premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is either not old or funny is brave or quiet. Everyone who is not wise or happy is both creative and wise. If someone is rich or not creative then someone is not curious or old. If susan is both not curious and happy then someone is both not rich and not tall and vice versa. If someone is either wise or quiet then paul is both creative and not creative and vice versa. If susan is both not humble and not old then mary is curious or not old. If someone is both not humble and not patient then susan is not quiet and vice versa. Everyone who is not rich is brave and vice versa. Everyone who is both old and kind is not funny. If someone is either not quiet or not strong then john is wise. If someone is either generous or not quiet then mary is both funny and not rich. Everyone who is either quiet or curious is either creative or rich and vice versa. If someone is not patient then alice is not funny. Everyone who is not curious or strong is both not kind and not brave and vice versa. If mary is either not rich or strong then fred is kind or happy and vice versa. If lucy is both patient and kind then someone is both not old and tall and vice versa. Mary is generous or not wise. Lucy is either not tall or not patient. Lucy is not funny or calm. Someone is either not funny or not creative. Fred is kind. Someone is either wise or not kind. Mary is kind. | Mary is not creative. | entailment | (![X]:((~old(X)<~>funny(X))=>(brave(X)|quiet(X))))&
(![X]:((~wise(X)|happy(X))=>(creative(X)&wise(X))))&
((?[X]:((rich(X)|~creative(X))))=>(?[X]:((~curious(X)|old(X)))))&
(((~curious(susan)&happy(susan)))<=>(?[X]:((~rich(X)&~tall(X)))))&
((?[X]:((wise(X)<~>quiet(X))))<=>((creative(paul)&~creative(paul))))&
(((~humble(susan)&~old(susan)))=>((curious(mary)|~old(mary))))&
((?[X]:((~humble(X)&~patient(X))))<=>(~quiet(susan)))&
(![X]:(~rich(X)<=>brave(X)))&
(![X]:((old(X)&kind(X))=>~funny(X)))&
((?[X]:((~quiet(X)<~>~strong(X))))=>(wise(john)))&
((?[X]:((generous(X)<~>~quiet(X))))=>((funny(mary)&~rich(mary))))&
(![X]:((quiet(X)<~>curious(X))<=>(creative(X)<~>rich(X))))&
((?[X]:(~patient(X)))=>(~funny(alice)))&
(![X]:((~curious(X)|strong(X))<=>(~kind(X)&~brave(X))))&
(((~rich(mary)<~>strong(mary)))<=>((kind(fred)|happy(fred))))&
(((patient(lucy)&kind(lucy)))<=>(?[X]:((~old(X)&tall(X)))))&
((generous(mary)|~wise(mary)))&
((~tall(lucy)<~>~patient(lucy)))&
((~funny(lucy)|calm(lucy)))&
(?[X]:((~funny(X)<~>~creative(X))))&
(kind(fred))&
(?[X]:((wise(X)<~>~kind(X))))&
(kind(mary)) | ~creative(mary) | [
"p1",
"p4",
"p10",
"p11",
"p13",
"p16",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7297740106041751683380703
% SZS output start Proof for 7297740106041751683380703
2. ! [X0] : ((happy(X0) | ~wise(X0)) => (wise(X0) & creative(X0))) [input p1]
5. ? [X0] : (wise(X0) <~> quiet(X0)) <=> (~creative(paul) & creative(paul)) [input p4]
11. ? [X0] : (generous(X0) <~> ~quiet(X0)) => (~rich(mary) & funny(mary)) [input p10]
12. ! [X0] : ((quiet(X0) <~> curious(X0)) <=> (creative(X0) <~> rich(X0))) [input p11]
14. ! [X0] : ((strong(X0) | ~curious(X0)) <=> (~brave(X0) & ~kind(X0))) [input p13]
17. ~wise(mary) | generous(mary) [input p16]
23. kind(mary) [input p22]
24. creative(mary) [input hypothesis]
29. ! [X0] : ((wise(X0) & creative(X0)) | (~happy(X0) & wise(X0))) [ennf transformation 2]
36. (~rich(mary) & funny(mary)) | ! [X0] : (generous(X0) <=> ~quiet(X0)) [ennf transformation 11]
47. (? [X0] : ((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) | (creative(paul) | ~creative(paul))) & ((~creative(paul) & creative(paul)) | ! [X0] : ((wise(X0) | ~quiet(X0)) & (quiet(X0) | ~wise(X0)))) [nnf transformation 5]
48. (? [X0] : ((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) | creative(paul) | ~creative(paul)) & ((~creative(paul) & creative(paul)) | ! [X0] : ((wise(X0) | ~quiet(X0)) & (quiet(X0) | ~wise(X0)))) [flattening 47]
49. (? [X0] : ((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) | creative(paul) | ~creative(paul)) & ((~creative(paul) & creative(paul)) | ! [X1] : ((wise(X1) | ~quiet(X1)) & (quiet(X1) | ~wise(X1)))) [rectify 48]
50. ? [X0] : ((~quiet(X0) | ~wise(X0)) & (quiet(X0) | wise(X0))) => ((~quiet(sK2) | ~wise(sK2)) & (quiet(sK2) | wise(sK2))) [choice axiom]
51. (((~quiet(sK2) | ~wise(sK2)) & (quiet(sK2) | wise(sK2))) | creative(paul) | ~creative(paul)) & ((~creative(paul) & creative(paul)) | ! [X1] : ((wise(X1) | ~quiet(X1)) & (quiet(X1) | ~wise(X1)))) [skolemisation 49,50]
58. (~rich(mary) & funny(mary)) | ! [X0] : ((generous(X0) | quiet(X0)) & (~quiet(X0) | ~generous(X0))) [nnf transformation 36]
59. ! [X0] : ((((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0)))) & (((~rich(X0) | ~creative(X0)) & (rich(X0) | creative(X0))) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0))))) [nnf transformation 12]
60. ! [X0] : (((strong(X0) | ~curious(X0)) | (brave(X0) | kind(X0))) & ((~brave(X0) & ~kind(X0)) | (~strong(X0) & curious(X0)))) [nnf transformation 14]
61. ! [X0] : ((strong(X0) | ~curious(X0) | brave(X0) | kind(X0)) & ((~brave(X0) & ~kind(X0)) | (~strong(X0) & curious(X0)))) [flattening 60]
80. wise(X0) | wise(X0) [cnf transformation 29]
88. creative(paul) | quiet(X1) | ~wise(X1) [cnf transformation 51]
90. ~creative(paul) | quiet(X1) | ~wise(X1) [cnf transformation 51]
105. ~rich(mary) | ~quiet(X0) | ~generous(X0) [cnf transformation 58]
113. ~curious(X0) | ~quiet(X0) | rich(X0) | ~creative(X0) [cnf transformation 59]
116. ~kind(X0) | curious(X0) [cnf transformation 61]
131. ~wise(mary) | generous(mary) [cnf transformation 17]
139. kind(mary) [cnf transformation 23]
140. creative(mary) [cnf transformation 24]
141. wise(X0) [duplicate literal removal 80]
181. ~creative(paul) | quiet(X1) [subsumption resolution 90,141]
183. 10 <=> ! [X1] : quiet(X1) [avatar definition]
184. quiet(X1) <- (10) [avatar component clause 183]
186. 11 <=> creative(paul) [avatar definition]
189. 10 | ~11 [avatar split clause 181,186,183]
190. creative(paul) | quiet(X1) [subsumption resolution 88,141]
191. 10 | 11 [avatar split clause 190,186,183]
201. 14 <=> curious(mary) [avatar definition]
203. curious(mary) <- (14) [avatar component clause 201]
231. 21 <=> rich(mary) [avatar definition]
233. ~rich(mary) <- (~21) [avatar component clause 231]
236. 22 <=> ! [X0] : (~quiet(X0) | ~generous(X0)) [avatar definition]
237. ~generous(X0) | ~quiet(X0) <- (22) [avatar component clause 236]
238. 22 | ~21 [avatar split clause 105,231,236]
294. generous(mary) [subsumption resolution 131,141]
317. curious(mary) [resolution 116,139]
320. 14 [avatar split clause 317,201]
327. ~quiet(mary) <- (22) [resolution 237,294]
329. $false <- (10, 22) [subsumption resolution 327,184]
330. ~10 | ~22 [avatar contradiction clause 329]
404. ~quiet(mary) | rich(mary) | ~creative(mary) <- (14) [resolution 113,203]
409. rich(mary) | ~creative(mary) <- (10, 14) [subsumption resolution 404,184]
410. ~creative(mary) <- (10, 14, ~21) [subsumption resolution 409,233]
411. $false <- (10, 14, ~21) [subsumption resolution 410,140]
412. ~10 | ~14 | 21 [avatar contradiction clause 411]
435. $false [avatar sat refutation 189,191,238,320,330,412]
% SZS output end Proof for 7297740106041751683380703
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and curious is patient and vice versa.
Everyone who is either not humble or not calm is brave and vice versa.
Everyone who is both happy and not strong is both strong and funny.
Everyone who is old or funny is not brave or curious and vice versa.
If someone is both not funny and creative then paul is either curious or patient.
Everyone who is both not kind and not strong is either rich or calm and vice versa.
If alice is creative or old then someone is curious or not quiet and vice versa.
If fred is both patient and not humble then susan is both not curious and calm and vice versa.
Everyone who is strong or not patient is not kind or not calm and vice versa.
Everyone who is both happy and not kind is both not creative and not humble.
If paul is creative or not funny then someone is rich and vice versa.
If lucy is either not brave or not patient then someone is humble or calm and vice versa.
Everyone who is calm or not wise is both happy and not funny and vice versa.
Everyone who is either patient or not funny is both strong and funny and vice versa.
If someone is not humble or wise then john is either old or not old and vice versa.
If lucy is both humble and not wise then fred is not kind.
Someone is not rich or wise.
Someone is not generous or patient.
Someone is not brave or not tall.
Someone is not calm. | Paul is tall. | neutral | (![X]:((~strong(X)&curious(X))<=>patient(X)))&
(![X]:((~humble(X)<~>~calm(X))<=>brave(X)))&
(![X]:((happy(X)&~strong(X))=>(strong(X)&funny(X))))&
(![X]:((old(X)|funny(X))<=>(~brave(X)|curious(X))))&
((?[X]:((~funny(X)&creative(X))))=>((curious(paul)<~>patient(paul))))&
(![X]:((~kind(X)&~strong(X))<=>(rich(X)<~>calm(X))))&
(((creative(alice)|old(alice)))<=>(?[X]:((curious(X)|~quiet(X)))))&
(((patient(fred)&~humble(fred)))<=>((~curious(susan)&calm(susan))))&
(![X]:((strong(X)|~patient(X))<=>(~kind(X)|~calm(X))))&
(![X]:((happy(X)&~kind(X))=>(~creative(X)&~humble(X))))&
(((creative(paul)|~funny(paul)))<=>(?[X]:(rich(X))))&
(((~brave(lucy)<~>~patient(lucy)))<=>(?[X]:((humble(X)|calm(X)))))&
(![X]:((calm(X)|~wise(X))<=>(happy(X)&~funny(X))))&
(![X]:((patient(X)<~>~funny(X))<=>(strong(X)&funny(X))))&
((?[X]:((~humble(X)|wise(X))))<=>((old(john)<~>~old(john))))&
(((humble(lucy)&~wise(lucy)))=>(~kind(fred)))&
(?[X]:((~rich(X)|wise(X))))&
(?[X]:((~generous(X)|patient(X))))&
(?[X]:((~brave(X)|~tall(X))))&
(?[X]:(~calm(X))) | tall(paul) | [] | null | 0 |
Everyone who is not patient or humble is both funny and not funny.
If lucy is not generous or not happy then someone is either calm or humble.
Everyone who is old is strong or not kind.
Everyone who is brave or curious is not creative.
If someone is either not curious or not funny then susan is not patient.
If alice is not brave or not happy then someone is generous or curious.
Everyone who is both patient and not generous is either not creative or not happy and vice versa.
If alice is happy or generous then fred is both not curious and not rich.
If alice is happy then someone is curious or humble and vice versa.
Everyone who is funny is either not brave or rich and vice versa.
Everyone who is both not generous and funny is wise or not creative and vice versa.
Everyone who is calm or happy is not calm or not patient.
Everyone who is either quiet or not happy is tall or humble.
If mary is not humble or not brave then susan is both not old and not wise and vice versa.
Everyone who is creative is not funny or creative and vice versa.
If someone is both wise and not rich then paul is funny and vice versa.
Lucy is not generous or not humble.
Someone is either humble or not calm.
Susan is calm or not calm.
Alice is either creative or tall.
Paul is not old.
Someone is either curious or not kind.
Someone is kind. | Susan is rich. | entailment | (![X]:((~patient(X)|humble(X))=>(funny(X)&~funny(X))))&
(((~generous(lucy)|~happy(lucy)))=>(?[X]:((calm(X)<~>humble(X)))))&
(![X]:(old(X)=>(strong(X)|~kind(X))))&
(![X]:((brave(X)|curious(X))=>~creative(X)))&
((?[X]:((~curious(X)<~>~funny(X))))=>(~patient(susan)))&
(((~brave(alice)|~happy(alice)))=>(?[X]:((generous(X)|curious(X)))))&
(![X]:((patient(X)&~generous(X))<=>(~creative(X)<~>~happy(X))))&
(((happy(alice)|generous(alice)))=>((~curious(fred)&~rich(fred))))&
((happy(alice))<=>(?[X]:((curious(X)|humble(X)))))&
(![X]:(funny(X)<=>(~brave(X)<~>rich(X))))&
(![X]:((~generous(X)&funny(X))<=>(wise(X)|~creative(X))))&
(![X]:((calm(X)|happy(X))=>(~calm(X)|~patient(X))))&
(![X]:((quiet(X)<~>~happy(X))=>(tall(X)|humble(X))))&
(((~humble(mary)|~brave(mary)))<=>((~old(susan)&~wise(susan))))&
(![X]:(creative(X)<=>(~funny(X)|creative(X))))&
((?[X]:((wise(X)&~rich(X))))<=>(funny(paul)))&
((~generous(lucy)|~humble(lucy)))&
(?[X]:((humble(X)<~>~calm(X))))&
((calm(susan)|~calm(susan)))&
((creative(alice)<~>tall(alice)))&
(~old(paul))&
(?[X]:((curious(X)<~>~kind(X))))&
(?[X]:(kind(X))) | rich(susan) | [
"p0",
"p3",
"p4",
"p7",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 287610935998669303805583
% SZS output start Proof for 287610935998669303805583
1. ! [X0] : ((humble(X0) | ~patient(X0)) => (~funny(X0) & funny(X0))) [input p0]
4. ! [X0] : ((curious(X0) | brave(X0)) => ~creative(X0)) [input p3]
5. ? [X0] : (~curious(X0) <~> ~funny(X0)) => ~patient(susan) [input p4]
8. (generous(alice) | happy(alice)) => (~rich(fred) & ~curious(fred)) [input p7]
9. happy(alice) <=> ? [X0] : (humble(X0) | curious(X0)) [input p8]
10. ! [X0] : (funny(X0) <=> (~brave(X0) <~> rich(X0))) [input p9]
11. ! [X0] : ((funny(X0) & ~generous(X0)) <=> (~creative(X0) | wise(X0))) [input p10]
24. ~rich(susan) [input hypothesis]
26. ! [X0] : ((~funny(X0) & funny(X0)) | (~humble(X0) & patient(X0))) [ennf transformation 1]
28. ! [X0] : (~creative(X0) | (~curious(X0) & ~brave(X0))) [ennf transformation 4]
29. ~patient(susan) | ! [X0] : (~curious(X0) <=> ~funny(X0)) [ennf transformation 5]
31. (~rich(fred) & ~curious(fred)) | (~generous(alice) & ~happy(alice)) [ennf transformation 8]
39. ~patient(susan) | ! [X0] : ((~curious(X0) | funny(X0)) & (~funny(X0) | curious(X0))) [nnf transformation 29]
44. (happy(alice) | ! [X0] : (~humble(X0) & ~curious(X0))) & (? [X0] : (humble(X0) | curious(X0)) | ~happy(alice)) [nnf transformation 9]
45. (happy(alice) | ! [X0] : (~humble(X0) & ~curious(X0))) & (? [X1] : (humble(X1) | curious(X1)) | ~happy(alice)) [rectify 44]
46. ? [X1] : (humble(X1) | curious(X1)) => (humble(sK2) | curious(sK2)) [choice axiom]
47. (happy(alice) | ! [X0] : (~humble(X0) & ~curious(X0))) & ((humble(sK2) | curious(sK2)) | ~happy(alice)) [skolemisation 45,46]
48. ! [X0] : ((funny(X0) | ((~brave(X0) | ~rich(X0)) & (rich(X0) | brave(X0)))) & (((~rich(X0) | brave(X0)) & (rich(X0) | ~brave(X0))) | ~funny(X0))) [nnf transformation 10]
49. ! [X0] : (((funny(X0) & ~generous(X0)) | (creative(X0) & ~wise(X0))) & ((~creative(X0) | wise(X0)) | (~funny(X0) | generous(X0)))) [nnf transformation 11]
50. ! [X0] : (((funny(X0) & ~generous(X0)) | (creative(X0) & ~wise(X0))) & (~creative(X0) | wise(X0) | ~funny(X0) | generous(X0))) [flattening 49]
69. funny(X0) | patient(X0) [cnf transformation 26]
71. ~funny(X0) | patient(X0) [cnf transformation 26]
77. ~creative(X0) | ~brave(X0) [cnf transformation 28]
79. ~patient(susan) | ~funny(X0) | curious(X0) [cnf transformation 39]
89. ~curious(fred) | ~happy(alice) [cnf transformation 31]
91. ~rich(fred) | ~happy(alice) [cnf transformation 31]
94. happy(alice) | ~curious(X0) [cnf transformation 47]
98. rich(X0) | funny(X0) | brave(X0) [cnf transformation 48]
104. creative(X0) | funny(X0) [cnf transformation 50]
130. ~rich(susan) [cnf transformation 24]
133. patient(X0) [subsumption resolution 69,71]
151. ~funny(X0) | curious(X0) [subsumption resolution 79,133]
153. 4 <=> happy(alice) [avatar definition]
177. 9 <=> rich(fred) [avatar definition]
179. ~rich(fred) <- (~9) [avatar component clause 177]
181. ~4 | ~9 [avatar split clause 91,177,153]
183. 10 <=> curious(fred) [avatar definition]
185. ~curious(fred) <- (~10) [avatar component clause 183]
187. ~4 | ~10 [avatar split clause 89,183,153]
189. 11 <=> ! [X0] : ~curious(X0) [avatar definition]
190. ~curious(X0) <- (11) [avatar component clause 189]
191. 11 | 4 [avatar split clause 94,153,189]
272. ~brave(X1) | funny(X1) [resolution 104,77]
290. funny(susan) | brave(susan) [resolution 98,130]
294. funny(susan) [subsumption resolution 290,272]
298. curious(susan) [resolution 294,151]
301. $false <- (11) [subsumption resolution 298,190]
302. ~11 [avatar contradiction clause 301]
305. funny(fred) | brave(fred) <- (~9) [resolution 179,98]
306. funny(fred) <- (~9) [subsumption resolution 305,272]
326. curious(fred) <- (~9) [resolution 306,151]
329. $false <- (~9, ~10) [subsumption resolution 326,185]
330. 9 | 10 [avatar contradiction clause 329]
331. $false [avatar sat refutation 181,187,191,302,330]
% SZS output end Proof for 287610935998669303805583
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or patient is not happy and vice versa.
Everyone who is both not strong and not old is both curious and strong.
Everyone who is both generous and rich is both not strong and rich.
Everyone who is both not kind and not generous is not patient and vice versa.
Everyone who is wise or not quiet is patient or wise and vice versa.
Everyone who is brave or happy is both not generous and happy and vice versa.
If fred is humble or not curious then someone is both not generous and tall and vice versa.
If susan is curious or happy then john is either not generous or funny.
If fred is either not quiet or kind then someone is not patient or not generous.
Everyone who is not humble is both not humble and not old and vice versa.
If fred is not funny or not creative then alice is both not curious and not tall.
Everyone who is either not strong or generous is either not happy or not brave and vice versa.
If someone is both not rich and not old then someone is wise or patient.
If someone is patient or not kind then someone is generous or rich.
If john is curious or not kind then fred is both not creative and humble and vice versa.
Everyone who is rich is wise or not funny.
Fred is both not calm and not humble.
Fred is not humble.
Someone is both quiet and not brave.
Mary is either not creative or not rich.
Someone is either not happy or calm.
John is not generous or curious. | Fred is not happy. | neutral | (![X]:((~curious(X)<~>patient(X))<=>~happy(X)))&
(![X]:((~strong(X)&~old(X))=>(curious(X)&strong(X))))&
(![X]:((generous(X)&rich(X))=>(~strong(X)&rich(X))))&
(![X]:((~kind(X)&~generous(X))<=>~patient(X)))&
(![X]:((wise(X)|~quiet(X))<=>(patient(X)|wise(X))))&
(![X]:((brave(X)|happy(X))<=>(~generous(X)&happy(X))))&
(((humble(fred)|~curious(fred)))<=>(?[X]:((~generous(X)&tall(X)))))&
(((curious(susan)|happy(susan)))=>((~generous(john)<~>funny(john))))&
(((~quiet(fred)<~>kind(fred)))=>(?[X]:((~patient(X)|~generous(X)))))&
(![X]:(~humble(X)<=>(~humble(X)&~old(X))))&
(((~funny(fred)|~creative(fred)))=>((~curious(alice)&~tall(alice))))&
(![X]:((~strong(X)<~>generous(X))<=>(~happy(X)<~>~brave(X))))&
((?[X]:((~rich(X)&~old(X))))=>(?[X]:((wise(X)|patient(X)))))&
((?[X]:((patient(X)|~kind(X))))=>(?[X]:((generous(X)|rich(X)))))&
(((curious(john)|~kind(john)))<=>((~creative(fred)&humble(fred))))&
(![X]:(rich(X)=>(wise(X)|~funny(X))))&
((~calm(fred)&~humble(fred)))&
(~humble(fred))&
(?[X]:((quiet(X)&~brave(X))))&
((~creative(mary)<~>~rich(mary)))&
(?[X]:((~happy(X)<~>calm(X))))&
((~generous(john)|curious(john))) | ~happy(fred) | [] | null | 0 |
Everyone who is not humble or not creative is rich or wise and vice versa.
Everyone who is calm or not wise is both not patient and not calm and vice versa.
If paul is creative or brave then someone is not humble and vice versa.
Everyone who is both brave and tall is not rich.
Everyone who is either generous or not rich is both not kind and not humble and vice versa.
If someone is both strong and not old then john is quiet and vice versa.
Everyone who is both curious and not brave is quiet or tall.
If someone is not tall then lucy is either brave or tall.
Everyone who is happy or not old is both not happy and not funny.
Everyone who is not wise is generous.
If someone is humble then alice is kind.
Everyone who is strong is not wise or happy and vice versa.
Everyone who is either humble or not strong is both not humble and funny and vice versa.
Everyone who is both wise and not tall is not old or not generous.
Everyone who is either not creative or humble is generous or not strong and vice versa.
If john is either calm or not strong then someone is either wise or old.
Susan is not strong or not curious.
Mary is not strong.
Someone is either not happy or not old.
Someone is not tall or brave.
Someone is either patient or not generous.
Someone is either not calm or happy.
Someone is not funny. | Paul is creative. | contradiction | (![X]:((~humble(X)|~creative(X))<=>(rich(X)|wise(X))))&
(![X]:((calm(X)|~wise(X))<=>(~patient(X)&~calm(X))))&
(((creative(paul)|brave(paul)))<=>(?[X]:(~humble(X))))&
(![X]:((brave(X)&tall(X))=>~rich(X)))&
(![X]:((generous(X)<~>~rich(X))<=>(~kind(X)&~humble(X))))&
((?[X]:((strong(X)&~old(X))))<=>(quiet(john)))&
(![X]:((curious(X)&~brave(X))=>(quiet(X)|tall(X))))&
((?[X]:(~tall(X)))=>((brave(lucy)<~>tall(lucy))))&
(![X]:((happy(X)|~old(X))=>(~happy(X)&~funny(X))))&
(![X]:(~wise(X)=>generous(X)))&
((?[X]:(humble(X)))=>(kind(alice)))&
(![X]:(strong(X)<=>(~wise(X)|happy(X))))&
(![X]:((humble(X)<~>~strong(X))<=>(~humble(X)&funny(X))))&
(![X]:((wise(X)&~tall(X))=>(~old(X)|~generous(X))))&
(![X]:((~creative(X)<~>humble(X))<=>(generous(X)|~strong(X))))&
(((calm(john)<~>~strong(john)))=>(?[X]:((wise(X)<~>old(X)))))&
((~strong(susan)|~curious(susan)))&
(~strong(mary))&
(?[X]:((~happy(X)<~>~old(X))))&
(?[X]:((~tall(X)|brave(X))))&
(?[X]:((patient(X)<~>~generous(X))))&
(?[X]:((~calm(X)<~>happy(X))))&
(?[X]:(~funny(X))) | creative(paul) | [
"p0",
"p8",
"p9",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4712095772631433296950482
% SZS output start Proof for 4712095772631433296950482
1. ! [X0] : ((~creative(X0) | ~humble(X0)) <=> (wise(X0) | rich(X0))) [input p0]
9. ! [X0] : ((~old(X0) | happy(X0)) => (~funny(X0) & ~happy(X0))) [input p8]
10. ! [X0] : (~wise(X0) => generous(X0)) [input p9]
12. ! [X0] : (strong(X0) <=> (happy(X0) | ~wise(X0))) [input p11]
13. ! [X0] : ((humble(X0) <~> ~strong(X0)) <=> (funny(X0) & ~humble(X0))) [input p12]
15. ! [X0] : ((~creative(X0) <~> humble(X0)) <=> (~strong(X0) | generous(X0))) [input p14]
24. creative(paul) [input hypothesis]
30. ! [X0] : ((~funny(X0) & ~happy(X0)) | (old(X0) & ~happy(X0))) [ennf transformation 9]
31. ! [X0] : (generous(X0) | wise(X0)) [ennf transformation 10]
36. ! [X0] : (((~creative(X0) | ~humble(X0)) | (~wise(X0) & ~rich(X0))) & ((wise(X0) | rich(X0)) | (creative(X0) & humble(X0)))) [nnf transformation 1]
37. ! [X0] : ((~creative(X0) | ~humble(X0) | (~wise(X0) & ~rich(X0))) & (wise(X0) | rich(X0) | (creative(X0) & humble(X0)))) [flattening 36]
52. ! [X0] : ((strong(X0) | (~happy(X0) & wise(X0))) & ((happy(X0) | ~wise(X0)) | ~strong(X0))) [nnf transformation 12]
53. ! [X0] : ((strong(X0) | (~happy(X0) & wise(X0))) & (happy(X0) | ~wise(X0) | ~strong(X0))) [flattening 52]
54. ! [X0] : ((((strong(X0) | ~humble(X0)) & (~strong(X0) | humble(X0))) | (~funny(X0) | humble(X0))) & ((funny(X0) & ~humble(X0)) | ((humble(X0) | strong(X0)) & (~strong(X0) | ~humble(X0))))) [nnf transformation 13]
55. ! [X0] : ((((strong(X0) | ~humble(X0)) & (~strong(X0) | humble(X0))) | ~funny(X0) | humble(X0)) & ((funny(X0) & ~humble(X0)) | ((humble(X0) | strong(X0)) & (~strong(X0) | ~humble(X0))))) [flattening 54]
56. ! [X0] : ((((~humble(X0) | creative(X0)) & (humble(X0) | ~creative(X0))) | (strong(X0) & ~generous(X0))) & ((~strong(X0) | generous(X0)) | ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0))))) [nnf transformation 15]
57. ! [X0] : ((((~humble(X0) | creative(X0)) & (humble(X0) | ~creative(X0))) | (strong(X0) & ~generous(X0))) & (~strong(X0) | generous(X0) | ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0))))) [flattening 56]
77. ~wise(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 37]
98. ~happy(X0) | ~happy(X0) [cnf transformation 30]
102. generous(X0) | wise(X0) [cnf transformation 31]
104. happy(X0) | ~wise(X0) | ~strong(X0) [cnf transformation 53]
105. strong(X0) | wise(X0) [cnf transformation 53]
107. ~humble(X0) | ~strong(X0) | ~humble(X0) [cnf transformation 55]
116. ~generous(X0) | ~creative(X0) | humble(X0) [cnf transformation 57]
117. ~creative(X0) | humble(X0) | strong(X0) [cnf transformation 57]
133. creative(paul) [cnf transformation 24]
134. ~strong(X0) | ~humble(X0) [duplicate literal removal 107]
136. ~happy(X0) [duplicate literal removal 98]
143. 2 <=> creative(paul) [avatar definition]
145. creative(paul) <- (2) [avatar component clause 143]
196. ~strong(X0) | ~wise(X0) [subsumption resolution 104,136]
235. 2 [avatar split clause 133,143]
242. ~humble(X0) | wise(X0) [resolution 134,105]
270. ~creative(X0) | humble(X0) | wise(X0) [resolution 116,102]
357. humble(paul) | strong(paul) <- (2) [resolution 117,145]
426. 40 <=> strong(paul) [avatar definition]
428. strong(paul) <- (40) [avatar component clause 426]
430. 41 <=> humble(paul) [avatar definition]
431. ~humble(paul) <- (~41) [avatar component clause 430]
432. humble(paul) <- (41) [avatar component clause 430]
433. 40 | 41 | ~2 [avatar split clause 357,143,430,426]
467. ~wise(paul) <- (40) [resolution 428,196]
536. humble(paul) | wise(paul) <- (2) [resolution 270,145]
537. wise(paul) <- (2, ~41) [subsumption resolution 536,431]
538. $false <- (2, 40, ~41) [subsumption resolution 537,467]
539. ~2 | ~40 | 41 [avatar contradiction clause 538]
540. wise(paul) <- (2) [subsumption resolution 536,242]
607. ~humble(paul) | ~creative(paul) <- (2) [resolution 540,77]
609. ~creative(paul) <- (2, 41) [subsumption resolution 607,432]
610. $false <- (2, 41) [subsumption resolution 609,145]
611. ~2 | ~41 [avatar contradiction clause 610]
612. $false [avatar sat refutation 235,433,539,611]
% SZS output end Proof for 4712095772631433296950482
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or quiet is happy and vice versa.
If someone is both curious and not patient then someone is brave and vice versa.
Everyone who is not wise or not quiet is either quiet or tall and vice versa.
If someone is both creative and curious then someone is both strong and not tall.
Everyone who is not funny or not rich is old and vice versa.
Everyone who is both not old and tall is either funny or quiet and vice versa.
Everyone who is tall is both not tall and humble.
Everyone who is not strong is tall or not happy.
Everyone who is either quiet or not tall is both not kind and not funny and vice versa.
If someone is both brave and not old then someone is not old and vice versa.
If someone is either brave or tall then someone is kind and vice versa.
Everyone who is not brave or quiet is old.
If someone is either strong or not tall then susan is either strong or not calm.
If someone is either not kind or curious then someone is both brave and not tall and vice versa.
Everyone who is creative is not patient and vice versa.
If someone is either not old or not kind then lucy is either patient or happy and vice versa.
Someone is not humble or not quiet.
Someone is creative.
Alice is either not funny or quiet.
Someone is either quiet or not happy.
Someone is either kind or not strong.
Alice is not funny or humble. | Susan is strong. | entailment | (![X]:((strong(X)|quiet(X))<=>happy(X)))&
((?[X]:((curious(X)&~patient(X))))<=>(?[X]:(brave(X))))&
(![X]:((~wise(X)|~quiet(X))<=>(quiet(X)<~>tall(X))))&
((?[X]:((creative(X)&curious(X))))=>(?[X]:((strong(X)&~tall(X)))))&
(![X]:((~funny(X)|~rich(X))<=>old(X)))&
(![X]:((~old(X)&tall(X))<=>(funny(X)<~>quiet(X))))&
(![X]:(tall(X)=>(~tall(X)&humble(X))))&
(![X]:(~strong(X)=>(tall(X)|~happy(X))))&
(![X]:((quiet(X)<~>~tall(X))<=>(~kind(X)&~funny(X))))&
((?[X]:((brave(X)&~old(X))))<=>(?[X]:(~old(X))))&
((?[X]:((brave(X)<~>tall(X))))<=>(?[X]:(kind(X))))&
(![X]:((~brave(X)|quiet(X))=>old(X)))&
((?[X]:((strong(X)<~>~tall(X))))=>((strong(susan)<~>~calm(susan))))&
((?[X]:((~kind(X)<~>curious(X))))<=>(?[X]:((brave(X)&~tall(X)))))&
(![X]:(creative(X)<=>~patient(X)))&
((?[X]:((~old(X)<~>~kind(X))))<=>((patient(lucy)<~>happy(lucy))))&
(?[X]:((~humble(X)|~quiet(X))))&
(?[X]:(creative(X)))&
((~funny(alice)<~>quiet(alice)))&
(?[X]:((quiet(X)<~>~happy(X))))&
(?[X]:((kind(X)<~>~strong(X))))&
((~funny(alice)|humble(alice))) | strong(susan) | [
"p0",
"p2",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 961446655236673688258051
% SZS output start Proof for 961446655236673688258051
1. ! [X0] : ((quiet(X0) | strong(X0)) <=> happy(X0)) [input p0]
3. ! [X0] : ((~quiet(X0) | ~wise(X0)) <=> (quiet(X0) <~> tall(X0))) [input p2]
7. ! [X0] : (tall(X0) => (humble(X0) & ~tall(X0))) [input p6]
8. ! [X0] : (~strong(X0) => (~happy(X0) | tall(X0))) [input p7]
23. ~strong(susan) [input hypothesis]
30. ! [X0] : ((humble(X0) & ~tall(X0)) | ~tall(X0)) [ennf transformation 7]
31. ! [X0] : ((~happy(X0) | tall(X0)) | strong(X0)) [ennf transformation 8]
32. ! [X0] : (~happy(X0) | tall(X0) | strong(X0)) [flattening 31]
35. ! [X0] : (((quiet(X0) | strong(X0)) | ~happy(X0)) & (happy(X0) | (~quiet(X0) & ~strong(X0)))) [nnf transformation 1]
36. ! [X0] : ((quiet(X0) | strong(X0) | ~happy(X0)) & (happy(X0) | (~quiet(X0) & ~strong(X0)))) [flattening 35]
42. ! [X0] : (((~quiet(X0) | ~wise(X0)) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0)))) & (((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (quiet(X0) & wise(X0)))) [nnf transformation 3]
43. ! [X0] : ((~quiet(X0) | ~wise(X0) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0)))) & (((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (quiet(X0) & wise(X0)))) [flattening 42]
86. ~quiet(X0) | happy(X0) [cnf transformation 36]
92. tall(X0) | quiet(X0) | quiet(X0) [cnf transformation 43]
108. ~tall(X0) | ~tall(X0) [cnf transformation 30]
110. ~happy(X0) | tall(X0) | strong(X0) [cnf transformation 32]
155. ~strong(susan) [cnf transformation 23]
156. ~tall(X0) [duplicate literal removal 108]
157. tall(X0) | quiet(X0) [duplicate literal removal 92]
196. ~happy(X0) | strong(X0) [subsumption resolution 110,156]
235. 17 <=> ! [X0] : strong(X0) [avatar definition]
236. strong(X0) <- (17) [avatar component clause 235]
238. 18 <=> strong(susan) [avatar definition]
240. ~strong(susan) <- (~18) [avatar component clause 238]
344. ~18 [avatar split clause 155,238]
360. quiet(X1) [resolution 157,156]
372. happy(X1) [resolution 360,86]
386. strong(X1) [resolution 372,196]
388. 17 [avatar split clause 386,235]
389. $false <- (17, ~18) [resolution 236,240]
393. ~17 | 18 [avatar contradiction clause 389]
394. $false [avatar sat refutation 344,388,393]
% SZS output end Proof for 961446655236673688258051
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is brave.
Everyone who is either old or not rich is generous and vice versa.
If paul is either generous or not old then alice is not calm or old and vice versa.
If someone is curious or kind then someone is not tall or funny.
If someone is rich then fred is kind and vice versa.
Everyone who is not happy is both creative and not tall.
If fred is either patient or quiet then someone is either not strong or funny and vice versa.
Everyone who is both patient and not quiet is calm and vice versa.
Everyone who is not patient is either calm or not quiet.
Everyone who is either not happy or not brave is either not old or quiet and vice versa.
Everyone who is old or not quiet is both strong and patient.
If someone is both not patient and quiet then mary is either creative or old.
Everyone who is either creative or rich is both strong and patient and vice versa.
If john is both wise and quiet then alice is not brave and vice versa.
Everyone who is not tall is not brave.
If alice is not curious or calm then someone is either kind or funny.
Someone is both not happy and kind.
Fred is both not wise and brave.
Fred is either kind or tall.
Someone is either generous or rich.
Fred is either happy or kind.
Someone is either tall or not creative.
Paul is either not brave or not strong. | Alice is not generous. | contradiction | (![X]:(~strong(X)=>brave(X)))&
(![X]:((old(X)<~>~rich(X))<=>generous(X)))&
(((generous(paul)<~>~old(paul)))<=>((~calm(alice)|old(alice))))&
((?[X]:((curious(X)|kind(X))))=>(?[X]:((~tall(X)|funny(X)))))&
((?[X]:(rich(X)))<=>(kind(fred)))&
(![X]:(~happy(X)=>(creative(X)&~tall(X))))&
(((patient(fred)<~>quiet(fred)))<=>(?[X]:((~strong(X)<~>funny(X)))))&
(![X]:((patient(X)&~quiet(X))<=>calm(X)))&
(![X]:(~patient(X)=>(calm(X)<~>~quiet(X))))&
(![X]:((~happy(X)<~>~brave(X))<=>(~old(X)<~>quiet(X))))&
(![X]:((old(X)|~quiet(X))=>(strong(X)&patient(X))))&
((?[X]:((~patient(X)&quiet(X))))=>((creative(mary)<~>old(mary))))&
(![X]:((creative(X)<~>rich(X))<=>(strong(X)&patient(X))))&
(((wise(john)&quiet(john)))<=>(~brave(alice)))&
(![X]:(~tall(X)=>~brave(X)))&
(((~curious(alice)|calm(alice)))=>(?[X]:((kind(X)<~>funny(X)))))&
(?[X]:((~happy(X)&kind(X))))&
((~wise(fred)&brave(fred)))&
((kind(fred)<~>tall(fred)))&
(?[X]:((generous(X)<~>rich(X))))&
((happy(fred)<~>kind(fred)))&
(?[X]:((tall(X)<~>~creative(X))))&
((~brave(paul)<~>~strong(paul))) | ~generous(alice) | [
"p1",
"p2",
"p4",
"p14",
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2568045573847106819258223
% SZS output start Proof for 2568045573847106819258223
2. ! [X0] : ((old(X0) <~> ~rich(X0)) <=> generous(X0)) [input p1]
3. (generous(paul) <~> ~old(paul)) <=> (old(alice) | ~calm(alice)) [input p2]
5. ? [X0] : rich(X0) <=> kind(fred) [input p4]
15. ! [X0] : (~tall(X0) => ~brave(X0)) [input p14]
18. brave(fred) & ~wise(fred) [input p17]
19. kind(fred) <~> tall(fred) [input p18]
24. ~generous(alice) [input hypothesis]
32. ! [X0] : (~brave(X0) | tall(X0)) [ennf transformation 15]
34. ! [X0] : ((((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | ~generous(X0)) & (generous(X0) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))))) [nnf transformation 2]
35. (((old(paul) | ~generous(paul)) & (~old(paul) | generous(paul))) | (~old(alice) & calm(alice))) & ((old(alice) | ~calm(alice)) | ((generous(paul) | old(paul)) & (~old(paul) | ~generous(paul)))) [nnf transformation 3]
36. (((old(paul) | ~generous(paul)) & (~old(paul) | generous(paul))) | (~old(alice) & calm(alice))) & (old(alice) | ~calm(alice) | ((generous(paul) | old(paul)) & (~old(paul) | ~generous(paul)))) [flattening 35]
40. (? [X0] : rich(X0) | ~kind(fred)) & (kind(fred) | ! [X0] : ~rich(X0)) [nnf transformation 5]
41. (? [X0] : rich(X0) | ~kind(fred)) & (kind(fred) | ! [X1] : ~rich(X1)) [rectify 40]
42. ? [X0] : rich(X0) => rich(sK1) [choice axiom]
43. (rich(sK1) | ~kind(fred)) & (kind(fred) | ! [X1] : ~rich(X1)) [skolemisation 41,42]
62. (~tall(fred) | ~kind(fred)) & (tall(fred) | kind(fred)) [nnf transformation 19]
73. generous(X0) | old(X0) | rich(X0) [cnf transformation 34]
75. ~generous(X0) | ~old(X0) | rich(X0) [cnf transformation 34]
79. ~old(paul) | generous(paul) | ~old(alice) [cnf transformation 36]
81. old(paul) | ~generous(paul) | ~old(alice) [cnf transformation 36]
84. kind(fred) | ~rich(X1) [cnf transformation 43]
124. ~brave(X0) | tall(X0) [cnf transformation 32]
132. brave(fred) [cnf transformation 18]
134. ~tall(fred) | ~kind(fred) [cnf transformation 62]
143. ~generous(alice) [cnf transformation 24]
145. 1 <=> old(alice) [avatar definition]
149. 2 <=> generous(paul) [avatar definition]
150. generous(paul) <- (2) [avatar component clause 149]
151. ~generous(paul) <- (~2) [avatar component clause 149]
153. 3 <=> old(paul) [avatar definition]
154. ~old(paul) <- (~3) [avatar component clause 153]
155. old(paul) <- (3) [avatar component clause 153]
156. ~1 | ~2 | 3 [avatar split clause 81,153,149,145]
162. ~1 | 2 | ~3 [avatar split clause 79,153,149,145]
183. 9 <=> kind(fred) [avatar definition]
192. 11 <=> ! [X1] : ~rich(X1) [avatar definition]
193. ~rich(X1) <- (11) [avatar component clause 192]
194. 11 | 9 [avatar split clause 84,183,192]
261. 24 <=> tall(fred) [avatar definition]
264. ~9 | ~24 [avatar split clause 134,261,183]
304. tall(fred) [resolution 124,132]
309. 24 [avatar split clause 304,261]
315. old(alice) | rich(alice) [resolution 73,143]
316. old(paul) | rich(paul) <- (~2) [resolution 73,151]
317. old(alice) <- (11) [subsumption resolution 315,193]
318. 1 | ~11 [avatar split clause 317,192,145]
319. rich(paul) <- (~2, ~3) [subsumption resolution 316,154]
320. $false <- (~2, ~3, 11) [subsumption resolution 319,193]
321. 2 | 3 | ~11 [avatar contradiction clause 320]
334. ~old(paul) | rich(paul) <- (2) [resolution 75,150]
337. rich(paul) <- (2, 3) [subsumption resolution 334,155]
338. $false <- (2, 3, 11) [subsumption resolution 337,193]
339. ~2 | ~3 | ~11 [avatar contradiction clause 338]
340. $false [avatar sat refutation 156,162,194,264,309,318,321,339]
% SZS output end Proof for 2568045573847106819258223
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or kind is both tall and wise.
If mary is either not rich or not quiet then alice is either not strong or not quiet and vice versa.
Everyone who is either kind or not generous is both not generous and not strong.
Everyone who is strong is not funny and vice versa.
Everyone who is brave or rich is both not rich and not creative and vice versa.
Everyone who is both kind and not old is either rich or not tall.
If alice is humble then susan is both not strong and not happy.
Everyone who is rich or not funny is generous or not rich and vice versa.
Everyone who is not curious or funny is both not strong and not wise and vice versa.
Everyone who is calm or curious is brave or not rich.
If susan is quiet then someone is not calm or kind.
Everyone who is not wise or wise is not tall.
Everyone who is both rich and not generous is either not creative or not curious.
Everyone who is not humble or not old is generous or happy.
If someone is both quiet and not rich then someone is either not creative or patient.
Someone is calm or not brave.
Someone is not creative.
Someone is either brave or not curious.
Someone is both generous and not calm.
Someone is either not kind or calm. | Alice is rich. | contradiction | (![X]:((~wise(X)|kind(X))=>(tall(X)&wise(X))))&
(((~rich(mary)<~>~quiet(mary)))<=>((~strong(alice)<~>~quiet(alice))))&
(![X]:((kind(X)<~>~generous(X))=>(~generous(X)&~strong(X))))&
(![X]:(strong(X)<=>~funny(X)))&
(![X]:((brave(X)|rich(X))<=>(~rich(X)&~creative(X))))&
(![X]:((kind(X)&~old(X))=>(rich(X)<~>~tall(X))))&
((humble(alice))=>((~strong(susan)&~happy(susan))))&
(![X]:((rich(X)|~funny(X))<=>(generous(X)|~rich(X))))&
(![X]:((~curious(X)|funny(X))<=>(~strong(X)&~wise(X))))&
(![X]:((calm(X)|curious(X))=>(brave(X)|~rich(X))))&
((quiet(susan))=>(?[X]:((~calm(X)|kind(X)))))&
(![X]:((~wise(X)|wise(X))=>~tall(X)))&
(![X]:((rich(X)&~generous(X))=>(~creative(X)<~>~curious(X))))&
(![X]:((~humble(X)|~old(X))=>(generous(X)|happy(X))))&
((?[X]:((quiet(X)&~rich(X))))=>(?[X]:((~creative(X)<~>patient(X)))))&
(?[X]:((calm(X)|~brave(X))))&
(?[X]:(~creative(X)))&
(?[X]:((brave(X)<~>~curious(X))))&
(?[X]:((generous(X)&~calm(X))))&
(?[X]:((~kind(X)<~>calm(X)))) | rich(alice) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 5815703114365895433827407
% SZS output start Proof for 5815703114365895433827407
5. ! [X0] : ((rich(X0) | brave(X0)) <=> (~creative(X0) & ~rich(X0))) [input p4]
21. rich(alice) [input hypothesis]
40. ! [X0] : (((rich(X0) | brave(X0)) | (creative(X0) | rich(X0))) & ((~creative(X0) & ~rich(X0)) | (~rich(X0) & ~brave(X0)))) [nnf transformation 5]
41. ! [X0] : ((rich(X0) | brave(X0) | creative(X0) | rich(X0)) & ((~creative(X0) & ~rich(X0)) | (~rich(X0) & ~brave(X0)))) [flattening 40]
84. ~rich(X0) | ~rich(X0) [cnf transformation 41]
117. rich(alice) [cnf transformation 21]
120. ~rich(X0) [duplicate literal removal 84]
213. $false [subsumption resolution 117,120]
% SZS output end Proof for 5815703114365895433827407
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If alice is humble then someone is old or not creative.
Everyone who is not strong or not funny is both not humble and generous and vice versa.
If someone is not tall or not curious then someone is either brave or not wise and vice versa.
If fred is both old and not tall then lucy is humble and vice versa.
Everyone who is either not strong or not creative is not creative and vice versa.
If paul is not strong then someone is quiet.
Everyone who is not curious is not strong and vice versa.
Everyone who is strong is both creative and not quiet and vice versa.
Everyone who is both not curious and strong is either strong or rich.
Everyone who is both quiet and not calm is both curious and not strong.
If susan is either not quiet or tall then someone is either brave or not strong.
Everyone who is not patient is quiet.
If someone is either not strong or brave then someone is either not strong or calm and vice versa.
If someone is either wise or quiet then someone is not happy or not creative and vice versa.
Everyone who is not humble or not kind is rich or not tall and vice versa.
Alice is either not strong or patient.
Someone is funny or humble.
Paul is generous or not rich.
Alice is strong or humble.
Paul is both not humble and creative.
Paul is either curious or not calm.
John is calm. | Paul is not strong. | contradiction | ((humble(alice))=>(?[X]:((old(X)|~creative(X)))))&
(![X]:((~strong(X)|~funny(X))<=>(~humble(X)&generous(X))))&
((?[X]:((~tall(X)|~curious(X))))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(((old(fred)&~tall(fred)))<=>(humble(lucy)))&
(![X]:((~strong(X)<~>~creative(X))<=>~creative(X)))&
((~strong(paul))=>(?[X]:(quiet(X))))&
(![X]:(~curious(X)<=>~strong(X)))&
(![X]:(strong(X)<=>(creative(X)&~quiet(X))))&
(![X]:((~curious(X)&strong(X))=>(strong(X)<~>rich(X))))&
(![X]:((quiet(X)&~calm(X))=>(curious(X)&~strong(X))))&
(((~quiet(susan)<~>tall(susan)))=>(?[X]:((brave(X)<~>~strong(X)))))&
(![X]:(~patient(X)=>quiet(X)))&
((?[X]:((~strong(X)<~>brave(X))))<=>(?[X]:((~strong(X)<~>calm(X)))))&
((?[X]:((wise(X)<~>quiet(X))))<=>(?[X]:((~happy(X)|~creative(X)))))&
(![X]:((~humble(X)|~kind(X))<=>(rich(X)|~tall(X))))&
((~strong(alice)<~>patient(alice)))&
(?[X]:((funny(X)|humble(X))))&
((generous(paul)|~rich(paul)))&
((strong(alice)|humble(alice)))&
((~humble(paul)&creative(paul)))&
((curious(paul)<~>~calm(paul)))&
(calm(john)) | ~strong(paul) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 1870281264767333766824481
% SZS output start Proof for 1870281264767333766824481
5. ! [X0] : ((~strong(X0) <~> ~creative(X0)) <=> ~creative(X0)) [input p4]
23. ~strong(paul) [input hypothesis]
46. ! [X0] : ((((creative(X0) | strong(X0)) & (~creative(X0) | ~strong(X0))) | creative(X0)) & (~creative(X0) | ((~strong(X0) | creative(X0)) & (~creative(X0) | strong(X0))))) [nnf transformation 5]
87. ~creative(X0) | ~creative(X0) | strong(X0) [cnf transformation 46]
90. creative(X0) | strong(X0) | creative(X0) [cnf transformation 46]
134. ~strong(paul) [cnf transformation 23]
136. ~creative(X0) | strong(X0) [duplicate literal removal 87]
137. creative(X0) | strong(X0) [duplicate literal removal 90]
200. strong(X0) [subsumption resolution 136,137]
277. $false [subsumption resolution 134,200]
% SZS output end Proof for 1870281264767333766824481
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and tall is either not old or not kind. Everyone who is patient or not old is not old. Everyone who is both not wise and strong is not creative and vice versa. Everyone who is not brave or strong is either not calm or not strong. If fred is not old then someone is not humble or not funny and vice versa. Everyone who is not humble is not curious and vice versa. Everyone who is not old or strong is not humble. Everyone who is both not wise and not rich is both wise and calm and vice versa. If john is curious then fred is humble and vice versa. If someone is both not curious and not generous then fred is both not curious and generous. Everyone who is calm is either wise or humble. If someone is either not funny or quiet then alice is either not kind or not rich and vice versa. If paul is generous or not kind then someone is both not creative and not funny. Everyone who is not curious is happy or old and vice versa. Everyone who is not rich or not brave is either brave or generous. If fred is both generous and not happy then someone is brave. Someone is brave. Someone is patient or not quiet. Alice is not strong. Someone is not generous. Mary is not patient or patient. Someone is not calm. | John is not strong. | neutral | (![X]:((~strong(X)&tall(X))=>(~old(X)<~>~kind(X))))&
(![X]:((patient(X)|~old(X))=>~old(X)))&
(![X]:((~wise(X)&strong(X))<=>~creative(X)))&
(![X]:((~brave(X)|strong(X))=>(~calm(X)<~>~strong(X))))&
((~old(fred))<=>(?[X]:((~humble(X)|~funny(X)))))&
(![X]:(~humble(X)<=>~curious(X)))&
(![X]:((~old(X)|strong(X))=>~humble(X)))&
(![X]:((~wise(X)&~rich(X))<=>(wise(X)&calm(X))))&
((curious(john))<=>(humble(fred)))&
((?[X]:((~curious(X)&~generous(X))))=>((~curious(fred)&generous(fred))))&
(![X]:(calm(X)=>(wise(X)<~>humble(X))))&
((?[X]:((~funny(X)<~>quiet(X))))<=>((~kind(alice)<~>~rich(alice))))&
(((generous(paul)|~kind(paul)))=>(?[X]:((~creative(X)&~funny(X)))))&
(![X]:(~curious(X)<=>(happy(X)|old(X))))&
(![X]:((~rich(X)|~brave(X))=>(brave(X)<~>generous(X))))&
(((generous(fred)&~happy(fred)))=>(?[X]:(brave(X))))&
(?[X]:(brave(X)))&
(?[X]:((patient(X)|~quiet(X))))&
(~strong(alice))&
(?[X]:(~generous(X)))&
((~patient(mary)|patient(mary)))&
(?[X]:(~calm(X))) | ~strong(john) | [] | null | 0 |
If mary is not happy or curious then someone is strong or not tall. Everyone who is both calm and happy is both strong and not tall and vice versa. Everyone who is rich is both wise and kind and vice versa. Everyone who is not creative or not humble is funny and vice versa. Everyone who is either curious or kind is brave and vice versa. Everyone who is wise or curious is humble or not calm. If lucy is quiet or brave then someone is funny. If someone is both not funny and not curious then alice is funny and vice versa. Everyone who is not wise or quiet is both curious and not humble and vice versa. If john is both calm and not tall then paul is both calm and happy. If mary is both not strong and old then fred is both funny and not brave and vice versa. If someone is patient or not humble then paul is happy or wise. Everyone who is either humble or funny is not kind or not strong. If susan is not kind then susan is both generous and not old and vice versa. Everyone who is funny or tall is patient and vice versa. Everyone who is either happy or humble is either not brave or not calm. Someone is not humble or not kind. Someone is both funny and strong. Paul is wise. Someone is not humble. Someone is humble. Someone is generous. Mary is not generous. Lucy is both creative and not patient. | Paul is patient. | neutral | (((~happy(mary)|curious(mary)))=>(?[X]:((strong(X)|~tall(X)))))&
(![X]:((calm(X)&happy(X))<=>(strong(X)&~tall(X))))&
(![X]:(rich(X)<=>(wise(X)&kind(X))))&
(![X]:((~creative(X)|~humble(X))<=>funny(X)))&
(![X]:((curious(X)<~>kind(X))<=>brave(X)))&
(![X]:((wise(X)|curious(X))=>(humble(X)|~calm(X))))&
(((quiet(lucy)|brave(lucy)))=>(?[X]:(funny(X))))&
((?[X]:((~funny(X)&~curious(X))))<=>(funny(alice)))&
(![X]:((~wise(X)|quiet(X))<=>(curious(X)&~humble(X))))&
(((calm(john)&~tall(john)))=>((calm(paul)&happy(paul))))&
(((~strong(mary)&old(mary)))<=>((funny(fred)&~brave(fred))))&
((?[X]:((patient(X)|~humble(X))))=>((happy(paul)|wise(paul))))&
(![X]:((humble(X)<~>funny(X))=>(~kind(X)|~strong(X))))&
((~kind(susan))<=>((generous(susan)&~old(susan))))&
(![X]:((funny(X)|tall(X))<=>patient(X)))&
(![X]:((happy(X)<~>humble(X))=>(~brave(X)<~>~calm(X))))&
(?[X]:((~humble(X)|~kind(X))))&
(?[X]:((funny(X)&strong(X))))&
(wise(paul))&
(?[X]:(~humble(X)))&
(?[X]:(humble(X)))&
(?[X]:(generous(X)))&
(~generous(mary))&
((creative(lucy)&~patient(lucy))) | patient(paul) | [] | null | 0 |
Everyone who is either not quiet or kind is both not humble and not happy. Everyone who is rich or kind is not generous or funny and vice versa. If someone is either not creative or funny then mary is both not quiet and not curious. If susan is kind or not old then lucy is wise or not curious. Everyone who is not calm or brave is both funny and rich and vice versa. Everyone who is happy or not happy is not creative and vice versa. Everyone who is not tall or rich is both not wise and wise. Everyone who is not old is both not quiet and humble. Everyone who is both humble and not happy is not happy. If someone is curious then mary is curious or creative and vice versa. If someone is patient then someone is not kind or old. Everyone who is not patient is not rich or humble and vice versa. Everyone who is either quiet or not creative is patient or rich. Everyone who is either not brave or not happy is strong or not wise. Alice is not creative. John is curious or not curious. Someone is both quiet and strong. Someone is humble or curious. Someone is both curious and not happy. Alice is not curious. | Mary is humble. | contradiction | (![X]:((~quiet(X)<~>kind(X))=>(~humble(X)&~happy(X))))&
(![X]:((rich(X)|kind(X))<=>(~generous(X)|funny(X))))&
((?[X]:((~creative(X)<~>funny(X))))=>((~quiet(mary)&~curious(mary))))&
(((kind(susan)|~old(susan)))=>((wise(lucy)|~curious(lucy))))&
(![X]:((~calm(X)|brave(X))<=>(funny(X)&rich(X))))&
(![X]:((happy(X)|~happy(X))<=>~creative(X)))&
(![X]:((~tall(X)|rich(X))=>(~wise(X)&wise(X))))&
(![X]:(~old(X)=>(~quiet(X)&humble(X))))&
(![X]:((humble(X)&~happy(X))=>~happy(X)))&
((?[X]:(curious(X)))<=>((curious(mary)|creative(mary))))&
((?[X]:(patient(X)))=>(?[X]:((~kind(X)|old(X)))))&
(![X]:(~patient(X)<=>(~rich(X)|humble(X))))&
(![X]:((quiet(X)<~>~creative(X))=>(patient(X)|rich(X))))&
(![X]:((~brave(X)<~>~happy(X))=>(strong(X)|~wise(X))))&
(~creative(alice))&
((curious(john)|~curious(john)))&
(?[X]:((quiet(X)&strong(X))))&
(?[X]:((humble(X)|curious(X))))&
(?[X]:((curious(X)&~happy(X))))&
(~curious(alice)) | humble(mary) | [
"p0",
"p1",
"p2",
"p5",
"p6",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2439098466520303618146168
% SZS output start Proof for 2439098466520303618146168
1. ! [X0] : ((~quiet(X0) <~> kind(X0)) => (~happy(X0) & ~humble(X0))) [input p0]
2. ! [X0] : ((kind(X0) | rich(X0)) <=> (funny(X0) | ~generous(X0))) [input p1]
3. ? [X0] : (~creative(X0) <~> funny(X0)) => (~curious(mary) & ~quiet(mary)) [input p2]
6. ! [X0] : ((~happy(X0) | happy(X0)) <=> ~creative(X0)) [input p5]
7. ! [X0] : ((rich(X0) | ~tall(X0)) => (wise(X0) & ~wise(X0))) [input p6]
12. ! [X0] : (~patient(X0) <=> (humble(X0) | ~rich(X0))) [input p11]
13. ! [X0] : ((quiet(X0) <~> ~creative(X0)) => (rich(X0) | patient(X0))) [input p12]
21. humble(mary) [input hypothesis]
25. ! [X0] : (rich(X0) => (wise(X0) & ~wise(X0))) [pure predicate removal 7]
29. ! [X0] : ((humble(X0) | ~rich(X0)) => ~patient(X0)) [unused predicate definition removal 12]
30. ! [X0] : ((~happy(X0) & ~humble(X0)) | (~quiet(X0) <=> kind(X0))) [ennf transformation 1]
31. (~curious(mary) & ~quiet(mary)) | ! [X0] : (~creative(X0) <=> funny(X0)) [ennf transformation 3]
34. ! [X0] : ((wise(X0) & ~wise(X0)) | ~rich(X0)) [ennf transformation 25]
37. ! [X0] : (~patient(X0) | (~humble(X0) & rich(X0))) [ennf transformation 29]
38. ! [X0] : ((rich(X0) | patient(X0)) | (quiet(X0) <=> ~creative(X0))) [ennf transformation 13]
39. ! [X0] : (rich(X0) | patient(X0) | (quiet(X0) <=> ~creative(X0))) [flattening 38]
40. ! [X0] : ((~happy(X0) & ~humble(X0)) | ((~quiet(X0) | ~kind(X0)) & (kind(X0) | quiet(X0)))) [nnf transformation 30]
41. ! [X0] : (((kind(X0) | rich(X0)) | (~funny(X0) & generous(X0))) & ((funny(X0) | ~generous(X0)) | (~kind(X0) & ~rich(X0)))) [nnf transformation 2]
42. ! [X0] : ((kind(X0) | rich(X0) | (~funny(X0) & generous(X0))) & (funny(X0) | ~generous(X0) | (~kind(X0) & ~rich(X0)))) [flattening 41]
43. (~curious(mary) & ~quiet(mary)) | ! [X0] : ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0))) [nnf transformation 31]
46. ! [X0] : (((~happy(X0) | happy(X0)) | creative(X0)) & (~creative(X0) | (happy(X0) & ~happy(X0)))) [nnf transformation 6]
47. ! [X0] : ((~happy(X0) | happy(X0) | creative(X0)) & (~creative(X0) | (happy(X0) & ~happy(X0)))) [flattening 46]
53. ! [X0] : (rich(X0) | patient(X0) | ((quiet(X0) | creative(X0)) & (~creative(X0) | ~quiet(X0)))) [nnf transformation 39]
61. ~humble(X0) | ~quiet(X0) | ~kind(X0) [cnf transformation 40]
67. ~funny(X0) | rich(X0) | kind(X0) [cnf transformation 42]
68. ~quiet(mary) | funny(X0) | creative(X0) [cnf transformation 43]
78. ~creative(X0) | ~happy(X0) [cnf transformation 47]
79. ~creative(X0) | happy(X0) [cnf transformation 47]
81. ~wise(X0) | ~rich(X0) [cnf transformation 34]
82. ~rich(X0) | wise(X0) [cnf transformation 34]
87. ~patient(X0) | rich(X0) [cnf transformation 37]
90. rich(X0) | patient(X0) | quiet(X0) | creative(X0) [cnf transformation 53]
98. humble(mary) [cnf transformation 21]
108. 3 <=> ! [X0] : (funny(X0) | creative(X0)) [avatar definition]
109. funny(X0) | creative(X0) <- (3) [avatar component clause 108]
112. 4 <=> quiet(mary) [avatar definition]
114. ~quiet(mary) <- (~4) [avatar component clause 112]
116. 3 | ~4 [avatar split clause 68,112,108]
130. ~creative(X0) [subsumption resolution 78,79]
131. ~rich(X0) [subsumption resolution 81,82]
142. ~patient(X0) [subsumption resolution 87,131]
143. patient(X0) | quiet(X0) | creative(X0) [subsumption resolution 90,131]
144. quiet(X0) | creative(X0) [subsumption resolution 143,142]
145. quiet(X0) [subsumption resolution 144,130]
155. $false <- (~4) [subsumption resolution 114,145]
156. 4 [avatar contradiction clause 155]
157. funny(X0) <- (3) [subsumption resolution 109,130]
162. ~quiet(mary) | ~kind(mary) [resolution 61,98]
164. ~kind(mary) [subsumption resolution 162,145]
168. rich(X0) | kind(X0) <- (3) [resolution 67,157]
169. kind(X0) <- (3) [subsumption resolution 168,131]
172. $false <- (3) [resolution 169,164]
175. ~3 [avatar contradiction clause 172]
176. $false [avatar sat refutation 116,156,175]
% SZS output end Proof for 2439098466520303618146168
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not old or not quiet then fred is not rich and vice versa.
