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
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is both calm and not happy is either patient or not patient and vice versa.
If someone is creative or not tall then lucy is either not happy or funny.
Everyone who is creative or not funny is both not strong and kind.
If someone is either funny or humble then someone is both not curious and generous and vice versa.
Everyone who is not funny is either rich or strong and vice versa.
Everyone who is kind is either not rich or not humble and vice versa.
Everyone who is either not old or not humble is either strong or generous.
Everyone who is not creative is either strong or rich.
If someone is either not old or humble then susan is happy or calm.
Everyone who is both quiet and not tall is both not curious and wise.
Everyone who is both not funny and happy is not strong or strong.
If someone is funny then someone is either not quiet or creative.
If someone is both not humble and creative then someone is strong or curious.
If someone is not patient then someone is either brave or not generous and vice versa.
If someone is either strong or not happy then someone is curious or patient.
If someone is both creative and not tall then someone is tall or not patient.
Someone is either brave or patient.
Lucy is either not calm or rich.
Susan is not patient or not kind.
Mary is not rich.
Someone is not quiet or curious.
Someone is both kind and generous. | Lucy is humble. | contradiction | (![X]:((calm(X)&~happy(X))<=>(patient(X)<~>~patient(X))))&
((?[X]:((creative(X)|~tall(X))))=>((~happy(lucy)<~>funny(lucy))))&
(![X]:((creative(X)|~funny(X))=>(~strong(X)&kind(X))))&
((?[X]:((funny(X)<~>humble(X))))<=>(?[X]:((~curious(X)&generous(X)))))&
(![X]:(~funny(X)<=>(rich(X)<~>strong(X))))&
(![X]:(kind(X)<=>(~rich(X)<~>~humble(X))))&
(![X]:((~old(X)<~>~humble(X))=>(strong(X)<~>generous(X))))&
(![X]:(~creative(X)=>(strong(X)<~>rich(X))))&
((?[X]:((~old(X)<~>humble(X))))=>((happy(susan)|calm(susan))))&
(![X]:((quiet(X)&~tall(X))=>(~curious(X)&wise(X))))&
(![X]:((~funny(X)&happy(X))=>(~strong(X)|strong(X))))&
((?[X]:(funny(X)))=>(?[X]:((~quiet(X)<~>creative(X)))))&
((?[X]:((~humble(X)&creative(X))))=>(?[X]:((strong(X)|curious(X)))))&
((?[X]:(~patient(X)))<=>(?[X]:((brave(X)<~>~generous(X)))))&
((?[X]:((strong(X)<~>~happy(X))))=>(?[X]:((curious(X)|patient(X)))))&
((?[X]:((creative(X)&~tall(X))))=>(?[X]:((tall(X)|~patient(X)))))&
(?[X]:((brave(X)<~>patient(X))))&
((~calm(lucy)<~>rich(lucy)))&
((~patient(susan)|~kind(susan)))&
(~rich(mary))&
(?[X]:((~quiet(X)|curious(X))))&
(?[X]:((kind(X)&generous(X)))) | humble(lucy) | [
"p0",
"p1",
"p2",
"p4",
"p5",
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1235960804310830677708886
% SZS output start Proof for 1235960804310830677708886
1. ! [X0] : ((~happy(X0) & calm(X0)) <=> (patient(X0) <~> ~patient(X0))) [input p0]
2. ? [X0] : (~tall(X0) | creative(X0)) => (~happy(lucy) <~> funny(lucy)) [input p1]
3. ! [X0] : ((~funny(X0) | creative(X0)) => (kind(X0) & ~strong(X0))) [input p2]
5. ! [X0] : (~funny(X0) <=> (rich(X0) <~> strong(X0))) [input p4]
6. ! [X0] : (kind(X0) <=> (~rich(X0) <~> ~humble(X0))) [input p5]
8. ! [X0] : (~creative(X0) => (strong(X0) <~> rich(X0))) [input p7]
20. ~rich(mary) [input p19]
23. humble(lucy) [input hypothesis]
31. ? [X0] : creative(X0) => (~happy(lucy) <~> funny(lucy)) [pure predicate removal 2]
34. (~happy(lucy) <~> funny(lucy)) | ! [X0] : ~creative(X0) [ennf transformation 31]
35. ! [X0] : ((kind(X0) & ~strong(X0)) | (funny(X0) & ~creative(X0))) [ennf transformation 3]
37. ! [X0] : ((strong(X0) <~> rich(X0)) | creative(X0)) [ennf transformation 8]
45. ! [X0] : (((~happy(X0) & calm(X0)) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0)))) & (((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | (happy(X0) | ~calm(X0)))) [nnf transformation 1]
46. ! [X0] : (((~happy(X0) & calm(X0)) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0)))) & (((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | happy(X0) | ~calm(X0))) [flattening 45]
47. ((~funny(lucy) | happy(lucy)) & (funny(lucy) | ~happy(lucy))) | ! [X0] : ~creative(X0) [nnf transformation 34]
53. ! [X0] : ((~funny(X0) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0)))) & (((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | funny(X0))) [nnf transformation 5]
54. ! [X0] : ((kind(X0) | ((~rich(X0) | humble(X0)) & (~humble(X0) | rich(X0)))) & (((humble(X0) | rich(X0)) & (~humble(X0) | ~rich(X0))) | ~kind(X0))) [nnf transformation 6]
56. ! [X0] : (((~rich(X0) | ~strong(X0)) & (rich(X0) | strong(X0))) | creative(X0)) [nnf transformation 37]
86. ~happy(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 46]
87. ~happy(X0) | patient(X0) | patient(X0) [cnf transformation 46]
89. ~funny(lucy) | happy(lucy) | ~creative(X0) [cnf transformation 47]
90. ~strong(X0) | ~creative(X0) [cnf transformation 35]
91. ~strong(X0) | funny(X0) [cnf transformation 35]
93. kind(X0) | funny(X0) [cnf transformation 35]
100. strong(X0) | rich(X0) | funny(X0) [cnf transformation 53]
103. ~funny(X0) | rich(X0) | ~strong(X0) [cnf transformation 53]
104. ~rich(X0) | ~humble(X0) | ~kind(X0) [cnf transformation 54]
112. rich(X0) | strong(X0) | creative(X0) [cnf transformation 56]
113. ~rich(X0) | ~strong(X0) | creative(X0) [cnf transformation 56]
131. ~rich(mary) [cnf transformation 20]
135. humble(lucy) [cnf transformation 23]
138. ~happy(X0) | ~patient(X0) [duplicate literal removal 86]
139. ~happy(X0) | patient(X0) [duplicate literal removal 87]
140. ~happy(X0) [subsumption resolution 138,139]
142. ~funny(lucy) | ~creative(X0) [subsumption resolution 89,140]
144. 1 <=> ! [X0] : ~creative(X0) [avatar definition]
145. ~creative(X0) <- (1) [avatar component clause 144]
147. 2 <=> funny(lucy) [avatar definition]
150. 1 | ~2 [avatar split clause 142,147,144]
165. 6 <=> ! [X3] : (funny(X3) | ~humble(X3)) [avatar definition]
166. ~humble(X3) | funny(X3) <- (6) [avatar component clause 165]
182. ~strong(X0) | rich(X0) [subsumption resolution 103,91]
183. rich(X0) | funny(X0) [subsumption resolution 100,182]
184. ~strong(X0) | creative(X0) [subsumption resolution 113,182]
185. ~strong(X0) [subsumption resolution 184,90]
186. rich(X0) | creative(X0) [subsumption resolution 112,185]
281. funny(lucy) <- (6) [resolution 166,135]
284. 2 | ~6 [avatar split clause 281,165,147]
290. creative(mary) [resolution 186,131]
291. $false <- (1) [subsumption resolution 290,145]
292. ~1 [avatar contradiction clause 291]
301. ~humble(X1) | ~kind(X1) | funny(X1) [resolution 104,183]
303. ~humble(X1) | funny(X1) [subsumption resolution 301,93]
304. 6 [avatar split clause 303,165]
305. $false [avatar sat refutation 150,284,292,304]
% SZS output end Proof for 1235960804310830677708886
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous or humble is either kind or wise and vice versa.
If someone is both quiet and tall then susan is either not rich or generous and vice versa.
Everyone who is not brave is old and vice versa.
If mary is both humble and not humble then john is old and vice versa.
Everyone who is not quiet is either not funny or not kind and vice versa.
If someone is both not patient and funny then paul is either not humble or brave and vice versa.
Everyone who is not strong or not patient is either not funny or not strong.
If someone is either not generous or happy then john is both not old and not calm and vice versa.
Everyone who is either calm or not creative is either not patient or not rich and vice versa.
Everyone who is both humble and not funny is tall.
Everyone who is either creative or not strong is either funny or strong and vice versa.
If someone is both not curious and not funny then alice is both not kind and tall.
If lucy is both wise and not kind then paul is not tall and vice versa.
Everyone who is wise or not creative is humble or not calm.
If susan is either not quiet or brave then alice is either not quiet or not kind.
John is not brave or not quiet.
Someone is quiet.
Alice is not calm.
Someone is both humble and quiet.
Paul is either tall or not quiet.
Susan is both not old and patient.
Mary is not rich or calm.
Susan is both curious and not humble. | Paul is not humble. | neutral | (![X]:((generous(X)|humble(X))<=>(kind(X)<~>wise(X))))&
((?[X]:((quiet(X)&tall(X))))<=>((~rich(susan)<~>generous(susan))))&
(![X]:(~brave(X)<=>old(X)))&
(((humble(mary)&~humble(mary)))<=>(old(john)))&
(![X]:(~quiet(X)<=>(~funny(X)<~>~kind(X))))&
((?[X]:((~patient(X)&funny(X))))<=>((~humble(paul)<~>brave(paul))))&
(![X]:((~strong(X)|~patient(X))=>(~funny(X)<~>~strong(X))))&
((?[X]:((~generous(X)<~>happy(X))))<=>((~old(john)&~calm(john))))&
(![X]:((calm(X)<~>~creative(X))<=>(~patient(X)<~>~rich(X))))&
(![X]:((humble(X)&~funny(X))=>tall(X)))&
(![X]:((creative(X)<~>~strong(X))<=>(funny(X)<~>strong(X))))&
((?[X]:((~curious(X)&~funny(X))))=>((~kind(alice)&tall(alice))))&
(((wise(lucy)&~kind(lucy)))<=>(~tall(paul)))&
(![X]:((wise(X)|~creative(X))=>(humble(X)|~calm(X))))&
(((~quiet(susan)<~>brave(susan)))=>((~quiet(alice)<~>~kind(alice))))&
((~brave(john)|~quiet(john)))&
(?[X]:(quiet(X)))&
(~calm(alice))&
(?[X]:((humble(X)&quiet(X))))&
((tall(paul)<~>~quiet(paul)))&
((~old(susan)&patient(susan)))&
((~rich(mary)|calm(mary)))&
((curious(susan)&~humble(susan))) | ~humble(paul) | [] | null | 0 |
If someone is either calm or kind then susan is not kind or brave and vice versa.
If paul is curious or old then paul is tall or not generous.
If alice is both not wise and calm then alice is either not tall or not quiet and vice versa.
Everyone who is both not rich and generous is both not old and not brave and vice versa.
If lucy is not rich or tall then fred is both creative and not tall.
If alice is both not humble and strong then someone is either not funny or not tall.
Everyone who is both not humble and not patient is brave or rich and vice versa.
Everyone who is either funny or tall is rich or brave and vice versa.
Everyone who is either wise or not calm is not quiet and vice versa.
Everyone who is either not quiet or not creative is generous.
Everyone who is creative is either funny or old and vice versa.
If someone is not old or creative then someone is either tall or not kind and vice versa.
Everyone who is both creative and calm is old.
If someone is both not quiet and not calm then fred is not old or calm and vice versa.
Everyone who is both not creative and kind is not calm or rich and vice versa.
If alice is both old and not calm then someone is quiet or happy and vice versa.
Someone is happy.
Someone is not kind.
Someone is both humble and wise.
Someone is not tall or not calm.
Mary is both not generous and quiet.
Paul is not tall. | Lucy is tall. | neutral | ((?[X]:((calm(X)<~>kind(X))))<=>((~kind(susan)|brave(susan))))&
(((curious(paul)|old(paul)))=>((tall(paul)|~generous(paul))))&
(((~wise(alice)&calm(alice)))<=>((~tall(alice)<~>~quiet(alice))))&
(![X]:((~rich(X)&generous(X))<=>(~old(X)&~brave(X))))&
(((~rich(lucy)|tall(lucy)))=>((creative(fred)&~tall(fred))))&
(((~humble(alice)&strong(alice)))=>(?[X]:((~funny(X)<~>~tall(X)))))&
(![X]:((~humble(X)&~patient(X))<=>(brave(X)|rich(X))))&
(![X]:((funny(X)<~>tall(X))<=>(rich(X)|brave(X))))&
(![X]:((wise(X)<~>~calm(X))<=>~quiet(X)))&
(![X]:((~quiet(X)<~>~creative(X))=>generous(X)))&
(![X]:(creative(X)<=>(funny(X)<~>old(X))))&
((?[X]:((~old(X)|creative(X))))<=>(?[X]:((tall(X)<~>~kind(X)))))&
(![X]:((creative(X)&calm(X))=>old(X)))&
((?[X]:((~quiet(X)&~calm(X))))<=>((~old(fred)|calm(fred))))&
(![X]:((~creative(X)&kind(X))<=>(~calm(X)|rich(X))))&
(((old(alice)&~calm(alice)))<=>(?[X]:((quiet(X)|happy(X)))))&
(?[X]:(happy(X)))&
(?[X]:(~kind(X)))&
(?[X]:((humble(X)&wise(X))))&
(?[X]:((~tall(X)|~calm(X))))&
((~generous(mary)&quiet(mary)))&
(~tall(paul)) | tall(lucy) | [] | null | 0 |
If mary is not kind or not tall then mary is both not brave and funny and vice versa.
If someone is either strong or not happy then someone is not old and vice versa.
If someone is happy or not patient then fred is humble or funny.
If mary is either not creative or kind then someone is not strong and vice versa.
Everyone who is both not quiet and strong is not happy.
If someone is either not curious or brave then someone is not patient or not humble.
If someone is not calm or wise then john is both not wise and funny and vice versa.
If mary is brave or creative then lucy is not funny or calm.
Everyone who is funny is both not humble and funny and vice versa.
Everyone who is wise is either not generous or funny and vice versa.
Everyone who is both brave and happy is not rich or patient.
If someone is both not generous and not old then someone is both not quiet and not wise.
If mary is not calm or patient then someone is not happy or not patient and vice versa.
Everyone who is creative or not humble is generous or not wise and vice versa.
If alice is rich or not generous then mary is not brave.
If someone is quiet then someone is not humble.
Mary is both calm and not happy.
Susan is both old and brave.
Someone is patient.
Someone is not kind or old.
Alice is either not kind or old.
Someone is both patient and funny.
Mary is both humble and wise.
Paul is not humble or not patient. | Mary is not creative. | entailment | (((~kind(mary)|~tall(mary)))<=>((~brave(mary)&funny(mary))))&
((?[X]:((strong(X)<~>~happy(X))))<=>(?[X]:(~old(X))))&
((?[X]:((happy(X)|~patient(X))))=>((humble(fred)|funny(fred))))&
(((~creative(mary)<~>kind(mary)))<=>(?[X]:(~strong(X))))&
(![X]:((~quiet(X)&strong(X))=>~happy(X)))&
((?[X]:((~curious(X)<~>brave(X))))=>(?[X]:((~patient(X)|~humble(X)))))&
((?[X]:((~calm(X)|wise(X))))<=>((~wise(john)&funny(john))))&
(((brave(mary)|creative(mary)))=>((~funny(lucy)|calm(lucy))))&
(![X]:(funny(X)<=>(~humble(X)&funny(X))))&
(![X]:(wise(X)<=>(~generous(X)<~>funny(X))))&
(![X]:((brave(X)&happy(X))=>(~rich(X)|patient(X))))&
((?[X]:((~generous(X)&~old(X))))=>(?[X]:((~quiet(X)&~wise(X)))))&
(((~calm(mary)|patient(mary)))<=>(?[X]:((~happy(X)|~patient(X)))))&
(![X]:((creative(X)|~humble(X))<=>(generous(X)|~wise(X))))&
(((rich(alice)|~generous(alice)))=>(~brave(mary)))&
((?[X]:(quiet(X)))=>(?[X]:(~humble(X))))&
((calm(mary)&~happy(mary)))&
((old(susan)&brave(susan)))&
(?[X]:(patient(X)))&
(?[X]:((~kind(X)|old(X))))&
((~kind(alice)<~>old(alice)))&
(?[X]:((patient(X)&funny(X))))&
((humble(mary)&wise(mary)))&
((~humble(paul)|~patient(paul))) | ~creative(mary) | [
"p8",
"p9",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2949127117036968552881732
% SZS output start Proof for 2949127117036968552881732
9. ! [X0] : (funny(X0) <=> (funny(X0) & ~humble(X0))) [input p8]
10. ! [X0] : (wise(X0) <=> (~generous(X0) <~> funny(X0))) [input p9]
14. ! [X0] : ((~humble(X0) | creative(X0)) <=> (~wise(X0) | generous(X0))) [input p13]
23. wise(mary) & humble(mary) [input p22]
25. creative(mary) [input hypothesis]
62. ! [X0] : ((funny(X0) | (~funny(X0) | humble(X0))) & ((funny(X0) & ~humble(X0)) | ~funny(X0))) [nnf transformation 9]
63. ! [X0] : ((funny(X0) | ~funny(X0) | humble(X0)) & ((funny(X0) & ~humble(X0)) | ~funny(X0))) [flattening 62]
64. ! [X0] : ((wise(X0) | ((~generous(X0) | ~funny(X0)) & (funny(X0) | generous(X0)))) & (((~funny(X0) | generous(X0)) & (funny(X0) | ~generous(X0))) | ~wise(X0))) [nnf transformation 10]
73. ! [X0] : (((~humble(X0) | creative(X0)) | (wise(X0) & ~generous(X0))) & ((~wise(X0) | generous(X0)) | (humble(X0) & ~creative(X0)))) [nnf transformation 14]
74. ! [X0] : ((~humble(X0) | creative(X0) | (wise(X0) & ~generous(X0))) & (~wise(X0) | generous(X0) | (humble(X0) & ~creative(X0)))) [flattening 73]
110. ~humble(X0) | ~funny(X0) [cnf transformation 63]
113. ~generous(X0) | funny(X0) | ~wise(X0) [cnf transformation 64]
123. ~wise(X0) | generous(X0) | ~creative(X0) [cnf transformation 74]
139. humble(mary) [cnf transformation 23]
140. wise(mary) [cnf transformation 23]
142. creative(mary) [cnf transformation 25]
148. 2 <=> funny(mary) [avatar definition]
150. ~funny(mary) <- (~2) [avatar component clause 148]
209. 16 <=> creative(mary) [avatar definition]
211. creative(mary) <- (16) [avatar component clause 209]
351. 16 [avatar split clause 142,209]
352. ~funny(mary) [resolution 110,139]
357. ~2 [avatar split clause 352,148]
363. generous(mary) | ~creative(mary) [resolution 123,140]
364. generous(mary) <- (16) [subsumption resolution 363,211]
367. funny(mary) | ~wise(mary) <- (16) [resolution 364,113]
368. ~wise(mary) <- (~2, 16) [subsumption resolution 367,150]
369. $false <- (~2, 16) [subsumption resolution 368,140]
370. 2 | ~16 [avatar contradiction clause 369]
371. $false [avatar sat refutation 351,357,370]
% SZS output end Proof for 2949127117036968552881732
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is both patient and not old and vice versa. Everyone who is humble is either not tall or not old. If someone is not old then someone is either not brave or quiet and vice versa. Everyone who is old is both wise and not rich and vice versa. Everyone who is patient or old is both quiet and not kind. Everyone who is not patient or not wise is either quiet or old and vice versa. Everyone who is both not calm and calm is either calm or humble. Everyone who is calm is either not old or rich. Everyone who is not curious or rich is either not rich or tall. Everyone who is not wise or not patient is either kind or humble and vice versa. Everyone who is happy is either not curious or not old and vice versa. Everyone who is both not humble and happy is humble or curious and vice versa. Everyone who is not wise is not curious. If fred is either calm or not quiet then lucy is both not patient and wise. Everyone who is not wise is either not kind or not creative and vice versa. If john is rich then someone is not brave and vice versa. Mary is either not humble or strong. John is not wise. Someone is not generous. Lucy is not strong or not creative. Someone is both wise and not brave. Someone is either not rich or curious. | Mary is strong. | contradiction | (![X]:(~funny(X)<=>(patient(X)&~old(X))))&
(![X]:(humble(X)=>(~tall(X)<~>~old(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~brave(X)<~>quiet(X)))))&
(![X]:(old(X)<=>(wise(X)&~rich(X))))&
(![X]:((patient(X)|old(X))=>(quiet(X)&~kind(X))))&
(![X]:((~patient(X)|~wise(X))<=>(quiet(X)<~>old(X))))&
(![X]:((~calm(X)&calm(X))=>(calm(X)<~>humble(X))))&
(![X]:(calm(X)=>(~old(X)<~>rich(X))))&
(![X]:((~curious(X)|rich(X))=>(~rich(X)<~>tall(X))))&
(![X]:((~wise(X)|~patient(X))<=>(kind(X)<~>humble(X))))&
(![X]:(happy(X)<=>(~curious(X)<~>~old(X))))&
(![X]:((~humble(X)&happy(X))<=>(humble(X)|curious(X))))&
(![X]:(~wise(X)=>~curious(X)))&
(((calm(fred)<~>~quiet(fred)))=>((~patient(lucy)&wise(lucy))))&
(![X]:(~wise(X)<=>(~kind(X)<~>~creative(X))))&
((rich(john))<=>(?[X]:(~brave(X))))&
((~humble(mary)<~>strong(mary)))&
(~wise(john))&
(?[X]:(~generous(X)))&
((~strong(lucy)|~creative(lucy)))&
(?[X]:((wise(X)&~brave(X))))&
(?[X]:((~rich(X)<~>curious(X)))) | strong(mary) | [
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4364234770509692564225246
% SZS output start Proof for 4364234770509692564225246
12. ! [X0] : ((happy(X0) & ~humble(X0)) <=> (curious(X0) | humble(X0))) [input p11]
17. ~humble(mary) <~> strong(mary) [input p16]
23. strong(mary) [input hypothesis]
50. ! [X0] : (((happy(X0) & ~humble(X0)) | (~curious(X0) & ~humble(X0))) & ((curious(X0) | humble(X0)) | (~happy(X0) | humble(X0)))) [nnf transformation 12]
51. ! [X0] : (((happy(X0) & ~humble(X0)) | (~curious(X0) & ~humble(X0))) & (curious(X0) | humble(X0) | ~happy(X0) | humble(X0))) [flattening 50]
58. (~strong(mary) | humble(mary)) & (strong(mary) | ~humble(mary)) [nnf transformation 17]
102. ~humble(X0) | ~humble(X0) [cnf transformation 51]
118. ~strong(mary) | humble(mary) [cnf transformation 58]
125. strong(mary) [cnf transformation 23]
127. ~humble(X0) [duplicate literal removal 102]
195. ~strong(mary) [subsumption resolution 118,127]
215. $false [subsumption resolution 125,195]
% SZS output end Proof for 4364234770509692564225246
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind or humble then lucy is humble or wise and vice versa.
If someone is either not rich or rich then susan is both old and funny.
Everyone who is both not calm and kind is not happy.
If mary is both not wise and happy then someone is quiet or not curious.
Everyone who is not humble is both kind and not creative and vice versa.
If alice is both quiet and not kind then john is tall or brave and vice versa.
Everyone who is either not strong or not calm is not old.
Everyone who is both creative and patient is tall and vice versa.
Everyone who is either not calm or not wise is either not funny or not creative.
If someone is wise or old then someone is funny and vice versa.
If someone is either tall or not patient then someone is both brave and not calm.
Everyone who is not generous or brave is creative or not kind.
If someone is both tall and patient then someone is both creative and tall and vice versa.
If someone is not tall or not creative then someone is either wise or strong and vice versa.
Everyone who is either creative or funny is not quiet or not rich.
If lucy is both not wise and calm then lucy is funny or not calm and vice versa.
Someone is not calm or not happy.
Alice is both rich and curious.
Someone is kind or not wise.
Someone is both creative and not funny.
Someone is not generous or not quiet.
Someone is both not quiet and not kind.
Someone is creative.
Fred is either calm or curious. | Susan is old. | entailment | ((?[X]:((~kind(X)|humble(X))))<=>((humble(lucy)|wise(lucy))))&
((?[X]:((~rich(X)<~>rich(X))))=>((old(susan)&funny(susan))))&
(![X]:((~calm(X)&kind(X))=>~happy(X)))&
(((~wise(mary)&happy(mary)))=>(?[X]:((quiet(X)|~curious(X)))))&
(![X]:(~humble(X)<=>(kind(X)&~creative(X))))&
(((quiet(alice)&~kind(alice)))<=>((tall(john)|brave(john))))&
(![X]:((~strong(X)<~>~calm(X))=>~old(X)))&
(![X]:((creative(X)&patient(X))<=>tall(X)))&
(![X]:((~calm(X)<~>~wise(X))=>(~funny(X)<~>~creative(X))))&
((?[X]:((wise(X)|old(X))))<=>(?[X]:(funny(X))))&
((?[X]:((tall(X)<~>~patient(X))))=>(?[X]:((brave(X)&~calm(X)))))&
(![X]:((~generous(X)|brave(X))=>(creative(X)|~kind(X))))&
((?[X]:((tall(X)&patient(X))))<=>(?[X]:((creative(X)&tall(X)))))&
((?[X]:((~tall(X)|~creative(X))))<=>(?[X]:((wise(X)<~>strong(X)))))&
(![X]:((creative(X)<~>funny(X))=>(~quiet(X)|~rich(X))))&
(((~wise(lucy)&calm(lucy)))<=>((funny(lucy)|~calm(lucy))))&
(?[X]:((~calm(X)|~happy(X))))&
((rich(alice)&curious(alice)))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((creative(X)&~funny(X))))&
(?[X]:((~generous(X)|~quiet(X))))&
(?[X]:((~quiet(X)&~kind(X))))&
(?[X]:(creative(X)))&
((calm(fred)<~>curious(fred))) | old(susan) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 3038608130674683674356339
% SZS output start Proof for 3038608130674683674356339
2. ? [X0] : (~rich(X0) <~> rich(X0)) => (funny(susan) & old(susan)) [input p1]
25. ~old(susan) [input hypothesis]
33. (funny(susan) & old(susan)) | ! [X0] : (~rich(X0) <=> rich(X0)) [ennf transformation 2]
46. (funny(susan) & old(susan)) | ! [X0] : ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0))) [nnf transformation 33]
92. old(susan) | rich(X0) | rich(X0) [cnf transformation 46]
93. old(susan) | ~rich(X0) | ~rich(X0) [cnf transformation 46]
150. ~old(susan) [cnf transformation 25]
153. old(susan) | rich(X0) [duplicate literal removal 92]
154. old(susan) | ~rich(X0) [duplicate literal removal 93]
184. 7 <=> ! [X0] : ~rich(X0) [avatar definition]
185. ~rich(X0) <- (7) [avatar component clause 184]
192. 9 <=> ! [X0] : rich(X0) [avatar definition]
193. rich(X0) <- (9) [avatar component clause 192]
196. 10 <=> old(susan) [avatar definition]
199. 7 | 10 [avatar split clause 154,196,184]
200. 9 | 10 [avatar split clause 153,196,192]
359. ~10 [avatar split clause 150,196]
360. $false <- (7, 9) [subsumption resolution 185,193]
361. ~7 | ~9 [avatar contradiction clause 360]
362. $false [avatar sat refutation 199,200,359,361]
% SZS output end Proof for 3038608130674683674356339
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is either curious or not humble.
If someone is both not tall and not kind then someone is both strong and generous.
Everyone who is not brave or not curious is tall or not old.
Everyone who is either not old or quiet is either quiet or not rich and vice versa.
If someone is funny or not calm then fred is either not curious or not calm and vice versa.
Everyone who is not calm or not strong is both humble and not creative.
If someone is both creative and not creative then someone is either not curious or quiet.
Everyone who is not patient or not old is both not brave and patient and vice versa.
Everyone who is quiet or not brave is both not old and wise.
Everyone who is both strong and not calm is not funny or funny and vice versa.
If someone is either not funny or not creative then fred is not wise or not creative and vice versa.
If john is either funny or humble then susan is not generous or quiet and vice versa.
Everyone who is not humble is both not patient and humble and vice versa.
If alice is tall then someone is not humble and vice versa.
Everyone who is either happy or quiet is not funny and vice versa.
Someone is old or patient.
Someone is humble.
Someone is either generous or not funny.
Someone is both quiet and not funny.
Susan is funny or curious.
Lucy is strong.
Fred is humble. | Susan is humble. | entailment | (![X]:(curious(X)=>(curious(X)<~>~humble(X))))&
((?[X]:((~tall(X)&~kind(X))))=>(?[X]:((strong(X)&generous(X)))))&
(![X]:((~brave(X)|~curious(X))=>(tall(X)|~old(X))))&
(![X]:((~old(X)<~>quiet(X))<=>(quiet(X)<~>~rich(X))))&
((?[X]:((funny(X)|~calm(X))))<=>((~curious(fred)<~>~calm(fred))))&
(![X]:((~calm(X)|~strong(X))=>(humble(X)&~creative(X))))&
((?[X]:((creative(X)&~creative(X))))=>(?[X]:((~curious(X)<~>quiet(X)))))&
(![X]:((~patient(X)|~old(X))<=>(~brave(X)&patient(X))))&
(![X]:((quiet(X)|~brave(X))=>(~old(X)&wise(X))))&
(![X]:((strong(X)&~calm(X))<=>(~funny(X)|funny(X))))&
((?[X]:((~funny(X)<~>~creative(X))))<=>((~wise(fred)|~creative(fred))))&
(((funny(john)<~>humble(john)))<=>((~generous(susan)|quiet(susan))))&
(![X]:(~humble(X)<=>(~patient(X)&humble(X))))&
((tall(alice))<=>(?[X]:(~humble(X))))&
(![X]:((happy(X)<~>quiet(X))<=>~funny(X)))&
(?[X]:((old(X)|patient(X))))&
(?[X]:(humble(X)))&
(?[X]:((generous(X)<~>~funny(X))))&
(?[X]:((quiet(X)&~funny(X))))&
((funny(susan)|curious(susan)))&
(strong(lucy))&
(humble(fred)) | humble(susan) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7955093897908005257992865
% SZS output start Proof for 7955093897908005257992865
13. ! [X0] : (~humble(X0) <=> (humble(X0) & ~patient(X0))) [input p12]
23. ~humble(susan) [input hypothesis]
54. ! [X0] : ((~humble(X0) | (~humble(X0) | patient(X0))) & ((humble(X0) & ~patient(X0)) | humble(X0))) [nnf transformation 13]
55. ! [X0] : ((~humble(X0) | ~humble(X0) | patient(X0)) & ((humble(X0) & ~patient(X0)) | humble(X0))) [flattening 54]
121. humble(X0) | humble(X0) [cnf transformation 55]
138. ~humble(susan) [cnf transformation 23]
139. humble(X0) [duplicate literal removal 121]
250. $false [subsumption resolution 138,139]
% SZS output end Proof for 7955093897908005257992865
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not happy or not strong then lucy is both not generous and not happy. Everyone who is not kind is strong and vice versa. Everyone who is not kind or kind is happy or rich. If mary is either happy or not happy then someone is not brave or humble. Everyone who is not kind is not old. If susan is either curious or not happy then someone is both not curious and not strong. Everyone who is both quiet and not patient is strong and vice versa. If someone is not brave then someone is not wise or humble and vice versa. If someone is creative or not rich then mary is either old or calm and vice versa. If susan is both not old and not quiet then someone is both kind and not strong and vice versa. If someone is either not brave or not kind then john is either humble or curious and vice versa. Everyone who is not wise is patient or curious and vice versa. Everyone who is either happy or funny is not curious or strong. Everyone who is not quiet is not old and vice versa. Everyone who is either not rich or not brave is either not curious or not rich. If fred is either brave or not brave then lucy is either not rich or calm. John is not curious. Lucy is quiet. Someone is both not calm and not humble. Someone is generous. Someone is either creative or happy. Someone is not wise or happy. Someone is old. Fred is either not curious or rich. | Mary is old. | neutral | ((?[X]:((~happy(X)<~>~strong(X))))=>((~generous(lucy)&~happy(lucy))))&
(![X]:(~kind(X)<=>strong(X)))&
(![X]:((~kind(X)|kind(X))=>(happy(X)|rich(X))))&
(((happy(mary)<~>~happy(mary)))=>(?[X]:((~brave(X)|humble(X)))))&
(![X]:(~kind(X)=>~old(X)))&
(((curious(susan)<~>~happy(susan)))=>(?[X]:((~curious(X)&~strong(X)))))&
(![X]:((quiet(X)&~patient(X))<=>strong(X)))&
((?[X]:(~brave(X)))<=>(?[X]:((~wise(X)|humble(X)))))&
((?[X]:((creative(X)|~rich(X))))<=>((old(mary)<~>calm(mary))))&
(((~old(susan)&~quiet(susan)))<=>(?[X]:((kind(X)&~strong(X)))))&
((?[X]:((~brave(X)<~>~kind(X))))<=>((humble(john)<~>curious(john))))&
(![X]:(~wise(X)<=>(patient(X)|curious(X))))&
(![X]:((happy(X)<~>funny(X))=>(~curious(X)|strong(X))))&
(![X]:(~quiet(X)<=>~old(X)))&
(![X]:((~rich(X)<~>~brave(X))=>(~curious(X)<~>~rich(X))))&
(((brave(fred)<~>~brave(fred)))=>((~rich(lucy)<~>calm(lucy))))&
(~curious(john))&
(quiet(lucy))&
(?[X]:((~calm(X)&~humble(X))))&
(?[X]:(generous(X)))&
(?[X]:((creative(X)<~>happy(X))))&
(?[X]:((~wise(X)|happy(X))))&
(?[X]:(old(X)))&
((~curious(fred)<~>rich(fred))) | old(mary) | [] | null | 0 |
If someone is both calm and not kind then someone is either rich or not brave and vice versa.
Everyone who is not wise or not quiet is generous or wise.
If paul is kind or rich then fred is both brave and tall and vice versa.
If someone is both not calm and humble then someone is either not strong or brave and vice versa.
Everyone who is either not kind or calm is not creative or wise and vice versa.
Everyone who is curious or generous is rich or not quiet.
Everyone who is both not kind and wise is both not wise and not rich and vice versa.
If someone is both not creative and not happy then someone is both not patient and not kind and vice versa.
Everyone who is calm is not old or quiet.
If someone is not calm then someone is both kind and strong.
Everyone who is strong is either not happy or not strong.
Everyone who is quiet or not patient is both not old and not calm.
Everyone who is not old is both humble and not happy.
Everyone who is either not happy or not funny is kind or not wise and vice versa.
If someone is both creative and wise then fred is not brave or not calm and vice versa.
Everyone who is either not funny or kind is happy or not strong.
Mary is generous or not wise.
Fred is not patient or not wise.
Someone is not patient or humble.
Someone is either rich or strong.
Someone is both brave and generous. | Mary is not wise. | entailment | ((?[X]:((calm(X)&~kind(X))))<=>(?[X]:((rich(X)<~>~brave(X)))))&
(![X]:((~wise(X)|~quiet(X))=>(generous(X)|wise(X))))&
(((kind(paul)|rich(paul)))<=>((brave(fred)&tall(fred))))&
((?[X]:((~calm(X)&humble(X))))<=>(?[X]:((~strong(X)<~>brave(X)))))&
(![X]:((~kind(X)<~>calm(X))<=>(~creative(X)|wise(X))))&
(![X]:((curious(X)|generous(X))=>(rich(X)|~quiet(X))))&
(![X]:((~kind(X)&wise(X))<=>(~wise(X)&~rich(X))))&
((?[X]:((~creative(X)&~happy(X))))<=>(?[X]:((~patient(X)&~kind(X)))))&
(![X]:(calm(X)=>(~old(X)|quiet(X))))&
((?[X]:(~calm(X)))=>(?[X]:((kind(X)&strong(X)))))&
(![X]:(strong(X)=>(~happy(X)<~>~strong(X))))&
(![X]:((quiet(X)|~patient(X))=>(~old(X)&~calm(X))))&
(![X]:(~old(X)=>(humble(X)&~happy(X))))&
(![X]:((~happy(X)<~>~funny(X))<=>(kind(X)|~wise(X))))&
((?[X]:((creative(X)&wise(X))))<=>((~brave(fred)|~calm(fred))))&
(![X]:((~funny(X)<~>kind(X))=>(happy(X)|~strong(X))))&
((generous(mary)|~wise(mary)))&
((~patient(fred)|~wise(fred)))&
(?[X]:((~patient(X)|humble(X))))&
(?[X]:((rich(X)<~>strong(X))))&
(?[X]:((brave(X)&generous(X)))) | ~wise(mary) | [
"p2",
"p6",
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4699212509048077594495275
% SZS output start Proof for 4699212509048077594495275
3. (rich(paul) | kind(paul)) <=> (tall(fred) & brave(fred)) [input p2]
7. ! [X0] : ((wise(X0) & ~kind(X0)) <=> (~rich(X0) & ~wise(X0))) [input p6]
8. ? [X0] : (~happy(X0) & ~creative(X0)) <=> ? [X0] : (~kind(X0) & ~patient(X0)) [input p7]
9. ! [X0] : (calm(X0) => (quiet(X0) | ~old(X0))) [input p8]
10. ? [X0] : ~calm(X0) => ? [X0] : (strong(X0) & kind(X0)) [input p9]
11. ! [X0] : (strong(X0) => (~happy(X0) <~> ~strong(X0))) [input p10]
12. ! [X0] : ((~patient(X0) | quiet(X0)) => (~calm(X0) & ~old(X0))) [input p11]
13. ! [X0] : (~old(X0) => (~happy(X0) & humble(X0))) [input p12]
14. ! [X0] : ((~happy(X0) <~> ~funny(X0)) <=> (~wise(X0) | kind(X0))) [input p13]
15. ? [X0] : (wise(X0) & creative(X0)) <=> (~calm(fred) | ~brave(fred)) [input p14]
16. ! [X0] : ((~funny(X0) <~> kind(X0)) => (~strong(X0) | happy(X0))) [input p15]
22. wise(mary) [input hypothesis]
25. ? [X0] : (~happy(X0) & ~creative(X0)) <=> ? [X1] : (~kind(X1) & ~patient(X1)) [rectify 8]
26. ? [X0] : ~calm(X0) => ? [X1] : (strong(X1) & kind(X1)) [rectify 10]
32. ! [X0] : ((quiet(X0) | ~old(X0)) | ~calm(X0)) [ennf transformation 9]
33. ! [X0] : (quiet(X0) | ~old(X0) | ~calm(X0)) [flattening 32]
34. ? [X1] : (strong(X1) & kind(X1)) | ! [X0] : calm(X0) [ennf transformation 26]
35. ! [X0] : ((~happy(X0) <~> ~strong(X0)) | ~strong(X0)) [ennf transformation 11]
36. ! [X0] : ((~calm(X0) & ~old(X0)) | (patient(X0) & ~quiet(X0))) [ennf transformation 12]
37. ! [X0] : ((~happy(X0) & humble(X0)) | old(X0)) [ennf transformation 13]
38. ! [X0] : ((~strong(X0) | happy(X0)) | (~funny(X0) <=> kind(X0))) [ennf transformation 16]
39. ! [X0] : (~strong(X0) | happy(X0) | (~funny(X0) <=> kind(X0))) [flattening 38]
45. ((rich(paul) | kind(paul)) | (~tall(fred) | ~brave(fred))) & ((tall(fred) & brave(fred)) | (~rich(paul) & ~kind(paul))) [nnf transformation 3]
46. (rich(paul) | kind(paul) | ~tall(fred) | ~brave(fred)) & ((tall(fred) & brave(fred)) | (~rich(paul) & ~kind(paul))) [flattening 45]
54. ! [X0] : (((wise(X0) & ~kind(X0)) | (rich(X0) | wise(X0))) & ((~rich(X0) & ~wise(X0)) | (~wise(X0) | kind(X0)))) [nnf transformation 7]
55. ! [X0] : (((wise(X0) & ~kind(X0)) | rich(X0) | wise(X0)) & ((~rich(X0) & ~wise(X0)) | ~wise(X0) | kind(X0))) [flattening 54]
56. (? [X0] : (~happy(X0) & ~creative(X0)) | ! [X1] : (kind(X1) | patient(X1))) & (? [X1] : (~kind(X1) & ~patient(X1)) | ! [X0] : (happy(X0) | creative(X0))) [nnf transformation 25]
57. (? [X0] : (~happy(X0) & ~creative(X0)) | ! [X1] : (kind(X1) | patient(X1))) & (? [X2] : (~kind(X2) & ~patient(X2)) | ! [X3] : (happy(X3) | creative(X3))) [rectify 56]
58. ? [X0] : (~happy(X0) & ~creative(X0)) => (~happy(sK4) & ~creative(sK4)) [choice axiom]
59. ? [X2] : (~kind(X2) & ~patient(X2)) => (~kind(sK5) & ~patient(sK5)) [choice axiom]
60. ((~happy(sK4) & ~creative(sK4)) | ! [X1] : (kind(X1) | patient(X1))) & ((~kind(sK5) & ~patient(sK5)) | ! [X3] : (happy(X3) | creative(X3))) [skolemisation 57,59,58]
61. ? [X0] : (strong(X0) & kind(X0)) | ! [X1] : calm(X1) [rectify 34]
62. ? [X0] : (strong(X0) & kind(X0)) => (strong(sK6) & kind(sK6)) [choice axiom]
63. (strong(sK6) & kind(sK6)) | ! [X1] : calm(X1) [skolemisation 61,62]
64. ! [X0] : (((strong(X0) | happy(X0)) & (~strong(X0) | ~happy(X0))) | ~strong(X0)) [nnf transformation 35]
65. ! [X0] : ((((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | (wise(X0) & ~kind(X0))) & ((~wise(X0) | kind(X0)) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0))))) [nnf transformation 14]
66. ! [X0] : ((((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | (wise(X0) & ~kind(X0))) & (~wise(X0) | kind(X0) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0))))) [flattening 65]
67. (? [X0] : (wise(X0) & creative(X0)) | (calm(fred) & brave(fred))) & ((~calm(fred) | ~brave(fred)) | ! [X0] : (~wise(X0) | ~creative(X0))) [nnf transformation 15]
68. (? [X0] : (wise(X0) & creative(X0)) | (calm(fred) & brave(fred))) & (~calm(fred) | ~brave(fred) | ! [X0] : (~wise(X0) | ~creative(X0))) [flattening 67]
69. (? [X0] : (wise(X0) & creative(X0)) | (calm(fred) & brave(fred))) & (~calm(fred) | ~brave(fred) | ! [X1] : (~wise(X1) | ~creative(X1))) [rectify 68]
70. ? [X0] : (wise(X0) & creative(X0)) => (wise(sK7) & creative(sK7)) [choice axiom]
71. ((wise(sK7) & creative(sK7)) | (calm(fred) & brave(fred))) & (~calm(fred) | ~brave(fred) | ! [X1] : (~wise(X1) | ~creative(X1))) [skolemisation 69,70]
72. ! [X0] : (~strong(X0) | happy(X0) | ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0)))) [nnf transformation 39]
88. brave(fred) | ~kind(paul) [cnf transformation 46]
89. brave(fred) | ~rich(paul) [cnf transformation 46]
106. ~wise(X0) | ~wise(X0) | kind(X0) [cnf transformation 55]
109. wise(X0) | rich(X0) | wise(X0) [cnf transformation 55]
110. ~patient(sK5) | happy(X3) | creative(X3) [cnf transformation 60]
114. ~old(X0) | quiet(X0) | ~calm(X0) [cnf transformation 33]
115. kind(sK6) | calm(X1) [cnf transformation 63]
116. strong(sK6) | calm(X1) [cnf transformation 63]
117. ~strong(X0) | ~happy(X0) | ~strong(X0) [cnf transformation 64]
119. ~old(X0) | ~quiet(X0) [cnf transformation 36]
122. ~calm(X0) | patient(X0) [cnf transformation 36]
124. ~happy(X0) | old(X0) [cnf transformation 37]
127. ~funny(X0) | ~happy(X0) | ~kind(X0) [cnf transformation 66]
129. ~kind(X0) | happy(X0) | funny(X0) [cnf transformation 66]
131. ~calm(fred) | ~brave(fred) | ~wise(X1) | ~creative(X1) [cnf transformation 71]
136. ~strong(X0) | happy(X0) | kind(X0) | funny(X0) [cnf transformation 72]
137. ~strong(X0) | happy(X0) | ~funny(X0) | ~kind(X0) [cnf transformation 72]
145. wise(mary) [cnf transformation 22]
146. ~happy(X0) | ~strong(X0) [duplicate literal removal 117]
147. ~wise(X0) | kind(X0) [duplicate literal removal 106]
148. wise(X0) | rich(X0) [duplicate literal removal 109]
182. 8 <=> brave(fred) [avatar definition]
190. 10 <=> kind(paul) [avatar definition]
191. ~kind(paul) <- (~10) [avatar component clause 190]
194. 11 <=> rich(paul) [avatar definition]
195. ~rich(paul) <- (~11) [avatar component clause 194]
200. ~11 | 8 [avatar split clause 89,182,194]
201. ~10 | 8 [avatar split clause 88,182,190]
247. 22 <=> ! [X3] : (happy(X3) | creative(X3)) [avatar definition]
248. happy(X3) | creative(X3) <- (22) [avatar component clause 247]
255. 24 <=> patient(sK5) [avatar definition]
257. ~patient(sK5) <- (~24) [avatar component clause 255]
258. 22 | ~24 [avatar split clause 110,255,247]
260. 25 <=> ! [X1] : calm(X1) [avatar definition]
261. calm(X1) <- (25) [avatar component clause 260]
263. 26 <=> strong(sK6) [avatar definition]
265. strong(sK6) <- (26) [avatar component clause 263]
266. 25 | 26 [avatar split clause 116,263,260]
268. 27 <=> kind(sK6) [avatar definition]
271. 25 | 27 [avatar split clause 115,268,260]
273. 28 <=> calm(fred) [avatar definition]
274. ~calm(fred) <- (~28) [avatar component clause 273]
289. 31 <=> ! [X1] : (~wise(X1) | ~creative(X1)) [avatar definition]
290. ~creative(X1) | ~wise(X1) <- (31) [avatar component clause 289]
291. 31 | ~8 | ~28 [avatar split clause 131,273,182,289]
292. ~funny(X0) | ~strong(X0) | ~kind(X0) [subsumption resolution 137,127]
293. ~strong(X0) | happy(X0) | funny(X0) [subsumption resolution 136,129]
294. ~strong(X0) | funny(X0) [subsumption resolution 293,146]
324. $false <- (25, ~28) [resolution 274,261]
325. ~25 | 28 [avatar contradiction clause 324]
331. rich(X0) | kind(X0) [resolution 148,147]
338. funny(sK6) <- (26) [resolution 294,265]
352. 40 <=> creative(mary) [avatar definition]
353. ~creative(mary) <- (~40) [avatar component clause 352]
354. creative(mary) <- (40) [avatar component clause 352]
434. ~strong(sK6) | ~kind(sK6) <- (26) [resolution 292,338]
436. ~kind(sK6) <- (26) [subsumption resolution 434,265]
440. ~27 | ~26 [avatar split clause 436,263,268]
454. patient(X1) <- (25) [resolution 261,122]
466. ~wise(mary) <- (31, 40) [resolution 290,354]
470. $false <- (31, 40) [subsumption resolution 466,145]
471. ~31 | ~40 [avatar contradiction clause 470]
480. $false <- (~24, 25) [resolution 454,257]
485. 24 | ~25 [avatar contradiction clause 480]
489. old(X1) | creative(X1) <- (22) [resolution 248,124]
541. kind(paul) <- (~11) [resolution 331,195]
542. $false <- (~10, ~11) [subsumption resolution 541,191]
543. 10 | 11 [avatar contradiction clause 542]
567. creative(X0) | quiet(X0) | ~calm(X0) <- (22) [resolution 489,114]
569. creative(X2) | ~quiet(X2) <- (22) [resolution 489,119]
570. creative(X0) | quiet(X0) <- (22, 25) [subsumption resolution 567,261]
571. creative(X2) <- (22, 25) [subsumption resolution 569,570]
594. $false <- (22, 25, ~40) [resolution 571,353]
595. ~22 | ~25 | 40 [avatar contradiction clause 594]
597. $false [avatar sat refutation 200,201,258,266,271,291,325,440,471,485,543,595]
% SZS output end Proof for 4699212509048077594495275
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or not creative is not curious and vice versa. If susan is strong or not quiet then fred is tall and vice versa. Everyone who is not humble is both not brave and rich and vice versa. If alice is tall or creative then someone is both not happy and not curious and vice versa. If mary is both creative and wise then someone is creative or patient and vice versa. Everyone who is not quiet or brave is both calm and not strong. Everyone who is either not generous or not patient is not old or calm and vice versa. Everyone who is either not kind or not quiet is either not happy or not calm and vice versa. Everyone who is either tall or kind is either kind or not curious and vice versa. Everyone who is funny is either humble or calm. If alice is both brave and kind then someone is brave. Everyone who is tall is either not brave or brave. If someone is patient or not funny then john is kind or old and vice versa. Everyone who is funny is not tall. Everyone who is not curious or happy is not rich or not brave and vice versa. If fred is not creative then paul is either funny or not rich and vice versa. Someone is either not curious or not calm. Fred is both strong and old. Someone is generous. Someone is both wise and tall. Lucy is not strong or generous. Someone is old. Someone is not happy. | Paul is not funny. | entailment | (![X]:((funny(X)|~creative(X))<=>~curious(X)))&
(((strong(susan)|~quiet(susan)))<=>(tall(fred)))&
(![X]:(~humble(X)<=>(~brave(X)&rich(X))))&
(((tall(alice)|creative(alice)))<=>(?[X]:((~happy(X)&~curious(X)))))&
(((creative(mary)&wise(mary)))<=>(?[X]:((creative(X)|patient(X)))))&
(![X]:((~quiet(X)|brave(X))=>(calm(X)&~strong(X))))&
(![X]:((~generous(X)<~>~patient(X))<=>(~old(X)|calm(X))))&
(![X]:((~kind(X)<~>~quiet(X))<=>(~happy(X)<~>~calm(X))))&
(![X]:((tall(X)<~>kind(X))<=>(kind(X)<~>~curious(X))))&
(![X]:(funny(X)=>(humble(X)<~>calm(X))))&
(((brave(alice)&kind(alice)))=>(?[X]:(brave(X))))&
(![X]:(tall(X)=>(~brave(X)<~>brave(X))))&
((?[X]:((patient(X)|~funny(X))))<=>((kind(john)|old(john))))&
(![X]:(funny(X)=>~tall(X)))&
(![X]:((~curious(X)|happy(X))<=>(~rich(X)|~brave(X))))&
((~creative(fred))<=>((funny(paul)<~>~rich(paul))))&
(?[X]:((~curious(X)<~>~calm(X))))&
((strong(fred)&old(fred)))&
(?[X]:(generous(X)))&
(?[X]:((wise(X)&tall(X))))&
((~strong(lucy)|generous(lucy)))&
(?[X]:(old(X)))&
(?[X]:(~happy(X))) | ~funny(paul) | [
"p0",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2793304529560931445157081
% SZS output start Proof for 2793304529560931445157081
1. ! [X0] : ((~creative(X0) | funny(X0)) <=> ~curious(X0)) [input p0]
9. ! [X0] : ((tall(X0) <~> kind(X0)) <=> (kind(X0) <~> ~curious(X0))) [input p8]
14. ! [X0] : (funny(X0) => ~tall(X0)) [input p13]
24. funny(paul) [input hypothesis]
30. ! [X0] : (~tall(X0) | ~funny(X0)) [ennf transformation 14]
31. ! [X0] : (((~creative(X0) | funny(X0)) | curious(X0)) & (~curious(X0) | (creative(X0) & ~funny(X0)))) [nnf transformation 1]
32. ! [X0] : ((~creative(X0) | funny(X0) | curious(X0)) & (~curious(X0) | (creative(X0) & ~funny(X0)))) [flattening 31]
50. ! [X0] : ((((~kind(X0) | ~tall(X0)) & (kind(X0) | tall(X0))) | ((kind(X0) | curious(X0)) & (~curious(X0) | ~kind(X0)))) & (((curious(X0) | ~kind(X0)) & (~curious(X0) | kind(X0))) | ((tall(X0) | ~kind(X0)) & (kind(X0) | ~tall(X0))))) [nnf transformation 9]
74. ~curious(X0) | ~funny(X0) [cnf transformation 32]
114. curious(X0) | ~kind(X0) | tall(X0) | ~kind(X0) [cnf transformation 50]
116. kind(X0) | tall(X0) | kind(X0) | curious(X0) [cnf transformation 50]
128. ~tall(X0) | ~funny(X0) [cnf transformation 30]
147. funny(paul) [cnf transformation 24]
149. curious(X0) | ~kind(X0) | tall(X0) [duplicate literal removal 114]
150. kind(X0) | tall(X0) | curious(X0) [duplicate literal removal 116]
222. tall(X0) | curious(X0) [subsumption resolution 149,150]
265. 24 <=> funny(paul) [avatar definition]
267. funny(paul) <- (24) [avatar component clause 265]
295. 24 [avatar split clause 147,265]
311. curious(X0) | ~funny(X0) [resolution 222,128]
313. ~funny(X0) [subsumption resolution 311,74]
354. $false <- (24) [resolution 313,267]
355. ~24 [avatar contradiction clause 354]
356. $false [avatar sat refutation 295,355]
% SZS output end Proof for 2793304529560931445157081
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or quiet is either not curious or not brave.
Everyone who is creative or not kind is patient or not rich and vice versa.
If paul is both not wise and brave then john is humble or not creative and vice versa.
Everyone who is happy or not strong is not wise and vice versa.
If someone is either not patient or humble then someone is either not calm or humble.
If someone is both not strong and curious then fred is both not kind and not curious and vice versa.
Everyone who is either not creative or rich is either not creative or quiet and vice versa.
Everyone who is generous is either humble or rich and vice versa.
Everyone who is brave is either not generous or not tall and vice versa.
Everyone who is both not happy and curious is either not curious or kind and vice versa.
Everyone who is not patient or not happy is either not calm or curious and vice versa.
Everyone who is either not wise or curious is not brave or not tall and vice versa.
If someone is both not brave and patient then someone is either tall or not patient.
Everyone who is both not strong and not curious is either not humble or quiet and vice versa.
Everyone who is happy is not curious or not patient.
Everyone who is either tall or funny is brave and vice versa.
Mary is both not funny and not strong.
Someone is either not kind or not rich.
Someone is either old or creative.
Someone is old or not humble.
Someone is either not tall or not patient.
Someone is both calm and strong.
Paul is either not tall or not funny. | Paul is brave. | entailment | (![X]:((calm(X)<~>quiet(X))=>(~curious(X)<~>~brave(X))))&
(![X]:((creative(X)|~kind(X))<=>(patient(X)|~rich(X))))&
(((~wise(paul)&brave(paul)))<=>((humble(john)|~creative(john))))&
(![X]:((happy(X)|~strong(X))<=>~wise(X)))&
((?[X]:((~patient(X)<~>humble(X))))=>(?[X]:((~calm(X)<~>humble(X)))))&
((?[X]:((~strong(X)&curious(X))))<=>((~kind(fred)&~curious(fred))))&
(![X]:((~creative(X)<~>rich(X))<=>(~creative(X)<~>quiet(X))))&
(![X]:(generous(X)<=>(humble(X)<~>rich(X))))&
(![X]:(brave(X)<=>(~generous(X)<~>~tall(X))))&
(![X]:((~happy(X)&curious(X))<=>(~curious(X)<~>kind(X))))&
(![X]:((~patient(X)|~happy(X))<=>(~calm(X)<~>curious(X))))&
(![X]:((~wise(X)<~>curious(X))<=>(~brave(X)|~tall(X))))&
((?[X]:((~brave(X)&patient(X))))=>(?[X]:((tall(X)<~>~patient(X)))))&
(![X]:((~strong(X)&~curious(X))<=>(~humble(X)<~>quiet(X))))&
(![X]:(happy(X)=>(~curious(X)|~patient(X))))&
(![X]:((tall(X)<~>funny(X))<=>brave(X)))&
((~funny(mary)&~strong(mary)))&
(?[X]:((~kind(X)<~>~rich(X))))&
(?[X]:((old(X)<~>creative(X))))&
(?[X]:((old(X)|~humble(X))))&
(?[X]:((~tall(X)<~>~patient(X))))&
(?[X]:((calm(X)&strong(X))))&
((~tall(paul)<~>~funny(paul))) | brave(paul) | [
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8918530268237360335618174
% SZS output start Proof for 8918530268237360335618174
16. ! [X0] : ((tall(X0) <~> funny(X0)) <=> brave(X0)) [input p15]
23. ~tall(paul) <~> ~funny(paul) [input p22]
24. ~brave(paul) [input hypothesis]
63. ! [X0] : ((((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | ~brave(X0)) & (brave(X0) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0))))) [nnf transformation 16]
77. (funny(paul) | tall(paul)) & (~funny(paul) | ~tall(paul)) [nnf transformation 23]
145. ~tall(X0) | funny(X0) | brave(X0) [cnf transformation 63]
146. ~funny(X0) | tall(X0) | brave(X0) [cnf transformation 63]
160. ~funny(paul) | ~tall(paul) [cnf transformation 77]
161. funny(paul) | tall(paul) [cnf transformation 77]
162. ~brave(paul) [cnf transformation 24]
174. 2 <=> brave(paul) [avatar definition]
175. ~brave(paul) <- (~2) [avatar component clause 174]
287. 25 <=> tall(paul) [avatar definition]
288. ~tall(paul) <- (~25) [avatar component clause 287]
289. tall(paul) <- (25) [avatar component clause 287]
291. 26 <=> funny(paul) [avatar definition]
292. ~funny(paul) <- (~26) [avatar component clause 291]
293. funny(paul) <- (26) [avatar component clause 291]
294. 25 | 26 [avatar split clause 161,291,287]
295. ~25 | ~26 [avatar split clause 160,291,287]
296. ~2 [avatar split clause 162,174]
489. funny(paul) | brave(paul) <- (25) [resolution 145,289]
492. brave(paul) <- (25, ~26) [subsumption resolution 489,292]
493. $false <- (~2, 25, ~26) [subsumption resolution 492,175]
494. 2 | ~25 | 26 [avatar contradiction clause 493]
496. tall(paul) | brave(paul) <- (26) [resolution 146,293]
498. brave(paul) <- (~25, 26) [subsumption resolution 496,288]
499. $false <- (~2, ~25, 26) [subsumption resolution 498,175]
500. 2 | 25 | ~26 [avatar contradiction clause 499]
501. $false [avatar sat refutation 294,295,296,494,500]
% SZS output end Proof for 8918530268237360335618174
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet and tall is both not wise and curious.
If lucy is both not curious and not happy then someone is either not happy or not rich.
Everyone who is not funny is either not patient or rich and vice versa.
If someone is not happy or strong then susan is either kind or quiet.
Everyone who is funny or humble is either not funny or brave.
Everyone who is not funny is both quiet and kind.
If someone is both not calm and not strong then john is both not quiet and generous and vice versa.
If john is not tall then someone is both tall and strong and vice versa.
Everyone who is both not wise and curious is either not wise or not quiet.
If lucy is both not creative and not rich then alice is both creative and not old and vice versa.
If lucy is both not humble and rich then someone is both humble and not generous and vice versa.
If someone is both generous and curious then someone is kind or old.
Everyone who is not patient is brave and vice versa.
