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
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⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
If someone is kind then someone is not kind or curious.
Everyone who is both not wise and quiet is both not quiet and not rich.
Everyone who is not rich or not happy is not happy or tall.
Everyone who is generous or kind is both not kind and creative.
If someone is both not calm and not funny then someone is humble or not funny.
If someone is wise or not tall then lucy is humble.
If someone is both not rich and not patient then lucy is both rich and funny.
Everyone who is either not quiet or not old is either not wise or generous.
Everyone who is both not creative and not quiet is both generous and tall.
If mary is both not tall and not generous then someone is humble or creative and vice versa.
Everyone who is funny is both tall and old.
Everyone who is either kind or not generous is not wise or not calm.
Everyone who is either not rich or wise is creative.
If alice is either wise or not generous then someone is both wise and not kind and vice versa.
Everyone who is either not humble or not tall is patient or quiet.
Everyone who is either quiet or not funny is not tall.
Someone is both not curious and calm.
Someone is either rich or kind.
Susan is brave or not brave.
Fred is either not old or not funny.
Lucy is both not generous and calm.
Fred is humble or generous.
Someone is both generous and not funny.
Someone is wise or old. | Lucy is not creative. | contradiction | ((?[X]:(kind(X)))=>(?[X]:((~kind(X)|curious(X)))))&
(![X]:((~wise(X)&quiet(X))=>(~quiet(X)&~rich(X))))&
(![X]:((~rich(X)|~happy(X))=>(~happy(X)|tall(X))))&
(![X]:((generous(X)|kind(X))=>(~kind(X)&creative(X))))&
((?[X]:((~calm(X)&~funny(X))))=>(?[X]:((humble(X)|~funny(X)))))&
((?[X]:((wise(X)|~tall(X))))=>(humble(lucy)))&
((?[X]:((~rich(X)&~patient(X))))=>((rich(lucy)&funny(lucy))))&
(![X]:((~quiet(X)<~>~old(X))=>(~wise(X)<~>generous(X))))&
(![X]:((~creative(X)&~quiet(X))=>(generous(X)&tall(X))))&
(((~tall(mary)&~generous(mary)))<=>(?[X]:((humble(X)|creative(X)))))&
(![X]:(funny(X)=>(tall(X)&old(X))))&
(![X]:((kind(X)<~>~generous(X))=>(~wise(X)|~calm(X))))&
(![X]:((~rich(X)<~>wise(X))=>creative(X)))&
(((wise(alice)<~>~generous(alice)))<=>(?[X]:((wise(X)&~kind(X)))))&
(![X]:((~humble(X)<~>~tall(X))=>(patient(X)|quiet(X))))&
(![X]:((quiet(X)<~>~funny(X))=>~tall(X)))&
(?[X]:((~curious(X)&calm(X))))&
(?[X]:((rich(X)<~>kind(X))))&
((brave(susan)|~brave(susan)))&
((~old(fred)<~>~funny(fred)))&
((~generous(lucy)&calm(lucy)))&
((humble(fred)|generous(fred)))&
(?[X]:((generous(X)&~funny(X))))&
(?[X]:((wise(X)|old(X)))) | ~creative(lucy) | [
"p1",
"p3",
"p8",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3929972866800707751877849
% SZS output start Proof for 3929972866800707751877849
2. ! [X0] : ((quiet(X0) & ~wise(X0)) => (~rich(X0) & ~quiet(X0))) [input p1]
4. ! [X0] : ((kind(X0) | generous(X0)) => (creative(X0) & ~kind(X0))) [input p3]
9. ! [X0] : ((~quiet(X0) & ~creative(X0)) => (tall(X0) & generous(X0))) [input p8]
12. ! [X0] : ((kind(X0) <~> ~generous(X0)) => (~calm(X0) | ~wise(X0))) [input p11]
21. calm(lucy) & ~generous(lucy) [input p20]
25. ~creative(lucy) [input hypothesis]
31. ! [X0] : ((~rich(X0) & ~quiet(X0)) | (~quiet(X0) | wise(X0))) [ennf transformation 2]
32. ! [X0] : ((~rich(X0) & ~quiet(X0)) | ~quiet(X0) | wise(X0)) [flattening 31]
35. ! [X0] : ((creative(X0) & ~kind(X0)) | (~kind(X0) & ~generous(X0))) [ennf transformation 4]
39. ! [X0] : ((tall(X0) & generous(X0)) | (quiet(X0) | creative(X0))) [ennf transformation 9]
40. ! [X0] : ((tall(X0) & generous(X0)) | quiet(X0) | creative(X0)) [flattening 39]
42. ! [X0] : ((~calm(X0) | ~wise(X0)) | (kind(X0) <=> ~generous(X0))) [ennf transformation 12]
43. ! [X0] : (~calm(X0) | ~wise(X0) | (kind(X0) <=> ~generous(X0))) [flattening 42]
58. ! [X0] : (~calm(X0) | ~wise(X0) | ((kind(X0) | generous(X0)) & (~generous(X0) | ~kind(X0)))) [nnf transformation 43]
76. ~quiet(X0) | ~quiet(X0) | wise(X0) [cnf transformation 32]
81. ~kind(X0) | ~kind(X0) [cnf transformation 35]
82. ~generous(X0) | creative(X0) [cnf transformation 35]
91. generous(X0) | quiet(X0) | creative(X0) [cnf transformation 40]
101. ~calm(X0) | ~wise(X0) | kind(X0) | generous(X0) [cnf transformation 58]
119. ~generous(lucy) [cnf transformation 21]
120. calm(lucy) [cnf transformation 21]
125. ~creative(lucy) [cnf transformation 25]
126. ~kind(X0) [duplicate literal removal 81]
127. ~quiet(X0) | wise(X0) [duplicate literal removal 76]
129. 1 <=> ! [X1] : ~kind(X1) [avatar definition]
130. ~kind(X1) <- (1) [avatar component clause 129]
140. 1 [avatar split clause 126,129]
167. creative(X0) | quiet(X0) [subsumption resolution 91,82]
261. quiet(lucy) [resolution 167,125]
262. wise(lucy) [resolution 261,127]
300. ~wise(lucy) | kind(lucy) | generous(lucy) [resolution 101,120]
311. kind(lucy) | generous(lucy) [subsumption resolution 300,262]
312. generous(lucy) <- (1) [subsumption resolution 311,130]
313. $false <- (1) [subsumption resolution 312,119]
314. ~1 [avatar contradiction clause 313]
315. $false [avatar sat refutation 140,314]
% SZS output end Proof for 3929972866800707751877849
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not calm or not rich then john is both not old and not creative and vice versa.
If someone is either not wise or not tall then mary is funny or brave and vice versa.
Everyone who is strong or quiet is not tall and vice versa.
If mary is both not rich and not kind then susan is either not strong or not rich and vice versa.
Everyone who is either not tall or strong is not calm or tall and vice versa.
If someone is kind or not strong then mary is either calm or not old.
Everyone who is generous or strong is not humble or patient and vice versa.
If mary is either kind or old then fred is curious.
If someone is both not creative and not curious then john is both patient and quiet and vice versa.
Everyone who is not quiet or not rich is not brave and vice versa.
Everyone who is not brave is either not generous or calm.
Everyone who is not patient or not old is either happy or wise.
Everyone who is funny is not calm.
Everyone who is not generous or calm is either not funny or not calm and vice versa.
If alice is both not wise and not old then susan is either old or strong and vice versa.
If someone is not rich or happy then lucy is both not quiet and not strong and vice versa.
Mary is strong or tall.
Susan is not creative or quiet.
Someone is both not strong and not kind.
Mary is not tall or creative.
Susan is happy or kind.
Someone is both not patient and brave.
Someone is not quiet.
Someone is tall or quiet. | Susan is old. | entailment | (((~calm(susan)<~>~rich(susan)))<=>((~old(john)&~creative(john))))&
((?[X]:((~wise(X)<~>~tall(X))))<=>((funny(mary)|brave(mary))))&
(![X]:((strong(X)|quiet(X))<=>~tall(X)))&
(((~rich(mary)&~kind(mary)))<=>((~strong(susan)<~>~rich(susan))))&
(![X]:((~tall(X)<~>strong(X))<=>(~calm(X)|tall(X))))&
((?[X]:((kind(X)|~strong(X))))=>((calm(mary)<~>~old(mary))))&
(![X]:((generous(X)|strong(X))<=>(~humble(X)|patient(X))))&
(((kind(mary)<~>old(mary)))=>(curious(fred)))&
((?[X]:((~creative(X)&~curious(X))))<=>((patient(john)&quiet(john))))&
(![X]:((~quiet(X)|~rich(X))<=>~brave(X)))&
(![X]:(~brave(X)=>(~generous(X)<~>calm(X))))&
(![X]:((~patient(X)|~old(X))=>(happy(X)<~>wise(X))))&
(![X]:(funny(X)=>~calm(X)))&
(![X]:((~generous(X)|calm(X))<=>(~funny(X)<~>~calm(X))))&
(((~wise(alice)&~old(alice)))<=>((old(susan)<~>strong(susan))))&
((?[X]:((~rich(X)|happy(X))))<=>((~quiet(lucy)&~strong(lucy))))&
((strong(mary)|tall(mary)))&
((~creative(susan)|quiet(susan)))&
(?[X]:((~strong(X)&~kind(X))))&
((~tall(mary)|creative(mary)))&
((happy(susan)|kind(susan)))&
(?[X]:((~patient(X)&brave(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((tall(X)|quiet(X)))) | old(susan) | [
"p2",
"p3",
"p4",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4425378817115741660667418
% SZS output start Proof for 4425378817115741660667418
3. ! [X0] : ((quiet(X0) | strong(X0)) <=> ~tall(X0)) [input p2]
4. (~kind(mary) & ~rich(mary)) <=> (~strong(susan) <~> ~rich(susan)) [input p3]
5. ! [X0] : ((~tall(X0) <~> strong(X0)) <=> (tall(X0) | ~calm(X0))) [input p4]
12. ! [X0] : ((~old(X0) | ~patient(X0)) => (happy(X0) <~> wise(X0))) [input p11]
15. (~old(alice) & ~wise(alice)) <=> (old(susan) <~> strong(susan)) [input p14]
16. ? [X0] : (happy(X0) | ~rich(X0)) <=> (~strong(lucy) & ~quiet(lucy)) [input p15]
25. ~old(susan) [input hypothesis]
29. ! [X0] : ((happy(X0) <~> wise(X0)) | (old(X0) & patient(X0))) [ennf transformation 12]
38. ! [X0] : (((quiet(X0) | strong(X0)) | tall(X0)) & (~tall(X0) | (~quiet(X0) & ~strong(X0)))) [nnf transformation 3]
39. ! [X0] : ((quiet(X0) | strong(X0) | tall(X0)) & (~tall(X0) | (~quiet(X0) & ~strong(X0)))) [flattening 38]
40. ((~kind(mary) & ~rich(mary)) | ((~strong(susan) | rich(susan)) & (~rich(susan) | strong(susan)))) & (((rich(susan) | strong(susan)) & (~rich(susan) | ~strong(susan))) | (kind(mary) | rich(mary))) [nnf transformation 4]
41. ((~kind(mary) & ~rich(mary)) | ((~strong(susan) | rich(susan)) & (~rich(susan) | strong(susan)))) & (((rich(susan) | strong(susan)) & (~rich(susan) | ~strong(susan))) | kind(mary) | rich(mary)) [flattening 40]
42. ! [X0] : ((((~strong(X0) | tall(X0)) & (strong(X0) | ~tall(X0))) | (~tall(X0) & calm(X0))) & ((tall(X0) | ~calm(X0)) | ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0))))) [nnf transformation 5]
43. ! [X0] : ((((~strong(X0) | tall(X0)) & (strong(X0) | ~tall(X0))) | (~tall(X0) & calm(X0))) & (tall(X0) | ~calm(X0) | ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0))))) [flattening 42]
56. ! [X0] : (((~wise(X0) | ~happy(X0)) & (wise(X0) | happy(X0))) | (old(X0) & patient(X0))) [nnf transformation 29]
59. ((~old(alice) & ~wise(alice)) | ((old(susan) | ~strong(susan)) & (strong(susan) | ~old(susan)))) & (((~strong(susan) | ~old(susan)) & (strong(susan) | old(susan))) | (old(alice) | wise(alice))) [nnf transformation 15]
60. ((~old(alice) & ~wise(alice)) | ((old(susan) | ~strong(susan)) & (strong(susan) | ~old(susan)))) & (((~strong(susan) | ~old(susan)) & (strong(susan) | old(susan))) | old(alice) | wise(alice)) [flattening 59]
61. (? [X0] : (happy(X0) | ~rich(X0)) | (strong(lucy) | quiet(lucy))) & ((~strong(lucy) & ~quiet(lucy)) | ! [X0] : (~happy(X0) & rich(X0))) [nnf transformation 16]
62. (? [X0] : (happy(X0) | ~rich(X0)) | strong(lucy) | quiet(lucy)) & ((~strong(lucy) & ~quiet(lucy)) | ! [X0] : (~happy(X0) & rich(X0))) [flattening 61]
63. (? [X0] : (happy(X0) | ~rich(X0)) | strong(lucy) | quiet(lucy)) & ((~strong(lucy) & ~quiet(lucy)) | ! [X1] : (~happy(X1) & rich(X1))) [rectify 62]
64. ? [X0] : (happy(X0) | ~rich(X0)) => (happy(sK2) | ~rich(sK2)) [choice axiom]
65. ((happy(sK2) | ~rich(sK2)) | strong(lucy) | quiet(lucy)) & ((~strong(lucy) & ~quiet(lucy)) | ! [X1] : (~happy(X1) & rich(X1))) [skolemisation 63,64]
86. ~strong(X0) | ~tall(X0) [cnf transformation 39]
88. quiet(X0) | strong(X0) | tall(X0) [cnf transformation 39]
91. ~rich(mary) | ~rich(susan) | strong(susan) [cnf transformation 41]
98. strong(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 43]
121. happy(X0) | wise(X0) | old(X0) [cnf transformation 56]
134. ~wise(alice) | old(susan) | ~strong(susan) [cnf transformation 60]
136. ~old(alice) | old(susan) | ~strong(susan) [cnf transformation 60]
137. ~quiet(lucy) | rich(X1) [cnf transformation 65]
138. ~quiet(lucy) | ~happy(X1) [cnf transformation 65]
139. ~strong(lucy) | rich(X1) [cnf transformation 65]
140. ~strong(lucy) | ~happy(X1) [cnf transformation 65]
152. ~old(susan) [cnf transformation 25]
156. strong(X0) | ~tall(X0) [duplicate literal removal 98]
170. 4 <=> rich(susan) [avatar definition]
171. ~rich(susan) <- (~4) [avatar component clause 170]
208. 11 <=> strong(susan) [avatar definition]
218. 13 <=> rich(mary) [avatar definition]
220. ~rich(mary) <- (~13) [avatar component clause 218]
222. 11 | ~4 | ~13 [avatar split clause 91,218,170,208]
226. ~tall(X0) [subsumption resolution 156,86]
277. 24 <=> old(susan) [avatar definition]
281. 25 <=> old(alice) [avatar definition]
283. ~old(alice) <- (~25) [avatar component clause 281]
284. ~11 | 24 | ~25 [avatar split clause 136,281,277,208]
287. 26 <=> wise(alice) [avatar definition]
289. ~wise(alice) <- (~26) [avatar component clause 287]
290. ~11 | 24 | ~26 [avatar split clause 134,287,277,208]
295. 27 <=> quiet(lucy) [avatar definition]
296. ~quiet(lucy) <- (~27) [avatar component clause 295]
299. 28 <=> strong(lucy) [avatar definition]
312. 31 <=> ! [X1] : ~happy(X1) [avatar definition]
313. ~happy(X1) <- (31) [avatar component clause 312]
314. 31 | ~28 [avatar split clause 140,299,312]
316. 32 <=> ! [X1] : rich(X1) [avatar definition]
317. rich(X1) <- (32) [avatar component clause 316]
318. 32 | ~28 [avatar split clause 139,299,316]
319. 31 | ~27 [avatar split clause 138,295,312]
320. 32 | ~27 [avatar split clause 137,295,316]
341. ~24 [avatar split clause 152,277]
369. strong(lucy) | tall(lucy) <- (~27) [resolution 88,296]
375. strong(lucy) <- (~27) [subsumption resolution 369,226]
376. 28 | 27 [avatar split clause 375,295,299]
445. $false <- (~4, 32) [subsumption resolution 171,317]
446. 4 | ~32 [avatar contradiction clause 445]
452. $false <- (~13, 32) [subsumption resolution 220,317]
453. 13 | ~32 [avatar contradiction clause 452]
478. wise(X0) | old(X0) <- (31) [resolution 121,313]
503. old(alice) <- (~26, 31) [resolution 478,289]
504. $false <- (~25, ~26, 31) [subsumption resolution 503,283]
505. 25 | 26 | ~31 [avatar contradiction clause 504]
506. $false [avatar sat refutation 222,284,290,314,318,319,320,341,376,446,453,505]
% SZS output end Proof for 4425378817115741660667418
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or not curious is either funny or brave and vice versa.
Everyone who is either not kind or not strong is either not patient or not tall and vice versa.
Everyone who is both not tall and happy is not curious or not funny and vice versa.
If someone is both not old and old then susan is either curious or not happy.
Everyone who is either not kind or not wise is not creative.
If mary is either not patient or not strong then paul is tall or not kind.
If alice is not creative or brave then someone is both wise and not strong.
Everyone who is both not creative and not old is both not rich and strong.
Everyone who is not old is not strong.
Everyone who is not rich is both calm and strong.
Everyone who is both funny and not humble is not curious.
Everyone who is not generous is not brave.
If alice is not funny then alice is either not happy or curious and vice versa.
Everyone who is either rich or happy is either not humble or humble.
If lucy is both not humble and not generous then someone is kind and vice versa.
Alice is both not humble and not old.
John is either quiet or not kind.
Someone is not happy.
Someone is either quiet or brave.
Fred is either curious or strong.
Susan is either wise or not wise.
Fred is both funny and not creative.
Alice is quiet or not creative. | Lucy is not quiet. | neutral | (![X]:((~old(X)<~>~curious(X))<=>(funny(X)<~>brave(X))))&
(![X]:((~kind(X)<~>~strong(X))<=>(~patient(X)<~>~tall(X))))&
(![X]:((~tall(X)&happy(X))<=>(~curious(X)|~funny(X))))&
((?[X]:((~old(X)&old(X))))=>((curious(susan)<~>~happy(susan))))&
(![X]:((~kind(X)<~>~wise(X))=>~creative(X)))&
(((~patient(mary)<~>~strong(mary)))=>((tall(paul)|~kind(paul))))&
(((~creative(alice)|brave(alice)))=>(?[X]:((wise(X)&~strong(X)))))&
(![X]:((~creative(X)&~old(X))=>(~rich(X)&strong(X))))&
(![X]:(~old(X)=>~strong(X)))&
(![X]:(~rich(X)=>(calm(X)&strong(X))))&
(![X]:((funny(X)&~humble(X))=>~curious(X)))&
(![X]:(~generous(X)=>~brave(X)))&
((~funny(alice))<=>((~happy(alice)<~>curious(alice))))&
(![X]:((rich(X)<~>happy(X))=>(~humble(X)<~>humble(X))))&
(((~humble(lucy)&~generous(lucy)))<=>(?[X]:(kind(X))))&
((~humble(alice)&~old(alice)))&
((quiet(john)<~>~kind(john)))&
(?[X]:(~happy(X)))&
(?[X]:((quiet(X)<~>brave(X))))&
((curious(fred)<~>strong(fred)))&
((wise(susan)<~>~wise(susan)))&
((funny(fred)&~creative(fred)))&
((quiet(alice)|~creative(alice))) | ~quiet(lucy) | [] | null | 0 |
Everyone who is either not curious or funny is both patient and not generous and vice versa.
Everyone who is both quiet and wise is both strong and not curious.
If alice is not happy or strong then john is not rich or wise.
If someone is either not kind or not brave then someone is either not patient or rich.
If someone is either humble or happy then fred is both not strong and kind and vice versa.
If mary is quiet then lucy is old.
Everyone who is either not wise or not tall is not creative or not generous.
Everyone who is either calm or not wise is either not kind or not patient and vice versa.
Everyone who is both not quiet and strong is kind and vice versa.
If someone is brave or not kind then mary is both happy and not happy and vice versa.
If someone is humble or not quiet then someone is not tall or rich.
Everyone who is not calm or not happy is both happy and curious.
If alice is both not happy and kind then lucy is both calm and not brave and vice versa.
Everyone who is both not patient and kind is either kind or creative and vice versa.
If someone is old then susan is generous.
Paul is either rich or not generous.
Someone is not old or calm.
Someone is either not patient or not happy.
Alice is kind.
Lucy is both patient and funny.
Someone is both generous and not creative.
Someone is not calm.
Someone is not old or humble. | Mary is not quiet. | entailment | (![X]:((~curious(X)<~>funny(X))<=>(patient(X)&~generous(X))))&
(![X]:((quiet(X)&wise(X))=>(strong(X)&~curious(X))))&
(((~happy(alice)|strong(alice)))=>((~rich(john)|wise(john))))&
((?[X]:((~kind(X)<~>~brave(X))))=>(?[X]:((~patient(X)<~>rich(X)))))&
((?[X]:((humble(X)<~>happy(X))))<=>((~strong(fred)&kind(fred))))&
((quiet(mary))=>(old(lucy)))&
(![X]:((~wise(X)<~>~tall(X))=>(~creative(X)|~generous(X))))&
(![X]:((calm(X)<~>~wise(X))<=>(~kind(X)<~>~patient(X))))&
(![X]:((~quiet(X)&strong(X))<=>kind(X)))&
((?[X]:((brave(X)|~kind(X))))<=>((happy(mary)&~happy(mary))))&
((?[X]:((humble(X)|~quiet(X))))=>(?[X]:((~tall(X)|rich(X)))))&
(![X]:((~calm(X)|~happy(X))=>(happy(X)&curious(X))))&
(((~happy(alice)&kind(alice)))<=>((calm(lucy)&~brave(lucy))))&
(![X]:((~patient(X)&kind(X))<=>(kind(X)<~>creative(X))))&
((?[X]:(old(X)))=>(generous(susan)))&
((rich(paul)<~>~generous(paul)))&
(?[X]:((~old(X)|calm(X))))&
(?[X]:((~patient(X)<~>~happy(X))))&
(kind(alice))&
((patient(lucy)&funny(lucy)))&
(?[X]:((generous(X)&~creative(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~old(X)|humble(X)))) | ~quiet(mary) | [
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3908258856984294434256934
% SZS output start Proof for 3908258856984294434256934
9. ! [X0] : ((strong(X0) & ~quiet(X0)) <=> kind(X0)) [input p8]
10. ? [X0] : (~kind(X0) | brave(X0)) <=> (~happy(mary) & happy(mary)) [input p9]
24. quiet(mary) [input hypothesis]
51. ! [X0] : (((strong(X0) & ~quiet(X0)) | ~kind(X0)) & (kind(X0) | (~strong(X0) | quiet(X0)))) [nnf transformation 9]
52. ! [X0] : (((strong(X0) & ~quiet(X0)) | ~kind(X0)) & (kind(X0) | ~strong(X0) | quiet(X0))) [flattening 51]
53. (? [X0] : (~kind(X0) | brave(X0)) | (happy(mary) | ~happy(mary))) & ((~happy(mary) & happy(mary)) | ! [X0] : (kind(X0) & ~brave(X0))) [nnf transformation 10]
54. (? [X0] : (~kind(X0) | brave(X0)) | happy(mary) | ~happy(mary)) & ((~happy(mary) & happy(mary)) | ! [X0] : (kind(X0) & ~brave(X0))) [flattening 53]
55. (? [X0] : (~kind(X0) | brave(X0)) | happy(mary) | ~happy(mary)) & ((~happy(mary) & happy(mary)) | ! [X1] : (kind(X1) & ~brave(X1))) [rectify 54]
56. ? [X0] : (~kind(X0) | brave(X0)) => (~kind(sK2) | brave(sK2)) [choice axiom]
57. ((~kind(sK2) | brave(sK2)) | happy(mary) | ~happy(mary)) & ((~happy(mary) & happy(mary)) | ! [X1] : (kind(X1) & ~brave(X1))) [skolemisation 55,56]
109. ~kind(X0) | ~quiet(X0) [cnf transformation 52]
112. happy(mary) | kind(X1) [cnf transformation 57]
114. ~happy(mary) | kind(X1) [cnf transformation 57]
145. quiet(mary) [cnf transformation 24]
214. 15 <=> quiet(mary) [avatar definition]
215. quiet(mary) <- (15) [avatar component clause 214]
223. 17 <=> ! [X1] : kind(X1) [avatar definition]
224. kind(X1) <- (17) [avatar component clause 223]
226. 18 <=> happy(mary) [avatar definition]
229. 17 | ~18 [avatar split clause 114,226,223]
234. 17 | 18 [avatar split clause 112,226,223]
306. 15 [avatar split clause 145,214]
311. ~quiet(X0) <- (17) [resolution 109,224]
315. $false <- (15, 17) [resolution 311,215]
316. ~15 | ~17 [avatar contradiction clause 315]
317. $false [avatar sat refutation 229,234,306,316]
% SZS output end Proof for 3908258856984294434256934
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or not old is not patient. Everyone who is not calm is either not old or humble and vice versa. If alice is both not funny and not wise then someone is generous. Everyone who is strong or humble is not funny and vice versa. If susan is happy or not creative then someone is patient and vice versa. Everyone who is either not tall or curious is not generous or not happy. If someone is patient or calm then alice is not strong or not creative and vice versa. If john is not creative or patient then susan is not happy and vice versa. If lucy is old then paul is kind. If someone is not quiet or not curious then someone is not kind or not old and vice versa. If lucy is either generous or not curious then someone is not tall or not curious and vice versa. Everyone who is both rich and not happy is not curious or not generous. Everyone who is both not strong and curious is not rich or not brave. Everyone who is not tall or old is curious and vice versa. Everyone who is both kind and patient is both funny and not quiet and vice versa. Everyone who is either old or not patient is not tall and vice versa. Mary is either not old or happy. Susan is both not creative and kind. Someone is either not wise or not old. Lucy is calm. Mary is both happy and generous. Someone is either curious or calm. Someone is tall or not humble. Someone is either not funny or calm. | Mary is not funny. | entailment | (![X]:((funny(X)<~>~old(X))=>~patient(X)))&
(![X]:(~calm(X)<=>(~old(X)<~>humble(X))))&
(((~funny(alice)&~wise(alice)))=>(?[X]:(generous(X))))&
(![X]:((strong(X)|humble(X))<=>~funny(X)))&
(((happy(susan)|~creative(susan)))<=>(?[X]:(patient(X))))&
(![X]:((~tall(X)<~>curious(X))=>(~generous(X)|~happy(X))))&
((?[X]:((patient(X)|calm(X))))<=>((~strong(alice)|~creative(alice))))&
(((~creative(john)|patient(john)))<=>(~happy(susan)))&
((old(lucy))=>(kind(paul)))&
((?[X]:((~quiet(X)|~curious(X))))<=>(?[X]:((~kind(X)|~old(X)))))&
(((generous(lucy)<~>~curious(lucy)))<=>(?[X]:((~tall(X)|~curious(X)))))&
(![X]:((rich(X)&~happy(X))=>(~curious(X)|~generous(X))))&
(![X]:((~strong(X)&curious(X))=>(~rich(X)|~brave(X))))&
(![X]:((~tall(X)|old(X))<=>curious(X)))&
(![X]:((kind(X)&patient(X))<=>(funny(X)&~quiet(X))))&
(![X]:((old(X)<~>~patient(X))<=>~tall(X)))&
((~old(mary)<~>happy(mary)))&
((~creative(susan)&kind(susan)))&
(?[X]:((~wise(X)<~>~old(X))))&
(calm(lucy))&
((happy(mary)&generous(mary)))&
(?[X]:((curious(X)<~>calm(X))))&
(?[X]:((tall(X)|~humble(X))))&
(?[X]:((~funny(X)<~>calm(X)))) | ~funny(mary) | [
"p0",
"p5",
"p13",
"p15",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4576304922269197367771354
% SZS output start Proof for 4576304922269197367771354
1. ! [X0] : ((funny(X0) <~> ~old(X0)) => ~patient(X0)) [input p0]
6. ! [X0] : ((~tall(X0) <~> curious(X0)) => (~happy(X0) | ~generous(X0))) [input p5]
14. ! [X0] : ((old(X0) | ~tall(X0)) <=> curious(X0)) [input p13]
16. ! [X0] : ((old(X0) <~> ~patient(X0)) <=> ~tall(X0)) [input p15]
17. ~old(mary) <~> happy(mary) [input p16]
21. generous(mary) & happy(mary) [input p20]
25. funny(mary) [input hypothesis]
29. ! [X0] : (~patient(X0) | (funny(X0) <=> ~old(X0))) [ennf transformation 1]
32. ! [X0] : ((~happy(X0) | ~generous(X0)) | (~tall(X0) <=> curious(X0))) [ennf transformation 6]
33. ! [X0] : (~happy(X0) | ~generous(X0) | (~tall(X0) <=> curious(X0))) [flattening 32]
35. ! [X0] : (~patient(X0) | ((funny(X0) | old(X0)) & (~old(X0) | ~funny(X0)))) [nnf transformation 29]
46. ! [X0] : (~happy(X0) | ~generous(X0) | ((~tall(X0) | ~curious(X0)) & (curious(X0) | tall(X0)))) [nnf transformation 33]
63. ! [X0] : (((old(X0) | ~tall(X0)) | ~curious(X0)) & (curious(X0) | (~old(X0) & tall(X0)))) [nnf transformation 14]
64. ! [X0] : ((old(X0) | ~tall(X0) | ~curious(X0)) & (curious(X0) | (~old(X0) & tall(X0)))) [flattening 63]
67. ! [X0] : ((((patient(X0) | ~old(X0)) & (~patient(X0) | old(X0))) | tall(X0)) & (~tall(X0) | ((old(X0) | patient(X0)) & (~patient(X0) | ~old(X0))))) [nnf transformation 16]
68. (~happy(mary) | old(mary)) & (happy(mary) | ~old(mary)) [nnf transformation 17]
80. ~patient(X0) | ~old(X0) | ~funny(X0) [cnf transformation 35]
94. ~curious(X0) | ~generous(X0) | ~tall(X0) | ~happy(X0) [cnf transformation 46]
114. ~old(X0) | curious(X0) [cnf transformation 64]
123. ~old(X0) | patient(X0) | tall(X0) [cnf transformation 67]
125. ~happy(mary) | old(mary) [cnf transformation 68]
131. happy(mary) [cnf transformation 21]
132. generous(mary) [cnf transformation 21]
138. funny(mary) [cnf transformation 25]
271. 30 <=> old(mary) [avatar definition]
273. old(mary) <- (30) [avatar component clause 271]
275. 31 <=> happy(mary) [avatar definition]
276. happy(mary) <- (31) [avatar component clause 275]
278. 30 | ~31 [avatar split clause 125,275,271]
291. 31 [avatar split clause 131,275]
324. curious(mary) <- (30) [resolution 114,273]
436. 57 <=> patient(mary) [avatar definition]
438. patient(mary) <- (57) [avatar component clause 436]
472. patient(mary) | tall(mary) <- (30) [resolution 123,273]
474. 62 <=> tall(mary) [avatar definition]
477. 62 | 57 | ~30 [avatar split clause 472,271,436,474]
481. ~generous(mary) | ~tall(mary) | ~happy(mary) <- (30) [resolution 94,324]
484. ~tall(mary) | ~happy(mary) <- (30) [subsumption resolution 481,132]
485. ~tall(mary) <- (30, 31) [subsumption resolution 484,276]
486. ~62 | ~30 | ~31 [avatar split clause 485,275,271,474]
494. ~old(mary) | ~funny(mary) <- (57) [resolution 438,80]
495. ~funny(mary) <- (30, 57) [subsumption resolution 494,273]
496. $false <- (30, 57) [subsumption resolution 495,138]
497. ~30 | ~57 [avatar contradiction clause 496]
498. $false [avatar sat refutation 278,291,477,486,497]
% SZS output end Proof for 4576304922269197367771354
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not old is either humble or kind and vice versa.
Everyone who is not kind is both brave and creative and vice versa.
Everyone who is both strong and not strong is both not kind and not strong and vice versa.
Everyone who is either not funny or not curious is either strong or quiet and vice versa.
If someone is not old then lucy is humble.
If someone is funny then someone is either patient or kind and vice versa.
Everyone who is both brave and creative is not quiet or generous and vice versa.
Everyone who is both quiet and not brave is not creative and vice versa.
Everyone who is both happy and strong is patient.
Everyone who is calm or not rich is not humble and vice versa.
Everyone who is both not quiet and old is both not creative and not wise and vice versa.
If susan is either quiet or creative then susan is either not patient or rich and vice versa.
Everyone who is not happy is either not patient or patient.
Everyone who is old is either not strong or not old and vice versa.
Everyone who is not curious is either not generous or not creative.
Someone is not generous or humble.
Someone is not tall.
Someone is both not humble and not happy.
Lucy is not rich or not patient.
Alice is wise or not kind.
Lucy is not wise or wise. | Susan is happy. | neutral | (![X]:((old(X)<~>~old(X))<=>(humble(X)<~>kind(X))))&
(![X]:(~kind(X)<=>(brave(X)&creative(X))))&
(![X]:((strong(X)&~strong(X))<=>(~kind(X)&~strong(X))))&
(![X]:((~funny(X)<~>~curious(X))<=>(strong(X)<~>quiet(X))))&
((?[X]:(~old(X)))=>(humble(lucy)))&
((?[X]:(funny(X)))<=>(?[X]:((patient(X)<~>kind(X)))))&
(![X]:((brave(X)&creative(X))<=>(~quiet(X)|generous(X))))&
(![X]:((quiet(X)&~brave(X))<=>~creative(X)))&
(![X]:((happy(X)&strong(X))=>patient(X)))&
(![X]:((calm(X)|~rich(X))<=>~humble(X)))&
(![X]:((~quiet(X)&old(X))<=>(~creative(X)&~wise(X))))&
(((quiet(susan)<~>creative(susan)))<=>((~patient(susan)<~>rich(susan))))&
(![X]:(~happy(X)=>(~patient(X)<~>patient(X))))&
(![X]:(old(X)<=>(~strong(X)<~>~old(X))))&
(![X]:(~curious(X)=>(~generous(X)<~>~creative(X))))&
(?[X]:((~generous(X)|humble(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~humble(X)&~happy(X))))&
((~rich(lucy)|~patient(lucy)))&
((wise(alice)|~kind(alice)))&
((~wise(lucy)|wise(lucy))) | happy(susan) | [] | null | 0 |
Everyone who is both quiet and calm is not curious or not rich and vice versa. If susan is curious then susan is not creative or not quiet and vice versa. If paul is kind then mary is both not quiet and old. Everyone who is not kind or not strong is either quiet or tall. If someone is not happy then mary is wise and vice versa. Everyone who is not creative is both not happy and not brave and vice versa. Everyone who is either not quiet or rich is either happy or old and vice versa. Everyone who is wise is either generous or rich and vice versa. Everyone who is either not rich or happy is either old or quiet. Everyone who is either not curious or patient is wise and vice versa. Everyone who is either wise or generous is funny and vice versa. If alice is not brave or creative then someone is both strong and not humble. If john is either generous or not humble then someone is not tall and vice versa. Everyone who is either curious or not old is both not old and patient. Everyone who is both wise and not patient is curious or quiet and vice versa. Everyone who is either not curious or not tall is not humble or happy and vice versa. Someone is both not curious and tall. Someone is patient or calm. Alice is patient or happy. Someone is either not brave or patient. Someone is not patient. Someone is both not strong and old. | Paul is not old. | contradiction | (![X]:((quiet(X)&calm(X))<=>(~curious(X)|~rich(X))))&
((curious(susan))<=>((~creative(susan)|~quiet(susan))))&
((kind(paul))=>((~quiet(mary)&old(mary))))&
(![X]:((~kind(X)|~strong(X))=>(quiet(X)<~>tall(X))))&
((?[X]:(~happy(X)))<=>(wise(mary)))&
(![X]:(~creative(X)<=>(~happy(X)&~brave(X))))&
(![X]:((~quiet(X)<~>rich(X))<=>(happy(X)<~>old(X))))&
(![X]:(wise(X)<=>(generous(X)<~>rich(X))))&
(![X]:((~rich(X)<~>happy(X))=>(old(X)<~>quiet(X))))&
(![X]:((~curious(X)<~>patient(X))<=>wise(X)))&
(![X]:((wise(X)<~>generous(X))<=>funny(X)))&
(((~brave(alice)|creative(alice)))=>(?[X]:((strong(X)&~humble(X)))))&
(((generous(john)<~>~humble(john)))<=>(?[X]:(~tall(X))))&
(![X]:((curious(X)<~>~old(X))=>(~old(X)&patient(X))))&
(![X]:((wise(X)&~patient(X))<=>(curious(X)|quiet(X))))&
(![X]:((~curious(X)<~>~tall(X))<=>(~humble(X)|happy(X))))&
(?[X]:((~curious(X)&tall(X))))&
(?[X]:((patient(X)|calm(X))))&
((patient(alice)|happy(alice)))&
(?[X]:((~brave(X)<~>patient(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~strong(X)&old(X)))) | ~old(paul) | [
"p0",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8246030287291086038212538
% SZS output start Proof for 8246030287291086038212538
1. ! [X0] : ((calm(X0) & quiet(X0)) <=> (~rich(X0) | ~curious(X0))) [input p0]
10. ! [X0] : ((~curious(X0) <~> patient(X0)) <=> wise(X0)) [input p9]
14. ! [X0] : ((curious(X0) <~> ~old(X0)) => (patient(X0) & ~old(X0))) [input p13]
15. ! [X0] : ((~patient(X0) & wise(X0)) <=> (quiet(X0) | curious(X0))) [input p14]
23. ~old(paul) [input hypothesis]
28. ! [X0] : ((patient(X0) & ~old(X0)) | (curious(X0) <=> ~old(X0))) [ennf transformation 14]
29. ! [X0] : (((calm(X0) & quiet(X0)) | (rich(X0) & curious(X0))) & ((~rich(X0) | ~curious(X0)) | (~calm(X0) | ~quiet(X0)))) [nnf transformation 1]
30. ! [X0] : (((calm(X0) & quiet(X0)) | (rich(X0) & curious(X0))) & (~rich(X0) | ~curious(X0) | ~calm(X0) | ~quiet(X0))) [flattening 29]
43. ! [X0] : ((((~patient(X0) | curious(X0)) & (patient(X0) | ~curious(X0))) | ~wise(X0)) & (wise(X0) | ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0))))) [nnf transformation 10]
50. ! [X0] : ((patient(X0) & ~old(X0)) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) [nnf transformation 28]
51. ! [X0] : (((~patient(X0) & wise(X0)) | (~quiet(X0) & ~curious(X0))) & ((quiet(X0) | curious(X0)) | (patient(X0) | ~wise(X0)))) [nnf transformation 15]
52. ! [X0] : (((~patient(X0) & wise(X0)) | (~quiet(X0) & ~curious(X0))) & (quiet(X0) | curious(X0) | patient(X0) | ~wise(X0))) [flattening 51]
67. curious(X0) | quiet(X0) [cnf transformation 30]
103. ~wise(X0) | ~curious(X0) | patient(X0) [cnf transformation 43]
104. ~patient(X0) | curious(X0) | ~wise(X0) [cnf transformation 43]
116. patient(X0) | curious(X0) | old(X0) [cnf transformation 50]
118. ~curious(X0) | wise(X0) [cnf transformation 52]
119. ~quiet(X0) | wise(X0) [cnf transformation 52]
120. ~patient(X0) | ~curious(X0) [cnf transformation 52]
137. ~old(paul) [cnf transformation 23]
259. wise(X1) | quiet(X1) [resolution 118,67]
260. wise(X1) [subsumption resolution 259,119]
352. ~curious(X1) | patient(X1) [resolution 103,260]
355. ~curious(X1) [subsumption resolution 352,120]
375. curious(X0) | old(X0) | curious(X0) | ~wise(X0) [resolution 116,104]
383. curious(X0) | old(X0) | ~wise(X0) [duplicate literal removal 375]
384. old(X0) | ~wise(X0) [subsumption resolution 383,355]
385. old(X0) [subsumption resolution 384,260]
386. $false [resolution 385,137]
% SZS output end Proof for 8246030287291086038212538
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or happy then lucy is creative and vice versa. Everyone who is humble is both not rich and not patient. If fred is not strong then someone is brave or not calm. Everyone who is wise or brave is both not brave and not kind. Everyone who is both not old and calm is both not brave and not strong. Everyone who is quiet or not strong is not wise and vice versa. If john is both creative and not calm then lucy is not kind or quiet and vice versa. Everyone who is strong or quiet is both not humble and not brave and vice versa. If susan is funny then mary is either humble or funny and vice versa. Everyone who is happy is patient. If someone is both not wise and not strong then fred is quiet or wise. If someone is not funny then someone is both not strong and kind. If susan is not rich or not kind then mary is patient. Everyone who is not old is generous or funny and vice versa. Everyone who is either rich or generous is not rich. Everyone who is either generous or brave is generous or not patient and vice versa. Mary is calm. Alice is not creative. Paul is happy or wise. Someone is wise. Someone is either humble or not humble. Lucy is not brave. Alice is not curious or funny. Paul is either creative or calm. | John is brave. | contradiction | (((~patient(paul)<~>happy(paul)))<=>(creative(lucy)))&
(![X]:(humble(X)=>(~rich(X)&~patient(X))))&
((~strong(fred))=>(?[X]:((brave(X)|~calm(X)))))&
(![X]:((wise(X)|brave(X))=>(~brave(X)&~kind(X))))&
(![X]:((~old(X)&calm(X))=>(~brave(X)&~strong(X))))&
(![X]:((quiet(X)|~strong(X))<=>~wise(X)))&
(((creative(john)&~calm(john)))<=>((~kind(lucy)|quiet(lucy))))&
(![X]:((strong(X)|quiet(X))<=>(~humble(X)&~brave(X))))&
((funny(susan))<=>((humble(mary)<~>funny(mary))))&
(![X]:(happy(X)=>patient(X)))&
((?[X]:((~wise(X)&~strong(X))))=>((quiet(fred)|wise(fred))))&
((?[X]:(~funny(X)))=>(?[X]:((~strong(X)&kind(X)))))&
(((~rich(susan)|~kind(susan)))=>(patient(mary)))&
(![X]:(~old(X)<=>(generous(X)|funny(X))))&
(![X]:((rich(X)<~>generous(X))=>~rich(X)))&
(![X]:((generous(X)<~>brave(X))<=>(generous(X)|~patient(X))))&
(calm(mary))&
(~creative(alice))&
((happy(paul)|wise(paul)))&
(?[X]:(wise(X)))&
(?[X]:((humble(X)<~>~humble(X))))&
(~brave(lucy))&
((~curious(alice)|funny(alice)))&
((creative(paul)<~>calm(paul))) | brave(john) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 2436686780419764299637374
% SZS output start Proof for 2436686780419764299637374
4. ! [X0] : ((brave(X0) | wise(X0)) => (~kind(X0) & ~brave(X0))) [input p3]
25. brave(john) [input hypothesis]
31. ! [X0] : ((~kind(X0) & ~brave(X0)) | (~brave(X0) & ~wise(X0))) [ennf transformation 4]
71. ~brave(X0) | ~brave(X0) [cnf transformation 31]
118. brave(john) [cnf transformation 25]
122. ~brave(X0) [duplicate literal removal 71]
246. $false [subsumption resolution 118,122]
% SZS output end Proof for 2436686780419764299637374
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either curious or not patient then someone is strong or generous and vice versa.
Everyone who is not calm or quiet is either curious or kind.
If someone is wise then lucy is wise and vice versa.
Everyone who is both not tall and not humble is both not wise and not creative and vice versa.
Everyone who is not patient is both generous and humble and vice versa.
If someone is both not brave and not calm then someone is either not brave or happy and vice versa.
Everyone who is not curious or not kind is both not rich and not funny.
If susan is happy then someone is not patient or patient and vice versa.
If fred is old or generous then someone is both quiet and not happy.
If someone is not funny or not happy then mary is not creative or not curious.
Everyone who is either not kind or not calm is wise or not wise and vice versa.
Everyone who is not happy is either curious or not creative.
If someone is humble or creative then someone is both rich and not old.
Everyone who is either not brave or not kind is either not rich or brave.
Everyone who is not tall is not creative and vice versa.
Everyone who is not calm is not patient or wise and vice versa.
Fred is either not patient or not creative.
Someone is both not brave and not funny.
Someone is not brave.
Someone is either not kind or not quiet.
Someone is both not curious and not rich. | Mary is brave. | contradiction | (((curious(lucy)<~>~patient(lucy)))<=>(?[X]:((strong(X)|generous(X)))))&
(![X]:((~calm(X)|quiet(X))=>(curious(X)<~>kind(X))))&
((?[X]:(wise(X)))<=>(wise(lucy)))&
(![X]:((~tall(X)&~humble(X))<=>(~wise(X)&~creative(X))))&
(![X]:(~patient(X)<=>(generous(X)&humble(X))))&
((?[X]:((~brave(X)&~calm(X))))<=>(?[X]:((~brave(X)<~>happy(X)))))&
(![X]:((~curious(X)|~kind(X))=>(~rich(X)&~funny(X))))&
((happy(susan))<=>(?[X]:((~patient(X)|patient(X)))))&
(((old(fred)|generous(fred)))=>(?[X]:((quiet(X)&~happy(X)))))&
((?[X]:((~funny(X)|~happy(X))))=>((~creative(mary)|~curious(mary))))&
(![X]:((~kind(X)<~>~calm(X))<=>(wise(X)|~wise(X))))&
(![X]:(~happy(X)=>(curious(X)<~>~creative(X))))&
((?[X]:((humble(X)|creative(X))))=>(?[X]:((rich(X)&~old(X)))))&
(![X]:((~brave(X)<~>~kind(X))=>(~rich(X)<~>brave(X))))&
(![X]:(~tall(X)<=>~creative(X)))&
(![X]:(~calm(X)<=>(~patient(X)|wise(X))))&
((~patient(fred)<~>~creative(fred)))&
(?[X]:((~brave(X)&~funny(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~kind(X)<~>~quiet(X))))&
(?[X]:((~curious(X)&~rich(X)))) | brave(mary) | [
"p1",
"p2",
"p3",
"p4",
"p6",
"p10",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1376260893851005791801335
% SZS output start Proof for 1376260893851005791801335
2. ! [X0] : ((quiet(X0) | ~calm(X0)) => (curious(X0) <~> kind(X0))) [input p1]
3. ? [X0] : wise(X0) <=> wise(lucy) [input p2]
4. ! [X0] : ((~humble(X0) & ~tall(X0)) <=> (~creative(X0) & ~wise(X0))) [input p3]
5. ! [X0] : (~patient(X0) <=> (humble(X0) & generous(X0))) [input p4]
7. ! [X0] : ((~kind(X0) | ~curious(X0)) => (~funny(X0) & ~rich(X0))) [input p6]
11. ! [X0] : ((~kind(X0) <~> ~calm(X0)) <=> (~wise(X0) | wise(X0))) [input p10]
13. ? [X0] : (creative(X0) | humble(X0)) => ? [X0] : (~old(X0) & rich(X0)) [input p12]
14. ! [X0] : ((~brave(X0) <~> ~kind(X0)) => (~rich(X0) <~> brave(X0))) [input p13]
15. ! [X0] : (~tall(X0) <=> ~creative(X0)) [input p14]
16. ! [X0] : (~calm(X0) <=> (wise(X0) | ~patient(X0))) [input p15]
22. brave(mary) [input hypothesis]
24. ? [X0] : (creative(X0) | humble(X0)) => ? [X1] : (~old(X1) & rich(X1)) [rectify 13]
26. ? [X0] : (creative(X0) | humble(X0)) => ? [X1] : rich(X1) [pure predicate removal 24]
27. ! [X0] : ((curious(X0) <~> kind(X0)) | (~quiet(X0) & calm(X0))) [ennf transformation 2]
28. ! [X0] : ((~funny(X0) & ~rich(X0)) | (kind(X0) & curious(X0))) [ennf transformation 7]
33. ? [X1] : rich(X1) | ! [X0] : (~creative(X0) & ~humble(X0)) [ennf transformation 26]
34. ! [X0] : ((~rich(X0) <~> brave(X0)) | (~brave(X0) <=> ~kind(X0))) [ennf transformation 14]
39. ! [X0] : (((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | (~quiet(X0) & calm(X0))) [nnf transformation 27]
40. (? [X0] : wise(X0) | ~wise(lucy)) & (wise(lucy) | ! [X0] : ~wise(X0)) [nnf transformation 3]
41. (? [X0] : wise(X0) | ~wise(lucy)) & (wise(lucy) | ! [X1] : ~wise(X1)) [rectify 40]
42. ? [X0] : wise(X0) => wise(sK1) [choice axiom]
43. (wise(sK1) | ~wise(lucy)) & (wise(lucy) | ! [X1] : ~wise(X1)) [skolemisation 41,42]
44. ! [X0] : (((~humble(X0) & ~tall(X0)) | (creative(X0) | wise(X0))) & ((~creative(X0) & ~wise(X0)) | (humble(X0) | tall(X0)))) [nnf transformation 4]
45. ! [X0] : (((~humble(X0) & ~tall(X0)) | creative(X0) | wise(X0)) & ((~creative(X0) & ~wise(X0)) | humble(X0) | tall(X0))) [flattening 44]
46. ! [X0] : ((~patient(X0) | (~humble(X0) | ~generous(X0))) & ((humble(X0) & generous(X0)) | patient(X0))) [nnf transformation 5]
47. ! [X0] : ((~patient(X0) | ~humble(X0) | ~generous(X0)) & ((humble(X0) & generous(X0)) | patient(X0))) [flattening 46]
59. ! [X0] : ((((calm(X0) | kind(X0)) & (~calm(X0) | ~kind(X0))) | (wise(X0) & ~wise(X0))) & ((~wise(X0) | wise(X0)) | ((~kind(X0) | calm(X0)) & (~calm(X0) | kind(X0))))) [nnf transformation 11]
60. ! [X0] : ((((calm(X0) | kind(X0)) & (~calm(X0) | ~kind(X0))) | (wise(X0) & ~wise(X0))) & (~wise(X0) | wise(X0) | ((~kind(X0) | calm(X0)) & (~calm(X0) | kind(X0))))) [flattening 59]
62. ? [X0] : rich(X0) | ! [X1] : (~creative(X1) & ~humble(X1)) [rectify 33]
63. ? [X0] : rich(X0) => rich(sK6) [choice axiom]
64. rich(sK6) | ! [X1] : (~creative(X1) & ~humble(X1)) [skolemisation 62,63]
65. ! [X0] : (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | ((~brave(X0) | kind(X0)) & (~kind(X0) | brave(X0)))) [nnf transformation 34]
66. ! [X0] : ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))) [nnf transformation 15]
67. ! [X0] : ((~calm(X0) | (~wise(X0) & patient(X0))) & ((wise(X0) | ~patient(X0)) | calm(X0))) [nnf transformation 16]
68. ! [X0] : ((~calm(X0) | (~wise(X0) & patient(X0))) & (wise(X0) | ~patient(X0) | calm(X0))) [flattening 67]
87. ~kind(X0) | ~curious(X0) | calm(X0) [cnf transformation 39]
89. wise(lucy) | ~wise(X1) [cnf transformation 43]
91. ~wise(X0) | humble(X0) | tall(X0) [cnf transformation 45]
96. humble(X0) | patient(X0) [cnf transformation 47]
104. ~rich(X0) | curious(X0) [cnf transformation 28]
105. ~rich(X0) | kind(X0) [cnf transformation 28]
117. ~calm(X0) | ~kind(X0) | ~wise(X0) [cnf transformation 60]
118. ~kind(X0) | ~calm(X0) | wise(X0) [cnf transformation 60]
119. calm(X0) | kind(X0) | ~wise(X0) [cnf transformation 60]
120. wise(X0) | kind(X0) | calm(X0) [cnf transformation 60]
123. rich(sK6) | ~humble(X1) [cnf transformation 64]
124. rich(sK6) | ~creative(X1) [cnf transformation 64]
128. ~brave(X0) | rich(X0) | ~brave(X0) | kind(X0) [cnf transformation 65]
130. ~tall(X0) | creative(X0) [cnf transformation 66]
131. ~patient(X0) | wise(X0) | calm(X0) [cnf transformation 68]
143. brave(mary) [cnf transformation 22]
145. ~brave(X0) | rich(X0) | kind(X0) [duplicate literal removal 128]
175. 7 <=> wise(lucy) [avatar definition]
176. wise(lucy) <- (7) [avatar component clause 175]
184. 9 <=> ! [X1] : ~wise(X1) [avatar definition]
185. ~wise(X1) <- (9) [avatar component clause 184]
186. 9 | 7 [avatar split clause 89,175,184]
227. 19 <=> ! [X0] : patient(X0) [avatar definition]
228. patient(X0) <- (19) [avatar component clause 227]
260. kind(X0) | calm(X0) [subsumption resolution 119,120]
261. ~kind(X0) | ~calm(X0) [subsumption resolution 117,118]
263. 27 <=> ! [X1] : ~creative(X1) [avatar definition]
264. ~creative(X1) <- (27) [avatar component clause 263]
266. 28 <=> rich(sK6) [avatar definition]
268. rich(sK6) <- (28) [avatar component clause 266]
269. 27 | 28 [avatar split clause 124,266,263]
271. 29 <=> ! [X1] : ~humble(X1) [avatar definition]
272. ~humble(X1) <- (29) [avatar component clause 271]
273. 29 | 28 [avatar split clause 123,266,271]
274. ~brave(X0) | kind(X0) [subsumption resolution 145,105]
297. curious(sK6) <- (28) [resolution 104,268]
298. kind(sK6) <- (28) [resolution 105,268]
302. ~calm(sK6) <- (28) [resolution 261,298]
304. kind(mary) [resolution 274,143]
306. ~calm(mary) [resolution 304,261]
310. ~curious(X1) | calm(X1) | calm(X1) [resolution 87,260]
314. ~curious(X1) | calm(X1) [duplicate literal removal 310]
322. humble(lucy) | tall(lucy) <- (7) [resolution 91,176]
325. 34 <=> tall(lucy) [avatar definition]
327. tall(lucy) <- (34) [avatar component clause 325]
329. 35 <=> humble(lucy) [avatar definition]
331. humble(lucy) <- (35) [avatar component clause 329]
332. 34 | 35 | ~7 [avatar split clause 322,175,329,325]
342. calm(sK6) <- (28) [resolution 314,297]
343. $false <- (28) [subsumption resolution 342,302]
344. ~28 [avatar contradiction clause 343]
345. patient(X0) <- (29) [resolution 272,96]
346. $false <- (29, 35) [resolution 272,331]
349. ~29 | ~35 [avatar contradiction clause 346]
350. 19 | ~29 [avatar split clause 345,271,227]
366. wise(X0) | calm(X0) <- (19) [resolution 131,228]
368. calm(X0) <- (9, 19) [subsumption resolution 366,185]
371. $false <- (9, 19) [resolution 368,306]
376. ~9 | ~19 [avatar contradiction clause 371]
382. creative(lucy) <- (34) [resolution 327,130]
383. $false <- (27, 34) [subsumption resolution 382,264]
384. ~27 | ~34 [avatar contradiction clause 383]
385. $false [avatar sat refutation 186,269,273,332,344,349,350,376,384]
% SZS output end Proof for 1376260893851005791801335
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is generous and vice versa.
If someone is rich then someone is not funny.
Everyone who is both not calm and not generous is not brave or quiet.
If alice is either not wise or strong then paul is both brave and creative.
Everyone who is both calm and patient is both not generous and not patient.
Everyone who is kind or not strong is both quiet and not happy.
If mary is not old or strong then someone is not brave or tall and vice versa.
If alice is either calm or not curious then john is strong.
If alice is happy then someone is either not kind or patient and vice versa.
Everyone who is both happy and generous is both happy and curious and vice versa.
Everyone who is either wise or not humble is both humble and not patient.
Everyone who is either funny or strong is either not tall or funny.
Everyone who is not happy is brave.
Everyone who is not strong or not quiet is both rich and happy.
Everyone who is both calm and not curious is either strong or kind and vice versa.
If mary is not funny then mary is either not humble or creative.
Someone is rich.
Someone is either not wise or not strong.
Someone is wise.
Someone is not quiet or creative.
Alice is either not wise or not creative.
Mary is not creative or not old.
Susan is both not generous and not humble. | Mary is not funny. | neutral | (![X]:(~kind(X)<=>generous(X)))&
((?[X]:(rich(X)))=>(?[X]:(~funny(X))))&
(![X]:((~calm(X)&~generous(X))=>(~brave(X)|quiet(X))))&
(((~wise(alice)<~>strong(alice)))=>((brave(paul)&creative(paul))))&
(![X]:((calm(X)&patient(X))=>(~generous(X)&~patient(X))))&
(![X]:((kind(X)|~strong(X))=>(quiet(X)&~happy(X))))&
(((~old(mary)|strong(mary)))<=>(?[X]:((~brave(X)|tall(X)))))&
(((calm(alice)<~>~curious(alice)))=>(strong(john)))&
((happy(alice))<=>(?[X]:((~kind(X)<~>patient(X)))))&
(![X]:((happy(X)&generous(X))<=>(happy(X)&curious(X))))&
(![X]:((wise(X)<~>~humble(X))=>(humble(X)&~patient(X))))&
(![X]:((funny(X)<~>strong(X))=>(~tall(X)<~>funny(X))))&
(![X]:(~happy(X)=>brave(X)))&
(![X]:((~strong(X)|~quiet(X))=>(rich(X)&happy(X))))&
(![X]:((calm(X)&~curious(X))<=>(strong(X)<~>kind(X))))&
((~funny(mary))=>((~humble(mary)<~>creative(mary))))&
(?[X]:(rich(X)))&
(?[X]:((~wise(X)<~>~strong(X))))&
(?[X]:(wise(X)))&
(?[X]:((~quiet(X)|creative(X))))&
((~wise(alice)<~>~creative(alice)))&
((~creative(mary)|~old(mary)))&
((~generous(susan)&~humble(susan))) | ~funny(mary) | [] | null | 0 |
If someone is not kind then john is either kind or brave and vice versa. If paul is both generous and not quiet then someone is both not happy and wise and vice versa. If susan is either kind or tall then lucy is either rich or generous. Everyone who is quiet is both not generous and calm. If someone is either not old or happy then mary is both not calm and generous and vice versa. Everyone who is either quiet or not funny is not humble or not creative and vice versa. Everyone who is curious is not generous or not humble and vice versa. Everyone who is not brave or kind is creative or not patient and vice versa. Everyone who is funny is either generous or calm and vice versa. Everyone who is wise or not calm is either creative or old and vice versa. Everyone who is either not humble or generous is not rich or brave and vice versa. If fred is both not tall and tall then someone is not funny. Everyone who is either tall or happy is quiet or tall and vice versa. Everyone who is either not generous or not kind is tall or not tall and vice versa. Everyone who is both not humble and creative is either not calm or brave. If someone is not curious then john is happy or not tall. Someone is not kind or not creative. Someone is either tall or generous. Lucy is not calm or rich. Someone is both not funny and not happy. Lucy is both brave and not generous. Someone is wise or brave. Someone is wise. | John is not patient. | neutral | ((?[X]:(~kind(X)))<=>((kind(john)<~>brave(john))))&
(((generous(paul)&~quiet(paul)))<=>(?[X]:((~happy(X)&wise(X)))))&
(((kind(susan)<~>tall(susan)))=>((rich(lucy)<~>generous(lucy))))&
(![X]:(quiet(X)=>(~generous(X)&calm(X))))&
((?[X]:((~old(X)<~>happy(X))))<=>((~calm(mary)&generous(mary))))&
(![X]:((quiet(X)<~>~funny(X))<=>(~humble(X)|~creative(X))))&
(![X]:(curious(X)<=>(~generous(X)|~humble(X))))&
(![X]:((~brave(X)|kind(X))<=>(creative(X)|~patient(X))))&
(![X]:(funny(X)<=>(generous(X)<~>calm(X))))&
(![X]:((wise(X)|~calm(X))<=>(creative(X)<~>old(X))))&
(![X]:((~humble(X)<~>generous(X))<=>(~rich(X)|brave(X))))&
(((~tall(fred)&tall(fred)))=>(?[X]:(~funny(X))))&
(![X]:((tall(X)<~>happy(X))<=>(quiet(X)|tall(X))))&
(![X]:((~generous(X)<~>~kind(X))<=>(tall(X)|~tall(X))))&
(![X]:((~humble(X)&creative(X))=>(~calm(X)<~>brave(X))))&
((?[X]:(~curious(X)))=>((happy(john)|~tall(john))))&
(?[X]:((~kind(X)|~creative(X))))&
(?[X]:((tall(X)<~>generous(X))))&
((~calm(lucy)|rich(lucy)))&
(?[X]:((~funny(X)&~happy(X))))&
((brave(lucy)&~generous(lucy)))&
(?[X]:((wise(X)|brave(X))))&
(?[X]:(wise(X))) | ~patient(john) | [] | null | 0 |
Everyone who is patient is not old and vice versa.
Everyone who is not calm or generous is not rich or not humble and vice versa.
Everyone who is not strong is both happy and quiet.
Everyone who is funny is not calm and vice versa.
Everyone who is wise is both not patient and not curious and vice versa.
Everyone who is both humble and not strong is strong and vice versa.
If someone is either not curious or patient then lucy is generous or not calm.
Everyone who is not tall is both not creative and not patient and vice versa.
If someone is curious or patient then paul is kind or funny and vice versa.
Everyone who is kind or old is not happy or patient and vice versa.
Everyone who is either not generous or tall is both funny and not humble and vice versa.
If mary is not generous or kind then alice is brave and vice versa.
Everyone who is either not tall or creative is both humble and old.
Everyone who is either kind or rich is either not quiet or tall.
If someone is not generous then someone is not strong.
Susan is both tall and not wise.
Mary is not humble.
Someone is patient or brave.
Paul is calm or not strong. | Lucy is rich. | neutral | (![X]:(patient(X)<=>~old(X)))&
(![X]:((~calm(X)|generous(X))<=>(~rich(X)|~humble(X))))&
(![X]:(~strong(X)=>(happy(X)&quiet(X))))&
(![X]:(funny(X)<=>~calm(X)))&
(![X]:(wise(X)<=>(~patient(X)&~curious(X))))&
(![X]:((humble(X)&~strong(X))<=>strong(X)))&
((?[X]:((~curious(X)<~>patient(X))))=>((generous(lucy)|~calm(lucy))))&
(![X]:(~tall(X)<=>(~creative(X)&~patient(X))))&
((?[X]:((curious(X)|patient(X))))<=>((kind(paul)|funny(paul))))&
(![X]:((kind(X)|old(X))<=>(~happy(X)|patient(X))))&
(![X]:((~generous(X)<~>tall(X))<=>(funny(X)&~humble(X))))&
(((~generous(mary)|kind(mary)))<=>(brave(alice)))&
(![X]:((~tall(X)<~>creative(X))=>(humble(X)&old(X))))&
(![X]:((kind(X)<~>rich(X))=>(~quiet(X)<~>tall(X))))&
((?[X]:(~generous(X)))=>(?[X]:(~strong(X))))&
((tall(susan)&~wise(susan)))&
(~humble(mary))&
(?[X]:((patient(X)|brave(X))))&
((calm(paul)|~strong(paul))) | rich(lucy) | [] | null | 0 |
If susan is not strong then someone is either old or not patient.
If someone is either not creative or happy then someone is happy or not old.
Everyone who is either not strong or funny is quiet and vice versa.
If someone is either brave or old then fred is not strong or creative.
If mary is not tall or not generous then someone is either brave or calm.
Everyone who is not brave is either wise or not funny and vice versa.
If someone is not rich or not curious then someone is both not humble and not creative and vice versa.
If someone is wise then someone is not wise or strong.
If lucy is both creative and not rich then someone is brave.
If someone is funny then someone is wise and vice versa.
Everyone who is both funny and kind is not wise.
If someone is not calm or kind then someone is strong.
Everyone who is both not tall and not rich is either tall or curious.
Everyone who is either not old or not quiet is brave or not curious and vice versa.
Everyone who is not kind is either not generous or not brave and vice versa.
Everyone who is either funny or curious is not funny and vice versa.
Someone is both not strong and not happy.
Someone is either old or wise.
Someone is quiet or not funny.
Mary is not patient.
Someone is not generous or humble.
Fred is wise.
Someone is either not strong or humble.