Everyone who is either old or not rich is not rich.
Everyone who is both old and wise is either old or not old.
Everyone who is either not curious or funny is both tall and not wise and vice versa.
Everyone who is either humble or funny is not happy and vice versa.
Everyone who is not happy or not funny is both not curious and not calm.
Everyone who is both patient and not rich is funny.
If someone is both not quiet and happy then paul is old or not funny and vice versa.
If mary is not brave or not old then someone is either rich or generous.
If someone is either humble or not calm then alice is both wise and not quiet and vice versa.
Everyone who is either not tall or not old is not generous.
If mary is not rich or not old then someone is tall or not brave and vice versa.
Everyone who is both not brave and not creative is generous and vice versa.
If someone is both not creative and patient then someone is either not curious or old.
If mary is generous then susan is both quiet and happy.
Everyone who is not calm or not wise is kind or quiet and vice versa.
Someone is both not wise and not generous.
Mary is generous or not creative.
Someone is both not tall and calm.
Someone is both generous and not creative.
Someone is either funny or calm.
Paul is tall or not old.
Someone is not tall.
Lucy is not quiet. | Mary is creative. | contradiction | ((?[X]:((~old(X)<~>~quiet(X))))<=>(~rich(fred)))&
(![X]:((old(X)<~>~rich(X))=>~rich(X)))&
(![X]:((old(X)&wise(X))=>(old(X)<~>~old(X))))&
(![X]:((~curious(X)<~>funny(X))<=>(tall(X)&~wise(X))))&
(![X]:((humble(X)<~>funny(X))<=>~happy(X)))&
(![X]:((~happy(X)|~funny(X))=>(~curious(X)&~calm(X))))&
(![X]:((patient(X)&~rich(X))=>funny(X)))&
((?[X]:((~quiet(X)&happy(X))))<=>((old(paul)|~funny(paul))))&
(((~brave(mary)|~old(mary)))=>(?[X]:((rich(X)<~>generous(X)))))&
((?[X]:((humble(X)<~>~calm(X))))<=>((wise(alice)&~quiet(alice))))&
(![X]:((~tall(X)<~>~old(X))=>~generous(X)))&
(((~rich(mary)|~old(mary)))<=>(?[X]:((tall(X)|~brave(X)))))&
(![X]:((~brave(X)&~creative(X))<=>generous(X)))&
((?[X]:((~creative(X)&patient(X))))=>(?[X]:((~curious(X)<~>old(X)))))&
((generous(mary))=>((quiet(susan)&happy(susan))))&
(![X]:((~calm(X)|~wise(X))<=>(kind(X)|quiet(X))))&
(?[X]:((~wise(X)&~generous(X))))&
((generous(mary)|~creative(mary)))&
(?[X]:((~tall(X)&calm(X))))&
(?[X]:((generous(X)&~creative(X))))&
(?[X]:((funny(X)<~>calm(X))))&
((tall(paul)|~old(paul)))&
(?[X]:(~tall(X)))&
(~quiet(lucy)) | creative(mary) | [
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8817164170273948874365818
% SZS output start Proof for 8817164170273948874365818
13. ! [X0] : ((~creative(X0) & ~brave(X0)) <=> generous(X0)) [input p12]
18. ~creative(mary) | generous(mary) [input p17]
25. creative(mary) [input hypothesis]
64. ! [X0] : (((~creative(X0) & ~brave(X0)) | ~generous(X0)) & (generous(X0) | (creative(X0) | brave(X0)))) [nnf transformation 13]
65. ! [X0] : (((~creative(X0) & ~brave(X0)) | ~generous(X0)) & (generous(X0) | creative(X0) | brave(X0))) [flattening 64]
124. ~creative(X0) | ~generous(X0) [cnf transformation 65]
133. ~creative(mary) | generous(mary) [cnf transformation 18]
143. creative(mary) [cnf transformation 25]
269. ~creative(mary) [subsumption resolution 133,124]
277. $false [subsumption resolution 143,269]
% SZS output end Proof for 8817164170273948874365818
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is both not curious and not wise. Everyone who is brave or creative is either not creative or not humble. If john is both not rich and not happy then someone is either curious or happy. Everyone who is tall is both not creative and not quiet. Everyone who is patient is humble or not wise. Everyone who is not patient is curious or not calm. If someone is tall then john is either not wise or not kind and vice versa. If mary is not generous then susan is both rich and not happy and vice versa. If someone is both not wise and kind then lucy is either curious or not humble. Everyone who is either curious or old is both patient and not strong. Everyone who is wise is either not patient or kind and vice versa. If someone is both not brave and not old then someone is both not strong and not brave. Everyone who is not rich or creative is either humble or calm and vice versa. Everyone who is either strong or generous is calm and vice versa. If someone is both tall and not tall then fred is not brave or generous and vice versa. Everyone who is either not kind or not patient is not calm or tall and vice versa. Alice is brave. Someone is either not brave or generous. Fred is not rich or not brave. Paul is not generous. Someone is both old and happy. John is not wise. | Paul is rich. | neutral | (![X]:(calm(X)=>(~curious(X)&~wise(X))))&
(![X]:((brave(X)|creative(X))=>(~creative(X)<~>~humble(X))))&
(((~rich(john)&~happy(john)))=>(?[X]:((curious(X)<~>happy(X)))))&
(![X]:(tall(X)=>(~creative(X)&~quiet(X))))&
(![X]:(patient(X)=>(humble(X)|~wise(X))))&
(![X]:(~patient(X)=>(curious(X)|~calm(X))))&
((?[X]:(tall(X)))<=>((~wise(john)<~>~kind(john))))&
((~generous(mary))<=>((rich(susan)&~happy(susan))))&
((?[X]:((~wise(X)&kind(X))))=>((curious(lucy)<~>~humble(lucy))))&
(![X]:((curious(X)<~>old(X))=>(patient(X)&~strong(X))))&
(![X]:(wise(X)<=>(~patient(X)<~>kind(X))))&
((?[X]:((~brave(X)&~old(X))))=>(?[X]:((~strong(X)&~brave(X)))))&
(![X]:((~rich(X)|creative(X))<=>(humble(X)<~>calm(X))))&
(![X]:((strong(X)<~>generous(X))<=>calm(X)))&
((?[X]:((tall(X)&~tall(X))))<=>((~brave(fred)|generous(fred))))&
(![X]:((~kind(X)<~>~patient(X))<=>(~calm(X)|tall(X))))&
(brave(alice))&
(?[X]:((~brave(X)<~>generous(X))))&
((~rich(fred)|~brave(fred)))&
(~generous(paul))&
(?[X]:((old(X)&happy(X))))&
(~wise(john)) | rich(paul) | [] | null | 0 |
If someone is not creative then someone is not tall.
If paul is either curious or patient then paul is both not happy and rich and vice versa.
If john is either patient or not brave then mary is either not generous or not calm and vice versa.
If lucy is both not kind and curious then someone is creative or not quiet.
Everyone who is either not strong or not patient is both not strong and not happy and vice versa.
If someone is both happy and not creative then mary is quiet and vice versa.
If paul is not happy or not tall then someone is happy or humble and vice versa.
Everyone who is either curious or not happy is both curious and kind and vice versa.
Everyone who is both not calm and tall is calm and vice versa.
Everyone who is both tall and funny is either funny or quiet.
If fred is either not strong or not kind then someone is funny or rich.
Everyone who is both not creative and not patient is either not old or not wise and vice versa.
If paul is tall then fred is happy and vice versa.
Everyone who is either not creative or quiet is either curious or not patient.
If someone is kind then paul is humble.
If someone is both humble and strong then paul is either tall or not strong and vice versa.
Someone is not kind or not generous.
Someone is quiet.
Someone is strong.
Mary is both not tall and humble.
Alice is wise.
Mary is brave. | Alice is not curious. | neutral | ((?[X]:(~creative(X)))=>(?[X]:(~tall(X))))&
(((curious(paul)<~>patient(paul)))<=>((~happy(paul)&rich(paul))))&
(((patient(john)<~>~brave(john)))<=>((~generous(mary)<~>~calm(mary))))&
(((~kind(lucy)&curious(lucy)))=>(?[X]:((creative(X)|~quiet(X)))))&
(![X]:((~strong(X)<~>~patient(X))<=>(~strong(X)&~happy(X))))&
((?[X]:((happy(X)&~creative(X))))<=>(quiet(mary)))&
(((~happy(paul)|~tall(paul)))<=>(?[X]:((happy(X)|humble(X)))))&
(![X]:((curious(X)<~>~happy(X))<=>(curious(X)&kind(X))))&
(![X]:((~calm(X)&tall(X))<=>calm(X)))&
(![X]:((tall(X)&funny(X))=>(funny(X)<~>quiet(X))))&
(((~strong(fred)<~>~kind(fred)))=>(?[X]:((funny(X)|rich(X)))))&
(![X]:((~creative(X)&~patient(X))<=>(~old(X)<~>~wise(X))))&
((tall(paul))<=>(happy(fred)))&
(![X]:((~creative(X)<~>quiet(X))=>(curious(X)<~>~patient(X))))&
((?[X]:(kind(X)))=>(humble(paul)))&
((?[X]:((humble(X)&strong(X))))<=>((tall(paul)<~>~strong(paul))))&
(?[X]:((~kind(X)|~generous(X))))&
(?[X]:(quiet(X)))&
(?[X]:(strong(X)))&
((~tall(mary)&humble(mary)))&
(wise(alice))&
(brave(mary)) | ~curious(alice) | [] | null | 0 |
Everyone who is either not quiet or not curious is not kind or not brave and vice versa.
Everyone who is either not brave or rich is not calm or not rich.
Everyone who is either not tall or not curious is both curious and creative.
Everyone who is either not curious or generous is not old or strong and vice versa.
If someone is strong then fred is not funny and vice versa.
If someone is both rich and quiet then paul is tall and vice versa.
If someone is either not kind or not humble then someone is both not funny and funny and vice versa.
If someone is either happy or wise then lucy is tall or not happy.
Everyone who is both curious and calm is both not tall and strong.
Everyone who is not wise or wise is both humble and brave and vice versa.
If someone is not wise then lucy is either not generous or not happy and vice versa.
Everyone who is old or not old is either curious or not quiet.
Everyone who is either strong or patient is both not wise and not old and vice versa.
If alice is both not kind and not funny then lucy is either not calm or funny.
If susan is kind then fred is both not old and tall.
Everyone who is not wise is not brave and vice versa.
Alice is both not generous and old.
Mary is not funny or funny.
Someone is either not patient or not wise.
John is wise or generous.
Someone is both humble and quiet.
John is wise.
John is both strong and rich.
Susan is quiet. | Paul is not humble. | contradiction | (![X]:((~quiet(X)<~>~curious(X))<=>(~kind(X)|~brave(X))))&
(![X]:((~brave(X)<~>rich(X))=>(~calm(X)|~rich(X))))&
(![X]:((~tall(X)<~>~curious(X))=>(curious(X)&creative(X))))&
(![X]:((~curious(X)<~>generous(X))<=>(~old(X)|strong(X))))&
((?[X]:(strong(X)))<=>(~funny(fred)))&
((?[X]:((rich(X)&quiet(X))))<=>(tall(paul)))&
((?[X]:((~kind(X)<~>~humble(X))))<=>(?[X]:((~funny(X)&funny(X)))))&
((?[X]:((happy(X)<~>wise(X))))=>((tall(lucy)|~happy(lucy))))&
(![X]:((curious(X)&calm(X))=>(~tall(X)&strong(X))))&
(![X]:((~wise(X)|wise(X))<=>(humble(X)&brave(X))))&
((?[X]:(~wise(X)))<=>((~generous(lucy)<~>~happy(lucy))))&
(![X]:((old(X)|~old(X))=>(curious(X)<~>~quiet(X))))&
(![X]:((strong(X)<~>patient(X))<=>(~wise(X)&~old(X))))&
(((~kind(alice)&~funny(alice)))=>((~calm(lucy)<~>funny(lucy))))&
((kind(susan))=>((~old(fred)&tall(fred))))&
(![X]:(~wise(X)<=>~brave(X)))&
((~generous(alice)&old(alice)))&
((~funny(mary)|funny(mary)))&
(?[X]:((~patient(X)<~>~wise(X))))&
((wise(john)|generous(john)))&
(?[X]:((humble(X)&quiet(X))))&
(wise(john))&
((strong(john)&rich(john)))&
(quiet(susan)) | ~humble(paul) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2624905660753075699608288
% SZS output start Proof for 2624905660753075699608288
10. ! [X0] : ((wise(X0) | ~wise(X0)) <=> (brave(X0) & humble(X0))) [input p9]
25. ~humble(paul) [input hypothesis]
59. ! [X0] : (((wise(X0) | ~wise(X0)) | (~brave(X0) | ~humble(X0))) & ((brave(X0) & humble(X0)) | (~wise(X0) & wise(X0)))) [nnf transformation 10]
60. ! [X0] : ((wise(X0) | ~wise(X0) | ~brave(X0) | ~humble(X0)) & ((brave(X0) & humble(X0)) | (~wise(X0) & wise(X0)))) [flattening 59]
106. humble(X0) | wise(X0) [cnf transformation 60]
107. humble(X0) | ~wise(X0) [cnf transformation 60]
143. ~humble(paul) [cnf transformation 25]
209. humble(X0) [subsumption resolution 106,107]
281. $false [subsumption resolution 143,209]
% SZS output end Proof for 2624905660753075699608288
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or not tall is not rich or not quiet and vice versa. If lucy is both not patient and creative then fred is not patient. Everyone who is patient is not generous. If someone is both old and not old then someone is both not strong and not humble and vice versa. Everyone who is both generous and kind is not generous. Everyone who is either not generous or not quiet is both not humble and curious and vice versa. Everyone who is not happy or curious is not funny or funny and vice versa. Everyone who is both generous and not humble is creative and vice versa. If paul is both not funny and tall then someone is both wise and rich. Everyone who is both brave and not happy is patient or not calm. Everyone who is not quiet or strong is both not brave and curious and vice versa. If someone is both not happy and brave then someone is both curious and not patient and vice versa. If someone is both not happy and kind then someone is creative and vice versa. If mary is both tall and not humble then someone is both creative and tall. Everyone who is either not old or patient is kind and vice versa. Everyone who is both kind and not tall is either not strong or curious. Mary is either tall or funny. John is either quiet or patient. Paul is humble. Susan is not humble or not generous. Someone is either not strong or not rich. Alice is curious. Someone is not kind. Fred is not humble or not wise. | John is calm. | neutral | (![X]:((kind(X)|~tall(X))<=>(~rich(X)|~quiet(X))))&
(((~patient(lucy)&creative(lucy)))=>(~patient(fred)))&
(![X]:(patient(X)=>~generous(X)))&
((?[X]:((old(X)&~old(X))))<=>(?[X]:((~strong(X)&~humble(X)))))&
(![X]:((generous(X)&kind(X))=>~generous(X)))&
(![X]:((~generous(X)<~>~quiet(X))<=>(~humble(X)&curious(X))))&
(![X]:((~happy(X)|curious(X))<=>(~funny(X)|funny(X))))&
(![X]:((generous(X)&~humble(X))<=>creative(X)))&
(((~funny(paul)&tall(paul)))=>(?[X]:((wise(X)&rich(X)))))&
(![X]:((brave(X)&~happy(X))=>(patient(X)|~calm(X))))&
(![X]:((~quiet(X)|strong(X))<=>(~brave(X)&curious(X))))&
((?[X]:((~happy(X)&brave(X))))<=>(?[X]:((curious(X)&~patient(X)))))&
((?[X]:((~happy(X)&kind(X))))<=>(?[X]:(creative(X))))&
(((tall(mary)&~humble(mary)))=>(?[X]:((creative(X)&tall(X)))))&
(![X]:((~old(X)<~>patient(X))<=>kind(X)))&
(![X]:((kind(X)&~tall(X))=>(~strong(X)<~>curious(X))))&
((tall(mary)<~>funny(mary)))&
((quiet(john)<~>patient(john)))&
(humble(paul))&
((~humble(susan)|~generous(susan)))&
(?[X]:((~strong(X)<~>~rich(X))))&
(curious(alice))&
(?[X]:(~kind(X)))&
((~humble(fred)|~wise(fred))) | calm(john) | [] | null | 0 |
If someone is not calm then someone is happy or brave.
If someone is either not wise or strong then someone is not wise or happy and vice versa.
Everyone who is either not calm or generous is not calm or brave and vice versa.
Everyone who is both not humble and happy is either tall or humble and vice versa.
Everyone who is both not old and not rich is both not generous and strong.
Everyone who is not patient is both not wise and calm.
If someone is either patient or calm then john is either not calm or happy and vice versa.
If john is not generous or not rich then someone is not generous or wise.
If mary is wise then susan is either patient or not tall and vice versa.
Everyone who is not wise or rich is both not rich and not patient.
If someone is either not generous or patient then lucy is rich.
Everyone who is patient or not calm is both kind and old.
Everyone who is happy is both not generous and not quiet.
If someone is either rich or not patient then someone is both patient and funny.
If paul is humble then someone is both not patient and not rich and vice versa.
If someone is not quiet or strong then susan is not brave and vice versa.
Paul is either not creative or quiet.
Paul is either not rich or strong.
Alice is generous or not brave.
Someone is old.
Alice is either not curious or not generous.
Susan is not kind or not curious.
Someone is either old or strong. | Susan is not old. | contradiction | ((?[X]:(~calm(X)))=>(?[X]:((happy(X)|brave(X)))))&
((?[X]:((~wise(X)<~>strong(X))))<=>(?[X]:((~wise(X)|happy(X)))))&
(![X]:((~calm(X)<~>generous(X))<=>(~calm(X)|brave(X))))&
(![X]:((~humble(X)&happy(X))<=>(tall(X)<~>humble(X))))&
(![X]:((~old(X)&~rich(X))=>(~generous(X)&strong(X))))&
(![X]:(~patient(X)=>(~wise(X)&calm(X))))&
((?[X]:((patient(X)<~>calm(X))))<=>((~calm(john)<~>happy(john))))&
(((~generous(john)|~rich(john)))=>(?[X]:((~generous(X)|wise(X)))))&
((wise(mary))<=>((patient(susan)<~>~tall(susan))))&
(![X]:((~wise(X)|rich(X))=>(~rich(X)&~patient(X))))&
((?[X]:((~generous(X)<~>patient(X))))=>(rich(lucy)))&
(![X]:((patient(X)|~calm(X))=>(kind(X)&old(X))))&
(![X]:(happy(X)=>(~generous(X)&~quiet(X))))&
((?[X]:((rich(X)<~>~patient(X))))=>(?[X]:((patient(X)&funny(X)))))&
((humble(paul))<=>(?[X]:((~patient(X)&~rich(X)))))&
((?[X]:((~quiet(X)|strong(X))))<=>(~brave(susan)))&
((~creative(paul)<~>quiet(paul)))&
((~rich(paul)<~>strong(paul)))&
((generous(alice)|~brave(alice)))&
(?[X]:(old(X)))&
((~curious(alice)<~>~generous(alice)))&
((~kind(susan)|~curious(susan)))&
(?[X]:((old(X)<~>strong(X)))) | ~old(susan) | [
"p4",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6062716859222720750567051
% SZS output start Proof for 6062716859222720750567051
5. ! [X0] : ((~rich(X0) & ~old(X0)) => (strong(X0) & ~generous(X0))) [input p4]
10. ! [X0] : ((rich(X0) | ~wise(X0)) => (~patient(X0) & ~rich(X0))) [input p9]
11. ? [X0] : (~generous(X0) <~> patient(X0)) => rich(lucy) [input p10]
12. ! [X0] : ((~calm(X0) | patient(X0)) => (old(X0) & kind(X0))) [input p11]
24. ~old(susan) [input hypothesis]
30. ! [X0] : ((strong(X0) & ~generous(X0)) | (rich(X0) | old(X0))) [ennf transformation 5]
31. ! [X0] : ((strong(X0) & ~generous(X0)) | rich(X0) | old(X0)) [flattening 30]
34. ! [X0] : ((~patient(X0) & ~rich(X0)) | (~rich(X0) & wise(X0))) [ennf transformation 10]
35. rich(lucy) | ! [X0] : (~generous(X0) <=> patient(X0)) [ennf transformation 11]
36. ! [X0] : ((old(X0) & kind(X0)) | (calm(X0) & ~patient(X0))) [ennf transformation 12]
58. rich(lucy) | ! [X0] : ((~generous(X0) | ~patient(X0)) & (patient(X0) | generous(X0))) [nnf transformation 35]
98. ~generous(X0) | rich(X0) | old(X0) [cnf transformation 31]
117. ~rich(X0) | ~rich(X0) [cnf transformation 34]
120. rich(lucy) | patient(X0) | generous(X0) [cnf transformation 58]
124. ~patient(X0) | old(X0) [cnf transformation 36]
147. ~old(susan) [cnf transformation 24]
148. ~rich(X0) [duplicate literal removal 117]
253. 22 <=> patient(susan) [avatar definition]
254. ~patient(susan) <- (~22) [avatar component clause 253]
255. patient(susan) <- (22) [avatar component clause 253]
265. patient(X0) | generous(X0) [subsumption resolution 120,148]
403. old(susan) <- (22) [resolution 255,124]
407. $false <- (22) [subsumption resolution 403,147]
408. ~22 [avatar contradiction clause 407]
421. generous(susan) <- (~22) [resolution 254,265]
438. rich(susan) | old(susan) <- (~22) [resolution 98,421]
441. old(susan) <- (~22) [subsumption resolution 438,148]
442. $false <- (~22) [subsumption resolution 441,147]
443. 22 [avatar contradiction clause 442]
444. $false [avatar sat refutation 408,443]
% SZS output end Proof for 6062716859222720750567051
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or kind is either not happy or not funny and vice versa.
Everyone who is either tall or not strong is both calm and wise and vice versa.
Everyone who is both strong and not old is either not creative or brave and vice versa.
If susan is both tall and not strong then someone is not tall and vice versa.
Everyone who is either strong or not funny is both rich and not strong and vice versa.
If mary is not brave then fred is not kind or quiet and vice versa.
Everyone who is not patient is not quiet or not patient.
If someone is generous then someone is not tall and vice versa.
If someone is either kind or generous then paul is not funny.
Everyone who is either not quiet or funny is not generous or not wise and vice versa.
If someone is either not patient or rich then alice is not quiet and vice versa.
Everyone who is either not rich or not kind is happy.
Everyone who is both patient and not funny is not happy or curious.
If someone is not quiet or not strong then someone is old.
If someone is both quiet and funny then someone is both calm and not tall and vice versa.
Everyone who is not generous or not curious is generous or not funny.
Someone is generous.
Paul is not patient or creative.
Lucy is kind.
Someone is not calm or creative.
Someone is both calm and quiet.
Someone is either not quiet or curious.
John is either not funny or humble.
Someone is both not kind and not patient. | Lucy is happy. | entailment | (![X]:((~patient(X)|kind(X))<=>(~happy(X)<~>~funny(X))))&
(![X]:((tall(X)<~>~strong(X))<=>(calm(X)&wise(X))))&
(![X]:((strong(X)&~old(X))<=>(~creative(X)<~>brave(X))))&
(((tall(susan)&~strong(susan)))<=>(?[X]:(~tall(X))))&
(![X]:((strong(X)<~>~funny(X))<=>(rich(X)&~strong(X))))&
((~brave(mary))<=>((~kind(fred)|quiet(fred))))&
(![X]:(~patient(X)=>(~quiet(X)|~patient(X))))&
((?[X]:(generous(X)))<=>(?[X]:(~tall(X))))&
((?[X]:((kind(X)<~>generous(X))))=>(~funny(paul)))&
(![X]:((~quiet(X)<~>funny(X))<=>(~generous(X)|~wise(X))))&
((?[X]:((~patient(X)<~>rich(X))))<=>(~quiet(alice)))&
(![X]:((~rich(X)<~>~kind(X))=>happy(X)))&
(![X]:((patient(X)&~funny(X))=>(~happy(X)|curious(X))))&
((?[X]:((~quiet(X)|~strong(X))))=>(?[X]:(old(X))))&
((?[X]:((quiet(X)&funny(X))))<=>(?[X]:((calm(X)&~tall(X)))))&
(![X]:((~generous(X)|~curious(X))=>(generous(X)|~funny(X))))&
(?[X]:(generous(X)))&
((~patient(paul)|creative(paul)))&
(kind(lucy))&
(?[X]:((~calm(X)|creative(X))))&
(?[X]:((calm(X)&quiet(X))))&
(?[X]:((~quiet(X)<~>curious(X))))&
((~funny(john)<~>humble(john)))&
(?[X]:((~kind(X)&~patient(X)))) | happy(lucy) | [
"p0",
"p4",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7218739889426917450141444
% SZS output start Proof for 7218739889426917450141444
1. ! [X0] : ((kind(X0) | ~patient(X0)) <=> (~happy(X0) <~> ~funny(X0))) [input p0]
5. ! [X0] : ((strong(X0) <~> ~funny(X0)) <=> (~strong(X0) & rich(X0))) [input p4]
12. ! [X0] : ((~rich(X0) <~> ~kind(X0)) => happy(X0)) [input p11]
19. kind(lucy) [input p18]
25. ~happy(lucy) [input hypothesis]
32. ! [X0] : (happy(X0) | (~rich(X0) <=> ~kind(X0))) [ennf transformation 12]
38. ! [X0] : (((kind(X0) | ~patient(X0)) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0)))) & (((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | (~kind(X0) & patient(X0)))) [nnf transformation 1]
39. ! [X0] : ((kind(X0) | ~patient(X0) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0)))) & (((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | (~kind(X0) & patient(X0)))) [flattening 38]
49. ! [X0] : ((((funny(X0) | ~strong(X0)) & (~funny(X0) | strong(X0))) | (strong(X0) | ~rich(X0))) & ((~strong(X0) & rich(X0)) | ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0))))) [nnf transformation 5]
50. ! [X0] : ((((funny(X0) | ~strong(X0)) & (~funny(X0) | strong(X0))) | strong(X0) | ~rich(X0)) & ((~strong(X0) & rich(X0)) | ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0))))) [flattening 49]
65. ! [X0] : (happy(X0) | ((~rich(X0) | kind(X0)) & (~kind(X0) | rich(X0)))) [nnf transformation 32]
89. ~kind(X0) | happy(X0) | funny(X0) [cnf transformation 39]
109. ~strong(X0) | ~funny(X0) | ~strong(X0) [cnf transformation 50]
111. ~funny(X0) | strong(X0) | strong(X0) | ~rich(X0) [cnf transformation 50]
131. ~kind(X0) | happy(X0) | rich(X0) [cnf transformation 65]
144. kind(lucy) [cnf transformation 19]
154. ~happy(lucy) [cnf transformation 25]
156. ~strong(X0) | ~funny(X0) [duplicate literal removal 109]
157. ~rich(X0) | strong(X0) | ~funny(X0) [duplicate literal removal 111]
371. happy(lucy) | funny(lucy) [resolution 89,144]
372. funny(lucy) [subsumption resolution 371,154]
515. happy(lucy) | rich(lucy) [resolution 131,144]
516. rich(lucy) [subsumption resolution 515,154]
601. strong(lucy) | ~funny(lucy) [resolution 157,516]
605. strong(lucy) [subsumption resolution 601,372]
859. ~funny(lucy) [resolution 605,156]
862. $false [subsumption resolution 859,372]
% SZS output end Proof for 7218739889426917450141444
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is tall or not happy and vice versa.
Everyone who is not humble is not happy or not wise.
If mary is not funny then mary is not old or not patient and vice versa.
Everyone who is not strong is either not kind or funny and vice versa.
If someone is not tall or not wise then mary is brave or not rich and vice versa.
If susan is either creative or old then mary is either curious or brave and vice versa.
Everyone who is generous is both calm and generous.
Everyone who is not wise or happy is calm or not calm.
Everyone who is brave or not wise is funny or not generous and vice versa.
If someone is either not quiet or quiet then someone is not funny or not calm.
If someone is creative then someone is both quiet and generous and vice versa.
If mary is not happy or kind then mary is both tall and not creative.
If someone is both kind and generous then someone is either not curious or not tall and vice versa.
If someone is not brave or tall then someone is not funny or curious.
If paul is both brave and creative then someone is creative and vice versa.
Everyone who is not rich or funny is both not humble and curious and vice versa.
Paul is both not tall and humble.
John is either wise or not kind.
Mary is not strong or not calm.
John is both calm and wise.
Susan is both not patient and creative.
Someone is not calm or quiet.
Someone is both not creative and not tall.
Someone is brave or not curious. | Paul is rich. | entailment | (![X]:(creative(X)<=>(tall(X)|~happy(X))))&
(![X]:(~humble(X)=>(~happy(X)|~wise(X))))&
((~funny(mary))<=>((~old(mary)|~patient(mary))))&
(![X]:(~strong(X)<=>(~kind(X)<~>funny(X))))&
((?[X]:((~tall(X)|~wise(X))))<=>((brave(mary)|~rich(mary))))&
(((creative(susan)<~>old(susan)))<=>((curious(mary)<~>brave(mary))))&
(![X]:(generous(X)=>(calm(X)&generous(X))))&
(![X]:((~wise(X)|happy(X))=>(calm(X)|~calm(X))))&
(![X]:((brave(X)|~wise(X))<=>(funny(X)|~generous(X))))&
((?[X]:((~quiet(X)<~>quiet(X))))=>(?[X]:((~funny(X)|~calm(X)))))&
((?[X]:(creative(X)))<=>(?[X]:((quiet(X)&generous(X)))))&
(((~happy(mary)|kind(mary)))=>((tall(mary)&~creative(mary))))&
((?[X]:((kind(X)&generous(X))))<=>(?[X]:((~curious(X)<~>~tall(X)))))&
((?[X]:((~brave(X)|tall(X))))=>(?[X]:((~funny(X)|curious(X)))))&
(((brave(paul)&creative(paul)))<=>(?[X]:(creative(X))))&
(![X]:((~rich(X)|funny(X))<=>(~humble(X)&curious(X))))&
((~tall(paul)&humble(paul)))&
((wise(john)<~>~kind(john)))&
((~strong(mary)|~calm(mary)))&
((calm(john)&wise(john)))&
((~patient(susan)&creative(susan)))&
(?[X]:((~calm(X)|quiet(X))))&
(?[X]:((~creative(X)&~tall(X))))&
(?[X]:((brave(X)|~curious(X)))) | rich(paul) | [
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6635939700345145760637653
% SZS output start Proof for 6635939700345145760637653
16. ! [X0] : ((funny(X0) | ~rich(X0)) <=> (curious(X0) & ~humble(X0))) [input p15]
17. humble(paul) & ~tall(paul) [input p16]
25. ~rich(paul) [input hypothesis]
75. ! [X0] : (((funny(X0) | ~rich(X0)) | (~curious(X0) | humble(X0))) & ((curious(X0) & ~humble(X0)) | (~funny(X0) & rich(X0)))) [nnf transformation 16]
76. ! [X0] : ((funny(X0) | ~rich(X0) | ~curious(X0) | humble(X0)) & ((curious(X0) & ~humble(X0)) | (~funny(X0) & rich(X0)))) [flattening 75]
133. ~humble(X0) | rich(X0) [cnf transformation 76]
139. humble(paul) [cnf transformation 17]
151. ~rich(paul) [cnf transformation 25]
371. rich(paul) [resolution 133,139]
372. $false [subsumption resolution 371,151]
% SZS output end Proof for 6635939700345145760637653
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is both not old and humble then susan is both tall and generous.
Everyone who is quiet is both humble and not old.
Everyone who is either kind or patient is both kind and not curious and vice versa.
If lucy is either not strong or not tall then john is not funny and vice versa.
Everyone who is both creative and kind is not old or not strong and vice versa.
Everyone who is funny is either not wise or not strong and vice versa.
Everyone who is either not curious or not brave is either kind or rich.
If someone is strong or not strong then lucy is strong or rich.
If paul is not quiet then someone is not old and vice versa.
Everyone who is not humble is tall.
If fred is both not curious and not wise then susan is both not old and humble and vice versa.
Everyone who is quiet or wise is both calm and quiet.
Everyone who is not happy or not generous is not kind and vice versa.
If fred is patient then someone is not wise or creative and vice versa.
If someone is not brave then mary is both kind and not rich and vice versa.
Everyone who is not quiet is both humble and old and vice versa.
Lucy is funny.
Someone is both not generous and not happy.
Fred is either not curious or old.
Someone is both not wise and not funny.
Someone is calm or not kind.
Someone is either not rich or happy. | Paul is happy. | neutral | (((~old(alice)&humble(alice)))=>((tall(susan)&generous(susan))))&
(![X]:(quiet(X)=>(humble(X)&~old(X))))&
(![X]:((kind(X)<~>patient(X))<=>(kind(X)&~curious(X))))&
(((~strong(lucy)<~>~tall(lucy)))<=>(~funny(john)))&
(![X]:((creative(X)&kind(X))<=>(~old(X)|~strong(X))))&
(![X]:(funny(X)<=>(~wise(X)<~>~strong(X))))&
(![X]:((~curious(X)<~>~brave(X))=>(kind(X)<~>rich(X))))&
((?[X]:((strong(X)|~strong(X))))=>((strong(lucy)|rich(lucy))))&
((~quiet(paul))<=>(?[X]:(~old(X))))&
(![X]:(~humble(X)=>tall(X)))&
(((~curious(fred)&~wise(fred)))<=>((~old(susan)&humble(susan))))&
(![X]:((quiet(X)|wise(X))=>(calm(X)&quiet(X))))&
(![X]:((~happy(X)|~generous(X))<=>~kind(X)))&
((patient(fred))<=>(?[X]:((~wise(X)|creative(X)))))&
((?[X]:(~brave(X)))<=>((kind(mary)&~rich(mary))))&
(![X]:(~quiet(X)<=>(humble(X)&old(X))))&
(funny(lucy))&
(?[X]:((~generous(X)&~happy(X))))&
((~curious(fred)<~>old(fred)))&
(?[X]:((~wise(X)&~funny(X))))&
(?[X]:((calm(X)|~kind(X))))&
(?[X]:((~rich(X)<~>happy(X)))) | happy(paul) | [] | null | 0 |
If someone is not humble then someone is either humble or not curious.
Everyone who is not curious is calm or patient and vice versa.
Everyone who is both old and not brave is either creative or not old and vice versa.
Everyone who is both creative and not generous is old and vice versa.
Everyone who is either old or not happy is not creative and vice versa.
If someone is kind then fred is both not happy and calm.
Everyone who is not calm is both not rich and creative.
If susan is strong or tall then someone is tall.
Everyone who is not curious or kind is either not kind or not wise.
Everyone who is either rich or not quiet is either kind or not old and vice versa.
If lucy is either wise or not quiet then lucy is not funny and vice versa.
If someone is both patient and rich then someone is both not quiet and not funny.
If someone is not humble or happy then someone is either not generous or not creative.
Everyone who is either not brave or humble is both curious and not rich.
Everyone who is curious or not funny is patient or not quiet.
Everyone who is either not humble or wise is both humble and not humble and vice versa.
Someone is calm.
Someone is both humble and not old.
Someone is humble or strong.
Paul is not patient or curious.
Someone is either not humble or not happy.
Mary is not rich. | Fred is curious. | contradiction | ((?[X]:(~humble(X)))=>(?[X]:((humble(X)<~>~curious(X)))))&
(![X]:(~curious(X)<=>(calm(X)|patient(X))))&
(![X]:((old(X)&~brave(X))<=>(creative(X)<~>~old(X))))&
(![X]:((creative(X)&~generous(X))<=>old(X)))&
(![X]:((old(X)<~>~happy(X))<=>~creative(X)))&
((?[X]:(kind(X)))=>((~happy(fred)&calm(fred))))&
(![X]:(~calm(X)=>(~rich(X)&creative(X))))&
(((strong(susan)|tall(susan)))=>(?[X]:(tall(X))))&
(![X]:((~curious(X)|kind(X))=>(~kind(X)<~>~wise(X))))&
(![X]:((rich(X)<~>~quiet(X))<=>(kind(X)<~>~old(X))))&
(((wise(lucy)<~>~quiet(lucy)))<=>(~funny(lucy)))&
((?[X]:((patient(X)&rich(X))))=>(?[X]:((~quiet(X)&~funny(X)))))&
((?[X]:((~humble(X)|happy(X))))=>(?[X]:((~generous(X)<~>~creative(X)))))&
(![X]:((~brave(X)<~>humble(X))=>(curious(X)&~rich(X))))&
(![X]:((curious(X)|~funny(X))=>(patient(X)|~quiet(X))))&
(![X]:((~humble(X)<~>wise(X))<=>(humble(X)&~humble(X))))&
(?[X]:(calm(X)))&
(?[X]:((humble(X)&~old(X))))&
(?[X]:((humble(X)|strong(X))))&
((~patient(paul)|curious(paul)))&
(?[X]:((~humble(X)<~>~happy(X))))&
(~rich(mary)) | curious(fred) | [
"p1",
"p2",
"p3",
"p4",
"p5",
"p6",
"p8",
"p9",
"p12",
"p13",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2109235022828055437652651
% SZS output start Proof for 2109235022828055437652651
2. ! [X0] : (~curious(X0) <=> (patient(X0) | calm(X0))) [input p1]
3. ! [X0] : ((~brave(X0) & old(X0)) <=> (creative(X0) <~> ~old(X0))) [input p2]
4. ! [X0] : ((~generous(X0) & creative(X0)) <=> old(X0)) [input p3]
5. ! [X0] : ((old(X0) <~> ~happy(X0)) <=> ~creative(X0)) [input p4]
6. ? [X0] : kind(X0) => (calm(fred) & ~happy(fred)) [input p5]
7. ! [X0] : (~calm(X0) => (creative(X0) & ~rich(X0))) [input p6]
9. ! [X0] : ((kind(X0) | ~curious(X0)) => (~kind(X0) <~> ~wise(X0))) [input p8]
10. ! [X0] : ((rich(X0) <~> ~quiet(X0)) <=> (kind(X0) <~> ~old(X0))) [input p9]
13. ? [X0] : (happy(X0) | ~humble(X0)) => ? [X0] : (~generous(X0) <~> ~creative(X0)) [input p12]
14. ! [X0] : ((~brave(X0) <~> humble(X0)) => (~rich(X0) & curious(X0))) [input p13]
15. ! [X0] : ((~funny(X0) | curious(X0)) => (~quiet(X0) | patient(X0))) [input p14]
16. ! [X0] : ((~humble(X0) <~> wise(X0)) <=> (~humble(X0) & humble(X0))) [input p15]
18. ? [X0] : (~old(X0) & humble(X0)) [input p17]
23. curious(fred) [input hypothesis]
26. ? [X0] : (happy(X0) | ~humble(X0)) => ? [X1] : (~generous(X1) <~> ~creative(X1)) [rectify 13]
28. (calm(fred) & ~happy(fred)) | ! [X0] : ~kind(X0) [ennf transformation 6]
29. ! [X0] : ((creative(X0) & ~rich(X0)) | calm(X0)) [ennf transformation 7]
31. ! [X0] : ((~kind(X0) <~> ~wise(X0)) | (~kind(X0) & curious(X0))) [ennf transformation 9]
33. ? [X1] : (~generous(X1) <~> ~creative(X1)) | ! [X0] : (~happy(X0) & humble(X0)) [ennf transformation 26]
34. ! [X0] : ((~rich(X0) & curious(X0)) | (~brave(X0) <=> humble(X0))) [ennf transformation 14]
35. ! [X0] : ((~quiet(X0) | patient(X0)) | (funny(X0) & ~curious(X0))) [ennf transformation 15]
36. ! [X0] : (~quiet(X0) | patient(X0) | (funny(X0) & ~curious(X0))) [flattening 35]
41. ! [X0] : ((~curious(X0) | (~patient(X0) & ~calm(X0))) & ((patient(X0) | calm(X0)) | curious(X0))) [nnf transformation 2]
42. ! [X0] : ((~curious(X0) | (~patient(X0) & ~calm(X0))) & (patient(X0) | calm(X0) | curious(X0))) [flattening 41]
43. ! [X0] : (((~brave(X0) & old(X0)) | ((creative(X0) | old(X0)) & (~old(X0) | ~creative(X0)))) & (((old(X0) | ~creative(X0)) & (~old(X0) | creative(X0))) | (brave(X0) | ~old(X0)))) [nnf transformation 3]
44. ! [X0] : (((~brave(X0) & old(X0)) | ((creative(X0) | old(X0)) & (~old(X0) | ~creative(X0)))) & (((old(X0) | ~creative(X0)) & (~old(X0) | creative(X0))) | brave(X0) | ~old(X0))) [flattening 43]
45. ! [X0] : (((~generous(X0) & creative(X0)) | ~old(X0)) & (old(X0) | (generous(X0) | ~creative(X0)))) [nnf transformation 4]
46. ! [X0] : (((~generous(X0) & creative(X0)) | ~old(X0)) & (old(X0) | generous(X0) | ~creative(X0))) [flattening 45]
47. ! [X0] : ((((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | creative(X0)) & (~creative(X0) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0))))) [nnf transformation 5]
50. ! [X0] : (((wise(X0) | kind(X0)) & (~wise(X0) | ~kind(X0))) | (~kind(X0) & curious(X0))) [nnf transformation 31]
51. ! [X0] : ((((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | ((kind(X0) | old(X0)) & (~old(X0) | ~kind(X0)))) & (((old(X0) | ~kind(X0)) & (~old(X0) | kind(X0))) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0))))) [nnf transformation 10]
56. ? [X1] : ((creative(X1) | generous(X1)) & (~creative(X1) | ~generous(X1))) | ! [X0] : (~happy(X0) & humble(X0)) [nnf transformation 33]
57. ? [X0] : ((creative(X0) | generous(X0)) & (~creative(X0) | ~generous(X0))) | ! [X1] : (~happy(X1) & humble(X1)) [rectify 56]
58. ? [X0] : ((creative(X0) | generous(X0)) & (~creative(X0) | ~generous(X0))) => ((creative(sK3) | generous(sK3)) & (~creative(sK3) | ~generous(sK3))) [choice axiom]
59. ((creative(sK3) | generous(sK3)) & (~creative(sK3) | ~generous(sK3))) | ! [X1] : (~happy(X1) & humble(X1)) [skolemisation 57,58]
60. ! [X0] : ((~rich(X0) & curious(X0)) | ((~brave(X0) | ~humble(X0)) & (humble(X0) | brave(X0)))) [nnf transformation 34]
61. ! [X0] : ((((~wise(X0) | humble(X0)) & (wise(X0) | ~humble(X0))) | (humble(X0) | ~humble(X0))) & ((~humble(X0) & humble(X0)) | ((~humble(X0) | ~wise(X0)) & (wise(X0) | humble(X0))))) [nnf transformation 16]
62. ! [X0] : ((((~wise(X0) | humble(X0)) & (wise(X0) | ~humble(X0))) | humble(X0) | ~humble(X0)) & ((~humble(X0) & humble(X0)) | ((~humble(X0) | ~wise(X0)) & (wise(X0) | humble(X0))))) [flattening 61]
65. ? [X0] : (~old(X0) & humble(X0)) => (~old(sK5) & humble(sK5)) [choice axiom]
66. ~old(sK5) & humble(sK5) [skolemisation 18,65]
75. ~calm(X0) | ~curious(X0) [cnf transformation 42]
76. ~patient(X0) | ~curious(X0) [cnf transformation 42]
80. old(X0) | creative(X0) | old(X0) [cnf transformation 44]
81. ~creative(X0) | ~old(X0) | ~brave(X0) [cnf transformation 44]
83. old(X0) | generous(X0) | ~creative(X0) [cnf transformation 46]
84. creative(X0) | ~old(X0) [cnf transformation 46]
87. ~creative(X0) | old(X0) | happy(X0) [cnf transformation 47]
91. calm(fred) | ~kind(X0) [cnf transformation 28]
92. ~rich(X0) | calm(X0) [cnf transformation 29]
98. wise(X0) | kind(X0) | curious(X0) [cnf transformation 50]
101. ~old(X0) | kind(X0) | rich(X0) | quiet(X0) [cnf transformation 51]
115. ~creative(sK3) | ~generous(sK3) | ~happy(X1) [cnf transformation 59]
118. brave(X0) | humble(X0) | curious(X0) [cnf transformation 60]
122. ~quiet(X0) | patient(X0) | ~curious(X0) [cnf transformation 36]
127. ~humble(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 62]
132. ~old(sK5) [cnf transformation 66]
138. curious(fred) [cnf transformation 23]
140. ~wise(X0) | ~humble(X0) [duplicate literal removal 127]
145. creative(X0) | old(X0) [duplicate literal removal 80]
160. creative(X0) [subsumption resolution 84,145]
161. generous(X0) | old(X0) [subsumption resolution 83,160]
162. happy(X0) | old(X0) [subsumption resolution 87,160]
165. 4 <=> ! [X0] : ~kind(X0) [avatar definition]
166. ~kind(X0) <- (4) [avatar component clause 165]
168. 5 <=> calm(fred) [avatar definition]
170. calm(fred) <- (5) [avatar component clause 168]
171. 4 | 5 [avatar split clause 91,168,165]
220. ~generous(sK3) | ~happy(X1) [subsumption resolution 115,160]
222. 16 <=> ! [X1] : ~happy(X1) [avatar definition]
223. ~happy(X1) <- (16) [avatar component clause 222]
225. 17 <=> generous(sK3) [avatar definition]
227. ~generous(sK3) <- (~17) [avatar component clause 225]
228. 16 | ~17 [avatar split clause 220,225,222]
231. ~quiet(X0) | ~curious(X0) [subsumption resolution 122,76]
273. ~brave(X2) | ~old(X2) [resolution 81,160]
276. kind(X1) | curious(X1) | ~humble(X1) [resolution 98,140]
279. humble(X0) | curious(X0) | ~old(X0) [resolution 118,273]
294. 24 <=> quiet(sK3) [avatar definition]
296. quiet(sK3) <- (24) [avatar component clause 294]
298. 25 <=> rich(sK3) [avatar definition]
300. rich(sK3) <- (25) [avatar component clause 298]
315. old(X0) <- (16) [resolution 223,162]
320. ~curious(fred) <- (5) [resolution 170,75]
321. $false <- (5) [subsumption resolution 320,138]
322. ~5 [avatar contradiction clause 321]
323. old(sK3) <- (~17) [resolution 227,161]
327. ~humble(X1) | curious(X1) <- (4) [subsumption resolution 276,166]
335. $false <- (16) [resolution 315,132]
337. ~16 [avatar contradiction clause 335]
339. ~old(X0) | curious(X0) <- (4) [subsumption resolution 279,327]
342. kind(sK3) | rich(sK3) | quiet(sK3) <- (~17) [resolution 323,101]
374. rich(sK3) | quiet(sK3) <- (4, ~17) [subsumption resolution 342,166]
375. 24 | 25 | ~4 | 17 [avatar split clause 374,225,165,298,294]
400. ~curious(sK3) <- (24) [resolution 296,231]
422. curious(sK3) <- (4, ~17) [resolution 339,323]
423. $false <- (4, ~17, 24) [subsumption resolution 422,400]
424. ~4 | 17 | ~24 [avatar contradiction clause 423]
429. calm(sK3) <- (25) [resolution 300,92]
432. ~curious(sK3) <- (25) [resolution 429,75]
433. $false <- (4, ~17, 25) [subsumption resolution 432,422]
434. ~4 | 17 | ~25 [avatar contradiction clause 433]
435. $false [avatar sat refutation 171,228,322,337,375,424,434]
% SZS output end Proof for 2109235022828055437652651
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not calm and not generous then someone is either not happy or not patient. Everyone who is not generous is patient or wise and vice versa. Everyone who is not curious or funny is either not tall or not generous. If someone is not old then someone is not kind or creative and vice versa. If john is not curious then someone is not rich or not generous and vice versa. Everyone who is both not patient and funny is either not creative or not generous and vice versa. If susan is humble or not generous then john is kind. Everyone who is either patient or not brave is both creative and not wise. Everyone who is both not happy and not humble is not old or not patient. Everyone who is either not old or not brave is both tall and funny. If someone is not curious then fred is either quiet or not tall and vice versa. If someone is both strong and quiet then alice is either not creative or not quiet and vice versa. If paul is old or not humble then someone is either not patient or not calm and vice versa. If someone is either calm or patient then someone is either not kind or wise. Everyone who is not rich is both not tall and not funny. If someone is both wise and tall then fred is either not quiet or not kind and vice versa. Susan is brave or not old. Someone is both tall and not humble. Fred is either not curious or tall. Paul is not brave. Alice is either humble or not brave. Mary is either kind or not tall. Someone is either tall or not wise. | Alice is not tall. | neutral | ((?[X]:((~calm(X)&~generous(X))))=>(?[X]:((~happy(X)<~>~patient(X)))))&
(![X]:(~generous(X)<=>(patient(X)|wise(X))))&
(![X]:((~curious(X)|funny(X))=>(~tall(X)<~>~generous(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~kind(X)|creative(X)))))&
((~curious(john))<=>(?[X]:((~rich(X)|~generous(X)))))&
(![X]:((~patient(X)&funny(X))<=>(~creative(X)<~>~generous(X))))&
(((humble(susan)|~generous(susan)))=>(kind(john)))&
(![X]:((patient(X)<~>~brave(X))=>(creative(X)&~wise(X))))&
(![X]:((~happy(X)&~humble(X))=>(~old(X)|~patient(X))))&
(![X]:((~old(X)<~>~brave(X))=>(tall(X)&funny(X))))&
((?[X]:(~curious(X)))<=>((quiet(fred)<~>~tall(fred))))&
((?[X]:((strong(X)&quiet(X))))<=>((~creative(alice)<~>~quiet(alice))))&
(((old(paul)|~humble(paul)))<=>(?[X]:((~patient(X)<~>~calm(X)))))&
((?[X]:((calm(X)<~>patient(X))))=>(?[X]:((~kind(X)<~>wise(X)))))&
(![X]:(~rich(X)=>(~tall(X)&~funny(X))))&
((?[X]:((wise(X)&tall(X))))<=>((~quiet(fred)<~>~kind(fred))))&
((brave(susan)|~old(susan)))&
(?[X]:((tall(X)&~humble(X))))&
((~curious(fred)<~>tall(fred)))&
(~brave(paul))&
((humble(alice)<~>~brave(alice)))&
((kind(mary)<~>~tall(mary)))&
(?[X]:((tall(X)<~>~wise(X)))) | ~tall(alice) | [] | null | 0 |
If someone is both generous and not wise then someone is happy and vice versa. Everyone who is either not kind or not wise is both not old and rich. If someone is rich then alice is not tall. If alice is either happy or funny then fred is either not creative or not old. If someone is rich or tall then someone is either strong or not rich and vice versa. Everyone who is wise or strong is both not kind and not creative and vice versa. Everyone who is humble or quiet is not creative and vice versa. Everyone who is either not wise or not strong is patient or not patient. Everyone who is both curious and tall is curious or old. If someone is both funny and not brave then fred is not funny or old and vice versa. Everyone who is humble is not old and vice versa. If fred is not tall or not generous then someone is either quiet or kind and vice versa. If alice is wise or not funny then someone is not strong and vice versa. If someone is calm then lucy is both rich and wise and vice versa. If someone is patient or curious then susan is either not old or quiet and vice versa. Everyone who is not tall or old is creative or humble and vice versa. Lucy is creative. Fred is brave or not happy. Paul is both curious and creative. Someone is happy. Someone is patient. Paul is not strong or not quiet. Someone is either happy or not kind. | Susan is tall. | contradiction | ((?[X]:((generous(X)&~wise(X))))<=>(?[X]:(happy(X))))&
(![X]:((~kind(X)<~>~wise(X))=>(~old(X)&rich(X))))&
((?[X]:(rich(X)))=>(~tall(alice)))&
(((happy(alice)<~>funny(alice)))=>((~creative(fred)<~>~old(fred))))&
((?[X]:((rich(X)|tall(X))))<=>(?[X]:((strong(X)<~>~rich(X)))))&
(![X]:((wise(X)|strong(X))<=>(~kind(X)&~creative(X))))&
(![X]:((humble(X)|quiet(X))<=>~creative(X)))&
(![X]:((~wise(X)<~>~strong(X))=>(patient(X)|~patient(X))))&
(![X]:((curious(X)&tall(X))=>(curious(X)|old(X))))&
((?[X]:((funny(X)&~brave(X))))<=>((~funny(fred)|old(fred))))&
(![X]:(humble(X)<=>~old(X)))&
(((~tall(fred)|~generous(fred)))<=>(?[X]:((quiet(X)<~>kind(X)))))&
(((wise(alice)|~funny(alice)))<=>(?[X]:(~strong(X))))&
((?[X]:(calm(X)))<=>((rich(lucy)&wise(lucy))))&
((?[X]:((patient(X)|curious(X))))<=>((~old(susan)<~>quiet(susan))))&
(![X]:((~tall(X)|old(X))<=>(creative(X)|humble(X))))&
(creative(lucy))&
((brave(fred)|~happy(fred)))&
((curious(paul)&creative(paul)))&
(?[X]:(happy(X)))&
(?[X]:(patient(X)))&
((~strong(paul)|~quiet(paul)))&
(?[X]:((happy(X)<~>~kind(X)))) | tall(susan) | [
"p6",
"p10",
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3463555016353642874279834
% SZS output start Proof for 3463555016353642874279834
7. ! [X0] : ((quiet(X0) | humble(X0)) <=> ~creative(X0)) [input p6]
11. ! [X0] : (humble(X0) <=> ~old(X0)) [input p10]
15. ? [X0] : (curious(X0) | patient(X0)) <=> (~old(susan) <~> quiet(susan)) [input p14]
16. ! [X0] : ((old(X0) | ~tall(X0)) <=> (humble(X0) | creative(X0))) [input p15]
21. ? [X0] : patient(X0) [input p20]
24. tall(susan) [input hypothesis]
48. ! [X0] : (((quiet(X0) | humble(X0)) | creative(X0)) & (~creative(X0) | (~quiet(X0) & ~humble(X0)))) [nnf transformation 7]
49. ! [X0] : ((quiet(X0) | humble(X0) | creative(X0)) & (~creative(X0) | (~quiet(X0) & ~humble(X0)))) [flattening 48]
56. ! [X0] : ((humble(X0) | old(X0)) & (~old(X0) | ~humble(X0))) [nnf transformation 11]
72. (? [X0] : (curious(X0) | patient(X0)) | ((~old(susan) | ~quiet(susan)) & (quiet(susan) | old(susan)))) & (((~quiet(susan) | old(susan)) & (quiet(susan) | ~old(susan))) | ! [X0] : (~curious(X0) & ~patient(X0))) [nnf transformation 15]
73. (? [X0] : (curious(X0) | patient(X0)) | ((~old(susan) | ~quiet(susan)) & (quiet(susan) | old(susan)))) & (((~quiet(susan) | old(susan)) & (quiet(susan) | ~old(susan))) | ! [X1] : (~curious(X1) & ~patient(X1))) [rectify 72]
74. ? [X0] : (curious(X0) | patient(X0)) => (curious(sK8) | patient(sK8)) [choice axiom]
75. ((curious(sK8) | patient(sK8)) | ((~old(susan) | ~quiet(susan)) & (quiet(susan) | old(susan)))) & (((~quiet(susan) | old(susan)) & (quiet(susan) | ~old(susan))) | ! [X1] : (~curious(X1) & ~patient(X1))) [skolemisation 73,74]
76. ! [X0] : (((old(X0) | ~tall(X0)) | (~humble(X0) & ~creative(X0))) & ((humble(X0) | creative(X0)) | (~old(X0) & tall(X0)))) [nnf transformation 16]
77. ! [X0] : ((old(X0) | ~tall(X0) | (~humble(X0) & ~creative(X0))) & (humble(X0) | creative(X0) | (~old(X0) & tall(X0)))) [flattening 76]
80. ? [X0] : patient(X0) => patient(sK10) [choice axiom]
81. patient(sK10) [skolemisation 21,80]
109. ~quiet(X0) | ~creative(X0) [cnf transformation 49]
119. ~humble(X0) | ~old(X0) [cnf transformation 56]
120. humble(X0) | old(X0) [cnf transformation 56]
133. quiet(susan) | ~old(susan) | ~patient(X1) [cnf transformation 75]
140. humble(X0) | creative(X0) | ~old(X0) [cnf transformation 77]
142. old(X0) | ~tall(X0) | ~humble(X0) [cnf transformation 77]
148. patient(sK10) [cnf transformation 81]
152. tall(susan) [cnf transformation 24]
314. 36 <=> quiet(susan) [avatar definition]
315. quiet(susan) <- (36) [avatar component clause 314]
318. 37 <=> old(susan) [avatar definition]
336. 41 <=> ! [X1] : ~patient(X1) [avatar definition]
337. ~patient(X1) <- (41) [avatar component clause 336]
340. 41 | ~37 | 36 [avatar split clause 133,314,318,336]
341. ~humble(X0) | ~tall(X0) [subsumption resolution 142,119]
342. humble(X0) | creative(X0) [subsumption resolution 140,120]
380. ~tall(X0) | old(X0) [resolution 341,120]
381. ~tall(X0) | creative(X0) [resolution 342,341]
445. old(susan) [resolution 380,152]
449. 37 [avatar split clause 445,318]
457. ~creative(susan) <- (36) [resolution 315,109]
461. $false <- (41) [resolution 337,148]
464. ~41 [avatar contradiction clause 461]
465. creative(susan) [resolution 381,152]
466. $false <- (36) [subsumption resolution 465,457]
467. ~36 [avatar contradiction clause 466]
468. $false [avatar sat refutation 340,449,464,467]
% SZS output end Proof for 3463555016353642874279834
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is kind then someone is both not rich and not wise and vice versa.