Everyone who is either funny or rich is either not brave or not funny.
Everyone who is not quiet is patient or not happy.
Everyone who is either not tall or funny is brave.
Fred is either generous or not kind.
Someone is either tall or not creative.
Fred is either old or not calm.
Mary is both not patient and not generous.
Mary is not wise or brave.
Fred is tall or not happy.
Someone is either rich or not generous.
Someone is not wise or not happy. | Fred is patient. | contradiction | (![X]:((~quiet(X)&tall(X))=>(~wise(X)&curious(X))))&
(((~curious(lucy)&~happy(lucy)))=>(?[X]:((~happy(X)<~>~rich(X)))))&
(![X]:(~funny(X)<=>(~patient(X)<~>rich(X))))&
((?[X]:((~happy(X)|strong(X))))=>((kind(susan)<~>quiet(susan))))&
(![X]:((funny(X)|humble(X))=>(~funny(X)<~>brave(X))))&
(![X]:(~funny(X)=>(quiet(X)&kind(X))))&
((?[X]:((~calm(X)&~strong(X))))<=>((~quiet(john)&generous(john))))&
((~tall(john))<=>(?[X]:((tall(X)&strong(X)))))&
(![X]:((~wise(X)&curious(X))=>(~wise(X)<~>~quiet(X))))&
(((~creative(lucy)&~rich(lucy)))<=>((creative(alice)&~old(alice))))&
(((~humble(lucy)&rich(lucy)))<=>(?[X]:((humble(X)&~generous(X)))))&
((?[X]:((generous(X)&curious(X))))=>(?[X]:((kind(X)|old(X)))))&
(![X]:(~patient(X)<=>brave(X)))&
(![X]:((funny(X)<~>rich(X))=>(~brave(X)<~>~funny(X))))&
(![X]:(~quiet(X)=>(patient(X)|~happy(X))))&
(![X]:((~tall(X)<~>funny(X))=>brave(X)))&
((generous(fred)<~>~kind(fred)))&
(?[X]:((tall(X)<~>~creative(X))))&
((old(fred)<~>~calm(fred)))&
((~patient(mary)&~generous(mary)))&
((~wise(mary)|brave(mary)))&
((tall(fred)|~happy(fred)))&
(?[X]:((rich(X)<~>~generous(X))))&
(?[X]:((~wise(X)|~happy(X)))) | patient(fred) | [
"p2",
"p4",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7374085161753974831863190
% SZS output start Proof for 7374085161753974831863190
3. ! [X0] : (~funny(X0) <=> (~patient(X0) <~> rich(X0))) [input p2]
5. ! [X0] : ((humble(X0) | funny(X0)) => (~funny(X0) <~> brave(X0))) [input p4]
13. ! [X0] : (~patient(X0) <=> brave(X0)) [input p12]
14. ! [X0] : ((funny(X0) <~> rich(X0)) => (~brave(X0) <~> ~funny(X0))) [input p13]
25. patient(fred) [input hypothesis]
32. ! [X0] : ((~funny(X0) <~> brave(X0)) | (~humble(X0) & ~funny(X0))) [ennf transformation 5]
37. ! [X0] : ((~brave(X0) <~> ~funny(X0)) | (funny(X0) <=> rich(X0))) [ennf transformation 14]
44. ! [X0] : ((~funny(X0) | ((~patient(X0) | ~rich(X0)) & (rich(X0) | patient(X0)))) & (((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | funny(X0))) [nnf transformation 3]
46. ! [X0] : (((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | (~humble(X0) & ~funny(X0))) [nnf transformation 32]
67. ! [X0] : ((~patient(X0) | ~brave(X0)) & (brave(X0) | patient(X0))) [nnf transformation 13]
68. ! [X0] : (((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | ((funny(X0) | ~rich(X0)) & (rich(X0) | ~funny(X0)))) [nnf transformation 37]
84. ~patient(X0) | rich(X0) | funny(X0) [cnf transformation 44]
92. brave(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 46]
117. ~brave(X0) | ~patient(X0) [cnf transformation 67]
118. ~funny(X0) | ~brave(X0) | rich(X0) | ~funny(X0) [cnf transformation 68]
121. funny(X0) | brave(X0) | funny(X0) | ~rich(X0) [cnf transformation 68]
138. patient(fred) [cnf transformation 25]
139. ~funny(X0) | ~brave(X0) | rich(X0) [duplicate literal removal 118]
140. funny(X0) | brave(X0) | ~rich(X0) [duplicate literal removal 121]
142. ~funny(X0) | brave(X0) [duplicate literal removal 92]
271. ~rich(X0) | brave(X0) [subsumption resolution 140,142]
272. ~funny(X0) | rich(X0) [subsumption resolution 139,142]
362. rich(fred) | funny(fred) [resolution 84,138]
363. rich(fred) [subsumption resolution 362,272]
367. brave(fred) [resolution 363,271]
369. ~patient(fred) [resolution 367,117]
370. $false [subsumption resolution 369,138]
% SZS output end Proof for 7374085161753974831863190
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich then alice is either brave or not funny.
Everyone who is both not funny and patient is both not funny and not rich and vice versa.
Everyone who is both not tall and curious is not curious or creative and vice versa.
If alice is either not strong or curious then someone is either kind or wise.
Everyone who is patient or old is both quiet and not creative.
If john is both not generous and not tall then susan is both not wise and generous and vice versa.
If john is not happy or creative then someone is either not patient or brave and vice versa.
If john is old or quiet then lucy is both happy and old.
If lucy is either not patient or not generous then alice is both not old and not curious and vice versa.
Everyone who is creative is quiet and vice versa.
Everyone who is either generous or not curious is humble.
If john is both tall and rich then alice is both creative and patient and vice versa.
If alice is either not kind or not funny then someone is both curious and happy.
If paul is either not quiet or brave then susan is generous and vice versa.
If mary is either not creative or old then susan is not calm.
Everyone who is curious is either old or not strong and vice versa.
Lucy is quiet or not happy.
Someone is wise or not rich.
Someone is both happy and not quiet.
Someone is not kind or tall.
Someone is calm.
Someone is either happy or not creative.
John is not generous or not humble. | Alice is strong. | contradiction | ((?[X]:(~rich(X)))=>((brave(alice)<~>~funny(alice))))&
(![X]:((~funny(X)&patient(X))<=>(~funny(X)&~rich(X))))&
(![X]:((~tall(X)&curious(X))<=>(~curious(X)|creative(X))))&
(((~strong(alice)<~>curious(alice)))=>(?[X]:((kind(X)<~>wise(X)))))&
(![X]:((patient(X)|old(X))=>(quiet(X)&~creative(X))))&
(((~generous(john)&~tall(john)))<=>((~wise(susan)&generous(susan))))&
(((~happy(john)|creative(john)))<=>(?[X]:((~patient(X)<~>brave(X)))))&
(((old(john)|quiet(john)))=>((happy(lucy)&old(lucy))))&
(((~patient(lucy)<~>~generous(lucy)))<=>((~old(alice)&~curious(alice))))&
(![X]:(creative(X)<=>quiet(X)))&
(![X]:((generous(X)<~>~curious(X))=>humble(X)))&
(((tall(john)&rich(john)))<=>((creative(alice)&patient(alice))))&
(((~kind(alice)<~>~funny(alice)))=>(?[X]:((curious(X)&happy(X)))))&
(((~quiet(paul)<~>brave(paul)))<=>(generous(susan)))&
(((~creative(mary)<~>old(mary)))=>(~calm(susan)))&
(![X]:(curious(X)<=>(old(X)<~>~strong(X))))&
((quiet(lucy)|~happy(lucy)))&
(?[X]:((wise(X)|~rich(X))))&
(?[X]:((happy(X)&~quiet(X))))&
(?[X]:((~kind(X)|tall(X))))&
(?[X]:(calm(X)))&
(?[X]:((happy(X)<~>~creative(X))))&
((~generous(john)|~humble(john))) | strong(alice) | [
"p2",
"p4",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2366003271738936579496093
% SZS output start Proof for 2366003271738936579496093
3. ! [X0] : ((curious(X0) & ~tall(X0)) <=> (creative(X0) | ~curious(X0))) [input p2]
5. ! [X0] : ((old(X0) | patient(X0)) => (~creative(X0) & quiet(X0))) [input p4]
10. ! [X0] : (creative(X0) <=> quiet(X0)) [input p9]
16. ! [X0] : (curious(X0) <=> (old(X0) <~> ~strong(X0))) [input p15]
24. strong(alice) [input hypothesis]
27. ! [X0] : ((~creative(X0) & quiet(X0)) | (~old(X0) & ~patient(X0))) [ennf transformation 5]
35. ! [X0] : (((curious(X0) & ~tall(X0)) | (~creative(X0) & curious(X0))) & ((creative(X0) | ~curious(X0)) | (~curious(X0) | tall(X0)))) [nnf transformation 3]
36. ! [X0] : (((curious(X0) & ~tall(X0)) | (~creative(X0) & curious(X0))) & (creative(X0) | ~curious(X0) | ~curious(X0) | tall(X0))) [flattening 35]
49. ! [X0] : ((creative(X0) | ~quiet(X0)) & (quiet(X0) | ~creative(X0))) [nnf transformation 10]
58. ! [X0] : ((curious(X0) | ((old(X0) | strong(X0)) & (~strong(X0) | ~old(X0)))) & (((strong(X0) | ~old(X0)) & (~strong(X0) | old(X0))) | ~curious(X0))) [nnf transformation 16]
79. curious(X0) | curious(X0) [cnf transformation 36]
86. ~old(X0) | quiet(X0) [cnf transformation 27]
88. ~old(X0) | ~creative(X0) [cnf transformation 27]
110. ~quiet(X0) | creative(X0) [cnf transformation 49]
127. ~strong(X0) | old(X0) | ~curious(X0) [cnf transformation 58]
140. strong(alice) [cnf transformation 24]
142. curious(X0) [duplicate literal removal 79]
159. 4 <=> strong(alice) [avatar definition]
160. strong(alice) <- (4) [avatar component clause 159]
254. 23 <=> old(alice) [avatar definition]
255. old(alice) <- (23) [avatar component clause 254]
270. 26 <=> creative(alice) [avatar definition]
271. ~creative(alice) <- (~26) [avatar component clause 270]
310. ~strong(X0) | old(X0) [subsumption resolution 127,142]
346. 4 [avatar split clause 140,159]
357. old(alice) <- (4) [resolution 310,160]
358. 23 | ~4 [avatar split clause 357,159,254]
360. ~creative(alice) <- (23) [resolution 255,88]
361. quiet(alice) <- (23) [resolution 255,86]
362. ~26 | ~23 [avatar split clause 360,254,270]
364. creative(alice) <- (23) [resolution 361,110]
365. $false <- (23, ~26) [subsumption resolution 364,271]
366. ~23 | 26 [avatar contradiction clause 365]
367. $false [avatar sat refutation 346,358,362,366]
% SZS output end Proof for 2366003271738936579496093
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not humble is rich.
Everyone who is tall or not happy is both not generous and calm.
If mary is not generous or not happy then susan is either not funny or not generous and vice versa.
If fred is either not tall or not calm then someone is brave and vice versa.
Everyone who is both calm and not wise is either brave or not patient.
If someone is both not curious and patient then alice is not happy and vice versa.
If someone is wise then mary is either strong or not quiet and vice versa.
If john is not quiet then someone is both not calm and wise.
Everyone who is creative is not funny and vice versa.
If someone is both not tall and quiet then someone is not curious or generous and vice versa.
If someone is wise or not strong then someone is brave or happy and vice versa.
If mary is old or strong then someone is curious and vice versa.
Everyone who is not kind is brave or quiet and vice versa.
If mary is both not strong and not calm then mary is not patient and vice versa.
If lucy is both funny and not happy then someone is creative or patient.
Someone is either not happy or curious.
Someone is old or not calm.
Someone is not rich or old.
John is both not brave and humble.
Fred is either not funny or not rich.
Someone is not wise or wise.
Fred is generous.
John is either creative or tall. | Fred is not creative. | contradiction | (![X]:((funny(X)|~humble(X))=>rich(X)))&
(![X]:((tall(X)|~happy(X))=>(~generous(X)&calm(X))))&
(((~generous(mary)|~happy(mary)))<=>((~funny(susan)<~>~generous(susan))))&
(((~tall(fred)<~>~calm(fred)))<=>(?[X]:(brave(X))))&
(![X]:((calm(X)&~wise(X))=>(brave(X)<~>~patient(X))))&
((?[X]:((~curious(X)&patient(X))))<=>(~happy(alice)))&
((?[X]:(wise(X)))<=>((strong(mary)<~>~quiet(mary))))&
((~quiet(john))=>(?[X]:((~calm(X)&wise(X)))))&
(![X]:(creative(X)<=>~funny(X)))&
((?[X]:((~tall(X)&quiet(X))))<=>(?[X]:((~curious(X)|generous(X)))))&
((?[X]:((wise(X)|~strong(X))))<=>(?[X]:((brave(X)|happy(X)))))&
(((old(mary)|strong(mary)))<=>(?[X]:(curious(X))))&
(![X]:(~kind(X)<=>(brave(X)|quiet(X))))&
(((~strong(mary)&~calm(mary)))<=>(~patient(mary)))&
(((funny(lucy)&~happy(lucy)))=>(?[X]:((creative(X)|patient(X)))))&
(?[X]:((~happy(X)<~>curious(X))))&
(?[X]:((old(X)|~calm(X))))&
(?[X]:((~rich(X)|old(X))))&
((~brave(john)&humble(john)))&
((~funny(fred)<~>~rich(fred)))&
(?[X]:((~wise(X)|wise(X))))&
(generous(fred))&
((creative(john)<~>tall(john))) | ~creative(fred) | [
"p0",
"p8",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4695064761701511251182704
% SZS output start Proof for 4695064761701511251182704
1. ! [X0] : ((~humble(X0) | funny(X0)) => rich(X0)) [input p0]
9. ! [X0] : (creative(X0) <=> ~funny(X0)) [input p8]
20. ~funny(fred) <~> ~rich(fred) [input p19]
24. ~creative(fred) [input hypothesis]
27. ! [X0] : (funny(X0) => rich(X0)) [pure predicate removal 1]
29. ! [X0] : (rich(X0) | ~funny(X0)) [ennf transformation 27]
53. ! [X0] : ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0))) [nnf transformation 9]
80. (rich(fred) | funny(fred)) & (~rich(fred) | ~funny(fred)) [nnf transformation 20]
84. ~funny(X0) | rich(X0) [cnf transformation 29]
111. creative(X0) | funny(X0) [cnf transformation 53]
133. ~rich(fred) | ~funny(fred) [cnf transformation 80]
134. rich(fred) | funny(fred) [cnf transformation 80]
139. ~creative(fred) [cnf transformation 24]
361. rich(fred) [subsumption resolution 134,84]
362. ~funny(fred) [subsumption resolution 133,361]
386. funny(fred) [resolution 111,139]
388. $false [subsumption resolution 386,362]
% SZS output end Proof for 4695064761701511251182704
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall is either not happy or curious and vice versa. Everyone who is either kind or old is both not curious and not calm and vice versa. If someone is not brave then someone is both calm and not brave and vice versa. If susan is both not happy and curious then susan is kind or humble and vice versa. Everyone who is both not generous and strong is calm. If someone is not kind then someone is both not generous and brave. Everyone who is wise or funny is both kind and not generous and vice versa. Everyone who is quiet is both not patient and not old. If fred is both not brave and not strong then alice is not patient and vice versa. If mary is either brave or patient then john is either old or creative and vice versa. If john is calm or kind then alice is both old and not happy. If someone is not brave then someone is funny and vice versa. If lucy is both happy and not wise then john is patient or not happy. Everyone who is not calm or old is either not quiet or happy and vice versa. If mary is either kind or curious then someone is strong. Everyone who is either patient or brave is both not wise and wise and vice versa. Someone is both not curious and old. Alice is not calm or happy. Someone is either not quiet or not generous. John is both rich and not kind. Someone is either wise or not wise. Fred is quiet. Susan is both not calm and quiet. Fred is calm. | Susan is funny. | contradiction | (![X]:(tall(X)<=>(~happy(X)<~>curious(X))))&
(![X]:((kind(X)<~>old(X))<=>(~curious(X)&~calm(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((calm(X)&~brave(X)))))&
(((~happy(susan)&curious(susan)))<=>((kind(susan)|humble(susan))))&
(![X]:((~generous(X)&strong(X))=>calm(X)))&
((?[X]:(~kind(X)))=>(?[X]:((~generous(X)&brave(X)))))&
(![X]:((wise(X)|funny(X))<=>(kind(X)&~generous(X))))&
(![X]:(quiet(X)=>(~patient(X)&~old(X))))&
(((~brave(fred)&~strong(fred)))<=>(~patient(alice)))&
(((brave(mary)<~>patient(mary)))<=>((old(john)<~>creative(john))))&
(((calm(john)|kind(john)))=>((old(alice)&~happy(alice))))&
((?[X]:(~brave(X)))<=>(?[X]:(funny(X))))&
(((happy(lucy)&~wise(lucy)))=>((patient(john)|~happy(john))))&
(![X]:((~calm(X)|old(X))<=>(~quiet(X)<~>happy(X))))&
(((kind(mary)<~>curious(mary)))=>(?[X]:(strong(X))))&
(![X]:((patient(X)<~>brave(X))<=>(~wise(X)&wise(X))))&
(?[X]:((~curious(X)&old(X))))&
((~calm(alice)|happy(alice)))&
(?[X]:((~quiet(X)<~>~generous(X))))&
((rich(john)&~kind(john)))&
(?[X]:((wise(X)<~>~wise(X))))&
(quiet(fred))&
((~calm(susan)&quiet(susan)))&
(calm(fred)) | funny(susan) | [
"p1",
"p3",
"p6",
"p7",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1814822158149684155514813
% SZS output start Proof for 1814822158149684155514813
2. ! [X0] : ((kind(X0) <~> old(X0)) <=> (~calm(X0) & ~curious(X0))) [input p1]
4. (curious(susan) & ~happy(susan)) <=> (humble(susan) | kind(susan)) [input p3]
7. ! [X0] : ((funny(X0) | wise(X0)) <=> (~generous(X0) & kind(X0))) [input p6]
8. ! [X0] : (quiet(X0) => (~old(X0) & ~patient(X0))) [input p7]
23. quiet(susan) & ~calm(susan) [input p22]
25. funny(susan) [input hypothesis]
33. ! [X0] : ((~old(X0) & ~patient(X0)) | ~quiet(X0)) [ennf transformation 8]
38. ! [X0] : ((((~old(X0) | ~kind(X0)) & (old(X0) | kind(X0))) | (calm(X0) | curious(X0))) & ((~calm(X0) & ~curious(X0)) | ((kind(X0) | ~old(X0)) & (old(X0) | ~kind(X0))))) [nnf transformation 2]
39. ! [X0] : ((((~old(X0) | ~kind(X0)) & (old(X0) | kind(X0))) | calm(X0) | curious(X0)) & ((~calm(X0) & ~curious(X0)) | ((kind(X0) | ~old(X0)) & (old(X0) | ~kind(X0))))) [flattening 38]
45. ((curious(susan) & ~happy(susan)) | (~humble(susan) & ~kind(susan))) & ((humble(susan) | kind(susan)) | (~curious(susan) | happy(susan))) [nnf transformation 4]
46. ((curious(susan) & ~happy(susan)) | (~humble(susan) & ~kind(susan))) & (humble(susan) | kind(susan) | ~curious(susan) | happy(susan)) [flattening 45]
50. ! [X0] : (((funny(X0) | wise(X0)) | (generous(X0) | ~kind(X0))) & ((~generous(X0) & kind(X0)) | (~funny(X0) & ~wise(X0)))) [nnf transformation 7]
51. ! [X0] : ((funny(X0) | wise(X0) | generous(X0) | ~kind(X0)) & ((~generous(X0) & kind(X0)) | (~funny(X0) & ~wise(X0)))) [flattening 50]
75. ~kind(X0) | old(X0) | ~curious(X0) [cnf transformation 39]
87. curious(susan) | ~kind(susan) [cnf transformation 46]
93. ~funny(X0) | kind(X0) [cnf transformation 51]
98. ~quiet(X0) | ~old(X0) [cnf transformation 33]
141. quiet(susan) [cnf transformation 23]
143. funny(susan) [cnf transformation 25]
170. 7 <=> curious(susan) [avatar definition]
172. curious(susan) <- (7) [avatar component clause 170]
175. 8 <=> kind(susan) [avatar definition]
176. kind(susan) <- (8) [avatar component clause 175]
178. ~8 | 7 [avatar split clause 87,170,175]
328. kind(susan) [resolution 93,143]
333. ~old(susan) [resolution 98,141]
337. old(susan) | ~curious(susan) <- (8) [resolution 75,176]
339. ~curious(susan) <- (8) [subsumption resolution 337,333]
340. $false <- (7, 8) [subsumption resolution 339,172]
341. ~7 | ~8 [avatar contradiction clause 340]
351. 8 [avatar split clause 328,175]
352. $false [avatar sat refutation 178,341,351]
% SZS output end Proof for 1814822158149684155514813
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both rich and brave then someone is either not generous or brave.
Everyone who is old is either not quiet or tall.
Everyone who is funny is both generous and not brave.
If someone is both not strong and strong then someone is creative.
Everyone who is either humble or not humble is not funny and vice versa.
If susan is not humble or funny then john is either patient or brave.
Everyone who is brave or not kind is happy.
Everyone who is not strong or not funny is both old and patient.
Everyone who is happy is both generous and not creative.
Everyone who is not patient or funny is both not funny and wise.
Everyone who is not patient or quiet is curious or tall and vice versa.
If susan is both rich and not happy then alice is either not rich or not calm.
If someone is both brave and not calm then someone is both creative and not strong and vice versa.
Everyone who is humble or not strong is either not brave or humble.
If someone is either rich or old then susan is patient.
If someone is old or brave then john is not kind or old.
Fred is curious.
Mary is not funny.
Susan is both wise and tall.
Someone is both not humble and not brave.
Someone is both not quiet and not rich.
Someone is patient or kind.
Someone is both kind and not happy. | Susan is quiet. | entailment | ((?[X]:((rich(X)&brave(X))))=>(?[X]:((~generous(X)<~>brave(X)))))&
(![X]:(old(X)=>(~quiet(X)<~>tall(X))))&
(![X]:(funny(X)=>(generous(X)&~brave(X))))&
((?[X]:((~strong(X)&strong(X))))=>(?[X]:(creative(X))))&
(![X]:((humble(X)<~>~humble(X))<=>~funny(X)))&
(((~humble(susan)|funny(susan)))=>((patient(john)<~>brave(john))))&
(![X]:((brave(X)|~kind(X))=>happy(X)))&
(![X]:((~strong(X)|~funny(X))=>(old(X)&patient(X))))&
(![X]:(happy(X)=>(generous(X)&~creative(X))))&
(![X]:((~patient(X)|funny(X))=>(~funny(X)&wise(X))))&
(![X]:((~patient(X)|quiet(X))<=>(curious(X)|tall(X))))&
(((rich(susan)&~happy(susan)))=>((~rich(alice)<~>~calm(alice))))&
((?[X]:((brave(X)&~calm(X))))<=>(?[X]:((creative(X)&~strong(X)))))&
(![X]:((humble(X)|~strong(X))=>(~brave(X)<~>humble(X))))&
((?[X]:((rich(X)<~>old(X))))=>(patient(susan)))&
((?[X]:((old(X)|brave(X))))=>((~kind(john)|old(john))))&
(curious(fred))&
(~funny(mary))&
((wise(susan)&tall(susan)))&
(?[X]:((~humble(X)&~brave(X))))&
(?[X]:((~quiet(X)&~rich(X))))&
(?[X]:((patient(X)|kind(X))))&
(?[X]:((kind(X)&~happy(X)))) | quiet(susan) | [
"p4",
"p7",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4162948223163462990844614
% SZS output start Proof for 4162948223163462990844614
5. ! [X0] : ((humble(X0) <~> ~humble(X0)) <=> ~funny(X0)) [input p4]
8. ! [X0] : ((~funny(X0) | ~strong(X0)) => (patient(X0) & old(X0))) [input p7]
11. ! [X0] : ((quiet(X0) | ~patient(X0)) <=> (tall(X0) | curious(X0))) [input p10]
19. tall(susan) & wise(susan) [input p18]
24. ~quiet(susan) [input hypothesis]
29. tall(susan) [pure predicate removal 19]
36. ! [X0] : ((patient(X0) & old(X0)) | (funny(X0) & strong(X0))) [ennf transformation 8]
53. ! [X0] : ((((humble(X0) | ~humble(X0)) & (~humble(X0) | humble(X0))) | funny(X0)) & (~funny(X0) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0))))) [nnf transformation 5]
55. ! [X0] : (((quiet(X0) | ~patient(X0)) | (~tall(X0) & ~curious(X0))) & ((tall(X0) | curious(X0)) | (~quiet(X0) & patient(X0)))) [nnf transformation 11]
56. ! [X0] : ((quiet(X0) | ~patient(X0) | (~tall(X0) & ~curious(X0))) & (tall(X0) | curious(X0) | (~quiet(X0) & patient(X0)))) [flattening 55]
80. ~funny(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 53]
81. ~funny(X0) | humble(X0) | humble(X0) [cnf transformation 53]
93. patient(X0) | funny(X0) [cnf transformation 36]
101. quiet(X0) | ~patient(X0) | ~tall(X0) [cnf transformation 56]
118. tall(susan) [cnf transformation 29]
126. ~quiet(susan) [cnf transformation 24]
129. ~funny(X0) | ~humble(X0) [duplicate literal removal 80]
130. ~funny(X0) | humble(X0) [duplicate literal removal 81]
144. ~funny(X0) [subsumption resolution 129,130]
159. patient(X0) [subsumption resolution 93,144]
161. ~tall(X0) | quiet(X0) [subsumption resolution 101,159]
213. quiet(susan) [resolution 161,118]
214. $false [subsumption resolution 213,126]
% SZS output end Proof for 4162948223163462990844614
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is not rich or not funny then lucy is not tall or creative.
If lucy is not calm then fred is quiet and vice versa.
If someone is calm or not funny then john is not rich or creative and vice versa.
Everyone who is either not wise or not quiet is both not quiet and humble and vice versa.
Everyone who is happy or old is not quiet or not old and vice versa.
If fred is not funny or rich then fred is funny or old.
Everyone who is not tall is both strong and humble.
Everyone who is either curious or not old is both not strong and patient.
If someone is either not humble or not funny then someone is either strong or not rich.
If someone is both tall and not curious then paul is strong and vice versa.
Everyone who is creative is old or generous and vice versa.
Everyone who is not happy is both not creative and not calm.
If someone is strong or tall then someone is either old or happy and vice versa.
If someone is both happy and not brave then alice is both not curious and strong and vice versa.
If alice is both not old and patient then someone is either not generous or happy.
Everyone who is not happy or not humble is happy and vice versa.
Paul is not curious.
Fred is both calm and tall.
Susan is not wise or not funny.
Alice is tall or strong.
Someone is both calm and rich.
Alice is quiet.
Someone is generous or not old.
Fred is both tall and kind. | Susan is not brave. | contradiction | ((?[X]:((~rich(X)|~funny(X))))=>((~tall(lucy)|creative(lucy))))&
((~calm(lucy))<=>(quiet(fred)))&
((?[X]:((calm(X)|~funny(X))))<=>((~rich(john)|creative(john))))&
(![X]:((~wise(X)<~>~quiet(X))<=>(~quiet(X)&humble(X))))&
(![X]:((happy(X)|old(X))<=>(~quiet(X)|~old(X))))&
(((~funny(fred)|rich(fred)))=>((funny(fred)|old(fred))))&
(![X]:(~tall(X)=>(strong(X)&humble(X))))&
(![X]:((curious(X)<~>~old(X))=>(~strong(X)&patient(X))))&
((?[X]:((~humble(X)<~>~funny(X))))=>(?[X]:((strong(X)<~>~rich(X)))))&
((?[X]:((tall(X)&~curious(X))))<=>(strong(paul)))&
(![X]:(creative(X)<=>(old(X)|generous(X))))&
(![X]:(~happy(X)=>(~creative(X)&~calm(X))))&
((?[X]:((strong(X)|tall(X))))<=>(?[X]:((old(X)<~>happy(X)))))&
((?[X]:((happy(X)&~brave(X))))<=>((~curious(alice)&strong(alice))))&
(((~old(alice)&patient(alice)))=>(?[X]:((~generous(X)<~>happy(X)))))&
(![X]:((~happy(X)|~humble(X))<=>happy(X)))&
(~curious(paul))&
((calm(fred)&tall(fred)))&
((~wise(susan)|~funny(susan)))&
((tall(alice)|strong(alice)))&
(?[X]:((calm(X)&rich(X))))&
(quiet(alice))&
(?[X]:((generous(X)|~old(X))))&
((tall(fred)&kind(fred))) | ~brave(susan) | [
"p4",
"p7",
"p13",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6172138716377258090352238
% SZS output start Proof for 6172138716377258090352238
5. ! [X0] : ((old(X0) | happy(X0)) <=> (~old(X0) | ~quiet(X0))) [input p4]
8. ! [X0] : ((curious(X0) <~> ~old(X0)) => (patient(X0) & ~strong(X0))) [input p7]
14. ? [X0] : (~brave(X0) & happy(X0)) <=> (strong(alice) & ~curious(alice)) [input p13]
16. ! [X0] : ((~humble(X0) | ~happy(X0)) <=> happy(X0)) [input p15]
22. quiet(alice) [input p21]
25. ~brave(susan) [input hypothesis]
34. ! [X0] : ((patient(X0) & ~strong(X0)) | (curious(X0) <=> ~old(X0))) [ennf transformation 8]
47. ! [X0] : (((old(X0) | happy(X0)) | (old(X0) & quiet(X0))) & ((~old(X0) | ~quiet(X0)) | (~old(X0) & ~happy(X0)))) [nnf transformation 5]
48. ! [X0] : ((old(X0) | happy(X0) | (old(X0) & quiet(X0))) & (~old(X0) | ~quiet(X0) | (~old(X0) & ~happy(X0)))) [flattening 47]
49. ! [X0] : ((patient(X0) & ~strong(X0)) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) [nnf transformation 34]
65. (? [X0] : (~brave(X0) & happy(X0)) | (~strong(alice) | curious(alice))) & ((strong(alice) & ~curious(alice)) | ! [X0] : (brave(X0) | ~happy(X0))) [nnf transformation 14]
66. (? [X0] : (~brave(X0) & happy(X0)) | ~strong(alice) | curious(alice)) & ((strong(alice) & ~curious(alice)) | ! [X0] : (brave(X0) | ~happy(X0))) [flattening 65]
67. (? [X0] : (~brave(X0) & happy(X0)) | ~strong(alice) | curious(alice)) & ((strong(alice) & ~curious(alice)) | ! [X1] : (brave(X1) | ~happy(X1))) [rectify 66]
68. ? [X0] : (~brave(X0) & happy(X0)) => (~brave(sK5) & happy(sK5)) [choice axiom]
69. ((~brave(sK5) & happy(sK5)) | ~strong(alice) | curious(alice)) & ((strong(alice) & ~curious(alice)) | ! [X1] : (brave(X1) | ~happy(X1))) [skolemisation 67,68]
73. ! [X0] : (((~humble(X0) | ~happy(X0)) | ~happy(X0)) & (happy(X0) | (humble(X0) & happy(X0)))) [nnf transformation 16]
74. ! [X0] : ((~humble(X0) | ~happy(X0) | ~happy(X0)) & (happy(X0) | (humble(X0) & happy(X0)))) [flattening 73]
94. ~old(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 48]
102. ~strong(X0) | curious(X0) | old(X0) [cnf transformation 49]
123. ~curious(alice) | brave(X1) | ~happy(X1) [cnf transformation 69]
124. strong(alice) | brave(X1) | ~happy(X1) [cnf transformation 69]
129. happy(X0) | happy(X0) [cnf transformation 74]
139. quiet(alice) [cnf transformation 22]
142. ~brave(susan) [cnf transformation 25]
143. happy(X0) [duplicate literal removal 129]
146. ~old(X0) | ~quiet(X0) [duplicate literal removal 94]
266. 27 <=> curious(alice) [avatar definition]
267. ~curious(alice) <- (~27) [avatar component clause 266]
270. 28 <=> strong(alice) [avatar definition]
271. strong(alice) <- (28) [avatar component clause 270]
284. 31 <=> ! [X1] : (brave(X1) | ~happy(X1)) [avatar definition]
285. brave(X1) | ~happy(X1) <- (31) [avatar component clause 284]
286. 31 | 28 [avatar split clause 124,270,284]
287. 31 | ~27 [avatar split clause 123,266,284]
289. 32 <=> old(alice) [avatar definition]
291. old(alice) <- (32) [avatar component clause 289]
344. curious(alice) | old(alice) <- (28) [resolution 102,271]
347. old(alice) <- (~27, 28) [subsumption resolution 344,267]
348. 32 | 27 | ~28 [avatar split clause 347,270,266,289]
349. brave(X1) <- (31) [subsumption resolution 285,143]
351. $false <- (31) [resolution 349,142]
354. ~31 [avatar contradiction clause 351]
356. ~quiet(alice) <- (32) [resolution 291,146]
358. $false <- (32) [subsumption resolution 356,139]
359. ~32 [avatar contradiction clause 358]
360. $false [avatar sat refutation 286,287,348,354,359]
% SZS output end Proof for 6172138716377258090352238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not old and generous then lucy is not humble and vice versa.
If alice is both brave and not old then someone is either wise or brave and vice versa.
If someone is both happy and not curious then fred is both not patient and funny.
Everyone who is tall or not kind is strong and vice versa.
If someone is either not quiet or rich then fred is old or not creative.
Everyone who is not kind or calm is both not curious and not tall.
If someone is both old and generous then someone is both not old and not humble.
If paul is tall or not happy then john is either calm or not generous.
If someone is not creative then fred is happy or strong.
If someone is either not happy or funny then someone is quiet and vice versa.
Everyone who is either patient or not calm is both rich and not patient and vice versa.
Everyone who is not wise is quiet or humble.
If susan is not creative or kind then lucy is both tall and creative.
Everyone who is not calm or not creative is either kind or calm and vice versa.
If someone is not rich then lucy is patient or not happy and vice versa.
Everyone who is brave is either generous or not kind.
John is calm.
Fred is either not curious or not tall.
John is either not brave or not rich.
Mary is both not curious and not quiet.
Someone is not quiet.
Someone is not funny or rich.
Someone is rich.
Paul is either not calm or quiet. | John is rich. | contradiction | ((?[X]:((~old(X)&generous(X))))<=>(~humble(lucy)))&
(((brave(alice)&~old(alice)))<=>(?[X]:((wise(X)<~>brave(X)))))&
((?[X]:((happy(X)&~curious(X))))=>((~patient(fred)&funny(fred))))&
(![X]:((tall(X)|~kind(X))<=>strong(X)))&
((?[X]:((~quiet(X)<~>rich(X))))=>((old(fred)|~creative(fred))))&
(![X]:((~kind(X)|calm(X))=>(~curious(X)&~tall(X))))&
((?[X]:((old(X)&generous(X))))=>(?[X]:((~old(X)&~humble(X)))))&
(((tall(paul)|~happy(paul)))=>((calm(john)<~>~generous(john))))&
((?[X]:(~creative(X)))=>((happy(fred)|strong(fred))))&
((?[X]:((~happy(X)<~>funny(X))))<=>(?[X]:(quiet(X))))&
(![X]:((patient(X)<~>~calm(X))<=>(rich(X)&~patient(X))))&
(![X]:(~wise(X)=>(quiet(X)|humble(X))))&
(((~creative(susan)|kind(susan)))=>((tall(lucy)&creative(lucy))))&
(![X]:((~calm(X)|~creative(X))<=>(kind(X)<~>calm(X))))&
((?[X]:(~rich(X)))<=>((patient(lucy)|~happy(lucy))))&
(![X]:(brave(X)=>(generous(X)<~>~kind(X))))&
(calm(john))&
((~curious(fred)<~>~tall(fred)))&
((~brave(john)<~>~rich(john)))&
((~curious(mary)&~quiet(mary)))&
(?[X]:(~quiet(X)))&
(?[X]:((~funny(X)|rich(X))))&
(?[X]:(rich(X)))&
((~calm(paul)<~>quiet(paul))) | rich(john) | [
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1618548618743377566280322
% SZS output start Proof for 1618548618743377566280322
11. ! [X0] : ((patient(X0) <~> ~calm(X0)) <=> (~patient(X0) & rich(X0))) [input p10]
17. calm(john) [input p16]
25. rich(john) [input hypothesis]
62. ! [X0] : ((((calm(X0) | ~patient(X0)) & (~calm(X0) | patient(X0))) | (patient(X0) | ~rich(X0))) & ((~patient(X0) & rich(X0)) | ((patient(X0) | calm(X0)) & (~calm(X0) | ~patient(X0))))) [nnf transformation 11]
63. ! [X0] : ((((calm(X0) | ~patient(X0)) & (~calm(X0) | patient(X0))) | patient(X0) | ~rich(X0)) & ((~patient(X0) & rich(X0)) | ((patient(X0) | calm(X0)) & (~calm(X0) | ~patient(X0))))) [flattening 62]
112. ~patient(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 63]
114. ~calm(X0) | patient(X0) | patient(X0) | ~rich(X0) [cnf transformation 63]
132. calm(john) [cnf transformation 17]
144. rich(john) [cnf transformation 25]
147. ~calm(X0) | ~patient(X0) [duplicate literal removal 112]
148. ~calm(X0) | patient(X0) | ~rich(X0) [duplicate literal removal 114]
242. 22 <=> calm(john) [avatar definition]
243. calm(john) <- (22) [avatar component clause 242]
332. 22 [avatar split clause 132,242]
348. 45 <=> rich(john) [avatar definition]
350. rich(john) <- (45) [avatar component clause 348]
372. 45 [avatar split clause 144,348]
381. ~patient(john) <- (22) [resolution 147,243]
479. patient(john) | ~rich(john) <- (22) [resolution 148,243]
485. ~rich(john) <- (22) [subsumption resolution 479,381]
486. $false <- (22, 45) [subsumption resolution 485,350]
487. ~22 | ~45 [avatar contradiction clause 486]
490. $false [avatar sat refutation 332,372,487]
% SZS output end Proof for 1618548618743377566280322
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both creative and tall then lucy is not brave.
Everyone who is generous or not generous is not patient or generous.
Everyone who is both not old and not patient is old.
If someone is not humble then someone is both brave and generous.
Everyone who is not happy is not rich.
If someone is happy then someone is both not quiet and strong.
Everyone who is both tall and rich is either funny or wise and vice versa.
If someone is humble or rich then mary is not brave or curious.
Everyone who is not wise is both not brave and happy and vice versa.
Everyone who is both brave and not rich is both patient and creative and vice versa.
Everyone who is not wise or not rich is both not strong and curious.
If fred is both not curious and calm then paul is kind or not quiet and vice versa.
If someone is not kind or not tall then paul is either brave or not old and vice versa.
Everyone who is both curious and not kind is both not brave and brave and vice versa.
Everyone who is both generous and not kind is not generous.
Everyone who is not patient is not kind.
Lucy is both quiet and not calm.
John is both tall and not calm.
Someone is quiet.
Alice is both tall and not creative.
Lucy is curious or happy.
Alice is not calm.
Lucy is not happy. | Mary is calm. | neutral | (((creative(alice)&tall(alice)))=>(~brave(lucy)))&
(![X]:((generous(X)|~generous(X))=>(~patient(X)|generous(X))))&
(![X]:((~old(X)&~patient(X))=>old(X)))&
((?[X]:(~humble(X)))=>(?[X]:((brave(X)&generous(X)))))&
(![X]:(~happy(X)=>~rich(X)))&
((?[X]:(happy(X)))=>(?[X]:((~quiet(X)&strong(X)))))&
(![X]:((tall(X)&rich(X))<=>(funny(X)<~>wise(X))))&
((?[X]:((humble(X)|rich(X))))=>((~brave(mary)|curious(mary))))&
(![X]:(~wise(X)<=>(~brave(X)&happy(X))))&
(![X]:((brave(X)&~rich(X))<=>(patient(X)&creative(X))))&
(![X]:((~wise(X)|~rich(X))=>(~strong(X)&curious(X))))&
(((~curious(fred)&calm(fred)))<=>((kind(paul)|~quiet(paul))))&
((?[X]:((~kind(X)|~tall(X))))<=>((brave(paul)<~>~old(paul))))&
(![X]:((curious(X)&~kind(X))<=>(~brave(X)&brave(X))))&
(![X]:((generous(X)&~kind(X))=>~generous(X)))&
(![X]:(~patient(X)=>~kind(X)))&
((quiet(lucy)&~calm(lucy)))&
((tall(john)&~calm(john)))&
(?[X]:(quiet(X)))&
((tall(alice)&~creative(alice)))&
((curious(lucy)|happy(lucy)))&
(~calm(alice))&
(~happy(lucy)) | calm(mary) | [] | null | 0 |
If paul is not calm or old then someone is not happy or curious. If susan is not generous or quiet then someone is either happy or creative. Everyone who is funny or creative is not generous or not happy. Everyone who is generous is both patient and funny. If mary is not rich or strong then paul is both patient and not old and vice versa. If lucy is either not humble or not happy then fred is not brave or not funny. If fred is quiet then john is either rich or not generous. If john is generous then someone is old or not rich. Everyone who is both quiet and curious is not patient and vice versa. Everyone who is not funny or happy is not generous. If someone is quiet or not humble then someone is funny and vice versa. Everyone who is happy or not curious is not brave or creative and vice versa. Everyone who is both wise and creative is both not rich and curious and vice versa. Everyone who is either brave or not quiet is generous and vice versa. Everyone who is not wise or not curious is both tall and not quiet and vice versa. Everyone who is both not humble and kind is patient or not old and vice versa. Someone is calm. Someone is patient or not curious. Someone is either rich or not kind. Someone is old or not wise. Lucy is not rich or not humble. Someone is patient. Fred is not calm. | John is brave. | neutral | (((~calm(paul)|old(paul)))=>(?[X]:((~happy(X)|curious(X)))))&
(((~generous(susan)|quiet(susan)))=>(?[X]:((happy(X)<~>creative(X)))))&
(![X]:((funny(X)|creative(X))=>(~generous(X)|~happy(X))))&
(![X]:(generous(X)=>(patient(X)&funny(X))))&
(((~rich(mary)|strong(mary)))<=>((patient(paul)&~old(paul))))&
(((~humble(lucy)<~>~happy(lucy)))=>((~brave(fred)|~funny(fred))))&
((quiet(fred))=>((rich(john)<~>~generous(john))))&
((generous(john))=>(?[X]:((old(X)|~rich(X)))))&
(![X]:((quiet(X)&curious(X))<=>~patient(X)))&
(![X]:((~funny(X)|happy(X))=>~generous(X)))&
((?[X]:((quiet(X)|~humble(X))))<=>(?[X]:(funny(X))))&
(![X]:((happy(X)|~curious(X))<=>(~brave(X)|creative(X))))&
(![X]:((wise(X)&creative(X))<=>(~rich(X)&curious(X))))&
(![X]:((brave(X)<~>~quiet(X))<=>generous(X)))&
(![X]:((~wise(X)|~curious(X))<=>(tall(X)&~quiet(X))))&
(![X]:((~humble(X)&kind(X))<=>(patient(X)|~old(X))))&
(?[X]:(calm(X)))&
(?[X]:((patient(X)|~curious(X))))&
(?[X]:((rich(X)<~>~kind(X))))&
(?[X]:((old(X)|~wise(X))))&
((~rich(lucy)|~humble(lucy)))&
(?[X]:(patient(X)))&
(~calm(fred)) | brave(john) | [] | null | 0 |
Everyone who is not curious is both strong and kind and vice versa.
If susan is not kind or not funny then lucy is not wise or creative.
If someone is strong then someone is either wise or not generous and vice versa.
Everyone who is either not humble or not strong is either not wise or not quiet.
Everyone who is either strong or wise is not wise.
Everyone who is not kind or not curious is both not patient and not old.
If someone is calm or rich then lucy is not happy or tall.
Everyone who is either not rich or not happy is patient or generous and vice versa.
If someone is both brave and not calm then someone is not tall or not old and vice versa.
If susan is either not curious or patient then someone is both not wise and kind.
If someone is both not funny and quiet then someone is funny and vice versa.
Everyone who is either not humble or funny is either not brave or generous.
If someone is not brave or happy then john is both creative and funny and vice versa.
Everyone who is both calm and happy is either curious or quiet and vice versa.
Everyone who is either kind or generous is old or not patient.
Everyone who is either happy or generous is both patient and old.
Someone is both not brave and calm.
Paul is generous or not old.
Someone is both not happy and not curious.
Someone is not creative or not tall.
Paul is either not creative or not rich.
Someone is either not happy or not curious. | Paul is humble. | neutral | (![X]:(~curious(X)<=>(strong(X)&kind(X))))&
(((~kind(susan)|~funny(susan)))=>((~wise(lucy)|creative(lucy))))&
((?[X]:(strong(X)))<=>(?[X]:((wise(X)<~>~generous(X)))))&
(![X]:((~humble(X)<~>~strong(X))=>(~wise(X)<~>~quiet(X))))&
(![X]:((strong(X)<~>wise(X))=>~wise(X)))&
(![X]:((~kind(X)|~curious(X))=>(~patient(X)&~old(X))))&
((?[X]:((calm(X)|rich(X))))=>((~happy(lucy)|tall(lucy))))&
(![X]:((~rich(X)<~>~happy(X))<=>(patient(X)|generous(X))))&
((?[X]:((brave(X)&~calm(X))))<=>(?[X]:((~tall(X)|~old(X)))))&
(((~curious(susan)<~>patient(susan)))=>(?[X]:((~wise(X)&kind(X)))))&
((?[X]:((~funny(X)&quiet(X))))<=>(?[X]:(funny(X))))&
(![X]:((~humble(X)<~>funny(X))=>(~brave(X)<~>generous(X))))&
((?[X]:((~brave(X)|happy(X))))<=>((creative(john)&funny(john))))&
(![X]:((calm(X)&happy(X))<=>(curious(X)<~>quiet(X))))&
(![X]:((kind(X)<~>generous(X))=>(old(X)|~patient(X))))&
(![X]:((happy(X)<~>generous(X))=>(patient(X)&old(X))))&
(?[X]:((~brave(X)&calm(X))))&
((generous(paul)|~old(paul)))&
(?[X]:((~happy(X)&~curious(X))))&
(?[X]:((~creative(X)|~tall(X))))&
((~creative(paul)<~>~rich(paul)))&
(?[X]:((~happy(X)<~>~curious(X)))) | humble(paul) | [] | null | 0 |
If someone is not quiet or brave then someone is not generous and vice versa.
If someone is both old and not kind then mary is not funny or kind.
Everyone who is both not old and not tall is old.
Everyone who is brave or wise is not humble or rich and vice versa.
If susan is not tall or not brave then lucy is both rich and quiet and vice versa.
If someone is either not patient or patient then someone is generous.
If paul is both kind and not rich then alice is tall and vice versa.
If someone is either not strong or creative then susan is quiet or not brave and vice versa.
If someone is not happy then someone is either kind or funny and vice versa.
Everyone who is both tall and not creative is both generous and rich.
If fred is both not old and brave then someone is either not calm or not old.
If john is not curious or rich then someone is old.
Everyone who is old or rich is both not wise and strong.
If john is both not wise and not creative then someone is not patient.
Everyone who is either not humble or not wise is both not tall and not rich.
Everyone who is both not creative and not wise is both happy and not kind and vice versa.
Someone is both happy and generous.
Someone is rich or patient.
Someone is rich or not wise.
Someone is not strong or strong.
Someone is humble or kind.
Someone is quiet.
Lucy is not tall. | Susan is wise. | contradiction | ((?[X]:((~quiet(X)|brave(X))))<=>(?[X]:(~generous(X))))&
((?[X]:((old(X)&~kind(X))))=>((~funny(mary)|kind(mary))))&
(![X]:((~old(X)&~tall(X))=>old(X)))&
(![X]:((brave(X)|wise(X))<=>(~humble(X)|rich(X))))&
(((~tall(susan)|~brave(susan)))<=>((rich(lucy)&quiet(lucy))))&
((?[X]:((~patient(X)<~>patient(X))))=>(?[X]:(generous(X))))&
(((kind(paul)&~rich(paul)))<=>(tall(alice)))&
((?[X]:((~strong(X)<~>creative(X))))<=>((quiet(susan)|~brave(susan))))&
((?[X]:(~happy(X)))<=>(?[X]:((kind(X)<~>funny(X)))))&
(![X]:((tall(X)&~creative(X))=>(generous(X)&rich(X))))&
(((~old(fred)&brave(fred)))=>(?[X]:((~calm(X)<~>~old(X)))))&
(((~curious(john)|rich(john)))=>(?[X]:(old(X))))&
(![X]:((old(X)|rich(X))=>(~wise(X)&strong(X))))&
(((~wise(john)&~creative(john)))=>(?[X]:(~patient(X))))&
(![X]:((~humble(X)<~>~wise(X))=>(~tall(X)&~rich(X))))&
(![X]:((~creative(X)&~wise(X))<=>(happy(X)&~kind(X))))&
(?[X]:((happy(X)&generous(X))))&
(?[X]:((rich(X)|patient(X))))&
(?[X]:((rich(X)|~wise(X))))&
(?[X]:((~strong(X)|strong(X))))&
(?[X]:((humble(X)|kind(X))))&
(?[X]:(quiet(X)))&
(~tall(lucy)) | wise(susan) | [
"p2",
"p3",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2220279279972751541813493
% SZS output start Proof for 2220279279972751541813493
3. ! [X0] : ((~tall(X0) & ~old(X0)) => old(X0)) [input p2]
4. ! [X0] : ((wise(X0) | brave(X0)) <=> (rich(X0) | ~humble(X0))) [input p3]
13. ! [X0] : ((rich(X0) | old(X0)) => (strong(X0) & ~wise(X0))) [input p12]
15. ! [X0] : ((~humble(X0) <~> ~wise(X0)) => (~rich(X0) & ~tall(X0))) [input p14]
24. wise(susan) [input hypothesis]
31. ! [X0] : (old(X0) | (tall(X0) | old(X0))) [ennf transformation 3]
32. ! [X0] : (old(X0) | tall(X0) | old(X0)) [flattening 31]
39. ! [X0] : ((strong(X0) & ~wise(X0)) | (~rich(X0) & ~old(X0))) [ennf transformation 13]
42. ! [X0] : ((~rich(X0) & ~tall(X0)) | (~humble(X0) <=> ~wise(X0))) [ennf transformation 15]
48. ! [X0] : (((wise(X0) | brave(X0)) | (~rich(X0) & humble(X0))) & ((rich(X0) | ~humble(X0)) | (~wise(X0) & ~brave(X0)))) [nnf transformation 4]
49. ! [X0] : ((wise(X0) | brave(X0) | (~rich(X0) & humble(X0))) & (rich(X0) | ~humble(X0) | (~wise(X0) & ~brave(X0)))) [flattening 48]
75. ! [X0] : ((~rich(X0) & ~tall(X0)) | ((~humble(X0) | wise(X0)) & (~wise(X0) | humble(X0)))) [nnf transformation 42]
94. old(X0) | tall(X0) | old(X0) [cnf transformation 32]
96. ~humble(X0) | rich(X0) | ~wise(X0) [cnf transformation 49]
124. ~wise(X0) | ~old(X0) [cnf transformation 39]
125. ~rich(X0) | ~wise(X0) [cnf transformation 39]
129. ~wise(X0) | ~tall(X0) | humble(X0) [cnf transformation 75]
145. wise(susan) [cnf transformation 24]
148. tall(X0) | old(X0) [duplicate literal removal 94]
194. 12 <=> tall(susan) [avatar definition]
196. ~tall(susan) <- (~12) [avatar component clause 194]
344. ~old(susan) [resolution 124,145]
377. ~tall(susan) | humble(susan) [resolution 129,145]
379. 46 <=> humble(susan) [avatar definition]
381. humble(susan) <- (46) [avatar component clause 379]
382. 46 | ~12 [avatar split clause 377,194,379]
383. old(susan) <- (~12) [resolution 196,148]
384. $false <- (~12) [subsumption resolution 383,344]
385. 12 [avatar contradiction clause 384]
389. 47 <=> rich(susan) [avatar definition]
391. rich(susan) <- (47) [avatar component clause 389]
402. rich(susan) | ~wise(susan) <- (46) [resolution 381,96]
404. rich(susan) <- (46) [subsumption resolution 402,145]
405. 47 | ~46 [avatar split clause 404,379,389]
414. ~wise(susan) <- (47) [resolution 391,125]
417. $false <- (47) [subsumption resolution 414,145]
418. ~47 [avatar contradiction clause 417]
419. $false [avatar sat refutation 382,385,405,418]
% SZS output end Proof for 2220279279972751541813493
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not happy is kind and vice versa.
If someone is not old or humble then someone is kind.
Everyone who is both not tall and not kind is either not kind or rich.
Everyone who is both not old and not generous is both quiet and rich.
If paul is not generous then lucy is kind.
If paul is both humble and not strong then someone is tall and vice versa.
Everyone who is both not kind and not curious is kind and vice versa.
If mary is funny or rich then john is either not strong or not quiet and vice versa.
If someone is both not brave and tall then paul is not strong and vice versa.
Everyone who is not rich is both not kind and not quiet and vice versa.
If alice is both not rich and not creative then fred is not strong and vice versa.
If lucy is not wise then lucy is both generous and funny.
Everyone who is not rich or not creative is funny and vice versa.
Everyone who is not rich is either not tall or not patient.
If mary is either strong or calm then paul is not humble.
If john is both not quiet and not rich then someone is either not wise or brave.
Someone is not wise or tall.
Someone is not brave.
Susan is not generous.
Alice is not kind or calm.
Someone is either kind or not tall. | Paul is not strong. | contradiction | (![X]:((creative(X)|~happy(X))<=>kind(X)))&
((?[X]:((~old(X)|humble(X))))=>(?[X]:(kind(X))))&
(![X]:((~tall(X)&~kind(X))=>(~kind(X)<~>rich(X))))&
(![X]:((~old(X)&~generous(X))=>(quiet(X)&rich(X))))&
((~generous(paul))=>(kind(lucy)))&
(((humble(paul)&~strong(paul)))<=>(?[X]:(tall(X))))&
(![X]:((~kind(X)&~curious(X))<=>kind(X)))&
(((funny(mary)|rich(mary)))<=>((~strong(john)<~>~quiet(john))))&
((?[X]:((~brave(X)&tall(X))))<=>(~strong(paul)))&
(![X]:(~rich(X)<=>(~kind(X)&~quiet(X))))&
(((~rich(alice)&~creative(alice)))<=>(~strong(fred)))&
((~wise(lucy))=>((generous(lucy)&funny(lucy))))&
(![X]:((~rich(X)|~creative(X))<=>funny(X)))&
(![X]:(~rich(X)=>(~tall(X)<~>~patient(X))))&
(((strong(mary)<~>calm(mary)))=>(~humble(paul)))&
(((~quiet(john)&~rich(john)))=>(?[X]:((~wise(X)<~>brave(X)))))&
(?[X]:((~wise(X)|tall(X))))&
(?[X]:(~brave(X)))&
(~generous(susan))&
((~kind(alice)|calm(alice)))&
(?[X]:((kind(X)<~>~tall(X)))) | ~strong(paul) | [
"p1",
"p5",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2855636708087171648994710
% SZS output start Proof for 2855636708087171648994710
2. ? [X0] : (humble(X0) | ~old(X0)) => ? [X0] : kind(X0) [input p1]
6. (~strong(paul) & humble(paul)) <=> ? [X0] : tall(X0) [input p5]
7. ! [X0] : ((~curious(X0) & ~kind(X0)) <=> kind(X0)) [input p6]
9. ? [X0] : (tall(X0) & ~brave(X0)) <=> ~strong(paul) [input p8]
22. ~strong(paul) [input hypothesis]
23. ? [X0] : (humble(X0) | ~old(X0)) => ? [X1] : kind(X1) [rectify 2]
25. ? [X0] : humble(X0) => ? [X1] : kind(X1) [pure predicate removal 23]
26. ? [X1] : kind(X1) | ! [X0] : ~humble(X0) [ennf transformation 25]
37. ? [X0] : kind(X0) | ! [X1] : ~humble(X1) [rectify 26]
38. ? [X0] : kind(X0) => kind(sK0) [choice axiom]
39. kind(sK0) | ! [X1] : ~humble(X1) [skolemisation 37,38]
41. ((~strong(paul) & humble(paul)) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | (strong(paul) | ~humble(paul))) [nnf transformation 6]
42. ((~strong(paul) & humble(paul)) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | strong(paul) | ~humble(paul)) [flattening 41]
43. ((~strong(paul) & humble(paul)) | ! [X0] : ~tall(X0)) & (? [X1] : tall(X1) | strong(paul) | ~humble(paul)) [rectify 42]
44. ? [X1] : tall(X1) => tall(sK1) [choice axiom]
45. ((~strong(paul) & humble(paul)) | ! [X0] : ~tall(X0)) & (tall(sK1) | strong(paul) | ~humble(paul)) [skolemisation 43,44]
46. ! [X0] : (((~curious(X0) & ~kind(X0)) | ~kind(X0)) & (kind(X0) | (curious(X0) | kind(X0)))) [nnf transformation 7]
47. ! [X0] : (((~curious(X0) & ~kind(X0)) | ~kind(X0)) & (kind(X0) | curious(X0) | kind(X0))) [flattening 46]
50. (? [X0] : (tall(X0) & ~brave(X0)) | strong(paul)) & (~strong(paul) | ! [X0] : (~tall(X0) | brave(X0))) [nnf transformation 9]
51. (? [X0] : (tall(X0) & ~brave(X0)) | strong(paul)) & (~strong(paul) | ! [X1] : (~tall(X1) | brave(X1))) [rectify 50]
52. ? [X0] : (tall(X0) & ~brave(X0)) => (tall(sK2) & ~brave(sK2)) [choice axiom]
53. ((tall(sK2) & ~brave(sK2)) | strong(paul)) & (~strong(paul) | ! [X1] : (~tall(X1) | brave(X1))) [skolemisation 51,52]
75. kind(sK0) | ~humble(X1) [cnf transformation 39]
80. humble(paul) | ~tall(X0) [cnf transformation 45]
83. ~kind(X0) | ~kind(X0) [cnf transformation 47]
93. tall(sK2) | strong(paul) [cnf transformation 53]
117. ~strong(paul) [cnf transformation 22]
119. ~kind(X0) [duplicate literal removal 83]
122. 1 <=> ! [X1] : ~humble(X1) [avatar definition]
123. ~humble(X1) <- (1) [avatar component clause 122]
125. 2 <=> kind(sK0) [avatar definition]
127. kind(sK0) <- (2) [avatar component clause 125]
128. 1 | 2 [avatar split clause 75,125,122]
139. 5 <=> ! [X0] : ~tall(X0) [avatar definition]
140. ~tall(X0) <- (5) [avatar component clause 139]
142. 6 <=> strong(paul) [avatar definition]
147. 7 <=> humble(paul) [avatar definition]
149. humble(paul) <- (7) [avatar component clause 147]
150. 5 | 7 [avatar split clause 80,147,139]
180. 13 <=> tall(sK2) [avatar definition]
182. tall(sK2) <- (13) [avatar component clause 180]
183. 6 | 13 [avatar split clause 93,180,142]
255. ~6 [avatar split clause 117,142]
256. $false <- (2) [subsumption resolution 127,119]
257. ~2 [avatar contradiction clause 256]
258. $false <- (5, 13) [resolution 182,140]
259. ~5 | ~13 [avatar contradiction clause 258]
260. $false <- (1, 7) [subsumption resolution 149,123]
261. ~1 | ~7 [avatar contradiction clause 260]
262. $false [avatar sat refutation 128,150,183,255,257,259,261]
% SZS output end Proof for 2855636708087171648994710
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich is both not brave and funny.
