (~curious(X0) | wise(X0))) | (wise(X0) & ~calm(X0)))) [nnf transformation 13]
68. ! [X0] : ((~wise(X0) | calm(X0) | ((wise(X0) | curious(X0)) & (~curious(X0) | ~wise(X0)))) & (((curious(X0) | ~wise(X0)) & (~curious(X0) | wise(X0))) | (wise(X0) & ~calm(X0)))) [flattening 67]
129. ~wise(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 66]
130. ~wise(X0) | rich(X0) | rich(X0) [cnf transformation 66]
134. ~curious(X0) | wise(X0) | wise(X0) [cnf transformation 68]
159. curious(paul) [cnf transformation 24]
161. ~curious(X0) | wise(X0) [duplicate literal removal 134]
163. ~wise(X0) | ~rich(X0) [duplicate literal removal 129]
164. ~wise(X0) | rich(X0) [duplicate literal removal 130]
312. ~wise(X0) [subsumption resolution 163,164]
313. ~curious(X0) [subsumption resolution 161,312]
355. $false [subsumption resolution 159,313]
% SZS output end Proof for 9150646423556628838619446
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or kind is not humble. Everyone who is either not strong or rich is not tall or not curious and vice versa. If someone is either brave or not tall then someone is not kind or patient and vice versa. If someone is tall or not curious then someone is not rich and vice versa. If someone is both not curious and brave then john is not funny and vice versa. Everyone who is not old is not quiet or not generous. If fred is not generous then someone is happy or not brave and vice versa. If lucy is both not brave and brave then someone is strong or brave. If mary is not kind then fred is not happy and vice versa. Everyone who is not rich or not wise is both not curious and rich and vice versa. Everyone who is not quiet is either rich or not brave. Everyone who is either generous or tall is both not curious and not happy and vice versa. If lucy is not wise or not quiet then someone is either not patient or patient. If lucy is not old or not kind then someone is either funny or not brave. If lucy is both not quiet and generous then john is either rich or not generous. If someone is both not happy and quiet then someone is both not patient and generous and vice versa. Someone is either not patient or not tall. Paul is both not funny and not creative. John is both curious and happy. Paul is both not tall and quiet. Mary is patient. | Lucy is happy. | neutral | (![X]:((curious(X)|kind(X))=>~humble(X)))&
(![X]:((~strong(X)<~>rich(X))<=>(~tall(X)|~curious(X))))&
((?[X]:((brave(X)<~>~tall(X))))<=>(?[X]:((~kind(X)|patient(X)))))&
((?[X]:((tall(X)|~curious(X))))<=>(?[X]:(~rich(X))))&
((?[X]:((~curious(X)&brave(X))))<=>(~funny(john)))&
(![X]:(~old(X)=>(~quiet(X)|~generous(X))))&
((~generous(fred))<=>(?[X]:((happy(X)|~brave(X)))))&
(((~brave(lucy)&brave(lucy)))=>(?[X]:((strong(X)|brave(X)))))&
((~kind(mary))<=>(~happy(fred)))&
(![X]:((~rich(X)|~wise(X))<=>(~curious(X)&rich(X))))&
(![X]:(~quiet(X)=>(rich(X)<~>~brave(X))))&
(![X]:((generous(X)<~>tall(X))<=>(~curious(X)&~happy(X))))&
(((~wise(lucy)|~quiet(lucy)))=>(?[X]:((~patient(X)<~>patient(X)))))&
(((~old(lucy)|~kind(lucy)))=>(?[X]:((funny(X)<~>~brave(X)))))&
(((~quiet(lucy)&generous(lucy)))=>((rich(john)<~>~generous(john))))&
((?[X]:((~happy(X)&quiet(X))))<=>(?[X]:((~patient(X)&generous(X)))))&
(?[X]:((~patient(X)<~>~tall(X))))&
((~funny(paul)&~creative(paul)))&
((curious(john)&happy(john)))&
((~tall(paul)&quiet(paul)))&
(patient(mary)) | happy(lucy) | [] | null | 0 |
If someone is both not tall and strong then someone is curious.
Everyone who is not tall or not creative is both quiet and not brave and vice versa.
If someone is both old and happy then john is not wise or generous and vice versa.
If lucy is either old or not kind then paul is either not generous or creative.
If someone is creative or not tall then fred is not generous.
Everyone who is either not curious or kind is either not creative or not happy.
If someone is brave or not strong then susan is wise or tall and vice versa.
Everyone who is kind is both not quiet and creative and vice versa.
If someone is both kind and not wise then mary is not brave or not strong and vice versa.
Everyone who is both not wise and not patient is either generous or funny.
If someone is either not curious or not brave then alice is either not creative or not wise and vice versa.
Everyone who is not old is either rich or calm.
Everyone who is either not creative or not old is both brave and not happy.
Everyone who is not funny or brave is either not calm or humble.
Everyone who is both creative and not humble is both not rich and not creative.
If mary is both creative and quiet then someone is generous or humble and vice versa.
Paul is both creative and not old.
Someone is not quiet or not funny.
Someone is not kind or not rich.
Paul is not old or not quiet.
Alice is either not tall or wise.
Someone is not curious.
Alice is both not rich and not calm.
Paul is not generous. | Lucy is not creative. | contradiction | ((?[X]:((~tall(X)&strong(X))))=>(?[X]:(curious(X))))&
(![X]:((~tall(X)|~creative(X))<=>(quiet(X)&~brave(X))))&
((?[X]:((old(X)&happy(X))))<=>((~wise(john)|generous(john))))&
(((old(lucy)<~>~kind(lucy)))=>((~generous(paul)<~>creative(paul))))&
((?[X]:((creative(X)|~tall(X))))=>(~generous(fred)))&
(![X]:((~curious(X)<~>kind(X))=>(~creative(X)<~>~happy(X))))&
((?[X]:((brave(X)|~strong(X))))<=>((wise(susan)|tall(susan))))&
(![X]:(kind(X)<=>(~quiet(X)&creative(X))))&
((?[X]:((kind(X)&~wise(X))))<=>((~brave(mary)|~strong(mary))))&
(![X]:((~wise(X)&~patient(X))=>(generous(X)<~>funny(X))))&
((?[X]:((~curious(X)<~>~brave(X))))<=>((~creative(alice)<~>~wise(alice))))&
(![X]:(~old(X)=>(rich(X)<~>calm(X))))&
(![X]:((~creative(X)<~>~old(X))=>(brave(X)&~happy(X))))&
(![X]:((~funny(X)|brave(X))=>(~calm(X)<~>humble(X))))&
(![X]:((creative(X)&~humble(X))=>(~rich(X)&~creative(X))))&
(((creative(mary)&quiet(mary)))<=>(?[X]:((generous(X)|humble(X)))))&
((creative(paul)&~old(paul)))&
(?[X]:((~quiet(X)|~funny(X))))&
(?[X]:((~kind(X)|~rich(X))))&
((~old(paul)|~quiet(paul)))&
((~tall(alice)<~>wise(alice)))&
(?[X]:(~curious(X)))&
((~rich(alice)&~calm(alice)))&
(~generous(paul)) | ~creative(lucy) | [
"p1",
"p3",
"p7",
"p12",
"p16",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3914344970206190088476416
% SZS output start Proof for 3914344970206190088476416
2. ! [X0] : ((~creative(X0) | ~tall(X0)) <=> (~brave(X0) & quiet(X0))) [input p1]
4. (old(lucy) <~> ~kind(lucy)) => (~generous(paul) <~> creative(paul)) [input p3]
8. ! [X0] : (kind(X0) <=> (creative(X0) & ~quiet(X0))) [input p7]
13. ! [X0] : ((~creative(X0) <~> ~old(X0)) => (~happy(X0) & brave(X0))) [input p12]
17. ~old(paul) & creative(paul) [input p16]
24. ~generous(paul) [input p23]
25. ~creative(lucy) [input hypothesis]
29. (~generous(paul) <~> creative(paul)) | (old(lucy) <=> ~kind(lucy)) [ennf transformation 4]
33. ! [X0] : ((~happy(X0) & brave(X0)) | (~creative(X0) <=> ~old(X0))) [ennf transformation 13]
40. ! [X0] : (((~creative(X0) | ~tall(X0)) | (brave(X0) | ~quiet(X0))) & ((~brave(X0) & quiet(X0)) | (creative(X0) & tall(X0)))) [nnf transformation 2]
41. ! [X0] : ((~creative(X0) | ~tall(X0) | brave(X0) | ~quiet(X0)) & ((~brave(X0) & quiet(X0)) | (creative(X0) & tall(X0)))) [flattening 40]
47. ((~creative(paul) | generous(paul)) & (creative(paul) | ~generous(paul))) | ((old(lucy) | kind(lucy)) & (~kind(lucy) | ~old(lucy))) [nnf transformation 29]
54. ! [X0] : ((kind(X0) | (~creative(X0) | quiet(X0))) & ((creative(X0) & ~quiet(X0)) | ~kind(X0))) [nnf transformation 8]
55. ! [X0] : ((kind(X0) | ~creative(X0) | quiet(X0)) & ((creative(X0) & ~quiet(X0)) | ~kind(X0))) [flattening 54]
66. ! [X0] : ((~happy(X0) & brave(X0)) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0)))) [nnf transformation 33]
84. ~brave(X0) | creative(X0) [cnf transformation 41]
94. ~creative(paul) | generous(paul) | old(lucy) | kind(lucy) [cnf transformation 47]
106. ~kind(X0) | creative(X0) [cnf transformation 55]
123. brave(X0) | ~old(X0) | creative(X0) [cnf transformation 66]
138. creative(paul) [cnf transformation 17]
148. ~generous(paul) [cnf transformation 24]
149. ~creative(lucy) [cnf transformation 25]
184. 8 <=> kind(lucy) [avatar definition]
186. kind(lucy) <- (8) [avatar component clause 184]
188. 9 <=> old(lucy) [avatar definition]
190. old(lucy) <- (9) [avatar component clause 188]
192. 10 <=> generous(paul) [avatar definition]
196. 11 <=> creative(paul) [avatar definition]
199. 8 | 9 | 10 | ~11 [avatar split clause 94,196,192,188,184]
296. ~old(X0) | creative(X0) [subsumption resolution 123,84]
324. 11 [avatar split clause 138,196]
349. ~10 [avatar split clause 148,192]
357. creative(lucy) <- (8) [resolution 106,186]
359. $false <- (8) [subsumption resolution 357,149]
360. ~8 [avatar contradiction clause 359]
381. creative(lucy) <- (9) [resolution 296,190]
382. $false <- (9) [subsumption resolution 381,149]
383. ~9 [avatar contradiction clause 382]
384. $false [avatar sat refutation 199,324,349,360,383]
% SZS output end Proof for 3914344970206190088476416
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and strong is both happy and not funny.
If someone is patient or not calm then paul is both not rich and not happy and vice versa.
If someone is both rich and not patient then someone is both not strong and happy and vice versa.
If susan is old or strong then susan is not funny or not kind.
Everyone who is both not funny and not creative is not wise and vice versa.
Everyone who is not tall or not generous is not strong or wise and vice versa.
If mary is creative then fred is both kind and not generous and vice versa.
Everyone who is not patient is not quiet or not rich and vice versa.
If alice is not kind or not patient then susan is not patient and vice versa.
If someone is either funny or wise then paul is both funny and calm and vice versa.
If someone is not brave or not wise then someone is either old or strong.
If someone is both not quiet and not wise then someone is both not quiet and tall and vice versa.
Everyone who is not strong or tall is either kind or not wise.
Everyone who is not brave or not strong is both happy and humble.
Everyone who is either not curious or not quiet is both happy and not wise and vice versa.
If someone is curious or happy then john is either tall or creative.
Paul is not wise or patient.
Lucy is not funny.
Someone is wise or calm.
Mary is calm.
Susan is rich or not kind.
Someone is both happy and creative.
Someone is not brave or humble. | Fred is not quiet. | neutral | (![X]:((wise(X)&strong(X))=>(happy(X)&~funny(X))))&
((?[X]:((patient(X)|~calm(X))))<=>((~rich(paul)&~happy(paul))))&
((?[X]:((rich(X)&~patient(X))))<=>(?[X]:((~strong(X)&happy(X)))))&
(((old(susan)|strong(susan)))=>((~funny(susan)|~kind(susan))))&
(![X]:((~funny(X)&~creative(X))<=>~wise(X)))&
(![X]:((~tall(X)|~generous(X))<=>(~strong(X)|wise(X))))&
((creative(mary))<=>((kind(fred)&~generous(fred))))&
(![X]:(~patient(X)<=>(~quiet(X)|~rich(X))))&
(((~kind(alice)|~patient(alice)))<=>(~patient(susan)))&
((?[X]:((funny(X)<~>wise(X))))<=>((funny(paul)&calm(paul))))&
((?[X]:((~brave(X)|~wise(X))))=>(?[X]:((old(X)<~>strong(X)))))&
((?[X]:((~quiet(X)&~wise(X))))<=>(?[X]:((~quiet(X)&tall(X)))))&
(![X]:((~strong(X)|tall(X))=>(kind(X)<~>~wise(X))))&
(![X]:((~brave(X)|~strong(X))=>(happy(X)&humble(X))))&
(![X]:((~curious(X)<~>~quiet(X))<=>(happy(X)&~wise(X))))&
((?[X]:((curious(X)|happy(X))))=>((tall(john)<~>creative(john))))&
((~wise(paul)|patient(paul)))&
(~funny(lucy))&
(?[X]:((wise(X)|calm(X))))&
(calm(mary))&
((rich(susan)|~kind(susan)))&
(?[X]:((happy(X)&creative(X))))&
(?[X]:((~brave(X)|humble(X)))) | ~quiet(fred) | [] | null | 0 |
If john is not kind or not humble then someone is both not strong and not generous.
Everyone who is either not rich or not happy is old and vice versa.
If someone is both not brave and not funny then someone is either not funny or generous and vice versa.
If someone is funny or not tall then john is both not tall and wise and vice versa.
If paul is either wise or humble then lucy is either funny or rich and vice versa.
Everyone who is either not happy or tall is tall.
If someone is not quiet then john is both not calm and curious.
Everyone who is either not rich or not old is either quiet or rich and vice versa.
If someone is generous or not funny then john is not strong.
Everyone who is not kind is not quiet and vice versa.
Everyone who is not wise or not calm is either not generous or not patient.
If fred is either patient or old then paul is not funny and vice versa.
If someone is both not quiet and not humble then john is both not generous and not funny.
Everyone who is not patient is both patient and not patient and vice versa.
Everyone who is not strong or not curious is both humble and not humble and vice versa.
Everyone who is not funny is either happy or curious and vice versa.
Someone is kind or not curious.
Someone is both calm and not wise.
John is either creative or kind.
John is either happy or not wise.
Susan is tall.
Alice is both not old and strong.
John is calm or wise. | Fred is not kind. | contradiction | (((~kind(john)|~humble(john)))=>(?[X]:((~strong(X)&~generous(X)))))&
(![X]:((~rich(X)<~>~happy(X))<=>old(X)))&
((?[X]:((~brave(X)&~funny(X))))<=>(?[X]:((~funny(X)<~>generous(X)))))&
((?[X]:((funny(X)|~tall(X))))<=>((~tall(john)&wise(john))))&
(((wise(paul)<~>humble(paul)))<=>((funny(lucy)<~>rich(lucy))))&
(![X]:((~happy(X)<~>tall(X))=>tall(X)))&
((?[X]:(~quiet(X)))=>((~calm(john)&curious(john))))&
(![X]:((~rich(X)<~>~old(X))<=>(quiet(X)<~>rich(X))))&
((?[X]:((generous(X)|~funny(X))))=>(~strong(john)))&
(![X]:(~kind(X)<=>~quiet(X)))&
(![X]:((~wise(X)|~calm(X))=>(~generous(X)<~>~patient(X))))&
(((patient(fred)<~>old(fred)))<=>(~funny(paul)))&
((?[X]:((~quiet(X)&~humble(X))))=>((~generous(john)&~funny(john))))&
(![X]:(~patient(X)<=>(patient(X)&~patient(X))))&
(![X]:((~strong(X)|~curious(X))<=>(humble(X)&~humble(X))))&
(![X]:(~funny(X)<=>(happy(X)<~>curious(X))))&
(?[X]:((kind(X)|~curious(X))))&
(?[X]:((calm(X)&~wise(X))))&
((creative(john)<~>kind(john)))&
((happy(john)<~>~wise(john)))&
(tall(susan))&
((~old(alice)&strong(alice)))&
((calm(john)|wise(john))) | ~kind(fred) | [
"p7",
"p8",
"p9",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 222930505423144311478062
% SZS output start Proof for 222930505423144311478062
8. ! [X0] : ((~rich(X0) <~> ~old(X0)) <=> (quiet(X0) <~> rich(X0))) [input p7]
9. ? [X0] : (~funny(X0) | generous(X0)) => ~strong(john) [input p8]
10. ! [X0] : (~kind(X0) <=> ~quiet(X0)) [input p9]
12. (patient(fred) <~> old(fred)) <=> ~funny(paul) [input p11]
14. ! [X0] : (~patient(X0) <=> (~patient(X0) & patient(X0))) [input p13]
15. ! [X0] : ((~curious(X0) | ~strong(X0)) <=> (~humble(X0) & humble(X0))) [input p14]
24. ~kind(fred) [input hypothesis]
29. ~strong(john) | ! [X0] : (funny(X0) & ~generous(X0)) [ennf transformation 9]
47. ! [X0] : ((((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0)))) & (((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0))))) [nnf transformation 8]
48. ! [X0] : ((~kind(X0) | quiet(X0)) & (~quiet(X0) | kind(X0))) [nnf transformation 10]
50. (((~old(fred) | ~patient(fred)) & (old(fred) | patient(fred))) | funny(paul)) & (~funny(paul) | ((patient(fred) | ~old(fred)) & (old(fred) | ~patient(fred)))) [nnf transformation 12]
51. ! [X0] : ((~patient(X0) | (patient(X0) | ~patient(X0))) & ((~patient(X0) & patient(X0)) | patient(X0))) [nnf transformation 14]
52. ! [X0] : ((~patient(X0) | patient(X0) | ~patient(X0)) & ((~patient(X0) & patient(X0)) | patient(X0))) [flattening 51]
53. ! [X0] : (((~curious(X0) | ~strong(X0)) | (humble(X0) | ~humble(X0))) & ((~humble(X0) & humble(X0)) | (curious(X0) & strong(X0)))) [nnf transformation 15]
54. ! [X0] : ((~curious(X0) | ~strong(X0) | humble(X0) | ~humble(X0)) & ((~humble(X0) & humble(X0)) | (curious(X0) & strong(X0)))) [flattening 53]
93. rich(X0) | quiet(X0) | ~old(X0) | rich(X0) [cnf transformation 47]
98. ~old(X0) | ~rich(X0) | quiet(X0) | ~rich(X0) [cnf transformation 47]
102. ~strong(john) | funny(X0) [cnf transformation 29]
103. ~quiet(X0) | kind(X0) [cnf transformation 48]
109. ~funny(paul) | old(fred) | ~patient(fred) [cnf transformation 50]
115. patient(X0) | patient(X0) [cnf transformation 52]
118. humble(X0) | strong(X0) [cnf transformation 54]
120. ~humble(X0) | strong(X0) [cnf transformation 54]
138. ~kind(fred) [cnf transformation 24]
139. patient(X0) [duplicate literal removal 115]
141. rich(X0) | quiet(X0) | ~old(X0) [duplicate literal removal 93]
143. ~old(X0) | ~rich(X0) | quiet(X0) [duplicate literal removal 98]
262. ~old(X0) | quiet(X0) [subsumption resolution 141,143]
264. 25 <=> ! [X0] : funny(X0) [avatar definition]
265. funny(X0) <- (25) [avatar component clause 264]
267. 26 <=> strong(john) [avatar definition]
269. ~strong(john) <- (~26) [avatar component clause 267]
270. 25 | ~26 [avatar split clause 102,267,264]
276. 28 <=> funny(paul) [avatar definition]
277. ~funny(paul) <- (~28) [avatar component clause 276]
280. 29 <=> patient(fred) [avatar definition]
282. ~patient(fred) <- (~29) [avatar component clause 280]
284. 30 <=> old(fred) [avatar definition]
285. old(fred) <- (30) [avatar component clause 284]
290. ~29 | 30 | ~28 [avatar split clause 109,276,284,280]
305. strong(X0) [subsumption resolution 118,120]
322. $false <- (~29) [subsumption resolution 282,139]
323. 29 [avatar contradiction clause 322]
324. $false <- (~26) [subsumption resolution 269,305]
325. 26 [avatar contradiction clause 324]
332. $false <- (25, ~28) [subsumption resolution 277,265]
333. ~25 | 28 [avatar contradiction clause 332]
355. quiet(fred) <- (30) [resolution 262,285]
358. kind(fred) <- (30) [resolution 355,103]
359. $false <- (30) [subsumption resolution 358,138]
360. ~30 [avatar contradiction clause 359]
361. $false [avatar sat refutation 270,290,323,325,333,360]
% SZS output end Proof for 222930505423144311478062
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and rich is either not patient or funny and vice versa.
Everyone who is either not calm or calm is both not old and not tall and vice versa.
Everyone who is either tall or old is either not kind or curious and vice versa.
Everyone who is both not brave and strong is not humble and vice versa.
If fred is either not old or happy then someone is kind or patient.
If someone is both creative and not rich then someone is not funny and vice versa.
Everyone who is wise or not happy is both not kind and tall.
Everyone who is humble or not wise is not old and vice versa.
Everyone who is not brave or creative is patient.
Everyone who is not generous or tall is both not old and not wise and vice versa.
Everyone who is brave is both not generous and not strong.
If john is both not humble and not old then mary is either brave or not happy and vice versa.
If someone is not patient then someone is rich and vice versa.
If someone is both quiet and not creative then john is both not happy and not brave.
If lucy is either funny or tall then fred is either not brave or funny and vice versa.
If someone is either not rich or kind then alice is either not quiet or patient and vice versa.
John is either not humble or not generous.
Someone is not strong.
John is funny or patient.
Someone is both not kind and not generous.
Someone is not calm or old.
Susan is either not creative or not brave.
Susan is either not quiet or wise. | Fred is not funny. | neutral | (![X]:((patient(X)&rich(X))<=>(~patient(X)<~>funny(X))))&
(![X]:((~calm(X)<~>calm(X))<=>(~old(X)&~tall(X))))&
(![X]:((tall(X)<~>old(X))<=>(~kind(X)<~>curious(X))))&
(![X]:((~brave(X)&strong(X))<=>~humble(X)))&
(((~old(fred)<~>happy(fred)))=>(?[X]:((kind(X)|patient(X)))))&
((?[X]:((creative(X)&~rich(X))))<=>(?[X]:(~funny(X))))&
(![X]:((wise(X)|~happy(X))=>(~kind(X)&tall(X))))&
(![X]:((humble(X)|~wise(X))<=>~old(X)))&
(![X]:((~brave(X)|creative(X))=>patient(X)))&
(![X]:((~generous(X)|tall(X))<=>(~old(X)&~wise(X))))&
(![X]:(brave(X)=>(~generous(X)&~strong(X))))&
(((~humble(john)&~old(john)))<=>((brave(mary)<~>~happy(mary))))&
((?[X]:(~patient(X)))<=>(?[X]:(rich(X))))&
((?[X]:((quiet(X)&~creative(X))))=>((~happy(john)&~brave(john))))&
(((funny(lucy)<~>tall(lucy)))<=>((~brave(fred)<~>funny(fred))))&
((?[X]:((~rich(X)<~>kind(X))))<=>((~quiet(alice)<~>patient(alice))))&
((~humble(john)<~>~generous(john)))&
(?[X]:(~strong(X)))&
((funny(john)|patient(john)))&
(?[X]:((~kind(X)&~generous(X))))&
(?[X]:((~calm(X)|old(X))))&
((~creative(susan)<~>~brave(susan)))&
((~quiet(susan)<~>wise(susan))) | ~funny(fred) | [] | null | 0 |
Everyone who is humble is strong or not humble.
Everyone who is both not strong and not tall is either creative or not creative.
Everyone who is both not strong and curious is both not brave and not old and vice versa.
If someone is not wise or not happy then john is both not quiet and funny.
If mary is not calm then susan is both curious and rich.
Everyone who is both not kind and calm is calm or not old and vice versa.
Everyone who is either old or not creative is not happy.
If alice is both not wise and not tall then someone is strong.
If alice is not brave then paul is quiet or curious and vice versa.
If someone is both not quiet and creative then mary is brave and vice versa.
Everyone who is not old is both humble and kind and vice versa.
If someone is not strong then someone is generous or old and vice versa.
If someone is both quiet and strong then someone is both patient and not generous.
Everyone who is not kind is either not brave or kind and vice versa.
If someone is humble or not brave then someone is not kind and vice versa.
Lucy is both happy and not tall.
Fred is patient.
Someone is either not humble or humble.
Someone is not creative.
Someone is not calm.
Someone is old. | Alice is not tall. | neutral | (![X]:(humble(X)=>(strong(X)|~humble(X))))&
(![X]:((~strong(X)&~tall(X))=>(creative(X)<~>~creative(X))))&
(![X]:((~strong(X)&curious(X))<=>(~brave(X)&~old(X))))&
((?[X]:((~wise(X)|~happy(X))))=>((~quiet(john)&funny(john))))&
((~calm(mary))=>((curious(susan)&rich(susan))))&
(![X]:((~kind(X)&calm(X))<=>(calm(X)|~old(X))))&
(![X]:((old(X)<~>~creative(X))=>~happy(X)))&
(((~wise(alice)&~tall(alice)))=>(?[X]:(strong(X))))&
((~brave(alice))<=>((quiet(paul)|curious(paul))))&
((?[X]:((~quiet(X)&creative(X))))<=>(brave(mary)))&
(![X]:(~old(X)<=>(humble(X)&kind(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((generous(X)|old(X)))))&
((?[X]:((quiet(X)&strong(X))))=>(?[X]:((patient(X)&~generous(X)))))&
(![X]:(~kind(X)<=>(~brave(X)<~>kind(X))))&
((?[X]:((humble(X)|~brave(X))))<=>(?[X]:(~kind(X))))&
((happy(lucy)&~tall(lucy)))&
(patient(fred))&
(?[X]:((~humble(X)<~>humble(X))))&
(?[X]:(~creative(X)))&
(?[X]:(~calm(X)))&
(?[X]:(old(X))) | ~tall(alice) | [] | null | 0 |
If alice is strong or quiet then susan is not brave and vice versa.
If someone is not brave then someone is not patient.
Everyone who is either rich or not tall is both not tall and not quiet.
Everyone who is strong or humble is calm or not tall.
If john is either not curious or not calm then someone is wise or tall.
If someone is kind or creative then someone is either quiet or not generous.
Everyone who is either generous or not tall is both humble and not calm and vice versa.
If susan is both not kind and not strong then someone is either not funny or not generous.
If someone is not old or not strong then someone is calm and vice versa.
Everyone who is either rich or not humble is either not rich or quiet and vice versa.
Everyone who is both not strong and not rich is both old and quiet.
Everyone who is either happy or not strong is patient and vice versa.
Everyone who is either generous or tall is either funny or not old.
If someone is both not brave and brave then john is not funny or curious and vice versa.
Everyone who is not kind is both not brave and not funny.
If mary is both not kind and brave then someone is strong or rich.
Someone is either tall or creative.
Alice is not wise or not creative.
Someone is creative or not strong.
Someone is creative or not rich.
Someone is generous.
Alice is either not brave or quiet.
Susan is humble.
Someone is not quiet. | Alice is not brave. | neutral | (((strong(alice)|quiet(alice)))<=>(~brave(susan)))&
((?[X]:(~brave(X)))=>(?[X]:(~patient(X))))&
(![X]:((rich(X)<~>~tall(X))=>(~tall(X)&~quiet(X))))&
(![X]:((strong(X)|humble(X))=>(calm(X)|~tall(X))))&
(((~curious(john)<~>~calm(john)))=>(?[X]:((wise(X)|tall(X)))))&
((?[X]:((kind(X)|creative(X))))=>(?[X]:((quiet(X)<~>~generous(X)))))&
(![X]:((generous(X)<~>~tall(X))<=>(humble(X)&~calm(X))))&
(((~kind(susan)&~strong(susan)))=>(?[X]:((~funny(X)<~>~generous(X)))))&
((?[X]:((~old(X)|~strong(X))))<=>(?[X]:(calm(X))))&
(![X]:((rich(X)<~>~humble(X))<=>(~rich(X)<~>quiet(X))))&
(![X]:((~strong(X)&~rich(X))=>(old(X)&quiet(X))))&
(![X]:((happy(X)<~>~strong(X))<=>patient(X)))&
(![X]:((generous(X)<~>tall(X))=>(funny(X)<~>~old(X))))&
((?[X]:((~brave(X)&brave(X))))<=>((~funny(john)|curious(john))))&
(![X]:(~kind(X)=>(~brave(X)&~funny(X))))&
(((~kind(mary)&brave(mary)))=>(?[X]:((strong(X)|rich(X)))))&
(?[X]:((tall(X)<~>creative(X))))&
((~wise(alice)|~creative(alice)))&
(?[X]:((creative(X)|~strong(X))))&
(?[X]:((creative(X)|~rich(X))))&
(?[X]:(generous(X)))&
((~brave(alice)<~>quiet(alice)))&
(humble(susan))&
(?[X]:(~quiet(X))) | ~brave(alice) | [] | null | 0 |
Everyone who is either calm or not creative is not quiet. If lucy is either old or happy then mary is both strong and old and vice versa. If someone is generous or happy then fred is generous or not humble. Everyone who is either not calm or brave is not funny or curious and vice versa. Everyone who is either creative or wise is not rich or strong. If someone is quiet then someone is generous or not curious and vice versa. Everyone who is either brave or not old is either not strong or not funny and vice versa. If john is not old or brave then someone is either quiet or not quiet. Everyone who is not kind is not curious or not quiet and vice versa. If someone is tall then someone is both not old and kind. If fred is both not strong and not funny then someone is both not patient and old. Everyone who is either kind or not strong is either tall or strong and vice versa. Everyone who is either not strong or brave is not tall. Everyone who is not generous is both not brave and generous and vice versa. If someone is not calm then susan is either not curious or not creative and vice versa. Everyone who is both not strong and not quiet is both humble and happy and vice versa. Someone is strong. Fred is kind or not funny. Lucy is funny or wise. Someone is not creative or not brave. Someone is either happy or humble. | John is not tall. | neutral | (![X]:((calm(X)<~>~creative(X))=>~quiet(X)))&
(((old(lucy)<~>happy(lucy)))<=>((strong(mary)&old(mary))))&
((?[X]:((generous(X)|happy(X))))=>((generous(fred)|~humble(fred))))&
(![X]:((~calm(X)<~>brave(X))<=>(~funny(X)|curious(X))))&
(![X]:((creative(X)<~>wise(X))=>(~rich(X)|strong(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((generous(X)|~curious(X)))))&
(![X]:((brave(X)<~>~old(X))<=>(~strong(X)<~>~funny(X))))&
(((~old(john)|brave(john)))=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:(~kind(X)<=>(~curious(X)|~quiet(X))))&
((?[X]:(tall(X)))=>(?[X]:((~old(X)&kind(X)))))&
(((~strong(fred)&~funny(fred)))=>(?[X]:((~patient(X)&old(X)))))&
(![X]:((kind(X)<~>~strong(X))<=>(tall(X)<~>strong(X))))&
(![X]:((~strong(X)<~>brave(X))=>~tall(X)))&
(![X]:(~generous(X)<=>(~brave(X)&generous(X))))&
((?[X]:(~calm(X)))<=>((~curious(susan)<~>~creative(susan))))&
(![X]:((~strong(X)&~quiet(X))<=>(humble(X)&happy(X))))&
(?[X]:(strong(X)))&
((kind(fred)|~funny(fred)))&
((funny(lucy)|wise(lucy)))&
(?[X]:((~creative(X)|~brave(X))))&
(?[X]:((happy(X)<~>humble(X)))) | ~tall(john) | [] | null | 0 |
If alice is either curious or not funny then someone is not brave or wise and vice versa.
If someone is tall or calm then alice is not curious and vice versa.
Everyone who is not wise or not creative is either curious or not tall.
Everyone who is either brave or not generous is not curious or rich.
Everyone who is either not tall or not strong is generous or not generous and vice versa.
Everyone who is both quiet and humble is old.
If mary is calm then someone is not generous and vice versa.
Everyone who is both not calm and strong is strong and vice versa.
If fred is not patient or not curious then someone is both quiet and curious and vice versa.
Everyone who is both kind and humble is both not brave and humble and vice versa.
Everyone who is either not tall or rich is generous and vice versa.
If fred is either not calm or curious then someone is rich or not funny.
Everyone who is either not brave or not kind is not funny or quiet.
If someone is not funny or kind then someone is rich and vice versa.
If someone is funny then mary is either not wise or creative.
Everyone who is either funny or not tall is either strong or patient.
Alice is both patient and not tall.
Someone is both not calm and not humble.
Lucy is either brave or not strong.
Lucy is both wise and quiet.
Someone is either patient or calm.
Mary is strong or not happy. | Lucy is curious. | contradiction | (((curious(alice)<~>~funny(alice)))<=>(?[X]:((~brave(X)|wise(X)))))&
((?[X]:((tall(X)|calm(X))))<=>(~curious(alice)))&
(![X]:((~wise(X)|~creative(X))=>(curious(X)<~>~tall(X))))&
(![X]:((brave(X)<~>~generous(X))=>(~curious(X)|rich(X))))&
(![X]:((~tall(X)<~>~strong(X))<=>(generous(X)|~generous(X))))&
(![X]:((quiet(X)&humble(X))=>old(X)))&
((calm(mary))<=>(?[X]:(~generous(X))))&
(![X]:((~calm(X)&strong(X))<=>strong(X)))&
(((~patient(fred)|~curious(fred)))<=>(?[X]:((quiet(X)&curious(X)))))&
(![X]:((kind(X)&humble(X))<=>(~brave(X)&humble(X))))&
(![X]:((~tall(X)<~>rich(X))<=>generous(X)))&
(((~calm(fred)<~>curious(fred)))=>(?[X]:((rich(X)|~funny(X)))))&
(![X]:((~brave(X)<~>~kind(X))=>(~funny(X)|quiet(X))))&
((?[X]:((~funny(X)|kind(X))))<=>(?[X]:(rich(X))))&
((?[X]:(funny(X)))=>((~wise(mary)<~>creative(mary))))&
(![X]:((funny(X)<~>~tall(X))=>(strong(X)<~>patient(X))))&
((patient(alice)&~tall(alice)))&
(?[X]:((~calm(X)&~humble(X))))&
((brave(lucy)<~>~strong(lucy)))&
((wise(lucy)&quiet(lucy)))&
(?[X]:((patient(X)<~>calm(X))))&
((strong(mary)|~happy(mary))) | curious(lucy) | [
"p0",
"p1",
"p3",
"p4",
"p6",
"p10",
"p13",
"p15",
"p16",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6012571430120996898269064
% SZS output start Proof for 6012571430120996898269064
1. (curious(alice) <~> ~funny(alice)) <=> ? [X0] : (wise(X0) | ~brave(X0)) [input p0]
2. ? [X0] : (calm(X0) | tall(X0)) <=> ~curious(alice) [input p1]
4. ! [X0] : ((brave(X0) <~> ~generous(X0)) => (rich(X0) | ~curious(X0))) [input p3]
5. ! [X0] : ((~tall(X0) <~> ~strong(X0)) <=> (~generous(X0) | generous(X0))) [input p4]
7. calm(mary) <=> ? [X0] : ~generous(X0) [input p6]
11. ! [X0] : ((~tall(X0) <~> rich(X0)) <=> generous(X0)) [input p10]
14. ? [X0] : (kind(X0) | ~funny(X0)) <=> ? [X0] : rich(X0) [input p13]
16. ! [X0] : ((funny(X0) <~> ~tall(X0)) => (strong(X0) <~> patient(X0))) [input p15]
17. ~tall(alice) & patient(alice) [input p16]
19. brave(lucy) <~> ~strong(lucy) [input p18]
20. quiet(lucy) & wise(lucy) [input p19]
23. curious(lucy) [input hypothesis]
24. ? [X0] : (kind(X0) | ~funny(X0)) <=> ? [X1] : rich(X1) [rectify 14]
28. ! [X0] : ((rich(X0) | ~curious(X0)) | (brave(X0) <=> ~generous(X0))) [ennf transformation 4]
29. ! [X0] : (rich(X0) | ~curious(X0) | (brave(X0) <=> ~generous(X0))) [flattening 28]
34. ! [X0] : ((strong(X0) <~> patient(X0)) | (funny(X0) <=> ~tall(X0))) [ennf transformation 16]
35. (((funny(alice) | ~curious(alice)) & (~funny(alice) | curious(alice))) | ! [X0] : (~wise(X0) & brave(X0))) & (? [X0] : (wise(X0) | ~brave(X0)) | ((curious(alice) | funny(alice)) & (~funny(alice) | ~curious(alice)))) [nnf transformation 1]
36. (((funny(alice) | ~curious(alice)) & (~funny(alice) | curious(alice))) | ! [X0] : (~wise(X0) & brave(X0))) & (? [X1] : (wise(X1) | ~brave(X1)) | ((curious(alice) | funny(alice)) & (~funny(alice) | ~curious(alice)))) [rectify 35]
37. ? [X1] : (wise(X1) | ~brave(X1)) => (wise(sK0) | ~brave(sK0)) [choice axiom]
38. (((funny(alice) | ~curious(alice)) & (~funny(alice) | curious(alice))) | ! [X0] : (~wise(X0) & brave(X0))) & ((wise(sK0) | ~brave(sK0)) | ((curious(alice) | funny(alice)) & (~funny(alice) | ~curious(alice)))) [skolemisation 36,37]
39. (? [X0] : (calm(X0) | tall(X0)) | curious(alice)) & (~curious(alice) | ! [X0] : (~calm(X0) & ~tall(X0))) [nnf transformation 2]
40. (? [X0] : (calm(X0) | tall(X0)) | curious(alice)) & (~curious(alice) | ! [X1] : (~calm(X1) & ~tall(X1))) [rectify 39]
41. ? [X0] : (calm(X0) | tall(X0)) => (calm(sK1) | tall(sK1)) [choice axiom]
42. ((calm(sK1) | tall(sK1)) | curious(alice)) & (~curious(alice) | ! [X1] : (~calm(X1) & ~tall(X1))) [skolemisation 40,41]
44. ! [X0] : (rich(X0) | ~curious(X0) | ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0)))) [nnf transformation 29]
45. ! [X0] : ((((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) | (generous(X0) & ~generous(X0))) & ((~generous(X0) | generous(X0)) | ((~tall(X0) | strong(X0)) & (~strong(X0) | tall(X0))))) [nnf transformation 5]
46. ! [X0] : ((((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) | (generous(X0) & ~generous(X0))) & (~generous(X0) | generous(X0) | ((~tall(X0) | strong(X0)) & (~strong(X0) | tall(X0))))) [flattening 45]
47. (calm(mary) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | ~calm(mary)) [nnf transformation 7]
48. (calm(mary) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | ~calm(mary)) [rectify 47]
49. ? [X1] : ~generous(X1) => ~generous(sK2) [choice axiom]
50. (calm(mary) | ! [X0] : generous(X0)) & (~generous(sK2) | ~calm(mary)) [skolemisation 48,49]
60. ! [X0] : ((((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | ~generous(X0)) & (generous(X0) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0))))) [nnf transformation 11]
65. (? [X0] : (kind(X0) | ~funny(X0)) | ! [X1] : ~rich(X1)) & (? [X1] : rich(X1) | ! [X0] : (~kind(X0) & funny(X0))) [nnf transformation 24]
66. (? [X0] : (kind(X0) | ~funny(X0)) | ! [X1] : ~rich(X1)) & (? [X2] : rich(X2) | ! [X3] : (~kind(X3) & funny(X3))) [rectify 65]
67. ? [X0] : (kind(X0) | ~funny(X0)) => (kind(sK5) | ~funny(sK5)) [choice axiom]
68. ? [X2] : rich(X2) => rich(sK6) [choice axiom]
69. ((kind(sK5) | ~funny(sK5)) | ! [X1] : ~rich(X1)) & (rich(sK6) | ! [X3] : (~kind(X3) & funny(X3))) [skolemisation 66,68,67]
71. ! [X0] : (((~patient(X0) | ~strong(X0)) & (patient(X0) | strong(X0))) | ((funny(X0) | tall(X0)) & (~tall(X0) | ~funny(X0)))) [nnf transformation 34]
74. (strong(lucy) | ~brave(lucy)) & (~strong(lucy) | brave(lucy)) [nnf transformation 19]
81. ~funny(alice) | curious(alice) | ~wise(X0) [cnf transformation 38]
84. ~curious(alice) | ~tall(X1) [cnf transformation 42]
85. ~curious(alice) | ~calm(X1) [cnf transformation 42]
91. ~generous(X0) | ~curious(X0) | rich(X0) | ~brave(X0) [cnf transformation 44]
95. ~strong(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 46]
96. ~strong(X0) | ~tall(X0) | generous(X0) [cnf transformation 46]
97. strong(X0) | tall(X0) | ~generous(X0) [cnf transformation 46]
98. strong(X0) | tall(X0) | generous(X0) [cnf transformation 46]
100. calm(mary) | generous(X0) [cnf transformation 50]
116. ~rich(X0) | tall(X0) | ~generous(X0) [cnf transformation 60]
121. rich(sK6) | funny(X3) [cnf transformation 69]
122. rich(sK6) | ~kind(X3) [cnf transformation 69]
123. kind(sK5) | ~funny(sK5) | ~rich(X1) [cnf transformation 69]
129. ~patient(X0) | ~strong(X0) | funny(X0) | tall(X0) [cnf transformation 71]
130. patient(alice) [cnf transformation 17]
131. ~tall(alice) [cnf transformation 17]
134. ~strong(lucy) | brave(lucy) [cnf transformation 74]
136. wise(lucy) [cnf transformation 20]
140. curious(lucy) [cnf transformation 23]
142. 1 <=> ! [X0] : ~wise(X0) [avatar definition]
143. ~wise(X0) <- (1) [avatar component clause 142]
145. 2 <=> curious(alice) [avatar definition]
149. 3 <=> funny(alice) [avatar definition]
150. ~funny(alice) <- (~3) [avatar component clause 149]
157. 1 | 2 | ~3 [avatar split clause 81,149,145,142]
179. 9 <=> ! [X1] : ~calm(X1) [avatar definition]
180. ~calm(X1) <- (9) [avatar component clause 179]
181. 9 | ~2 [avatar split clause 85,145,179]
183. 10 <=> ! [X1] : ~tall(X1) [avatar definition]
184. ~tall(X1) <- (10) [avatar component clause 183]
185. 10 | ~2 [avatar split clause 84,145,183]
186. strong(X0) | tall(X0) [subsumption resolution 97,98]
187. ~strong(X0) | ~tall(X0) [subsumption resolution 95,96]
189. 11 <=> ! [X0] : generous(X0) [avatar definition]
190. generous(X0) <- (11) [avatar component clause 189]
192. 12 <=> calm(mary) [avatar definition]
194. calm(mary) <- (12) [avatar component clause 192]
195. 11 | 12 [avatar split clause 100,192,189]
240. 22 <=> ! [X1] : ~rich(X1) [avatar definition]
241. ~rich(X1) <- (22) [avatar component clause 240]
243. 23 <=> funny(sK5) [avatar definition]
245. ~funny(sK5) <- (~23) [avatar component clause 243]
247. 24 <=> kind(sK5) [avatar definition]
249. kind(sK5) <- (24) [avatar component clause 247]
250. 22 | ~23 | 24 [avatar split clause 123,247,243,240]
252. 25 <=> ! [X3] : ~kind(X3) [avatar definition]
253. ~kind(X3) <- (25) [avatar component clause 252]
255. 26 <=> rich(sK6) [avatar definition]
257. rich(sK6) <- (26) [avatar component clause 255]
258. 25 | 26 [avatar split clause 122,255,252]
260. 27 <=> ! [X3] : funny(X3) [avatar definition]
261. funny(X3) <- (27) [avatar component clause 260]
262. 27 | 26 [avatar split clause 121,255,260]
276. ~patient(X0) | ~strong(X0) | funny(X0) [subsumption resolution 129,187]
279. 31 <=> brave(lucy) [avatar definition]
280. brave(lucy) <- (31) [avatar component clause 279]
283. 32 <=> strong(lucy) [avatar definition]
284. ~strong(lucy) <- (~32) [avatar component clause 283]
287. 31 | ~32 [avatar split clause 134,283,279]
300. tall(lucy) <- (~32) [resolution 186,284]
352. 39 <=> generous(sK6) [avatar definition]
353. ~generous(sK6) <- (~39) [avatar component clause 352]
356. 40 <=> tall(sK6) [avatar definition]
357. tall(sK6) <- (40) [avatar component clause 356]
358. ~tall(sK6) <- (~40) [avatar component clause 356]
360. tall(sK6) | ~generous(sK6) <- (26) [resolution 116,257]
363. ~generous(sK6) <- (26, ~40) [subsumption resolution 360,358]
364. ~39 | ~26 | 40 [avatar split clause 363,356,255,352]
365. ~strong(alice) | funny(alice) [resolution 276,130]
368. ~strong(alice) <- (~3) [subsumption resolution 365,150]
388. tall(alice) <- (~3) [resolution 368,186]
390. $false <- (~3) [subsumption resolution 388,131]
391. 3 [avatar contradiction clause 390]
397. $false <- (1) [resolution 143,136]
398. ~1 [avatar contradiction clause 397]
407. $false <- (9, 12) [resolution 180,194]
408. ~9 | ~12 [avatar contradiction clause 407]
409. $false <- (10, ~32) [resolution 184,300]
414. ~10 | 32 [avatar contradiction clause 409]
420. $false <- (11, ~39) [resolution 190,353]
422. ~11 | 39 [avatar contradiction clause 420]
426. $false <- (~23, 27) [resolution 261,245]
427. 23 | ~27 [avatar contradiction clause 426]
433. $false <- (24, 25) [subsumption resolution 249,253]
434. ~24 | ~25 [avatar contradiction clause 433]
435. $false <- (10, 40) [subsumption resolution 357,184]
436. ~10 | ~40 [avatar contradiction clause 435]
448. ~curious(X0) | rich(X0) | ~brave(X0) <- (11) [resolution 91,190]
450. ~brave(X0) | ~curious(X0) <- (11, 22) [subsumption resolution 448,241]
476. ~curious(lucy) <- (11, 22, 31) [resolution 450,280]
477. $false <- (11, 22, 31) [subsumption resolution 476,140]
478. ~11 | ~22 | ~31 [avatar contradiction clause 477]
479. $false [avatar sat refutation 157,181,185,195,250,258,262,287,364,391,398,408,414,422,427,434,436,478]
% SZS output end Proof for 6012571430120996898269064
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is old or not kind and vice versa. If someone is not creative or not wise then alice is both not rich and rich and vice versa. Everyone who is not strong or patient is not humble and vice versa. If someone is both old and quiet then someone is both kind and not kind and vice versa. Everyone who is not funny or not wise is either not strong or quiet. Everyone who is either brave or creative is either strong or happy and vice versa. If john is either not quiet or strong then susan is brave or rich and vice versa. Everyone who is both not calm and not rich is curious and vice versa. If john is wise or not humble then mary is either humble or not funny. If someone is not generous or funny then mary is not creative or generous. Everyone who is either not humble or calm is either not calm or not rich and vice versa. Everyone who is both tall and not kind is both funny and curious. Everyone who is not rich is either humble or creative. If fred is not wise or not curious then someone is both creative and happy. Everyone who is both quiet and not generous is both brave and calm. Everyone who is both funny and wise is strong or happy and vice versa. Paul is not calm or not strong. Susan is humble or not tall. Someone is not kind. Someone is either kind or humble. Lucy is either happy or not kind. Paul is either not calm or patient. | Susan is humble. | contradiction | (![X]:(~calm(X)<=>(old(X)|~kind(X))))&
((?[X]:((~creative(X)|~wise(X))))<=>((~rich(alice)&rich(alice))))&
(![X]:((~strong(X)|patient(X))<=>~humble(X)))&
((?[X]:((old(X)&quiet(X))))<=>(?[X]:((kind(X)&~kind(X)))))&
(![X]:((~funny(X)|~wise(X))=>(~strong(X)<~>quiet(X))))&
(![X]:((brave(X)<~>creative(X))<=>(strong(X)<~>happy(X))))&
(((~quiet(john)<~>strong(john)))<=>((brave(susan)|rich(susan))))&
(![X]:((~calm(X)&~rich(X))<=>curious(X)))&
(((wise(john)|~humble(john)))=>((humble(mary)<~>~funny(mary))))&
((?[X]:((~generous(X)|funny(X))))=>((~creative(mary)|generous(mary))))&
(![X]:((~humble(X)<~>calm(X))<=>(~calm(X)<~>~rich(X))))&
(![X]:((tall(X)&~kind(X))=>(funny(X)&curious(X))))&
(![X]:(~rich(X)=>(humble(X)<~>creative(X))))&
(((~wise(fred)|~curious(fred)))=>(?[X]:((creative(X)&happy(X)))))&
(![X]:((quiet(X)&~generous(X))=>(brave(X)&calm(X))))&
(![X]:((funny(X)&wise(X))<=>(strong(X)|happy(X))))&
((~calm(paul)|~strong(paul)))&
((humble(susan)|~tall(susan)))&
(?[X]:(~kind(X)))&
(?[X]:((kind(X)<~>humble(X))))&
((happy(lucy)<~>~kind(lucy)))&
((~calm(paul)<~>patient(paul))) | humble(susan) | [
"p1",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 9050711704325562372484658
% SZS output start Proof for 9050711704325562372484658
2. ? [X0] : (~wise(X0) | ~creative(X0)) <=> (rich(alice) & ~rich(alice)) [input p1]
11. ! [X0] : ((~humble(X0) <~> calm(X0)) <=> (~calm(X0) <~> ~rich(X0))) [input p10]
13. ! [X0] : (~rich(X0) => (humble(X0) <~> creative(X0))) [input p12]
23. humble(susan) [input hypothesis]
33. ! [X0] : ((humble(X0) <~> creative(X0)) | rich(X0)) [ennf transformation 13]
37. (? [X0] : (~wise(X0) | ~creative(X0)) | (~rich(alice) | rich(alice))) & ((rich(alice) & ~rich(alice)) | ! [X0] : (wise(X0) & creative(X0))) [nnf transformation 2]
38. (? [X0] : (~wise(X0) | ~creative(X0)) | ~rich(alice) | rich(alice)) & ((rich(alice) & ~rich(alice)) | ! [X0] : (wise(X0) & creative(X0))) [flattening 37]
39. (? [X0] : (~wise(X0) | ~creative(X0)) | ~rich(alice) | rich(alice)) & ((rich(alice) & ~rich(alice)) | ! [X1] : (wise(X1) & creative(X1))) [rectify 38]
40. ? [X0] : (~wise(X0) | ~creative(X0)) => (~wise(sK0) | ~creative(sK0)) [choice axiom]
41. ((~wise(sK0) | ~creative(sK0)) | ~rich(alice) | rich(alice)) & ((rich(alice) & ~rich(alice)) | ! [X1] : (wise(X1) & creative(X1))) [skolemisation 39,40]
54. ! [X0] : ((((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | ((~calm(X0) | rich(X0)) & (~rich(X0) | calm(X0)))) & (((rich(X0) | calm(X0)) & (~rich(X0) | ~calm(X0))) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0))))) [nnf transformation 11]
55. ! [X0] : (((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | rich(X0)) [nnf transformation 33]
70. ~rich(alice) | creative(X1) [cnf transformation 41]
72. rich(alice) | creative(X1) [cnf transformation 41]
107. ~rich(X0) | ~calm(X0) | ~humble(X0) | ~calm(X0) [cnf transformation 54]
108. rich(X0) | calm(X0) | calm(X0) | humble(X0) [cnf transformation 54]
110. calm(X0) | ~humble(X0) | ~rich(X0) | calm(X0) [cnf transformation 54]
113. ~calm(X0) | humble(X0) | ~calm(X0) | rich(X0) [cnf transformation 54]
115. ~creative(X0) | ~humble(X0) | rich(X0) [cnf transformation 55]
133. humble(susan) [cnf transformation 23]
134. ~rich(X0) | ~calm(X0) | ~humble(X0) [duplicate literal removal 107]
135. rich(X0) | calm(X0) | humble(X0) [duplicate literal removal 108]
136. calm(X0) | ~humble(X0) | ~rich(X0) [duplicate literal removal 110]
137. ~calm(X0) | humble(X0) | rich(X0) [duplicate literal removal 113]
142. 2 <=> rich(alice) [avatar definition]
147. 3 <=> ! [X1] : creative(X1) [avatar definition]
148. creative(X1) <- (3) [avatar component clause 147]
149. 3 | 2 [avatar split clause 72,142,147]
151. 3 | ~2 [avatar split clause 70,142,147]
203. humble(X0) | rich(X0) [subsumption resolution 135,137]
204. ~humble(X0) | ~rich(X0) [subsumption resolution 134,136]
205. ~creative(X0) | rich(X0) [subsumption resolution 115,203]
272. ~rich(susan) [resolution 204,133]
274. rich(X0) <- (3) [resolution 205,148]
279. $false <- (3) [subsumption resolution 272,274]
280. ~3 [avatar contradiction clause 279]
281. $false [avatar sat refutation 149,151,280]
% SZS output end Proof for 9050711704325562372484658
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and not generous is wise or not creative. If someone is strong or generous then someone is not funny or not rich and vice versa. Everyone who is either humble or not humble is either kind or not brave and vice versa. Everyone who is wise or not strong is not old or happy and vice versa. Everyone who is both not brave and wise is both curious and not strong. Everyone who is both not patient and quiet is both not creative and tall and vice versa. Everyone who is tall or not curious is not happy and vice versa. Everyone who is either brave or not humble is curious and vice versa. Everyone who is either funny or curious is kind or not funny and vice versa. If lucy is both not tall and wise then alice is calm and vice versa. If someone is either creative or wise then someone is both not kind and old. Everyone who is funny is both old and not strong and vice versa. Everyone who is not brave or not strong is tall and vice versa. If mary is both wise and patient then lucy is wise or tall and vice versa. If someone is both old and calm then mary is not strong and vice versa. If john is both wise and not humble then mary is not rich. Paul is brave. Lucy is not brave. Someone is either wise or curious. Fred is both not patient and not creative. Someone is not rich or wise. Fred is either not brave or calm. John is not strong. | John is not old. | entailment | (![X]:((rich(X)&~generous(X))=>(wise(X)|~creative(X))))&
((?[X]:((strong(X)|generous(X))))<=>(?[X]:((~funny(X)|~rich(X)))))&
(![X]:((humble(X)<~>~humble(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((wise(X)|~strong(X))<=>(~old(X)|happy(X))))&
(![X]:((~brave(X)&wise(X))=>(curious(X)&~strong(X))))&
(![X]:((~patient(X)&quiet(X))<=>(~creative(X)&tall(X))))&
(![X]:((tall(X)|~curious(X))<=>~happy(X)))&
(![X]:((brave(X)<~>~humble(X))<=>curious(X)))&
(![X]:((funny(X)<~>curious(X))<=>(kind(X)|~funny(X))))&
(((~tall(lucy)&wise(lucy)))<=>(calm(alice)))&
((?[X]:((creative(X)<~>wise(X))))=>(?[X]:((~kind(X)&old(X)))))&
(![X]:(funny(X)<=>(old(X)&~strong(X))))&
(![X]:((~brave(X)|~strong(X))<=>tall(X)))&
(((wise(mary)&patient(mary)))<=>((wise(lucy)|tall(lucy))))&
((?[X]:((old(X)&calm(X))))<=>(~strong(mary)))&
(((wise(john)&~humble(john)))=>(~rich(mary)))&
(brave(paul))&
(~brave(lucy))&
(?[X]:((wise(X)<~>curious(X))))&
((~patient(fred)&~creative(fred)))&
(?[X]:((~rich(X)|wise(X))))&
((~brave(fred)<~>calm(fred)))&
(~strong(john)) | ~old(john) | [
"p3",
"p6",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8686953140586980212209656
% SZS output start Proof for 8686953140586980212209656
4. ! [X0] : ((~strong(X0) | wise(X0)) <=> (happy(X0) | ~old(X0))) [input p3]
7. ! [X0] : ((~curious(X0) | tall(X0)) <=> ~happy(X0)) [input p6]
13. ! [X0] : ((~strong(X0) | ~brave(X0)) <=> tall(X0)) [input p12]
23. ~strong(john) [input p22]
24. old(john) [input hypothesis]
40. ! [X0] : (((~strong(X0) | wise(X0)) | (~happy(X0) & old(X0))) & ((happy(X0) | ~old(X0)) | (strong(X0) & ~wise(X0)))) [nnf transformation 4]
41. ! [X0] : ((~strong(X0) | wise(X0) | (~happy(X0) & old(X0))) & (happy(X0) | ~old(X0) | (strong(X0) & ~wise(X0)))) [flattening 40]
44. ! [X0] : (((~curious(X0) | tall(X0)) | happy(X0)) & (~happy(X0) | (curious(X0) & ~tall(X0)))) [nnf transformation 7]
45. ! [X0] : ((~curious(X0) | tall(X0) | happy(X0)) & (~happy(X0) | (curious(X0) & ~tall(X0)))) [flattening 44]
57. ! [X0] : (((~strong(X0) | ~brave(X0)) | ~tall(X0)) & (tall(X0) | (strong(X0) & brave(X0)))) [nnf transformation 13]
58. ! [X0] : ((~strong(X0) | ~brave(X0) | ~tall(X0)) & (tall(X0) | (strong(X0) & brave(X0)))) [flattening 57]
85. ~old(X0) | happy(X0) | strong(X0) [cnf transformation 41]
94. ~tall(X0) | ~happy(X0) [cnf transformation 45]
118. tall(X0) | strong(X0) [cnf transformation 58]
138. ~strong(john) [cnf transformation 23]
139. old(john) [cnf transformation 24]
292. ~happy(X0) | strong(X0) [resolution 118,94]
304. 31 <=> happy(john) [avatar definition]
306. happy(john) <- (31) [avatar component clause 304]
326. happy(john) | strong(john) [resolution 85,139]
329. happy(john) [subsumption resolution 326,138]
330. 31 [avatar split clause 329,304]
520. strong(john) <- (31) [resolution 292,306]
522. $false <- (31) [subsumption resolution 520,138]
523. ~31 [avatar contradiction clause 522]
526. $false [avatar sat refutation 330,523]
% SZS output end Proof for 8686953140586980212209656
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is humble then susan is either not calm or not patient and vice versa. Everyone who is not old is calm. Everyone who is both old and rich is happy. If someone is rich or not wise then susan is not creative. Everyone who is curious or generous is either patient or happy and vice versa. Everyone who is either not happy or not kind is not quiet. Everyone who is either not generous or not wise is either curious or brave and vice versa. Everyone who is not quiet or not kind is both not brave and not creative. Everyone who is both funny and old is humble. If someone is both patient and not quiet then someone is either humble or not generous and vice versa. Everyone who is both not happy and tall is either humble or tall and vice versa. If susan is not calm then mary is quiet or rich and vice versa. Everyone who is patient is both brave and wise and vice versa. Everyone who is brave is curious. Everyone who is both not patient and quiet is both curious and not humble. Everyone who is creative or not funny is calm. Lucy is not patient. Lucy is either not patient or not kind. Someone is both not curious and not humble. John is generous or not happy. Someone is not generous. Someone is not happy or calm. Someone is either kind or tall. John is not patient or wise. | Mary is rich. | neutral | ((humble(fred))<=>((~calm(susan)<~>~patient(susan))))&
(![X]:(~old(X)=>calm(X)))&
(![X]:((old(X)&rich(X))=>happy(X)))&
((?[X]:((rich(X)|~wise(X))))=>(~creative(susan)))&
(![X]:((curious(X)|generous(X))<=>(patient(X)<~>happy(X))))&
(![X]:((~happy(X)<~>~kind(X))=>~quiet(X)))&
(![X]:((~generous(X)<~>~wise(X))<=>(curious(X)<~>brave(X))))&
(![X]:((~quiet(X)|~kind(X))=>(~brave(X)&~creative(X))))&
(![X]:((funny(X)&old(X))=>humble(X)))&
((?[X]:((patient(X)&~quiet(X))))<=>(?[X]:((humble(X)<~>~generous(X)))))&
(![X]:((~happy(X)&tall(X))<=>(humble(X)<~>tall(X))))&
((~calm(susan))<=>((quiet(mary)|rich(mary))))&
(![X]:(patient(X)<=>(brave(X)&wise(X))))&
(![X]:(brave(X)=>curious(X)))&
(![X]:((~patient(X)&quiet(X))=>(curious(X)&~humble(X))))&
(![X]:((creative(X)|~funny(X))=>calm(X)))&
(~patient(lucy))&
((~patient(lucy)<~>~kind(lucy)))&
(?[X]:((~curious(X)&~humble(X))))&
((generous(john)|~happy(john)))&
(?[X]:(~generous(X)))&
(?[X]:((~happy(X)|calm(X))))&
(?[X]:((kind(X)<~>tall(X))))&
((~patient(john)|wise(john))) | rich(mary) | [] | null | 0 |
If john is funny then susan is both not curious and creative and vice versa.