Everyone who is either strong or curious is not funny and vice versa.
Everyone who is not tall is both happy and creative and vice versa.
If someone is both calm and humble then someone is either curious or not happy.
If paul is either strong or curious then someone is calm or not tall and vice versa.
Everyone who is generous or happy is either generous or not kind.
Everyone who is both not wise and brave is either rich or creative and vice versa.
Everyone who is brave is not happy or funny and vice versa.
If someone is either not patient or curious then paul is not humble or not tall and vice versa.
Everyone who is not old or rich is either not wise or happy and vice versa.
If lucy is brave then someone is either not happy or creative and vice versa.
If susan is either not tall or quiet then someone is not happy or not quiet and vice versa.
If fred is either funny or not funny then someone is either not strong or generous and vice versa.
Everyone who is either not old or old is either not happy or kind and vice versa.
Everyone who is not rich or tall is either not funny or not generous.
Everyone who is either not quiet or not strong is brave and vice versa.
Someone is both not curious and not creative.
Someone is both not funny and not patient.
Someone is either brave or not generous.
Someone is not curious.
Someone is both strong and not old.
Someone is both wise and not funny.
Someone is happy.
Someone is both tall and not brave. | Paul is happy. | entailment | ((kind(paul))<=>(?[X]:((~rich(X)&~wise(X)))))&
(![X]:((strong(X)<~>curious(X))<=>~funny(X)))&
(![X]:(~tall(X)<=>(happy(X)&creative(X))))&
((?[X]:((calm(X)&humble(X))))=>(?[X]:((curious(X)<~>~happy(X)))))&
(((strong(paul)<~>curious(paul)))<=>(?[X]:((calm(X)|~tall(X)))))&
(![X]:((generous(X)|happy(X))=>(generous(X)<~>~kind(X))))&
(![X]:((~wise(X)&brave(X))<=>(rich(X)<~>creative(X))))&
(![X]:(brave(X)<=>(~happy(X)|funny(X))))&
((?[X]:((~patient(X)<~>curious(X))))<=>((~humble(paul)|~tall(paul))))&
(![X]:((~old(X)|rich(X))<=>(~wise(X)<~>happy(X))))&
((brave(lucy))<=>(?[X]:((~happy(X)<~>creative(X)))))&
(((~tall(susan)<~>quiet(susan)))<=>(?[X]:((~happy(X)|~quiet(X)))))&
(((funny(fred)<~>~funny(fred)))<=>(?[X]:((~strong(X)<~>generous(X)))))&
(![X]:((~old(X)<~>old(X))<=>(~happy(X)<~>kind(X))))&
(![X]:((~rich(X)|tall(X))=>(~funny(X)<~>~generous(X))))&
(![X]:((~quiet(X)<~>~strong(X))<=>brave(X)))&
(?[X]:((~curious(X)&~creative(X))))&
(?[X]:((~funny(X)&~patient(X))))&
(?[X]:((brave(X)<~>~generous(X))))&
(?[X]:(~curious(X)))&
(?[X]:((strong(X)&~old(X))))&
(?[X]:((wise(X)&~funny(X))))&
(?[X]:(happy(X)))&
(?[X]:((tall(X)&~brave(X)))) | happy(paul) | [
"p1",
"p2",
"p4",
"p5",
"p7",
"p13",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8314882615499395116456953
% SZS output start Proof for 8314882615499395116456953
2. ! [X0] : ((strong(X0) <~> curious(X0)) <=> ~funny(X0)) [input p1]
3. ! [X0] : (~tall(X0) <=> (creative(X0) & happy(X0))) [input p2]
5. (strong(paul) <~> curious(paul)) <=> ? [X0] : (~tall(X0) | calm(X0)) [input p4]
6. ! [X0] : ((happy(X0) | generous(X0)) => (generous(X0) <~> ~kind(X0))) [input p5]
8. ! [X0] : (brave(X0) <=> (funny(X0) | ~happy(X0))) [input p7]
14. ! [X0] : ((~old(X0) <~> old(X0)) <=> (~happy(X0) <~> kind(X0))) [input p13]
15. ! [X0] : ((tall(X0) | ~rich(X0)) => (~funny(X0) <~> ~generous(X0))) [input p14]
19. ? [X0] : (brave(X0) <~> ~generous(X0)) [input p18]
25. ~happy(paul) [input hypothesis]
28. ! [X0] : ((generous(X0) <~> ~kind(X0)) | (~happy(X0) & ~generous(X0))) [ennf transformation 6]
29. ! [X0] : ((~funny(X0) <~> ~generous(X0)) | (~tall(X0) & rich(X0))) [ennf transformation 15]
34. ! [X0] : ((((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | funny(X0)) & (~funny(X0) | ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0))))) [nnf transformation 2]
35. ! [X0] : ((~tall(X0) | (~creative(X0) | ~happy(X0))) & ((creative(X0) & happy(X0)) | tall(X0))) [nnf transformation 3]
36. ! [X0] : ((~tall(X0) | ~creative(X0) | ~happy(X0)) & ((creative(X0) & happy(X0)) | tall(X0))) [flattening 35]
41. (((~curious(paul) | ~strong(paul)) & (curious(paul) | strong(paul))) | ! [X0] : (tall(X0) & ~calm(X0))) & (? [X0] : (~tall(X0) | calm(X0)) | ((strong(paul) | ~curious(paul)) & (curious(paul) | ~strong(paul)))) [nnf transformation 5]
42. (((~curious(paul) | ~strong(paul)) & (curious(paul) | strong(paul))) | ! [X0] : (tall(X0) & ~calm(X0))) & (? [X1] : (~tall(X1) | calm(X1)) | ((strong(paul) | ~curious(paul)) & (curious(paul) | ~strong(paul)))) [rectify 41]
43. ? [X1] : (~tall(X1) | calm(X1)) => (~tall(sK2) | calm(sK2)) [choice axiom]
44. (((~curious(paul) | ~strong(paul)) & (curious(paul) | strong(paul))) | ! [X0] : (tall(X0) & ~calm(X0))) & ((~tall(sK2) | calm(sK2)) | ((strong(paul) | ~curious(paul)) & (curious(paul) | ~strong(paul)))) [skolemisation 42,43]
45. ! [X0] : (((kind(X0) | ~generous(X0)) & (~kind(X0) | generous(X0))) | (~happy(X0) & ~generous(X0))) [nnf transformation 28]
48. ! [X0] : ((brave(X0) | (~funny(X0) & happy(X0))) & ((funny(X0) | ~happy(X0)) | ~brave(X0))) [nnf transformation 8]
49. ! [X0] : ((brave(X0) | (~funny(X0) & happy(X0))) & (funny(X0) | ~happy(X0) | ~brave(X0))) [flattening 48]
69. ! [X0] : ((((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0)))) & (((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0))))) [nnf transformation 14]
70. ! [X0] : (((generous(X0) | funny(X0)) & (~generous(X0) | ~funny(X0))) | (~tall(X0) & rich(X0))) [nnf transformation 29]
76. ? [X0] : ((generous(X0) | ~brave(X0)) & (~generous(X0) | brave(X0))) [nnf transformation 19]
77. ? [X0] : ((generous(X0) | ~brave(X0)) & (~generous(X0) | brave(X0))) => ((generous(sK9) | ~brave(sK9)) & (~generous(sK9) | brave(sK9))) [choice axiom]
78. (generous(sK9) | ~brave(sK9)) & (~generous(sK9) | brave(sK9)) [skolemisation 76,77]
92. ~funny(X0) | curious(X0) | ~strong(X0) [cnf transformation 34]
93. ~funny(X0) | strong(X0) | ~curious(X0) [cnf transformation 34]
96. happy(X0) | tall(X0) [cnf transformation 36]
104. curious(paul) | strong(paul) | tall(X0) [cnf transformation 44]
106. ~curious(paul) | ~strong(paul) | tall(X0) [cnf transformation 44]
108. ~happy(X0) | generous(X0) | ~kind(X0) [cnf transformation 45]
109. kind(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 45]
117. ~brave(X0) | ~happy(X0) | funny(X0) [cnf transformation 49]
118. brave(X0) | happy(X0) [cnf transformation 49]
150. kind(X0) | ~happy(X0) | old(X0) | old(X0) [cnf transformation 69]
151. kind(X0) | ~happy(X0) | ~old(X0) | ~old(X0) [cnf transformation 69]
152. ~kind(X0) | happy(X0) | old(X0) | old(X0) [cnf transformation 69]
153. ~kind(X0) | happy(X0) | ~old(X0) | ~old(X0) [cnf transformation 69]
159. ~generous(X0) | ~funny(X0) | ~tall(X0) [cnf transformation 70]
161. ~tall(X0) | funny(X0) | generous(X0) [cnf transformation 70]
170. ~generous(sK9) | brave(sK9) [cnf transformation 78]
171. generous(sK9) | ~brave(sK9) [cnf transformation 78]
180. ~happy(paul) [cnf transformation 25]
181. kind(X0) | ~happy(X0) | old(X0) [duplicate literal removal 150]
182. kind(X0) | ~happy(X0) | ~old(X0) [duplicate literal removal 151]
183. ~kind(X0) | happy(X0) | old(X0) [duplicate literal removal 152]
184. ~kind(X0) | happy(X0) | ~old(X0) [duplicate literal removal 153]
189. ~generous(X0) | kind(X0) [duplicate literal removal 109]
194. 2 <=> kind(paul) [avatar definition]
195. ~kind(paul) <- (~2) [avatar component clause 194]
196. kind(paul) <- (2) [avatar component clause 194]
222. 8 <=> ! [X0] : tall(X0) [avatar definition]
223. tall(X0) <- (8) [avatar component clause 222]
225. 9 <=> strong(paul) [avatar definition]
229. 10 <=> curious(paul) [avatar definition]
232. 8 | ~9 | ~10 [avatar split clause 106,229,225,222]
237. 8 | 9 | 10 [avatar split clause 104,229,225,222]
250. 14 <=> tall(paul) [avatar definition]
252. tall(paul) <- (14) [avatar component clause 250]
343. ~kind(X0) | happy(X0) [subsumption resolution 183,184]
344. ~happy(X0) | kind(X0) [subsumption resolution 181,182]
346. 34 <=> brave(sK9) [avatar definition]
347. brave(sK9) <- (34) [avatar component clause 346]
348. ~brave(sK9) <- (~34) [avatar component clause 346]
350. 35 <=> generous(sK9) [avatar definition]
351. ~generous(sK9) <- (~35) [avatar component clause 350]
352. generous(sK9) <- (35) [avatar component clause 350]
353. ~34 | 35 [avatar split clause 171,350,346]
354. 34 | ~35 [avatar split clause 170,350,346]
355. tall(paul) [resolution 96,180]
361. 14 [avatar split clause 355,250]
365. happy(sK9) <- (~34) [resolution 118,348]
366. happy(paul) <- (2) [resolution 343,196]
367. $false <- (2) [subsumption resolution 366,180]
368. ~2 [avatar contradiction clause 367]
375. kind(sK9) <- (~34) [resolution 365,344]
410. generous(sK9) | ~kind(sK9) <- (~34) [resolution 108,365]
414. ~kind(sK9) <- (~34, ~35) [subsumption resolution 410,351]
415. $false <- (~34, ~35) [subsumption resolution 414,375]
416. 34 | 35 [avatar contradiction clause 415]
419. kind(sK9) <- (35) [resolution 352,189]
435. happy(sK9) <- (35) [resolution 419,343]
444. ~happy(sK9) | funny(sK9) <- (34) [resolution 117,347]
454. funny(sK9) <- (34, 35) [subsumption resolution 444,435]
565. ~funny(sK9) | ~tall(sK9) <- (35) [resolution 159,352]
568. ~tall(sK9) <- (34, 35) [subsumption resolution 565,454]
595. funny(paul) | generous(paul) <- (14) [resolution 161,252]
602. 64 <=> generous(paul) [avatar definition]
604. generous(paul) <- (64) [avatar component clause 602]
606. 65 <=> funny(paul) [avatar definition]
608. funny(paul) <- (65) [avatar component clause 606]
609. 64 | 65 | ~14 [avatar split clause 595,250,606,602]
724. kind(paul) <- (64) [resolution 604,189]
732. $false <- (~2, 64) [subsumption resolution 724,195]
733. 2 | ~64 [avatar contradiction clause 732]
748. strong(paul) | ~curious(paul) <- (65) [resolution 608,93]
749. curious(paul) | ~strong(paul) <- (65) [resolution 608,92]
754. ~10 | 9 | ~65 [avatar split clause 748,606,225,229]
755. ~9 | 10 | ~65 [avatar split clause 749,606,229,225]
759. $false <- (8, 34, 35) [resolution 223,568]
760. ~8 | ~34 | ~35 [avatar contradiction clause 759]
763. $false [avatar sat refutation 232,237,353,354,361,368,416,609,733,754,755,760]
% SZS output end Proof for 8314882615499395116456953
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet is generous or not old.
If someone is both not generous and not wise then someone is old or not curious.
If someone is either funny or not old then john is both humble and not wise.
Everyone who is brave is both not tall and calm and vice versa.
Everyone who is not quiet is not patient and vice versa.
Everyone who is either not generous or not kind is either strong or not rich.
If someone is not quiet then lucy is not quiet and vice versa.
If john is both strong and not generous then alice is not rich or not wise.
Everyone who is both curious and patient is not old or not calm 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. | John is not tall. | neutral | (![X]:(quiet(X)=>(generous(X)|~old(X))))&
((?[X]:((~generous(X)&~wise(X))))=>(?[X]:((old(X)|~curious(X)))))&
((?[X]:((funny(X)<~>~old(X))))=>((humble(john)&~wise(john))))&
(![X]:(brave(X)<=>(~tall(X)&calm(X))))&
(![X]:(~quiet(X)<=>~patient(X)))&
(![X]:((~generous(X)<~>~kind(X))=>(strong(X)<~>~rich(X))))&
((?[X]:(~quiet(X)))<=>(~quiet(lucy)))&
(((strong(john)&~generous(john)))=>((~rich(alice)|~wise(alice))))&
(![X]:((curious(X)&patient(X))<=>(~old(X)|~calm(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)))) | ~tall(john) | [] | null | 0 |
Everyone who is either not rich or generous is either kind or not curious and vice versa.
If fred is rich or quiet then someone is both not strong and patient.
Everyone who is not funny or not strong is generous.
Everyone who is either not brave or not rich is not wise.
Everyone who is both not wise and happy is not patient and vice versa.
Everyone who is tall or humble is both happy and tall and vice versa.
If someone is either old or wise then paul is not kind and vice versa.
Everyone who is either not funny or rich is not generous or curious.
If john is not calm or not wise then fred is rich or not generous.
If susan is not creative then someone is both not rich and not kind and vice versa.
If alice is both not brave and not quiet then someone is happy or not funny.
Everyone who is strong is either not creative or not rich and vice versa.
If susan is either not funny or generous then fred is happy or not generous.
If alice is curious or not patient then someone is calm.
Everyone who is not rich is both not generous and not humble.
Everyone who is wise or humble is generous.
Susan is either creative or not brave.
John is not calm or funny.
Someone is both tall and not wise.
Someone is not old.
Someone is both tall and not curious.
Someone is either humble or strong.
Someone is patient.
Someone is not humble or wise. | Alice is patient. | neutral | (![X]:((~rich(X)<~>generous(X))<=>(kind(X)<~>~curious(X))))&
(((rich(fred)|quiet(fred)))=>(?[X]:((~strong(X)&patient(X)))))&
(![X]:((~funny(X)|~strong(X))=>generous(X)))&
(![X]:((~brave(X)<~>~rich(X))=>~wise(X)))&
(![X]:((~wise(X)&happy(X))<=>~patient(X)))&
(![X]:((tall(X)|humble(X))<=>(happy(X)&tall(X))))&
((?[X]:((old(X)<~>wise(X))))<=>(~kind(paul)))&
(![X]:((~funny(X)<~>rich(X))=>(~generous(X)|curious(X))))&
(((~calm(john)|~wise(john)))=>((rich(fred)|~generous(fred))))&
((~creative(susan))<=>(?[X]:((~rich(X)&~kind(X)))))&
(((~brave(alice)&~quiet(alice)))=>(?[X]:((happy(X)|~funny(X)))))&
(![X]:(strong(X)<=>(~creative(X)<~>~rich(X))))&
(((~funny(susan)<~>generous(susan)))=>((happy(fred)|~generous(fred))))&
(((curious(alice)|~patient(alice)))=>(?[X]:(calm(X))))&
(![X]:(~rich(X)=>(~generous(X)&~humble(X))))&
(![X]:((wise(X)|humble(X))=>generous(X)))&
((creative(susan)<~>~brave(susan)))&
((~calm(john)|funny(john)))&
(?[X]:((tall(X)&~wise(X))))&
(?[X]:(~old(X)))&
(?[X]:((tall(X)&~curious(X))))&
(?[X]:((humble(X)<~>strong(X))))&
(?[X]:(patient(X)))&
(?[X]:((~humble(X)|wise(X)))) | patient(alice) | [] | null | 0 |
Everyone who is either not rich or old is not tall or funny and vice versa. If alice is both wise and patient then someone is both not creative and not calm. If mary is brave or not tall then susan is calm or not patient. If paul is both wise and funny then alice is not creative or not rich. Everyone who is strong is both not humble and not strong and vice versa. If alice is kind or curious then alice is not old and vice versa. If susan is either not brave or creative then someone is either wise or generous and vice versa. Everyone who is both kind and quiet is happy or not tall and vice versa. Everyone who is quiet is not brave. Everyone who is either not calm or not rich is either not tall or not quiet and vice versa. If mary is not kind then someone is funny or not humble. If someone is either old or not curious then susan is either not patient or not brave. Everyone who is old or not calm is both strong and old and vice versa. If john is kind then someone is both old and quiet and vice versa. If someone is not strong then someone is both not patient and not curious. If someone is not brave then paul is either tall or not brave and vice versa. Paul is either not funny or not old. Someone is either not generous or not calm. John is strong or not funny. Lucy is not quiet or not creative. Mary is both not curious and patient. Alice is patient or tall. | John is not brave. | entailment | (![X]:((~rich(X)<~>old(X))<=>(~tall(X)|funny(X))))&
(((wise(alice)&patient(alice)))=>(?[X]:((~creative(X)&~calm(X)))))&
(((brave(mary)|~tall(mary)))=>((calm(susan)|~patient(susan))))&
(((wise(paul)&funny(paul)))=>((~creative(alice)|~rich(alice))))&
(![X]:(strong(X)<=>(~humble(X)&~strong(X))))&
(((kind(alice)|curious(alice)))<=>(~old(alice)))&
(((~brave(susan)<~>creative(susan)))<=>(?[X]:((wise(X)<~>generous(X)))))&
(![X]:((kind(X)&quiet(X))<=>(happy(X)|~tall(X))))&
(![X]:(quiet(X)=>~brave(X)))&
(![X]:((~calm(X)<~>~rich(X))<=>(~tall(X)<~>~quiet(X))))&
((~kind(mary))=>(?[X]:((funny(X)|~humble(X)))))&
((?[X]:((old(X)<~>~curious(X))))=>((~patient(susan)<~>~brave(susan))))&
(![X]:((old(X)|~calm(X))<=>(strong(X)&old(X))))&
((kind(john))<=>(?[X]:((old(X)&quiet(X)))))&
((?[X]:(~strong(X)))=>(?[X]:((~patient(X)&~curious(X)))))&
((?[X]:(~brave(X)))<=>((tall(paul)<~>~brave(paul))))&
((~funny(paul)<~>~old(paul)))&
(?[X]:((~generous(X)<~>~calm(X))))&
((strong(john)|~funny(john)))&
((~quiet(lucy)|~creative(lucy)))&
((~curious(mary)&patient(mary)))&
((patient(alice)|tall(alice))) | ~brave(john) | [
"p0",
"p4",
"p7",
"p8",
"p9",
"p12",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8425725013811423721318358
% SZS output start Proof for 8425725013811423721318358
1. ! [X0] : ((~rich(X0) <~> old(X0)) <=> (funny(X0) | ~tall(X0))) [input p0]
5. ! [X0] : (strong(X0) <=> (~strong(X0) & ~humble(X0))) [input p4]
8. ! [X0] : ((quiet(X0) & kind(X0)) <=> (~tall(X0) | happy(X0))) [input p7]
9. ! [X0] : (quiet(X0) => ~brave(X0)) [input p8]
10. ! [X0] : ((~calm(X0) <~> ~rich(X0)) <=> (~tall(X0) <~> ~quiet(X0))) [input p9]
13. ! [X0] : ((~calm(X0) | old(X0)) <=> (old(X0) & strong(X0))) [input p12]
14. kind(john) <=> ? [X0] : (quiet(X0) & old(X0)) [input p13]
19. ~funny(john) | strong(john) [input p18]
23. brave(john) [input hypothesis]
31. ! [X0] : (~brave(X0) | ~quiet(X0)) [ennf transformation 9]
35. ! [X0] : ((((~old(X0) | rich(X0)) & (old(X0) | ~rich(X0))) | (~funny(X0) & tall(X0))) & ((funny(X0) | ~tall(X0)) | ((~rich(X0) | ~old(X0)) & (old(X0) | rich(X0))))) [nnf transformation 1]
36. ! [X0] : ((((~old(X0) | rich(X0)) & (old(X0) | ~rich(X0))) | (~funny(X0) & tall(X0))) & (funny(X0) | ~tall(X0) | ((~rich(X0) | ~old(X0)) & (old(X0) | rich(X0))))) [flattening 35]
39. ! [X0] : ((strong(X0) | (strong(X0) | humble(X0))) & ((~strong(X0) & ~humble(X0)) | ~strong(X0))) [nnf transformation 5]
40. ! [X0] : ((strong(X0) | strong(X0) | humble(X0)) & ((~strong(X0) & ~humble(X0)) | ~strong(X0))) [flattening 39]
47. ! [X0] : (((quiet(X0) & kind(X0)) | (tall(X0) & ~happy(X0))) & ((~tall(X0) | happy(X0)) | (~quiet(X0) | ~kind(X0)))) [nnf transformation 8]
48. ! [X0] : (((quiet(X0) & kind(X0)) | (tall(X0) & ~happy(X0))) & (~tall(X0) | happy(X0) | ~quiet(X0) | ~kind(X0))) [flattening 47]
49. ! [X0] : ((((rich(X0) | calm(X0)) & (~rich(X0) | ~calm(X0))) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0)))) & (((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | ((~calm(X0) | rich(X0)) & (~rich(X0) | calm(X0))))) [nnf transformation 10]
53. ! [X0] : (((~calm(X0) | old(X0)) | (~old(X0) | ~strong(X0))) & ((old(X0) & strong(X0)) | (calm(X0) & ~old(X0)))) [nnf transformation 13]
54. ! [X0] : ((~calm(X0) | old(X0) | ~old(X0) | ~strong(X0)) & ((old(X0) & strong(X0)) | (calm(X0) & ~old(X0)))) [flattening 53]
55. (kind(john) | ! [X0] : (~quiet(X0) | ~old(X0))) & (? [X0] : (quiet(X0) & old(X0)) | ~kind(john)) [nnf transformation 14]
56. (kind(john) | ! [X0] : (~quiet(X0) | ~old(X0))) & (? [X1] : (quiet(X1) & old(X1)) | ~kind(john)) [rectify 55]
57. ? [X1] : (quiet(X1) & old(X1)) => (quiet(sK3) & old(sK3)) [choice axiom]
58. (kind(john) | ! [X0] : (~quiet(X0) | ~old(X0))) & ((quiet(sK3) & old(sK3)) | ~kind(john)) [skolemisation 56,57]
70. ~tall(X0) | funny(X0) | old(X0) | rich(X0) [cnf transformation 36]
82. ~strong(X0) | ~strong(X0) [cnf transformation 40]
97. kind(X0) | tall(X0) [cnf transformation 48]
99. quiet(X0) | tall(X0) [cnf transformation 48]
100. ~quiet(X0) | ~brave(X0) [cnf transformation 31]
106. ~rich(X0) | ~calm(X0) | ~tall(X0) | quiet(X0) [cnf transformation 49]
114. strong(X0) | ~old(X0) [cnf transformation 54]
117. calm(X0) | old(X0) [cnf transformation 54]
119. old(sK3) | ~kind(john) [cnf transformation 58]
132. ~funny(john) | strong(john) [cnf transformation 19]
137. brave(john) [cnf transformation 23]
138. ~strong(X0) [duplicate literal removal 82]
240. ~calm(X0) | ~rich(X0) | quiet(X0) [subsumption resolution 106,99]
266. ~old(X0) [subsumption resolution 114,138]
268. 27 <=> kind(john) [avatar definition]
270. ~kind(john) <- (~27) [avatar component clause 268]
276. ~kind(john) [subsumption resolution 119,266]
277. ~27 [avatar split clause 276,268]
302. ~funny(john) [subsumption resolution 132,138]
319. tall(john) <- (~27) [resolution 97,270]
334. ~rich(X1) | quiet(X1) | old(X1) [resolution 240,117]
336. ~rich(X1) | quiet(X1) [subsumption resolution 334,266]
341. funny(john) | old(john) | rich(john) <- (~27) [resolution 70,319]
343. old(john) | rich(john) <- (~27) [subsumption resolution 341,302]
344. rich(john) <- (~27) [subsumption resolution 343,266]
356. quiet(john) <- (~27) [resolution 344,336]
366. ~brave(john) <- (~27) [resolution 356,100]
367. $false <- (~27) [subsumption resolution 366,137]
368. 27 [avatar contradiction clause 367]
369. $false [avatar sat refutation 277,368]
% SZS output end Proof for 8425725013811423721318358
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not quiet is both curious and tall.
If someone is generous then fred is either quiet or not old and vice versa.
Everyone who is both funny and tall is old or not rich and vice versa.
If mary is both not happy and patient then someone is generous.
Everyone who is not funny or not tall is both creative and patient and vice versa.
If lucy is curious then someone is calm or generous and vice versa.
Everyone who is not curious or not funny is both not quiet and humble and vice versa.
If someone is wise then someone is not generous and vice versa.
If someone is either not wise or funny then someone is either humble or not curious.
Everyone who is humble is generous or brave and vice versa.
Everyone who is not quiet or rich is not patient or rich.
If susan is both happy and not tall then someone is either not curious or old and vice versa.
If someone is both not happy and wise then susan is either not creative or not old and vice versa.
If fred is both not generous and not rich then someone is either humble or not kind.
Everyone who is both humble and strong is brave or not wise and vice versa.
If someone is not creative then someone is both not curious and not generous and vice versa.
Lucy is not old.
Someone is not curious or not funny.
Someone is patient or humble.
John is kind.
Someone is generous or brave.
Alice is not calm or curious.
Someone is either quiet or not happy. | Fred is not wise. | neutral | (![X]:((~happy(X)|~quiet(X))=>(curious(X)&tall(X))))&
((?[X]:(generous(X)))<=>((quiet(fred)<~>~old(fred))))&
(![X]:((funny(X)&tall(X))<=>(old(X)|~rich(X))))&
(((~happy(mary)&patient(mary)))=>(?[X]:(generous(X))))&
(![X]:((~funny(X)|~tall(X))<=>(creative(X)&patient(X))))&
((curious(lucy))<=>(?[X]:((calm(X)|generous(X)))))&
(![X]:((~curious(X)|~funny(X))<=>(~quiet(X)&humble(X))))&
((?[X]:(wise(X)))<=>(?[X]:(~generous(X))))&
((?[X]:((~wise(X)<~>funny(X))))=>(?[X]:((humble(X)<~>~curious(X)))))&
(![X]:(humble(X)<=>(generous(X)|brave(X))))&
(![X]:((~quiet(X)|rich(X))=>(~patient(X)|rich(X))))&
(((happy(susan)&~tall(susan)))<=>(?[X]:((~curious(X)<~>old(X)))))&
((?[X]:((~happy(X)&wise(X))))<=>((~creative(susan)<~>~old(susan))))&
(((~generous(fred)&~rich(fred)))=>(?[X]:((humble(X)<~>~kind(X)))))&
(![X]:((humble(X)&strong(X))<=>(brave(X)|~wise(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~curious(X)&~generous(X)))))&
(~old(lucy))&
(?[X]:((~curious(X)|~funny(X))))&
(?[X]:((patient(X)|humble(X))))&
(kind(john))&
(?[X]:((generous(X)|brave(X))))&
((~calm(alice)|curious(alice)))&
(?[X]:((quiet(X)<~>~happy(X)))) | ~wise(fred) | [] | null | 0 |
If someone is creative or old then lucy is not brave and vice versa. Everyone who is either curious or not old is not old or strong and vice versa. Everyone who is kind or calm is either not happy or brave and vice versa. If someone is both not brave and quiet then someone is kind or brave and vice versa. Everyone who is both kind and not happy is kind or patient and vice versa. If someone is both not strong and not curious then fred is calm. Everyone who is humble or not wise is both wise and not calm and vice versa. Everyone who is either creative or not patient is either not quiet or not wise and vice versa. If someone is quiet then someone is both calm and brave and vice versa. If someone is both humble and not humble then someone is both not quiet and kind. Everyone who is either rich or not wise is patient or not creative and vice versa. Everyone who is not curious is not quiet or tall and vice versa. Everyone who is either not happy or creative is not happy or kind. Everyone who is funny or creative is either not creative or patient. If susan is both not creative and not old then someone is either kind or happy and vice versa. Everyone who is both not funny and not tall is not generous and vice versa. Mary is tall. John is both humble and not tall. Mary is calm or not brave. Mary is not quiet. Alice is not funny. Mary is either curious or not funny. | Lucy is not rich. | contradiction | ((?[X]:((creative(X)|old(X))))<=>(~brave(lucy)))&
(![X]:((curious(X)<~>~old(X))<=>(~old(X)|strong(X))))&
(![X]:((kind(X)|calm(X))<=>(~happy(X)<~>brave(X))))&
((?[X]:((~brave(X)&quiet(X))))<=>(?[X]:((kind(X)|brave(X)))))&
(![X]:((kind(X)&~happy(X))<=>(kind(X)|patient(X))))&
((?[X]:((~strong(X)&~curious(X))))=>(calm(fred)))&
(![X]:((humble(X)|~wise(X))<=>(wise(X)&~calm(X))))&
(![X]:((creative(X)<~>~patient(X))<=>(~quiet(X)<~>~wise(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((calm(X)&brave(X)))))&
((?[X]:((humble(X)&~humble(X))))=>(?[X]:((~quiet(X)&kind(X)))))&
(![X]:((rich(X)<~>~wise(X))<=>(patient(X)|~creative(X))))&
(![X]:(~curious(X)<=>(~quiet(X)|tall(X))))&
(![X]:((~happy(X)<~>creative(X))=>(~happy(X)|kind(X))))&
(![X]:((funny(X)|creative(X))=>(~creative(X)<~>patient(X))))&
(((~creative(susan)&~old(susan)))<=>(?[X]:((kind(X)<~>happy(X)))))&
(![X]:((~funny(X)&~tall(X))<=>~generous(X)))&
(tall(mary))&
((humble(john)&~tall(john)))&
((calm(mary)|~brave(mary)))&
(~quiet(mary))&
(~funny(alice))&
((curious(mary)<~>~funny(mary))) | ~rich(lucy) | [
"p6",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8727594601204111835921566
% SZS output start Proof for 8727594601204111835921566
7. ! [X0] : ((~wise(X0) | humble(X0)) <=> (~calm(X0) & wise(X0))) [input p6]
11. ! [X0] : ((rich(X0) <~> ~wise(X0)) <=> (~creative(X0) | patient(X0))) [input p10]
14. ! [X0] : ((creative(X0) | funny(X0)) => (~creative(X0) <~> patient(X0))) [input p13]
23. ~rich(lucy) [input hypothesis]
31. ! [X0] : ((~creative(X0) <~> patient(X0)) | (~creative(X0) & ~funny(X0))) [ennf transformation 14]
47. ! [X0] : (((~wise(X0) | humble(X0)) | (calm(X0) | ~wise(X0))) & ((~calm(X0) & wise(X0)) | (wise(X0) & ~humble(X0)))) [nnf transformation 7]
48. ! [X0] : ((~wise(X0) | humble(X0) | calm(X0) | ~wise(X0)) & ((~calm(X0) & wise(X0)) | (wise(X0) & ~humble(X0)))) [flattening 47]
58. ! [X0] : ((((wise(X0) | ~rich(X0)) & (~wise(X0) | rich(X0))) | (creative(X0) & ~patient(X0))) & ((~creative(X0) | patient(X0)) | ((rich(X0) | wise(X0)) & (~wise(X0) | ~rich(X0))))) [nnf transformation 11]
59. ! [X0] : ((((wise(X0) | ~rich(X0)) & (~wise(X0) | rich(X0))) | (creative(X0) & ~patient(X0))) & (~creative(X0) | patient(X0) | ((rich(X0) | wise(X0)) & (~wise(X0) | ~rich(X0))))) [flattening 58]
63. ! [X0] : (((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) | (~creative(X0) & ~funny(X0))) [nnf transformation 31]
97. wise(X0) | wise(X0) [cnf transformation 48]
116. ~wise(X0) | rich(X0) | ~patient(X0) [cnf transformation 59]
117. ~wise(X0) | rich(X0) | creative(X0) [cnf transformation 59]
126. patient(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 63]
143. ~rich(lucy) [cnf transformation 23]
144. ~creative(X0) | patient(X0) [duplicate literal removal 126]
146. wise(X0) [duplicate literal removal 97]
236. rich(X0) | creative(X0) [subsumption resolution 117,146]
237. ~patient(X0) | rich(X0) [subsumption resolution 116,146]
307. creative(lucy) [resolution 236,143]
309. patient(lucy) [resolution 307,144]
311. rich(lucy) [resolution 309,237]
314. $false [subsumption resolution 311,143]
% SZS output end Proof for 8727594601204111835921566
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and calm is not wise or not happy and vice versa.
Everyone who is both not funny and calm is not quiet or not tall.
If someone is funny then alice is not humble or generous.
If paul is both brave and calm then paul is not kind.
If someone is kind or not funny then someone is rich.
Everyone who is both funny and calm is strong or patient.
Everyone who is rich or not old is kind and vice versa.
If alice is not brave or not happy then paul is not quiet and vice versa.
If someone is either not funny or not curious then alice is either not old or not calm and vice versa.
Everyone who is not generous or not creative is not quiet and vice versa.
If someone is both not creative and not curious then someone is funny.
If someone is tall then alice is both humble and not rich and vice versa.
Everyone who is not strong or not funny is either not patient or humble.
Everyone who is not old or calm is not calm.
Everyone who is both not generous and kind is either not strong or tall and vice versa.
If someone is not quiet then john is tall.
Mary is humble.
Someone is kind.
Mary is either not patient or not wise.
Susan is not tall or not funny.
Fred is curious.
Someone is either brave or generous.
Someone is both not rich and strong.
Someone is both not calm and not old. | John is happy. | entailment | (![X]:((humble(X)&calm(X))<=>(~wise(X)|~happy(X))))&
(![X]:((~funny(X)&calm(X))=>(~quiet(X)|~tall(X))))&
((?[X]:(funny(X)))=>((~humble(alice)|generous(alice))))&
(((brave(paul)&calm(paul)))=>(~kind(paul)))&
((?[X]:((kind(X)|~funny(X))))=>(?[X]:(rich(X))))&
(![X]:((funny(X)&calm(X))=>(strong(X)|patient(X))))&
(![X]:((rich(X)|~old(X))<=>kind(X)))&
(((~brave(alice)|~happy(alice)))<=>(~quiet(paul)))&
((?[X]:((~funny(X)<~>~curious(X))))<=>((~old(alice)<~>~calm(alice))))&
(![X]:((~generous(X)|~creative(X))<=>~quiet(X)))&
((?[X]:((~creative(X)&~curious(X))))=>(?[X]:(funny(X))))&
((?[X]:(tall(X)))<=>((humble(alice)&~rich(alice))))&
(![X]:((~strong(X)|~funny(X))=>(~patient(X)<~>humble(X))))&
(![X]:((~old(X)|calm(X))=>~calm(X)))&
(![X]:((~generous(X)&kind(X))<=>(~strong(X)<~>tall(X))))&
((?[X]:(~quiet(X)))=>(tall(john)))&
(humble(mary))&
(?[X]:(kind(X)))&
((~patient(mary)<~>~wise(mary)))&
((~tall(susan)|~funny(susan)))&
(curious(fred))&
(?[X]:((brave(X)<~>generous(X))))&
(?[X]:((~rich(X)&strong(X))))&
(?[X]:((~calm(X)&~old(X)))) | happy(john) | [
"p0",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1200874194043014586843190
% SZS output start Proof for 1200874194043014586843190
1. ! [X0] : ((calm(X0) & humble(X0)) <=> (~happy(X0) | ~wise(X0))) [input p0]
14. ! [X0] : ((calm(X0) | ~old(X0)) => ~calm(X0)) [input p13]
25. ~happy(john) [input hypothesis]
39. ! [X0] : (~calm(X0) | (~calm(X0) & old(X0))) [ennf transformation 14]
41. ! [X0] : (((calm(X0) & humble(X0)) | (happy(X0) & wise(X0))) & ((~happy(X0) | ~wise(X0)) | (~calm(X0) | ~humble(X0)))) [nnf transformation 1]
42. ! [X0] : (((calm(X0) & humble(X0)) | (happy(X0) & wise(X0))) & (~happy(X0) | ~wise(X0) | ~calm(X0) | ~humble(X0))) [flattening 41]
81. happy(X0) | calm(X0) [cnf transformation 42]
114. ~calm(X0) | ~calm(X0) [cnf transformation 39]
134. ~happy(john) [cnf transformation 25]
135. ~calm(X0) [duplicate literal removal 114]
286. calm(john) [resolution 81,134]
287. $false [subsumption resolution 286,135]
% SZS output end Proof for 1200874194043014586843190
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not creative is kind and vice versa.
If mary is both curious and not kind then fred is not patient and vice versa.
Everyone who is not tall or not humble is both not generous and creative.
If someone is not funny then alice is either not brave or kind and vice versa.
Everyone who is not patient or not old is not kind or strong and vice versa.
Everyone who is either brave or patient is both kind and patient.
If fred is either generous or humble then someone is creative or not old and vice versa.
Everyone who is either not patient or tall is quiet or brave and vice versa.
If john is either funny or not happy then someone is kind and vice versa.
If someone is either not kind or tall then alice is not wise or wise.
Everyone who is both funny and rich is either not quiet or not patient and vice versa.
Everyone who is tall or not generous is not calm or creative.
Everyone who is not strong is not quiet and vice versa.
If someone is either generous or not humble then susan is not old and vice versa.
Everyone who is either happy or funny is curious or happy and vice versa.
Everyone who is either not calm or patient is generous.
Lucy is old.
Lucy is both creative and not generous.
Someone is both not rich and not curious.
Fred is both not curious and patient.
Someone is funny. | John is not curious. | neutral | (![X]:((~humble(X)&~creative(X))<=>kind(X)))&
(((curious(mary)&~kind(mary)))<=>(~patient(fred)))&
(![X]:((~tall(X)|~humble(X))=>(~generous(X)&creative(X))))&
((?[X]:(~funny(X)))<=>((~brave(alice)<~>kind(alice))))&
(![X]:((~patient(X)|~old(X))<=>(~kind(X)|strong(X))))&
(![X]:((brave(X)<~>patient(X))=>(kind(X)&patient(X))))&
(((generous(fred)<~>humble(fred)))<=>(?[X]:((creative(X)|~old(X)))))&
(![X]:((~patient(X)<~>tall(X))<=>(quiet(X)|brave(X))))&
(((funny(john)<~>~happy(john)))<=>(?[X]:(kind(X))))&
((?[X]:((~kind(X)<~>tall(X))))=>((~wise(alice)|wise(alice))))&
(![X]:((funny(X)&rich(X))<=>(~quiet(X)<~>~patient(X))))&
(![X]:((tall(X)|~generous(X))=>(~calm(X)|creative(X))))&
(![X]:(~strong(X)<=>~quiet(X)))&
((?[X]:((generous(X)<~>~humble(X))))<=>(~old(susan)))&
(![X]:((happy(X)<~>funny(X))<=>(curious(X)|happy(X))))&
(![X]:((~calm(X)<~>patient(X))=>generous(X)))&
(old(lucy))&
((creative(lucy)&~generous(lucy)))&
(?[X]:((~rich(X)&~curious(X))))&
((~curious(fred)&patient(fred)))&
(?[X]:(funny(X))) | ~curious(john) | [] | null | 0 |
Everyone who is both not wise and not generous is not generous and vice versa.
Everyone who is either curious or not old is not rich or not generous and vice versa.
Everyone who is either quiet or generous is both tall and old and vice versa.
If someone is not kind or not generous then fred is either kind or brave.
If susan is not funny then mary is both old and not tall and vice versa.
Everyone who is both not generous and not tall is not kind or quiet and vice versa.
If mary is not patient then someone is either brave or strong and vice versa.
If paul is strong or brave then mary is both not creative and humble and vice versa.
If someone is not brave or curious then alice is both not creative and rich and vice versa.
If susan is either not happy or not calm then someone is both not funny and creative.
Everyone who is not kind or happy is kind or not happy.
If paul is kind or not patient then paul is brave or not wise and vice versa.
Everyone who is both humble and not humble is both funny and not humble and vice versa.
If someone is not patient or not quiet then someone is funny or wise.
Everyone who is not strong is humble or not patient.
Everyone who is not strong is not wise.
Someone is patient.
Someone is not calm.
Fred is both generous and not humble.
Someone is both brave and rich.
Someone is both not generous and kind.
Someone is either not quiet or strong.
Someone is not funny or quiet. | Mary is tall. | neutral | (![X]:((~wise(X)&~generous(X))<=>~generous(X)))&
(![X]:((curious(X)<~>~old(X))<=>(~rich(X)|~generous(X))))&
(![X]:((quiet(X)<~>generous(X))<=>(tall(X)&old(X))))&
((?[X]:((~kind(X)|~generous(X))))=>((kind(fred)<~>brave(fred))))&
((~funny(susan))<=>((old(mary)&~tall(mary))))&
(![X]:((~generous(X)&~tall(X))<=>(~kind(X)|quiet(X))))&
((~patient(mary))<=>(?[X]:((brave(X)<~>strong(X)))))&
(((strong(paul)|brave(paul)))<=>((~creative(mary)&humble(mary))))&
((?[X]:((~brave(X)|curious(X))))<=>((~creative(alice)&rich(alice))))&
(((~happy(susan)<~>~calm(susan)))=>(?[X]:((~funny(X)&creative(X)))))&
(![X]:((~kind(X)|happy(X))=>(kind(X)|~happy(X))))&
(((kind(paul)|~patient(paul)))<=>((brave(paul)|~wise(paul))))&
(![X]:((humble(X)&~humble(X))<=>(funny(X)&~humble(X))))&
((?[X]:((~patient(X)|~quiet(X))))=>(?[X]:((funny(X)|wise(X)))))&
(![X]:(~strong(X)=>(humble(X)|~patient(X))))&
(![X]:(~strong(X)=>~wise(X)))&
(?[X]:(patient(X)))&
(?[X]:(~calm(X)))&
((generous(fred)&~humble(fred)))&
(?[X]:((brave(X)&rich(X))))&
(?[X]:((~generous(X)&kind(X))))&
(?[X]:((~quiet(X)<~>strong(X))))&
(?[X]:((~funny(X)|quiet(X)))) | tall(mary) | [] | null | 0 |
Everyone who is not curious or not wise is rich and vice versa. If lucy is either wise or not creative then alice is either not strong or calm. Everyone who is either not old or not happy is both patient and not funny and vice versa. Everyone who is happy or humble is both not quiet and not happy. If someone is both not happy and tall then someone is happy. If someone is rich then someone is both not humble and strong. If someone is both not humble and humble then alice is not creative or not curious and vice versa. If susan is old or not brave then someone is either not rich or calm and vice versa. If someone is tall then someone is both creative and not kind and vice versa. Everyone who is not wise or quiet is both not wise and not tall and vice versa. If someone is either not happy or not wise then someone is both old and quiet. If someone is creative or generous then lucy is funny or creative. Everyone who is generous is not curious or strong. Everyone who is not curious is humble or not patient and vice versa. Everyone who is brave is either creative or not humble. Everyone who is both rich and not generous is both kind and not curious. John is both humble and brave. Someone is both rich and patient. Someone is not happy. Someone is happy or not generous. Someone is quiet. Paul is generous or rich. Susan is not calm. Mary is not brave or funny. | Susan is old. | neutral | (![X]:((~curious(X)|~wise(X))<=>rich(X)))&
(((wise(lucy)<~>~creative(lucy)))=>((~strong(alice)<~>calm(alice))))&
(![X]:((~old(X)<~>~happy(X))<=>(patient(X)&~funny(X))))&
(![X]:((happy(X)|humble(X))=>(~quiet(X)&~happy(X))))&
((?[X]:((~happy(X)&tall(X))))=>(?[X]:(happy(X))))&
((?[X]:(rich(X)))=>(?[X]:((~humble(X)&strong(X)))))&
((?[X]:((~humble(X)&humble(X))))<=>((~creative(alice)|~curious(alice))))&
(((old(susan)|~brave(susan)))<=>(?[X]:((~rich(X)<~>calm(X)))))&
((?[X]:(tall(X)))<=>(?[X]:((creative(X)&~kind(X)))))&
(![X]:((~wise(X)|quiet(X))<=>(~wise(X)&~tall(X))))&
((?[X]:((~happy(X)<~>~wise(X))))=>(?[X]:((old(X)&quiet(X)))))&
((?[X]:((creative(X)|generous(X))))=>((funny(lucy)|creative(lucy))))&
(![X]:(generous(X)=>(~curious(X)|strong(X))))&
(![X]:(~curious(X)<=>(humble(X)|~patient(X))))&
(![X]:(brave(X)=>(creative(X)<~>~humble(X))))&
(![X]:((rich(X)&~generous(X))=>(kind(X)&~curious(X))))&
((humble(john)&brave(john)))&
(?[X]:((rich(X)&patient(X))))&
(?[X]:(~happy(X)))&
(?[X]:((happy(X)|~generous(X))))&
(?[X]:(quiet(X)))&
((generous(paul)|rich(paul)))&
(~calm(susan))&
((~brave(mary)|funny(mary))) | old(susan) | [] | null | 0 |
If someone is not rich then paul is humble or generous and vice versa.
If alice is either funny or calm then mary is both strong and rich and vice versa.
Everyone who is rich or not funny is strong.
If alice is not curious then someone is not patient and vice versa.
If someone is both humble and kind then alice is both generous and not funny.
If someone is either not creative or kind then alice is both generous and not patient and vice versa.
Everyone who is both strong and tall is either not strong or not calm and vice versa.
Everyone who is both calm and not strong is brave and vice versa.
Everyone who is either not strong or not happy is both not quiet and not curious.
Everyone who is either rich or not patient is rich and vice versa.
If lucy is not humble then someone is not curious.
If someone is either patient or not patient then lucy is both not creative and happy.
Everyone who is rich or quiet is brave or old.
Everyone who is generous is either not curious or not creative.
Everyone who is either funny or generous is either brave or not funny.
If someone is not brave then someone is both humble and quiet.
Someone is either humble or not creative.
Someone is either not rich or not humble.
Someone is generous.
Alice is not tall or rich.
Someone is not generous.
Paul is not rich.
Someone is either not old or happy.
Someone is quiet or not brave. | Mary is patient. | entailment | ((?[X]:(~rich(X)))<=>((humble(paul)|generous(paul))))&
(((funny(alice)<~>calm(alice)))<=>((strong(mary)&rich(mary))))&
(![X]:((rich(X)|~funny(X))=>strong(X)))&
((~curious(alice))<=>(?[X]:(~patient(X))))&
((?[X]:((humble(X)&kind(X))))=>((generous(alice)&~funny(alice))))&
((?[X]:((~creative(X)<~>kind(X))))<=>((generous(alice)&~patient(alice))))&
(![X]:((strong(X)&tall(X))<=>(~strong(X)<~>~calm(X))))&
(![X]:((calm(X)&~strong(X))<=>brave(X)))&
(![X]:((~strong(X)<~>~happy(X))=>(~quiet(X)&~curious(X))))&
(![X]:((rich(X)<~>~patient(X))<=>rich(X)))&
((~humble(lucy))=>(?[X]:(~curious(X))))&
((?[X]:((patient(X)<~>~patient(X))))=>((~creative(lucy)&happy(lucy))))&
(![X]:((rich(X)|quiet(X))=>(brave(X)|old(X))))&
(![X]:(generous(X)=>(~curious(X)<~>~creative(X))))&
(![X]:((funny(X)<~>generous(X))=>(brave(X)<~>~funny(X))))&
((?[X]:(~brave(X)))=>(?[X]:((humble(X)&quiet(X)))))&
(?[X]:((humble(X)<~>~creative(X))))&
(?[X]:((~rich(X)<~>~humble(X))))&
(?[X]:(generous(X)))&
((~tall(alice)|rich(alice)))&
(?[X]:(~generous(X)))&
(~rich(paul))&
(?[X]:((~old(X)<~>happy(X))))&
(?[X]:((quiet(X)|~brave(X)))) | patient(mary) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3077501893679705061616946
% SZS output start Proof for 3077501893679705061616946
10. ! [X0] : ((rich(X0) <~> ~patient(X0)) <=> rich(X0)) [input p9]
25. ~patient(mary) [input hypothesis]
58. ! [X0] : ((((patient(X0) | ~rich(X0)) & (~patient(X0) | rich(X0))) | ~rich(X0)) & (rich(X0) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0))))) [nnf transformation 10]
117. rich(X0) | rich(X0) | patient(X0) [cnf transformation 58]
119. patient(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 58]
146. ~patient(mary) [cnf transformation 25]
153. rich(X0) | patient(X0) [duplicate literal removal 117]
154. patient(X0) | ~rich(X0) [duplicate literal removal 119]
198. 9 <=> ! [X0] : patient(X0) [avatar definition]
199. patient(X0) <- (9) [avatar component clause 198]
244. patient(X0) [subsumption resolution 153,154]
245. 9 [avatar split clause 244,198]
331. $false <- (9) [resolution 199,146]
332. ~9 [avatar contradiction clause 331]
333. $false [avatar sat refutation 245,332]
% SZS output end Proof for 3077501893679705061616946
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is happy or brave and vice versa.
If susan is either creative or tall then fred is not strong.
If fred is quiet or not rich then susan is not happy or not old.
Everyone who is rich or not wise is not brave.
Everyone who is not strong or not generous is strong.
If fred is either not old or kind then someone is strong and vice versa.
Everyone who is not brave is both happy and not wise and vice versa.
Everyone who is both not wise and rich is either generous or brave and vice versa.
If susan is either strong or happy then paul is either patient or not tall and vice versa.
Everyone who is brave is either tall or not brave and vice versa.
Everyone who is either not humble or not old is both tall and old and vice versa.
Everyone who is both patient and calm is humble or not happy.
If someone is not creative then susan is not rich or happy.
Everyone who is either patient or not wise is rich.
If someone is both not curious and not kind then someone is patient and vice versa.
If alice is not tall or not wise then someone is both not creative and tall.
Someone is both not calm and quiet.
John is either not patient or wise.
Someone is patient.
Alice is calm or not creative.
Someone is not kind. | Susan is not rich. | neutral | (![X]:(funny(X)<=>(happy(X)|brave(X))))&
(((creative(susan)<~>tall(susan)))=>(~strong(fred)))&
(((quiet(fred)|~rich(fred)))=>((~happy(susan)|~old(susan))))&
(![X]:((rich(X)|~wise(X))=>~brave(X)))&
(![X]:((~strong(X)|~generous(X))=>strong(X)))&
(((~old(fred)<~>kind(fred)))<=>(?[X]:(strong(X))))&
(![X]:(~brave(X)<=>(happy(X)&~wise(X))))&
(![X]:((~wise(X)&rich(X))<=>(generous(X)<~>brave(X))))&
(((strong(susan)<~>happy(susan)))<=>((patient(paul)<~>~tall(paul))))&
(![X]:(brave(X)<=>(tall(X)<~>~brave(X))))&
(![X]:((~humble(X)<~>~old(X))<=>(tall(X)&old(X))))&
(![X]:((patient(X)&calm(X))=>(humble(X)|~happy(X))))&
((?[X]:(~creative(X)))=>((~rich(susan)|happy(susan))))&
(![X]:((patient(X)<~>~wise(X))=>rich(X)))&
((?[X]:((~curious(X)&~kind(X))))<=>(?[X]:(patient(X))))&
(((~tall(alice)|~wise(alice)))=>(?[X]:((~creative(X)&tall(X)))))&
(?[X]:((~calm(X)&quiet(X))))&
((~patient(john)<~>wise(john)))&
(?[X]:(patient(X)))&
((calm(alice)|~creative(alice)))&
(?[X]:(~kind(X))) | ~rich(susan) | [] | null | 0 |
Everyone who is both not patient and not tall is not patient or not humble.
If fred is both not quiet and not kind then someone is either curious or not calm and vice versa.
Everyone who is not rich is either not tall or rich and vice versa.
Everyone who is either brave or not rich is either not happy or not strong.
Everyone who is either creative or not old is both brave and not wise.
If john is either not creative or not wise then someone is old or creative and vice versa.
If someone is not tall then paul is both humble and patient.
If someone is both generous and brave then john is not tall or not humble and vice versa.
If fred is not happy or not creative then mary is rich or not generous.
If susan is funny then someone is either not tall or not curious.
If fred is either not patient or humble then someone is not tall.
Everyone who is either creative or calm is not creative or happy.
Everyone who is funny is either tall or creative and vice versa.
If john is not creative then someone is happy and vice versa.
If paul is not happy or kind then someone is either tall or not brave.
Everyone who is not happy or old is both not quiet and tall.
John is tall or not old.
Someone is not strong.
Susan is not tall or not brave.
Someone is not rich.
Someone is curious or not generous.
Someone is either humble or funny.
