premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is rich or not quiet is either curious or humble.
If someone is funny then susan is either old or not quiet.
Everyone who is both not calm and not wise is not humble.
If someone is both not curious and kind then someone is not strong and vice versa.
Everyone who is both not brave and generous is humble.
If someone is brave then paul is either not rich or not old.
Everyone who is not tall is either curious or tall and vice versa.
If someone is either not rich or not strong then someone is not tall or not generous.
If lucy is both not quiet and not tall then someone is either not wise or generous.
If susan is happy then someone is both not old and not humble.
Everyone who is either wise or funny is brave and vice versa.
If someone is not rich then alice is not brave and vice versa.
Everyone who is either not creative or quiet is humble or not patient.
Everyone who is either patient or tall is both curious and not rich and vice versa.
Everyone who is both calm and patient is either not calm or patient.
Susan is both calm and rich.
Someone is both old and not patient.
Susan is humble or not kind.
Someone is happy.
Paul is not kind.
Someone is strong or curious.
Fred is tall. | Alice is strong. | entailment | (![X]:((rich(X)|~quiet(X))=>(curious(X)<~>humble(X))))&
((?[X]:(funny(X)))=>((old(susan)<~>~quiet(susan))))&
(![X]:((~calm(X)&~wise(X))=>~humble(X)))&
((?[X]:((~curious(X)&kind(X))))<=>(?[X]:(~strong(X))))&
(![X]:((~brave(X)&generous(X))=>humble(X)))&
((?[X]:(brave(X)))=>((~rich(paul)<~>~old(paul))))&
(![X]:(~tall(X)<=>(curious(X)<~>tall(X))))&
((?[X]:((~rich(X)<~>~strong(X))))=>(?[X]:((~tall(X)|~generous(X)))))&
(((~quiet(lucy)&~tall(lucy)))=>(?[X]:((~wise(X)<~>generous(X)))))&
((happy(susan))=>(?[X]:((~old(X)&~humble(X)))))&
(![X]:((wise(X)<~>funny(X))<=>brave(X)))&
((?[X]:(~rich(X)))<=>(~brave(alice)))&
(![X]:((~creative(X)<~>quiet(X))=>(humble(X)|~patient(X))))&
(![X]:((patient(X)<~>tall(X))<=>(curious(X)&~rich(X))))&
(![X]:((calm(X)&patient(X))=>(~calm(X)<~>patient(X))))&
((calm(susan)&rich(susan)))&
(?[X]:((old(X)&~patient(X))))&
((humble(susan)|~kind(susan)))&
(?[X]:(happy(X)))&
(~kind(paul))&
(?[X]:((strong(X)|curious(X))))&
(tall(fred)) | strong(alice) | [
"p3",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 4245126294361086844278237
% SZS output start Proof for 4245126294361086844278237
4. ? [X0] : (kind(X0) & ~curious(X0)) <=> ? [X0] : ~strong(X0) [input p3]
7. ! [X0] : (~tall(X0) <=> (curious(X0) <~> tall(X0))) [input p6]
23. ~strong(alice) [input hypothesis]
24. ? [X0] : (kind(X0) & ~curious(X0)) <=> ? [X1] : ~strong(X1) [rectify 4]
43. (? [X0] : (kind(X0) & ~curious(X0)) | ! [X1] : strong(X1)) & (? [X1] : ~strong(X1) | ! [X0] : (~kind(X0) | curious(X0))) [nnf transformation 24]
44. (? [X0] : (kind(X0) & ~curious(X0)) | ! [X1] : strong(X1)) & (? [X2] : ~strong(X2) | ! [X3] : (~kind(X3) | curious(X3))) [rectify 43]
45. ? [X0] : (kind(X0) & ~curious(X0)) => (kind(sK0) & ~curious(sK0)) [choice axiom]
46. ? [X2] : ~strong(X2) => ~strong(sK1) [choice axiom]
47. ((kind(sK0) & ~curious(sK0)) | ! [X1] : strong(X1)) & (~strong(sK1) | ! [X3] : (~kind(X3) | curious(X3))) [skolemisation 44,46,45]
49. ! [X0] : ((~tall(X0) | ((curious(X0) | ~tall(X0)) & (tall(X0) | ~curious(X0)))) & (((~tall(X0) | ~curious(X0)) & (tall(X0) | curious(X0))) | tall(X0))) [nnf transformation 7]
82. ~curious(sK0) | strong(X1) [cnf transformation 47]
87. tall(X0) | curious(X0) | tall(X0) [cnf transformation 49]
90. ~tall(X0) | curious(X0) | ~tall(X0) [cnf transformation 49]
122. ~strong(alice) [cnf transformation 23]
125. tall(X0) | curious(X0) [duplicate literal removal 87]
126. ~tall(X0) | curious(X0) [duplicate literal removal 90]
141. 4 <=> ! [X1] : strong(X1) [avatar definition]
142. strong(X1) <- (4) [avatar component clause 141]
149. 6 <=> curious(sK0) [avatar definition]
151. ~curious(sK0) <- (~6) [avatar component clause 149]
152. 4 | ~6 [avatar split clause 82,149,141]
174. curious(X0) [subsumption resolution 125,126]
247. $false <- (4) [resolution 142,122]
248. ~4 [avatar contradiction clause 247]
249. $false <- (~6) [subsumption resolution 151,174]
250. 6 [avatar contradiction clause 249]
251. $false [avatar sat refutation 152,248,250]
% SZS output end Proof for 4245126294361086844278237
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either curious or not brave then someone is both wise and not old and vice versa. Everyone who is either generous or not patient is not brave. Everyone who is brave or tall is not wise. Everyone who is either happy or funny is either brave or not tall and vice versa. Everyone who is tall or humble is not patient or calm. Everyone who is either not kind or brave is not creative. Everyone who is either generous or not rich is both generous and not calm and vice versa. Everyone who is either strong or creative is rich or humble and vice versa. If fred is both not humble and patient then susan is both not brave and happy. If fred is happy or not tall then someone is both tall and creative and vice versa. If lucy is both not calm and not creative then paul is not curious or curious and vice versa. Everyone who is not funny is not rich or happy and vice versa. Everyone who is either not wise or not calm is both patient and rich. If someone is either not rich or not funny then someone is rich or strong. Everyone who is both not calm and curious is not rich or not happy and vice versa. Everyone who is either wise or humble is not wise and vice versa. Paul is not old. Someone is both not funny and creative. Someone is both not quiet and not strong. Someone is not generous. Someone is creative. Someone is quiet. | Susan is not humble. | contradiction | (((curious(paul)<~>~brave(paul)))<=>(?[X]:((wise(X)&~old(X)))))&
(![X]:((generous(X)<~>~patient(X))=>~brave(X)))&
(![X]:((brave(X)|tall(X))=>~wise(X)))&
(![X]:((happy(X)<~>funny(X))<=>(brave(X)<~>~tall(X))))&
(![X]:((tall(X)|humble(X))=>(~patient(X)|calm(X))))&
(![X]:((~kind(X)<~>brave(X))=>~creative(X)))&
(![X]:((generous(X)<~>~rich(X))<=>(generous(X)&~calm(X))))&
(![X]:((strong(X)<~>creative(X))<=>(rich(X)|humble(X))))&
(((~humble(fred)&patient(fred)))=>((~brave(susan)&happy(susan))))&
(((happy(fred)|~tall(fred)))<=>(?[X]:((tall(X)&creative(X)))))&
(((~calm(lucy)&~creative(lucy)))<=>((~curious(paul)|curious(paul))))&
(![X]:(~funny(X)<=>(~rich(X)|happy(X))))&
(![X]:((~wise(X)<~>~calm(X))=>(patient(X)&rich(X))))&
((?[X]:((~rich(X)<~>~funny(X))))=>(?[X]:((rich(X)|strong(X)))))&
(![X]:((~calm(X)&curious(X))<=>(~rich(X)|~happy(X))))&
(![X]:((wise(X)<~>humble(X))<=>~wise(X)))&
(~old(paul))&
(?[X]:((~funny(X)&creative(X))))&
(?[X]:((~quiet(X)&~strong(X))))&
(?[X]:(~generous(X)))&
(?[X]:(creative(X)))&
(?[X]:(quiet(X))) | ~humble(susan) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1449826751150666269792332
% SZS output start Proof for 1449826751150666269792332
16. ! [X0] : ((wise(X0) <~> humble(X0)) <=> ~wise(X0)) [input p15]
23. ~humble(susan) [input hypothesis]
61. ! [X0] : ((((~humble(X0) | ~wise(X0)) & (humble(X0) | wise(X0))) | wise(X0)) & (~wise(X0) | ((wise(X0) | ~humble(X0)) & (humble(X0) | ~wise(X0))))) [nnf transformation 16]
132. ~wise(X0) | humble(X0) | ~wise(X0) [cnf transformation 61]
134. humble(X0) | wise(X0) | wise(X0) [cnf transformation 61]
144. ~humble(susan) [cnf transformation 23]
145. ~wise(X0) | humble(X0) [duplicate literal removal 132]
146. humble(X0) | wise(X0) [duplicate literal removal 134]
240. humble(X0) [subsumption resolution 145,146]
241. $false [subsumption resolution 144,240]
% SZS output end Proof for 1449826751150666269792332
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or tall is not creative or calm.
Everyone who is not rich is tall.
Everyone who is not quiet or strong is happy.
If someone is not curious then someone is either old or wise and vice versa.
Everyone who is either brave or kind is both not funny and generous.
Everyone who is happy or rich is quiet or happy.
If someone is both not calm and not funny then someone is wise or not tall.
Everyone who is both not calm and tall is not humble or old.
If someone is both creative and kind then someone is either happy or old.
If someone is either brave or not wise then fred is not brave.
If someone is creative or calm then someone is either not old or not brave and vice versa.
Everyone who is not calm is generous and vice versa.
Everyone who is not patient is wise or creative.
Everyone who is both creative and not brave is either calm or not wise and vice versa.
Everyone who is not brave is rich or wise and vice versa.
If someone is not wise then paul is either not humble or not patient and vice versa.
Alice is not creative or happy.
Someone is creative.
Susan is both curious and kind.
Someone is either patient or not funny.
Someone is either not tall or kind.
Fred is wise or generous.
Mary is not tall or humble. | Fred is calm. | neutral | (![X]:((generous(X)|tall(X))=>(~creative(X)|calm(X))))&
(![X]:(~rich(X)=>tall(X)))&
(![X]:((~quiet(X)|strong(X))=>happy(X)))&
((?[X]:(~curious(X)))<=>(?[X]:((old(X)<~>wise(X)))))&
(![X]:((brave(X)<~>kind(X))=>(~funny(X)&generous(X))))&
(![X]:((happy(X)|rich(X))=>(quiet(X)|happy(X))))&
((?[X]:((~calm(X)&~funny(X))))=>(?[X]:((wise(X)|~tall(X)))))&
(![X]:((~calm(X)&tall(X))=>(~humble(X)|old(X))))&
((?[X]:((creative(X)&kind(X))))=>(?[X]:((happy(X)<~>old(X)))))&
((?[X]:((brave(X)<~>~wise(X))))=>(~brave(fred)))&
((?[X]:((creative(X)|calm(X))))<=>(?[X]:((~old(X)<~>~brave(X)))))&
(![X]:(~calm(X)<=>generous(X)))&
(![X]:(~patient(X)=>(wise(X)|creative(X))))&
(![X]:((creative(X)&~brave(X))<=>(calm(X)<~>~wise(X))))&
(![X]:(~brave(X)<=>(rich(X)|wise(X))))&
((?[X]:(~wise(X)))<=>((~humble(paul)<~>~patient(paul))))&
((~creative(alice)|happy(alice)))&
(?[X]:(creative(X)))&
((curious(susan)&kind(susan)))&
(?[X]:((patient(X)<~>~funny(X))))&
(?[X]:((~tall(X)<~>kind(X))))&
((wise(fred)|generous(fred)))&
((~tall(mary)|humble(mary))) | calm(fred) | [] | null | 0 |
If paul is both wise and not humble then lucy is both calm and not old.
Everyone who is both funny and not happy is not old or not kind and vice versa.
If someone is not wise or not calm then someone is wise or not brave.
Everyone who is wise is calm or creative and vice versa.
If someone is not tall or not calm then alice is both not humble and not patient.
If someone is either patient or creative then someone is either not curious or not calm and vice versa.
Everyone who is both generous and calm is generous or rich.
Everyone who is kind is both tall and not wise and vice versa.
If paul is either not rich or patient then someone is either not quiet or old and vice versa.
Everyone who is both not kind and not happy is not funny.
If someone is not calm then alice is both quiet and not curious.
Everyone who is either wise or brave is tall or not rich.
Everyone who is not quiet or not wise is either patient or kind and vice versa.
If someone is wise then someone is happy or rich.
Everyone who is either tall or not funny is patient and vice versa.
If mary is humble or tall then paul is funny or kind and vice versa.
Fred is either not quiet or brave.
Someone is either not wise or not kind. | Mary is rich. | neutral | (((wise(paul)&~humble(paul)))=>((calm(lucy)&~old(lucy))))&
(![X]:((funny(X)&~happy(X))<=>(~old(X)|~kind(X))))&
((?[X]:((~wise(X)|~calm(X))))=>(?[X]:((wise(X)|~brave(X)))))&
(![X]:(wise(X)<=>(calm(X)|creative(X))))&
((?[X]:((~tall(X)|~calm(X))))=>((~humble(alice)&~patient(alice))))&
((?[X]:((patient(X)<~>creative(X))))<=>(?[X]:((~curious(X)<~>~calm(X)))))&
(![X]:((generous(X)&calm(X))=>(generous(X)|rich(X))))&
(![X]:(kind(X)<=>(tall(X)&~wise(X))))&
(((~rich(paul)<~>patient(paul)))<=>(?[X]:((~quiet(X)<~>old(X)))))&
(![X]:((~kind(X)&~happy(X))=>~funny(X)))&
((?[X]:(~calm(X)))=>((quiet(alice)&~curious(alice))))&
(![X]:((wise(X)<~>brave(X))=>(tall(X)|~rich(X))))&
(![X]:((~quiet(X)|~wise(X))<=>(patient(X)<~>kind(X))))&
((?[X]:(wise(X)))=>(?[X]:((happy(X)|rich(X)))))&
(![X]:((tall(X)<~>~funny(X))<=>patient(X)))&
(((humble(mary)|tall(mary)))<=>((funny(paul)|kind(paul))))&
((~quiet(fred)<~>brave(fred)))&
(?[X]:((~wise(X)<~>~kind(X)))) | rich(mary) | [] | null | 0 |
Everyone who is both generous and strong is not generous or not curious and vice versa. If alice is kind or curious then alice is either not calm or not curious and vice versa. If fred is both humble and not calm then someone is not curious. If someone is not creative or not happy then someone is either kind or brave and vice versa. If someone is either not creative or strong then someone is both quiet and not calm and vice versa. Everyone who is both not old and not funny is not patient or quiet. If someone is funny then someone is either rich or not calm. If lucy is kind or humble then john is not old. Everyone who is not happy or curious is tall and vice versa. If someone is not humble then someone is both wise and not happy and vice versa. Everyone who is either not rich or rich is both not happy and not creative. If someone is not tall or humble then someone is funny or not calm and vice versa. Everyone who is both funny and creative is both not humble and brave and vice versa. Everyone who is not brave is either funny or humble. If paul is both not happy and not wise then fred is kind and vice versa. Everyone who is both not curious and old is either not calm or humble and vice versa. Someone is not wise or curious. Mary is generous or not kind. Someone is brave. Someone is quiet or kind. Someone is rich or not rich. Someone is either brave or kind. Someone is not creative or not funny. | John is happy. | contradiction | (![X]:((generous(X)&strong(X))<=>(~generous(X)|~curious(X))))&
(((kind(alice)|curious(alice)))<=>((~calm(alice)<~>~curious(alice))))&
(((humble(fred)&~calm(fred)))=>(?[X]:(~curious(X))))&
((?[X]:((~creative(X)|~happy(X))))<=>(?[X]:((kind(X)<~>brave(X)))))&
((?[X]:((~creative(X)<~>strong(X))))<=>(?[X]:((quiet(X)&~calm(X)))))&
(![X]:((~old(X)&~funny(X))=>(~patient(X)|quiet(X))))&
((?[X]:(funny(X)))=>(?[X]:((rich(X)<~>~calm(X)))))&
(((kind(lucy)|humble(lucy)))=>(~old(john)))&
(![X]:((~happy(X)|curious(X))<=>tall(X)))&
((?[X]:(~humble(X)))<=>(?[X]:((wise(X)&~happy(X)))))&
(![X]:((~rich(X)<~>rich(X))=>(~happy(X)&~creative(X))))&
((?[X]:((~tall(X)|humble(X))))<=>(?[X]:((funny(X)|~calm(X)))))&
(![X]:((funny(X)&creative(X))<=>(~humble(X)&brave(X))))&
(![X]:(~brave(X)=>(funny(X)<~>humble(X))))&
(((~happy(paul)&~wise(paul)))<=>(kind(fred)))&
(![X]:((~curious(X)&old(X))<=>(~calm(X)<~>humble(X))))&
(?[X]:((~wise(X)|curious(X))))&
((generous(mary)|~kind(mary)))&
(?[X]:(brave(X)))&
(?[X]:((quiet(X)|kind(X))))&
(?[X]:((rich(X)|~rich(X))))&
(?[X]:((brave(X)<~>kind(X))))&
(?[X]:((~creative(X)|~funny(X)))) | happy(john) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6958634970658011531360902
% SZS output start Proof for 6958634970658011531360902
11. ! [X0] : ((~rich(X0) <~> rich(X0)) => (~creative(X0) & ~happy(X0))) [input p10]
24. happy(john) [input hypothesis]
35. ! [X0] : ((~creative(X0) & ~happy(X0)) | (~rich(X0) <=> rich(X0))) [ennf transformation 11]
64. ! [X0] : ((~creative(X0) & ~happy(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0)))) [nnf transformation 35]
124. ~happy(X0) | rich(X0) | rich(X0) [cnf transformation 64]
125. ~happy(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 64]
155. happy(john) [cnf transformation 24]
156. ~happy(X0) | rich(X0) [duplicate literal removal 124]
157. ~happy(X0) | ~rich(X0) [duplicate literal removal 125]
308. ~happy(X0) [subsumption resolution 156,157]
379. $false [subsumption resolution 155,308]
% SZS output end Proof for 6958634970658011531360902
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and not rich then someone is either not rich or not humble and vice versa.
Everyone who is either not creative or kind is not patient.
Everyone who is not happy is both not wise and not old.
If fred is humble then someone is either not humble or not tall.
If someone is both not quiet and tall then someone is quiet and vice versa.
Everyone who is not creative is not tall or creative and vice versa.
Everyone who is not quiet or not old is both not quiet and calm.
Everyone who is both calm and not generous is both kind and not rich and vice versa.
Everyone who is either generous or patient is both old and not old.
Everyone who is curious or not funny is not brave or strong.
If lucy is rich or generous then someone is either not old or not humble and vice versa.
Everyone who is not humble or kind is either not curious or brave and vice versa.
Everyone who is not wise is both not humble and kind and vice versa.
If someone is both humble and not quiet then someone is not quiet.
If fred is either generous or not patient then susan is not patient or tall and vice versa.
Someone is strong or happy.
Someone is either curious or not quiet.
Susan is either funny or generous.
Someone is curious or not rich.
John is wise.
Alice is not rich or humble.
Fred is not creative or happy. | Lucy is not calm. | contradiction | ((?[X]:((~curious(X)&~rich(X))))<=>(?[X]:((~rich(X)<~>~humble(X)))))&
(![X]:((~creative(X)<~>kind(X))=>~patient(X)))&
(![X]:(~happy(X)=>(~wise(X)&~old(X))))&
((humble(fred))=>(?[X]:((~humble(X)<~>~tall(X)))))&
((?[X]:((~quiet(X)&tall(X))))<=>(?[X]:(quiet(X))))&
(![X]:(~creative(X)<=>(~tall(X)|creative(X))))&
(![X]:((~quiet(X)|~old(X))=>(~quiet(X)&calm(X))))&
(![X]:((calm(X)&~generous(X))<=>(kind(X)&~rich(X))))&
(![X]:((generous(X)<~>patient(X))=>(old(X)&~old(X))))&
(![X]:((curious(X)|~funny(X))=>(~brave(X)|strong(X))))&
(((rich(lucy)|generous(lucy)))<=>(?[X]:((~old(X)<~>~humble(X)))))&
(![X]:((~humble(X)|kind(X))<=>(~curious(X)<~>brave(X))))&
(![X]:(~wise(X)<=>(~humble(X)&kind(X))))&
((?[X]:((humble(X)&~quiet(X))))=>(?[X]:(~quiet(X))))&
(((generous(fred)<~>~patient(fred)))<=>((~patient(susan)|tall(susan))))&
(?[X]:((strong(X)|happy(X))))&
(?[X]:((curious(X)<~>~quiet(X))))&
((funny(susan)<~>generous(susan)))&
(?[X]:((curious(X)|~rich(X))))&
(wise(john))&
((~rich(alice)|humble(alice)))&
((~creative(fred)|happy(fred))) | ~calm(lucy) | [
"p4",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 388187697039182066361951
% SZS output start Proof for 388187697039182066361951
5. ? [X0] : (tall(X0) & ~quiet(X0)) <=> ? [X0] : quiet(X0) [input p4]
6. ! [X0] : (~creative(X0) <=> (creative(X0) | ~tall(X0))) [input p5]
7. ! [X0] : ((~old(X0) | ~quiet(X0)) => (calm(X0) & ~quiet(X0))) [input p6]
23. ~calm(lucy) [input hypothesis]
25. ? [X0] : (tall(X0) & ~quiet(X0)) <=> ? [X1] : quiet(X1) [rectify 5]
34. ! [X0] : ((calm(X0) & ~quiet(X0)) | (old(X0) & quiet(X0))) [ennf transformation 7]
48. (? [X0] : (tall(X0) & ~quiet(X0)) | ! [X1] : ~quiet(X1)) & (? [X1] : quiet(X1) | ! [X0] : (~tall(X0) | quiet(X0))) [nnf transformation 25]
49. (? [X0] : (tall(X0) & ~quiet(X0)) | ! [X1] : ~quiet(X1)) & (? [X2] : quiet(X2) | ! [X3] : (~tall(X3) | quiet(X3))) [rectify 48]
50. ? [X0] : (tall(X0) & ~quiet(X0)) => (tall(sK3) & ~quiet(sK3)) [choice axiom]
51. ? [X2] : quiet(X2) => quiet(sK4) [choice axiom]
52. ((tall(sK3) & ~quiet(sK3)) | ! [X1] : ~quiet(X1)) & (quiet(sK4) | ! [X3] : (~tall(X3) | quiet(X3))) [skolemisation 49,51,50]
53. ! [X0] : ((~creative(X0) | (~creative(X0) & tall(X0))) & ((creative(X0) | ~tall(X0)) | creative(X0))) [nnf transformation 6]
54. ! [X0] : ((~creative(X0) | (~creative(X0) & tall(X0))) & (creative(X0) | ~tall(X0) | creative(X0))) [flattening 53]
88. tall(sK3) | ~quiet(X1) [cnf transformation 52]
89. creative(X0) | ~tall(X0) | creative(X0) [cnf transformation 54]
91. ~creative(X0) | ~creative(X0) [cnf transformation 54]
94. calm(X0) | quiet(X0) [cnf transformation 34]
131. ~calm(lucy) [cnf transformation 23]
132. creative(X0) | ~tall(X0) [duplicate literal removal 89]
133. ~creative(X0) [duplicate literal removal 91]
180. 11 <=> ! [X1] : ~quiet(X1) [avatar definition]
181. ~quiet(X1) <- (11) [avatar component clause 180]
183. 12 <=> tall(sK3) [avatar definition]
185. tall(sK3) <- (12) [avatar component clause 183]
186. 11 | 12 [avatar split clause 88,183,180]
200. ~tall(X0) [subsumption resolution 132,133]
291. quiet(lucy) [resolution 94,131]
292. $false <- (11) [subsumption resolution 291,181]
293. ~11 [avatar contradiction clause 292]
294. $false <- (12) [subsumption resolution 185,200]
295. ~12 [avatar contradiction clause 294]
296. $false [avatar sat refutation 186,293,295]
% SZS output end Proof for 388187697039182066361951
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not strong or old then someone is either humble or curious and vice versa.
Everyone who is both calm and not happy is calm and vice versa.
Everyone who is calm or generous is both brave and not tall and vice versa.
If someone is either not tall or not strong then someone is both happy and not quiet and vice versa.
Everyone who is not strong or old is both creative and patient.
If mary is either quiet or patient then fred is either not patient or not calm.
If john is both not quiet and not patient then fred is both patient and not strong and vice versa.
Everyone who is rich or patient is either not kind or not happy and vice versa.
If alice is both curious and not kind then alice is not humble or tall and vice versa.
If someone is both not calm and not happy then john is either not old or strong.
If mary is either not funny or not creative then mary is not humble and vice versa.
Everyone who is not old is both not humble and funny and vice versa.
If susan is either not creative or not humble then paul is curious and vice versa.
Everyone who is either not quiet or wise is wise and vice versa.
Everyone who is not wise or not funny is not calm and vice versa.
Everyone who is either not happy or wise is both creative and wise and vice versa.
Someone is either not kind or not happy.
Lucy is not kind or funny.
Someone is not patient or quiet.
John is both quiet and kind.
Someone is not calm.
Someone is both generous and rich.