If someone is either strong or not kind then lucy is both funny and patient.
If someone is both patient and creative then mary is not humble and vice versa.
Everyone who is both patient and not quiet is either humble or not calm.
Everyone who is not creative is both curious and strong.
Everyone who is either not curious or not old is both generous and not funny and vice versa.
Everyone who is kind or not generous is both not creative and not tall and vice versa.
Everyone who is not wise or curious is humble.
Everyone who is either not calm or rich is both not happy and generous.
If someone is not rich or not patient then someone is both strong and creative and vice versa.
Everyone who is either not strong or not kind is both brave and not calm and vice versa.
Everyone who is patient is either quiet or not old and vice versa.
Everyone who is both not creative and quiet is either not creative or generous.
Everyone who is not rich is both patient and curious.
If mary is either not wise or funny then susan is not tall or not old.
If someone is either calm or not curious then someone is not creative or not humble and vice versa.
Someone is old or strong.
Someone is creative.
John is either tall or not quiet.
John is curious.
Susan is both rich and not tall.
Someone is both not rich and not strong.
Susan is either tall or generous.
Mary is both rich and not quiet. | Mary is generous. | entailment | (![X]:(rich(X)=>(~brave(X)&funny(X))))&
((?[X]:((strong(X)<~>~kind(X))))=>((funny(lucy)&patient(lucy))))&
((?[X]:((patient(X)&creative(X))))<=>(~humble(mary)))&
(![X]:((patient(X)&~quiet(X))=>(humble(X)<~>~calm(X))))&
(![X]:(~creative(X)=>(curious(X)&strong(X))))&
(![X]:((~curious(X)<~>~old(X))<=>(generous(X)&~funny(X))))&
(![X]:((kind(X)|~generous(X))<=>(~creative(X)&~tall(X))))&
(![X]:((~wise(X)|curious(X))=>humble(X)))&
(![X]:((~calm(X)<~>rich(X))=>(~happy(X)&generous(X))))&
((?[X]:((~rich(X)|~patient(X))))<=>(?[X]:((strong(X)&creative(X)))))&
(![X]:((~strong(X)<~>~kind(X))<=>(brave(X)&~calm(X))))&
(![X]:(patient(X)<=>(quiet(X)<~>~old(X))))&
(![X]:((~creative(X)&quiet(X))=>(~creative(X)<~>generous(X))))&
(![X]:(~rich(X)=>(patient(X)&curious(X))))&
(((~wise(mary)<~>funny(mary)))=>((~tall(susan)|~old(susan))))&
((?[X]:((calm(X)<~>~curious(X))))<=>(?[X]:((~creative(X)|~humble(X)))))&
(?[X]:((old(X)|strong(X))))&
(?[X]:(creative(X)))&
((tall(john)<~>~quiet(john)))&
(curious(john))&
((rich(susan)&~tall(susan)))&
(?[X]:((~rich(X)&~strong(X))))&
((tall(susan)<~>generous(susan)))&
((rich(mary)&~quiet(mary))) | generous(mary) | [
"p0",
"p2",
"p4",
"p6",
"p7",
"p9",
"p10",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5813286065665028453795726
% SZS output start Proof for 5813286065665028453795726
1. ! [X0] : (rich(X0) => (funny(X0) & ~brave(X0))) [input p0]
3. ? [X0] : (creative(X0) & patient(X0)) <=> ~humble(mary) [input p2]
5. ! [X0] : (~creative(X0) => (strong(X0) & curious(X0))) [input p4]
7. ! [X0] : ((~generous(X0) | kind(X0)) <=> (~tall(X0) & ~creative(X0))) [input p6]
8. ! [X0] : ((curious(X0) | ~wise(X0)) => humble(X0)) [input p7]
10. ? [X0] : (~patient(X0) | ~rich(X0)) <=> ? [X0] : (creative(X0) & strong(X0)) [input p9]
11. ! [X0] : ((~strong(X0) <~> ~kind(X0)) <=> (~calm(X0) & brave(X0))) [input p10]
14. ! [X0] : (~rich(X0) => (curious(X0) & patient(X0))) [input p13]
22. ? [X0] : (~strong(X0) & ~rich(X0)) [input p21]
25. ~generous(mary) [input hypothesis]
26. ? [X0] : (~patient(X0) | ~rich(X0)) <=> ? [X1] : (creative(X1) & strong(X1)) [rectify 10]
29. ! [X0] : ((funny(X0) & ~brave(X0)) | ~rich(X0)) [ennf transformation 1]
33. ! [X0] : ((strong(X0) & curious(X0)) | creative(X0)) [ennf transformation 5]
34. ! [X0] : (humble(X0) | (~curious(X0) & wise(X0))) [ennf transformation 8]
38. ! [X0] : ((curious(X0) & patient(X0)) | rich(X0)) [ennf transformation 14]
42. (? [X0] : (creative(X0) & patient(X0)) | humble(mary)) & (~humble(mary) | ! [X0] : (~creative(X0) | ~patient(X0))) [nnf transformation 3]
43. (? [X0] : (creative(X0) & patient(X0)) | humble(mary)) & (~humble(mary) | ! [X1] : (~creative(X1) | ~patient(X1))) [rectify 42]
44. ? [X0] : (creative(X0) & patient(X0)) => (creative(sK0) & patient(sK0)) [choice axiom]
45. ((creative(sK0) & patient(sK0)) | humble(mary)) & (~humble(mary) | ! [X1] : (~creative(X1) | ~patient(X1))) [skolemisation 43,44]
49. ! [X0] : (((~generous(X0) | kind(X0)) | (tall(X0) | creative(X0))) & ((~tall(X0) & ~creative(X0)) | (generous(X0) & ~kind(X0)))) [nnf transformation 7]
50. ! [X0] : ((~generous(X0) | kind(X0) | tall(X0) | creative(X0)) & ((~tall(X0) & ~creative(X0)) | (generous(X0) & ~kind(X0)))) [flattening 49]
52. (? [X0] : (~patient(X0) | ~rich(X0)) | ! [X1] : (~creative(X1) | ~strong(X1))) & (? [X1] : (creative(X1) & strong(X1)) | ! [X0] : (patient(X0) & rich(X0))) [nnf transformation 26]
53. (? [X0] : (~patient(X0) | ~rich(X0)) | ! [X1] : (~creative(X1) | ~strong(X1))) & (? [X2] : (creative(X2) & strong(X2)) | ! [X3] : (patient(X3) & rich(X3))) [rectify 52]
54. ? [X0] : (~patient(X0) | ~rich(X0)) => (~patient(sK1) | ~rich(sK1)) [choice axiom]
55. ? [X2] : (creative(X2) & strong(X2)) => (creative(sK2) & strong(sK2)) [choice axiom]
56. ((~patient(sK1) | ~rich(sK1)) | ! [X1] : (~creative(X1) | ~strong(X1))) & ((creative(sK2) & strong(sK2)) | ! [X3] : (patient(X3) & rich(X3))) [skolemisation 53,55,54]
57. ! [X0] : ((((kind(X0) | strong(X0)) & (~kind(X0) | ~strong(X0))) | (calm(X0) | ~brave(X0))) & ((~calm(X0) & brave(X0)) | ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0))))) [nnf transformation 11]
58. ! [X0] : ((((kind(X0) | strong(X0)) & (~kind(X0) | ~strong(X0))) | calm(X0) | ~brave(X0)) & ((~calm(X0) & brave(X0)) | ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0))))) [flattening 57]
72. ? [X0] : (~strong(X0) & ~rich(X0)) => (~strong(sK7) & ~rich(sK7)) [choice axiom]
73. ~strong(sK7) & ~rich(sK7) [skolemisation 22,72]
75. ~brave(X0) | ~rich(X0) [cnf transformation 29]
81. ~humble(mary) | ~creative(X1) | ~patient(X1) [cnf transformation 45]
86. curious(X0) | creative(X0) [cnf transformation 33]
94. ~creative(X0) | ~kind(X0) [cnf transformation 50]
95. ~creative(X0) | generous(X0) [cnf transformation 50]
100. ~curious(X0) | humble(X0) [cnf transformation 34]
103. strong(sK2) | rich(X3) [cnf transformation 56]
105. creative(sK2) | rich(X3) [cnf transformation 56]
109. ~strong(X0) | brave(X0) | kind(X0) [cnf transformation 58]
120. patient(X0) | rich(X0) [cnf transformation 38]
137. ~rich(sK7) [cnf transformation 73]
143. ~generous(mary) [cnf transformation 25]
164. 5 <=> humble(mary) [avatar definition]
165. ~humble(mary) <- (~5) [avatar component clause 164]
178. 8 <=> ! [X1] : (~creative(X1) | ~patient(X1)) [avatar definition]
179. ~creative(X1) | ~patient(X1) <- (8) [avatar component clause 178]
180. 8 | ~5 [avatar split clause 81,164,178]
197. 13 <=> creative(sK2) [avatar definition]
199. creative(sK2) <- (13) [avatar component clause 197]
202. 14 <=> ! [X3] : rich(X3) [avatar definition]
203. rich(X3) <- (14) [avatar component clause 202]
204. 14 | 13 [avatar split clause 105,197,202]
206. 15 <=> strong(sK2) [avatar definition]
208. strong(sK2) <- (15) [avatar component clause 206]
210. 14 | 15 [avatar split clause 103,206,202]
290. $false <- (14) [resolution 203,137]
291. ~14 [avatar contradiction clause 290]
300. ~kind(sK2) <- (13) [resolution 94,199]
309. humble(X0) | creative(X0) [resolution 100,86]
349. brave(sK2) | kind(sK2) <- (15) [resolution 109,208]
352. brave(sK2) <- (13, 15) [subsumption resolution 349,300]
379. ~rich(sK2) <- (13, 15) [resolution 352,75]
515. ~patient(sK2) <- (8, 13) [resolution 179,199]
554. rich(sK2) <- (8, 13) [resolution 515,120]
555. $false <- (8, 13, 15) [subsumption resolution 554,379]
556. ~8 | ~13 | ~15 [avatar contradiction clause 555]
577. creative(mary) <- (~5) [resolution 309,165]
970. generous(mary) <- (~5) [resolution 577,95]
972. $false <- (~5) [subsumption resolution 970,143]
973. 5 [avatar contradiction clause 972]
976. $false [avatar sat refutation 180,204,210,291,556,973]
% SZS output end Proof for 5813286065665028453795726
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not calm is tall and vice versa.
Everyone who is both tall and not funny is not kind or kind and vice versa.
Everyone who is patient or tall is brave and vice versa.
If paul is quiet or patient then someone is rich and vice versa.
If john is both happy and old then susan is both kind and strong and vice versa.
If susan is both generous and funny then someone is either not happy or generous and vice versa.
Everyone who is not humble or strong is quiet.
Everyone who is either creative or not patient is both not brave and rich.
If john is both not calm and not wise then someone is either funny or not strong and vice versa.
If someone is not curious then paul is either wise or calm and vice versa.
If john is wise then john is either not strong or not funny and vice versa.
If alice is either not strong or brave then fred is curious and vice versa.
If someone is generous then lucy is not patient and vice versa.
Everyone who is either not rich or not wise is not creative and vice versa.
If susan is not funny or humble then lucy is funny or not rich.
Someone is not patient or not happy.
Someone is brave or not happy.
Paul is not tall or not patient.
Mary is both not wise and quiet.
Someone is not generous or not brave.
Susan is not funny or brave. | Lucy is funny. | contradiction | (![X]:((~patient(X)<~>~calm(X))<=>tall(X)))&
(![X]:((tall(X)&~funny(X))<=>(~kind(X)|kind(X))))&
(![X]:((patient(X)|tall(X))<=>brave(X)))&
(((quiet(paul)|patient(paul)))<=>(?[X]:(rich(X))))&
(((happy(john)&old(john)))<=>((kind(susan)&strong(susan))))&
(((generous(susan)&funny(susan)))<=>(?[X]:((~happy(X)<~>generous(X)))))&
(![X]:((~humble(X)|strong(X))=>quiet(X)))&
(![X]:((creative(X)<~>~patient(X))=>(~brave(X)&rich(X))))&
(((~calm(john)&~wise(john)))<=>(?[X]:((funny(X)<~>~strong(X)))))&
((?[X]:(~curious(X)))<=>((wise(paul)<~>calm(paul))))&
((wise(john))<=>((~strong(john)<~>~funny(john))))&
(((~strong(alice)<~>brave(alice)))<=>(curious(fred)))&
((?[X]:(generous(X)))<=>(~patient(lucy)))&
(![X]:((~rich(X)<~>~wise(X))<=>~creative(X)))&
(((~funny(susan)|humble(susan)))=>((funny(lucy)|~rich(lucy))))&
(?[X]:((~patient(X)|~happy(X))))&
(?[X]:((brave(X)|~happy(X))))&
((~tall(paul)|~patient(paul)))&
((~wise(mary)&quiet(mary)))&
(?[X]:((~generous(X)|~brave(X))))&
((~funny(susan)|brave(susan))) | funny(lucy) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 1890395139438628917634134
% SZS output start Proof for 1890395139438628917634134
2. ! [X0] : ((~funny(X0) & tall(X0)) <=> (kind(X0) | ~kind(X0))) [input p1]
22. funny(lucy) [input hypothesis]
28. ! [X0] : (((~funny(X0) & tall(X0)) | (~kind(X0) & kind(X0))) & ((kind(X0) | ~kind(X0)) | (funny(X0) | ~tall(X0)))) [nnf transformation 2]
29. ! [X0] : (((~funny(X0) & tall(X0)) | (~kind(X0) & kind(X0))) & (kind(X0) | ~kind(X0) | funny(X0) | ~tall(X0))) [flattening 28]
74. ~funny(X0) | kind(X0) [cnf transformation 29]
75. ~funny(X0) | ~kind(X0) [cnf transformation 29]
131. funny(lucy) [cnf transformation 22]
132. ~funny(X0) [subsumption resolution 74,75]
275. $false [subsumption resolution 131,132]
% SZS output end Proof for 1890395139438628917634134
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not generous or rich then fred is not calm or not rich and vice versa. If alice is either patient or not humble then someone is not happy and vice versa. Everyone who is both tall and quiet is either brave or not kind. Everyone who is both not wise and not curious is rich. Everyone who is both tall and kind is both not generous and not brave. If someone is both brave and not tall then fred is not quiet. Everyone who is strong or not funny is both not patient and rich. If paul is not calm then susan is not generous or patient and vice versa. Everyone who is either not old or strong is not rich or happy and vice versa. If someone is not humble or not quiet then someone is either not wise or not curious and vice versa. Everyone who is kind or quiet is either not strong or not old and vice versa. Everyone who is not kind or old is not strong or curious. If someone is either quiet or rich then someone is either not tall or not wise. Everyone who is either wise or not patient is strong or not rich. If someone is both creative and quiet then paul is creative or not creative. Everyone who is either quiet or rich is not patient and vice versa. Mary is either wise or humble. Someone is either not happy or kind. Someone is humble or rich. Someone is not strong. Someone is funny or not funny. Someone is either tall or not quiet. Susan is both wise and generous. Susan is wise. | Susan is not quiet. | entailment | (((~generous(lucy)|rich(lucy)))<=>((~calm(fred)|~rich(fred))))&
(((patient(alice)<~>~humble(alice)))<=>(?[X]:(~happy(X))))&
(![X]:((tall(X)&quiet(X))=>(brave(X)<~>~kind(X))))&
(![X]:((~wise(X)&~curious(X))=>rich(X)))&
(![X]:((tall(X)&kind(X))=>(~generous(X)&~brave(X))))&
((?[X]:((brave(X)&~tall(X))))=>(~quiet(fred)))&
(![X]:((strong(X)|~funny(X))=>(~patient(X)&rich(X))))&
((~calm(paul))<=>((~generous(susan)|patient(susan))))&
(![X]:((~old(X)<~>strong(X))<=>(~rich(X)|happy(X))))&
((?[X]:((~humble(X)|~quiet(X))))<=>(?[X]:((~wise(X)<~>~curious(X)))))&
(![X]:((kind(X)|quiet(X))<=>(~strong(X)<~>~old(X))))&
(![X]:((~kind(X)|old(X))=>(~strong(X)|curious(X))))&
((?[X]:((quiet(X)<~>rich(X))))=>(?[X]:((~tall(X)<~>~wise(X)))))&
(![X]:((wise(X)<~>~patient(X))=>(strong(X)|~rich(X))))&
((?[X]:((creative(X)&quiet(X))))=>((creative(paul)|~creative(paul))))&
(![X]:((quiet(X)<~>rich(X))<=>~patient(X)))&
((wise(mary)<~>humble(mary)))&
(?[X]:((~happy(X)<~>kind(X))))&
(?[X]:((humble(X)|rich(X))))&
(?[X]:(~strong(X)))&
(?[X]:((funny(X)|~funny(X))))&
(?[X]:((tall(X)<~>~quiet(X))))&
((wise(susan)&generous(susan)))&
(wise(susan)) | ~quiet(susan) | [
"p6",
"p8",
"p10",
"p13",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7218151994535449487886936
% SZS output start Proof for 7218151994535449487886936
7. ! [X0] : ((~funny(X0) | strong(X0)) => (rich(X0) & ~patient(X0))) [input p6]
9. ! [X0] : ((~old(X0) <~> strong(X0)) <=> (happy(X0) | ~rich(X0))) [input p8]
11. ! [X0] : ((quiet(X0) | kind(X0)) <=> (~strong(X0) <~> ~old(X0))) [input p10]
14. ! [X0] : ((wise(X0) <~> ~patient(X0)) => (~rich(X0) | strong(X0))) [input p13]
16. ! [X0] : ((quiet(X0) <~> rich(X0)) <=> ~patient(X0)) [input p15]
23. generous(susan) & wise(susan) [input p22]
25. quiet(susan) [input hypothesis]
35. ! [X0] : ((rich(X0) & ~patient(X0)) | (funny(X0) & ~strong(X0))) [ennf transformation 7]
39. ! [X0] : ((~rich(X0) | strong(X0)) | (wise(X0) <=> ~patient(X0))) [ennf transformation 14]
40. ! [X0] : (~rich(X0) | strong(X0) | (wise(X0) <=> ~patient(X0))) [flattening 39]
52. ! [X0] : ((((~strong(X0) | old(X0)) & (strong(X0) | ~old(X0))) | (~happy(X0) & rich(X0))) & ((happy(X0) | ~rich(X0)) | ((~old(X0) | ~strong(X0)) & (strong(X0) | old(X0))))) [nnf transformation 9]
53. ! [X0] : ((((~strong(X0) | old(X0)) & (strong(X0) | ~old(X0))) | (~happy(X0) & rich(X0))) & (happy(X0) | ~rich(X0) | ((~old(X0) | ~strong(X0)) & (strong(X0) | old(X0))))) [flattening 52]
59. ! [X0] : (((quiet(X0) | kind(X0)) | ((~strong(X0) | old(X0)) & (~old(X0) | strong(X0)))) & (((old(X0) | strong(X0)) & (~old(X0) | ~strong(X0))) | (~quiet(X0) & ~kind(X0)))) [nnf transformation 11]
60. ! [X0] : ((quiet(X0) | kind(X0) | ((~strong(X0) | old(X0)) & (~old(X0) | strong(X0)))) & (((old(X0) | strong(X0)) & (~old(X0) | ~strong(X0))) | (~quiet(X0) & ~kind(X0)))) [flattening 59]
65. ! [X0] : (~rich(X0) | strong(X0) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0)))) [nnf transformation 40]
66. ! [X0] : ((((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | patient(X0)) & (~patient(X0) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0))))) [nnf transformation 16]
94. ~strong(X0) | ~patient(X0) [cnf transformation 35]
96. ~strong(X0) | rich(X0) [cnf transformation 35]
103. strong(X0) | ~old(X0) | rich(X0) [cnf transformation 53]
116. ~quiet(X0) | strong(X0) | old(X0) [cnf transformation 60]
125. ~rich(X0) | strong(X0) | ~patient(X0) | ~wise(X0) [cnf transformation 65]
131. ~quiet(X0) | ~rich(X0) | patient(X0) [cnf transformation 66]
141. wise(susan) [cnf transformation 23]
144. quiet(susan) [cnf transformation 25]
193. 11 <=> patient(susan) [avatar definition]
207. ~old(X0) | rich(X0) [subsumption resolution 103,96]
261. ~wise(X0) | ~patient(X0) | ~rich(X0) [subsumption resolution 125,94]
304. strong(susan) | old(susan) [resolution 116,144]
306. 34 <=> old(susan) [avatar definition]
308. old(susan) <- (34) [avatar component clause 306]
310. 35 <=> strong(susan) [avatar definition]
312. strong(susan) <- (35) [avatar component clause 310]
313. 34 | 35 [avatar split clause 304,310,306]
317. rich(susan) <- (34) [resolution 308,207]
366. ~rich(susan) | patient(susan) [resolution 131,144]
374. ~patient(susan) | ~rich(susan) [resolution 261,141]
398. ~patient(susan) <- (34) [subsumption resolution 374,317]
399. ~11 | ~34 [avatar split clause 398,306,193]
400. patient(susan) <- (34) [subsumption resolution 366,317]
401. 11 | ~34 [avatar split clause 400,306,193]
405. rich(susan) <- (35) [resolution 312,96]
415. ~patient(susan) <- (35) [subsumption resolution 374,405]
416. ~11 | ~35 [avatar split clause 415,310,193]
417. patient(susan) <- (35) [subsumption resolution 366,405]
418. 11 | ~35 [avatar split clause 417,310,193]
419. $false [avatar sat refutation 313,399,401,416,418]
% SZS output end Proof for 7218151994535449487886936
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not patient then someone is either happy or not calm and vice versa.
Everyone who is wise is calm or not rich.
Everyone who is either not patient or old is both quiet and generous.
Everyone who is not kind or kind is not happy and vice versa.
Everyone who is either not humble or not happy is wise or old.
Everyone who is curious or funny is not generous or not quiet.
If fred is either not funny or not curious then john is funny or wise and vice versa.
Everyone who is not rich is either not patient or not brave.
Everyone who is either not quiet or creative is strong or patient and vice versa.
If someone is either funny or not generous then lucy is not old or not kind.
If someone is not creative or not curious then susan is not curious or old and vice versa.
If someone is not happy then someone is either strong or happy and vice versa.
Everyone who is not patient is either not happy or not wise.
Everyone who is rich or funny is both creative and not strong and vice versa.
Everyone who is not quiet or not curious is calm.
If susan is either not wise or not brave then alice is humble.
Someone is either calm or not humble.
Someone is either tall or generous.
Lucy is curious or quiet.
Susan is either old or not funny.
Paul is strong or not patient.
Alice is humble.
John is not generous.
Lucy is wise or calm. | Paul is not patient. | neutral | ((~patient(susan))<=>(?[X]:((happy(X)<~>~calm(X)))))&
(![X]:(wise(X)=>(calm(X)|~rich(X))))&
(![X]:((~patient(X)<~>old(X))=>(quiet(X)&generous(X))))&
(![X]:((~kind(X)|kind(X))<=>~happy(X)))&
(![X]:((~humble(X)<~>~happy(X))=>(wise(X)|old(X))))&
(![X]:((curious(X)|funny(X))=>(~generous(X)|~quiet(X))))&
(((~funny(fred)<~>~curious(fred)))<=>((funny(john)|wise(john))))&
(![X]:(~rich(X)=>(~patient(X)<~>~brave(X))))&
(![X]:((~quiet(X)<~>creative(X))<=>(strong(X)|patient(X))))&
((?[X]:((funny(X)<~>~generous(X))))=>((~old(lucy)|~kind(lucy))))&
((?[X]:((~creative(X)|~curious(X))))<=>((~curious(susan)|old(susan))))&
((?[X]:(~happy(X)))<=>(?[X]:((strong(X)<~>happy(X)))))&
(![X]:(~patient(X)=>(~happy(X)<~>~wise(X))))&
(![X]:((rich(X)|funny(X))<=>(creative(X)&~strong(X))))&
(![X]:((~quiet(X)|~curious(X))=>calm(X)))&
(((~wise(susan)<~>~brave(susan)))=>(humble(alice)))&
(?[X]:((calm(X)<~>~humble(X))))&
(?[X]:((tall(X)<~>generous(X))))&
((curious(lucy)|quiet(lucy)))&
((old(susan)<~>~funny(susan)))&
((strong(paul)|~patient(paul)))&
(humble(alice))&
(~generous(john))&
((wise(lucy)|calm(lucy))) | ~patient(paul) | [] | null | 0 |
If someone is both funny and not happy then paul is quiet.
Everyone who is not wise or not creative is both old and not creative and vice versa.
If someone is both not patient and calm then john is both rich and not generous.
If someone is either not patient or creative then someone is not funny.
Everyone who is both not brave and kind is funny.
If susan is both curious and happy then alice is either quiet or not old.
Everyone who is humble or kind is generous or not patient.
Everyone who is not humble is both kind and not rich and vice versa.
Everyone who is not patient or not creative is either brave or not funny.
If someone is either not tall or not strong then someone is both not wise and not old.
Everyone who is not funny or curious is calm.
Everyone who is not brave is not strong.
Everyone who is either tall or kind is generous or humble and vice versa.
If someone is both patient and not funny then someone is happy and vice versa.
Everyone who is not old or humble is both not humble and creative and vice versa.
Everyone who is old or calm is not kind.
Fred is generous or curious.
Someone is either curious or tall.
Alice is either not curious or old.
Fred is funny.
John is wise.
Fred is kind or not quiet.
Someone is strong. | Alice is funny. | entailment | ((?[X]:((funny(X)&~happy(X))))=>(quiet(paul)))&
(![X]:((~wise(X)|~creative(X))<=>(old(X)&~creative(X))))&
((?[X]:((~patient(X)&calm(X))))=>((rich(john)&~generous(john))))&
((?[X]:((~patient(X)<~>creative(X))))=>(?[X]:(~funny(X))))&
(![X]:((~brave(X)&kind(X))=>funny(X)))&
(((curious(susan)&happy(susan)))=>((quiet(alice)<~>~old(alice))))&
(![X]:((humble(X)|kind(X))=>(generous(X)|~patient(X))))&
(![X]:(~humble(X)<=>(kind(X)&~rich(X))))&
(![X]:((~patient(X)|~creative(X))=>(brave(X)<~>~funny(X))))&
((?[X]:((~tall(X)<~>~strong(X))))=>(?[X]:((~wise(X)&~old(X)))))&
(![X]:((~funny(X)|curious(X))=>calm(X)))&
(![X]:(~brave(X)=>~strong(X)))&
(![X]:((tall(X)<~>kind(X))<=>(generous(X)|humble(X))))&
((?[X]:((patient(X)&~funny(X))))<=>(?[X]:(happy(X))))&
(![X]:((~old(X)|humble(X))<=>(~humble(X)&creative(X))))&
(![X]:((old(X)|calm(X))=>~kind(X)))&
((generous(fred)|curious(fred)))&
(?[X]:((curious(X)<~>tall(X))))&
((~curious(alice)<~>old(alice)))&
(funny(fred))&
(wise(john))&
((kind(fred)|~quiet(fred)))&
(?[X]:(strong(X))) | funny(alice) | [
"p7",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4096467844600652223212658
% SZS output start Proof for 4096467844600652223212658
8. ! [X0] : (~humble(X0) <=> (~rich(X0) & kind(X0))) [input p7]
11. ! [X0] : ((curious(X0) | ~funny(X0)) => calm(X0)) [input p10]
15. ! [X0] : ((humble(X0) | ~old(X0)) <=> (creative(X0) & ~humble(X0))) [input p14]
16. ! [X0] : ((calm(X0) | old(X0)) => ~kind(X0)) [input p15]
24. ~funny(alice) [input hypothesis]
39. ! [X0] : (calm(X0) | (~curious(X0) & funny(X0))) [ennf transformation 11]
41. ! [X0] : (~kind(X0) | (~calm(X0) & ~old(X0))) [ennf transformation 16]
49. ! [X0] : ((~humble(X0) | (rich(X0) | ~kind(X0))) & ((~rich(X0) & kind(X0)) | humble(X0))) [nnf transformation 8]
50. ! [X0] : ((~humble(X0) | rich(X0) | ~kind(X0)) & ((~rich(X0) & kind(X0)) | humble(X0))) [flattening 49]
63. ! [X0] : (((humble(X0) | ~old(X0)) | (~creative(X0) | humble(X0))) & ((creative(X0) & ~humble(X0)) | (~humble(X0) & old(X0)))) [nnf transformation 15]
64. ! [X0] : ((humble(X0) | ~old(X0) | ~creative(X0) | humble(X0)) & ((creative(X0) & ~humble(X0)) | (~humble(X0) & old(X0)))) [flattening 63]
86. humble(X0) | kind(X0) [cnf transformation 50]
97. calm(X0) | funny(X0) [cnf transformation 39]
110. ~humble(X0) | ~humble(X0) [cnf transformation 64]
115. ~kind(X0) | ~calm(X0) [cnf transformation 41]
125. ~funny(alice) [cnf transformation 24]
126. ~humble(X0) [duplicate literal removal 110]
260. kind(X0) [resolution 86,126]
265. ~calm(X0) [resolution 115,260]
282. funny(X0) [resolution 265,97]
296. $false [resolution 282,125]
% SZS output end Proof for 4096467844600652223212658
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or old then john is either brave or calm and vice versa.
Everyone who is not humble is humble.
If lucy is both curious and tall then someone is strong or not patient and vice versa.
Everyone who is happy is both rich and not kind and vice versa.
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. | John is creative. | contradiction | ((?[X]:((kind(X)<~>old(X))))<=>((brave(john)<~>calm(john))))&
(![X]:(~humble(X)=>humble(X)))&
(((curious(lucy)&tall(lucy)))<=>(?[X]:((strong(X)|~patient(X)))))&
(![X]:(happy(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))) | creative(john) | [
"p1",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2754672495824431196250474
% SZS output start Proof for 2754672495824431196250474
2. ! [X0] : (~humble(X0) => humble(X0)) [input p1]
15. ? [X0] : (kind(X0) | creative(X0)) <=> ? [X0] : ~humble(X0) [input p14]
25. creative(john) [input hypothesis]
28. ? [X0] : (kind(X0) | creative(X0)) <=> ? [X1] : ~humble(X1) [rectify 15]
30. ! [X0] : (humble(X0) | humble(X0)) [ennf transformation 2]
66. (? [X0] : (kind(X0) | creative(X0)) | ! [X1] : humble(X1)) & (? [X1] : ~humble(X1) | ! [X0] : (~kind(X0) & ~creative(X0))) [nnf transformation 28]
67. (? [X0] : (kind(X0) | creative(X0)) | ! [X1] : humble(X1)) & (? [X2] : ~humble(X2) | ! [X3] : (~kind(X3) & ~creative(X3))) [rectify 66]
68. ? [X0] : (kind(X0) | creative(X0)) => (kind(sK6) | creative(sK6)) [choice axiom]
69. ? [X2] : ~humble(X2) => ~humble(sK7) [choice axiom]
70. ((kind(sK6) | creative(sK6)) | ! [X1] : humble(X1)) & (~humble(sK7) | ! [X3] : (~kind(X3) & ~creative(X3))) [skolemisation 67,69,68]
90. humble(X0) | humble(X0) [cnf transformation 30]
135. ~humble(sK7) | ~creative(X3) [cnf transformation 70]
154. creative(john) [cnf transformation 25]
155. humble(X0) [duplicate literal removal 90]
329. ~creative(X3) [subsumption resolution 135,155]
390. $false [subsumption resolution 154,329]
% SZS output end Proof for 2754672495824431196250474
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not curious and generous then someone is either not curious or not rich and vice versa.
Everyone who is curious is both not patient and not curious and vice versa.
If someone is not happy then someone is wise or creative and vice versa.
Everyone who is both wise and not funny is rich or not happy and vice versa.
If someone is old or not brave then susan is both humble and not quiet and vice versa.
If mary is not calm or humble then someone is brave or not funny and vice versa.
Everyone who is both kind and patient is happy or not wise.
Everyone who is either not tall or quiet is either not curious or not quiet and vice versa.
If john is both funny and strong then someone is either creative or old and vice versa.
Everyone who is both not kind and old is both funny and quiet.
If lucy is not generous then fred is both not funny and not patient.
Everyone who is both not brave and not calm is brave or creative and vice versa.
If someone is not strong or creative then john is either not tall or tall and vice versa.
If fred is generous or not brave then someone is not curious or not brave.
If fred is either not humble or generous then someone is either not funny or not humble.
Everyone who is quiet is generous or calm and vice versa.
Someone is generous.
Mary is not generous.
Someone is not humble.
John is old.
Paul is both not generous and not wise.
Someone is not humble or old. | Mary is tall. | entailment | (((~curious(fred)&generous(fred)))<=>(?[X]:((~curious(X)<~>~rich(X)))))&
(![X]:(curious(X)<=>(~patient(X)&~curious(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((wise(X)|creative(X)))))&
(![X]:((wise(X)&~funny(X))<=>(rich(X)|~happy(X))))&
((?[X]:((old(X)|~brave(X))))<=>((humble(susan)&~quiet(susan))))&
(((~calm(mary)|humble(mary)))<=>(?[X]:((brave(X)|~funny(X)))))&
(![X]:((kind(X)&patient(X))=>(happy(X)|~wise(X))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~curious(X)<~>~quiet(X))))&
(((funny(john)&strong(john)))<=>(?[X]:((creative(X)<~>old(X)))))&
(![X]:((~kind(X)&old(X))=>(funny(X)&quiet(X))))&
((~generous(lucy))=>((~funny(fred)&~patient(fred))))&
(![X]:((~brave(X)&~calm(X))<=>(brave(X)|creative(X))))&
((?[X]:((~strong(X)|creative(X))))<=>((~tall(john)<~>tall(john))))&
(((generous(fred)|~brave(fred)))=>(?[X]:((~curious(X)|~brave(X)))))&
(((~humble(fred)<~>generous(fred)))=>(?[X]:((~funny(X)<~>~humble(X)))))&
(![X]:(quiet(X)<=>(generous(X)|calm(X))))&
(?[X]:(generous(X)))&
(~generous(mary))&
(?[X]:(~humble(X)))&
(old(john))&
((~generous(paul)&~wise(paul)))&
(?[X]:((~humble(X)|old(X)))) | tall(mary) | [
"p1",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2838398373956372455547833
% SZS output start Proof for 2838398373956372455547833
2. ! [X0] : (curious(X0) <=> (~curious(X0) & ~patient(X0))) [input p1]
8. ! [X0] : ((~tall(X0) <~> quiet(X0)) <=> (~curious(X0) <~> ~quiet(X0))) [input p7]
23. ~tall(mary) [input hypothesis]
37. ! [X0] : ((curious(X0) | (curious(X0) | patient(X0))) & ((~curious(X0) & ~patient(X0)) | ~curious(X0))) [nnf transformation 2]
38. ! [X0] : ((curious(X0) | curious(X0) | patient(X0)) & ((~curious(X0) & ~patient(X0)) | ~curious(X0))) [flattening 37]
56. ! [X0] : ((((~quiet(X0) | tall(X0)) & (quiet(X0) | ~tall(X0))) | ((~curious(X0) | quiet(X0)) & (~quiet(X0) | curious(X0)))) & (((quiet(X0) | curious(X0)) & (~quiet(X0) | ~curious(X0))) | ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))))) [nnf transformation 8]
88. ~curious(X0) | ~curious(X0) [cnf transformation 38]
110. quiet(X0) | curious(X0) | quiet(X0) | tall(X0) [cnf transformation 56]
114. ~quiet(X0) | tall(X0) | ~quiet(X0) | curious(X0) [cnf transformation 56]
153. ~tall(mary) [cnf transformation 23]
159. quiet(X0) | curious(X0) | tall(X0) [duplicate literal removal 110]
161. ~quiet(X0) | tall(X0) | curious(X0) [duplicate literal removal 114]
162. ~curious(X0) [duplicate literal removal 88]
270. ~quiet(X0) | tall(X0) [subsumption resolution 161,162]
271. quiet(X0) | tall(X0) [subsumption resolution 159,162]
272. tall(X0) [subsumption resolution 271,270]
351. $false [subsumption resolution 153,272]
% SZS output end Proof for 2838398373956372455547833
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not rich is both quiet and not tall.
If someone is kind or curious then someone is both not rich and tall and vice versa.
Everyone who is either creative or not kind is both not funny and quiet and vice versa.
Everyone who is either humble or not quiet is both not happy and not calm.
If someone is tall or not strong then someone is either not happy or creative and vice versa.
If someone is not calm or tall then someone is calm and vice versa.
Everyone who is strong is both curious and not curious and vice versa.
Everyone who is both quiet and patient is humble or calm.
Everyone who is both not funny and old is not happy.
Everyone who is calm is curious and vice versa.
Everyone who is patient is either old or creative and vice versa.
If alice is both curious and old then someone is not rich or not funny.
If someone is either funny or strong then mary is either not funny or brave and vice versa.
Everyone who is curious or kind is not generous or not strong.
If someone is brave then someone is both not brave and not curious and vice versa.
Someone is not happy.
Someone is either not funny or happy.
John is both not old and brave.
Alice is either not generous or creative.
Someone is not patient or funny.
Paul is either not kind or calm. | Alice is not humble. | neutral | (![X]:((generous(X)<~>~rich(X))=>(quiet(X)&~tall(X))))&
((?[X]:((kind(X)|curious(X))))<=>(?[X]:((~rich(X)&tall(X)))))&
(![X]:((creative(X)<~>~kind(X))<=>(~funny(X)&quiet(X))))&
(![X]:((humble(X)<~>~quiet(X))=>(~happy(X)&~calm(X))))&
((?[X]:((tall(X)|~strong(X))))<=>(?[X]:((~happy(X)<~>creative(X)))))&
((?[X]:((~calm(X)|tall(X))))<=>(?[X]:(calm(X))))&
(![X]:(strong(X)<=>(curious(X)&~curious(X))))&
(![X]:((quiet(X)&patient(X))=>(humble(X)|calm(X))))&
(![X]:((~funny(X)&old(X))=>~happy(X)))&
(![X]:(calm(X)<=>curious(X)))&
(![X]:(patient(X)<=>(old(X)<~>creative(X))))&
(((curious(alice)&old(alice)))=>(?[X]:((~rich(X)|~funny(X)))))&
((?[X]:((funny(X)<~>strong(X))))<=>((~funny(mary)<~>brave(mary))))&
(![X]:((curious(X)|kind(X))=>(~generous(X)|~strong(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~brave(X)&~curious(X)))))&
(?[X]:(~happy(X)))&
(?[X]:((~funny(X)<~>happy(X))))&
((~old(john)&brave(john)))&
((~generous(alice)<~>creative(alice)))&
(?[X]:((~patient(X)|funny(X))))&
((~kind(paul)<~>calm(paul))) | ~humble(alice) | [] | null | 0 |
If susan is not happy or not wise then lucy is both tall and not tall. If susan is calm then someone is tall and vice versa. Everyone who is either not generous or not happy is rich and vice versa. If someone is both generous and creative then someone is brave or not calm. Everyone who is rich is tall. If someone is not wise or not calm then someone is either rich or wise and vice versa. If susan is not tall then susan is both generous and funny. Everyone who is either patient or not generous is not tall or not happy and vice versa. If susan is either quiet or not strong then mary is either curious or not wise and vice versa. Everyone who is either not tall or not creative is either creative or quiet and vice versa. If someone is either not old or not calm then someone is not funny and vice versa. Everyone who is not old or calm is humble. Everyone who is not humble or tall is either rich or not creative and vice versa. Everyone who is not humble or not funny is either wise or not funny. Everyone who is curious or humble is both creative and quiet. Everyone who is both not strong and happy is either not strong or not calm and vice versa. Someone is not tall. John is generous or not rich. Someone is either not brave or wise. Someone is either happy or not old. Someone is not patient. Someone is either not humble or not tall. Someone is not calm or strong. | Lucy is curious. | neutral | (((~happy(susan)|~wise(susan)))=>((tall(lucy)&~tall(lucy))))&
((calm(susan))<=>(?[X]:(tall(X))))&
(![X]:((~generous(X)<~>~happy(X))<=>rich(X)))&
((?[X]:((generous(X)&creative(X))))=>(?[X]:((brave(X)|~calm(X)))))&
(![X]:(rich(X)=>tall(X)))&
((?[X]:((~wise(X)|~calm(X))))<=>(?[X]:((rich(X)<~>wise(X)))))&
((~tall(susan))=>((generous(susan)&funny(susan))))&
(![X]:((patient(X)<~>~generous(X))<=>(~tall(X)|~happy(X))))&
(((quiet(susan)<~>~strong(susan)))<=>((curious(mary)<~>~wise(mary))))&
(![X]:((~tall(X)<~>~creative(X))<=>(creative(X)<~>quiet(X))))&
((?[X]:((~old(X)<~>~calm(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~old(X)|calm(X))=>humble(X)))&
(![X]:((~humble(X)|tall(X))<=>(rich(X)<~>~creative(X))))&
(![X]:((~humble(X)|~funny(X))=>(wise(X)<~>~funny(X))))&
(![X]:((curious(X)|humble(X))=>(creative(X)&quiet(X))))&
(![X]:((~strong(X)&happy(X))<=>(~strong(X)<~>~calm(X))))&
(?[X]:(~tall(X)))&
((generous(john)|~rich(john)))&
(?[X]:((~brave(X)<~>wise(X))))&
(?[X]:((happy(X)<~>~old(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~humble(X)<~>~tall(X))))&
(?[X]:((~calm(X)|strong(X)))) | curious(lucy) | [] | null | 0 |
If someone is both not calm and funny then someone is either strong or tall. If alice is not funny or not quiet then mary is either tall or strong. If someone is brave then paul is either rich or strong and vice versa. If someone is either funny or not quiet then john is either not humble or not generous. Everyone who is not wise or strong is both calm and generous. Everyone who is either not calm or quiet is both old and not humble. Everyone who is either not kind or tall is either old or not wise. Everyone who is not strong or patient is either not old or kind. Everyone who is not funny or not tall is both tall and not brave and vice versa. If paul is brave or patient then someone is either strong or not happy and vice versa. Everyone who is both tall and kind is either wise or old and vice versa. If someone is old then someone is both not calm and not tall and vice versa. If someone is both creative and not funny then paul is both generous and funny. Everyone who is both calm and not kind is either not humble or not funny and vice versa. Everyone who is both not humble and happy is not old or generous and vice versa. If paul is both not quiet and happy then alice is not rich and vice versa. Paul is either not funny or happy. Someone is both curious and not quiet. Alice is not funny or not creative. Someone is not kind or patient. | Paul is quiet. | contradiction | ((?[X]:((~calm(X)&funny(X))))=>(?[X]:((strong(X)<~>tall(X)))))&
(((~funny(alice)|~quiet(alice)))=>((tall(mary)<~>strong(mary))))&
((?[X]:(brave(X)))<=>((rich(paul)<~>strong(paul))))&
((?[X]:((funny(X)<~>~quiet(X))))=>((~humble(john)<~>~generous(john))))&
(![X]:((~wise(X)|strong(X))=>(calm(X)&generous(X))))&
(![X]:((~calm(X)<~>quiet(X))=>(old(X)&~humble(X))))&
(![X]:((~kind(X)<~>tall(X))=>(old(X)<~>~wise(X))))&
(![X]:((~strong(X)|patient(X))=>(~old(X)<~>kind(X))))&
(![X]:((~funny(X)|~tall(X))<=>(tall(X)&~brave(X))))&
(((brave(paul)|patient(paul)))<=>(?[X]:((strong(X)<~>~happy(X)))))&
(![X]:((tall(X)&kind(X))<=>(wise(X)<~>old(X))))&
((?[X]:(old(X)))<=>(?[X]:((~calm(X)&~tall(X)))))&
((?[X]:((creative(X)&~funny(X))))=>((generous(paul)&funny(paul))))&
(![X]:((calm(X)&~kind(X))<=>(~humble(X)<~>~funny(X))))&
(![X]:((~humble(X)&happy(X))<=>(~old(X)|generous(X))))&
(((~quiet(paul)&happy(paul)))<=>(~rich(alice)))&
((~funny(paul)<~>happy(paul)))&
(?[X]:((curious(X)&~quiet(X))))&
((~funny(alice)|~creative(alice)))&
(?[X]:((~kind(X)|patient(X)))) | quiet(paul) | [
"p5",
"p8",
"p11",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7962122403277397422940119
% SZS output start Proof for 7962122403277397422940119
6. ! [X0] : ((~calm(X0) <~> quiet(X0)) => (~humble(X0) & old(X0))) [input p5]
9. ! [X0] : ((~tall(X0) | ~funny(X0)) <=> (~brave(X0) & tall(X0))) [input p8]
12. ? [X0] : old(X0) <=> ? [X0] : (~tall(X0) & ~calm(X0)) [input p11]
14. ! [X0] : ((~kind(X0) & calm(X0)) <=> (~humble(X0) <~> ~funny(X0))) [input p13]
15. ! [X0] : ((happy(X0) & ~humble(X0)) <=> (generous(X0) | ~old(X0))) [input p14]
17. ~funny(paul) <~> happy(paul) [input p16]
21. quiet(paul) [input hypothesis]
23. ? [X0] : old(X0) <=> ? [X1] : (~tall(X1) & ~calm(X1)) [rectify 12]
31. ! [X0] : ((~humble(X0) & old(X0)) | (~calm(X0) <=> quiet(X0))) [ennf transformation 6]
44. ! [X0] : ((~humble(X0) & old(X0)) | ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0)))) [nnf transformation 31]
47. ! [X0] : (((~tall(X0) | ~funny(X0)) | (brave(X0) | ~tall(X0))) & ((~brave(X0) & tall(X0)) | (tall(X0) & funny(X0)))) [nnf transformation 9]
48. ! [X0] : ((~tall(X0) | ~funny(X0) | brave(X0) | ~tall(X0)) & ((~brave(X0) & tall(X0)) | (tall(X0) & funny(X0)))) [flattening 47]
56. (? [X0] : old(X0) | ! [X1] : (tall(X1) | calm(X1))) & (? [X1] : (~tall(X1) & ~calm(X1)) | ! [X0] : ~old(X0)) [nnf transformation 23]
57. (? [X0] : old(X0) | ! [X1] : (tall(X1) | calm(X1))) & (? [X2] : (~tall(X2) & ~calm(X2)) | ! [X3] : ~old(X3)) [rectify 56]
58. ? [X0] : old(X0) => old(sK3) [choice axiom]
59. ? [X2] : (~tall(X2) & ~calm(X2)) => (~tall(sK4) & ~calm(sK4)) [choice axiom]
60. (old(sK3) | ! [X1] : (tall(X1) | calm(X1))) & ((~tall(sK4) & ~calm(sK4)) | ! [X3] : ~old(X3)) [skolemisation 57,59,58]
61. ! [X0] : (((~kind(X0) & calm(X0)) | ((~humble(X0) | funny(X0)) & (~funny(X0) | humble(X0)))) & (((funny(X0) | humble(X0)) & (~funny(X0) | ~humble(X0))) | (kind(X0) | ~calm(X0)))) [nnf transformation 14]
62. ! [X0] : (((~kind(X0) & calm(X0)) | ((~humble(X0) | funny(X0)) & (~funny(X0) | humble(X0)))) & (((funny(X0) | humble(X0)) & (~funny(X0) | ~humble(X0))) | kind(X0) | ~calm(X0))) [flattening 61]
63. ! [X0] : (((happy(X0) & ~humble(X0)) | (~generous(X0) & old(X0))) & ((generous(X0) | ~old(X0)) | (~happy(X0) | humble(X0)))) [nnf transformation 15]
64. ! [X0] : (((happy(X0) & ~humble(X0)) | (~generous(X0) & old(X0))) & (generous(X0) | ~old(X0) | ~happy(X0) | humble(X0))) [flattening 63]
67. (~happy(paul) | funny(paul)) & (happy(paul) | ~funny(paul)) [nnf transformation 17]
91. ~quiet(X0) | ~calm(X0) | old(X0) [cnf transformation 44]
103. tall(X0) | tall(X0) [cnf transformation 48]
120. ~tall(sK4) | ~old(X3) [cnf transformation 60]
124. ~funny(X0) | calm(X0) | humble(X0) [cnf transformation 62]
129. ~humble(X0) | old(X0) [cnf transformation 64]
131. happy(X0) | old(X0) [cnf transformation 64]
137. ~happy(paul) | funny(paul) [cnf transformation 67]
140. quiet(paul) [cnf transformation 21]
141. tall(X0) [duplicate literal removal 103]
243. ~old(X3) [subsumption resolution 120,141]
244. happy(X0) [subsumption resolution 131,243]
245. ~humble(X0) [subsumption resolution 129,243]
251. 23 <=> quiet(paul) [avatar definition]
252. quiet(paul) <- (23) [avatar component clause 251]
257. funny(paul) [subsumption resolution 137,244]
267. 23 [avatar split clause 140,251]
288. ~calm(paul) | old(paul) <- (23) [resolution 91,252]
292. ~calm(paul) <- (23) [subsumption resolution 288,243]
313. calm(paul) | humble(paul) [resolution 124,257]
315. humble(paul) <- (23) [subsumption resolution 313,292]
316. $false <- (23) [subsumption resolution 315,245]
317. ~23 [avatar contradiction clause 316]
319. $false [avatar sat refutation 267,317]
% SZS output end Proof for 7962122403277397422940119
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and curious is not strong or quiet and vice versa.
Everyone who is not curious is not old and vice versa.
If john is either kind or not old then alice is either not calm or patient.
If someone is kind then fred is not kind or not funny.
Everyone who is humble or not creative is both creative and not rich and vice versa.
Everyone who is not kind or not creative is not kind or not patient.
Everyone who is both not quiet and humble is not funny.
If someone is not calm or not creative then someone is funny or not old.
Everyone who is either not quiet or brave is old and vice versa.
If someone is either kind or generous then someone is not brave or not rich and vice versa.
If someone is not happy or old then someone is not quiet.
Everyone who is curious or rich is both not old and wise and vice versa.
Everyone who is happy or not old is not wise and vice versa.
Everyone who is curious is either not brave or creative.
If paul is both not creative and not happy then lucy is either not creative or not generous and vice versa.
Someone is strong or not creative.
Someone is either not patient or not curious.
Someone is brave.
Someone is both creative and tall.
Someone is both patient and calm. | Fred is curious. | contradiction | (![X]:((~happy(X)&curious(X))<=>(~strong(X)|quiet(X))))&
(![X]:(~curious(X)<=>~old(X)))&
(((kind(john)<~>~old(john)))=>((~calm(alice)<~>patient(alice))))&
((?[X]:(kind(X)))=>((~kind(fred)|~funny(fred))))&
(![X]:((humble(X)|~creative(X))<=>(creative(X)&~rich(X))))&
(![X]:((~kind(X)|~creative(X))=>(~kind(X)|~patient(X))))&
(![X]:((~quiet(X)&humble(X))=>~funny(X)))&
((?[X]:((~calm(X)|~creative(X))))=>(?[X]:((funny(X)|~old(X)))))&
(![X]:((~quiet(X)<~>brave(X))<=>old(X)))&
((?[X]:((kind(X)<~>generous(X))))<=>(?[X]:((~brave(X)|~rich(X)))))&
((?[X]:((~happy(X)|old(X))))=>(?[X]:(~quiet(X))))&
(![X]:((curious(X)|rich(X))<=>(~old(X)&wise(X))))&
(![X]:((happy(X)|~old(X))<=>~wise(X)))&
(![X]:(curious(X)=>(~brave(X)<~>creative(X))))&
(((~creative(paul)&~happy(paul)))<=>((~creative(lucy)<~>~generous(lucy))))&
(?[X]:((strong(X)|~creative(X))))&
(?[X]:((~patient(X)<~>~curious(X))))&
(?[X]:(brave(X)))&
(?[X]:((creative(X)&tall(X))))&
(?[X]:((patient(X)&calm(X)))) | curious(fred) | [
"p1",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5895170848072855386930628
% SZS output start Proof for 5895170848072855386930628
2. ! [X0] : (~curious(X0) <=> ~old(X0)) [input p1]
12. ! [X0] : ((rich(X0) | curious(X0)) <=> (wise(X0) & ~old(X0))) [input p11]
21. curious(fred) [input hypothesis]
38. ! [X0] : ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0))) [nnf transformation 2]
54. ! [X0] : (((rich(X0) | curious(X0)) | (~wise(X0) | old(X0))) & ((wise(X0) & ~old(X0)) | (~rich(X0) & ~curious(X0)))) [nnf transformation 12]
55. ! [X0] : ((rich(X0) | curious(X0) | ~wise(X0) | old(X0)) & ((wise(X0) & ~old(X0)) | (~rich(X0) & ~curious(X0)))) [flattening 54]
77. ~old(X0) | curious(X0) [cnf transformation 38]
78. ~curious(X0) | old(X0) [cnf transformation 38]
106. ~old(X0) | ~curious(X0) [cnf transformation 55]
129. curious(fred) [cnf transformation 21]
211. 19 <=> ! [X1] : ~old(X1) [avatar definition]
212. ~old(X1) <- (19) [avatar component clause 211]
223. ~old(X0) [subsumption resolution 106,77]
224. 19 [avatar split clause 223,211]
250. old(fred) [resolution 78,129]
251. $false <- (19) [subsumption resolution 250,212]
252. ~19 [avatar contradiction clause 251]
253. $false [avatar sat refutation 224,252]
% SZS output end Proof for 5895170848072855386930628
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is both rich and not curious and vice versa. If someone is not tall or brave then someone is tall or quiet and vice versa. Everyone who is not happy or not wise is rich or tall and vice versa. If someone is either tall or not strong then mary is both not tall and funny. If someone is not wise or not kind then someone is not rich. If someone is brave or curious then fred is either not happy or not brave. If john is both patient and not funny then someone is not old or not tall and vice versa. Everyone who is both not brave and happy is humble or not tall and vice versa. If john is both brave and generous then susan is not funny. Everyone who is both not humble and not strong is kind and vice versa. If john is either tall or not funny then someone is old. If someone is not old then fred is happy or patient. Everyone who is not generous is patient or not old and vice versa. Everyone who is either kind or not creative is not humble and vice versa. Everyone who is either strong or happy is creative and vice versa. If susan is patient then someone is both not curious and not rich and vice versa. Someone is not kind. Someone is both old and tall. Someone is generous or not kind. Someone is either wise or patient. Mary is quiet. Mary is calm. Someone is either rich or not old. John is humble or strong. | Fred is not funny. | neutral | (![X]:(creative(X)<=>(rich(X)&~curious(X))))&
((?[X]:((~tall(X)|brave(X))))<=>(?[X]:((tall(X)|quiet(X)))))&
(![X]:((~happy(X)|~wise(X))<=>(rich(X)|tall(X))))&
((?[X]:((tall(X)<~>~strong(X))))=>((~tall(mary)&funny(mary))))&
((?[X]:((~wise(X)|~kind(X))))=>(?[X]:(~rich(X))))&
((?[X]:((brave(X)|curious(X))))=>((~happy(fred)<~>~brave(fred))))&
(((patient(john)&~funny(john)))<=>(?[X]:((~old(X)|~tall(X)))))&
(![X]:((~brave(X)&happy(X))<=>(humble(X)|~tall(X))))&
(((brave(john)&generous(john)))=>(~funny(susan)))&
(![X]:((~humble(X)&~strong(X))<=>kind(X)))&
(((tall(john)<~>~funny(john)))=>(?[X]:(old(X))))&
((?[X]:(~old(X)))=>((happy(fred)|patient(fred))))&
(![X]:(~generous(X)<=>(patient(X)|~old(X))))&
(![X]:((kind(X)<~>~creative(X))<=>~humble(X)))&
(![X]:((strong(X)<~>happy(X))<=>creative(X)))&
((patient(susan))<=>(?[X]:((~curious(X)&~rich(X)))))&
(?[X]:(~kind(X)))&
(?[X]:((old(X)&tall(X))))&
(?[X]:((generous(X)|~kind(X))))&
(?[X]:((wise(X)<~>patient(X))))&
(quiet(mary))&
(calm(mary))&
(?[X]:((rich(X)<~>~old(X))))&
((humble(john)|strong(john))) | ~funny(fred) | [] | null | 0 |
If lucy is not funny then someone is both not calm and patient.
If someone is humble or not calm then fred is both not brave and quiet.
If someone is either funny or not tall then mary is not humble or not curious.
Everyone who is both creative and old is rich.
Everyone who is generous is both rich and strong and vice versa.
If someone is creative then someone is either funny or brave.
If someone is not brave or kind then someone is both tall and not kind and vice versa.
If alice is not creative then alice is both curious and not funny and vice versa.
Everyone who is both wise and not creative is not strong or not funny.
If someone is both happy and not wise then fred is either not creative or brave and vice versa.
If someone is old then someone is either funny or curious.
Everyone who is not patient or not strong is both funny and not quiet.
Everyone who is either old or humble is not quiet or not humble and vice versa.
If someone is not creative or not quiet then fred is both not quiet and tall.
Everyone who is not quiet is both creative and not rich and vice versa.
If alice is either not old or creative then someone is kind and vice versa.
Someone is either not funny or rich.
Susan is happy.