Mary is both not creative and curious. | Mary is not brave. | contradiction | (![X]:((~patient(X)&~tall(X))=>(~patient(X)|~humble(X))))&
(((~quiet(fred)&~kind(fred)))<=>(?[X]:((curious(X)<~>~calm(X)))))&
(![X]:(~rich(X)<=>(~tall(X)<~>rich(X))))&
(![X]:((brave(X)<~>~rich(X))=>(~happy(X)<~>~strong(X))))&
(![X]:((creative(X)<~>~old(X))=>(brave(X)&~wise(X))))&
(((~creative(john)<~>~wise(john)))<=>(?[X]:((old(X)|creative(X)))))&
((?[X]:(~tall(X)))=>((humble(paul)&patient(paul))))&
((?[X]:((generous(X)&brave(X))))<=>((~tall(john)|~humble(john))))&
(((~happy(fred)|~creative(fred)))=>((rich(mary)|~generous(mary))))&
((funny(susan))=>(?[X]:((~tall(X)<~>~curious(X)))))&
(((~patient(fred)<~>humble(fred)))=>(?[X]:(~tall(X))))&
(![X]:((creative(X)<~>calm(X))=>(~creative(X)|happy(X))))&
(![X]:(funny(X)<=>(tall(X)<~>creative(X))))&
((~creative(john))<=>(?[X]:(happy(X))))&
(((~happy(paul)|kind(paul)))=>(?[X]:((tall(X)<~>~brave(X)))))&
(![X]:((~happy(X)|old(X))=>(~quiet(X)&tall(X))))&
((tall(john)|~old(john)))&
(?[X]:(~strong(X)))&
((~tall(susan)|~brave(susan)))&
(?[X]:(~rich(X)))&
(?[X]:((curious(X)|~generous(X))))&
(?[X]:((humble(X)<~>funny(X))))&
((~creative(mary)&curious(mary))) | ~brave(mary) | [
"p2",
"p4",
"p5",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7876986714625072154894092
% SZS output start Proof for 7876986714625072154894092
3. ! [X0] : (~rich(X0) <=> (~tall(X0) <~> rich(X0))) [input p2]
5. ! [X0] : ((creative(X0) <~> ~old(X0)) => (~wise(X0) & brave(X0))) [input p4]
6. (~creative(john) <~> ~wise(john)) <=> ? [X0] : (creative(X0) | old(X0)) [input p5]
14. ~creative(john) <=> ? [X0] : happy(X0) [input p13]
16. ! [X0] : ((old(X0) | ~happy(X0)) => (tall(X0) & ~quiet(X0))) [input p15]
17. ~old(john) | tall(john) [input p16]
24. ~brave(mary) [input hypothesis]
28. ! [X0] : ((~wise(X0) & brave(X0)) | (creative(X0) <=> ~old(X0))) [ennf transformation 5]
37. ! [X0] : ((tall(X0) & ~quiet(X0)) | (~old(X0) & happy(X0))) [ennf transformation 16]
43. ! [X0] : ((~rich(X0) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0)))) & (((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | rich(X0))) [nnf transformation 3]
45. ! [X0] : ((~wise(X0) & brave(X0)) | ((creative(X0) | old(X0)) & (~old(X0) | ~creative(X0)))) [nnf transformation 28]
46. (((wise(john) | creative(john)) & (~wise(john) | ~creative(john))) | ! [X0] : (~creative(X0) & ~old(X0))) & (? [X0] : (creative(X0) | old(X0)) | ((~creative(john) | wise(john)) & (~wise(john) | creative(john)))) [nnf transformation 6]
47. (((wise(john) | creative(john)) & (~wise(john) | ~creative(john))) | ! [X0] : (~creative(X0) & ~old(X0))) & (? [X1] : (creative(X1) | old(X1)) | ((~creative(john) | wise(john)) & (~wise(john) | creative(john)))) [rectify 46]
48. ? [X1] : (creative(X1) | old(X1)) => (creative(sK1) | old(sK1)) [choice axiom]
49. (((wise(john) | creative(john)) & (~wise(john) | ~creative(john))) | ! [X0] : (~creative(X0) & ~old(X0))) & ((creative(sK1) | old(sK1)) | ((~creative(john) | wise(john)) & (~wise(john) | creative(john)))) [skolemisation 47,48]
63. (~creative(john) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | creative(john)) [nnf transformation 14]
64. (~creative(john) | ! [X0] : ~happy(X0)) & (? [X1] : happy(X1) | creative(john)) [rectify 63]
65. ? [X1] : happy(X1) => happy(sK5) [choice axiom]
66. (~creative(john) | ! [X0] : ~happy(X0)) & (happy(sK5) | creative(john)) [skolemisation 64,65]
86. rich(X0) | ~tall(X0) | rich(X0) [cnf transformation 43]
89. ~rich(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 43]
95. old(X0) | creative(X0) | brave(X0) [cnf transformation 45]
97. ~wise(X0) | creative(X0) | old(X0) [cnf transformation 45]
103. wise(john) | creative(john) | ~creative(X0) [cnf transformation 49]
124. ~creative(john) | ~happy(X0) [cnf transformation 66]
131. tall(X0) | happy(X0) [cnf transformation 37]
132. tall(X0) | ~old(X0) [cnf transformation 37]
133. ~old(john) | tall(john) [cnf transformation 17]
142. ~brave(mary) [cnf transformation 24]
144. rich(X0) | ~tall(X0) [duplicate literal removal 86]
145. ~rich(X0) | ~tall(X0) [duplicate literal removal 89]
174. ~tall(X0) [subsumption resolution 144,145]
176. 7 <=> ! [X0] : ~creative(X0) [avatar definition]
177. ~creative(X0) <- (7) [avatar component clause 176]
179. 8 <=> creative(john) [avatar definition]
180. ~creative(john) <- (~8) [avatar component clause 179]
183. 9 <=> wise(john) [avatar definition]
185. wise(john) <- (9) [avatar component clause 183]
186. 7 | 8 | 9 [avatar split clause 103,183,179,176]
188. 10 <=> ! [X0] : ~old(X0) [avatar definition]
189. ~old(X0) <- (10) [avatar component clause 188]
254. 22 <=> ! [X0] : ~happy(X0) [avatar definition]
255. ~happy(X0) <- (22) [avatar component clause 254]
256. 22 | ~8 [avatar split clause 124,179,254]
278. ~old(X0) [subsumption resolution 132,174]
279. 10 [avatar split clause 278,188]
280. happy(X0) [subsumption resolution 131,174]
281. ~old(john) [subsumption resolution 133,174]
301. $false <- (22) [subsumption resolution 255,280]
302. ~22 [avatar contradiction clause 301]
305. creative(X2) | brave(X2) <- (10) [resolution 95,189]
309. brave(X2) <- (7, 10) [subsumption resolution 305,177]
310. $false <- (7, 10) [resolution 309,142]
313. ~7 | ~10 [avatar contradiction clause 310]
323. creative(john) | old(john) <- (9) [resolution 97,185]
324. old(john) <- (~8, 9) [subsumption resolution 323,180]
325. $false <- (~8, 9) [subsumption resolution 324,281]
326. 8 | ~9 [avatar contradiction clause 325]
327. $false [avatar sat refutation 186,256,279,302,313,326]
% SZS output end Proof for 7876986714625072154894092
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not quiet is wise and vice versa.
If paul is not curious or old then someone is not tall or happy.
Everyone who is not generous is either not creative or not funny and vice versa.
Everyone who is generous or happy is tall and vice versa.
If someone is either not tall or not creative then mary is both rich and not wise.
Everyone who is not humble is either happy or strong and vice versa.
If someone is both creative and not old then someone is either wise or generous and vice versa.
Everyone who is both curious and not curious is both rich and quiet and vice versa.
If mary is humble or happy then alice is not patient or not strong.
If alice is both calm and not kind then mary is not wise or creative and vice versa.
Everyone who is kind or not humble is rich and vice versa.
If paul is either kind or not strong then someone is rich or patient and vice versa.
Everyone who is not strong is not curious and vice versa.
If someone is either not brave or not curious then someone is either tall or happy and vice versa.
If someone is both not happy and brave then someone is rich or happy and vice versa.
Everyone who is either wise or kind is generous and vice versa.
Fred is not creative.
Alice is not calm or quiet.
Alice is either not generous or not rich.
Someone is generous or not kind.
Someone is happy or not funny.
Lucy is either generous or not humble.
Lucy is both not wise and not patient.
John is wise or happy. | Lucy is curious. | contradiction | (![X]:((curious(X)&~quiet(X))<=>wise(X)))&
(((~curious(paul)|old(paul)))=>(?[X]:((~tall(X)|happy(X)))))&
(![X]:(~generous(X)<=>(~creative(X)<~>~funny(X))))&
(![X]:((generous(X)|happy(X))<=>tall(X)))&
((?[X]:((~tall(X)<~>~creative(X))))=>((rich(mary)&~wise(mary))))&
(![X]:(~humble(X)<=>(happy(X)<~>strong(X))))&
((?[X]:((creative(X)&~old(X))))<=>(?[X]:((wise(X)<~>generous(X)))))&
(![X]:((curious(X)&~curious(X))<=>(rich(X)&quiet(X))))&
(((humble(mary)|happy(mary)))=>((~patient(alice)|~strong(alice))))&
(((calm(alice)&~kind(alice)))<=>((~wise(mary)|creative(mary))))&
(![X]:((kind(X)|~humble(X))<=>rich(X)))&
(((kind(paul)<~>~strong(paul)))<=>(?[X]:((rich(X)|patient(X)))))&
(![X]:(~strong(X)<=>~curious(X)))&
((?[X]:((~brave(X)<~>~curious(X))))<=>(?[X]:((tall(X)<~>happy(X)))))&
((?[X]:((~happy(X)&brave(X))))<=>(?[X]:((rich(X)|happy(X)))))&
(![X]:((wise(X)<~>kind(X))<=>generous(X)))&
(~creative(fred))&
((~calm(alice)|quiet(alice)))&
((~generous(alice)<~>~rich(alice)))&
(?[X]:((generous(X)|~kind(X))))&
(?[X]:((happy(X)|~funny(X))))&
((generous(lucy)<~>~humble(lucy)))&
((~wise(lucy)&~patient(lucy)))&
((wise(john)|happy(john))) | curious(lucy) | [
"p0",
"p7",
"p10",
"p15",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7321960362319640436808809
% SZS output start Proof for 7321960362319640436808809
1. ! [X0] : ((~quiet(X0) & curious(X0)) <=> wise(X0)) [input p0]
8. ! [X0] : ((~curious(X0) & curious(X0)) <=> (quiet(X0) & rich(X0))) [input p7]
11. ! [X0] : ((~humble(X0) | kind(X0)) <=> rich(X0)) [input p10]
16. ! [X0] : ((wise(X0) <~> kind(X0)) <=> generous(X0)) [input p15]
22. generous(lucy) <~> ~humble(lucy) [input p21]
23. ~patient(lucy) & ~wise(lucy) [input p22]
25. curious(lucy) [input hypothesis]
33. ! [X0] : (((~quiet(X0) & curious(X0)) | ~wise(X0)) & (wise(X0) | (quiet(X0) | ~curious(X0)))) [nnf transformation 1]
34. ! [X0] : (((~quiet(X0) & curious(X0)) | ~wise(X0)) & (wise(X0) | quiet(X0) | ~curious(X0))) [flattening 33]
47. ! [X0] : (((~curious(X0) & curious(X0)) | (~quiet(X0) | ~rich(X0))) & ((quiet(X0) & rich(X0)) | (curious(X0) | ~curious(X0)))) [nnf transformation 8]
48. ! [X0] : (((~curious(X0) & curious(X0)) | ~quiet(X0) | ~rich(X0)) & ((quiet(X0) & rich(X0)) | curious(X0) | ~curious(X0))) [flattening 47]
51. ! [X0] : (((~humble(X0) | kind(X0)) | ~rich(X0)) & (rich(X0) | (humble(X0) & ~kind(X0)))) [nnf transformation 11]
52. ! [X0] : ((~humble(X0) | kind(X0) | ~rich(X0)) & (rich(X0) | (humble(X0) & ~kind(X0)))) [flattening 51]
68. ! [X0] : ((((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | ~generous(X0)) & (generous(X0) | ((wise(X0) | ~kind(X0)) & (kind(X0) | ~wise(X0))))) [nnf transformation 16]
74. (humble(lucy) | ~generous(lucy)) & (~humble(lucy) | generous(lucy)) [nnf transformation 22]
75. ~curious(X0) | quiet(X0) | wise(X0) [cnf transformation 34]
103. curious(X0) | ~quiet(X0) | ~rich(X0) [cnf transformation 48]
104. ~rich(X0) | ~quiet(X0) | ~curious(X0) [cnf transformation 48]
112. ~kind(X0) | rich(X0) [cnf transformation 52]
113. humble(X0) | rich(X0) [cnf transformation 52]
138. ~generous(X0) | wise(X0) | kind(X0) [cnf transformation 68]
146. ~humble(lucy) | generous(lucy) [cnf transformation 74]
148. ~wise(lucy) [cnf transformation 23]
151. curious(lucy) [cnf transformation 25]
219. ~rich(X0) | ~quiet(X0) [subsumption resolution 103,104]
379. 49 <=> generous(lucy) [avatar definition]
380. generous(lucy) <- (49) [avatar component clause 379]
383. 50 <=> humble(lucy) [avatar definition]
384. ~humble(lucy) <- (~50) [avatar component clause 383]
387. 49 | ~50 [avatar split clause 146,383,379]
409. rich(lucy) <- (~50) [resolution 113,384]
431. ~quiet(lucy) <- (~50) [resolution 219,409]
452. quiet(lucy) | wise(lucy) [resolution 75,151]
456. wise(lucy) <- (~50) [subsumption resolution 452,431]
457. $false <- (~50) [subsumption resolution 456,148]
458. 50 [avatar contradiction clause 457]
477. quiet(lucy) [subsumption resolution 452,148]
598. 68 <=> rich(lucy) [avatar definition]
599. rich(lucy) <- (68) [avatar component clause 598]
602. 69 <=> kind(lucy) [avatar definition]
604. kind(lucy) <- (69) [avatar component clause 602]
632. wise(lucy) | kind(lucy) <- (49) [resolution 138,380]
639. kind(lucy) <- (49) [subsumption resolution 632,148]
640. 69 | ~49 [avatar split clause 639,379,602]
651. rich(lucy) <- (69) [resolution 604,112]
654. 68 | ~69 [avatar split clause 651,602,598]
660. ~quiet(lucy) <- (68) [resolution 599,219]
664. $false <- (68) [subsumption resolution 660,477]
665. ~68 [avatar contradiction clause 664]
666. $false [avatar sat refutation 387,458,640,654,665]
% SZS output end Proof for 7321960362319640436808809
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either humble or not wise then paul is both wise and not wise and vice versa. If lucy is both kind and old then paul is not strong and vice versa. Everyone who is either calm or wise is calm and vice versa. Everyone who is happy or funny is wise. If mary is not humble then someone is not brave. If someone is funny then someone is curious or calm and vice versa. Everyone who is calm is both curious and rich and vice versa. If someone is both not old and rich then someone is either brave or old. If someone is both brave and not funny then someone is either generous or not kind and vice versa. If someone is both quiet and not generous then lucy is not curious or not old. If john is either humble or not tall then susan is funny or not rich and vice versa. Everyone who is both funny and not funny is curious or funny. If susan is not funny or not humble then someone is either not patient or patient. If someone is patient or funny then lucy is not curious. John is either not creative or kind. Someone is not creative. Someone is either not creative or creative. Lucy is either not strong or not quiet. Susan is not patient or not rich. Someone is wise or not curious. Lucy is strong or not curious. | Susan is not curious. | entailment | ((?[X]:((humble(X)<~>~wise(X))))<=>((wise(paul)&~wise(paul))))&
(((kind(lucy)&old(lucy)))<=>(~strong(paul)))&
(![X]:((calm(X)<~>wise(X))<=>calm(X)))&
(![X]:((happy(X)|funny(X))=>wise(X)))&
((~humble(mary))=>(?[X]:(~brave(X))))&
((?[X]:(funny(X)))<=>(?[X]:((curious(X)|calm(X)))))&
(![X]:(calm(X)<=>(curious(X)&rich(X))))&
((?[X]:((~old(X)&rich(X))))=>(?[X]:((brave(X)<~>old(X)))))&
((?[X]:((brave(X)&~funny(X))))<=>(?[X]:((generous(X)<~>~kind(X)))))&
((?[X]:((quiet(X)&~generous(X))))=>((~curious(lucy)|~old(lucy))))&
(((humble(john)<~>~tall(john)))<=>((funny(susan)|~rich(susan))))&
(![X]:((funny(X)&~funny(X))=>(curious(X)|funny(X))))&
(((~funny(susan)|~humble(susan)))=>(?[X]:((~patient(X)<~>patient(X)))))&
((?[X]:((patient(X)|funny(X))))=>(~curious(lucy)))&
((~creative(john)<~>kind(john)))&
(?[X]:(~creative(X)))&
(?[X]:((~creative(X)<~>creative(X))))&
((~strong(lucy)<~>~quiet(lucy)))&
((~patient(susan)|~rich(susan)))&
(?[X]:((wise(X)|~curious(X))))&
((strong(lucy)|~curious(lucy))) | ~curious(susan) | [
"p2",
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 8156343827296474251237823
% SZS output start Proof for 8156343827296474251237823
3. ! [X0] : ((calm(X0) <~> wise(X0)) <=> calm(X0)) [input p2]
4. ! [X0] : ((funny(X0) | happy(X0)) => wise(X0)) [input p3]
6. ? [X0] : funny(X0) <=> ? [X0] : (calm(X0) | curious(X0)) [input p5]
22. curious(susan) [input hypothesis]
23. ? [X0] : funny(X0) <=> ? [X1] : (calm(X1) | curious(X1)) [rectify 6]
26. ! [X0] : (funny(X0) => wise(X0)) [pure predicate removal 4]
27. ! [X0] : (wise(X0) | ~funny(X0)) [ennf transformation 26]
43. ! [X0] : ((((~wise(X0) | ~calm(X0)) & (wise(X0) | calm(X0))) | ~calm(X0)) & (calm(X0) | ((calm(X0) | ~wise(X0)) & (wise(X0) | ~calm(X0))))) [nnf transformation 3]
46. (? [X0] : funny(X0) | ! [X1] : (~calm(X1) & ~curious(X1))) & (? [X1] : (calm(X1) | curious(X1)) | ! [X0] : ~funny(X0)) [nnf transformation 23]
47. (? [X0] : funny(X0) | ! [X1] : (~calm(X1) & ~curious(X1))) & (? [X2] : (calm(X2) | curious(X2)) | ! [X3] : ~funny(X3)) [rectify 46]
48. ? [X0] : funny(X0) => funny(sK2) [choice axiom]
49. ? [X2] : (calm(X2) | curious(X2)) => (calm(sK3) | curious(sK3)) [choice axiom]
50. (funny(sK2) | ! [X1] : (~calm(X1) & ~curious(X1))) & ((calm(sK3) | curious(sK3)) | ! [X3] : ~funny(X3)) [skolemisation 47,49,48]
86. calm(X0) | calm(X0) | ~wise(X0) [cnf transformation 43]
88. ~wise(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 43]
89. wise(X0) | ~funny(X0) [cnf transformation 27]
92. funny(sK2) | ~curious(X1) [cnf transformation 50]
129. curious(susan) [cnf transformation 22]
131. calm(X0) | ~wise(X0) [duplicate literal removal 86]
132. ~wise(X0) | ~calm(X0) [duplicate literal removal 88]
162. ~wise(X0) [subsumption resolution 131,132]
163. ~funny(X0) [subsumption resolution 89,162]
174. ~curious(X1) [subsumption resolution 92,163]
258. $false [subsumption resolution 129,174]
% SZS output end Proof for 8156343827296474251237823
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not happy or not calm then fred is not brave.
If lucy is both patient and not patient then alice is either calm or strong.
Everyone who is kind or creative is both generous and not tall and vice versa.
Everyone who is either not generous or happy is quiet or not brave.
Everyone who is not rich is both strong and not rich and vice versa.
If someone is both happy and patient then someone is humble.
If susan is not humble then someone is rich and vice versa.
Everyone who is both not generous and not creative is either not strong or quiet and vice versa.
Everyone who is not brave is both not rich and not humble and vice versa.
Everyone who is patient or not wise is not tall.
Everyone who is rich or not strong is brave or not creative and vice versa.
Everyone who is either not generous or not funny is not curious or not tall and vice versa.
If someone is rich then mary is not creative or happy.
Everyone who is either not wise or rich is not old and vice versa.
Everyone who is quiet or not tall is old or strong and vice versa.
If someone is not tall or rich then susan is either not rich or wise.
Someone is wise or not curious.
Lucy is both not kind and not calm.
Someone is either strong or not tall.
Lucy is either quiet or not rich.
Someone is either not creative or not kind.
Someone is tall.
Mary is both not patient and happy.
Lucy is both not brave and not quiet. | Lucy is not tall. | entailment | (((~happy(susan)<~>~calm(susan)))=>(~brave(fred)))&
(((patient(lucy)&~patient(lucy)))=>((calm(alice)<~>strong(alice))))&
(![X]:((kind(X)|creative(X))<=>(generous(X)&~tall(X))))&
(![X]:((~generous(X)<~>happy(X))=>(quiet(X)|~brave(X))))&
(![X]:(~rich(X)<=>(strong(X)&~rich(X))))&
((?[X]:((happy(X)&patient(X))))=>(?[X]:(humble(X))))&
((~humble(susan))<=>(?[X]:(rich(X))))&
(![X]:((~generous(X)&~creative(X))<=>(~strong(X)<~>quiet(X))))&
(![X]:(~brave(X)<=>(~rich(X)&~humble(X))))&
(![X]:((patient(X)|~wise(X))=>~tall(X)))&
(![X]:((rich(X)|~strong(X))<=>(brave(X)|~creative(X))))&
(![X]:((~generous(X)<~>~funny(X))<=>(~curious(X)|~tall(X))))&
((?[X]:(rich(X)))=>((~creative(mary)|happy(mary))))&
(![X]:((~wise(X)<~>rich(X))<=>~old(X)))&
(![X]:((quiet(X)|~tall(X))<=>(old(X)|strong(X))))&
((?[X]:((~tall(X)|rich(X))))=>((~rich(susan)<~>wise(susan))))&
(?[X]:((wise(X)|~curious(X))))&
((~kind(lucy)&~calm(lucy)))&
(?[X]:((strong(X)<~>~tall(X))))&
((quiet(lucy)<~>~rich(lucy)))&
(?[X]:((~creative(X)<~>~kind(X))))&
(?[X]:(tall(X)))&
((~patient(mary)&happy(mary)))&
((~brave(lucy)&~quiet(lucy))) | ~tall(lucy) | [
"p2",
"p4",
"p10",
"p19",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8850819574399570257757665
% SZS output start Proof for 8850819574399570257757665
3. ! [X0] : ((creative(X0) | kind(X0)) <=> (~tall(X0) & generous(X0))) [input p2]
5. ! [X0] : (~rich(X0) <=> (~rich(X0) & strong(X0))) [input p4]
11. ! [X0] : ((~strong(X0) | rich(X0)) <=> (~creative(X0) | brave(X0))) [input p10]
20. quiet(lucy) <~> ~rich(lucy) [input p19]
24. ~quiet(lucy) & ~brave(lucy) [input p23]
25. tall(lucy) [input hypothesis]
39. ! [X0] : (((creative(X0) | kind(X0)) | (tall(X0) | ~generous(X0))) & ((~tall(X0) & generous(X0)) | (~creative(X0) & ~kind(X0)))) [nnf transformation 3]
40. ! [X0] : ((creative(X0) | kind(X0) | tall(X0) | ~generous(X0)) & ((~tall(X0) & generous(X0)) | (~creative(X0) & ~kind(X0)))) [flattening 39]
42. ! [X0] : ((~rich(X0) | (rich(X0) | ~strong(X0))) & ((~rich(X0) & strong(X0)) | rich(X0))) [nnf transformation 5]
43. ! [X0] : ((~rich(X0) | rich(X0) | ~strong(X0)) & ((~rich(X0) & strong(X0)) | rich(X0))) [flattening 42]
55. ! [X0] : (((~strong(X0) | rich(X0)) | (creative(X0) & ~brave(X0))) & ((~creative(X0) | brave(X0)) | (strong(X0) & ~rich(X0)))) [nnf transformation 11]
56. ! [X0] : ((~strong(X0) | rich(X0) | (creative(X0) & ~brave(X0))) & (~creative(X0) | brave(X0) | (strong(X0) & ~rich(X0)))) [flattening 55]
68. (rich(lucy) | ~quiet(lucy)) & (~rich(lucy) | quiet(lucy)) [nnf transformation 20]
81. ~tall(X0) | ~creative(X0) [cnf transformation 40]
85. rich(X0) | strong(X0) [cnf transformation 43]
105. ~strong(X0) | rich(X0) | creative(X0) [cnf transformation 56]
130. ~rich(lucy) | quiet(lucy) [cnf transformation 68]
138. ~quiet(lucy) [cnf transformation 24]
139. tall(lucy) [cnf transformation 25]
177. rich(X0) | creative(X0) [subsumption resolution 105,85]
223. 18 <=> quiet(lucy) [avatar definition]
227. 19 <=> rich(lucy) [avatar definition]
228. ~rich(lucy) <- (~19) [avatar component clause 227]
231. 18 | ~19 [avatar split clause 130,227,223]
243. ~18 [avatar split clause 138,223]
248. ~creative(lucy) [resolution 81,139]
263. creative(lucy) <- (~19) [resolution 177,228]
264. $false <- (~19) [subsumption resolution 263,248]
265. 19 [avatar contradiction clause 264]
266. $false [avatar sat refutation 231,243,265]
% SZS output end Proof for 8850819574399570257757665
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or not generous is not quiet. If someone is generous then mary is not curious. Everyone who is either not calm or rich is both not calm and not funny. Everyone who is not calm is either not wise or not rich. If someone is tall then paul is not funny or creative and vice versa. Everyone who is not funny is either brave or rich. If someone is humble or not humble then alice is both rich and funny. Everyone who is both not generous and humble is not rich or not happy. Everyone who is either not strong or curious is brave or not brave and vice versa. Everyone who is patient is not old or not strong. If someone is either quiet or not curious then someone is not wise and vice versa. Everyone who is strong or old is not patient or rich. If fred is both not creative and not patient then someone is not humble and vice versa. Everyone who is brave is not humble or happy. If someone is strong or not calm then susan is not tall or patient. If someone is happy or not creative then lucy is both calm and strong and vice versa. Alice is not quiet or tall. Someone is either quiet or not tall. Mary is either happy or not happy. Paul is either not generous or not strong. Someone is wise. Susan is either curious or happy. Someone is funny. John is brave. | Paul is not funny. | neutral | (![X]:((~rich(X)<~>~generous(X))=>~quiet(X)))&
((?[X]:(generous(X)))=>(~curious(mary)))&
(![X]:((~calm(X)<~>rich(X))=>(~calm(X)&~funny(X))))&
(![X]:(~calm(X)=>(~wise(X)<~>~rich(X))))&
((?[X]:(tall(X)))<=>((~funny(paul)|creative(paul))))&
(![X]:(~funny(X)=>(brave(X)<~>rich(X))))&
((?[X]:((humble(X)|~humble(X))))=>((rich(alice)&funny(alice))))&
(![X]:((~generous(X)&humble(X))=>(~rich(X)|~happy(X))))&
(![X]:((~strong(X)<~>curious(X))<=>(brave(X)|~brave(X))))&
(![X]:(patient(X)=>(~old(X)|~strong(X))))&
((?[X]:((quiet(X)<~>~curious(X))))<=>(?[X]:(~wise(X))))&
(![X]:((strong(X)|old(X))=>(~patient(X)|rich(X))))&
(((~creative(fred)&~patient(fred)))<=>(?[X]:(~humble(X))))&
(![X]:(brave(X)=>(~humble(X)|happy(X))))&
((?[X]:((strong(X)|~calm(X))))=>((~tall(susan)|patient(susan))))&
((?[X]:((happy(X)|~creative(X))))<=>((calm(lucy)&strong(lucy))))&
((~quiet(alice)|tall(alice)))&
(?[X]:((quiet(X)<~>~tall(X))))&
((happy(mary)<~>~happy(mary)))&
((~generous(paul)<~>~strong(paul)))&
(?[X]:(wise(X)))&
((curious(susan)<~>happy(susan)))&
(?[X]:(funny(X)))&
(brave(john)) | ~funny(paul) | [] | null | 0 |
If someone is old or wise then alice is calm. Everyone who is either not kind or not happy is either not quiet or old and vice versa. If someone is not old then susan is not funny. If mary is patient then someone is not calm and vice versa. If john is either not happy or rich then someone is old or not strong and vice versa. Everyone who is not quiet or not happy is both not funny and rich and vice versa. Everyone who is either not quiet or calm is both kind and not brave and vice versa. Everyone who is either old or not strong is both patient and not happy and vice versa. Everyone who is both not curious and rich is not strong. Everyone who is both not calm and not quiet is both calm and not creative. Everyone who is both not calm and curious is not funny or not quiet and vice versa. If someone is not creative or strong then fred is quiet or humble. If mary is either humble or happy then someone is not happy or humble and vice versa. Everyone who is either quiet or tall is either not tall or brave and vice versa. Everyone who is quiet or not rich is both quiet and not wise. Someone is kind or funny. Someone is rich or not kind. Someone is either strong or not tall. Someone is either generous or not quiet. Susan is not rich or old. Mary is not kind or not tall. | Susan is kind. | contradiction | ((?[X]:((old(X)|wise(X))))=>(calm(alice)))&
(![X]:((~kind(X)<~>~happy(X))<=>(~quiet(X)<~>old(X))))&
((?[X]:(~old(X)))=>(~funny(susan)))&
((patient(mary))<=>(?[X]:(~calm(X))))&
(((~happy(john)<~>rich(john)))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((~quiet(X)|~happy(X))<=>(~funny(X)&rich(X))))&
(![X]:((~quiet(X)<~>calm(X))<=>(kind(X)&~brave(X))))&
(![X]:((old(X)<~>~strong(X))<=>(patient(X)&~happy(X))))&
(![X]:((~curious(X)&rich(X))=>~strong(X)))&
(![X]:((~calm(X)&~quiet(X))=>(calm(X)&~creative(X))))&
(![X]:((~calm(X)&curious(X))<=>(~funny(X)|~quiet(X))))&
((?[X]:((~creative(X)|strong(X))))=>((quiet(fred)|humble(fred))))&
(((humble(mary)<~>happy(mary)))<=>(?[X]:((~happy(X)|humble(X)))))&
(![X]:((quiet(X)<~>tall(X))<=>(~tall(X)<~>brave(X))))&
(![X]:((quiet(X)|~rich(X))=>(quiet(X)&~wise(X))))&
(?[X]:((kind(X)|funny(X))))&
(?[X]:((rich(X)|~kind(X))))&
(?[X]:((strong(X)<~>~tall(X))))&
(?[X]:((generous(X)<~>~quiet(X))))&
((~rich(susan)|old(susan)))&
((~kind(mary)|~tall(mary))) | kind(susan) | [
"p0",
"p1",
"p2",
"p5",
"p6",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1208553261166562904835975
% SZS output start Proof for 1208553261166562904835975
1. ? [X0] : (wise(X0) | old(X0)) => calm(alice) [input p0]
2. ! [X0] : ((~kind(X0) <~> ~happy(X0)) <=> (~quiet(X0) <~> old(X0))) [input p1]
3. ? [X0] : ~old(X0) => ~funny(susan) [input p2]
6. ! [X0] : ((~happy(X0) | ~quiet(X0)) <=> (rich(X0) & ~funny(X0))) [input p5]
7. ! [X0] : ((~quiet(X0) <~> calm(X0)) <=> (~brave(X0) & kind(X0))) [input p6]
10. ! [X0] : ((~quiet(X0) & ~calm(X0)) => (~creative(X0) & calm(X0))) [input p9]
11. ! [X0] : ((curious(X0) & ~calm(X0)) <=> (~quiet(X0) | ~funny(X0))) [input p10]
14. ! [X0] : ((quiet(X0) <~> tall(X0)) <=> (~tall(X0) <~> brave(X0))) [input p13]
22. kind(susan) [input hypothesis]
23. ? [X0] : old(X0) => calm(alice) [pure predicate removal 1]
25. calm(alice) | ! [X0] : ~old(X0) [ennf transformation 23]
26. ~funny(susan) | ! [X0] : old(X0) [ennf transformation 3]
29. ! [X0] : ((~creative(X0) & calm(X0)) | (quiet(X0) | calm(X0))) [ennf transformation 10]
30. ! [X0] : ((~creative(X0) & calm(X0)) | quiet(X0) | calm(X0)) [flattening 29]
34. ! [X0] : ((((happy(X0) | kind(X0)) & (~happy(X0) | ~kind(X0))) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | ((~kind(X0) | happy(X0)) & (~happy(X0) | kind(X0))))) [nnf transformation 2]
43. ! [X0] : (((~happy(X0) | ~quiet(X0)) | (~rich(X0) | funny(X0))) & ((rich(X0) & ~funny(X0)) | (happy(X0) & quiet(X0)))) [nnf transformation 6]
44. ! [X0] : ((~happy(X0) | ~quiet(X0) | ~rich(X0) | funny(X0)) & ((rich(X0) & ~funny(X0)) | (happy(X0) & quiet(X0)))) [flattening 43]
45. ! [X0] : ((((~calm(X0) | quiet(X0)) & (calm(X0) | ~quiet(X0))) | (brave(X0) | ~kind(X0))) & ((~brave(X0) & kind(X0)) | ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0))))) [nnf transformation 7]
46. ! [X0] : ((((~calm(X0) | quiet(X0)) & (calm(X0) | ~quiet(X0))) | brave(X0) | ~kind(X0)) & ((~brave(X0) & kind(X0)) | ((~quiet(X0) | ~calm(X0)) & (calm(X0) | quiet(X0))))) [flattening 45]
49. ! [X0] : (((curious(X0) & ~calm(X0)) | (quiet(X0) & funny(X0))) & ((~quiet(X0) | ~funny(X0)) | (~curious(X0) | calm(X0)))) [nnf transformation 11]
50. ! [X0] : (((curious(X0) & ~calm(X0)) | (quiet(X0) & funny(X0))) & (~quiet(X0) | ~funny(X0) | ~curious(X0) | calm(X0))) [flattening 49]
55. ! [X0] : ((((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | ((~tall(X0) | ~brave(X0)) & (brave(X0) | tall(X0)))) & (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0))))) [nnf transformation 14]
66. calm(alice) | ~old(X0) [cnf transformation 25]
72. ~quiet(X0) | ~kind(X0) | ~happy(X0) | ~old(X0) [cnf transformation 34]
75. ~funny(susan) | old(X0) [cnf transformation 26]
85. ~funny(X0) | happy(X0) [cnf transformation 44]
90. ~quiet(X0) | kind(X0) | ~calm(X0) [cnf transformation 46]
93. ~quiet(X0) | calm(X0) | brave(X0) | ~kind(X0) [cnf transformation 46]
102. calm(X0) | quiet(X0) | calm(X0) [cnf transformation 30]
105. ~calm(X0) | funny(X0) [cnf transformation 50]
106. ~calm(X0) | quiet(X0) [cnf transformation 50]
119. ~brave(X0) | tall(X0) | tall(X0) | ~quiet(X0) [cnf transformation 55]
124. ~tall(X0) | ~quiet(X0) | ~tall(X0) | ~brave(X0) [cnf transformation 55]
135. kind(susan) [cnf transformation 22]
137. ~brave(X0) | tall(X0) | ~quiet(X0) [duplicate literal removal 119]
139. ~tall(X0) | ~quiet(X0) | ~brave(X0) [duplicate literal removal 124]
140. quiet(X0) | calm(X0) [duplicate literal removal 102]
142. 1 <=> ! [X0] : ~old(X0) [avatar definition]
143. ~old(X0) <- (1) [avatar component clause 142]
145. 2 <=> calm(alice) [avatar definition]
147. calm(alice) <- (2) [avatar component clause 145]
148. 1 | 2 [avatar split clause 66,145,142]
150. 3 <=> ! [X0] : old(X0) [avatar definition]
151. old(X0) <- (3) [avatar component clause 150]
153. 4 <=> funny(susan) [avatar definition]
156. 3 | ~4 [avatar split clause 75,153,150]
195. quiet(X0) [subsumption resolution 106,140]
225. ~tall(X0) | ~brave(X0) [subsumption resolution 139,195]
226. ~brave(X0) | tall(X0) [subsumption resolution 137,195]
227. ~brave(X0) [subsumption resolution 226,225]
283. funny(alice) <- (2) [resolution 105,147]
284. happy(alice) <- (2) [resolution 283,85]
288. ~calm(X2) | kind(X2) [resolution 90,195]
290. kind(alice) <- (2) [resolution 288,147]
405. ~happy(X2) | ~kind(X2) | ~old(X2) [resolution 72,195]
458. calm(X2) | brave(X2) | ~kind(X2) | calm(X2) [resolution 93,140]
460. calm(X2) | brave(X2) | ~kind(X2) [duplicate literal removal 458]
462. ~kind(X2) | calm(X2) [subsumption resolution 460,227]
472. calm(susan) [resolution 462,135]
493. funny(susan) [resolution 472,105]
496. 4 [avatar split clause 493,153]
527. ~kind(alice) | ~old(alice) <- (2) [resolution 405,284]
532. ~old(alice) <- (2) [subsumption resolution 527,290]
533. $false <- (2, 3) [subsumption resolution 532,151]
534. ~2 | ~3 [avatar contradiction clause 533]
552. $false <- (1, 3) [subsumption resolution 143,151]
553. ~1 | ~3 [avatar contradiction clause 552]
554. $false [avatar sat refutation 148,156,496,534,553]
% SZS output end Proof for 1208553261166562904835975
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either patient or rich then someone is not happy or not creative.
Everyone who is both calm and not happy is both not funny and happy and vice versa.
If paul is both not creative and patient then someone is not brave.
If fred is not calm or not tall then susan is not old or not brave and vice versa.
Everyone who is either not calm or not funny is not generous or funny.
Everyone who is not curious or old is tall and vice versa.
Everyone who is either kind or not humble is either kind or not creative.
Everyone who is both not brave and generous is brave or generous and vice versa.
If someone is both not brave and not happy then lucy is patient and vice versa.
If mary is not humble then mary is not tall or not happy and vice versa.
If someone is both calm and generous then mary is not calm.
If someone is either calm or not strong then lucy is both rich and calm and vice versa.
If someone is either not calm or not generous then john is not brave.
Everyone who is not kind is both calm and not funny.
If someone is happy then someone is both creative and tall.
Someone is not brave or quiet.
Someone is both curious and not creative.
Someone is not humble.
Someone is funny or not curious.
Someone is either not funny or not brave.
Someone is both wise and not creative.
Someone is both not old and not patient. | Fred is not brave. | entailment | (((patient(lucy)<~>rich(lucy)))=>(?[X]:((~happy(X)|~creative(X)))))&
(![X]:((calm(X)&~happy(X))<=>(~funny(X)&happy(X))))&
(((~creative(paul)&patient(paul)))=>(?[X]:(~brave(X))))&
(((~calm(fred)|~tall(fred)))<=>((~old(susan)|~brave(susan))))&
(![X]:((~calm(X)<~>~funny(X))=>(~generous(X)|funny(X))))&
(![X]:((~curious(X)|old(X))<=>tall(X)))&
(![X]:((kind(X)<~>~humble(X))=>(kind(X)<~>~creative(X))))&
(![X]:((~brave(X)&generous(X))<=>(brave(X)|generous(X))))&
((?[X]:((~brave(X)&~happy(X))))<=>(patient(lucy)))&
((~humble(mary))<=>((~tall(mary)|~happy(mary))))&
((?[X]:((calm(X)&generous(X))))=>(~calm(mary)))&
((?[X]:((calm(X)<~>~strong(X))))<=>((rich(lucy)&calm(lucy))))&
((?[X]:((~calm(X)<~>~generous(X))))=>(~brave(john)))&
(![X]:(~kind(X)=>(calm(X)&~funny(X))))&
((?[X]:(happy(X)))=>(?[X]:((creative(X)&tall(X)))))&
(?[X]:((~brave(X)|quiet(X))))&
(?[X]:((curious(X)&~creative(X))))&
(?[X]:(~humble(X)))&
(?[X]:((funny(X)|~curious(X))))&
(?[X]:((~funny(X)<~>~brave(X))))&
(?[X]:((wise(X)&~creative(X))))&
(?[X]:((~old(X)&~patient(X)))) | ~brave(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1946512045165075663543771
% SZS output start Proof for 1946512045165075663543771
8. ! [X0] : ((generous(X0) & ~brave(X0)) <=> (generous(X0) | brave(X0))) [input p7]
23. brave(fred) [input hypothesis]
50. ! [X0] : (((generous(X0) & ~brave(X0)) | (~generous(X0) & ~brave(X0))) & ((generous(X0) | brave(X0)) | (~generous(X0) | brave(X0)))) [nnf transformation 8]
51. ! [X0] : (((generous(X0) & ~brave(X0)) | (~generous(X0) & ~brave(X0))) & (generous(X0) | brave(X0) | ~generous(X0) | brave(X0))) [flattening 50]
102. ~brave(X0) | ~generous(X0) [cnf transformation 51]
103. generous(X0) | ~brave(X0) [cnf transformation 51]
133. brave(fred) [cnf transformation 23]
192. ~brave(X0) [subsumption resolution 102,103]
273. $false [subsumption resolution 133,192]
% SZS output end Proof for 1946512045165075663543771
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or curious is kind.
Everyone who is not humble or curious is generous.
Everyone who is not quiet is not strong and vice versa.
Everyone who is not happy is both not kind and not calm and vice versa.
If john is not curious or not humble then someone is both calm and not quiet.
Everyone who is not calm or funny is not funny and vice versa.
If paul is not creative or funny then someone is not calm or not happy.
Everyone who is not calm or old is either not patient or tall.
Everyone who is patient or not tall is patient or funny.
If someone is either curious or not funny then susan is either not quiet or not old and vice versa.
If someone is strong then someone is not funny and vice versa.
If someone is either not happy or creative then susan is not wise or generous and vice versa.
If someone is both tall and not curious then someone is not tall and vice versa.
Everyone who is either creative or not tall is humble or not creative.
If paul is not generous then someone is not old.
Everyone who is both creative and not quiet is either not old or creative and vice versa.
Paul is strong.
Mary is either strong or not quiet.
Susan is calm or not brave.
Mary is either calm or not quiet.
Lucy is either wise or creative. | Susan is curious. | entailment | (![X]:((~wise(X)|curious(X))=>kind(X)))&
(![X]:((~humble(X)|curious(X))=>generous(X)))&
(![X]:(~quiet(X)<=>~strong(X)))&
(![X]:(~happy(X)<=>(~kind(X)&~calm(X))))&
(((~curious(john)|~humble(john)))=>(?[X]:((calm(X)&~quiet(X)))))&
(![X]:((~calm(X)|funny(X))<=>~funny(X)))&
(((~creative(paul)|funny(paul)))=>(?[X]:((~calm(X)|~happy(X)))))&
(![X]:((~calm(X)|old(X))=>(~patient(X)<~>tall(X))))&
(![X]:((patient(X)|~tall(X))=>(patient(X)|funny(X))))&
((?[X]:((curious(X)<~>~funny(X))))<=>((~quiet(susan)<~>~old(susan))))&
((?[X]:(strong(X)))<=>(?[X]:(~funny(X))))&
((?[X]:((~happy(X)<~>creative(X))))<=>((~wise(susan)|generous(susan))))&
((?[X]:((tall(X)&~curious(X))))<=>(?[X]:(~tall(X))))&
(![X]:((creative(X)<~>~tall(X))=>(humble(X)|~creative(X))))&
((~generous(paul))=>(?[X]:(~old(X))))&
(![X]:((creative(X)&~quiet(X))<=>(~old(X)<~>creative(X))))&
(strong(paul))&
((strong(mary)<~>~quiet(mary)))&
((calm(susan)|~brave(susan)))&
((calm(mary)<~>~quiet(mary)))&
((wise(lucy)<~>creative(lucy))) | curious(susan) | [
"p5",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4102543481180468852673012
% SZS output start Proof for 4102543481180468852673012
6. ! [X0] : ((funny(X0) | ~calm(X0)) <=> ~funny(X0)) [input p5]
8. ! [X0] : ((old(X0) | ~calm(X0)) => (~patient(X0) <~> tall(X0))) [input p7]
9. ! [X0] : ((~tall(X0) | patient(X0)) => (funny(X0) | patient(X0))) [input p8]
13. ? [X0] : (~curious(X0) & tall(X0)) <=> ? [X0] : ~tall(X0) [input p12]
22. ~curious(susan) [input hypothesis]
24. ? [X0] : (~curious(X0) & tall(X0)) <=> ? [X1] : ~tall(X1) [rectify 13]
33. ! [X0] : ((~patient(X0) <~> tall(X0)) | (~old(X0) & calm(X0))) [ennf transformation 8]
34. ! [X0] : ((funny(X0) | patient(X0)) | (tall(X0) & ~patient(X0))) [ennf transformation 9]
35. ! [X0] : (funny(X0) | patient(X0) | (tall(X0) & ~patient(X0))) [flattening 34]
42. ! [X0] : (((funny(X0) | ~calm(X0)) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [nnf transformation 6]
43. ! [X0] : ((funny(X0) | ~calm(X0) | funny(X0)) & (~funny(X0) | (~funny(X0) & calm(X0)))) [flattening 42]
46. ! [X0] : (((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | (~old(X0) & calm(X0))) [nnf transformation 33]
61. (? [X0] : (~curious(X0) & tall(X0)) | ! [X1] : tall(X1)) & (? [X1] : ~tall(X1) | ! [X0] : (curious(X0) | ~tall(X0))) [nnf transformation 24]
62. (? [X0] : (~curious(X0) & tall(X0)) | ! [X1] : tall(X1)) & (? [X2] : ~tall(X2) | ! [X3] : (curious(X3) | ~tall(X3))) [rectify 61]
63. ? [X0] : (~curious(X0) & tall(X0)) => (~curious(sK6) & tall(sK6)) [choice axiom]
64. ? [X2] : ~tall(X2) => ~tall(sK7) [choice axiom]
65. ((~curious(sK6) & tall(sK6)) | ! [X1] : tall(X1)) & (~tall(sK7) | ! [X3] : (curious(X3) | ~tall(X3))) [skolemisation 62,64,63]
84. ~funny(X0) | ~funny(X0) [cnf transformation 43]
85. funny(X0) | ~calm(X0) | funny(X0) [cnf transformation 43]
88. ~patient(X0) | tall(X0) | calm(X0) [cnf transformation 46]
93. funny(X0) | patient(X0) | tall(X0) [cnf transformation 35]
110. ~tall(sK7) | curious(X3) | ~tall(X3) [cnf transformation 65]
111. tall(sK6) | tall(X1) [cnf transformation 65]
112. ~curious(sK6) | tall(X1) [cnf transformation 65]
127. ~curious(susan) [cnf transformation 22]
130. ~funny(X0) [duplicate literal removal 84]
131. ~calm(X0) | funny(X0) [duplicate literal removal 85]
156. tall(X0) | patient(X0) [subsumption resolution 93,130]
175. 9 <=> ! [X1] : curious(X1) [avatar definition]
176. curious(X1) <- (9) [avatar component clause 175]
210. 16 <=> ! [X1] : tall(X1) [avatar definition]
211. tall(X1) <- (16) [avatar component clause 210]
213. 17 <=> curious(sK6) [avatar definition]
215. ~curious(sK6) <- (~17) [avatar component clause 213]
216. 16 | ~17 [avatar split clause 112,213,210]
218. 18 <=> tall(sK6) [avatar definition]
220. tall(sK6) <- (18) [avatar component clause 218]
221. 16 | 18 [avatar split clause 111,218,210]
223. 19 <=> ! [X3] : (curious(X3) | ~tall(X3)) [avatar definition]
224. ~tall(X3) | curious(X3) <- (19) [avatar component clause 223]
226. 20 <=> tall(sK7) [avatar definition]
228. ~tall(sK7) <- (~20) [avatar component clause 226]
229. 19 | ~20 [avatar split clause 110,226,223]
301. curious(X0) <- (16, 19) [resolution 224,211]
304. 9 | ~16 | ~19 [avatar split clause 301,223,210,175]
307. $false <- (9) [resolution 176,127]
312. ~9 [avatar contradiction clause 307]
313. curious(sK6) <- (18, 19) [resolution 220,224]
315. $false <- (~17, 18, 19) [subsumption resolution 313,215]
316. 17 | ~18 | ~19 [avatar contradiction clause 315]
317. patient(sK7) <- (~20) [resolution 228,156]
334. tall(sK7) | calm(sK7) <- (~20) [resolution 317,88]
336. calm(sK7) <- (~20) [subsumption resolution 334,228]
345. funny(sK7) <- (~20) [resolution 336,131]
347. $false <- (~20) [subsumption resolution 345,130]
348. 20 [avatar contradiction clause 347]
349. $false [avatar sat refutation 216,221,229,304,312,316,348]
% SZS output end Proof for 4102543481180468852673012
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or rich is both not happy and tall.
Everyone who is either old or brave is not tall or not calm and vice versa.
If fred is either not strong or not curious then paul is either not brave or not old and vice versa.
Everyone who is both not humble and not patient is either rich or not strong.
If susan is not rich then fred is either generous or not calm and vice versa.
Everyone who is not humble or not brave is not calm.
Everyone who is either not brave or kind is not kind.
If paul is kind then alice is patient or wise and vice versa.
If lucy is not wise then john is not curious or not humble and vice versa.
Everyone who is not calm is either old or kind.
Everyone who is either not tall or not quiet is either not creative or not brave.
If someone is not old or quiet then lucy is not generous or humble and vice versa.
If lucy is calm or patient then paul is not brave.
If susan is both generous and humble then lucy is either not strong or not brave and vice versa.
If someone is either calm or strong then someone is not quiet or calm and vice versa.
Everyone who is either quiet or not brave is both not curious and not brave.
Fred is either not rich or wise.
Someone is not generous or curious.
Someone is either funny or not tall.
Someone is both rich and not wise.
Alice is not strong.
Someone is either not patient or tall.
Alice is not calm.
Someone is either not calm or not quiet. | John is not kind. | entailment | (![X]:((~rich(X)<~>rich(X))=>(~happy(X)&tall(X))))&
(![X]:((old(X)<~>brave(X))<=>(~tall(X)|~calm(X))))&
(((~strong(fred)<~>~curious(fred)))<=>((~brave(paul)<~>~old(paul))))&
(![X]:((~humble(X)&~patient(X))=>(rich(X)<~>~strong(X))))&
((~rich(susan))<=>((generous(fred)<~>~calm(fred))))&
(![X]:((~humble(X)|~brave(X))=>~calm(X)))&
(![X]:((~brave(X)<~>kind(X))=>~kind(X)))&
((kind(paul))<=>((patient(alice)|wise(alice))))&
((~wise(lucy))<=>((~curious(john)|~humble(john))))&
(![X]:(~calm(X)=>(old(X)<~>kind(X))))&
(![X]:((~tall(X)<~>~quiet(X))=>(~creative(X)<~>~brave(X))))&
((?[X]:((~old(X)|quiet(X))))<=>((~generous(lucy)|humble(lucy))))&
(((calm(lucy)|patient(lucy)))=>(~brave(paul)))&
(((generous(susan)&humble(susan)))<=>((~strong(lucy)<~>~brave(lucy))))&
((?[X]:((calm(X)<~>strong(X))))<=>(?[X]:((~quiet(X)|calm(X)))))&
(![X]:((quiet(X)<~>~brave(X))=>(~curious(X)&~brave(X))))&
((~rich(fred)<~>wise(fred)))&
(?[X]:((~generous(X)|curious(X))))&
(?[X]:((funny(X)<~>~tall(X))))&
(?[X]:((rich(X)&~wise(X))))&
(~strong(alice))&
(?[X]:((~patient(X)<~>tall(X))))&
(~calm(alice))&
(?[X]:((~calm(X)<~>~quiet(X)))) | ~kind(john) | [
"p0",
"p1",
"p5",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2352655126471309108916738
% SZS output start Proof for 2352655126471309108916738
1. ! [X0] : ((~rich(X0) <~> rich(X0)) => (tall(X0) & ~happy(X0))) [input p0]
2. ! [X0] : ((old(X0) <~> brave(X0)) <=> (~calm(X0) | ~tall(X0))) [input p1]
6. ! [X0] : ((~brave(X0) | ~humble(X0)) => ~calm(X0)) [input p5]
7. ! [X0] : ((~brave(X0) <~> kind(X0)) => ~kind(X0)) [input p6]
10. ! [X0] : (~calm(X0) => (old(X0) <~> kind(X0))) [input p9]
25. kind(john) [input hypothesis]
27. ! [X0] : ((~rich(X0) <~> rich(X0)) => tall(X0)) [pure predicate removal 1]
28. ! [X0] : (tall(X0) | (~rich(X0) <=> rich(X0))) [ennf transformation 27]
31. ! [X0] : (~calm(X0) | (brave(X0) & humble(X0))) [ennf transformation 6]
32. ! [X0] : (~kind(X0) | (~brave(X0) <=> kind(X0))) [ennf transformation 7]
33. ! [X0] : ((old(X0) <~> kind(X0)) | calm(X0)) [ennf transformation 10]
37. ! [X0] : (tall(X0) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0)))) [nnf transformation 28]
38. ! [X0] : ((((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | (calm(X0) & tall(X0))) & ((~calm(X0) | ~tall(X0)) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0))))) [nnf transformation 2]
39. ! [X0] : ((((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | (calm(X0) & tall(X0))) & (~calm(X0) | ~tall(X0) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0))))) [flattening 38]
43. ! [X0] : (~kind(X0) | ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0)))) [nnf transformation 32]
48. ! [X0] : (((~kind(X0) | ~old(X0)) & (kind(X0) | old(X0))) | calm(X0)) [nnf transformation 33]
77. tall(X0) | rich(X0) | rich(X0) [cnf transformation 37]
78. tall(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 37]
80. ~calm(X0) | ~tall(X0) | old(X0) | ~brave(X0) [cnf transformation 39]
82. calm(X0) | old(X0) | brave(X0) [cnf transformation 39]
100. ~calm(X0) | brave(X0) [cnf transformation 31]
102. ~kind(X0) | ~brave(X0) | ~kind(X0) [cnf transformation 43]
109. kind(X0) | old(X0) | calm(X0) [cnf transformation 48]
110. ~kind(X0) | ~old(X0) | calm(X0) [cnf transformation 48]
150. kind(john) [cnf transformation 25]
152. ~kind(X0) | ~brave(X0) [duplicate literal removal 102]
153. tall(X0) | rich(X0) [duplicate literal removal 77]
154. ~rich(X0) | tall(X0) [duplicate literal removal 78]
155. tall(X0) [subsumption resolution 153,154]
156. ~calm(X0) | old(X0) | ~brave(X0) [subsumption resolution 80,155]
253. 19 <=> ! [X1] : old(X1) [avatar definition]
254. old(X1) <- (19) [avatar component clause 253]
357. ~brave(john) [resolution 152,150]
361. old(X0) | brave(X0) | brave(X0) [resolution 82,100]
363. old(X0) | brave(X0) [duplicate literal removal 361]
391. old(X0) | calm(X0) | ~brave(X0) [resolution 109,152]
393. old(X0) | ~brave(X0) [subsumption resolution 391,156]
394. old(X0) [subsumption resolution 393,363]
395. 19 [avatar split clause 394,253]
403. ~old(john) | calm(john) [resolution 110,150]
406. calm(john) <- (19) [subsumption resolution 403,254]
421. brave(john) <- (19) [resolution 406,100]
426. $false <- (19) [subsumption resolution 421,357]
427. ~19 [avatar contradiction clause 426]
429. $false [avatar sat refutation 395,427]
% SZS output end Proof for 2352655126471309108916738
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and kind is either not calm or funny and vice versa.
Everyone who is not old is not generous or quiet and vice versa.
If someone is happy or creative then john is both rich and creative and vice versa.
Everyone who is both not patient and not strong is both not creative and strong.
If paul is either not funny or not creative then lucy is either humble or kind.
If alice is either wise or not funny then mary is either patient or creative.
If fred is either funny or brave then lucy is both not strong and strong.
Everyone who is both creative and rich is either quiet or calm and vice versa.
Everyone who is either brave or not humble is not rich.
Everyone who is both not rich and happy is either old or not quiet and vice versa.
Everyone who is either not generous or not calm is not quiet and vice versa.
Everyone who is either not old or wise is both humble and tall.
Everyone who is not brave or brave is both old and wise.
Everyone who is either not old or not funny is curious and vice versa.
If someone is both not old and not strong then someone is both funny and kind and vice versa.
Everyone who is not rich is not creative or patient and vice versa.
Lucy is generous.
Someone is not calm.
Someone is not brave or brave.
Alice is both not rich and not quiet.
Mary is generous.
Mary is either old or strong. | John is not quiet. | entailment | (![X]:((happy(X)&kind(X))<=>(~calm(X)<~>funny(X))))&
(![X]:(~old(X)<=>(~generous(X)|quiet(X))))&
((?[X]:((happy(X)|creative(X))))<=>((rich(john)&creative(john))))&
(![X]:((~patient(X)&~strong(X))=>(~creative(X)&strong(X))))&
(((~funny(paul)<~>~creative(paul)))=>((humble(lucy)<~>kind(lucy))))&
(((wise(alice)<~>~funny(alice)))=>((patient(mary)<~>creative(mary))))&
(((funny(fred)<~>brave(fred)))=>((~strong(lucy)&strong(lucy))))&
(![X]:((creative(X)&rich(X))<=>(quiet(X)<~>calm(X))))&
(![X]:((brave(X)<~>~humble(X))=>~rich(X)))&
(![X]:((~rich(X)&happy(X))<=>(old(X)<~>~quiet(X))))&
(![X]:((~generous(X)<~>~calm(X))<=>~quiet(X)))&
(![X]:((~old(X)<~>wise(X))=>(humble(X)&tall(X))))&
(![X]:((~brave(X)|brave(X))=>(old(X)&wise(X))))&
(![X]:((~old(X)<~>~funny(X))<=>curious(X)))&
((?[X]:((~old(X)&~strong(X))))<=>(?[X]:((funny(X)&kind(X)))))&
(![X]:(~rich(X)<=>(~creative(X)|patient(X))))&
(generous(lucy))&
(?[X]:(~calm(X)))&
(?[X]:((~brave(X)|brave(X))))&
((~rich(alice)&~quiet(alice)))&
(generous(mary))&
((old(mary)<~>strong(mary))) | ~quiet(john) | [
"p1",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 195274082981120003518341
% SZS output start Proof for 195274082981120003518341
2. ! [X0] : (~old(X0) <=> (quiet(X0) | ~generous(X0))) [input p1]
13. ! [X0] : ((brave(X0) | ~brave(X0)) => (wise(X0) & old(X0))) [input p12]
23. quiet(john) [input hypothesis]
33. ! [X0] : ((wise(X0) & old(X0)) | (~brave(X0) & brave(X0))) [ennf transformation 13]
36. ! [X0] : ((~old(X0) | (~quiet(X0) & generous(X0))) & ((quiet(X0) | ~generous(X0)) | old(X0))) [nnf transformation 2]
37. ! [X0] : ((~old(X0) | (~quiet(X0) & generous(X0))) & (quiet(X0) | ~generous(X0) | old(X0))) [flattening 36]
73. ~quiet(X0) | ~old(X0) [cnf transformation 37]
113. old(X0) | brave(X0) [cnf transformation 33]
114. old(X0) | ~brave(X0) [cnf transformation 33]
132. quiet(john) [cnf transformation 23]
220. old(X0) [subsumption resolution 113,114]
235. ~old(john) [resolution 73,132]
236. $false [subsumption resolution 235,220]
% SZS output end Proof for 195274082981120003518341
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or calm is patient. Everyone who is humble or not humble is not patient or funny. If someone is patient or not strong then someone is generous and vice versa. Everyone who is curious is not humble or not generous. If lucy is not wise or curious then someone is both not strong and creative. If someone is either not patient or not humble then someone is not old. If someone is not wise then paul is both not happy and old and vice versa. If someone is either not creative or not funny then someone is quiet and vice versa. If alice is either not curious or tall then alice is quiet and vice versa. Everyone who is wise is either tall or not humble. Everyone who is both funny and tall is both not rich and wise and vice versa. Everyone who is not strong is either not generous or creative and vice versa. If someone is either quiet or not brave then susan is both not happy and creative and vice versa. If susan is quiet then someone is either kind or not funny. Everyone who is not humble is not kind or strong. If mary is either not tall or not calm then fred is funny and vice versa. Susan is strong. Paul is not calm or patient. John is creative. Someone is patient. Someone is both wise and happy. Fred is calm or not strong. Paul is either not strong or not calm. | Paul is old. | neutral | (![X]:((creative(X)|calm(X))=>patient(X)))&
(![X]:((humble(X)|~humble(X))=>(~patient(X)|funny(X))))&
((?[X]:((patient(X)|~strong(X))))<=>(?[X]:(generous(X))))&
(![X]:(curious(X)=>(~humble(X)|~generous(X))))&
(((~wise(lucy)|curious(lucy)))=>(?[X]:((~strong(X)&creative(X)))))&
((?[X]:((~patient(X)<~>~humble(X))))=>(?[X]:(~old(X))))&
((?[X]:(~wise(X)))<=>((~happy(paul)&old(paul))))&
((?[X]:((~creative(X)<~>~funny(X))))<=>(?[X]:(quiet(X))))&
(((~curious(alice)<~>tall(alice)))<=>(quiet(alice)))&
(![X]:(wise(X)=>(tall(X)<~>~humble(X))))&
(![X]:((funny(X)&tall(X))<=>(~rich(X)&wise(X))))&
(![X]:(~strong(X)<=>(~generous(X)<~>creative(X))))&
((?[X]:((quiet(X)<~>~brave(X))))<=>((~happy(susan)&creative(susan))))&
((quiet(susan))=>(?[X]:((kind(X)<~>~funny(X)))))&
(![X]:(~humble(X)=>(~kind(X)|strong(X))))&
(((~tall(mary)<~>~calm(mary)))<=>(funny(fred)))&
(strong(susan))&
((~calm(paul)|patient(paul)))&
(creative(john))&
(?[X]:(patient(X)))&
(?[X]:((wise(X)&happy(X))))&
((calm(fred)|~strong(fred)))&
((~strong(paul)<~>~calm(paul))) | old(paul) | [] | null | 0 |
If someone is either not brave or calm then someone is funny or strong and vice versa.