If someone is funny or rich then alice is tall or rich.
If someone is not calm or humble then susan is not strong.
Everyone who is not brave is either not humble or wise.
Everyone who is not quiet is not rich.
Everyone who is both not quiet and wise is either not curious or not tall.
Everyone who is not quiet or not patient is not patient or generous.
Everyone who is happy or not patient is curious and vice versa.
Everyone who is creative is both strong and generous.
Everyone who is not creative or funny is kind or not funny.
Everyone who is either not quiet or old is not quiet or creative and vice versa.
If someone is either kind or not brave then someone is both happy and not rich and vice versa.
Everyone who is either not funny or rich is either not creative or humble and vice versa.
If someone is either not humble or generous then someone is both not brave and calm and vice versa.
Everyone who is either not funny or funny is not creative or strong and vice versa.
Everyone who is both calm and funny is both kind and not kind.
Alice is not creative.
Someone is either patient or not patient.
Someone is not funny or generous.
Someone is both kind and calm.
Someone is both kind and strong.
Someone is either creative or not old.
John is either wise or not strong.
Someone is both happy and curious. | Alice is tall. | neutral | ((funny(john))<=>((~curious(susan)&creative(susan))))&
((?[X]:((funny(X)|rich(X))))=>((tall(alice)|rich(alice))))&
((?[X]:((~calm(X)|humble(X))))=>(~strong(susan)))&
(![X]:(~brave(X)=>(~humble(X)<~>wise(X))))&
(![X]:(~quiet(X)=>~rich(X)))&
(![X]:((~quiet(X)&wise(X))=>(~curious(X)<~>~tall(X))))&
(![X]:((~quiet(X)|~patient(X))=>(~patient(X)|generous(X))))&
(![X]:((happy(X)|~patient(X))<=>curious(X)))&
(![X]:(creative(X)=>(strong(X)&generous(X))))&
(![X]:((~creative(X)|funny(X))=>(kind(X)|~funny(X))))&
(![X]:((~quiet(X)<~>old(X))<=>(~quiet(X)|creative(X))))&
((?[X]:((kind(X)<~>~brave(X))))<=>(?[X]:((happy(X)&~rich(X)))))&
(![X]:((~funny(X)<~>rich(X))<=>(~creative(X)<~>humble(X))))&
((?[X]:((~humble(X)<~>generous(X))))<=>(?[X]:((~brave(X)&calm(X)))))&
(![X]:((~funny(X)<~>funny(X))<=>(~creative(X)|strong(X))))&
(![X]:((calm(X)&funny(X))=>(kind(X)&~kind(X))))&
(~creative(alice))&
(?[X]:((patient(X)<~>~patient(X))))&
(?[X]:((~funny(X)|generous(X))))&
(?[X]:((kind(X)&calm(X))))&
(?[X]:((kind(X)&strong(X))))&
(?[X]:((creative(X)<~>~old(X))))&
((wise(john)<~>~strong(john)))&
(?[X]:((happy(X)&curious(X)))) | tall(alice) | [] | null | 0 |
Everyone who is either happy or not old is not creative. Everyone who is either quiet or not happy is either curious or not tall and vice versa. If someone is kind or calm then someone is not tall and vice versa. Everyone who is either humble or not quiet is not funny. If someone is both not patient and quiet then mary is both curious and happy. Everyone who is not quiet is both not creative and calm and vice versa. Everyone who is either wise or creative is either happy or not patient. Everyone who is not generous is not curious. Everyone who is not patient is not old or strong and vice versa. If alice is both kind and tall then someone is either generous or not old. Everyone who is rich is generous. Everyone who is calm or not patient is either not old or humble. Everyone who is either old or generous is not old or creative. Everyone who is both not quiet and humble is humble and vice versa. Everyone who is either happy or not old is both quiet and generous and vice versa. If john is both not generous and creative then alice is patient. Susan is brave. Fred is strong. Someone is both patient and not happy. Alice is not humble. Someone is both not patient and creative. Fred is both strong and brave. Someone is strong or happy. | Mary is creative. | contradiction | (![X]:((happy(X)<~>~old(X))=>~creative(X)))&
(![X]:((quiet(X)<~>~happy(X))<=>(curious(X)<~>~tall(X))))&
((?[X]:((kind(X)|calm(X))))<=>(?[X]:(~tall(X))))&
(![X]:((humble(X)<~>~quiet(X))=>~funny(X)))&
((?[X]:((~patient(X)&quiet(X))))=>((curious(mary)&happy(mary))))&
(![X]:(~quiet(X)<=>(~creative(X)&calm(X))))&
(![X]:((wise(X)<~>creative(X))=>(happy(X)<~>~patient(X))))&
(![X]:(~generous(X)=>~curious(X)))&
(![X]:(~patient(X)<=>(~old(X)|strong(X))))&
(((kind(alice)&tall(alice)))=>(?[X]:((generous(X)<~>~old(X)))))&
(![X]:(rich(X)=>generous(X)))&
(![X]:((calm(X)|~patient(X))=>(~old(X)<~>humble(X))))&
(![X]:((old(X)<~>generous(X))=>(~old(X)|creative(X))))&
(![X]:((~quiet(X)&humble(X))<=>humble(X)))&
(![X]:((happy(X)<~>~old(X))<=>(quiet(X)&generous(X))))&
(((~generous(john)&creative(john)))=>(patient(alice)))&
(brave(susan))&
(strong(fred))&
(?[X]:((patient(X)&~happy(X))))&
(~humble(alice))&
(?[X]:((~patient(X)&creative(X))))&
((strong(fred)&brave(fred)))&
(?[X]:((strong(X)|happy(X)))) | creative(mary) | [
"p0",
"p4",
"p5",
"p7",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1636878082464642930134465
% SZS output start Proof for 1636878082464642930134465
1. ! [X0] : ((happy(X0) <~> ~old(X0)) => ~creative(X0)) [input p0]
5. ? [X0] : (quiet(X0) & ~patient(X0)) => (happy(mary) & curious(mary)) [input p4]
6. ! [X0] : (~quiet(X0) <=> (calm(X0) & ~creative(X0))) [input p5]
8. ! [X0] : (~generous(X0) => ~curious(X0)) [input p7]
15. ! [X0] : ((happy(X0) <~> ~old(X0)) <=> (generous(X0) & quiet(X0))) [input p14]
21. ? [X0] : (creative(X0) & ~patient(X0)) [input p20]
24. creative(mary) [input hypothesis]
30. ! [X0] : (~creative(X0) | (happy(X0) <=> ~old(X0))) [ennf transformation 1]
31. (happy(mary) & curious(mary)) | ! [X0] : (~quiet(X0) | patient(X0)) [ennf transformation 5]
33. ! [X0] : (~curious(X0) | generous(X0)) [ennf transformation 8]
41. ! [X0] : (~creative(X0) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0)))) [nnf transformation 30]
48. ! [X0] : ((~quiet(X0) | (~calm(X0) | creative(X0))) & ((calm(X0) & ~creative(X0)) | quiet(X0))) [nnf transformation 6]
49. ! [X0] : ((~quiet(X0) | ~calm(X0) | creative(X0)) & ((calm(X0) & ~creative(X0)) | quiet(X0))) [flattening 48]
60. ! [X0] : ((((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | (~generous(X0) | ~quiet(X0))) & ((generous(X0) & quiet(X0)) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0))))) [nnf transformation 15]
61. ! [X0] : ((((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | ~generous(X0) | ~quiet(X0)) & ((generous(X0) & quiet(X0)) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0))))) [flattening 60]
64. ? [X0] : (creative(X0) & ~patient(X0)) => (creative(sK4) & ~patient(sK4)) [choice axiom]
65. creative(sK4) & ~patient(sK4) [skolemisation 21,64]
68. ~creative(X0) | ~old(X0) | ~happy(X0) [cnf transformation 41]
81. curious(mary) | ~quiet(X0) | patient(X0) [cnf transformation 31]
82. happy(mary) | ~quiet(X0) | patient(X0) [cnf transformation 31]
83. ~creative(X0) | quiet(X0) [cnf transformation 49]
90. ~curious(X0) | generous(X0) [cnf transformation 33]
110. ~generous(X0) | ~happy(X0) | old(X0) | ~quiet(X0) [cnf transformation 61]
116. ~patient(sK4) [cnf transformation 65]
117. creative(sK4) [cnf transformation 65]
120. creative(mary) [cnf transformation 24]
147. 7 <=> ! [X0] : (~quiet(X0) | patient(X0)) [avatar definition]
148. ~quiet(X0) | patient(X0) <- (7) [avatar component clause 147]
150. 8 <=> happy(mary) [avatar definition]
152. happy(mary) <- (8) [avatar component clause 150]
153. 7 | 8 [avatar split clause 82,150,147]
155. 9 <=> curious(mary) [avatar definition]
157. curious(mary) <- (9) [avatar component clause 155]
158. 7 | 9 [avatar split clause 81,155,147]
200. quiet(sK4) [resolution 83,117]
201. quiet(mary) [resolution 83,120]
205. patient(sK4) <- (7) [resolution 148,200]
207. $false <- (7) [subsumption resolution 205,116]
208. ~7 [avatar contradiction clause 207]
209. generous(mary) <- (9) [resolution 157,90]
211. ~old(mary) | ~happy(mary) [resolution 68,120]
221. ~old(mary) <- (8) [subsumption resolution 211,152]
308. ~happy(mary) | old(mary) | ~quiet(mary) <- (9) [resolution 110,209]
312. old(mary) | ~quiet(mary) <- (8, 9) [subsumption resolution 308,152]
313. ~quiet(mary) <- (8, 9) [subsumption resolution 312,221]
314. $false <- (8, 9) [subsumption resolution 313,201]
315. ~8 | ~9 [avatar contradiction clause 314]
316. $false [avatar sat refutation 153,158,208,315]
% SZS output end Proof for 1636878082464642930134465
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both not strong and funny then someone is both happy and not tall.
Everyone who is not kind or not happy is not rich.
Everyone who is either creative or not funny is patient or not strong and vice versa.
Everyone who is both not curious and rich is not creative.
Everyone who is humble or creative is both not tall and not old and vice versa.
Everyone who is not generous is funny.
Everyone who is not patient or calm is not tall and vice versa.
If mary is either quiet or not curious then someone is both not kind and not strong.
If someone is either not patient or not strong then someone is creative or humble.
Everyone who is both quiet and not kind is both calm and happy and vice versa.
Everyone who is not happy or happy is both not wise and not brave and vice versa.
Everyone who is both not strong and kind is both not kind and rich.
Everyone who is either happy or not old is both quiet and not humble and vice versa.
Everyone who is either rich or quiet is both not rich and curious.
Everyone who is both not curious and kind is both not wise and not creative.
Everyone who is happy or curious is either kind or not brave.
Someone is either kind or not rich.
Mary is kind.
Someone is both tall and not strong.
Alice is both quiet and humble.
Alice is not tall or old.
Someone is either brave or not creative.
Susan is both not curious and funny. | Mary is not creative. | entailment | (((~strong(paul)&funny(paul)))=>(?[X]:((happy(X)&~tall(X)))))&
(![X]:((~kind(X)|~happy(X))=>~rich(X)))&
(![X]:((creative(X)<~>~funny(X))<=>(patient(X)|~strong(X))))&
(![X]:((~curious(X)&rich(X))=>~creative(X)))&
(![X]:((humble(X)|creative(X))<=>(~tall(X)&~old(X))))&
(![X]:(~generous(X)=>funny(X)))&
(![X]:((~patient(X)|calm(X))<=>~tall(X)))&
(((quiet(mary)<~>~curious(mary)))=>(?[X]:((~kind(X)&~strong(X)))))&
((?[X]:((~patient(X)<~>~strong(X))))=>(?[X]:((creative(X)|humble(X)))))&
(![X]:((quiet(X)&~kind(X))<=>(calm(X)&happy(X))))&
(![X]:((~happy(X)|happy(X))<=>(~wise(X)&~brave(X))))&
(![X]:((~strong(X)&kind(X))=>(~kind(X)&rich(X))))&
(![X]:((happy(X)<~>~old(X))<=>(quiet(X)&~humble(X))))&
(![X]:((rich(X)<~>quiet(X))=>(~rich(X)&curious(X))))&
(![X]:((~curious(X)&kind(X))=>(~wise(X)&~creative(X))))&
(![X]:((happy(X)|curious(X))=>(kind(X)<~>~brave(X))))&
(?[X]:((kind(X)<~>~rich(X))))&
(kind(mary))&
(?[X]:((tall(X)&~strong(X))))&
((quiet(alice)&humble(alice)))&
((~tall(alice)|old(alice)))&
(?[X]:((brave(X)<~>~creative(X))))&
((~curious(susan)&funny(susan))) | ~creative(mary) | [
"p3",
"p4",
"p10",
"p12",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5641350377824264088213098
% SZS output start Proof for 5641350377824264088213098
4. ! [X0] : ((rich(X0) & ~curious(X0)) => ~creative(X0)) [input p3]
5. ! [X0] : ((creative(X0) | humble(X0)) <=> (~old(X0) & ~tall(X0))) [input p4]
11. ! [X0] : ((happy(X0) | ~happy(X0)) <=> (~brave(X0) & ~wise(X0))) [input p10]
13. ! [X0] : ((happy(X0) <~> ~old(X0)) <=> (~humble(X0) & quiet(X0))) [input p12]
14. ! [X0] : ((rich(X0) <~> quiet(X0)) => (curious(X0) & ~rich(X0))) [input p13]
16. ! [X0] : ((curious(X0) | happy(X0)) => (kind(X0) <~> ~brave(X0))) [input p15]
18. kind(mary) [input p17]
24. creative(mary) [input hypothesis]
30. ! [X0] : (~creative(X0) | (~rich(X0) | curious(X0))) [ennf transformation 4]
31. ! [X0] : (~creative(X0) | ~rich(X0) | curious(X0)) [flattening 30]
36. ! [X0] : ((curious(X0) & ~rich(X0)) | (rich(X0) <=> quiet(X0))) [ennf transformation 14]
39. ! [X0] : ((kind(X0) <~> ~brave(X0)) | (~curious(X0) & ~happy(X0))) [ennf transformation 16]
44. ! [X0] : (((creative(X0) | humble(X0)) | (old(X0) | tall(X0))) & ((~old(X0) & ~tall(X0)) | (~creative(X0) & ~humble(X0)))) [nnf transformation 5]
45. ! [X0] : ((creative(X0) | humble(X0) | old(X0) | tall(X0)) & ((~old(X0) & ~tall(X0)) | (~creative(X0) & ~humble(X0)))) [flattening 44]
57. ! [X0] : (((happy(X0) | ~happy(X0)) | (brave(X0) | wise(X0))) & ((~brave(X0) & ~wise(X0)) | (~happy(X0) & happy(X0)))) [nnf transformation 11]
58. ! [X0] : ((happy(X0) | ~happy(X0) | brave(X0) | wise(X0)) & ((~brave(X0) & ~wise(X0)) | (~happy(X0) & happy(X0)))) [flattening 57]
59. ! [X0] : ((((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | (humble(X0) | ~quiet(X0))) & ((~humble(X0) & quiet(X0)) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0))))) [nnf transformation 13]
60. ! [X0] : ((((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | humble(X0) | ~quiet(X0)) & ((~humble(X0) & quiet(X0)) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0))))) [flattening 59]
61. ! [X0] : ((curious(X0) & ~rich(X0)) | ((rich(X0) | ~quiet(X0)) & (quiet(X0) | ~rich(X0)))) [nnf transformation 36]
62. ! [X0] : (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | (~curious(X0) & ~happy(X0))) [nnf transformation 39]
81. ~creative(X0) | ~rich(X0) | curious(X0) [cnf transformation 31]
85. ~old(X0) | ~creative(X0) [cnf transformation 45]
102. ~brave(X0) | happy(X0) [cnf transformation 58]
103. ~brave(X0) | ~happy(X0) [cnf transformation 58]
108. quiet(X0) | happy(X0) | old(X0) [cnf transformation 60]
116. ~quiet(X0) | rich(X0) | curious(X0) [cnf transformation 61]
121. brave(X0) | ~kind(X0) | ~happy(X0) [cnf transformation 62]
122. brave(X0) | ~kind(X0) | ~curious(X0) [cnf transformation 62]
125. kind(mary) [cnf transformation 18]
135. creative(mary) [cnf transformation 24]
157. 5 <=> curious(mary) [avatar definition]
159. curious(mary) <- (5) [avatar component clause 157]
161. 6 <=> quiet(mary) [avatar definition]
162. ~quiet(mary) <- (~6) [avatar component clause 161]
163. quiet(mary) <- (6) [avatar component clause 161]
192. ~brave(X0) [subsumption resolution 102,103]
196. ~curious(X0) | ~kind(X0) [subsumption resolution 122,192]
197. ~kind(X0) | ~happy(X0) [subsumption resolution 121,192]
223. ~happy(mary) [resolution 197,125]
260. ~rich(mary) | curious(mary) [resolution 81,135]
262. 23 <=> rich(mary) [avatar definition]
264. ~rich(mary) <- (~23) [avatar component clause 262]
265. 5 | ~23 [avatar split clause 260,262,157]
282. happy(mary) | old(mary) <- (~6) [resolution 108,162]
286. old(mary) <- (~6) [subsumption resolution 282,223]
288. ~creative(mary) <- (~6) [resolution 286,85]
290. $false <- (~6) [subsumption resolution 288,135]
291. 6 [avatar contradiction clause 290]
296. rich(mary) | curious(mary) <- (6) [resolution 116,163]
307. curious(mary) <- (6, ~23) [subsumption resolution 296,264]
308. 5 | ~6 | 23 [avatar split clause 307,262,161,157]
309. ~kind(mary) <- (5) [resolution 159,196]
310. $false <- (5) [subsumption resolution 309,125]
311. ~5 [avatar contradiction clause 310]
312. $false [avatar sat refutation 265,291,308,311]
% SZS output end Proof for 5641350377824264088213098
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and strong is not brave or not rich. Everyone who is either not curious or not rich is either not generous or not quiet and vice versa. If alice is both calm and not generous then fred is not tall and vice versa. Everyone who is not brave or not calm is either funny or not rich and vice versa. If fred is quiet then someone is not humble or rich. If mary is either not humble or generous then someone is funny or not kind and vice versa. If alice is either creative or calm then someone is not old or not brave and vice versa. If fred is both not rich and not strong then someone is both calm and funny. Everyone who is both humble and not tall is both not calm and not rich and vice versa. If paul is not generous then mary is either strong or not generous and vice versa. Everyone who is either not patient or not strong is not tall. Everyone who is wise or humble is patient or creative. Everyone who is quiet or not quiet is both not calm and not wise and vice versa. Everyone who is not tall is both not strong and creative and vice versa. If someone is happy or not brave then someone is strong or not wise and vice versa. If someone is wise or not happy then someone is both brave and not happy. Mary is either kind or not strong. Mary is not funny or old. Fred is both not generous and creative. Someone is either not wise or not kind. Someone is not rich or humble. Alice is not quiet. Fred is not generous or not humble. Alice is both patient and generous. | Mary is not generous. | neutral | (![X]:((humble(X)&strong(X))=>(~brave(X)|~rich(X))))&
(![X]:((~curious(X)<~>~rich(X))<=>(~generous(X)<~>~quiet(X))))&
(((calm(alice)&~generous(alice)))<=>(~tall(fred)))&
(![X]:((~brave(X)|~calm(X))<=>(funny(X)<~>~rich(X))))&
((quiet(fred))=>(?[X]:((~humble(X)|rich(X)))))&
(((~humble(mary)<~>generous(mary)))<=>(?[X]:((funny(X)|~kind(X)))))&
(((creative(alice)<~>calm(alice)))<=>(?[X]:((~old(X)|~brave(X)))))&
(((~rich(fred)&~strong(fred)))=>(?[X]:((calm(X)&funny(X)))))&
(![X]:((humble(X)&~tall(X))<=>(~calm(X)&~rich(X))))&
((~generous(paul))<=>((strong(mary)<~>~generous(mary))))&
(![X]:((~patient(X)<~>~strong(X))=>~tall(X)))&
(![X]:((wise(X)|humble(X))=>(patient(X)|creative(X))))&
(![X]:((quiet(X)|~quiet(X))<=>(~calm(X)&~wise(X))))&
(![X]:(~tall(X)<=>(~strong(X)&creative(X))))&
((?[X]:((happy(X)|~brave(X))))<=>(?[X]:((strong(X)|~wise(X)))))&
((?[X]:((wise(X)|~happy(X))))=>(?[X]:((brave(X)&~happy(X)))))&
((kind(mary)<~>~strong(mary)))&
((~funny(mary)|old(mary)))&
((~generous(fred)&creative(fred)))&
(?[X]:((~wise(X)<~>~kind(X))))&
(?[X]:((~rich(X)|humble(X))))&
(~quiet(alice))&
((~generous(fred)|~humble(fred)))&
((patient(alice)&generous(alice))) | ~generous(mary) | [] | null | 0 |
Everyone who is not tall or happy is kind and vice versa.
If fred is not funny or strong then fred is both not brave and not quiet.
Everyone who is either patient or funny is both curious and humble.
If susan is both quiet and tall then lucy is not rich.
Everyone who is both creative and not tall is not quiet or not generous.
If susan is both happy and not tall then alice is rich and vice versa.
If someone is not creative or not wise then lucy is both not curious and patient.
If paul is either not funny or not kind then paul is rich or not creative.
Everyone who is tall or not happy is either curious or wise and vice versa.
Everyone who is both not creative and wise is strong and vice versa.
Everyone who is not funny or not happy is both not rich and not strong and vice versa.
Everyone who is not patient or not quiet is old or calm and vice versa.
Everyone who is happy is both funny and not old.
Everyone who is humble is either strong or not patient.
Everyone who is either not happy or brave is not old or funny and vice versa.
Everyone who is either brave or not old is wise or kind and vice versa.
John is either not tall or brave.
Someone is not calm or calm.
Someone is either not patient or not rich.
Someone is wise.
Alice is both tall and not old.
Someone is not old or not generous. | Lucy is wise. | entailment | (![X]:((~tall(X)|happy(X))<=>kind(X)))&
(((~funny(fred)|strong(fred)))=>((~brave(fred)&~quiet(fred))))&
(![X]:((patient(X)<~>funny(X))=>(curious(X)&humble(X))))&
(((quiet(susan)&tall(susan)))=>(~rich(lucy)))&
(![X]:((creative(X)&~tall(X))=>(~quiet(X)|~generous(X))))&
(((happy(susan)&~tall(susan)))<=>(rich(alice)))&
((?[X]:((~creative(X)|~wise(X))))=>((~curious(lucy)&patient(lucy))))&
(((~funny(paul)<~>~kind(paul)))=>((rich(paul)|~creative(paul))))&
(![X]:((tall(X)|~happy(X))<=>(curious(X)<~>wise(X))))&
(![X]:((~creative(X)&wise(X))<=>strong(X)))&
(![X]:((~funny(X)|~happy(X))<=>(~rich(X)&~strong(X))))&
(![X]:((~patient(X)|~quiet(X))<=>(old(X)|calm(X))))&
(![X]:(happy(X)=>(funny(X)&~old(X))))&
(![X]:(humble(X)=>(strong(X)<~>~patient(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~old(X)|funny(X))))&
(![X]:((brave(X)<~>~old(X))<=>(wise(X)|kind(X))))&
((~tall(john)<~>brave(john)))&
(?[X]:((~calm(X)|calm(X))))&
(?[X]:((~patient(X)<~>~rich(X))))&
(?[X]:(wise(X)))&
((tall(alice)&~old(alice)))&
(?[X]:((~old(X)|~generous(X)))) | wise(lucy) | [
"p0",
"p6",
"p8",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6294270022687137281654787
% SZS output start Proof for 6294270022687137281654787
1. ! [X0] : ((happy(X0) | ~tall(X0)) <=> kind(X0)) [input p0]
7. ? [X0] : (~wise(X0) | ~creative(X0)) => (patient(lucy) & ~curious(lucy)) [input p6]
9. ! [X0] : ((~happy(X0) | tall(X0)) <=> (curious(X0) <~> wise(X0))) [input p8]
13. ! [X0] : (happy(X0) => (~old(X0) & funny(X0))) [input p12]
15. ! [X0] : ((~happy(X0) <~> brave(X0)) <=> (funny(X0) | ~old(X0))) [input p14]
16. ! [X0] : ((brave(X0) <~> ~old(X0)) <=> (kind(X0) | wise(X0))) [input p15]
23. ~wise(lucy) [input hypothesis]
30. (patient(lucy) & ~curious(lucy)) | ! [X0] : (wise(X0) & creative(X0)) [ennf transformation 7]
33. ! [X0] : ((~old(X0) & funny(X0)) | ~happy(X0)) [ennf transformation 13]
35. ! [X0] : (((happy(X0) | ~tall(X0)) | ~kind(X0)) & (kind(X0) | (~happy(X0) & tall(X0)))) [nnf transformation 1]
36. ! [X0] : ((happy(X0) | ~tall(X0) | ~kind(X0)) & (kind(X0) | (~happy(X0) & tall(X0)))) [flattening 35]
41. ! [X0] : (((~happy(X0) | tall(X0)) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0)))) & (((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (happy(X0) & ~tall(X0)))) [nnf transformation 9]
42. ! [X0] : ((~happy(X0) | tall(X0) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0)))) & (((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (happy(X0) & ~tall(X0)))) [flattening 41]
50. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) & old(X0))) & ((funny(X0) | ~old(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [nnf transformation 15]
51. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) & old(X0))) & (funny(X0) | ~old(X0) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [flattening 50]
52. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (~kind(X0) & ~wise(X0))) & ((kind(X0) | wise(X0)) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [nnf transformation 16]
53. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (~kind(X0) & ~wise(X0))) & (kind(X0) | wise(X0) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [flattening 52]
63. ~happy(X0) | kind(X0) [cnf transformation 36]
78. ~curious(lucy) | wise(X0) [cnf transformation 30]
84. wise(X0) | curious(X0) | happy(X0) [cnf transformation 42]
101. ~happy(X0) | funny(X0) [cnf transformation 33]
102. ~old(X0) | ~happy(X0) [cnf transformation 33]
108. brave(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 51]
116. ~brave(X0) | old(X0) | ~kind(X0) [cnf transformation 53]
125. ~wise(lucy) [cnf transformation 23]
171. 10 <=> ! [X0] : wise(X0) [avatar definition]
172. wise(X0) <- (10) [avatar component clause 171]
183. 13 <=> curious(lucy) [avatar definition]
185. ~curious(lucy) <- (~13) [avatar component clause 183]
186. 10 | ~13 [avatar split clause 78,183,171]
206. ~happy(X0) | brave(X0) [subsumption resolution 108,101]
273. curious(lucy) | happy(lucy) [resolution 84,125]
274. happy(lucy) <- (~13) [subsumption resolution 273,185]
293. brave(lucy) <- (~13) [resolution 274,206]
295. kind(lucy) <- (~13) [resolution 274,63]
363. old(lucy) | ~kind(lucy) <- (~13) [resolution 116,293]
365. old(lucy) <- (~13) [subsumption resolution 363,295]
569. ~happy(lucy) <- (~13) [resolution 365,102]
571. $false <- (~13) [subsumption resolution 569,274]
572. 13 [avatar contradiction clause 571]
587. $false <- (10) [resolution 172,125]
593. ~10 [avatar contradiction clause 587]
594. $false [avatar sat refutation 186,572,593]
% SZS output end Proof for 6294270022687137281654787
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is not creative or not funny then someone is either not brave or not quiet and vice versa.
If alice is not patient or patient then someone is either old or quiet.
Everyone who is either humble or not humble is both generous and wise.
If someone is creative then fred is both wise and not brave and vice versa.
If alice is calm or not quiet then lucy is both happy and curious and vice versa.
If someone is tall then someone is both patient and not generous.
Everyone who is either kind or not curious is either happy or not calm and vice versa.
Everyone who is both generous and not quiet is not strong and vice versa.
Everyone who is both not humble and calm is curious.
If lucy is both not rich and not wise then someone is both funny and quiet.
If lucy is both calm and strong then fred is both not patient and not funny.
If someone is quiet or happy then alice is either not calm or not generous.
Everyone who is humble is either not kind or tall and vice versa.
Everyone who is both not calm and not old is creative or happy and vice versa.
If alice is either not funny or old then someone is either not generous or old and vice versa.
Everyone who is happy or brave is both wise and quiet.
Lucy is not tall or funny.
Someone is both rich and not curious.
Someone is not quiet or creative.
John is not brave or not calm.
Fred is both wise and not kind.
Someone is old. | Alice is rich. | neutral | (((~creative(alice)|~funny(alice)))<=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(((~patient(alice)|patient(alice)))=>(?[X]:((old(X)<~>quiet(X)))))&
(![X]:((humble(X)<~>~humble(X))=>(generous(X)&wise(X))))&
((?[X]:(creative(X)))<=>((wise(fred)&~brave(fred))))&
(((calm(alice)|~quiet(alice)))<=>((happy(lucy)&curious(lucy))))&
((?[X]:(tall(X)))=>(?[X]:((patient(X)&~generous(X)))))&
(![X]:((kind(X)<~>~curious(X))<=>(happy(X)<~>~calm(X))))&
(![X]:((generous(X)&~quiet(X))<=>~strong(X)))&
(![X]:((~humble(X)&calm(X))=>curious(X)))&
(((~rich(lucy)&~wise(lucy)))=>(?[X]:((funny(X)&quiet(X)))))&
(((calm(lucy)&strong(lucy)))=>((~patient(fred)&~funny(fred))))&
((?[X]:((quiet(X)|happy(X))))=>((~calm(alice)<~>~generous(alice))))&
(![X]:(humble(X)<=>(~kind(X)<~>tall(X))))&
(![X]:((~calm(X)&~old(X))<=>(creative(X)|happy(X))))&
(((~funny(alice)<~>old(alice)))<=>(?[X]:((~generous(X)<~>old(X)))))&
(![X]:((happy(X)|brave(X))=>(wise(X)&quiet(X))))&
((~tall(lucy)|funny(lucy)))&
(?[X]:((rich(X)&~curious(X))))&
(?[X]:((~quiet(X)|creative(X))))&
((~brave(john)|~calm(john)))&
((wise(fred)&~kind(fred)))&
(?[X]:(old(X))) | rich(alice) | [] | null | 0 |
If susan is curious or creative then susan is generous and vice versa. If paul is not curious then someone is both not creative and not happy and vice versa. Everyone who is either wise or patient is not funny. If alice is not happy or patient then someone is either not tall or generous and vice versa. If paul is both happy and tall then someone is both old and not kind. If alice is both not old and not creative then someone is both old and not old and vice versa. If someone is not strong then someone is both humble and not creative and vice versa. If lucy is tall or wise then mary is not calm or generous. If someone is creative or not wise then someone is not old or kind and vice versa. If mary is creative then paul is either old or not old and vice versa. Everyone who is both not wise and quiet is both not funny and strong and vice versa. If someone is either quiet or not humble then someone is either not happy or patient. Everyone who is happy or not wise is both rich and not strong and vice versa. If john is curious then mary is curious or not calm and vice versa. If someone is rich then someone is both tall and not tall and vice versa. If alice is either creative or rich then paul is not tall or not generous. Someone is not wise or not strong. Someone is brave or not curious. Paul is not kind. Someone is not strong. Fred is wise or not humble. Lucy is not strong or not curious. Someone is not brave. | Mary is wise. | entailment | (((curious(susan)|creative(susan)))<=>(generous(susan)))&
((~curious(paul))<=>(?[X]:((~creative(X)&~happy(X)))))&
(![X]:((wise(X)<~>patient(X))=>~funny(X)))&
(((~happy(alice)|patient(alice)))<=>(?[X]:((~tall(X)<~>generous(X)))))&
(((happy(paul)&tall(paul)))=>(?[X]:((old(X)&~kind(X)))))&
(((~old(alice)&~creative(alice)))<=>(?[X]:((old(X)&~old(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((humble(X)&~creative(X)))))&
(((tall(lucy)|wise(lucy)))=>((~calm(mary)|generous(mary))))&
((?[X]:((creative(X)|~wise(X))))<=>(?[X]:((~old(X)|kind(X)))))&
((creative(mary))<=>((old(paul)<~>~old(paul))))&
(![X]:((~wise(X)&quiet(X))<=>(~funny(X)&strong(X))))&
((?[X]:((quiet(X)<~>~humble(X))))=>(?[X]:((~happy(X)<~>patient(X)))))&
(![X]:((happy(X)|~wise(X))<=>(rich(X)&~strong(X))))&
((curious(john))<=>((curious(mary)|~calm(mary))))&
((?[X]:(rich(X)))<=>(?[X]:((tall(X)&~tall(X)))))&
(((creative(alice)<~>rich(alice)))=>((~tall(paul)|~generous(paul))))&
(?[X]:((~wise(X)|~strong(X))))&
(?[X]:((brave(X)|~curious(X))))&
(~kind(paul))&
(?[X]:(~strong(X)))&
((wise(fred)|~humble(fred)))&
((~strong(lucy)|~curious(lucy)))&
(?[X]:(~brave(X))) | wise(mary) | [
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9156298321212121781402345
% SZS output start Proof for 9156298321212121781402345
13. ! [X0] : ((~wise(X0) | happy(X0)) <=> (~strong(X0) & rich(X0))) [input p12]
15. ? [X0] : rich(X0) <=> ? [X0] : (~tall(X0) & tall(X0)) [input p14]
24. ~wise(mary) [input hypothesis]
28. ? [X0] : rich(X0) <=> ? [X1] : (~tall(X1) & tall(X1)) [rectify 15]
73. ! [X0] : (((~wise(X0) | happy(X0)) | (strong(X0) | ~rich(X0))) & ((~strong(X0) & rich(X0)) | (wise(X0) & ~happy(X0)))) [nnf transformation 13]
74. ! [X0] : ((~wise(X0) | happy(X0) | strong(X0) | ~rich(X0)) & ((~strong(X0) & rich(X0)) | (wise(X0) & ~happy(X0)))) [flattening 73]
77. (? [X0] : rich(X0) | ! [X1] : (tall(X1) | ~tall(X1))) & (? [X1] : (~tall(X1) & tall(X1)) | ! [X0] : ~rich(X0)) [nnf transformation 28]
78. (? [X0] : rich(X0) | ! [X1] : (tall(X1) | ~tall(X1))) & (? [X2] : (~tall(X2) & tall(X2)) | ! [X3] : ~rich(X3)) [rectify 77]
79. ? [X0] : rich(X0) => rich(sK9) [choice axiom]
80. ? [X2] : (~tall(X2) & tall(X2)) => (~tall(sK10) & tall(sK10)) [choice axiom]
81. (rich(sK9) | ! [X1] : (tall(X1) | ~tall(X1))) & ((~tall(sK10) & tall(sK10)) | ! [X3] : ~rich(X3)) [skolemisation 78,80,79]
133. rich(X0) | wise(X0) [cnf transformation 74]
140. tall(sK10) | ~rich(X3) [cnf transformation 81]
141. ~tall(sK10) | ~rich(X3) [cnf transformation 81]
152. ~wise(mary) [cnf transformation 24]
304. 34 <=> ! [X3] : wise(X3) [avatar definition]
305. wise(X3) <- (34) [avatar component clause 304]
359. 46 <=> ! [X3] : ~rich(X3) [avatar definition]
360. ~rich(X3) <- (46) [avatar component clause 359]
362. 47 <=> tall(sK10) [avatar definition]
365. 46 | ~47 [avatar split clause 141,362,359]
366. 46 | 47 [avatar split clause 140,362,359]
409. wise(X0) <- (46) [resolution 133,360]
410. 34 | ~46 [avatar split clause 409,359,304]
411. $false <- (34) [resolution 305,152]
416. ~34 [avatar contradiction clause 411]
417. $false [avatar sat refutation 365,366,410,416]
% SZS output end Proof for 9156298321212121781402345
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or not curious is not curious and vice versa.
Everyone who is brave or not generous is not patient or happy and vice versa.
If alice is both patient and not humble then someone is not brave and vice versa.
If alice is not humble or not rich then someone is both not happy and strong.
Everyone who is patient or not humble is not kind or funny and vice versa.
If susan is both funny and not happy then someone is not calm.
If someone is not happy then someone is not patient and vice versa.
If alice is both tall and not curious then john is both not creative and not generous.
If lucy is either generous or not wise then someone is either not kind or humble.
Everyone who is either funny or rich is not creative and vice versa.
Everyone who is not calm or not rich is either humble or not strong.
Everyone who is either calm or funny is either patient or not strong.
If someone is either strong or wise then lucy is not funny or not patient and vice versa.
If someone is rich then someone is both not strong and happy and vice versa.
Everyone who is either not happy or not calm is curious.
Everyone who is both calm and creative is patient and vice versa.
Someone is both strong and not kind.
Someone is generous or calm.
Paul is either wise or not humble.
Susan is either not tall or brave.
Someone is both happy and funny.
Someone is funny or not generous.
Someone is both not wise and curious.
Lucy is either funny or not patient. | Susan is tall. | neutral | (![X]:((~creative(X)|~curious(X))<=>~curious(X)))&
(![X]:((brave(X)|~generous(X))<=>(~patient(X)|happy(X))))&
(((patient(alice)&~humble(alice)))<=>(?[X]:(~brave(X))))&
(((~humble(alice)|~rich(alice)))=>(?[X]:((~happy(X)&strong(X)))))&
(![X]:((patient(X)|~humble(X))<=>(~kind(X)|funny(X))))&
(((funny(susan)&~happy(susan)))=>(?[X]:(~calm(X))))&
((?[X]:(~happy(X)))<=>(?[X]:(~patient(X))))&
(((tall(alice)&~curious(alice)))=>((~creative(john)&~generous(john))))&
(((generous(lucy)<~>~wise(lucy)))=>(?[X]:((~kind(X)<~>humble(X)))))&
(![X]:((funny(X)<~>rich(X))<=>~creative(X)))&
(![X]:((~calm(X)|~rich(X))=>(humble(X)<~>~strong(X))))&
(![X]:((calm(X)<~>funny(X))=>(patient(X)<~>~strong(X))))&
((?[X]:((strong(X)<~>wise(X))))<=>((~funny(lucy)|~patient(lucy))))&
((?[X]:(rich(X)))<=>(?[X]:((~strong(X)&happy(X)))))&
(![X]:((~happy(X)<~>~calm(X))=>curious(X)))&
(![X]:((calm(X)&creative(X))<=>patient(X)))&
(?[X]:((strong(X)&~kind(X))))&
(?[X]:((generous(X)|calm(X))))&
((wise(paul)<~>~humble(paul)))&
((~tall(susan)<~>brave(susan)))&
(?[X]:((happy(X)&funny(X))))&
(?[X]:((funny(X)|~generous(X))))&
(?[X]:((~wise(X)&curious(X))))&
((funny(lucy)<~>~patient(lucy))) | tall(susan) | [] | null | 0 |
Everyone who is both not patient and not curious is rich.
If someone is both humble and not creative then someone is both humble and happy.
Everyone who is either rich or old is not humble and vice versa.
If someone is both calm and not wise then someone is either not wise or quiet.
Everyone who is generous or not funny is curious or not curious and vice versa.
If someone is not curious or not kind then mary is strong and vice versa.
Everyone who is either funny or generous is not strong or not old and vice versa.
If someone is not funny then susan is not wise.
Everyone who is kind or strong is either not strong or humble and vice versa.
If someone is either not patient or humble then lucy is either humble or not tall and vice versa.
If alice is tall or not patient then john is not brave.
Everyone who is not old is not generous or funny and vice versa.
If susan is not tall then john is either not curious or funny and vice versa.
Everyone who is both not happy and strong is both rich and strong and vice versa.
If someone is both not patient and not quiet then lucy is both not strong and not rich.
Everyone who is either funny or not tall is patient and vice versa.
Alice is both tall and not calm.
Lucy is not old or not rich.
Someone is both kind and not quiet.
Someone is both not happy and patient.
Someone is both not patient and not wise.
Someone is both not happy and generous. | John is kind. | entailment | (![X]:((~patient(X)&~curious(X))=>rich(X)))&
((?[X]:((humble(X)&~creative(X))))=>(?[X]:((humble(X)&happy(X)))))&
(![X]:((rich(X)<~>old(X))<=>~humble(X)))&
((?[X]:((calm(X)&~wise(X))))=>(?[X]:((~wise(X)<~>quiet(X)))))&
(![X]:((generous(X)|~funny(X))<=>(curious(X)|~curious(X))))&
((?[X]:((~curious(X)|~kind(X))))<=>(strong(mary)))&
(![X]:((funny(X)<~>generous(X))<=>(~strong(X)|~old(X))))&
((?[X]:(~funny(X)))=>(~wise(susan)))&
(![X]:((kind(X)|strong(X))<=>(~strong(X)<~>humble(X))))&
((?[X]:((~patient(X)<~>humble(X))))<=>((humble(lucy)<~>~tall(lucy))))&
(((tall(alice)|~patient(alice)))=>(~brave(john)))&
(![X]:(~old(X)<=>(~generous(X)|funny(X))))&
((~tall(susan))<=>((~curious(john)<~>funny(john))))&
(![X]:((~happy(X)&strong(X))<=>(rich(X)&strong(X))))&
((?[X]:((~patient(X)&~quiet(X))))=>((~strong(lucy)&~rich(lucy))))&
(![X]:((funny(X)<~>~tall(X))<=>patient(X)))&
((tall(alice)&~calm(alice)))&
((~old(lucy)|~rich(lucy)))&
(?[X]:((kind(X)&~quiet(X))))&
(?[X]:((~happy(X)&patient(X))))&
(?[X]:((~patient(X)&~wise(X))))&
(?[X]:((~happy(X)&generous(X)))) | kind(john) | [
"p4",
"p5",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8611592557346177311517533
% SZS output start Proof for 8611592557346177311517533
5. ! [X0] : ((~funny(X0) | generous(X0)) <=> (~curious(X0) | curious(X0))) [input p4]
6. ? [X0] : (~kind(X0) | ~curious(X0)) <=> strong(mary) [input p5]
7. ! [X0] : ((funny(X0) <~> generous(X0)) <=> (~old(X0) | ~strong(X0))) [input p6]
12. ! [X0] : (~old(X0) <=> (funny(X0) | ~generous(X0))) [input p11]
23. ~kind(john) [input hypothesis]
36. ! [X0] : (((~funny(X0) | generous(X0)) | (curious(X0) & ~curious(X0))) & ((~curious(X0) | curious(X0)) | (funny(X0) & ~generous(X0)))) [nnf transformation 5]
37. ! [X0] : ((~funny(X0) | generous(X0) | (curious(X0) & ~curious(X0))) & (~curious(X0) | curious(X0) | (funny(X0) & ~generous(X0)))) [flattening 36]
38. (? [X0] : (~kind(X0) | ~curious(X0)) | ~strong(mary)) & (strong(mary) | ! [X0] : (kind(X0) & curious(X0))) [nnf transformation 6]
39. (? [X0] : (~kind(X0) | ~curious(X0)) | ~strong(mary)) & (strong(mary) | ! [X1] : (kind(X1) & curious(X1))) [rectify 38]
40. ? [X0] : (~kind(X0) | ~curious(X0)) => (~kind(sK0) | ~curious(sK0)) [choice axiom]
41. ((~kind(sK0) | ~curious(sK0)) | ~strong(mary)) & (strong(mary) | ! [X1] : (kind(X1) & curious(X1))) [skolemisation 39,40]
42. ! [X0] : ((((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (old(X0) & strong(X0))) & ((~old(X0) | ~strong(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0))))) [nnf transformation 7]
43. ! [X0] : ((((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (old(X0) & strong(X0))) & (~old(X0) | ~strong(X0) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0))))) [flattening 42]
50. ! [X0] : ((~old(X0) | (~funny(X0) & generous(X0))) & ((funny(X0) | ~generous(X0)) | old(X0))) [nnf transformation 12]
51. ! [X0] : ((~old(X0) | (~funny(X0) & generous(X0))) & (funny(X0) | ~generous(X0) | old(X0))) [flattening 50]
71. ~funny(X0) | generous(X0) | ~curious(X0) [cnf transformation 37]
72. ~funny(X0) | generous(X0) | curious(X0) [cnf transformation 37]
74. strong(mary) | kind(X1) [cnf transformation 41]
77. ~strong(X0) | ~old(X0) | funny(X0) | ~generous(X0) [cnf transformation 43]
79. generous(X0) | funny(X0) | old(X0) [cnf transformation 43]
81. ~generous(X0) | ~funny(X0) | old(X0) [cnf transformation 43]
96. funny(X0) | ~generous(X0) | old(X0) [cnf transformation 51]
97. ~old(X0) | generous(X0) [cnf transformation 51]
98. ~old(X0) | ~funny(X0) [cnf transformation 51]
122. ~kind(john) [cnf transformation 23]
125. ~funny(X0) | generous(X0) [subsumption resolution 71,72]
127. 1 <=> strong(mary) [avatar definition]
128. strong(mary) <- (1) [avatar component clause 127]
140. 4 <=> ! [X1] : kind(X1) [avatar definition]
141. kind(X1) <- (4) [avatar component clause 140]
142. 4 | 1 [avatar split clause 74,127,140]
147. ~funny(X0) | old(X0) [subsumption resolution 81,125]
149. generous(X0) | old(X0) [subsumption resolution 79,147]
181. ~funny(X0) [subsumption resolution 98,147]
182. generous(X0) [subsumption resolution 97,149]
183. ~generous(X0) | old(X0) [subsumption resolution 96,181]
184. old(X0) [subsumption resolution 183,182]
216. $false <- (4) [resolution 141,122]
217. ~4 [avatar contradiction clause 216]
258. ~old(mary) | funny(mary) | ~generous(mary) <- (1) [resolution 77,128]
261. funny(mary) | ~generous(mary) <- (1) [subsumption resolution 258,184]
262. ~generous(mary) <- (1) [subsumption resolution 261,181]
263. $false <- (1) [subsumption resolution 262,182]
264. ~1 [avatar contradiction clause 263]
265. $false [avatar sat refutation 142,217,264]
% SZS output end Proof for 8611592557346177311517533
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or strong is not humble and vice versa. If fred is either not old or strong then mary is strong. If someone is both not tall and not wise then paul is either calm or not creative. Everyone who is not quiet or curious is either not happy or not wise. If mary is not happy or curious then someone is both calm and old and vice versa. If mary is either creative or not tall then alice is calm or not brave and vice versa. If john is both not tall and not brave then lucy is either not calm or not rich and vice versa. Everyone who is not old is either not creative or calm and vice versa. If someone is quiet then someone is curious and vice versa. Everyone who is both not humble and strong is both not funny and funny and vice versa. If mary is either not quiet or not generous then susan is not funny or not curious and vice versa. Everyone who is not calm is both not humble and tall. Everyone who is generous is either wise or not generous. Everyone who is tall or not creative is both creative and curious. Everyone who is creative or not happy is either not patient or not brave and vice versa. If paul is both not wise and not kind then susan is not quiet or happy and vice versa. Someone is either funny or not tall. Someone is not quiet or not calm. Someone is both happy and creative. Lucy is both calm and not tall. Someone is not calm. John is creative. Someone is either creative or strong. | Alice is calm. | contradiction | (![X]:((wise(X)|strong(X))<=>~humble(X)))&
(((~old(fred)<~>strong(fred)))=>(strong(mary)))&
((?[X]:((~tall(X)&~wise(X))))=>((calm(paul)<~>~creative(paul))))&
(![X]:((~quiet(X)|curious(X))=>(~happy(X)<~>~wise(X))))&
(((~happy(mary)|curious(mary)))<=>(?[X]:((calm(X)&old(X)))))&
(((creative(mary)<~>~tall(mary)))<=>((calm(alice)|~brave(alice))))&
(((~tall(john)&~brave(john)))<=>((~calm(lucy)<~>~rich(lucy))))&
(![X]:(~old(X)<=>(~creative(X)<~>calm(X))))&
((?[X]:(quiet(X)))<=>(?[X]:(curious(X))))&
(![X]:((~humble(X)&strong(X))<=>(~funny(X)&funny(X))))&
(((~quiet(mary)<~>~generous(mary)))<=>((~funny(susan)|~curious(susan))))&
(![X]:(~calm(X)=>(~humble(X)&tall(X))))&
(![X]:(generous(X)=>(wise(X)<~>~generous(X))))&
(![X]:((tall(X)|~creative(X))=>(creative(X)&curious(X))))&
(![X]:((creative(X)|~happy(X))<=>(~patient(X)<~>~brave(X))))&
(((~wise(paul)&~kind(paul)))<=>((~quiet(susan)|happy(susan))))&
(?[X]:((funny(X)<~>~tall(X))))&
(?[X]:((~quiet(X)|~calm(X))))&
(?[X]:((happy(X)&creative(X))))&
((calm(lucy)&~tall(lucy)))&
(?[X]:(~calm(X)))&
(creative(john))&
(?[X]:((creative(X)<~>strong(X)))) | calm(alice) | [
"p4",
"p5",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 549819474189486304089880
% SZS output start Proof for 549819474189486304089880
5. (curious(mary) | ~happy(mary)) <=> ? [X0] : (old(X0) & calm(X0)) [input p4]
6. (creative(mary) <~> ~tall(mary)) <=> (~brave(alice) | calm(alice)) [input p5]
8. ! [X0] : (~old(X0) <=> (~creative(X0) <~> calm(X0))) [input p7]
14. ! [X0] : ((~creative(X0) | tall(X0)) => (curious(X0) & creative(X0))) [input p13]
24. calm(alice) [input hypothesis]
31. ! [X0] : ((curious(X0) & creative(X0)) | (creative(X0) & ~tall(X0))) [ennf transformation 14]
37. ((curious(mary) | ~happy(mary)) | ! [X0] : (~old(X0) | ~calm(X0))) & (? [X0] : (old(X0) & calm(X0)) | (~curious(mary) & happy(mary))) [nnf transformation 5]
38. (curious(mary) | ~happy(mary) | ! [X0] : (~old(X0) | ~calm(X0))) & (? [X0] : (old(X0) & calm(X0)) | (~curious(mary) & happy(mary))) [flattening 37]
39. (curious(mary) | ~happy(mary) | ! [X0] : (~old(X0) | ~calm(X0))) & (? [X1] : (old(X1) & calm(X1)) | (~curious(mary) & happy(mary))) [rectify 38]
40. ? [X1] : (old(X1) & calm(X1)) => (old(sK0) & calm(sK0)) [choice axiom]
41. (curious(mary) | ~happy(mary) | ! [X0] : (~old(X0) | ~calm(X0))) & ((old(sK0) & calm(sK0)) | (~curious(mary) & happy(mary))) [skolemisation 39,40]
42. (((tall(mary) | ~creative(mary)) & (~tall(mary) | creative(mary))) | (brave(alice) & ~calm(alice))) & ((~brave(alice) | calm(alice)) | ((creative(mary) | tall(mary)) & (~tall(mary) | ~creative(mary)))) [nnf transformation 6]
43. (((tall(mary) | ~creative(mary)) & (~tall(mary) | creative(mary))) | (brave(alice) & ~calm(alice))) & (~brave(alice) | calm(alice) | ((creative(mary) | tall(mary)) & (~tall(mary) | ~creative(mary)))) [flattening 42]
46. ! [X0] : ((~old(X0) | ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0)))) & (((~calm(X0) | creative(X0)) & (calm(X0) | ~creative(X0))) | old(X0))) [nnf transformation 8]
85. calm(sK0) | ~curious(mary) [cnf transformation 41]
87. old(sK0) | ~curious(mary) [cnf transformation 41]
93. tall(mary) | ~creative(mary) | ~calm(alice) [cnf transformation 43]
104. ~creative(X0) | ~old(X0) | ~calm(X0) [cnf transformation 46]
122. creative(X0) | creative(X0) [cnf transformation 31]
123. ~tall(X0) | curious(X0) [cnf transformation 31]
147. calm(alice) [cnf transformation 24]
148. creative(X0) [duplicate literal removal 122]
178. 7 <=> ! [X0] : (~old(X0) | ~calm(X0)) [avatar definition]
179. ~calm(X0) | ~old(X0) <- (7) [avatar component clause 178]
185. 9 <=> curious(mary) [avatar definition]
190. 10 <=> old(sK0) [avatar definition]
192. old(sK0) <- (10) [avatar component clause 190]
193. ~9 | 10 [avatar split clause 87,190,185]
196. 11 <=> calm(sK0) [avatar definition]
198. calm(sK0) <- (11) [avatar component clause 196]
199. ~9 | 11 [avatar split clause 85,196,185]
206. 13 <=> creative(mary) [avatar definition]
208. ~creative(mary) <- (~13) [avatar component clause 206]
210. 14 <=> tall(mary) [avatar definition]
212. tall(mary) <- (14) [avatar component clause 210]
215. 15 <=> calm(alice) [avatar definition]
218. ~15 | ~13 | 14 [avatar split clause 93,210,206,215]
329. 15 [avatar split clause 147,215]
330. $false <- (~13) [subsumption resolution 208,148]
331. 13 [avatar contradiction clause 330]
341. curious(mary) <- (14) [resolution 123,212]
344. 9 | ~14 [avatar split clause 341,210,185]
355. ~old(sK0) <- (7, 11) [resolution 179,198]
356. $false <- (7, 10, 11) [subsumption resolution 355,192]
357. ~7 | ~10 | ~11 [avatar contradiction clause 356]
438. ~old(X0) | ~calm(X0) [resolution 104,148]
439. 7 [avatar split clause 438,178]
440. $false [avatar sat refutation 193,199,218,329,331,344,357,439]
% SZS output end Proof for 549819474189486304089880
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not calm or not rich then paul is not patient.
