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
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|---|---|---|---|---|---|---|---|
Everyone who is rich or patient is both curious and not curious. If lucy is kind or not rich then someone is either tall or kind and vice versa. Everyone who is either not curious or humble is both funny and curious. Everyone who is not generous or funny is both not creative and not quiet. Everyone who is brave or curious is not humble or not tall and vice versa. Everyone who is not patient is old or happy. If john is strong or not brave then someone is either not happy or not strong. Everyone who is not quiet is patient. If someone is curious then alice is both creative and generous. If someone is either calm or quiet then mary is curious or not creative. If john is not happy then someone is happy and vice versa. Everyone who is both creative and wise is not funny or strong and vice versa. Everyone who is both patient and not humble is humble and vice versa. Everyone who is not generous is both kind and not old and vice versa. John is not calm. Lucy is wise. Paul is either rich or not brave. Someone is calm. John is either not old or not tall. | Paul is kind. | neutral | (![X]:((rich(X)|patient(X))=>(curious(X)&~curious(X))))&
(((kind(lucy)|~rich(lucy)))<=>(?[X]:((tall(X)<~>kind(X)))))&
(![X]:((~curious(X)<~>humble(X))=>(funny(X)&curious(X))))&
(![X]:((~generous(X)|funny(X))=>(~creative(X)&~quiet(X))))&
(![X]:((brave(X)|curious(X))<=>(~humble(X)|~tall(X))))&
(![X]:(~patient(X)=>(old(X)|happy(X))))&
(((strong(john)|~brave(john)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:(~quiet(X)=>patient(X)))&
((?[X]:(curious(X)))=>((creative(alice)&generous(alice))))&
((?[X]:((calm(X)<~>quiet(X))))=>((curious(mary)|~creative(mary))))&
((~happy(john))<=>(?[X]:(happy(X))))&
(![X]:((creative(X)&wise(X))<=>(~funny(X)|strong(X))))&
(![X]:((patient(X)&~humble(X))<=>humble(X)))&
(![X]:(~generous(X)<=>(kind(X)&~old(X))))&
(~calm(john))&
(wise(lucy))&
((rich(paul)<~>~brave(paul)))&
(?[X]:(calm(X)))&
((~old(john)<~>~tall(john))) | kind(paul) | [] | null | 0 |
Everyone who is both funny and not strong is not funny or calm.
Everyone who is curious or not humble is not rich.
Everyone who is rich is not tall and vice versa.
If someone is both not quiet and strong then someone is not patient or not old.
Everyone who is not rich or old is either strong or not calm.
Everyone who is kind or not generous is either not calm or not funny.
Everyone who is not kind or calm is both not brave and not curious.
If someone is not wise then mary is either brave or not wise and vice versa.
Everyone who is both not curious and not humble is calm and vice versa.
Everyone who is brave is not brave.
If someone is happy then someone is not strong or not happy.
Everyone who is not kind is not wise or not calm and vice versa.
Everyone who is either old or tall is both not quiet and not funny.
If susan is both not kind and funny then someone is not humble and vice versa.
If john is either happy or not humble then susan is both curious and not wise.
Lucy is both quiet and not old.
Alice is not kind or wise.
Someone is strong or not quiet.
Fred is curious or not patient.
Someone is either old or not wise.
Alice is brave or not kind.
Paul is either funny or calm. | Paul is strong. | entailment | (![X]:((funny(X)&~strong(X))=>(~funny(X)|calm(X))))&
(![X]:((curious(X)|~humble(X))=>~rich(X)))&
(![X]:(rich(X)<=>~tall(X)))&
((?[X]:((~quiet(X)&strong(X))))=>(?[X]:((~patient(X)|~old(X)))))&
(![X]:((~rich(X)|old(X))=>(strong(X)<~>~calm(X))))&
(![X]:((kind(X)|~generous(X))=>(~calm(X)<~>~funny(X))))&
(![X]:((~kind(X)|calm(X))=>(~brave(X)&~curious(X))))&
((?[X]:(~wise(X)))<=>((brave(mary)<~>~wise(mary))))&
(![X]:((~curious(X)&~humble(X))<=>calm(X)))&
(![X]:(brave(X)=>~brave(X)))&
((?[X]:(happy(X)))=>(?[X]:((~strong(X)|~happy(X)))))&
(![X]:(~kind(X)<=>(~wise(X)|~calm(X))))&
(![X]:((old(X)<~>tall(X))=>(~quiet(X)&~funny(X))))&
(((~kind(susan)&funny(susan)))<=>(?[X]:(~humble(X))))&
(((happy(john)<~>~humble(john)))=>((curious(susan)&~wise(susan))))&
((quiet(lucy)&~old(lucy)))&
((~kind(alice)|wise(alice)))&
(?[X]:((strong(X)|~quiet(X))))&
((curious(fred)|~patient(fred)))&
(?[X]:((old(X)<~>~wise(X))))&
((brave(alice)|~kind(alice)))&
((funny(paul)<~>calm(paul))) | strong(paul) | [
"p0",
"p1",
"p4",
"p8",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4110242483989338381819452
% SZS output start Proof for 4110242483989338381819452
1. ! [X0] : ((~strong(X0) & funny(X0)) => (calm(X0) | ~funny(X0))) [input p0]
2. ! [X0] : ((~humble(X0) | curious(X0)) => ~rich(X0)) [input p1]
5. ! [X0] : ((old(X0) | ~rich(X0)) => (strong(X0) <~> ~calm(X0))) [input p4]
9. ! [X0] : ((~humble(X0) & ~curious(X0)) <=> calm(X0)) [input p8]
22. funny(paul) <~> calm(paul) [input p21]
23. ~strong(paul) [input hypothesis]
29. ! [X0] : ((calm(X0) | ~funny(X0)) | (strong(X0) | ~funny(X0))) [ennf transformation 1]
30. ! [X0] : (calm(X0) | ~funny(X0) | strong(X0) | ~funny(X0)) [flattening 29]
31. ! [X0] : (~rich(X0) | (humble(X0) & ~curious(X0))) [ennf transformation 2]
32. ! [X0] : ((strong(X0) <~> ~calm(X0)) | (~old(X0) & rich(X0))) [ennf transformation 5]
40. ! [X0] : (((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | (~old(X0) & rich(X0))) [nnf transformation 32]
46. ! [X0] : (((~humble(X0) & ~curious(X0)) | ~calm(X0)) & (calm(X0) | (humble(X0) | curious(X0)))) [nnf transformation 9]
47. ! [X0] : (((~humble(X0) & ~curious(X0)) | ~calm(X0)) & (calm(X0) | humble(X0) | curious(X0))) [flattening 46]
65. (~calm(paul) | ~funny(paul)) & (calm(paul) | funny(paul)) [nnf transformation 22]
66. calm(X0) | ~funny(X0) | strong(X0) | ~funny(X0) [cnf transformation 30]
68. ~rich(X0) | humble(X0) [cnf transformation 31]
71. ~calm(X0) | strong(X0) | rich(X0) [cnf transformation 40]
87. ~humble(X0) | ~calm(X0) [cnf transformation 47]
111. calm(paul) | funny(paul) [cnf transformation 65]
113. ~strong(paul) [cnf transformation 23]
115. ~funny(X0) | calm(X0) | strong(X0) [duplicate literal removal 66]
206. 20 <=> funny(paul) [avatar definition]
207. funny(paul) <- (20) [avatar component clause 206]
210. 21 <=> calm(paul) [avatar definition]
211. calm(paul) <- (21) [avatar component clause 210]
212. ~calm(paul) <- (~21) [avatar component clause 210]
214. 20 | 21 [avatar split clause 111,210,206]
238. calm(paul) | strong(paul) <- (20) [resolution 115,207]
239. strong(paul) <- (20, ~21) [subsumption resolution 238,212]
240. $false <- (20, ~21) [subsumption resolution 239,113]
241. ~20 | 21 [avatar contradiction clause 240]
255. strong(paul) | rich(paul) <- (21) [resolution 211,71]
256. rich(paul) <- (21) [subsumption resolution 255,113]
267. humble(paul) <- (21) [resolution 256,68]
293. ~calm(paul) <- (21) [resolution 267,87]
294. $false <- (21) [subsumption resolution 293,211]
295. ~21 [avatar contradiction clause 294]
296. $false [avatar sat refutation 214,241,295]
% SZS output end Proof for 4110242483989338381819452
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or brave then mary is both wise and not strong.
Everyone who is either not strong or generous is kind or not tall and vice versa.
Everyone who is either tall or not funny is both not quiet and brave.
If fred is both not patient and not generous then paul is curious.
Everyone who is brave or humble is both patient and rich.
If susan is not funny then someone is not brave or calm.
If someone is both not humble and not rich then paul is either happy or not tall.
Everyone who is funny is not strong or funny and vice versa.
If susan is either tall or humble then paul is either brave or not tall and vice versa.
Everyone who is old is not tall or happy.
Everyone who is not calm or not rich is not curious and vice versa.
If susan is either not kind or not tall then someone is both funny and old and vice versa.
Everyone who is strong is not funny or not strong and vice versa.
If someone is both curious and not humble then someone is either not calm or not rich and vice versa.
If lucy is not patient then someone is both not creative and not rich.
Everyone who is either brave or old is happy.
Someone is either funny or not generous.
Paul is both not happy and patient.
Someone is not humble or not creative.
Lucy is happy or wise.
Paul is not curious or not kind.
Mary is not generous. | Fred is not old. | entailment | ((?[X]:((happy(X)|brave(X))))=>((wise(mary)&~strong(mary))))&
(![X]:((~strong(X)<~>generous(X))<=>(kind(X)|~tall(X))))&
(![X]:((tall(X)<~>~funny(X))=>(~quiet(X)&brave(X))))&
(((~patient(fred)&~generous(fred)))=>(curious(paul)))&
(![X]:((brave(X)|humble(X))=>(patient(X)&rich(X))))&
((~funny(susan))=>(?[X]:((~brave(X)|calm(X)))))&
((?[X]:((~humble(X)&~rich(X))))=>((happy(paul)<~>~tall(paul))))&
(![X]:(funny(X)<=>(~strong(X)|funny(X))))&
(((tall(susan)<~>humble(susan)))<=>((brave(paul)<~>~tall(paul))))&
(![X]:(old(X)=>(~tall(X)|happy(X))))&
(![X]:((~calm(X)|~rich(X))<=>~curious(X)))&
(((~kind(susan)<~>~tall(susan)))<=>(?[X]:((funny(X)&old(X)))))&
(![X]:(strong(X)<=>(~funny(X)|~strong(X))))&
((?[X]:((curious(X)&~humble(X))))<=>(?[X]:((~calm(X)<~>~rich(X)))))&
((~patient(lucy))=>(?[X]:((~creative(X)&~rich(X)))))&
(![X]:((brave(X)<~>old(X))=>happy(X)))&
(?[X]:((funny(X)<~>~generous(X))))&
((~happy(paul)&patient(paul)))&
(?[X]:((~humble(X)|~creative(X))))&
((happy(lucy)|wise(lucy)))&
((~curious(paul)|~kind(paul)))&
(~generous(mary)) | ~old(fred) | [
"p0",
"p2",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6385373171026053376348382
% SZS output start Proof for 6385373171026053376348382
1. ? [X0] : (brave(X0) | happy(X0)) => (~strong(mary) & wise(mary)) [input p0]
3. ! [X0] : ((tall(X0) <~> ~funny(X0)) => (brave(X0) & ~quiet(X0))) [input p2]
10. ! [X0] : (old(X0) => (happy(X0) | ~tall(X0))) [input p9]
13. ! [X0] : (strong(X0) <=> (~strong(X0) | ~funny(X0))) [input p12]
23. old(fred) [input hypothesis]
31. ! [X0] : ((tall(X0) <~> ~funny(X0)) => brave(X0)) [pure predicate removal 3]
32. ? [X0] : (brave(X0) | happy(X0)) => ~strong(mary) [pure predicate removal 1]
34. ~strong(mary) | ! [X0] : (~brave(X0) & ~happy(X0)) [ennf transformation 32]
35. ! [X0] : (brave(X0) | (tall(X0) <=> ~funny(X0))) [ennf transformation 31]
39. ! [X0] : ((happy(X0) | ~tall(X0)) | ~old(X0)) [ennf transformation 10]
40. ! [X0] : (happy(X0) | ~tall(X0) | ~old(X0)) [flattening 39]
44. ! [X0] : (brave(X0) | ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0)))) [nnf transformation 35]
57. ! [X0] : ((strong(X0) | (strong(X0) & funny(X0))) & ((~strong(X0) | ~funny(X0)) | ~strong(X0))) [nnf transformation 13]
58. ! [X0] : ((strong(X0) | (strong(X0) & funny(X0))) & (~strong(X0) | ~funny(X0) | ~strong(X0))) [flattening 57]
68. ~strong(mary) | ~happy(X0) [cnf transformation 34]
69. ~strong(mary) | ~brave(X0) [cnf transformation 34]
77. funny(X0) | tall(X0) | brave(X0) [cnf transformation 44]
94. ~old(X0) | ~tall(X0) | happy(X0) [cnf transformation 40]
104. ~strong(X0) | ~funny(X0) | ~strong(X0) [cnf transformation 58]
106. strong(X0) | strong(X0) [cnf transformation 58]
120. old(fred) [cnf transformation 23]
121. ~strong(X0) | ~funny(X0) [duplicate literal removal 104]
122. strong(X0) [duplicate literal removal 106]
124. 1 <=> ! [X0] : ~brave(X0) [avatar definition]
125. ~brave(X0) <- (1) [avatar component clause 124]
127. 2 <=> strong(mary) [avatar definition]
129. ~strong(mary) <- (~2) [avatar component clause 127]
130. 1 | ~2 [avatar split clause 69,127,124]
132. 3 <=> ! [X0] : ~happy(X0) [avatar definition]
133. ~happy(X0) <- (3) [avatar component clause 132]
134. 3 | ~2 [avatar split clause 68,127,132]
204. ~funny(X0) [subsumption resolution 121,122]
247. $false <- (~2) [subsumption resolution 129,122]
248. 2 [avatar contradiction clause 247]
257. tall(X1) | brave(X1) [resolution 77,204]
259. tall(X1) <- (1) [subsumption resolution 257,125]
260. ~tall(fred) | happy(fred) [resolution 94,120]
261. happy(fred) <- (1) [subsumption resolution 260,259]
262. $false <- (1, 3) [subsumption resolution 261,133]
263. ~1 | ~3 [avatar contradiction clause 262]
264. $false [avatar sat refutation 130,134,248,263]
% SZS output end Proof for 6385373171026053376348382
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is not wise or not generous.
If someone is not creative then susan is either quiet or not generous.
Everyone who is both humble and not old is both not happy and not creative.
If mary is not generous then fred is patient.
If lucy is brave or not tall then fred is either rich or not patient.
Everyone who is not kind is creative or funny.
If someone is either creative or not wise then someone is generous and vice versa.
If paul is not wise then fred is both tall and kind.
Everyone who is either calm or quiet is not happy or not tall.
If someone is both not happy and not creative then someone is both not strong and brave and vice versa.
If mary is either not funny or quiet then someone is either rich or not tall.
If john is quiet then lucy is both not wise and calm and vice versa.
Everyone who is happy or kind is both not patient and not strong.
Everyone who is curious or calm is either creative or not rich.
Everyone who is both not happy and not quiet is happy and vice versa.
Everyone who is patient is not calm or strong and vice versa.
Someone is funny.
Someone is not generous or patient.
Mary is not humble.
Alice is not strong.
Fred is either not kind or not humble.
Someone is not old or not generous.
Paul is both humble and not patient.
Someone is kind or strong. | Susan is quiet. | entailment | (![X]:(funny(X)=>(~wise(X)|~generous(X))))&
((?[X]:(~creative(X)))=>((quiet(susan)<~>~generous(susan))))&
(![X]:((humble(X)&~old(X))=>(~happy(X)&~creative(X))))&
((~generous(mary))=>(patient(fred)))&
(((brave(lucy)|~tall(lucy)))=>((rich(fred)<~>~patient(fred))))&
(![X]:(~kind(X)=>(creative(X)|funny(X))))&
((?[X]:((creative(X)<~>~wise(X))))<=>(?[X]:(generous(X))))&
((~wise(paul))=>((tall(fred)&kind(fred))))&
(![X]:((calm(X)<~>quiet(X))=>(~happy(X)|~tall(X))))&
((?[X]:((~happy(X)&~creative(X))))<=>(?[X]:((~strong(X)&brave(X)))))&
(((~funny(mary)<~>quiet(mary)))=>(?[X]:((rich(X)<~>~tall(X)))))&
((quiet(john))<=>((~wise(lucy)&calm(lucy))))&
(![X]:((happy(X)|kind(X))=>(~patient(X)&~strong(X))))&
(![X]:((curious(X)|calm(X))=>(creative(X)<~>~rich(X))))&
(![X]:((~happy(X)&~quiet(X))<=>happy(X)))&
(![X]:(patient(X)<=>(~calm(X)|strong(X))))&
(?[X]:(funny(X)))&
(?[X]:((~generous(X)|patient(X))))&
(~humble(mary))&
(~strong(alice))&
((~kind(fred)<~>~humble(fred)))&
(?[X]:((~old(X)|~generous(X))))&
((humble(paul)&~patient(paul)))&
(?[X]:((kind(X)|strong(X)))) | quiet(susan) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3313789196627401327634427
% SZS output start Proof for 3313789196627401327634427
15. ! [X0] : ((~quiet(X0) & ~happy(X0)) <=> happy(X0)) [input p14]
25. ~quiet(susan) [input hypothesis]
63. ! [X0] : (((~quiet(X0) & ~happy(X0)) | ~happy(X0)) & (happy(X0) | (quiet(X0) | happy(X0)))) [nnf transformation 15]
64. ! [X0] : (((~quiet(X0) & ~happy(X0)) | ~happy(X0)) & (happy(X0) | quiet(X0) | happy(X0))) [flattening 63]
112. happy(X0) | quiet(X0) | happy(X0) [cnf transformation 64]
113. ~happy(X0) | ~happy(X0) [cnf transformation 64]
128. ~quiet(susan) [cnf transformation 25]
129. happy(X0) | quiet(X0) [duplicate literal removal 112]
130. ~happy(X0) [duplicate literal removal 113]
269. quiet(X0) [subsumption resolution 129,130]
303. $false [subsumption resolution 128,269]
% SZS output end Proof for 3313789196627401327634427
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or old is either creative or curious and vice versa. If john is not patient or not wise then alice is not tall. Everyone who is either happy or rich is both not curious and generous. Everyone who is either kind or not kind is not tall and vice versa. Everyone who is not calm is either calm or not rich. Everyone who is either curious or strong is either not brave or not rich. Everyone who is tall is either strong or not generous. Everyone who is either not brave or wise is not old or not brave and vice versa. Everyone who is both not happy and funny is either not humble or patient. If alice is old then someone is not kind. Everyone who is either quiet or not funny is old or not old and vice versa. If mary is both not wise and happy then alice is either humble or not happy. If john is either strong or not humble then john is both brave and not wise. Everyone who is not funny or not wise is both strong and not wise. Everyone who is both not curious and tall is both brave and not wise and vice versa. Everyone who is both not tall and tall is not wise or not calm and vice versa. Fred is creative. Alice is creative. John is both strong and not tall. Paul is either not old or not humble. | Mary is calm. | entailment | (![X]:((~humble(X)<~>old(X))<=>(creative(X)<~>curious(X))))&
(((~patient(john)|~wise(john)))=>(~tall(alice)))&
(![X]:((happy(X)<~>rich(X))=>(~curious(X)&generous(X))))&
(![X]:((kind(X)<~>~kind(X))<=>~tall(X)))&
(![X]:(~calm(X)=>(calm(X)<~>~rich(X))))&
(![X]:((curious(X)<~>strong(X))=>(~brave(X)<~>~rich(X))))&
(![X]:(tall(X)=>(strong(X)<~>~generous(X))))&
(![X]:((~brave(X)<~>wise(X))<=>(~old(X)|~brave(X))))&
(![X]:((~happy(X)&funny(X))=>(~humble(X)<~>patient(X))))&
((old(alice))=>(?[X]:(~kind(X))))&
(![X]:((quiet(X)<~>~funny(X))<=>(old(X)|~old(X))))&
(((~wise(mary)&happy(mary)))=>((humble(alice)<~>~happy(alice))))&
(((strong(john)<~>~humble(john)))=>((brave(john)&~wise(john))))&
(![X]:((~funny(X)|~wise(X))=>(strong(X)&~wise(X))))&
(![X]:((~curious(X)&tall(X))<=>(brave(X)&~wise(X))))&
(![X]:((~tall(X)&tall(X))<=>(~wise(X)|~calm(X))))&
(creative(fred))&
(creative(alice))&
((strong(john)&~tall(john)))&
((~old(paul)<~>~humble(paul))) | calm(mary) | [
"p3",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6656682756420641182101373
% SZS output start Proof for 6656682756420641182101373
4. ! [X0] : ((kind(X0) <~> ~kind(X0)) <=> ~tall(X0)) [input p3]
16. ! [X0] : ((tall(X0) & ~tall(X0)) <=> (~calm(X0) | ~wise(X0))) [input p15]
21. ~calm(mary) [input hypothesis]
36. ! [X0] : ((((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | tall(X0)) & (~tall(X0) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0))))) [nnf transformation 4]
51. ! [X0] : (((tall(X0) & ~tall(X0)) | (calm(X0) & wise(X0))) & ((~calm(X0) | ~wise(X0)) | (~tall(X0) | tall(X0)))) [nnf transformation 16]
52. ! [X0] : (((tall(X0) & ~tall(X0)) | (calm(X0) & wise(X0))) & (~calm(X0) | ~wise(X0) | ~tall(X0) | tall(X0))) [flattening 51]
68. ~tall(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 36]
69. ~tall(X0) | kind(X0) | kind(X0) [cnf transformation 36]
113. tall(X0) | calm(X0) [cnf transformation 52]
120. ~calm(mary) [cnf transformation 21]
124. ~tall(X0) | ~kind(X0) [duplicate literal removal 68]
125. ~tall(X0) | kind(X0) [duplicate literal removal 69]
140. ~tall(X0) [subsumption resolution 124,125]
188. calm(X0) [subsumption resolution 113,140]
201. $false [subsumption resolution 120,188]
% SZS output end Proof for 6656682756420641182101373
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then someone is both not wise and not calm and vice versa.
Everyone who is not calm or not tall is either old or not humble and vice versa.
Everyone who is patient or wise is both humble and not old and vice versa.
Everyone who is creative or funny is creative or quiet.
If someone is both not tall and humble then susan is brave.
Everyone who is both not wise and not curious is both not happy and not calm and vice versa.
If john is old then someone is either not generous or curious and vice versa.
If someone is wise or not rich then someone is both not calm and not creative.
Everyone who is calm is both not calm and humble.
If someone is either happy or not funny then someone is not kind and vice versa.
Everyone who is calm or curious is both kind and not rich.
Everyone who is not strong or not kind is wise.
Everyone who is strong is old or not creative.
Everyone who is curious or not curious is not happy and vice versa.
Everyone who is either not happy or strong is either not happy or not generous and vice versa.
Everyone who is either funny or not brave is curious or not calm.
Someone is both brave and not tall.
John is not creative or happy.
Someone is not rich.
Lucy is kind.
Someone is rich or not curious. | Susan is not strong. | contradiction | ((?[X]:(~old(X)))<=>(?[X]:((~wise(X)&~calm(X)))))&
(![X]:((~calm(X)|~tall(X))<=>(old(X)<~>~humble(X))))&
(![X]:((patient(X)|wise(X))<=>(humble(X)&~old(X))))&
(![X]:((creative(X)|funny(X))=>(creative(X)|quiet(X))))&
((?[X]:((~tall(X)&humble(X))))=>(brave(susan)))&
(![X]:((~wise(X)&~curious(X))<=>(~happy(X)&~calm(X))))&
((old(john))<=>(?[X]:((~generous(X)<~>curious(X)))))&
((?[X]:((wise(X)|~rich(X))))=>(?[X]:((~calm(X)&~creative(X)))))&
(![X]:(calm(X)=>(~calm(X)&humble(X))))&
((?[X]:((happy(X)<~>~funny(X))))<=>(?[X]:(~kind(X))))&
(![X]:((calm(X)|curious(X))=>(kind(X)&~rich(X))))&
(![X]:((~strong(X)|~kind(X))=>wise(X)))&
(![X]:(strong(X)=>(old(X)|~creative(X))))&
(![X]:((curious(X)|~curious(X))<=>~happy(X)))&
(![X]:((~happy(X)<~>strong(X))<=>(~happy(X)<~>~generous(X))))&
(![X]:((funny(X)<~>~brave(X))=>(curious(X)|~calm(X))))&
(?[X]:((brave(X)&~tall(X))))&
((~creative(john)|happy(john)))&
(?[X]:(~rich(X)))&
(kind(lucy))&
(?[X]:((rich(X)|~curious(X)))) | ~strong(susan) | [
"p1",
"p2",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3641342157940583356856079
% SZS output start Proof for 3641342157940583356856079
2. ! [X0] : ((~tall(X0) | ~calm(X0)) <=> (old(X0) <~> ~humble(X0))) [input p1]
3. ! [X0] : ((wise(X0) | patient(X0)) <=> (~old(X0) & humble(X0))) [input p2]
9. ! [X0] : (calm(X0) => (humble(X0) & ~calm(X0))) [input p8]
12. ! [X0] : ((~kind(X0) | ~strong(X0)) => wise(X0)) [input p11]
22. ~strong(susan) [input hypothesis]
32. ! [X0] : ((humble(X0) & ~calm(X0)) | ~calm(X0)) [ennf transformation 9]
34. ! [X0] : (wise(X0) | (kind(X0) & strong(X0))) [ennf transformation 12]
42. ! [X0] : (((~tall(X0) | ~calm(X0)) | ((old(X0) | humble(X0)) & (~humble(X0) | ~old(X0)))) & (((humble(X0) | ~old(X0)) & (~humble(X0) | old(X0))) | (tall(X0) & calm(X0)))) [nnf transformation 2]
43. ! [X0] : ((~tall(X0) | ~calm(X0) | ((old(X0) | humble(X0)) & (~humble(X0) | ~old(X0)))) & (((humble(X0) | ~old(X0)) & (~humble(X0) | old(X0))) | (tall(X0) & calm(X0)))) [flattening 42]
44. ! [X0] : (((wise(X0) | patient(X0)) | (old(X0) | ~humble(X0))) & ((~old(X0) & humble(X0)) | (~wise(X0) & ~patient(X0)))) [nnf transformation 3]
45. ! [X0] : ((wise(X0) | patient(X0) | old(X0) | ~humble(X0)) & ((~old(X0) & humble(X0)) | (~wise(X0) & ~patient(X0)))) [flattening 44]
73. ~humble(X0) | old(X0) | calm(X0) [cnf transformation 43]
80. ~wise(X0) | humble(X0) [cnf transformation 45]
82. ~wise(X0) | ~old(X0) [cnf transformation 45]
95. ~calm(X0) | ~calm(X0) [cnf transformation 32]
105. strong(X0) | wise(X0) [cnf transformation 34]
125. ~strong(susan) [cnf transformation 22]
130. ~calm(X0) [duplicate literal removal 95]
223. wise(susan) [resolution 105,125]
225. ~old(susan) [resolution 223,82]
226. humble(susan) [resolution 223,80]
233. old(susan) | calm(susan) [resolution 73,226]
234. calm(susan) [subsumption resolution 233,225]
235. $false [subsumption resolution 234,130]
% SZS output end Proof for 3641342157940583356856079
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is quiet or not kind then someone is either wise or not kind and vice versa. Everyone who is both patient and not wise is strong. Everyone who is both rich and not quiet is not old or creative and vice versa. Everyone who is both happy and not kind is not humble or not tall and vice versa. Everyone who is both calm and tall is humble or old and vice versa. Everyone who is not funny is rich and vice versa. Everyone who is both not kind and not quiet is both strong and not rich and vice versa. Everyone who is curious is both rich and not curious. If someone is both not quiet and wise then fred is not strong or kind and vice versa. Everyone who is both kind and not humble is not curious or not tall. Everyone who is either not brave or curious is not happy or strong. Everyone who is either calm or not funny is either not strong or funny. Everyone who is both not old and humble is both humble and patient. If someone is both not brave and not generous then someone is creative or not strong. If someone is generous or creative then fred is both humble and creative and vice versa. Everyone who is either not generous or wise is either not kind or not curious. Lucy is patient. Someone is not wise. Someone is kind or wise. Paul is either not creative or not curious. John is either calm or brave. Someone is quiet or calm. Someone is both old and rich. | Fred is not humble. | contradiction | (((quiet(paul)|~kind(paul)))<=>(?[X]:((wise(X)<~>~kind(X)))))&
(![X]:((patient(X)&~wise(X))=>strong(X)))&
(![X]:((rich(X)&~quiet(X))<=>(~old(X)|creative(X))))&
(![X]:((happy(X)&~kind(X))<=>(~humble(X)|~tall(X))))&
(![X]:((calm(X)&tall(X))<=>(humble(X)|old(X))))&
(![X]:(~funny(X)<=>rich(X)))&
(![X]:((~kind(X)&~quiet(X))<=>(strong(X)&~rich(X))))&
(![X]:(curious(X)=>(rich(X)&~curious(X))))&
((?[X]:((~quiet(X)&wise(X))))<=>((~strong(fred)|kind(fred))))&
(![X]:((kind(X)&~humble(X))=>(~curious(X)|~tall(X))))&
(![X]:((~brave(X)<~>curious(X))=>(~happy(X)|strong(X))))&
(![X]:((calm(X)<~>~funny(X))=>(~strong(X)<~>funny(X))))&
(![X]:((~old(X)&humble(X))=>(humble(X)&patient(X))))&
((?[X]:((~brave(X)&~generous(X))))=>(?[X]:((creative(X)|~strong(X)))))&
((?[X]:((generous(X)|creative(X))))<=>((humble(fred)&creative(fred))))&
(![X]:((~generous(X)<~>wise(X))=>(~kind(X)<~>~curious(X))))&
(patient(lucy))&
(?[X]:(~wise(X)))&
(?[X]:((kind(X)|wise(X))))&
((~creative(paul)<~>~curious(paul)))&
((calm(john)<~>brave(john)))&
(?[X]:((quiet(X)|calm(X))))&
(?[X]:((old(X)&rich(X)))) | ~humble(fred) | [
"p7",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4448283373534728010566973
% SZS output start Proof for 4448283373534728010566973
8. ! [X0] : (curious(X0) => (~curious(X0) & rich(X0))) [input p7]
15. ? [X0] : (creative(X0) | generous(X0)) <=> (creative(fred) & humble(fred)) [input p14]
20. ~creative(paul) <~> ~curious(paul) [input p19]
24. ~humble(fred) [input hypothesis]
28. ! [X0] : ((~curious(X0) & rich(X0)) | ~curious(X0)) [ennf transformation 8]
62. (? [X0] : (creative(X0) | generous(X0)) | (~creative(fred) | ~humble(fred))) & ((creative(fred) & humble(fred)) | ! [X0] : (~creative(X0) & ~generous(X0))) [nnf transformation 15]
63. (? [X0] : (creative(X0) | generous(X0)) | ~creative(fred) | ~humble(fred)) & ((creative(fred) & humble(fred)) | ! [X0] : (~creative(X0) & ~generous(X0))) [flattening 62]
64. (? [X0] : (creative(X0) | generous(X0)) | ~creative(fred) | ~humble(fred)) & ((creative(fred) & humble(fred)) | ! [X1] : (~creative(X1) & ~generous(X1))) [rectify 63]
65. ? [X0] : (creative(X0) | generous(X0)) => (creative(sK3) | generous(sK3)) [choice axiom]
66. ((creative(sK3) | generous(sK3)) | ~creative(fred) | ~humble(fred)) & ((creative(fred) & humble(fred)) | ! [X1] : (~creative(X1) & ~generous(X1))) [skolemisation 64,65]
72. (curious(paul) | creative(paul)) & (~curious(paul) | ~creative(paul)) [nnf transformation 20]
107. ~curious(X0) | ~curious(X0) [cnf transformation 28]
124. humble(fred) | ~creative(X1) [cnf transformation 66]
136. curious(paul) | creative(paul) [cnf transformation 72]
142. ~humble(fred) [cnf transformation 24]
145. ~curious(X0) [duplicate literal removal 107]
212. 15 <=> humble(fred) [avatar definition]
229. 19 <=> ! [X1] : ~creative(X1) [avatar definition]
230. ~creative(X1) <- (19) [avatar component clause 229]
236. 19 | 15 [avatar split clause 124,212,229]
249. creative(paul) [subsumption resolution 136,145]
269. ~15 [avatar split clause 142,212]
270. $false <- (19) [resolution 249,230]
271. ~19 [avatar contradiction clause 270]
272. $false [avatar sat refutation 236,269,271]
% SZS output end Proof for 4448283373534728010566973
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If paul is brave then someone is both old and not generous and vice versa.
Everyone who is both not wise and strong is rich or curious and vice versa.
Everyone who is not funny is not kind and vice versa.
If john is either not patient or not curious then someone is brave and vice versa.
If someone is not patient then someone is either humble or not brave and vice versa.
If someone is both funny and rich then someone is not creative and vice versa.
Everyone who is either curious or rich is both strong and wise.
Everyone who is both happy and not curious is funny and vice versa.
If alice is not humble or old then fred is either funny or not old and vice versa.
Everyone who is both not creative and happy is generous and vice versa.
Everyone who is rich or brave is not patient.
If alice is not humble then someone is either not kind or not happy and vice versa.
If paul is both brave and wise then fred is not tall or curious and vice versa.
If someone is brave or creative then paul is either kind or brave.
Everyone who is rich is old and vice versa.
If john is not quiet then alice is not generous and vice versa.
Lucy is brave.
Someone is strong.
Fred is either generous or happy.
Someone is not strong or rich.
Someone is either strong or not kind.
Mary is calm.
Someone is either not calm or not humble.
Someone is not brave or generous. | Alice is not humble. | contradiction | ((brave(paul))<=>(?[X]:((old(X)&~generous(X)))))&
(![X]:((~wise(X)&strong(X))<=>(rich(X)|curious(X))))&
(![X]:(~funny(X)<=>~kind(X)))&
(((~patient(john)<~>~curious(john)))<=>(?[X]:(brave(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((humble(X)<~>~brave(X)))))&
((?[X]:((funny(X)&rich(X))))<=>(?[X]:(~creative(X))))&
(![X]:((curious(X)<~>rich(X))=>(strong(X)&wise(X))))&
(![X]:((happy(X)&~curious(X))<=>funny(X)))&
(((~humble(alice)|old(alice)))<=>((funny(fred)<~>~old(fred))))&
(![X]:((~creative(X)&happy(X))<=>generous(X)))&
(![X]:((rich(X)|brave(X))=>~patient(X)))&
((~humble(alice))<=>(?[X]:((~kind(X)<~>~happy(X)))))&
(((brave(paul)&wise(paul)))<=>((~tall(fred)|curious(fred))))&
((?[X]:((brave(X)|creative(X))))=>((kind(paul)<~>brave(paul))))&
(![X]:(rich(X)<=>old(X)))&
((~quiet(john))<=>(~generous(alice)))&
(brave(lucy))&
(?[X]:(strong(X)))&
((generous(fred)<~>happy(fred)))&
(?[X]:((~strong(X)|rich(X))))&
(?[X]:((strong(X)<~>~kind(X))))&
(calm(mary))&
(?[X]:((~calm(X)<~>~humble(X))))&
(?[X]:((~brave(X)|generous(X)))) | ~humble(alice) | [
"p1",
"p5",
"p6",
"p7",
"p8",
"p9",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 226125636359069709815028
% SZS output start Proof for 226125636359069709815028
2. ! [X0] : ((strong(X0) & ~wise(X0)) <=> (curious(X0) | rich(X0))) [input p1]
6. ? [X0] : (rich(X0) & funny(X0)) <=> ? [X0] : ~creative(X0) [input p5]
7. ! [X0] : ((curious(X0) <~> rich(X0)) => (wise(X0) & strong(X0))) [input p6]
8. ! [X0] : ((~curious(X0) & happy(X0)) <=> funny(X0)) [input p7]
9. (old(alice) | ~humble(alice)) <=> (funny(fred) <~> ~old(fred)) [input p8]
10. ! [X0] : ((happy(X0) & ~creative(X0)) <=> generous(X0)) [input p9]
15. ! [X0] : (rich(X0) <=> old(X0)) [input p14]
19. generous(fred) <~> happy(fred) [input p18]
25. ~humble(alice) [input hypothesis]
27. ? [X0] : (rich(X0) & funny(X0)) <=> ? [X1] : ~creative(X1) [rectify 6]
28. ! [X0] : ((wise(X0) & strong(X0)) | (curious(X0) <=> rich(X0))) [ennf transformation 7]
35. ! [X0] : (((strong(X0) & ~wise(X0)) | (~curious(X0) & ~rich(X0))) & ((curious(X0) | rich(X0)) | (~strong(X0) | wise(X0)))) [nnf transformation 2]
36. ! [X0] : (((strong(X0) & ~wise(X0)) | (~curious(X0) & ~rich(X0))) & (curious(X0) | rich(X0) | ~strong(X0) | wise(X0))) [flattening 35]
47. (? [X0] : (rich(X0) & funny(X0)) | ! [X1] : creative(X1)) & (? [X1] : ~creative(X1) | ! [X0] : (~rich(X0) | ~funny(X0))) [nnf transformation 27]
48. (? [X0] : (rich(X0) & funny(X0)) | ! [X1] : creative(X1)) & (? [X2] : ~creative(X2) | ! [X3] : (~rich(X3) | ~funny(X3))) [rectify 47]
49. ? [X0] : (rich(X0) & funny(X0)) => (rich(sK4) & funny(sK4)) [choice axiom]
50. ? [X2] : ~creative(X2) => ~creative(sK5) [choice axiom]
51. ((rich(sK4) & funny(sK4)) | ! [X1] : creative(X1)) & (~creative(sK5) | ! [X3] : (~rich(X3) | ~funny(X3))) [skolemisation 48,50,49]
52. ! [X0] : ((wise(X0) & strong(X0)) | ((curious(X0) | ~rich(X0)) & (rich(X0) | ~curious(X0)))) [nnf transformation 28]
53. ! [X0] : (((~curious(X0) & happy(X0)) | ~funny(X0)) & (funny(X0) | (curious(X0) | ~happy(X0)))) [nnf transformation 8]
54. ! [X0] : (((~curious(X0) & happy(X0)) | ~funny(X0)) & (funny(X0) | curious(X0) | ~happy(X0))) [flattening 53]
55. ((old(alice) | ~humble(alice)) | ((funny(fred) | old(fred)) & (~old(fred) | ~funny(fred)))) & (((old(fred) | ~funny(fred)) & (~old(fred) | funny(fred))) | (~old(alice) & humble(alice))) [nnf transformation 9]
56. (old(alice) | ~humble(alice) | ((funny(fred) | old(fred)) & (~old(fred) | ~funny(fred)))) & (((old(fred) | ~funny(fred)) & (~old(fred) | funny(fred))) | (~old(alice) & humble(alice))) [flattening 55]
57. ! [X0] : (((happy(X0) & ~creative(X0)) | ~generous(X0)) & (generous(X0) | (~happy(X0) | creative(X0)))) [nnf transformation 10]
58. ! [X0] : (((happy(X0) & ~creative(X0)) | ~generous(X0)) & (generous(X0) | ~happy(X0) | creative(X0))) [flattening 57]
66. ! [X0] : ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0))) [nnf transformation 15]
70. (~happy(fred) | ~generous(fred)) & (happy(fred) | generous(fred)) [nnf transformation 19]
85. ~rich(X0) | ~wise(X0) [cnf transformation 36]
86. ~curious(X0) | ~wise(X0) [cnf transformation 36]
99. ~creative(sK5) | ~rich(X3) | ~funny(X3) [cnf transformation 51]
100. funny(sK4) | creative(X1) [cnf transformation 51]
101. rich(sK4) | creative(X1) [cnf transformation 51]
104. wise(X0) | rich(X0) | ~curious(X0) [cnf transformation 52]
105. wise(X0) | curious(X0) | ~rich(X0) [cnf transformation 52]
106. ~happy(X0) | curious(X0) | funny(X0) [cnf transformation 54]
108. ~funny(X0) | ~curious(X0) [cnf transformation 54]
109. ~old(fred) | funny(fred) | humble(alice) [cnf transformation 56]
111. old(fred) | ~funny(fred) | humble(alice) [cnf transformation 56]
117. ~generous(X0) | happy(X0) [cnf transformation 58]
133. ~rich(X0) | old(X0) [cnf transformation 66]
134. ~old(X0) | rich(X0) [cnf transformation 66]
139. happy(fred) | generous(fred) [cnf transformation 70]
140. ~happy(fred) | ~generous(fred) [cnf transformation 70]
148. ~humble(alice) [cnf transformation 25]
212. 15 <=> ! [X1] : creative(X1) [avatar definition]
213. creative(X1) <- (15) [avatar component clause 212]
215. 16 <=> rich(sK4) [avatar definition]
217. rich(sK4) <- (16) [avatar component clause 215]
218. 15 | 16 [avatar split clause 101,215,212]
220. 17 <=> funny(sK4) [avatar definition]
222. funny(sK4) <- (17) [avatar component clause 220]
223. 15 | 17 [avatar split clause 100,220,212]
225. 18 <=> ! [X3] : (~rich(X3) | ~funny(X3)) [avatar definition]
226. ~funny(X3) | ~rich(X3) <- (18) [avatar component clause 225]
228. 19 <=> creative(sK5) [avatar definition]
230. ~creative(sK5) <- (~19) [avatar component clause 228]
231. 18 | ~19 [avatar split clause 99,228,225]
232. ~rich(X0) | curious(X0) [subsumption resolution 105,85]
233. ~curious(X0) | rich(X0) [subsumption resolution 104,86]
235. 20 <=> old(fred) [avatar definition]
236. ~old(fred) <- (~20) [avatar component clause 235]
237. old(fred) <- (20) [avatar component clause 235]
239. 21 <=> funny(fred) [avatar definition]
241. funny(fred) <- (21) [avatar component clause 239]
243. 22 <=> humble(alice) [avatar definition]
253. 22 | ~21 | 20 [avatar split clause 111,235,239,243]
255. 22 | 21 | ~20 [avatar split clause 109,235,239,243]
275. 28 <=> curious(fred) [avatar definition]
276. curious(fred) <- (28) [avatar component clause 275]
312. ~generous(fred) [subsumption resolution 140,117]
313. happy(fred) [subsumption resolution 139,312]
352. ~22 [avatar split clause 148,243]
371. ~curious(sK4) <- (17) [resolution 108,222]
384. curious(sK4) <- (16) [resolution 232,217]
386. $false <- (16, 17) [subsumption resolution 384,371]
387. ~16 | ~17 [avatar contradiction clause 386]
388. $false <- (15, ~19) [resolution 213,230]
390. ~15 | 19 [avatar contradiction clause 388]
393. rich(fred) <- (28) [resolution 233,276]
396. old(fred) <- (28) [resolution 393,133]
399. $false <- (~20, 28) [subsumption resolution 396,236]
400. 20 | ~28 [avatar contradiction clause 399]
401. curious(fred) | funny(fred) [resolution 106,313]
415. 21 | 28 [avatar split clause 401,275,239]
416. rich(fred) <- (20) [resolution 237,134]
417. ~rich(fred) <- (18, 21) [resolution 241,226]
421. $false <- (18, 20, 21) [subsumption resolution 417,416]
422. ~18 | ~20 | ~21 [avatar contradiction clause 421]
425. $false [avatar sat refutation 218,223,231,253,255,352,387,390,400,415,422]
% SZS output end Proof for 226125636359069709815028
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either not tall or happy then someone is not tall or creative.
If susan is not curious then someone is creative or curious and vice versa.
Everyone who is quiet or not funny is brave and vice versa.
Everyone who is not brave is both not brave and calm and vice versa.
If someone is not rich then someone is not strong and vice versa.
Everyone who is humble or not humble is both not brave and not strong and vice versa.
If alice is not creative or tall then alice is not happy or not tall.
Everyone who is humble is curious and vice versa.
If someone is not creative or not patient then someone is not funny and vice versa.
If john is either humble or strong then john is either not creative or creative and vice versa.
Everyone who is both strong and tall is either not brave or patient and vice versa.
Everyone who is both not calm and not generous is patient or not humble.
If paul is not brave then someone is old and vice versa.
Everyone who is either brave or not kind is both not creative and calm and vice versa.
If susan is not strong or curious then someone is calm.
Someone is not old or humble.
Someone is rich or quiet.
Lucy is happy or not creative.
Someone is kind.
Someone is either happy or rich.
Lucy is not old.
Someone is not humble. | Fred is funny. | entailment | (((~tall(fred)<~>happy(fred)))=>(?[X]:((~tall(X)|creative(X)))))&
((~curious(susan))<=>(?[X]:((creative(X)|curious(X)))))&
(![X]:((quiet(X)|~funny(X))<=>brave(X)))&
(![X]:(~brave(X)<=>(~brave(X)&calm(X))))&
((?[X]:(~rich(X)))<=>(?[X]:(~strong(X))))&
(![X]:((humble(X)|~humble(X))<=>(~brave(X)&~strong(X))))&
(((~creative(alice)|tall(alice)))=>((~happy(alice)|~tall(alice))))&
(![X]:(humble(X)<=>curious(X)))&
((?[X]:((~creative(X)|~patient(X))))<=>(?[X]:(~funny(X))))&
(((humble(john)<~>strong(john)))<=>((~creative(john)<~>creative(john))))&
(![X]:((strong(X)&tall(X))<=>(~brave(X)<~>patient(X))))&
(![X]:((~calm(X)&~generous(X))=>(patient(X)|~humble(X))))&
((~brave(paul))<=>(?[X]:(old(X))))&
(![X]:((brave(X)<~>~kind(X))<=>(~creative(X)&calm(X))))&
(((~strong(susan)|curious(susan)))=>(?[X]:(calm(X))))&
(?[X]:((~old(X)|humble(X))))&
(?[X]:((rich(X)|quiet(X))))&
((happy(lucy)|~creative(lucy)))&
(?[X]:(kind(X)))&
(?[X]:((happy(X)<~>rich(X))))&
(~old(lucy))&
(?[X]:(~humble(X))) | funny(fred) | [
"p2",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 5909200112336178531567692
% SZS output start Proof for 5909200112336178531567692
3. ! [X0] : ((~funny(X0) | quiet(X0)) <=> brave(X0)) [input p2]
6. ! [X0] : ((~humble(X0) | humble(X0)) <=> (~strong(X0) & ~brave(X0))) [input p5]
23. ~funny(fred) [input hypothesis]
38. ! [X0] : (((~funny(X0) | quiet(X0)) | ~brave(X0)) & (brave(X0) | (funny(X0) & ~quiet(X0)))) [nnf transformation 3]
39. ! [X0] : ((~funny(X0) | quiet(X0) | ~brave(X0)) & (brave(X0) | (funny(X0) & ~quiet(X0)))) [flattening 38]
47. ! [X0] : (((~humble(X0) | humble(X0)) | (strong(X0) | brave(X0))) & ((~strong(X0) & ~brave(X0)) | (humble(X0) & ~humble(X0)))) [nnf transformation 6]
48. ! [X0] : ((~humble(X0) | humble(X0) | strong(X0) | brave(X0)) & ((~strong(X0) & ~brave(X0)) | (humble(X0) & ~humble(X0)))) [flattening 47]
83. brave(X0) | funny(X0) [cnf transformation 39]
90. ~brave(X0) | ~humble(X0) [cnf transformation 48]
91. ~brave(X0) | humble(X0) [cnf transformation 48]
134. ~funny(fred) [cnf transformation 23]
196. ~brave(X0) [subsumption resolution 90,91]
212. 17 <=> ! [X1] : funny(X1) [avatar definition]
213. funny(X1) <- (17) [avatar component clause 212]
300. funny(X0) [resolution 83,196]
301. 17 [avatar split clause 300,212]
302. $false <- (17) [resolution 213,134]
305. ~17 [avatar contradiction clause 302]
306. $false [avatar sat refutation 301,305]
% SZS output end Proof for 5909200112336178531567692
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is not curious and vice versa.
If susan is not tall then someone is tall or not old and vice versa.
If john is not curious or not creative then someone is either generous or tall and vice versa.
Everyone who is patient or not rich is not brave or not curious and vice versa.
If someone is calm or wise then someone is either brave or curious.
Everyone who is strong or not creative is not creative or curious and vice versa.
Everyone who is both humble and tall is wise and vice versa.
If paul is both not kind and quiet then someone is old or not quiet.
Everyone who is either quiet or patient is curious or rich.
Everyone who is not brave is calm or not brave.
Everyone who is not happy is not tall or not brave.
Everyone who is not patient or not generous is both not calm and not patient and vice versa.
If someone is both happy and not patient then mary is tall.
Everyone who is patient is either not brave or curious and vice versa.
Everyone who is not curious is either generous or not humble.
If alice is not calm or not creative then susan is not funny or not old and vice versa.
Paul is not creative.
Paul is either not quiet or not strong.
Someone is happy or wise.
Someone is not strong or not kind.
Alice is not calm or kind.
Fred is either quiet or creative.
Someone is strong. | Paul is not rich. | entailment | (![X]:(~generous(X)<=>~curious(X)))&
((~tall(susan))<=>(?[X]:((tall(X)|~old(X)))))&
(((~curious(john)|~creative(john)))<=>(?[X]:((generous(X)<~>tall(X)))))&
(![X]:((patient(X)|~rich(X))<=>(~brave(X)|~curious(X))))&
((?[X]:((calm(X)|wise(X))))=>(?[X]:((brave(X)<~>curious(X)))))&
(![X]:((strong(X)|~creative(X))<=>(~creative(X)|curious(X))))&
(![X]:((humble(X)&tall(X))<=>wise(X)))&
(((~kind(paul)&quiet(paul)))=>(?[X]:((old(X)|~quiet(X)))))&
(![X]:((quiet(X)<~>patient(X))=>(curious(X)|rich(X))))&
(![X]:(~brave(X)=>(calm(X)|~brave(X))))&
(![X]:(~happy(X)=>(~tall(X)|~brave(X))))&
(![X]:((~patient(X)|~generous(X))<=>(~calm(X)&~patient(X))))&
((?[X]:((happy(X)&~patient(X))))=>(tall(mary)))&
(![X]:(patient(X)<=>(~brave(X)<~>curious(X))))&
(![X]:(~curious(X)=>(generous(X)<~>~humble(X))))&
(((~calm(alice)|~creative(alice)))<=>((~funny(susan)|~old(susan))))&
(~creative(paul))&
((~quiet(paul)<~>~strong(paul)))&
(?[X]:((happy(X)|wise(X))))&
(?[X]:((~strong(X)|~kind(X))))&
((~calm(alice)|kind(alice)))&
((quiet(fred)<~>creative(fred)))&
(?[X]:(strong(X))) | ~rich(paul) | [
"p0",
"p3",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4674238452360612543422544
% SZS output start Proof for 4674238452360612543422544
1. ! [X0] : (~generous(X0) <=> ~curious(X0)) [input p0]
4. ! [X0] : ((~rich(X0) | patient(X0)) <=> (~curious(X0) | ~brave(X0))) [input p3]
12. ! [X0] : ((~generous(X0) | ~patient(X0)) <=> (~patient(X0) & ~calm(X0))) [input p11]
14. ! [X0] : (patient(X0) <=> (~brave(X0) <~> curious(X0))) [input p13]
24. rich(paul) [input hypothesis]
37. ! [X0] : ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0))) [nnf transformation 1]
47. ! [X0] : (((~rich(X0) | patient(X0)) | (curious(X0) & brave(X0))) & ((~curious(X0) | ~brave(X0)) | (rich(X0) & ~patient(X0)))) [nnf transformation 4]
48. ! [X0] : ((~rich(X0) | patient(X0) | (curious(X0) & brave(X0))) & (~curious(X0) | ~brave(X0) | (rich(X0) & ~patient(X0)))) [flattening 47]
60. ! [X0] : (((~generous(X0) | ~patient(X0)) | (patient(X0) | calm(X0))) & ((~patient(X0) & ~calm(X0)) | (generous(X0) & patient(X0)))) [nnf transformation 12]
61. ! [X0] : ((~generous(X0) | ~patient(X0) | patient(X0) | calm(X0)) & ((~patient(X0) & ~calm(X0)) | (generous(X0) & patient(X0)))) [flattening 60]
62. ! [X0] : ((patient(X0) | ((~brave(X0) | ~curious(X0)) & (curious(X0) | brave(X0)))) & (((~curious(X0) | brave(X0)) & (curious(X0) | ~brave(X0))) | ~patient(X0))) [nnf transformation 14]
75. ~generous(X0) | curious(X0) [cnf transformation 37]
85. ~brave(X0) | ~curious(X0) | ~patient(X0) [cnf transformation 48]
87. ~rich(X0) | patient(X0) | brave(X0) [cnf transformation 48]
88. ~rich(X0) | patient(X0) | curious(X0) [cnf transformation 48]
108. ~patient(X0) | generous(X0) [cnf transformation 61]
112. ~curious(X0) | brave(X0) | ~patient(X0) [cnf transformation 62]
114. patient(X0) | ~brave(X0) | ~curious(X0) [cnf transformation 62]
130. rich(paul) [cnf transformation 24]
224. ~brave(X0) | ~curious(X0) [subsumption resolution 114,85]
225. ~patient(X0) | ~curious(X0) [subsumption resolution 112,85]
306. patient(paul) | brave(paul) [resolution 87,130]
308. 34 <=> brave(paul) [avatar definition]
310. brave(paul) <- (34) [avatar component clause 308]
312. 35 <=> patient(paul) [avatar definition]
314. patient(paul) <- (35) [avatar component clause 312]
315. 34 | 35 [avatar split clause 306,312,308]
316. patient(paul) | curious(paul) [resolution 88,130]
318. 36 <=> curious(paul) [avatar definition]
319. ~curious(paul) <- (~36) [avatar component clause 318]
321. 36 | 35 [avatar split clause 316,312,318]
325. ~curious(paul) <- (34) [resolution 310,224]
328. ~36 | ~34 [avatar split clause 325,308,318]
341. ~curious(paul) <- (35) [resolution 314,225]
342. generous(paul) <- (35) [resolution 314,108]
343. ~36 | ~35 [avatar split clause 341,312,318]
382. curious(paul) <- (35) [resolution 342,75]
383. $false <- (35, ~36) [subsumption resolution 382,319]
384. ~35 | 36 [avatar contradiction clause 383]
385. $false [avatar sat refutation 315,321,328,343,384]
% SZS output end Proof for 4674238452360612543422544
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and not quiet is not generous or not quiet and vice versa. If alice is both not humble and not tall then someone is quiet or humble. If john is either not kind or humble then someone is either old or not kind. Everyone who is funny is not brave or not kind. If someone is both not happy and creative then lucy is both brave and patient and vice versa. Everyone who is happy or not tall is not creative or wise. Everyone who is either curious or kind is both old and not curious. If someone is either not curious or wise then john is either wise or not quiet. If alice is not kind then fred is either strong or not curious and vice versa. If susan is both tall and rich then someone is both not generous and not calm and vice versa. Everyone who is both not patient and quiet is not curious. Everyone who is not generous or patient is both old and kind. Everyone who is both wise and tall is both strong and tall and vice versa. Everyone who is not kind is curious or not generous. Everyone who is either not strong or humble is strong or happy and vice versa. If someone is both strong and not calm then paul is happy. Someone is not happy. Someone is both generous and rich. Alice is both humble and kind. Someone is either not creative or not patient. Alice is either not rich or funny. Someone is both not strong and humble. Susan is both not happy and not rich. | Susan is not humble. | contradiction | (![X]:((~old(X)&~quiet(X))<=>(~generous(X)|~quiet(X))))&
(((~humble(alice)&~tall(alice)))=>(?[X]:((quiet(X)|humble(X)))))&
(((~kind(john)<~>humble(john)))=>(?[X]:((old(X)<~>~kind(X)))))&
(![X]:(funny(X)=>(~brave(X)|~kind(X))))&
((?[X]:((~happy(X)&creative(X))))<=>((brave(lucy)&patient(lucy))))&
(![X]:((happy(X)|~tall(X))=>(~creative(X)|wise(X))))&
(![X]:((curious(X)<~>kind(X))=>(old(X)&~curious(X))))&
((?[X]:((~curious(X)<~>wise(X))))=>((wise(john)<~>~quiet(john))))&
((~kind(alice))<=>((strong(fred)<~>~curious(fred))))&
(((tall(susan)&rich(susan)))<=>(?[X]:((~generous(X)&~calm(X)))))&
(![X]:((~patient(X)&quiet(X))=>~curious(X)))&
(![X]:((~generous(X)|patient(X))=>(old(X)&kind(X))))&
(![X]:((wise(X)&tall(X))<=>(strong(X)&tall(X))))&
(![X]:(~kind(X)=>(curious(X)|~generous(X))))&
(![X]:((~strong(X)<~>humble(X))<=>(strong(X)|happy(X))))&
((?[X]:((strong(X)&~calm(X))))=>(happy(paul)))&
(?[X]:(~happy(X)))&
(?[X]:((generous(X)&rich(X))))&
((humble(alice)&kind(alice)))&
(?[X]:((~creative(X)<~>~patient(X))))&
((~rich(alice)<~>funny(alice)))&
(?[X]:((~strong(X)&humble(X))))&
((~happy(susan)&~rich(susan))) | ~humble(susan) | [
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7872467947953424596194131
% SZS output start Proof for 7872467947953424596194131
15. ! [X0] : ((~strong(X0) <~> humble(X0)) <=> (happy(X0) | strong(X0))) [input p14]
23. ~rich(susan) & ~happy(susan) [input p22]
24. ~humble(susan) [input hypothesis]
62. ! [X0] : ((((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | (~happy(X0) & ~strong(X0))) & ((happy(X0) | strong(X0)) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0))))) [nnf transformation 15]
63. ! [X0] : ((((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | (~happy(X0) & ~strong(X0))) & (happy(X0) | strong(X0) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0))))) [flattening 62]
117. happy(X0) | strong(X0) | humble(X0) | strong(X0) [cnf transformation 63]
119. humble(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 63]
135. ~happy(susan) [cnf transformation 23]
137. ~humble(susan) [cnf transformation 24]
138. happy(X0) | strong(X0) | humble(X0) [duplicate literal removal 117]
139. ~strong(X0) | humble(X0) [duplicate literal removal 119]
261. happy(X0) | humble(X0) [subsumption resolution 138,139]
305. humble(susan) [resolution 261,135]
307. $false [subsumption resolution 305,137]
% SZS output end Proof for 7872467947953424596194131
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not generous and patient then fred is strong. If paul is humble or not brave then alice is not curious and vice versa. If mary is both humble and not tall then fred is either rich or not strong. If susan is rich or creative then someone is not brave. Everyone who is either curious or old is both rich and brave and vice versa. If mary is either calm or not quiet then someone is brave or not creative and vice versa. Everyone who is both not creative and not tall is humble and vice versa. If lucy is either kind or calm then paul is not quiet. Everyone who is generous or funny is both strong and patient and vice versa. If lucy is both curious and patient then lucy is not tall. If someone is either not strong or funny then someone is not generous or humble and vice versa. Everyone who is not funny or creative is both not humble and wise and vice versa. Everyone who is both not patient and old is both funny and not humble. Everyone who is either not strong or not happy is old or not humble. Everyone who is either not happy or tall is not curious or creative and vice versa. Everyone who is calm or not old is patient and vice versa. Someone is both curious and quiet. Someone is not generous. Susan is not strong. John is both not tall and not kind. Someone is either not kind or rich. Someone is not old or not creative. Someone is not wise or calm. | Lucy is tall. | neutral | (((~generous(mary)&patient(mary)))=>(strong(fred)))&
(((humble(paul)|~brave(paul)))<=>(~curious(alice)))&
(((humble(mary)&~tall(mary)))=>((rich(fred)<~>~strong(fred))))&
(((rich(susan)|creative(susan)))=>(?[X]:(~brave(X))))&
(![X]:((curious(X)<~>old(X))<=>(rich(X)&brave(X))))&
(((calm(mary)<~>~quiet(mary)))<=>(?[X]:((brave(X)|~creative(X)))))&
(![X]:((~creative(X)&~tall(X))<=>humble(X)))&
(((kind(lucy)<~>calm(lucy)))=>(~quiet(paul)))&
(![X]:((generous(X)|funny(X))<=>(strong(X)&patient(X))))&
(((curious(lucy)&patient(lucy)))=>(~tall(lucy)))&
((?[X]:((~strong(X)<~>funny(X))))<=>(?[X]:((~generous(X)|humble(X)))))&
(![X]:((~funny(X)|creative(X))<=>(~humble(X)&wise(X))))&
(![X]:((~patient(X)&old(X))=>(funny(X)&~humble(X))))&
(![X]:((~strong(X)<~>~happy(X))=>(old(X)|~humble(X))))&
(![X]:((~happy(X)<~>tall(X))<=>(~curious(X)|creative(X))))&
(![X]:((calm(X)|~old(X))<=>patient(X)))&
(?[X]:((curious(X)&quiet(X))))&
(?[X]:(~generous(X)))&
(~strong(susan))&
((~tall(john)&~kind(john)))&
(?[X]:((~kind(X)<~>rich(X))))&
(?[X]:((~old(X)|~creative(X))))&
(?[X]:((~wise(X)|calm(X)))) | tall(lucy) | [] | null | 0 |
Everyone who is not creative is both not calm and old. If fred is either strong or not happy then someone is not curious and vice versa. If someone is both curious and not tall then someone is not quiet or not brave and vice versa. Everyone who is either not old or funny is either happy or not calm and vice versa. Everyone who is not strong is not brave or not old and vice versa. Everyone who is either humble or not wise is not patient. If paul is not wise then paul is both humble and patient and vice versa. If mary is either not wise or not curious then john is creative or not rich and vice versa. Everyone who is not funny is both not kind and calm and vice versa. Everyone who is either curious or old is either not kind or not happy and vice versa. If someone is wise then someone is humble. Everyone who is both calm and creative is not humble. Everyone who is both quiet and humble is either rich or tall. Everyone who is either not patient or brave is both not calm and patient. If fred is not happy or happy then someone is funny and vice versa. If someone is not generous or quiet then someone is funny or humble. Someone is either not tall or curious. Someone is tall. Someone is either not happy or not tall. Alice is either not brave or funny. Fred is not funny. Paul is rich. Someone is not generous or tall. Someone is either not old or quiet. | Fred is not creative. | contradiction | (![X]:(~creative(X)=>(~calm(X)&old(X))))&
(((strong(fred)<~>~happy(fred)))<=>(?[X]:(~curious(X))))&
((?[X]:((curious(X)&~tall(X))))<=>(?[X]:((~quiet(X)|~brave(X)))))&
(![X]:((~old(X)<~>funny(X))<=>(happy(X)<~>~calm(X))))&
(![X]:(~strong(X)<=>(~brave(X)|~old(X))))&
(![X]:((humble(X)<~>~wise(X))=>~patient(X)))&
((~wise(paul))<=>((humble(paul)&patient(paul))))&
(((~wise(mary)<~>~curious(mary)))<=>((creative(john)|~rich(john))))&
(![X]:(~funny(X)<=>(~kind(X)&calm(X))))&
(![X]:((curious(X)<~>old(X))<=>(~kind(X)<~>~happy(X))))&
((?[X]:(wise(X)))=>(?[X]:(humble(X))))&
(![X]:((calm(X)&creative(X))=>~humble(X)))&
(![X]:((quiet(X)&humble(X))=>(rich(X)<~>tall(X))))&
(![X]:((~patient(X)<~>brave(X))=>(~calm(X)&patient(X))))&
(((~happy(fred)|happy(fred)))<=>(?[X]:(funny(X))))&
((?[X]:((~generous(X)|quiet(X))))=>(?[X]:((funny(X)|humble(X)))))&
(?[X]:((~tall(X)<~>curious(X))))&
(?[X]:(tall(X)))&
(?[X]:((~happy(X)<~>~tall(X))))&
((~brave(alice)<~>funny(alice)))&
(~funny(fred))&
(rich(paul))&
(?[X]:((~generous(X)|tall(X))))&
(?[X]:((~old(X)<~>quiet(X)))) | ~creative(fred) | [
"p0",
"p8",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3743737515286651936347941
% SZS output start Proof for 3743737515286651936347941
1. ! [X0] : (~creative(X0) => (old(X0) & ~calm(X0))) [input p0]
9. ! [X0] : (~funny(X0) <=> (calm(X0) & ~kind(X0))) [input p8]
21. ~funny(fred) [input p20]
25. ~creative(fred) [input hypothesis]
29. ! [X0] : ((old(X0) & ~calm(X0)) | creative(X0)) [ennf transformation 1]
55. ! [X0] : ((~funny(X0) | (~calm(X0) | kind(X0))) & ((calm(X0) & ~kind(X0)) | funny(X0))) [nnf transformation 9]
56. ! [X0] : ((~funny(X0) | ~calm(X0) | kind(X0)) & ((calm(X0) & ~kind(X0)) | funny(X0))) [flattening 55]
85. ~calm(X0) | creative(X0) [cnf transformation 29]
119. funny(X0) | calm(X0) [cnf transformation 56]
149. ~funny(fred) [cnf transformation 21]
154. ~creative(fred) [cnf transformation 25]
322. calm(fred) [resolution 119,149]
324. creative(fred) [resolution 322,85]
325. $false [subsumption resolution 324,154]
% SZS output end Proof for 3743737515286651936347941
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and not creative is either brave or not brave and vice versa.
If someone is either tall or not old then fred is not old.
If mary is both not funny and rich then someone is not tall and vice versa.
If someone is humble then fred is not brave or not strong and vice versa.
If someone is both not calm and not wise then someone is strong or not kind.
If someone is either rich or not quiet then susan is not humble or not generous.
Everyone who is not humble or quiet is both not humble and old and vice versa.
If john is not wise then someone is strong.