Someone is both brave and curious. | John is not tall. | contradiction | ((?[X]:((~strong(X)<~>old(X))))<=>(?[X]:((humble(X)<~>curious(X)))))&
(![X]:((calm(X)&~happy(X))<=>calm(X)))&
(![X]:((calm(X)|generous(X))<=>(brave(X)&~tall(X))))&
((?[X]:((~tall(X)<~>~strong(X))))<=>(?[X]:((happy(X)&~quiet(X)))))&
(![X]:((~strong(X)|old(X))=>(creative(X)&patient(X))))&
(((quiet(mary)<~>patient(mary)))=>((~patient(fred)<~>~calm(fred))))&
(((~quiet(john)&~patient(john)))<=>((patient(fred)&~strong(fred))))&
(![X]:((rich(X)|patient(X))<=>(~kind(X)<~>~happy(X))))&
(((curious(alice)&~kind(alice)))<=>((~humble(alice)|tall(alice))))&
((?[X]:((~calm(X)&~happy(X))))=>((~old(john)<~>strong(john))))&
(((~funny(mary)<~>~creative(mary)))<=>(~humble(mary)))&
(![X]:(~old(X)<=>(~humble(X)&funny(X))))&
(((~creative(susan)<~>~humble(susan)))<=>(curious(paul)))&
(![X]:((~quiet(X)<~>wise(X))<=>wise(X)))&
(![X]:((~wise(X)|~funny(X))<=>~calm(X)))&
(![X]:((~happy(X)<~>wise(X))<=>(creative(X)&wise(X))))&
(?[X]:((~kind(X)<~>~happy(X))))&
((~kind(lucy)|funny(lucy)))&
(?[X]:((~patient(X)|quiet(X))))&
((quiet(john)&kind(john)))&
(?[X]:(~calm(X)))&
(?[X]:((generous(X)&rich(X))))&
(?[X]:((brave(X)&curious(X)))) | ~tall(john) | [
"p3",
"p4",
"p7",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2630746751659467794420274
% SZS output start Proof for 2630746751659467794420274
4. ? [X0] : (~tall(X0) <~> ~strong(X0)) <=> ? [X0] : (~quiet(X0) & happy(X0)) [input p3]
5. ! [X0] : ((old(X0) | ~strong(X0)) => (patient(X0) & creative(X0))) [input p4]
8. ! [X0] : ((patient(X0) | rich(X0)) <=> (~kind(X0) <~> ~happy(X0))) [input p7]
14. ! [X0] : ((~quiet(X0) <~> wise(X0)) <=> wise(X0)) [input p13]
16. ! [X0] : ((~happy(X0) <~> wise(X0)) <=> (wise(X0) & creative(X0))) [input p15]
20. kind(john) & quiet(john) [input p19]
24. ~tall(john) [input hypothesis]
26. ? [X0] : (~tall(X0) <~> ~strong(X0)) <=> ? [X1] : (~quiet(X1) & happy(X1)) [rectify 4]
27. ! [X0] : ((patient(X0) & creative(X0)) | (~old(X0) & strong(X0))) [ennf transformation 5]
39. (? [X0] : ((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) | ! [X1] : (quiet(X1) | ~happy(X1))) & (? [X1] : (~quiet(X1) & happy(X1)) | ! [X0] : ((~tall(X0) | strong(X0)) & (~strong(X0) | tall(X0)))) [nnf transformation 26]
40. (? [X0] : ((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) | ! [X1] : (quiet(X1) | ~happy(X1))) & (? [X2] : (~quiet(X2) & happy(X2)) | ! [X3] : ((~tall(X3) | strong(X3)) & (~strong(X3) | tall(X3)))) [rectify 39]
41. ? [X0] : ((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) => ((strong(sK2) | tall(sK2)) & (~strong(sK2) | ~tall(sK2))) [choice axiom]
42. ? [X2] : (~quiet(X2) & happy(X2)) => (~quiet(sK3) & happy(sK3)) [choice axiom]
43. (((strong(sK2) | tall(sK2)) & (~strong(sK2) | ~tall(sK2))) | ! [X1] : (quiet(X1) | ~happy(X1))) & ((~quiet(sK3) & happy(sK3)) | ! [X3] : ((~tall(X3) | strong(X3)) & (~strong(X3) | tall(X3)))) [skolemisation 40,42,41]
47. ! [X0] : (((patient(X0) | rich(X0)) | ((~kind(X0) | happy(X0)) & (~happy(X0) | kind(X0)))) & (((happy(X0) | kind(X0)) & (~happy(X0) | ~kind(X0))) | (~patient(X0) & ~rich(X0)))) [nnf transformation 8]
48. ! [X0] : ((patient(X0) | rich(X0) | ((~kind(X0) | happy(X0)) & (~happy(X0) | kind(X0)))) & (((happy(X0) | kind(X0)) & (~happy(X0) | ~kind(X0))) | (~patient(X0) & ~rich(X0)))) [flattening 47]
56. ! [X0] : ((((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | ~wise(X0)) & (wise(X0) | ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0))))) [nnf transformation 14]
59. ! [X0] : ((((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | (~wise(X0) | ~creative(X0))) & ((wise(X0) & creative(X0)) | ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0))))) [nnf transformation 16]
60. ! [X0] : ((((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | ~wise(X0) | ~creative(X0)) & ((wise(X0) & creative(X0)) | ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0))))) [flattening 59]
90. ~quiet(sK3) | ~strong(X3) | tall(X3) [cnf transformation 43]
94. creative(X0) | strong(X0) [cnf transformation 27]
96. patient(X0) | strong(X0) [cnf transformation 27]
107. ~kind(X0) | ~happy(X0) | ~patient(X0) [cnf transformation 48]
130. wise(X0) | wise(X0) | quiet(X0) [cnf transformation 56]
133. ~wise(X0) | quiet(X0) | ~wise(X0) [cnf transformation 56]
139. wise(X0) | wise(X0) | happy(X0) [cnf transformation 60]
142. ~wise(X0) | happy(X0) | ~wise(X0) | ~creative(X0) [cnf transformation 60]
148. kind(john) [cnf transformation 20]
154. ~tall(john) [cnf transformation 24]
155. wise(X0) | happy(X0) [duplicate literal removal 139]
156. ~wise(X0) | happy(X0) | ~creative(X0) [duplicate literal removal 142]
157. wise(X0) | quiet(X0) [duplicate literal removal 130]
158. ~wise(X0) | quiet(X0) [duplicate literal removal 133]
212. 13 <=> quiet(sK3) [avatar definition]
214. ~quiet(sK3) <- (~13) [avatar component clause 212]
217. 14 <=> ! [X3] : (~strong(X3) | tall(X3)) [avatar definition]
218. ~strong(X3) | tall(X3) <- (14) [avatar component clause 217]
219. 14 | ~13 [avatar split clause 90,212,217]
252. 21 <=> patient(john) [avatar definition]
253. patient(john) <- (21) [avatar component clause 252]
254. ~patient(john) <- (~21) [avatar component clause 252]
293. 29 <=> strong(john) [avatar definition]
294. strong(john) <- (29) [avatar component clause 293]
295. ~strong(john) <- (~29) [avatar component clause 293]
330. quiet(X0) [subsumption resolution 157,158]
355. strong(john) <- (~21) [resolution 96,254]
356. $false <- (~21, ~29) [subsumption resolution 355,295]
357. 21 | 29 [avatar contradiction clause 356]
385. 41 <=> happy(john) [avatar definition]
387. ~happy(john) <- (~41) [avatar component clause 385]
389. ~happy(john) | ~patient(john) [resolution 107,148]
391. ~happy(john) <- (21) [subsumption resolution 389,253]
392. ~41 | ~21 [avatar split clause 391,252,385]
445. $false <- (~13) [subsumption resolution 214,330]
446. 13 [avatar contradiction clause 445]
471. happy(X0) | ~creative(X0) | happy(X0) [resolution 156,155]
472. ~creative(X0) | happy(X0) [duplicate literal removal 471]
529. happy(X0) | strong(X0) [resolution 472,94]
559. strong(john) <- (~41) [resolution 529,387]
563. 29 | 41 [avatar split clause 559,385,293]
564. tall(john) <- (14, 29) [resolution 294,218]
565. $false <- (14, 29) [subsumption resolution 564,154]
566. ~14 | ~29 [avatar contradiction clause 565]
567. $false [avatar sat refutation 219,357,392,446,563,566]
% SZS output end Proof for 2630746751659467794420274
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not happy.
Everyone who is both not quiet and brave is creative and vice versa.
Everyone who is both quiet and not old is rich or calm and vice versa.
If someone is both quiet and not happy then someone is generous and vice versa.
If mary is not humble or calm then paul is kind or not brave and vice versa.
If mary is either creative or curious then fred is rich or humble.
Everyone who is tall is rich or not rich and vice versa.
If someone is either calm or quiet then someone is either not old or not patient.
Everyone who is tall or curious is both curious and generous and vice versa.
Everyone who is humble is kind.
Everyone who is both wise and generous is funny or wise and vice versa.
If alice is both not kind and not old then someone is both not funny and creative and vice versa.
If fred is not rich then lucy is wise and vice versa.
Everyone who is curious or not quiet is not calm or calm and vice versa.
If susan is not rich or funny then someone is not tall or tall and vice versa.
Everyone who is not curious or tall is either calm or brave and vice versa.
Someone is both generous and funny.
Someone is both patient and tall.
Someone is either not curious or old.
Someone is not wise or brave.
Paul is not funny.
Mary is strong.
Susan is either not humble or calm.
Someone is both not happy and calm. | Fred is tall. | entailment | (![X]:(~generous(X)=>~happy(X)))&
(![X]:((~quiet(X)&brave(X))<=>creative(X)))&
(![X]:((quiet(X)&~old(X))<=>(rich(X)|calm(X))))&
((?[X]:((quiet(X)&~happy(X))))<=>(?[X]:(generous(X))))&
(((~humble(mary)|calm(mary)))<=>((kind(paul)|~brave(paul))))&
(((creative(mary)<~>curious(mary)))=>((rich(fred)|humble(fred))))&
(![X]:(tall(X)<=>(rich(X)|~rich(X))))&
((?[X]:((calm(X)<~>quiet(X))))=>(?[X]:((~old(X)<~>~patient(X)))))&
(![X]:((tall(X)|curious(X))<=>(curious(X)&generous(X))))&
(![X]:(humble(X)=>kind(X)))&
(![X]:((wise(X)&generous(X))<=>(funny(X)|wise(X))))&
(((~kind(alice)&~old(alice)))<=>(?[X]:((~funny(X)&creative(X)))))&
((~rich(fred))<=>(wise(lucy)))&
(![X]:((curious(X)|~quiet(X))<=>(~calm(X)|calm(X))))&
(((~rich(susan)|funny(susan)))<=>(?[X]:((~tall(X)|tall(X)))))&
(![X]:((~curious(X)|tall(X))<=>(calm(X)<~>brave(X))))&
(?[X]:((generous(X)&funny(X))))&
(?[X]:((patient(X)&tall(X))))&
(?[X]:((~curious(X)<~>old(X))))&
(?[X]:((~wise(X)|brave(X))))&
(~funny(paul))&
(strong(mary))&
((~humble(susan)<~>calm(susan)))&
(?[X]:((~happy(X)&calm(X)))) | tall(fred) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2022701093325323335377618
% SZS output start Proof for 2022701093325323335377618
7. ! [X0] : (tall(X0) <=> (~rich(X0) | rich(X0))) [input p6]
25. ~tall(fred) [input hypothesis]
46. ! [X0] : ((tall(X0) | (rich(X0) & ~rich(X0))) & ((~rich(X0) | rich(X0)) | ~tall(X0))) [nnf transformation 7]
47. ! [X0] : ((tall(X0) | (rich(X0) & ~rich(X0))) & (~rich(X0) | rich(X0) | ~tall(X0))) [flattening 46]
102. tall(X0) | ~rich(X0) [cnf transformation 47]
103. tall(X0) | rich(X0) [cnf transformation 47]
151. ~tall(fred) [cnf transformation 25]
211. tall(X0) [subsumption resolution 102,103]
288. $false [subsumption resolution 151,211]
% SZS output end Proof for 2022701093325323335377618
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and creative is funny or not quiet.
Everyone who is quiet or old is both not funny and not kind and vice versa.
Everyone who is happy or patient is either humble or old and vice versa.
If someone is curious or tall then paul is both not quiet and quiet.
Everyone who is brave is both not funny and patient and vice versa.
Everyone who is tall or funny is either quiet or calm and vice versa.
If alice is wise or quiet then alice is brave and vice versa.
Everyone who is both brave and not wise is not old.
If paul is not kind or rich then john is curious.
If susan is not rich then someone is either wise or not rich.
Everyone who is not kind or not wise is either kind or creative.
If someone is humble then john is both kind and old.
Everyone who is brave or not generous is not patient or not strong.
Everyone who is both not creative and generous is not happy or tall and vice versa.
If someone is both not curious and old then john is either not rich or funny and vice versa.
If someone is not quiet then someone is patient and vice versa.
Someone is happy or strong.
Someone is either not kind or not brave.
Fred is either creative or generous.
Someone is either quiet or not patient.
Someone is both generous and funny.
Someone is either funny or not kind. | Fred is humble. | contradiction | (![X]:((quiet(X)&creative(X))=>(funny(X)|~quiet(X))))&
(![X]:((quiet(X)|old(X))<=>(~funny(X)&~kind(X))))&
(![X]:((happy(X)|patient(X))<=>(humble(X)<~>old(X))))&
((?[X]:((curious(X)|tall(X))))=>((~quiet(paul)&quiet(paul))))&
(![X]:(brave(X)<=>(~funny(X)&patient(X))))&
(![X]:((tall(X)|funny(X))<=>(quiet(X)<~>calm(X))))&
(((wise(alice)|quiet(alice)))<=>(brave(alice)))&
(![X]:((brave(X)&~wise(X))=>~old(X)))&
(((~kind(paul)|rich(paul)))=>(curious(john)))&
((~rich(susan))=>(?[X]:((wise(X)<~>~rich(X)))))&
(![X]:((~kind(X)|~wise(X))=>(kind(X)<~>creative(X))))&
((?[X]:(humble(X)))=>((kind(john)&old(john))))&
(![X]:((brave(X)|~generous(X))=>(~patient(X)|~strong(X))))&
(![X]:((~creative(X)&generous(X))<=>(~happy(X)|tall(X))))&
((?[X]:((~curious(X)&old(X))))<=>((~rich(john)<~>funny(john))))&
((?[X]:(~quiet(X)))<=>(?[X]:(patient(X))))&
(?[X]:((happy(X)|strong(X))))&
(?[X]:((~kind(X)<~>~brave(X))))&
((creative(fred)<~>generous(fred)))&
(?[X]:((quiet(X)<~>~patient(X))))&
(?[X]:((generous(X)&funny(X))))&
(?[X]:((funny(X)<~>~kind(X)))) | humble(fred) | [
"p1",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2169248925844130388702986
% SZS output start Proof for 2169248925844130388702986
2. ! [X0] : ((old(X0) | quiet(X0)) <=> (~kind(X0) & ~funny(X0))) [input p1]
12. ? [X0] : humble(X0) => (old(john) & kind(john)) [input p11]
23. humble(fred) [input hypothesis]
33. (old(john) & kind(john)) | ! [X0] : ~humble(X0) [ennf transformation 12]
36. ! [X0] : (((old(X0) | quiet(X0)) | (kind(X0) | funny(X0))) & ((~kind(X0) & ~funny(X0)) | (~old(X0) & ~quiet(X0)))) [nnf transformation 2]
37. ! [X0] : ((old(X0) | quiet(X0) | kind(X0) | funny(X0)) & ((~kind(X0) & ~funny(X0)) | (~old(X0) & ~quiet(X0)))) [flattening 36]
79. ~kind(X0) | ~old(X0) [cnf transformation 37]
112. kind(john) | ~humble(X0) [cnf transformation 33]
113. old(john) | ~humble(X0) [cnf transformation 33]
140. humble(fred) [cnf transformation 23]
203. 13 <=> ! [X0] : ~humble(X0) [avatar definition]
204. ~humble(X0) <- (13) [avatar component clause 203]
206. 14 <=> old(john) [avatar definition]
208. old(john) <- (14) [avatar component clause 206]
209. 13 | 14 [avatar split clause 113,206,203]
211. 15 <=> kind(john) [avatar definition]
213. kind(john) <- (15) [avatar component clause 211]
214. 13 | 15 [avatar split clause 112,211,203]
310. $false <- (13) [resolution 204,140]
311. ~13 [avatar contradiction clause 310]
327. ~old(john) <- (15) [resolution 79,213]
329. $false <- (14, 15) [subsumption resolution 327,208]
330. ~14 | ~15 [avatar contradiction clause 329]
331. $false [avatar sat refutation 209,214,311,330]
% SZS output end Proof for 2169248925844130388702986
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not strong or wise then fred is curious and vice versa. If paul is not patient then someone is not wise and vice versa. If someone is both not wise and humble then alice is not wise or happy. Everyone who is both calm and not patient is both funny and not wise and vice versa. If someone is either tall or not tall then someone is kind. If someone is not kind or not wise then someone is not creative and vice versa. If someone is both not old and not funny then lucy is calm or not old and vice versa. Everyone who is both not generous and not curious is not old and vice versa. Everyone who is not brave or happy is either strong or happy and vice versa. Everyone who is either not curious or not patient is not happy or not brave and vice versa. If john is not generous or strong then someone is either rich or kind and vice versa. Everyone who is either tall or not calm is not generous or strong. If susan is both quiet and not kind then someone is not patient or tall and vice versa. Everyone who is creative or not wise is not strong and vice versa. Everyone who is not kind or not happy is both not kind and not happy. If someone is both not kind and not quiet then fred is both old and strong and vice versa. John is both brave and not strong. Alice is not strong. Someone is not creative. Alice is not funny or not creative. Mary is either not brave or not happy. John is creative. Alice is either not funny or old. Someone is not brave. | John is strong. | contradiction | ((?[X]:((~strong(X)<~>wise(X))))<=>(curious(fred)))&
((~patient(paul))<=>(?[X]:(~wise(X))))&
((?[X]:((~wise(X)&humble(X))))=>((~wise(alice)|happy(alice))))&
(![X]:((calm(X)&~patient(X))<=>(funny(X)&~wise(X))))&
((?[X]:((tall(X)<~>~tall(X))))=>(?[X]:(kind(X))))&
((?[X]:((~kind(X)|~wise(X))))<=>(?[X]:(~creative(X))))&
((?[X]:((~old(X)&~funny(X))))<=>((calm(lucy)|~old(lucy))))&
(![X]:((~generous(X)&~curious(X))<=>~old(X)))&
(![X]:((~brave(X)|happy(X))<=>(strong(X)<~>happy(X))))&
(![X]:((~curious(X)<~>~patient(X))<=>(~happy(X)|~brave(X))))&
(((~generous(john)|strong(john)))<=>(?[X]:((rich(X)<~>kind(X)))))&
(![X]:((tall(X)<~>~calm(X))=>(~generous(X)|strong(X))))&
(((quiet(susan)&~kind(susan)))<=>(?[X]:((~patient(X)|tall(X)))))&
(![X]:((creative(X)|~wise(X))<=>~strong(X)))&
(![X]:((~kind(X)|~happy(X))=>(~kind(X)&~happy(X))))&
((?[X]:((~kind(X)&~quiet(X))))<=>((old(fred)&strong(fred))))&
((brave(john)&~strong(john)))&
(~strong(alice))&
(?[X]:(~creative(X)))&
((~funny(alice)|~creative(alice)))&
((~brave(mary)<~>~happy(mary)))&
(creative(john))&
((~funny(alice)<~>old(alice)))&
(?[X]:(~brave(X))) | strong(john) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8820427579526217935935356
% SZS output start Proof for 8820427579526217935935356
17. ~strong(john) & brave(john) [input p16]
25. strong(john) [input hypothesis]
147. ~strong(john) [cnf transformation 17]
157. strong(john) [cnf transformation 25]
262. 24 <=> strong(john) [avatar definition]
329. ~24 [avatar split clause 147,262]
355. 24 [avatar split clause 157,262]
356. $false [avatar sat refutation 329,355]
% SZS output end Proof for 8820427579526217935935356
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and not generous is kind or happy. If someone is either not tall or not quiet then someone is funny or creative and vice versa. Everyone who is either not humble or strong is not happy or not kind. Everyone who is not kind is both creative and not kind. If someone is either not creative or not rich then lucy is wise and vice versa. Everyone who is not patient or funny is either not generous or creative. Everyone who is either humble or not happy is both kind and calm. If someone is both kind and not tall then someone is either not quiet or not rich and vice versa. Everyone who is not strong or not rich is both generous and not patient. Everyone who is both not funny and not tall is wise. If mary is either calm or not wise then someone is not kind. If someone is not strong then john is not happy or tall and vice versa. Everyone who is wise or calm is not creative. Everyone who is both not quiet and not strong is both kind and not wise and vice versa. If someone is either not wise or not quiet then paul is both not patient and brave. Everyone who is either not happy or old is either not humble or strong. Fred is both not humble and not kind. Someone is either happy or not happy. Someone is not curious or curious. Someone is both creative and not quiet. Paul is wise. Mary is either kind or wise. Someone is not funny. | Paul is kind. | entailment | (![X]:((creative(X)&~generous(X))=>(kind(X)|happy(X))))&
((?[X]:((~tall(X)<~>~quiet(X))))<=>(?[X]:((funny(X)|creative(X)))))&
(![X]:((~humble(X)<~>strong(X))=>(~happy(X)|~kind(X))))&
(![X]:(~kind(X)=>(creative(X)&~kind(X))))&
((?[X]:((~creative(X)<~>~rich(X))))<=>(wise(lucy)))&
(![X]:((~patient(X)|funny(X))=>(~generous(X)<~>creative(X))))&
(![X]:((humble(X)<~>~happy(X))=>(kind(X)&calm(X))))&
((?[X]:((kind(X)&~tall(X))))<=>(?[X]:((~quiet(X)<~>~rich(X)))))&
(![X]:((~strong(X)|~rich(X))=>(generous(X)&~patient(X))))&
(![X]:((~funny(X)&~tall(X))=>wise(X)))&
(((calm(mary)<~>~wise(mary)))=>(?[X]:(~kind(X))))&
((?[X]:(~strong(X)))<=>((~happy(john)|tall(john))))&
(![X]:((wise(X)|calm(X))=>~creative(X)))&
(![X]:((~quiet(X)&~strong(X))<=>(kind(X)&~wise(X))))&
((?[X]:((~wise(X)<~>~quiet(X))))=>((~patient(paul)&brave(paul))))&
(![X]:((~happy(X)<~>old(X))=>(~humble(X)<~>strong(X))))&
((~humble(fred)&~kind(fred)))&
(?[X]:((happy(X)<~>~happy(X))))&
(?[X]:((~curious(X)|curious(X))))&
(?[X]:((creative(X)&~quiet(X))))&
(wise(paul))&
((kind(mary)<~>wise(mary)))&
(?[X]:(~funny(X))) | kind(paul) | [
"p3",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6160472646436017406949048
% SZS output start Proof for 6160472646436017406949048
4. ! [X0] : (~kind(X0) => (~kind(X0) & creative(X0))) [input p3]
13. ! [X0] : ((calm(X0) | wise(X0)) => ~creative(X0)) [input p12]
21. wise(paul) [input p20]
24. ~kind(paul) [input hypothesis]
32. ! [X0] : ((~kind(X0) & creative(X0)) | kind(X0)) [ennf transformation 4]
39. ! [X0] : (~creative(X0) | (~calm(X0) & ~wise(X0))) [ennf transformation 13]
90. kind(X0) | creative(X0) [cnf transformation 32]
120. ~wise(X0) | ~creative(X0) [cnf transformation 39]
139. wise(paul) [cnf transformation 21]
143. ~kind(paul) [cnf transformation 24]
282. creative(paul) [resolution 90,143]
287. ~creative(paul) [resolution 120,139]
290. $false [subsumption resolution 287,282]
% SZS output end Proof for 6160472646436017406949048
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious is both wise and not creative and vice versa.
Everyone who is both not generous and tall is both not strong and not old and vice versa.
Everyone who is calm is both not quiet and patient and vice versa.
If mary is both happy and funny then someone is not funny or not humble and vice versa.
If paul is wise or not calm then someone is not kind or not happy.
If someone is both not calm and not old then fred is old.
If lucy is both patient and not strong then someone is not wise.
Everyone who is both curious and not rich is tall or rich.
Everyone who is either strong or generous is both tall and not generous.
If someone is happy or not calm then someone is kind or not humble and vice versa.
Everyone who is not strong is old or not curious.
If susan is both wise and quiet then mary is quiet or strong and vice versa.
Everyone who is strong or rich is either not wise or not kind and vice versa.
If lucy is either not wise or old then john is both not brave and generous.
Everyone who is not calm or creative is kind and vice versa.
Everyone who is not curious or wise is both not generous and not creative.
Someone is both not old and funny.
Someone is either not funny or tall.
Someone is both not funny and not humble.
Someone is not rich.
Paul is not funny or not happy.
Mary is either patient or not patient.