If someone is creative or wise then someone is either not kind or generous.
If someone is either patient or not funny then john is not happy.
If someone is either patient or tall then someone is both not patient and brave and vice versa.
If mary is either strong or not patient then someone is both not generous and funny.
Everyone who is brave is kind and vice versa.
Everyone who is either patient or kind is not creative or brave and vice versa.
Everyone who is both old and quiet is both not kind and patient and vice versa.
If someone is wise then someone is either funny or curious and vice versa.
Everyone who is both not happy and not patient is not creative.
If someone is either kind or not quiet then someone is not creative or not old.
Everyone who is tall or wise is either not creative or wise and vice versa.
Everyone who is not generous or not funny is rich or creative and vice versa.
If paul is not wise or creative then someone is quiet.
Everyone who is not happy or patient is both not old and not rich.
If susan is both not funny and not creative then someone is not wise or not strong and vice versa.
Someone is not curious.
Someone is not humble or wise.
Someone is both brave and generous.
Susan is both not curious and not funny.
Someone is not patient.
Fred is not wise or wise.
Someone is either not rich or not wise. | Susan is not brave. | contradiction | ((?[X]:((~calm(X)<~>~rich(X))))=>(~patient(paul)))&
((?[X]:((creative(X)|wise(X))))=>(?[X]:((~kind(X)<~>generous(X)))))&
((?[X]:((patient(X)<~>~funny(X))))=>(~happy(john)))&
((?[X]:((patient(X)<~>tall(X))))<=>(?[X]:((~patient(X)&brave(X)))))&
(((strong(mary)<~>~patient(mary)))=>(?[X]:((~generous(X)&funny(X)))))&
(![X]:(brave(X)<=>kind(X)))&
(![X]:((patient(X)<~>kind(X))<=>(~creative(X)|brave(X))))&
(![X]:((old(X)&quiet(X))<=>(~kind(X)&patient(X))))&
((?[X]:(wise(X)))<=>(?[X]:((funny(X)<~>curious(X)))))&
(![X]:((~happy(X)&~patient(X))=>~creative(X)))&
((?[X]:((kind(X)<~>~quiet(X))))=>(?[X]:((~creative(X)|~old(X)))))&
(![X]:((tall(X)|wise(X))<=>(~creative(X)<~>wise(X))))&
(![X]:((~generous(X)|~funny(X))<=>(rich(X)|creative(X))))&
(((~wise(paul)|creative(paul)))=>(?[X]:(quiet(X))))&
(![X]:((~happy(X)|patient(X))=>(~old(X)&~rich(X))))&
(((~funny(susan)&~creative(susan)))<=>(?[X]:((~wise(X)|~strong(X)))))&
(?[X]:(~curious(X)))&
(?[X]:((~humble(X)|wise(X))))&
(?[X]:((brave(X)&generous(X))))&
((~curious(susan)&~funny(susan)))&
(?[X]:(~patient(X)))&
((~wise(fred)|wise(fred)))&
(?[X]:((~rich(X)<~>~wise(X)))) | ~brave(susan) | [
"p2",
"p5",
"p6",
"p9",
"p11",
"p12",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 629700145186044139868682
% SZS output start Proof for 629700145186044139868682
3. ? [X0] : (patient(X0) <~> ~funny(X0)) => ~happy(john) [input p2]
6. ! [X0] : (brave(X0) <=> kind(X0)) [input p5]
7. ! [X0] : ((patient(X0) <~> kind(X0)) <=> (brave(X0) | ~creative(X0))) [input p6]
10. ! [X0] : ((~patient(X0) & ~happy(X0)) => ~creative(X0)) [input p9]
12. ! [X0] : ((wise(X0) | tall(X0)) <=> (~creative(X0) <~> wise(X0))) [input p11]
13. ! [X0] : ((~funny(X0) | ~generous(X0)) <=> (creative(X0) | rich(X0))) [input p12]
15. ! [X0] : ((patient(X0) | ~happy(X0)) => (~rich(X0) & ~old(X0))) [input p14]
16. (~creative(susan) & ~funny(susan)) <=> ? [X0] : (~strong(X0) | ~wise(X0)) [input p15]
20. ~funny(susan) & ~curious(susan) [input p19]
24. ~brave(susan) [input hypothesis]
32. ~happy(john) | ! [X0] : (patient(X0) <=> ~funny(X0)) [ennf transformation 3]
34. ! [X0] : (~creative(X0) | (patient(X0) | happy(X0))) [ennf transformation 10]
35. ! [X0] : (~creative(X0) | patient(X0) | happy(X0)) [flattening 34]
38. ! [X0] : ((~rich(X0) & ~old(X0)) | (~patient(X0) & happy(X0))) [ennf transformation 15]
44. ~happy(john) | ! [X0] : ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0))) [nnf transformation 32]
53. ! [X0] : ((brave(X0) | ~kind(X0)) & (kind(X0) | ~brave(X0))) [nnf transformation 6]
54. ! [X0] : ((((~kind(X0) | ~patient(X0)) & (kind(X0) | patient(X0))) | (~brave(X0) & creative(X0))) & ((brave(X0) | ~creative(X0)) | ((patient(X0) | ~kind(X0)) & (kind(X0) | ~patient(X0))))) [nnf transformation 7]
55. ! [X0] : ((((~kind(X0) | ~patient(X0)) & (kind(X0) | patient(X0))) | (~brave(X0) & creative(X0))) & (brave(X0) | ~creative(X0) | ((patient(X0) | ~kind(X0)) & (kind(X0) | ~patient(X0))))) [flattening 54]
67. ! [X0] : (((wise(X0) | tall(X0)) | ((~creative(X0) | ~wise(X0)) & (wise(X0) | creative(X0)))) & (((~wise(X0) | creative(X0)) & (wise(X0) | ~creative(X0))) | (~wise(X0) & ~tall(X0)))) [nnf transformation 12]
68. ! [X0] : ((wise(X0) | tall(X0) | ((~creative(X0) | ~wise(X0)) & (wise(X0) | creative(X0)))) & (((~wise(X0) | creative(X0)) & (wise(X0) | ~creative(X0))) | (~wise(X0) & ~tall(X0)))) [flattening 67]
69. ! [X0] : (((~funny(X0) | ~generous(X0)) | (~creative(X0) & ~rich(X0))) & ((creative(X0) | rich(X0)) | (funny(X0) & generous(X0)))) [nnf transformation 13]
70. ! [X0] : ((~funny(X0) | ~generous(X0) | (~creative(X0) & ~rich(X0))) & (creative(X0) | rich(X0) | (funny(X0) & generous(X0)))) [flattening 69]
73. ((~creative(susan) & ~funny(susan)) | ! [X0] : (strong(X0) & wise(X0))) & (? [X0] : (~strong(X0) | ~wise(X0)) | (creative(susan) | funny(susan))) [nnf transformation 16]
74. ((~creative(susan) & ~funny(susan)) | ! [X0] : (strong(X0) & wise(X0))) & (? [X0] : (~strong(X0) | ~wise(X0)) | creative(susan) | funny(susan)) [flattening 73]
75. ((~creative(susan) & ~funny(susan)) | ! [X0] : (strong(X0) & wise(X0))) & (? [X1] : (~strong(X1) | ~wise(X1)) | creative(susan) | funny(susan)) [rectify 74]
76. ? [X1] : (~strong(X1) | ~wise(X1)) => (~strong(sK8) | ~wise(sK8)) [choice axiom]
77. ((~creative(susan) & ~funny(susan)) | ! [X0] : (strong(X0) & wise(X0))) & ((~strong(sK8) | ~wise(sK8)) | creative(susan) | funny(susan)) [skolemisation 75,76]
94. ~happy(john) | patient(X0) | funny(X0) [cnf transformation 44]
105. ~brave(X0) | kind(X0) [cnf transformation 53]
106. ~kind(X0) | brave(X0) [cnf transformation 53]
107. brave(X0) | ~creative(X0) | kind(X0) | ~patient(X0) [cnf transformation 55]
109. kind(X0) | patient(X0) | creative(X0) [cnf transformation 55]
112. ~kind(X0) | ~patient(X0) | ~brave(X0) [cnf transformation 55]
121. ~creative(X0) | patient(X0) | happy(X0) [cnf transformation 35]
127. ~wise(X0) | creative(X0) | ~wise(X0) [cnf transformation 68]
131. funny(X0) | rich(X0) | creative(X0) [cnf transformation 70]
139. ~patient(X0) | ~rich(X0) [cnf transformation 38]
143. ~creative(susan) | wise(X0) [cnf transformation 77]
149. ~funny(susan) [cnf transformation 20]
154. ~brave(susan) [cnf transformation 24]
155. ~wise(X0) | creative(X0) [duplicate literal removal 127]
188. 8 <=> ! [X0] : (patient(X0) | funny(X0)) [avatar definition]
189. patient(X0) | funny(X0) <- (8) [avatar component clause 188]
191. 9 <=> happy(john) [avatar definition]
193. ~happy(john) <- (~9) [avatar component clause 191]
194. 8 | ~9 [avatar split clause 94,191,188]
250. ~brave(X0) | ~patient(X0) [subsumption resolution 112,105]
251. brave(X0) | ~creative(X0) | ~patient(X0) [subsumption resolution 107,106]
252. ~creative(X0) | ~patient(X0) [subsumption resolution 251,250]
275. ~creative(X0) | happy(X0) [subsumption resolution 121,252]
310. 35 <=> creative(susan) [avatar definition]
312. ~creative(susan) <- (~35) [avatar component clause 310]
315. 36 <=> ! [X0] : wise(X0) [avatar definition]
316. wise(X0) <- (36) [avatar component clause 315]
317. 36 | ~35 [avatar split clause 143,310,315]
319. 37 <=> funny(susan) [avatar definition]
321. ~funny(susan) <- (~37) [avatar component clause 319]
333. ~37 [avatar split clause 149,319]
361. brave(X0) | creative(X0) | patient(X0) [resolution 109,106]
414. rich(susan) | creative(susan) <- (~37) [resolution 131,321]
416. rich(susan) <- (~35, ~37) [subsumption resolution 414,312]
422. creative(susan) | patient(susan) [resolution 361,154]
425. patient(susan) <- (~35) [subsumption resolution 422,312]
472. ~rich(susan) <- (~35) [resolution 425,139]
487. $false <- (~35, ~37) [subsumption resolution 472,416]
488. 35 | 37 [avatar contradiction clause 487]
504. creative(X0) <- (36) [resolution 316,155]
507. happy(X0) <- (36) [resolution 504,275]
508. ~patient(X1) <- (36) [resolution 504,252]
518. $false <- (~9, 36) [resolution 507,193]
519. 9 | ~36 [avatar contradiction clause 518]
520. funny(X0) <- (8, 36) [subsumption resolution 189,508]
521. $false <- (8, 36, ~37) [resolution 520,321]
524. ~8 | ~36 | 37 [avatar contradiction clause 521]
526. $false [avatar sat refutation 194,317,333,488,519,524]
% SZS output end Proof for 629700145186044139868682
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not wise and not curious then someone is either not strong or not generous.
Everyone who is funny or not curious is wise and vice versa.
Everyone who is rich is not wise or not patient.
Everyone who is humble is either not rich or not old.
Everyone who is either not creative or old is humble or funny and vice versa.
Everyone who is both not humble and not curious is both tall and not strong and vice versa.
If lucy is not quiet then someone is wise and vice versa.
Everyone who is either strong or not funny is not calm and vice versa.
If someone is either not humble or brave then someone is not creative or quiet.
If fred is patient then lucy is calm or not creative and vice versa.
Everyone who is either not generous or not old is both kind and curious.
Everyone who is not rich or old is either not tall or creative.
If susan is both not tall and funny then someone is both not curious and kind and vice versa.
Everyone who is either rich or not brave is either happy or not curious and vice versa.
Everyone who is not tall or humble is tall or calm and vice versa.
Everyone who is rich or not rich is either tall or patient and vice versa.
Susan is not funny or brave.
Fred is funny or humble.
Fred is either not creative or not patient.
Someone is quiet or brave.
Mary is either not kind or not strong.
Susan is both kind and old.
Someone is strong.
Someone is both not curious and rich. | Mary is wise. | neutral | (((~wise(mary)&~curious(mary)))=>(?[X]:((~strong(X)<~>~generous(X)))))&
(![X]:((funny(X)|~curious(X))<=>wise(X)))&
(![X]:(rich(X)=>(~wise(X)|~patient(X))))&
(![X]:(humble(X)=>(~rich(X)<~>~old(X))))&
(![X]:((~creative(X)<~>old(X))<=>(humble(X)|funny(X))))&
(![X]:((~humble(X)&~curious(X))<=>(tall(X)&~strong(X))))&
((~quiet(lucy))<=>(?[X]:(wise(X))))&
(![X]:((strong(X)<~>~funny(X))<=>~calm(X)))&
((?[X]:((~humble(X)<~>brave(X))))=>(?[X]:((~creative(X)|quiet(X)))))&
((patient(fred))<=>((calm(lucy)|~creative(lucy))))&
(![X]:((~generous(X)<~>~old(X))=>(kind(X)&curious(X))))&
(![X]:((~rich(X)|old(X))=>(~tall(X)<~>creative(X))))&
(((~tall(susan)&funny(susan)))<=>(?[X]:((~curious(X)&kind(X)))))&
(![X]:((rich(X)<~>~brave(X))<=>(happy(X)<~>~curious(X))))&
(![X]:((~tall(X)|humble(X))<=>(tall(X)|calm(X))))&
(![X]:((rich(X)|~rich(X))<=>(tall(X)<~>patient(X))))&
((~funny(susan)|brave(susan)))&
((funny(fred)|humble(fred)))&
((~creative(fred)<~>~patient(fred)))&
(?[X]:((quiet(X)|brave(X))))&
((~kind(mary)<~>~strong(mary)))&
((kind(susan)&old(susan)))&
(?[X]:(strong(X)))&
(?[X]:((~curious(X)&rich(X)))) | wise(mary) | [] | null | 0 |
If alice is not happy or old then someone is either happy or not tall. If someone is either not curious or calm then fred is both patient and strong. If mary is either not quiet or not strong then someone is either creative or curious. Everyone who is strong is not tall. If someone is happy or calm then mary is not quiet. Everyone who is not curious or not calm is both not curious and funny and vice versa. Everyone who is curious or humble is both kind and not creative. Everyone who is both creative and not brave is not funny and vice versa. Everyone who is both creative and calm is wise or not rich and vice versa. If someone is not tall or patient then mary is both wise and curious and vice versa. Everyone who is either not kind or not curious is humble. If alice is both tall and generous then someone is either not rich or not wise and vice versa. Everyone who is either generous or humble is both not calm and patient and vice versa. Everyone who is both not curious and not funny is either strong or not humble and vice versa. If lucy is either not creative or not old then fred is both kind and not wise and vice versa. If someone is both not calm and funny then someone is strong or quiet. Someone is not patient. Susan is both not happy and kind. Someone is rich. Someone is brave or wise. Lucy is both old and tall. | Alice is not humble. | contradiction | (((~happy(alice)|old(alice)))=>(?[X]:((happy(X)<~>~tall(X)))))&
((?[X]:((~curious(X)<~>calm(X))))=>((patient(fred)&strong(fred))))&
(((~quiet(mary)<~>~strong(mary)))=>(?[X]:((creative(X)<~>curious(X)))))&
(![X]:(strong(X)=>~tall(X)))&
((?[X]:((happy(X)|calm(X))))=>(~quiet(mary)))&
(![X]:((~curious(X)|~calm(X))<=>(~curious(X)&funny(X))))&
(![X]:((curious(X)|humble(X))=>(kind(X)&~creative(X))))&
(![X]:((creative(X)&~brave(X))<=>~funny(X)))&
(![X]:((creative(X)&calm(X))<=>(wise(X)|~rich(X))))&
((?[X]:((~tall(X)|patient(X))))<=>((wise(mary)&curious(mary))))&
(![X]:((~kind(X)<~>~curious(X))=>humble(X)))&
(((tall(alice)&generous(alice)))<=>(?[X]:((~rich(X)<~>~wise(X)))))&
(![X]:((generous(X)<~>humble(X))<=>(~calm(X)&patient(X))))&
(![X]:((~curious(X)&~funny(X))<=>(strong(X)<~>~humble(X))))&
(((~creative(lucy)<~>~old(lucy)))<=>((kind(fred)&~wise(fred))))&
((?[X]:((~calm(X)&funny(X))))=>(?[X]:((strong(X)|quiet(X)))))&
(?[X]:(~patient(X)))&
((~happy(susan)&kind(susan)))&
(?[X]:(rich(X)))&
(?[X]:((brave(X)|wise(X))))&
((old(lucy)&tall(lucy))) | ~humble(alice) | [
"p1",
"p5",
"p6",
"p8",
"p9",
"p10",
"p11",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8724102584368227742367367
% SZS output start Proof for 8724102584368227742367367
2. ? [X0] : (~curious(X0) <~> calm(X0)) => (strong(fred) & patient(fred)) [input p1]
6. ! [X0] : ((~calm(X0) | ~curious(X0)) <=> (funny(X0) & ~curious(X0))) [input p5]
7. ! [X0] : ((humble(X0) | curious(X0)) => (~creative(X0) & kind(X0))) [input p6]
9. ! [X0] : ((calm(X0) & creative(X0)) <=> (~rich(X0) | wise(X0))) [input p8]
10. ? [X0] : (patient(X0) | ~tall(X0)) <=> (curious(mary) & wise(mary)) [input p9]
11. ! [X0] : ((~kind(X0) <~> ~curious(X0)) => humble(X0)) [input p10]
12. (generous(alice) & tall(alice)) <=> ? [X0] : (~rich(X0) <~> ~wise(X0)) [input p11]
13. ! [X0] : ((generous(X0) <~> humble(X0)) <=> (patient(X0) & ~calm(X0))) [input p12]
18. kind(susan) & ~happy(susan) [input p17]
22. ~humble(alice) [input hypothesis]
25. (strong(fred) & patient(fred)) | ! [X0] : (~curious(X0) <=> calm(X0)) [ennf transformation 2]
29. ! [X0] : ((~creative(X0) & kind(X0)) | (~humble(X0) & ~curious(X0))) [ennf transformation 7]
30. ! [X0] : (humble(X0) | (~kind(X0) <=> ~curious(X0))) [ennf transformation 11]
35. (strong(fred) & patient(fred)) | ! [X0] : ((~curious(X0) | ~calm(X0)) & (calm(X0) | curious(X0))) [nnf transformation 25]
39. ! [X0] : (((~calm(X0) | ~curious(X0)) | (~funny(X0) | curious(X0))) & ((funny(X0) & ~curious(X0)) | (calm(X0) & curious(X0)))) [nnf transformation 6]
40. ! [X0] : ((~calm(X0) | ~curious(X0) | ~funny(X0) | curious(X0)) & ((funny(X0) & ~curious(X0)) | (calm(X0) & curious(X0)))) [flattening 39]
43. ! [X0] : (((calm(X0) & creative(X0)) | (rich(X0) & ~wise(X0))) & ((~rich(X0) | wise(X0)) | (~calm(X0) | ~creative(X0)))) [nnf transformation 9]
44. ! [X0] : (((calm(X0) & creative(X0)) | (rich(X0) & ~wise(X0))) & (~rich(X0) | wise(X0) | ~calm(X0) | ~creative(X0))) [flattening 43]
45. (? [X0] : (patient(X0) | ~tall(X0)) | (~curious(mary) | ~wise(mary))) & ((curious(mary) & wise(mary)) | ! [X0] : (~patient(X0) & tall(X0))) [nnf transformation 10]
46. (? [X0] : (patient(X0) | ~tall(X0)) | ~curious(mary) | ~wise(mary)) & ((curious(mary) & wise(mary)) | ! [X0] : (~patient(X0) & tall(X0))) [flattening 45]
47. (? [X0] : (patient(X0) | ~tall(X0)) | ~curious(mary) | ~wise(mary)) & ((curious(mary) & wise(mary)) | ! [X1] : (~patient(X1) & tall(X1))) [rectify 46]
48. ? [X0] : (patient(X0) | ~tall(X0)) => (patient(sK2) | ~tall(sK2)) [choice axiom]
49. ((patient(sK2) | ~tall(sK2)) | ~curious(mary) | ~wise(mary)) & ((curious(mary) & wise(mary)) | ! [X1] : (~patient(X1) & tall(X1))) [skolemisation 47,48]
50. ! [X0] : (humble(X0) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0)))) [nnf transformation 30]
51. ((generous(alice) & tall(alice)) | ! [X0] : ((~rich(X0) | wise(X0)) & (~wise(X0) | rich(X0)))) & (? [X0] : ((wise(X0) | rich(X0)) & (~wise(X0) | ~rich(X0))) | (~generous(alice) | ~tall(alice))) [nnf transformation 12]
52. ((generous(alice) & tall(alice)) | ! [X0] : ((~rich(X0) | wise(X0)) & (~wise(X0) | rich(X0)))) & (? [X0] : ((wise(X0) | rich(X0)) & (~wise(X0) | ~rich(X0))) | ~generous(alice) | ~tall(alice)) [flattening 51]
53. ((generous(alice) & tall(alice)) | ! [X0] : ((~rich(X0) | wise(X0)) & (~wise(X0) | rich(X0)))) & (? [X1] : ((wise(X1) | rich(X1)) & (~wise(X1) | ~rich(X1))) | ~generous(alice) | ~tall(alice)) [rectify 52]
54. ? [X1] : ((wise(X1) | rich(X1)) & (~wise(X1) | ~rich(X1))) => ((wise(sK3) | rich(sK3)) & (~wise(sK3) | ~rich(sK3))) [choice axiom]
55. ((generous(alice) & tall(alice)) | ! [X0] : ((~rich(X0) | wise(X0)) & (~wise(X0) | rich(X0)))) & (((wise(sK3) | rich(sK3)) & (~wise(sK3) | ~rich(sK3))) | ~generous(alice) | ~tall(alice)) [skolemisation 53,54]
56. ! [X0] : ((((~humble(X0) | ~generous(X0)) & (humble(X0) | generous(X0))) | (~patient(X0) | calm(X0))) & ((patient(X0) & ~calm(X0)) | ((generous(X0) | ~humble(X0)) & (humble(X0) | ~generous(X0))))) [nnf transformation 13]
57. ! [X0] : ((((~humble(X0) | ~generous(X0)) & (humble(X0) | generous(X0))) | ~patient(X0) | calm(X0)) & ((patient(X0) & ~calm(X0)) | ((generous(X0) | ~humble(X0)) & (humble(X0) | ~generous(X0))))) [flattening 56]
75. patient(fred) | calm(X0) | curious(X0) [cnf transformation 35]
76. patient(fred) | ~curious(X0) | ~calm(X0) [cnf transformation 35]
87. ~curious(X0) | calm(X0) [cnf transformation 40]
93. ~creative(X0) | ~curious(X0) [cnf transformation 29]
94. ~humble(X0) | ~creative(X0) [cnf transformation 29]
99. ~wise(X0) | creative(X0) [cnf transformation 44]
100. rich(X0) | creative(X0) [cnf transformation 44]
104. wise(mary) | ~patient(X1) [cnf transformation 49]
106. curious(mary) | ~patient(X1) [cnf transformation 49]
109. ~kind(X0) | humble(X0) | curious(X0) [cnf transformation 50]
115. generous(alice) | ~rich(X0) | wise(X0) [cnf transformation 55]
116. ~generous(X0) | humble(X0) | ~calm(X0) [cnf transformation 57]
137. kind(susan) [cnf transformation 18]
142. ~humble(alice) [cnf transformation 22]
164. 5 <=> ! [X0] : (~curious(X0) | ~calm(X0)) [avatar definition]
165. ~curious(X0) | ~calm(X0) <- (5) [avatar component clause 164]
172. 7 <=> ! [X0] : (calm(X0) | curious(X0)) [avatar definition]
173. calm(X0) | curious(X0) <- (7) [avatar component clause 172]
176. 8 <=> patient(fred) [avatar definition]
178. patient(fred) <- (8) [avatar component clause 176]
179. 5 | 8 [avatar split clause 76,176,164]
180. 7 | 8 [avatar split clause 75,176,172]
210. 15 <=> wise(mary) [avatar definition]
211. wise(mary) <- (15) [avatar component clause 210]
214. 16 <=> curious(mary) [avatar definition]
215. curious(mary) <- (16) [avatar component clause 214]
227. 19 <=> ! [X1] : ~patient(X1) [avatar definition]
228. ~patient(X1) <- (19) [avatar component clause 227]
229. 19 | 16 [avatar split clause 106,214,227]
234. 19 | 15 [avatar split clause 104,210,227]
237. 21 <=> ! [X0] : (~rich(X0) | wise(X0)) [avatar definition]
238. ~rich(X0) | wise(X0) <- (21) [avatar component clause 237]
240. 22 <=> generous(alice) [avatar definition]
242. generous(alice) <- (22) [avatar component clause 240]
243. 21 | 22 [avatar split clause 115,240,237]
288. 31 <=> ! [X1] : calm(X1) [avatar definition]
289. calm(X1) <- (31) [avatar component clause 288]
316. creative(mary) <- (15) [resolution 99,211]
317. ~curious(mary) <- (15) [resolution 316,93]
318. $false <- (15, 16) [subsumption resolution 317,215]
319. ~15 | ~16 [avatar contradiction clause 318]
320. $false <- (8, 19) [resolution 228,178]
321. ~8 | ~19 [avatar contradiction clause 320]
322. calm(X0) <- (7) [subsumption resolution 173,87]
323. 31 | ~7 [avatar split clause 322,172,288]
324. ~curious(X0) <- (5) [subsumption resolution 165,87]
338. wise(X1) | creative(X1) <- (21) [resolution 238,100]
339. creative(X1) <- (21) [subsumption resolution 338,99]
353. humble(susan) | curious(susan) [resolution 109,137]
354. humble(susan) <- (5) [subsumption resolution 353,324]
355. ~creative(susan) <- (5) [resolution 354,94]
357. $false <- (5, 21) [subsumption resolution 355,339]
358. ~5 | ~21 [avatar contradiction clause 357]
361. humble(alice) | ~calm(alice) <- (22) [resolution 116,242]
362. ~calm(alice) <- (22) [subsumption resolution 361,142]
363. $false <- (22, 31) [subsumption resolution 362,289]
364. ~22 | ~31 [avatar contradiction clause 363]
365. $false [avatar sat refutation 179,180,229,234,243,319,321,323,358,364]
% SZS output end Proof for 8724102584368227742367367
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is strong or calm. Everyone who is not brave is either not rich or brave and vice versa. Everyone who is either not brave or old is tall or not happy. Everyone who is creative is either not quiet or not patient and vice versa. If fred is either not happy or funny then mary is calm or patient. If someone is either wise or not wise then lucy is not kind or old and vice versa. Everyone who is not strong or not curious is both strong and wise. If someone is either not patient or not rich then someone is wise and vice versa. If alice is both not brave and not kind then someone is not humble or not happy. Everyone who is not funny or not generous is both brave and generous. Everyone who is either not generous or kind is both calm and patient. Everyone who is rich is both not tall and kind and vice versa. If someone is strong then susan is old or calm and vice versa. Everyone who is both curious and calm is funny. If someone is funny or not happy then someone is either not quiet or tall and vice versa. Everyone who is brave is either creative or tall. Someone is not wise. Someone is either not generous or not humble. Someone is strong. Someone is both not tall and not kind. Someone is both generous and not humble. Someone is both not quiet and strong. Someone is calm or strong. | Mary is generous. | entailment | (![X]:(~strong(X)=>(strong(X)|calm(X))))&
(![X]:(~brave(X)<=>(~rich(X)<~>brave(X))))&
(![X]:((~brave(X)<~>old(X))=>(tall(X)|~happy(X))))&
(![X]:(creative(X)<=>(~quiet(X)<~>~patient(X))))&
(((~happy(fred)<~>funny(fred)))=>((calm(mary)|patient(mary))))&
((?[X]:((wise(X)<~>~wise(X))))<=>((~kind(lucy)|old(lucy))))&
(![X]:((~strong(X)|~curious(X))=>(strong(X)&wise(X))))&
((?[X]:((~patient(X)<~>~rich(X))))<=>(?[X]:(wise(X))))&
(((~brave(alice)&~kind(alice)))=>(?[X]:((~humble(X)|~happy(X)))))&
(![X]:((~funny(X)|~generous(X))=>(brave(X)&generous(X))))&
(![X]:((~generous(X)<~>kind(X))=>(calm(X)&patient(X))))&
(![X]:(rich(X)<=>(~tall(X)&kind(X))))&
((?[X]:(strong(X)))<=>((old(susan)|calm(susan))))&
(![X]:((curious(X)&calm(X))=>funny(X)))&
((?[X]:((funny(X)|~happy(X))))<=>(?[X]:((~quiet(X)<~>tall(X)))))&
(![X]:(brave(X)=>(creative(X)<~>tall(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~generous(X)<~>~humble(X))))&
(?[X]:(strong(X)))&
(?[X]:((~tall(X)&~kind(X))))&
(?[X]:((generous(X)&~humble(X))))&
(?[X]:((~quiet(X)&strong(X))))&
(?[X]:((calm(X)|strong(X)))) | generous(mary) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8996313504575949791485942
% SZS output start Proof for 8996313504575949791485942
10. ! [X0] : ((~generous(X0) | ~funny(X0)) => (generous(X0) & brave(X0))) [input p9]
24. ~generous(mary) [input hypothesis]
36. ! [X0] : ((generous(X0) & brave(X0)) | (generous(X0) & funny(X0))) [ennf transformation 10]
117. generous(X0) | generous(X0) [cnf transformation 36]
148. ~generous(mary) [cnf transformation 24]
149. generous(X0) [duplicate literal removal 117]
271. $false [subsumption resolution 148,149]
% SZS output end Proof for 8996313504575949791485942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not creative then someone is wise. Everyone who is funny or patient is old and vice versa. Everyone who is rich or not quiet is not happy or generous and vice versa. Everyone who is both not funny and strong is not brave. If someone is both not generous and not patient then john is happy. If someone is either old or not rich then lucy is both not old and tall and vice versa. Everyone who is funny or not brave is either not funny or not curious and vice versa. Everyone who is not humble is not rich or generous and vice versa. If paul is either calm or not happy then john is curious or not brave and vice versa. Everyone who is funny is both not creative and not curious. If mary is both not kind and humble then someone is generous and vice versa. Everyone who is both rich and creative is both not rich and patient. Everyone who is not curious is not funny and vice versa. Everyone who is old or not rich is either rich or not wise. Alice is tall. Mary is either wise or tall. Paul is not strong. Someone is both not strong and tall. John is not funny. Someone is not creative or not happy. | John is not happy. | neutral | ((?[X]:((~funny(X)|~creative(X))))=>(?[X]:(wise(X))))&
(![X]:((funny(X)|patient(X))<=>old(X)))&
(![X]:((rich(X)|~quiet(X))<=>(~happy(X)|generous(X))))&
(![X]:((~funny(X)&strong(X))=>~brave(X)))&
((?[X]:((~generous(X)&~patient(X))))=>(happy(john)))&
((?[X]:((old(X)<~>~rich(X))))<=>((~old(lucy)&tall(lucy))))&
(![X]:((funny(X)|~brave(X))<=>(~funny(X)<~>~curious(X))))&
(![X]:(~humble(X)<=>(~rich(X)|generous(X))))&
(((calm(paul)<~>~happy(paul)))<=>((curious(john)|~brave(john))))&
(![X]:(funny(X)=>(~creative(X)&~curious(X))))&
(((~kind(mary)&humble(mary)))<=>(?[X]:(generous(X))))&
(![X]:((rich(X)&creative(X))=>(~rich(X)&patient(X))))&
(![X]:(~curious(X)<=>~funny(X)))&
(![X]:((old(X)|~rich(X))=>(rich(X)<~>~wise(X))))&
(tall(alice))&
((wise(mary)<~>tall(mary)))&
(~strong(paul))&
(?[X]:((~strong(X)&tall(X))))&
(~funny(john))&
(?[X]:((~creative(X)|~happy(X)))) | ~happy(john) | [] | null | 0 |
Everyone who is both strong and kind is funny. If someone is not brave then someone is not curious and vice versa. Everyone who is not calm is both tall and creative and vice versa. If someone is not creative then someone is either not quiet or not old. If susan is both not quiet and not kind then someone is either not rich or tall and vice versa. If paul is not humble then someone is not old or patient. If fred is brave then fred is either not happy or creative and vice versa. Everyone who is calm or not happy is not happy. If someone is not rich then susan is happy. Everyone who is both generous and humble is both not quiet and not rich. If someone is rich then john is not tall or not generous and vice versa. Everyone who is not curious is happy or not quiet and vice versa. If alice is strong or generous then susan is either not rich or not curious and vice versa. If alice is not humble then paul is not quiet or not strong. If someone is either not patient or curious then john is not brave. If someone is both not creative and not calm then someone is both not generous and not curious and vice versa. Someone is both humble and not creative. Someone is not curious. Someone is old or not quiet. Lucy is not rich. Someone is either not old or not strong. Someone is tall or brave. Someone is both funny and not kind. Someone is funny or not patient. | Susan is creative. | entailment | (![X]:((strong(X)&kind(X))=>funny(X)))&
((?[X]:(~brave(X)))<=>(?[X]:(~curious(X))))&
(![X]:(~calm(X)<=>(tall(X)&creative(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~quiet(X)<~>~old(X)))))&
(((~quiet(susan)&~kind(susan)))<=>(?[X]:((~rich(X)<~>tall(X)))))&
((~humble(paul))=>(?[X]:((~old(X)|patient(X)))))&
((brave(fred))<=>((~happy(fred)<~>creative(fred))))&
(![X]:((calm(X)|~happy(X))=>~happy(X)))&
((?[X]:(~rich(X)))=>(happy(susan)))&
(![X]:((generous(X)&humble(X))=>(~quiet(X)&~rich(X))))&
((?[X]:(rich(X)))<=>((~tall(john)|~generous(john))))&
(![X]:(~curious(X)<=>(happy(X)|~quiet(X))))&
(((strong(alice)|generous(alice)))<=>((~rich(susan)<~>~curious(susan))))&
((~humble(alice))=>((~quiet(paul)|~strong(paul))))&
((?[X]:((~patient(X)<~>curious(X))))=>(~brave(john)))&
((?[X]:((~creative(X)&~calm(X))))<=>(?[X]:((~generous(X)&~curious(X)))))&
(?[X]:((humble(X)&~creative(X))))&
(?[X]:(~curious(X)))&
(?[X]:((old(X)|~quiet(X))))&
(~rich(lucy))&
(?[X]:((~old(X)<~>~strong(X))))&
(?[X]:((tall(X)|brave(X))))&
(?[X]:((funny(X)&~kind(X))))&
(?[X]:((funny(X)|~patient(X)))) | creative(susan) | [
"p2",
"p7",
"p8",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4441097162458928900481533
% SZS output start Proof for 4441097162458928900481533
3. ! [X0] : (~calm(X0) <=> (creative(X0) & tall(X0))) [input p2]
8. ! [X0] : ((~happy(X0) | calm(X0)) => ~happy(X0)) [input p7]
9. ? [X0] : ~rich(X0) => happy(susan) [input p8]
20. ~rich(lucy) [input p19]
25. ~creative(susan) [input hypothesis]
34. ! [X0] : (~happy(X0) | (happy(X0) & ~calm(X0))) [ennf transformation 8]
35. happy(susan) | ! [X0] : rich(X0) [ennf transformation 9]
46. ! [X0] : ((~calm(X0) | (~creative(X0) | ~tall(X0))) & ((creative(X0) & tall(X0)) | calm(X0))) [nnf transformation 3]
47. ! [X0] : ((~calm(X0) | ~creative(X0) | ~tall(X0)) & ((creative(X0) & tall(X0)) | calm(X0))) [flattening 46]
91. creative(X0) | calm(X0) [cnf transformation 47]
106. ~happy(X0) | ~calm(X0) [cnf transformation 34]
108. happy(susan) | rich(X0) [cnf transformation 35]
134. ~rich(lucy) [cnf transformation 20]
139. ~creative(susan) [cnf transformation 25]
227. 20 <=> ! [X0] : rich(X0) [avatar definition]
228. rich(X0) <- (20) [avatar component clause 227]
230. 21 <=> happy(susan) [avatar definition]
232. happy(susan) <- (21) [avatar component clause 230]
233. 20 | 21 [avatar split clause 108,230,227]
347. $false <- (20) [resolution 228,134]
348. ~20 [avatar contradiction clause 347]
352. calm(susan) [resolution 91,139]
357. ~calm(susan) <- (21) [resolution 106,232]
358. $false <- (21) [subsumption resolution 357,352]
359. ~21 [avatar contradiction clause 358]
360. $false [avatar sat refutation 233,348,359]
% SZS output end Proof for 4441097162458928900481533
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either old or tall then someone is not brave.
Everyone who is happy is not patient and vice versa.
Everyone who is happy or not old is not curious.
Everyone who is both brave and happy is both rich and not funny and vice versa.
If someone is both not patient and not rich then someone is generous.
Everyone who is not kind is funny and vice versa.
Everyone who is humble is either old or not brave and vice versa.
If someone is either not humble or not rich then someone is both not humble and humble.
If john is brave then someone is both generous and creative and vice versa.
If john is not patient then lucy is funny and vice versa.
If fred is either tall or strong then someone is not curious and vice versa.
Everyone who is both happy and not old is creative and vice versa.
Everyone who is either old or not creative is not curious or not brave and vice versa.
If someone is either not strong or strong then someone is either not quiet or wise.
If someone is not kind then alice is curious and vice versa.
If someone is not generous or strong then someone is not generous.
Someone is not happy or not brave.
Someone is generous.
John is calm or not strong.
Paul is not calm or not creative.
Someone is humble or not brave.
Lucy is either not quiet or kind.
Paul is not generous or humble.
John is rich. | John is humble. | entailment | (((old(mary)<~>tall(mary)))=>(?[X]:(~brave(X))))&
(![X]:(happy(X)<=>~patient(X)))&
(![X]:((happy(X)|~old(X))=>~curious(X)))&
(![X]:((brave(X)&happy(X))<=>(rich(X)&~funny(X))))&
((?[X]:((~patient(X)&~rich(X))))=>(?[X]:(generous(X))))&
(![X]:(~kind(X)<=>funny(X)))&
(![X]:(humble(X)<=>(old(X)<~>~brave(X))))&
((?[X]:((~humble(X)<~>~rich(X))))=>(?[X]:((~humble(X)&humble(X)))))&
((brave(john))<=>(?[X]:((generous(X)&creative(X)))))&
((~patient(john))<=>(funny(lucy)))&
(((tall(fred)<~>strong(fred)))<=>(?[X]:(~curious(X))))&
(![X]:((happy(X)&~old(X))<=>creative(X)))&
(![X]:((old(X)<~>~creative(X))<=>(~curious(X)|~brave(X))))&
((?[X]:((~strong(X)<~>strong(X))))=>(?[X]:((~quiet(X)<~>wise(X)))))&
((?[X]:(~kind(X)))<=>(curious(alice)))&
((?[X]:((~generous(X)|strong(X))))=>(?[X]:(~generous(X))))&
(?[X]:((~happy(X)|~brave(X))))&
(?[X]:(generous(X)))&
((calm(john)|~strong(john)))&
((~calm(paul)|~creative(paul)))&
(?[X]:((humble(X)|~brave(X))))&
((~quiet(lucy)<~>kind(lucy)))&
((~generous(paul)|humble(paul)))&
(rich(john)) | humble(john) | [
"p7",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3062326525538076829438527
% SZS output start Proof for 3062326525538076829438527
8. ? [X0] : (~humble(X0) <~> ~rich(X0)) => ? [X0] : (humble(X0) & ~humble(X0)) [input p7]
24. rich(john) [input p23]
25. ~humble(john) [input hypothesis]
27. ? [X0] : (~humble(X0) <~> ~rich(X0)) => ? [X1] : (humble(X1) & ~humble(X1)) [rectify 8]
33. ? [X1] : (humble(X1) & ~humble(X1)) | ! [X0] : (~humble(X0) <=> ~rich(X0)) [ennf transformation 27]
47. ? [X1] : (humble(X1) & ~humble(X1)) | ! [X0] : ((~humble(X0) | rich(X0)) & (~rich(X0) | humble(X0))) [nnf transformation 33]
48. ? [X0] : (humble(X0) & ~humble(X0)) | ! [X1] : ((~humble(X1) | rich(X1)) & (~rich(X1) | humble(X1))) [rectify 47]
49. ? [X0] : (humble(X0) & ~humble(X0)) => (humble(sK2) & ~humble(sK2)) [choice axiom]
50. (humble(sK2) & ~humble(sK2)) | ! [X1] : ((~humble(X1) | rich(X1)) & (~rich(X1) | humble(X1))) [skolemisation 48,49]
99. ~humble(sK2) | ~rich(X1) | humble(X1) [cnf transformation 50]
101. humble(sK2) | ~rich(X1) | humble(X1) [cnf transformation 50]
137. rich(john) [cnf transformation 24]
138. ~humble(john) [cnf transformation 25]
169. 7 <=> humble(sK2) [avatar definition]
174. 8 <=> ! [X1] : (~rich(X1) | humble(X1)) [avatar definition]
175. ~rich(X1) | humble(X1) <- (8) [avatar component clause 174]
176. 8 | 7 [avatar split clause 101,169,174]
178. 8 | ~7 [avatar split clause 99,169,174]
334. humble(john) <- (8) [resolution 175,137]
336. $false <- (8) [subsumption resolution 334,138]
337. ~8 [avatar contradiction clause 336]
338. $false [avatar sat refutation 176,178,337]
% SZS output end Proof for 3062326525538076829438527
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and not kind is not kind. If someone is curious or not strong then paul is both not kind and not rich. Everyone who is both not tall and strong is either patient or humble and vice versa. Everyone who is generous or quiet is not quiet and vice versa. Everyone who is not old is both happy and not humble. If susan is not generous or not patient then lucy is not tall or not curious and vice versa. Everyone who is not patient is either not curious or tall and vice versa. Everyone who is not tall is either not quiet or not happy. Everyone who is either quiet or rich is both not creative and not strong. Everyone who is both tall and not curious is either not patient or happy. Everyone who is either creative or wise is calm and vice versa. If susan is not generous or not humble then someone is either not old or not patient. Everyone who is brave or not generous is both not tall and not old and vice versa. Everyone who is not generous is both not humble and funny and vice versa. Everyone who is both wise and rich is both kind and old. If someone is either not happy or not old then someone is rich or not funny. Alice is both not calm and not brave. Alice is both not old and not funny. Mary is either curious or strong. Someone is old. Fred is not curious or funny. Mary is either not patient or not funny. Alice is both not creative and kind. | Mary is not happy. | contradiction | (![X]:((rich(X)&~kind(X))=>~kind(X)))&
((?[X]:((curious(X)|~strong(X))))=>((~kind(paul)&~rich(paul))))&
(![X]:((~tall(X)&strong(X))<=>(patient(X)<~>humble(X))))&
(![X]:((generous(X)|quiet(X))<=>~quiet(X)))&
(![X]:(~old(X)=>(happy(X)&~humble(X))))&
(((~generous(susan)|~patient(susan)))<=>((~tall(lucy)|~curious(lucy))))&
(![X]:(~patient(X)<=>(~curious(X)<~>tall(X))))&
(![X]:(~tall(X)=>(~quiet(X)<~>~happy(X))))&
(![X]:((quiet(X)<~>rich(X))=>(~creative(X)&~strong(X))))&
(![X]:((tall(X)&~curious(X))=>(~patient(X)<~>happy(X))))&
(![X]:((creative(X)<~>wise(X))<=>calm(X)))&
(((~generous(susan)|~humble(susan)))=>(?[X]:((~old(X)<~>~patient(X)))))&
(![X]:((brave(X)|~generous(X))<=>(~tall(X)&~old(X))))&
(![X]:(~generous(X)<=>(~humble(X)&funny(X))))&
(![X]:((wise(X)&rich(X))=>(kind(X)&old(X))))&
((?[X]:((~happy(X)<~>~old(X))))=>(?[X]:((rich(X)|~funny(X)))))&
((~calm(alice)&~brave(alice)))&
((~old(alice)&~funny(alice)))&
((curious(mary)<~>strong(mary)))&
(?[X]:(old(X)))&
((~curious(fred)|funny(fred)))&
((~patient(mary)<~>~funny(mary)))&
((~creative(alice)&kind(alice))) | ~happy(mary) | [
"p2",
"p3",
"p4",
"p6",
"p7",
"p9",
"p12",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 906066332396797072516313
% SZS output start Proof for 906066332396797072516313
3. ! [X0] : ((strong(X0) & ~tall(X0)) <=> (patient(X0) <~> humble(X0))) [input p2]
4. ! [X0] : ((quiet(X0) | generous(X0)) <=> ~quiet(X0)) [input p3]
5. ! [X0] : (~old(X0) => (~humble(X0) & happy(X0))) [input p4]
7. ! [X0] : (~patient(X0) <=> (~curious(X0) <~> tall(X0))) [input p6]
8. ! [X0] : (~tall(X0) => (~quiet(X0) <~> ~happy(X0))) [input p7]
10. ! [X0] : ((~curious(X0) & tall(X0)) => (~patient(X0) <~> happy(X0))) [input p9]
13. ! [X0] : ((~generous(X0) | brave(X0)) <=> (~old(X0) & ~tall(X0))) [input p12]
14. ! [X0] : (~generous(X0) <=> (funny(X0) & ~humble(X0))) [input p13]
22. ~patient(mary) <~> ~funny(mary) [input p21]
24. ~happy(mary) [input hypothesis]
30. ! [X0] : ((~humble(X0) & happy(X0)) | old(X0)) [ennf transformation 5]
31. ! [X0] : ((~quiet(X0) <~> ~happy(X0)) | tall(X0)) [ennf transformation 8]
33. ! [X0] : ((~patient(X0) <~> happy(X0)) | (curious(X0) | ~tall(X0))) [ennf transformation 10]
34. ! [X0] : ((~patient(X0) <~> happy(X0)) | curious(X0) | ~tall(X0)) [flattening 33]
40. ! [X0] : (((strong(X0) & ~tall(X0)) | ((patient(X0) | ~humble(X0)) & (humble(X0) | ~patient(X0)))) & (((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | (~strong(X0) | tall(X0)))) [nnf transformation 3]
41. ! [X0] : (((strong(X0) & ~tall(X0)) | ((patient(X0) | ~humble(X0)) & (humble(X0) | ~patient(X0)))) & (((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | ~strong(X0) | tall(X0))) [flattening 40]
42. ! [X0] : (((quiet(X0) | generous(X0)) | quiet(X0)) & (~quiet(X0) | (~quiet(X0) & ~generous(X0)))) [nnf transformation 4]
43. ! [X0] : ((quiet(X0) | generous(X0) | quiet(X0)) & (~quiet(X0) | (~quiet(X0) & ~generous(X0)))) [flattening 42]
46. ! [X0] : ((~patient(X0) | ((~curious(X0) | ~tall(X0)) & (tall(X0) | curious(X0)))) & (((~tall(X0) | curious(X0)) & (tall(X0) | ~curious(X0))) | patient(X0))) [nnf transformation 7]
47. ! [X0] : (((happy(X0) | quiet(X0)) & (~happy(X0) | ~quiet(X0))) | tall(X0)) [nnf transformation 31]
49. ! [X0] : (((~happy(X0) | patient(X0)) & (happy(X0) | ~patient(X0))) | curious(X0) | ~tall(X0)) [nnf transformation 34]
54. ! [X0] : (((~generous(X0) | brave(X0)) | (old(X0) | tall(X0))) & ((~old(X0) & ~tall(X0)) | (generous(X0) & ~brave(X0)))) [nnf transformation 13]
55. ! [X0] : ((~generous(X0) | brave(X0) | old(X0) | tall(X0)) & ((~old(X0) & ~tall(X0)) | (generous(X0) & ~brave(X0)))) [flattening 54]
56. ! [X0] : ((~generous(X0) | (~funny(X0) | humble(X0))) & ((funny(X0) & ~humble(X0)) | generous(X0))) [nnf transformation 14]
57. ! [X0] : ((~generous(X0) | ~funny(X0) | humble(X0)) & ((funny(X0) & ~humble(X0)) | generous(X0))) [flattening 56]
65. (funny(mary) | patient(mary)) & (~funny(mary) | ~patient(mary)) [nnf transformation 22]
74. ~humble(X0) | patient(X0) | ~tall(X0) [cnf transformation 41]
78. ~quiet(X0) | ~quiet(X0) [cnf transformation 43]
80. happy(X0) | old(X0) [cnf transformation 30]
88. ~patient(X0) | tall(X0) | curious(X0) [cnf transformation 46]
89. ~patient(X0) | ~curious(X0) | ~tall(X0) [cnf transformation 46]
91. happy(X0) | quiet(X0) | tall(X0) [cnf transformation 47]
96. happy(X0) | ~patient(X0) | curious(X0) | ~tall(X0) [cnf transformation 49]
107. ~old(X0) | generous(X0) [cnf transformation 55]
111. ~funny(X0) | ~generous(X0) | humble(X0) [cnf transformation 57]
125. funny(mary) | patient(mary) [cnf transformation 65]
128. ~happy(mary) [cnf transformation 24]
129. ~quiet(X0) [duplicate literal removal 78]
169. happy(X0) | tall(X0) [subsumption resolution 91,129]
172. ~patient(X0) | happy(X0) | curious(X0) [subsumption resolution 96,88]
208. 16 <=> curious(mary) [avatar definition]
210. ~curious(mary) <- (~16) [avatar component clause 208]
227. 20 <=> patient(mary) [avatar definition]
228. ~patient(mary) <- (~20) [avatar component clause 227]
229. patient(mary) <- (20) [avatar component clause 227]
231. 21 <=> funny(mary) [avatar definition]
233. funny(mary) <- (21) [avatar component clause 231]
234. 20 | 21 [avatar split clause 125,231,227]
236. old(mary) [resolution 80,128]
239. generous(mary) [resolution 107,236]
246. tall(mary) [resolution 169,128]
263. ~curious(mary) | ~tall(mary) <- (20) [resolution 89,229]
267. ~curious(mary) <- (20) [subsumption resolution 263,246]
268. ~16 | ~20 [avatar split clause 267,227,208]
271. happy(mary) | curious(mary) <- (20) [resolution 172,229]
272. curious(mary) <- (20) [subsumption resolution 271,128]
273. $false <- (~16, 20) [subsumption resolution 272,210]
274. 16 | ~20 [avatar contradiction clause 273]
280. ~generous(mary) | humble(mary) <- (21) [resolution 233,111]
281. humble(mary) <- (21) [subsumption resolution 280,239]
283. patient(mary) | ~tall(mary) <- (21) [resolution 281,74]
289. ~tall(mary) <- (~20, 21) [subsumption resolution 283,228]
290. $false <- (~20, 21) [subsumption resolution 289,246]
291. 20 | ~21 [avatar contradiction clause 290]
292. $false [avatar sat refutation 234,268,274,291]
% SZS output end Proof for 906066332396797072516313
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and not kind is not happy or not patient. Everyone who is generous is old or calm and vice versa. If someone is not wise or not creative then someone is both happy and not old. If someone is not strong or not funny then fred is brave or not rich. Everyone who is both calm and not tall is funny and vice versa. If someone is either happy or tall then someone is both curious and not calm. If john is both not kind and humble then john is patient or not rich. Everyone who is either not generous or strong is not brave or quiet and vice versa. Everyone who is either generous or strong is not old or not tall. If someone is calm or not rich then someone is quiet or generous and vice versa. Everyone who is either calm or not brave is both old and not curious and vice versa. Everyone who is not patient is either not humble or not patient and vice versa. Everyone who is either not wise or not strong is both not humble and not happy. Everyone who is wise is not old or calm. If someone is both kind and old then someone is not patient. Everyone who is not patient or not kind is not curious or not wise and vice versa. Fred is not funny or not quiet. Fred is not humble or not brave. Fred is either not rich or old. Someone is rich. Someone is either not tall or not humble. Someone is not funny or not rich. Lucy is either not quiet or old. Susan is patient or not quiet. | John is curious. | neutral | (![X]:((patient(X)&~kind(X))=>(~happy(X)|~patient(X))))&
(![X]:(generous(X)<=>(old(X)|calm(X))))&
((?[X]:((~wise(X)|~creative(X))))=>(?[X]:((happy(X)&~old(X)))))&
((?[X]:((~strong(X)|~funny(X))))=>((brave(fred)|~rich(fred))))&
(![X]:((calm(X)&~tall(X))<=>funny(X)))&
((?[X]:((happy(X)<~>tall(X))))=>(?[X]:((curious(X)&~calm(X)))))&
(((~kind(john)&humble(john)))=>((patient(john)|~rich(john))))&
(![X]:((~generous(X)<~>strong(X))<=>(~brave(X)|quiet(X))))&
(![X]:((generous(X)<~>strong(X))=>(~old(X)|~tall(X))))&
((?[X]:((calm(X)|~rich(X))))<=>(?[X]:((quiet(X)|generous(X)))))&
(![X]:((calm(X)<~>~brave(X))<=>(old(X)&~curious(X))))&
(![X]:(~patient(X)<=>(~humble(X)<~>~patient(X))))&
(![X]:((~wise(X)<~>~strong(X))=>(~humble(X)&~happy(X))))&
(![X]:(wise(X)=>(~old(X)|calm(X))))&
((?[X]:((kind(X)&old(X))))=>(?[X]:(~patient(X))))&
(![X]:((~patient(X)|~kind(X))<=>(~curious(X)|~wise(X))))&
((~funny(fred)|~quiet(fred)))&
((~humble(fred)|~brave(fred)))&
((~rich(fred)<~>old(fred)))&
(?[X]:(rich(X)))&
(?[X]:((~tall(X)<~>~humble(X))))&
(?[X]:((~funny(X)|~rich(X))))&
((~quiet(lucy)<~>old(lucy)))&
((patient(susan)|~quiet(susan))) | curious(john) | [] | null | 0 |
Everyone who is both not old and not rich is rich and vice versa.