Everyone who is not kind is not happy and vice versa.
Everyone who is either not wise or not old is happy or kind.
Everyone who is creative is both not creative and not happy.
Everyone who is humble or not wise is not curious or strong and vice versa.
Everyone who is not kind or not tall is either not creative or not happy and vice versa.
Everyone who is not patient is either not curious or humble and vice versa.
Everyone who is both tall and not generous is either not brave or brave.
Everyone who is creative is not kind or not patient.
Everyone who is either not funny or creative is both not rich and wise and vice versa.
If someone is both not wise and not calm then someone is humble or not kind and vice versa.
Everyone who is either not brave or quiet is either tall or not happy.
Everyone who is either curious or tall is rich or not strong.
If alice is both rich and not patient then mary is both brave and strong.
Everyone who is either quiet or calm is not humble or not strong.
Everyone who is either not humble or calm is both happy and funny and vice versa.
Someone is not old.
Someone is creative or old.
Paul is not funny.
Someone is funny.
Someone is kind or brave.
Susan is not patient or not humble. | Susan is not strong. | neutral | ((?[X]:((~brave(X)<~>calm(X))))<=>(?[X]:((funny(X)|strong(X)))))&
(![X]:(~kind(X)<=>~happy(X)))&
(![X]:((~wise(X)<~>~old(X))=>(happy(X)|kind(X))))&
(![X]:(creative(X)=>(~creative(X)&~happy(X))))&
(![X]:((humble(X)|~wise(X))<=>(~curious(X)|strong(X))))&
(![X]:((~kind(X)|~tall(X))<=>(~creative(X)<~>~happy(X))))&
(![X]:(~patient(X)<=>(~curious(X)<~>humble(X))))&
(![X]:((tall(X)&~generous(X))=>(~brave(X)<~>brave(X))))&
(![X]:(creative(X)=>(~kind(X)|~patient(X))))&
(![X]:((~funny(X)<~>creative(X))<=>(~rich(X)&wise(X))))&
((?[X]:((~wise(X)&~calm(X))))<=>(?[X]:((humble(X)|~kind(X)))))&
(![X]:((~brave(X)<~>quiet(X))=>(tall(X)<~>~happy(X))))&
(![X]:((curious(X)<~>tall(X))=>(rich(X)|~strong(X))))&
(((rich(alice)&~patient(alice)))=>((brave(mary)&strong(mary))))&
(![X]:((quiet(X)<~>calm(X))=>(~humble(X)|~strong(X))))&
(![X]:((~humble(X)<~>calm(X))<=>(happy(X)&funny(X))))&
(?[X]:(~old(X)))&
(?[X]:((creative(X)|old(X))))&
(~funny(paul))&
(?[X]:(funny(X)))&
(?[X]:((kind(X)|brave(X))))&
((~patient(susan)|~humble(susan))) | ~strong(susan) | [] | null | 0 |
If mary is not brave then mary is not strong or generous and vice versa. Everyone who is both tall and brave is tall or not quiet. If alice is either generous or kind then susan is happy. Everyone who is either quiet or not curious is both calm and kind and vice versa. If someone is patient then fred is generous or funny. Everyone who is creative is not kind or generous and vice versa. Everyone who is rich is both tall and not old and vice versa. If someone is not wise or funny then someone is both humble and not generous. If someone is both not curious and not patient then fred is not generous. If paul is both kind and not strong then john is not patient. Everyone who is both not brave and not rich is humble or not humble and vice versa. Everyone who is not wise or not kind is kind and vice versa. If someone is not generous or rich then mary is not curious or not kind. Everyone who is quiet or not calm is either funny or humble. Susan is curious or not quiet. Someone is either not old or brave. Someone is kind. Someone is either not old or not calm. Susan is either rich or not funny. John is either not tall or not happy. Susan is generous or calm. | Paul is not strong. | neutral | ((~brave(mary))<=>((~strong(mary)|generous(mary))))&
(![X]:((tall(X)&brave(X))=>(tall(X)|~quiet(X))))&
(((generous(alice)<~>kind(alice)))=>(happy(susan)))&
(![X]:((quiet(X)<~>~curious(X))<=>(calm(X)&kind(X))))&
((?[X]:(patient(X)))=>((generous(fred)|funny(fred))))&
(![X]:(creative(X)<=>(~kind(X)|generous(X))))&
(![X]:(rich(X)<=>(tall(X)&~old(X))))&
((?[X]:((~wise(X)|funny(X))))=>(?[X]:((humble(X)&~generous(X)))))&
((?[X]:((~curious(X)&~patient(X))))=>(~generous(fred)))&
(((kind(paul)&~strong(paul)))=>(~patient(john)))&
(![X]:((~brave(X)&~rich(X))<=>(humble(X)|~humble(X))))&
(![X]:((~wise(X)|~kind(X))<=>kind(X)))&
((?[X]:((~generous(X)|rich(X))))=>((~curious(mary)|~kind(mary))))&
(![X]:((quiet(X)|~calm(X))=>(funny(X)<~>humble(X))))&
((curious(susan)|~quiet(susan)))&
(?[X]:((~old(X)<~>brave(X))))&
(?[X]:(kind(X)))&
(?[X]:((~old(X)<~>~calm(X))))&
((rich(susan)<~>~funny(susan)))&
((~tall(john)<~>~happy(john)))&
((generous(susan)|calm(susan))) | ~strong(paul) | [] | null | 0 |
Everyone who is both creative and not rich is either quiet or not funny and vice versa.
Everyone who is humble is not wise.
Everyone who is quiet or wise is wise and vice versa.
Everyone who is either quiet or old is not tall.
Everyone who is happy is old and vice versa.
Everyone who is both creative and tall is not generous and vice versa.
If someone is either curious or not kind then alice is not patient.
If someone is funny or not wise then someone is both funny and not curious and vice versa.
If john is both not strong and not creative then mary is calm or not creative.
If lucy is both not kind and not brave then fred is not rich or quiet.
If someone is wise then someone is not strong or not humble.
Everyone who is both brave and strong is either curious or tall and vice versa.
Everyone who is not rich or happy is not quiet.
If someone is both not generous and happy then someone is not strong.
Everyone who is not wise or brave is either quiet or not strong.
Everyone who is not happy is not strong and vice versa.
Someone is not creative or not calm.
Someone is not curious.
Mary is either generous or not creative.
Someone is not generous.
Someone is both brave and patient.
Alice is humble or not tall. | John is not generous. | neutral | (![X]:((creative(X)&~rich(X))<=>(quiet(X)<~>~funny(X))))&
(![X]:(humble(X)=>~wise(X)))&
(![X]:((quiet(X)|wise(X))<=>wise(X)))&
(![X]:((quiet(X)<~>old(X))=>~tall(X)))&
(![X]:(happy(X)<=>old(X)))&
(![X]:((creative(X)&tall(X))<=>~generous(X)))&
((?[X]:((curious(X)<~>~kind(X))))=>(~patient(alice)))&
((?[X]:((funny(X)|~wise(X))))<=>(?[X]:((funny(X)&~curious(X)))))&
(((~strong(john)&~creative(john)))=>((calm(mary)|~creative(mary))))&
(((~kind(lucy)&~brave(lucy)))=>((~rich(fred)|quiet(fred))))&
((?[X]:(wise(X)))=>(?[X]:((~strong(X)|~humble(X)))))&
(![X]:((brave(X)&strong(X))<=>(curious(X)<~>tall(X))))&
(![X]:((~rich(X)|happy(X))=>~quiet(X)))&
((?[X]:((~generous(X)&happy(X))))=>(?[X]:(~strong(X))))&
(![X]:((~wise(X)|brave(X))=>(quiet(X)<~>~strong(X))))&
(![X]:(~happy(X)<=>~strong(X)))&
(?[X]:((~creative(X)|~calm(X))))&
(?[X]:(~curious(X)))&
((generous(mary)<~>~creative(mary)))&
(?[X]:(~generous(X)))&
(?[X]:((brave(X)&patient(X))))&
((humble(alice)|~tall(alice))) | ~generous(john) | [] | null | 0 |
Everyone who is either wise or rich is not quiet or patient and vice versa.
Everyone who is both not generous and not patient is both humble and happy.
Everyone who is not tall or not brave is either not happy or not curious.
If someone is both old and humble then lucy is not creative and vice versa.
If paul is either creative or brave then john is not strong and vice versa.
Everyone who is both not curious and not generous is humble or rich and vice versa.
Everyone who is either not creative or not tall is not strong and vice versa.
If someone is both not happy and not creative then lucy is either patient or not quiet.
Everyone who is not kind or rich is both strong and generous.
If someone is not happy then mary is both kind and not kind.
If someone is not quiet or funny then paul is both not tall and not wise.
Everyone who is not kind is not calm or not kind and vice versa.
Everyone who is either humble or wise is not curious or creative.
Everyone who is not creative is either not calm or not wise and vice versa.
Everyone who is both strong and not funny is rich and vice versa.
If fred is tall then someone is brave and vice versa.
Someone is patient.
Someone is creative or strong.
Fred is not brave.
Mary is kind or quiet.
Someone is either not rich or creative.
Someone is both brave and not curious.
Paul is wise. | Paul is brave. | contradiction | (![X]:((wise(X)<~>rich(X))<=>(~quiet(X)|patient(X))))&
(![X]:((~generous(X)&~patient(X))=>(humble(X)&happy(X))))&
(![X]:((~tall(X)|~brave(X))=>(~happy(X)<~>~curious(X))))&
((?[X]:((old(X)&humble(X))))<=>(~creative(lucy)))&
(((creative(paul)<~>brave(paul)))<=>(~strong(john)))&
(![X]:((~curious(X)&~generous(X))<=>(humble(X)|rich(X))))&
(![X]:((~creative(X)<~>~tall(X))<=>~strong(X)))&
((?[X]:((~happy(X)&~creative(X))))=>((patient(lucy)<~>~quiet(lucy))))&
(![X]:((~kind(X)|rich(X))=>(strong(X)&generous(X))))&
((?[X]:(~happy(X)))=>((kind(mary)&~kind(mary))))&
((?[X]:((~quiet(X)|funny(X))))=>((~tall(paul)&~wise(paul))))&
(![X]:(~kind(X)<=>(~calm(X)|~kind(X))))&
(![X]:((humble(X)<~>wise(X))=>(~curious(X)|creative(X))))&
(![X]:(~creative(X)<=>(~calm(X)<~>~wise(X))))&
(![X]:((strong(X)&~funny(X))<=>rich(X)))&
((tall(fred))<=>(?[X]:(brave(X))))&
(?[X]:(patient(X)))&
(?[X]:((creative(X)|strong(X))))&
(~brave(fred))&
((kind(mary)|quiet(mary)))&
(?[X]:((~rich(X)<~>creative(X))))&
(?[X]:((brave(X)&~curious(X))))&
(wise(paul)) | brave(paul) | [
"p4",
"p5",
"p8",
"p10",
"p11",
"p13",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1089676358432147808784947
% SZS output start Proof for 1089676358432147808784947
5. (creative(paul) <~> brave(paul)) <=> ~strong(john) [input p4]
6. ! [X0] : ((~generous(X0) & ~curious(X0)) <=> (rich(X0) | humble(X0))) [input p5]
9. ! [X0] : ((rich(X0) | ~kind(X0)) => (generous(X0) & strong(X0))) [input p8]
11. ? [X0] : (funny(X0) | ~quiet(X0)) => (~wise(paul) & ~tall(paul)) [input p10]
12. ! [X0] : (~kind(X0) <=> (~kind(X0) | ~calm(X0))) [input p11]
14. ! [X0] : (~creative(X0) <=> (~calm(X0) <~> ~wise(X0))) [input p13]
15. ! [X0] : ((~funny(X0) & strong(X0)) <=> rich(X0)) [input p14]
23. wise(paul) [input p22]
24. brave(paul) [input hypothesis]
29. ! [X0] : ((generous(X0) & strong(X0)) | (~rich(X0) & kind(X0))) [ennf transformation 9]
31. (~wise(paul) & ~tall(paul)) | ! [X0] : (~funny(X0) & quiet(X0)) [ennf transformation 11]
41. (((~brave(paul) | ~creative(paul)) & (brave(paul) | creative(paul))) | strong(john)) & (~strong(john) | ((creative(paul) | ~brave(paul)) & (brave(paul) | ~creative(paul)))) [nnf transformation 5]
42. ! [X0] : (((~generous(X0) & ~curious(X0)) | (~rich(X0) & ~humble(X0))) & ((rich(X0) | humble(X0)) | (generous(X0) | curious(X0)))) [nnf transformation 6]
43. ! [X0] : (((~generous(X0) & ~curious(X0)) | (~rich(X0) & ~humble(X0))) & (rich(X0) | humble(X0) | generous(X0) | curious(X0))) [flattening 42]
46. ! [X0] : ((~kind(X0) | (kind(X0) & calm(X0))) & ((~kind(X0) | ~calm(X0)) | kind(X0))) [nnf transformation 12]
47. ! [X0] : ((~kind(X0) | (kind(X0) & calm(X0))) & (~kind(X0) | ~calm(X0) | kind(X0))) [flattening 46]
49. ! [X0] : ((~creative(X0) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) & (((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | creative(X0))) [nnf transformation 14]
50. ! [X0] : (((~funny(X0) & strong(X0)) | ~rich(X0)) & (rich(X0) | (funny(X0) | ~strong(X0)))) [nnf transformation 15]
51. ! [X0] : (((~funny(X0) & strong(X0)) | ~rich(X0)) & (rich(X0) | funny(X0) | ~strong(X0))) [flattening 50]
83. ~brave(paul) | ~creative(paul) | strong(john) [cnf transformation 41]
88. ~generous(X0) | ~rich(X0) [cnf transformation 43]
95. kind(X0) | strong(X0) [cnf transformation 29]
98. generous(X0) | ~rich(X0) [cnf transformation 29]
104. ~wise(paul) | ~funny(X0) [cnf transformation 31]
106. ~kind(X0) | calm(X0) [cnf transformation 47]
110. ~calm(X0) | ~wise(X0) | creative(X0) [cnf transformation 49]
114. rich(X0) | funny(X0) | ~strong(X0) [cnf transformation 51]
127. wise(paul) [cnf transformation 23]
128. brave(paul) [cnf transformation 24]
148. 5 <=> strong(john) [avatar definition]
150. strong(john) <- (5) [avatar component clause 148]
152. 6 <=> creative(paul) [avatar definition]
154. ~creative(paul) <- (~6) [avatar component clause 152]
156. 7 <=> brave(paul) [avatar definition]
159. 5 | ~6 | ~7 [avatar split clause 83,156,152,148]
176. ~rich(X0) [subsumption resolution 98,88]
187. 13 <=> ! [X0] : ~funny(X0) [avatar definition]
188. ~funny(X0) <- (13) [avatar component clause 187]
190. 14 <=> wise(paul) [avatar definition]
191. wise(paul) <- (14) [avatar component clause 190]
193. 13 | ~14 [avatar split clause 104,190,187]
205. ~strong(X0) | funny(X0) [subsumption resolution 114,176]
234. 14 [avatar split clause 127,190]
235. 7 [avatar split clause 128,156]
243. calm(X1) | strong(X1) [resolution 106,95]
284. funny(john) <- (5) [resolution 150,205]
289. $false <- (5, 13) [subsumption resolution 284,188]
290. ~5 | ~13 [avatar contradiction clause 289]
293. ~wise(X0) | creative(X0) | strong(X0) [resolution 110,243]
395. creative(paul) | strong(paul) <- (14) [resolution 293,191]
397. strong(paul) <- (~6, 14) [subsumption resolution 395,154]
409. funny(paul) <- (~6, 14) [resolution 397,205]
413. $false <- (~6, 13, 14) [subsumption resolution 409,188]
414. 6 | ~13 | ~14 [avatar contradiction clause 413]
415. $false [avatar sat refutation 159,193,234,235,290,414]
% SZS output end Proof for 1089676358432147808784947
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is both not quiet and not strong and vice versa.
Everyone who is not strong or tall is either not rich or not calm and vice versa.
If john is not generous then mary is either creative or not quiet and vice versa.
Everyone who is either not kind or old is either rich or not kind.
Everyone who is not strong or not happy is not funny or calm and vice versa.
If fred is rich or wise then mary is both not tall and not calm and vice versa.
Everyone who is not generous is calm or brave and vice versa.
If fred is not creative then lucy is quiet and vice versa.
Everyone who is either not quiet or not calm is tall or not patient and vice versa.
If someone is both brave and not tall then someone is both curious and strong and vice versa.
If mary is either happy or not kind then lucy is either funny or brave and vice versa.
If someone is kind or not generous then someone is quiet.
If fred is both not funny and tall then lucy is funny.
If lucy is curious then someone is both not quiet and kind.
If someone is creative or kind then someone is not humble and vice versa.
Everyone who is calm or not happy is either not humble or not old.
Someone is either old or not brave.
Someone is not curious or not strong.
Mary is not old.
John is either patient or quiet.
Mary is either rich or not wise.
Mary is not curious.
Someone is either rich or calm.
John is not tall or not strong. | Mary is not kind. | neutral | (![X]:(creative(X)<=>(~quiet(X)&~strong(X))))&
(![X]:((~strong(X)|tall(X))<=>(~rich(X)<~>~calm(X))))&
((~generous(john))<=>((creative(mary)<~>~quiet(mary))))&
(![X]:((~kind(X)<~>old(X))=>(rich(X)<~>~kind(X))))&
(![X]:((~strong(X)|~happy(X))<=>(~funny(X)|calm(X))))&
(((rich(fred)|wise(fred)))<=>((~tall(mary)&~calm(mary))))&
(![X]:(~generous(X)<=>(calm(X)|brave(X))))&
((~creative(fred))<=>(quiet(lucy)))&
(![X]:((~quiet(X)<~>~calm(X))<=>(tall(X)|~patient(X))))&
((?[X]:((brave(X)&~tall(X))))<=>(?[X]:((curious(X)&strong(X)))))&
(((happy(mary)<~>~kind(mary)))<=>((funny(lucy)<~>brave(lucy))))&
((?[X]:((kind(X)|~generous(X))))=>(?[X]:(quiet(X))))&
(((~funny(fred)&tall(fred)))=>(funny(lucy)))&
((curious(lucy))=>(?[X]:((~quiet(X)&kind(X)))))&
((?[X]:((creative(X)|kind(X))))<=>(?[X]:(~humble(X))))&
(![X]:((calm(X)|~happy(X))=>(~humble(X)<~>~old(X))))&
(?[X]:((old(X)<~>~brave(X))))&
(?[X]:((~curious(X)|~strong(X))))&
(~old(mary))&
((patient(john)<~>quiet(john)))&
((rich(mary)<~>~wise(mary)))&
(~curious(mary))&
(?[X]:((rich(X)<~>calm(X))))&
((~tall(john)|~strong(john))) | ~kind(mary) | [] | null | 0 |
Everyone who is old or wise is both funny and not creative and vice versa.
If someone is both strong and wise then someone is either not quiet or quiet.
Everyone who is strong is happy or not rich.
If someone is humble or not old then fred is old and vice versa.
Everyone who is calm or not creative is either not humble or calm.
If someone is both not kind and not calm then someone is either not creative or not patient and vice versa.
If susan is rich then someone is brave or not creative and vice versa.
Everyone who is both happy and old is not strong or calm and vice versa.
Everyone who is creative or funny is calm or not strong.
If fred is both patient and not quiet then someone is either not quiet or not strong and vice versa.
Everyone who is not wise is both not tall and quiet.
If alice is not old or strong then someone is not generous or not funny.
If susan is not old then someone is both not generous and creative.
If lucy is happy then someone is not curious and vice versa.
Everyone who is both generous and old is either rich or not calm and vice versa.
If someone is quiet or not calm then paul is not old.
Someone is not generous.
Paul is wise.
Someone is either not calm or not curious.
Fred is either not kind or patient.
Fred is not tall.
Someone is either not brave or calm.
Fred is both not kind and old. | Lucy is not humble. | contradiction | (![X]:((old(X)|wise(X))<=>(funny(X)&~creative(X))))&
((?[X]:((strong(X)&wise(X))))=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:(strong(X)=>(happy(X)|~rich(X))))&
((?[X]:((humble(X)|~old(X))))<=>(old(fred)))&
(![X]:((calm(X)|~creative(X))=>(~humble(X)<~>calm(X))))&
((?[X]:((~kind(X)&~calm(X))))<=>(?[X]:((~creative(X)<~>~patient(X)))))&
((rich(susan))<=>(?[X]:((brave(X)|~creative(X)))))&
(![X]:((happy(X)&old(X))<=>(~strong(X)|calm(X))))&
(![X]:((creative(X)|funny(X))=>(calm(X)|~strong(X))))&
(((patient(fred)&~quiet(fred)))<=>(?[X]:((~quiet(X)<~>~strong(X)))))&
(![X]:(~wise(X)=>(~tall(X)&quiet(X))))&
(((~old(alice)|strong(alice)))=>(?[X]:((~generous(X)|~funny(X)))))&
((~old(susan))=>(?[X]:((~generous(X)&creative(X)))))&
((happy(lucy))<=>(?[X]:(~curious(X))))&
(![X]:((generous(X)&old(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((quiet(X)|~calm(X))))=>(~old(paul)))&
(?[X]:(~generous(X)))&
(wise(paul))&
(?[X]:((~calm(X)<~>~curious(X))))&
((~kind(fred)<~>patient(fred)))&
(~tall(fred))&
(?[X]:((~brave(X)<~>calm(X))))&
((~kind(fred)&old(fred))) | ~humble(lucy) | [
"p0",
"p4",
"p7",
"p8",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2403697331315853618472331
% SZS output start Proof for 2403697331315853618472331
1. ! [X0] : ((wise(X0) | old(X0)) <=> (~creative(X0) & funny(X0))) [input p0]
5. ! [X0] : ((~creative(X0) | calm(X0)) => (~humble(X0) <~> calm(X0))) [input p4]
8. ! [X0] : ((old(X0) & happy(X0)) <=> (calm(X0) | ~strong(X0))) [input p7]
9. ! [X0] : ((funny(X0) | creative(X0)) => (~strong(X0) | calm(X0))) [input p8]
16. ? [X0] : (~calm(X0) | quiet(X0)) => ~old(paul) [input p15]
18. wise(paul) [input p17]
24. ~humble(lucy) [input hypothesis]
32. ! [X0] : ((~humble(X0) <~> calm(X0)) | (creative(X0) & ~calm(X0))) [ennf transformation 5]
33. ! [X0] : ((~strong(X0) | calm(X0)) | (~funny(X0) & ~creative(X0))) [ennf transformation 9]
34. ! [X0] : (~strong(X0) | calm(X0) | (~funny(X0) & ~creative(X0))) [flattening 33]
38. ~old(paul) | ! [X0] : (calm(X0) & ~quiet(X0)) [ennf transformation 16]
39. ! [X0] : (((wise(X0) | old(X0)) | (creative(X0) | ~funny(X0))) & ((~creative(X0) & funny(X0)) | (~wise(X0) & ~old(X0)))) [nnf transformation 1]
40. ! [X0] : ((wise(X0) | old(X0) | creative(X0) | ~funny(X0)) & ((~creative(X0) & funny(X0)) | (~wise(X0) & ~old(X0)))) [flattening 39]
49. ! [X0] : (((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | (creative(X0) & ~calm(X0))) [nnf transformation 32]
59. ! [X0] : (((old(X0) & happy(X0)) | (~calm(X0) & strong(X0))) & ((calm(X0) | ~strong(X0)) | (~old(X0) | ~happy(X0)))) [nnf transformation 8]
60. ! [X0] : (((old(X0) & happy(X0)) | (~calm(X0) & strong(X0))) & (calm(X0) | ~strong(X0) | ~old(X0) | ~happy(X0))) [flattening 59]
86. ~wise(X0) | funny(X0) [cnf transformation 40]
87. ~creative(X0) | ~old(X0) [cnf transformation 40]
99. ~calm(X0) | humble(X0) | creative(X0) [cnf transformation 49]
112. strong(X0) | old(X0) [cnf transformation 60]
113. ~calm(X0) | old(X0) [cnf transformation 60]
114. ~strong(X0) | calm(X0) | ~creative(X0) [cnf transformation 34]
115. ~strong(X0) | calm(X0) | ~funny(X0) [cnf transformation 34]
136. ~old(paul) | calm(X0) [cnf transformation 38]
138. wise(paul) [cnf transformation 18]
147. ~humble(lucy) [cnf transformation 24]
298. 34 <=> ! [X0] : calm(X0) [avatar definition]
299. calm(X0) <- (34) [avatar component clause 298]
301. 35 <=> old(paul) [avatar definition]
304. 34 | ~35 [avatar split clause 136,301,298]
341. funny(paul) [resolution 86,138]
370. calm(X0) | ~creative(X0) | old(X0) [resolution 114,112]
371. ~creative(X0) | old(X0) [subsumption resolution 370,113]
372. ~creative(X0) [subsumption resolution 371,87]
373. calm(X0) | ~funny(X0) | old(X0) [resolution 115,112]
374. ~funny(X0) | old(X0) [subsumption resolution 373,113]
500. old(paul) [resolution 374,341]
505. 35 [avatar split clause 500,301]
507. humble(X1) | creative(X1) <- (34) [resolution 299,99]
515. humble(X1) <- (34) [subsumption resolution 507,372]
526. $false <- (34) [resolution 515,147]
528. ~34 [avatar contradiction clause 526]
529. $false [avatar sat refutation 304,505,528]
% SZS output end Proof for 2403697331315853618472331
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is both not quiet and not wise and vice versa. If someone is brave or kind then john is either not patient or not quiet and vice versa. Everyone who is not creative is both not funny and not old and vice versa. If mary is not old then someone is both not strong and patient. Everyone who is not creative or happy is either tall or not quiet and vice versa. If someone is both not funny and old then someone is not brave or not kind. Everyone who is either creative or not humble is both strong and not creative. Everyone who is both not kind and strong is calm or not kind. Everyone who is not humble is either not quiet or not wise. Everyone who is not old or calm is not humble or patient and vice versa. Everyone who is either not happy or patient is either curious or not brave. Someone is quiet or wise. Susan is not happy or tall. Mary is not quiet or not rich. Someone is either not strong or not old. Alice is not generous. Mary is tall. Susan is not happy or not rich. | Alice is old. | neutral | (![X]:(wise(X)<=>(~quiet(X)&~wise(X))))&
((?[X]:((brave(X)|kind(X))))<=>((~patient(john)<~>~quiet(john))))&
(![X]:(~creative(X)<=>(~funny(X)&~old(X))))&
((~old(mary))=>(?[X]:((~strong(X)&patient(X)))))&
(![X]:((~creative(X)|happy(X))<=>(tall(X)<~>~quiet(X))))&
((?[X]:((~funny(X)&old(X))))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((creative(X)<~>~humble(X))=>(strong(X)&~creative(X))))&
(![X]:((~kind(X)&strong(X))=>(calm(X)|~kind(X))))&
(![X]:(~humble(X)=>(~quiet(X)<~>~wise(X))))&
(![X]:((~old(X)|calm(X))<=>(~humble(X)|patient(X))))&
(![X]:((~happy(X)<~>patient(X))=>(curious(X)<~>~brave(X))))&
(?[X]:((quiet(X)|wise(X))))&
((~happy(susan)|tall(susan)))&
((~quiet(mary)|~rich(mary)))&
(?[X]:((~strong(X)<~>~old(X))))&
(~generous(alice))&
(tall(mary))&
((~happy(susan)|~rich(susan))) | old(alice) | [] | null | 0 |
If fred is both calm and not calm then lucy is both humble and old and vice versa.
If lucy is both not curious and wise then paul is either not tall or not strong and vice versa.
Everyone who is both not patient and not strong is either happy or strong.
If john is quiet then fred is either patient or not strong.
If someone is not curious then someone is old or strong.
If someone is not tall then someone is both calm and not happy and vice versa.
If alice is tall then susan is not happy or creative and vice versa.
Everyone who is both kind and funny is not happy or kind.
If lucy is creative then fred is calm or not curious.
Everyone who is both not generous and not strong is both not patient and creative.
Everyone who is old or curious is calm and vice versa.
If lucy is both not brave and strong then susan is strong.
Everyone who is tall is both curious and not creative and vice versa.
Everyone who is either not rich or rich is both not wise and old and vice versa.
Everyone who is strong or not kind is not generous and vice versa.
Everyone who is not creative is either funny or not wise and vice versa.
Someone is not curious or patient.
Someone is not quiet or strong.
Someone is old or not creative.
Someone is either curious or not curious.
Someone is both happy and not quiet.
Susan is generous or not patient.
Alice is either patient or not curious. | Lucy is old. | entailment | (((calm(fred)&~calm(fred)))<=>((humble(lucy)&old(lucy))))&
(((~curious(lucy)&wise(lucy)))<=>((~tall(paul)<~>~strong(paul))))&
(![X]:((~patient(X)&~strong(X))=>(happy(X)<~>strong(X))))&
((quiet(john))=>((patient(fred)<~>~strong(fred))))&
((?[X]:(~curious(X)))=>(?[X]:((old(X)|strong(X)))))&
((?[X]:(~tall(X)))<=>(?[X]:((calm(X)&~happy(X)))))&
((tall(alice))<=>((~happy(susan)|creative(susan))))&
(![X]:((kind(X)&funny(X))=>(~happy(X)|kind(X))))&
((creative(lucy))=>((calm(fred)|~curious(fred))))&
(![X]:((~generous(X)&~strong(X))=>(~patient(X)&creative(X))))&
(![X]:((old(X)|curious(X))<=>calm(X)))&
(((~brave(lucy)&strong(lucy)))=>(strong(susan)))&
(![X]:(tall(X)<=>(curious(X)&~creative(X))))&
(![X]:((~rich(X)<~>rich(X))<=>(~wise(X)&old(X))))&
(![X]:((strong(X)|~kind(X))<=>~generous(X)))&
(![X]:(~creative(X)<=>(funny(X)<~>~wise(X))))&
(?[X]:((~curious(X)|patient(X))))&
(?[X]:((~quiet(X)|strong(X))))&
(?[X]:((old(X)|~creative(X))))&
(?[X]:((curious(X)<~>~curious(X))))&
(?[X]:((happy(X)&~quiet(X))))&
((generous(susan)|~patient(susan)))&
((patient(alice)<~>~curious(alice))) | old(lucy) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8740893776957523225742293
% SZS output start Proof for 8740893776957523225742293
14. ! [X0] : ((~rich(X0) <~> rich(X0)) <=> (old(X0) & ~wise(X0))) [input p13]
24. ~old(lucy) [input hypothesis]
61. ! [X0] : ((((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | (~old(X0) | wise(X0))) & ((old(X0) & ~wise(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0))))) [nnf transformation 14]
62. ! [X0] : ((((~rich(X0) | rich(X0)) & (rich(X0) | ~rich(X0))) | ~old(X0) | wise(X0)) & ((old(X0) & ~wise(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0))))) [flattening 61]
105. old(X0) | rich(X0) | rich(X0) [cnf transformation 62]
106. old(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 62]
123. ~old(lucy) [cnf transformation 24]
126. old(X0) | rich(X0) [duplicate literal removal 105]
127. old(X0) | ~rich(X0) [duplicate literal removal 106]
222. old(X0) [subsumption resolution 126,127]
254. $false [subsumption resolution 123,222]
% SZS output end Proof for 8740893776957523225742293
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If susan is either not rich or old then lucy is both not curious and not kind. If someone is old or brave then fred is not patient and vice versa. Everyone who is either brave or not generous is quiet or old. Everyone who is not patient or humble is not tall and vice versa. If someone is not happy then mary is not happy. Everyone who is generous or rich is either curious or not funny. Everyone who is both not happy and happy is quiet or not curious and vice versa. If alice is not wise or not rich then susan is either calm or not quiet and vice versa. Everyone who is either not rich or not humble is not tall or not quiet. Everyone who is either tall or generous is not quiet and vice versa. Everyone who is both not kind and not creative is either rich or wise and vice versa. If lucy is both calm and tall then someone is not generous and vice versa. Everyone who is kind is patient. If mary is old then susan is not wise or not calm. Everyone who is not generous is not kind and vice versa. If someone is creative or humble then lucy is not calm. Fred is not calm. Someone is either not creative or not curious. Someone is not kind or not creative. John is curious. Someone is both wise and happy. Alice is either tall or funny. | John is not kind. | contradiction | (((~rich(susan)<~>old(susan)))=>((~curious(lucy)&~kind(lucy))))&
((?[X]:((old(X)|brave(X))))<=>(~patient(fred)))&
(![X]:((brave(X)<~>~generous(X))=>(quiet(X)|old(X))))&
(![X]:((~patient(X)|humble(X))<=>~tall(X)))&
((?[X]:(~happy(X)))=>(~happy(mary)))&
(![X]:((generous(X)|rich(X))=>(curious(X)<~>~funny(X))))&
(![X]:((~happy(X)&happy(X))<=>(quiet(X)|~curious(X))))&
(((~wise(alice)|~rich(alice)))<=>((calm(susan)<~>~quiet(susan))))&
(![X]:((~rich(X)<~>~humble(X))=>(~tall(X)|~quiet(X))))&
(![X]:((tall(X)<~>generous(X))<=>~quiet(X)))&
(![X]:((~kind(X)&~creative(X))<=>(rich(X)<~>wise(X))))&
(((calm(lucy)&tall(lucy)))<=>(?[X]:(~generous(X))))&
(![X]:(kind(X)=>patient(X)))&
((old(mary))=>((~wise(susan)|~calm(susan))))&
(![X]:(~generous(X)<=>~kind(X)))&
((?[X]:((creative(X)|humble(X))))=>(~calm(lucy)))&
(~calm(fred))&
(?[X]:((~creative(X)<~>~curious(X))))&
(?[X]:((~kind(X)|~creative(X))))&
(curious(john))&
(?[X]:((wise(X)&happy(X))))&
((tall(alice)<~>funny(alice))) | ~kind(john) | [
"p1",
"p2",
"p3",
"p6",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3953611135568210607747448
% SZS output start Proof for 3953611135568210607747448
2. ? [X0] : (brave(X0) | old(X0)) <=> ~patient(fred) [input p1]
3. ! [X0] : ((brave(X0) <~> ~generous(X0)) => (old(X0) | quiet(X0))) [input p2]
4. ! [X0] : ((humble(X0) | ~patient(X0)) <=> ~tall(X0)) [input p3]
7. ! [X0] : ((happy(X0) & ~happy(X0)) <=> (~curious(X0) | quiet(X0))) [input p6]
10. ! [X0] : ((tall(X0) <~> generous(X0)) <=> ~quiet(X0)) [input p9]
13. ! [X0] : (kind(X0) => patient(X0)) [input p12]
15. ! [X0] : (~generous(X0) <=> ~kind(X0)) [input p14]
23. ~kind(john) [input hypothesis]
25. ! [X0] : ((old(X0) | quiet(X0)) | (brave(X0) <=> ~generous(X0))) [ennf transformation 3]
26. ! [X0] : (old(X0) | quiet(X0) | (brave(X0) <=> ~generous(X0))) [flattening 25]
31. ! [X0] : (patient(X0) | ~kind(X0)) [ennf transformation 13]
36. (? [X0] : (brave(X0) | old(X0)) | patient(fred)) & (~patient(fred) | ! [X0] : (~brave(X0) & ~old(X0))) [nnf transformation 2]
37. (? [X0] : (brave(X0) | old(X0)) | patient(fred)) & (~patient(fred) | ! [X1] : (~brave(X1) & ~old(X1))) [rectify 36]
38. ? [X0] : (brave(X0) | old(X0)) => (brave(sK0) | old(sK0)) [choice axiom]
39. ((brave(sK0) | old(sK0)) | patient(fred)) & (~patient(fred) | ! [X1] : (~brave(X1) & ~old(X1))) [skolemisation 37,38]
40. ! [X0] : (old(X0) | quiet(X0) | ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0)))) [nnf transformation 26]
41. ! [X0] : (((humble(X0) | ~patient(X0)) | tall(X0)) & (~tall(X0) | (~humble(X0) & patient(X0)))) [nnf transformation 4]
42. ! [X0] : ((humble(X0) | ~patient(X0) | tall(X0)) & (~tall(X0) | (~humble(X0) & patient(X0)))) [flattening 41]
44. ! [X0] : (((happy(X0) & ~happy(X0)) | (curious(X0) & ~quiet(X0))) & ((~curious(X0) | quiet(X0)) | (~happy(X0) | happy(X0)))) [nnf transformation 7]
45. ! [X0] : (((happy(X0) & ~happy(X0)) | (curious(X0) & ~quiet(X0))) & (~curious(X0) | quiet(X0) | ~happy(X0) | happy(X0))) [flattening 44]
49. ! [X0] : ((((~generous(X0) | ~tall(X0)) & (generous(X0) | tall(X0))) | quiet(X0)) & (~quiet(X0) | ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0))))) [nnf transformation 10]
57. ! [X0] : ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0))) [nnf transformation 15]
70. ~patient(fred) | ~old(X1) [cnf transformation 39]
71. ~patient(fred) | ~brave(X1) [cnf transformation 39]
74. quiet(X0) | old(X0) | brave(X0) | generous(X0) [cnf transformation 40]
75. ~tall(X0) | patient(X0) [cnf transformation 42]
84. ~happy(X0) | ~quiet(X0) [cnf transformation 45]
86. ~quiet(X0) | happy(X0) [cnf transformation 45]
98. generous(X0) | tall(X0) | quiet(X0) [cnf transformation 49]
109. ~kind(X0) | patient(X0) [cnf transformation 31]
112. ~generous(X0) | kind(X0) [cnf transformation 57]
124. ~kind(john) [cnf transformation 23]
146. 5 <=> patient(fred) [avatar definition]
147. ~patient(fred) <- (~5) [avatar component clause 146]
159. 8 <=> ! [X1] : ~brave(X1) [avatar definition]
160. ~brave(X1) <- (8) [avatar component clause 159]
161. 8 | ~5 [avatar split clause 71,146,159]
163. 9 <=> ! [X1] : ~old(X1) [avatar definition]
164. ~old(X1) <- (9) [avatar component clause 163]
165. 9 | ~5 [avatar split clause 70,146,163]
175. ~quiet(X0) [subsumption resolution 84,86]
195. tall(X0) | generous(X0) [subsumption resolution 98,175]
197. 15 <=> ! [X0] : generous(X0) [avatar definition]
198. generous(X0) <- (15) [avatar component clause 197]
265. generous(X2) | patient(X2) [resolution 195,75]
268. patient(X0) | kind(X0) [resolution 265,112]
272. patient(X0) [subsumption resolution 268,109]
274. $false <- (~5) [resolution 272,147]
276. 5 [avatar contradiction clause 274]
302. old(X1) | brave(X1) | generous(X1) [resolution 74,175]
307. brave(X1) | generous(X1) <- (9) [subsumption resolution 302,164]
308. generous(X1) <- (8, 9) [subsumption resolution 307,160]
311. 15 | ~8 | ~9 [avatar split clause 308,163,159,197]
314. kind(X2) <- (15) [resolution 198,112]
334. $false <- (15) [resolution 314,124]
339. ~15 [avatar contradiction clause 334]
341. $false [avatar sat refutation 161,165,276,311,339]
% SZS output end Proof for 3953611135568210607747448
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or creative is not old and vice versa.
Everyone who is not creative is brave.
Everyone who is not humble or not creative is both not kind and humble and vice versa.
Everyone who is either not tall or happy is both happy and rich and vice versa.
Everyone who is both not happy and generous is either not strong or not calm and vice versa.
If mary is either generous or not old then mary is both humble and not quiet and vice versa.
If john is not creative then lucy is brave or not rich and vice versa.
If someone is not brave or not humble then paul is rich or not old and vice versa.
Everyone who is either not humble or wise is not rich or tall and vice versa.
Everyone who is creative is either not kind or tall and vice versa.
Everyone who is both quiet and not calm is strong or not wise and vice versa.
If susan is not rich or not humble then someone is either not funny or not kind.
Everyone who is not strong is either not kind or curious and vice versa.
Everyone who is either not patient or patient is creative or strong.
If fred is both not tall and strong then someone is both brave and not tall.
Everyone who is generous or not happy is not humble.
Someone is humble or not curious.
Someone is not funny.
Someone is not humble or tall.
Someone is either quiet or not patient. | Fred is wise. | entailment | (![X]:((humble(X)|creative(X))<=>~old(X)))&
(![X]:(~creative(X)=>brave(X)))&
(![X]:((~humble(X)|~creative(X))<=>(~kind(X)&humble(X))))&
(![X]:((~tall(X)<~>happy(X))<=>(happy(X)&rich(X))))&
(![X]:((~happy(X)&generous(X))<=>(~strong(X)<~>~calm(X))))&
(((generous(mary)<~>~old(mary)))<=>((humble(mary)&~quiet(mary))))&
((~creative(john))<=>((brave(lucy)|~rich(lucy))))&
((?[X]:((~brave(X)|~humble(X))))<=>((rich(paul)|~old(paul))))&
(![X]:((~humble(X)<~>wise(X))<=>(~rich(X)|tall(X))))&
(![X]:(creative(X)<=>(~kind(X)<~>tall(X))))&
(![X]:((quiet(X)&~calm(X))<=>(strong(X)|~wise(X))))&
(((~rich(susan)|~humble(susan)))=>(?[X]:((~funny(X)<~>~kind(X)))))&
(![X]:(~strong(X)<=>(~kind(X)<~>curious(X))))&
(![X]:((~patient(X)<~>patient(X))=>(creative(X)|strong(X))))&
(((~tall(fred)&strong(fred)))=>(?[X]:((brave(X)&~tall(X)))))&
(![X]:((generous(X)|~happy(X))=>~humble(X)))&
(?[X]:((humble(X)|~curious(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~humble(X)|tall(X))))&
(?[X]:((quiet(X)<~>~patient(X)))) | wise(fred) | [
"p2",
"p3",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7758225002945024454786507
% SZS output start Proof for 7758225002945024454786507
3. ! [X0] : ((~creative(X0) | ~humble(X0)) <=> (humble(X0) & ~kind(X0))) [input p2]
4. ! [X0] : ((~tall(X0) <~> happy(X0)) <=> (rich(X0) & happy(X0))) [input p3]
9. ! [X0] : ((~humble(X0) <~> wise(X0)) <=> (tall(X0) | ~rich(X0))) [input p8]
16. ! [X0] : ((~happy(X0) | generous(X0)) => ~humble(X0)) [input p15]
21. ~wise(fred) [input hypothesis]
28. ! [X0] : (~humble(X0) | (happy(X0) & ~generous(X0))) [ennf transformation 16]
31. ! [X0] : (((~creative(X0) | ~humble(X0)) | (~humble(X0) | kind(X0))) & ((humble(X0) & ~kind(X0)) | (creative(X0) & humble(X0)))) [nnf transformation 3]
32. ! [X0] : ((~creative(X0) | ~humble(X0) | ~humble(X0) | kind(X0)) & ((humble(X0) & ~kind(X0)) | (creative(X0) & humble(X0)))) [flattening 31]
33. ! [X0] : ((((~happy(X0) | tall(X0)) & (happy(X0) | ~tall(X0))) | (~rich(X0) | ~happy(X0))) & ((rich(X0) & happy(X0)) | ((~tall(X0) | ~happy(X0)) & (happy(X0) | tall(X0))))) [nnf transformation 4]
34. ! [X0] : ((((~happy(X0) | tall(X0)) & (happy(X0) | ~tall(X0))) | ~rich(X0) | ~happy(X0)) & ((rich(X0) & happy(X0)) | ((~tall(X0) | ~happy(X0)) & (happy(X0) | tall(X0))))) [flattening 33]
46. ! [X0] : ((((~wise(X0) | humble(X0)) & (wise(X0) | ~humble(X0))) | (~tall(X0) & rich(X0))) & ((tall(X0) | ~rich(X0)) | ((~humble(X0) | ~wise(X0)) & (wise(X0) | humble(X0))))) [nnf transformation 9]
47. ! [X0] : ((((~wise(X0) | humble(X0)) & (wise(X0) | ~humble(X0))) | (~tall(X0) & rich(X0))) & (tall(X0) | ~rich(X0) | ((~humble(X0) | ~wise(X0)) & (wise(X0) | humble(X0))))) [flattening 46]
73. humble(X0) | humble(X0) [cnf transformation 32]
81. ~happy(X0) | tall(X0) | ~rich(X0) | ~happy(X0) [cnf transformation 34]
103. wise(X0) | ~humble(X0) | rich(X0) [cnf transformation 47]
104. wise(X0) | ~humble(X0) | ~tall(X0) [cnf transformation 47]
129. ~humble(X0) | happy(X0) [cnf transformation 28]
135. ~wise(fred) [cnf transformation 21]
139. ~rich(X0) | tall(X0) | ~happy(X0) [duplicate literal removal 81]
140. humble(X0) [duplicate literal removal 73]
193. ~tall(X0) | wise(X0) [subsumption resolution 104,140]
194. wise(X0) | rich(X0) [subsumption resolution 103,140]
214. 14 <=> tall(fred) [avatar definition]
216. tall(fred) <- (14) [avatar component clause 214]
231. happy(X0) [subsumption resolution 129,140]
248. rich(fred) [resolution 194,135]
305. tall(fred) | ~happy(fred) [resolution 139,248]
310. tall(fred) [subsumption resolution 305,231]
311. 14 [avatar split clause 310,214]
314. wise(fred) <- (14) [resolution 216,193]
316. $false <- (14) [subsumption resolution 314,135]
317. ~14 [avatar contradiction clause 316]
318. $false [avatar sat refutation 311,317]
% SZS output end Proof for 7758225002945024454786507
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not happy or not old is not quiet or tall. Everyone who is either calm or old is not brave or not rich and vice versa. If susan is either not generous or old then fred is generous and vice versa. If someone is either not old or brave then someone is either not wise or not humble. Everyone who is either not rich or creative is either creative or tall and vice versa. Everyone who is both creative and not rich is both creative and tall and vice versa. Everyone who is not old or not kind is not rich or not patient. Everyone who is either happy or not humble is tall and vice versa. Everyone who is not rich is either not creative or rich. If someone is humble then someone is not quiet or not patient and vice versa. Everyone who is both generous and not generous is not quiet and vice versa. If mary is either not curious or not quiet then susan is generous or strong. Everyone who is wise or not creative is both not brave and not calm and vice versa. If someone is not tall or not kind then susan is both not quiet and creative and vice versa. If someone is both not tall and tall then paul is either not creative or not quiet. Everyone who is either not brave or not tall is old or curious and vice versa. Someone is humble or happy. Mary is both not patient and not funny. Someone is not strong or patient. Mary is not funny. Someone is both kind and happy. | Mary is not kind. | contradiction | (![X]:((~happy(X)<~>~old(X))=>(~quiet(X)|tall(X))))&
(![X]:((calm(X)<~>old(X))<=>(~brave(X)|~rich(X))))&
(((~generous(susan)<~>old(susan)))<=>(generous(fred)))&
((?[X]:((~old(X)<~>brave(X))))=>(?[X]:((~wise(X)<~>~humble(X)))))&
(![X]:((~rich(X)<~>creative(X))<=>(creative(X)<~>tall(X))))&
(![X]:((creative(X)&~rich(X))<=>(creative(X)&tall(X))))&
(![X]:((~old(X)|~kind(X))=>(~rich(X)|~patient(X))))&
(![X]:((happy(X)<~>~humble(X))<=>tall(X)))&
(![X]:(~rich(X)=>(~creative(X)<~>rich(X))))&
((?[X]:(humble(X)))<=>(?[X]:((~quiet(X)|~patient(X)))))&
(![X]:((generous(X)&~generous(X))<=>~quiet(X)))&
(((~curious(mary)<~>~quiet(mary)))=>((generous(susan)|strong(susan))))&
(![X]:((wise(X)|~creative(X))<=>(~brave(X)&~calm(X))))&
((?[X]:((~tall(X)|~kind(X))))<=>((~quiet(susan)&creative(susan))))&
((?[X]:((~tall(X)&tall(X))))=>((~creative(paul)<~>~quiet(paul))))&
(![X]:((~brave(X)<~>~tall(X))<=>(old(X)|curious(X))))&
(?[X]:((humble(X)|happy(X))))&
((~patient(mary)&~funny(mary)))&
(?[X]:((~strong(X)|patient(X))))&
(~funny(mary))&
(?[X]:((kind(X)&happy(X)))) | ~kind(mary) | [
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5907170284390567838133798
% SZS output start Proof for 5907170284390567838133798
11. ! [X0] : ((~generous(X0) & generous(X0)) <=> ~quiet(X0)) [input p10]
14. ? [X0] : (~kind(X0) | ~tall(X0)) <=> (creative(susan) & ~quiet(susan)) [input p13]
22. ~kind(mary) [input hypothesis]
54. ! [X0] : (((~generous(X0) & generous(X0)) | quiet(X0)) & (~quiet(X0) | (generous(X0) | ~generous(X0)))) [nnf transformation 11]
55. ! [X0] : (((~generous(X0) & generous(X0)) | quiet(X0)) & (~quiet(X0) | generous(X0) | ~generous(X0))) [flattening 54]
59. (? [X0] : (~kind(X0) | ~tall(X0)) | (~creative(susan) | quiet(susan))) & ((creative(susan) & ~quiet(susan)) | ! [X0] : (kind(X0) & tall(X0))) [nnf transformation 14]
60. (? [X0] : (~kind(X0) | ~tall(X0)) | ~creative(susan) | quiet(susan)) & ((creative(susan) & ~quiet(susan)) | ! [X0] : (kind(X0) & tall(X0))) [flattening 59]
61. (? [X0] : (~kind(X0) | ~tall(X0)) | ~creative(susan) | quiet(susan)) & ((creative(susan) & ~quiet(susan)) | ! [X1] : (kind(X1) & tall(X1))) [rectify 60]
62. ? [X0] : (~kind(X0) | ~tall(X0)) => (~kind(sK3) | ~tall(sK3)) [choice axiom]
63. ((~kind(sK3) | ~tall(sK3)) | ~creative(susan) | quiet(susan)) & ((creative(susan) & ~quiet(susan)) | ! [X1] : (kind(X1) & tall(X1))) [skolemisation 61,62]
113. generous(X0) | quiet(X0) [cnf transformation 55]
114. ~generous(X0) | quiet(X0) [cnf transformation 55]
123. ~quiet(susan) | kind(X1) [cnf transformation 63]
140. ~kind(mary) [cnf transformation 22]
191. 10 <=> ! [X1] : quiet(X1) [avatar definition]
192. quiet(X1) <- (10) [avatar component clause 191]
206. quiet(X0) [subsumption resolution 113,114]
207. 10 [avatar split clause 206,191]
223. 17 <=> quiet(susan) [avatar definition]
224. ~quiet(susan) <- (~17) [avatar component clause 223]
240. 21 <=> ! [X1] : kind(X1) [avatar definition]
241. kind(X1) <- (21) [avatar component clause 240]
247. 21 | ~17 [avatar split clause 123,223,240]
269. $false <- (10, ~17) [resolution 224,192]
270. ~10 | 17 [avatar contradiction clause 269]
271. $false <- (21) [resolution 241,140]
274. ~21 [avatar contradiction clause 271]
275. $false [avatar sat refutation 207,247,270,274]
% SZS output end Proof for 5907170284390567838133798
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is old or curious then lucy is either not wise or humble and vice versa. If someone is curious then someone is either not tall or tall and vice versa. If someone is not patient then someone is not old or curious. Everyone who is either rich or quiet is either not humble or not happy and vice versa. If someone is not generous or happy then mary is kind. If paul is both not tall and generous then lucy is strong and vice versa. Everyone who is funny or not curious is both happy and creative. Everyone who is either not happy or not rich is either humble or not patient. Everyone who is either not strong or not funny is not quiet and vice versa. If mary is not rich or quiet then someone is either not humble or not wise. Everyone who is either not rich or not curious is not brave or not kind. If paul is not curious then susan is either patient or humble. If paul is not wise then alice is not rich or not patient and vice versa. Everyone who is happy is both not patient and not old and vice versa. If paul is not brave or not kind then mary is both quiet and not wise and vice versa. Everyone who is not quiet or kind is not patient or not humble and vice versa. Fred is either not funny or not old. Someone is both funny and creative. Mary is both not creative and not happy. Someone is not curious. John is both humble and quiet. John is happy or not old. Someone is either kind or brave. Fred is not patient or not humble. | John is not humble. | contradiction | (((old(lucy)|curious(lucy)))<=>((~wise(lucy)<~>humble(lucy))))&
((?[X]:(curious(X)))<=>(?[X]:((~tall(X)<~>tall(X)))))&
((?[X]:(~patient(X)))=>(?[X]:((~old(X)|curious(X)))))&
(![X]:((rich(X)<~>quiet(X))<=>(~humble(X)<~>~happy(X))))&
((?[X]:((~generous(X)|happy(X))))=>(kind(mary)))&
(((~tall(paul)&generous(paul)))<=>(strong(lucy)))&
(![X]:((funny(X)|~curious(X))=>(happy(X)&creative(X))))&
(![X]:((~happy(X)<~>~rich(X))=>(humble(X)<~>~patient(X))))&
(![X]:((~strong(X)<~>~funny(X))<=>~quiet(X)))&
(((~rich(mary)|quiet(mary)))=>(?[X]:((~humble(X)<~>~wise(X)))))&
(![X]:((~rich(X)<~>~curious(X))=>(~brave(X)|~kind(X))))&
((~curious(paul))=>((patient(susan)<~>humble(susan))))&
((~wise(paul))<=>((~rich(alice)|~patient(alice))))&
(![X]:(happy(X)<=>(~patient(X)&~old(X))))&
(((~brave(paul)|~kind(paul)))<=>((quiet(mary)&~wise(mary))))&
(![X]:((~quiet(X)|kind(X))<=>(~patient(X)|~humble(X))))&
((~funny(fred)<~>~old(fred)))&
(?[X]:((funny(X)&creative(X))))&
((~creative(mary)&~happy(mary)))&
(?[X]:(~curious(X)))&
((humble(john)&quiet(john)))&
((happy(john)|~old(john)))&
(?[X]:((kind(X)<~>brave(X))))&
((~patient(fred)|~humble(fred))) | ~humble(john) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5007088485143619204786154
% SZS output start Proof for 5007088485143619204786154
21. quiet(john) & humble(john) [input p20]
25. ~humble(john) [input hypothesis]
138. humble(john) [cnf transformation 21]
144. ~humble(john) [cnf transformation 25]
316. $false [subsumption resolution 144,138]
% SZS output end Proof for 5007088485143619204786154
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and happy is both tall and humble and vice versa.
If susan is not kind or not patient then someone is either not quiet or happy and vice versa.
If paul is not quiet then someone is not brave or not generous.
If someone is either not strong or not rich then someone is either tall or not curious.
Everyone who is not happy is either not kind or funny and vice versa.
If john is both patient and not quiet then someone is both not brave and quiet and vice versa.
If lucy is happy then alice is not calm or rich.
Everyone who is not happy or not curious is both tall and brave.
If someone is not happy then someone is both not brave and wise and vice versa.
Everyone who is not patient is both not strong and creative and vice versa.
Everyone who is both quiet and not calm is not happy or happy and vice versa.
Everyone who is either curious or strong is not quiet or not brave and vice versa.
If someone is creative then paul is not patient and vice versa.
If someone is not old then someone is both not brave and not tall.
Everyone who is either humble or strong is strong or patient and vice versa.
Paul is both strong and rich.
Lucy is either not calm or not rich.
Fred is curious.
John is both not funny and not wise.