Lucy is not creative or not generous. | Lucy is strong. | contradiction | (![X]:(curious(X)<=>(wise(X)&~creative(X))))&
(![X]:((~generous(X)&tall(X))<=>(~strong(X)&~old(X))))&
(![X]:(calm(X)<=>(~quiet(X)&patient(X))))&
(((happy(mary)&funny(mary)))<=>(?[X]:((~funny(X)|~humble(X)))))&
(((wise(paul)|~calm(paul)))=>(?[X]:((~kind(X)|~happy(X)))))&
((?[X]:((~calm(X)&~old(X))))=>(old(fred)))&
(((patient(lucy)&~strong(lucy)))=>(?[X]:(~wise(X))))&
(![X]:((curious(X)&~rich(X))=>(tall(X)|rich(X))))&
(![X]:((strong(X)<~>generous(X))=>(tall(X)&~generous(X))))&
((?[X]:((happy(X)|~calm(X))))<=>(?[X]:((kind(X)|~humble(X)))))&
(![X]:(~strong(X)=>(old(X)|~curious(X))))&
(((wise(susan)&quiet(susan)))<=>((quiet(mary)|strong(mary))))&
(![X]:((strong(X)|rich(X))<=>(~wise(X)<~>~kind(X))))&
(((~wise(lucy)<~>old(lucy)))=>((~brave(john)&generous(john))))&
(![X]:((~calm(X)|creative(X))<=>kind(X)))&
(![X]:((~curious(X)|wise(X))=>(~generous(X)&~creative(X))))&
(?[X]:((~old(X)&funny(X))))&
(?[X]:((~funny(X)<~>tall(X))))&
(?[X]:((~funny(X)&~humble(X))))&
(?[X]:(~rich(X)))&
((~funny(paul)|~happy(paul)))&
((patient(mary)<~>~patient(mary)))&
((~creative(lucy)|~generous(lucy))) | strong(lucy) | [
"p0",
"p1",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 94462222211790249385218
% SZS output start Proof for 94462222211790249385218
1. ! [X0] : (curious(X0) <=> (~creative(X0) & wise(X0))) [input p0]
2. ! [X0] : ((tall(X0) & ~generous(X0)) <=> (~old(X0) & ~strong(X0))) [input p1]
9. ! [X0] : ((strong(X0) <~> generous(X0)) => (~generous(X0) & tall(X0))) [input p8]
16. ! [X0] : ((wise(X0) | ~curious(X0)) => (~creative(X0) & ~generous(X0))) [input p15]
24. strong(lucy) [input hypothesis]
33. ! [X0] : ((~generous(X0) & tall(X0)) | (strong(X0) <=> generous(X0))) [ennf transformation 9]
37. ! [X0] : ((~creative(X0) & ~generous(X0)) | (~wise(X0) & curious(X0))) [ennf transformation 16]
38. ! [X0] : ((curious(X0) | (creative(X0) | ~wise(X0))) & ((~creative(X0) & wise(X0)) | ~curious(X0))) [nnf transformation 1]
39. ! [X0] : ((curious(X0) | creative(X0) | ~wise(X0)) & ((~creative(X0) & wise(X0)) | ~curious(X0))) [flattening 38]
40. ! [X0] : (((tall(X0) & ~generous(X0)) | (old(X0) | strong(X0))) & ((~old(X0) & ~strong(X0)) | (~tall(X0) | generous(X0)))) [nnf transformation 2]
41. ! [X0] : (((tall(X0) & ~generous(X0)) | old(X0) | strong(X0)) & ((~old(X0) & ~strong(X0)) | ~tall(X0) | generous(X0))) [flattening 40]
53. ! [X0] : ((~generous(X0) & tall(X0)) | ((strong(X0) | ~generous(X0)) & (generous(X0) | ~strong(X0)))) [nnf transformation 33]
76. ~curious(X0) | wise(X0) [cnf transformation 39]
79. ~strong(X0) | ~tall(X0) | generous(X0) [cnf transformation 41]
96. tall(X0) | generous(X0) | ~strong(X0) [cnf transformation 53]
121. ~generous(X0) | curious(X0) [cnf transformation 37]
122. ~generous(X0) | ~wise(X0) [cnf transformation 37]
136. strong(lucy) [cnf transformation 24]
197. 14 <=> strong(lucy) [avatar definition]
199. strong(lucy) <- (14) [avatar component clause 197]
205. ~strong(X0) | generous(X0) [subsumption resolution 96,79]
261. 28 <=> wise(lucy) [avatar definition]
290. 14 [avatar split clause 136,197]
295. generous(lucy) <- (14) [resolution 205,199]
297. ~wise(lucy) <- (14) [resolution 295,122]
298. curious(lucy) <- (14) [resolution 295,121]
299. wise(lucy) <- (14) [resolution 298,76]
302. 28 | ~14 [avatar split clause 299,197,261]
303. ~28 | ~14 [avatar split clause 297,197,261]
304. $false [avatar sat refutation 290,302,303]
% SZS output end Proof for 94462222211790249385218
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then paul is either not brave or patient and vice versa. If someone is both not quiet and strong then someone is not wise or humble. Everyone who is either not tall or not calm is either not brave or not creative and vice versa. If someone is not brave or kind then someone is not funny or brave and vice versa. Everyone who is both not funny and brave is creative or not brave and vice versa. Everyone who is either not old or happy is both not happy and creative. If lucy is both patient and not happy then someone is funny. Everyone who is either humble or happy is both strong and not curious and vice versa. Everyone who is both kind and not rich is either brave or wise and vice versa. If fred is either wise or creative then paul is humble or patient. Everyone who is both old and quiet is both not humble and rich and vice versa. Everyone who is not wise or not patient is humble or generous. Everyone who is both patient and funny is not wise or old and vice versa. Everyone who is not old or creative is both not tall and calm. Someone is humble or not strong. Someone is either not funny or patient. Susan is both strong and not kind. Someone is not creative or not rich. Alice is either calm or funny. Someone is patient. Someone is not tall or not patient. | Alice is calm. | contradiction | ((?[X]:(~kind(X)))<=>((~brave(paul)<~>patient(paul))))&
((?[X]:((~quiet(X)&strong(X))))=>(?[X]:((~wise(X)|humble(X)))))&
(![X]:((~tall(X)<~>~calm(X))<=>(~brave(X)<~>~creative(X))))&
((?[X]:((~brave(X)|kind(X))))<=>(?[X]:((~funny(X)|brave(X)))))&
(![X]:((~funny(X)&brave(X))<=>(creative(X)|~brave(X))))&
(![X]:((~old(X)<~>happy(X))=>(~happy(X)&creative(X))))&
(((patient(lucy)&~happy(lucy)))=>(?[X]:(funny(X))))&
(![X]:((humble(X)<~>happy(X))<=>(strong(X)&~curious(X))))&
(![X]:((kind(X)&~rich(X))<=>(brave(X)<~>wise(X))))&
(((wise(fred)<~>creative(fred)))=>((humble(paul)|patient(paul))))&
(![X]:((old(X)&quiet(X))<=>(~humble(X)&rich(X))))&
(![X]:((~wise(X)|~patient(X))=>(humble(X)|generous(X))))&
(![X]:((patient(X)&funny(X))<=>(~wise(X)|old(X))))&
(![X]:((~old(X)|creative(X))=>(~tall(X)&calm(X))))&
(?[X]:((humble(X)|~strong(X))))&
(?[X]:((~funny(X)<~>patient(X))))&
((strong(susan)&~kind(susan)))&
(?[X]:((~creative(X)|~rich(X))))&
((calm(alice)<~>funny(alice)))&
(?[X]:(patient(X)))&
(?[X]:((~tall(X)|~patient(X)))) | calm(alice) | [
"p2",
"p4",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 517085011910883006449052
% SZS output start Proof for 517085011910883006449052
3. ! [X0] : ((~tall(X0) <~> ~calm(X0)) <=> (~brave(X0) <~> ~creative(X0))) [input p2]
5. ! [X0] : ((brave(X0) & ~funny(X0)) <=> (~brave(X0) | creative(X0))) [input p4]
14. ! [X0] : ((creative(X0) | ~old(X0)) => (calm(X0) & ~tall(X0))) [input p13]
19. calm(alice) <~> funny(alice) [input p18]
22. calm(alice) [input hypothesis]
32. ! [X0] : ((calm(X0) & ~tall(X0)) | (~creative(X0) & old(X0))) [ennf transformation 14]
40. ! [X0] : ((((calm(X0) | tall(X0)) & (~calm(X0) | ~tall(X0))) | ((~brave(X0) | creative(X0)) & (~creative(X0) | brave(X0)))) & (((creative(X0) | brave(X0)) & (~creative(X0) | ~brave(X0))) | ((~tall(X0) | calm(X0)) & (~calm(X0) | tall(X0))))) [nnf transformation 3]
46. ! [X0] : (((brave(X0) & ~funny(X0)) | (brave(X0) & ~creative(X0))) & ((~brave(X0) | creative(X0)) | (~brave(X0) | funny(X0)))) [nnf transformation 5]
47. ! [X0] : (((brave(X0) & ~funny(X0)) | (brave(X0) & ~creative(X0))) & (~brave(X0) | creative(X0) | ~brave(X0) | funny(X0))) [flattening 46]
67. (~funny(alice) | ~calm(alice)) & (funny(alice) | calm(alice)) [nnf transformation 19]
77. ~creative(X0) | ~brave(X0) | ~calm(X0) | tall(X0) [cnf transformation 40]
89. ~brave(X0) | creative(X0) | ~brave(X0) | funny(X0) [cnf transformation 47]
93. brave(X0) | brave(X0) [cnf transformation 47]
123. ~creative(X0) | ~tall(X0) [cnf transformation 32]
133. ~funny(alice) | ~calm(alice) [cnf transformation 67]
136. calm(alice) [cnf transformation 22]
138. ~brave(X0) | creative(X0) | funny(X0) [duplicate literal removal 89]
139. brave(X0) [duplicate literal removal 93]
200. 15 <=> ! [X3] : brave(X3) [avatar definition]
201. brave(X3) <- (15) [avatar component clause 200]
203. 15 [avatar split clause 139,200]
260. 28 <=> calm(alice) [avatar definition]
261. calm(alice) <- (28) [avatar component clause 260]
264. 29 <=> funny(alice) [avatar definition]
266. ~funny(alice) <- (~29) [avatar component clause 264]
267. ~28 | ~29 [avatar split clause 133,264,260]
278. 28 [avatar split clause 136,260]
316. funny(X0) | creative(X0) <- (15) [resolution 138,201]
319. creative(alice) <- (15, ~29) [resolution 316,266]
323. ~brave(alice) | ~calm(alice) | tall(alice) <- (15, ~29) [resolution 319,77]
326. ~tall(alice) <- (15, ~29) [resolution 319,123]
328. ~calm(alice) | tall(alice) <- (15, ~29) [subsumption resolution 323,201]
329. tall(alice) <- (15, 28, ~29) [subsumption resolution 328,261]
330. $false <- (15, 28, ~29) [subsumption resolution 326,329]
331. ~15 | ~28 | 29 [avatar contradiction clause 330]
332. $false [avatar sat refutation 203,267,278,331]
% SZS output end Proof for 517085011910883006449052
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both quiet and generous then someone is old or happy. Everyone who is both funny and kind is both humble and not rich. Everyone who is not funny or calm is not funny and vice versa. Everyone who is both generous and humble is wise or brave and vice versa. Everyone who is calm is not generous. If susan is either creative or not humble then paul is not patient and vice versa. Everyone who is either wise or patient is either not generous or not humble. If susan is generous then susan is happy and vice versa. If someone is both kind and not humble then fred is either not funny or creative. Everyone who is curious or wise is not curious. Everyone who is both humble and rich is not brave and vice versa. If mary is not patient or funny then john is either strong or not patient and vice versa. Everyone who is either patient or kind is either strong or happy. Everyone who is either wise or happy is happy. If someone is not rich or kind then lucy is curious and vice versa. Everyone who is either not strong or not quiet is not rich and vice versa. Susan is either patient or not wise. Someone is not calm. Someone is creative or not patient. Someone is not tall or old. John is either not humble or patient. Someone is either funny or not kind. Alice is funny or old. | Susan is not calm. | neutral | (((quiet(fred)&generous(fred)))=>(?[X]:((old(X)|happy(X)))))&
(![X]:((funny(X)&kind(X))=>(humble(X)&~rich(X))))&
(![X]:((~funny(X)|calm(X))<=>~funny(X)))&
(![X]:((generous(X)&humble(X))<=>(wise(X)|brave(X))))&
(![X]:(calm(X)=>~generous(X)))&
(((creative(susan)<~>~humble(susan)))<=>(~patient(paul)))&
(![X]:((wise(X)<~>patient(X))=>(~generous(X)<~>~humble(X))))&
((generous(susan))<=>(happy(susan)))&
((?[X]:((kind(X)&~humble(X))))=>((~funny(fred)<~>creative(fred))))&
(![X]:((curious(X)|wise(X))=>~curious(X)))&
(![X]:((humble(X)&rich(X))<=>~brave(X)))&
(((~patient(mary)|funny(mary)))<=>((strong(john)<~>~patient(john))))&
(![X]:((patient(X)<~>kind(X))=>(strong(X)<~>happy(X))))&
(![X]:((wise(X)<~>happy(X))=>happy(X)))&
((?[X]:((~rich(X)|kind(X))))<=>(curious(lucy)))&
(![X]:((~strong(X)<~>~quiet(X))<=>~rich(X)))&
((patient(susan)<~>~wise(susan)))&
(?[X]:(~calm(X)))&
(?[X]:((creative(X)|~patient(X))))&
(?[X]:((~tall(X)|old(X))))&
((~humble(john)<~>patient(john)))&
(?[X]:((funny(X)<~>~kind(X))))&
((funny(alice)|old(alice))) | ~calm(susan) | [] | null | 0 |
If paul is not brave then someone is not brave or not curious and vice versa.
If someone is either kind or not strong then lucy is tall or not creative.
Everyone who is either not patient or not rich is brave or generous.
If someone is funny or not creative then someone is both not creative and not funny and vice versa.
If paul is not funny then someone is calm and vice versa.
Everyone who is strong is not happy or humble and vice versa.
Everyone who is not quiet or not humble is tall or patient and vice versa.
If someone is not wise or brave then fred is either not humble or not brave and vice versa.
Everyone who is either not generous or creative is both humble and not funny and vice versa.
If someone is both generous and not wise then mary is wise or curious and vice versa.
Everyone who is either not patient or humble is not brave.
Everyone who is curious is not wise and vice versa.
Everyone who is either not wise or not happy is both humble and kind and vice versa.
Everyone who is old or kind is both not creative and strong and vice versa.
Everyone who is either creative or kind is both curious and not generous and vice versa.
Everyone who is either tall or not humble is either brave or not calm and vice versa.
Someone is both strong and funny.
Mary is happy.
Someone is rich.
Someone is both creative and not patient.
John is either not kind or happy.
Fred is not patient or not creative.
Susan is both not happy and not wise. | Fred is not creative. | neutral | ((~brave(paul))<=>(?[X]:((~brave(X)|~curious(X)))))&
((?[X]:((kind(X)<~>~strong(X))))=>((tall(lucy)|~creative(lucy))))&
(![X]:((~patient(X)<~>~rich(X))=>(brave(X)|generous(X))))&
((?[X]:((funny(X)|~creative(X))))<=>(?[X]:((~creative(X)&~funny(X)))))&
((~funny(paul))<=>(?[X]:(calm(X))))&
(![X]:(strong(X)<=>(~happy(X)|humble(X))))&
(![X]:((~quiet(X)|~humble(X))<=>(tall(X)|patient(X))))&
((?[X]:((~wise(X)|brave(X))))<=>((~humble(fred)<~>~brave(fred))))&
(![X]:((~generous(X)<~>creative(X))<=>(humble(X)&~funny(X))))&
((?[X]:((generous(X)&~wise(X))))<=>((wise(mary)|curious(mary))))&
(![X]:((~patient(X)<~>humble(X))=>~brave(X)))&
(![X]:(curious(X)<=>~wise(X)))&
(![X]:((~wise(X)<~>~happy(X))<=>(humble(X)&kind(X))))&
(![X]:((old(X)|kind(X))<=>(~creative(X)&strong(X))))&
(![X]:((creative(X)<~>kind(X))<=>(curious(X)&~generous(X))))&
(![X]:((tall(X)<~>~humble(X))<=>(brave(X)<~>~calm(X))))&
(?[X]:((strong(X)&funny(X))))&
(happy(mary))&
(?[X]:(rich(X)))&
(?[X]:((creative(X)&~patient(X))))&
((~kind(john)<~>happy(john)))&
((~patient(fred)|~creative(fred)))&
((~happy(susan)&~wise(susan))) | ~creative(fred) | [] | null | 0 |
If john is both not patient and old then someone is both kind and not calm and vice versa.
Everyone who is generous or curious is both strong and generous.
Everyone who is both patient and not funny is either quiet or not generous.
If paul is both tall and wise then mary is not kind and vice versa.
Everyone who is both patient and wise is calm or not wise.
Everyone who is both not humble and happy is both not quiet and patient and vice versa.
If someone is both quiet and not funny then someone is either not happy or curious and vice versa.
If paul is both not calm and not strong then someone is both funny and patient and vice versa.
If john is quiet then lucy is either not humble or wise and vice versa.
Everyone who is either not generous or generous is not brave and vice versa.
Everyone who is calm or humble is either not kind or kind.
If john is either generous or quiet then fred is old.
Everyone who is kind is not old.
If someone is either not curious or patient then mary is wise or not quiet and vice versa.
If someone is either not calm or humble then paul is both not creative and curious and vice versa.
If someone is either patient or not strong then mary is not brave and vice versa.
Someone is humble.
Someone is either creative or curious.
Paul is not generous or wise.
John is either calm or creative.
John is not funny or not patient.
Someone is not old.
Lucy is not calm or strong. | Paul is not calm. | neutral | (((~patient(john)&old(john)))<=>(?[X]:((kind(X)&~calm(X)))))&
(![X]:((generous(X)|curious(X))=>(strong(X)&generous(X))))&
(![X]:((patient(X)&~funny(X))=>(quiet(X)<~>~generous(X))))&
(((tall(paul)&wise(paul)))<=>(~kind(mary)))&
(![X]:((patient(X)&wise(X))=>(calm(X)|~wise(X))))&
(![X]:((~humble(X)&happy(X))<=>(~quiet(X)&patient(X))))&
((?[X]:((quiet(X)&~funny(X))))<=>(?[X]:((~happy(X)<~>curious(X)))))&
(((~calm(paul)&~strong(paul)))<=>(?[X]:((funny(X)&patient(X)))))&
((quiet(john))<=>((~humble(lucy)<~>wise(lucy))))&
(![X]:((~generous(X)<~>generous(X))<=>~brave(X)))&
(![X]:((calm(X)|humble(X))=>(~kind(X)<~>kind(X))))&
(((generous(john)<~>quiet(john)))=>(old(fred)))&
(![X]:(kind(X)=>~old(X)))&
((?[X]:((~curious(X)<~>patient(X))))<=>((wise(mary)|~quiet(mary))))&
((?[X]:((~calm(X)<~>humble(X))))<=>((~creative(paul)&curious(paul))))&
((?[X]:((patient(X)<~>~strong(X))))<=>(~brave(mary)))&
(?[X]:(humble(X)))&
(?[X]:((creative(X)<~>curious(X))))&
((~generous(paul)|wise(paul)))&
((calm(john)<~>creative(john)))&
((~funny(john)|~patient(john)))&
(?[X]:(~old(X)))&
((~calm(lucy)|strong(lucy))) | ~calm(paul) | [] | null | 0 |
If lucy is curious or brave then someone is curious 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. If someone is creative then susan is either not quiet or strong. If someone is both happy and curious then lucy is either rich or curious and vice versa. If someone is either humble or not curious then john is strong or wise and vice versa. Someone is old or not generous. John is either strong or kind. Paul is not humble. Someone is both kind and humble. Someone is either rich or patient. Someone is not humble or funny. Lucy is either funny or not curious. Someone is either not humble or not wise. | Paul is quiet. | neutral | (((curious(lucy)|brave(lucy)))<=>(?[X]:(curious(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))))&
((?[X]:(creative(X)))=>((~quiet(susan)<~>strong(susan))))&
((?[X]:((happy(X)&curious(X))))<=>((rich(lucy)<~>curious(lucy))))&
((?[X]:((humble(X)<~>~curious(X))))<=>((strong(john)|wise(john))))&
(?[X]:((old(X)|~generous(X))))&
((strong(john)<~>kind(john)))&
(~humble(paul))&
(?[X]:((kind(X)&humble(X))))&
(?[X]:((rich(X)<~>patient(X))))&
(?[X]:((~humble(X)|funny(X))))&
((funny(lucy)<~>~curious(lucy)))&
(?[X]:((~humble(X)<~>~wise(X)))) | quiet(paul) | [] | null | 0 |
Everyone who is both not generous and not curious is brave. If someone is both rich and happy then fred is both not quiet and calm and vice versa. Everyone who is both not humble and creative is funny. If lucy is strong or not kind then paul is strong or curious and vice versa. Everyone who is tall or not strong is both curious and not kind. Everyone who is either not strong or not humble is not funny. If mary is not rich or tall then someone is funny or happy. If someone is both strong and not old then alice is humble or not funny. Everyone who is brave or not patient is either kind or not quiet and vice versa. If paul is both calm and not old then paul is both curious and not rich. If alice is both not brave and not tall then someone is not patient. Everyone who is tall or not quiet is kind. Everyone who is both rich and not creative is calm or not calm and vice versa. If someone is either funny or not kind then someone is both not curious and happy and vice versa. Everyone who is both not funny and not kind is not brave or not quiet and vice versa. If someone is not happy or patient then someone is both not curious and patient. Fred is either strong or not old. Paul is humble. Fred is either not curious or humble. Someone is either generous or not quiet. John is not calm or funny. Someone is either not curious or not quiet. | Mary is strong. | entailment | (![X]:((~generous(X)&~curious(X))=>brave(X)))&
((?[X]:((rich(X)&happy(X))))<=>((~quiet(fred)&calm(fred))))&
(![X]:((~humble(X)&creative(X))=>funny(X)))&
(((strong(lucy)|~kind(lucy)))<=>((strong(paul)|curious(paul))))&
(![X]:((tall(X)|~strong(X))=>(curious(X)&~kind(X))))&
(![X]:((~strong(X)<~>~humble(X))=>~funny(X)))&
(((~rich(mary)|tall(mary)))=>(?[X]:((funny(X)|happy(X)))))&
((?[X]:((strong(X)&~old(X))))=>((humble(alice)|~funny(alice))))&
(![X]:((brave(X)|~patient(X))<=>(kind(X)<~>~quiet(X))))&
(((calm(paul)&~old(paul)))=>((curious(paul)&~rich(paul))))&
(((~brave(alice)&~tall(alice)))=>(?[X]:(~patient(X))))&
(![X]:((tall(X)|~quiet(X))=>kind(X)))&
(![X]:((rich(X)&~creative(X))<=>(calm(X)|~calm(X))))&
((?[X]:((funny(X)<~>~kind(X))))<=>(?[X]:((~curious(X)&happy(X)))))&
(![X]:((~funny(X)&~kind(X))<=>(~brave(X)|~quiet(X))))&
((?[X]:((~happy(X)|patient(X))))=>(?[X]:((~curious(X)&patient(X)))))&
((strong(fred)<~>~old(fred)))&
(humble(paul))&
((~curious(fred)<~>humble(fred)))&
(?[X]:((generous(X)<~>~quiet(X))))&
((~calm(john)|funny(john)))&
(?[X]:((~curious(X)<~>~quiet(X)))) | strong(mary) | [
"p1",
"p4",
"p8",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5388111886623859061624660
% SZS output start Proof for 5388111886623859061624660
2. ? [X0] : (happy(X0) & rich(X0)) <=> (calm(fred) & ~quiet(fred)) [input p1]
5. ! [X0] : ((~strong(X0) | tall(X0)) => (~kind(X0) & curious(X0))) [input p4]
9. ! [X0] : ((~patient(X0) | brave(X0)) <=> (kind(X0) <~> ~quiet(X0))) [input p8]
12. ! [X0] : ((~quiet(X0) | tall(X0)) => kind(X0)) [input p11]
13. ! [X0] : ((~creative(X0) & rich(X0)) <=> (~calm(X0) | calm(X0))) [input p12]
14. ? [X0] : (funny(X0) <~> ~kind(X0)) <=> ? [X0] : (happy(X0) & ~curious(X0)) [input p13]
15. ! [X0] : ((~kind(X0) & ~funny(X0)) <=> (~quiet(X0) | ~brave(X0))) [input p14]
23. ~strong(mary) [input hypothesis]
24. ? [X0] : (funny(X0) <~> ~kind(X0)) <=> ? [X1] : (happy(X1) & ~curious(X1)) [rectify 14]
30. ! [X0] : ((~kind(X0) & curious(X0)) | (strong(X0) & ~tall(X0))) [ennf transformation 5]
39. ! [X0] : (kind(X0) | (quiet(X0) & ~tall(X0))) [ennf transformation 12]
41. (? [X0] : (happy(X0) & rich(X0)) | (~calm(fred) | quiet(fred))) & ((calm(fred) & ~quiet(fred)) | ! [X0] : (~happy(X0) | ~rich(X0))) [nnf transformation 2]
42. (? [X0] : (happy(X0) & rich(X0)) | ~calm(fred) | quiet(fred)) & ((calm(fred) & ~quiet(fred)) | ! [X0] : (~happy(X0) | ~rich(X0))) [flattening 41]
43. (? [X0] : (happy(X0) & rich(X0)) | ~calm(fred) | quiet(fred)) & ((calm(fred) & ~quiet(fred)) | ! [X1] : (~happy(X1) | ~rich(X1))) [rectify 42]
44. ? [X0] : (happy(X0) & rich(X0)) => (happy(sK0) & rich(sK0)) [choice axiom]
45. ((happy(sK0) & rich(sK0)) | ~calm(fred) | quiet(fred)) & ((calm(fred) & ~quiet(fred)) | ! [X1] : (~happy(X1) | ~rich(X1))) [skolemisation 43,44]
51. ! [X0] : (((~patient(X0) | brave(X0)) | ((kind(X0) | quiet(X0)) & (~quiet(X0) | ~kind(X0)))) & (((quiet(X0) | ~kind(X0)) & (~quiet(X0) | kind(X0))) | (patient(X0) & ~brave(X0)))) [nnf transformation 9]
52. ! [X0] : ((~patient(X0) | brave(X0) | ((kind(X0) | quiet(X0)) & (~quiet(X0) | ~kind(X0)))) & (((quiet(X0) | ~kind(X0)) & (~quiet(X0) | kind(X0))) | (patient(X0) & ~brave(X0)))) [flattening 51]
55. ! [X0] : (((~creative(X0) & rich(X0)) | (calm(X0) & ~calm(X0))) & ((~calm(X0) | calm(X0)) | (creative(X0) | ~rich(X0)))) [nnf transformation 13]
56. ! [X0] : (((~creative(X0) & rich(X0)) | (calm(X0) & ~calm(X0))) & (~calm(X0) | calm(X0) | creative(X0) | ~rich(X0))) [flattening 55]
57. (? [X0] : ((kind(X0) | ~funny(X0)) & (~kind(X0) | funny(X0))) | ! [X1] : (~happy(X1) | curious(X1))) & (? [X1] : (happy(X1) & ~curious(X1)) | ! [X0] : ((funny(X0) | kind(X0)) & (~kind(X0) | ~funny(X0)))) [nnf transformation 24]
58. (? [X0] : ((kind(X0) | ~funny(X0)) & (~kind(X0) | funny(X0))) | ! [X1] : (~happy(X1) | curious(X1))) & (? [X2] : (happy(X2) & ~curious(X2)) | ! [X3] : ((funny(X3) | kind(X3)) & (~kind(X3) | ~funny(X3)))) [rectify 57]
59. ? [X0] : ((kind(X0) | ~funny(X0)) & (~kind(X0) | funny(X0))) => ((kind(sK3) | ~funny(sK3)) & (~kind(sK3) | funny(sK3))) [choice axiom]
60. ? [X2] : (happy(X2) & ~curious(X2)) => (happy(sK4) & ~curious(sK4)) [choice axiom]
61. (((kind(sK3) | ~funny(sK3)) & (~kind(sK3) | funny(sK3))) | ! [X1] : (~happy(X1) | curious(X1))) & ((happy(sK4) & ~curious(sK4)) | ! [X3] : ((funny(X3) | kind(X3)) & (~kind(X3) | ~funny(X3)))) [skolemisation 58,60,59]
62. ! [X0] : (((~kind(X0) & ~funny(X0)) | (quiet(X0) & brave(X0))) & ((~quiet(X0) | ~brave(X0)) | (kind(X0) | funny(X0)))) [nnf transformation 15]
63. ! [X0] : (((~kind(X0) & ~funny(X0)) | (quiet(X0) & brave(X0))) & (~quiet(X0) | ~brave(X0) | kind(X0) | funny(X0))) [flattening 62]
76. ~quiet(fred) | ~happy(X1) | ~rich(X1) [cnf transformation 45]
88. ~kind(X0) | strong(X0) [cnf transformation 30]
94. ~quiet(X0) | kind(X0) | ~brave(X0) [cnf transformation 52]
104. kind(X0) | quiet(X0) [cnf transformation 39]
106. rich(X0) | ~calm(X0) [cnf transformation 56]
107. calm(X0) | rich(X0) [cnf transformation 56]
112. happy(sK4) | ~kind(X3) | ~funny(X3) [cnf transformation 61]
113. happy(sK4) | funny(X3) | kind(X3) [cnf transformation 61]
117. ~funny(X0) | brave(X0) [cnf transformation 63]
119. ~kind(X0) | brave(X0) [cnf transformation 63]
120. ~kind(X0) | quiet(X0) [cnf transformation 63]
135. ~strong(mary) [cnf transformation 23]
137. 1 <=> quiet(fred) [avatar definition]
138. ~quiet(fred) <- (~1) [avatar component clause 137]
155. 5 <=> ! [X1] : (~happy(X1) | ~rich(X1)) [avatar definition]
156. ~happy(X1) | ~rich(X1) <- (5) [avatar component clause 155]
158. 5 | ~1 [avatar split clause 76,137,155]
238. rich(X0) [subsumption resolution 106,107]
253. 26 <=> ! [X3] : (funny(X3) | kind(X3)) [avatar definition]
254. kind(X3) | funny(X3) <- (26) [avatar component clause 253]
256. 27 <=> happy(sK4) [avatar definition]
258. happy(sK4) <- (27) [avatar component clause 256]
259. 26 | 27 [avatar split clause 113,256,253]
261. 28 <=> ! [X3] : (~kind(X3) | ~funny(X3)) [avatar definition]
262. ~kind(X3) | ~funny(X3) <- (28) [avatar component clause 261]
263. 28 | 27 [avatar split clause 112,256,261]
270. quiet(X0) [subsumption resolution 120,104]
322. $false <- (~1) [subsumption resolution 138,270]
323. 1 [avatar contradiction clause 322]
324. ~happy(X1) <- (5) [subsumption resolution 156,238]
326. $false <- (5, 27) [resolution 324,258]
327. ~5 | ~27 [avatar contradiction clause 326]
342. funny(X0) | brave(X0) <- (26) [resolution 254,119]
343. strong(X1) | funny(X1) <- (26) [resolution 254,88]
346. brave(X0) <- (26) [subsumption resolution 342,117]
352. funny(mary) <- (26) [resolution 343,135]
383. kind(X0) | ~brave(X0) [resolution 94,270]
384. kind(X0) <- (26) [subsumption resolution 383,346]
388. ~funny(X0) <- (26, 28) [resolution 384,262]
409. $false <- (26, 28) [resolution 388,352]
410. ~26 | ~28 [avatar contradiction clause 409]
413. $false [avatar sat refutation 158,259,263,323,327,410]
% SZS output end Proof for 5388111886623859061624660
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or old then someone is both wise and old and vice versa.
Everyone who is either curious or happy is kind or not humble.
If someone is both humble and not happy then someone is not tall and vice versa.
If john is either not happy or strong then john is curious or brave.
Everyone who is either not funny or not tall is happy.
Everyone who is either generous or not generous is not curious or creative and vice versa.
If someone is either brave or not funny then susan is not patient or generous.
Everyone who is both strong and old is kind and vice versa.
If someone is quiet then someone is both not creative and not generous and vice versa.
Everyone who is either not quiet or not generous is brave or creative.
Everyone who is not calm or wise is happy and vice versa.
If someone is wise then mary is not happy.
Everyone who is calm is not tall or creative and vice versa.
If mary is either not generous or not rich then susan is not curious or generous and vice versa.
Everyone who is not strong is not brave or generous and vice versa.
If someone is either generous or not creative then lucy is both not quiet and happy.
Someone is tall.
Mary is both not funny and not patient.
Mary is both not strong and not patient.
Someone is not curious or strong.
Someone is both humble and tall.
Someone is not calm or not patient.
Someone is both not quiet and kind.
Alice is patient. | Susan is not patient. | neutral | ((?[X]:((quiet(X)|old(X))))<=>(?[X]:((wise(X)&old(X)))))&
(![X]:((curious(X)<~>happy(X))=>(kind(X)|~humble(X))))&
((?[X]:((humble(X)&~happy(X))))<=>(?[X]:(~tall(X))))&
(((~happy(john)<~>strong(john)))=>((curious(john)|brave(john))))&
(![X]:((~funny(X)<~>~tall(X))=>happy(X)))&
(![X]:((generous(X)<~>~generous(X))<=>(~curious(X)|creative(X))))&
((?[X]:((brave(X)<~>~funny(X))))=>((~patient(susan)|generous(susan))))&
(![X]:((strong(X)&old(X))<=>kind(X)))&
((?[X]:(quiet(X)))<=>(?[X]:((~creative(X)&~generous(X)))))&
(![X]:((~quiet(X)<~>~generous(X))=>(brave(X)|creative(X))))&
(![X]:((~calm(X)|wise(X))<=>happy(X)))&
((?[X]:(wise(X)))=>(~happy(mary)))&
(![X]:(calm(X)<=>(~tall(X)|creative(X))))&
(((~generous(mary)<~>~rich(mary)))<=>((~curious(susan)|generous(susan))))&
(![X]:(~strong(X)<=>(~brave(X)|generous(X))))&
((?[X]:((generous(X)<~>~creative(X))))=>((~quiet(lucy)&happy(lucy))))&
(?[X]:(tall(X)))&
((~funny(mary)&~patient(mary)))&
((~strong(mary)&~patient(mary)))&
(?[X]:((~curious(X)|strong(X))))&
(?[X]:((humble(X)&tall(X))))&
(?[X]:((~calm(X)|~patient(X))))&
(?[X]:((~quiet(X)&kind(X))))&
(patient(alice)) | ~patient(susan) | [] | null | 0 |
If lucy is both tall and not tall then fred is either not patient or not tall and vice versa.
Everyone who is not humble or not generous is not quiet and vice versa.