Someone is creative or patient. | Mary is generous. | entailment | ((~funny(lucy))=>(?[X]:((~calm(X)&patient(X)))))&
((?[X]:((humble(X)|~calm(X))))=>((~brave(fred)&quiet(fred))))&
((?[X]:((funny(X)<~>~tall(X))))=>((~humble(mary)|~curious(mary))))&
(![X]:((creative(X)&old(X))=>rich(X)))&
(![X]:(generous(X)<=>(rich(X)&strong(X))))&
((?[X]:(creative(X)))=>(?[X]:((funny(X)<~>brave(X)))))&
((?[X]:((~brave(X)|kind(X))))<=>(?[X]:((tall(X)&~kind(X)))))&
((~creative(alice))<=>((curious(alice)&~funny(alice))))&
(![X]:((wise(X)&~creative(X))=>(~strong(X)|~funny(X))))&
((?[X]:((happy(X)&~wise(X))))<=>((~creative(fred)<~>brave(fred))))&
((?[X]:(old(X)))=>(?[X]:((funny(X)<~>curious(X)))))&
(![X]:((~patient(X)|~strong(X))=>(funny(X)&~quiet(X))))&
(![X]:((old(X)<~>humble(X))<=>(~quiet(X)|~humble(X))))&
((?[X]:((~creative(X)|~quiet(X))))=>((~quiet(fred)&tall(fred))))&
(![X]:(~quiet(X)<=>(creative(X)&~rich(X))))&
(((~old(alice)<~>creative(alice)))<=>(?[X]:(kind(X))))&
(?[X]:((~funny(X)<~>rich(X))))&
(happy(susan))&
(?[X]:((creative(X)|patient(X)))) | generous(mary) | [
"p1",
"p3",
"p4",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1693258031228057071233246
% SZS output start Proof for 1693258031228057071233246
2. ? [X0] : (~calm(X0) | humble(X0)) => (quiet(fred) & ~brave(fred)) [input p1]
4. ! [X0] : ((old(X0) & creative(X0)) => rich(X0)) [input p3]
5. ! [X0] : (generous(X0) <=> (strong(X0) & rich(X0))) [input p4]
12. ! [X0] : ((~strong(X0) | ~patient(X0)) => (~quiet(X0) & funny(X0))) [input p11]
13. ! [X0] : ((old(X0) <~> humble(X0)) <=> (~humble(X0) | ~quiet(X0))) [input p12]
14. ? [X0] : (~quiet(X0) | ~creative(X0)) => (tall(fred) & ~quiet(fred)) [input p13]
15. ! [X0] : (~quiet(X0) <=> (~rich(X0) & creative(X0))) [input p14]
20. ~generous(mary) [input hypothesis]
24. ! [X0] : ((strong(X0) & rich(X0)) => generous(X0)) [unused predicate definition removal 5]
27. ! [X0] : (~strong(X0) => (~quiet(X0) & funny(X0))) [pure predicate removal 12]
29. (quiet(fred) & ~brave(fred)) | ! [X0] : (calm(X0) & ~humble(X0)) [ennf transformation 2]
32. ! [X0] : (rich(X0) | (~old(X0) | ~creative(X0))) [ennf transformation 4]
33. ! [X0] : (rich(X0) | ~old(X0) | ~creative(X0)) [flattening 32]
34. ! [X0] : (generous(X0) | (~strong(X0) | ~rich(X0))) [ennf transformation 24]
35. ! [X0] : (generous(X0) | ~strong(X0) | ~rich(X0)) [flattening 34]
40. ! [X0] : ((~quiet(X0) & funny(X0)) | strong(X0)) [ennf transformation 27]
41. (tall(fred) & ~quiet(fred)) | ! [X0] : (quiet(X0) & creative(X0)) [ennf transformation 14]
64. ! [X0] : ((((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | (humble(X0) & quiet(X0))) & ((~humble(X0) | ~quiet(X0)) | ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0))))) [nnf transformation 13]
65. ! [X0] : ((((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | (humble(X0) & quiet(X0))) & (~humble(X0) | ~quiet(X0) | ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0))))) [flattening 64]
66. ! [X0] : ((~quiet(X0) | (rich(X0) | ~creative(X0))) & ((~rich(X0) & creative(X0)) | quiet(X0))) [nnf transformation 15]
67. ! [X0] : ((~quiet(X0) | rich(X0) | ~creative(X0)) & ((~rich(X0) & creative(X0)) | quiet(X0))) [flattening 66]
78. quiet(fred) | ~humble(X0) [cnf transformation 29]
82. ~old(X0) | rich(X0) | ~creative(X0) [cnf transformation 33]
83. ~strong(X0) | generous(X0) | ~rich(X0) [cnf transformation 35]
104. ~quiet(X0) | strong(X0) [cnf transformation 40]
106. ~humble(X0) | ~quiet(X0) | old(X0) | ~humble(X0) [cnf transformation 65]
108. humble(X0) | old(X0) | humble(X0) [cnf transformation 65]
111. ~quiet(fred) | creative(X0) [cnf transformation 41]
112. ~quiet(fred) | quiet(X0) [cnf transformation 41]
115. creative(X0) | quiet(X0) [cnf transformation 67]
116. ~rich(X0) | quiet(X0) [cnf transformation 67]
125. ~generous(mary) [cnf transformation 20]
126. ~humble(X0) | ~quiet(X0) | old(X0) [duplicate literal removal 106]
127. old(X0) | humble(X0) [duplicate literal removal 108]
141. 4 <=> quiet(fred) [avatar definition]
142. ~quiet(fred) <- (~4) [avatar component clause 141]
146. 5 <=> ! [X0] : ~humble(X0) [avatar definition]
147. ~humble(X0) <- (5) [avatar component clause 146]
148. 5 | 4 [avatar split clause 78,141,146]
263. ~quiet(X0) | old(X0) [subsumption resolution 126,127]
265. 31 <=> ! [X0] : quiet(X0) [avatar definition]
266. quiet(X0) <- (31) [avatar component clause 265]
273. 33 <=> ! [X0] : creative(X0) [avatar definition]
274. creative(X0) <- (33) [avatar component clause 273]
276. 31 | ~4 [avatar split clause 112,141,265]
277. 33 | ~4 [avatar split clause 111,141,273]
312. strong(X0) <- (31) [resolution 266,104]
328. old(X0) <- (31) [resolution 263,266]
329. rich(X0) | ~creative(X0) <- (31) [resolution 82,328]
330. rich(X1) | ~creative(X1) | humble(X1) [resolution 82,127]
332. rich(X0) <- (31, 33) [subsumption resolution 329,274]
336. generous(X0) | ~rich(X0) <- (31) [resolution 83,312]
338. generous(X0) <- (31, 33) [subsumption resolution 336,332]
342. $false <- (31, 33) [resolution 338,125]
343. ~31 | ~33 [avatar contradiction clause 342]
382. ~creative(X1) | rich(X1) <- (5) [subsumption resolution 330,147]
389. rich(X0) | quiet(X0) <- (5) [resolution 382,115]
391. quiet(X0) <- (5) [subsumption resolution 389,116]
392. 31 | ~5 [avatar split clause 391,146,265]
395. $false <- (~4, 31) [resolution 266,142]
396. 4 | ~31 [avatar contradiction clause 395]
397. $false [avatar sat refutation 148,276,277,343,392,396]
% SZS output end Proof for 1693258031228057071233246
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or kind is both not brave and not funny.
If someone is not patient or generous then someone is both creative and wise and vice versa.
If mary is not strong then someone is both old and wise.
Everyone who is not kind or not curious is either calm or not funny.
If someone is not humble then someone is either humble or rich and vice versa.
Everyone who is either not calm or patient is not patient or kind and vice versa.
Everyone who is either not rich or curious is not calm or curious.
If someone is both not tall and curious then someone is not calm or not curious and vice versa.
If someone is not quiet or wise then someone is not happy and vice versa.
Everyone who is both old and not old is not calm or not curious and vice versa.
If john is not curious or not patient then john is both not calm and tall and vice versa.
Everyone who is either not generous or not happy is either not funny or quiet and vice versa.
Everyone who is not tall or not brave is either not creative or rich and vice versa.
Everyone who is not creative is either not creative or rich and vice versa.
If someone is either curious or not funny then john is not wise and vice versa.
Everyone who is humble is either wise or rich and vice versa.
Susan is strong.
Someone is either not old or not funny.
Someone is calm.
Someone is either rich or not brave.
Someone is not creative or not kind. | Susan is not kind. | contradiction | (![X]:((calm(X)|kind(X))=>(~brave(X)&~funny(X))))&
((?[X]:((~patient(X)|generous(X))))<=>(?[X]:((creative(X)&wise(X)))))&
((~strong(mary))=>(?[X]:((old(X)&wise(X)))))&
(![X]:((~kind(X)|~curious(X))=>(calm(X)<~>~funny(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((humble(X)<~>rich(X)))))&
(![X]:((~calm(X)<~>patient(X))<=>(~patient(X)|kind(X))))&
(![X]:((~rich(X)<~>curious(X))=>(~calm(X)|curious(X))))&
((?[X]:((~tall(X)&curious(X))))<=>(?[X]:((~calm(X)|~curious(X)))))&
((?[X]:((~quiet(X)|wise(X))))<=>(?[X]:(~happy(X))))&
(![X]:((old(X)&~old(X))<=>(~calm(X)|~curious(X))))&
(((~curious(john)|~patient(john)))<=>((~calm(john)&tall(john))))&
(![X]:((~generous(X)<~>~happy(X))<=>(~funny(X)<~>quiet(X))))&
(![X]:((~tall(X)|~brave(X))<=>(~creative(X)<~>rich(X))))&
(![X]:(~creative(X)<=>(~creative(X)<~>rich(X))))&
((?[X]:((curious(X)<~>~funny(X))))<=>(~wise(john)))&
(![X]:(humble(X)<=>(wise(X)<~>rich(X))))&
(strong(susan))&
(?[X]:((~old(X)<~>~funny(X))))&
(?[X]:(calm(X)))&
(?[X]:((rich(X)<~>~brave(X))))&
(?[X]:((~creative(X)|~kind(X)))) | ~kind(susan) | [
"p0",
"p3",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7679251475459532478354155
% SZS output start Proof for 7679251475459532478354155
1. ! [X0] : ((kind(X0) | calm(X0)) => (~funny(X0) & ~brave(X0))) [input p0]
4. ! [X0] : ((~curious(X0) | ~kind(X0)) => (calm(X0) <~> ~funny(X0))) [input p3]
10. ! [X0] : ((~old(X0) & old(X0)) <=> (~curious(X0) | ~calm(X0))) [input p9]
22. ~kind(susan) [input hypothesis]
29. ! [X0] : ((~funny(X0) & ~brave(X0)) | (~kind(X0) & ~calm(X0))) [ennf transformation 1]
30. ! [X0] : ((calm(X0) <~> ~funny(X0)) | (curious(X0) & kind(X0))) [ennf transformation 4]
38. ! [X0] : (((funny(X0) | ~calm(X0)) & (~funny(X0) | calm(X0))) | (curious(X0) & kind(X0))) [nnf transformation 30]
57. ! [X0] : (((~old(X0) & old(X0)) | (curious(X0) & calm(X0))) & ((~curious(X0) | ~calm(X0)) | (old(X0) | ~old(X0)))) [nnf transformation 10]
58. ! [X0] : (((~old(X0) & old(X0)) | (curious(X0) & calm(X0))) & (~curious(X0) | ~calm(X0) | old(X0) | ~old(X0))) [flattening 57]
82. ~funny(X0) | ~calm(X0) [cnf transformation 29]
91. funny(X0) | ~calm(X0) | kind(X0) [cnf transformation 38]
114. old(X0) | calm(X0) [cnf transformation 58]
116. ~old(X0) | calm(X0) [cnf transformation 58]
155. ~kind(susan) [cnf transformation 22]
192. ~calm(X0) | kind(X0) [subsumption resolution 91,82]
231. 16 <=> ! [X1] : calm(X1) [avatar definition]
232. calm(X1) <- (16) [avatar component clause 231]
275. calm(X0) [subsumption resolution 114,116]
276. 16 [avatar split clause 275,231]
347. kind(X0) <- (16) [resolution 192,232]
348. $false <- (16) [resolution 347,155]
349. ~16 [avatar contradiction clause 348]
350. $false [avatar sat refutation 276,349]
% SZS output end Proof for 7679251475459532478354155
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and generous is humble and vice versa.
Everyone who is either wise or not humble is both not tall and not patient.
If alice is either not creative or not patient then someone is both not happy and not creative.
If someone is tall then someone is either rich or funny and vice versa.
Everyone who is both quiet and not creative is not humble or not funny.
If paul is either not tall or not wise then alice is humble or tall.
If someone is old then mary is kind.
If paul is brave or kind then someone is either not creative or old.
Everyone who is either not rich or generous is old and vice versa.
Everyone who is both not humble and not wise is both brave and quiet and vice versa.
If someone is strong or generous then mary is funny and vice versa.
Everyone who is not calm is both curious and not brave.
If paul is both curious and not funny then mary is both not old and not generous and vice versa.
Everyone who is both brave and not brave is kind and vice versa.
Everyone who is both kind and happy is tall and vice versa.
If someone is calm or creative then paul is generous or funny and vice versa.
John is not strong.
Someone is not patient or happy.
Paul is either not generous or not rich.
Mary is either not wise or curious.
Someone is not old or quiet.
Someone is happy.
Someone is brave.
Someone is both curious and not happy. | Paul is wise. | contradiction | (![X]:((funny(X)&generous(X))<=>humble(X)))&
(![X]:((wise(X)<~>~humble(X))=>(~tall(X)&~patient(X))))&
(((~creative(alice)<~>~patient(alice)))=>(?[X]:((~happy(X)&~creative(X)))))&
((?[X]:(tall(X)))<=>(?[X]:((rich(X)<~>funny(X)))))&
(![X]:((quiet(X)&~creative(X))=>(~humble(X)|~funny(X))))&
(((~tall(paul)<~>~wise(paul)))=>((humble(alice)|tall(alice))))&
((?[X]:(old(X)))=>(kind(mary)))&
(((brave(paul)|kind(paul)))=>(?[X]:((~creative(X)<~>old(X)))))&
(![X]:((~rich(X)<~>generous(X))<=>old(X)))&
(![X]:((~humble(X)&~wise(X))<=>(brave(X)&quiet(X))))&
((?[X]:((strong(X)|generous(X))))<=>(funny(mary)))&
(![X]:(~calm(X)=>(curious(X)&~brave(X))))&
(((curious(paul)&~funny(paul)))<=>((~old(mary)&~generous(mary))))&
(![X]:((brave(X)&~brave(X))<=>kind(X)))&
(![X]:((kind(X)&happy(X))<=>tall(X)))&
((?[X]:((calm(X)|creative(X))))<=>((generous(paul)|funny(paul))))&
(~strong(john))&
(?[X]:((~patient(X)|happy(X))))&
((~generous(paul)<~>~rich(paul)))&
((~wise(mary)<~>curious(mary)))&
(?[X]:((~old(X)|quiet(X))))&
(?[X]:(happy(X)))&
(?[X]:(brave(X)))&
(?[X]:((curious(X)&~happy(X)))) | wise(paul) | [
"p0",
"p3",
"p5",
"p6",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7577567079207411001476852
% SZS output start Proof for 7577567079207411001476852
1. ! [X0] : ((generous(X0) & funny(X0)) <=> humble(X0)) [input p0]
4. ? [X0] : tall(X0) <=> ? [X0] : (rich(X0) <~> funny(X0)) [input p3]
6. (~tall(paul) <~> ~wise(paul)) => (tall(alice) | humble(alice)) [input p5]
7. ? [X0] : old(X0) => kind(mary) [input p6]
9. ! [X0] : ((~rich(X0) <~> generous(X0)) <=> old(X0)) [input p8]
14. ! [X0] : ((~brave(X0) & brave(X0)) <=> kind(X0)) [input p13]
15. ! [X0] : ((happy(X0) & kind(X0)) <=> tall(X0)) [input p14]
25. wise(paul) [input hypothesis]
26. ? [X0] : tall(X0) <=> ? [X1] : (rich(X1) <~> funny(X1)) [rectify 4]
31. (tall(alice) | humble(alice)) | (~tall(paul) <=> ~wise(paul)) [ennf transformation 6]
32. tall(alice) | humble(alice) | (~tall(paul) <=> ~wise(paul)) [flattening 31]
33. kind(mary) | ! [X0] : ~old(X0) [ennf transformation 7]
36. ! [X0] : (((generous(X0) & funny(X0)) | ~humble(X0)) & (humble(X0) | (~generous(X0) | ~funny(X0)))) [nnf transformation 1]
37. ! [X0] : (((generous(X0) & funny(X0)) | ~humble(X0)) & (humble(X0) | ~generous(X0) | ~funny(X0))) [flattening 36]
42. (? [X0] : tall(X0) | ! [X1] : ((rich(X1) | ~funny(X1)) & (funny(X1) | ~rich(X1)))) & (? [X1] : ((~funny(X1) | ~rich(X1)) & (funny(X1) | rich(X1))) | ! [X0] : ~tall(X0)) [nnf transformation 26]
43. (? [X0] : tall(X0) | ! [X1] : ((rich(X1) | ~funny(X1)) & (funny(X1) | ~rich(X1)))) & (? [X2] : ((~funny(X2) | ~rich(X2)) & (funny(X2) | rich(X2))) | ! [X3] : ~tall(X3)) [rectify 42]
44. ? [X0] : tall(X0) => tall(sK1) [choice axiom]
45. ? [X2] : ((~funny(X2) | ~rich(X2)) & (funny(X2) | rich(X2))) => ((~funny(sK2) | ~rich(sK2)) & (funny(sK2) | rich(sK2))) [choice axiom]
46. (tall(sK1) | ! [X1] : ((rich(X1) | ~funny(X1)) & (funny(X1) | ~rich(X1)))) & (((~funny(sK2) | ~rich(sK2)) & (funny(sK2) | rich(sK2))) | ! [X3] : ~tall(X3)) [skolemisation 43,45,44]
47. tall(alice) | humble(alice) | ((~tall(paul) | wise(paul)) & (~wise(paul) | tall(paul))) [nnf transformation 32]
51. ! [X0] : ((((~generous(X0) | rich(X0)) & (generous(X0) | ~rich(X0))) | ~old(X0)) & (old(X0) | ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0))))) [nnf transformation 9]
60. ! [X0] : (((~brave(X0) & brave(X0)) | ~kind(X0)) & (kind(X0) | (brave(X0) | ~brave(X0)))) [nnf transformation 14]
61. ! [X0] : (((~brave(X0) & brave(X0)) | ~kind(X0)) & (kind(X0) | brave(X0) | ~brave(X0))) [flattening 60]
62. ! [X0] : (((happy(X0) & kind(X0)) | ~tall(X0)) & (tall(X0) | (~happy(X0) | ~kind(X0)))) [nnf transformation 15]
63. ! [X0] : (((happy(X0) & kind(X0)) | ~tall(X0)) & (tall(X0) | ~happy(X0) | ~kind(X0))) [flattening 62]
82. ~humble(X0) | funny(X0) [cnf transformation 37]
83. ~humble(X0) | generous(X0) [cnf transformation 37]
95. tall(sK1) | rich(X1) | ~funny(X1) [cnf transformation 46]
97. tall(alice) | humble(alice) | ~wise(paul) | tall(paul) [cnf transformation 47]
99. kind(mary) | ~old(X0) [cnf transformation 33]
105. ~rich(X0) | old(X0) | ~generous(X0) [cnf transformation 51]
122. brave(X0) | ~kind(X0) [cnf transformation 61]
123. ~brave(X0) | ~kind(X0) [cnf transformation 61]
125. kind(X0) | ~tall(X0) [cnf transformation 63]
142. wise(paul) [cnf transformation 25]
164. 5 <=> ! [X1] : (rich(X1) | ~funny(X1)) [avatar definition]
165. ~funny(X1) | rich(X1) <- (5) [avatar component clause 164]
167. 6 <=> tall(sK1) [avatar definition]
169. tall(sK1) <- (6) [avatar component clause 167]
170. 5 | 6 [avatar split clause 95,167,164]
176. 8 <=> ! [X3] : ~tall(X3) [avatar definition]
177. ~tall(X3) <- (8) [avatar component clause 176]
190. 11 <=> wise(paul) [avatar definition]
194. 12 <=> tall(paul) [avatar definition]
195. tall(paul) <- (12) [avatar component clause 194]
198. 13 <=> humble(alice) [avatar definition]
200. humble(alice) <- (13) [avatar component clause 198]
202. 14 <=> tall(alice) [avatar definition]
204. tall(alice) <- (14) [avatar component clause 202]
206. 12 | ~11 | 13 | 14 [avatar split clause 97,202,198,190,194]
208. 15 <=> ! [X0] : ~old(X0) [avatar definition]
209. ~old(X0) <- (15) [avatar component clause 208]
211. 16 <=> kind(mary) [avatar definition]
213. kind(mary) <- (16) [avatar component clause 211]
214. 15 | 16 [avatar split clause 99,211,208]
276. ~kind(X0) [subsumption resolution 122,123]
277. ~tall(X0) [subsumption resolution 125,276]
278. 8 [avatar split clause 277,176]
335. 11 [avatar split clause 142,190]
336. $false <- (6, 8) [subsumption resolution 169,177]
337. ~6 | ~8 [avatar contradiction clause 336]
338. $false <- (8, 12) [resolution 195,177]
339. ~8 | ~12 [avatar contradiction clause 338]
342. $false <- (16) [subsumption resolution 213,276]
343. ~16 [avatar contradiction clause 342]
344. funny(alice) <- (13) [resolution 82,200]
345. generous(alice) <- (13) [resolution 83,200]
351. rich(alice) <- (5, 13) [resolution 165,344]
364. old(alice) | ~generous(alice) <- (5, 13) [resolution 105,351]
368. ~generous(alice) <- (5, 13, 15) [subsumption resolution 364,209]
369. $false <- (5, 13, 15) [subsumption resolution 368,345]
370. ~5 | ~13 | ~15 [avatar contradiction clause 369]
376. $false <- (8, 14) [subsumption resolution 204,177]
377. ~8 | ~14 [avatar contradiction clause 376]
378. $false [avatar sat refutation 170,206,214,278,335,337,339,343,370,377]
% SZS output end Proof for 7577567079207411001476852
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and funny is not tall and vice versa.
If john is both not humble and not funny then someone is both not wise and not brave and vice versa.
Everyone who is not brave or not curious is generous and vice versa.
If someone is creative then mary is both generous and not wise and vice versa.
Everyone who is both not kind and not funny is not rich or kind and vice versa.
Everyone who is not creative is either not humble or not patient.
If susan is either not patient or not brave then john is both not tall and not happy.
Everyone who is funny or calm is happy or creative.
Everyone who is both old and not strong is either strong or wise.
If alice is tall then fred is not quiet and vice versa.
If someone is either not funny or not creative then someone is calm or not strong and vice versa.
Everyone who is either old or tall is both brave and creative and vice versa.
Everyone who is both not funny and not calm is not kind or funny and vice versa.
Everyone who is either not rich or not curious is either not generous or not strong and vice versa.
If someone is either brave or patient then someone is either strong or humble and vice versa.
If paul is both funny and not rich then someone is not quiet or rich.
Someone is both not humble and generous.
Alice is not wise.
Someone is not quiet.
Someone is patient.
Someone is not wise or wise.
Someone is both brave and not humble.
Someone is either tall or happy. | Fred is happy. | neutral | (![X]:((wise(X)&funny(X))<=>~tall(X)))&
(((~humble(john)&~funny(john)))<=>(?[X]:((~wise(X)&~brave(X)))))&
(![X]:((~brave(X)|~curious(X))<=>generous(X)))&
((?[X]:(creative(X)))<=>((generous(mary)&~wise(mary))))&
(![X]:((~kind(X)&~funny(X))<=>(~rich(X)|kind(X))))&
(![X]:(~creative(X)=>(~humble(X)<~>~patient(X))))&
(((~patient(susan)<~>~brave(susan)))=>((~tall(john)&~happy(john))))&
(![X]:((funny(X)|calm(X))=>(happy(X)|creative(X))))&
(![X]:((old(X)&~strong(X))=>(strong(X)<~>wise(X))))&
((tall(alice))<=>(~quiet(fred)))&
((?[X]:((~funny(X)<~>~creative(X))))<=>(?[X]:((calm(X)|~strong(X)))))&
(![X]:((old(X)<~>tall(X))<=>(brave(X)&creative(X))))&
(![X]:((~funny(X)&~calm(X))<=>(~kind(X)|funny(X))))&
(![X]:((~rich(X)<~>~curious(X))<=>(~generous(X)<~>~strong(X))))&
((?[X]:((brave(X)<~>patient(X))))<=>(?[X]:((strong(X)<~>humble(X)))))&
(((funny(paul)&~rich(paul)))=>(?[X]:((~quiet(X)|rich(X)))))&
(?[X]:((~humble(X)&generous(X))))&
(~wise(alice))&
(?[X]:(~quiet(X)))&
(?[X]:(patient(X)))&
(?[X]:((~wise(X)|wise(X))))&
(?[X]:((brave(X)&~humble(X))))&
(?[X]:((tall(X)<~>happy(X)))) | happy(fred) | [] | null | 0 |
Everyone who is not happy or not calm is either not humble or patient and vice versa.
If alice is both not rich and tall then someone is either not tall or not funny.
Everyone who is either not patient or quiet is not calm and vice versa.
Everyone who is generous or not generous is either wise or funny and vice versa.
Everyone who is both not strong and not wise is not kind.
If mary is both patient and not happy then john is both not calm and rich and vice versa.
If mary is either not rich or not humble then fred is both not patient and generous and vice versa.
If mary is either not tall or old then someone is either not brave or not kind and vice versa.
Everyone who is not generous is not patient or kind.
If mary is either creative or not old then someone is either not calm or calm and vice versa.
Everyone who is curious is quiet and vice versa.
If someone is old then susan is either not wise or not curious and vice versa.
If mary is either curious or not creative then someone is not brave and vice versa.
If fred is rich then someone is not kind or calm and vice versa.
Everyone who is not funny or not wise is both not tall and rich and vice versa.
Everyone who is not curious is not kind or not tall.
Someone is either strong or patient.
Someone is both not funny and not creative.
Someone is creative or brave.
Fred is either not kind or not rich.
Susan is both not humble and kind.
John is both funny and not old.
Fred is rich. | Susan is not kind. | contradiction | (![X]:((~happy(X)|~calm(X))<=>(~humble(X)<~>patient(X))))&
(((~rich(alice)&tall(alice)))=>(?[X]:((~tall(X)<~>~funny(X)))))&
(![X]:((~patient(X)<~>quiet(X))<=>~calm(X)))&
(![X]:((generous(X)|~generous(X))<=>(wise(X)<~>funny(X))))&
(![X]:((~strong(X)&~wise(X))=>~kind(X)))&
(((patient(mary)&~happy(mary)))<=>((~calm(john)&rich(john))))&
(((~rich(mary)<~>~humble(mary)))<=>((~patient(fred)&generous(fred))))&
(((~tall(mary)<~>old(mary)))<=>(?[X]:((~brave(X)<~>~kind(X)))))&
(![X]:(~generous(X)=>(~patient(X)|kind(X))))&
(((creative(mary)<~>~old(mary)))<=>(?[X]:((~calm(X)<~>calm(X)))))&
(![X]:(curious(X)<=>quiet(X)))&
((?[X]:(old(X)))<=>((~wise(susan)<~>~curious(susan))))&
(((curious(mary)<~>~creative(mary)))<=>(?[X]:(~brave(X))))&
((rich(fred))<=>(?[X]:((~kind(X)|calm(X)))))&
(![X]:((~funny(X)|~wise(X))<=>(~tall(X)&rich(X))))&
(![X]:(~curious(X)=>(~kind(X)|~tall(X))))&
(?[X]:((strong(X)<~>patient(X))))&
(?[X]:((~funny(X)&~creative(X))))&
(?[X]:((creative(X)|brave(X))))&
((~kind(fred)<~>~rich(fred)))&
((~humble(susan)&kind(susan)))&
((funny(john)&~old(john)))&
(rich(fred)) | ~kind(susan) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3641966047783588816623001
% SZS output start Proof for 3641966047783588816623001
21. kind(susan) & ~humble(susan) [input p20]
24. ~kind(susan) [input hypothesis]
149. kind(susan) [cnf transformation 21]
153. ~kind(susan) [cnf transformation 24]
342. $false [subsumption resolution 153,149]
% SZS output end Proof for 3641966047783588816623001
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and not creative is patient or creative and vice versa.
If someone is happy then someone is not creative or not funny and vice versa.
Everyone who is not patient is not generous and vice versa.
Everyone who is not creative is either not humble or creative and vice versa.
Everyone who is both not happy and rich is both patient and not humble and vice versa.
If someone is either quiet or not humble then someone is rich.
Everyone who is brave or not creative is strong and vice versa.
If someone is creative or strong then someone is quiet or not happy and vice versa.
If fred is both calm and not kind then susan is both rich and not rich and vice versa.
Everyone who is not quiet is quiet.
Everyone who is either not happy or tall is both tall and wise.
If john is not calm or wise then someone is patient or not rich.
If paul is either old or kind then susan is either not old or quiet and vice versa.
Everyone who is both not kind and not wise is rich.
If alice is either kind or wise then fred is both not rich and kind and vice versa.
Fred is both wise and not calm.
Someone is curious or not calm.
Someone is either tall or creative.
Someone is either calm or not brave.
Someone is not curious or quiet.
Someone is funny or humble.
Alice is both kind and not brave. | Paul is not creative. | entailment | (![X]:((calm(X)&~creative(X))<=>(patient(X)|creative(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~creative(X)|~funny(X)))))&
(![X]:(~patient(X)<=>~generous(X)))&
(![X]:(~creative(X)<=>(~humble(X)<~>creative(X))))&
(![X]:((~happy(X)&rich(X))<=>(patient(X)&~humble(X))))&
((?[X]:((quiet(X)<~>~humble(X))))=>(?[X]:(rich(X))))&
(![X]:((brave(X)|~creative(X))<=>strong(X)))&
((?[X]:((creative(X)|strong(X))))<=>(?[X]:((quiet(X)|~happy(X)))))&
(((calm(fred)&~kind(fred)))<=>((rich(susan)&~rich(susan))))&
(![X]:(~quiet(X)=>quiet(X)))&
(![X]:((~happy(X)<~>tall(X))=>(tall(X)&wise(X))))&
(((~calm(john)|wise(john)))=>(?[X]:((patient(X)|~rich(X)))))&
(((old(paul)<~>kind(paul)))<=>((~old(susan)<~>quiet(susan))))&
(![X]:((~kind(X)&~wise(X))=>rich(X)))&
(((kind(alice)<~>wise(alice)))<=>((~rich(fred)&kind(fred))))&
((wise(fred)&~calm(fred)))&
(?[X]:((curious(X)|~calm(X))))&
(?[X]:((tall(X)<~>creative(X))))&
(?[X]:((calm(X)<~>~brave(X))))&
(?[X]:((~curious(X)|quiet(X))))&
(?[X]:((funny(X)|humble(X))))&
((kind(alice)&~brave(alice))) | ~creative(paul) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 5457157819825553280545727
% SZS output start Proof for 5457157819825553280545727
1. ! [X0] : ((~creative(X0) & calm(X0)) <=> (creative(X0) | patient(X0))) [input p0]
23. creative(paul) [input hypothesis]
33. ! [X0] : (((~creative(X0) & calm(X0)) | (~creative(X0) & ~patient(X0))) & ((creative(X0) | patient(X0)) | (creative(X0) | ~calm(X0)))) [nnf transformation 1]
34. ! [X0] : (((~creative(X0) & calm(X0)) | (~creative(X0) & ~patient(X0))) & (creative(X0) | patient(X0) | creative(X0) | ~calm(X0))) [flattening 33]
79. ~creative(X0) | ~creative(X0) [cnf transformation 34]
139. creative(paul) [cnf transformation 23]
145. ~creative(X0) [duplicate literal removal 79]
287. $false [subsumption resolution 139,145]
% SZS output end Proof for 5457157819825553280545727
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and tall is both not funny and not generous.
If someone is happy or not funny then john is wise or not funny.
Everyone who is not patient or not generous is both not curious and brave.
Everyone who is strong is either quiet or not funny and vice versa.
Everyone who is not wise or curious is kind or humble and vice versa.
If susan is tall then john is either not calm or not old and vice versa.
If john is happy then paul is both not patient and not rich.
Everyone who is strong is both funny and not happy and vice versa.
If someone is both not happy and not wise then mary is both not quiet and not tall.
If someone is both not curious and not patient then someone is quiet or not brave and vice versa.
Everyone who is not strong or humble is both not quiet and not brave and vice versa.
Everyone who is both patient and not rich is both not old and not brave and vice versa.
Everyone who is patient or quiet is both wise and rich and vice versa.
If mary is both tall and not quiet then someone is either kind or old.
If someone is not tall or tall then someone is not brave.
Everyone who is either curious or not quiet is both not brave and humble.
Someone is not old.
Someone is both not brave and strong.
John is either not creative or not happy.
Lucy is both not humble and not tall.
Paul is quiet or not wise.
Mary is both not old and quiet. | Susan is not generous. | neutral | (![X]:((quiet(X)&tall(X))=>(~funny(X)&~generous(X))))&
((?[X]:((happy(X)|~funny(X))))=>((wise(john)|~funny(john))))&
(![X]:((~patient(X)|~generous(X))=>(~curious(X)&brave(X))))&
(![X]:(strong(X)<=>(quiet(X)<~>~funny(X))))&
(![X]:((~wise(X)|curious(X))<=>(kind(X)|humble(X))))&
((tall(susan))<=>((~calm(john)<~>~old(john))))&
((happy(john))=>((~patient(paul)&~rich(paul))))&
(![X]:(strong(X)<=>(funny(X)&~happy(X))))&
((?[X]:((~happy(X)&~wise(X))))=>((~quiet(mary)&~tall(mary))))&
((?[X]:((~curious(X)&~patient(X))))<=>(?[X]:((quiet(X)|~brave(X)))))&
(![X]:((~strong(X)|humble(X))<=>(~quiet(X)&~brave(X))))&
(![X]:((patient(X)&~rich(X))<=>(~old(X)&~brave(X))))&
(![X]:((patient(X)|quiet(X))<=>(wise(X)&rich(X))))&
(((tall(mary)&~quiet(mary)))=>(?[X]:((kind(X)<~>old(X)))))&
((?[X]:((~tall(X)|tall(X))))=>(?[X]:(~brave(X))))&
(![X]:((curious(X)<~>~quiet(X))=>(~brave(X)&humble(X))))&
(?[X]:(~old(X)))&
(?[X]:((~brave(X)&strong(X))))&
((~creative(john)<~>~happy(john)))&
((~humble(lucy)&~tall(lucy)))&
((quiet(paul)|~wise(paul)))&
((~old(mary)&quiet(mary))) | ~generous(susan) | [] | null | 0 |
If alice is brave then fred is both old and brave.
Everyone who is not kind is happy.
Everyone who is not calm is either patient or not strong and vice versa.
Everyone who is both not kind and generous is not quiet or rich and vice versa.
If mary is either calm or rich then john is both not kind and rich and vice versa.
If mary is not rich then susan is both not quiet and tall.
Everyone who is not quiet is both tall and old.
If someone is either funny or not tall then someone is not creative or not rich and vice versa.
Everyone who is either quiet or not calm is both not strong and not quiet and vice versa.
Everyone who is wise or calm is not funny and vice versa.
If someone is both humble and not patient then john is both quiet and creative and vice versa.
If someone is not brave or not patient then alice is rich or humble.
If mary is both humble and not patient then lucy is old or not tall and vice versa.
If lucy is both not quiet and not creative then paul is either calm or brave and vice versa.
Everyone who is both curious and not strong is either not wise or curious.
Everyone who is either not calm or not generous is not brave or not rich and vice versa.
Someone is rich.
Susan is not strong.
Someone is funny.
Someone is not humble.
Lucy is generous.
John is either not curious or not quiet. | Fred is not humble. | neutral | ((brave(alice))=>((old(fred)&brave(fred))))&
(![X]:(~kind(X)=>happy(X)))&
(![X]:(~calm(X)<=>(patient(X)<~>~strong(X))))&
(![X]:((~kind(X)&generous(X))<=>(~quiet(X)|rich(X))))&
(((calm(mary)<~>rich(mary)))<=>((~kind(john)&rich(john))))&
((~rich(mary))=>((~quiet(susan)&tall(susan))))&
(![X]:(~quiet(X)=>(tall(X)&old(X))))&
((?[X]:((funny(X)<~>~tall(X))))<=>(?[X]:((~creative(X)|~rich(X)))))&
(![X]:((quiet(X)<~>~calm(X))<=>(~strong(X)&~quiet(X))))&
(![X]:((wise(X)|calm(X))<=>~funny(X)))&
((?[X]:((humble(X)&~patient(X))))<=>((quiet(john)&creative(john))))&
((?[X]:((~brave(X)|~patient(X))))=>((rich(alice)|humble(alice))))&
(((humble(mary)&~patient(mary)))<=>((old(lucy)|~tall(lucy))))&
(((~quiet(lucy)&~creative(lucy)))<=>((calm(paul)<~>brave(paul))))&
(![X]:((curious(X)&~strong(X))=>(~wise(X)<~>curious(X))))&
(![X]:((~calm(X)<~>~generous(X))<=>(~brave(X)|~rich(X))))&
(?[X]:(rich(X)))&
(~strong(susan))&
(?[X]:(funny(X)))&
(?[X]:(~humble(X)))&
(generous(lucy))&
((~curious(john)<~>~quiet(john))) | ~humble(fred) | [] | null | 0 |
Everyone who is both not funny and not patient is either funny or old and vice versa. Everyone who is both brave and not brave is either not humble or not old and vice versa. Everyone who is both creative and not curious is kind. If mary is either not humble or wise then susan is either not creative or not funny and vice versa. Everyone who is not creative or not curious is both not patient and patient. Everyone who is both not generous and not patient is not tall. Everyone who is both happy and rich is either not quiet or patient. If someone is either calm or not kind then paul is not strong and vice versa. If someone is not calm or curious then lucy is kind. Everyone who is not tall or not rich is both tall and not happy. Everyone who is both creative and not strong is old. Everyone who is either not strong or tall is not wise or not humble. Everyone who is not rich or creative is either not wise or not curious and vice versa. Everyone who is both quiet and creative is both not calm and not rich. If alice is not brave then someone is not rich. Everyone who is not calm is brave or not brave and vice versa. Paul is either not strong or not wise. Someone is not creative or not quiet. Lucy is rich. Someone is funny or not funny. Someone is funny. | Paul is not tall. | contradiction | (![X]:((~funny(X)&~patient(X))<=>(funny(X)<~>old(X))))&
(![X]:((brave(X)&~brave(X))<=>(~humble(X)<~>~old(X))))&
(![X]:((creative(X)&~curious(X))=>kind(X)))&
(((~humble(mary)<~>wise(mary)))<=>((~creative(susan)<~>~funny(susan))))&
(![X]:((~creative(X)|~curious(X))=>(~patient(X)&patient(X))))&
(![X]:((~generous(X)&~patient(X))=>~tall(X)))&
(![X]:((happy(X)&rich(X))=>(~quiet(X)<~>patient(X))))&
((?[X]:((calm(X)<~>~kind(X))))<=>(~strong(paul)))&
((?[X]:((~calm(X)|curious(X))))=>(kind(lucy)))&
(![X]:((~tall(X)|~rich(X))=>(tall(X)&~happy(X))))&
(![X]:((creative(X)&~strong(X))=>old(X)))&
(![X]:((~strong(X)<~>tall(X))=>(~wise(X)|~humble(X))))&
(![X]:((~rich(X)|creative(X))<=>(~wise(X)<~>~curious(X))))&
(![X]:((quiet(X)&creative(X))=>(~calm(X)&~rich(X))))&
((~brave(alice))=>(?[X]:(~rich(X))))&
(![X]:(~calm(X)<=>(brave(X)|~brave(X))))&
((~strong(paul)<~>~wise(paul)))&
(?[X]:((~creative(X)|~quiet(X))))&
(rich(lucy))&
(?[X]:((funny(X)|~funny(X))))&
(?[X]:(funny(X))) | ~tall(paul) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3573276707497596309696500
% SZS output start Proof for 3573276707497596309696500
10. ! [X0] : ((~rich(X0) | ~tall(X0)) => (~happy(X0) & tall(X0))) [input p9]
22. ~tall(paul) [input hypothesis]
23. ! [X0] : ((~rich(X0) | ~tall(X0)) => tall(X0)) [pure predicate removal 10]
32. ! [X0] : (tall(X0) | (rich(X0) & tall(X0))) [ennf transformation 23]
90. tall(X0) | tall(X0) [cnf transformation 32]
110. ~tall(paul) [cnf transformation 22]
111. tall(X0) [duplicate literal removal 90]
182. $false [subsumption resolution 110,111]
% SZS output end Proof for 3573276707497596309696500
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not curious is not happy or not tall and vice versa. Everyone who is calm is not creative or strong and vice versa. Everyone who is both creative and brave is tall or not old and vice versa. Everyone who is both not generous and not funny is rich or not wise. Everyone who is kind or humble is not wise and vice versa. Everyone who is either not creative or not strong is strong and vice versa. If john is not calm then someone is tall or not patient. If someone is both not curious and not wise then someone is either not tall or not strong and vice versa. Everyone who is not funny or not curious is not strong or old and vice versa. If someone is happy then someone is either not patient or kind and vice versa. Everyone who is generous or brave is both happy and not strong. Everyone who is wise is patient and vice versa. Everyone who is rich or not old is both creative and curious and vice versa. Someone is both not humble and old. John is both generous and old. Lucy is not creative. Someone is not rich or brave. John is not wise or generous. Fred is both not creative and not strong. | John is not funny. | neutral | (![X]:((~brave(X)<~>~curious(X))<=>(~happy(X)|~tall(X))))&
(![X]:(calm(X)<=>(~creative(X)|strong(X))))&
(![X]:((creative(X)&brave(X))<=>(tall(X)|~old(X))))&
(![X]:((~generous(X)&~funny(X))=>(rich(X)|~wise(X))))&
(![X]:((kind(X)|humble(X))<=>~wise(X)))&
(![X]:((~creative(X)<~>~strong(X))<=>strong(X)))&
((~calm(john))=>(?[X]:((tall(X)|~patient(X)))))&
((?[X]:((~curious(X)&~wise(X))))<=>(?[X]:((~tall(X)<~>~strong(X)))))&
(![X]:((~funny(X)|~curious(X))<=>(~strong(X)|old(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~patient(X)<~>kind(X)))))&
(![X]:((generous(X)|brave(X))=>(happy(X)&~strong(X))))&
(![X]:(wise(X)<=>patient(X)))&
(![X]:((rich(X)|~old(X))<=>(creative(X)&curious(X))))&
(?[X]:((~humble(X)&old(X))))&
((generous(john)&old(john)))&
(~creative(lucy))&
(?[X]:((~rich(X)|brave(X))))&
((~wise(john)|generous(john)))&
((~creative(fred)&~strong(fred))) | ~funny(john) | [] | null | 0 |
Everyone who is either tall or not strong is not creative.
Everyone who is not generous or wise is patient or brave.
If alice is not kind or not creative then lucy is either not old or rich and vice versa.
If someone is patient then someone is calm.
Everyone who is either happy or not rich is creative or not wise and vice versa.
Everyone who is both not funny and brave is either not humble or curious.
Everyone who is either not happy or not quiet is strong or kind and vice versa.
Everyone who is both not wise and rich is both brave and not funny.
If someone is either not patient or tall then someone is kind and vice versa.
Everyone who is not rich is not happy.
Everyone who is not strong or strong is both creative and curious and vice versa.
Everyone who is happy is not creative and vice versa.
Everyone who is both calm and not kind is not wise.
Everyone who is either not calm or quiet is either not happy or quiet.
If susan is creative or not rich then fred is either not patient or not happy.
Everyone who is brave is either kind or brave and vice versa.
Fred is both not kind and curious.
Paul is either not funny or not strong.
Someone is humble or not old.
Someone is not strong.
Susan is not strong or wise.
Lucy is not humble or not happy. | Fred is calm. | contradiction | (![X]:((tall(X)<~>~strong(X))=>~creative(X)))&
(![X]:((~generous(X)|wise(X))=>(patient(X)|brave(X))))&
(((~kind(alice)|~creative(alice)))<=>((~old(lucy)<~>rich(lucy))))&
((?[X]:(patient(X)))=>(?[X]:(calm(X))))&
(![X]:((happy(X)<~>~rich(X))<=>(creative(X)|~wise(X))))&
(![X]:((~funny(X)&brave(X))=>(~humble(X)<~>curious(X))))&
(![X]:((~happy(X)<~>~quiet(X))<=>(strong(X)|kind(X))))&
(![X]:((~wise(X)&rich(X))=>(brave(X)&~funny(X))))&
((?[X]:((~patient(X)<~>tall(X))))<=>(?[X]:(kind(X))))&
(![X]:(~rich(X)=>~happy(X)))&
(![X]:((~strong(X)|strong(X))<=>(creative(X)&curious(X))))&
(![X]:(happy(X)<=>~creative(X)))&
(![X]:((calm(X)&~kind(X))=>~wise(X)))&
(![X]:((~calm(X)<~>quiet(X))=>(~happy(X)<~>quiet(X))))&
(((creative(susan)|~rich(susan)))=>((~patient(fred)<~>~happy(fred))))&
(![X]:(brave(X)<=>(kind(X)<~>brave(X))))&
((~kind(fred)&curious(fred)))&
((~funny(paul)<~>~strong(paul)))&
(?[X]:((humble(X)|~old(X))))&
(?[X]:(~strong(X)))&
((~strong(susan)|wise(susan)))&
((~humble(lucy)|~happy(lucy))) | calm(fred) | [
"p0",
"p6",
"p8",
"p10",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4447941837155124267499107
% SZS output start Proof for 4447941837155124267499107
1. ! [X0] : ((tall(X0) <~> ~strong(X0)) => ~creative(X0)) [input p0]
7. ! [X0] : ((~happy(X0) <~> ~quiet(X0)) <=> (kind(X0) | strong(X0))) [input p6]
9. ? [X0] : (~patient(X0) <~> tall(X0)) <=> ? [X0] : kind(X0) [input p8]
11. ! [X0] : ((strong(X0) | ~strong(X0)) <=> (curious(X0) & creative(X0))) [input p10]
12. ! [X0] : (happy(X0) <=> ~creative(X0)) [input p11]
14. ! [X0] : ((~calm(X0) <~> quiet(X0)) => (~happy(X0) <~> quiet(X0))) [input p13]
15. (~rich(susan) | creative(susan)) => (~patient(fred) <~> ~happy(fred)) [input p14]
16. ! [X0] : (brave(X0) <=> (kind(X0) <~> brave(X0))) [input p15]
23. calm(fred) [input hypothesis]
25. ? [X0] : (~patient(X0) <~> tall(X0)) <=> ? [X1] : kind(X1) [rectify 9]
27. ! [X0] : (~creative(X0) | (tall(X0) <=> ~strong(X0))) [ennf transformation 1]
38. ! [X0] : ((~happy(X0) <~> quiet(X0)) | (~calm(X0) <=> quiet(X0))) [ennf transformation 14]
39. (~patient(fred) <~> ~happy(fred)) | (rich(susan) & ~creative(susan)) [ennf transformation 15]
40. ! [X0] : (~creative(X0) | ((tall(X0) | strong(X0)) & (~strong(X0) | ~tall(X0)))) [nnf transformation 27]
49. ! [X0] : ((((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | (~kind(X0) & ~strong(X0))) & ((kind(X0) | strong(X0)) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0))))) [nnf transformation 7]
50. ! [X0] : ((((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | (~kind(X0) & ~strong(X0))) & (kind(X0) | strong(X0) | ((~happy(X0) | quiet(X0)) & (~quiet(X0) | happy(X0))))) [flattening 49]
51. (? [X0] : ((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | ! [X1] : ~kind(X1)) & (? [X1] : kind(X1) | ! [X0] : ((~patient(X0) | ~tall(X0)) & (tall(X0) | patient(X0)))) [nnf transformation 25]
52. (? [X0] : ((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | ! [X1] : ~kind(X1)) & (? [X2] : kind(X2) | ! [X3] : ((~patient(X3) | ~tall(X3)) & (tall(X3) | patient(X3)))) [rectify 51]
53. ? [X0] : ((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) => ((~tall(sK1) | patient(sK1)) & (tall(sK1) | ~patient(sK1))) [choice axiom]
54. ? [X2] : kind(X2) => kind(sK2) [choice axiom]
55. (((~tall(sK1) | patient(sK1)) & (tall(sK1) | ~patient(sK1))) | ! [X1] : ~kind(X1)) & (kind(sK2) | ! [X3] : ((~patient(X3) | ~tall(X3)) & (tall(X3) | patient(X3)))) [skolemisation 52,54,53]
56. ! [X0] : (((strong(X0) | ~strong(X0)) | (~curious(X0) | ~creative(X0))) & ((curious(X0) & creative(X0)) | (~strong(X0) & strong(X0)))) [nnf transformation 11]
57. ! [X0] : ((strong(X0) | ~strong(X0) | ~curious(X0) | ~creative(X0)) & ((curious(X0) & creative(X0)) | (~strong(X0) & strong(X0)))) [flattening 56]
58. ! [X0] : ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0))) [nnf transformation 12]
59. ! [X0] : (((~quiet(X0) | happy(X0)) & (quiet(X0) | ~happy(X0))) | ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0)))) [nnf transformation 38]
60. ((happy(fred) | patient(fred)) & (~happy(fred) | ~patient(fred))) | (rich(susan) & ~creative(susan)) [nnf transformation 39]
61. ! [X0] : ((brave(X0) | ((kind(X0) | ~brave(X0)) & (brave(X0) | ~kind(X0)))) & (((~brave(X0) | ~kind(X0)) & (brave(X0) | kind(X0))) | ~brave(X0))) [nnf transformation 16]
68. ~creative(X0) | tall(X0) | strong(X0) [cnf transformation 40]
89. ~strong(X0) | happy(X0) | quiet(X0) [cnf transformation 50]
94. kind(sK2) | ~patient(X3) | ~tall(X3) [cnf transformation 55]
98. creative(X0) | strong(X0) [cnf transformation 57]
99. ~strong(X0) | creative(X0) [cnf transformation 57]
103. ~creative(X0) | ~happy(X0) [cnf transformation 58]
109. ~quiet(X0) | happy(X0) | ~calm(X0) | ~quiet(X0) [cnf transformation 59]
112. happy(fred) | patient(fred) | ~creative(susan) [cnf transformation 60]
115. ~brave(X0) | ~kind(X0) | ~brave(X0) [cnf transformation 61]
116. brave(X0) | brave(X0) | ~kind(X0) [cnf transformation 61]
126. calm(fred) [cnf transformation 23]
127. ~brave(X0) | ~kind(X0) [duplicate literal removal 115]
128. ~kind(X0) | brave(X0) [duplicate literal removal 116]
130. ~quiet(X0) | happy(X0) | ~calm(X0) [duplicate literal removal 109]
162. 7 <=> ! [X1] : ~kind(X1) [avatar definition]
163. ~kind(X1) <- (7) [avatar component clause 162]
175. 10 <=> ! [X3] : (~patient(X3) | ~tall(X3)) [avatar definition]
176. ~patient(X3) | ~tall(X3) <- (10) [avatar component clause 175]
178. 11 <=> kind(sK2) [avatar definition]
180. kind(sK2) <- (11) [avatar component clause 178]
181. 10 | 11 [avatar split clause 94,178,175]
187. creative(X0) [subsumption resolution 98,99]
188. ~happy(X0) [subsumption resolution 103,187]
189. ~quiet(X0) | ~calm(X0) [subsumption resolution 130,188]
196. 14 <=> patient(fred) [avatar definition]
198. patient(fred) <- (14) [avatar component clause 196]
200. patient(fred) | ~creative(susan) [subsumption resolution 112,188]
201. patient(fred) [subsumption resolution 200,187]
202. 14 [avatar split clause 201,196]
203. ~kind(X0) [subsumption resolution 127,128]
204. 7 [avatar split clause 203,162]
233. $false <- (7, 11) [resolution 180,163]
234. ~7 | ~11 [avatar contradiction clause 233]
238. ~tall(fred) <- (10, 14) [resolution 176,198]
241. strong(X0) | tall(X0) [resolution 68,187]
248. happy(X0) | quiet(X0) | tall(X0) [resolution 89,241]
249. quiet(X0) | tall(X0) [subsumption resolution 248,188]
252. ~calm(X2) | tall(X2) [resolution 249,189]
253. tall(fred) [resolution 252,126]
255. $false <- (10, 14) [subsumption resolution 253,238]
256. ~10 | ~14 [avatar contradiction clause 255]
257. $false [avatar sat refutation 181,202,204,234,256]
% SZS output end Proof for 4447941837155124267499107
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not tall is both not brave and creative and vice versa.
Everyone who is tall or not brave is both wise and not old and vice versa.
Everyone who is both curious and calm is creative and vice versa.
If john is not happy or not patient then someone is kind.
If someone is both funny and not funny then someone is patient and vice versa.
Everyone who is generous or quiet is tall or not happy.
Everyone who is not calm is either rich or not quiet and vice versa.
Everyone who is creative is either rich or creative and vice versa.
If someone is both not generous and not kind then someone is either not funny or not generous.
If mary is old then someone is strong or humble.
Everyone who is either not old or quiet is not creative.
Everyone who is either not strong or old is not wise or calm.
Everyone who is old or not strong is not happy or not funny and vice versa.
If someone is both strong and not brave then lucy is both old and not curious.
If someone is patient then someone is generous.
Everyone who is not strong is not tall and vice versa.
Susan is both not rich and not funny.
Fred is brave or humble.
Lucy is funny.
Someone is both not generous and curious.
Alice is strong or not creative.
Someone is not happy or not wise.
John is generous. | Mary is not wise. | contradiction | (![X]:((patient(X)<~>~tall(X))<=>(~brave(X)&creative(X))))&
(![X]:((tall(X)|~brave(X))<=>(wise(X)&~old(X))))&
(![X]:((curious(X)&calm(X))<=>creative(X)))&
(((~happy(john)|~patient(john)))=>(?[X]:(kind(X))))&
((?[X]:((funny(X)&~funny(X))))<=>(?[X]:(patient(X))))&
(![X]:((generous(X)|quiet(X))=>(tall(X)|~happy(X))))&
(![X]:(~calm(X)<=>(rich(X)<~>~quiet(X))))&
(![X]:(creative(X)<=>(rich(X)<~>creative(X))))&
((?[X]:((~generous(X)&~kind(X))))=>(?[X]:((~funny(X)<~>~generous(X)))))&
((old(mary))=>(?[X]:((strong(X)|humble(X)))))&
(![X]:((~old(X)<~>quiet(X))=>~creative(X)))&
(![X]:((~strong(X)<~>old(X))=>(~wise(X)|calm(X))))&
(![X]:((old(X)|~strong(X))<=>(~happy(X)|~funny(X))))&
((?[X]:((strong(X)&~brave(X))))=>((old(lucy)&~curious(lucy))))&
((?[X]:(patient(X)))=>(?[X]:(generous(X))))&
(![X]:(~strong(X)<=>~tall(X)))&
((~rich(susan)&~funny(susan)))&
((brave(fred)|humble(fred)))&
(funny(lucy))&
(?[X]:((~generous(X)&curious(X))))&
((strong(alice)|~creative(alice)))&
(?[X]:((~happy(X)|~wise(X))))&
(generous(john)) | ~wise(mary) | [
"p0",
"p1",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 1562986313077857246450771
% SZS output start Proof for 1562986313077857246450771
1. ! [X0] : ((patient(X0) <~> ~tall(X0)) <=> (creative(X0) & ~brave(X0))) [input p0]
2. ! [X0] : ((~brave(X0) | tall(X0)) <=> (~old(X0) & wise(X0))) [input p1]
5. ? [X0] : (~funny(X0) & funny(X0)) <=> ? [X0] : patient(X0) [input p4]
24. ~wise(mary) [input hypothesis]
25. ? [X0] : (~funny(X0) & funny(X0)) <=> ? [X1] : patient(X1) [rectify 5]
39. ! [X0] : ((((tall(X0) | ~patient(X0)) & (~tall(X0) | patient(X0))) | (~creative(X0) | brave(X0))) & ((creative(X0) & ~brave(X0)) | ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0))))) [nnf transformation 1]
40. ! [X0] : ((((tall(X0) | ~patient(X0)) & (~tall(X0) | patient(X0))) | ~creative(X0) | brave(X0)) & ((creative(X0) & ~brave(X0)) | ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0))))) [flattening 39]
41. ! [X0] : (((~brave(X0) | tall(X0)) | (old(X0) | ~wise(X0))) & ((~old(X0) & wise(X0)) | (brave(X0) & ~tall(X0)))) [nnf transformation 2]
42. ! [X0] : ((~brave(X0) | tall(X0) | old(X0) | ~wise(X0)) & ((~old(X0) & wise(X0)) | (brave(X0) & ~tall(X0)))) [flattening 41]
45. (? [X0] : (~funny(X0) & funny(X0)) | ! [X1] : ~patient(X1)) & (? [X1] : patient(X1) | ! [X0] : (funny(X0) | ~funny(X0))) [nnf transformation 25]
46. (? [X0] : (~funny(X0) & funny(X0)) | ! [X1] : ~patient(X1)) & (? [X2] : patient(X2) | ! [X3] : (funny(X3) | ~funny(X3))) [rectify 45]
47. ? [X0] : (~funny(X0) & funny(X0)) => (~funny(sK0) & funny(sK0)) [choice axiom]
48. ? [X2] : patient(X2) => patient(sK1) [choice axiom]
49. ((~funny(sK0) & funny(sK0)) | ! [X1] : ~patient(X1)) & (patient(sK1) | ! [X3] : (funny(X3) | ~funny(X3))) [skolemisation 46,48,47]
65. ~brave(X0) | patient(X0) | tall(X0) [cnf transformation 40]
70. ~tall(X0) | wise(X0) [cnf transformation 42]
71. wise(X0) | brave(X0) [cnf transformation 42]
79. funny(sK0) | ~patient(X1) [cnf transformation 49]
80. ~funny(sK0) | ~patient(X1) [cnf transformation 49]
112. ~wise(mary) [cnf transformation 24]
116. 1 <=> ! [X1] : ~patient(X1) [avatar definition]
117. ~patient(X1) <- (1) [avatar component clause 116]
119. 2 <=> funny(sK0) [avatar definition]
122. 1 | ~2 [avatar split clause 80,119,116]
123. 1 | 2 [avatar split clause 79,119,116]
161. brave(mary) [resolution 71,112]
168. patient(mary) | tall(mary) [resolution 65,161]
171. tall(mary) <- (1) [subsumption resolution 168,117]
177. wise(mary) <- (1) [resolution 171,70]
178. $false <- (1) [subsumption resolution 177,112]
179. ~1 [avatar contradiction clause 178]
180. $false [avatar sat refutation 122,123,179]
% SZS output end Proof for 1562986313077857246450771
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise then lucy is both calm and patient and vice versa.
If mary is both not brave and rich then someone is either not patient or kind and vice versa.
Everyone who is both quiet and not rich is either not creative or tall and vice versa.
If someone is quiet or not kind then susan is not funny or not humble and vice versa.
If someone is both not funny and quiet then someone is either not calm or not generous.
Everyone who is curious or not creative is old and vice versa.
Everyone who is both not generous and rich is both old and calm.
If someone is either not wise or kind then paul is either wise or calm.
Everyone who is not generous is not old and vice versa.
If someone is both not wise and not rich then susan is either brave or tall.
If someone is either not kind or not old then someone is not kind and vice versa.
If someone is humble then lucy is both old and not generous.
Everyone who is brave is happy.
Everyone who is quiet is both not curious and not old and vice versa.
If someone is brave then someone is not humble or not brave and vice versa.
If someone is not happy or not calm then paul is either rich or tall and vice versa.
Someone is not wise or not creative.
Paul is happy or not calm.
Someone is both quiet and not calm.
Susan is both not brave and not old.
Lucy is generous.
Alice is not humble.
Someone is creative. | Susan is humble. | contradiction | ((?[X]:(~wise(X)))<=>((calm(lucy)&patient(lucy))))&
(((~brave(mary)&rich(mary)))<=>(?[X]:((~patient(X)<~>kind(X)))))&
(![X]:((quiet(X)&~rich(X))<=>(~creative(X)<~>tall(X))))&
((?[X]:((quiet(X)|~kind(X))))<=>((~funny(susan)|~humble(susan))))&
((?[X]:((~funny(X)&quiet(X))))=>(?[X]:((~calm(X)<~>~generous(X)))))&
(![X]:((curious(X)|~creative(X))<=>old(X)))&
(![X]:((~generous(X)&rich(X))=>(old(X)&calm(X))))&
((?[X]:((~wise(X)<~>kind(X))))=>((wise(paul)<~>calm(paul))))&
(![X]:(~generous(X)<=>~old(X)))&
((?[X]:((~wise(X)&~rich(X))))=>((brave(susan)<~>tall(susan))))&
((?[X]:((~kind(X)<~>~old(X))))<=>(?[X]:(~kind(X))))&
((?[X]:(humble(X)))=>((old(lucy)&~generous(lucy))))&
(![X]:(brave(X)=>happy(X)))&
(![X]:(quiet(X)<=>(~curious(X)&~old(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~humble(X)|~brave(X)))))&
((?[X]:((~happy(X)|~calm(X))))<=>((rich(paul)<~>tall(paul))))&
(?[X]:((~wise(X)|~creative(X))))&
((happy(paul)|~calm(paul)))&
(?[X]:((quiet(X)&~calm(X))))&
((~brave(susan)&~old(susan)))&
(generous(lucy))&
(~humble(alice))&
(?[X]:(creative(X))) | humble(susan) | [
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6410273255647619420289337
% SZS output start Proof for 6410273255647619420289337
12. ? [X0] : humble(X0) => (~generous(lucy) & old(lucy)) [input p11]
21. generous(lucy) [input p20]
24. humble(susan) [input hypothesis]
33. (~generous(lucy) & old(lucy)) | ! [X0] : ~humble(X0) [ennf transformation 12]
122. ~generous(lucy) | ~humble(X0) [cnf transformation 33]
142. generous(lucy) [cnf transformation 21]
145. humble(susan) [cnf transformation 24]
193. 11 <=> humble(susan) [avatar definition]
195. humble(susan) <- (11) [avatar component clause 193]
285. 32 <=> ! [X0] : ~humble(X0) [avatar definition]
286. ~humble(X0) <- (32) [avatar component clause 285]
288. 33 <=> generous(lucy) [avatar definition]
291. 32 | ~33 [avatar split clause 122,288,285]
365. 33 [avatar split clause 142,288]
366. 11 [avatar split clause 145,193]
369. $false <- (11, 32) [subsumption resolution 195,286]
370. ~11 | ~32 [avatar contradiction clause 369]
373. $false [avatar sat refutation 291,365,366,370]
% SZS output end Proof for 6410273255647619420289337
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or not happy is either rich or wise and vice versa.