Everyone who is both strong and not happy is either not brave or quiet and vice versa.
If someone is not patient or humble then alice is both curious and calm.
Everyone who is either not tall or curious is not generous or not creative and vice versa.
Everyone who is wise or patient is not generous or not curious.
Everyone who is both not generous and rich is creative or not funny and vice versa.
Everyone who is not calm is not quiet or happy and vice versa.
If someone is both not kind and strong then someone is both not creative and not wise and vice versa.
Everyone who is wise or not rich is not patient and vice versa.
Someone is either not rich or old.
Susan is both kind and not curious.
Alice is not funny or not creative.
Paul is not strong or not wise.
Someone is both not humble and calm.
Someone is generous or not curious.
Mary is not wise.
Someone is both not patient and not happy. | Mary is funny. | contradiction | (![X]:((~generous(X)&~creative(X))<=>(brave(X)<~>~brave(X))))&
((?[X]:((tall(X)<~>~old(X))))=>(~old(fred)))&
(((~funny(mary)&rich(mary)))<=>(?[X]:(~tall(X))))&
((?[X]:(humble(X)))<=>((~brave(fred)|~strong(fred))))&
((?[X]:((~calm(X)&~wise(X))))=>(?[X]:((strong(X)|~kind(X)))))&
((?[X]:((rich(X)<~>~quiet(X))))=>((~humble(susan)|~generous(susan))))&
(![X]:((~humble(X)|quiet(X))<=>(~humble(X)&old(X))))&
((~wise(john))=>(?[X]:(strong(X))))&
(![X]:((strong(X)&~happy(X))<=>(~brave(X)<~>quiet(X))))&
((?[X]:((~patient(X)|humble(X))))=>((curious(alice)&calm(alice))))&
(![X]:((~tall(X)<~>curious(X))<=>(~generous(X)|~creative(X))))&
(![X]:((wise(X)|patient(X))=>(~generous(X)|~curious(X))))&
(![X]:((~generous(X)&rich(X))<=>(creative(X)|~funny(X))))&
(![X]:(~calm(X)<=>(~quiet(X)|happy(X))))&
((?[X]:((~kind(X)&strong(X))))<=>(?[X]:((~creative(X)&~wise(X)))))&
(![X]:((wise(X)|~rich(X))<=>~patient(X)))&
(?[X]:((~rich(X)<~>old(X))))&
((kind(susan)&~curious(susan)))&
((~funny(alice)|~creative(alice)))&
((~strong(paul)|~wise(paul)))&
(?[X]:((~humble(X)&calm(X))))&
(?[X]:((generous(X)|~curious(X))))&
(~wise(mary))&
(?[X]:((~patient(X)&~happy(X)))) | funny(mary) | [
"p0",
"p2",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 663984301238443893728309
% SZS output start Proof for 663984301238443893728309
1. ! [X0] : ((~creative(X0) & ~generous(X0)) <=> (brave(X0) <~> ~brave(X0))) [input p0]
3. (rich(mary) & ~funny(mary)) <=> ? [X0] : ~tall(X0) [input p2]
11. ! [X0] : ((~tall(X0) <~> curious(X0)) <=> (~creative(X0) | ~generous(X0))) [input p10]
18. ~curious(susan) & kind(susan) [input p17]
25. funny(mary) [input hypothesis]
38. ! [X0] : (((~creative(X0) & ~generous(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | (creative(X0) | generous(X0)))) [nnf transformation 1]
39. ! [X0] : (((~creative(X0) & ~generous(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | creative(X0) | generous(X0))) [flattening 38]
41. ((rich(mary) & ~funny(mary)) | ! [X0] : tall(X0)) & (? [X0] : ~tall(X0) | (~rich(mary) | funny(mary))) [nnf transformation 3]
42. ((rich(mary) & ~funny(mary)) | ! [X0] : tall(X0)) & (? [X0] : ~tall(X0) | ~rich(mary) | funny(mary)) [flattening 41]
43. ((rich(mary) & ~funny(mary)) | ! [X0] : tall(X0)) & (? [X1] : ~tall(X1) | ~rich(mary) | funny(mary)) [rectify 42]
44. ? [X1] : ~tall(X1) => ~tall(sK0) [choice axiom]
45. ((rich(mary) & ~funny(mary)) | ! [X0] : tall(X0)) & (~tall(sK0) | ~rich(mary) | funny(mary)) [skolemisation 43,44]
61. ! [X0] : ((((~curious(X0) | tall(X0)) & (curious(X0) | ~tall(X0))) | (creative(X0) & generous(X0))) & ((~creative(X0) | ~generous(X0)) | ((~tall(X0) | ~curious(X0)) & (curious(X0) | tall(X0))))) [nnf transformation 11]
62. ! [X0] : ((((~curious(X0) | tall(X0)) & (curious(X0) | ~tall(X0))) | (creative(X0) & generous(X0))) & (~creative(X0) | ~generous(X0) | ((~tall(X0) | ~curious(X0)) & (curious(X0) | tall(X0))))) [flattening 61]
85. ~creative(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 39]
86. ~creative(X0) | brave(X0) | brave(X0) [cnf transformation 39]
90. ~funny(mary) | tall(X0) [cnf transformation 45]
117. curious(X0) | ~tall(X0) | creative(X0) [cnf transformation 62]
139. ~curious(susan) [cnf transformation 18]
148. funny(mary) [cnf transformation 25]
151. ~creative(X0) | ~brave(X0) [duplicate literal removal 85]
152. ~creative(X0) | brave(X0) [duplicate literal removal 86]
153. ~creative(X0) [subsumption resolution 151,152]
168. 4 <=> ! [X0] : tall(X0) [avatar definition]
169. tall(X0) <- (4) [avatar component clause 168]
176. 6 <=> funny(mary) [avatar definition]
179. 4 | ~6 [avatar split clause 90,176,168]
240. ~tall(X0) | curious(X0) [subsumption resolution 117,153]
286. 6 [avatar split clause 148,176]
308. curious(X0) <- (4) [resolution 240,169]
310. $false <- (4) [resolution 308,139]
314. ~4 [avatar contradiction clause 310]
315. $false [avatar sat refutation 179,286,314]
% SZS output end Proof for 663984301238443893728309
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not wise then someone is not tall.
If fred is both funny and not humble then alice is tall or not happy and vice versa.
Everyone who is both wise and generous is not creative or not funny.
If someone is either humble or not brave then lucy is not quiet or not brave and vice versa.
If someone is not wise or not patient then alice is both wise and not creative and vice versa.
Everyone who is both not quiet and tall is either curious or funny.
If someone is either strong or happy then someone is not quiet or kind and vice versa.
Everyone who is not generous is both generous and strong.
Everyone who is either not generous or not strong is generous or wise and vice versa.
If someone is not patient then someone is either not wise or strong and vice versa.
Everyone who is not rich is not strong or not wise and vice versa.
Everyone who is both curious and creative is patient and vice versa.
If paul is both not happy and curious then someone is both not generous and not kind and vice versa.
Everyone who is not patient is old or creative.
Everyone who is both generous and tall is both kind and not humble.
If someone is brave then fred is both not quiet and not tall and vice versa.
Someone is happy or not curious.
Someone is not humble.
Someone is not quiet.
Someone is either creative or not old.
Mary is kind or not curious.
Someone is old or quiet.
Someone is not patient.
Lucy is both not funny and generous. | Susan is not generous. | contradiction | ((~wise(susan))=>(?[X]:(~tall(X))))&
(((funny(fred)&~humble(fred)))<=>((tall(alice)|~happy(alice))))&
(![X]:((wise(X)&generous(X))=>(~creative(X)|~funny(X))))&
((?[X]:((humble(X)<~>~brave(X))))<=>((~quiet(lucy)|~brave(lucy))))&
((?[X]:((~wise(X)|~patient(X))))<=>((wise(alice)&~creative(alice))))&
(![X]:((~quiet(X)&tall(X))=>(curious(X)<~>funny(X))))&
((?[X]:((strong(X)<~>happy(X))))<=>(?[X]:((~quiet(X)|kind(X)))))&
(![X]:(~generous(X)=>(generous(X)&strong(X))))&
(![X]:((~generous(X)<~>~strong(X))<=>(generous(X)|wise(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~wise(X)<~>strong(X)))))&
(![X]:(~rich(X)<=>(~strong(X)|~wise(X))))&
(![X]:((curious(X)&creative(X))<=>patient(X)))&
(((~happy(paul)&curious(paul)))<=>(?[X]:((~generous(X)&~kind(X)))))&
(![X]:(~patient(X)=>(old(X)|creative(X))))&
(![X]:((generous(X)&tall(X))=>(kind(X)&~humble(X))))&
((?[X]:(brave(X)))<=>((~quiet(fred)&~tall(fred))))&
(?[X]:((happy(X)|~curious(X))))&
(?[X]:(~humble(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((creative(X)<~>~old(X))))&
((kind(mary)|~curious(mary)))&
(?[X]:((old(X)|quiet(X))))&
(?[X]:(~patient(X)))&
((~funny(lucy)&generous(lucy))) | ~generous(susan) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 443069370651589337721755
% SZS output start Proof for 443069370651589337721755
8. ! [X0] : (~generous(X0) => (strong(X0) & generous(X0))) [input p7]
25. ~generous(susan) [input hypothesis]
33. ! [X0] : ((strong(X0) & generous(X0)) | generous(X0)) [ennf transformation 8]
116. generous(X0) | generous(X0) [cnf transformation 33]
151. ~generous(susan) [cnf transformation 25]
154. generous(X0) [duplicate literal removal 116]
353. $false [subsumption resolution 151,154]
% SZS output end Proof for 443069370651589337721755
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not strong and strong then someone is both calm and not brave and vice versa.
If mary is either not tall or not funny then mary is both happy and not humble.
Everyone who is calm or not tall is both rich and not old.
If someone is patient or generous then lucy is both generous and not funny.
If paul is both not calm and not patient then someone is either strong or curious and vice versa.
Everyone who is either not curious or not brave is either creative or not happy.
If fred is either not humble or not creative then lucy is both not generous and humble.
Everyone who is creative or not tall is not happy.
Everyone who is both not old and strong is either calm or brave and vice versa.
If someone is both brave and not calm then someone is either not wise or creative and vice versa.
Everyone who is both not strong and not curious is creative and vice versa.
If paul is both brave and not kind then someone is not old or not funny and vice versa.
Everyone who is generous or strong is both rich and kind.
If fred is brave or generous then mary is generous or calm.
Someone is not wise.
Someone is happy or not generous.
Someone is not brave or not rich.
Someone is either not quiet or not funny.
Someone is either not happy or not tall.
Someone is wise or humble. | Mary is tall. | entailment | ((?[X]:((~strong(X)&strong(X))))<=>(?[X]:((calm(X)&~brave(X)))))&
(((~tall(mary)<~>~funny(mary)))=>((happy(mary)&~humble(mary))))&
(![X]:((calm(X)|~tall(X))=>(rich(X)&~old(X))))&
((?[X]:((patient(X)|generous(X))))=>((generous(lucy)&~funny(lucy))))&
(((~calm(paul)&~patient(paul)))<=>(?[X]:((strong(X)<~>curious(X)))))&
(![X]:((~curious(X)<~>~brave(X))=>(creative(X)<~>~happy(X))))&
(((~humble(fred)<~>~creative(fred)))=>((~generous(lucy)&humble(lucy))))&
(![X]:((creative(X)|~tall(X))=>~happy(X)))&
(![X]:((~old(X)&strong(X))<=>(calm(X)<~>brave(X))))&
((?[X]:((brave(X)&~calm(X))))<=>(?[X]:((~wise(X)<~>creative(X)))))&
(![X]:((~strong(X)&~curious(X))<=>creative(X)))&
(((brave(paul)&~kind(paul)))<=>(?[X]:((~old(X)|~funny(X)))))&
(![X]:((generous(X)|strong(X))=>(rich(X)&kind(X))))&
(((brave(fred)|generous(fred)))=>((generous(mary)|calm(mary))))&
(?[X]:(~wise(X)))&
(?[X]:((happy(X)|~generous(X))))&
(?[X]:((~brave(X)|~rich(X))))&
(?[X]:((~quiet(X)<~>~funny(X))))&
(?[X]:((~happy(X)<~>~tall(X))))&
(?[X]:((wise(X)|humble(X)))) | tall(mary) | [
"p1",
"p2",
"p4",
"p5",
"p7",
"p8",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 9150640079082644109394535
% SZS output start Proof for 9150640079082644109394535
2. (~tall(mary) <~> ~funny(mary)) => (~humble(mary) & happy(mary)) [input p1]
3. ! [X0] : ((~tall(X0) | calm(X0)) => (~old(X0) & rich(X0))) [input p2]
5. (~patient(paul) & ~calm(paul)) <=> ? [X0] : (strong(X0) <~> curious(X0)) [input p4]
6. ! [X0] : ((~curious(X0) <~> ~brave(X0)) => (creative(X0) <~> ~happy(X0))) [input p5]
8. ! [X0] : ((~tall(X0) | creative(X0)) => ~happy(X0)) [input p7]
9. ! [X0] : ((strong(X0) & ~old(X0)) <=> (calm(X0) <~> brave(X0))) [input p8]
11. ! [X0] : ((~curious(X0) & ~strong(X0)) <=> creative(X0)) [input p10]
12. (~kind(paul) & brave(paul)) <=> ? [X0] : (~funny(X0) | ~old(X0)) [input p11]
13. ! [X0] : ((strong(X0) | generous(X0)) => (kind(X0) & rich(X0))) [input p12]
21. ~tall(mary) [input hypothesis]
24. (~humble(mary) & happy(mary)) | (~tall(mary) <=> ~funny(mary)) [ennf transformation 2]
25. ! [X0] : ((~old(X0) & rich(X0)) | (tall(X0) & ~calm(X0))) [ennf transformation 3]
27. ! [X0] : ((creative(X0) <~> ~happy(X0)) | (~curious(X0) <=> ~brave(X0))) [ennf transformation 6]
29. ! [X0] : (~happy(X0) | (tall(X0) & ~creative(X0))) [ennf transformation 8]
30. ! [X0] : ((kind(X0) & rich(X0)) | (~strong(X0) & ~generous(X0))) [ennf transformation 13]
38. (~humble(mary) & happy(mary)) | ((~tall(mary) | funny(mary)) & (~funny(mary) | tall(mary))) [nnf transformation 24]
39. ((~patient(paul) & ~calm(paul)) | ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (? [X0] : ((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | (patient(paul) | calm(paul))) [nnf transformation 5]
40. ((~patient(paul) & ~calm(paul)) | ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (? [X0] : ((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | patient(paul) | calm(paul)) [flattening 39]
41. ((~patient(paul) & ~calm(paul)) | ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (? [X1] : ((~curious(X1) | ~strong(X1)) & (curious(X1) | strong(X1))) | patient(paul) | calm(paul)) [rectify 40]
42. ? [X1] : ((~curious(X1) | ~strong(X1)) & (curious(X1) | strong(X1))) => ((~curious(sK2) | ~strong(sK2)) & (curious(sK2) | strong(sK2))) [choice axiom]
43. ((~patient(paul) & ~calm(paul)) | ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) & (((~curious(sK2) | ~strong(sK2)) & (curious(sK2) | strong(sK2))) | patient(paul) | calm(paul)) [skolemisation 41,42]
44. ! [X0] : (((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0)))) [nnf transformation 27]
46. ! [X0] : (((strong(X0) & ~old(X0)) | ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0)))) & (((~brave(X0) | ~calm(X0)) & (brave(X0) | calm(X0))) | (~strong(X0) | old(X0)))) [nnf transformation 9]
47. ! [X0] : (((strong(X0) & ~old(X0)) | ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0)))) & (((~brave(X0) | ~calm(X0)) & (brave(X0) | calm(X0))) | ~strong(X0) | old(X0))) [flattening 46]
53. ! [X0] : (((~curious(X0) & ~strong(X0)) | ~creative(X0)) & (creative(X0) | (curious(X0) | strong(X0)))) [nnf transformation 11]
54. ! [X0] : (((~curious(X0) & ~strong(X0)) | ~creative(X0)) & (creative(X0) | curious(X0) | strong(X0))) [flattening 53]
55. ((~kind(paul) & brave(paul)) | ! [X0] : (funny(X0) & old(X0))) & (? [X0] : (~funny(X0) | ~old(X0)) | (kind(paul) | ~brave(paul))) [nnf transformation 12]
56. ((~kind(paul) & brave(paul)) | ! [X0] : (funny(X0) & old(X0))) & (? [X0] : (~funny(X0) | ~old(X0)) | kind(paul) | ~brave(paul)) [flattening 55]
57. ((~kind(paul) & brave(paul)) | ! [X0] : (funny(X0) & old(X0))) & (? [X1] : (~funny(X1) | ~old(X1)) | kind(paul) | ~brave(paul)) [rectify 56]
58. ? [X1] : (~funny(X1) | ~old(X1)) => (~funny(sK5) | ~old(sK5)) [choice axiom]
59. ((~kind(paul) & brave(paul)) | ! [X0] : (funny(X0) & old(X0))) & ((~funny(sK5) | ~old(sK5)) | kind(paul) | ~brave(paul)) [skolemisation 57,58]
78. happy(mary) | ~funny(mary) | tall(mary) [cnf transformation 38]
84. ~old(X0) | ~calm(X0) [cnf transformation 25]
92. ~calm(paul) | curious(X0) | ~strong(X0) [cnf transformation 43]
93. ~calm(paul) | strong(X0) | ~curious(X0) [cnf transformation 43]
98. ~creative(X0) | happy(X0) | ~brave(X0) | curious(X0) [cnf transformation 44]
104. ~creative(X0) | ~happy(X0) [cnf transformation 29]
105. ~happy(X0) | tall(X0) [cnf transformation 29]
107. ~brave(X0) | ~calm(X0) | ~strong(X0) | old(X0) [cnf transformation 47]
111. ~brave(X0) | calm(X0) | strong(X0) [cnf transformation 47]
118. creative(X0) | curious(X0) | strong(X0) [cnf transformation 54]
123. brave(paul) | funny(X0) [cnf transformation 59]
125. ~kind(paul) | funny(X0) [cnf transformation 59]
129. ~strong(X0) | kind(X0) [cnf transformation 30]
140. ~tall(mary) [cnf transformation 21]
151. 3 <=> funny(mary) [avatar definition]
152. ~funny(mary) <- (~3) [avatar component clause 151]
155. 4 <=> tall(mary) [avatar definition]
157. ~tall(mary) <- (~4) [avatar component clause 155]
165. 6 <=> happy(mary) [avatar definition]
167. happy(mary) <- (6) [avatar component clause 165]
169. 4 | ~3 | 6 [avatar split clause 78,165,151,155]
189. 11 <=> ! [X0] : (strong(X0) | ~curious(X0)) [avatar definition]
190. ~curious(X0) | strong(X0) <- (11) [avatar component clause 189]
197. 13 <=> ! [X0] : (curious(X0) | ~strong(X0)) [avatar definition]
198. ~strong(X0) | curious(X0) <- (13) [avatar component clause 197]
201. 14 <=> calm(paul) [avatar definition]
202. calm(paul) <- (14) [avatar component clause 201]
203. ~calm(paul) <- (~14) [avatar component clause 201]
204. 11 | ~14 [avatar split clause 93,201,189]
205. 13 | ~14 [avatar split clause 92,201,197]
233. ~brave(X0) | ~calm(X0) | ~strong(X0) [subsumption resolution 107,84]
266. 27 <=> ! [X0] : funny(X0) [avatar definition]
267. funny(X0) <- (27) [avatar component clause 266]
269. 28 <=> kind(paul) [avatar definition]
271. ~kind(paul) <- (~28) [avatar component clause 269]
272. 27 | ~28 [avatar split clause 125,269,266]
278. 30 <=> brave(paul) [avatar definition]
280. brave(paul) <- (30) [avatar component clause 278]
281. 27 | 30 [avatar split clause 123,278,266]
349. ~4 [avatar split clause 140,155]
352. $false <- (~3, 27) [subsumption resolution 152,267]
353. 3 | ~27 [avatar contradiction clause 352]
358. tall(mary) <- (6) [resolution 105,167]
359. $false <- (~4, 6) [subsumption resolution 358,157]
360. 4 | ~6 [avatar contradiction clause 359]
368. calm(paul) | strong(paul) <- (30) [resolution 111,280]
370. strong(paul) <- (~14, 30) [subsumption resolution 368,203]
372. kind(paul) <- (~14, 30) [resolution 370,129]
374. $false <- (~14, ~28, 30) [subsumption resolution 372,271]
375. 14 | 28 | ~30 [avatar contradiction clause 374]
377. 45 <=> strong(paul) [avatar definition]
378. ~strong(paul) <- (~45) [avatar component clause 377]
394. curious(X2) | strong(X2) | ~happy(X2) [resolution 118,104]
397. ~happy(X2) | curious(X2) <- (13) [subsumption resolution 394,198]
399. ~calm(paul) | ~strong(paul) <- (30) [resolution 233,280]
401. ~strong(paul) <- (14, 30) [subsumption resolution 399,202]
402. ~45 | ~14 | ~30 [avatar split clause 401,278,201,377]
418. happy(X0) | ~brave(X0) | curious(X0) | curious(X0) | strong(X0) [resolution 98,118]
419. happy(X0) | ~brave(X0) | curious(X0) | strong(X0) [duplicate literal removal 418]
420. happy(X0) | ~brave(X0) | curious(X0) <- (13) [subsumption resolution 419,198]
421. ~brave(X0) | curious(X0) <- (13) [subsumption resolution 420,397]
516. curious(paul) <- (13, 30) [resolution 421,280]
519. strong(paul) <- (11, 13, 30) [resolution 516,190]
520. $false <- (11, 13, 30, ~45) [subsumption resolution 519,378]
521. ~11 | ~13 | ~30 | 45 [avatar contradiction clause 520]
522. $false [avatar sat refutation 169,204,205,272,281,349,353,360,375,402,521]
% SZS output end Proof for 9150640079082644109394535
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either old or brave then someone is either not calm or generous and vice versa.
Everyone who is not tall or not curious is both curious and not creative and vice versa.
Everyone who is old or not creative is not calm and vice versa.
Everyone who is not rich is either not strong or happy and vice versa.
If alice is not tall or tall then mary is not happy and vice versa.
Everyone who is kind is both funny and not quiet.
Everyone who is not calm or funny is either not humble or not strong.
Everyone who is not strong is either curious or old.
If john is not generous or not rich then someone is not generous and vice versa.
Everyone who is calm or happy is wise and vice versa.
Everyone who is not funny or wise is rich or not humble and vice versa.
Everyone who is not happy is both not wise and not kind.
If fred is both patient and old then fred is both not curious and wise and vice versa.
Everyone who is either rich or strong is not wise.
If john is not calm then someone is both not strong and funny.
Fred is either tall or not patient.
Someone is either generous or humble.
Fred is either strong or kind.
Susan is funny.
Mary is not patient or humble.
Someone is not creative.
Someone is not curious or funny. | Alice is not strong. | neutral | (((old(paul)<~>brave(paul)))<=>(?[X]:((~calm(X)<~>generous(X)))))&
(![X]:((~tall(X)|~curious(X))<=>(curious(X)&~creative(X))))&
(![X]:((old(X)|~creative(X))<=>~calm(X)))&
(![X]:(~rich(X)<=>(~strong(X)<~>happy(X))))&
(((~tall(alice)|tall(alice)))<=>(~happy(mary)))&
(![X]:(kind(X)=>(funny(X)&~quiet(X))))&
(![X]:((~calm(X)|funny(X))=>(~humble(X)<~>~strong(X))))&
(![X]:(~strong(X)=>(curious(X)<~>old(X))))&
(((~generous(john)|~rich(john)))<=>(?[X]:(~generous(X))))&
(![X]:((calm(X)|happy(X))<=>wise(X)))&
(![X]:((~funny(X)|wise(X))<=>(rich(X)|~humble(X))))&
(![X]:(~happy(X)=>(~wise(X)&~kind(X))))&
(((patient(fred)&old(fred)))<=>((~curious(fred)&wise(fred))))&
(![X]:((rich(X)<~>strong(X))=>~wise(X)))&
((~calm(john))=>(?[X]:((~strong(X)&funny(X)))))&
((tall(fred)<~>~patient(fred)))&
(?[X]:((generous(X)<~>humble(X))))&
((strong(fred)<~>kind(fred)))&
(funny(susan))&
((~patient(mary)|humble(mary)))&
(?[X]:(~creative(X)))&
(?[X]:((~curious(X)|funny(X)))) | ~strong(alice) | [] | null | 0 |
Everyone who is both not quiet and generous is not happy or creative and vice versa.
Everyone who is calm is strong and vice versa.
If someone is not patient then someone is either not curious or not brave.
If fred is not creative or not wise then john is both quiet and rich and vice versa.
Everyone who is either patient or not creative is not curious and vice versa.
Everyone who is both quiet and not tall is old and vice versa.
Everyone who is either rich or old is not humble or not generous and vice versa.
If john is generous then someone is kind or not quiet.
If someone is tall or quiet then susan is tall or calm.
Everyone who is both not generous and funny is both calm and not curious and vice versa.
If someone is not strong then someone is either happy or not strong and vice versa.
Everyone who is humble is either not patient or wise.
If someone is not kind then susan is both tall and not funny and vice versa.
Everyone who is either strong or not brave is kind.
If someone is happy then lucy is humble or not creative.
If mary is not brave or not funny then fred is either happy or wise and vice versa.
Fred is not curious.
Alice is not brave or old.
Someone is not curious.
Someone is either wise or not wise.
Someone is both tall and not kind.
Mary is not old or strong.
Paul is both happy and not calm.
Someone is both not generous and not calm. | Susan is not tall. | contradiction | (![X]:((~quiet(X)&generous(X))<=>(~happy(X)|creative(X))))&
(![X]:(calm(X)<=>strong(X)))&
((?[X]:(~patient(X)))=>(?[X]:((~curious(X)<~>~brave(X)))))&
(((~creative(fred)|~wise(fred)))<=>((quiet(john)&rich(john))))&
(![X]:((patient(X)<~>~creative(X))<=>~curious(X)))&
(![X]:((quiet(X)&~tall(X))<=>old(X)))&
(![X]:((rich(X)<~>old(X))<=>(~humble(X)|~generous(X))))&
((generous(john))=>(?[X]:((kind(X)|~quiet(X)))))&
((?[X]:((tall(X)|quiet(X))))=>((tall(susan)|calm(susan))))&
(![X]:((~generous(X)&funny(X))<=>(calm(X)&~curious(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((happy(X)<~>~strong(X)))))&
(![X]:(humble(X)=>(~patient(X)<~>wise(X))))&
((?[X]:(~kind(X)))<=>((tall(susan)&~funny(susan))))&
(![X]:((strong(X)<~>~brave(X))=>kind(X)))&
((?[X]:(happy(X)))=>((humble(lucy)|~creative(lucy))))&
(((~brave(mary)|~funny(mary)))<=>((happy(fred)<~>wise(fred))))&
(~curious(fred))&
((~brave(alice)|old(alice)))&
(?[X]:(~curious(X)))&
(?[X]:((wise(X)<~>~wise(X))))&
(?[X]:((tall(X)&~kind(X))))&
((~old(mary)|strong(mary)))&
((happy(paul)&~calm(paul)))&
(?[X]:((~generous(X)&~calm(X)))) | ~tall(susan) | [
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3078160154685643872214999
% SZS output start Proof for 3078160154685643872214999
13. ? [X0] : ~kind(X0) <=> (~funny(susan) & tall(susan)) [input p12]
21. ? [X0] : (~kind(X0) & tall(X0)) [input p20]
25. ~tall(susan) [input hypothesis]
60. (? [X0] : ~kind(X0) | (funny(susan) | ~tall(susan))) & ((~funny(susan) & tall(susan)) | ! [X0] : kind(X0)) [nnf transformation 13]
61. (? [X0] : ~kind(X0) | funny(susan) | ~tall(susan)) & ((~funny(susan) & tall(susan)) | ! [X0] : kind(X0)) [flattening 60]
62. (? [X0] : ~kind(X0) | funny(susan) | ~tall(susan)) & ((~funny(susan) & tall(susan)) | ! [X1] : kind(X1)) [rectify 61]
63. ? [X0] : ~kind(X0) => ~kind(sK4) [choice axiom]
64. (~kind(sK4) | funny(susan) | ~tall(susan)) & ((~funny(susan) & tall(susan)) | ! [X1] : kind(X1)) [skolemisation 62,63]
73. ? [X0] : (~kind(X0) & tall(X0)) => (~kind(sK7) & tall(sK7)) [choice axiom]
74. ~kind(sK7) & tall(sK7) [skolemisation 21,73]
117. tall(susan) | kind(X1) [cnf transformation 64]
135. ~kind(sK7) [cnf transformation 74]
141. ~tall(susan) [cnf transformation 25]
193. 12 <=> tall(susan) [avatar definition]
240. 23 <=> ! [X1] : kind(X1) [avatar definition]
241. kind(X1) <- (23) [avatar component clause 240]
243. 23 | 12 [avatar split clause 117,193,240]
292. ~12 [avatar split clause 141,193]
293. $false <- (23) [resolution 241,135]
294. ~23 [avatar contradiction clause 293]
295. $false [avatar sat refutation 243,292,294]
% SZS output end Proof for 3078160154685643872214999
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or creative is not quiet or patient and vice versa. Everyone who is kind or rich is both tall and not calm. Everyone who is wise or curious is quiet or happy. Everyone who is both not wise and creative is both not funny and not creative and vice versa. If susan is brave then lucy is calm or not rich and vice versa. Everyone who is funny is both not curious and curious and vice versa. If someone is not strong then someone is humble. If alice is either curious or generous then someone is old or happy and vice versa. If susan is quiet or old then paul is both not old and curious and vice versa. Everyone who is not creative is either wise or creative. Everyone who is tall or not kind is both happy and wise. Everyone who is creative is calm or not funny. Everyone who is wise is not strong or not rich and vice versa. If someone is patient or not funny then fred is both not generous and patient. Everyone who is both not patient and not tall is calm and vice versa. If someone is both not patient and rich then someone is not curious. Someone is happy. Someone is either brave or not rich. Someone is not quiet or rich. Someone is both not humble and generous. Someone is not quiet. Someone is patient. Someone is not wise or wise. | Lucy is happy. | entailment | (![X]:((~funny(X)|creative(X))<=>(~quiet(X)|patient(X))))&
(![X]:((kind(X)|rich(X))=>(tall(X)&~calm(X))))&
(![X]:((wise(X)|curious(X))=>(quiet(X)|happy(X))))&
(![X]:((~wise(X)&creative(X))<=>(~funny(X)&~creative(X))))&
((brave(susan))<=>((calm(lucy)|~rich(lucy))))&
(![X]:(funny(X)<=>(~curious(X)&curious(X))))&
((?[X]:(~strong(X)))=>(?[X]:(humble(X))))&
(((curious(alice)<~>generous(alice)))<=>(?[X]:((old(X)|happy(X)))))&
(((quiet(susan)|old(susan)))<=>((~old(paul)&curious(paul))))&
(![X]:(~creative(X)=>(wise(X)<~>creative(X))))&
(![X]:((tall(X)|~kind(X))=>(happy(X)&wise(X))))&
(![X]:(creative(X)=>(calm(X)|~funny(X))))&
(![X]:(wise(X)<=>(~strong(X)|~rich(X))))&
((?[X]:((patient(X)|~funny(X))))=>((~generous(fred)&patient(fred))))&
(![X]:((~patient(X)&~tall(X))<=>calm(X)))&
((?[X]:((~patient(X)&rich(X))))=>(?[X]:(~curious(X))))&
(?[X]:(happy(X)))&
(?[X]:((brave(X)<~>~rich(X))))&
(?[X]:((~quiet(X)|rich(X))))&
(?[X]:((~humble(X)&generous(X))))&
(?[X]:(~quiet(X)))&
(?[X]:(patient(X)))&
(?[X]:((~wise(X)|wise(X)))) | happy(lucy) | [
"p1",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1713502529420220553967423
% SZS output start Proof for 1713502529420220553967423
2. ! [X0] : ((rich(X0) | kind(X0)) => (~calm(X0) & tall(X0))) [input p1]
11. ! [X0] : ((~kind(X0) | tall(X0)) => (wise(X0) & happy(X0))) [input p10]
24. ~happy(lucy) [input hypothesis]
27. ! [X0] : ((~calm(X0) & tall(X0)) | (~rich(X0) & ~kind(X0))) [ennf transformation 2]
32. ! [X0] : ((wise(X0) & happy(X0)) | (kind(X0) & ~tall(X0))) [ennf transformation 11]
81. ~kind(X0) | tall(X0) [cnf transformation 27]
111. ~tall(X0) | happy(X0) [cnf transformation 32]
112. happy(X0) | kind(X0) [cnf transformation 32]
136. ~happy(lucy) [cnf transformation 24]
247. kind(lucy) [resolution 112,136]
248. tall(lucy) [resolution 247,81]
249. happy(lucy) [resolution 248,111]
250. $false [subsumption resolution 249,136]
% SZS output end Proof for 1713502529420220553967423
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or not generous is both old and not tall and vice versa.
Everyone who is both tall and not creative is both not funny and quiet and vice versa.
Everyone who is rich or not strong is both not funny and not patient and vice versa.
Everyone who is curious is either not quiet or not rich.
If someone is both not wise and brave then alice is either tall or not wise and vice versa.
Everyone who is creative or not funny is not old or funny.
Everyone who is creative or not creative is not generous or not old and vice versa.
Everyone who is not generous is patient or not rich and vice versa.
If lucy is both not patient and creative then someone is calm.
Everyone who is not humble is either not creative or not tall.
If paul is either calm or not strong then someone is not quiet and vice versa.
If fred is not rich or not curious then alice is happy.
If someone is rich then paul is not humble and vice versa.
If mary is either curious or not strong then lucy is either not happy or not calm and vice versa.
Everyone who is creative is both quiet and humble and vice versa.
If mary is both not kind and creative then someone is not kind or happy and vice versa.
Mary is not brave.
John is not creative.
Paul is both not kind and not brave.
Alice is either funny or curious.
Someone is wise.
Alice is either wise or not calm.
Someone is both not generous and not tall. | Paul is happy. | neutral | (![X]:((~strong(X)|~generous(X))<=>(old(X)&~tall(X))))&
(![X]:((tall(X)&~creative(X))<=>(~funny(X)&quiet(X))))&
(![X]:((rich(X)|~strong(X))<=>(~funny(X)&~patient(X))))&
(![X]:(curious(X)=>(~quiet(X)<~>~rich(X))))&
((?[X]:((~wise(X)&brave(X))))<=>((tall(alice)<~>~wise(alice))))&
(![X]:((creative(X)|~funny(X))=>(~old(X)|funny(X))))&
(![X]:((creative(X)|~creative(X))<=>(~generous(X)|~old(X))))&
(![X]:(~generous(X)<=>(patient(X)|~rich(X))))&
(((~patient(lucy)&creative(lucy)))=>(?[X]:(calm(X))))&
(![X]:(~humble(X)=>(~creative(X)<~>~tall(X))))&
(((calm(paul)<~>~strong(paul)))<=>(?[X]:(~quiet(X))))&
(((~rich(fred)|~curious(fred)))=>(happy(alice)))&
((?[X]:(rich(X)))<=>(~humble(paul)))&
(((curious(mary)<~>~strong(mary)))<=>((~happy(lucy)<~>~calm(lucy))))&
(![X]:(creative(X)<=>(quiet(X)&humble(X))))&
(((~kind(mary)&creative(mary)))<=>(?[X]:((~kind(X)|happy(X)))))&
(~brave(mary))&
(~creative(john))&
((~kind(paul)&~brave(paul)))&
((funny(alice)<~>curious(alice)))&
(?[X]:(wise(X)))&
((wise(alice)<~>~calm(alice)))&
(?[X]:((~generous(X)&~tall(X)))) | happy(paul) | [] | null | 0 |
Everyone who is not generous or strong is both not calm and creative.
If fred is both creative and not tall then mary is not quiet.
Everyone who is either calm or funny is not generous and vice versa.
If someone is not rich or tall then someone is both happy and not funny and vice versa.
If someone is old then alice is both patient and happy.
Everyone who is not strong or calm is both brave and not kind and vice versa.
If lucy is both wise and old then john is both not creative and patient and vice versa.
Everyone who is tall is both not funny and generous.
Everyone who is either funny or rich is kind.
If someone is both happy and not wise then someone is both not calm and not brave and vice versa.
Everyone who is not tall is both not creative and generous.
If lucy is either brave or not wise then fred is both curious and not brave.
If paul is not patient then susan is not humble or funny and vice versa.
Everyone who is both not quiet and not happy is both not strong and tall.
If someone is both humble and tall then susan is either old or strong and vice versa.
Paul is not brave or not curious.
Someone is happy or tall.
Someone is both brave and not old.
Lucy is both strong and not funny.
Someone is both creative and not funny. | Susan is not calm. | neutral | (![X]:((~generous(X)|strong(X))=>(~calm(X)&creative(X))))&
(((creative(fred)&~tall(fred)))=>(~quiet(mary)))&
(![X]:((calm(X)<~>funny(X))<=>~generous(X)))&
((?[X]:((~rich(X)|tall(X))))<=>(?[X]:((happy(X)&~funny(X)))))&
((?[X]:(old(X)))=>((patient(alice)&happy(alice))))&
(![X]:((~strong(X)|calm(X))<=>(brave(X)&~kind(X))))&
(((wise(lucy)&old(lucy)))<=>((~creative(john)&patient(john))))&
(![X]:(tall(X)=>(~funny(X)&generous(X))))&
(![X]:((funny(X)<~>rich(X))=>kind(X)))&
((?[X]:((happy(X)&~wise(X))))<=>(?[X]:((~calm(X)&~brave(X)))))&
(![X]:(~tall(X)=>(~creative(X)&generous(X))))&
(((brave(lucy)<~>~wise(lucy)))=>((curious(fred)&~brave(fred))))&
((~patient(paul))<=>((~humble(susan)|funny(susan))))&
(![X]:((~quiet(X)&~happy(X))=>(~strong(X)&tall(X))))&
((?[X]:((humble(X)&tall(X))))<=>((old(susan)<~>strong(susan))))&
((~brave(paul)|~curious(paul)))&
(?[X]:((happy(X)|tall(X))))&
(?[X]:((brave(X)&~old(X))))&
((strong(lucy)&~funny(lucy)))&
(?[X]:((creative(X)&~funny(X)))) | ~calm(susan) | [] | null | 0 |
Everyone who is tall is funny and vice versa.
Everyone who is not tall or kind is both happy and funny.
If someone is either not rich or not old then someone is not tall and vice versa.
Everyone who is not rich is wise or humble and vice versa.
If susan is both rich and not funny then someone is either not kind or not rich.
Everyone who is both funny and old is both not brave and not old and vice versa.
Everyone who is calm is generous.
If someone is not tall or not strong then someone is either patient or kind and vice versa.
If lucy is rich then someone is calm or not wise and vice versa.
Everyone who is curious is either not generous or rich and vice versa.
Everyone who is either not wise or not happy is either curious or not calm.
Everyone who is not brave or not strong is either creative or not patient.
If someone is either rich or not rich then john is both not strong and funny.
Everyone who is quiet is either not happy or kind and vice versa.
Everyone who is either not funny or humble is either not old or happy.
Everyone who is not happy or old is either not kind or tall.
Someone is not generous or not happy.
Mary is not quiet or not kind.
Someone is both happy and curious.
Someone is both creative and brave.
Paul is either calm or not old.
Someone is either not curious or patient. | Susan is creative. | neutral | (![X]:(tall(X)<=>funny(X)))&
(![X]:((~tall(X)|kind(X))=>(happy(X)&funny(X))))&
((?[X]:((~rich(X)<~>~old(X))))<=>(?[X]:(~tall(X))))&
(![X]:(~rich(X)<=>(wise(X)|humble(X))))&
(((rich(susan)&~funny(susan)))=>(?[X]:((~kind(X)<~>~rich(X)))))&
(![X]:((funny(X)&old(X))<=>(~brave(X)&~old(X))))&
(![X]:(calm(X)=>generous(X)))&
((?[X]:((~tall(X)|~strong(X))))<=>(?[X]:((patient(X)<~>kind(X)))))&
((rich(lucy))<=>(?[X]:((calm(X)|~wise(X)))))&
(![X]:(curious(X)<=>(~generous(X)<~>rich(X))))&
(![X]:((~wise(X)<~>~happy(X))=>(curious(X)<~>~calm(X))))&
(![X]:((~brave(X)|~strong(X))=>(creative(X)<~>~patient(X))))&
((?[X]:((rich(X)<~>~rich(X))))=>((~strong(john)&funny(john))))&
(![X]:(quiet(X)<=>(~happy(X)<~>kind(X))))&
(![X]:((~funny(X)<~>humble(X))=>(~old(X)<~>happy(X))))&
(![X]:((~happy(X)|old(X))=>(~kind(X)<~>tall(X))))&
(?[X]:((~generous(X)|~happy(X))))&
((~quiet(mary)|~kind(mary)))&
(?[X]:((happy(X)&curious(X))))&
(?[X]:((creative(X)&brave(X))))&
((calm(paul)<~>~old(paul)))&
(?[X]:((~curious(X)<~>patient(X)))) | creative(susan) | [] | null | 0 |
Everyone who is both wise and not quiet is rich. If susan is rich then mary is either funny or not old. If susan is both tall and calm then paul is curious and vice versa. Everyone who is either not wise or not humble is either wise or not old. Everyone who is not old is wise. Everyone who is either not quiet or not happy is brave and vice versa. If susan is both not patient and quiet then someone is not patient or rich. Everyone who is not happy is not curious and vice versa. Everyone who is both rich and calm is either happy or calm and vice versa. Everyone who is both tall and generous is either not funny or not wise and vice versa. If john is both not humble and not creative then susan is either not strong or happy and vice versa. If someone is either old or humble then someone is not quiet and vice versa. If john is generous or not wise then john is either not tall or curious and vice versa. If susan is either curious or not happy then mary is strong or happy and vice versa. Everyone who is both generous and not curious is not kind or not rich and vice versa. Everyone who is both quiet and curious is both not happy and not old. Someone is not wise or patient. Fred is not funny or wise. Someone is either curious or brave. Paul is both quiet and funny. Someone is not curious or not funny. Someone is strong or not old. Fred is not creative or not wise. Paul is happy or humble. | Paul is brave. | entailment | (![X]:((wise(X)&~quiet(X))=>rich(X)))&
((rich(susan))=>((funny(mary)<~>~old(mary))))&
(((tall(susan)&calm(susan)))<=>(curious(paul)))&
(![X]:((~wise(X)<~>~humble(X))=>(wise(X)<~>~old(X))))&
(![X]:(~old(X)=>wise(X)))&
(![X]:((~quiet(X)<~>~happy(X))<=>brave(X)))&
(((~patient(susan)&quiet(susan)))=>(?[X]:((~patient(X)|rich(X)))))&
(![X]:(~happy(X)<=>~curious(X)))&
(![X]:((rich(X)&calm(X))<=>(happy(X)<~>calm(X))))&
(![X]:((tall(X)&generous(X))<=>(~funny(X)<~>~wise(X))))&
(((~humble(john)&~creative(john)))<=>((~strong(susan)<~>happy(susan))))&
((?[X]:((old(X)<~>humble(X))))<=>(?[X]:(~quiet(X))))&
(((generous(john)|~wise(john)))<=>((~tall(john)<~>curious(john))))&
(((curious(susan)<~>~happy(susan)))<=>((strong(mary)|happy(mary))))&
(![X]:((generous(X)&~curious(X))<=>(~kind(X)|~rich(X))))&
(![X]:((quiet(X)&curious(X))=>(~happy(X)&~old(X))))&
(?[X]:((~wise(X)|patient(X))))&
((~funny(fred)|wise(fred)))&
(?[X]:((curious(X)<~>brave(X))))&
((quiet(paul)&funny(paul)))&
(?[X]:((~curious(X)|~funny(X))))&
(?[X]:((strong(X)|~old(X))))&
((~creative(fred)|~wise(fred)))&
((happy(paul)|humble(paul))) | brave(paul) | [
"p5",
"p7",
"p8",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7485575434848318127355
% SZS output start Proof for 7485575434848318127355
6. ! [X0] : ((~quiet(X0) <~> ~happy(X0)) <=> brave(X0)) [input p5]
8. ! [X0] : (~happy(X0) <=> ~curious(X0)) [input p7]
9. ! [X0] : ((calm(X0) & rich(X0)) <=> (happy(X0) <~> calm(X0))) [input p8]
15. ! [X0] : ((~curious(X0) & generous(X0)) <=> (~rich(X0) | ~kind(X0))) [input p14]
20. funny(paul) & quiet(paul) [input p19]
25. ~brave(paul) [input hypothesis]
40. ! [X0] : ((((happy(X0) | quiet(X0)) & (~happy(X0) | ~quiet(X0))) | ~brave(X0)) & (brave(X0) | ((~quiet(X0) | happy(X0)) & (~happy(X0) | quiet(X0))))) [nnf transformation 6]
43. ! [X0] : ((~happy(X0) | curious(X0)) & (~curious(X0) | happy(X0))) [nnf transformation 8]
44. ! [X0] : (((calm(X0) & rich(X0)) | ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0)))) & (((~calm(X0) | ~happy(X0)) & (calm(X0) | happy(X0))) | (~calm(X0) | ~rich(X0)))) [nnf transformation 9]
45. ! [X0] : (((calm(X0) & rich(X0)) | ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0)))) & (((~calm(X0) | ~happy(X0)) & (calm(X0) | happy(X0))) | ~calm(X0) | ~rich(X0))) [flattening 44]
59. ! [X0] : (((~curious(X0) & generous(X0)) | (rich(X0) & kind(X0))) & ((~rich(X0) | ~kind(X0)) | (curious(X0) | ~generous(X0)))) [nnf transformation 15]
60. ! [X0] : (((~curious(X0) & generous(X0)) | (rich(X0) & kind(X0))) & (~rich(X0) | ~kind(X0) | curious(X0) | ~generous(X0))) [flattening 59]
82. ~quiet(X0) | brave(X0) | happy(X0) [cnf transformation 40]
87. ~happy(X0) | curious(X0) [cnf transformation 43]
89. ~calm(X0) | ~happy(X0) | ~calm(X0) | ~rich(X0) [cnf transformation 45]
92. calm(X0) | calm(X0) | ~happy(X0) [cnf transformation 45]
126. ~curious(X0) | rich(X0) [cnf transformation 60]
133. quiet(paul) [cnf transformation 20]
139. ~brave(paul) [cnf transformation 25]
140. ~calm(X0) | ~happy(X0) | ~rich(X0) [duplicate literal removal 89]
141. ~happy(X0) | calm(X0) [duplicate literal removal 92]
159. 4 <=> curious(paul) [avatar definition]
160. curious(paul) <- (4) [avatar component clause 159]
190. ~happy(X0) | ~rich(X0) [subsumption resolution 140,141]
329. 39 <=> happy(paul) [avatar definition]
330. ~happy(paul) <- (~39) [avatar component clause 329]
331. happy(paul) <- (39) [avatar component clause 329]
341. curious(paul) <- (39) [resolution 87,331]
345. 4 | ~39 [avatar split clause 341,329,159]
350. rich(paul) <- (4) [resolution 126,160]
353. ~rich(paul) <- (39) [resolution 190,331]
355. $false <- (4, 39) [subsumption resolution 353,350]
356. ~4 | ~39 [avatar contradiction clause 355]
370. brave(paul) | happy(paul) [resolution 82,133]
371. happy(paul) [subsumption resolution 370,139]
372. $false <- (~39) [subsumption resolution 371,330]
373. 39 [avatar contradiction clause 372]
374. $false [avatar sat refutation 345,356,373]
% SZS output end Proof for 7485575434848318127355
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not generous and kind is either humble or wise. Everyone who is not tall or patient is not happy or happy and vice versa. If someone is both not rich and not curious then susan is both not funny and not wise. Everyone who is not tall is not brave or old. If john is quiet then someone is either generous or not quiet. If someone is not strong or not funny then lucy is either brave or not strong. Everyone who is either not tall or happy is not patient and vice versa. If alice is either not funny or wise then susan is both not generous and not patient and vice versa. Everyone who is brave or creative is calm and vice versa. Everyone who is not kind or wise is not tall. Everyone who is generous or not creative is not quiet or calm. Everyone who is both wise and not rich is either not tall or not patient. Everyone who is not tall is not calm. Everyone who is either not brave or not tall is not curious and vice versa. If susan is either not funny or happy then someone is both not happy and not funny and vice versa. Everyone who is both not curious and rich is brave and vice versa. Someone is generous or strong. John is either humble or not calm. Paul is generous. Someone is not brave or not kind. Susan is rich. Susan is not calm or creative. Someone is both not patient and not rich. | Susan is creative. | contradiction | (![X]:((~generous(X)&kind(X))=>(humble(X)<~>wise(X))))&
(![X]:((~tall(X)|patient(X))<=>(~happy(X)|happy(X))))&
((?[X]:((~rich(X)&~curious(X))))=>((~funny(susan)&~wise(susan))))&
(![X]:(~tall(X)=>(~brave(X)|old(X))))&
((quiet(john))=>(?[X]:((generous(X)<~>~quiet(X)))))&
((?[X]:((~strong(X)|~funny(X))))=>((brave(lucy)<~>~strong(lucy))))&
(![X]:((~tall(X)<~>happy(X))<=>~patient(X)))&
(((~funny(alice)<~>wise(alice)))<=>((~generous(susan)&~patient(susan))))&
(![X]:((brave(X)|creative(X))<=>calm(X)))&
(![X]:((~kind(X)|wise(X))=>~tall(X)))&
(![X]:((generous(X)|~creative(X))=>(~quiet(X)|calm(X))))&
(![X]:((wise(X)&~rich(X))=>(~tall(X)<~>~patient(X))))&
(![X]:(~tall(X)=>~calm(X)))&
(![X]:((~brave(X)<~>~tall(X))<=>~curious(X)))&
(((~funny(susan)<~>happy(susan)))<=>(?[X]:((~happy(X)&~funny(X)))))&
(![X]:((~curious(X)&rich(X))<=>brave(X)))&
(?[X]:((generous(X)|strong(X))))&
((humble(john)<~>~calm(john)))&
(generous(paul))&
(?[X]:((~brave(X)|~kind(X))))&
(rich(susan))&
((~calm(susan)|creative(susan)))&
(?[X]:((~patient(X)&~rich(X)))) | creative(susan) | [
"p8",
"p12",
"p13",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1641859721100542450185376
% SZS output start Proof for 1641859721100542450185376
9. ! [X0] : ((creative(X0) | brave(X0)) <=> calm(X0)) [input p8]
13. ! [X0] : (~tall(X0) => ~calm(X0)) [input p12]
14. ! [X0] : ((~brave(X0) <~> ~tall(X0)) <=> ~curious(X0)) [input p13]
16. ! [X0] : ((rich(X0) & ~curious(X0)) <=> brave(X0)) [input p15]
21. rich(susan) [input p20]
24. creative(susan) [input hypothesis]
36. ! [X0] : (~calm(X0) | tall(X0)) [ennf transformation 13]
47. ! [X0] : (((creative(X0) | brave(X0)) | ~calm(X0)) & (calm(X0) | (~creative(X0) & ~brave(X0)))) [nnf transformation 9]
48. ! [X0] : ((creative(X0) | brave(X0) | ~calm(X0)) & (calm(X0) | (~creative(X0) & ~brave(X0)))) [flattening 47]
50. ! [X0] : ((((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | curious(X0)) & (~curious(X0) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0))))) [nnf transformation 14]
55. ! [X0] : (((rich(X0) & ~curious(X0)) | ~brave(X0)) & (brave(X0) | (~rich(X0) | curious(X0)))) [nnf transformation 16]
56. ! [X0] : (((rich(X0) & ~curious(X0)) | ~brave(X0)) & (brave(X0) | ~rich(X0) | curious(X0))) [flattening 55]
89. ~creative(X0) | calm(X0) [cnf transformation 48]
97. ~calm(X0) | tall(X0) [cnf transformation 36]
98. ~curious(X0) | ~tall(X0) | brave(X0) [cnf transformation 50]
100. ~brave(X0) | ~tall(X0) | curious(X0) [cnf transformation 50]
108. ~rich(X0) | brave(X0) | curious(X0) [cnf transformation 56]
109. ~brave(X0) | ~curious(X0) [cnf transformation 56]
116. rich(susan) [cnf transformation 21]
120. creative(susan) [cnf transformation 24]
243. 25 <=> calm(susan) [avatar definition]
244. calm(susan) <- (25) [avatar component clause 243]
247. 26 <=> creative(susan) [avatar definition]
249. creative(susan) <- (26) [avatar component clause 247]
251. 26 [avatar split clause 120,247]
252. calm(susan) <- (26) [resolution 89,249]
253. 25 | ~26 [avatar split clause 252,247,243]
254. tall(susan) <- (25) [resolution 97,244]
316. brave(susan) | curious(susan) [resolution 108,116]
318. 31 <=> curious(susan) [avatar definition]
320. curious(susan) <- (31) [avatar component clause 318]
322. 32 <=> brave(susan) [avatar definition]
324. brave(susan) <- (32) [avatar component clause 322]
325. 31 | 32 [avatar split clause 316,322,318]
332. ~tall(susan) | brave(susan) <- (31) [resolution 320,98]
333. brave(susan) <- (25, 31) [subsumption resolution 332,254]
334. 32 | ~25 | ~31 [avatar split clause 333,318,243,322]
335. ~tall(susan) | curious(susan) <- (32) [resolution 324,100]
338. ~curious(susan) <- (32) [resolution 324,109]
342. ~31 | ~32 [avatar split clause 338,322,318]
343. curious(susan) <- (25, 32) [subsumption resolution 335,254]
344. 31 | ~25 | ~32 [avatar split clause 343,322,243,318]
345. $false [avatar sat refutation 251,253,325,334,342,344]
% SZS output end Proof for 1641859721100542450185376
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not rich is both not tall and not old.
Everyone who is not quiet is not curious or humble and vice versa.
Everyone who is either patient or not patient is both rich and wise and vice versa.
Everyone who is either not strong or not rich is not kind or not funny and vice versa.
If someone is quiet then someone is either patient or not wise and vice versa.
Everyone who is both wise and calm is either old or not patient and vice versa.
If fred is either quiet or happy then lucy is both humble and creative.
If someone is either strong or rich then someone is not funny and vice versa.
If someone is not humble then someone is not quiet.
Everyone who is brave or wise is both old and not funny and vice versa.
Everyone who is both not old and wise is both wise and quiet.
Everyone who is curious is wise.
Everyone who is both tall and funny is either not strong or not humble.
If someone is either not patient or wise then fred is either not strong or wise.
If paul is either not generous or rich then fred is generous and vice versa.
If paul is both kind and strong then someone is either not brave or brave.
Someone is both tall and rich.
Susan is not curious.
Mary is both not funny and creative.
Susan is either brave or not strong.
Someone is not strong or not generous.
Someone is not funny.
Someone is both not calm and not patient.
Mary is not strong. | Mary is patient. | contradiction | (![X]:((generous(X)&~rich(X))=>(~tall(X)&~old(X))))&
(![X]:(~quiet(X)<=>(~curious(X)|humble(X))))&
(![X]:((patient(X)<~>~patient(X))<=>(rich(X)&wise(X))))&
(![X]:((~strong(X)<~>~rich(X))<=>(~kind(X)|~funny(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((patient(X)<~>~wise(X)))))&
(![X]:((wise(X)&calm(X))<=>(old(X)<~>~patient(X))))&
(((quiet(fred)<~>happy(fred)))=>((humble(lucy)&creative(lucy))))&
((?[X]:((strong(X)<~>rich(X))))<=>(?[X]:(~funny(X))))&
((?[X]:(~humble(X)))=>(?[X]:(~quiet(X))))&
(![X]:((brave(X)|wise(X))<=>(old(X)&~funny(X))))&
(![X]:((~old(X)&wise(X))=>(wise(X)&quiet(X))))&
(![X]:(curious(X)=>wise(X)))&
(![X]:((tall(X)&funny(X))=>(~strong(X)<~>~humble(X))))&
((?[X]:((~patient(X)<~>wise(X))))=>((~strong(fred)<~>wise(fred))))&
(((~generous(paul)<~>rich(paul)))<=>(generous(fred)))&
(((kind(paul)&strong(paul)))=>(?[X]:((~brave(X)<~>brave(X)))))&
(?[X]:((tall(X)&rich(X))))&
(~curious(susan))&
((~funny(mary)&creative(mary)))&
((brave(susan)<~>~strong(susan)))&
(?[X]:((~strong(X)|~generous(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~calm(X)&~patient(X))))&
(~strong(mary)) | patient(mary) | [
"p2",
"p3",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3806469277426788257572371
% SZS output start Proof for 3806469277426788257572371
3. ! [X0] : ((patient(X0) <~> ~patient(X0)) <=> (wise(X0) & rich(X0))) [input p2]
4. ! [X0] : ((~strong(X0) <~> ~rich(X0)) <=> (~funny(X0) | ~kind(X0))) [input p3]
10. ! [X0] : ((wise(X0) | brave(X0)) <=> (~funny(X0) & old(X0))) [input p9]
14. ? [X0] : (~patient(X0) <~> wise(X0)) => (~strong(fred) <~> wise(fred)) [input p13]
25. patient(mary) [input hypothesis]
40. (~strong(fred) <~> wise(fred)) | ! [X0] : (~patient(X0) <=> wise(X0)) [ennf transformation 14]
45. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | (~wise(X0) | ~rich(X0))) & ((wise(X0) & rich(X0)) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [nnf transformation 3]
46. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | ~wise(X0) | ~rich(X0)) & ((wise(X0) & rich(X0)) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [flattening 45]
47. ! [X0] : ((((rich(X0) | strong(X0)) & (~rich(X0) | ~strong(X0))) | (funny(X0) & kind(X0))) & ((~funny(X0) | ~kind(X0)) | ((~strong(X0) | rich(X0)) & (~rich(X0) | strong(X0))))) [nnf transformation 4]
48. ! [X0] : ((((rich(X0) | strong(X0)) & (~rich(X0) | ~strong(X0))) | (funny(X0) & kind(X0))) & (~funny(X0) | ~kind(X0) | ((~strong(X0) | rich(X0)) & (~rich(X0) | strong(X0))))) [flattening 47]
65. ! [X0] : (((wise(X0) | brave(X0)) | (funny(X0) | ~old(X0))) & ((~funny(X0) & old(X0)) | (~wise(X0) & ~brave(X0)))) [nnf transformation 10]
66. ! [X0] : ((wise(X0) | brave(X0) | funny(X0) | ~old(X0)) & ((~funny(X0) & old(X0)) | (~wise(X0) & ~brave(X0)))) [flattening 65]
68. ((~wise(fred) | strong(fred)) & (wise(fred) | ~strong(fred))) | ! [X0] : ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0))) [nnf transformation 40]
87. rich(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 46]
88. rich(X0) | patient(X0) | patient(X0) [cnf transformation 46]
89. wise(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 46]
90. wise(X0) | patient(X0) | patient(X0) [cnf transformation 46]
96. ~rich(X0) | ~strong(X0) | funny(X0) [cnf transformation 48]
119. ~funny(X0) | ~wise(X0) [cnf transformation 66]
129. ~wise(fred) | strong(fred) | ~patient(X0) | ~wise(X0) [cnf transformation 68]
147. patient(mary) [cnf transformation 25]
148. rich(X0) | ~patient(X0) [duplicate literal removal 87]
149. patient(X0) | rich(X0) [duplicate literal removal 88]
150. wise(X0) | ~patient(X0) [duplicate literal removal 89]
151. wise(X0) | patient(X0) [duplicate literal removal 90]
152. wise(X0) [subsumption resolution 150,151]
153. rich(X0) [subsumption resolution 148,149]
154. ~strong(X0) | funny(X0) [subsumption resolution 96,153]
159. 1 <=> ! [X1] : ~patient(X1) [avatar definition]
160. ~patient(X1) <- (1) [avatar component clause 159]
217. ~funny(X0) [subsumption resolution 119,152]
219. strong(fred) | ~patient(X0) | ~wise(X0) [subsumption resolution 129,152]
220. strong(fred) | ~patient(X0) [subsumption resolution 219,152]
222. 14 <=> strong(fred) [avatar definition]
224. strong(fred) <- (14) [avatar component clause 222]
225. 1 | 14 [avatar split clause 220,222,159]
259. $false <- (1) [resolution 160,147]
260. ~1 [avatar contradiction clause 259]
263. funny(fred) <- (14) [resolution 154,224]
264. $false <- (14) [subsumption resolution 263,217]
265. ~14 [avatar contradiction clause 264]
266. $false [avatar sat refutation 225,260,265]
% SZS output end Proof for 3806469277426788257572371
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not happy or not rich then someone is both not strong and happy and vice versa.
Everyone who is both not kind and not old is funny or not strong.
Everyone who is not calm is either not rich or wise and vice versa.
If mary is brave then someone is both happy and kind and vice versa.
Everyone who is either patient or not funny is funny and vice versa.
Everyone who is either wise or not funny is humble or patient and vice versa.
If someone is both generous and not funny then john is either happy or not generous and vice versa.
Everyone who is both not rich and not brave is not rich or not happy and vice versa.
Everyone who is both humble and rich is either kind or not brave and vice versa.
Everyone who is either funny or rich is brave or wise and vice versa.
If someone is generous then fred is happy.
If fred is calm or not creative then fred is both not curious and not old.
If mary is either not tall or happy then alice is either funny or not creative.
Everyone who is not old or curious is either not patient or not tall and vice versa.
If susan is not strong then alice is generous.
Everyone who is calm or not kind is humble and vice versa.
John is not funny or tall.
Paul is not patient or calm.
John is funny.
Paul is generous or not kind.
Someone is rich.
Someone is both not curious and rich.