Everyone who is either not strong or old is either humble or not happy and vice versa.
If someone is both not kind and not humble then paul is either not humble or rich and vice versa.
If someone is either humble or not funny then someone is not generous or not wise and vice versa.
Everyone who is not generous or old is rich or wise.
If someone is brave or not old then someone is not curious.
Everyone who is either quiet or not generous is generous.
If someone is either not generous or not old then someone is calm and vice versa.
Everyone who is either humble or not curious is kind or calm.
If someone is either not happy or not wise then someone is either not happy or not calm.
Everyone who is calm or not humble is not kind and vice versa.
Everyone who is not calm is quiet or not quiet and vice versa.
If lucy is not strong or not curious then fred is both not generous and patient and vice versa.
If someone is not creative then lucy is patient or strong and vice versa.
If paul is either tall or happy then susan is both patient and not creative and vice versa.
Susan is not curious or not happy.
Paul is generous or not generous.
John is both not rich and humble.
Someone is not strong or not brave.
Someone is not patient or not calm.
Someone is creative.
Someone is strong or tall. | Fred is old. | entailment | (((tall(lucy)&~tall(lucy)))<=>((~patient(fred)<~>~tall(fred))))&
(![X]:((~humble(X)|~generous(X))<=>~quiet(X)))&
(![X]:((~strong(X)<~>old(X))<=>(humble(X)<~>~happy(X))))&
((?[X]:((~kind(X)&~humble(X))))<=>((~humble(paul)<~>rich(paul))))&
((?[X]:((humble(X)<~>~funny(X))))<=>(?[X]:((~generous(X)|~wise(X)))))&
(![X]:((~generous(X)|old(X))=>(rich(X)|wise(X))))&
((?[X]:((brave(X)|~old(X))))=>(?[X]:(~curious(X))))&
(![X]:((quiet(X)<~>~generous(X))=>generous(X)))&
((?[X]:((~generous(X)<~>~old(X))))<=>(?[X]:(calm(X))))&
(![X]:((humble(X)<~>~curious(X))=>(kind(X)|calm(X))))&
((?[X]:((~happy(X)<~>~wise(X))))=>(?[X]:((~happy(X)<~>~calm(X)))))&
(![X]:((calm(X)|~humble(X))<=>~kind(X)))&
(![X]:(~calm(X)<=>(quiet(X)|~quiet(X))))&
(((~strong(lucy)|~curious(lucy)))<=>((~generous(fred)&patient(fred))))&
((?[X]:(~creative(X)))<=>((patient(lucy)|strong(lucy))))&
(((tall(paul)<~>happy(paul)))<=>((patient(susan)&~creative(susan))))&
((~curious(susan)|~happy(susan)))&
((generous(paul)|~generous(paul)))&
((~rich(john)&humble(john)))&
(?[X]:((~strong(X)|~brave(X))))&
(?[X]:((~patient(X)|~calm(X))))&
(?[X]:(creative(X)))&
(?[X]:((strong(X)|tall(X)))) | old(fred) | [
"p1",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1199945933784885727123605
% SZS output start Proof for 1199945933784885727123605
2. ! [X0] : ((~generous(X0) | ~humble(X0)) <=> ~quiet(X0)) [input p1]
8. ! [X0] : ((quiet(X0) <~> ~generous(X0)) => generous(X0)) [input p7]
9. ? [X0] : (~generous(X0) <~> ~old(X0)) <=> ? [X0] : calm(X0) [input p8]
13. ! [X0] : (~calm(X0) <=> (~quiet(X0) | quiet(X0))) [input p12]
24. ~old(fred) [input hypothesis]
27. ? [X0] : (~generous(X0) <~> ~old(X0)) <=> ? [X1] : calm(X1) [rectify 9]
34. ! [X0] : (generous(X0) | (quiet(X0) <=> ~generous(X0))) [ennf transformation 8]
40. ! [X0] : (((~generous(X0) | ~humble(X0)) | quiet(X0)) & (~quiet(X0) | (generous(X0) & humble(X0)))) [nnf transformation 2]
41. ! [X0] : ((~generous(X0) | ~humble(X0) | quiet(X0)) & (~quiet(X0) | (generous(X0) & humble(X0)))) [flattening 40]
55. ! [X0] : (generous(X0) | ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0)))) [nnf transformation 34]
56. (? [X0] : ((old(X0) | generous(X0)) & (~old(X0) | ~generous(X0))) | ! [X1] : ~calm(X1)) & (? [X1] : calm(X1) | ! [X0] : ((~generous(X0) | old(X0)) & (~old(X0) | generous(X0)))) [nnf transformation 27]
57. (? [X0] : ((old(X0) | generous(X0)) & (~old(X0) | ~generous(X0))) | ! [X1] : ~calm(X1)) & (? [X2] : calm(X2) | ! [X3] : ((~generous(X3) | old(X3)) & (~old(X3) | generous(X3)))) [rectify 56]
58. ? [X0] : ((old(X0) | generous(X0)) & (~old(X0) | ~generous(X0))) => ((old(sK4) | generous(sK4)) & (~old(sK4) | ~generous(sK4))) [choice axiom]
59. ? [X2] : calm(X2) => calm(sK5) [choice axiom]
60. (((old(sK4) | generous(sK4)) & (~old(sK4) | ~generous(sK4))) | ! [X1] : ~calm(X1)) & (calm(sK5) | ! [X3] : ((~generous(X3) | old(X3)) & (~old(X3) | generous(X3)))) [skolemisation 57,59,58]
68. ! [X0] : ((~calm(X0) | (quiet(X0) & ~quiet(X0))) & ((~quiet(X0) | quiet(X0)) | calm(X0))) [nnf transformation 13]
69. ! [X0] : ((~calm(X0) | (quiet(X0) & ~quiet(X0))) & (~quiet(X0) | quiet(X0) | calm(X0))) [flattening 68]
92. ~quiet(X0) | generous(X0) [cnf transformation 41]
118. generous(X0) | quiet(X0) | generous(X0) [cnf transformation 55]
120. calm(sK5) | ~generous(X3) | old(X3) [cnf transformation 60]
133. ~calm(X0) | ~quiet(X0) [cnf transformation 69]
134. ~calm(X0) | quiet(X0) [cnf transformation 69]
156. ~old(fred) [cnf transformation 24]
157. generous(X0) | quiet(X0) [duplicate literal removal 118]
212. 12 <=> ! [X1] : generous(X1) [avatar definition]
213. generous(X1) <- (12) [avatar component clause 212]
234. 17 <=> ! [X1] : old(X1) [avatar definition]
235. old(X1) <- (17) [avatar component clause 234]
241. generous(X0) [subsumption resolution 157,92]
242. 12 [avatar split clause 241,212]
244. 19 <=> ! [X1] : ~calm(X1) [avatar definition]
245. ~calm(X1) <- (19) [avatar component clause 244]
257. 22 <=> ! [X3] : (~generous(X3) | old(X3)) [avatar definition]
258. ~generous(X3) | old(X3) <- (22) [avatar component clause 257]
260. 23 <=> calm(sK5) [avatar definition]
262. calm(sK5) <- (23) [avatar component clause 260]
263. 22 | 23 [avatar split clause 120,260,257]
286. ~calm(X0) [subsumption resolution 133,134]
287. 19 [avatar split clause 286,244]
370. $false <- (19, 23) [resolution 262,245]
371. ~19 | ~23 [avatar contradiction clause 370]
372. old(X3) <- (12, 22) [subsumption resolution 258,213]
373. 17 | ~12 | ~22 [avatar split clause 372,257,212,234]
374. $false <- (17) [resolution 235,156]
375. ~17 [avatar contradiction clause 374]
376. $false [avatar sat refutation 242,263,287,371,373,375]
% SZS output end Proof for 1199945933784885727123605
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and happy is kind. Everyone who is both curious and not patient is generous and vice versa. Everyone who is not old or not calm is either curious or not generous. If paul is rich then paul is both happy and not generous. If someone is both not rich and not old then someone is not brave. Everyone who is either happy or not old is old or calm and vice versa. Everyone who is old is both not rich and not curious and vice versa. Everyone who is both strong and not patient is not rich or not tall and vice versa. Everyone who is either not wise or tall is both not happy and generous and vice versa. If someone is either calm or not kind then lucy is not brave or patient. If someone is not humble or patient then paul is both curious and not patient and vice versa. Everyone who is not funny is both brave and not curious. If someone is calm then someone is either not old or funny and vice versa. Everyone who is either creative or not happy is both humble and not old. Everyone who is both not funny and happy is not kind or happy. Everyone who is both not wise and curious is either not creative or creative and vice versa. Someone is old or funny. Susan is not old. Susan is not humble. Someone is either tall or not rich. Someone is both not brave and not strong. | Susan is not creative. | entailment | (![X]:((creative(X)&happy(X))=>kind(X)))&
(![X]:((curious(X)&~patient(X))<=>generous(X)))&
(![X]:((~old(X)|~calm(X))=>(curious(X)<~>~generous(X))))&
((rich(paul))=>((happy(paul)&~generous(paul))))&
((?[X]:((~rich(X)&~old(X))))=>(?[X]:(~brave(X))))&
(![X]:((happy(X)<~>~old(X))<=>(old(X)|calm(X))))&
(![X]:(old(X)<=>(~rich(X)&~curious(X))))&
(![X]:((strong(X)&~patient(X))<=>(~rich(X)|~tall(X))))&
(![X]:((~wise(X)<~>tall(X))<=>(~happy(X)&generous(X))))&
((?[X]:((calm(X)<~>~kind(X))))=>((~brave(lucy)|patient(lucy))))&
((?[X]:((~humble(X)|patient(X))))<=>((curious(paul)&~patient(paul))))&
(![X]:(~funny(X)=>(brave(X)&~curious(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~old(X)<~>funny(X)))))&
(![X]:((creative(X)<~>~happy(X))=>(humble(X)&~old(X))))&
(![X]:((~funny(X)&happy(X))=>(~kind(X)|happy(X))))&
(![X]:((~wise(X)&curious(X))<=>(~creative(X)<~>creative(X))))&
(?[X]:((old(X)|funny(X))))&
(~old(susan))&
(~humble(susan))&
(?[X]:((tall(X)<~>~rich(X))))&
(?[X]:((~brave(X)&~strong(X)))) | ~creative(susan) | [
"p5",
"p6",
"p11",
"p12",
"p13",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2636717158013967627827060
% SZS output start Proof for 2636717158013967627827060
6. ! [X0] : ((happy(X0) <~> ~old(X0)) <=> (calm(X0) | old(X0))) [input p5]
7. ! [X0] : (old(X0) <=> (~curious(X0) & ~rich(X0))) [input p6]
12. ! [X0] : (~funny(X0) => (~curious(X0) & brave(X0))) [input p11]
13. ? [X0] : calm(X0) <=> ? [X0] : (~old(X0) <~> funny(X0)) [input p12]
14. ! [X0] : ((creative(X0) <~> ~happy(X0)) => (~old(X0) & humble(X0))) [input p13]
16. ! [X0] : ((curious(X0) & ~wise(X0)) <=> (~creative(X0) <~> creative(X0))) [input p15]
19. ~humble(susan) [input p18]
22. creative(susan) [input hypothesis]
24. ? [X0] : calm(X0) <=> ? [X1] : (~old(X1) <~> funny(X1)) [rectify 13]
32. ! [X0] : ((~curious(X0) & brave(X0)) | funny(X0)) [ennf transformation 12]
33. ! [X0] : ((~old(X0) & humble(X0)) | (creative(X0) <=> ~happy(X0))) [ennf transformation 14]
42. ! [X0] : ((((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | (~calm(X0) & ~old(X0))) & ((calm(X0) | old(X0)) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0))))) [nnf transformation 6]
43. ! [X0] : ((((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | (~calm(X0) & ~old(X0))) & (calm(X0) | old(X0) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0))))) [flattening 42]
44. ! [X0] : ((old(X0) | (curious(X0) | rich(X0))) & ((~curious(X0) & ~rich(X0)) | ~old(X0))) [nnf transformation 7]
45. ! [X0] : ((old(X0) | curious(X0) | rich(X0)) & ((~curious(X0) & ~rich(X0)) | ~old(X0))) [flattening 44]
56. (? [X0] : calm(X0) | ! [X1] : ((~old(X1) | ~funny(X1)) & (funny(X1) | old(X1)))) & (? [X1] : ((~funny(X1) | old(X1)) & (funny(X1) | ~old(X1))) | ! [X0] : ~calm(X0)) [nnf transformation 24]
57. (? [X0] : calm(X0) | ! [X1] : ((~old(X1) | ~funny(X1)) & (funny(X1) | old(X1)))) & (? [X2] : ((~funny(X2) | old(X2)) & (funny(X2) | ~old(X2))) | ! [X3] : ~calm(X3)) [rectify 56]
58. ? [X0] : calm(X0) => calm(sK2) [choice axiom]
59. ? [X2] : ((~funny(X2) | old(X2)) & (funny(X2) | ~old(X2))) => ((~funny(sK3) | old(sK3)) & (funny(sK3) | ~old(sK3))) [choice axiom]
60. (calm(sK2) | ! [X1] : ((~old(X1) | ~funny(X1)) & (funny(X1) | old(X1)))) & (((~funny(sK3) | old(sK3)) & (funny(sK3) | ~old(sK3))) | ! [X3] : ~calm(X3)) [skolemisation 57,59,58]
61. ! [X0] : ((~old(X0) & humble(X0)) | ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) [nnf transformation 33]
62. ! [X0] : (((curious(X0) & ~wise(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) & (((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (~curious(X0) | wise(X0)))) [nnf transformation 16]
63. ! [X0] : (((curious(X0) & ~wise(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) & (((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | ~curious(X0) | wise(X0))) [flattening 62]
83. calm(X0) | old(X0) | happy(X0) | old(X0) [cnf transformation 43]
84. ~old(X0) | happy(X0) | ~old(X0) [cnf transformation 43]
89. ~old(X0) | ~curious(X0) [cnf transformation 45]
110. ~curious(X0) | funny(X0) [cnf transformation 32]
112. ~funny(sK3) | old(sK3) | ~calm(X3) [cnf transformation 60]
115. ~happy(X0) | humble(X0) | ~creative(X0) [cnf transformation 61]
124. curious(X0) | creative(X0) | creative(X0) [cnf transformation 63]
125. curious(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 63]
128. ~humble(susan) [cnf transformation 19]
133. creative(susan) [cnf transformation 22]
136. curious(X0) | creative(X0) [duplicate literal removal 124]
137. ~creative(X0) | curious(X0) [duplicate literal removal 125]
138. calm(X0) | old(X0) | happy(X0) [duplicate literal removal 83]
139. ~old(X0) | happy(X0) [duplicate literal removal 84]
162. calm(X0) | happy(X0) [subsumption resolution 138,139]
219. 19 <=> ! [X3] : ~calm(X3) [avatar definition]
220. ~calm(X3) <- (19) [avatar component clause 219]
222. 20 <=> old(sK3) [avatar definition]
224. old(sK3) <- (20) [avatar component clause 222]
226. 21 <=> funny(sK3) [avatar definition]
228. ~funny(sK3) <- (~21) [avatar component clause 226]
229. 19 | 20 | ~21 [avatar split clause 112,226,222,219]
232. curious(X0) [subsumption resolution 136,137]
260. funny(X0) [resolution 110,232]
261. $false <- (~21) [resolution 260,228]
262. 21 [avatar contradiction clause 261]
304. ~curious(sK3) <- (20) [resolution 224,89]
305. $false <- (20) [subsumption resolution 304,232]
306. ~20 [avatar contradiction clause 305]
308. happy(X0) <- (19) [resolution 220,162]
328. ~creative(X0) | humble(X0) <- (19) [resolution 115,308]
346. humble(susan) <- (19) [resolution 328,133]
347. $false <- (19) [subsumption resolution 346,128]
348. ~19 [avatar contradiction clause 347]
349. $false [avatar sat refutation 229,262,306,348]
% SZS output end Proof for 2636717158013967627827060
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not curious or not quiet then someone is not generous or not patient.
If fred is either not tall or not kind then someone is both strong and brave.
Everyone who is wise is not happy and vice versa.
Everyone who is both not creative and old is not calm or old and vice versa.
If someone is both calm and happy then john is both not happy and not kind and vice versa.
If mary is either curious or not patient then someone is not rich or strong and vice versa.
Everyone who is not brave is either wise or creative and vice versa.
If someone is not generous or strong then paul is patient and vice versa.
If someone is either not strong or not rich then someone is both brave and curious and vice versa.
If someone is both not generous and happy then someone is both quiet and old.
Everyone who is both not old and not calm is old or not kind.
If someone is either not old or not curious then john is both humble and not wise and vice versa.
Everyone who is calm or curious is either happy or not brave.
If someone is tall or not wise then someone is both tall and creative.
If someone is not tall then someone is either not wise or not quiet.
Everyone who is brave is either not rich or not funny and vice versa.
Someone is both not patient and not kind.
Mary is either strong or humble.
Someone is both not brave and kind.
Fred is not curious.
Paul is not funny or not generous.
Someone is both quiet and funny.
Fred is not quiet or not generous.
Someone is not humble or not calm. | Fred is not brave. | entailment | ((?[X]:((~curious(X)<~>~quiet(X))))=>(?[X]:((~generous(X)|~patient(X)))))&
(((~tall(fred)<~>~kind(fred)))=>(?[X]:((strong(X)&brave(X)))))&
(![X]:(wise(X)<=>~happy(X)))&
(![X]:((~creative(X)&old(X))<=>(~calm(X)|old(X))))&
((?[X]:((calm(X)&happy(X))))<=>((~happy(john)&~kind(john))))&
(((curious(mary)<~>~patient(mary)))<=>(?[X]:((~rich(X)|strong(X)))))&
(![X]:(~brave(X)<=>(wise(X)<~>creative(X))))&
((?[X]:((~generous(X)|strong(X))))<=>(patient(paul)))&
((?[X]:((~strong(X)<~>~rich(X))))<=>(?[X]:((brave(X)&curious(X)))))&
((?[X]:((~generous(X)&happy(X))))=>(?[X]:((quiet(X)&old(X)))))&
(![X]:((~old(X)&~calm(X))=>(old(X)|~kind(X))))&
((?[X]:((~old(X)<~>~curious(X))))<=>((humble(john)&~wise(john))))&
(![X]:((calm(X)|curious(X))=>(happy(X)<~>~brave(X))))&
((?[X]:((tall(X)|~wise(X))))=>(?[X]:((tall(X)&creative(X)))))&
((?[X]:(~tall(X)))=>(?[X]:((~wise(X)<~>~quiet(X)))))&
(![X]:(brave(X)<=>(~rich(X)<~>~funny(X))))&
(?[X]:((~patient(X)&~kind(X))))&
((strong(mary)<~>humble(mary)))&
(?[X]:((~brave(X)&kind(X))))&
(~curious(fred))&
((~funny(paul)|~generous(paul)))&
(?[X]:((quiet(X)&funny(X))))&
((~quiet(fred)|~generous(fred)))&
(?[X]:((~humble(X)|~calm(X)))) | ~brave(fred) | [
"p2",
"p3",
"p4",
"p6",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3622545797186639558219215
% SZS output start Proof for 3622545797186639558219215
3. ! [X0] : (wise(X0) <=> ~happy(X0)) [input p2]
4. ! [X0] : ((old(X0) & ~creative(X0)) <=> (old(X0) | ~calm(X0))) [input p3]
5. ? [X0] : (happy(X0) & calm(X0)) <=> (~kind(john) & ~happy(john)) [input p4]
7. ! [X0] : (~brave(X0) <=> (wise(X0) <~> creative(X0))) [input p6]
13. ! [X0] : ((curious(X0) | calm(X0)) => (happy(X0) <~> ~brave(X0))) [input p12]
14. ? [X0] : (~wise(X0) | tall(X0)) => ? [X0] : (creative(X0) & tall(X0)) [input p13]
25. brave(fred) [input hypothesis]
29. ? [X0] : (~wise(X0) | tall(X0)) => ? [X1] : (creative(X1) & tall(X1)) [rectify 14]
36. ! [X0] : ((happy(X0) <~> ~brave(X0)) | (~curious(X0) & ~calm(X0))) [ennf transformation 13]
37. ? [X1] : (creative(X1) & tall(X1)) | ! [X0] : (wise(X0) & ~tall(X0)) [ennf transformation 29]
46. ! [X0] : ((wise(X0) | happy(X0)) & (~happy(X0) | ~wise(X0))) [nnf transformation 3]
47. ! [X0] : (((old(X0) & ~creative(X0)) | (~old(X0) & calm(X0))) & ((old(X0) | ~calm(X0)) | (~old(X0) | creative(X0)))) [nnf transformation 4]
48. ! [X0] : (((old(X0) & ~creative(X0)) | (~old(X0) & calm(X0))) & (old(X0) | ~calm(X0) | ~old(X0) | creative(X0))) [flattening 47]
49. (? [X0] : (happy(X0) & calm(X0)) | (kind(john) | happy(john))) & ((~kind(john) & ~happy(john)) | ! [X0] : (~happy(X0) | ~calm(X0))) [nnf transformation 5]
50. (? [X0] : (happy(X0) & calm(X0)) | kind(john) | happy(john)) & ((~kind(john) & ~happy(john)) | ! [X0] : (~happy(X0) | ~calm(X0))) [flattening 49]
51. (? [X0] : (happy(X0) & calm(X0)) | kind(john) | happy(john)) & ((~kind(john) & ~happy(john)) | ! [X1] : (~happy(X1) | ~calm(X1))) [rectify 50]
52. ? [X0] : (happy(X0) & calm(X0)) => (happy(sK2) & calm(sK2)) [choice axiom]
53. ((happy(sK2) & calm(sK2)) | kind(john) | happy(john)) & ((~kind(john) & ~happy(john)) | ! [X1] : (~happy(X1) | ~calm(X1))) [skolemisation 51,52]
58. ! [X0] : ((~brave(X0) | ((wise(X0) | ~creative(X0)) & (creative(X0) | ~wise(X0)))) & (((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | brave(X0))) [nnf transformation 7]
76. ! [X0] : (((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | (~curious(X0) & ~calm(X0))) [nnf transformation 36]
77. ? [X0] : (creative(X0) & tall(X0)) | ! [X1] : (wise(X1) & ~tall(X1)) [rectify 37]
78. ? [X0] : (creative(X0) & tall(X0)) => (creative(sK9) & tall(sK9)) [choice axiom]
79. (creative(sK9) & tall(sK9)) | ! [X1] : (wise(X1) & ~tall(X1)) [skolemisation 77,78]
100. ~happy(X0) | ~wise(X0) [cnf transformation 46]
101. happy(X0) | wise(X0) [cnf transformation 46]
103. ~creative(X0) | calm(X0) [cnf transformation 48]
104. ~old(X0) | ~creative(X0) [cnf transformation 48]
105. calm(X0) | old(X0) [cnf transformation 48]
107. ~happy(john) | ~happy(X1) | ~calm(X1) [cnf transformation 53]
108. ~kind(john) | ~happy(X1) | ~calm(X1) [cnf transformation 53]
110. happy(sK2) | kind(john) | happy(john) [cnf transformation 53]
117. creative(X0) | wise(X0) | brave(X0) [cnf transformation 58]
118. ~creative(X0) | ~wise(X0) | brave(X0) [cnf transformation 58]
119. ~wise(X0) | creative(X0) | ~brave(X0) [cnf transformation 58]
120. ~creative(X0) | wise(X0) | ~brave(X0) [cnf transformation 58]
139. ~calm(X0) | happy(X0) | ~brave(X0) [cnf transformation 76]
141. ~calm(X0) | ~happy(X0) | brave(X0) [cnf transformation 76]
144. tall(sK9) | wise(X1) [cnf transformation 79]
145. creative(sK9) | ~tall(X1) [cnf transformation 79]
165. brave(fred) [cnf transformation 25]
204. 9 <=> happy(john) [avatar definition]
208. 10 <=> kind(john) [avatar definition]
212. 11 <=> happy(sK2) [avatar definition]
214. happy(sK2) <- (11) [avatar component clause 212]
215. 9 | 10 | 11 [avatar split clause 110,212,208,204]
222. 13 <=> ! [X1] : (~happy(X1) | ~calm(X1)) [avatar definition]
223. ~calm(X1) | ~happy(X1) <- (13) [avatar component clause 222]
224. 13 | ~10 [avatar split clause 108,208,222]
225. 13 | ~9 [avatar split clause 107,204,222]
345. 40 <=> ! [X1] : wise(X1) [avatar definition]
346. wise(X1) <- (40) [avatar component clause 345]
348. 41 <=> creative(sK9) [avatar definition]
350. creative(sK9) <- (41) [avatar component clause 348]
353. 42 <=> ! [X1] : ~tall(X1) [avatar definition]
354. ~tall(X1) <- (42) [avatar component clause 353]
355. 42 | 41 [avatar split clause 145,348,353]
357. 43 <=> tall(sK9) [avatar definition]
359. tall(sK9) <- (43) [avatar component clause 357]
360. 40 | 43 [avatar split clause 144,357,345]
418. ~wise(sK2) <- (11) [resolution 100,214]
419. $false <- (11, 40) [subsumption resolution 418,346]
420. ~11 | ~40 [avatar contradiction clause 419]
428. ~happy(X0) | old(X0) <- (13) [resolution 223,105]
437. calm(X0) | brave(X0) | wise(X0) [resolution 117,103]
452. ~brave(X0) | happy(X0) | old(X0) [resolution 139,105]
457. ~brave(X0) | old(X0) <- (13) [subsumption resolution 452,428]
472. ~brave(X0) | creative(X0) <- (40) [resolution 346,119]
476. $false <- (42, 43) [resolution 359,354]
477. ~42 | ~43 [avatar contradiction clause 476]
525. old(fred) <- (13) [resolution 457,165]
530. creative(fred) <- (40) [resolution 472,165]
531. brave(X0) | wise(X0) | ~happy(X0) | brave(X0) [resolution 437,141]
534. brave(X0) | wise(X0) | ~happy(X0) [duplicate literal removal 531]
536. ~creative(fred) <- (13) [resolution 525,104]
539. $false <- (13, 40) [subsumption resolution 536,530]
540. ~13 | ~40 [avatar contradiction clause 539]
547. ~happy(X0) | brave(X0) [subsumption resolution 534,100]
561. wise(sK9) | ~brave(sK9) <- (41) [resolution 350,120]
562. ~wise(sK9) | brave(sK9) <- (41) [resolution 350,118]
563. calm(sK9) <- (41) [resolution 350,103]
565. 66 <=> brave(sK9) [avatar definition]
567. ~brave(sK9) <- (~66) [avatar component clause 565]
569. 67 <=> wise(sK9) [avatar definition]
570. ~wise(sK9) <- (~67) [avatar component clause 569]
571. wise(sK9) <- (67) [avatar component clause 569]
572. ~66 | 67 | ~41 [avatar split clause 561,348,569,565]
573. 66 | ~67 | ~41 [avatar split clause 562,348,569,565]
588. happy(sK9) | ~brave(sK9) <- (41) [resolution 563,139]
624. wise(X0) | brave(X0) [resolution 547,101]
634. brave(sK9) <- (~67) [resolution 624,570]
635. $false <- (~66, ~67) [subsumption resolution 634,567]
636. 66 | 67 [avatar contradiction clause 635]
638. 72 <=> happy(sK9) [avatar definition]
640. happy(sK9) <- (72) [avatar component clause 638]
641. ~66 | 72 | ~41 [avatar split clause 588,348,638,565]
659. ~wise(sK9) <- (72) [resolution 640,100]
660. $false <- (67, 72) [subsumption resolution 659,571]
661. ~67 | ~72 [avatar contradiction clause 660]
662. $false [avatar sat refutation 215,224,225,355,360,420,477,540,572,573,636,641,661]
% SZS output end Proof for 3622545797186639558219215
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative then someone is both not funny and not happy. Everyone who is quiet or tall is humble or calm and vice versa. Everyone who is either humble or not calm is quiet or curious. Everyone who is not happy or rich is both brave and not tall. Everyone who is both rich and not humble is both quiet and not creative and vice versa. If someone is both not brave and happy then lucy is quiet or creative. Everyone who is not kind is both strong and not curious and vice versa. Everyone who is happy is either not tall or humble. Everyone who is either humble or creative is not kind or not quiet and vice versa. If lucy is either not calm or not creative then someone is funny or generous and vice versa. Everyone who is both creative and happy is both not humble and not happy and vice versa. Everyone who is both happy and not patient is patient. Everyone who is either funny or wise is quiet or rich. Everyone who is not rich is either strong or happy and vice versa. Everyone who is rich or humble is either not creative or strong and vice versa. If john is patient then susan is either tall or not generous. Lucy is either not patient or not strong. Someone is not patient or calm. Someone is not wise. Someone is not brave or funny. Paul is both generous and not calm. Susan is not patient or not wise. Someone is both not brave and not curious. | Lucy is strong. | entailment | ((?[X]:(creative(X)))=>(?[X]:((~funny(X)&~happy(X)))))&
(![X]:((quiet(X)|tall(X))<=>(humble(X)|calm(X))))&
(![X]:((humble(X)<~>~calm(X))=>(quiet(X)|curious(X))))&