Everyone who is both tall and not wise is both patient and quiet.
If someone is both not happy and kind then alice is both brave and not humble.
Everyone who is not strong is kind.
Everyone who is funny or generous is both brave and generous and vice versa.
Everyone who is brave is not happy.
Everyone who is tall is brave.
If someone is generous then john is old.
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.
Everyone who is both happy and patient is both not happy and old and vice versa.
If someone is not rich then fred is wise.
Everyone who is both not quiet and not funny is either not quiet or not rich.
Everyone who is either not happy or quiet is not old.
Everyone who is both rich and patient is either kind or patient and vice versa.
If someone is curious or creative then someone is either humble or patient.
Someone is not creative.
Paul is not funny.
Alice is either wise or not kind.
Someone is not wise.
Mary is either not brave or quiet.
Paul is either not creative or not calm.
Someone is brave or humble. | John is not funny. | entailment | (![X]:((curious(X)<~>~happy(X))<=>(rich(X)<~>wise(X))))&
(![X]:((tall(X)&~wise(X))=>(patient(X)&quiet(X))))&
((?[X]:((~happy(X)&kind(X))))=>((brave(alice)&~humble(alice))))&
(![X]:(~strong(X)=>kind(X)))&
(![X]:((funny(X)|generous(X))<=>(brave(X)&generous(X))))&
(![X]:(brave(X)=>~happy(X)))&
(![X]:(tall(X)=>brave(X)))&
((?[X]:(generous(X)))=>(old(john)))&
(((humble(alice)<~>~wise(alice)))<=>(?[X]:(~kind(X))))&
(![X]:((~strong(X)<~>~kind(X))<=>(~rich(X)|~strong(X))))&
(![X]:((happy(X)&patient(X))<=>(~happy(X)&old(X))))&
((?[X]:(~rich(X)))=>(wise(fred)))&
(![X]:((~quiet(X)&~funny(X))=>(~quiet(X)<~>~rich(X))))&
(![X]:((~happy(X)<~>quiet(X))=>~old(X)))&
(![X]:((rich(X)&patient(X))<=>(kind(X)<~>patient(X))))&
((?[X]:((curious(X)|creative(X))))=>(?[X]:((humble(X)<~>patient(X)))))&
(?[X]:(~creative(X)))&
(~funny(paul))&
((wise(alice)<~>~kind(alice)))&
(?[X]:(~wise(X)))&
((~brave(mary)<~>quiet(mary)))&
((~creative(paul)<~>~calm(paul)))&
(?[X]:((brave(X)|humble(X)))) | ~funny(john) | [
"p4",
"p5",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6514947540706417503831879
% SZS output start Proof for 6514947540706417503831879
5. ! [X0] : ((generous(X0) | funny(X0)) <=> (generous(X0) & brave(X0))) [input p4]
6. ! [X0] : (brave(X0) => ~happy(X0)) [input p5]
8. ? [X0] : generous(X0) => old(john) [input p7]
11. ! [X0] : ((patient(X0) & happy(X0)) <=> (old(X0) & ~happy(X0))) [input p10]
24. funny(john) [input hypothesis]
30. ! [X0] : (~happy(X0) | ~brave(X0)) [ennf transformation 6]
31. old(john) | ! [X0] : ~generous(X0) [ennf transformation 8]
38. ! [X0] : (((generous(X0) | funny(X0)) | (~generous(X0) | ~brave(X0))) & ((generous(X0) & brave(X0)) | (~generous(X0) & ~funny(X0)))) [nnf transformation 5]
39. ! [X0] : ((generous(X0) | funny(X0) | ~generous(X0) | ~brave(X0)) & ((generous(X0) & brave(X0)) | (~generous(X0) & ~funny(X0)))) [flattening 38]
46. ! [X0] : (((patient(X0) & happy(X0)) | (~old(X0) | happy(X0))) & ((old(X0) & ~happy(X0)) | (~patient(X0) | ~happy(X0)))) [nnf transformation 11]
47. ! [X0] : (((patient(X0) & happy(X0)) | ~old(X0) | happy(X0)) & ((old(X0) & ~happy(X0)) | ~patient(X0) | ~happy(X0))) [flattening 46]
76. ~funny(X0) | brave(X0) [cnf transformation 39]
78. ~funny(X0) | generous(X0) [cnf transformation 39]
81. ~brave(X0) | ~happy(X0) [cnf transformation 30]
82. old(john) | ~generous(X0) [cnf transformation 31]
95. happy(X0) | ~old(X0) | happy(X0) [cnf transformation 47]
122. funny(john) [cnf transformation 24]
127. ~old(X0) | happy(X0) [duplicate literal removal 95]
144. 4 <=> ! [X0] : ~generous(X0) [avatar definition]
145. ~generous(X0) <- (4) [avatar component clause 144]
147. 5 <=> old(john) [avatar definition]
149. old(john) <- (5) [avatar component clause 147]
150. 4 | 5 [avatar split clause 82,147,144]
231. brave(john) [resolution 76,122]
232. generous(john) [resolution 78,122]
233. $false <- (4) [subsumption resolution 232,145]
234. ~4 [avatar contradiction clause 233]
238. ~happy(john) [resolution 81,231]
239. happy(john) <- (5) [resolution 127,149]
240. $false <- (5) [subsumption resolution 239,238]
241. ~5 [avatar contradiction clause 240]
242. $false [avatar sat refutation 150,234,241]
% SZS output end Proof for 6514947540706417503831879
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is both wise and brave.
If someone is not wise or not funny then john is either not quiet or funny and vice versa.
Everyone who is not happy is not strong.
Everyone who is creative or not generous is not funny or not curious.
Everyone who is creative is creative or not generous and vice versa.
Everyone who is funny is not tall and vice versa.
Everyone who is not calm or curious is not brave and vice versa.
If someone is generous then fred is either not happy or not creative and vice versa.
If someone is patient then alice is both strong and not generous and vice versa.
Everyone who is either humble or not patient is funny or curious and vice versa.
Everyone who is not quiet is both not old and tall.
Everyone who is kind is generous and vice versa.
Everyone who is both generous and not creative is both strong and generous.
If fred is both funny and quiet then john is both not kind and not curious.
Everyone who is strong is not humble or tall and vice versa.
If mary is not humble or not generous then someone is not calm or not strong.
Paul is both not curious and not strong.
Someone is either not strong or not humble.
Someone is either not brave or funny.
Someone is not brave.
Fred is both strong and not creative.
John is calm or generous. | Paul is happy. | neutral | (![X]:(calm(X)=>(wise(X)&brave(X))))&
((?[X]:((~wise(X)|~funny(X))))<=>((~quiet(john)<~>funny(john))))&
(![X]:(~happy(X)=>~strong(X)))&
(![X]:((creative(X)|~generous(X))=>(~funny(X)|~curious(X))))&
(![X]:(creative(X)<=>(creative(X)|~generous(X))))&
(![X]:(funny(X)<=>~tall(X)))&
(![X]:((~calm(X)|curious(X))<=>~brave(X)))&
((?[X]:(generous(X)))<=>((~happy(fred)<~>~creative(fred))))&
((?[X]:(patient(X)))<=>((strong(alice)&~generous(alice))))&
(![X]:((humble(X)<~>~patient(X))<=>(funny(X)|curious(X))))&
(![X]:(~quiet(X)=>(~old(X)&tall(X))))&
(![X]:(kind(X)<=>generous(X)))&
(![X]:((generous(X)&~creative(X))=>(strong(X)&generous(X))))&
(((funny(fred)&quiet(fred)))=>((~kind(john)&~curious(john))))&
(![X]:(strong(X)<=>(~humble(X)|tall(X))))&
(((~humble(mary)|~generous(mary)))=>(?[X]:((~calm(X)|~strong(X)))))&
((~curious(paul)&~strong(paul)))&
(?[X]:((~strong(X)<~>~humble(X))))&
(?[X]:((~brave(X)<~>funny(X))))&
(?[X]:(~brave(X)))&
((strong(fred)&~creative(fred)))&
((calm(john)|generous(john))) | happy(paul) | [] | null | 0 |
Everyone who is old is quiet.
If susan is not kind then someone is both happy and not rich.
Everyone who is either funny or kind is creative or not strong and vice versa.
Everyone who is both tall and not kind is curious.
If john is either not brave or rich then someone is not rich or patient.
Everyone who is wise or not patient is both curious and humble.
Everyone who is generous or not quiet is both not patient and wise.
If lucy is funny or not creative then someone is either not curious or not brave and vice versa.
Everyone who is either creative or rich is not funny or old and vice versa.
Everyone who is either not tall or not kind is both not strong and not patient and vice versa.
If susan is both curious and generous then someone is curious and vice versa.
Everyone who is both generous and not humble is not strong and vice versa.
Everyone who is either creative or old is both tall and humble and vice versa.
Everyone who is either strong or creative is both generous and curious.
If someone is not tall then fred is not wise or not rich and vice versa.
Everyone who is not strong is patient or happy and vice versa.
Fred is either not happy or not rich.
Someone is not happy or happy.
Someone is either brave or kind.
Mary is either brave or not generous.
Susan is either not quiet or not old.
Someone is either creative or strong.
Mary is either not patient or not wise.
Someone is not funny or kind. | Fred is wise. | entailment | (![X]:(old(X)=>quiet(X)))&
((~kind(susan))=>(?[X]:((happy(X)&~rich(X)))))&
(![X]:((funny(X)<~>kind(X))<=>(creative(X)|~strong(X))))&
(![X]:((tall(X)&~kind(X))=>curious(X)))&
(((~brave(john)<~>rich(john)))=>(?[X]:((~rich(X)|patient(X)))))&
(![X]:((wise(X)|~patient(X))=>(curious(X)&humble(X))))&
(![X]:((generous(X)|~quiet(X))=>(~patient(X)&wise(X))))&
(((funny(lucy)|~creative(lucy)))<=>(?[X]:((~curious(X)<~>~brave(X)))))&
(![X]:((creative(X)<~>rich(X))<=>(~funny(X)|old(X))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~strong(X)&~patient(X))))&
(((curious(susan)&generous(susan)))<=>(?[X]:(curious(X))))&
(![X]:((generous(X)&~humble(X))<=>~strong(X)))&
(![X]:((creative(X)<~>old(X))<=>(tall(X)&humble(X))))&
(![X]:((strong(X)<~>creative(X))=>(generous(X)&curious(X))))&
((?[X]:(~tall(X)))<=>((~wise(fred)|~rich(fred))))&
(![X]:(~strong(X)<=>(patient(X)|happy(X))))&
((~happy(fred)<~>~rich(fred)))&
(?[X]:((~happy(X)|happy(X))))&
(?[X]:((brave(X)<~>kind(X))))&
((brave(mary)<~>~generous(mary)))&
((~quiet(susan)<~>~old(susan)))&
(?[X]:((creative(X)<~>strong(X))))&
((~patient(mary)<~>~wise(mary)))&
(?[X]:((~funny(X)|kind(X)))) | wise(fred) | [
"p2",
"p5",
"p6",
"p8",
"p9",
"p11",
"p12",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 476746977782447436550449
% SZS output start Proof for 476746977782447436550449
3. ! [X0] : ((funny(X0) <~> kind(X0)) <=> (~strong(X0) | creative(X0))) [input p2]
6. ! [X0] : ((~patient(X0) | wise(X0)) => (humble(X0) & curious(X0))) [input p5]
7. ! [X0] : ((~quiet(X0) | generous(X0)) => (wise(X0) & ~patient(X0))) [input p6]
9. ! [X0] : ((creative(X0) <~> rich(X0)) <=> (old(X0) | ~funny(X0))) [input p8]
10. ! [X0] : ((~tall(X0) <~> ~kind(X0)) <=> (~patient(X0) & ~strong(X0))) [input p9]
12. ! [X0] : ((~humble(X0) & generous(X0)) <=> ~strong(X0)) [input p11]
13. ! [X0] : ((creative(X0) <~> old(X0)) <=> (humble(X0) & tall(X0))) [input p12]
14. ! [X0] : ((strong(X0) <~> creative(X0)) => (curious(X0) & generous(X0))) [input p13]
16. ! [X0] : (~strong(X0) <=> (happy(X0) | patient(X0))) [input p15]
17. ~happy(fred) <~> ~rich(fred) [input p16]
25. ~wise(fred) [input hypothesis]
31. ! [X0] : ((humble(X0) & curious(X0)) | (patient(X0) & ~wise(X0))) [ennf transformation 6]
32. ! [X0] : ((wise(X0) & ~patient(X0)) | (quiet(X0) & ~generous(X0))) [ennf transformation 7]
33. ! [X0] : ((curious(X0) & generous(X0)) | (strong(X0) <=> creative(X0))) [ennf transformation 14]
36. ! [X0] : ((((~kind(X0) | ~funny(X0)) & (kind(X0) | funny(X0))) | (strong(X0) & ~creative(X0))) & ((~strong(X0) | creative(X0)) | ((funny(X0) | ~kind(X0)) & (kind(X0) | ~funny(X0))))) [nnf transformation 3]
37. ! [X0] : ((((~kind(X0) | ~funny(X0)) & (kind(X0) | funny(X0))) | (strong(X0) & ~creative(X0))) & (~strong(X0) | creative(X0) | ((funny(X0) | ~kind(X0)) & (kind(X0) | ~funny(X0))))) [flattening 36]
46. ! [X0] : ((((~rich(X0) | ~creative(X0)) & (rich(X0) | creative(X0))) | (~old(X0) & funny(X0))) & ((old(X0) | ~funny(X0)) | ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0))))) [nnf transformation 9]
47. ! [X0] : ((((~rich(X0) | ~creative(X0)) & (rich(X0) | creative(X0))) | (~old(X0) & funny(X0))) & (old(X0) | ~funny(X0) | ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0))))) [flattening 46]
48. ! [X0] : ((((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) | (patient(X0) | strong(X0))) & ((~patient(X0) & ~strong(X0)) | ((~tall(X0) | kind(X0)) & (~kind(X0) | tall(X0))))) [nnf transformation 10]
49. ! [X0] : ((((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) | patient(X0) | strong(X0)) & ((~patient(X0) & ~strong(X0)) | ((~tall(X0) | kind(X0)) & (~kind(X0) | tall(X0))))) [flattening 48]
55. ! [X0] : (((~humble(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | (humble(X0) | ~generous(X0)))) [nnf transformation 12]
56. ! [X0] : (((~humble(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | humble(X0) | ~generous(X0))) [flattening 55]
57. ! [X0] : ((((~old(X0) | ~creative(X0)) & (old(X0) | creative(X0))) | (~humble(X0) | ~tall(X0))) & ((humble(X0) & tall(X0)) | ((creative(X0) | ~old(X0)) & (old(X0) | ~creative(X0))))) [nnf transformation 13]
58. ! [X0] : ((((~old(X0) | ~creative(X0)) & (old(X0) | creative(X0))) | ~humble(X0) | ~tall(X0)) & ((humble(X0) & tall(X0)) | ((creative(X0) | ~old(X0)) & (old(X0) | ~creative(X0))))) [flattening 57]
59. ! [X0] : ((curious(X0) & generous(X0)) | ((strong(X0) | ~creative(X0)) & (creative(X0) | ~strong(X0)))) [nnf transformation 33]
65. ! [X0] : ((~strong(X0) | (~happy(X0) & ~patient(X0))) & ((happy(X0) | patient(X0)) | strong(X0))) [nnf transformation 16]
66. ! [X0] : ((~strong(X0) | (~happy(X0) & ~patient(X0))) & (happy(X0) | patient(X0) | strong(X0))) [flattening 65]
67. (rich(fred) | happy(fred)) & (~rich(fred) | ~happy(fred)) [nnf transformation 17]
88. ~creative(X0) | ~funny(X0) | ~kind(X0) [cnf transformation 37]
96. humble(X0) | patient(X0) [cnf transformation 31]
97. ~generous(X0) | ~patient(X0) [cnf transformation 32]
99. ~generous(X0) | wise(X0) [cnf transformation 32]
111. ~creative(X0) | ~rich(X0) | funny(X0) [cnf transformation 47]
112. ~creative(X0) | ~rich(X0) | ~old(X0) [cnf transformation 47]
114. ~tall(X0) | ~strong(X0) | kind(X0) [cnf transformation 49]
123. generous(X0) | strong(X0) [cnf transformation 56]
124. ~humble(X0) | strong(X0) [cnf transformation 56]
125. ~creative(X0) | old(X0) | tall(X0) [cnf transformation 58]
131. generous(X0) | creative(X0) | ~strong(X0) [cnf transformation 59]
139. ~patient(X0) | ~strong(X0) [cnf transformation 66]
140. ~strong(X0) | ~happy(X0) [cnf transformation 66]
142. rich(fred) | happy(fred) [cnf transformation 67]
155. ~wise(fred) [cnf transformation 25]
234. generous(X0) | creative(X0) [subsumption resolution 131,123]
236. 18 <=> rich(fred) [avatar definition]
238. rich(fred) <- (18) [avatar component clause 236]
245. 20 <=> wise(fred) [avatar definition]
246. ~wise(fred) <- (~20) [avatar component clause 245]
254. 22 <=> happy(fred) [avatar definition]
256. happy(fred) <- (22) [avatar component clause 254]
257. 22 | 18 [avatar split clause 142,236,254]
310. ~20 [avatar split clause 155,245]
329. strong(X1) | ~patient(X1) [resolution 123,97]
330. ~patient(X1) [subsumption resolution 329,139]
331. strong(X0) | patient(X0) [resolution 124,96]
332. strong(X0) [subsumption resolution 331,330]
351. ~happy(X0) [resolution 332,140]
353. wise(X0) | creative(X0) [resolution 234,99]
364. creative(fred) <- (~20) [resolution 353,246]
385. ~rich(fred) | funny(fred) <- (~20) [resolution 364,111]
386. ~funny(fred) | ~kind(fred) <- (~20) [resolution 364,88]
388. funny(fred) <- (18, ~20) [subsumption resolution 385,238]
389. ~kind(fred) <- (18, ~20) [subsumption resolution 386,388]
391. ~rich(fred) | ~old(fred) <- (~20) [resolution 112,364]
392. ~old(fred) <- (18, ~20) [subsumption resolution 391,238]
407. old(fred) | tall(fred) <- (~20) [resolution 125,364]
408. tall(fred) <- (18, ~20) [subsumption resolution 407,392]
409. ~strong(fred) | kind(fred) <- (18, ~20) [resolution 408,114]
411. kind(fred) <- (18, ~20) [subsumption resolution 409,332]
412. $false <- (18, ~20) [subsumption resolution 411,389]
413. ~18 | 20 [avatar contradiction clause 412]
435. $false <- (22) [subsumption resolution 256,351]
436. ~22 [avatar contradiction clause 435]
437. $false [avatar sat refutation 257,310,413,436]
% SZS output end Proof for 476746977782447436550449
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is not old or not happy and vice versa.
Everyone who is not humble is either not patient or not happy.
Everyone who is not curious is both not quiet and wise and vice versa.
Everyone who is not kind or patient is both not rich and not creative and vice versa.
Everyone who is not funny or happy is either tall or wise.
If someone is not funny then john is both not calm and funny and vice versa.
If someone is either not creative or kind then someone is not funny and vice versa.
If someone is not funny or patient then someone is both not creative and not happy and vice versa.
If susan is rich then paul is creative.
If someone is curious or not quiet then john is not creative or not wise and vice versa.
If lucy is calm then someone is humble.
Everyone who is rich or curious is wise.
If lucy is both not patient and not quiet then someone is not strong or funny and vice versa.
If someone is not wise or kind then lucy is patient.
Everyone who is happy is both not patient and not old.
Everyone who is generous or not strong is funny or not kind and vice versa.
Alice is old.
Fred is both quiet and curious.
Lucy is either not generous or rich.
Someone is brave.
Someone is both not rich and not creative.
Someone is funny.
Someone is either not tall or not curious. | Fred is not quiet. | contradiction | (![X]:(~strong(X)<=>(~old(X)|~happy(X))))&
(![X]:(~humble(X)=>(~patient(X)<~>~happy(X))))&
(![X]:(~curious(X)<=>(~quiet(X)&wise(X))))&
(![X]:((~kind(X)|patient(X))<=>(~rich(X)&~creative(X))))&
(![X]:((~funny(X)|happy(X))=>(tall(X)<~>wise(X))))&
((?[X]:(~funny(X)))<=>((~calm(john)&funny(john))))&
((?[X]:((~creative(X)<~>kind(X))))<=>(?[X]:(~funny(X))))&
((?[X]:((~funny(X)|patient(X))))<=>(?[X]:((~creative(X)&~happy(X)))))&
((rich(susan))=>(creative(paul)))&
((?[X]:((curious(X)|~quiet(X))))<=>((~creative(john)|~wise(john))))&
((calm(lucy))=>(?[X]:(humble(X))))&
(![X]:((rich(X)|curious(X))=>wise(X)))&
(((~patient(lucy)&~quiet(lucy)))<=>(?[X]:((~strong(X)|funny(X)))))&
((?[X]:((~wise(X)|kind(X))))=>(patient(lucy)))&
(![X]:(happy(X)=>(~patient(X)&~old(X))))&
(![X]:((generous(X)|~strong(X))<=>(funny(X)|~kind(X))))&
(old(alice))&
((quiet(fred)&curious(fred)))&
((~generous(lucy)<~>rich(lucy)))&
(?[X]:(brave(X)))&
(?[X]:((~rich(X)&~creative(X))))&
(?[X]:(funny(X)))&
(?[X]:((~tall(X)<~>~curious(X)))) | ~quiet(fred) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 758139867849224817822325
% SZS output start Proof for 758139867849224817822325
18. curious(fred) & quiet(fred) [input p17]
24. ~quiet(fred) [input hypothesis]
125. quiet(fred) [cnf transformation 18]
134. ~quiet(fred) [cnf transformation 24]
280. $false [subsumption resolution 134,125]
% SZS output end Proof for 758139867849224817822325
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not humble and brave then someone is both tall and not wise and vice versa.
Everyone who is both not happy and not generous is both happy and quiet and vice versa.
Everyone who is not brave or humble is not generous or not funny.
Everyone who is either quiet or calm is both not brave and not strong and vice versa.
Everyone who is old or not rich is not wise or not old and vice versa.
Everyone who is both strong and brave is both old and creative.
Everyone who is creative or not patient is both not kind and humble.
Everyone who is not rich or not strong is calm.
If someone is not humble or not happy then john is not humble and vice versa.
Everyone who is either not wise or tall is both not wise and happy and vice versa.
Everyone who is not creative is either humble or not quiet and vice versa.
Everyone who is humble or not old is either rich or not strong and vice versa.
If susan is creative or not brave then someone is not generous and vice versa.
If paul is not old then someone is not generous or tall.
If someone is not creative or not patient then someone is either not curious or happy and vice versa.
If paul is rich or not quiet then lucy is both not rich and not quiet and vice versa.
Lucy is tall or quiet.
Mary is either not old or brave.
Someone is both not strong and curious.
Someone is both not humble and not curious.
Someone is creative. | John is not wise. | neutral | ((?[X]:((~humble(X)&brave(X))))<=>(?[X]:((tall(X)&~wise(X)))))&
(![X]:((~happy(X)&~generous(X))<=>(happy(X)&quiet(X))))&
(![X]:((~brave(X)|humble(X))=>(~generous(X)|~funny(X))))&
(![X]:((quiet(X)<~>calm(X))<=>(~brave(X)&~strong(X))))&
(![X]:((old(X)|~rich(X))<=>(~wise(X)|~old(X))))&
(![X]:((strong(X)&brave(X))=>(old(X)&creative(X))))&
(![X]:((creative(X)|~patient(X))=>(~kind(X)&humble(X))))&
(![X]:((~rich(X)|~strong(X))=>calm(X)))&
((?[X]:((~humble(X)|~happy(X))))<=>(~humble(john)))&
(![X]:((~wise(X)<~>tall(X))<=>(~wise(X)&happy(X))))&
(![X]:(~creative(X)<=>(humble(X)<~>~quiet(X))))&
(![X]:((humble(X)|~old(X))<=>(rich(X)<~>~strong(X))))&
(((creative(susan)|~brave(susan)))<=>(?[X]:(~generous(X))))&
((~old(paul))=>(?[X]:((~generous(X)|tall(X)))))&
((?[X]:((~creative(X)|~patient(X))))<=>(?[X]:((~curious(X)<~>happy(X)))))&
(((rich(paul)|~quiet(paul)))<=>((~rich(lucy)&~quiet(lucy))))&
((tall(lucy)|quiet(lucy)))&
((~old(mary)<~>brave(mary)))&
(?[X]:((~strong(X)&curious(X))))&
(?[X]:((~humble(X)&~curious(X))))&
(?[X]:(creative(X))) | ~wise(john) | [] | null | 0 |
Everyone who is not patient is either curious or tall and vice versa.
Everyone who is either not rich or not creative is either patient or not generous.
If fred is either not creative or creative then paul is both happy and strong and vice versa.
If john is rich or quiet then someone is both not strong and brave.
Everyone who is not creative is not calm or not generous.
Everyone who is not kind is either rich or old.
If lucy is wise then john is calm or not strong and vice versa.
Everyone who is not quiet is either wise or not rich and vice versa.
Everyone who is not tall or humble is both not old and not brave and vice versa.
If john is kind or patient then fred is both calm and kind.
If someone is both strong and not patient then someone is not creative or patient.
If susan is either humble or quiet then someone is both happy and not humble and vice versa.
If someone is humble then someone is either not rich or not kind and vice versa.
Everyone who is both not patient and curious is not calm or not generous and vice versa.
Everyone who is not brave is not old and vice versa.
If mary is either calm or not rich then someone is not funny or not kind.
Someone is either happy or not tall.
Lucy is patient or not old.
Someone is either not patient or not generous.
Someone is kind.
John is either brave or funny.
Someone is not patient or happy.
Lucy is not strong.
Mary is both not wise and tall. | Susan is patient. | neutral | (![X]:(~patient(X)<=>(curious(X)<~>tall(X))))&
(![X]:((~rich(X)<~>~creative(X))=>(patient(X)<~>~generous(X))))&
(((~creative(fred)<~>creative(fred)))<=>((happy(paul)&strong(paul))))&
(((rich(john)|quiet(john)))=>(?[X]:((~strong(X)&brave(X)))))&
(![X]:(~creative(X)=>(~calm(X)|~generous(X))))&
(![X]:(~kind(X)=>(rich(X)<~>old(X))))&
((wise(lucy))<=>((calm(john)|~strong(john))))&
(![X]:(~quiet(X)<=>(wise(X)<~>~rich(X))))&
(![X]:((~tall(X)|humble(X))<=>(~old(X)&~brave(X))))&
(((kind(john)|patient(john)))=>((calm(fred)&kind(fred))))&
((?[X]:((strong(X)&~patient(X))))=>(?[X]:((~creative(X)|patient(X)))))&
(((humble(susan)<~>quiet(susan)))<=>(?[X]:((happy(X)&~humble(X)))))&
((?[X]:(humble(X)))<=>(?[X]:((~rich(X)<~>~kind(X)))))&
(![X]:((~patient(X)&curious(X))<=>(~calm(X)|~generous(X))))&
(![X]:(~brave(X)<=>~old(X)))&
(((calm(mary)<~>~rich(mary)))=>(?[X]:((~funny(X)|~kind(X)))))&
(?[X]:((happy(X)<~>~tall(X))))&
((patient(lucy)|~old(lucy)))&
(?[X]:((~patient(X)<~>~generous(X))))&
(?[X]:(kind(X)))&
((brave(john)<~>funny(john)))&
(?[X]:((~patient(X)|happy(X))))&
(~strong(lucy))&
((~wise(mary)&tall(mary))) | patient(susan) | [] | null | 0 |
If someone is not calm then someone is generous.
Everyone who is both not funny and not generous is not old and vice versa.
If someone is either not generous or quiet then mary is either strong or funny.
If someone is both brave and humble then susan is either not tall or quiet.
If lucy is both old and curious then fred is either quiet or not quiet and vice versa.
Everyone who is creative or not generous is both generous and not calm and vice versa.
If susan is not wise then someone is both old and rich.
If lucy is either creative or wise then someone is both not curious and humble.
Everyone who is brave or not tall is both tall and quiet.
Everyone who is both wise and not quiet is either not patient or not generous.
If someone is not happy or not patient then someone is not humble.
If fred is either not curious or tall then someone is curious.
If fred is curious or strong then mary is either not happy or brave.
If mary is quiet then someone is rich or not brave.
If someone is not quiet then someone is either not creative or curious and vice versa.
Everyone who is both not happy and funny is generous or not old and vice versa.
Someone is calm or not brave.
Alice is both humble and tall.
Fred is curious.
Susan is not patient or curious.
Paul is either happy or not brave.
Fred is both humble and not patient. | Fred is not happy. | entailment | ((?[X]:(~calm(X)))=>(?[X]:(generous(X))))&
(![X]:((~funny(X)&~generous(X))<=>~old(X)))&
((?[X]:((~generous(X)<~>quiet(X))))=>((strong(mary)<~>funny(mary))))&
((?[X]:((brave(X)&humble(X))))=>((~tall(susan)<~>quiet(susan))))&
(((old(lucy)&curious(lucy)))<=>((quiet(fred)<~>~quiet(fred))))&
(![X]:((creative(X)|~generous(X))<=>(generous(X)&~calm(X))))&
((~wise(susan))=>(?[X]:((old(X)&rich(X)))))&
(((creative(lucy)<~>wise(lucy)))=>(?[X]:((~curious(X)&humble(X)))))&
(![X]:((brave(X)|~tall(X))=>(tall(X)&quiet(X))))&
(![X]:((wise(X)&~quiet(X))=>(~patient(X)<~>~generous(X))))&
((?[X]:((~happy(X)|~patient(X))))=>(?[X]:(~humble(X))))&
(((~curious(fred)<~>tall(fred)))=>(?[X]:(curious(X))))&
(((curious(fred)|strong(fred)))=>((~happy(mary)<~>brave(mary))))&
((quiet(mary))=>(?[X]:((rich(X)|~brave(X)))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~creative(X)<~>curious(X)))))&
(![X]:((~happy(X)&funny(X))<=>(generous(X)|~old(X))))&
(?[X]:((calm(X)|~brave(X))))&
((humble(alice)&tall(alice)))&
(curious(fred))&
((~patient(susan)|curious(susan)))&
((happy(paul)<~>~brave(paul)))&
((humble(fred)&~patient(fred))) | ~happy(fred) | [
"p5",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7887301712512245749312514
% SZS output start Proof for 7887301712512245749312514
6. ! [X0] : ((~generous(X0) | creative(X0)) <=> (~calm(X0) & generous(X0))) [input p5]
16. ! [X0] : ((funny(X0) & ~happy(X0)) <=> (~old(X0) | generous(X0))) [input p15]
23. happy(fred) [input hypothesis]
49. ! [X0] : (((~generous(X0) | creative(X0)) | (calm(X0) | ~generous(X0))) & ((~calm(X0) & generous(X0)) | (generous(X0) & ~creative(X0)))) [nnf transformation 6]
50. ! [X0] : ((~generous(X0) | creative(X0) | calm(X0) | ~generous(X0)) & ((~calm(X0) & generous(X0)) | (generous(X0) & ~creative(X0)))) [flattening 49]
69. ! [X0] : (((funny(X0) & ~happy(X0)) | (old(X0) & ~generous(X0))) & ((~old(X0) | generous(X0)) | (~funny(X0) | happy(X0)))) [nnf transformation 16]
70. ! [X0] : (((funny(X0) & ~happy(X0)) | (old(X0) & ~generous(X0))) & (~old(X0) | generous(X0) | ~funny(X0) | happy(X0))) [flattening 69]
91. generous(X0) | generous(X0) [cnf transformation 50]
119. ~happy(X0) | ~generous(X0) [cnf transformation 70]
132. happy(fred) [cnf transformation 23]
134. generous(X0) [duplicate literal removal 91]
290. ~happy(X0) [subsumption resolution 119,134]
311. $false [subsumption resolution 132,290]
% SZS output end Proof for 7887301712512245749312514
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both funny and rich then lucy is either patient or happy.
Everyone who is not rich or quiet is not generous or calm and vice versa.
Everyone who is not happy is not kind.
Everyone who is kind is patient.
Everyone who is strong or not patient is either curious or not strong.
Everyone who is not curious is tall or strong and vice versa.
Everyone who is not funny or not generous is calm and vice versa.
If john is either not curious or not brave then susan is not wise.
Everyone who is humble or not strong is either strong or not kind and vice versa.
If someone is not brave then john is not strong or not wise and vice versa.
Everyone who is patient or not happy is either not humble or brave.
If someone is not happy then paul is not wise and vice versa.
If susan is either not generous or not calm then paul is not happy and vice versa.
Everyone who is both brave and not tall is both not humble and creative.
Everyone who is either funny or not tall is both not strong and not wise and vice versa.
If someone is not kind then someone is not creative.
Susan is both not wise and not curious.
Alice is both creative and not funny.
Lucy is both not happy and not generous.
Fred is strong or happy.
Paul is either not brave or not tall.
Someone is either not old or humble.
Someone is not calm.
Someone is either not tall or not curious. | Paul is not humble. | entailment | ((?[X]:((funny(X)&rich(X))))=>((patient(lucy)<~>happy(lucy))))&
(![X]:((~rich(X)|quiet(X))<=>(~generous(X)|calm(X))))&
(![X]:(~happy(X)=>~kind(X)))&
(![X]:(kind(X)=>patient(X)))&
(![X]:((strong(X)|~patient(X))=>(curious(X)<~>~strong(X))))&
(![X]:(~curious(X)<=>(tall(X)|strong(X))))&
(![X]:((~funny(X)|~generous(X))<=>calm(X)))&
(((~curious(john)<~>~brave(john)))=>(~wise(susan)))&
(![X]:((humble(X)|~strong(X))<=>(strong(X)<~>~kind(X))))&
((?[X]:(~brave(X)))<=>((~strong(john)|~wise(john))))&
(![X]:((patient(X)|~happy(X))=>(~humble(X)<~>brave(X))))&
((?[X]:(~happy(X)))<=>(~wise(paul)))&
(((~generous(susan)<~>~calm(susan)))<=>(~happy(paul)))&
(![X]:((brave(X)&~tall(X))=>(~humble(X)&creative(X))))&
(![X]:((funny(X)<~>~tall(X))<=>(~strong(X)&~wise(X))))&
((?[X]:(~kind(X)))=>(?[X]:(~creative(X))))&
((~wise(susan)&~curious(susan)))&
((creative(alice)&~funny(alice)))&
((~happy(lucy)&~generous(lucy)))&
((strong(fred)|happy(fred)))&
((~brave(paul)<~>~tall(paul)))&
(?[X]:((~old(X)<~>humble(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~tall(X)<~>~curious(X)))) | ~humble(paul) | [
"p4",
"p5",
"p6",
"p10",
"p12",
"p13",
"p14",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4594135088017972171816254
% SZS output start Proof for 4594135088017972171816254
5. ! [X0] : ((~patient(X0) | strong(X0)) => (curious(X0) <~> ~strong(X0))) [input p4]
6. ! [X0] : (~curious(X0) <=> (strong(X0) | tall(X0))) [input p5]
7. ! [X0] : ((~generous(X0) | ~funny(X0)) <=> calm(X0)) [input p6]
11. ! [X0] : ((~happy(X0) | patient(X0)) => (~humble(X0) <~> brave(X0))) [input p10]
13. (~generous(susan) <~> ~calm(susan)) <=> ~happy(paul) [input p12]
14. ! [X0] : ((~tall(X0) & brave(X0)) => (creative(X0) & ~humble(X0))) [input p13]
15. ! [X0] : ((funny(X0) <~> ~tall(X0)) <=> (~wise(X0) & ~strong(X0))) [input p14]
17. ~curious(susan) & ~wise(susan) [input p16]
21. ~brave(paul) <~> ~tall(paul) [input p20]
25. humble(paul) [input hypothesis]
30. ! [X0] : ((curious(X0) <~> ~strong(X0)) | (patient(X0) & ~strong(X0))) [ennf transformation 5]
32. ! [X0] : ((~humble(X0) <~> brave(X0)) | (happy(X0) & ~patient(X0))) [ennf transformation 11]
33. ! [X0] : ((creative(X0) & ~humble(X0)) | (tall(X0) | ~brave(X0))) [ennf transformation 14]
34. ! [X0] : ((creative(X0) & ~humble(X0)) | tall(X0) | ~brave(X0)) [flattening 33]
39. ! [X0] : (((strong(X0) | ~curious(X0)) & (~strong(X0) | curious(X0))) | (patient(X0) & ~strong(X0))) [nnf transformation 30]
40. ! [X0] : ((~curious(X0) | (~strong(X0) & ~tall(X0))) & ((strong(X0) | tall(X0)) | curious(X0))) [nnf transformation 6]
41. ! [X0] : ((~curious(X0) | (~strong(X0) & ~tall(X0))) & (strong(X0) | tall(X0) | curious(X0))) [flattening 40]
42. ! [X0] : (((~generous(X0) | ~funny(X0)) | ~calm(X0)) & (calm(X0) | (generous(X0) & funny(X0)))) [nnf transformation 7]
43. ! [X0] : ((~generous(X0) | ~funny(X0) | ~calm(X0)) & (calm(X0) | (generous(X0) & funny(X0)))) [flattening 42]
52. ! [X0] : (((~brave(X0) | humble(X0)) & (brave(X0) | ~humble(X0))) | (happy(X0) & ~patient(X0))) [nnf transformation 32]
57. (((calm(susan) | generous(susan)) & (~calm(susan) | ~generous(susan))) | happy(paul)) & (~happy(paul) | ((~generous(susan) | calm(susan)) & (~calm(susan) | generous(susan)))) [nnf transformation 13]
58. ! [X0] : ((((tall(X0) | ~funny(X0)) & (~tall(X0) | funny(X0))) | (wise(X0) | strong(X0))) & ((~wise(X0) & ~strong(X0)) | ((funny(X0) | tall(X0)) & (~tall(X0) | ~funny(X0))))) [nnf transformation 15]
59. ! [X0] : ((((tall(X0) | ~funny(X0)) & (~tall(X0) | funny(X0))) | wise(X0) | strong(X0)) & ((~wise(X0) & ~strong(X0)) | ((funny(X0) | tall(X0)) & (~tall(X0) | ~funny(X0))))) [flattening 58]
63. (tall(paul) | brave(paul)) & (~tall(paul) | ~brave(paul)) [nnf transformation 21]
80. ~strong(X0) | curious(X0) | ~strong(X0) [cnf transformation 39]
84. strong(X0) | tall(X0) | curious(X0) [cnf transformation 41]
86. ~curious(X0) | ~strong(X0) [cnf transformation 41]
88. calm(X0) | generous(X0) [cnf transformation 43]
89. ~calm(X0) | ~funny(X0) | ~generous(X0) [cnf transformation 43]
102. ~humble(X0) | brave(X0) | happy(X0) [cnf transformation 52]
107. ~happy(paul) | ~calm(susan) | generous(susan) [cnf transformation 57]
108. ~happy(paul) | ~generous(susan) | calm(susan) [cnf transformation 57]
111. ~humble(X0) | tall(X0) | ~brave(X0) [cnf transformation 34]
117. ~tall(X0) | funny(X0) | wise(X0) | strong(X0) [cnf transformation 59]
120. ~wise(susan) [cnf transformation 17]
121. ~curious(susan) [cnf transformation 17]
127. ~tall(paul) | ~brave(paul) [cnf transformation 63]
128. tall(paul) | brave(paul) [cnf transformation 63]
134. humble(paul) [cnf transformation 25]
137. ~strong(X0) | curious(X0) [duplicate literal removal 80]
151. ~strong(X0) [subsumption resolution 86,137]
152. tall(X0) | curious(X0) [subsumption resolution 84,151]
162. 6 <=> wise(susan) [avatar definition]
164. ~wise(susan) <- (~6) [avatar component clause 162]
193. 12 <=> happy(paul) [avatar definition]
197. 13 <=> generous(susan) [avatar definition]
198. generous(susan) <- (13) [avatar component clause 197]
201. 14 <=> calm(susan) [avatar definition]
202. calm(susan) <- (14) [avatar component clause 201]
205. ~happy(paul) | calm(susan) [subsumption resolution 108,88]
206. 14 | ~12 [avatar split clause 205,193,201]
207. ~happy(paul) | generous(susan) [subsumption resolution 107,88]
208. 13 | ~12 [avatar split clause 207,193,197]
210. ~tall(X0) | funny(X0) | wise(X0) [subsumption resolution 117,151]
212. ~6 [avatar split clause 120,162]
216. 15 <=> brave(paul) [avatar definition]
217. ~brave(paul) <- (~15) [avatar component clause 216]
220. 16 <=> tall(paul) [avatar definition]
223. 15 | 16 [avatar split clause 128,220,216]
224. ~15 | ~16 [avatar split clause 127,220,216]
259. brave(paul) | happy(paul) [resolution 102,134]
262. tall(paul) | ~brave(paul) [resolution 111,134]
273. ~15 | 16 [avatar split clause 262,220,216]
274. happy(paul) <- (~15) [subsumption resolution 259,217]
275. 12 | 15 [avatar split clause 274,216,193]
286. ~funny(susan) | ~generous(susan) <- (14) [resolution 202,89]
288. ~funny(susan) <- (13, 14) [subsumption resolution 286,198]
301. wise(X0) | funny(X0) | curious(X0) [resolution 210,152]
310. funny(susan) | curious(susan) <- (~6) [resolution 301,164]
315. curious(susan) <- (~6, 13, 14) [subsumption resolution 310,288]
316. $false <- (~6, 13, 14) [subsumption resolution 315,121]
317. 6 | ~13 | ~14 [avatar contradiction clause 316]
318. $false [avatar sat refutation 206,208,212,223,224,273,275,317]
% SZS output end Proof for 4594135088017972171816254
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 then john is both not tall and wise and vice versa.
Everyone who is creative is not funny or not humble and vice versa.
Everyone who is quiet or strong is tall or rich and vice versa.
If someone is both quiet and strong then someone is quiet or funny and vice versa.
Everyone who is creative or not funny is either quiet or rich and vice versa.
Everyone who is both not funny and tall is not kind or not happy and vice versa.
If someone is either not happy or not brave then someone is not wise and vice versa.
If mary is wise or not rich then mary is either not creative or generous and vice versa.
Everyone who is not happy or happy is both brave and not tall.
Everyone who is both not curious and patient is either not kind or not creative and vice versa.
If someone is not kind or old then someone is both not curious and not wise and vice versa.
Everyone who is funny or not creative is quiet and vice versa.
If someone is not rich or not humble then fred is not strong and vice versa.
If susan is either not strong or not rich then someone is old or not kind.
Everyone who is both not rich and not humble is not happy or strong.
Everyone who is generous is either creative or calm.
Susan is calm or generous.
John is not funny or strong.
Mary is rich.
Someone is either not curious or not rich.
Mary is quiet.
Someone is not curious or not wise.
Mary is either generous or calm. | Mary is not kind. | contradiction | ((?[X]:(calm(X)))<=>((~tall(john)&wise(john))))&
(![X]:(creative(X)<=>(~funny(X)|~humble(X))))&
(![X]:((quiet(X)|strong(X))<=>(tall(X)|rich(X))))&
((?[X]:((quiet(X)&strong(X))))<=>(?[X]:((quiet(X)|funny(X)))))&
(![X]:((creative(X)|~funny(X))<=>(quiet(X)<~>rich(X))))&
(![X]:((~funny(X)&tall(X))<=>(~kind(X)|~happy(X))))&
((?[X]:((~happy(X)<~>~brave(X))))<=>(?[X]:(~wise(X))))&
(((wise(mary)|~rich(mary)))<=>((~creative(mary)<~>generous(mary))))&
(![X]:((~happy(X)|happy(X))=>(brave(X)&~tall(X))))&
(![X]:((~curious(X)&patient(X))<=>(~kind(X)<~>~creative(X))))&
((?[X]:((~kind(X)|old(X))))<=>(?[X]:((~curious(X)&~wise(X)))))&
(![X]:((funny(X)|~creative(X))<=>quiet(X)))&
((?[X]:((~rich(X)|~humble(X))))<=>(~strong(fred)))&
(((~strong(susan)<~>~rich(susan)))=>(?[X]:((old(X)|~kind(X)))))&
(![X]:((~rich(X)&~humble(X))=>(~happy(X)|strong(X))))&
(![X]:(generous(X)=>(creative(X)<~>calm(X))))&
((calm(susan)|generous(susan)))&
((~funny(john)|strong(john)))&
(rich(mary))&
(?[X]:((~curious(X)<~>~rich(X))))&
(quiet(mary))&
(?[X]:((~curious(X)|~wise(X))))&
((generous(mary)<~>calm(mary))) | ~kind(mary) | [
"p5",
"p6",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3515485789083449656525674
% SZS output start Proof for 3515485789083449656525674
6. ! [X0] : ((tall(X0) & ~funny(X0)) <=> (~happy(X0) | ~kind(X0))) [input p5]
7. ? [X0] : (~happy(X0) <~> ~brave(X0)) <=> ? [X0] : ~wise(X0) [input p6]
9. ! [X0] : ((happy(X0) | ~happy(X0)) => (~tall(X0) & brave(X0))) [input p8]
11. ? [X0] : (old(X0) | ~kind(X0)) <=> ? [X0] : (~wise(X0) & ~curious(X0)) [input p10]
24. ~kind(mary) [input hypothesis]
26. ? [X0] : (~happy(X0) <~> ~brave(X0)) <=> ? [X1] : ~wise(X1) [rectify 7]
27. ? [X0] : (old(X0) | ~kind(X0)) <=> ? [X1] : (~wise(X1) & ~curious(X1)) [rectify 11]
28. ! [X0] : ((~tall(X0) & brave(X0)) | (~happy(X0) & happy(X0))) [ennf transformation 9]
49. ! [X0] : (((tall(X0) & ~funny(X0)) | (happy(X0) & kind(X0))) & ((~happy(X0) | ~kind(X0)) | (~tall(X0) | funny(X0)))) [nnf transformation 6]
50. ! [X0] : (((tall(X0) & ~funny(X0)) | (happy(X0) & kind(X0))) & (~happy(X0) | ~kind(X0) | ~tall(X0) | funny(X0))) [flattening 49]
51. (? [X0] : ((brave(X0) | happy(X0)) & (~brave(X0) | ~happy(X0))) | ! [X1] : wise(X1)) & (? [X1] : ~wise(X1) | ! [X0] : ((~happy(X0) | brave(X0)) & (~brave(X0) | happy(X0)))) [nnf transformation 26]
52. (? [X0] : ((brave(X0) | happy(X0)) & (~brave(X0) | ~happy(X0))) | ! [X1] : wise(X1)) & (? [X2] : ~wise(X2) | ! [X3] : ((~happy(X3) | brave(X3)) & (~brave(X3) | happy(X3)))) [rectify 51]
53. ? [X0] : ((brave(X0) | happy(X0)) & (~brave(X0) | ~happy(X0))) => ((brave(sK3) | happy(sK3)) & (~brave(sK3) | ~happy(sK3))) [choice axiom]
54. ? [X2] : ~wise(X2) => ~wise(sK4) [choice axiom]
55. (((brave(sK3) | happy(sK3)) & (~brave(sK3) | ~happy(sK3))) | ! [X1] : wise(X1)) & (~wise(sK4) | ! [X3] : ((~happy(X3) | brave(X3)) & (~brave(X3) | happy(X3)))) [skolemisation 52,54,53]
60. (? [X0] : (old(X0) | ~kind(X0)) | ! [X1] : (wise(X1) | curious(X1))) & (? [X1] : (~wise(X1) & ~curious(X1)) | ! [X0] : (~old(X0) & kind(X0))) [nnf transformation 27]
61. (? [X0] : (old(X0) | ~kind(X0)) | ! [X1] : (wise(X1) | curious(X1))) & (? [X2] : (~wise(X2) & ~curious(X2)) | ! [X3] : (~old(X3) & kind(X3))) [rectify 60]
62. ? [X0] : (old(X0) | ~kind(X0)) => (old(sK5) | ~kind(sK5)) [choice axiom]
63. ? [X2] : (~wise(X2) & ~curious(X2)) => (~wise(sK6) & ~curious(sK6)) [choice axiom]
64. ((old(sK5) | ~kind(sK5)) | ! [X1] : (wise(X1) | curious(X1))) & ((~wise(sK6) & ~curious(sK6)) | ! [X3] : (~old(X3) & kind(X3))) [skolemisation 61,63,62]
106. tall(X0) | happy(X0) [cnf transformation 50]
109. ~brave(sK3) | ~happy(sK3) | wise(X1) [cnf transformation 55]
118. brave(X0) | ~happy(X0) [cnf transformation 28]
119. ~tall(X0) | happy(X0) [cnf transformation 28]
129. ~wise(sK6) | kind(X3) [cnf transformation 64]
152. ~kind(mary) [cnf transformation 24]
204. 12 <=> ! [X1] : wise(X1) [avatar definition]
205. wise(X1) <- (12) [avatar component clause 204]
207. 13 <=> happy(sK3) [avatar definition]
208. ~happy(sK3) <- (~13) [avatar component clause 207]
211. 14 <=> brave(sK3) [avatar definition]
212. ~brave(sK3) <- (~14) [avatar component clause 211]
215. 12 | ~13 | ~14 [avatar split clause 109,211,207,204]
250. happy(X0) [subsumption resolution 119,106]
251. brave(X0) [subsumption resolution 118,250]
268. 26 <=> wise(sK6) [avatar definition]
270. ~wise(sK6) <- (~26) [avatar component clause 268]
273. 27 <=> ! [X3] : kind(X3) [avatar definition]
274. kind(X3) <- (27) [avatar component clause 273]
275. 27 | ~26 [avatar split clause 129,268,273]
371. $false <- (~14) [subsumption resolution 212,251]
372. 14 [avatar contradiction clause 371]
373. $false <- (~13) [subsumption resolution 208,250]
374. 13 [avatar contradiction clause 373]
377. $false <- (12, ~26) [resolution 270,205]
378. ~12 | 26 [avatar contradiction clause 377]
379. $false <- (27) [resolution 274,152]
382. ~27 [avatar contradiction clause 379]
383. $false [avatar sat refutation 215,275,372,374,378,382]
% SZS output end Proof for 3515485789083449656525674
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not funny and strong then fred is not old or not strong.
If mary is either not brave or happy then alice is both strong and not wise and vice versa.
Everyone who is either strong or not strong is strong or not kind and vice versa.
Everyone who is both not strong and brave is either rich or not curious and vice versa.
If someone is strong or not generous then someone is either not patient or brave and vice versa.
Everyone who is kind is both not tall and tall.
If lucy is calm then paul is not generous.
Everyone who is either not curious or rich is calm.
Everyone who is rich is either not creative or not funny.
If someone is either not brave or quiet then someone is curious.
Everyone who is not wise or not patient is both funny and not funny and vice versa.
If someone is kind then someone is rich or curious and vice versa.
If fred is either not brave or rich then susan is both not kind and calm.
If john is both strong and not calm then paul is either generous or not humble and vice versa.
Everyone who is both not quiet and not happy is not curious and vice versa.
Everyone who is both rich and not rich is either patient or not rich.
Someone is generous.
Paul is either quiet or not rich.
Someone is both not humble and funny.
Someone is not kind or curious.
Alice is both not quiet and calm. | Lucy is rich. | contradiction | ((?[X]:((~funny(X)&strong(X))))=>((~old(fred)|~strong(fred))))&
(((~brave(mary)<~>happy(mary)))<=>((strong(alice)&~wise(alice))))&
(![X]:((strong(X)<~>~strong(X))<=>(strong(X)|~kind(X))))&
(![X]:((~strong(X)&brave(X))<=>(rich(X)<~>~curious(X))))&
((?[X]:((strong(X)|~generous(X))))<=>(?[X]:((~patient(X)<~>brave(X)))))&
(![X]:(kind(X)=>(~tall(X)&tall(X))))&
((calm(lucy))=>(~generous(paul)))&
(![X]:((~curious(X)<~>rich(X))=>calm(X)))&
(![X]:(rich(X)=>(~creative(X)<~>~funny(X))))&
((?[X]:((~brave(X)<~>quiet(X))))=>(?[X]:(curious(X))))&
(![X]:((~wise(X)|~patient(X))<=>(funny(X)&~funny(X))))&
((?[X]:(kind(X)))<=>(?[X]:((rich(X)|curious(X)))))&
(((~brave(fred)<~>rich(fred)))=>((~kind(susan)&calm(susan))))&
(((strong(john)&~calm(john)))<=>((generous(paul)<~>~humble(paul))))&
(![X]:((~quiet(X)&~happy(X))<=>~curious(X)))&
(![X]:((rich(X)&~rich(X))=>(patient(X)<~>~rich(X))))&
(?[X]:(generous(X)))&
((quiet(paul)<~>~rich(paul)))&
(?[X]:((~humble(X)&funny(X))))&
(?[X]:((~kind(X)|curious(X))))&
((~quiet(alice)&calm(alice))) | rich(lucy) | [
"p5",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1062087343831793811749031
% SZS output start Proof for 1062087343831793811749031
6. ! [X0] : (kind(X0) => (tall(X0) & ~tall(X0))) [input p5]
12. ? [X0] : kind(X0) <=> ? [X0] : (curious(X0) | rich(X0)) [input p11]
22. rich(lucy) [input hypothesis]
25. ? [X0] : kind(X0) <=> ? [X1] : (curious(X1) | rich(X1)) [rectify 12]
27. ! [X0] : ((tall(X0) & ~tall(X0)) | ~kind(X0)) [ennf transformation 6]
54. (? [X0] : kind(X0) | ! [X1] : (~curious(X1) & ~rich(X1))) & (? [X1] : (curious(X1) | rich(X1)) | ! [X0] : ~kind(X0)) [nnf transformation 25]
55. (? [X0] : kind(X0) | ! [X1] : (~curious(X1) & ~rich(X1))) & (? [X2] : (curious(X2) | rich(X2)) | ! [X3] : ~kind(X3)) [rectify 54]
56. ? [X0] : kind(X0) => kind(sK3) [choice axiom]
57. ? [X2] : (curious(X2) | rich(X2)) => (curious(sK4) | rich(sK4)) [choice axiom]
58. (kind(sK3) | ! [X1] : (~curious(X1) & ~rich(X1))) & ((curious(sK4) | rich(sK4)) | ! [X3] : ~kind(X3)) [skolemisation 55,57,56]
96. ~tall(X0) | ~kind(X0) [cnf transformation 27]
97. tall(X0) | ~kind(X0) [cnf transformation 27]
111. kind(sK3) | ~rich(X1) [cnf transformation 58]
136. rich(lucy) [cnf transformation 22]
199. ~kind(X0) [subsumption resolution 96,97]
224. ~rich(X1) [subsumption resolution 111,199]
255. $false [subsumption resolution 136,224]
% SZS output end Proof for 1062087343831793811749031
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not patient is either not kind or strong and vice versa. If someone is both not calm and humble then susan is creative and vice versa. If someone is either not wise or not happy then someone is both humble and tall and vice versa. Everyone who is both not strong and quiet is either brave or not rich. Everyone who is wise is both patient and calm. If mary is not humble then someone is brave or calm. Everyone who is not old or not patient is not generous. Everyone who is either tall or not brave is not quiet or not kind. If someone is rich then lucy is not creative or rich and vice versa. If someone is either kind or old then someone is both not tall and not happy and vice versa. Everyone who is generous or not happy is either not kind or calm. If fred is either humble or rich then someone is either not generous or not happy and vice versa. If someone is either not curious or not quiet then someone is either not strong or not happy and vice versa. Everyone who is kind or not calm is either creative or not tall and vice versa. Everyone who is either curious or quiet is both not old and not curious and vice versa. If paul is not patient then someone is both generous and not wise and vice versa. Someone is both brave and humble. Mary is happy. Someone is either not generous or wise. Someone is both wise and patient. Someone is not brave. Susan is either not creative or not happy. Someone is curious. Mary is both not wise and not brave. | Mary is not humble. | neutral | (![X]:((wise(X)<~>~patient(X))<=>(~kind(X)<~>strong(X))))&
((?[X]:((~calm(X)&humble(X))))<=>(creative(susan)))&
((?[X]:((~wise(X)<~>~happy(X))))<=>(?[X]:((humble(X)&tall(X)))))&
(![X]:((~strong(X)&quiet(X))=>(brave(X)<~>~rich(X))))&
(![X]:(wise(X)=>(patient(X)&calm(X))))&
((~humble(mary))=>(?[X]:((brave(X)|calm(X)))))&
(![X]:((~old(X)|~patient(X))=>~generous(X)))&
(![X]:((tall(X)<~>~brave(X))=>(~quiet(X)|~kind(X))))&
((?[X]:(rich(X)))<=>((~creative(lucy)|rich(lucy))))&
((?[X]:((kind(X)<~>old(X))))<=>(?[X]:((~tall(X)&~happy(X)))))&
(![X]:((generous(X)|~happy(X))=>(~kind(X)<~>calm(X))))&
(((humble(fred)<~>rich(fred)))<=>(?[X]:((~generous(X)<~>~happy(X)))))&
((?[X]:((~curious(X)<~>~quiet(X))))<=>(?[X]:((~strong(X)<~>~happy(X)))))&
(![X]:((kind(X)|~calm(X))<=>(creative(X)<~>~tall(X))))&
(![X]:((curious(X)<~>quiet(X))<=>(~old(X)&~curious(X))))&
((~patient(paul))<=>(?[X]:((generous(X)&~wise(X)))))&
(?[X]:((brave(X)&humble(X))))&
(happy(mary))&
(?[X]:((~generous(X)<~>wise(X))))&
(?[X]:((wise(X)&patient(X))))&
(?[X]:(~brave(X)))&
((~creative(susan)<~>~happy(susan)))&
(?[X]:(curious(X)))&
((~wise(mary)&~brave(mary))) | ~humble(mary) | [] | null | 0 |
Everyone who is tall or humble is not brave or not old. Everyone who is both not funny and brave is happy or curious. Everyone who is rich is both strong and not quiet and vice versa. Everyone who is either creative or not strong is not rich and vice versa. Everyone who is either happy or not creative is either not rich or not tall and vice versa. If someone is either not strong or brave then someone is generous or not creative and vice versa. Everyone who is wise or not strong is not patient and vice versa. If john is not old then lucy is brave or not tall. If someone is both tall and curious then lucy is either not rich or generous and vice versa. Everyone who is calm or kind is kind or tall and vice versa. Everyone who is happy is not creative or not happy and vice versa. If fred is not wise then lucy is both curious and patient and vice versa. If someone is either not humble or creative then someone is both not old and funny and vice versa. If susan is either quiet or kind then someone is tall. Everyone who is funny or not old is either generous or not old. If john is both tall and patient then someone is humble and vice versa. Alice is not old. Someone is not wise. Someone is kind or not creative. Someone is both wise and not old. Someone is either humble or kind. Someone is either calm or not tall. Someone is not calm. Lucy is both not old and not tall. | Lucy is not patient. | entailment | (![X]:((tall(X)|humble(X))=>(~brave(X)|~old(X))))&
(![X]:((~funny(X)&brave(X))=>(happy(X)|curious(X))))&
(![X]:(rich(X)<=>(strong(X)&~quiet(X))))&
(![X]:((creative(X)<~>~strong(X))<=>~rich(X)))&
(![X]:((happy(X)<~>~creative(X))<=>(~rich(X)<~>~tall(X))))&
((?[X]:((~strong(X)<~>brave(X))))<=>(?[X]:((generous(X)|~creative(X)))))&
(![X]:((wise(X)|~strong(X))<=>~patient(X)))&
((~old(john))=>((brave(lucy)|~tall(lucy))))&
((?[X]:((tall(X)&curious(X))))<=>((~rich(lucy)<~>generous(lucy))))&
(![X]:((calm(X)|kind(X))<=>(kind(X)|tall(X))))&
(![X]:(happy(X)<=>(~creative(X)|~happy(X))))&
((~wise(fred))<=>((curious(lucy)&patient(lucy))))&
((?[X]:((~humble(X)<~>creative(X))))<=>(?[X]:((~old(X)&funny(X)))))&
(((quiet(susan)<~>kind(susan)))=>(?[X]:(tall(X))))&
(![X]:((funny(X)|~old(X))=>(generous(X)<~>~old(X))))&
(((tall(john)&patient(john)))<=>(?[X]:(humble(X))))&
(~old(alice))&
(?[X]:(~wise(X)))&
(?[X]:((kind(X)|~creative(X))))&
(?[X]:((wise(X)&~old(X))))&
(?[X]:((humble(X)<~>kind(X))))&
(?[X]:((calm(X)<~>~tall(X))))&
(?[X]:(~calm(X)))&
((~old(lucy)&~tall(lucy))) | ~patient(lucy) | [
"p2",
"p3",
"p4",
"p6",
"p10",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8045203378339616398440663
% SZS output start Proof for 8045203378339616398440663
3. ! [X0] : (rich(X0) <=> (~quiet(X0) & strong(X0))) [input p2]
4. ! [X0] : ((creative(X0) <~> ~strong(X0)) <=> ~rich(X0)) [input p3]
5. ! [X0] : ((happy(X0) <~> ~creative(X0)) <=> (~rich(X0) <~> ~tall(X0))) [input p4]
7. ! [X0] : ((~strong(X0) | wise(X0)) <=> ~patient(X0)) [input p6]
11. ! [X0] : (happy(X0) <=> (~happy(X0) | ~creative(X0))) [input p10]
24. ~tall(lucy) & ~old(lucy) [input p23]
25. patient(lucy) [input hypothesis]
36. ! [X0] : ((rich(X0) | (quiet(X0) | ~strong(X0))) & ((~quiet(X0) & strong(X0)) | ~rich(X0))) [nnf transformation 3]
37. ! [X0] : ((rich(X0) | quiet(X0) | ~strong(X0)) & ((~quiet(X0) & strong(X0)) | ~rich(X0))) [flattening 36]
38. ! [X0] : ((((strong(X0) | ~creative(X0)) & (~strong(X0) | creative(X0))) | rich(X0)) & (~rich(X0) | ((creative(X0) | strong(X0)) & (~strong(X0) | ~creative(X0))))) [nnf transformation 4]
39. ! [X0] : ((((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0)))) & (((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0))))) [nnf transformation 5]
45. ! [X0] : (((~strong(X0) | wise(X0)) | patient(X0)) & (~patient(X0) | (strong(X0) & ~wise(X0)))) [nnf transformation 7]
46. ! [X0] : ((~strong(X0) | wise(X0) | patient(X0)) & (~patient(X0) | (strong(X0) & ~wise(X0)))) [flattening 45]
53. ! [X0] : ((happy(X0) | (happy(X0) & creative(X0))) & ((~happy(X0) | ~creative(X0)) | ~happy(X0))) [nnf transformation 11]
54. ! [X0] : ((happy(X0) | (happy(X0) & creative(X0))) & (~happy(X0) | ~creative(X0) | ~happy(X0))) [flattening 53]
88. ~rich(X0) | strong(X0) [cnf transformation 37]
91. ~rich(X0) | ~strong(X0) | ~creative(X0) [cnf transformation 38]
93. ~strong(X0) | creative(X0) | rich(X0) [cnf transformation 38]
94. strong(X0) | ~creative(X0) | rich(X0) [cnf transformation 38]
102. creative(X0) | ~happy(X0) | ~rich(X0) | tall(X0) [cnf transformation 39]
110. ~patient(X0) | strong(X0) [cnf transformation 46]
123. ~happy(X0) | ~creative(X0) | ~happy(X0) [cnf transformation 54]
125. happy(X0) | happy(X0) [cnf transformation 54]
155. ~tall(lucy) [cnf transformation 24]
156. patient(lucy) [cnf transformation 25]
158. ~happy(X0) | ~creative(X0) [duplicate literal removal 123]
159. happy(X0) [duplicate literal removal 125]
160. ~creative(X0) | strong(X0) [subsumption resolution 94,88]
161. ~creative(X0) | ~rich(X0) [subsumption resolution 91,160]
162. ~rich(X0) | ~happy(X0) | tall(X0) [subsumption resolution 102,161]
209. 11 <=> tall(lucy) [avatar definition]
211. ~tall(lucy) <- (~11) [avatar component clause 209]
218. 13 <=> rich(lucy) [avatar definition]
219. rich(lucy) <- (13) [avatar component clause 218]
238. ~creative(X0) [subsumption resolution 158,159]
244. 18 <=> patient(lucy) [avatar definition]
245. patient(lucy) <- (18) [avatar component clause 244]
330. ~11 [avatar split clause 155,209]
331. 18 [avatar split clause 156,244]
338. strong(lucy) <- (18) [resolution 110,245]
353. creative(lucy) | rich(lucy) <- (18) [resolution 93,338]
355. rich(lucy) <- (18) [subsumption resolution 353,238]
358. 13 | ~18 [avatar split clause 355,244,218]
384. ~happy(lucy) | tall(lucy) <- (13) [resolution 162,219]
386. tall(lucy) <- (13) [subsumption resolution 384,159]
387. $false <- (~11, 13) [subsumption resolution 386,211]
388. 11 | ~13 [avatar contradiction clause 387]
389. $false [avatar sat refutation 330,331,358,388]
% SZS output end Proof for 8045203378339616398440663
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or not humble is both not funny and not curious and vice versa.