Everyone who is either not tall or not brave is both not patient and generous.
If mary is both not funny and not humble then someone is either rich or generous.
Everyone who is either tall or not creative is either curious or not brave and vice versa.
If john is either calm or not humble then someone is not funny or strong.
Everyone who is not old is not curious and vice versa.
If someone is brave or curious then paul is not funny or not calm.
If fred is humble then someone is both calm and not generous and vice versa.
Everyone who is both happy and kind is not creative and vice versa.
Everyone who is not funny is either strong or not old.
If fred is either not creative or tall then alice is both funny and happy and vice versa.
If fred is either not patient or curious then paul is either quiet or happy and vice versa.
Everyone who is both not quiet and rich is either not kind or brave.
If paul is both tall and not creative then lucy is not wise and vice versa.
Everyone who is both not tall and not creative is not brave.
Everyone who is wise or kind is both wise and happy.
Someone is quiet.
Fred is both not generous and happy.
Someone is either happy or strong.
Alice is not rich or not old.
Someone is both not funny and curious.
Lucy is either not patient or funny. | John is not tall. | neutral | (![X]:((~old(X)&~rich(X))<=>rich(X)))&
(![X]:((~tall(X)<~>~brave(X))=>(~patient(X)&generous(X))))&
(((~funny(mary)&~humble(mary)))=>(?[X]:((rich(X)<~>generous(X)))))&
(![X]:((tall(X)<~>~creative(X))<=>(curious(X)<~>~brave(X))))&
(((calm(john)<~>~humble(john)))=>(?[X]:((~funny(X)|strong(X)))))&
(![X]:(~old(X)<=>~curious(X)))&
((?[X]:((brave(X)|curious(X))))=>((~funny(paul)|~calm(paul))))&
((humble(fred))<=>(?[X]:((calm(X)&~generous(X)))))&
(![X]:((happy(X)&kind(X))<=>~creative(X)))&
(![X]:(~funny(X)=>(strong(X)<~>~old(X))))&
(((~creative(fred)<~>tall(fred)))<=>((funny(alice)&happy(alice))))&
(((~patient(fred)<~>curious(fred)))<=>((quiet(paul)<~>happy(paul))))&
(![X]:((~quiet(X)&rich(X))=>(~kind(X)<~>brave(X))))&
(((tall(paul)&~creative(paul)))<=>(~wise(lucy)))&
(![X]:((~tall(X)&~creative(X))=>~brave(X)))&
(![X]:((wise(X)|kind(X))=>(wise(X)&happy(X))))&
(?[X]:(quiet(X)))&
((~generous(fred)&happy(fred)))&
(?[X]:((happy(X)<~>strong(X))))&
((~rich(alice)|~old(alice)))&
(?[X]:((~funny(X)&curious(X))))&
((~patient(lucy)<~>funny(lucy))) | ~tall(john) | [] | null | 0 |
Everyone who is brave or tall is either rich or wise. If john is either curious or strong then lucy is tall. If paul is both quiet and not humble then fred is generous. If someone is wise or old then someone is not rich or not kind. Everyone who is either not quiet or not humble is creative. If fred is either not happy or not generous then someone is either not curious or not brave. Everyone who is creative or not rich is both strong and brave. Everyone who is both old and wise is either curious or patient and vice versa. Everyone who is not patient is not kind or not old and vice versa. Everyone who is curious or quiet is either not old or not strong. Everyone who is old or funny is either quiet or not calm. If someone is both not old and kind then someone is both not tall and not patient. Everyone who is either rich or not patient is not quiet or not tall. Everyone who is either wise or strong is old. If someone is either strong or not quiet then someone is both strong and rich. Everyone who is either not creative or kind is not patient or curious. Lucy is either generous or not creative. John is both not calm and not strong. Mary is tall. Someone is not old. Fred is brave or patient. Someone is quiet. | John is strong. | contradiction | (![X]:((brave(X)|tall(X))=>(rich(X)<~>wise(X))))&
(((curious(john)<~>strong(john)))=>(tall(lucy)))&
(((quiet(paul)&~humble(paul)))=>(generous(fred)))&
((?[X]:((wise(X)|old(X))))=>(?[X]:((~rich(X)|~kind(X)))))&
(![X]:((~quiet(X)<~>~humble(X))=>creative(X)))&
(((~happy(fred)<~>~generous(fred)))=>(?[X]:((~curious(X)<~>~brave(X)))))&
(![X]:((creative(X)|~rich(X))=>(strong(X)&brave(X))))&
(![X]:((old(X)&wise(X))<=>(curious(X)<~>patient(X))))&
(![X]:(~patient(X)<=>(~kind(X)|~old(X))))&
(![X]:((curious(X)|quiet(X))=>(~old(X)<~>~strong(X))))&
(![X]:((old(X)|funny(X))=>(quiet(X)<~>~calm(X))))&
((?[X]:((~old(X)&kind(X))))=>(?[X]:((~tall(X)&~patient(X)))))&
(![X]:((rich(X)<~>~patient(X))=>(~quiet(X)|~tall(X))))&
(![X]:((wise(X)<~>strong(X))=>old(X)))&
((?[X]:((strong(X)<~>~quiet(X))))=>(?[X]:((strong(X)&rich(X)))))&
(![X]:((~creative(X)<~>kind(X))=>(~patient(X)|curious(X))))&
((generous(lucy)<~>~creative(lucy)))&
((~calm(john)&~strong(john)))&
(tall(mary))&
(?[X]:(~old(X)))&
((brave(fred)|patient(fred)))&
(?[X]:(quiet(X))) | strong(john) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7157322523496490393630794
% SZS output start Proof for 7157322523496490393630794
18. ~strong(john) & ~calm(john) [input p17]
23. strong(john) [input hypothesis]
124. ~strong(john) [cnf transformation 18]
129. strong(john) [cnf transformation 23]
131. 1 <=> strong(john) [avatar definition]
231. ~1 [avatar split clause 124,131]
241. 1 [avatar split clause 129,131]
242. $false [avatar sat refutation 231,241]
% SZS output end Proof for 7157322523496490393630794
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not happy is not funny. Everyone who is not quiet or not curious is not kind or not humble. Everyone who is either brave or not rich is not calm and vice versa. Everyone who is brave or not tall is brave or strong and vice versa. If someone is creative then someone is both calm and not calm 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. Everyone who is not patient is not quiet. If someone is both strong and not rich then john is both not tall and not happy. Everyone who is not brave or not quiet is either strong or happy and vice versa. Someone is generous. Fred is either not old or kind. John is happy or curious. Someone is both not wise and not calm. Lucy is not generous or curious. | Paul is tall. | neutral | (![X]:((~brave(X)<~>~happy(X))=>~funny(X)))&
(![X]:((~quiet(X)|~curious(X))=>(~kind(X)|~humble(X))))&
(![X]:((brave(X)<~>~rich(X))<=>~calm(X)))&
(![X]:((brave(X)|~tall(X))<=>(brave(X)|strong(X))))&
((?[X]:(creative(X)))<=>(?[X]:((calm(X)&~calm(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))))&
(![X]:(~patient(X)=>~quiet(X)))&
((?[X]:((strong(X)&~rich(X))))=>((~tall(john)&~happy(john))))&
(![X]:((~brave(X)|~quiet(X))<=>(strong(X)<~>happy(X))))&
(?[X]:(generous(X)))&
((~old(fred)<~>kind(fred)))&
((happy(john)|curious(john)))&
(?[X]:((~wise(X)&~calm(X))))&
((~generous(lucy)|curious(lucy))) | tall(paul) | [] | null | 0 |
If fred is either not tall or not kind then paul is creative or brave and vice versa.
Everyone who is not curious or funny is both brave and not strong and vice versa.
Everyone who is humble or not strong is funny and vice versa.
Everyone who is generous is not old or quiet and vice versa.
If someone is not humble then john is either not funny or funny.
Everyone who is wise is not happy.
Everyone who is both wise and funny is both patient and not generous and vice versa.
If someone is curious or not calm then mary is strong.
If susan is both not patient and not quiet then mary is either not strong or not curious and vice versa.
Everyone who is both humble and not strong is rich or not funny and vice versa.
Everyone who is either not generous or not happy is curious and vice versa.
Everyone who is not generous or not kind is not creative and vice versa.
If someone is either not quiet or creative then susan is not happy or not creative.
Everyone who is both calm and not tall is not humble and vice versa.
If someone is either not wise or not rich then fred is humble or funny.
If alice is either not wise or not creative then someone is either quiet or brave and vice versa.
Someone is not strong.
Alice is not kind or quiet.
Someone is not humble or patient.
Mary is creative.
Susan is either rich or not funny.
Mary is either strong or generous. | Mary is not tall. | neutral | (((~tall(fred)<~>~kind(fred)))<=>((creative(paul)|brave(paul))))&
(![X]:((~curious(X)|funny(X))<=>(brave(X)&~strong(X))))&
(![X]:((humble(X)|~strong(X))<=>funny(X)))&
(![X]:(generous(X)<=>(~old(X)|quiet(X))))&
((?[X]:(~humble(X)))=>((~funny(john)<~>funny(john))))&
(![X]:(wise(X)=>~happy(X)))&
(![X]:((wise(X)&funny(X))<=>(patient(X)&~generous(X))))&
((?[X]:((curious(X)|~calm(X))))=>(strong(mary)))&
(((~patient(susan)&~quiet(susan)))<=>((~strong(mary)<~>~curious(mary))))&
(![X]:((humble(X)&~strong(X))<=>(rich(X)|~funny(X))))&
(![X]:((~generous(X)<~>~happy(X))<=>curious(X)))&
(![X]:((~generous(X)|~kind(X))<=>~creative(X)))&
((?[X]:((~quiet(X)<~>creative(X))))=>((~happy(susan)|~creative(susan))))&
(![X]:((calm(X)&~tall(X))<=>~humble(X)))&
((?[X]:((~wise(X)<~>~rich(X))))=>((humble(fred)|funny(fred))))&
(((~wise(alice)<~>~creative(alice)))<=>(?[X]:((quiet(X)<~>brave(X)))))&
(?[X]:(~strong(X)))&
((~kind(alice)|quiet(alice)))&
(?[X]:((~humble(X)|patient(X))))&
(creative(mary))&
((rich(susan)<~>~funny(susan)))&
((strong(mary)<~>generous(mary))) | ~tall(mary) | [] | null | 0 |
If mary is creative or kind then paul is old.
If lucy is old or not humble then lucy is not rich.
Everyone who is both old and not generous is tall.
Everyone who is not patient or not funny is not brave or not happy and vice versa.
If paul is not old or funny then someone is not wise and vice versa.
Everyone who is not funny or curious is patient and vice versa.
If someone is either humble or not curious then someone is not kind and vice versa.
If someone is both funny and not curious then susan is either not strong or not old and vice versa.
If someone is brave or patient then someone is both funny and wise and vice versa.
Everyone who is creative is rich.
Everyone who is not strong is generous.
If alice is not patient then paul is either not rich or not kind and vice versa.
If someone is not wise then paul is patient or not funny and vice versa.
If john is not rich or quiet then lucy is either not brave or not tall and vice versa.
Everyone who is not patient or happy is calm or not quiet and vice versa.
Everyone who is old or curious is strong and vice versa.
Paul is either not curious or rich.
Paul is wise or not wise.
Someone is both not humble and not kind.
Lucy is either calm or not funny.
Fred is either tall or not old.
Someone is both kind and not happy.
Alice is not strong. | Lucy is patient. | neutral | (((creative(mary)|kind(mary)))=>(old(paul)))&
(((old(lucy)|~humble(lucy)))=>(~rich(lucy)))&
(![X]:((old(X)&~generous(X))=>tall(X)))&
(![X]:((~patient(X)|~funny(X))<=>(~brave(X)|~happy(X))))&
(((~old(paul)|funny(paul)))<=>(?[X]:(~wise(X))))&
(![X]:((~funny(X)|curious(X))<=>patient(X)))&
((?[X]:((humble(X)<~>~curious(X))))<=>(?[X]:(~kind(X))))&
((?[X]:((funny(X)&~curious(X))))<=>((~strong(susan)<~>~old(susan))))&
((?[X]:((brave(X)|patient(X))))<=>(?[X]:((funny(X)&wise(X)))))&
(![X]:(creative(X)=>rich(X)))&
(![X]:(~strong(X)=>generous(X)))&
((~patient(alice))<=>((~rich(paul)<~>~kind(paul))))&
((?[X]:(~wise(X)))<=>((patient(paul)|~funny(paul))))&
(((~rich(john)|quiet(john)))<=>((~brave(lucy)<~>~tall(lucy))))&
(![X]:((~patient(X)|happy(X))<=>(calm(X)|~quiet(X))))&
(![X]:((old(X)|curious(X))<=>strong(X)))&
((~curious(paul)<~>rich(paul)))&
((wise(paul)|~wise(paul)))&
(?[X]:((~humble(X)&~kind(X))))&
((calm(lucy)<~>~funny(lucy)))&
((tall(fred)<~>~old(fred)))&
(?[X]:((kind(X)&~happy(X))))&
(~strong(alice)) | patient(lucy) | [] | null | 0 |
Everyone who is generous or creative is both not calm and not kind and vice versa.
If lucy is either strong or generous then someone is both patient and not humble.
Everyone who is happy or not quiet is both curious and kind and vice versa.
Everyone who is not happy or not humble is not creative.
Everyone who is either wise or not wise is either generous or not happy and vice versa.
If paul is both not curious and not strong then susan is either generous or not brave and vice versa.
Everyone who is either not rich or funny is both strong and calm and vice versa.
Everyone who is old is not humble or not wise and vice versa.
If someone is either kind or not tall then fred is either not humble or humble and vice versa.
Everyone who is brave is both not strong and humble and vice versa.
Everyone who is both wise and rich is not old or not wise and vice versa.
Everyone who is either quiet or generous is brave or not brave and vice versa.
If susan is not quiet then mary is both not humble and wise and vice versa.
Everyone who is either strong or kind is either generous or not rich and vice versa.
If someone is calm then alice is not strong or not humble.
Everyone who is not old is both not generous and not curious.
Someone is old.
Alice is either calm or funny.
Someone is either old or not quiet.
Someone is either brave or quiet.
Someone is either quiet or funny.
Fred is either not strong or not wise. | Mary is not rich. | contradiction | (![X]:((generous(X)|creative(X))<=>(~calm(X)&~kind(X))))&
(((strong(lucy)<~>generous(lucy)))=>(?[X]:((patient(X)&~humble(X)))))&
(![X]:((happy(X)|~quiet(X))<=>(curious(X)&kind(X))))&
(![X]:((~happy(X)|~humble(X))=>~creative(X)))&
(![X]:((wise(X)<~>~wise(X))<=>(generous(X)<~>~happy(X))))&
(((~curious(paul)&~strong(paul)))<=>((generous(susan)<~>~brave(susan))))&
(![X]:((~rich(X)<~>funny(X))<=>(strong(X)&calm(X))))&
(![X]:(old(X)<=>(~humble(X)|~wise(X))))&
((?[X]:((kind(X)<~>~tall(X))))<=>((~humble(fred)<~>humble(fred))))&
(![X]:(brave(X)<=>(~strong(X)&humble(X))))&
(![X]:((wise(X)&rich(X))<=>(~old(X)|~wise(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(brave(X)|~brave(X))))&
((~quiet(susan))<=>((~humble(mary)&wise(mary))))&
(![X]:((strong(X)<~>kind(X))<=>(generous(X)<~>~rich(X))))&
((?[X]:(calm(X)))=>((~strong(alice)|~humble(alice))))&
(![X]:(~old(X)=>(~generous(X)&~curious(X))))&
(?[X]:(old(X)))&
((calm(alice)<~>funny(alice)))&
(?[X]:((old(X)<~>~quiet(X))))&
(?[X]:((brave(X)<~>quiet(X))))&
(?[X]:((quiet(X)<~>funny(X))))&
((~strong(fred)<~>~wise(fred))) | ~rich(mary) | [
"p0",
"p2",
"p7",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7143942553434416739928893
% SZS output start Proof for 7143942553434416739928893
1. ! [X0] : ((creative(X0) | generous(X0)) <=> (~kind(X0) & ~calm(X0))) [input p0]
3. ! [X0] : ((~quiet(X0) | happy(X0)) <=> (kind(X0) & curious(X0))) [input p2]
8. ! [X0] : (old(X0) <=> (~wise(X0) | ~humble(X0))) [input p7]
11. ! [X0] : ((rich(X0) & wise(X0)) <=> (~wise(X0) | ~old(X0))) [input p10]
12. ! [X0] : ((quiet(X0) <~> generous(X0)) <=> (~brave(X0) | brave(X0))) [input p11]
13. ~quiet(susan) <=> (wise(mary) & ~humble(mary)) [input p12]
23. ~rich(mary) [input hypothesis]
30. ! [X0] : (((creative(X0) | generous(X0)) | (kind(X0) | calm(X0))) & ((~kind(X0) & ~calm(X0)) | (~creative(X0) & ~generous(X0)))) [nnf transformation 1]
31. ! [X0] : ((creative(X0) | generous(X0) | kind(X0) | calm(X0)) & ((~kind(X0) & ~calm(X0)) | (~creative(X0) & ~generous(X0)))) [flattening 30]
35. ! [X0] : (((~quiet(X0) | happy(X0)) | (~kind(X0) | ~curious(X0))) & ((kind(X0) & curious(X0)) | (quiet(X0) & ~happy(X0)))) [nnf transformation 3]
36. ! [X0] : ((~quiet(X0) | happy(X0) | ~kind(X0) | ~curious(X0)) & ((kind(X0) & curious(X0)) | (quiet(X0) & ~happy(X0)))) [flattening 35]
42. ! [X0] : ((old(X0) | (wise(X0) & humble(X0))) & ((~wise(X0) | ~humble(X0)) | ~old(X0))) [nnf transformation 8]
43. ! [X0] : ((old(X0) | (wise(X0) & humble(X0))) & (~wise(X0) | ~humble(X0) | ~old(X0))) [flattening 42]
50. ! [X0] : (((rich(X0) & wise(X0)) | (wise(X0) & old(X0))) & ((~wise(X0) | ~old(X0)) | (~rich(X0) | ~wise(X0)))) [nnf transformation 11]
51. ! [X0] : (((rich(X0) & wise(X0)) | (wise(X0) & old(X0))) & (~wise(X0) | ~old(X0) | ~rich(X0) | ~wise(X0))) [flattening 50]
52. ! [X0] : ((((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | (brave(X0) & ~brave(X0))) & ((~brave(X0) | brave(X0)) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))))) [nnf transformation 12]
53. ! [X0] : ((((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | (brave(X0) & ~brave(X0))) & (~brave(X0) | brave(X0) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))))) [flattening 52]
54. (~quiet(susan) | (~wise(mary) | humble(mary))) & ((wise(mary) & ~humble(mary)) | quiet(susan)) [nnf transformation 13]
55. (~quiet(susan) | ~wise(mary) | humble(mary)) & ((wise(mary) & ~humble(mary)) | quiet(susan)) [flattening 54]
72. ~kind(X0) | ~generous(X0) [cnf transformation 31]
80. quiet(X0) | kind(X0) [cnf transformation 36]
104. ~old(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 43]
120. wise(X0) | wise(X0) [cnf transformation 51]
121. old(X0) | rich(X0) [cnf transformation 51]
125. generous(X0) | quiet(X0) | ~brave(X0) [cnf transformation 53]
126. brave(X0) | quiet(X0) | generous(X0) [cnf transformation 53]
127. ~generous(X0) | ~quiet(X0) | ~brave(X0) [cnf transformation 53]
128. ~quiet(X0) | ~generous(X0) | brave(X0) [cnf transformation 53]
131. ~quiet(susan) | ~wise(mary) | humble(mary) [cnf transformation 55]
154. ~rich(mary) [cnf transformation 23]
156. wise(X0) [duplicate literal removal 120]
220. ~quiet(X0) | ~generous(X0) [subsumption resolution 127,128]
221. quiet(X0) | generous(X0) [subsumption resolution 125,126]
222. ~quiet(susan) | humble(mary) [subsumption resolution 131,156]
224. 11 <=> humble(mary) [avatar definition]
226. humble(mary) <- (11) [avatar component clause 224]
228. 12 <=> quiet(susan) [avatar definition]
230. ~quiet(susan) <- (~12) [avatar component clause 228]
231. 11 | ~12 [avatar split clause 222,228,224]
315. ~generous(X0) | kind(X0) [resolution 220,80]
316. ~generous(X0) [subsumption resolution 315,72]
319. generous(susan) <- (~12) [resolution 221,230]
328. $false <- (~12) [subsumption resolution 319,316]
329. 12 [avatar contradiction clause 328]
368. ~humble(X0) | ~wise(X0) | rich(X0) [resolution 104,121]
373. ~humble(X0) | rich(X0) [subsumption resolution 368,156]
423. rich(mary) <- (11) [resolution 373,226]
425. $false <- (11) [subsumption resolution 423,154]
426. ~11 [avatar contradiction clause 425]
427. $false [avatar sat refutation 231,329,426]
% SZS output end Proof for 7143942553434416739928893
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is both patient and rich then john is quiet or not happy and vice versa.
If someone is both not generous and patient then someone is not patient or not generous and vice versa.
Everyone who is both not patient and rich is both generous and happy.
Everyone who is both not tall and tall is either not humble or not generous and vice versa.
If fred is not tall then susan is both not old and not curious.
Everyone who is funny is not kind or curious.
If lucy is kind or not happy then someone is curious and vice versa.
If alice is both quiet and not generous then someone is not patient or patient and vice versa.
If lucy is not funny then mary is either not calm or quiet.
Everyone who is both old and not quiet is not calm.
If john is creative then someone is both not curious and not patient and vice versa.
If susan is both not strong and not calm then someone is tall or not brave and vice versa.
Everyone who is either not brave or not happy is either funny or happy.
If john is both not calm and not tall then john is both humble and wise and vice versa.
Everyone who is both brave and not generous is wise.
If someone is both not strong and humble then someone is not strong or not kind and vice versa.
Someone is not humble.
Someone is not happy or humble.
Paul is either kind or not old.
Someone is not quiet.
Someone is both not brave and not calm.
Someone is both not rich and not happy.
Someone is either kind or happy. | Alice is not generous. | entailment | (((patient(john)&rich(john)))<=>((quiet(john)|~happy(john))))&
((?[X]:((~generous(X)&patient(X))))<=>(?[X]:((~patient(X)|~generous(X)))))&
(![X]:((~patient(X)&rich(X))=>(generous(X)&happy(X))))&
(![X]:((~tall(X)&tall(X))<=>(~humble(X)<~>~generous(X))))&
((~tall(fred))=>((~old(susan)&~curious(susan))))&
(![X]:(funny(X)=>(~kind(X)|curious(X))))&
(((kind(lucy)|~happy(lucy)))<=>(?[X]:(curious(X))))&
(((quiet(alice)&~generous(alice)))<=>(?[X]:((~patient(X)|patient(X)))))&
((~funny(lucy))=>((~calm(mary)<~>quiet(mary))))&
(![X]:((old(X)&~quiet(X))=>~calm(X)))&
((creative(john))<=>(?[X]:((~curious(X)&~patient(X)))))&
(((~strong(susan)&~calm(susan)))<=>(?[X]:((tall(X)|~brave(X)))))&
(![X]:((~brave(X)<~>~happy(X))=>(funny(X)<~>happy(X))))&
(((~calm(john)&~tall(john)))<=>((humble(john)&wise(john))))&
(![X]:((brave(X)&~generous(X))=>wise(X)))&
((?[X]:((~strong(X)&humble(X))))<=>(?[X]:((~strong(X)|~kind(X)))))&
(?[X]:(~humble(X)))&
(?[X]:((~happy(X)|humble(X))))&
((kind(paul)<~>~old(paul)))&
(?[X]:(~quiet(X)))&
(?[X]:((~brave(X)&~calm(X))))&
(?[X]:((~rich(X)&~happy(X))))&
(?[X]:((kind(X)<~>happy(X)))) | ~generous(alice) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5907566843053920687279006
% SZS output start Proof for 5907566843053920687279006
8. (~generous(alice) & quiet(alice)) <=> ? [X0] : (patient(X0) | ~patient(X0)) [input p7]
24. generous(alice) [input hypothesis]
52. ((~generous(alice) & quiet(alice)) | ! [X0] : (~patient(X0) & patient(X0))) & (? [X0] : (patient(X0) | ~patient(X0)) | (generous(alice) | ~quiet(alice))) [nnf transformation 8]
53. ((~generous(alice) & quiet(alice)) | ! [X0] : (~patient(X0) & patient(X0))) & (? [X0] : (patient(X0) | ~patient(X0)) | generous(alice) | ~quiet(alice)) [flattening 52]
54. ((~generous(alice) & quiet(alice)) | ! [X0] : (~patient(X0) & patient(X0))) & (? [X1] : (patient(X1) | ~patient(X1)) | generous(alice) | ~quiet(alice)) [rectify 53]
55. ? [X1] : (patient(X1) | ~patient(X1)) => (patient(sK3) | ~patient(sK3)) [choice axiom]
56. ((~generous(alice) & quiet(alice)) | ! [X0] : (~patient(X0) & patient(X0))) & ((patient(sK3) | ~patient(sK3)) | generous(alice) | ~quiet(alice)) [skolemisation 54,55]
116. ~generous(alice) | patient(X0) [cnf transformation 56]
117. ~generous(alice) | ~patient(X0) [cnf transformation 56]
154. generous(alice) [cnf transformation 24]
187. 7 <=> ! [X1] : patient(X1) [avatar definition]
188. patient(X1) <- (7) [avatar component clause 187]
243. 19 <=> ! [X0] : ~patient(X0) [avatar definition]
244. ~patient(X0) <- (19) [avatar component clause 243]
246. 20 <=> generous(alice) [avatar definition]
249. 19 | ~20 [avatar split clause 117,246,243]
250. 7 | ~20 [avatar split clause 116,246,187]
395. 20 [avatar split clause 154,246]
396. $false <- (7, 19) [subsumption resolution 188,244]
397. ~7 | ~19 [avatar contradiction clause 396]
400. $false [avatar sat refutation 249,250,395,397]
% SZS output end Proof for 5907566843053920687279006
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not happy and not curious then someone is either generous or happy.
If john is wise then someone is old or not wise and vice versa.
Everyone who is either calm or not creative is either wise or not kind.
Everyone who is either not kind or not wise is not happy and vice versa.
Everyone who is either wise or old is either not old or generous.
If fred is curious then someone is rich.
If mary is both not strong and creative then someone is either not generous or humble and vice versa.
If someone is not strong or not old then someone is either not curious or creative and vice versa.
If someone is wise then someone is not happy or patient and vice versa.
Everyone who is not patient or funny is not patient.
Everyone who is not wise is not quiet or not rich.
Everyone who is either old or calm is quiet and vice versa.
Everyone who is creative or not creative is not tall and vice versa.
If fred is not brave then someone is either not tall or brave.
Everyone who is curious or not rich is not humble or not tall.
Everyone who is not humble is not quiet or not kind and vice versa.
Paul is calm or not brave.
Someone is not tall.
Susan is happy.
Someone is both not creative and not funny.
Someone is either not creative or tall.
Someone is creative.
Lucy is either not creative or not wise. | Fred is strong. | neutral | (((~happy(susan)&~curious(susan)))=>(?[X]:((generous(X)<~>happy(X)))))&
((wise(john))<=>(?[X]:((old(X)|~wise(X)))))&
(![X]:((calm(X)<~>~creative(X))=>(wise(X)<~>~kind(X))))&
(![X]:((~kind(X)<~>~wise(X))<=>~happy(X)))&
(![X]:((wise(X)<~>old(X))=>(~old(X)<~>generous(X))))&
((curious(fred))=>(?[X]:(rich(X))))&
(((~strong(mary)&creative(mary)))<=>(?[X]:((~generous(X)<~>humble(X)))))&
((?[X]:((~strong(X)|~old(X))))<=>(?[X]:((~curious(X)<~>creative(X)))))&
((?[X]:(wise(X)))<=>(?[X]:((~happy(X)|patient(X)))))&
(![X]:((~patient(X)|funny(X))=>~patient(X)))&
(![X]:(~wise(X)=>(~quiet(X)|~rich(X))))&
(![X]:((old(X)<~>calm(X))<=>quiet(X)))&
(![X]:((creative(X)|~creative(X))<=>~tall(X)))&
((~brave(fred))=>(?[X]:((~tall(X)<~>brave(X)))))&
(![X]:((curious(X)|~rich(X))=>(~humble(X)|~tall(X))))&
(![X]:(~humble(X)<=>(~quiet(X)|~kind(X))))&
((calm(paul)|~brave(paul)))&
(?[X]:(~tall(X)))&
(happy(susan))&
(?[X]:((~creative(X)&~funny(X))))&
(?[X]:((~creative(X)<~>tall(X))))&
(?[X]:(creative(X)))&
((~creative(lucy)<~>~wise(lucy))) | strong(fred) | [] | null | 0 |
Everyone who is both wise and not humble is both not patient and not funny and vice versa.
If someone is not funny then someone is both creative and not brave.
If someone is either funny or humble then someone is not old or tall.
If susan is either strong or not quiet then someone is either not humble or not brave.
If someone is either rich or not creative then someone is both not brave and creative.
If someone is either old or not happy then fred is either rich or curious and vice versa.
If lucy is not wise then mary is old or rich and vice versa.
Everyone who is either wise or generous is both humble and kind and vice versa.
If paul is not wise or curious then someone is either not patient or happy.
If susan is patient or not happy then someone is both old and not happy and vice versa.
If someone is not old then someone is calm or creative and vice versa.
Everyone who is strong or not strong is both wise and curious and vice versa.
If someone is not creative then someone is funny or wise and vice versa.
If mary is funny or patient then fred is either happy or tall and vice versa.
Everyone who is either brave or tall is not funny or happy and vice versa.
Everyone who is either patient or humble is curious.
Alice is both not happy and tall.
Someone is not kind or not old.
Paul is either wise or not kind.
Someone is either not patient or kind.
John is both not old and not strong.
Lucy is both not generous and not rich. | Fred is kind. | neutral | (![X]:((wise(X)&~humble(X))<=>(~patient(X)&~funny(X))))&
((?[X]:(~funny(X)))=>(?[X]:((creative(X)&~brave(X)))))&
((?[X]:((funny(X)<~>humble(X))))=>(?[X]:((~old(X)|tall(X)))))&
(((strong(susan)<~>~quiet(susan)))=>(?[X]:((~humble(X)<~>~brave(X)))))&
((?[X]:((rich(X)<~>~creative(X))))=>(?[X]:((~brave(X)&creative(X)))))&
((?[X]:((old(X)<~>~happy(X))))<=>((rich(fred)<~>curious(fred))))&
((~wise(lucy))<=>((old(mary)|rich(mary))))&
(![X]:((wise(X)<~>generous(X))<=>(humble(X)&kind(X))))&
(((~wise(paul)|curious(paul)))=>(?[X]:((~patient(X)<~>happy(X)))))&
(((patient(susan)|~happy(susan)))<=>(?[X]:((old(X)&~happy(X)))))&
((?[X]:(~old(X)))<=>(?[X]:((calm(X)|creative(X)))))&
(![X]:((strong(X)|~strong(X))<=>(wise(X)&curious(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((funny(X)|wise(X)))))&
(((funny(mary)|patient(mary)))<=>((happy(fred)<~>tall(fred))))&
(![X]:((brave(X)<~>tall(X))<=>(~funny(X)|happy(X))))&
(![X]:((patient(X)<~>humble(X))=>curious(X)))&
((~happy(alice)&tall(alice)))&
(?[X]:((~kind(X)|~old(X))))&
((wise(paul)<~>~kind(paul)))&
(?[X]:((~patient(X)<~>kind(X))))&
((~old(john)&~strong(john)))&
((~generous(lucy)&~rich(lucy))) | kind(fred) | [] | null | 0 |
If susan is not kind then john is either quiet or not calm. Everyone who is creative is humble and vice versa. Everyone who is both kind and not happy is either not happy or rich and vice versa. Everyone who is not quiet or not brave is calm or not wise. Everyone who is not tall or tall is brave and vice versa. If john is either quiet or not tall then someone is not old or happy and vice versa. If alice is creative then mary is curious and vice versa. Everyone who is quiet or generous is not curious. Everyone who is not kind is both not brave and funny. If someone is either humble or not tall then susan is both brave and patient and vice versa. If someone is wise or rich then someone is either old or not calm and vice versa. Everyone who is rich or funny is not quiet and vice versa. If someone is either not calm or not tall then mary is both not rich and tall and vice versa. If fred is both patient and calm then john is creative. Everyone who is not rich or rich is either patient or quiet. Everyone who is not tall is not quiet or not wise. John is either not generous or happy. Someone is either not generous or not strong. Someone is humble. Someone is either not brave or not curious. John is both not patient and creative. Someone is either old or patient. John is either not quiet or generous. Someone is either not brave or not happy. | John is not generous. | contradiction | ((~kind(susan))=>((quiet(john)<~>~calm(john))))&
(![X]:(creative(X)<=>humble(X)))&
(![X]:((kind(X)&~happy(X))<=>(~happy(X)<~>rich(X))))&
(![X]:((~quiet(X)|~brave(X))=>(calm(X)|~wise(X))))&
(![X]:((~tall(X)|tall(X))<=>brave(X)))&
(((quiet(john)<~>~tall(john)))<=>(?[X]:((~old(X)|happy(X)))))&
((creative(alice))<=>(curious(mary)))&
(![X]:((quiet(X)|generous(X))=>~curious(X)))&
(![X]:(~kind(X)=>(~brave(X)&funny(X))))&
((?[X]:((humble(X)<~>~tall(X))))<=>((brave(susan)&patient(susan))))&
((?[X]:((wise(X)|rich(X))))<=>(?[X]:((old(X)<~>~calm(X)))))&
(![X]:((rich(X)|funny(X))<=>~quiet(X)))&
((?[X]:((~calm(X)<~>~tall(X))))<=>((~rich(mary)&tall(mary))))&
(((patient(fred)&calm(fred)))=>(creative(john)))&
(![X]:((~rich(X)|rich(X))=>(patient(X)<~>quiet(X))))&
(![X]:(~tall(X)=>(~quiet(X)|~wise(X))))&
((~generous(john)<~>happy(john)))&
(?[X]:((~generous(X)<~>~strong(X))))&
(?[X]:(humble(X)))&
(?[X]:((~brave(X)<~>~curious(X))))&
((~patient(john)&creative(john)))&
(?[X]:((old(X)<~>patient(X))))&
((~quiet(john)<~>generous(john)))&
(?[X]:((~brave(X)<~>~happy(X)))) | ~generous(john) | [
"p11",
"p14",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8917845078971713232991613
% SZS output start Proof for 8917845078971713232991613
12. ! [X0] : ((funny(X0) | rich(X0)) <=> ~quiet(X0)) [input p11]
15. ! [X0] : ((rich(X0) | ~rich(X0)) => (patient(X0) <~> quiet(X0))) [input p14]
21. creative(john) & ~patient(john) [input p20]
23. ~quiet(john) <~> generous(john) [input p22]
25. ~generous(john) [input hypothesis]
34. ! [X0] : ((patient(X0) <~> quiet(X0)) | (~rich(X0) & rich(X0))) [ennf transformation 15]
58. ! [X0] : (((funny(X0) | rich(X0)) | quiet(X0)) & (~quiet(X0) | (~funny(X0) & ~rich(X0)))) [nnf transformation 12]
59. ! [X0] : ((funny(X0) | rich(X0) | quiet(X0)) & (~quiet(X0) | (~funny(X0) & ~rich(X0)))) [flattening 58]
65. ! [X0] : (((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (~rich(X0) & rich(X0))) [nnf transformation 34]
78. (~generous(john) | quiet(john)) & (generous(john) | ~quiet(john)) [nnf transformation 23]
121. ~rich(X0) | ~quiet(X0) [cnf transformation 59]
131. quiet(X0) | patient(X0) | rich(X0) [cnf transformation 65]
132. quiet(X0) | patient(X0) | ~rich(X0) [cnf transformation 65]
143. ~patient(john) [cnf transformation 21]
147. generous(john) | ~quiet(john) [cnf transformation 78]
151. ~generous(john) [cnf transformation 25]
159. 2 <=> quiet(john) [avatar definition]
161. ~quiet(john) <- (~2) [avatar component clause 159]
305. ~rich(X0) | patient(X0) [subsumption resolution 132,121]
306. patient(X0) | quiet(X0) [subsumption resolution 131,305]
308. 33 <=> generous(john) [avatar definition]
340. ~2 | 33 [avatar split clause 147,308,159]
342. ~33 [avatar split clause 151,308]
351. quiet(john) [resolution 306,143]
354. $false <- (~2) [subsumption resolution 351,161]
355. 2 [avatar contradiction clause 354]
356. $false [avatar sat refutation 340,342,355]
% SZS output end Proof for 8917845078971713232991613
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm then paul is both not rich and happy and vice versa. Everyone who is not kind is not curious. If someone is either patient or not humble then someone is either humble or not strong. If mary is not calm or creative then john is not brave or not rich. If susan is both funny and not funny then someone is either not curious or creative. Everyone who is creative or not creative is either not rich or old and vice versa. If mary is wise or not funny then fred is either brave or old. Everyone who is not brave or creative is both rich and not happy and vice versa. Everyone who is both brave and strong is either not tall or not quiet and vice versa. Everyone who is either not calm or old is not strong or wise and vice versa. Everyone who is not patient is not calm. Everyone who is not brave is either not patient or generous. If someone is either not creative or not old then john is wise. Everyone who is calm or happy is humble and vice versa. If lucy is creative or kind then paul is both not wise and not strong. Everyone who is not happy is both generous and not funny. Someone is both creative and not funny. Susan is either not brave or not tall. John is kind. Fred is either not tall or tall. John is either rich or not patient. Susan is tall or not brave. Fred is not rich or not quiet. | Paul is rich. | neutral | ((?[X]:(calm(X)))<=>((~rich(paul)&happy(paul))))&
(![X]:(~kind(X)=>~curious(X)))&
((?[X]:((patient(X)<~>~humble(X))))=>(?[X]:((humble(X)<~>~strong(X)))))&
(((~calm(mary)|creative(mary)))=>((~brave(john)|~rich(john))))&
(((funny(susan)&~funny(susan)))=>(?[X]:((~curious(X)<~>creative(X)))))&
(![X]:((creative(X)|~creative(X))<=>(~rich(X)<~>old(X))))&
(((wise(mary)|~funny(mary)))=>((brave(fred)<~>old(fred))))&
(![X]:((~brave(X)|creative(X))<=>(rich(X)&~happy(X))))&
(![X]:((brave(X)&strong(X))<=>(~tall(X)<~>~quiet(X))))&
(![X]:((~calm(X)<~>old(X))<=>(~strong(X)|wise(X))))&
(![X]:(~patient(X)=>~calm(X)))&
(![X]:(~brave(X)=>(~patient(X)<~>generous(X))))&
((?[X]:((~creative(X)<~>~old(X))))=>(wise(john)))&
(![X]:((calm(X)|happy(X))<=>humble(X)))&
(((creative(lucy)|kind(lucy)))=>((~wise(paul)&~strong(paul))))&
(![X]:(~happy(X)=>(generous(X)&~funny(X))))&
(?[X]:((creative(X)&~funny(X))))&
((~brave(susan)<~>~tall(susan)))&
(kind(john))&
((~tall(fred)<~>tall(fred)))&
((rich(john)<~>~patient(john)))&
((tall(susan)|~brave(susan)))&
((~rich(fred)|~quiet(fred))) | rich(paul) | [] | null | 0 |
Everyone who is either old or kind is either not rich or not strong.
Everyone who is both not patient and not wise is both patient and not brave.
If someone is either creative or strong then someone is not quiet.
If someone is not happy or rich then lucy is either creative or not calm.
If someone is not strong or old then someone is both brave and not happy and vice versa.
If mary is brave or funny then someone is both quiet and not rich.
Everyone who is not wise or not rich is either wise or strong and vice versa.
If someone is not brave or not rich then lucy is curious and vice versa.
Everyone who is either brave or not brave is either creative or not humble.
Everyone who is either not rich or creative is either funny or happy.
If fred is either not generous or not curious then lucy is rich and vice versa.
Everyone who is both not rich and rich is not tall and vice versa.
Everyone who is kind is either humble or not rich and vice versa.
If someone is tall then paul is both not curious and not strong.
Everyone who is brave is either not brave or patient.
Someone is both funny and humble.
Someone is both not patient and not humble.
Someone is not humble.
Someone is happy.
Alice is humble or not tall.
Paul is either quiet or wise. | Alice is not creative. | contradiction | (![X]:((old(X)<~>kind(X))=>(~rich(X)<~>~strong(X))))&
(![X]:((~patient(X)&~wise(X))=>(patient(X)&~brave(X))))&
((?[X]:((creative(X)<~>strong(X))))=>(?[X]:(~quiet(X))))&
((?[X]:((~happy(X)|rich(X))))=>((creative(lucy)<~>~calm(lucy))))&
((?[X]:((~strong(X)|old(X))))<=>(?[X]:((brave(X)&~happy(X)))))&
(((brave(mary)|funny(mary)))=>(?[X]:((quiet(X)&~rich(X)))))&
(![X]:((~wise(X)|~rich(X))<=>(wise(X)<~>strong(X))))&
((?[X]:((~brave(X)|~rich(X))))<=>(curious(lucy)))&
(![X]:((brave(X)<~>~brave(X))=>(creative(X)<~>~humble(X))))&
(![X]:((~rich(X)<~>creative(X))=>(funny(X)<~>happy(X))))&
(((~generous(fred)<~>~curious(fred)))<=>(rich(lucy)))&
(![X]:((~rich(X)&rich(X))<=>~tall(X)))&
(![X]:(kind(X)<=>(humble(X)<~>~rich(X))))&
((?[X]:(tall(X)))=>((~curious(paul)&~strong(paul))))&
(![X]:(brave(X)=>(~brave(X)<~>patient(X))))&
(?[X]:((funny(X)&humble(X))))&
(?[X]:((~patient(X)&~humble(X))))&
(?[X]:(~humble(X)))&
(?[X]:(happy(X)))&
((humble(alice)|~tall(alice)))&
((quiet(paul)<~>wise(paul))) | ~creative(alice) | [
"p8",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2767016764338182523954418
% SZS output start Proof for 2767016764338182523954418
9. ! [X0] : ((brave(X0) <~> ~brave(X0)) => (creative(X0) <~> ~humble(X0))) [input p8]
12. ! [X0] : ((rich(X0) & ~rich(X0)) <=> ~tall(X0)) [input p11]
20. ~tall(alice) | humble(alice) [input p19]
22. ~creative(alice) [input hypothesis]
25. ! [X0] : (~tall(X0) => (rich(X0) & ~rich(X0))) [unused predicate definition removal 12]
32. ! [X0] : ((creative(X0) <~> ~humble(X0)) | (brave(X0) <=> ~brave(X0))) [ennf transformation 9]
34. ! [X0] : ((rich(X0) & ~rich(X0)) | tall(X0)) [ennf transformation 25]
56. ! [X0] : (((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) [nnf transformation 32]
100. ~humble(X0) | creative(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 56]
101. ~humble(X0) | creative(X0) | brave(X0) | brave(X0) [cnf transformation 56]
112. ~rich(X0) | tall(X0) [cnf transformation 34]
113. tall(X0) | rich(X0) [cnf transformation 34]
128. ~tall(alice) | humble(alice) [cnf transformation 20]
131. ~creative(alice) [cnf transformation 22]
133. ~humble(X0) | creative(X0) | ~brave(X0) [duplicate literal removal 100]
134. ~humble(X0) | creative(X0) | brave(X0) [duplicate literal removal 101]
242. ~humble(X0) | creative(X0) [subsumption resolution 133,134]
259. tall(X0) [subsumption resolution 112,113]
262. humble(alice) [subsumption resolution 128,259]
285. creative(alice) [resolution 242,262]
286. $false [subsumption resolution 285,131]
% SZS output end Proof for 2767016764338182523954418
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is quiet then someone is both not calm and not quiet. If lucy is either rich or not strong then someone is both not creative and wise. Everyone who is not curious is both generous and funny and vice versa. Everyone who is not happy or not creative is both brave and not rich. If mary is either not calm or not happy then mary is tall or not creative and vice versa. If mary is not curious then paul is not happy or rich and vice versa. Everyone who is not curious or not rich is either quiet or not old and vice versa. Everyone who is quiet is either patient or not curious and vice versa. If someone is not old then john is both calm and patient and vice versa. If fred is either not brave or tall then john is not wise or not kind. If someone is not strong or not creative then susan is both humble and not rich. Everyone who is both not curious and rich is both patient and not calm and vice versa. Everyone who is both not old and not patient is either old or creative. If mary is both strong and humble then someone is both not calm and not curious and vice versa. Everyone who is either patient or not creative is both not funny and generous. Everyone who is not patient is either not wise or rich and vice versa. Someone is creative or not patient. Paul is both not curious and not humble. John is not funny. Someone is patient. Someone is both humble and not old. Mary is rich or brave. Someone is curious or brave. Mary is funny. | John is not quiet. | contradiction | ((quiet(lucy))=>(?[X]:((~calm(X)&~quiet(X)))))&
(((rich(lucy)<~>~strong(lucy)))=>(?[X]:((~creative(X)&wise(X)))))&
(![X]:(~curious(X)<=>(generous(X)&funny(X))))&
(![X]:((~happy(X)|~creative(X))=>(brave(X)&~rich(X))))&
(((~calm(mary)<~>~happy(mary)))<=>((tall(mary)|~creative(mary))))&
((~curious(mary))<=>((~happy(paul)|rich(paul))))&
(![X]:((~curious(X)|~rich(X))<=>(quiet(X)<~>~old(X))))&
(![X]:(quiet(X)<=>(patient(X)<~>~curious(X))))&
((?[X]:(~old(X)))<=>((calm(john)&patient(john))))&
(((~brave(fred)<~>tall(fred)))=>((~wise(john)|~kind(john))))&
((?[X]:((~strong(X)|~creative(X))))=>((humble(susan)&~rich(susan))))&
(![X]:((~curious(X)&rich(X))<=>(patient(X)&~calm(X))))&
(![X]:((~old(X)&~patient(X))=>(old(X)<~>creative(X))))&
(((strong(mary)&humble(mary)))<=>(?[X]:((~calm(X)&~curious(X)))))&
(![X]:((patient(X)<~>~creative(X))=>(~funny(X)&generous(X))))&
(![X]:(~patient(X)<=>(~wise(X)<~>rich(X))))&
(?[X]:((creative(X)|~patient(X))))&
((~curious(paul)&~humble(paul)))&
(~funny(john))&
(?[X]:(patient(X)))&
(?[X]:((humble(X)&~old(X))))&
((rich(mary)|brave(mary)))&
(?[X]:((curious(X)|brave(X))))&
(funny(mary)) | ~quiet(john) | [
"p2",
"p7",
"p8",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1989578447713447103298674
% SZS output start Proof for 1989578447713447103298674
3. ! [X0] : (~curious(X0) <=> (funny(X0) & generous(X0))) [input p2]
8. ! [X0] : (quiet(X0) <=> (patient(X0) <~> ~curious(X0))) [input p7]
9. ? [X0] : ~old(X0) <=> (patient(john) & calm(john)) [input p8]
19. ~funny(john) [input p18]
21. ? [X0] : (~old(X0) & humble(X0)) [input p20]
25. ~quiet(john) [input hypothesis]
42. ! [X0] : ((~curious(X0) | (~funny(X0) | ~generous(X0))) & ((funny(X0) & generous(X0)) | curious(X0))) [nnf transformation 3]
43. ! [X0] : ((~curious(X0) | ~funny(X0) | ~generous(X0)) & ((funny(X0) & generous(X0)) | curious(X0))) [flattening 42]
50. ! [X0] : ((quiet(X0) | ((patient(X0) | curious(X0)) & (~curious(X0) | ~patient(X0)))) & (((curious(X0) | ~patient(X0)) & (~curious(X0) | patient(X0))) | ~quiet(X0))) [nnf transformation 8]
51. (? [X0] : ~old(X0) | (~patient(john) | ~calm(john))) & ((patient(john) & calm(john)) | ! [X0] : old(X0)) [nnf transformation 9]
52. (? [X0] : ~old(X0) | ~patient(john) | ~calm(john)) & ((patient(john) & calm(john)) | ! [X0] : old(X0)) [flattening 51]
53. (? [X0] : ~old(X0) | ~patient(john) | ~calm(john)) & ((patient(john) & calm(john)) | ! [X1] : old(X1)) [rectify 52]
54. ? [X0] : ~old(X0) => ~old(sK2) [choice axiom]
55. (~old(sK2) | ~patient(john) | ~calm(john)) & ((patient(john) & calm(john)) | ! [X1] : old(X1)) [skolemisation 53,54]
70. ? [X0] : (~old(X0) & humble(X0)) => (~old(sK6) & humble(sK6)) [choice axiom]
71. ~old(sK6) & humble(sK6) [skolemisation 21,70]
79. funny(X0) | curious(X0) [cnf transformation 43]
100. ~patient(X0) | ~curious(X0) | quiet(X0) [cnf transformation 50]
103. patient(john) | old(X1) [cnf transformation 55]
130. ~funny(john) [cnf transformation 19]
133. ~old(sK6) [cnf transformation 71]
135. ~quiet(john) [cnf transformation 25]
213. 16 <=> patient(john) [avatar definition]
214. patient(john) <- (16) [avatar component clause 213]
222. 18 <=> ! [X1] : old(X1) [avatar definition]
223. old(X1) <- (18) [avatar component clause 222]
224. 18 | 16 [avatar split clause 103,213,222]
276. curious(john) [resolution 79,130]
300. ~curious(john) | quiet(john) <- (16) [resolution 100,214]
303. quiet(john) <- (16) [subsumption resolution 300,276]
304. $false <- (16) [subsumption resolution 303,135]
305. ~16 [avatar contradiction clause 304]
306. $false <- (18) [resolution 223,133]
311. ~18 [avatar contradiction clause 306]
312. $false [avatar sat refutation 224,305,311]
% SZS output end Proof for 1989578447713447103298674
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not wise is both kind and not curious. Everyone who is not creative is either brave or not rich and vice versa. Everyone who is old is not rich and vice versa. If fred is patient then lucy is not curious or happy. Everyone who is both not patient and rich is both creative and not humble and vice versa. Everyone who is not old or rich is generous or not kind and vice versa. Everyone who is either not brave or creative is not quiet or quiet and vice versa. Everyone who is not happy is either generous or not generous. If john is quiet then someone is either old or kind. If alice is not kind then alice is either not happy or not generous. Everyone who is funny is either not calm or not old and vice versa. If mary is not calm or not brave then someone is both kind and creative and vice versa. If someone is not generous or creative then john is happy or kind. Everyone who is either not kind or not tall is either not kind or not generous. Everyone who is either not rich or wise is calm. If paul is either generous or kind then alice is either not calm or not tall. Fred is either kind or wise. Lucy is either not humble or curious. Someone is happy or not brave. Someone is either happy or not happy. Someone is both funny and not humble. Someone is either old or strong. Paul is both not wise and strong. Someone is not tall. | Lucy is generous. | contradiction | (![X]:((rich(X)|~wise(X))=>(kind(X)&~curious(X))))&
(![X]:(~creative(X)<=>(brave(X)<~>~rich(X))))&
(![X]:(old(X)<=>~rich(X)))&
((patient(fred))=>((~curious(lucy)|happy(lucy))))&
(![X]:((~patient(X)&rich(X))<=>(creative(X)&~humble(X))))&
(![X]:((~old(X)|rich(X))<=>(generous(X)|~kind(X))))&
(![X]:((~brave(X)<~>creative(X))<=>(~quiet(X)|quiet(X))))&
(![X]:(~happy(X)=>(generous(X)<~>~generous(X))))&
((quiet(john))=>(?[X]:((old(X)<~>kind(X)))))&
((~kind(alice))=>((~happy(alice)<~>~generous(alice))))&
(![X]:(funny(X)<=>(~calm(X)<~>~old(X))))&
(((~calm(mary)|~brave(mary)))<=>(?[X]:((kind(X)&creative(X)))))&
((?[X]:((~generous(X)|creative(X))))=>((happy(john)|kind(john))))&
(![X]:((~kind(X)<~>~tall(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((~rich(X)<~>wise(X))=>calm(X)))&
(((generous(paul)<~>kind(paul)))=>((~calm(alice)<~>~tall(alice))))&
((kind(fred)<~>wise(fred)))&
((~humble(lucy)<~>curious(lucy)))&
(?[X]:((happy(X)|~brave(X))))&
(?[X]:((happy(X)<~>~happy(X))))&
(?[X]:((funny(X)&~humble(X))))&
(?[X]:((old(X)<~>strong(X))))&
((~wise(paul)&strong(paul)))&
(?[X]:(~tall(X))) | generous(lucy) | [
"p1",
"p2",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8087215015705502210286300
% SZS output start Proof for 8087215015705502210286300
2. ! [X0] : (~creative(X0) <=> (brave(X0) <~> ~rich(X0))) [input p1]
3. ! [X0] : (old(X0) <=> ~rich(X0)) [input p2]
6. ! [X0] : ((rich(X0) | ~old(X0)) <=> (~kind(X0) | generous(X0))) [input p5]
7. ! [X0] : ((~brave(X0) <~> creative(X0)) <=> (quiet(X0) | ~quiet(X0))) [input p6]
25. generous(lucy) [input hypothesis]
39. ! [X0] : ((~creative(X0) | ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0)))) & (((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | creative(X0))) [nnf transformation 2]
40. ! [X0] : ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))) [nnf transformation 3]
43. ! [X0] : (((rich(X0) | ~old(X0)) | (kind(X0) & ~generous(X0))) & ((~kind(X0) | generous(X0)) | (~rich(X0) & old(X0)))) [nnf transformation 6]
44. ! [X0] : ((rich(X0) | ~old(X0) | (kind(X0) & ~generous(X0))) & (~kind(X0) | generous(X0) | (~rich(X0) & old(X0)))) [flattening 43]
45. ! [X0] : ((((~creative(X0) | brave(X0)) & (creative(X0) | ~brave(X0))) | (~quiet(X0) & quiet(X0))) & ((quiet(X0) | ~quiet(X0)) | ((~brave(X0) | ~creative(X0)) & (creative(X0) | brave(X0))))) [nnf transformation 7]
46. ! [X0] : ((((~creative(X0) | brave(X0)) & (creative(X0) | ~brave(X0))) | (~quiet(X0) & quiet(X0))) & (quiet(X0) | ~quiet(X0) | ((~brave(X0) | ~creative(X0)) & (creative(X0) | brave(X0))))) [flattening 45]
79. ~rich(X0) | brave(X0) | creative(X0) [cnf transformation 39]
81. ~brave(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 39]
83. ~old(X0) | ~rich(X0) [cnf transformation 40]
84. old(X0) | rich(X0) [cnf transformation 40]
92. rich(X0) | ~old(X0) | ~generous(X0) [cnf transformation 44]
96. creative(X0) | ~brave(X0) | quiet(X0) [cnf transformation 46]
97. creative(X0) | ~brave(X0) | ~quiet(X0) [cnf transformation 46]
98. ~creative(X0) | brave(X0) | quiet(X0) [cnf transformation 46]
99. ~creative(X0) | brave(X0) | ~quiet(X0) [cnf transformation 46]
139. generous(lucy) [cnf transformation 25]
156. ~generous(X0) | ~old(X0) [subsumption resolution 92,83]
158. ~creative(X0) | brave(X0) [subsumption resolution 98,99]
159. ~brave(X0) | creative(X0) [subsumption resolution 96,97]
294. ~old(lucy) [resolution 156,139]
296. rich(lucy) [resolution 294,84]
306. brave(lucy) | creative(lucy) [resolution 296,79]
309. brave(lucy) [subsumption resolution 306,158]
324. 31 <=> creative(lucy) [avatar definition]
337. ~rich(lucy) | ~creative(lucy) [resolution 309,81]
339. creative(lucy) [resolution 309,159]
340. ~creative(lucy) [subsumption resolution 337,296]
341. ~31 [avatar split clause 340,324]
342. 31 [avatar split clause 339,324]
343. $false [avatar sat refutation 341,342]
% SZS output end Proof for 8087215015705502210286300
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or brave then someone is rich or not funny.