(![X]:((~happy(X)|rich(X))=>(brave(X)&~tall(X))))&
(![X]:((rich(X)&~humble(X))<=>(quiet(X)&~creative(X))))&
((?[X]:((~brave(X)&happy(X))))=>((quiet(lucy)|creative(lucy))))&
(![X]:(~kind(X)<=>(strong(X)&~curious(X))))&
(![X]:(happy(X)=>(~tall(X)<~>humble(X))))&
(![X]:((humble(X)<~>creative(X))<=>(~kind(X)|~quiet(X))))&
(((~calm(lucy)<~>~creative(lucy)))<=>(?[X]:((funny(X)|generous(X)))))&
(![X]:((creative(X)&happy(X))<=>(~humble(X)&~happy(X))))&
(![X]:((happy(X)&~patient(X))=>patient(X)))&
(![X]:((funny(X)<~>wise(X))=>(quiet(X)|rich(X))))&
(![X]:(~rich(X)<=>(strong(X)<~>happy(X))))&
(![X]:((rich(X)|humble(X))<=>(~creative(X)<~>strong(X))))&
((patient(john))=>((tall(susan)<~>~generous(susan))))&
((~patient(lucy)<~>~strong(lucy)))&
(?[X]:((~patient(X)|calm(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~brave(X)|funny(X))))&
((generous(paul)&~calm(paul)))&
((~patient(susan)|~wise(susan)))&
(?[X]:((~brave(X)&~curious(X)))) | strong(lucy) | [
"p1",
"p3",
"p4",
"p5",
"p10",
"p13",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8232702049777174505581580
% SZS output start Proof for 8232702049777174505581580
2. ! [X0] : ((tall(X0) | quiet(X0)) <=> (calm(X0) | humble(X0))) [input p1]
4. ! [X0] : ((rich(X0) | ~happy(X0)) => (~tall(X0) & brave(X0))) [input p3]
5. ! [X0] : ((~humble(X0) & rich(X0)) <=> (~creative(X0) & quiet(X0))) [input p4]
6. ? [X0] : (happy(X0) & ~brave(X0)) => (creative(lucy) | quiet(lucy)) [input p5]
11. ! [X0] : ((happy(X0) & creative(X0)) <=> (~happy(X0) & ~humble(X0))) [input p10]
14. ! [X0] : (~rich(X0) <=> (strong(X0) <~> happy(X0))) [input p13]
15. ! [X0] : ((humble(X0) | rich(X0)) <=> (~creative(X0) <~> strong(X0))) [input p14]
23. ? [X0] : (~curious(X0) & ~brave(X0)) [input p22]
24. ~strong(lucy) [input hypothesis]
29. ! [X0] : ((~tall(X0) & brave(X0)) | (~rich(X0) & happy(X0))) [ennf transformation 4]
30. (creative(lucy) | quiet(lucy)) | ! [X0] : (~happy(X0) | brave(X0)) [ennf transformation 6]
31. creative(lucy) | quiet(lucy) | ! [X0] : (~happy(X0) | brave(X0)) [flattening 30]
41. ! [X0] : (((tall(X0) | quiet(X0)) | (~calm(X0) & ~humble(X0))) & ((calm(X0) | humble(X0)) | (~tall(X0) & ~quiet(X0)))) [nnf transformation 2]
42. ! [X0] : ((tall(X0) | quiet(X0) | (~calm(X0) & ~humble(X0))) & (calm(X0) | humble(X0) | (~tall(X0) & ~quiet(X0)))) [flattening 41]
44. ! [X0] : (((~humble(X0) & rich(X0)) | (creative(X0) | ~quiet(X0))) & ((~creative(X0) & quiet(X0)) | (humble(X0) | ~rich(X0)))) [nnf transformation 5]
45. ! [X0] : (((~humble(X0) & rich(X0)) | creative(X0) | ~quiet(X0)) & ((~creative(X0) & quiet(X0)) | humble(X0) | ~rich(X0))) [flattening 44]
55. ! [X0] : (((happy(X0) & creative(X0)) | (happy(X0) | humble(X0))) & ((~happy(X0) & ~humble(X0)) | (~happy(X0) | ~creative(X0)))) [nnf transformation 11]
56. ! [X0] : (((happy(X0) & creative(X0)) | happy(X0) | humble(X0)) & ((~happy(X0) & ~humble(X0)) | ~happy(X0) | ~creative(X0))) [flattening 55]
58. ! [X0] : ((~rich(X0) | ((strong(X0) | ~happy(X0)) & (happy(X0) | ~strong(X0)))) & (((~happy(X0) | ~strong(X0)) & (happy(X0) | strong(X0))) | rich(X0))) [nnf transformation 14]
59. ! [X0] : (((humble(X0) | rich(X0)) | ((~creative(X0) | ~strong(X0)) & (strong(X0) | creative(X0)))) & (((~strong(X0) | creative(X0)) & (strong(X0) | ~creative(X0))) | (~humble(X0) & ~rich(X0)))) [nnf transformation 15]
60. ! [X0] : ((humble(X0) | rich(X0) | ((~creative(X0) | ~strong(X0)) & (strong(X0) | creative(X0)))) & (((~strong(X0) | creative(X0)) & (strong(X0) | ~creative(X0))) | (~humble(X0) & ~rich(X0)))) [flattening 59]
69. ? [X0] : (~curious(X0) & ~brave(X0)) => (~curious(sK5) & ~brave(sK5)) [choice axiom]
70. ~curious(sK5) & ~brave(sK5) [skolemisation 23,69]
75. ~humble(X0) | quiet(X0) | tall(X0) [cnf transformation 42]
79. brave(X0) | happy(X0) [cnf transformation 29]
81. ~tall(X0) | happy(X0) [cnf transformation 29]
85. ~quiet(X0) | creative(X0) | rich(X0) [cnf transformation 45]
86. ~humble(X0) | creative(X0) | ~quiet(X0) [cnf transformation 45]
87. creative(lucy) | quiet(lucy) | ~happy(X0) | brave(X0) [cnf transformation 31]
106. ~happy(X0) | ~happy(X0) | ~creative(X0) [cnf transformation 56]
108. happy(X0) | happy(X0) | humble(X0) [cnf transformation 56]
112. strong(X0) | happy(X0) | rich(X0) [cnf transformation 58]
115. ~rich(X0) | strong(X0) | ~happy(X0) [cnf transformation 58]
116. ~rich(X0) | ~creative(X0) | strong(X0) [cnf transformation 60]
132. ~brave(sK5) [cnf transformation 70]
134. ~strong(lucy) [cnf transformation 24]
136. ~happy(X0) | ~creative(X0) [duplicate literal removal 106]
137. humble(X0) | happy(X0) [duplicate literal removal 108]
152. creative(lucy) | quiet(lucy) | brave(X0) [subsumption resolution 87,79]
154. 4 <=> ! [X0] : brave(X0) [avatar definition]
155. brave(X0) <- (4) [avatar component clause 154]
157. 5 <=> quiet(lucy) [avatar definition]
159. quiet(lucy) <- (5) [avatar component clause 157]
161. 6 <=> creative(lucy) [avatar definition]
162. ~creative(lucy) <- (~6) [avatar component clause 161]
163. creative(lucy) <- (6) [avatar component clause 161]
164. 4 | 5 | 6 [avatar split clause 152,161,157,154]
210. 16 <=> strong(lucy) [avatar definition]
211. ~strong(lucy) <- (~16) [avatar component clause 210]
242. ~16 [avatar split clause 134,210]
243. $false <- (4) [resolution 155,132]
244. ~4 [avatar contradiction clause 243]
256. quiet(X0) | tall(X0) | happy(X0) [resolution 75,137]
258. quiet(X0) | happy(X0) [subsumption resolution 256,81]
262. creative(X0) | ~quiet(X0) | happy(X0) [resolution 86,137]
264. happy(X0) | creative(X0) [subsumption resolution 262,258]
272. 23 <=> happy(lucy) [avatar definition]
273. happy(lucy) <- (23) [avatar component clause 272]
274. ~happy(lucy) <- (~23) [avatar component clause 272]
298. happy(lucy) | rich(lucy) <- (~16) [resolution 112,211]
300. rich(lucy) <- (~16, ~23) [subsumption resolution 298,274]
315. ~creative(lucy) | strong(lucy) <- (~16, ~23) [resolution 116,300]
316. strong(lucy) <- (6, ~16, ~23) [subsumption resolution 315,163]
317. $false <- (6, ~16, ~23) [subsumption resolution 316,211]
318. ~6 | 16 | 23 [avatar contradiction clause 317]
320. 25 <=> rich(lucy) [avatar definition]
322. rich(lucy) <- (25) [avatar component clause 320]
323. 25 | 23 | 16 [avatar split clause 298,210,272,320]
328. ~creative(lucy) <- (23) [resolution 273,136]
332. ~6 | ~23 [avatar split clause 328,272,161]
333. creative(lucy) | rich(lucy) <- (5) [resolution 159,85]
335. rich(lucy) <- (5, ~6) [subsumption resolution 333,162]
336. 25 | ~5 | 6 [avatar split clause 335,161,157,320]
339. strong(lucy) | ~happy(lucy) <- (25) [resolution 322,115]
344. ~happy(lucy) <- (~16, 25) [subsumption resolution 339,211]
347. ~23 | 16 | ~25 [avatar split clause 344,320,210,272]
351. creative(lucy) <- (~23) [resolution 274,264]
352. $false <- (~6, ~23) [subsumption resolution 351,162]
353. 6 | 23 [avatar contradiction clause 352]
354. $false [avatar sat refutation 164,242,244,318,323,332,336,347,353]
% SZS output end Proof for 8232702049777174505581580
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is not creative or curious and vice versa. Everyone who is either not brave or brave is both creative and quiet. Everyone who is not strong or not curious is both funny and not rich and vice versa. If susan is either not curious or not brave then someone is both rich and strong and vice versa. Everyone who is either not creative or creative is not funny or not strong and vice versa. Everyone who is both not quiet and not brave is both not funny and old. If someone is brave then paul is strong and vice versa. Everyone who is both tall and quiet is generous and vice versa. If alice is either calm or curious then john is not quiet or not humble and vice versa. Everyone who is not generous or not brave is funny or not generous and vice versa. Everyone who is creative is not patient or not happy. Everyone who is both wise and not patient is either wise or not generous. Everyone who is creative or rich is not generous. Everyone who is either brave or humble is not curious or curious and vice versa. If someone is either creative or not happy then someone is calm or humble and vice versa. Susan is both not humble and kind. Someone is both not generous and not tall. Someone is either happy or not generous. Someone is either old or funny. Someone is both not humble and not strong. Lucy is patient. Someone is either not patient or not kind. Paul is both not rich and happy. | Paul is curious. | entailment | (![X]:(~rich(X)<=>(~creative(X)|curious(X))))&
(![X]:((~brave(X)<~>brave(X))=>(creative(X)&quiet(X))))&
(![X]:((~strong(X)|~curious(X))<=>(funny(X)&~rich(X))))&
(((~curious(susan)<~>~brave(susan)))<=>(?[X]:((rich(X)&strong(X)))))&
(![X]:((~creative(X)<~>creative(X))<=>(~funny(X)|~strong(X))))&
(![X]:((~quiet(X)&~brave(X))=>(~funny(X)&old(X))))&
((?[X]:(brave(X)))<=>(strong(paul)))&
(![X]:((tall(X)&quiet(X))<=>generous(X)))&
(((calm(alice)<~>curious(alice)))<=>((~quiet(john)|~humble(john))))&
(![X]:((~generous(X)|~brave(X))<=>(funny(X)|~generous(X))))&
(![X]:(creative(X)=>(~patient(X)|~happy(X))))&
(![X]:((wise(X)&~patient(X))=>(wise(X)<~>~generous(X))))&
(![X]:((creative(X)|rich(X))=>~generous(X)))&
(![X]:((brave(X)<~>humble(X))<=>(~curious(X)|curious(X))))&
((?[X]:((creative(X)<~>~happy(X))))<=>(?[X]:((calm(X)|humble(X)))))&
((~humble(susan)&kind(susan)))&
(?[X]:((~generous(X)&~tall(X))))&
(?[X]:((happy(X)<~>~generous(X))))&
(?[X]:((old(X)<~>funny(X))))&
(?[X]:((~humble(X)&~strong(X))))&
(patient(lucy))&
(?[X]:((~patient(X)<~>~kind(X))))&
((~rich(paul)&happy(paul))) | curious(paul) | [
"p0",
"p1",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 1669119767988519402887822
% SZS output start Proof for 1669119767988519402887822
1. ! [X0] : (~rich(X0) <=> (curious(X0) | ~creative(X0))) [input p0]
2. ! [X0] : ((~brave(X0) <~> brave(X0)) => (quiet(X0) & creative(X0))) [input p1]
3. ! [X0] : ((~curious(X0) | ~strong(X0)) <=> (~rich(X0) & funny(X0))) [input p2]
24. ~curious(paul) [input hypothesis]
26. ! [X0] : ((quiet(X0) & creative(X0)) | (~brave(X0) <=> brave(X0))) [ennf transformation 2]
34. ! [X0] : ((~rich(X0) | (~curious(X0) & creative(X0))) & ((curious(X0) | ~creative(X0)) | rich(X0))) [nnf transformation 1]
35. ! [X0] : ((~rich(X0) | (~curious(X0) & creative(X0))) & (curious(X0) | ~creative(X0) | rich(X0))) [flattening 34]
36. ! [X0] : ((quiet(X0) & creative(X0)) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) [nnf transformation 26]
37. ! [X0] : (((~curious(X0) | ~strong(X0)) | (rich(X0) | ~funny(X0))) & ((~rich(X0) & funny(X0)) | (curious(X0) & strong(X0)))) [nnf transformation 3]
38. ! [X0] : ((~curious(X0) | ~strong(X0) | rich(X0) | ~funny(X0)) & ((~rich(X0) & funny(X0)) | (curious(X0) & strong(X0)))) [flattening 37]
76. ~creative(X0) | curious(X0) | rich(X0) [cnf transformation 35]
78. ~curious(X0) | ~rich(X0) [cnf transformation 35]
79. creative(X0) | brave(X0) | brave(X0) [cnf transformation 36]
80. creative(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 36]
86. ~rich(X0) | curious(X0) [cnf transformation 38]
149. ~curious(paul) [cnf transformation 24]
153. creative(X0) | brave(X0) [duplicate literal removal 79]
154. ~brave(X0) | creative(X0) [duplicate literal removal 80]
158. creative(X0) [subsumption resolution 153,154]
160. ~rich(X0) [subsumption resolution 86,78]
291. curious(X0) | rich(X0) [resolution 76,158]
292. curious(X0) [subsumption resolution 291,160]
300. $false [resolution 292,149]
% SZS output end Proof for 1669119767988519402887822
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not generous then lucy is not happy or rich.
Everyone who is not quiet or rich is patient.
Everyone who is both not old and happy is both not wise and patient and vice versa.
If john is either not happy or creative then someone is not brave or not tall.
Everyone who is either not funny or not creative is either not brave or wise and vice versa.
If someone is rich or wise then someone is either not brave or not wise and vice versa.
If john is not curious then someone is wise.
If mary is both humble and kind then someone is quiet and vice versa.
Everyone who is both not quiet and not old is either old or not wise and vice versa.
Everyone who is strong or rich is kind.
Everyone who is rich or not curious is both not wise and calm.
Everyone who is both curious and kind is either not rich or brave and vice versa.
Everyone who is patient is not brave and vice versa.
If mary is kind or humble then someone is either happy or wise.
If lucy is not generous or strong then someone is both creative and curious.
If alice is both not funny and not curious then susan is generous or not quiet.
Someone is not rich.
Someone is strong.
Mary is not humble.
John is either not happy or calm.
Someone is funny.
Lucy is brave or tall.
Paul is either humble or not strong. | Lucy is kind. | entailment | ((~generous(paul))=>((~happy(lucy)|rich(lucy))))&
(![X]:((~quiet(X)|rich(X))=>patient(X)))&
(![X]:((~old(X)&happy(X))<=>(~wise(X)&patient(X))))&
(((~happy(john)<~>creative(john)))=>(?[X]:((~brave(X)|~tall(X)))))&
(![X]:((~funny(X)<~>~creative(X))<=>(~brave(X)<~>wise(X))))&
((?[X]:((rich(X)|wise(X))))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
((~curious(john))=>(?[X]:(wise(X))))&
(((humble(mary)&kind(mary)))<=>(?[X]:(quiet(X))))&
(![X]:((~quiet(X)&~old(X))<=>(old(X)<~>~wise(X))))&
(![X]:((strong(X)|rich(X))=>kind(X)))&
(![X]:((rich(X)|~curious(X))=>(~wise(X)&calm(X))))&
(![X]:((curious(X)&kind(X))<=>(~rich(X)<~>brave(X))))&
(![X]:(patient(X)<=>~brave(X)))&
(((kind(mary)|humble(mary)))=>(?[X]:((happy(X)<~>wise(X)))))&
(((~generous(lucy)|strong(lucy)))=>(?[X]:((creative(X)&curious(X)))))&
(((~funny(alice)&~curious(alice)))=>((generous(susan)|~quiet(susan))))&
(?[X]:(~rich(X)))&
(?[X]:(strong(X)))&
(~humble(mary))&
((~happy(john)<~>calm(john)))&
(?[X]:(funny(X)))&
((brave(lucy)|tall(lucy)))&
((humble(paul)<~>~strong(paul))) | kind(lucy) | [
"p1",
"p7",
"p9",
"p11",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5739938550723551534209647
% SZS output start Proof for 5739938550723551534209647
2. ! [X0] : ((rich(X0) | ~quiet(X0)) => patient(X0)) [input p1]
8. (kind(mary) & humble(mary)) <=> ? [X0] : quiet(X0) [input p7]
10. ! [X0] : ((rich(X0) | strong(X0)) => kind(X0)) [input p9]
12. ! [X0] : ((kind(X0) & curious(X0)) <=> (~rich(X0) <~> brave(X0))) [input p11]
13. ! [X0] : (patient(X0) <=> ~brave(X0)) [input p12]
19. ~humble(mary) [input p18]
24. ~kind(lucy) [input hypothesis]
29. ! [X0] : (patient(X0) | (~rich(X0) & quiet(X0))) [ennf transformation 2]
32. ! [X0] : (kind(X0) | (~rich(X0) & ~strong(X0))) [ennf transformation 10]
49. ((kind(mary) & humble(mary)) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | (~kind(mary) | ~humble(mary))) [nnf transformation 8]
50. ((kind(mary) & humble(mary)) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | ~kind(mary) | ~humble(mary)) [flattening 49]
51. ((kind(mary) & humble(mary)) | ! [X0] : ~quiet(X0)) & (? [X1] : quiet(X1) | ~kind(mary) | ~humble(mary)) [rectify 50]
52. ? [X1] : quiet(X1) => quiet(sK4) [choice axiom]
53. ((kind(mary) & humble(mary)) | ! [X0] : ~quiet(X0)) & (quiet(sK4) | ~kind(mary) | ~humble(mary)) [skolemisation 51,52]
56. ! [X0] : (((kind(X0) & curious(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~kind(X0) | ~curious(X0)))) [nnf transformation 12]
57. ! [X0] : (((kind(X0) & curious(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | ~kind(X0) | ~curious(X0))) [flattening 56]
58. ! [X0] : ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0))) [nnf transformation 13]
72. patient(X0) | quiet(X0) [cnf transformation 29]
96. humble(mary) | ~quiet(X0) [cnf transformation 53]
105. ~rich(X0) | kind(X0) [cnf transformation 32]
114. kind(X0) | brave(X0) | rich(X0) [cnf transformation 57]
116. ~brave(X0) | ~patient(X0) [cnf transformation 58]
126. ~humble(mary) [cnf transformation 19]
133. ~kind(lucy) [cnf transformation 24]
198. 15 <=> ! [X0] : ~quiet(X0) [avatar definition]
199. ~quiet(X0) <- (15) [avatar component clause 198]
206. 17 <=> humble(mary) [avatar definition]
209. 15 | 17 [avatar split clause 96,206,198]
216. kind(X0) | brave(X0) [subsumption resolution 114,105]
244. ~17 [avatar split clause 126,206]
252. 25 <=> brave(lucy) [avatar definition]
253. ~brave(lucy) <- (~25) [avatar component clause 252]
254. brave(lucy) <- (25) [avatar component clause 252]
276. ~patient(lucy) <- (25) [resolution 116,254]
285. quiet(lucy) <- (25) [resolution 276,72]
286. $false <- (15, 25) [subsumption resolution 285,199]
287. ~15 | ~25 [avatar contradiction clause 286]
298. brave(lucy) [resolution 216,133]
300. $false <- (~25) [subsumption resolution 298,253]
301. 25 [avatar contradiction clause 300]
304. $false [avatar sat refutation 209,244,287,301]
% SZS output end Proof for 5739938550723551534209647
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not generous then someone is either not rich or quiet and vice versa.
Everyone who is humble is either not rich or happy.
If someone is not rich then someone is rich or not creative.
Everyone who is not creative or rich is not quiet and vice versa.
Everyone who is tall is both not rich and patient and vice versa.
If someone is kind then someone is both not creative and strong and vice versa.
If lucy is not curious or happy then someone is happy or funny and vice versa.
Everyone who is both not tall and humble is both curious and funny.
Everyone who is either brave or wise is both creative and rich.
Everyone who is not patient or curious is old and vice versa.
Everyone who is both strong and not quiet is both creative and calm and vice versa.
If someone is not happy then lucy is either not patient or rich and vice versa.
If someone is funny then someone is either not tall or strong and vice versa.
Everyone who is either not happy or patient is both not calm and brave and vice versa.
If someone is either generous or not creative then someone is patient or not calm.
If someone is not old then someone is not patient.
Mary is not kind.
Someone is either generous or not brave.
Someone is both tall and calm.
Someone is curious or not tall.
Someone is not kind or not creative.
Someone is not wise or not quiet.
Someone is not strong or not happy.
Mary is either not generous or not curious. | Mary is curious. | neutral | (((~happy(lucy)|~generous(lucy)))<=>(?[X]:((~rich(X)<~>quiet(X)))))&
(![X]:(humble(X)=>(~rich(X)<~>happy(X))))&
((?[X]:(~rich(X)))=>(?[X]:((rich(X)|~creative(X)))))&
(![X]:((~creative(X)|rich(X))<=>~quiet(X)))&
(![X]:(tall(X)<=>(~rich(X)&patient(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~creative(X)&strong(X)))))&
(((~curious(lucy)|happy(lucy)))<=>(?[X]:((happy(X)|funny(X)))))&
(![X]:((~tall(X)&humble(X))=>(curious(X)&funny(X))))&
(![X]:((brave(X)<~>wise(X))=>(creative(X)&rich(X))))&
(![X]:((~patient(X)|curious(X))<=>old(X)))&
(![X]:((strong(X)&~quiet(X))<=>(creative(X)&calm(X))))&
((?[X]:(~happy(X)))<=>((~patient(lucy)<~>rich(lucy))))&
((?[X]:(funny(X)))<=>(?[X]:((~tall(X)<~>strong(X)))))&
(![X]:((~happy(X)<~>patient(X))<=>(~calm(X)&brave(X))))&
((?[X]:((generous(X)<~>~creative(X))))=>(?[X]:((patient(X)|~calm(X)))))&
((?[X]:(~old(X)))=>(?[X]:(~patient(X))))&
(~kind(mary))&
(?[X]:((generous(X)<~>~brave(X))))&
(?[X]:((tall(X)&calm(X))))&
(?[X]:((curious(X)|~tall(X))))&
(?[X]:((~kind(X)|~creative(X))))&
(?[X]:((~wise(X)|~quiet(X))))&
(?[X]:((~strong(X)|~happy(X))))&
((~generous(mary)<~>~curious(mary))) | curious(mary) | [] | null | 0 |
Everyone who is not happy or not curious is both patient and old and vice versa.
Everyone who is not generous or funny is not old or not strong and vice versa.
Everyone who is either happy or not brave is strong or not creative.
If someone is both happy and curious then someone is not strong or not quiet.
If someone is either curious or creative then someone is both not patient and curious.
Everyone who is not kind or old is not wise and vice versa.
If susan is funny or not happy then john is both kind and not strong.
Everyone who is not brave or not kind is patient and vice versa.
If john is calm or old then someone is either not brave or not funny and vice versa.
If someone is both not patient and not kind then someone is not rich and vice versa.
Everyone who is both not old and strong is rich or creative.
If lucy is either not curious or not humble then paul is rich.
Everyone who is both not generous and happy is both rich and not kind and vice versa.
Everyone who is either tall or funny is kind or tall and vice versa.
Everyone who is both tall and happy is either not calm or not quiet.
Everyone who is generous or funny is both strong and patient and vice versa.
Someone is not calm.
Lucy is kind.
Fred is not tall.
Someone is not wise.
John is kind or not generous.
Someone is both creative and not funny.
Someone is creative or not tall. | Lucy is not patient. | contradiction | (![X]:((~happy(X)|~curious(X))<=>(patient(X)&old(X))))&
(![X]:((~generous(X)|funny(X))<=>(~old(X)|~strong(X))))&
(![X]:((happy(X)<~>~brave(X))=>(strong(X)|~creative(X))))&
((?[X]:((happy(X)&curious(X))))=>(?[X]:((~strong(X)|~quiet(X)))))&
((?[X]:((curious(X)<~>creative(X))))=>(?[X]:((~patient(X)&curious(X)))))&
(![X]:((~kind(X)|old(X))<=>~wise(X)))&
(((funny(susan)|~happy(susan)))=>((kind(john)&~strong(john))))&
(![X]:((~brave(X)|~kind(X))<=>patient(X)))&
(((calm(john)|old(john)))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
((?[X]:((~patient(X)&~kind(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~old(X)&strong(X))=>(rich(X)|creative(X))))&
(((~curious(lucy)<~>~humble(lucy)))=>(rich(paul)))&
(![X]:((~generous(X)&happy(X))<=>(rich(X)&~kind(X))))&
(![X]:((tall(X)<~>funny(X))<=>(kind(X)|tall(X))))&
(![X]:((tall(X)&happy(X))=>(~calm(X)<~>~quiet(X))))&
(![X]:((generous(X)|funny(X))<=>(strong(X)&patient(X))))&
(?[X]:(~calm(X)))&
(kind(lucy))&
(~tall(fred))&
(?[X]:(~wise(X)))&
((kind(john)|~generous(john)))&
(?[X]:((creative(X)&~funny(X))))&
(?[X]:((creative(X)|~tall(X)))) | ~patient(lucy) | [
"p0",
"p7",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 306620705094952276831469
% SZS output start Proof for 306620705094952276831469
1. ! [X0] : ((~curious(X0) | ~happy(X0)) <=> (old(X0) & patient(X0))) [input p0]
8. ! [X0] : ((~kind(X0) | ~brave(X0)) <=> patient(X0)) [input p7]
13. ! [X0] : ((happy(X0) & ~generous(X0)) <=> (~kind(X0) & rich(X0))) [input p12]
16. ! [X0] : ((funny(X0) | generous(X0)) <=> (patient(X0) & strong(X0))) [input p15]
24. ~patient(lucy) [input hypothesis]
41. ! [X0] : (((~curious(X0) | ~happy(X0)) | (~old(X0) | ~patient(X0))) & ((old(X0) & patient(X0)) | (curious(X0) & happy(X0)))) [nnf transformation 1]
42. ! [X0] : ((~curious(X0) | ~happy(X0) | ~old(X0) | ~patient(X0)) & ((old(X0) & patient(X0)) | (curious(X0) & happy(X0)))) [flattening 41]
53. ! [X0] : (((~kind(X0) | ~brave(X0)) | ~patient(X0)) & (patient(X0) | (kind(X0) & brave(X0)))) [nnf transformation 8]
54. ! [X0] : ((~kind(X0) | ~brave(X0) | ~patient(X0)) & (patient(X0) | (kind(X0) & brave(X0)))) [flattening 53]
66. ! [X0] : (((happy(X0) & ~generous(X0)) | (kind(X0) | ~rich(X0))) & ((~kind(X0) & rich(X0)) | (~happy(X0) | generous(X0)))) [nnf transformation 13]
67. ! [X0] : (((happy(X0) & ~generous(X0)) | kind(X0) | ~rich(X0)) & ((~kind(X0) & rich(X0)) | ~happy(X0) | generous(X0))) [flattening 66]
71. ! [X0] : (((funny(X0) | generous(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~funny(X0) & ~generous(X0)))) [nnf transformation 16]
72. ! [X0] : ((funny(X0) | generous(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~funny(X0) & ~generous(X0)))) [flattening 71]
81. patient(X0) | happy(X0) [cnf transformation 42]
103. kind(X0) | patient(X0) [cnf transformation 54]
118. ~kind(X0) | ~happy(X0) | generous(X0) [cnf transformation 67]
131. ~generous(X0) | patient(X0) [cnf transformation 72]
142. ~patient(lucy) [cnf transformation 24]
316. ~happy(X0) | generous(X0) | patient(X0) [resolution 118,103]
319. generous(X0) | patient(X0) [subsumption resolution 316,81]
320. patient(X0) [subsumption resolution 319,131]
328. $false [resolution 320,142]
% SZS output end Proof for 306620705094952276831469
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not brave is either funny or not wise.