John is either funny or not tall. | Mary is curious. | entailment | ((~strong(susan))=>(?[X]:((old(X)<~>~patient(X)))))&
((?[X]:((~creative(X)<~>happy(X))))=>(?[X]:((happy(X)|~old(X)))))&
(![X]:((~strong(X)<~>funny(X))<=>quiet(X)))&
((?[X]:((brave(X)<~>old(X))))=>((~strong(fred)|creative(fred))))&
(((~tall(mary)|~generous(mary)))=>(?[X]:((brave(X)<~>calm(X)))))&
(![X]:(~brave(X)<=>(wise(X)<~>~funny(X))))&
((?[X]:((~rich(X)|~curious(X))))<=>(?[X]:((~humble(X)&~creative(X)))))&
((?[X]:(wise(X)))=>(?[X]:((~wise(X)|strong(X)))))&
(((creative(lucy)&~rich(lucy)))=>(?[X]:(brave(X))))&
((?[X]:(funny(X)))<=>(?[X]:(wise(X))))&
(![X]:((funny(X)&kind(X))=>~wise(X)))&
((?[X]:((~calm(X)|kind(X))))=>(?[X]:(strong(X))))&
(![X]:((~tall(X)&~rich(X))=>(tall(X)<~>curious(X))))&
(![X]:((~old(X)<~>~quiet(X))<=>(brave(X)|~curious(X))))&
(![X]:(~kind(X)<=>(~generous(X)<~>~brave(X))))&
(![X]:((funny(X)<~>curious(X))<=>~funny(X)))&
(?[X]:((~strong(X)&~happy(X))))&
(?[X]:((old(X)<~>wise(X))))&
(?[X]:((quiet(X)|~funny(X))))&
(~patient(mary))&
(?[X]:((~generous(X)|humble(X))))&
(wise(fred))&
(?[X]:((~strong(X)<~>humble(X))))&
((funny(john)<~>~tall(john))) | curious(mary) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2445174568948972313468588
% SZS output start Proof for 2445174568948972313468588
16. ! [X0] : ((funny(X0) <~> curious(X0)) <=> ~funny(X0)) [input p15]
25. ~curious(mary) [input hypothesis]
81. ! [X0] : ((((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | funny(X0)) & (~funny(X0) | ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0))))) [nnf transformation 16]
135. ~funny(X0) | curious(X0) | ~funny(X0) [cnf transformation 81]
137. curious(X0) | funny(X0) | funny(X0) [cnf transformation 81]
151. ~curious(mary) [cnf transformation 25]
152. ~funny(X0) | curious(X0) [duplicate literal removal 135]
153. curious(X0) | funny(X0) [duplicate literal removal 137]
234. 19 <=> ! [X3] : curious(X3) [avatar definition]
235. curious(X3) <- (19) [avatar component clause 234]
301. curious(X0) [subsumption resolution 152,153]
302. 19 [avatar split clause 301,234]
351. $false <- (19) [resolution 235,151]
352. ~19 [avatar contradiction clause 351]
353. $false [avatar sat refutation 302,352]
% SZS output end Proof for 2445174568948972313468588
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both not brave and quiet then alice is both not calm and creative. Everyone who is not quiet is not strong and vice versa. If someone is not creative then alice is either not strong or old. If someone is either calm or quiet then lucy is not generous. Everyone who is either rich or not brave is both humble and not creative. If fred is old or not humble then susan is either generous or curious. Everyone who is not creative or kind is not calm or not creative and vice versa. Everyone who is either brave or not happy is both not wise and not rich. If someone is not calm then lucy is either curious or not calm. Everyone who is rich or not strong is either not kind or kind and vice versa. If someone is either not strong or not wise then someone is either not wise or not tall. Everyone who is both not rich and not happy is either not brave or not funny and vice versa. If lucy is both not wise and wise then paul is either not generous or not funny and vice versa. If someone is not curious then someone is not brave or not patient and vice versa. If paul is tall or not kind then someone is old and vice versa. Everyone who is not brave or strong is both not happy and patient and vice versa. Paul is strong. Alice is not old. Someone is both humble and quiet. Mary is either brave or strong. Mary is brave or not calm. Someone is creative or not kind. Paul is quiet. Fred is not happy or not patient. | Mary is not quiet. | entailment | (((~brave(alice)&quiet(alice)))=>((~calm(alice)&creative(alice))))&
(![X]:(~quiet(X)<=>~strong(X)))&
((?[X]:(~creative(X)))=>((~strong(alice)<~>old(alice))))&
((?[X]:((calm(X)<~>quiet(X))))=>(~generous(lucy)))&
(![X]:((rich(X)<~>~brave(X))=>(humble(X)&~creative(X))))&
(((old(fred)|~humble(fred)))=>((generous(susan)<~>curious(susan))))&
(![X]:((~creative(X)|kind(X))<=>(~calm(X)|~creative(X))))&
(![X]:((brave(X)<~>~happy(X))=>(~wise(X)&~rich(X))))&
((?[X]:(~calm(X)))=>((curious(lucy)<~>~calm(lucy))))&
(![X]:((rich(X)|~strong(X))<=>(~kind(X)<~>kind(X))))&
((?[X]:((~strong(X)<~>~wise(X))))=>(?[X]:((~wise(X)<~>~tall(X)))))&
(![X]:((~rich(X)&~happy(X))<=>(~brave(X)<~>~funny(X))))&
(((~wise(lucy)&wise(lucy)))<=>((~generous(paul)<~>~funny(paul))))&
((?[X]:(~curious(X)))<=>(?[X]:((~brave(X)|~patient(X)))))&
(((tall(paul)|~kind(paul)))<=>(?[X]:(old(X))))&
(![X]:((~brave(X)|strong(X))<=>(~happy(X)&patient(X))))&
(strong(paul))&
(~old(alice))&
(?[X]:((humble(X)&quiet(X))))&
((brave(mary)<~>strong(mary)))&
((brave(mary)|~calm(mary)))&
(?[X]:((creative(X)|~kind(X))))&
(quiet(paul))&
((~happy(fred)|~patient(fred))) | ~quiet(mary) | [
"p1",
"p7",
"p9",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4801833732545574654667539
% SZS output start Proof for 4801833732545574654667539
2. ! [X0] : (~quiet(X0) <=> ~strong(X0)) [input p1]
8. ! [X0] : ((brave(X0) <~> ~happy(X0)) => (~rich(X0) & ~wise(X0))) [input p7]
10. ! [X0] : ((~strong(X0) | rich(X0)) <=> (~kind(X0) <~> kind(X0))) [input p9]
16. ! [X0] : ((strong(X0) | ~brave(X0)) <=> (patient(X0) & ~happy(X0))) [input p15]
20. brave(mary) <~> strong(mary) [input p19]
25. quiet(mary) [input hypothesis]
37. ! [X0] : ((~rich(X0) & ~wise(X0)) | (brave(X0) <=> ~happy(X0))) [ennf transformation 8]
40. ! [X0] : ((~quiet(X0) | strong(X0)) & (~strong(X0) | quiet(X0))) [nnf transformation 2]
47. ! [X0] : ((~rich(X0) & ~wise(X0)) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0)))) [nnf transformation 37]
49. ! [X0] : (((~strong(X0) | rich(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | (strong(X0) & ~rich(X0)))) [nnf transformation 10]
50. ! [X0] : ((~strong(X0) | rich(X0) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | (strong(X0) & ~rich(X0)))) [flattening 49]
69. ! [X0] : (((strong(X0) | ~brave(X0)) | (~patient(X0) | happy(X0))) & ((patient(X0) & ~happy(X0)) | (~strong(X0) & brave(X0)))) [nnf transformation 16]
70. ! [X0] : ((strong(X0) | ~brave(X0) | ~patient(X0) | happy(X0)) & ((patient(X0) & ~happy(X0)) | (~strong(X0) & brave(X0)))) [flattening 69]
73. (~strong(mary) | ~brave(mary)) & (strong(mary) | brave(mary)) [nnf transformation 20]
79. ~quiet(X0) | strong(X0) [cnf transformation 40]
95. ~rich(X0) | brave(X0) | happy(X0) [cnf transformation 47]
102. ~strong(X0) | rich(X0) | kind(X0) | kind(X0) [cnf transformation 50]
103. ~strong(X0) | rich(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 50]
126. ~happy(X0) | brave(X0) [cnf transformation 70]
135. ~strong(mary) | ~brave(mary) [cnf transformation 73]
140. quiet(mary) [cnf transformation 25]
141. ~strong(X0) | rich(X0) | kind(X0) [duplicate literal removal 102]
142. ~strong(X0) | rich(X0) | ~kind(X0) [duplicate literal removal 103]
213. ~strong(X0) | rich(X0) [subsumption resolution 141,142]
293. 34 <=> brave(mary) [avatar definition]
295. ~brave(mary) <- (~34) [avatar component clause 293]
297. 35 <=> strong(mary) [avatar definition]
298. strong(mary) <- (35) [avatar component clause 297]
300. ~34 | ~35 [avatar split clause 135,297,293]
328. strong(mary) [resolution 79,140]
331. 35 [avatar split clause 328,297]
340. rich(mary) <- (35) [resolution 213,298]
369. brave(mary) | happy(mary) <- (35) [resolution 95,340]
373. happy(mary) <- (~34, 35) [subsumption resolution 369,295]
387. brave(mary) <- (~34, 35) [resolution 373,126]
390. $false <- (~34, 35) [subsumption resolution 387,295]
391. 34 | ~35 [avatar contradiction clause 390]
392. $false [avatar sat refutation 300,331,391]
% SZS output end Proof for 4801833732545574654667539
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or quiet is both happy and patient and vice versa.
Everyone who is rich is either calm or not brave.
Everyone who is either not old or not kind is not wise.
Everyone who is not calm is both not wise and not kind.
Everyone who is both happy and not wise is both rich and not humble.
Everyone who is funny or brave is both not calm and calm.
If someone is either rich or curious then john is both funny and not humble and vice versa.
If john is creative or calm then fred is either kind or calm.
Everyone who is not generous is both strong and not old.
Everyone who is either quiet or generous is either funny or not humble and vice versa.
If paul is old then someone is either not happy or patient and vice versa.
Everyone who is creative is tall or humble and vice versa.
Everyone who is both not curious and not brave is either patient or brave.
If john is humble then someone is either strong or brave and vice versa.
If someone is not patient or kind then someone is both not rich and quiet.
If someone is creative then paul is kind.
Mary is either quiet or not wise.
Someone is strong or not curious.
Someone is wise.
Someone is either not rich or not calm.
Someone is either not strong or not brave.
Paul is both creative and happy. | Fred is not patient. | contradiction | (![X]:((wise(X)|quiet(X))<=>(happy(X)&patient(X))))&
(![X]:(rich(X)=>(calm(X)<~>~brave(X))))&
(![X]:((~old(X)<~>~kind(X))=>~wise(X)))&
(![X]:(~calm(X)=>(~wise(X)&~kind(X))))&
(![X]:((happy(X)&~wise(X))=>(rich(X)&~humble(X))))&
(![X]:((funny(X)|brave(X))=>(~calm(X)&calm(X))))&
((?[X]:((rich(X)<~>curious(X))))<=>((funny(john)&~humble(john))))&
(((creative(john)|calm(john)))=>((kind(fred)<~>calm(fred))))&
(![X]:(~generous(X)=>(strong(X)&~old(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(funny(X)<~>~humble(X))))&
((old(paul))<=>(?[X]:((~happy(X)<~>patient(X)))))&
(![X]:(creative(X)<=>(tall(X)|humble(X))))&
(![X]:((~curious(X)&~brave(X))=>(patient(X)<~>brave(X))))&
((humble(john))<=>(?[X]:((strong(X)<~>brave(X)))))&
((?[X]:((~patient(X)|kind(X))))=>(?[X]:((~rich(X)&quiet(X)))))&
((?[X]:(creative(X)))=>(kind(paul)))&
((quiet(mary)<~>~wise(mary)))&
(?[X]:((strong(X)|~curious(X))))&
(?[X]:(wise(X)))&
(?[X]:((~rich(X)<~>~calm(X))))&
(?[X]:((~strong(X)<~>~brave(X))))&
((creative(paul)&happy(paul))) | ~patient(fred) | [
"p1",
"p3",
"p5",
"p6",
"p7",
"p11",
"p12",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4708376964713014514325776
% SZS output start Proof for 4708376964713014514325776
2. ! [X0] : (rich(X0) => (calm(X0) <~> ~brave(X0))) [input p1]
4. ! [X0] : (~calm(X0) => (~kind(X0) & ~wise(X0))) [input p3]
6. ! [X0] : ((brave(X0) | funny(X0)) => (calm(X0) & ~calm(X0))) [input p5]
7. ? [X0] : (rich(X0) <~> curious(X0)) <=> (~humble(john) & funny(john)) [input p6]
8. (calm(john) | creative(john)) => (kind(fred) <~> calm(fred)) [input p7]
12. ! [X0] : (creative(X0) <=> (humble(X0) | tall(X0))) [input p11]
13. ! [X0] : ((~brave(X0) & ~curious(X0)) => (patient(X0) <~> brave(X0))) [input p12]
14. humble(john) <=> ? [X0] : (strong(X0) <~> brave(X0)) [input p13]
21. ? [X0] : (~strong(X0) <~> ~brave(X0)) [input p20]
23. ~patient(fred) [input hypothesis]
25. ! [X0] : ((calm(X0) <~> ~brave(X0)) | ~rich(X0)) [ennf transformation 2]
27. ! [X0] : ((~kind(X0) & ~wise(X0)) | calm(X0)) [ennf transformation 4]
30. ! [X0] : ((calm(X0) & ~calm(X0)) | (~brave(X0) & ~funny(X0))) [ennf transformation 6]
31. (kind(fred) <~> calm(fred)) | (~calm(john) & ~creative(john)) [ennf transformation 8]
33. ! [X0] : ((patient(X0) <~> brave(X0)) | (brave(X0) | curious(X0))) [ennf transformation 13]
34. ! [X0] : ((patient(X0) <~> brave(X0)) | brave(X0) | curious(X0)) [flattening 33]
39. ! [X0] : (((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | ~rich(X0)) [nnf transformation 25]
41. (? [X0] : ((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | (humble(john) | ~funny(john))) & ((~humble(john) & funny(john)) | ! [X0] : ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0)))) [nnf transformation 7]
42. (? [X0] : ((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | humble(john) | ~funny(john)) & ((~humble(john) & funny(john)) | ! [X0] : ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0)))) [flattening 41]
43. (? [X0] : ((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | humble(john) | ~funny(john)) & ((~humble(john) & funny(john)) | ! [X1] : ((rich(X1) | ~curious(X1)) & (curious(X1) | ~rich(X1)))) [rectify 42]
44. ? [X0] : ((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) => ((~curious(sK0) | ~rich(sK0)) & (curious(sK0) | rich(sK0))) [choice axiom]
45. (((~curious(sK0) | ~rich(sK0)) & (curious(sK0) | rich(sK0))) | humble(john) | ~funny(john)) & ((~humble(john) & funny(john)) | ! [X1] : ((rich(X1) | ~curious(X1)) & (curious(X1) | ~rich(X1)))) [skolemisation 43,44]
46. ((~calm(fred) | ~kind(fred)) & (calm(fred) | kind(fred))) | (~calm(john) & ~creative(john)) [nnf transformation 31]
52. ! [X0] : ((creative(X0) | (~humble(X0) & ~tall(X0))) & ((humble(X0) | tall(X0)) | ~creative(X0))) [nnf transformation 12]
53. ! [X0] : ((creative(X0) | (~humble(X0) & ~tall(X0))) & (humble(X0) | tall(X0) | ~creative(X0))) [flattening 52]
54. ! [X0] : (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | brave(X0) | curious(X0)) [nnf transformation 34]
55. (humble(john) | ! [X0] : ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0)))) & (? [X0] : ((~brave(X0) | ~strong(X0)) & (brave(X0) | strong(X0))) | ~humble(john)) [nnf transformation 14]
56. (humble(john) | ! [X0] : ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0)))) & (? [X1] : ((~brave(X1) | ~strong(X1)) & (brave(X1) | strong(X1))) | ~humble(john)) [rectify 55]
57. ? [X1] : ((~brave(X1) | ~strong(X1)) & (brave(X1) | strong(X1))) => ((~brave(sK2) | ~strong(sK2)) & (brave(sK2) | strong(sK2))) [choice axiom]
58. (humble(john) | ! [X0] : ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0)))) & (((~brave(sK2) | ~strong(sK2)) & (brave(sK2) | strong(sK2))) | ~humble(john)) [skolemisation 56,57]
70. ? [X0] : ((brave(X0) | strong(X0)) & (~brave(X0) | ~strong(X0))) [nnf transformation 21]
71. ? [X0] : ((brave(X0) | strong(X0)) & (~brave(X0) | ~strong(X0))) => ((brave(sK7) | strong(sK7)) & (~brave(sK7) | ~strong(sK7))) [choice axiom]
72. (brave(sK7) | strong(sK7)) & (~brave(sK7) | ~strong(sK7)) [skolemisation 70,71]
79. ~calm(X0) | brave(X0) | ~rich(X0) [cnf transformation 39]
83. ~kind(X0) | calm(X0) [cnf transformation 27]
86. ~calm(X0) | ~funny(X0) [cnf transformation 30]
87. ~calm(X0) | ~brave(X0) [cnf transformation 30]
88. ~funny(X0) | calm(X0) [cnf transformation 30]
89. ~brave(X0) | calm(X0) [cnf transformation 30]
91. funny(john) | rich(X1) | ~curious(X1) [cnf transformation 45]
96. calm(fred) | kind(fred) | ~creative(john) [cnf transformation 46]
116. ~humble(X0) | creative(X0) [cnf transformation 53]
117. brave(X0) | patient(X0) | brave(X0) | curious(X0) [cnf transformation 54]
121. humble(john) | brave(X0) | ~strong(X0) [cnf transformation 58]
135. brave(sK7) | strong(sK7) [cnf transformation 72]
138. ~patient(fred) [cnf transformation 23]
139. brave(X0) | patient(X0) | curious(X0) [duplicate literal removal 117]
140. ~brave(X0) [subsumption resolution 87,89]
141. ~funny(X0) [subsumption resolution 86,88]
143. 1 <=> ! [X1] : (rich(X1) | ~curious(X1)) [avatar definition]
144. ~curious(X1) | rich(X1) <- (1) [avatar component clause 143]
146. 2 <=> humble(john) [avatar definition]
147. humble(john) <- (2) [avatar component clause 146]
154. rich(X1) | ~curious(X1) [subsumption resolution 91,141]
155. 1 [avatar split clause 154,143]
170. 6 <=> creative(john) [avatar definition]
176. 7 <=> calm(fred) [avatar definition]
178. calm(fred) <- (7) [avatar component clause 176]
180. calm(fred) | ~creative(john) [subsumption resolution 96,83]
181. ~6 | 7 [avatar split clause 180,176,170]
208. curious(X0) | patient(X0) [subsumption resolution 139,140]
209. humble(john) | ~strong(X0) [subsumption resolution 121,140]
211. 13 <=> ! [X0] : ~strong(X0) [avatar definition]
212. ~strong(X0) <- (13) [avatar component clause 211]
213. 13 | 2 [avatar split clause 209,146,211]
275. strong(sK7) [subsumption resolution 135,140]
278. $false <- (13) [resolution 275,212]
279. ~13 [avatar contradiction clause 278]
287. creative(john) <- (2) [resolution 116,147]
290. 6 | ~2 [avatar split clause 287,146,170]
293. rich(X0) | patient(X0) <- (1) [resolution 208,144]
297. brave(fred) | ~rich(fred) <- (7) [resolution 79,178]
300. ~rich(fred) <- (7) [subsumption resolution 297,140]
375. patient(fred) <- (1, 7) [resolution 293,300]
379. $false <- (1, 7) [subsumption resolution 375,138]
380. ~1 | ~7 [avatar contradiction clause 379]
381. $false [avatar sat refutation 155,181,213,279,290,380]
% SZS output end Proof for 4708376964713014514325776
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or old is not wise.
Everyone who is both funny and not wise is not old and vice versa.
Everyone who is calm or not happy is quiet or funny and vice versa.
Everyone who is brave or not old is both humble and quiet and vice versa.
If someone is not tall or creative then someone is either not curious or calm.
If someone is not curious then alice is curious and vice versa.
If someone is not rich then fred is both not funny and patient.
If someone is either rich or not strong then someone is not wise or not quiet.
Everyone who is either not humble or not kind is either quiet or not quiet and vice versa.
If someone is both not rich and quiet then lucy is not calm or not rich.
Everyone who is old or not brave is either happy or not wise.
Everyone who is either not brave or not happy is not rich.
Everyone who is wise is both strong and generous.
If someone is not happy then someone is brave or not calm and vice versa.
Everyone who is both strong and rich is creative.
Everyone who is both kind and happy is both not curious and happy and vice versa.
Lucy is either not quiet or not creative.
Someone is either not quiet or curious.
John is not calm.
Someone is both not generous and brave.
Paul is calm.
Fred is not wise.
Someone is both kind and tall.
Someone is either not humble or old. | Fred is not happy. | entailment | (![X]:((~curious(X)|old(X))=>~wise(X)))&
(![X]:((funny(X)&~wise(X))<=>~old(X)))&
(![X]:((calm(X)|~happy(X))<=>(quiet(X)|funny(X))))&
(![X]:((brave(X)|~old(X))<=>(humble(X)&quiet(X))))&
((?[X]:((~tall(X)|creative(X))))=>(?[X]:((~curious(X)<~>calm(X)))))&
((?[X]:(~curious(X)))<=>(curious(alice)))&
((?[X]:(~rich(X)))=>((~funny(fred)&patient(fred))))&
((?[X]:((rich(X)<~>~strong(X))))=>(?[X]:((~wise(X)|~quiet(X)))))&
(![X]:((~humble(X)<~>~kind(X))<=>(quiet(X)<~>~quiet(X))))&
((?[X]:((~rich(X)&quiet(X))))=>((~calm(lucy)|~rich(lucy))))&
(![X]:((old(X)|~brave(X))=>(happy(X)<~>~wise(X))))&
(![X]:((~brave(X)<~>~happy(X))=>~rich(X)))&
(![X]:(wise(X)=>(strong(X)&generous(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((brave(X)|~calm(X)))))&
(![X]:((strong(X)&rich(X))=>creative(X)))&
(![X]:((kind(X)&happy(X))<=>(~curious(X)&happy(X))))&
((~quiet(lucy)<~>~creative(lucy)))&
(?[X]:((~quiet(X)<~>curious(X))))&
(~calm(john))&
(?[X]:((~generous(X)&brave(X))))&
(calm(paul))&
(~wise(fred))&
(?[X]:((kind(X)&tall(X))))&
(?[X]:((~humble(X)<~>old(X)))) | ~happy(fred) | [
"p0",
"p1",
"p2",
"p3",
"p6",
"p10",
"p11",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4622463219540654974205748
% SZS output start Proof for 4622463219540654974205748
1. ! [X0] : ((old(X0) | ~curious(X0)) => ~wise(X0)) [input p0]
2. ! [X0] : ((~wise(X0) & funny(X0)) <=> ~old(X0)) [input p1]
3. ! [X0] : ((~happy(X0) | calm(X0)) <=> (funny(X0) | quiet(X0))) [input p2]
4. ! [X0] : ((~old(X0) | brave(X0)) <=> (quiet(X0) & humble(X0))) [input p3]
7. ? [X0] : ~rich(X0) => (patient(fred) & ~funny(fred)) [input p6]
11. ! [X0] : ((~brave(X0) | old(X0)) => (happy(X0) <~> ~wise(X0))) [input p10]
12. ! [X0] : ((~brave(X0) <~> ~happy(X0)) => ~rich(X0)) [input p11]
24. ? [X0] : (~humble(X0) <~> old(X0)) [input p23]
25. happy(fred) [input hypothesis]
29. ? [X0] : ~rich(X0) => ~funny(fred) [pure predicate removal 7]
32. ! [X0] : (~wise(X0) | (~old(X0) & curious(X0))) [ennf transformation 1]
34. ~funny(fred) | ! [X0] : rich(X0) [ennf transformation 29]
38. ! [X0] : ((happy(X0) <~> ~wise(X0)) | (brave(X0) & ~old(X0))) [ennf transformation 11]
39. ! [X0] : (~rich(X0) | (~brave(X0) <=> ~happy(X0))) [ennf transformation 12]
43. ! [X0] : (((~wise(X0) & funny(X0)) | old(X0)) & (~old(X0) | (wise(X0) | ~funny(X0)))) [nnf transformation 2]
44. ! [X0] : (((~wise(X0) & funny(X0)) | old(X0)) & (~old(X0) | wise(X0) | ~funny(X0))) [flattening 43]
45. ! [X0] : (((~happy(X0) | calm(X0)) | (~funny(X0) & ~quiet(X0))) & ((funny(X0) | quiet(X0)) | (happy(X0) & ~calm(X0)))) [nnf transformation 3]
46. ! [X0] : ((~happy(X0) | calm(X0) | (~funny(X0) & ~quiet(X0))) & (funny(X0) | quiet(X0) | (happy(X0) & ~calm(X0)))) [flattening 45]
47. ! [X0] : (((~old(X0) | brave(X0)) | (~quiet(X0) | ~humble(X0))) & ((quiet(X0) & humble(X0)) | (old(X0) & ~brave(X0)))) [nnf transformation 4]
48. ! [X0] : ((~old(X0) | brave(X0) | ~quiet(X0) | ~humble(X0)) & ((quiet(X0) & humble(X0)) | (old(X0) & ~brave(X0)))) [flattening 47]
62. ! [X0] : (((wise(X0) | ~happy(X0)) & (~wise(X0) | happy(X0))) | (brave(X0) & ~old(X0))) [nnf transformation 38]
63. ! [X0] : (~rich(X0) | ((~brave(X0) | happy(X0)) & (~happy(X0) | brave(X0)))) [nnf transformation 39]
79. ? [X0] : ((~old(X0) | humble(X0)) & (old(X0) | ~humble(X0))) [nnf transformation 24]
80. ? [X0] : ((~old(X0) | humble(X0)) & (old(X0) | ~humble(X0))) => ((~old(sK8) | humble(sK8)) & (old(sK8) | ~humble(sK8))) [choice axiom]
81. (~old(sK8) | humble(sK8)) & (old(sK8) | ~humble(sK8)) [skolemisation 79,80]
83. ~wise(X0) | ~old(X0) [cnf transformation 32]
84. ~old(X0) | wise(X0) | ~funny(X0) [cnf transformation 44]
85. funny(X0) | old(X0) [cnf transformation 44]
86. ~wise(X0) | old(X0) [cnf transformation 44]
88. quiet(X0) | funny(X0) | happy(X0) [cnf transformation 46]
92. humble(X0) | old(X0) [cnf transformation 48]
95. ~humble(X0) | brave(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 48]
100. ~funny(fred) | rich(X0) [cnf transformation 34]
114. wise(X0) | ~happy(X0) | ~old(X0) [cnf transformation 62]
117. ~rich(X0) | ~brave(X0) | happy(X0) [cnf transformation 63]
138. old(sK8) | ~humble(sK8) [cnf transformation 81]
139. ~old(sK8) | humble(sK8) [cnf transformation 81]
140. happy(fred) [cnf transformation 25]
145. ~wise(X0) [subsumption resolution 86,83]
146. ~funny(X0) | ~old(X0) [subsumption resolution 84,145]
174. 7 <=> ! [X0] : rich(X0) [avatar definition]
175. rich(X0) <- (7) [avatar component clause 174]
177. 8 <=> funny(fred) [avatar definition]
179. ~funny(fred) <- (~8) [avatar component clause 177]
180. 7 | ~8 [avatar split clause 100,177,174]
196. ~happy(X0) | ~old(X0) [subsumption resolution 114,145]
241. humble(sK8) [subsumption resolution 139,92]
242. old(sK8) [subsumption resolution 138,241]
243. old(fred) <- (~8) [resolution 85,179]
252. ~old(fred) [resolution 196,140]
253. $false <- (~8) [subsumption resolution 252,243]
254. 8 [avatar contradiction clause 253]
290. ~brave(X0) | happy(X0) <- (7) [resolution 117,175]
322. brave(sK8) | ~quiet(sK8) | ~old(sK8) [resolution 95,241]
323. brave(sK8) | ~quiet(sK8) [subsumption resolution 322,242]
325. 30 <=> quiet(sK8) [avatar definition]
327. ~quiet(sK8) <- (~30) [avatar component clause 325]
329. 31 <=> brave(sK8) [avatar definition]
331. brave(sK8) <- (31) [avatar component clause 329]
332. ~30 | 31 [avatar split clause 323,329,325]
336. 32 <=> happy(sK8) [avatar definition]
338. happy(sK8) <- (32) [avatar component clause 336]
340. 33 <=> funny(sK8) [avatar definition]
342. funny(sK8) <- (33) [avatar component clause 340]
350. happy(sK8) <- (7, 31) [resolution 290,331]
351. 32 | ~7 | ~31 [avatar split clause 350,329,174,336]
352. funny(sK8) | happy(sK8) <- (~30) [resolution 327,88]
357. ~old(sK8) <- (32) [resolution 338,196]
368. $false <- (32) [subsumption resolution 357,242]
369. ~32 [avatar contradiction clause 368]
371. 32 | 33 | 30 [avatar split clause 352,325,340,336]
373. ~old(sK8) <- (33) [resolution 342,146]
374. $false <- (33) [subsumption resolution 373,242]
375. ~33 [avatar contradiction clause 374]
376. $false [avatar sat refutation 180,254,332,351,369,371,375]
% SZS output end Proof for 4622463219540654974205748
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then alice is curious and vice versa. Everyone who is tall is not happy or wise and vice versa. Everyone who is not rich or strong is happy. Everyone who is either not creative or generous is not creative. Everyone who is not patient is not brave or brave and vice versa. Everyone who is not brave or not strong is brave or not rich and vice versa. If someone is both not old and wise then mary is either quiet or not generous and vice versa. If someone is both kind and not calm then someone is not tall or not wise and vice versa. If paul is funny or not brave then someone is either not rich or not curious and vice versa. If someone is not humble then mary is not tall and vice versa. If someone is patient or not calm then fred is either old or not patient and vice versa. Everyone who is either happy or wise is both not creative and creative and vice versa. If someone is both not happy and not creative then someone is either quiet or not patient. Everyone who is either not creative or humble is both quiet and not calm and vice versa. If someone is tall or not curious then alice is either old or not rich and vice versa. Everyone who is both tall and not brave is creative or not humble. Fred is either not wise or generous. Paul is not calm. Fred is creative. Someone is both wise and old. Someone is both kind and brave. Someone is either not quiet or happy. Someone is both not kind and not generous. Alice is both happy and not funny. | Mary is old. | neutral | ((?[X]:(kind(X)))<=>(curious(alice)))&
(![X]:(tall(X)<=>(~happy(X)|wise(X))))&
(![X]:((~rich(X)|strong(X))=>happy(X)))&
(![X]:((~creative(X)<~>generous(X))=>~creative(X)))&
(![X]:(~patient(X)<=>(~brave(X)|brave(X))))&
(![X]:((~brave(X)|~strong(X))<=>(brave(X)|~rich(X))))&
((?[X]:((~old(X)&wise(X))))<=>((quiet(mary)<~>~generous(mary))))&
((?[X]:((kind(X)&~calm(X))))<=>(?[X]:((~tall(X)|~wise(X)))))&
(((funny(paul)|~brave(paul)))<=>(?[X]:((~rich(X)<~>~curious(X)))))&
((?[X]:(~humble(X)))<=>(~tall(mary)))&
((?[X]:((patient(X)|~calm(X))))<=>((old(fred)<~>~patient(fred))))&
(![X]:((happy(X)<~>wise(X))<=>(~creative(X)&creative(X))))&
((?[X]:((~happy(X)&~creative(X))))=>(?[X]:((quiet(X)<~>~patient(X)))))&
(![X]:((~creative(X)<~>humble(X))<=>(quiet(X)&~calm(X))))&
((?[X]:((tall(X)|~curious(X))))<=>((old(alice)<~>~rich(alice))))&
(![X]:((tall(X)&~brave(X))=>(creative(X)|~humble(X))))&
((~wise(fred)<~>generous(fred)))&
(~calm(paul))&
(creative(fred))&
(?[X]:((wise(X)&old(X))))&
(?[X]:((kind(X)&brave(X))))&
(?[X]:((~quiet(X)<~>happy(X))))&
(?[X]:((~kind(X)&~generous(X))))&
((happy(alice)&~funny(alice))) | old(mary) | [] | null | 0 |
If someone is either calm or not curious then someone is either not brave or not wise and vice versa.
Everyone who is both calm and brave is strong.
Everyone who is not rich is both not brave and not humble.
If susan is either quiet or not wise then alice is not rich or strong and vice versa.
If someone is either patient or kind then someone is both not happy and happy.
Everyone who is not calm is either humble or patient and vice versa.
If someone is either humble or patient then paul is not quiet or not wise and vice versa.
Everyone who is both patient and not creative is not brave and vice versa.
If paul is either not calm or not generous then susan is funny and vice versa.
Everyone who is old is not strong.
If lucy is both strong and not curious then someone is calm or not funny.
If someone is either old or strong then lucy is both patient and not patient and vice versa.
Everyone who is not brave or humble is not brave and vice versa.
Everyone who is strong or not humble is curious or not calm and vice versa.
Everyone who is both not tall and not humble is either not curious or happy and vice versa.
Alice is not creative.
Lucy is either tall or old.
Alice is happy or rich.
Someone is not creative or not rich. | Lucy is kind. | entailment | ((?[X]:((calm(X)<~>~curious(X))))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
(![X]:((calm(X)&brave(X))=>strong(X)))&
(![X]:(~rich(X)=>(~brave(X)&~humble(X))))&
(((quiet(susan)<~>~wise(susan)))<=>((~rich(alice)|strong(alice))))&
((?[X]:((patient(X)<~>kind(X))))=>(?[X]:((~happy(X)&happy(X)))))&
(![X]:(~calm(X)<=>(humble(X)<~>patient(X))))&
((?[X]:((humble(X)<~>patient(X))))<=>((~quiet(paul)|~wise(paul))))&
(![X]:((patient(X)&~creative(X))<=>~brave(X)))&
(((~calm(paul)<~>~generous(paul)))<=>(funny(susan)))&
(![X]:(old(X)=>~strong(X)))&
(((strong(lucy)&~curious(lucy)))=>(?[X]:((calm(X)|~funny(X)))))&
((?[X]:((old(X)<~>strong(X))))<=>((patient(lucy)&~patient(lucy))))&
(![X]:((~brave(X)|humble(X))<=>~brave(X)))&
(![X]:((strong(X)|~humble(X))<=>(curious(X)|~calm(X))))&
(![X]:((~tall(X)&~humble(X))<=>(~curious(X)<~>happy(X))))&
(~creative(alice))&
((tall(lucy)<~>old(lucy)))&
((happy(alice)|rich(alice)))&
(?[X]:((~creative(X)|~rich(X)))) | kind(lucy) | [
"p1",
"p4",
"p5",
"p7",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3241957958371462022487908
% SZS output start Proof for 3241957958371462022487908
2. ! [X0] : ((brave(X0) & calm(X0)) => strong(X0)) [input p1]
5. ? [X0] : (patient(X0) <~> kind(X0)) => ? [X0] : (happy(X0) & ~happy(X0)) [input p4]
6. ! [X0] : (~calm(X0) <=> (humble(X0) <~> patient(X0))) [input p5]
8. ! [X0] : ((~creative(X0) & patient(X0)) <=> ~brave(X0)) [input p7]
10. ! [X0] : (old(X0) => ~strong(X0)) [input p9]
12. ? [X0] : (old(X0) <~> strong(X0)) <=> (~patient(lucy) & patient(lucy)) [input p11]
13. ! [X0] : ((humble(X0) | ~brave(X0)) <=> ~brave(X0)) [input p12]
20. ~kind(lucy) [input hypothesis]
22. ? [X0] : (patient(X0) <~> kind(X0)) => ? [X1] : (happy(X1) & ~happy(X1)) [rectify 5]
23. ! [X0] : (strong(X0) | (~brave(X0) | ~calm(X0))) [ennf transformation 2]
24. ! [X0] : (strong(X0) | ~brave(X0) | ~calm(X0)) [flattening 23]
26. ? [X1] : (happy(X1) & ~happy(X1)) | ! [X0] : (patient(X0) <=> kind(X0)) [ennf transformation 22]
27. ! [X0] : (~strong(X0) | ~old(X0)) [ennf transformation 10]
37. ? [X1] : (happy(X1) & ~happy(X1)) | ! [X0] : ((patient(X0) | ~kind(X0)) & (kind(X0) | ~patient(X0))) [nnf transformation 26]
38. ? [X0] : (happy(X0) & ~happy(X0)) | ! [X1] : ((patient(X1) | ~kind(X1)) & (kind(X1) | ~patient(X1))) [rectify 37]
39. ? [X0] : (happy(X0) & ~happy(X0)) => (happy(sK2) & ~happy(sK2)) [choice axiom]
40. (happy(sK2) & ~happy(sK2)) | ! [X1] : ((patient(X1) | ~kind(X1)) & (kind(X1) | ~patient(X1))) [skolemisation 38,39]
41. ! [X0] : ((~calm(X0) | ((humble(X0) | ~patient(X0)) & (patient(X0) | ~humble(X0)))) & (((~patient(X0) | ~humble(X0)) & (patient(X0) | humble(X0))) | calm(X0))) [nnf transformation 6]
47. ! [X0] : (((~creative(X0) & patient(X0)) | brave(X0)) & (~brave(X0) | (creative(X0) | ~patient(X0)))) [nnf transformation 8]
48. ! [X0] : (((~creative(X0) & patient(X0)) | brave(X0)) & (~brave(X0) | creative(X0) | ~patient(X0))) [flattening 47]
52. (? [X0] : ((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (patient(lucy) | ~patient(lucy))) & ((~patient(lucy) & patient(lucy)) | ! [X0] : ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0)))) [nnf transformation 12]
53. (? [X0] : ((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | patient(lucy) | ~patient(lucy)) & ((~patient(lucy) & patient(lucy)) | ! [X0] : ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0)))) [flattening 52]
54. (? [X0] : ((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | patient(lucy) | ~patient(lucy)) & ((~patient(lucy) & patient(lucy)) | ! [X1] : ((old(X1) | ~strong(X1)) & (strong(X1) | ~old(X1)))) [rectify 53]
55. ? [X0] : ((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) => ((~strong(sK5) | ~old(sK5)) & (strong(sK5) | old(sK5))) [choice axiom]
56. (((~strong(sK5) | ~old(sK5)) & (strong(sK5) | old(sK5))) | patient(lucy) | ~patient(lucy)) & ((~patient(lucy) & patient(lucy)) | ! [X1] : ((old(X1) | ~strong(X1)) & (strong(X1) | ~old(X1)))) [skolemisation 54,55]
57. ! [X0] : (((humble(X0) | ~brave(X0)) | brave(X0)) & (~brave(X0) | (~humble(X0) & brave(X0)))) [nnf transformation 13]
58. ! [X0] : ((humble(X0) | ~brave(X0) | brave(X0)) & (~brave(X0) | (~humble(X0) & brave(X0)))) [flattening 57]
74. ~brave(X0) | strong(X0) | ~calm(X0) [cnf transformation 24]
83. ~happy(sK2) | kind(X1) | ~patient(X1) [cnf transformation 40]
85. happy(sK2) | kind(X1) | ~patient(X1) [cnf transformation 40]
87. patient(X0) | humble(X0) | calm(X0) [cnf transformation 41]
88. ~patient(X0) | ~humble(X0) | calm(X0) [cnf transformation 41]
98. patient(X0) | brave(X0) [cnf transformation 48]
104. ~old(X0) | ~strong(X0) [cnf transformation 27]
107. patient(lucy) | old(X1) | ~strong(X1) [cnf transformation 56]
109. ~patient(lucy) | old(X1) | ~strong(X1) [cnf transformation 56]
113. ~humble(X0) | ~brave(X0) [cnf transformation 58]
130. ~kind(lucy) [cnf transformation 20]
193. 14 <=> happy(sK2) [avatar definition]
198. 15 <=> ! [X1] : (kind(X1) | ~patient(X1)) [avatar definition]
199. ~patient(X1) | kind(X1) <- (15) [avatar component clause 198]
200. 15 | 14 [avatar split clause 85,193,198]
202. 15 | ~14 [avatar split clause 83,193,198]
264. ~patient(lucy) | ~strong(X1) [subsumption resolution 109,104]
266. 29 <=> ! [X1] : ~strong(X1) [avatar definition]
267. ~strong(X1) <- (29) [avatar component clause 266]
269. 30 <=> patient(lucy) [avatar definition]
272. 29 | ~30 [avatar split clause 264,269,266]
278. patient(lucy) | ~strong(X1) [subsumption resolution 107,104]
279. 29 | 30 [avatar split clause 278,269,266]
315. kind(X0) | brave(X0) <- (15) [resolution 199,98]
320. kind(X0) | calm(X0) | humble(X0) <- (15) [resolution 87,199]
322. ~humble(X1) | calm(X1) | brave(X1) [resolution 88,98]
325. ~humble(X1) | calm(X1) [subsumption resolution 322,113]
326. brave(lucy) <- (15) [resolution 315,130]
328. strong(lucy) | ~calm(lucy) <- (15) [resolution 326,74]
330. ~calm(lucy) <- (15, 29) [subsumption resolution 328,267]
359. calm(lucy) | humble(lucy) <- (15) [resolution 320,130]
361. humble(lucy) <- (15, 29) [subsumption resolution 359,330]
368. calm(lucy) <- (15, 29) [resolution 361,325]
374. $false <- (15, 29) [subsumption resolution 368,330]
375. ~15 | ~29 [avatar contradiction clause 374]
376. $false [avatar sat refutation 200,202,272,279,375]
% SZS output end Proof for 3241957958371462022487908
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is either old or not calm and vice versa.
Everyone who is not old is both quiet and strong.
If someone is either rich or kind then john is either kind or wise.
Everyone who is patient or not happy is calm and vice versa.
If alice is calm then someone is wise.
Everyone who is rich or creative is happy.
If someone is either creative or not generous then mary is either not curious or not creative and vice versa.
Everyone who is brave or rich is not quiet.
Everyone who is rich or not wise is either not strong or tall and vice versa.
Everyone who is strong is not generous or brave and vice versa.
Everyone who is both not old and curious is not quiet or rich and vice versa.
If someone is not old or not calm then alice is not quiet or creative and vice versa.
If someone is either not generous or kind then alice is curious or not kind and vice versa.
If fred is rich then someone is both not strong and strong and vice versa.
Everyone who is both not curious and generous is either not happy or not patient.
If someone is generous then someone is both generous and funny and vice versa.
Fred is either not funny or not quiet.
Someone is either not strong or not wise.
Someone is kind.
Someone is either creative or quiet.
Alice is curious or not rich.
Alice is either not humble or happy. | John is rich. | contradiction | (![X]:(generous(X)<=>(old(X)<~>~calm(X))))&
(![X]:(~old(X)=>(quiet(X)&strong(X))))&
((?[X]:((rich(X)<~>kind(X))))=>((kind(john)<~>wise(john))))&
(![X]:((patient(X)|~happy(X))<=>calm(X)))&
((calm(alice))=>(?[X]:(wise(X))))&
(![X]:((rich(X)|creative(X))=>happy(X)))&
((?[X]:((creative(X)<~>~generous(X))))<=>((~curious(mary)<~>~creative(mary))))&
(![X]:((brave(X)|rich(X))=>~quiet(X)))&
(![X]:((rich(X)|~wise(X))<=>(~strong(X)<~>tall(X))))&
(![X]:(strong(X)<=>(~generous(X)|brave(X))))&
(![X]:((~old(X)&curious(X))<=>(~quiet(X)|rich(X))))&
((?[X]:((~old(X)|~calm(X))))<=>((~quiet(alice)|creative(alice))))&
((?[X]:((~generous(X)<~>kind(X))))<=>((curious(alice)|~kind(alice))))&
((rich(fred))<=>(?[X]:((~strong(X)&strong(X)))))&
(![X]:((~curious(X)&generous(X))=>(~happy(X)<~>~patient(X))))&
((?[X]:(generous(X)))<=>(?[X]:((generous(X)&funny(X)))))&
((~funny(fred)<~>~quiet(fred)))&
(?[X]:((~strong(X)<~>~wise(X))))&
(?[X]:(kind(X)))&
(?[X]:((creative(X)<~>quiet(X))))&
((curious(alice)|~rich(alice)))&
((~humble(alice)<~>happy(alice))) | rich(john) | [
"p1",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2172946767341809287175390
% SZS output start Proof for 2172946767341809287175390
2. ! [X0] : (~old(X0) => (strong(X0) & quiet(X0))) [input p1]
8. ! [X0] : ((rich(X0) | brave(X0)) => ~quiet(X0)) [input p7]
11. ! [X0] : ((curious(X0) & ~old(X0)) <=> (rich(X0) | ~quiet(X0))) [input p10]
23. rich(john) [input hypothesis]
25. ! [X0] : ((strong(X0) & quiet(X0)) | old(X0)) [ennf transformation 2]
29. ! [X0] : (~quiet(X0) | (~rich(X0) & ~brave(X0))) [ennf transformation 8]
46. ! [X0] : (((curious(X0) & ~old(X0)) | (~rich(X0) & quiet(X0))) & ((rich(X0) | ~quiet(X0)) | (~curious(X0) | old(X0)))) [nnf transformation 11]
47. ! [X0] : (((curious(X0) & ~old(X0)) | (~rich(X0) & quiet(X0))) & (rich(X0) | ~quiet(X0) | ~curious(X0) | old(X0))) [flattening 46]
82. quiet(X0) | old(X0) [cnf transformation 25]
103. ~rich(X0) | ~quiet(X0) [cnf transformation 29]
114. ~old(X0) | quiet(X0) [cnf transformation 47]
146. rich(john) [cnf transformation 23]
204. quiet(X0) [subsumption resolution 114,82]
321. ~quiet(john) [resolution 103,146]
322. $false [subsumption resolution 321,204]
% SZS output end Proof for 2172946767341809287175390
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and quiet is not curious or not creative and vice versa.
If someone is both tall and not kind then alice is strong and vice versa.
If someone is not rich then someone is both not curious and quiet.
Everyone who is not kind is both kind and tall and vice versa.
Everyone who is humble or quiet is either not rich or not strong.
Everyone who is not humble is either curious or quiet.
If fred is not kind then alice is either generous or wise and vice versa.
If someone is both funny and not curious then fred is creative or not curious.
Everyone who is either not old or brave is patient.
Everyone who is funny is both tall and not humble and vice versa.
Everyone who is both not happy and rich is rich or curious and vice versa.
If someone is both tall and old then fred is not brave or creative.
Everyone who is tall is wise and vice versa.
Everyone who is happy is both humble and wise and vice versa.
Everyone who is either not creative or not quiet is not strong and vice versa.
John is both not calm and not old.
Someone is not kind or strong.
Someone is not old or not quiet.
Susan is both not patient and quiet.
Someone is either not patient or not old.
Someone is either brave or not quiet. | Alice is not curious. | contradiction | (![X]:((strong(X)&quiet(X))<=>(~curious(X)|~creative(X))))&
((?[X]:((tall(X)&~kind(X))))<=>(strong(alice)))&
((?[X]:(~rich(X)))=>(?[X]:((~curious(X)&quiet(X)))))&
(![X]:(~kind(X)<=>(kind(X)&tall(X))))&
(![X]:((humble(X)|quiet(X))=>(~rich(X)<~>~strong(X))))&
(![X]:(~humble(X)=>(curious(X)<~>quiet(X))))&
((~kind(fred))<=>((generous(alice)<~>wise(alice))))&
((?[X]:((funny(X)&~curious(X))))=>((creative(fred)|~curious(fred))))&
(![X]:((~old(X)<~>brave(X))=>patient(X)))&
(![X]:(funny(X)<=>(tall(X)&~humble(X))))&
(![X]:((~happy(X)&rich(X))<=>(rich(X)|curious(X))))&
((?[X]:((tall(X)&old(X))))=>((~brave(fred)|creative(fred))))&
(![X]:(tall(X)<=>wise(X)))&
(![X]:(happy(X)<=>(humble(X)&wise(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>~strong(X)))&
((~calm(john)&~old(john)))&
(?[X]:((~kind(X)|strong(X))))&
(?[X]:((~old(X)|~quiet(X))))&
((~patient(susan)&quiet(susan)))&
(?[X]:((~patient(X)<~>~old(X))))&
(?[X]:((brave(X)<~>~quiet(X)))) | ~curious(alice) | [
"p0",
"p1",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 1801511435815869805604472
% SZS output start Proof for 1801511435815869805604472
1. ! [X0] : ((quiet(X0) & strong(X0)) <=> (~creative(X0) | ~curious(X0))) [input p0]
2. ? [X0] : (~kind(X0) & tall(X0)) <=> strong(alice) [input p1]
4. ! [X0] : (~kind(X0) <=> (tall(X0) & kind(X0))) [input p3]
22. ~curious(alice) [input hypothesis]
36. ! [X0] : (((quiet(X0) & strong(X0)) | (creative(X0) & curious(X0))) & ((~creative(X0) | ~curious(X0)) | (~quiet(X0) | ~strong(X0)))) [nnf transformation 1]
37. ! [X0] : (((quiet(X0) & strong(X0)) | (creative(X0) & curious(X0))) & (~creative(X0) | ~curious(X0) | ~quiet(X0) | ~strong(X0))) [flattening 36]
38. (? [X0] : (~kind(X0) & tall(X0)) | ~strong(alice)) & (strong(alice) | ! [X0] : (kind(X0) | ~tall(X0))) [nnf transformation 2]
39. (? [X0] : (~kind(X0) & tall(X0)) | ~strong(alice)) & (strong(alice) | ! [X1] : (kind(X1) | ~tall(X1))) [rectify 38]
40. ? [X0] : (~kind(X0) & tall(X0)) => (~kind(sK0) & tall(sK0)) [choice axiom]
41. ((~kind(sK0) & tall(sK0)) | ~strong(alice)) & (strong(alice) | ! [X1] : (kind(X1) | ~tall(X1))) [skolemisation 39,40]
45. ! [X0] : ((~kind(X0) | (~tall(X0) | ~kind(X0))) & ((tall(X0) & kind(X0)) | kind(X0))) [nnf transformation 4]
46. ! [X0] : ((~kind(X0) | ~tall(X0) | ~kind(X0)) & ((tall(X0) & kind(X0)) | kind(X0))) [flattening 45]
68. curious(X0) | strong(X0) [cnf transformation 37]
74. ~kind(sK0) | ~strong(alice) [cnf transformation 41]
77. kind(X0) | kind(X0) [cnf transformation 46]
118. ~curious(alice) [cnf transformation 22]
119. kind(X0) [duplicate literal removal 77]
122. 1 <=> strong(alice) [avatar definition]
126. 2 <=> kind(sK0) [avatar definition]
128. ~kind(sK0) <- (~2) [avatar component clause 126]
129. ~1 | ~2 [avatar split clause 74,126,122]
218. strong(alice) [resolution 68,118]
222. 1 [avatar split clause 218,122]
223. $false <- (~2) [subsumption resolution 128,119]
224. 2 [avatar contradiction clause 223]
225. $false [avatar sat refutation 129,222,224]
% SZS output end Proof for 1801511435815869805604472
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or funny then someone is not brave.
If mary is not strong or strong then john is calm or generous.
Everyone who is both not happy and tall is either not humble or not old.
If mary is not rich then someone is both not happy and old.
Everyone who is generous is both strong and not patient.
Everyone who is quiet or kind is happy or funny and vice versa.
Everyone who is both generous and wise is not humble and vice versa.
If someone is both not tall and not old then someone is brave or not generous and vice versa.
If susan is kind then someone is both funny and patient and vice versa.
Everyone who is not quiet is both creative and funny and vice versa.
Everyone who is not kind or not humble is not generous or not curious.
If john is not curious then someone is wise or not rich.
If someone is kind then someone is both curious and not kind.
Everyone who is kind or quiet is both strong and patient and vice versa.
Everyone who is both kind and calm is quiet.
If someone is both rich and curious then john is generous or humble and vice versa.
Someone is both creative and not generous.
Someone is either tall or calm.
Mary is either humble or creative.
Someone is not calm.
Someone is wise.
Someone is not funny or rich.
Someone is both funny and not curious. | John is strong. | entailment | ((?[X]:((~brave(X)|funny(X))))=>(?[X]:(~brave(X))))&
(((~strong(mary)|strong(mary)))=>((calm(john)|generous(john))))&
(![X]:((~happy(X)&tall(X))=>(~humble(X)<~>~old(X))))&
((~rich(mary))=>(?[X]:((~happy(X)&old(X)))))&
(![X]:(generous(X)=>(strong(X)&~patient(X))))&
(![X]:((quiet(X)|kind(X))<=>(happy(X)|funny(X))))&
(![X]:((generous(X)&wise(X))<=>~humble(X)))&
((?[X]:((~tall(X)&~old(X))))<=>(?[X]:((brave(X)|~generous(X)))))&
((kind(susan))<=>(?[X]:((funny(X)&patient(X)))))&
(![X]:(~quiet(X)<=>(creative(X)&funny(X))))&
(![X]:((~kind(X)|~humble(X))=>(~generous(X)|~curious(X))))&
((~curious(john))=>(?[X]:((wise(X)|~rich(X)))))&
((?[X]:(kind(X)))=>(?[X]:((curious(X)&~kind(X)))))&
(![X]:((kind(X)|quiet(X))<=>(strong(X)&patient(X))))&
(![X]:((kind(X)&calm(X))=>quiet(X)))&
((?[X]:((rich(X)&curious(X))))<=>((generous(john)|humble(john))))&
(?[X]:((creative(X)&~generous(X))))&
(?[X]:((tall(X)<~>calm(X))))&
((humble(mary)<~>creative(mary)))&
(?[X]:(~calm(X)))&
(?[X]:(wise(X)))&
(?[X]:((~funny(X)|rich(X))))&
(?[X]:((funny(X)&~curious(X)))) | strong(john) | [
"p5",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7453724499578637795864639
% SZS output start Proof for 7453724499578637795864639
6. ! [X0] : ((kind(X0) | quiet(X0)) <=> (funny(X0) | happy(X0))) [input p5]
10. ! [X0] : (~quiet(X0) <=> (funny(X0) & creative(X0))) [input p9]
14. ! [X0] : ((quiet(X0) | kind(X0)) <=> (patient(X0) & strong(X0))) [input p13]
24. ~strong(john) [input hypothesis]
47. ! [X0] : (((kind(X0) | quiet(X0)) | (~funny(X0) & ~happy(X0))) & ((funny(X0) | happy(X0)) | (~kind(X0) & ~quiet(X0)))) [nnf transformation 6]
48. ! [X0] : ((kind(X0) | quiet(X0) | (~funny(X0) & ~happy(X0))) & (funny(X0) | happy(X0) | (~kind(X0) & ~quiet(X0)))) [flattening 47]
60. ! [X0] : ((~quiet(X0) | (~funny(X0) | ~creative(X0))) & ((funny(X0) & creative(X0)) | quiet(X0))) [nnf transformation 10]
61. ! [X0] : ((~quiet(X0) | ~funny(X0) | ~creative(X0)) & ((funny(X0) & creative(X0)) | quiet(X0))) [flattening 60]
67. ! [X0] : (((quiet(X0) | kind(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [nnf transformation 14]
68. ! [X0] : ((quiet(X0) | kind(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [flattening 67]
101. ~funny(X0) | quiet(X0) | kind(X0) [cnf transformation 48]
114. quiet(X0) | funny(X0) [cnf transformation 61]
121. ~kind(X0) | strong(X0) [cnf transformation 68]
122. ~quiet(X0) | strong(X0) [cnf transformation 68]
143. ~strong(john) [cnf transformation 24]
309. strong(X0) | funny(X0) [resolution 122,114]
318. funny(john) [resolution 309,143]
322. quiet(john) | kind(john) [resolution 101,318]
408. 47 <=> kind(john) [avatar definition]
410. kind(john) <- (47) [avatar component clause 408]
412. 48 <=> quiet(john) [avatar definition]
414. quiet(john) <- (48) [avatar component clause 412]
415. 47 | 48 [avatar split clause 322,412,408]
483. strong(john) <- (48) [resolution 414,122]
484. $false <- (48) [subsumption resolution 483,143]
485. ~48 [avatar contradiction clause 484]
502. strong(john) <- (47) [resolution 410,121]
506. $false <- (47) [subsumption resolution 502,143]
507. ~47 [avatar contradiction clause 506]
508. $false [avatar sat refutation 415,485,507]
% SZS output end Proof for 7453724499578637795864639
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is both patient and old and vice versa.
Everyone who is not generous or not quiet is not brave or happy and vice versa.
Everyone who is both not wise and not quiet is brave or kind.
Everyone who is either funny or not quiet is not funny and vice versa.
Everyone who is creative is either not brave or not creative and vice versa.
Everyone who is not calm is either curious or not quiet.
Everyone who is both calm and funny is both not strong and creative and vice versa.
If lucy is old then someone is funny and vice versa.
Everyone who is both not old and old is not wise and vice versa.
If susan is funny or not happy then john is both kind and not strong.
Everyone who is not brave or not kind is patient and vice versa.
If john is calm or old then someone is either not brave or not funny and vice versa.
If someone is both not patient and not kind then someone is not rich and vice versa.
Everyone who is both not old and strong is rich or creative.
If lucy is either not curious or not humble then paul is rich.
Everyone who is both not generous and happy is both rich and not kind and vice versa.
John is either not rich or not tall.
Lucy is not tall.
Someone is either humble or creative.
Someone is either not generous or calm.
Someone is humble or not brave.
Someone is not generous or not brave.
John is not calm.
Lucy is kind. | Paul is not wise. | contradiction | (![X]:((~happy(X)|~curious(X))<=>(patient(X)&old(X))))&
(![X]:((~generous(X)|~quiet(X))<=>(~brave(X)|happy(X))))&
(![X]:((~wise(X)&~quiet(X))=>(brave(X)|kind(X))))&
(![X]:((funny(X)<~>~quiet(X))<=>~funny(X)))&
(![X]:(creative(X)<=>(~brave(X)<~>~creative(X))))&
(![X]:(~calm(X)=>(curious(X)<~>~quiet(X))))&
(![X]:((calm(X)&funny(X))<=>(~strong(X)&creative(X))))&
((old(lucy))<=>(?[X]:(funny(X))))&
(![X]:((~old(X)&old(X))<=>~wise(X)))&
(((funny(susan)|~happy(susan)))=>((kind(john)&~strong(john))))&
(![X]:((~brave(X)|~kind(X))<=>patient(X)))&
(((calm(john)|old(john)))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
((?[X]:((~patient(X)&~kind(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~old(X)&strong(X))=>(rich(X)|creative(X))))&
(((~curious(lucy)<~>~humble(lucy)))=>(rich(paul)))&
(![X]:((~generous(X)&happy(X))<=>(rich(X)&~kind(X))))&
((~rich(john)<~>~tall(john)))&
(~tall(lucy))&
(?[X]:((humble(X)<~>creative(X))))&
(?[X]:((~generous(X)<~>calm(X))))&
(?[X]:((humble(X)|~brave(X))))&
(?[X]:((~generous(X)|~brave(X))))&
(~calm(john))&
(kind(lucy)) | ~wise(paul) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6633085997312498765297030
% SZS output start Proof for 6633085997312498765297030
9. ! [X0] : ((old(X0) & ~old(X0)) <=> ~wise(X0)) [input p8]
25. ~wise(paul) [input hypothesis]
47. ! [X0] : (((old(X0) & ~old(X0)) | wise(X0)) & (~wise(X0) | (~old(X0) | old(X0)))) [nnf transformation 9]
48. ! [X0] : (((old(X0) & ~old(X0)) | wise(X0)) & (~wise(X0) | ~old(X0) | old(X0))) [flattening 47]
102. ~old(X0) | wise(X0) [cnf transformation 48]
103. old(X0) | wise(X0) [cnf transformation 48]
138. ~wise(paul) [cnf transformation 25]
159. wise(X0) [subsumption resolution 102,103]
254. $false [subsumption resolution 138,159]
% SZS output end Proof for 6633085997312498765297030
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is happy or not wise then someone is curious or not old.
If someone is both not brave and not curious then alice is both kind and tall.
If lucy is either rich or not happy then someone is kind or tall and vice versa.
Everyone who is both rich and brave is strong.
Everyone who is funny or quiet is either not curious or calm and vice versa.
If someone is brave or quiet then paul is both not happy and not strong and vice versa.
Everyone who is either not tall or not curious is not generous and vice versa.
If someone is either not wise or tall then fred is either old or not brave and vice versa.
If john is either not patient or generous then lucy is either calm or generous.
If someone is kind then someone is both creative and not brave and vice versa.
Everyone who is not calm or old is curious and vice versa.
Everyone who is not old is both funny and not patient.
Everyone who is both not old and quiet is both wise and old and vice versa.
If mary is quiet then someone is either not rich or not creative and vice versa.
Everyone who is not funny or curious is either not creative or not strong.
If someone is brave or creative then someone is generous.
Mary is not calm.
Lucy is either generous or happy.
Alice is not wise or tall.
Alice is kind.
Susan is patient or not strong.
Susan is patient or not generous. | Susan is old. | entailment | (((happy(paul)|~wise(paul)))=>(?[X]:((curious(X)|~old(X)))))&
((?[X]:((~brave(X)&~curious(X))))=>((kind(alice)&tall(alice))))&
(((rich(lucy)<~>~happy(lucy)))<=>(?[X]:((kind(X)|tall(X)))))&
(![X]:((rich(X)&brave(X))=>strong(X)))&
(![X]:((funny(X)|quiet(X))<=>(~curious(X)<~>calm(X))))&
((?[X]:((brave(X)|quiet(X))))<=>((~happy(paul)&~strong(paul))))&
(![X]:((~tall(X)<~>~curious(X))<=>~generous(X)))&
((?[X]:((~wise(X)<~>tall(X))))<=>((old(fred)<~>~brave(fred))))&
(((~patient(john)<~>generous(john)))=>((calm(lucy)<~>generous(lucy))))&
((?[X]:(kind(X)))<=>(?[X]:((creative(X)&~brave(X)))))&
(![X]:((~calm(X)|old(X))<=>curious(X)))&
(![X]:(~old(X)=>(funny(X)&~patient(X))))&
(![X]:((~old(X)&quiet(X))<=>(wise(X)&old(X))))&
((quiet(mary))<=>(?[X]:((~rich(X)<~>~creative(X)))))&
(![X]:((~funny(X)|curious(X))=>(~creative(X)<~>~strong(X))))&
((?[X]:((brave(X)|creative(X))))=>(?[X]:(generous(X))))&
(~calm(mary))&
((generous(lucy)<~>happy(lucy)))&
((~wise(alice)|tall(alice)))&
(kind(alice))&
((patient(susan)|~strong(susan)))&
((patient(susan)|~generous(susan))) | old(susan) | [
"p4",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7937659249233413999441427
% SZS output start Proof for 7937659249233413999441427
5. ! [X0] : ((quiet(X0) | funny(X0)) <=> (~curious(X0) <~> calm(X0))) [input p4]
11. ! [X0] : ((old(X0) | ~calm(X0)) <=> curious(X0)) [input p10]
12. ! [X0] : (~old(X0) => (~patient(X0) & funny(X0))) [input p11]
23. ~old(susan) [input hypothesis]
31. ! [X0] : ((~patient(X0) & funny(X0)) | old(X0)) [ennf transformation 12]
40. ! [X0] : (((quiet(X0) | funny(X0)) | ((~curious(X0) | ~calm(X0)) & (calm(X0) | curious(X0)))) & (((~calm(X0) | curious(X0)) & (calm(X0) | ~curious(X0))) | (~quiet(X0) & ~funny(X0)))) [nnf transformation 5]
41. ! [X0] : ((quiet(X0) | funny(X0) | ((~curious(X0) | ~calm(X0)) & (calm(X0) | curious(X0)))) & (((~calm(X0) | curious(X0)) & (calm(X0) | ~curious(X0))) | (~quiet(X0) & ~funny(X0)))) [flattening 40]
58. ! [X0] : (((old(X0) | ~calm(X0)) | ~curious(X0)) & (curious(X0) | (~old(X0) & calm(X0)))) [nnf transformation 11]
59. ! [X0] : ((old(X0) | ~calm(X0) | ~curious(X0)) & (curious(X0) | (~old(X0) & calm(X0)))) [flattening 58]
82. ~funny(X0) | ~curious(X0) | calm(X0) [cnf transformation 41]
84. ~calm(X0) | curious(X0) | ~funny(X0) [cnf transformation 41]
112. calm(X0) | curious(X0) [cnf transformation 59]
114. ~calm(X0) | old(X0) | ~curious(X0) [cnf transformation 59]
115. funny(X0) | old(X0) [cnf transformation 31]
138. ~old(susan) [cnf transformation 23]
381. ~curious(X0) | calm(X0) | old(X0) [resolution 82,115]
382. calm(X0) | old(X0) [subsumption resolution 381,112]
386. curious(X0) | ~funny(X0) | curious(X0) [resolution 84,112]
388. ~funny(X0) | curious(X0) [duplicate literal removal 386]
408. old(X0) | ~curious(X0) | old(X0) [resolution 114,382]
411. old(X0) | ~curious(X0) [duplicate literal removal 408]
438. curious(X0) | old(X0) [resolution 388,115]
439. old(X0) [subsumption resolution 438,411]
494. $false [resolution 439,138]
% SZS output end Proof for 7937659249233413999441427
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not brave and quiet then someone is tall and vice versa.
Everyone who is both kind and not quiet is old.
Everyone who is both not patient and wise is either not rich or wise and vice versa.
If someone is not brave or not kind then susan is not calm and vice versa.
Everyone who is not funny or funny is either not calm or not tall and vice versa.
If someone is not kind then someone is not strong and vice versa.
Everyone who is either wise or not wise is not tall.
If someone is not quiet or happy then someone is not tall or not kind.
If susan is either not old or not creative then someone is either curious or funny.
If lucy is wise then mary is either not patient or happy and vice versa.
Everyone who is either not curious or quiet is either old or calm and vice versa.
If john is both strong and patient then someone is calm and vice versa.
If someone is calm or curious then fred is either not humble or not calm and vice versa.
If someone is both tall and not strong then someone is both calm and rich.
Someone is either strong or old.
Someone is both not generous and strong.
Someone is either kind or not funny.
Paul is either not creative or curious.
Someone is quiet or not funny.
Someone is either creative or not curious.