If someone is either not wise or not old then someone is both calm and not quiet and vice versa.
If mary is not old then someone is both generous and not happy.
If someone is not rich or not calm then someone is not generous or patient.
If paul is both old and curious then someone is both not rich and curious and vice versa.
If someone is both curious and funny then alice is curious or not wise and vice versa.
Everyone who is funny is tall and vice versa.
If john is either quiet or not rich then fred is either not curious or kind.
Everyone who is brave is both funny and not kind.
Everyone who is either tall or wise is both wise and not strong and vice versa.
Everyone who is both curious and not quiet is not creative or humble and vice versa.
If someone is not brave then susan is either quiet or humble and vice versa.
Everyone who is not tall is both wise and not wise.
If someone is both not funny and not brave then someone is not quiet.
If john is either humble or brave then mary is both happy and not old and vice versa.
If someone is both kind and wise then someone is not kind or humble.
Fred is both strong and not calm.
Someone is not creative or not generous.
Alice is creative.
John is not kind.
Alice is both not brave and not calm.
Someone is brave. | Fred is funny. | entailment | ((?[X]:((happy(X)|brave(X))))=>(?[X]:((rich(X)|~funny(X)))))&
((?[X]:((~wise(X)<~>~old(X))))<=>(?[X]:((calm(X)&~quiet(X)))))&
((~old(mary))=>(?[X]:((generous(X)&~happy(X)))))&
((?[X]:((~rich(X)|~calm(X))))=>(?[X]:((~generous(X)|patient(X)))))&
(((old(paul)&curious(paul)))<=>(?[X]:((~rich(X)&curious(X)))))&
((?[X]:((curious(X)&funny(X))))<=>((curious(alice)|~wise(alice))))&
(![X]:(funny(X)<=>tall(X)))&
(((quiet(john)<~>~rich(john)))=>((~curious(fred)<~>kind(fred))))&
(![X]:(brave(X)=>(funny(X)&~kind(X))))&
(![X]:((tall(X)<~>wise(X))<=>(wise(X)&~strong(X))))&
(![X]:((curious(X)&~quiet(X))<=>(~creative(X)|humble(X))))&
((?[X]:(~brave(X)))<=>((quiet(susan)<~>humble(susan))))&
(![X]:(~tall(X)=>(wise(X)&~wise(X))))&
((?[X]:((~funny(X)&~brave(X))))=>(?[X]:(~quiet(X))))&
(((humble(john)<~>brave(john)))<=>((happy(mary)&~old(mary))))&
((?[X]:((kind(X)&wise(X))))=>(?[X]:((~kind(X)|humble(X)))))&
((strong(fred)&~calm(fred)))&
(?[X]:((~creative(X)|~generous(X))))&
(creative(alice))&
(~kind(john))&
((~brave(alice)&~calm(alice)))&
(?[X]:(brave(X))) | funny(fred) | [
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 164256702707816942455360
% SZS output start Proof for 164256702707816942455360
7. ! [X0] : (funny(X0) <=> tall(X0)) [input p6]
13. ! [X0] : (~tall(X0) => (~wise(X0) & wise(X0))) [input p12]
23. ~funny(fred) [input hypothesis]
34. ! [X0] : ((~wise(X0) & wise(X0)) | tall(X0)) [ennf transformation 13]
57. ! [X0] : ((funny(X0) | ~tall(X0)) & (tall(X0) | ~funny(X0))) [nnf transformation 7]
99. ~tall(X0) | funny(X0) [cnf transformation 57]
121. wise(X0) | tall(X0) [cnf transformation 34]
122. ~wise(X0) | tall(X0) [cnf transformation 34]
139. ~funny(fred) [cnf transformation 23]
290. tall(X0) [subsumption resolution 121,122]
293. 33 <=> ! [X1] : funny(X1) [avatar definition]
294. funny(X1) <- (33) [avatar component clause 293]
340. funny(X0) [resolution 99,290]
341. 33 [avatar split clause 340,293]
342. $false <- (33) [resolution 294,139]
346. ~33 [avatar contradiction clause 342]
347. $false [avatar sat refutation 341,346]
% SZS output end Proof for 164256702707816942455360
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or funny is either not happy or generous and vice versa. If susan is both creative and kind then someone is generous. If fred is not rich or quiet then someone is either not tall or generous. Everyone who is not brave is either not quiet or old and vice versa. If someone is not patient or funny then mary is both not humble and not funny and vice versa. Everyone who is not tall is either humble or not tall. If someone is both humble and not kind then someone is either calm or strong. If lucy is brave or not old then someone is both wise and not wise and vice versa. Everyone who is not kind is happy or funny. Everyone who is both funny and old is both not curious and not calm and vice versa. If someone is rich or funny then john is creative or not calm. Everyone who is humble is both not funny and not old. Everyone who is not old is not happy and vice versa. Everyone who is quiet is both not humble and wise and vice versa. Everyone who is either not kind or tall is not wise and vice versa. Someone is both not happy and not patient. Fred is either wise or happy. John is not humble or not brave. Paul is wise or funny. Someone is happy or old. Paul is either not humble or curious. Someone is old or quiet. | John is creative. | neutral | (![X]:((~funny(X)|funny(X))<=>(~happy(X)<~>generous(X))))&
(((creative(susan)&kind(susan)))=>(?[X]:(generous(X))))&
(((~rich(fred)|quiet(fred)))=>(?[X]:((~tall(X)<~>generous(X)))))&
(![X]:(~brave(X)<=>(~quiet(X)<~>old(X))))&
((?[X]:((~patient(X)|funny(X))))<=>((~humble(mary)&~funny(mary))))&
(![X]:(~tall(X)=>(humble(X)<~>~tall(X))))&
((?[X]:((humble(X)&~kind(X))))=>(?[X]:((calm(X)<~>strong(X)))))&
(((brave(lucy)|~old(lucy)))<=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:(~kind(X)=>(happy(X)|funny(X))))&
(![X]:((funny(X)&old(X))<=>(~curious(X)&~calm(X))))&
((?[X]:((rich(X)|funny(X))))=>((creative(john)|~calm(john))))&
(![X]:(humble(X)=>(~funny(X)&~old(X))))&
(![X]:(~old(X)<=>~happy(X)))&
(![X]:(quiet(X)<=>(~humble(X)&wise(X))))&
(![X]:((~kind(X)<~>tall(X))<=>~wise(X)))&
(?[X]:((~happy(X)&~patient(X))))&
((wise(fred)<~>happy(fred)))&
((~humble(john)|~brave(john)))&
((wise(paul)|funny(paul)))&
(?[X]:((happy(X)|old(X))))&
((~humble(paul)<~>curious(paul)))&
(?[X]:((old(X)|quiet(X)))) | creative(john) | [] | null | 0 |
Everyone who is both not kind and calm is not strong or creative and vice versa.
Everyone who is both not old and not tall is either not kind or not humble.
If someone is either rich or not rich then mary is not brave.
If mary is not wise or rich then fred is not brave or not calm and vice versa.
Everyone who is both wise and not curious is not creative and vice versa.
Everyone who is either not humble or not kind is not strong or not humble.
If someone is either patient or happy then someone is old.
Everyone who is not creative is either kind or not generous.
Everyone who is both not strong and not wise is not happy.
Everyone who is both not tall and happy is either not kind or generous and vice versa.
Everyone who is either tall or strong is calm or kind.
If lucy is funny then john is kind or brave and vice versa.
Everyone who is both kind and not curious is both not kind and not old.
Everyone who is rich or tall is happy or curious and vice versa.
If someone is both not old and strong then susan is both not quiet and not funny and vice versa.
Everyone who is both not creative and brave is quiet.
Mary is both not funny and not kind.
Paul is either not rich or humble.
Fred is either not kind or not generous.
Someone is not humble.
Alice is tall or creative.
Lucy is wise or not quiet.
Mary is curious. | Fred is not kind. | entailment | (![X]:((~kind(X)&calm(X))<=>(~strong(X)|creative(X))))&
(![X]:((~old(X)&~tall(X))=>(~kind(X)<~>~humble(X))))&
((?[X]:((rich(X)<~>~rich(X))))=>(~brave(mary)))&
(((~wise(mary)|rich(mary)))<=>((~brave(fred)|~calm(fred))))&
(![X]:((wise(X)&~curious(X))<=>~creative(X)))&
(![X]:((~humble(X)<~>~kind(X))=>(~strong(X)|~humble(X))))&
((?[X]:((patient(X)<~>happy(X))))=>(?[X]:(old(X))))&
(![X]:(~creative(X)=>(kind(X)<~>~generous(X))))&
(![X]:((~strong(X)&~wise(X))=>~happy(X)))&
(![X]:((~tall(X)&happy(X))<=>(~kind(X)<~>generous(X))))&
(![X]:((tall(X)<~>strong(X))=>(calm(X)|kind(X))))&
((funny(lucy))<=>((kind(john)|brave(john))))&
(![X]:((kind(X)&~curious(X))=>(~kind(X)&~old(X))))&
(![X]:((rich(X)|tall(X))<=>(happy(X)|curious(X))))&
((?[X]:((~old(X)&strong(X))))<=>((~quiet(susan)&~funny(susan))))&
(![X]:((~creative(X)&brave(X))=>quiet(X)))&
((~funny(mary)&~kind(mary)))&
((~rich(paul)<~>humble(paul)))&
((~kind(fred)<~>~generous(fred)))&
(?[X]:(~humble(X)))&
((tall(alice)|creative(alice)))&
((wise(lucy)|~quiet(lucy)))&
(curious(mary)) | ~kind(fred) | [
"p0",
"p7",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7652857740826690558521756
% SZS output start Proof for 7652857740826690558521756
1. ! [X0] : ((calm(X0) & ~kind(X0)) <=> (creative(X0) | ~strong(X0))) [input p0]
8. ! [X0] : (~creative(X0) => (kind(X0) <~> ~generous(X0))) [input p7]
19. ~kind(fred) <~> ~generous(fred) [input p18]
24. kind(fred) [input hypothesis]
32. ! [X0] : ((kind(X0) <~> ~generous(X0)) | creative(X0)) [ennf transformation 8]
41. ! [X0] : (((calm(X0) & ~kind(X0)) | (~creative(X0) & strong(X0))) & ((creative(X0) | ~strong(X0)) | (~calm(X0) | kind(X0)))) [nnf transformation 1]
42. ! [X0] : (((calm(X0) & ~kind(X0)) | (~creative(X0) & strong(X0))) & (creative(X0) | ~strong(X0) | ~calm(X0) | kind(X0))) [flattening 41]
54. ! [X0] : (((generous(X0) | ~kind(X0)) & (~generous(X0) | kind(X0))) | creative(X0)) [nnf transformation 32]
68. (generous(fred) | kind(fred)) & (~generous(fred) | ~kind(fred)) [nnf transformation 19]
73. ~kind(X0) | ~creative(X0) [cnf transformation 42]
92. generous(X0) | ~kind(X0) | creative(X0) [cnf transformation 54]
120. ~generous(fred) | ~kind(fred) [cnf transformation 68]
121. generous(fred) | kind(fred) [cnf transformation 68]
126. kind(fred) [cnf transformation 24]
175. generous(X0) | ~kind(X0) [subsumption resolution 92,73]
229. generous(fred) [subsumption resolution 121,175]
230. ~kind(fred) [subsumption resolution 120,229]
249. $false [subsumption resolution 126,230]
% SZS output end Proof for 7652857740826690558521756
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is not humble.
If someone is not strong or not tall then someone is both not old and funny and vice versa.
Everyone who is both generous and not wise is either not strong or not happy and vice versa.
Everyone who is either tall or patient is both humble and wise.
If someone is both happy and tall then alice is either creative or not funny and vice versa.
Everyone who is either not rich or patient is rich or wise.
If someone is either humble or generous then someone is kind.
Everyone who is not tall or humble is patient and vice versa.
If someone is generous or not tall then alice is either not creative or calm and vice versa.
If someone is both not kind and not calm then someone is either happy or brave and vice versa.
Everyone who is either tall or not old is kind.
Everyone who is not generous is not calm and vice versa.
If lucy is patient or rich then someone is old or not rich and vice versa.
Everyone who is not quiet or not patient is both creative and not happy.
If paul is both strong and not tall then someone is not creative or not generous and vice versa.
Everyone who is generous is both not curious and quiet.
Someone is either not tall or rich.
Mary is both happy and wise.
John is either not humble or wise.
Alice is funny or not wise.
Fred is both not tall and wise.
Someone is either creative or not strong. | Paul is calm. | entailment | (![X]:(~generous(X)=>~humble(X)))&
((?[X]:((~strong(X)|~tall(X))))<=>(?[X]:((~old(X)&funny(X)))))&
(![X]:((generous(X)&~wise(X))<=>(~strong(X)<~>~happy(X))))&
(![X]:((tall(X)<~>patient(X))=>(humble(X)&wise(X))))&
((?[X]:((happy(X)&tall(X))))<=>((creative(alice)<~>~funny(alice))))&
(![X]:((~rich(X)<~>patient(X))=>(rich(X)|wise(X))))&
((?[X]:((humble(X)<~>generous(X))))=>(?[X]:(kind(X))))&
(![X]:((~tall(X)|humble(X))<=>patient(X)))&
((?[X]:((generous(X)|~tall(X))))<=>((~creative(alice)<~>calm(alice))))&
((?[X]:((~kind(X)&~calm(X))))<=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:((tall(X)<~>~old(X))=>kind(X)))&
(![X]:(~generous(X)<=>~calm(X)))&
(((patient(lucy)|rich(lucy)))<=>(?[X]:((old(X)|~rich(X)))))&
(![X]:((~quiet(X)|~patient(X))=>(creative(X)&~happy(X))))&
(((strong(paul)&~tall(paul)))<=>(?[X]:((~creative(X)|~generous(X)))))&
(![X]:(generous(X)=>(~curious(X)&quiet(X))))&
(?[X]:((~tall(X)<~>rich(X))))&
((happy(mary)&wise(mary)))&
((~humble(john)<~>wise(john)))&
((funny(alice)|~wise(alice)))&
((~tall(fred)&wise(fred)))&
(?[X]:((creative(X)<~>~strong(X)))) | calm(paul) | [
"p0",
"p3",
"p7",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5544640480691002618412822
% SZS output start Proof for 5544640480691002618412822
1. ! [X0] : (~generous(X0) => ~humble(X0)) [input p0]
4. ! [X0] : ((tall(X0) <~> patient(X0)) => (wise(X0) & humble(X0))) [input p3]
8. ! [X0] : ((humble(X0) | ~tall(X0)) <=> patient(X0)) [input p7]
12. ! [X0] : (~generous(X0) <=> ~calm(X0)) [input p11]
15. (~tall(paul) & strong(paul)) <=> ? [X0] : (~generous(X0) | ~creative(X0)) [input p14]
23. ~calm(paul) [input hypothesis]
30. ! [X0] : (~humble(X0) | generous(X0)) [ennf transformation 1]
31. ! [X0] : ((wise(X0) & humble(X0)) | (tall(X0) <=> patient(X0))) [ennf transformation 4]
44. ! [X0] : ((wise(X0) & humble(X0)) | ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0)))) [nnf transformation 31]
54. ! [X0] : (((humble(X0) | ~tall(X0)) | ~patient(X0)) & (patient(X0) | (~humble(X0) & tall(X0)))) [nnf transformation 8]
55. ! [X0] : ((humble(X0) | ~tall(X0) | ~patient(X0)) & (patient(X0) | (~humble(X0) & tall(X0)))) [flattening 54]
66. ! [X0] : ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0))) [nnf transformation 12]
72. ((~tall(paul) & strong(paul)) | ! [X0] : (generous(X0) & creative(X0))) & (? [X0] : (~generous(X0) | ~creative(X0)) | (tall(paul) | ~strong(paul))) [nnf transformation 15]
73. ((~tall(paul) & strong(paul)) | ! [X0] : (generous(X0) & creative(X0))) & (? [X0] : (~generous(X0) | ~creative(X0)) | tall(paul) | ~strong(paul)) [flattening 72]
74. ((~tall(paul) & strong(paul)) | ! [X0] : (generous(X0) & creative(X0))) & (? [X1] : (~generous(X1) | ~creative(X1)) | tall(paul) | ~strong(paul)) [rectify 73]
75. ? [X1] : (~generous(X1) | ~creative(X1)) => (~generous(sK8) | ~creative(sK8)) [choice axiom]
76. ((~tall(paul) & strong(paul)) | ! [X0] : (generous(X0) & creative(X0))) & ((~generous(sK8) | ~creative(sK8)) | tall(paul) | ~strong(paul)) [skolemisation 74,75]
84. ~humble(X0) | generous(X0) [cnf transformation 30]
97. ~patient(X0) | tall(X0) | humble(X0) [cnf transformation 44]
110. patient(X0) | tall(X0) [cnf transformation 55]
112. humble(X0) | ~tall(X0) | ~patient(X0) [cnf transformation 55]
128. ~generous(X0) | calm(X0) [cnf transformation 66]
139. ~tall(paul) | generous(X0) [cnf transformation 76]
151. ~calm(paul) [cnf transformation 23]
216. ~patient(X0) | humble(X0) [subsumption resolution 112,97]
296. 32 <=> ! [X0] : generous(X0) [avatar definition]
297. generous(X0) <- (32) [avatar component clause 296]
299. 33 <=> tall(paul) [avatar definition]
301. ~tall(paul) <- (~33) [avatar component clause 299]
302. 32 | ~33 [avatar split clause 139,299,296]
370. tall(X0) | humble(X0) [resolution 216,110]
414. 50 <=> generous(paul) [avatar definition]
416. generous(paul) <- (50) [avatar component clause 414]
419. calm(X1) <- (32) [resolution 297,128]
444. $false <- (32) [resolution 419,151]
446. ~32 [avatar contradiction clause 444]
658. humble(paul) <- (~33) [resolution 370,301]
741. generous(paul) <- (~33) [resolution 658,84]
744. 50 | 33 [avatar split clause 741,299,414]
746. calm(paul) <- (50) [resolution 416,128]
747. $false <- (50) [subsumption resolution 746,151]
748. ~50 [avatar contradiction clause 747]
749. $false [avatar sat refutation 302,446,744,748]
% SZS output end Proof for 5544640480691002618412822
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or not funny then susan is both humble and funny.
Everyone who is both not tall and not humble is either humble or tall and vice versa.
Everyone who is either not strong or patient is both funny and not curious.
Everyone who is both tall and not tall is not strong and vice versa.
If someone is tall then john is humble.
Everyone who is creative is rich and vice versa.
If someone is creative then john is not wise and vice versa.
Everyone who is both not creative and brave is not old or not humble and vice versa.
If alice is not rich or not kind then susan is funny or not rich and vice versa.
Everyone who is brave or not funny is humble.
If mary is strong or not calm then someone is either not rich or not humble and vice versa.
Everyone who is brave or not humble is either not quiet or not creative and vice versa.
Everyone who is strong or not quiet is either calm or curious and vice versa.
If lucy is either not humble or not quiet then john is either quiet or not kind and vice versa.
Everyone who is not brave is either not creative or strong and vice versa.
Someone is either brave or funny.
Someone is quiet.
Mary is funny.
Susan is not happy or not brave.
John is tall or not funny.
Someone is not creative or patient.
Lucy is either quiet or funny.
Lucy is either not quiet or brave. | Lucy is rich. | contradiction | ((?[X]:((kind(X)<~>~funny(X))))=>((humble(susan)&funny(susan))))&
(![X]:((~tall(X)&~humble(X))<=>(humble(X)<~>tall(X))))&
(![X]:((~strong(X)<~>patient(X))=>(funny(X)&~curious(X))))&
(![X]:((tall(X)&~tall(X))<=>~strong(X)))&
((?[X]:(tall(X)))=>(humble(john)))&
(![X]:(creative(X)<=>rich(X)))&
((?[X]:(creative(X)))<=>(~wise(john)))&
(![X]:((~creative(X)&brave(X))<=>(~old(X)|~humble(X))))&
(((~rich(alice)|~kind(alice)))<=>((funny(susan)|~rich(susan))))&
(![X]:((brave(X)|~funny(X))=>humble(X)))&
(((strong(mary)|~calm(mary)))<=>(?[X]:((~rich(X)<~>~humble(X)))))&
(![X]:((brave(X)|~humble(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((strong(X)|~quiet(X))<=>(calm(X)<~>curious(X))))&
(((~humble(lucy)<~>~quiet(lucy)))<=>((quiet(john)<~>~kind(john))))&
(![X]:(~brave(X)<=>(~creative(X)<~>strong(X))))&
(?[X]:((brave(X)<~>funny(X))))&
(?[X]:(quiet(X)))&
(funny(mary))&
((~happy(susan)|~brave(susan)))&
((tall(john)|~funny(john)))&
(?[X]:((~creative(X)|patient(X))))&
((quiet(lucy)<~>funny(lucy)))&
((~quiet(lucy)<~>brave(lucy))) | rich(lucy) | [
"p1",
"p3",
"p5",
"p11",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2192637976424206946175641
% SZS output start Proof for 2192637976424206946175641
2. ! [X0] : ((~humble(X0) & ~tall(X0)) <=> (humble(X0) <~> tall(X0))) [input p1]
4. ! [X0] : ((~tall(X0) & tall(X0)) <=> ~strong(X0)) [input p3]
6. ! [X0] : (creative(X0) <=> rich(X0)) [input p5]
12. ! [X0] : ((~humble(X0) | brave(X0)) <=> (~quiet(X0) <~> ~creative(X0))) [input p11]
15. ! [X0] : (~brave(X0) <=> (~creative(X0) <~> strong(X0))) [input p14]
23. ~quiet(lucy) <~> brave(lucy) [input p22]
24. rich(lucy) [input hypothesis]
31. ! [X0] : (((~humble(X0) & ~tall(X0)) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) & (((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | (humble(X0) | tall(X0)))) [nnf transformation 2]
32. ! [X0] : (((~humble(X0) & ~tall(X0)) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) & (((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | humble(X0) | tall(X0))) [flattening 31]
34. ! [X0] : (((~tall(X0) & tall(X0)) | strong(X0)) & (~strong(X0) | (tall(X0) | ~tall(X0)))) [nnf transformation 4]
35. ! [X0] : (((~tall(X0) & tall(X0)) | strong(X0)) & (~strong(X0) | tall(X0) | ~tall(X0))) [flattening 34]
36. ! [X0] : ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0))) [nnf transformation 6]
50. ! [X0] : (((~humble(X0) | brave(X0)) | ((~quiet(X0) | creative(X0)) & (~creative(X0) | quiet(X0)))) & (((creative(X0) | quiet(X0)) & (~creative(X0) | ~quiet(X0))) | (humble(X0) & ~brave(X0)))) [nnf transformation 12]
51. ! [X0] : ((~humble(X0) | brave(X0) | ((~quiet(X0) | creative(X0)) & (~creative(X0) | quiet(X0)))) & (((creative(X0) | quiet(X0)) & (~creative(X0) | ~quiet(X0))) | (humble(X0) & ~brave(X0)))) [flattening 50]
55. ! [X0] : ((~brave(X0) | ((~creative(X0) | ~strong(X0)) & (strong(X0) | creative(X0)))) & (((~strong(X0) | creative(X0)) & (strong(X0) | ~creative(X0))) | brave(X0))) [nnf transformation 15]
64. (~brave(lucy) | quiet(lucy)) & (brave(lucy) | ~quiet(lucy)) [nnf transformation 23]
69. tall(X0) | humble(X0) | humble(X0) | tall(X0) [cnf transformation 32]
72. ~tall(X0) | humble(X0) | ~tall(X0) [cnf transformation 32]
80. tall(X0) | strong(X0) [cnf transformation 35]
81. ~tall(X0) | strong(X0) [cnf transformation 35]
84. ~rich(X0) | creative(X0) [cnf transformation 36]
108. ~humble(X0) | brave(X0) | ~creative(X0) | quiet(X0) [cnf transformation 51]
127. ~brave(X0) | ~creative(X0) | ~strong(X0) [cnf transformation 55]
136. brave(lucy) | ~quiet(lucy) [cnf transformation 64]
138. rich(lucy) [cnf transformation 24]
139. tall(X0) | humble(X0) [duplicate literal removal 69]
140. ~tall(X0) | humble(X0) [duplicate literal removal 72]
160. humble(X0) [subsumption resolution 139,140]
161. strong(X0) [subsumption resolution 80,81]
206. ~creative(X0) | brave(X0) | quiet(X0) [subsumption resolution 108,160]
219. 15 <=> quiet(lucy) [avatar definition]
229. ~brave(X0) | ~creative(X0) [subsumption resolution 127,161]
266. 23 <=> brave(lucy) [avatar definition]
267. brave(lucy) <- (23) [avatar component clause 266]
270. ~15 | 23 [avatar split clause 136,266,219]
272. creative(lucy) [resolution 84,138]
312. brave(lucy) | quiet(lucy) [resolution 206,272]
327. 15 | 23 [avatar split clause 312,266,219]
338. ~creative(lucy) <- (23) [resolution 267,229]
339. $false <- (23) [subsumption resolution 338,272]
340. ~23 [avatar contradiction clause 339]
341. $false [avatar sat refutation 270,327,340]
% SZS output end Proof for 2192637976424206946175641
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or not wise is both old and quiet and vice versa.
Everyone who is both not brave and not generous is either not quiet or tall and vice versa.
If someone is either not brave or old then someone is both not happy and not quiet and vice versa.
If someone is either old or quiet then lucy is not generous and vice versa.
If someone is either not quiet or rich then someone is both strong and funny and vice versa.
Everyone who is not old or not creative is not kind and vice versa.
Everyone who is not generous is either kind or happy and vice versa.
If alice is either not patient or curious then someone is both kind and not kind.
Everyone who is calm or funny is not curious or funny and vice versa.
If mary is strong or not curious then someone is not generous and vice versa.
If john is both not quiet and not patient then someone is either not creative or wise.
If lucy is either old or not strong then susan is patient or not humble.
Everyone who is not quiet is either old or rich and vice versa.
Everyone who is generous or old is funny or not happy and vice versa.
If alice is both creative and strong then lucy is kind.
Everyone who is not happy or not humble is either not old or creative and vice versa.
Someone is both kind and generous.
Someone is generous.
Someone is strong or happy.
Someone is creative or kind.
John is not rich or quiet.
Someone is both not happy and kind.
Someone is not creative or wise.
Someone is calm or humble. | John is old. | entailment | (![X]:((~rich(X)|~wise(X))<=>(old(X)&quiet(X))))&
(![X]:((~brave(X)&~generous(X))<=>(~quiet(X)<~>tall(X))))&
((?[X]:((~brave(X)<~>old(X))))<=>(?[X]:((~happy(X)&~quiet(X)))))&
((?[X]:((old(X)<~>quiet(X))))<=>(~generous(lucy)))&
((?[X]:((~quiet(X)<~>rich(X))))<=>(?[X]:((strong(X)&funny(X)))))&
(![X]:((~old(X)|~creative(X))<=>~kind(X)))&
(![X]:(~generous(X)<=>(kind(X)<~>happy(X))))&
(((~patient(alice)<~>curious(alice)))=>(?[X]:((kind(X)&~kind(X)))))&
(![X]:((calm(X)|funny(X))<=>(~curious(X)|funny(X))))&
(((strong(mary)|~curious(mary)))<=>(?[X]:(~generous(X))))&
(((~quiet(john)&~patient(john)))=>(?[X]:((~creative(X)<~>wise(X)))))&
(((old(lucy)<~>~strong(lucy)))=>((patient(susan)|~humble(susan))))&
(![X]:(~quiet(X)<=>(old(X)<~>rich(X))))&
(![X]:((generous(X)|old(X))<=>(funny(X)|~happy(X))))&
(((creative(alice)&strong(alice)))=>(kind(lucy)))&
(![X]:((~happy(X)|~humble(X))<=>(~old(X)<~>creative(X))))&
(?[X]:((kind(X)&generous(X))))&
(?[X]:(generous(X)))&
(?[X]:((strong(X)|happy(X))))&
(?[X]:((creative(X)|kind(X))))&
((~rich(john)|quiet(john)))&
(?[X]:((~happy(X)&kind(X))))&
(?[X]:((~creative(X)|wise(X))))&
(?[X]:((calm(X)|humble(X)))) | old(john) | [
"p0",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1399048230710104072174608
% SZS output start Proof for 1399048230710104072174608
1. ! [X0] : ((~wise(X0) | ~rich(X0)) <=> (quiet(X0) & old(X0))) [input p0]
13. ! [X0] : (~quiet(X0) <=> (old(X0) <~> rich(X0))) [input p12]
21. quiet(john) | ~rich(john) [input p20]
25. ~old(john) [input hypothesis]
35. ! [X0] : (((~wise(X0) | ~rich(X0)) | (~quiet(X0) | ~old(X0))) & ((quiet(X0) & old(X0)) | (wise(X0) & rich(X0)))) [nnf transformation 1]
36. ! [X0] : ((~wise(X0) | ~rich(X0) | ~quiet(X0) | ~old(X0)) & ((quiet(X0) & old(X0)) | (wise(X0) & rich(X0)))) [flattening 35]
70. ! [X0] : ((~quiet(X0) | ((old(X0) | ~rich(X0)) & (rich(X0) | ~old(X0)))) & (((~rich(X0) | ~old(X0)) & (rich(X0) | old(X0))) | quiet(X0))) [nnf transformation 13]
89. old(X0) | rich(X0) [cnf transformation 36]
91. quiet(X0) | rich(X0) [cnf transformation 36]
140. ~quiet(X0) | rich(X0) | ~old(X0) [cnf transformation 70]
141. ~quiet(X0) | old(X0) | ~rich(X0) [cnf transformation 70]
158. quiet(john) | ~rich(john) [cnf transformation 21]
163. ~old(john) [cnf transformation 25]
210. 11 <=> ! [X1] : (old(X1) | ~quiet(X1)) [avatar definition]
211. ~quiet(X1) | old(X1) <- (11) [avatar component clause 210]
280. 26 <=> quiet(john) [avatar definition]
282. quiet(john) <- (26) [avatar component clause 280]
315. ~quiet(X0) | old(X0) [subsumption resolution 141,89]
316. 11 [avatar split clause 315,210]
317. rich(X0) | ~old(X0) [subsumption resolution 140,91]
318. rich(X0) [subsumption resolution 317,89]
344. quiet(john) [subsumption resolution 158,318]
345. 26 [avatar split clause 344,280]
378. old(john) <- (11, 26) [resolution 211,282]
381. $false <- (11, 26) [subsumption resolution 378,163]
382. ~11 | ~26 [avatar contradiction clause 381]
383. $false [avatar sat refutation 316,345,382]
% SZS output end Proof for 1399048230710104072174608
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or patient is generous or not creative and vice versa. Everyone who is not kind is both not funny and not old. Everyone who is not humble or wise is not brave or rich and vice versa. Everyone who is either not calm or generous is both patient and not curious and vice versa. Everyone who is both not rich and brave is not calm or generous. Everyone who is either not patient or wise is either happy or not creative. If fred is not 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. Everyone who is either not strong or happy is not tall or calm. If fred is old or not brave then john is not strong or curious and vice versa. If susan is either not kind or tall then someone is not brave or patient. Everyone who is not quiet or humble is strong. Someone is either patient or old. Someone is either wise or not creative. Someone is not brave or not strong. Someone is creative or brave. Mary is not creative or curious. Someone is either not wise or wise. Mary is calm or strong. | Mary is generous. | neutral | (![X]:((~curious(X)|patient(X))<=>(generous(X)|~creative(X))))&
(![X]:(~kind(X)=>(~funny(X)&~old(X))))&
(![X]:((~humble(X)|wise(X))<=>(~brave(X)|rich(X))))&
(![X]:((~calm(X)<~>generous(X))<=>(patient(X)&~curious(X))))&
(![X]:((~rich(X)&brave(X))=>(~calm(X)|generous(X))))&
(![X]:((~patient(X)<~>wise(X))=>(happy(X)<~>~creative(X))))&
((~curious(fred))<=>(?[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]:((~strong(X)<~>happy(X))=>(~tall(X)|calm(X))))&
(((old(fred)|~brave(fred)))<=>((~strong(john)|curious(john))))&
(((~kind(susan)<~>tall(susan)))=>(?[X]:((~brave(X)|patient(X)))))&
(![X]:((~quiet(X)|humble(X))=>strong(X)))&
(?[X]:((patient(X)<~>old(X))))&
(?[X]:((wise(X)<~>~creative(X))))&
(?[X]:((~brave(X)|~strong(X))))&
(?[X]:((creative(X)|brave(X))))&
((~creative(mary)|curious(mary)))&
(?[X]:((~wise(X)<~>wise(X))))&
((calm(mary)|strong(mary))) | generous(mary) | [] | null | 0 |
Everyone who is both not patient and patient is rich or kind and vice versa.
If someone is both not funny and not happy then mary is either tall or not generous and vice versa.
Everyone who is both calm and not generous is either not creative or not funny.
Everyone who is not rich or not happy is not rich.
If someone is both not quiet and not wise then someone is not generous and vice versa.
Everyone who is either tall or not brave is patient and vice versa.
If someone is not humble or not curious then someone is both quiet and creative.
If someone is either tall or creative then someone is patient or not brave.
If alice is both not rich and old then susan is either not calm or patient.
If fred is quiet then someone is not funny or kind.
Everyone who is both calm and not creative is either not funny or wise and vice versa.
If someone is both humble and rich then fred is either not brave or curious and vice versa.
If someone is rich or creative then someone is not humble.
If susan is not strong or not patient then someone is not patient or not wise and vice versa.
Everyone who is both not creative and patient is either rich or not creative and vice versa.
If alice is both strong and patient then fred is either not quiet or generous.
Someone is old or creative.
John is both strong and wise.
Lucy is not wise or creative.
Lucy is both not wise and not brave.
Lucy is not humble or humble.
Someone is either brave or tall.
Fred is either not generous or rich. | Alice is not rich. | entailment | (![X]:((~patient(X)&patient(X))<=>(rich(X)|kind(X))))&
((?[X]:((~funny(X)&~happy(X))))<=>((tall(mary)<~>~generous(mary))))&
(![X]:((calm(X)&~generous(X))=>(~creative(X)<~>~funny(X))))&
(![X]:((~rich(X)|~happy(X))=>~rich(X)))&
((?[X]:((~quiet(X)&~wise(X))))<=>(?[X]:(~generous(X))))&
(![X]:((tall(X)<~>~brave(X))<=>patient(X)))&
((?[X]:((~humble(X)|~curious(X))))=>(?[X]:((quiet(X)&creative(X)))))&
((?[X]:((tall(X)<~>creative(X))))=>(?[X]:((patient(X)|~brave(X)))))&
(((~rich(alice)&old(alice)))=>((~calm(susan)<~>patient(susan))))&
((quiet(fred))=>(?[X]:((~funny(X)|kind(X)))))&
(![X]:((calm(X)&~creative(X))<=>(~funny(X)<~>wise(X))))&
((?[X]:((humble(X)&rich(X))))<=>((~brave(fred)<~>curious(fred))))&
((?[X]:((rich(X)|creative(X))))=>(?[X]:(~humble(X))))&
(((~strong(susan)|~patient(susan)))<=>(?[X]:((~patient(X)|~wise(X)))))&
(![X]:((~creative(X)&patient(X))<=>(rich(X)<~>~creative(X))))&
(((strong(alice)&patient(alice)))=>((~quiet(fred)<~>generous(fred))))&
(?[X]:((old(X)|creative(X))))&
((strong(john)&wise(john)))&
((~wise(lucy)|creative(lucy)))&
((~wise(lucy)&~brave(lucy)))&
((~humble(lucy)|humble(lucy)))&
(?[X]:((brave(X)<~>tall(X))))&
((~generous(fred)<~>rich(fred))) | ~rich(alice) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 5330742689167711609230440
% SZS output start Proof for 5330742689167711609230440
1. ! [X0] : ((patient(X0) & ~patient(X0)) <=> (kind(X0) | rich(X0))) [input p0]
24. rich(alice) [input hypothesis]
40. ! [X0] : (((patient(X0) & ~patient(X0)) | (~kind(X0) & ~rich(X0))) & ((kind(X0) | rich(X0)) | (~patient(X0) | patient(X0)))) [nnf transformation 1]
41. ! [X0] : (((patient(X0) & ~patient(X0)) | (~kind(X0) & ~rich(X0))) & (kind(X0) | rich(X0) | ~patient(X0) | patient(X0))) [flattening 40]
87. ~patient(X0) | ~rich(X0) [cnf transformation 41]
89. patient(X0) | ~rich(X0) [cnf transformation 41]
154. rich(alice) [cnf transformation 24]
158. ~rich(X0) [subsumption resolution 87,89]
359. $false [subsumption resolution 154,158]
% SZS output end Proof for 5330742689167711609230440
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is brave.
Everyone who is both not wise and humble is generous.
Everyone who is both curious and not wise is both creative and not generous.
Everyone who is either patient or quiet is either not creative or not brave and vice versa.
If someone is either not kind or not quiet then mary is not calm.
Everyone who is tall is rich or wise and vice versa.
If someone is humble or quiet then fred is not wise.
Everyone who is both calm and not happy is brave or strong and vice versa.
Everyone who is both not creative and funny is not calm or happy.
If someone is both tall and not funny then someone is humble or rich and vice versa.
Everyone who is rich is calm or brave.
If someone is both creative and strong then mary is both not kind and happy and vice versa.
If susan is not brave or kind then fred is either not old or not funny.
If lucy is both not patient and happy then paul is not generous or not calm.
If someone is creative then paul is both brave and rich and vice versa.
If someone is not humble then paul is both quiet and wise.
Someone is not brave.
Someone is not kind or not funny.
Someone is not humble or generous.
Someone is old.
Paul is not calm.
Lucy is funny.
Someone is not rich or not old.
Someone is either humble or not calm. | Paul is rich. | contradiction | (![X]:(generous(X)=>brave(X)))&
(![X]:((~wise(X)&humble(X))=>generous(X)))&
(![X]:((curious(X)&~wise(X))=>(creative(X)&~generous(X))))&
(![X]:((patient(X)<~>quiet(X))<=>(~creative(X)<~>~brave(X))))&
((?[X]:((~kind(X)<~>~quiet(X))))=>(~calm(mary)))&
(![X]:(tall(X)<=>(rich(X)|wise(X))))&
((?[X]:((humble(X)|quiet(X))))=>(~wise(fred)))&
(![X]:((calm(X)&~happy(X))<=>(brave(X)|strong(X))))&
(![X]:((~creative(X)&funny(X))=>(~calm(X)|happy(X))))&
((?[X]:((tall(X)&~funny(X))))<=>(?[X]:((humble(X)|rich(X)))))&
(![X]:(rich(X)=>(calm(X)|brave(X))))&
((?[X]:((creative(X)&strong(X))))<=>((~kind(mary)&happy(mary))))&
(((~brave(susan)|kind(susan)))=>((~old(fred)<~>~funny(fred))))&
(((~patient(lucy)&happy(lucy)))=>((~generous(paul)|~calm(paul))))&
((?[X]:(creative(X)))<=>((brave(paul)&rich(paul))))&
((?[X]:(~humble(X)))=>((quiet(paul)&wise(paul))))&
(?[X]:(~brave(X)))&
(?[X]:((~kind(X)|~funny(X))))&
(?[X]:((~humble(X)|generous(X))))&
(?[X]:(old(X)))&
(~calm(paul))&
(funny(lucy))&
(?[X]:((~rich(X)|~old(X))))&
(?[X]:((humble(X)<~>~calm(X)))) | rich(paul) | [
"p7",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7530540011429230182590419
% SZS output start Proof for 7530540011429230182590419
8. ! [X0] : ((~happy(X0) & calm(X0)) <=> (strong(X0) | brave(X0))) [input p7]
11. ! [X0] : (rich(X0) => (brave(X0) | calm(X0))) [input p10]
21. ~calm(paul) [input p20]
25. rich(paul) [input hypothesis]
35. ! [X0] : ((brave(X0) | calm(X0)) | ~rich(X0)) [ennf transformation 11]
36. ! [X0] : (brave(X0) | calm(X0) | ~rich(X0)) [flattening 35]
45. ! [X0] : (((~happy(X0) & calm(X0)) | (~strong(X0) & ~brave(X0))) & ((strong(X0) | brave(X0)) | (happy(X0) | ~calm(X0)))) [nnf transformation 8]
46. ! [X0] : (((~happy(X0) & calm(X0)) | (~strong(X0) & ~brave(X0))) & (strong(X0) | brave(X0) | happy(X0) | ~calm(X0))) [flattening 45]
94. ~brave(X0) | calm(X0) [cnf transformation 46]
104. brave(X0) | calm(X0) | ~rich(X0) [cnf transformation 36]
123. ~calm(paul) [cnf transformation 21]
128. rich(paul) [cnf transformation 25]
180. ~rich(X0) | calm(X0) [subsumption resolution 104,94]
237. 25 <=> calm(paul) [avatar definition]
239. ~calm(paul) <- (~25) [avatar component clause 237]
246. 27 <=> rich(paul) [avatar definition]
247. rich(paul) <- (27) [avatar component clause 246]
290. ~25 [avatar split clause 123,237]
310. 27 [avatar split clause 128,246]
332. calm(paul) <- (27) [resolution 180,247]
333. $false <- (~25, 27) [subsumption resolution 332,239]
334. 25 | ~27 [avatar contradiction clause 333]
335. $false [avatar sat refutation 290,310,334]
% SZS output end Proof for 7530540011429230182590419
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative is either not tall or not humble and vice versa.
If someone is humble or not humble then someone is both humble and not funny and vice versa.
If mary is not brave or not strong then mary is both tall and not patient.
Everyone who is not rich is both not funny and funny and vice versa.
Everyone who is happy is either calm or kind.
If susan is not kind then alice is both patient and not humble and vice versa.
Everyone who is not creative is generous or creative and vice versa.
If lucy is either not creative or humble then mary is either not brave or not humble.
If john is not curious then someone is calm or not humble.
Everyone who is either kind or not generous is rich.
Everyone who is either not patient or not old is not generous and vice versa.
If someone is patient or not wise then someone is both not curious and not funny.
Everyone who is both curious and not calm is not patient and vice versa.
Everyone who is both quiet and calm is not humble and vice versa.
John is not brave.
Paul is both not happy and brave.
Mary is quiet.
John is both strong and not humble. | John is not calm. | contradiction | (![X]:(~creative(X)<=>(~tall(X)<~>~humble(X))))&
((?[X]:((humble(X)|~humble(X))))<=>(?[X]:((humble(X)&~funny(X)))))&
(((~brave(mary)|~strong(mary)))=>((tall(mary)&~patient(mary))))&
(![X]:(~rich(X)<=>(~funny(X)&funny(X))))&
(![X]:(happy(X)=>(calm(X)<~>kind(X))))&
((~kind(susan))<=>((patient(alice)&~humble(alice))))&
(![X]:(~creative(X)<=>(generous(X)|creative(X))))&
(((~creative(lucy)<~>humble(lucy)))=>((~brave(mary)<~>~humble(mary))))&
((~curious(john))=>(?[X]:((calm(X)|~humble(X)))))&
(![X]:((kind(X)<~>~generous(X))=>rich(X)))&
(![X]:((~patient(X)<~>~old(X))<=>~generous(X)))&
((?[X]:((patient(X)|~wise(X))))=>(?[X]:((~curious(X)&~funny(X)))))&
(![X]:((curious(X)&~calm(X))<=>~patient(X)))&
(![X]:((quiet(X)&calm(X))<=>~humble(X)))&
(~brave(john))&
((~happy(paul)&brave(paul)))&
(quiet(mary))&
((strong(john)&~humble(john))) | ~calm(john) | [
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1414551966231277746137333
% SZS output start Proof for 1414551966231277746137333
14. ! [X0] : ((calm(X0) & quiet(X0)) <=> ~humble(X0)) [input p13]
18. ~humble(john) & strong(john) [input p17]
19. ~calm(john) [input hypothesis]
27. ~humble(john) [pure predicate removal 18]
55. ! [X0] : (((calm(X0) & quiet(X0)) | humble(X0)) & (~humble(X0) | (~calm(X0) | ~quiet(X0)))) [nnf transformation 14]
56. ! [X0] : (((calm(X0) & quiet(X0)) | humble(X0)) & (~humble(X0) | ~calm(X0) | ~quiet(X0))) [flattening 55]
93. calm(X0) | humble(X0) [cnf transformation 56]
97. ~humble(john) [cnf transformation 27]
98. ~calm(john) [cnf transformation 19]
191. humble(john) [resolution 93,98]
193. $false [subsumption resolution 191,97]
% SZS output end Proof for 1414551966231277746137333
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is both curious and humble then paul is both tall and not happy. Everyone who is both not brave and old is either patient or wise. Everyone who is not calm is both strong and old. If lucy is either not creative or not rich then someone is both generous and wise. If alice is patient then someone is not happy and vice versa. Everyone who is not strong or kind is both not rich and not patient and vice versa. Everyone who is not rich or not wise is both generous and quiet and vice versa. Everyone who is happy is creative and vice versa. If someone is both brave and not funny then someone is either curious or not kind. If mary is not rich or not wise then someone is happy. If john is old or funny then susan is either not wise or calm and vice versa. Everyone who is both not kind and old is not happy. If someone is both not wise and funny then fred is not creative or not strong. If someone is humble then someone is not strong and vice versa. Everyone who is either patient or humble is old. Everyone who is both not happy and generous is not humble or calm. Susan is not creative or not funny. Paul is either rich or not wise. Paul is both brave and not kind. Alice is not rich or humble. Someone is curious or brave. Someone is wise or not strong. Someone is not creative or curious. Fred is both patient and brave. | Fred is not quiet. | neutral | ((?[X]:((curious(X)&humble(X))))=>((tall(paul)&~happy(paul))))&
(![X]:((~brave(X)&old(X))=>(patient(X)<~>wise(X))))&
(![X]:(~calm(X)=>(strong(X)&old(X))))&
(((~creative(lucy)<~>~rich(lucy)))=>(?[X]:((generous(X)&wise(X)))))&
((patient(alice))<=>(?[X]:(~happy(X))))&
(![X]:((~strong(X)|kind(X))<=>(~rich(X)&~patient(X))))&
(![X]:((~rich(X)|~wise(X))<=>(generous(X)&quiet(X))))&
(![X]:(happy(X)<=>creative(X)))&
((?[X]:((brave(X)&~funny(X))))=>(?[X]:((curious(X)<~>~kind(X)))))&
(((~rich(mary)|~wise(mary)))=>(?[X]:(happy(X))))&
(((old(john)|funny(john)))<=>((~wise(susan)<~>calm(susan))))&
(![X]:((~kind(X)&old(X))=>~happy(X)))&
((?[X]:((~wise(X)&funny(X))))=>((~creative(fred)|~strong(fred))))&
((?[X]:(humble(X)))<=>(?[X]:(~strong(X))))&
(![X]:((patient(X)<~>humble(X))=>old(X)))&
(![X]:((~happy(X)&generous(X))=>(~humble(X)|calm(X))))&
((~creative(susan)|~funny(susan)))&
((rich(paul)<~>~wise(paul)))&
((brave(paul)&~kind(paul)))&
((~rich(alice)|humble(alice)))&
(?[X]:((curious(X)|brave(X))))&
(?[X]:((wise(X)|~strong(X))))&
(?[X]:((~creative(X)|curious(X))))&
((patient(fred)&brave(fred))) | ~quiet(fred) | [] | null | 0 |
Everyone who is both patient and not tall is both curious and funny.
Everyone who is both curious and humble is either not creative or curious and vice versa.
If lucy is both not wise and not quiet then someone is both strong and not quiet and vice versa.
Everyone who is either strong or rich is either not strong or tall.
If someone is calm then lucy is curious and vice versa.
If mary is either old or not generous then someone is either not kind or generous and vice versa.
Everyone who is not strong or tall is tall and vice versa.
If paul is either patient or rich then someone is either not funny or not happy and vice versa.
If fred is either not wise or humble then someone is not generous or quiet.
If lucy is rich then someone is either strong or not curious.
If someone is either wise or brave then john is not brave.
If someone is both creative and patient then someone is either patient or not quiet.
Everyone who is both not quiet and wise is tall or old and vice versa.
If someone is not quiet then someone is both rich and not patient.
If someone is not funny then paul is rich.
If someone is rich or generous then alice is both old and not brave and vice versa.
John is both kind and not tall.
Fred is not humble.
Alice is strong.
Someone is not rich or not humble.
Someone is either not generous or funny.
Susan is not creative or not kind.
Someone is not funny. | Alice is not old. | contradiction | (![X]:((patient(X)&~tall(X))=>(curious(X)&funny(X))))&
(![X]:((curious(X)&humble(X))<=>(~creative(X)<~>curious(X))))&
(((~wise(lucy)&~quiet(lucy)))<=>(?[X]:((strong(X)&~quiet(X)))))&
(![X]:((strong(X)<~>rich(X))=>(~strong(X)<~>tall(X))))&
((?[X]:(calm(X)))<=>(curious(lucy)))&
(((old(mary)<~>~generous(mary)))<=>(?[X]:((~kind(X)<~>generous(X)))))&
(![X]:((~strong(X)|tall(X))<=>tall(X)))&
(((patient(paul)<~>rich(paul)))<=>(?[X]:((~funny(X)<~>~happy(X)))))&
(((~wise(fred)<~>humble(fred)))=>(?[X]:((~generous(X)|quiet(X)))))&
((rich(lucy))=>(?[X]:((strong(X)<~>~curious(X)))))&
((?[X]:((wise(X)<~>brave(X))))=>(~brave(john)))&
((?[X]:((creative(X)&patient(X))))=>(?[X]:((patient(X)<~>~quiet(X)))))&
(![X]:((~quiet(X)&wise(X))<=>(tall(X)|old(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((rich(X)&~patient(X)))))&
((?[X]:(~funny(X)))=>(rich(paul)))&
((?[X]:((rich(X)|generous(X))))<=>((old(alice)&~brave(alice))))&
((kind(john)&~tall(john)))&
(~humble(fred))&
(strong(alice))&
(?[X]:((~rich(X)|~humble(X))))&
(?[X]:((~generous(X)<~>funny(X))))&
((~creative(susan)|~kind(susan)))&
(?[X]:(~funny(X))) | ~old(alice) | [
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8662070715940320496607428
% SZS output start Proof for 8662070715940320496607428
15. ? [X0] : ~funny(X0) => rich(paul) [input p14]
16. ? [X0] : (generous(X0) | rich(X0)) <=> (~brave(alice) & old(alice)) [input p15]
23. ? [X0] : ~funny(X0) [input p22]
24. ~old(alice) [input hypothesis]
35. rich(paul) | ! [X0] : funny(X0) [ennf transformation 15]
74. (? [X0] : (generous(X0) | rich(X0)) | (brave(alice) | ~old(alice))) & ((~brave(alice) & old(alice)) | ! [X0] : (~generous(X0) & ~rich(X0))) [nnf transformation 16]
75. (? [X0] : (generous(X0) | rich(X0)) | brave(alice) | ~old(alice)) & ((~brave(alice) & old(alice)) | ! [X0] : (~generous(X0) & ~rich(X0))) [flattening 74]
76. (? [X0] : (generous(X0) | rich(X0)) | brave(alice) | ~old(alice)) & ((~brave(alice) & old(alice)) | ! [X1] : (~generous(X1) & ~rich(X1))) [rectify 75]
77. ? [X0] : (generous(X0) | rich(X0)) => (generous(sK8) | rich(sK8)) [choice axiom]
78. ((generous(sK8) | rich(sK8)) | brave(alice) | ~old(alice)) & ((~brave(alice) & old(alice)) | ! [X1] : (~generous(X1) & ~rich(X1))) [skolemisation 76,77]
84. ? [X0] : ~funny(X0) => ~funny(sK11) [choice axiom]
85. ~funny(sK11) [skolemisation 23,84]
138. rich(paul) | funny(X0) [cnf transformation 35]
139. old(alice) | ~rich(X1) [cnf transformation 78]
152. ~funny(sK11) [cnf transformation 85]
153. ~old(alice) [cnf transformation 24]
233. 17 <=> rich(paul) [avatar definition]
234. rich(paul) <- (17) [avatar component clause 233]
326. 37 <=> ! [X0] : funny(X0) [avatar definition]
327. funny(X0) <- (37) [avatar component clause 326]
328. 37 | 17 [avatar split clause 138,233,326]
330. 38 <=> old(alice) [avatar definition]
351. 43 <=> ! [X1] : ~rich(X1) [avatar definition]
352. ~rich(X1) <- (43) [avatar component clause 351]
355. 43 | 38 [avatar split clause 139,330,351]
385. ~38 [avatar split clause 153,330]
388. $false <- (17, 43) [subsumption resolution 234,352]
389. ~17 | ~43 [avatar contradiction clause 388]
396. $false <- (37) [resolution 327,152]
397. ~37 [avatar contradiction clause 396]
398. $false [avatar sat refutation 328,355,385,389,397]
% SZS output end Proof for 8662070715940320496607428
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not rich or patient then alice is not kind. Everyone who is either not creative or wise is both not calm and not happy and vice versa. Everyone who is wise or brave is either not funny or generous. Everyone who is not happy is quiet or not strong and vice versa. If fred is both not creative and old then john is either not old or not quiet and vice versa. Everyone who is not rich or tall is both not wise and not kind and vice versa. If someone is generous or not humble then susan is both happy and strong and vice versa. Everyone who is either wise or not wise is both not strong and not rich. If paul is calm then someone is both creative and happy and vice versa. Everyone who is both brave and not rich is brave or wise and vice versa. Everyone who is either not humble or strong is not patient and vice versa. If someone is both not brave and funny then someone is either happy or not curious and vice versa. If fred is both not generous and kind then someone is generous or wise and vice versa. Everyone who is not generous is either calm or not tall and vice versa. Someone is generous or humble. Mary is either not generous or calm. Someone is either not humble or quiet. Someone is both quiet and old. Someone is not brave or quiet. | John is tall. | neutral | ((?[X]:((~rich(X)|patient(X))))=>(~kind(alice)))&
(![X]:((~creative(X)<~>wise(X))<=>(~calm(X)&~happy(X))))&
(![X]:((wise(X)|brave(X))=>(~funny(X)<~>generous(X))))&
(![X]:(~happy(X)<=>(quiet(X)|~strong(X))))&
(((~creative(fred)&old(fred)))<=>((~old(john)<~>~quiet(john))))&
(![X]:((~rich(X)|tall(X))<=>(~wise(X)&~kind(X))))&
((?[X]:((generous(X)|~humble(X))))<=>((happy(susan)&strong(susan))))&
(![X]:((wise(X)<~>~wise(X))=>(~strong(X)&~rich(X))))&
((calm(paul))<=>(?[X]:((creative(X)&happy(X)))))&
(![X]:((brave(X)&~rich(X))<=>(brave(X)|wise(X))))&
(![X]:((~humble(X)<~>strong(X))<=>~patient(X)))&
((?[X]:((~brave(X)&funny(X))))<=>(?[X]:((happy(X)<~>~curious(X)))))&
(((~generous(fred)&kind(fred)))<=>(?[X]:((generous(X)|wise(X)))))&
(![X]:(~generous(X)<=>(calm(X)<~>~tall(X))))&
(?[X]:((generous(X)|humble(X))))&
((~generous(mary)<~>calm(mary)))&
(?[X]:((~humble(X)<~>quiet(X))))&
(?[X]:((quiet(X)&old(X))))&
(?[X]:((~brave(X)|quiet(X)))) | tall(john) | [] | null | 0 |
If paul is both not funny and creative then someone is either not patient or not creative and vice versa.