Someone is not brave or patient. | Susan is not curious. | contradiction | (![X]:((creative(X)&happy(X))<=>(tall(X)&humble(X))))&
(((~kind(susan)|~patient(susan)))<=>(?[X]:((~quiet(X)<~>happy(X)))))&
((~quiet(paul))=>(?[X]:((~brave(X)|~generous(X)))))&
((?[X]:((~strong(X)<~>~rich(X))))=>(?[X]:((tall(X)<~>~curious(X)))))&
(![X]:(~happy(X)<=>(~kind(X)<~>funny(X))))&
(((patient(john)&~quiet(john)))<=>(?[X]:((~brave(X)&quiet(X)))))&
((happy(lucy))=>((~calm(alice)|rich(alice))))&
(![X]:((~happy(X)|~curious(X))=>(tall(X)&brave(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~brave(X)&wise(X)))))&
(![X]:(~patient(X)<=>(~strong(X)&creative(X))))&
(![X]:((quiet(X)&~calm(X))<=>(~happy(X)|happy(X))))&
(![X]:((curious(X)<~>strong(X))<=>(~quiet(X)|~brave(X))))&
((?[X]:(creative(X)))<=>(~patient(paul)))&
((?[X]:(~old(X)))=>(?[X]:((~brave(X)&~tall(X)))))&
(![X]:((humble(X)<~>strong(X))<=>(strong(X)|patient(X))))&
((strong(paul)&rich(paul)))&
((~calm(lucy)<~>~rich(lucy)))&
(curious(fred))&
((~funny(john)&~wise(john)))&
(?[X]:((~brave(X)|patient(X)))) | ~curious(susan) | [
"p0",
"p7",
"p9",
"p10",
"p11",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4549814141978429114378168
% SZS output start Proof for 4549814141978429114378168
1. ! [X0] : ((happy(X0) & creative(X0)) <=> (humble(X0) & tall(X0))) [input p0]
8. ! [X0] : ((~curious(X0) | ~happy(X0)) => (brave(X0) & tall(X0))) [input p7]
10. ! [X0] : (~patient(X0) <=> (creative(X0) & ~strong(X0))) [input p9]
11. ! [X0] : ((~calm(X0) & quiet(X0)) <=> (happy(X0) | ~happy(X0))) [input p10]
12. ! [X0] : ((curious(X0) <~> strong(X0)) <=> (~brave(X0) | ~quiet(X0))) [input p11]
13. ? [X0] : creative(X0) <=> ~patient(paul) [input p12]
15. ! [X0] : ((humble(X0) <~> strong(X0)) <=> (patient(X0) | strong(X0))) [input p14]
16. rich(paul) & strong(paul) [input p15]
21. ~curious(susan) [input hypothesis]
30. ! [X0] : ((brave(X0) & tall(X0)) | (curious(X0) & happy(X0))) [ennf transformation 8]
31. ! [X0] : (((happy(X0) & creative(X0)) | (~humble(X0) | ~tall(X0))) & ((humble(X0) & tall(X0)) | (~happy(X0) | ~creative(X0)))) [nnf transformation 1]
32. ! [X0] : (((happy(X0) & creative(X0)) | ~humble(X0) | ~tall(X0)) & ((humble(X0) & tall(X0)) | ~happy(X0) | ~creative(X0))) [flattening 31]
53. ! [X0] : ((~patient(X0) | (~creative(X0) | strong(X0))) & ((creative(X0) & ~strong(X0)) | patient(X0))) [nnf transformation 10]
54. ! [X0] : ((~patient(X0) | ~creative(X0) | strong(X0)) & ((creative(X0) & ~strong(X0)) | patient(X0))) [flattening 53]
55. ! [X0] : (((~calm(X0) & quiet(X0)) | (~happy(X0) & happy(X0))) & ((happy(X0) | ~happy(X0)) | (calm(X0) | ~quiet(X0)))) [nnf transformation 11]
56. ! [X0] : (((~calm(X0) & quiet(X0)) | (~happy(X0) & happy(X0))) & (happy(X0) | ~happy(X0) | calm(X0) | ~quiet(X0))) [flattening 55]
57. ! [X0] : ((((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | (brave(X0) & quiet(X0))) & ((~brave(X0) | ~quiet(X0)) | ((curious(X0) | ~strong(X0)) & (strong(X0) | ~curious(X0))))) [nnf transformation 12]
58. ! [X0] : ((((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | (brave(X0) & quiet(X0))) & (~brave(X0) | ~quiet(X0) | ((curious(X0) | ~strong(X0)) & (strong(X0) | ~curious(X0))))) [flattening 57]
59. (? [X0] : creative(X0) | patient(paul)) & (~patient(paul) | ! [X0] : ~creative(X0)) [nnf transformation 13]
60. (? [X0] : creative(X0) | patient(paul)) & (~patient(paul) | ! [X1] : ~creative(X1)) [rectify 59]
61. ? [X0] : creative(X0) => creative(sK5) [choice axiom]
62. (creative(sK5) | patient(paul)) & (~patient(paul) | ! [X1] : ~creative(X1)) [skolemisation 60,61]
63. ! [X0] : ((((~strong(X0) | ~humble(X0)) & (strong(X0) | humble(X0))) | (~patient(X0) & ~strong(X0))) & ((patient(X0) | strong(X0)) | ((humble(X0) | ~strong(X0)) & (strong(X0) | ~humble(X0))))) [nnf transformation 15]
64. ! [X0] : ((((~strong(X0) | ~humble(X0)) & (strong(X0) | humble(X0))) | (~patient(X0) & ~strong(X0))) & (patient(X0) | strong(X0) | ((humble(X0) | ~strong(X0)) & (strong(X0) | ~humble(X0))))) [flattening 63]
70. ~humble(X0) | creative(X0) | ~tall(X0) [cnf transformation 32]
92. curious(X0) | tall(X0) [cnf transformation 30]
94. curious(X0) | brave(X0) [cnf transformation 30]
98. ~strong(X0) | patient(X0) [cnf transformation 54]
99. patient(X0) | creative(X0) [cnf transformation 54]
102. quiet(X0) | happy(X0) [cnf transformation 56]
103. ~happy(X0) | quiet(X0) [cnf transformation 56]
107. ~brave(X0) | ~quiet(X0) | curious(X0) | ~strong(X0) [cnf transformation 58]
111. ~strong(X0) | ~curious(X0) | brave(X0) [cnf transformation 58]
112. ~patient(paul) | ~creative(X1) [cnf transformation 62]
117. ~patient(X0) | humble(X0) | strong(X0) [cnf transformation 64]
120. strong(paul) [cnf transformation 16]
128. ~curious(susan) [cnf transformation 21]
235. quiet(X0) [subsumption resolution 102,103]
236. ~strong(X0) | brave(X0) [subsumption resolution 111,94]
237. ~brave(X0) | curious(X0) | ~strong(X0) [subsumption resolution 107,235]
238. ~strong(X0) | curious(X0) [subsumption resolution 237,236]
241. 24 <=> patient(paul) [avatar definition]
250. 26 <=> ! [X1] : ~creative(X1) [avatar definition]
251. ~creative(X1) <- (26) [avatar component clause 250]
252. 26 | ~24 [avatar split clause 112,241,250]
282. tall(susan) [resolution 92,128]
287. patient(paul) [resolution 98,120]
290. 24 [avatar split clause 287,241]
309. humble(X0) | strong(X0) | creative(X0) [resolution 117,99]
313. strong(X0) | humble(X0) <- (26) [subsumption resolution 309,251]
331. curious(X1) | humble(X1) <- (26) [resolution 313,238]
345. humble(susan) <- (26) [resolution 331,128]
348. creative(susan) | ~tall(susan) <- (26) [resolution 345,70]
350. ~tall(susan) <- (26) [subsumption resolution 348,251]
351. $false <- (26) [subsumption resolution 350,282]
352. ~26 [avatar contradiction clause 351]
353. $false [avatar sat refutation 252,290,352]
% SZS output end Proof for 4549814141978429114378168
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or not funny is both strong and curious.
If lucy is not generous then someone is not rich and vice versa.
If someone is both humble and not calm then fred is both not quiet and not calm.
If someone is not humble or brave then someone is both wise and strong and vice versa.
Everyone who is not curious is both humble and calm and vice versa.
Everyone who is either old or creative is both not kind and not curious and vice versa.
Everyone who is strong is humble and vice versa.
Everyone who is both curious and tall is curious and vice versa.
Everyone who is either strong or quiet is either patient or not brave.
If someone is both not quiet and not kind then susan is funny or not patient.
If lucy is either patient or not happy then paul is either brave or not brave and vice versa.
Everyone who is both brave and not old is kind and vice versa.
If mary is either not strong or strong then fred is not calm or old and vice versa.
Everyone who is either quiet or not humble is old or not creative.
If someone is either strong or not brave then john is both wise and not curious.
Everyone who is either kind or not happy is both funny and not brave and vice versa.
Mary is either not funny or not curious.
Fred is both calm and not strong.
Someone is brave.
John is either strong or creative.
John is not wise.
Paul is old.
Someone is wise.
Someone is both not tall and not kind. | Mary is not strong. | contradiction | (![X]:((kind(X)|~funny(X))=>(strong(X)&curious(X))))&
((~generous(lucy))<=>(?[X]:(~rich(X))))&
((?[X]:((humble(X)&~calm(X))))=>((~quiet(fred)&~calm(fred))))&
((?[X]:((~humble(X)|brave(X))))<=>(?[X]:((wise(X)&strong(X)))))&
(![X]:(~curious(X)<=>(humble(X)&calm(X))))&
(![X]:((old(X)<~>creative(X))<=>(~kind(X)&~curious(X))))&
(![X]:(strong(X)<=>humble(X)))&
(![X]:((curious(X)&tall(X))<=>curious(X)))&
(![X]:((strong(X)<~>quiet(X))=>(patient(X)<~>~brave(X))))&
((?[X]:((~quiet(X)&~kind(X))))=>((funny(susan)|~patient(susan))))&
(((patient(lucy)<~>~happy(lucy)))<=>((brave(paul)<~>~brave(paul))))&
(![X]:((brave(X)&~old(X))<=>kind(X)))&
(((~strong(mary)<~>strong(mary)))<=>((~calm(fred)|old(fred))))&
(![X]:((quiet(X)<~>~humble(X))=>(old(X)|~creative(X))))&
((?[X]:((strong(X)<~>~brave(X))))=>((wise(john)&~curious(john))))&
(![X]:((kind(X)<~>~happy(X))<=>(funny(X)&~brave(X))))&
((~funny(mary)<~>~curious(mary)))&
((calm(fred)&~strong(fred)))&
(?[X]:(brave(X)))&
((strong(john)<~>creative(john)))&
(~wise(john))&
(old(paul))&
(?[X]:(wise(X)))&
(?[X]:((~tall(X)&~kind(X)))) | ~strong(mary) | [
"p0",
"p4",
"p6",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4430963069377863687493586
% SZS output start Proof for 4430963069377863687493586
1. ! [X0] : ((~funny(X0) | kind(X0)) => (curious(X0) & strong(X0))) [input p0]
5. ! [X0] : (~curious(X0) <=> (calm(X0) & humble(X0))) [input p4]
7. ! [X0] : (strong(X0) <=> humble(X0)) [input p6]
17. ~funny(mary) <~> ~curious(mary) [input p16]
25. ~strong(mary) [input hypothesis]
27. ! [X0] : ((curious(X0) & strong(X0)) | (funny(X0) & ~kind(X0))) [ennf transformation 1]
44. ! [X0] : ((~curious(X0) | (~calm(X0) | ~humble(X0))) & ((calm(X0) & humble(X0)) | curious(X0))) [nnf transformation 5]
45. ! [X0] : ((~curious(X0) | ~calm(X0) | ~humble(X0)) & ((calm(X0) & humble(X0)) | curious(X0))) [flattening 44]
48. ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0))) [nnf transformation 7]
61. (curious(mary) | funny(mary)) & (~curious(mary) | ~funny(mary)) [nnf transformation 17]
70. strong(X0) | funny(X0) [cnf transformation 27]
82. humble(X0) | curious(X0) [cnf transformation 45]
92. ~humble(X0) | strong(X0) [cnf transformation 48]
130. ~curious(mary) | ~funny(mary) [cnf transformation 61]
142. ~strong(mary) [cnf transformation 25]
236. 20 <=> strong(mary) [avatar definition]
238. ~strong(mary) <- (~20) [avatar component clause 236]
266. 26 <=> funny(mary) [avatar definition]
270. 27 <=> curious(mary) [avatar definition]
272. ~curious(mary) <- (~27) [avatar component clause 270]
273. ~26 | ~27 [avatar split clause 130,270,266]
286. ~20 [avatar split clause 142,236]
293. funny(mary) <- (~20) [resolution 70,238]
296. 26 | 20 [avatar split clause 293,236,266]
301. curious(X0) | strong(X0) [resolution 92,82]
469. strong(mary) <- (~27) [resolution 301,272]
473. $false <- (~20, ~27) [subsumption resolution 469,238]
474. 20 | 27 [avatar contradiction clause 473]
475. $false [avatar sat refutation 273,286,296,474]
% SZS output end Proof for 4430963069377863687493586
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both not patient and creative then susan is funny.
Everyone who is rich or happy is either brave or not happy and vice versa.
Everyone who is both not humble and quiet is either patient or old and vice versa.
If paul is humble or not patient then someone is old or quiet.
Everyone who is both not kind and funny is quiet.
If alice is either not calm or generous then susan is both not strong and kind.
Everyone who is not tall or calm is either not wise or not funny and vice versa.
Everyone who is either brave or creative is both happy and old.
If susan is either tall or not happy then someone is both generous and not creative.
Everyone who is either not creative or not rich is not funny or creative and vice versa.
Everyone who is brave is both not creative and not generous.
If someone is either not creative or not old then mary is not happy and vice versa.
If paul is either not tall or happy then someone is both brave and tall.
If alice is old or not kind then alice is either tall or wise.
If paul is both brave and funny then susan is not old or not creative and vice versa.
Everyone who is tall is either quiet or rich and vice versa.
Fred is quiet.
Fred is not funny or not humble.
Someone is both generous and not strong.
Someone is humble.
Someone is not wise or tall.
Fred is rich or old.
Lucy is either not old or not rich.
Someone is patient or old. | Paul is creative. | contradiction | (((~patient(paul)&creative(paul)))=>(funny(susan)))&
(![X]:((rich(X)|happy(X))<=>(brave(X)<~>~happy(X))))&
(![X]:((~humble(X)&quiet(X))<=>(patient(X)<~>old(X))))&
(((humble(paul)|~patient(paul)))=>(?[X]:((old(X)|quiet(X)))))&
(![X]:((~kind(X)&funny(X))=>quiet(X)))&
(((~calm(alice)<~>generous(alice)))=>((~strong(susan)&kind(susan))))&
(![X]:((~tall(X)|calm(X))<=>(~wise(X)<~>~funny(X))))&
(![X]:((brave(X)<~>creative(X))=>(happy(X)&old(X))))&
(((tall(susan)<~>~happy(susan)))=>(?[X]:((generous(X)&~creative(X)))))&
(![X]:((~creative(X)<~>~rich(X))<=>(~funny(X)|creative(X))))&
(![X]:(brave(X)=>(~creative(X)&~generous(X))))&
((?[X]:((~creative(X)<~>~old(X))))<=>(~happy(mary)))&
(((~tall(paul)<~>happy(paul)))=>(?[X]:((brave(X)&tall(X)))))&
(((old(alice)|~kind(alice)))=>((tall(alice)<~>wise(alice))))&
(((brave(paul)&funny(paul)))<=>((~old(susan)|~creative(susan))))&
(![X]:(tall(X)<=>(quiet(X)<~>rich(X))))&
(quiet(fred))&
((~funny(fred)|~humble(fred)))&
(?[X]:((generous(X)&~strong(X))))&
(?[X]:(humble(X)))&
(?[X]:((~wise(X)|tall(X))))&
((rich(fred)|old(fred)))&
((~old(lucy)<~>~rich(lucy)))&
(?[X]:((patient(X)|old(X)))) | creative(paul) | [
"p1",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1784794288477314655552600
% SZS output start Proof for 1784794288477314655552600
2. ! [X0] : ((happy(X0) | rich(X0)) <=> (brave(X0) <~> ~happy(X0))) [input p1]
8. ! [X0] : ((brave(X0) <~> creative(X0)) => (old(X0) & happy(X0))) [input p7]
11. ! [X0] : (brave(X0) => (~generous(X0) & ~creative(X0))) [input p10]
25. creative(paul) [input hypothesis]
34. ! [X0] : ((old(X0) & happy(X0)) | (brave(X0) <=> creative(X0))) [ennf transformation 8]
36. ! [X0] : ((~generous(X0) & ~creative(X0)) | ~brave(X0)) [ennf transformation 11]
39. ! [X0] : (((happy(X0) | rich(X0)) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0)))) & (((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | (~happy(X0) & ~rich(X0)))) [nnf transformation 2]
40. ! [X0] : ((happy(X0) | rich(X0) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0)))) & (((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | (~happy(X0) & ~rich(X0)))) [flattening 39]
47. ! [X0] : ((old(X0) & happy(X0)) | ((brave(X0) | ~creative(X0)) & (creative(X0) | ~brave(X0)))) [nnf transformation 34]
75. ~happy(X0) | brave(X0) | ~happy(X0) [cnf transformation 40]
95. happy(X0) | brave(X0) | ~creative(X0) [cnf transformation 47]
108. ~creative(X0) | ~brave(X0) [cnf transformation 36]
138. creative(paul) [cnf transformation 25]
141. ~happy(X0) | brave(X0) [duplicate literal removal 75]
170. brave(X0) | ~creative(X0) [subsumption resolution 95,141]
192. ~creative(X0) [subsumption resolution 108,170]
290. $false [subsumption resolution 138,192]
% SZS output end Proof for 1784794288477314655552600
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not humble is rich and vice versa. Everyone who is either generous or calm is not funny. Everyone who is not funny or strong is either kind or wise. Everyone who is brave or not humble is both brave and not rich and vice versa. Everyone who is rich is not creative. If mary is either brave or humble then john is both calm and not old and vice versa. Everyone who is either quiet or not happy is humble and vice versa. Everyone who is not creative is happy and vice versa. Everyone who is strong is both not humble and not brave. If someone is tall or rich then susan is both humble and not wise. Everyone who is not rich is both not rich and brave. Everyone who is either strong or generous is either not humble or happy. Everyone who is not generous is both creative and not wise. If someone is not wise or not quiet then paul is either curious or not funny and vice versa. If lucy is either not happy or funny then someone is both not funny and patient and vice versa. If someone is not wise then fred is humble or not humble. Paul is both funny and not curious. Paul is wise. Paul is old or not quiet. Lucy is either generous or not patient. John is quiet. Susan is either not rich or rich. | Mary is old. | neutral | (![X]:((tall(X)|~humble(X))<=>rich(X)))&
(![X]:((generous(X)<~>calm(X))=>~funny(X)))&
(![X]:((~funny(X)|strong(X))=>(kind(X)<~>wise(X))))&
(![X]:((brave(X)|~humble(X))<=>(brave(X)&~rich(X))))&
(![X]:(rich(X)=>~creative(X)))&
(((brave(mary)<~>humble(mary)))<=>((calm(john)&~old(john))))&
(![X]:((quiet(X)<~>~happy(X))<=>humble(X)))&
(![X]:(~creative(X)<=>happy(X)))&
(![X]:(strong(X)=>(~humble(X)&~brave(X))))&
((?[X]:((tall(X)|rich(X))))=>((humble(susan)&~wise(susan))))&
(![X]:(~rich(X)=>(~rich(X)&brave(X))))&
(![X]:((strong(X)<~>generous(X))=>(~humble(X)<~>happy(X))))&
(![X]:(~generous(X)=>(creative(X)&~wise(X))))&
((?[X]:((~wise(X)|~quiet(X))))<=>((curious(paul)<~>~funny(paul))))&
(((~happy(lucy)<~>funny(lucy)))<=>(?[X]:((~funny(X)&patient(X)))))&
((?[X]:(~wise(X)))=>((humble(fred)|~humble(fred))))&
((funny(paul)&~curious(paul)))&
(wise(paul))&
((old(paul)|~quiet(paul)))&
((generous(lucy)<~>~patient(lucy)))&
(quiet(john))&
((~rich(susan)<~>rich(susan))) | old(mary) | [] | null | 0 |
Everyone who is old is curious and vice versa.
If lucy is not quiet then someone is curious or quiet and vice versa.
Everyone who is either curious or patient is both not happy and creative and vice versa.
If someone is either calm or funny then someone is quiet or not humble and vice versa.
If lucy is calm then paul is wise.
Everyone who is not humble or not rich is not funny or funny.
If paul is quiet then someone is both tall and not happy.
Everyone who is old is both not wise and not quiet.
Everyone who is both not humble and curious is either creative or not creative and vice versa.
If lucy is either calm or not patient then someone is not old or not strong.
Everyone who is both creative and strong is both tall and not strong and vice versa.
Everyone who is either not generous or humble is both kind and not rich.
If someone is not curious or quiet then susan is either not rich or not calm.
Everyone who is not tall or old is both creative and funny.
Everyone who is both not tall and not curious is humble and vice versa.
Someone is both generous and not calm.
Someone is either not funny or not wise.
Someone is either generous or not curious.
Alice is not rich.
Mary is both old and calm.
Someone is both patient and generous.
Fred is not kind. | Lucy is patient. | neutral | (![X]:(old(X)<=>curious(X)))&
((~quiet(lucy))<=>(?[X]:((curious(X)|quiet(X)))))&
(![X]:((curious(X)<~>patient(X))<=>(~happy(X)&creative(X))))&
((?[X]:((calm(X)<~>funny(X))))<=>(?[X]:((quiet(X)|~humble(X)))))&
((calm(lucy))=>(wise(paul)))&
(![X]:((~humble(X)|~rich(X))=>(~funny(X)|funny(X))))&
((quiet(paul))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:(old(X)=>(~wise(X)&~quiet(X))))&
(![X]:((~humble(X)&curious(X))<=>(creative(X)<~>~creative(X))))&
(((calm(lucy)<~>~patient(lucy)))=>(?[X]:((~old(X)|~strong(X)))))&
(![X]:((creative(X)&strong(X))<=>(tall(X)&~strong(X))))&
(![X]:((~generous(X)<~>humble(X))=>(kind(X)&~rich(X))))&
((?[X]:((~curious(X)|quiet(X))))=>((~rich(susan)<~>~calm(susan))))&
(![X]:((~tall(X)|old(X))=>(creative(X)&funny(X))))&
(![X]:((~tall(X)&~curious(X))<=>humble(X)))&
(?[X]:((generous(X)&~calm(X))))&
(?[X]:((~funny(X)<~>~wise(X))))&
(?[X]:((generous(X)<~>~curious(X))))&
(~rich(alice))&
((old(mary)&calm(mary)))&
(?[X]:((patient(X)&generous(X))))&
(~kind(fred)) | patient(lucy) | [] | null | 0 |
Everyone who is either rich or wise is quiet or not old.
Everyone who is not funny or not rich is happy and vice versa.
Everyone who is strong or not patient is either humble or tall and vice versa.
If john is happy or not strong then someone is generous or funny.
If fred is strong then paul is not funny and vice versa.
If someone is either not humble or not tall then fred is not humble and vice versa.
If fred is rich then susan is not strong or funny.
If lucy is not brave then fred is either not wise or not strong and vice versa.
If john is either creative or kind then someone is funny or not quiet and vice versa.
If john is either not rich or old then someone is tall or strong.
If someone is not funny or tall then someone is not creative or strong and vice versa.
If someone is both not wise and creative then someone is either not calm or not old.
If someone is either old or not happy then someone is rich or not generous.
Everyone who is both humble and calm is old or not quiet and vice versa.
If someone is quiet then someone is not wise and vice versa.
If mary is both not happy and brave then someone is not humble or not curious and vice versa.
Someone is not wise or wise.
Paul is kind.
Someone is both not rich and strong.
Alice is either happy or brave.
Lucy is rich.
Lucy is patient or not happy.
Someone is patient or funny.
Fred is not rich or not tall. | Fred is not quiet. | contradiction | (![X]:((rich(X)<~>wise(X))=>(quiet(X)|~old(X))))&
(![X]:((~funny(X)|~rich(X))<=>happy(X)))&
(![X]:((strong(X)|~patient(X))<=>(humble(X)<~>tall(X))))&
(((happy(john)|~strong(john)))=>(?[X]:((generous(X)|funny(X)))))&
((strong(fred))<=>(~funny(paul)))&
((?[X]:((~humble(X)<~>~tall(X))))<=>(~humble(fred)))&
((rich(fred))=>((~strong(susan)|funny(susan))))&
((~brave(lucy))<=>((~wise(fred)<~>~strong(fred))))&
(((creative(john)<~>kind(john)))<=>(?[X]:((funny(X)|~quiet(X)))))&
(((~rich(john)<~>old(john)))=>(?[X]:((tall(X)|strong(X)))))&
((?[X]:((~funny(X)|tall(X))))<=>(?[X]:((~creative(X)|strong(X)))))&
((?[X]:((~wise(X)&creative(X))))=>(?[X]:((~calm(X)<~>~old(X)))))&
((?[X]:((old(X)<~>~happy(X))))=>(?[X]:((rich(X)|~generous(X)))))&
(![X]:((humble(X)&calm(X))<=>(old(X)|~quiet(X))))&
((?[X]:(quiet(X)))<=>(?[X]:(~wise(X))))&
(((~happy(mary)&brave(mary)))<=>(?[X]:((~humble(X)|~curious(X)))))&
(?[X]:((~wise(X)|wise(X))))&
(kind(paul))&
(?[X]:((~rich(X)&strong(X))))&
((happy(alice)<~>brave(alice)))&
(rich(lucy))&
((patient(lucy)|~happy(lucy)))&
(?[X]:((patient(X)|funny(X))))&
((~rich(fred)|~tall(fred))) | ~quiet(fred) | [
"p2",
"p5",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 266280317729531905880579
% SZS output start Proof for 266280317729531905880579
3. ! [X0] : ((~patient(X0) | strong(X0)) <=> (humble(X0) <~> tall(X0))) [input p2]
6. ? [X0] : (~humble(X0) <~> ~tall(X0)) <=> ~humble(fred) [input p5]
14. ! [X0] : ((calm(X0) & humble(X0)) <=> (~quiet(X0) | old(X0))) [input p13]
19. ? [X0] : (strong(X0) & ~rich(X0)) [input p18]
25. ~quiet(fred) [input hypothesis]
41. ! [X0] : (((~patient(X0) | strong(X0)) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) & (((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | (patient(X0) & ~strong(X0)))) [nnf transformation 3]
42. ! [X0] : ((~patient(X0) | strong(X0) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) & (((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | (patient(X0) & ~strong(X0)))) [flattening 41]
46. (? [X0] : ((tall(X0) | humble(X0)) & (~tall(X0) | ~humble(X0))) | humble(fred)) & (~humble(fred) | ! [X0] : ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) [nnf transformation 6]
47. (? [X0] : ((tall(X0) | humble(X0)) & (~tall(X0) | ~humble(X0))) | humble(fred)) & (~humble(fred) | ! [X1] : ((~humble(X1) | tall(X1)) & (~tall(X1) | humble(X1)))) [rectify 46]
48. ? [X0] : ((tall(X0) | humble(X0)) & (~tall(X0) | ~humble(X0))) => ((tall(sK1) | humble(sK1)) & (~tall(sK1) | ~humble(sK1))) [choice axiom]
49. (((tall(sK1) | humble(sK1)) & (~tall(sK1) | ~humble(sK1))) | humble(fred)) & (~humble(fred) | ! [X1] : ((~humble(X1) | tall(X1)) & (~tall(X1) | humble(X1)))) [skolemisation 47,48]
71. ! [X0] : (((calm(X0) & humble(X0)) | (quiet(X0) & ~old(X0))) & ((~quiet(X0) | old(X0)) | (~calm(X0) | ~humble(X0)))) [nnf transformation 14]
72. ! [X0] : (((calm(X0) & humble(X0)) | (quiet(X0) & ~old(X0))) & (~quiet(X0) | old(X0) | ~calm(X0) | ~humble(X0))) [flattening 71]
85. ? [X0] : (strong(X0) & ~rich(X0)) => (strong(sK12) & ~rich(sK12)) [choice axiom]
86. strong(sK12) & ~rich(sK12) [skolemisation 19,85]
95. ~strong(X0) | humble(X0) | tall(X0) [cnf transformation 42]
97. ~tall(X0) | ~humble(X0) | ~strong(X0) [cnf transformation 42]
105. ~humble(fred) | ~tall(X1) | humble(X1) [cnf transformation 49]
106. ~humble(fred) | ~humble(X1) | tall(X1) [cnf transformation 49]
132. humble(X0) | quiet(X0) [cnf transformation 72]
145. strong(sK12) [cnf transformation 86]
152. ~quiet(fred) [cnf transformation 25]
182. 7 <=> humble(fred) [avatar definition]
183. ~humble(fred) <- (~7) [avatar component clause 182]
196. 10 <=> ! [X1] : (~humble(X1) | tall(X1)) [avatar definition]
197. ~humble(X1) | tall(X1) <- (10) [avatar component clause 196]
198. 10 | ~7 [avatar split clause 106,182,196]
200. 11 <=> ! [X1] : (~tall(X1) | humble(X1)) [avatar definition]
201. ~tall(X1) | humble(X1) <- (11) [avatar component clause 200]
202. 11 | ~7 [avatar split clause 105,182,200]
420. quiet(fred) <- (~7) [resolution 132,183]
421. $false <- (~7) [subsumption resolution 420,152]
422. 7 [avatar contradiction clause 421]
446. humble(sK12) | tall(sK12) [resolution 95,145]
447. tall(sK12) <- (10) [subsumption resolution 446,197]
448. humble(sK12) <- (10, 11) [resolution 447,201]
454. ~humble(sK12) | ~strong(sK12) <- (10) [resolution 97,447]
456. ~strong(sK12) <- (10, 11) [subsumption resolution 454,448]
457. $false <- (10, 11) [subsumption resolution 456,145]
458. ~10 | ~11 [avatar contradiction clause 457]
459. $false [avatar sat refutation 198,202,422,458]
% SZS output end Proof for 266280317729531905880579
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not old is not quiet or tall. Everyone who is either calm or old is not brave or not rich and vice versa. If susan is either not generous or old then fred is generous and vice versa. If someone is either not old or brave then someone is either not wise or not humble. Everyone who is either not rich or creative is either creative or tall and vice versa. Everyone who is both creative and not rich is both creative and tall and vice versa. Everyone who is not old or not kind is not rich or not patient. Everyone who is either happy or not humble is tall and vice versa. Everyone who is not rich is either not creative or rich. If someone is humble then someone is not quiet or not patient and vice versa. Everyone who is both generous and not generous is not quiet and vice versa. If mary is either not curious or not quiet then susan is generous or strong. Everyone who is wise or not creative is both not brave and not calm and vice versa. If someone is not tall or not kind then susan is both not quiet and creative and vice versa. If someone is both not tall and tall then paul is either not creative or not quiet. Everyone who is either not brave or not tall is old or curious and vice versa. Someone is humble or happy. Mary is both not patient and not funny. Someone is not strong or patient. Mary is not funny. Someone is both kind and happy. | Paul is calm. | contradiction | (![X]:((~happy(X)<~>~old(X))=>(~quiet(X)|tall(X))))&
(![X]:((calm(X)<~>old(X))<=>(~brave(X)|~rich(X))))&
(((~generous(susan)<~>old(susan)))<=>(generous(fred)))&
((?[X]:((~old(X)<~>brave(X))))=>(?[X]:((~wise(X)<~>~humble(X)))))&
(![X]:((~rich(X)<~>creative(X))<=>(creative(X)<~>tall(X))))&
(![X]:((creative(X)&~rich(X))<=>(creative(X)&tall(X))))&
(![X]:((~old(X)|~kind(X))=>(~rich(X)|~patient(X))))&
(![X]:((happy(X)<~>~humble(X))<=>tall(X)))&
(![X]:(~rich(X)=>(~creative(X)<~>rich(X))))&
((?[X]:(humble(X)))<=>(?[X]:((~quiet(X)|~patient(X)))))&
(![X]:((generous(X)&~generous(X))<=>~quiet(X)))&
(((~curious(mary)<~>~quiet(mary)))=>((generous(susan)|strong(susan))))&
(![X]:((wise(X)|~creative(X))<=>(~brave(X)&~calm(X))))&
((?[X]:((~tall(X)|~kind(X))))<=>((~quiet(susan)&creative(susan))))&
((?[X]:((~tall(X)&tall(X))))=>((~creative(paul)<~>~quiet(paul))))&
(![X]:((~brave(X)<~>~tall(X))<=>(old(X)|curious(X))))&
(?[X]:((humble(X)|happy(X))))&
((~patient(mary)&~funny(mary)))&
(?[X]:((~strong(X)|patient(X))))&
(~funny(mary))&
(?[X]:((kind(X)&happy(X)))) | calm(paul) | [
"p4",
"p8",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1990084719858097246673414
% SZS output start Proof for 1990084719858097246673414
5. ! [X0] : ((~rich(X0) <~> creative(X0)) <=> (creative(X0) <~> tall(X0))) [input p4]
9. ! [X0] : (~rich(X0) => (~creative(X0) <~> rich(X0))) [input p8]
11. ! [X0] : ((~generous(X0) & generous(X0)) <=> ~quiet(X0)) [input p10]
13. ! [X0] : ((~creative(X0) | wise(X0)) <=> (~calm(X0) & ~brave(X0))) [input p12]
14. ? [X0] : (~kind(X0) | ~tall(X0)) <=> (creative(susan) & ~quiet(susan)) [input p13]
22. calm(paul) [input hypothesis]
32. ! [X0] : ((~creative(X0) <~> rich(X0)) | rich(X0)) [ennf transformation 9]
44. ! [X0] : ((((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) & (((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0))))) [nnf transformation 5]
48. ! [X0] : (((~rich(X0) | creative(X0)) & (rich(X0) | ~creative(X0))) | rich(X0)) [nnf transformation 32]
54. ! [X0] : (((~generous(X0) & generous(X0)) | quiet(X0)) & (~quiet(X0) | (generous(X0) | ~generous(X0)))) [nnf transformation 11]
55. ! [X0] : (((~generous(X0) & generous(X0)) | quiet(X0)) & (~quiet(X0) | generous(X0) | ~generous(X0))) [flattening 54]
57. ! [X0] : (((~creative(X0) | wise(X0)) | (calm(X0) | brave(X0))) & ((~calm(X0) & ~brave(X0)) | (creative(X0) & ~wise(X0)))) [nnf transformation 13]
58. ! [X0] : ((~creative(X0) | wise(X0) | calm(X0) | brave(X0)) & ((~calm(X0) & ~brave(X0)) | (creative(X0) & ~wise(X0)))) [flattening 57]
59. (? [X0] : (~kind(X0) | ~tall(X0)) | (~creative(susan) | quiet(susan))) & ((creative(susan) & ~quiet(susan)) | ! [X0] : (kind(X0) & tall(X0))) [nnf transformation 14]
60. (? [X0] : (~kind(X0) | ~tall(X0)) | ~creative(susan) | quiet(susan)) & ((creative(susan) & ~quiet(susan)) | ! [X0] : (kind(X0) & tall(X0))) [flattening 59]
61. (? [X0] : (~kind(X0) | ~tall(X0)) | ~creative(susan) | quiet(susan)) & ((creative(susan) & ~quiet(susan)) | ! [X1] : (kind(X1) & tall(X1))) [rectify 60]
62. ? [X0] : (~kind(X0) | ~tall(X0)) => (~kind(sK3) | ~tall(sK3)) [choice axiom]
63. ((~kind(sK3) | ~tall(sK3)) | ~creative(susan) | quiet(susan)) & ((creative(susan) & ~quiet(susan)) | ! [X1] : (kind(X1) & tall(X1))) [skolemisation 61,62]
92. ~tall(X0) | ~creative(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 44]
94. creative(X0) | ~rich(X0) | creative(X0) | ~tall(X0) [cnf transformation 44]
107. rich(X0) | ~creative(X0) | rich(X0) [cnf transformation 48]
113. generous(X0) | quiet(X0) [cnf transformation 55]
114. ~generous(X0) | quiet(X0) [cnf transformation 55]
120. ~calm(X0) | creative(X0) [cnf transformation 58]
122. ~quiet(susan) | tall(X1) [cnf transformation 63]
140. calm(paul) [cnf transformation 22]
141. ~creative(X0) | rich(X0) [duplicate literal removal 107]
143. ~tall(X0) | ~creative(X0) | ~rich(X0) [duplicate literal removal 92]
144. creative(X0) | ~rich(X0) | ~tall(X0) [duplicate literal removal 94]
180. ~rich(X0) | ~tall(X0) [subsumption resolution 143,144]
191. 10 <=> ! [X1] : quiet(X1) [avatar definition]
192. quiet(X1) <- (10) [avatar component clause 191]
206. quiet(X0) [subsumption resolution 113,114]
207. 10 [avatar split clause 206,191]
223. 17 <=> quiet(susan) [avatar definition]
224. ~quiet(susan) <- (~17) [avatar component clause 223]
244. 22 <=> ! [X1] : tall(X1) [avatar definition]
245. tall(X1) <- (22) [avatar component clause 244]
248. 22 | ~17 [avatar split clause 122,223,244]
269. $false <- (10, ~17) [resolution 224,192]
270. ~10 | 17 [avatar contradiction clause 269]
276. creative(paul) [resolution 120,140]
278. rich(paul) [resolution 276,141]
282. ~tall(paul) [resolution 278,180]
283. $false <- (22) [subsumption resolution 282,245]
284. ~22 [avatar contradiction clause 283]
285. $false [avatar sat refutation 207,248,270,284]
% SZS output end Proof for 1990084719858097246673414
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not rich and not patient then john is either not humble or humble and vice versa.
If mary is old then someone is either tall or not calm.
Everyone who is either not wise or funny is either not strong or not kind.
If lucy is not old or not patient then someone is not creative.
If someone is not wise then mary is either kind or rich.
Everyone who is generous or not curious is both generous and not humble and vice versa.
If someone is either not calm or creative then someone is either not generous or calm.
Everyone who is not brave is either not brave or not curious.
If someone is either not rich or funny then alice is not humble or not happy.
Everyone who is both curious and not happy is either rich or not curious.
Everyone who is either not old or not quiet is strong or not curious.
Everyone who is not tall or quiet is either happy or not calm and vice versa.
Everyone who is not generous is either rich or calm and vice versa.
If john is patient or brave then someone is either generous or not tall.
If someone is either tall or old then someone is both not curious and rich and vice versa.
Everyone who is either brave or not brave is either generous or not humble.
Lucy is creative or happy.
Someone is either quiet or not kind.
Alice is both happy and not humble.
Someone is creative or not curious.
Mary is creative.
Someone is patient.
Someone is quiet. | John is patient. | neutral | (((~rich(paul)&~patient(paul)))<=>((~humble(john)<~>humble(john))))&
((old(mary))=>(?[X]:((tall(X)<~>~calm(X)))))&
(![X]:((~wise(X)<~>funny(X))=>(~strong(X)<~>~kind(X))))&
(((~old(lucy)|~patient(lucy)))=>(?[X]:(~creative(X))))&
((?[X]:(~wise(X)))=>((kind(mary)<~>rich(mary))))&
(![X]:((generous(X)|~curious(X))<=>(generous(X)&~humble(X))))&
((?[X]:((~calm(X)<~>creative(X))))=>(?[X]:((~generous(X)<~>calm(X)))))&
(![X]:(~brave(X)=>(~brave(X)<~>~curious(X))))&
((?[X]:((~rich(X)<~>funny(X))))=>((~humble(alice)|~happy(alice))))&
(![X]:((curious(X)&~happy(X))=>(rich(X)<~>~curious(X))))&
(![X]:((~old(X)<~>~quiet(X))=>(strong(X)|~curious(X))))&
(![X]:((~tall(X)|quiet(X))<=>(happy(X)<~>~calm(X))))&
(![X]:(~generous(X)<=>(rich(X)<~>calm(X))))&
(((patient(john)|brave(john)))=>(?[X]:((generous(X)<~>~tall(X)))))&
((?[X]:((tall(X)<~>old(X))))<=>(?[X]:((~curious(X)&rich(X)))))&
(![X]:((brave(X)<~>~brave(X))=>(generous(X)<~>~humble(X))))&
((creative(lucy)|happy(lucy)))&
(?[X]:((quiet(X)<~>~kind(X))))&
((happy(alice)&~humble(alice)))&
(?[X]:((creative(X)|~curious(X))))&
(creative(mary))&
(?[X]:(patient(X)))&
(?[X]:(quiet(X))) | patient(john) | [] | null | 0 |
If john is strong or not happy then someone is either tall or not brave and vice versa.
If someone is happy or not rich then fred is not curious or not happy and vice versa.
If mary is tall or not old then someone is both wise and not creative.
Everyone who is not patient is both generous and not strong and vice versa.
Everyone who is either not rich or old is brave or not curious and vice versa.
If paul is either not wise or not generous then fred is not curious or kind.
Everyone who is both not strong and strong is both not happy and rich and vice versa.
Everyone who is either not tall or tall is not happy.
Everyone who is both generous and strong is not happy.
Everyone who is either rich or brave is not old and vice versa.
Everyone who is generous is not humble and vice versa.
If someone is either wise or not strong then fred is either funny or old and vice versa.
If someone is both not tall and not happy then fred is not creative.
Everyone who is strong is both old and not tall and vice versa.
If alice is either humble or not wise then someone is not kind and vice versa.
Everyone who is either not strong or not kind is not rich or not strong and vice versa.
Someone is both not curious and not strong.
John is both not humble and not tall.
Someone is not strong or not calm.
Someone is not kind.
Someone is not funny.
Alice is both brave and not creative.
Someone is both wise and humble. | John is funny. | neutral | (((strong(john)|~happy(john)))<=>(?[X]:((tall(X)<~>~brave(X)))))&
((?[X]:((happy(X)|~rich(X))))<=>((~curious(fred)|~happy(fred))))&
(((tall(mary)|~old(mary)))=>(?[X]:((wise(X)&~creative(X)))))&
(![X]:(~patient(X)<=>(generous(X)&~strong(X))))&
(![X]:((~rich(X)<~>old(X))<=>(brave(X)|~curious(X))))&
(((~wise(paul)<~>~generous(paul)))=>((~curious(fred)|kind(fred))))&
(![X]:((~strong(X)&strong(X))<=>(~happy(X)&rich(X))))&
(![X]:((~tall(X)<~>tall(X))=>~happy(X)))&
(![X]:((generous(X)&strong(X))=>~happy(X)))&
(![X]:((rich(X)<~>brave(X))<=>~old(X)))&
(![X]:(generous(X)<=>~humble(X)))&
((?[X]:((wise(X)<~>~strong(X))))<=>((funny(fred)<~>old(fred))))&
((?[X]:((~tall(X)&~happy(X))))=>(~creative(fred)))&
(![X]:(strong(X)<=>(old(X)&~tall(X))))&
(((humble(alice)<~>~wise(alice)))<=>(?[X]:(~kind(X))))&
(![X]:((~strong(X)<~>~kind(X))<=>(~rich(X)|~strong(X))))&
(?[X]:((~curious(X)&~strong(X))))&
((~humble(john)&~tall(john)))&
(?[X]:((~strong(X)|~calm(X))))&
(?[X]:(~kind(X)))&
(?[X]:(~funny(X)))&
((brave(alice)&~creative(alice)))&
(?[X]:((wise(X)&humble(X)))) | funny(john) | [] | null | 0 |
Everyone who is both not humble and not curious is strong or not wise.
Everyone who is either happy or not humble is not funny and vice versa.
If someone is not funny or humble then alice is quiet.
If mary is not funny then mary is not humble.
Everyone who is not calm is strong or wise.
If john is both not wise and wise then alice is not happy.
Everyone who is either not rich or calm is quiet.
Everyone who is strong is not brave or not curious and vice versa.
If lucy is both curious and not humble then alice is not calm or not patient and vice versa.
Everyone who is either not generous or tall is either patient or kind and vice versa.
If someone is both not calm and not wise then someone is funny and vice versa.
Everyone who is not humble or generous is both not quiet and humble.
If someone is not brave then paul is both curious and not strong and vice versa.
Everyone who is not happy or creative is quiet or old and vice versa.
Everyone who is both rich and old is not creative or funny and vice versa.
John is both rich and not tall.
Someone is generous.
Someone is either old or not brave.
Fred is both curious and not old.
Fred is either not creative or kind.
Someone is both patient and not rich. | Fred is not funny. | entailment | (![X]:((~humble(X)&~curious(X))=>(strong(X)|~wise(X))))&
(![X]:((happy(X)<~>~humble(X))<=>~funny(X)))&
((?[X]:((~funny(X)|humble(X))))=>(quiet(alice)))&
((~funny(mary))=>(~humble(mary)))&
(![X]:(~calm(X)=>(strong(X)|wise(X))))&
(((~wise(john)&wise(john)))=>(~happy(alice)))&
(![X]:((~rich(X)<~>calm(X))=>quiet(X)))&
(![X]:(strong(X)<=>(~brave(X)|~curious(X))))&
(((curious(lucy)&~humble(lucy)))<=>((~calm(alice)|~patient(alice))))&
(![X]:((~generous(X)<~>tall(X))<=>(patient(X)<~>kind(X))))&
((?[X]:((~calm(X)&~wise(X))))<=>(?[X]:(funny(X))))&
(![X]:((~humble(X)|generous(X))=>(~quiet(X)&humble(X))))&
((?[X]:(~brave(X)))<=>((curious(paul)&~strong(paul))))&
(![X]:((~happy(X)|creative(X))<=>(quiet(X)|old(X))))&
(![X]:((rich(X)&old(X))<=>(~creative(X)|funny(X))))&
((rich(john)&~tall(john)))&
(?[X]:(generous(X)))&
(?[X]:((old(X)<~>~brave(X))))&
((curious(fred)&~old(fred)))&
((~creative(fred)<~>kind(fred)))&
(?[X]:((patient(X)&~rich(X)))) | ~funny(fred) | [
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7860789988603605964796360
% SZS output start Proof for 7860789988603605964796360
15. ! [X0] : ((old(X0) & rich(X0)) <=> (funny(X0) | ~creative(X0))) [input p14]
19. ~old(fred) & curious(fred) [input p18]
22. funny(fred) [input hypothesis]
53. ! [X0] : (((old(X0) & rich(X0)) | (~funny(X0) & creative(X0))) & ((funny(X0) | ~creative(X0)) | (~old(X0) | ~rich(X0)))) [nnf transformation 15]
54. ! [X0] : (((old(X0) & rich(X0)) | (~funny(X0) & creative(X0))) & (funny(X0) | ~creative(X0) | ~old(X0) | ~rich(X0))) [flattening 53]
109. ~funny(X0) | old(X0) [cnf transformation 54]
116. ~old(fred) [cnf transformation 19]
121. funny(fred) [cnf transformation 22]
246. old(fred) [resolution 109,121]
248. $false [subsumption resolution 246,116]
% SZS output end Proof for 7860789988603605964796360
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not tall is both old and kind and vice versa.
If susan is generous or not brave then susan is generous or not tall and vice versa.
Everyone who is rich is both calm and not strong.
If someone is strong then someone is wise and vice versa.
Everyone who is both wise and creative is either not happy or not rich and vice versa.
Everyone who is not curious is old.
Everyone who is both wise and tall is not humble or curious and vice versa.
Everyone who is both not rich and funny is not quiet.
If alice is both not kind and quiet then alice is not rich or humble.
Everyone who is either strong or wise is either not calm or not old and vice versa.
Everyone who is not old or rich is wise or not curious and vice versa.
If susan is happy or tall then paul is generous or wise.
If fred is not quiet then susan is curious or not quiet.
Everyone who is both not patient and not old is either not tall or not generous.
Everyone who is not kind is both not quiet and not calm.
Everyone who is not tall or not wise is either not happy or not wise and vice versa.
Someone is both rich and kind.
Fred is either not wise or tall.
Fred is both not rich and not patient.
Someone is kind or strong.
Alice is either funny or wise.
Alice is strong.
Lucy is quiet or not calm.
Someone is not happy or tall. | Alice is not happy. | contradiction | (![X]:((humble(X)<~>~tall(X))<=>(old(X)&kind(X))))&
(((generous(susan)|~brave(susan)))<=>((generous(susan)|~tall(susan))))&
(![X]:(rich(X)=>(calm(X)&~strong(X))))&
((?[X]:(strong(X)))<=>(?[X]:(wise(X))))&
(![X]:((wise(X)&creative(X))<=>(~happy(X)<~>~rich(X))))&
(![X]:(~curious(X)=>old(X)))&
(![X]:((wise(X)&tall(X))<=>(~humble(X)|curious(X))))&
(![X]:((~rich(X)&funny(X))=>~quiet(X)))&
(((~kind(alice)&quiet(alice)))=>((~rich(alice)|humble(alice))))&
(![X]:((strong(X)<~>wise(X))<=>(~calm(X)<~>~old(X))))&
(![X]:((~old(X)|rich(X))<=>(wise(X)|~curious(X))))&
(((happy(susan)|tall(susan)))=>((generous(paul)|wise(paul))))&
((~quiet(fred))=>((curious(susan)|~quiet(susan))))&
(![X]:((~patient(X)&~old(X))=>(~tall(X)<~>~generous(X))))&
(![X]:(~kind(X)=>(~quiet(X)&~calm(X))))&
(![X]:((~tall(X)|~wise(X))<=>(~happy(X)<~>~wise(X))))&
(?[X]:((rich(X)&kind(X))))&
((~wise(fred)<~>tall(fred)))&
((~rich(fred)&~patient(fred)))&
(?[X]:((kind(X)|strong(X))))&
((funny(alice)<~>wise(alice)))&
(strong(alice))&
((quiet(lucy)|~calm(lucy)))&
(?[X]:((~happy(X)|tall(X)))) | ~happy(alice) | [
"p2",
"p5",
"p6",
"p10",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1498357201644692328796173
% SZS output start Proof for 1498357201644692328796173
3. ! [X0] : (rich(X0) => (~strong(X0) & calm(X0))) [input p2]
6. ! [X0] : (~curious(X0) => old(X0)) [input p5]
7. ! [X0] : ((tall(X0) & wise(X0)) <=> (curious(X0) | ~humble(X0))) [input p6]
11. ! [X0] : ((rich(X0) | ~old(X0)) <=> (~curious(X0) | wise(X0))) [input p10]
16. ! [X0] : ((~wise(X0) | ~tall(X0)) <=> (~happy(X0) <~> ~wise(X0))) [input p15]
22. strong(alice) [input p21]
25. ~happy(alice) [input hypothesis]
27. ! [X0] : ((~strong(X0) & calm(X0)) | ~rich(X0)) [ennf transformation 3]
28. ! [X0] : (old(X0) | curious(X0)) [ennf transformation 6]
51. ! [X0] : (((tall(X0) & wise(X0)) | (~curious(X0) & humble(X0))) & ((curious(X0) | ~humble(X0)) | (~tall(X0) | ~wise(X0)))) [nnf transformation 7]
52. ! [X0] : (((tall(X0) & wise(X0)) | (~curious(X0) & humble(X0))) & (curious(X0) | ~humble(X0) | ~tall(X0) | ~wise(X0))) [flattening 51]
54. ! [X0] : (((rich(X0) | ~old(X0)) | (curious(X0) & ~wise(X0))) & ((~curious(X0) | wise(X0)) | (~rich(X0) & old(X0)))) [nnf transformation 11]
55. ! [X0] : ((rich(X0) | ~old(X0) | (curious(X0) & ~wise(X0))) & (~curious(X0) | wise(X0) | (~rich(X0) & old(X0)))) [flattening 54]
57. ! [X0] : (((~wise(X0) | ~tall(X0)) | ((~happy(X0) | wise(X0)) & (~wise(X0) | happy(X0)))) & (((wise(X0) | happy(X0)) & (~wise(X0) | ~happy(X0))) | (wise(X0) & tall(X0)))) [nnf transformation 16]
58. ! [X0] : ((~wise(X0) | ~tall(X0) | ((~happy(X0) | wise(X0)) & (~wise(X0) | happy(X0)))) & (((wise(X0) | happy(X0)) & (~wise(X0) | ~happy(X0))) | (wise(X0) & tall(X0)))) [flattening 57]
78. ~strong(X0) | ~rich(X0) [cnf transformation 27]
87. curious(X0) | old(X0) [cnf transformation 28]
92. ~curious(X0) | tall(X0) [cnf transformation 52]
106. rich(X0) | ~old(X0) | curious(X0) [cnf transformation 55]
117. wise(X0) | happy(X0) | wise(X0) [cnf transformation 58]
118. ~wise(X0) | ~tall(X0) | ~wise(X0) | happy(X0) [cnf transformation 58]
129. strong(alice) [cnf transformation 22]
132. ~happy(alice) [cnf transformation 25]
133. happy(X0) | wise(X0) [duplicate literal removal 117]
134. ~wise(X0) | ~tall(X0) | happy(X0) [duplicate literal removal 118]
174. 10 <=> rich(alice) [avatar definition]
176. ~rich(alice) <- (~10) [avatar component clause 174]
182. curious(X0) | rich(X0) [subsumption resolution 106,87]
234. 23 <=> wise(alice) [avatar definition]
235. wise(alice) <- (23) [avatar component clause 234]
262. ~rich(alice) [resolution 78,129]
272. wise(alice) [resolution 133,132]
277. 23 [avatar split clause 272,234]
278. rich(X0) | tall(X0) [resolution 182,92]
286. tall(alice) <- (~10) [resolution 278,176]
407. ~tall(alice) | happy(alice) <- (23) [resolution 134,235]
413. happy(alice) <- (~10, 23) [subsumption resolution 407,286]
414. $false <- (~10, 23) [subsumption resolution 413,132]
415. 10 | ~23 [avatar contradiction clause 414]
421. ~10 [avatar split clause 262,174]
422. $false [avatar sat refutation 277,415,421]
% SZS output end Proof for 1498357201644692328796173
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is not old then someone is happy.
Everyone who is old is either not humble or brave and vice versa.
Everyone who is either not curious or not quiet is not creative and vice versa.
If john is either creative or not funny then paul is happy or humble and vice versa.
Everyone who is kind is curious.
If mary is happy then someone is either not old or not generous.
Everyone who is happy or not wise is either kind or not generous and vice versa.
Everyone who is not quiet is either not quiet or not creative.
Everyone who is generous or creative is wise.
If mary is not patient or not happy then alice is not calm and vice versa.
If someone is kind or not funny then lucy is old or not happy and vice versa.
If alice is both brave and not tall then alice is kind and vice versa.
Everyone who is not patient is not tall or humble and vice versa.
Everyone who is not rich is not creative or curious.
Everyone who is either old or kind is not rich or happy.
Everyone who is calm or not creative is either not patient or calm and vice versa.
Alice is patient or not creative.
John is both kind and old.
Fred is tall.
Someone is not funny or not calm.
Someone is not tall or calm.
Someone is both funny and not kind.
Alice is patient. | Paul is tall. | neutral | ((~old(alice))=>(?[X]:(happy(X))))&
(![X]:(old(X)<=>(~humble(X)<~>brave(X))))&
(![X]:((~curious(X)<~>~quiet(X))<=>~creative(X)))&
(((creative(john)<~>~funny(john)))<=>((happy(paul)|humble(paul))))&
(![X]:(kind(X)=>curious(X)))&
((happy(mary))=>(?[X]:((~old(X)<~>~generous(X)))))&
(![X]:((happy(X)|~wise(X))<=>(kind(X)<~>~generous(X))))&
(![X]:(~quiet(X)=>(~quiet(X)<~>~creative(X))))&
(![X]:((generous(X)|creative(X))=>wise(X)))&
(((~patient(mary)|~happy(mary)))<=>(~calm(alice)))&
((?[X]:((kind(X)|~funny(X))))<=>((old(lucy)|~happy(lucy))))&
(((brave(alice)&~tall(alice)))<=>(kind(alice)))&
(![X]:(~patient(X)<=>(~tall(X)|humble(X))))&
(![X]:(~rich(X)=>(~creative(X)|curious(X))))&
(![X]:((old(X)<~>kind(X))=>(~rich(X)|happy(X))))&
(![X]:((calm(X)|~creative(X))<=>(~patient(X)<~>calm(X))))&
((patient(alice)|~creative(alice)))&
((kind(john)&old(john)))&
(tall(fred))&
(?[X]:((~funny(X)|~calm(X))))&
(?[X]:((~tall(X)|calm(X))))&
(?[X]:((funny(X)&~kind(X))))&
(patient(alice)) | tall(paul) | [] | null | 0 |
Everyone who is wise is generous and vice versa.
If susan is either not kind or old then paul is not happy.
If someone is quiet then paul is not old or not kind.
Everyone who is wise is humble and vice versa.
Everyone who is generous is either not funny or rich.
If mary is strong or calm then someone is both brave and happy and vice versa.
If fred is either not funny or patient then someone is not quiet and vice versa.
If someone is not quiet or not humble then paul is calm and vice versa.
Everyone who is either not strong or happy is not happy and vice versa.
Everyone who is both curious and tall is rich and vice versa.
If alice is both tall and not patient then someone is happy and vice versa.
Everyone who is either kind or patient is humble and vice versa.
Everyone who is not patient or not wise is both not kind and brave.
If someone is generous or wise then someone is not tall or generous.
Everyone who is either curious or wise is not rich and vice versa.
Mary is either tall or not generous.
Susan is funny.
Someone is creative.
Someone is either not creative or strong.
Someone is both wise and not strong.
Lucy is not old or not creative.
Someone is not tall.
Mary is either not quiet or not rich. | Lucy is not strong. | entailment | (![X]:(wise(X)<=>generous(X)))&
(((~kind(susan)<~>old(susan)))=>(~happy(paul)))&
((?[X]:(quiet(X)))=>((~old(paul)|~kind(paul))))&
(![X]:(wise(X)<=>humble(X)))&
(![X]:(generous(X)=>(~funny(X)<~>rich(X))))&
(((strong(mary)|calm(mary)))<=>(?[X]:((brave(X)&happy(X)))))&
(((~funny(fred)<~>patient(fred)))<=>(?[X]:(~quiet(X))))&
((?[X]:((~quiet(X)|~humble(X))))<=>(calm(paul)))&
(![X]:((~strong(X)<~>happy(X))<=>~happy(X)))&
(![X]:((curious(X)&tall(X))<=>rich(X)))&
(((tall(alice)&~patient(alice)))<=>(?[X]:(happy(X))))&
(![X]:((kind(X)<~>patient(X))<=>humble(X)))&
(![X]:((~patient(X)|~wise(X))=>(~kind(X)&brave(X))))&
((?[X]:((generous(X)|wise(X))))=>(?[X]:((~tall(X)|generous(X)))))&
(![X]:((curious(X)<~>wise(X))<=>~rich(X)))&
((tall(mary)<~>~generous(mary)))&
(funny(susan))&
(?[X]:(creative(X)))&
(?[X]:((~creative(X)<~>strong(X))))&
(?[X]:((wise(X)&~strong(X))))&
((~old(lucy)|~creative(lucy)))&
(?[X]:(~tall(X)))&
((~quiet(mary)<~>~rich(mary))) | ~strong(lucy) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8406137614171157921182849
% SZS output start Proof for 8406137614171157921182849
9. ! [X0] : ((~strong(X0) <~> happy(X0)) <=> ~happy(X0)) [input p8]
24. strong(lucy) [input hypothesis]
49. ! [X0] : ((((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | happy(X0)) & (~happy(X0) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0))))) [nnf transformation 9]
95. ~happy(X0) | ~strong(X0) | ~happy(X0) [cnf transformation 49]
96. happy(X0) | ~strong(X0) | happy(X0) [cnf transformation 49]
130. strong(lucy) [cnf transformation 24]
131. ~happy(X0) | ~strong(X0) [duplicate literal removal 95]
132. happy(X0) | ~strong(X0) [duplicate literal removal 96]
220. ~strong(X0) [subsumption resolution 131,132]
287. $false [subsumption resolution 130,220]
% SZS output end Proof for 8406137614171157921182849
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is both happy and not calm and vice versa. If someone is either brave or not old then someone is quiet or not happy and vice versa. Everyone who is both not creative and not quiet is not curious. Everyone who is curious or funny is not strong and vice versa. Everyone who is wise is both humble and not kind and vice versa. If someone is wise or not curious then someone is both not calm and not curious. Everyone who is calm or curious is both humble and creative. Everyone who is both wise and not rich is either not old or not calm and vice versa. If someone is calm then mary is both funny and tall. Everyone who is either not generous or not funny is not patient or brave. Everyone who is not old or wise is both strong and not old. Everyone who is not tall or not brave is not patient or not curious and vice versa. Everyone who is funny is not happy. Everyone who is both not wise and not calm is not strong. Everyone who is happy or not wise is tall. If susan is either curious or old then susan is either kind or not rich and vice versa. Lucy is both humble and happy. Someone is generous or not happy. John is either not curious or not happy. Susan is both creative and wise. Someone is not happy or wise. Someone is either quiet or tall. Mary is both not old and not brave. | Mary is strong. | entailment | (![X]:((wise(X)|funny(X))<=>(happy(X)&~calm(X))))&
((?[X]:((brave(X)<~>~old(X))))<=>(?[X]:((quiet(X)|~happy(X)))))&
(![X]:((~creative(X)&~quiet(X))=>~curious(X)))&
(![X]:((curious(X)|funny(X))<=>~strong(X)))&
(![X]:(wise(X)<=>(humble(X)&~kind(X))))&
((?[X]:((wise(X)|~curious(X))))=>(?[X]:((~calm(X)&~curious(X)))))&
(![X]:((calm(X)|curious(X))=>(humble(X)&creative(X))))&
(![X]:((wise(X)&~rich(X))<=>(~old(X)<~>~calm(X))))&
((?[X]:(calm(X)))=>((funny(mary)&tall(mary))))&
(![X]:((~generous(X)<~>~funny(X))=>(~patient(X)|brave(X))))&
(![X]:((~old(X)|wise(X))=>(strong(X)&~old(X))))&
(![X]:((~tall(X)|~brave(X))<=>(~patient(X)|~curious(X))))&
(![X]:(funny(X)=>~happy(X)))&
(![X]:((~wise(X)&~calm(X))=>~strong(X)))&
(![X]:((happy(X)|~wise(X))=>tall(X)))&
(((curious(susan)<~>old(susan)))<=>((kind(susan)<~>~rich(susan))))&
((humble(lucy)&happy(lucy)))&
(?[X]:((generous(X)|~happy(X))))&
((~curious(john)<~>~happy(john)))&
((creative(susan)&wise(susan)))&
(?[X]:((~happy(X)|wise(X))))&
(?[X]:((quiet(X)<~>tall(X))))&
((~old(mary)&~brave(mary))) | strong(mary) | [
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4277484864325510505908854
% SZS output start Proof for 4277484864325510505908854
11. ! [X0] : ((wise(X0) | ~old(X0)) => (~old(X0) & strong(X0))) [input p10]
23. ~brave(mary) & ~old(mary) [input p22]
24. ~strong(mary) [input hypothesis]
35. ! [X0] : ((~old(X0) & strong(X0)) | (~wise(X0) & old(X0))) [ennf transformation 11]
101. strong(X0) | old(X0) [cnf transformation 35]
130. ~old(mary) [cnf transformation 23]
132. ~strong(mary) [cnf transformation 24]
266. old(mary) [resolution 101,132]
269. $false [subsumption resolution 266,130]
% SZS output end Proof for 4277484864325510505908854
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not generous is generous and vice versa.