Everyone who is curious or humble is not strong.
Everyone who is either wise or generous is either happy or not patient and vice versa.
Everyone who is both not patient and strong is patient or not funny and vice versa.
Everyone who is rich is brave and vice versa.
Everyone who is brave is patient and vice versa.
Everyone who is both not old and not humble is either tall or not rich.
If alice is strong then mary is both not quiet and not patient and vice versa.
If mary is not generous or old then fred is not calm or happy and vice versa.
Everyone who is not creative is kind or calm.
If someone is generous or funny then someone is both not generous and not happy.
If paul is either funny or not funny then lucy is happy.
If mary is not quiet then someone is rich or not tall.
If someone is not brave then john is old or not humble.
Everyone who is either funny or wise is not rich or not brave.
Someone is happy or not quiet.
Someone is either old or calm.
John is either not generous or tall.
Lucy is both creative and not patient.
Someone is both not generous and kind.
Someone is either strong or funny. | Lucy is generous. | neutral | (![X]:((~patient(X)<~>~brave(X))=>(funny(X)<~>~wise(X))))&
(![X]:((curious(X)|humble(X))=>~strong(X)))&
(![X]:((wise(X)<~>generous(X))<=>(happy(X)<~>~patient(X))))&
(![X]:((~patient(X)&strong(X))<=>(patient(X)|~funny(X))))&
(![X]:(rich(X)<=>brave(X)))&
(![X]:(brave(X)<=>patient(X)))&
(![X]:((~old(X)&~humble(X))=>(tall(X)<~>~rich(X))))&
((strong(alice))<=>((~quiet(mary)&~patient(mary))))&
(((~generous(mary)|old(mary)))<=>((~calm(fred)|happy(fred))))&
(![X]:(~creative(X)=>(kind(X)|calm(X))))&
((?[X]:((generous(X)|funny(X))))=>(?[X]:((~generous(X)&~happy(X)))))&
(((funny(paul)<~>~funny(paul)))=>(happy(lucy)))&
((~quiet(mary))=>(?[X]:((rich(X)|~tall(X)))))&
((?[X]:(~brave(X)))=>((old(john)|~humble(john))))&
(![X]:((funny(X)<~>wise(X))=>(~rich(X)|~brave(X))))&
(?[X]:((happy(X)|~quiet(X))))&
(?[X]:((old(X)<~>calm(X))))&
((~generous(john)<~>tall(john)))&
((creative(lucy)&~patient(lucy)))&
(?[X]:((~generous(X)&kind(X))))&
(?[X]:((strong(X)<~>funny(X)))) | generous(lucy) | [] | null | 0 |
Everyone who is both generous and calm is creative and vice versa.
If someone is either happy or not wise then paul is not generous.
If someone is not creative or not generous then fred is either not kind or not wise and vice versa.
If mary is not tall or generous then fred is not patient and vice versa.
Everyone who is not creative is both not rich and not funny and vice versa.
If someone is not happy or not patient then mary is not old.
Everyone who is not quiet is either not generous or quiet.
Everyone who is both humble and patient is not old or creative.
If someone is both wise and brave then fred is either creative or tall.
Everyone who is either not rich or curious is either not happy or quiet and vice versa.
If paul is not happy or not funny then someone is either brave or not curious and vice versa.
Everyone who is either not rich or not creative is both brave and kind.
If paul is quiet or not generous then someone is tall or not generous and vice versa.
Everyone who is either calm or not curious is not curious and vice versa.
Everyone who is not wise or creative is both tall and calm and vice versa.
Everyone who is either not wise or not humble is both not wise and not brave and vice versa.
Alice is both not patient and not generous.
Someone is either not strong or not funny.
Someone is not patient or not quiet.
Alice is either kind or not wise.
Someone is not brave.
Someone is either rich or patient. | Mary is strong. | neutral | (![X]:((generous(X)&calm(X))<=>creative(X)))&
((?[X]:((happy(X)<~>~wise(X))))=>(~generous(paul)))&
((?[X]:((~creative(X)|~generous(X))))<=>((~kind(fred)<~>~wise(fred))))&
(((~tall(mary)|generous(mary)))<=>(~patient(fred)))&
(![X]:(~creative(X)<=>(~rich(X)&~funny(X))))&
((?[X]:((~happy(X)|~patient(X))))=>(~old(mary)))&
(![X]:(~quiet(X)=>(~generous(X)<~>quiet(X))))&
(![X]:((humble(X)&patient(X))=>(~old(X)|creative(X))))&
((?[X]:((wise(X)&brave(X))))=>((creative(fred)<~>tall(fred))))&
(![X]:((~rich(X)<~>curious(X))<=>(~happy(X)<~>quiet(X))))&
(((~happy(paul)|~funny(paul)))<=>(?[X]:((brave(X)<~>~curious(X)))))&
(![X]:((~rich(X)<~>~creative(X))=>(brave(X)&kind(X))))&
(((quiet(paul)|~generous(paul)))<=>(?[X]:((tall(X)|~generous(X)))))&
(![X]:((calm(X)<~>~curious(X))<=>~curious(X)))&
(![X]:((~wise(X)|creative(X))<=>(tall(X)&calm(X))))&
(![X]:((~wise(X)<~>~humble(X))<=>(~wise(X)&~brave(X))))&
((~patient(alice)&~generous(alice)))&
(?[X]:((~strong(X)<~>~funny(X))))&
(?[X]:((~patient(X)|~quiet(X))))&
((kind(alice)<~>~wise(alice)))&
(?[X]:(~brave(X)))&
(?[X]:((rich(X)<~>patient(X)))) | strong(mary) | [] | null | 0 |
If someone is both not patient and humble then alice is both not calm and patient.
If mary is not humble or not calm then someone is not rich or patient and vice versa.
Everyone who is both not creative and not happy is both patient and not rich and vice versa.
Everyone who is not old or curious is both not rich and not funny.
Everyone who is not patient or not wise is not curious.
If someone is not strong then someone is curious or not quiet and vice versa.
Everyone who is both brave and humble is both tall and rich.
If alice is both curious and wise then alice is either not creative or not happy.
Everyone who is not calm is creative or not happy.
If fred is either not funny or not curious then mary is rich or not quiet and vice versa.
Everyone who is not humble is not generous or brave.
Everyone who is both rich and not old is either rich or not happy and vice versa.
Everyone who is old or not rich is patient or not funny and vice versa.
If someone is both rich and not calm then someone is both not curious and curious and vice versa.
Everyone who is generous or calm is not patient or brave and vice versa.
Someone is not old.
Someone is funny.
Mary is brave or not funny.
Someone is both not kind and not patient.
Someone is either not wise or not patient.
Someone is not generous.
Susan is both not happy and tall.
Alice is humble. | Susan is funny. | neutral | ((?[X]:((~patient(X)&humble(X))))=>((~calm(alice)&patient(alice))))&
(((~humble(mary)|~calm(mary)))<=>(?[X]:((~rich(X)|patient(X)))))&
(![X]:((~creative(X)&~happy(X))<=>(patient(X)&~rich(X))))&
(![X]:((~old(X)|curious(X))=>(~rich(X)&~funny(X))))&
(![X]:((~patient(X)|~wise(X))=>~curious(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((curious(X)|~quiet(X)))))&
(![X]:((brave(X)&humble(X))=>(tall(X)&rich(X))))&
(((curious(alice)&wise(alice)))=>((~creative(alice)<~>~happy(alice))))&
(![X]:(~calm(X)=>(creative(X)|~happy(X))))&
(((~funny(fred)<~>~curious(fred)))<=>((rich(mary)|~quiet(mary))))&
(![X]:(~humble(X)=>(~generous(X)|brave(X))))&
(![X]:((rich(X)&~old(X))<=>(rich(X)<~>~happy(X))))&
(![X]:((old(X)|~rich(X))<=>(patient(X)|~funny(X))))&
((?[X]:((rich(X)&~calm(X))))<=>(?[X]:((~curious(X)&curious(X)))))&
(![X]:((generous(X)|calm(X))<=>(~patient(X)|brave(X))))&
(?[X]:(~old(X)))&
(?[X]:(funny(X)))&
((brave(mary)|~funny(mary)))&
(?[X]:((~kind(X)&~patient(X))))&
(?[X]:((~wise(X)<~>~patient(X))))&
(?[X]:(~generous(X)))&
((~happy(susan)&tall(susan)))&
(humble(alice)) | funny(susan) | [] | null | 0 |
Everyone who is either funny or not quiet is quiet.
Everyone who is strong is both not generous and not quiet and vice versa.
Everyone who is either wise or not funny is not old.
If mary is either calm or kind then alice is funny or not patient and vice versa.
Everyone who is kind or strong is both funny and rich and vice versa.
If mary is calm then someone is rich.
If someone is funny then susan is happy or tall and vice versa.
If john is calm or happy then someone is not funny.
Everyone who is either curious or patient is either wise or quiet and vice versa.
Everyone who is not creative is not patient or not old.
If susan is both not funny and not generous then someone is not brave or not funny and vice versa.
If someone is either not humble or not tall then someone is not quiet and vice versa.
If someone is either not kind or kind then susan is creative.
Everyone who is not quiet or not rich is both rich and not wise.
Everyone who is both old and quiet is both strong and kind.
Everyone who is both patient and not old is either calm or brave and vice versa.
Someone is either patient or happy.
Someone is not quiet.
Someone is brave.
Someone is both rich and tall.
Paul is not strong or not rich.
Lucy is either rich or quiet.
Paul is both not creative and brave. | Alice is funny. | neutral | (![X]:((funny(X)<~>~quiet(X))=>quiet(X)))&
(![X]:(strong(X)<=>(~generous(X)&~quiet(X))))&
(![X]:((wise(X)<~>~funny(X))=>~old(X)))&
(((calm(mary)<~>kind(mary)))<=>((funny(alice)|~patient(alice))))&
(![X]:((kind(X)|strong(X))<=>(funny(X)&rich(X))))&
((calm(mary))=>(?[X]:(rich(X))))&
((?[X]:(funny(X)))<=>((happy(susan)|tall(susan))))&
(((calm(john)|happy(john)))=>(?[X]:(~funny(X))))&
(![X]:((curious(X)<~>patient(X))<=>(wise(X)<~>quiet(X))))&
(![X]:(~creative(X)=>(~patient(X)|~old(X))))&
(((~funny(susan)&~generous(susan)))<=>(?[X]:((~brave(X)|~funny(X)))))&
((?[X]:((~humble(X)<~>~tall(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:((~kind(X)<~>kind(X))))=>(creative(susan)))&
(![X]:((~quiet(X)|~rich(X))=>(rich(X)&~wise(X))))&
(![X]:((old(X)&quiet(X))=>(strong(X)&kind(X))))&
(![X]:((patient(X)&~old(X))<=>(calm(X)<~>brave(X))))&
(?[X]:((patient(X)<~>happy(X))))&
(?[X]:(~quiet(X)))&
(?[X]:(brave(X)))&
(?[X]:((rich(X)&tall(X))))&
((~strong(paul)|~rich(paul)))&
((rich(lucy)<~>quiet(lucy)))&
((~creative(paul)&brave(paul))) | funny(alice) | [] | null | 0 |
Everyone who is both calm and not rich is not calm or funny.
Everyone who is both wise and patient is either kind or tall and vice versa.
Everyone who is both kind and old is both funny and not patient.
Everyone who is not rich or not quiet is either rich or creative and vice versa.
If mary is patient then someone is old.
Everyone who is both quiet and not calm is both brave and not creative.
If susan is not old then susan is both tall and quiet.
Everyone who is not old or not funny is both tall and not brave and vice versa.
Everyone who is both not humble and not tall is both curious and not happy and vice versa.
If someone is wise or not old then alice is either not quiet or not wise and vice versa.
If lucy is calm or not generous then someone is not humble or not funny and vice versa.
Everyone who is kind or quiet is either kind or patient and vice versa.
If alice is not kind or kind then alice is either curious or generous.
If john is either not kind or quiet then someone is both not happy and not patient.
Everyone who is not rich is not funny and vice versa.
Everyone who is both rich and not strong is both brave and not happy and vice versa.
Someone is either happy or not happy.
Someone is both tall and old.
Someone is either not brave or calm.
Someone is rich or strong.
Someone is both not humble and not generous.
John is humble.
Mary is both not rich and not generous.
Someone is both kind and quiet. | Lucy is funny. | neutral | (![X]:((calm(X)&~rich(X))=>(~calm(X)|funny(X))))&
(![X]:((wise(X)&patient(X))<=>(kind(X)<~>tall(X))))&
(![X]:((kind(X)&old(X))=>(funny(X)&~patient(X))))&
(![X]:((~rich(X)|~quiet(X))<=>(rich(X)<~>creative(X))))&
((patient(mary))=>(?[X]:(old(X))))&
(![X]:((quiet(X)&~calm(X))=>(brave(X)&~creative(X))))&
((~old(susan))=>((tall(susan)&quiet(susan))))&
(![X]:((~old(X)|~funny(X))<=>(tall(X)&~brave(X))))&
(![X]:((~humble(X)&~tall(X))<=>(curious(X)&~happy(X))))&
((?[X]:((wise(X)|~old(X))))<=>((~quiet(alice)<~>~wise(alice))))&
(((calm(lucy)|~generous(lucy)))<=>(?[X]:((~humble(X)|~funny(X)))))&
(![X]:((kind(X)|quiet(X))<=>(kind(X)<~>patient(X))))&
(((~kind(alice)|kind(alice)))=>((curious(alice)<~>generous(alice))))&
(((~kind(john)<~>quiet(john)))=>(?[X]:((~happy(X)&~patient(X)))))&
(![X]:(~rich(X)<=>~funny(X)))&
(![X]:((rich(X)&~strong(X))<=>(brave(X)&~happy(X))))&
(?[X]:((happy(X)<~>~happy(X))))&
(?[X]:((tall(X)&old(X))))&
(?[X]:((~brave(X)<~>calm(X))))&
(?[X]:((rich(X)|strong(X))))&
(?[X]:((~humble(X)&~generous(X))))&
(humble(john))&
((~rich(mary)&~generous(mary)))&
(?[X]:((kind(X)&quiet(X)))) | funny(lucy) | [] | null | 0 |
Everyone who is tall is both kind and curious.
If lucy is generous or not tall then paul is both not generous and generous.
Everyone who is either curious or not strong is both not rich and calm.
Everyone who is quiet or humble is either not brave or creative and vice versa.
Everyone who is rich or not kind is not wise or not humble and vice versa.
If susan is both funny and happy then someone is both not patient and not generous.
Everyone who is both not funny and not patient is rich or happy and vice versa.
If someone is both not wise and calm then fred is not creative or creative.
Everyone who is both brave and not happy is not calm.
Everyone who is both brave and quiet is not old and vice versa.
Everyone who is either rich or wise is both old and calm and vice versa.
If someone is both not strong and not humble then john is both not happy and happy and vice versa.
Everyone who is both creative and funny is both not quiet and not generous.
Everyone who is not old or tall is not quiet and vice versa.
If someone is either not old or kind then fred is both happy and not generous.
If someone is generous then someone is either not kind or not curious and vice versa.
Someone is both calm and not generous.
Paul is not generous.
Fred is not generous or creative.
Someone is not quiet.
Alice is not wise.
Susan is old or not wise.
Mary is not rich or not calm. | Susan is not happy. | neutral | (![X]:(tall(X)=>(kind(X)&curious(X))))&
(((generous(lucy)|~tall(lucy)))=>((~generous(paul)&generous(paul))))&
(![X]:((curious(X)<~>~strong(X))=>(~rich(X)&calm(X))))&
(![X]:((quiet(X)|humble(X))<=>(~brave(X)<~>creative(X))))&
(![X]:((rich(X)|~kind(X))<=>(~wise(X)|~humble(X))))&
(((funny(susan)&happy(susan)))=>(?[X]:((~patient(X)&~generous(X)))))&
(![X]:((~funny(X)&~patient(X))<=>(rich(X)|happy(X))))&
((?[X]:((~wise(X)&calm(X))))=>((~creative(fred)|creative(fred))))&
(![X]:((brave(X)&~happy(X))=>~calm(X)))&
(![X]:((brave(X)&quiet(X))<=>~old(X)))&
(![X]:((rich(X)<~>wise(X))<=>(old(X)&calm(X))))&
((?[X]:((~strong(X)&~humble(X))))<=>((~happy(john)&happy(john))))&
(![X]:((creative(X)&funny(X))=>(~quiet(X)&~generous(X))))&
(![X]:((~old(X)|tall(X))<=>~quiet(X)))&
((?[X]:((~old(X)<~>kind(X))))=>((happy(fred)&~generous(fred))))&
((?[X]:(generous(X)))<=>(?[X]:((~kind(X)<~>~curious(X)))))&
(?[X]:((calm(X)&~generous(X))))&
(~generous(paul))&
((~generous(fred)|creative(fred)))&
(?[X]:(~quiet(X)))&
(~wise(alice))&
((old(susan)|~wise(susan)))&
((~rich(mary)|~calm(mary))) | ~happy(susan) | [] | null | 0 |
Everyone who is either not wise or quiet is both not calm and not kind and vice versa.
Everyone who is funny or not patient is not creative or wise and vice versa.
If someone is strong then someone is not tall and vice versa.
Everyone who is not brave or not humble is either not generous or not calm and vice versa.
Everyone who is not calm is humble.
Everyone who is either quiet or not kind is both patient and not funny and vice versa.
Everyone who is either brave or old is patient and vice versa.
If someone is either old or not tall then someone is kind and vice versa.
Everyone who is either creative or curious is rich and vice versa.
If someone is both patient and not creative then someone is not curious.
Everyone who is either not curious or strong is either not rich or patient and vice versa.
Everyone who is both rich and humble is both brave and tall.
If lucy is strong then lucy is both old and calm and vice versa.
If someone is either wise or rich then someone is not generous or curious.
Everyone who is not happy or not rich is brave or kind.
Everyone who is not quiet or tall is not strong or humble and vice versa.
Someone is not brave or happy.
Alice is both strong and not wise.
Someone is either calm or generous.
Alice is not humble.
Someone is both happy and not old.
Someone is not tall.
Someone is either curious or not rich.
Paul is either happy or tall. | Alice is not generous. | entailment | (![X]:((~wise(X)<~>quiet(X))<=>(~calm(X)&~kind(X))))&
(![X]:((funny(X)|~patient(X))<=>(~creative(X)|wise(X))))&
((?[X]:(strong(X)))<=>(?[X]:(~tall(X))))&
(![X]:((~brave(X)|~humble(X))<=>(~generous(X)<~>~calm(X))))&
(![X]:(~calm(X)=>humble(X)))&
(![X]:((quiet(X)<~>~kind(X))<=>(patient(X)&~funny(X))))&
(![X]:((brave(X)<~>old(X))<=>patient(X)))&
((?[X]:((old(X)<~>~tall(X))))<=>(?[X]:(kind(X))))&
(![X]:((creative(X)<~>curious(X))<=>rich(X)))&
((?[X]:((patient(X)&~creative(X))))=>(?[X]:(~curious(X))))&
(![X]:((~curious(X)<~>strong(X))<=>(~rich(X)<~>patient(X))))&
(![X]:((rich(X)&humble(X))=>(brave(X)&tall(X))))&
((strong(lucy))<=>((old(lucy)&calm(lucy))))&
((?[X]:((wise(X)<~>rich(X))))=>(?[X]:((~generous(X)|curious(X)))))&
(![X]:((~happy(X)|~rich(X))=>(brave(X)|kind(X))))&
(![X]:((~quiet(X)|tall(X))<=>(~strong(X)|humble(X))))&
(?[X]:((~brave(X)|happy(X))))&
((strong(alice)&~wise(alice)))&
(?[X]:((calm(X)<~>generous(X))))&
(~humble(alice))&
(?[X]:((happy(X)&~old(X))))&
(?[X]:(~tall(X)))&
(?[X]:((curious(X)<~>~rich(X))))&
((happy(paul)<~>tall(paul))) | ~generous(alice) | [
"p3",
"p4",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5616498736012607584761598
% SZS output start Proof for 5616498736012607584761598
4. ! [X0] : ((~humble(X0) | ~brave(X0)) <=> (~generous(X0) <~> ~calm(X0))) [input p3]
5. ! [X0] : (~calm(X0) => humble(X0)) [input p4]
20. ~humble(alice) [input p19]
25. generous(alice) [input hypothesis]
30. ! [X0] : (humble(X0) | calm(X0)) [ennf transformation 5]
46. ! [X0] : (((~humble(X0) | ~brave(X0)) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0)))) & (((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | (humble(X0) & brave(X0)))) [nnf transformation 4]
47. ! [X0] : ((~humble(X0) | ~brave(X0) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0)))) & (((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | (humble(X0) & brave(X0)))) [flattening 46]
95. ~generous(X0) | ~calm(X0) | humble(X0) [cnf transformation 47]
100. humble(X0) | calm(X0) [cnf transformation 30]
146. ~humble(alice) [cnf transformation 20]
154. generous(alice) [cnf transformation 25]
274. calm(alice) [resolution 100,146]
309. ~calm(alice) | humble(alice) [resolution 95,154]
311. humble(alice) [subsumption resolution 309,274]
312. $false [subsumption resolution 311,146]
% SZS output end Proof for 5616498736012607584761598
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall then susan is quiet or creative.
Everyone who is both generous and not brave is either calm or not old.
If someone is not old or not generous then someone is happy.
If alice is both not kind and curious then someone is both patient and not quiet.
If lucy is creative or not strong then susan is both happy and brave.
Everyone who is generous or curious is not humble or not patient and vice versa.
Everyone who is either quiet or curious is happy or not happy.
Everyone who is both not funny and creative is generous and vice versa.
If fred is creative or funny then john is not brave or tall and vice versa.
If someone is both not brave and brave then someone is either patient or curious and vice versa.
If john is both curious and calm then someone is both not strong and not curious and vice versa.
If someone is both generous and brave then someone is curious or not curious.
Everyone who is both humble and not rich is not happy and vice versa.
Everyone who is humble is not kind and vice versa.
If someone is both old and not humble then lucy is either not brave or patient.
Everyone who is not calm or not patient is either creative or generous and vice versa.
Someone is both calm and curious.
Fred is either quiet or calm.
Someone is both not tall and not humble.
Someone is either wise or strong.
Mary is not curious or not tall.
Paul is either patient or not curious.