Everyone who is not tall or brave is either not patient or not calm.
If someone is patient then someone is not brave.
If someone is not generous or kind then mary is strong and vice versa.
Everyone who is humble or not quiet is not kind.
If someone is calm then mary is generous and vice versa.
If someone is happy then someone is both curious and not rich.
Everyone who is not patient or brave is not generous or generous.
If someone is not creative or funny then fred is both patient and not brave.
Everyone who is happy is both creative and not calm.
Everyone who is either quiet or not calm is kind.
Everyone who is not strong or humble is both patient and brave.
If someone is patient then john is tall.
Everyone who is not curious is patient or not funny.
If alice is either creative or not funny then john is quiet and vice versa.
Everyone who is either not wise or not humble is both not wise and not calm and vice versa.
Susan is either curious or humble.
Fred is either not wise or not old.
Someone is not creative or not wise.
John is not kind.
Someone is not wise.
John is not brave or not happy.
Susan is both not generous and not quiet.
Paul is either not quiet or not old. | Fred is not old. | neutral | (((~funny(paul)&creative(paul)))<=>(?[X]:((~patient(X)<~>~creative(X)))))&
(![X]:((~tall(X)|brave(X))=>(~patient(X)<~>~calm(X))))&
((?[X]:(patient(X)))=>(?[X]:(~brave(X))))&
((?[X]:((~generous(X)|kind(X))))<=>(strong(mary)))&
(![X]:((humble(X)|~quiet(X))=>~kind(X)))&
((?[X]:(calm(X)))<=>(generous(mary)))&
((?[X]:(happy(X)))=>(?[X]:((curious(X)&~rich(X)))))&
(![X]:((~patient(X)|brave(X))=>(~generous(X)|generous(X))))&
((?[X]:((~creative(X)|funny(X))))=>((patient(fred)&~brave(fred))))&
(![X]:(happy(X)=>(creative(X)&~calm(X))))&
(![X]:((quiet(X)<~>~calm(X))=>kind(X)))&
(![X]:((~strong(X)|humble(X))=>(patient(X)&brave(X))))&
((?[X]:(patient(X)))=>(tall(john)))&
(![X]:(~curious(X)=>(patient(X)|~funny(X))))&
(((creative(alice)<~>~funny(alice)))<=>(quiet(john)))&
(![X]:((~wise(X)<~>~humble(X))<=>(~wise(X)&~calm(X))))&
((curious(susan)<~>humble(susan)))&
((~wise(fred)<~>~old(fred)))&
(?[X]:((~creative(X)|~wise(X))))&
(~kind(john))&
(?[X]:(~wise(X)))&
((~brave(john)|~happy(john)))&
((~generous(susan)&~quiet(susan)))&
((~quiet(paul)<~>~old(paul))) | ~old(fred) | [] | null | 0 |
Everyone who is either not rich or not generous is tall or patient and vice versa.
Everyone who is both generous and not kind is both humble and not calm and vice versa.
If someone is not rich then alice is tall or generous and vice versa.
If someone is not humble or patient then paul is either not strong or not tall and vice versa.
Everyone who is both not funny and not quiet is funny.
Everyone who is both quiet and brave is not patient.
Everyone who is not curious is either patient or kind and vice versa.
If someone is either calm or humble then susan is humble or tall and vice versa.
If susan is curious then someone is quiet or creative.
Everyone who is not patient is not brave.
Everyone who is either funny or not brave is either not wise or not quiet.
If alice is both tall and not kind then john is both rich and generous.
If mary is either not calm or not rich then someone is not kind or not calm.
If someone is both not wise and not patient then someone is either happy or not calm and vice versa.
If susan is either not rich or rich then someone is both brave and generous and vice versa.
If susan is both creative and humble then someone is not tall or not old and vice versa.
Paul is not happy or not old.
Susan is not funny.
Someone is not wise or not strong.
Someone is not curious or rich.
John is both not humble and not wise.
Someone is curious or funny.
Someone is either patient or not happy.
Susan is either not funny or not creative. | Susan is not funny. | entailment | (![X]:((~rich(X)<~>~generous(X))<=>(tall(X)|patient(X))))&
(![X]:((generous(X)&~kind(X))<=>(humble(X)&~calm(X))))&
((?[X]:(~rich(X)))<=>((tall(alice)|generous(alice))))&
((?[X]:((~humble(X)|patient(X))))<=>((~strong(paul)<~>~tall(paul))))&
(![X]:((~funny(X)&~quiet(X))=>funny(X)))&
(![X]:((quiet(X)&brave(X))=>~patient(X)))&
(![X]:(~curious(X)<=>(patient(X)<~>kind(X))))&
((?[X]:((calm(X)<~>humble(X))))<=>((humble(susan)|tall(susan))))&
((curious(susan))=>(?[X]:((quiet(X)|creative(X)))))&
(![X]:(~patient(X)=>~brave(X)))&
(![X]:((funny(X)<~>~brave(X))=>(~wise(X)<~>~quiet(X))))&
(((tall(alice)&~kind(alice)))=>((rich(john)&generous(john))))&
(((~calm(mary)<~>~rich(mary)))=>(?[X]:((~kind(X)|~calm(X)))))&
((?[X]:((~wise(X)&~patient(X))))<=>(?[X]:((happy(X)<~>~calm(X)))))&
(((~rich(susan)<~>rich(susan)))<=>(?[X]:((brave(X)&generous(X)))))&
(((creative(susan)&humble(susan)))<=>(?[X]:((~tall(X)|~old(X)))))&
((~happy(paul)|~old(paul)))&
(~funny(susan))&
(?[X]:((~wise(X)|~strong(X))))&
(?[X]:((~curious(X)|rich(X))))&
((~humble(john)&~wise(john)))&
(?[X]:((curious(X)|funny(X))))&
(?[X]:((patient(X)<~>~happy(X))))&
((~funny(susan)<~>~creative(susan))) | ~funny(susan) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7700362307498152236346392
% SZS output start Proof for 7700362307498152236346392
18. ~funny(susan) [input p17]
25. funny(susan) [input hypothesis]
145. ~funny(susan) [cnf transformation 18]
155. funny(susan) [cnf transformation 25]
400. $false [subsumption resolution 155,145]
% SZS output end Proof for 7700362307498152236346392
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is not generous or calm then paul is not strong.
Everyone who is both humble and patient is either not tall or happy.
If someone is not generous then john is generous and vice versa.
Everyone who is happy or creative is not patient or quiet and vice versa.
Everyone who is both calm and quiet is not kind or not tall.
Everyone who is either not patient or not happy is not quiet and vice versa.
Everyone who is both kind and not tall is both creative and rich and vice versa.
If someone is kind or not generous then john is kind.
Everyone who is both not humble and not tall is patient or calm and vice versa.
If susan is not patient then someone is both not wise and not calm.
Everyone who is curious or generous is creative or not happy.
If someone is either generous or not calm then paul is both not patient and not wise.
Everyone who is not tall or rich is not patient.
Everyone who is wise or tall is either calm or not funny.
Everyone who is either not calm or not brave is either patient or kind.
Susan is strong or not wise.
Someone is brave.
Someone is wise.
Paul is kind.
John is both not happy and not tall.
Lucy is kind.
John is either not patient or tall. | Paul is calm. | neutral | ((?[X]:((~generous(X)|calm(X))))=>(~strong(paul)))&
(![X]:((humble(X)&patient(X))=>(~tall(X)<~>happy(X))))&
((?[X]:(~generous(X)))<=>(generous(john)))&
(![X]:((happy(X)|creative(X))<=>(~patient(X)|quiet(X))))&
(![X]:((calm(X)&quiet(X))=>(~kind(X)|~tall(X))))&
(![X]:((~patient(X)<~>~happy(X))<=>~quiet(X)))&
(![X]:((kind(X)&~tall(X))<=>(creative(X)&rich(X))))&
((?[X]:((kind(X)|~generous(X))))=>(kind(john)))&
(![X]:((~humble(X)&~tall(X))<=>(patient(X)|calm(X))))&
((~patient(susan))=>(?[X]:((~wise(X)&~calm(X)))))&
(![X]:((curious(X)|generous(X))=>(creative(X)|~happy(X))))&
((?[X]:((generous(X)<~>~calm(X))))=>((~patient(paul)&~wise(paul))))&
(![X]:((~tall(X)|rich(X))=>~patient(X)))&
(![X]:((wise(X)|tall(X))=>(calm(X)<~>~funny(X))))&
(![X]:((~calm(X)<~>~brave(X))=>(patient(X)<~>kind(X))))&
((strong(susan)|~wise(susan)))&
(?[X]:(brave(X)))&
(?[X]:(wise(X)))&
(kind(paul))&
((~happy(john)&~tall(john)))&
(kind(lucy))&
((~patient(john)<~>tall(john))) | calm(paul) | [] | null | 0 |
If someone is funny or not rich then paul is both happy and not quiet.
If someone is both not wise and not happy then lucy is either patient or not rich and vice versa.
Everyone who is patient or tall is not quiet and vice versa.
If fred is both patient and not generous then susan is either strong or curious and vice versa.
Everyone who is not old or calm is not happy or patient.
Everyone who is either not curious or not humble is not wise.
Everyone who is either not brave or quiet is both wise and not quiet and vice versa.
Everyone who is strong is not curious and vice versa.
If alice is rich then someone is funny or not quiet.
Everyone who is not generous or not quiet is both not generous and wise.
Everyone who is either not tall or old is either not curious or not quiet and vice versa.
If john is creative or tall then someone is both curious and patient and vice versa.
Everyone who is both funny and patient is not happy or not humble.
Everyone who is not strong or not brave is patient or not happy and vice versa.
Everyone who is either tall or not generous is patient or not patient and vice versa.
If someone is either not creative or tall then someone is either curious or not patient and vice versa.
Alice is both not kind and not brave.
Someone is brave or kind.
Susan is not patient.
Someone is either humble or strong.
Susan is calm.
Lucy is curious or not creative.
Paul is both humble and not old. | Paul is not patient. | contradiction | ((?[X]:((funny(X)|~rich(X))))=>((happy(paul)&~quiet(paul))))&
((?[X]:((~wise(X)&~happy(X))))<=>((patient(lucy)<~>~rich(lucy))))&
(![X]:((patient(X)|tall(X))<=>~quiet(X)))&
(((patient(fred)&~generous(fred)))<=>((strong(susan)<~>curious(susan))))&
(![X]:((~old(X)|calm(X))=>(~happy(X)|patient(X))))&
(![X]:((~curious(X)<~>~humble(X))=>~wise(X)))&
(![X]:((~brave(X)<~>quiet(X))<=>(wise(X)&~quiet(X))))&
(![X]:(strong(X)<=>~curious(X)))&
((rich(alice))=>(?[X]:((funny(X)|~quiet(X)))))&
(![X]:((~generous(X)|~quiet(X))=>(~generous(X)&wise(X))))&
(![X]:((~tall(X)<~>old(X))<=>(~curious(X)<~>~quiet(X))))&
(((creative(john)|tall(john)))<=>(?[X]:((curious(X)&patient(X)))))&
(![X]:((funny(X)&patient(X))=>(~happy(X)|~humble(X))))&
(![X]:((~strong(X)|~brave(X))<=>(patient(X)|~happy(X))))&
(![X]:((tall(X)<~>~generous(X))<=>(patient(X)|~patient(X))))&
((?[X]:((~creative(X)<~>tall(X))))<=>(?[X]:((curious(X)<~>~patient(X)))))&
((~kind(alice)&~brave(alice)))&
(?[X]:((brave(X)|kind(X))))&
(~patient(susan))&
(?[X]:((humble(X)<~>strong(X))))&
(calm(susan))&
((curious(lucy)|~creative(lucy)))&
((humble(paul)&~old(paul))) | ~patient(paul) | [
"p2",
"p5",
"p9",
"p10",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 140124339326663766241727
% SZS output start Proof for 140124339326663766241727
3. ! [X0] : ((tall(X0) | patient(X0)) <=> ~quiet(X0)) [input p2]
6. ! [X0] : ((~curious(X0) <~> ~humble(X0)) => ~wise(X0)) [input p5]
10. ! [X0] : ((~quiet(X0) | ~generous(X0)) => (wise(X0) & ~generous(X0))) [input p9]
11. ! [X0] : ((~tall(X0) <~> old(X0)) <=> (~curious(X0) <~> ~quiet(X0))) [input p10]
15. ! [X0] : ((tall(X0) <~> ~generous(X0)) <=> (~patient(X0) | patient(X0))) [input p14]
23. ~old(paul) & humble(paul) [input p22]
24. ~patient(paul) [input hypothesis]
29. ! [X0] : (~wise(X0) | (~curious(X0) <=> ~humble(X0))) [ennf transformation 6]
31. ! [X0] : ((wise(X0) & ~generous(X0)) | (quiet(X0) & generous(X0))) [ennf transformation 10]
38. ! [X0] : (((tall(X0) | patient(X0)) | quiet(X0)) & (~quiet(X0) | (~tall(X0) & ~patient(X0)))) [nnf transformation 3]
39. ! [X0] : ((tall(X0) | patient(X0) | quiet(X0)) & (~quiet(X0) | (~tall(X0) & ~patient(X0)))) [flattening 38]
42. ! [X0] : (~wise(X0) | ((~curious(X0) | humble(X0)) & (~humble(X0) | curious(X0)))) [nnf transformation 29]
48. ! [X0] : ((((~old(X0) | tall(X0)) & (old(X0) | ~tall(X0))) | ((~curious(X0) | quiet(X0)) & (~quiet(X0) | curious(X0)))) & (((quiet(X0) | curious(X0)) & (~quiet(X0) | ~curious(X0))) | ((~tall(X0) | ~old(X0)) & (old(X0) | tall(X0))))) [nnf transformation 11]
56. ! [X0] : ((((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | (patient(X0) & ~patient(X0))) & ((~patient(X0) | patient(X0)) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0))))) [nnf transformation 15]
57. ! [X0] : ((((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | (patient(X0) & ~patient(X0))) & (~patient(X0) | patient(X0) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0))))) [flattening 56]
79. ~tall(X0) | ~quiet(X0) [cnf transformation 39]
80. tall(X0) | patient(X0) | quiet(X0) [cnf transformation 39]
89. ~humble(X0) | ~wise(X0) | curious(X0) [cnf transformation 42]
101. ~generous(X0) | quiet(X0) [cnf transformation 31]
102. generous(X0) | wise(X0) [cnf transformation 31]
103. wise(X0) | quiet(X0) [cnf transformation 31]
104. ~quiet(X0) | ~curious(X0) | old(X0) | tall(X0) [cnf transformation 48]
109. old(X0) | ~tall(X0) | ~curious(X0) | quiet(X0) [cnf transformation 48]
124. ~generous(X0) | tall(X0) | ~patient(X0) [cnf transformation 57]
125. ~generous(X0) | tall(X0) | patient(X0) [cnf transformation 57]
126. generous(X0) | ~tall(X0) | ~patient(X0) [cnf transformation 57]
127. ~tall(X0) | generous(X0) | patient(X0) [cnf transformation 57]
144. humble(paul) [cnf transformation 23]
145. ~old(paul) [cnf transformation 23]
146. ~patient(paul) [cnf transformation 24]
153. 2 <=> quiet(paul) [avatar definition]
228. ~curious(X0) | ~tall(X0) | old(X0) [subsumption resolution 109,79]
230. ~curious(X0) | ~quiet(X0) | old(X0) [subsumption resolution 104,228]
255. ~tall(X0) | generous(X0) [subsumption resolution 126,127]
256. ~generous(X0) | tall(X0) [subsumption resolution 124,125]
334. tall(X0) | wise(X0) [resolution 256,102]
337. patient(X0) | quiet(X0) | generous(X0) [resolution 80,255]
357. patient(X0) | quiet(X0) [subsumption resolution 337,101]
377. ~wise(paul) | curious(paul) [resolution 89,144]
380. 39 <=> curious(paul) [avatar definition]
382. curious(paul) <- (39) [avatar component clause 380]
384. 40 <=> wise(paul) [avatar definition]
386. ~wise(paul) <- (~40) [avatar component clause 384]
387. 39 | ~40 [avatar split clause 377,384,380]
494. ~quiet(paul) | old(paul) <- (39) [resolution 230,382]
520. wise(X2) | ~quiet(X2) [resolution 334,79]
525. wise(X2) [subsumption resolution 520,103]
527. quiet(paul) [resolution 357,146]
533. 2 [avatar split clause 527,153]
534. ~quiet(paul) <- (39) [subsumption resolution 494,145]
535. ~2 | ~39 [avatar split clause 534,380,153]
536. $false <- (~40) [subsumption resolution 386,525]
537. 40 [avatar contradiction clause 536]
538. $false [avatar sat refutation 387,533,535,537]
% SZS output end Proof for 140124339326663766241727
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative then someone is not wise or not strong and vice versa. If someone is either not kind or not calm then someone is wise or not happy. If mary is curious then lucy is both not strong and strong. Everyone who is either not generous or not funny is old or not kind. If lucy is quiet or not quiet then someone is either humble or patient. Everyone who is humble is either creative or not kind and vice versa. Everyone who is humble or creative is either not creative or kind and vice versa. Everyone who is either not calm or not brave is not quiet and vice versa. Everyone who is funny is either not generous or calm and vice versa. Everyone who is not strong or kind is not brave or brave and vice versa. Everyone who is funny or generous is both humble and not happy and vice versa. Everyone who is either tall or not funny is not humble and vice versa. If mary is creative then paul is both kind and rich and vice versa. Everyone who is both not patient and old is not quiet and vice versa. Everyone who is brave is humble. Everyone who is not patient is either quiet or not tall and vice versa. Alice is either old or funny. Mary is both tall and not curious. Someone is either not happy or wise. Someone is not wise. Fred is not wise. Fred is either kind or curious. Someone is not tall or wise. Someone is generous. | Mary is not humble. | contradiction | ((?[X]:(~creative(X)))<=>(?[X]:((~wise(X)|~strong(X)))))&
((?[X]:((~kind(X)<~>~calm(X))))=>(?[X]:((wise(X)|~happy(X)))))&
((curious(mary))=>((~strong(lucy)&strong(lucy))))&
(![X]:((~generous(X)<~>~funny(X))=>(old(X)|~kind(X))))&
(((quiet(lucy)|~quiet(lucy)))=>(?[X]:((humble(X)<~>patient(X)))))&
(![X]:(humble(X)<=>(creative(X)<~>~kind(X))))&
(![X]:((humble(X)|creative(X))<=>(~creative(X)<~>kind(X))))&
(![X]:((~calm(X)<~>~brave(X))<=>~quiet(X)))&
(![X]:(funny(X)<=>(~generous(X)<~>calm(X))))&
(![X]:((~strong(X)|kind(X))<=>(~brave(X)|brave(X))))&
(![X]:((funny(X)|generous(X))<=>(humble(X)&~happy(X))))&
(![X]:((tall(X)<~>~funny(X))<=>~humble(X)))&
((creative(mary))<=>((kind(paul)&rich(paul))))&
(![X]:((~patient(X)&old(X))<=>~quiet(X)))&
(![X]:(brave(X)=>humble(X)))&
(![X]:(~patient(X)<=>(quiet(X)<~>~tall(X))))&
((old(alice)<~>funny(alice)))&
((tall(mary)&~curious(mary)))&
(?[X]:((~happy(X)<~>wise(X))))&
(?[X]:(~wise(X)))&
(~wise(fred))&
((kind(fred)<~>curious(fred)))&
(?[X]:((~tall(X)|wise(X))))&
(?[X]:(generous(X))) | ~humble(mary) | [
"p10",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4626038863586326436134560
% SZS output start Proof for 4626038863586326436134560
11. ! [X0] : ((generous(X0) | funny(X0)) <=> (~happy(X0) & humble(X0))) [input p10]
12. ! [X0] : ((tall(X0) <~> ~funny(X0)) <=> ~humble(X0)) [input p11]
18. ~curious(mary) & tall(mary) [input p17]
25. ~humble(mary) [input hypothesis]
54. ! [X0] : (((generous(X0) | funny(X0)) | (happy(X0) | ~humble(X0))) & ((~happy(X0) & humble(X0)) | (~generous(X0) & ~funny(X0)))) [nnf transformation 11]
55. ! [X0] : ((generous(X0) | funny(X0) | happy(X0) | ~humble(X0)) & ((~happy(X0) & humble(X0)) | (~generous(X0) & ~funny(X0)))) [flattening 54]
56. ! [X0] : ((((funny(X0) | ~tall(X0)) & (~funny(X0) | tall(X0))) | humble(X0)) & (~humble(X0) | ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0))))) [nnf transformation 12]
108. ~funny(X0) | humble(X0) [cnf transformation 55]
116. funny(X0) | ~tall(X0) | humble(X0) [cnf transformation 56]
130. tall(mary) [cnf transformation 18]
140. ~humble(mary) [cnf transformation 25]
210. ~tall(X0) | humble(X0) [subsumption resolution 116,108]
271. humble(mary) [resolution 210,130]
272. $false [subsumption resolution 271,140]
% SZS output end Proof for 4626038863586326436134560
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is not wise and vice versa. Everyone who is not brave or generous is not happy. If susan is curious then someone is either curious or humble and vice versa. Everyone who is either not patient or not old is not happy or not humble. Everyone who is happy or tall is either creative or not kind and vice versa. Everyone who is both calm and not curious is not happy or not generous and vice versa. If paul is strong or brave then lucy is tall and vice versa. Everyone who is wise or not strong is not calm or not humble. If someone is not rich or not creative then lucy is either not tall or patient and vice versa. Everyone who is not humble or not curious is not patient or quiet and vice versa. Everyone who is both generous and not quiet is not curious and vice versa. If alice is either rich or not tall then someone is patient or not calm and vice versa. If someone is not wise then paul is curious or not generous. Everyone who is not funny is either brave or quiet and vice versa. If john is either calm or curious then lucy is generous and vice versa. John is strong or not creative. Someone is not strong or not happy. Mary is generous. | Susan is creative. | entailment | (![X]:(~strong(X)<=>~wise(X)))&
(![X]:((~brave(X)|generous(X))=>~happy(X)))&
((curious(susan))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((~patient(X)<~>~old(X))=>(~happy(X)|~humble(X))))&
(![X]:((happy(X)|tall(X))<=>(creative(X)<~>~kind(X))))&
(![X]:((calm(X)&~curious(X))<=>(~happy(X)|~generous(X))))&
(((strong(paul)|brave(paul)))<=>(tall(lucy)))&
(![X]:((wise(X)|~strong(X))=>(~calm(X)|~humble(X))))&
((?[X]:((~rich(X)|~creative(X))))<=>((~tall(lucy)<~>patient(lucy))))&
(![X]:((~humble(X)|~curious(X))<=>(~patient(X)|quiet(X))))&
(![X]:((generous(X)&~quiet(X))<=>~curious(X)))&
(((rich(alice)<~>~tall(alice)))<=>(?[X]:((patient(X)|~calm(X)))))&
((?[X]:(~wise(X)))=>((curious(paul)|~generous(paul))))&
(![X]:(~funny(X)<=>(brave(X)<~>quiet(X))))&
(((calm(john)<~>curious(john)))<=>(generous(lucy)))&
((strong(john)|~creative(john)))&
(?[X]:((~strong(X)|~happy(X))))&
(generous(mary)) | creative(susan) | [
"p0",
"p1",
"p2",
"p5",
"p6",
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5405049063853985698886086
% SZS output start Proof for 5405049063853985698886086
1. ! [X0] : (~strong(X0) <=> ~wise(X0)) [input p0]
2. ! [X0] : ((generous(X0) | ~brave(X0)) => ~happy(X0)) [input p1]
3. curious(susan) <=> ? [X0] : (curious(X0) <~> humble(X0)) [input p2]
6. ! [X0] : ((~curious(X0) & calm(X0)) <=> (~generous(X0) | ~happy(X0))) [input p5]
7. (brave(paul) | strong(paul)) <=> tall(lucy) [input p6]
8. ! [X0] : ((~strong(X0) | wise(X0)) => (~humble(X0) | ~calm(X0))) [input p7]
9. ? [X0] : (~creative(X0) | ~rich(X0)) <=> (~tall(lucy) <~> patient(lucy)) [input p8]
10. ! [X0] : ((~curious(X0) | ~humble(X0)) <=> (quiet(X0) | ~patient(X0))) [input p9]
11. ! [X0] : ((~quiet(X0) & generous(X0)) <=> ~curious(X0)) [input p10]
12. (rich(alice) <~> ~tall(alice)) <=> ? [X0] : (~calm(X0) | patient(X0)) [input p11]
13. ? [X0] : ~wise(X0) => (~generous(paul) | curious(paul)) [input p12]
19. ~creative(susan) [input hypothesis]
20. ! [X0] : (~happy(X0) | (~generous(X0) & brave(X0))) [ennf transformation 2]
23. ! [X0] : ((~humble(X0) | ~calm(X0)) | (strong(X0) & ~wise(X0))) [ennf transformation 8]
24. ! [X0] : (~humble(X0) | ~calm(X0) | (strong(X0) & ~wise(X0))) [flattening 23]
25. (~generous(paul) | curious(paul)) | ! [X0] : wise(X0) [ennf transformation 13]
26. ~generous(paul) | curious(paul) | ! [X0] : wise(X0) [flattening 25]
27. ! [X0] : ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0))) [nnf transformation 1]
28. (curious(susan) | ! [X0] : ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) & (? [X0] : ((~humble(X0) | ~curious(X0)) & (humble(X0) | curious(X0))) | ~curious(susan)) [nnf transformation 3]
29. (curious(susan) | ! [X0] : ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) & (? [X1] : ((~humble(X1) | ~curious(X1)) & (humble(X1) | curious(X1))) | ~curious(susan)) [rectify 28]
30. ? [X1] : ((~humble(X1) | ~curious(X1)) & (humble(X1) | curious(X1))) => ((~humble(sK0) | ~curious(sK0)) & (humble(sK0) | curious(sK0))) [choice axiom]
31. (curious(susan) | ! [X0] : ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0)))) & (((~humble(sK0) | ~curious(sK0)) & (humble(sK0) | curious(sK0))) | ~curious(susan)) [skolemisation 29,30]
35. ! [X0] : (((~curious(X0) & calm(X0)) | (generous(X0) & happy(X0))) & ((~generous(X0) | ~happy(X0)) | (curious(X0) | ~calm(X0)))) [nnf transformation 6]
36. ! [X0] : (((~curious(X0) & calm(X0)) | (generous(X0) & happy(X0))) & (~generous(X0) | ~happy(X0) | curious(X0) | ~calm(X0))) [flattening 35]
37. ((brave(paul) | strong(paul)) | ~tall(lucy)) & (tall(lucy) | (~brave(paul) & ~strong(paul))) [nnf transformation 7]
38. (brave(paul) | strong(paul) | ~tall(lucy)) & (tall(lucy) | (~brave(paul) & ~strong(paul))) [flattening 37]
39. (? [X0] : (~creative(X0) | ~rich(X0)) | ((~tall(lucy) | ~patient(lucy)) & (patient(lucy) | tall(lucy)))) & (((~patient(lucy) | tall(lucy)) & (patient(lucy) | ~tall(lucy))) | ! [X0] : (creative(X0) & rich(X0))) [nnf transformation 9]
40. (? [X0] : (~creative(X0) | ~rich(X0)) | ((~tall(lucy) | ~patient(lucy)) & (patient(lucy) | tall(lucy)))) & (((~patient(lucy) | tall(lucy)) & (patient(lucy) | ~tall(lucy))) | ! [X1] : (creative(X1) & rich(X1))) [rectify 39]
41. ? [X0] : (~creative(X0) | ~rich(X0)) => (~creative(sK1) | ~rich(sK1)) [choice axiom]
42. ((~creative(sK1) | ~rich(sK1)) | ((~tall(lucy) | ~patient(lucy)) & (patient(lucy) | tall(lucy)))) & (((~patient(lucy) | tall(lucy)) & (patient(lucy) | ~tall(lucy))) | ! [X1] : (creative(X1) & rich(X1))) [skolemisation 40,41]
43. ! [X0] : (((~curious(X0) | ~humble(X0)) | (~quiet(X0) & patient(X0))) & ((quiet(X0) | ~patient(X0)) | (curious(X0) & humble(X0)))) [nnf transformation 10]
44. ! [X0] : ((~curious(X0) | ~humble(X0) | (~quiet(X0) & patient(X0))) & (quiet(X0) | ~patient(X0) | (curious(X0) & humble(X0)))) [flattening 43]
45. ! [X0] : (((~quiet(X0) & generous(X0)) | curious(X0)) & (~curious(X0) | (quiet(X0) | ~generous(X0)))) [nnf transformation 11]
46. ! [X0] : (((~quiet(X0) & generous(X0)) | curious(X0)) & (~curious(X0) | quiet(X0) | ~generous(X0))) [flattening 45]
47. (((tall(alice) | ~rich(alice)) & (~tall(alice) | rich(alice))) | ! [X0] : (calm(X0) & ~patient(X0))) & (? [X0] : (~calm(X0) | patient(X0)) | ((rich(alice) | tall(alice)) & (~tall(alice) | ~rich(alice)))) [nnf transformation 12]
48. (((tall(alice) | ~rich(alice)) & (~tall(alice) | rich(alice))) | ! [X0] : (calm(X0) & ~patient(X0))) & (? [X1] : (~calm(X1) | patient(X1)) | ((rich(alice) | tall(alice)) & (~tall(alice) | ~rich(alice)))) [rectify 47]
49. ? [X1] : (~calm(X1) | patient(X1)) => (~calm(sK2) | patient(sK2)) [choice axiom]
50. (((tall(alice) | ~rich(alice)) & (~tall(alice) | rich(alice))) | ! [X0] : (calm(X0) & ~patient(X0))) & ((~calm(sK2) | patient(sK2)) | ((rich(alice) | tall(alice)) & (~tall(alice) | ~rich(alice)))) [skolemisation 48,49]
54. ~wise(X0) | strong(X0) [cnf transformation 27]
57. ~happy(X0) | ~generous(X0) [cnf transformation 20]
60. curious(susan) | humble(X0) | ~curious(X0) [cnf transformation 31]
71. calm(X0) | happy(X0) [cnf transformation 36]
73. ~curious(X0) | happy(X0) [cnf transformation 36]
74. ~curious(X0) | generous(X0) [cnf transformation 36]
75. tall(lucy) | ~strong(paul) [cnf transformation 38]
78. ~calm(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 24]
81. patient(lucy) | ~tall(lucy) | creative(X1) [cnf transformation 42]
87. ~patient(X0) | quiet(X0) | curious(X0) [cnf transformation 44]
90. ~curious(X0) | quiet(X0) | ~generous(X0) [cnf transformation 46]
91. generous(X0) | curious(X0) [cnf transformation 46]
92. ~quiet(X0) | curious(X0) [cnf transformation 46]
93. ~calm(sK2) | patient(sK2) | ~tall(alice) | ~rich(alice) [cnf transformation 50]
94. ~calm(sK2) | patient(sK2) | rich(alice) | tall(alice) [cnf transformation 50]
95. ~tall(alice) | rich(alice) | ~patient(X0) [cnf transformation 50]
97. tall(alice) | ~rich(alice) | ~patient(X0) [cnf transformation 50]
99. ~generous(paul) | curious(paul) | wise(X0) [cnf transformation 26]
107. ~creative(susan) [cnf transformation 19]
112. 2 <=> curious(susan) [avatar definition]
114. curious(susan) <- (2) [avatar component clause 112]
117. 3 <=> ! [X0] : (humble(X0) | ~curious(X0)) [avatar definition]
118. ~curious(X0) | humble(X0) <- (3) [avatar component clause 117]
119. 3 | 2 [avatar split clause 60,112,117]
131. 6 <=> tall(lucy) [avatar definition]
135. 7 <=> strong(paul) [avatar definition]
136. ~strong(paul) <- (~7) [avatar component clause 135]
144. ~7 | 6 [avatar split clause 75,131,135]
146. 9 <=> patient(lucy) [avatar definition]
147. patient(lucy) <- (9) [avatar component clause 146]
160. 12 <=> ! [X1] : creative(X1) [avatar definition]
161. creative(X1) <- (12) [avatar component clause 160]
167. 12 | ~6 | 9 [avatar split clause 81,146,131,160]
169. generous(X0) [subsumption resolution 91,74]
170. ~curious(X0) | quiet(X0) [subsumption resolution 90,169]
175. 15 <=> rich(alice) [avatar definition]
179. 16 <=> tall(alice) [avatar definition]
184. 17 <=> ! [X0] : ~patient(X0) [avatar definition]
185. ~patient(X0) <- (17) [avatar component clause 184]
186. 17 | ~15 | 16 [avatar split clause 97,179,175,184]
188. 17 | 15 | ~16 [avatar split clause 95,179,175,184]
190. 18 <=> patient(sK2) [avatar definition]
192. patient(sK2) <- (18) [avatar component clause 190]
194. 19 <=> calm(sK2) [avatar definition]
195. calm(sK2) <- (19) [avatar component clause 194]
196. ~calm(sK2) <- (~19) [avatar component clause 194]
197. 16 | 15 | 18 | ~19 [avatar split clause 94,194,190,175,179]
198. ~15 | ~16 | 18 | ~19 [avatar split clause 93,194,190,179,175]
199. curious(paul) | wise(X0) [subsumption resolution 99,169]
201. 20 <=> ! [X0] : wise(X0) [avatar definition]
202. wise(X0) <- (20) [avatar component clause 201]
204. 21 <=> curious(paul) [avatar definition]
206. curious(paul) <- (21) [avatar component clause 204]
207. 20 | 21 [avatar split clause 199,204,201]
238. strong(X0) <- (20) [resolution 54,202]
239. $false <- (~7, 20) [resolution 238,136]
241. 7 | ~20 [avatar contradiction clause 239]
242. happy(sK2) <- (~19) [resolution 71,196]
243. ~generous(sK2) <- (~19) [resolution 242,57]
245. $false <- (~19) [subsumption resolution 243,169]
246. 19 [avatar contradiction clause 245]
247. $false <- (9, 17) [resolution 185,147]
248. ~9 | ~17 [avatar contradiction clause 247]
249. $false <- (12) [resolution 161,107]
254. ~12 [avatar contradiction clause 249]
255. happy(susan) <- (2) [resolution 73,114]
257. happy(paul) <- (21) [resolution 73,206]
258. ~generous(susan) <- (2) [resolution 255,57]
260. $false <- (2) [subsumption resolution 258,169]
261. ~2 [avatar contradiction clause 260]
266. ~generous(paul) <- (21) [resolution 257,57]
268. $false <- (21) [subsumption resolution 266,169]
269. ~21 [avatar contradiction clause 268]
281. ~humble(sK2) | ~wise(sK2) <- (19) [resolution 78,195]
294. quiet(sK2) | curious(sK2) <- (18) [resolution 87,192]
305. quiet(sK2) <- (18) [subsumption resolution 294,170]
307. ~humble(sK2) <- (19, 20) [subsumption resolution 281,202]
310. curious(sK2) <- (18) [resolution 305,92]
332. humble(sK2) <- (3, 18) [resolution 310,118]
335. $false <- (3, 18, 19, 20) [subsumption resolution 332,307]
336. ~3 | ~18 | ~19 | ~20 [avatar contradiction clause 335]
337. $false [avatar sat refutation 119,144,167,186,188,197,198,207,241,246,248,254,261,269,336]
% SZS output end Proof for 5405049063853985698886086
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not creative is either not creative or creative and vice versa.
If fred is either not patient or creative then lucy is quiet or generous and vice versa.
If someone is both calm and brave then john is wise or not wise and vice versa.
Everyone who is tall or not generous is strong.
If someone is not funny then paul is both creative and not brave and vice versa.
If someone is not tall or not creative then someone is either not happy or not calm.
Everyone who is either calm or not curious is generous and vice versa.
Everyone who is both creative and curious is either humble or calm and vice versa.
Everyone who is either calm or kind is not curious and vice versa.
Everyone who is not old is happy.
Everyone who is both not curious and not happy is either curious or happy.
If susan is not creative then someone is either quiet or brave.
Everyone who is not rich is not happy or curious and vice versa.
If someone is both kind and tall then paul is not happy or not strong.
Someone is calm or not old.
Fred is humble or brave.
Someone is both not brave and humble.
Someone is both not wise and not tall.
Someone is either kind or not humble.
Susan is both not brave and not rich. | Fred is not rich. | neutral | (![X]:((~strong(X)&~creative(X))<=>(~creative(X)<~>creative(X))))&
(((~patient(fred)<~>creative(fred)))<=>((quiet(lucy)|generous(lucy))))&
((?[X]:((calm(X)&brave(X))))<=>((wise(john)|~wise(john))))&
(![X]:((tall(X)|~generous(X))=>strong(X)))&
((?[X]:(~funny(X)))<=>((creative(paul)&~brave(paul))))&
((?[X]:((~tall(X)|~creative(X))))=>(?[X]:((~happy(X)<~>~calm(X)))))&
(![X]:((calm(X)<~>~curious(X))<=>generous(X)))&
(![X]:((creative(X)&curious(X))<=>(humble(X)<~>calm(X))))&
(![X]:((calm(X)<~>kind(X))<=>~curious(X)))&
(![X]:(~old(X)=>happy(X)))&
(![X]:((~curious(X)&~happy(X))=>(curious(X)<~>happy(X))))&
((~creative(susan))=>(?[X]:((quiet(X)<~>brave(X)))))&
(![X]:(~rich(X)<=>(~happy(X)|curious(X))))&
((?[X]:((kind(X)&tall(X))))=>((~happy(paul)|~strong(paul))))&
(?[X]:((calm(X)|~old(X))))&
((humble(fred)|brave(fred)))&
(?[X]:((~brave(X)&humble(X))))&
(?[X]:((~wise(X)&~tall(X))))&
(?[X]:((kind(X)<~>~humble(X))))&
((~brave(susan)&~rich(susan))) | ~rich(fred) | [] | null | 0 |
Everyone who is either not tall or happy is either not tall or strong and vice versa. Everyone who is funny is either not curious or tall and vice versa. If susan is curious then susan is both funny and not humble and vice versa. Everyone who is not funny is tall. Everyone who is either patient or old is both rich and wise. If someone is both rich and happy then someone is strong and vice versa. Everyone who is not kind or not tall is wise. If someone is either creative or not rich then mary is not brave or tall. If someone is both calm and patient then fred is both not humble and not calm and vice versa. Everyone who is not kind or old is both not humble and kind. Everyone who is not calm or not quiet is both not calm and not strong and vice versa. Everyone who is not generous or not patient is calm. Everyone who is either tall or not wise is brave and vice versa. If someone is not brave then someone is both not generous and generous and vice versa. If lucy is both humble and not happy then fred is not old and vice versa. Everyone who is not old or not rich is either rich or not humble and vice versa. Someone is both not rich and calm. Paul is not curious. Fred is not quiet. John is not old or rich. Alice is either curious or happy. John is either curious or not brave. Someone is creative or not funny. | Susan is not strong. | neutral | (![X]:((~tall(X)<~>happy(X))<=>(~tall(X)<~>strong(X))))&
(![X]:(funny(X)<=>(~curious(X)<~>tall(X))))&
((curious(susan))<=>((funny(susan)&~humble(susan))))&
(![X]:(~funny(X)=>tall(X)))&
(![X]:((patient(X)<~>old(X))=>(rich(X)&wise(X))))&
((?[X]:((rich(X)&happy(X))))<=>(?[X]:(strong(X))))&
(![X]:((~kind(X)|~tall(X))=>wise(X)))&
((?[X]:((creative(X)<~>~rich(X))))=>((~brave(mary)|tall(mary))))&
((?[X]:((calm(X)&patient(X))))<=>((~humble(fred)&~calm(fred))))&
(![X]:((~kind(X)|old(X))=>(~humble(X)&kind(X))))&
(![X]:((~calm(X)|~quiet(X))<=>(~calm(X)&~strong(X))))&
(![X]:((~generous(X)|~patient(X))=>calm(X)))&
(![X]:((tall(X)<~>~wise(X))<=>brave(X)))&
((?[X]:(~brave(X)))<=>(?[X]:((~generous(X)&generous(X)))))&
(((humble(lucy)&~happy(lucy)))<=>(~old(fred)))&
(![X]:((~old(X)|~rich(X))<=>(rich(X)<~>~humble(X))))&
(?[X]:((~rich(X)&calm(X))))&
(~curious(paul))&
(~quiet(fred))&
((~old(john)|rich(john)))&
((curious(alice)<~>happy(alice)))&
((curious(john)<~>~brave(john)))&
(?[X]:((creative(X)|~funny(X)))) | ~strong(susan) | [] | null | 0 |
If fred is both brave and not strong then fred is either curious or not tall. Everyone who is happy or not patient is both tall and not wise. Everyone who is not brave or generous is either not strong or patient and vice versa. Everyone who is not humble is not brave or generous and vice versa. Everyone who is both quiet and not wise is not generous and vice versa. If someone is not old or rich then paul is not humble. Everyone who is patient is either generous or not patient and vice versa. If someone is not patient or not tall then mary is both not quiet and calm. Everyone who is funny or patient is quiet and vice versa. If mary is either not strong or not kind then someone is both not tall and brave. Everyone who is both not old and kind is wise or kind and vice versa. Everyone who is wise is not strong. Everyone who is either strong or not quiet is both not funny and not kind and vice versa. Everyone who is either not patient or not quiet is either strong or funny. If mary is both not rich and calm then fred is either not calm or rich. If susan is either wise or generous then lucy is not happy and vice versa. Lucy is curious. John is both not rich and not calm. Fred is either not strong or not rich. Alice is creative or not tall. John is either not quiet or not creative. | Lucy is not calm. | neutral | (((brave(fred)&~strong(fred)))=>((curious(fred)<~>~tall(fred))))&
(![X]:((happy(X)|~patient(X))=>(tall(X)&~wise(X))))&
(![X]:((~brave(X)|generous(X))<=>(~strong(X)<~>patient(X))))&
(![X]:(~humble(X)<=>(~brave(X)|generous(X))))&
(![X]:((quiet(X)&~wise(X))<=>~generous(X)))&
((?[X]:((~old(X)|rich(X))))=>(~humble(paul)))&
(![X]:(patient(X)<=>(generous(X)<~>~patient(X))))&
((?[X]:((~patient(X)|~tall(X))))=>((~quiet(mary)&calm(mary))))&
(![X]:((funny(X)|patient(X))<=>quiet(X)))&
(((~strong(mary)<~>~kind(mary)))=>(?[X]:((~tall(X)&brave(X)))))&
(![X]:((~old(X)&kind(X))<=>(wise(X)|kind(X))))&
(![X]:(wise(X)=>~strong(X)))&
(![X]:((strong(X)<~>~quiet(X))<=>(~funny(X)&~kind(X))))&
(![X]:((~patient(X)<~>~quiet(X))=>(strong(X)<~>funny(X))))&
(((~rich(mary)&calm(mary)))=>((~calm(fred)<~>rich(fred))))&
(((wise(susan)<~>generous(susan)))<=>(~happy(lucy)))&
(curious(lucy))&
((~rich(john)&~calm(john)))&
((~strong(fred)<~>~rich(fred)))&
((creative(alice)|~tall(alice)))&
((~quiet(john)<~>~creative(john))) | ~calm(lucy) | [] | null | 0 |
Everyone who is generous is both curious and not tall.
Everyone who is either not creative or tall is either happy or not wise and vice versa.
Everyone who is curious is not old and vice versa.
Everyone who is both not humble and not funny is either funny or kind and vice versa.
If paul is both brave and not creative then someone is creative or not calm.
Everyone who is both not tall and funny is both not quiet and calm and vice versa.
Everyone who is wise is kind or brave.
Everyone who is generous or not calm is not rich.
If paul is generous then someone is curious.
If someone is brave then someone is either not kind or brave and vice versa.
If fred is not humble or curious then susan is curious or brave.
If fred is generous then someone is both not funny and not brave.
Everyone who is either not tall or not wise is both creative and old.
If someone is both not patient and humble then someone is curious or not patient and vice versa.
If someone is not patient or not kind then mary is not brave and vice versa.
If someone is not patient then someone is both not brave and not old and vice versa.
Paul is both kind and humble.
Lucy is not funny or patient.
Someone is not strong or strong.
Susan is either not calm or creative.
Someone is not quiet or quiet.
Fred is either strong or creative.
Someone is not curious or not tall. | Lucy is not funny. | neutral | (![X]:(generous(X)=>(curious(X)&~tall(X))))&
(![X]:((~creative(X)<~>tall(X))<=>(happy(X)<~>~wise(X))))&
(![X]:(curious(X)<=>~old(X)))&
(![X]:((~humble(X)&~funny(X))<=>(funny(X)<~>kind(X))))&
(((brave(paul)&~creative(paul)))=>(?[X]:((creative(X)|~calm(X)))))&
(![X]:((~tall(X)&funny(X))<=>(~quiet(X)&calm(X))))&
(![X]:(wise(X)=>(kind(X)|brave(X))))&
(![X]:((generous(X)|~calm(X))=>~rich(X)))&
((generous(paul))=>(?[X]:(curious(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~kind(X)<~>brave(X)))))&
(((~humble(fred)|curious(fred)))=>((curious(susan)|brave(susan))))&
((generous(fred))=>(?[X]:((~funny(X)&~brave(X)))))&
(![X]:((~tall(X)<~>~wise(X))=>(creative(X)&old(X))))&
((?[X]:((~patient(X)&humble(X))))<=>(?[X]:((curious(X)|~patient(X)))))&
((?[X]:((~patient(X)|~kind(X))))<=>(~brave(mary)))&
((?[X]:(~patient(X)))<=>(?[X]:((~brave(X)&~old(X)))))&
((kind(paul)&humble(paul)))&
((~funny(lucy)|patient(lucy)))&
(?[X]:((~strong(X)|strong(X))))&
((~calm(susan)<~>creative(susan)))&
(?[X]:((~quiet(X)|quiet(X))))&
((strong(fred)<~>creative(fred)))&
(?[X]:((~curious(X)|~tall(X)))) | ~funny(lucy) | [] | null | 0 |
Everyone who is both kind and not happy is creative or not funny.
Everyone who is brave is both curious and not creative and vice versa.
Everyone who is either not humble or brave is patient.
Everyone who is not curious is both not happy and not rich.
Everyone who is either not strong or not happy is tall.
Everyone who is both humble and not quiet is not old and vice versa.
If lucy is either not creative or not happy then fred is calm or not happy and vice versa.
Everyone who is either creative or curious is not calm and vice versa.
Everyone who is not wise is creative and vice versa.
If fred is both not wise and funny then someone is both not kind and not brave.
Everyone who is either funny or old is not creative or not wise and vice versa.
Everyone who is both not old and not kind is kind or not humble.
Everyone who is happy or brave is both not brave and calm and vice versa.
If someone is not rich or rich then someone is either rich or not happy and vice versa.
Everyone who is either not wise or patient is both not humble and humble and vice versa.
Someone is either not funny or kind.
Susan is not patient or kind.
Someone is not kind.
Someone is tall or not patient.
Paul is old.
Mary is either calm or kind.
Paul is kind. | Fred is not calm. | neutral | (![X]:((kind(X)&~happy(X))=>(creative(X)|~funny(X))))&
(![X]:(brave(X)<=>(curious(X)&~creative(X))))&
(![X]:((~humble(X)<~>brave(X))=>patient(X)))&
(![X]:(~curious(X)=>(~happy(X)&~rich(X))))&
(![X]:((~strong(X)<~>~happy(X))=>tall(X)))&
(![X]:((humble(X)&~quiet(X))<=>~old(X)))&
(((~creative(lucy)<~>~happy(lucy)))<=>((calm(fred)|~happy(fred))))&
(![X]:((creative(X)<~>curious(X))<=>~calm(X)))&
(![X]:(~wise(X)<=>creative(X)))&
(((~wise(fred)&funny(fred)))=>(?[X]:((~kind(X)&~brave(X)))))&
(![X]:((funny(X)<~>old(X))<=>(~creative(X)|~wise(X))))&
(![X]:((~old(X)&~kind(X))=>(kind(X)|~humble(X))))&
(![X]:((happy(X)|brave(X))<=>(~brave(X)&calm(X))))&
((?[X]:((~rich(X)|rich(X))))<=>(?[X]:((rich(X)<~>~happy(X)))))&
(![X]:((~wise(X)<~>patient(X))<=>(~humble(X)&humble(X))))&
(?[X]:((~funny(X)<~>kind(X))))&
((~patient(susan)|kind(susan)))&
(?[X]:(~kind(X)))&
(?[X]:((tall(X)|~patient(X))))&
(old(paul))&
((calm(mary)<~>kind(mary)))&
(kind(paul)) | ~calm(fred) | [] | null | 0 |
Everyone who is tall is both rich and calm and vice versa.
If someone is not humble or wise then someone is not generous and vice versa.
Everyone who is not quiet is both tall and not generous.
If fred is both not patient and not brave then fred is both not generous and not humble and vice versa.
Everyone who is either not old or patient is not happy and vice versa.
If mary is creative then someone is either tall or not strong and vice versa.
If someone is kind then someone is either wise or rich.
If someone is generous then someone is wise or humble and vice versa.
Everyone who is both happy and not rich is either old or not happy and vice versa.
Everyone who is quiet is creative and vice versa.
If fred is happy or not quiet then someone is either strong or patient and vice versa.
Everyone who is funny is either not curious or happy and vice versa.
Everyone who is calm is both strong and generous and vice versa.
Everyone who is not patient is both humble and not funny.
If lucy is happy then someone is funny or patient.
Everyone who is old or not kind is both old and not curious.
Someone is old or not quiet.
Lucy is not rich.
Someone is either not old or not strong.
Someone is tall or brave.
Someone is both funny and not kind.
Someone is funny or not patient.
Someone is old or not old.
Someone is not creative or not rich. | Fred is creative. | entailment | (![X]:(tall(X)<=>(rich(X)&calm(X))))&
((?[X]:((~humble(X)|wise(X))))<=>(?[X]:(~generous(X))))&
(![X]:(~quiet(X)=>(tall(X)&~generous(X))))&
(((~patient(fred)&~brave(fred)))<=>((~generous(fred)&~humble(fred))))&
(![X]:((~old(X)<~>patient(X))<=>~happy(X)))&
((creative(mary))<=>(?[X]:((tall(X)<~>~strong(X)))))&
((?[X]:(kind(X)))=>(?[X]:((wise(X)<~>rich(X)))))&
((?[X]:(generous(X)))<=>(?[X]:((wise(X)|humble(X)))))&
(![X]:((happy(X)&~rich(X))<=>(old(X)<~>~happy(X))))&
(![X]:(quiet(X)<=>creative(X)))&
(((happy(fred)|~quiet(fred)))<=>(?[X]:((strong(X)<~>patient(X)))))&
(![X]:(funny(X)<=>(~curious(X)<~>happy(X))))&
(![X]:(calm(X)<=>(strong(X)&generous(X))))&
(![X]:(~patient(X)=>(humble(X)&~funny(X))))&
((happy(lucy))=>(?[X]:((funny(X)|patient(X)))))&
(![X]:((old(X)|~kind(X))=>(old(X)&~curious(X))))&
(?[X]:((old(X)|~quiet(X))))&
(~rich(lucy))&
(?[X]:((~old(X)<~>~strong(X))))&
(?[X]:((tall(X)|brave(X))))&
(?[X]:((funny(X)&~kind(X))))&
(?[X]:((funny(X)|~patient(X))))&
(?[X]:((old(X)|~old(X))))&
(?[X]:((~creative(X)|~rich(X)))) | creative(fred) | [
"p0",
"p2",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 857728925273119899472060
% SZS output start Proof for 857728925273119899472060
1. ! [X0] : (tall(X0) <=> (calm(X0) & rich(X0))) [input p0]
3. ! [X0] : (~quiet(X0) => (~generous(X0) & tall(X0))) [input p2]
10. ! [X0] : (quiet(X0) <=> creative(X0)) [input p9]
13. ! [X0] : (calm(X0) <=> (generous(X0) & strong(X0))) [input p12]
25. ~creative(fred) [input hypothesis]
29. ! [X0] : ((~generous(X0) & tall(X0)) | quiet(X0)) [ennf transformation 3]
34. ! [X0] : ((tall(X0) | (~calm(X0) | ~rich(X0))) & ((calm(X0) & rich(X0)) | ~tall(X0))) [nnf transformation 1]
35. ! [X0] : ((tall(X0) | ~calm(X0) | ~rich(X0)) & ((calm(X0) & rich(X0)) | ~tall(X0))) [flattening 34]
59. ! [X0] : ((quiet(X0) | ~creative(X0)) & (creative(X0) | ~quiet(X0))) [nnf transformation 10]
66. ! [X0] : ((calm(X0) | (~generous(X0) | ~strong(X0))) & ((generous(X0) & strong(X0)) | ~calm(X0))) [nnf transformation 13]
67. ! [X0] : ((calm(X0) | ~generous(X0) | ~strong(X0)) & ((generous(X0) & strong(X0)) | ~calm(X0))) [flattening 66]
86. ~tall(X0) | calm(X0) [cnf transformation 35]
91. quiet(X0) | tall(X0) [cnf transformation 29]
92. ~generous(X0) | quiet(X0) [cnf transformation 29]
116. ~quiet(X0) | creative(X0) [cnf transformation 59]
129. ~calm(X0) | generous(X0) [cnf transformation 67]
148. ~creative(fred) [cnf transformation 25]
176. 7 <=> generous(fred) [avatar definition]
178. generous(fred) <- (7) [avatar component clause 176]
260. 26 <=> quiet(fred) [avatar definition]
261. quiet(fred) <- (26) [avatar component clause 260]
262. ~quiet(fred) <- (~26) [avatar component clause 260]
341. creative(fred) <- (26) [resolution 116,261]
343. $false <- (26) [subsumption resolution 341,148]
344. ~26 [avatar contradiction clause 343]
345. tall(fred) <- (~26) [resolution 262,91]
347. calm(fred) <- (~26) [resolution 345,86]
380. generous(fred) <- (~26) [resolution 347,129]
384. 7 | 26 [avatar split clause 380,260,176]
385. quiet(fred) <- (7) [resolution 178,92]
386. $false <- (7, ~26) [subsumption resolution 385,262]
387. ~7 | 26 [avatar contradiction clause 386]
388. $false [avatar sat refutation 344,384,387]
% SZS output end Proof for 857728925273119899472060
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not quiet then someone is brave and vice versa.
Everyone who is wise is not curious and vice versa.
Everyone who is not happy or patient is not strong.
If john is either old or happy then john is either curious or happy and vice versa.
Everyone who is both not rich and old is curious or generous.
Everyone who is both not creative and creative is happy and vice versa.
If alice is humble then someone is both not wise and strong and vice versa.
Everyone who is not quiet is not calm.
Everyone who is both brave and curious is not tall or not rich and vice versa.
If paul is either not funny or not calm then someone is not quiet or not creative and vice versa.
Everyone who is either not strong or tall is both not kind and generous.
If someone is patient then mary is either humble or calm.
Everyone who is both not tall and patient is either not old or not brave and vice versa.
Everyone who is both not humble and brave is both not brave and not rich.
Everyone who is not generous is curious or not happy.
Paul is not old or not funny.
Paul is not funny or funny.
Susan is not wise.
Someone is humble or not brave.
Fred is not happy or not generous.
John is either rich or not generous.
Someone is both curious and not creative. | Susan is calm. | neutral | ((~quiet(paul))<=>(?[X]:(brave(X))))&
(![X]:(wise(X)<=>~curious(X)))&
(![X]:((~happy(X)|patient(X))=>~strong(X)))&
(((old(john)<~>happy(john)))<=>((curious(john)<~>happy(john))))&
(![X]:((~rich(X)&old(X))=>(curious(X)|generous(X))))&
(![X]:((~creative(X)&creative(X))<=>happy(X)))&
((humble(alice))<=>(?[X]:((~wise(X)&strong(X)))))&
(![X]:(~quiet(X)=>~calm(X)))&
(![X]:((brave(X)&curious(X))<=>(~tall(X)|~rich(X))))&
(((~funny(paul)<~>~calm(paul)))<=>(?[X]:((~quiet(X)|~creative(X)))))&
(![X]:((~strong(X)<~>tall(X))=>(~kind(X)&generous(X))))&
((?[X]:(patient(X)))=>((humble(mary)<~>calm(mary))))&
(![X]:((~tall(X)&patient(X))<=>(~old(X)<~>~brave(X))))&
(![X]:((~humble(X)&brave(X))=>(~brave(X)&~rich(X))))&
(![X]:(~generous(X)=>(curious(X)|~happy(X))))&
((~old(paul)|~funny(paul)))&
((~funny(paul)|funny(paul)))&
(~wise(susan))&
(?[X]:((humble(X)|~brave(X))))&
((~happy(fred)|~generous(fred)))&
((rich(john)<~>~generous(john)))&
(?[X]:((curious(X)&~creative(X)))) | calm(susan) | [] | null | 0 |
If lucy is not strong or funny then someone is quiet.