Someone is rich or wise. | Fred is not happy. | contradiction | (((~happy(mary)|~rich(mary)))<=>(?[X]:((~strong(X)&happy(X)))))&
(![X]:((~kind(X)&~old(X))=>(funny(X)|~strong(X))))&
(![X]:(~calm(X)<=>(~rich(X)<~>wise(X))))&
((brave(mary))<=>(?[X]:((happy(X)&kind(X)))))&
(![X]:((patient(X)<~>~funny(X))<=>funny(X)))&
(![X]:((wise(X)<~>~funny(X))<=>(humble(X)|patient(X))))&
((?[X]:((generous(X)&~funny(X))))<=>((happy(john)<~>~generous(john))))&
(![X]:((~rich(X)&~brave(X))<=>(~rich(X)|~happy(X))))&
(![X]:((humble(X)&rich(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((funny(X)<~>rich(X))<=>(brave(X)|wise(X))))&
((?[X]:(generous(X)))=>(happy(fred)))&
(((calm(fred)|~creative(fred)))=>((~curious(fred)&~old(fred))))&
(((~tall(mary)<~>happy(mary)))=>((funny(alice)<~>~creative(alice))))&
(![X]:((~old(X)|curious(X))<=>(~patient(X)<~>~tall(X))))&
((~strong(susan))=>(generous(alice)))&
(![X]:((calm(X)|~kind(X))<=>humble(X)))&
((~funny(john)|tall(john)))&
((~patient(paul)|calm(paul)))&
(funny(john))&
((generous(paul)|~kind(paul)))&
(?[X]:(rich(X)))&
(?[X]:((~curious(X)&rich(X))))&
(?[X]:((rich(X)|wise(X)))) | ~happy(fred) | [
"p4",
"p5",
"p7",
"p8",
"p9",
"p10",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5870870355441637179826657
% SZS output start Proof for 5870870355441637179826657
5. ! [X0] : ((patient(X0) <~> ~funny(X0)) <=> funny(X0)) [input p4]
6. ! [X0] : ((wise(X0) <~> ~funny(X0)) <=> (patient(X0) | humble(X0))) [input p5]
8. ! [X0] : ((~brave(X0) & ~rich(X0)) <=> (~happy(X0) | ~rich(X0))) [input p7]
9. ! [X0] : ((rich(X0) & humble(X0)) <=> (kind(X0) <~> ~brave(X0))) [input p8]
10. ! [X0] : ((funny(X0) <~> rich(X0)) <=> (wise(X0) | brave(X0))) [input p9]
11. ? [X0] : generous(X0) => happy(fred) [input p10]
16. ! [X0] : ((~kind(X0) | calm(X0)) <=> humble(X0)) [input p15]
20. ~kind(paul) | generous(paul) [input p19]
24. ~happy(fred) [input hypothesis]
27. happy(fred) | ! [X0] : ~generous(X0) [ennf transformation 11]
41. ! [X0] : ((((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | ~funny(X0)) & (funny(X0) | ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0))))) [nnf transformation 5]
42. ! [X0] : ((((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | (~patient(X0) & ~humble(X0))) & ((patient(X0) | humble(X0)) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0))))) [nnf transformation 6]
43. ! [X0] : ((((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | (~patient(X0) & ~humble(X0))) & (patient(X0) | humble(X0) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0))))) [flattening 42]
48. ! [X0] : (((~brave(X0) & ~rich(X0)) | (happy(X0) & rich(X0))) & ((~happy(X0) | ~rich(X0)) | (brave(X0) | rich(X0)))) [nnf transformation 8]
49. ! [X0] : (((~brave(X0) & ~rich(X0)) | (happy(X0) & rich(X0))) & (~happy(X0) | ~rich(X0) | brave(X0) | rich(X0))) [flattening 48]
50. ! [X0] : (((rich(X0) & humble(X0)) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | (~rich(X0) | ~humble(X0)))) [nnf transformation 9]
51. ! [X0] : (((rich(X0) & humble(X0)) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | ~rich(X0) | ~humble(X0))) [flattening 50]
52. ! [X0] : ((((~rich(X0) | ~funny(X0)) & (rich(X0) | funny(X0))) | (~wise(X0) & ~brave(X0))) & ((wise(X0) | brave(X0)) | ((funny(X0) | ~rich(X0)) & (rich(X0) | ~funny(X0))))) [nnf transformation 10]
53. ! [X0] : ((((~rich(X0) | ~funny(X0)) & (rich(X0) | funny(X0))) | (~wise(X0) & ~brave(X0))) & (wise(X0) | brave(X0) | ((funny(X0) | ~rich(X0)) & (rich(X0) | ~funny(X0))))) [flattening 52]
57. ! [X0] : (((~kind(X0) | calm(X0)) | ~humble(X0)) & (humble(X0) | (kind(X0) & ~calm(X0)))) [nnf transformation 16]
58. ! [X0] : ((~kind(X0) | calm(X0) | ~humble(X0)) & (humble(X0) | (kind(X0) & ~calm(X0)))) [flattening 57]
79. funny(X0) | patient(X0) | funny(X0) [cnf transformation 41]
80. ~funny(X0) | patient(X0) | ~funny(X0) [cnf transformation 41]
85. ~funny(X0) | wise(X0) | ~patient(X0) [cnf transformation 43]
87. funny(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 43]
97. ~brave(X0) | rich(X0) [cnf transformation 49]
99. ~brave(X0) | kind(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 51]
104. rich(X0) | kind(X0) | brave(X0) [cnf transformation 51]
106. wise(X0) | brave(X0) | funny(X0) | ~rich(X0) [cnf transformation 53]
110. ~rich(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 53]
111. happy(fred) | ~generous(X0) [cnf transformation 27]
128. humble(X0) | kind(X0) [cnf transformation 58]
133. ~kind(paul) | generous(paul) [cnf transformation 20]
138. ~happy(fred) [cnf transformation 24]
139. funny(X0) | patient(X0) [duplicate literal removal 79]
140. ~funny(X0) | patient(X0) [duplicate literal removal 80]
183. patient(X0) [subsumption resolution 139,140]
184. ~wise(X0) | funny(X0) [subsumption resolution 87,183]
185. ~funny(X0) | wise(X0) [subsumption resolution 85,183]
211. kind(X0) | rich(X0) [subsumption resolution 104,97]
212. ~humble(X0) | kind(X0) | ~brave(X0) [subsumption resolution 99,97]
213. ~wise(X0) | ~rich(X0) [subsumption resolution 110,184]
215. ~rich(X0) | funny(X0) | brave(X0) [subsumption resolution 106,213]
217. 15 <=> ! [X0] : ~generous(X0) [avatar definition]
218. ~generous(X0) <- (15) [avatar component clause 217]
220. 16 <=> happy(fred) [avatar definition]
223. 15 | 16 [avatar split clause 111,220,217]
284. 28 <=> generous(paul) [avatar definition]
286. generous(paul) <- (28) [avatar component clause 284]
288. 29 <=> kind(paul) [avatar definition]
290. ~kind(paul) <- (~29) [avatar component clause 288]
291. 28 | ~29 [avatar split clause 133,288,284]
301. ~16 [avatar split clause 138,220]
368. kind(X1) | ~brave(X1) | kind(X1) [resolution 212,128]
372. ~brave(X1) | kind(X1) [duplicate literal removal 368]
381. 37 <=> brave(paul) [avatar definition]
383. brave(paul) <- (37) [avatar component clause 381]
385. 38 <=> funny(paul) [avatar definition]
387. funny(paul) <- (38) [avatar component clause 385]
417. 45 <=> rich(paul) [avatar definition]
419. rich(paul) <- (45) [avatar component clause 417]
421. 46 <=> wise(paul) [avatar definition]
422. ~wise(paul) <- (~46) [avatar component clause 421]
423. wise(paul) <- (46) [avatar component clause 421]
425. $false <- (15, 28) [subsumption resolution 286,218]
426. ~15 | ~28 [avatar contradiction clause 425]
427. rich(paul) <- (~29) [resolution 290,211]
428. 45 | 29 [avatar split clause 427,288,417]
466. funny(paul) | brave(paul) <- (45) [resolution 419,215]
471. ~rich(paul) <- (46) [resolution 423,213]
476. $false <- (45, 46) [subsumption resolution 471,419]
477. ~45 | ~46 [avatar contradiction clause 476]
550. kind(paul) <- (37) [resolution 372,383]
554. $false <- (~29, 37) [subsumption resolution 550,290]
555. 29 | ~37 [avatar contradiction clause 554]
556. 37 | 38 | ~45 [avatar split clause 466,417,385,381]
557. wise(paul) <- (38) [resolution 387,185]
559. $false <- (38, ~46) [subsumption resolution 557,422]
560. ~38 | 46 [avatar contradiction clause 559]
561. $false [avatar sat refutation 223,291,301,426,428,477,555,556,560]
% SZS output end Proof for 5870870355441637179826657
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then lucy is generous or not happy and vice versa.
Everyone who is either happy or not rich is either not creative or rich.
If paul is not rich or not patient then someone is brave or tall.
Everyone who is not generous is tall or not old and vice versa.
Everyone who is not generous is both patient and not funny and vice versa.
If paul is humble then someone is either not strong or generous and vice versa.
If someone is curious or not quiet then someone is both not patient and not funny and vice versa.
Everyone who is both calm and quiet is both not happy and not kind and vice versa.
Everyone who is both not humble and brave is generous or creative.
Everyone who is either curious or creative is either brave or not quiet.
Everyone who is both not patient and kind is not rich or not curious.
Everyone who is strong is brave or happy.
If paul is not strong then someone is not quiet and vice versa.
If susan is not strong or creative then lucy is not old or not wise.
If someone is not happy or not creative then alice is both not old and not humble and vice versa.
Everyone who is not rich is patient and vice versa.
Someone is both not happy and calm.
John is not humble or not funny.
Someone is humble or creative.
Susan is quiet.
Mary is strong or old.
Paul is not strong or not patient.
Susan is either tall or not old.
Someone is either not happy or quiet. | Paul is not curious. | neutral | ((?[X]:(~quiet(X)))<=>((generous(lucy)|~happy(lucy))))&
(![X]:((happy(X)<~>~rich(X))=>(~creative(X)<~>rich(X))))&
(((~rich(paul)|~patient(paul)))=>(?[X]:((brave(X)|tall(X)))))&
(![X]:(~generous(X)<=>(tall(X)|~old(X))))&
(![X]:(~generous(X)<=>(patient(X)&~funny(X))))&
((humble(paul))<=>(?[X]:((~strong(X)<~>generous(X)))))&
((?[X]:((curious(X)|~quiet(X))))<=>(?[X]:((~patient(X)&~funny(X)))))&
(![X]:((calm(X)&quiet(X))<=>(~happy(X)&~kind(X))))&
(![X]:((~humble(X)&brave(X))=>(generous(X)|creative(X))))&
(![X]:((curious(X)<~>creative(X))=>(brave(X)<~>~quiet(X))))&
(![X]:((~patient(X)&kind(X))=>(~rich(X)|~curious(X))))&
(![X]:(strong(X)=>(brave(X)|happy(X))))&
((~strong(paul))<=>(?[X]:(~quiet(X))))&
(((~strong(susan)|creative(susan)))=>((~old(lucy)|~wise(lucy))))&
((?[X]:((~happy(X)|~creative(X))))<=>((~old(alice)&~humble(alice))))&
(![X]:(~rich(X)<=>patient(X)))&
(?[X]:((~happy(X)&calm(X))))&
((~humble(john)|~funny(john)))&
(?[X]:((humble(X)|creative(X))))&
(quiet(susan))&
((strong(mary)|old(mary)))&
((~strong(paul)|~patient(paul)))&
((tall(susan)<~>~old(susan)))&
(?[X]:((~happy(X)<~>quiet(X)))) | ~curious(paul) | [] | null | 0 |
If someone is not curious then paul is generous. If someone is both not wise and not brave then someone is both not tall and old. If someone is not quiet or rich then susan is tall. If someone is either not old or not creative then mary is either not happy or not quiet. If susan is both not happy and funny then john is patient and vice versa. If someone is not curious then someone is not wise. Everyone who is either strong or not calm is either rich or not wise. Everyone who is humble or rich is both wise and not quiet and vice versa. If someone is either humble or generous then susan is not humble. Everyone who is either not brave or patient is not old. Everyone who is not creative or generous is not patient or patient and vice versa. If john is not curious then someone is not creative or not generous. If lucy is either not generous or not tall then susan is either funny or not humble and vice versa. If someone is either not wise or tall then susan is not wise. Everyone who is patient or not wise is both curious and rich. If someone is both not patient and not wise then susan is both not generous and not kind and vice versa. Someone is not humble or not calm. Someone is wise or not happy. Fred is curious or not wise. Someone is not humble. Someone is calm or not generous. Someone is not patient. John is both not strong and not generous. Susan is either quiet or calm. | Susan is not quiet. | contradiction | ((?[X]:(~curious(X)))=>(generous(paul)))&
((?[X]:((~wise(X)&~brave(X))))=>(?[X]:((~tall(X)&old(X)))))&
((?[X]:((~quiet(X)|rich(X))))=>(tall(susan)))&
((?[X]:((~old(X)<~>~creative(X))))=>((~happy(mary)<~>~quiet(mary))))&
(((~happy(susan)&funny(susan)))<=>(patient(john)))&
((?[X]:(~curious(X)))=>(?[X]:(~wise(X))))&
(![X]:((strong(X)<~>~calm(X))=>(rich(X)<~>~wise(X))))&
(![X]:((humble(X)|rich(X))<=>(wise(X)&~quiet(X))))&
((?[X]:((humble(X)<~>generous(X))))=>(~humble(susan)))&
(![X]:((~brave(X)<~>patient(X))=>~old(X)))&
(![X]:((~creative(X)|generous(X))<=>(~patient(X)|patient(X))))&
((~curious(john))=>(?[X]:((~creative(X)|~generous(X)))))&
(((~generous(lucy)<~>~tall(lucy)))<=>((funny(susan)<~>~humble(susan))))&
((?[X]:((~wise(X)<~>tall(X))))=>(~wise(susan)))&
(![X]:((patient(X)|~wise(X))=>(curious(X)&rich(X))))&
((?[X]:((~patient(X)&~wise(X))))<=>((~generous(susan)&~kind(susan))))&
(?[X]:((~humble(X)|~calm(X))))&
(?[X]:((wise(X)|~happy(X))))&
((curious(fred)|~wise(fred)))&
(?[X]:(~humble(X)))&
(?[X]:((calm(X)|~generous(X))))&
(?[X]:(~patient(X)))&
((~strong(john)&~generous(john)))&
((quiet(susan)<~>calm(susan))) | ~quiet(susan) | [
"p2",
"p7",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8195152186643067659352223
% SZS output start Proof for 8195152186643067659352223
3. ? [X0] : (rich(X0) | ~quiet(X0)) => tall(susan) [input p2]
8. ! [X0] : ((rich(X0) | humble(X0)) <=> (~quiet(X0) & wise(X0))) [input p7]
14. ? [X0] : (~wise(X0) <~> tall(X0)) => ~wise(susan) [input p13]
15. ! [X0] : ((~wise(X0) | patient(X0)) => (rich(X0) & curious(X0))) [input p14]
25. ~quiet(susan) [input hypothesis]
31. ! [X0] : ((~wise(X0) | patient(X0)) => rich(X0)) [pure predicate removal 15]
34. tall(susan) | ! [X0] : (~rich(X0) & quiet(X0)) [ennf transformation 3]
39. ~wise(susan) | ! [X0] : (~wise(X0) <=> tall(X0)) [ennf transformation 14]
40. ! [X0] : (rich(X0) | (wise(X0) & ~patient(X0))) [ennf transformation 31]
48. ! [X0] : (((rich(X0) | humble(X0)) | (quiet(X0) | ~wise(X0))) & ((~quiet(X0) & wise(X0)) | (~rich(X0) & ~humble(X0)))) [nnf transformation 8]
49. ! [X0] : ((rich(X0) | humble(X0) | quiet(X0) | ~wise(X0)) & ((~quiet(X0) & wise(X0)) | (~rich(X0) & ~humble(X0)))) [flattening 48]
55. ~wise(susan) | ! [X0] : ((~wise(X0) | ~tall(X0)) & (tall(X0) | wise(X0))) [nnf transformation 39]
74. tall(susan) | quiet(X0) [cnf transformation 34]
88. wise(X0) | ~rich(X0) [cnf transformation 49]
109. ~wise(susan) | ~wise(X0) | ~tall(X0) [cnf transformation 55]
111. rich(X0) | wise(X0) [cnf transformation 40]
125. ~quiet(susan) [cnf transformation 25]
143. 5 <=> tall(susan) [avatar definition]
145. tall(susan) <- (5) [avatar component clause 143]
148. 6 <=> ! [X0] : quiet(X0) [avatar definition]
149. quiet(X0) <- (6) [avatar component clause 148]
150. 6 | 5 [avatar split clause 74,143,148]
214. 19 <=> ! [X0] : (~wise(X0) | ~tall(X0)) [avatar definition]
215. ~wise(X0) | ~tall(X0) <- (19) [avatar component clause 214]
217. 20 <=> wise(susan) [avatar definition]
219. ~wise(susan) <- (~20) [avatar component clause 217]
220. 19 | ~20 [avatar split clause 109,217,214]
225. wise(X0) [subsumption resolution 111,88]
260. 29 <=> quiet(susan) [avatar definition]
262. ~quiet(susan) <- (~29) [avatar component clause 260]
269. ~29 [avatar split clause 125,260]
270. $false <- (~20) [subsumption resolution 219,225]
271. 20 [avatar contradiction clause 270]
272. ~tall(X0) <- (19) [subsumption resolution 215,225]
273. $false <- (5, 19) [resolution 272,145]
274. ~5 | ~19 [avatar contradiction clause 273]
276. $false <- (6, ~29) [resolution 149,262]
277. ~6 | 29 [avatar contradiction clause 276]
279. $false [avatar sat refutation 150,220,269,271,274,277]
% SZS output end Proof for 8195152186643067659352223
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not old then john is not funny.
Everyone who is both kind and not humble is curious or rich.
Everyone who is both generous and not brave is either not rich or humble and vice versa.
Everyone who is old is not creative or not old and vice versa.
Everyone who is rich is not strong.
Everyone who is both not rich and happy is either generous or not happy.
If someone is either not humble or wise then fred is either not old or not strong and vice versa.
Everyone who is both curious and creative is both tall and funny.
Everyone who is both not funny and not rich is either not wise or not tall.
If susan is either patient or rich then lucy is wise or quiet and vice versa.
If someone is both strong and not old then someone is either not strong or not patient and vice versa.
If mary is not rich then someone is either not humble or not patient and vice versa.
Everyone who is both curious and old is either quiet or old and vice versa.
Everyone who is both not kind and not happy is not wise.
Everyone who is either not quiet or not old is not old and vice versa.
Everyone who is either not old or not happy is both not creative and old and vice versa.
Someone is not calm or calm.
John is both not brave and not funny.
Someone is either generous or creative.
Lucy is either not happy or not wise.
Someone is both rich and old.
Someone is either humble or not wise.
Mary is brave.
Paul is both generous and brave. | Lucy is not rich. | neutral | ((~old(fred))=>(~funny(john)))&
(![X]:((kind(X)&~humble(X))=>(curious(X)|rich(X))))&
(![X]:((generous(X)&~brave(X))<=>(~rich(X)<~>humble(X))))&
(![X]:(old(X)<=>(~creative(X)|~old(X))))&
(![X]:(rich(X)=>~strong(X)))&
(![X]:((~rich(X)&happy(X))=>(generous(X)<~>~happy(X))))&
((?[X]:((~humble(X)<~>wise(X))))<=>((~old(fred)<~>~strong(fred))))&
(![X]:((curious(X)&creative(X))=>(tall(X)&funny(X))))&
(![X]:((~funny(X)&~rich(X))=>(~wise(X)<~>~tall(X))))&
(((patient(susan)<~>rich(susan)))<=>((wise(lucy)|quiet(lucy))))&
((?[X]:((strong(X)&~old(X))))<=>(?[X]:((~strong(X)<~>~patient(X)))))&
((~rich(mary))<=>(?[X]:((~humble(X)<~>~patient(X)))))&
(![X]:((curious(X)&old(X))<=>(quiet(X)<~>old(X))))&
(![X]:((~kind(X)&~happy(X))=>~wise(X)))&
(![X]:((~quiet(X)<~>~old(X))<=>~old(X)))&
(![X]:((~old(X)<~>~happy(X))<=>(~creative(X)&old(X))))&
(?[X]:((~calm(X)|calm(X))))&
((~brave(john)&~funny(john)))&
(?[X]:((generous(X)<~>creative(X))))&
((~happy(lucy)<~>~wise(lucy)))&
(?[X]:((rich(X)&old(X))))&
(?[X]:((humble(X)<~>~wise(X))))&
(brave(mary))&
((generous(paul)&brave(paul))) | ~rich(lucy) | [] | null | 0 |
If fred is either not creative or not brave then someone is either not rich or not patient and vice versa. Everyone who is both not old and patient is either not happy or rich. Everyone who is either not tall or quiet is both kind and not wise and vice versa. If paul is both rich and not quiet then someone is both not curious and not brave and vice versa. Everyone who is either wise or creative is not tall and vice versa. If mary is not brave or happy then someone is not calm and vice versa. Everyone who is either strong or not creative is either not calm or not strong and vice versa. If alice is not generous then alice is both curious and not strong and vice versa. If alice is either not brave or not wise then lucy is old. Everyone who is not generous or not humble is not curious or patient and vice versa. Everyone who is both humble and not curious is not tall and vice versa. Everyone who is not kind is strong and vice versa. Everyone who is tall or not quiet is both not creative and not curious and vice versa. Everyone who is tall is both rich and not quiet and vice versa. If someone is either not creative or not strong then john is either generous or strong and vice versa. Everyone who is either happy or curious is either kind or tall. Someone is not brave. Lucy is not tall. Paul is either curious or not brave. Someone is not happy. Fred is either not generous or humble. Someone is both generous and not humble. Lucy is both strong and not old. | Paul is not humble. | entailment | (((~creative(fred)<~>~brave(fred)))<=>(?[X]:((~rich(X)<~>~patient(X)))))&
(![X]:((~old(X)&patient(X))=>(~happy(X)<~>rich(X))))&
(![X]:((~tall(X)<~>quiet(X))<=>(kind(X)&~wise(X))))&
(((rich(paul)&~quiet(paul)))<=>(?[X]:((~curious(X)&~brave(X)))))&
(![X]:((wise(X)<~>creative(X))<=>~tall(X)))&
(((~brave(mary)|happy(mary)))<=>(?[X]:(~calm(X))))&
(![X]:((strong(X)<~>~creative(X))<=>(~calm(X)<~>~strong(X))))&
((~generous(alice))<=>((curious(alice)&~strong(alice))))&
(((~brave(alice)<~>~wise(alice)))=>(old(lucy)))&
(![X]:((~generous(X)|~humble(X))<=>(~curious(X)|patient(X))))&
(![X]:((humble(X)&~curious(X))<=>~tall(X)))&
(![X]:(~kind(X)<=>strong(X)))&
(![X]:((tall(X)|~quiet(X))<=>(~creative(X)&~curious(X))))&
(![X]:(tall(X)<=>(rich(X)&~quiet(X))))&
((?[X]:((~creative(X)<~>~strong(X))))<=>((generous(john)<~>strong(john))))&
(![X]:((happy(X)<~>curious(X))=>(kind(X)<~>tall(X))))&
(?[X]:(~brave(X)))&
(~tall(lucy))&
((curious(paul)<~>~brave(paul)))&
(?[X]:(~happy(X)))&
((~generous(fred)<~>humble(fred)))&
(?[X]:((generous(X)&~humble(X))))&
((strong(lucy)&~old(lucy))) | ~humble(paul) | [
"p2",
"p3",
"p4",
"p10",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2302145824920629111414232
% SZS output start Proof for 2302145824920629111414232
3. ! [X0] : ((~tall(X0) <~> quiet(X0)) <=> (~wise(X0) & kind(X0))) [input p2]
4. (~quiet(paul) & rich(paul)) <=> ? [X0] : (~brave(X0) & ~curious(X0)) [input p3]
5. ! [X0] : ((wise(X0) <~> creative(X0)) <=> ~tall(X0)) [input p4]
11. ! [X0] : ((~curious(X0) & humble(X0)) <=> ~tall(X0)) [input p10]
13. ! [X0] : ((~quiet(X0) | tall(X0)) <=> (~curious(X0) & ~creative(X0))) [input p12]
19. curious(paul) <~> ~brave(paul) [input p18]
24. humble(paul) [input hypothesis]
34. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | (wise(X0) | ~kind(X0))) & ((~wise(X0) & kind(X0)) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [nnf transformation 3]
35. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | wise(X0) | ~kind(X0)) & ((~wise(X0) & kind(X0)) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [flattening 34]
36. ((~quiet(paul) & rich(paul)) | ! [X0] : (brave(X0) | curious(X0))) & (? [X0] : (~brave(X0) & ~curious(X0)) | (quiet(paul) | ~rich(paul))) [nnf transformation 4]
37. ((~quiet(paul) & rich(paul)) | ! [X0] : (brave(X0) | curious(X0))) & (? [X0] : (~brave(X0) & ~curious(X0)) | quiet(paul) | ~rich(paul)) [flattening 36]
38. ((~quiet(paul) & rich(paul)) | ! [X0] : (brave(X0) | curious(X0))) & (? [X1] : (~brave(X1) & ~curious(X1)) | quiet(paul) | ~rich(paul)) [rectify 37]
39. ? [X1] : (~brave(X1) & ~curious(X1)) => (~brave(sK1) & ~curious(sK1)) [choice axiom]
40. ((~quiet(paul) & rich(paul)) | ! [X0] : (brave(X0) | curious(X0))) & ((~brave(sK1) & ~curious(sK1)) | quiet(paul) | ~rich(paul)) [skolemisation 38,39]
41. ! [X0] : ((((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | tall(X0)) & (~tall(X0) | ((wise(X0) | ~creative(X0)) & (creative(X0) | ~wise(X0))))) [nnf transformation 5]
53. ! [X0] : (((~curious(X0) & humble(X0)) | tall(X0)) & (~tall(X0) | (curious(X0) | ~humble(X0)))) [nnf transformation 11]
54. ! [X0] : (((~curious(X0) & humble(X0)) | tall(X0)) & (~tall(X0) | curious(X0) | ~humble(X0))) [flattening 53]
56. ! [X0] : (((~quiet(X0) | tall(X0)) | (curious(X0) | creative(X0))) & ((~curious(X0) & ~creative(X0)) | (quiet(X0) & ~tall(X0)))) [nnf transformation 13]
57. ! [X0] : ((~quiet(X0) | tall(X0) | curious(X0) | creative(X0)) & ((~curious(X0) & ~creative(X0)) | (quiet(X0) & ~tall(X0)))) [flattening 56]
67. (brave(paul) | ~curious(paul)) & (~brave(paul) | curious(paul)) [nnf transformation 19]
85. ~wise(X0) | quiet(X0) | tall(X0) [cnf transformation 35]
92. ~quiet(paul) | brave(X0) | curious(X0) [cnf transformation 40]
95. wise(X0) | creative(X0) | tall(X0) [cnf transformation 41]
117. ~humble(X0) | curious(X0) | ~tall(X0) [cnf transformation 54]
119. ~curious(X0) | tall(X0) [cnf transformation 54]
123. ~creative(X0) | quiet(X0) [cnf transformation 57]
124. ~curious(X0) | ~tall(X0) [cnf transformation 57]
144. ~brave(paul) | curious(paul) [cnf transformation 67]
153. humble(paul) [cnf transformation 24]
189. 7 <=> ! [X0] : (brave(X0) | curious(X0)) [avatar definition]
190. brave(X0) | curious(X0) <- (7) [avatar component clause 189]
192. 8 <=> quiet(paul) [avatar definition]
194. ~quiet(paul) <- (~8) [avatar component clause 192]
195. 7 | ~8 [avatar split clause 92,192,189]
261. ~curious(X0) [subsumption resolution 124,119]
294. ~brave(paul) [subsumption resolution 144,261]
308. brave(X0) <- (7) [subsumption resolution 190,261]
309. $false <- (7) [resolution 308,294]
316. ~7 [avatar contradiction clause 309]
370. creative(X2) | tall(X2) | quiet(X2) | tall(X2) [resolution 95,85]
371. creative(X2) | tall(X2) | quiet(X2) [duplicate literal removal 370]
382. quiet(X2) | tall(X2) [subsumption resolution 371,123]
391. tall(paul) <- (~8) [resolution 382,194]
413. curious(paul) | ~tall(paul) [resolution 117,153]
415. ~tall(paul) [subsumption resolution 413,261]
416. $false <- (~8) [subsumption resolution 415,391]
417. 8 [avatar contradiction clause 416]
418. $false [avatar sat refutation 195,316,417]
% SZS output end Proof for 2302145824920629111414232
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not calm or happy then alice is not calm and vice versa.
Everyone who is happy is both not curious and not creative and vice versa.
Everyone who is both strong and creative is wise.
Everyone who is rich is not patient.
Everyone who is both not humble and not kind is not happy.
Everyone who is both curious and not wise is not brave and vice versa.
If someone is either not funny or not creative then paul is both not curious and not calm.
Everyone who is not patient or not wise is either not patient or not creative and vice versa.
Everyone who is not strong is rich.
If someone is both wise and happy then mary is both rich and happy and vice versa.
Everyone who is both generous and patient is either curious or creative.
Everyone who is not strong is not calm or strong and vice versa.
Everyone who is both strong and humble is creative.
If susan is wise or not funny then someone is either quiet or not rich and vice versa.
If john is either quiet or not patient then someone is both not quiet and not humble.
If someone is either not strong or patient then someone is either not rich or wise and vice versa.
Mary is kind.
Someone is both generous and kind.
Lucy is either not rich or not wise.
Alice is strong or tall.
Susan is not happy.
Someone is rich.
Susan is not quiet.
Someone is curious or quiet. | Mary is not strong. | entailment | (((~calm(mary)|happy(mary)))<=>(~calm(alice)))&
(![X]:(happy(X)<=>(~curious(X)&~creative(X))))&
(![X]:((strong(X)&creative(X))=>wise(X)))&
(![X]:(rich(X)=>~patient(X)))&
(![X]:((~humble(X)&~kind(X))=>~happy(X)))&
(![X]:((curious(X)&~wise(X))<=>~brave(X)))&
((?[X]:((~funny(X)<~>~creative(X))))=>((~curious(paul)&~calm(paul))))&
(![X]:((~patient(X)|~wise(X))<=>(~patient(X)<~>~creative(X))))&
(![X]:(~strong(X)=>rich(X)))&
((?[X]:((wise(X)&happy(X))))<=>((rich(mary)&happy(mary))))&
(![X]:((generous(X)&patient(X))=>(curious(X)<~>creative(X))))&
(![X]:(~strong(X)<=>(~calm(X)|strong(X))))&
(![X]:((strong(X)&humble(X))=>creative(X)))&
(((wise(susan)|~funny(susan)))<=>(?[X]:((quiet(X)<~>~rich(X)))))&
(((quiet(john)<~>~patient(john)))=>(?[X]:((~quiet(X)&~humble(X)))))&
((?[X]:((~strong(X)<~>patient(X))))<=>(?[X]:((~rich(X)<~>wise(X)))))&
(kind(mary))&
(?[X]:((generous(X)&kind(X))))&
((~rich(lucy)<~>~wise(lucy)))&
((strong(alice)|tall(alice)))&
(~happy(susan))&
(?[X]:(rich(X)))&
(~quiet(susan))&
(?[X]:((curious(X)|quiet(X)))) | ~strong(mary) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 326025439836316102515314
% SZS output start Proof for 326025439836316102515314
12. ! [X0] : (~strong(X0) <=> (strong(X0) | ~calm(X0))) [input p11]
25. strong(mary) [input hypothesis]
54. ! [X0] : ((~strong(X0) | (~strong(X0) & calm(X0))) & ((strong(X0) | ~calm(X0)) | strong(X0))) [nnf transformation 12]
55. ! [X0] : ((~strong(X0) | (~strong(X0) & calm(X0))) & (strong(X0) | ~calm(X0) | strong(X0))) [flattening 54]
103. ~strong(X0) | ~strong(X0) [cnf transformation 55]
127. strong(mary) [cnf transformation 25]
129. ~strong(X0) [duplicate literal removal 103]
276. $false [subsumption resolution 127,129]
% SZS output end Proof for 326025439836316102515314
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich or brave then paul is not creative or not wise.
Everyone who is not curious or funny is either creative or tall.
Everyone who is both not humble and not creative is not calm.
Everyone who is both not humble and humble is not calm.
If susan is wise or not wise then someone is both not happy and creative.
Everyone who is patient or strong is both not calm and not rich and vice versa.
Everyone who is not kind or strong is both calm and rich and vice versa.
If someone is both not old and not rich then someone is either not kind or not brave and vice versa.
Everyone who is funny is either funny or calm.
If someone is both tall and not old then lucy is humble and vice versa.
If fred is quiet or creative then someone is either humble or tall and vice versa.
If fred is not generous then lucy is tall or not tall and vice versa.
Everyone who is generous is generous or not generous.
Everyone who is either rich or humble is creative or brave.
If alice is either not happy or not strong then paul is not quiet and vice versa.
If paul is both generous and quiet then paul is both not old and happy and vice versa.
Lucy is not strong.
Someone is both rich and not creative.
Mary is not rich or kind.
Fred is either tall or rich.
Alice is both not rich and brave.
Alice is not kind or not quiet.
Paul is either tall or creative.
Mary is curious. | Mary is kind. | entailment | ((?[X]:((~rich(X)|brave(X))))=>((~creative(paul)|~wise(paul))))&
(![X]:((~curious(X)|funny(X))=>(creative(X)<~>tall(X))))&
(![X]:((~humble(X)&~creative(X))=>~calm(X)))&
(![X]:((~humble(X)&humble(X))=>~calm(X)))&
(((wise(susan)|~wise(susan)))=>(?[X]:((~happy(X)&creative(X)))))&
(![X]:((patient(X)|strong(X))<=>(~calm(X)&~rich(X))))&
(![X]:((~kind(X)|strong(X))<=>(calm(X)&rich(X))))&
((?[X]:((~old(X)&~rich(X))))<=>(?[X]:((~kind(X)<~>~brave(X)))))&
(![X]:(funny(X)=>(funny(X)<~>calm(X))))&
((?[X]:((tall(X)&~old(X))))<=>(humble(lucy)))&
(((quiet(fred)|creative(fred)))<=>(?[X]:((humble(X)<~>tall(X)))))&
((~generous(fred))<=>((tall(lucy)|~tall(lucy))))&
(![X]:(generous(X)=>(generous(X)|~generous(X))))&
(![X]:((rich(X)<~>humble(X))=>(creative(X)|brave(X))))&
(((~happy(alice)<~>~strong(alice)))<=>(~quiet(paul)))&
(((generous(paul)&quiet(paul)))<=>((~old(paul)&happy(paul))))&
(~strong(lucy))&
(?[X]:((rich(X)&~creative(X))))&
((~rich(mary)|kind(mary)))&
((tall(fred)<~>rich(fred)))&
((~rich(alice)&brave(alice)))&
((~kind(alice)|~quiet(alice)))&
((tall(paul)<~>creative(paul)))&
(curious(mary)) | kind(mary) | [
"p6",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4904581464859610409282489
% SZS output start Proof for 4904581464859610409282489
7. ! [X0] : ((strong(X0) | ~kind(X0)) <=> (rich(X0) & calm(X0))) [input p6]
19. kind(mary) | ~rich(mary) [input p18]
25. ~kind(mary) [input hypothesis]
47. ! [X0] : (((strong(X0) | ~kind(X0)) | (~rich(X0) | ~calm(X0))) & ((rich(X0) & calm(X0)) | (~strong(X0) & kind(X0)))) [nnf transformation 7]
48. ! [X0] : ((strong(X0) | ~kind(X0) | ~rich(X0) | ~calm(X0)) & ((rich(X0) & calm(X0)) | (~strong(X0) & kind(X0)))) [flattening 47]
91. rich(X0) | kind(X0) [cnf transformation 48]
128. kind(mary) | ~rich(mary) [cnf transformation 19]
136. ~kind(mary) [cnf transformation 25]
288. kind(mary) [subsumption resolution 128,91]
314. $false [subsumption resolution 136,288]
% SZS output end Proof for 4904581464859610409282489
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both brave and not brave then fred is humble or not patient.
Everyone who is not strong is not patient and vice versa.
If someone is either not funny or kind then someone is either creative or not funny and vice versa.
If john is not humble then mary is both not strong and not patient and vice versa.
Everyone who is both not old and not rich is either rich or calm and vice versa.
Everyone who is either not old or not strong is strong and vice versa.
If someone is not kind or not tall then someone is kind or brave.
Everyone who is rich or quiet is funny and vice versa.
Everyone who is not brave is either not kind or not generous.
Everyone who is either not wise or happy is both patient and funny.
Everyone who is either not wise or not brave is both not tall and strong.
If susan is wise or not rich then paul is not rich or old and vice versa.
Everyone who is either not calm or not tall is both calm and curious.
If alice is creative then someone is either creative or brave and vice versa.
If fred is generous or tall then lucy is either quiet or humble.
Everyone who is calm or funny is generous and vice versa.
Someone is happy or not funny.
Someone is not humble or strong.
John is both not happy and wise.
Someone is humble.
Someone is both not quiet and calm.
Someone is not happy or strong.
Alice is not wise. | Mary is not strong. | neutral | ((?[X]:((brave(X)&~brave(X))))=>((humble(fred)|~patient(fred))))&
(![X]:(~strong(X)<=>~patient(X)))&
((?[X]:((~funny(X)<~>kind(X))))<=>(?[X]:((creative(X)<~>~funny(X)))))&
((~humble(john))<=>((~strong(mary)&~patient(mary))))&
(![X]:((~old(X)&~rich(X))<=>(rich(X)<~>calm(X))))&
(![X]:((~old(X)<~>~strong(X))<=>strong(X)))&
((?[X]:((~kind(X)|~tall(X))))=>(?[X]:((kind(X)|brave(X)))))&
(![X]:((rich(X)|quiet(X))<=>funny(X)))&
(![X]:(~brave(X)=>(~kind(X)<~>~generous(X))))&
(![X]:((~wise(X)<~>happy(X))=>(patient(X)&funny(X))))&
(![X]:((~wise(X)<~>~brave(X))=>(~tall(X)&strong(X))))&
(((wise(susan)|~rich(susan)))<=>((~rich(paul)|old(paul))))&
(![X]:((~calm(X)<~>~tall(X))=>(calm(X)&curious(X))))&
((creative(alice))<=>(?[X]:((creative(X)<~>brave(X)))))&
(((generous(fred)|tall(fred)))=>((quiet(lucy)<~>humble(lucy))))&
(![X]:((calm(X)|funny(X))<=>generous(X)))&
(?[X]:((happy(X)|~funny(X))))&
(?[X]:((~humble(X)|strong(X))))&
((~happy(john)&wise(john)))&
(?[X]:(humble(X)))&
(?[X]:((~quiet(X)&calm(X))))&
(?[X]:((~happy(X)|strong(X))))&
(~wise(alice)) | ~strong(mary) | [] | null | 0 |
Everyone who is either generous or calm is either not generous or wise and vice versa.
If someone is either not tall or not patient then lucy is both not calm and humble.
Everyone who is strong or not patient is curious and vice versa.
Everyone who is either humble or not patient is not generous or not patient.
Everyone who is both funny and old is kind or calm.
If someone is patient or generous then someone is not generous and vice versa.
Everyone who is strong or curious is both quiet and not humble.
Everyone who is either tall or humble is curious.
Everyone who is both funny and not strong is both not humble and not old and vice versa.
Everyone who is not curious is happy or not tall and vice versa.
If someone is both kind and strong then alice is not generous or not wise.
Everyone who is either not tall or not creative is either curious or strong and vice versa.
If lucy is either curious or not brave then alice is not tall.
If someone is either not happy or happy then mary is not wise and vice versa.
Everyone who is calm or kind is both old and kind.
Everyone who is either curious or wise is both rich and happy and vice versa.
Alice is either not tall or humble.
Someone is both not brave and not funny.
Fred is both wise and patient.
Someone is either happy or not patient.
Mary is generous or rich.
Someone is not tall or strong.
Mary is not curious or brave.
Someone is both curious and tall. | Lucy is not rich. | contradiction | (![X]:((generous(X)<~>calm(X))<=>(~generous(X)<~>wise(X))))&
((?[X]:((~tall(X)<~>~patient(X))))=>((~calm(lucy)&humble(lucy))))&
(![X]:((strong(X)|~patient(X))<=>curious(X)))&
(![X]:((humble(X)<~>~patient(X))=>(~generous(X)|~patient(X))))&
(![X]:((funny(X)&old(X))=>(kind(X)|calm(X))))&
((?[X]:((patient(X)|generous(X))))<=>(?[X]:(~generous(X))))&
(![X]:((strong(X)|curious(X))=>(quiet(X)&~humble(X))))&
(![X]:((tall(X)<~>humble(X))=>curious(X)))&
(![X]:((funny(X)&~strong(X))<=>(~humble(X)&~old(X))))&
(![X]:(~curious(X)<=>(happy(X)|~tall(X))))&
((?[X]:((kind(X)&strong(X))))=>((~generous(alice)|~wise(alice))))&
(![X]:((~tall(X)<~>~creative(X))<=>(curious(X)<~>strong(X))))&
(((curious(lucy)<~>~brave(lucy)))=>(~tall(alice)))&
((?[X]:((~happy(X)<~>happy(X))))<=>(~wise(mary)))&
(![X]:((calm(X)|kind(X))=>(old(X)&kind(X))))&
(![X]:((curious(X)<~>wise(X))<=>(rich(X)&happy(X))))&
((~tall(alice)<~>humble(alice)))&
(?[X]:((~brave(X)&~funny(X))))&
((wise(fred)&patient(fred)))&
(?[X]:((happy(X)<~>~patient(X))))&
((generous(mary)|rich(mary)))&
(?[X]:((~tall(X)|strong(X))))&
((~curious(mary)|brave(mary)))&
(?[X]:((curious(X)&tall(X)))) | ~rich(lucy) | [
"p0",
"p1",
"p2",
"p3",
"p6",
"p7",
"p9",
"p13",
"p15",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3136030375424775057171212
% SZS output start Proof for 3136030375424775057171212
1. ! [X0] : ((generous(X0) <~> calm(X0)) <=> (~generous(X0) <~> wise(X0))) [input p0]
2. ? [X0] : (~tall(X0) <~> ~patient(X0)) => (humble(lucy) & ~calm(lucy)) [input p1]
3. ! [X0] : ((~patient(X0) | strong(X0)) <=> curious(X0)) [input p2]
4. ! [X0] : ((humble(X0) <~> ~patient(X0)) => (~patient(X0) | ~generous(X0))) [input p3]
7. ! [X0] : ((curious(X0) | strong(X0)) => (~humble(X0) & quiet(X0))) [input p6]
8. ! [X0] : ((tall(X0) <~> humble(X0)) => curious(X0)) [input p7]
10. ! [X0] : (~curious(X0) <=> (~tall(X0) | happy(X0))) [input p9]
14. ? [X0] : (~happy(X0) <~> happy(X0)) <=> ~wise(mary) [input p13]
16. ! [X0] : ((curious(X0) <~> wise(X0)) <=> (happy(X0) & rich(X0))) [input p15]
20. ? [X0] : (happy(X0) <~> ~patient(X0)) [input p19]
21. rich(mary) | generous(mary) [input p20]
25. ~rich(lucy) [input hypothesis]
27. ! [X0] : ((curious(X0) | strong(X0)) => ~humble(X0)) [pure predicate removal 7]
28. (humble(lucy) & ~calm(lucy)) | ! [X0] : (~tall(X0) <=> ~patient(X0)) [ennf transformation 2]
29. ! [X0] : ((~patient(X0) | ~generous(X0)) | (humble(X0) <=> ~patient(X0))) [ennf transformation 4]
30. ! [X0] : (~patient(X0) | ~generous(X0) | (humble(X0) <=> ~patient(X0))) [flattening 29]
33. ! [X0] : (~humble(X0) | (~curious(X0) & ~strong(X0))) [ennf transformation 27]
34. ! [X0] : (curious(X0) | (tall(X0) <=> humble(X0))) [ennf transformation 8]
39. ! [X0] : ((((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) | ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0)))) & (((~wise(X0) | generous(X0)) & (wise(X0) | ~generous(X0))) | ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0))))) [nnf transformation 1]
40. (humble(lucy) & ~calm(lucy)) | ! [X0] : ((~tall(X0) | patient(X0)) & (~patient(X0) | tall(X0))) [nnf transformation 28]
41. ! [X0] : (((~patient(X0) | strong(X0)) | ~curious(X0)) & (curious(X0) | (patient(X0) & ~strong(X0)))) [nnf transformation 3]
42. ! [X0] : ((~patient(X0) | strong(X0) | ~curious(X0)) & (curious(X0) | (patient(X0) & ~strong(X0)))) [flattening 41]
43. ! [X0] : (~patient(X0) | ~generous(X0) | ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0)))) [nnf transformation 30]
49. ! [X0] : (curious(X0) | ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0)))) [nnf transformation 34]
52. ! [X0] : ((~curious(X0) | (tall(X0) & ~happy(X0))) & ((~tall(X0) | happy(X0)) | curious(X0))) [nnf transformation 10]
53. ! [X0] : ((~curious(X0) | (tall(X0) & ~happy(X0))) & (~tall(X0) | happy(X0) | curious(X0))) [flattening 52]
56. (? [X0] : ((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | wise(mary)) & (~wise(mary) | ! [X0] : ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) [nnf transformation 14]
57. (? [X0] : ((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | wise(mary)) & (~wise(mary) | ! [X1] : ((~happy(X1) | ~happy(X1)) & (happy(X1) | happy(X1)))) [rectify 56]
58. ? [X0] : ((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) => ((~happy(sK2) | happy(sK2)) & (happy(sK2) | ~happy(sK2))) [choice axiom]
59. (((~happy(sK2) | happy(sK2)) & (happy(sK2) | ~happy(sK2))) | wise(mary)) & (~wise(mary) | ! [X1] : ((~happy(X1) | ~happy(X1)) & (happy(X1) | happy(X1)))) [skolemisation 57,58]
60. ! [X0] : ((((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (~happy(X0) | ~rich(X0))) & ((happy(X0) & rich(X0)) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0))))) [nnf transformation 16]
61. ! [X0] : ((((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | ~happy(X0) | ~rich(X0)) & ((happy(X0) & rich(X0)) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0))))) [flattening 60]
65. ? [X0] : ((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) [nnf transformation 20]
66. ? [X0] : ((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) => ((patient(sK4) | ~happy(sK4)) & (~patient(sK4) | happy(sK4))) [choice axiom]
67. (patient(sK4) | ~happy(sK4)) & (~patient(sK4) | happy(sK4)) [skolemisation 65,66]
72. wise(X0) | ~generous(X0) | calm(X0) | ~generous(X0) [cnf transformation 39]
76. calm(X0) | generous(X0) | wise(X0) | generous(X0) [cnf transformation 39]
80. ~calm(lucy) | ~patient(X0) | tall(X0) [cnf transformation 40]
82. humble(lucy) | ~patient(X0) | tall(X0) [cnf transformation 40]
83. humble(lucy) | ~tall(X0) | patient(X0) [cnf transformation 40]
85. curious(X0) | patient(X0) [cnf transformation 42]
87. ~patient(X0) | ~generous(X0) | ~patient(X0) | ~humble(X0) [cnf transformation 43]
94. ~curious(X0) | ~humble(X0) [cnf transformation 33]
95. ~tall(X0) | humble(X0) | curious(X0) [cnf transformation 49]
96. curious(X0) | tall(X0) | ~humble(X0) [cnf transformation 49]
101. ~tall(X0) | happy(X0) | curious(X0) [cnf transformation 53]
102. ~happy(X0) | ~curious(X0) [cnf transformation 53]
103. ~curious(X0) | tall(X0) [cnf transformation 53]
116. ~wise(mary) | ~happy(X1) | ~happy(X1) [cnf transformation 59]
124. ~wise(X0) | curious(X0) | rich(X0) [cnf transformation 61]
125. happy(X0) | wise(X0) | ~curious(X0) [cnf transformation 61]
127. wise(X0) | curious(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 61]
135. ~patient(sK4) | happy(sK4) [cnf transformation 67]
137. rich(mary) | generous(mary) [cnf transformation 21]
142. ~rich(lucy) [cnf transformation 25]
144. ~wise(mary) | ~happy(X1) [duplicate literal removal 116]
145. ~humble(X0) | ~generous(X0) | ~patient(X0) [duplicate literal removal 87]
146. wise(X0) | ~generous(X0) | calm(X0) [duplicate literal removal 72]
148. wise(X0) | generous(X0) | calm(X0) [duplicate literal removal 76]
151. wise(X0) | calm(X0) [subsumption resolution 146,148]
153. 1 <=> ! [X0] : (~tall(X0) | patient(X0)) [avatar definition]
154. ~tall(X0) | patient(X0) <- (1) [avatar component clause 153]
156. 2 <=> humble(lucy) [avatar definition]
158. humble(lucy) <- (2) [avatar component clause 156]
159. 1 | 2 [avatar split clause 83,156,153]
161. 3 <=> ! [X0] : (~patient(X0) | tall(X0)) [avatar definition]
162. ~patient(X0) | tall(X0) <- (3) [avatar component clause 161]
163. 3 | 2 [avatar split clause 82,156,161]
165. 4 <=> calm(lucy) [avatar definition]
169. 3 | ~4 [avatar split clause 80,165,161]
194. ~humble(X0) | tall(X0) [subsumption resolution 96,94]
219. 15 <=> curious(lucy) [avatar definition]
220. ~curious(lucy) <- (~15) [avatar component clause 219]
221. curious(lucy) <- (15) [avatar component clause 219]
229. 17 <=> ! [X1] : ~happy(X1) [avatar definition]
230. ~happy(X1) <- (17) [avatar component clause 229]
232. 18 <=> wise(mary) [avatar definition]
234. ~wise(mary) <- (~18) [avatar component clause 232]
235. 17 | ~18 [avatar split clause 144,232,229]
240. ~rich(X0) | ~happy(X0) | wise(X0) [subsumption resolution 127,102]
241. ~curious(X0) | wise(X0) [subsumption resolution 125,102]
248. 21 <=> happy(sK4) [avatar definition]
249. happy(sK4) <- (21) [avatar component clause 248]
252. 22 <=> patient(sK4) [avatar definition]
253. ~patient(sK4) <- (~22) [avatar component clause 252]
256. 21 | ~22 [avatar split clause 135,252,248]
258. 23 <=> generous(mary) [avatar definition]
260. generous(mary) <- (23) [avatar component clause 258]
262. 24 <=> rich(mary) [avatar definition]
264. rich(mary) <- (24) [avatar component clause 262]
265. 23 | 24 [avatar split clause 137,262,258]
276. 27 <=> curious(mary) [avatar definition]
277. curious(mary) <- (27) [avatar component clause 276]
278. ~curious(mary) <- (~27) [avatar component clause 276]
286. patient(mary) <- (~27) [resolution 85,278]
290. patient(X0) | tall(X0) [resolution 103,85]
296. tall(lucy) <- (2) [resolution 194,158]
326. happy(lucy) | curious(lucy) <- (2) [resolution 101,296]
328. 33 <=> happy(lucy) [avatar definition]
330. happy(lucy) <- (33) [avatar component clause 328]
331. 15 | 33 | ~2 [avatar split clause 326,156,328,219]
335. ~humble(lucy) <- (15) [resolution 221,94]
347. ~2 | ~15 [avatar split clause 335,219,156]
348. tall(X0) <- (3) [subsumption resolution 162,290]
349. patient(X0) <- (1, 3) [subsumption resolution 154,348]
352. happy(X0) | curious(X0) <- (3) [resolution 348,101]
353. curious(X1) | humble(X1) <- (3) [resolution 348,95]
361. $false <- (1, 3, ~22) [resolution 349,253]
364. ~1 | ~3 | 22 [avatar contradiction clause 361]
371. rich(X0) | curious(X0) | calm(X0) [resolution 124,151]
461. humble(mary) <- (3, ~27) [resolution 353,278]
484. curious(lucy) | calm(lucy) [resolution 371,142]
487. ~generous(mary) | ~patient(mary) <- (3, ~27) [resolution 461,145]
489. ~patient(mary) <- (3, 23, ~27) [subsumption resolution 487,260]
490. $false <- (3, 23, ~27) [subsumption resolution 489,286]
491. ~3 | ~23 | 27 [avatar contradiction clause 490]
493. wise(mary) <- (27) [resolution 277,241]
500. 18 | ~27 [avatar split clause 493,276,232]
503. $false <- (17, 21) [resolution 230,249]
505. ~17 | ~21 [avatar contradiction clause 503]
507. $false <- (17, 33) [subsumption resolution 330,230]
508. ~17 | ~33 [avatar contradiction clause 507]
511. calm(lucy) <- (~15) [subsumption resolution 484,220]
514. 4 | 15 [avatar split clause 511,219,165]
529. ~happy(mary) | wise(mary) <- (24) [resolution 264,240]
530. ~happy(mary) <- (~18, 24) [subsumption resolution 529,234]
539. curious(mary) <- (3, ~18, 24) [resolution 530,352]
540. $false <- (3, ~18, 24, ~27) [subsumption resolution 539,278]
541. ~3 | 18 | ~24 | 27 [avatar contradiction clause 540]
542. $false [avatar sat refutation 159,163,169,235,256,265,331,347,364,491,500,505,508,514,541]
% SZS output end Proof for 3136030375424775057171212
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either curious or not strong then susan is either not generous or not rich and vice versa.
If someone is quiet then someone is both not tall and not curious and vice versa.
If alice is not rich then fred is both not generous and generous.
If john is not quiet or humble then someone is both generous and brave and vice versa.
Everyone who is either not old or strong is old and vice versa.
Everyone who is both strong and not funny is generous and vice versa.
If someone is either kind or happy then mary is quiet and vice versa.
Everyone who is not happy or humble is not patient.
If paul is old or kind then someone is not curious.
If john is wise then someone is old or funny and vice versa.
If someone is both old and not happy then someone is either not funny or not curious.
If lucy is not rich or wise then someone is not funny or not calm.
Everyone who is both not funny and not kind is both curious and not curious and vice versa.
If someone is both not rich and old then someone is both not kind and not brave and vice versa.
Everyone who is either not strong or wise is not happy and vice versa.
If someone is not quiet or not curious then paul is not patient or not kind.
Fred is either not calm or rich.
Someone is happy.
Someone is either not humble or kind.
Someone is either not rich or strong.
Someone is tall.
Fred is either not old or kind.
Someone is not wise or quiet.
Someone is both kind and brave. | John is patient. | contradiction | (((curious(fred)<~>~strong(fred)))<=>((~generous(susan)<~>~rich(susan))))&
((?[X]:(quiet(X)))<=>(?[X]:((~tall(X)&~curious(X)))))&
((~rich(alice))=>((~generous(fred)&generous(fred))))&
(((~quiet(john)|humble(john)))<=>(?[X]:((generous(X)&brave(X)))))&
(![X]:((~old(X)<~>strong(X))<=>old(X)))&
(![X]:((strong(X)&~funny(X))<=>generous(X)))&
((?[X]:((kind(X)<~>happy(X))))<=>(quiet(mary)))&
(![X]:((~happy(X)|humble(X))=>~patient(X)))&
(((old(paul)|kind(paul)))=>(?[X]:(~curious(X))))&
((wise(john))<=>(?[X]:((old(X)|funny(X)))))&
((?[X]:((old(X)&~happy(X))))=>(?[X]:((~funny(X)<~>~curious(X)))))&
(((~rich(lucy)|wise(lucy)))=>(?[X]:((~funny(X)|~calm(X)))))&
(![X]:((~funny(X)&~kind(X))<=>(curious(X)&~curious(X))))&
((?[X]:((~rich(X)&old(X))))<=>(?[X]:((~kind(X)&~brave(X)))))&
(![X]:((~strong(X)<~>wise(X))<=>~happy(X)))&
((?[X]:((~quiet(X)|~curious(X))))=>((~patient(paul)|~kind(paul))))&
((~calm(fred)<~>rich(fred)))&
(?[X]:(happy(X)))&
(?[X]:((~humble(X)<~>kind(X))))&
(?[X]:((~rich(X)<~>strong(X))))&
(?[X]:(tall(X)))&
((~old(fred)<~>kind(fred)))&
(?[X]:((~wise(X)|quiet(X))))&
(?[X]:((kind(X)&brave(X)))) | patient(john) | [
"p4",
"p7",
"p9",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7790235215330893455703076
% SZS output start Proof for 7790235215330893455703076
5. ! [X0] : ((~old(X0) <~> strong(X0)) <=> old(X0)) [input p4]
8. ! [X0] : ((humble(X0) | ~happy(X0)) => ~patient(X0)) [input p7]
10. wise(john) <=> ? [X0] : (funny(X0) | old(X0)) [input p9]
13. ! [X0] : ((~kind(X0) & ~funny(X0)) <=> (~curious(X0) & curious(X0))) [input p12]
15. ! [X0] : ((~strong(X0) <~> wise(X0)) <=> ~happy(X0)) [input p14]
22. ~old(fred) <~> kind(fred) [input p21]
25. patient(john) [input hypothesis]
30. ! [X0] : (~patient(X0) | (~humble(X0) & happy(X0))) [ennf transformation 8]
47. ! [X0] : ((((~strong(X0) | old(X0)) & (strong(X0) | ~old(X0))) | ~old(X0)) & (old(X0) | ((~old(X0) | ~strong(X0)) & (strong(X0) | old(X0))))) [nnf transformation 5]
56. (wise(john) | ! [X0] : (~funny(X0) & ~old(X0))) & (? [X0] : (funny(X0) | old(X0)) | ~wise(john)) [nnf transformation 10]
57. (wise(john) | ! [X0] : (~funny(X0) & ~old(X0))) & (? [X1] : (funny(X1) | old(X1)) | ~wise(john)) [rectify 56]
58. ? [X1] : (funny(X1) | old(X1)) => (funny(sK5) | old(sK5)) [choice axiom]
59. (wise(john) | ! [X0] : (~funny(X0) & ~old(X0))) & ((funny(sK5) | old(sK5)) | ~wise(john)) [skolemisation 57,58]
66. ! [X0] : (((~kind(X0) & ~funny(X0)) | (curious(X0) | ~curious(X0))) & ((~curious(X0) & curious(X0)) | (kind(X0) | funny(X0)))) [nnf transformation 13]
67. ! [X0] : (((~kind(X0) & ~funny(X0)) | curious(X0) | ~curious(X0)) & ((~curious(X0) & curious(X0)) | kind(X0) | funny(X0))) [flattening 66]
73. ! [X0] : ((((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | happy(X0)) & (~happy(X0) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0))))) [nnf transformation 15]
85. (~kind(fred) | old(fred)) & (kind(fred) | ~old(fred)) [nnf transformation 22]
108. old(X0) | strong(X0) | old(X0) [cnf transformation 47]
110. strong(X0) | ~old(X0) | ~old(X0) [cnf transformation 47]
119. ~patient(X0) | happy(X0) [cnf transformation 30]
124. wise(john) | ~old(X0) [cnf transformation 59]
125. wise(john) | ~funny(X0) [cnf transformation 59]
130. curious(X0) | kind(X0) | funny(X0) [cnf transformation 67]
131. ~curious(X0) | kind(X0) | funny(X0) [cnf transformation 67]
139. ~happy(X0) | ~strong(X0) | ~wise(X0) [cnf transformation 73]
153. ~kind(fred) | old(fred) [cnf transformation 85]
157. patient(john) [cnf transformation 25]
158. old(X0) | strong(X0) [duplicate literal removal 108]
159. ~old(X0) | strong(X0) [duplicate literal removal 110]
239. strong(X0) [subsumption resolution 158,159]
278. 25 <=> ! [X0] : ~funny(X0) [avatar definition]
279. ~funny(X0) <- (25) [avatar component clause 278]
281. 26 <=> wise(john) [avatar definition]
283. wise(john) <- (26) [avatar component clause 281]
284. 25 | 26 [avatar split clause 125,281,278]
286. 27 <=> ! [X0] : ~old(X0) [avatar definition]
287. ~old(X0) <- (27) [avatar component clause 286]
288. 27 | 26 [avatar split clause 124,281,286]
329. kind(X0) | funny(X0) [subsumption resolution 130,131]
357. ~wise(X0) | ~happy(X0) [subsumption resolution 139,239]
392. 50 <=> old(fred) [avatar definition]
394. old(fred) <- (50) [avatar component clause 392]
396. 51 <=> kind(fred) [avatar definition]
398. ~kind(fred) <- (~51) [avatar component clause 396]
399. 50 | ~51 [avatar split clause 153,396,392]
412. happy(john) [resolution 119,157]
429. funny(fred) <- (~51) [resolution 329,398]
433. $false <- (25, ~51) [subsumption resolution 429,279]
434. ~25 | 51 [avatar contradiction clause 433]
457. ~happy(john) <- (26) [resolution 357,283]
459. $false <- (26) [subsumption resolution 457,412]
460. ~26 [avatar contradiction clause 459]
465. $false <- (27, 50) [resolution 394,287]
468. ~27 | ~50 [avatar contradiction clause 465]
469. $false [avatar sat refutation 284,288,399,434,460,468]
% SZS output end Proof for 7790235215330893455703076
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not kind and generous is both not calm and patient. If paul is brave or generous then john is either not generous or not happy and vice versa. Everyone who is both patient and kind is either not rich or not old. If someone is not tall then alice is both calm and patient. If someone is both kind and rich then susan is humble and vice versa. Everyone who is rich is not patient and vice versa. If someone is both tall and not quiet then someone is not creative or not strong and vice versa. Everyone who is both calm and not quiet is creative. Everyone who is not quiet or not creative is not tall and vice versa. Everyone who is both tall and rich is both not generous and not happy. Everyone who is both generous and tall is patient and vice versa. If lucy is both not rich and wise then someone is both kind and quiet. If someone is both tall and not brave then someone is both not old and creative and vice versa. Everyone who is humble is not patient or not funny and vice versa. Everyone who is both not strong and not humble is both tall and not patient and vice versa. Everyone who is both funny and not brave is rich or strong. Lucy is both calm and old. John is both rich and old. Someone is not rich or creative. Alice is not funny. Someone is not generous. Someone is not tall. | John is not funny. | neutral | (![X]:((~kind(X)&generous(X))=>(~calm(X)&patient(X))))&
(((brave(paul)|generous(paul)))<=>((~generous(john)<~>~happy(john))))&
(![X]:((patient(X)&kind(X))=>(~rich(X)<~>~old(X))))&
((?[X]:(~tall(X)))=>((calm(alice)&patient(alice))))&
((?[X]:((kind(X)&rich(X))))<=>(humble(susan)))&
(![X]:(rich(X)<=>~patient(X)))&
((?[X]:((tall(X)&~quiet(X))))<=>(?[X]:((~creative(X)|~strong(X)))))&
(![X]:((calm(X)&~quiet(X))=>creative(X)))&
(![X]:((~quiet(X)|~creative(X))<=>~tall(X)))&
(![X]:((tall(X)&rich(X))=>(~generous(X)&~happy(X))))&
(![X]:((generous(X)&tall(X))<=>patient(X)))&
(((~rich(lucy)&wise(lucy)))=>(?[X]:((kind(X)&quiet(X)))))&
((?[X]:((tall(X)&~brave(X))))<=>(?[X]:((~old(X)&creative(X)))))&
(![X]:(humble(X)<=>(~patient(X)|~funny(X))))&
(![X]:((~strong(X)&~humble(X))<=>(tall(X)&~patient(X))))&
(![X]:((funny(X)&~brave(X))=>(rich(X)|strong(X))))&
((calm(lucy)&old(lucy)))&
((rich(john)&old(john)))&
(?[X]:((~rich(X)|creative(X))))&
(~funny(alice))&
(?[X]:(~generous(X)))&
(?[X]:(~tall(X))) | ~funny(john) | [] | null | 0 |
Everyone who is both tall and not kind is happy and vice versa.
If paul is both strong and not calm then someone is both not quiet and tall and vice versa.
If paul is not happy then someone is not creative or not brave.
Everyone who is rich is not patient or kind.
Everyone who is patient or not tall is not funny or brave.
Everyone who is not wise or tall is patient.
Everyone who is not calm or not kind is both humble and strong.
Everyone who is not curious or strong is wise and vice versa.
Everyone who is both not brave and not patient is brave or humble and vice versa.
If someone is strong or not funny then someone is not happy or not brave and vice versa.
Everyone who is either curious or not funny is either kind or not brave and vice versa.
Everyone who is both patient and not old is both not patient and funny and vice versa.
Everyone who is both not happy and not generous is either not creative or not funny.
If john is not brave or old then fred is rich and vice versa.
Everyone who is strong is either not patient or not strong and vice versa.
Everyone who is not rich is either not calm or not brave.
Someone is either calm or rich.
Someone is not old.
Someone is strong.
Someone is quiet or not strong.
John is either humble or not wise.
Fred is both old and not patient.
Paul is not wise or not kind. | John is rich. | neutral | (![X]:((tall(X)&~kind(X))<=>happy(X)))&
(((strong(paul)&~calm(paul)))<=>(?[X]:((~quiet(X)&tall(X)))))&
((~happy(paul))=>(?[X]:((~creative(X)|~brave(X)))))&
(![X]:(rich(X)=>(~patient(X)|kind(X))))&
(![X]:((patient(X)|~tall(X))=>(~funny(X)|brave(X))))&
(![X]:((~wise(X)|tall(X))=>patient(X)))&
(![X]:((~calm(X)|~kind(X))=>(humble(X)&strong(X))))&
(![X]:((~curious(X)|strong(X))<=>wise(X)))&
(![X]:((~brave(X)&~patient(X))<=>(brave(X)|humble(X))))&
((?[X]:((strong(X)|~funny(X))))<=>(?[X]:((~happy(X)|~brave(X)))))&
(![X]:((curious(X)<~>~funny(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((patient(X)&~old(X))<=>(~patient(X)&funny(X))))&
(![X]:((~happy(X)&~generous(X))=>(~creative(X)<~>~funny(X))))&
(((~brave(john)|old(john)))<=>(rich(fred)))&
(![X]:(strong(X)<=>(~patient(X)<~>~strong(X))))&
(![X]:(~rich(X)=>(~calm(X)<~>~brave(X))))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:(~old(X)))&
(?[X]:(strong(X)))&
(?[X]:((quiet(X)|~strong(X))))&
((humble(john)<~>~wise(john)))&
((old(fred)&~patient(fred)))&
((~wise(paul)|~kind(paul))) | rich(john) | [] | null | 0 |
Everyone who is either not generous or not calm is both not funny and not creative and vice versa.
If someone is both tall and not tall then paul is happy or kind.
If someone is rich or quiet then someone is quiet or not wise.
Everyone who is not creative or tall is both not patient and not tall.
If someone is not tall then someone is either kind or rich.
If someone is humble then someone is not strong or humble.
If paul is not old or patient then someone is rich or strong.
Everyone who is kind or not curious is happy or tall and vice versa.
If john is both not curious and curious then someone is both wise and not patient and vice versa.
Everyone who is humble or not happy is either patient or not patient.
If someone is both calm and wise then fred is not brave or not old and vice versa.
If someone is both patient and not rich then someone is not brave or not rich and vice versa.
If fred is not brave then someone is not patient.
If john is not patient then someone is either not strong or rich.
Everyone who is not kind or kind is both brave and not creative and vice versa.
Everyone who is either creative or not strong is creative or not strong.
Alice is not tall or not happy.
Someone is funny or not happy.
Susan is either happy or not tall.
Fred is both curious and not calm.
Alice is either not rich or kind.
Someone is both happy and not funny.
Someone is not calm.