Everyone who is curious is both tall and strong.
If someone is either not funny or not old then someone is calm.
If someone is patient or not strong then someone is both patient and not curious.
If someone is not strong or not rich then someone is both old and tall.
Everyone who is both creative and not calm is generous or not wise and vice versa.
If susan is both strong and not humble then someone is both not creative and patient and vice versa.
If someone is both quiet and wise then alice is both generous and not strong.
Everyone who is not funny or not patient is both creative and not old.
Everyone who is both strong and wise is either not creative or not kind and vice versa.
If someone is both curious and strong then susan is not curious and vice versa.
Everyone who is both old and generous is either funny or rich.
Everyone who is either not kind or tall is not creative.
If someone is not curious then someone is both kind and not rich and vice versa.
Everyone who is either quiet or brave is not calm.
Paul is either not funny or creative.
Someone is either patient or not strong.
Susan is either not generous or generous.
Someone is both strong and tall.
Someone is not patient or not happy.
Someone is not funny or happy.
Susan is either not patient or brave.
Someone is quiet or creative. | Susan is not creative. | contradiction | (![X]:((~strong(X)<~>~humble(X))<=>(~funny(X)&~curious(X))))&
(![X]:(curious(X)=>(tall(X)&strong(X))))&
((?[X]:((~funny(X)<~>~old(X))))=>(?[X]:(calm(X))))&
((?[X]:((patient(X)|~strong(X))))=>(?[X]:((patient(X)&~curious(X)))))&
((?[X]:((~strong(X)|~rich(X))))=>(?[X]:((old(X)&tall(X)))))&
(![X]:((creative(X)&~calm(X))<=>(generous(X)|~wise(X))))&
(((strong(susan)&~humble(susan)))<=>(?[X]:((~creative(X)&patient(X)))))&
((?[X]:((quiet(X)&wise(X))))=>((generous(alice)&~strong(alice))))&
(![X]:((~funny(X)|~patient(X))=>(creative(X)&~old(X))))&
(![X]:((strong(X)&wise(X))<=>(~creative(X)<~>~kind(X))))&
((?[X]:((curious(X)&strong(X))))<=>(~curious(susan)))&
(![X]:((old(X)&generous(X))=>(funny(X)<~>rich(X))))&
(![X]:((~kind(X)<~>tall(X))=>~creative(X)))&
((?[X]:(~curious(X)))<=>(?[X]:((kind(X)&~rich(X)))))&
(![X]:((quiet(X)<~>brave(X))=>~calm(X)))&
((~funny(paul)<~>creative(paul)))&
(?[X]:((patient(X)<~>~strong(X))))&
((~generous(susan)<~>generous(susan)))&
(?[X]:((strong(X)&tall(X))))&
(?[X]:((~patient(X)|~happy(X))))&
(?[X]:((~funny(X)|happy(X))))&
((~patient(susan)<~>brave(susan)))&
(?[X]:((quiet(X)|creative(X)))) | ~creative(susan) | [
"p0",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8952612882599366165926803
% SZS output start Proof for 8952612882599366165926803
1. ! [X0] : ((~strong(X0) <~> ~humble(X0)) <=> (~curious(X0) & ~funny(X0))) [input p0]
7. (~humble(susan) & strong(susan)) <=> ? [X0] : (patient(X0) & ~creative(X0)) [input p6]
9. ! [X0] : ((~patient(X0) | ~funny(X0)) => (~old(X0) & creative(X0))) [input p8]
24. ~creative(susan) [input hypothesis]
34. ! [X0] : ((~old(X0) & creative(X0)) | (patient(X0) & funny(X0))) [ennf transformation 9]
39. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | (curious(X0) | funny(X0))) & ((~curious(X0) & ~funny(X0)) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [nnf transformation 1]
40. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | curious(X0) | funny(X0)) & ((~curious(X0) & ~funny(X0)) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [flattening 39]
53. ((~humble(susan) & strong(susan)) | ! [X0] : (~patient(X0) | creative(X0))) & (? [X0] : (patient(X0) & ~creative(X0)) | (humble(susan) | ~strong(susan))) [nnf transformation 7]
54. ((~humble(susan) & strong(susan)) | ! [X0] : (~patient(X0) | creative(X0))) & (? [X0] : (patient(X0) & ~creative(X0)) | humble(susan) | ~strong(susan)) [flattening 53]
55. ((~humble(susan) & strong(susan)) | ! [X0] : (~patient(X0) | creative(X0))) & (? [X1] : (patient(X1) & ~creative(X1)) | humble(susan) | ~strong(susan)) [rectify 54]
56. ? [X1] : (patient(X1) & ~creative(X1)) => (patient(sK3) & ~creative(sK3)) [choice axiom]
57. ((~humble(susan) & strong(susan)) | ! [X0] : (~patient(X0) | creative(X0))) & ((patient(sK3) & ~creative(sK3)) | humble(susan) | ~strong(susan)) [skolemisation 55,56]
87. ~funny(X0) | ~strong(X0) | humble(X0) [cnf transformation 40]
111. strong(susan) | ~patient(X0) | creative(X0) [cnf transformation 57]
112. ~humble(susan) | ~patient(X0) | creative(X0) [cnf transformation 57]
115. creative(X0) | funny(X0) [cnf transformation 34]
116. creative(X0) | patient(X0) [cnf transformation 34]
150. ~creative(susan) [cnf transformation 24]
197. 11 <=> ! [X0] : (~patient(X0) | creative(X0)) [avatar definition]
198. ~patient(X0) | creative(X0) <- (11) [avatar component clause 197]
200. 12 <=> humble(susan) [avatar definition]
202. ~humble(susan) <- (~12) [avatar component clause 200]
203. 11 | ~12 [avatar split clause 112,200,197]
205. 13 <=> strong(susan) [avatar definition]
207. strong(susan) <- (13) [avatar component clause 205]
208. 11 | 13 [avatar split clause 111,205,197]
328. creative(X0) <- (11) [subsumption resolution 198,116]
343. $false <- (11) [resolution 328,150]
344. ~11 [avatar contradiction clause 343]
348. funny(susan) [resolution 115,150]
397. ~strong(susan) | humble(susan) [resolution 87,348]
401. humble(susan) <- (13) [subsumption resolution 397,207]
402. $false <- (~12, 13) [subsumption resolution 401,202]
403. 12 | ~13 [avatar contradiction clause 402]
410. $false [avatar sat refutation 203,208,344,403]
% SZS output end Proof for 8952612882599366165926803
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not old and not patient then someone is brave or not patient.
Everyone who is both humble and brave is either happy or creative.
Everyone who is both not funny and not happy is not calm and vice versa.
Everyone who is both funny and not curious is both not generous and funny and vice versa.
Everyone who is both not brave and humble is old or not generous and vice versa.
If lucy is kind then someone is rich.
Everyone who is creative is not patient or not generous and vice versa.
Everyone who is not generous is both strong and not brave and vice versa.
Everyone who is both not calm and not brave is calm or tall and vice versa.
If susan is not brave or curious then susan is either not quiet or not happy.
If someone is both not rich and brave then john is either quiet or patient and vice versa.
Everyone who is both tall and not curious is both patient and not tall and vice versa.
If alice is both not strong and not curious then someone is calm and vice versa.
Everyone who is not creative is both not humble and creative.
Everyone who is either strong or not brave is both creative and not wise and vice versa.
If mary is not quiet or old then john is both not rich and calm and vice versa.
Alice is not happy or rich.
Fred is not happy.
Someone is not calm or not strong.
Someone is not brave.
Lucy is both not humble and wise.
Paul is not kind or creative.
Paul is either calm or old. | Fred is funny. | contradiction | ((?[X]:((~old(X)&~patient(X))))=>(?[X]:((brave(X)|~patient(X)))))&
(![X]:((humble(X)&brave(X))=>(happy(X)<~>creative(X))))&
(![X]:((~funny(X)&~happy(X))<=>~calm(X)))&
(![X]:((funny(X)&~curious(X))<=>(~generous(X)&funny(X))))&
(![X]:((~brave(X)&humble(X))<=>(old(X)|~generous(X))))&
((kind(lucy))=>(?[X]:(rich(X))))&
(![X]:(creative(X)<=>(~patient(X)|~generous(X))))&
(![X]:(~generous(X)<=>(strong(X)&~brave(X))))&
(![X]:((~calm(X)&~brave(X))<=>(calm(X)|tall(X))))&
(((~brave(susan)|curious(susan)))=>((~quiet(susan)<~>~happy(susan))))&
((?[X]:((~rich(X)&brave(X))))<=>((quiet(john)<~>patient(john))))&
(![X]:((tall(X)&~curious(X))<=>(patient(X)&~tall(X))))&
(((~strong(alice)&~curious(alice)))<=>(?[X]:(calm(X))))&
(![X]:(~creative(X)=>(~humble(X)&creative(X))))&
(![X]:((strong(X)<~>~brave(X))<=>(creative(X)&~wise(X))))&
(((~quiet(mary)|old(mary)))<=>((~rich(john)&calm(john))))&
((~happy(alice)|rich(alice)))&
(~happy(fred))&
(?[X]:((~calm(X)|~strong(X))))&
(?[X]:(~brave(X)))&
((~humble(lucy)&wise(lucy)))&
((~kind(paul)|creative(paul)))&
((calm(paul)<~>old(paul))) | funny(fred) | [
"p2",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4388191185967895736346969
% SZS output start Proof for 4388191185967895736346969
3. ! [X0] : ((~happy(X0) & ~funny(X0)) <=> ~calm(X0)) [input p2]
9. ! [X0] : ((~brave(X0) & ~calm(X0)) <=> (tall(X0) | calm(X0))) [input p8]
24. funny(fred) [input hypothesis]
37. ! [X0] : (((~happy(X0) & ~funny(X0)) | calm(X0)) & (~calm(X0) | (happy(X0) | funny(X0)))) [nnf transformation 3]
38. ! [X0] : (((~happy(X0) & ~funny(X0)) | calm(X0)) & (~calm(X0) | happy(X0) | funny(X0))) [flattening 37]
47. ! [X0] : (((~brave(X0) & ~calm(X0)) | (~tall(X0) & ~calm(X0))) & ((tall(X0) | calm(X0)) | (brave(X0) | calm(X0)))) [nnf transformation 9]
48. ! [X0] : (((~brave(X0) & ~calm(X0)) | (~tall(X0) & ~calm(X0))) & (tall(X0) | calm(X0) | brave(X0) | calm(X0))) [flattening 47]
74. ~funny(X0) | calm(X0) [cnf transformation 38]
92. ~calm(X0) | ~calm(X0) [cnf transformation 48]
134. funny(fred) [cnf transformation 24]
139. ~calm(X0) [duplicate literal removal 92]
222. calm(fred) [resolution 74,134]
223. $false [subsumption resolution 222,139]
% SZS output end Proof for 4388191185967895736346969
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either tall or patient then paul is either not curious or wise and vice versa.
If alice is either calm or quiet then paul is both rich and not creative.
If someone is both happy and kind then someone is both not funny and not creative.
Everyone who is either wise or patient is both generous and funny.
Everyone who is not old is both not quiet and brave and vice versa.
Everyone who is both creative and funny is not humble or not rich.
Everyone who is not humble or kind is both generous and not brave and vice versa.
Everyone who is creative is not wise.
Everyone who is both not quiet and rich is both not tall and rich and vice versa.
If someone is both tall and not kind then john is brave.
If someone is either not brave or not creative then fred is both strong and not old.
If fred is both generous and rich then paul is not humble or old.
If someone is both brave and not creative then someone is either humble or not calm and vice versa.
If lucy is not funny then alice is either not generous or funny and vice versa.
If someone is happy then mary is both strong and humble and vice versa.
Everyone who is both brave and not happy is not calm.
Paul is both not happy and curious.
Lucy is both old and strong.
Someone is either not generous or rich.
Fred is humble.
Lucy is either not brave or wise.
Someone is both curious and patient.
Someone is curious.
Fred is both creative and humble. | Mary is not happy. | neutral | ((?[X]:((tall(X)<~>patient(X))))<=>((~curious(paul)<~>wise(paul))))&
(((calm(alice)<~>quiet(alice)))=>((rich(paul)&~creative(paul))))&
((?[X]:((happy(X)&kind(X))))=>(?[X]:((~funny(X)&~creative(X)))))&
(![X]:((wise(X)<~>patient(X))=>(generous(X)&funny(X))))&
(![X]:(~old(X)<=>(~quiet(X)&brave(X))))&
(![X]:((creative(X)&funny(X))=>(~humble(X)|~rich(X))))&
(![X]:((~humble(X)|kind(X))<=>(generous(X)&~brave(X))))&
(![X]:(creative(X)=>~wise(X)))&
(![X]:((~quiet(X)&rich(X))<=>(~tall(X)&rich(X))))&
((?[X]:((tall(X)&~kind(X))))=>(brave(john)))&
((?[X]:((~brave(X)<~>~creative(X))))=>((strong(fred)&~old(fred))))&
(((generous(fred)&rich(fred)))=>((~humble(paul)|old(paul))))&
((?[X]:((brave(X)&~creative(X))))<=>(?[X]:((humble(X)<~>~calm(X)))))&
((~funny(lucy))<=>((~generous(alice)<~>funny(alice))))&
((?[X]:(happy(X)))<=>((strong(mary)&humble(mary))))&
(![X]:((brave(X)&~happy(X))=>~calm(X)))&
((~happy(paul)&curious(paul)))&
((old(lucy)&strong(lucy)))&
(?[X]:((~generous(X)<~>rich(X))))&
(humble(fred))&
((~brave(lucy)<~>wise(lucy)))&
(?[X]:((curious(X)&patient(X))))&
(?[X]:(curious(X)))&
((creative(fred)&humble(fred))) | ~happy(mary) | [] | null | 0 |
If mary is both not kind and brave then someone is both generous and not patient.
Everyone who is either not happy or tall is wise and vice versa.
If someone is both wise and not wise then alice is both not curious and not humble and vice versa.
Everyone who is not old is either wise or strong.
Everyone who is patient is both not generous and happy.
Everyone who is either wise or not wise is not old.
If someone is either humble or not curious then someone is strong or not tall.
If alice is both not strong and generous then someone is brave and vice versa.
If someone is not rich or not patient then susan is either not patient or not humble.
If fred is quiet then lucy is both happy and not strong.
Everyone who is both not old and not strong is old or not creative and vice versa.
Everyone who is both quiet and curious is both kind and not wise and vice versa.
Everyone who is patient or not wise is either wise or not brave.
Everyone who is both calm and not brave is not humble or calm.
If mary is both curious and not wise then john is both not kind and not calm.
If someone is both not happy and not kind then someone is not curious or not happy and vice versa.
Someone is tall or quiet.
Someone is rich or brave.
Someone is not quiet.
Someone is either generous or not creative.
Someone is not kind or not patient.
Someone is either funny or not calm.
Paul is either quiet or not generous. | Mary is not tall. | neutral | (((~kind(mary)&brave(mary)))=>(?[X]:((generous(X)&~patient(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>wise(X)))&
((?[X]:((wise(X)&~wise(X))))<=>((~curious(alice)&~humble(alice))))&
(![X]:(~old(X)=>(wise(X)<~>strong(X))))&
(![X]:(patient(X)=>(~generous(X)&happy(X))))&
(![X]:((wise(X)<~>~wise(X))=>~old(X)))&
((?[X]:((humble(X)<~>~curious(X))))=>(?[X]:((strong(X)|~tall(X)))))&
(((~strong(alice)&generous(alice)))<=>(?[X]:(brave(X))))&
((?[X]:((~rich(X)|~patient(X))))=>((~patient(susan)<~>~humble(susan))))&
((quiet(fred))=>((happy(lucy)&~strong(lucy))))&
(![X]:((~old(X)&~strong(X))<=>(old(X)|~creative(X))))&
(![X]:((quiet(X)&curious(X))<=>(kind(X)&~wise(X))))&
(![X]:((patient(X)|~wise(X))=>(wise(X)<~>~brave(X))))&
(![X]:((calm(X)&~brave(X))=>(~humble(X)|calm(X))))&
(((curious(mary)&~wise(mary)))=>((~kind(john)&~calm(john))))&
((?[X]:((~happy(X)&~kind(X))))<=>(?[X]:((~curious(X)|~happy(X)))))&
(?[X]:((tall(X)|quiet(X))))&
(?[X]:((rich(X)|brave(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((generous(X)<~>~creative(X))))&
(?[X]:((~kind(X)|~patient(X))))&
(?[X]:((funny(X)<~>~calm(X))))&
((quiet(paul)<~>~generous(paul))) | ~tall(mary) | [] | null | 0 |
Everyone who is either curious or not kind is both not generous and not wise.
Everyone who is not calm or not strong is either kind or not curious.
Everyone who is both not calm and not patient is either brave or calm.
Everyone who is both calm and curious is wise.
If someone is either rich or not kind then susan is either old or not humble and vice versa.
Everyone who is either funny or not humble is generous or not happy.
If susan is not happy then someone is either not strong or not humble and vice versa.
If susan is generous then someone is both not creative and kind and vice versa.
If someone is strong or not wise then paul is not creative or old and vice versa.
Everyone who is both generous and not kind is not generous.
If alice is both kind and not old then john is either not generous or not brave.
If someone is rich then paul is both calm and not happy and vice versa.
Everyone who is either kind or not curious is wise or not happy and vice versa.
If paul is not happy then someone is rich.
If someone is both wise and not funny then someone is either not brave or creative and vice versa.
If lucy is both curious and not wise then someone is tall and vice versa.
Someone is not creative.
Someone is generous.
Someone is not quiet or generous.
Fred is either quiet or strong.
Someone is humble.
Fred is generous or quiet. | Paul is not brave. | neutral | (![X]:((curious(X)<~>~kind(X))=>(~generous(X)&~wise(X))))&
(![X]:((~calm(X)|~strong(X))=>(kind(X)<~>~curious(X))))&
(![X]:((~calm(X)&~patient(X))=>(brave(X)<~>calm(X))))&
(![X]:((calm(X)&curious(X))=>wise(X)))&
((?[X]:((rich(X)<~>~kind(X))))<=>((old(susan)<~>~humble(susan))))&
(![X]:((funny(X)<~>~humble(X))=>(generous(X)|~happy(X))))&
((~happy(susan))<=>(?[X]:((~strong(X)<~>~humble(X)))))&
((generous(susan))<=>(?[X]:((~creative(X)&kind(X)))))&
((?[X]:((strong(X)|~wise(X))))<=>((~creative(paul)|old(paul))))&
(![X]:((generous(X)&~kind(X))=>~generous(X)))&
(((kind(alice)&~old(alice)))=>((~generous(john)<~>~brave(john))))&
((?[X]:(rich(X)))<=>((calm(paul)&~happy(paul))))&
(![X]:((kind(X)<~>~curious(X))<=>(wise(X)|~happy(X))))&
((~happy(paul))=>(?[X]:(rich(X))))&
((?[X]:((wise(X)&~funny(X))))<=>(?[X]:((~brave(X)<~>creative(X)))))&
(((curious(lucy)&~wise(lucy)))<=>(?[X]:(tall(X))))&
(?[X]:(~creative(X)))&
(?[X]:(generous(X)))&
(?[X]:((~quiet(X)|generous(X))))&
((quiet(fred)<~>strong(fred)))&
(?[X]:(humble(X)))&
((generous(fred)|quiet(fred))) | ~brave(paul) | [] | null | 0 |
Everyone who is either not patient or wise is not curious and vice versa.
Everyone who is patient or old is both not tall and brave and vice versa.
Everyone who is either not tall or creative is both not curious and happy and vice versa.
Everyone who is not funny is not wise.
Everyone who is not quiet is happy or tall and vice versa.
Everyone who is curious or old is either not wise or curious.
If john is not patient or old then someone is not creative or not humble and vice versa.
Everyone who is not strong or not old is not curious or not brave.
Everyone who is either not funny or not quiet is not curious.
If someone is either not creative or not rich then someone is either not tall or creative and vice versa.
Everyone who is both patient and old is either tall or not kind.
Everyone who is not quiet or not rich is either not old or wise.
If susan is both not happy and not funny then someone is not calm or calm and vice versa.
If someone is both not creative and not humble then lucy is both not funny and not kind.
Everyone who is happy or not strong is both funny and creative and vice versa.
Everyone who is both creative and not tall is kind and vice versa.
Someone is either not old or not generous.
Someone is both not strong and not humble.
Someone is not rich.
Someone is not generous or funny.
Fred is both not happy and not brave.
Someone is both kind and humble.
Someone is either rich or not old.
Someone is patient or curious. | John is wise. | neutral | (![X]:((~patient(X)<~>wise(X))<=>~curious(X)))&
(![X]:((patient(X)|old(X))<=>(~tall(X)&brave(X))))&
(![X]:((~tall(X)<~>creative(X))<=>(~curious(X)&happy(X))))&
(![X]:(~funny(X)=>~wise(X)))&
(![X]:(~quiet(X)<=>(happy(X)|tall(X))))&
(![X]:((curious(X)|old(X))=>(~wise(X)<~>curious(X))))&
(((~patient(john)|old(john)))<=>(?[X]:((~creative(X)|~humble(X)))))&
(![X]:((~strong(X)|~old(X))=>(~curious(X)|~brave(X))))&
(![X]:((~funny(X)<~>~quiet(X))=>~curious(X)))&
((?[X]:((~creative(X)<~>~rich(X))))<=>(?[X]:((~tall(X)<~>creative(X)))))&
(![X]:((patient(X)&old(X))=>(tall(X)<~>~kind(X))))&
(![X]:((~quiet(X)|~rich(X))=>(~old(X)<~>wise(X))))&
(((~happy(susan)&~funny(susan)))<=>(?[X]:((~calm(X)|calm(X)))))&
((?[X]:((~creative(X)&~humble(X))))=>((~funny(lucy)&~kind(lucy))))&
(![X]:((happy(X)|~strong(X))<=>(funny(X)&creative(X))))&
(![X]:((creative(X)&~tall(X))<=>kind(X)))&
(?[X]:((~old(X)<~>~generous(X))))&
(?[X]:((~strong(X)&~humble(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~generous(X)|funny(X))))&
((~happy(fred)&~brave(fred)))&
(?[X]:((kind(X)&humble(X))))&
(?[X]:((rich(X)<~>~old(X))))&
(?[X]:((patient(X)|curious(X)))) | wise(john) | [] | null | 0 |
Everyone who is both funny and not creative is either tall or generous. If paul is either brave or not generous then john is not creative and vice versa. Everyone who is either not brave or not funny is not humble and vice versa. Everyone who is either curious or creative is both not quiet and curious and vice versa. Everyone who is not curious is not old or brave and vice versa. If someone is either quiet or creative then lucy is both not quiet and not generous. Everyone who is both not strong and tall is both not curious and funny. Everyone who is either generous or calm is both not calm and happy and vice versa. Everyone who is both tall and quiet is not patient or rich and vice versa. Everyone who is not kind is quiet or wise and vice versa. Everyone who is both not brave and not wise is either old or not generous and vice versa. Everyone who is not curious is old or not kind. Everyone who is both not old and not happy is both not old and not rich and vice versa. Everyone who is either curious or not humble is not generous and vice versa. If mary is both not creative and curious then mary is not happy. Everyone who is both curious and not kind is not funny. Someone is both not generous and brave. Paul is not kind. Someone is not strong. Fred is not curious or wise. Someone is either brave or not happy. Fred is patient or happy. Someone is humble. Someone is curious. | Lucy is tall. | neutral | (![X]:((funny(X)&~creative(X))=>(tall(X)<~>generous(X))))&
(((brave(paul)<~>~generous(paul)))<=>(~creative(john)))&
(![X]:((~brave(X)<~>~funny(X))<=>~humble(X)))&
(![X]:((curious(X)<~>creative(X))<=>(~quiet(X)&curious(X))))&
(![X]:(~curious(X)<=>(~old(X)|brave(X))))&
((?[X]:((quiet(X)<~>creative(X))))=>((~quiet(lucy)&~generous(lucy))))&
(![X]:((~strong(X)&tall(X))=>(~curious(X)&funny(X))))&
(![X]:((generous(X)<~>calm(X))<=>(~calm(X)&happy(X))))&
(![X]:((tall(X)&quiet(X))<=>(~patient(X)|rich(X))))&
(![X]:(~kind(X)<=>(quiet(X)|wise(X))))&
(![X]:((~brave(X)&~wise(X))<=>(old(X)<~>~generous(X))))&
(![X]:(~curious(X)=>(old(X)|~kind(X))))&
(![X]:((~old(X)&~happy(X))<=>(~old(X)&~rich(X))))&
(![X]:((curious(X)<~>~humble(X))<=>~generous(X)))&
(((~creative(mary)&curious(mary)))=>(~happy(mary)))&
(![X]:((curious(X)&~kind(X))=>~funny(X)))&
(?[X]:((~generous(X)&brave(X))))&
(~kind(paul))&
(?[X]:(~strong(X)))&
((~curious(fred)|wise(fred)))&
(?[X]:((brave(X)<~>~happy(X))))&
((patient(fred)|happy(fred)))&
(?[X]:(humble(X)))&
(?[X]:(curious(X))) | tall(lucy) | [] | null | 0 |
If someone is strong or quiet then someone is either wise or not rich.
Everyone who is both not brave and not happy is wise or not humble and vice versa.
Everyone who is either not generous or not rich is both not patient and not wise and vice versa.
Everyone who is both not generous and happy is not funny or not happy and vice versa.
Everyone who is either humble or happy is either funny or not creative.
If someone is generous or funny then mary is quiet or not strong and vice versa.
If someone is funny then fred is either brave or quiet.
If someone is either not strong or generous then someone is either old or not tall and vice versa.
Everyone who is both not curious and patient is either not tall or not calm.
If mary is both quiet and humble then someone is either not rich or brave and vice versa.
Everyone who is not humble or not kind is both quiet and not funny.
Everyone who is either wise or old is both not funny and old and vice versa.
Everyone who is not brave or creative is either not calm or not strong.
If lucy is either creative or not old then alice is both not old and not tall.
If john is both quiet and creative then someone is either curious or patient and vice versa.
If paul is not brave then paul is both not calm and not happy.
Someone is either funny or not wise.
Alice is not calm or old.
Someone is not patient or curious.
Alice is both old and not funny.
Alice is both not tall and rich.
John is funny or not quiet. | Lucy is creative. | neutral | ((?[X]:((strong(X)|quiet(X))))=>(?[X]:((wise(X)<~>~rich(X)))))&
(![X]:((~brave(X)&~happy(X))<=>(wise(X)|~humble(X))))&
(![X]:((~generous(X)<~>~rich(X))<=>(~patient(X)&~wise(X))))&
(![X]:((~generous(X)&happy(X))<=>(~funny(X)|~happy(X))))&
(![X]:((humble(X)<~>happy(X))=>(funny(X)<~>~creative(X))))&
((?[X]:((generous(X)|funny(X))))<=>((quiet(mary)|~strong(mary))))&
((?[X]:(funny(X)))=>((brave(fred)<~>quiet(fred))))&
((?[X]:((~strong(X)<~>generous(X))))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:((~curious(X)&patient(X))=>(~tall(X)<~>~calm(X))))&
(((quiet(mary)&humble(mary)))<=>(?[X]:((~rich(X)<~>brave(X)))))&
(![X]:((~humble(X)|~kind(X))=>(quiet(X)&~funny(X))))&
(![X]:((wise(X)<~>old(X))<=>(~funny(X)&old(X))))&
(![X]:((~brave(X)|creative(X))=>(~calm(X)<~>~strong(X))))&
(((creative(lucy)<~>~old(lucy)))=>((~old(alice)&~tall(alice))))&
(((quiet(john)&creative(john)))<=>(?[X]:((curious(X)<~>patient(X)))))&
((~brave(paul))=>((~calm(paul)&~happy(paul))))&
(?[X]:((funny(X)<~>~wise(X))))&
((~calm(alice)|old(alice)))&
(?[X]:((~patient(X)|curious(X))))&
((old(alice)&~funny(alice)))&
((~tall(alice)&rich(alice)))&
((funny(john)|~quiet(john))) | creative(lucy) | [] | null | 0 |
Everyone who is not curious is patient or not curious.
Everyone who is both not generous and not curious is calm or creative and vice versa.
If someone is generous then john is not patient.
Everyone who is not strong is both not old and humble.
Everyone who is both creative and kind is either patient or curious and vice versa.
If someone is not tall or curious then someone is both calm and curious and vice versa.
If mary is both kind and not calm then paul is both quiet and calm.
If mary is either not strong or old then someone is either brave or funny.
If someone is happy then someone is either not quiet or strong.
Everyone who is not generous is funny and vice versa.
Everyone who is strong or happy is creative or not funny and vice versa.
If someone is either brave or not happy then someone is both not curious and not tall and vice versa.
Everyone who is either rich or not strong is patient and vice versa.
Everyone who is either patient or not rich is not calm.
Everyone who is rich is either creative or not old and vice versa.
Paul is not old or kind.
Fred is both not curious and calm.
John is both not happy and calm.
Someone is either not happy or curious.
Mary is not creative.
Lucy is both not kind and not calm. | Fred is not happy. | neutral | (![X]:(~curious(X)=>(patient(X)|~curious(X))))&
(![X]:((~generous(X)&~curious(X))<=>(calm(X)|creative(X))))&
((?[X]:(generous(X)))=>(~patient(john)))&
(![X]:(~strong(X)=>(~old(X)&humble(X))))&
(![X]:((creative(X)&kind(X))<=>(patient(X)<~>curious(X))))&
((?[X]:((~tall(X)|curious(X))))<=>(?[X]:((calm(X)&curious(X)))))&
(((kind(mary)&~calm(mary)))=>((quiet(paul)&calm(paul))))&
(((~strong(mary)<~>old(mary)))=>(?[X]:((brave(X)<~>funny(X)))))&
((?[X]:(happy(X)))=>(?[X]:((~quiet(X)<~>strong(X)))))&
(![X]:(~generous(X)<=>funny(X)))&
(![X]:((strong(X)|happy(X))<=>(creative(X)|~funny(X))))&
((?[X]:((brave(X)<~>~happy(X))))<=>(?[X]:((~curious(X)&~tall(X)))))&
(![X]:((rich(X)<~>~strong(X))<=>patient(X)))&
(![X]:((patient(X)<~>~rich(X))=>~calm(X)))&
(![X]:(rich(X)<=>(creative(X)<~>~old(X))))&
((~old(paul)|kind(paul)))&
((~curious(fred)&calm(fred)))&
((~happy(john)&calm(john)))&
(?[X]:((~happy(X)<~>curious(X))))&
(~creative(mary))&
((~kind(lucy)&~calm(lucy))) | ~happy(fred) | [] | null | 0 |
Everyone who is not patient or wise is both not brave and patient and vice versa.
If alice is generous or quiet then paul is either not tall or kind and vice versa.
Everyone who is either humble or rich is both not brave and brave and vice versa.
If someone is not wise or not curious then someone is quiet or not wise.
Everyone who is quiet or not wise is both not kind and kind.
Everyone who is either funny or not tall is both not strong and not wise.
If lucy is either happy or not humble then alice is either not humble or not quiet.
Everyone who is both curious and not generous is strong.
If someone is either not happy or tall then someone is quiet and vice versa.
If someone is either calm or creative then lucy is either strong or tall and vice versa.
Everyone who is both not generous and not patient is either not old or quiet.
If someone is either humble or old then someone is both not generous and kind and vice versa.
If someone is both happy and old then alice is both not happy and not rich.
If someone is not happy then john is not brave.
Mary is not tall.
Mary is kind.
Paul is not happy or not generous.
Someone is either generous or wise.
Mary is either wise or not creative. | Alice is not calm. | neutral | (![X]:((~patient(X)|wise(X))<=>(~brave(X)&patient(X))))&
(((generous(alice)|quiet(alice)))<=>((~tall(paul)<~>kind(paul))))&
(![X]:((humble(X)<~>rich(X))<=>(~brave(X)&brave(X))))&
((?[X]:((~wise(X)|~curious(X))))=>(?[X]:((quiet(X)|~wise(X)))))&
(![X]:((quiet(X)|~wise(X))=>(~kind(X)&kind(X))))&
(![X]:((funny(X)<~>~tall(X))=>(~strong(X)&~wise(X))))&
(((happy(lucy)<~>~humble(lucy)))=>((~humble(alice)<~>~quiet(alice))))&
(![X]:((curious(X)&~generous(X))=>strong(X)))&
((?[X]:((~happy(X)<~>tall(X))))<=>(?[X]:(quiet(X))))&
((?[X]:((calm(X)<~>creative(X))))<=>((strong(lucy)<~>tall(lucy))))&
(![X]:((~generous(X)&~patient(X))=>(~old(X)<~>quiet(X))))&
((?[X]:((humble(X)<~>old(X))))<=>(?[X]:((~generous(X)&kind(X)))))&
((?[X]:((happy(X)&old(X))))=>((~happy(alice)&~rich(alice))))&
((?[X]:(~happy(X)))=>(~brave(john)))&
(~tall(mary))&
(kind(mary))&
((~happy(paul)|~generous(paul)))&
(?[X]:((generous(X)<~>wise(X))))&
((wise(mary)<~>~creative(mary))) | ~calm(alice) | [] | null | 0 |
Everyone who is either not humble or creative is either not kind or not strong.
Everyone who is not kind is not funny or not humble and vice versa.
If someone is either not rich or not wise then lucy is not wise and vice versa.
Everyone who is not tall or happy is not old or not humble and vice versa.
Everyone who is both not curious and happy is not rich or not funny and vice versa.
Everyone who is both not wise and not curious is quiet.
Everyone who is not calm or wise is not patient or not creative.
Everyone who is tall or not rich is kind.
Everyone who is happy or not wise is both not rich and funny.
Everyone who is either not humble or tall is not strong.
If susan is both not strong and not old then someone is generous.
Everyone who is brave or funny is either not old or funny.
Everyone who is not generous or not tall is kind.
Everyone who is either not creative or old is either old or not kind and vice versa.
If someone is patient or not curious then someone is not creative.
Everyone who is both not strong and not creative is both not brave and not strong and vice versa.
Someone is funny.
Lucy is either not wise or calm.
Paul is quiet.
Someone is either not funny or tall.
Someone is both funny and tall. | Paul is not generous. | neutral | (![X]:((~humble(X)<~>creative(X))=>(~kind(X)<~>~strong(X))))&
(![X]:(~kind(X)<=>(~funny(X)|~humble(X))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>(~wise(lucy)))&
(![X]:((~tall(X)|happy(X))<=>(~old(X)|~humble(X))))&
(![X]:((~curious(X)&happy(X))<=>(~rich(X)|~funny(X))))&
(![X]:((~wise(X)&~curious(X))=>quiet(X)))&
(![X]:((~calm(X)|wise(X))=>(~patient(X)|~creative(X))))&
(![X]:((tall(X)|~rich(X))=>kind(X)))&
(![X]:((happy(X)|~wise(X))=>(~rich(X)&funny(X))))&
(![X]:((~humble(X)<~>tall(X))=>~strong(X)))&
(((~strong(susan)&~old(susan)))=>(?[X]:(generous(X))))&
(![X]:((brave(X)|funny(X))=>(~old(X)<~>funny(X))))&
(![X]:((~generous(X)|~tall(X))=>kind(X)))&
(![X]:((~creative(X)<~>old(X))<=>(old(X)<~>~kind(X))))&
((?[X]:((patient(X)|~curious(X))))=>(?[X]:(~creative(X))))&
(![X]:((~strong(X)&~creative(X))<=>(~brave(X)&~strong(X))))&
(?[X]:(funny(X)))&
((~wise(lucy)<~>calm(lucy)))&
(quiet(paul))&
(?[X]:((~funny(X)<~>tall(X))))&
(?[X]:((funny(X)&tall(X)))) | ~generous(paul) | [] | null | 0 |
Everyone who is not wise or old is both quiet and not patient and vice versa. Everyone who is both brave and patient is not generous or not happy and vice versa. Everyone who is either not tall or strong is tall or not funny. If someone is both humble and happy then susan is happy and vice versa. Everyone who is not strong is rich. If paul is tall then someone is not happy and vice versa. Everyone who is both not wise and curious is both not rich and generous. If someone is not calm then susan is both not old and tall. Everyone who is not funny is not creative and vice versa. Everyone who is not brave or not humble is not happy or calm and vice versa. If john is either not humble or wise then someone is not rich and vice versa. If lucy is both kind and tall then mary is both not calm and calm. Everyone who is either not wise or not strong is either not strong or not rich. If fred is quiet then someone is quiet or not creative and vice versa. Everyone who is not generous is both not kind and tall and vice versa. If someone is both patient and creative then paul is not patient or not strong. Mary is either not curious or kind. Paul is creative. Someone is both not kind and creative. Alice is both generous and not patient. Someone is humble or not curious. Someone is not rich or not curious. Paul is both kind and not wise. Someone is not funny. | Susan is not generous. | neutral | (![X]:((~wise(X)|old(X))<=>(quiet(X)&~patient(X))))&
(![X]:((brave(X)&patient(X))<=>(~generous(X)|~happy(X))))&
(![X]:((~tall(X)<~>strong(X))=>(tall(X)|~funny(X))))&
((?[X]:((humble(X)&happy(X))))<=>(happy(susan)))&
(![X]:(~strong(X)=>rich(X)))&
((tall(paul))<=>(?[X]:(~happy(X))))&
(![X]:((~wise(X)&curious(X))=>(~rich(X)&generous(X))))&
((?[X]:(~calm(X)))=>((~old(susan)&tall(susan))))&
(![X]:(~funny(X)<=>~creative(X)))&
(![X]:((~brave(X)|~humble(X))<=>(~happy(X)|calm(X))))&
(((~humble(john)<~>wise(john)))<=>(?[X]:(~rich(X))))&
(((kind(lucy)&tall(lucy)))=>((~calm(mary)&calm(mary))))&
(![X]:((~wise(X)<~>~strong(X))=>(~strong(X)<~>~rich(X))))&
((quiet(fred))<=>(?[X]:((quiet(X)|~creative(X)))))&
(![X]:(~generous(X)<=>(~kind(X)&tall(X))))&
((?[X]:((patient(X)&creative(X))))=>((~patient(paul)|~strong(paul))))&
((~curious(mary)<~>kind(mary)))&
(creative(paul))&
(?[X]:((~kind(X)&creative(X))))&
((generous(alice)&~patient(alice)))&
(?[X]:((humble(X)|~curious(X))))&
(?[X]:((~rich(X)|~curious(X))))&
((kind(paul)&~wise(paul)))&
(?[X]:(~funny(X))) | ~generous(susan) | [] | null | 0 |
Everyone who is not wise is both not wise and not humble and vice versa.
Everyone who is either not rich or not quiet is either wise or brave.
Everyone who is either not calm or not strong is curious or old and vice versa.
Everyone who is humble is either funny or humble and vice versa.
If alice is either brave or not generous then someone is not wise.
Everyone who is not funny or not wise is either patient or not old and vice versa.
Everyone who is either not rich or not wise is either not generous or curious and vice versa.
If lucy is strong or curious then someone is not strong and vice versa.
Everyone who is either rich or not kind is either old or not brave and vice versa.
If someone is brave or calm then mary is not brave.
If someone is either rich or brave then someone is not calm.
Everyone who is both funny and kind is not creative or strong and vice versa.
If john is either not curious or not creative then someone is both not creative and curious.
If fred is not happy then someone is not quiet or calm.
If alice is both quiet and not strong then paul is calm or not patient and vice versa.
Someone is wise.
Mary is not humble or rich.
Alice is humble.
Lucy is either quiet or not curious.
Someone is old.
Someone is humble or not generous. | Paul is generous. | neutral | (![X]:(~wise(X)<=>(~wise(X)&~humble(X))))&
(![X]:((~rich(X)<~>~quiet(X))=>(wise(X)<~>brave(X))))&
(![X]:((~calm(X)<~>~strong(X))<=>(curious(X)|old(X))))&
(![X]:(humble(X)<=>(funny(X)<~>humble(X))))&
(((brave(alice)<~>~generous(alice)))=>(?[X]:(~wise(X))))&
(![X]:((~funny(X)|~wise(X))<=>(patient(X)<~>~old(X))))&
(![X]:((~rich(X)<~>~wise(X))<=>(~generous(X)<~>curious(X))))&
(((strong(lucy)|curious(lucy)))<=>(?[X]:(~strong(X))))&
(![X]:((rich(X)<~>~kind(X))<=>(old(X)<~>~brave(X))))&
((?[X]:((brave(X)|calm(X))))=>(~brave(mary)))&
((?[X]:((rich(X)<~>brave(X))))=>(?[X]:(~calm(X))))&
(![X]:((funny(X)&kind(X))<=>(~creative(X)|strong(X))))&
(((~curious(john)<~>~creative(john)))=>(?[X]:((~creative(X)&curious(X)))))&
((~happy(fred))=>(?[X]:((~quiet(X)|calm(X)))))&
(((quiet(alice)&~strong(alice)))<=>((calm(paul)|~patient(paul))))&
(?[X]:(wise(X)))&
((~humble(mary)|rich(mary)))&
(humble(alice))&
((quiet(lucy)<~>~curious(lucy)))&
(?[X]:(old(X)))&
(?[X]:((humble(X)|~generous(X)))) | generous(paul) | [] | null | 0 |
If someone is old then someone is both happy and not creative and vice versa.
If alice is both not wise and happy then lucy is not generous or kind.
Everyone who is not happy is happy or not strong and vice versa.
If paul is either funny or not kind then fred is not kind.
If fred is funny then fred is humble and vice versa.
If someone is strong then someone is funny and vice versa.
If john is not rich then lucy is both not old and not funny and vice versa.
Everyone who is either not humble or quiet is both not old and not patient.
If someone is either funny or rich then john is both kind and brave and vice versa.
Everyone who is both creative and not calm is either calm or funny and vice versa.
If someone is both not happy and curious then someone is creative or happy.
Everyone who is humble or quiet is either funny or not generous.
Everyone who is either not wise or patient is curious.
If someone is either tall or strong then someone is either not curious or not quiet.
Everyone who is kind or not tall is either kind or not happy and vice versa.
If someone is both wise and rich then someone is not generous or strong and vice versa.
Someone is either not rich or curious.
Mary is not happy.
Someone is not brave or funny.
Someone is both not creative and not funny. | Lucy is not kind. | entailment | ((?[X]:(old(X)))<=>(?[X]:((happy(X)&~creative(X)))))&
(((~wise(alice)&happy(alice)))=>((~generous(lucy)|kind(lucy))))&
(![X]:(~happy(X)<=>(happy(X)|~strong(X))))&
(((funny(paul)<~>~kind(paul)))=>(~kind(fred)))&
((funny(fred))<=>(humble(fred)))&
((?[X]:(strong(X)))<=>(?[X]:(funny(X))))&
((~rich(john))<=>((~old(lucy)&~funny(lucy))))&
(![X]:((~humble(X)<~>quiet(X))=>(~old(X)&~patient(X))))&
((?[X]:((funny(X)<~>rich(X))))<=>((kind(john)&brave(john))))&
(![X]:((creative(X)&~calm(X))<=>(calm(X)<~>funny(X))))&
((?[X]:((~happy(X)&curious(X))))=>(?[X]:((creative(X)|happy(X)))))&
(![X]:((humble(X)|quiet(X))=>(funny(X)<~>~generous(X))))&
(![X]:((~wise(X)<~>patient(X))=>curious(X)))&
((?[X]:((tall(X)<~>strong(X))))=>(?[X]:((~curious(X)<~>~quiet(X)))))&
(![X]:((kind(X)|~tall(X))<=>(kind(X)<~>~happy(X))))&
((?[X]:((wise(X)&rich(X))))<=>(?[X]:((~generous(X)|strong(X)))))&
(?[X]:((~rich(X)<~>curious(X))))&
(~happy(mary))&
(?[X]:((~brave(X)|funny(X))))&
(?[X]:((~creative(X)&~funny(X)))) | ~kind(lucy) | [
"p2",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7552921405335664682966766
% SZS output start Proof for 7552921405335664682966766
3. ! [X0] : (~happy(X0) <=> (~strong(X0) | happy(X0))) [input p2]
15. ! [X0] : ((~tall(X0) | kind(X0)) <=> (kind(X0) <~> ~happy(X0))) [input p14]
21. kind(lucy) [input hypothesis]
40. ! [X0] : ((~happy(X0) | (strong(X0) & ~happy(X0))) & ((~strong(X0) | happy(X0)) | happy(X0))) [nnf transformation 3]
41. ! [X0] : ((~happy(X0) | (strong(X0) & ~happy(X0))) & (~strong(X0) | happy(X0) | happy(X0))) [flattening 40]
68. ! [X0] : (((~tall(X0) | kind(X0)) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0)))) & (((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | (tall(X0) & ~kind(X0)))) [nnf transformation 15]
69. ! [X0] : ((~tall(X0) | kind(X0) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0)))) & (((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | (tall(X0) & ~kind(X0)))) [flattening 68]
87. ~happy(X0) | ~happy(X0) [cnf transformation 41]
127. happy(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 69]
142. kind(lucy) [cnf transformation 21]
143. happy(X0) | ~kind(X0) [duplicate literal removal 127]
148. ~happy(X0) [duplicate literal removal 87]
267. ~kind(X0) [subsumption resolution 143,148]
292. $false [subsumption resolution 142,267]
% SZS output end Proof for 7552921405335664682966766
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not calm and curious then someone is either kind or patient.
Everyone who is not quiet is either not happy or curious and vice versa.
Everyone who is not kind or not strong is not kind or strong.
Everyone who is either not curious or funny is either not kind or not patient.
Everyone who is not patient or not strong is both not strong and not curious.
Everyone who is not curious is not creative or brave.
If paul is strong or not patient then someone is not patient or funny.
Everyone who is both not quiet and not generous is calm or wise.
If john is both old and strong then someone is both not kind and not tall and vice versa.
If someone is not kind or kind then john is wise or creative and vice versa.
If someone is tall or not patient then someone is old or not strong.
Everyone who is not calm is not curious and vice versa.
If john is both not funny and not curious then mary is either not curious or old and vice versa.
Everyone who is not humble is not kind or rich.
Everyone who is either calm or not calm is happy or tall.
Everyone who is rich or calm is not old and vice versa.
Someone is both not wise and not rich.
Lucy is not rich.
Mary is both not calm and not humble.
Someone is either patient or not patient.
Someone is either rich or curious.
Someone is not kind or kind.
Someone is not rich or not strong.
Mary is both not rich and wise. | Mary is tall. | neutral | (((~calm(john)&curious(john)))=>(?[X]:((kind(X)<~>patient(X)))))&
(![X]:(~quiet(X)<=>(~happy(X)<~>curious(X))))&
(![X]:((~kind(X)|~strong(X))=>(~kind(X)|strong(X))))&
(![X]:((~curious(X)<~>funny(X))=>(~kind(X)<~>~patient(X))))&
(![X]:((~patient(X)|~strong(X))=>(~strong(X)&~curious(X))))&
(![X]:(~curious(X)=>(~creative(X)|brave(X))))&
(((strong(paul)|~patient(paul)))=>(?[X]:((~patient(X)|funny(X)))))&
(![X]:((~quiet(X)&~generous(X))=>(calm(X)|wise(X))))&
(((old(john)&strong(john)))<=>(?[X]:((~kind(X)&~tall(X)))))&
((?[X]:((~kind(X)|kind(X))))<=>((wise(john)|creative(john))))&
((?[X]:((tall(X)|~patient(X))))=>(?[X]:((old(X)|~strong(X)))))&
(![X]:(~calm(X)<=>~curious(X)))&
(((~funny(john)&~curious(john)))<=>((~curious(mary)<~>old(mary))))&
(![X]:(~humble(X)=>(~kind(X)|rich(X))))&
(![X]:((calm(X)<~>~calm(X))=>(happy(X)|tall(X))))&
(![X]:((rich(X)|calm(X))<=>~old(X)))&
(?[X]:((~wise(X)&~rich(X))))&
(~rich(lucy))&
((~calm(mary)&~humble(mary)))&
(?[X]:((patient(X)<~>~patient(X))))&
(?[X]:((rich(X)<~>curious(X))))&
(?[X]:((~kind(X)|kind(X))))&
(?[X]:((~rich(X)|~strong(X))))&
((~rich(mary)&wise(mary))) | tall(mary) | [] | null | 0 |
If someone is both not quiet and patient then someone is not quiet or quiet and vice versa. Everyone who is either not creative or kind is both kind and creative and vice versa. If someone is both brave and patient then someone is either not curious or not rich and vice versa. If someone is tall then fred is not curious and vice versa. Everyone who is both quiet and not patient is funny. Everyone who is either not kind or not creative is either kind or generous and vice versa. If someone is both kind and not humble then alice is tall and vice versa. Everyone who is either strong or not humble is both generous and not quiet. If fred is both creative and not tall then alice is either kind or not brave and vice versa. Everyone who is both not curious and not humble is both not humble and old. If john is both not patient and quiet then john is creative or not generous and vice versa. If someone is not rich then someone is both not creative and generous and vice versa. If lucy is happy then someone is either rich or old and vice versa. Everyone who is patient is either not creative or quiet and vice versa. Everyone who is either humble or old is not happy or rich and vice versa. Everyone who is old or not old is both not wise and not happy. Someone is either not tall or funny. Mary is not creative. Mary is either not patient or not tall. Someone is either generous or old. Paul is both not wise and not patient. Someone is both rich and not generous. Someone is creative. | John is generous. | contradiction | ((?[X]:((~quiet(X)&patient(X))))<=>(?[X]:((~quiet(X)|quiet(X)))))&
(![X]:((~creative(X)<~>kind(X))<=>(kind(X)&creative(X))))&
((?[X]:((brave(X)&patient(X))))<=>(?[X]:((~curious(X)<~>~rich(X)))))&
((?[X]:(tall(X)))<=>(~curious(fred)))&
(![X]:((quiet(X)&~patient(X))=>funny(X)))&
(![X]:((~kind(X)<~>~creative(X))<=>(kind(X)<~>generous(X))))&
((?[X]:((kind(X)&~humble(X))))<=>(tall(alice)))&
(![X]:((strong(X)<~>~humble(X))=>(generous(X)&~quiet(X))))&
(((creative(fred)&~tall(fred)))<=>((kind(alice)<~>~brave(alice))))&
(![X]:((~curious(X)&~humble(X))=>(~humble(X)&old(X))))&
(((~patient(john)&quiet(john)))<=>((creative(john)|~generous(john))))&
((?[X]:(~rich(X)))<=>(?[X]:((~creative(X)&generous(X)))))&
((happy(lucy))<=>(?[X]:((rich(X)<~>old(X)))))&
(![X]:(patient(X)<=>(~creative(X)<~>quiet(X))))&
(![X]:((humble(X)<~>old(X))<=>(~happy(X)|rich(X))))&
(![X]:((old(X)|~old(X))=>(~wise(X)&~happy(X))))&
(?[X]:((~tall(X)<~>funny(X))))&
(~creative(mary))&
((~patient(mary)<~>~tall(mary)))&
(?[X]:((generous(X)<~>old(X))))&
((~wise(paul)&~patient(paul)))&
(?[X]:((rich(X)&~generous(X))))&
(?[X]:(creative(X))) | generous(john) | [
"p1",
"p5",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1756551949699245019113737
% SZS output start Proof for 1756551949699245019113737
2. ! [X0] : ((~creative(X0) <~> kind(X0)) <=> (creative(X0) & kind(X0))) [input p1]
6. ! [X0] : ((~kind(X0) <~> ~creative(X0)) <=> (kind(X0) <~> generous(X0))) [input p5]
11. (quiet(john) & ~patient(john)) <=> (~generous(john) | creative(john)) [input p10]
14. ! [X0] : (patient(X0) <=> (~creative(X0) <~> quiet(X0))) [input p13]
24. generous(john) [input hypothesis]
41. ! [X0] : ((((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | (~creative(X0) | ~kind(X0))) & ((creative(X0) & kind(X0)) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0))))) [nnf transformation 2]
42. ! [X0] : ((((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | ~creative(X0) | ~kind(X0)) & ((creative(X0) & kind(X0)) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0))))) [flattening 41]
52. ! [X0] : ((((creative(X0) | kind(X0)) & (~creative(X0) | ~kind(X0))) | ((kind(X0) | ~generous(X0)) & (generous(X0) | ~kind(X0)))) & (((~generous(X0) | ~kind(X0)) & (generous(X0) | kind(X0))) | ((~kind(X0) | creative(X0)) & (~creative(X0) | kind(X0))))) [nnf transformation 6]
60. ((quiet(john) & ~patient(john)) | (generous(john) & ~creative(john))) & ((~generous(john) | creative(john)) | (~quiet(john) | patient(john))) [nnf transformation 11]
61. ((quiet(john) & ~patient(john)) | (generous(john) & ~creative(john))) & (~generous(john) | creative(john) | ~quiet(john) | patient(john)) [flattening 60]
71. ! [X0] : ((patient(X0) | ((~creative(X0) | ~quiet(X0)) & (quiet(X0) | creative(X0)))) & (((~quiet(X0) | creative(X0)) & (quiet(X0) | ~creative(X0))) | ~patient(X0))) [nnf transformation 14]
92. creative(X0) | kind(X0) | creative(X0) [cnf transformation 42]
108. ~generous(X0) | ~kind(X0) | ~kind(X0) | creative(X0) [cnf transformation 52]
129. ~patient(john) | ~creative(john) [cnf transformation 61]
131. quiet(john) | ~creative(john) [cnf transformation 61]
143. ~creative(X0) | patient(X0) | ~quiet(X0) [cnf transformation 71]
163. generous(john) [cnf transformation 24]
165. ~generous(X0) | ~kind(X0) | creative(X0) [duplicate literal removal 108]
169. kind(X0) | creative(X0) [duplicate literal removal 92]
234. ~generous(X0) | creative(X0) [subsumption resolution 165,169]
277. 23 <=> generous(john) [avatar definition]
279. generous(john) <- (23) [avatar component clause 277]
281. 24 <=> quiet(john) [avatar definition]
283. quiet(john) <- (24) [avatar component clause 281]
286. 25 <=> creative(john) [avatar definition]
287. creative(john) <- (25) [avatar component clause 286]
289. ~25 | 24 [avatar split clause 131,281,286]
291. 26 <=> patient(john) [avatar definition]
293. ~patient(john) <- (~26) [avatar component clause 291]
295. ~25 | ~26 [avatar split clause 129,291,286]
362. 23 [avatar split clause 163,277]
380. creative(john) <- (23) [resolution 234,279]
384. 25 | ~23 [avatar split clause 380,277,286]
484. patient(john) | ~quiet(john) <- (25) [resolution 143,287]
489. ~quiet(john) <- (25, ~26) [subsumption resolution 484,293]
490. $false <- (24, 25, ~26) [subsumption resolution 489,283]
491. ~24 | ~25 | 26 [avatar contradiction clause 490]
496. $false [avatar sat refutation 289,295,362,384,491]
% SZS output end Proof for 1756551949699245019113737
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or kind is both generous and not quiet and vice versa.