Everyone who is both not old and wise is not creative or brave.
If someone is either not creative or not wise then paul is either not rich or not funny.
If someone is either not patient or quiet then paul is either not strong or not curious.
Everyone who is both not humble and quiet is either not wise or not tall.
Everyone who is not funny is not curious or rich.
Everyone who is not creative or calm is both not calm and not patient and vice versa.
If someone is both not calm and not humble then someone is not humble or curious and vice versa.
Everyone who is not patient is creative or humble and vice versa.
If paul is tall or not generous then someone is funny or quiet.
Everyone who is not funny or not brave is creative and vice versa.
If john is both not generous and humble then susan is either calm or brave and vice versa.
If someone is either tall or brave then someone is not funny.
If someone is both kind and not patient then someone is both old and not tall.
Mary is brave.
Someone is either not brave or quiet.
Someone is not creative or quiet.
Alice is either not kind or wise.
Someone is not kind or not strong. | Mary is strong. | neutral | (((~strong(lucy)|funny(lucy)))=>(?[X]:(quiet(X))))&
(![X]:((~old(X)&wise(X))=>(~creative(X)|brave(X))))&
((?[X]:((~creative(X)<~>~wise(X))))=>((~rich(paul)<~>~funny(paul))))&
((?[X]:((~patient(X)<~>quiet(X))))=>((~strong(paul)<~>~curious(paul))))&
(![X]:((~humble(X)&quiet(X))=>(~wise(X)<~>~tall(X))))&
(![X]:(~funny(X)=>(~curious(X)|rich(X))))&
(![X]:((~creative(X)|calm(X))<=>(~calm(X)&~patient(X))))&
((?[X]:((~calm(X)&~humble(X))))<=>(?[X]:((~humble(X)|curious(X)))))&
(![X]:(~patient(X)<=>(creative(X)|humble(X))))&
(((tall(paul)|~generous(paul)))=>(?[X]:((funny(X)|quiet(X)))))&
(![X]:((~funny(X)|~brave(X))<=>creative(X)))&
(((~generous(john)&humble(john)))<=>((calm(susan)<~>brave(susan))))&
((?[X]:((tall(X)<~>brave(X))))=>(?[X]:(~funny(X))))&
((?[X]:((kind(X)&~patient(X))))=>(?[X]:((old(X)&~tall(X)))))&
(brave(mary))&
(?[X]:((~brave(X)<~>quiet(X))))&
(?[X]:((~creative(X)|quiet(X))))&
((~kind(alice)<~>wise(alice)))&
(?[X]:((~kind(X)|~strong(X)))) | strong(mary) | [] | null | 0 |
If someone is not funny or quiet then someone is not quiet.
If someone is not old then mary is either generous or brave.
Everyone who is not curious is not generous or not kind.
If susan is not generous then alice is strong or rich and vice versa.
Everyone who is patient is creative and vice versa.
If susan is either not creative or creative then someone is not strong.
Everyone who is either not strong or not creative is not brave and vice versa.
Everyone who is wise or not calm is both not kind and patient and vice versa.
If paul is not happy then susan is either not brave or old.
Everyone who is creative or generous is both not old and not calm and vice versa.
If john is both not quiet and creative then john is calm and vice versa.
Everyone who is both not creative and not curious is both rich and patient and vice versa.
If someone is not wise or tall then someone is both not wise and not patient.
If john is either happy or quiet then someone is both calm and not calm.
If someone is both not strong and not happy then someone is both patient and creative and vice versa.
Everyone who is both funny and not old is both not brave and wise.
Paul is not generous or not quiet.
John is wise or not happy.
Susan is both creative and patient.
Lucy is either creative or not humble.
Lucy is not strong.
Someone is kind.
Someone is not rich or not kind.
Someone is both not curious and strong. | John is not rich. | entailment | ((?[X]:((~funny(X)|quiet(X))))=>(?[X]:(~quiet(X))))&
((?[X]:(~old(X)))=>((generous(mary)<~>brave(mary))))&
(![X]:(~curious(X)=>(~generous(X)|~kind(X))))&
((~generous(susan))<=>((strong(alice)|rich(alice))))&
(![X]:(patient(X)<=>creative(X)))&
(((~creative(susan)<~>creative(susan)))=>(?[X]:(~strong(X))))&
(![X]:((~strong(X)<~>~creative(X))<=>~brave(X)))&
(![X]:((wise(X)|~calm(X))<=>(~kind(X)&patient(X))))&
((~happy(paul))=>((~brave(susan)<~>old(susan))))&
(![X]:((creative(X)|generous(X))<=>(~old(X)&~calm(X))))&
(((~quiet(john)&creative(john)))<=>(calm(john)))&
(![X]:((~creative(X)&~curious(X))<=>(rich(X)&patient(X))))&
((?[X]:((~wise(X)|tall(X))))=>(?[X]:((~wise(X)&~patient(X)))))&
(((happy(john)<~>quiet(john)))=>(?[X]:((calm(X)&~calm(X)))))&
((?[X]:((~strong(X)&~happy(X))))<=>(?[X]:((patient(X)&creative(X)))))&
(![X]:((funny(X)&~old(X))=>(~brave(X)&wise(X))))&
((~generous(paul)|~quiet(paul)))&
((wise(john)|~happy(john)))&
((creative(susan)&patient(susan)))&
((creative(lucy)<~>~humble(lucy)))&
(~strong(lucy))&
(?[X]:(kind(X)))&
(?[X]:((~rich(X)|~kind(X))))&
(?[X]:((~curious(X)&strong(X)))) | ~rich(john) | [
"p4",
"p7",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 580543678814672622112477
% SZS output start Proof for 580543678814672622112477
5. ! [X0] : (patient(X0) <=> creative(X0)) [input p4]
8. ! [X0] : ((~calm(X0) | wise(X0)) <=> (patient(X0) & ~kind(X0))) [input p7]
10. ! [X0] : ((generous(X0) | creative(X0)) <=> (~calm(X0) & ~old(X0))) [input p9]
11. (creative(john) & ~quiet(john)) <=> calm(john) [input p10]
12. ! [X0] : ((~curious(X0) & ~creative(X0)) <=> (patient(X0) & rich(X0))) [input p11]
25. rich(john) [input hypothesis]
46. ! [X0] : ((patient(X0) | ~creative(X0)) & (creative(X0) | ~patient(X0))) [nnf transformation 5]
51. ! [X0] : (((~calm(X0) | wise(X0)) | (~patient(X0) | kind(X0))) & ((patient(X0) & ~kind(X0)) | (calm(X0) & ~wise(X0)))) [nnf transformation 8]
52. ! [X0] : ((~calm(X0) | wise(X0) | ~patient(X0) | kind(X0)) & ((patient(X0) & ~kind(X0)) | (calm(X0) & ~wise(X0)))) [flattening 51]
54. ! [X0] : (((generous(X0) | creative(X0)) | (calm(X0) | old(X0))) & ((~calm(X0) & ~old(X0)) | (~generous(X0) & ~creative(X0)))) [nnf transformation 10]
55. ! [X0] : ((generous(X0) | creative(X0) | calm(X0) | old(X0)) & ((~calm(X0) & ~old(X0)) | (~generous(X0) & ~creative(X0)))) [flattening 54]
56. ((creative(john) & ~quiet(john)) | ~calm(john)) & (calm(john) | (~creative(john) | quiet(john))) [nnf transformation 11]
57. ((creative(john) & ~quiet(john)) | ~calm(john)) & (calm(john) | ~creative(john) | quiet(john)) [flattening 56]
58. ! [X0] : (((~curious(X0) & ~creative(X0)) | (~patient(X0) | ~rich(X0))) & ((patient(X0) & rich(X0)) | (curious(X0) | creative(X0)))) [nnf transformation 12]
59. ! [X0] : (((~curious(X0) & ~creative(X0)) | ~patient(X0) | ~rich(X0)) & ((patient(X0) & rich(X0)) | curious(X0) | creative(X0))) [flattening 58]
86. ~patient(X0) | creative(X0) [cnf transformation 46]
97. calm(X0) | patient(X0) [cnf transformation 52]
103. ~calm(X0) | ~creative(X0) [cnf transformation 55]
108. creative(john) | ~calm(john) [cnf transformation 57]
111. ~creative(X0) | ~patient(X0) | ~rich(X0) [cnf transformation 59]
136. rich(john) [cnf transformation 25]
203. ~calm(john) [subsumption resolution 108,103]
214. ~patient(X0) | ~rich(X0) [subsumption resolution 111,86]
308. patient(john) [resolution 97,203]
324. ~rich(john) [resolution 214,308]
325. $false [subsumption resolution 324,136]
% SZS output end Proof for 580543678814672622112477
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is quiet and vice versa. Everyone who is either quiet or brave is either not funny or not rich. Everyone who is not kind or not generous is either not happy or brave and vice versa. Everyone who is either not tall or quiet is both brave and not brave. Everyone who is both creative and happy is not humble or generous and vice versa. If someone is both quiet and not kind then someone is either wise or kind and vice versa. If someone is either rich or funny then fred is either not kind or not generous and vice versa. Everyone who is not generous or not wise is not patient. If john is both calm and brave then someone is both not tall and happy and vice versa. Everyone who is not strong is not rich or not kind and vice versa. If someone is both tall and quiet then mary is either not calm or not curious. Everyone who is both not brave and brave is tall or wise and vice versa. If susan is not curious or not old then someone is either not calm or not curious. If someone is not patient or creative then paul is not kind. Someone is not brave or not calm. Lucy is both humble and funny. Someone is not rich. Mary is not calm. Someone is both not funny and not humble. Someone is funny or not kind. | John is happy. | entailment | (![X]:(~rich(X)<=>quiet(X)))&
(![X]:((quiet(X)<~>brave(X))=>(~funny(X)<~>~rich(X))))&
(![X]:((~kind(X)|~generous(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((~tall(X)<~>quiet(X))=>(brave(X)&~brave(X))))&
(![X]:((creative(X)&happy(X))<=>(~humble(X)|generous(X))))&
((?[X]:((quiet(X)&~kind(X))))<=>(?[X]:((wise(X)<~>kind(X)))))&
((?[X]:((rich(X)<~>funny(X))))<=>((~kind(fred)<~>~generous(fred))))&
(![X]:((~generous(X)|~wise(X))=>~patient(X)))&
(((calm(john)&brave(john)))<=>(?[X]:((~tall(X)&happy(X)))))&
(![X]:(~strong(X)<=>(~rich(X)|~kind(X))))&
((?[X]:((tall(X)&quiet(X))))=>((~calm(mary)<~>~curious(mary))))&
(![X]:((~brave(X)&brave(X))<=>(tall(X)|wise(X))))&
(((~curious(susan)|~old(susan)))=>(?[X]:((~calm(X)<~>~curious(X)))))&
((?[X]:((~patient(X)|creative(X))))=>(~kind(paul)))&
(?[X]:((~brave(X)|~calm(X))))&
((humble(lucy)&funny(lucy)))&
(?[X]:(~rich(X)))&
(~calm(mary))&
(?[X]:((~funny(X)&~humble(X))))&
(?[X]:((funny(X)|~kind(X)))) | happy(john) | [
"p2",
"p4",
"p8",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 101588668770963919996946
% SZS output start Proof for 101588668770963919996946
3. ! [X0] : ((~generous(X0) | ~kind(X0)) <=> (~happy(X0) <~> brave(X0))) [input p2]
5. ! [X0] : ((happy(X0) & creative(X0)) <=> (generous(X0) | ~humble(X0))) [input p4]
9. (brave(john) & calm(john)) <=> ? [X0] : (happy(X0) & ~tall(X0)) [input p8]
12. ! [X0] : ((brave(X0) & ~brave(X0)) <=> (wise(X0) | tall(X0))) [input p11]
19. ? [X0] : (~humble(X0) & ~funny(X0)) [input p18]
21. ~happy(john) [input hypothesis]
32. ! [X0] : (((~generous(X0) | ~kind(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) & (((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (generous(X0) & kind(X0)))) [nnf transformation 3]
33. ! [X0] : ((~generous(X0) | ~kind(X0) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) & (((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (generous(X0) & kind(X0)))) [flattening 32]
35. ! [X0] : (((happy(X0) & creative(X0)) | (~generous(X0) & humble(X0))) & ((generous(X0) | ~humble(X0)) | (~happy(X0) | ~creative(X0)))) [nnf transformation 5]
36. ! [X0] : (((happy(X0) & creative(X0)) | (~generous(X0) & humble(X0))) & (generous(X0) | ~humble(X0) | ~happy(X0) | ~creative(X0))) [flattening 35]
46. ((brave(john) & calm(john)) | ! [X0] : (~happy(X0) | tall(X0))) & (? [X0] : (happy(X0) & ~tall(X0)) | (~brave(john) | ~calm(john))) [nnf transformation 9]
47. ((brave(john) & calm(john)) | ! [X0] : (~happy(X0) | tall(X0))) & (? [X0] : (happy(X0) & ~tall(X0)) | ~brave(john) | ~calm(john)) [flattening 46]
48. ((brave(john) & calm(john)) | ! [X0] : (~happy(X0) | tall(X0))) & (? [X1] : (happy(X1) & ~tall(X1)) | ~brave(john) | ~calm(john)) [rectify 47]
49. ? [X1] : (happy(X1) & ~tall(X1)) => (happy(sK3) & ~tall(sK3)) [choice axiom]
50. ((brave(john) & calm(john)) | ! [X0] : (~happy(X0) | tall(X0))) & ((happy(sK3) & ~tall(sK3)) | ~brave(john) | ~calm(john)) [skolemisation 48,49]
52. ! [X0] : (((brave(X0) & ~brave(X0)) | (~wise(X0) & ~tall(X0))) & ((wise(X0) | tall(X0)) | (~brave(X0) | brave(X0)))) [nnf transformation 12]
53. ! [X0] : (((brave(X0) & ~brave(X0)) | (~wise(X0) & ~tall(X0))) & (wise(X0) | tall(X0) | ~brave(X0) | brave(X0))) [flattening 52]
61. ? [X0] : (~humble(X0) & ~funny(X0)) => (~humble(sK7) & ~funny(sK7)) [choice axiom]
62. ~humble(sK7) & ~funny(sK7) [skolemisation 19,61]
74. ~brave(X0) | happy(X0) | generous(X0) [cnf transformation 33]
84. humble(X0) | happy(X0) [cnf transformation 36]
85. ~generous(X0) | happy(X0) [cnf transformation 36]
105. brave(john) | ~happy(X0) | tall(X0) [cnf transformation 50]
109. ~brave(X0) | ~tall(X0) [cnf transformation 53]
111. ~tall(X0) | brave(X0) [cnf transformation 53]
123. ~humble(sK7) [cnf transformation 62]
125. ~happy(john) [cnf transformation 21]
192. 14 <=> ! [X0] : (~happy(X0) | tall(X0)) [avatar definition]
193. ~happy(X0) | tall(X0) <- (14) [avatar component clause 192]
195. 15 <=> brave(john) [avatar definition]
197. brave(john) <- (15) [avatar component clause 195]
198. 14 | 15 [avatar split clause 105,195,192]
215. ~tall(X0) [subsumption resolution 109,111]
260. ~happy(X0) <- (14) [subsumption resolution 193,215]
265. happy(sK7) [resolution 84,123]
266. $false <- (14) [subsumption resolution 265,260]
267. ~14 [avatar contradiction clause 266]
313. happy(john) | generous(john) <- (15) [resolution 74,197]
314. generous(john) <- (15) [subsumption resolution 313,125]
316. happy(john) <- (15) [resolution 314,85]
318. $false <- (15) [subsumption resolution 316,125]
319. ~15 [avatar contradiction clause 318]
320. $false [avatar sat refutation 198,267,319]
% SZS output end Proof for 101588668770963919996946
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either not generous or old then lucy is either not brave or not tall and vice versa.
Everyone who is not tall is tall.
Everyone who is not curious or humble is brave.
If alice is both not strong and not old then john is funny or not happy.
If susan is either happy or not calm then someone is not brave.
Everyone who is either strong or not strong is either not humble or kind.
Everyone who is both rich and curious is not strong or not brave.
If susan is either not old or calm then john is calm or not tall and vice versa.
Everyone who is not creative or curious is either wise or tall and vice versa.
If someone is both creative and brave then someone is both rich and not funny and vice versa.
Everyone who is not quiet is not kind or calm and vice versa.
If someone is not creative or not old then fred is not kind or humble.
Everyone who is not humble is both not curious and not funny and vice versa.
If mary is both not curious and not generous then alice is either not curious or creative.
Everyone who is both not tall and old is either not kind or creative.
Everyone who is not strong or not tall is not curious and vice versa.
Someone is both curious and tall.
Someone is both not curious and not rich.
Lucy is not generous or brave.
Fred is wise or curious.
Mary is both brave and wise.
Alice is tall or not creative. | Lucy is tall. | entailment | (((~generous(lucy)<~>old(lucy)))<=>((~brave(lucy)<~>~tall(lucy))))&
(![X]:(~tall(X)=>tall(X)))&
(![X]:((~curious(X)|humble(X))=>brave(X)))&
(((~strong(alice)&~old(alice)))=>((funny(john)|~happy(john))))&
(((happy(susan)<~>~calm(susan)))=>(?[X]:(~brave(X))))&
(![X]:((strong(X)<~>~strong(X))=>(~humble(X)<~>kind(X))))&
(![X]:((rich(X)&curious(X))=>(~strong(X)|~brave(X))))&
(((~old(susan)<~>calm(susan)))<=>((calm(john)|~tall(john))))&
(![X]:((~creative(X)|curious(X))<=>(wise(X)<~>tall(X))))&
((?[X]:((creative(X)&brave(X))))<=>(?[X]:((rich(X)&~funny(X)))))&
(![X]:(~quiet(X)<=>(~kind(X)|calm(X))))&
((?[X]:((~creative(X)|~old(X))))=>((~kind(fred)|humble(fred))))&
(![X]:(~humble(X)<=>(~curious(X)&~funny(X))))&
(((~curious(mary)&~generous(mary)))=>((~curious(alice)<~>creative(alice))))&
(![X]:((~tall(X)&old(X))=>(~kind(X)<~>creative(X))))&
(![X]:((~strong(X)|~tall(X))<=>~curious(X)))&
(?[X]:((curious(X)&tall(X))))&
(?[X]:((~curious(X)&~rich(X))))&
((~generous(lucy)|brave(lucy)))&
((wise(fred)|curious(fred)))&
((brave(mary)&wise(mary)))&
((tall(alice)|~creative(alice))) | tall(lucy) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 4057569858819231273507872
% SZS output start Proof for 4057569858819231273507872
2. ! [X0] : (~tall(X0) => tall(X0)) [input p1]
23. ~tall(lucy) [input hypothesis]
25. ! [X0] : (tall(X0) | tall(X0)) [ennf transformation 2]
71. tall(X0) | tall(X0) [cnf transformation 25]
119. ~tall(lucy) [cnf transformation 23]
124. tall(X0) [duplicate literal removal 71]
254. $false [subsumption resolution 119,124]
% SZS output end Proof for 4057569858819231273507872
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both funny and not old is curious.
If susan is not humble then someone is not humble and vice versa.
Everyone who is patient is either tall or curious and vice versa.
If someone is both not patient and not tall then someone is not creative.
Everyone who is either not creative or quiet is both curious and not kind.
If someone is both old and not strong then susan is not strong.
Everyone who is either creative or old is either brave or not quiet.
If someone is not wise or not curious then someone is kind.
Everyone who is wise is brave or quiet.
Everyone who is both kind and calm is not humble.
If someone is both calm and brave then mary is happy.
Everyone who is old is both not tall and not quiet and vice versa.
Everyone who is either happy or tall is not happy and vice versa.
If someone is either not happy or rich then fred is not humble or not calm and vice versa.
Everyone who is either not tall or quiet is either not tall or creative and vice versa.
If john is generous then someone is kind and vice versa.
Someone is not calm.
Someone is both wise and humble.
Mary is not patient.
Lucy is either humble or generous.
Someone is both curious and not happy.
Fred is either not kind or not rich.
Lucy is old or not old. | Mary is not funny. | neutral | (![X]:((funny(X)&~old(X))=>curious(X)))&
((~humble(susan))<=>(?[X]:(~humble(X))))&
(![X]:(patient(X)<=>(tall(X)<~>curious(X))))&
((?[X]:((~patient(X)&~tall(X))))=>(?[X]:(~creative(X))))&
(![X]:((~creative(X)<~>quiet(X))=>(curious(X)&~kind(X))))&
((?[X]:((old(X)&~strong(X))))=>(~strong(susan)))&
(![X]:((creative(X)<~>old(X))=>(brave(X)<~>~quiet(X))))&
((?[X]:((~wise(X)|~curious(X))))=>(?[X]:(kind(X))))&
(![X]:(wise(X)=>(brave(X)|quiet(X))))&
(![X]:((kind(X)&calm(X))=>~humble(X)))&
((?[X]:((calm(X)&brave(X))))=>(happy(mary)))&
(![X]:(old(X)<=>(~tall(X)&~quiet(X))))&
(![X]:((happy(X)<~>tall(X))<=>~happy(X)))&
((?[X]:((~happy(X)<~>rich(X))))<=>((~humble(fred)|~calm(fred))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~tall(X)<~>creative(X))))&
((generous(john))<=>(?[X]:(kind(X))))&
(?[X]:(~calm(X)))&
(?[X]:((wise(X)&humble(X))))&
(~patient(mary))&
((humble(lucy)<~>generous(lucy)))&
(?[X]:((curious(X)&~happy(X))))&
((~kind(fred)<~>~rich(fred)))&
((old(lucy)|~old(lucy))) | ~funny(mary) | [] | null | 0 |
If someone is not creative or not humble then susan is both not tall and humble and vice versa.
Everyone who is both not patient and creative is both not funny and not strong and vice versa.
If someone is brave or not funny then someone is both not humble and happy.
Everyone who is not strong is both strong and tall.
If alice is either not old or kind then alice is humble or wise.
Everyone who is not quiet or quiet is either not funny or strong.
If someone is either not humble or not kind then lucy is curious.
Everyone who is not old is either funny or not wise.
If someone is either not quiet or curious then someone is either not calm or calm.
Everyone who is both calm and not calm is rich and vice versa.
Everyone who is both quiet and not calm is not happy and vice versa.
Everyone who is both patient and not quiet is both not patient and rich.
If alice is brave or not creative then someone is quiet or not patient and vice versa.
If john is not generous then susan is not generous or old and vice versa.
If alice is tall then someone is either not funny or not calm.
Someone is both wise and kind.
Someone is old or strong.
Someone is kind or not curious.
Susan is old.
Someone is either funny or wise.
Paul is strong or not old.
Someone is either not generous or not wise. | Susan is not tall. | entailment | ((?[X]:((~creative(X)|~humble(X))))<=>((~tall(susan)&humble(susan))))&
(![X]:((~patient(X)&creative(X))<=>(~funny(X)&~strong(X))))&
((?[X]:((brave(X)|~funny(X))))=>(?[X]:((~humble(X)&happy(X)))))&
(![X]:(~strong(X)=>(strong(X)&tall(X))))&
(((~old(alice)<~>kind(alice)))=>((humble(alice)|wise(alice))))&
(![X]:((~quiet(X)|quiet(X))=>(~funny(X)<~>strong(X))))&
((?[X]:((~humble(X)<~>~kind(X))))=>(curious(lucy)))&
(![X]:(~old(X)=>(funny(X)<~>~wise(X))))&
((?[X]:((~quiet(X)<~>curious(X))))=>(?[X]:((~calm(X)<~>calm(X)))))&
(![X]:((calm(X)&~calm(X))<=>rich(X)))&
(![X]:((quiet(X)&~calm(X))<=>~happy(X)))&
(![X]:((patient(X)&~quiet(X))=>(~patient(X)&rich(X))))&
(((brave(alice)|~creative(alice)))<=>(?[X]:((quiet(X)|~patient(X)))))&
((~generous(john))<=>((~generous(susan)|old(susan))))&
((tall(alice))=>(?[X]:((~funny(X)<~>~calm(X)))))&
(?[X]:((wise(X)&kind(X))))&
(?[X]:((old(X)|strong(X))))&
(?[X]:((kind(X)|~curious(X))))&
(old(susan))&
(?[X]:((funny(X)<~>wise(X))))&
((strong(paul)|~old(paul)))&
(?[X]:((~generous(X)<~>~wise(X)))) | ~tall(susan) | [
"p0",
"p2",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1745038984222338520796028
% SZS output start Proof for 1745038984222338520796028
1. ? [X0] : (~humble(X0) | ~creative(X0)) <=> (humble(susan) & ~tall(susan)) [input p0]
3. ? [X0] : (~funny(X0) | brave(X0)) => ? [X0] : (happy(X0) & ~humble(X0)) [input p2]
10. ! [X0] : ((~calm(X0) & calm(X0)) <=> rich(X0)) [input p9]
12. ! [X0] : ((~quiet(X0) & patient(X0)) => (rich(X0) & ~patient(X0))) [input p11]
13. (~creative(alice) | brave(alice)) <=> ? [X0] : (~patient(X0) | quiet(X0)) [input p12]
23. tall(susan) [input hypothesis]
24. ? [X0] : (~funny(X0) | brave(X0)) => ? [X1] : (happy(X1) & ~humble(X1)) [rectify 3]
26. ! [X0] : (rich(X0) => (~calm(X0) & calm(X0))) [unused predicate definition removal 10]
28. ? [X1] : (happy(X1) & ~humble(X1)) | ! [X0] : (funny(X0) & ~brave(X0)) [ennf transformation 24]
36. ! [X0] : ((~calm(X0) & calm(X0)) | ~rich(X0)) [ennf transformation 26]
39. ! [X0] : ((rich(X0) & ~patient(X0)) | (quiet(X0) | ~patient(X0))) [ennf transformation 12]
40. ! [X0] : ((rich(X0) & ~patient(X0)) | quiet(X0) | ~patient(X0)) [flattening 39]
42. (? [X0] : (~humble(X0) | ~creative(X0)) | (~humble(susan) | tall(susan))) & ((humble(susan) & ~tall(susan)) | ! [X0] : (humble(X0) & creative(X0))) [nnf transformation 1]
43. (? [X0] : (~humble(X0) | ~creative(X0)) | ~humble(susan) | tall(susan)) & ((humble(susan) & ~tall(susan)) | ! [X0] : (humble(X0) & creative(X0))) [flattening 42]
44. (? [X0] : (~humble(X0) | ~creative(X0)) | ~humble(susan) | tall(susan)) & ((humble(susan) & ~tall(susan)) | ! [X1] : (humble(X1) & creative(X1))) [rectify 43]
45. ? [X0] : (~humble(X0) | ~creative(X0)) => (~humble(sK0) | ~creative(sK0)) [choice axiom]
46. ((~humble(sK0) | ~creative(sK0)) | ~humble(susan) | tall(susan)) & ((humble(susan) & ~tall(susan)) | ! [X1] : (humble(X1) & creative(X1))) [skolemisation 44,45]
49. ? [X0] : (happy(X0) & ~humble(X0)) | ! [X1] : (funny(X1) & ~brave(X1)) [rectify 28]
50. ? [X0] : (happy(X0) & ~humble(X0)) => (happy(sK1) & ~humble(sK1)) [choice axiom]
51. (happy(sK1) & ~humble(sK1)) | ! [X1] : (funny(X1) & ~brave(X1)) [skolemisation 49,50]
60. ((~creative(alice) | brave(alice)) | ! [X0] : (patient(X0) & ~quiet(X0))) & (? [X0] : (~patient(X0) | quiet(X0)) | (creative(alice) & ~brave(alice))) [nnf transformation 13]
61. (~creative(alice) | brave(alice) | ! [X0] : (patient(X0) & ~quiet(X0))) & (? [X0] : (~patient(X0) | quiet(X0)) | (creative(alice) & ~brave(alice))) [flattening 60]
62. (~creative(alice) | brave(alice) | ! [X0] : (patient(X0) & ~quiet(X0))) & (? [X1] : (~patient(X1) | quiet(X1)) | (creative(alice) & ~brave(alice))) [rectify 61]
63. ? [X1] : (~patient(X1) | quiet(X1)) => (~patient(sK3) | quiet(sK3)) [choice axiom]
64. (~creative(alice) | brave(alice) | ! [X0] : (patient(X0) & ~quiet(X0))) & ((~patient(sK3) | quiet(sK3)) | (creative(alice) & ~brave(alice))) [skolemisation 62,63]
82. ~tall(susan) | creative(X1) [cnf transformation 46]
83. ~tall(susan) | humble(X1) [cnf transformation 46]
91. ~humble(sK1) | ~brave(X1) [cnf transformation 51]
111. calm(X0) | ~rich(X0) [cnf transformation 36]
112. ~rich(X0) | ~calm(X0) [cnf transformation 36]
115. rich(X0) | quiet(X0) | ~patient(X0) [cnf transformation 40]
118. ~creative(alice) | brave(alice) | ~quiet(X0) [cnf transformation 64]
119. ~creative(alice) | brave(alice) | patient(X0) [cnf transformation 64]
135. tall(susan) [cnf transformation 23]
139. 1 <=> tall(susan) [avatar definition]
156. 5 <=> ! [X1] : humble(X1) [avatar definition]
157. humble(X1) <- (5) [avatar component clause 156]
160. 6 <=> ! [X1] : creative(X1) [avatar definition]
161. creative(X1) <- (6) [avatar component clause 160]
163. 5 | ~1 [avatar split clause 83,139,156]
164. 6 | ~1 [avatar split clause 82,139,160]
174. 9 <=> ! [X1] : ~brave(X1) [avatar definition]
175. ~brave(X1) <- (9) [avatar component clause 174]
178. 10 <=> humble(sK1) [avatar definition]
180. ~humble(sK1) <- (~10) [avatar component clause 178]
182. 9 | ~10 [avatar split clause 91,178,174]
217. ~rich(X0) [subsumption resolution 111,112]
218. ~patient(X0) | quiet(X0) [subsumption resolution 115,217]
220. 18 <=> ! [X0] : patient(X0) [avatar definition]
221. patient(X0) <- (18) [avatar component clause 220]
223. 19 <=> brave(alice) [avatar definition]
225. brave(alice) <- (19) [avatar component clause 223]
227. 20 <=> creative(alice) [avatar definition]
229. ~creative(alice) <- (~20) [avatar component clause 227]
230. 18 | 19 | ~20 [avatar split clause 119,227,223,220]
232. 21 <=> ! [X0] : ~quiet(X0) [avatar definition]
233. ~quiet(X0) <- (21) [avatar component clause 232]
234. 21 | 19 | ~20 [avatar split clause 118,227,223,232]
294. 1 [avatar split clause 135,139]
295. $false <- (5, ~10) [resolution 180,157]
296. ~5 | 10 [avatar contradiction clause 295]
297. $false <- (6, ~20) [resolution 229,161]
298. ~6 | 20 [avatar contradiction clause 297]
299. $false <- (9, 19) [subsumption resolution 225,175]
300. ~9 | ~19 [avatar contradiction clause 299]
301. quiet(X0) <- (18) [resolution 218,221]
302. $false <- (18, 21) [subsumption resolution 301,233]
303. ~18 | ~21 [avatar contradiction clause 302]
304. $false [avatar sat refutation 163,164,182,230,234,294,296,298,300,303]
% SZS output end Proof for 1745038984222338520796028
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is quiet or funny then alice is both not funny and rich. If someone is quiet then someone is calm or not wise and vice versa. Everyone who is not wise is generous or not humble. Everyone who is either not rich or strong is creative. Everyone who is calm is brave or funny and vice versa. Everyone who is both not happy and not kind is curious. If someone is not brave or not humble then lucy is both not rich and not patient and vice versa. Everyone who is either not kind or not funny is calm or wise. Everyone who is either not creative or creative is strong or tall. Everyone who is kind is not patient or not funny. Everyone who is not happy is not old or curious and vice versa. Everyone who is not humble is either not strong or not patient and vice versa. If someone is creative or not kind then someone is not calm and vice versa. If fred is both tall and not quiet then someone is either not kind or not calm. Everyone who is not calm is either not patient or not strong. If alice is patient or funny then someone is either not patient or strong. Someone is both not curious and not funny. Someone is both not generous and creative. Someone is not strong. Someone is not strong or funny. Mary is not rich. Paul is quiet. Susan is not wise or not quiet. Someone is wise or not calm. | Lucy is not rich. | entailment | (((quiet(susan)|funny(susan)))=>((~funny(alice)&rich(alice))))&
((?[X]:(quiet(X)))<=>(?[X]:((calm(X)|~wise(X)))))&
(![X]:(~wise(X)=>(generous(X)|~humble(X))))&
(![X]:((~rich(X)<~>strong(X))=>creative(X)))&
(![X]:(calm(X)<=>(brave(X)|funny(X))))&
(![X]:((~happy(X)&~kind(X))=>curious(X)))&
((?[X]:((~brave(X)|~humble(X))))<=>((~rich(lucy)&~patient(lucy))))&
(![X]:((~kind(X)<~>~funny(X))=>(calm(X)|wise(X))))&
(![X]:((~creative(X)<~>creative(X))=>(strong(X)|tall(X))))&
(![X]:(kind(X)=>(~patient(X)|~funny(X))))&
(![X]:(~happy(X)<=>(~old(X)|curious(X))))&
(![X]:(~humble(X)<=>(~strong(X)<~>~patient(X))))&
((?[X]:((creative(X)|~kind(X))))<=>(?[X]:(~calm(X))))&
(((tall(fred)&~quiet(fred)))=>(?[X]:((~kind(X)<~>~calm(X)))))&
(![X]:(~calm(X)=>(~patient(X)<~>~strong(X))))&
(((patient(alice)|funny(alice)))=>(?[X]:((~patient(X)<~>strong(X)))))&
(?[X]:((~curious(X)&~funny(X))))&
(?[X]:((~generous(X)&creative(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~strong(X)|funny(X))))&
(~rich(mary))&
(quiet(paul))&
((~wise(susan)|~quiet(susan)))&
(?[X]:((wise(X)|~calm(X)))) | ~rich(lucy) | [
"p4",
"p6",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1706569154657084727829270
% SZS output start Proof for 1706569154657084727829270
5. ! [X0] : (calm(X0) <=> (funny(X0) | brave(X0))) [input p4]
7. ? [X0] : (~humble(X0) | ~brave(X0)) <=> (~patient(lucy) & ~rich(lucy)) [input p6]
13. ? [X0] : (~kind(X0) | creative(X0)) <=> ? [X0] : ~calm(X0) [input p12]
18. ? [X0] : (creative(X0) & ~generous(X0)) [input p17]
25. rich(lucy) [input hypothesis]
27. ? [X0] : (~kind(X0) | creative(X0)) <=> ? [X1] : ~calm(X1) [rectify 13]
53. ! [X0] : ((calm(X0) | (~funny(X0) & ~brave(X0))) & ((funny(X0) | brave(X0)) | ~calm(X0))) [nnf transformation 5]
54. ! [X0] : ((calm(X0) | (~funny(X0) & ~brave(X0))) & (funny(X0) | brave(X0) | ~calm(X0))) [flattening 53]
55. (? [X0] : (~humble(X0) | ~brave(X0)) | (patient(lucy) | rich(lucy))) & ((~patient(lucy) & ~rich(lucy)) | ! [X0] : (humble(X0) & brave(X0))) [nnf transformation 7]
56. (? [X0] : (~humble(X0) | ~brave(X0)) | patient(lucy) | rich(lucy)) & ((~patient(lucy) & ~rich(lucy)) | ! [X0] : (humble(X0) & brave(X0))) [flattening 55]
57. (? [X0] : (~humble(X0) | ~brave(X0)) | patient(lucy) | rich(lucy)) & ((~patient(lucy) & ~rich(lucy)) | ! [X1] : (humble(X1) & brave(X1))) [rectify 56]
58. ? [X0] : (~humble(X0) | ~brave(X0)) => (~humble(sK2) | ~brave(sK2)) [choice axiom]
59. ((~humble(sK2) | ~brave(sK2)) | patient(lucy) | rich(lucy)) & ((~patient(lucy) & ~rich(lucy)) | ! [X1] : (humble(X1) & brave(X1))) [skolemisation 57,58]
63. (? [X0] : (~kind(X0) | creative(X0)) | ! [X1] : calm(X1)) & (? [X1] : ~calm(X1) | ! [X0] : (kind(X0) & ~creative(X0))) [nnf transformation 27]
64. (? [X0] : (~kind(X0) | creative(X0)) | ! [X1] : calm(X1)) & (? [X2] : ~calm(X2) | ! [X3] : (kind(X3) & ~creative(X3))) [rectify 63]
65. ? [X0] : (~kind(X0) | creative(X0)) => (~kind(sK3) | creative(sK3)) [choice axiom]
66. ? [X2] : ~calm(X2) => ~calm(sK4) [choice axiom]
67. ((~kind(sK3) | creative(sK3)) | ! [X1] : calm(X1)) & (~calm(sK4) | ! [X3] : (kind(X3) & ~creative(X3))) [skolemisation 64,66,65]
77. ? [X0] : (creative(X0) & ~generous(X0)) => (creative(sK8) & ~generous(sK8)) [choice axiom]
78. creative(sK8) & ~generous(sK8) [skolemisation 18,77]
96. ~brave(X0) | calm(X0) [cnf transformation 54]
99. ~rich(lucy) | brave(X1) [cnf transformation 59]
114. ~calm(sK4) | ~creative(X3) [cnf transformation 67]
128. creative(sK8) [cnf transformation 78]
135. rich(lucy) [cnf transformation 25]
183. 11 <=> rich(lucy) [avatar definition]
204. 16 <=> ! [X1] : brave(X1) [avatar definition]
205. brave(X1) <- (16) [avatar component clause 204]
208. 16 | ~11 [avatar split clause 99,183,204]
212. 17 <=> ! [X1] : calm(X1) [avatar definition]
213. calm(X1) <- (17) [avatar component clause 212]
227. 21 <=> calm(sK4) [avatar definition]
229. ~calm(sK4) <- (~21) [avatar component clause 227]
232. 22 <=> ! [X3] : ~creative(X3) [avatar definition]
233. ~creative(X3) <- (22) [avatar component clause 232]
234. 22 | ~21 [avatar split clause 114,227,232]
292. 11 [avatar split clause 135,183]
293. calm(X0) <- (16) [resolution 96,205]
294. 17 | ~16 [avatar split clause 293,204,212]
295. $false <- (17, ~21) [resolution 213,229]
298. ~17 | 21 [avatar contradiction clause 295]
301. $false <- (22) [resolution 233,128]
302. ~22 [avatar contradiction clause 301]
303. $false [avatar sat refutation 208,234,292,294,298,302]
% SZS output end Proof for 1706569154657084727829270
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or kind is either not brave or not quiet. Everyone who is not humble is either not calm or humble and vice versa. If susan is not brave or not rich then someone is old and vice versa. Everyone who is quiet or not rich is happy and vice versa. Everyone who is both funny and not kind is both rich and not kind. If someone is either brave or kind then someone is either tall or patient and vice versa. Everyone who is not curious is not generous and vice versa. If john is either kind or not generous then someone is not tall or happy. Everyone who is both happy and patient is either not strong or quiet. If someone is kind or brave then paul is not quiet. If someone is happy then someone is both not humble and curious. Everyone who is both not curious and happy is not quiet. Everyone who is not happy is either funny or kind. If someone is both not happy and not brave then someone is creative or happy and vice versa. If susan is either curious or not generous then someone is not wise or patient and vice versa. Everyone who is both wise and not calm is either not strong or curious. Lucy is both not strong and not generous. Someone is kind or happy. John is either creative or not wise. Susan is either quiet or not calm. Susan is both not calm and not wise. | Lucy is not brave. | contradiction | (![X]:((~calm(X)|kind(X))=>(~brave(X)<~>~quiet(X))))&
(![X]:(~humble(X)<=>(~calm(X)<~>humble(X))))&
(((~brave(susan)|~rich(susan)))<=>(?[X]:(old(X))))&
(![X]:((quiet(X)|~rich(X))<=>happy(X)))&
(![X]:((funny(X)&~kind(X))=>(rich(X)&~kind(X))))&
((?[X]:((brave(X)<~>kind(X))))<=>(?[X]:((tall(X)<~>patient(X)))))&
(![X]:(~curious(X)<=>~generous(X)))&
(((kind(john)<~>~generous(john)))=>(?[X]:((~tall(X)|happy(X)))))&
(![X]:((happy(X)&patient(X))=>(~strong(X)<~>quiet(X))))&
((?[X]:((kind(X)|brave(X))))=>(~quiet(paul)))&
((?[X]:(happy(X)))=>(?[X]:((~humble(X)&curious(X)))))&
(![X]:((~curious(X)&happy(X))=>~quiet(X)))&
(![X]:(~happy(X)=>(funny(X)<~>kind(X))))&
((?[X]:((~happy(X)&~brave(X))))<=>(?[X]:((creative(X)|happy(X)))))&
(((curious(susan)<~>~generous(susan)))<=>(?[X]:((~wise(X)|patient(X)))))&
(![X]:((wise(X)&~calm(X))=>(~strong(X)<~>curious(X))))&
((~strong(lucy)&~generous(lucy)))&
(?[X]:((kind(X)|happy(X))))&
((creative(john)<~>~wise(john)))&
((quiet(susan)<~>~calm(susan)))&
((~calm(susan)&~wise(susan))) | ~brave(lucy) | [
"p0",
"p1",
"p3",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2282991183203413371640585
% SZS output start Proof for 2282991183203413371640585
1. ! [X0] : ((kind(X0) | ~calm(X0)) => (~brave(X0) <~> ~quiet(X0))) [input p0]
2. ! [X0] : (~humble(X0) <=> (~calm(X0) <~> humble(X0))) [input p1]
4. ! [X0] : ((~rich(X0) | quiet(X0)) <=> happy(X0)) [input p3]
14. ? [X0] : (~brave(X0) & ~happy(X0)) <=> ? [X0] : (happy(X0) | creative(X0)) [input p13]
22. ~brave(lucy) [input hypothesis]
25. ? [X0] : (~brave(X0) & ~happy(X0)) <=> ? [X1] : (happy(X1) | creative(X1)) [rectify 14]
26. ! [X0] : ((~brave(X0) <~> ~quiet(X0)) | (~kind(X0) & calm(X0))) [ennf transformation 1]
39. ! [X0] : (((quiet(X0) | brave(X0)) & (~quiet(X0) | ~brave(X0))) | (~kind(X0) & calm(X0))) [nnf transformation 26]
40. ! [X0] : ((~humble(X0) | ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0)))) & (((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | humble(X0))) [nnf transformation 2]
46. ! [X0] : (((~rich(X0) | quiet(X0)) | ~happy(X0)) & (happy(X0) | (rich(X0) & ~quiet(X0)))) [nnf transformation 4]
47. ! [X0] : ((~rich(X0) | quiet(X0) | ~happy(X0)) & (happy(X0) | (rich(X0) & ~quiet(X0)))) [flattening 46]
62. (? [X0] : (~brave(X0) & ~happy(X0)) | ! [X1] : (~happy(X1) & ~creative(X1))) & (? [X1] : (happy(X1) | creative(X1)) | ! [X0] : (brave(X0) | happy(X0))) [nnf transformation 25]
63. (? [X0] : (~brave(X0) & ~happy(X0)) | ! [X1] : (~happy(X1) & ~creative(X1))) & (? [X2] : (happy(X2) | creative(X2)) | ! [X3] : (brave(X3) | happy(X3))) [rectify 62]
64. ? [X0] : (~brave(X0) & ~happy(X0)) => (~brave(sK5) & ~happy(sK5)) [choice axiom]
65. ? [X2] : (happy(X2) | creative(X2)) => (happy(sK6) | creative(sK6)) [choice axiom]
66. ((~brave(sK5) & ~happy(sK5)) | ! [X1] : (~happy(X1) & ~creative(X1))) & ((happy(sK6) | creative(sK6)) | ! [X3] : (brave(X3) | happy(X3))) [skolemisation 63,65,64]
78. quiet(X0) | brave(X0) | calm(X0) [cnf transformation 39]
80. humble(X0) | ~calm(X0) | humble(X0) [cnf transformation 40]
83. ~humble(X0) | ~calm(X0) | ~humble(X0) [cnf transformation 40]
87. ~quiet(X0) | happy(X0) [cnf transformation 47]
115. ~happy(sK5) | ~happy(X1) [cnf transformation 66]
117. ~brave(sK5) | ~happy(X1) [cnf transformation 66]
135. ~brave(lucy) [cnf transformation 22]
136. humble(X0) | ~calm(X0) [duplicate literal removal 80]
137. ~humble(X0) | ~calm(X0) [duplicate literal removal 83]
138. ~calm(X0) [subsumption resolution 136,137]
225. 20 <=> ! [X1] : ~happy(X1) [avatar definition]
226. ~happy(X1) <- (20) [avatar component clause 225]
239. 23 <=> brave(sK5) [avatar definition]
241. ~brave(sK5) <- (~23) [avatar component clause 239]
242. 20 | ~23 [avatar split clause 117,239,225]
248. 25 <=> happy(sK5) [avatar definition]
250. ~happy(sK5) <- (~25) [avatar component clause 248]
251. 20 | ~25 [avatar split clause 115,248,225]
254. 26 <=> ! [X3] : (brave(X3) | happy(X3)) [avatar definition]
255. happy(X3) | brave(X3) <- (26) [avatar component clause 254]
309. brave(sK5) <- (~25, 26) [resolution 255,250]
310. $false <- (~23, ~25, 26) [subsumption resolution 309,241]
311. 23 | 25 | ~26 [avatar contradiction clause 310]
317. brave(X3) | calm(X3) | happy(X3) [resolution 78,87]
323. brave(X3) | happy(X3) [subsumption resolution 317,138]
324. 26 [avatar split clause 323,254]
331. brave(X0) <- (20, 26) [resolution 255,226]
335. $false <- (20, 26) [resolution 331,135]
336. ~20 | ~26 [avatar contradiction clause 335]
337. $false [avatar sat refutation 242,251,311,324,336]
% SZS output end Proof for 2282991183203413371640585
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and not old is either not brave or not curious and vice versa.
Everyone who is both not rich and not generous is both not generous and not creative and vice versa.
Everyone who is both calm and not tall is not humble and vice versa.
If fred is either not tall or not curious then someone is both not tall and not wise.
Everyone who is not rich or not brave is kind or not funny and vice versa.
Everyone who is not patient is not calm or not kind and vice versa.
Everyone who is either not brave or not old is curious or rich and vice versa.
If someone is both patient and quiet then fred is either creative or rich and vice versa.
If mary is not rich then alice is humble and vice versa.
Everyone who is tall is both not creative and not wise.
If mary is both rich and not strong then someone is either not creative or funny and vice versa.
If someone is old then alice is not humble and vice versa.
If john is both old and calm then someone is brave and vice versa.
If fred is not quiet or generous then someone is both not patient and rich.
If someone is either not generous or generous then someone is both patient and not happy and vice versa.
Everyone who is quiet is both not old and not quiet.
Someone is both not wise and happy.
Alice is either tall or not old.
Alice is brave or wise.
Someone is either calm or brave.
Susan is not curious.
Fred is not patient.
Someone is old.
Someone is not wise or curious. | John is curious. | contradiction | (![X]:((rich(X)&~old(X))<=>(~brave(X)<~>~curious(X))))&
(![X]:((~rich(X)&~generous(X))<=>(~generous(X)&~creative(X))))&
(![X]:((calm(X)&~tall(X))<=>~humble(X)))&
(((~tall(fred)<~>~curious(fred)))=>(?[X]:((~tall(X)&~wise(X)))))&
(![X]:((~rich(X)|~brave(X))<=>(kind(X)|~funny(X))))&
(![X]:(~patient(X)<=>(~calm(X)|~kind(X))))&
(![X]:((~brave(X)<~>~old(X))<=>(curious(X)|rich(X))))&
((?[X]:((patient(X)&quiet(X))))<=>((creative(fred)<~>rich(fred))))&
((~rich(mary))<=>(humble(alice)))&
(![X]:(tall(X)=>(~creative(X)&~wise(X))))&
(((rich(mary)&~strong(mary)))<=>(?[X]:((~creative(X)<~>funny(X)))))&
((?[X]:(old(X)))<=>(~humble(alice)))&
(((old(john)&calm(john)))<=>(?[X]:(brave(X))))&
(((~quiet(fred)|generous(fred)))=>(?[X]:((~patient(X)&rich(X)))))&
((?[X]:((~generous(X)<~>generous(X))))<=>(?[X]:((patient(X)&~happy(X)))))&
(![X]:(quiet(X)=>(~old(X)&~quiet(X))))&
(?[X]:((~wise(X)&happy(X))))&
((tall(alice)<~>~old(alice)))&
((brave(alice)|wise(alice)))&
(?[X]:((calm(X)<~>brave(X))))&
(~curious(susan))&
(~patient(fred))&
(?[X]:(old(X)))&
(?[X]:((~wise(X)|curious(X)))) | curious(john) | [
"p0",
"p6",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3703039884893518433337204
% SZS output start Proof for 3703039884893518433337204
1. ! [X0] : ((~old(X0) & rich(X0)) <=> (~brave(X0) <~> ~curious(X0))) [input p0]
7. ! [X0] : ((~brave(X0) <~> ~old(X0)) <=> (rich(X0) | curious(X0))) [input p6]
13. (calm(john) & old(john)) <=> ? [X0] : brave(X0) [input p12]
25. curious(john) [input hypothesis]
31. ! [X0] : (((~old(X0) & rich(X0)) | ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0)))) & (((curious(X0) | brave(X0)) & (~curious(X0) | ~brave(X0))) | (old(X0) | ~rich(X0)))) [nnf transformation 1]
32. ! [X0] : (((~old(X0) & rich(X0)) | ((~brave(X0) | curious(X0)) & (~curious(X0) | brave(X0)))) & (((curious(X0) | brave(X0)) & (~curious(X0) | ~brave(X0))) | old(X0) | ~rich(X0))) [flattening 31]
44. ! [X0] : ((((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | (~rich(X0) & ~curious(X0))) & ((rich(X0) | curious(X0)) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0))))) [nnf transformation 7]
45. ! [X0] : ((((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | (~rich(X0) & ~curious(X0))) & (rich(X0) | curious(X0) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0))))) [flattening 44]
60. ((calm(john) & old(john)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | (~calm(john) | ~old(john))) [nnf transformation 13]
61. ((calm(john) & old(john)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | ~calm(john) | ~old(john)) [flattening 60]
62. ((calm(john) & old(john)) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | ~calm(john) | ~old(john)) [rectify 61]
63. ? [X1] : brave(X1) => brave(sK4) [choice axiom]
64. ((calm(john) & old(john)) | ! [X0] : ~brave(X0)) & (brave(sK4) | ~calm(john) | ~old(john)) [skolemisation 62,63]
86. ~old(X0) | ~curious(X0) | brave(X0) [cnf transformation 32]
108. ~old(X0) | ~brave(X0) | ~curious(X0) [cnf transformation 45]
110. old(X0) | brave(X0) | ~curious(X0) [cnf transformation 45]
131. old(john) | ~brave(X0) [cnf transformation 64]
156. curious(john) [cnf transformation 25]
182. ~curious(X0) | brave(X0) [subsumption resolution 110,86]
183. ~curious(X0) | ~old(X0) [subsumption resolution 108,86]
255. 19 <=> ! [X0] : ~brave(X0) [avatar definition]
256. ~brave(X0) <- (19) [avatar component clause 255]
263. 21 <=> old(john) [avatar definition]
266. 19 | 21 [avatar split clause 131,263,255]
361. brave(john) [resolution 182,156]
362. ~old(john) [resolution 183,156]
365. ~21 [avatar split clause 362,263]
366. $false <- (19) [resolution 256,361]
369. ~19 [avatar contradiction clause 366]
370. $false [avatar sat refutation 266,365,369]
% SZS output end Proof for 3703039884893518433337204
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not strong is not happy or not creative and vice versa.
If someone is both kind and old then someone is both happy and old.
Everyone who is not rich is strong and vice versa.
If someone is wise then someone is either tall or not calm and vice versa.
Everyone who is kind is both not wise and calm and vice versa.
Everyone who is both not happy and not wise is both not quiet and tall and vice versa.
Everyone who is either not brave or not old is both quiet and wise.
If someone is both strong and humble then someone is not creative or old and vice versa.
Everyone who is both not patient and not happy is quiet or old and vice versa.
If susan is not generous or creative then mary is not rich or not brave.
Everyone who is both brave and strong is both not curious and brave.
Everyone who is both not curious and not happy is both not kind and not calm.
If someone is either creative or not calm then someone is wise and vice versa.
Everyone who is strong is either happy or brave and vice versa.
Everyone who is not generous or not strong is not curious.
Everyone who is kind or not rich is happy and vice versa.
Paul is both kind and humble.
Someone is not humble.
John is both strong and not rich.
Paul is either quiet or humble.
Paul is either humble or quiet.