Someone is either not calm or rich. | John is funny. | entailment | ((~tall(paul))=>((quiet(susan)|creative(susan))))&
(![X]:((generous(X)&~brave(X))=>(calm(X)<~>~old(X))))&
((?[X]:((~old(X)|~generous(X))))=>(?[X]:(happy(X))))&
(((~kind(alice)&curious(alice)))=>(?[X]:((patient(X)&~quiet(X)))))&
(((creative(lucy)|~strong(lucy)))=>((happy(susan)&brave(susan))))&
(![X]:((generous(X)|curious(X))<=>(~humble(X)|~patient(X))))&
(![X]:((quiet(X)<~>curious(X))=>(happy(X)|~happy(X))))&
(![X]:((~funny(X)&creative(X))<=>generous(X)))&
(((creative(fred)|funny(fred)))<=>((~brave(john)|tall(john))))&
((?[X]:((~brave(X)&brave(X))))<=>(?[X]:((patient(X)<~>curious(X)))))&
(((curious(john)&calm(john)))<=>(?[X]:((~strong(X)&~curious(X)))))&
((?[X]:((generous(X)&brave(X))))=>(?[X]:((curious(X)|~curious(X)))))&
(![X]:((humble(X)&~rich(X))<=>~happy(X)))&
(![X]:(humble(X)<=>~kind(X)))&
((?[X]:((old(X)&~humble(X))))=>((~brave(lucy)<~>patient(lucy))))&
(![X]:((~calm(X)|~patient(X))<=>(creative(X)<~>generous(X))))&
(?[X]:((calm(X)&curious(X))))&
((quiet(fred)<~>calm(fred)))&
(?[X]:((~tall(X)&~humble(X))))&
(?[X]:((wise(X)<~>strong(X))))&
((~curious(mary)|~tall(mary)))&
((patient(paul)<~>~curious(paul)))&
(?[X]:((~calm(X)<~>rich(X)))) | funny(john) | [
"p5",
"p7",
"p9",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7238037374620275689584051
% SZS output start Proof for 7238037374620275689584051
6. ! [X0] : ((curious(X0) | generous(X0)) <=> (~patient(X0) | ~humble(X0))) [input p5]
8. ! [X0] : ((creative(X0) & ~funny(X0)) <=> generous(X0)) [input p7]
10. ? [X0] : (brave(X0) & ~brave(X0)) <=> ? [X0] : (patient(X0) <~> curious(X0)) [input p9]
11. (calm(john) & curious(john)) <=> ? [X0] : (~curious(X0) & ~strong(X0)) [input p10]
16. ! [X0] : ((~patient(X0) | ~calm(X0)) <=> (creative(X0) <~> generous(X0))) [input p15]
24. ~funny(john) [input hypothesis]
26. ? [X0] : (brave(X0) & ~brave(X0)) <=> ? [X1] : (patient(X1) <~> curious(X1)) [rectify 10]
46. ! [X0] : (((curious(X0) | generous(X0)) | (patient(X0) & humble(X0))) & ((~patient(X0) | ~humble(X0)) | (~curious(X0) & ~generous(X0)))) [nnf transformation 6]
47. ! [X0] : ((curious(X0) | generous(X0) | (patient(X0) & humble(X0))) & (~patient(X0) | ~humble(X0) | (~curious(X0) & ~generous(X0)))) [flattening 46]
49. ! [X0] : (((creative(X0) & ~funny(X0)) | ~generous(X0)) & (generous(X0) | (~creative(X0) | funny(X0)))) [nnf transformation 8]
50. ! [X0] : (((creative(X0) & ~funny(X0)) | ~generous(X0)) & (generous(X0) | ~creative(X0) | funny(X0))) [flattening 49]
53. (? [X0] : (brave(X0) & ~brave(X0)) | ! [X1] : ((patient(X1) | ~curious(X1)) & (curious(X1) | ~patient(X1)))) & (? [X1] : ((~curious(X1) | ~patient(X1)) & (curious(X1) | patient(X1))) | ! [X0] : (~brave(X0) | brave(X0))) [nnf transformation 26]
54. (? [X0] : (brave(X0) & ~brave(X0)) | ! [X1] : ((patient(X1) | ~curious(X1)) & (curious(X1) | ~patient(X1)))) & (? [X2] : ((~curious(X2) | ~patient(X2)) & (curious(X2) | patient(X2))) | ! [X3] : (~brave(X3) | brave(X3))) [rectify 53]
55. ? [X0] : (brave(X0) & ~brave(X0)) => (brave(sK2) & ~brave(sK2)) [choice axiom]
56. ? [X2] : ((~curious(X2) | ~patient(X2)) & (curious(X2) | patient(X2))) => ((~curious(sK3) | ~patient(sK3)) & (curious(sK3) | patient(sK3))) [choice axiom]
57. ((brave(sK2) & ~brave(sK2)) | ! [X1] : ((patient(X1) | ~curious(X1)) & (curious(X1) | ~patient(X1)))) & (((~curious(sK3) | ~patient(sK3)) & (curious(sK3) | patient(sK3))) | ! [X3] : (~brave(X3) | brave(X3))) [skolemisation 54,56,55]
58. ((calm(john) & curious(john)) | ! [X0] : (curious(X0) | strong(X0))) & (? [X0] : (~curious(X0) & ~strong(X0)) | (~calm(john) | ~curious(john))) [nnf transformation 11]
59. ((calm(john) & curious(john)) | ! [X0] : (curious(X0) | strong(X0))) & (? [X0] : (~curious(X0) & ~strong(X0)) | ~calm(john) | ~curious(john)) [flattening 58]
60. ((calm(john) & curious(john)) | ! [X0] : (curious(X0) | strong(X0))) & (? [X1] : (~curious(X1) & ~strong(X1)) | ~calm(john) | ~curious(john)) [rectify 59]
61. ? [X1] : (~curious(X1) & ~strong(X1)) => (~curious(sK4) & ~strong(sK4)) [choice axiom]
62. ((calm(john) & curious(john)) | ! [X0] : (curious(X0) | strong(X0))) & ((~curious(sK4) & ~strong(sK4)) | ~calm(john) | ~curious(john)) [skolemisation 60,61]
70. ! [X0] : (((~patient(X0) | ~calm(X0)) | ((creative(X0) | ~generous(X0)) & (generous(X0) | ~creative(X0)))) & (((~generous(X0) | ~creative(X0)) & (generous(X0) | creative(X0))) | (patient(X0) & calm(X0)))) [nnf transformation 16]
71. ! [X0] : ((~patient(X0) | ~calm(X0) | ((creative(X0) | ~generous(X0)) & (generous(X0) | ~creative(X0)))) & (((~generous(X0) | ~creative(X0)) & (generous(X0) | creative(X0))) | (patient(X0) & calm(X0)))) [flattening 70]
98. patient(X0) | generous(X0) | curious(X0) [cnf transformation 47]
101. ~creative(X0) | generous(X0) | funny(X0) [cnf transformation 50]
103. ~generous(X0) | creative(X0) [cnf transformation 50]
110. ~brave(sK2) | curious(X1) | ~patient(X1) [cnf transformation 57]
111. ~brave(sK2) | patient(X1) | ~curious(X1) [cnf transformation 57]
112. brave(sK2) | curious(X1) | ~patient(X1) [cnf transformation 57]
113. brave(sK2) | patient(X1) | ~curious(X1) [cnf transformation 57]
115. ~curious(sK4) | ~calm(john) | ~curious(john) [cnf transformation 62]
126. generous(X0) | creative(X0) | calm(X0) [cnf transformation 71]
128. ~generous(X0) | ~creative(X0) | calm(X0) [cnf transformation 71]
129. ~generous(X0) | ~creative(X0) | patient(X0) [cnf transformation 71]
145. ~funny(john) [cnf transformation 24]
230. 19 <=> ! [X1] : (patient(X1) | ~curious(X1)) [avatar definition]
231. ~curious(X1) | patient(X1) <- (19) [avatar component clause 230]
233. 20 <=> brave(sK2) [avatar definition]
236. 19 | 20 [avatar split clause 113,233,230]
238. 21 <=> ! [X1] : (curious(X1) | ~patient(X1)) [avatar definition]
239. ~patient(X1) | curious(X1) <- (21) [avatar component clause 238]
240. 21 | 20 [avatar split clause 112,233,238]
241. 19 | ~20 [avatar split clause 111,233,230]
242. 21 | ~20 [avatar split clause 110,233,238]
247. 23 <=> calm(john) [avatar definition]
248. ~calm(john) <- (~23) [avatar component clause 247]
252. 24 <=> curious(john) [avatar definition]
253. ~curious(john) <- (~24) [avatar component clause 252]
257. 25 <=> curious(sK4) [avatar definition]
259. ~curious(sK4) <- (~25) [avatar component clause 257]
260. ~24 | ~23 | ~25 [avatar split clause 115,257,247,252]
279. ~generous(X0) | patient(X0) [subsumption resolution 129,103]
280. ~generous(X0) | calm(X0) [subsumption resolution 128,103]
282. calm(X0) | creative(X0) [subsumption resolution 126,103]
384. generous(X0) | curious(X0) | curious(X0) <- (21) [resolution 98,239]
385. curious(X0) | generous(X0) <- (21) [duplicate literal removal 384]
529. generous(X2) | patient(X2) <- (19, 21) [resolution 385,231]
534. patient(X2) <- (19, 21) [subsumption resolution 529,279]
555. curious(X1) <- (19, 21) [resolution 534,239]
573. creative(john) <- (~23) [resolution 248,282]
574. generous(john) | funny(john) <- (~23) [resolution 573,101]
575. generous(john) <- (~23) [subsumption resolution 574,145]
578. calm(john) <- (~23) [resolution 575,280]
581. $false <- (~23) [subsumption resolution 578,248]
582. 23 [avatar contradiction clause 581]
583. $false <- (19, 21, ~25) [subsumption resolution 259,555]
584. ~19 | ~21 | 25 [avatar contradiction clause 583]
585. $false <- (19, 21, ~24) [subsumption resolution 253,555]
586. ~19 | ~21 | 24 [avatar contradiction clause 585]
587. $false [avatar sat refutation 236,240,241,242,260,582,584,586]
% SZS output end Proof for 7238037374620275689584051
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or wise is both not funny and not curious and vice versa.
Everyone who is not patient is not funny.
If susan is not funny then lucy is old and vice versa.
If someone is either not kind or not humble then lucy is both curious and wise and vice versa.
Everyone who is not calm or creative is old and vice versa.
If fred is either humble or not patient then susan is not strong.
If someone is quiet then someone is funny or not rich.
If mary is not calm or old then fred is not humble or old and vice versa.
If someone is not humble or happy then someone is kind or brave.
Everyone who is wise is either not humble or not strong and vice versa.
Everyone who is either not kind or not curious is patient.
If someone is either not tall or not rich then someone is tall and vice versa.
If fred is not rich or not patient then someone is both humble and curious and vice versa.
If someone is either creative or not rich then mary is both kind and not calm and vice versa.
Everyone who is either quiet or not creative is not curious.
Everyone who is either rich or curious is both humble and tall.
Someone is both brave and old.
Someone is not wise or not brave.
Someone is brave or funny.
Lucy is either brave or humble.
Fred is creative.
Paul is not humble.
Paul is either generous or not generous.
Alice is either funny or not old. | Alice is curious. | contradiction | (![X]:((~wise(X)<~>wise(X))<=>(~funny(X)&~curious(X))))&
(![X]:(~patient(X)=>~funny(X)))&
((~funny(susan))<=>(old(lucy)))&
((?[X]:((~kind(X)<~>~humble(X))))<=>((curious(lucy)&wise(lucy))))&
(![X]:((~calm(X)|creative(X))<=>old(X)))&
(((humble(fred)<~>~patient(fred)))=>(~strong(susan)))&
((?[X]:(quiet(X)))=>(?[X]:((funny(X)|~rich(X)))))&
(((~calm(mary)|old(mary)))<=>((~humble(fred)|old(fred))))&
((?[X]:((~humble(X)|happy(X))))=>(?[X]:((kind(X)|brave(X)))))&
(![X]:(wise(X)<=>(~humble(X)<~>~strong(X))))&
(![X]:((~kind(X)<~>~curious(X))=>patient(X)))&
((?[X]:((~tall(X)<~>~rich(X))))<=>(?[X]:(tall(X))))&
(((~rich(fred)|~patient(fred)))<=>(?[X]:((humble(X)&curious(X)))))&
((?[X]:((creative(X)<~>~rich(X))))<=>((kind(mary)&~calm(mary))))&
(![X]:((quiet(X)<~>~creative(X))=>~curious(X)))&
(![X]:((rich(X)<~>curious(X))=>(humble(X)&tall(X))))&
(?[X]:((brave(X)&old(X))))&
(?[X]:((~wise(X)|~brave(X))))&
(?[X]:((brave(X)|funny(X))))&
((brave(lucy)<~>humble(lucy)))&
(creative(fred))&
(~humble(paul))&
((generous(paul)<~>~generous(paul)))&
((funny(alice)<~>~old(alice))) | curious(alice) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 2940336782498697895726475
% SZS output start Proof for 2940336782498697895726475
1. ! [X0] : ((~wise(X0) <~> wise(X0)) <=> (~curious(X0) & ~funny(X0))) [input p0]
25. curious(alice) [input hypothesis]
37. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (curious(X0) | funny(X0))) & ((~curious(X0) & ~funny(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [nnf transformation 1]
38. ! [X0] : ((((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | curious(X0) | funny(X0)) & ((~curious(X0) & ~funny(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0))))) [flattening 37]
86. ~curious(X0) | wise(X0) | wise(X0) [cnf transformation 38]
87. ~curious(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 38]
149. curious(alice) [cnf transformation 25]
152. ~curious(X0) | wise(X0) [duplicate literal removal 86]
153. ~curious(X0) | ~wise(X0) [duplicate literal removal 87]
154. ~curious(X0) [subsumption resolution 152,153]
308. $false [subsumption resolution 149,154]
% SZS output end Proof for 2940336782498697895726475
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or not strong is both curious and brave and vice versa.
If someone is either not creative or old then mary is both old and strong and vice versa.
If lucy is either kind or patient then alice is strong.
If someone is either not humble or brave then someone is humble or not kind.
If john is tall or not quiet then fred is not curious or happy and vice versa.
If susan is quiet then someone is both humble and not curious.
Everyone who is both not wise and rich is both not kind and quiet.
Everyone who is not brave is creative and vice versa.
If fred is both patient and strong then lucy is humble.
If someone is not happy or not curious then susan is not curious.
Everyone who is old is both humble and creative and vice versa.
Everyone who is curious or not generous is either curious or generous.
If someone is both patient and not happy then someone is not kind or humble.
If paul is both brave and happy then someone is not quiet and vice versa.
If john is not calm then mary is both not quiet and rich and vice versa.
Everyone who is not quiet is creative.
Someone is humble or wise.
Someone is wise or generous.
Someone is not quiet.
Alice is not brave or not creative.
Someone is quiet or generous.
Someone is both not old and not creative.
Mary is both calm and not curious.
Someone is both strong and not tall. | Mary is not creative. | contradiction | (![X]:((wise(X)|~strong(X))<=>(curious(X)&brave(X))))&
((?[X]:((~creative(X)<~>old(X))))<=>((old(mary)&strong(mary))))&
(((kind(lucy)<~>patient(lucy)))=>(strong(alice)))&
((?[X]:((~humble(X)<~>brave(X))))=>(?[X]:((humble(X)|~kind(X)))))&
(((tall(john)|~quiet(john)))<=>((~curious(fred)|happy(fred))))&
((quiet(susan))=>(?[X]:((humble(X)&~curious(X)))))&
(![X]:((~wise(X)&rich(X))=>(~kind(X)&quiet(X))))&
(![X]:(~brave(X)<=>creative(X)))&
(((patient(fred)&strong(fred)))=>(humble(lucy)))&
((?[X]:((~happy(X)|~curious(X))))=>(~curious(susan)))&
(![X]:(old(X)<=>(humble(X)&creative(X))))&
(![X]:((curious(X)|~generous(X))=>(curious(X)<~>generous(X))))&
((?[X]:((patient(X)&~happy(X))))=>(?[X]:((~kind(X)|humble(X)))))&
(((brave(paul)&happy(paul)))<=>(?[X]:(~quiet(X))))&
((~calm(john))<=>((~quiet(mary)&rich(mary))))&
(![X]:(~quiet(X)=>creative(X)))&
(?[X]:((humble(X)|wise(X))))&
(?[X]:((wise(X)|generous(X))))&
(?[X]:(~quiet(X)))&
((~brave(alice)|~creative(alice)))&
(?[X]:((quiet(X)|generous(X))))&
(?[X]:((~old(X)&~creative(X))))&
((calm(mary)&~curious(mary)))&
(?[X]:((strong(X)&~tall(X)))) | ~creative(mary) | [
"p1",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7333522897820658413158801
% SZS output start Proof for 7333522897820658413158801
2. ? [X0] : (~creative(X0) <~> old(X0)) <=> (strong(mary) & old(mary)) [input p1]
11. ! [X0] : (old(X0) <=> (creative(X0) & humble(X0))) [input p10]
22. ? [X0] : (~creative(X0) & ~old(X0)) [input p21]
25. ~creative(mary) [input hypothesis]
41. (? [X0] : ((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | (~strong(mary) | ~old(mary))) & ((strong(mary) & old(mary)) | ! [X0] : ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0)))) [nnf transformation 2]
42. (? [X0] : ((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | ~strong(mary) | ~old(mary)) & ((strong(mary) & old(mary)) | ! [X0] : ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0)))) [flattening 41]
43. (? [X0] : ((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | ~strong(mary) | ~old(mary)) & ((strong(mary) & old(mary)) | ! [X1] : ((~creative(X1) | ~old(X1)) & (old(X1) | creative(X1)))) [rectify 42]
44. ? [X0] : ((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) => ((~old(sK0) | creative(sK0)) & (old(sK0) | ~creative(sK0))) [choice axiom]
45. (((~old(sK0) | creative(sK0)) & (old(sK0) | ~creative(sK0))) | ~strong(mary) | ~old(mary)) & ((strong(mary) & old(mary)) | ! [X1] : ((~creative(X1) | ~old(X1)) & (old(X1) | creative(X1)))) [skolemisation 43,44]
56. ! [X0] : ((old(X0) | (~creative(X0) | ~humble(X0))) & ((creative(X0) & humble(X0)) | ~old(X0))) [nnf transformation 11]
57. ! [X0] : ((old(X0) | ~creative(X0) | ~humble(X0)) & ((creative(X0) & humble(X0)) | ~old(X0))) [flattening 56]
77. ? [X0] : (~creative(X0) & ~old(X0)) => (~creative(sK9) & ~old(sK9)) [choice axiom]
78. ~creative(sK9) & ~old(sK9) [skolemisation 22,77]
86. old(mary) | old(X1) | creative(X1) [cnf transformation 45]
110. ~old(X0) | creative(X0) [cnf transformation 57]
130. ~creative(sK9) [cnf transformation 78]
135. ~creative(mary) [cnf transformation 25]
139. 1 <=> old(mary) [avatar definition]
140. old(mary) <- (1) [avatar component clause 139]
161. 6 <=> ! [X1] : (old(X1) | creative(X1)) [avatar definition]
162. old(X1) | creative(X1) <- (6) [avatar component clause 161]
165. 6 | 1 [avatar split clause 86,139,161]
331. creative(X1) <- (6) [subsumption resolution 162,110]
335. $false <- (6) [resolution 331,130]
338. ~6 [avatar contradiction clause 335]
354. creative(mary) <- (1) [resolution 110,140]
355. $false <- (1) [subsumption resolution 354,135]
356. ~1 [avatar contradiction clause 355]
357. $false [avatar sat refutation 165,338,356]
% SZS output end Proof for 7333522897820658413158801
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not old is both not funny and calm and vice versa.
Everyone who is both rich and not brave is either not wise or creative and vice versa.
If alice is humble then someone is either not wise or wise.
If someone is either not tall or not patient then lucy is either strong or happy and vice versa.
Everyone who is both not wise and patient is not generous.
If someone is brave then someone is either tall or not happy and vice versa.
If paul is not rich then someone is not humble and vice versa.
Everyone who is patient or not humble is not tall.
Everyone who is both strong and not patient is both not kind and not curious.
If susan is either patient or curious then someone is strong or brave.
If someone is patient or not calm then mary is either happy or humble and vice versa.
If someone is both humble and not old then someone is both wise and not old and vice versa.
If someone is happy then lucy is both not wise and curious and vice versa.
Everyone who is both strong and not patient is not wise or not calm and vice versa.
If john is either tall or not funny then someone is either tall or not humble.
Everyone who is not curious is either not brave or creative and vice versa.
Someone is either not generous or not happy.
Someone is not generous or strong.
Susan is not quiet or not strong.
Fred is either calm or wise.
Someone is patient or not strong.
Susan is both funny and not humble.
Someone is not tall or brave.
Someone is not calm. | Susan is not humble. | entailment | (![X]:((~strong(X)<~>~old(X))<=>(~funny(X)&calm(X))))&
(![X]:((rich(X)&~brave(X))<=>(~wise(X)<~>creative(X))))&
((humble(alice))=>(?[X]:((~wise(X)<~>wise(X)))))&
((?[X]:((~tall(X)<~>~patient(X))))<=>((strong(lucy)<~>happy(lucy))))&
(![X]:((~wise(X)&patient(X))=>~generous(X)))&
((?[X]:(brave(X)))<=>(?[X]:((tall(X)<~>~happy(X)))))&
((~rich(paul))<=>(?[X]:(~humble(X))))&
(![X]:((patient(X)|~humble(X))=>~tall(X)))&
(![X]:((strong(X)&~patient(X))=>(~kind(X)&~curious(X))))&
(((patient(susan)<~>curious(susan)))=>(?[X]:((strong(X)|brave(X)))))&
((?[X]:((patient(X)|~calm(X))))<=>((happy(mary)<~>humble(mary))))&
((?[X]:((humble(X)&~old(X))))<=>(?[X]:((wise(X)&~old(X)))))&
((?[X]:(happy(X)))<=>((~wise(lucy)&curious(lucy))))&
(![X]:((strong(X)&~patient(X))<=>(~wise(X)|~calm(X))))&
(((tall(john)<~>~funny(john)))=>(?[X]:((tall(X)<~>~humble(X)))))&
(![X]:(~curious(X)<=>(~brave(X)<~>creative(X))))&
(?[X]:((~generous(X)<~>~happy(X))))&
(?[X]:((~generous(X)|strong(X))))&
((~quiet(susan)|~strong(susan)))&
((calm(fred)<~>wise(fred)))&
(?[X]:((patient(X)|~strong(X))))&
((funny(susan)&~humble(susan)))&
(?[X]:((~tall(X)|brave(X))))&
(?[X]:(~calm(X))) | ~humble(susan) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 9133079254750334638994087
% SZS output start Proof for 9133079254750334638994087
22. ~humble(susan) & funny(susan) [input p21]
25. humble(susan) [input hypothesis]
160. ~humble(susan) [cnf transformation 22]
163. humble(susan) [cnf transformation 25]
387. $false [subsumption resolution 163,160]
% SZS output end Proof for 9133079254750334638994087
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is either patient or not old.
If someone is not kind then someone is either generous or not curious.
If susan is either not funny or not rich then someone is either not happy or not strong.
If someone is happy or not creative then someone is both quiet and generous and vice versa.
If mary is not creative then fred is either funny or not old and vice versa.
Everyone who is not tall or not brave is not patient and vice versa.
Everyone who is not patient is strong.
If someone is both tall and not generous then someone is not rich and vice versa.
If mary is either humble or calm then someone is both old and curious.
Everyone who is quiet is both not rich and curious.
Everyone who is tall or happy is either patient or funny.
Everyone who is strong is creative or tall.
Everyone who is not creative is either not patient or not happy and vice versa.
Everyone who is not kind or rich is happy and vice versa.
If someone is either not strong or kind then lucy is both brave and strong.
Everyone who is not old or happy is both not creative and kind and vice versa.
John is either not strong or tall.
Someone is both humble and not creative.
Susan is not old.
Someone is quiet or funny.
Someone is rich.
Someone is patient or rich.
Someone is rich or brave.
Someone is wise or not creative. | Susan is funny. | entailment | (![X]:(patient(X)=>(patient(X)<~>~old(X))))&
((?[X]:(~kind(X)))=>(?[X]:((generous(X)<~>~curious(X)))))&
(((~funny(susan)<~>~rich(susan)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
((?[X]:((happy(X)|~creative(X))))<=>(?[X]:((quiet(X)&generous(X)))))&
((~creative(mary))<=>((funny(fred)<~>~old(fred))))&
(![X]:((~tall(X)|~brave(X))<=>~patient(X)))&
(![X]:(~patient(X)=>strong(X)))&
((?[X]:((tall(X)&~generous(X))))<=>(?[X]:(~rich(X))))&
(((humble(mary)<~>calm(mary)))=>(?[X]:((old(X)&curious(X)))))&
(![X]:(quiet(X)=>(~rich(X)&curious(X))))&
(![X]:((tall(X)|happy(X))=>(patient(X)<~>funny(X))))&
(![X]:(strong(X)=>(creative(X)|tall(X))))&
(![X]:(~creative(X)<=>(~patient(X)<~>~happy(X))))&
(![X]:((~kind(X)|rich(X))<=>happy(X)))&
((?[X]:((~strong(X)<~>kind(X))))=>((brave(lucy)&strong(lucy))))&
(![X]:((~old(X)|happy(X))<=>(~creative(X)&kind(X))))&
((~strong(john)<~>tall(john)))&
(?[X]:((humble(X)&~creative(X))))&
(~old(susan))&
(?[X]:((quiet(X)|funny(X))))&
(?[X]:(rich(X)))&
(?[X]:((patient(X)|rich(X))))&
(?[X]:((rich(X)|brave(X))))&
(?[X]:((wise(X)|~creative(X)))) | funny(susan) | [
"p0",
"p10",
"p12",
"p13",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 40211907188334875938635
% SZS output start Proof for 40211907188334875938635
1. ! [X0] : (patient(X0) => (patient(X0) <~> ~old(X0))) [input p0]
11. ! [X0] : ((happy(X0) | tall(X0)) => (patient(X0) <~> funny(X0))) [input p10]
13. ! [X0] : (~creative(X0) <=> (~patient(X0) <~> ~happy(X0))) [input p12]
14. ! [X0] : ((rich(X0) | ~kind(X0)) <=> happy(X0)) [input p13]
16. ! [X0] : ((happy(X0) | ~old(X0)) <=> (kind(X0) & ~creative(X0))) [input p15]
19. ~old(susan) [input p18]
25. ~funny(susan) [input hypothesis]
30. ! [X0] : ((patient(X0) <~> ~old(X0)) | ~patient(X0)) [ennf transformation 1]
36. ! [X0] : ((patient(X0) <~> funny(X0)) | (~happy(X0) & ~tall(X0))) [ennf transformation 11]
40. ! [X0] : (((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | ~patient(X0)) [nnf transformation 30]
64. ! [X0] : (((~funny(X0) | ~patient(X0)) & (funny(X0) | patient(X0))) | (~happy(X0) & ~tall(X0))) [nnf transformation 36]
65. ! [X0] : ((~creative(X0) | ((~patient(X0) | happy(X0)) & (~happy(X0) | patient(X0)))) & (((happy(X0) | patient(X0)) & (~happy(X0) | ~patient(X0))) | creative(X0))) [nnf transformation 13]
66. ! [X0] : (((rich(X0) | ~kind(X0)) | ~happy(X0)) & (happy(X0) | (~rich(X0) & kind(X0)))) [nnf transformation 14]
67. ! [X0] : ((rich(X0) | ~kind(X0) | ~happy(X0)) & (happy(X0) | (~rich(X0) & kind(X0)))) [flattening 66]
69. ! [X0] : (((happy(X0) | ~old(X0)) | (~kind(X0) | creative(X0))) & ((kind(X0) & ~creative(X0)) | (~happy(X0) & old(X0)))) [nnf transformation 16]
70. ! [X0] : ((happy(X0) | ~old(X0) | ~kind(X0) | creative(X0)) & ((kind(X0) & ~creative(X0)) | (~happy(X0) & old(X0)))) [flattening 69]
83. old(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 40]
113. ~happy(X0) | patient(X0) | funny(X0) [cnf transformation 64]
117. ~happy(X0) | ~patient(X0) | creative(X0) [cnf transformation 65]
118. creative(X0) | patient(X0) | happy(X0) [cnf transformation 65]
121. happy(X0) | kind(X0) [cnf transformation 67]
122. ~rich(X0) | happy(X0) [cnf transformation 67]
123. ~happy(X0) | ~kind(X0) | rich(X0) [cnf transformation 67]
128. ~creative(X0) | old(X0) [cnf transformation 70]
131. kind(X0) | ~happy(X0) [cnf transformation 70]
137. ~old(susan) [cnf transformation 19]
142. ~funny(susan) [cnf transformation 25]
143. ~patient(X0) | old(X0) [duplicate literal removal 83]
145. 1 <=> ! [X1] : kind(X1) [avatar definition]
146. kind(X1) <- (1) [avatar component clause 145]
158. 4 <=> rich(susan) [avatar definition]
159. ~rich(susan) <- (~4) [avatar component clause 158]
160. rich(susan) <- (4) [avatar component clause 158]
162. 5 <=> funny(susan) [avatar definition]
164. ~funny(susan) <- (~5) [avatar component clause 162]
284. kind(X0) [subsumption resolution 131,121]
285. 1 [avatar split clause 284,145]
323. ~5 [avatar split clause 142,162]
467. patient(X1) | happy(X1) | old(X1) [resolution 118,128]
471. happy(X1) | old(X1) [subsumption resolution 467,143]
554. old(X0) | ~kind(X0) | rich(X0) [resolution 471,123]
562. rich(X0) | old(X0) <- (1) [subsumption resolution 554,146]
662. old(susan) <- (1, ~4) [resolution 562,159]
667. $false <- (1, ~4) [subsumption resolution 662,137]
668. ~1 | 4 [avatar contradiction clause 667]
669. happy(susan) <- (4) [resolution 160,122]
671. ~patient(susan) | creative(susan) <- (4) [resolution 669,117]
673. patient(susan) | funny(susan) <- (4) [resolution 669,113]
675. 63 <=> creative(susan) [avatar definition]
677. creative(susan) <- (63) [avatar component clause 675]
679. 64 <=> patient(susan) [avatar definition]
682. 63 | ~64 | ~4 [avatar split clause 671,158,679,675]
683. patient(susan) <- (4, ~5) [subsumption resolution 673,164]
684. 64 | ~4 | 5 [avatar split clause 683,162,158,679]
688. old(susan) <- (63) [resolution 677,128]
691. $false <- (63) [subsumption resolution 688,137]
692. ~63 [avatar contradiction clause 691]
693. $false [avatar sat refutation 285,323,668,682,684,692]
% SZS output end Proof for 40211907188334875938635
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either strong or not old then someone is both not tall and humble.
Everyone who is either not strong or tall is either funny or not creative.
If someone is old or not generous then lucy is not strong or not creative and vice versa.
Everyone who is calm or not kind is not calm.
Everyone who is either not curious or not happy is either not quiet or not curious.
If someone is patient or not patient then someone is not old or not curious.
Everyone who is both rich and not calm is curious or not patient.
Everyone who is strong is both not kind and not tall.
If someone is either not wise or calm then john is generous.
If someone is either not generous or happy then someone is both generous and not calm.
If someone is curious then someone is not tall or patient.
Everyone who is both old and tall is both wise and kind and vice versa.
Everyone who is both not humble and brave is creative or not humble.
If someone is not humble or not old then someone is not rich or not kind and vice versa.
Everyone who is old or not tall is both not old and not rich and vice versa.
Everyone who is not old is humble and vice versa.
Lucy is patient.
Mary is not curious or strong.
Susan is brave or not brave.
Someone is not kind.
Someone is generous.
Susan is humble or brave. | Mary is not curious. | neutral | (((strong(mary)<~>~old(mary)))=>(?[X]:((~tall(X)&humble(X)))))&
(![X]:((~strong(X)<~>tall(X))=>(funny(X)<~>~creative(X))))&
((?[X]:((old(X)|~generous(X))))<=>((~strong(lucy)|~creative(lucy))))&
(![X]:((calm(X)|~kind(X))=>~calm(X)))&
(![X]:((~curious(X)<~>~happy(X))=>(~quiet(X)<~>~curious(X))))&
((?[X]:((patient(X)|~patient(X))))=>(?[X]:((~old(X)|~curious(X)))))&
(![X]:((rich(X)&~calm(X))=>(curious(X)|~patient(X))))&
(![X]:(strong(X)=>(~kind(X)&~tall(X))))&
((?[X]:((~wise(X)<~>calm(X))))=>(generous(john)))&
((?[X]:((~generous(X)<~>happy(X))))=>(?[X]:((generous(X)&~calm(X)))))&
((?[X]:(curious(X)))=>(?[X]:((~tall(X)|patient(X)))))&
(![X]:((old(X)&tall(X))<=>(wise(X)&kind(X))))&
(![X]:((~humble(X)&brave(X))=>(creative(X)|~humble(X))))&
((?[X]:((~humble(X)|~old(X))))<=>(?[X]:((~rich(X)|~kind(X)))))&
(![X]:((old(X)|~tall(X))<=>(~old(X)&~rich(X))))&
(![X]:(~old(X)<=>humble(X)))&
(patient(lucy))&
((~curious(mary)|strong(mary)))&
((brave(susan)|~brave(susan)))&
(?[X]:(~kind(X)))&
(?[X]:(generous(X)))&
((humble(susan)|brave(susan))) | ~curious(mary) | [] | null | 0 |
Everyone who is either creative or rich is both not funny and not patient.