Paul is either brave or old. | Alice is not creative. | entailment | (![X]:((~generous(X)<~>~calm(X))<=>(~funny(X)&~creative(X))))&
((?[X]:((tall(X)&~tall(X))))=>((happy(paul)|kind(paul))))&
((?[X]:((rich(X)|quiet(X))))=>(?[X]:((quiet(X)|~wise(X)))))&
(![X]:((~creative(X)|tall(X))=>(~patient(X)&~tall(X))))&
((?[X]:(~tall(X)))=>(?[X]:((kind(X)<~>rich(X)))))&
((?[X]:(humble(X)))=>(?[X]:((~strong(X)|humble(X)))))&
(((~old(paul)|patient(paul)))=>(?[X]:((rich(X)|strong(X)))))&
(![X]:((kind(X)|~curious(X))<=>(happy(X)|tall(X))))&
(((~curious(john)&curious(john)))<=>(?[X]:((wise(X)&~patient(X)))))&
(![X]:((humble(X)|~happy(X))=>(patient(X)<~>~patient(X))))&
((?[X]:((calm(X)&wise(X))))<=>((~brave(fred)|~old(fred))))&
((?[X]:((patient(X)&~rich(X))))<=>(?[X]:((~brave(X)|~rich(X)))))&
((~brave(fred))=>(?[X]:(~patient(X))))&
((~patient(john))=>(?[X]:((~strong(X)<~>rich(X)))))&
(![X]:((~kind(X)|kind(X))<=>(brave(X)&~creative(X))))&
(![X]:((creative(X)<~>~strong(X))=>(creative(X)|~strong(X))))&
((~tall(alice)|~happy(alice)))&
(?[X]:((funny(X)|~happy(X))))&
((happy(susan)<~>~tall(susan)))&
((curious(fred)&~calm(fred)))&
((~rich(alice)<~>kind(alice)))&
(?[X]:((happy(X)&~funny(X))))&
(?[X]:(~calm(X)))&
((brave(paul)<~>old(paul))) | ~creative(alice) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 404971573232755690016325
% SZS output start Proof for 404971573232755690016325
15. ! [X0] : ((kind(X0) | ~kind(X0)) <=> (~creative(X0) & brave(X0))) [input p14]
25. creative(alice) [input hypothesis]
79. ! [X0] : (((kind(X0) | ~kind(X0)) | (creative(X0) | ~brave(X0))) & ((~creative(X0) & brave(X0)) | (~kind(X0) & kind(X0)))) [nnf transformation 15]
80. ! [X0] : ((kind(X0) | ~kind(X0) | creative(X0) | ~brave(X0)) & ((~creative(X0) & brave(X0)) | (~kind(X0) & kind(X0)))) [flattening 79]
136. ~creative(X0) | kind(X0) [cnf transformation 80]
137. ~creative(X0) | ~kind(X0) [cnf transformation 80]
154. creative(alice) [cnf transformation 25]
300. ~creative(X0) [subsumption resolution 136,137]
329. $false [subsumption resolution 154,300]
% SZS output end Proof for 404971573232755690016325
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and rich is strong or not strong and vice versa. Everyone who is humble is creative or not patient and vice versa. If paul is either humble or generous then someone is either brave or not quiet and vice versa. If someone is both old and tall then someone is either humble or not quiet. Everyone who is not tall or wise is not creative. If mary is either quiet or not humble then someone is both not humble and strong and vice versa. If susan is not tall then someone is strong or not patient and vice versa. If someone is curious or old then lucy is both not old and rich and vice versa. Everyone who is not rich or not brave is funny and vice versa. If someone is not generous then mary is both curious and not happy and vice versa. Everyone who is either not strong or strong is creative or calm. Everyone who is both not quiet and funny is not brave or generous. Everyone who is not tall or not generous is strong or not rich and vice versa. If someone is not calm then someone is rich or kind. If alice is either not humble or patient then someone is calm or not happy. Everyone who is not humble or not tall is both old and not humble and vice versa. Someone is brave or not curious. Someone is either funny or tall. Lucy is funny. Someone is happy or not tall. Susan is not strong or not old. Someone is both not happy and kind. | Alice is not strong. | entailment | (![X]:((patient(X)&rich(X))<=>(strong(X)|~strong(X))))&
(![X]:(humble(X)<=>(creative(X)|~patient(X))))&
(((humble(paul)<~>generous(paul)))<=>(?[X]:((brave(X)<~>~quiet(X)))))&
((?[X]:((old(X)&tall(X))))=>(?[X]:((humble(X)<~>~quiet(X)))))&
(![X]:((~tall(X)|wise(X))=>~creative(X)))&
(((quiet(mary)<~>~humble(mary)))<=>(?[X]:((~humble(X)&strong(X)))))&
((~tall(susan))<=>(?[X]:((strong(X)|~patient(X)))))&
((?[X]:((curious(X)|old(X))))<=>((~old(lucy)&rich(lucy))))&
(![X]:((~rich(X)|~brave(X))<=>funny(X)))&
((?[X]:(~generous(X)))<=>((curious(mary)&~happy(mary))))&
(![X]:((~strong(X)<~>strong(X))=>(creative(X)|calm(X))))&
(![X]:((~quiet(X)&funny(X))=>(~brave(X)|generous(X))))&
(![X]:((~tall(X)|~generous(X))<=>(strong(X)|~rich(X))))&
((?[X]:(~calm(X)))=>(?[X]:((rich(X)|kind(X)))))&
(((~humble(alice)<~>patient(alice)))=>(?[X]:((calm(X)|~happy(X)))))&
(![X]:((~humble(X)|~tall(X))<=>(old(X)&~humble(X))))&
(?[X]:((brave(X)|~curious(X))))&
(?[X]:((funny(X)<~>tall(X))))&
(funny(lucy))&
(?[X]:((happy(X)|~tall(X))))&
((~strong(susan)|~old(susan)))&
(?[X]:((~happy(X)&kind(X)))) | ~strong(alice) | [
"p0",
"p6",
"p12",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1352943039669695067432543
% SZS output start Proof for 1352943039669695067432543
1. ! [X0] : ((rich(X0) & patient(X0)) <=> (~strong(X0) | strong(X0))) [input p0]
7. ~tall(susan) <=> ? [X0] : (~patient(X0) | strong(X0)) [input p6]
13. ! [X0] : ((~generous(X0) | ~tall(X0)) <=> (~rich(X0) | strong(X0))) [input p12]
16. ! [X0] : ((~tall(X0) | ~humble(X0)) <=> (~humble(X0) & old(X0))) [input p15]
21. ~old(susan) | ~strong(susan) [input p20]
23. strong(alice) [input hypothesis]
35. ! [X0] : (((rich(X0) & patient(X0)) | (strong(X0) & ~strong(X0))) & ((~strong(X0) | strong(X0)) | (~rich(X0) | ~patient(X0)))) [nnf transformation 1]
36. ! [X0] : (((rich(X0) & patient(X0)) | (strong(X0) & ~strong(X0))) & (~strong(X0) | strong(X0) | ~rich(X0) | ~patient(X0))) [flattening 35]
51. (~tall(susan) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X0] : (~patient(X0) | strong(X0)) | tall(susan)) [nnf transformation 7]
52. (~tall(susan) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X1] : (~patient(X1) | strong(X1)) | tall(susan)) [rectify 51]
53. ? [X1] : (~patient(X1) | strong(X1)) => (~patient(sK3) | strong(sK3)) [choice axiom]
54. (~tall(susan) | ! [X0] : (patient(X0) & ~strong(X0))) & ((~patient(sK3) | strong(sK3)) | tall(susan)) [skolemisation 52,53]
67. ! [X0] : (((~generous(X0) | ~tall(X0)) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | (generous(X0) & tall(X0)))) [nnf transformation 13]
68. ! [X0] : ((~generous(X0) | ~tall(X0) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | (generous(X0) & tall(X0)))) [flattening 67]
69. ! [X0] : (((~tall(X0) | ~humble(X0)) | (humble(X0) | ~old(X0))) & ((~humble(X0) & old(X0)) | (tall(X0) & humble(X0)))) [nnf transformation 16]
70. ! [X0] : ((~tall(X0) | ~humble(X0) | humble(X0) | ~old(X0)) & ((~humble(X0) & old(X0)) | (tall(X0) & humble(X0)))) [flattening 69]
83. rich(X0) | ~strong(X0) [cnf transformation 36]
84. strong(X0) | rich(X0) [cnf transformation 36]
106. ~tall(susan) | ~strong(X0) [cnf transformation 54]
120. ~rich(X0) | strong(X0) | tall(X0) [cnf transformation 68]
125. tall(X0) | old(X0) [cnf transformation 70]
134. ~old(susan) | ~strong(susan) [cnf transformation 21]
136. strong(alice) [cnf transformation 23]
137. rich(X0) [subsumption resolution 83,84]
209. 15 <=> ! [X0] : ~strong(X0) [avatar definition]
210. ~strong(X0) <- (15) [avatar component clause 209]
212. 16 <=> tall(susan) [avatar definition]
214. ~tall(susan) <- (~16) [avatar component clause 212]
215. 15 | ~16 [avatar split clause 106,212,209]
264. tall(X0) | strong(X0) [subsumption resolution 120,137]
294. 33 <=> strong(susan) [avatar definition]
296. ~strong(susan) <- (~33) [avatar component clause 294]
298. 34 <=> old(susan) [avatar definition]
301. ~33 | ~34 [avatar split clause 134,298,294]
302. $false <- (15) [resolution 210,136]
303. ~15 [avatar contradiction clause 302]
306. old(susan) <- (~16) [resolution 125,214]
311. 34 | 16 [avatar split clause 306,212,298]
333. strong(susan) <- (~16) [resolution 264,214]
336. $false <- (~16, ~33) [subsumption resolution 333,296]
337. 16 | 33 [avatar contradiction clause 336]
338. $false [avatar sat refutation 215,301,303,311,337]
% SZS output end Proof for 1352943039669695067432543
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is patient or old then john is not funny or happy and vice versa.
Everyone who is both old and not kind is either rich or curious.
Everyone who is tall is not patient or not rich.
If someone is generous then someone is patient.
If someone is tall or not patient then lucy is tall or old.
Everyone who is either kind or wise is not strong or tall and vice versa.
Everyone who is patient or generous is not old or not tall.
If someone is either not tall or not wise then someone is both generous and not wise.
Everyone who is either not strong or not patient is either humble or not old.
Everyone who is both kind and rich is old or not brave and vice versa.
Everyone who is not patient or patient is both not patient and not calm and vice versa.
Everyone who is wise or not old is either not calm or not curious.
If susan is quiet then paul is either not patient or not kind and vice versa.
Everyone who is either strong or humble is calm.
Everyone who is calm is both patient and not wise.
Everyone who is both curious and not tall is tall.
Fred is not kind.
Someone is rich.
Susan is either not brave or happy.
John is either not brave or not patient.
Susan is either not brave or curious.
Someone is either kind or not strong. | Lucy is not humble. | entailment | ((?[X]:((patient(X)|old(X))))<=>((~funny(john)|happy(john))))&
(![X]:((old(X)&~kind(X))=>(rich(X)<~>curious(X))))&
(![X]:(tall(X)=>(~patient(X)|~rich(X))))&
((?[X]:(generous(X)))=>(?[X]:(patient(X))))&
((?[X]:((tall(X)|~patient(X))))=>((tall(lucy)|old(lucy))))&
(![X]:((kind(X)<~>wise(X))<=>(~strong(X)|tall(X))))&
(![X]:((patient(X)|generous(X))=>(~old(X)|~tall(X))))&
((?[X]:((~tall(X)<~>~wise(X))))=>(?[X]:((generous(X)&~wise(X)))))&
(![X]:((~strong(X)<~>~patient(X))=>(humble(X)<~>~old(X))))&
(![X]:((kind(X)&rich(X))<=>(old(X)|~brave(X))))&
(![X]:((~patient(X)|patient(X))<=>(~patient(X)&~calm(X))))&
(![X]:((wise(X)|~old(X))=>(~calm(X)<~>~curious(X))))&
((quiet(susan))<=>((~patient(paul)<~>~kind(paul))))&
(![X]:((strong(X)<~>humble(X))=>calm(X)))&
(![X]:(calm(X)=>(patient(X)&~wise(X))))&
(![X]:((curious(X)&~tall(X))=>tall(X)))&
(~kind(fred))&
(?[X]:(rich(X)))&
((~brave(susan)<~>happy(susan)))&
((~brave(john)<~>~patient(john)))&
((~brave(susan)<~>curious(susan)))&
(?[X]:((kind(X)<~>~strong(X)))) | ~humble(lucy) | [
"p3",
"p5",
"p7",
"p8",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1864029795980984347775119
% SZS output start Proof for 1864029795980984347775119
4. ? [X0] : generous(X0) => ? [X0] : patient(X0) [input p3]
6. ! [X0] : ((kind(X0) <~> wise(X0)) <=> (tall(X0) | ~strong(X0))) [input p5]
8. ? [X0] : (~tall(X0) <~> ~wise(X0)) => ? [X0] : (~wise(X0) & generous(X0)) [input p7]
9. ! [X0] : ((~strong(X0) <~> ~patient(X0)) => (humble(X0) <~> ~old(X0))) [input p8]
10. ! [X0] : ((rich(X0) & kind(X0)) <=> (~brave(X0) | old(X0))) [input p9]
11. ! [X0] : ((patient(X0) | ~patient(X0)) <=> (~calm(X0) & ~patient(X0))) [input p10]
14. ! [X0] : ((strong(X0) <~> humble(X0)) => calm(X0)) [input p13]
23. humble(lucy) [input hypothesis]
24. ? [X0] : generous(X0) => ? [X1] : patient(X1) [rectify 4]
25. ? [X0] : (~tall(X0) <~> ~wise(X0)) => ? [X1] : (~wise(X1) & generous(X1)) [rectify 8]
30. ? [X1] : patient(X1) | ! [X0] : ~generous(X0) [ennf transformation 24]
35. ? [X1] : (~wise(X1) & generous(X1)) | ! [X0] : (~tall(X0) <=> ~wise(X0)) [ennf transformation 25]
36. ! [X0] : ((humble(X0) <~> ~old(X0)) | (~strong(X0) <=> ~patient(X0))) [ennf transformation 9]
38. ! [X0] : (calm(X0) | (strong(X0) <=> humble(X0))) [ennf transformation 14]
48. ? [X0] : patient(X0) | ! [X1] : ~generous(X1) [rectify 30]
49. ? [X0] : patient(X0) => patient(sK1) [choice axiom]
50. patient(sK1) | ! [X1] : ~generous(X1) [skolemisation 48,49]
51. ! [X0] : ((((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) | (~tall(X0) & strong(X0))) & ((tall(X0) | ~strong(X0)) | ((kind(X0) | ~wise(X0)) & (wise(X0) | ~kind(X0))))) [nnf transformation 6]
52. ! [X0] : ((((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) | (~tall(X0) & strong(X0))) & (tall(X0) | ~strong(X0) | ((kind(X0) | ~wise(X0)) & (wise(X0) | ~kind(X0))))) [flattening 51]
53. ? [X1] : (~wise(X1) & generous(X1)) | ! [X0] : ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))) [nnf transformation 35]
54. ? [X0] : (~wise(X0) & generous(X0)) | ! [X1] : ((~tall(X1) | wise(X1)) & (~wise(X1) | tall(X1))) [rectify 53]
55. ? [X0] : (~wise(X0) & generous(X0)) => (~wise(sK2) & generous(sK2)) [choice axiom]
56. (~wise(sK2) & generous(sK2)) | ! [X1] : ((~tall(X1) | wise(X1)) & (~wise(X1) | tall(X1))) [skolemisation 54,55]
57. ! [X0] : (((old(X0) | ~humble(X0)) & (~old(X0) | humble(X0))) | ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) [nnf transformation 36]
58. ! [X0] : (((rich(X0) & kind(X0)) | (brave(X0) & ~old(X0))) & ((~brave(X0) | old(X0)) | (~rich(X0) | ~kind(X0)))) [nnf transformation 10]
59. ! [X0] : (((rich(X0) & kind(X0)) | (brave(X0) & ~old(X0))) & (~brave(X0) | old(X0) | ~rich(X0) | ~kind(X0))) [flattening 58]
60. ! [X0] : (((patient(X0) | ~patient(X0)) | (calm(X0) | patient(X0))) & ((~calm(X0) & ~patient(X0)) | (~patient(X0) & patient(X0)))) [nnf transformation 11]
61. ! [X0] : ((patient(X0) | ~patient(X0) | calm(X0) | patient(X0)) & ((~calm(X0) & ~patient(X0)) | (~patient(X0) & patient(X0)))) [flattening 60]
64. ! [X0] : (calm(X0) | ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0)))) [nnf transformation 38]
80. patient(sK1) | ~generous(X1) [cnf transformation 50]
83. ~strong(X0) | tall(X0) | wise(X0) | ~kind(X0) [cnf transformation 52]
88. ~wise(X0) | ~kind(X0) | ~tall(X0) [cnf transformation 52]
91. generous(sK2) | ~wise(X1) | tall(X1) [cnf transformation 56]
92. generous(sK2) | ~tall(X1) | wise(X1) [cnf transformation 56]
98. ~humble(X0) | old(X0) | ~strong(X0) | patient(X0) [cnf transformation 57]
100. ~old(X0) | kind(X0) [cnf transformation 59]
105. ~patient(X0) | ~patient(X0) [cnf transformation 61]
106. ~calm(X0) | patient(X0) [cnf transformation 61]
107. ~calm(X0) | ~patient(X0) [cnf transformation 61]
118. calm(X0) | strong(X0) | ~humble(X0) [cnf transformation 64]
132. humble(lucy) [cnf transformation 23]
134. ~patient(X0) [duplicate literal removal 105]
159. 6 <=> ! [X1] : ~patient(X1) [avatar definition]
160. ~patient(X1) <- (6) [avatar component clause 159]
163. 7 <=> ! [X1] : ~generous(X1) [avatar definition]
164. ~generous(X1) <- (7) [avatar component clause 163]
166. 8 <=> patient(sK1) [avatar definition]
168. patient(sK1) <- (8) [avatar component clause 166]
169. 7 | 8 [avatar split clause 80,166,163]
174. 10 <=> tall(lucy) [avatar definition]
175. ~tall(lucy) <- (~10) [avatar component clause 174]
176. tall(lucy) <- (10) [avatar component clause 174]
178. 11 <=> old(lucy) [avatar definition]
180. old(lucy) <- (11) [avatar component clause 178]
187. 13 <=> ! [X1] : (~tall(X1) | wise(X1)) [avatar definition]
188. ~tall(X1) | wise(X1) <- (13) [avatar component clause 187]
195. 15 <=> ! [X1] : (~wise(X1) | tall(X1)) [avatar definition]
196. ~wise(X1) | tall(X1) <- (15) [avatar component clause 195]
199. 16 <=> generous(sK2) [avatar definition]
201. generous(sK2) <- (16) [avatar component clause 199]
202. 13 | 16 [avatar split clause 92,199,187]
203. 15 | 16 [avatar split clause 91,199,195]
204. ~calm(X0) [subsumption resolution 106,107]
205. 6 [avatar split clause 134,159]
224. ~humble(X0) | strong(X0) [subsumption resolution 118,204]
268. wise(lucy) <- (10, 13) [resolution 188,176]
275. strong(lucy) [resolution 224,132]
294. ~kind(lucy) | ~tall(lucy) <- (10, 13) [resolution 88,268]
296. ~kind(lucy) <- (10, 13) [subsumption resolution 294,176]
313. tall(lucy) | wise(lucy) | ~kind(lucy) [resolution 83,275]
325. old(lucy) | ~strong(lucy) | patient(lucy) [resolution 98,132]
327. old(lucy) | patient(lucy) [subsumption resolution 325,275]
328. old(lucy) <- (6) [subsumption resolution 327,160]
329. 11 | ~6 [avatar split clause 328,159,178]
333. kind(lucy) <- (11) [resolution 180,100]
334. $false <- (10, 11, 13) [subsumption resolution 333,296]
335. ~10 | ~11 | ~13 [avatar contradiction clause 334]
336. tall(lucy) | wise(lucy) <- (11) [subsumption resolution 313,333]
337. wise(lucy) <- (11, 13) [subsumption resolution 336,188]
346. tall(lucy) <- (11, 13, 15) [resolution 337,196]
347. $false <- (~10, 11, 13, 15) [subsumption resolution 346,175]
348. 10 | ~11 | ~13 | ~15 [avatar contradiction clause 347]
349. $false <- (7, 16) [subsumption resolution 201,164]
350. ~7 | ~16 [avatar contradiction clause 349]
351. $false <- (6, 8) [subsumption resolution 168,160]
352. ~6 | ~8 [avatar contradiction clause 351]
353. $false [avatar sat refutation 169,202,203,205,329,335,348,350,352]
% SZS output end Proof for 1864029795980984347775119
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet or kind then someone is humble or creative and vice versa.
Everyone who is happy is either not rich or not patient.
Everyone who is both not rich and not tall is not wise.
If someone is both strong and humble then someone is either not humble or rich.
Everyone who is either not curious or strong is not curious or old.
Everyone who is not curious is not patient or brave and vice versa.
Everyone who is not brave is both not wise and not strong.
If someone is curious then someone is rich.
If someone is both not quiet and not strong then someone is both strong and curious and vice versa.
Everyone who is both tall and not generous is funny and vice versa.
Everyone who is either quiet or not kind is not curious and vice versa.
Everyone who is both curious and not happy is both tall and brave.
If paul is both not kind and not strong then someone is patient or strong and vice versa.
Everyone who is curious or not old is either not strong or funny and vice versa.
If someone is either strong or not brave then susan is both generous and calm and vice versa.
If someone is not kind or not patient then someone is patient or funny and vice versa.
Alice is not generous.
Someone is both not strong and not funny.
Alice is both curious and not old.
Someone is either patient or creative.
John is either not wise or rich.
Someone is both generous and rich.
Paul is either tall or not old. | Susan is funny. | contradiction | ((?[X]:((~quiet(X)<~>kind(X))))<=>(?[X]:((humble(X)|creative(X)))))&
(![X]:(happy(X)=>(~rich(X)<~>~patient(X))))&
(![X]:((~rich(X)&~tall(X))=>~wise(X)))&
((?[X]:((strong(X)&humble(X))))=>(?[X]:((~humble(X)<~>rich(X)))))&
(![X]:((~curious(X)<~>strong(X))=>(~curious(X)|old(X))))&
(![X]:(~curious(X)<=>(~patient(X)|brave(X))))&
(![X]:(~brave(X)=>(~wise(X)&~strong(X))))&
((?[X]:(curious(X)))=>(?[X]:(rich(X))))&
((?[X]:((~quiet(X)&~strong(X))))<=>(?[X]:((strong(X)&curious(X)))))&
(![X]:((tall(X)&~generous(X))<=>funny(X)))&
(![X]:((quiet(X)<~>~kind(X))<=>~curious(X)))&
(![X]:((curious(X)&~happy(X))=>(tall(X)&brave(X))))&
(((~kind(paul)&~strong(paul)))<=>(?[X]:((patient(X)|strong(X)))))&
(![X]:((curious(X)|~old(X))<=>(~strong(X)<~>funny(X))))&
((?[X]:((strong(X)<~>~brave(X))))<=>((generous(susan)&calm(susan))))&
((?[X]:((~kind(X)|~patient(X))))<=>(?[X]:((patient(X)|funny(X)))))&
(~generous(alice))&
(?[X]:((~strong(X)&~funny(X))))&
((curious(alice)&~old(alice)))&
(?[X]:((patient(X)<~>creative(X))))&
((~wise(john)<~>rich(john)))&
(?[X]:((generous(X)&rich(X))))&
((tall(paul)<~>~old(paul))) | funny(susan) | [
"p5",
"p6",
"p9",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4744698182912287963864437
% SZS output start Proof for 4744698182912287963864437
6. ! [X0] : (~curious(X0) <=> (brave(X0) | ~patient(X0))) [input p5]
7. ! [X0] : (~brave(X0) => (~strong(X0) & ~wise(X0))) [input p6]
10. ! [X0] : ((~generous(X0) & tall(X0)) <=> funny(X0)) [input p9]
15. ? [X0] : (strong(X0) <~> ~brave(X0)) <=> (calm(susan) & generous(susan)) [input p14]
19. ~old(alice) & curious(alice) [input p18]
24. funny(susan) [input hypothesis]
36. ! [X0] : ((~strong(X0) & ~wise(X0)) | brave(X0)) [ennf transformation 7]
51. ! [X0] : ((~curious(X0) | (~brave(X0) & patient(X0))) & ((brave(X0) | ~patient(X0)) | curious(X0))) [nnf transformation 6]
52. ! [X0] : ((~curious(X0) | (~brave(X0) & patient(X0))) & (brave(X0) | ~patient(X0) | curious(X0))) [flattening 51]
61. ! [X0] : (((~generous(X0) & tall(X0)) | ~funny(X0)) & (funny(X0) | (generous(X0) | ~tall(X0)))) [nnf transformation 10]
62. ! [X0] : (((~generous(X0) & tall(X0)) | ~funny(X0)) & (funny(X0) | generous(X0) | ~tall(X0))) [flattening 61]
71. (? [X0] : ((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | (~calm(susan) | ~generous(susan))) & ((calm(susan) & generous(susan)) | ! [X0] : ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0)))) [nnf transformation 15]
72. (? [X0] : ((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | ~calm(susan) | ~generous(susan)) & ((calm(susan) & generous(susan)) | ! [X0] : ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0)))) [flattening 71]
73. (? [X0] : ((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | ~calm(susan) | ~generous(susan)) & ((calm(susan) & generous(susan)) | ! [X1] : ((strong(X1) | brave(X1)) & (~brave(X1) | ~strong(X1)))) [rectify 72]
74. ? [X0] : ((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) => ((brave(sK7) | ~strong(sK7)) & (~brave(sK7) | strong(sK7))) [choice axiom]
75. (((brave(sK7) | ~strong(sK7)) & (~brave(sK7) | strong(sK7))) | ~calm(susan) | ~generous(susan)) & ((calm(susan) & generous(susan)) | ! [X1] : ((strong(X1) | brave(X1)) & (~brave(X1) | ~strong(X1)))) [skolemisation 73,74]
105. ~brave(X0) | ~curious(X0) [cnf transformation 52]
107. ~strong(X0) | brave(X0) [cnf transformation 36]
115. ~funny(X0) | ~generous(X0) [cnf transformation 62]
134. generous(susan) | strong(X1) | brave(X1) [cnf transformation 75]
146. curious(alice) [cnf transformation 19]
156. funny(susan) [cnf transformation 24]
206. 12 <=> ! [X1] : ~curious(X1) [avatar definition]
207. ~curious(X1) <- (12) [avatar component clause 206]
268. 26 <=> generous(susan) [avatar definition]
286. 30 <=> ! [X1] : brave(X1) [avatar definition]
287. brave(X1) <- (30) [avatar component clause 286]
291. generous(susan) | brave(X1) [subsumption resolution 134,107]
292. 30 | 26 [avatar split clause 291,268,286]
365. $false <- (12) [resolution 207,146]
366. ~12 [avatar contradiction clause 365]
369. ~generous(susan) [resolution 115,156]
372. ~26 [avatar split clause 369,268]
376. ~curious(X0) <- (30) [resolution 287,105]
378. 12 | ~30 [avatar split clause 376,286,206]
379. $false [avatar sat refutation 292,366,372,378]
% SZS output end Proof for 4744698182912287963864437
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is both calm and curious.
If john is not tall then someone is either not patient or not creative and vice versa.
Everyone who is humble or brave is rich or brave.
If someone is either not old or quiet then someone is creative and vice versa.
Everyone who is not tall or strong is curious or quiet.
Everyone who is both generous and not curious is not patient and vice versa.
If someone is creative then someone is both not brave and not tall and vice versa.
If someone is funny or not generous then fred is not calm.
If alice is not kind then someone is either not rich or humble and vice versa.
If someone is rich then someone is not brave and vice versa.
If someone is not curious or not patient then someone is not patient and vice versa.
Everyone who is old or curious is both strong and calm.
Everyone who is happy or not calm is both not old and not funny.
Everyone who is either old or not quiet is either not curious or wise.
If someone is brave or wise then someone is not strong and vice versa.
If someone is either creative or not strong then fred is either not happy or not creative and vice versa.
Someone is both not strong and not quiet.
Someone is either quiet or generous.
Someone is not patient or not happy.
Mary is not old or not strong.
John is not quiet.
Alice is both not rich and not brave.
Someone is not funny.
Mary is not calm. | Fred is funny. | contradiction | (![X]:(~generous(X)=>(calm(X)&curious(X))))&
((~tall(john))<=>(?[X]:((~patient(X)<~>~creative(X)))))&
(![X]:((humble(X)|brave(X))=>(rich(X)|brave(X))))&
((?[X]:((~old(X)<~>quiet(X))))<=>(?[X]:(creative(X))))&
(![X]:((~tall(X)|strong(X))=>(curious(X)|quiet(X))))&
(![X]:((generous(X)&~curious(X))<=>~patient(X)))&
((?[X]:(creative(X)))<=>(?[X]:((~brave(X)&~tall(X)))))&
((?[X]:((funny(X)|~generous(X))))=>(~calm(fred)))&
((~kind(alice))<=>(?[X]:((~rich(X)<~>humble(X)))))&
((?[X]:(rich(X)))<=>(?[X]:(~brave(X))))&
((?[X]:((~curious(X)|~patient(X))))<=>(?[X]:(~patient(X))))&
(![X]:((old(X)|curious(X))=>(strong(X)&calm(X))))&
(![X]:((happy(X)|~calm(X))=>(~old(X)&~funny(X))))&
(![X]:((old(X)<~>~quiet(X))=>(~curious(X)<~>wise(X))))&
((?[X]:((brave(X)|wise(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((creative(X)<~>~strong(X))))<=>((~happy(fred)<~>~creative(fred))))&
(?[X]:((~strong(X)&~quiet(X))))&
(?[X]:((quiet(X)<~>generous(X))))&
(?[X]:((~patient(X)|~happy(X))))&
((~old(mary)|~strong(mary)))&
(~quiet(john))&
((~rich(alice)&~brave(alice)))&
(?[X]:(~funny(X)))&
(~calm(mary)) | funny(fred) | [
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5890241021228653773302865
% SZS output start Proof for 5890241021228653773302865
8. ? [X0] : (~generous(X0) | funny(X0)) => ~calm(fred) [input p7]
13. ! [X0] : ((~calm(X0) | happy(X0)) => (~funny(X0) & ~old(X0))) [input p12]
25. funny(fred) [input hypothesis]
36. ~calm(fred) | ! [X0] : (generous(X0) & ~funny(X0)) [ennf transformation 8]
38. ! [X0] : ((~funny(X0) & ~old(X0)) | (calm(X0) & ~happy(X0))) [ennf transformation 13]
109. ~calm(fred) | ~funny(X0) [cnf transformation 36]
127. ~funny(X0) | calm(X0) [cnf transformation 38]
154. funny(fred) [cnf transformation 25]
225. 17 <=> calm(fred) [avatar definition]
230. 18 <=> ! [X0] : ~funny(X0) [avatar definition]
231. ~funny(X0) <- (18) [avatar component clause 230]
232. 18 | ~17 [avatar split clause 109,225,230]
380. calm(fred) [resolution 127,154]
383. 17 [avatar split clause 380,225]
386. $false <- (18) [resolution 231,154]
387. ~18 [avatar contradiction clause 386]
388. $false [avatar sat refutation 232,383,387]
% SZS output end Proof for 5890241021228653773302865
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is generous or not patient then someone is not strong or happy and vice versa.
If someone is both not wise and tall then someone is not kind or patient and vice versa.
Everyone who is brave is not wise.
Everyone who is brave is both not generous and not happy.
If someone is not patient then someone is humble or curious.
Everyone who is not quiet is tall.
If paul is either not strong or quiet then someone is both not wise and not tall and vice versa.
If someone is not rich then susan is both curious and strong.
If alice is both not rich and not wise then lucy is creative and vice versa.
If paul is not wise then susan is not patient or brave.
Everyone who is generous or not humble is funny or not patient.
Everyone who is not tall is not funny and vice versa.
If fred is quiet or not strong then someone is strong or not funny and vice versa.
Everyone who is not old or tall is not funny or generous.
If someone is generous then someone is either not wise or calm.
Everyone who is not calm is not rich.
Lucy is not calm.
Someone is both not quiet and tall.
Paul is not generous or not curious.
Someone is creative.
Mary is either not patient or not tall.
Someone is patient.
John is not kind or not rich.
John is not humble or not generous. | Susan is not strong. | contradiction | (((generous(alice)|~patient(alice)))<=>(?[X]:((~strong(X)|happy(X)))))&
((?[X]:((~wise(X)&tall(X))))<=>(?[X]:((~kind(X)|patient(X)))))&
(![X]:(brave(X)=>~wise(X)))&
(![X]:(brave(X)=>(~generous(X)&~happy(X))))&
((?[X]:(~patient(X)))=>(?[X]:((humble(X)|curious(X)))))&
(![X]:(~quiet(X)=>tall(X)))&
(((~strong(paul)<~>quiet(paul)))<=>(?[X]:((~wise(X)&~tall(X)))))&
((?[X]:(~rich(X)))=>((curious(susan)&strong(susan))))&
(((~rich(alice)&~wise(alice)))<=>(creative(lucy)))&
((~wise(paul))=>((~patient(susan)|brave(susan))))&
(![X]:((generous(X)|~humble(X))=>(funny(X)|~patient(X))))&
(![X]:(~tall(X)<=>~funny(X)))&
(((quiet(fred)|~strong(fred)))<=>(?[X]:((strong(X)|~funny(X)))))&
(![X]:((~old(X)|tall(X))=>(~funny(X)|generous(X))))&
((?[X]:(generous(X)))=>(?[X]:((~wise(X)<~>calm(X)))))&
(![X]:(~calm(X)=>~rich(X)))&
(~calm(lucy))&
(?[X]:((~quiet(X)&tall(X))))&
((~generous(paul)|~curious(paul)))&
(?[X]:(creative(X)))&
((~patient(mary)<~>~tall(mary)))&
(?[X]:(patient(X)))&
((~kind(john)|~rich(john)))&
((~humble(john)|~generous(john))) | ~strong(susan) | [
"p7",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2163478156498610259197200
% SZS output start Proof for 2163478156498610259197200
8. ? [X0] : ~rich(X0) => (strong(susan) & curious(susan)) [input p7]
16. ! [X0] : (~calm(X0) => ~rich(X0)) [input p15]
17. ~calm(lucy) [input p16]
25. ~strong(susan) [input hypothesis]
34. (strong(susan) & curious(susan)) | ! [X0] : rich(X0) [ennf transformation 8]
42. ! [X0] : (~rich(X0) | calm(X0)) [ennf transformation 16]
100. strong(susan) | rich(X0) [cnf transformation 34]
116. ~rich(X0) | calm(X0) [cnf transformation 42]
117. ~calm(lucy) [cnf transformation 17]
127. ~strong(susan) [cnf transformation 25]
222. 22 <=> ! [X0] : rich(X0) [avatar definition]
223. rich(X0) <- (22) [avatar component clause 222]
225. 23 <=> strong(susan) [avatar definition]
228. 22 | 23 [avatar split clause 100,225,222]
339. ~23 [avatar split clause 127,225]
351. calm(X0) <- (22) [resolution 116,223]
376. $false <- (22) [resolution 351,117]
379. ~22 [avatar contradiction clause 376]
380. $false [avatar sat refutation 228,339,379]
% SZS output end Proof for 2163478156498610259197200
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or quiet is both quiet and old and vice versa. If alice is both old and not tall then susan is both generous and not old and vice versa. Everyone who is either quiet or not brave is either not curious or not rich and vice versa. Everyone who is not happy is either not old or not brave. If paul is both generous and not tall then mary is both kind and generous and vice versa. Everyone who is either not kind or not calm is not quiet. Everyone who is not creative or funny is kind. Everyone who is both quiet and not tall is either not patient or not old. If fred is curious then lucy is old or wise. If someone is not tall then alice is either not funny or not old and vice versa. If fred is either not generous or brave then someone is brave or not rich and vice versa. If someone is both quiet and not strong then someone is kind and vice versa. Everyone who is both not wise and patient is either not rich or strong and vice versa. Everyone who is both not patient and not tall is happy or humble and vice versa. Everyone who is rich or not wise is either quiet or not funny and vice versa. Everyone who is either not strong or generous is wise or not patient and vice versa. Someone is both not funny and humble. Someone is both not funny and not quiet. Fred is both not curious and calm. Someone is both not happy and tall. Someone is either quiet or kind. Susan is not curious or not strong. Alice is both not strong and funny. Mary is not rich. | Alice is funny. | entailment | (![X]:((~old(X)<~>quiet(X))<=>(quiet(X)&old(X))))&
(((old(alice)&~tall(alice)))<=>((generous(susan)&~old(susan))))&
(![X]:((quiet(X)<~>~brave(X))<=>(~curious(X)<~>~rich(X))))&
(![X]:(~happy(X)=>(~old(X)<~>~brave(X))))&
(((generous(paul)&~tall(paul)))<=>((kind(mary)&generous(mary))))&
(![X]:((~kind(X)<~>~calm(X))=>~quiet(X)))&
(![X]:((~creative(X)|funny(X))=>kind(X)))&
(![X]:((quiet(X)&~tall(X))=>(~patient(X)<~>~old(X))))&
((curious(fred))=>((old(lucy)|wise(lucy))))&
((?[X]:(~tall(X)))<=>((~funny(alice)<~>~old(alice))))&
(((~generous(fred)<~>brave(fred)))<=>(?[X]:((brave(X)|~rich(X)))))&
((?[X]:((quiet(X)&~strong(X))))<=>(?[X]:(kind(X))))&
(![X]:((~wise(X)&patient(X))<=>(~rich(X)<~>strong(X))))&
(![X]:((~patient(X)&~tall(X))<=>(happy(X)|humble(X))))&
(![X]:((rich(X)|~wise(X))<=>(quiet(X)<~>~funny(X))))&
(![X]:((~strong(X)<~>generous(X))<=>(wise(X)|~patient(X))))&
(?[X]:((~funny(X)&humble(X))))&
(?[X]:((~funny(X)&~quiet(X))))&
((~curious(fred)&calm(fred)))&
(?[X]:((~happy(X)&tall(X))))&
(?[X]:((quiet(X)<~>kind(X))))&
((~curious(susan)|~strong(susan)))&
((~strong(alice)&funny(alice)))&
(~rich(mary)) | funny(alice) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 312199142091716742992757
% SZS output start Proof for 312199142091716742992757
23. funny(alice) & ~strong(alice) [input p22]
25. ~funny(alice) [input hypothesis]
153. funny(alice) [cnf transformation 23]
155. ~funny(alice) [cnf transformation 25]
215. 12 <=> funny(alice) [avatar definition]
298. 12 [avatar split clause 153,215]
299. ~12 [avatar split clause 155,215]
300. $false [avatar sat refutation 298,299]
% SZS output end Proof for 312199142091716742992757
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If john is calm or generous then someone is not happy. Everyone who is both not wise and calm is old. If alice is both not tall and creative then fred is either not funny or not kind and vice versa. If fred is old or not strong then someone is old or kind and vice versa. Everyone who is both not creative and happy is both patient and not generous. If alice is both brave and not funny then someone is rich and vice versa. Everyone who is not happy is either not creative or quiet and vice versa. Everyone who is either funny or creative is both wise and creative. Everyone who is either quiet or generous is either not strong or not wise and vice versa. Everyone who is both not curious and old is either not kind or tall. If susan is either not brave or tall then someone is tall or curious and vice versa. Everyone who is quiet is strong or not quiet and vice versa. Everyone who is wise is not strong or curious and vice versa. If someone is both not strong and old then mary is not wise or not generous and vice versa. If someone is generous or quiet then someone is not patient or not old. Everyone who is not wise is either quiet or not patient. Lucy is both tall and not wise. Paul is both happy and old. Alice is either not wise or not strong. Someone is not wise or wise. Someone is both patient and not curious. Someone is either not calm or rich. Someone is not creative or not old. | Mary is not strong. | contradiction | (((calm(john)|generous(john)))=>(?[X]:(~happy(X))))&
(![X]:((~wise(X)&calm(X))=>old(X)))&
(((~tall(alice)&creative(alice)))<=>((~funny(fred)<~>~kind(fred))))&
(((old(fred)|~strong(fred)))<=>(?[X]:((old(X)|kind(X)))))&
(![X]:((~creative(X)&happy(X))=>(patient(X)&~generous(X))))&
(((brave(alice)&~funny(alice)))<=>(?[X]:(rich(X))))&
(![X]:(~happy(X)<=>(~creative(X)<~>quiet(X))))&
(![X]:((funny(X)<~>creative(X))=>(wise(X)&creative(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(~strong(X)<~>~wise(X))))&
(![X]:((~curious(X)&old(X))=>(~kind(X)<~>tall(X))))&
(((~brave(susan)<~>tall(susan)))<=>(?[X]:((tall(X)|curious(X)))))&
(![X]:(quiet(X)<=>(strong(X)|~quiet(X))))&
(![X]:(wise(X)<=>(~strong(X)|curious(X))))&
((?[X]:((~strong(X)&old(X))))<=>((~wise(mary)|~generous(mary))))&
((?[X]:((generous(X)|quiet(X))))=>(?[X]:((~patient(X)|~old(X)))))&
(![X]:(~wise(X)=>(quiet(X)<~>~patient(X))))&
((tall(lucy)&~wise(lucy)))&
((happy(paul)&old(paul)))&
((~wise(alice)<~>~strong(alice)))&
(?[X]:((~wise(X)|wise(X))))&
(?[X]:((patient(X)&~curious(X))))&
(?[X]:((~calm(X)<~>rich(X))))&
(?[X]:((~creative(X)|~old(X)))) | ~strong(mary) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 79191526127920719538035
% SZS output start Proof for 79191526127920719538035
12. ! [X0] : (quiet(X0) <=> (~quiet(X0) | strong(X0))) [input p11]
24. ~strong(mary) [input hypothesis]
58. ! [X0] : ((quiet(X0) | (quiet(X0) & ~strong(X0))) & ((~quiet(X0) | strong(X0)) | ~quiet(X0))) [nnf transformation 12]
59. ! [X0] : ((quiet(X0) | (quiet(X0) & ~strong(X0))) & (~quiet(X0) | strong(X0) | ~quiet(X0))) [flattening 58]
123. ~quiet(X0) | strong(X0) | ~quiet(X0) [cnf transformation 59]
125. quiet(X0) | quiet(X0) [cnf transformation 59]
150. ~strong(mary) [cnf transformation 24]
151. ~quiet(X0) | strong(X0) [duplicate literal removal 123]
152. quiet(X0) [duplicate literal removal 125]
262. strong(X0) [subsumption resolution 151,152]
317. $false [subsumption resolution 150,262]
% SZS output end Proof for 79191526127920719538035
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not happy or not quiet then someone is not creative or quiet. If someone is kind then john is not old. Everyone who is both humble and not tall is both not curious and not rich and vice versa. Everyone who is either strong or kind is either happy or wise. Everyone who is both kind and strong is either not strong or strong and vice versa. Everyone who is either generous or funny is both curious and quiet and vice versa. Everyone who is strong or quiet is not old. Everyone who is not rich is not patient and vice versa. Everyone who is both wise and rich is either not calm or not old and vice versa. If susan is quiet or not calm then paul is both not patient and funny and vice versa. Everyone who is not patient is not wise or brave. If someone is either patient or humble then someone is not strong and vice versa. Everyone who is both not calm and calm is either not tall or brave. Everyone who is either kind or not funny is humble. If mary is either funny or creative then susan is humble and vice versa. Everyone who is not curious is curious or creative and vice versa. Alice is strong or not creative. Lucy is not happy or strong. Someone is tall or not curious. Susan is not generous or not creative. Alice is both creative and not generous. Susan is not happy. Fred is rich or patient. | Susan is not old. | entailment | ((?[X]:((~happy(X)<~>~quiet(X))))=>(?[X]:((~creative(X)|quiet(X)))))&
((?[X]:(kind(X)))=>(~old(john)))&
(![X]:((humble(X)&~tall(X))<=>(~curious(X)&~rich(X))))&
(![X]:((strong(X)<~>kind(X))=>(happy(X)<~>wise(X))))&
(![X]:((kind(X)&strong(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((generous(X)<~>funny(X))<=>(curious(X)&quiet(X))))&
(![X]:((strong(X)|quiet(X))=>~old(X)))&
(![X]:(~rich(X)<=>~patient(X)))&
(![X]:((wise(X)&rich(X))<=>(~calm(X)<~>~old(X))))&
(((quiet(susan)|~calm(susan)))<=>((~patient(paul)&funny(paul))))&
(![X]:(~patient(X)=>(~wise(X)|brave(X))))&
((?[X]:((patient(X)<~>humble(X))))<=>(?[X]:(~strong(X))))&
(![X]:((~calm(X)&calm(X))=>(~tall(X)<~>brave(X))))&
(![X]:((kind(X)<~>~funny(X))=>humble(X)))&
(((funny(mary)<~>creative(mary)))<=>(humble(susan)))&
(![X]:(~curious(X)<=>(curious(X)|creative(X))))&
((strong(alice)|~creative(alice)))&
((~happy(lucy)|strong(lucy)))&
(?[X]:((tall(X)|~curious(X))))&
((~generous(susan)|~creative(susan)))&
((creative(alice)&~generous(alice)))&
(~happy(susan))&
((rich(fred)|patient(fred))) | ~old(susan) | [
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 869541812147091080810360
% SZS output start Proof for 869541812147091080810360
5. ! [X0] : ((strong(X0) & kind(X0)) <=> (~strong(X0) <~> strong(X0))) [input p4]
7. ! [X0] : ((quiet(X0) | strong(X0)) => ~old(X0)) [input p6]
24. old(susan) [input hypothesis]
30. ! [X0] : (~old(X0) | (~quiet(X0) & ~strong(X0))) [ennf transformation 7]
43. ! [X0] : (((strong(X0) & kind(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) & (((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | (~strong(X0) | ~kind(X0)))) [nnf transformation 5]
44. ! [X0] : (((strong(X0) & kind(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) & (((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | ~strong(X0) | ~kind(X0))) [flattening 43]
79. strong(X0) | strong(X0) | strong(X0) [cnf transformation 44]
87. ~old(X0) | ~strong(X0) [cnf transformation 30]
126. old(susan) [cnf transformation 24]
133. strong(X0) [duplicate literal removal 79]
160. ~old(X0) [subsumption resolution 87,133]
207. $false [subsumption resolution 126,160]
% SZS output end Proof for 869541812147091080810360
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both brave and wise then someone is both not patient and not wise and vice versa.
If john is either not happy or not curious then paul is both tall and funny and vice versa.
If someone is not happy then someone is strong or not creative and vice versa.
Everyone who is not funny or humble is either not strong or brave and vice versa.
Everyone who is not old or old is either old or brave and vice versa.
If someone is old or not happy then susan is not patient or not humble and vice versa.
If someone is curious or not wise then someone is not strong and vice versa.
If someone is not humble or not calm then john is funny and vice versa.
If paul is not humble or not generous then john is wise and vice versa.
If john is either not curious or not brave then someone is both quiet and strong and vice versa.
Everyone who is not brave is creative or not old and vice versa.
If someone is either old or funny then someone is both kind and old and vice versa.
Everyone who is either happy or curious is both quiet and not strong.
Everyone who is not calm is both happy and humble.
Everyone who is not generous or old is either tall or patient.
Fred is happy or not generous.
Someone is tall or not humble.
Paul is either kind or not humble.
Lucy is either brave or not tall.
Susan is either strong or happy. | Paul is quiet. | neutral | ((?[X]:((brave(X)&wise(X))))<=>(?[X]:((~patient(X)&~wise(X)))))&
(((~happy(john)<~>~curious(john)))<=>((tall(paul)&funny(paul))))&
((?[X]:(~happy(X)))<=>(?[X]:((strong(X)|~creative(X)))))&
(![X]:((~funny(X)|humble(X))<=>(~strong(X)<~>brave(X))))&
(![X]:((~old(X)|old(X))<=>(old(X)<~>brave(X))))&
((?[X]:((old(X)|~happy(X))))<=>((~patient(susan)|~humble(susan))))&
((?[X]:((curious(X)|~wise(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((~humble(X)|~calm(X))))<=>(funny(john)))&
(((~humble(paul)|~generous(paul)))<=>(wise(john)))&
(((~curious(john)<~>~brave(john)))<=>(?[X]:((quiet(X)&strong(X)))))&
(![X]:(~brave(X)<=>(creative(X)|~old(X))))&
((?[X]:((old(X)<~>funny(X))))<=>(?[X]:((kind(X)&old(X)))))&
(![X]:((happy(X)<~>curious(X))=>(quiet(X)&~strong(X))))&
(![X]:(~calm(X)=>(happy(X)&humble(X))))&
(![X]:((~generous(X)|old(X))=>(tall(X)<~>patient(X))))&
((happy(fred)|~generous(fred)))&
(?[X]:((tall(X)|~humble(X))))&
((kind(paul)<~>~humble(paul)))&
((brave(lucy)<~>~tall(lucy)))&
((strong(susan)<~>happy(susan))) | quiet(paul) | [] | null | 0 |
Everyone who is not strong or not quiet is brave.
If someone is either not kind or rich then alice is brave or not humble and vice versa.
If someone is both not brave and not humble then someone is both not creative and not rich.
If paul is either not happy or patient then john is both not rich and funny and vice versa.
If fred is not funny or old then susan is both brave and kind and vice versa.
If someone is both not wise and not tall then someone is either strong or wise.
Everyone who is not strong is not tall.
If someone is both not creative and not humble then someone is either not happy or not creative and vice versa.
If john is either humble or not brave then lucy is calm.
Everyone who is both not calm and curious is either brave or curious.
Everyone who is calm or old is humble or funny and vice versa.
Everyone who is not wise is not humble or not calm and vice versa.
Everyone who is not rich is either patient or kind and vice versa.
Everyone who is old is both not old and creative.
If lucy is tall then fred is wise or creative.
Everyone who is either not curious or happy is not kind and vice versa.
Mary is both not old and quiet.
Someone is wise.
Lucy is either not strong or not happy.
Someone is not brave or not rich.
Someone is humble or wise.
Someone is not patient.
Someone is happy or not rich.
Lucy is old or not kind. | John is not old. | entailment | (![X]:((~strong(X)|~quiet(X))=>brave(X)))&
((?[X]:((~kind(X)<~>rich(X))))<=>((brave(alice)|~humble(alice))))&
((?[X]:((~brave(X)&~humble(X))))=>(?[X]:((~creative(X)&~rich(X)))))&
(((~happy(paul)<~>patient(paul)))<=>((~rich(john)&funny(john))))&
(((~funny(fred)|old(fred)))<=>((brave(susan)&kind(susan))))&
((?[X]:((~wise(X)&~tall(X))))=>(?[X]:((strong(X)<~>wise(X)))))&
(![X]:(~strong(X)=>~tall(X)))&
((?[X]:((~creative(X)&~humble(X))))<=>(?[X]:((~happy(X)<~>~creative(X)))))&
(((humble(john)<~>~brave(john)))=>(calm(lucy)))&
(![X]:((~calm(X)&curious(X))=>(brave(X)<~>curious(X))))&
(![X]:((calm(X)|old(X))<=>(humble(X)|funny(X))))&
(![X]:(~wise(X)<=>(~humble(X)|~calm(X))))&
(![X]:(~rich(X)<=>(patient(X)<~>kind(X))))&
(![X]:(old(X)=>(~old(X)&creative(X))))&
((tall(lucy))=>((wise(fred)|creative(fred))))&
(![X]:((~curious(X)<~>happy(X))<=>~kind(X)))&
((~old(mary)&quiet(mary)))&
(?[X]:(wise(X)))&
((~strong(lucy)<~>~happy(lucy)))&
(?[X]:((~brave(X)|~rich(X))))&
(?[X]:((humble(X)|wise(X))))&
(?[X]:(~patient(X)))&
(?[X]:((happy(X)|~rich(X))))&
((old(lucy)|~kind(lucy))) | ~old(john) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 857766319964417055936245
% SZS output start Proof for 857766319964417055936245
14. ! [X0] : (old(X0) => (creative(X0) & ~old(X0))) [input p13]
25. old(john) [input hypothesis]
38. ! [X0] : ((creative(X0) & ~old(X0)) | ~old(X0)) [ennf transformation 14]
125. ~old(X0) | ~old(X0) [cnf transformation 38]
141. old(john) [cnf transformation 25]
142. ~old(X0) [duplicate literal removal 125]
329. $false [subsumption resolution 141,142]
% SZS output end Proof for 857766319964417055936245
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not wise is both wise and calm and vice versa.
If lucy is tall or not brave then mary is either funny or not brave and vice versa.
If someone is patient then someone is happy and vice versa.
If someone is both strong and old then susan is calm and vice versa.
Everyone who is both generous and not calm is not brave.
Everyone who is either not kind or tall is either not strong or tall and vice versa.
If someone is either tall or calm then john is either not creative or wise.
If lucy is both not kind and not humble then fred is both not generous and not curious.
Everyone who is either patient or tall is strong or not tall and vice versa.
Everyone who is not quiet is not wise or not calm.
Everyone who is either not wise or tall is both not rich and not quiet.
If mary is calm or not curious then mary is not old.
Everyone who is either calm or wise is both not patient and not strong.
If fred is both not quiet and not patient then someone is both tall and not happy.
Everyone who is not calm or humble is either not curious or not tall and vice versa.
If mary is not patient or not old then someone is not humble and vice versa.
Someone is not patient or tall.
Someone is either brave or calm.
Paul is brave.
Someone is generous or wise.
Someone is either kind or not rich.
Someone is kind or not wise.
Someone is not patient or funny.
Alice is both not rich and not wise. | Fred is not strong. | contradiction | (![X]:((~patient(X)<~>~wise(X))<=>(wise(X)&calm(X))))&
(((tall(lucy)|~brave(lucy)))<=>((funny(mary)<~>~brave(mary))))&
((?[X]:(patient(X)))<=>(?[X]:(happy(X))))&
((?[X]:((strong(X)&old(X))))<=>(calm(susan)))&
(![X]:((generous(X)&~calm(X))=>~brave(X)))&
(![X]:((~kind(X)<~>tall(X))<=>(~strong(X)<~>tall(X))))&
((?[X]:((tall(X)<~>calm(X))))=>((~creative(john)<~>wise(john))))&
(((~kind(lucy)&~humble(lucy)))=>((~generous(fred)&~curious(fred))))&
(![X]:((patient(X)<~>tall(X))<=>(strong(X)|~tall(X))))&
(![X]:(~quiet(X)=>(~wise(X)|~calm(X))))&
(![X]:((~wise(X)<~>tall(X))=>(~rich(X)&~quiet(X))))&
(((calm(mary)|~curious(mary)))=>(~old(mary)))&
(![X]:((calm(X)<~>wise(X))=>(~patient(X)&~strong(X))))&
(((~quiet(fred)&~patient(fred)))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((~calm(X)|humble(X))<=>(~curious(X)<~>~tall(X))))&
(((~patient(mary)|~old(mary)))<=>(?[X]:(~humble(X))))&
(?[X]:((~patient(X)|tall(X))))&
(?[X]:((brave(X)<~>calm(X))))&
(brave(paul))&
(?[X]:((generous(X)|wise(X))))&
(?[X]:((kind(X)<~>~rich(X))))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((~patient(X)|funny(X))))&
((~rich(alice)&~wise(alice))) | ~strong(fred) | [
"p0",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3563698405030062271361982
% SZS output start Proof for 3563698405030062271361982
1. ! [X0] : ((~patient(X0) <~> ~wise(X0)) <=> (calm(X0) & wise(X0))) [input p0]
9. ! [X0] : ((patient(X0) <~> tall(X0)) <=> (~tall(X0) | strong(X0))) [input p8]
13. ! [X0] : ((calm(X0) <~> wise(X0)) => (~strong(X0) & ~patient(X0))) [input p12]
25. ~strong(fred) [input hypothesis]
36. ! [X0] : ((~strong(X0) & ~patient(X0)) | (calm(X0) <=> wise(X0))) [ennf transformation 13]
39. ! [X0] : ((((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | (~calm(X0) | ~wise(X0))) & ((calm(X0) & wise(X0)) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))))) [nnf transformation 1]
40. ! [X0] : ((((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | ~calm(X0) | ~wise(X0)) & ((calm(X0) & wise(X0)) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))))) [flattening 39]
54. ! [X0] : ((((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (tall(X0) & ~strong(X0))) & ((~tall(X0) | strong(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0))))) [nnf transformation 9]
55. ! [X0] : ((((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (tall(X0) & ~strong(X0))) & (~tall(X0) | strong(X0) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0))))) [flattening 54]
57. ! [X0] : ((~strong(X0) & ~patient(X0)) | ((calm(X0) | ~wise(X0)) & (wise(X0) | ~calm(X0)))) [nnf transformation 36]
82. wise(X0) | ~patient(X0) | wise(X0) [cnf transformation 40]
84. ~patient(X0) | calm(X0) | wise(X0) [cnf transformation 40]
85. ~wise(X0) | ~patient(X0) | ~calm(X0) | ~wise(X0) [cnf transformation 40]
114. ~tall(X0) | strong(X0) | patient(X0) | ~tall(X0) [cnf transformation 55]
116. tall(X0) | patient(X0) | tall(X0) [cnf transformation 55]
127. ~patient(X0) | calm(X0) | ~wise(X0) [cnf transformation 57]
152. ~strong(fred) [cnf transformation 25]
153. ~tall(X0) | strong(X0) | patient(X0) [duplicate literal removal 114]
154. tall(X0) | patient(X0) [duplicate literal removal 116]
159. ~patient(X0) | wise(X0) [duplicate literal removal 82]
160. ~calm(X0) | ~patient(X0) | ~wise(X0) [duplicate literal removal 85]
255. strong(X0) | patient(X0) [subsumption resolution 153,154]
270. ~patient(X0) | calm(X0) [subsumption resolution 127,84]
276. 25 <=> patient(fred) [avatar definition]
278. patient(fred) <- (25) [avatar component clause 276]
352. patient(fred) [resolution 255,152]
357. 25 [avatar split clause 352,276]
361. wise(fred) <- (25) [resolution 278,159]
363. calm(fred) <- (25) [resolution 270,278]
446. ~patient(fred) | ~wise(fred) <- (25) [resolution 160,363]
449. ~wise(fred) <- (25) [subsumption resolution 446,278]
450. $false <- (25) [subsumption resolution 449,361]
451. ~25 [avatar contradiction clause 450]
458. $false [avatar sat refutation 357,451]
% SZS output end Proof for 3563698405030062271361982
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and not generous is either rich or not patient and vice versa. Everyone who is both not wise and kind is not humble. Everyone who is happy is patient or not happy. If alice is brave or not tall then someone is quiet. If lucy is both not quiet and creative then fred is tall and vice versa. If someone is not old or not funny then paul is calm and vice versa. Everyone who is not humble is rich or not calm and vice versa. Everyone who is either not rich or not generous is not wise and vice versa. If lucy is either not calm or not patient then john is not wise. Everyone who is not patient is not wise and vice versa. Everyone who is either not creative or not quiet is both not patient and rich. If alice is not quiet then someone is either not happy or generous. Everyone who is either quiet or patient is creative or not old and vice versa. Everyone who is both tall and not rich is not creative and vice versa. If someone is both not rich and strong then paul is creative and vice versa. Everyone who is not brave or strong is not calm and vice versa. John is not happy. Mary is not strong or not quiet. Someone is not generous. Someone is not quiet or not kind. John is either happy or wise. Mary is calm. Mary is either curious or strong. | Fred is not happy. | entailment | (![X]:((~brave(X)&~generous(X))<=>(rich(X)<~>~patient(X))))&
(![X]:((~wise(X)&kind(X))=>~humble(X)))&
(![X]:(happy(X)=>(patient(X)|~happy(X))))&
(((brave(alice)|~tall(alice)))=>(?[X]:(quiet(X))))&
(((~quiet(lucy)&creative(lucy)))<=>(tall(fred)))&
((?[X]:((~old(X)|~funny(X))))<=>(calm(paul)))&
(![X]:(~humble(X)<=>(rich(X)|~calm(X))))&
(![X]:((~rich(X)<~>~generous(X))<=>~wise(X)))&
(((~calm(lucy)<~>~patient(lucy)))=>(~wise(john)))&
(![X]:(~patient(X)<=>~wise(X)))&
(![X]:((~creative(X)<~>~quiet(X))=>(~patient(X)&rich(X))))&
((~quiet(alice))=>(?[X]:((~happy(X)<~>generous(X)))))&
(![X]:((quiet(X)<~>patient(X))<=>(creative(X)|~old(X))))&
(![X]:((tall(X)&~rich(X))<=>~creative(X)))&
((?[X]:((~rich(X)&strong(X))))<=>(creative(paul)))&
(![X]:((~brave(X)|strong(X))<=>~calm(X)))&
(~happy(john))&
((~strong(mary)|~quiet(mary)))&
(?[X]:(~generous(X)))&
(?[X]:((~quiet(X)|~kind(X))))&
((happy(john)<~>wise(john)))&
(calm(mary))&
((curious(mary)<~>strong(mary))) | ~happy(fred) | [
"p2",
"p4",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3572827619053487012448072
% SZS output start Proof for 3572827619053487012448072
3. ! [X0] : (happy(X0) => (~happy(X0) | patient(X0))) [input p2]
5. (creative(lucy) & ~quiet(lucy)) <=> tall(fred) [input p4]
11. ! [X0] : ((~creative(X0) <~> ~quiet(X0)) => (rich(X0) & ~patient(X0))) [input p10]
13. ! [X0] : ((quiet(X0) <~> patient(X0)) <=> (~old(X0) | creative(X0))) [input p12]
14. ! [X0] : ((~rich(X0) & tall(X0)) <=> ~creative(X0)) [input p13]
24. happy(fred) [input hypothesis]
29. ! [X0] : ((~happy(X0) | patient(X0)) | ~happy(X0)) [ennf transformation 3]
30. ! [X0] : (~happy(X0) | patient(X0) | ~happy(X0)) [flattening 29]
33. ! [X0] : ((rich(X0) & ~patient(X0)) | (~creative(X0) <=> ~quiet(X0))) [ennf transformation 11]
39. ((creative(lucy) & ~quiet(lucy)) | ~tall(fred)) & (tall(fred) | (~creative(lucy) | quiet(lucy))) [nnf transformation 5]
40. ((creative(lucy) & ~quiet(lucy)) | ~tall(fred)) & (tall(fred) | ~creative(lucy) | quiet(lucy)) [flattening 39]
48. ! [X0] : ((rich(X0) & ~patient(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0)))) [nnf transformation 33]
52. ! [X0] : ((((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | (old(X0) & ~creative(X0))) & ((~old(X0) | creative(X0)) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0))))) [nnf transformation 13]
53. ! [X0] : ((((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | (old(X0) & ~creative(X0))) & (~old(X0) | creative(X0) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0))))) [flattening 52]
54. ! [X0] : (((~rich(X0) & tall(X0)) | creative(X0)) & (~creative(X0) | (rich(X0) | ~tall(X0)))) [nnf transformation 14]
55. ! [X0] : (((~rich(X0) & tall(X0)) | creative(X0)) & (~creative(X0) | rich(X0) | ~tall(X0))) [flattening 54]
72. ~happy(X0) | patient(X0) | ~happy(X0) [cnf transformation 30]
76. ~quiet(lucy) | ~tall(fred) [cnf transformation 40]
77. creative(lucy) | ~tall(fred) [cnf transformation 40]
90. ~creative(X0) | ~patient(X0) | quiet(X0) [cnf transformation 48]
97. patient(X0) | quiet(X0) | ~creative(X0) [cnf transformation 53]
99. ~patient(X0) | ~quiet(X0) | ~creative(X0) [cnf transformation 53]
102. creative(X0) | tall(X0) [cnf transformation 55]
118. happy(fred) [cnf transformation 24]
119. ~happy(X0) | patient(X0) [duplicate literal removal 72]
135. 4 <=> tall(fred) [avatar definition]
139. 5 <=> creative(lucy) [avatar definition]
141. creative(lucy) <- (5) [avatar component clause 139]
142. ~4 | 5 [avatar split clause 77,139,135]
144. 6 <=> quiet(lucy) [avatar definition]
146. ~quiet(lucy) <- (~6) [avatar component clause 144]
147. ~4 | ~6 [avatar split clause 76,144,135]
198. ~creative(X0) | ~patient(X0) [subsumption resolution 99,90]
199. ~creative(X0) | quiet(X0) [subsumption resolution 97,90]
246. patient(fred) [resolution 119,118]
248. ~patient(X0) | tall(X0) [resolution 198,102]
365. tall(fred) [resolution 248,246]
369. 4 [avatar split clause 365,135]
373. quiet(lucy) <- (5) [resolution 141,199]
386. $false <- (5, ~6) [subsumption resolution 373,146]
387. ~5 | 6 [avatar contradiction clause 386]
388. $false [avatar sat refutation 142,147,369,387]
% SZS output end Proof for 3572827619053487012448072
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both not tall and not funny then paul is either not curious or happy and vice versa.
If mary is both creative and strong then mary is both not old and not calm.
If john is both not curious and strong then mary is either tall or rich and vice versa.
Everyone who is both kind and generous is either patient or not brave.
If lucy is not funny then paul is humble and vice versa.
Everyone who is both not funny and not wise is not kind and vice versa.
Everyone who is both calm and patient is both brave and quiet.
If someone is both not kind and strong then mary is not patient and vice versa.
If paul is not kind or generous then someone is not quiet or not humble and vice versa.
If john is not wise or not rich then lucy is not quiet and vice versa.
Everyone who is both happy and brave is both strong and quiet.
If someone is old then someone is both not funny and humble and vice versa.
Everyone who is either not tall or quiet is both not tall and not patient and vice versa.
Everyone who is both not tall and creative is funny or curious and vice versa.
Everyone who is strong is humble.
If someone is not old or not patient then paul is both creative and strong.
Mary is both not patient and brave.
Mary is old.
Someone is quiet or not wise.
Someone is generous or wise.
Someone is not rich or not generous.
Paul is rich.
Someone is both old and brave. | Lucy is not kind. | neutral | (((~tall(mary)&~funny(mary)))<=>((~curious(paul)<~>happy(paul))))&
(((creative(mary)&strong(mary)))=>((~old(mary)&~calm(mary))))&
(((~curious(john)&strong(john)))<=>((tall(mary)<~>rich(mary))))&
(![X]:((kind(X)&generous(X))=>(patient(X)<~>~brave(X))))&
((~funny(lucy))<=>(humble(paul)))&
(![X]:((~funny(X)&~wise(X))<=>~kind(X)))&
(![X]:((calm(X)&patient(X))=>(brave(X)&quiet(X))))&
((?[X]:((~kind(X)&strong(X))))<=>(~patient(mary)))&
(((~kind(paul)|generous(paul)))<=>(?[X]:((~quiet(X)|~humble(X)))))&
(((~wise(john)|~rich(john)))<=>(~quiet(lucy)))&
(![X]:((happy(X)&brave(X))=>(strong(X)&quiet(X))))&
((?[X]:(old(X)))<=>(?[X]:((~funny(X)&humble(X)))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~tall(X)&~patient(X))))&
(![X]:((~tall(X)&creative(X))<=>(funny(X)|curious(X))))&
(![X]:(strong(X)=>humble(X)))&
((?[X]:((~old(X)|~patient(X))))=>((creative(paul)&strong(paul))))&
((~patient(mary)&brave(mary)))&
(old(mary))&
(?[X]:((quiet(X)|~wise(X))))&
(?[X]:((generous(X)|wise(X))))&
(?[X]:((~rich(X)|~generous(X))))&
(rich(paul))&
(?[X]:((old(X)&brave(X)))) | ~kind(lucy) | [] | null | 0 |
If alice is not funny or not happy then someone is quiet or wise and vice versa.
Everyone who is not wise is not humble or strong and vice versa.
If someone is both not creative and not patient then fred is either generous or humble and vice versa.
If mary is creative or old then someone is curious.
Everyone who is either brave or not patient is either humble or not tall.
If someone is both creative and wise then someone is generous or quiet and vice versa.
If someone is both not calm and calm then someone is either humble or generous and vice versa.
If someone is not curious or not happy then susan is either not wise or not strong and vice versa.
Everyone who is funny is both not calm and generous and vice versa.