Someone is either not curious or brave. | Mary is strong. | entailment | (((~brave(mary)&quiet(mary)))<=>(?[X]:(tall(X))))&
(![X]:((kind(X)&~quiet(X))=>old(X)))&
(![X]:((~patient(X)&wise(X))<=>(~rich(X)<~>wise(X))))&
((?[X]:((~brave(X)|~kind(X))))<=>(~calm(susan)))&
(![X]:((~funny(X)|funny(X))<=>(~calm(X)<~>~tall(X))))&
((?[X]:(~kind(X)))<=>(?[X]:(~strong(X))))&
(![X]:((wise(X)<~>~wise(X))=>~tall(X)))&
((?[X]:((~quiet(X)|happy(X))))=>(?[X]:((~tall(X)|~kind(X)))))&
(((~old(susan)<~>~creative(susan)))=>(?[X]:((curious(X)<~>funny(X)))))&
((wise(lucy))<=>((~patient(mary)<~>happy(mary))))&
(![X]:((~curious(X)<~>quiet(X))<=>(old(X)<~>calm(X))))&
(((strong(john)&patient(john)))<=>(?[X]:(calm(X))))&
((?[X]:((calm(X)|curious(X))))<=>((~humble(fred)<~>~calm(fred))))&
((?[X]:((tall(X)&~strong(X))))=>(?[X]:((calm(X)&rich(X)))))&
(?[X]:((strong(X)<~>old(X))))&
(?[X]:((~generous(X)&strong(X))))&
(?[X]:((kind(X)<~>~funny(X))))&
((~creative(paul)<~>curious(paul)))&
(?[X]:((quiet(X)|~funny(X))))&
(?[X]:((creative(X)<~>~curious(X))))&
(?[X]:((~curious(X)<~>brave(X)))) | strong(mary) | [
"p3",
"p4",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 7920977675786437188999703
% SZS output start Proof for 7920977675786437188999703
4. ? [X0] : (~kind(X0) | ~brave(X0)) <=> ~calm(susan) [input p3]
5. ! [X0] : ((funny(X0) | ~funny(X0)) <=> (~calm(X0) <~> ~tall(X0))) [input p4]
6. ? [X0] : ~kind(X0) <=> ? [X0] : ~strong(X0) [input p5]
7. ! [X0] : ((wise(X0) <~> ~wise(X0)) => ~tall(X0)) [input p6]
22. ~strong(mary) [input hypothesis]
23. ? [X0] : ~kind(X0) <=> ? [X1] : ~strong(X1) [rectify 6]
29. ! [X0] : (~tall(X0) | (wise(X0) <=> ~wise(X0))) [ennf transformation 7]
40. (? [X0] : (~kind(X0) | ~brave(X0)) | calm(susan)) & (~calm(susan) | ! [X0] : (kind(X0) & brave(X0))) [nnf transformation 4]
41. (? [X0] : (~kind(X0) | ~brave(X0)) | calm(susan)) & (~calm(susan) | ! [X1] : (kind(X1) & brave(X1))) [rectify 40]
42. ? [X0] : (~kind(X0) | ~brave(X0)) => (~kind(sK1) | ~brave(sK1)) [choice axiom]
43. ((~kind(sK1) | ~brave(sK1)) | calm(susan)) & (~calm(susan) | ! [X1] : (kind(X1) & brave(X1))) [skolemisation 41,42]
44. ! [X0] : (((funny(X0) | ~funny(X0)) | ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0)))) & (((tall(X0) | calm(X0)) & (~tall(X0) | ~calm(X0))) | (~funny(X0) & funny(X0)))) [nnf transformation 5]
45. ! [X0] : ((funny(X0) | ~funny(X0) | ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0)))) & (((tall(X0) | calm(X0)) & (~tall(X0) | ~calm(X0))) | (~funny(X0) & funny(X0)))) [flattening 44]
46. (? [X0] : ~kind(X0) | ! [X1] : strong(X1)) & (? [X1] : ~strong(X1) | ! [X0] : kind(X0)) [nnf transformation 23]
47. (? [X0] : ~kind(X0) | ! [X1] : strong(X1)) & (? [X2] : ~strong(X2) | ! [X3] : kind(X3)) [rectify 46]
48. ? [X0] : ~kind(X0) => ~kind(sK2) [choice axiom]
49. ? [X2] : ~strong(X2) => ~strong(sK3) [choice axiom]
50. (~kind(sK2) | ! [X1] : strong(X1)) & (~strong(sK3) | ! [X3] : kind(X3)) [skolemisation 47,49,48]
51. ! [X0] : (~tall(X0) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) [nnf transformation 29]
100. ~calm(susan) | kind(X1) [cnf transformation 43]
104. tall(X0) | calm(X0) | funny(X0) [cnf transformation 45]
105. tall(X0) | calm(X0) | ~funny(X0) [cnf transformation 45]
109. ~kind(sK2) | strong(X1) [cnf transformation 50]
110. ~tall(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 51]
111. ~tall(X0) | wise(X0) | wise(X0) [cnf transformation 51]
153. ~strong(mary) [cnf transformation 22]
154. ~tall(X0) | ~wise(X0) [duplicate literal removal 110]
155. ~tall(X0) | wise(X0) [duplicate literal removal 111]
159. 1 <=> ! [X0] : ~tall(X0) [avatar definition]
160. ~tall(X0) <- (1) [avatar component clause 159]
178. 5 <=> calm(susan) [avatar definition]
179. ~calm(susan) <- (~5) [avatar component clause 178]
191. 8 <=> ! [X1] : kind(X1) [avatar definition]
192. kind(X1) <- (8) [avatar component clause 191]
193. 8 | ~5 [avatar split clause 100,178,191]
198. calm(X0) | tall(X0) [subsumption resolution 104,105]
201. 10 <=> ! [X1] : strong(X1) [avatar definition]
202. strong(X1) <- (10) [avatar component clause 201]
204. 11 <=> kind(sK2) [avatar definition]
206. ~kind(sK2) <- (~11) [avatar component clause 204]
207. 10 | ~11 [avatar split clause 109,204,201]
213. ~tall(X0) [subsumption resolution 154,155]
214. 1 [avatar split clause 213,159]
384. tall(susan) <- (~5) [resolution 198,179]
385. $false <- (1, ~5) [subsumption resolution 384,160]
386. ~1 | 5 [avatar contradiction clause 385]
388. $false <- (8, ~11) [resolution 192,206]
393. ~8 | 11 [avatar contradiction clause 388]
397. $false <- (10) [resolution 202,153]
400. ~10 [avatar contradiction clause 397]
401. $false [avatar sat refutation 193,207,214,386,393,400]
% SZS output end Proof for 7920977675786437188999703
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is 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. | Paul is not brave. | 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)))) | ~brave(paul) | [
"p2",
"p4",
"p7",
"p8",
"p10",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3738315995950904502173129
% SZS output start Proof for 3738315995950904502173129
3. ! [X0] : (rich(X0) => (~kind(X0) & ~brave(X0))) [input p2]
5. ! [X0] : (~rich(X0) <=> (old(X0) & funny(X0))) [input p4]
8. ? [X0] : (~calm(X0) | ~patient(X0)) <=> (patient(paul) <~> funny(paul)) [input p7]
9. ! [X0] : ((calm(X0) | ~patient(X0)) <=> ~wise(X0)) [input p8]
11. ! [X0] : ((rich(X0) | ~patient(X0)) <=> ~old(X0)) [input p10]
24. ? [X0] : (~generous(X0) & wise(X0)) [input p23]
25. brave(paul) [input hypothesis]
31. ! [X0] : ((~kind(X0) & ~brave(X0)) | ~rich(X0)) [ennf transformation 3]
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]
39. (? [X0] : (~calm(X0) | ~patient(X0)) | ((patient(paul) | ~funny(paul)) & (funny(paul) | ~patient(paul)))) & (((~funny(paul) | ~patient(paul)) & (funny(paul) | patient(paul))) | ! [X0] : (calm(X0) & patient(X0))) [nnf transformation 8]
40. (? [X0] : (~calm(X0) | ~patient(X0)) | ((patient(paul) | ~funny(paul)) & (funny(paul) | ~patient(paul)))) & (((~funny(paul) | ~patient(paul)) & (funny(paul) | patient(paul))) | ! [X1] : (calm(X1) & patient(X1))) [rectify 39]
41. ? [X0] : (~calm(X0) | ~patient(X0)) => (~calm(sK0) | ~patient(sK0)) [choice axiom]
42. ((~calm(sK0) | ~patient(sK0)) | ((patient(paul) | ~funny(paul)) & (funny(paul) | ~patient(paul)))) & (((~funny(paul) | ~patient(paul)) & (funny(paul) | patient(paul))) | ! [X1] : (calm(X1) & patient(X1))) [skolemisation 40,41]
43. ! [X0] : (((calm(X0) | ~patient(X0)) | wise(X0)) & (~wise(X0) | (~calm(X0) & patient(X0)))) [nnf transformation 9]
44. ! [X0] : ((calm(X0) | ~patient(X0) | wise(X0)) & (~wise(X0) | (~calm(X0) & patient(X0)))) [flattening 43]
47. ! [X0] : (((rich(X0) | ~patient(X0)) | old(X0)) & (~old(X0) | (~rich(X0) & patient(X0)))) [nnf transformation 11]
48. ! [X0] : ((rich(X0) | ~patient(X0) | old(X0)) & (~old(X0) | (~rich(X0) & patient(X0)))) [flattening 47]
70. ? [X0] : (~generous(X0) & wise(X0)) => (~generous(sK6) & wise(sK6)) [choice axiom]
71. ~generous(sK6) & wise(sK6) [skolemisation 24,70]
75. ~brave(X0) | ~rich(X0) [cnf transformation 31]
78. funny(X0) | rich(X0) [cnf transformation 37]
79. rich(X0) | old(X0) [cnf transformation 37]
86. ~funny(paul) | ~patient(paul) | calm(X1) [cnf transformation 42]
90. ~wise(X0) | ~calm(X0) [cnf transformation 44]
98. ~old(X0) | patient(X0) [cnf transformation 48]
122. wise(sK6) [cnf transformation 71]
124. brave(paul) [cnf transformation 25]
161. 9 <=> funny(paul) [avatar definition]
163. ~funny(paul) <- (~9) [avatar component clause 161]
165. 10 <=> patient(paul) [avatar definition]
179. 13 <=> ! [X1] : calm(X1) [avatar definition]
180. calm(X1) <- (13) [avatar component clause 179]
181. 13 | ~10 | ~9 [avatar split clause 86,161,165,179]
282. ~rich(paul) [resolution 75,124]
283. old(paul) [resolution 79,282]
286. ~calm(sK6) [resolution 90,122]
288. patient(paul) [resolution 98,283]
291. 10 [avatar split clause 288,165]
292. rich(paul) <- (~9) [resolution 163,78]
293. $false <- (~9) [subsumption resolution 292,282]
294. 9 [avatar contradiction clause 293]
296. $false <- (13) [resolution 180,286]
297. ~13 [avatar contradiction clause 296]
299. $false [avatar sat refutation 181,291,294,297]
% SZS output end Proof for 3738315995950904502173129
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both old and not quiet then alice is strong and vice versa.
Everyone who is not kind is old.
Everyone who is both not generous and not wise is either not funny or not happy.
Everyone who is either not brave or not strong is either brave or calm and vice versa.
Everyone who is not curious or tall is either not wise or patient.
If john is not humble or not brave then susan is both not old and not kind and vice versa.
Everyone who is either not creative or not funny is both not kind and creative.
Everyone who is not rich is both brave and wise.
If mary is wise or old then susan is not patient and vice versa.
Everyone who is quiet is both not tall and not kind and vice versa.
Everyone who is either kind or not generous is not rich.
Everyone who is wise or not creative is rich or not quiet and vice versa.
If someone is either not kind or wise then someone is both not quiet and not funny.
Everyone who is either old or not funny is not tall or not old and vice versa.
Everyone who is either not patient or quiet is both not old and not happy.
Everyone who is both not old and not rich is either not happy or not wise.
John is both calm and funny.
Someone is rich.
Mary is both not patient and quiet.
Paul is rich or generous.
Someone is both creative and not rich.
Someone is old or calm.
Susan is either not curious or not rich. | Susan is not kind. | contradiction | (((old(paul)&~quiet(paul)))<=>(strong(alice)))&
(![X]:(~kind(X)=>old(X)))&
(![X]:((~generous(X)&~wise(X))=>(~funny(X)<~>~happy(X))))&
(![X]:((~brave(X)<~>~strong(X))<=>(brave(X)<~>calm(X))))&
(![X]:((~curious(X)|tall(X))=>(~wise(X)<~>patient(X))))&
(((~humble(john)|~brave(john)))<=>((~old(susan)&~kind(susan))))&
(![X]:((~creative(X)<~>~funny(X))=>(~kind(X)&creative(X))))&
(![X]:(~rich(X)=>(brave(X)&wise(X))))&
(((wise(mary)|old(mary)))<=>(~patient(susan)))&
(![X]:(quiet(X)<=>(~tall(X)&~kind(X))))&
(![X]:((kind(X)<~>~generous(X))=>~rich(X)))&
(![X]:((wise(X)|~creative(X))<=>(rich(X)|~quiet(X))))&
((?[X]:((~kind(X)<~>wise(X))))=>(?[X]:((~quiet(X)&~funny(X)))))&
(![X]:((old(X)<~>~funny(X))<=>(~tall(X)|~old(X))))&
(![X]:((~patient(X)<~>quiet(X))=>(~old(X)&~happy(X))))&
(![X]:((~old(X)&~rich(X))=>(~happy(X)<~>~wise(X))))&
((calm(john)&funny(john)))&
(?[X]:(rich(X)))&
((~patient(mary)&quiet(mary)))&
((rich(paul)|generous(paul)))&
(?[X]:((creative(X)&~rich(X))))&
(?[X]:((old(X)|calm(X))))&
((~curious(susan)<~>~rich(susan))) | ~kind(susan) | [
"p1",
"p4",
"p6",
"p7",
"p8",
"p9",
"p11",
"p13",
"p14",
"p18",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2573113075739802987707684
% SZS output start Proof for 2573113075739802987707684
2. ! [X0] : (~kind(X0) => old(X0)) [input p1]
5. ! [X0] : ((tall(X0) | ~curious(X0)) => (~wise(X0) <~> patient(X0))) [input p4]
7. ! [X0] : ((~creative(X0) <~> ~funny(X0)) => (creative(X0) & ~kind(X0))) [input p6]
8. ! [X0] : (~rich(X0) => (wise(X0) & brave(X0))) [input p7]
9. (old(mary) | wise(mary)) <=> ~patient(susan) [input p8]
10. ! [X0] : (quiet(X0) <=> (~kind(X0) & ~tall(X0))) [input p9]
12. ! [X0] : ((~creative(X0) | wise(X0)) <=> (~quiet(X0) | rich(X0))) [input p11]
14. ! [X0] : ((old(X0) <~> ~funny(X0)) <=> (~old(X0) | ~tall(X0))) [input p13]
15. ! [X0] : ((~patient(X0) <~> quiet(X0)) => (~happy(X0) & ~old(X0))) [input p14]
19. quiet(mary) & ~patient(mary) [input p18]
23. ~curious(susan) <~> ~rich(susan) [input p22]
24. ~kind(susan) [input hypothesis]
26. ! [X0] : (old(X0) | kind(X0)) [ennf transformation 2]
29. ! [X0] : ((~wise(X0) <~> patient(X0)) | (~tall(X0) & curious(X0))) [ennf transformation 5]
30. ! [X0] : ((creative(X0) & ~kind(X0)) | (~creative(X0) <=> ~funny(X0))) [ennf transformation 7]
31. ! [X0] : ((wise(X0) & brave(X0)) | rich(X0)) [ennf transformation 8]
34. ! [X0] : ((~happy(X0) & ~old(X0)) | (~patient(X0) <=> quiet(X0))) [ennf transformation 15]
41. ! [X0] : (((~patient(X0) | wise(X0)) & (patient(X0) | ~wise(X0))) | (~tall(X0) & curious(X0))) [nnf transformation 29]
44. ! [X0] : ((creative(X0) & ~kind(X0)) | ((~creative(X0) | funny(X0)) & (~funny(X0) | creative(X0)))) [nnf transformation 30]
45. ((old(mary) | wise(mary)) | patient(susan)) & (~patient(susan) | (~old(mary) & ~wise(mary))) [nnf transformation 9]
46. (old(mary) | wise(mary) | patient(susan)) & (~patient(susan) | (~old(mary) & ~wise(mary))) [flattening 45]
47. ! [X0] : ((quiet(X0) | (kind(X0) | tall(X0))) & ((~kind(X0) & ~tall(X0)) | ~quiet(X0))) [nnf transformation 10]
48. ! [X0] : ((quiet(X0) | kind(X0) | tall(X0)) & ((~kind(X0) & ~tall(X0)) | ~quiet(X0))) [flattening 47]
50. ! [X0] : (((~creative(X0) | wise(X0)) | (quiet(X0) & ~rich(X0))) & ((~quiet(X0) | rich(X0)) | (creative(X0) & ~wise(X0)))) [nnf transformation 12]
51. ! [X0] : ((~creative(X0) | wise(X0) | (quiet(X0) & ~rich(X0))) & (~quiet(X0) | rich(X0) | (creative(X0) & ~wise(X0)))) [flattening 50]
56. ! [X0] : ((((funny(X0) | ~old(X0)) & (~funny(X0) | old(X0))) | (old(X0) & tall(X0))) & ((~old(X0) | ~tall(X0)) | ((old(X0) | funny(X0)) & (~funny(X0) | ~old(X0))))) [nnf transformation 14]
57. ! [X0] : ((((funny(X0) | ~old(X0)) & (~funny(X0) | old(X0))) | (old(X0) & tall(X0))) & (~old(X0) | ~tall(X0) | ((old(X0) | funny(X0)) & (~funny(X0) | ~old(X0))))) [flattening 56]
58. ! [X0] : ((~happy(X0) & ~old(X0)) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0)))) [nnf transformation 34]
66. (rich(susan) | curious(susan)) & (~rich(susan) | ~curious(susan)) [nnf transformation 23]
70. kind(X0) | old(X0) [cnf transformation 26]
81. ~wise(X0) | patient(X0) | curious(X0) [cnf transformation 41]
92. creative(X0) | ~funny(X0) | creative(X0) [cnf transformation 44]
95. rich(X0) | wise(X0) [cnf transformation 31]
96. ~patient(susan) | ~wise(mary) [cnf transformation 46]
99. ~tall(X0) | ~quiet(X0) [cnf transformation 48]
100. ~kind(X0) | ~quiet(X0) [cnf transformation 48]
104. ~quiet(X0) | rich(X0) | ~wise(X0) [cnf transformation 51]
106. ~creative(X0) | wise(X0) | ~rich(X0) [cnf transformation 51]
116. ~old(X0) | funny(X0) | tall(X0) [cnf transformation 57]
118. ~old(X0) | quiet(X0) | patient(X0) [cnf transformation 58]
128. quiet(mary) [cnf transformation 19]
133. ~rich(susan) | ~curious(susan) [cnf transformation 66]
135. ~kind(susan) [cnf transformation 24]
138. ~funny(X0) | creative(X0) [duplicate literal removal 92]
165. 5 <=> kind(susan) [avatar definition]
167. ~kind(susan) <- (~5) [avatar component clause 165]
175. 7 <=> old(susan) [avatar definition]
176. old(susan) <- (7) [avatar component clause 175]
181. 8 <=> patient(susan) [avatar definition]
182. ~patient(susan) <- (~8) [avatar component clause 181]
185. 9 <=> wise(mary) [avatar definition]
189. 10 <=> old(mary) [avatar definition]
191. old(mary) <- (10) [avatar component clause 189]
194. ~9 | ~8 [avatar split clause 96,181,185]
195. ~creative(X0) | wise(X0) [subsumption resolution 106,95]
196. ~quiet(X0) | rich(X0) [subsumption resolution 104,95]
236. 19 <=> curious(susan) [avatar definition]
237. ~curious(susan) <- (~19) [avatar component clause 236]
240. 20 <=> rich(susan) [avatar definition]
244. ~19 | ~20 [avatar split clause 133,240,236]
245. ~5 [avatar split clause 135,165]
246. old(susan) <- (~5) [resolution 70,167]
249. 7 | 5 [avatar split clause 246,165,175]
254. ~quiet(X0) | old(X0) [resolution 100,70]
262. old(mary) [resolution 254,128]
265. 10 [avatar split clause 262,189]
353. funny(susan) | tall(susan) <- (7) [resolution 116,176]
354. funny(mary) | tall(mary) <- (10) [resolution 116,191]
367. 34 <=> tall(susan) [avatar definition]
369. tall(susan) <- (34) [avatar component clause 367]
371. 35 <=> funny(susan) [avatar definition]
373. funny(susan) <- (35) [avatar component clause 371]
374. 34 | 35 | ~7 [avatar split clause 353,175,371,367]
376. 36 <=> tall(mary) [avatar definition]
378. tall(mary) <- (36) [avatar component clause 376]
380. 37 <=> funny(mary) [avatar definition]
382. funny(mary) <- (37) [avatar component clause 380]
383. 36 | 37 | ~10 [avatar split clause 354,189,380,376]
402. quiet(susan) | patient(susan) <- (7) [resolution 118,176]
412. quiet(susan) <- (7, ~8) [subsumption resolution 402,182]
434. ~quiet(susan) <- (34) [resolution 369,99]
439. $false <- (7, ~8, 34) [subsumption resolution 434,412]
440. ~7 | 8 | ~34 [avatar contradiction clause 439]
447. creative(susan) <- (35) [resolution 373,138]
451. ~quiet(mary) <- (36) [resolution 378,99]
453. $false <- (36) [subsumption resolution 451,128]
454. ~36 [avatar contradiction clause 453]
460. creative(mary) <- (37) [resolution 382,138]
474. rich(susan) <- (7, ~8) [resolution 412,196]
477. 20 | ~7 | 8 [avatar split clause 474,181,175,240]
543. wise(susan) <- (35) [resolution 447,195]
546. wise(mary) <- (37) [resolution 460,195]
549. 9 | ~37 [avatar split clause 546,380,185]
577. patient(susan) | curious(susan) <- (35) [resolution 543,81]
578. curious(susan) <- (~8, 35) [subsumption resolution 577,182]
579. $false <- (~8, ~19, 35) [subsumption resolution 578,237]
580. 8 | 19 | ~35 [avatar contradiction clause 579]
581. $false [avatar sat refutation 194,244,245,249,265,374,383,440,454,477,549,580]
% SZS output end Proof for 2573113075739802987707684
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is not wise or kind then someone is not humble.
If someone is both not happy and not funny then someone is both wise and not kind and vice versa.
If mary is not happy then alice is either not tall or humble.
Everyone who is either quiet or kind is not wise and vice versa.
If paul is not curious or funny then someone is not quiet and vice versa.
Everyone who is happy is both creative and not strong and vice versa.
Everyone who is quiet is creative or not generous.
If paul is not kind then fred is both curious and not happy.
If someone is quiet or not generous then someone is both not old and not tall and vice versa.
Everyone who is curious or strong is both not wise and not humble and vice versa.
If someone is both not generous and not humble then susan is not generous.
If paul is creative or wise then lucy is rich or happy and vice versa.
Everyone who is both calm and not quiet is not rich or not wise.
Everyone who is patient or wise is quiet and vice versa.
Everyone who is both tall and generous is not tall or not creative and vice versa.
Mary is funny or not wise.
Someone is not curious.
Mary is both not wise and kind.
Mary is not quiet or curious.
Someone is kind or not rich.
John is not curious or old.
Someone is either strong or not kind. | Paul is wise. | contradiction | ((?[X]:((~wise(X)|kind(X))))=>(?[X]:(~humble(X))))&
((?[X]:((~happy(X)&~funny(X))))<=>(?[X]:((wise(X)&~kind(X)))))&
((~happy(mary))=>((~tall(alice)<~>humble(alice))))&
(![X]:((quiet(X)<~>kind(X))<=>~wise(X)))&
(((~curious(paul)|funny(paul)))<=>(?[X]:(~quiet(X))))&
(![X]:(happy(X)<=>(creative(X)&~strong(X))))&
(![X]:(quiet(X)=>(creative(X)|~generous(X))))&
((~kind(paul))=>((curious(fred)&~happy(fred))))&
((?[X]:((quiet(X)|~generous(X))))<=>(?[X]:((~old(X)&~tall(X)))))&
(![X]:((curious(X)|strong(X))<=>(~wise(X)&~humble(X))))&
((?[X]:((~generous(X)&~humble(X))))=>(~generous(susan)))&
(((creative(paul)|wise(paul)))<=>((rich(lucy)|happy(lucy))))&
(![X]:((calm(X)&~quiet(X))=>(~rich(X)|~wise(X))))&
(![X]:((patient(X)|wise(X))<=>quiet(X)))&
(![X]:((tall(X)&generous(X))<=>(~tall(X)|~creative(X))))&
((funny(mary)|~wise(mary)))&
(?[X]:(~curious(X)))&
((~wise(mary)&kind(mary)))&
((~quiet(mary)|curious(mary)))&
(?[X]:((kind(X)|~rich(X))))&
((~curious(john)|old(john)))&
(?[X]:((strong(X)<~>~kind(X)))) | wise(paul) | [
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3549997803451977597475496
% SZS output start Proof for 3549997803451977597475496
9. ? [X0] : (~generous(X0) | quiet(X0)) <=> ? [X0] : (~tall(X0) & ~old(X0)) [input p8]
14. ! [X0] : ((wise(X0) | patient(X0)) <=> quiet(X0)) [input p13]
15. ! [X0] : ((generous(X0) & tall(X0)) <=> (~creative(X0) | ~tall(X0))) [input p14]
23. wise(paul) [input hypothesis]
26. ? [X0] : (~generous(X0) | quiet(X0)) <=> ? [X1] : (~tall(X1) & ~old(X1)) [rectify 9]
51. (? [X0] : (~generous(X0) | quiet(X0)) | ! [X1] : (tall(X1) | old(X1))) & (? [X1] : (~tall(X1) & ~old(X1)) | ! [X0] : (generous(X0) & ~quiet(X0))) [nnf transformation 26]
52. (? [X0] : (~generous(X0) | quiet(X0)) | ! [X1] : (tall(X1) | old(X1))) & (? [X2] : (~tall(X2) & ~old(X2)) | ! [X3] : (generous(X3) & ~quiet(X3))) [rectify 51]
53. ? [X0] : (~generous(X0) | quiet(X0)) => (~generous(sK4) | quiet(sK4)) [choice axiom]
54. ? [X2] : (~tall(X2) & ~old(X2)) => (~tall(sK5) & ~old(sK5)) [choice axiom]
55. ((~generous(sK4) | quiet(sK4)) | ! [X1] : (tall(X1) | old(X1))) & ((~tall(sK5) & ~old(sK5)) | ! [X3] : (generous(X3) & ~quiet(X3))) [skolemisation 52,54,53]
60. ! [X0] : (((wise(X0) | patient(X0)) | ~quiet(X0)) & (quiet(X0) | (~wise(X0) & ~patient(X0)))) [nnf transformation 14]
61. ! [X0] : ((wise(X0) | patient(X0) | ~quiet(X0)) & (quiet(X0) | (~wise(X0) & ~patient(X0)))) [flattening 60]
62. ! [X0] : (((generous(X0) & tall(X0)) | (creative(X0) & tall(X0))) & ((~creative(X0) | ~tall(X0)) | (~generous(X0) | ~tall(X0)))) [nnf transformation 15]
63. ! [X0] : (((generous(X0) & tall(X0)) | (creative(X0) & tall(X0))) & (~creative(X0) | ~tall(X0) | ~generous(X0) | ~tall(X0))) [flattening 62]
94. ~tall(sK5) | ~quiet(X3) [cnf transformation 55]
108. ~wise(X0) | quiet(X0) [cnf transformation 61]
111. tall(X0) | tall(X0) [cnf transformation 63]
124. wise(paul) [cnf transformation 23]
126. tall(X0) [duplicate literal removal 111]
227. 24 <=> tall(sK5) [avatar definition]
229. ~tall(sK5) <- (~24) [avatar component clause 227]
232. 25 <=> ! [X3] : ~quiet(X3) [avatar definition]
233. ~quiet(X3) <- (25) [avatar component clause 232]
234. 25 | ~24 [avatar split clause 94,227,232]
258. 31 <=> wise(paul) [avatar definition]
260. wise(paul) <- (31) [avatar component clause 258]
317. 31 [avatar split clause 124,258]
318. $false <- (~24) [subsumption resolution 229,126]
319. 24 [avatar contradiction clause 318]
328. quiet(paul) <- (31) [resolution 108,260]
329. $false <- (25, 31) [subsumption resolution 328,233]
330. ~25 | ~31 [avatar contradiction clause 329]
331. $false [avatar sat refutation 234,317,319,330]
% SZS output end Proof for 3549997803451977597475496
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy is not creative.
Everyone who is both not strong and not humble is both generous and not brave.
Everyone who is both not humble and funny is either wise or strong and vice versa.
Everyone who is both strong and not patient is kind and vice versa.
If someone is wise or not brave then someone is either rich or not quiet.
Everyone who is either not wise or kind is both happy and tall.
Everyone who is either funny or not creative is not quiet.
Everyone who is either not strong or not rich is either happy or not funny and vice versa.
If someone is both wise and happy then susan is both not curious and not brave.
Everyone who is either happy or kind is not tall and vice versa.
If fred is brave then alice is not generous or not brave.
Everyone who is not strong is either strong or brave and vice versa.
If someone is not happy or quiet then someone is old.
If someone is humble or not happy then alice is curious or not funny.
Everyone who is either not quiet or strong is either creative or humble.
Everyone who is wise is both not brave and wise and vice versa.
Susan is not patient.
Paul is creative.
Someone is not generous.
Mary is not rich.
Someone is either brave or old. | Paul is tall. | contradiction | (![X]:(happy(X)=>~creative(X)))&
(![X]:((~strong(X)&~humble(X))=>(generous(X)&~brave(X))))&
(![X]:((~humble(X)&funny(X))<=>(wise(X)<~>strong(X))))&
(![X]:((strong(X)&~patient(X))<=>kind(X)))&
((?[X]:((wise(X)|~brave(X))))=>(?[X]:((rich(X)<~>~quiet(X)))))&
(![X]:((~wise(X)<~>kind(X))=>(happy(X)&tall(X))))&
(![X]:((funny(X)<~>~creative(X))=>~quiet(X)))&
(![X]:((~strong(X)<~>~rich(X))<=>(happy(X)<~>~funny(X))))&
((?[X]:((wise(X)&happy(X))))=>((~curious(susan)&~brave(susan))))&
(![X]:((happy(X)<~>kind(X))<=>~tall(X)))&
((brave(fred))=>((~generous(alice)|~brave(alice))))&
(![X]:(~strong(X)<=>(strong(X)<~>brave(X))))&
((?[X]:((~happy(X)|quiet(X))))=>(?[X]:(old(X))))&
((?[X]:((humble(X)|~happy(X))))=>((curious(alice)|~funny(alice))))&
(![X]:((~quiet(X)<~>strong(X))=>(creative(X)<~>humble(X))))&
(![X]:(wise(X)<=>(~brave(X)&wise(X))))&
(~patient(susan))&
(creative(paul))&
(?[X]:(~generous(X)))&
(~rich(mary))&
(?[X]:((brave(X)<~>old(X)))) | tall(paul) | [
"p0",
"p5",
"p9",
"p11",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3756209818224943884124181
% SZS output start Proof for 3756209818224943884124181
1. ! [X0] : (happy(X0) => ~creative(X0)) [input p0]
6. ! [X0] : ((~wise(X0) <~> kind(X0)) => (tall(X0) & happy(X0))) [input p5]
10. ! [X0] : ((happy(X0) <~> kind(X0)) <=> ~tall(X0)) [input p9]
12. ! [X0] : (~strong(X0) <=> (strong(X0) <~> brave(X0))) [input p11]
16. ! [X0] : (wise(X0) <=> (wise(X0) & ~brave(X0))) [input p15]
18. creative(paul) [input p17]
22. tall(paul) [input hypothesis]
25. ! [X0] : ((happy(X0) <~> kind(X0)) => ~tall(X0)) [unused predicate definition removal 10]
26. ! [X0] : (~creative(X0) | ~happy(X0)) [ennf transformation 1]
30. ! [X0] : ((tall(X0) & happy(X0)) | (~wise(X0) <=> kind(X0))) [ennf transformation 6]
33. ! [X0] : (~tall(X0) | (happy(X0) <=> kind(X0))) [ennf transformation 25]
48. ! [X0] : ((tall(X0) & happy(X0)) | ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0)))) [nnf transformation 30]
51. ! [X0] : (~tall(X0) | ((happy(X0) | ~kind(X0)) & (kind(X0) | ~happy(X0)))) [nnf transformation 33]
52. ! [X0] : ((~strong(X0) | ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0)))) & (((~brave(X0) | ~strong(X0)) & (brave(X0) | strong(X0))) | strong(X0))) [nnf transformation 12]
57. ! [X0] : ((wise(X0) | (~wise(X0) | brave(X0))) & ((wise(X0) & ~brave(X0)) | ~wise(X0))) [nnf transformation 16]
58. ! [X0] : ((wise(X0) | ~wise(X0) | brave(X0)) & ((wise(X0) & ~brave(X0)) | ~wise(X0))) [flattening 57]
64. ~creative(X0) | ~happy(X0) [cnf transformation 26]
80. kind(X0) | happy(X0) | wise(X0) [cnf transformation 48]
97. ~tall(X0) | happy(X0) | ~kind(X0) [cnf transformation 51]
99. brave(X0) | strong(X0) | strong(X0) [cnf transformation 52]
101. ~strong(X0) | brave(X0) | ~strong(X0) [cnf transformation 52]
111. ~wise(X0) | ~brave(X0) [cnf transformation 58]
115. creative(paul) [cnf transformation 18]
120. tall(paul) [cnf transformation 22]
121. brave(X0) | strong(X0) [duplicate literal removal 99]
122. ~strong(X0) | brave(X0) [duplicate literal removal 101]
124. 1 <=> ! [X1] : brave(X1) [avatar definition]
125. brave(X1) <- (1) [avatar component clause 124]
167. brave(X0) [subsumption resolution 121,122]
168. 1 [avatar split clause 167,124]
210. ~happy(paul) [resolution 64,115]
269. happy(paul) | ~kind(paul) [resolution 97,120]
271. ~kind(paul) [subsumption resolution 269,210]
272. happy(paul) | wise(paul) [resolution 271,80]
273. wise(paul) [subsumption resolution 272,210]
277. ~brave(paul) [resolution 273,111]
289. $false <- (1) [subsumption resolution 277,125]
290. ~1 [avatar contradiction clause 289]
291. $false [avatar sat refutation 168,290]
% SZS output end Proof for 3756209818224943884124181
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and not strong is both calm and kind. If alice is both quiet and creative then john is both calm and tall. If lucy is both not humble and curious then paul is not patient and vice versa. If mary is both not creative and old then lucy is either not tall or generous. Everyone who is both not quiet and not creative is both tall and kind and vice versa. If lucy is both old and not rich then fred is not brave and vice versa. Everyone who is not kind or not wise is generous. Everyone who is creative or humble is both humble and old and vice versa. Everyone who is either not generous or rich is either not quiet or curious. Everyone who is calm or brave is either not patient or rich and vice versa. Everyone who is not rich is both brave and tall. Everyone who is both not curious and not wise is kind or not rich and vice versa. If someone is both not old and not tall then alice is either funny or not wise and vice versa. If someone is either not creative or quiet then someone is not patient and vice versa. Everyone who is not curious is both patient and old and vice versa. Everyone who is curious is not kind. Someone is either not calm or humble. Someone is not calm or happy. Someone is curious. Alice is both brave and not calm. Someone is either not humble or generous. Alice is either not humble or rich. Paul is both not calm and not tall. Susan is both tall and not calm. | Lucy is generous. | entailment | (![X]:((~quiet(X)&~strong(X))=>(calm(X)&kind(X))))&
(((quiet(alice)&creative(alice)))=>((calm(john)&tall(john))))&
(((~humble(lucy)&curious(lucy)))<=>(~patient(paul)))&
(((~creative(mary)&old(mary)))=>((~tall(lucy)<~>generous(lucy))))&
(![X]:((~quiet(X)&~creative(X))<=>(tall(X)&kind(X))))&
(((old(lucy)&~rich(lucy)))<=>(~brave(fred)))&
(![X]:((~kind(X)|~wise(X))=>generous(X)))&
(![X]:((creative(X)|humble(X))<=>(humble(X)&old(X))))&
(![X]:((~generous(X)<~>rich(X))=>(~quiet(X)<~>curious(X))))&
(![X]:((calm(X)|brave(X))<=>(~patient(X)<~>rich(X))))&
(![X]:(~rich(X)=>(brave(X)&tall(X))))&
(![X]:((~curious(X)&~wise(X))<=>(kind(X)|~rich(X))))&
((?[X]:((~old(X)&~tall(X))))<=>((funny(alice)<~>~wise(alice))))&
((?[X]:((~creative(X)<~>quiet(X))))<=>(?[X]:(~patient(X))))&
(![X]:(~curious(X)<=>(patient(X)&old(X))))&
(![X]:(curious(X)=>~kind(X)))&
(?[X]:((~calm(X)<~>humble(X))))&
(?[X]:((~calm(X)|happy(X))))&
(?[X]:(curious(X)))&
((brave(alice)&~calm(alice)))&
(?[X]:((~humble(X)<~>generous(X))))&
((~humble(alice)<~>rich(alice)))&
((~calm(paul)&~tall(paul)))&
((tall(susan)&~calm(susan))) | generous(lucy) | [
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 99215154667302374199999
% SZS output start Proof for 99215154667302374199999
7. ! [X0] : ((~wise(X0) | ~kind(X0)) => generous(X0)) [input p6]
12. ! [X0] : ((~wise(X0) & ~curious(X0)) <=> (~rich(X0) | kind(X0))) [input p11]
25. ~generous(lucy) [input hypothesis]
33. ! [X0] : (generous(X0) | (wise(X0) & kind(X0))) [ennf transformation 7]
49. ! [X0] : (((~wise(X0) & ~curious(X0)) | (rich(X0) & ~kind(X0))) & ((~rich(X0) | kind(X0)) | (wise(X0) | curious(X0)))) [nnf transformation 12]
50. ! [X0] : (((~wise(X0) & ~curious(X0)) | (rich(X0) & ~kind(X0))) & (~rich(X0) | kind(X0) | wise(X0) | curious(X0))) [flattening 49]
85. generous(X0) | kind(X0) [cnf transformation 33]
86. wise(X0) | generous(X0) [cnf transformation 33]
107. ~wise(X0) | ~kind(X0) [cnf transformation 50]
136. ~generous(lucy) [cnf transformation 25]
183. 11 <=> generous(lucy) [avatar definition]
185. ~generous(lucy) <- (~11) [avatar component clause 183]
283. ~11 [avatar split clause 136,183]
290. ~kind(X0) | generous(X0) [resolution 107,86]
291. generous(X0) [subsumption resolution 290,85]
293. $false <- (~11) [resolution 291,185]
296. 11 [avatar contradiction clause 293]
297. $false [avatar sat refutation 283,296]
% SZS output end Proof for 99215154667302374199999
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and tall is creative or not quiet.
If someone is either not quiet or not strong then someone is not old or rich and vice versa.
Everyone who is not old is not humble.
Everyone who is funny or not strong is both quiet and strong and vice versa.
Everyone who is either not strong or not patient is curious and vice versa.
Everyone who is not rich or not generous is tall and vice versa.
Everyone who is humble is not kind and vice versa.
If someone is either not rich or strong then someone is either not strong or curious and vice versa.
Everyone who is both not humble and not kind is kind.
If someone is both not humble and strong then mary is not old and vice versa.
Everyone who is either not curious or tall is not generous or patient.
Everyone who is both patient and not calm is either not brave or not funny and vice versa.
Everyone who is old is not generous and vice versa.
If someone is not happy then paul is funny or not creative and vice versa.
If alice is both not brave and old then someone is both not strong and quiet.
Everyone who is both curious and not quiet is either curious or funny.
Someone is both creative and funny.
Fred is not rich.
Someone is not rich.
Fred is either not kind or rich.
Someone is either not humble or quiet.
Mary is both not calm and not brave.
Someone is either generous or rich. | Alice is not quiet. | neutral | (![X]:((~happy(X)&tall(X))=>(creative(X)|~quiet(X))))&
((?[X]:((~quiet(X)<~>~strong(X))))<=>(?[X]:((~old(X)|rich(X)))))&
(![X]:(~old(X)=>~humble(X)))&
(![X]:((funny(X)|~strong(X))<=>(quiet(X)&strong(X))))&
(![X]:((~strong(X)<~>~patient(X))<=>curious(X)))&
(![X]:((~rich(X)|~generous(X))<=>tall(X)))&
(![X]:(humble(X)<=>~kind(X)))&
((?[X]:((~rich(X)<~>strong(X))))<=>(?[X]:((~strong(X)<~>curious(X)))))&
(![X]:((~humble(X)&~kind(X))=>kind(X)))&
((?[X]:((~humble(X)&strong(X))))<=>(~old(mary)))&
(![X]:((~curious(X)<~>tall(X))=>(~generous(X)|patient(X))))&
(![X]:((patient(X)&~calm(X))<=>(~brave(X)<~>~funny(X))))&
(![X]:(old(X)<=>~generous(X)))&
((?[X]:(~happy(X)))<=>((funny(paul)|~creative(paul))))&
(((~brave(alice)&old(alice)))=>(?[X]:((~strong(X)&quiet(X)))))&
(![X]:((curious(X)&~quiet(X))=>(curious(X)<~>funny(X))))&
(?[X]:((creative(X)&funny(X))))&
(~rich(fred))&
(?[X]:(~rich(X)))&
((~kind(fred)<~>rich(fred)))&
(?[X]:((~humble(X)<~>quiet(X))))&
((~calm(mary)&~brave(mary)))&
(?[X]:((generous(X)<~>rich(X)))) | ~quiet(alice) | [] | null | 0 |
If someone is not strong then someone is not old.
Everyone who is not strong is either old or not rich and vice versa.
Everyone who is brave or quiet is kind and vice versa.
Everyone who is not tall or not funny is not kind.
Everyone who is not rich is both not calm and happy and vice versa.
Everyone who is not strong is both not kind and patient and vice versa.
Everyone who is not humble is happy or kind and vice versa.
If someone is either curious or not quiet then fred is wise.
If fred is not wise then someone is not humble and vice versa.
If alice is either brave or not humble then someone is tall or not rich and vice versa.
If someone is both not humble and patient then someone is both not wise and curious and vice versa.
If someone is not rich then susan is not calm.
Everyone who is not wise is not tall.
If someone is either not kind or generous then mary is humble or calm.
If paul is both old and not quiet then lucy is either not humble or not calm.
Everyone who is both not rich and not old is brave and vice versa.
Lucy is not brave or happy.
Someone is both creative and generous.
Mary is both not strong and not calm.
Someone is either calm or not curious.
Someone is not strong or not brave.
Someone is either not humble or not happy.
Someone is wise.
Someone is both strong and not generous. | Mary is not kind. | entailment | ((?[X]:(~strong(X)))=>(?[X]:(~old(X))))&
(![X]:(~strong(X)<=>(old(X)<~>~rich(X))))&
(![X]:((brave(X)|quiet(X))<=>kind(X)))&
(![X]:((~tall(X)|~funny(X))=>~kind(X)))&
(![X]:(~rich(X)<=>(~calm(X)&happy(X))))&
(![X]:(~strong(X)<=>(~kind(X)&patient(X))))&
(![X]:(~humble(X)<=>(happy(X)|kind(X))))&
((?[X]:((curious(X)<~>~quiet(X))))=>(wise(fred)))&
((~wise(fred))<=>(?[X]:(~humble(X))))&
(((brave(alice)<~>~humble(alice)))<=>(?[X]:((tall(X)|~rich(X)))))&
((?[X]:((~humble(X)&patient(X))))<=>(?[X]:((~wise(X)&curious(X)))))&
((?[X]:(~rich(X)))=>(~calm(susan)))&
(![X]:(~wise(X)=>~tall(X)))&
((?[X]:((~kind(X)<~>generous(X))))=>((humble(mary)|calm(mary))))&
(((old(paul)&~quiet(paul)))=>((~humble(lucy)<~>~calm(lucy))))&
(![X]:((~rich(X)&~old(X))<=>brave(X)))&
((~brave(lucy)|happy(lucy)))&
(?[X]:((creative(X)&generous(X))))&
((~strong(mary)&~calm(mary)))&
(?[X]:((calm(X)<~>~curious(X))))&
(?[X]:((~strong(X)|~brave(X))))&
(?[X]:((~humble(X)<~>~happy(X))))&
(?[X]:(wise(X)))&
(?[X]:((strong(X)&~generous(X)))) | ~kind(mary) | [
"p5",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6390595510766356068477289
% SZS output start Proof for 6390595510766356068477289
6. ! [X0] : (~strong(X0) <=> (patient(X0) & ~kind(X0))) [input p5]
19. ~calm(mary) & ~strong(mary) [input p18]
25. kind(mary) [input hypothesis]
47. ! [X0] : ((~strong(X0) | (~patient(X0) | kind(X0))) & ((patient(X0) & ~kind(X0)) | strong(X0))) [nnf transformation 6]
48. ! [X0] : ((~strong(X0) | ~patient(X0) | kind(X0)) & ((patient(X0) & ~kind(X0)) | strong(X0))) [flattening 47]
95. ~kind(X0) | strong(X0) [cnf transformation 48]
126. ~strong(mary) [cnf transformation 19]
136. kind(mary) [cnf transformation 25]
298. strong(mary) [resolution 95,136]
299. $false [subsumption resolution 298,126]
% SZS output end Proof for 6390595510766356068477289
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not old and not brave then lucy is either calm or not creative.
If someone is kind or not humble then someone is both rich and wise.
If someone is both funny and not wise then someone is generous or kind and vice versa.
If lucy is either not rich or not kind then someone is calm or not generous.
Everyone who is both old and not creative is not funny and vice versa.
Everyone who is both brave and happy is either not kind or not patient and vice versa.
Everyone who is happy or not happy is not happy and vice versa.
Everyone who is both not calm and strong is tall.
Everyone who is kind or funny is both not rich and brave and vice versa.
Everyone who is both not calm and not brave is both not brave and not curious.
Everyone who is either tall or rich is not creative.
Everyone who is either not patient or not wise is creative and vice versa.
If fred is not humble or old then someone is brave or creative and vice versa.
If susan is both not patient and curious then susan is either calm or not happy.
If someone is either quiet or not creative then someone is both brave and not happy.
Mary is either quiet or brave.
Someone is old.
Someone is both quiet and not wise.
Alice is both rich and not curious.
Mary is either brave or generous.
Someone is not kind.
Susan is not brave or calm. | Fred is humble. | entailment | (((~old(fred)&~brave(fred)))=>((calm(lucy)<~>~creative(lucy))))&
((?[X]:((kind(X)|~humble(X))))=>(?[X]:((rich(X)&wise(X)))))&
((?[X]:((funny(X)&~wise(X))))<=>(?[X]:((generous(X)|kind(X)))))&
(((~rich(lucy)<~>~kind(lucy)))=>(?[X]:((calm(X)|~generous(X)))))&
(![X]:((old(X)&~creative(X))<=>~funny(X)))&
(![X]:((brave(X)&happy(X))<=>(~kind(X)<~>~patient(X))))&
(![X]:((happy(X)|~happy(X))<=>~happy(X)))&
(![X]:((~calm(X)&strong(X))=>tall(X)))&
(![X]:((kind(X)|funny(X))<=>(~rich(X)&brave(X))))&
(![X]:((~calm(X)&~brave(X))=>(~brave(X)&~curious(X))))&
(![X]:((tall(X)<~>rich(X))=>~creative(X)))&
(![X]:((~patient(X)<~>~wise(X))<=>creative(X)))&
(((~humble(fred)|old(fred)))<=>(?[X]:((brave(X)|creative(X)))))&
(((~patient(susan)&curious(susan)))=>((calm(susan)<~>~happy(susan))))&
((?[X]:((quiet(X)<~>~creative(X))))=>(?[X]:((brave(X)&~happy(X)))))&
((quiet(mary)<~>brave(mary)))&
(?[X]:(old(X)))&
(?[X]:((quiet(X)&~wise(X))))&
((rich(alice)&~curious(alice)))&
((brave(mary)<~>generous(mary)))&
(?[X]:(~kind(X)))&
((~brave(susan)|calm(susan))) | humble(fred) | [
"p1",
"p4",
"p5",
"p6",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5967211168183919699892321
% SZS output start Proof for 5967211168183919699892321
2. ? [X0] : (~humble(X0) | kind(X0)) => ? [X0] : (wise(X0) & rich(X0)) [input p1]
5. ! [X0] : ((~creative(X0) & old(X0)) <=> ~funny(X0)) [input p4]
6. ! [X0] : ((happy(X0) & brave(X0)) <=> (~kind(X0) <~> ~patient(X0))) [input p5]
7. ! [X0] : ((~happy(X0) | happy(X0)) <=> ~happy(X0)) [input p6]
9. ! [X0] : ((funny(X0) | kind(X0)) <=> (brave(X0) & ~rich(X0))) [input p8]
12. ! [X0] : ((~patient(X0) <~> ~wise(X0)) <=> creative(X0)) [input p11]
23. ~humble(fred) [input hypothesis]
24. ? [X0] : (~humble(X0) | kind(X0)) => ? [X1] : (wise(X1) & rich(X1)) [rectify 2]
33. ? [X1] : (wise(X1) & rich(X1)) | ! [X0] : (humble(X0) & ~kind(X0)) [ennf transformation 24]
40. ? [X0] : (wise(X0) & rich(X0)) | ! [X1] : (humble(X1) & ~kind(X1)) [rectify 33]
41. ? [X0] : (wise(X0) & rich(X0)) => (wise(sK0) & rich(sK0)) [choice axiom]
42. (wise(sK0) & rich(sK0)) | ! [X1] : (humble(X1) & ~kind(X1)) [skolemisation 40,41]
51. ! [X0] : (((~creative(X0) & old(X0)) | funny(X0)) & (~funny(X0) | (creative(X0) | ~old(X0)))) [nnf transformation 5]
52. ! [X0] : (((~creative(X0) & old(X0)) | funny(X0)) & (~funny(X0) | creative(X0) | ~old(X0))) [flattening 51]
53. ! [X0] : (((happy(X0) & brave(X0)) | ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0)))) & (((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | (~happy(X0) | ~brave(X0)))) [nnf transformation 6]
54. ! [X0] : (((happy(X0) & brave(X0)) | ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0)))) & (((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | ~happy(X0) | ~brave(X0))) [flattening 53]
55. ! [X0] : (((~happy(X0) | happy(X0)) | happy(X0)) & (~happy(X0) | (happy(X0) & ~happy(X0)))) [nnf transformation 7]
56. ! [X0] : ((~happy(X0) | happy(X0) | happy(X0)) & (~happy(X0) | (happy(X0) & ~happy(X0)))) [flattening 55]
57. ! [X0] : (((funny(X0) | kind(X0)) | (~brave(X0) | rich(X0))) & ((brave(X0) & ~rich(X0)) | (~funny(X0) & ~kind(X0)))) [nnf transformation 9]
58. ! [X0] : ((funny(X0) | kind(X0) | ~brave(X0) | rich(X0)) & ((brave(X0) & ~rich(X0)) | (~funny(X0) & ~kind(X0)))) [flattening 57]
60. ! [X0] : ((((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | ~creative(X0)) & (creative(X0) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0))))) [nnf transformation 12]
81. rich(sK0) | humble(X1) [cnf transformation 42]
83. wise(sK0) | humble(X1) [cnf transformation 42]
93. ~creative(X0) | funny(X0) [cnf transformation 52]
98. ~patient(X0) | happy(X0) | kind(X0) [cnf transformation 54]
100. ~happy(X0) | ~happy(X0) [cnf transformation 56]
103. ~rich(X0) | ~kind(X0) [cnf transformation 58]
104. ~funny(X0) | ~rich(X0) [cnf transformation 58]
111. ~wise(X0) | creative(X0) | patient(X0) [cnf transformation 60]
133. ~humble(fred) [cnf transformation 23]
134. ~happy(X0) [duplicate literal removal 100]
155. 5 <=> ! [X1] : humble(X1) [avatar definition]
156. humble(X1) <- (5) [avatar component clause 155]
158. 6 <=> wise(sK0) [avatar definition]
160. wise(sK0) <- (6) [avatar component clause 158]
161. 5 | 6 [avatar split clause 83,158,155]
167. 8 <=> rich(sK0) [avatar definition]
169. rich(sK0) <- (8) [avatar component clause 167]
170. 5 | 8 [avatar split clause 81,167,155]
221. 20 <=> humble(fred) [avatar definition]
223. ~humble(fred) <- (~20) [avatar component clause 221]
276. ~20 [avatar split clause 133,221]
277. $false <- (5, ~20) [resolution 223,156]
278. ~5 | 20 [avatar contradiction clause 277]
280. ~kind(sK0) <- (8) [resolution 103,169]
301. 34 <=> creative(sK0) [avatar definition]
302. creative(sK0) <- (34) [avatar component clause 301]
303. ~creative(sK0) <- (~34) [avatar component clause 301]
309. creative(sK0) | patient(sK0) <- (6) [resolution 111,160]
311. patient(sK0) <- (6, ~34) [subsumption resolution 309,303]
313. happy(sK0) | kind(sK0) <- (6, ~34) [resolution 311,98]
315. kind(sK0) <- (6, ~34) [subsumption resolution 313,134]
320. $false <- (6, 8, ~34) [subsumption resolution 280,315]
321. ~6 | ~8 | 34 [avatar contradiction clause 320]
360. funny(sK0) <- (34) [resolution 302,93]
427. ~rich(sK0) <- (34) [resolution 360,104]
428. $false <- (8, 34) [subsumption resolution 427,169]
429. ~8 | ~34 [avatar contradiction clause 428]
430. $false [avatar sat refutation 161,170,276,278,321,429]
% SZS output end Proof for 5967211168183919699892321
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is either tall or not curious is both not kind and curious and vice versa.
Everyone who is both tall and not rich is both creative and curious.
Everyone who is kind is brave and vice versa.
If someone is funny or generous then mary is tall or not patient.
If someone is either humble or tall then alice is quiet and vice versa.
If alice is both not old and rich then someone is both patient and not quiet.
Everyone who is either rich or not humble is not calm and vice versa.
Everyone who is both humble and not curious is either humble or not calm.
If alice is either not funny or patient then someone is both brave and wise.
If mary is not patient then someone is tall and vice versa.
If fred is both kind and not curious then alice is both not quiet and creative and vice versa.
Everyone who is either not wise or not strong is not humble or tall.
Everyone who is curious or not humble is both not funny and old.
Everyone who is both not patient and not quiet is both strong and brave.
Everyone who is either rich or quiet is brave or kind and vice versa.
Everyone who is quiet or happy is both not old and rich and vice versa.
Paul is both calm and kind.
John is both not kind and curious.
Someone is calm.
Mary is either not humble or not brave.
Someone is either happy or wise.
Someone is not rich. | John is not humble. | contradiction | (![X]:((tall(X)<~>~curious(X))<=>(~kind(X)&curious(X))))&
(![X]:((tall(X)&~rich(X))=>(creative(X)&curious(X))))&
(![X]:(kind(X)<=>brave(X)))&
((?[X]:((funny(X)|generous(X))))=>((tall(mary)|~patient(mary))))&
((?[X]:((humble(X)<~>tall(X))))<=>(quiet(alice)))&
(((~old(alice)&rich(alice)))=>(?[X]:((patient(X)&~quiet(X)))))&
(![X]:((rich(X)<~>~humble(X))<=>~calm(X)))&
(![X]:((humble(X)&~curious(X))=>(humble(X)<~>~calm(X))))&
(((~funny(alice)<~>patient(alice)))=>(?[X]:((brave(X)&wise(X)))))&
((~patient(mary))<=>(?[X]:(tall(X))))&
(((kind(fred)&~curious(fred)))<=>((~quiet(alice)&creative(alice))))&
(![X]:((~wise(X)<~>~strong(X))=>(~humble(X)|tall(X))))&
(![X]:((curious(X)|~humble(X))=>(~funny(X)&old(X))))&
(![X]:((~patient(X)&~quiet(X))=>(strong(X)&brave(X))))&
(![X]:((rich(X)<~>quiet(X))<=>(brave(X)|kind(X))))&
(![X]:((quiet(X)|happy(X))<=>(~old(X)&rich(X))))&
((calm(paul)&kind(paul)))&
((~kind(john)&curious(john)))&
(?[X]:(calm(X)))&
((~humble(mary)<~>~brave(mary)))&
(?[X]:((happy(X)<~>wise(X))))&
(?[X]:(~rich(X))) | ~humble(john) | [
"p0",
"p1",
"p4",
"p6",
"p7",
"p12",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5463992888287424218672705
% SZS output start Proof for 5463992888287424218672705
1. ! [X0] : ((tall(X0) <~> ~curious(X0)) <=> (curious(X0) & ~kind(X0))) [input p0]
2. ! [X0] : ((~rich(X0) & tall(X0)) => (curious(X0) & creative(X0))) [input p1]
5. ? [X0] : (humble(X0) <~> tall(X0)) <=> quiet(alice) [input p4]
7. ! [X0] : ((rich(X0) <~> ~humble(X0)) <=> ~calm(X0)) [input p6]
8. ! [X0] : ((~curious(X0) & humble(X0)) => (humble(X0) <~> ~calm(X0))) [input p7]
13. ! [X0] : ((~humble(X0) | curious(X0)) => (old(X0) & ~funny(X0))) [input p12]
16. ! [X0] : ((happy(X0) | quiet(X0)) <=> (rich(X0) & ~old(X0))) [input p15]
18. curious(john) & ~kind(john) [input p17]
23. ~humble(john) [input hypothesis]
25. ! [X0] : ((curious(X0) & creative(X0)) | (rich(X0) | ~tall(X0))) [ennf transformation 2]
26. ! [X0] : ((curious(X0) & creative(X0)) | rich(X0) | ~tall(X0)) [flattening 25]
31. ! [X0] : ((humble(X0) <~> ~calm(X0)) | (curious(X0) | ~humble(X0))) [ennf transformation 8]
32. ! [X0] : ((humble(X0) <~> ~calm(X0)) | curious(X0) | ~humble(X0)) [flattening 31]
36. ! [X0] : ((old(X0) & ~funny(X0)) | (humble(X0) & ~curious(X0))) [ennf transformation 13]
39. ! [X0] : ((((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | (~curious(X0) | kind(X0))) & ((curious(X0) & ~kind(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0))))) [nnf transformation 1]
40. ! [X0] : ((((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | ~curious(X0) | kind(X0)) & ((curious(X0) & ~kind(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0))))) [flattening 39]
42. (? [X0] : ((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | ~quiet(alice)) & (quiet(alice) | ! [X0] : ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) [nnf transformation 5]
43. (? [X0] : ((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | ~quiet(alice)) & (quiet(alice) | ! [X1] : ((humble(X1) | ~tall(X1)) & (tall(X1) | ~humble(X1)))) [rectify 42]
44. ? [X0] : ((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) => ((~tall(sK0) | ~humble(sK0)) & (tall(sK0) | humble(sK0))) [choice axiom]
45. (((~tall(sK0) | ~humble(sK0)) & (tall(sK0) | humble(sK0))) | ~quiet(alice)) & (quiet(alice) | ! [X1] : ((humble(X1) | ~tall(X1)) & (tall(X1) | ~humble(X1)))) [skolemisation 43,44]
48. ! [X0] : ((((humble(X0) | ~rich(X0)) & (~humble(X0) | rich(X0))) | calm(X0)) & (~calm(X0) | ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0))))) [nnf transformation 7]
49. ! [X0] : (((calm(X0) | ~humble(X0)) & (~calm(X0) | humble(X0))) | curious(X0) | ~humble(X0)) [nnf transformation 32]
62. ! [X0] : (((happy(X0) | quiet(X0)) | (~rich(X0) | old(X0))) & ((rich(X0) & ~old(X0)) | (~happy(X0) & ~quiet(X0)))) [nnf transformation 16]
63. ! [X0] : ((happy(X0) | quiet(X0) | ~rich(X0) | old(X0)) & ((rich(X0) & ~old(X0)) | (~happy(X0) & ~quiet(X0)))) [flattening 62]
75. curious(X0) | tall(X0) | curious(X0) [cnf transformation 40]
76. ~curious(X0) | tall(X0) | ~curious(X0) | kind(X0) [cnf transformation 40]
79. curious(X0) | rich(X0) | ~tall(X0) [cnf transformation 26]
84. quiet(alice) | humble(X1) | ~tall(X1) [cnf transformation 45]
89. ~calm(X0) | ~humble(X0) | ~rich(X0) [cnf transformation 48]
92. ~rich(X0) | humble(X0) | calm(X0) [cnf transformation 48]
94. calm(X0) | ~humble(X0) | curious(X0) | ~humble(X0) [cnf transformation 49]
109. ~curious(X0) | old(X0) [cnf transformation 36]
110. old(X0) | humble(X0) [cnf transformation 36]
119. ~old(X0) | ~quiet(X0) [cnf transformation 63]
126. ~kind(john) [cnf transformation 18]
134. ~humble(john) [cnf transformation 23]
135. ~humble(X0) | calm(X0) | curious(X0) [duplicate literal removal 94]
136. curious(X0) | tall(X0) [duplicate literal removal 75]
137. ~curious(X0) | tall(X0) | kind(X0) [duplicate literal removal 76]
138. rich(X0) | curious(X0) [subsumption resolution 79,136]
152. 4 <=> quiet(alice) [avatar definition]
153. quiet(alice) <- (4) [avatar component clause 152]
166. 7 <=> ! [X1] : (humble(X1) | ~tall(X1)) [avatar definition]
167. ~tall(X1) | humble(X1) <- (7) [avatar component clause 166]
168. 7 | 4 [avatar split clause 84,152,166]
174. 9 <=> old(alice) [avatar definition]
175. ~old(alice) <- (~9) [avatar component clause 174]
176. old(alice) <- (9) [avatar component clause 174]
263. ~quiet(X0) | humble(X0) [resolution 119,110]
271. ~quiet(alice) <- (9) [resolution 176,119]
272. $false <- (4, 9) [subsumption resolution 271,153]
273. ~4 | ~9 [avatar contradiction clause 272]
350. humble(X0) | calm(X0) | curious(X0) [resolution 92,138]
354. calm(X0) | curious(X0) [subsumption resolution 350,135]
389. tall(X0) | kind(X0) | tall(X0) [resolution 137,136]
393. kind(X0) | tall(X0) [duplicate literal removal 389]
470. curious(X1) | ~humble(X1) | ~rich(X1) [resolution 354,89]
471. ~humble(X1) | curious(X1) [subsumption resolution 470,138]
479. tall(john) [resolution 393,126]
610. humble(john) <- (7) [resolution 167,479]
613. $false <- (7) [subsumption resolution 610,134]
614. ~7 [avatar contradiction clause 613]
616. humble(alice) <- (4) [resolution 153,263]
642. curious(alice) <- (4) [resolution 616,471]
717. old(alice) <- (4) [resolution 642,109]
718. $false <- (4, ~9) [subsumption resolution 717,175]
719. ~4 | 9 [avatar contradiction clause 718]
720. $false [avatar sat refutation 168,273,614,719]
% SZS output end Proof for 5463992888287424218672705
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not patient or curious then someone is either kind or quiet and vice versa.
Everyone who is both not happy and not wise is either quiet or curious.
If someone is happy then someone is both not strong and generous and vice versa.
Everyone who is either patient or not calm is both not quiet and not happy.
Everyone who is not old is generous and vice versa.
Everyone who is both not wise and rich is generous or not humble and vice versa.
Everyone who is either quiet or generous is either happy or not quiet and vice versa.
Everyone who is either not kind or kind is not humble or generous and vice versa.
Everyone who is both patient and not funny is not patient or happy and vice versa.
Everyone who is either brave or not rich is not creative and vice versa.
If john is old or humble then someone is both quiet and not patient.
Everyone who is either patient or kind is both brave and not funny and vice versa.
If someone is generous or calm then someone is kind and vice versa.
If someone is either tall or old then fred is humble.
Everyone who is not generous or not quiet is kind or humble.
Everyone who is both brave and not happy is either not kind or curious and vice versa.
Paul is both rich and not happy.
Mary is either brave or not tall.
Someone is either creative or kind.
Someone is not creative or tall.
Someone is not humble.
Fred is both not calm and patient.
Someone is not humble or not kind. | Paul is wise. | contradiction | ((?[X]:((~patient(X)<~>curious(X))))<=>(?[X]:((kind(X)<~>quiet(X)))))&
(![X]:((~happy(X)&~wise(X))=>(quiet(X)<~>curious(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~strong(X)&generous(X)))))&
(![X]:((patient(X)<~>~calm(X))=>(~quiet(X)&~happy(X))))&
(![X]:(~old(X)<=>generous(X)))&
(![X]:((~wise(X)&rich(X))<=>(generous(X)|~humble(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(happy(X)<~>~quiet(X))))&
(![X]:((~kind(X)<~>kind(X))<=>(~humble(X)|generous(X))))&
(![X]:((patient(X)&~funny(X))<=>(~patient(X)|happy(X))))&
(![X]:((brave(X)<~>~rich(X))<=>~creative(X)))&
(((old(john)|humble(john)))=>(?[X]:((quiet(X)&~patient(X)))))&
(![X]:((patient(X)<~>kind(X))<=>(brave(X)&~funny(X))))&
((?[X]:((generous(X)|calm(X))))<=>(?[X]:(kind(X))))&
((?[X]:((tall(X)<~>old(X))))=>(humble(fred)))&
(![X]:((~generous(X)|~quiet(X))=>(kind(X)|humble(X))))&
(![X]:((brave(X)&~happy(X))<=>(~kind(X)<~>curious(X))))&
((rich(paul)&~happy(paul)))&
((brave(mary)<~>~tall(mary)))&
(?[X]:((creative(X)<~>kind(X))))&
(?[X]:((~creative(X)|tall(X))))&
(?[X]:(~humble(X)))&
((~calm(fred)&patient(fred)))&
(?[X]:((~humble(X)|~kind(X)))) | wise(paul) | [
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 714719414550289955775794
% SZS output start Proof for 714719414550289955775794
6. ! [X0] : ((rich(X0) & ~wise(X0)) <=> (~humble(X0) | generous(X0))) [input p5]
8. ! [X0] : ((~kind(X0) <~> kind(X0)) <=> (generous(X0) | ~humble(X0))) [input p7]
24. wise(paul) [input hypothesis]
48. ! [X0] : (((rich(X0) & ~wise(X0)) | (humble(X0) & ~generous(X0))) & ((~humble(X0) | generous(X0)) | (~rich(X0) | wise(X0)))) [nnf transformation 6]
49. ! [X0] : (((rich(X0) & ~wise(X0)) | (humble(X0) & ~generous(X0))) & (~humble(X0) | generous(X0) | ~rich(X0) | wise(X0))) [flattening 48]
51. ! [X0] : ((((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | (~generous(X0) & humble(X0))) & ((generous(X0) | ~humble(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0))))) [nnf transformation 8]
52. ! [X0] : ((((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | (~generous(X0) & humble(X0))) & (generous(X0) | ~humble(X0) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0))))) [flattening 51]
98. ~generous(X0) | ~wise(X0) [cnf transformation 49]
99. ~wise(X0) | humble(X0) [cnf transformation 49]
110. generous(X0) | ~humble(X0) | kind(X0) | kind(X0) [cnf transformation 52]
111. generous(X0) | ~humble(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 52]
159. wise(paul) [cnf transformation 24]
162. generous(X0) | ~humble(X0) | kind(X0) [duplicate literal removal 110]
163. generous(X0) | ~humble(X0) | ~kind(X0) [duplicate literal removal 111]
227. ~humble(X0) | generous(X0) [subsumption resolution 162,163]
321. humble(paul) [resolution 99,159]
338. generous(paul) [resolution 227,321]
373. ~wise(paul) [resolution 338,98]
374. $false [subsumption resolution 373,159]
% SZS output end Proof for 714719414550289955775794
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is both not patient and curious then someone is not generous and vice versa. Everyone who is both generous and humble is both creative and not kind and vice versa. If alice is either calm or tall then lucy is not patient or funny. Everyone who is both old and not happy is rich and vice versa. Everyone who is not brave is both generous and not patient. If lucy is not generous then paul is generous. If someone is not creative then mary is not quiet and vice versa. If someone is both creative and wise then someone is both not patient and not tall. Everyone who is funny or not patient is rich or not calm and vice versa. If someone is either not brave or not creative then fred is not wise or calm and vice versa. If mary is both curious and not humble then susan is either not happy or creative and vice versa. If susan is either not patient or funny then someone is not wise or rich. If lucy is old then someone is either not wise or not patient and vice versa. Everyone who is not rich or rich is rich and vice versa. Everyone who is happy is both quiet and not calm and vice versa. If someone is kind then john is both creative and not patient and vice versa. Alice is either not curious or not kind. Someone is both not tall and not generous. Paul is not tall or not kind. Someone is not brave. Someone is either not strong or not funny. Fred is generous or not generous. Paul is not brave. | Alice is not rich. | contradiction | ((?[X]:((~patient(X)&curious(X))))<=>(?[X]:(~generous(X))))&
(![X]:((generous(X)&humble(X))<=>(creative(X)&~kind(X))))&
(((calm(alice)<~>tall(alice)))=>((~patient(lucy)|funny(lucy))))&
(![X]:((old(X)&~happy(X))<=>rich(X)))&
(![X]:(~brave(X)=>(generous(X)&~patient(X))))&
((~generous(lucy))=>(generous(paul)))&
((?[X]:(~creative(X)))<=>(~quiet(mary)))&
((?[X]:((creative(X)&wise(X))))=>(?[X]:((~patient(X)&~tall(X)))))&
(![X]:((funny(X)|~patient(X))<=>(rich(X)|~calm(X))))&
((?[X]:((~brave(X)<~>~creative(X))))<=>((~wise(fred)|calm(fred))))&
(((curious(mary)&~humble(mary)))<=>((~happy(susan)<~>creative(susan))))&
(((~patient(susan)<~>funny(susan)))=>(?[X]:((~wise(X)|rich(X)))))&
((old(lucy))<=>(?[X]:((~wise(X)<~>~patient(X)))))&
(![X]:((~rich(X)|rich(X))<=>rich(X)))&
(![X]:(happy(X)<=>(quiet(X)&~calm(X))))&
((?[X]:(kind(X)))<=>((creative(john)&~patient(john))))&
((~curious(alice)<~>~kind(alice)))&
(?[X]:((~tall(X)&~generous(X))))&
((~tall(paul)|~kind(paul)))&
(?[X]:(~brave(X)))&
(?[X]:((~strong(X)<~>~funny(X))))&
((generous(fred)|~generous(fred)))&
(~brave(paul)) | ~rich(alice) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7328327852689021635755808
% SZS output start Proof for 7328327852689021635755808
14. ! [X0] : ((rich(X0) | ~rich(X0)) <=> rich(X0)) [input p13]
24. ~rich(alice) [input hypothesis]
66. ! [X0] : (((rich(X0) | ~rich(X0)) | ~rich(X0)) & (rich(X0) | (~rich(X0) & rich(X0)))) [nnf transformation 14]
67. ! [X0] : ((rich(X0) | ~rich(X0) | ~rich(X0)) & (rich(X0) | (~rich(X0) & rich(X0)))) [flattening 66]
124. rich(X0) | rich(X0) [cnf transformation 67]
143. ~rich(alice) [cnf transformation 24]
144. rich(X0) [duplicate literal removal 124]
357. $false [subsumption resolution 143,144]
% SZS output end Proof for 7328327852689021635755808
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not strong or generous then paul is happy or curious. Everyone who is happy or not wise is both not rich and not curious. Everyone who is both not curious and not quiet is not creative or not generous and vice versa. If someone is both not kind and curious then someone is both wise and curious. Everyone who is both not rich and creative is brave or not rich. If someone is humble or tall then someone is not quiet or rich and vice versa. If someone is either humble or not kind then lucy is strong. Everyone who is both humble and not calm is either not rich or calm. If someone is quiet then paul is not tall or not old and vice versa. Everyone who is not calm or not kind is creative or patient and vice versa. Everyone who is calm is humble or not generous. Everyone who is not happy or not old is both not kind and not happy. Everyone who is brave or not creative is brave and vice versa. If lucy is wise or funny then fred is not tall or humble. Everyone who is not rich or tall is both wise and not curious and vice versa. Everyone who is creative is not brave or happy and vice versa. Susan is brave. Someone is old. Someone is not funny. Susan is not funny. Someone is either not rich or humble. Lucy is not happy. Someone is both not funny and not old. | Paul is quiet. | neutral | ((?[X]:((~strong(X)<~>generous(X))))=>((happy(paul)|curious(paul))))&
(![X]:((happy(X)|~wise(X))=>(~rich(X)&~curious(X))))&
(![X]:((~curious(X)&~quiet(X))<=>(~creative(X)|~generous(X))))&
((?[X]:((~kind(X)&curious(X))))=>(?[X]:((wise(X)&curious(X)))))&
(![X]:((~rich(X)&creative(X))=>(brave(X)|~rich(X))))&
((?[X]:((humble(X)|tall(X))))<=>(?[X]:((~quiet(X)|rich(X)))))&
((?[X]:((humble(X)<~>~kind(X))))=>(strong(lucy)))&
(![X]:((humble(X)&~calm(X))=>(~rich(X)<~>calm(X))))&
((?[X]:(quiet(X)))<=>((~tall(paul)|~old(paul))))&
(![X]:((~calm(X)|~kind(X))<=>(creative(X)|patient(X))))&
(![X]:(calm(X)=>(humble(X)|~generous(X))))&
(![X]:((~happy(X)|~old(X))=>(~kind(X)&~happy(X))))&
(![X]:((brave(X)|~creative(X))<=>brave(X)))&
(((wise(lucy)|funny(lucy)))=>((~tall(fred)|humble(fred))))&
(![X]:((~rich(X)|tall(X))<=>(wise(X)&~curious(X))))&
(![X]:(creative(X)<=>(~brave(X)|happy(X))))&
(brave(susan))&
(?[X]:(old(X)))&
(?[X]:(~funny(X)))&
(~funny(susan))&
(?[X]:((~rich(X)<~>humble(X))))&
(~happy(lucy))&
(?[X]:((~funny(X)&~old(X)))) | quiet(paul) | [] | null | 0 |
If someone is not rich or not calm then someone is not curious or humble and vice versa.