If susan is not calm then someone is either not strong or not wise and vice versa.
Everyone who is either not wise or quiet is either not wise or curious.
Everyone who is either curious or not curious is either not tall or old and vice versa.
If someone is both rich and not old then someone is strong and vice versa.
If mary is happy then alice is both calm and not calm and vice versa.
If someone is not humble or not wise then fred is not patient and vice versa.
If someone is both not old and not creative then paul is not funny.
If fred is either tall or brave then lucy is either not creative or generous and vice versa.
If fred is both not funny and quiet then someone is both funny and rich and vice versa.
Everyone who is curious or wise is both calm and not tall.
Everyone who is brave or not kind is not kind or rich and vice versa.
If alice is generous or humble then paul is not calm.
If someone is either rich or kind then someone is wise and vice versa.
Someone is not kind or generous.
Paul is either kind or rich.
Someone is happy or not old.
Susan is either old or not funny.
Someone is either not wise or kind. | Mary is brave. | neutral | (![X]:((strong(X)<~>~generous(X))<=>generous(X)))&
((~calm(susan))<=>(?[X]:((~strong(X)<~>~wise(X)))))&
(![X]:((~wise(X)<~>quiet(X))=>(~wise(X)<~>curious(X))))&
(![X]:((curious(X)<~>~curious(X))<=>(~tall(X)<~>old(X))))&
((?[X]:((rich(X)&~old(X))))<=>(?[X]:(strong(X))))&
((happy(mary))<=>((calm(alice)&~calm(alice))))&
((?[X]:((~humble(X)|~wise(X))))<=>(~patient(fred)))&
((?[X]:((~old(X)&~creative(X))))=>(~funny(paul)))&
(((tall(fred)<~>brave(fred)))<=>((~creative(lucy)<~>generous(lucy))))&
(((~funny(fred)&quiet(fred)))<=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((curious(X)|wise(X))=>(calm(X)&~tall(X))))&
(![X]:((brave(X)|~kind(X))<=>(~kind(X)|rich(X))))&
(((generous(alice)|humble(alice)))=>(~calm(paul)))&
((?[X]:((rich(X)<~>kind(X))))<=>(?[X]:(wise(X))))&
(?[X]:((~kind(X)|generous(X))))&
((kind(paul)<~>rich(paul)))&
(?[X]:((happy(X)|~old(X))))&
((old(susan)<~>~funny(susan)))&
(?[X]:((~wise(X)<~>kind(X)))) | brave(mary) | [] | null | 0 |
If mary is kind or creative then mary is either rich or not brave and vice versa.
Everyone who is either wise or not creative is not generous.
If someone is both not humble and happy then susan is patient and vice versa.
Everyone who is both kind and rich is strong or quiet.
If someone is both humble and not generous then someone is both not happy and not creative.
If someone is kind then someone is patient.
Everyone who is not kind or humble is not curious.
If john is either not humble or old then fred is both calm and quiet and vice versa.
Everyone who is strong is funny and vice versa.
Everyone who is happy or rich is either wise or humble and vice versa.
Everyone who is both not rich and not brave is both old and generous and vice versa.
Everyone who is not patient is not curious.
If john is either calm or funny then someone is either generous or not humble.
If paul is not funny or old then lucy is generous and vice versa.
If someone is not wise then mary is either not humble or not old.
Everyone who is either strong or calm is not wise or not quiet and vice versa.
Lucy is not rich or not kind.
Alice is either brave or kind.
Someone is not strong.
Someone is humble.
Alice is not tall.
Someone is calm or brave.
Someone is either not curious or happy.
Fred is both not curious and not strong. | Fred is not funny. | entailment | (((kind(mary)|creative(mary)))<=>((rich(mary)<~>~brave(mary))))&
(![X]:((wise(X)<~>~creative(X))=>~generous(X)))&
((?[X]:((~humble(X)&happy(X))))<=>(patient(susan)))&
(![X]:((kind(X)&rich(X))=>(strong(X)|quiet(X))))&
((?[X]:((humble(X)&~generous(X))))=>(?[X]:((~happy(X)&~creative(X)))))&
((?[X]:(kind(X)))=>(?[X]:(patient(X))))&
(![X]:((~kind(X)|humble(X))=>~curious(X)))&
(((~humble(john)<~>old(john)))<=>((calm(fred)&quiet(fred))))&
(![X]:(strong(X)<=>funny(X)))&
(![X]:((happy(X)|rich(X))<=>(wise(X)<~>humble(X))))&
(![X]:((~rich(X)&~brave(X))<=>(old(X)&generous(X))))&
(![X]:(~patient(X)=>~curious(X)))&
(((calm(john)<~>funny(john)))=>(?[X]:((generous(X)<~>~humble(X)))))&
(((~funny(paul)|old(paul)))<=>(generous(lucy)))&
((?[X]:(~wise(X)))=>((~humble(mary)<~>~old(mary))))&
(![X]:((strong(X)<~>calm(X))<=>(~wise(X)|~quiet(X))))&
((~rich(lucy)|~kind(lucy)))&
((brave(alice)<~>kind(alice)))&
(?[X]:(~strong(X)))&
(?[X]:(humble(X)))&
(~tall(alice))&
(?[X]:((calm(X)|brave(X))))&
(?[X]:((~curious(X)<~>happy(X))))&
((~curious(fred)&~strong(fred))) | ~funny(fred) | [
"p8",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2462153424418448386487235
% SZS output start Proof for 2462153424418448386487235
9. ! [X0] : (strong(X0) <=> funny(X0)) [input p8]
24. ~strong(fred) & ~curious(fred) [input p23]
25. funny(fred) [input hypothesis]
53. ! [X0] : ((strong(X0) | ~funny(X0)) & (funny(X0) | ~strong(X0))) [nnf transformation 9]
100. ~funny(X0) | strong(X0) [cnf transformation 53]
136. ~strong(fred) [cnf transformation 24]
137. funny(fred) [cnf transformation 25]
307. strong(fred) [resolution 100,137]
308. $false [subsumption resolution 307,136]
% SZS output end Proof for 2462153424418448386487235
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not wise then john is not brave and vice versa.
Everyone who is generous is wise and vice versa.
If lucy is not kind or quiet then someone is either creative or strong.
Everyone who is patient is not creative or patient.
If someone is old or calm then someone is not kind and vice versa.
Everyone who is either not kind or old is humble and vice versa.
If lucy is both rich and not patient then someone is both not humble and not happy.
Everyone who is both not patient and not old is brave or not happy.
Everyone who is either not humble or not wise is strong or kind and vice versa.
Everyone who is either not quiet or wise is not creative or tall.
If fred is not curious then mary is either brave or not old.
If john is not curious then lucy is not funny.
If someone is both generous and curious then susan is not patient or quiet.
If susan is not quiet or brave then someone is either not patient or not creative.
Mary is either not humble or humble.
Paul is happy or wise.
Alice is either wise or quiet.
Lucy is both not calm and not kind.
Paul is either not kind or not old.
Someone is either not happy or brave. | Mary is not happy. | neutral | ((?[X]:((generous(X)|~wise(X))))<=>(~brave(john)))&
(![X]:(generous(X)<=>wise(X)))&
(((~kind(lucy)|quiet(lucy)))=>(?[X]:((creative(X)<~>strong(X)))))&
(![X]:(patient(X)=>(~creative(X)|patient(X))))&
((?[X]:((old(X)|calm(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~kind(X)<~>old(X))<=>humble(X)))&
(((rich(lucy)&~patient(lucy)))=>(?[X]:((~humble(X)&~happy(X)))))&
(![X]:((~patient(X)&~old(X))=>(brave(X)|~happy(X))))&
(![X]:((~humble(X)<~>~wise(X))<=>(strong(X)|kind(X))))&
(![X]:((~quiet(X)<~>wise(X))=>(~creative(X)|tall(X))))&
((~curious(fred))=>((brave(mary)<~>~old(mary))))&
((~curious(john))=>(~funny(lucy)))&
((?[X]:((generous(X)&curious(X))))=>((~patient(susan)|quiet(susan))))&
(((~quiet(susan)|brave(susan)))=>(?[X]:((~patient(X)<~>~creative(X)))))&
((~humble(mary)<~>humble(mary)))&
((happy(paul)|wise(paul)))&
((wise(alice)<~>quiet(alice)))&
((~calm(lucy)&~kind(lucy)))&
((~kind(paul)<~>~old(paul)))&
(?[X]:((~happy(X)<~>brave(X)))) | ~happy(mary) | [] | null | 0 |
If paul is both not funny and tall then someone is old or not brave and vice versa.
If someone is rich or not calm then someone is both calm and not strong and vice versa.
If lucy is either not quiet or not calm then john is either not funny or wise.
Everyone who is both happy and funny is both happy and strong and vice versa.
Everyone who is humble or generous is tall.
If someone is both not happy and curious then someone is not brave or creative and vice versa.
Everyone who is both happy and not creative is generous.
Everyone who is strong is quiet or old.
Everyone who is not strong is either kind or not generous and vice versa.
Everyone who is kind or calm is either happy or not humble and vice versa.
Everyone who is either funny or kind is either not generous or not curious and vice versa.
Everyone who is patient is tall and vice versa.
Everyone who is patient is both kind and not creative.
Everyone who is humble or not humble is either not brave or not funny.
If paul is creative then someone is either quiet or brave and vice versa.
If john is both curious and rich then someone is calm.
Lucy is both strong and not wise.
Someone is either quiet or strong.
Someone is either not rich or not calm.
Alice is humble or brave.
Someone is not kind or humble.
Susan is either rich or old.
Someone is either not old or old.
Alice is both not quiet and not patient. | Lucy is not happy. | entailment | (((~funny(paul)&tall(paul)))<=>(?[X]:((old(X)|~brave(X)))))&
((?[X]:((rich(X)|~calm(X))))<=>(?[X]:((calm(X)&~strong(X)))))&
(((~quiet(lucy)<~>~calm(lucy)))=>((~funny(john)<~>wise(john))))&
(![X]:((happy(X)&funny(X))<=>(happy(X)&strong(X))))&
(![X]:((humble(X)|generous(X))=>tall(X)))&
((?[X]:((~happy(X)&curious(X))))<=>(?[X]:((~brave(X)|creative(X)))))&
(![X]:((happy(X)&~creative(X))=>generous(X)))&
(![X]:(strong(X)=>(quiet(X)|old(X))))&
(![X]:(~strong(X)<=>(kind(X)<~>~generous(X))))&
(![X]:((kind(X)|calm(X))<=>(happy(X)<~>~humble(X))))&
(![X]:((funny(X)<~>kind(X))<=>(~generous(X)<~>~curious(X))))&
(![X]:(patient(X)<=>tall(X)))&
(![X]:(patient(X)=>(kind(X)&~creative(X))))&
(![X]:((humble(X)|~humble(X))=>(~brave(X)<~>~funny(X))))&
((creative(paul))<=>(?[X]:((quiet(X)<~>brave(X)))))&
(((curious(john)&rich(john)))=>(?[X]:(calm(X))))&
((strong(lucy)&~wise(lucy)))&
(?[X]:((quiet(X)<~>strong(X))))&
(?[X]:((~rich(X)<~>~calm(X))))&
((humble(alice)|brave(alice)))&
(?[X]:((~kind(X)|humble(X))))&
((rich(susan)<~>old(susan)))&
(?[X]:((~old(X)<~>old(X))))&
((~quiet(alice)&~patient(alice))) | ~happy(lucy) | [
"p0",
"p3",
"p4",
"p11",
"p12",
"p13",
"p14",
"p16",
"p19",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1935123192432723999939874
% SZS output start Proof for 1935123192432723999939874
1. (tall(paul) & ~funny(paul)) <=> ? [X0] : (~brave(X0) | old(X0)) [input p0]
4. ! [X0] : ((funny(X0) & happy(X0)) <=> (strong(X0) & happy(X0))) [input p3]
5. ! [X0] : ((generous(X0) | humble(X0)) => tall(X0)) [input p4]
12. ! [X0] : (patient(X0) <=> tall(X0)) [input p11]
13. ! [X0] : (patient(X0) => (~creative(X0) & kind(X0))) [input p12]
14. ! [X0] : ((~humble(X0) | humble(X0)) => (~brave(X0) <~> ~funny(X0))) [input p13]
15. creative(paul) <=> ? [X0] : (quiet(X0) <~> brave(X0)) [input p14]
17. ~wise(lucy) & strong(lucy) [input p16]
20. brave(alice) | humble(alice) [input p19]
24. ~patient(alice) & ~quiet(alice) [input p23]
25. happy(lucy) [input hypothesis]
28. ! [X0] : (tall(X0) => patient(X0)) [unused predicate definition removal 12]
30. ! [X0] : (tall(X0) | (~generous(X0) & ~humble(X0))) [ennf transformation 5]
35. ! [X0] : (patient(X0) | ~tall(X0)) [ennf transformation 28]
36. ! [X0] : ((~creative(X0) & kind(X0)) | ~patient(X0)) [ennf transformation 13]
37. ! [X0] : ((~brave(X0) <~> ~funny(X0)) | (humble(X0) & ~humble(X0))) [ennf transformation 14]
40. ((tall(paul) & ~funny(paul)) | ! [X0] : (brave(X0) & ~old(X0))) & (? [X0] : (~brave(X0) | old(X0)) | (~tall(paul) | funny(paul))) [nnf transformation 1]
41. ((tall(paul) & ~funny(paul)) | ! [X0] : (brave(X0) & ~old(X0))) & (? [X0] : (~brave(X0) | old(X0)) | ~tall(paul) | funny(paul)) [flattening 40]
42. ((tall(paul) & ~funny(paul)) | ! [X0] : (brave(X0) & ~old(X0))) & (? [X1] : (~brave(X1) | old(X1)) | ~tall(paul) | funny(paul)) [rectify 41]
43. ? [X1] : (~brave(X1) | old(X1)) => (~brave(sK0) | old(sK0)) [choice axiom]
44. ((tall(paul) & ~funny(paul)) | ! [X0] : (brave(X0) & ~old(X0))) & ((~brave(sK0) | old(sK0)) | ~tall(paul) | funny(paul)) [skolemisation 42,43]
51. ! [X0] : (((funny(X0) & happy(X0)) | (~strong(X0) | ~happy(X0))) & ((strong(X0) & happy(X0)) | (~funny(X0) | ~happy(X0)))) [nnf transformation 4]
52. ! [X0] : (((funny(X0) & happy(X0)) | ~strong(X0) | ~happy(X0)) & ((strong(X0) & happy(X0)) | ~funny(X0) | ~happy(X0))) [flattening 51]
62. ! [X0] : (((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | (humble(X0) & ~humble(X0))) [nnf transformation 37]
63. (creative(paul) | ! [X0] : ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0)))) & (? [X0] : ((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | ~creative(paul)) [nnf transformation 15]
64. (creative(paul) | ! [X0] : ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0)))) & (? [X1] : ((~brave(X1) | ~quiet(X1)) & (brave(X1) | quiet(X1))) | ~creative(paul)) [rectify 63]
65. ? [X1] : ((~brave(X1) | ~quiet(X1)) & (brave(X1) | quiet(X1))) => ((~brave(sK5) | ~quiet(sK5)) & (brave(sK5) | quiet(sK5))) [choice axiom]
66. (creative(paul) | ! [X0] : ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0)))) & (((~brave(sK5) | ~quiet(sK5)) & (brave(sK5) | quiet(sK5))) | ~creative(paul)) [skolemisation 64,65]
85. tall(paul) | brave(X0) [cnf transformation 44]
98. ~happy(X0) | ~strong(X0) | funny(X0) [cnf transformation 52]
99. ~humble(X0) | tall(X0) [cnf transformation 30]
126. ~tall(X0) | patient(X0) [cnf transformation 35]
128. ~patient(X0) | ~creative(X0) [cnf transformation 36]
129. ~funny(X0) | ~brave(X0) | ~humble(X0) [cnf transformation 62]
130. ~funny(X0) | ~brave(X0) | humble(X0) [cnf transformation 62]
136. creative(paul) | quiet(X0) | ~brave(X0) [cnf transformation 66]
138. strong(lucy) [cnf transformation 17]
144. brave(alice) | humble(alice) [cnf transformation 20]
150. ~quiet(alice) [cnf transformation 24]
151. ~patient(alice) [cnf transformation 24]
152. happy(lucy) [cnf transformation 25]
154. 1 <=> ! [X0] : brave(X0) [avatar definition]
155. brave(X0) <- (1) [avatar component clause 154]
157. 2 <=> tall(paul) [avatar definition]
159. tall(paul) <- (2) [avatar component clause 157]
160. 1 | 2 [avatar split clause 85,157,154]
258. ~brave(X0) | ~funny(X0) [subsumption resolution 129,130]
260. 24 <=> ! [X0] : (quiet(X0) | ~brave(X0)) [avatar definition]
261. ~brave(X0) | quiet(X0) <- (24) [avatar component clause 260]
263. 25 <=> creative(paul) [avatar definition]
266. 24 | 25 [avatar split clause 136,263,260]
315. 36 <=> humble(alice) [avatar definition]
317. humble(alice) <- (36) [avatar component clause 315]
319. 37 <=> brave(alice) [avatar definition]
321. brave(alice) <- (37) [avatar component clause 319]
322. 36 | 37 [avatar split clause 144,319,315]
349. tall(alice) <- (36) [resolution 99,317]
350. patient(paul) <- (2) [resolution 126,159]
351. patient(alice) <- (36) [resolution 126,349]
352. $false <- (36) [subsumption resolution 351,151]
353. ~36 [avatar contradiction clause 352]
355. ~creative(paul) <- (2) [resolution 128,350]
364. quiet(alice) <- (24, 37) [resolution 261,321]
366. $false <- (24, 37) [subsumption resolution 364,150]
367. ~24 | ~37 [avatar contradiction clause 366]
368. ~25 | ~2 [avatar split clause 355,157,263]
371. ~funny(X0) <- (1) [resolution 155,258]
386. ~strong(lucy) | funny(lucy) [resolution 98,152]
387. funny(lucy) [subsumption resolution 386,138]
388. $false <- (1) [subsumption resolution 387,371]
389. ~1 [avatar contradiction clause 388]
390. $false [avatar sat refutation 160,266,322,353,367,368,389]
% SZS output end Proof for 1935123192432723999939874
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and not generous then someone is both curious and not rich and vice versa.
If paul is either not curious or quiet then susan is both not wise and not curious.
Everyone who is either curious or funny is funny and vice versa.
If alice is either quiet or wise then someone is both curious and not rich and vice versa.
Everyone who is not wise is both brave and generous and vice versa.
If john is not kind or not quiet then someone is not wise or not kind.
If someone is either not calm or not happy then someone is kind or rich and vice versa.
Everyone who is both brave and creative is either tall or generous.
If susan is not creative or kind then paul is happy and vice versa.
If someone is both patient and not curious then paul is brave.
If someone is not rich or wise then paul is strong or not tall.
Everyone who is either not brave or not happy is creative or brave and vice versa.
If someone is wise or happy then someone is not tall and vice versa.
If someone is not creative or not strong then paul is either strong or kind and vice versa.
If mary is both not humble and curious then someone is not brave or creative.
If someone is calm then someone is humble.
Mary is either not wise or curious.
Someone is not generous.
Someone is either curious or quiet.
Susan is either brave or strong.
Someone is both tall and wise.
Paul is both not quiet and rich.
Someone is both not happy and calm.
Someone is not humble. | Mary is not generous. | contradiction | ((?[X]:((~tall(X)&~generous(X))))<=>(?[X]:((curious(X)&~rich(X)))))&
(((~curious(paul)<~>quiet(paul)))=>((~wise(susan)&~curious(susan))))&
(![X]:((curious(X)<~>funny(X))<=>funny(X)))&
(((quiet(alice)<~>wise(alice)))<=>(?[X]:((curious(X)&~rich(X)))))&
(![X]:(~wise(X)<=>(brave(X)&generous(X))))&
(((~kind(john)|~quiet(john)))=>(?[X]:((~wise(X)|~kind(X)))))&
((?[X]:((~calm(X)<~>~happy(X))))<=>(?[X]:((kind(X)|rich(X)))))&
(![X]:((brave(X)&creative(X))=>(tall(X)<~>generous(X))))&
(((~creative(susan)|kind(susan)))<=>(happy(paul)))&
((?[X]:((patient(X)&~curious(X))))=>(brave(paul)))&
((?[X]:((~rich(X)|wise(X))))=>((strong(paul)|~tall(paul))))&
(![X]:((~brave(X)<~>~happy(X))<=>(creative(X)|brave(X))))&
((?[X]:((wise(X)|happy(X))))<=>(?[X]:(~tall(X))))&
((?[X]:((~creative(X)|~strong(X))))<=>((strong(paul)<~>kind(paul))))&
(((~humble(mary)&curious(mary)))=>(?[X]:((~brave(X)|creative(X)))))&
((?[X]:(calm(X)))=>(?[X]:(humble(X))))&
((~wise(mary)<~>curious(mary)))&
(?[X]:(~generous(X)))&
(?[X]:((curious(X)<~>quiet(X))))&
((brave(susan)<~>strong(susan)))&
(?[X]:((tall(X)&wise(X))))&
((~quiet(paul)&rich(paul)))&
(?[X]:((~happy(X)&calm(X))))&
(?[X]:(~humble(X))) | ~generous(mary) | [
"p2",
"p4",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1353877747712883240413222
% SZS output start Proof for 1353877747712883240413222
3. ! [X0] : ((curious(X0) <~> funny(X0)) <=> funny(X0)) [input p2]
5. ! [X0] : (~wise(X0) <=> (generous(X0) & brave(X0))) [input p4]
17. ~wise(mary) <~> curious(mary) [input p16]
25. ~generous(mary) [input hypothesis]
46. ! [X0] : ((((~funny(X0) | ~curious(X0)) & (funny(X0) | curious(X0))) | ~funny(X0)) & (funny(X0) | ((curious(X0) | ~funny(X0)) & (funny(X0) | ~curious(X0))))) [nnf transformation 3]
51. ! [X0] : ((~wise(X0) | (~generous(X0) | ~brave(X0))) & ((generous(X0) & brave(X0)) | wise(X0))) [nnf transformation 5]
52. ! [X0] : ((~wise(X0) | ~generous(X0) | ~brave(X0)) & ((generous(X0) & brave(X0)) | wise(X0))) [flattening 51]
79. (~curious(mary) | wise(mary)) & (curious(mary) | ~wise(mary)) [nnf transformation 17]
100. funny(X0) | funny(X0) | ~curious(X0) [cnf transformation 46]
103. ~funny(X0) | ~curious(X0) | ~funny(X0) [cnf transformation 46]
111. wise(X0) | generous(X0) [cnf transformation 52]
145. curious(mary) | ~wise(mary) [cnf transformation 79]
159. ~generous(mary) [cnf transformation 25]
162. funny(X0) | ~curious(X0) [duplicate literal removal 100]
163. ~funny(X0) | ~curious(X0) [duplicate literal removal 103]
210. ~curious(X0) [subsumption resolution 162,163]
366. ~wise(mary) [subsumption resolution 145,210]
387. generous(mary) [resolution 111,366]
389. $false [subsumption resolution 387,159]
% SZS output end Proof for 1353877747712883240413222
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is humble and vice versa.
If someone is old or not funny then someone is not old and vice versa.
If someone is both not kind and wise then someone is either brave or not rich.
Everyone who is not quiet is both not brave and curious.
If susan is both not curious and calm then someone is both not patient and not rich and vice versa.
If someone is both creative and curious then someone is patient or not funny and vice versa.
If someone is humble or not quiet then someone is both rich and old and vice versa.
If susan is either not funny or not generous then fred is both not calm and not happy.
Everyone who is creative or not strong is not creative.
Everyone who is creative is tall.
Everyone who is both patient and not kind is kind or not generous and vice versa.
Everyone who is both not kind and not creative is either curious or not humble and vice versa.
Everyone who is both brave and not rich is either curious or not wise and vice versa.
Everyone who is both wise and not rich is both not happy and not kind.
Someone is either quiet or strong.
Someone is not brave or creative.
Someone is not rich.
Someone is both strong and not rich.
Someone is not creative. | Susan is not patient. | entailment | (![X]:(~funny(X)<=>humble(X)))&
((?[X]:((old(X)|~funny(X))))<=>(?[X]:(~old(X))))&
((?[X]:((~kind(X)&wise(X))))=>(?[X]:((brave(X)<~>~rich(X)))))&
(![X]:(~quiet(X)=>(~brave(X)&curious(X))))&
(((~curious(susan)&calm(susan)))<=>(?[X]:((~patient(X)&~rich(X)))))&
((?[X]:((creative(X)&curious(X))))<=>(?[X]:((patient(X)|~funny(X)))))&
((?[X]:((humble(X)|~quiet(X))))<=>(?[X]:((rich(X)&old(X)))))&
(((~funny(susan)<~>~generous(susan)))=>((~calm(fred)&~happy(fred))))&
(![X]:((creative(X)|~strong(X))=>~creative(X)))&
(![X]:(creative(X)=>tall(X)))&
(![X]:((patient(X)&~kind(X))<=>(kind(X)|~generous(X))))&
(![X]:((~kind(X)&~creative(X))<=>(curious(X)<~>~humble(X))))&
(![X]:((brave(X)&~rich(X))<=>(curious(X)<~>~wise(X))))&
(![X]:((wise(X)&~rich(X))=>(~happy(X)&~kind(X))))&
(?[X]:((quiet(X)<~>strong(X))))&
(?[X]:((~brave(X)|creative(X))))&
(?[X]:(~rich(X)))&
(?[X]:((strong(X)&~rich(X))))&
(?[X]:(~creative(X))) | ~patient(susan) | [
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4940316061650503529601539
% SZS output start Proof for 4940316061650503529601539
6. ? [X0] : (curious(X0) & creative(X0)) <=> ? [X0] : (~funny(X0) | patient(X0)) [input p5]
9. ! [X0] : ((~strong(X0) | creative(X0)) => ~creative(X0)) [input p8]
20. patient(susan) [input hypothesis]
23. ? [X0] : (curious(X0) & creative(X0)) <=> ? [X1] : (~funny(X1) | patient(X1)) [rectify 6]
31. ! [X0] : (~creative(X0) | (strong(X0) & ~creative(X0))) [ennf transformation 9]
49. (? [X0] : (curious(X0) & creative(X0)) | ! [X1] : (funny(X1) & ~patient(X1))) & (? [X1] : (~funny(X1) | patient(X1)) | ! [X0] : (~curious(X0) | ~creative(X0))) [nnf transformation 23]
50. (? [X0] : (curious(X0) & creative(X0)) | ! [X1] : (funny(X1) & ~patient(X1))) & (? [X2] : (~funny(X2) | patient(X2)) | ! [X3] : (~curious(X3) | ~creative(X3))) [rectify 49]
51. ? [X0] : (curious(X0) & creative(X0)) => (curious(sK4) & creative(sK4)) [choice axiom]
52. ? [X2] : (~funny(X2) | patient(X2)) => (~funny(sK5) | patient(sK5)) [choice axiom]
53. ((curious(sK4) & creative(sK4)) | ! [X1] : (funny(X1) & ~patient(X1))) & ((~funny(sK5) | patient(sK5)) | ! [X3] : (~curious(X3) | ~creative(X3))) [skolemisation 50,52,51]
91. creative(sK4) | ~patient(X1) [cnf transformation 53]
102. ~creative(X0) | ~creative(X0) [cnf transformation 31]
129. patient(susan) [cnf transformation 20]
132. ~creative(X0) [duplicate literal removal 102]
199. 16 <=> ! [X1] : ~patient(X1) [avatar definition]
200. ~patient(X1) <- (16) [avatar component clause 199]
203. 17 <=> creative(sK4) [avatar definition]
205. creative(sK4) <- (17) [avatar component clause 203]
207. 16 | 17 [avatar split clause 91,203,199]
289. $false <- (17) [subsumption resolution 205,132]
290. ~17 [avatar contradiction clause 289]
294. $false <- (16) [resolution 200,129]
295. ~16 [avatar contradiction clause 294]
296. $false [avatar sat refutation 207,290,295]
% SZS output end Proof for 4940316061650503529601539
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious or not happy then someone is either quiet or not funny and vice versa.
Everyone who is not curious or not tall is not tall or kind.
Everyone who is calm is quiet or generous.
If someone is both not calm and not happy then john is not generous or funny and vice versa.
If someone is either happy or brave then fred is not curious or not calm.
Everyone who is rich is old or not patient and vice versa.
If lucy is either tall or not wise then someone is not patient or not wise and vice versa.
If fred is tall then someone is not happy.
Everyone who is not generous is not generous or rich and vice versa.
Everyone who is not quiet is both quiet and rich and vice versa.
If someone is both kind and humble then someone is quiet.
Everyone who is either patient or not strong is patient.
Everyone who is not quiet or not tall is not generous and vice versa.
If someone is both generous and not kind then someone is not creative and vice versa.
Everyone who is both generous and not calm is kind or not wise.
If someone is both quiet and wise then john is not happy and vice versa.
Lucy is either not patient or brave.
Someone is curious or rich.
Mary is not tall or not strong.
Paul is not happy or not tall.
Mary is kind.
Someone is not rich or not creative. | Mary is rich. | contradiction | ((?[X]:((~curious(X)|~happy(X))))<=>(?[X]:((quiet(X)<~>~funny(X)))))&
(![X]:((~curious(X)|~tall(X))=>(~tall(X)|kind(X))))&
(![X]:(calm(X)=>(quiet(X)|generous(X))))&
((?[X]:((~calm(X)&~happy(X))))<=>((~generous(john)|funny(john))))&
((?[X]:((happy(X)<~>brave(X))))=>((~curious(fred)|~calm(fred))))&
(![X]:(rich(X)<=>(old(X)|~patient(X))))&
(((tall(lucy)<~>~wise(lucy)))<=>(?[X]:((~patient(X)|~wise(X)))))&
((tall(fred))=>(?[X]:(~happy(X))))&
(![X]:(~generous(X)<=>(~generous(X)|rich(X))))&
(![X]:(~quiet(X)<=>(quiet(X)&rich(X))))&
((?[X]:((kind(X)&humble(X))))=>(?[X]:(quiet(X))))&
(![X]:((patient(X)<~>~strong(X))=>patient(X)))&
(![X]:((~quiet(X)|~tall(X))<=>~generous(X)))&
((?[X]:((generous(X)&~kind(X))))<=>(?[X]:(~creative(X))))&
(![X]:((generous(X)&~calm(X))=>(kind(X)|~wise(X))))&
((?[X]:((quiet(X)&wise(X))))<=>(~happy(john)))&
((~patient(lucy)<~>brave(lucy)))&
(?[X]:((curious(X)|rich(X))))&
((~tall(mary)|~strong(mary)))&
((~happy(paul)|~tall(paul)))&
(kind(mary))&
(?[X]:((~rich(X)|~creative(X)))) | rich(mary) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6502785730264809605603539
% SZS output start Proof for 6502785730264809605603539
10. ! [X0] : (~quiet(X0) <=> (rich(X0) & quiet(X0))) [input p9]
23. rich(mary) [input hypothesis]
59. ! [X0] : ((~quiet(X0) | (~rich(X0) | ~quiet(X0))) & ((rich(X0) & quiet(X0)) | quiet(X0))) [nnf transformation 10]
60. ! [X0] : ((~quiet(X0) | ~rich(X0) | ~quiet(X0)) & ((rich(X0) & quiet(X0)) | quiet(X0))) [flattening 59]
107. quiet(X0) | quiet(X0) [cnf transformation 60]
109. ~quiet(X0) | ~rich(X0) | ~quiet(X0) [cnf transformation 60]
129. rich(mary) [cnf transformation 23]
131. quiet(X0) [duplicate literal removal 107]
132. ~rich(X0) | ~quiet(X0) [duplicate literal removal 109]
341. ~quiet(mary) [resolution 132,129]
345. $false [subsumption resolution 341,131]
% SZS output end Proof for 6502785730264809605603539
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious or not old then someone is not strong or not happy and vice versa.
Everyone who is quiet or curious is both not curious and calm.
Everyone who is both not quiet and not tall is not strong or not curious and vice versa.
Everyone who is both wise and not patient is either not wise or quiet.
If lucy is either patient or not old then someone is not funny or curious.
If someone is wise then mary is patient or funny and vice versa.
Everyone who is both not generous and happy is not quiet or not old.
If paul is both curious and generous then lucy is either old or not funny.
Everyone who is both strong and wise is wise or strong.
Everyone who is patient is both not creative and not rich and vice versa.
If paul is both funny and wise then lucy is brave.
Everyone who is not old is either kind or happy and vice versa.
Everyone who is either not rich or old is both happy and rich and vice versa.
Everyone who is both creative and happy is both not wise and not calm.
If someone is kind or generous then lucy is not patient and vice versa.
If alice is happy or brave then john is either calm or funny.
Alice is not rich.
Someone is not generous or not strong.
Someone is either not funny or not kind.
Someone is not patient.
Fred is either not rich or tall.
John is not wise. | Alice is curious. | contradiction | ((?[X]:((curious(X)|~old(X))))<=>(?[X]:((~strong(X)|~happy(X)))))&
(![X]:((quiet(X)|curious(X))=>(~curious(X)&calm(X))))&
(![X]:((~quiet(X)&~tall(X))<=>(~strong(X)|~curious(X))))&
(![X]:((wise(X)&~patient(X))=>(~wise(X)<~>quiet(X))))&
(((patient(lucy)<~>~old(lucy)))=>(?[X]:((~funny(X)|curious(X)))))&
((?[X]:(wise(X)))<=>((patient(mary)|funny(mary))))&
(![X]:((~generous(X)&happy(X))=>(~quiet(X)|~old(X))))&
(((curious(paul)&generous(paul)))=>((old(lucy)<~>~funny(lucy))))&
(![X]:((strong(X)&wise(X))=>(wise(X)|strong(X))))&
(![X]:(patient(X)<=>(~creative(X)&~rich(X))))&
(((funny(paul)&wise(paul)))=>(brave(lucy)))&
(![X]:(~old(X)<=>(kind(X)<~>happy(X))))&
(![X]:((~rich(X)<~>old(X))<=>(happy(X)&rich(X))))&
(![X]:((creative(X)&happy(X))=>(~wise(X)&~calm(X))))&
((?[X]:((kind(X)|generous(X))))<=>(~patient(lucy)))&
(((happy(alice)|brave(alice)))=>((calm(john)<~>funny(john))))&
(~rich(alice))&
(?[X]:((~generous(X)|~strong(X))))&
(?[X]:((~funny(X)<~>~kind(X))))&
(?[X]:(~patient(X)))&
((~rich(fred)<~>tall(fred)))&
(~wise(john)) | curious(alice) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 6933738883215328628966123
% SZS output start Proof for 6933738883215328628966123
2. ! [X0] : ((curious(X0) | quiet(X0)) => (calm(X0) & ~curious(X0))) [input p1]
23. curious(alice) [input hypothesis]
25. ! [X0] : ((calm(X0) & ~curious(X0)) | (~curious(X0) & ~quiet(X0))) [ennf transformation 2]
80. ~curious(X0) | ~curious(X0) [cnf transformation 25]
130. curious(alice) [cnf transformation 23]
134. ~curious(X0) [duplicate literal removal 80]
164. 8 <=> ! [X3] : ~curious(X3) [avatar definition]
165. ~curious(X3) <- (8) [avatar component clause 164]
167. 8 [avatar split clause 134,164]
300. $false <- (8) [resolution 165,130]
301. ~8 [avatar contradiction clause 300]
302. $false [avatar sat refutation 167,301]
% SZS output end Proof for 6933738883215328628966123
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and calm is either not rich or brave and vice versa.
Everyone who is not curious or not humble is either not creative or not calm and vice versa.
If someone is not old then susan is not calm and vice versa.
Everyone who is strong or not creative is not curious.
Everyone who is either not rich or brave is humble or old and vice versa.
Everyone who is both not rich and not kind is generous or not funny and vice versa.
If someone is either not creative or happy then mary is both not tall and not generous and vice versa.
If someone is brave then fred is both kind and not rich and vice versa.
Everyone who is both not funny and not brave is not old and vice versa.
Everyone who is either not creative or old is either humble or generous.
If paul is either not funny or not calm then susan is both not quiet and not creative and vice versa.
Everyone who is not strong is brave.
Everyone who is either happy or patient is either kind or strong.
If lucy is both old and tall then lucy is humble.
Everyone who is both curious and patient is either not humble or not happy and vice versa.
Fred is humble or not quiet.
Fred is creative or not curious.
Lucy is either brave or not patient.
Someone is either not rich or not happy.
Someone is funny or tall. | Mary is not rich. | entailment | (![X]:((generous(X)&calm(X))<=>(~rich(X)<~>brave(X))))&
(![X]:((~curious(X)|~humble(X))<=>(~creative(X)<~>~calm(X))))&
((?[X]:(~old(X)))<=>(~calm(susan)))&
(![X]:((strong(X)|~creative(X))=>~curious(X)))&
(![X]:((~rich(X)<~>brave(X))<=>(humble(X)|old(X))))&
(![X]:((~rich(X)&~kind(X))<=>(generous(X)|~funny(X))))&
((?[X]:((~creative(X)<~>happy(X))))<=>((~tall(mary)&~generous(mary))))&
((?[X]:(brave(X)))<=>((kind(fred)&~rich(fred))))&
(![X]:((~funny(X)&~brave(X))<=>~old(X)))&
(![X]:((~creative(X)<~>old(X))=>(humble(X)<~>generous(X))))&
(((~funny(paul)<~>~calm(paul)))<=>((~quiet(susan)&~creative(susan))))&
(![X]:(~strong(X)=>brave(X)))&
(![X]:((happy(X)<~>patient(X))=>(kind(X)<~>strong(X))))&
(((old(lucy)&tall(lucy)))=>(humble(lucy)))&
(![X]:((curious(X)&patient(X))<=>(~humble(X)<~>~happy(X))))&
((humble(fred)|~quiet(fred)))&
((creative(fred)|~curious(fred)))&
((brave(lucy)<~>~patient(lucy)))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:((funny(X)|tall(X)))) | ~rich(mary) | [
"p0",
"p4",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4212181466493636478848905
% SZS output start Proof for 4212181466493636478848905
1. ! [X0] : ((calm(X0) & generous(X0)) <=> (~rich(X0) <~> brave(X0))) [input p0]
5. ! [X0] : ((~rich(X0) <~> brave(X0)) <=> (old(X0) | humble(X0))) [input p4]
6. ! [X0] : ((~kind(X0) & ~rich(X0)) <=> (~funny(X0) | generous(X0))) [input p5]
9. ! [X0] : ((~brave(X0) & ~funny(X0)) <=> ~old(X0)) [input p8]
21. rich(mary) [input hypothesis]
28. ! [X0] : (((calm(X0) & generous(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~calm(X0) | ~generous(X0)))) [nnf transformation 1]
29. ! [X0] : (((calm(X0) & generous(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | ~calm(X0) | ~generous(X0))) [flattening 28]
36. ! [X0] : ((((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~old(X0) & ~humble(X0))) & ((old(X0) | humble(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))))) [nnf transformation 5]
37. ! [X0] : ((((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~old(X0) & ~humble(X0))) & (old(X0) | humble(X0) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))))) [flattening 36]
38. ! [X0] : (((~kind(X0) & ~rich(X0)) | (funny(X0) & ~generous(X0))) & ((~funny(X0) | generous(X0)) | (kind(X0) | rich(X0)))) [nnf transformation 6]
39. ! [X0] : (((~kind(X0) & ~rich(X0)) | (funny(X0) & ~generous(X0))) & (~funny(X0) | generous(X0) | kind(X0) | rich(X0))) [flattening 38]
50. ! [X0] : (((~brave(X0) & ~funny(X0)) | old(X0)) & (~old(X0) | (brave(X0) | funny(X0)))) [nnf transformation 9]
51. ! [X0] : (((~brave(X0) & ~funny(X0)) | old(X0)) & (~old(X0) | brave(X0) | funny(X0))) [flattening 50]
67. ~brave(X0) | ~rich(X0) | generous(X0) [cnf transformation 29]
83. ~old(X0) | ~rich(X0) | brave(X0) [cnf transformation 37]
87. ~rich(X0) | ~generous(X0) [cnf transformation 39]
88. ~rich(X0) | funny(X0) [cnf transformation 39]
101. ~funny(X0) | old(X0) [cnf transformation 51]
132. rich(mary) [cnf transformation 21]
151. 5 <=> generous(mary) [avatar definition]
265. ~generous(mary) [resolution 87,132]
267. funny(mary) [resolution 88,132]
272. old(mary) [resolution 101,267]
328. ~rich(mary) | brave(mary) [resolution 83,272]
334. brave(mary) [subsumption resolution 328,132]
346. ~rich(mary) | generous(mary) [resolution 334,67]
349. generous(mary) [subsumption resolution 346,132]
352. 5 [avatar split clause 349,151]
353. ~5 [avatar split clause 265,151]
354. $false [avatar sat refutation 352,353]
% SZS output end Proof for 4212181466493636478848905
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both brave and patient then mary is humble. Everyone who is either wise or not humble is both not old and not wise. If someone is both not humble and funny then paul is either not funny or not curious. If mary is not happy or not humble then someone is either creative or curious. Everyone who is not generous is wise or not quiet. Everyone who is not happy is not generous or not strong. Everyone who is old or brave is both strong and not old and vice versa. If mary is both funny and not brave then someone is tall. Everyone who is both tall and not funny is rich or not rich and vice versa. Everyone who is either not kind or creative is either not patient or not creative and vice versa. Everyone who is both quiet and rich is both not creative and rich and vice versa. Everyone who is either not happy or humble is not humble. If alice is either not wise or calm then someone is both wise and patient and vice versa. Everyone who is either calm or rich is either curious or not quiet. Everyone who is strong or humble is either wise or not creative and vice versa. Everyone who is not quiet or creative is either patient or creative. Mary is not curious. Someone is not patient. Someone is not funny. Someone is wise or not generous. Someone is patient. | Mary is not calm. | neutral | (((brave(lucy)&patient(lucy)))=>(humble(mary)))&
(![X]:((wise(X)<~>~humble(X))=>(~old(X)&~wise(X))))&
((?[X]:((~humble(X)&funny(X))))=>((~funny(paul)<~>~curious(paul))))&
(((~happy(mary)|~humble(mary)))=>(?[X]:((creative(X)<~>curious(X)))))&
(![X]:(~generous(X)=>(wise(X)|~quiet(X))))&
(![X]:(~happy(X)=>(~generous(X)|~strong(X))))&
(![X]:((old(X)|brave(X))<=>(strong(X)&~old(X))))&
(((funny(mary)&~brave(mary)))=>(?[X]:(tall(X))))&
(![X]:((tall(X)&~funny(X))<=>(rich(X)|~rich(X))))&
(![X]:((~kind(X)<~>creative(X))<=>(~patient(X)<~>~creative(X))))&
(![X]:((quiet(X)&rich(X))<=>(~creative(X)&rich(X))))&
(![X]:((~happy(X)<~>humble(X))=>~humble(X)))&
(((~wise(alice)<~>calm(alice)))<=>(?[X]:((wise(X)&patient(X)))))&
(![X]:((calm(X)<~>rich(X))=>(curious(X)<~>~quiet(X))))&
(![X]:((strong(X)|humble(X))<=>(wise(X)<~>~creative(X))))&
(![X]:((~quiet(X)|creative(X))=>(patient(X)<~>creative(X))))&
(~curious(mary))&
(?[X]:(~patient(X)))&
(?[X]:(~funny(X)))&
(?[X]:((wise(X)|~generous(X))))&
(?[X]:(patient(X))) | ~calm(mary) | [] | null | 0 |
If someone is rich then mary is not patient and vice versa.
If someone is calm then someone is both not tall and not humble and vice versa.
If paul is both quiet and not rich then mary is kind or generous and vice versa.
Everyone who is calm or happy is not funny.
Everyone who is old is both wise and generous.
Everyone who is both creative and not creative is happy or not happy.
If someone is either not old or not quiet then someone is quiet or rich and vice versa.
Everyone who is happy or not kind is not wise and vice versa.
Everyone who is either curious or tall is not kind and vice versa.
If mary is not patient then someone is not rich or not creative.
Everyone who is not wise is both not strong and wise and vice versa.
Everyone who is either not generous or not calm is both not kind and not tall.
Everyone who is both kind and quiet is not humble or not curious.
Everyone who is happy or not wise is not calm or patient and vice versa.
Everyone who is not quiet is either not old or rich.
If john is either not wise or generous then fred is rich.
Paul is either not curious or happy.
Someone is curious or strong.
Mary is calm.
Someone is wise or not brave.
Mary is either not humble or creative.
Someone is not calm or wise.
Mary is not old.
John is not quiet. | Fred is rich. | entailment | ((?[X]:(rich(X)))<=>(~patient(mary)))&
((?[X]:(calm(X)))<=>(?[X]:((~tall(X)&~humble(X)))))&
(((quiet(paul)&~rich(paul)))<=>((kind(mary)|generous(mary))))&
(![X]:((calm(X)|happy(X))=>~funny(X)))&
(![X]:(old(X)=>(wise(X)&generous(X))))&
(![X]:((creative(X)&~creative(X))=>(happy(X)|~happy(X))))&
((?[X]:((~old(X)<~>~quiet(X))))<=>(?[X]:((quiet(X)|rich(X)))))&
(![X]:((happy(X)|~kind(X))<=>~wise(X)))&
(![X]:((curious(X)<~>tall(X))<=>~kind(X)))&
((~patient(mary))=>(?[X]:((~rich(X)|~creative(X)))))&
(![X]:(~wise(X)<=>(~strong(X)&wise(X))))&
(![X]:((~generous(X)<~>~calm(X))=>(~kind(X)&~tall(X))))&
(![X]:((kind(X)&quiet(X))=>(~humble(X)|~curious(X))))&
(![X]:((happy(X)|~wise(X))<=>(~calm(X)|patient(X))))&
(![X]:(~quiet(X)=>(~old(X)<~>rich(X))))&
(((~wise(john)<~>generous(john)))=>(rich(fred)))&
((~curious(paul)<~>happy(paul)))&
(?[X]:((curious(X)|strong(X))))&
(calm(mary))&
(?[X]:((wise(X)|~brave(X))))&
((~humble(mary)<~>creative(mary)))&
(?[X]:((~calm(X)|wise(X))))&
(~old(mary))&
(~quiet(john)) | rich(fred) | [
"p7",
"p10",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 381966914203162224991196
% SZS output start Proof for 381966914203162224991196
8. ! [X0] : ((~kind(X0) | happy(X0)) <=> ~wise(X0)) [input p7]
11. ! [X0] : (~wise(X0) <=> (wise(X0) & ~strong(X0))) [input p10]
12. ! [X0] : ((~generous(X0) <~> ~calm(X0)) => (~tall(X0) & ~kind(X0))) [input p11]
14. ! [X0] : ((~wise(X0) | happy(X0)) <=> (patient(X0) | ~calm(X0))) [input p13]
16. (~wise(john) <~> generous(john)) => rich(fred) [input p15]
25. ~rich(fred) [input hypothesis]
34. ! [X0] : ((~tall(X0) & ~kind(X0)) | (~generous(X0) <=> ~calm(X0))) [ennf transformation 12]
38. rich(fred) | (~wise(john) <=> generous(john)) [ennf transformation 16]
55. ! [X0] : (((~kind(X0) | happy(X0)) | wise(X0)) & (~wise(X0) | (kind(X0) & ~happy(X0)))) [nnf transformation 8]
56. ! [X0] : ((~kind(X0) | happy(X0) | wise(X0)) & (~wise(X0) | (kind(X0) & ~happy(X0)))) [flattening 55]
60. ! [X0] : ((~wise(X0) | (~wise(X0) | strong(X0))) & ((wise(X0) & ~strong(X0)) | wise(X0))) [nnf transformation 11]
61. ! [X0] : ((~wise(X0) | ~wise(X0) | strong(X0)) & ((wise(X0) & ~strong(X0)) | wise(X0))) [flattening 60]
62. ! [X0] : ((~tall(X0) & ~kind(X0)) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0)))) [nnf transformation 34]
63. ! [X0] : (((~wise(X0) | happy(X0)) | (~patient(X0) & calm(X0))) & ((patient(X0) | ~calm(X0)) | (wise(X0) & ~happy(X0)))) [nnf transformation 14]
64. ! [X0] : ((~wise(X0) | happy(X0) | (~patient(X0) & calm(X0))) & (patient(X0) | ~calm(X0) | (wise(X0) & ~happy(X0)))) [flattening 63]
66. rich(fred) | ((~wise(john) | ~generous(john)) & (generous(john) | wise(john))) [nnf transformation 38]
92. ~wise(X0) | ~happy(X0) [cnf transformation 56]
93. ~wise(X0) | kind(X0) [cnf transformation 56]
101. wise(X0) | wise(X0) [cnf transformation 61]
103. ~kind(X0) | ~calm(X0) | generous(X0) [cnf transformation 62]
110. ~wise(X0) | happy(X0) | calm(X0) [cnf transformation 64]
115. rich(fred) | ~wise(john) | ~generous(john) [cnf transformation 66]
125. ~rich(fred) [cnf transformation 25]
126. wise(X0) [duplicate literal removal 101]
224. happy(X0) | calm(X0) [subsumption resolution 110,126]
225. rich(fred) | ~generous(john) [subsumption resolution 115,126]
227. 22 <=> generous(john) [avatar definition]
229. ~generous(john) <- (~22) [avatar component clause 227]
231. 23 <=> rich(fred) [avatar definition]
234. ~22 | 23 [avatar split clause 225,231,227]
264. ~23 [avatar split clause 125,231]
267. ~happy(X0) [resolution 92,126]
268. kind(X0) [resolution 93,126]
277. calm(X0) [resolution 224,267]
289. ~calm(X0) | generous(X0) [resolution 103,268]
290. generous(X0) [subsumption resolution 289,277]
293. $false <- (~22) [resolution 290,229]
295. 22 [avatar contradiction clause 293]
297. $false [avatar sat refutation 234,264,295]
% SZS output end Proof for 381966914203162224991196
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm or not wise then paul is brave and vice versa.
Everyone who is both brave and curious is quiet.
If someone is happy then susan is quiet.
If someone is either curious or not calm then someone is either not funny or not generous.
If john is quiet then mary is both not brave and brave and vice versa.
If someone is either not tall or not creative then alice is not funny and vice versa.
If mary is both not tall and not old then alice is either happy or funny and vice versa.
Everyone who is not tall is brave or not happy.
If someone is not quiet or not kind then john is funny or not brave and vice versa.
If lucy is both not wise and not rich then fred is both not creative and humble.
If someone is not tall then mary is either not quiet or humble and vice versa.
Everyone who is both not tall and not creative is not generous and vice versa.
Everyone who is not kind or strong is either not quiet or wise and vice versa.
Everyone who is not wise or not brave is not humble.
Everyone who is not humble is both brave and strong and vice versa.
If someone is old then mary is both funny and brave.
Mary is not happy or curious.
Lucy is creative.
John is either not strong or not quiet.
Someone is old.
Someone is either not brave or rich.
Fred is tall.
Paul is brave. | Mary is not funny. | contradiction | ((?[X]:((calm(X)|~wise(X))))<=>(brave(paul)))&
(![X]:((brave(X)&curious(X))=>quiet(X)))&
((?[X]:(happy(X)))=>(quiet(susan)))&
((?[X]:((curious(X)<~>~calm(X))))=>(?[X]:((~funny(X)<~>~generous(X)))))&
((quiet(john))<=>((~brave(mary)&brave(mary))))&
((?[X]:((~tall(X)<~>~creative(X))))<=>(~funny(alice)))&
(((~tall(mary)&~old(mary)))<=>((happy(alice)<~>funny(alice))))&
(![X]:(~tall(X)=>(brave(X)|~happy(X))))&
((?[X]:((~quiet(X)|~kind(X))))<=>((funny(john)|~brave(john))))&
(((~wise(lucy)&~rich(lucy)))=>((~creative(fred)&humble(fred))))&
((?[X]:(~tall(X)))<=>((~quiet(mary)<~>humble(mary))))&
(![X]:((~tall(X)&~creative(X))<=>~generous(X)))&
(![X]:((~kind(X)|strong(X))<=>(~quiet(X)<~>wise(X))))&
(![X]:((~wise(X)|~brave(X))=>~humble(X)))&
(![X]:(~humble(X)<=>(brave(X)&strong(X))))&
((?[X]:(old(X)))=>((funny(mary)&brave(mary))))&
((~happy(mary)|curious(mary)))&
(creative(lucy))&
((~strong(john)<~>~quiet(john)))&
(?[X]:(old(X)))&
(?[X]:((~brave(X)<~>rich(X))))&
(tall(fred))&
(brave(paul)) | ~funny(mary) | [
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 398379707410053213666765
% SZS output start Proof for 398379707410053213666765
16. ? [X0] : old(X0) => (brave(mary) & funny(mary)) [input p15]
20. ? [X0] : old(X0) [input p19]
24. ~funny(mary) [input hypothesis]
35. (brave(mary) & funny(mary)) | ! [X0] : ~old(X0) [ennf transformation 16]
68. ? [X0] : old(X0) => old(sK5) [choice axiom]
69. old(sK5) [skolemisation 20,68]
120. funny(mary) | ~old(X0) [cnf transformation 35]
126. old(sK5) [cnf transformation 69]
131. ~funny(mary) [cnf transformation 24]
295. 36 <=> ! [X0] : ~old(X0) [avatar definition]
296. ~old(X0) <- (36) [avatar component clause 295]
298. 37 <=> funny(mary) [avatar definition]
301. 36 | 37 [avatar split clause 120,298,295]
318. ~37 [avatar split clause 131,298]
325. $false <- (36) [resolution 296,126]
326. ~36 [avatar contradiction clause 325]
327. $false [avatar sat refutation 301,318,326]
% SZS output end Proof for 398379707410053213666765
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and curious is not brave and vice versa. Everyone who is quiet or old is rich or old and vice versa. Everyone who is both not wise and not humble is either not tall or not calm. If lucy is not brave or creative then someone is both rich and not calm. Everyone who is not funny or brave is both funny and not quiet. Everyone who is both happy and not happy is curious. Everyone who is not funny or humble is either wise or not humble and vice versa. If someone is brave then lucy is both curious and old. Everyone who is quiet is both not patient and patient and vice versa. Everyone who is not calm is generous or funny and vice versa. Everyone who is both tall and kind is both curious and brave and vice versa. If susan is both old and not tall then susan is not tall or brave and vice versa. Everyone who is curious is either not rich or patient and vice versa. If someone is strong or not strong then someone is both not old and kind and vice versa. Everyone who is either curious or old is both not kind and strong. Everyone who is both happy and not brave is either not humble or not generous. Alice is not generous. Fred is rich. John is not curious or humble. Someone is either curious or not patient. Someone is either humble or not humble. Someone is either not happy or not wise. Someone is kind or not quiet. Someone is either generous or not patient. | Fred is wise. | entailment | (![X]:((~strong(X)&curious(X))<=>~brave(X)))&
(![X]:((quiet(X)|old(X))<=>(rich(X)|old(X))))&
(![X]:((~wise(X)&~humble(X))=>(~tall(X)<~>~calm(X))))&
(((~brave(lucy)|creative(lucy)))=>(?[X]:((rich(X)&~calm(X)))))&
(![X]:((~funny(X)|brave(X))=>(funny(X)&~quiet(X))))&
(![X]:((happy(X)&~happy(X))=>curious(X)))&
(![X]:((~funny(X)|humble(X))<=>(wise(X)<~>~humble(X))))&
((?[X]:(brave(X)))=>((curious(lucy)&old(lucy))))&
(![X]:(quiet(X)<=>(~patient(X)&patient(X))))&
(![X]:(~calm(X)<=>(generous(X)|funny(X))))&
(![X]:((tall(X)&kind(X))<=>(curious(X)&brave(X))))&
(((old(susan)&~tall(susan)))<=>((~tall(susan)|brave(susan))))&
(![X]:(curious(X)<=>(~rich(X)<~>patient(X))))&
((?[X]:((strong(X)|~strong(X))))<=>(?[X]:((~old(X)&kind(X)))))&
(![X]:((curious(X)<~>old(X))=>(~kind(X)&strong(X))))&
(![X]:((happy(X)&~brave(X))=>(~humble(X)<~>~generous(X))))&
(~generous(alice))&
(rich(fred))&
((~curious(john)|humble(john)))&
(?[X]:((curious(X)<~>~patient(X))))&
(?[X]:((humble(X)<~>~humble(X))))&
(?[X]:((~happy(X)<~>~wise(X))))&
(?[X]:((kind(X)|~quiet(X))))&
(?[X]:((generous(X)<~>~patient(X)))) | wise(fred) | [
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2534503309105223413889370
% SZS output start Proof for 2534503309105223413889370
5. ! [X0] : ((brave(X0) | ~funny(X0)) => (~quiet(X0) & funny(X0))) [input p4]
7. ! [X0] : ((humble(X0) | ~funny(X0)) <=> (wise(X0) <~> ~humble(X0))) [input p6]
25. ~wise(fred) [input hypothesis]
31. ! [X0] : ((~quiet(X0) & funny(X0)) | (~brave(X0) & funny(X0))) [ennf transformation 5]
45. ! [X0] : (((humble(X0) | ~funny(X0)) | ((wise(X0) | humble(X0)) & (~humble(X0) | ~wise(X0)))) & (((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) | (~humble(X0) & funny(X0)))) [nnf transformation 7]
46. ! [X0] : ((humble(X0) | ~funny(X0) | ((wise(X0) | humble(X0)) & (~humble(X0) | ~wise(X0)))) & (((humble(X0) | ~wise(X0)) & (~humble(X0) | wise(X0))) | (~humble(X0) & funny(X0)))) [flattening 45]
88. funny(X0) | funny(X0) [cnf transformation 31]
94. ~humble(X0) | wise(X0) | ~humble(X0) [cnf transformation 46]
98. humble(X0) | ~funny(X0) | wise(X0) | humble(X0) [cnf transformation 46]
143. ~wise(fred) [cnf transformation 25]
144. ~humble(X0) | wise(X0) [duplicate literal removal 94]
145. humble(X0) | ~funny(X0) | wise(X0) [duplicate literal removal 98]
146. funny(X0) [duplicate literal removal 88]
161. humble(X0) | wise(X0) [subsumption resolution 145,146]
162. wise(X0) [subsumption resolution 144,161]
241. $false [subsumption resolution 143,162]
% SZS output end Proof for 2534503309105223413889370
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not quiet then someone is either funny or not old and vice versa. If john is not quiet or not humble then john is both not funny and old and vice versa. If mary is both not quiet and rich then someone is tall and vice versa. Everyone who is not quiet or not rich is not rich or not wise. Everyone who is not calm or curious is both not kind and not calm. Everyone who is either calm or brave is both brave and kind. If susan is both not strong and funny then susan is either not generous or kind and vice versa. Everyone who is humble or not tall is not quiet or wise. Everyone who is brave or tall is not wise or not patient and vice versa. If someone is both not kind and not old then lucy is either strong or tall. If someone is quiet or not generous then lucy is both not calm and wise and vice versa. Everyone who is either funny or generous is both not quiet and kind. If alice is both not quiet and wise then someone is either wise or not brave. If fred is not quiet then paul is creative or calm. Everyone who is not quiet is not tall or not quiet and vice versa. If someone is both not patient and not kind then someone is wise. Paul is generous or tall. Susan is not humble or patient. Someone is kind or rich. Someone is not curious. Alice is old. Someone is either not generous or not wise. Alice is strong. Someone is either rich or not generous. | John is quiet. | neutral | (((generous(alice)|~quiet(alice)))<=>(?[X]:((funny(X)<~>~old(X)))))&
(((~quiet(john)|~humble(john)))<=>((~funny(john)&old(john))))&
(((~quiet(mary)&rich(mary)))<=>(?[X]:(tall(X))))&
(![X]:((~quiet(X)|~rich(X))=>(~rich(X)|~wise(X))))&
(![X]:((~calm(X)|curious(X))=>(~kind(X)&~calm(X))))&
(![X]:((calm(X)<~>brave(X))=>(brave(X)&kind(X))))&
(((~strong(susan)&funny(susan)))<=>((~generous(susan)<~>kind(susan))))&
(![X]:((humble(X)|~tall(X))=>(~quiet(X)|wise(X))))&
(![X]:((brave(X)|tall(X))<=>(~wise(X)|~patient(X))))&
((?[X]:((~kind(X)&~old(X))))=>((strong(lucy)<~>tall(lucy))))&
((?[X]:((quiet(X)|~generous(X))))<=>((~calm(lucy)&wise(lucy))))&
(![X]:((funny(X)<~>generous(X))=>(~quiet(X)&kind(X))))&
(((~quiet(alice)&wise(alice)))=>(?[X]:((wise(X)<~>~brave(X)))))&
((~quiet(fred))=>((creative(paul)|calm(paul))))&
(![X]:(~quiet(X)<=>(~tall(X)|~quiet(X))))&
((?[X]:((~patient(X)&~kind(X))))=>(?[X]:(wise(X))))&
((generous(paul)|tall(paul)))&
((~humble(susan)|patient(susan)))&
(?[X]:((kind(X)|rich(X))))&
(?[X]:(~curious(X)))&
(old(alice))&
(?[X]:((~generous(X)<~>~wise(X))))&
(strong(alice))&
(?[X]:((rich(X)<~>~generous(X)))) | quiet(john) | [] | null | 0 |
If someone is rich or not funny then john is patient or not quiet and vice versa.