If alice is kind or not quiet then someone is brave.
Everyone who is either happy or strong is not tall and vice versa.
Everyone who is both calm and generous is both happy and not wise and vice versa.
Everyone who is not humble is curious or rich and vice versa.
If someone is either humble or not calm then paul is either generous or not kind and vice versa.
If alice is either not quiet or not patient then someone is both not strong and old and vice versa.
Everyone who is not kind or not calm is both creative and wise and vice versa.
Someone is not curious or curious.
Someone is quiet or not creative.
Susan is either brave or humble.
Someone is either old or not calm.
Someone is either kind or not rich.
Susan is wise.
Someone is either not rich or creative.
Mary is rich or not old. | Susan is not curious. | entailment | (((~funny(alice)|~happy(alice)))<=>(?[X]:((quiet(X)|wise(X)))))&
(![X]:(~wise(X)<=>(~humble(X)|strong(X))))&
((?[X]:((~creative(X)&~patient(X))))<=>((generous(fred)<~>humble(fred))))&
(((creative(mary)|old(mary)))=>(?[X]:(curious(X))))&
(![X]:((brave(X)<~>~patient(X))=>(humble(X)<~>~tall(X))))&
((?[X]:((creative(X)&wise(X))))<=>(?[X]:((generous(X)|quiet(X)))))&
((?[X]:((~calm(X)&calm(X))))<=>(?[X]:((humble(X)<~>generous(X)))))&
((?[X]:((~curious(X)|~happy(X))))<=>((~wise(susan)<~>~strong(susan))))&
(![X]:(funny(X)<=>(~calm(X)&generous(X))))&
(((kind(alice)|~quiet(alice)))=>(?[X]:(brave(X))))&
(![X]:((happy(X)<~>strong(X))<=>~tall(X)))&
(![X]:((calm(X)&generous(X))<=>(happy(X)&~wise(X))))&
(![X]:(~humble(X)<=>(curious(X)|rich(X))))&
((?[X]:((humble(X)<~>~calm(X))))<=>((generous(paul)<~>~kind(paul))))&
(((~quiet(alice)<~>~patient(alice)))<=>(?[X]:((~strong(X)&old(X)))))&
(![X]:((~kind(X)|~calm(X))<=>(creative(X)&wise(X))))&
(?[X]:((~curious(X)|curious(X))))&
(?[X]:((quiet(X)|~creative(X))))&
((brave(susan)<~>humble(susan)))&
(?[X]:((old(X)<~>~calm(X))))&
(?[X]:((kind(X)<~>~rich(X))))&
(wise(susan))&
(?[X]:((~rich(X)<~>creative(X))))&
((rich(mary)|~old(mary))) | ~curious(susan) | [
"p1",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1270886998419202310961091
% SZS output start Proof for 1270886998419202310961091
2. ! [X0] : (~wise(X0) <=> (strong(X0) | ~humble(X0))) [input p1]
13. ! [X0] : (~humble(X0) <=> (rich(X0) | curious(X0))) [input p12]
22. wise(susan) [input p21]
25. curious(susan) [input hypothesis]
36. ! [X0] : ((~wise(X0) | (~strong(X0) & humble(X0))) & ((strong(X0) | ~humble(X0)) | wise(X0))) [nnf transformation 2]
37. ! [X0] : ((~wise(X0) | (~strong(X0) & humble(X0))) & (strong(X0) | ~humble(X0) | wise(X0))) [flattening 36]
66. ! [X0] : ((~humble(X0) | (~rich(X0) & ~curious(X0))) & ((rich(X0) | curious(X0)) | humble(X0))) [nnf transformation 13]
67. ! [X0] : ((~humble(X0) | (~rich(X0) & ~curious(X0))) & (rich(X0) | curious(X0) | humble(X0))) [flattening 66]
97. ~wise(X0) | humble(X0) [cnf transformation 37]
142. ~curious(X0) | ~humble(X0) [cnf transformation 67]
171. wise(susan) [cnf transformation 22]
175. curious(susan) [cnf transformation 25]
284. 24 <=> wise(susan) [avatar definition]
285. wise(susan) <- (24) [avatar component clause 284]
389. 46 <=> humble(susan) [avatar definition]
390. humble(susan) <- (46) [avatar component clause 389]
414. 24 [avatar split clause 171,284]
432. humble(susan) <- (24) [resolution 97,285]
436. 46 | ~24 [avatar split clause 432,284,389]
437. ~humble(susan) [resolution 142,175]
438. $false <- (46) [subsumption resolution 437,390]
439. ~46 [avatar contradiction clause 438]
440. $false [avatar sat refutation 414,436,439]
% SZS output end Proof for 1270886998419202310961091
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not tall and patient then someone is either not creative or curious and vice versa. Everyone who is not humble is either not creative or old and vice versa. Everyone who is both calm and not patient is patient or funny and vice versa. Everyone who is wise is either not kind or not humble and vice versa. Everyone who is both patient and creative is not tall or wise and vice versa. If fred is both quiet and calm then someone is patient. If someone is generous or tall then susan is not humble or old and vice versa. If someone is not happy then lucy is both tall and creative and vice versa. Everyone who is either not old or not creative is funny and vice versa. If fred is strong then mary is not wise or kind and vice versa. Everyone who is both not strong and old is funny. Everyone who is tall or not humble is either not curious or not old. Everyone who is either not funny or creative is both not generous and not strong and vice versa. Everyone who is not happy or not old is either not quiet or not funny. If alice is not generous or patient then mary is generous and vice versa. Someone is not brave or patient. Someone is not rich or wise. Someone is not curious. Alice is both not funny and not brave. John is either not kind or happy. Someone is either tall or patient. Mary is tall. | Alice is not humble. | entailment | (((~tall(paul)&patient(paul)))<=>(?[X]:((~creative(X)<~>curious(X)))))&
(![X]:(~humble(X)<=>(~creative(X)<~>old(X))))&
(![X]:((calm(X)&~patient(X))<=>(patient(X)|funny(X))))&
(![X]:(wise(X)<=>(~kind(X)<~>~humble(X))))&
(![X]:((patient(X)&creative(X))<=>(~tall(X)|wise(X))))&
(((quiet(fred)&calm(fred)))=>(?[X]:(patient(X))))&
((?[X]:((generous(X)|tall(X))))<=>((~humble(susan)|old(susan))))&
((?[X]:(~happy(X)))<=>((tall(lucy)&creative(lucy))))&
(![X]:((~old(X)<~>~creative(X))<=>funny(X)))&
((strong(fred))<=>((~wise(mary)|kind(mary))))&
(![X]:((~strong(X)&old(X))=>funny(X)))&
(![X]:((tall(X)|~humble(X))=>(~curious(X)<~>~old(X))))&
(![X]:((~funny(X)<~>creative(X))<=>(~generous(X)&~strong(X))))&
(![X]:((~happy(X)|~old(X))=>(~quiet(X)<~>~funny(X))))&
(((~generous(alice)|patient(alice)))<=>(generous(mary)))&
(?[X]:((~brave(X)|patient(X))))&
(?[X]:((~rich(X)|wise(X))))&
(?[X]:(~curious(X)))&
((~funny(alice)&~brave(alice)))&
((~kind(john)<~>happy(john)))&
(?[X]:((tall(X)<~>patient(X))))&
(tall(mary)) | ~humble(alice) | [
"p0",
"p1",
"p2",
"p4",
"p8",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7007797584149331923753572
% SZS output start Proof for 7007797584149331923753572
1. (patient(paul) & ~tall(paul)) <=> ? [X0] : (~creative(X0) <~> curious(X0)) [input p0]
2. ! [X0] : (~humble(X0) <=> (~creative(X0) <~> old(X0))) [input p1]
3. ! [X0] : ((~patient(X0) & calm(X0)) <=> (funny(X0) | patient(X0))) [input p2]
5. ! [X0] : ((creative(X0) & patient(X0)) <=> (wise(X0) | ~tall(X0))) [input p4]
9. ! [X0] : ((~old(X0) <~> ~creative(X0)) <=> funny(X0)) [input p8]
12. ! [X0] : ((~humble(X0) | tall(X0)) => (~curious(X0) <~> ~old(X0))) [input p11]
19. ~brave(alice) & ~funny(alice) [input p18]
23. humble(alice) [input hypothesis]
25. ~funny(alice) [pure predicate removal 19]
31. ! [X0] : ((~curious(X0) <~> ~old(X0)) | (humble(X0) & ~tall(X0))) [ennf transformation 12]
33. ((patient(paul) & ~tall(paul)) | ! [X0] : ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0)))) & (? [X0] : ((~curious(X0) | creative(X0)) & (curious(X0) | ~creative(X0))) | (~patient(paul) | tall(paul))) [nnf transformation 1]
34. ((patient(paul) & ~tall(paul)) | ! [X0] : ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0)))) & (? [X0] : ((~curious(X0) | creative(X0)) & (curious(X0) | ~creative(X0))) | ~patient(paul) | tall(paul)) [flattening 33]
35. ((patient(paul) & ~tall(paul)) | ! [X0] : ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0)))) & (? [X1] : ((~curious(X1) | creative(X1)) & (curious(X1) | ~creative(X1))) | ~patient(paul) | tall(paul)) [rectify 34]
36. ? [X1] : ((~curious(X1) | creative(X1)) & (curious(X1) | ~creative(X1))) => ((~curious(sK0) | creative(sK0)) & (curious(sK0) | ~creative(sK0))) [choice axiom]
37. ((patient(paul) & ~tall(paul)) | ! [X0] : ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0)))) & (((~curious(sK0) | creative(sK0)) & (curious(sK0) | ~creative(sK0))) | ~patient(paul) | tall(paul)) [skolemisation 35,36]
38. ! [X0] : ((~humble(X0) | ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0)))) & (((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | humble(X0))) [nnf transformation 2]
39. ! [X0] : (((~patient(X0) & calm(X0)) | (~funny(X0) & ~patient(X0))) & ((funny(X0) | patient(X0)) | (patient(X0) | ~calm(X0)))) [nnf transformation 3]
40. ! [X0] : (((~patient(X0) & calm(X0)) | (~funny(X0) & ~patient(X0))) & (funny(X0) | patient(X0) | patient(X0) | ~calm(X0))) [flattening 39]
42. ! [X0] : (((creative(X0) & patient(X0)) | (~wise(X0) & tall(X0))) & ((wise(X0) | ~tall(X0)) | (~creative(X0) | ~patient(X0)))) [nnf transformation 5]
43. ! [X0] : (((creative(X0) & patient(X0)) | (~wise(X0) & tall(X0))) & (wise(X0) | ~tall(X0) | ~creative(X0) | ~patient(X0))) [flattening 42]
56. ! [X0] : ((((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | ~funny(X0)) & (funny(X0) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0))))) [nnf transformation 9]
59. ! [X0] : (((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | (humble(X0) & ~tall(X0))) [nnf transformation 31]
73. ~tall(paul) | curious(X0) | creative(X0) [cnf transformation 37]
79. ~humble(X0) | old(X0) | creative(X0) [cnf transformation 38]
80. ~old(X0) | ~creative(X0) | ~humble(X0) [cnf transformation 38]
84. ~patient(X0) | ~patient(X0) [cnf transformation 40]
91. patient(X0) | tall(X0) [cnf transformation 43]
103. ~creative(X0) | funny(X0) | old(X0) [cnf transformation 56]
111. ~old(X0) | ~curious(X0) | ~tall(X0) [cnf transformation 59]
113. old(X0) | curious(X0) | ~tall(X0) [cnf transformation 59]
129. ~funny(alice) [cnf transformation 25]
135. humble(alice) [cnf transformation 23]
137. ~patient(X0) [duplicate literal removal 84]
147. 3 <=> ! [X0] : (curious(X0) | creative(X0)) [avatar definition]
148. curious(X0) | creative(X0) <- (3) [avatar component clause 147]
151. 4 <=> tall(paul) [avatar definition]
153. ~tall(paul) <- (~4) [avatar component clause 151]
155. 3 | ~4 [avatar split clause 73,151,147]
168. tall(X0) [subsumption resolution 91,137]
218. old(X0) | curious(X0) [subsumption resolution 113,168]
219. ~old(X0) | ~curious(X0) [subsumption resolution 111,168]
241. $false <- (~4) [subsumption resolution 153,168]
242. 4 [avatar contradiction clause 241]
280. old(alice) | creative(alice) [resolution 79,135]
283. 25 <=> creative(alice) [avatar definition]
285. creative(alice) <- (25) [avatar component clause 283]
287. 26 <=> old(alice) [avatar definition]
289. old(alice) <- (26) [avatar component clause 287]
290. 25 | 26 [avatar split clause 280,287,283]
291. ~creative(X0) | ~humble(X0) | curious(X0) [resolution 80,218]
292. ~humble(X0) | curious(X0) <- (3) [subsumption resolution 291,148]
295. curious(alice) <- (3) [resolution 292,135]
320. funny(alice) | old(alice) <- (25) [resolution 103,285]
327. old(alice) <- (25) [subsumption resolution 320,129]
328. 26 | ~25 [avatar split clause 327,283,287]
347. ~curious(alice) <- (26) [resolution 289,219]
351. $false <- (3, 26) [subsumption resolution 347,295]
352. ~3 | ~26 [avatar contradiction clause 351]
353. $false [avatar sat refutation 155,242,290,328,352]
% SZS output end Proof for 7007797584149331923753572
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not brave then someone is either creative or not curious. Everyone who is rich is not brave or not wise. If mary is either not patient or wise then someone is either not brave or not rich. If someone is both old and not tall then lucy is tall or not tall and vice versa. If someone is both tall and not calm then someone is either funny or wise and vice versa. Everyone who is not tall or not quiet is strong. If someone is happy or generous then someone is both not strong and not happy. If someone is strong or creative then paul is not old or quiet and vice versa. If someone is brave or humble then lucy is both old and not kind and vice versa. If mary is not happy or not quiet then someone is both rich and brave and vice versa. If someone is both strong and not curious then someone is both wise and not happy. If someone is not strong then someone is both calm and patient and vice versa. Everyone who is rich is both not rich and tall. Everyone who is quiet or not kind is tall or not kind. If someone is either not creative or calm then susan is funny and vice versa. If someone is both wise and old then fred is both brave and creative. Someone is humble or not rich. Someone is patient. Paul is either brave or rich. Someone is not quiet. Someone is both wise and old. Someone is either not curious or quiet. Lucy is either wise or kind. Paul is tall or not brave. | Mary is patient. | neutral | ((?[X]:((brave(X)|~brave(X))))=>(?[X]:((creative(X)<~>~curious(X)))))&
(![X]:(rich(X)=>(~brave(X)|~wise(X))))&
(((~patient(mary)<~>wise(mary)))=>(?[X]:((~brave(X)<~>~rich(X)))))&
((?[X]:((old(X)&~tall(X))))<=>((tall(lucy)|~tall(lucy))))&
((?[X]:((tall(X)&~calm(X))))<=>(?[X]:((funny(X)<~>wise(X)))))&
(![X]:((~tall(X)|~quiet(X))=>strong(X)))&
((?[X]:((happy(X)|generous(X))))=>(?[X]:((~strong(X)&~happy(X)))))&
((?[X]:((strong(X)|creative(X))))<=>((~old(paul)|quiet(paul))))&
((?[X]:((brave(X)|humble(X))))<=>((old(lucy)&~kind(lucy))))&
(((~happy(mary)|~quiet(mary)))<=>(?[X]:((rich(X)&brave(X)))))&
((?[X]:((strong(X)&~curious(X))))=>(?[X]:((wise(X)&~happy(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((calm(X)&patient(X)))))&
(![X]:(rich(X)=>(~rich(X)&tall(X))))&
(![X]:((quiet(X)|~kind(X))=>(tall(X)|~kind(X))))&
((?[X]:((~creative(X)<~>calm(X))))<=>(funny(susan)))&
((?[X]:((wise(X)&old(X))))=>((brave(fred)&creative(fred))))&
(?[X]:((humble(X)|~rich(X))))&
(?[X]:(patient(X)))&
((brave(paul)<~>rich(paul)))&
(?[X]:(~quiet(X)))&
(?[X]:((wise(X)&old(X))))&
(?[X]:((~curious(X)<~>quiet(X))))&
((wise(lucy)<~>kind(lucy)))&
((tall(paul)|~brave(paul))) | patient(mary) | [] | null | 0 |
If lucy is both not strong and kind then susan is either patient or old.
If someone is either patient or not funny then john is not funny and vice versa.
If alice is either not wise or humble then someone is either not calm or curious and vice versa.
Everyone who is not generous is brave and vice versa.
Everyone who is both not patient and brave is both generous and tall.
Everyone who is either tall or wise is not rich or brave.
If mary is either creative or not tall then john is both kind and calm.
Everyone who is not patient is humble.
Everyone who is not funny is brave or tall.
Everyone who is both not happy and curious is humble or quiet.
If someone is both not old and not happy then susan is not calm and vice versa.
If someone is not happy or strong then someone is wise and vice versa.
Everyone who is not rich or not old is both wise and old and vice versa.
If someone is not wise or calm then someone is both quiet and funny and vice versa.
If john is not wise or curious then mary is tall or quiet.
Everyone who is not curious or not generous is both quiet and not brave and vice versa.
Mary is either happy or not wise.
Fred is either not funny or not brave.
Susan is both funny and not quiet.
Susan is both strong and curious.
Someone is either humble or not rich. | John is not strong. | neutral | (((~strong(lucy)&kind(lucy)))=>((patient(susan)<~>old(susan))))&
((?[X]:((patient(X)<~>~funny(X))))<=>(~funny(john)))&
(((~wise(alice)<~>humble(alice)))<=>(?[X]:((~calm(X)<~>curious(X)))))&
(![X]:(~generous(X)<=>brave(X)))&
(![X]:((~patient(X)&brave(X))=>(generous(X)&tall(X))))&
(![X]:((tall(X)<~>wise(X))=>(~rich(X)|brave(X))))&
(((creative(mary)<~>~tall(mary)))=>((kind(john)&calm(john))))&
(![X]:(~patient(X)=>humble(X)))&
(![X]:(~funny(X)=>(brave(X)|tall(X))))&
(![X]:((~happy(X)&curious(X))=>(humble(X)|quiet(X))))&
((?[X]:((~old(X)&~happy(X))))<=>(~calm(susan)))&
((?[X]:((~happy(X)|strong(X))))<=>(?[X]:(wise(X))))&
(![X]:((~rich(X)|~old(X))<=>(wise(X)&old(X))))&
((?[X]:((~wise(X)|calm(X))))<=>(?[X]:((quiet(X)&funny(X)))))&
(((~wise(john)|curious(john)))=>((tall(mary)|quiet(mary))))&
(![X]:((~curious(X)|~generous(X))<=>(quiet(X)&~brave(X))))&
((happy(mary)<~>~wise(mary)))&
((~funny(fred)<~>~brave(fred)))&
((funny(susan)&~quiet(susan)))&
((strong(susan)&curious(susan)))&
(?[X]:((humble(X)<~>~rich(X)))) | ~strong(john) | [] | null | 0 |
Everyone who is not brave is not calm and vice versa.
Everyone who is not rich is both humble and patient.
If paul is both generous and not generous then someone is not rich or kind and vice versa.
Everyone who is either not strong or not calm is patient.
Everyone who is either strong or brave is either not creative or humble.
If mary is rich then alice is not patient or not happy and vice versa.
Everyone who is both creative and not kind is not creative.
If paul is funny or not wise then paul is both not funny and not kind and vice versa.
Everyone who is both old and curious is not humble or kind and vice versa.
If someone is not calm or not rich then john is both not calm and not quiet.
If mary is strong or not happy then fred is either not generous or not wise.
If someone is either curious or not rich then someone is either not funny or not patient and vice versa.
If someone is not patient or not generous then someone is either not kind or not brave and vice versa.
If alice is not funny then someone is either not kind or not happy.
If someone is not patient or not happy then john is tall or not strong and vice versa.
Everyone who is both not quiet and not curious is either calm or brave and vice versa.
Someone is either strong or quiet.
Fred is both not patient and not curious.
Someone is both not funny and not calm.
Someone is either not generous or wise.
Someone is not old or old.
John is happy or old.
Someone is strong or not curious. | Mary is not quiet. | neutral | (![X]:(~brave(X)<=>~calm(X)))&
(![X]:(~rich(X)=>(humble(X)&patient(X))))&
(((generous(paul)&~generous(paul)))<=>(?[X]:((~rich(X)|kind(X)))))&
(![X]:((~strong(X)<~>~calm(X))=>patient(X)))&
(![X]:((strong(X)<~>brave(X))=>(~creative(X)<~>humble(X))))&
((rich(mary))<=>((~patient(alice)|~happy(alice))))&
(![X]:((creative(X)&~kind(X))=>~creative(X)))&
(((funny(paul)|~wise(paul)))<=>((~funny(paul)&~kind(paul))))&
(![X]:((old(X)&curious(X))<=>(~humble(X)|kind(X))))&
((?[X]:((~calm(X)|~rich(X))))=>((~calm(john)&~quiet(john))))&
(((strong(mary)|~happy(mary)))=>((~generous(fred)<~>~wise(fred))))&
((?[X]:((curious(X)<~>~rich(X))))<=>(?[X]:((~funny(X)<~>~patient(X)))))&
((?[X]:((~patient(X)|~generous(X))))<=>(?[X]:((~kind(X)<~>~brave(X)))))&
((~funny(alice))=>(?[X]:((~kind(X)<~>~happy(X)))))&
((?[X]:((~patient(X)|~happy(X))))<=>((tall(john)|~strong(john))))&
(![X]:((~quiet(X)&~curious(X))<=>(calm(X)<~>brave(X))))&
(?[X]:((strong(X)<~>quiet(X))))&
((~patient(fred)&~curious(fred)))&
(?[X]:((~funny(X)&~calm(X))))&
(?[X]:((~generous(X)<~>wise(X))))&
(?[X]:((~old(X)|old(X))))&
((happy(john)|old(john)))&
(?[X]:((strong(X)|~curious(X)))) | ~quiet(mary) | [] | null | 0 |
If paul is calm then mary is quiet and vice versa.
Everyone who is either not strong or strong is both not strong and happy and vice versa.
If someone is curious or quiet then someone is both not rich and not happy.
Everyone who is not rich is both brave and not creative.
If mary is either creative or calm then alice is either not old or not tall.
Everyone who is not strong or not creative is both not quiet and not curious.
Everyone who is both kind and generous is wise or patient.
Everyone who is not humble or happy is either curious or funny.
Everyone who is both humble and calm is both happy and kind.
If someone is not calm or old then alice is either not wise or generous.
Everyone who is not funny is either rich or not calm.
If someone is either kind or not wise then fred is both not rich and not patient and vice versa.
If someone is either not funny or kind then someone is both generous and not kind and vice versa.
Everyone who is either not kind or not calm is both rich and old.
Someone is not old.
Fred is not calm.
Paul is wise or humble.
Paul is either kind or not calm.
Paul is creative or not generous.
Susan is quiet or not brave.
Someone is tall or old.
Someone is not strong. | Mary is not happy. | contradiction | ((calm(paul))<=>(quiet(mary)))&
(![X]:((~strong(X)<~>strong(X))<=>(~strong(X)&happy(X))))&
((?[X]:((curious(X)|quiet(X))))=>(?[X]:((~rich(X)&~happy(X)))))&
(![X]:(~rich(X)=>(brave(X)&~creative(X))))&
(((creative(mary)<~>calm(mary)))=>((~old(alice)<~>~tall(alice))))&
(![X]:((~strong(X)|~creative(X))=>(~quiet(X)&~curious(X))))&
(![X]:((kind(X)&generous(X))=>(wise(X)|patient(X))))&
(![X]:((~humble(X)|happy(X))=>(curious(X)<~>funny(X))))&
(![X]:((humble(X)&calm(X))=>(happy(X)&kind(X))))&
((?[X]:((~calm(X)|old(X))))=>((~wise(alice)<~>generous(alice))))&
(![X]:(~funny(X)=>(rich(X)<~>~calm(X))))&
((?[X]:((kind(X)<~>~wise(X))))<=>((~rich(fred)&~patient(fred))))&
((?[X]:((~funny(X)<~>kind(X))))<=>(?[X]:((generous(X)&~kind(X)))))&
(![X]:((~kind(X)<~>~calm(X))=>(rich(X)&old(X))))&
(?[X]:(~old(X)))&
(~calm(fred))&
((wise(paul)|humble(paul)))&
((kind(paul)<~>~calm(paul)))&
((creative(paul)|~generous(paul)))&
((quiet(susan)|~brave(susan)))&
(?[X]:((tall(X)|old(X))))&
(?[X]:(~strong(X))) | ~happy(mary) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 4250541595793419813942485
% SZS output start Proof for 4250541595793419813942485
2. ! [X0] : ((~strong(X0) <~> strong(X0)) <=> (happy(X0) & ~strong(X0))) [input p1]
23. ~happy(mary) [input hypothesis]
39. ! [X0] : ((((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | (~happy(X0) | strong(X0))) & ((happy(X0) & ~strong(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0))))) [nnf transformation 2]
40. ! [X0] : ((((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | ~happy(X0) | strong(X0)) & ((happy(X0) & ~strong(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0))))) [flattening 39]
70. happy(X0) | strong(X0) | strong(X0) [cnf transformation 40]
71. happy(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 40]
126. ~happy(mary) [cnf transformation 23]
129. happy(X0) | strong(X0) [duplicate literal removal 70]
130. happy(X0) | ~strong(X0) [duplicate literal removal 71]
143. happy(X0) [subsumption resolution 129,130]
272. $false [subsumption resolution 126,143]
% SZS output end Proof for 4250541595793419813942485
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and generous then someone is either kind or not brave. If fred is wise or brave then someone is not curious or patient and vice versa. Everyone who is both not humble and not brave is not kind. Everyone who is both not wise and old is either not old or happy and vice versa. If someone is either curious or not calm then lucy is kind and vice versa. Everyone who is creative or not old is both tall and not patient and vice versa. Everyone who is either humble or not strong is not kind. If someone is either not old or humble then someone is not tall or not curious. If lucy is both happy and creative then someone is either not wise or not generous. If mary is not generous then someone is curious or not strong. Everyone who is either not old or not brave is both not funny and strong. Everyone who is brave or strong is both not brave and calm and vice versa. Everyone who is wise is not funny or quiet and vice versa. Everyone who is humble or not wise is wise. Everyone who is either not old or not calm is not curious. If john is either patient or not tall then alice is generous or not quiet and vice versa. Someone is both not brave and funny. Lucy is funny or strong. Paul is strong or not rich. Mary is old or wise. Someone is both not rich and not funny. Someone is rich or not humble. | Fred is quiet. | neutral | ((?[X]:((strong(X)&generous(X))))=>(?[X]:((kind(X)<~>~brave(X)))))&
(((wise(fred)|brave(fred)))<=>(?[X]:((~curious(X)|patient(X)))))&
(![X]:((~humble(X)&~brave(X))=>~kind(X)))&
(![X]:((~wise(X)&old(X))<=>(~old(X)<~>happy(X))))&
((?[X]:((curious(X)<~>~calm(X))))<=>(kind(lucy)))&
(![X]:((creative(X)|~old(X))<=>(tall(X)&~patient(X))))&
(![X]:((humble(X)<~>~strong(X))=>~kind(X)))&
((?[X]:((~old(X)<~>humble(X))))=>(?[X]:((~tall(X)|~curious(X)))))&
(((happy(lucy)&creative(lucy)))=>(?[X]:((~wise(X)<~>~generous(X)))))&
((~generous(mary))=>(?[X]:((curious(X)|~strong(X)))))&
(![X]:((~old(X)<~>~brave(X))=>(~funny(X)&strong(X))))&
(![X]:((brave(X)|strong(X))<=>(~brave(X)&calm(X))))&
(![X]:(wise(X)<=>(~funny(X)|quiet(X))))&
(![X]:((humble(X)|~wise(X))=>wise(X)))&
(![X]:((~old(X)<~>~calm(X))=>~curious(X)))&
(((patient(john)<~>~tall(john)))<=>((generous(alice)|~quiet(alice))))&
(?[X]:((~brave(X)&funny(X))))&
((funny(lucy)|strong(lucy)))&
((strong(paul)|~rich(paul)))&
((old(mary)|wise(mary)))&
(?[X]:((~rich(X)&~funny(X))))&
(?[X]:((rich(X)|~humble(X)))) | quiet(fred) | [] | null | 0 |
Everyone who is both creative and funny is not humble and vice versa.
If someone is either strong or rich then paul is both not humble and not calm.
If fred is both not brave and not humble then john is either not happy or strong.
Everyone who is not brave is not kind.
Everyone who is either happy or strong is not brave and vice versa.
If someone is not humble then someone is not patient or not kind and vice versa.
If susan is either creative or not wise then someone is either not happy or generous and vice versa.
If someone is strong or not rich then someone is tall.
If lucy is both not kind and rich then someone is either kind or funny.
If mary is not calm then alice is both not calm and strong.
Everyone who is either strong or tall is both tall and strong.
Everyone who is not brave or kind is not kind and vice versa.
If someone is not calm then lucy is either creative or not brave.
If someone is not strong then alice is not brave and vice versa.
If someone is both rich and calm then someone is not brave and vice versa.
Lucy is calm or funny.
Alice is either not kind or not rich.
Fred is both not funny and not happy.
Susan is not brave or not strong.
Susan is either kind or not funny.
Mary is not wise or happy.
Someone is quiet or humble. | Susan is brave. | contradiction | (![X]:((creative(X)&funny(X))<=>~humble(X)))&
((?[X]:((strong(X)<~>rich(X))))=>((~humble(paul)&~calm(paul))))&
(((~brave(fred)&~humble(fred)))=>((~happy(john)<~>strong(john))))&
(![X]:(~brave(X)=>~kind(X)))&
(![X]:((happy(X)<~>strong(X))<=>~brave(X)))&
((?[X]:(~humble(X)))<=>(?[X]:((~patient(X)|~kind(X)))))&
(((creative(susan)<~>~wise(susan)))<=>(?[X]:((~happy(X)<~>generous(X)))))&
((?[X]:((strong(X)|~rich(X))))=>(?[X]:(tall(X))))&
(((~kind(lucy)&rich(lucy)))=>(?[X]:((kind(X)<~>funny(X)))))&
((~calm(mary))=>((~calm(alice)&strong(alice))))&
(![X]:((strong(X)<~>tall(X))=>(tall(X)&strong(X))))&
(![X]:((~brave(X)|kind(X))<=>~kind(X)))&
((?[X]:(~calm(X)))=>((creative(lucy)<~>~brave(lucy))))&
((?[X]:(~strong(X)))<=>(~brave(alice)))&
((?[X]:((rich(X)&calm(X))))<=>(?[X]:(~brave(X))))&
((calm(lucy)|funny(lucy)))&
((~kind(alice)<~>~rich(alice)))&
((~funny(fred)&~happy(fred)))&
((~brave(susan)|~strong(susan)))&
((kind(susan)<~>~funny(susan)))&
((~wise(mary)|happy(mary)))&
(?[X]:((quiet(X)|humble(X)))) | brave(susan) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6593351939422652196239281
% SZS output start Proof for 6593351939422652196239281
12. ! [X0] : ((kind(X0) | ~brave(X0)) <=> ~kind(X0)) [input p11]
23. brave(susan) [input hypothesis]
59. ! [X0] : (((kind(X0) | ~brave(X0)) | kind(X0)) & (~kind(X0) | (~kind(X0) & brave(X0)))) [nnf transformation 12]
60. ! [X0] : ((kind(X0) | ~brave(X0) | kind(X0)) & (~kind(X0) | (~kind(X0) & brave(X0)))) [flattening 59]
109. ~kind(X0) | ~kind(X0) [cnf transformation 60]
110. kind(X0) | ~brave(X0) | kind(X0) [cnf transformation 60]
127. brave(susan) [cnf transformation 23]
128. ~kind(X0) [duplicate literal removal 109]
129. ~brave(X0) | kind(X0) [duplicate literal removal 110]
324. 44 <=> brave(susan) [avatar definition]
325. brave(susan) <- (44) [avatar component clause 324]
342. 44 [avatar split clause 127,324]
362. kind(susan) <- (44) [resolution 129,325]
365. $false <- (44) [subsumption resolution 362,128]
366. ~44 [avatar contradiction clause 365]
367. $false [avatar sat refutation 342,366]
% SZS output end Proof for 6593351939422652196239281
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is not funny and vice versa.
Everyone who is both funny and quiet is rich or happy and vice versa.
Everyone who is both not kind and not humble is either quiet or not strong.
Everyone who is both not curious and not strong is not humble and vice versa.
Everyone who is happy or old is both generous and strong.
If someone is either wise or not calm then someone is both kind and not brave and vice versa.
If susan is not curious or generous then susan is both not happy and not wise.
If fred is both not quiet and not generous then someone is creative.
If mary is quiet or not tall then someone is both rich and generous and vice versa.
Everyone who is tall is not happy or creative and vice versa.
If mary is generous then someone is both kind and not happy and vice versa.
If lucy is both not creative and wise then someone is either generous or quiet and vice versa.
If someone is not kind then someone is either generous or patient.
Everyone who is not humble is not brave or not generous and vice versa.
Everyone who is both not funny and not kind is not brave and vice versa.
Everyone who is either generous or brave is rich and vice versa.
Someone is either not strong or not wise.
Someone is curious or brave.
Mary is either calm or not humble.
Someone is not patient.
Someone is quiet or not rich.
Someone is both not humble and not funny.
John is either not old or not tall. | Susan is calm. | entailment | (![X]:(~curious(X)<=>~funny(X)))&
(![X]:((funny(X)&quiet(X))<=>(rich(X)|happy(X))))&
(![X]:((~kind(X)&~humble(X))=>(quiet(X)<~>~strong(X))))&
(![X]:((~curious(X)&~strong(X))<=>~humble(X)))&
(![X]:((happy(X)|old(X))=>(generous(X)&strong(X))))&
((?[X]:((wise(X)<~>~calm(X))))<=>(?[X]:((kind(X)&~brave(X)))))&
(((~curious(susan)|generous(susan)))=>((~happy(susan)&~wise(susan))))&
(((~quiet(fred)&~generous(fred)))=>(?[X]:(creative(X))))&
(((quiet(mary)|~tall(mary)))<=>(?[X]:((rich(X)&generous(X)))))&
(![X]:(tall(X)<=>(~happy(X)|creative(X))))&
((generous(mary))<=>(?[X]:((kind(X)&~happy(X)))))&
(((~creative(lucy)&wise(lucy)))<=>(?[X]:((generous(X)<~>quiet(X)))))&
((?[X]:(~kind(X)))=>(?[X]:((generous(X)<~>patient(X)))))&
(![X]:(~humble(X)<=>(~brave(X)|~generous(X))))&
(![X]:((~funny(X)&~kind(X))<=>~brave(X)))&
(![X]:((generous(X)<~>brave(X))<=>rich(X)))&
(?[X]:((~strong(X)<~>~wise(X))))&
(?[X]:((curious(X)|brave(X))))&
((calm(mary)<~>~humble(mary)))&
(?[X]:(~patient(X)))&
(?[X]:((quiet(X)|~rich(X))))&
(?[X]:((~humble(X)&~funny(X))))&
((~old(john)<~>~tall(john))) | calm(susan) | [
"p3",
"p5",
"p6",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5503646321133503667727290
% SZS output start Proof for 5503646321133503667727290
4. ! [X0] : ((~strong(X0) & ~curious(X0)) <=> ~humble(X0)) [input p3]
6. ? [X0] : (wise(X0) <~> ~calm(X0)) <=> ? [X0] : (~brave(X0) & kind(X0)) [input p5]
7. (generous(susan) | ~curious(susan)) => (~wise(susan) & ~happy(susan)) [input p6]
14. ! [X0] : (~humble(X0) <=> (~generous(X0) | ~brave(X0))) [input p13]
15. ! [X0] : ((~kind(X0) & ~funny(X0)) <=> ~brave(X0)) [input p14]
24. ~calm(susan) [input hypothesis]
25. ? [X0] : (wise(X0) <~> ~calm(X0)) <=> ? [X1] : (~brave(X1) & kind(X1)) [rectify 6]
30. (~wise(susan) & ~happy(susan)) | (~generous(susan) & curious(susan)) [ennf transformation 7]
38. ! [X0] : (((~strong(X0) & ~curious(X0)) | humble(X0)) & (~humble(X0) | (strong(X0) | curious(X0)))) [nnf transformation 4]
39. ! [X0] : (((~strong(X0) & ~curious(X0)) | humble(X0)) & (~humble(X0) | strong(X0) | curious(X0))) [flattening 38]
40. (? [X0] : ((calm(X0) | ~wise(X0)) & (~calm(X0) | wise(X0))) | ! [X1] : (brave(X1) | ~kind(X1))) & (? [X1] : (~brave(X1) & kind(X1)) | ! [X0] : ((wise(X0) | calm(X0)) & (~calm(X0) | ~wise(X0)))) [nnf transformation 25]
41. (? [X0] : ((calm(X0) | ~wise(X0)) & (~calm(X0) | wise(X0))) | ! [X1] : (brave(X1) | ~kind(X1))) & (? [X2] : (~brave(X2) & kind(X2)) | ! [X3] : ((wise(X3) | calm(X3)) & (~calm(X3) | ~wise(X3)))) [rectify 40]
42. ? [X0] : ((calm(X0) | ~wise(X0)) & (~calm(X0) | wise(X0))) => ((calm(sK0) | ~wise(sK0)) & (~calm(sK0) | wise(sK0))) [choice axiom]
43. ? [X2] : (~brave(X2) & kind(X2)) => (~brave(sK1) & kind(sK1)) [choice axiom]
44. (((calm(sK0) | ~wise(sK0)) & (~calm(sK0) | wise(sK0))) | ! [X1] : (brave(X1) | ~kind(X1))) & ((~brave(sK1) & kind(sK1)) | ! [X3] : ((wise(X3) | calm(X3)) & (~calm(X3) | ~wise(X3)))) [skolemisation 41,43,42]
67. ! [X0] : ((~humble(X0) | (generous(X0) & brave(X0))) & ((~generous(X0) | ~brave(X0)) | humble(X0))) [nnf transformation 14]
68. ! [X0] : ((~humble(X0) | (generous(X0) & brave(X0))) & (~generous(X0) | ~brave(X0) | humble(X0))) [flattening 67]
69. ! [X0] : (((~kind(X0) & ~funny(X0)) | brave(X0)) & (~brave(X0) | (kind(X0) | funny(X0)))) [nnf transformation 15]
70. ! [X0] : (((~kind(X0) & ~funny(X0)) | brave(X0)) & (~brave(X0) | kind(X0) | funny(X0))) [flattening 69]
95. ~curious(X0) | humble(X0) [cnf transformation 39]
102. kind(sK1) | wise(X3) | calm(X3) [cnf transformation 44]
104. ~brave(sK1) | wise(X3) | calm(X3) [cnf transformation 44]
109. ~wise(susan) | curious(susan) [cnf transformation 30]
110. ~wise(susan) | ~generous(susan) [cnf transformation 30]
133. ~humble(X0) | generous(X0) [cnf transformation 68]
136. ~kind(X0) | brave(X0) [cnf transformation 70]
152. ~calm(susan) [cnf transformation 24]
154. 1 <=> ! [X1] : (brave(X1) | ~kind(X1)) [avatar definition]
155. ~kind(X1) | brave(X1) <- (1) [avatar component clause 154]
167. 4 <=> ! [X3] : (wise(X3) | calm(X3)) [avatar definition]
168. calm(X3) | wise(X3) <- (4) [avatar component clause 167]
170. 5 <=> brave(sK1) [avatar definition]
173. 4 | ~5 [avatar split clause 104,170,167]
179. 7 <=> kind(sK1) [avatar definition]
181. kind(sK1) <- (7) [avatar component clause 179]
182. 4 | 7 [avatar split clause 102,179,167]
185. 8 <=> generous(susan) [avatar definition]
187. ~generous(susan) <- (~8) [avatar component clause 185]
189. 9 <=> wise(susan) [avatar definition]
191. ~wise(susan) <- (~9) [avatar component clause 189]
192. ~8 | ~9 [avatar split clause 110,189,185]
194. 10 <=> curious(susan) [avatar definition]
196. curious(susan) <- (10) [avatar component clause 194]
197. 10 | ~9 [avatar split clause 109,189,194]
295. 1 [avatar split clause 136,154]
360. wise(susan) <- (4) [resolution 168,152]
362. $false <- (4, ~9) [subsumption resolution 360,191]
363. ~4 | 9 [avatar contradiction clause 362]
368. brave(sK1) <- (1, 7) [resolution 155,181]
372. 5 | ~1 | ~7 [avatar split clause 368,179,154,170]
373. humble(susan) <- (10) [resolution 196,95]
377. generous(susan) <- (10) [resolution 373,133]
379. $false <- (~8, 10) [subsumption resolution 377,187]
380. 8 | ~10 [avatar contradiction clause 379]
381. $false [avatar sat refutation 173,182,192,197,295,363,372,380]
% SZS output end Proof for 5503646321133503667727290
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and not tall is humble. If lucy is not patient then mary is both not curious and wise. Everyone who is not quiet or quiet is patient. Everyone who is not wise is not rich and vice versa. If someone is either not strong or not quiet then paul is either curious or brave and vice versa. Everyone who is both not curious and curious is not calm or old. Everyone who is both wise and calm is patient and vice versa. If someone is both not brave and not kind then alice is funny or brave and vice versa. Everyone who is not creative is not happy and vice versa. Everyone who is not funny or calm is curious and vice versa. Everyone who is either not happy or not kind is not old. If someone is not kind then lucy is both not funny and tall. Everyone who is not old or tall is either not strong or happy and vice versa. If alice is both not old and generous then fred is both strong and wise. Everyone who is tall is brave and vice versa. Someone is rich. Someone is both generous and not creative. Fred is either old or happy. Someone is either not happy or not kind. Someone is either not old or wise. Someone is funny or kind. | Fred is calm. | entailment | (![X]:((humble(X)&~tall(X))=>humble(X)))&
((~patient(lucy))=>((~curious(mary)&wise(mary))))&
(![X]:((~quiet(X)|quiet(X))=>patient(X)))&
(![X]:(~wise(X)<=>~rich(X)))&
((?[X]:((~strong(X)<~>~quiet(X))))<=>((curious(paul)<~>brave(paul))))&
(![X]:((~curious(X)&curious(X))=>(~calm(X)|old(X))))&
(![X]:((wise(X)&calm(X))<=>patient(X)))&
((?[X]:((~brave(X)&~kind(X))))<=>((funny(alice)|brave(alice))))&
(![X]:(~creative(X)<=>~happy(X)))&
(![X]:((~funny(X)|calm(X))<=>curious(X)))&
(![X]:((~happy(X)<~>~kind(X))=>~old(X)))&
((?[X]:(~kind(X)))=>((~funny(lucy)&tall(lucy))))&
(![X]:((~old(X)|tall(X))<=>(~strong(X)<~>happy(X))))&
(((~old(alice)&generous(alice)))=>((strong(fred)&wise(fred))))&
(![X]:(tall(X)<=>brave(X)))&
(?[X]:(rich(X)))&
(?[X]:((generous(X)&~creative(X))))&
((old(fred)<~>happy(fred)))&
(?[X]:((~happy(X)<~>~kind(X))))&
(?[X]:((~old(X)<~>wise(X))))&
(?[X]:((funny(X)|kind(X)))) | calm(fred) | [
"p2",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8513128575251842495521963
% SZS output start Proof for 8513128575251842495521963
3. ! [X0] : ((quiet(X0) | ~quiet(X0)) => patient(X0)) [input p2]
7. ! [X0] : ((calm(X0) & wise(X0)) <=> patient(X0)) [input p6]
22. ~calm(fred) [input hypothesis]
24. ! [X0] : (patient(X0) => (calm(X0) & wise(X0))) [unused predicate definition removal 7]
28. ! [X0] : (patient(X0) | (~quiet(X0) & quiet(X0))) [ennf transformation 3]
31. ! [X0] : ((calm(X0) & wise(X0)) | ~patient(X0)) [ennf transformation 24]
69. patient(X0) | quiet(X0) [cnf transformation 28]
70. patient(X0) | ~quiet(X0) [cnf transformation 28]
83. calm(X0) | ~patient(X0) [cnf transformation 31]
117. ~calm(fred) [cnf transformation 22]
132. patient(X0) [subsumption resolution 69,70]
163. calm(X0) [subsumption resolution 83,132]
246. $false [subsumption resolution 117,163]
% SZS output end Proof for 8513128575251842495521963
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is both creative and not happy then fred is not strong and vice versa.
If someone is both humble and not quiet then john is either brave or not tall and vice versa.
If lucy is either not generous or not old then someone is patient or not rich and vice versa.
Everyone who is not tall or quiet is not generous.
Everyone who is either humble or curious is both calm and patient and vice versa.
Everyone who is both not quiet and wise is brave.
Everyone who is not curious or not old is either not calm or not humble and vice versa.
Everyone who is strong or not calm is either not strong or quiet.
Everyone who is not curious is either not brave or not old.
If paul is generous or not happy then paul is not quiet or not curious.
Everyone who is either humble or not kind is not brave and vice versa.
If someone is either not creative or not tall then someone is both tall and kind and vice versa.
Everyone who is not kind is not kind or not humble.
If paul is not curious or not wise then someone is both not old and calm.
Everyone who is not kind is both kind and not curious.
Everyone who is either not calm or strong is not generous and vice versa.
John is both not rich and not wise.
Mary is happy or not tall.
Someone is either quiet or not happy.
Someone is both brave and patient.
Someone is either calm or strong.
Paul is either quiet or not quiet.
Someone is not old or strong.
Lucy is old. | Mary is not calm. | neutral | (((creative(john)&~happy(john)))<=>(~strong(fred)))&
((?[X]:((humble(X)&~quiet(X))))<=>((brave(john)<~>~tall(john))))&
(((~generous(lucy)<~>~old(lucy)))<=>(?[X]:((patient(X)|~rich(X)))))&
(![X]:((~tall(X)|quiet(X))=>~generous(X)))&
(![X]:((humble(X)<~>curious(X))<=>(calm(X)&patient(X))))&
(![X]:((~quiet(X)&wise(X))=>brave(X)))&
(![X]:((~curious(X)|~old(X))<=>(~calm(X)<~>~humble(X))))&
(![X]:((strong(X)|~calm(X))=>(~strong(X)<~>quiet(X))))&
(![X]:(~curious(X)=>(~brave(X)<~>~old(X))))&
(((generous(paul)|~happy(paul)))=>((~quiet(paul)|~curious(paul))))&
(![X]:((humble(X)<~>~kind(X))<=>~brave(X)))&
((?[X]:((~creative(X)<~>~tall(X))))<=>(?[X]:((tall(X)&kind(X)))))&
(![X]:(~kind(X)=>(~kind(X)|~humble(X))))&
(((~curious(paul)|~wise(paul)))=>(?[X]:((~old(X)&calm(X)))))&
(![X]:(~kind(X)=>(kind(X)&~curious(X))))&
(![X]:((~calm(X)<~>strong(X))<=>~generous(X)))&
((~rich(john)&~wise(john)))&
((happy(mary)|~tall(mary)))&
(?[X]:((quiet(X)<~>~happy(X))))&
(?[X]:((brave(X)&patient(X))))&
(?[X]:((calm(X)<~>strong(X))))&
((quiet(paul)<~>~quiet(paul)))&
(?[X]:((~old(X)|strong(X))))&
(old(lucy)) | ~calm(mary) | [] | null | 0 |
Everyone who is both patient and not brave is either not creative or not old and vice versa.
Everyone who is either brave or kind is either happy or brave.
Everyone who is not kind is both not humble and generous.
If susan is both not generous and generous then lucy is not wise or not funny.
Everyone who is either old or not happy is happy.
Everyone who is both quiet and not brave is not curious or old.
Everyone who is humble is not quiet or strong.
If fred is not tall or humble then fred is not creative or humble and vice versa.
If fred is quiet or strong then someone is either funny or not creative and vice versa.
Everyone who is rich or quiet is both humble and calm.
Everyone who is both not patient and not kind is both generous and strong and vice versa.
Everyone who is not generous or not humble is not tall.
Everyone who is either kind or strong is both old and not calm.
Everyone who is old is either tall or wise and vice versa.
If alice is either not tall or not kind then someone is not brave or not calm and vice versa.
If alice is either humble or generous then fred is either wise or not wise and vice versa.
Someone is not funny or not humble.
Someone is humble or tall.
Someone is not happy or not strong.
Someone is both not humble and happy.
Susan is both not creative and not happy.
Someone is either not tall or calm.
Someone is both not curious and happy.
Someone is calm. | Susan is not wise. | contradiction | (![X]:((patient(X)&~brave(X))<=>(~creative(X)<~>~old(X))))&
(![X]:((brave(X)<~>kind(X))=>(happy(X)<~>brave(X))))&
(![X]:(~kind(X)=>(~humble(X)&generous(X))))&
(((~generous(susan)&generous(susan)))=>((~wise(lucy)|~funny(lucy))))&
(![X]:((old(X)<~>~happy(X))=>happy(X)))&
(![X]:((quiet(X)&~brave(X))=>(~curious(X)|old(X))))&
(![X]:(humble(X)=>(~quiet(X)|strong(X))))&
(((~tall(fred)|humble(fred)))<=>((~creative(fred)|humble(fred))))&
(((quiet(fred)|strong(fred)))<=>(?[X]:((funny(X)<~>~creative(X)))))&
(![X]:((rich(X)|quiet(X))=>(humble(X)&calm(X))))&
(![X]:((~patient(X)&~kind(X))<=>(generous(X)&strong(X))))&
(![X]:((~generous(X)|~humble(X))=>~tall(X)))&
(![X]:((kind(X)<~>strong(X))=>(old(X)&~calm(X))))&
(![X]:(old(X)<=>(tall(X)<~>wise(X))))&
(((~tall(alice)<~>~kind(alice)))<=>(?[X]:((~brave(X)|~calm(X)))))&
(((humble(alice)<~>generous(alice)))<=>((wise(fred)<~>~wise(fred))))&
(?[X]:((~funny(X)|~humble(X))))&
(?[X]:((humble(X)|tall(X))))&
(?[X]:((~happy(X)|~strong(X))))&
(?[X]:((~humble(X)&happy(X))))&
((~creative(susan)&~happy(susan)))&
(?[X]:((~tall(X)<~>calm(X))))&
(?[X]:((~curious(X)&happy(X))))&
(?[X]:(calm(X))) | ~wise(susan) | [
"p0",
"p1",
"p2",
"p4",
"p11",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6363712894333771339125796
% SZS output start Proof for 6363712894333771339125796
1. ! [X0] : ((~brave(X0) & patient(X0)) <=> (~creative(X0) <~> ~old(X0))) [input p0]
2. ! [X0] : ((brave(X0) <~> kind(X0)) => (happy(X0) <~> brave(X0))) [input p1]
3. ! [X0] : (~kind(X0) => (generous(X0) & ~humble(X0))) [input p2]
5. ! [X0] : ((old(X0) <~> ~happy(X0)) => happy(X0)) [input p4]
12. ! [X0] : ((~humble(X0) | ~generous(X0)) => ~tall(X0)) [input p11]
14. ! [X0] : (old(X0) <=> (tall(X0) <~> wise(X0))) [input p13]
21. ~happy(susan) & ~creative(susan) [input p20]
25. ~wise(susan) [input hypothesis]
29. ! [X0] : ((happy(X0) <~> brave(X0)) | (brave(X0) <=> kind(X0))) [ennf transformation 2]
30. ! [X0] : ((generous(X0) & ~humble(X0)) | kind(X0)) [ennf transformation 3]
33. ! [X0] : (happy(X0) | (old(X0) <=> ~happy(X0))) [ennf transformation 5]
37. ! [X0] : (~tall(X0) | (humble(X0) & generous(X0))) [ennf transformation 12]
39. ! [X0] : (((~brave(X0) & patient(X0)) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0)))) & (((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | (brave(X0) | ~patient(X0)))) [nnf transformation 1]
40. ! [X0] : (((~brave(X0) & patient(X0)) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0)))) & (((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | brave(X0) | ~patient(X0))) [flattening 39]
41. ! [X0] : (((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ((brave(X0) | ~kind(X0)) & (kind(X0) | ~brave(X0)))) [nnf transformation 29]
42. ! [X0] : (happy(X0) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) [nnf transformation 33]
53. ! [X0] : ((old(X0) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0)))) & (((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | ~old(X0))) [nnf transformation 14]
78. ~old(X0) | ~brave(X0) | creative(X0) [cnf transformation 40]
81. brave(X0) | happy(X0) | brave(X0) | ~kind(X0) [cnf transformation 41]
84. ~humble(X0) | kind(X0) [cnf transformation 30]
88. happy(X0) | old(X0) | happy(X0) [cnf transformation 42]
107. ~tall(X0) | humble(X0) [cnf transformation 37]
112. ~old(X0) | tall(X0) | wise(X0) [cnf transformation 53]
135. ~creative(susan) [cnf transformation 21]
136. ~happy(susan) [cnf transformation 21]
141. ~wise(susan) [cnf transformation 25]
146. happy(X0) | old(X0) [duplicate literal removal 88]
147. ~kind(X0) | happy(X0) | brave(X0) [duplicate literal removal 81]
274. old(susan) [resolution 146,136]
288. ~brave(susan) | creative(susan) [resolution 78,274]
290. ~brave(susan) [subsumption resolution 288,135]
389. tall(susan) | wise(susan) [resolution 112,274]
393. tall(susan) [subsumption resolution 389,141]
498. humble(susan) [resolution 393,107]
520. kind(susan) [resolution 498,84]
521. happy(susan) | brave(susan) [resolution 520,147]
523. brave(susan) [subsumption resolution 521,136]
524. $false [subsumption resolution 523,290]
% SZS output end Proof for 6363712894333771339125796
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong is kind and vice versa.
If someone is either not brave or funny then someone is not quiet or not patient and vice versa.
If susan is both not calm and not generous then someone is not generous.
If susan is not brave then someone is happy or patient and vice versa.
If someone is not curious or rich then lucy is either not happy or rich and vice versa.
Everyone who is curious is either humble or not kind and vice versa.
If someone is both not kind and not calm then alice is both not strong and not quiet and vice versa.
If alice is not brave or strong then someone is quiet.
If john is not quiet or tall then someone is both not strong and brave.
If alice is humble or quiet then lucy is both funny and happy and vice versa.
If someone is both not funny and patient then susan is both not patient and funny and vice versa.
Everyone who is either happy or generous is humble or not kind and vice versa.
Everyone who is both curious and generous is both not humble and not calm.
Everyone who is wise or quiet is both not old and not kind and vice versa.
Everyone who is either not wise or creative is either tall or funny.
Everyone who is either humble or old is not brave or wise and vice versa.
Someone is not humble.
Someone is not creative.
Fred is not rich or tall.
Someone is either not humble or generous.
Susan is either not old or humble.
John is either not calm or wise.
Mary is either old or calm.
Someone is not old or not tall. | Susan is brave. | entailment | (![X]:(strong(X)<=>kind(X)))&
((?[X]:((~brave(X)<~>funny(X))))<=>(?[X]:((~quiet(X)|~patient(X)))))&
(((~calm(susan)&~generous(susan)))=>(?[X]:(~generous(X))))&
((~brave(susan))<=>(?[X]:((happy(X)|patient(X)))))&
((?[X]:((~curious(X)|rich(X))))<=>((~happy(lucy)<~>rich(lucy))))&
(![X]:(curious(X)<=>(humble(X)<~>~kind(X))))&
((?[X]:((~kind(X)&~calm(X))))<=>((~strong(alice)&~quiet(alice))))&
(((~brave(alice)|strong(alice)))=>(?[X]:(quiet(X))))&
(((~quiet(john)|tall(john)))=>(?[X]:((~strong(X)&brave(X)))))&
(((humble(alice)|quiet(alice)))<=>((funny(lucy)&happy(lucy))))&
((?[X]:((~funny(X)&patient(X))))<=>((~patient(susan)&funny(susan))))&
(![X]:((happy(X)<~>generous(X))<=>(humble(X)|~kind(X))))&
(![X]:((curious(X)&generous(X))=>(~humble(X)&~calm(X))))&
(![X]:((wise(X)|quiet(X))<=>(~old(X)&~kind(X))))&
(![X]:((~wise(X)<~>creative(X))=>(tall(X)<~>funny(X))))&
(![X]:((humble(X)<~>old(X))<=>(~brave(X)|wise(X))))&
(?[X]:(~humble(X)))&
(?[X]:(~creative(X)))&
((~rich(fred)|tall(fred)))&
(?[X]:((~humble(X)<~>generous(X))))&
((~old(susan)<~>humble(susan)))&
((~calm(john)<~>wise(john)))&
((old(mary)<~>calm(mary)))&
(?[X]:((~old(X)|~tall(X)))) | brave(susan) | [
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8992371942635339523425267
% SZS output start Proof for 8992371942635339523425267
16. ! [X0] : ((humble(X0) <~> old(X0)) <=> (wise(X0) | ~brave(X0))) [input p15]
21. ~old(susan) <~> humble(susan) [input p20]
25. ~brave(susan) [input hypothesis]
72. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | (~wise(X0) & brave(X0))) & ((wise(X0) | ~brave(X0)) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [nnf transformation 16]
73. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | (~wise(X0) & brave(X0))) & (wise(X0) | ~brave(X0) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [flattening 72]
81. (~humble(susan) | old(susan)) & (humble(susan) | ~old(susan)) [nnf transformation 21]
146. old(X0) | humble(X0) | brave(X0) [cnf transformation 73]
148. ~old(X0) | ~humble(X0) | brave(X0) [cnf transformation 73]
155. humble(susan) | ~old(susan) [cnf transformation 81]
156. ~humble(susan) | old(susan) [cnf transformation 81]
162. ~brave(susan) [cnf transformation 25]
214. 13 <=> brave(susan) [avatar definition]
216. ~brave(susan) <- (~13) [avatar component clause 214]
370. 45 <=> old(susan) [avatar definition]
371. ~old(susan) <- (~45) [avatar component clause 370]
372. old(susan) <- (45) [avatar component clause 370]
374. 46 <=> humble(susan) [avatar definition]
375. humble(susan) <- (46) [avatar component clause 374]
376. ~humble(susan) <- (~46) [avatar component clause 374]
377. 45 | ~46 [avatar split clause 156,374,370]
378. ~45 | 46 [avatar split clause 155,374,370]
408. ~13 [avatar split clause 162,214]
534. ~humble(susan) | brave(susan) <- (45) [resolution 148,372]
546. brave(susan) <- (45, 46) [subsumption resolution 534,375]
547. $false <- (~13, 45, 46) [subsumption resolution 546,216]
548. 13 | ~45 | ~46 [avatar contradiction clause 547]
549. humble(susan) | brave(susan) <- (~45) [resolution 371,146]
550. brave(susan) <- (~45, ~46) [subsumption resolution 549,376]
551. $false <- (~13, ~45, ~46) [subsumption resolution 550,216]
552. 13 | 45 | 46 [avatar contradiction clause 551]
553. $false [avatar sat refutation 377,378,408,548,552]
% SZS output end Proof for 8992371942635339523425267
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not quiet or curious then lucy is both funny and not kind. If someone is either not calm or funny then someone is old or quiet. If someone is old or wise then someone is kind or not curious. Everyone who is wise or generous is both not kind and tall. Everyone who is both brave and not curious is either not generous or not curious and vice versa. Everyone who is tall is not patient or not funny. Everyone who is either not calm or not generous is either not curious or not creative and vice versa. Everyone who is not generous or not strong is both not strong and kind and vice versa. If alice is both quiet and strong then mary is both wise and not funny. Everyone who is either not curious or brave is quiet or wise. If someone is wise then someone is either creative or not quiet. If someone is not creative then alice is either not rich or not quiet and vice versa. Everyone who is either old or not strong is both rich and not brave and vice versa. Everyone who is both happy and kind is not wise. If someone is not humble or not creative then someone is either happy or not calm and vice versa. Everyone who is happy is both tall and quiet. Fred is either calm or not curious. Someone is both happy and not brave. Someone is not creative. Someone is humble or not brave. Someone is either not wise or not kind. Alice is quiet. Fred is either not rich or not calm. Someone is wise. | Fred is old. | contradiction | ((?[X]:((~quiet(X)|curious(X))))=>((funny(lucy)&~kind(lucy))))&
((?[X]:((~calm(X)<~>funny(X))))=>(?[X]:((old(X)|quiet(X)))))&
((?[X]:((old(X)|wise(X))))=>(?[X]:((kind(X)|~curious(X)))))&
(![X]:((wise(X)|generous(X))=>(~kind(X)&tall(X))))&
(![X]:((brave(X)&~curious(X))<=>(~generous(X)<~>~curious(X))))&
(![X]:(tall(X)=>(~patient(X)|~funny(X))))&
(![X]:((~calm(X)<~>~generous(X))<=>(~curious(X)<~>~creative(X))))&
(![X]:((~generous(X)|~strong(X))<=>(~strong(X)&kind(X))))&
(((quiet(alice)&strong(alice)))=>((wise(mary)&~funny(mary))))&
(![X]:((~curious(X)<~>brave(X))=>(quiet(X)|wise(X))))&
((?[X]:(wise(X)))=>(?[X]:((creative(X)<~>~quiet(X)))))&
((?[X]:(~creative(X)))<=>((~rich(alice)<~>~quiet(alice))))&
(![X]:((old(X)<~>~strong(X))<=>(rich(X)&~brave(X))))&
(![X]:((happy(X)&kind(X))=>~wise(X)))&
((?[X]:((~humble(X)|~creative(X))))<=>(?[X]:((happy(X)<~>~calm(X)))))&
(![X]:(happy(X)=>(tall(X)&quiet(X))))&
((calm(fred)<~>~curious(fred)))&
(?[X]:((happy(X)&~brave(X))))&
(?[X]:(~creative(X)))&
(?[X]:((humble(X)|~brave(X))))&
(?[X]:((~wise(X)<~>~kind(X))))&
(quiet(alice))&
((~rich(fred)<~>~calm(fred)))&
(?[X]:(wise(X))) | old(fred) | [
"p3",
"p4",
"p7",
"p12",
"p16",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6456821530264404636497127
% SZS output start Proof for 6456821530264404636497127
4. ! [X0] : ((generous(X0) | wise(X0)) => (tall(X0) & ~kind(X0))) [input p3]
5. ! [X0] : ((~curious(X0) & brave(X0)) <=> (~generous(X0) <~> ~curious(X0))) [input p4]
8. ! [X0] : ((~strong(X0) | ~generous(X0)) <=> (kind(X0) & ~strong(X0))) [input p7]
13. ! [X0] : ((old(X0) <~> ~strong(X0)) <=> (~brave(X0) & rich(X0))) [input p12]
17. calm(fred) <~> ~curious(fred) [input p16]
23. ~rich(fred) <~> ~calm(fred) [input p22]
25. old(fred) [input hypothesis]
32. ! [X0] : ((generous(X0) | wise(X0)) => ~kind(X0)) [pure predicate removal 4]
36. ! [X0] : (~kind(X0) | (~generous(X0) & ~wise(X0))) [ennf transformation 32]
52. ! [X0] : (((~curious(X0) & brave(X0)) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0)))) & (((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | (curious(X0) | ~brave(X0)))) [nnf transformation 5]
53. ! [X0] : (((~curious(X0) & brave(X0)) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0)))) & (((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | curious(X0) | ~brave(X0))) [flattening 52]
55. ! [X0] : (((~strong(X0) | ~generous(X0)) | (~kind(X0) | strong(X0))) & ((kind(X0) & ~strong(X0)) | (strong(X0) & generous(X0)))) [nnf transformation 8]
56. ! [X0] : ((~strong(X0) | ~generous(X0) | ~kind(X0) | strong(X0)) & ((kind(X0) & ~strong(X0)) | (strong(X0) & generous(X0)))) [flattening 55]
66. ! [X0] : ((((strong(X0) | ~old(X0)) & (~strong(X0) | old(X0))) | (brave(X0) | ~rich(X0))) & ((~brave(X0) & rich(X0)) | ((old(X0) | strong(X0)) & (~strong(X0) | ~old(X0))))) [nnf transformation 13]
67. ! [X0] : ((((strong(X0) | ~old(X0)) & (~strong(X0) | old(X0))) | brave(X0) | ~rich(X0)) & ((~brave(X0) & rich(X0)) | ((old(X0) | strong(X0)) & (~strong(X0) | ~old(X0))))) [flattening 66]
73. (curious(fred) | ~calm(fred)) & (~curious(fred) | calm(fred)) [nnf transformation 17]
83. (calm(fred) | rich(fred)) & (~calm(fred) | ~rich(fred)) [nnf transformation 23]
95. ~generous(X0) | ~kind(X0) [cnf transformation 36]
97. curious(X0) | generous(X0) | curious(X0) | ~brave(X0) [cnf transformation 53]
99. ~generous(X0) | brave(X0) | curious(X0) [cnf transformation 53]
100. ~curious(X0) | ~curious(X0) | generous(X0) [cnf transformation 53]
110. ~strong(X0) | generous(X0) [cnf transformation 56]
113. strong(X0) | kind(X0) [cnf transformation 56]
125. ~strong(X0) | rich(X0) | ~old(X0) [cnf transformation 67]
127. ~strong(X0) | ~brave(X0) | ~old(X0) [cnf transformation 67]
130. ~rich(X0) | ~old(X0) | brave(X0) | strong(X0) [cnf transformation 67]
139. ~curious(fred) | calm(fred) [cnf transformation 73]
140. curious(fred) | ~calm(fred) [cnf transformation 73]
148. ~calm(fred) | ~rich(fred) [cnf transformation 83]
149. calm(fred) | rich(fred) [cnf transformation 83]
151. old(fred) [cnf transformation 25]
152. curious(X0) | generous(X0) | ~brave(X0) [duplicate literal removal 97]
153. ~curious(X0) | generous(X0) [duplicate literal removal 100]
204. ~brave(X0) | generous(X0) [subsumption resolution 152,153]
284. 29 <=> calm(fred) [avatar definition]
288. 30 <=> curious(fred) [avatar definition]
289. ~curious(fred) <- (~30) [avatar component clause 288]
290. curious(fred) <- (30) [avatar component clause 288]
291. ~29 | 30 [avatar split clause 140,288,284]
292. 29 | ~30 [avatar split clause 139,288,284]
313. 35 <=> rich(fred) [avatar definition]
314. ~rich(fred) <- (~35) [avatar component clause 313]
315. rich(fred) <- (35) [avatar component clause 313]
316. 35 | 29 [avatar split clause 149,284,313]
317. ~35 | ~29 [avatar split clause 148,284,313]
325. generous(fred) <- (30) [resolution 153,290]
326. ~kind(fred) <- (30) [resolution 325,95]
329. ~old(X0) | rich(X0) | kind(X0) [resolution 125,113]
376. rich(fred) | kind(fred) [resolution 329,151]
379. kind(fred) <- (~35) [subsumption resolution 376,314]
380. $false <- (30, ~35) [subsumption resolution 379,326]
381. ~30 | 35 [avatar contradiction clause 380]
392. 44 <=> kind(fred) [avatar definition]
394. kind(fred) <- (44) [avatar component clause 392]
423. ~old(fred) | brave(fred) | strong(fred) <- (35) [resolution 130,315]
425. brave(fred) | strong(fred) <- (35) [subsumption resolution 423,151]
427. 47 <=> strong(fred) [avatar definition]
428. ~strong(fred) <- (~47) [avatar component clause 427]
429. strong(fred) <- (47) [avatar component clause 427]
431. 48 <=> brave(fred) [avatar definition]
432. ~brave(fred) <- (~48) [avatar component clause 431]
433. brave(fred) <- (48) [avatar component clause 431]
434. 47 | 48 | ~35 [avatar split clause 425,313,431,427]
435. ~brave(fred) | ~old(fred) <- (47) [resolution 429,127]
438. ~brave(fred) <- (47) [subsumption resolution 435,151]
439. ~48 | ~47 [avatar split clause 438,427,431]
454. kind(fred) <- (~47) [resolution 428,113]
455. 44 | 47 [avatar split clause 454,427,392]
458. generous(fred) <- (48) [resolution 433,204]
465. ~kind(fred) <- (48) [resolution 458,95]
468. $false <- (44, 48) [subsumption resolution 465,394]
469. ~44 | ~48 [avatar contradiction clause 468]
472. generous(fred) <- (47) [resolution 429,110]
628. brave(fred) | curious(fred) <- (47) [resolution 472,99]
632. curious(fred) <- (47, ~48) [subsumption resolution 628,432]
633. $false <- (~30, 47, ~48) [subsumption resolution 632,289]
634. 30 | ~47 | 48 [avatar contradiction clause 633]
637. $false [avatar sat refutation 291,292,316,317,381,434,439,455,469,634]
% SZS output end Proof for 6456821530264404636497127
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or curious is both patient and brave.