Everyone who is wise is both patient and rich and vice versa.
Everyone who is kind is both rich and patient and vice versa.
Everyone who is happy or creative is curious and vice versa.
If someone is both rich and not patient then mary is not tall or not calm.
Everyone who is both happy and brave is kind.
Everyone who is not brave is both creative and generous and vice versa.
Everyone who is not humble or old is funny or not wise and vice versa.
If mary is humble then someone is either humble or not brave and vice versa.
Everyone who is both not tall and not curious is both not strong and not generous.
Everyone who is both not tall and not patient is not curious or wise and vice versa.
If susan is both not happy and funny then someone is old.
If someone is not brave then lucy is both tall and not generous.
If alice is either curious or generous then john is not rich.
If paul is strong or not happy then mary is rich.
If alice is either not funny or not calm then someone is happy and vice versa.
Susan is not wise or rich.
Someone is either not happy or not creative.
Someone is both not rich and not patient.
Someone is both humble and tall.
Susan is both old and not generous.
John is generous.
Someone is strong. | Lucy is happy. | contradiction | ((?[X]:((~rich(X)|~calm(X))))<=>(?[X]:((~curious(X)|humble(X)))))&
(![X]:(wise(X)<=>(patient(X)&rich(X))))&
(![X]:(kind(X)<=>(rich(X)&patient(X))))&
(![X]:((happy(X)|creative(X))<=>curious(X)))&
((?[X]:((rich(X)&~patient(X))))=>((~tall(mary)|~calm(mary))))&
(![X]:((happy(X)&brave(X))=>kind(X)))&
(![X]:(~brave(X)<=>(creative(X)&generous(X))))&
(![X]:((~humble(X)|old(X))<=>(funny(X)|~wise(X))))&
((humble(mary))<=>(?[X]:((humble(X)<~>~brave(X)))))&
(![X]:((~tall(X)&~curious(X))=>(~strong(X)&~generous(X))))&
(![X]:((~tall(X)&~patient(X))<=>(~curious(X)|wise(X))))&
(((~happy(susan)&funny(susan)))=>(?[X]:(old(X))))&
((?[X]:(~brave(X)))=>((tall(lucy)&~generous(lucy))))&
(((curious(alice)<~>generous(alice)))=>(~rich(john)))&
(((strong(paul)|~happy(paul)))=>(rich(mary)))&
(((~funny(alice)<~>~calm(alice)))<=>(?[X]:(happy(X))))&
((~wise(susan)|rich(susan)))&
(?[X]:((~happy(X)<~>~creative(X))))&
(?[X]:((~rich(X)&~patient(X))))&
(?[X]:((humble(X)&tall(X))))&
((old(susan)&~generous(susan)))&
(generous(john))&
(?[X]:(strong(X))) | happy(lucy) | [
"p1",
"p2",
"p5",
"p6",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7481947555219557957505792
% SZS output start Proof for 7481947555219557957505792
2. ! [X0] : (wise(X0) <=> (rich(X0) & patient(X0))) [input p1]
3. ! [X0] : (kind(X0) <=> (patient(X0) & rich(X0))) [input p2]
6. ! [X0] : ((brave(X0) & happy(X0)) => kind(X0)) [input p5]
7. ! [X0] : (~brave(X0) <=> (generous(X0) & creative(X0))) [input p6]
11. ! [X0] : ((~patient(X0) & ~tall(X0)) <=> (wise(X0) | ~curious(X0))) [input p10]
13. ? [X0] : ~brave(X0) => (~generous(lucy) & tall(lucy)) [input p12]
16. (~funny(alice) <~> ~calm(alice)) <=> ? [X0] : happy(X0) [input p15]
24. happy(lucy) [input hypothesis]
26. ! [X0] : (kind(X0) => (patient(X0) & rich(X0))) [unused predicate definition removal 3]
27. ! [X0] : ((patient(X0) & rich(X0)) | ~kind(X0)) [ennf transformation 26]
30. ! [X0] : (kind(X0) | (~brave(X0) | ~happy(X0))) [ennf transformation 6]
31. ! [X0] : (kind(X0) | ~brave(X0) | ~happy(X0)) [flattening 30]
36. (~generous(lucy) & tall(lucy)) | ! [X0] : brave(X0) [ennf transformation 13]
44. ! [X0] : ((wise(X0) | (~rich(X0) | ~patient(X0))) & ((rich(X0) & patient(X0)) | ~wise(X0))) [nnf transformation 2]
45. ! [X0] : ((wise(X0) | ~rich(X0) | ~patient(X0)) & ((rich(X0) & patient(X0)) | ~wise(X0))) [flattening 44]
48. ! [X0] : ((~brave(X0) | (~generous(X0) | ~creative(X0))) & ((generous(X0) & creative(X0)) | brave(X0))) [nnf transformation 7]
49. ! [X0] : ((~brave(X0) | ~generous(X0) | ~creative(X0)) & ((generous(X0) & creative(X0)) | brave(X0))) [flattening 48]
56. ! [X0] : (((~patient(X0) & ~tall(X0)) | (~wise(X0) & curious(X0))) & ((wise(X0) | ~curious(X0)) | (patient(X0) | tall(X0)))) [nnf transformation 11]
57. ! [X0] : (((~patient(X0) & ~tall(X0)) | (~wise(X0) & curious(X0))) & (wise(X0) | ~curious(X0) | patient(X0) | tall(X0))) [flattening 56]
61. (((calm(alice) | funny(alice)) & (~calm(alice) | ~funny(alice))) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | ((~funny(alice) | calm(alice)) & (~calm(alice) | funny(alice)))) [nnf transformation 16]
62. (((calm(alice) | funny(alice)) & (~calm(alice) | ~funny(alice))) | ! [X0] : ~happy(X0)) & (? [X1] : happy(X1) | ((~funny(alice) | calm(alice)) & (~calm(alice) | funny(alice)))) [rectify 61]
63. ? [X1] : happy(X1) => happy(sK4) [choice axiom]
64. (((calm(alice) | funny(alice)) & (~calm(alice) | ~funny(alice))) | ! [X0] : ~happy(X0)) & (happy(sK4) | ((~funny(alice) | calm(alice)) & (~calm(alice) | funny(alice)))) [skolemisation 62,63]
78. ~wise(X0) | patient(X0) [cnf transformation 45]
80. ~patient(X0) | ~rich(X0) | wise(X0) [cnf transformation 45]
81. ~kind(X0) | rich(X0) [cnf transformation 27]
82. ~kind(X0) | patient(X0) [cnf transformation 27]
87. ~brave(X0) | kind(X0) | ~happy(X0) [cnf transformation 31]
89. generous(X0) | brave(X0) [cnf transformation 49]
105. ~patient(X0) | ~wise(X0) [cnf transformation 57]
108. ~generous(lucy) | brave(X0) [cnf transformation 36]
113. happy(sK4) | ~calm(alice) | funny(alice) [cnf transformation 64]
114. happy(sK4) | ~funny(alice) | calm(alice) [cnf transformation 64]
115. ~calm(alice) | ~funny(alice) | ~happy(X0) [cnf transformation 64]
116. calm(alice) | funny(alice) | ~happy(X0) [cnf transformation 64]
128. happy(lucy) [cnf transformation 24]
195. ~wise(X0) [subsumption resolution 105,78]
211. 20 <=> ! [X0] : brave(X0) [avatar definition]
212. brave(X0) <- (20) [avatar component clause 211]
214. 21 <=> generous(lucy) [avatar definition]
216. ~generous(lucy) <- (~21) [avatar component clause 214]
217. 20 | ~21 [avatar split clause 108,214,211]
252. 29 <=> ! [X0] : ~happy(X0) [avatar definition]
253. ~happy(X0) <- (29) [avatar component clause 252]
255. 30 <=> funny(alice) [avatar definition]
259. 31 <=> calm(alice) [avatar definition]
262. 29 | 30 | 31 [avatar split clause 116,259,255,252]
263. 29 | ~30 | ~31 [avatar split clause 115,259,255,252]
265. 32 <=> happy(sK4) [avatar definition]
267. happy(sK4) <- (32) [avatar component clause 265]
268. 31 | ~30 | 32 [avatar split clause 114,265,255,259]
269. 30 | ~31 | 32 [avatar split clause 113,265,259,255]
286. $false <- (29) [resolution 253,128]
287. ~29 [avatar contradiction clause 286]
307. ~happy(X1) | kind(X1) <- (20) [resolution 87,212]
313. kind(sK4) <- (20, 32) [resolution 307,267]
352. 40 <=> patient(sK4) [avatar definition]
354. patient(sK4) <- (40) [avatar component clause 352]
397. patient(sK4) <- (20, 32) [resolution 313,82]
399. 40 | ~20 | ~32 [avatar split clause 397,265,211,352]
410. 51 <=> patient(lucy) [avatar definition]
412. patient(lucy) <- (51) [avatar component clause 410]
430. brave(lucy) <- (~21) [resolution 216,89]
441. kind(lucy) | ~happy(lucy) <- (~21) [resolution 430,87]
442. kind(lucy) <- (~21) [subsumption resolution 441,128]
458. 57 <=> kind(sK4) [avatar definition]
460. kind(sK4) <- (57) [avatar component clause 458]
496. patient(lucy) <- (~21) [resolution 442,82]
497. rich(lucy) <- (~21) [resolution 442,81]
498. 51 | 21 [avatar split clause 496,214,410]
499. ~rich(lucy) | wise(lucy) <- (51) [resolution 412,80]
501. wise(lucy) <- (~21, 51) [subsumption resolution 499,497]
502. $false <- (~21, 51) [subsumption resolution 501,195]
503. 21 | ~51 [avatar contradiction clause 502]
519. ~happy(X0) | kind(X0) <- (20) [resolution 212,87]
526. ~rich(sK4) | wise(sK4) <- (40) [resolution 354,80]
528. ~rich(sK4) <- (40) [subsumption resolution 526,195]
530. kind(sK4) <- (20, 32) [resolution 519,267]
534. 57 | ~20 | ~32 [avatar split clause 530,265,211,458]
541. rich(sK4) <- (57) [resolution 460,81]
542. $false <- (40, 57) [subsumption resolution 541,528]
543. ~40 | ~57 [avatar contradiction clause 542]
544. $false [avatar sat refutation 217,262,263,268,269,287,399,498,503,534,543]
% SZS output end Proof for 7481947555219557957505792
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either patient or not strong then someone is either not strong or not humble.
If someone is not funny then alice is not old or not wise and vice versa.
Everyone who is both not patient and strong is not kind or calm and vice versa.
Everyone who is funny or not rich is not tall and vice versa.
If someone is old then paul is both not generous and creative and vice versa.
Everyone who is old is not generous or not strong and vice versa.
If someone is either not generous or not happy then susan is not patient or not brave.
If paul is both not brave and not rich then john is not rich.
If mary is both rich and not patient then someone is not creative or creative and vice versa.
If someone is either kind or not tall then someone is both not kind and tall and vice versa.
If alice is either not rich or old then someone is both not brave and kind.
If mary is either not brave or not patient then lucy is both rich and not happy and vice versa.
If john is kind then fred is old.
Everyone who is not kind or quiet is either not tall or not strong and vice versa.
If alice is not happy or kind then mary is both humble and not old and vice versa.
If alice is both not tall and not rich then alice is both not old and not curious and vice versa.
Alice is patient or kind.
Someone is wise.
Someone is not wise or humble.
Someone is generous.
Susan is not kind or not curious.
Paul is strong.
Someone is curious or not funny.
Fred is curious or strong. | Mary is not funny. | contradiction | ((?[X]:((patient(X)<~>~strong(X))))=>(?[X]:((~strong(X)<~>~humble(X)))))&
((?[X]:(~funny(X)))<=>((~old(alice)|~wise(alice))))&
(![X]:((~patient(X)&strong(X))<=>(~kind(X)|calm(X))))&
(![X]:((funny(X)|~rich(X))<=>~tall(X)))&
((?[X]:(old(X)))<=>((~generous(paul)&creative(paul))))&
(![X]:(old(X)<=>(~generous(X)|~strong(X))))&
((?[X]:((~generous(X)<~>~happy(X))))=>((~patient(susan)|~brave(susan))))&
(((~brave(paul)&~rich(paul)))=>(~rich(john)))&
(((rich(mary)&~patient(mary)))<=>(?[X]:((~creative(X)|creative(X)))))&
((?[X]:((kind(X)<~>~tall(X))))<=>(?[X]:((~kind(X)&tall(X)))))&
(((~rich(alice)<~>old(alice)))=>(?[X]:((~brave(X)&kind(X)))))&
(((~brave(mary)<~>~patient(mary)))<=>((rich(lucy)&~happy(lucy))))&
((kind(john))=>(old(fred)))&
(![X]:((~kind(X)|quiet(X))<=>(~tall(X)<~>~strong(X))))&
(((~happy(alice)|kind(alice)))<=>((humble(mary)&~old(mary))))&
(((~tall(alice)&~rich(alice)))<=>((~old(alice)&~curious(alice))))&
((patient(alice)|kind(alice)))&
(?[X]:(wise(X)))&
(?[X]:((~wise(X)|humble(X))))&
(?[X]:(generous(X)))&
((~kind(susan)|~curious(susan)))&
(strong(paul))&
(?[X]:((curious(X)|~funny(X))))&
((curious(fred)|strong(fred))) | ~funny(mary) | [
"p2",
"p3",
"p8",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8584250838042364312436537
% SZS output start Proof for 8584250838042364312436537
3. ! [X0] : ((strong(X0) & ~patient(X0)) <=> (calm(X0) | ~kind(X0))) [input p2]
4. ! [X0] : ((~rich(X0) | funny(X0)) <=> ~tall(X0)) [input p3]
9. (~patient(mary) & rich(mary)) <=> ? [X0] : (creative(X0) | ~creative(X0)) [input p8]
10. ? [X0] : (kind(X0) <~> ~tall(X0)) <=> ? [X0] : (tall(X0) & ~kind(X0)) [input p9]
14. ! [X0] : ((quiet(X0) | ~kind(X0)) <=> (~tall(X0) <~> ~strong(X0))) [input p13]
25. ~funny(mary) [input hypothesis]
27. ? [X0] : (kind(X0) <~> ~tall(X0)) <=> ? [X1] : (tall(X1) & ~kind(X1)) [rectify 10]
44. ! [X0] : (((strong(X0) & ~patient(X0)) | (~calm(X0) & kind(X0))) & ((calm(X0) | ~kind(X0)) | (~strong(X0) | patient(X0)))) [nnf transformation 3]
45. ! [X0] : (((strong(X0) & ~patient(X0)) | (~calm(X0) & kind(X0))) & (calm(X0) | ~kind(X0) | ~strong(X0) | patient(X0))) [flattening 44]
46. ! [X0] : (((~rich(X0) | funny(X0)) | tall(X0)) & (~tall(X0) | (rich(X0) & ~funny(X0)))) [nnf transformation 4]
47. ! [X0] : ((~rich(X0) | funny(X0) | tall(X0)) & (~tall(X0) | (rich(X0) & ~funny(X0)))) [flattening 46]
56. ((~patient(mary) & rich(mary)) | ! [X0] : (~creative(X0) & creative(X0))) & (? [X0] : (creative(X0) | ~creative(X0)) | (patient(mary) | ~rich(mary))) [nnf transformation 9]
57. ((~patient(mary) & rich(mary)) | ! [X0] : (~creative(X0) & creative(X0))) & (? [X0] : (creative(X0) | ~creative(X0)) | patient(mary) | ~rich(mary)) [flattening 56]
58. ((~patient(mary) & rich(mary)) | ! [X0] : (~creative(X0) & creative(X0))) & (? [X1] : (creative(X1) | ~creative(X1)) | patient(mary) | ~rich(mary)) [rectify 57]
59. ? [X1] : (creative(X1) | ~creative(X1)) => (creative(sK3) | ~creative(sK3)) [choice axiom]
60. ((~patient(mary) & rich(mary)) | ! [X0] : (~creative(X0) & creative(X0))) & ((creative(sK3) | ~creative(sK3)) | patient(mary) | ~rich(mary)) [skolemisation 58,59]
61. (? [X0] : ((tall(X0) | ~kind(X0)) & (~tall(X0) | kind(X0))) | ! [X1] : (~tall(X1) | kind(X1))) & (? [X1] : (tall(X1) & ~kind(X1)) | ! [X0] : ((kind(X0) | tall(X0)) & (~tall(X0) | ~kind(X0)))) [nnf transformation 27]
62. (? [X0] : ((tall(X0) | ~kind(X0)) & (~tall(X0) | kind(X0))) | ! [X1] : (~tall(X1) | kind(X1))) & (? [X2] : (tall(X2) & ~kind(X2)) | ! [X3] : ((kind(X3) | tall(X3)) & (~tall(X3) | ~kind(X3)))) [rectify 61]
63. ? [X0] : ((tall(X0) | ~kind(X0)) & (~tall(X0) | kind(X0))) => ((tall(sK4) | ~kind(sK4)) & (~tall(sK4) | kind(sK4))) [choice axiom]
64. ? [X2] : (tall(X2) & ~kind(X2)) => (tall(sK5) & ~kind(sK5)) [choice axiom]
65. (((tall(sK4) | ~kind(sK4)) & (~tall(sK4) | kind(sK4))) | ! [X1] : (~tall(X1) | kind(X1))) & ((tall(sK5) & ~kind(sK5)) | ! [X3] : ((kind(X3) | tall(X3)) & (~tall(X3) | ~kind(X3)))) [skolemisation 62,64,63]
71. ! [X0] : (((quiet(X0) | ~kind(X0)) | ((~tall(X0) | strong(X0)) & (~strong(X0) | tall(X0)))) & (((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) | (~quiet(X0) & kind(X0)))) [nnf transformation 14]
72. ! [X0] : ((quiet(X0) | ~kind(X0) | ((~tall(X0) | strong(X0)) & (~strong(X0) | tall(X0)))) & (((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) | (~quiet(X0) & kind(X0)))) [flattening 71]
95. kind(X0) | strong(X0) [cnf transformation 45]
99. ~rich(X0) | funny(X0) | tall(X0) [cnf transformation 47]
110. rich(mary) | creative(X0) [cnf transformation 60]
111. rich(mary) | ~creative(X0) [cnf transformation 60]
114. ~kind(sK5) | ~tall(X3) | ~kind(X3) [cnf transformation 65]
116. tall(sK5) | ~tall(X3) | ~kind(X3) [cnf transformation 65]
131. ~strong(X0) | ~tall(X0) | kind(X0) [cnf transformation 72]
154. ~funny(mary) [cnf transformation 25]
239. 20 <=> ! [X0] : ~creative(X0) [avatar definition]
240. ~creative(X0) <- (20) [avatar component clause 239]
247. 22 <=> ! [X0] : creative(X0) [avatar definition]
248. creative(X0) <- (22) [avatar component clause 247]
251. 23 <=> rich(mary) [avatar definition]
253. rich(mary) <- (23) [avatar component clause 251]
254. 20 | 23 [avatar split clause 111,251,239]
255. 22 | 23 [avatar split clause 110,251,247]
257. 24 <=> ! [X1] : (~tall(X1) | kind(X1)) [avatar definition]
258. ~tall(X1) | kind(X1) <- (24) [avatar component clause 257]
273. 28 <=> tall(sK5) [avatar definition]
275. tall(sK5) <- (28) [avatar component clause 273]
278. 29 <=> ! [X3] : (~tall(X3) | ~kind(X3)) [avatar definition]
279. ~tall(X3) | ~kind(X3) <- (29) [avatar component clause 278]
280. 29 | 28 [avatar split clause 116,273,278]
282. 30 <=> kind(sK5) [avatar definition]
284. ~kind(sK5) <- (~30) [avatar component clause 282]
286. 29 | ~30 [avatar split clause 114,282,278]
331. ~tall(X0) | kind(X0) [subsumption resolution 131,95]
332. 24 [avatar split clause 331,257]
406. $false <- (20, 22) [subsumption resolution 240,248]
407. ~20 | ~22 [avatar contradiction clause 406]
415. kind(sK5) <- (24, 28) [resolution 258,275]
416. $false <- (24, 28, ~30) [subsumption resolution 415,284]
417. ~24 | ~28 | 30 [avatar contradiction clause 416]
418. ~tall(X3) <- (24, 29) [subsumption resolution 279,258]
424. funny(mary) | tall(mary) <- (23) [resolution 99,253]
425. tall(mary) <- (23) [subsumption resolution 424,154]
426. $false <- (23, 24, 29) [subsumption resolution 425,418]
427. ~23 | ~24 | ~29 [avatar contradiction clause 426]
428. $false [avatar sat refutation 254,255,280,286,332,407,417,427]
% SZS output end Proof for 8584250838042364312436537
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either old or not wise is either kind or not generous and vice versa.
Everyone who is both not calm and not generous is not funny or not old and vice versa.
If someone is happy or not rich then someone is both not happy and strong and vice versa.
Everyone who is both rich and brave is not patient.
If someone is both not funny and generous then someone is old or not humble.
Everyone who is either tall or strong is not strong and vice versa.
Everyone who is generous or tall is both not brave and not rich and vice versa.
Everyone who is tall is either not calm or humble.
If someone is both not brave and curious then paul is both not strong and happy.
Everyone who is rich or not happy is either kind or curious and vice versa.
Everyone who is not patient is not humble.
Everyone who is either kind or not calm is not humble or not strong and vice versa.
Everyone who is both not generous and old is funny or brave.
Everyone who is not humble is both creative and not brave.
Everyone who is either not wise or creative is either rich or patient and vice versa.
If mary is either humble or not calm then someone is not creative and vice versa.
Someone is both not wise and not brave.
Lucy is either not humble or old.
Mary is either tall or not happy.
Someone is both not humble and quiet.
Alice is either quiet or not wise.
Someone is either not calm or calm.
Someone is happy.
Fred is kind or not strong. | Fred is strong. | contradiction | (![X]:((old(X)<~>~wise(X))<=>(kind(X)<~>~generous(X))))&
(![X]:((~calm(X)&~generous(X))<=>(~funny(X)|~old(X))))&
((?[X]:((happy(X)|~rich(X))))<=>(?[X]:((~happy(X)&strong(X)))))&
(![X]:((rich(X)&brave(X))=>~patient(X)))&
((?[X]:((~funny(X)&generous(X))))=>(?[X]:((old(X)|~humble(X)))))&
(![X]:((tall(X)<~>strong(X))<=>~strong(X)))&
(![X]:((generous(X)|tall(X))<=>(~brave(X)&~rich(X))))&
(![X]:(tall(X)=>(~calm(X)<~>humble(X))))&
((?[X]:((~brave(X)&curious(X))))=>((~strong(paul)&happy(paul))))&
(![X]:((rich(X)|~happy(X))<=>(kind(X)<~>curious(X))))&
(![X]:(~patient(X)=>~humble(X)))&
(![X]:((kind(X)<~>~calm(X))<=>(~humble(X)|~strong(X))))&
(![X]:((~generous(X)&old(X))=>(funny(X)|brave(X))))&
(![X]:(~humble(X)=>(creative(X)&~brave(X))))&
(![X]:((~wise(X)<~>creative(X))<=>(rich(X)<~>patient(X))))&
(((humble(mary)<~>~calm(mary)))<=>(?[X]:(~creative(X))))&
(?[X]:((~wise(X)&~brave(X))))&
((~humble(lucy)<~>old(lucy)))&
((tall(mary)<~>~happy(mary)))&
(?[X]:((~humble(X)&quiet(X))))&
((quiet(alice)<~>~wise(alice)))&
(?[X]:((~calm(X)<~>calm(X))))&
(?[X]:(happy(X)))&
((kind(fred)|~strong(fred))) | strong(fred) | [
"p5",
"p7",
"p11",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7968553660927883176678223
% SZS output start Proof for 7968553660927883176678223
6. ! [X0] : ((tall(X0) <~> strong(X0)) <=> ~strong(X0)) [input p5]
8. ! [X0] : (tall(X0) => (~calm(X0) <~> humble(X0))) [input p7]
12. ! [X0] : ((kind(X0) <~> ~calm(X0)) <=> (~strong(X0) | ~humble(X0))) [input p11]
24. ~strong(fred) | kind(fred) [input p23]
25. strong(fred) [input hypothesis]
31. ! [X0] : ((~calm(X0) <~> humble(X0)) | ~tall(X0)) [ennf transformation 8]
48. ! [X0] : ((((~strong(X0) | ~tall(X0)) & (strong(X0) | tall(X0))) | strong(X0)) & (~strong(X0) | ((tall(X0) | ~strong(X0)) & (strong(X0) | ~tall(X0))))) [nnf transformation 6]
51. ! [X0] : (((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | ~tall(X0)) [nnf transformation 31]
54. ! [X0] : ((((calm(X0) | ~kind(X0)) & (~calm(X0) | kind(X0))) | (strong(X0) & humble(X0))) & ((~strong(X0) | ~humble(X0)) | ((kind(X0) | calm(X0)) & (~calm(X0) | ~kind(X0))))) [nnf transformation 12]
55. ! [X0] : ((((calm(X0) | ~kind(X0)) & (~calm(X0) | kind(X0))) | (strong(X0) & humble(X0))) & (~strong(X0) | ~humble(X0) | ((kind(X0) | calm(X0)) & (~calm(X0) | ~kind(X0))))) [flattening 54]
94. ~strong(X0) | tall(X0) | ~strong(X0) [cnf transformation 48]
95. strong(X0) | tall(X0) | strong(X0) [cnf transformation 48]
102. humble(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 51]
103. ~humble(X0) | calm(X0) | ~tall(X0) [cnf transformation 51]
113. ~strong(X0) | ~humble(X0) | ~calm(X0) | ~kind(X0) [cnf transformation 55]
117. calm(X0) | ~kind(X0) | humble(X0) [cnf transformation 55]
147. ~strong(fred) | kind(fred) [cnf transformation 24]
148. strong(fred) [cnf transformation 25]
149. ~strong(X0) | tall(X0) [duplicate literal removal 94]
150. tall(X0) | strong(X0) [duplicate literal removal 95]
181. tall(X0) [subsumption resolution 149,150]
184. ~humble(X0) | calm(X0) [subsumption resolution 103,181]
185. ~calm(X0) | humble(X0) [subsumption resolution 102,181]
203. ~kind(X0) | humble(X0) [subsumption resolution 117,185]
204. ~strong(X0) | ~calm(X0) | ~kind(X0) [subsumption resolution 113,203]
245. 17 <=> kind(fred) [avatar definition]
247. kind(fred) <- (17) [avatar component clause 245]
249. 18 <=> strong(fred) [avatar definition]
250. strong(fred) <- (18) [avatar component clause 249]
252. 17 | ~18 [avatar split clause 147,249,245]
253. 18 [avatar split clause 148,249]
260. humble(fred) <- (17) [resolution 203,247]
261. calm(fred) <- (17) [resolution 260,184]
294. ~calm(fred) | ~kind(fred) <- (18) [resolution 204,250]
297. ~kind(fred) <- (17, 18) [subsumption resolution 294,261]
298. $false <- (17, 18) [subsumption resolution 297,247]
299. ~17 | ~18 [avatar contradiction clause 298]
302. $false [avatar sat refutation 252,253,299]
% SZS output end Proof for 7968553660927883176678223
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and not old is creative and vice versa.
Everyone who is both not curious and brave is either curious or tall and vice versa.
Everyone who is not kind or not brave is either not rich or curious and vice versa.
Everyone who is happy is tall or rich and vice versa.
If someone is either not kind or not patient then paul is either not funny or brave.
Everyone who is both not humble and not brave is not rich and vice versa.
Everyone who is humble or not funny is both quiet and strong and vice versa.
If alice is not patient or calm then someone is not funny or not strong and vice versa.
If susan is either not creative or humble then susan is not quiet.
If someone is not creative then alice is not wise and vice versa.
Everyone who is creative or patient is either humble or not brave and vice versa.
If susan is creative then someone is both not patient and generous.
If susan is happy or not calm then someone is both rich and not old.
If someone is both not strong and not humble then someone is not kind or not old.
Everyone who is calm or patient is either wise or not rich.
Everyone who is patient is either kind or funny.
Someone is both not rich and not brave.
Someone is not quiet.
Alice is either not funny or not tall.
Someone is not kind or not old.
Someone is either not brave or tall.
Someone is either not generous or rich.
Fred is not strong.
Someone is curious or creative. | Fred is funny. | entailment | (![X]:((rich(X)&~old(X))<=>creative(X)))&
(![X]:((~curious(X)&brave(X))<=>(curious(X)<~>tall(X))))&
(![X]:((~kind(X)|~brave(X))<=>(~rich(X)<~>curious(X))))&
(![X]:(happy(X)<=>(tall(X)|rich(X))))&
((?[X]:((~kind(X)<~>~patient(X))))=>((~funny(paul)<~>brave(paul))))&
(![X]:((~humble(X)&~brave(X))<=>~rich(X)))&
(![X]:((humble(X)|~funny(X))<=>(quiet(X)&strong(X))))&
(((~patient(alice)|calm(alice)))<=>(?[X]:((~funny(X)|~strong(X)))))&
(((~creative(susan)<~>humble(susan)))=>(~quiet(susan)))&
((?[X]:(~creative(X)))<=>(~wise(alice)))&
(![X]:((creative(X)|patient(X))<=>(humble(X)<~>~brave(X))))&
((creative(susan))=>(?[X]:((~patient(X)&generous(X)))))&
(((happy(susan)|~calm(susan)))=>(?[X]:((rich(X)&~old(X)))))&
((?[X]:((~strong(X)&~humble(X))))=>(?[X]:((~kind(X)|~old(X)))))&
(![X]:((calm(X)|patient(X))=>(wise(X)<~>~rich(X))))&
(![X]:(patient(X)=>(kind(X)<~>funny(X))))&
(?[X]:((~rich(X)&~brave(X))))&
(?[X]:(~quiet(X)))&
((~funny(alice)<~>~tall(alice)))&
(?[X]:((~kind(X)|~old(X))))&
(?[X]:((~brave(X)<~>tall(X))))&
(?[X]:((~generous(X)<~>rich(X))))&
(~strong(fred))&
(?[X]:((curious(X)|creative(X)))) | funny(fred) | [
"p6",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 867787712142708688587793
% SZS output start Proof for 867787712142708688587793
7. ! [X0] : ((~funny(X0) | humble(X0)) <=> (strong(X0) & quiet(X0))) [input p6]
23. ~strong(fred) [input p22]
25. ~funny(fred) [input hypothesis]
45. ! [X0] : (((~funny(X0) | humble(X0)) | (~strong(X0) | ~quiet(X0))) & ((strong(X0) & quiet(X0)) | (funny(X0) & ~humble(X0)))) [nnf transformation 7]
46. ! [X0] : ((~funny(X0) | humble(X0) | ~strong(X0) | ~quiet(X0)) & ((strong(X0) & quiet(X0)) | (funny(X0) & ~humble(X0)))) [flattening 45]
110. strong(X0) | funny(X0) [cnf transformation 46]
149. ~strong(fred) [cnf transformation 23]
151. ~funny(fred) [cnf transformation 25]
316. funny(fred) [resolution 110,149]
317. $false [subsumption resolution 316,151]
% SZS output end Proof for 867787712142708688587793
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet then fred is funny and vice versa. If someone is either not happy or creative then mary is either quiet or old and vice versa. If john is old or curious then paul is either tall or old. If someone is not kind or not curious then fred is either kind or not funny and vice versa. If someone is not happy then lucy is not rich or not humble and vice versa. If mary is generous then someone is both rich and humble and vice versa. If lucy is rich then someone is both not calm and not kind and vice versa. If someone is not wise then someone is curious or not brave and vice versa. Everyone who is not wise is both kind and quiet. Everyone who is not quiet or not happy is calm or happy and vice versa. Everyone who is both not strong and not tall is both strong and brave and vice versa. If someone is tall or generous then susan is happy. Everyone who is not happy is not patient or happy. Everyone who is either wise or not patient is not quiet. If someone is both not tall and patient then someone is both not old and not funny. If someone is both not funny and kind then fred is both not quiet and not kind and vice versa. Someone is not patient or strong. Someone is generous or not happy. Someone is either humble or not patient. Mary is not happy or not wise. Susan is not creative. Susan is either not humble or not kind. Fred is not old or not kind. Someone is not old or not calm. | Mary is not curious. | entailment | ((?[X]:(quiet(X)))<=>(funny(fred)))&
((?[X]:((~happy(X)<~>creative(X))))<=>((quiet(mary)<~>old(mary))))&
(((old(john)|curious(john)))=>((tall(paul)<~>old(paul))))&
((?[X]:((~kind(X)|~curious(X))))<=>((kind(fred)<~>~funny(fred))))&
((?[X]:(~happy(X)))<=>((~rich(lucy)|~humble(lucy))))&
((generous(mary))<=>(?[X]:((rich(X)&humble(X)))))&
((rich(lucy))<=>(?[X]:((~calm(X)&~kind(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((curious(X)|~brave(X)))))&
(![X]:(~wise(X)=>(kind(X)&quiet(X))))&
(![X]:((~quiet(X)|~happy(X))<=>(calm(X)|happy(X))))&
(![X]:((~strong(X)&~tall(X))<=>(strong(X)&brave(X))))&
((?[X]:((tall(X)|generous(X))))=>(happy(susan)))&
(![X]:(~happy(X)=>(~patient(X)|happy(X))))&
(![X]:((wise(X)<~>~patient(X))=>~quiet(X)))&
((?[X]:((~tall(X)&patient(X))))=>(?[X]:((~old(X)&~funny(X)))))&
((?[X]:((~funny(X)&kind(X))))<=>((~quiet(fred)&~kind(fred))))&
(?[X]:((~patient(X)|strong(X))))&
(?[X]:((generous(X)|~happy(X))))&
(?[X]:((humble(X)<~>~patient(X))))&
((~happy(mary)|~wise(mary)))&
(~creative(susan))&
((~humble(susan)<~>~kind(susan)))&
((~old(fred)|~kind(fred)))&
(?[X]:((~old(X)|~calm(X)))) | ~curious(mary) | [
"p7",
"p8",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 190478937724629593662200
% SZS output start Proof for 190478937724629593662200
8. ? [X0] : ~wise(X0) <=> ? [X0] : (~brave(X0) | curious(X0)) [input p7]
9. ! [X0] : (~wise(X0) => (quiet(X0) & kind(X0))) [input p8]
10. ! [X0] : ((~happy(X0) | ~quiet(X0)) <=> (happy(X0) | calm(X0))) [input p9]
13. ! [X0] : (~happy(X0) => (happy(X0) | ~patient(X0))) [input p12]
14. ! [X0] : ((wise(X0) <~> ~patient(X0)) => ~quiet(X0)) [input p13]
25. curious(mary) [input hypothesis]
26. ? [X0] : ~wise(X0) <=> ? [X1] : (~brave(X1) | curious(X1)) [rectify 8]
29. ! [X0] : ((quiet(X0) & kind(X0)) | wise(X0)) [ennf transformation 9]
31. ! [X0] : ((happy(X0) | ~patient(X0)) | happy(X0)) [ennf transformation 13]
32. ! [X0] : (happy(X0) | ~patient(X0) | happy(X0)) [flattening 31]
33. ! [X0] : (~quiet(X0) | (wise(X0) <=> ~patient(X0))) [ennf transformation 14]
61. (? [X0] : ~wise(X0) | ! [X1] : (brave(X1) & ~curious(X1))) & (? [X1] : (~brave(X1) | curious(X1)) | ! [X0] : wise(X0)) [nnf transformation 26]
62. (? [X0] : ~wise(X0) | ! [X1] : (brave(X1) & ~curious(X1))) & (? [X2] : (~brave(X2) | curious(X2)) | ! [X3] : wise(X3)) [rectify 61]
63. ? [X0] : ~wise(X0) => ~wise(sK6) [choice axiom]
64. ? [X2] : (~brave(X2) | curious(X2)) => (~brave(sK7) | curious(sK7)) [choice axiom]
65. (~wise(sK6) | ! [X1] : (brave(X1) & ~curious(X1))) & ((~brave(sK7) | curious(sK7)) | ! [X3] : wise(X3)) [skolemisation 62,64,63]
66. ! [X0] : (((~happy(X0) | ~quiet(X0)) | (~happy(X0) & ~calm(X0))) & ((happy(X0) | calm(X0)) | (happy(X0) & quiet(X0)))) [nnf transformation 10]
67. ! [X0] : ((~happy(X0) | ~quiet(X0) | (~happy(X0) & ~calm(X0))) & (happy(X0) | calm(X0) | (happy(X0) & quiet(X0)))) [flattening 66]
70. ! [X0] : (~quiet(X0) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0)))) [nnf transformation 33]
119. ~wise(sK6) | ~curious(X1) [cnf transformation 65]
122. wise(X0) | quiet(X0) [cnf transformation 29]
126. ~happy(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 67]
133. happy(X0) | ~patient(X0) | happy(X0) [cnf transformation 32]
135. ~quiet(X0) | wise(X0) | patient(X0) [cnf transformation 70]
152. curious(mary) [cnf transformation 25]
153. ~patient(X0) | happy(X0) [duplicate literal removal 133]
157. ~happy(X0) | ~quiet(X0) [duplicate literal removal 126]
299. 31 <=> wise(sK6) [avatar definition]
301. ~wise(sK6) <- (~31) [avatar component clause 299]
304. 32 <=> ! [X1] : ~curious(X1) [avatar definition]
305. ~curious(X1) <- (32) [avatar component clause 304]
306. 32 | ~31 [avatar split clause 119,299,304]
331. patient(X0) | wise(X0) [subsumption resolution 135,122]
431. $false <- (32) [resolution 305,152]
432. ~32 [avatar contradiction clause 431]
445. quiet(sK6) <- (~31) [resolution 301,122]
457. wise(X0) | happy(X0) [resolution 331,153]
467. happy(sK6) <- (~31) [resolution 457,301]
468. ~quiet(sK6) <- (~31) [resolution 467,157]
469. $false <- (~31) [subsumption resolution 468,445]
470. 31 [avatar contradiction clause 469]
471. $false [avatar sat refutation 306,432,470]
% SZS output end Proof for 190478937724629593662200
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is generous and vice versa.
Everyone who is not tall or not funny is either rich or not calm and vice versa.
Everyone who is either not kind or not wise is brave and vice versa.
If someone is either not brave or not patient then someone is not funny or not curious.
Everyone who is not humble or not calm is not patient or not creative and vice versa.
If someone is generous then alice is either happy or funny and vice versa.
If fred is not calm or funny then mary is both not creative and not kind and vice versa.
Everyone who is both kind and not rich is not generous or quiet and vice versa.
If someone is either not strong or creative then john is creative or not wise.
Everyone who is either tall or not brave is both not tall and not rich.
Everyone who is either old or patient is calm or not calm and vice versa.
If someone is either wise or not calm then alice is happy and vice versa.
Everyone who is wise is both brave and quiet.
If someone is humble or patient then alice is either not calm or brave.
Everyone who is funny is either curious or not happy.
If lucy is both not rich and rich then paul is both not patient and quiet and vice versa.
Fred is not funny.
Someone is either not happy or old.
Lucy is quiet or not wise.
Someone is kind or not generous.
Mary is kind or not wise.
Fred is either not generous or not kind.
Lucy is not tall.
Someone is either not wise or not patient. | Mary is creative. | contradiction | (![X]:(~calm(X)<=>generous(X)))&
(![X]:((~tall(X)|~funny(X))<=>(rich(X)<~>~calm(X))))&
(![X]:((~kind(X)<~>~wise(X))<=>brave(X)))&
((?[X]:((~brave(X)<~>~patient(X))))=>(?[X]:((~funny(X)|~curious(X)))))&
(![X]:((~humble(X)|~calm(X))<=>(~patient(X)|~creative(X))))&
((?[X]:(generous(X)))<=>((happy(alice)<~>funny(alice))))&
(((~calm(fred)|funny(fred)))<=>((~creative(mary)&~kind(mary))))&
(![X]:((kind(X)&~rich(X))<=>(~generous(X)|quiet(X))))&
((?[X]:((~strong(X)<~>creative(X))))=>((creative(john)|~wise(john))))&
(![X]:((tall(X)<~>~brave(X))=>(~tall(X)&~rich(X))))&
(![X]:((old(X)<~>patient(X))<=>(calm(X)|~calm(X))))&
((?[X]:((wise(X)<~>~calm(X))))<=>(happy(alice)))&
(![X]:(wise(X)=>(brave(X)&quiet(X))))&
((?[X]:((humble(X)|patient(X))))=>((~calm(alice)<~>brave(alice))))&
(![X]:(funny(X)=>(curious(X)<~>~happy(X))))&
(((~rich(lucy)&rich(lucy)))<=>((~patient(paul)&quiet(paul))))&
(~funny(fred))&
(?[X]:((~happy(X)<~>old(X))))&
((quiet(lucy)|~wise(lucy)))&
(?[X]:((kind(X)|~generous(X))))&
((kind(mary)|~wise(mary)))&
((~generous(fred)<~>~kind(fred)))&
(~tall(lucy))&
(?[X]:((~wise(X)<~>~patient(X)))) | creative(mary) | [
"p0",
"p1",
"p6",
"p7",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8935440199569800233993745
% SZS output start Proof for 8935440199569800233993745
1. ! [X0] : (~calm(X0) <=> generous(X0)) [input p0]
2. ! [X0] : ((~funny(X0) | ~tall(X0)) <=> (rich(X0) <~> ~calm(X0))) [input p1]
7. (funny(fred) | ~calm(fred)) <=> (~kind(mary) & ~creative(mary)) [input p6]
8. ! [X0] : ((~rich(X0) & kind(X0)) <=> (quiet(X0) | ~generous(X0))) [input p7]
17. ~funny(fred) [input p16]
25. creative(mary) [input hypothesis]
34. ! [X0] : ((~calm(X0) | ~generous(X0)) & (generous(X0) | calm(X0))) [nnf transformation 1]
35. ! [X0] : (((~funny(X0) | ~tall(X0)) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0)))) & (((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | (funny(X0) & tall(X0)))) [nnf transformation 2]
36. ! [X0] : ((~funny(X0) | ~tall(X0) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0)))) & (((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | (funny(X0) & tall(X0)))) [flattening 35]
48. ((funny(fred) | ~calm(fred)) | (kind(mary) | creative(mary))) & ((~kind(mary) & ~creative(mary)) | (~funny(fred) & calm(fred))) [nnf transformation 7]
49. (funny(fred) | ~calm(fred) | kind(mary) | creative(mary)) & ((~kind(mary) & ~creative(mary)) | (~funny(fred) & calm(fred))) [flattening 48]
50. ! [X0] : (((~rich(X0) & kind(X0)) | (~quiet(X0) & generous(X0))) & ((quiet(X0) | ~generous(X0)) | (rich(X0) | ~kind(X0)))) [nnf transformation 8]
51. ! [X0] : (((~rich(X0) & kind(X0)) | (~quiet(X0) & generous(X0))) & (quiet(X0) | ~generous(X0) | rich(X0) | ~kind(X0))) [flattening 50]
74. ~generous(X0) | ~calm(X0) [cnf transformation 34]
76. ~calm(X0) | rich(X0) | funny(X0) [cnf transformation 36]
95. ~creative(mary) | calm(fred) [cnf transformation 49]
103. ~rich(X0) | generous(X0) [cnf transformation 51]
133. ~funny(fred) [cnf transformation 17]
144. creative(mary) [cnf transformation 25]
182. 9 <=> creative(mary) [avatar definition]
190. 11 <=> calm(fred) [avatar definition]
191. calm(fred) <- (11) [avatar component clause 190]
194. 12 <=> funny(fred) [avatar definition]
195. ~funny(fred) <- (~12) [avatar component clause 194]
201. 11 | ~9 [avatar split clause 95,182,190]
270. ~12 [avatar split clause 133,194]
288. 31 <=> generous(fred) [avatar definition]
289. generous(fred) <- (31) [avatar component clause 288]
306. 9 [avatar split clause 144,182]
323. 36 <=> rich(fred) [avatar definition]
325. rich(fred) <- (36) [avatar component clause 323]
327. rich(fred) | funny(fred) <- (11) [resolution 76,191]
328. rich(fred) <- (11, ~12) [subsumption resolution 327,195]
329. 36 | ~11 | 12 [avatar split clause 328,194,190,323]
330. generous(fred) <- (36) [resolution 325,103]
333. 31 | ~36 [avatar split clause 330,323,288]
334. ~calm(fred) <- (31) [resolution 289,74]
335. $false <- (11, 31) [subsumption resolution 334,191]
336. ~11 | ~31 [avatar contradiction clause 335]
337. $false [avatar sat refutation 201,270,306,329,333,336]
% SZS output end Proof for 8935440199569800233993745
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is both happy and curious. Everyone who is quiet or generous is calm or not kind. Everyone who is not wise is tall or not old. Everyone who is wise or not quiet is not generous or brave and vice versa. If mary is not humble or old then someone is not happy or not old and vice versa. If someone is curious or wise then someone is not kind or not wise and vice versa. Everyone who is not old is both not wise and humble. If susan is tall then mary is both quiet and brave and vice versa. If someone is brave or creative then susan is not patient and vice versa. Everyone who is not curious is not happy. Everyone who is quiet is funny. If someone is kind then someone is both not rich and not patient. Everyone who is both brave and tall is both generous and happy and vice versa. Everyone who is either generous or creative is either quiet or not tall and vice versa. Everyone who is calm is curious. If someone is either patient or not old then susan is both not happy and not funny and vice versa. Someone is not rich or generous. Alice is not brave or not curious. Someone is either rich or not quiet. Paul is either not old or calm. Paul is both quiet and creative. Someone is either quiet or strong. Mary is kind or not patient. Someone is either not humble or not old. | Mary is not old. | contradiction | (![X]:(~patient(X)=>(happy(X)&curious(X))))&
(![X]:((quiet(X)|generous(X))=>(calm(X)|~kind(X))))&
(![X]:(~wise(X)=>(tall(X)|~old(X))))&
(![X]:((wise(X)|~quiet(X))<=>(~generous(X)|brave(X))))&
(((~humble(mary)|old(mary)))<=>(?[X]:((~happy(X)|~old(X)))))&
((?[X]:((curious(X)|wise(X))))<=>(?[X]:((~kind(X)|~wise(X)))))&
(![X]:(~old(X)=>(~wise(X)&humble(X))))&
((tall(susan))<=>((quiet(mary)&brave(mary))))&
((?[X]:((brave(X)|creative(X))))<=>(~patient(susan)))&
(![X]:(~curious(X)=>~happy(X)))&
(![X]:(quiet(X)=>funny(X)))&
((?[X]:(kind(X)))=>(?[X]:((~rich(X)&~patient(X)))))&
(![X]:((brave(X)&tall(X))<=>(generous(X)&happy(X))))&
(![X]:((generous(X)<~>creative(X))<=>(quiet(X)<~>~tall(X))))&
(![X]:(calm(X)=>curious(X)))&
((?[X]:((patient(X)<~>~old(X))))<=>((~happy(susan)&~funny(susan))))&
(?[X]:((~rich(X)|generous(X))))&
((~brave(alice)|~curious(alice)))&
(?[X]:((rich(X)<~>~quiet(X))))&
((~old(paul)<~>calm(paul)))&
((quiet(paul)&creative(paul)))&
(?[X]:((quiet(X)<~>strong(X))))&
((kind(mary)|~patient(mary)))&
(?[X]:((~humble(X)<~>~old(X)))) | ~old(mary) | [
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 4455857736335126219449620
% SZS output start Proof for 4455857736335126219449620
5. (old(mary) | ~humble(mary)) <=> ? [X0] : (~old(X0) | ~happy(X0)) [input p4]
7. ! [X0] : (~old(X0) => (humble(X0) & ~wise(X0))) [input p6]
25. ~old(mary) [input hypothesis]
33. ! [X0] : ((humble(X0) & ~wise(X0)) | old(X0)) [ennf transformation 7]
40. ((old(mary) | ~humble(mary)) | ! [X0] : (old(X0) & happy(X0))) & (? [X0] : (~old(X0) | ~happy(X0)) | (~old(mary) & humble(mary))) [nnf transformation 5]
41. (old(mary) | ~humble(mary) | ! [X0] : (old(X0) & happy(X0))) & (? [X0] : (~old(X0) | ~happy(X0)) | (~old(mary) & humble(mary))) [flattening 40]
42. (old(mary) | ~humble(mary) | ! [X0] : (old(X0) & happy(X0))) & (? [X1] : (~old(X1) | ~happy(X1)) | (~old(mary) & humble(mary))) [rectify 41]
43. ? [X1] : (~old(X1) | ~happy(X1)) => (~old(sK0) | ~happy(sK0)) [choice axiom]
44. (old(mary) | ~humble(mary) | ! [X0] : (old(X0) & happy(X0))) & ((~old(sK0) | ~happy(sK0)) | (~old(mary) & humble(mary))) [skolemisation 42,43]
91. old(mary) | ~humble(mary) | old(X0) [cnf transformation 44]
97. humble(X0) | old(X0) [cnf transformation 33]
140. ~old(mary) [cnf transformation 25]
142. 1 <=> ! [X0] : old(X0) [avatar definition]
143. old(X0) <- (1) [avatar component clause 142]
145. 2 <=> humble(mary) [avatar definition]
147. ~humble(mary) <- (~2) [avatar component clause 145]
149. 3 <=> old(mary) [avatar definition]
150. ~old(mary) <- (~3) [avatar component clause 149]
152. 1 | ~2 | 3 [avatar split clause 91,149,145,142]
342. ~3 [avatar split clause 140,149]
353. old(mary) <- (~2) [resolution 97,147]
354. $false <- (~2, ~3) [subsumption resolution 353,150]
355. 2 | 3 [avatar contradiction clause 354]
356. $false <- (1, ~3) [resolution 143,150]
363. ~1 | 3 [avatar contradiction clause 356]
364. $false [avatar sat refutation 152,342,355,363]
% SZS output end Proof for 4455857736335126219449620
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or curious is old or rich and vice versa.
Everyone who is not creative or not curious is either not tall or tall.
If someone is patient then mary is happy or rich.
If someone is not wise then fred is both funny and not tall and vice versa.
If someone is not patient then susan is quiet or not funny and vice versa.
Everyone who is curious is not tall or not happy and vice versa.
If mary is both not quiet and strong then someone is not quiet.
Everyone who is either not quiet or tall is both old and funny and vice versa.
If someone is either rich or not old then mary is either not humble or not happy.
If someone is not quiet then paul is brave and vice versa.
Everyone who is either not patient or humble is either not kind or not tall.
If alice is both not kind and not patient then someone is not quiet.
Everyone who is not rich or not curious is either not curious or tall and vice versa.
Everyone who is either not old or quiet is both not rich and not generous and vice versa.
Everyone who is either not rich or not brave is humble.
Everyone who is old is happy.
Someone is kind or old.
Someone is generous or not rich.
Paul is not kind or kind.
Someone is not tall or not creative.
Paul is happy or rich. | Paul is kind. | neutral | (![X]:((old(X)<~>curious(X))<=>(old(X)|rich(X))))&
(![X]:((~creative(X)|~curious(X))=>(~tall(X)<~>tall(X))))&
((?[X]:(patient(X)))=>((happy(mary)|rich(mary))))&
((?[X]:(~wise(X)))<=>((funny(fred)&~tall(fred))))&
((?[X]:(~patient(X)))<=>((quiet(susan)|~funny(susan))))&
(![X]:(curious(X)<=>(~tall(X)|~happy(X))))&
(((~quiet(mary)&strong(mary)))=>(?[X]:(~quiet(X))))&
(![X]:((~quiet(X)<~>tall(X))<=>(old(X)&funny(X))))&
((?[X]:((rich(X)<~>~old(X))))=>((~humble(mary)<~>~happy(mary))))&
((?[X]:(~quiet(X)))<=>(brave(paul)))&
(![X]:((~patient(X)<~>humble(X))=>(~kind(X)<~>~tall(X))))&
(((~kind(alice)&~patient(alice)))=>(?[X]:(~quiet(X))))&
(![X]:((~rich(X)|~curious(X))<=>(~curious(X)<~>tall(X))))&
(![X]:((~old(X)<~>quiet(X))<=>(~rich(X)&~generous(X))))&
(![X]:((~rich(X)<~>~brave(X))=>humble(X)))&
(![X]:(old(X)=>happy(X)))&
(?[X]:((kind(X)|old(X))))&
(?[X]:((generous(X)|~rich(X))))&
((~kind(paul)|kind(paul)))&
(?[X]:((~tall(X)|~creative(X))))&
((happy(paul)|rich(paul))) | kind(paul) | [] | null | 0 |
If john is brave then fred is both calm and curious. Everyone who is not rich is calm and vice versa. Everyone who is both not tall and creative is not curious. If fred is not wise or tall then mary is both not funny and happy and vice versa. Everyone who is both curious and rich is either not curious or not generous. If someone is either strong or not happy then lucy is generous and vice versa. If susan is old then someone is both humble and not patient and vice versa. If fred is both humble and not calm then someone is either not calm or quiet. If someone is old or not humble then john is not brave or patient and vice versa. Everyone who is both happy and not happy is either not happy or not quiet and vice versa. Everyone who is strong or quiet is not quiet. Everyone who is calm is either creative or patient. If someone is both calm and wise then paul is kind or humble and vice versa. Everyone who is not generous is not patient and vice versa. Everyone who is not brave or not quiet is both rich and not patient and vice versa. Lucy is both not old and not quiet. Fred is either rich or old. Someone is either not kind or not humble. Susan is old or curious. Someone is not tall. Alice is not calm. Someone is funny or not generous. | Paul is strong. | entailment | ((brave(john))=>((calm(fred)&curious(fred))))&
(![X]:(~rich(X)<=>calm(X)))&
(![X]:((~tall(X)&creative(X))=>~curious(X)))&
(((~wise(fred)|tall(fred)))<=>((~funny(mary)&happy(mary))))&
(![X]:((curious(X)&rich(X))=>(~curious(X)<~>~generous(X))))&
((?[X]:((strong(X)<~>~happy(X))))<=>(generous(lucy)))&
((old(susan))<=>(?[X]:((humble(X)&~patient(X)))))&
(((humble(fred)&~calm(fred)))=>(?[X]:((~calm(X)<~>quiet(X)))))&
((?[X]:((old(X)|~humble(X))))<=>((~brave(john)|patient(john))))&
(![X]:((happy(X)&~happy(X))<=>(~happy(X)<~>~quiet(X))))&
(![X]:((strong(X)|quiet(X))=>~quiet(X)))&
(![X]:(calm(X)=>(creative(X)<~>patient(X))))&
((?[X]:((calm(X)&wise(X))))<=>((kind(paul)|humble(paul))))&
(![X]:(~generous(X)<=>~patient(X)))&
(![X]:((~brave(X)|~quiet(X))<=>(rich(X)&~patient(X))))&
((~old(lucy)&~quiet(lucy)))&
((rich(fred)<~>old(fred)))&
(?[X]:((~kind(X)<~>~humble(X))))&
((old(susan)|curious(susan)))&
(?[X]:(~tall(X)))&
(~calm(alice))&
(?[X]:((funny(X)|~generous(X)))) | strong(paul) | [
"p5",
"p9",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 399351639385625414635528
% SZS output start Proof for 399351639385625414635528
6. ? [X0] : (strong(X0) <~> ~happy(X0)) <=> generous(lucy) [input p5]
10. ! [X0] : ((~happy(X0) & happy(X0)) <=> (~happy(X0) <~> ~quiet(X0))) [input p9]
11. ! [X0] : ((quiet(X0) | strong(X0)) => ~quiet(X0)) [input p10]
14. ! [X0] : (~generous(X0) <=> ~patient(X0)) [input p13]
15. ! [X0] : ((~quiet(X0) | ~brave(X0)) <=> (~patient(X0) & rich(X0))) [input p14]
23. ~strong(paul) [input hypothesis]
31. ! [X0] : (~quiet(X0) | (~quiet(X0) & ~strong(X0))) [ennf transformation 11]
37. (? [X0] : ((happy(X0) | ~strong(X0)) & (~happy(X0) | strong(X0))) | ~generous(lucy)) & (generous(lucy) | ! [X0] : ((strong(X0) | happy(X0)) & (~happy(X0) | ~strong(X0)))) [nnf transformation 6]
38. (? [X0] : ((happy(X0) | ~strong(X0)) & (~happy(X0) | strong(X0))) | ~generous(lucy)) & (generous(lucy) | ! [X1] : ((strong(X1) | happy(X1)) & (~happy(X1) | ~strong(X1)))) [rectify 37]
39. ? [X0] : ((happy(X0) | ~strong(X0)) & (~happy(X0) | strong(X0))) => ((happy(sK0) | ~strong(sK0)) & (~happy(sK0) | strong(sK0))) [choice axiom]
40. (((happy(sK0) | ~strong(sK0)) & (~happy(sK0) | strong(sK0))) | ~generous(lucy)) & (generous(lucy) | ! [X1] : ((strong(X1) | happy(X1)) & (~happy(X1) | ~strong(X1)))) [skolemisation 38,39]
53. ! [X0] : (((~happy(X0) & happy(X0)) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0)))) & (((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | (happy(X0) | ~happy(X0)))) [nnf transformation 10]
54. ! [X0] : (((~happy(X0) & happy(X0)) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0)))) & (((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | happy(X0) | ~happy(X0))) [flattening 53]
61. ! [X0] : ((~generous(X0) | patient(X0)) & (~patient(X0) | generous(X0))) [nnf transformation 14]
62. ! [X0] : (((~quiet(X0) | ~brave(X0)) | (patient(X0) | ~rich(X0))) & ((~patient(X0) & rich(X0)) | (quiet(X0) & brave(X0)))) [nnf transformation 15]
63. ! [X0] : ((~quiet(X0) | ~brave(X0) | patient(X0) | ~rich(X0)) & ((~patient(X0) & rich(X0)) | (quiet(X0) & brave(X0)))) [flattening 62]
85. generous(lucy) | strong(X1) | happy(X1) [cnf transformation 40]
102. ~happy(X0) | ~happy(X0) | quiet(X0) [cnf transformation 54]
104. ~quiet(X0) | ~quiet(X0) [cnf transformation 31]
113. ~generous(X0) | patient(X0) [cnf transformation 61]
117. ~patient(X0) | quiet(X0) [cnf transformation 63]
129. ~strong(paul) [cnf transformation 23]
130. ~quiet(X0) [duplicate literal removal 104]
134. ~happy(X0) | quiet(X0) [duplicate literal removal 102]
172. 8 <=> generous(lucy) [avatar definition]
173. generous(lucy) <- (8) [avatar component clause 172]
186. 11 <=> ! [X1] : (strong(X1) | happy(X1)) [avatar definition]
187. strong(X1) | happy(X1) <- (11) [avatar component clause 186]
188. 11 | 8 [avatar split clause 85,172,186]
271. ~patient(X0) [subsumption resolution 117,130]
302. patient(lucy) <- (8) [resolution 113,173]
303. $false <- (8) [subsumption resolution 302,271]
304. ~8 [avatar contradiction clause 303]
308. happy(paul) <- (11) [resolution 187,129]
312. quiet(paul) <- (11) [resolution 308,134]
313. $false <- (11) [subsumption resolution 312,130]
314. ~11 [avatar contradiction clause 313]
315. $false [avatar sat refutation 188,304,314]
% SZS output end Proof for 399351639385625414635528
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and generous is patient or rich. Everyone who is both not strong and patient is not curious or curious. If someone is not rich or strong then someone is not generous or not happy and vice versa. Everyone who is not rich is not humble or curious. Everyone who is not calm or wise is wise. Everyone who is both funny and not creative is creative or not tall and vice versa. If someone is either not calm or old then someone is both creative and not calm and vice versa. Everyone who is not kind or not strong is both not brave and tall and vice versa. Everyone who is funny is both brave and not humble and vice versa. If lucy is patient or not patient then someone is not funny and vice versa. Everyone who is either not kind or wise is not calm or not rich and vice versa. If someone is both wise and curious then someone is not humble and vice versa. If fred is not tall or strong then someone is both not old and creative. If someone is old then someone is not happy or strong. If paul is both old and strong then someone is both calm and not kind. If alice is both tall and not old then someone is either curious or not calm and vice versa. John is brave or not calm. Lucy is not old. Someone is both not funny and not old. Lucy is both rich and not kind. Alice is either wise or patient. Someone is not quiet or not old. Someone is calm. | John is not kind. | contradiction | (![X]:((funny(X)&generous(X))=>(patient(X)|rich(X))))&
(![X]:((~strong(X)&patient(X))=>(~curious(X)|curious(X))))&
((?[X]:((~rich(X)|strong(X))))<=>(?[X]:((~generous(X)|~happy(X)))))&
(![X]:(~rich(X)=>(~humble(X)|curious(X))))&
(![X]:((~calm(X)|wise(X))=>wise(X)))&
(![X]:((funny(X)&~creative(X))<=>(creative(X)|~tall(X))))&
((?[X]:((~calm(X)<~>old(X))))<=>(?[X]:((creative(X)&~calm(X)))))&
(![X]:((~kind(X)|~strong(X))<=>(~brave(X)&tall(X))))&
(![X]:(funny(X)<=>(brave(X)&~humble(X))))&
(((patient(lucy)|~patient(lucy)))<=>(?[X]:(~funny(X))))&
(![X]:((~kind(X)<~>wise(X))<=>(~calm(X)|~rich(X))))&
((?[X]:((wise(X)&curious(X))))<=>(?[X]:(~humble(X))))&
(((~tall(fred)|strong(fred)))=>(?[X]:((~old(X)&creative(X)))))&
((?[X]:(old(X)))=>(?[X]:((~happy(X)|strong(X)))))&
(((old(paul)&strong(paul)))=>(?[X]:((calm(X)&~kind(X)))))&
(((tall(alice)&~old(alice)))<=>(?[X]:((curious(X)<~>~calm(X)))))&
((brave(john)|~calm(john)))&
(~old(lucy))&
(?[X]:((~funny(X)&~old(X))))&
((rich(lucy)&~kind(lucy)))&
((wise(alice)<~>patient(alice)))&
(?[X]:((~quiet(X)|~old(X))))&
(?[X]:(calm(X))) | ~kind(john) | [
"p4",
"p7",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2146491753046011448759095
% SZS output start Proof for 2146491753046011448759095
5. ! [X0] : ((wise(X0) | ~calm(X0)) => wise(X0)) [input p4]
8. ! [X0] : ((~strong(X0) | ~kind(X0)) <=> (tall(X0) & ~brave(X0))) [input p7]
11. ! [X0] : ((~kind(X0) <~> wise(X0)) <=> (~rich(X0) | ~calm(X0))) [input p10]
17. ~calm(john) | brave(john) [input p16]
24. ~kind(john) [input hypothesis]
36. ! [X0] : (wise(X0) | (~wise(X0) & calm(X0))) [ennf transformation 5]
53. ! [X0] : (((~strong(X0) | ~kind(X0)) | (~tall(X0) | brave(X0))) & ((tall(X0) & ~brave(X0)) | (strong(X0) & kind(X0)))) [nnf transformation 8]
54. ! [X0] : ((~strong(X0) | ~kind(X0) | ~tall(X0) | brave(X0)) & ((tall(X0) & ~brave(X0)) | (strong(X0) & kind(X0)))) [flattening 53]
62. ! [X0] : ((((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) | (rich(X0) & calm(X0))) & ((~rich(X0) | ~calm(X0)) | ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0))))) [nnf transformation 11]
63. ! [X0] : ((((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) | (rich(X0) & calm(X0))) & (~rich(X0) | ~calm(X0) | ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0))))) [flattening 62]
93. wise(X0) | calm(X0) [cnf transformation 36]
106. ~brave(X0) | kind(X0) [cnf transformation 54]
121. ~wise(X0) | kind(X0) | calm(X0) [cnf transformation 63]
139. ~calm(john) | brave(john) [cnf transformation 17]
148. ~kind(john) [cnf transformation 24]
210. kind(X0) | calm(X0) [subsumption resolution 121,93]
294. 32 <=> brave(john) [avatar definition]
296. brave(john) <- (32) [avatar component clause 294]
298. 33 <=> calm(john) [avatar definition]
301. 32 | ~33 [avatar split clause 139,298,294]
331. calm(john) [resolution 210,148]
334. 33 [avatar split clause 331,298]
336. kind(john) <- (32) [resolution 296,106]
337. $false <- (32) [subsumption resolution 336,148]
338. ~32 [avatar contradiction clause 337]
339. $false [avatar sat refutation 301,334,338]
% SZS output end Proof for 2146491753046011448759095
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not curious or patient then mary is both not patient and not tall and vice versa. Everyone who is old is tall and vice versa. Everyone who is either quiet or generous is both not rich and not funny. Everyone who is either not strong or patient is humble or wise and vice versa. If lucy is both quiet and not quiet then susan is curious and vice versa. Everyone who is either not quiet or not tall is either not brave or not creative and vice versa. If someone is either kind or not brave then someone is patient or kind and vice versa. If someone is both quiet and not tall then alice is both tall and happy and vice versa. If susan is either not patient or brave then john is old or strong and vice versa. Everyone who is not old or not strong is both funny and kind and vice versa. Everyone who is either not curious or happy is not calm. Everyone who is not generous is brave or kind and vice versa. Everyone who is strong or calm is quiet and vice versa. Everyone who is not generous is humble. Everyone who is both not rich and generous is not kind and vice versa. Everyone who is not calm is not rich and vice versa. Someone is not wise. Susan is not strong or generous. Alice is brave or patient. John is either wise or not brave. John is either not patient or not quiet. Someone is funny or not creative. John is not brave. Lucy is not tall. | John is rich. | contradiction | ((?[X]:((~curious(X)<~>patient(X))))<=>((~patient(mary)&~tall(mary))))&
(![X]:(old(X)<=>tall(X)))&
(![X]:((quiet(X)<~>generous(X))=>(~rich(X)&~funny(X))))&
(![X]:((~strong(X)<~>patient(X))<=>(humble(X)|wise(X))))&
(((quiet(lucy)&~quiet(lucy)))<=>(curious(susan)))&
(![X]:((~quiet(X)<~>~tall(X))<=>(~brave(X)<~>~creative(X))))&
((?[X]:((kind(X)<~>~brave(X))))<=>(?[X]:((patient(X)|kind(X)))))&
((?[X]:((quiet(X)&~tall(X))))<=>((tall(alice)&happy(alice))))&
(((~patient(susan)<~>brave(susan)))<=>((old(john)|strong(john))))&
(![X]:((~old(X)|~strong(X))<=>(funny(X)&kind(X))))&
(![X]:((~curious(X)<~>happy(X))=>~calm(X)))&
(![X]:(~generous(X)<=>(brave(X)|kind(X))))&
(![X]:((strong(X)|calm(X))<=>quiet(X)))&
(![X]:(~generous(X)=>humble(X)))&
(![X]:((~rich(X)&generous(X))<=>~kind(X)))&
(![X]:(~calm(X)<=>~rich(X)))&
(?[X]:(~wise(X)))&
((~strong(susan)|generous(susan)))&
((brave(alice)|patient(alice)))&
((wise(john)<~>~brave(john)))&
((~patient(john)<~>~quiet(john)))&
(?[X]:((funny(X)|~creative(X))))&
(~brave(john))&
(~tall(lucy)) | rich(john) | [
"p2",
"p11",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8183903474027618799670652
% SZS output start Proof for 8183903474027618799670652
3. ! [X0] : ((quiet(X0) <~> generous(X0)) => (~funny(X0) & ~rich(X0))) [input p2]
12. ! [X0] : (~generous(X0) <=> (kind(X0) | brave(X0))) [input p11]
13. ! [X0] : ((calm(X0) | strong(X0)) <=> quiet(X0)) [input p12]
15. ! [X0] : ((generous(X0) & ~rich(X0)) <=> ~kind(X0)) [input p14]
16. ! [X0] : (~calm(X0) <=> ~rich(X0)) [input p15]
25. rich(john) [input hypothesis]
27. ! [X0] : ((~funny(X0) & ~rich(X0)) | (quiet(X0) <=> generous(X0))) [ennf transformation 3]
36. ! [X0] : ((~funny(X0) & ~rich(X0)) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0)))) [nnf transformation 27]
57. ! [X0] : ((~generous(X0) | (~kind(X0) & ~brave(X0))) & ((kind(X0) | brave(X0)) | generous(X0))) [nnf transformation 12]
58. ! [X0] : ((~generous(X0) | (~kind(X0) & ~brave(X0))) & (kind(X0) | brave(X0) | generous(X0))) [flattening 57]
59. ! [X0] : (((calm(X0) | strong(X0)) | ~quiet(X0)) & (quiet(X0) | (~calm(X0) & ~strong(X0)))) [nnf transformation 13]
60. ! [X0] : ((calm(X0) | strong(X0) | ~quiet(X0)) & (quiet(X0) | (~calm(X0) & ~strong(X0)))) [flattening 59]
61. ! [X0] : (((generous(X0) & ~rich(X0)) | kind(X0)) & (~kind(X0) | (~generous(X0) | rich(X0)))) [nnf transformation 15]
62. ! [X0] : (((generous(X0) & ~rich(X0)) | kind(X0)) & (~kind(X0) | ~generous(X0) | rich(X0))) [flattening 61]
63. ! [X0] : ((~calm(X0) | rich(X0)) & (~rich(X0) | calm(X0))) [nnf transformation 16]
78. ~rich(X0) | generous(X0) | ~quiet(X0) [cnf transformation 36]
124. ~kind(X0) | ~generous(X0) [cnf transformation 58]
126. ~calm(X0) | quiet(X0) [cnf transformation 60]
130. ~rich(X0) | kind(X0) [cnf transformation 62]
132. ~rich(X0) | calm(X0) [cnf transformation 63]
144. rich(john) [cnf transformation 25]
295. 33 <=> quiet(john) [avatar definition]
297. quiet(john) <- (33) [avatar component clause 295]
326. kind(john) [resolution 130,144]
327. ~generous(john) [resolution 326,124]
330. calm(john) [resolution 132,144]
331. quiet(john) [resolution 330,126]
334. 33 [avatar split clause 331,295]
336. generous(john) | ~quiet(john) [resolution 78,144]
337. ~quiet(john) [subsumption resolution 336,327]
338. $false <- (33) [subsumption resolution 337,297]
339. ~33 [avatar contradiction clause 338]
340. $false [avatar sat refutation 334,339]
% SZS output end Proof for 8183903474027618799670652
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and not brave is both tall and not curious and vice versa.