If someone is curious then fred is rich.
If lucy is not brave then paul is funny or calm.
Everyone who is brave is creative or not patient and vice versa.
Everyone who is either not calm or kind is either curious or not calm.
Everyone who is not quiet or tall is either not patient or brave.
If alice is not patient then alice is rich or old and vice versa.
Everyone who is either calm or not quiet is both not quiet and not happy and vice versa.
If lucy is both not patient and kind then someone is either not tall or patient.
If mary is both not kind and not happy then someone is either not calm or not tall and vice versa.
If susan is either not calm or not brave then lucy is not kind and vice versa.
Everyone who is not kind is not rich and vice versa.
Everyone who is either not happy or old is tall or quiet.
Everyone who is either not calm or not generous is happy and vice versa.
If john is both not kind and not humble then susan is curious or not calm.
Everyone who is both not old and not happy is both calm and not patient and vice versa.
Alice is old or rich.
Lucy is both funny and old.
Lucy is both not humble and not kind.
Someone is not rich.
Someone is both curious and not funny.
Someone is either not old or not brave.
Someone is both strong and kind.
Someone is either happy or not humble. | Alice is not tall. | entailment | (![X]:((~old(X)<~>kind(X))<=>(generous(X)&~quiet(X))))&
((?[X]:(curious(X)))=>(rich(fred)))&
((~brave(lucy))=>((funny(paul)|calm(paul))))&
(![X]:(brave(X)<=>(creative(X)|~patient(X))))&
(![X]:((~calm(X)<~>kind(X))=>(curious(X)<~>~calm(X))))&
(![X]:((~quiet(X)|tall(X))=>(~patient(X)<~>brave(X))))&
((~patient(alice))<=>((rich(alice)|old(alice))))&
(![X]:((calm(X)<~>~quiet(X))<=>(~quiet(X)&~happy(X))))&
(((~patient(lucy)&kind(lucy)))=>(?[X]:((~tall(X)<~>patient(X)))))&
(((~kind(mary)&~happy(mary)))<=>(?[X]:((~calm(X)<~>~tall(X)))))&
(((~calm(susan)<~>~brave(susan)))<=>(~kind(lucy)))&
(![X]:(~kind(X)<=>~rich(X)))&
(![X]:((~happy(X)<~>old(X))=>(tall(X)|quiet(X))))&
(![X]:((~calm(X)<~>~generous(X))<=>happy(X)))&
(((~kind(john)&~humble(john)))=>((curious(susan)|~calm(susan))))&
(![X]:((~old(X)&~happy(X))<=>(calm(X)&~patient(X))))&
((old(alice)|rich(alice)))&
((funny(lucy)&old(lucy)))&
((~humble(lucy)&~kind(lucy)))&
(?[X]:(~rich(X)))&
(?[X]:((curious(X)&~funny(X))))&
(?[X]:((~old(X)<~>~brave(X))))&
(?[X]:((strong(X)&kind(X))))&
(?[X]:((happy(X)<~>~humble(X)))) | ~tall(alice) | [
"p3",
"p5",
"p6",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 474796063079885577611975
% SZS output start Proof for 474796063079885577611975
4. ! [X0] : (brave(X0) <=> (~patient(X0) | creative(X0))) [input p3]
6. ! [X0] : ((tall(X0) | ~quiet(X0)) => (~patient(X0) <~> brave(X0))) [input p5]
7. ~patient(alice) <=> (old(alice) | rich(alice)) [input p6]
17. rich(alice) | old(alice) [input p16]
25. tall(alice) [input hypothesis]
31. ! [X0] : ((~patient(X0) <~> brave(X0)) | (~tall(X0) & quiet(X0))) [ennf transformation 6]
40. ! [X0] : ((brave(X0) | (patient(X0) & ~creative(X0))) & ((~patient(X0) | creative(X0)) | ~brave(X0))) [nnf transformation 4]
41. ! [X0] : ((brave(X0) | (patient(X0) & ~creative(X0))) & (~patient(X0) | creative(X0) | ~brave(X0))) [flattening 40]
43. ! [X0] : (((~brave(X0) | patient(X0)) & (brave(X0) | ~patient(X0))) | (~tall(X0) & quiet(X0))) [nnf transformation 31]
44. (~patient(alice) | (~old(alice) & ~rich(alice))) & ((old(alice) | rich(alice)) | patient(alice)) [nnf transformation 7]
45. (~patient(alice) | (~old(alice) & ~rich(alice))) & (old(alice) | rich(alice) | patient(alice)) [flattening 44]
84. patient(X0) | brave(X0) [cnf transformation 41]
92. ~brave(X0) | patient(X0) | ~tall(X0) [cnf transformation 43]
94. ~patient(alice) | ~rich(alice) [cnf transformation 45]
95. ~patient(alice) | ~old(alice) [cnf transformation 45]
127. rich(alice) | old(alice) [cnf transformation 17]
140. tall(alice) [cnf transformation 25]
166. ~tall(X0) | patient(X0) [subsumption resolution 92,84]
171. 6 <=> old(alice) [avatar definition]
175. 7 <=> patient(alice) [avatar definition]
177. ~patient(alice) <- (~7) [avatar component clause 175]
178. ~6 | ~7 [avatar split clause 95,175,171]
180. 8 <=> rich(alice) [avatar definition]
183. ~8 | ~7 [avatar split clause 94,175,180]
255. 6 | 8 [avatar split clause 127,180,171]
282. patient(alice) [resolution 166,140]
283. $false <- (~7) [subsumption resolution 282,177]
284. 7 [avatar contradiction clause 283]
285. $false [avatar sat refutation 178,183,255,284]
% SZS output end Proof for 474796063079885577611975
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or wise is humble or not tall. Everyone who is happy or not patient is not happy or not tall and vice versa. Everyone who is quiet is quiet or not quiet. If susan is rich then lucy is either not kind or not funny and vice versa. Everyone who is wise or quiet is either not funny or not quiet and vice versa. Everyone who is both not generous and not strong is tall. Everyone who is both brave and creative is both rich and not happy. If someone is both tall and not happy then someone is not humble or not wise. Everyone who is not humble or not brave is not old or rich and vice versa. Everyone who is not rich is not humble and vice versa. Everyone who is patient is both not old and creative. If someone is creative or patient then susan is not patient or generous. Everyone who is calm is wise and vice versa. Everyone who is tall or not funny is either funny or tall. If lucy is both curious and strong then someone is either patient or not tall and vice versa. Everyone who is both quiet and not creative is both not curious and not calm. Fred is either kind or not creative. Someone is rich or not wise. Someone is either not old or not kind. Paul is quiet. Mary is both curious and not old. Someone is both tall and quiet. Someone is either not creative or humble. | Fred is curious. | neutral | (![X]:((patient(X)|wise(X))=>(humble(X)|~tall(X))))&
(![X]:((happy(X)|~patient(X))<=>(~happy(X)|~tall(X))))&
(![X]:(quiet(X)=>(quiet(X)|~quiet(X))))&
((rich(susan))<=>((~kind(lucy)<~>~funny(lucy))))&
(![X]:((wise(X)|quiet(X))<=>(~funny(X)<~>~quiet(X))))&
(![X]:((~generous(X)&~strong(X))=>tall(X)))&
(![X]:((brave(X)&creative(X))=>(rich(X)&~happy(X))))&
((?[X]:((tall(X)&~happy(X))))=>(?[X]:((~humble(X)|~wise(X)))))&
(![X]:((~humble(X)|~brave(X))<=>(~old(X)|rich(X))))&
(![X]:(~rich(X)<=>~humble(X)))&
(![X]:(patient(X)=>(~old(X)&creative(X))))&
((?[X]:((creative(X)|patient(X))))=>((~patient(susan)|generous(susan))))&
(![X]:(calm(X)<=>wise(X)))&
(![X]:((tall(X)|~funny(X))=>(funny(X)<~>tall(X))))&
(((curious(lucy)&strong(lucy)))<=>(?[X]:((patient(X)<~>~tall(X)))))&
(![X]:((quiet(X)&~creative(X))=>(~curious(X)&~calm(X))))&
((kind(fred)<~>~creative(fred)))&
(?[X]:((rich(X)|~wise(X))))&
(?[X]:((~old(X)<~>~kind(X))))&
(quiet(paul))&
((curious(mary)&~old(mary)))&
(?[X]:((tall(X)&quiet(X))))&
(?[X]:((~creative(X)<~>humble(X)))) | curious(fred) | [] | null | 0 |
Everyone who is both happy and generous is both not curious and brave and vice versa. If fred is not creative then someone is either humble or not quiet. Everyone who is both not generous and tall is strong. Everyone who is not curious or not quiet is funny or wise. If someone is not tall or happy then someone is not quiet or strong. Everyone who is either not curious or not strong is either kind or curious and vice versa. Everyone who is creative is rich or old and vice versa. Everyone who is happy is rich. Everyone who is either kind or creative is both kind and not rich and vice versa. Everyone who is humble is either not wise or happy. If john is both not generous and not creative then someone is not patient. Everyone who is not kind is both not wise and rich. Everyone who is not patient or happy is not humble. If someone is quiet then fred is either not calm or happy. If alice is either strong or not humble then someone is either not quiet or not old. Everyone who is humble is both curious and not brave. Someone is old or not generous. Someone is either not humble or not quiet. Someone is not generous or not kind. Alice is either calm or not kind. Someone is patient. Paul is both calm and kind. Someone is either not strong or not funny. | John is not generous. | neutral | (![X]:((happy(X)&generous(X))<=>(~curious(X)&brave(X))))&
((~creative(fred))=>(?[X]:((humble(X)<~>~quiet(X)))))&
(![X]:((~generous(X)&tall(X))=>strong(X)))&
(![X]:((~curious(X)|~quiet(X))=>(funny(X)|wise(X))))&
((?[X]:((~tall(X)|happy(X))))=>(?[X]:((~quiet(X)|strong(X)))))&
(![X]:((~curious(X)<~>~strong(X))<=>(kind(X)<~>curious(X))))&
(![X]:(creative(X)<=>(rich(X)|old(X))))&
(![X]:(happy(X)=>rich(X)))&
(![X]:((kind(X)<~>creative(X))<=>(kind(X)&~rich(X))))&
(![X]:(humble(X)=>(~wise(X)<~>happy(X))))&
(((~generous(john)&~creative(john)))=>(?[X]:(~patient(X))))&
(![X]:(~kind(X)=>(~wise(X)&rich(X))))&
(![X]:((~patient(X)|happy(X))=>~humble(X)))&
((?[X]:(quiet(X)))=>((~calm(fred)<~>happy(fred))))&
(((strong(alice)<~>~humble(alice)))=>(?[X]:((~quiet(X)<~>~old(X)))))&
(![X]:(humble(X)=>(curious(X)&~brave(X))))&
(?[X]:((old(X)|~generous(X))))&
(?[X]:((~humble(X)<~>~quiet(X))))&
(?[X]:((~generous(X)|~kind(X))))&
((calm(alice)<~>~kind(alice)))&
(?[X]:(patient(X)))&
((calm(paul)&kind(paul)))&
(?[X]:((~strong(X)<~>~funny(X)))) | ~generous(john) | [] | null | 0 |
Everyone who is both rich and not rich is not happy.
If susan is not creative or not quiet then susan is both not happy and not creative and vice versa.
Everyone who is not funny or not wise is both not tall and rich and vice versa.
Everyone who is not curious is not kind or not tall.
Everyone who is both strong and patient is not funny and vice versa.
Everyone who is both not brave and not calm is both not calm and creative and vice versa.
If someone is not wise or not patient then someone is both curious and old.
If someone is not curious or not rich then someone is generous or rich.
If someone is either funny or not strong then someone is both not curious and old.
If paul is quiet then paul is humble and vice versa.
If lucy is generous or not tall then someone is not brave or old.
If lucy is either calm or strong then someone is not wise and vice versa.
If someone is kind or humble then lucy is both brave and not happy and vice versa.
Everyone who is either rich or patient is both tall and not funny and vice versa.
If lucy is both brave and not curious then john is either funny or creative and vice versa.
If john is funny then someone is both not brave and not patient.
Susan is tall or not curious.
Alice is not old.
Paul is creative.
Someone is either curious or quiet.
Someone is kind.
John is not quiet or creative.
Someone is both not tall and not curious.
Someone is not strong. | Alice is curious. | neutral | (![X]:((rich(X)&~rich(X))=>~happy(X)))&
(((~creative(susan)|~quiet(susan)))<=>((~happy(susan)&~creative(susan))))&
(![X]:((~funny(X)|~wise(X))<=>(~tall(X)&rich(X))))&
(![X]:(~curious(X)=>(~kind(X)|~tall(X))))&
(![X]:((strong(X)&patient(X))<=>~funny(X)))&
(![X]:((~brave(X)&~calm(X))<=>(~calm(X)&creative(X))))&
((?[X]:((~wise(X)|~patient(X))))=>(?[X]:((curious(X)&old(X)))))&
((?[X]:((~curious(X)|~rich(X))))=>(?[X]:((generous(X)|rich(X)))))&
((?[X]:((funny(X)<~>~strong(X))))=>(?[X]:((~curious(X)&old(X)))))&
((quiet(paul))<=>(humble(paul)))&
(((generous(lucy)|~tall(lucy)))=>(?[X]:((~brave(X)|old(X)))))&
(((calm(lucy)<~>strong(lucy)))<=>(?[X]:(~wise(X))))&
((?[X]:((kind(X)|humble(X))))<=>((brave(lucy)&~happy(lucy))))&
(![X]:((rich(X)<~>patient(X))<=>(tall(X)&~funny(X))))&
(((brave(lucy)&~curious(lucy)))<=>((funny(john)<~>creative(john))))&
((funny(john))=>(?[X]:((~brave(X)&~patient(X)))))&
((tall(susan)|~curious(susan)))&
(~old(alice))&
(creative(paul))&
(?[X]:((curious(X)<~>quiet(X))))&
(?[X]:(kind(X)))&
((~quiet(john)|creative(john)))&
(?[X]:((~tall(X)&~curious(X))))&
(?[X]:(~strong(X))) | curious(alice) | [] | null | 0 |
Everyone who is not creative or not curious is either not tall or humble and vice versa.
If alice is not funny or quiet then john is either funny or curious and vice versa.
Everyone who is wise or not funny is not funny or rich and vice versa.
Everyone who is both not curious and brave is both not wise and not strong.
Everyone who is either funny or kind is kind and vice versa.
If someone is both not rich and not brave then susan is both not happy and generous and vice versa.
If someone is not old or not humble then mary is calm or tall.
Everyone who is not strong is both wise and calm.
Everyone who is either not curious or creative is not generous and vice versa.
Everyone who is both creative and curious is both not old and rich.
Everyone who is tall or funny is not humble.
If lucy is not funny or not tall then someone is either not patient or generous and vice versa.
Everyone who is either not creative or not rich is both not quiet and not humble.
Everyone who is not curious or happy is wise or not patient and vice versa.
If fred is either happy or not old then someone is both not strong and brave and vice versa.
If susan is both strong and patient then someone is both not happy and not kind.
Paul is both not generous and patient.
Fred is either creative or tall.
Someone is both not curious and not funny.
Mary is not wise or not funny.
Mary is not quiet.
Someone is both not strong and patient.
Fred is both kind and brave. | John is not kind. | neutral | (![X]:((~creative(X)|~curious(X))<=>(~tall(X)<~>humble(X))))&
(((~funny(alice)|quiet(alice)))<=>((funny(john)<~>curious(john))))&
(![X]:((wise(X)|~funny(X))<=>(~funny(X)|rich(X))))&
(![X]:((~curious(X)&brave(X))=>(~wise(X)&~strong(X))))&
(![X]:((funny(X)<~>kind(X))<=>kind(X)))&
((?[X]:((~rich(X)&~brave(X))))<=>((~happy(susan)&generous(susan))))&
((?[X]:((~old(X)|~humble(X))))=>((calm(mary)|tall(mary))))&
(![X]:(~strong(X)=>(wise(X)&calm(X))))&
(![X]:((~curious(X)<~>creative(X))<=>~generous(X)))&
(![X]:((creative(X)&curious(X))=>(~old(X)&rich(X))))&
(![X]:((tall(X)|funny(X))=>~humble(X)))&
(((~funny(lucy)|~tall(lucy)))<=>(?[X]:((~patient(X)<~>generous(X)))))&
(![X]:((~creative(X)<~>~rich(X))=>(~quiet(X)&~humble(X))))&
(![X]:((~curious(X)|happy(X))<=>(wise(X)|~patient(X))))&
(((happy(fred)<~>~old(fred)))<=>(?[X]:((~strong(X)&brave(X)))))&
(((strong(susan)&patient(susan)))=>(?[X]:((~happy(X)&~kind(X)))))&
((~generous(paul)&patient(paul)))&
((creative(fred)<~>tall(fred)))&
(?[X]:((~curious(X)&~funny(X))))&
((~wise(mary)|~funny(mary)))&
(~quiet(mary))&
(?[X]:((~strong(X)&patient(X))))&
((kind(fred)&brave(fred))) | ~kind(john) | [] | null | 0 |
If fred is patient then someone is not curious or curious and vice versa.
If fred is old or calm then paul is curious and vice versa.
Everyone who is both not happy and funny is either old or not creative.
If someone is tall or not quiet then paul is both not strong and not old and vice versa.
If susan is tall then someone is calm.
Everyone who is tall or rich is either not calm or rich.
If lucy is either quiet or not generous then susan is both strong and not old.
Everyone who is both humble and not old is both not old and rich and vice versa.
Everyone who is either patient or not humble is not old or curious and vice versa.
Everyone who is funny is both not brave and not wise and vice versa.
If someone is tall then someone is not strong and vice versa.
Everyone who is either not patient or creative is both not calm and rich.
If someone is either wise or not happy then paul is rich or tall.
Everyone who is either not kind or not humble is both curious and not creative and vice versa.
Everyone who is patient is both not generous and kind.
Everyone who is both not humble and tall is either not quiet or not happy and vice versa.
Someone is either not old or rich.
Paul is both not humble and rich.
Susan is both quiet and not brave.
Someone is either creative or tall.
Someone is either not creative or curious.
Someone is either not humble or kind. | Paul is not patient. | entailment | ((patient(fred))<=>(?[X]:((~curious(X)|curious(X)))))&
(((old(fred)|calm(fred)))<=>(curious(paul)))&
(![X]:((~happy(X)&funny(X))=>(old(X)<~>~creative(X))))&
((?[X]:((tall(X)|~quiet(X))))<=>((~strong(paul)&~old(paul))))&
((tall(susan))=>(?[X]:(calm(X))))&
(![X]:((tall(X)|rich(X))=>(~calm(X)<~>rich(X))))&
(((quiet(lucy)<~>~generous(lucy)))=>((strong(susan)&~old(susan))))&
(![X]:((humble(X)&~old(X))<=>(~old(X)&rich(X))))&
(![X]:((patient(X)<~>~humble(X))<=>(~old(X)|curious(X))))&
(![X]:(funny(X)<=>(~brave(X)&~wise(X))))&
((?[X]:(tall(X)))<=>(?[X]:(~strong(X))))&
(![X]:((~patient(X)<~>creative(X))=>(~calm(X)&rich(X))))&
((?[X]:((wise(X)<~>~happy(X))))=>((rich(paul)|tall(paul))))&
(![X]:((~kind(X)<~>~humble(X))<=>(curious(X)&~creative(X))))&
(![X]:(patient(X)=>(~generous(X)&kind(X))))&
(![X]:((~humble(X)&tall(X))<=>(~quiet(X)<~>~happy(X))))&
(?[X]:((~old(X)<~>rich(X))))&
((~humble(paul)&rich(paul)))&
((quiet(susan)&~brave(susan)))&
(?[X]:((creative(X)<~>tall(X))))&
(?[X]:((~creative(X)<~>curious(X))))&
(?[X]:((~humble(X)<~>kind(X)))) | ~patient(paul) | [
"p0",
"p1",
"p5",
"p7",
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7148278540211036073988236
% SZS output start Proof for 7148278540211036073988236
1. patient(fred) <=> ? [X0] : (curious(X0) | ~curious(X0)) [input p0]
2. (calm(fred) | old(fred)) <=> curious(paul) [input p1]
6. ! [X0] : ((rich(X0) | tall(X0)) => (~calm(X0) <~> rich(X0))) [input p5]
8. ! [X0] : ((~old(X0) & humble(X0)) <=> (rich(X0) & ~old(X0))) [input p7]
9. ! [X0] : ((patient(X0) <~> ~humble(X0)) <=> (curious(X0) | ~old(X0))) [input p8]
18. rich(paul) & ~humble(paul) [input p17]
23. patient(paul) [input hypothesis]
29. ! [X0] : ((~calm(X0) <~> rich(X0)) | (~rich(X0) & ~tall(X0))) [ennf transformation 6]
37. (patient(fred) | ! [X0] : (~curious(X0) & curious(X0))) & (? [X0] : (curious(X0) | ~curious(X0)) | ~patient(fred)) [nnf transformation 1]
38. (patient(fred) | ! [X0] : (~curious(X0) & curious(X0))) & (? [X1] : (curious(X1) | ~curious(X1)) | ~patient(fred)) [rectify 37]
39. ? [X1] : (curious(X1) | ~curious(X1)) => (curious(sK0) | ~curious(sK0)) [choice axiom]
40. (patient(fred) | ! [X0] : (~curious(X0) & curious(X0))) & ((curious(sK0) | ~curious(sK0)) | ~patient(fred)) [skolemisation 38,39]
41. ((calm(fred) | old(fred)) | ~curious(paul)) & (curious(paul) | (~calm(fred) & ~old(fred))) [nnf transformation 2]
42. (calm(fred) | old(fred) | ~curious(paul)) & (curious(paul) | (~calm(fred) & ~old(fred))) [flattening 41]
51. ! [X0] : (((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | (~rich(X0) & ~tall(X0))) [nnf transformation 29]
53. ! [X0] : (((~old(X0) & humble(X0)) | (~rich(X0) | old(X0))) & ((rich(X0) & ~old(X0)) | (old(X0) | ~humble(X0)))) [nnf transformation 8]
54. ! [X0] : (((~old(X0) & humble(X0)) | ~rich(X0) | old(X0)) & ((rich(X0) & ~old(X0)) | old(X0) | ~humble(X0))) [flattening 53]
55. ! [X0] : ((((humble(X0) | ~patient(X0)) & (~humble(X0) | patient(X0))) | (~curious(X0) & old(X0))) & ((curious(X0) | ~old(X0)) | ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0))))) [nnf transformation 9]
56. ! [X0] : ((((humble(X0) | ~patient(X0)) & (~humble(X0) | patient(X0))) | (~curious(X0) & old(X0))) & (curious(X0) | ~old(X0) | ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0))))) [flattening 55]
81. patient(fred) | curious(X0) [cnf transformation 40]
82. patient(fred) | ~curious(X0) [cnf transformation 40]
83. curious(paul) | ~old(fred) [cnf transformation 42]
84. curious(paul) | ~calm(fred) [cnf transformation 42]
97. ~rich(X0) | calm(X0) | ~rich(X0) [cnf transformation 51]
103. ~humble(X0) | old(X0) | rich(X0) [cnf transformation 54]
110. ~patient(X0) | humble(X0) | old(X0) [cnf transformation 56]
111. ~curious(X0) | ~patient(X0) | humble(X0) [cnf transformation 56]
137. ~humble(paul) [cnf transformation 18]
147. patient(paul) [cnf transformation 23]
148. ~rich(X0) | calm(X0) [duplicate literal removal 97]
150. 1 <=> ! [X0] : ~curious(X0) [avatar definition]
151. ~curious(X0) <- (1) [avatar component clause 150]
153. 2 <=> patient(fred) [avatar definition]
155. patient(fred) <- (2) [avatar component clause 153]
156. 1 | 2 [avatar split clause 82,153,150]
158. 3 <=> ! [X0] : curious(X0) [avatar definition]
159. curious(X0) <- (3) [avatar component clause 158]
160. 3 | 2 [avatar split clause 81,153,158]
162. 4 <=> curious(paul) [avatar definition]
163. curious(paul) <- (4) [avatar component clause 162]
166. 5 <=> old(fred) [avatar definition]
167. ~old(fred) <- (~5) [avatar component clause 166]
170. 6 <=> calm(fred) [avatar definition]
171. ~calm(fred) <- (~6) [avatar component clause 170]
174. ~6 | 4 [avatar split clause 84,162,170]
175. ~5 | 4 [avatar split clause 83,162,166]
331. humble(fred) | old(fred) <- (2) [resolution 110,155]
332. humble(fred) <- (2, ~5) [subsumption resolution 331,167]
335. old(fred) | rich(fred) <- (2, ~5) [resolution 332,103]
336. rich(fred) <- (2, ~5) [subsumption resolution 335,167]
338. calm(fred) <- (2, ~5) [resolution 336,148]
339. $false <- (2, ~5, ~6) [subsumption resolution 338,171]
340. ~2 | 5 | 6 [avatar contradiction clause 339]
341. $false <- (1, 3) [subsumption resolution 151,159]
342. ~1 | ~3 [avatar contradiction clause 341]
352. ~patient(paul) | humble(paul) <- (4) [resolution 163,111]
353. humble(paul) <- (4) [subsumption resolution 352,147]
354. $false <- (4) [subsumption resolution 353,137]
355. ~4 [avatar contradiction clause 354]
356. $false [avatar sat refutation 156,160,174,175,340,342,355]
% SZS output end Proof for 7148278540211036073988236
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both not brave and not happy then someone is happy and vice versa.
Everyone who is both not old and humble is not wise and vice versa.
Everyone who is not generous is generous.
If alice is not kind then someone is not creative or rich and vice versa.
If alice is strong then lucy is not curious and vice versa.
Everyone who is creative or not funny is not funny and vice versa.
If someone is kind then someone is either not brave or not kind.
If someone is humble or not brave then someone is not creative or not quiet.
If someone is not brave or not tall then someone is calm.
Everyone who is quiet or happy is calm.
Everyone who is calm or curious is not brave or not old and vice versa.
Everyone who is both not curious and not brave is not old or brave and vice versa.
Everyone who is either kind or wise is not happy and vice versa.
Everyone who is old is both not curious and curious.
Someone is not patient or not funny.
John is either humble or wise.
Someone is either not kind or not strong.
Lucy is kind or not funny.
Someone is both kind and not quiet.
Fred is both tall and not curious.
Someone is either brave or generous.
Someone is patient. | Lucy is patient. | neutral | (((~brave(fred)&~happy(fred)))<=>(?[X]:(happy(X))))&
(![X]:((~old(X)&humble(X))<=>~wise(X)))&
(![X]:(~generous(X)=>generous(X)))&
((~kind(alice))<=>(?[X]:((~creative(X)|rich(X)))))&
((strong(alice))<=>(~curious(lucy)))&
(![X]:((creative(X)|~funny(X))<=>~funny(X)))&
((?[X]:(kind(X)))=>(?[X]:((~brave(X)<~>~kind(X)))))&
((?[X]:((humble(X)|~brave(X))))=>(?[X]:((~creative(X)|~quiet(X)))))&
((?[X]:((~brave(X)|~tall(X))))=>(?[X]:(calm(X))))&
(![X]:((quiet(X)|happy(X))=>calm(X)))&
(![X]:((calm(X)|curious(X))<=>(~brave(X)|~old(X))))&
(![X]:((~curious(X)&~brave(X))<=>(~old(X)|brave(X))))&
(![X]:((kind(X)<~>wise(X))<=>~happy(X)))&
(![X]:(old(X)=>(~curious(X)&curious(X))))&
(?[X]:((~patient(X)|~funny(X))))&
((humble(john)<~>wise(john)))&
(?[X]:((~kind(X)<~>~strong(X))))&
((kind(lucy)|~funny(lucy)))&
(?[X]:((kind(X)&~quiet(X))))&
((tall(fred)&~curious(fred)))&
(?[X]:((brave(X)<~>generous(X))))&
(?[X]:(patient(X))) | patient(lucy) | [] | null | 0 |
Everyone who is either generous or curious is either not funny or rich and vice versa. Everyone who is brave or not brave is not funny or humble. Everyone who is either curious or kind is either not kind or not patient and vice versa. Everyone who is both not old and not kind is not strong and vice versa. Everyone who is not tall is both not old and calm and vice versa. Everyone who is not curious or not humble is rich. Everyone who is both not quiet and wise is curious and vice versa. If john is not generous then someone is either tall or curious. Everyone who is not generous is both not rich and brave. Everyone who is not patient or not brave is tall and vice versa. If susan is both brave and wise then someone is not humble or calm and vice versa. Everyone who is either generous or old is either not patient or creative and vice versa. Everyone who is not funny or not curious is either wise or not calm. Everyone who is either not humble or not funny is humble or kind. Everyone who is either not brave or not calm is not quiet or wise and vice versa. Everyone who is not brave is either old or creative. Someone is both not quiet and not curious. Fred is either not creative or brave. Mary is both brave and funny. John is both not quiet and kind. Someone is both not curious and old. | Fred is not generous. | contradiction | (![X]:((generous(X)<~>curious(X))<=>(~funny(X)<~>rich(X))))&
(![X]:((brave(X)|~brave(X))=>(~funny(X)|humble(X))))&
(![X]:((curious(X)<~>kind(X))<=>(~kind(X)<~>~patient(X))))&
(![X]:((~old(X)&~kind(X))<=>~strong(X)))&
(![X]:(~tall(X)<=>(~old(X)&calm(X))))&
(![X]:((~curious(X)|~humble(X))=>rich(X)))&
(![X]:((~quiet(X)&wise(X))<=>curious(X)))&
((~generous(john))=>(?[X]:((tall(X)<~>curious(X)))))&
(![X]:(~generous(X)=>(~rich(X)&brave(X))))&
(![X]:((~patient(X)|~brave(X))<=>tall(X)))&
(((brave(susan)&wise(susan)))<=>(?[X]:((~humble(X)|calm(X)))))&
(![X]:((generous(X)<~>old(X))<=>(~patient(X)<~>creative(X))))&
(![X]:((~funny(X)|~curious(X))=>(wise(X)<~>~calm(X))))&
(![X]:((~humble(X)<~>~funny(X))=>(humble(X)|kind(X))))&
(![X]:((~brave(X)<~>~calm(X))<=>(~quiet(X)|wise(X))))&
(![X]:(~brave(X)=>(old(X)<~>creative(X))))&
(?[X]:((~quiet(X)&~curious(X))))&
((~creative(fred)<~>brave(fred)))&
((brave(mary)&funny(mary)))&
((~quiet(john)&kind(john)))&
(?[X]:((~curious(X)&old(X)))) | ~generous(fred) | [
"p2",
"p4",
"p5",
"p6",
"p8",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5801202640596852049477666
% SZS output start Proof for 5801202640596852049477666
3. ! [X0] : ((curious(X0) <~> kind(X0)) <=> (~kind(X0) <~> ~patient(X0))) [input p2]
5. ! [X0] : (~tall(X0) <=> (calm(X0) & ~old(X0))) [input p4]
6. ! [X0] : ((~humble(X0) | ~curious(X0)) => rich(X0)) [input p5]
7. ! [X0] : ((wise(X0) & ~quiet(X0)) <=> curious(X0)) [input p6]
9. ! [X0] : (~generous(X0) => (brave(X0) & ~rich(X0))) [input p8]
10. ! [X0] : ((~brave(X0) | ~patient(X0)) <=> tall(X0)) [input p9]
13. ! [X0] : ((~curious(X0) | ~funny(X0)) => (wise(X0) <~> ~calm(X0))) [input p12]
15. ! [X0] : ((~brave(X0) <~> ~calm(X0)) <=> (wise(X0) | ~quiet(X0))) [input p14]
22. ~generous(fred) [input hypothesis]
25. ! [X0] : (rich(X0) | (humble(X0) & curious(X0))) [ennf transformation 6]
27. ! [X0] : ((brave(X0) & ~rich(X0)) | generous(X0)) [ennf transformation 9]
28. ! [X0] : ((wise(X0) <~> ~calm(X0)) | (curious(X0) & funny(X0))) [ennf transformation 13]
33. ! [X0] : ((((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0)))) & (((patient(X0) | kind(X0)) & (~patient(X0) | ~kind(X0))) | ((curious(X0) | ~kind(X0)) & (kind(X0) | ~curious(X0))))) [nnf transformation 3]
34. ! [X0] : ((~tall(X0) | (~calm(X0) | old(X0))) & ((calm(X0) & ~old(X0)) | tall(X0))) [nnf transformation 5]
35. ! [X0] : ((~tall(X0) | ~calm(X0) | old(X0)) & ((calm(X0) & ~old(X0)) | tall(X0))) [flattening 34]
36. ! [X0] : (((wise(X0) & ~quiet(X0)) | ~curious(X0)) & (curious(X0) | (~wise(X0) | quiet(X0)))) [nnf transformation 7]
37. ! [X0] : (((wise(X0) & ~quiet(X0)) | ~curious(X0)) & (curious(X0) | ~wise(X0) | quiet(X0))) [flattening 36]
41. ! [X0] : (((~brave(X0) | ~patient(X0)) | ~tall(X0)) & (tall(X0) | (brave(X0) & patient(X0)))) [nnf transformation 10]
42. ! [X0] : ((~brave(X0) | ~patient(X0) | ~tall(X0)) & (tall(X0) | (brave(X0) & patient(X0)))) [flattening 41]
49. ! [X0] : (((calm(X0) | ~wise(X0)) & (~calm(X0) | wise(X0))) | (curious(X0) & funny(X0))) [nnf transformation 28]
51. ! [X0] : ((((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | (~wise(X0) & quiet(X0))) & ((wise(X0) | ~quiet(X0)) | ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0))))) [nnf transformation 15]
52. ! [X0] : ((((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | (~wise(X0) & quiet(X0))) & (wise(X0) | ~quiet(X0) | ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0))))) [flattening 51]
71. patient(X0) | kind(X0) | kind(X0) | ~curious(X0) [cnf transformation 33]
76. ~kind(X0) | ~curious(X0) | ~kind(X0) | patient(X0) [cnf transformation 33]
78. calm(X0) | tall(X0) [cnf transformation 35]
80. rich(X0) | curious(X0) [cnf transformation 25]
84. ~curious(X0) | wise(X0) [cnf transformation 37]
87. ~rich(X0) | generous(X0) [cnf transformation 27]
88. brave(X0) | generous(X0) [cnf transformation 27]
90. tall(X0) | brave(X0) [cnf transformation 42]
91. ~tall(X0) | ~patient(X0) | ~brave(X0) [cnf transformation 42]
106. ~calm(X0) | wise(X0) | curious(X0) [cnf transformation 49]
114. ~calm(X0) | ~brave(X0) | ~wise(X0) [cnf transformation 52]
129. ~generous(fred) [cnf transformation 22]
132. patient(X0) | kind(X0) | ~curious(X0) [duplicate literal removal 71]
134. ~kind(X0) | ~curious(X0) | patient(X0) [duplicate literal removal 76]
136. ~curious(X0) | patient(X0) [subsumption resolution 132,134]
179. ~calm(X0) | wise(X0) [subsumption resolution 106,84]
180. ~calm(X0) | ~brave(X0) [subsumption resolution 114,179]
187. 11 <=> brave(fred) [avatar definition]
188. brave(fred) <- (11) [avatar component clause 187]
189. ~brave(fred) <- (~11) [avatar component clause 187]
197. curious(X0) | generous(X0) [resolution 87,80]
199. generous(fred) <- (~11) [resolution 88,189]
200. $false <- (~11) [subsumption resolution 199,129]
201. 11 [avatar contradiction clause 200]
204. ~brave(X0) | tall(X0) [resolution 180,78]
205. patient(X0) | generous(X0) [resolution 197,136]
290. tall(X0) [subsumption resolution 204,90]
341. ~patient(X0) | ~brave(X0) [resolution 290,91]
411. 28 <=> patient(fred) [avatar definition]
412. patient(fred) <- (28) [avatar component clause 411]
413. ~patient(fred) <- (~28) [avatar component clause 411]
445. generous(fred) <- (~28) [resolution 413,205]
446. $false <- (~28) [subsumption resolution 445,129]
447. 28 [avatar contradiction clause 446]
568. ~brave(fred) <- (28) [resolution 341,412]
573. $false <- (11, 28) [subsumption resolution 568,188]
574. ~11 | ~28 [avatar contradiction clause 573]
575. $false [avatar sat refutation 201,447,574]
% SZS output end Proof for 5801202640596852049477666
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is not humble and vice versa.
If someone is not wise or not humble then someone is both not patient and not tall.
Everyone who is not generous is both tall and not old and vice versa.
Everyone who is both not patient and not wise is both kind and creative and vice versa.
Everyone who is not quiet or not funny is not quiet.
Everyone who is strong or not generous is curious or not funny and vice versa.
If someone is not tall or patient then fred is either not old or not happy.
Everyone who is happy is tall and vice versa.
If susan is both not humble and curious then someone is not brave or quiet and vice versa.
Everyone who is old is not calm.
Everyone who is not calm is either not funny or not creative.
If paul is kind or not generous then someone is both happy and rich.
Everyone who is not patient is creative or happy and vice versa.
Everyone who is both not calm and brave is either creative or not humble and vice versa.
If someone is both kind and not creative then someone is patient and vice versa.
Everyone who is both not patient and humble is both strong and not patient.
Fred is both humble and not quiet.
Someone is both not patient and not creative.
John is not creative or wise.
Mary is either old or funny.
Mary is curious or old.
Mary is not rich or wise.
Paul is not tall or old.
Susan is both rich and old. | John is not wise. | neutral | (![X]:(~funny(X)<=>~humble(X)))&
((?[X]:((~wise(X)|~humble(X))))=>(?[X]:((~patient(X)&~tall(X)))))&
(![X]:(~generous(X)<=>(tall(X)&~old(X))))&
(![X]:((~patient(X)&~wise(X))<=>(kind(X)&creative(X))))&
(![X]:((~quiet(X)|~funny(X))=>~quiet(X)))&
(![X]:((strong(X)|~generous(X))<=>(curious(X)|~funny(X))))&
((?[X]:((~tall(X)|patient(X))))=>((~old(fred)<~>~happy(fred))))&
(![X]:(happy(X)<=>tall(X)))&
(((~humble(susan)&curious(susan)))<=>(?[X]:((~brave(X)|quiet(X)))))&
(![X]:(old(X)=>~calm(X)))&
(![X]:(~calm(X)=>(~funny(X)<~>~creative(X))))&
(((kind(paul)|~generous(paul)))=>(?[X]:((happy(X)&rich(X)))))&
(![X]:(~patient(X)<=>(creative(X)|happy(X))))&
(![X]:((~calm(X)&brave(X))<=>(creative(X)<~>~humble(X))))&
((?[X]:((kind(X)&~creative(X))))<=>(?[X]:(patient(X))))&
(![X]:((~patient(X)&humble(X))=>(strong(X)&~patient(X))))&
((humble(fred)&~quiet(fred)))&
(?[X]:((~patient(X)&~creative(X))))&
((~creative(john)|wise(john)))&
((old(mary)<~>funny(mary)))&
((curious(mary)|old(mary)))&
((~rich(mary)|wise(mary)))&
((~tall(paul)|old(paul)))&
((rich(susan)&old(susan))) | ~wise(john) | [] | null | 0 |
If mary is either funny or old then fred is quiet and vice versa.
If someone is calm then susan is funny.
If someone is both not patient and humble then someone is calm or not old and vice versa.
Everyone who is not wise is rich.
Everyone who is either not kind or kind is both happy and wise and vice versa.
If someone is not wise then someone is not patient.
Everyone who is happy or not brave is both not quiet and not old and vice versa.
If fred is either not tall or funny then alice is calm or not curious and vice versa.
If someone is not humble or strong then john is not humble or not patient and vice versa.
If susan is patient then mary is either brave or not wise and vice versa.
If someone is either not humble or strong then someone is either curious or kind and vice versa.
Everyone who is not generous is either not tall or not humble.
If someone is funny then someone is not wise or humble and vice versa.
Everyone who is not creative is not patient.
If susan is either kind or patient then john is both calm and not patient and vice versa.
John is tall.
Someone is wise or kind.
Fred is wise.
Someone is both brave and not strong.
Paul is either creative or kind.
Alice is quiet or not funny. | John is old. | contradiction | (((funny(mary)<~>old(mary)))<=>(quiet(fred)))&
((?[X]:(calm(X)))=>(funny(susan)))&
((?[X]:((~patient(X)&humble(X))))<=>(?[X]:((calm(X)|~old(X)))))&
(![X]:(~wise(X)=>rich(X)))&
(![X]:((~kind(X)<~>kind(X))<=>(happy(X)&wise(X))))&
((?[X]:(~wise(X)))=>(?[X]:(~patient(X))))&
(![X]:((happy(X)|~brave(X))<=>(~quiet(X)&~old(X))))&
(((~tall(fred)<~>funny(fred)))<=>((calm(alice)|~curious(alice))))&
((?[X]:((~humble(X)|strong(X))))<=>((~humble(john)|~patient(john))))&
((patient(susan))<=>((brave(mary)<~>~wise(mary))))&
((?[X]:((~humble(X)<~>strong(X))))<=>(?[X]:((curious(X)<~>kind(X)))))&
(![X]:(~generous(X)=>(~tall(X)<~>~humble(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~wise(X)|humble(X)))))&
(![X]:(~creative(X)=>~patient(X)))&
(((kind(susan)<~>patient(susan)))<=>((calm(john)&~patient(john))))&
(tall(john))&
(?[X]:((wise(X)|kind(X))))&
(wise(fred))&
(?[X]:((brave(X)&~strong(X))))&
((creative(paul)<~>kind(paul)))&
((quiet(alice)|~funny(alice))) | old(john) | [
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 109453733011222790109796
% SZS output start Proof for 109453733011222790109796
5. ! [X0] : ((~kind(X0) <~> kind(X0)) <=> (wise(X0) & happy(X0))) [input p4]
7. ! [X0] : ((~brave(X0) | happy(X0)) <=> (~old(X0) & ~quiet(X0))) [input p6]
22. old(john) [input hypothesis]
38. ! [X0] : ((((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | (~wise(X0) | ~happy(X0))) & ((wise(X0) & happy(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0))))) [nnf transformation 5]
39. ! [X0] : ((((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ~wise(X0) | ~happy(X0)) & ((wise(X0) & happy(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0))))) [flattening 38]
43. ! [X0] : (((~brave(X0) | happy(X0)) | (old(X0) | quiet(X0))) & ((~old(X0) & ~quiet(X0)) | (brave(X0) & ~happy(X0)))) [nnf transformation 7]
44. ! [X0] : ((~brave(X0) | happy(X0) | old(X0) | quiet(X0)) & ((~old(X0) & ~quiet(X0)) | (brave(X0) & ~happy(X0)))) [flattening 43]
80. happy(X0) | kind(X0) | kind(X0) [cnf transformation 39]
81. happy(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 39]
89. ~old(X0) | ~happy(X0) [cnf transformation 44]
132. old(john) [cnf transformation 22]
133. happy(X0) | kind(X0) [duplicate literal removal 80]
134. happy(X0) | ~kind(X0) [duplicate literal removal 81]
189. happy(X0) [subsumption resolution 133,134]
190. ~old(X0) [subsumption resolution 89,189]
330. $false [subsumption resolution 132,190]
% SZS output end Proof for 109453733011222790109796
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not quiet then someone is both old and not rich and vice versa. Everyone who is both brave and calm is not kind or old and vice versa. If lucy is either creative or patient then susan is curious or not creative. Everyone who is both creative and rich is either not quiet or generous. If someone is calm then alice is patient. If fred is either strong or not quiet then susan is kind. Everyone who is brave is either wise or patient. Everyone who is not calm or curious is both quiet and creative. If lucy is both not quiet and not tall then susan is generous. If paul is both generous and kind then susan is brave and vice versa. If someone is either happy or brave then someone is quiet and vice versa. If paul is old then someone is both not old and not rich and vice versa. Everyone who is both not patient and tall is both old and patient. Everyone who is either old or not calm is both calm and old and vice versa. If lucy is either generous or not humble then lucy is kind and vice versa. Everyone who is both not rich and not calm is not strong or tall. Someone is not strong. Alice is not happy or not funny. Mary is patient or not generous. Someone is either not quiet or not rich. Susan is kind. Lucy is either brave or quiet. Someone is either not brave or curious. Someone is strong or humble. | Lucy is not calm. | contradiction | ((~quiet(paul))<=>(?[X]:((old(X)&~rich(X)))))&
(![X]:((brave(X)&calm(X))<=>(~kind(X)|old(X))))&
(((creative(lucy)<~>patient(lucy)))=>((curious(susan)|~creative(susan))))&
(![X]:((creative(X)&rich(X))=>(~quiet(X)<~>generous(X))))&
((?[X]:(calm(X)))=>(patient(alice)))&
(((strong(fred)<~>~quiet(fred)))=>(kind(susan)))&
(![X]:(brave(X)=>(wise(X)<~>patient(X))))&
(![X]:((~calm(X)|curious(X))=>(quiet(X)&creative(X))))&
(((~quiet(lucy)&~tall(lucy)))=>(generous(susan)))&
(((generous(paul)&kind(paul)))<=>(brave(susan)))&
((?[X]:((happy(X)<~>brave(X))))<=>(?[X]:(quiet(X))))&
((old(paul))<=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:((~patient(X)&tall(X))=>(old(X)&patient(X))))&
(![X]:((old(X)<~>~calm(X))<=>(calm(X)&old(X))))&
(((generous(lucy)<~>~humble(lucy)))<=>(kind(lucy)))&
(![X]:((~rich(X)&~calm(X))=>(~strong(X)|tall(X))))&
(?[X]:(~strong(X)))&
((~happy(alice)|~funny(alice)))&
((patient(mary)|~generous(mary)))&
(?[X]:((~quiet(X)<~>~rich(X))))&
(kind(susan))&
((brave(lucy)<~>quiet(lucy)))&
(?[X]:((~brave(X)<~>curious(X))))&
(?[X]:((strong(X)|humble(X)))) | ~calm(lucy) | [
"p1",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1963451098335796582478498
% SZS output start Proof for 1963451098335796582478498
2. ! [X0] : ((calm(X0) & brave(X0)) <=> (old(X0) | ~kind(X0))) [input p1]
14. ! [X0] : ((old(X0) <~> ~calm(X0)) <=> (old(X0) & calm(X0))) [input p13]
25. ~calm(lucy) [input hypothesis]
46. ! [X0] : (((calm(X0) & brave(X0)) | (~old(X0) & kind(X0))) & ((old(X0) | ~kind(X0)) | (~calm(X0) | ~brave(X0)))) [nnf transformation 2]
47. ! [X0] : (((calm(X0) & brave(X0)) | (~old(X0) & kind(X0))) & (old(X0) | ~kind(X0) | ~calm(X0) | ~brave(X0))) [flattening 46]
63. ! [X0] : ((((calm(X0) | ~old(X0)) & (~calm(X0) | old(X0))) | (~old(X0) | ~calm(X0))) & ((old(X0) & calm(X0)) | ((old(X0) | calm(X0)) & (~calm(X0) | ~old(X0))))) [nnf transformation 14]
64. ! [X0] : ((((calm(X0) | ~old(X0)) & (~calm(X0) | old(X0))) | ~old(X0) | ~calm(X0)) & ((old(X0) & calm(X0)) | ((old(X0) | calm(X0)) & (~calm(X0) | ~old(X0))))) [flattening 63]
84. calm(X0) | ~old(X0) [cnf transformation 47]
114. old(X0) | old(X0) | calm(X0) [cnf transformation 64]
132. ~calm(lucy) [cnf transformation 25]
134. old(X0) | calm(X0) [duplicate literal removal 114]
267. calm(X0) [subsumption resolution 134,84]
329. $false [subsumption resolution 132,267]
% SZS output end Proof for 1963451098335796582478498
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not curious or happy then someone is not creative. Everyone who is either not funny or not humble is not brave. If someone is either tall or strong then someone is either not quiet or calm and vice versa. If someone is strong or not funny then someone is either not curious or not humble and vice versa. If someone is both funny and not brave then mary is not old or not tall and vice versa. Everyone who is either not happy or tall is creative. If alice is happy or not quiet then someone is rich. If someone is happy or not creative then someone is both not wise and not patient and vice versa. If john is old then alice is not rich. Everyone who is rich or not calm is brave and vice versa. Everyone who is not happy is not humble or funny and vice versa. Everyone who is either not calm or not rich is either not rich or not creative. If susan is either strong or creative then someone is tall or not kind. Everyone who is both kind and humble is not funny or patient and vice versa. If lucy is tall or not generous then someone is either curious or not patient and vice versa. Everyone who is not humble is both not wise and not patient. Mary is not funny. Someone is not tall or old. Paul is both not strong and calm. Susan is not wise or brave. Mary is either tall or kind. Fred is brave. Mary is not old or brave. | Mary is creative. | entailment | (((~curious(paul)|happy(paul)))=>(?[X]:(~creative(X))))&
(![X]:((~funny(X)<~>~humble(X))=>~brave(X)))&
((?[X]:((tall(X)<~>strong(X))))<=>(?[X]:((~quiet(X)<~>calm(X)))))&
((?[X]:((strong(X)|~funny(X))))<=>(?[X]:((~curious(X)<~>~humble(X)))))&
((?[X]:((funny(X)&~brave(X))))<=>((~old(mary)|~tall(mary))))&
(![X]:((~happy(X)<~>tall(X))=>creative(X)))&
(((happy(alice)|~quiet(alice)))=>(?[X]:(rich(X))))&
((?[X]:((happy(X)|~creative(X))))<=>(?[X]:((~wise(X)&~patient(X)))))&
((old(john))=>(~rich(alice)))&
(![X]:((rich(X)|~calm(X))<=>brave(X)))&
(![X]:(~happy(X)<=>(~humble(X)|funny(X))))&
(![X]:((~calm(X)<~>~rich(X))=>(~rich(X)<~>~creative(X))))&
(((strong(susan)<~>creative(susan)))=>(?[X]:((tall(X)|~kind(X)))))&
(![X]:((kind(X)&humble(X))<=>(~funny(X)|patient(X))))&
(((tall(lucy)|~generous(lucy)))<=>(?[X]:((curious(X)<~>~patient(X)))))&
(![X]:(~humble(X)=>(~wise(X)&~patient(X))))&
(~funny(mary))&
(?[X]:((~tall(X)|old(X))))&
((~strong(paul)&calm(paul)))&
((~wise(susan)|brave(susan)))&
((tall(mary)<~>kind(mary)))&
(brave(fred))&
((~old(mary)|brave(mary))) | creative(mary) | [
"p1",
"p9",
"p11",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 9027721753176955294149760
% SZS output start Proof for 9027721753176955294149760
2. ! [X0] : ((~funny(X0) <~> ~humble(X0)) => ~brave(X0)) [input p1]
10. ! [X0] : ((~calm(X0) | rich(X0)) <=> brave(X0)) [input p9]
12. ! [X0] : ((~calm(X0) <~> ~rich(X0)) => (~rich(X0) <~> ~creative(X0))) [input p11]
14. ! [X0] : ((humble(X0) & kind(X0)) <=> (patient(X0) | ~funny(X0))) [input p13]
17. ~funny(mary) [input p16]
24. ~creative(mary) [input hypothesis]
29. ! [X0] : (~brave(X0) | (~funny(X0) <=> ~humble(X0))) [ennf transformation 2]
33. ! [X0] : ((~rich(X0) <~> ~creative(X0)) | (~calm(X0) <=> ~rich(X0))) [ennf transformation 12]
38. ! [X0] : (~brave(X0) | ((~funny(X0) | humble(X0)) & (~humble(X0) | funny(X0)))) [nnf transformation 29]
62. ! [X0] : (((~calm(X0) | rich(X0)) | ~brave(X0)) & (brave(X0) | (calm(X0) & ~rich(X0)))) [nnf transformation 10]
63. ! [X0] : ((~calm(X0) | rich(X0) | ~brave(X0)) & (brave(X0) | (calm(X0) & ~rich(X0)))) [flattening 62]
66. ! [X0] : (((creative(X0) | rich(X0)) & (~creative(X0) | ~rich(X0))) | ((~calm(X0) | rich(X0)) & (~rich(X0) | calm(X0)))) [nnf transformation 33]
70. ! [X0] : (((humble(X0) & kind(X0)) | (~patient(X0) & funny(X0))) & ((patient(X0) | ~funny(X0)) | (~humble(X0) | ~kind(X0)))) [nnf transformation 14]
71. ! [X0] : (((humble(X0) & kind(X0)) | (~patient(X0) & funny(X0))) & (patient(X0) | ~funny(X0) | ~humble(X0) | ~kind(X0))) [flattening 70]
82. ~brave(X0) | ~humble(X0) | funny(X0) [cnf transformation 38]
83. ~brave(X0) | ~funny(X0) | humble(X0) [cnf transformation 38]
113. ~rich(X0) | brave(X0) [cnf transformation 63]
114. calm(X0) | brave(X0) [cnf transformation 63]
122. creative(X0) | rich(X0) | ~calm(X0) | rich(X0) [cnf transformation 66]
128. humble(X0) | funny(X0) [cnf transformation 71]
138. ~funny(mary) [cnf transformation 17]
147. ~creative(mary) [cnf transformation 24]
149. ~calm(X0) | rich(X0) | creative(X0) [duplicate literal removal 122]
447. rich(X0) | creative(X0) | brave(X0) [resolution 149,114]
453. brave(X0) | creative(X0) [subsumption resolution 447,113]
469. creative(X0) | ~funny(X0) | humble(X0) [resolution 453,83]
470. creative(X1) | ~humble(X1) | funny(X1) [resolution 453,82]
471. humble(X0) | creative(X0) [subsumption resolution 469,128]
472. funny(X1) | creative(X1) [subsumption resolution 470,471]
481. creative(mary) [resolution 472,138]
484. $false [subsumption resolution 481,147]
% SZS output end Proof for 9027721753176955294149760
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not tall then someone is brave or happy. Everyone who is not curious is patient and vice versa. Everyone who is not generous is curious and vice versa. Everyone who is not strong or old is both funny and not tall. Everyone who is not creative or not brave is both tall and curious and vice versa. Everyone who is both funny and not patient is either rich or not calm and vice versa. If someone is not generous or funny then someone is funny and vice versa. Everyone who is either not old or not calm is not strong or strong and vice versa. Everyone who is both curious and tall is both not patient and creative. Everyone who is either not quiet or generous is rich or creative and vice versa. Everyone who is either not patient or not rich is both quiet and calm. Everyone who is either not brave or not wise is either not funny or curious. Everyone who is funny is either not brave or wise and vice versa. Everyone who is both patient and strong is strong and vice versa. If someone is either not patient or not humble then someone is both creative and not creative. Everyone who is both patient and not funny is both not funny and funny and vice versa. Fred is not quiet or not strong. Lucy is either kind or funny. Susan is either not tall or not wise. Susan is not calm. Paul is creative or old. Someone is happy or tall. Someone is generous. | Lucy is happy. | neutral | (((brave(paul)|~tall(paul)))=>(?[X]:((brave(X)|happy(X)))))&
(![X]:(~curious(X)<=>patient(X)))&
(![X]:(~generous(X)<=>curious(X)))&
(![X]:((~strong(X)|old(X))=>(funny(X)&~tall(X))))&
(![X]:((~creative(X)|~brave(X))<=>(tall(X)&curious(X))))&
(![X]:((funny(X)&~patient(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((~generous(X)|funny(X))))<=>(?[X]:(funny(X))))&
(![X]:((~old(X)<~>~calm(X))<=>(~strong(X)|strong(X))))&
(![X]:((curious(X)&tall(X))=>(~patient(X)&creative(X))))&
(![X]:((~quiet(X)<~>generous(X))<=>(rich(X)|creative(X))))&
(![X]:((~patient(X)<~>~rich(X))=>(quiet(X)&calm(X))))&
(![X]:((~brave(X)<~>~wise(X))=>(~funny(X)<~>curious(X))))&
(![X]:(funny(X)<=>(~brave(X)<~>wise(X))))&
(![X]:((patient(X)&strong(X))<=>strong(X)))&
((?[X]:((~patient(X)<~>~humble(X))))=>(?[X]:((creative(X)&~creative(X)))))&
(![X]:((patient(X)&~funny(X))<=>(~funny(X)&funny(X))))&
((~quiet(fred)|~strong(fred)))&
((kind(lucy)<~>funny(lucy)))&
((~tall(susan)<~>~wise(susan)))&
(~calm(susan))&
((creative(paul)|old(paul)))&
(?[X]:((happy(X)|tall(X))))&
(?[X]:(generous(X))) | happy(lucy) | [] | null | 0 |
Everyone who is not happy or old is both not funny and not quiet.
Everyone who is both humble and curious is both not generous and calm and vice versa.
Everyone who is both not brave and not tall is either brave or not creative and vice versa.
Everyone who is not tall is either rich or not curious.
If someone is either not tall or not kind then john is both not humble and old and vice versa.
Everyone who is either not kind or creative is not kind or tall and vice versa.
If alice is either strong or not kind then someone is both not humble and rich.
If fred is either not creative or strong then lucy is both strong and old.
If fred is not kind then paul is calm and vice versa.
If lucy is both happy and not humble then someone is both not quiet and calm and vice versa.
If someone is both not tall and strong then someone is tall.
Everyone who is not rich is both wise and patient and vice versa.
Everyone who is not quiet is either generous or rich.
Everyone who is both funny and not old is not creative.
If mary is both calm and not quiet then someone is calm or not quiet and vice versa.
If alice is either not brave or not generous then someone is humble and vice versa.
Mary is both rich and funny.
Mary is both strong and not patient.
Mary is either not funny or generous.
Lucy is humble or not old.