Everyone who is both happy and patient is not brave.
Everyone who is brave or rich is not creative and vice versa.
If alice is either not generous or not brave then someone is both wise and not brave and vice versa.
If paul is brave or curious then lucy is not curious or quiet and vice versa.
Everyone who is either not strong or rich is not rich or not calm.
If someone is quiet then someone is both quiet and not happy.
Everyone who is not happy is both old and not old.
If fred is not humble then mary is either not quiet or not humble.
If mary is wise then fred is kind and vice versa.
Everyone who is humble or wise is either not brave or old and vice versa.
Everyone who is generous or funny is both not funny and not quiet.
If susan is kind or wise then someone is either generous or old and vice versa.
Everyone who is both quiet and calm is both not happy and patient and vice versa.
Everyone who is both not kind and curious is wise or rich and vice versa.
Fred is both tall and calm.
John is calm.
John is not generous or not quiet.
Someone is quiet or creative.
Fred is calm.
Susan is both humble and kind.
John is both not tall and not old. | John is quiet. | contradiction | (![X]:((~brave(X)<~>curious(X))=>(patient(X)&brave(X))))&
(![X]:((happy(X)&patient(X))=>~brave(X)))&
(![X]:((brave(X)|rich(X))<=>~creative(X)))&
(((~generous(alice)<~>~brave(alice)))<=>(?[X]:((wise(X)&~brave(X)))))&
(((brave(paul)|curious(paul)))<=>((~curious(lucy)|quiet(lucy))))&
(![X]:((~strong(X)<~>rich(X))=>(~rich(X)|~calm(X))))&
((?[X]:(quiet(X)))=>(?[X]:((quiet(X)&~happy(X)))))&
(![X]:(~happy(X)=>(old(X)&~old(X))))&
((~humble(fred))=>((~quiet(mary)<~>~humble(mary))))&
((wise(mary))<=>(kind(fred)))&
(![X]:((humble(X)|wise(X))<=>(~brave(X)<~>old(X))))&
(![X]:((generous(X)|funny(X))=>(~funny(X)&~quiet(X))))&
(((kind(susan)|wise(susan)))<=>(?[X]:((generous(X)<~>old(X)))))&
(![X]:((quiet(X)&calm(X))<=>(~happy(X)&patient(X))))&
(![X]:((~kind(X)&curious(X))<=>(wise(X)|rich(X))))&
((tall(fred)&calm(fred)))&
(calm(john))&
((~generous(john)|~quiet(john)))&
(?[X]:((quiet(X)|creative(X))))&
(calm(fred))&
((humble(susan)&kind(susan)))&
((~tall(john)&~old(john))) | quiet(john) | [
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2391316973959955028229666
% SZS output start Proof for 2391316973959955028229666
7. ? [X0] : quiet(X0) => ? [X0] : (~happy(X0) & quiet(X0)) [input p6]
8. ! [X0] : (~happy(X0) => (~old(X0) & old(X0))) [input p7]
23. quiet(john) [input hypothesis]
24. ? [X0] : quiet(X0) => ? [X1] : (~happy(X1) & quiet(X1)) [rectify 7]
33. ? [X1] : (~happy(X1) & quiet(X1)) | ! [X0] : ~quiet(X0) [ennf transformation 24]
34. ! [X0] : ((~old(X0) & old(X0)) | happy(X0)) [ennf transformation 8]
45. ? [X0] : (~happy(X0) & quiet(X0)) | ! [X1] : ~quiet(X1) [rectify 33]
46. ? [X0] : (~happy(X0) & quiet(X0)) => (~happy(sK1) & quiet(sK1)) [choice axiom]
47. (~happy(sK1) & quiet(sK1)) | ! [X1] : ~quiet(X1) [skolemisation 45,46]
83. ~happy(sK1) | ~quiet(X1) [cnf transformation 47]
84. old(X0) | happy(X0) [cnf transformation 34]
85. ~old(X0) | happy(X0) [cnf transformation 34]
122. quiet(john) [cnf transformation 23]
169. 10 <=> ! [X1] : ~quiet(X1) [avatar definition]
170. ~quiet(X1) <- (10) [avatar component clause 169]
172. 11 <=> happy(sK1) [avatar definition]
174. ~happy(sK1) <- (~11) [avatar component clause 172]
175. 10 | ~11 [avatar split clause 83,172,169]
181. happy(X0) [subsumption resolution 84,85]
245. $false <- (10) [resolution 170,122]
246. ~10 [avatar contradiction clause 245]
247. $false <- (~11) [subsumption resolution 174,181]
248. 11 [avatar contradiction clause 247]
249. $false [avatar sat refutation 175,246,248]
% SZS output end Proof for 2391316973959955028229666
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is both calm and not generous.
Everyone who is either not humble or not wise is generous.
If alice is either brave or rich then fred is not funny or not calm and vice versa.
If someone is both happy and not tall then mary is strong or not happy.
Everyone who is not tall or quiet is both creative and calm and vice versa.
If someone is both tall and not funny then susan is not brave or not curious.
If someone is either not humble or not wise then susan is patient or tall and vice versa.
Everyone who is either kind or not curious is not creative or curious.
Everyone who is either curious or strong is either brave or not generous.
Everyone who is either not curious or generous is either not old or not kind and vice versa.
Everyone who is quiet is old and vice versa.
Everyone who is both not happy and funny is not calm and vice versa.
Everyone who is either not happy or happy is curious and vice versa.
Everyone who is brave is generous and vice versa.
If fred is calm or creative then someone is both not tall and generous and vice versa.
Everyone who is both strong and happy is both creative and calm and vice versa.
Someone is not old.
Someone is not rich or kind.
Someone is patient or not rich.
Someone is curious or not brave.
Someone is both brave and not kind.
Someone is not funny or not humble. | Susan is not quiet. | neutral | (![X]:(rich(X)=>(calm(X)&~generous(X))))&
(![X]:((~humble(X)<~>~wise(X))=>generous(X)))&
(((brave(alice)<~>rich(alice)))<=>((~funny(fred)|~calm(fred))))&
((?[X]:((happy(X)&~tall(X))))=>((strong(mary)|~happy(mary))))&
(![X]:((~tall(X)|quiet(X))<=>(creative(X)&calm(X))))&
((?[X]:((tall(X)&~funny(X))))=>((~brave(susan)|~curious(susan))))&
((?[X]:((~humble(X)<~>~wise(X))))<=>((patient(susan)|tall(susan))))&
(![X]:((kind(X)<~>~curious(X))=>(~creative(X)|curious(X))))&
(![X]:((curious(X)<~>strong(X))=>(brave(X)<~>~generous(X))))&
(![X]:((~curious(X)<~>generous(X))<=>(~old(X)<~>~kind(X))))&
(![X]:(quiet(X)<=>old(X)))&
(![X]:((~happy(X)&funny(X))<=>~calm(X)))&
(![X]:((~happy(X)<~>happy(X))<=>curious(X)))&
(![X]:(brave(X)<=>generous(X)))&
(((calm(fred)|creative(fred)))<=>(?[X]:((~tall(X)&generous(X)))))&
(![X]:((strong(X)&happy(X))<=>(creative(X)&calm(X))))&
(?[X]:(~old(X)))&
(?[X]:((~rich(X)|kind(X))))&
(?[X]:((patient(X)|~rich(X))))&
(?[X]:((curious(X)|~brave(X))))&
(?[X]:((brave(X)&~kind(X))))&
(?[X]:((~funny(X)|~humble(X)))) | ~quiet(susan) | [] | null | 0 |
If paul is not quiet or not strong then someone is not generous and vice versa.
Everyone who is brave is kind.
If john is not patient or kind then someone is either patient or creative and vice versa.
Everyone who is both not tall and old is rich or curious and vice versa.
If alice is tall then lucy is either not old or not curious.
Everyone who is quiet is either rich or creative and vice versa.
If lucy is not patient then someone is not kind or funny and vice versa.
Everyone who is not happy is wise.
Everyone who is either strong or not creative is both not generous and not humble and vice versa.
If someone is old or humble then paul is both wise and quiet.
If john is not wise then fred is either curious or wise and vice versa.
If someone is not brave or not patient then someone is both old and patient and vice versa.
If someone is both quiet and not old then john is either old or curious and vice versa.
If someone is old or kind then lucy is both not humble and not funny.
If someone is wise or not patient then paul is not brave.
Everyone who is both generous and calm is not brave and vice versa.
Someone is either not wise or not strong.
Someone is not humble or not creative.
John is either strong or brave.
Alice is not patient.
Susan is either not strong or brave.
Someone is patient or not humble.
Someone is wise or funny.
John is curious. | Paul is not brave. | entailment | (((~quiet(paul)|~strong(paul)))<=>(?[X]:(~generous(X))))&
(![X]:(brave(X)=>kind(X)))&
(((~patient(john)|kind(john)))<=>(?[X]:((patient(X)<~>creative(X)))))&
(![X]:((~tall(X)&old(X))<=>(rich(X)|curious(X))))&
((tall(alice))=>((~old(lucy)<~>~curious(lucy))))&
(![X]:(quiet(X)<=>(rich(X)<~>creative(X))))&
((~patient(lucy))<=>(?[X]:((~kind(X)|funny(X)))))&
(![X]:(~happy(X)=>wise(X)))&
(![X]:((strong(X)<~>~creative(X))<=>(~generous(X)&~humble(X))))&
((?[X]:((old(X)|humble(X))))=>((wise(paul)&quiet(paul))))&
((~wise(john))<=>((curious(fred)<~>wise(fred))))&
((?[X]:((~brave(X)|~patient(X))))<=>(?[X]:((old(X)&patient(X)))))&
((?[X]:((quiet(X)&~old(X))))<=>((old(john)<~>curious(john))))&
((?[X]:((old(X)|kind(X))))=>((~humble(lucy)&~funny(lucy))))&
((?[X]:((wise(X)|~patient(X))))=>(~brave(paul)))&
(![X]:((generous(X)&calm(X))<=>~brave(X)))&
(?[X]:((~wise(X)<~>~strong(X))))&
(?[X]:((~humble(X)|~creative(X))))&
((strong(john)<~>brave(john)))&
(~patient(alice))&
((~strong(susan)<~>brave(susan)))&
(?[X]:((patient(X)|~humble(X))))&
(?[X]:((wise(X)|funny(X))))&
(curious(john)) | ~brave(paul) | [
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4024399597927743363455567
% SZS output start Proof for 4024399597927743363455567
15. ? [X0] : (~patient(X0) | wise(X0)) => ~brave(paul) [input p14]
20. ~patient(alice) [input p19]
25. brave(paul) [input hypothesis]
32. ~brave(paul) | ! [X0] : (patient(X0) & ~wise(X0)) [ennf transformation 15]
130. ~brave(paul) | patient(X0) [cnf transformation 32]
139. ~patient(alice) [cnf transformation 20]
145. brave(paul) [cnf transformation 25]
272. 28 <=> ! [X3] : patient(X3) [avatar definition]
273. patient(X3) <- (28) [avatar component clause 272]
330. 40 <=> brave(paul) [avatar definition]
333. 28 | ~40 [avatar split clause 130,330,272]
396. 40 [avatar split clause 145,330]
414. $false <- (28) [resolution 273,139]
415. ~28 [avatar contradiction clause 414]
416. $false [avatar sat refutation 333,396,415]
% SZS output end Proof for 4024399597927743363455567
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy or not wise is either not creative or kind and vice versa.
If paul is both not patient and not rich then someone is either not curious or creative.
Everyone who is either not patient or tall is creative or curious and vice versa.
Everyone who is wise or not rich is both wise and kind.
If fred is not humble or tall then someone is patient and vice versa.
Everyone who is not tall or happy is both wise and not old and vice versa.
If alice is kind then susan is both old and strong.
If john is both not curious and kind then someone is either not patient or not quiet.
If susan is either rich or not happy then someone is not generous or not rich.
Everyone who is both not tall and not generous is happy or brave.
If fred is humble then someone is calm or not happy.
Everyone who is rich is not tall or creative.
Everyone who is either not patient or creative is not creative or quiet and vice versa.
Everyone who is not patient or generous is either quiet or tall.
Everyone who is either not tall or not humble is both not creative and curious.
Everyone who is either not quiet or not curious is not brave or not curious and vice versa.
Someone is kind or creative.
Someone is either patient or not old.
Someone is either not creative or not wise.
Paul is brave.
Paul is not kind or not curious.
Mary is calm or not rich.
Someone is both humble and not patient.
Fred is either generous or funny. | Susan is not generous. | entailment | (![X]:((~happy(X)|~wise(X))<=>(~creative(X)<~>kind(X))))&
(((~patient(paul)&~rich(paul)))=>(?[X]:((~curious(X)<~>creative(X)))))&
(![X]:((~patient(X)<~>tall(X))<=>(creative(X)|curious(X))))&
(![X]:((wise(X)|~rich(X))=>(wise(X)&kind(X))))&
(((~humble(fred)|tall(fred)))<=>(?[X]:(patient(X))))&
(![X]:((~tall(X)|happy(X))<=>(wise(X)&~old(X))))&
((kind(alice))=>((old(susan)&strong(susan))))&
(((~curious(john)&kind(john)))=>(?[X]:((~patient(X)<~>~quiet(X)))))&
(((rich(susan)<~>~happy(susan)))=>(?[X]:((~generous(X)|~rich(X)))))&
(![X]:((~tall(X)&~generous(X))=>(happy(X)|brave(X))))&
((humble(fred))=>(?[X]:((calm(X)|~happy(X)))))&
(![X]:(rich(X)=>(~tall(X)|creative(X))))&
(![X]:((~patient(X)<~>creative(X))<=>(~creative(X)|quiet(X))))&
(![X]:((~patient(X)|generous(X))=>(quiet(X)<~>tall(X))))&
(![X]:((~tall(X)<~>~humble(X))=>(~creative(X)&curious(X))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~brave(X)|~curious(X))))&
(?[X]:((kind(X)|creative(X))))&
(?[X]:((patient(X)<~>~old(X))))&
(?[X]:((~creative(X)<~>~wise(X))))&
(brave(paul))&
((~kind(paul)|~curious(paul)))&
((calm(mary)|~rich(mary)))&
(?[X]:((humble(X)&~patient(X))))&
((generous(fred)<~>funny(fred))) | ~generous(susan) | [
"p0",
"p2",
"p3",
"p5",
"p6",
"p11",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7877069041362496303719160
% SZS output start Proof for 7877069041362496303719160
1. ! [X0] : ((~wise(X0) | ~happy(X0)) <=> (~creative(X0) <~> kind(X0))) [input p0]
3. ! [X0] : ((~patient(X0) <~> tall(X0)) <=> (curious(X0) | creative(X0))) [input p2]
4. ! [X0] : ((~rich(X0) | wise(X0)) => (kind(X0) & wise(X0))) [input p3]
6. ! [X0] : ((happy(X0) | ~tall(X0)) <=> (~old(X0) & wise(X0))) [input p5]
7. kind(alice) => (strong(susan) & old(susan)) [input p6]
12. ! [X0] : (rich(X0) => (creative(X0) | ~tall(X0))) [input p11]
13. ! [X0] : ((~patient(X0) <~> creative(X0)) <=> (quiet(X0) | ~creative(X0))) [input p12]
14. ! [X0] : ((generous(X0) | ~patient(X0)) => (quiet(X0) <~> tall(X0))) [input p13]
16. ! [X0] : ((~quiet(X0) <~> ~curious(X0)) <=> (~curious(X0) | ~brave(X0))) [input p15]
25. generous(susan) [input hypothesis]
28. kind(alice) => old(susan) [pure predicate removal 7]
31. ! [X0] : ((kind(X0) & wise(X0)) | (rich(X0) & ~wise(X0))) [ennf transformation 4]
32. old(susan) | ~kind(alice) [ennf transformation 28]
38. ! [X0] : ((creative(X0) | ~tall(X0)) | ~rich(X0)) [ennf transformation 12]
39. ! [X0] : (creative(X0) | ~tall(X0) | ~rich(X0)) [flattening 38]
40. ! [X0] : ((quiet(X0) <~> tall(X0)) | (~generous(X0) & patient(X0))) [ennf transformation 14]
42. ! [X0] : (((~wise(X0) | ~happy(X0)) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0)))) & (((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | (wise(X0) & happy(X0)))) [nnf transformation 1]
43. ! [X0] : ((~wise(X0) | ~happy(X0) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0)))) & (((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | (wise(X0) & happy(X0)))) [flattening 42]
47. ! [X0] : ((((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | (~curious(X0) & ~creative(X0))) & ((curious(X0) | creative(X0)) | ((~patient(X0) | ~tall(X0)) & (tall(X0) | patient(X0))))) [nnf transformation 3]
48. ! [X0] : ((((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | (~curious(X0) & ~creative(X0))) & (curious(X0) | creative(X0) | ((~patient(X0) | ~tall(X0)) & (tall(X0) | patient(X0))))) [flattening 47]
54. ! [X0] : (((happy(X0) | ~tall(X0)) | (old(X0) | ~wise(X0))) & ((~old(X0) & wise(X0)) | (~happy(X0) & tall(X0)))) [nnf transformation 6]
55. ! [X0] : ((happy(X0) | ~tall(X0) | old(X0) | ~wise(X0)) & ((~old(X0) & wise(X0)) | (~happy(X0) & tall(X0)))) [flattening 54]
62. ! [X0] : ((((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | (~quiet(X0) & creative(X0))) & ((quiet(X0) | ~creative(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))))) [nnf transformation 13]
63. ! [X0] : ((((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | (~quiet(X0) & creative(X0))) & (quiet(X0) | ~creative(X0) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))))) [flattening 62]
64. ! [X0] : (((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (~generous(X0) & patient(X0))) [nnf transformation 40]
66. ! [X0] : ((((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | (curious(X0) & brave(X0))) & ((~curious(X0) | ~brave(X0)) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0))))) [nnf transformation 16]
67. ! [X0] : ((((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | (curious(X0) & brave(X0))) & (~curious(X0) | ~brave(X0) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0))))) [flattening 66]
80. ~creative(X0) | kind(X0) | wise(X0) [cnf transformation 43]
92. ~tall(X0) | patient(X0) | ~curious(X0) [cnf transformation 48]
94. rich(X0) | wise(X0) [cnf transformation 31]
95. ~wise(X0) | kind(X0) [cnf transformation 31]
100. tall(X0) | wise(X0) [cnf transformation 55]
102. ~old(X0) | tall(X0) [cnf transformation 55]
105. old(susan) | ~kind(alice) [cnf transformation 32]
111. ~tall(X0) | creative(X0) | ~rich(X0) [cnf transformation 39]
113. quiet(X0) | ~creative(X0) | ~patient(X0) | ~creative(X0) [cnf transformation 63]
114. creative(X0) | ~patient(X0) | creative(X0) [cnf transformation 63]
121. ~generous(X0) | ~quiet(X0) | ~tall(X0) [cnf transformation 64]
131. curious(X0) | quiet(X0) | curious(X0) [cnf transformation 67]
143. generous(susan) [cnf transformation 25]
145. quiet(X0) | curious(X0) [duplicate literal removal 131]
146. quiet(X0) | ~creative(X0) | ~patient(X0) [duplicate literal removal 113]
147. ~patient(X0) | creative(X0) [duplicate literal removal 114]
185. 9 <=> kind(alice) [avatar definition]
187. ~kind(alice) <- (~9) [avatar component clause 185]
189. 10 <=> old(susan) [avatar definition]
191. old(susan) <- (10) [avatar component clause 189]
192. ~9 | 10 [avatar split clause 105,189,185]
229. ~patient(X0) | quiet(X0) [subsumption resolution 146,147]
357. creative(X0) | ~rich(X0) | wise(X0) [resolution 111,100]
359. creative(X0) | wise(X0) [subsumption resolution 357,94]
390. ~quiet(susan) | ~tall(susan) [resolution 121,143]
393. 39 <=> tall(susan) [avatar definition]
394. tall(susan) <- (39) [avatar component clause 393]
395. ~tall(susan) <- (~39) [avatar component clause 393]
397. 40 <=> quiet(susan) [avatar definition]
399. ~quiet(susan) <- (~40) [avatar component clause 397]
400. ~39 | ~40 [avatar split clause 390,397,393]
487. 47 <=> patient(susan) [avatar definition]
489. patient(susan) <- (47) [avatar component clause 487]
491. 48 <=> curious(susan) [avatar definition]
498. patient(susan) | ~curious(susan) <- (39) [resolution 394,92]
511. ~48 | 47 | ~39 [avatar split clause 498,393,487,491]
516. curious(susan) <- (~40) [resolution 399,145]
520. 48 | 40 [avatar split clause 516,397,491]
580. wise(X0) | kind(X0) | wise(X0) [resolution 359,80]
583. wise(X0) | kind(X0) [duplicate literal removal 580]
584. kind(X0) [subsumption resolution 583,95]
659. quiet(susan) <- (47) [resolution 489,229]
677. 40 | ~47 [avatar split clause 659,487,397]
718. $false <- (~9) [resolution 584,187]
721. 9 [avatar contradiction clause 718]
725. tall(susan) <- (10) [resolution 191,102]
728. $false <- (10, ~39) [subsumption resolution 725,395]
729. ~10 | 39 [avatar contradiction clause 728]
730. $false [avatar sat refutation 192,400,511,520,677,721,729]
% SZS output end Proof for 7877069041362496303719160
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous then lucy is either old or kind. If someone is both not happy and curious then fred is not generous or old. Everyone who is rich is both not brave and not kind. Everyone who is not strong or not calm is curious or not rich. Everyone who is not rich is both funny and old and vice versa. If alice is not old or not funny then lucy is strong or humble. If paul is kind then paul is not generous and vice versa. If someone is not patient or not calm then paul is either patient or funny and vice versa. Everyone who is not patient or calm is not wise and vice versa. Everyone who is either not happy or wise is both not generous and not old and vice versa. Everyone who is not patient or rich is not old and vice versa. Everyone who is not calm or not rich is creative and vice versa. Everyone who is either not curious or calm is wise. Everyone who is not happy is curious and vice versa. If someone is not kind then fred is both not wise and not patient and vice versa. If mary is both not curious and not brave then someone is not generous and vice versa. Susan is both not generous and not tall. Alice is either not funny or not brave. John is either curious or calm. Someone is either generous or not quiet. Someone is tall or calm. Someone is quiet or old. Alice is quiet or wise. Someone is both wise and not generous. | Mary is calm. | entailment | ((?[X]:(generous(X)))=>((old(lucy)<~>kind(lucy))))&
((?[X]:((~happy(X)&curious(X))))=>((~generous(fred)|old(fred))))&
(![X]:(rich(X)=>(~brave(X)&~kind(X))))&
(![X]:((~strong(X)|~calm(X))=>(curious(X)|~rich(X))))&
(![X]:(~rich(X)<=>(funny(X)&old(X))))&
(((~old(alice)|~funny(alice)))=>((strong(lucy)|humble(lucy))))&
((kind(paul))<=>(~generous(paul)))&
((?[X]:((~patient(X)|~calm(X))))<=>((patient(paul)<~>funny(paul))))&
(![X]:((~patient(X)|calm(X))<=>~wise(X)))&
(![X]:((~happy(X)<~>wise(X))<=>(~generous(X)&~old(X))))&
(![X]:((~patient(X)|rich(X))<=>~old(X)))&
(![X]:((~calm(X)|~rich(X))<=>creative(X)))&
(![X]:((~curious(X)<~>calm(X))=>wise(X)))&
(![X]:(~happy(X)<=>curious(X)))&
((?[X]:(~kind(X)))<=>((~wise(fred)&~patient(fred))))&
(((~curious(mary)&~brave(mary)))<=>(?[X]:(~generous(X))))&
((~generous(susan)&~tall(susan)))&
((~funny(alice)<~>~brave(alice)))&
((curious(john)<~>calm(john)))&
(?[X]:((generous(X)<~>~quiet(X))))&
(?[X]:((tall(X)|calm(X))))&
(?[X]:((quiet(X)|old(X))))&
((quiet(alice)|wise(alice)))&
(?[X]:((wise(X)&~generous(X)))) | calm(mary) | [
"p3",
"p4",
"p9",
"p12",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4708135987388194745374961
% SZS output start Proof for 4708135987388194745374961
4. ! [X0] : ((~calm(X0) | ~strong(X0)) => (~rich(X0) | curious(X0))) [input p3]
5. ! [X0] : (~rich(X0) <=> (old(X0) & funny(X0))) [input p4]
10. ! [X0] : ((~happy(X0) <~> wise(X0)) <=> (~old(X0) & ~generous(X0))) [input p9]
13. ! [X0] : ((~curious(X0) <~> calm(X0)) => wise(X0)) [input p12]
14. ! [X0] : (~happy(X0) <=> curious(X0)) [input p13]
16. (~brave(mary) & ~curious(mary)) <=> ? [X0] : ~generous(X0) [input p15]
17. ~tall(susan) & ~generous(susan) [input p16]
25. ~calm(mary) [input hypothesis]
27. ! [X0] : (~calm(X0) => (~rich(X0) | curious(X0))) [pure predicate removal 4]
32. ! [X0] : ((~rich(X0) | curious(X0)) | calm(X0)) [ennf transformation 27]
33. ! [X0] : (~rich(X0) | curious(X0) | calm(X0)) [flattening 32]
34. ! [X0] : (wise(X0) | (~curious(X0) <=> calm(X0))) [ennf transformation 13]
36. ! [X0] : ((~rich(X0) | (~old(X0) | ~funny(X0))) & ((old(X0) & funny(X0)) | rich(X0))) [nnf transformation 5]
37. ! [X0] : ((~rich(X0) | ~old(X0) | ~funny(X0)) & ((old(X0) & funny(X0)) | rich(X0))) [flattening 36]
45. ! [X0] : ((((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | (old(X0) | generous(X0))) & ((~old(X0) & ~generous(X0)) | ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0))))) [nnf transformation 10]
46. ! [X0] : ((((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | old(X0) | generous(X0)) & ((~old(X0) & ~generous(X0)) | ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0))))) [flattening 45]
49. ! [X0] : (wise(X0) | ((~curious(X0) | ~calm(X0)) & (calm(X0) | curious(X0)))) [nnf transformation 34]
50. ! [X0] : ((~happy(X0) | ~curious(X0)) & (curious(X0) | happy(X0))) [nnf transformation 14]
56. ((~brave(mary) & ~curious(mary)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | (brave(mary) | curious(mary))) [nnf transformation 16]
57. ((~brave(mary) & ~curious(mary)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | brave(mary) | curious(mary)) [flattening 56]
58. ((~brave(mary) & ~curious(mary)) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | brave(mary) | curious(mary)) [rectify 57]
59. ? [X1] : ~generous(X1) => ~generous(sK2) [choice axiom]
60. ((~brave(mary) & ~curious(mary)) | ! [X0] : generous(X0)) & (~generous(sK2) | brave(mary) | curious(mary)) [skolemisation 58,59]
77. ~rich(X0) | curious(X0) | calm(X0) [cnf transformation 33]
79. rich(X0) | old(X0) [cnf transformation 37]
95. ~wise(X0) | ~happy(X0) | ~old(X0) [cnf transformation 46]
101. wise(X0) | calm(X0) | curious(X0) [cnf transformation 49]
103. curious(X0) | happy(X0) [cnf transformation 50]
109. ~curious(mary) | generous(X0) [cnf transformation 60]
111. ~generous(susan) [cnf transformation 17]
124. ~calm(mary) [cnf transformation 25]
209. 19 <=> ! [X0] : generous(X0) [avatar definition]
210. generous(X0) <- (19) [avatar component clause 209]
217. 21 <=> curious(mary) [avatar definition]
220. 19 | ~21 [avatar split clause 109,217,209]
290. curious(X0) | calm(X0) | old(X0) [resolution 77,79]
351. calm(X0) | curious(X0) | ~happy(X0) | ~old(X0) [resolution 101,95]
364. calm(X0) | curious(X0) | ~old(X0) [subsumption resolution 351,103]
365. calm(X0) | curious(X0) [subsumption resolution 364,290]
392. curious(mary) [resolution 365,124]
397. 21 [avatar split clause 392,217]
400. $false <- (19) [resolution 210,111]
407. ~19 [avatar contradiction clause 400]
409. $false [avatar sat refutation 220,397,407]
% SZS output end Proof for 4708135987388194745374961
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is happy or not curious then susan is not quiet and vice versa.
Everyone who is wise is old.
Everyone who is both not old and not rich is old or not strong and vice versa.
Everyone who is either rich or not humble is either not rich or funny.
Everyone who is either quiet or not patient is either not wise or creative.
Everyone who is happy is not wise and vice versa.
If someone is both not tall and not happy then susan is brave and vice versa.
If someone is patient or not curious then paul is generous.
If lucy is both quiet and not tall then paul is both kind and not old and vice versa.
Everyone who is either funny or not calm is not old or wise and vice versa.
Everyone who is either wise or rich is both not humble and patient.
Everyone who is either not brave or patient is either not quiet or not calm and vice versa.
If someone is either not calm or not tall then susan is either wise or not rich and vice versa.
Everyone who is not creative is not quiet.
If someone is both funny and not patient then lucy is either funny or not wise and vice versa.
Everyone who is strong is not quiet.
John is both not old and not brave.
Paul is both not calm and curious.
Someone is either calm or not happy.
Someone is either not curious or funny.
Mary is not rich or happy. | Paul is not funny. | entailment | (((happy(john)|~curious(john)))<=>(~quiet(susan)))&
(![X]:(wise(X)=>old(X)))&
(![X]:((~old(X)&~rich(X))<=>(old(X)|~strong(X))))&
(![X]:((rich(X)<~>~humble(X))=>(~rich(X)<~>funny(X))))&
(![X]:((quiet(X)<~>~patient(X))=>(~wise(X)<~>creative(X))))&
(![X]:(happy(X)<=>~wise(X)))&
((?[X]:((~tall(X)&~happy(X))))<=>(brave(susan)))&
((?[X]:((patient(X)|~curious(X))))=>(generous(paul)))&
(((quiet(lucy)&~tall(lucy)))<=>((kind(paul)&~old(paul))))&
(![X]:((funny(X)<~>~calm(X))<=>(~old(X)|wise(X))))&
(![X]:((wise(X)<~>rich(X))=>(~humble(X)&patient(X))))&
(![X]:((~brave(X)<~>patient(X))<=>(~quiet(X)<~>~calm(X))))&
((?[X]:((~calm(X)<~>~tall(X))))<=>((wise(susan)<~>~rich(susan))))&
(![X]:(~creative(X)=>~quiet(X)))&
((?[X]:((funny(X)&~patient(X))))<=>((funny(lucy)<~>~wise(lucy))))&
(![X]:(strong(X)=>~quiet(X)))&
((~old(john)&~brave(john)))&
((~calm(paul)&curious(paul)))&
(?[X]:((calm(X)<~>~happy(X))))&
(?[X]:((~curious(X)<~>funny(X))))&
((~rich(mary)|happy(mary))) | ~funny(paul) | [
"p2",
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4537543082885746211260530
% SZS output start Proof for 4537543082885746211260530
3. ! [X0] : ((~rich(X0) & ~old(X0)) <=> (~strong(X0) | old(X0))) [input p2]
10. ! [X0] : ((funny(X0) <~> ~calm(X0)) <=> (wise(X0) | ~old(X0))) [input p9]
18. curious(paul) & ~calm(paul) [input p17]
22. funny(paul) [input hypothesis]
32. ! [X0] : (((~rich(X0) & ~old(X0)) | (strong(X0) & ~old(X0))) & ((~strong(X0) | old(X0)) | (rich(X0) | old(X0)))) [nnf transformation 3]
33. ! [X0] : (((~rich(X0) & ~old(X0)) | (strong(X0) & ~old(X0))) & (~strong(X0) | old(X0) | rich(X0) | old(X0))) [flattening 32]
43. ! [X0] : ((((calm(X0) | ~funny(X0)) & (~calm(X0) | funny(X0))) | (~wise(X0) & old(X0))) & ((wise(X0) | ~old(X0)) | ((funny(X0) | calm(X0)) & (~calm(X0) | ~funny(X0))))) [nnf transformation 10]
44. ! [X0] : ((((calm(X0) | ~funny(X0)) & (~calm(X0) | funny(X0))) | (~wise(X0) & old(X0))) & (wise(X0) | ~old(X0) | ((funny(X0) | calm(X0)) & (~calm(X0) | ~funny(X0))))) [flattening 43]
66. ~old(X0) | ~old(X0) [cnf transformation 33]
91. calm(X0) | ~funny(X0) | old(X0) [cnf transformation 44]
123. ~calm(paul) [cnf transformation 18]
130. funny(paul) [cnf transformation 22]
134. ~old(X0) [duplicate literal removal 66]
186. ~funny(X0) | calm(X0) [subsumption resolution 91,134]
280. calm(paul) [resolution 186,130]
282. $false [subsumption resolution 280,123]
% SZS output end Proof for 4537543082885746211260530
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not happy and curious then someone is either not humble or not quiet and vice versa. If fred is patient or not rich then alice is not wise. If fred is not brave or not old then someone is both kind and not strong. If susan is either kind or funny then susan is not patient. Everyone who is both not curious and not tall is either not kind or not quiet and vice versa. If someone is not humble or calm then someone is quiet or not strong and vice versa. Everyone who is both not curious and not brave is both quiet and not strong. Everyone who is not patient is not strong and vice versa. If someone is creative or not strong then paul is either kind or not strong and vice versa. If alice is either not patient or not creative then fred is either kind or rich. If someone is humble or generous then someone is either not happy or happy. Everyone who is both not tall and not calm is both not humble and not creative and vice versa. If someone is either not wise or not curious then john is either not happy or not quiet and vice versa. Everyone who is either tall or brave is not tall or not old. If mary is both tall and not tall then alice is both not funny and generous. Everyone who is not calm or not patient is both humble and patient. Paul is kind or not quiet. John is not patient or calm. Mary is either strong or calm. Fred is both curious and not humble. Someone is not wise or wise. John is either brave or not old. | John is not humble. | neutral | ((?[X]:((~happy(X)&curious(X))))<=>(?[X]:((~humble(X)<~>~quiet(X)))))&
(((patient(fred)|~rich(fred)))=>(~wise(alice)))&
(((~brave(fred)|~old(fred)))=>(?[X]:((kind(X)&~strong(X)))))&
(((kind(susan)<~>funny(susan)))=>(~patient(susan)))&
(![X]:((~curious(X)&~tall(X))<=>(~kind(X)<~>~quiet(X))))&
((?[X]:((~humble(X)|calm(X))))<=>(?[X]:((quiet(X)|~strong(X)))))&
(![X]:((~curious(X)&~brave(X))=>(quiet(X)&~strong(X))))&
(![X]:(~patient(X)<=>~strong(X)))&
((?[X]:((creative(X)|~strong(X))))<=>((kind(paul)<~>~strong(paul))))&
(((~patient(alice)<~>~creative(alice)))=>((kind(fred)<~>rich(fred))))&
((?[X]:((humble(X)|generous(X))))=>(?[X]:((~happy(X)<~>happy(X)))))&
(![X]:((~tall(X)&~calm(X))<=>(~humble(X)&~creative(X))))&
((?[X]:((~wise(X)<~>~curious(X))))<=>((~happy(john)<~>~quiet(john))))&
(![X]:((tall(X)<~>brave(X))=>(~tall(X)|~old(X))))&
(((tall(mary)&~tall(mary)))=>((~funny(alice)&generous(alice))))&
(![X]:((~calm(X)|~patient(X))=>(humble(X)&patient(X))))&
((kind(paul)|~quiet(paul)))&
((~patient(john)|calm(john)))&
((strong(mary)<~>calm(mary)))&
((curious(fred)&~humble(fred)))&
(?[X]:((~wise(X)|wise(X))))&
((brave(john)<~>~old(john))) | ~humble(john) | [] | null | 0 |
Everyone who is funny or wise is happy.
Everyone who is both patient and rich is not funny and vice versa.
If lucy is not humble or happy then susan is either not wise or happy and vice versa.
If someone is not brave or brave then lucy is either not quiet or curious.
Everyone who is either old or wise is both not creative and not funny and vice versa.
Everyone who is either not quiet or curious is kind and vice versa.
If someone is not quiet then someone is both not old and patient.
If paul is not calm then susan is not strong.
Everyone who is either not curious or not strong is both kind and not happy and vice versa.
Everyone who is both not kind and strong is wise or not rich and vice versa.
Everyone who is not happy or not funny is either curious or quiet.
If mary is both strong and not tall then someone is both strong and creative and vice versa.
Everyone who is either humble or tall is either old or rich.
Everyone who is either happy or not old is either old or not old.
Everyone who is either generous or wise is both humble and not happy.
If someone is funny or calm then someone is both rich and not patient.
Someone is not humble or old.
Fred is either wise or not funny.
John is creative.
Paul is not kind or not rich. | Fred is calm. | neutral | (![X]:((funny(X)|wise(X))=>happy(X)))&
(![X]:((patient(X)&rich(X))<=>~funny(X)))&
(((~humble(lucy)|happy(lucy)))<=>((~wise(susan)<~>happy(susan))))&
((?[X]:((~brave(X)|brave(X))))=>((~quiet(lucy)<~>curious(lucy))))&
(![X]:((old(X)<~>wise(X))<=>(~creative(X)&~funny(X))))&
(![X]:((~quiet(X)<~>curious(X))<=>kind(X)))&
((?[X]:(~quiet(X)))=>(?[X]:((~old(X)&patient(X)))))&
((~calm(paul))=>(~strong(susan)))&
(![X]:((~curious(X)<~>~strong(X))<=>(kind(X)&~happy(X))))&
(![X]:((~kind(X)&strong(X))<=>(wise(X)|~rich(X))))&
(![X]:((~happy(X)|~funny(X))=>(curious(X)<~>quiet(X))))&
(((strong(mary)&~tall(mary)))<=>(?[X]:((strong(X)&creative(X)))))&
(![X]:((humble(X)<~>tall(X))=>(old(X)<~>rich(X))))&
(![X]:((happy(X)<~>~old(X))=>(old(X)<~>~old(X))))&
(![X]:((generous(X)<~>wise(X))=>(humble(X)&~happy(X))))&
((?[X]:((funny(X)|calm(X))))=>(?[X]:((rich(X)&~patient(X)))))&
(?[X]:((~humble(X)|old(X))))&
((wise(fred)<~>~funny(fred)))&
(creative(john))&
((~kind(paul)|~rich(paul))) | calm(fred) | [] | null | 0 |
Everyone who is either strong or not old is strong and vice versa.
Everyone who is not quiet or generous is either kind or curious and vice versa.
If someone is curious then mary is both not humble and not wise.
Everyone who is either strong or not curious is both not humble and wise and vice versa.
Everyone who is both curious and patient is strong or happy and vice versa.
If susan is either not quiet or not funny then someone is both kind and quiet.
If john is not rich then fred is not old.
Everyone who is not curious is both not quiet and wise and vice versa.
If mary is both not funny and not happy then paul is not curious or brave.
Everyone who is not happy or tall is either not generous or not funny and vice versa.
If susan is not curious then mary is both not quiet and not creative and vice versa.
Everyone who is humble is both quiet and generous and vice versa.
Everyone who is both not wise and not quiet is either brave or patient and vice versa.
Everyone who is wise is not humble or wise and vice versa.
Everyone who is both not old and tall is both happy and generous and vice versa.
Someone is funny.
Someone is either not patient or not calm.
Susan is both creative and rich.
Someone is either not tall or not happy.
Susan is tall.
Someone is both creative and not calm. | Mary is not quiet. | entailment | (![X]:((strong(X)<~>~old(X))<=>strong(X)))&
(![X]:((~quiet(X)|generous(X))<=>(kind(X)<~>curious(X))))&
((?[X]:(curious(X)))=>((~humble(mary)&~wise(mary))))&
(![X]:((strong(X)<~>~curious(X))<=>(~humble(X)&wise(X))))&
(![X]:((curious(X)&patient(X))<=>(strong(X)|happy(X))))&
(((~quiet(susan)<~>~funny(susan)))=>(?[X]:((kind(X)&quiet(X)))))&
((~rich(john))=>(~old(fred)))&
(![X]:(~curious(X)<=>(~quiet(X)&wise(X))))&
(((~funny(mary)&~happy(mary)))=>((~curious(paul)|brave(paul))))&
(![X]:((~happy(X)|tall(X))<=>(~generous(X)<~>~funny(X))))&
((~curious(susan))<=>((~quiet(mary)&~creative(mary))))&
(![X]:(humble(X)<=>(quiet(X)&generous(X))))&
(![X]:((~wise(X)&~quiet(X))<=>(brave(X)<~>patient(X))))&
(![X]:(wise(X)<=>(~humble(X)|wise(X))))&
(![X]:((~old(X)&tall(X))<=>(happy(X)&generous(X))))&
(?[X]:(funny(X)))&
(?[X]:((~patient(X)<~>~calm(X))))&
((creative(susan)&rich(susan)))&
(?[X]:((~tall(X)<~>~happy(X))))&
(tall(susan))&
(?[X]:((creative(X)&~calm(X)))) | ~quiet(mary) | [
"p2",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2640976981241820905303082
% SZS output start Proof for 2640976981241820905303082
3. ? [X0] : curious(X0) => (~wise(mary) & ~humble(mary)) [input p2]
8. ! [X0] : (~curious(X0) <=> (wise(X0) & ~quiet(X0))) [input p7]
14. ! [X0] : (wise(X0) <=> (wise(X0) | ~humble(X0))) [input p13]
22. quiet(mary) [input hypothesis]
25. (~wise(mary) & ~humble(mary)) | ! [X0] : ~curious(X0) [ennf transformation 3]
39. ! [X0] : ((~curious(X0) | (~wise(X0) | quiet(X0))) & ((wise(X0) & ~quiet(X0)) | curious(X0))) [nnf transformation 8]
40. ! [X0] : ((~curious(X0) | ~wise(X0) | quiet(X0)) & ((wise(X0) & ~quiet(X0)) | curious(X0))) [flattening 39]
49. ! [X0] : ((wise(X0) | (~wise(X0) & humble(X0))) & ((wise(X0) | ~humble(X0)) | ~wise(X0))) [nnf transformation 14]
50. ! [X0] : ((wise(X0) | (~wise(X0) & humble(X0))) & (wise(X0) | ~humble(X0) | ~wise(X0))) [flattening 49]
73. ~humble(mary) | ~curious(X0) [cnf transformation 25]
74. ~wise(mary) | ~curious(X0) [cnf transformation 25]
90. ~quiet(X0) | curious(X0) [cnf transformation 40]
113. wise(X0) | humble(X0) [cnf transformation 50]
128. quiet(mary) [cnf transformation 22]
133. 1 <=> ! [X0] : ~curious(X0) [avatar definition]
134. ~curious(X0) <- (1) [avatar component clause 133]
136. 2 <=> wise(mary) [avatar definition]
138. ~wise(mary) <- (~2) [avatar component clause 136]
139. 1 | ~2 [avatar split clause 74,136,133]
141. 3 <=> humble(mary) [avatar definition]
143. ~humble(mary) <- (~3) [avatar component clause 141]
144. 1 | ~3 [avatar split clause 73,141,133]
183. 12 <=> quiet(mary) [avatar definition]
185. quiet(mary) <- (12) [avatar component clause 183]
218. 12 [avatar split clause 128,183]
219. curious(mary) <- (12) [resolution 90,185]
221. humble(mary) <- (~2) [resolution 113,138]
222. $false <- (~2, ~3) [subsumption resolution 221,143]
223. 2 | 3 [avatar contradiction clause 222]
225. $false <- (1, 12) [resolution 134,219]
226. ~1 | ~12 [avatar contradiction clause 225]
228. $false [avatar sat refutation 139,144,218,223,226]
% SZS output end Proof for 2640976981241820905303082
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or not tall is calm. If susan is both not happy and patient then someone is brave or not wise. Everyone who is not happy or patient is either not old or not happy and vice versa. Everyone who is generous is calm or not wise and vice versa. Everyone who is old or strong is both old and not rich and vice versa. If someone is both wise and not patient then someone is either wise or not wise and vice versa. Everyone who is either not quiet or not curious is either not funny or happy and vice versa. If someone is not tall or tall then fred is both tall and not patient and vice versa. If lucy is either not wise or not rich then someone is both calm and not brave. Everyone who is either not creative or not curious is tall or patient and vice versa. If susan is either not quiet or not old then susan is creative or not happy and vice versa. If susan is either not tall or generous then alice is not happy and vice versa. If someone is either humble or strong then someone is tall or not creative. Everyone who is either not quiet or quiet is both quiet and not kind and vice versa. Everyone who is both creative and not kind is either not wise or calm and vice versa. Everyone who is tall is either not funny or not creative. John is either quiet or humble. Fred is wise. Someone is brave or not rich. Someone is tall. Someone is either patient or funny. Lucy is happy or not curious. Lucy is both not patient and old. Susan is both not rich and not wise. | Lucy is calm. | entailment | (![X]:((~rich(X)|~tall(X))=>calm(X)))&
(((~happy(susan)&patient(susan)))=>(?[X]:((brave(X)|~wise(X)))))&
(![X]:((~happy(X)|patient(X))<=>(~old(X)<~>~happy(X))))&
(![X]:(generous(X)<=>(calm(X)|~wise(X))))&
(![X]:((old(X)|strong(X))<=>(old(X)&~rich(X))))&
((?[X]:((wise(X)&~patient(X))))<=>(?[X]:((wise(X)<~>~wise(X)))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~funny(X)<~>happy(X))))&
((?[X]:((~tall(X)|tall(X))))<=>((tall(fred)&~patient(fred))))&
(((~wise(lucy)<~>~rich(lucy)))=>(?[X]:((calm(X)&~brave(X)))))&
(![X]:((~creative(X)<~>~curious(X))<=>(tall(X)|patient(X))))&
(((~quiet(susan)<~>~old(susan)))<=>((creative(susan)|~happy(susan))))&
(((~tall(susan)<~>generous(susan)))<=>(~happy(alice)))&
((?[X]:((humble(X)<~>strong(X))))=>(?[X]:((tall(X)|~creative(X)))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(quiet(X)&~kind(X))))&
(![X]:((creative(X)&~kind(X))<=>(~wise(X)<~>calm(X))))&
(![X]:(tall(X)=>(~funny(X)<~>~creative(X))))&
((quiet(john)<~>humble(john)))&
(wise(fred))&
(?[X]:((brave(X)|~rich(X))))&
(?[X]:(tall(X)))&
(?[X]:((patient(X)<~>funny(X))))&
((happy(lucy)|~curious(lucy)))&
((~patient(lucy)&old(lucy)))&
((~rich(susan)&~wise(susan))) | calm(lucy) | [
"p0",
"p4",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8316113093519406137931971
% SZS output start Proof for 8316113093519406137931971
1. ! [X0] : ((~tall(X0) | ~rich(X0)) => calm(X0)) [input p0]
5. ! [X0] : ((strong(X0) | old(X0)) <=> (~rich(X0) & old(X0))) [input p4]
23. old(lucy) & ~patient(lucy) [input p22]
25. ~calm(lucy) [input hypothesis]
28. ! [X0] : (calm(X0) | (tall(X0) & rich(X0))) [ennf transformation 1]
40. ! [X0] : (((strong(X0) | old(X0)) | (rich(X0) | ~old(X0))) & ((~rich(X0) & old(X0)) | (~strong(X0) & ~old(X0)))) [nnf transformation 5]
41. ! [X0] : ((strong(X0) | old(X0) | rich(X0) | ~old(X0)) & ((~rich(X0) & old(X0)) | (~strong(X0) & ~old(X0)))) [flattening 40]
78. calm(X0) | rich(X0) [cnf transformation 28]
92. ~old(X0) | ~rich(X0) [cnf transformation 41]
159. old(lucy) [cnf transformation 23]
162. ~calm(lucy) [cnf transformation 25]
229. 13 <=> rich(lucy) [avatar definition]
231. rich(lucy) <- (13) [avatar component clause 229]
341. rich(lucy) [resolution 78,162]
344. 13 [avatar split clause 341,229]
352. ~rich(lucy) [resolution 92,159]
353. $false <- (13) [subsumption resolution 352,231]
354. ~13 [avatar contradiction clause 353]
355. $false [avatar sat refutation 344,354]
% SZS output end Proof for 8316113093519406137931971
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not happy is not calm. Everyone who is not old or wise is either rich or strong. If someone is both wise and not humble then someone is not generous or happy. Everyone who is not rich or not kind is either happy or not funny and vice versa. If someone is old then alice is not funny or old. Everyone who is both not rich and not curious is both not kind and generous and vice versa. Everyone who is either not funny or not patient is both kind and old. If someone is either not happy or not old then someone is not curious or rich. If someone is not tall then alice is not curious or not patient. If lucy is both strong and not creative then someone is not rich or funny and vice versa. Everyone who is old or creative is either not quiet or not rich. Everyone who is funny or creative is either not creative or strong. Everyone who is both not wise and patient is both not calm and not old. Everyone who is both funny and old is funny or wise. If john is both funny and calm then fred is funny or not rich and vice versa. Everyone who is kind is wise. Someone is not wise. John is both not quiet and funny. Lucy is both rich and not kind. Someone is both not patient and not funny. Someone is either curious or not wise. Paul is generous. John is either not quiet or patient. Someone is either not curious or curious. | Lucy is generous. | contradiction | (![X]:((~patient(X)<~>~happy(X))=>~calm(X)))&
(![X]:((~old(X)|wise(X))=>(rich(X)<~>strong(X))))&
((?[X]:((wise(X)&~humble(X))))=>(?[X]:((~generous(X)|happy(X)))))&
(![X]:((~rich(X)|~kind(X))<=>(happy(X)<~>~funny(X))))&
((?[X]:(old(X)))=>((~funny(alice)|old(alice))))&
(![X]:((~rich(X)&~curious(X))<=>(~kind(X)&generous(X))))&
(![X]:((~funny(X)<~>~patient(X))=>(kind(X)&old(X))))&
((?[X]:((~happy(X)<~>~old(X))))=>(?[X]:((~curious(X)|rich(X)))))&
((?[X]:(~tall(X)))=>((~curious(alice)|~patient(alice))))&
(((strong(lucy)&~creative(lucy)))<=>(?[X]:((~rich(X)|funny(X)))))&
(![X]:((old(X)|creative(X))=>(~quiet(X)<~>~rich(X))))&
(![X]:((funny(X)|creative(X))=>(~creative(X)<~>strong(X))))&
(![X]:((~wise(X)&patient(X))=>(~calm(X)&~old(X))))&
(![X]:((funny(X)&old(X))=>(funny(X)|wise(X))))&
(((funny(john)&calm(john)))<=>((funny(fred)|~rich(fred))))&
(![X]:(kind(X)=>wise(X)))&
(?[X]:(~wise(X)))&
((~quiet(john)&funny(john)))&
((rich(lucy)&~kind(lucy)))&
(?[X]:((~patient(X)&~funny(X))))&
(?[X]:((curious(X)<~>~wise(X))))&
(generous(paul))&
((~quiet(john)<~>patient(john)))&
(?[X]:((~curious(X)<~>curious(X)))) | generous(lucy) | [
"p5",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7553537415072827946333812
% SZS output start Proof for 7553537415072827946333812
6. ! [X0] : ((~curious(X0) & ~rich(X0)) <=> (generous(X0) & ~kind(X0))) [input p5]
19. ~kind(lucy) & rich(lucy) [input p18]
25. generous(lucy) [input hypothesis]
47. ! [X0] : (((~curious(X0) & ~rich(X0)) | (~generous(X0) | kind(X0))) & ((generous(X0) & ~kind(X0)) | (curious(X0) | rich(X0)))) [nnf transformation 6]
48. ! [X0] : (((~curious(X0) & ~rich(X0)) | ~generous(X0) | kind(X0)) & ((generous(X0) & ~kind(X0)) | curious(X0) | rich(X0))) [flattening 47]
89. ~generous(X0) | ~rich(X0) | kind(X0) [cnf transformation 48]
122. rich(lucy) [cnf transformation 19]
123. ~kind(lucy) [cnf transformation 19]
133. generous(lucy) [cnf transformation 25]
275. ~rich(lucy) | kind(lucy) [resolution 89,133]
285. kind(lucy) [subsumption resolution 275,122]
286. $false [subsumption resolution 285,123]
% SZS output end Proof for 7553537415072827946333812
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is creative or not quiet and vice versa. Everyone who is not happy or not generous is old or funny and vice versa. Everyone who is funny is both not humble and not wise and vice versa. If mary is tall then someone is both strong and curious and vice versa. If mary is either not creative or not happy then susan is brave or not humble. If paul is strong then someone is both wise and rich and vice versa. Everyone who is not old or curious is humble. Everyone who is creative or curious is both not rich and not curious and vice versa. If someone is both brave and tall then someone is either not rich or not kind and vice versa. If someone is both not humble and not calm then susan is not wise or quiet and vice versa. Everyone who is both creative and not funny is both not quiet and not creative. If alice is both brave and generous then susan is either kind or not happy and vice versa. If fred is curious or creative then susan is either not happy or tall and vice versa. Everyone who is not kind or humble is funny. If someone is not strong then someone is either not old or humble and vice versa. Someone is either not happy or not humble. Someone is not brave. Someone is not rich or brave. John is either kind or brave. Mary is both not patient and rich. John is either patient or tall. Susan is not kind. Someone is either not old or tall. | John is not humble. | entailment | (![X]:(tall(X)<=>(creative(X)|~quiet(X))))&
(![X]:((~happy(X)|~generous(X))<=>(old(X)|funny(X))))&
(![X]:(funny(X)<=>(~humble(X)&~wise(X))))&
((tall(mary))<=>(?[X]:((strong(X)&curious(X)))))&
(((~creative(mary)<~>~happy(mary)))=>((brave(susan)|~humble(susan))))&
((strong(paul))<=>(?[X]:((wise(X)&rich(X)))))&
(![X]:((~old(X)|curious(X))=>humble(X)))&
(![X]:((creative(X)|curious(X))<=>(~rich(X)&~curious(X))))&
((?[X]:((brave(X)&tall(X))))<=>(?[X]:((~rich(X)<~>~kind(X)))))&
((?[X]:((~humble(X)&~calm(X))))<=>((~wise(susan)|quiet(susan))))&
(![X]:((creative(X)&~funny(X))=>(~quiet(X)&~creative(X))))&
(((brave(alice)&generous(alice)))<=>((kind(susan)<~>~happy(susan))))&
(((curious(fred)|creative(fred)))<=>((~happy(susan)<~>tall(susan))))&
(![X]:((~kind(X)|humble(X))=>funny(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((~old(X)<~>humble(X)))))&
(?[X]:((~happy(X)<~>~humble(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~rich(X)|brave(X))))&
((kind(john)<~>brave(john)))&
((~patient(mary)&rich(mary)))&
((patient(john)<~>tall(john)))&
(~kind(susan))&
(?[X]:((~old(X)<~>tall(X)))) | ~humble(john) | [
"p2",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1043685140752382665515409
% SZS output start Proof for 1043685140752382665515409
3. ! [X0] : (funny(X0) <=> (~wise(X0) & ~humble(X0))) [input p2]
14. ! [X0] : ((humble(X0) | ~kind(X0)) => funny(X0)) [input p13]
24. humble(john) [input hypothesis]
32. ! [X0] : (funny(X0) | (~humble(X0) & kind(X0))) [ennf transformation 14]
37. ! [X0] : ((funny(X0) | (wise(X0) | humble(X0))) & ((~wise(X0) & ~humble(X0)) | ~funny(X0))) [nnf transformation 3]
38. ! [X0] : ((funny(X0) | wise(X0) | humble(X0)) & ((~wise(X0) & ~humble(X0)) | ~funny(X0))) [flattening 37]
88. ~humble(X0) | ~funny(X0) [cnf transformation 38]
132. funny(X0) | ~humble(X0) [cnf transformation 32]
150. humble(john) [cnf transformation 24]
299. ~humble(X0) [subsumption resolution 132,88]
350. $false [subsumption resolution 150,299]
% SZS output end Proof for 1043685140752382665515409
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble then someone is both happy and creative.
If someone is both not old and not quiet then someone is either wise or not tall and vice versa.
If paul is quiet then someone is both not wise and not funny.
If mary is both brave and rich then paul is not curious.
Everyone who is both curious and brave is funny and vice versa.
If lucy is tall then lucy is kind and vice versa.
If john is both not creative and not happy then susan is both creative and kind and vice versa.
If someone is not quiet then susan is either not tall or not creative and vice versa.
Everyone who is either not kind or generous is rich.
Everyone who is curious is either not generous or brave.
If someone is both quiet and curious then someone is both creative and brave and vice versa.
Everyone who is not rich is either humble or not old.
If someone is either not happy or generous then someone is both not rich and curious.
If mary is not creative or not curious then someone is creative and vice versa.
If mary is either not happy or calm then john is both not tall and not kind and vice versa.
Everyone who is either old or not curious is curious and vice versa.
Paul is tall.
Susan is not brave.
Someone is not old or tall.
Someone is patient or not funny.
Susan is either wise or not strong.
Someone is either tall or generous.
Lucy is both not brave and not patient. | Mary is calm. | neutral | ((?[X]:(humble(X)))=>(?[X]:((happy(X)&creative(X)))))&
((?[X]:((~old(X)&~quiet(X))))<=>(?[X]:((wise(X)<~>~tall(X)))))&
((quiet(paul))=>(?[X]:((~wise(X)&~funny(X)))))&
(((brave(mary)&rich(mary)))=>(~curious(paul)))&
(![X]:((curious(X)&brave(X))<=>funny(X)))&
((tall(lucy))<=>(kind(lucy)))&
(((~creative(john)&~happy(john)))<=>((creative(susan)&kind(susan))))&
((?[X]:(~quiet(X)))<=>((~tall(susan)<~>~creative(susan))))&
(![X]:((~kind(X)<~>generous(X))=>rich(X)))&
(![X]:(curious(X)=>(~generous(X)<~>brave(X))))&
((?[X]:((quiet(X)&curious(X))))<=>(?[X]:((creative(X)&brave(X)))))&
(![X]:(~rich(X)=>(humble(X)<~>~old(X))))&
((?[X]:((~happy(X)<~>generous(X))))=>(?[X]:((~rich(X)&curious(X)))))&
(((~creative(mary)|~curious(mary)))<=>(?[X]:(creative(X))))&
(((~happy(mary)<~>calm(mary)))<=>((~tall(john)&~kind(john))))&
(![X]:((old(X)<~>~curious(X))<=>curious(X)))&
(tall(paul))&
(~brave(susan))&
(?[X]:((~old(X)|tall(X))))&
(?[X]:((patient(X)|~funny(X))))&
((wise(susan)<~>~strong(susan)))&
(?[X]:((tall(X)<~>generous(X))))&
((~brave(lucy)&~patient(lucy))) | calm(mary) | [] | null | 0 |
If alice is both not old and not quiet then someone is either not patient or old.
If someone is patient then fred is not kind and vice versa.
Everyone who is tall or quiet is either not kind or not rich.
Everyone who is either humble or not wise is either calm or not quiet and vice versa.
If someone is humble then fred is both calm and rich.
Everyone who is rich or strong is either patient or quiet.
If someone is happy or calm then someone is both not wise and not calm.
Everyone who is not calm or not happy is not kind.
If someone is wise then john is both not generous and not creative.
Everyone who is not generous is happy.
Everyone who is either not humble or wise is humble.
If someone is either not calm or patient then john is not strong or not happy and vice versa.
If someone is either not quiet or not funny then someone is not brave or not quiet and vice versa.
Everyone who is both tall and kind is both not generous and not patient and vice versa.
If someone is both wise and not curious then someone is both wise and strong and vice versa.
Everyone who is patient or not funny is both not wise and generous.
Someone is either tall or wise.
Paul is both old and not humble.
Alice is either happy or strong.
Someone is both not funny and not brave.
John is both curious and kind.
Mary is not humble or kind.
John is curious or old.
Someone is rich or creative. | Fred is not rich. | contradiction | (((~old(alice)&~quiet(alice)))=>(?[X]:((~patient(X)<~>old(X)))))&
((?[X]:(patient(X)))<=>(~kind(fred)))&
(![X]:((tall(X)|quiet(X))=>(~kind(X)<~>~rich(X))))&
(![X]:((humble(X)<~>~wise(X))<=>(calm(X)<~>~quiet(X))))&
((?[X]:(humble(X)))=>((calm(fred)&rich(fred))))&
(![X]:((rich(X)|strong(X))=>(patient(X)<~>quiet(X))))&
((?[X]:((happy(X)|calm(X))))=>(?[X]:((~wise(X)&~calm(X)))))&
(![X]:((~calm(X)|~happy(X))=>~kind(X)))&
((?[X]:(wise(X)))=>((~generous(john)&~creative(john))))&
(![X]:(~generous(X)=>happy(X)))&
(![X]:((~humble(X)<~>wise(X))=>humble(X)))&
((?[X]:((~calm(X)<~>patient(X))))<=>((~strong(john)|~happy(john))))&
((?[X]:((~quiet(X)<~>~funny(X))))<=>(?[X]:((~brave(X)|~quiet(X)))))&
(![X]:((tall(X)&kind(X))<=>(~generous(X)&~patient(X))))&
((?[X]:((wise(X)&~curious(X))))<=>(?[X]:((wise(X)&strong(X)))))&
(![X]:((patient(X)|~funny(X))=>(~wise(X)&generous(X))))&
(?[X]:((tall(X)<~>wise(X))))&
((old(paul)&~humble(paul)))&
((happy(alice)<~>strong(alice)))&
(?[X]:((~funny(X)&~brave(X))))&
((curious(john)&kind(john)))&
((~humble(mary)|kind(mary)))&
((curious(john)|old(john)))&
(?[X]:((rich(X)|creative(X)))) | ~rich(fred) | [
"p1",
"p4",
"p6",
"p7",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3068369844945571797495754
% SZS output start Proof for 3068369844945571797495754
2. ? [X0] : patient(X0) <=> ~kind(fred) [input p1]
5. ? [X0] : humble(X0) => (rich(fred) & calm(fred)) [input p4]
7. ? [X0] : (calm(X0) | happy(X0)) => ? [X0] : (~calm(X0) & ~wise(X0)) [input p6]
8. ! [X0] : ((~happy(X0) | ~calm(X0)) => ~kind(X0)) [input p7]
11. ! [X0] : ((~humble(X0) <~> wise(X0)) => humble(X0)) [input p10]
16. ! [X0] : ((~funny(X0) | patient(X0)) => (generous(X0) & ~wise(X0))) [input p15]
25. ~rich(fred) [input hypothesis]
26. ? [X0] : (calm(X0) | happy(X0)) => ? [X1] : (~calm(X1) & ~wise(X1)) [rectify 7]
32. (rich(fred) & calm(fred)) | ! [X0] : ~humble(X0) [ennf transformation 5]
34. ? [X1] : (~calm(X1) & ~wise(X1)) | ! [X0] : (~calm(X0) & ~happy(X0)) [ennf transformation 26]
35. ! [X0] : (~kind(X0) | (happy(X0) & calm(X0))) [ennf transformation 8]
38. ! [X0] : (humble(X0) | (~humble(X0) <=> wise(X0))) [ennf transformation 11]
39. ! [X0] : ((generous(X0) & ~wise(X0)) | (funny(X0) & ~patient(X0))) [ennf transformation 16]
43. (? [X0] : patient(X0) | kind(fred)) & (~kind(fred) | ! [X0] : ~patient(X0)) [nnf transformation 2]
44. (? [X0] : patient(X0) | kind(fred)) & (~kind(fred) | ! [X1] : ~patient(X1)) [rectify 43]
45. ? [X0] : patient(X0) => patient(sK1) [choice axiom]
46. (patient(sK1) | kind(fred)) & (~kind(fred) | ! [X1] : ~patient(X1)) [skolemisation 44,45]
50. ? [X0] : (~calm(X0) & ~wise(X0)) | ! [X1] : (~calm(X1) & ~happy(X1)) [rectify 34]
51. ? [X0] : (~calm(X0) & ~wise(X0)) => (~calm(sK2) & ~wise(sK2)) [choice axiom]
52. (~calm(sK2) & ~wise(sK2)) | ! [X1] : (~calm(X1) & ~happy(X1)) [skolemisation 50,51]
53. ! [X0] : (humble(X0) | ((~humble(X0) | ~wise(X0)) & (wise(X0) | humble(X0)))) [nnf transformation 38]
82. patient(sK1) | kind(fred) [cnf transformation 46]
96. rich(fred) | ~humble(X0) [cnf transformation 32]
101. ~wise(sK2) | ~happy(X1) [cnf transformation 52]
106. ~kind(X0) | happy(X0) [cnf transformation 35]
110. humble(X0) | wise(X0) | humble(X0) [cnf transformation 53]
132. ~wise(X0) | ~patient(X0) [cnf transformation 39]
149. ~rich(fred) [cnf transformation 25]
150. wise(X0) | humble(X0) [duplicate literal removal 110]
170. 5 <=> kind(fred) [avatar definition]
172. kind(fred) <- (5) [avatar component clause 170]
174. 6 <=> patient(sK1) [avatar definition]
176. patient(sK1) <- (6) [avatar component clause 174]
177. 5 | 6 [avatar split clause 82,174,170]
179. 7 <=> ! [X1] : ~patient(X1) [avatar definition]
180. ~patient(X1) <- (7) [avatar component clause 179]
183. 8 <=> ! [X0] : ~humble(X0) [avatar definition]
184. ~humble(X0) <- (8) [avatar component clause 183]
186. 9 <=> rich(fred) [avatar definition]
189. 8 | 9 [avatar split clause 96,186,183]
204. 13 <=> ! [X1] : ~happy(X1) [avatar definition]
205. ~happy(X1) <- (13) [avatar component clause 204]
208. 14 <=> wise(sK2) [avatar definition]
210. ~wise(sK2) <- (~14) [avatar component clause 208]
212. 13 | ~14 [avatar split clause 101,208,204]
352. ~9 [avatar split clause 149,186]
362. humble(sK2) <- (~14) [resolution 150,210]
365. humble(X1) | ~patient(X1) [resolution 150,132]
366. $false <- (8, ~14) [subsumption resolution 362,184]
367. ~8 | 14 [avatar contradiction clause 366]
371. ~patient(X1) <- (8) [subsumption resolution 365,184]
372. 7 | ~8 [avatar split clause 371,183,179]
373. $false <- (6, 7) [resolution 180,176]
374. ~6 | ~7 [avatar contradiction clause 373]
375. happy(fred) <- (5) [resolution 172,106]
377. $false <- (5, 13) [subsumption resolution 375,205]
378. ~5 | ~13 [avatar contradiction clause 377]
381. $false [avatar sat refutation 177,189,212,352,367,372,374,378]
% SZS output end Proof for 3068369844945571797495754
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind or curious then someone is either not curious or rich.