Everyone who is not humble or not brave is creative or kind.
If someone is either quiet or rich then someone is either not kind or patient.
Everyone who is rich is old or generous.
Everyone who is both not old and not happy is strong or curious and vice versa.
If john is either humble or not funny then someone is both not happy and not brave.
Everyone who is not calm or not happy is not brave or not humble and vice versa.
Everyone who is tall is not happy.
If john is both old and brave then fred is not calm and vice versa.
If lucy is both not calm and not tall then someone is either humble or not creative and vice versa.
If alice is not funny or rich then someone is generous and vice versa.
Everyone who is either not kind or not funny is either not wise or not brave.
Everyone who is generous is both not calm and not curious and vice versa.
Everyone who is both not old and not strong is either quiet or not brave and vice versa.
Everyone who is not creative is not rich.
Everyone who is either generous or rich is both strong and not wise and vice versa.
Someone is rich or kind.
Someone is either wise or generous.
Someone is not generous or calm.
Susan is either curious or old.
Someone is not funny.
Someone is both not brave and funny.
Someone is curious or not funny.
Mary is both creative and curious. | Mary is humble. | contradiction | (![X]:((creative(X)&~brave(X))<=>(tall(X)&~curious(X))))&
(![X]:((~humble(X)|~brave(X))=>(creative(X)|kind(X))))&
((?[X]:((quiet(X)<~>rich(X))))=>(?[X]:((~kind(X)<~>patient(X)))))&
(![X]:(rich(X)=>(old(X)|generous(X))))&
(![X]:((~old(X)&~happy(X))<=>(strong(X)|curious(X))))&
(((humble(john)<~>~funny(john)))=>(?[X]:((~happy(X)&~brave(X)))))&
(![X]:((~calm(X)|~happy(X))<=>(~brave(X)|~humble(X))))&
(![X]:(tall(X)=>~happy(X)))&
(((old(john)&brave(john)))<=>(~calm(fred)))&
(((~calm(lucy)&~tall(lucy)))<=>(?[X]:((humble(X)<~>~creative(X)))))&
(((~funny(alice)|rich(alice)))<=>(?[X]:(generous(X))))&
(![X]:((~kind(X)<~>~funny(X))=>(~wise(X)<~>~brave(X))))&
(![X]:(generous(X)<=>(~calm(X)&~curious(X))))&
(![X]:((~old(X)&~strong(X))<=>(quiet(X)<~>~brave(X))))&
(![X]:(~creative(X)=>~rich(X)))&
(![X]:((generous(X)<~>rich(X))<=>(strong(X)&~wise(X))))&
(?[X]:((rich(X)|kind(X))))&
(?[X]:((wise(X)<~>generous(X))))&
(?[X]:((~generous(X)|calm(X))))&
((curious(susan)<~>old(susan)))&
(?[X]:(~funny(X)))&
(?[X]:((~brave(X)&funny(X))))&
(?[X]:((curious(X)|~funny(X))))&
((creative(mary)&curious(mary))) | humble(mary) | [
"p0",
"p4",
"p6",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4557093925338788366773981
% SZS output start Proof for 4557093925338788366773981
1. ! [X0] : ((~brave(X0) & creative(X0)) <=> (~curious(X0) & tall(X0))) [input p0]
5. ! [X0] : ((~happy(X0) & ~old(X0)) <=> (curious(X0) | strong(X0))) [input p4]
7. ! [X0] : ((~happy(X0) | ~calm(X0)) <=> (~humble(X0) | ~brave(X0))) [input p6]
24. curious(mary) & creative(mary) [input p23]
25. humble(mary) [input hypothesis]
36. ! [X0] : (((~brave(X0) & creative(X0)) | (curious(X0) | ~tall(X0))) & ((~curious(X0) & tall(X0)) | (brave(X0) | ~creative(X0)))) [nnf transformation 1]
37. ! [X0] : (((~brave(X0) & creative(X0)) | curious(X0) | ~tall(X0)) & ((~curious(X0) & tall(X0)) | brave(X0) | ~creative(X0))) [flattening 36]
42. ! [X0] : (((~happy(X0) & ~old(X0)) | (~curious(X0) & ~strong(X0))) & ((curious(X0) | strong(X0)) | (happy(X0) | old(X0)))) [nnf transformation 5]
43. ! [X0] : (((~happy(X0) & ~old(X0)) | (~curious(X0) & ~strong(X0))) & (curious(X0) | strong(X0) | happy(X0) | old(X0))) [flattening 42]
47. ! [X0] : (((~happy(X0) | ~calm(X0)) | (humble(X0) & brave(X0))) & ((~humble(X0) | ~brave(X0)) | (happy(X0) & calm(X0)))) [nnf transformation 7]
48. ! [X0] : ((~happy(X0) | ~calm(X0) | (humble(X0) & brave(X0))) & (~humble(X0) | ~brave(X0) | (happy(X0) & calm(X0)))) [flattening 47]
83. ~curious(X0) | brave(X0) | ~creative(X0) [cnf transformation 37]
97. ~happy(X0) | ~curious(X0) [cnf transformation 43]
103. ~humble(X0) | ~brave(X0) | happy(X0) [cnf transformation 48]
149. creative(mary) [cnf transformation 24]
150. curious(mary) [cnf transformation 24]
151. humble(mary) [cnf transformation 25]
298. 31 <=> brave(mary) [avatar definition]
300. brave(mary) <- (31) [avatar component clause 298]
311. brave(mary) | ~creative(mary) [resolution 83,150]
313. brave(mary) [subsumption resolution 311,149]
314. 31 [avatar split clause 313,298]
339. ~brave(mary) | happy(mary) [resolution 103,151]
340. happy(mary) <- (31) [subsumption resolution 339,300]
342. ~curious(mary) <- (31) [resolution 340,97]
345. $false <- (31) [subsumption resolution 342,150]
346. ~31 [avatar contradiction clause 345]
347. $false [avatar sat refutation 314,346]
% SZS output end Proof for 4557093925338788366773981
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and not calm is not quiet and vice versa.
Everyone who is happy is both not curious and curious.
If paul is both not quiet and happy then someone is either rich or not creative and vice versa.
Everyone who is either not rich or not strong is strong and vice versa.
If susan is both not brave and not quiet then someone is either brave or not strong.
If someone is not humble then someone is both funny and not brave.
Everyone who is both not tall and generous is either strong or kind.
Everyone who is either patient or old is kind or not creative and vice versa.
Everyone who is not tall is both not funny and not calm.
If lucy is not funny then paul is not curious.
Everyone who is both curious and strong is brave and vice versa.
Everyone who is either rich or tall is happy and vice versa.
Everyone who is humble or not generous is old and vice versa.
Everyone who is either not curious or generous is either old or not quiet and vice versa.
Everyone who is either humble or not wise is either happy or not rich.
If lucy is both wise and not wise then fred is both not strong and not generous.
Someone is creative or not wise.
Someone is both curious and not kind.
Someone is either not curious or quiet.
Lucy is both brave and not funny.
Lucy is either not happy or calm.
Someone is not generous. | Lucy is quiet. | contradiction | (![X]:((strong(X)&~calm(X))<=>~quiet(X)))&
(![X]:(happy(X)=>(~curious(X)&curious(X))))&
(((~quiet(paul)&happy(paul)))<=>(?[X]:((rich(X)<~>~creative(X)))))&
(![X]:((~rich(X)<~>~strong(X))<=>strong(X)))&
(((~brave(susan)&~quiet(susan)))=>(?[X]:((brave(X)<~>~strong(X)))))&
((?[X]:(~humble(X)))=>(?[X]:((funny(X)&~brave(X)))))&
(![X]:((~tall(X)&generous(X))=>(strong(X)<~>kind(X))))&
(![X]:((patient(X)<~>old(X))<=>(kind(X)|~creative(X))))&
(![X]:(~tall(X)=>(~funny(X)&~calm(X))))&
((~funny(lucy))=>(~curious(paul)))&
(![X]:((curious(X)&strong(X))<=>brave(X)))&
(![X]:((rich(X)<~>tall(X))<=>happy(X)))&
(![X]:((humble(X)|~generous(X))<=>old(X)))&
(![X]:((~curious(X)<~>generous(X))<=>(old(X)<~>~quiet(X))))&
(![X]:((humble(X)<~>~wise(X))=>(happy(X)<~>~rich(X))))&
(((wise(lucy)&~wise(lucy)))=>((~strong(fred)&~generous(fred))))&
(?[X]:((creative(X)|~wise(X))))&
(?[X]:((curious(X)&~kind(X))))&
(?[X]:((~curious(X)<~>quiet(X))))&
((brave(lucy)&~funny(lucy)))&
((~happy(lucy)<~>calm(lucy)))&
(?[X]:(~generous(X))) | quiet(lucy) | [
"p0",
"p1",
"p10",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 36304771809205939702859
% SZS output start Proof for 36304771809205939702859
1. ! [X0] : ((~calm(X0) & strong(X0)) <=> ~quiet(X0)) [input p0]
2. ! [X0] : (happy(X0) => (curious(X0) & ~curious(X0))) [input p1]
11. ! [X0] : ((strong(X0) & curious(X0)) <=> brave(X0)) [input p10]
20. ~funny(lucy) & brave(lucy) [input p19]
21. ~happy(lucy) <~> calm(lucy) [input p20]
23. quiet(lucy) [input hypothesis]
25. ! [X0] : ((curious(X0) & ~curious(X0)) | ~happy(X0)) [ennf transformation 2]
36. ! [X0] : (((~calm(X0) & strong(X0)) | quiet(X0)) & (~quiet(X0) | (calm(X0) | ~strong(X0)))) [nnf transformation 1]
37. ! [X0] : (((~calm(X0) & strong(X0)) | quiet(X0)) & (~quiet(X0) | calm(X0) | ~strong(X0))) [flattening 36]
53. ! [X0] : (((strong(X0) & curious(X0)) | ~brave(X0)) & (brave(X0) | (~strong(X0) | ~curious(X0)))) [nnf transformation 11]
54. ! [X0] : (((strong(X0) & curious(X0)) | ~brave(X0)) & (brave(X0) | ~strong(X0) | ~curious(X0))) [flattening 53]
67. (~calm(lucy) | happy(lucy)) & (calm(lucy) | ~happy(lucy)) [nnf transformation 21]
70. ~quiet(X0) | calm(X0) | ~strong(X0) [cnf transformation 37]
73. ~curious(X0) | ~happy(X0) [cnf transformation 25]
74. ~happy(X0) | curious(X0) [cnf transformation 25]
102. ~brave(X0) | strong(X0) [cnf transformation 54]
129. brave(lucy) [cnf transformation 20]
132. ~calm(lucy) | happy(lucy) [cnf transformation 67]
134. quiet(lucy) [cnf transformation 23]
137. ~happy(X0) [subsumption resolution 73,74]
207. ~calm(lucy) [subsumption resolution 132,137]
210. strong(lucy) [resolution 102,129]
213. calm(lucy) | ~strong(lucy) [resolution 70,134]
215. ~strong(lucy) [subsumption resolution 213,207]
216. $false [subsumption resolution 215,210]
% SZS output end Proof for 36304771809205939702859
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not creative is either not brave or not tall and vice versa. Everyone who is either not curious or not rich is either not quiet or not kind. Everyone who is either not strong or not generous is both not brave and tall. Everyone who is humble or not kind is not humble or not wise and vice versa. If someone is not strong then someone is kind or tall and vice versa. If someone is either not kind or not funny then someone is rich or not old and vice versa. If lucy is both strong and not funny then john is either not kind or not calm and vice versa. Everyone who is either not generous or not humble is not happy. If someone is both not rich and not funny then someone is patient. Everyone who is either not funny or not generous is funny or brave. If fred is patient or not happy then fred is not old or not humble. Everyone who is either not wise or not curious is not humble. If someone is both not funny and tall then alice is generous and vice versa. Everyone who is both humble and wise is not patient or humble and vice versa. If someone is both not patient and generous then someone is not old or not wise. If lucy is not humble or not calm then someone is either happy or brave. Fred is not funny. Someone is happy or brave. Someone is tall or not rich. Mary is both not wise and not curious. Someone is either funny or quiet. Alice is both strong and not curious. | Lucy is not kind. | entailment | (![X]:((happy(X)<~>~creative(X))<=>(~brave(X)<~>~tall(X))))&
(![X]:((~curious(X)<~>~rich(X))=>(~quiet(X)<~>~kind(X))))&
(![X]:((~strong(X)<~>~generous(X))=>(~brave(X)&tall(X))))&
(![X]:((humble(X)|~kind(X))<=>(~humble(X)|~wise(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((kind(X)|tall(X)))))&
((?[X]:((~kind(X)<~>~funny(X))))<=>(?[X]:((rich(X)|~old(X)))))&
(((strong(lucy)&~funny(lucy)))<=>((~kind(john)<~>~calm(john))))&
(![X]:((~generous(X)<~>~humble(X))=>~happy(X)))&
((?[X]:((~rich(X)&~funny(X))))=>(?[X]:(patient(X))))&
(![X]:((~funny(X)<~>~generous(X))=>(funny(X)|brave(X))))&
(((patient(fred)|~happy(fred)))=>((~old(fred)|~humble(fred))))&
(![X]:((~wise(X)<~>~curious(X))=>~humble(X)))&
((?[X]:((~funny(X)&tall(X))))<=>(generous(alice)))&
(![X]:((humble(X)&wise(X))<=>(~patient(X)|humble(X))))&
((?[X]:((~patient(X)&generous(X))))=>(?[X]:((~old(X)|~wise(X)))))&
(((~humble(lucy)|~calm(lucy)))=>(?[X]:((happy(X)<~>brave(X)))))&
(~funny(fred))&
(?[X]:((happy(X)|brave(X))))&
(?[X]:((tall(X)|~rich(X))))&
((~wise(mary)&~curious(mary)))&
(?[X]:((funny(X)<~>quiet(X))))&
((strong(alice)&~curious(alice))) | ~kind(lucy) | [
"p3",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5480244890830510697440787
% SZS output start Proof for 5480244890830510697440787
4. ! [X0] : ((~kind(X0) | humble(X0)) <=> (~wise(X0) | ~humble(X0))) [input p3]
14. ! [X0] : ((wise(X0) & humble(X0)) <=> (humble(X0) | ~patient(X0))) [input p13]
23. kind(lucy) [input hypothesis]
42. ! [X0] : (((~kind(X0) | humble(X0)) | (wise(X0) & humble(X0))) & ((~wise(X0) | ~humble(X0)) | (kind(X0) & ~humble(X0)))) [nnf transformation 4]
43. ! [X0] : ((~kind(X0) | humble(X0) | (wise(X0) & humble(X0))) & (~wise(X0) | ~humble(X0) | (kind(X0) & ~humble(X0)))) [flattening 42]
66. ! [X0] : (((wise(X0) & humble(X0)) | (~humble(X0) & patient(X0))) & ((humble(X0) | ~patient(X0)) | (~wise(X0) | ~humble(X0)))) [nnf transformation 14]
67. ! [X0] : (((wise(X0) & humble(X0)) | (~humble(X0) & patient(X0))) & (humble(X0) | ~patient(X0) | ~wise(X0) | ~humble(X0))) [flattening 66]
97. ~wise(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 43]
99. ~kind(X0) | humble(X0) | humble(X0) [cnf transformation 43]
132. wise(X0) | ~humble(X0) [cnf transformation 67]
147. kind(lucy) [cnf transformation 23]
149. ~wise(X0) | ~humble(X0) [duplicate literal removal 97]
150. ~kind(X0) | humble(X0) [duplicate literal removal 99]
276. ~humble(X0) [subsumption resolution 132,149]
326. humble(lucy) [resolution 150,147]
329. $false [subsumption resolution 326,276]
% SZS output end Proof for 5480244890830510697440787
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or patient is either humble or funny.
If fred is old then alice is old.
Everyone who is both rich and strong is patient or brave and vice versa.
Everyone who is not kind or not strong is not creative and vice versa.
Everyone who is either rich or old is both strong and not generous.
Everyone who is either not creative or kind is both not funny and not brave and vice versa.
Everyone who is not patient is both patient and not patient and vice versa.
If mary is both brave and not creative then someone is not generous or quiet.
If someone is not humble then john is either calm or funny and vice versa.
If someone is not patient then someone is both old and rich and vice versa.
Everyone who is either not curious or creative is kind or brave.
Everyone who is not wise is either not tall or not creative and vice versa.
If alice is both not brave and wise then susan is calm or funny.
If someone is both old and not creative then fred is not curious or not creative.
If mary is both tall and wise then someone is both humble and not kind.
Someone is not creative or not kind.
Someone is both not old and not tall.
Fred is either quiet or creative. | Susan is not strong. | contradiction | (![X]:((~quiet(X)|patient(X))=>(humble(X)<~>funny(X))))&
((old(fred))=>(old(alice)))&
(![X]:((rich(X)&strong(X))<=>(patient(X)|brave(X))))&
(![X]:((~kind(X)|~strong(X))<=>~creative(X)))&
(![X]:((rich(X)<~>old(X))=>(strong(X)&~generous(X))))&
(![X]:((~creative(X)<~>kind(X))<=>(~funny(X)&~brave(X))))&
(![X]:(~patient(X)<=>(patient(X)&~patient(X))))&
(((brave(mary)&~creative(mary)))=>(?[X]:((~generous(X)|quiet(X)))))&
((?[X]:(~humble(X)))<=>((calm(john)<~>funny(john))))&
((?[X]:(~patient(X)))<=>(?[X]:((old(X)&rich(X)))))&
(![X]:((~curious(X)<~>creative(X))=>(kind(X)|brave(X))))&
(![X]:(~wise(X)<=>(~tall(X)<~>~creative(X))))&
(((~brave(alice)&wise(alice)))=>((calm(susan)|funny(susan))))&
((?[X]:((old(X)&~creative(X))))=>((~curious(fred)|~creative(fred))))&
(((tall(mary)&wise(mary)))=>(?[X]:((humble(X)&~kind(X)))))&
(?[X]:((~creative(X)|~kind(X))))&
(?[X]:((~old(X)&~tall(X))))&
((quiet(fred)<~>creative(fred))) | ~strong(susan) | [
"p2",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 7559918586008997971979986
% SZS output start Proof for 7559918586008997971979986
3. ! [X0] : ((strong(X0) & rich(X0)) <=> (brave(X0) | patient(X0))) [input p2]
7. ! [X0] : (~patient(X0) <=> (~patient(X0) & patient(X0))) [input p6]
19. ~strong(susan) [input hypothesis]
37. ! [X0] : (((strong(X0) & rich(X0)) | (~brave(X0) & ~patient(X0))) & ((brave(X0) | patient(X0)) | (~strong(X0) | ~rich(X0)))) [nnf transformation 3]
38. ! [X0] : (((strong(X0) & rich(X0)) | (~brave(X0) & ~patient(X0))) & (brave(X0) | patient(X0) | ~strong(X0) | ~rich(X0))) [flattening 37]
44. ! [X0] : ((~patient(X0) | (patient(X0) | ~patient(X0))) & ((~patient(X0) & patient(X0)) | patient(X0))) [nnf transformation 7]
45. ! [X0] : ((~patient(X0) | patient(X0) | ~patient(X0)) & ((~patient(X0) & patient(X0)) | patient(X0))) [flattening 44]
72. ~patient(X0) | strong(X0) [cnf transformation 38]
85. patient(X0) | patient(X0) [cnf transformation 45]
108. ~strong(susan) [cnf transformation 19]
109. patient(X0) [duplicate literal removal 85]
201. strong(X0) [resolution 72,109]
202. $false [resolution 201,108]
% SZS output end Proof for 7559918586008997971979986
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and strong is funny. If someone is either kind or happy then someone is kind and vice versa. Everyone who is not patient is not old and vice versa. Everyone who is funny is either strong or humble and vice versa. Everyone who is generous or not calm is either not funny or not kind. If someone is not calm or not happy then paul is wise or not curious and vice versa. Everyone who is humble is both patient and not generous. Everyone who is not old or wise is both not funny and quiet. Everyone who is not patient or not funny is patient or not calm and vice versa. If someone is both quiet and not quiet then someone is not curious. If fred is both rich and kind then susan is not funny. If paul is both not old and not tall then someone is not brave or not happy. Everyone who is not happy or patient is both creative and not happy and vice versa. Everyone who is not humble or not wise is both generous and old. If someone is both wise and old then someone is either funny or not humble. Everyone who is both not wise and not quiet is not calm or funny and vice versa. Someone is patient or calm. John is wise or brave. Someone is either not strong or not creative. John is humble. Someone is both not rich and not generous. Someone is both not wise and not quiet. | John is not rich. | neutral | (![X]:((~curious(X)&strong(X))=>funny(X)))&
((?[X]:((kind(X)<~>happy(X))))<=>(?[X]:(kind(X))))&
(![X]:(~patient(X)<=>~old(X)))&
(![X]:(funny(X)<=>(strong(X)<~>humble(X))))&
(![X]:((generous(X)|~calm(X))=>(~funny(X)<~>~kind(X))))&
((?[X]:((~calm(X)|~happy(X))))<=>((wise(paul)|~curious(paul))))&
(![X]:(humble(X)=>(patient(X)&~generous(X))))&
(![X]:((~old(X)|wise(X))=>(~funny(X)&quiet(X))))&
(![X]:((~patient(X)|~funny(X))<=>(patient(X)|~calm(X))))&
((?[X]:((quiet(X)&~quiet(X))))=>(?[X]:(~curious(X))))&
(((rich(fred)&kind(fred)))=>(~funny(susan)))&
(((~old(paul)&~tall(paul)))=>(?[X]:((~brave(X)|~happy(X)))))&
(![X]:((~happy(X)|patient(X))<=>(creative(X)&~happy(X))))&
(![X]:((~humble(X)|~wise(X))=>(generous(X)&old(X))))&
((?[X]:((wise(X)&old(X))))=>(?[X]:((funny(X)<~>~humble(X)))))&
(![X]:((~wise(X)&~quiet(X))<=>(~calm(X)|funny(X))))&
(?[X]:((patient(X)|calm(X))))&
((wise(john)|brave(john)))&
(?[X]:((~strong(X)<~>~creative(X))))&
(humble(john))&
(?[X]:((~rich(X)&~generous(X))))&
(?[X]:((~wise(X)&~quiet(X)))) | ~rich(john) | [] | null | 0 |
If alice is brave then susan is both not tall and not happy and vice versa. Everyone who is not tall is both wise and generous. If alice is curious then someone is curious or not tall and vice versa. If susan is both not funny and not calm then someone is either not curious or not strong and vice versa. If someone is either not creative or generous then paul is tall or patient. Everyone who is rich is humble. Everyone who is both rich and generous is not old or not quiet. Everyone who is wise is both not wise and old and vice versa. Everyone who is both not happy and not funny is not funny or patient and vice versa. Everyone who is not creative is not curious or not old and vice versa. If susan is both not strong and not quiet then someone is either funny or not happy and vice versa. If someone is funny or calm then alice is either creative or not brave and vice versa. Everyone who is not old is kind. Everyone who is not generous is tall or not strong and vice versa. If someone is old or not brave then susan is not patient or not kind and vice versa. Someone is either not generous or brave. Someone is funny. Susan is funny. Alice is either calm or not strong. Paul is both not funny and not curious. Someone is either not curious or not humble. Lucy is both happy and kind. Lucy is either humble or not calm. | Alice is creative. | contradiction | ((brave(alice))<=>((~tall(susan)&~happy(susan))))&
(![X]:(~tall(X)=>(wise(X)&generous(X))))&
((curious(alice))<=>(?[X]:((curious(X)|~tall(X)))))&
(((~funny(susan)&~calm(susan)))<=>(?[X]:((~curious(X)<~>~strong(X)))))&
((?[X]:((~creative(X)<~>generous(X))))=>((tall(paul)|patient(paul))))&
(![X]:(rich(X)=>humble(X)))&
(![X]:((rich(X)&generous(X))=>(~old(X)|~quiet(X))))&
(![X]:(wise(X)<=>(~wise(X)&old(X))))&
(![X]:((~happy(X)&~funny(X))<=>(~funny(X)|patient(X))))&
(![X]:(~creative(X)<=>(~curious(X)|~old(X))))&
(((~strong(susan)&~quiet(susan)))<=>(?[X]:((funny(X)<~>~happy(X)))))&
((?[X]:((funny(X)|calm(X))))<=>((creative(alice)<~>~brave(alice))))&
(![X]:(~old(X)=>kind(X)))&
(![X]:(~generous(X)<=>(tall(X)|~strong(X))))&
((?[X]:((old(X)|~brave(X))))<=>((~patient(susan)|~kind(susan))))&
(?[X]:((~generous(X)<~>brave(X))))&
(?[X]:(funny(X)))&
(funny(susan))&
((calm(alice)<~>~strong(alice)))&
((~funny(paul)&~curious(paul)))&
(?[X]:((~curious(X)<~>~humble(X))))&
((happy(lucy)&kind(lucy)))&
((humble(lucy)<~>~calm(lucy))) | creative(alice) | [
"p0",
"p1",
"p7",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2986134508223150278569845
% SZS output start Proof for 2986134508223150278569845
1. brave(alice) <=> (~happy(susan) & ~tall(susan)) [input p0]
2. ! [X0] : (~tall(X0) => (generous(X0) & wise(X0))) [input p1]
8. ! [X0] : (wise(X0) <=> (old(X0) & ~wise(X0))) [input p7]
12. ? [X0] : (calm(X0) | funny(X0)) <=> (creative(alice) <~> ~brave(alice)) [input p11]
17. ? [X0] : funny(X0) [input p16]
24. creative(alice) [input hypothesis]
27. ! [X0] : ((generous(X0) & wise(X0)) | tall(X0)) [ennf transformation 2]
31. (brave(alice) | (happy(susan) | tall(susan))) & ((~happy(susan) & ~tall(susan)) | ~brave(alice)) [nnf transformation 1]
32. (brave(alice) | happy(susan) | tall(susan)) & ((~happy(susan) & ~tall(susan)) | ~brave(alice)) [flattening 31]
43. ! [X0] : ((wise(X0) | (~old(X0) | wise(X0))) & ((old(X0) & ~wise(X0)) | ~wise(X0))) [nnf transformation 8]
44. ! [X0] : ((wise(X0) | ~old(X0) | wise(X0)) & ((old(X0) & ~wise(X0)) | ~wise(X0))) [flattening 43]
54. (? [X0] : (calm(X0) | funny(X0)) | ((creative(alice) | brave(alice)) & (~brave(alice) | ~creative(alice)))) & (((brave(alice) | ~creative(alice)) & (~brave(alice) | creative(alice))) | ! [X0] : (~calm(X0) & ~funny(X0))) [nnf transformation 12]
55. (? [X0] : (calm(X0) | funny(X0)) | ((creative(alice) | brave(alice)) & (~brave(alice) | ~creative(alice)))) & (((brave(alice) | ~creative(alice)) & (~brave(alice) | creative(alice))) | ! [X1] : (~calm(X1) & ~funny(X1))) [rectify 54]
56. ? [X0] : (calm(X0) | funny(X0)) => (calm(sK3) | funny(sK3)) [choice axiom]
57. ((calm(sK3) | funny(sK3)) | ((creative(alice) | brave(alice)) & (~brave(alice) | ~creative(alice)))) & (((brave(alice) | ~creative(alice)) & (~brave(alice) | creative(alice))) | ! [X1] : (~calm(X1) & ~funny(X1))) [skolemisation 55,56]
68. ? [X0] : funny(X0) => funny(sK6) [choice axiom]
69. funny(sK6) [skolemisation 17,68]
75. ~tall(susan) | ~brave(alice) [cnf transformation 32]
78. wise(X0) | tall(X0) [cnf transformation 27]
91. ~wise(X0) | ~wise(X0) [cnf transformation 44]
110. brave(alice) | ~creative(alice) | ~funny(X1) [cnf transformation 57]
124. funny(sK6) [cnf transformation 69]
136. creative(alice) [cnf transformation 24]
137. ~wise(X0) [duplicate literal removal 91]
140. 1 <=> tall(susan) [avatar definition]
141. ~tall(susan) <- (~1) [avatar component clause 140]
148. 3 <=> brave(alice) [avatar definition]
153. ~3 | ~1 [avatar split clause 75,140,148]
155. 4 <=> ! [X0] : tall(X0) [avatar definition]
156. tall(X0) <- (4) [avatar component clause 155]
251. 25 <=> creative(alice) [avatar definition]
269. 29 <=> ! [X1] : ~funny(X1) [avatar definition]
270. ~funny(X1) <- (29) [avatar component clause 269]
271. 29 | ~25 | 3 [avatar split clause 110,148,251,269]
341. 25 [avatar split clause 136,251]
342. tall(X0) [resolution 78,137]
343. 4 [avatar split clause 342,155]
344. $false <- (~1, 4) [resolution 156,141]
347. 1 | ~4 [avatar contradiction clause 344]
350. $false <- (29) [resolution 270,124]
355. ~29 [avatar contradiction clause 350]
356. $false [avatar sat refutation 153,271,341,343,347,355]
% SZS output end Proof for 2986134508223150278569845
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or not strong is not wise.
If susan is kind or not brave then lucy is either not curious or not tall and vice versa.
If someone is both not quiet and funny then someone is either not patient or not humble and vice versa.
If lucy is both generous and calm then someone is not brave and vice versa.
Everyone who is both not creative and brave is quiet or not kind and vice versa.
If paul is brave then mary is either not rich or calm.
If someone is patient then john is not generous or not humble.
Everyone who is not quiet is tall or humble.
Everyone who is not curious is both not funny and not patient and vice versa.
If someone is either not kind or not strong then susan is not old or wise and vice versa.
If fred is either not happy or quiet then mary is either not humble or not funny.
Everyone who is both curious and creative is not funny.
If someone is both old and not old then someone is not humble or not kind.
Everyone who is either not quiet or quiet is either not old or strong and vice versa.
If someone is not creative then john is both happy and humble.
Everyone who is both patient and old is not funny or not old.
Someone is either not happy or not calm.
John is not humble.
Someone is brave.
Someone is calm.
Someone is not strong.
Someone is both calm and tall.
Someone is either not quiet or wise. | John is quiet. | contradiction | (![X]:((patient(X)|~strong(X))=>~wise(X)))&
(((kind(susan)|~brave(susan)))<=>((~curious(lucy)<~>~tall(lucy))))&
((?[X]:((~quiet(X)&funny(X))))<=>(?[X]:((~patient(X)<~>~humble(X)))))&
(((generous(lucy)&calm(lucy)))<=>(?[X]:(~brave(X))))&
(![X]:((~creative(X)&brave(X))<=>(quiet(X)|~kind(X))))&
((brave(paul))=>((~rich(mary)<~>calm(mary))))&
((?[X]:(patient(X)))=>((~generous(john)|~humble(john))))&
(![X]:(~quiet(X)=>(tall(X)|humble(X))))&
(![X]:(~curious(X)<=>(~funny(X)&~patient(X))))&
((?[X]:((~kind(X)<~>~strong(X))))<=>((~old(susan)|wise(susan))))&
(((~happy(fred)<~>quiet(fred)))=>((~humble(mary)<~>~funny(mary))))&
(![X]:((curious(X)&creative(X))=>~funny(X)))&
((?[X]:((old(X)&~old(X))))=>(?[X]:((~humble(X)|~kind(X)))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(~old(X)<~>strong(X))))&
((?[X]:(~creative(X)))=>((happy(john)&humble(john))))&
(![X]:((patient(X)&old(X))=>(~funny(X)|~old(X))))&
(?[X]:((~happy(X)<~>~calm(X))))&
(~humble(john))&
(?[X]:(brave(X)))&
(?[X]:(calm(X)))&
(?[X]:(~strong(X)))&
(?[X]:((calm(X)&tall(X))))&
(?[X]:((~quiet(X)<~>wise(X)))) | quiet(john) | [
"p4",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 879834114523457482843019
% SZS output start Proof for 879834114523457482843019
5. ! [X0] : ((brave(X0) & ~creative(X0)) <=> (~kind(X0) | quiet(X0))) [input p4]
15. ? [X0] : ~creative(X0) => (humble(john) & happy(john)) [input p14]
18. ~humble(john) [input p17]
24. quiet(john) [input hypothesis]
37. (humble(john) & happy(john)) | ! [X0] : creative(X0) [ennf transformation 15]
52. ! [X0] : (((brave(X0) & ~creative(X0)) | (kind(X0) & ~quiet(X0))) & ((~kind(X0) | quiet(X0)) | (~brave(X0) | creative(X0)))) [nnf transformation 5]
53. ! [X0] : (((brave(X0) & ~creative(X0)) | (kind(X0) & ~quiet(X0))) & (~kind(X0) | quiet(X0) | ~brave(X0) | creative(X0))) [flattening 52]
99. ~creative(X0) | ~quiet(X0) [cnf transformation 53]
131. humble(john) | creative(X0) [cnf transformation 37]
135. ~humble(john) [cnf transformation 18]
143. quiet(john) [cnf transformation 24]
242. 21 <=> humble(john) [avatar definition]
298. 32 <=> ! [X0] : creative(X0) [avatar definition]
299. creative(X0) <- (32) [avatar component clause 298]
300. 32 | 21 [avatar split clause 131,242,298]
316. ~21 [avatar split clause 135,242]
331. ~quiet(X0) <- (32) [resolution 99,299]
332. $false <- (32) [resolution 331,143]
335. ~32 [avatar contradiction clause 332]
336. $false [avatar sat refutation 300,316,335]
% SZS output end Proof for 879834114523457482843019
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not kind is both not tall and not generous and vice versa. Everyone who is wise is tall. If paul is not rich then susan is both not humble and creative and vice versa. Everyone who is not strong or not humble is both not patient and humble and vice versa. If paul is both calm and not patient then someone is both strong and tall. Everyone who is quiet or not strong is both tall and calm. If john is both not rich and calm then someone is both not patient and happy and vice versa. If paul is either not calm or curious then susan is both not rich and curious and vice versa. Everyone who is both not strong and happy is either brave or not calm. If mary is not curious or brave then fred is not strong or happy. If mary is not generous then someone is both not brave and calm. If someone is curious or quiet then someone is curious and vice versa. If lucy is either brave or quiet then someone is both funny and rich and vice versa. Everyone who is either not wise or curious is not wise or not strong and vice versa. Everyone who is calm or rich is not creative or not rich and vice versa. Everyone who is happy or creative is curious or not creative. Susan is both not old and calm. Susan is either brave or not generous. Fred is either generous or not quiet. Susan is either not wise or happy. Someone is both brave and tall. Someone is not quiet or not generous. | Fred is not humble. | contradiction | (![X]:((quiet(X)|~kind(X))<=>(~tall(X)&~generous(X))))&
(![X]:(wise(X)=>tall(X)))&
((~rich(paul))<=>((~humble(susan)&creative(susan))))&
(![X]:((~strong(X)|~humble(X))<=>(~patient(X)&humble(X))))&
(((calm(paul)&~patient(paul)))=>(?[X]:((strong(X)&tall(X)))))&
(![X]:((quiet(X)|~strong(X))=>(tall(X)&calm(X))))&
(((~rich(john)&calm(john)))<=>(?[X]:((~patient(X)&happy(X)))))&
(((~calm(paul)<~>curious(paul)))<=>((~rich(susan)&curious(susan))))&
(![X]:((~strong(X)&happy(X))=>(brave(X)<~>~calm(X))))&
(((~curious(mary)|brave(mary)))=>((~strong(fred)|happy(fred))))&
((~generous(mary))=>(?[X]:((~brave(X)&calm(X)))))&
((?[X]:((curious(X)|quiet(X))))<=>(?[X]:(curious(X))))&
(((brave(lucy)<~>quiet(lucy)))<=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((~wise(X)<~>curious(X))<=>(~wise(X)|~strong(X))))&
(![X]:((calm(X)|rich(X))<=>(~creative(X)|~rich(X))))&
(![X]:((happy(X)|creative(X))=>(curious(X)|~creative(X))))&
((~old(susan)&calm(susan)))&
((brave(susan)<~>~generous(susan)))&
((generous(fred)<~>~quiet(fred)))&
((~wise(susan)<~>happy(susan)))&
(?[X]:((brave(X)&tall(X))))&
(?[X]:((~quiet(X)|~generous(X)))) | ~humble(fred) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 7237007276143279042532199
% SZS output start Proof for 7237007276143279042532199
4. ! [X0] : ((~humble(X0) | ~strong(X0)) <=> (humble(X0) & ~patient(X0))) [input p3]
23. ~humble(fred) [input hypothesis]
41. ! [X0] : (((~humble(X0) | ~strong(X0)) | (~humble(X0) | patient(X0))) & ((humble(X0) & ~patient(X0)) | (humble(X0) & strong(X0)))) [nnf transformation 4]
42. ! [X0] : ((~humble(X0) | ~strong(X0) | ~humble(X0) | patient(X0)) & ((humble(X0) & ~patient(X0)) | (humble(X0) & strong(X0)))) [flattening 41]
87. humble(X0) | humble(X0) [cnf transformation 42]
142. ~humble(fred) [cnf transformation 23]
148. humble(X0) [duplicate literal removal 87]
315. $false [subsumption resolution 142,148]
% SZS output end Proof for 7237007276143279042532199
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not wise is not brave or not calm and vice versa.
Everyone who is funny is either happy or curious.
If someone is both not kind and happy then paul is both happy and rich and vice versa.
Everyone who is both not generous and not quiet is curious and vice versa.
Everyone who is both not rich and funny is humble or generous.
Everyone who is not brave or old is wise.
Everyone who is both not wise and old is not humble or old.
Everyone who is both not calm and happy is either not creative or old.
If someone is not calm or not rich then susan is rich or not calm.
If someone is both humble and strong then fred is humble.
If someone is both not calm and funny then mary is both not patient and not quiet and vice versa.
Everyone who is both not happy and kind is kind.
If susan is both generous and rich then someone is either not kind or not brave and vice versa.
If someone is both not generous and quiet then susan is either not generous or wise.
If john is either old or creative then someone is not funny and vice versa.
If someone is curious or not tall then someone is either not brave or not kind and vice versa.
Someone is both tall and not old.
Alice is not wise.
Alice is not humble or old.
Someone is generous or curious.
Fred is both happy and not kind.
John is wise.
Paul is old.
Someone is both not kind and not curious. | Susan is not brave. | contradiction | (![X]:((~generous(X)<~>~wise(X))<=>(~brave(X)|~calm(X))))&
(![X]:(funny(X)=>(happy(X)<~>curious(X))))&
((?[X]:((~kind(X)&happy(X))))<=>((happy(paul)&rich(paul))))&
(![X]:((~generous(X)&~quiet(X))<=>curious(X)))&
(![X]:((~rich(X)&funny(X))=>(humble(X)|generous(X))))&
(![X]:((~brave(X)|old(X))=>wise(X)))&
(![X]:((~wise(X)&old(X))=>(~humble(X)|old(X))))&
(![X]:((~calm(X)&happy(X))=>(~creative(X)<~>old(X))))&
((?[X]:((~calm(X)|~rich(X))))=>((rich(susan)|~calm(susan))))&
((?[X]:((humble(X)&strong(X))))=>(humble(fred)))&
((?[X]:((~calm(X)&funny(X))))<=>((~patient(mary)&~quiet(mary))))&
(![X]:((~happy(X)&kind(X))=>kind(X)))&
(((generous(susan)&rich(susan)))<=>(?[X]:((~kind(X)<~>~brave(X)))))&
((?[X]:((~generous(X)&quiet(X))))=>((~generous(susan)<~>wise(susan))))&
(((old(john)<~>creative(john)))<=>(?[X]:(~funny(X))))&
((?[X]:((curious(X)|~tall(X))))<=>(?[X]:((~brave(X)<~>~kind(X)))))&
(?[X]:((tall(X)&~old(X))))&
(~wise(alice))&
((~humble(alice)|old(alice)))&
(?[X]:((generous(X)|curious(X))))&
((happy(fred)&~kind(fred)))&
(wise(john))&
(old(paul))&
(?[X]:((~kind(X)&~curious(X)))) | ~brave(susan) | [
"p0",
"p3",
"p5",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 770263859086942222719845
% SZS output start Proof for 770263859086942222719845
1. ! [X0] : ((~generous(X0) <~> ~wise(X0)) <=> (~calm(X0) | ~brave(X0))) [input p0]
4. ! [X0] : ((~quiet(X0) & ~generous(X0)) <=> curious(X0)) [input p3]
6. ! [X0] : ((old(X0) | ~brave(X0)) => wise(X0)) [input p5]
13. (rich(susan) & generous(susan)) <=> ? [X0] : (~kind(X0) <~> ~brave(X0)) [input p12]
14. ? [X0] : (quiet(X0) & ~generous(X0)) => (~generous(susan) <~> wise(susan)) [input p13]
16. ? [X0] : (~tall(X0) | curious(X0)) <=> ? [X0] : (~brave(X0) <~> ~kind(X0)) [input p15]
25. ~brave(susan) [input hypothesis]
26. ? [X0] : (~tall(X0) | curious(X0)) <=> ? [X1] : (~brave(X1) <~> ~kind(X1)) [rectify 16]
31. ! [X0] : (wise(X0) | (~old(X0) & brave(X0))) [ennf transformation 6]
40. (~generous(susan) <~> wise(susan)) | ! [X0] : (~quiet(X0) | generous(X0)) [ennf transformation 14]
41. ! [X0] : ((((wise(X0) | generous(X0)) & (~wise(X0) | ~generous(X0))) | (calm(X0) & brave(X0))) & ((~calm(X0) | ~brave(X0)) | ((~generous(X0) | wise(X0)) & (~wise(X0) | generous(X0))))) [nnf transformation 1]
42. ! [X0] : ((((wise(X0) | generous(X0)) & (~wise(X0) | ~generous(X0))) | (calm(X0) & brave(X0))) & (~calm(X0) | ~brave(X0) | ((~generous(X0) | wise(X0)) & (~wise(X0) | generous(X0))))) [flattening 41]
49. ! [X0] : (((~quiet(X0) & ~generous(X0)) | ~curious(X0)) & (curious(X0) | (quiet(X0) | generous(X0)))) [nnf transformation 4]
50. ! [X0] : (((~quiet(X0) & ~generous(X0)) | ~curious(X0)) & (curious(X0) | quiet(X0) | generous(X0))) [flattening 49]
57. ((rich(susan) & generous(susan)) | ! [X0] : ((~kind(X0) | brave(X0)) & (~brave(X0) | kind(X0)))) & (? [X0] : ((brave(X0) | kind(X0)) & (~brave(X0) | ~kind(X0))) | (~rich(susan) | ~generous(susan))) [nnf transformation 13]
58. ((rich(susan) & generous(susan)) | ! [X0] : ((~kind(X0) | brave(X0)) & (~brave(X0) | kind(X0)))) & (? [X0] : ((brave(X0) | kind(X0)) & (~brave(X0) | ~kind(X0))) | ~rich(susan) | ~generous(susan)) [flattening 57]
59. ((rich(susan) & generous(susan)) | ! [X0] : ((~kind(X0) | brave(X0)) & (~brave(X0) | kind(X0)))) & (? [X1] : ((brave(X1) | kind(X1)) & (~brave(X1) | ~kind(X1))) | ~rich(susan) | ~generous(susan)) [rectify 58]
60. ? [X1] : ((brave(X1) | kind(X1)) & (~brave(X1) | ~kind(X1))) => ((brave(sK2) | kind(sK2)) & (~brave(sK2) | ~kind(sK2))) [choice axiom]
61. ((rich(susan) & generous(susan)) | ! [X0] : ((~kind(X0) | brave(X0)) & (~brave(X0) | kind(X0)))) & (((brave(sK2) | kind(sK2)) & (~brave(sK2) | ~kind(sK2))) | ~rich(susan) | ~generous(susan)) [skolemisation 59,60]
62. ((~wise(susan) | generous(susan)) & (wise(susan) | ~generous(susan))) | ! [X0] : (~quiet(X0) | generous(X0)) [nnf transformation 40]
67. (? [X0] : (~tall(X0) | curious(X0)) | ! [X1] : ((~brave(X1) | kind(X1)) & (~kind(X1) | brave(X1)))) & (? [X1] : ((kind(X1) | brave(X1)) & (~kind(X1) | ~brave(X1))) | ! [X0] : (tall(X0) & ~curious(X0))) [nnf transformation 26]
68. (? [X0] : (~tall(X0) | curious(X0)) | ! [X1] : ((~brave(X1) | kind(X1)) & (~kind(X1) | brave(X1)))) & (? [X2] : ((kind(X2) | brave(X2)) & (~kind(X2) | ~brave(X2))) | ! [X3] : (tall(X3) & ~curious(X3))) [rectify 67]
69. ? [X0] : (~tall(X0) | curious(X0)) => (~tall(sK4) | curious(sK4)) [choice axiom]
70. ? [X2] : ((kind(X2) | brave(X2)) & (~kind(X2) | ~brave(X2))) => ((kind(sK5) | brave(sK5)) & (~kind(sK5) | ~brave(sK5))) [choice axiom]
71. ((~tall(sK4) | curious(sK4)) | ! [X1] : ((~brave(X1) | kind(X1)) & (~kind(X1) | brave(X1)))) & (((kind(sK5) | brave(sK5)) & (~kind(sK5) | ~brave(sK5))) | ! [X3] : (tall(X3) & ~curious(X3))) [skolemisation 68,70,69]
80. ~wise(X0) | ~generous(X0) | brave(X0) [cnf transformation 42]
90. quiet(X0) | curious(X0) | generous(X0) [cnf transformation 50]
94. brave(X0) | wise(X0) [cnf transformation 31]
108. generous(susan) | ~brave(X0) | kind(X0) [cnf transformation 61]
109. generous(susan) | ~kind(X0) | brave(X0) [cnf transformation 61]
113. ~wise(susan) | generous(susan) | ~quiet(X0) | generous(X0) [cnf transformation 62]
118. ~kind(sK5) | ~brave(sK5) | ~curious(X3) [cnf transformation 71]
120. kind(sK5) | brave(sK5) | ~curious(X3) [cnf transformation 71]
135. ~brave(susan) [cnf transformation 25]
199. 15 <=> ! [X0] : (~kind(X0) | brave(X0)) [avatar definition]
200. ~kind(X0) | brave(X0) <- (15) [avatar component clause 199]
203. 16 <=> ! [X0] : (~brave(X0) | kind(X0)) [avatar definition]
204. ~brave(X0) | kind(X0) <- (16) [avatar component clause 203]
207. 17 <=> generous(susan) [avatar definition]
208. ~generous(susan) <- (~17) [avatar component clause 207]
210. 15 | 17 [avatar split clause 109,207,199]
211. 16 | 17 [avatar split clause 108,207,203]
223. 20 <=> ! [X0] : (~quiet(X0) | generous(X0)) [avatar definition]
224. ~quiet(X0) | generous(X0) <- (20) [avatar component clause 223]
226. 21 <=> wise(susan) [avatar definition]
227. wise(susan) <- (21) [avatar component clause 226]
229. 20 | 17 | ~21 [avatar split clause 113,226,207,223]
264. 29 <=> brave(sK5) [avatar definition]
265. ~brave(sK5) <- (~29) [avatar component clause 264]
266. brave(sK5) <- (29) [avatar component clause 264]
268. 30 <=> kind(sK5) [avatar definition]
269. ~kind(sK5) <- (~30) [avatar component clause 268]
270. kind(sK5) <- (30) [avatar component clause 268]
273. 31 <=> ! [X3] : ~curious(X3) [avatar definition]
274. ~curious(X3) <- (31) [avatar component clause 273]
275. 31 | 29 | 30 [avatar split clause 120,268,264,273]
277. 31 | ~29 | ~30 [avatar split clause 118,268,264,273]
298. wise(susan) [resolution 94,135]
301. 21 [avatar split clause 298,226]
307. kind(sK5) <- (16, 29) [resolution 204,266]
309. $false <- (16, 29, ~30) [subsumption resolution 307,269]
310. ~16 | ~29 | 30 [avatar contradiction clause 309]
316. ~generous(susan) | brave(susan) <- (21) [resolution 80,227]
339. ~generous(susan) <- (21) [subsumption resolution 316,135]
340. ~17 | ~21 [avatar split clause 339,226,207]
344. brave(sK5) <- (15, 30) [resolution 200,270]
345. $false <- (15, ~29, 30) [subsumption resolution 344,265]
346. ~15 | 29 | ~30 [avatar contradiction clause 345]
384. curious(X0) | generous(X0) | generous(X0) <- (20) [resolution 90,224]
386. curious(X0) | generous(X0) <- (20) [duplicate literal removal 384]
388. generous(X0) <- (20, 31) [subsumption resolution 386,274]
392. $false <- (~17, 20, 31) [resolution 388,208]
399. 17 | ~20 | ~31 [avatar contradiction clause 392]
401. $false [avatar sat refutation 210,211,229,275,277,301,310,340,346,399]
% SZS output end Proof for 770263859086942222719845
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave then alice is generous or kind and vice versa. Everyone who is both not curious and rich is either happy or creative. Everyone who is strong or kind is both not strong and calm and vice versa. Everyone who is strong is either not wise or generous. If alice is old then someone is both rich and patient and vice versa. Everyone who is either brave or not rich is both tall and not quiet and vice versa. If lucy is either humble or not curious then someone is either not brave or not wise and vice versa. If someone is not strong or not funny then someone is not kind and vice versa. Everyone who is curious is kind or not strong and vice versa. If someone is either brave or kind then susan is both not brave and wise and vice versa. Everyone who is brave is not calm and vice versa. Everyone who is kind is not tall or curious. Everyone who is either kind or not patient is strong. If someone is either humble or not humble then alice is both happy and old and vice versa. Mary is either not funny or old. Susan is not kind or not happy. Someone is both not old and not creative. Lucy is not humble or not strong. Lucy is either wise or quiet. Someone is either not rich or not curious. | Lucy is not humble. | contradiction | ((?[X]:(brave(X)))<=>((generous(alice)|kind(alice))))&
(![X]:((~curious(X)&rich(X))=>(happy(X)<~>creative(X))))&
(![X]:((strong(X)|kind(X))<=>(~strong(X)&calm(X))))&
(![X]:(strong(X)=>(~wise(X)<~>generous(X))))&
((old(alice))<=>(?[X]:((rich(X)&patient(X)))))&
(![X]:((brave(X)<~>~rich(X))<=>(tall(X)&~quiet(X))))&
(((humble(lucy)<~>~curious(lucy)))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
((?[X]:((~strong(X)|~funny(X))))<=>(?[X]:(~kind(X))))&
(![X]:(curious(X)<=>(kind(X)|~strong(X))))&
((?[X]:((brave(X)<~>kind(X))))<=>((~brave(susan)&wise(susan))))&
(![X]:(brave(X)<=>~calm(X)))&
(![X]:(kind(X)=>(~tall(X)|curious(X))))&
(![X]:((kind(X)<~>~patient(X))=>strong(X)))&
((?[X]:((humble(X)<~>~humble(X))))<=>((happy(alice)&old(alice))))&
((~funny(mary)<~>old(mary)))&
((~kind(susan)|~happy(susan)))&
(?[X]:((~old(X)&~creative(X))))&
((~humble(lucy)|~strong(lucy)))&
((wise(lucy)<~>quiet(lucy)))&
(?[X]:((~rich(X)<~>~curious(X)))) | ~humble(lucy) | [
"p0",
"p2",
"p6",
"p7",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4798039218355917468966073
% SZS output start Proof for 4798039218355917468966073
1. ? [X0] : brave(X0) <=> (kind(alice) | generous(alice)) [input p0]
3. ! [X0] : ((kind(X0) | strong(X0)) <=> (calm(X0) & ~strong(X0))) [input p2]
7. (humble(lucy) <~> ~curious(lucy)) <=> ? [X0] : (~brave(X0) <~> ~wise(X0)) [input p6]
8. ? [X0] : (~funny(X0) | ~strong(X0)) <=> ? [X0] : ~kind(X0) [input p7]
9. ! [X0] : (curious(X0) <=> (~strong(X0) | kind(X0))) [input p8]
10. ? [X0] : (brave(X0) <~> kind(X0)) <=> (wise(susan) & ~brave(susan)) [input p9]
11. ! [X0] : (brave(X0) <=> ~calm(X0)) [input p10]
21. ~humble(lucy) [input hypothesis]
22. ? [X0] : (~funny(X0) | ~strong(X0)) <=> ? [X1] : ~kind(X1) [rectify 8]
29. (? [X0] : brave(X0) | (~kind(alice) & ~generous(alice))) & ((kind(alice) | generous(alice)) | ! [X0] : ~brave(X0)) [nnf transformation 1]
30. (? [X0] : brave(X0) | (~kind(alice) & ~generous(alice))) & (kind(alice) | generous(alice) | ! [X0] : ~brave(X0)) [flattening 29]
31. (? [X0] : brave(X0) | (~kind(alice) & ~generous(alice))) & (kind(alice) | generous(alice) | ! [X1] : ~brave(X1)) [rectify 30]
32. ? [X0] : brave(X0) => brave(sK0) [choice axiom]
33. (brave(sK0) | (~kind(alice) & ~generous(alice))) & (kind(alice) | generous(alice) | ! [X1] : ~brave(X1)) [skolemisation 31,32]
35. ! [X0] : (((kind(X0) | strong(X0)) | (~calm(X0) | strong(X0))) & ((calm(X0) & ~strong(X0)) | (~kind(X0) & ~strong(X0)))) [nnf transformation 3]
36. ! [X0] : ((kind(X0) | strong(X0) | ~calm(X0) | strong(X0)) & ((calm(X0) & ~strong(X0)) | (~kind(X0) & ~strong(X0)))) [flattening 35]
44. (((curious(lucy) | ~humble(lucy)) & (~curious(lucy) | humble(lucy))) | ! [X0] : ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0)))) & (? [X0] : ((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | ((humble(lucy) | curious(lucy)) & (~curious(lucy) | ~humble(lucy)))) [nnf transformation 7]
45. (((curious(lucy) | ~humble(lucy)) & (~curious(lucy) | humble(lucy))) | ! [X0] : ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0)))) & (? [X1] : ((wise(X1) | brave(X1)) & (~wise(X1) | ~brave(X1))) | ((humble(lucy) | curious(lucy)) & (~curious(lucy) | ~humble(lucy)))) [rectify 44]
46. ? [X1] : ((wise(X1) | brave(X1)) & (~wise(X1) | ~brave(X1))) => ((wise(sK2) | brave(sK2)) & (~wise(sK2) | ~brave(sK2))) [choice axiom]
47. (((curious(lucy) | ~humble(lucy)) & (~curious(lucy) | humble(lucy))) | ! [X0] : ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0)))) & (((wise(sK2) | brave(sK2)) & (~wise(sK2) | ~brave(sK2))) | ((humble(lucy) | curious(lucy)) & (~curious(lucy) | ~humble(lucy)))) [skolemisation 45,46]
48. (? [X0] : (~funny(X0) | ~strong(X0)) | ! [X1] : kind(X1)) & (? [X1] : ~kind(X1) | ! [X0] : (funny(X0) & strong(X0))) [nnf transformation 22]
49. (? [X0] : (~funny(X0) | ~strong(X0)) | ! [X1] : kind(X1)) & (? [X2] : ~kind(X2) | ! [X3] : (funny(X3) & strong(X3))) [rectify 48]
50. ? [X0] : (~funny(X0) | ~strong(X0)) => (~funny(sK3) | ~strong(sK3)) [choice axiom]
51. ? [X2] : ~kind(X2) => ~kind(sK4) [choice axiom]
52. ((~funny(sK3) | ~strong(sK3)) | ! [X1] : kind(X1)) & (~kind(sK4) | ! [X3] : (funny(X3) & strong(X3))) [skolemisation 49,51,50]
53. ! [X0] : ((curious(X0) | (strong(X0) & ~kind(X0))) & ((~strong(X0) | kind(X0)) | ~curious(X0))) [nnf transformation 9]
54. ! [X0] : ((curious(X0) | (strong(X0) & ~kind(X0))) & (~strong(X0) | kind(X0) | ~curious(X0))) [flattening 53]
55. (? [X0] : ((~kind(X0) | ~brave(X0)) & (kind(X0) | brave(X0))) | (~wise(susan) | brave(susan))) & ((wise(susan) & ~brave(susan)) | ! [X0] : ((brave(X0) | ~kind(X0)) & (kind(X0) | ~brave(X0)))) [nnf transformation 10]
56. (? [X0] : ((~kind(X0) | ~brave(X0)) & (kind(X0) | brave(X0))) | ~wise(susan) | brave(susan)) & ((wise(susan) & ~brave(susan)) | ! [X0] : ((brave(X0) | ~kind(X0)) & (kind(X0) | ~brave(X0)))) [flattening 55]
57. (? [X0] : ((~kind(X0) | ~brave(X0)) & (kind(X0) | brave(X0))) | ~wise(susan) | brave(susan)) & ((wise(susan) & ~brave(susan)) | ! [X1] : ((brave(X1) | ~kind(X1)) & (kind(X1) | ~brave(X1)))) [rectify 56]
58. ? [X0] : ((~kind(X0) | ~brave(X0)) & (kind(X0) | brave(X0))) => ((~kind(sK5) | ~brave(sK5)) & (kind(sK5) | brave(sK5))) [choice axiom]
59. (((~kind(sK5) | ~brave(sK5)) & (kind(sK5) | brave(sK5))) | ~wise(susan) | brave(susan)) & ((wise(susan) & ~brave(susan)) | ! [X1] : ((brave(X1) | ~kind(X1)) & (kind(X1) | ~brave(X1)))) [skolemisation 57,58]
60. ! [X0] : ((brave(X0) | calm(X0)) & (~calm(X0) | ~brave(X0))) [nnf transformation 11]
74. kind(alice) | generous(alice) | ~brave(X1) [cnf transformation 33]
75. brave(sK0) | ~generous(alice) [cnf transformation 33]
76. brave(sK0) | ~kind(alice) [cnf transformation 33]
79. ~strong(X0) | ~strong(X0) [cnf transformation 36]
82. ~kind(X0) | calm(X0) [cnf transformation 36]
83. kind(X0) | strong(X0) | ~calm(X0) | strong(X0) [cnf transformation 36]
99. ~curious(lucy) | humble(lucy) | ~wise(X0) | brave(X0) [cnf transformation 47]
103. ~kind(sK4) | strong(X3) [cnf transformation 52]
108. curious(X0) | strong(X0) [cnf transformation 54]
109. ~brave(susan) | kind(X1) | ~brave(X1) [cnf transformation 59]
111. wise(susan) | kind(X1) | ~brave(X1) [cnf transformation 59]
115. ~calm(X0) | ~brave(X0) [cnf transformation 60]
116. calm(X0) | brave(X0) [cnf transformation 60]
136. ~humble(lucy) [cnf transformation 21]
141. ~strong(X0) [duplicate literal removal 79]
142. ~calm(X0) | strong(X0) | kind(X0) [duplicate literal removal 83]
144. 1 <=> kind(alice) [avatar definition]
148. 2 <=> brave(sK0) [avatar definition]
150. brave(sK0) <- (2) [avatar component clause 148]
151. ~1 | 2 [avatar split clause 76,148,144]
153. 3 <=> generous(alice) [avatar definition]
156. ~3 | 2 [avatar split clause 75,148,153]
158. 4 <=> ! [X1] : ~brave(X1) [avatar definition]
159. ~brave(X1) <- (4) [avatar component clause 158]
160. 4 | 3 | 1 [avatar split clause 74,144,153,158]
183. 10 <=> humble(lucy) [avatar definition]
187. 11 <=> curious(lucy) [avatar definition]
188. ~curious(lucy) <- (~11) [avatar component clause 187]
192. 12 <=> ! [X0] : (~wise(X0) | brave(X0)) [avatar definition]
193. ~wise(X0) | brave(X0) <- (12) [avatar component clause 192]
196. 12 | 10 | ~11 [avatar split clause 99,187,183,192]
213. 16 <=> kind(sK4) [avatar definition]
215. ~kind(sK4) <- (~16) [avatar component clause 213]
217. ~kind(sK4) [subsumption resolution 103,141]
218. ~16 [avatar split clause 217,213]
219. curious(X0) [subsumption resolution 108,141]
221. 17 <=> brave(susan) [avatar definition]
222. ~brave(susan) <- (~17) [avatar component clause 221]
225. 18 <=> wise(susan) [avatar definition]
226. wise(susan) <- (18) [avatar component clause 225]
243. 22 <=> ! [X1] : (kind(X1) | ~brave(X1)) [avatar definition]
244. ~brave(X1) | kind(X1) <- (22) [avatar component clause 243]
245. 22 | 18 [avatar split clause 111,225,243]
247. 22 | ~17 [avatar split clause 109,221,243]
294. ~10 [avatar split clause 136,183]
303. brave(susan) <- (12, 18) [resolution 193,226]
305. $false <- (12, ~17, 18) [subsumption resolution 303,222]
306. ~12 | 17 | ~18 [avatar contradiction clause 305]
308. kind(sK0) <- (2, 22) [resolution 244,150]
317. calm(sK0) <- (2, 22) [resolution 308,82]
330. ~brave(sK0) <- (2, 22) [resolution 317,115]
331. $false <- (2, 22) [subsumption resolution 330,150]
332. ~2 | ~22 [avatar contradiction clause 331]
339. strong(X0) | kind(X0) | brave(X0) [resolution 142,116]
340. kind(X0) | brave(X0) [subsumption resolution 339,141]
341. kind(X0) <- (4) [subsumption resolution 340,159]
346. $false <- (4, ~16) [resolution 341,215]
349. ~4 | 16 [avatar contradiction clause 346]
356. $false <- (~11) [subsumption resolution 188,219]
357. 11 [avatar contradiction clause 356]
358. $false [avatar sat refutation 151,156,160,196,218,245,247,294,306,332,349,357]
% SZS output end Proof for 4798039218355917468966073
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or not rich is either not patient or generous.
If someone is either humble or strong then someone is not creative.
Everyone who is not quiet or not wise is both wise and not brave and vice versa.
Everyone who is not happy or rich is both happy and not strong and vice versa.
Everyone who is either brave or humble is not calm or not creative and vice versa.
Everyone who is both calm and patient is not brave and vice versa.
Everyone who is either creative or quiet is not tall or strong.
If someone is humble then someone is not tall.
Everyone who is quiet or happy is brave or calm and vice versa.
Everyone who is either calm or patient is happy.
Everyone who is either not creative or old is not tall or not calm.
If someone is both wise and not old then someone is both not patient and creative and vice versa.
If someone is either patient or not brave then someone is either not patient or not strong.
If susan is either curious or wise then mary is strong or old.
If someone is both funny and not rich then mary is either not brave or strong and vice versa.
Everyone who is not strong is either not happy or kind.
Susan is brave or old.
Fred is both brave and tall.
Someone is either not wise or wise.
Someone is both not rich and not old.
Someone is both not rich and tall.