If someone is creative or not tall then someone is kind.
Everyone who is both strong and funny is strong or brave.
If mary is both not quiet and curious then alice is either not kind or wise.
Everyone who is either not wise or not curious is curious.
Everyone who is not old is patient or humble.
Everyone who is both not humble and not old is not quiet or not curious and vice versa.
Everyone who is rich is either not strong or not patient.
Everyone who is creative is not rich and vice versa.
If someone is either generous or humble then someone is both not strong and not quiet.
Everyone who is not calm or not kind is not funny and vice versa.
Everyone who is happy is wise.
If someone is not kind or not patient then someone is either not generous or not brave and vice versa.
Everyone who is either not rich or creative is humble or not calm and vice versa.
Everyone who is both generous and funny is generous or quiet.
Everyone who is either kind or not funny is either not tall or not calm and vice versa.
Someone is not rich or funny.
Someone is either brave or curious.
Susan is rich.
Someone is not curious or not patient.
Someone is both calm and rich.
Someone is either humble or generous. | Mary is not strong. | neutral | ((?[X]:((rich(X)|~funny(X))))<=>((patient(john)|~quiet(john))))&
((?[X]:((creative(X)|~tall(X))))=>(?[X]:(kind(X))))&
(![X]:((strong(X)&funny(X))=>(strong(X)|brave(X))))&
(((~quiet(mary)&curious(mary)))=>((~kind(alice)<~>wise(alice))))&
(![X]:((~wise(X)<~>~curious(X))=>curious(X)))&
(![X]:(~old(X)=>(patient(X)|humble(X))))&
(![X]:((~humble(X)&~old(X))<=>(~quiet(X)|~curious(X))))&
(![X]:(rich(X)=>(~strong(X)<~>~patient(X))))&
(![X]:(creative(X)<=>~rich(X)))&
((?[X]:((generous(X)<~>humble(X))))=>(?[X]:((~strong(X)&~quiet(X)))))&
(![X]:((~calm(X)|~kind(X))<=>~funny(X)))&
(![X]:(happy(X)=>wise(X)))&
((?[X]:((~kind(X)|~patient(X))))<=>(?[X]:((~generous(X)<~>~brave(X)))))&
(![X]:((~rich(X)<~>creative(X))<=>(humble(X)|~calm(X))))&
(![X]:((generous(X)&funny(X))=>(generous(X)|quiet(X))))&
(![X]:((kind(X)<~>~funny(X))<=>(~tall(X)<~>~calm(X))))&
(?[X]:((~rich(X)|funny(X))))&
(?[X]:((brave(X)<~>curious(X))))&
(rich(susan))&
(?[X]:((~curious(X)|~patient(X))))&
(?[X]:((calm(X)&rich(X))))&
(?[X]:((humble(X)<~>generous(X)))) | ~strong(mary) | [] | null | 0 |
Everyone who is kind or not humble is both not quiet and calm and vice versa.
If someone is both brave and calm then mary is patient or not generous and vice versa.
Everyone who is not old or not humble is not tall or happy and vice versa.
Everyone who is both curious and quiet is not brave.
Everyone who is not old is both not tall and not happy.
If someone is brave or not creative then susan is both brave and not kind and vice versa.
Everyone who is not calm or not humble is not tall and vice versa.
Everyone who is not funny or kind is either not patient or humble and vice versa.
If someone is either not patient or not creative then someone is humble and vice versa.
Everyone who is either not curious or curious is rich and vice versa.
Everyone who is either happy or not creative is both not brave and funny and vice versa.
If alice is not wise or calm then john is both not kind and old.
Everyone who is not patient is both not creative and not old.
Everyone who is both brave and not humble is not tall.
Everyone who is happy or curious is either not calm or old.
If fred is calm or not calm then alice is not tall.
Mary is either tall or generous.
Someone is either not rich or creative.
Someone is either tall or funny.
Someone is both not strong and not patient.
Mary is both brave and not calm.
Someone is either not generous or humble.
Fred is either creative or old.
Someone is not tall. | Alice is patient. | neutral | (![X]:((kind(X)|~humble(X))<=>(~quiet(X)&calm(X))))&
((?[X]:((brave(X)&calm(X))))<=>((patient(mary)|~generous(mary))))&
(![X]:((~old(X)|~humble(X))<=>(~tall(X)|happy(X))))&
(![X]:((curious(X)&quiet(X))=>~brave(X)))&
(![X]:(~old(X)=>(~tall(X)&~happy(X))))&
((?[X]:((brave(X)|~creative(X))))<=>((brave(susan)&~kind(susan))))&
(![X]:((~calm(X)|~humble(X))<=>~tall(X)))&
(![X]:((~funny(X)|kind(X))<=>(~patient(X)<~>humble(X))))&
((?[X]:((~patient(X)<~>~creative(X))))<=>(?[X]:(humble(X))))&
(![X]:((~curious(X)<~>curious(X))<=>rich(X)))&
(![X]:((happy(X)<~>~creative(X))<=>(~brave(X)&funny(X))))&
(((~wise(alice)|calm(alice)))=>((~kind(john)&old(john))))&
(![X]:(~patient(X)=>(~creative(X)&~old(X))))&
(![X]:((brave(X)&~humble(X))=>~tall(X)))&
(![X]:((happy(X)|curious(X))=>(~calm(X)<~>old(X))))&
(((calm(fred)|~calm(fred)))=>(~tall(alice)))&
((tall(mary)<~>generous(mary)))&
(?[X]:((~rich(X)<~>creative(X))))&
(?[X]:((tall(X)<~>funny(X))))&
(?[X]:((~strong(X)&~patient(X))))&
((brave(mary)&~calm(mary)))&
(?[X]:((~generous(X)<~>humble(X))))&
((creative(fred)<~>old(fred)))&
(?[X]:(~tall(X))) | patient(alice) | [] | null | 0 |
If someone is not old then alice is either not humble or not quiet and vice versa.
If someone is both curious and not quiet then someone is both not wise and not generous.
If john is strong then someone is not tall or kind.
Everyone who is both not patient and not wise is both not humble and not patient.
Everyone who is strong or not tall is both not calm and rich.
Everyone who is not quiet or not humble is either old or quiet.
Everyone who is not generous is funny.
If susan is not creative then someone is not brave.
Everyone who is calm or not humble is wise.
If someone is kind then alice is either quiet or not kind.
Everyone who is not old is not brave.
Everyone who is humble or not brave is both not happy and happy.
Everyone who is not brave or happy is not patient or strong and vice versa.
Everyone who is both old and calm is either kind or not patient and vice versa.
If someone is either not happy or quiet then someone is curious or funny.
Everyone who is both not curious and funny is both wise and not patient.
Someone is either generous or old.
Alice is brave or not patient.
Someone is either kind or not rich.
Someone is not humble.
Susan is both not happy and not strong.
Someone is both not rich and not patient. | Susan is patient. | entailment | ((?[X]:(~old(X)))<=>((~humble(alice)<~>~quiet(alice))))&
((?[X]:((curious(X)&~quiet(X))))=>(?[X]:((~wise(X)&~generous(X)))))&
((strong(john))=>(?[X]:((~tall(X)|kind(X)))))&
(![X]:((~patient(X)&~wise(X))=>(~humble(X)&~patient(X))))&
(![X]:((strong(X)|~tall(X))=>(~calm(X)&rich(X))))&
(![X]:((~quiet(X)|~humble(X))=>(old(X)<~>quiet(X))))&
(![X]:(~generous(X)=>funny(X)))&
((~creative(susan))=>(?[X]:(~brave(X))))&
(![X]:((calm(X)|~humble(X))=>wise(X)))&
((?[X]:(kind(X)))=>((quiet(alice)<~>~kind(alice))))&
(![X]:(~old(X)=>~brave(X)))&
(![X]:((humble(X)|~brave(X))=>(~happy(X)&happy(X))))&
(![X]:((~brave(X)|happy(X))<=>(~patient(X)|strong(X))))&
(![X]:((old(X)&calm(X))<=>(kind(X)<~>~patient(X))))&
((?[X]:((~happy(X)<~>quiet(X))))=>(?[X]:((curious(X)|funny(X)))))&
(![X]:((~curious(X)&funny(X))=>(wise(X)&~patient(X))))&
(?[X]:((generous(X)<~>old(X))))&
((brave(alice)|~patient(alice)))&
(?[X]:((kind(X)<~>~rich(X))))&
(?[X]:(~humble(X)))&
((~happy(susan)&~strong(susan)))&
(?[X]:((~rich(X)&~patient(X)))) | patient(susan) | [
"p11",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 409845142539520760983679
% SZS output start Proof for 409845142539520760983679
12. ! [X0] : ((~brave(X0) | humble(X0)) => (happy(X0) & ~happy(X0))) [input p11]
13. ! [X0] : ((happy(X0) | ~brave(X0)) <=> (strong(X0) | ~patient(X0))) [input p12]
21. ~strong(susan) & ~happy(susan) [input p20]
23. ~patient(susan) [input hypothesis]
37. ! [X0] : ((happy(X0) & ~happy(X0)) | (brave(X0) & ~humble(X0))) [ennf transformation 12]
52. ! [X0] : (((happy(X0) | ~brave(X0)) | (~strong(X0) & patient(X0))) & ((strong(X0) | ~patient(X0)) | (~happy(X0) & brave(X0)))) [nnf transformation 13]
53. ! [X0] : ((happy(X0) | ~brave(X0) | (~strong(X0) & patient(X0))) & (strong(X0) | ~patient(X0) | (~happy(X0) & brave(X0)))) [flattening 52]
94. ~happy(X0) | brave(X0) [cnf transformation 37]
96. happy(X0) | brave(X0) [cnf transformation 37]
99. happy(X0) | ~brave(X0) | patient(X0) [cnf transformation 53]
117. ~happy(susan) [cnf transformation 21]
121. ~patient(susan) [cnf transformation 23]
177. brave(X0) [subsumption resolution 94,96]
180. happy(X0) | patient(X0) [subsumption resolution 99,177]
232. patient(susan) [resolution 180,117]
233. $false [subsumption resolution 232,121]
% SZS output end Proof for 409845142539520760983679
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both funny and not funny then mary is not humble.
If someone is both calm and not humble then someone is both not curious and not kind and vice versa.
If someone is both kind and not creative then paul is either quiet or old and vice versa.
Everyone who is not creative is not quiet or not generous.
If someone is not kind then someone is both calm and not generous and vice versa.
If susan is both not generous and not wise then paul is kind or brave and vice versa.
If someone is not wise or not brave then alice is both not happy and strong.
Everyone who is either not creative or strong is both quiet and rich and vice versa.
Everyone who is both not quiet and humble is both not humble and not strong and vice versa.
If someone is not quiet or not rich then paul is both quiet and not creative.
Everyone who is both wise and not curious is not humble and vice versa.
Everyone who is both rich and patient is tall.
If alice is not quiet then paul is either not generous or not kind and vice versa.
Everyone who is either not happy or not funny is curious.
If someone is either not old or wise then alice is funny and vice versa.
Everyone who is both not wise and strong is both rich and old.
Lucy is funny.
Someone is funny or curious.
Someone is either brave or not happy.
Paul is either not curious or kind.
Someone is brave or funny.
Susan is both humble and not patient.
John is both calm and not tall.
Alice is both humble and not patient. | Susan is patient. | contradiction | ((?[X]:((funny(X)&~funny(X))))=>(~humble(mary)))&
((?[X]:((calm(X)&~humble(X))))<=>(?[X]:((~curious(X)&~kind(X)))))&
((?[X]:((kind(X)&~creative(X))))<=>((quiet(paul)<~>old(paul))))&
(![X]:(~creative(X)=>(~quiet(X)|~generous(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((calm(X)&~generous(X)))))&
(((~generous(susan)&~wise(susan)))<=>((kind(paul)|brave(paul))))&
((?[X]:((~wise(X)|~brave(X))))=>((~happy(alice)&strong(alice))))&
(![X]:((~creative(X)<~>strong(X))<=>(quiet(X)&rich(X))))&
(![X]:((~quiet(X)&humble(X))<=>(~humble(X)&~strong(X))))&
((?[X]:((~quiet(X)|~rich(X))))=>((quiet(paul)&~creative(paul))))&
(![X]:((wise(X)&~curious(X))<=>~humble(X)))&
(![X]:((rich(X)&patient(X))=>tall(X)))&
((~quiet(alice))<=>((~generous(paul)<~>~kind(paul))))&
(![X]:((~happy(X)<~>~funny(X))=>curious(X)))&
((?[X]:((~old(X)<~>wise(X))))<=>(funny(alice)))&
(![X]:((~wise(X)&strong(X))=>(rich(X)&old(X))))&
(funny(lucy))&
(?[X]:((funny(X)|curious(X))))&
(?[X]:((brave(X)<~>~happy(X))))&
((~curious(paul)<~>kind(paul)))&
(?[X]:((brave(X)|funny(X))))&
((humble(susan)&~patient(susan)))&
((calm(john)&~tall(john)))&
((humble(alice)&~patient(alice))) | patient(susan) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 504500427623756356615817
% SZS output start Proof for 504500427623756356615817
22. ~patient(susan) & humble(susan) [input p21]
25. patient(susan) [input hypothesis]
136. ~patient(susan) [cnf transformation 22]
141. patient(susan) [cnf transformation 25]
337. $false [subsumption resolution 141,136]
% SZS output end Proof for 504500427623756356615817
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is tall then someone is both curious and brave.
If john is not tall or not strong then paul is not generous or not happy and vice versa.
Everyone who is both not creative and not kind is funny and vice versa.
If someone is brave or curious then someone is not rich and vice versa.
If fred is either not funny or creative then paul is both not humble and not funny and vice versa.
If john is not creative then someone is not generous or generous and vice versa.
Everyone who is funny is both funny and not curious and vice versa.
Everyone who is both generous and not patient is either not old or brave and vice versa.
If paul is not creative or not rich then someone is not strong and vice versa.
If lucy is either quiet or tall then john is either not old or not creative and vice versa.
Everyone who is not tall or not strong is either funny or not humble.
If lucy is not generous then john is kind or creative.
Everyone who is humble or patient is both not brave and kind and vice versa.
Everyone who is not old is either humble or not kind and vice versa.
Everyone who is not calm is both not kind and not funny and vice versa.
Everyone who is both old and tall is brave or not funny and vice versa.
Mary is not patient or quiet.
Lucy is funny.
Someone is both not old and not rich.
Someone is either not happy or not generous.
Someone is both not humble and not happy.
Lucy is either not kind or curious. | Fred is creative. | neutral | ((?[X]:(tall(X)))=>(?[X]:((curious(X)&brave(X)))))&
(((~tall(john)|~strong(john)))<=>((~generous(paul)|~happy(paul))))&
(![X]:((~creative(X)&~kind(X))<=>funny(X)))&
((?[X]:((brave(X)|curious(X))))<=>(?[X]:(~rich(X))))&
(((~funny(fred)<~>creative(fred)))<=>((~humble(paul)&~funny(paul))))&
((~creative(john))<=>(?[X]:((~generous(X)|generous(X)))))&
(![X]:(funny(X)<=>(funny(X)&~curious(X))))&
(![X]:((generous(X)&~patient(X))<=>(~old(X)<~>brave(X))))&
(((~creative(paul)|~rich(paul)))<=>(?[X]:(~strong(X))))&
(((quiet(lucy)<~>tall(lucy)))<=>((~old(john)<~>~creative(john))))&
(![X]:((~tall(X)|~strong(X))=>(funny(X)<~>~humble(X))))&
((~generous(lucy))=>((kind(john)|creative(john))))&
(![X]:((humble(X)|patient(X))<=>(~brave(X)&kind(X))))&
(![X]:(~old(X)<=>(humble(X)<~>~kind(X))))&
(![X]:(~calm(X)<=>(~kind(X)&~funny(X))))&
(![X]:((old(X)&tall(X))<=>(brave(X)|~funny(X))))&
((~patient(mary)|quiet(mary)))&
(funny(lucy))&
(?[X]:((~old(X)&~rich(X))))&
(?[X]:((~happy(X)<~>~generous(X))))&
(?[X]:((~humble(X)&~happy(X))))&
((~kind(lucy)<~>curious(lucy))) | creative(fred) | [] | null | 0 |
If someone is both strong and not happy then someone is both not brave and not tall and vice versa.
Everyone who is either creative or wise is both brave and not creative and vice versa.
Everyone who is either generous or not rich is either quiet or rich and vice versa.
Everyone who is not calm is either quiet or not patient.
Everyone who is not creative is strong or rich.
Everyone who is not old or generous is both happy and quiet.
If mary is rich or patient then lucy is both curious and wise.
Everyone who is both not kind and rich is both not curious and funny.
If someone is both old and not calm then someone is creative.
Everyone who is both not curious and happy is both calm and not humble.
Everyone who is creative is generous and vice versa.
If alice is not funny then someone is not calm.
If paul is either not patient or not tall then someone is both not generous and not rich.
Everyone who is not rich is rich or brave and vice versa.
Everyone who is not brave is both curious and tall.
Everyone who is not calm or not strong is not strong.
Paul is not strong or happy.
Someone is either not old or not wise.
Someone is happy.
Fred is not funny or wise.
Fred is wise.
Someone is both curious and not rich. | Alice is not quiet. | contradiction | ((?[X]:((strong(X)&~happy(X))))<=>(?[X]:((~brave(X)&~tall(X)))))&
(![X]:((creative(X)<~>wise(X))<=>(brave(X)&~creative(X))))&
(![X]:((generous(X)<~>~rich(X))<=>(quiet(X)<~>rich(X))))&
(![X]:(~calm(X)=>(quiet(X)<~>~patient(X))))&
(![X]:(~creative(X)=>(strong(X)|rich(X))))&
(![X]:((~old(X)|generous(X))=>(happy(X)&quiet(X))))&
(((rich(mary)|patient(mary)))=>((curious(lucy)&wise(lucy))))&
(![X]:((~kind(X)&rich(X))=>(~curious(X)&funny(X))))&
((?[X]:((old(X)&~calm(X))))=>(?[X]:(creative(X))))&
(![X]:((~curious(X)&happy(X))=>(calm(X)&~humble(X))))&
(![X]:(creative(X)<=>generous(X)))&
((~funny(alice))=>(?[X]:(~calm(X))))&
(((~patient(paul)<~>~tall(paul)))=>(?[X]:((~generous(X)&~rich(X)))))&
(![X]:(~rich(X)<=>(rich(X)|brave(X))))&
(![X]:(~brave(X)=>(curious(X)&tall(X))))&
(![X]:((~calm(X)|~strong(X))=>~strong(X)))&
((~strong(paul)|happy(paul)))&
(?[X]:((~old(X)<~>~wise(X))))&
(?[X]:(happy(X)))&
((~funny(fred)|wise(fred)))&
(wise(fred))&
(?[X]:((curious(X)&~rich(X)))) | ~quiet(alice) | [
"p2",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 4110460933215244481363993
% SZS output start Proof for 4110460933215244481363993
3. ! [X0] : ((generous(X0) <~> ~rich(X0)) <=> (quiet(X0) <~> rich(X0))) [input p2]
6. ! [X0] : ((generous(X0) | ~old(X0)) => (quiet(X0) & happy(X0))) [input p5]
23. ~quiet(alice) [input hypothesis]
35. ! [X0] : ((quiet(X0) & happy(X0)) | (~generous(X0) & old(X0))) [ennf transformation 6]
49. ! [X0] : ((((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0)))) & (((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0))))) [nnf transformation 3]
80. rich(X0) | quiet(X0) | generous(X0) | rich(X0) [cnf transformation 49]
84. ~rich(X0) | generous(X0) | quiet(X0) | ~rich(X0) [cnf transformation 49]
93. quiet(X0) | ~generous(X0) [cnf transformation 35]
117. ~quiet(alice) [cnf transformation 23]
120. rich(X0) | quiet(X0) | generous(X0) [duplicate literal removal 80]
122. ~rich(X0) | generous(X0) | quiet(X0) [duplicate literal removal 84]
153. quiet(X0) | generous(X0) [subsumption resolution 120,122]
154. quiet(X0) [subsumption resolution 93,153]
236. $false [subsumption resolution 117,154]
% SZS output end Proof for 4110460933215244481363993
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not rich is either creative or not rich.
If someone is not calm or not tall then someone is quiet and vice versa.
Everyone who is not quiet or quiet is quiet.
Everyone who is quiet or curious is either old or not tall.
If susan is either not calm or not humble then alice is wise and vice versa.
If someone is either patient or old then someone is not generous or creative.
If john is both not humble and brave then alice is either not rich or curious.
If lucy is not patient then susan is strong.
Everyone who is both not creative and brave is not creative.
If someone is both not creative and wise then lucy is either creative or not tall.
Everyone who is both not old and old is not generous or funny and vice versa.
If someone is not curious or not quiet then john is generous or quiet and vice versa.
Everyone who is not generous or not humble is both not generous and not quiet and vice versa.
Everyone who is both quiet and not brave is either not curious or not wise.
If someone is either not wise or curious then susan is either funny or creative.
Someone is creative.
Susan is both brave and not strong.
Someone is patient.
Someone is either tall or not curious.
John is both curious and not tall.
Someone is not calm. | John is not generous. | contradiction | (![X]:((~wise(X)<~>~rich(X))=>(creative(X)<~>~rich(X))))&
((?[X]:((~calm(X)|~tall(X))))<=>(?[X]:(quiet(X))))&
(![X]:((~quiet(X)|quiet(X))=>quiet(X)))&
(![X]:((quiet(X)|curious(X))=>(old(X)<~>~tall(X))))&
(((~calm(susan)<~>~humble(susan)))<=>(wise(alice)))&
((?[X]:((patient(X)<~>old(X))))=>(?[X]:((~generous(X)|creative(X)))))&
(((~humble(john)&brave(john)))=>((~rich(alice)<~>curious(alice))))&
((~patient(lucy))=>(strong(susan)))&
(![X]:((~creative(X)&brave(X))=>~creative(X)))&
((?[X]:((~creative(X)&wise(X))))=>((creative(lucy)<~>~tall(lucy))))&
(![X]:((~old(X)&old(X))<=>(~generous(X)|funny(X))))&
((?[X]:((~curious(X)|~quiet(X))))<=>((generous(john)|quiet(john))))&
(![X]:((~generous(X)|~humble(X))<=>(~generous(X)&~quiet(X))))&
(![X]:((quiet(X)&~brave(X))=>(~curious(X)<~>~wise(X))))&
((?[X]:((~wise(X)<~>curious(X))))=>((funny(susan)<~>creative(susan))))&
(?[X]:(creative(X)))&
((brave(susan)&~strong(susan)))&
(?[X]:(patient(X)))&
(?[X]:((tall(X)<~>~curious(X))))&
((curious(john)&~tall(john)))&
(?[X]:(~calm(X))) | ~generous(john) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4552590452144690697854720
% SZS output start Proof for 4552590452144690697854720
11. ! [X0] : ((old(X0) & ~old(X0)) <=> (funny(X0) | ~generous(X0))) [input p10]
22. ~generous(john) [input hypothesis]
52. ! [X0] : (((old(X0) & ~old(X0)) | (~funny(X0) & generous(X0))) & ((funny(X0) | ~generous(X0)) | (~old(X0) | old(X0)))) [nnf transformation 11]
53. ! [X0] : (((old(X0) & ~old(X0)) | (~funny(X0) & generous(X0))) & (funny(X0) | ~generous(X0) | ~old(X0) | old(X0))) [flattening 52]
98. ~old(X0) | generous(X0) [cnf transformation 53]
100. old(X0) | generous(X0) [cnf transformation 53]
126. ~generous(john) [cnf transformation 22]
229. generous(X0) [subsumption resolution 98,100]
260. $false [subsumption resolution 126,229]
% SZS output end Proof for 4552590452144690697854720
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not creative is creative.
If mary is either strong or not quiet then lucy is either wise or curious and vice versa.
Everyone who is either wise or brave is not wise or not strong and vice versa.
If someone is either quiet or creative then john is either rich or not curious and vice versa.
Everyone who is not rich or brave is both calm and not calm.
If lucy is either not brave or not creative then someone is old or happy.
If lucy is both brave and not curious then someone is not happy and vice versa.
Everyone who is either not strong or patient is not rich and vice versa.
Everyone who is either not humble or not creative is either not generous or not happy and vice versa.
If paul is brave then someone is not strong.
Everyone who is either not brave or rich is not happy or happy.
Everyone who is kind or not brave is not creative and vice versa.
Everyone who is not kind or curious is not humble.
Everyone who is both not curious and funny is either not happy or brave and vice versa.
Everyone who is either curious or creative is either brave or kind.
If someone is either not happy or not calm then paul is both funny and kind and vice versa.
Someone is funny or happy.
Paul is either happy or not rich.
Someone is both not brave and generous.
Someone is happy.
Paul is kind. | Mary is tall. | contradiction | (![X]:((~tall(X)<~>~creative(X))=>creative(X)))&
(((strong(mary)<~>~quiet(mary)))<=>((wise(lucy)<~>curious(lucy))))&
(![X]:((wise(X)<~>brave(X))<=>(~wise(X)|~strong(X))))&
((?[X]:((quiet(X)<~>creative(X))))<=>((rich(john)<~>~curious(john))))&
(![X]:((~rich(X)|brave(X))=>(calm(X)&~calm(X))))&
(((~brave(lucy)<~>~creative(lucy)))=>(?[X]:((old(X)|happy(X)))))&
(((brave(lucy)&~curious(lucy)))<=>(?[X]:(~happy(X))))&
(![X]:((~strong(X)<~>patient(X))<=>~rich(X)))&
(![X]:((~humble(X)<~>~creative(X))<=>(~generous(X)<~>~happy(X))))&
((brave(paul))=>(?[X]:(~strong(X))))&
(![X]:((~brave(X)<~>rich(X))=>(~happy(X)|happy(X))))&
(![X]:((kind(X)|~brave(X))<=>~creative(X)))&
(![X]:((~kind(X)|curious(X))=>~humble(X)))&
(![X]:((~curious(X)&funny(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((curious(X)<~>creative(X))=>(brave(X)<~>kind(X))))&
((?[X]:((~happy(X)<~>~calm(X))))<=>((funny(paul)&kind(paul))))&
(?[X]:((funny(X)|happy(X))))&
((happy(paul)<~>~rich(paul)))&
(?[X]:((~brave(X)&generous(X))))&
(?[X]:(happy(X)))&
(kind(paul)) | tall(mary) | [
"p0",
"p4",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3332501767360049273160359
% SZS output start Proof for 3332501767360049273160359
1. ! [X0] : ((~tall(X0) <~> ~creative(X0)) => creative(X0)) [input p0]
5. ! [X0] : ((brave(X0) | ~rich(X0)) => (~calm(X0) & calm(X0))) [input p4]
12. ! [X0] : ((~brave(X0) | kind(X0)) <=> ~creative(X0)) [input p11]
22. tall(mary) [input hypothesis]
24. ! [X0] : (creative(X0) | (~tall(X0) <=> ~creative(X0))) [ennf transformation 1]
25. ! [X0] : ((~calm(X0) & calm(X0)) | (~brave(X0) & rich(X0))) [ennf transformation 5]
31. ! [X0] : (creative(X0) | ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0)))) [nnf transformation 24]
49. ! [X0] : (((~brave(X0) | kind(X0)) | creative(X0)) & (~creative(X0) | (brave(X0) & ~kind(X0)))) [nnf transformation 12]
50. ! [X0] : ((~brave(X0) | kind(X0) | creative(X0)) & (~creative(X0) | (brave(X0) & ~kind(X0)))) [flattening 49]
67. creative(X0) | ~tall(X0) | creative(X0) [cnf transformation 31]
91. calm(X0) | ~brave(X0) [cnf transformation 25]
93. ~calm(X0) | ~brave(X0) [cnf transformation 25]
113. ~creative(X0) | brave(X0) [cnf transformation 50]
140. tall(mary) [cnf transformation 22]
143. ~tall(X0) | creative(X0) [duplicate literal removal 67]
199. ~brave(X0) [subsumption resolution 91,93]
209. ~creative(X0) [subsumption resolution 113,199]
251. creative(mary) [resolution 143,140]
252. $false [subsumption resolution 251,209]
% SZS output end Proof for 3332501767360049273160359
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or tall then fred is not patient or kind.
If alice is both not funny and not happy then someone is either rich or not curious and vice versa.
If john is not humble or calm then john is either brave or not rich and vice versa.
Everyone who is both quiet and happy is old or happy and vice versa.
If mary is both not curious and rich then someone is both rich and not strong.
Everyone who is both calm and happy is patient.
Everyone who is either quiet or not funny is both generous and creative and vice versa.
Everyone who is tall or calm is not generous.
If someone is wise then john is patient.
Everyone who is both not curious and not quiet is not generous and vice versa.
Everyone who is not generous or generous is either not funny or curious.
If someone is not strong then susan is curious or wise and vice versa.
Everyone who is either not calm or not curious is not creative and vice versa.
Everyone who is either wise or old is either not funny or not patient.
Everyone who is curious or not generous is not quiet or not humble and vice versa.
Everyone who is old or generous is either not humble or patient.
Someone is curious.
Someone is calm or not quiet.
John is strong.
Someone is tall or not quiet. | John is not creative. | entailment | ((?[X]:((~curious(X)<~>tall(X))))=>((~patient(fred)|kind(fred))))&
(((~funny(alice)&~happy(alice)))<=>(?[X]:((rich(X)<~>~curious(X)))))&
(((~humble(john)|calm(john)))<=>((brave(john)<~>~rich(john))))&
(![X]:((quiet(X)&happy(X))<=>(old(X)|happy(X))))&
(((~curious(mary)&rich(mary)))=>(?[X]:((rich(X)&~strong(X)))))&
(![X]:((calm(X)&happy(X))=>patient(X)))&
(![X]:((quiet(X)<~>~funny(X))<=>(generous(X)&creative(X))))&
(![X]:((tall(X)|calm(X))=>~generous(X)))&
((?[X]:(wise(X)))=>(patient(john)))&
(![X]:((~curious(X)&~quiet(X))<=>~generous(X)))&
(![X]:((~generous(X)|generous(X))=>(~funny(X)<~>curious(X))))&
((?[X]:(~strong(X)))<=>((curious(susan)|wise(susan))))&
(![X]:((~calm(X)<~>~curious(X))<=>~creative(X)))&
(![X]:((wise(X)<~>old(X))=>(~funny(X)<~>~patient(X))))&
(![X]:((curious(X)|~generous(X))<=>(~quiet(X)|~humble(X))))&
(![X]:((old(X)|generous(X))=>(~humble(X)<~>patient(X))))&
(?[X]:(curious(X)))&
(?[X]:((calm(X)|~quiet(X))))&
(strong(john))&
(?[X]:((tall(X)|~quiet(X)))) | ~creative(john) | [
"p6",
"p7",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1996502539912456827675332
% SZS output start Proof for 1996502539912456827675332
7. ! [X0] : ((quiet(X0) <~> ~funny(X0)) <=> (creative(X0) & generous(X0))) [input p6]
8. ! [X0] : ((calm(X0) | tall(X0)) => ~generous(X0)) [input p7]
10. ! [X0] : ((~quiet(X0) & ~curious(X0)) <=> ~generous(X0)) [input p9]
11. ! [X0] : ((generous(X0) | ~generous(X0)) => (~funny(X0) <~> curious(X0))) [input p10]
13. ! [X0] : ((~calm(X0) <~> ~curious(X0)) <=> ~creative(X0)) [input p12]
21. creative(john) [input hypothesis]
27. ! [X0] : (~generous(X0) | (~calm(X0) & ~tall(X0))) [ennf transformation 8]
29. ! [X0] : ((~funny(X0) <~> curious(X0)) | (~generous(X0) & generous(X0))) [ennf transformation 11]
43. ! [X0] : ((((funny(X0) | ~quiet(X0)) & (~funny(X0) | quiet(X0))) | (~creative(X0) | ~generous(X0))) & ((creative(X0) & generous(X0)) | ((quiet(X0) | funny(X0)) & (~funny(X0) | ~quiet(X0))))) [nnf transformation 7]
44. ! [X0] : ((((funny(X0) | ~quiet(X0)) & (~funny(X0) | quiet(X0))) | ~creative(X0) | ~generous(X0)) & ((creative(X0) & generous(X0)) | ((quiet(X0) | funny(X0)) & (~funny(X0) | ~quiet(X0))))) [flattening 43]
45. ! [X0] : (((~quiet(X0) & ~curious(X0)) | generous(X0)) & (~generous(X0) | (quiet(X0) | curious(X0)))) [nnf transformation 10]
46. ! [X0] : (((~quiet(X0) & ~curious(X0)) | generous(X0)) & (~generous(X0) | quiet(X0) | curious(X0))) [flattening 45]
47. ! [X0] : (((~curious(X0) | funny(X0)) & (curious(X0) | ~funny(X0))) | (~generous(X0) & generous(X0))) [nnf transformation 29]
53. ! [X0] : ((((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | creative(X0)) & (~creative(X0) | ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0))))) [nnf transformation 13]
85. generous(X0) | quiet(X0) | funny(X0) [cnf transformation 44]
88. ~creative(X0) | quiet(X0) | ~funny(X0) | ~generous(X0) [cnf transformation 44]
89. ~creative(X0) | ~quiet(X0) | funny(X0) | ~generous(X0) [cnf transformation 44]
91. ~generous(X0) | ~calm(X0) [cnf transformation 27]
93. ~generous(X0) | quiet(X0) | curious(X0) [cnf transformation 46]
94. ~curious(X0) | generous(X0) [cnf transformation 46]
95. ~quiet(X0) | generous(X0) [cnf transformation 46]
96. curious(X0) | ~funny(X0) | generous(X0) [cnf transformation 47]
97. ~generous(X0) | ~funny(X0) | curious(X0) [cnf transformation 47]
99. ~curious(X0) | funny(X0) | ~generous(X0) [cnf transformation 47]
103. ~creative(X0) | ~curious(X0) | calm(X0) [cnf transformation 53]
123. creative(john) [cnf transformation 21]
165. 10 <=> calm(john) [avatar definition]
167. calm(john) <- (10) [avatar component clause 165]
200. ~curious(X0) | funny(X0) [subsumption resolution 99,94]
201. ~funny(X0) | generous(X0) [subsumption resolution 96,94]
248. quiet(X0) | curious(X0) | quiet(X0) | funny(X0) [resolution 93,85]
249. quiet(X0) | curious(X0) | funny(X0) [duplicate literal removal 248]
250. quiet(X0) | funny(X0) [subsumption resolution 249,200]
255. funny(X2) | generous(X2) [resolution 250,95]
256. generous(X2) [subsumption resolution 255,201]
260. ~curious(john) | calm(john) [resolution 103,123]
263. 25 <=> curious(john) [avatar definition]
266. 10 | ~25 [avatar split clause 260,263,165]
276. ~funny(X0) | curious(X0) [resolution 256,97]
278. ~calm(X2) [resolution 256,91]
306. quiet(john) | ~funny(john) | ~generous(john) [resolution 88,123]
310. quiet(john) | ~funny(john) [subsumption resolution 306,256]
311. quiet(john) [subsumption resolution 310,250]
316. ~quiet(john) | funny(john) | ~generous(john) [resolution 89,123]
320. funny(john) | ~generous(john) [subsumption resolution 316,311]
321. funny(john) [subsumption resolution 320,256]
326. curious(john) [resolution 321,276]
330. 25 [avatar split clause 326,263]
331. $false <- (10) [subsumption resolution 167,278]
332. ~10 [avatar contradiction clause 331]
333. $false [avatar sat refutation 266,330,332]
% SZS output end Proof for 1996502539912456827675332
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and curious is either strong or wise and vice versa.
Everyone who is not curious or funny is either not strong or not generous and vice versa.
If someone is not wise or calm then mary is either old or not kind and vice versa.
If alice is not funny or not old then someone is both curious and not patient.
Everyone who is not old or not strong is both not generous and tall and vice versa.
Everyone who is either humble or happy is not quiet.
If alice is not quiet or happy then alice is both not brave and not calm and vice versa.
If someone is brave or not funny then lucy is either funny or calm.
If someone is not funny then someone is kind and vice versa.
Everyone who is not funny or tall is both generous and funny and vice versa.
Everyone who is either not curious or happy is both brave and calm.
If mary is not wise or not patient then alice is quiet or kind and vice versa.
Everyone who is either not creative or old is not happy or generous and vice versa.
Everyone who is happy or not humble is not strong.
Everyone who is both not strong and not generous is tall or not creative.
Everyone who is creative is funny or creative and vice versa.
Mary is humble or not patient.
Lucy is patient.
Someone is both brave and not kind.
Paul is not quiet.
Someone is either not kind or patient.
Someone is curious. | Lucy is not humble. | contradiction | (![X]:((~creative(X)&curious(X))<=>(strong(X)<~>wise(X))))&
(![X]:((~curious(X)|funny(X))<=>(~strong(X)<~>~generous(X))))&
((?[X]:((~wise(X)|calm(X))))<=>((old(mary)<~>~kind(mary))))&
(((~funny(alice)|~old(alice)))=>(?[X]:((curious(X)&~patient(X)))))&
(![X]:((~old(X)|~strong(X))<=>(~generous(X)&tall(X))))&
(![X]:((humble(X)<~>happy(X))=>~quiet(X)))&
(((~quiet(alice)|happy(alice)))<=>((~brave(alice)&~calm(alice))))&
((?[X]:((brave(X)|~funny(X))))=>((funny(lucy)<~>calm(lucy))))&
((?[X]:(~funny(X)))<=>(?[X]:(kind(X))))&
(![X]:((~funny(X)|tall(X))<=>(generous(X)&funny(X))))&
(![X]:((~curious(X)<~>happy(X))=>(brave(X)&calm(X))))&
(((~wise(mary)|~patient(mary)))<=>((quiet(alice)|kind(alice))))&
(![X]:((~creative(X)<~>old(X))<=>(~happy(X)|generous(X))))&
(![X]:((happy(X)|~humble(X))=>~strong(X)))&
(![X]:((~strong(X)&~generous(X))=>(tall(X)|~creative(X))))&
(![X]:(creative(X)<=>(funny(X)|creative(X))))&
((humble(mary)|~patient(mary)))&
(patient(lucy))&
(?[X]:((brave(X)&~kind(X))))&
(~quiet(paul))&
(?[X]:((~kind(X)<~>patient(X))))&
(?[X]:(curious(X))) | ~humble(lucy) | [
"p4",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4379434240628453698468339
% SZS output start Proof for 4379434240628453698468339
5. ! [X0] : ((~strong(X0) | ~old(X0)) <=> (tall(X0) & ~generous(X0))) [input p4]
10. ! [X0] : ((tall(X0) | ~funny(X0)) <=> (funny(X0) & generous(X0))) [input p9]
14. ! [X0] : ((~humble(X0) | happy(X0)) => ~strong(X0)) [input p13]
23. ~humble(lucy) [input hypothesis]
29. ! [X0] : (~strong(X0) | (humble(X0) & ~happy(X0))) [ennf transformation 14]
42. ! [X0] : (((~strong(X0) | ~old(X0)) | (~tall(X0) | generous(X0))) & ((tall(X0) & ~generous(X0)) | (strong(X0) & old(X0)))) [nnf transformation 5]
43. ! [X0] : ((~strong(X0) | ~old(X0) | ~tall(X0) | generous(X0)) & ((tall(X0) & ~generous(X0)) | (strong(X0) & old(X0)))) [flattening 42]
53. ! [X0] : (((tall(X0) | ~funny(X0)) | (~funny(X0) | ~generous(X0))) & ((funny(X0) & generous(X0)) | (~tall(X0) & funny(X0)))) [nnf transformation 10]
54. ! [X0] : ((tall(X0) | ~funny(X0) | ~funny(X0) | ~generous(X0)) & ((funny(X0) & generous(X0)) | (~tall(X0) & funny(X0)))) [flattening 53]
92. ~generous(X0) | strong(X0) [cnf transformation 43]
94. tall(X0) | strong(X0) [cnf transformation 43]
110. ~tall(X0) | generous(X0) [cnf transformation 54]
129. ~strong(X0) | humble(X0) [cnf transformation 29]
142. ~humble(lucy) [cnf transformation 23]
283. generous(X0) | strong(X0) [resolution 110,94]
285. strong(X0) [subsumption resolution 283,92]
293. humble(X0) [resolution 129,285]
294. $false [resolution 293,142]
% SZS output end Proof for 4379434240628453698468339
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not curious and brave then someone is both not calm and happy. Everyone who is funny is both rich and strong and vice versa. Everyone who is not creative or rich is not calm and vice versa. Everyone who is both not old and not calm is both patient and not funny and vice versa. Everyone who is not quiet is either wise or not funny. Everyone who is either creative or wise is not happy or not patient. If john is not calm or not rich then someone is not patient and vice versa. If someone is both patient and tall then someone is both not generous and not strong. Everyone who is either not funny or funny is both generous and not wise and vice versa. Everyone who is generous or not kind is either not wise or not funny and vice versa. If alice is happy then susan is wise or not wise. If someone is both strong and not brave then mary is not kind or old. Everyone who is not tall or not wise is strong. If mary is either humble or not funny then mary is either not patient or not rich and vice versa. If someone is quiet then alice is both old and creative and vice versa. If someone is not funny then someone is both not generous and patient. Mary is not brave. Susan is not calm. John is strong or not generous. John is not tall. | Mary is not old. | contradiction | ((?[X]:((~curious(X)&brave(X))))=>(?[X]:((~calm(X)&happy(X)))))&
(![X]:(funny(X)<=>(rich(X)&strong(X))))&
(![X]:((~creative(X)|rich(X))<=>~calm(X)))&
(![X]:((~old(X)&~calm(X))<=>(patient(X)&~funny(X))))&
(![X]:(~quiet(X)=>(wise(X)<~>~funny(X))))&
(![X]:((creative(X)<~>wise(X))=>(~happy(X)|~patient(X))))&
(((~calm(john)|~rich(john)))<=>(?[X]:(~patient(X))))&
((?[X]:((patient(X)&tall(X))))=>(?[X]:((~generous(X)&~strong(X)))))&
(![X]:((~funny(X)<~>funny(X))<=>(generous(X)&~wise(X))))&
(![X]:((generous(X)|~kind(X))<=>(~wise(X)<~>~funny(X))))&
((happy(alice))=>((wise(susan)|~wise(susan))))&
((?[X]:((strong(X)&~brave(X))))=>((~kind(mary)|old(mary))))&
(![X]:((~tall(X)|~wise(X))=>strong(X)))&
(((humble(mary)<~>~funny(mary)))<=>((~patient(mary)<~>~rich(mary))))&
((?[X]:(quiet(X)))<=>((old(alice)&creative(alice))))&
((?[X]:(~funny(X)))=>(?[X]:((~generous(X)&patient(X)))))&
(~brave(mary))&
(~calm(susan))&
((strong(john)|~generous(john)))&
(~tall(john)) | ~old(mary) | [
"p1",
"p2",
"p3",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2623673238130999813235304
% SZS output start Proof for 2623673238130999813235304
2. ! [X0] : (funny(X0) <=> (strong(X0) & rich(X0))) [input p1]
3. ! [X0] : ((rich(X0) | ~creative(X0)) <=> ~calm(X0)) [input p2]
4. ! [X0] : ((~calm(X0) & ~old(X0)) <=> (~funny(X0) & patient(X0))) [input p3]
9. ! [X0] : ((~funny(X0) <~> funny(X0)) <=> (~wise(X0) & generous(X0))) [input p8]
10. ! [X0] : ((~kind(X0) | generous(X0)) <=> (~wise(X0) <~> ~funny(X0))) [input p9]
21. ~old(mary) [input hypothesis]
34. ! [X0] : ((funny(X0) | (~strong(X0) | ~rich(X0))) & ((strong(X0) & rich(X0)) | ~funny(X0))) [nnf transformation 2]
35. ! [X0] : ((funny(X0) | ~strong(X0) | ~rich(X0)) & ((strong(X0) & rich(X0)) | ~funny(X0))) [flattening 34]
36. ! [X0] : (((rich(X0) | ~creative(X0)) | calm(X0)) & (~calm(X0) | (~rich(X0) & creative(X0)))) [nnf transformation 3]
37. ! [X0] : ((rich(X0) | ~creative(X0) | calm(X0)) & (~calm(X0) | (~rich(X0) & creative(X0)))) [flattening 36]
38. ! [X0] : (((~calm(X0) & ~old(X0)) | (funny(X0) | ~patient(X0))) & ((~funny(X0) & patient(X0)) | (calm(X0) | old(X0)))) [nnf transformation 4]
39. ! [X0] : (((~calm(X0) & ~old(X0)) | funny(X0) | ~patient(X0)) & ((~funny(X0) & patient(X0)) | calm(X0) | old(X0))) [flattening 38]
49. ! [X0] : ((((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | (wise(X0) | ~generous(X0))) & ((~wise(X0) & generous(X0)) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0))))) [nnf transformation 9]
50. ! [X0] : ((((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | wise(X0) | ~generous(X0)) & ((~wise(X0) & generous(X0)) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0))))) [flattening 49]
51. ! [X0] : (((~kind(X0) | generous(X0)) | ((~wise(X0) | funny(X0)) & (~funny(X0) | wise(X0)))) & (((funny(X0) | wise(X0)) & (~funny(X0) | ~wise(X0))) | (kind(X0) & ~generous(X0)))) [nnf transformation 10]
52. ! [X0] : ((~kind(X0) | generous(X0) | ((~wise(X0) | funny(X0)) & (~funny(X0) | wise(X0)))) & (((funny(X0) | wise(X0)) & (~funny(X0) | ~wise(X0))) | (kind(X0) & ~generous(X0)))) [flattening 51]
62. ~funny(X0) | rich(X0) [cnf transformation 35]
66. ~rich(X0) | ~calm(X0) [cnf transformation 37]
69. ~funny(X0) | calm(X0) | old(X0) [cnf transformation 39]
79. generous(X0) | funny(X0) | funny(X0) [cnf transformation 50]
80. generous(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 50]
81. ~wise(X0) | funny(X0) | funny(X0) [cnf transformation 50]
82. ~wise(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 50]
87. funny(X0) | wise(X0) | ~generous(X0) [cnf transformation 52]
111. ~old(mary) [cnf transformation 21]
112. generous(X0) | funny(X0) [duplicate literal removal 79]
113. ~funny(X0) | generous(X0) [duplicate literal removal 80]
114. ~wise(X0) | funny(X0) [duplicate literal removal 81]
115. ~wise(X0) | ~funny(X0) [duplicate literal removal 82]
143. ~wise(X0) [subsumption resolution 114,115]
144. generous(X0) [subsumption resolution 112,113]
146. funny(X0) | ~generous(X0) [subsumption resolution 87,143]
147. funny(X0) [subsumption resolution 146,144]
156. 9 <=> old(mary) [avatar definition]
157. ~old(mary) <- (~9) [avatar component clause 156]
195. ~9 [avatar split clause 111,156]
200. rich(X0) [resolution 62,147]
204. ~calm(X0) [resolution 66,200]
211. calm(X0) | old(X0) [resolution 69,147]
212. old(X0) [subsumption resolution 211,204]
215. $false <- (~9) [resolution 212,157]
216. 9 [avatar contradiction clause 215]
217. $false [avatar sat refutation 195,216]
% SZS output end Proof for 2623673238130999813235304
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not creative is both happy and humble.
If susan is either not curious or old then john is either not kind or strong and vice versa.
Everyone who is both not funny and patient is not calm and vice versa.
Everyone who is either not quiet or not old is either not quiet or not strong and vice versa.
Everyone who is happy is not tall.
If lucy is either curious or strong then someone is not strong or tall.
If someone is kind or generous then someone is not happy or not wise and vice versa.
Everyone who is strong is both not generous and strong.
Everyone who is strong is both rich and not rich.
If someone is both generous and patient then fred is both kind and happy.
If someone is either funny or not wise then someone is not funny.
Everyone who is either wise or calm is both not old and calm.
If someone is either calm or not patient then paul is either wise or strong.
If lucy is both old and not old then someone is either not rich or strong and vice versa.
Everyone who is not quiet is patient and vice versa.
If susan is both generous and not curious then mary is not calm or generous and vice versa.
John is not quiet or not rich.
Someone is both not old and not funny.
Someone is not happy or old.
Someone is both curious and not humble.
John is either humble or not strong.
Susan is either not quiet or rich.
Someone is not calm.
Lucy is not old or not creative. | Mary is rich. | entailment | (![X]:((generous(X)&~creative(X))=>(happy(X)&humble(X))))&
(((~curious(susan)<~>old(susan)))<=>((~kind(john)<~>strong(john))))&
(![X]:((~funny(X)&patient(X))<=>~calm(X)))&
(![X]:((~quiet(X)<~>~old(X))<=>(~quiet(X)<~>~strong(X))))&
(![X]:(happy(X)=>~tall(X)))&
(((curious(lucy)<~>strong(lucy)))=>(?[X]:((~strong(X)|tall(X)))))&
((?[X]:((kind(X)|generous(X))))<=>(?[X]:((~happy(X)|~wise(X)))))&
(![X]:(strong(X)=>(~generous(X)&strong(X))))&
(![X]:(strong(X)=>(rich(X)&~rich(X))))&
((?[X]:((generous(X)&patient(X))))=>((kind(fred)&happy(fred))))&
((?[X]:((funny(X)<~>~wise(X))))=>(?[X]:(~funny(X))))&
(![X]:((wise(X)<~>calm(X))=>(~old(X)&calm(X))))&
((?[X]:((calm(X)<~>~patient(X))))=>((wise(paul)<~>strong(paul))))&
(((old(lucy)&~old(lucy)))<=>(?[X]:((~rich(X)<~>strong(X)))))&
(![X]:(~quiet(X)<=>patient(X)))&
(((generous(susan)&~curious(susan)))<=>((~calm(mary)|generous(mary))))&
((~quiet(john)|~rich(john)))&
(?[X]:((~old(X)&~funny(X))))&
(?[X]:((~happy(X)|old(X))))&
(?[X]:((curious(X)&~humble(X))))&
((humble(john)<~>~strong(john)))&
((~quiet(susan)<~>rich(susan)))&
(?[X]:(~calm(X)))&
((~old(lucy)|~creative(lucy))) | rich(mary) | [
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1391961478629388377267337
% SZS output start Proof for 1391961478629388377267337
9. ! [X0] : (strong(X0) => (~rich(X0) & rich(X0))) [input p8]
14. (~old(lucy) & old(lucy)) <=> ? [X0] : (~rich(X0) <~> strong(X0)) [input p13]
25. ~rich(mary) [input hypothesis]
33. ! [X0] : ((~rich(X0) & rich(X0)) | ~strong(X0)) [ennf transformation 9]
56. ((~old(lucy) & old(lucy)) | ! [X0] : ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (? [X0] : ((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | (old(lucy) | ~old(lucy))) [nnf transformation 14]
57. ((~old(lucy) & old(lucy)) | ! [X0] : ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (? [X0] : ((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | old(lucy) | ~old(lucy)) [flattening 56]
58. ((~old(lucy) & old(lucy)) | ! [X0] : ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (? [X1] : ((~strong(X1) | rich(X1)) & (strong(X1) | ~rich(X1))) | old(lucy) | ~old(lucy)) [rectify 57]
59. ? [X1] : ((~strong(X1) | rich(X1)) & (strong(X1) | ~rich(X1))) => ((~strong(sK4) | rich(sK4)) & (strong(sK4) | ~rich(sK4))) [choice axiom]
60. ((~old(lucy) & old(lucy)) | ! [X0] : ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (((~strong(sK4) | rich(sK4)) & (strong(sK4) | ~rich(sK4))) | old(lucy) | ~old(lucy)) [skolemisation 58,59]
104. rich(X0) | ~strong(X0) [cnf transformation 33]
105. ~rich(X0) | ~strong(X0) [cnf transformation 33]
120. old(lucy) | strong(X0) | rich(X0) [cnf transformation 60]
122. ~old(lucy) | strong(X0) | rich(X0) [cnf transformation 60]
143. ~rich(mary) [cnf transformation 25]
225. ~strong(X0) [subsumption resolution 104,105]
260. ~old(lucy) | rich(X0) [subsumption resolution 122,225]
262. 25 <=> ! [X0] : rich(X0) [avatar definition]
263. rich(X0) <- (25) [avatar component clause 262]
265. 26 <=> old(lucy) [avatar definition]
268. 25 | ~26 [avatar split clause 260,265,262]
269. old(lucy) | rich(X0) [subsumption resolution 120,225]
270. 25 | 26 [avatar split clause 269,265,262]
322. $false <- (25) [resolution 263,143]
323. ~25 [avatar contradiction clause 322]
324. $false [avatar sat refutation 268,270,323]
% SZS output end Proof for 1391961478629388377267337
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is both quiet and calm then someone is patient or kind and vice versa.
If alice is both not funny and not tall then mary is both creative and not creative and vice versa.
Everyone who is not tall is both humble and not calm and vice versa.
If someone is tall then someone is either generous or not generous and vice versa.
Everyone who is either not tall or not calm is both not generous and not strong.
Everyone who is both not happy and creative is wise and vice versa.
If john is not curious then alice is not funny or not happy and vice versa.
If someone is kind or not rich then someone is both not wise and creative and vice versa.
If alice is either not funny or wise then someone is kind or quiet.
If someone is not generous then someone is calm or not patient.
Everyone who is either not creative or not tall is both not strong and not wise.
Everyone who is happy or not generous is either not rich or not generous.
If fred is either brave or curious then someone is either not happy or brave.
Everyone who is not humble or quiet is both not quiet and creative.
If susan is wise or strong then alice is both patient and not curious and vice versa.
Everyone who is kind or funny is curious or not funny.
Someone is both happy and not calm.
Someone is either funny or rich.
Someone is both not calm and funny.
Alice is either not quiet or creative.
Paul is not wise or curious.
Someone is both curious and calm.
Someone is strong.
Someone is either old or not curious. | John is not quiet. | entailment | ((?[X]:((quiet(X)&calm(X))))<=>(?[X]:((patient(X)|kind(X)))))&
(((~funny(alice)&~tall(alice)))<=>((creative(mary)&~creative(mary))))&
(![X]:(~tall(X)<=>(humble(X)&~calm(X))))&
((?[X]:(tall(X)))<=>(?[X]:((generous(X)<~>~generous(X)))))&
(![X]:((~tall(X)<~>~calm(X))=>(~generous(X)&~strong(X))))&
(![X]:((~happy(X)&creative(X))<=>wise(X)))&
((~curious(john))<=>((~funny(alice)|~happy(alice))))&
((?[X]:((kind(X)|~rich(X))))<=>(?[X]:((~wise(X)&creative(X)))))&
(((~funny(alice)<~>wise(alice)))=>(?[X]:((kind(X)|quiet(X)))))&
((?[X]:(~generous(X)))=>(?[X]:((calm(X)|~patient(X)))))&
(![X]:((~creative(X)<~>~tall(X))=>(~strong(X)&~wise(X))))&
(![X]:((happy(X)|~generous(X))=>(~rich(X)<~>~generous(X))))&
(((brave(fred)<~>curious(fred)))=>(?[X]:((~happy(X)<~>brave(X)))))&
(![X]:((~humble(X)|quiet(X))=>(~quiet(X)&creative(X))))&
(((wise(susan)|strong(susan)))<=>((patient(alice)&~curious(alice))))&
(![X]:((kind(X)|funny(X))=>(curious(X)|~funny(X))))&
(?[X]:((happy(X)&~calm(X))))&
(?[X]:((funny(X)<~>rich(X))))&
(?[X]:((~calm(X)&funny(X))))&
((~quiet(alice)<~>creative(alice)))&
((~wise(paul)|curious(paul)))&
(?[X]:((curious(X)&calm(X))))&
(?[X]:(strong(X)))&
(?[X]:((old(X)<~>~curious(X)))) | ~quiet(john) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7707110497085233219998927
% SZS output start Proof for 7707110497085233219998927
14. ! [X0] : ((quiet(X0) | ~humble(X0)) => (creative(X0) & ~quiet(X0))) [input p13]
25. quiet(john) [input hypothesis]
36. ! [X0] : ((creative(X0) & ~quiet(X0)) | (~quiet(X0) & humble(X0))) [ennf transformation 14]
138. ~quiet(X0) | ~quiet(X0) [cnf transformation 36]
162. quiet(john) [cnf transformation 25]
164. ~quiet(X0) [duplicate literal removal 138]
357. $false [subsumption resolution 162,164]
% SZS output end Proof for 7707110497085233219998927
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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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