Everyone who is either rich or wise is happy and vice versa.
If someone is both creative and not wise then lucy is tall or creative and vice versa.
Everyone who is happy is not creative and vice versa.
If someone is quiet or not old then someone is not creative or not funny.
If lucy is both not happy and not generous then paul is either not calm or funny.
If someone is either not happy or generous then john is either funny or humble and vice versa.
Everyone who is patient is both quiet and calm and vice versa.
If susan is not humble then someone is not rich or not curious.
Everyone who is patient or calm is not wise or rich and vice versa.
If someone is both not patient and not happy then someone is not rich or not brave and vice versa.
If someone is both not calm and not wise then john is either strong or funny and vice versa.
Everyone who is both rich and kind is either not creative or generous and vice versa.
Everyone who is calm or kind is not humble.
If john is not wise then fred is rich and vice versa.
Everyone who is both humble and not funny is either not brave or not strong and vice versa.
Someone is either not rich or not happy.
John is tall.
Someone is either generous or tall.
Paul is either not wise or not tall.
John is either humble or not strong.
John is not patient or tall. | Fred is not humble. | entailment | ((?[X]:((kind(X)|curious(X))))=>(?[X]:((~curious(X)<~>rich(X)))))&
(![X]:((rich(X)<~>wise(X))<=>happy(X)))&
((?[X]:((creative(X)&~wise(X))))<=>((tall(lucy)|creative(lucy))))&
(![X]:(happy(X)<=>~creative(X)))&
((?[X]:((quiet(X)|~old(X))))=>(?[X]:((~creative(X)|~funny(X)))))&
(((~happy(lucy)&~generous(lucy)))=>((~calm(paul)<~>funny(paul))))&
((?[X]:((~happy(X)<~>generous(X))))<=>((funny(john)<~>humble(john))))&
(![X]:(patient(X)<=>(quiet(X)&calm(X))))&
((~humble(susan))=>(?[X]:((~rich(X)|~curious(X)))))&
(![X]:((patient(X)|calm(X))<=>(~wise(X)|rich(X))))&
((?[X]:((~patient(X)&~happy(X))))<=>(?[X]:((~rich(X)|~brave(X)))))&
((?[X]:((~calm(X)&~wise(X))))<=>((strong(john)<~>funny(john))))&
(![X]:((rich(X)&kind(X))<=>(~creative(X)<~>generous(X))))&
(![X]:((calm(X)|kind(X))=>~humble(X)))&
((~wise(john))<=>(rich(fred)))&
(![X]:((humble(X)&~funny(X))<=>(~brave(X)<~>~strong(X))))&
(?[X]:((~rich(X)<~>~happy(X))))&
(tall(john))&
(?[X]:((generous(X)<~>tall(X))))&
((~wise(paul)<~>~tall(paul)))&
((humble(john)<~>~strong(john)))&
((~patient(john)|tall(john))) | ~humble(fred) | [
"p3",
"p6",
"p7",
"p9",
"p11",
"p12",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 217252412199845142383759
% SZS output start Proof for 217252412199845142383759
4. ! [X0] : (happy(X0) <=> ~creative(X0)) [input p3]
7. ? [X0] : (~happy(X0) <~> generous(X0)) <=> (funny(john) <~> humble(john)) [input p6]
8. ! [X0] : (patient(X0) <=> (calm(X0) & quiet(X0))) [input p7]
10. ! [X0] : ((calm(X0) | patient(X0)) <=> (rich(X0) | ~wise(X0))) [input p9]
12. ? [X0] : (~wise(X0) & ~calm(X0)) <=> (strong(john) <~> funny(john)) [input p11]
13. ! [X0] : ((kind(X0) & rich(X0)) <=> (~creative(X0) <~> generous(X0))) [input p12]
14. ! [X0] : ((kind(X0) | calm(X0)) => ~humble(X0)) [input p13]
21. humble(john) <~> ~strong(john) [input p20]
23. humble(fred) [input hypothesis]
33. ! [X0] : (~humble(X0) | (~kind(X0) & ~calm(X0))) [ennf transformation 14]
44. ! [X0] : ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0))) [nnf transformation 4]
49. (? [X0] : ((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | ((funny(john) | ~humble(john)) & (humble(john) | ~funny(john)))) & (((~humble(john) | ~funny(john)) & (humble(john) | funny(john))) | ! [X0] : ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0)))) [nnf transformation 7]
50. (? [X0] : ((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | ((funny(john) | ~humble(john)) & (humble(john) | ~funny(john)))) & (((~humble(john) | ~funny(john)) & (humble(john) | funny(john))) | ! [X1] : ((~happy(X1) | ~generous(X1)) & (generous(X1) | happy(X1)))) [rectify 49]
51. ? [X0] : ((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) => ((~generous(sK3) | happy(sK3)) & (generous(sK3) | ~happy(sK3))) [choice axiom]
52. (((~generous(sK3) | happy(sK3)) & (generous(sK3) | ~happy(sK3))) | ((funny(john) | ~humble(john)) & (humble(john) | ~funny(john)))) & (((~humble(john) | ~funny(john)) & (humble(john) | funny(john))) | ! [X1] : ((~happy(X1) | ~generous(X1)) & (generous(X1) | happy(X1)))) [skolemisation 50,51]
53. ! [X0] : ((patient(X0) | (~calm(X0) | ~quiet(X0))) & ((calm(X0) & quiet(X0)) | ~patient(X0))) [nnf transformation 8]
54. ! [X0] : ((patient(X0) | ~calm(X0) | ~quiet(X0)) & ((calm(X0) & quiet(X0)) | ~patient(X0))) [flattening 53]
57. ! [X0] : (((calm(X0) | patient(X0)) | (~rich(X0) & wise(X0))) & ((rich(X0) | ~wise(X0)) | (~calm(X0) & ~patient(X0)))) [nnf transformation 10]
58. ! [X0] : ((calm(X0) | patient(X0) | (~rich(X0) & wise(X0))) & (rich(X0) | ~wise(X0) | (~calm(X0) & ~patient(X0)))) [flattening 57]
64. (? [X0] : (~wise(X0) & ~calm(X0)) | ((strong(john) | ~funny(john)) & (funny(john) | ~strong(john)))) & (((~funny(john) | ~strong(john)) & (funny(john) | strong(john))) | ! [X0] : (wise(X0) | calm(X0))) [nnf transformation 12]
65. (? [X0] : (~wise(X0) & ~calm(X0)) | ((strong(john) | ~funny(john)) & (funny(john) | ~strong(john)))) & (((~funny(john) | ~strong(john)) & (funny(john) | strong(john))) | ! [X1] : (wise(X1) | calm(X1))) [rectify 64]
66. ? [X0] : (~wise(X0) & ~calm(X0)) => (~wise(sK7) & ~calm(sK7)) [choice axiom]
67. ((~wise(sK7) & ~calm(sK7)) | ((strong(john) | ~funny(john)) & (funny(john) | ~strong(john)))) & (((~funny(john) | ~strong(john)) & (funny(john) | strong(john))) | ! [X1] : (wise(X1) | calm(X1))) [skolemisation 65,66]
68. ! [X0] : (((kind(X0) & rich(X0)) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0)))) & (((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | (~kind(X0) | ~rich(X0)))) [nnf transformation 13]
69. ! [X0] : (((kind(X0) & rich(X0)) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0)))) & (((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | ~kind(X0) | ~rich(X0))) [flattening 68]
80. (strong(john) | ~humble(john)) & (~strong(john) | humble(john)) [nnf transformation 21]
94. ~creative(X0) | ~happy(X0) [cnf transformation 44]
95. creative(X0) | happy(X0) [cnf transformation 44]
99. humble(john) | funny(john) | generous(X1) | happy(X1) [cnf transformation 52]
100. humble(john) | funny(john) | ~happy(X1) | ~generous(X1) [cnf transformation 52]
101. ~humble(john) | ~funny(john) | generous(X1) | happy(X1) [cnf transformation 52]
102. ~humble(john) | ~funny(john) | ~happy(X1) | ~generous(X1) [cnf transformation 52]
108. ~patient(X0) | calm(X0) [cnf transformation 54]
113. calm(X0) | patient(X0) | wise(X0) [cnf transformation 58]
114. calm(X0) | patient(X0) | ~rich(X0) [cnf transformation 58]
122. ~calm(sK7) | funny(john) | ~strong(john) [cnf transformation 67]
123. ~calm(sK7) | strong(john) | ~funny(john) [cnf transformation 67]
124. ~wise(sK7) | funny(john) | ~strong(john) [cnf transformation 67]
125. ~wise(sK7) | strong(john) | ~funny(john) [cnf transformation 67]
128. generous(X0) | rich(X0) | creative(X0) [cnf transformation 69]
129. ~generous(X0) | ~creative(X0) | rich(X0) [cnf transformation 69]
132. ~humble(X0) | ~calm(X0) [cnf transformation 33]
149. ~strong(john) | humble(john) [cnf transformation 80]
150. strong(john) | ~humble(john) [cnf transformation 80]
152. humble(fred) [cnf transformation 23]
226. 17 <=> humble(john) [avatar definition]
230. 18 <=> funny(john) [avatar definition]
246. 21 <=> ! [X1] : (~happy(X1) | ~generous(X1)) [avatar definition]
247. ~generous(X1) | ~happy(X1) <- (21) [avatar component clause 246]
248. 21 | ~18 | ~17 [avatar split clause 102,226,230,246]
250. 22 <=> ! [X1] : (generous(X1) | happy(X1)) [avatar definition]
251. generous(X1) | happy(X1) <- (22) [avatar component clause 250]
252. 22 | ~18 | ~17 [avatar split clause 101,226,230,250]
253. 21 | 18 | 17 [avatar split clause 100,226,230,246]
254. 22 | 18 | 17 [avatar split clause 99,226,230,250]
268. ~rich(X0) | calm(X0) [subsumption resolution 114,108]
269. calm(X0) | wise(X0) [subsumption resolution 113,108]
279. 28 <=> ! [X1] : rich(X1) [avatar definition]
280. rich(X1) <- (28) [avatar component clause 279]
301. 33 <=> strong(john) [avatar definition]
305. 34 <=> wise(sK7) [avatar definition]
308. ~18 | 33 | ~34 [avatar split clause 125,305,301,230]
309. ~33 | 18 | ~34 [avatar split clause 124,305,230,301]
311. 35 <=> calm(sK7) [avatar definition]
313. ~calm(sK7) <- (~35) [avatar component clause 311]
314. ~18 | 33 | ~35 [avatar split clause 123,311,301,230]
315. ~33 | 18 | ~35 [avatar split clause 122,311,230,301]
317. 36 <=> rich(fred) [avatar definition]
318. rich(fred) <- (36) [avatar component clause 317]
319. ~rich(fred) <- (~36) [avatar component clause 317]
356. ~17 | 33 [avatar split clause 150,301,226]
357. 17 | ~33 [avatar split clause 149,301,226]
362. ~calm(fred) [resolution 132,152]
364. calm(fred) <- (36) [resolution 268,318]
366. $false <- (36) [subsumption resolution 364,362]
367. ~36 [avatar contradiction clause 366]
369. wise(sK7) <- (~35) [resolution 269,313]
373. 34 | 35 [avatar split clause 369,311,305]
461. rich(X0) | creative(X0) | ~happy(X0) <- (21) [resolution 128,247]
463. rich(X0) | ~happy(X0) <- (21) [subsumption resolution 461,94]
475. ~creative(X1) | rich(X1) | happy(X1) <- (22) [resolution 129,251]
486. rich(X1) | happy(X1) <- (22) [subsumption resolution 475,95]
487. rich(X1) <- (21, 22) [subsumption resolution 486,463]
488. 28 | ~21 | ~22 [avatar split clause 487,250,246,279]
491. $false <- (28, ~36) [resolution 280,319]
496. ~28 | 36 [avatar contradiction clause 491]
497. $false [avatar sat refutation 248,252,253,254,308,309,314,315,356,357,367,373,488,496]
% SZS output end Proof for 217252412199845142383759
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is both quiet and funny.
Everyone who is both curious and quiet is not calm and vice versa.
Everyone who is calm or not patient is happy or not creative.
Everyone who is kind or wise is not funny or not happy.
If mary is generous then alice is patient or not old and vice versa.
If someone is curious or not brave then someone is brave or not strong.
Everyone who is either generous or happy is funny and vice versa.
If fred is either kind or not old then someone is both curious and rich.
If john is old or humble then paul is not patient.
Everyone who is both generous and not funny is either not happy or not rich and vice versa.
If paul is wise then someone is both not wise and not calm and vice versa.
If someone is both happy and not humble then susan is strong or not wise.
If someone is curious or old then fred is curious.
If someone is either happy or strong then someone is funny or curious and vice versa.
Everyone who is not calm or not brave is not humble or tall.
Everyone who is either tall or kind is curious or not creative.
Someone is not patient.
Paul is not humble or calm.
Someone is wise or not tall.
Fred is generous.
Someone is both not humble and not patient.
Susan is either not rich or creative.
Someone is brave.
Someone is not happy. | John is old. | neutral | (![X]:(brave(X)=>(quiet(X)&funny(X))))&
(![X]:((curious(X)&quiet(X))<=>~calm(X)))&
(![X]:((calm(X)|~patient(X))=>(happy(X)|~creative(X))))&
(![X]:((kind(X)|wise(X))=>(~funny(X)|~happy(X))))&
((generous(mary))<=>((patient(alice)|~old(alice))))&
((?[X]:((curious(X)|~brave(X))))=>(?[X]:((brave(X)|~strong(X)))))&
(![X]:((generous(X)<~>happy(X))<=>funny(X)))&
(((kind(fred)<~>~old(fred)))=>(?[X]:((curious(X)&rich(X)))))&
(((old(john)|humble(john)))=>(~patient(paul)))&
(![X]:((generous(X)&~funny(X))<=>(~happy(X)<~>~rich(X))))&
((wise(paul))<=>(?[X]:((~wise(X)&~calm(X)))))&
((?[X]:((happy(X)&~humble(X))))=>((strong(susan)|~wise(susan))))&
((?[X]:((curious(X)|old(X))))=>(curious(fred)))&
((?[X]:((happy(X)<~>strong(X))))<=>(?[X]:((funny(X)|curious(X)))))&
(![X]:((~calm(X)|~brave(X))=>(~humble(X)|tall(X))))&
(![X]:((tall(X)<~>kind(X))=>(curious(X)|~creative(X))))&
(?[X]:(~patient(X)))&
((~humble(paul)|calm(paul)))&
(?[X]:((wise(X)|~tall(X))))&
(generous(fred))&
(?[X]:((~humble(X)&~patient(X))))&
((~rich(susan)<~>creative(susan)))&
(?[X]:(brave(X)))&
(?[X]:(~happy(X))) | old(john) | [] | null | 0 |
Everyone who is both not quiet and happy is either not kind or not humble. Everyone who is curious or not brave is both not funny and tall. If mary is tall or not rich then someone is patient or kind and vice versa. Everyone who is either not funny or not quiet is not kind or not happy and vice versa. If fred is not kind or wise then someone is both not old and not patient. Everyone who is not strong is not quiet or generous. If someone is not brave then someone is both not tall and funny. Everyone who is not generous or not wise is old or not rich and vice versa. If someone is calm or kind then susan is both curious and not patient. Everyone who is rich or old is not calm. Everyone who is tall or generous is both not kind and funny and vice versa. If someone is not generous then lucy is not patient. If someone is not tall then someone is old and vice versa. If someone is calm or funny then fred is either not funny or happy. If alice is not creative then someone is not calm and vice versa. Everyone who is not kind or tall is either curious or not strong and vice versa. Someone is rich or strong. John is both humble and not curious. Mary is either not happy or not kind. John is not old. Someone is either not wise or not rich. | Susan is not strong. | entailment | (![X]:((~quiet(X)&happy(X))=>(~kind(X)<~>~humble(X))))&
(![X]:((curious(X)|~brave(X))=>(~funny(X)&tall(X))))&
(((tall(mary)|~rich(mary)))<=>(?[X]:((patient(X)|kind(X)))))&
(![X]:((~funny(X)<~>~quiet(X))<=>(~kind(X)|~happy(X))))&
(((~kind(fred)|wise(fred)))=>(?[X]:((~old(X)&~patient(X)))))&
(![X]:(~strong(X)=>(~quiet(X)|generous(X))))&
((?[X]:(~brave(X)))=>(?[X]:((~tall(X)&funny(X)))))&
(![X]:((~generous(X)|~wise(X))<=>(old(X)|~rich(X))))&
((?[X]:((calm(X)|kind(X))))=>((curious(susan)&~patient(susan))))&
(![X]:((rich(X)|old(X))=>~calm(X)))&
(![X]:((tall(X)|generous(X))<=>(~kind(X)&funny(X))))&
((?[X]:(~generous(X)))=>(~patient(lucy)))&
((?[X]:(~tall(X)))<=>(?[X]:(old(X))))&
((?[X]:((calm(X)|funny(X))))=>((~funny(fred)<~>happy(fred))))&
((~creative(alice))<=>(?[X]:(~calm(X))))&
(![X]:((~kind(X)|tall(X))<=>(curious(X)<~>~strong(X))))&
(?[X]:((rich(X)|strong(X))))&
((humble(john)&~curious(john)))&
((~happy(mary)<~>~kind(mary)))&
(~old(john))&
(?[X]:((~wise(X)<~>~rich(X)))) | ~strong(susan) | [
"p1",
"p8",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 813670851187647766859298
% SZS output start Proof for 813670851187647766859298
2. ! [X0] : ((~brave(X0) | curious(X0)) => (tall(X0) & ~funny(X0))) [input p1]
9. ? [X0] : (kind(X0) | calm(X0)) => (~patient(susan) & curious(susan)) [input p8]
11. ! [X0] : ((generous(X0) | tall(X0)) <=> (funny(X0) & ~kind(X0))) [input p10]
16. ! [X0] : ((tall(X0) | ~kind(X0)) <=> (curious(X0) <~> ~strong(X0))) [input p15]
22. strong(susan) [input hypothesis]
25. ! [X0] : (curious(X0) => (tall(X0) & ~funny(X0))) [pure predicate removal 2]
29. ! [X0] : ((tall(X0) & ~funny(X0)) | ~curious(X0)) [ennf transformation 25]
33. (~patient(susan) & curious(susan)) | ! [X0] : (~kind(X0) & ~calm(X0)) [ennf transformation 9]
49. ! [X0] : (((generous(X0) | tall(X0)) | (~funny(X0) | kind(X0))) & ((funny(X0) & ~kind(X0)) | (~generous(X0) & ~tall(X0)))) [nnf transformation 11]
50. ! [X0] : ((generous(X0) | tall(X0) | ~funny(X0) | kind(X0)) & ((funny(X0) & ~kind(X0)) | (~generous(X0) & ~tall(X0)))) [flattening 49]
61. ! [X0] : (((tall(X0) | ~kind(X0)) | ((curious(X0) | strong(X0)) & (~strong(X0) | ~curious(X0)))) & (((strong(X0) | ~curious(X0)) & (~strong(X0) | curious(X0))) | (~tall(X0) & kind(X0)))) [nnf transformation 16]
62. ! [X0] : ((tall(X0) | ~kind(X0) | ((curious(X0) | strong(X0)) & (~strong(X0) | ~curious(X0)))) & (((strong(X0) | ~curious(X0)) & (~strong(X0) | curious(X0))) | (~tall(X0) & kind(X0)))) [flattening 61]
71. ~funny(X0) | ~curious(X0) [cnf transformation 29]
72. ~curious(X0) | tall(X0) [cnf transformation 29]
93. curious(susan) | ~kind(X0) [cnf transformation 33]
100. ~tall(X0) | funny(X0) [cnf transformation 50]
112. ~strong(X0) | curious(X0) | kind(X0) [cnf transformation 62]
126. strong(susan) [cnf transformation 22]
128. 1 <=> ! [X0] : ~kind(X0) [avatar definition]
129. ~kind(X0) <- (1) [avatar component clause 128]
183. 13 <=> curious(susan) [avatar definition]
184. ~curious(susan) <- (~13) [avatar component clause 183]
185. curious(susan) <- (13) [avatar component clause 183]
186. 1 | 13 [avatar split clause 93,183,128]
273. tall(susan) <- (13) [resolution 72,185]
279. funny(susan) <- (13) [resolution 100,273]
280. ~curious(susan) <- (13) [resolution 279,71]
281. $false <- (13) [subsumption resolution 280,185]
282. ~13 [avatar contradiction clause 281]
331. curious(susan) | kind(susan) [resolution 112,126]
333. kind(susan) <- (~13) [subsumption resolution 331,184]
334. $false <- (1, ~13) [subsumption resolution 333,129]
335. ~1 | 13 [avatar contradiction clause 334]
337. $false [avatar sat refutation 186,282,335]
% SZS output end Proof for 813670851187647766859298
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both wise and calm then alice is either creative or not happy and vice versa. Everyone who is both happy and quiet is not rich or not brave and vice versa. If someone is calm or curious then mary is either creative or humble. Everyone who is not humble or not wise is either humble or not quiet. If paul is both generous and tall then susan is both strong and not tall. If lucy is not funny then someone is both kind and not happy and vice versa. Everyone who is both not quiet and not humble is both tall and not calm and vice versa. If susan is both not generous and not rich then fred is not calm or kind. Everyone who is either not creative or creative is both brave and funny and vice versa. Everyone who is not brave or not strong is wise or not creative. Everyone who is either not quiet or not brave is wise and vice versa. Everyone who is not kind is either calm or not calm and vice versa. Everyone who is curious or strong is not funny or not kind and vice versa. Everyone who is both not generous and strong is both curious and wise and vice versa. If someone is both not creative and strong then fred is both old and not happy and vice versa. Everyone who is both not tall and happy is not kind and vice versa. Someone is not curious. Susan is both not calm and not kind. Someone is either not wise or curious. Fred is either not brave or humble. Someone is either creative or not generous. Lucy is either not brave or calm. Someone is not rich. | Susan is quiet. | neutral | ((?[X]:((wise(X)&calm(X))))<=>((creative(alice)<~>~happy(alice))))&
(![X]:((happy(X)&quiet(X))<=>(~rich(X)|~brave(X))))&
((?[X]:((calm(X)|curious(X))))=>((creative(mary)<~>humble(mary))))&
(![X]:((~humble(X)|~wise(X))=>(humble(X)<~>~quiet(X))))&
(((generous(paul)&tall(paul)))=>((strong(susan)&~tall(susan))))&
((~funny(lucy))<=>(?[X]:((kind(X)&~happy(X)))))&
(![X]:((~quiet(X)&~humble(X))<=>(tall(X)&~calm(X))))&
(((~generous(susan)&~rich(susan)))=>((~calm(fred)|kind(fred))))&
(![X]:((~creative(X)<~>creative(X))<=>(brave(X)&funny(X))))&
(![X]:((~brave(X)|~strong(X))=>(wise(X)|~creative(X))))&
(![X]:((~quiet(X)<~>~brave(X))<=>wise(X)))&
(![X]:(~kind(X)<=>(calm(X)<~>~calm(X))))&
(![X]:((curious(X)|strong(X))<=>(~funny(X)|~kind(X))))&
(![X]:((~generous(X)&strong(X))<=>(curious(X)&wise(X))))&
((?[X]:((~creative(X)&strong(X))))<=>((old(fred)&~happy(fred))))&
(![X]:((~tall(X)&happy(X))<=>~kind(X)))&
(?[X]:(~curious(X)))&
((~calm(susan)&~kind(susan)))&
(?[X]:((~wise(X)<~>curious(X))))&
((~brave(fred)<~>humble(fred)))&
(?[X]:((creative(X)<~>~generous(X))))&
((~brave(lucy)<~>calm(lucy)))&
(?[X]:(~rich(X))) | quiet(susan) | [] | null | 0 |
If someone is either brave or not tall then someone is both calm and quiet. Everyone who is not strong is both not strong and old. Everyone who is both quiet and not kind is both not strong and old. Everyone who is both quiet and not calm is not quiet or not kind. If mary is not funny then someone is generous or brave and vice versa. Everyone who is both not creative and strong is not quiet and vice versa. Everyone who is both not tall and not funny is either not strong or calm and vice versa. Everyone who is not quiet is either generous or calm and vice versa. Everyone who is brave or generous is calm or generous. Everyone who is funny is not creative and vice versa. If john is old then someone is either rich or not humble. Everyone who is both humble and old is either curious or wise and vice versa. Everyone who is not tall is either calm or not old. If someone is wise or not kind then alice is tall or patient. If someone is wise then john is either quiet or not curious and vice versa. If someone is not calm then lucy is either tall or funny. Paul is not rich. Someone is either not old or not humble. Someone is quiet. Alice is either brave or not tall. Someone is either generous or patient. Someone is either curious or not wise. Alice is either not quiet or generous. | Lucy is generous. | entailment | ((?[X]:((brave(X)<~>~tall(X))))=>(?[X]:((calm(X)&quiet(X)))))&
(![X]:(~strong(X)=>(~strong(X)&old(X))))&
(![X]:((quiet(X)&~kind(X))=>(~strong(X)&old(X))))&
(![X]:((quiet(X)&~calm(X))=>(~quiet(X)|~kind(X))))&
((~funny(mary))<=>(?[X]:((generous(X)|brave(X)))))&
(![X]:((~creative(X)&strong(X))<=>~quiet(X)))&
(![X]:((~tall(X)&~funny(X))<=>(~strong(X)<~>calm(X))))&
(![X]:(~quiet(X)<=>(generous(X)<~>calm(X))))&
(![X]:((brave(X)|generous(X))=>(calm(X)|generous(X))))&
(![X]:(funny(X)<=>~creative(X)))&
((old(john))=>(?[X]:((rich(X)<~>~humble(X)))))&
(![X]:((humble(X)&old(X))<=>(curious(X)<~>wise(X))))&
(![X]:(~tall(X)=>(calm(X)<~>~old(X))))&
((?[X]:((wise(X)|~kind(X))))=>((tall(alice)|patient(alice))))&
((?[X]:(wise(X)))<=>((quiet(john)<~>~curious(john))))&
((?[X]:(~calm(X)))=>((tall(lucy)<~>funny(lucy))))&
(~rich(paul))&
(?[X]:((~old(X)<~>~humble(X))))&
(?[X]:(quiet(X)))&
((brave(alice)<~>~tall(alice)))&
(?[X]:((generous(X)<~>patient(X))))&
(?[X]:((curious(X)<~>~wise(X))))&
((~quiet(alice)<~>generous(alice))) | generous(lucy) | [
"p1",
"p2",
"p3",
"p5",
"p6",
"p7",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 212445894915845614793519
% SZS output start Proof for 212445894915845614793519
2. ! [X0] : (~strong(X0) => (old(X0) & ~strong(X0))) [input p1]
3. ! [X0] : ((~kind(X0) & quiet(X0)) => (old(X0) & ~strong(X0))) [input p2]
4. ! [X0] : ((~calm(X0) & quiet(X0)) => (~kind(X0) | ~quiet(X0))) [input p3]
6. ! [X0] : ((strong(X0) & ~creative(X0)) <=> ~quiet(X0)) [input p5]
7. ! [X0] : ((~funny(X0) & ~tall(X0)) <=> (~strong(X0) <~> calm(X0))) [input p6]
8. ! [X0] : (~quiet(X0) <=> (generous(X0) <~> calm(X0))) [input p7]
10. ! [X0] : (funny(X0) <=> ~creative(X0)) [input p9]
13. ! [X0] : (~tall(X0) => (calm(X0) <~> ~old(X0))) [input p12]
24. ~generous(lucy) [input hypothesis]
27. ! [X0] : ((old(X0) & ~strong(X0)) | strong(X0)) [ennf transformation 2]
28. ! [X0] : ((old(X0) & ~strong(X0)) | (kind(X0) | ~quiet(X0))) [ennf transformation 3]
29. ! [X0] : ((old(X0) & ~strong(X0)) | kind(X0) | ~quiet(X0)) [flattening 28]
30. ! [X0] : ((~kind(X0) | ~quiet(X0)) | (calm(X0) | ~quiet(X0))) [ennf transformation 4]
31. ! [X0] : (~kind(X0) | ~quiet(X0) | calm(X0) | ~quiet(X0)) [flattening 30]
35. ! [X0] : ((calm(X0) <~> ~old(X0)) | tall(X0)) [ennf transformation 13]
47. ! [X0] : (((strong(X0) & ~creative(X0)) | quiet(X0)) & (~quiet(X0) | (~strong(X0) | creative(X0)))) [nnf transformation 6]
48. ! [X0] : (((strong(X0) & ~creative(X0)) | quiet(X0)) & (~quiet(X0) | ~strong(X0) | creative(X0))) [flattening 47]
49. ! [X0] : (((~funny(X0) & ~tall(X0)) | ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) & (((~calm(X0) | strong(X0)) & (calm(X0) | ~strong(X0))) | (funny(X0) | tall(X0)))) [nnf transformation 7]
50. ! [X0] : (((~funny(X0) & ~tall(X0)) | ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) & (((~calm(X0) | strong(X0)) & (calm(X0) | ~strong(X0))) | funny(X0) | tall(X0))) [flattening 49]
51. ! [X0] : ((~quiet(X0) | ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0)))) & (((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) | quiet(X0))) [nnf transformation 8]
52. ! [X0] : ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0))) [nnf transformation 10]
58. ! [X0] : (((old(X0) | ~calm(X0)) & (~old(X0) | calm(X0))) | tall(X0)) [nnf transformation 35]
82. old(X0) | strong(X0) [cnf transformation 27]
83. ~strong(X0) | kind(X0) | ~quiet(X0) [cnf transformation 29]
85. ~kind(X0) | ~quiet(X0) | calm(X0) | ~quiet(X0) [cnf transformation 31]
89. ~strong(X0) | ~quiet(X0) | creative(X0) [cnf transformation 48]
90. ~creative(X0) | quiet(X0) [cnf transformation 48]
91. strong(X0) | quiet(X0) [cnf transformation 48]
94. ~tall(X0) | calm(X0) | strong(X0) [cnf transformation 50]
96. ~funny(X0) | calm(X0) | strong(X0) [cnf transformation 50]
97. ~funny(X0) | ~strong(X0) | ~calm(X0) [cnf transformation 50]
98. generous(X0) | calm(X0) | quiet(X0) [cnf transformation 51]
101. ~quiet(X0) | generous(X0) | ~calm(X0) [cnf transformation 51]
104. ~creative(X0) | ~funny(X0) [cnf transformation 52]
105. creative(X0) | funny(X0) [cnf transformation 52]
114. ~old(X0) | calm(X0) | tall(X0) [cnf transformation 58]
136. ~generous(lucy) [cnf transformation 24]
137. ~kind(X0) | ~quiet(X0) | calm(X0) [duplicate literal removal 85]
231. 22 <=> funny(lucy) [avatar definition]
232. funny(lucy) <- (22) [avatar component clause 231]
233. ~funny(lucy) <- (~22) [avatar component clause 231]
286. funny(X1) | quiet(X1) [resolution 105,90]
300. ~strong(X0) | ~calm(X0) | quiet(X0) [resolution 97,286]
308. ~calm(X0) | quiet(X0) [subsumption resolution 300,91]
320. 34 <=> strong(lucy) [avatar definition]
322. strong(lucy) <- (34) [avatar component clause 320]
324. 35 <=> calm(lucy) [avatar definition]
325. ~calm(lucy) <- (~35) [avatar component clause 324]
326. calm(lucy) <- (35) [avatar component clause 324]
329. calm(lucy) | strong(lucy) <- (22) [resolution 232,96]
331. 34 | 35 | ~22 [avatar split clause 329,231,324,320]
338. quiet(lucy) <- (~22) [resolution 233,286]
340. calm(lucy) | quiet(lucy) [resolution 98,136]
342. ~quiet(lucy) | creative(lucy) <- (34) [resolution 322,89]
409. calm(X0) | tall(X0) | strong(X0) [resolution 114,82]
420. strong(X0) | calm(X0) [subsumption resolution 409,94]
482. calm(X3) | kind(X3) | ~quiet(X3) [resolution 420,83]
495. ~quiet(X3) | calm(X3) [subsumption resolution 482,137]
590. calm(lucy) <- (~22) [resolution 495,338]
597. $false <- (~22, ~35) [subsumption resolution 590,325]
598. 22 | 35 [avatar contradiction clause 597]
602. 64 <=> creative(lucy) [avatar definition]
604. creative(lucy) <- (64) [avatar component clause 602]
606. 65 <=> quiet(lucy) [avatar definition]
607. quiet(lucy) <- (65) [avatar component clause 606]
609. 64 | ~65 | ~34 [avatar split clause 342,320,606,602]
641. ~funny(lucy) <- (64) [resolution 604,104]
643. $false <- (22, 64) [subsumption resolution 641,232]
644. ~22 | ~64 [avatar contradiction clause 643]
646. quiet(lucy) [subsumption resolution 340,308]
647. 65 [avatar split clause 646,606]
657. generous(lucy) | ~calm(lucy) <- (65) [resolution 607,101]
659. ~calm(lucy) <- (65) [subsumption resolution 657,136]
660. $false <- (35, 65) [subsumption resolution 659,326]
661. ~35 | ~65 [avatar contradiction clause 660]
662. $false [avatar sat refutation 331,598,609,644,647,661]
% SZS output end Proof for 212445894915845614793519
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or not funny is either funny or not curious and vice versa.
If someone is not kind then someone is humble or not calm.
Everyone who is not patient is not funny and vice versa.
If someone is calm then susan is strong or quiet and vice versa.
If someone is curious then someone is either not old or not strong.
Everyone who is old is both not patient and old.
Everyone who is brave is both not creative and not wise and vice versa.
Everyone who is both funny and not quiet is either not quiet or not curious.
If john is both not wise and strong then fred is tall and vice versa.
If paul is not generous or not humble then someone is not patient.
If alice is either funny or not wise then someone is both not strong and humble and vice versa.
Everyone who is not patient is both not wise and curious and vice versa.
If someone is both not old and not kind then someone is kind and vice versa.
If lucy is humble or old then someone is not calm or not tall and vice versa.
If someone is either calm or not rich then someone is either not tall or not wise and vice versa.
If someone is not funny or rich then susan is not humble or old and vice versa.
Someone is generous.
Someone is brave.
Someone is either not humble or not rich.
Someone is brave or patient.
Someone is both not calm and rich.
Someone is both curious and humble.
Someone is either not old or not kind.
Susan is not wise. | Paul is old. | contradiction | (![X]:((~rich(X)|~funny(X))<=>(funny(X)<~>~curious(X))))&
((?[X]:(~kind(X)))=>(?[X]:((humble(X)|~calm(X)))))&
(![X]:(~patient(X)<=>~funny(X)))&
((?[X]:(calm(X)))<=>((strong(susan)|quiet(susan))))&
((?[X]:(curious(X)))=>(?[X]:((~old(X)<~>~strong(X)))))&
(![X]:(old(X)=>(~patient(X)&old(X))))&
(![X]:(brave(X)<=>(~creative(X)&~wise(X))))&
(![X]:((funny(X)&~quiet(X))=>(~quiet(X)<~>~curious(X))))&
(((~wise(john)&strong(john)))<=>(tall(fred)))&
(((~generous(paul)|~humble(paul)))=>(?[X]:(~patient(X))))&
(((funny(alice)<~>~wise(alice)))<=>(?[X]:((~strong(X)&humble(X)))))&
(![X]:(~patient(X)<=>(~wise(X)&curious(X))))&
((?[X]:((~old(X)&~kind(X))))<=>(?[X]:(kind(X))))&
(((humble(lucy)|old(lucy)))<=>(?[X]:((~calm(X)|~tall(X)))))&
((?[X]:((calm(X)<~>~rich(X))))<=>(?[X]:((~tall(X)<~>~wise(X)))))&
((?[X]:((~funny(X)|rich(X))))<=>((~humble(susan)|old(susan))))&
(?[X]:(generous(X)))&
(?[X]:(brave(X)))&
(?[X]:((~humble(X)<~>~rich(X))))&
(?[X]:((brave(X)|patient(X))))&
(?[X]:((~calm(X)&rich(X))))&
(?[X]:((curious(X)&humble(X))))&
(?[X]:((~old(X)<~>~kind(X))))&
(~wise(susan)) | old(paul) | [
"p0",
"p2",
"p5",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 26762546866089091502926
% SZS output start Proof for 26762546866089091502926
1. ! [X0] : ((~funny(X0) | ~rich(X0)) <=> (funny(X0) <~> ~curious(X0))) [input p0]
3. ! [X0] : (~patient(X0) <=> ~funny(X0)) [input p2]
6. ! [X0] : (old(X0) => (old(X0) & ~patient(X0))) [input p5]
12. ! [X0] : (~patient(X0) <=> (curious(X0) & ~wise(X0))) [input p11]
25. old(paul) [input hypothesis]
36. ! [X0] : ((old(X0) & ~patient(X0)) | ~old(X0)) [ennf transformation 6]
41. ! [X0] : (((~funny(X0) | ~rich(X0)) | ((funny(X0) | curious(X0)) & (~curious(X0) | ~funny(X0)))) & (((curious(X0) | ~funny(X0)) & (~curious(X0) | funny(X0))) | (funny(X0) & rich(X0)))) [nnf transformation 1]
42. ! [X0] : ((~funny(X0) | ~rich(X0) | ((funny(X0) | curious(X0)) & (~curious(X0) | ~funny(X0)))) & (((curious(X0) | ~funny(X0)) & (~curious(X0) | funny(X0))) | (funny(X0) & rich(X0)))) [flattening 41]
46. ! [X0] : ((~patient(X0) | funny(X0)) & (~funny(X0) | patient(X0))) [nnf transformation 3]
65. ! [X0] : ((~patient(X0) | (~curious(X0) | wise(X0))) & ((curious(X0) & ~wise(X0)) | patient(X0))) [nnf transformation 12]
66. ! [X0] : ((~patient(X0) | ~curious(X0) | wise(X0)) & ((curious(X0) & ~wise(X0)) | patient(X0))) [flattening 65]
102. ~curious(X0) | funny(X0) | funny(X0) [cnf transformation 42]
108. ~funny(X0) | patient(X0) [cnf transformation 46]
109. ~patient(X0) | funny(X0) [cnf transformation 46]
115. ~old(X0) | ~patient(X0) [cnf transformation 36]
131. patient(X0) | curious(X0) [cnf transformation 66]
163. old(paul) [cnf transformation 25]
165. ~curious(X0) | funny(X0) [duplicate literal removal 102]
365. 45 <=> ! [X1] : funny(X1) [avatar definition]
366. funny(X1) <- (45) [avatar component clause 365]
401. ~patient(paul) [resolution 115,163]
404. curious(X0) | funny(X0) [resolution 131,109]
408. funny(X0) [subsumption resolution 404,165]
409. 45 [avatar split clause 408,365]
411. patient(X0) <- (45) [resolution 366,108]
420. $false <- (45) [resolution 411,401]
427. ~45 [avatar contradiction clause 420]
428. $false [avatar sat refutation 409,427]
% SZS output end Proof for 26762546866089091502926
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or not wise is patient and vice versa.
Everyone who is not kind is not rich.
If john is both not rich and quiet then someone is both not funny and creative and vice versa.
Everyone who is both kind and happy is either not wise or old and vice versa.
Everyone who is not funny is both tall and not brave.
Everyone who is both calm and curious is not humble or not funny.
Everyone who is both kind and curious is not creative.
If john is both patient and not curious then someone is both not curious and not rich and vice versa.
If susan is not tall then someone is not happy or patient.
Everyone who is either tall or not kind is brave or not curious and vice versa.
If alice is generous or not creative then fred is both brave and not funny and vice versa.
If someone is both not humble and rich then someone is either patient or not patient.
Everyone who is strong is not old.
If someone is not brave or not patient then someone is either rich or creative and vice versa.
If someone is kind then paul is not quiet or not creative and vice versa.
If someone is kind or funny then lucy is both kind and not calm and vice versa.
Someone is not old or funny.
Paul is both not strong and not curious.
Alice is either quiet or old.
Someone is both calm and wise.
Mary is either not strong or happy.
John is quiet or not tall.
Susan is curious or not wise.
Someone is either quiet or brave. | Alice is generous. | contradiction | (![X]:((wise(X)|~wise(X))<=>patient(X)))&
(![X]:(~kind(X)=>~rich(X)))&
(((~rich(john)&quiet(john)))<=>(?[X]:((~funny(X)&creative(X)))))&
(![X]:((kind(X)&happy(X))<=>(~wise(X)<~>old(X))))&
(![X]:(~funny(X)=>(tall(X)&~brave(X))))&
(![X]:((calm(X)&curious(X))=>(~humble(X)|~funny(X))))&
(![X]:((kind(X)&curious(X))=>~creative(X)))&
(((patient(john)&~curious(john)))<=>(?[X]:((~curious(X)&~rich(X)))))&
((~tall(susan))=>(?[X]:((~happy(X)|patient(X)))))&
(![X]:((tall(X)<~>~kind(X))<=>(brave(X)|~curious(X))))&
(((generous(alice)|~creative(alice)))<=>((brave(fred)&~funny(fred))))&
((?[X]:((~humble(X)&rich(X))))=>(?[X]:((patient(X)<~>~patient(X)))))&
(![X]:(strong(X)=>~old(X)))&
((?[X]:((~brave(X)|~patient(X))))<=>(?[X]:((rich(X)<~>creative(X)))))&
((?[X]:(kind(X)))<=>((~quiet(paul)|~creative(paul))))&
((?[X]:((kind(X)|funny(X))))<=>((kind(lucy)&~calm(lucy))))&
(?[X]:((~old(X)|funny(X))))&
((~strong(paul)&~curious(paul)))&
((quiet(alice)<~>old(alice)))&
(?[X]:((calm(X)&wise(X))))&
((~strong(mary)<~>happy(mary)))&
((quiet(john)|~tall(john)))&
((curious(susan)|~wise(susan)))&
(?[X]:((quiet(X)<~>brave(X)))) | generous(alice) | [
"p4",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 850086422631026243759555
% SZS output start Proof for 850086422631026243759555
5. ! [X0] : (~funny(X0) => (~brave(X0) & tall(X0))) [input p4]
11. (~creative(alice) | generous(alice)) <=> (~funny(fred) & brave(fred)) [input p10]
25. generous(alice) [input hypothesis]
29. ! [X0] : ((~brave(X0) & tall(X0)) | funny(X0)) [ennf transformation 5]
55. ((~creative(alice) | generous(alice)) | (funny(fred) | ~brave(fred))) & ((~funny(fred) & brave(fred)) | (creative(alice) & ~generous(alice))) [nnf transformation 11]
56. (~creative(alice) | generous(alice) | funny(fred) | ~brave(fred)) & ((~funny(fred) & brave(fred)) | (creative(alice) & ~generous(alice))) [flattening 55]
100. ~brave(X0) | funny(X0) [cnf transformation 29]
114. brave(fred) | ~generous(alice) [cnf transformation 56]
116. ~funny(fred) | ~generous(alice) [cnf transformation 56]
149. generous(alice) [cnf transformation 25]
199. 11 <=> funny(fred) [avatar definition]
201. ~funny(fred) <- (~11) [avatar component clause 199]
204. 12 <=> generous(alice) [avatar definition]
207. ~12 | ~11 [avatar split clause 116,199,204]
209. 13 <=> brave(fred) [avatar definition]
211. brave(fred) <- (13) [avatar component clause 209]
213. ~12 | 13 [avatar split clause 114,209,204]
336. 12 [avatar split clause 149,204]
342. funny(fred) <- (13) [resolution 100,211]
344. $false <- (~11, 13) [subsumption resolution 342,201]
345. 11 | ~13 [avatar contradiction clause 344]
346. $false [avatar sat refutation 207,213,336,345]
% SZS output end Proof for 850086422631026243759555
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not generous or kind then someone is not happy.
If lucy is not strong or not humble then someone is patient or happy.
Everyone who is both brave and creative is not humble and vice versa.
Everyone who is not funny is funny or calm and vice versa.
Everyone who is not funny is creative or rich and vice versa.
If someone is both curious and wise then mary is either happy or strong and vice versa.
If paul is calm or wise then someone is not funny and vice versa.
Everyone who is either not patient or wise is both not old and kind.
Everyone who is both not funny and not creative is happy and vice versa.
If alice is either happy or not wise then someone is both not creative and quiet and vice versa.
Everyone who is both not patient and happy is either not calm or creative and vice versa.
If someone is not kind then someone is tall and vice versa.
Everyone who is both creative and not happy is either generous or patient and vice versa.
Everyone who is either not curious or funny is either generous or not quiet and vice versa.
If john is either not happy or happy then susan is either not happy or generous and vice versa.
If someone is creative or curious then paul is not strong or not happy.
Someone is not kind.
Someone is both patient and not quiet.
Fred is not strong or not patient.
Fred is either not brave or not kind.
Someone is not wise.
Susan is both not strong and humble. | Fred is not quiet. | entailment | ((?[X]:((~generous(X)<~>kind(X))))=>(?[X]:(~happy(X))))&
(((~strong(lucy)|~humble(lucy)))=>(?[X]:((patient(X)|happy(X)))))&
(![X]:((brave(X)&creative(X))<=>~humble(X)))&
(![X]:(~funny(X)<=>(funny(X)|calm(X))))&
(![X]:(~funny(X)<=>(creative(X)|rich(X))))&
((?[X]:((curious(X)&wise(X))))<=>((happy(mary)<~>strong(mary))))&
(((calm(paul)|wise(paul)))<=>(?[X]:(~funny(X))))&
(![X]:((~patient(X)<~>wise(X))=>(~old(X)&kind(X))))&
(![X]:((~funny(X)&~creative(X))<=>happy(X)))&
(((happy(alice)<~>~wise(alice)))<=>(?[X]:((~creative(X)&quiet(X)))))&
(![X]:((~patient(X)&happy(X))<=>(~calm(X)<~>creative(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(tall(X))))&
(![X]:((creative(X)&~happy(X))<=>(generous(X)<~>patient(X))))&
(![X]:((~curious(X)<~>funny(X))<=>(generous(X)<~>~quiet(X))))&
(((~happy(john)<~>happy(john)))<=>((~happy(susan)<~>generous(susan))))&
((?[X]:((creative(X)|curious(X))))=>((~strong(paul)|~happy(paul))))&
(?[X]:(~kind(X)))&
(?[X]:((patient(X)&~quiet(X))))&
((~strong(fred)|~patient(fred)))&
((~brave(fred)<~>~kind(fred)))&
(?[X]:(~wise(X)))&
((~strong(susan)&humble(susan))) | ~quiet(fred) | [
"p0",
"p3",
"p7",
"p8",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2111931039520306260990957
% SZS output start Proof for 2111931039520306260990957
1. ? [X0] : (~generous(X0) <~> kind(X0)) => ? [X0] : ~happy(X0) [input p0]
4. ! [X0] : (~funny(X0) <=> (calm(X0) | funny(X0))) [input p3]
8. ! [X0] : ((~patient(X0) <~> wise(X0)) => (kind(X0) & ~old(X0))) [input p7]
9. ! [X0] : ((~creative(X0) & ~funny(X0)) <=> happy(X0)) [input p8]
10. (happy(alice) <~> ~wise(alice)) <=> ? [X0] : (quiet(X0) & ~creative(X0)) [input p9]
11. ! [X0] : ((happy(X0) & ~patient(X0)) <=> (~calm(X0) <~> creative(X0))) [input p10]
13. ! [X0] : ((~happy(X0) & creative(X0)) <=> (generous(X0) <~> patient(X0))) [input p12]
23. quiet(fred) [input hypothesis]
24. ? [X0] : (~generous(X0) <~> kind(X0)) => ? [X1] : ~happy(X1) [rectify 1]
27. ! [X0] : ((~patient(X0) <~> wise(X0)) => kind(X0)) [pure predicate removal 8]
28. ? [X1] : ~happy(X1) | ! [X0] : (~generous(X0) <=> kind(X0)) [ennf transformation 24]
32. ! [X0] : (kind(X0) | (~patient(X0) <=> wise(X0))) [ennf transformation 27]
35. ? [X1] : ~happy(X1) | ! [X0] : ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0))) [nnf transformation 28]
36. ? [X0] : ~happy(X0) | ! [X1] : ((~generous(X1) | ~kind(X1)) & (kind(X1) | generous(X1))) [rectify 35]
37. ? [X0] : ~happy(X0) => ~happy(sK0) [choice axiom]
38. ~happy(sK0) | ! [X1] : ((~generous(X1) | ~kind(X1)) & (kind(X1) | generous(X1))) [skolemisation 36,37]
41. ! [X0] : ((~funny(X0) | (~calm(X0) & ~funny(X0))) & ((calm(X0) | funny(X0)) | funny(X0))) [nnf transformation 4]
42. ! [X0] : ((~funny(X0) | (~calm(X0) & ~funny(X0))) & (calm(X0) | funny(X0) | funny(X0))) [flattening 41]
54. ! [X0] : (kind(X0) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) [nnf transformation 32]
55. ! [X0] : (((~creative(X0) & ~funny(X0)) | ~happy(X0)) & (happy(X0) | (creative(X0) | funny(X0)))) [nnf transformation 9]
56. ! [X0] : (((~creative(X0) & ~funny(X0)) | ~happy(X0)) & (happy(X0) | creative(X0) | funny(X0))) [flattening 55]
57. (((wise(alice) | ~happy(alice)) & (~wise(alice) | happy(alice))) | ! [X0] : (~quiet(X0) | creative(X0))) & (? [X0] : (quiet(X0) & ~creative(X0)) | ((happy(alice) | wise(alice)) & (~wise(alice) | ~happy(alice)))) [nnf transformation 10]
58. (((wise(alice) | ~happy(alice)) & (~wise(alice) | happy(alice))) | ! [X0] : (~quiet(X0) | creative(X0))) & (? [X1] : (quiet(X1) & ~creative(X1)) | ((happy(alice) | wise(alice)) & (~wise(alice) | ~happy(alice)))) [rectify 57]
59. ? [X1] : (quiet(X1) & ~creative(X1)) => (quiet(sK4) & ~creative(sK4)) [choice axiom]
60. (((wise(alice) | ~happy(alice)) & (~wise(alice) | happy(alice))) | ! [X0] : (~quiet(X0) | creative(X0))) & ((quiet(sK4) & ~creative(sK4)) | ((happy(alice) | wise(alice)) & (~wise(alice) | ~happy(alice)))) [skolemisation 58,59]
61. ! [X0] : (((happy(X0) & ~patient(X0)) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0)))) & (((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | (~happy(X0) | patient(X0)))) [nnf transformation 11]
62. ! [X0] : (((happy(X0) & ~patient(X0)) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0)))) & (((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | ~happy(X0) | patient(X0))) [flattening 61]
68. ! [X0] : (((~happy(X0) & creative(X0)) | ((generous(X0) | ~patient(X0)) & (patient(X0) | ~generous(X0)))) & (((~patient(X0) | ~generous(X0)) & (patient(X0) | generous(X0))) | (happy(X0) | ~creative(X0)))) [nnf transformation 13]
69. ! [X0] : (((~happy(X0) & creative(X0)) | ((generous(X0) | ~patient(X0)) & (patient(X0) | ~generous(X0)))) & (((~patient(X0) | ~generous(X0)) & (patient(X0) | generous(X0))) | happy(X0) | ~creative(X0))) [flattening 68]
80. ~happy(sK0) | ~generous(X1) | ~kind(X1) [cnf transformation 38]
84. calm(X0) | funny(X0) | funny(X0) [cnf transformation 42]
85. ~funny(X0) | ~funny(X0) [cnf transformation 42]
100. ~wise(X0) | ~patient(X0) | kind(X0) [cnf transformation 54]
101. happy(X0) | creative(X0) | funny(X0) [cnf transformation 56]
103. ~creative(X0) | ~happy(X0) [cnf transformation 56]
109. wise(alice) | ~happy(alice) | ~quiet(X0) | creative(X0) [cnf transformation 60]
110. creative(X0) | ~calm(X0) | ~happy(X0) | patient(X0) [cnf transformation 62]
115. happy(X0) | ~calm(X0) | ~creative(X0) [cnf transformation 62]
123. ~happy(X0) | generous(X0) | ~patient(X0) [cnf transformation 69]
151. quiet(fred) [cnf transformation 23]
156. calm(X0) | funny(X0) [duplicate literal removal 84]
157. ~funny(X0) [duplicate literal removal 85]
159. 1 <=> ! [X1] : (~generous(X1) | ~kind(X1)) [avatar definition]
160. ~kind(X1) | ~generous(X1) <- (1) [avatar component clause 159]
162. 2 <=> happy(sK0) [avatar definition]
164. ~happy(sK0) <- (~2) [avatar component clause 162]
165. 1 | ~2 [avatar split clause 80,162,159]
188. calm(X0) [subsumption resolution 156,157]
215. creative(X0) | happy(X0) [subsumption resolution 101,157]
217. 13 <=> ! [X0] : (~quiet(X0) | creative(X0)) [avatar definition]
218. ~quiet(X0) | creative(X0) <- (13) [avatar component clause 217]
220. 14 <=> happy(alice) [avatar definition]
221. happy(alice) <- (14) [avatar component clause 220]
222. ~happy(alice) <- (~14) [avatar component clause 220]
224. 15 <=> wise(alice) [avatar definition]
226. wise(alice) <- (15) [avatar component clause 224]
227. 13 | ~14 | 15 [avatar split clause 109,224,220,217]
241. happy(X0) | ~creative(X0) [subsumption resolution 115,188]
242. ~creative(X0) [subsumption resolution 241,103]
243. ~calm(X0) | ~happy(X0) | patient(X0) [subsumption resolution 110,242]
244. ~happy(X0) | patient(X0) [subsumption resolution 243,188]
261. ~happy(X0) | generous(X0) [subsumption resolution 123,244]
315. ~quiet(X0) <- (13) [subsumption resolution 218,242]
320. $false <- (13) [resolution 315,151]
321. ~13 [avatar contradiction clause 320]
324. happy(X1) [resolution 215,242]
325. $false <- (~2) [resolution 324,164]
328. 2 [avatar contradiction clause 325]
333. patient(alice) <- (14) [resolution 244,221]
335. generous(alice) <- (14) [resolution 261,221]
351. ~patient(alice) | kind(alice) <- (15) [resolution 100,226]
355. kind(alice) <- (14, 15) [subsumption resolution 351,333]
362. ~generous(alice) <- (1, 14, 15) [resolution 355,160]
363. $false <- (1, 14, 15) [subsumption resolution 362,335]
364. ~1 | ~14 | ~15 [avatar contradiction clause 363]
365. $false <- (~14) [subsumption resolution 222,324]
366. 14 [avatar contradiction clause 365]
367. $false [avatar sat refutation 165,227,321,328,364,366]
% SZS output end Proof for 2111931039520306260990957
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or strong then alice is calm or not generous.
Everyone who is not strong or not brave is not humble.
If someone is not creative or tall then someone is not funny or not tall and vice versa.
Everyone who is funny or curious is creative and vice versa.
Everyone who is either kind or not humble is either not calm or creative and vice versa.
Everyone who is either not brave or not strong is calm and vice versa.
If paul is either not humble or not rich then mary is not wise.
Everyone who is both not humble and strong is either calm or tall.
If susan is not rich or old then someone is wise or not brave and vice versa.
Everyone who is both humble and not kind is either kind or not tall.
Everyone who is brave is both tall and not humble.
Everyone who is both brave and not generous is not calm.
Everyone who is not brave is both curious and not wise.
If john is either not wise or not rich then someone is not humble.
If someone is both kind and not kind then someone is not generous or creative.
If someone is both strong and not wise then fred is not funny and vice versa.
Someone is not calm.
Someone is brave.
Someone is either not curious or curious.
John is either quiet or funny.
Someone is either creative or tall.
Lucy is not kind.
Someone is either not humble or not creative.
Paul is both quiet and old. | Mary is humble. | contradiction | ((?[X]:((kind(X)<~>strong(X))))=>((calm(alice)|~generous(alice))))&
(![X]:((~strong(X)|~brave(X))=>~humble(X)))&
((?[X]:((~creative(X)|tall(X))))<=>(?[X]:((~funny(X)|~tall(X)))))&
(![X]:((funny(X)|curious(X))<=>creative(X)))&
(![X]:((kind(X)<~>~humble(X))<=>(~calm(X)<~>creative(X))))&
(![X]:((~brave(X)<~>~strong(X))<=>calm(X)))&
(((~humble(paul)<~>~rich(paul)))=>(~wise(mary)))&
(![X]:((~humble(X)&strong(X))=>(calm(X)<~>tall(X))))&
(((~rich(susan)|old(susan)))<=>(?[X]:((wise(X)|~brave(X)))))&
(![X]:((humble(X)&~kind(X))=>(kind(X)<~>~tall(X))))&
(![X]:(brave(X)=>(tall(X)&~humble(X))))&
(![X]:((brave(X)&~generous(X))=>~calm(X)))&
(![X]:(~brave(X)=>(curious(X)&~wise(X))))&
(((~wise(john)<~>~rich(john)))=>(?[X]:(~humble(X))))&
((?[X]:((kind(X)&~kind(X))))=>(?[X]:((~generous(X)|creative(X)))))&
((?[X]:((strong(X)&~wise(X))))<=>(~funny(fred)))&
(?[X]:(~calm(X)))&
(?[X]:(brave(X)))&
(?[X]:((~curious(X)<~>curious(X))))&
((quiet(john)<~>funny(john)))&
(?[X]:((creative(X)<~>tall(X))))&
(~kind(lucy))&
(?[X]:((~humble(X)<~>~creative(X))))&
((quiet(paul)&old(paul))) | humble(mary) | [
"p1",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 94369894700900625923491
% SZS output start Proof for 94369894700900625923491
2. ! [X0] : ((~brave(X0) | ~strong(X0)) => ~humble(X0)) [input p1]
11. ! [X0] : (brave(X0) => (~humble(X0) & tall(X0))) [input p10]
25. humble(mary) [input hypothesis]
30. ! [X0] : (~humble(X0) | (brave(X0) & strong(X0))) [ennf transformation 2]
36. ! [X0] : ((~humble(X0) & tall(X0)) | ~brave(X0)) [ennf transformation 11]
87. ~humble(X0) | brave(X0) [cnf transformation 30]
118. ~humble(X0) | ~brave(X0) [cnf transformation 36]
141. humble(mary) [cnf transformation 25]
231. ~humble(X0) [subsumption resolution 118,87]
271. $false [subsumption resolution 141,231]
% SZS output end Proof for 94369894700900625923491
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either not creative or not brave then someone is either not rich or not patient and vice versa. Everyone who is both not old and patient is either not happy or rich. Everyone who is either not tall or quiet is both kind and not wise and vice versa. If paul is both rich and not quiet then someone is both not curious and not brave and vice versa. Everyone who is either wise or creative is not tall and vice versa. If mary is not brave or happy then someone is not calm and vice versa. Everyone who is either strong or not creative is either not calm or not strong and vice versa. If alice is not generous then alice is both curious and not strong and vice versa. If alice is either not brave or not wise then lucy is old. Everyone who is not generous or not humble is not curious or patient and vice versa. Everyone who is both humble and not curious is not tall and vice versa. Everyone who is not kind is strong and vice versa. Everyone who is tall or not quiet is both not creative and not curious and vice versa. Everyone who is tall is both rich and not quiet and vice versa. If someone is either not creative or not strong then john is either generous or strong and vice versa. Everyone who is either happy or curious is either kind or tall. Someone is not brave. Lucy is not tall. Paul is either curious or not brave. Someone is not happy. Fred is either not generous or humble. Someone is both generous and not humble. Lucy is both strong and not old. | Paul is not humble. | entailment | (((~creative(fred)<~>~brave(fred)))<=>(?[X]:((~rich(X)<~>~patient(X)))))&
(![X]:((~old(X)&patient(X))=>(~happy(X)<~>rich(X))))&
(![X]:((~tall(X)<~>quiet(X))<=>(kind(X)&~wise(X))))&
(((rich(paul)&~quiet(paul)))<=>(?[X]:((~curious(X)&~brave(X)))))&
(![X]:((wise(X)<~>creative(X))<=>~tall(X)))&
(((~brave(mary)|happy(mary)))<=>(?[X]:(~calm(X))))&
(![X]:((strong(X)<~>~creative(X))<=>(~calm(X)<~>~strong(X))))&
((~generous(alice))<=>((curious(alice)&~strong(alice))))&
(((~brave(alice)<~>~wise(alice)))=>(old(lucy)))&
(![X]:((~generous(X)|~humble(X))<=>(~curious(X)|patient(X))))&
(![X]:((humble(X)&~curious(X))<=>~tall(X)))&
(![X]:(~kind(X)<=>strong(X)))&
(![X]:((tall(X)|~quiet(X))<=>(~creative(X)&~curious(X))))&
(![X]:(tall(X)<=>(rich(X)&~quiet(X))))&
((?[X]:((~creative(X)<~>~strong(X))))<=>((generous(john)<~>strong(john))))&
(![X]:((happy(X)<~>curious(X))=>(kind(X)<~>tall(X))))&
(?[X]:(~brave(X)))&
(~tall(lucy))&
((curious(paul)<~>~brave(paul)))&
(?[X]:(~happy(X)))&
((~generous(fred)<~>humble(fred)))&
(?[X]:((generous(X)&~humble(X))))&
((strong(lucy)&~old(lucy))) | ~humble(paul) | [
"p2",
"p3",
"p4",
"p10",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2302145824920629111463932
% SZS output start Proof for 2302145824920629111463932
3. ! [X0] : ((~tall(X0) <~> quiet(X0)) <=> (~wise(X0) & kind(X0))) [input p2]
4. (~quiet(paul) & rich(paul)) <=> ? [X0] : (~brave(X0) & ~curious(X0)) [input p3]
5. ! [X0] : ((wise(X0) <~> creative(X0)) <=> ~tall(X0)) [input p4]
11. ! [X0] : ((~curious(X0) & humble(X0)) <=> ~tall(X0)) [input p10]
13. ! [X0] : ((~quiet(X0) | tall(X0)) <=> (~curious(X0) & ~creative(X0))) [input p12]
19. curious(paul) <~> ~brave(paul) [input p18]
24. humble(paul) [input hypothesis]
34. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | (wise(X0) | ~kind(X0))) & ((~wise(X0) & kind(X0)) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [nnf transformation 3]
35. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | wise(X0) | ~kind(X0)) & ((~wise(X0) & kind(X0)) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [flattening 34]
36. ((~quiet(paul) & rich(paul)) | ! [X0] : (brave(X0) | curious(X0))) & (? [X0] : (~brave(X0) & ~curious(X0)) | (quiet(paul) | ~rich(paul))) [nnf transformation 4]
37. ((~quiet(paul) & rich(paul)) | ! [X0] : (brave(X0) | curious(X0))) & (? [X0] : (~brave(X0) & ~curious(X0)) | quiet(paul) | ~rich(paul)) [flattening 36]
38. ((~quiet(paul) & rich(paul)) | ! [X0] : (brave(X0) | curious(X0))) & (? [X1] : (~brave(X1) & ~curious(X1)) | quiet(paul) | ~rich(paul)) [rectify 37]
39. ? [X1] : (~brave(X1) & ~curious(X1)) => (~brave(sK1) & ~curious(sK1)) [choice axiom]
40. ((~quiet(paul) & rich(paul)) | ! [X0] : (brave(X0) | curious(X0))) & ((~brave(sK1) & ~curious(sK1)) | quiet(paul) | ~rich(paul)) [skolemisation 38,39]
41. ! [X0] : ((((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | tall(X0)) & (~tall(X0) | ((wise(X0) | ~creative(X0)) & (creative(X0) | ~wise(X0))))) [nnf transformation 5]
53. ! [X0] : (((~curious(X0) & humble(X0)) | tall(X0)) & (~tall(X0) | (curious(X0) | ~humble(X0)))) [nnf transformation 11]
54. ! [X0] : (((~curious(X0) & humble(X0)) | tall(X0)) & (~tall(X0) | curious(X0) | ~humble(X0))) [flattening 53]
56. ! [X0] : (((~quiet(X0) | tall(X0)) | (curious(X0) | creative(X0))) & ((~curious(X0) & ~creative(X0)) | (quiet(X0) & ~tall(X0)))) [nnf transformation 13]
57. ! [X0] : ((~quiet(X0) | tall(X0) | curious(X0) | creative(X0)) & ((~curious(X0) & ~creative(X0)) | (quiet(X0) & ~tall(X0)))) [flattening 56]
67. (brave(paul) | ~curious(paul)) & (~brave(paul) | curious(paul)) [nnf transformation 19]
85. ~wise(X0) | quiet(X0) | tall(X0) [cnf transformation 35]
92. ~quiet(paul) | brave(X0) | curious(X0) [cnf transformation 40]
95. wise(X0) | creative(X0) | tall(X0) [cnf transformation 41]
117. ~humble(X0) | curious(X0) | ~tall(X0) [cnf transformation 54]
119. ~curious(X0) | tall(X0) [cnf transformation 54]
123. ~creative(X0) | quiet(X0) [cnf transformation 57]
124. ~curious(X0) | ~tall(X0) [cnf transformation 57]
144. ~brave(paul) | curious(paul) [cnf transformation 67]
153. humble(paul) [cnf transformation 24]
189. 7 <=> ! [X0] : (brave(X0) | curious(X0)) [avatar definition]
190. brave(X0) | curious(X0) <- (7) [avatar component clause 189]
192. 8 <=> quiet(paul) [avatar definition]
194. ~quiet(paul) <- (~8) [avatar component clause 192]
195. 7 | ~8 [avatar split clause 92,192,189]
261. ~curious(X0) [subsumption resolution 124,119]
294. ~brave(paul) [subsumption resolution 144,261]
308. brave(X0) <- (7) [subsumption resolution 190,261]
309. $false <- (7) [resolution 308,294]
316. ~7 [avatar contradiction clause 309]
370. creative(X2) | tall(X2) | quiet(X2) | tall(X2) [resolution 95,85]
371. creative(X2) | tall(X2) | quiet(X2) [duplicate literal removal 370]
382. quiet(X2) | tall(X2) [subsumption resolution 371,123]
391. tall(paul) <- (~8) [resolution 382,194]
413. curious(paul) | ~tall(paul) [resolution 117,153]
415. ~tall(paul) [subsumption resolution 413,261]
416. $false <- (~8) [subsumption resolution 415,391]
417. 8 [avatar contradiction clause 416]
418. $false [avatar sat refutation 195,316,417]
% SZS output end Proof for 2302145824920629111463932
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or generous then mary is not wise and vice versa.