Someone is not kind. | Mary is calm. | neutral | (![X]:((~happy(X)<~>~rich(X))=>(~patient(X)<~>generous(X))))&
((?[X]:((humble(X)<~>strong(X))))=>(?[X]:(~creative(X))))&
(![X]:((~quiet(X)|~wise(X))<=>(wise(X)&~brave(X))))&
(![X]:((~happy(X)|rich(X))<=>(happy(X)&~strong(X))))&
(![X]:((brave(X)<~>humble(X))<=>(~calm(X)|~creative(X))))&
(![X]:((calm(X)&patient(X))<=>~brave(X)))&
(![X]:((creative(X)<~>quiet(X))=>(~tall(X)|strong(X))))&
((?[X]:(humble(X)))=>(?[X]:(~tall(X))))&
(![X]:((quiet(X)|happy(X))<=>(brave(X)|calm(X))))&
(![X]:((calm(X)<~>patient(X))=>happy(X)))&
(![X]:((~creative(X)<~>old(X))=>(~tall(X)|~calm(X))))&
((?[X]:((wise(X)&~old(X))))<=>(?[X]:((~patient(X)&creative(X)))))&
((?[X]:((patient(X)<~>~brave(X))))=>(?[X]:((~patient(X)<~>~strong(X)))))&
(((curious(susan)<~>wise(susan)))=>((strong(mary)|old(mary))))&
((?[X]:((funny(X)&~rich(X))))<=>((~brave(mary)<~>strong(mary))))&
(![X]:(~strong(X)=>(~happy(X)<~>kind(X))))&
((brave(susan)|old(susan)))&
((brave(fred)&tall(fred)))&
(?[X]:((~wise(X)<~>wise(X))))&
(?[X]:((~rich(X)&~old(X))))&
(?[X]:((~rich(X)&tall(X))))&
(?[X]:(~kind(X))) | calm(mary) | [] | null | 0 |
If alice is rich or not creative then someone is not kind and vice versa. If paul is not kind then fred is both tall and not calm. If susan is not kind or not quiet then lucy is old. If someone is both not patient and funny then lucy is not rich or not brave. Everyone who is calm or not brave is not kind or not rich and vice versa. Everyone who is old is either not creative or kind. Everyone who is either not patient or not calm is creative or patient. Everyone who is either not calm or not generous is both patient and tall and vice versa. If someone is calm then someone is both old and happy. If susan is both rich and generous then someone is both quiet and happy and vice versa. Everyone who is not quiet or not tall is both kind and not funny. If someone is curious or tall then someone is both kind and not kind and vice versa. Everyone who is either rich or not kind is either tall or calm and vice versa. If someone is strong then someone is either not tall or not brave. If susan is not humble then john is tall. Someone is humble or not funny. Someone is either old or funny. Someone is strong or patient. Someone is not brave or happy. Susan is both not generous and not creative. John is both not happy and not old. Paul is not generous. | John is not strong. | entailment | (((rich(alice)|~creative(alice)))<=>(?[X]:(~kind(X))))&
((~kind(paul))=>((tall(fred)&~calm(fred))))&
(((~kind(susan)|~quiet(susan)))=>(old(lucy)))&
((?[X]:((~patient(X)&funny(X))))=>((~rich(lucy)|~brave(lucy))))&
(![X]:((calm(X)|~brave(X))<=>(~kind(X)|~rich(X))))&
(![X]:(old(X)=>(~creative(X)<~>kind(X))))&
(![X]:((~patient(X)<~>~calm(X))=>(creative(X)|patient(X))))&
(![X]:((~calm(X)<~>~generous(X))<=>(patient(X)&tall(X))))&
((?[X]:(calm(X)))=>(?[X]:((old(X)&happy(X)))))&
(((rich(susan)&generous(susan)))<=>(?[X]:((quiet(X)&happy(X)))))&
(![X]:((~quiet(X)|~tall(X))=>(kind(X)&~funny(X))))&
((?[X]:((curious(X)|tall(X))))<=>(?[X]:((kind(X)&~kind(X)))))&
(![X]:((rich(X)<~>~kind(X))<=>(tall(X)<~>calm(X))))&
((?[X]:(strong(X)))=>(?[X]:((~tall(X)<~>~brave(X)))))&
((~humble(susan))=>(tall(john)))&
(?[X]:((humble(X)|~funny(X))))&
(?[X]:((old(X)<~>funny(X))))&
(?[X]:((strong(X)|patient(X))))&
(?[X]:((~brave(X)|happy(X))))&
((~generous(susan)&~creative(susan)))&
((~happy(john)&~old(john)))&
(~generous(paul)) | ~strong(john) | [
"p4",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 121962283106332315232257
% SZS output start Proof for 121962283106332315232257
5. ! [X0] : ((~brave(X0) | calm(X0)) <=> (~rich(X0) | ~kind(X0))) [input p4]
11. ! [X0] : ((~tall(X0) | ~quiet(X0)) => (~funny(X0) & kind(X0))) [input p10]
12. ? [X0] : (tall(X0) | curious(X0)) <=> ? [X0] : (~kind(X0) & kind(X0)) [input p11]
13. ! [X0] : ((rich(X0) <~> ~kind(X0)) <=> (tall(X0) <~> calm(X0))) [input p12]
14. ? [X0] : strong(X0) => ? [X0] : (~tall(X0) <~> ~brave(X0)) [input p13]
23. strong(john) [input hypothesis]
25. ? [X0] : (tall(X0) | curious(X0)) <=> ? [X1] : (~kind(X1) & kind(X1)) [rectify 12]
26. ? [X0] : strong(X0) => ? [X1] : (~tall(X1) <~> ~brave(X1)) [rectify 14]
37. ! [X0] : ((~funny(X0) & kind(X0)) | (tall(X0) & quiet(X0))) [ennf transformation 11]
38. ? [X1] : (~tall(X1) <~> ~brave(X1)) | ! [X0] : ~strong(X0) [ennf transformation 26]
44. ! [X0] : (((~brave(X0) | calm(X0)) | (rich(X0) & kind(X0))) & ((~rich(X0) | ~kind(X0)) | (brave(X0) & ~calm(X0)))) [nnf transformation 5]
45. ! [X0] : ((~brave(X0) | calm(X0) | (rich(X0) & kind(X0))) & (~rich(X0) | ~kind(X0) | (brave(X0) & ~calm(X0)))) [flattening 44]
58. (? [X0] : (tall(X0) | curious(X0)) | ! [X1] : (kind(X1) | ~kind(X1))) & (? [X1] : (~kind(X1) & kind(X1)) | ! [X0] : (~tall(X0) & ~curious(X0))) [nnf transformation 25]
59. (? [X0] : (tall(X0) | curious(X0)) | ! [X1] : (kind(X1) | ~kind(X1))) & (? [X2] : (~kind(X2) & kind(X2)) | ! [X3] : (~tall(X3) & ~curious(X3))) [rectify 58]
60. ? [X0] : (tall(X0) | curious(X0)) => (tall(sK3) | curious(sK3)) [choice axiom]
61. ? [X2] : (~kind(X2) & kind(X2)) => (~kind(sK4) & kind(sK4)) [choice axiom]
62. ((tall(sK3) | curious(sK3)) | ! [X1] : (kind(X1) | ~kind(X1))) & ((~kind(sK4) & kind(sK4)) | ! [X3] : (~tall(X3) & ~curious(X3))) [skolemisation 59,61,60]
63. ! [X0] : ((((kind(X0) | ~rich(X0)) & (~kind(X0) | rich(X0))) | ((tall(X0) | ~calm(X0)) & (calm(X0) | ~tall(X0)))) & (((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0))))) [nnf transformation 13]
64. ? [X1] : ((brave(X1) | tall(X1)) & (~brave(X1) | ~tall(X1))) | ! [X0] : ~strong(X0) [nnf transformation 38]
65. ? [X0] : ((brave(X0) | tall(X0)) & (~brave(X0) | ~tall(X0))) | ! [X1] : ~strong(X1) [rectify 64]
66. ? [X0] : ((brave(X0) | tall(X0)) & (~brave(X0) | ~tall(X0))) => ((brave(sK5) | tall(sK5)) & (~brave(sK5) | ~tall(sK5))) [choice axiom]
67. ((brave(sK5) | tall(sK5)) & (~brave(sK5) | ~tall(sK5))) | ! [X1] : ~strong(X1) [skolemisation 65,66]
83. ~calm(X0) | ~kind(X0) | ~rich(X0) [cnf transformation 45]
86. ~brave(X0) | calm(X0) | rich(X0) [cnf transformation 45]
104. tall(X0) | kind(X0) [cnf transformation 37]
108. kind(sK4) | ~tall(X3) [cnf transformation 62]
110. ~kind(sK4) | ~tall(X3) [cnf transformation 62]
112. calm(X0) | tall(X0) | ~kind(X0) | ~rich(X0) [cnf transformation 63]
117. ~kind(X0) | rich(X0) | tall(X0) | ~calm(X0) [cnf transformation 63]
118. kind(X0) | ~rich(X0) | calm(X0) | ~tall(X0) [cnf transformation 63]
121. brave(sK5) | tall(sK5) | ~strong(X1) [cnf transformation 67]
131. strong(john) [cnf transformation 23]
228. 22 <=> ! [X3] : ~tall(X3) [avatar definition]
229. ~tall(X3) <- (22) [avatar component clause 228]
231. 23 <=> kind(sK4) [avatar definition]
234. 22 | ~23 [avatar split clause 110,231,228]
239. 22 | 23 [avatar split clause 108,231,228]
241. kind(X0) | ~rich(X0) | calm(X0) [subsumption resolution 118,104]
242. ~kind(X0) | tall(X0) | ~calm(X0) [subsumption resolution 117,83]
243. ~calm(X0) | tall(X0) [subsumption resolution 242,104]
245. calm(X0) | tall(X0) | ~rich(X0) [subsumption resolution 112,241]
246. ~rich(X0) | tall(X0) [subsumption resolution 245,243]
248. 25 <=> ! [X1] : ~strong(X1) [avatar definition]
249. ~strong(X1) <- (25) [avatar component clause 248]
251. 26 <=> tall(sK5) [avatar definition]
253. tall(sK5) <- (26) [avatar component clause 251]
255. 27 <=> brave(sK5) [avatar definition]
257. brave(sK5) <- (27) [avatar component clause 255]
258. 25 | 26 | 27 [avatar split clause 121,255,251,248]
291. $false <- (25) [resolution 249,131]
292. ~25 [avatar contradiction clause 291]
293. $false <- (22, 26) [subsumption resolution 253,229]
294. ~22 | ~26 [avatar contradiction clause 293]
311. calm(sK5) | rich(sK5) <- (27) [resolution 86,257]
318. 36 <=> rich(sK5) [avatar definition]
320. rich(sK5) <- (36) [avatar component clause 318]
322. 37 <=> calm(sK5) [avatar definition]
324. calm(sK5) <- (37) [avatar component clause 322]
325. 36 | 37 | ~27 [avatar split clause 311,255,322,318]
328. tall(sK5) <- (36) [resolution 320,246]
329. $false <- (22, 36) [subsumption resolution 328,229]
330. ~22 | ~36 [avatar contradiction clause 329]
341. tall(sK5) <- (37) [resolution 324,243]
342. $false <- (22, 37) [subsumption resolution 341,229]
343. ~22 | ~37 [avatar contradiction clause 342]
344. $false [avatar sat refutation 234,239,258,292,294,325,330,343]
% SZS output end Proof for 121962283106332315232257
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not strong then someone is wise or quiet.
Everyone who is both not happy and not tall is either tall or happy.
If someone is not patient then fred is either not creative or generous.
Everyone who is either not strong or quiet is both not humble and not happy and vice versa.
If mary is either humble or wise then someone is either rich or happy and vice versa.
If paul is either not quiet or strong then someone is calm or not rich and vice versa.
Everyone who is not old is wise and vice versa.
Everyone who is not old or not rich is creative and vice versa.
If mary is either not calm or strong then someone is not calm or not brave and vice versa.
If someone is either not wise or not humble then someone is wise.
Everyone who is not humble is not creative or old and vice versa.
Everyone who is not rich is humble and vice versa.
Everyone who is not happy or not calm is either not tall or not brave.
If susan is both not humble and generous then someone is both rich and not humble.
Everyone who is not tall or funny is not funny.
Everyone who is strong is not funny or not brave.
John is both not quiet and not wise.
Someone is brave.
Alice is both not wise and not generous.
Susan is not patient or strong.
Someone is not quiet or generous. | Mary is not creative. | entailment | ((~strong(mary))=>(?[X]:((wise(X)|quiet(X)))))&
(![X]:((~happy(X)&~tall(X))=>(tall(X)<~>happy(X))))&
((?[X]:(~patient(X)))=>((~creative(fred)<~>generous(fred))))&
(![X]:((~strong(X)<~>quiet(X))<=>(~humble(X)&~happy(X))))&
(((humble(mary)<~>wise(mary)))<=>(?[X]:((rich(X)<~>happy(X)))))&
(((~quiet(paul)<~>strong(paul)))<=>(?[X]:((calm(X)|~rich(X)))))&
(![X]:(~old(X)<=>wise(X)))&
(![X]:((~old(X)|~rich(X))<=>creative(X)))&
(((~calm(mary)<~>strong(mary)))<=>(?[X]:((~calm(X)|~brave(X)))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:(wise(X))))&
(![X]:(~humble(X)<=>(~creative(X)|old(X))))&
(![X]:(~rich(X)<=>humble(X)))&
(![X]:((~happy(X)|~calm(X))=>(~tall(X)<~>~brave(X))))&
(((~humble(susan)&generous(susan)))=>(?[X]:((rich(X)&~humble(X)))))&
(![X]:((~tall(X)|funny(X))=>~funny(X)))&
(![X]:(strong(X)=>(~funny(X)|~brave(X))))&
((~quiet(john)&~wise(john)))&
(?[X]:(brave(X)))&
((~wise(alice)&~generous(alice)))&
((~patient(susan)|strong(susan)))&
(?[X]:((~quiet(X)|generous(X)))) | ~creative(mary) | [
"p3",
"p4",
"p5",
"p6",
"p7",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4463486017520204117916291
% SZS output start Proof for 4463486017520204117916291
4. ! [X0] : ((~strong(X0) <~> quiet(X0)) <=> (~happy(X0) & ~humble(X0))) [input p3]
5. (humble(mary) <~> wise(mary)) <=> ? [X0] : (rich(X0) <~> happy(X0)) [input p4]
6. (~quiet(paul) <~> strong(paul)) <=> ? [X0] : (~rich(X0) | calm(X0)) [input p5]
7. ! [X0] : (~old(X0) <=> wise(X0)) [input p6]
8. ! [X0] : ((~rich(X0) | ~old(X0)) <=> creative(X0)) [input p7]
11. ! [X0] : (~humble(X0) <=> (old(X0) | ~creative(X0))) [input p10]
12. ! [X0] : (~rich(X0) <=> humble(X0)) [input p11]
22. creative(mary) [input hypothesis]
38. ! [X0] : ((((~quiet(X0) | strong(X0)) & (quiet(X0) | ~strong(X0))) | (happy(X0) | humble(X0))) & ((~happy(X0) & ~humble(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0))))) [nnf transformation 4]
39. ! [X0] : ((((~quiet(X0) | strong(X0)) & (quiet(X0) | ~strong(X0))) | happy(X0) | humble(X0)) & ((~happy(X0) & ~humble(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0))))) [flattening 38]
40. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (? [X0] : ((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [nnf transformation 5]
41. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (? [X1] : ((~happy(X1) | ~rich(X1)) & (happy(X1) | rich(X1))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [rectify 40]
42. ? [X1] : ((~happy(X1) | ~rich(X1)) & (happy(X1) | rich(X1))) => ((~happy(sK1) | ~rich(sK1)) & (happy(sK1) | rich(sK1))) [choice axiom]
43. (((~wise(mary) | ~humble(mary)) & (wise(mary) | humble(mary))) | ! [X0] : ((rich(X0) | ~happy(X0)) & (happy(X0) | ~rich(X0)))) & (((~happy(sK1) | ~rich(sK1)) & (happy(sK1) | rich(sK1))) | ((humble(mary) | ~wise(mary)) & (wise(mary) | ~humble(mary)))) [skolemisation 41,42]
44. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & (? [X0] : (~rich(X0) | calm(X0)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [nnf transformation 6]
45. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & (? [X1] : (~rich(X1) | calm(X1)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [rectify 44]
46. ? [X1] : (~rich(X1) | calm(X1)) => (~rich(sK2) | calm(sK2)) [choice axiom]
47. (((~strong(paul) | quiet(paul)) & (strong(paul) | ~quiet(paul))) | ! [X0] : (rich(X0) & ~calm(X0))) & ((~rich(sK2) | calm(sK2)) | ((~quiet(paul) | ~strong(paul)) & (strong(paul) | quiet(paul)))) [skolemisation 45,46]
48. ! [X0] : ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0))) [nnf transformation 7]
49. ! [X0] : (((~rich(X0) | ~old(X0)) | ~creative(X0)) & (creative(X0) | (rich(X0) & old(X0)))) [nnf transformation 8]
50. ! [X0] : ((~rich(X0) | ~old(X0) | ~creative(X0)) & (creative(X0) | (rich(X0) & old(X0)))) [flattening 49]
59. ! [X0] : ((~humble(X0) | (~old(X0) & creative(X0))) & ((old(X0) | ~creative(X0)) | humble(X0))) [nnf transformation 11]
60. ! [X0] : ((~humble(X0) | (~old(X0) & creative(X0))) & (old(X0) | ~creative(X0) | humble(X0))) [flattening 59]
61. ! [X0] : ((~rich(X0) | ~humble(X0)) & (humble(X0) | rich(X0))) [nnf transformation 12]
74. ~humble(X0) | quiet(X0) | strong(X0) [cnf transformation 39]
75. ~humble(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 39]
76. ~happy(X0) | quiet(X0) | strong(X0) [cnf transformation 39]
77. ~happy(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 39]
84. wise(mary) | humble(mary) | happy(X0) | ~rich(X0) [cnf transformation 43]
86. ~wise(mary) | ~humble(mary) | happy(X0) | ~rich(X0) [cnf transformation 43]
91. strong(paul) | ~quiet(paul) | rich(X0) [cnf transformation 47]
93. ~strong(paul) | quiet(paul) | rich(X0) [cnf transformation 47]
94. old(X0) | wise(X0) [cnf transformation 48]
95. ~old(X0) | ~wise(X0) [cnf transformation 48]
96. old(X0) | creative(X0) [cnf transformation 50]
98. ~old(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 50]
107. old(X0) | ~creative(X0) | humble(X0) [cnf transformation 60]
109. ~old(X0) | ~humble(X0) [cnf transformation 60]
110. rich(X0) | humble(X0) [cnf transformation 61]
111. ~rich(X0) | ~humble(X0) [cnf transformation 61]
125. creative(mary) [cnf transformation 22]
157. 8 <=> humble(mary) [avatar definition]
158. humble(mary) <- (8) [avatar component clause 157]
159. ~humble(mary) <- (~8) [avatar component clause 157]
161. 9 <=> wise(mary) [avatar definition]
162. wise(mary) <- (9) [avatar component clause 161]
163. ~wise(mary) <- (~9) [avatar component clause 161]
166. 10 <=> ! [X0] : (happy(X0) | ~rich(X0)) [avatar definition]
167. ~rich(X0) | happy(X0) <- (10) [avatar component clause 166]
168. 10 | ~8 | ~9 [avatar split clause 86,161,157,166]
170. 10 | 8 | 9 [avatar split clause 84,161,157,166]
184. 13 <=> ! [X0] : rich(X0) [avatar definition]
185. rich(X0) <- (13) [avatar component clause 184]
187. 14 <=> quiet(paul) [avatar definition]
188. ~quiet(paul) <- (~14) [avatar component clause 187]
189. quiet(paul) <- (14) [avatar component clause 187]
191. 15 <=> strong(paul) [avatar definition]
192. strong(paul) <- (15) [avatar component clause 191]
193. ~strong(paul) <- (~15) [avatar component clause 191]
194. 13 | 14 | ~15 [avatar split clause 93,191,187,184]
199. 13 | ~14 | 15 [avatar split clause 91,191,187,184]
236. 24 <=> ! [X1] : (~wise(X1) | humble(X1)) [avatar definition]
237. ~wise(X1) | humble(X1) <- (24) [avatar component clause 236]
244. 26 <=> ! [X1] : (~humble(X1) | wise(X1)) [avatar definition]
245. ~humble(X1) | wise(X1) <- (26) [avatar component clause 244]
247. old(X0) | humble(X0) [subsumption resolution 107,96]
289. ~humble(X1) | wise(X1) [resolution 109,94]
290. 26 [avatar split clause 289,244]
295. humble(X0) | happy(X0) <- (10) [resolution 167,110]
299. humble(X1) | ~wise(X1) [resolution 247,95]
300. 24 [avatar split clause 299,236]
348. ~rich(X0) | ~creative(X0) | humble(X0) [resolution 98,247]
351. ~rich(X0) | ~creative(X0) [subsumption resolution 348,111]
396. happy(X0) | ~strong(X0) | ~quiet(X0) <- (10) [resolution 295,75]
397. happy(X1) | quiet(X1) | strong(X1) <- (10) [resolution 295,74]
400. ~quiet(X0) | ~strong(X0) <- (10) [subsumption resolution 396,77]
401. quiet(X1) | strong(X1) <- (10) [subsumption resolution 397,76]
428. strong(paul) <- (10, ~14) [resolution 401,188]
434. $false <- (10, ~14, ~15) [subsumption resolution 428,193]
435. ~10 | 14 | 15 [avatar contradiction clause 434]
441. ~strong(paul) <- (10, 14) [resolution 189,400]
443. $false <- (10, 14, 15) [subsumption resolution 441,192]
444. ~10 | ~14 | ~15 [avatar contradiction clause 443]
445. ~creative(X0) <- (13) [resolution 185,351]
460. $false <- (13) [resolution 445,125]
461. ~13 [avatar contradiction clause 460]
500. wise(mary) <- (8, 26) [resolution 158,245]
503. $false <- (8, ~9, 26) [subsumption resolution 500,163]
504. ~8 | 9 | ~26 [avatar contradiction clause 503]
506. humble(mary) <- (9, 24) [resolution 162,237]
507. $false <- (~8, 9, 24) [subsumption resolution 506,159]
508. 8 | ~9 | ~24 [avatar contradiction clause 507]
509. $false [avatar sat refutation 168,170,194,199,290,300,435,444,461,504,508]
% SZS output end Proof for 4463486017520204117916291
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or calm is both not creative and not curious and vice versa. If someone is not creative then someone is both kind and not old and vice versa. Everyone who is not old or not calm is either not calm or rich. If someone is not generous then paul is humble or patient and vice versa. Everyone who is not happy is not strong and vice versa. Everyone who is calm is both calm and not strong. Everyone who is either kind or tall is not quiet or not old. If mary is curious or not kind then john is not quiet or wise and vice versa. Everyone who is not kind or not tall is both not generous and happy and vice versa. If someone is either not curious or not brave then someone is not quiet or not happy and vice versa. Everyone who is rich is not humble or not calm and vice versa. Everyone who is happy or curious is both old and not calm and vice versa. Everyone who is humble is not strong. If john is not brave or generous then someone is either tall or creative. Paul is either not curious or brave. Paul is either creative or strong. Someone is both generous and not brave. Alice is not patient or creative. Someone is either not tall or not curious. | Paul is patient. | neutral | (![X]:((~quiet(X)<~>calm(X))<=>(~creative(X)&~curious(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((kind(X)&~old(X)))))&
(![X]:((~old(X)|~calm(X))=>(~calm(X)<~>rich(X))))&
((?[X]:(~generous(X)))<=>((humble(paul)|patient(paul))))&
(![X]:(~happy(X)<=>~strong(X)))&
(![X]:(calm(X)=>(calm(X)&~strong(X))))&
(![X]:((kind(X)<~>tall(X))=>(~quiet(X)|~old(X))))&
(((curious(mary)|~kind(mary)))<=>((~quiet(john)|wise(john))))&
(![X]:((~kind(X)|~tall(X))<=>(~generous(X)&happy(X))))&
((?[X]:((~curious(X)<~>~brave(X))))<=>(?[X]:((~quiet(X)|~happy(X)))))&
(![X]:(rich(X)<=>(~humble(X)|~calm(X))))&
(![X]:((happy(X)|curious(X))<=>(old(X)&~calm(X))))&
(![X]:(humble(X)=>~strong(X)))&
(((~brave(john)|generous(john)))=>(?[X]:((tall(X)<~>creative(X)))))&
((~curious(paul)<~>brave(paul)))&
((creative(paul)<~>strong(paul)))&
(?[X]:((generous(X)&~brave(X))))&
((~patient(alice)|creative(alice)))&
(?[X]:((~tall(X)<~>~curious(X)))) | patient(paul) | [] | null | 0 |
Everyone who is rich or quiet is either creative or not generous.
If mary is either funny or wise then mary is both not wise and not patient.
Everyone who is not strong or not wise is not funny and vice versa.
Everyone who is both tall and wise is not funny or patient and vice versa.
Everyone who is either not calm or curious is not old or not kind.
If paul is kind then someone is old or not creative.
Everyone who is both not funny and not kind is both not rich and not happy and vice versa.
Everyone who is either brave or patient is calm.
Everyone who is either not brave or patient is quiet and vice versa.
If someone is quiet then someone is wise and vice versa.
Everyone who is both happy and not strong is not happy or not kind.
Everyone who is creative or wise is funny.
If someone is rich then someone is both creative and old.
If someone is both happy and not funny then someone is not creative and vice versa.
Everyone who is either not quiet or calm is not creative.
Someone is either not humble or rich.
Alice is both strong and not old.
Someone is either brave or happy.
John is quiet.
Fred is creative or not generous. | Alice is not generous. | neutral | (![X]:((rich(X)|quiet(X))=>(creative(X)<~>~generous(X))))&
(((funny(mary)<~>wise(mary)))=>((~wise(mary)&~patient(mary))))&
(![X]:((~strong(X)|~wise(X))<=>~funny(X)))&
(![X]:((tall(X)&wise(X))<=>(~funny(X)|patient(X))))&
(![X]:((~calm(X)<~>curious(X))=>(~old(X)|~kind(X))))&
((kind(paul))=>(?[X]:((old(X)|~creative(X)))))&
(![X]:((~funny(X)&~kind(X))<=>(~rich(X)&~happy(X))))&
(![X]:((brave(X)<~>patient(X))=>calm(X)))&
(![X]:((~brave(X)<~>patient(X))<=>quiet(X)))&
((?[X]:(quiet(X)))<=>(?[X]:(wise(X))))&
(![X]:((happy(X)&~strong(X))=>(~happy(X)|~kind(X))))&
(![X]:((creative(X)|wise(X))=>funny(X)))&
((?[X]:(rich(X)))=>(?[X]:((creative(X)&old(X)))))&
((?[X]:((happy(X)&~funny(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~quiet(X)<~>calm(X))=>~creative(X)))&
(?[X]:((~humble(X)<~>rich(X))))&
((strong(alice)&~old(alice)))&
(?[X]:((brave(X)<~>happy(X))))&
(quiet(john))&
((creative(fred)|~generous(fred))) | ~generous(alice) | [] | null | 0 |
Everyone who is either not generous or brave is not quiet and vice versa.
Everyone who is either funny or not tall is funny or not tall and vice versa.
Everyone who is both tall and not curious is calm.
Everyone who is not generous or not brave is humble and vice versa.
Everyone who is both not generous and brave is rich and vice versa.
Everyone who is old is generous.
Everyone who is both creative and happy is happy or curious and vice versa.
Everyone who is either not calm or not wise is wise.
Everyone who is both strong and humble is either not creative or not quiet and vice versa.
If fred is both not quiet and tall then someone is curious.
Everyone who is kind is not calm and vice versa.
If susan is either patient or not wise then mary is not wise or curious.
If mary is not funny or not calm then susan is not curious.
If someone is not strong then fred is both generous and kind and vice versa.
Everyone who is both not quiet and creative is funny or happy.
If someone is not old or not rich then someone is either not quiet or kind.
Someone is both rich and tall.
Someone is not kind or wise.
Alice is either old or tall.
Someone is curious or kind.
Alice is both not calm and tall.
Alice is either kind or rich.
Someone is calm or not calm.
Someone is calm or not kind. | Alice is not brave. | entailment | (![X]:((~generous(X)<~>brave(X))<=>~quiet(X)))&
(![X]:((funny(X)<~>~tall(X))<=>(funny(X)|~tall(X))))&
(![X]:((tall(X)&~curious(X))=>calm(X)))&
(![X]:((~generous(X)|~brave(X))<=>humble(X)))&
(![X]:((~generous(X)&brave(X))<=>rich(X)))&
(![X]:(old(X)=>generous(X)))&
(![X]:((creative(X)&happy(X))<=>(happy(X)|curious(X))))&
(![X]:((~calm(X)<~>~wise(X))=>wise(X)))&
(![X]:((strong(X)&humble(X))<=>(~creative(X)<~>~quiet(X))))&
(((~quiet(fred)&tall(fred)))=>(?[X]:(curious(X))))&
(![X]:(kind(X)<=>~calm(X)))&
(((patient(susan)<~>~wise(susan)))=>((~wise(mary)|curious(mary))))&
(((~funny(mary)|~calm(mary)))=>(~curious(susan)))&
((?[X]:(~strong(X)))<=>((generous(fred)&kind(fred))))&
(![X]:((~quiet(X)&creative(X))=>(funny(X)|happy(X))))&
((?[X]:((~old(X)|~rich(X))))=>(?[X]:((~quiet(X)<~>kind(X)))))&
(?[X]:((rich(X)&tall(X))))&
(?[X]:((~kind(X)|wise(X))))&
((old(alice)<~>tall(alice)))&
(?[X]:((curious(X)|kind(X))))&
((~calm(alice)&tall(alice)))&
((kind(alice)<~>rich(alice)))&
(?[X]:((calm(X)|~calm(X))))&
(?[X]:((calm(X)|~kind(X)))) | ~brave(alice) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p8",
"p10",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4106318879089938867842615
% SZS output start Proof for 4106318879089938867842615
1. ! [X0] : ((~generous(X0) <~> brave(X0)) <=> ~quiet(X0)) [input p0]
3. ! [X0] : ((~curious(X0) & tall(X0)) => calm(X0)) [input p2]
4. ! [X0] : ((~brave(X0) | ~generous(X0)) <=> humble(X0)) [input p3]
5. ! [X0] : ((brave(X0) & ~generous(X0)) <=> rich(X0)) [input p4]
7. ! [X0] : ((happy(X0) & creative(X0)) <=> (curious(X0) | happy(X0))) [input p6]
9. ! [X0] : ((humble(X0) & strong(X0)) <=> (~creative(X0) <~> ~quiet(X0))) [input p8]
11. ! [X0] : (kind(X0) <=> ~calm(X0)) [input p10]
21. tall(alice) & ~calm(alice) [input p20]
22. kind(alice) <~> rich(alice) [input p21]
25. brave(alice) [input hypothesis]
27. ! [X0] : (calm(X0) | (curious(X0) | ~tall(X0))) [ennf transformation 3]
28. ! [X0] : (calm(X0) | curious(X0) | ~tall(X0)) [flattening 27]
39. ! [X0] : ((((~brave(X0) | generous(X0)) & (brave(X0) | ~generous(X0))) | quiet(X0)) & (~quiet(X0) | ((~generous(X0) | ~brave(X0)) & (brave(X0) | generous(X0))))) [nnf transformation 1]
42. ! [X0] : (((~brave(X0) | ~generous(X0)) | ~humble(X0)) & (humble(X0) | (brave(X0) & generous(X0)))) [nnf transformation 4]
43. ! [X0] : ((~brave(X0) | ~generous(X0) | ~humble(X0)) & (humble(X0) | (brave(X0) & generous(X0)))) [flattening 42]
44. ! [X0] : (((brave(X0) & ~generous(X0)) | ~rich(X0)) & (rich(X0) | (~brave(X0) | generous(X0)))) [nnf transformation 5]
45. ! [X0] : (((brave(X0) & ~generous(X0)) | ~rich(X0)) & (rich(X0) | ~brave(X0) | generous(X0))) [flattening 44]
46. ! [X0] : (((happy(X0) & creative(X0)) | (~curious(X0) & ~happy(X0))) & ((curious(X0) | happy(X0)) | (~happy(X0) | ~creative(X0)))) [nnf transformation 7]
47. ! [X0] : (((happy(X0) & creative(X0)) | (~curious(X0) & ~happy(X0))) & (curious(X0) | happy(X0) | ~happy(X0) | ~creative(X0))) [flattening 46]
49. ! [X0] : (((humble(X0) & strong(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0)))) & (((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | (~humble(X0) | ~strong(X0)))) [nnf transformation 9]
50. ! [X0] : (((humble(X0) & strong(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0)))) & (((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | ~humble(X0) | ~strong(X0))) [flattening 49]
53. ! [X0] : ((kind(X0) | calm(X0)) & (~calm(X0) | ~kind(X0))) [nnf transformation 11]
71. (~rich(alice) | ~kind(alice)) & (rich(alice) | kind(alice)) [nnf transformation 22]
77. ~quiet(X0) | ~generous(X0) | ~brave(X0) [cnf transformation 39]
86. ~tall(X0) | curious(X0) | calm(X0) [cnf transformation 28]
89. ~humble(X0) | ~generous(X0) | ~brave(X0) [cnf transformation 43]
90. ~brave(X0) | rich(X0) | generous(X0) [cnf transformation 45]
96. ~curious(X0) | creative(X0) [cnf transformation 47]
106. ~creative(X0) | humble(X0) | quiet(X0) [cnf transformation 50]
109. kind(X0) | calm(X0) [cnf transformation 53]
128. ~calm(alice) [cnf transformation 21]
129. tall(alice) [cnf transformation 21]
131. ~rich(alice) | ~kind(alice) [cnf transformation 71]
134. brave(alice) [cnf transformation 25]
235. 22 <=> tall(alice) [avatar definition]
236. tall(alice) <- (22) [avatar component clause 235]
249. 22 [avatar split clause 129,235]
251. 25 <=> kind(alice) [avatar definition]
253. ~kind(alice) <- (~25) [avatar component clause 251]
255. 26 <=> rich(alice) [avatar definition]
258. ~25 | ~26 [avatar split clause 131,255,251]
289. 28 <=> quiet(alice) [avatar definition]
290. ~quiet(alice) <- (~28) [avatar component clause 289]
291. quiet(alice) <- (28) [avatar component clause 289]
293. 29 <=> generous(alice) [avatar definition]
295. generous(alice) <- (29) [avatar component clause 293]
298. ~generous(alice) | ~brave(alice) <- (28) [resolution 291,77]
300. ~generous(alice) <- (28) [subsumption resolution 298,134]
301. ~29 | ~28 [avatar split clause 300,289,293]
303. curious(alice) | calm(alice) <- (22) [resolution 86,236]
313. curious(alice) <- (22) [subsumption resolution 303,128]
317. rich(alice) | generous(alice) [resolution 90,134]
338. creative(alice) <- (22) [resolution 313,96]
368. humble(alice) | quiet(alice) <- (22) [resolution 338,106]
370. humble(alice) <- (22, ~28) [subsumption resolution 368,290]
395. ~generous(alice) | ~brave(alice) <- (22, ~28) [resolution 370,89]
396. ~brave(alice) <- (22, ~28, 29) [subsumption resolution 395,295]
397. $false <- (22, ~28, 29) [subsumption resolution 396,134]
398. ~22 | 28 | ~29 [avatar contradiction clause 397]
399. 29 | 26 [avatar split clause 317,255,293]
410. calm(alice) <- (~25) [resolution 253,109]
411. $false <- (~25) [subsumption resolution 410,128]
412. 25 [avatar contradiction clause 411]
413. $false [avatar sat refutation 249,258,301,398,399,412]
% SZS output end Proof for 4106318879089938867842615
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative and not old then lucy is either not kind or funny. Everyone who is not quiet or happy is both not patient and not strong and vice versa. Everyone who is both patient and not tall is not wise. Everyone who is either curious or happy is not tall. Everyone who is either not funny or not wise is both not happy and not curious and vice versa. If fred is not happy then susan is not rich or curious. Everyone who is either happy or strong is not humble or kind. Everyone who is brave or not brave is either not generous or tall. If someone is either not creative or not wise then mary is rich. Everyone who is not rich is quiet or not humble. Everyone who is not generous is not creative. If someone is old or not tall then john is either not curious or not rich. If someone is either rich or patient then someone is not generous and vice versa. If fred is not quiet then susan is not brave or kind. Everyone who is wise or calm is both not happy and rich. Everyone who is not generous is strong or not generous and vice versa. Someone is both not funny and generous. Paul is not calm or not funny. Paul is both calm and not kind. Paul is both humble and not wise. Mary is calm or not old. Lucy is either funny or not kind. Mary is strong or quiet. | Paul is funny. | contradiction | ((?[X]:((~creative(X)&~old(X))))=>((~kind(lucy)<~>funny(lucy))))&
(![X]:((~quiet(X)|happy(X))<=>(~patient(X)&~strong(X))))&
(![X]:((patient(X)&~tall(X))=>~wise(X)))&
(![X]:((curious(X)<~>happy(X))=>~tall(X)))&
(![X]:((~funny(X)<~>~wise(X))<=>(~happy(X)&~curious(X))))&
((~happy(fred))=>((~rich(susan)|curious(susan))))&
(![X]:((happy(X)<~>strong(X))=>(~humble(X)|kind(X))))&
(![X]:((brave(X)|~brave(X))=>(~generous(X)<~>tall(X))))&
((?[X]:((~creative(X)<~>~wise(X))))=>(rich(mary)))&
(![X]:(~rich(X)=>(quiet(X)|~humble(X))))&
(![X]:(~generous(X)=>~creative(X)))&
((?[X]:((old(X)|~tall(X))))=>((~curious(john)<~>~rich(john))))&
((?[X]:((rich(X)<~>patient(X))))<=>(?[X]:(~generous(X))))&
((~quiet(fred))=>((~brave(susan)|kind(susan))))&
(![X]:((wise(X)|calm(X))=>(~happy(X)&rich(X))))&
(![X]:(~generous(X)<=>(strong(X)|~generous(X))))&
(?[X]:((~funny(X)&generous(X))))&
((~calm(paul)|~funny(paul)))&
((calm(paul)&~kind(paul)))&
((humble(paul)&~wise(paul)))&
((calm(mary)|~old(mary)))&
((funny(lucy)<~>~kind(lucy)))&
((strong(mary)|quiet(mary))) | funny(paul) | [
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 623227114894677294360055
% SZS output start Proof for 623227114894677294360055
18. ~funny(paul) | ~calm(paul) [input p17]
19. ~kind(paul) & calm(paul) [input p18]
24. funny(paul) [input hypothesis]
108. ~funny(paul) | ~calm(paul) [cnf transformation 18]
109. calm(paul) [cnf transformation 19]
117. funny(paul) [cnf transformation 24]
217. 23 <=> calm(paul) [avatar definition]
221. 24 <=> funny(paul) [avatar definition]
224. ~23 | ~24 [avatar split clause 108,221,217]
225. 23 [avatar split clause 109,217]
238. 24 [avatar split clause 117,221]
239. $false [avatar sat refutation 224,225,238]
% SZS output end Proof for 623227114894677294360055
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or not kind is either not rich or kind.
Everyone who is humble or creative is both not quiet and not kind.
If john is either not rich or not strong then someone is both rich and not strong.
Everyone who is either not old or not generous is curious and vice versa.
If lucy is funny or tall then someone is funny.
Everyone who is both not funny and not old is not generous and vice versa.
Everyone who is either not calm or brave is either funny or not kind.
Everyone who is either old or kind is both not kind and curious and vice versa.
If paul is not rich or happy then alice is both quiet and generous.
Everyone who is both not funny and rich is happy or tall and vice versa.
If alice is happy or not calm then someone is rich and vice versa.
If someone is either old or not rich then someone is kind.
Everyone who is either not curious or not tall is not humble or wise.
If lucy is both generous and old then someone is either funny or creative.
John is either not wise or rich.
Paul is old or not brave.
Lucy is not kind or not brave.
Paul is calm or not strong.
Someone is either brave or strong.
Alice is calm or not kind.
Alice is either not patient or rich. | John is patient. | neutral | (![X]:((~tall(X)|~kind(X))=>(~rich(X)<~>kind(X))))&
(![X]:((humble(X)|creative(X))=>(~quiet(X)&~kind(X))))&
(((~rich(john)<~>~strong(john)))=>(?[X]:((rich(X)&~strong(X)))))&
(![X]:((~old(X)<~>~generous(X))<=>curious(X)))&
(((funny(lucy)|tall(lucy)))=>(?[X]:(funny(X))))&
(![X]:((~funny(X)&~old(X))<=>~generous(X)))&
(![X]:((~calm(X)<~>brave(X))=>(funny(X)<~>~kind(X))))&
(![X]:((old(X)<~>kind(X))<=>(~kind(X)&curious(X))))&
(((~rich(paul)|happy(paul)))=>((quiet(alice)&generous(alice))))&
(![X]:((~funny(X)&rich(X))<=>(happy(X)|tall(X))))&
(((happy(alice)|~calm(alice)))<=>(?[X]:(rich(X))))&
((?[X]:((old(X)<~>~rich(X))))=>(?[X]:(kind(X))))&
(![X]:((~curious(X)<~>~tall(X))=>(~humble(X)|wise(X))))&
(((generous(lucy)&old(lucy)))=>(?[X]:((funny(X)<~>creative(X)))))&
((~wise(john)<~>rich(john)))&
((old(paul)|~brave(paul)))&
((~kind(lucy)|~brave(lucy)))&
((calm(paul)|~strong(paul)))&
(?[X]:((brave(X)<~>strong(X))))&
((calm(alice)|~kind(alice)))&
((~patient(alice)<~>rich(alice))) | patient(john) | [] | null | 0 |
Everyone who is either not generous or happy is either brave or rich and vice versa.
Everyone who is both curious and not patient is not strong or not humble and vice versa.
Everyone who is not happy is not funny.
If john is strong or calm then someone is humble.
If someone is either creative or rich then john is both not generous and not happy.
If john is kind or not rich then someone is both not funny and strong and vice versa.
Everyone who is either not old or humble is both not old and not strong and vice versa.
Everyone who is not tall is both not tall and not strong.
Everyone who is both not strong and strong is funny.
Everyone who is not quiet or humble is both old and not brave and vice versa.
Everyone who is not patient is generous or wise.
Everyone who is not quiet or not strong is kind or not calm and vice versa.
If lucy is not curious or funny then john is either not quiet or calm and vice versa.
Everyone who is both humble and old is old.
Everyone who is either patient or not humble is both happy and not quiet.
Someone is funny or kind.
Fred is either not curious or tall.
Someone is either generous or not calm.
John is not calm or kind.
Mary is not patient or funny. | Lucy is not strong. | neutral | (![X]:((~generous(X)<~>happy(X))<=>(brave(X)<~>rich(X))))&
(![X]:((curious(X)&~patient(X))<=>(~strong(X)|~humble(X))))&
(![X]:(~happy(X)=>~funny(X)))&
(((strong(john)|calm(john)))=>(?[X]:(humble(X))))&
((?[X]:((creative(X)<~>rich(X))))=>((~generous(john)&~happy(john))))&
(((kind(john)|~rich(john)))<=>(?[X]:((~funny(X)&strong(X)))))&
(![X]:((~old(X)<~>humble(X))<=>(~old(X)&~strong(X))))&
(![X]:(~tall(X)=>(~tall(X)&~strong(X))))&
(![X]:((~strong(X)&strong(X))=>funny(X)))&
(![X]:((~quiet(X)|humble(X))<=>(old(X)&~brave(X))))&
(![X]:(~patient(X)=>(generous(X)|wise(X))))&
(![X]:((~quiet(X)|~strong(X))<=>(kind(X)|~calm(X))))&
(((~curious(lucy)|funny(lucy)))<=>((~quiet(john)<~>calm(john))))&
(![X]:((humble(X)&old(X))=>old(X)))&
(![X]:((patient(X)<~>~humble(X))=>(happy(X)&~quiet(X))))&
(?[X]:((funny(X)|kind(X))))&
((~curious(fred)<~>tall(fred)))&
(?[X]:((generous(X)<~>~calm(X))))&
((~calm(john)|kind(john)))&
((~patient(mary)|funny(mary))) | ~strong(lucy) | [] | null | 0 |
If someone is both strong and happy then fred is both not humble and rich.
If mary is rich or happy then fred is either not tall or happy and vice versa.
Everyone who is not rich or humble is not funny or not humble.
If someone is either quiet or not strong then someone is not generous.
Everyone who is not creative is either old or patient and vice versa.
If someone is either not strong or happy then paul is both funny and not brave.
Everyone who is both not humble and not calm is either rich or humble.
If someone is either not calm or not wise then someone is strong or wise and vice versa.
Everyone who is not calm or happy is not humble and vice versa.
Everyone who is either not funny or calm is both funny and not rich.
Everyone who is both brave and not quiet is both generous and not calm and vice versa.
If susan is not tall then someone is either not happy or not old and vice versa.
Everyone who is not calm or not old is not happy.
If someone is humble or old then someone is both happy and not calm and vice versa.
Everyone who is either old or not funny is either quiet or calm.
Everyone who is both quiet and curious is wise or kind and vice versa.
Someone is happy or strong.
John is either not wise or not happy.
Fred is funny.
John is either tall or not kind.
Someone is both curious and not brave. | Mary is funny. | entailment | ((?[X]:((strong(X)&happy(X))))=>((~humble(fred)&rich(fred))))&
(((rich(mary)|happy(mary)))<=>((~tall(fred)<~>happy(fred))))&
(![X]:((~rich(X)|humble(X))=>(~funny(X)|~humble(X))))&
((?[X]:((quiet(X)<~>~strong(X))))=>(?[X]:(~generous(X))))&
(![X]:(~creative(X)<=>(old(X)<~>patient(X))))&
((?[X]:((~strong(X)<~>happy(X))))=>((funny(paul)&~brave(paul))))&
(![X]:((~humble(X)&~calm(X))=>(rich(X)<~>humble(X))))&
((?[X]:((~calm(X)<~>~wise(X))))<=>(?[X]:((strong(X)|wise(X)))))&
(![X]:((~calm(X)|happy(X))<=>~humble(X)))&
(![X]:((~funny(X)<~>calm(X))=>(funny(X)&~rich(X))))&
(![X]:((brave(X)&~quiet(X))<=>(generous(X)&~calm(X))))&
((~tall(susan))<=>(?[X]:((~happy(X)<~>~old(X)))))&
(![X]:((~calm(X)|~old(X))=>~happy(X)))&
((?[X]:((humble(X)|old(X))))<=>(?[X]:((happy(X)&~calm(X)))))&
(![X]:((old(X)<~>~funny(X))=>(quiet(X)<~>calm(X))))&
(![X]:((quiet(X)&curious(X))<=>(wise(X)|kind(X))))&
(?[X]:((happy(X)|strong(X))))&
((~wise(john)<~>~happy(john)))&
(funny(fred))&
((tall(john)<~>~kind(john)))&
(?[X]:((curious(X)&~brave(X)))) | funny(mary) | [
"p8",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7126387694606842797639608
% SZS output start Proof for 7126387694606842797639608
9. ! [X0] : ((happy(X0) | ~calm(X0)) <=> ~humble(X0)) [input p8]
10. ! [X0] : ((~funny(X0) <~> calm(X0)) => (~rich(X0) & funny(X0))) [input p9]
13. ! [X0] : ((~old(X0) | ~calm(X0)) => ~happy(X0)) [input p12]
14. ? [X0] : (old(X0) | humble(X0)) <=> ? [X0] : (~calm(X0) & happy(X0)) [input p13]
22. ~funny(mary) [input hypothesis]
25. ? [X0] : (old(X0) | humble(X0)) <=> ? [X1] : (~calm(X1) & happy(X1)) [rectify 14]
33. ! [X0] : ((~rich(X0) & funny(X0)) | (~funny(X0) <=> calm(X0))) [ennf transformation 10]
34. ! [X0] : (~happy(X0) | (old(X0) & calm(X0))) [ennf transformation 13]
49. ! [X0] : (((happy(X0) | ~calm(X0)) | humble(X0)) & (~humble(X0) | (~happy(X0) & calm(X0)))) [nnf transformation 9]
50. ! [X0] : ((happy(X0) | ~calm(X0) | humble(X0)) & (~humble(X0) | (~happy(X0) & calm(X0)))) [flattening 49]
51. ! [X0] : ((~rich(X0) & funny(X0)) | ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0)))) [nnf transformation 33]
58. (? [X0] : (old(X0) | humble(X0)) | ! [X1] : (calm(X1) | ~happy(X1))) & (? [X1] : (~calm(X1) & happy(X1)) | ! [X0] : (~old(X0) & ~humble(X0))) [nnf transformation 25]
59. (? [X0] : (old(X0) | humble(X0)) | ! [X1] : (calm(X1) | ~happy(X1))) & (? [X2] : (~calm(X2) & happy(X2)) | ! [X3] : (~old(X3) & ~humble(X3))) [rectify 58]
60. ? [X0] : (old(X0) | humble(X0)) => (old(sK4) | humble(sK4)) [choice axiom]
61. ? [X2] : (~calm(X2) & happy(X2)) => (~calm(sK5) & happy(sK5)) [choice axiom]
62. ((old(sK4) | humble(sK4)) | ! [X1] : (calm(X1) | ~happy(X1))) & ((~calm(sK5) & happy(sK5)) | ! [X3] : (~old(X3) & ~humble(X3))) [skolemisation 59,61,60]
98. ~calm(X0) | happy(X0) | humble(X0) [cnf transformation 50]
99. funny(X0) | calm(X0) | funny(X0) [cnf transformation 51]
111. ~happy(X0) | calm(X0) [cnf transformation 34]
112. ~happy(X0) | old(X0) [cnf transformation 34]
113. happy(sK5) | ~humble(X3) [cnf transformation 62]
114. happy(sK5) | ~old(X3) [cnf transformation 62]
116. ~calm(sK5) | ~old(X3) [cnf transformation 62]
135. ~funny(mary) [cnf transformation 22]
136. calm(X0) | funny(X0) [duplicate literal removal 99]
165. 7 <=> happy(mary) [avatar definition]
166. ~happy(mary) <- (~7) [avatar component clause 165]
167. happy(mary) <- (7) [avatar component clause 165]
236. 22 <=> ! [X0] : (~happy(X0) | old(X0)) [avatar definition]
237. ~happy(X0) | old(X0) <- (22) [avatar component clause 236]
257. 22 [avatar split clause 112,236]
259. 27 <=> ! [X3] : ~old(X3) [avatar definition]
260. ~old(X3) <- (27) [avatar component clause 259]
262. 28 <=> calm(sK5) [avatar definition]
265. 27 | ~28 [avatar split clause 116,262,259]
267. 29 <=> ! [X3] : ~humble(X3) [avatar definition]
268. ~humble(X3) <- (29) [avatar component clause 267]
271. 30 <=> happy(sK5) [avatar definition]
273. happy(sK5) <- (30) [avatar component clause 271]
274. 27 | 30 [avatar split clause 114,271,259]
275. 29 | 30 [avatar split clause 113,271,267]
311. calm(sK5) <- (30) [resolution 111,273]
315. 28 | ~30 [avatar split clause 311,271,262]
322. old(sK5) <- (22, 30) [resolution 237,273]
323. old(mary) <- (7, 22) [resolution 237,167]
326. $false <- (22, 27, 30) [subsumption resolution 322,260]
327. ~22 | ~27 | ~30 [avatar contradiction clause 326]
328. $false <- (7, 22, 27) [subsumption resolution 323,260]
329. ~7 | ~22 | ~27 [avatar contradiction clause 328]
330. happy(X0) | humble(X0) | funny(X0) [resolution 98,136]
333. funny(X0) | happy(X0) <- (29) [subsumption resolution 330,268]
352. happy(mary) <- (29) [resolution 333,135]
354. $false <- (~7, 29) [subsumption resolution 352,166]
355. 7 | ~29 [avatar contradiction clause 354]
356. $false [avatar sat refutation 257,265,274,275,315,327,329,355]
% SZS output end Proof for 7126387694606842797639608
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and brave is not brave and vice versa.
If paul is both not curious and wise then someone is quiet or not tall.
Everyone who is either calm or not kind is generous and vice versa.
Everyone who is not quiet or strong is both tall and not brave and vice versa.
Everyone who is happy or not strong is old or not patient.
If fred is both not humble and not happy then someone is rich or not rich.
Everyone who is brave is both old and not calm and vice versa.
Everyone who is patient or not calm is rich or not wise and vice versa.
Everyone who is both not happy and not humble is tall or not tall.
If someone is quiet or old then lucy is not strong and vice versa.
If mary is both not strong and humble then mary is either not generous or not calm and vice versa.
Everyone who is not patient is generous and vice versa.
Everyone who is happy is not strong.
If someone is either not calm or kind then susan is both generous and not brave and vice versa.
If someone is tall or not creative then john is either not humble or not happy.
Mary is not curious.
Someone is not creative.
Mary is wise.
Someone is not calm or not happy.
Someone is either not old or happy.
Fred is either not old or funny.
Alice is tall. | Susan is not kind. | contradiction | (![X]:((curious(X)&brave(X))<=>~brave(X)))&
(((~curious(paul)&wise(paul)))=>(?[X]:((quiet(X)|~tall(X)))))&
(![X]:((calm(X)<~>~kind(X))<=>generous(X)))&
(![X]:((~quiet(X)|strong(X))<=>(tall(X)&~brave(X))))&
(![X]:((happy(X)|~strong(X))=>(old(X)|~patient(X))))&
(((~humble(fred)&~happy(fred)))=>(?[X]:((rich(X)|~rich(X)))))&
(![X]:(brave(X)<=>(old(X)&~calm(X))))&
(![X]:((patient(X)|~calm(X))<=>(rich(X)|~wise(X))))&
(![X]:((~happy(X)&~humble(X))=>(tall(X)|~tall(X))))&
((?[X]:((quiet(X)|old(X))))<=>(~strong(lucy)))&
(((~strong(mary)&humble(mary)))<=>((~generous(mary)<~>~calm(mary))))&
(![X]:(~patient(X)<=>generous(X)))&
(![X]:(happy(X)=>~strong(X)))&
((?[X]:((~calm(X)<~>kind(X))))<=>((generous(susan)&~brave(susan))))&
((?[X]:((tall(X)|~creative(X))))=>((~humble(john)<~>~happy(john))))&
(~curious(mary))&
(?[X]:(~creative(X)))&
(wise(mary))&
(?[X]:((~calm(X)|~happy(X))))&
(?[X]:((~old(X)<~>happy(X))))&
((~old(fred)<~>funny(fred)))&
(tall(alice)) | ~kind(susan) | [
"p0",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2122053095852952685443702
% SZS output start Proof for 2122053095852952685443702
1. ! [X0] : ((brave(X0) & curious(X0)) <=> ~brave(X0)) [input p0]
7. ! [X0] : (brave(X0) <=> (~calm(X0) & old(X0))) [input p6]
14. ? [X0] : (~calm(X0) <~> kind(X0)) <=> (~brave(susan) & generous(susan)) [input p13]
23. ~kind(susan) [input hypothesis]
34. ! [X0] : (((brave(X0) & curious(X0)) | brave(X0)) & (~brave(X0) | (~brave(X0) | ~curious(X0)))) [nnf transformation 1]
35. ! [X0] : (((brave(X0) & curious(X0)) | brave(X0)) & (~brave(X0) | ~brave(X0) | ~curious(X0))) [flattening 34]
43. ! [X0] : ((brave(X0) | (calm(X0) | ~old(X0))) & ((~calm(X0) & old(X0)) | ~brave(X0))) [nnf transformation 7]
44. ! [X0] : ((brave(X0) | calm(X0) | ~old(X0)) & ((~calm(X0) & old(X0)) | ~brave(X0))) [flattening 43]
54. (? [X0] : ((~kind(X0) | calm(X0)) & (kind(X0) | ~calm(X0))) | (brave(susan) | ~generous(susan))) & ((~brave(susan) & generous(susan)) | ! [X0] : ((~calm(X0) | ~kind(X0)) & (kind(X0) | calm(X0)))) [nnf transformation 14]
55. (? [X0] : ((~kind(X0) | calm(X0)) & (kind(X0) | ~calm(X0))) | brave(susan) | ~generous(susan)) & ((~brave(susan) & generous(susan)) | ! [X0] : ((~calm(X0) | ~kind(X0)) & (kind(X0) | calm(X0)))) [flattening 54]
56. (? [X0] : ((~kind(X0) | calm(X0)) & (kind(X0) | ~calm(X0))) | brave(susan) | ~generous(susan)) & ((~brave(susan) & generous(susan)) | ! [X1] : ((~calm(X1) | ~kind(X1)) & (kind(X1) | calm(X1)))) [rectify 55]
57. ? [X0] : ((~kind(X0) | calm(X0)) & (kind(X0) | ~calm(X0))) => ((~kind(sK3) | calm(sK3)) & (kind(sK3) | ~calm(sK3))) [choice axiom]
58. (((~kind(sK3) | calm(sK3)) & (kind(sK3) | ~calm(sK3))) | brave(susan) | ~generous(susan)) & ((~brave(susan) & generous(susan)) | ! [X1] : ((~calm(X1) | ~kind(X1)) & (kind(X1) | calm(X1)))) [skolemisation 56,57]
70. brave(X0) | brave(X0) [cnf transformation 35]
85. ~calm(X0) | ~brave(X0) [cnf transformation 44]
106. ~brave(susan) | kind(X1) | calm(X1) [cnf transformation 58]
123. ~kind(susan) [cnf transformation 23]
125. brave(X0) [duplicate literal removal 70]
144. ~calm(X0) [subsumption resolution 85,125]
160. kind(X1) | calm(X1) [subsumption resolution 106,125]
161. kind(X1) [subsumption resolution 160,144]
182. $false [subsumption resolution 123,161]
% SZS output end Proof for 2122053095852952685443702
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is not tall or curious.
Everyone who is curious is either not kind or not humble and vice versa.
If john is patient or not strong then fred is not old or not happy and vice versa.
Everyone who is either not rich or generous is calm or not funny and vice versa.
Everyone who is not quiet is not generous.
Everyone who is humble or funny is calm or kind and vice versa.
Everyone who is both not quiet and not creative is not old or creative and vice versa.
If someone is both creative and kind then lucy is generous.
Everyone who is either kind or curious is not quiet and vice versa.
Everyone who is both not curious and not quiet is kind and vice versa.
Everyone who is either brave or not happy is either not rich or not old and vice versa.
Everyone who is both funny and not curious is either not curious or not rich and vice versa.
Everyone who is either strong or not old is both calm and not patient and vice versa.
Everyone who is both not old and not strong is curious or tall and vice versa.
Everyone who is not kind is both quiet and patient and vice versa.
If alice is not calm or strong then someone is not humble and vice versa.
Someone is not calm or patient.
Someone is not happy or humble.
Someone is both funny and rich.
Fred is wise.
Someone is not old or not wise.
Lucy is both generous and funny.
Someone is humble or not generous.
Someone is either not happy or not tall. | Lucy is calm. | entailment | (![X]:(~quiet(X)=>(~tall(X)|curious(X))))&
(![X]:(curious(X)<=>(~kind(X)<~>~humble(X))))&
(((patient(john)|~strong(john)))<=>((~old(fred)|~happy(fred))))&
(![X]:((~rich(X)<~>generous(X))<=>(calm(X)|~funny(X))))&
(![X]:(~quiet(X)=>~generous(X)))&
(![X]:((humble(X)|funny(X))<=>(calm(X)|kind(X))))&
(![X]:((~quiet(X)&~creative(X))<=>(~old(X)|creative(X))))&
((?[X]:((creative(X)&kind(X))))=>(generous(lucy)))&
(![X]:((kind(X)<~>curious(X))<=>~quiet(X)))&
(![X]:((~curious(X)&~quiet(X))<=>kind(X)))&
(![X]:((brave(X)<~>~happy(X))<=>(~rich(X)<~>~old(X))))&
(![X]:((funny(X)&~curious(X))<=>(~curious(X)<~>~rich(X))))&
(![X]:((strong(X)<~>~old(X))<=>(calm(X)&~patient(X))))&
(![X]:((~old(X)&~strong(X))<=>(curious(X)|tall(X))))&
(![X]:(~kind(X)<=>(quiet(X)&patient(X))))&
(((~calm(alice)|strong(alice)))<=>(?[X]:(~humble(X))))&
(?[X]:((~calm(X)|patient(X))))&
(?[X]:((~happy(X)|humble(X))))&
(?[X]:((funny(X)&rich(X))))&
(wise(fred))&
(?[X]:((~old(X)|~wise(X))))&
((generous(lucy)&funny(lucy)))&
(?[X]:((humble(X)|~generous(X))))&
(?[X]:((~happy(X)<~>~tall(X)))) | calm(lucy) | [
"p4",
"p5",
"p6",
"p8",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 42304280771588146884177
% SZS output start Proof for 42304280771588146884177
5. ! [X0] : (~quiet(X0) => ~generous(X0)) [input p4]
6. ! [X0] : ((funny(X0) | humble(X0)) <=> (kind(X0) | calm(X0))) [input p5]
7. ! [X0] : ((~creative(X0) & ~quiet(X0)) <=> (creative(X0) | ~old(X0))) [input p6]
9. ! [X0] : ((kind(X0) <~> curious(X0)) <=> ~quiet(X0)) [input p8]
14. ! [X0] : ((~strong(X0) & ~old(X0)) <=> (tall(X0) | curious(X0))) [input p13]
22. funny(lucy) & generous(lucy) [input p21]
25. ~calm(lucy) [input hypothesis]
28. ! [X0] : (~generous(X0) | quiet(X0)) [ennf transformation 5]
35. ! [X0] : (((funny(X0) | humble(X0)) | (~kind(X0) & ~calm(X0))) & ((kind(X0) | calm(X0)) | (~funny(X0) & ~humble(X0)))) [nnf transformation 6]
36. ! [X0] : ((funny(X0) | humble(X0) | (~kind(X0) & ~calm(X0))) & (kind(X0) | calm(X0) | (~funny(X0) & ~humble(X0)))) [flattening 35]
37. ! [X0] : (((~creative(X0) & ~quiet(X0)) | (~creative(X0) & old(X0))) & ((creative(X0) | ~old(X0)) | (creative(X0) | quiet(X0)))) [nnf transformation 7]
38. ! [X0] : (((~creative(X0) & ~quiet(X0)) | (~creative(X0) & old(X0))) & (creative(X0) | ~old(X0) | creative(X0) | quiet(X0))) [flattening 37]
39. ! [X0] : ((((~curious(X0) | ~kind(X0)) & (curious(X0) | kind(X0))) | quiet(X0)) & (~quiet(X0) | ((kind(X0) | ~curious(X0)) & (curious(X0) | ~kind(X0))))) [nnf transformation 9]
47. ! [X0] : (((~strong(X0) & ~old(X0)) | (~tall(X0) & ~curious(X0))) & ((tall(X0) | curious(X0)) | (strong(X0) | old(X0)))) [nnf transformation 14]
48. ! [X0] : (((~strong(X0) & ~old(X0)) | (~tall(X0) & ~curious(X0))) & (tall(X0) | curious(X0) | strong(X0) | old(X0))) [flattening 47]
84. ~generous(X0) | quiet(X0) [cnf transformation 28]
86. ~funny(X0) | calm(X0) | kind(X0) [cnf transformation 36]
90. ~quiet(X0) | old(X0) [cnf transformation 38]
95. ~kind(X0) | curious(X0) | ~quiet(X0) [cnf transformation 39]
123. ~old(X0) | ~curious(X0) [cnf transformation 48]
139. generous(lucy) [cnf transformation 22]
140. funny(lucy) [cnf transformation 22]
144. ~calm(lucy) [cnf transformation 25]
235. quiet(lucy) [resolution 84,139]
236. old(lucy) [resolution 90,235]
237. ~curious(lucy) [resolution 123,236]
258. calm(lucy) | kind(lucy) [resolution 86,140]
268. kind(lucy) [subsumption resolution 258,144]
289. curious(lucy) | ~quiet(lucy) [resolution 268,95]
294. ~quiet(lucy) [subsumption resolution 289,237]
295. $false [subsumption resolution 294,235]
% SZS output end Proof for 42304280771588146884177
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and kind is both curious and not tall and vice versa.
Everyone who is both happy and not humble is both rich and kind.
Everyone who is either creative or calm is both not wise and not funny and vice versa.
If susan is either calm or funny then someone is generous.
If susan is not calm then someone is either humble or not creative and vice versa.
Everyone who is not kind or curious is either creative or not happy and vice versa.
Everyone who is either calm or wise is brave or patient.
Everyone who is both brave and curious is both not humble and not generous and vice versa.
If someone is both not humble and brave then fred is not rich.
If susan is both curious and funny then someone is both brave and wise.
Everyone who is both rich and not quiet is not wise.
Everyone who is generous is not quiet and vice versa.
Everyone who is happy is both not rich and not brave and vice versa.
Everyone who is not old or not wise is not old and vice versa.
Everyone who is not quiet is rich and vice versa.
If fred is calm then someone is not curious or not funny and vice versa.
Paul is patient or calm.
John is both kind and not rich.
Mary is either strong or creative.
Lucy is not quiet or calm.
Lucy is not curious.
Someone is both wise and not generous.
Someone is both brave and funny.
Someone is not wise. | Susan is happy. | neutral | (![X]:((~humble(X)&kind(X))<=>(curious(X)&~tall(X))))&
(![X]:((happy(X)&~humble(X))=>(rich(X)&kind(X))))&
(![X]:((creative(X)<~>calm(X))<=>(~wise(X)&~funny(X))))&
(((calm(susan)<~>funny(susan)))=>(?[X]:(generous(X))))&
((~calm(susan))<=>(?[X]:((humble(X)<~>~creative(X)))))&
(![X]:((~kind(X)|curious(X))<=>(creative(X)<~>~happy(X))))&
(![X]:((calm(X)<~>wise(X))=>(brave(X)|patient(X))))&
(![X]:((brave(X)&curious(X))<=>(~humble(X)&~generous(X))))&
((?[X]:((~humble(X)&brave(X))))=>(~rich(fred)))&
(((curious(susan)&funny(susan)))=>(?[X]:((brave(X)&wise(X)))))&
(![X]:((rich(X)&~quiet(X))=>~wise(X)))&
(![X]:(generous(X)<=>~quiet(X)))&
(![X]:(happy(X)<=>(~rich(X)&~brave(X))))&
(![X]:((~old(X)|~wise(X))<=>~old(X)))&
(![X]:(~quiet(X)<=>rich(X)))&
((calm(fred))<=>(?[X]:((~curious(X)|~funny(X)))))&
((patient(paul)|calm(paul)))&
((kind(john)&~rich(john)))&
((strong(mary)<~>creative(mary)))&
((~quiet(lucy)|calm(lucy)))&
(~curious(lucy))&
(?[X]:((wise(X)&~generous(X))))&
(?[X]:((brave(X)&funny(X))))&
(?[X]:(~wise(X))) | happy(susan) | [] | null | 0 |
If alice is both not wise and not funny then someone is both not funny and rich and vice versa.
If mary is both not humble and not funny then someone is not quiet or happy and vice versa.
If someone is strong then fred is both creative and not patient and vice versa.
If alice is either quiet or creative then someone is both not rich and not happy.
Everyone who is not funny is generous or brave.
If someone is either not funny or kind then someone is strong and vice versa.
Everyone who is both old and kind is either not rich or not calm.
If paul is either kind or tall then john is wise and vice versa.
Everyone who is either not old or not tall is kind and vice versa.
If someone is both not generous and rich then alice is quiet or rich and vice versa.
Everyone who is calm or not old is either not kind or old.
If someone is funny then someone is curious.
Everyone who is both not calm and kind is not funny or not patient and vice versa.
Everyone who is not quiet or strong is either not calm or not old and vice versa.
If someone is either brave or not brave then lucy is both not kind and strong.