Paul is humble. | Mary is brave. | contradiction | (![X]:((funny(X)|~strong(X))<=>(~happy(X)|~creative(X))))&
((?[X]:((kind(X)&old(X))))=>(?[X]:((happy(X)&old(X)))))&
(![X]:(~rich(X)<=>strong(X)))&
((?[X]:(wise(X)))<=>(?[X]:((tall(X)<~>~calm(X)))))&
(![X]:(kind(X)<=>(~wise(X)&calm(X))))&
(![X]:((~happy(X)&~wise(X))<=>(~quiet(X)&tall(X))))&
(![X]:((~brave(X)<~>~old(X))=>(quiet(X)&wise(X))))&
((?[X]:((strong(X)&humble(X))))<=>(?[X]:((~creative(X)|old(X)))))&
(![X]:((~patient(X)&~happy(X))<=>(quiet(X)|old(X))))&
(((~generous(susan)|creative(susan)))=>((~rich(mary)|~brave(mary))))&
(![X]:((brave(X)&strong(X))=>(~curious(X)&brave(X))))&
(![X]:((~curious(X)&~happy(X))=>(~kind(X)&~calm(X))))&
((?[X]:((creative(X)<~>~calm(X))))<=>(?[X]:(wise(X))))&
(![X]:(strong(X)<=>(happy(X)<~>brave(X))))&
(![X]:((~generous(X)|~strong(X))=>~curious(X)))&
(![X]:((kind(X)|~rich(X))<=>happy(X)))&
((kind(paul)&humble(paul)))&
(?[X]:(~humble(X)))&
((strong(john)&~rich(john)))&
((quiet(paul)<~>humble(paul)))&
((humble(paul)<~>quiet(paul)))&
(humble(paul)) | brave(mary) | [
"p2",
"p6",
"p8",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 534702973016449730988122
% SZS output start Proof for 534702973016449730988122
3. ! [X0] : (~rich(X0) <=> strong(X0)) [input p2]
7. ! [X0] : ((~brave(X0) <~> ~old(X0)) => (wise(X0) & quiet(X0))) [input p6]
9. ! [X0] : ((~happy(X0) & ~patient(X0)) <=> (old(X0) | quiet(X0))) [input p8]
14. ! [X0] : (strong(X0) <=> (happy(X0) <~> brave(X0))) [input p13]
16. ! [X0] : ((~rich(X0) | kind(X0)) <=> happy(X0)) [input p15]
23. brave(mary) [input hypothesis]
31. ! [X0] : ((wise(X0) & quiet(X0)) | (~brave(X0) <=> ~old(X0))) [ennf transformation 7]
44. ! [X0] : ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0))) [nnf transformation 3]
54. ! [X0] : ((wise(X0) & quiet(X0)) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0)))) [nnf transformation 31]
60. ! [X0] : (((~happy(X0) & ~patient(X0)) | (~old(X0) & ~quiet(X0))) & ((old(X0) | quiet(X0)) | (happy(X0) | patient(X0)))) [nnf transformation 9]
61. ! [X0] : (((~happy(X0) & ~patient(X0)) | (~old(X0) & ~quiet(X0))) & (old(X0) | quiet(X0) | happy(X0) | patient(X0))) [flattening 60]
67. ! [X0] : ((strong(X0) | ((happy(X0) | ~brave(X0)) & (brave(X0) | ~happy(X0)))) & (((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ~strong(X0))) [nnf transformation 14]
68. ! [X0] : (((~rich(X0) | kind(X0)) | ~happy(X0)) & (happy(X0) | (rich(X0) & ~kind(X0)))) [nnf transformation 16]
69. ! [X0] : ((~rich(X0) | kind(X0) | ~happy(X0)) & (happy(X0) | (rich(X0) & ~kind(X0)))) [flattening 68]
81. ~rich(X0) | ~strong(X0) [cnf transformation 44]
94. ~brave(X0) | quiet(X0) | old(X0) [cnf transformation 54]
105. ~quiet(X0) | ~happy(X0) [cnf transformation 61]
106. ~old(X0) | ~happy(X0) [cnf transformation 61]
119. ~brave(X0) | happy(X0) | strong(X0) [cnf transformation 67]
122. rich(X0) | happy(X0) [cnf transformation 69]
134. brave(mary) [cnf transformation 23]
208. 18 <=> rich(mary) [avatar definition]
209. rich(mary) <- (18) [avatar component clause 208]
210. ~rich(mary) <- (~18) [avatar component clause 208]
212. 19 <=> brave(mary) [avatar definition]
213. brave(mary) <- (19) [avatar component clause 212]
239. 19 [avatar split clause 134,212]
256. happy(mary) <- (~18) [resolution 122,210]
324. quiet(mary) | old(mary) <- (19) [resolution 94,213]
326. 35 <=> old(mary) [avatar definition]
328. old(mary) <- (35) [avatar component clause 326]
330. 36 <=> quiet(mary) [avatar definition]
332. quiet(mary) <- (36) [avatar component clause 330]
333. 35 | 36 | ~19 [avatar split clause 324,212,330,326]
339. ~happy(mary) <- (36) [resolution 332,105]
340. $false <- (~18, 36) [subsumption resolution 339,256]
341. 18 | ~36 [avatar contradiction clause 340]
343. ~strong(mary) <- (18) [resolution 209,81]
364. happy(mary) | strong(mary) <- (19) [resolution 119,213]
365. strong(mary) <- (19, 36) [subsumption resolution 364,339]
366. $false <- (18, 19, 36) [subsumption resolution 365,343]
367. ~18 | ~19 | ~36 [avatar contradiction clause 366]
368. happy(mary) <- (18, 19) [subsumption resolution 364,343]
377. ~happy(mary) <- (35) [resolution 328,106]
378. $false <- (18, 19, 35) [subsumption resolution 377,368]
379. ~18 | ~19 | ~35 [avatar contradiction clause 378]
381. happy(mary) <- (~18) [resolution 210,122]
383. $false <- (~18, 35) [subsumption resolution 381,377]
384. 18 | ~35 [avatar contradiction clause 383]
385. $false [avatar sat refutation 239,333,341,367,379,384]
% SZS output end Proof for 534702973016449730988122
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either quiet or not creative then someone is not happy or brave and vice versa.
Everyone who is both not old and calm is both funny and not wise and vice versa.
If someone is either quiet or not tall then someone is not patient.
If someone is both quiet and generous then someone is both brave and not curious.
If john is either humble or not strong then someone is creative or tall.
Everyone who is both tall and not old is kind.
Everyone who is generous is both not calm and happy and vice versa.
If lucy is creative then someone is funny or not humble.
If alice is strong or calm then someone is both old and not rich.
If someone is both not happy and creative then paul is not brave or not kind and vice versa.
If lucy is wise then susan is not brave.
Everyone who is both not tall and humble is not quiet.
Everyone who is either happy or quiet is both funny and not kind.
If susan is not happy then lucy is not old or brave.
If paul is both quiet and not quiet then someone is rich and vice versa.
Everyone who is not calm is not generous and vice versa.
Paul is both humble and old.
Fred is not rich or calm.
John is either happy or quiet.
Someone is not wise.
Someone is either not kind or not rich.
Someone is not creative or calm.
Someone is both strong and patient. | Lucy is wise. | neutral | ((?[X]:((quiet(X)<~>~creative(X))))<=>(?[X]:((~happy(X)|brave(X)))))&
(![X]:((~old(X)&calm(X))<=>(funny(X)&~wise(X))))&
((?[X]:((quiet(X)<~>~tall(X))))=>(?[X]:(~patient(X))))&
((?[X]:((quiet(X)&generous(X))))=>(?[X]:((brave(X)&~curious(X)))))&
(((humble(john)<~>~strong(john)))=>(?[X]:((creative(X)|tall(X)))))&
(![X]:((tall(X)&~old(X))=>kind(X)))&
(![X]:(generous(X)<=>(~calm(X)&happy(X))))&
((creative(lucy))=>(?[X]:((funny(X)|~humble(X)))))&
(((strong(alice)|calm(alice)))=>(?[X]:((old(X)&~rich(X)))))&
((?[X]:((~happy(X)&creative(X))))<=>((~brave(paul)|~kind(paul))))&
((wise(lucy))=>(~brave(susan)))&
(![X]:((~tall(X)&humble(X))=>~quiet(X)))&
(![X]:((happy(X)<~>quiet(X))=>(funny(X)&~kind(X))))&
((~happy(susan))=>((~old(lucy)|brave(lucy))))&
(((quiet(paul)&~quiet(paul)))<=>(?[X]:(rich(X))))&
(![X]:(~calm(X)<=>~generous(X)))&
((humble(paul)&old(paul)))&
((~rich(fred)|calm(fred)))&
((happy(john)<~>quiet(john)))&
(?[X]:(~wise(X)))&
(?[X]:((~kind(X)<~>~rich(X))))&
(?[X]:((~creative(X)|calm(X))))&
(?[X]:((strong(X)&patient(X)))) | wise(lucy) | [] | null | 0 |
Everyone who is patient or not tall is rich. If lucy is both rich and not old then someone is not brave. Everyone who is either not brave or not quiet is old and vice versa. Everyone who is both not brave and wise is not funny or happy and vice versa. If someone is calm or patient then paul is happy or not happy. Everyone who is not quiet is both not funny and not happy and vice versa. If someone is both calm and brave then someone is both not curious and tall and vice versa. Everyone who is either not creative or not strong is either generous or not rich. If someone is not strong or strong then someone is either wise or patient and vice versa. Everyone who is funny or wise is both not patient and wise. Everyone who is either generous or wise is either not wise or not happy. If someone is either not kind or not happy then someone is both strong and not patient and vice versa. If paul is not rich or curious then someone is kind and vice versa. Everyone who is either not wise or not happy is not funny and vice versa. If lucy is generous or not strong then someone is not brave or happy. Everyone who is both not tall and brave is either not happy or brave. Someone is either happy or not curious. Someone is not brave. Lucy is not curious. Mary is both generous and humble. Lucy is not funny. Alice is either old or patient. Alice is not strong. Lucy is tall or not humble. | Lucy is not quiet. | entailment | (![X]:((patient(X)|~tall(X))=>rich(X)))&
(((rich(lucy)&~old(lucy)))=>(?[X]:(~brave(X))))&
(![X]:((~brave(X)<~>~quiet(X))<=>old(X)))&
(![X]:((~brave(X)&wise(X))<=>(~funny(X)|happy(X))))&
((?[X]:((calm(X)|patient(X))))=>((happy(paul)|~happy(paul))))&
(![X]:(~quiet(X)<=>(~funny(X)&~happy(X))))&
((?[X]:((calm(X)&brave(X))))<=>(?[X]:((~curious(X)&tall(X)))))&
(![X]:((~creative(X)<~>~strong(X))=>(generous(X)<~>~rich(X))))&
((?[X]:((~strong(X)|strong(X))))<=>(?[X]:((wise(X)<~>patient(X)))))&
(![X]:((funny(X)|wise(X))=>(~patient(X)&wise(X))))&
(![X]:((generous(X)<~>wise(X))=>(~wise(X)<~>~happy(X))))&
((?[X]:((~kind(X)<~>~happy(X))))<=>(?[X]:((strong(X)&~patient(X)))))&
(((~rich(paul)|curious(paul)))<=>(?[X]:(kind(X))))&
(![X]:((~wise(X)<~>~happy(X))<=>~funny(X)))&
(((generous(lucy)|~strong(lucy)))=>(?[X]:((~brave(X)|happy(X)))))&
(![X]:((~tall(X)&brave(X))=>(~happy(X)<~>brave(X))))&
(?[X]:((happy(X)<~>~curious(X))))&
(?[X]:(~brave(X)))&
(~curious(lucy))&
((generous(mary)&humble(mary)))&
(~funny(lucy))&
((old(alice)<~>patient(alice)))&
(~strong(alice))&
((tall(lucy)|~humble(lucy))) | ~quiet(lucy) | [
"p3",
"p5",
"p9",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5962455922969624900115064
% SZS output start Proof for 5962455922969624900115064
4. ! [X0] : ((wise(X0) & ~brave(X0)) <=> (happy(X0) | ~funny(X0))) [input p3]
6. ! [X0] : (~quiet(X0) <=> (~happy(X0) & ~funny(X0))) [input p5]
10. ! [X0] : ((wise(X0) | funny(X0)) => (wise(X0) & ~patient(X0))) [input p9]
14. ! [X0] : ((~wise(X0) <~> ~happy(X0)) <=> ~funny(X0)) [input p13]
21. ~funny(lucy) [input p20]
25. quiet(lucy) [input hypothesis]
35. ! [X0] : ((wise(X0) & ~patient(X0)) | (~wise(X0) & ~funny(X0))) [ennf transformation 10]
43. ! [X0] : (((wise(X0) & ~brave(X0)) | (~happy(X0) & funny(X0))) & ((happy(X0) | ~funny(X0)) | (~wise(X0) | brave(X0)))) [nnf transformation 4]
44. ! [X0] : (((wise(X0) & ~brave(X0)) | (~happy(X0) & funny(X0))) & (happy(X0) | ~funny(X0) | ~wise(X0) | brave(X0))) [flattening 43]
45. ! [X0] : ((~quiet(X0) | (happy(X0) | funny(X0))) & ((~happy(X0) & ~funny(X0)) | quiet(X0))) [nnf transformation 6]
46. ! [X0] : ((~quiet(X0) | happy(X0) | funny(X0)) & ((~happy(X0) & ~funny(X0)) | quiet(X0))) [flattening 45]
69. ! [X0] : ((((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | funny(X0)) & (~funny(X0) | ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0))))) [nnf transformation 14]
89. funny(X0) | wise(X0) [cnf transformation 44]
95. ~quiet(X0) | happy(X0) | funny(X0) [cnf transformation 46]
112. wise(X0) | ~funny(X0) [cnf transformation 35]
129. ~happy(X0) | ~wise(X0) | funny(X0) [cnf transformation 69]
141. ~funny(lucy) [cnf transformation 21]
146. quiet(lucy) [cnf transformation 25]
207. wise(X0) [subsumption resolution 112,89]
252. ~happy(X0) | funny(X0) [subsumption resolution 129,207]
333. happy(lucy) | funny(lucy) [resolution 95,146]
336. happy(lucy) [subsumption resolution 333,141]
340. funny(lucy) [resolution 336,252]
345. $false [subsumption resolution 340,141]
% SZS output end Proof for 5962455922969624900115064
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is either quiet or not happy.
If fred is either wise or creative then alice is strong and vice versa.
If lucy is either not rich or brave then someone is not tall and vice versa.
Everyone who is wise or not patient is either strong or not humble.
If someone is either not creative or creative then someone is both old and not funny.
Everyone who is either not happy or not wise is not quiet or not tall and vice versa.
If someone is either not brave or happy then paul is both rich and not rich.
Everyone who is calm or generous is both rich and not brave and vice versa.
Everyone who is curious or not happy is not old or not humble and vice versa.
If paul is either not patient or not rich then someone is both not kind and not generous and vice versa.
Everyone who is not happy is rich or not generous.
If susan is strong or not old then fred is either not happy or strong and vice versa.
Everyone who is both wise and not quiet is not wise and vice versa.
Everyone who is happy is either rich or curious and vice versa.
Everyone who is happy or quiet is wise.
If someone is either not quiet or rich then someone is both not humble and calm and vice versa.
Lucy is not calm or happy.
Fred is not brave or funny.
Someone is old or generous.
Someone is both funny and curious.
Susan is both not tall and quiet.
Fred is not humble. | Susan is curious. | contradiction | (![X]:(kind(X)=>(quiet(X)<~>~happy(X))))&
(((wise(fred)<~>creative(fred)))<=>(strong(alice)))&
(((~rich(lucy)<~>brave(lucy)))<=>(?[X]:(~tall(X))))&
(![X]:((wise(X)|~patient(X))=>(strong(X)<~>~humble(X))))&
((?[X]:((~creative(X)<~>creative(X))))=>(?[X]:((old(X)&~funny(X)))))&
(![X]:((~happy(X)<~>~wise(X))<=>(~quiet(X)|~tall(X))))&
((?[X]:((~brave(X)<~>happy(X))))=>((rich(paul)&~rich(paul))))&
(![X]:((calm(X)|generous(X))<=>(rich(X)&~brave(X))))&
(![X]:((curious(X)|~happy(X))<=>(~old(X)|~humble(X))))&
(((~patient(paul)<~>~rich(paul)))<=>(?[X]:((~kind(X)&~generous(X)))))&
(![X]:(~happy(X)=>(rich(X)|~generous(X))))&
(((strong(susan)|~old(susan)))<=>((~happy(fred)<~>strong(fred))))&
(![X]:((wise(X)&~quiet(X))<=>~wise(X)))&
(![X]:(happy(X)<=>(rich(X)<~>curious(X))))&
(![X]:((happy(X)|quiet(X))=>wise(X)))&
((?[X]:((~quiet(X)<~>rich(X))))<=>(?[X]:((~humble(X)&calm(X)))))&
((~calm(lucy)|happy(lucy)))&
((~brave(fred)|funny(fred)))&
(?[X]:((old(X)|generous(X))))&
(?[X]:((funny(X)&curious(X))))&
((~tall(susan)&quiet(susan)))&
(~humble(fred)) | curious(susan) | [
"p5",
"p6",
"p7",
"p8",
"p12",
"p13",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6774544419215749024959922
% SZS output start Proof for 6774544419215749024959922
6. ! [X0] : ((~happy(X0) <~> ~wise(X0)) <=> (~tall(X0) | ~quiet(X0))) [input p5]
7. ? [X0] : (~brave(X0) <~> happy(X0)) => (~rich(paul) & rich(paul)) [input p6]
8. ! [X0] : ((generous(X0) | calm(X0)) <=> (~brave(X0) & rich(X0))) [input p7]
9. ! [X0] : ((~happy(X0) | curious(X0)) <=> (~humble(X0) | ~old(X0))) [input p8]
13. ! [X0] : ((~quiet(X0) & wise(X0)) <=> ~wise(X0)) [input p12]
14. ! [X0] : (happy(X0) <=> (rich(X0) <~> curious(X0))) [input p13]
16. ? [X0] : (~quiet(X0) <~> rich(X0)) <=> ? [X0] : (calm(X0) & ~humble(X0)) [input p15]
21. quiet(susan) & ~tall(susan) [input p20]
23. curious(susan) [input hypothesis]
25. ? [X0] : (~quiet(X0) <~> rich(X0)) <=> ? [X1] : (calm(X1) & ~humble(X1)) [rectify 16]
29. (~rich(paul) & rich(paul)) | ! [X0] : (~brave(X0) <=> happy(X0)) [ennf transformation 7]
44. ! [X0] : ((((wise(X0) | happy(X0)) & (~wise(X0) | ~happy(X0))) | (tall(X0) & quiet(X0))) & ((~tall(X0) | ~quiet(X0)) | ((~happy(X0) | wise(X0)) & (~wise(X0) | happy(X0))))) [nnf transformation 6]
45. ! [X0] : ((((wise(X0) | happy(X0)) & (~wise(X0) | ~happy(X0))) | (tall(X0) & quiet(X0))) & (~tall(X0) | ~quiet(X0) | ((~happy(X0) | wise(X0)) & (~wise(X0) | happy(X0))))) [flattening 44]
46. (~rich(paul) & rich(paul)) | ! [X0] : ((~brave(X0) | ~happy(X0)) & (happy(X0) | brave(X0))) [nnf transformation 29]
47. ! [X0] : (((generous(X0) | calm(X0)) | (brave(X0) | ~rich(X0))) & ((~brave(X0) & rich(X0)) | (~generous(X0) & ~calm(X0)))) [nnf transformation 8]
48. ! [X0] : ((generous(X0) | calm(X0) | brave(X0) | ~rich(X0)) & ((~brave(X0) & rich(X0)) | (~generous(X0) & ~calm(X0)))) [flattening 47]
49. ! [X0] : (((~happy(X0) | curious(X0)) | (humble(X0) & old(X0))) & ((~humble(X0) | ~old(X0)) | (happy(X0) & ~curious(X0)))) [nnf transformation 9]
50. ! [X0] : ((~happy(X0) | curious(X0) | (humble(X0) & old(X0))) & (~humble(X0) | ~old(X0) | (happy(X0) & ~curious(X0)))) [flattening 49]
57. ! [X0] : (((~quiet(X0) & wise(X0)) | wise(X0)) & (~wise(X0) | (quiet(X0) | ~wise(X0)))) [nnf transformation 13]
58. ! [X0] : (((~quiet(X0) & wise(X0)) | wise(X0)) & (~wise(X0) | quiet(X0) | ~wise(X0))) [flattening 57]
59. ! [X0] : ((happy(X0) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0)))) & (((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | ~happy(X0))) [nnf transformation 14]
60. (? [X0] : ((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | ! [X1] : (~calm(X1) | humble(X1))) & (? [X1] : (calm(X1) & ~humble(X1)) | ! [X0] : ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0)))) [nnf transformation 25]
61. (? [X0] : ((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | ! [X1] : (~calm(X1) | humble(X1))) & (? [X2] : (calm(X2) & ~humble(X2)) | ! [X3] : ((~quiet(X3) | ~rich(X3)) & (rich(X3) | quiet(X3)))) [rectify 60]
62. ? [X0] : ((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) => ((~rich(sK3) | quiet(sK3)) & (rich(sK3) | ~quiet(sK3))) [choice axiom]
63. ? [X2] : (calm(X2) & ~humble(X2)) => (calm(sK4) & ~humble(sK4)) [choice axiom]
64. (((~rich(sK3) | quiet(sK3)) & (rich(sK3) | ~quiet(sK3))) | ! [X1] : (~calm(X1) | humble(X1))) & ((calm(sK4) & ~humble(sK4)) | ! [X3] : ((~quiet(X3) | ~rich(X3)) & (rich(X3) | quiet(X3)))) [skolemisation 61,63,62]
90. ~wise(X0) | ~happy(X0) | tall(X0) [cnf transformation 45]
93. rich(paul) | happy(X0) | brave(X0) [cnf transformation 46]
95. ~rich(paul) | happy(X0) | brave(X0) [cnf transformation 46]
97. ~calm(X0) | rich(X0) [cnf transformation 48]
99. ~calm(X0) | ~brave(X0) [cnf transformation 48]
105. ~happy(X0) | curious(X0) | humble(X0) [cnf transformation 50]
119. ~wise(X0) | quiet(X0) | ~wise(X0) [cnf transformation 58]
120. wise(X0) | wise(X0) [cnf transformation 58]
123. ~curious(X0) | ~rich(X0) | ~happy(X0) [cnf transformation 59]
125. ~curious(X0) | rich(X0) | happy(X0) [cnf transformation 59]
129. ~humble(sK4) | ~quiet(X3) | ~rich(X3) [cnf transformation 64]
131. calm(sK4) | ~quiet(X3) | ~rich(X3) [cnf transformation 64]
139. ~tall(susan) [cnf transformation 21]
142. curious(susan) [cnf transformation 23]
143. ~wise(X0) | quiet(X0) [duplicate literal removal 119]
144. wise(X0) [duplicate literal removal 120]
206. 13 <=> rich(paul) [avatar definition]
211. 14 <=> ! [X0] : (happy(X0) | brave(X0)) [avatar definition]
212. brave(X0) | happy(X0) <- (14) [avatar component clause 211]
213. 14 | ~13 [avatar split clause 95,206,211]
215. 14 | 13 [avatar split clause 93,206,211]
259. quiet(X0) [subsumption resolution 143,144]
269. calm(sK4) | ~rich(X3) [subsumption resolution 131,259]
271. 25 <=> ! [X3] : ~rich(X3) [avatar definition]
272. ~rich(X3) <- (25) [avatar component clause 271]
274. 26 <=> calm(sK4) [avatar definition]
276. calm(sK4) <- (26) [avatar component clause 274]
277. 25 | 26 [avatar split clause 269,274,271]
278. ~humble(sK4) | ~rich(X3) [subsumption resolution 129,259]
280. 27 <=> humble(sK4) [avatar definition]
283. 25 | ~27 [avatar split clause 278,280,271]
334. ~brave(sK4) <- (26) [resolution 276,99]
335. rich(sK4) <- (26) [resolution 276,97]
348. happy(sK4) <- (14, 26) [resolution 334,212]
362. ~happy(X0) | tall(X0) [resolution 90,144]
419. 43 <=> curious(sK4) [avatar definition]
421. curious(sK4) <- (43) [avatar component clause 419]
424. curious(sK4) | humble(sK4) <- (14, 26) [resolution 105,348]
448. 47 <=> happy(susan) [avatar definition]
449. happy(susan) <- (47) [avatar component clause 448]
452. 48 <=> rich(susan) [avatar definition]
453. rich(susan) <- (48) [avatar component clause 452]
468. rich(susan) | happy(susan) [resolution 125,142]
481. tall(susan) <- (47) [resolution 449,362]
483. $false <- (47) [subsumption resolution 481,139]
484. ~47 [avatar contradiction clause 483]
485. 47 | 48 [avatar split clause 468,452,448]
575. ~rich(sK4) | ~happy(sK4) <- (43) [resolution 421,123]
577. ~happy(sK4) <- (26, 43) [subsumption resolution 575,335]
578. $false <- (14, 26, 43) [subsumption resolution 577,348]
579. ~14 | ~26 | ~43 [avatar contradiction clause 578]
580. 27 | 43 | ~14 | ~26 [avatar split clause 424,274,211,419,280]
581. $false <- (25, 48) [resolution 272,453]
588. ~25 | ~48 [avatar contradiction clause 581]
589. $false [avatar sat refutation 213,215,277,283,484,485,579,580,588]
% SZS output end Proof for 6774544419215749024959922
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not creative is either not quiet or generous and vice versa.
If someone is not quiet then fred is either not funny or tall and vice versa.
Everyone who is either creative or not calm is not happy.
Everyone who is strong or quiet is both kind and calm.
Everyone who is either not rich or tall is brave.
If alice is not rich or old then someone is not creative or quiet and vice versa.
If someone is not brave then someone is not quiet or tall.
If alice is not patient or humble then someone is both kind and not generous.
Everyone who is brave or curious is not strong or not happy.
Everyone who is both not rich and curious is kind and vice versa.
If someone is funny or tall then someone is either kind or not quiet.
If someone is both not creative and not rich then alice is happy.
Everyone who is both not happy and not funny is both not calm and not wise.
If someone is either kind or not generous then fred is brave or calm.
Everyone who is tall is not strong.
If alice is either funny or not curious then mary is not generous and vice versa.
Someone is happy or rich.
Someone is both humble and strong.
Someone is not strong or quiet.
Someone is either tall or old.
Someone is strong or creative.
Paul is both patient and not quiet.
Someone is both not kind and generous.
Someone is not humble or not curious. | Fred is strong. | contradiction | (![X]:((generous(X)<~>~creative(X))<=>(~quiet(X)<~>generous(X))))&
((?[X]:(~quiet(X)))<=>((~funny(fred)<~>tall(fred))))&
(![X]:((creative(X)<~>~calm(X))=>~happy(X)))&
(![X]:((strong(X)|quiet(X))=>(kind(X)&calm(X))))&
(![X]:((~rich(X)<~>tall(X))=>brave(X)))&
(((~rich(alice)|old(alice)))<=>(?[X]:((~creative(X)|quiet(X)))))&
((?[X]:(~brave(X)))=>(?[X]:((~quiet(X)|tall(X)))))&
(((~patient(alice)|humble(alice)))=>(?[X]:((kind(X)&~generous(X)))))&
(![X]:((brave(X)|curious(X))=>(~strong(X)|~happy(X))))&
(![X]:((~rich(X)&curious(X))<=>kind(X)))&
((?[X]:((funny(X)|tall(X))))=>(?[X]:((kind(X)<~>~quiet(X)))))&
((?[X]:((~creative(X)&~rich(X))))=>(happy(alice)))&
(![X]:((~happy(X)&~funny(X))=>(~calm(X)&~wise(X))))&
((?[X]:((kind(X)<~>~generous(X))))=>((brave(fred)|calm(fred))))&
(![X]:(tall(X)=>~strong(X)))&
(((funny(alice)<~>~curious(alice)))<=>(~generous(mary)))&
(?[X]:((happy(X)|rich(X))))&
(?[X]:((humble(X)&strong(X))))&
(?[X]:((~strong(X)|quiet(X))))&
(?[X]:((tall(X)<~>old(X))))&
(?[X]:((strong(X)|creative(X))))&
((patient(paul)&~quiet(paul)))&
(?[X]:((~kind(X)&generous(X))))&
(?[X]:((~humble(X)|~curious(X)))) | strong(fred) | [
"p1",
"p3",
"p8",
"p9",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1851988570519042010443171
% SZS output start Proof for 1851988570519042010443171
2. ? [X0] : ~quiet(X0) <=> (~funny(fred) <~> tall(fred)) [input p1]
4. ! [X0] : ((quiet(X0) | strong(X0)) => (calm(X0) & kind(X0))) [input p3]
9. ! [X0] : ((curious(X0) | brave(X0)) => (~happy(X0) | ~strong(X0))) [input p8]
10. ! [X0] : ((curious(X0) & ~rich(X0)) <=> kind(X0)) [input p9]
13. ! [X0] : ((~funny(X0) & ~happy(X0)) => (~wise(X0) & ~calm(X0))) [input p12]
15. ! [X0] : (tall(X0) => ~strong(X0)) [input p14]
22. ~quiet(paul) & patient(paul) [input p21]
25. strong(fred) [input hypothesis]
28. ! [X0] : ((~funny(X0) & ~happy(X0)) => ~calm(X0)) [pure predicate removal 13]
30. ~quiet(paul) [pure predicate removal 22]
32. ! [X0] : ((calm(X0) & kind(X0)) | (~quiet(X0) & ~strong(X0))) [ennf transformation 4]
36. ! [X0] : ((~happy(X0) | ~strong(X0)) | (~curious(X0) & ~brave(X0))) [ennf transformation 9]
37. ! [X0] : (~happy(X0) | ~strong(X0) | (~curious(X0) & ~brave(X0))) [flattening 36]
40. ! [X0] : (~calm(X0) | (funny(X0) | happy(X0))) [ennf transformation 28]
41. ! [X0] : (~calm(X0) | funny(X0) | happy(X0)) [flattening 40]
44. ! [X0] : (~strong(X0) | ~tall(X0)) [ennf transformation 15]
46. (? [X0] : ~quiet(X0) | ((~funny(fred) | ~tall(fred)) & (tall(fred) | funny(fred)))) & (((~tall(fred) | funny(fred)) & (tall(fred) | ~funny(fred))) | ! [X0] : quiet(X0)) [nnf transformation 2]
47. (? [X0] : ~quiet(X0) | ((~funny(fred) | ~tall(fred)) & (tall(fred) | funny(fred)))) & (((~tall(fred) | funny(fred)) & (tall(fred) | ~funny(fred))) | ! [X1] : quiet(X1)) [rectify 46]
48. ? [X0] : ~quiet(X0) => ~quiet(sK0) [choice axiom]
49. (~quiet(sK0) | ((~funny(fred) | ~tall(fred)) & (tall(fred) | funny(fred)))) & (((~tall(fred) | funny(fred)) & (tall(fred) | ~funny(fred))) | ! [X1] : quiet(X1)) [skolemisation 47,48]
62. ! [X0] : (((curious(X0) & ~rich(X0)) | ~kind(X0)) & (kind(X0) | (~curious(X0) | rich(X0)))) [nnf transformation 10]
63. ! [X0] : (((curious(X0) & ~rich(X0)) | ~kind(X0)) & (kind(X0) | ~curious(X0) | rich(X0))) [flattening 62]
93. tall(fred) | ~funny(fred) | quiet(X1) [cnf transformation 49]
99. ~strong(X0) | kind(X0) [cnf transformation 32]
101. ~strong(X0) | calm(X0) [cnf transformation 32]
113. ~curious(X0) | ~strong(X0) | ~happy(X0) [cnf transformation 37]
116. ~kind(X0) | curious(X0) [cnf transformation 63]
122. ~calm(X0) | funny(X0) | happy(X0) [cnf transformation 41]
125. ~strong(X0) | ~tall(X0) [cnf transformation 44]
137. ~quiet(paul) [cnf transformation 30]
141. strong(fred) [cnf transformation 25]
149. 1 <=> tall(fred) [avatar definition]
153. 2 <=> funny(fred) [avatar definition]
163. 4 <=> ! [X1] : quiet(X1) [avatar definition]
164. quiet(X1) <- (4) [avatar component clause 163]
166. 4 | ~2 | 1 [avatar split clause 93,149,153,163]
241. 23 <=> calm(fred) [avatar definition]
243. calm(fred) <- (23) [avatar component clause 241]
312. kind(fred) [resolution 99,141]
315. calm(fred) [resolution 101,141]
317. 23 [avatar split clause 315,241]
319. curious(fred) [resolution 116,312]
322. ~tall(fred) [resolution 125,141]
357. ~strong(fred) | ~happy(fred) [resolution 113,319]
367. funny(fred) | happy(fred) <- (23) [resolution 122,243]
375. ~happy(fred) [subsumption resolution 357,141]
378. funny(fred) <- (23) [subsumption resolution 367,375]
379. 2 | ~23 [avatar split clause 378,241,153]
383. $false <- (4) [resolution 164,137]
388. ~4 [avatar contradiction clause 383]
390. ~1 [avatar split clause 322,149]
391. $false [avatar sat refutation 166,317,379,388,390]
% SZS output end Proof for 1851988570519042010443171
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or not wise is both curious and quiet and vice versa.
Everyone who is both not brave and not generous is not rich or wise.
Everyone who is both patient and brave is not creative or not quiet.
If someone is either not wise or humble then alice is not creative and vice versa.
If someone is curious then mary is both creative and not tall.
Everyone who is quiet is both happy and curious.
If someone is both not funny and curious then someone is both patient and creative and vice versa.
If susan is either not happy or tall then mary is brave.
Everyone who is quiet is happy or humble.
If someone is not happy or not curious then mary is not patient or strong.
If someone is both not humble and not brave then john is not wise and vice versa.
Everyone who is both quiet and tall is not humble or not brave and vice versa.
Everyone who is kind or not creative is not curious or not rich and vice versa.
Everyone who is not strong or not rich is not brave or tall and vice versa.
If someone is wise or kind then mary is not kind or kind and vice versa.
Everyone who is either not brave or generous is both not old and rich and vice versa.
Lucy is not wise.
Fred is either generous or kind.
Alice is not creative.
Fred is kind.
Someone is strong or curious.
Mary is either generous or curious.
Susan is not kind. | Susan is curious. | entailment | (![X]:((~creative(X)|~wise(X))<=>(curious(X)&quiet(X))))&
(![X]:((~brave(X)&~generous(X))=>(~rich(X)|wise(X))))&
(![X]:((patient(X)&brave(X))=>(~creative(X)|~quiet(X))))&
((?[X]:((~wise(X)<~>humble(X))))<=>(~creative(alice)))&
((?[X]:(curious(X)))=>((creative(mary)&~tall(mary))))&
(![X]:(quiet(X)=>(happy(X)&curious(X))))&
((?[X]:((~funny(X)&curious(X))))<=>(?[X]:((patient(X)&creative(X)))))&
(((~happy(susan)<~>tall(susan)))=>(brave(mary)))&
(![X]:(quiet(X)=>(happy(X)|humble(X))))&
((?[X]:((~happy(X)|~curious(X))))=>((~patient(mary)|strong(mary))))&
((?[X]:((~humble(X)&~brave(X))))<=>(~wise(john)))&
(![X]:((quiet(X)&tall(X))<=>(~humble(X)|~brave(X))))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)|~rich(X))))&
(![X]:((~strong(X)|~rich(X))<=>(~brave(X)|tall(X))))&
((?[X]:((wise(X)|kind(X))))<=>((~kind(mary)|kind(mary))))&
(![X]:((~brave(X)<~>generous(X))<=>(~old(X)&rich(X))))&
(~wise(lucy))&
((generous(fred)<~>kind(fred)))&
(~creative(alice))&
(kind(fred))&
(?[X]:((strong(X)|curious(X))))&
((generous(mary)<~>curious(mary)))&
(~kind(susan)) | curious(susan) | [
"p0",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1498784923111848609270474
% SZS output start Proof for 1498784923111848609270474
1. ! [X0] : ((~wise(X0) | ~creative(X0)) <=> (quiet(X0) & curious(X0))) [input p0]
13. ! [X0] : ((~creative(X0) | kind(X0)) <=> (~rich(X0) | ~curious(X0))) [input p12]
23. ~kind(susan) [input p22]
24. ~curious(susan) [input hypothesis]
37. ! [X0] : (((~wise(X0) | ~creative(X0)) | (~quiet(X0) | ~curious(X0))) & ((quiet(X0) & curious(X0)) | (wise(X0) & creative(X0)))) [nnf transformation 1]
38. ! [X0] : ((~wise(X0) | ~creative(X0) | ~quiet(X0) | ~curious(X0)) & ((quiet(X0) & curious(X0)) | (wise(X0) & creative(X0)))) [flattening 37]
55. ! [X0] : (((~creative(X0) | kind(X0)) | (rich(X0) & curious(X0))) & ((~rich(X0) | ~curious(X0)) | (creative(X0) & ~kind(X0)))) [nnf transformation 13]
56. ! [X0] : ((~creative(X0) | kind(X0) | (rich(X0) & curious(X0))) & (~rich(X0) | ~curious(X0) | (creative(X0) & ~kind(X0)))) [flattening 55]
70. curious(X0) | creative(X0) [cnf transformation 38]
104. ~creative(X0) | kind(X0) | curious(X0) [cnf transformation 56]
128. ~kind(susan) [cnf transformation 23]
129. ~curious(susan) [cnf transformation 24]
239. kind(X0) | curious(X0) [subsumption resolution 104,70]
314. curious(susan) [resolution 239,128]
315. $false [subsumption resolution 314,129]
% SZS output end Proof for 1498784923111848609270474
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not brave is not quiet or not old and vice versa.
If lucy is either not strong or quiet then someone is either brave or not generous.
Everyone who is not creative or not strong is quiet and vice versa.
Everyone who is either not brave or strong is not calm.
If someone is either not kind or not patient then someone is either not strong or not patient.
Everyone who is not old or brave is either not tall or not strong and vice versa.
If fred is rich then someone is not quiet or brave.
Everyone who is either kind or not brave is both not quiet and wise and vice versa.
If fred is both funny and tall then someone is both not funny and not kind.
Everyone who is creative is both not strong and wise and vice versa.
Everyone who is either not tall or not happy is not patient or not rich and vice versa.
Everyone who is humble is either not calm or not creative.
Everyone who is not curious is not calm.
If fred is not calm then someone is either calm or not brave and vice versa.
Everyone who is either not rich or kind is both not funny and quiet.
Someone is not old or strong.
Someone is not strong.
Lucy is not creative.
Alice is either not strong or not curious.
Lucy is either not happy or funny.
Someone is rich.
Alice is both calm and humble. | Lucy is not quiet. | contradiction | (![X]:((~wise(X)&~brave(X))<=>(~quiet(X)|~old(X))))&
(((~strong(lucy)<~>quiet(lucy)))=>(?[X]:((brave(X)<~>~generous(X)))))&
(![X]:((~creative(X)|~strong(X))<=>quiet(X)))&
(![X]:((~brave(X)<~>strong(X))=>~calm(X)))&
((?[X]:((~kind(X)<~>~patient(X))))=>(?[X]:((~strong(X)<~>~patient(X)))))&
(![X]:((~old(X)|brave(X))<=>(~tall(X)<~>~strong(X))))&
((rich(fred))=>(?[X]:((~quiet(X)|brave(X)))))&
(![X]:((kind(X)<~>~brave(X))<=>(~quiet(X)&wise(X))))&
(((funny(fred)&tall(fred)))=>(?[X]:((~funny(X)&~kind(X)))))&
(![X]:(creative(X)<=>(~strong(X)&wise(X))))&
(![X]:((~tall(X)<~>~happy(X))<=>(~patient(X)|~rich(X))))&
(![X]:(humble(X)=>(~calm(X)<~>~creative(X))))&
(![X]:(~curious(X)=>~calm(X)))&
((~calm(fred))<=>(?[X]:((calm(X)<~>~brave(X)))))&
(![X]:((~rich(X)<~>kind(X))=>(~funny(X)&quiet(X))))&
(?[X]:((~old(X)|strong(X))))&
(?[X]:(~strong(X)))&
(~creative(lucy))&
((~strong(alice)<~>~curious(alice)))&
((~happy(lucy)<~>funny(lucy)))&
(?[X]:(rich(X)))&
((calm(alice)&humble(alice))) | ~quiet(lucy) | [
"p2",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2534772912354180001125061
% SZS output start Proof for 2534772912354180001125061
3. ! [X0] : ((~strong(X0) | ~creative(X0)) <=> quiet(X0)) [input p2]
18. ~creative(lucy) [input p17]
23. ~quiet(lucy) [input hypothesis]
39. ! [X0] : (((~strong(X0) | ~creative(X0)) | ~quiet(X0)) & (quiet(X0) | (strong(X0) & creative(X0)))) [nnf transformation 3]
40. ! [X0] : ((~strong(X0) | ~creative(X0) | ~quiet(X0)) & (quiet(X0) | (strong(X0) & creative(X0)))) [flattening 39]
81. creative(X0) | quiet(X0) [cnf transformation 40]
127. ~creative(lucy) [cnf transformation 18]
135. ~quiet(lucy) [cnf transformation 23]
137. 1 <=> quiet(lucy) [avatar definition]
139. ~quiet(lucy) <- (~1) [avatar component clause 137]
257. ~1 [avatar split clause 135,137]
258. quiet(lucy) [resolution 81,127]
259. $false <- (~1) [subsumption resolution 258,139]
260. 1 [avatar contradiction clause 259]
261. $false [avatar sat refutation 257,260]
% SZS output end Proof for 2534772912354180001125061
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or generous then someone is not curious and vice versa.
If fred is happy then someone is either not tall or creative.
If alice is both not rich and kind then someone is either not strong or wise.
Everyone who is not rich is either funny or not wise and vice versa.
Everyone who is either not tall or happy is both rich and not generous and vice versa.
If someone is not strong or curious then mary is either not quiet or not patient and vice versa.
If mary is either not patient or old then mary is not humble or not wise.
Everyone who is rich is brave and vice versa.
If alice is not generous or not old then john is wise.
If fred is not tall then lucy is either not brave or humble.
If susan is either happy or not tall then someone is both not wise and not creative and vice versa.
If fred is both calm and not strong then someone is either strong or not patient.
If fred is funny or not strong then alice is both not old and not funny.
Everyone who is either not funny or creative is not creative and vice versa.
If someone is generous or old then paul is either not calm or calm and vice versa.
Everyone who is both brave and not tall is either not curious or funny and vice versa.
Someone is strong or not happy.
Someone is either quiet or not kind.
Someone is tall or not strong.
Someone is not happy or curious.
Alice is not wise or rich.
Lucy is not rich or old.
John is either humble or not kind.
Susan is generous or patient. | Alice is funny. | contradiction | ((?[X]:((wise(X)<~>generous(X))))<=>(?[X]:(~curious(X))))&
((happy(fred))=>(?[X]:((~tall(X)<~>creative(X)))))&
(((~rich(alice)&kind(alice)))=>(?[X]:((~strong(X)<~>wise(X)))))&
(![X]:(~rich(X)<=>(funny(X)<~>~wise(X))))&
(![X]:((~tall(X)<~>happy(X))<=>(rich(X)&~generous(X))))&
((?[X]:((~strong(X)|curious(X))))<=>((~quiet(mary)<~>~patient(mary))))&
(((~patient(mary)<~>old(mary)))=>((~humble(mary)|~wise(mary))))&
(![X]:(rich(X)<=>brave(X)))&
(((~generous(alice)|~old(alice)))=>(wise(john)))&
((~tall(fred))=>((~brave(lucy)<~>humble(lucy))))&
(((happy(susan)<~>~tall(susan)))<=>(?[X]:((~wise(X)&~creative(X)))))&
(((calm(fred)&~strong(fred)))=>(?[X]:((strong(X)<~>~patient(X)))))&
(((funny(fred)|~strong(fred)))=>((~old(alice)&~funny(alice))))&
(![X]:((~funny(X)<~>creative(X))<=>~creative(X)))&
((?[X]:((generous(X)|old(X))))<=>((~calm(paul)<~>calm(paul))))&
(![X]:((brave(X)&~tall(X))<=>(~curious(X)<~>funny(X))))&
(?[X]:((strong(X)|~happy(X))))&
(?[X]:((quiet(X)<~>~kind(X))))&
(?[X]:((tall(X)|~strong(X))))&
(?[X]:((~happy(X)|curious(X))))&
((~wise(alice)|rich(alice)))&
((~rich(lucy)|old(lucy)))&
((humble(john)<~>~kind(john)))&
((generous(susan)|patient(susan))) | funny(alice) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4271362340044291781450118
% SZS output start Proof for 4271362340044291781450118
14. ! [X0] : ((~funny(X0) <~> creative(X0)) <=> ~creative(X0)) [input p13]
25. funny(alice) [input hypothesis]
65. ! [X0] : ((((~creative(X0) | funny(X0)) & (creative(X0) | ~funny(X0))) | creative(X0)) & (~creative(X0) | ((~funny(X0) | ~creative(X0)) & (creative(X0) | funny(X0))))) [nnf transformation 14]
127. ~creative(X0) | ~funny(X0) | ~creative(X0) [cnf transformation 65]
128. creative(X0) | ~funny(X0) | creative(X0) [cnf transformation 65]
152. funny(alice) [cnf transformation 25]
155. ~creative(X0) | ~funny(X0) [duplicate literal removal 127]
156. creative(X0) | ~funny(X0) [duplicate literal removal 128]
339. ~funny(X0) [subsumption resolution 155,156]
427. $false [subsumption resolution 152,339]
% SZS output end Proof for 4271362340044291781450118
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is tall. Everyone who is quiet or curious is both not kind and not humble. Everyone who is not tall is both not creative and not brave and vice versa. Everyone who is both happy and patient is both old and brave. Everyone who is both not patient and brave is not rich or not brave and vice versa. Everyone who is not brave or not wise is both not happy and strong. Everyone who is creative is both not generous and not curious and vice versa. Everyone who is not rich is brave and vice versa. Everyone who is strong or not creative is not calm or not wise. If someone is not curious or humble then someone is both calm and not creative and vice versa. If someone is wise then john is either patient or not patient. If susan is not strong then someone is both funny and patient and vice versa. If mary is not funny then john is humble or quiet. If someone is humble or patient then someone is not strong or funny and vice versa. Everyone who is kind is not quiet and vice versa. Everyone who is patient is funny or not wise. Someone is either not humble or kind. Susan is humble. Someone is either happy or wise. Someone is either wise or funny. Someone is either creative or not old. Someone is either not funny or not strong. Someone is old or patient. Someone is old or not happy. | Mary is patient. | contradiction | (![X]:(~calm(X)=>tall(X)))&
(![X]:((quiet(X)|curious(X))=>(~kind(X)&~humble(X))))&
(![X]:(~tall(X)<=>(~creative(X)&~brave(X))))&
(![X]:((happy(X)&patient(X))=>(old(X)&brave(X))))&
(![X]:((~patient(X)&brave(X))<=>(~rich(X)|~brave(X))))&
(![X]:((~brave(X)|~wise(X))=>(~happy(X)&strong(X))))&
(![X]:(creative(X)<=>(~generous(X)&~curious(X))))&
(![X]:(~rich(X)<=>brave(X)))&
(![X]:((strong(X)|~creative(X))=>(~calm(X)|~wise(X))))&
((?[X]:((~curious(X)|humble(X))))<=>(?[X]:((calm(X)&~creative(X)))))&
((?[X]:(wise(X)))=>((patient(john)<~>~patient(john))))&
((~strong(susan))<=>(?[X]:((funny(X)&patient(X)))))&
((~funny(mary))=>((humble(john)|quiet(john))))&
((?[X]:((humble(X)|patient(X))))<=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:(kind(X)<=>~quiet(X)))&
(![X]:(patient(X)=>(funny(X)|~wise(X))))&
(?[X]:((~humble(X)<~>kind(X))))&
(humble(susan))&
(?[X]:((happy(X)<~>wise(X))))&
(?[X]:((wise(X)<~>funny(X))))&
(?[X]:((creative(X)<~>~old(X))))&
(?[X]:((~funny(X)<~>~strong(X))))&
(?[X]:((old(X)|patient(X))))&
(?[X]:((old(X)|~happy(X)))) | patient(mary) | [
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7402230122765830457135865
% SZS output start Proof for 7402230122765830457135865
5. ! [X0] : ((brave(X0) & ~patient(X0)) <=> (~brave(X0) | ~rich(X0))) [input p4]
8. ! [X0] : (~rich(X0) <=> brave(X0)) [input p7]
25. patient(mary) [input hypothesis]
43. ! [X0] : (((brave(X0) & ~patient(X0)) | (brave(X0) & rich(X0))) & ((~brave(X0) | ~rich(X0)) | (~brave(X0) | patient(X0)))) [nnf transformation 5]
44. ! [X0] : (((brave(X0) & ~patient(X0)) | (brave(X0) & rich(X0))) & (~brave(X0) | ~rich(X0) | ~brave(X0) | patient(X0))) [flattening 43]
47. ! [X0] : ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))) [nnf transformation 8]
92. ~patient(X0) | rich(X0) [cnf transformation 44]
95. brave(X0) | brave(X0) [cnf transformation 44]
104. ~rich(X0) | ~brave(X0) [cnf transformation 47]
138. patient(mary) [cnf transformation 25]
140. brave(X0) [duplicate literal removal 95]
142. ~rich(X0) [subsumption resolution 104,140]
298. rich(mary) [resolution 92,138]
299. $false [subsumption resolution 298,142]
% SZS output end Proof for 7402230122765830457135865
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both creative and generous then someone is not kind or not creative.
Everyone who is not old or not strong is both kind and old and vice versa.
Everyone who is quiet or not curious is both brave and not wise.
Everyone who is both happy and kind is calm and vice versa.
Everyone who is not generous or calm is either not happy or not old and vice versa.
Everyone who is both happy and not kind is both humble and not calm.
Everyone who is quiet is not humble or humble.
If someone is not generous or not patient then someone is happy or curious and vice versa.
If alice is both not kind and not funny then fred is funny or strong and vice versa.
If someone is either kind or not kind then someone is both not patient and generous.
Everyone who is not funny is calm or not calm and vice versa.
Everyone who is either not old or brave is either not happy or not humble.
If fred is both not wise and not patient then someone is quiet.
If john is either creative or not strong then susan is happy or not curious.
Everyone who is either kind or calm is either patient or kind and vice versa.
Everyone who is tall is not funny.
Susan is either not brave or rich.
Someone is both wise and not creative.
Alice is both happy and not calm.
Lucy is either not quiet or not generous.
Alice is creative.
Someone is not curious. | Susan is calm. | contradiction | ((?[X]:((creative(X)&generous(X))))=>(?[X]:((~kind(X)|~creative(X)))))&
(![X]:((~old(X)|~strong(X))<=>(kind(X)&old(X))))&
(![X]:((quiet(X)|~curious(X))=>(brave(X)&~wise(X))))&
(![X]:((happy(X)&kind(X))<=>calm(X)))&
(![X]:((~generous(X)|calm(X))<=>(~happy(X)<~>~old(X))))&
(![X]:((happy(X)&~kind(X))=>(humble(X)&~calm(X))))&
(![X]:(quiet(X)=>(~humble(X)|humble(X))))&
((?[X]:((~generous(X)|~patient(X))))<=>(?[X]:((happy(X)|curious(X)))))&
(((~kind(alice)&~funny(alice)))<=>((funny(fred)|strong(fred))))&
((?[X]:((kind(X)<~>~kind(X))))=>(?[X]:((~patient(X)&generous(X)))))&
(![X]:(~funny(X)<=>(calm(X)|~calm(X))))&
(![X]:((~old(X)<~>brave(X))=>(~happy(X)<~>~humble(X))))&
(((~wise(fred)&~patient(fred)))=>(?[X]:(quiet(X))))&
(((creative(john)<~>~strong(john)))=>((happy(susan)|~curious(susan))))&
(![X]:((kind(X)<~>calm(X))<=>(patient(X)<~>kind(X))))&
(![X]:(tall(X)=>~funny(X)))&
((~brave(susan)<~>rich(susan)))&
(?[X]:((wise(X)&~creative(X))))&
((happy(alice)&~calm(alice)))&
((~quiet(lucy)<~>~generous(lucy)))&
(creative(alice))&
(?[X]:(~curious(X))) | calm(susan) | [
"p1",
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 5563353769417747903288968
% SZS output start Proof for 5563353769417747903288968
2. ! [X0] : ((~strong(X0) | ~old(X0)) <=> (old(X0) & kind(X0))) [input p1]
4. ! [X0] : ((kind(X0) & happy(X0)) <=> calm(X0)) [input p3]
5. ! [X0] : ((calm(X0) | ~generous(X0)) <=> (~happy(X0) <~> ~old(X0))) [input p4]
23. calm(susan) [input hypothesis]
43. ! [X0] : (((~strong(X0) | ~old(X0)) | (~old(X0) | ~kind(X0))) & ((old(X0) & kind(X0)) | (strong(X0) & old(X0)))) [nnf transformation 2]
44. ! [X0] : ((~strong(X0) | ~old(X0) | ~old(X0) | ~kind(X0)) & ((old(X0) & kind(X0)) | (strong(X0) & old(X0)))) [flattening 43]
45. ! [X0] : (((kind(X0) & happy(X0)) | ~calm(X0)) & (calm(X0) | (~kind(X0) | ~happy(X0)))) [nnf transformation 4]
46. ! [X0] : (((kind(X0) & happy(X0)) | ~calm(X0)) & (calm(X0) | ~kind(X0) | ~happy(X0))) [flattening 45]
47. ! [X0] : (((calm(X0) | ~generous(X0)) | ((~happy(X0) | old(X0)) & (~old(X0) | happy(X0)))) & (((old(X0) | happy(X0)) & (~old(X0) | ~happy(X0))) | (~calm(X0) & generous(X0)))) [nnf transformation 5]
48. ! [X0] : ((calm(X0) | ~generous(X0) | ((~happy(X0) | old(X0)) & (~old(X0) | happy(X0)))) & (((old(X0) | happy(X0)) & (~old(X0) | ~happy(X0))) | (~calm(X0) & generous(X0)))) [flattening 47]
76. old(X0) | old(X0) [cnf transformation 44]
84. happy(X0) | ~calm(X0) [cnf transformation 46]
87. ~old(X0) | ~happy(X0) | ~calm(X0) [cnf transformation 48]
136. calm(susan) [cnf transformation 23]
145. old(X0) [duplicate literal removal 76]
161. ~happy(X0) | ~calm(X0) [subsumption resolution 87,145]
162. ~calm(X0) [subsumption resolution 161,84]
292. $false [subsumption resolution 136,162]
% SZS output end Proof for 5563353769417747903288968
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
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% ------------------------------
| 0 |
Everyone who is not strong or not generous is not calm.
If fred is rich or not generous then mary is both patient and curious and vice versa.
Everyone who is both tall and brave is either not calm or not rich.
Everyone who is not generous is either wise or tall and vice versa.
Everyone who is either not curious or curious is brave.
If someone is generous or wise then someone is not creative.
If fred is both calm and not quiet then john is quiet and vice versa.
If john is not tall then someone is either curious or not calm and vice versa.
Everyone who is wise or not wise is both old and calm.
If someone is not creative or not tall then fred is both tall and strong and vice versa.
If john is happy then someone is either wise or old.
Everyone who is humble or kind is not patient or not wise and vice versa.
Everyone who is either not curious or humble is both curious and not kind and vice versa.
Everyone who is either not patient or not tall is brave or not quiet.
Everyone who is either not happy or old is not humble or curious and vice versa.
If mary is both brave and funny then lucy is either generous or strong and vice versa.
Alice is not tall.
Someone is either kind or not patient.
Someone is either not wise or strong.
Someone is both old and rich.
Someone is not happy or not kind.
Fred is either not curious or wise. | Mary is generous. | entailment | (![X]:((~strong(X)|~generous(X))=>~calm(X)))&
(((rich(fred)|~generous(fred)))<=>((patient(mary)&curious(mary))))&
(![X]:((tall(X)&brave(X))=>(~calm(X)<~>~rich(X))))&
(![X]:(~generous(X)<=>(wise(X)<~>tall(X))))&
(![X]:((~curious(X)<~>curious(X))=>brave(X)))&
((?[X]:((generous(X)|wise(X))))=>(?[X]:(~creative(X))))&
(((calm(fred)&~quiet(fred)))<=>(quiet(john)))&
((~tall(john))<=>(?[X]:((curious(X)<~>~calm(X)))))&
(![X]:((wise(X)|~wise(X))=>(old(X)&calm(X))))&
((?[X]:((~creative(X)|~tall(X))))<=>((tall(fred)&strong(fred))))&
((happy(john))=>(?[X]:((wise(X)<~>old(X)))))&
(![X]:((humble(X)|kind(X))<=>(~patient(X)|~wise(X))))&
(![X]:((~curious(X)<~>humble(X))<=>(curious(X)&~kind(X))))&
(![X]:((~patient(X)<~>~tall(X))=>(brave(X)|~quiet(X))))&
(![X]:((~happy(X)<~>old(X))<=>(~humble(X)|curious(X))))&
(((brave(mary)&funny(mary)))<=>((generous(lucy)<~>strong(lucy))))&
(~tall(alice))&
(?[X]:((kind(X)<~>~patient(X))))&
(?[X]:((~wise(X)<~>strong(X))))&
(?[X]:((old(X)&rich(X))))&
(?[X]:((~happy(X)|~kind(X))))&
((~curious(fred)<~>wise(fred))) | generous(mary) | [
"p0",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 483164405473494082606026
% SZS output start Proof for 483164405473494082606026
1. ! [X0] : ((~generous(X0) | ~strong(X0)) => ~calm(X0)) [input p0]
9. ! [X0] : ((~wise(X0) | wise(X0)) => (calm(X0) & old(X0))) [input p8]
23. ~generous(mary) [input hypothesis]
25. ! [X0] : (~calm(X0) | (generous(X0) & strong(X0))) [ennf transformation 1]
30. ! [X0] : ((calm(X0) & old(X0)) | (wise(X0) & ~wise(X0))) [ennf transformation 9]
77. ~calm(X0) | generous(X0) [cnf transformation 25]
102. calm(X0) | ~wise(X0) [cnf transformation 30]
103. calm(X0) | wise(X0) [cnf transformation 30]
145. ~generous(mary) [cnf transformation 23]
221. calm(X0) [subsumption resolution 102,103]
331. generous(X0) [resolution 77,221]
332. $false [resolution 331,145]
% SZS output end Proof for 483164405473494082606026
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
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