If paul is old or calm then alice is both wise and funny.
Everyone who is happy or patient is not old or creative.
If someone is happy or strong then lucy is either strong or rich and vice versa.
Everyone who is both not tall and rich is both not brave and tall.
Everyone who is not patient is both brave and humble.
Everyone who is either not tall or not patient is either funny or happy.
If someone is either not tall or not happy then lucy is not curious and vice versa.
If someone is not calm then mary is humble or patient and vice versa.
Everyone who is creative or not happy is both patient and not brave.
If someone is funny then someone is not happy or not old and vice versa.
Everyone who is not tall or generous is curious or quiet and vice versa.
If someone is humble or creative then lucy is both patient and happy and vice versa.
Everyone who is wise or not patient is wise or not strong.
If someone is not curious or patient then someone is either happy or not happy and vice versa.
Everyone who is curious or not generous is not humble or creative.
Someone is both not generous and strong.
Someone is creative.
Alice is brave.
Someone is either not brave or not tall.
Someone is both not funny and happy.
Mary is not wise.
Someone is generous.
Mary is either not creative or wise. | Alice is generous. | neutral | ((?[X]:((curious(X)|generous(X))))<=>(~wise(mary)))&
(((old(paul)|calm(paul)))=>((wise(alice)&funny(alice))))&
(![X]:((happy(X)|patient(X))=>(~old(X)|creative(X))))&
((?[X]:((happy(X)|strong(X))))<=>((strong(lucy)<~>rich(lucy))))&
(![X]:((~tall(X)&rich(X))=>(~brave(X)&tall(X))))&
(![X]:(~patient(X)=>(brave(X)&humble(X))))&
(![X]:((~tall(X)<~>~patient(X))=>(funny(X)<~>happy(X))))&
((?[X]:((~tall(X)<~>~happy(X))))<=>(~curious(lucy)))&
((?[X]:(~calm(X)))<=>((humble(mary)|patient(mary))))&
(![X]:((creative(X)|~happy(X))=>(patient(X)&~brave(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~happy(X)|~old(X)))))&
(![X]:((~tall(X)|generous(X))<=>(curious(X)|quiet(X))))&
((?[X]:((humble(X)|creative(X))))<=>((patient(lucy)&happy(lucy))))&
(![X]:((wise(X)|~patient(X))=>(wise(X)|~strong(X))))&
((?[X]:((~curious(X)|patient(X))))<=>(?[X]:((happy(X)<~>~happy(X)))))&
(![X]:((curious(X)|~generous(X))=>(~humble(X)|creative(X))))&
(?[X]:((~generous(X)&strong(X))))&
(?[X]:(creative(X)))&
(brave(alice))&
(?[X]:((~brave(X)<~>~tall(X))))&
(?[X]:((~funny(X)&happy(X))))&
(~wise(mary))&
(?[X]:(generous(X)))&
((~creative(mary)<~>wise(mary))) | generous(alice) | [] | null | 0 |
If someone is humble or not kind then mary is not wise or not rich.
Everyone who is both not tall and not rich is not happy and vice versa.
Everyone who is both not happy and patient is both brave and not brave.
If someone is not brave or generous then lucy is not tall and vice versa.
If someone is both not tall and old then someone is both old and not wise and vice versa.
If someone is either not brave or funny then lucy is not humble.
If someone is not kind then john is both tall and happy and vice versa.
If lucy is not creative or rich then someone is either not calm or funny and vice versa.
If lucy is both not old and humble then someone is not quiet or not curious.
If mary is not tall then someone is brave and vice versa.
If someone is not wise then mary is patient and vice versa.
Everyone who is rich or not creative is funny or brave and vice versa.
If someone is either tall or humble then someone is humble or calm and vice versa.
Everyone who is not funny or not generous is both not funny and not brave.
Everyone who is both not humble and funny is both rich and not tall.
Everyone who is either not old or not kind is either kind or generous.
Someone is either not quiet or not calm.
Alice is not rich.
Someone is tall or creative.
Someone is both not old and not brave.
Someone is either not calm or funny.
Someone is rich.
Someone is brave. | Lucy is not happy. | contradiction | ((?[X]:((humble(X)|~kind(X))))=>((~wise(mary)|~rich(mary))))&
(![X]:((~tall(X)&~rich(X))<=>~happy(X)))&
(![X]:((~happy(X)&patient(X))=>(brave(X)&~brave(X))))&
((?[X]:((~brave(X)|generous(X))))<=>(~tall(lucy)))&
((?[X]:((~tall(X)&old(X))))<=>(?[X]:((old(X)&~wise(X)))))&
((?[X]:((~brave(X)<~>funny(X))))=>(~humble(lucy)))&
((?[X]:(~kind(X)))<=>((tall(john)&happy(john))))&
(((~creative(lucy)|rich(lucy)))<=>(?[X]:((~calm(X)<~>funny(X)))))&
(((~old(lucy)&humble(lucy)))=>(?[X]:((~quiet(X)|~curious(X)))))&
((~tall(mary))<=>(?[X]:(brave(X))))&
((?[X]:(~wise(X)))<=>(patient(mary)))&
(![X]:((rich(X)|~creative(X))<=>(funny(X)|brave(X))))&
((?[X]:((tall(X)<~>humble(X))))<=>(?[X]:((humble(X)|calm(X)))))&
(![X]:((~funny(X)|~generous(X))=>(~funny(X)&~brave(X))))&
(![X]:((~humble(X)&funny(X))=>(rich(X)&~tall(X))))&
(![X]:((~old(X)<~>~kind(X))=>(kind(X)<~>generous(X))))&
(?[X]:((~quiet(X)<~>~calm(X))))&
(~rich(alice))&
(?[X]:((tall(X)|creative(X))))&
(?[X]:((~old(X)&~brave(X))))&
(?[X]:((~calm(X)<~>funny(X))))&
(?[X]:(rich(X)))&
(?[X]:(brave(X))) | ~happy(lucy) | [
"p1",
"p5",
"p7",
"p11",
"p13",
"p14",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6617334651235456865760342
% SZS output start Proof for 6617334651235456865760342
2. ! [X0] : ((~rich(X0) & ~tall(X0)) <=> ~happy(X0)) [input p1]
6. ? [X0] : (~brave(X0) <~> funny(X0)) => ~humble(lucy) [input p5]
8. (rich(lucy) | ~creative(lucy)) <=> ? [X0] : (~calm(X0) <~> funny(X0)) [input p7]
12. ! [X0] : ((~creative(X0) | rich(X0)) <=> (brave(X0) | funny(X0))) [input p11]
14. ! [X0] : ((~generous(X0) | ~funny(X0)) => (~brave(X0) & ~funny(X0))) [input p13]
15. ! [X0] : ((funny(X0) & ~humble(X0)) => (~tall(X0) & rich(X0))) [input p14]
21. ? [X0] : (~calm(X0) <~> funny(X0)) [input p20]
23. ? [X0] : brave(X0) [input p22]
24. ~happy(lucy) [input hypothesis]
32. ~humble(lucy) | ! [X0] : (~brave(X0) <=> funny(X0)) [ennf transformation 6]
33. ! [X0] : ((~brave(X0) & ~funny(X0)) | (generous(X0) & funny(X0))) [ennf transformation 14]
34. ! [X0] : ((~tall(X0) & rich(X0)) | (~funny(X0) | humble(X0))) [ennf transformation 15]
35. ! [X0] : ((~tall(X0) & rich(X0)) | ~funny(X0) | humble(X0)) [flattening 34]
37. ! [X0] : (((~rich(X0) & ~tall(X0)) | happy(X0)) & (~happy(X0) | (rich(X0) | tall(X0)))) [nnf transformation 2]
38. ! [X0] : (((~rich(X0) & ~tall(X0)) | happy(X0)) & (~happy(X0) | rich(X0) | tall(X0))) [flattening 37]
48. ~humble(lucy) | ! [X0] : ((~brave(X0) | ~funny(X0)) & (funny(X0) | brave(X0))) [nnf transformation 32]
54. ((rich(lucy) | ~creative(lucy)) | ! [X0] : ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0)))) & (? [X0] : ((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | (~rich(lucy) & creative(lucy))) [nnf transformation 8]
55. (rich(lucy) | ~creative(lucy) | ! [X0] : ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0)))) & (? [X0] : ((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | (~rich(lucy) & creative(lucy))) [flattening 54]
56. (rich(lucy) | ~creative(lucy) | ! [X0] : ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0)))) & (? [X1] : ((~funny(X1) | calm(X1)) & (funny(X1) | ~calm(X1))) | (~rich(lucy) & creative(lucy))) [rectify 55]
57. ? [X1] : ((~funny(X1) | calm(X1)) & (funny(X1) | ~calm(X1))) => ((~funny(sK4) | calm(sK4)) & (funny(sK4) | ~calm(sK4))) [choice axiom]
58. (rich(lucy) | ~creative(lucy) | ! [X0] : ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0)))) & (((~funny(sK4) | calm(sK4)) & (funny(sK4) | ~calm(sK4))) | (~rich(lucy) & creative(lucy))) [skolemisation 56,57]
67. ! [X0] : (((~creative(X0) | rich(X0)) | (~brave(X0) & ~funny(X0))) & ((brave(X0) | funny(X0)) | (creative(X0) & ~rich(X0)))) [nnf transformation 12]
68. ! [X0] : ((~creative(X0) | rich(X0) | (~brave(X0) & ~funny(X0))) & (brave(X0) | funny(X0) | (creative(X0) & ~rich(X0)))) [flattening 67]
82. ? [X0] : ((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) [nnf transformation 21]
83. ? [X0] : ((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) => ((~funny(sK12) | calm(sK12)) & (funny(sK12) | ~calm(sK12))) [choice axiom]
84. (~funny(sK12) | calm(sK12)) & (funny(sK12) | ~calm(sK12)) [skolemisation 82,83]
87. ? [X0] : brave(X0) => brave(sK14) [choice axiom]
88. brave(sK14) [skolemisation 23,87]
93. ~rich(X0) | happy(X0) [cnf transformation 38]
104. ~humble(lucy) | ~brave(X0) | ~funny(X0) [cnf transformation 48]
112. rich(lucy) | ~creative(lucy) | funny(X0) | calm(X0) [cnf transformation 58]
113. rich(lucy) | ~creative(lucy) | ~calm(X0) | ~funny(X0) [cnf transformation 58]
119. creative(X0) | funny(X0) | brave(X0) [cnf transformation 68]
130. ~brave(X0) | funny(X0) [cnf transformation 33]
132. ~funny(X0) | rich(X0) | humble(X0) [cnf transformation 35]
144. funny(sK12) | ~calm(sK12) [cnf transformation 84]
145. ~funny(sK12) | calm(sK12) [cnf transformation 84]
147. brave(sK14) [cnf transformation 88]
148. ~happy(lucy) [cnf transformation 24]
216. 16 <=> ! [X0] : (~brave(X0) | ~funny(X0)) [avatar definition]
217. ~brave(X0) | ~funny(X0) <- (16) [avatar component clause 216]
219. 17 <=> humble(lucy) [avatar definition]
222. 16 | ~17 [avatar split clause 104,219,216]
244. 22 <=> ! [X0] : (~calm(X0) | ~funny(X0)) [avatar definition]
245. ~calm(X0) | ~funny(X0) <- (22) [avatar component clause 244]
247. 23 <=> creative(lucy) [avatar definition]
249. ~creative(lucy) <- (~23) [avatar component clause 247]
251. 24 <=> rich(lucy) [avatar definition]
253. rich(lucy) <- (24) [avatar component clause 251]
254. 22 | ~23 | 24 [avatar split clause 113,251,247,244]
256. 25 <=> ! [X0] : (funny(X0) | calm(X0)) [avatar definition]
257. calm(X0) | funny(X0) <- (25) [avatar component clause 256]
258. 25 | ~23 | 24 [avatar split clause 112,251,247,256]
272. 28 <=> ! [X0] : ~brave(X0) [avatar definition]
273. ~brave(X0) <- (28) [avatar component clause 272]
348. 45 <=> calm(sK12) [avatar definition]
349. ~calm(sK12) <- (~45) [avatar component clause 348]
350. calm(sK12) <- (45) [avatar component clause 348]
352. 46 <=> funny(sK12) [avatar definition]
353. funny(sK12) <- (46) [avatar component clause 352]
354. ~funny(sK12) <- (~46) [avatar component clause 352]
355. 45 | ~46 [avatar split clause 145,352,348]
356. ~45 | 46 [avatar split clause 144,352,348]
357. $false <- (28) [resolution 273,147]
358. ~28 [avatar contradiction clause 357]
387. funny(lucy) | brave(lucy) <- (~23) [resolution 119,249]
388. funny(lucy) <- (~23) [subsumption resolution 387,130]
394. rich(lucy) | humble(lucy) <- (~23) [resolution 132,388]
418. 17 | 24 | 23 [avatar split clause 394,247,251,219]
422. ~brave(X0) <- (16) [subsumption resolution 217,130]
423. 28 | ~16 [avatar split clause 422,216,272]
425. happy(lucy) <- (24) [resolution 253,93]
426. $false <- (24) [subsumption resolution 425,148]
427. ~24 [avatar contradiction clause 426]
438. funny(sK12) <- (25, ~45) [resolution 257,349]
441. $false <- (25, ~45, ~46) [subsumption resolution 438,354]
442. ~25 | 45 | 46 [avatar contradiction clause 441]
444. ~funny(sK12) <- (22, 45) [resolution 350,245]
445. $false <- (22, 45, 46) [subsumption resolution 444,353]
446. ~22 | ~45 | ~46 [avatar contradiction clause 445]
447. $false [avatar sat refutation 222,254,258,355,356,358,418,423,427,442,446]
% SZS output end Proof for 6617334651235456865760342
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If mary is rich or quiet then lucy is either not patient or not tall.
If susan is both not tall and not happy then paul is funny.
Everyone who is both strong and not brave is either brave or not brave.
Everyone who is rich is either tall or not quiet.
If someone is not happy then someone is kind or not tall.
Everyone who is not wise is either wise or brave and vice versa.
Everyone who is not old or not strong is either not tall or wise and vice versa.
If fred is not kind or not happy then john is both not wise and not strong.
If mary is humble or not creative then paul is not tall.
Everyone who is both quiet and not humble is tall or not curious and vice versa.
Everyone who is either not patient or humble is not generous or not brave and vice versa.
If someone is not kind then someone is curious or humble.
If someone is either funny or not generous then someone is both not curious and not brave and vice versa.
Everyone who is not old or not generous is funny or calm and vice versa.
Everyone who is quiet or not creative is curious.
Everyone who is either funny or not generous is either wise or not creative and vice versa.
Someone is not creative.
Someone is either old or curious.
Someone is creative or not old.
Someone is either strong or not strong.
Someone is both not wise and not tall.
Someone is either funny or not old.
Someone is not tall or strong. | Mary is brave. | entailment | (((rich(mary)|quiet(mary)))=>((~patient(lucy)<~>~tall(lucy))))&
(((~tall(susan)&~happy(susan)))=>(funny(paul)))&
(![X]:((strong(X)&~brave(X))=>(brave(X)<~>~brave(X))))&
(![X]:(rich(X)=>(tall(X)<~>~quiet(X))))&
((?[X]:(~happy(X)))=>(?[X]:((kind(X)|~tall(X)))))&
(![X]:(~wise(X)<=>(wise(X)<~>brave(X))))&
(![X]:((~old(X)|~strong(X))<=>(~tall(X)<~>wise(X))))&
(((~kind(fred)|~happy(fred)))=>((~wise(john)&~strong(john))))&
(((humble(mary)|~creative(mary)))=>(~tall(paul)))&
(![X]:((quiet(X)&~humble(X))<=>(tall(X)|~curious(X))))&
(![X]:((~patient(X)<~>humble(X))<=>(~generous(X)|~brave(X))))&
((?[X]:(~kind(X)))=>(?[X]:((curious(X)|humble(X)))))&
((?[X]:((funny(X)<~>~generous(X))))<=>(?[X]:((~curious(X)&~brave(X)))))&
(![X]:((~old(X)|~generous(X))<=>(funny(X)|calm(X))))&
(![X]:((quiet(X)|~creative(X))=>curious(X)))&
(![X]:((funny(X)<~>~generous(X))<=>(wise(X)<~>~creative(X))))&
(?[X]:(~creative(X)))&
(?[X]:((old(X)<~>curious(X))))&
(?[X]:((creative(X)|~old(X))))&
(?[X]:((strong(X)<~>~strong(X))))&
(?[X]:((~wise(X)&~tall(X))))&
(?[X]:((funny(X)<~>~old(X))))&
(?[X]:((~tall(X)|strong(X)))) | brave(mary) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6249775967321636176440046
% SZS output start Proof for 6249775967321636176440046
6. ! [X0] : (~wise(X0) <=> (wise(X0) <~> brave(X0))) [input p5]
24. ~brave(mary) [input hypothesis]
42. ! [X0] : ((~wise(X0) | ((wise(X0) | ~brave(X0)) & (brave(X0) | ~wise(X0)))) & (((~brave(X0) | ~wise(X0)) & (brave(X0) | wise(X0))) | wise(X0))) [nnf transformation 6]
78. brave(X0) | wise(X0) | wise(X0) [cnf transformation 42]
80. ~wise(X0) | brave(X0) | ~wise(X0) [cnf transformation 42]
132. ~brave(mary) [cnf transformation 24]
133. brave(X0) | wise(X0) [duplicate literal removal 78]
134. ~wise(X0) | brave(X0) [duplicate literal removal 80]
151. brave(X0) [subsumption resolution 133,134]
206. $false [subsumption resolution 132,151]
% SZS output end Proof for 6249775967321636176440046
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or calm is happy or strong and vice versa. Everyone who is not quiet or old is not brave. Everyone who is either not calm or not rich is old. Everyone who is kind is not humble or not tall and vice versa. Everyone who is generous or not happy is not wise and vice versa. If john is both tall and rich then susan is both not humble and not calm and vice versa. Everyone who is not brave or rich is patient or not patient and vice versa. If lucy is both curious and not happy then alice is kind and vice versa. If lucy is curious or generous then someone is both not wise and not curious. Everyone who is brave or not brave is both patient and happy. If someone is not happy or quiet then someone is both not kind and patient. If alice is both not humble and happy then someone is not creative or humble. If someone is both not kind and curious then fred is not rich or not humble and vice versa. If john is not rich then someone is not curious. Everyone who is not strong or calm is either not happy or not rich and vice versa. Someone is rich or not creative. Alice is either kind or tall. Susan is not humble. Someone is either old or rich. Someone is both not brave and not creative. Someone is either brave or not kind. Someone is either not strong or brave. | Fred is old. | entailment | (![X]:((~happy(X)<~>calm(X))<=>(happy(X)|strong(X))))&
(![X]:((~quiet(X)|old(X))=>~brave(X)))&
(![X]:((~calm(X)<~>~rich(X))=>old(X)))&
(![X]:(kind(X)<=>(~humble(X)|~tall(X))))&
(![X]:((generous(X)|~happy(X))<=>~wise(X)))&
(((tall(john)&rich(john)))<=>((~humble(susan)&~calm(susan))))&
(![X]:((~brave(X)|rich(X))<=>(patient(X)|~patient(X))))&
(((curious(lucy)&~happy(lucy)))<=>(kind(alice)))&
(((curious(lucy)|generous(lucy)))=>(?[X]:((~wise(X)&~curious(X)))))&
(![X]:((brave(X)|~brave(X))=>(patient(X)&happy(X))))&
((?[X]:((~happy(X)|quiet(X))))=>(?[X]:((~kind(X)&patient(X)))))&
(((~humble(alice)&happy(alice)))=>(?[X]:((~creative(X)|humble(X)))))&
((?[X]:((~kind(X)&curious(X))))<=>((~rich(fred)|~humble(fred))))&
((~rich(john))=>(?[X]:(~curious(X))))&
(![X]:((~strong(X)|calm(X))<=>(~happy(X)<~>~rich(X))))&
(?[X]:((rich(X)|~creative(X))))&
((kind(alice)<~>tall(alice)))&
(~humble(susan))&
(?[X]:((old(X)<~>rich(X))))&
(?[X]:((~brave(X)&~creative(X))))&
(?[X]:((brave(X)<~>~kind(X))))&
(?[X]:((~strong(X)<~>brave(X)))) | old(fred) | [
"p0",
"p2",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 264428233060399105181918
% SZS output start Proof for 264428233060399105181918
1. ! [X0] : ((~happy(X0) <~> calm(X0)) <=> (strong(X0) | happy(X0))) [input p0]
3. ! [X0] : ((~calm(X0) <~> ~rich(X0)) => old(X0)) [input p2]
10. ! [X0] : ((~brave(X0) | brave(X0)) => (happy(X0) & patient(X0))) [input p9]
15. ! [X0] : ((calm(X0) | ~strong(X0)) <=> (~happy(X0) <~> ~rich(X0))) [input p14]
23. ~old(fred) [input hypothesis]
30. ! [X0] : (old(X0) | (~calm(X0) <=> ~rich(X0))) [ennf transformation 3]
34. ! [X0] : ((happy(X0) & patient(X0)) | (brave(X0) & ~brave(X0))) [ennf transformation 10]
37. ! [X0] : ((((~calm(X0) | happy(X0)) & (calm(X0) | ~happy(X0))) | (~strong(X0) & ~happy(X0))) & ((strong(X0) | happy(X0)) | ((~happy(X0) | ~calm(X0)) & (calm(X0) | happy(X0))))) [nnf transformation 1]
38. ! [X0] : ((((~calm(X0) | happy(X0)) & (calm(X0) | ~happy(X0))) | (~strong(X0) & ~happy(X0))) & (strong(X0) | happy(X0) | ((~happy(X0) | ~calm(X0)) & (calm(X0) | happy(X0))))) [flattening 37]
39. ! [X0] : (old(X0) | ((~calm(X0) | rich(X0)) & (~rich(X0) | calm(X0)))) [nnf transformation 30]
60. ! [X0] : (((calm(X0) | ~strong(X0)) | ((~happy(X0) | rich(X0)) & (~rich(X0) | happy(X0)))) & (((rich(X0) | happy(X0)) & (~rich(X0) | ~happy(X0))) | (~calm(X0) & strong(X0)))) [nnf transformation 15]
61. ! [X0] : ((calm(X0) | ~strong(X0) | ((~happy(X0) | rich(X0)) & (~rich(X0) | happy(X0)))) & (((rich(X0) | happy(X0)) & (~rich(X0) | ~happy(X0))) | (~calm(X0) & strong(X0)))) [flattening 60]
76. calm(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 38]
83. ~calm(X0) | old(X0) | rich(X0) [cnf transformation 39]
105. happy(X0) | ~brave(X0) [cnf transformation 34]
106. brave(X0) | happy(X0) [cnf transformation 34]
118. ~rich(X0) | ~happy(X0) | ~calm(X0) [cnf transformation 61]
133. ~old(fred) [cnf transformation 23]
135. ~happy(X0) | calm(X0) [duplicate literal removal 76]
189. happy(X0) [subsumption resolution 105,106]
228. ~rich(X0) | ~calm(X0) [subsumption resolution 118,189]
272. calm(X0) [resolution 135,189]
284. rich(X0) | old(X0) [resolution 83,272]
287. old(X2) | ~calm(X2) [resolution 284,228]
292. old(X2) [subsumption resolution 287,272]
294. $false [resolution 292,133]
% SZS output end Proof for 264428233060399105181918
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not generous then someone is not strong or not brave. If fred is either not rich or not patient then someone is kind. If someone is not calm then alice is both not kind and not generous. If john is either strong or not happy then mary is both not wise and not curious and vice versa. Everyone who is curious or strong is either not brave or not old. Everyone who is not brave is either kind or happy and vice versa. If someone is happy then susan is both not quiet and not rich and vice versa. Everyone who is both not happy and brave is either wise or strong and vice versa. Everyone who is either not funny or not generous is quiet and vice versa. If alice is both curious and calm then paul is either patient or not quiet. Everyone who is calm is either not old or rich. Everyone who is not curious or rich is either not rich or tall. Everyone who is not wise or not patient is either kind or humble and vice versa. Everyone who is happy is either not curious or not old and vice versa. Everyone who is both not humble and happy is humble or curious and vice versa. Everyone who is not wise is not curious. Someone is not generous. Susan is not quiet. Lucy is both not patient and wise. Someone is not wise. Someone is rich. Someone is not brave. Mary is either not humble or strong. | Lucy is brave. | entailment | ((~generous(john))=>(?[X]:((~strong(X)|~brave(X)))))&
(((~rich(fred)<~>~patient(fred)))=>(?[X]:(kind(X))))&
((?[X]:(~calm(X)))=>((~kind(alice)&~generous(alice))))&
(((strong(john)<~>~happy(john)))<=>((~wise(mary)&~curious(mary))))&
(![X]:((curious(X)|strong(X))=>(~brave(X)<~>~old(X))))&
(![X]:(~brave(X)<=>(kind(X)<~>happy(X))))&
((?[X]:(happy(X)))<=>((~quiet(susan)&~rich(susan))))&
(![X]:((~happy(X)&brave(X))<=>(wise(X)<~>strong(X))))&
(![X]:((~funny(X)<~>~generous(X))<=>quiet(X)))&
(((curious(alice)&calm(alice)))=>((patient(paul)<~>~quiet(paul))))&
(![X]:(calm(X)=>(~old(X)<~>rich(X))))&
(![X]:((~curious(X)|rich(X))=>(~rich(X)<~>tall(X))))&
(![X]:((~wise(X)|~patient(X))<=>(kind(X)<~>humble(X))))&
(![X]:(happy(X)<=>(~curious(X)<~>~old(X))))&
(![X]:((~humble(X)&happy(X))<=>(humble(X)|curious(X))))&
(![X]:(~wise(X)=>~curious(X)))&
(?[X]:(~generous(X)))&
(~quiet(susan))&
((~patient(lucy)&wise(lucy)))&
(?[X]:(~wise(X)))&
(?[X]:(rich(X)))&
(?[X]:(~brave(X)))&
((~humble(mary)<~>strong(mary))) | brave(lucy) | [
"p4",
"p7",
"p13",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3935590549807622663139369
% SZS output start Proof for 3935590549807622663139369
5. ! [X0] : ((strong(X0) | curious(X0)) => (~brave(X0) <~> ~old(X0))) [input p4]
8. ! [X0] : ((brave(X0) & ~happy(X0)) <=> (wise(X0) <~> strong(X0))) [input p7]
14. ! [X0] : (happy(X0) <=> (~curious(X0) <~> ~old(X0))) [input p13]
15. ! [X0] : ((happy(X0) & ~humble(X0)) <=> (curious(X0) | humble(X0))) [input p14]
19. wise(lucy) & ~patient(lucy) [input p18]
24. ~brave(lucy) [input hypothesis]
28. ! [X0] : ((~brave(X0) <~> ~old(X0)) | (~strong(X0) & ~curious(X0))) [ennf transformation 5]
41. ! [X0] : (((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | (~strong(X0) & ~curious(X0))) [nnf transformation 28]
48. ! [X0] : (((brave(X0) & ~happy(X0)) | ((wise(X0) | ~strong(X0)) & (strong(X0) | ~wise(X0)))) & (((~strong(X0) | ~wise(X0)) & (strong(X0) | wise(X0))) | (~brave(X0) | happy(X0)))) [nnf transformation 8]
49. ! [X0] : (((brave(X0) & ~happy(X0)) | ((wise(X0) | ~strong(X0)) & (strong(X0) | ~wise(X0)))) & (((~strong(X0) | ~wise(X0)) & (strong(X0) | wise(X0))) | ~brave(X0) | happy(X0))) [flattening 48]
56. ! [X0] : ((happy(X0) | ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0)))) & (((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | ~happy(X0))) [nnf transformation 14]
57. ! [X0] : (((happy(X0) & ~humble(X0)) | (~curious(X0) & ~humble(X0))) & ((curious(X0) | humble(X0)) | (~happy(X0) | humble(X0)))) [nnf transformation 15]
58. ! [X0] : (((happy(X0) & ~humble(X0)) | (~curious(X0) & ~humble(X0))) & (curious(X0) | humble(X0) | ~happy(X0) | humble(X0))) [flattening 57]
82. ~strong(X0) | brave(X0) | old(X0) [cnf transformation 41]
94. ~wise(X0) | strong(X0) | brave(X0) [cnf transformation 49]
114. ~old(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 56]
116. ~old(X0) | happy(X0) | curious(X0) [cnf transformation 56]
118. curious(X0) | humble(X0) | ~happy(X0) | humble(X0) [cnf transformation 58]
119. ~humble(X0) | ~humble(X0) [cnf transformation 58]
122. ~curious(X0) | happy(X0) [cnf transformation 58]
127. wise(lucy) [cnf transformation 19]
133. ~brave(lucy) [cnf transformation 24]
134. curious(X0) | humble(X0) | ~happy(X0) [duplicate literal removal 118]
135. ~humble(X0) [duplicate literal removal 119]
235. ~happy(X0) | curious(X0) [subsumption resolution 134,135]
301. 28 <=> happy(lucy) [avatar definition]
303. ~happy(lucy) <- (~28) [avatar component clause 301]
305. 29 <=> strong(lucy) [avatar definition]
307. strong(lucy) <- (29) [avatar component clause 305]
327. strong(lucy) | brave(lucy) [resolution 94,127]
329. strong(lucy) [subsumption resolution 327,133]
330. 29 [avatar split clause 329,305]
335. brave(lucy) | old(lucy) <- (29) [resolution 307,82]
336. old(lucy) <- (29) [subsumption resolution 335,133]
400. ~curious(lucy) | ~happy(lucy) <- (29) [resolution 114,336]
411. happy(lucy) | curious(lucy) <- (29) [resolution 116,336]
412. curious(lucy) <- (~28, 29) [subsumption resolution 411,303]
423. happy(lucy) <- (~28, 29) [resolution 412,122]
424. $false <- (~28, 29) [subsumption resolution 423,303]
425. 28 | ~29 [avatar contradiction clause 424]
426. curious(lucy) <- (29) [subsumption resolution 411,235]
427. ~happy(lucy) <- (29) [subsumption resolution 400,426]
428. ~28 | ~29 [avatar split clause 427,305,301]
429. $false [avatar sat refutation 330,425,428]
% SZS output end Proof for 3935590549807622663139369
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or creative is either generous or old and vice versa. Everyone who is strong or wise is either not brave or quiet and vice versa. Everyone who is kind or happy is not strong. Everyone who is not strong is both wise and not kind and vice versa. Everyone who is both brave and patient is not curious and vice versa. If someone is both kind and rich then mary is both not patient and happy. Everyone who is funny is either not happy or patient and vice versa. If someone is either patient or wise then fred is both not funny and not curious. Everyone who is both not brave and quiet is generous or funny. Everyone who is both rich and happy is patient or quiet and vice versa. Everyone who is not old is both not generous and not calm and vice versa. Everyone who is both wise and curious is not patient. If mary is both not curious and not humble then someone is both not tall and kind and vice versa. If someone is both patient and humble then someone is creative. If lucy is both not humble and quiet then alice is not old or rich. If john is either curious or not strong then lucy is either not generous or calm and vice versa. Someone is not humble. Susan is creative. Someone is either not happy or generous. Fred is both tall and humble. Someone is both brave and not humble. Alice is both old and creative. Mary is humble. | John is not funny. | contradiction | (![X]:((~wise(X)|creative(X))<=>(generous(X)<~>old(X))))&
(![X]:((strong(X)|wise(X))<=>(~brave(X)<~>quiet(X))))&
(![X]:((kind(X)|happy(X))=>~strong(X)))&
(![X]:(~strong(X)<=>(wise(X)&~kind(X))))&
(![X]:((brave(X)&patient(X))<=>~curious(X)))&
((?[X]:((kind(X)&rich(X))))=>((~patient(mary)&happy(mary))))&
(![X]:(funny(X)<=>(~happy(X)<~>patient(X))))&
((?[X]:((patient(X)<~>wise(X))))=>((~funny(fred)&~curious(fred))))&
(![X]:((~brave(X)&quiet(X))=>(generous(X)|funny(X))))&
(![X]:((rich(X)&happy(X))<=>(patient(X)|quiet(X))))&
(![X]:(~old(X)<=>(~generous(X)&~calm(X))))&
(![X]:((wise(X)&curious(X))=>~patient(X)))&
(((~curious(mary)&~humble(mary)))<=>(?[X]:((~tall(X)&kind(X)))))&
((?[X]:((patient(X)&humble(X))))=>(?[X]:(creative(X))))&
(((~humble(lucy)&quiet(lucy)))=>((~old(alice)|rich(alice))))&
(((curious(john)<~>~strong(john)))<=>((~generous(lucy)<~>calm(lucy))))&
(?[X]:(~humble(X)))&
(creative(susan))&
(?[X]:((~happy(X)<~>generous(X))))&
((tall(fred)&humble(fred)))&
(?[X]:((brave(X)&~humble(X))))&
((old(alice)&creative(alice)))&
(humble(mary)) | ~funny(john) | [
"p2",
"p3",
"p4",
"p6",
"p7",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5271177640421793624688626
% SZS output start Proof for 5271177640421793624688626
3. ! [X0] : ((happy(X0) | kind(X0)) => ~strong(X0)) [input p2]
4. ! [X0] : (~strong(X0) <=> (~kind(X0) & wise(X0))) [input p3]
5. ! [X0] : ((patient(X0) & brave(X0)) <=> ~curious(X0)) [input p4]
7. ! [X0] : (funny(X0) <=> (~happy(X0) <~> patient(X0))) [input p6]
8. ? [X0] : (patient(X0) <~> wise(X0)) => (~curious(fred) & ~funny(fred)) [input p7]
10. ! [X0] : ((happy(X0) & rich(X0)) <=> (quiet(X0) | patient(X0))) [input p9]
12. ! [X0] : ((curious(X0) & wise(X0)) => ~patient(X0)) [input p11]
24. ~funny(john) [input hypothesis]
26. ! [X0] : (~strong(X0) | (~happy(X0) & ~kind(X0))) [ennf transformation 3]
28. (~curious(fred) & ~funny(fred)) | ! [X0] : (patient(X0) <=> wise(X0)) [ennf transformation 8]
31. ! [X0] : (~patient(X0) | (~curious(X0) | ~wise(X0))) [ennf transformation 12]
32. ! [X0] : (~patient(X0) | ~curious(X0) | ~wise(X0)) [flattening 31]
40. ! [X0] : ((~strong(X0) | (kind(X0) | ~wise(X0))) & ((~kind(X0) & wise(X0)) | strong(X0))) [nnf transformation 4]
41. ! [X0] : ((~strong(X0) | kind(X0) | ~wise(X0)) & ((~kind(X0) & wise(X0)) | strong(X0))) [flattening 40]
42. ! [X0] : (((patient(X0) & brave(X0)) | curious(X0)) & (~curious(X0) | (~patient(X0) | ~brave(X0)))) [nnf transformation 5]
43. ! [X0] : (((patient(X0) & brave(X0)) | curious(X0)) & (~curious(X0) | ~patient(X0) | ~brave(X0))) [flattening 42]
44. ! [X0] : ((funny(X0) | ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0)))) & (((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) | ~funny(X0))) [nnf transformation 7]
45. (~curious(fred) & ~funny(fred)) | ! [X0] : ((patient(X0) | ~wise(X0)) & (wise(X0) | ~patient(X0))) [nnf transformation 28]
46. ! [X0] : (((happy(X0) & rich(X0)) | (~quiet(X0) & ~patient(X0))) & ((quiet(X0) | patient(X0)) | (~happy(X0) | ~rich(X0)))) [nnf transformation 10]
47. ! [X0] : (((happy(X0) & rich(X0)) | (~quiet(X0) & ~patient(X0))) & (quiet(X0) | patient(X0) | ~happy(X0) | ~rich(X0))) [flattening 46]
79. ~happy(X0) | ~strong(X0) [cnf transformation 26]
80. strong(X0) | wise(X0) [cnf transformation 41]
85. curious(X0) | patient(X0) [cnf transformation 43]
90. funny(X0) | patient(X0) | happy(X0) [cnf transformation 44]
91. ~patient(X0) | ~happy(X0) | funny(X0) [cnf transformation 44]
93. ~funny(fred) | patient(X0) | ~wise(X0) [cnf transformation 45]
95. ~curious(fred) | patient(X0) | ~wise(X0) [cnf transformation 45]
100. ~patient(X0) | happy(X0) [cnf transformation 47]
105. ~curious(X0) | ~patient(X0) | ~wise(X0) [cnf transformation 32]
131. ~funny(john) [cnf transformation 24]
135. 1 <=> ! [X0] : (patient(X0) | ~wise(X0)) [avatar definition]
136. ~wise(X0) | patient(X0) <- (1) [avatar component clause 135]
138. 2 <=> curious(fred) [avatar definition]
140. ~curious(fred) <- (~2) [avatar component clause 138]
141. 1 | ~2 [avatar split clause 95,138,135]
147. 4 <=> funny(fred) [avatar definition]
149. ~funny(fred) <- (~4) [avatar component clause 147]
150. 1 | ~4 [avatar split clause 93,147,135]
201. 16 <=> curious(john) [avatar definition]
202. curious(john) <- (16) [avatar component clause 201]
203. ~curious(john) <- (~16) [avatar component clause 201]
205. 17 <=> strong(john) [avatar definition]
206. ~strong(john) <- (~17) [avatar component clause 205]
231. patient(fred) <- (~2) [resolution 85,140]
232. patient(john) <- (~16) [resolution 85,203]
234. happy(fred) <- (~2) [resolution 100,231]
235. happy(john) <- (~16) [resolution 232,100]
320. patient(john) | happy(john) [resolution 90,131]
327. ~happy(fred) | funny(fred) <- (~2) [resolution 91,231]
328. ~happy(john) | funny(john) <- (~16) [resolution 91,232]
329. funny(fred) <- (~2) [subsumption resolution 327,234]
330. $false <- (~2, ~4) [subsumption resolution 329,149]
331. 2 | 4 [avatar contradiction clause 330]
332. funny(john) <- (~16) [subsumption resolution 328,235]
333. $false <- (~16) [subsumption resolution 332,131]
334. 16 [avatar contradiction clause 333]
336. happy(john) [subsumption resolution 320,100]
353. 31 <=> patient(john) [avatar definition]
355. ~patient(john) <- (~31) [avatar component clause 353]
360. ~strong(john) [resolution 336,79]
363. ~17 [avatar split clause 360,205]
365. wise(john) <- (~17) [resolution 206,80]
377. ~patient(john) | ~wise(john) <- (16) [resolution 105,202]
381. ~patient(john) <- (16, ~17) [subsumption resolution 377,365]
382. ~31 | ~16 | 17 [avatar split clause 381,205,201,353]
412. patient(john) <- (1, ~17) [resolution 365,136]
413. $false <- (1, ~17, ~31) [subsumption resolution 412,355]
414. ~1 | 17 | 31 [avatar contradiction clause 413]
415. $false [avatar sat refutation 141,150,331,334,363,382,414]
% SZS output end Proof for 5271177640421793624688626
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not strong then someone is both generous and not happy.
Everyone who is humble is either humble or strong.
If lucy is either creative or old then alice is not curious.
Everyone who is both creative and not brave is not curious or quiet and vice versa.
Everyone who is both not kind and not strong is either not patient or old and vice versa.
Everyone who is creative or patient is not brave and vice versa.
Everyone who is both creative and rich is either rich or not tall and vice versa.
Everyone who is both brave and not generous is either not funny or not rich.
Everyone who is not happy is both old and funny.
If someone is either rich or brave then paul is both not curious and quiet and vice versa.
Everyone who is either humble or rich is funny.
If mary is humble or not creative then alice is creative or not quiet and vice versa.
Everyone who is both not patient and rich is either happy or not patient and vice versa.
Everyone who is either old or not patient is not brave or not generous.
If lucy is generous then mary is funny.
If alice is quiet then someone is not brave or patient.
Susan is wise or not wise.
Someone is either wise or not wise.
Alice is patient or strong.
Someone is both not brave and not creative.
Susan is not old.
Paul is both not kind and generous.
Someone is both strong and happy.
John is brave or patient. | Susan is kind. | contradiction | ((~strong(susan))=>(?[X]:((generous(X)&~happy(X)))))&
(![X]:(humble(X)=>(humble(X)<~>strong(X))))&
(((creative(lucy)<~>old(lucy)))=>(~curious(alice)))&
(![X]:((creative(X)&~brave(X))<=>(~curious(X)|quiet(X))))&
(![X]:((~kind(X)&~strong(X))<=>(~patient(X)<~>old(X))))&
(![X]:((creative(X)|patient(X))<=>~brave(X)))&
(![X]:((creative(X)&rich(X))<=>(rich(X)<~>~tall(X))))&
(![X]:((brave(X)&~generous(X))=>(~funny(X)<~>~rich(X))))&
(![X]:(~happy(X)=>(old(X)&funny(X))))&
((?[X]:((rich(X)<~>brave(X))))<=>((~curious(paul)&quiet(paul))))&
(![X]:((humble(X)<~>rich(X))=>funny(X)))&
(((humble(mary)|~creative(mary)))<=>((creative(alice)|~quiet(alice))))&
(![X]:((~patient(X)&rich(X))<=>(happy(X)<~>~patient(X))))&
(![X]:((old(X)<~>~patient(X))=>(~brave(X)|~generous(X))))&
((generous(lucy))=>(funny(mary)))&
((quiet(alice))=>(?[X]:((~brave(X)|patient(X)))))&
((wise(susan)|~wise(susan)))&
(?[X]:((wise(X)<~>~wise(X))))&
((patient(alice)|strong(alice)))&
(?[X]:((~brave(X)&~creative(X))))&
(~old(susan))&
((~kind(paul)&generous(paul)))&
(?[X]:((strong(X)&happy(X))))&
((brave(john)|patient(john))) | kind(susan) | [
"p4",
"p8",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 315298992453886527228949
% SZS output start Proof for 315298992453886527228949
5. ! [X0] : ((~strong(X0) & ~kind(X0)) <=> (~patient(X0) <~> old(X0))) [input p4]
9. ! [X0] : (~happy(X0) => (funny(X0) & old(X0))) [input p8]
13. ! [X0] : ((rich(X0) & ~patient(X0)) <=> (happy(X0) <~> ~patient(X0))) [input p12]
21. ~old(susan) [input p20]
25. kind(susan) [input hypothesis]
31. ! [X0] : ((funny(X0) & old(X0)) | happy(X0)) [ennf transformation 9]
43. ! [X0] : (((~strong(X0) & ~kind(X0)) | ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) & (((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | (strong(X0) | kind(X0)))) [nnf transformation 5]
44. ! [X0] : (((~strong(X0) & ~kind(X0)) | ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) & (((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | strong(X0) | kind(X0))) [flattening 43]
58. ! [X0] : (((rich(X0) & ~patient(X0)) | ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0)))) & (((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | (~rich(X0) | patient(X0)))) [nnf transformation 13]
59. ! [X0] : (((rich(X0) & ~patient(X0)) | ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0)))) & (((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | ~rich(X0) | patient(X0))) [flattening 58]
83. ~kind(X0) | old(X0) | patient(X0) [cnf transformation 44]
98. old(X0) | happy(X0) [cnf transformation 31]
114. ~patient(X0) | ~patient(X0) | ~happy(X0) [cnf transformation 59]
128. ~old(susan) [cnf transformation 21]
134. kind(susan) [cnf transformation 25]
136. ~patient(X0) | ~happy(X0) [duplicate literal removal 114]
258. happy(susan) [resolution 98,128]
263. old(susan) | patient(susan) [resolution 83,134]
264. patient(susan) [subsumption resolution 263,128]
265. ~happy(susan) [resolution 264,136]
267. $false [subsumption resolution 265,258]
% SZS output end Proof for 315298992453886527228949
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or not quiet is wise.
Everyone who is both calm and not curious is happy.
Everyone who is not strong or kind is either strong or not humble.
If mary is both not rich and funny then someone is not funny.
If fred is funny or generous then mary is both humble and rich.
Everyone who is tall is not generous and vice versa.
If alice is wise or not old then someone is creative or tall and vice versa.
If alice is either old or not quiet then john is humble or not humble.
Everyone who is either humble or not tall is not creative and vice versa.
Everyone who is old or rich is funny or not creative and vice versa.
If someone is either creative or not humble then someone is both kind and quiet and vice versa.
If someone is either strong or curious then someone is not funny and vice versa.
Everyone who is either strong or not strong is both not brave and creative.
Everyone who is either tall or happy is tall or generous and vice versa.
Everyone who is not brave is funny or not generous and vice versa.
Everyone who is brave is humble or not humble.
Someone is not creative or not patient.
Alice is either not generous or old.
Someone is not kind or not calm.
Someone is not tall.
Someone is both curious and old.
Mary is both not rich and strong. | John is calm. | neutral | (![X]:((~old(X)<~>~quiet(X))=>wise(X)))&
(![X]:((calm(X)&~curious(X))=>happy(X)))&
(![X]:((~strong(X)|kind(X))=>(strong(X)<~>~humble(X))))&
(((~rich(mary)&funny(mary)))=>(?[X]:(~funny(X))))&
(((funny(fred)|generous(fred)))=>((humble(mary)&rich(mary))))&
(![X]:(tall(X)<=>~generous(X)))&
(((wise(alice)|~old(alice)))<=>(?[X]:((creative(X)|tall(X)))))&
(((old(alice)<~>~quiet(alice)))=>((humble(john)|~humble(john))))&
(![X]:((humble(X)<~>~tall(X))<=>~creative(X)))&
(![X]:((old(X)|rich(X))<=>(funny(X)|~creative(X))))&
((?[X]:((creative(X)<~>~humble(X))))<=>(?[X]:((kind(X)&quiet(X)))))&
((?[X]:((strong(X)<~>curious(X))))<=>(?[X]:(~funny(X))))&
(![X]:((strong(X)<~>~strong(X))=>(~brave(X)&creative(X))))&
(![X]:((tall(X)<~>happy(X))<=>(tall(X)|generous(X))))&
(![X]:(~brave(X)<=>(funny(X)|~generous(X))))&
(![X]:(brave(X)=>(humble(X)|~humble(X))))&
(?[X]:((~creative(X)|~patient(X))))&
((~generous(alice)<~>old(alice)))&
(?[X]:((~kind(X)|~calm(X))))&
(?[X]:(~tall(X)))&
(?[X]:((curious(X)&old(X))))&
((~rich(mary)&strong(mary))) | calm(john) | [] | null | 0 |
Everyone who is both strong and not rich is calm or creative and vice versa. If someone is either quiet or not old then paul is both calm and wise and vice versa. Everyone who is tall or calm is either strong or not humble and vice versa. Everyone who is both tall and brave is tall. If someone is not funny then someone is either not wise or calm and vice versa. Everyone who is curious or not wise is strong or generous. If susan is funny then paul is not humble or not creative. Everyone who is both tall and not humble is either strong or humble. If john is both tall and not happy then john is not happy. If someone is both brave and not brave then fred is kind. Everyone who is either not patient or not humble is creative or not happy and vice versa. If paul is either tall or not rich then someone is not humble. If someone is funny then someone is old or quiet. Everyone who is both not brave and not old is both not old and creative and vice versa. Everyone who is both not old and not happy is humble and vice versa. Everyone who is both not calm and creative is either creative or wise and vice versa. Someone is tall or generous. Alice is rich. Paul is either not curious or not quiet. Someone is either not humble or not wise. Paul is both curious and not old. Someone is not kind. Someone is brave. | Susan is funny. | contradiction | (![X]:((strong(X)&~rich(X))<=>(calm(X)|creative(X))))&
((?[X]:((quiet(X)<~>~old(X))))<=>((calm(paul)&wise(paul))))&
(![X]:((tall(X)|calm(X))<=>(strong(X)<~>~humble(X))))&
(![X]:((tall(X)&brave(X))=>tall(X)))&
((?[X]:(~funny(X)))<=>(?[X]:((~wise(X)<~>calm(X)))))&
(![X]:((curious(X)|~wise(X))=>(strong(X)|generous(X))))&
((funny(susan))=>((~humble(paul)|~creative(paul))))&
(![X]:((tall(X)&~humble(X))=>(strong(X)<~>humble(X))))&
(((tall(john)&~happy(john)))=>(~happy(john)))&
((?[X]:((brave(X)&~brave(X))))=>(kind(fred)))&
(![X]:((~patient(X)<~>~humble(X))<=>(creative(X)|~happy(X))))&
(((tall(paul)<~>~rich(paul)))=>(?[X]:(~humble(X))))&
((?[X]:(funny(X)))=>(?[X]:((old(X)|quiet(X)))))&
(![X]:((~brave(X)&~old(X))<=>(~old(X)&creative(X))))&
(![X]:((~old(X)&~happy(X))<=>humble(X)))&
(![X]:((~calm(X)&creative(X))<=>(creative(X)<~>wise(X))))&
(?[X]:((tall(X)|generous(X))))&
(rich(alice))&
((~curious(paul)<~>~quiet(paul)))&
(?[X]:((~humble(X)<~>~wise(X))))&
((curious(paul)&~old(paul)))&
(?[X]:(~kind(X)))&
(?[X]:(brave(X))) | funny(susan) | [
"p0",
"p1",
"p2",
"p6",
"p15",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1828308848236733918513136
% SZS output start Proof for 1828308848236733918513136
1. ! [X0] : ((~rich(X0) & strong(X0)) <=> (creative(X0) | calm(X0))) [input p0]
2. ? [X0] : (quiet(X0) <~> ~old(X0)) <=> (wise(paul) & calm(paul)) [input p1]
3. ! [X0] : ((calm(X0) | tall(X0)) <=> (strong(X0) <~> ~humble(X0))) [input p2]
7. funny(susan) => (~creative(paul) | ~humble(paul)) [input p6]
16. ! [X0] : ((creative(X0) & ~calm(X0)) <=> (creative(X0) <~> wise(X0))) [input p15]
19. ~curious(paul) <~> ~quiet(paul) [input p18]
21. ~old(paul) & curious(paul) [input p20]
24. funny(susan) [input hypothesis]
31. (~creative(paul) | ~humble(paul)) | ~funny(susan) [ennf transformation 7]
32. ~creative(paul) | ~humble(paul) | ~funny(susan) [flattening 31]
40. ! [X0] : (((~rich(X0) & strong(X0)) | (~creative(X0) & ~calm(X0))) & ((creative(X0) | calm(X0)) | (rich(X0) | ~strong(X0)))) [nnf transformation 1]
41. ! [X0] : (((~rich(X0) & strong(X0)) | (~creative(X0) & ~calm(X0))) & (creative(X0) | calm(X0) | rich(X0) | ~strong(X0))) [flattening 40]
42. (? [X0] : ((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | (~wise(paul) | ~calm(paul))) & ((wise(paul) & calm(paul)) | ! [X0] : ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0)))) [nnf transformation 2]
43. (? [X0] : ((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | ~wise(paul) | ~calm(paul)) & ((wise(paul) & calm(paul)) | ! [X0] : ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0)))) [flattening 42]
44. (? [X0] : ((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | ~wise(paul) | ~calm(paul)) & ((wise(paul) & calm(paul)) | ! [X1] : ((quiet(X1) | old(X1)) & (~old(X1) | ~quiet(X1)))) [rectify 43]
45. ? [X0] : ((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) => ((old(sK0) | ~quiet(sK0)) & (~old(sK0) | quiet(sK0))) [choice axiom]
46. (((old(sK0) | ~quiet(sK0)) & (~old(sK0) | quiet(sK0))) | ~wise(paul) | ~calm(paul)) & ((wise(paul) & calm(paul)) | ! [X1] : ((quiet(X1) | old(X1)) & (~old(X1) | ~quiet(X1)))) [skolemisation 44,45]
47. ! [X0] : (((calm(X0) | tall(X0)) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0)))) & (((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | (~calm(X0) & ~tall(X0)))) [nnf transformation 3]
48. ! [X0] : ((calm(X0) | tall(X0) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0)))) & (((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | (~calm(X0) & ~tall(X0)))) [flattening 47]
67. ! [X0] : (((creative(X0) & ~calm(X0)) | ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0)))) & (((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | (~creative(X0) | calm(X0)))) [nnf transformation 16]
68. ! [X0] : (((creative(X0) & ~calm(X0)) | ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0)))) & (((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | ~creative(X0) | calm(X0))) [flattening 67]
69. (quiet(paul) | curious(paul)) & (~quiet(paul) | ~curious(paul)) [nnf transformation 19]
78. ~calm(X0) | strong(X0) [cnf transformation 41]
83. calm(paul) | quiet(X1) | old(X1) [cnf transformation 46]
85. wise(paul) | quiet(X1) | old(X1) [cnf transformation 46]
91. humble(X0) | ~strong(X0) | ~calm(X0) [cnf transformation 48]
99. ~creative(paul) | ~humble(paul) | ~funny(susan) [cnf transformation 32]
125. creative(X0) | creative(X0) | ~wise(X0) [cnf transformation 68]
127. ~quiet(paul) | ~curious(paul) [cnf transformation 69]
131. curious(paul) [cnf transformation 21]
132. ~old(paul) [cnf transformation 21]
135. funny(susan) [cnf transformation 24]
137. ~wise(X0) | creative(X0) [duplicate literal removal 125]
140. 1 <=> calm(paul) [avatar definition]
141. calm(paul) <- (1) [avatar component clause 140]
144. 2 <=> wise(paul) [avatar definition]
145. wise(paul) <- (2) [avatar component clause 144]
158. 5 <=> ! [X1] : (quiet(X1) | old(X1)) [avatar definition]
159. old(X1) | quiet(X1) <- (5) [avatar component clause 158]
160. 5 | 2 [avatar split clause 85,144,158]
165. 5 | 1 [avatar split clause 83,140,158]
168. ~calm(X0) | humble(X0) [subsumption resolution 91,78]
195. 13 <=> funny(susan) [avatar definition]
199. 14 <=> humble(paul) [avatar definition]
201. ~humble(paul) <- (~14) [avatar component clause 199]
203. 15 <=> creative(paul) [avatar definition]
206. ~13 | ~14 | ~15 [avatar split clause 99,203,199,195]
236. 22 <=> curious(paul) [avatar definition]
240. 23 <=> quiet(paul) [avatar definition]
241. ~quiet(paul) <- (~23) [avatar component clause 240]
244. ~22 | ~23 [avatar split clause 127,240,236]
255. 22 [avatar split clause 131,236]
256. 13 [avatar split clause 135,195]
260. quiet(paul) <- (5) [resolution 159,132]
262. $false <- (5, ~23) [subsumption resolution 260,241]
263. ~5 | 23 [avatar contradiction clause 262]
267. creative(paul) <- (2) [resolution 145,137]
270. 15 | ~2 [avatar split clause 267,144,203]
275. humble(paul) <- (1) [resolution 168,141]
276. $false <- (1, ~14) [subsumption resolution 275,201]
277. ~1 | 14 [avatar contradiction clause 276]
278. $false [avatar sat refutation 160,165,206,244,255,256,263,270,277]
% SZS output end Proof for 1828308848236733918513136
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not curious or not creative then someone is not strong and vice versa.
If susan is not quiet or old then someone is either funny or happy.
Everyone who is wise or not brave is generous or humble and vice versa.
Everyone who is either rich or not creative is either not rich or not humble.
If someone is not quiet then someone is either tall or not brave and vice versa.
If john is either not curious or happy then mary is not humble and vice versa.
If mary is both brave and not creative then john is either curious or not quiet.
If someone is not curious then someone is rich.
If alice is either curious or wise then susan is humble and vice versa.
Everyone who is not quiet or not old is kind or funny and vice versa.
If someone is not creative or not funny then john is not quiet and vice versa.
If someone is brave or not creative then someone is rich or not quiet and vice versa.
If john is either not tall or not quiet then someone is either generous or not creative and vice versa.
If susan is either not brave or funny then mary is both not kind and not patient and vice versa.
If someone is both brave and not rich then someone is not tall or not patient.
If someone is not strong then susan is both strong and wise and vice versa.
Susan is either not tall or creative.
Lucy is not old.
Alice is not wise.
Lucy is either quiet or not quiet.
Fred is either not patient or old.
Susan is both generous and kind.
Paul is not humble.
Lucy is rich. | Susan is strong. | entailment | (((~curious(paul)<~>~creative(paul)))<=>(?[X]:(~strong(X))))&
(((~quiet(susan)|old(susan)))=>(?[X]:((funny(X)<~>happy(X)))))&
(![X]:((wise(X)|~brave(X))<=>(generous(X)|humble(X))))&
(![X]:((rich(X)<~>~creative(X))=>(~rich(X)<~>~humble(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((tall(X)<~>~brave(X)))))&
(((~curious(john)<~>happy(john)))<=>(~humble(mary)))&
(((brave(mary)&~creative(mary)))=>((curious(john)<~>~quiet(john))))&
((?[X]:(~curious(X)))=>(?[X]:(rich(X))))&
(((curious(alice)<~>wise(alice)))<=>(humble(susan)))&
(![X]:((~quiet(X)|~old(X))<=>(kind(X)|funny(X))))&
((?[X]:((~creative(X)|~funny(X))))<=>(~quiet(john)))&
((?[X]:((brave(X)|~creative(X))))<=>(?[X]:((rich(X)|~quiet(X)))))&
(((~tall(john)<~>~quiet(john)))<=>(?[X]:((generous(X)<~>~creative(X)))))&
(((~brave(susan)<~>funny(susan)))<=>((~kind(mary)&~patient(mary))))&
((?[X]:((brave(X)&~rich(X))))=>(?[X]:((~tall(X)|~patient(X)))))&
((?[X]:(~strong(X)))<=>((strong(susan)&wise(susan))))&
((~tall(susan)<~>creative(susan)))&
(~old(lucy))&
(~wise(alice))&
((quiet(lucy)<~>~quiet(lucy)))&
((~patient(fred)<~>old(fred)))&
((generous(susan)&kind(susan)))&
(~humble(paul))&
(rich(lucy)) | strong(susan) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8855069437246636296431528
% SZS output start Proof for 8855069437246636296431528
16. ? [X0] : ~strong(X0) <=> (wise(susan) & strong(susan)) [input p15]
25. ~strong(susan) [input hypothesis]
77. (? [X0] : ~strong(X0) | (~wise(susan) | ~strong(susan))) & ((wise(susan) & strong(susan)) | ! [X0] : strong(X0)) [nnf transformation 16]
78. (? [X0] : ~strong(X0) | ~wise(susan) | ~strong(susan)) & ((wise(susan) & strong(susan)) | ! [X0] : strong(X0)) [flattening 77]
79. (? [X0] : ~strong(X0) | ~wise(susan) | ~strong(susan)) & ((wise(susan) & strong(susan)) | ! [X1] : strong(X1)) [rectify 78]
80. ? [X0] : ~strong(X0) => ~strong(sK10) [choice axiom]
81. (~strong(sK10) | ~wise(susan) | ~strong(susan)) & ((wise(susan) & strong(susan)) | ! [X1] : strong(X1)) [skolemisation 79,80]
142. strong(susan) | strong(X1) [cnf transformation 81]
157. ~strong(susan) [cnf transformation 25]
161. 1 <=> ! [X0] : strong(X0) [avatar definition]
162. strong(X0) <- (1) [avatar component clause 161]
382. 48 <=> strong(susan) [avatar definition]
384. ~strong(susan) <- (~48) [avatar component clause 382]
395. 1 | 48 [avatar split clause 142,382,161]
417. ~48 [avatar split clause 157,382]
430. $false <- (1, ~48) [resolution 384,162]
431. ~1 | 48 [avatar contradiction clause 430]
432. $false [avatar sat refutation 395,417,431]
% SZS output end Proof for 8855069437246636296431528
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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
% ------------------------------
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If someone is rich or not happy then lucy is strong or not quiet and vice versa. If someone is both tall and not happy then someone is generous or not generous. Everyone who is both strong and not tall is either patient or strong and vice versa. If someone is either not kind or kind then someone is old and vice versa. Everyone who is not patient is both not creative and not curious. If paul is either tall or wise then alice is creative or quiet. Everyone who is both not funny and not curious is both strong and not patient. Everyone who is humble is both not patient and not curious. Everyone who is not happy is both old and funny and vice versa. If someone is curious then fred is generous. Everyone who is old is both not calm and patient. If someone is not creative or creative then someone is either curious or not humble. Everyone who is both kind and not patient is not kind or not generous. If alice is funny or not curious then someone is humble or tall and vice versa. Everyone who is wise or quiet is either not kind or not funny and vice versa. If someone is both kind and not rich then someone is not curious. Someone is either not generous or not creative. Susan is not calm. Someone is not humble. Paul is not funny. Someone is kind or strong. Mary is both not quiet and rich. John is either not tall or not old. | Fred is generous. | neutral | ((?[X]:((rich(X)|~happy(X))))<=>((strong(lucy)|~quiet(lucy))))&
((?[X]:((tall(X)&~happy(X))))=>(?[X]:((generous(X)|~generous(X)))))&
(![X]:((strong(X)&~tall(X))<=>(patient(X)<~>strong(X))))&
((?[X]:((~kind(X)<~>kind(X))))<=>(?[X]:(old(X))))&
(![X]:(~patient(X)=>(~creative(X)&~curious(X))))&
(((tall(paul)<~>wise(paul)))=>((creative(alice)|quiet(alice))))&
(![X]:((~funny(X)&~curious(X))=>(strong(X)&~patient(X))))&
(![X]:(humble(X)=>(~patient(X)&~curious(X))))&
(![X]:(~happy(X)<=>(old(X)&funny(X))))&
((?[X]:(curious(X)))=>(generous(fred)))&
(![X]:(old(X)=>(~calm(X)&patient(X))))&
((?[X]:((~creative(X)|creative(X))))=>(?[X]:((curious(X)<~>~humble(X)))))&
(![X]:((kind(X)&~patient(X))=>(~kind(X)|~generous(X))))&
(((funny(alice)|~curious(alice)))<=>(?[X]:((humble(X)|tall(X)))))&
(![X]:((wise(X)|quiet(X))<=>(~kind(X)<~>~funny(X))))&
((?[X]:((kind(X)&~rich(X))))=>(?[X]:(~curious(X))))&
(?[X]:((~generous(X)<~>~creative(X))))&
(~calm(susan))&
(?[X]:(~humble(X)))&
(~funny(paul))&
(?[X]:((kind(X)|strong(X))))&
((~quiet(mary)&rich(mary)))&
((~tall(john)<~>~old(john))) | generous(fred) | [] | null | 0 |
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