If fred is both humble and not old then mary is either wise or tall.
Lucy is strong or not quiet.
Susan is humble.
Mary is rich or patient.
Someone is both quiet and strong.
Mary is both not strong and not old.
Someone is creative.
Someone is old.
Someone is tall or not strong. | Alice is quiet. | entailment | (((~wise(alice)&~funny(alice)))<=>(?[X]:((~funny(X)&rich(X)))))&
(((~humble(mary)&~funny(mary)))<=>(?[X]:((~quiet(X)|happy(X)))))&
((?[X]:(strong(X)))<=>((creative(fred)&~patient(fred))))&
(((quiet(alice)<~>creative(alice)))=>(?[X]:((~rich(X)&~happy(X)))))&
(![X]:(~funny(X)=>(generous(X)|brave(X))))&
((?[X]:((~funny(X)<~>kind(X))))<=>(?[X]:(strong(X))))&
(![X]:((old(X)&kind(X))=>(~rich(X)<~>~calm(X))))&
(((kind(paul)<~>tall(paul)))<=>(wise(john)))&
(![X]:((~old(X)<~>~tall(X))<=>kind(X)))&
((?[X]:((~generous(X)&rich(X))))<=>((quiet(alice)|rich(alice))))&
(![X]:((calm(X)|~old(X))=>(~kind(X)<~>old(X))))&
((?[X]:(funny(X)))=>(?[X]:(curious(X))))&
(![X]:((~calm(X)&kind(X))<=>(~funny(X)|~patient(X))))&
(![X]:((~quiet(X)|strong(X))<=>(~calm(X)<~>~old(X))))&
((?[X]:((brave(X)<~>~brave(X))))=>((~kind(lucy)&strong(lucy))))&
(((humble(fred)&~old(fred)))=>((wise(mary)<~>tall(mary))))&
((strong(lucy)|~quiet(lucy)))&
(humble(susan))&
((rich(mary)|patient(mary)))&
(?[X]:((quiet(X)&strong(X))))&
((~strong(mary)&~old(mary)))&
(?[X]:(creative(X)))&
(?[X]:(old(X)))&
(?[X]:((tall(X)|~strong(X)))) | quiet(alice) | [
"p1",
"p10",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3742406336810291539965415
% SZS output start Proof for 3742406336810291539965415
2. (~funny(mary) & ~humble(mary)) <=> ? [X0] : (happy(X0) | ~quiet(X0)) [input p1]
11. ! [X0] : ((~old(X0) | calm(X0)) => (~kind(X0) <~> old(X0))) [input p10]
13. ! [X0] : ((kind(X0) & ~calm(X0)) <=> (~patient(X0) | ~funny(X0))) [input p12]
21. ~old(mary) & ~strong(mary) [input p20]
25. ~quiet(alice) [input hypothesis]
34. ! [X0] : ((~kind(X0) <~> old(X0)) | (old(X0) & ~calm(X0))) [ennf transformation 11]
43. ((~funny(mary) & ~humble(mary)) | ! [X0] : (~happy(X0) & quiet(X0))) & (? [X0] : (happy(X0) | ~quiet(X0)) | (funny(mary) | humble(mary))) [nnf transformation 2]
44. ((~funny(mary) & ~humble(mary)) | ! [X0] : (~happy(X0) & quiet(X0))) & (? [X0] : (happy(X0) | ~quiet(X0)) | funny(mary) | humble(mary)) [flattening 43]
45. ((~funny(mary) & ~humble(mary)) | ! [X0] : (~happy(X0) & quiet(X0))) & (? [X1] : (happy(X1) | ~quiet(X1)) | funny(mary) | humble(mary)) [rectify 44]
46. ? [X1] : (happy(X1) | ~quiet(X1)) => (happy(sK1) | ~quiet(sK1)) [choice axiom]
47. ((~funny(mary) & ~humble(mary)) | ! [X0] : (~happy(X0) & quiet(X0))) & ((happy(sK1) | ~quiet(sK1)) | funny(mary) | humble(mary)) [skolemisation 45,46]
69. ! [X0] : (((~old(X0) | kind(X0)) & (old(X0) | ~kind(X0))) | (old(X0) & ~calm(X0))) [nnf transformation 34]
70. ! [X0] : (((kind(X0) & ~calm(X0)) | (patient(X0) & funny(X0))) & ((~patient(X0) | ~funny(X0)) | (~kind(X0) | calm(X0)))) [nnf transformation 13]
71. ! [X0] : (((kind(X0) & ~calm(X0)) | (patient(X0) & funny(X0))) & (~patient(X0) | ~funny(X0) | ~kind(X0) | calm(X0))) [flattening 70]
91. ~funny(mary) | quiet(X0) [cnf transformation 47]
121. old(X0) | ~kind(X0) | old(X0) [cnf transformation 69]
127. kind(X0) | funny(X0) [cnf transformation 71]
147. ~old(mary) [cnf transformation 21]
151. ~quiet(alice) [cnf transformation 25]
156. ~kind(X0) | old(X0) [duplicate literal removal 121]
184. 7 <=> funny(mary) [avatar definition]
189. 8 <=> ! [X0] : quiet(X0) [avatar definition]
190. quiet(X0) <- (8) [avatar component clause 189]
191. 8 | ~7 [avatar split clause 91,184,189]
230. 17 <=> quiet(alice) [avatar definition]
231. ~quiet(alice) <- (~17) [avatar component clause 230]
264. 24 <=> ! [X3] : (kind(X3) | funny(X3)) [avatar definition]
265. kind(X3) | funny(X3) <- (24) [avatar component clause 264]
303. 24 [avatar split clause 127,264]
363. ~17 [avatar split clause 151,230]
370. old(X1) | funny(X1) <- (24) [resolution 265,156]
410. funny(mary) <- (24) [resolution 370,147]
414. 7 | ~24 [avatar split clause 410,264,184]
416. $false <- (8, ~17) [resolution 190,231]
417. ~8 | 17 [avatar contradiction clause 416]
419. $false [avatar sat refutation 191,303,363,414,417]
% SZS output end Proof for 3742406336810291539965415
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and funny is both strong and wise and vice versa. Everyone who is not rich is either not curious or quiet. If someone is calm then alice is both not calm and not quiet. Everyone who is not happy is not rich and vice versa. If mary is either strong or old then someone is not happy. If someone is funny then john is not brave or quiet and vice versa. Everyone who is not brave or not patient is not patient or calm and vice versa. If paul is not creative or not wise then john is rich and vice versa. Everyone who is not old or wise is kind and vice versa. Everyone who is not calm or curious is not funny. Everyone who is either not humble or funny is happy and vice versa. Everyone who is quiet or not brave is not humble or patient. Everyone who is not quiet or not brave is either brave or humble and vice versa. Everyone who is happy is both generous and kind and vice versa. Everyone who is both not generous and not calm is either not happy or not rich. If someone is both not calm and not happy then john is not curious. Someone is both not happy and old. Paul is brave or not curious. Someone is either patient or creative. Someone is either calm or happy. Someone is either not brave or not generous. Someone is kind. John is rich. Someone is not curious or not rich. | Alice is generous. | entailment | (![X]:((wise(X)&funny(X))<=>(strong(X)&wise(X))))&
(![X]:(~rich(X)=>(~curious(X)<~>quiet(X))))&
((?[X]:(calm(X)))=>((~calm(alice)&~quiet(alice))))&
(![X]:(~happy(X)<=>~rich(X)))&
(((strong(mary)<~>old(mary)))=>(?[X]:(~happy(X))))&
((?[X]:(funny(X)))<=>((~brave(john)|quiet(john))))&
(![X]:((~brave(X)|~patient(X))<=>(~patient(X)|calm(X))))&
(((~creative(paul)|~wise(paul)))<=>(rich(john)))&
(![X]:((~old(X)|wise(X))<=>kind(X)))&
(![X]:((~calm(X)|curious(X))=>~funny(X)))&
(![X]:((~humble(X)<~>funny(X))<=>happy(X)))&
(![X]:((quiet(X)|~brave(X))=>(~humble(X)|patient(X))))&
(![X]:((~quiet(X)|~brave(X))<=>(brave(X)<~>humble(X))))&
(![X]:(happy(X)<=>(generous(X)&kind(X))))&
(![X]:((~generous(X)&~calm(X))=>(~happy(X)<~>~rich(X))))&
((?[X]:((~calm(X)&~happy(X))))=>(~curious(john)))&
(?[X]:((~happy(X)&old(X))))&
((brave(paul)|~curious(paul)))&
(?[X]:((patient(X)<~>creative(X))))&
(?[X]:((calm(X)<~>happy(X))))&
(?[X]:((~brave(X)<~>~generous(X))))&
(?[X]:(kind(X)))&
(rich(john))&
(?[X]:((~curious(X)|~rich(X)))) | generous(alice) | [
"p2",
"p3",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9053877732704548508420833
% SZS output start Proof for 9053877732704548508420833
3. ? [X0] : calm(X0) => (~quiet(alice) & ~calm(alice)) [input p2]
4. ! [X0] : (~happy(X0) <=> ~rich(X0)) [input p3]
14. ! [X0] : (happy(X0) <=> (kind(X0) & generous(X0))) [input p13]
15. ! [X0] : ((~calm(X0) & ~generous(X0)) => (~happy(X0) <~> ~rich(X0))) [input p14]
25. ~generous(alice) [input hypothesis]
27. (~quiet(alice) & ~calm(alice)) | ! [X0] : ~calm(X0) [ennf transformation 3]
32. ! [X0] : ((~happy(X0) <~> ~rich(X0)) | (calm(X0) | generous(X0))) [ennf transformation 15]
33. ! [X0] : ((~happy(X0) <~> ~rich(X0)) | calm(X0) | generous(X0)) [flattening 32]
38. ! [X0] : ((~happy(X0) | rich(X0)) & (~rich(X0) | happy(X0))) [nnf transformation 4]
56. ! [X0] : ((happy(X0) | (~kind(X0) | ~generous(X0))) & ((kind(X0) & generous(X0)) | ~happy(X0))) [nnf transformation 14]
57. ! [X0] : ((happy(X0) | ~kind(X0) | ~generous(X0)) & ((kind(X0) & generous(X0)) | ~happy(X0))) [flattening 56]
58. ! [X0] : (((rich(X0) | happy(X0)) & (~rich(X0) | ~happy(X0))) | calm(X0) | generous(X0)) [nnf transformation 33]
80. ~calm(alice) | ~calm(X0) [cnf transformation 27]
82. ~rich(X0) | happy(X0) [cnf transformation 38]
113. ~happy(X0) | generous(X0) [cnf transformation 57]
117. rich(X0) | happy(X0) | calm(X0) | generous(X0) [cnf transformation 58]
131. ~generous(alice) [cnf transformation 25]
135. 1 <=> ! [X0] : ~calm(X0) [avatar definition]
136. ~calm(X0) <- (1) [avatar component clause 135]
143. 3 <=> calm(alice) [avatar definition]
144. calm(alice) <- (3) [avatar component clause 143]
145. ~calm(alice) <- (~3) [avatar component clause 143]
146. 1 | ~3 [avatar split clause 80,143,135]
194. generous(X0) | calm(X0) | rich(X0) [subsumption resolution 117,113]
350. calm(alice) | rich(alice) [resolution 194,131]
353. rich(alice) <- (~3) [subsumption resolution 350,145]
364. happy(alice) <- (~3) [resolution 353,82]
378. generous(alice) <- (~3) [resolution 364,113]
389. $false <- (~3) [subsumption resolution 378,131]
390. 3 [avatar contradiction clause 389]
400. $false <- (1, 3) [resolution 144,136]
401. ~1 | ~3 [avatar contradiction clause 400]
402. $false [avatar sat refutation 146,390,401]
% SZS output end Proof for 9053877732704548508420833
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not quiet and rich is either not strong or brave. If someone is not old or not tall then alice is not happy and vice versa. If someone is quiet then paul is either strong or not happy. If paul is not quiet or tall then someone is creative or not rich. Everyone who is generous is either not rich or kind. Everyone who is both funny and curious is both wise and not tall and vice versa. Everyone who is calm is not calm or not generous and vice versa. If someone is either not kind or not generous then fred is either not wise or not quiet and vice versa. Everyone who is both rich and not humble is both not creative and not brave. Everyone who is either curious or not tall is old. If john is happy or humble then paul is both happy and rich and vice versa. Everyone who is rich is old or wise. If fred is both not humble and strong then paul is both generous and funny and vice versa. If someone is either not wise or kind then mary is calm and vice versa. Everyone who is not calm or old is either patient or not tall. Everyone who is both humble and not wise is either not creative or not strong. Paul is either strong or not rich. Lucy is both not funny and old. Alice is either not humble or not quiet. John is not brave. John is both not strong and happy. Lucy is both not curious and not patient. Paul is both patient and humble. Someone is either not generous or curious. | Lucy is not wise. | entailment | (![X]:((~quiet(X)&rich(X))=>(~strong(X)<~>brave(X))))&
((?[X]:((~old(X)|~tall(X))))<=>(~happy(alice)))&
((?[X]:(quiet(X)))=>((strong(paul)<~>~happy(paul))))&
(((~quiet(paul)|tall(paul)))=>(?[X]:((creative(X)|~rich(X)))))&
(![X]:(generous(X)=>(~rich(X)<~>kind(X))))&
(![X]:((funny(X)&curious(X))<=>(wise(X)&~tall(X))))&
(![X]:(calm(X)<=>(~calm(X)|~generous(X))))&
((?[X]:((~kind(X)<~>~generous(X))))<=>((~wise(fred)<~>~quiet(fred))))&
(![X]:((rich(X)&~humble(X))=>(~creative(X)&~brave(X))))&
(![X]:((curious(X)<~>~tall(X))=>old(X)))&
(((happy(john)|humble(john)))<=>((happy(paul)&rich(paul))))&
(![X]:(rich(X)=>(old(X)|wise(X))))&
(((~humble(fred)&strong(fred)))<=>((generous(paul)&funny(paul))))&
((?[X]:((~wise(X)<~>kind(X))))<=>(calm(mary)))&
(![X]:((~calm(X)|old(X))=>(patient(X)<~>~tall(X))))&
(![X]:((humble(X)&~wise(X))=>(~creative(X)<~>~strong(X))))&
((strong(paul)<~>~rich(paul)))&
((~funny(lucy)&old(lucy)))&
((~humble(alice)<~>~quiet(alice)))&
(~brave(john))&
((~strong(john)&happy(john)))&
((~curious(lucy)&~patient(lucy)))&
((patient(paul)&humble(paul)))&
(?[X]:((~generous(X)<~>curious(X)))) | ~wise(lucy) | [
"p5",
"p14",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7795289053444925483139844
% SZS output start Proof for 7795289053444925483139844
6. ! [X0] : ((curious(X0) & funny(X0)) <=> (~tall(X0) & wise(X0))) [input p5]
15. ! [X0] : ((old(X0) | ~calm(X0)) => (patient(X0) <~> ~tall(X0))) [input p14]
18. old(lucy) & ~funny(lucy) [input p17]
22. ~patient(lucy) & ~curious(lucy) [input p21]
25. wise(lucy) [input hypothesis]
36. ! [X0] : ((patient(X0) <~> ~tall(X0)) | (~old(X0) & calm(X0))) [ennf transformation 15]
48. ! [X0] : (((curious(X0) & funny(X0)) | (tall(X0) | ~wise(X0))) & ((~tall(X0) & wise(X0)) | (~curious(X0) | ~funny(X0)))) [nnf transformation 6]
49. ! [X0] : (((curious(X0) & funny(X0)) | tall(X0) | ~wise(X0)) & ((~tall(X0) & wise(X0)) | ~curious(X0) | ~funny(X0))) [flattening 48]
65. ! [X0] : (((tall(X0) | ~patient(X0)) & (~tall(X0) | patient(X0))) | (~old(X0) & calm(X0))) [nnf transformation 36]
85. ~wise(X0) | tall(X0) | funny(X0) [cnf transformation 49]
117. ~tall(X0) | patient(X0) | ~old(X0) [cnf transformation 65]
124. ~funny(lucy) [cnf transformation 18]
125. old(lucy) [cnf transformation 18]
132. ~patient(lucy) [cnf transformation 22]
137. wise(lucy) [cnf transformation 25]
275. tall(lucy) | funny(lucy) [resolution 85,137]
276. tall(lucy) [subsumption resolution 275,124]
303. patient(lucy) | ~old(lucy) [resolution 117,276]
304. ~old(lucy) [subsumption resolution 303,132]
305. $false [subsumption resolution 304,125]
% SZS output end Proof for 7795289053444925483139844
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or funny is either not brave or not humble and vice versa.
If someone is both creative and happy then someone is either happy or not humble and vice versa.
Everyone who is curious or tall is brave.
Everyone who is creative or not funny is not creative and vice versa.
If someone is not funny or not strong then someone is either not funny or creative.
Everyone who is not generous or not curious is humble and vice versa.
Everyone who is either calm or not happy is both humble and not kind.
If john is either not old or not brave then someone is not happy or rich and vice versa.
Everyone who is not wise or tall is either not generous or not strong and vice versa.
If mary is both not curious and generous then someone is not creative and vice versa.
Everyone who is either not curious or not funny is either not calm or humble.
Everyone who is both wise and calm is not brave.
Everyone who is patient is both generous and not humble.
If fred is both tall and brave then someone is either wise or not strong and vice versa.
If susan is either not calm or curious then someone is either not funny or not rich.
Everyone who is both patient and happy is not calm and vice versa.
Someone is not happy.
Someone is either rich or happy.
Paul is not strong or curious.
Someone is generous or humble.
John is tall. | Mary is wise. | contradiction | (![X]:((creative(X)|funny(X))<=>(~brave(X)<~>~humble(X))))&
((?[X]:((creative(X)&happy(X))))<=>(?[X]:((happy(X)<~>~humble(X)))))&
(![X]:((curious(X)|tall(X))=>brave(X)))&
(![X]:((creative(X)|~funny(X))<=>~creative(X)))&
((?[X]:((~funny(X)|~strong(X))))=>(?[X]:((~funny(X)<~>creative(X)))))&
(![X]:((~generous(X)|~curious(X))<=>humble(X)))&
(![X]:((calm(X)<~>~happy(X))=>(humble(X)&~kind(X))))&
(((~old(john)<~>~brave(john)))<=>(?[X]:((~happy(X)|rich(X)))))&
(![X]:((~wise(X)|tall(X))<=>(~generous(X)<~>~strong(X))))&
(((~curious(mary)&generous(mary)))<=>(?[X]:(~creative(X))))&
(![X]:((~curious(X)<~>~funny(X))=>(~calm(X)<~>humble(X))))&
(![X]:((wise(X)&calm(X))=>~brave(X)))&
(![X]:(patient(X)=>(generous(X)&~humble(X))))&
(((tall(fred)&brave(fred)))<=>(?[X]:((wise(X)<~>~strong(X)))))&
(((~calm(susan)<~>curious(susan)))=>(?[X]:((~funny(X)<~>~rich(X)))))&
(![X]:((patient(X)&happy(X))<=>~calm(X)))&
(?[X]:(~happy(X)))&
(?[X]:((rich(X)<~>happy(X))))&
((~strong(paul)|curious(paul)))&
(?[X]:((generous(X)|humble(X))))&
(tall(john)) | wise(mary) | [
"p0",
"p2",
"p3",
"p5",
"p9",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 804785221911589239625065
% SZS output start Proof for 804785221911589239625065
1. ! [X0] : ((funny(X0) | creative(X0)) <=> (~brave(X0) <~> ~humble(X0))) [input p0]
3. ! [X0] : ((tall(X0) | curious(X0)) => brave(X0)) [input p2]
4. ! [X0] : ((~funny(X0) | creative(X0)) <=> ~creative(X0)) [input p3]
6. ! [X0] : ((~curious(X0) | ~generous(X0)) <=> humble(X0)) [input p5]
10. (generous(mary) & ~curious(mary)) <=> ? [X0] : ~creative(X0) [input p9]
12. ! [X0] : ((calm(X0) & wise(X0)) => ~brave(X0)) [input p11]
13. ! [X0] : (patient(X0) => (~humble(X0) & generous(X0))) [input p12]
16. ! [X0] : ((happy(X0) & patient(X0)) <=> ~calm(X0)) [input p15]
22. wise(mary) [input hypothesis]
26. ! [X0] : (brave(X0) | (~tall(X0) & ~curious(X0))) [ennf transformation 3]
30. ! [X0] : (~brave(X0) | (~calm(X0) | ~wise(X0))) [ennf transformation 12]
31. ! [X0] : (~brave(X0) | ~calm(X0) | ~wise(X0)) [flattening 30]
32. ! [X0] : ((~humble(X0) & generous(X0)) | ~patient(X0)) [ennf transformation 13]
34. ! [X0] : (((funny(X0) | creative(X0)) | ((~brave(X0) | humble(X0)) & (~humble(X0) | brave(X0)))) & (((humble(X0) | brave(X0)) & (~humble(X0) | ~brave(X0))) | (~funny(X0) & ~creative(X0)))) [nnf transformation 1]
35. ! [X0] : ((funny(X0) | creative(X0) | ((~brave(X0) | humble(X0)) & (~humble(X0) | brave(X0)))) & (((humble(X0) | brave(X0)) & (~humble(X0) | ~brave(X0))) | (~funny(X0) & ~creative(X0)))) [flattening 34]
41. ! [X0] : (((~funny(X0) | creative(X0)) | creative(X0)) & (~creative(X0) | (funny(X0) & ~creative(X0)))) [nnf transformation 4]
42. ! [X0] : ((~funny(X0) | creative(X0) | creative(X0)) & (~creative(X0) | (funny(X0) & ~creative(X0)))) [flattening 41]
47. ! [X0] : (((~curious(X0) | ~generous(X0)) | ~humble(X0)) & (humble(X0) | (curious(X0) & generous(X0)))) [nnf transformation 6]
48. ! [X0] : ((~curious(X0) | ~generous(X0) | ~humble(X0)) & (humble(X0) | (curious(X0) & generous(X0)))) [flattening 47]
56. ((generous(mary) & ~curious(mary)) | ! [X0] : creative(X0)) & (? [X0] : ~creative(X0) | (~generous(mary) | curious(mary))) [nnf transformation 10]
57. ((generous(mary) & ~curious(mary)) | ! [X0] : creative(X0)) & (? [X0] : ~creative(X0) | ~generous(mary) | curious(mary)) [flattening 56]
58. ((generous(mary) & ~curious(mary)) | ! [X0] : creative(X0)) & (? [X1] : ~creative(X1) | ~generous(mary) | curious(mary)) [rectify 57]
59. ? [X1] : ~creative(X1) => ~creative(sK4) [choice axiom]
60. ((generous(mary) & ~curious(mary)) | ! [X0] : creative(X0)) & (~creative(sK4) | ~generous(mary) | curious(mary)) [skolemisation 58,59]
70. ! [X0] : (((happy(X0) & patient(X0)) | calm(X0)) & (~calm(X0) | (~happy(X0) | ~patient(X0)))) [nnf transformation 16]
71. ! [X0] : (((happy(X0) & patient(X0)) | calm(X0)) & (~calm(X0) | ~happy(X0) | ~patient(X0))) [flattening 70]
83. ~humble(X0) | creative(X0) | funny(X0) | brave(X0) [cnf transformation 35]
91. ~curious(X0) | brave(X0) [cnf transformation 26]
93. ~creative(X0) | ~creative(X0) [cnf transformation 42]
95. ~funny(X0) | creative(X0) | creative(X0) [cnf transformation 42]
101. curious(X0) | humble(X0) [cnf transformation 48]
118. ~curious(mary) | creative(X0) [cnf transformation 60]
124. ~wise(X0) | ~calm(X0) | ~brave(X0) [cnf transformation 31]
126. ~patient(X0) | ~humble(X0) [cnf transformation 32]
138. patient(X0) | calm(X0) [cnf transformation 71]
146. wise(mary) [cnf transformation 22]
147. ~creative(X0) [duplicate literal removal 93]
148. ~funny(X0) | creative(X0) [duplicate literal removal 95]
209. ~curious(mary) [subsumption resolution 118,147]
288. humble(mary) [resolution 101,209]
289. humble(X0) | brave(X0) [resolution 101,91]
290. ~humble(X0) | calm(X0) [resolution 138,126]
317. 28 <=> funny(mary) [avatar definition]
318. funny(mary) <- (28) [avatar component clause 317]
321. 29 <=> brave(mary) [avatar definition]
323. ~brave(mary) <- (~29) [avatar component clause 321]
379. ~calm(mary) | ~brave(mary) [resolution 124,146]
383. 38 <=> calm(mary) [avatar definition]
386. ~29 | ~38 [avatar split clause 379,383,321]
390. calm(mary) [resolution 290,288]
394. 38 [avatar split clause 390,383]
400. creative(X0) | funny(X0) | brave(X0) | brave(X0) [resolution 83,289]
405. creative(X0) | funny(X0) | brave(X0) [duplicate literal removal 400]
406. brave(X0) | funny(X0) [subsumption resolution 405,147]
649. funny(mary) <- (~29) [resolution 406,323]
660. 28 | 29 [avatar split clause 649,321,317]
663. creative(mary) <- (28) [resolution 318,148]
664. $false <- (28) [subsumption resolution 663,147]
665. ~28 [avatar contradiction clause 664]
666. $false [avatar sat refutation 386,394,660,665]
% SZS output end Proof for 804785221911589239625065
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not patient is either generous or creative and vice versa. If john is both happy and not kind then someone is either not happy or not funny. If john is both happy and not funny then someone is happy and vice versa. If someone is not calm then mary is creative. Everyone who is not old or creative is both calm and not brave and vice versa. Everyone who is creative or not happy is strong. If alice is both not patient and quiet then someone is either not quiet or not generous and vice versa. Everyone who is not rich or not curious is not tall and vice versa. If someone is both rich and generous then someone is both generous and not funny and vice versa. If susan is both strong and old then mary is tall or not strong. Everyone who is not wise is happy or humble. Everyone who is not tall is both not creative and not happy. If someone is both funny and not humble then someone is both not happy and generous and vice versa. If john is either not happy or not kind then someone is not old or quiet and vice versa. If someone is strong or not tall then susan is either not generous or not wise and vice versa. If fred is not happy or not brave then mary is strong and vice versa. Someone is brave. Alice is either old or not old. Someone is wise or calm. Paul is creative. Alice is both not wise and happy. Someone is either generous or patient. Someone is quiet or rich. Alice is both generous and not wise. | Paul is rich. | entailment | (![X]:((~tall(X)<~>~patient(X))<=>(generous(X)<~>creative(X))))&
(((happy(john)&~kind(john)))=>(?[X]:((~happy(X)<~>~funny(X)))))&
(((happy(john)&~funny(john)))<=>(?[X]:(happy(X))))&
((?[X]:(~calm(X)))=>(creative(mary)))&
(![X]:((~old(X)|creative(X))<=>(calm(X)&~brave(X))))&
(![X]:((creative(X)|~happy(X))=>strong(X)))&
(((~patient(alice)&quiet(alice)))<=>(?[X]:((~quiet(X)<~>~generous(X)))))&
(![X]:((~rich(X)|~curious(X))<=>~tall(X)))&
((?[X]:((rich(X)&generous(X))))<=>(?[X]:((generous(X)&~funny(X)))))&
(((strong(susan)&old(susan)))=>((tall(mary)|~strong(mary))))&
(![X]:(~wise(X)=>(happy(X)|humble(X))))&
(![X]:(~tall(X)=>(~creative(X)&~happy(X))))&
((?[X]:((funny(X)&~humble(X))))<=>(?[X]:((~happy(X)&generous(X)))))&
(((~happy(john)<~>~kind(john)))<=>(?[X]:((~old(X)|quiet(X)))))&
((?[X]:((strong(X)|~tall(X))))<=>((~generous(susan)<~>~wise(susan))))&
(((~happy(fred)|~brave(fred)))<=>(strong(mary)))&
(?[X]:(brave(X)))&
((old(alice)<~>~old(alice)))&
(?[X]:((wise(X)|calm(X))))&
(creative(paul))&
((~wise(alice)&happy(alice)))&
(?[X]:((generous(X)<~>patient(X))))&
(?[X]:((quiet(X)|rich(X))))&
((generous(alice)&~wise(alice))) | rich(paul) | [
"p7",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5368938863310431902518007
% SZS output start Proof for 5368938863310431902518007
8. ! [X0] : ((~curious(X0) | ~rich(X0)) <=> ~tall(X0)) [input p7]
12. ! [X0] : (~tall(X0) => (~happy(X0) & ~creative(X0))) [input p11]
20. creative(paul) [input p19]
25. ~rich(paul) [input hypothesis]
36. ! [X0] : ((~happy(X0) & ~creative(X0)) | tall(X0)) [ennf transformation 12]
53. ! [X0] : (((~curious(X0) | ~rich(X0)) | tall(X0)) & (~tall(X0) | (curious(X0) & rich(X0)))) [nnf transformation 8]
54. ! [X0] : ((~curious(X0) | ~rich(X0) | tall(X0)) & (~tall(X0) | (curious(X0) & rich(X0)))) [flattening 53]
112. ~tall(X0) | rich(X0) [cnf transformation 54]
121. ~creative(X0) | tall(X0) [cnf transformation 36]
146. creative(paul) [cnf transformation 20]
154. ~rich(paul) [cnf transformation 25]
387. tall(paul) [resolution 121,146]
389. rich(paul) [resolution 387,112]
390. $false [subsumption resolution 389,154]
% SZS output end Proof for 5368938863310431902518007
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and patient is both not creative and not funny and vice versa. Everyone who is both wise and curious is either quiet or kind and vice versa. If paul is not kind then john is not humble or curious and vice versa. Everyone who is not wise is kind or not calm. Everyone who is not kind or not funny is both funny and not old. If someone is both generous and not rich then someone is not generous or not happy and vice versa. Everyone who is rich is not patient. Everyone who is both not kind and curious is either quiet or not old and vice versa. If paul is both creative and not strong then alice is creative and vice versa. Everyone who is old is either not brave or not quiet. If john is both kind and patient then someone is not generous. If paul is either calm or wise then someone is funny. Everyone who is calm is both creative and wise. Everyone who is either not wise or calm is either humble or not creative and vice versa. Everyone who is both not old and wise is either not quiet or not patient and vice versa. If someone is not happy or wise then paul is either not funny or kind. Someone is not generous or calm. Someone is curious or not curious. John is calm or not happy. Susan is either brave or not old. Someone is both not kind and happy. Mary is either not generous or quiet. Lucy is not rich or quiet. Someone is either not creative or not calm. | Susan is patient. | contradiction | (![X]:((~brave(X)&patient(X))<=>(~creative(X)&~funny(X))))&
(![X]:((wise(X)&curious(X))<=>(quiet(X)<~>kind(X))))&
((~kind(paul))<=>((~humble(john)|curious(john))))&
(![X]:(~wise(X)=>(kind(X)|~calm(X))))&
(![X]:((~kind(X)|~funny(X))=>(funny(X)&~old(X))))&
((?[X]:((generous(X)&~rich(X))))<=>(?[X]:((~generous(X)|~happy(X)))))&
(![X]:(rich(X)=>~patient(X)))&
(![X]:((~kind(X)&curious(X))<=>(quiet(X)<~>~old(X))))&
(((creative(paul)&~strong(paul)))<=>(creative(alice)))&
(![X]:(old(X)=>(~brave(X)<~>~quiet(X))))&
(((kind(john)&patient(john)))=>(?[X]:(~generous(X))))&
(((calm(paul)<~>wise(paul)))=>(?[X]:(funny(X))))&
(![X]:(calm(X)=>(creative(X)&wise(X))))&
(![X]:((~wise(X)<~>calm(X))<=>(humble(X)<~>~creative(X))))&
(![X]:((~old(X)&wise(X))<=>(~quiet(X)<~>~patient(X))))&
((?[X]:((~happy(X)|wise(X))))=>((~funny(paul)<~>kind(paul))))&
(?[X]:((~generous(X)|calm(X))))&
(?[X]:((curious(X)|~curious(X))))&
((calm(john)|~happy(john)))&
((brave(susan)<~>~old(susan)))&
(?[X]:((~kind(X)&happy(X))))&
((~generous(mary)<~>quiet(mary)))&
((~rich(lucy)|quiet(lucy)))&
(?[X]:((~creative(X)<~>~calm(X)))) | patient(susan) | [
"p0",
"p4",
"p7",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3100686138510612809853954
% SZS output start Proof for 3100686138510612809853954
1. ! [X0] : ((patient(X0) & ~brave(X0)) <=> (~funny(X0) & ~creative(X0))) [input p0]
5. ! [X0] : ((~funny(X0) | ~kind(X0)) => (~old(X0) & funny(X0))) [input p4]
8. ! [X0] : ((curious(X0) & ~kind(X0)) <=> (quiet(X0) <~> ~old(X0))) [input p7]
15. ! [X0] : ((wise(X0) & ~old(X0)) <=> (~quiet(X0) <~> ~patient(X0))) [input p14]
20. brave(susan) <~> ~old(susan) [input p19]
25. patient(susan) [input hypothesis]
29. ! [X0] : ((~old(X0) & funny(X0)) | (funny(X0) & kind(X0))) [ennf transformation 5]
37. ! [X0] : (((patient(X0) & ~brave(X0)) | (funny(X0) | creative(X0))) & ((~funny(X0) & ~creative(X0)) | (~patient(X0) | brave(X0)))) [nnf transformation 1]
38. ! [X0] : (((patient(X0) & ~brave(X0)) | funny(X0) | creative(X0)) & ((~funny(X0) & ~creative(X0)) | ~patient(X0) | brave(X0))) [flattening 37]
48. ! [X0] : (((curious(X0) & ~kind(X0)) | ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0)))) & (((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | (~curious(X0) | kind(X0)))) [nnf transformation 8]
49. ! [X0] : (((curious(X0) & ~kind(X0)) | ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0)))) & (((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | ~curious(X0) | kind(X0))) [flattening 48]
59. ! [X0] : (((wise(X0) & ~old(X0)) | ((~quiet(X0) | patient(X0)) & (~patient(X0) | quiet(X0)))) & (((patient(X0) | quiet(X0)) & (~patient(X0) | ~quiet(X0))) | (~wise(X0) | old(X0)))) [nnf transformation 15]
60. ! [X0] : (((wise(X0) & ~old(X0)) | ((~quiet(X0) | patient(X0)) & (~patient(X0) | quiet(X0)))) & (((patient(X0) | quiet(X0)) & (~patient(X0) | ~quiet(X0))) | ~wise(X0) | old(X0))) [flattening 59]
66. (old(susan) | ~brave(susan)) & (~old(susan) | brave(susan)) [nnf transformation 20]
74. ~funny(X0) | ~patient(X0) | brave(X0) [cnf transformation 38]
88. funny(X0) | funny(X0) [cnf transformation 29]
89. ~old(X0) | kind(X0) [cnf transformation 29]
99. ~kind(X0) | ~old(X0) | ~quiet(X0) [cnf transformation 49]
123. ~old(X0) | ~patient(X0) | quiet(X0) [cnf transformation 60]
135. old(susan) | ~brave(susan) [cnf transformation 66]
143. patient(susan) [cnf transformation 25]
144. funny(X0) [duplicate literal removal 88]
190. ~old(X0) | ~quiet(X0) [subsumption resolution 99,89]
227. ~old(X0) | ~patient(X0) [subsumption resolution 123,190]
255. 22 <=> brave(susan) [avatar definition]
259. 23 <=> old(susan) [avatar definition]
261. old(susan) <- (23) [avatar component clause 259]
262. ~22 | 23 [avatar split clause 135,259,255]
316. ~patient(X0) | brave(X0) [resolution 74,144]
318. brave(susan) [resolution 316,143]
321. 22 [avatar split clause 318,255]
323. ~patient(susan) <- (23) [resolution 261,227]
328. $false <- (23) [subsumption resolution 323,143]
329. ~23 [avatar contradiction clause 328]
330. $false [avatar sat refutation 262,321,329]
% SZS output end Proof for 3100686138510612809853954
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and curious is wise or happy. If someone is both not calm and quiet then someone is not brave or not tall and vice versa. Everyone who is both not generous and kind is either not kind or not funny and vice versa. Everyone who is wise or quiet is both not curious and brave and vice versa. If someone is either creative or old then someone is both calm and kind. Everyone who is both not curious and not old is brave or rich. Everyone who is either not creative or funny is either not curious or not rich. Everyone who is either not generous or generous is either not wise or happy. Everyone who is both brave and calm is not quiet and vice versa. If someone is either generous or not old then someone is both not curious and happy and vice versa. Everyone who is humble is either not quiet or not calm. Everyone who is not kind or not old is not patient. Everyone who is tall or not calm is both not humble and old and vice versa. If john is humble then someone is either not humble or not calm and vice versa. If someone is not generous then someone is either not old or not calm and vice versa. If someone is funny or not patient then john is either wise or happy and vice versa. Alice is either tall or rich. Fred is either old or not creative. Someone is rich. Mary is not humble. John is funny or tall. | John is kind. | entailment | (![X]:((calm(X)&curious(X))=>(wise(X)|happy(X))))&
((?[X]:((~calm(X)&quiet(X))))<=>(?[X]:((~brave(X)|~tall(X)))))&
(![X]:((~generous(X)&kind(X))<=>(~kind(X)<~>~funny(X))))&
(![X]:((wise(X)|quiet(X))<=>(~curious(X)&brave(X))))&
((?[X]:((creative(X)<~>old(X))))=>(?[X]:((calm(X)&kind(X)))))&
(![X]:((~curious(X)&~old(X))=>(brave(X)|rich(X))))&
(![X]:((~creative(X)<~>funny(X))=>(~curious(X)<~>~rich(X))))&
(![X]:((~generous(X)<~>generous(X))=>(~wise(X)<~>happy(X))))&
(![X]:((brave(X)&calm(X))<=>~quiet(X)))&
((?[X]:((generous(X)<~>~old(X))))<=>(?[X]:((~curious(X)&happy(X)))))&
(![X]:(humble(X)=>(~quiet(X)<~>~calm(X))))&
(![X]:((~kind(X)|~old(X))=>~patient(X)))&
(![X]:((tall(X)|~calm(X))<=>(~humble(X)&old(X))))&
((humble(john))<=>(?[X]:((~humble(X)<~>~calm(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((~old(X)<~>~calm(X)))))&
((?[X]:((funny(X)|~patient(X))))<=>((wise(john)<~>happy(john))))&
((tall(alice)<~>rich(alice)))&
((old(fred)<~>~creative(fred)))&
(?[X]:(rich(X)))&
(~humble(mary))&
((funny(john)|tall(john))) | kind(john) | [
"p7",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 40486939956852741633217
% SZS output start Proof for 40486939956852741633217
8. ! [X0] : ((~generous(X0) <~> generous(X0)) => (~wise(X0) <~> happy(X0))) [input p7]
12. ! [X0] : ((~old(X0) | ~kind(X0)) => ~patient(X0)) [input p11]
16. ? [X0] : (~patient(X0) | funny(X0)) <=> (wise(john) <~> happy(john)) [input p15]
22. ~kind(john) [input hypothesis]
33. ! [X0] : ((~wise(X0) <~> happy(X0)) | (~generous(X0) <=> generous(X0))) [ennf transformation 8]
35. ! [X0] : (~patient(X0) | (old(X0) & kind(X0))) [ennf transformation 12]
50. ! [X0] : (((~happy(X0) | wise(X0)) & (happy(X0) | ~wise(X0))) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) [nnf transformation 33]
70. (? [X0] : (~patient(X0) | funny(X0)) | ((wise(john) | ~happy(john)) & (happy(john) | ~wise(john)))) & (((~happy(john) | ~wise(john)) & (happy(john) | wise(john))) | ! [X0] : (patient(X0) & ~funny(X0))) [nnf transformation 16]
71. (? [X0] : (~patient(X0) | funny(X0)) | ((wise(john) | ~happy(john)) & (happy(john) | ~wise(john)))) & (((~happy(john) | ~wise(john)) & (happy(john) | wise(john))) | ! [X1] : (patient(X1) & ~funny(X1))) [rectify 70]
72. ? [X0] : (~patient(X0) | funny(X0)) => (~patient(sK8) | funny(sK8)) [choice axiom]
73. ((~patient(sK8) | funny(sK8)) | ((wise(john) | ~happy(john)) & (happy(john) | ~wise(john)))) & (((~happy(john) | ~wise(john)) & (happy(john) | wise(john))) | ! [X1] : (patient(X1) & ~funny(X1))) [skolemisation 71,72]
104. happy(X0) | ~wise(X0) | generous(X0) | generous(X0) [cnf transformation 50]
105. happy(X0) | ~wise(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 50]
106. ~happy(X0) | wise(X0) | generous(X0) | generous(X0) [cnf transformation 50]
107. ~happy(X0) | wise(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 50]
119. ~patient(X0) | kind(X0) [cnf transformation 35]
135. happy(john) | wise(john) | patient(X1) [cnf transformation 73]
137. ~happy(john) | ~wise(john) | patient(X1) [cnf transformation 73]
147. ~kind(john) [cnf transformation 22]
148. happy(X0) | ~wise(X0) | generous(X0) [duplicate literal removal 104]
149. happy(X0) | ~wise(X0) | ~generous(X0) [duplicate literal removal 105]
150. ~happy(X0) | wise(X0) | generous(X0) [duplicate literal removal 106]
151. ~happy(X0) | wise(X0) | ~generous(X0) [duplicate literal removal 107]
203. ~happy(X0) | wise(X0) [subsumption resolution 150,151]
204. happy(X0) | ~wise(X0) [subsumption resolution 148,149]
285. ~wise(john) | patient(X1) [subsumption resolution 137,204]
287. 29 <=> ! [X1] : patient(X1) [avatar definition]
288. patient(X1) <- (29) [avatar component clause 287]
290. 30 <=> wise(john) [avatar definition]
293. 29 | ~30 [avatar split clause 285,290,287]
299. wise(john) | patient(X1) [subsumption resolution 135,203]
300. 29 | 30 [avatar split clause 299,290,287]
338. kind(X0) <- (29) [resolution 119,288]
345. $false <- (29) [resolution 338,147]
346. ~29 [avatar contradiction clause 345]
347. $false [avatar sat refutation 293,300,346]
% SZS output end Proof for 40486939956852741633217
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is not happy. If someone is not curious then susan is either not strong or funny. If someone is either calm or curious then someone is either wise or not happy and vice versa. If someone is either happy or not old then lucy is strong. If someone is both curious and patient then someone is either not curious or wise and vice versa. If susan is both happy and not generous then someone is both patient and happy. If john is not wise or happy then someone is curious. Everyone who is either calm or rich is not wise or not brave and vice versa. Everyone who is both tall and curious is humble. Everyone who is either not humble or humble is wise and vice versa. If fred is either not generous or not wise then someone is quiet or not curious and vice versa. If john is not generous then paul is both strong and not humble and vice versa. If fred is not happy or generous then john is either old or not rich. If someone is not happy then susan is both calm and quiet and vice versa. Everyone who is both not humble and kind is quiet. Everyone who is either not generous or not strong is both not happy and not old. Fred is strong or rich. Paul is either not patient or creative. Someone is not funny or not calm. Someone is wise. Susan is tall. Someone is either creative or kind. Alice is not strong or wise. | Paul is wise. | entailment | (![X]:(kind(X)=>~happy(X)))&
((?[X]:(~curious(X)))=>((~strong(susan)<~>funny(susan))))&
((?[X]:((calm(X)<~>curious(X))))<=>(?[X]:((wise(X)<~>~happy(X)))))&
((?[X]:((happy(X)<~>~old(X))))=>(strong(lucy)))&
((?[X]:((curious(X)&patient(X))))<=>(?[X]:((~curious(X)<~>wise(X)))))&
(((happy(susan)&~generous(susan)))=>(?[X]:((patient(X)&happy(X)))))&
(((~wise(john)|happy(john)))=>(?[X]:(curious(X))))&
(![X]:((calm(X)<~>rich(X))<=>(~wise(X)|~brave(X))))&
(![X]:((tall(X)&curious(X))=>humble(X)))&
(![X]:((~humble(X)<~>humble(X))<=>wise(X)))&
(((~generous(fred)<~>~wise(fred)))<=>(?[X]:((quiet(X)|~curious(X)))))&
((~generous(john))<=>((strong(paul)&~humble(paul))))&
(((~happy(fred)|generous(fred)))=>((old(john)<~>~rich(john))))&
((?[X]:(~happy(X)))<=>((calm(susan)&quiet(susan))))&
(![X]:((~humble(X)&kind(X))=>quiet(X)))&
(![X]:((~generous(X)<~>~strong(X))=>(~happy(X)&~old(X))))&
((strong(fred)|rich(fred)))&
((~patient(paul)<~>creative(paul)))&
(?[X]:((~funny(X)|~calm(X))))&
(?[X]:(wise(X)))&
(tall(susan))&
(?[X]:((creative(X)<~>kind(X))))&
((~strong(alice)|wise(alice))) | wise(paul) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 173304292240314591825953
% SZS output start Proof for 173304292240314591825953
10. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> wise(X0)) [input p9]
24. ~wise(paul) [input hypothesis]
57. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | ~wise(X0)) & (wise(X0) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 10]
109. wise(X0) | humble(X0) | humble(X0) [cnf transformation 57]
110. wise(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 57]
143. ~wise(paul) [cnf transformation 24]
144. wise(X0) | humble(X0) [duplicate literal removal 109]
145. wise(X0) | ~humble(X0) [duplicate literal removal 110]
270. wise(X0) [subsumption resolution 144,145]
379. $false [subsumption resolution 143,270]
% SZS output end Proof for 173304292240314591825953
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or not wise is either creative or not old and vice versa. Everyone who is either not wise or not funny is both kind and creative. Everyone who is either funny or not wise is strong or humble and vice versa. Everyone who is quiet or funny is both humble and brave and vice versa. Everyone who is not patient is rich or not tall and vice versa. If someone is both funny and generous then lucy is both strong and not brave. If someone is creative or not patient then someone is not humble or quiet and vice versa. Everyone who is not old or brave is both generous and brave and vice versa. If john is not kind then someone is both not rich and not patient and vice versa. Everyone who is both humble and not strong is not tall and vice versa. Everyone who is brave is both not kind and not rich and vice versa. If someone is generous then john is funny or old and vice versa. Everyone who is either funny or strong is both not generous and not creative. If susan is both rich and not happy then alice is either not rich or not calm. Paul is either calm or not rich. John is not curious or not calm. Lucy is curious or brave. Someone is not patient or not wise. John is humble or tall. Lucy is old. | John is creative. | entailment | (![X]:((brave(X)|~wise(X))<=>(creative(X)<~>~old(X))))&
(![X]:((~wise(X)<~>~funny(X))=>(kind(X)&creative(X))))&
(![X]:((funny(X)<~>~wise(X))<=>(strong(X)|humble(X))))&
(![X]:((quiet(X)|funny(X))<=>(humble(X)&brave(X))))&
(![X]:(~patient(X)<=>(rich(X)|~tall(X))))&
((?[X]:((funny(X)&generous(X))))=>((strong(lucy)&~brave(lucy))))&
((?[X]:((creative(X)|~patient(X))))<=>(?[X]:((~humble(X)|quiet(X)))))&
(![X]:((~old(X)|brave(X))<=>(generous(X)&brave(X))))&
((~kind(john))<=>(?[X]:((~rich(X)&~patient(X)))))&
(![X]:((humble(X)&~strong(X))<=>~tall(X)))&
(![X]:(brave(X)<=>(~kind(X)&~rich(X))))&
((?[X]:(generous(X)))<=>((funny(john)|old(john))))&
(![X]:((funny(X)<~>strong(X))=>(~generous(X)&~creative(X))))&
(((rich(susan)&~happy(susan)))=>((~rich(alice)<~>~calm(alice))))&
((calm(paul)<~>~rich(paul)))&
((~curious(john)|~calm(john)))&
((curious(lucy)|brave(lucy)))&
(?[X]:((~patient(X)|~wise(X))))&
((humble(john)|tall(john)))&
(old(lucy)) | creative(john) | [
"p0",
"p1",
"p2",
"p3",
"p5",
"p7",
"p11",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6150748683501676089419048
% SZS output start Proof for 6150748683501676089419048
1. ! [X0] : ((~wise(X0) | brave(X0)) <=> (creative(X0) <~> ~old(X0))) [input p0]
2. ! [X0] : ((~wise(X0) <~> ~funny(X0)) => (creative(X0) & kind(X0))) [input p1]
3. ! [X0] : ((funny(X0) <~> ~wise(X0)) <=> (humble(X0) | strong(X0))) [input p2]
4. ! [X0] : ((funny(X0) | quiet(X0)) <=> (brave(X0) & humble(X0))) [input p3]
6. ? [X0] : (generous(X0) & funny(X0)) => (~brave(lucy) & strong(lucy)) [input p5]
8. ! [X0] : ((brave(X0) | ~old(X0)) <=> (brave(X0) & generous(X0))) [input p7]
12. ? [X0] : generous(X0) <=> (old(john) | funny(john)) [input p11]
13. ! [X0] : ((funny(X0) <~> strong(X0)) => (~creative(X0) & ~generous(X0))) [input p12]
20. old(lucy) [input p19]
21. ~creative(john) [input hypothesis]
24. ! [X0] : ((creative(X0) & kind(X0)) | (~wise(X0) <=> ~funny(X0))) [ennf transformation 2]
25. (~brave(lucy) & strong(lucy)) | ! [X0] : (~generous(X0) | ~funny(X0)) [ennf transformation 6]
26. ! [X0] : ((~creative(X0) & ~generous(X0)) | (funny(X0) <=> strong(X0))) [ennf transformation 13]
27. ! [X0] : (((~wise(X0) | brave(X0)) | ((creative(X0) | old(X0)) & (~old(X0) | ~creative(X0)))) & (((old(X0) | ~creative(X0)) & (~old(X0) | creative(X0))) | (wise(X0) & ~brave(X0)))) [nnf transformation 1]
28. ! [X0] : ((~wise(X0) | brave(X0) | ((creative(X0) | old(X0)) & (~old(X0) | ~creative(X0)))) & (((old(X0) | ~creative(X0)) & (~old(X0) | creative(X0))) | (wise(X0) & ~brave(X0)))) [flattening 27]
29. ! [X0] : ((creative(X0) & kind(X0)) | ((~wise(X0) | funny(X0)) & (~funny(X0) | wise(X0)))) [nnf transformation 24]
30. ! [X0] : ((((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | (~humble(X0) & ~strong(X0))) & ((humble(X0) | strong(X0)) | ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0))))) [nnf transformation 3]
31. ! [X0] : ((((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | (~humble(X0) & ~strong(X0))) & (humble(X0) | strong(X0) | ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0))))) [flattening 30]
32. ! [X0] : (((funny(X0) | quiet(X0)) | (~brave(X0) | ~humble(X0))) & ((brave(X0) & humble(X0)) | (~funny(X0) & ~quiet(X0)))) [nnf transformation 4]
33. ! [X0] : ((funny(X0) | quiet(X0) | ~brave(X0) | ~humble(X0)) & ((brave(X0) & humble(X0)) | (~funny(X0) & ~quiet(X0)))) [flattening 32]
41. ! [X0] : (((brave(X0) | ~old(X0)) | (~brave(X0) | ~generous(X0))) & ((brave(X0) & generous(X0)) | (~brave(X0) & old(X0)))) [nnf transformation 8]
42. ! [X0] : ((brave(X0) | ~old(X0) | ~brave(X0) | ~generous(X0)) & ((brave(X0) & generous(X0)) | (~brave(X0) & old(X0)))) [flattening 41]
51. (? [X0] : generous(X0) | (~old(john) & ~funny(john))) & ((old(john) | funny(john)) | ! [X0] : ~generous(X0)) [nnf transformation 12]
52. (? [X0] : generous(X0) | (~old(john) & ~funny(john))) & (old(john) | funny(john) | ! [X0] : ~generous(X0)) [flattening 51]
53. (? [X0] : generous(X0) | (~old(john) & ~funny(john))) & (old(john) | funny(john) | ! [X1] : ~generous(X1)) [rectify 52]
54. ? [X0] : generous(X0) => generous(sK3) [choice axiom]
55. (generous(sK3) | (~old(john) & ~funny(john))) & (old(john) | funny(john) | ! [X1] : ~generous(X1)) [skolemisation 53,54]
56. ! [X0] : ((~creative(X0) & ~generous(X0)) | ((funny(X0) | ~strong(X0)) & (strong(X0) | ~funny(X0)))) [nnf transformation 26]
61. ~old(X0) | creative(X0) | wise(X0) [cnf transformation 28]
69. ~wise(X0) | creative(X0) | funny(X0) [cnf transformation 29]
72. ~strong(X0) | funny(X0) | ~wise(X0) [cnf transformation 31]
79. ~funny(X0) | brave(X0) [cnf transformation 33]
84. strong(lucy) | ~generous(X0) | ~funny(X0) [cnf transformation 25]
85. ~brave(lucy) | ~generous(X0) | ~funny(X0) [cnf transformation 25]
90. generous(X0) | old(X0) [cnf transformation 42]
91. ~brave(X0) | generous(X0) [cnf transformation 42]
104. old(john) | funny(john) | ~generous(X1) [cnf transformation 55]
110. ~strong(X0) | funny(X0) | ~creative(X0) [cnf transformation 56]
117. old(lucy) [cnf transformation 20]
118. ~creative(john) [cnf transformation 21]
120. 1 <=> ! [X0] : (~generous(X0) | ~funny(X0)) [avatar definition]
121. ~generous(X0) | ~funny(X0) <- (1) [avatar component clause 120]
123. 2 <=> brave(lucy) [avatar definition]
125. ~brave(lucy) <- (~2) [avatar component clause 123]
126. 1 | ~2 [avatar split clause 85,123,120]
128. 3 <=> strong(lucy) [avatar definition]
130. strong(lucy) <- (3) [avatar component clause 128]
131. 1 | 3 [avatar split clause 84,128,120]
183. 16 <=> old(john) [avatar definition]
184. old(john) <- (16) [avatar component clause 183]
185. ~old(john) <- (~16) [avatar component clause 183]
192. 18 <=> funny(john) [avatar definition]
193. funny(john) <- (18) [avatar component clause 192]
197. 19 <=> ! [X1] : ~generous(X1) [avatar definition]
198. ~generous(X1) <- (19) [avatar component clause 197]
199. 19 | 18 | 16 [avatar split clause 104,183,192,197]
238. creative(lucy) | wise(lucy) [resolution 61,117]
239. creative(john) | wise(john) <- (16) [resolution 61,184]
242. 27 <=> wise(lucy) [avatar definition]
244. wise(lucy) <- (27) [avatar component clause 242]
246. 28 <=> creative(lucy) [avatar definition]
248. creative(lucy) <- (28) [avatar component clause 246]
249. 27 | 28 [avatar split clause 238,246,242]
250. wise(john) <- (16) [subsumption resolution 239,118]
254. 29 <=> funny(lucy) [avatar definition]
255. ~funny(lucy) <- (~29) [avatar component clause 254]
256. funny(lucy) <- (29) [avatar component clause 254]
276. creative(john) | funny(john) <- (16) [resolution 69,250]
277. funny(john) <- (16) [subsumption resolution 276,118]
278. 18 | ~16 [avatar split clause 277,183,192]
281. brave(john) <- (18) [resolution 193,79]
289. generous(john) <- (18) [resolution 281,91]
358. funny(lucy) | ~creative(lucy) <- (3) [resolution 110,130]
359. ~creative(lucy) <- (3, ~29) [subsumption resolution 358,255]
360. $false <- (3, 28, ~29) [subsumption resolution 359,248]
361. ~3 | ~28 | 29 [avatar contradiction clause 360]
364. ~funny(john) <- (1, 18) [resolution 121,289]
365. $false <- (1, 18) [subsumption resolution 364,193]
366. ~1 | ~18 [avatar contradiction clause 365]
369. funny(lucy) | ~wise(lucy) <- (3) [resolution 130,72]
374. funny(lucy) <- (3, 27) [subsumption resolution 369,244]
375. 29 | ~3 | ~27 [avatar split clause 374,242,128,254]
427. brave(lucy) <- (29) [resolution 256,79]
429. $false <- (~2, 29) [subsumption resolution 427,125]
430. 2 | ~29 [avatar contradiction clause 429]
442. old(X0) <- (19) [resolution 198,90]
449. $false <- (~16, 19) [resolution 442,185]
450. 16 | ~19 [avatar contradiction clause 449]
451. $false [avatar sat refutation 126,131,199,249,278,361,366,375,430,450]
% SZS output end Proof for 6150748683501676089419048
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or not calm is either rich or strong. If someone is not generous or tall then someone is kind and vice versa. Everyone who is both not quiet and not kind is not calm or patient and vice versa. Everyone who is both brave and not kind is not tall or not humble and vice versa. If someone is either funny or old then someone is both generous and not funny and vice versa. If susan is not patient then fred is either not old or humble. If mary is both rich and brave then john is not curious or old. If mary is not generous then someone is quiet or creative. Everyone who is either funny or strong is calm or kind. Everyone who is both not generous and not strong is both not rich and tall. If someone is both wise and not old then susan is not calm and vice versa. Everyone who is kind or old is quiet or not old. If lucy is happy then susan is brave or creative and vice versa. Everyone who is both happy and rich is creative or not generous. If someone is not wise or not creative then lucy is brave. Everyone who is curious or not kind is either happy or wise. Someone is not happy or rich. Mary is not strong or not calm. Fred is either funny or not tall. Someone is either not rich or not wise. Someone is happy. Alice is quiet. Susan is not rich. Alice is both creative and not curious. | Susan is brave. | neutral | (![X]:((~patient(X)|~calm(X))=>(rich(X)<~>strong(X))))&
((?[X]:((~generous(X)|tall(X))))<=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)&~kind(X))<=>(~calm(X)|patient(X))))&
(![X]:((brave(X)&~kind(X))<=>(~tall(X)|~humble(X))))&
((?[X]:((funny(X)<~>old(X))))<=>(?[X]:((generous(X)&~funny(X)))))&
((~patient(susan))=>((~old(fred)<~>humble(fred))))&
(((rich(mary)&brave(mary)))=>((~curious(john)|old(john))))&
((~generous(mary))=>(?[X]:((quiet(X)|creative(X)))))&
(![X]:((funny(X)<~>strong(X))=>(calm(X)|kind(X))))&
(![X]:((~generous(X)&~strong(X))=>(~rich(X)&tall(X))))&
((?[X]:((wise(X)&~old(X))))<=>(~calm(susan)))&
(![X]:((kind(X)|old(X))=>(quiet(X)|~old(X))))&
((happy(lucy))<=>((brave(susan)|creative(susan))))&
(![X]:((happy(X)&rich(X))=>(creative(X)|~generous(X))))&
((?[X]:((~wise(X)|~creative(X))))=>(brave(lucy)))&
(![X]:((curious(X)|~kind(X))=>(happy(X)<~>wise(X))))&
(?[X]:((~happy(X)|rich(X))))&
((~strong(mary)|~calm(mary)))&
((funny(fred)<~>~tall(fred)))&
(?[X]:((~rich(X)<~>~wise(X))))&
(?[X]:(happy(X)))&
(quiet(alice))&
(~rich(susan))&
((creative(alice)&~curious(alice))) | brave(susan) | [] | null | 0 |
If alice is either not quiet or not happy then someone is either creative or not old and vice versa.
Everyone who is not brave is both funny and not humble and vice versa.
If john is tall or not wise then someone is not strong.
Everyone who is both not funny and old is kind or rich.
Everyone who is strong or not creative is patient.
Everyone who is both happy and generous is quiet or not patient.
Everyone who is both kind and not patient is wise.
Everyone who is not humble is both not kind and calm and vice versa.
Everyone who is generous or not calm is generous.
Everyone who is tall is both humble and not generous.
Everyone who is tall is either strong or not patient and vice versa.
Everyone who is both not brave and not patient is either not calm or not funny and vice versa.
If fred is creative then someone is not strong or not creative and vice versa.
Everyone who is both patient and not rich is not generous and vice versa.
Everyone who is both not calm and kind is not strong and vice versa.
If someone is quiet or not old then fred is humble or not strong.
Someone is not quiet.
John is curious.
Someone is both not creative and tall.
Alice is not creative.
Mary is not old.
Susan is both not curious and funny.
Someone is not wise.
Someone is brave. | John is not humble. | contradiction | (((~quiet(alice)<~>~happy(alice)))<=>(?[X]:((creative(X)<~>~old(X)))))&
(![X]:(~brave(X)<=>(funny(X)&~humble(X))))&
(((tall(john)|~wise(john)))=>(?[X]:(~strong(X))))&
(![X]:((~funny(X)&old(X))=>(kind(X)|rich(X))))&
(![X]:((strong(X)|~creative(X))=>patient(X)))&
(![X]:((happy(X)&generous(X))=>(quiet(X)|~patient(X))))&
(![X]:((kind(X)&~patient(X))=>wise(X)))&
(![X]:(~humble(X)<=>(~kind(X)&calm(X))))&
(![X]:((generous(X)|~calm(X))=>generous(X)))&
(![X]:(tall(X)=>(humble(X)&~generous(X))))&
(![X]:(tall(X)<=>(strong(X)<~>~patient(X))))&
(![X]:((~brave(X)&~patient(X))<=>(~calm(X)<~>~funny(X))))&
((creative(fred))<=>(?[X]:((~strong(X)|~creative(X)))))&
(![X]:((patient(X)&~rich(X))<=>~generous(X)))&
(![X]:((~calm(X)&kind(X))<=>~strong(X)))&
((?[X]:((quiet(X)|~old(X))))=>((humble(fred)|~strong(fred))))&
(?[X]:(~quiet(X)))&
(curious(john))&
(?[X]:((~creative(X)&tall(X))))&
(~creative(alice))&
(~old(mary))&
((~curious(susan)&funny(susan)))&
(?[X]:(~wise(X)))&
(?[X]:(brave(X))) | ~humble(john) | [
"p4",
"p7",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4117707916675477220632621
% SZS output start Proof for 4117707916675477220632621
5. ! [X0] : ((~creative(X0) | strong(X0)) => patient(X0)) [input p4]
8. ! [X0] : (~humble(X0) <=> (calm(X0) & ~kind(X0))) [input p7]
10. ! [X0] : (tall(X0) => (~generous(X0) & humble(X0))) [input p9]
11. ! [X0] : (tall(X0) <=> (strong(X0) <~> ~patient(X0))) [input p10]
15. ! [X0] : ((kind(X0) & ~calm(X0)) <=> ~strong(X0)) [input p14]
25. ~humble(john) [input hypothesis]
29. ! [X0] : (patient(X0) | (creative(X0) & ~strong(X0))) [ennf transformation 5]
35. ! [X0] : ((~generous(X0) & humble(X0)) | ~tall(X0)) [ennf transformation 10]
46. ! [X0] : ((~humble(X0) | (~calm(X0) | kind(X0))) & ((calm(X0) & ~kind(X0)) | humble(X0))) [nnf transformation 8]
47. ! [X0] : ((~humble(X0) | ~calm(X0) | kind(X0)) & ((calm(X0) & ~kind(X0)) | humble(X0))) [flattening 46]
48. ! [X0] : ((tall(X0) | ((strong(X0) | patient(X0)) & (~patient(X0) | ~strong(X0)))) & (((patient(X0) | ~strong(X0)) & (~patient(X0) | strong(X0))) | ~tall(X0))) [nnf transformation 11]
57. ! [X0] : (((kind(X0) & ~calm(X0)) | strong(X0)) & (~strong(X0) | (~kind(X0) | calm(X0)))) [nnf transformation 15]
58. ! [X0] : (((kind(X0) & ~calm(X0)) | strong(X0)) & (~strong(X0) | ~kind(X0) | calm(X0))) [flattening 57]
81. ~strong(X0) | patient(X0) [cnf transformation 29]
86. calm(X0) | humble(X0) [cnf transformation 47]
90. ~tall(X0) | humble(X0) [cnf transformation 35]
94. tall(X0) | ~patient(X0) | ~strong(X0) [cnf transformation 48]
95. tall(X0) | strong(X0) | patient(X0) [cnf transformation 48]
109. ~calm(X0) | strong(X0) [cnf transformation 58]
123. ~humble(john) [cnf transformation 25]
168. patient(X0) | tall(X0) [subsumption resolution 95,81]
169. ~strong(X0) | tall(X0) [subsumption resolution 94,168]
214. strong(X1) | humble(X1) [resolution 109,86]
231. humble(X0) | tall(X0) [resolution 214,169]
236. humble(X0) [subsumption resolution 231,90]
240. $false [resolution 236,123]
% SZS output end Proof for 4117707916675477220632621
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is calm or generous then someone is not happy.
Everyone who is both not wise and calm is old.
If alice is either not strong or not brave then someone is funny and vice versa.
Everyone who is not tall or creative is either creative or not calm.
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.
Paul is either curious or quiet.
Susan is both funny and not kind.
Someone is not humble.
Someone is calm or funny.
Someone is both curious and old.
Alice is either not wise or not strong.
Someone is not wise or wise.
Someone is both patient and not curious. | Mary is not creative. | contradiction | (((calm(john)|generous(john)))=>(?[X]:(~happy(X))))&
(![X]:((~wise(X)&calm(X))=>old(X)))&
(((~strong(alice)<~>~brave(alice)))<=>(?[X]:(funny(X))))&
(![X]:((~tall(X)|creative(X))=>(creative(X)<~>~calm(X))))&
(((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)))))&
((curious(paul)<~>quiet(paul)))&
((funny(susan)&~kind(susan)))&
(?[X]:(~humble(X)))&
(?[X]:((calm(X)|funny(X))))&
(?[X]:((curious(X)&old(X))))&
((~wise(alice)<~>~strong(alice)))&
(?[X]:((~wise(X)|wise(X))))&
(?[X]:((patient(X)&~curious(X)))) | ~creative(mary) | [
"p5",
"p7",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8370889879778041010322369
% SZS output start Proof for 8370889879778041010322369
6. ! [X0] : ((happy(X0) & ~creative(X0)) => (~generous(X0) & patient(X0))) [input p5]
8. ! [X0] : (~happy(X0) <=> (~creative(X0) <~> quiet(X0))) [input p7]
13. ! [X0] : (quiet(X0) <=> (~quiet(X0) | strong(X0))) [input p12]
15. ? [X0] : (old(X0) & ~strong(X0)) <=> (~generous(mary) | ~wise(mary)) [input p14]
25. ~creative(mary) [input hypothesis]
27. ! [X0] : (~happy(X0) => (~creative(X0) <~> quiet(X0))) [unused predicate definition removal 8]
33. ! [X0] : ((~generous(X0) & patient(X0)) | (~happy(X0) | creative(X0))) [ennf transformation 6]
34. ! [X0] : ((~generous(X0) & patient(X0)) | ~happy(X0) | creative(X0)) [flattening 33]
35. ! [X0] : ((~creative(X0) <~> quiet(X0)) | happy(X0)) [ennf transformation 27]
57. ! [X0] : (((~quiet(X0) | creative(X0)) & (quiet(X0) | ~creative(X0))) | happy(X0)) [nnf transformation 35]
65. ! [X0] : ((quiet(X0) | (quiet(X0) & ~strong(X0))) & ((~quiet(X0) | strong(X0)) | ~quiet(X0))) [nnf transformation 13]
66. ! [X0] : ((quiet(X0) | (quiet(X0) & ~strong(X0))) & (~quiet(X0) | strong(X0) | ~quiet(X0))) [flattening 65]
69. (? [X0] : (old(X0) & ~strong(X0)) | (generous(mary) & wise(mary))) & ((~generous(mary) | ~wise(mary)) | ! [X0] : (~old(X0) | strong(X0))) [nnf transformation 15]
70. (? [X0] : (old(X0) & ~strong(X0)) | (generous(mary) & wise(mary))) & (~generous(mary) | ~wise(mary) | ! [X0] : (~old(X0) | strong(X0))) [flattening 69]
71. (? [X0] : (old(X0) & ~strong(X0)) | (generous(mary) & wise(mary))) & (~generous(mary) | ~wise(mary) | ! [X1] : (~old(X1) | strong(X1))) [rectify 70]
72. ? [X0] : (old(X0) & ~strong(X0)) => (old(sK5) & ~strong(sK5)) [choice axiom]
73. ((old(sK5) & ~strong(sK5)) | (generous(mary) & wise(mary))) & (~generous(mary) | ~wise(mary) | ! [X1] : (~old(X1) | strong(X1))) [skolemisation 71,72]
103. ~happy(X0) | ~generous(X0) | creative(X0) [cnf transformation 34]
108. ~quiet(X0) | creative(X0) | happy(X0) [cnf transformation 57]
129. ~quiet(X0) | strong(X0) | ~quiet(X0) [cnf transformation 66]
131. quiet(X0) | quiet(X0) [cnf transformation 66]
137. ~strong(sK5) | generous(mary) [cnf transformation 73]
154. ~creative(mary) [cnf transformation 25]
155. ~quiet(X0) | strong(X0) [duplicate literal removal 129]
156. quiet(X0) [duplicate literal removal 131]
260. strong(X0) [subsumption resolution 155,156]
263. 23 <=> generous(mary) [avatar definition]
265. generous(mary) <- (23) [avatar component clause 263]
276. generous(mary) [subsumption resolution 137,260]
277. 23 [avatar split clause 276,263]
369. creative(X0) | happy(X0) [resolution 108,156]
392. happy(mary) [resolution 369,154]
402. ~generous(mary) | creative(mary) [resolution 392,103]
404. creative(mary) <- (23) [subsumption resolution 402,265]
405. $false <- (23) [subsumption resolution 404,154]
406. ~23 [avatar contradiction clause 405]
408. $false [avatar sat refutation 277,406]
% SZS output end Proof for 8370889879778041010322369
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both not rich and rich then lucy is either rich or humble.