Someone is either wise or not strong. | Mary is curious. | entailment | (![X]:((~happy(X)|old(X))=>(~funny(X)&~quiet(X))))&
(![X]:((humble(X)&curious(X))<=>(~generous(X)&calm(X))))&
(![X]:((~brave(X)&~tall(X))<=>(brave(X)<~>~creative(X))))&
(![X]:(~tall(X)=>(rich(X)<~>~curious(X))))&
((?[X]:((~tall(X)<~>~kind(X))))<=>((~humble(john)&old(john))))&
(![X]:((~kind(X)<~>creative(X))<=>(~kind(X)|tall(X))))&
(((strong(alice)<~>~kind(alice)))=>(?[X]:((~humble(X)&rich(X)))))&
(((~creative(fred)<~>strong(fred)))=>((strong(lucy)&old(lucy))))&
((~kind(fred))<=>(calm(paul)))&
(((happy(lucy)&~humble(lucy)))<=>(?[X]:((~quiet(X)&calm(X)))))&
((?[X]:((~tall(X)&strong(X))))=>(?[X]:(tall(X))))&
(![X]:(~rich(X)<=>(wise(X)&patient(X))))&
(![X]:(~quiet(X)=>(generous(X)<~>rich(X))))&
(![X]:((funny(X)&~old(X))=>~creative(X)))&
(((calm(mary)&~quiet(mary)))<=>(?[X]:((calm(X)|~quiet(X)))))&
(((~brave(alice)<~>~generous(alice)))<=>(?[X]:(humble(X))))&
((rich(mary)&funny(mary)))&
((strong(mary)&~patient(mary)))&
((~funny(mary)<~>generous(mary)))&
((humble(lucy)|~old(lucy)))&
(?[X]:((wise(X)<~>~strong(X)))) | curious(mary) | [
"p0",
"p3",
"p4",
"p5",
"p12",
"p13",
"p14",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7237828685762741929150478
% SZS output start Proof for 7237828685762741929150478
1. ! [X0] : ((old(X0) | ~happy(X0)) => (~quiet(X0) & ~funny(X0))) [input p0]
4. ! [X0] : (~tall(X0) => (rich(X0) <~> ~curious(X0))) [input p3]
5. ? [X0] : (~tall(X0) <~> ~kind(X0)) <=> (old(john) & ~humble(john)) [input p4]
6. ! [X0] : ((~kind(X0) <~> creative(X0)) <=> (tall(X0) | ~kind(X0))) [input p5]
13. ! [X0] : (~quiet(X0) => (generous(X0) <~> rich(X0))) [input p12]
14. ! [X0] : ((~old(X0) & funny(X0)) => ~creative(X0)) [input p13]
15. (~quiet(mary) & calm(mary)) <=> ? [X0] : (~quiet(X0) | calm(X0)) [input p14]
17. funny(mary) & rich(mary) [input p16]
19. ~funny(mary) <~> generous(mary) [input p18]
22. ~curious(mary) [input hypothesis]
24. ! [X0] : ((~quiet(X0) & ~funny(X0)) | (~old(X0) & happy(X0))) [ennf transformation 1]
25. ! [X0] : ((rich(X0) <~> ~curious(X0)) | tall(X0)) [ennf transformation 4]
29. ! [X0] : ((generous(X0) <~> rich(X0)) | quiet(X0)) [ennf transformation 13]
30. ! [X0] : (~creative(X0) | (old(X0) | ~funny(X0))) [ennf transformation 14]
31. ! [X0] : (~creative(X0) | old(X0) | ~funny(X0)) [flattening 30]
36. ! [X0] : (((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | tall(X0)) [nnf transformation 25]
37. (? [X0] : ((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) | (~old(john) | humble(john))) & ((old(john) & ~humble(john)) | ! [X0] : ((~tall(X0) | kind(X0)) & (~kind(X0) | tall(X0)))) [nnf transformation 5]
38. (? [X0] : ((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) | ~old(john) | humble(john)) & ((old(john) & ~humble(john)) | ! [X0] : ((~tall(X0) | kind(X0)) & (~kind(X0) | tall(X0)))) [flattening 37]
39. (? [X0] : ((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) | ~old(john) | humble(john)) & ((old(john) & ~humble(john)) | ! [X1] : ((~tall(X1) | kind(X1)) & (~kind(X1) | tall(X1)))) [rectify 38]
40. ? [X0] : ((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) => ((kind(sK0) | tall(sK0)) & (~kind(sK0) | ~tall(sK0))) [choice axiom]
41. (((kind(sK0) | tall(sK0)) & (~kind(sK0) | ~tall(sK0))) | ~old(john) | humble(john)) & ((old(john) & ~humble(john)) | ! [X1] : ((~tall(X1) | kind(X1)) & (~kind(X1) | tall(X1)))) [skolemisation 39,40]
42. ! [X0] : ((((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | (~tall(X0) & kind(X0))) & ((tall(X0) | ~kind(X0)) | ((~kind(X0) | ~creative(X0)) & (creative(X0) | kind(X0))))) [nnf transformation 6]
43. ! [X0] : ((((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | (~tall(X0) & kind(X0))) & (tall(X0) | ~kind(X0) | ((~kind(X0) | ~creative(X0)) & (creative(X0) | kind(X0))))) [flattening 42]
59. ! [X0] : (((~rich(X0) | ~generous(X0)) & (rich(X0) | generous(X0))) | quiet(X0)) [nnf transformation 29]
60. ((~quiet(mary) & calm(mary)) | ! [X0] : (quiet(X0) & ~calm(X0))) & (? [X0] : (~quiet(X0) | calm(X0)) | (quiet(mary) | ~calm(mary))) [nnf transformation 15]
61. ((~quiet(mary) & calm(mary)) | ! [X0] : (quiet(X0) & ~calm(X0))) & (? [X0] : (~quiet(X0) | calm(X0)) | quiet(mary) | ~calm(mary)) [flattening 60]
62. ((~quiet(mary) & calm(mary)) | ! [X0] : (quiet(X0) & ~calm(X0))) & (? [X1] : (~quiet(X1) | calm(X1)) | quiet(mary) | ~calm(mary)) [rectify 61]
63. ? [X1] : (~quiet(X1) | calm(X1)) => (~quiet(sK4) | calm(sK4)) [choice axiom]
64. ((~quiet(mary) & calm(mary)) | ! [X0] : (quiet(X0) & ~calm(X0))) & ((~quiet(sK4) | calm(sK4)) | quiet(mary) | ~calm(mary)) [skolemisation 62,63]
69. (~generous(mary) | funny(mary)) & (generous(mary) | ~funny(mary)) [nnf transformation 19]
74. ~funny(X0) | ~old(X0) [cnf transformation 24]
76. ~quiet(X0) | ~old(X0) [cnf transformation 24]
88. ~rich(X0) | curious(X0) | tall(X0) [cnf transformation 36]
92. old(john) | ~tall(X1) | kind(X1) [cnf transformation 41]
98. ~kind(X0) | creative(X0) | ~tall(X0) [cnf transformation 43]
120. ~rich(X0) | ~generous(X0) | quiet(X0) [cnf transformation 59]
121. ~creative(X0) | old(X0) | ~funny(X0) [cnf transformation 31]
124. calm(mary) | quiet(X0) [cnf transformation 64]
125. ~quiet(mary) | ~calm(X0) [cnf transformation 64]
131. rich(mary) [cnf transformation 17]
132. funny(mary) [cnf transformation 17]
135. generous(mary) | ~funny(mary) [cnf transformation 69]
140. ~curious(mary) [cnf transformation 22]
151. 2 <=> old(john) [avatar definition]
152. old(john) <- (2) [avatar component clause 151]
165. 5 <=> ! [X1] : (~tall(X1) | kind(X1)) [avatar definition]
166. ~tall(X1) | kind(X1) <- (5) [avatar component clause 165]
167. 5 | 2 [avatar split clause 92,151,165]
256. ~creative(X0) | ~funny(X0) [subsumption resolution 121,74]
258. 24 <=> ! [X0] : quiet(X0) [avatar definition]
259. quiet(X0) <- (24) [avatar component clause 258]
261. 25 <=> quiet(mary) [avatar definition]
266. 26 <=> ! [X0] : ~calm(X0) [avatar definition]
267. ~calm(X0) <- (26) [avatar component clause 266]
268. 26 | ~25 [avatar split clause 125,261,266]
270. 27 <=> calm(mary) [avatar definition]
272. calm(mary) <- (27) [avatar component clause 270]
273. 24 | 27 [avatar split clause 124,270,258]
303. generous(mary) [subsumption resolution 135,132]
329. $false <- (26, 27) [subsumption resolution 272,267]
330. ~26 | ~27 [avatar contradiction clause 329]
331. ~old(X0) <- (24) [resolution 259,76]
338. $false <- (2, 24) [resolution 331,152]
339. ~2 | ~24 [avatar contradiction clause 338]
361. 36 <=> creative(mary) [avatar definition]
362. ~creative(mary) <- (~36) [avatar component clause 361]
363. creative(mary) <- (36) [avatar component clause 361]
386. curious(mary) | tall(mary) [resolution 88,131]
454. ~funny(mary) <- (36) [resolution 363,256]
460. $false <- (36) [subsumption resolution 454,132]
461. ~36 [avatar contradiction clause 460]
463. tall(mary) [subsumption resolution 386,140]
476. kind(mary) <- (5) [resolution 463,166]
480. ~generous(mary) | quiet(mary) [resolution 120,131]
515. creative(mary) | ~tall(mary) <- (5) [resolution 476,98]
517. ~tall(mary) <- (5, ~36) [subsumption resolution 515,362]
518. $false <- (5, ~36) [subsumption resolution 517,463]
519. ~5 | 36 [avatar contradiction clause 518]
540. quiet(mary) [subsumption resolution 480,303]
541. 25 [avatar split clause 540,261]
542. $false [avatar sat refutation 167,268,273,330,339,461,519,541]
% SZS output end Proof for 7237828685762741929150478
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or generous is humble or not generous.
If john is either tall or not brave then someone is not calm or quiet and vice versa.
Everyone who is either calm or not creative is funny or not happy.
Everyone who is both not patient and not calm is either calm or funny and vice versa.
Everyone who is humble is either not humble or brave.
Everyone who is either not creative or creative is either not funny or kind and vice versa.
Everyone who is rich or creative is not creative and vice versa.
Everyone who is quiet is rich or quiet and vice versa.
Everyone who is generous or not happy is not strong and vice versa.
If someone is both not quiet and calm then fred is happy or not generous and vice versa.
Everyone who is either not rich or not humble is both not quiet and not wise and vice versa.
If fred is not kind or not strong then fred is not tall or quiet and vice versa.
Everyone who is happy is patient.
Everyone who is both tall and not strong is both wise and not humble and vice versa.
Everyone who is either brave or not wise is rich.
If someone is either tall or not old then lucy is not humble.
Fred is both old and not calm.
Fred is not kind.
Someone is strong or not funny.
Lucy is either creative or humble.
Lucy is either not happy or humble.
Alice is not old. | Alice is calm. | entailment | (![X]:((rich(X)|generous(X))=>(humble(X)|~generous(X))))&
(((tall(john)<~>~brave(john)))<=>(?[X]:((~calm(X)|quiet(X)))))&
(![X]:((calm(X)<~>~creative(X))=>(funny(X)|~happy(X))))&
(![X]:((~patient(X)&~calm(X))<=>(calm(X)<~>funny(X))))&
(![X]:(humble(X)=>(~humble(X)<~>brave(X))))&
(![X]:((~creative(X)<~>creative(X))<=>(~funny(X)<~>kind(X))))&
(![X]:((rich(X)|creative(X))<=>~creative(X)))&
(![X]:(quiet(X)<=>(rich(X)|quiet(X))))&
(![X]:((generous(X)|~happy(X))<=>~strong(X)))&
((?[X]:((~quiet(X)&calm(X))))<=>((happy(fred)|~generous(fred))))&
(![X]:((~rich(X)<~>~humble(X))<=>(~quiet(X)&~wise(X))))&
(((~kind(fred)|~strong(fred)))<=>((~tall(fred)|quiet(fred))))&
(![X]:(happy(X)=>patient(X)))&
(![X]:((tall(X)&~strong(X))<=>(wise(X)&~humble(X))))&
(![X]:((brave(X)<~>~wise(X))=>rich(X)))&
((?[X]:((tall(X)<~>~old(X))))=>(~humble(lucy)))&
((old(fred)&~calm(fred)))&
(~kind(fred))&
(?[X]:((strong(X)|~funny(X))))&
((creative(lucy)<~>humble(lucy)))&
((~happy(lucy)<~>humble(lucy)))&
(~old(alice)) | calm(alice) | [
"p2",
"p3",
"p6",
"p7",
"p8",
"p10",
"p12",
"p13",
"p15",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 642814958572244789112242
% SZS output start Proof for 642814958572244789112242
3. ! [X0] : ((calm(X0) <~> ~creative(X0)) => (~happy(X0) | funny(X0))) [input p2]
4. ! [X0] : ((~calm(X0) & ~patient(X0)) <=> (calm(X0) <~> funny(X0))) [input p3]
7. ! [X0] : ((creative(X0) | rich(X0)) <=> ~creative(X0)) [input p6]
8. ! [X0] : (quiet(X0) <=> (quiet(X0) | rich(X0))) [input p7]
9. ! [X0] : ((~happy(X0) | generous(X0)) <=> ~strong(X0)) [input p8]
11. ! [X0] : ((~rich(X0) <~> ~humble(X0)) <=> (~wise(X0) & ~quiet(X0))) [input p10]
13. ! [X0] : (happy(X0) => patient(X0)) [input p12]
14. ! [X0] : ((~strong(X0) & tall(X0)) <=> (~humble(X0) & wise(X0))) [input p13]
16. ? [X0] : (tall(X0) <~> ~old(X0)) => ~humble(lucy) [input p15]
20. creative(lucy) <~> humble(lucy) [input p19]
22. ~old(alice) [input p21]
23. ~calm(alice) [input hypothesis]
26. ! [X0] : ((~happy(X0) | funny(X0)) | (calm(X0) <=> ~creative(X0))) [ennf transformation 3]
27. ! [X0] : (~happy(X0) | funny(X0) | (calm(X0) <=> ~creative(X0))) [flattening 26]
29. ! [X0] : (patient(X0) | ~happy(X0)) [ennf transformation 13]
31. ~humble(lucy) | ! [X0] : (tall(X0) <=> ~old(X0)) [ennf transformation 16]
36. ! [X0] : (~happy(X0) | funny(X0) | ((calm(X0) | creative(X0)) & (~creative(X0) | ~calm(X0)))) [nnf transformation 27]
37. ! [X0] : (((~calm(X0) & ~patient(X0)) | ((calm(X0) | ~funny(X0)) & (funny(X0) | ~calm(X0)))) & (((~funny(X0) | ~calm(X0)) & (funny(X0) | calm(X0))) | (calm(X0) | patient(X0)))) [nnf transformation 4]
38. ! [X0] : (((~calm(X0) & ~patient(X0)) | ((calm(X0) | ~funny(X0)) & (funny(X0) | ~calm(X0)))) & (((~funny(X0) | ~calm(X0)) & (funny(X0) | calm(X0))) | calm(X0) | patient(X0))) [flattening 37]
41. ! [X0] : (((creative(X0) | rich(X0)) | creative(X0)) & (~creative(X0) | (~creative(X0) & ~rich(X0)))) [nnf transformation 7]
42. ! [X0] : ((creative(X0) | rich(X0) | creative(X0)) & (~creative(X0) | (~creative(X0) & ~rich(X0)))) [flattening 41]
43. ! [X0] : ((quiet(X0) | (~quiet(X0) & ~rich(X0))) & ((quiet(X0) | rich(X0)) | ~quiet(X0))) [nnf transformation 8]
44. ! [X0] : ((quiet(X0) | (~quiet(X0) & ~rich(X0))) & (quiet(X0) | rich(X0) | ~quiet(X0))) [flattening 43]
45. ! [X0] : (((~happy(X0) | generous(X0)) | strong(X0)) & (~strong(X0) | (happy(X0) & ~generous(X0)))) [nnf transformation 9]
46. ! [X0] : ((~happy(X0) | generous(X0) | strong(X0)) & (~strong(X0) | (happy(X0) & ~generous(X0)))) [flattening 45]
52. ! [X0] : ((((humble(X0) | rich(X0)) & (~humble(X0) | ~rich(X0))) | (wise(X0) | quiet(X0))) & ((~wise(X0) & ~quiet(X0)) | ((~rich(X0) | humble(X0)) & (~humble(X0) | rich(X0))))) [nnf transformation 11]
53. ! [X0] : ((((humble(X0) | rich(X0)) & (~humble(X0) | ~rich(X0))) | wise(X0) | quiet(X0)) & ((~wise(X0) & ~quiet(X0)) | ((~rich(X0) | humble(X0)) & (~humble(X0) | rich(X0))))) [flattening 52]
56. ! [X0] : (((~strong(X0) & tall(X0)) | (humble(X0) | ~wise(X0))) & ((~humble(X0) & wise(X0)) | (strong(X0) | ~tall(X0)))) [nnf transformation 14]
57. ! [X0] : (((~strong(X0) & tall(X0)) | humble(X0) | ~wise(X0)) & ((~humble(X0) & wise(X0)) | strong(X0) | ~tall(X0))) [flattening 56]
59. ~humble(lucy) | ! [X0] : ((tall(X0) | old(X0)) & (~old(X0) | ~tall(X0))) [nnf transformation 31]
62. (~humble(lucy) | ~creative(lucy)) & (humble(lucy) | creative(lucy)) [nnf transformation 20]
73. ~happy(X0) | funny(X0) | calm(X0) | creative(X0) [cnf transformation 36]
77. ~patient(X0) | calm(X0) | ~funny(X0) [cnf transformation 38]
91. ~creative(X0) | ~creative(X0) [cnf transformation 42]
92. creative(X0) | rich(X0) | creative(X0) [cnf transformation 42]
94. ~rich(X0) | quiet(X0) [cnf transformation 44]
97. ~strong(X0) | happy(X0) [cnf transformation 46]
105. ~quiet(X0) | ~rich(X0) | humble(X0) [cnf transformation 53]
114. ~happy(X0) | patient(X0) [cnf transformation 29]
116. ~tall(X0) | strong(X0) | ~humble(X0) [cnf transformation 57]
122. ~humble(lucy) | tall(X0) | old(X0) [cnf transformation 59]
127. humble(lucy) | creative(lucy) [cnf transformation 62]
131. ~old(alice) [cnf transformation 22]
132. ~calm(alice) [cnf transformation 23]
133. ~creative(X0) [duplicate literal removal 91]
134. creative(X0) | rich(X0) [duplicate literal removal 92]
199. ~rich(X0) | humble(X0) [subsumption resolution 105,94]
221. 16 <=> ! [X0] : (tall(X0) | old(X0)) [avatar definition]
222. old(X0) | tall(X0) <- (16) [avatar component clause 221]
224. 17 <=> humble(lucy) [avatar definition]
227. 16 | ~17 [avatar split clause 122,224,221]
242. humble(lucy) [subsumption resolution 127,133]
243. 17 [avatar split clause 242,224]
251. rich(X0) [resolution 134,133]
261. humble(X0) [resolution 199,251]
263. tall(alice) <- (16) [resolution 222,131]
300. 27 <=> strong(alice) [avatar definition]
302. strong(alice) <- (27) [avatar component clause 300]
323. strong(alice) | ~humble(alice) <- (16) [resolution 116,263]
325. strong(alice) <- (16) [subsumption resolution 323,261]
326. 27 | ~16 [avatar split clause 325,221,300]
341. happy(alice) <- (27) [resolution 302,97]
355. patient(alice) <- (27) [resolution 341,114]
379. funny(alice) | calm(alice) | creative(alice) <- (27) [resolution 73,341]
386. funny(alice) | creative(alice) <- (27) [subsumption resolution 379,132]
387. funny(alice) <- (27) [subsumption resolution 386,133]
396. calm(alice) | ~funny(alice) <- (27) [resolution 355,77]
397. ~funny(alice) <- (27) [subsumption resolution 396,132]
398. $false <- (27) [subsumption resolution 397,387]
399. ~27 [avatar contradiction clause 398]
400. $false [avatar sat refutation 227,243,326,399]
% SZS output end Proof for 642814958572244789112242
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet or not brave then someone is rich or not calm.
If alice is both not funny and strong then mary is curious.
Everyone who is not happy or not creative is generous.
If susan is not strong or tall then someone is either quiet or not strong and vice versa.
If someone is both not patient and humble then someone is not kind or not wise and vice versa.
Everyone who is quiet or not wise is not strong and vice versa.
Everyone who is calm is patient.
Everyone who is calm or old is both not old and not rich.
If someone is brave or not strong then paul is wise.
Everyone who is both not old and curious is not curious.
Everyone who is not quiet is either not old or quiet and vice versa.
Everyone who is both old and happy is both strong and not calm and vice versa.
Everyone who is both not patient and not generous is both wise and quiet.
Everyone who is creative is both not calm and rich and vice versa.
If someone is both wise and not kind then someone is both not kind and happy and vice versa.
Everyone who is curious is not patient or not strong.
Paul is not humble or not patient.
Someone is not tall or not old.
Lucy is generous or not humble.
Paul is both tall and not creative.
Lucy is generous or not generous.
Mary is both happy and brave.
Someone is both not kind and not patient.
Alice is humble or kind. | Lucy is patient. | neutral | ((?[X]:((quiet(X)|~brave(X))))=>(?[X]:((rich(X)|~calm(X)))))&
(((~funny(alice)&strong(alice)))=>(curious(mary)))&
(![X]:((~happy(X)|~creative(X))=>generous(X)))&
(((~strong(susan)|tall(susan)))<=>(?[X]:((quiet(X)<~>~strong(X)))))&
((?[X]:((~patient(X)&humble(X))))<=>(?[X]:((~kind(X)|~wise(X)))))&
(![X]:((quiet(X)|~wise(X))<=>~strong(X)))&
(![X]:(calm(X)=>patient(X)))&
(![X]:((calm(X)|old(X))=>(~old(X)&~rich(X))))&
((?[X]:((brave(X)|~strong(X))))=>(wise(paul)))&
(![X]:((~old(X)&curious(X))=>~curious(X)))&
(![X]:(~quiet(X)<=>(~old(X)<~>quiet(X))))&
(![X]:((old(X)&happy(X))<=>(strong(X)&~calm(X))))&
(![X]:((~patient(X)&~generous(X))=>(wise(X)&quiet(X))))&
(![X]:(creative(X)<=>(~calm(X)&rich(X))))&
((?[X]:((wise(X)&~kind(X))))<=>(?[X]:((~kind(X)&happy(X)))))&
(![X]:(curious(X)=>(~patient(X)|~strong(X))))&
((~humble(paul)|~patient(paul)))&
(?[X]:((~tall(X)|~old(X))))&
((generous(lucy)|~humble(lucy)))&
((tall(paul)&~creative(paul)))&
((generous(lucy)|~generous(lucy)))&
((happy(mary)&brave(mary)))&
(?[X]:((~kind(X)&~patient(X))))&
((humble(alice)|kind(alice))) | patient(lucy) | [] | null | 0 |
Everyone who is either happy or brave is either happy or kind and vice versa.
If someone is both creative and not old then susan is brave.
If someone is not strong or humble then someone is either curious or old.
Everyone who is curious or brave is not funny and vice versa.
Everyone who is both old and not quiet is funny or patient and vice versa.
If paul is curious then someone is not brave and vice versa.
Everyone who is either not creative or not generous is not funny or not tall and vice versa.
If paul is not quiet or wise then alice is not humble or not tall and vice versa.
Everyone who is funny or not quiet is brave or not generous.
Everyone who is wise or not tall is either not curious or old and vice versa.
Everyone who is either not quiet or patient is both not old and not wise.
If someone is not humble or patient then someone is not humble or strong.
If someone is humble then lucy is not curious or old.
Everyone who is both creative and kind is not tall or not rich and vice versa.
If someone is both not quiet and quiet then someone is not funny.
Everyone who is either not curious or not quiet is tall or brave and vice versa.
Susan is either not curious or not quiet.
Susan is either creative or not humble.
Susan is either not curious or not strong.
Susan is both old and curious.
Paul is either not patient or not generous.
Susan is either not quiet or strong.
Someone is patient. | Susan is brave. | neutral | (![X]:((happy(X)<~>brave(X))<=>(happy(X)<~>kind(X))))&
((?[X]:((creative(X)&~old(X))))=>(brave(susan)))&
((?[X]:((~strong(X)|humble(X))))=>(?[X]:((curious(X)<~>old(X)))))&
(![X]:((curious(X)|brave(X))<=>~funny(X)))&
(![X]:((old(X)&~quiet(X))<=>(funny(X)|patient(X))))&
((curious(paul))<=>(?[X]:(~brave(X))))&
(![X]:((~creative(X)<~>~generous(X))<=>(~funny(X)|~tall(X))))&
(((~quiet(paul)|wise(paul)))<=>((~humble(alice)|~tall(alice))))&
(![X]:((funny(X)|~quiet(X))=>(brave(X)|~generous(X))))&
(![X]:((wise(X)|~tall(X))<=>(~curious(X)<~>old(X))))&
(![X]:((~quiet(X)<~>patient(X))=>(~old(X)&~wise(X))))&
((?[X]:((~humble(X)|patient(X))))=>(?[X]:((~humble(X)|strong(X)))))&
((?[X]:(humble(X)))=>((~curious(lucy)|old(lucy))))&
(![X]:((creative(X)&kind(X))<=>(~tall(X)|~rich(X))))&
((?[X]:((~quiet(X)&quiet(X))))=>(?[X]:(~funny(X))))&
(![X]:((~curious(X)<~>~quiet(X))<=>(tall(X)|brave(X))))&
((~curious(susan)<~>~quiet(susan)))&
((creative(susan)<~>~humble(susan)))&
((~curious(susan)<~>~strong(susan)))&
((old(susan)&curious(susan)))&
((~patient(paul)<~>~generous(paul)))&
((~quiet(susan)<~>strong(susan)))&
(?[X]:(patient(X))) | brave(susan) | [] | null | 0 |
Everyone who is both not creative and not rich is either not quiet or not old and vice versa. Everyone who is brave is kind or curious. If someone is generous then someone is not funny. Everyone who is not humble or creative is both old and not generous. If fred is not curious or old then mary is both not happy and brave. If mary is either wise or generous then someone is tall and vice versa. Everyone who is happy or not creative is both brave and patient. Everyone who is both funny and curious is both creative and not brave and vice versa. Everyone who is generous is strong or calm and vice versa. Everyone who is not wise is both not creative and not strong. If someone is both not kind and rich then someone is generous. Everyone who is both wise and not quiet is quiet. If alice is not generous then mary is either old or not rich. Everyone who is both not kind and calm is not quiet. Everyone who is both not rich and patient is not patient or not strong. Everyone who is both funny and not calm is brave or curious. Someone is not creative or creative. Mary is quiet. John is tall or not quiet. Someone is both kind and wise. Someone is both old and kind. Someone is both not quiet and not wise. Someone is either kind or happy. Someone is either old or not curious. | Alice is generous. | neutral | (![X]:((~creative(X)&~rich(X))<=>(~quiet(X)<~>~old(X))))&
(![X]:(brave(X)=>(kind(X)|curious(X))))&
((?[X]:(generous(X)))=>(?[X]:(~funny(X))))&
(![X]:((~humble(X)|creative(X))=>(old(X)&~generous(X))))&
(((~curious(fred)|old(fred)))=>((~happy(mary)&brave(mary))))&
(((wise(mary)<~>generous(mary)))<=>(?[X]:(tall(X))))&
(![X]:((happy(X)|~creative(X))=>(brave(X)&patient(X))))&
(![X]:((funny(X)&curious(X))<=>(creative(X)&~brave(X))))&
(![X]:(generous(X)<=>(strong(X)|calm(X))))&
(![X]:(~wise(X)=>(~creative(X)&~strong(X))))&
((?[X]:((~kind(X)&rich(X))))=>(?[X]:(generous(X))))&
(![X]:((wise(X)&~quiet(X))=>quiet(X)))&
((~generous(alice))=>((old(mary)<~>~rich(mary))))&
(![X]:((~kind(X)&calm(X))=>~quiet(X)))&
(![X]:((~rich(X)&patient(X))=>(~patient(X)|~strong(X))))&
(![X]:((funny(X)&~calm(X))=>(brave(X)|curious(X))))&
(?[X]:((~creative(X)|creative(X))))&
(quiet(mary))&
((tall(john)|~quiet(john)))&
(?[X]:((kind(X)&wise(X))))&
(?[X]:((old(X)&kind(X))))&
(?[X]:((~quiet(X)&~wise(X))))&
(?[X]:((kind(X)<~>happy(X))))&
(?[X]:((old(X)<~>~curious(X)))) | generous(alice) | [] | null | 0 |
Everyone who is not strong or happy is humble and vice versa. Everyone who is both strong and not kind is not tall or not wise and vice versa. If someone is not tall then alice is both happy and not patient and vice versa. If someone is both not quiet and not rich then someone is not kind or not humble and vice versa. Everyone who is either strong or not happy is strong or kind and vice versa. If someone is both not generous and humble then someone is either not calm or not quiet. If someone is either not happy or kind then someone is either not curious or not funny. If someone is strong then someone is both not tall and old and vice versa. Everyone who is not kind is either calm or not generous and vice versa. Everyone who is both not patient and not generous is either humble or not happy. Everyone who is curious or not calm is kind and vice versa. Everyone who is not generous or not humble is not calm. Everyone who is either generous or not funny is both not wise and not patient. Everyone who is not patient or humble is not brave or humble and vice versa. Everyone who is both curious and not quiet is not calm or not rich and vice versa. Everyone who is not old is not old or patient and vice versa. Paul is old or not quiet. Fred is generous. Someone is either not quiet or not happy. Fred is funny or not rich. Someone is either funny or not creative. Someone is either not tall or creative. Mary is both not patient and wise. | Alice is patient. | neutral | (![X]:((~strong(X)|happy(X))<=>humble(X)))&
(![X]:((strong(X)&~kind(X))<=>(~tall(X)|~wise(X))))&
((?[X]:(~tall(X)))<=>((happy(alice)&~patient(alice))))&
((?[X]:((~quiet(X)&~rich(X))))<=>(?[X]:((~kind(X)|~humble(X)))))&
(![X]:((strong(X)<~>~happy(X))<=>(strong(X)|kind(X))))&
((?[X]:((~generous(X)&humble(X))))=>(?[X]:((~calm(X)<~>~quiet(X)))))&
((?[X]:((~happy(X)<~>kind(X))))=>(?[X]:((~curious(X)<~>~funny(X)))))&
((?[X]:(strong(X)))<=>(?[X]:((~tall(X)&old(X)))))&
(![X]:(~kind(X)<=>(calm(X)<~>~generous(X))))&
(![X]:((~patient(X)&~generous(X))=>(humble(X)<~>~happy(X))))&
(![X]:((curious(X)|~calm(X))<=>kind(X)))&
(![X]:((~generous(X)|~humble(X))=>~calm(X)))&
(![X]:((generous(X)<~>~funny(X))=>(~wise(X)&~patient(X))))&
(![X]:((~patient(X)|humble(X))<=>(~brave(X)|humble(X))))&
(![X]:((curious(X)&~quiet(X))<=>(~calm(X)|~rich(X))))&
(![X]:(~old(X)<=>(~old(X)|patient(X))))&
((old(paul)|~quiet(paul)))&
(generous(fred))&
(?[X]:((~quiet(X)<~>~happy(X))))&
((funny(fred)|~rich(fred)))&
(?[X]:((funny(X)<~>~creative(X))))&
(?[X]:((~tall(X)<~>creative(X))))&
((~patient(mary)&wise(mary))) | patient(alice) | [] | null | 0 |
If someone is either not rich or kind then paul is humble.
Everyone who is either not tall or old is generous.
If fred is curious or humble then susan is either not wise or brave.
If alice is both wise and not brave then alice is either generous or quiet and vice versa.
If alice is either not quiet or not brave then someone is either not tall or curious.
Everyone who is either not humble or old is strong or not old.
Everyone who is both not brave and not quiet is not generous.
Everyone who is not kind is both wise and strong.
If someone is either quiet or not brave then someone is either not generous or not strong and vice versa.
Everyone who is not quiet or wise is both brave and not old and vice versa.
If susan is not funny or humble then alice is wise.
Everyone who is either humble or not quiet is brave.
Everyone who is tall or happy is both not curious and curious and vice versa.
If someone is both curious and rich then someone is calm.
Everyone who is not quiet is both happy and humble.
If someone is patient then paul is both strong and patient.
Someone is strong or not old.
Susan is strong.
Someone is both not wise and rich.
Someone is both curious and not kind.
Fred is both not generous and humble.
Susan is not funny.
Someone is either quiet or humble. | Fred is not strong. | contradiction | ((?[X]:((~rich(X)<~>kind(X))))=>(humble(paul)))&
(![X]:((~tall(X)<~>old(X))=>generous(X)))&
(((curious(fred)|humble(fred)))=>((~wise(susan)<~>brave(susan))))&
(((wise(alice)&~brave(alice)))<=>((generous(alice)<~>quiet(alice))))&
(((~quiet(alice)<~>~brave(alice)))=>(?[X]:((~tall(X)<~>curious(X)))))&
(![X]:((~humble(X)<~>old(X))=>(strong(X)|~old(X))))&
(![X]:((~brave(X)&~quiet(X))=>~generous(X)))&
(![X]:(~kind(X)=>(wise(X)&strong(X))))&
((?[X]:((quiet(X)<~>~brave(X))))<=>(?[X]:((~generous(X)<~>~strong(X)))))&
(![X]:((~quiet(X)|wise(X))<=>(brave(X)&~old(X))))&
(((~funny(susan)|humble(susan)))=>(wise(alice)))&
(![X]:((humble(X)<~>~quiet(X))=>brave(X)))&
(![X]:((tall(X)|happy(X))<=>(~curious(X)&curious(X))))&
((?[X]:((curious(X)&rich(X))))=>(?[X]:(calm(X))))&
(![X]:(~quiet(X)=>(happy(X)&humble(X))))&
((?[X]:(patient(X)))=>((strong(paul)&patient(paul))))&
(?[X]:((strong(X)|~old(X))))&
(strong(susan))&
(?[X]:((~wise(X)&rich(X))))&
(?[X]:((curious(X)&~kind(X))))&
((~generous(fred)&humble(fred)))&
(~funny(susan))&
(?[X]:((quiet(X)<~>humble(X)))) | ~strong(fred) | [
"p1",
"p5",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8108530672835790159989662
% SZS output start Proof for 8108530672835790159989662
2. ! [X0] : ((~tall(X0) <~> old(X0)) => generous(X0)) [input p1]
6. ! [X0] : ((~humble(X0) <~> old(X0)) => (~old(X0) | strong(X0))) [input p5]
13. ! [X0] : ((happy(X0) | tall(X0)) <=> (curious(X0) & ~curious(X0))) [input p12]
21. humble(fred) & ~generous(fred) [input p20]
24. ~strong(fred) [input hypothesis]
29. ! [X0] : (generous(X0) | (~tall(X0) <=> old(X0))) [ennf transformation 2]
32. ! [X0] : ((~old(X0) | strong(X0)) | (~humble(X0) <=> old(X0))) [ennf transformation 6]
33. ! [X0] : (~old(X0) | strong(X0) | (~humble(X0) <=> old(X0))) [flattening 32]
42. ! [X0] : (generous(X0) | ((~tall(X0) | ~old(X0)) & (old(X0) | tall(X0)))) [nnf transformation 29]
49. ! [X0] : (~old(X0) | strong(X0) | ((~humble(X0) | ~old(X0)) & (old(X0) | humble(X0)))) [nnf transformation 33]
58. ! [X0] : (((happy(X0) | tall(X0)) | (~curious(X0) | curious(X0))) & ((curious(X0) & ~curious(X0)) | (~happy(X0) & ~tall(X0)))) [nnf transformation 13]
59. ! [X0] : ((happy(X0) | tall(X0) | ~curious(X0) | curious(X0)) & ((curious(X0) & ~curious(X0)) | (~happy(X0) & ~tall(X0)))) [flattening 58]
71. generous(X0) | old(X0) | tall(X0) [cnf transformation 42]
88. ~old(X0) | strong(X0) | ~humble(X0) | ~old(X0) [cnf transformation 49]
109. ~curious(X0) | ~tall(X0) [cnf transformation 59]
111. ~tall(X0) | curious(X0) [cnf transformation 59]
124. ~generous(fred) [cnf transformation 21]
125. humble(fred) [cnf transformation 21]
129. ~strong(fred) [cnf transformation 24]
130. ~old(X0) | strong(X0) | ~humble(X0) [duplicate literal removal 88]
144. 4 <=> humble(fred) [avatar definition]
145. humble(fred) <- (4) [avatar component clause 144]
245. ~tall(X0) [subsumption resolution 109,111]
269. 4 [avatar split clause 125,144]
287. old(fred) | tall(fred) [resolution 71,124]
288. old(fred) [subsumption resolution 287,245]
302. strong(fred) | ~humble(fred) [resolution 130,288]
303. ~humble(fred) [subsumption resolution 302,129]
304. $false <- (4) [subsumption resolution 303,145]
305. ~4 [avatar contradiction clause 304]
306. $false [avatar sat refutation 269,305]
% SZS output end Proof for 8108530672835790159989662
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny or not humble then someone is kind and vice versa. Everyone who is either not quiet or funny is both kind and not funny and vice versa. Everyone who is either funny or curious is brave or curious and vice versa. Everyone who is kind or generous is generous or wise. If alice is happy then fred is both kind and old and vice versa. If john is not brave then fred is either wise or not humble. Everyone who is calm or not creative is either not curious or humble. If fred is not tall or calm then paul is either not tall or generous and vice versa. If someone is calm or not creative then john is either not creative or not old. Everyone who is both tall and not brave is brave or funny and vice versa. If someone is patient then fred is both not wise and not calm. Everyone who is not creative or old is both old and wise. If someone is not wise then alice is either curious or not brave and vice versa. Everyone who is either kind or not old is brave. Everyone who is creative or not curious is either not kind or humble. Mary is either not calm or tall. Lucy is not happy or not quiet. Someone is generous. Someone is not humble. Someone is both not rich and not wise. Someone is both not happy and not kind. | Alice is not wise. | neutral | ((?[X]:((~funny(X)|~humble(X))))<=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)<~>funny(X))<=>(kind(X)&~funny(X))))&
(![X]:((funny(X)<~>curious(X))<=>(brave(X)|curious(X))))&
(![X]:((kind(X)|generous(X))=>(generous(X)|wise(X))))&
((happy(alice))<=>((kind(fred)&old(fred))))&
((~brave(john))=>((wise(fred)<~>~humble(fred))))&
(![X]:((calm(X)|~creative(X))=>(~curious(X)<~>humble(X))))&
(((~tall(fred)|calm(fred)))<=>((~tall(paul)<~>generous(paul))))&
((?[X]:((calm(X)|~creative(X))))=>((~creative(john)<~>~old(john))))&
(![X]:((tall(X)&~brave(X))<=>(brave(X)|funny(X))))&
((?[X]:(patient(X)))=>((~wise(fred)&~calm(fred))))&
(![X]:((~creative(X)|old(X))=>(old(X)&wise(X))))&
((?[X]:(~wise(X)))<=>((curious(alice)<~>~brave(alice))))&
(![X]:((kind(X)<~>~old(X))=>brave(X)))&
(![X]:((creative(X)|~curious(X))=>(~kind(X)<~>humble(X))))&
((~calm(mary)<~>tall(mary)))&
((~happy(lucy)|~quiet(lucy)))&
(?[X]:(generous(X)))&
(?[X]:(~humble(X)))&
(?[X]:((~rich(X)&~wise(X))))&
(?[X]:((~happy(X)&~kind(X)))) | ~wise(alice) | [] | null | 0 |
Everyone who is either not creative or not patient is both brave and funny. Everyone who is not patient is not strong and vice versa. If susan is not funny or brave then someone is not strong or humble and vice versa. Everyone who is kind is not kind or happy. If fred is not curious or wise then someone is both not generous and not rich. Everyone who is either rich or not rich is either calm or not brave and vice versa. If someone is creative or old then someone is both kind and not kind and vice versa. Everyone who is not strong is both not humble and not kind. Everyone who is brave or not quiet is not old and vice versa. If fred is not curious then mary is both curious and quiet. Everyone who is rich or humble is rich and vice versa. Everyone who is both not happy and humble is both strong and not old and vice versa. Everyone who is either generous or not wise is calm. Everyone who is either not wise or not creative is both strong and creative. If someone is both calm and wise then someone is both curious and not calm and vice versa. If mary is both creative and not creative then someone is either not strong or calm and vice versa. Someone is both not rich and not humble. Someone is not wise. Alice is either not wise or patient. Someone is calm. John is not patient. | Mary is not kind. | entailment | (![X]:((~creative(X)<~>~patient(X))=>(brave(X)&funny(X))))&
(![X]:(~patient(X)<=>~strong(X)))&
(((~funny(susan)|brave(susan)))<=>(?[X]:((~strong(X)|humble(X)))))&
(![X]:(kind(X)=>(~kind(X)|happy(X))))&
(((~curious(fred)|wise(fred)))=>(?[X]:((~generous(X)&~rich(X)))))&
(![X]:((rich(X)<~>~rich(X))<=>(calm(X)<~>~brave(X))))&
((?[X]:((creative(X)|old(X))))<=>(?[X]:((kind(X)&~kind(X)))))&
(![X]:(~strong(X)=>(~humble(X)&~kind(X))))&
(![X]:((brave(X)|~quiet(X))<=>~old(X)))&
((~curious(fred))=>((curious(mary)&quiet(mary))))&
(![X]:((rich(X)|humble(X))<=>rich(X)))&
(![X]:((~happy(X)&humble(X))<=>(strong(X)&~old(X))))&
(![X]:((generous(X)<~>~wise(X))=>calm(X)))&
(![X]:((~wise(X)<~>~creative(X))=>(strong(X)&creative(X))))&
((?[X]:((calm(X)&wise(X))))<=>(?[X]:((curious(X)&~calm(X)))))&
(((creative(mary)&~creative(mary)))<=>(?[X]:((~strong(X)<~>calm(X)))))&
(?[X]:((~rich(X)&~humble(X))))&
(?[X]:(~wise(X)))&
((~wise(alice)<~>patient(alice)))&
(?[X]:(calm(X)))&
(~patient(john)) | ~kind(mary) | [
"p0",
"p1",
"p5",
"p6",
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4852996019480660434414421
% SZS output start Proof for 4852996019480660434414421
1. ! [X0] : ((~creative(X0) <~> ~patient(X0)) => (funny(X0) & brave(X0))) [input p0]
2. ! [X0] : (~patient(X0) <=> ~strong(X0)) [input p1]
6. ! [X0] : ((rich(X0) <~> ~rich(X0)) <=> (calm(X0) <~> ~brave(X0))) [input p5]
7. ? [X0] : (old(X0) | creative(X0)) <=> ? [X0] : (~kind(X0) & kind(X0)) [input p6]
8. ! [X0] : (~strong(X0) => (~kind(X0) & ~humble(X0))) [input p7]
16. (~creative(mary) & creative(mary)) <=> ? [X0] : (~strong(X0) <~> calm(X0)) [input p15]
22. kind(mary) [input hypothesis]
23. ? [X0] : (old(X0) | creative(X0)) <=> ? [X1] : (~kind(X1) & kind(X1)) [rectify 7]
25. ! [X0] : ((funny(X0) & brave(X0)) | (~creative(X0) <=> ~patient(X0))) [ennf transformation 1]
29. ! [X0] : ((~kind(X0) & ~humble(X0)) | strong(X0)) [ennf transformation 8]
33. ! [X0] : ((funny(X0) & brave(X0)) | ((~creative(X0) | patient(X0)) & (~patient(X0) | creative(X0)))) [nnf transformation 25]
34. ! [X0] : ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0))) [nnf transformation 2]
42. ! [X0] : ((((rich(X0) | ~rich(X0)) & (~rich(X0) | rich(X0))) | ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0)))) & (((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0))))) [nnf transformation 6]
43. (? [X0] : (old(X0) | creative(X0)) | ! [X1] : (kind(X1) | ~kind(X1))) & (? [X1] : (~kind(X1) & kind(X1)) | ! [X0] : (~old(X0) & ~creative(X0))) [nnf transformation 23]
44. (? [X0] : (old(X0) | creative(X0)) | ! [X1] : (kind(X1) | ~kind(X1))) & (? [X2] : (~kind(X2) & kind(X2)) | ! [X3] : (~old(X3) & ~creative(X3))) [rectify 43]
45. ? [X0] : (old(X0) | creative(X0)) => (old(sK2) | creative(sK2)) [choice axiom]
46. ? [X2] : (~kind(X2) & kind(X2)) => (~kind(sK3) & kind(sK3)) [choice axiom]
47. ((old(sK2) | creative(sK2)) | ! [X1] : (kind(X1) | ~kind(X1))) & ((~kind(sK3) & kind(sK3)) | ! [X3] : (~old(X3) & ~creative(X3))) [skolemisation 44,46,45]
61. ((~creative(mary) & creative(mary)) | ! [X0] : ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) & (? [X0] : ((~calm(X0) | strong(X0)) & (calm(X0) | ~strong(X0))) | (creative(mary) | ~creative(mary))) [nnf transformation 16]
62. ((~creative(mary) & creative(mary)) | ! [X0] : ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) & (? [X0] : ((~calm(X0) | strong(X0)) & (calm(X0) | ~strong(X0))) | creative(mary) | ~creative(mary)) [flattening 61]
63. ((~creative(mary) & creative(mary)) | ! [X0] : ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) & (? [X1] : ((~calm(X1) | strong(X1)) & (calm(X1) | ~strong(X1))) | creative(mary) | ~creative(mary)) [rectify 62]
64. ? [X1] : ((~calm(X1) | strong(X1)) & (calm(X1) | ~strong(X1))) => ((~calm(sK6) | strong(sK6)) & (calm(sK6) | ~strong(sK6))) [choice axiom]
65. ((~creative(mary) & creative(mary)) | ! [X0] : ((~strong(X0) | ~calm(X0)) & (calm(X0) | strong(X0)))) & (((~calm(sK6) | strong(sK6)) & (calm(sK6) | ~strong(sK6))) | creative(mary) | ~creative(mary)) [skolemisation 63,64]
73. ~patient(X0) | brave(X0) | creative(X0) [cnf transformation 33]
77. ~strong(X0) | patient(X0) [cnf transformation 34]
88. ~brave(X0) | calm(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 42]
89. ~brave(X0) | calm(X0) | rich(X0) | rich(X0) [cnf transformation 42]
96. kind(sK3) | ~creative(X3) [cnf transformation 47]
98. ~kind(sK3) | ~creative(X3) [cnf transformation 47]
102. ~kind(X0) | strong(X0) [cnf transformation 29]
128. creative(mary) | ~strong(X0) | ~calm(X0) [cnf transformation 65]
130. ~creative(mary) | ~strong(X0) | ~calm(X0) [cnf transformation 65]
138. kind(mary) [cnf transformation 22]
140. ~brave(X0) | calm(X0) | ~rich(X0) [duplicate literal removal 88]
141. ~brave(X0) | calm(X0) | rich(X0) [duplicate literal removal 89]
192. ~brave(X0) | calm(X0) [subsumption resolution 140,141]
197. 12 <=> kind(sK3) [avatar definition]
202. 13 <=> ! [X3] : ~creative(X3) [avatar definition]
203. ~creative(X3) <- (13) [avatar component clause 202]
204. 13 | ~12 [avatar split clause 98,197,202]
206. 13 | 12 [avatar split clause 96,197,202]
244. 22 <=> ! [X0] : (~strong(X0) | ~calm(X0)) [avatar definition]
245. ~calm(X0) | ~strong(X0) <- (22) [avatar component clause 244]
247. 23 <=> creative(mary) [avatar definition]
250. 22 | ~23 [avatar split clause 130,247,244]
255. 22 | 23 [avatar split clause 128,247,244]
267. strong(mary) [resolution 102,138]
268. patient(mary) [resolution 267,77]
283. brave(mary) | creative(mary) [resolution 73,268]
284. brave(mary) <- (13) [subsumption resolution 283,203]
285. calm(mary) <- (13) [resolution 284,192]
288. ~strong(mary) <- (13, 22) [resolution 285,245]
291. $false <- (13, 22) [subsumption resolution 288,267]
292. ~13 | ~22 [avatar contradiction clause 291]
293. $false [avatar sat refutation 204,206,250,255,292]
% SZS output end Proof for 4852996019480660434414421
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or curious is either not brave or rich.
If paul is either not strong or not happy then someone is either generous or not rich.
If someone is not old then fred is both not wise and not patient.
Everyone who is either strong or not humble is either curious or not curious.
Everyone who is both rich and not rich is not strong or humble and vice versa.
If someone is wise then fred is either funny or strong.
Everyone who is either not humble or rich is both tall and not old and vice versa.
Everyone who is both patient and kind is both curious and not strong and vice versa.
Everyone who is not kind is patient or rich.
If someone is both old and humble then someone is either not quiet or happy.
If someone is either tall or not kind then fred is both not tall and curious and vice versa.
Everyone who is not humble is either not calm or generous.
If mary is either kind or generous then john is both not generous and not funny.
Everyone who is calm or not funny is tall or wise.
Everyone who is not happy or not funny is either old or not patient.
Everyone who is both tall and not happy is either rich or not rich.
Someone is both happy and not wise.
Someone is both not generous and not old.
Someone is both not creative and brave.
Lucy is either creative or quiet.
Alice is not old.
John is either curious or old.
Someone is old.
Alice is either not calm or calm. | Alice is not strong. | contradiction | (![X]:((~tall(X)<~>curious(X))=>(~brave(X)<~>rich(X))))&
(((~strong(paul)<~>~happy(paul)))=>(?[X]:((generous(X)<~>~rich(X)))))&
((?[X]:(~old(X)))=>((~wise(fred)&~patient(fred))))&
(![X]:((strong(X)<~>~humble(X))=>(curious(X)<~>~curious(X))))&
(![X]:((rich(X)&~rich(X))<=>(~strong(X)|humble(X))))&
((?[X]:(wise(X)))=>((funny(fred)<~>strong(fred))))&
(![X]:((~humble(X)<~>rich(X))<=>(tall(X)&~old(X))))&
(![X]:((patient(X)&kind(X))<=>(curious(X)&~strong(X))))&
(![X]:(~kind(X)=>(patient(X)|rich(X))))&
((?[X]:((old(X)&humble(X))))=>(?[X]:((~quiet(X)<~>happy(X)))))&
((?[X]:((tall(X)<~>~kind(X))))<=>((~tall(fred)&curious(fred))))&
(![X]:(~humble(X)=>(~calm(X)<~>generous(X))))&
(((kind(mary)<~>generous(mary)))=>((~generous(john)&~funny(john))))&
(![X]:((calm(X)|~funny(X))=>(tall(X)|wise(X))))&
(![X]:((~happy(X)|~funny(X))=>(old(X)<~>~patient(X))))&
(![X]:((tall(X)&~happy(X))=>(rich(X)<~>~rich(X))))&
(?[X]:((happy(X)&~wise(X))))&
(?[X]:((~generous(X)&~old(X))))&
(?[X]:((~creative(X)&brave(X))))&
((creative(lucy)<~>quiet(lucy)))&
(~old(alice))&
((curious(john)<~>old(john)))&
(?[X]:(old(X)))&
((~calm(alice)<~>calm(alice))) | ~strong(alice) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 854168044515980771762971
% SZS output start Proof for 854168044515980771762971
5. ! [X0] : ((~rich(X0) & rich(X0)) <=> (humble(X0) | ~strong(X0))) [input p4]
25. ~strong(alice) [input hypothesis]
47. ! [X0] : (((~rich(X0) & rich(X0)) | (~humble(X0) & strong(X0))) & ((humble(X0) | ~strong(X0)) | (rich(X0) | ~rich(X0)))) [nnf transformation 5]
48. ! [X0] : (((~rich(X0) & rich(X0)) | (~humble(X0) & strong(X0))) & (humble(X0) | ~strong(X0) | rich(X0) | ~rich(X0))) [flattening 47]
93. rich(X0) | strong(X0) [cnf transformation 48]
95. ~rich(X0) | strong(X0) [cnf transformation 48]
146. ~strong(alice) [cnf transformation 25]
181. strong(X0) [subsumption resolution 93,95]
265. $false [subsumption resolution 146,181]
% SZS output end Proof for 854168044515980771762971
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either old or strong then someone is creative or not brave.
If alice is not rich or generous then susan is both not creative and humble.
Everyone who is either wise or not brave is not generous.
If fred is both not quiet and not creative then someone is creative.
Everyone who is both old and brave is not curious or not rich and vice versa.
Everyone who is either not old or not curious is both old and patient.
Everyone who is either humble or quiet is either generous or happy.
Everyone who is both wise and not calm is either not patient or old and vice versa.
If mary is either not brave or not happy then fred is not generous.
Everyone who is patient or not wise is not old or generous and vice versa.
If someone is strong then someone is either not curious or funny and vice versa.
If someone is not quiet then someone is funny and vice versa.
Everyone who is both not creative and quiet is both not old and not kind and vice versa.
Everyone who is not calm is funny or old and vice versa.
Everyone who is not quiet is wise or old and vice versa.
Everyone who is kind is not strong or happy and vice versa.
Paul is not curious or not kind.
Susan is both not rich and not wise.
Mary is either kind or not tall.
John is humble.
Someone is not generous or curious.
Fred is brave or quiet.
Someone is creative or wise.
Someone is both humble and creative. | Susan is not happy. | entailment | ((?[X]:((old(X)<~>strong(X))))=>(?[X]:((creative(X)|~brave(X)))))&
(((~rich(alice)|generous(alice)))=>((~creative(susan)&humble(susan))))&
(![X]:((wise(X)<~>~brave(X))=>~generous(X)))&
(((~quiet(fred)&~creative(fred)))=>(?[X]:(creative(X))))&
(![X]:((old(X)&brave(X))<=>(~curious(X)|~rich(X))))&
(![X]:((~old(X)<~>~curious(X))=>(old(X)&patient(X))))&
(![X]:((humble(X)<~>quiet(X))=>(generous(X)<~>happy(X))))&
(![X]:((wise(X)&~calm(X))<=>(~patient(X)<~>old(X))))&
(((~brave(mary)<~>~happy(mary)))=>(~generous(fred)))&
(![X]:((patient(X)|~wise(X))<=>(~old(X)|generous(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~curious(X)<~>funny(X)))))&
((?[X]:(~quiet(X)))<=>(?[X]:(funny(X))))&
(![X]:((~creative(X)&quiet(X))<=>(~old(X)&~kind(X))))&
(![X]:(~calm(X)<=>(funny(X)|old(X))))&
(![X]:(~quiet(X)<=>(wise(X)|old(X))))&
(![X]:(kind(X)<=>(~strong(X)|happy(X))))&
((~curious(paul)|~kind(paul)))&
((~rich(susan)&~wise(susan)))&
((kind(mary)<~>~tall(mary)))&
(humble(john))&
(?[X]:((~generous(X)|curious(X))))&
((brave(fred)|quiet(fred)))&
(?[X]:((creative(X)|wise(X))))&
(?[X]:((humble(X)&creative(X)))) | ~happy(susan) | [
"p1",
"p4",
"p5",
"p6",
"p7",
"p9",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5214946473005960393616582
% SZS output start Proof for 5214946473005960393616582
2. (generous(alice) | ~rich(alice)) => (humble(susan) & ~creative(susan)) [input p1]
5. ! [X0] : ((brave(X0) & old(X0)) <=> (~rich(X0) | ~curious(X0))) [input p4]
6. ! [X0] : ((~old(X0) <~> ~curious(X0)) => (patient(X0) & old(X0))) [input p5]
7. ! [X0] : ((humble(X0) <~> quiet(X0)) => (generous(X0) <~> happy(X0))) [input p6]
8. ! [X0] : ((~calm(X0) & wise(X0)) <=> (~patient(X0) <~> old(X0))) [input p7]
10. ! [X0] : ((~wise(X0) | patient(X0)) <=> (generous(X0) | ~old(X0))) [input p9]
14. ! [X0] : (~calm(X0) <=> (old(X0) | funny(X0))) [input p13]
15. ! [X0] : (~quiet(X0) <=> (old(X0) | wise(X0))) [input p14]
18. ~wise(susan) & ~rich(susan) [input p17]
25. happy(susan) [input hypothesis]
30. (humble(susan) & ~creative(susan)) | (~generous(alice) & rich(alice)) [ennf transformation 2]
34. ! [X0] : ((patient(X0) & old(X0)) | (~old(X0) <=> ~curious(X0))) [ennf transformation 6]
35. ! [X0] : ((generous(X0) <~> happy(X0)) | (humble(X0) <=> quiet(X0))) [ennf transformation 7]
44. ! [X0] : (((brave(X0) & old(X0)) | (rich(X0) & curious(X0))) & ((~rich(X0) | ~curious(X0)) | (~brave(X0) | ~old(X0)))) [nnf transformation 5]
45. ! [X0] : (((brave(X0) & old(X0)) | (rich(X0) & curious(X0))) & (~rich(X0) | ~curious(X0) | ~brave(X0) | ~old(X0))) [flattening 44]
46. ! [X0] : ((patient(X0) & old(X0)) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0)))) [nnf transformation 34]
47. ! [X0] : (((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | ((humble(X0) | ~quiet(X0)) & (quiet(X0) | ~humble(X0)))) [nnf transformation 35]
48. ! [X0] : (((~calm(X0) & wise(X0)) | ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) & (((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | (calm(X0) | ~wise(X0)))) [nnf transformation 8]
49. ! [X0] : (((~calm(X0) & wise(X0)) | ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) & (((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | calm(X0) | ~wise(X0))) [flattening 48]
51. ! [X0] : (((~wise(X0) | patient(X0)) | (~generous(X0) & old(X0))) & ((generous(X0) | ~old(X0)) | (wise(X0) & ~patient(X0)))) [nnf transformation 10]
52. ! [X0] : ((~wise(X0) | patient(X0) | (~generous(X0) & old(X0))) & (generous(X0) | ~old(X0) | (wise(X0) & ~patient(X0)))) [flattening 51]
65. ! [X0] : ((~calm(X0) | (~old(X0) & ~funny(X0))) & ((old(X0) | funny(X0)) | calm(X0))) [nnf transformation 14]
66. ! [X0] : ((~calm(X0) | (~old(X0) & ~funny(X0))) & (old(X0) | funny(X0) | calm(X0))) [flattening 65]
67. ! [X0] : ((~quiet(X0) | (~old(X0) & ~wise(X0))) & ((old(X0) | wise(X0)) | quiet(X0))) [nnf transformation 15]
68. ! [X0] : ((~quiet(X0) | (~old(X0) & ~wise(X0))) & (old(X0) | wise(X0) | quiet(X0))) [flattening 67]
83. humble(susan) | ~generous(alice) [cnf transformation 30]
88. curious(X0) | old(X0) [cnf transformation 45]
92. old(X0) | ~curious(X0) | old(X0) [cnf transformation 46]
98. ~happy(X0) | ~generous(X0) | quiet(X0) | ~humble(X0) [cnf transformation 47]
101. ~old(X0) | patient(X0) | calm(X0) | ~wise(X0) [cnf transformation 49]
108. generous(X0) | ~old(X0) | ~patient(X0) [cnf transformation 52]
109. generous(X0) | ~old(X0) | wise(X0) [cnf transformation 52]
124. ~calm(X0) | ~old(X0) [cnf transformation 66]
127. ~quiet(X0) | ~old(X0) [cnf transformation 68]
133. ~wise(susan) [cnf transformation 18]
142. happy(susan) [cnf transformation 25]
143. old(X0) | ~curious(X0) [duplicate literal removal 92]
161. 5 <=> generous(alice) [avatar definition]
163. ~generous(alice) <- (~5) [avatar component clause 161]
165. 6 <=> humble(susan) [avatar definition]
167. humble(susan) <- (6) [avatar component clause 165]
168. ~5 | 6 [avatar split clause 83,165,161]
195. old(X0) [subsumption resolution 143,88]
198. ~wise(X0) | calm(X0) | patient(X0) [subsumption resolution 101,195]
213. wise(X0) | generous(X0) [subsumption resolution 109,195]
214. ~patient(X0) | generous(X0) [subsumption resolution 108,195]
257. ~calm(X0) [subsumption resolution 124,195]
258. ~quiet(X0) [subsumption resolution 127,195]
310. generous(susan) [resolution 213,133]
333. calm(X0) | patient(X0) | generous(X0) [resolution 198,213]
334. patient(X0) | generous(X0) [subsumption resolution 333,257]
335. generous(X0) [subsumption resolution 334,214]
353. $false <- (~5) [resolution 335,163]
358. 5 [avatar contradiction clause 353]
378. ~generous(susan) | quiet(susan) | ~humble(susan) [resolution 98,142]
379. quiet(susan) | ~humble(susan) [subsumption resolution 378,310]
380. ~humble(susan) [subsumption resolution 379,258]
381. $false <- (6) [subsumption resolution 380,167]
382. ~6 [avatar contradiction clause 381]
383. $false [avatar sat refutation 168,358,382]
% SZS output end Proof for 5214946473005960393616582
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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