If someone is humble or brave then someone is kind.
If someone is both generous and not creative then paul is either quiet or not brave.
If someone is both not rich and rich then mary is rich and vice versa.
If susan is wise or not old then someone is either creative or not generous and vice versa.
Everyone who is not wise is not humble and vice versa.
If fred is not creative then mary is either generous or quiet and vice versa.
Everyone who is not curious is calm and vice versa.
If lucy is either not tall or not kind then someone is strong or kind.
If someone is tall or curious then paul is both not quiet and humble.
If someone is either not happy or happy then someone is not calm or not humble.
Everyone who is calm is not curious or not generous.
If someone is funny or curious then someone is both not rich and rich and vice versa.
If someone is kind then fred is both quiet and not humble and vice versa.
Everyone who is not wise is patient or not patient and vice versa.
If someone is strong then someone is both not funny and not old.
Alice is humble or not generous.
Fred is either not generous or generous.
John is both not curious and kind.
Susan is not brave.
Someone is both not curious and happy.
Someone is both not tall and not funny.
Paul is either not quiet or not generous. | Susan is tall. | contradiction | (((~rich(lucy)&rich(lucy)))=>((rich(lucy)<~>humble(lucy))))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(kind(X))))&
((?[X]:((generous(X)&~creative(X))))=>((quiet(paul)<~>~brave(paul))))&
((?[X]:((~rich(X)&rich(X))))<=>(rich(mary)))&
(((wise(susan)|~old(susan)))<=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:(~wise(X)<=>~humble(X)))&
((~creative(fred))<=>((generous(mary)<~>quiet(mary))))&
(![X]:(~curious(X)<=>calm(X)))&
(((~tall(lucy)<~>~kind(lucy)))=>(?[X]:((strong(X)|kind(X)))))&
((?[X]:((tall(X)|curious(X))))=>((~quiet(paul)&humble(paul))))&
((?[X]:((~happy(X)<~>happy(X))))=>(?[X]:((~calm(X)|~humble(X)))))&
(![X]:(calm(X)=>(~curious(X)|~generous(X))))&
((?[X]:((funny(X)|curious(X))))<=>(?[X]:((~rich(X)&rich(X)))))&
((?[X]:(kind(X)))<=>((quiet(fred)&~humble(fred))))&
(![X]:(~wise(X)<=>(patient(X)|~patient(X))))&
((?[X]:(strong(X)))=>(?[X]:((~funny(X)&~old(X)))))&
((humble(alice)|~generous(alice)))&
((~generous(fred)<~>generous(fred)))&
((~curious(john)&kind(john)))&
(~brave(susan))&
(?[X]:((~curious(X)&happy(X))))&
(?[X]:((~tall(X)&~funny(X))))&
((~quiet(paul)<~>~generous(paul))) | tall(susan) | [
"p5",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5383826150775252980956046
% SZS output start Proof for 5383826150775252980956046
6. ! [X0] : (~wise(X0) <=> ~humble(X0)) [input p5]
10. ? [X0] : (curious(X0) | tall(X0)) => (humble(paul) & ~quiet(paul)) [input p9]
15. ! [X0] : (~wise(X0) <=> (~patient(X0) | patient(X0))) [input p14]
24. tall(susan) [input hypothesis]
34. (humble(paul) & ~quiet(paul)) | ! [X0] : (~curious(X0) & ~tall(X0)) [ennf transformation 10]
53. ! [X0] : ((~wise(X0) | humble(X0)) & (~humble(X0) | wise(X0))) [nnf transformation 6]
73. ! [X0] : ((~wise(X0) | (patient(X0) & ~patient(X0))) & ((~patient(X0) | patient(X0)) | wise(X0))) [nnf transformation 15]
74. ! [X0] : ((~wise(X0) | (patient(X0) & ~patient(X0))) & (~patient(X0) | patient(X0) | wise(X0))) [flattening 73]
99. ~humble(X0) | wise(X0) [cnf transformation 53]
111. humble(paul) | ~tall(X0) [cnf transformation 34]
125. ~wise(X0) | ~patient(X0) [cnf transformation 74]
126. ~wise(X0) | patient(X0) [cnf transformation 74]
141. tall(susan) [cnf transformation 24]
247. 23 <=> humble(paul) [avatar definition]
249. humble(paul) <- (23) [avatar component clause 247]
252. 24 <=> ! [X0] : ~tall(X0) [avatar definition]
253. ~tall(X0) <- (24) [avatar component clause 252]
254. 24 | 23 [avatar split clause 111,247,252]
302. ~wise(X0) [subsumption resolution 125,126]
331. $false <- (24) [resolution 253,141]
332. ~24 [avatar contradiction clause 331]
333. wise(paul) <- (23) [resolution 99,249]
334. $false <- (23) [subsumption resolution 333,302]
335. ~23 [avatar contradiction clause 334]
336. $false [avatar sat refutation 254,332,335]
% SZS output end Proof for 5383826150775252980956046
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not kind and not happy then someone is either not rich or not happy.
If john is either calm or strong then someone is both not kind and not quiet.
Everyone who is both not kind and old is quiet and vice versa.
If fred is either old or generous then someone is happy or calm.
Everyone who is either creative or not curious is not creative or happy.
Everyone who is either humble or not quiet is not patient or not curious and vice versa.
Everyone who is both not happy and wise is both strong and rich and vice versa.
Everyone who is not old is kind or not generous and vice versa.
If someone is old then alice is both not brave and funny and vice versa.
Everyone who is both funny and calm is either tall or not tall and vice versa.
If someone is kind or not generous then someone is both not curious and curious and vice versa.
Everyone who is generous or calm is not patient or brave and vice versa.
If mary is not kind then fred is either strong or old and vice versa.
If fred is both brave and rich then someone is either not old or not humble and vice versa.
Someone is either wise or not patient.
Susan is not creative or not strong.
Susan is brave or old. | Alice is not tall. | neutral | ((?[X]:((~kind(X)&~happy(X))))=>(?[X]:((~rich(X)<~>~happy(X)))))&
(((calm(john)<~>strong(john)))=>(?[X]:((~kind(X)&~quiet(X)))))&
(![X]:((~kind(X)&old(X))<=>quiet(X)))&
(((old(fred)<~>generous(fred)))=>(?[X]:((happy(X)|calm(X)))))&
(![X]:((creative(X)<~>~curious(X))=>(~creative(X)|happy(X))))&
(![X]:((humble(X)<~>~quiet(X))<=>(~patient(X)|~curious(X))))&
(![X]:((~happy(X)&wise(X))<=>(strong(X)&rich(X))))&
(![X]:(~old(X)<=>(kind(X)|~generous(X))))&
((?[X]:(old(X)))<=>((~brave(alice)&funny(alice))))&
(![X]:((funny(X)&calm(X))<=>(tall(X)<~>~tall(X))))&
((?[X]:((kind(X)|~generous(X))))<=>(?[X]:((~curious(X)&curious(X)))))&
(![X]:((generous(X)|calm(X))<=>(~patient(X)|brave(X))))&
((~kind(mary))<=>((strong(fred)<~>old(fred))))&
(((brave(fred)&rich(fred)))<=>(?[X]:((~old(X)<~>~humble(X)))))&
(?[X]:((wise(X)<~>~patient(X))))&
((~creative(susan)|~strong(susan)))&
((brave(susan)|old(susan))) | ~tall(alice) | [] | null | 0 |
If someone is not rich then someone is either not quiet or quiet. If susan is not kind or not funny then someone is not rich or creative and vice versa. Everyone who is not strong is both humble and calm. Everyone who is wise or humble is both quiet and not funny and vice versa. Everyone who is not generous is not old. If paul is creative then lucy is both rich and not wise and vice versa. Everyone who is either tall or wise is either not strong or not calm. Everyone who is strong or creative is both not curious and generous. If someone is both wise and kind then alice is both humble and tall and vice versa. If someone is either not wise or not happy then paul is not humble or kind and vice versa. If someone is not happy or not rich then someone is both patient and generous and vice versa. Everyone who is patient is rich or not wise and vice versa. If fred is both funny and not patient then lucy is tall and vice versa. Everyone who is strong or not humble is not quiet or not generous and vice versa. Everyone who is not tall is both happy and not wise. Someone is either not strong or not quiet. Fred is both not calm and brave. Someone is both rich and not tall. Someone is either not humble or not generous. Someone is both wise and rich. | Susan is not happy. | neutral | ((?[X]:(~rich(X)))=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(((~kind(susan)|~funny(susan)))<=>(?[X]:((~rich(X)|creative(X)))))&
(![X]:(~strong(X)=>(humble(X)&calm(X))))&
(![X]:((wise(X)|humble(X))<=>(quiet(X)&~funny(X))))&
(![X]:(~generous(X)=>~old(X)))&
((creative(paul))<=>((rich(lucy)&~wise(lucy))))&
(![X]:((tall(X)<~>wise(X))=>(~strong(X)<~>~calm(X))))&
(![X]:((strong(X)|creative(X))=>(~curious(X)&generous(X))))&
((?[X]:((wise(X)&kind(X))))<=>((humble(alice)&tall(alice))))&
((?[X]:((~wise(X)<~>~happy(X))))<=>((~humble(paul)|kind(paul))))&
((?[X]:((~happy(X)|~rich(X))))<=>(?[X]:((patient(X)&generous(X)))))&
(![X]:(patient(X)<=>(rich(X)|~wise(X))))&
(((funny(fred)&~patient(fred)))<=>(tall(lucy)))&
(![X]:((strong(X)|~humble(X))<=>(~quiet(X)|~generous(X))))&
(![X]:(~tall(X)=>(happy(X)&~wise(X))))&
(?[X]:((~strong(X)<~>~quiet(X))))&
((~calm(fred)&brave(fred)))&
(?[X]:((rich(X)&~tall(X))))&
(?[X]:((~humble(X)<~>~generous(X))))&
(?[X]:((wise(X)&rich(X)))) | ~happy(susan) | [] | null | 0 |
Everyone who is brave is either quiet or not funny.
If someone is either not happy or not humble then someone is not creative.
Everyone who is either not kind or wise is not funny and vice versa.
If someone is either not humble or not brave then paul is tall or not brave.
Everyone who is not quiet or not rich is not quiet.
If someone is either generous or not generous then someone is either not curious or humble and vice versa.
Everyone who is either not rich or not wise is either strong or not wise.
If someone is both not humble and old then susan is both patient and not kind and vice versa.
Everyone who is not calm or brave is either patient or not wise and vice versa.
If someone is both not rich and kind then paul is both generous and quiet and vice versa.
If someone is both not calm and not patient then someone is not kind or not calm.
Everyone who is not calm is humble or old.
Everyone who is not happy or old is not funny.
Everyone who is either patient or not brave is both not calm and not tall.
If john is old then someone is not old and vice versa.
Everyone who is either wise or not happy is happy and vice versa.
John is strong or not kind.
Someone is happy or not rich.
Someone is both patient and kind.
Someone is either brave or not old.
Susan is not kind or not old.
Someone is either patient or brave.
Lucy is generous or not rich.
Someone is not patient or strong. | Lucy is generous. | neutral | (![X]:(brave(X)=>(quiet(X)<~>~funny(X))))&
((?[X]:((~happy(X)<~>~humble(X))))=>(?[X]:(~creative(X))))&
(![X]:((~kind(X)<~>wise(X))<=>~funny(X)))&
((?[X]:((~humble(X)<~>~brave(X))))=>((tall(paul)|~brave(paul))))&
(![X]:((~quiet(X)|~rich(X))=>~quiet(X)))&
((?[X]:((generous(X)<~>~generous(X))))<=>(?[X]:((~curious(X)<~>humble(X)))))&
(![X]:((~rich(X)<~>~wise(X))=>(strong(X)<~>~wise(X))))&
((?[X]:((~humble(X)&old(X))))<=>((patient(susan)&~kind(susan))))&
(![X]:((~calm(X)|brave(X))<=>(patient(X)<~>~wise(X))))&
((?[X]:((~rich(X)&kind(X))))<=>((generous(paul)&quiet(paul))))&
((?[X]:((~calm(X)&~patient(X))))=>(?[X]:((~kind(X)|~calm(X)))))&
(![X]:(~calm(X)=>(humble(X)|old(X))))&
(![X]:((~happy(X)|old(X))=>~funny(X)))&
(![X]:((patient(X)<~>~brave(X))=>(~calm(X)&~tall(X))))&
((old(john))<=>(?[X]:(~old(X))))&
(![X]:((wise(X)<~>~happy(X))<=>happy(X)))&
((strong(john)|~kind(john)))&
(?[X]:((happy(X)|~rich(X))))&
(?[X]:((patient(X)&kind(X))))&
(?[X]:((brave(X)<~>~old(X))))&
((~kind(susan)|~old(susan)))&
(?[X]:((patient(X)<~>brave(X))))&
((generous(lucy)|~rich(lucy)))&
(?[X]:((~patient(X)|strong(X)))) | generous(lucy) | [] | null | 0 |
Everyone who is not generous is funny or not patient.
Everyone who is either not brave or generous is both not tall and happy.
Everyone who is both not kind and not patient is not tall.
If paul is either humble or patient then someone is patient or not old.
Everyone who is both not happy and creative is not curious or brave.
Everyone who is either creative or not quiet is strong or not creative and vice versa.
If susan is not rich or quiet then someone is patient or funny.
If fred is not funny or curious then someone is both strong and not happy and vice versa.
Everyone who is funny is not strong and vice versa.
If someone is strong or generous then someone is not creative or not generous and vice versa.
If lucy is tall or happy then someone is not generous and vice versa.
If susan is brave then lucy is not generous and vice versa.
Everyone who is either not generous or generous is not creative or not generous and vice versa.
If alice is rich then someone is not calm and vice versa.
Everyone who is old is both humble and not funny and vice versa.
If susan is funny or calm then mary is happy.
Fred is not patient.
John is not calm.
Mary is not strong or humble.
Someone is not rich or not generous.
Paul is both not funny and not calm.
Lucy is both creative and quiet.
Someone is both funny and rich.
Susan is both old and wise. | Alice is not curious. | neutral | (![X]:(~generous(X)=>(funny(X)|~patient(X))))&
(![X]:((~brave(X)<~>generous(X))=>(~tall(X)&happy(X))))&
(![X]:((~kind(X)&~patient(X))=>~tall(X)))&
(((humble(paul)<~>patient(paul)))=>(?[X]:((patient(X)|~old(X)))))&
(![X]:((~happy(X)&creative(X))=>(~curious(X)|brave(X))))&
(![X]:((creative(X)<~>~quiet(X))<=>(strong(X)|~creative(X))))&
(((~rich(susan)|quiet(susan)))=>(?[X]:((patient(X)|funny(X)))))&
(((~funny(fred)|curious(fred)))<=>(?[X]:((strong(X)&~happy(X)))))&
(![X]:(funny(X)<=>~strong(X)))&
((?[X]:((strong(X)|generous(X))))<=>(?[X]:((~creative(X)|~generous(X)))))&
(((tall(lucy)|happy(lucy)))<=>(?[X]:(~generous(X))))&
((brave(susan))<=>(~generous(lucy)))&
(![X]:((~generous(X)<~>generous(X))<=>(~creative(X)|~generous(X))))&
((rich(alice))<=>(?[X]:(~calm(X))))&
(![X]:(old(X)<=>(humble(X)&~funny(X))))&
(((funny(susan)|calm(susan)))=>(happy(mary)))&
(~patient(fred))&
(~calm(john))&
((~strong(mary)|humble(mary)))&
(?[X]:((~rich(X)|~generous(X))))&
((~funny(paul)&~calm(paul)))&
((creative(lucy)&quiet(lucy)))&
(?[X]:((funny(X)&rich(X))))&
((old(susan)&wise(susan))) | ~curious(alice) | [] | null | 0 |
If fred is generous or not quiet then fred is kind or not rich. Everyone who is happy is not generous or quiet. Everyone who is not creative is generous or not wise and vice versa. Everyone who is either old or quiet is kind or not calm. If paul is either not happy or not quiet then paul is not tall or creative. Everyone who is creative or not wise is either wise or not calm. Everyone who is both not curious and tall is tall or creative and vice versa. Everyone who is not funny or generous is happy or not humble. If mary is not calm then susan is both not wise and patient and vice versa. If susan is either not curious or funny then paul is generous or quiet. Everyone who is both not old and happy is not patient or not humble. Everyone who is either not funny or creative is both old and happy and vice versa. Everyone who is not funny is both not curious and creative. If alice is either not brave or humble then someone is not kind or not strong and vice versa. If susan is not generous or not rich then john is not strong and vice versa. Everyone who is brave or not funny is not humble. Alice is both not wise and quiet. Lucy is not tall or not calm. Someone is creative or kind. Someone is not old. Paul is either curious or patient. Someone is not tall or not humble. Paul is humble. Someone is happy. | Fred is brave. | neutral | (((generous(fred)|~quiet(fred)))=>((kind(fred)|~rich(fred))))&
(![X]:(happy(X)=>(~generous(X)|quiet(X))))&
(![X]:(~creative(X)<=>(generous(X)|~wise(X))))&
(![X]:((old(X)<~>quiet(X))=>(kind(X)|~calm(X))))&
(((~happy(paul)<~>~quiet(paul)))=>((~tall(paul)|creative(paul))))&
(![X]:((creative(X)|~wise(X))=>(wise(X)<~>~calm(X))))&
(![X]:((~curious(X)&tall(X))<=>(tall(X)|creative(X))))&
(![X]:((~funny(X)|generous(X))=>(happy(X)|~humble(X))))&
((~calm(mary))<=>((~wise(susan)&patient(susan))))&
(((~curious(susan)<~>funny(susan)))=>((generous(paul)|quiet(paul))))&
(![X]:((~old(X)&happy(X))=>(~patient(X)|~humble(X))))&
(![X]:((~funny(X)<~>creative(X))<=>(old(X)&happy(X))))&
(![X]:(~funny(X)=>(~curious(X)&creative(X))))&
(((~brave(alice)<~>humble(alice)))<=>(?[X]:((~kind(X)|~strong(X)))))&
(((~generous(susan)|~rich(susan)))<=>(~strong(john)))&
(![X]:((brave(X)|~funny(X))=>~humble(X)))&
((~wise(alice)&quiet(alice)))&
((~tall(lucy)|~calm(lucy)))&
(?[X]:((creative(X)|kind(X))))&
(?[X]:(~old(X)))&
((curious(paul)<~>patient(paul)))&
(?[X]:((~tall(X)|~humble(X))))&
(humble(paul))&
(?[X]:(happy(X))) | brave(fred) | [] | null | 0 |
Everyone who is both not quiet and kind is curious and vice versa.
Everyone who is not curious or not happy is either curious or humble and vice versa.
If john is not generous then fred is not old or brave.
Everyone who is wise is not funny and vice versa.
If someone is both rich and not wise then someone is either quiet or brave.
If someone is old or curious then susan is not strong or curious and vice versa.
Everyone who is either brave or not creative is wise.
Everyone who is either creative or not old is not rich or quiet.
If someone is either not creative or not patient then someone is both not quiet and patient.
If paul is kind then paul is calm and vice versa.
If susan is not curious or curious then someone is not generous or strong.
If susan is both humble and old then john is both wise and funny.
Everyone who is quiet or old is old and vice versa.
Everyone who is either patient or funny is patient and vice versa.
Everyone who is not curious is not strong or patient.
Everyone who is old or funny is calm and vice versa.
Someone is both not quiet and brave.
Someone is not old.
Lucy is either not brave or not strong.
Lucy is not quiet or not tall.
Fred is both brave and happy.
Fred is not generous.
Someone is happy or not funny.
Someone is either old or not tall. | Lucy is not tall. | neutral | (![X]:((~quiet(X)&kind(X))<=>curious(X)))&
(![X]:((~curious(X)|~happy(X))<=>(curious(X)<~>humble(X))))&
((~generous(john))=>((~old(fred)|brave(fred))))&
(![X]:(wise(X)<=>~funny(X)))&
((?[X]:((rich(X)&~wise(X))))=>(?[X]:((quiet(X)<~>brave(X)))))&
((?[X]:((old(X)|curious(X))))<=>((~strong(susan)|curious(susan))))&
(![X]:((brave(X)<~>~creative(X))=>wise(X)))&
(![X]:((creative(X)<~>~old(X))=>(~rich(X)|quiet(X))))&
((?[X]:((~creative(X)<~>~patient(X))))=>(?[X]:((~quiet(X)&patient(X)))))&
((kind(paul))<=>(calm(paul)))&
(((~curious(susan)|curious(susan)))=>(?[X]:((~generous(X)|strong(X)))))&
(((humble(susan)&old(susan)))=>((wise(john)&funny(john))))&
(![X]:((quiet(X)|old(X))<=>old(X)))&
(![X]:((patient(X)<~>funny(X))<=>patient(X)))&
(![X]:(~curious(X)=>(~strong(X)|patient(X))))&
(![X]:((old(X)|funny(X))<=>calm(X)))&
(?[X]:((~quiet(X)&brave(X))))&
(?[X]:(~old(X)))&
((~brave(lucy)<~>~strong(lucy)))&
((~quiet(lucy)|~tall(lucy)))&
((brave(fred)&happy(fred)))&
(~generous(fred))&
(?[X]:((happy(X)|~funny(X))))&
(?[X]:((old(X)<~>~tall(X)))) | ~tall(lucy) | [] | null | 0 |
Everyone who is either not kind or not calm is creative or not kind and vice versa.
Everyone who is both funny and not calm is generous.
If someone is not strong then john is both not wise and not brave and vice versa.
Everyone who is quiet is both not strong and not brave.
Everyone who is kind or wise is both not brave and not calm.
If someone is not brave then someone is tall and vice versa.
Everyone who is both tall and patient is either not creative or not calm and vice versa.
If susan is both not happy and not calm then susan is both curious and not quiet.
Everyone who is both not patient and not kind is not creative and vice versa.
Everyone who is calm or not calm is either not creative or brave and vice versa.
Everyone who is both tall and not calm is not brave.
Everyone who is not quiet is both creative and strong.
If someone is both not funny and strong then mary is not quiet and vice versa.
Everyone who is both creative and not kind is either not rich or patient.
If someone is quiet or rich then susan is either calm or quiet and vice versa.
John is not quiet.
Someone is either humble or funny.
Susan is not old.
Lucy is not kind or kind.
Mary is both not kind and curious.
Fred is not rich or funny.
Someone is not quiet or calm. | Susan is not tall. | entailment | (![X]:((~kind(X)<~>~calm(X))<=>(creative(X)|~kind(X))))&
(![X]:((funny(X)&~calm(X))=>generous(X)))&
((?[X]:(~strong(X)))<=>((~wise(john)&~brave(john))))&
(![X]:(quiet(X)=>(~strong(X)&~brave(X))))&
(![X]:((kind(X)|wise(X))=>(~brave(X)&~calm(X))))&
((?[X]:(~brave(X)))<=>(?[X]:(tall(X))))&
(![X]:((tall(X)&patient(X))<=>(~creative(X)<~>~calm(X))))&
(((~happy(susan)&~calm(susan)))=>((curious(susan)&~quiet(susan))))&
(![X]:((~patient(X)&~kind(X))<=>~creative(X)))&
(![X]:((calm(X)|~calm(X))<=>(~creative(X)<~>brave(X))))&
(![X]:((tall(X)&~calm(X))=>~brave(X)))&
(![X]:(~quiet(X)=>(creative(X)&strong(X))))&
((?[X]:((~funny(X)&strong(X))))<=>(~quiet(mary)))&
(![X]:((creative(X)&~kind(X))=>(~rich(X)<~>patient(X))))&
((?[X]:((quiet(X)|rich(X))))<=>((calm(susan)<~>quiet(susan))))&
(~quiet(john))&
(?[X]:((humble(X)<~>funny(X))))&
(~old(susan))&
((~kind(lucy)|kind(lucy)))&
((~kind(mary)&curious(mary)))&
((~rich(fred)|funny(fred)))&
(?[X]:((~quiet(X)|calm(X)))) | ~tall(susan) | [
"p0",
"p5",
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8780880698565340827822612
% SZS output start Proof for 8780880698565340827822612
1. ! [X0] : ((~kind(X0) <~> ~calm(X0)) <=> (~kind(X0) | creative(X0))) [input p0]
6. ? [X0] : ~brave(X0) <=> ? [X0] : tall(X0) [input p5]
7. ! [X0] : ((patient(X0) & tall(X0)) <=> (~creative(X0) <~> ~calm(X0))) [input p6]
9. ! [X0] : ((~kind(X0) & ~patient(X0)) <=> ~creative(X0)) [input p8]
10. ! [X0] : ((~calm(X0) | calm(X0)) <=> (~creative(X0) <~> brave(X0))) [input p9]
23. tall(susan) [input hypothesis]
24. ? [X0] : ~brave(X0) <=> ? [X1] : tall(X1) [rectify 6]
37. ! [X0] : ((((calm(X0) | kind(X0)) & (~calm(X0) | ~kind(X0))) | (kind(X0) & ~creative(X0))) & ((~kind(X0) | creative(X0)) | ((~kind(X0) | calm(X0)) & (~calm(X0) | kind(X0))))) [nnf transformation 1]
38. ! [X0] : ((((calm(X0) | kind(X0)) & (~calm(X0) | ~kind(X0))) | (kind(X0) & ~creative(X0))) & (~kind(X0) | creative(X0) | ((~kind(X0) | calm(X0)) & (~calm(X0) | kind(X0))))) [flattening 37]
44. (? [X0] : ~brave(X0) | ! [X1] : ~tall(X1)) & (? [X1] : tall(X1) | ! [X0] : brave(X0)) [nnf transformation 24]
45. (? [X0] : ~brave(X0) | ! [X1] : ~tall(X1)) & (? [X2] : tall(X2) | ! [X3] : brave(X3)) [rectify 44]
46. ? [X0] : ~brave(X0) => ~brave(sK1) [choice axiom]
47. ? [X2] : tall(X2) => tall(sK2) [choice axiom]
48. (~brave(sK1) | ! [X1] : ~tall(X1)) & (tall(sK2) | ! [X3] : brave(X3)) [skolemisation 45,47,46]
49. ! [X0] : (((patient(X0) & tall(X0)) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0)))) & (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | (~patient(X0) | ~tall(X0)))) [nnf transformation 7]
50. ! [X0] : (((patient(X0) & tall(X0)) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0)))) & (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | ~patient(X0) | ~tall(X0))) [flattening 49]
51. ! [X0] : (((~kind(X0) & ~patient(X0)) | creative(X0)) & (~creative(X0) | (kind(X0) | patient(X0)))) [nnf transformation 9]
52. ! [X0] : (((~kind(X0) & ~patient(X0)) | creative(X0)) & (~creative(X0) | kind(X0) | patient(X0))) [flattening 51]
53. ! [X0] : (((~calm(X0) | calm(X0)) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | (calm(X0) & ~calm(X0)))) [nnf transformation 10]
54. ! [X0] : ((~calm(X0) | calm(X0) | ((~creative(X0) | ~brave(X0)) & (brave(X0) | creative(X0)))) & (((~brave(X0) | creative(X0)) & (brave(X0) | ~creative(X0))) | (calm(X0) & ~calm(X0)))) [flattening 53]
70. ~kind(X0) | creative(X0) | ~kind(X0) | calm(X0) [cnf transformation 38]
74. calm(X0) | kind(X0) | kind(X0) [cnf transformation 38]
85. ~brave(sK1) | ~tall(X1) [cnf transformation 48]
90. patient(X0) | ~calm(X0) | creative(X0) [cnf transformation 50]
93. ~patient(X0) | creative(X0) [cnf transformation 52]
95. brave(X0) | ~creative(X0) | ~calm(X0) [cnf transformation 54]
96. brave(X0) | ~creative(X0) | calm(X0) [cnf transformation 54]
122. tall(susan) [cnf transformation 23]
123. ~kind(X0) | creative(X0) | calm(X0) [duplicate literal removal 70]
124. calm(X0) | kind(X0) [duplicate literal removal 74]
125. creative(X0) | calm(X0) [subsumption resolution 123,124]
145. 5 <=> ! [X1] : ~tall(X1) [avatar definition]
146. ~tall(X1) <- (5) [avatar component clause 145]
148. 6 <=> brave(sK1) [avatar definition]
150. ~brave(sK1) <- (~6) [avatar component clause 148]
151. 5 | ~6 [avatar split clause 85,148,145]
153. 7 <=> ! [X3] : brave(X3) [avatar definition]
154. brave(X3) <- (7) [avatar component clause 153]
161. patient(X0) | creative(X0) [subsumption resolution 90,125]
164. creative(X0) [subsumption resolution 93,161]
166. brave(X0) | calm(X0) [subsumption resolution 96,164]
167. brave(X0) | ~calm(X0) [subsumption resolution 95,164]
168. brave(X0) [subsumption resolution 167,166]
169. 7 [avatar split clause 168,153]
235. $false <- (~6, 7) [subsumption resolution 150,154]
236. 6 | ~7 [avatar contradiction clause 235]
241. $false <- (5) [resolution 146,122]
242. ~5 [avatar contradiction clause 241]
243. $false [avatar sat refutation 151,169,236,242]
% SZS output end Proof for 8780880698565340827822612
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both calm and not brave then someone is either humble or not generous and vice versa. If lucy is happy or brave then mary is either not generous or rich. Everyone who is quiet or humble is either old or not wise and vice versa. Everyone who is not curious or not brave is not kind and vice versa. If someone is both curious and tall then paul is rich or not calm. If mary is both rich and quiet then someone is curious. Everyone who is not quiet is not strong or not brave and vice versa. Everyone who is not funny or not brave is not patient or brave and vice versa. If fred is not brave or not strong then someone is wise or not creative. If someone is not quiet then someone is curious and vice versa. If someone is generous or calm then someone is wise and vice versa. If someone is not quiet then someone is not old and vice versa. Everyone who is both not rich and not strong is creative. If fred is either wise or not kind then someone is patient and vice versa. Everyone who is both brave and kind is not tall or not kind and vice versa. Everyone who is not generous is either not calm or happy. Someone is both humble and not strong. Someone is either not brave or strong. Susan is either not funny or happy. Lucy is both curious and humble. Someone is either not humble or funny. Lucy is not quiet. | Susan is not rich. | neutral | (((calm(fred)&~brave(fred)))<=>(?[X]:((humble(X)<~>~generous(X)))))&
(((happy(lucy)|brave(lucy)))=>((~generous(mary)<~>rich(mary))))&
(![X]:((quiet(X)|humble(X))<=>(old(X)<~>~wise(X))))&
(![X]:((~curious(X)|~brave(X))<=>~kind(X)))&
((?[X]:((curious(X)&tall(X))))=>((rich(paul)|~calm(paul))))&
(((rich(mary)&quiet(mary)))=>(?[X]:(curious(X))))&
(![X]:(~quiet(X)<=>(~strong(X)|~brave(X))))&
(![X]:((~funny(X)|~brave(X))<=>(~patient(X)|brave(X))))&
(((~brave(fred)|~strong(fred)))=>(?[X]:((wise(X)|~creative(X)))))&
((?[X]:(~quiet(X)))<=>(?[X]:(curious(X))))&
((?[X]:((generous(X)|calm(X))))<=>(?[X]:(wise(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:(~old(X))))&
(![X]:((~rich(X)&~strong(X))=>creative(X)))&
(((wise(fred)<~>~kind(fred)))<=>(?[X]:(patient(X))))&
(![X]:((brave(X)&kind(X))<=>(~tall(X)|~kind(X))))&
(![X]:(~generous(X)=>(~calm(X)<~>happy(X))))&
(?[X]:((humble(X)&~strong(X))))&
(?[X]:((~brave(X)<~>strong(X))))&
((~funny(susan)<~>happy(susan)))&
((curious(lucy)&humble(lucy)))&
(?[X]:((~humble(X)<~>funny(X))))&
(~quiet(lucy)) | ~rich(susan) | [] | null | 0 |
Everyone who is not old is rich or patient and vice versa.
Everyone who is both creative and old is both strong and happy.
If someone is not creative or strong then someone is either not funny or tall and vice versa.
Everyone who is not strong or not old is strong or not old.
Everyone who is both quiet and tall is either happy or not rich and vice versa.
Everyone who is not tall or funny is either not happy or not wise.
If someone is kind then someone is brave.
If someone is brave then someone is either not strong or not kind.
Everyone who is not patient or not wise is not generous.
If paul is both not strong and not curious then john is not rich or rich and vice versa.
Everyone who is either generous or brave is either calm or not generous and vice versa.
If susan is generous then someone is both old and not wise and vice versa.
Everyone who is both not funny and kind is both funny and not rich.
Everyone who is both strong and rich is either quiet or rich.
Everyone who is not funny is both humble and curious and vice versa.
Everyone who is either quiet or not tall is not old or not patient.
Someone is kind or creative.
Paul is either not old or not patient.
Susan is both wise and patient.
Someone is both not tall and not happy.
Someone is either rich or not tall.
Someone is not rich or not strong.
Someone is rich or funny.
John is either not old or not curious. | Paul is wise. | neutral | (![X]:(~old(X)<=>(rich(X)|patient(X))))&
(![X]:((creative(X)&old(X))=>(strong(X)&happy(X))))&
((?[X]:((~creative(X)|strong(X))))<=>(?[X]:((~funny(X)<~>tall(X)))))&
(![X]:((~strong(X)|~old(X))=>(strong(X)|~old(X))))&
(![X]:((quiet(X)&tall(X))<=>(happy(X)<~>~rich(X))))&
(![X]:((~tall(X)|funny(X))=>(~happy(X)<~>~wise(X))))&
((?[X]:(kind(X)))=>(?[X]:(brave(X))))&
((?[X]:(brave(X)))=>(?[X]:((~strong(X)<~>~kind(X)))))&
(![X]:((~patient(X)|~wise(X))=>~generous(X)))&
(((~strong(paul)&~curious(paul)))<=>((~rich(john)|rich(john))))&
(![X]:((generous(X)<~>brave(X))<=>(calm(X)<~>~generous(X))))&
((generous(susan))<=>(?[X]:((old(X)&~wise(X)))))&
(![X]:((~funny(X)&kind(X))=>(funny(X)&~rich(X))))&
(![X]:((strong(X)&rich(X))=>(quiet(X)<~>rich(X))))&
(![X]:(~funny(X)<=>(humble(X)&curious(X))))&
(![X]:((quiet(X)<~>~tall(X))=>(~old(X)|~patient(X))))&
(?[X]:((kind(X)|creative(X))))&
((~old(paul)<~>~patient(paul)))&
((wise(susan)&patient(susan)))&
(?[X]:((~tall(X)&~happy(X))))&
(?[X]:((rich(X)<~>~tall(X))))&
(?[X]:((~rich(X)|~strong(X))))&
(?[X]:((rich(X)|funny(X))))&
((~old(john)<~>~curious(john))) | wise(paul) | [] | null | 0 |
Everyone who is either not strong or tall is either happy or not humble and vice versa.
If mary is either not creative or not quiet then alice is patient or not patient.
Everyone who is either not happy or old is either patient or not humble and vice versa.
Everyone who is old is not happy or not calm.
If someone is happy or tall then mary is both not patient and not tall.
Everyone who is curious is both not creative and rich and vice versa.
If alice is not curious then alice is both strong and creative and vice versa.
If someone is tall then lucy is kind or not creative.
Everyone who is funny or creative is either not tall or happy.
If someone is both quiet and humble then mary is either not rich or not creative.
Everyone who is not creative or not brave is either not patient or not rich and vice versa.
If susan is kind then fred is either funny or not brave and vice versa.
Everyone who is strong is not tall.
If someone is not patient or happy then someone is either calm or not calm.
Everyone who is both not patient and not rich is both wise and not patient and vice versa.
Everyone who is not generous or not patient is either patient or not quiet and vice versa.
Someone is both curious and not strong.
Mary is either not calm or humble.
John is not happy.
Lucy is quiet or funny.
Lucy is wise.
John is patient or not funny.
Someone is either quiet or brave.
Fred is either not rich or old. | Lucy is not curious. | entailment | (![X]:((~strong(X)<~>tall(X))<=>(happy(X)<~>~humble(X))))&
(((~creative(mary)<~>~quiet(mary)))=>((patient(alice)|~patient(alice))))&
(![X]:((~happy(X)<~>old(X))<=>(patient(X)<~>~humble(X))))&
(![X]:(old(X)=>(~happy(X)|~calm(X))))&
((?[X]:((happy(X)|tall(X))))=>((~patient(mary)&~tall(mary))))&
(![X]:(curious(X)<=>(~creative(X)&rich(X))))&
((~curious(alice))<=>((strong(alice)&creative(alice))))&
((?[X]:(tall(X)))=>((kind(lucy)|~creative(lucy))))&
(![X]:((funny(X)|creative(X))=>(~tall(X)<~>happy(X))))&
((?[X]:((quiet(X)&humble(X))))=>((~rich(mary)<~>~creative(mary))))&
(![X]:((~creative(X)|~brave(X))<=>(~patient(X)<~>~rich(X))))&
((kind(susan))<=>((funny(fred)<~>~brave(fred))))&
(![X]:(strong(X)=>~tall(X)))&
((?[X]:((~patient(X)|happy(X))))=>(?[X]:((calm(X)<~>~calm(X)))))&
(![X]:((~patient(X)&~rich(X))<=>(wise(X)&~patient(X))))&
(![X]:((~generous(X)|~patient(X))<=>(patient(X)<~>~quiet(X))))&
(?[X]:((curious(X)&~strong(X))))&
((~calm(mary)<~>humble(mary)))&
(~happy(john))&
((quiet(lucy)|funny(lucy)))&
(wise(lucy))&
((patient(john)|~funny(john)))&
(?[X]:((quiet(X)<~>brave(X))))&
((~rich(fred)<~>old(fred))) | ~curious(lucy) | [
"p5",
"p10",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 422739066928599001857440
% SZS output start Proof for 422739066928599001857440
6. ! [X0] : (curious(X0) <=> (rich(X0) & ~creative(X0))) [input p5]
11. ! [X0] : ((~brave(X0) | ~creative(X0)) <=> (~patient(X0) <~> ~rich(X0))) [input p10]
15. ! [X0] : ((~rich(X0) & ~patient(X0)) <=> (~patient(X0) & wise(X0))) [input p14]
21. wise(lucy) [input p20]
25. curious(lucy) [input hypothesis]
41. ! [X0] : ((curious(X0) | (~rich(X0) | creative(X0))) & ((rich(X0) & ~creative(X0)) | ~curious(X0))) [nnf transformation 6]
42. ! [X0] : ((curious(X0) | ~rich(X0) | creative(X0)) & ((rich(X0) & ~creative(X0)) | ~curious(X0))) [flattening 41]
47. ! [X0] : (((~brave(X0) | ~creative(X0)) | ((~patient(X0) | rich(X0)) & (~rich(X0) | patient(X0)))) & (((rich(X0) | patient(X0)) & (~rich(X0) | ~patient(X0))) | (brave(X0) & creative(X0)))) [nnf transformation 11]
48. ! [X0] : ((~brave(X0) | ~creative(X0) | ((~patient(X0) | rich(X0)) & (~rich(X0) | patient(X0)))) & (((rich(X0) | patient(X0)) & (~rich(X0) | ~patient(X0))) | (brave(X0) & creative(X0)))) [flattening 47]
54. ! [X0] : (((~rich(X0) & ~patient(X0)) | (patient(X0) | ~wise(X0))) & ((~patient(X0) & wise(X0)) | (rich(X0) | patient(X0)))) [nnf transformation 15]
55. ! [X0] : (((~rich(X0) & ~patient(X0)) | patient(X0) | ~wise(X0)) & ((~patient(X0) & wise(X0)) | rich(X0) | patient(X0))) [flattening 54]
88. ~curious(X0) | ~creative(X0) [cnf transformation 42]
89. ~curious(X0) | rich(X0) [cnf transformation 42]
101. ~rich(X0) | ~patient(X0) | creative(X0) [cnf transformation 48]
119. ~wise(X0) | patient(X0) | ~rich(X0) [cnf transformation 55]
132. wise(lucy) [cnf transformation 21]
138. curious(lucy) [cnf transformation 25]
178. 9 <=> creative(lucy) [avatar definition]
260. ~creative(lucy) [resolution 88,138]
264. rich(lucy) [resolution 89,138]
274. ~patient(lucy) | creative(lucy) [resolution 101,264]
282. ~9 [avatar split clause 260,178]
284. 26 <=> patient(lucy) [avatar definition]
286. ~patient(lucy) <- (~26) [avatar component clause 284]
287. 9 | ~26 [avatar split clause 274,284,178]
340. patient(lucy) | ~rich(lucy) [resolution 119,132]
343. ~rich(lucy) <- (~26) [subsumption resolution 340,286]
344. $false <- (~26) [subsumption resolution 343,264]
345. 26 [avatar contradiction clause 344]
346. $false [avatar sat refutation 282,287,345]
% SZS output end Proof for 422739066928599001857440
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and not wise then someone is either calm or curious.
Everyone who is calm or not creative is humble or not humble.
Everyone who is not rich or quiet is not patient and vice versa.
Everyone who is both not generous and not old is not funny and vice versa.
Everyone who is either happy or not kind is not wise or strong.
If someone is either not calm or not rich then someone is kind or not kind and vice versa.
Everyone who is either curious or not old is both creative and humble and vice versa.
Everyone who is both not brave and generous is not rich and vice versa.
If someone is either not quiet or creative then someone is patient and vice versa.
Everyone who is not funny or strong is strong or not generous and vice versa.
If someone is not quiet or curious then lucy is humble or happy.
Everyone who is either humble or curious is not humble.
Everyone who is calm or strong is both strong and not strong.
Everyone who is both brave and not funny is not strong or creative and vice versa.
Everyone who is wise is rich.
Mary is kind.
Paul is either tall or rich.
Alice is either old or patient.
Someone is either not happy or not kind.
Mary is not creative or wise.
Someone is either creative or funny.
Lucy is not old. | Lucy is tall. | neutral | ((?[X]:((~rich(X)&~wise(X))))=>(?[X]:((calm(X)<~>curious(X)))))&
(![X]:((calm(X)|~creative(X))=>(humble(X)|~humble(X))))&
(![X]:((~rich(X)|quiet(X))<=>~patient(X)))&
(![X]:((~generous(X)&~old(X))<=>~funny(X)))&
(![X]:((happy(X)<~>~kind(X))=>(~wise(X)|strong(X))))&
((?[X]:((~calm(X)<~>~rich(X))))<=>(?[X]:((kind(X)|~kind(X)))))&
(![X]:((curious(X)<~>~old(X))<=>(creative(X)&humble(X))))&
(![X]:((~brave(X)&generous(X))<=>~rich(X)))&
((?[X]:((~quiet(X)<~>creative(X))))<=>(?[X]:(patient(X))))&
(![X]:((~funny(X)|strong(X))<=>(strong(X)|~generous(X))))&
((?[X]:((~quiet(X)|curious(X))))=>((humble(lucy)|happy(lucy))))&
(![X]:((humble(X)<~>curious(X))=>~humble(X)))&
(![X]:((calm(X)|strong(X))=>(strong(X)&~strong(X))))&
(![X]:((brave(X)&~funny(X))<=>(~strong(X)|creative(X))))&
(![X]:(wise(X)=>rich(X)))&
(kind(mary))&
((tall(paul)<~>rich(paul)))&
((old(alice)<~>patient(alice)))&
(?[X]:((~happy(X)<~>~kind(X))))&
((~creative(mary)|wise(mary)))&
(?[X]:((creative(X)<~>funny(X))))&
(~old(lucy)) | tall(lucy) | [] | null | 0 |
Everyone who is old or patient is either kind or not quiet. Everyone who is creative or not generous is both generous and not calm and vice versa. If susan is not wise then someone is both old and rich. If lucy is either creative or wise then someone is both not curious and humble. Everyone who is brave or not tall is both tall and quiet. Everyone who is both wise and not quiet is either not patient or not generous. If someone is not happy or not patient then someone is not humble. If fred is either not curious or tall then someone is curious. If fred is curious or strong then mary is either not happy or brave. If mary is quiet then someone is rich or not brave. If someone is not quiet then someone is either not creative or curious and vice versa. Everyone who is both not happy and funny is generous or not old and vice versa. Everyone who is not calm or not brave is either old or tall and vice versa. Everyone who is either old or not calm is either not humble or funny and vice versa. If someone is both not calm and not humble then john is curious or not calm. If someone is both kind and humble then fred is old. Lucy is both not strong and old. John is not happy. Someone is old. Someone is either not quiet or tall. Fred is not creative. Paul is not happy. | Lucy is generous. | entailment | (![X]:((old(X)|patient(X))=>(kind(X)<~>~quiet(X))))&
(![X]:((creative(X)|~generous(X))<=>(generous(X)&~calm(X))))&
((~wise(susan))=>(?[X]:((old(X)&rich(X)))))&
(((creative(lucy)<~>wise(lucy)))=>(?[X]:((~curious(X)&humble(X)))))&
(![X]:((brave(X)|~tall(X))=>(tall(X)&quiet(X))))&
(![X]:((wise(X)&~quiet(X))=>(~patient(X)<~>~generous(X))))&
((?[X]:((~happy(X)|~patient(X))))=>(?[X]:(~humble(X))))&
(((~curious(fred)<~>tall(fred)))=>(?[X]:(curious(X))))&
(((curious(fred)|strong(fred)))=>((~happy(mary)<~>brave(mary))))&
((quiet(mary))=>(?[X]:((rich(X)|~brave(X)))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~creative(X)<~>curious(X)))))&
(![X]:((~happy(X)&funny(X))<=>(generous(X)|~old(X))))&
(![X]:((~calm(X)|~brave(X))<=>(old(X)<~>tall(X))))&
(![X]:((old(X)<~>~calm(X))<=>(~humble(X)<~>funny(X))))&
((?[X]:((~calm(X)&~humble(X))))=>((curious(john)|~calm(john))))&
((?[X]:((kind(X)&humble(X))))=>(old(fred)))&
((~strong(lucy)&old(lucy)))&
(~happy(john))&
(?[X]:(old(X)))&
(?[X]:((~quiet(X)<~>tall(X))))&
(~creative(fred))&
(~happy(paul)) | generous(lucy) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 5246090116571099166136317
% SZS output start Proof for 5246090116571099166136317
2. ! [X0] : ((~generous(X0) | creative(X0)) <=> (~calm(X0) & generous(X0))) [input p1]
23. ~generous(lucy) [input hypothesis]
43. ! [X0] : (((~generous(X0) | creative(X0)) | (calm(X0) | ~generous(X0))) & ((~calm(X0) & generous(X0)) | (generous(X0) & ~creative(X0)))) [nnf transformation 2]
44. ! [X0] : ((~generous(X0) | creative(X0) | calm(X0) | ~generous(X0)) & ((~calm(X0) & generous(X0)) | (generous(X0) & ~creative(X0)))) [flattening 43]
78. generous(X0) | generous(X0) [cnf transformation 44]
131. ~generous(lucy) [cnf transformation 23]
133. generous(X0) [duplicate literal removal 78]
241. $false [subsumption resolution 131,133]
% SZS output end Proof for 5246090116571099166136317
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or not generous is creative.
If alice is patient or not old then lucy is either calm or brave and vice versa.
Everyone who is both not tall and tall is either calm or not creative and vice versa.
Everyone who is not brave or not quiet is either rich or strong.
If alice is both funny and not creative then fred is funny or not calm and vice versa.
If fred is not happy or not humble then paul is happy and vice versa.
Everyone who is not old or calm is either wise or not old.
If alice is brave then lucy is both not kind and not humble and vice versa.
Everyone who is either not funny or not brave is humble and vice versa.
If someone is not strong or happy then someone is both not humble and quiet.
Everyone who is happy is not strong and vice versa.
Everyone who is both humble and not wise is not strong.
Everyone who is either not curious or not tall is either curious or not old and vice versa.
If someone is not tall then someone is happy.
If someone is both not generous and not strong then someone is creative and vice versa.
Everyone who is not quiet or happy is creative or not happy.
Lucy is either strong or quiet.
Someone is both not funny and curious.
Mary is funny.
Paul is either not strong or generous.
Someone is not wise or calm.
Someone is either kind or not tall.
Susan is both creative and funny.
Fred is both not quiet and not funny. | Lucy is calm. | neutral | (![X]:((funny(X)<~>~generous(X))=>creative(X)))&
(((patient(alice)|~old(alice)))<=>((calm(lucy)<~>brave(lucy))))&
(![X]:((~tall(X)&tall(X))<=>(calm(X)<~>~creative(X))))&
(![X]:((~brave(X)|~quiet(X))=>(rich(X)<~>strong(X))))&
(((funny(alice)&~creative(alice)))<=>((funny(fred)|~calm(fred))))&
(((~happy(fred)|~humble(fred)))<=>(happy(paul)))&
(![X]:((~old(X)|calm(X))=>(wise(X)<~>~old(X))))&
((brave(alice))<=>((~kind(lucy)&~humble(lucy))))&
(![X]:((~funny(X)<~>~brave(X))<=>humble(X)))&
((?[X]:((~strong(X)|happy(X))))=>(?[X]:((~humble(X)&quiet(X)))))&
(![X]:(happy(X)<=>~strong(X)))&
(![X]:((humble(X)&~wise(X))=>~strong(X)))&
(![X]:((~curious(X)<~>~tall(X))<=>(curious(X)<~>~old(X))))&
((?[X]:(~tall(X)))=>(?[X]:(happy(X))))&
((?[X]:((~generous(X)&~strong(X))))<=>(?[X]:(creative(X))))&
(![X]:((~quiet(X)|happy(X))=>(creative(X)|~happy(X))))&
((strong(lucy)<~>quiet(lucy)))&
(?[X]:((~funny(X)&curious(X))))&
(funny(mary))&
((~strong(paul)<~>generous(paul)))&
(?[X]:((~wise(X)|calm(X))))&
(?[X]:((kind(X)<~>~tall(X))))&
((creative(susan)&funny(susan)))&
((~quiet(fred)&~funny(fred))) | calm(lucy) | [] | null | 0 |
Everyone who is either strong or not wise is happy and vice versa. Everyone who is curious is calm. Everyone who is either curious or not brave is strong and vice versa. Everyone who is either not wise or not kind is both quiet and brave and vice versa. Everyone who is both curious and not creative is not funny or calm and vice versa. If fred is rich then someone is both not strong and kind. Everyone who is not brave or quiet is quiet and vice versa. If mary is not wise then someone is either not old or brave. Everyone who is not calm or not old is either not generous or calm and vice versa. If fred is calm or not kind then alice is old and vice versa. If someone is either generous or curious then someone is brave. Everyone who is not quiet or not funny is both strong and wise and vice versa. Everyone who is strong is brave and vice versa. If someone is both not happy and kind then someone is either not old or patient and vice versa. If alice is not funny or creative then someone is strong. Lucy is both brave and not kind. Susan is either not old or not happy. Someone is either humble or wise. Someone is not creative. Paul is not curious or not strong. John is both quiet and kind. | Fred is happy. | neutral | (![X]:((strong(X)<~>~wise(X))<=>happy(X)))&
(![X]:(curious(X)=>calm(X)))&
(![X]:((curious(X)<~>~brave(X))<=>strong(X)))&
(![X]:((~wise(X)<~>~kind(X))<=>(quiet(X)&brave(X))))&
(![X]:((curious(X)&~creative(X))<=>(~funny(X)|calm(X))))&
((rich(fred))=>(?[X]:((~strong(X)&kind(X)))))&
(![X]:((~brave(X)|quiet(X))<=>quiet(X)))&
((~wise(mary))=>(?[X]:((~old(X)<~>brave(X)))))&
(![X]:((~calm(X)|~old(X))<=>(~generous(X)<~>calm(X))))&
(((calm(fred)|~kind(fred)))<=>(old(alice)))&
((?[X]:((generous(X)<~>curious(X))))=>(?[X]:(brave(X))))&
(![X]:((~quiet(X)|~funny(X))<=>(strong(X)&wise(X))))&
(![X]:(strong(X)<=>brave(X)))&
((?[X]:((~happy(X)&kind(X))))<=>(?[X]:((~old(X)<~>patient(X)))))&
(((~funny(alice)|creative(alice)))=>(?[X]:(strong(X))))&
((brave(lucy)&~kind(lucy)))&
((~old(susan)<~>~happy(susan)))&
(?[X]:((humble(X)<~>wise(X))))&
(?[X]:(~creative(X)))&
((~curious(paul)|~strong(paul)))&
((quiet(john)&kind(john))) | happy(fred) | [] | null | 0 |
If someone is not old then someone is both not wise and not old and vice versa. If someone is happy then someone is both happy and tall. Everyone who is both rich and not strong is either humble or curious and vice versa. Everyone who is curious is tall. Everyone who is either strong or not curious is calm or not kind and vice versa. Everyone who is either not generous or not curious is not tall or patient and vice versa. If someone is kind then mary is not old and vice versa. Everyone who is either humble or happy is not calm. If john is both not brave and funny then someone is both not tall and not brave and vice versa. Everyone who is either not creative or not humble is both not creative and happy. Everyone who is not generous or old is funny. Everyone who is both not old and not strong is tall or generous. Everyone who is both rich and not calm is calm or generous and vice versa. Everyone who is not generous is not strong and vice versa. Everyone who is not rich or not humble is both generous and strong. Everyone who is both strong and not curious is both happy and not happy and vice versa. Lucy is either happy or not curious. Someone is humble or rich. Someone is old. Alice is not wise. Someone is either wise or strong. Susan is both not quiet and wise. Mary is tall or not old. | John is not strong. | contradiction | ((?[X]:(~old(X)))<=>(?[X]:((~wise(X)&~old(X)))))&
((?[X]:(happy(X)))=>(?[X]:((happy(X)&tall(X)))))&
(![X]:((rich(X)&~strong(X))<=>(humble(X)<~>curious(X))))&
(![X]:(curious(X)=>tall(X)))&
(![X]:((strong(X)<~>~curious(X))<=>(calm(X)|~kind(X))))&
(![X]:((~generous(X)<~>~curious(X))<=>(~tall(X)|patient(X))))&
((?[X]:(kind(X)))<=>(~old(mary)))&
(![X]:((humble(X)<~>happy(X))=>~calm(X)))&
(((~brave(john)&funny(john)))<=>(?[X]:((~tall(X)&~brave(X)))))&
(![X]:((~creative(X)<~>~humble(X))=>(~creative(X)&happy(X))))&
(![X]:((~generous(X)|old(X))=>funny(X)))&
(![X]:((~old(X)&~strong(X))=>(tall(X)|generous(X))))&
(![X]:((rich(X)&~calm(X))<=>(calm(X)|generous(X))))&
(![X]:(~generous(X)<=>~strong(X)))&
(![X]:((~rich(X)|~humble(X))=>(generous(X)&strong(X))))&
(![X]:((strong(X)&~curious(X))<=>(happy(X)&~happy(X))))&
((happy(lucy)<~>~curious(lucy)))&
(?[X]:((humble(X)|rich(X))))&
(?[X]:(old(X)))&
(~wise(alice))&
(?[X]:((wise(X)<~>strong(X))))&
((~quiet(susan)&wise(susan)))&
((tall(mary)|~old(mary))) | ~strong(john) | [
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7072896248591959096947692
% SZS output start Proof for 7072896248591959096947692
13. ! [X0] : ((~calm(X0) & rich(X0)) <=> (generous(X0) | calm(X0))) [input p12]
14. ! [X0] : (~generous(X0) <=> ~strong(X0)) [input p13]
15. ! [X0] : ((~humble(X0) | ~rich(X0)) => (strong(X0) & generous(X0))) [input p14]
24. ~strong(john) [input hypothesis]
35. ! [X0] : ((strong(X0) & generous(X0)) | (humble(X0) & rich(X0))) [ennf transformation 15]
61. ! [X0] : (((~calm(X0) & rich(X0)) | (~generous(X0) & ~calm(X0))) & ((generous(X0) | calm(X0)) | (calm(X0) | ~rich(X0)))) [nnf transformation 13]
62. ! [X0] : (((~calm(X0) & rich(X0)) | (~generous(X0) & ~calm(X0))) & (generous(X0) | calm(X0) | calm(X0) | ~rich(X0))) [flattening 61]
63. ! [X0] : ((~generous(X0) | strong(X0)) & (~strong(X0) | generous(X0))) [nnf transformation 14]
113. generous(X0) | calm(X0) | calm(X0) | ~rich(X0) [cnf transformation 62]
115. ~generous(X0) | rich(X0) [cnf transformation 62]
116. ~calm(X0) | ~calm(X0) [cnf transformation 62]
119. ~generous(X0) | strong(X0) [cnf transformation 63]
120. generous(X0) | rich(X0) [cnf transformation 35]
137. ~strong(john) [cnf transformation 24]
138. generous(X0) | calm(X0) | ~rich(X0) [duplicate literal removal 113]
139. ~calm(X0) [duplicate literal removal 116]
213. ~rich(X0) | generous(X0) [subsumption resolution 138,139]
214. rich(X0) [subsumption resolution 120,115]
260. generous(X0) [resolution 213,214]
262. strong(X0) [resolution 260,119]
266. $false [resolution 262,137]
% SZS output end Proof for 7072896248591959096947692
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or calm is both quiet and not wise. If mary is not brave then susan is either kind or not strong. If someone is both not wise and not brave then lucy is not strong or brave and vice versa. Everyone who is either quiet or old is calm. Everyone who is either not curious or not calm is not brave or quiet. If fred is both patient and happy then someone is either humble or kind and vice versa. If alice is not kind then someone is tall or humble and vice versa. If someone is both not calm and not happy then someone is kind or not strong. Everyone who is either not creative or humble is not curious and vice versa. Everyone who is quiet is not patient and vice versa. Everyone who is old is quiet and vice versa. Everyone who is both not happy and generous is rich or not humble and vice versa. Everyone who is creative or not strong is brave or kind and vice versa. Everyone who is not wise or curious is either kind or happy. Everyone who is both kind and not patient is not humble or curious. Someone is either not generous or creative. Someone is either not creative or not humble. Someone is old. Someone is funny. John is either not funny or not brave. Someone is not brave or not humble. Lucy is generous or not tall. | Susan is not quiet. | neutral | (![X]:((wise(X)|calm(X))=>(quiet(X)&~wise(X))))&
((~brave(mary))=>((kind(susan)<~>~strong(susan))))&
((?[X]:((~wise(X)&~brave(X))))<=>((~strong(lucy)|brave(lucy))))&
(![X]:((quiet(X)<~>old(X))=>calm(X)))&
(![X]:((~curious(X)<~>~calm(X))=>(~brave(X)|quiet(X))))&
(((patient(fred)&happy(fred)))<=>(?[X]:((humble(X)<~>kind(X)))))&
((~kind(alice))<=>(?[X]:((tall(X)|humble(X)))))&
((?[X]:((~calm(X)&~happy(X))))=>(?[X]:((kind(X)|~strong(X)))))&
(![X]:((~creative(X)<~>humble(X))<=>~curious(X)))&
(![X]:(quiet(X)<=>~patient(X)))&
(![X]:(old(X)<=>quiet(X)))&
(![X]:((~happy(X)&generous(X))<=>(rich(X)|~humble(X))))&
(![X]:((creative(X)|~strong(X))<=>(brave(X)|kind(X))))&
(![X]:((~wise(X)|curious(X))=>(kind(X)<~>happy(X))))&
(![X]:((kind(X)&~patient(X))=>(~humble(X)|curious(X))))&
(?[X]:((~generous(X)<~>creative(X))))&
(?[X]:((~creative(X)<~>~humble(X))))&
(?[X]:(old(X)))&
(?[X]:(funny(X)))&
((~funny(john)<~>~brave(john)))&
(?[X]:((~brave(X)|~humble(X))))&
((generous(lucy)|~tall(lucy))) | ~quiet(susan) | [] | null | 0 |
Everyone who is either old or not old is either humble or kind and vice versa.
Everyone who is not kind is both brave and creative and vice versa.
Everyone who is both strong and not strong is both not kind and not strong and vice versa.
Everyone who is either not funny or not curious is either strong or quiet and vice versa.
If someone is not old then lucy is humble.
If someone is funny then someone is either patient or kind and vice versa.
Everyone who is both brave and creative is not quiet or generous and vice versa.
Everyone who is both quiet and not brave is not creative and vice versa.
Everyone who is both happy and strong is patient.
Everyone who is calm or not rich is not humble and vice versa.
Everyone who is both not quiet and old is both not creative and not wise and vice versa.
If susan is either quiet or creative then susan is either not patient or rich and vice versa.
Everyone who is not happy is either not patient or patient.
Everyone who is old is either not strong or not old and vice versa.
Everyone who is not curious is either not generous or not creative.
Someone is not generous or humble.
Someone is not tall.
Someone is both not humble and not happy.
Lucy is not rich or not patient.
Alice is wise or not kind.
Lucy is not wise or wise. | Lucy is creative. | contradiction | (![X]:((old(X)<~>~old(X))<=>(humble(X)<~>kind(X))))&
(![X]:(~kind(X)<=>(brave(X)&creative(X))))&
(![X]:((strong(X)&~strong(X))<=>(~kind(X)&~strong(X))))&
(![X]:((~funny(X)<~>~curious(X))<=>(strong(X)<~>quiet(X))))&
((?[X]:(~old(X)))=>(humble(lucy)))&
((?[X]:(funny(X)))<=>(?[X]:((patient(X)<~>kind(X)))))&
(![X]:((brave(X)&creative(X))<=>(~quiet(X)|generous(X))))&
(![X]:((quiet(X)&~brave(X))<=>~creative(X)))&
(![X]:((happy(X)&strong(X))=>patient(X)))&
(![X]:((calm(X)|~rich(X))<=>~humble(X)))&
(![X]:((~quiet(X)&old(X))<=>(~creative(X)&~wise(X))))&
(((quiet(susan)<~>creative(susan)))<=>((~patient(susan)<~>rich(susan))))&
(![X]:(~happy(X)=>(~patient(X)<~>patient(X))))&
(![X]:(old(X)<=>(~strong(X)<~>~old(X))))&
(![X]:(~curious(X)=>(~generous(X)<~>~creative(X))))&
(?[X]:((~generous(X)|humble(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~humble(X)&~happy(X))))&
((~rich(lucy)|~patient(lucy)))&
((wise(alice)|~kind(alice)))&
((~wise(lucy)|wise(lucy))) | creative(lucy) | [
"p1",
"p2",
"p6",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3149564184493484916156355
% SZS output start Proof for 3149564184493484916156355
2. ! [X0] : (~kind(X0) <=> (creative(X0) & brave(X0))) [input p1]
3. ! [X0] : ((~strong(X0) & strong(X0)) <=> (~strong(X0) & ~kind(X0))) [input p2]
7. ! [X0] : ((creative(X0) & brave(X0)) <=> (generous(X0) | ~quiet(X0))) [input p6]
8. ! [X0] : ((~brave(X0) & quiet(X0)) <=> ~creative(X0)) [input p7]
14. ! [X0] : (old(X0) <=> (~strong(X0) <~> ~old(X0))) [input p13]
22. creative(lucy) [input hypothesis]
31. ! [X0] : ((~kind(X0) | (~creative(X0) | ~brave(X0))) & ((creative(X0) & brave(X0)) | kind(X0))) [nnf transformation 2]
32. ! [X0] : ((~kind(X0) | ~creative(X0) | ~brave(X0)) & ((creative(X0) & brave(X0)) | kind(X0))) [flattening 31]
33. ! [X0] : (((~strong(X0) & strong(X0)) | (strong(X0) | kind(X0))) & ((~strong(X0) & ~kind(X0)) | (strong(X0) | ~strong(X0)))) [nnf transformation 3]
34. ! [X0] : (((~strong(X0) & strong(X0)) | strong(X0) | kind(X0)) & ((~strong(X0) & ~kind(X0)) | strong(X0) | ~strong(X0))) [flattening 33]
41. ! [X0] : (((creative(X0) & brave(X0)) | (~generous(X0) & quiet(X0))) & ((generous(X0) | ~quiet(X0)) | (~creative(X0) | ~brave(X0)))) [nnf transformation 7]
42. ! [X0] : (((creative(X0) & brave(X0)) | (~generous(X0) & quiet(X0))) & (generous(X0) | ~quiet(X0) | ~creative(X0) | ~brave(X0))) [flattening 41]
43. ! [X0] : (((~brave(X0) & quiet(X0)) | creative(X0)) & (~creative(X0) | (brave(X0) | ~quiet(X0)))) [nnf transformation 8]
44. ! [X0] : (((~brave(X0) & quiet(X0)) | creative(X0)) & (~creative(X0) | brave(X0) | ~quiet(X0))) [flattening 43]
51. ! [X0] : ((old(X0) | ((~strong(X0) | old(X0)) & (~old(X0) | strong(X0)))) & (((old(X0) | strong(X0)) & (~old(X0) | ~strong(X0))) | ~old(X0))) [nnf transformation 14]
67. ~creative(X0) | ~kind(X0) | ~brave(X0) [cnf transformation 32]
70. strong(X0) | strong(X0) | kind(X0) [cnf transformation 34]
86. quiet(X0) | brave(X0) [cnf transformation 42]
90. ~creative(X0) | brave(X0) | ~quiet(X0) [cnf transformation 44]
111. ~old(X0) | ~strong(X0) | ~old(X0) [cnf transformation 51]
114. old(X0) | ~strong(X0) | old(X0) [cnf transformation 51]
123. creative(lucy) [cnf transformation 22]
124. ~old(X0) | ~strong(X0) [duplicate literal removal 111]
125. ~strong(X0) | old(X0) [duplicate literal removal 114]
127. strong(X0) | kind(X0) [duplicate literal removal 70]
167. ~creative(X0) | brave(X0) [subsumption resolution 90,86]
196. ~strong(X0) [subsumption resolution 124,125]
233. kind(X1) [resolution 127,196]
248. brave(lucy) [resolution 167,123]
252. ~kind(lucy) | ~brave(lucy) [resolution 67,123]
254. ~brave(lucy) [subsumption resolution 252,233]
255. $false [subsumption resolution 254,248]
% SZS output end Proof for 3149564184493484916156355
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
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