Everyone who is both calm and humble is funny and vice versa.
Everyone who is either strong or not curious is both humble and not patient and vice versa.
Everyone who is happy is both not calm and not strong.
Everyone who is not happy or not curious is old and vice versa.
Everyone who is either creative or not happy is not strong or patient.
If mary is happy or not wise then someone is either calm or kind.
If someone is either happy or not creative then someone is not rich and vice versa.
If mary is either not patient or happy then someone is either generous or not strong and vice versa.
Everyone who is both not creative and not quiet is kind or creative and vice versa.
Everyone who is not happy is not happy or not patient and vice versa.
If someone is both happy and not rich then paul is not strong.
Everyone who is not creative is old and vice versa.
Everyone who is not generous is strong or not quiet.
Everyone who is not creative is both humble and not calm and vice versa.
If someone is either not wise or tall then john is either tall or rich and vice versa.
Someone is either brave or creative.
Someone is either curious or not patient.
Someone is either quiet or not strong.
Someone is either strong or humble.
Susan is both not brave and not tall.
Mary is both not calm and not strong.
Mary is both old and not calm.
Someone is either tall or not quiet. | John is happy. | contradiction | (![X]:((creative(X)<~>rich(X))=>(~funny(X)&~patient(X))))&
(![X]:((calm(X)&humble(X))<=>funny(X)))&
(![X]:((strong(X)<~>~curious(X))<=>(humble(X)&~patient(X))))&
(![X]:(happy(X)=>(~calm(X)&~strong(X))))&
(![X]:((~happy(X)|~curious(X))<=>old(X)))&
(![X]:((creative(X)<~>~happy(X))=>(~strong(X)|patient(X))))&
(((happy(mary)|~wise(mary)))=>(?[X]:((calm(X)<~>kind(X)))))&
((?[X]:((happy(X)<~>~creative(X))))<=>(?[X]:(~rich(X))))&
(((~patient(mary)<~>happy(mary)))<=>(?[X]:((generous(X)<~>~strong(X)))))&
(![X]:((~creative(X)&~quiet(X))<=>(kind(X)|creative(X))))&
(![X]:(~happy(X)<=>(~happy(X)|~patient(X))))&
((?[X]:((happy(X)&~rich(X))))=>(~strong(paul)))&
(![X]:(~creative(X)<=>old(X)))&
(![X]:(~generous(X)=>(strong(X)|~quiet(X))))&
(![X]:(~creative(X)<=>(humble(X)&~calm(X))))&
((?[X]:((~wise(X)<~>tall(X))))<=>((tall(john)<~>rich(john))))&
(?[X]:((brave(X)<~>creative(X))))&
(?[X]:((curious(X)<~>~patient(X))))&
(?[X]:((quiet(X)<~>~strong(X))))&
(?[X]:((strong(X)<~>humble(X))))&
((~brave(susan)&~tall(susan)))&
((~calm(mary)&~strong(mary)))&
((old(mary)&~calm(mary)))&
(?[X]:((tall(X)<~>~quiet(X)))) | happy(john) | [
"p2",
"p3",
"p4",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2811849225053706223668550
% SZS output start Proof for 2811849225053706223668550
3. ! [X0] : ((strong(X0) <~> ~curious(X0)) <=> (~patient(X0) & humble(X0))) [input p2]
4. ! [X0] : (happy(X0) => (~strong(X0) & ~calm(X0))) [input p3]
5. ! [X0] : ((~curious(X0) | ~happy(X0)) <=> old(X0)) [input p4]
10. ! [X0] : ((~quiet(X0) & ~creative(X0)) <=> (creative(X0) | kind(X0))) [input p9]
11. ! [X0] : (~happy(X0) <=> (~patient(X0) | ~happy(X0))) [input p10]
13. ! [X0] : (~creative(X0) <=> old(X0)) [input p12]
25. happy(john) [input hypothesis]
31. ! [X0] : ((~strong(X0) & ~calm(X0)) | ~happy(X0)) [ennf transformation 4]
39. ! [X0] : ((((curious(X0) | ~strong(X0)) & (~curious(X0) | strong(X0))) | (patient(X0) | ~humble(X0))) & ((~patient(X0) & humble(X0)) | ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0))))) [nnf transformation 3]
40. ! [X0] : ((((curious(X0) | ~strong(X0)) & (~curious(X0) | strong(X0))) | patient(X0) | ~humble(X0)) & ((~patient(X0) & humble(X0)) | ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0))))) [flattening 39]
41. ! [X0] : (((~curious(X0) | ~happy(X0)) | ~old(X0)) & (old(X0) | (curious(X0) & happy(X0)))) [nnf transformation 5]
42. ! [X0] : ((~curious(X0) | ~happy(X0) | ~old(X0)) & (old(X0) | (curious(X0) & happy(X0)))) [flattening 41]
56. ! [X0] : (((~quiet(X0) & ~creative(X0)) | (~creative(X0) & ~kind(X0))) & ((creative(X0) | kind(X0)) | (quiet(X0) | creative(X0)))) [nnf transformation 10]
57. ! [X0] : (((~quiet(X0) & ~creative(X0)) | (~creative(X0) & ~kind(X0))) & (creative(X0) | kind(X0) | quiet(X0) | creative(X0))) [flattening 56]
58. ! [X0] : ((~happy(X0) | (patient(X0) & happy(X0))) & ((~patient(X0) | ~happy(X0)) | happy(X0))) [nnf transformation 11]
59. ! [X0] : ((~happy(X0) | (patient(X0) & happy(X0))) & (~patient(X0) | ~happy(X0) | happy(X0))) [flattening 58]
60. ! [X0] : ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0))) [nnf transformation 13]
90. ~patient(X0) | strong(X0) | curious(X0) [cnf transformation 40]
94. ~happy(X0) | ~strong(X0) [cnf transformation 31]
97. ~old(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 42]
118. ~creative(X0) | ~creative(X0) [cnf transformation 57]
123. ~happy(X0) | patient(X0) [cnf transformation 59]
125. old(X0) | creative(X0) [cnf transformation 60]
155. happy(john) [cnf transformation 25]
157. ~creative(X0) [duplicate literal removal 118]
239. old(X0) [subsumption resolution 125,157]
307. ~strong(john) [resolution 94,155]
308. patient(john) [resolution 123,155]
324. strong(john) | curious(john) [resolution 90,308]
325. curious(john) [subsumption resolution 324,307]
328. ~happy(X2) | ~curious(X2) [resolution 97,239]
332. ~curious(john) [resolution 328,155]
333. $false [subsumption resolution 332,325]
% SZS output end Proof for 2811849225053706223668550
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is either happy or not patient. Everyone who is not old is either patient or not kind and vice versa. If paul is not funny or strong then someone is rich or not strong. Everyone who is patient is not rich and vice versa. If someone is both not old and not rich then someone is both not old and not strong and vice versa. If lucy is strong then lucy is either tall or calm. If john is either not patient or not curious then someone is either patient or not funny and vice versa. If someone is calm then someone is either not quiet or strong. Everyone who is not old is both rich and not old. Everyone who is either not brave or not curious is not kind or not calm and vice versa. If susan is quiet or creative then someone is kind. If lucy is both not old and not kind then someone is both not wise and creative and vice versa. If someone is not rich or not creative then john is patient. Everyone who is both brave and rich is both calm and not wise. If someone is either generous or happy then john is either humble or not creative. Everyone who is not wise is both not tall and not creative and vice versa. Lucy is rich. Someone is either not quiet or not strong. John is both wise and not strong. Someone is either not rich or curious. Someone is not rich. Someone is rich. Paul is not patient. Lucy is either generous or brave. | John is happy. | entailment | (![X]:(wise(X)=>(happy(X)<~>~patient(X))))&
(![X]:(~old(X)<=>(patient(X)<~>~kind(X))))&
(((~funny(paul)|strong(paul)))=>(?[X]:((rich(X)|~strong(X)))))&
(![X]:(patient(X)<=>~rich(X)))&
((?[X]:((~old(X)&~rich(X))))<=>(?[X]:((~old(X)&~strong(X)))))&
((strong(lucy))=>((tall(lucy)<~>calm(lucy))))&
(((~patient(john)<~>~curious(john)))<=>(?[X]:((patient(X)<~>~funny(X)))))&
((?[X]:(calm(X)))=>(?[X]:((~quiet(X)<~>strong(X)))))&
(![X]:(~old(X)=>(rich(X)&~old(X))))&
(![X]:((~brave(X)<~>~curious(X))<=>(~kind(X)|~calm(X))))&
(((quiet(susan)|creative(susan)))=>(?[X]:(kind(X))))&
(((~old(lucy)&~kind(lucy)))<=>(?[X]:((~wise(X)&creative(X)))))&
((?[X]:((~rich(X)|~creative(X))))=>(patient(john)))&
(![X]:((brave(X)&rich(X))=>(calm(X)&~wise(X))))&
((?[X]:((generous(X)<~>happy(X))))=>((humble(john)<~>~creative(john))))&
(![X]:(~wise(X)<=>(~tall(X)&~creative(X))))&
(rich(lucy))&
(?[X]:((~quiet(X)<~>~strong(X))))&
((wise(john)&~strong(john)))&
(?[X]:((~rich(X)<~>curious(X))))&
(?[X]:(~rich(X)))&
(?[X]:(rich(X)))&
(~patient(paul))&
((generous(lucy)<~>brave(lucy))) | happy(john) | [
"p0",
"p12",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1924175089834916773606477
% SZS output start Proof for 1924175089834916773606477
1. ! [X0] : (wise(X0) => (happy(X0) <~> ~patient(X0))) [input p0]
13. ? [X0] : (~creative(X0) | ~rich(X0)) => patient(john) [input p12]
19. ~strong(john) & wise(john) [input p18]
21. ? [X0] : ~rich(X0) [input p20]
25. ~happy(john) [input hypothesis]
28. ! [X0] : ((happy(X0) <~> ~patient(X0)) | ~wise(X0)) [ennf transformation 1]
34. patient(john) | ! [X0] : (creative(X0) & rich(X0)) [ennf transformation 13]
38. ! [X0] : (((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | ~wise(X0)) [nnf transformation 28]
75. ? [X0] : ~rich(X0) => ~rich(sK9) [choice axiom]
76. ~rich(sK9) [skolemisation 21,75]
80. ~patient(X0) | happy(X0) | ~wise(X0) [cnf transformation 38]
120. patient(john) | rich(X0) [cnf transformation 34]
134. wise(john) [cnf transformation 19]
138. ~rich(sK9) [cnf transformation 76]
143. ~happy(john) [cnf transformation 25]
206. 15 <=> patient(john) [avatar definition]
208. patient(john) <- (15) [avatar component clause 206]
288. 32 <=> ! [X0] : rich(X0) [avatar definition]
289. rich(X0) <- (32) [avatar component clause 288]
290. 32 | 15 [avatar split clause 120,206,288]
360. happy(john) | ~wise(john) <- (15) [resolution 80,208]
363. ~wise(john) <- (15) [subsumption resolution 360,143]
364. $false <- (15) [subsumption resolution 363,134]
365. ~15 [avatar contradiction clause 364]
391. $false <- (32) [resolution 289,138]
392. ~32 [avatar contradiction clause 391]
394. $false [avatar sat refutation 290,365,392]
% SZS output end Proof for 1924175089834916773606477
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is calm.
If someone is brave then alice is not creative or patient and vice versa.
If paul is funny or generous then paul is not wise or not patient.
Everyone who is both not wise and creative is not wise and vice versa.
Everyone who is quiet is humble and vice versa.
Everyone who is not tall or curious is both not old and not kind and vice versa.
If paul is not strong then someone is creative and vice versa.
Everyone who is humble or not quiet is both not old and tall and vice versa.
If mary is not creative or curious then paul is tall or wise and vice versa.
Everyone who is either not funny or quiet is either quiet or not wise and vice versa.
Everyone who is not old or not strong is tall.
Everyone who is rich is not kind.
Everyone who is either curious or not creative is old and vice versa.
Everyone who is either not calm or not curious is strong or not kind.
If mary is not curious or not rich then john is not calm and vice versa.
If someone is either not rich or brave then alice is not calm and vice versa.
Someone is either not happy or not creative.
Alice is rich.
John is either not humble or kind.
Someone is both patient and not calm.
Someone is calm.
Someone is either kind or not happy.
Someone is either calm or not happy.
Someone is patient or not old. | Mary is not creative. | entailment | (![X]:(~humble(X)=>calm(X)))&
((?[X]:(brave(X)))<=>((~creative(alice)|patient(alice))))&
(((funny(paul)|generous(paul)))=>((~wise(paul)|~patient(paul))))&
(![X]:((~wise(X)&creative(X))<=>~wise(X)))&
(![X]:(quiet(X)<=>humble(X)))&
(![X]:((~tall(X)|curious(X))<=>(~old(X)&~kind(X))))&
((~strong(paul))<=>(?[X]:(creative(X))))&
(![X]:((humble(X)|~quiet(X))<=>(~old(X)&tall(X))))&
(((~creative(mary)|curious(mary)))<=>((tall(paul)|wise(paul))))&
(![X]:((~funny(X)<~>quiet(X))<=>(quiet(X)<~>~wise(X))))&
(![X]:((~old(X)|~strong(X))=>tall(X)))&
(![X]:(rich(X)=>~kind(X)))&
(![X]:((curious(X)<~>~creative(X))<=>old(X)))&
(![X]:((~calm(X)<~>~curious(X))=>(strong(X)|~kind(X))))&
(((~curious(mary)|~rich(mary)))<=>(~calm(john)))&
((?[X]:((~rich(X)<~>brave(X))))<=>(~calm(alice)))&
(?[X]:((~happy(X)<~>~creative(X))))&
(rich(alice))&
((~humble(john)<~>kind(john)))&
(?[X]:((patient(X)&~calm(X))))&
(?[X]:(calm(X)))&
(?[X]:((kind(X)<~>~happy(X))))&
(?[X]:((calm(X)<~>~happy(X))))&
(?[X]:((patient(X)|~old(X)))) | ~creative(mary) | [
"p5",
"p8",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7507331804039900931221626
% SZS output start Proof for 7507331804039900931221626
6. ! [X0] : ((curious(X0) | ~tall(X0)) <=> (~kind(X0) & ~old(X0))) [input p5]
9. (curious(mary) | ~creative(mary)) <=> (wise(paul) | tall(paul)) [input p8]
11. ! [X0] : ((~strong(X0) | ~old(X0)) => tall(X0)) [input p10]
13. ! [X0] : ((curious(X0) <~> ~creative(X0)) <=> old(X0)) [input p12]
25. creative(mary) [input hypothesis]
30. ! [X0] : (tall(X0) | (strong(X0) & old(X0))) [ennf transformation 11]
42. ! [X0] : (((curious(X0) | ~tall(X0)) | (kind(X0) | old(X0))) & ((~kind(X0) & ~old(X0)) | (~curious(X0) & tall(X0)))) [nnf transformation 6]
43. ! [X0] : ((curious(X0) | ~tall(X0) | kind(X0) | old(X0)) & ((~kind(X0) & ~old(X0)) | (~curious(X0) & tall(X0)))) [flattening 42]
50. ((curious(mary) | ~creative(mary)) | (~wise(paul) & ~tall(paul))) & ((wise(paul) | tall(paul)) | (~curious(mary) & creative(mary))) [nnf transformation 9]
51. (curious(mary) | ~creative(mary) | (~wise(paul) & ~tall(paul))) & (wise(paul) | tall(paul) | (~curious(mary) & creative(mary))) [flattening 50]
53. ! [X0] : ((((creative(X0) | ~curious(X0)) & (~creative(X0) | curious(X0))) | ~old(X0)) & (old(X0) | ((curious(X0) | creative(X0)) & (~creative(X0) | ~curious(X0))))) [nnf transformation 13]
87. ~old(X0) | tall(X0) [cnf transformation 43]
88. ~old(X0) | ~curious(X0) [cnf transformation 43]
101. curious(mary) | ~creative(mary) | ~tall(paul) [cnf transformation 51]
111. tall(X0) | old(X0) [cnf transformation 30]
114. old(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 53]
140. creative(mary) [cnf transformation 25]
190. 11 <=> creative(mary) [avatar definition]
191. creative(mary) <- (11) [avatar component clause 190]
194. 12 <=> curious(mary) [avatar definition]
196. curious(mary) <- (12) [avatar component clause 194]
199. 13 <=> tall(paul) [avatar definition]
201. ~tall(paul) <- (~13) [avatar component clause 199]
202. ~13 | ~11 | 12 [avatar split clause 101,194,190,199]
207. tall(X0) [subsumption resolution 111,87]
209. ~curious(X0) | ~creative(X0) [subsumption resolution 114,88]
293. 11 [avatar split clause 140,190]
294. $false <- (~13) [subsumption resolution 201,207]
295. 13 [avatar contradiction clause 294]
318. ~creative(mary) <- (12) [resolution 209,196]
319. $false <- (11, 12) [subsumption resolution 318,191]
320. ~11 | ~12 [avatar contradiction clause 319]
321. $false [avatar sat refutation 202,293,295,320]
% SZS output end Proof for 7507331804039900931221626
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is either not curious or not generous then alice is either brave or not generous and vice versa.
If mary is either not curious or not old then john is not quiet or humble and vice versa.
If fred is not old or not curious then someone is both not humble and patient and vice versa.
If someone is both not kind and calm then paul is either calm or strong.
Everyone who is either tall or not old is both not generous and creative and vice versa.
Everyone who is not happy or not funny is both kind and creative.
Everyone who is either humble or not funny is either not humble or humble and vice versa.
If someone is not rich or not old then fred is both not brave and strong and vice versa.
Everyone who is kind or quiet is both quiet and not rich.
Everyone who is not brave is generous.
If john is both not brave and not tall then susan is both not happy and creative.
If susan is both not calm and not old then susan is both strong and rich.
If lucy is both not generous and not funny then someone is either not happy or not wise and vice versa.
Everyone who is either happy or not tall is humble or not humble and vice versa.
Everyone who is both quiet and not funny is either not humble or not rich.
If someone is either quiet or not rich then someone is both humble and not patient.
Paul is either not tall or not funny.
Someone is not funny or quiet.
Paul is either not funny or patient.
Mary is both not patient and not rich.
John is not brave or not calm.
John is either brave or not old.
Someone is humble or rich.
Mary is either not generous or brave. | Fred is kind. | entailment | (((~curious(alice)<~>~generous(alice)))<=>((brave(alice)<~>~generous(alice))))&
(((~curious(mary)<~>~old(mary)))<=>((~quiet(john)|humble(john))))&
(((~old(fred)|~curious(fred)))<=>(?[X]:((~humble(X)&patient(X)))))&
((?[X]:((~kind(X)&calm(X))))=>((calm(paul)<~>strong(paul))))&
(![X]:((tall(X)<~>~old(X))<=>(~generous(X)&creative(X))))&
(![X]:((~happy(X)|~funny(X))=>(kind(X)&creative(X))))&
(![X]:((humble(X)<~>~funny(X))<=>(~humble(X)<~>humble(X))))&
((?[X]:((~rich(X)|~old(X))))<=>((~brave(fred)&strong(fred))))&
(![X]:((kind(X)|quiet(X))=>(quiet(X)&~rich(X))))&
(![X]:(~brave(X)=>generous(X)))&
(((~brave(john)&~tall(john)))=>((~happy(susan)&creative(susan))))&
(((~calm(susan)&~old(susan)))=>((strong(susan)&rich(susan))))&
(((~generous(lucy)&~funny(lucy)))<=>(?[X]:((~happy(X)<~>~wise(X)))))&
(![X]:((happy(X)<~>~tall(X))<=>(humble(X)|~humble(X))))&
(![X]:((quiet(X)&~funny(X))=>(~humble(X)<~>~rich(X))))&
((?[X]:((quiet(X)<~>~rich(X))))=>(?[X]:((humble(X)&~patient(X)))))&
((~tall(paul)<~>~funny(paul)))&
(?[X]:((~funny(X)|quiet(X))))&
((~funny(paul)<~>patient(paul)))&
((~patient(mary)&~rich(mary)))&
((~brave(john)|~calm(john)))&
((brave(john)<~>~old(john)))&
(?[X]:((humble(X)|rich(X))))&
((~generous(mary)<~>brave(mary))) | kind(fred) | [
"p2",
"p4",
"p5",
"p6",
"p7",
"p8",
"p9",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2231297891318661366856144
% SZS output start Proof for 2231297891318661366856144
3. (~curious(fred) | ~old(fred)) <=> ? [X0] : (patient(X0) & ~humble(X0)) [input p2]
5. ! [X0] : ((tall(X0) <~> ~old(X0)) <=> (creative(X0) & ~generous(X0))) [input p4]
6. ! [X0] : ((~funny(X0) | ~happy(X0)) => (creative(X0) & kind(X0))) [input p5]
7. ! [X0] : ((humble(X0) <~> ~funny(X0)) <=> (~humble(X0) <~> humble(X0))) [input p6]
8. ? [X0] : (~old(X0) | ~rich(X0)) <=> (strong(fred) & ~brave(fred)) [input p7]
9. ! [X0] : ((quiet(X0) | kind(X0)) => (~rich(X0) & quiet(X0))) [input p8]
10. ! [X0] : (~brave(X0) => generous(X0)) [input p9]
14. ! [X0] : ((happy(X0) <~> ~tall(X0)) <=> (~humble(X0) | humble(X0))) [input p13]
15. ! [X0] : ((~funny(X0) & quiet(X0)) => (~humble(X0) <~> ~rich(X0))) [input p14]
20. ~rich(mary) & ~patient(mary) [input p19]
25. ~kind(fred) [input hypothesis]
28. ! [X0] : ((creative(X0) & kind(X0)) | (funny(X0) & happy(X0))) [ennf transformation 6]
29. ! [X0] : ((~rich(X0) & quiet(X0)) | (~quiet(X0) & ~kind(X0))) [ennf transformation 9]
30. ! [X0] : (generous(X0) | brave(X0)) [ennf transformation 10]
35. ! [X0] : ((~humble(X0) <~> ~rich(X0)) | (funny(X0) | ~quiet(X0))) [ennf transformation 15]
36. ! [X0] : ((~humble(X0) <~> ~rich(X0)) | funny(X0) | ~quiet(X0)) [flattening 35]
41. ((~curious(fred) | ~old(fred)) | ! [X0] : (~patient(X0) | humble(X0))) & (? [X0] : (patient(X0) & ~humble(X0)) | (curious(fred) & old(fred))) [nnf transformation 3]
42. (~curious(fred) | ~old(fred) | ! [X0] : (~patient(X0) | humble(X0))) & (? [X0] : (patient(X0) & ~humble(X0)) | (curious(fred) & old(fred))) [flattening 41]
43. (~curious(fred) | ~old(fred) | ! [X0] : (~patient(X0) | humble(X0))) & (? [X1] : (patient(X1) & ~humble(X1)) | (curious(fred) & old(fred))) [rectify 42]
44. ? [X1] : (patient(X1) & ~humble(X1)) => (patient(sK0) & ~humble(sK0)) [choice axiom]
45. (~curious(fred) | ~old(fred) | ! [X0] : (~patient(X0) | humble(X0))) & ((patient(sK0) & ~humble(sK0)) | (curious(fred) & old(fred))) [skolemisation 43,44]
47. ! [X0] : ((((old(X0) | ~tall(X0)) & (~old(X0) | tall(X0))) | (~creative(X0) | generous(X0))) & ((creative(X0) & ~generous(X0)) | ((tall(X0) | old(X0)) & (~old(X0) | ~tall(X0))))) [nnf transformation 5]
48. ! [X0] : ((((old(X0) | ~tall(X0)) & (~old(X0) | tall(X0))) | ~creative(X0) | generous(X0)) & ((creative(X0) & ~generous(X0)) | ((tall(X0) | old(X0)) & (~old(X0) | ~tall(X0))))) [flattening 47]
49. ! [X0] : ((((funny(X0) | ~humble(X0)) & (~funny(X0) | humble(X0))) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) & (((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | ((humble(X0) | funny(X0)) & (~funny(X0) | ~humble(X0))))) [nnf transformation 7]
50. (? [X0] : (~old(X0) | ~rich(X0)) | (~strong(fred) | brave(fred))) & ((strong(fred) & ~brave(fred)) | ! [X0] : (old(X0) & rich(X0))) [nnf transformation 8]
51. (? [X0] : (~old(X0) | ~rich(X0)) | ~strong(fred) | brave(fred)) & ((strong(fred) & ~brave(fred)) | ! [X0] : (old(X0) & rich(X0))) [flattening 50]
52. (? [X0] : (~old(X0) | ~rich(X0)) | ~strong(fred) | brave(fred)) & ((strong(fred) & ~brave(fred)) | ! [X1] : (old(X1) & rich(X1))) [rectify 51]
53. ? [X0] : (~old(X0) | ~rich(X0)) => (~old(sK1) | ~rich(sK1)) [choice axiom]
54. ((~old(sK1) | ~rich(sK1)) | ~strong(fred) | brave(fred)) & ((strong(fred) & ~brave(fred)) | ! [X1] : (old(X1) & rich(X1))) [skolemisation 52,53]
60. ! [X0] : ((((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | (humble(X0) & ~humble(X0))) & ((~humble(X0) | humble(X0)) | ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0))))) [nnf transformation 14]
61. ! [X0] : ((((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | (humble(X0) & ~humble(X0))) & (~humble(X0) | humble(X0) | ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0))))) [flattening 60]
62. ! [X0] : (((rich(X0) | humble(X0)) & (~rich(X0) | ~humble(X0))) | funny(X0) | ~quiet(X0)) [nnf transformation 36]
89. ~humble(sK0) | old(fred) [cnf transformation 45]
96. ~tall(X0) | ~old(X0) | ~generous(X0) [cnf transformation 48]
102. happy(X0) | kind(X0) [cnf transformation 28]
103. funny(X0) | kind(X0) [cnf transformation 28]
110. ~funny(X0) | humble(X0) | humble(X0) | humble(X0) [cnf transformation 49]
113. funny(X0) | ~humble(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 49]
114. ~brave(fred) | rich(X1) [cnf transformation 54]
119. ~kind(X0) | quiet(X0) [cnf transformation 29]
122. ~rich(X0) | ~quiet(X0) [cnf transformation 29]
123. brave(X0) | generous(X0) [cnf transformation 30]
138. tall(X0) | ~happy(X0) | ~humble(X0) [cnf transformation 61]
139. ~happy(X0) | tall(X0) | humble(X0) [cnf transformation 61]
141. rich(X0) | humble(X0) | funny(X0) | ~quiet(X0) [cnf transformation 62]
152. ~rich(mary) [cnf transformation 20]
159. ~kind(fred) [cnf transformation 25]
164. ~funny(X0) | humble(X0) [duplicate literal removal 110]
167. ~humble(X0) | funny(X0) [duplicate literal removal 113]
214. 9 <=> old(fred) [avatar definition]
215. old(fred) <- (9) [avatar component clause 214]
229. 12 <=> humble(sK0) [avatar definition]
231. ~humble(sK0) <- (~12) [avatar component clause 229]
233. 9 | ~12 [avatar split clause 89,229,214]
248. 16 <=> brave(fred) [avatar definition]
249. ~brave(fred) <- (~16) [avatar component clause 248]
269. 21 <=> ! [X1] : rich(X1) [avatar definition]
270. rich(X1) <- (21) [avatar component clause 269]
273. 21 | ~16 [avatar split clause 114,248,269]
338. ~happy(X0) | tall(X0) [subsumption resolution 138,139]
340. humble(X0) | funny(X0) | ~quiet(X0) [subsumption resolution 141,122]
341. ~quiet(X0) | funny(X0) [subsumption resolution 340,167]
410. generous(fred) <- (~16) [resolution 123,249]
415. kind(X1) | humble(X1) [resolution 164,103]
424. tall(X1) | kind(X1) [resolution 338,102]
486. humble(X0) | quiet(X0) [resolution 415,119]
498. ~old(X2) | kind(X2) | ~generous(X2) [resolution 424,96]
502. quiet(X0) | funny(X0) [resolution 486,167]
503. funny(X0) [subsumption resolution 502,341]
509. humble(X0) [resolution 503,164]
510. kind(fred) | ~generous(fred) <- (9) [resolution 498,215]
511. ~generous(fred) <- (9) [subsumption resolution 510,159]
512. $false <- (9, ~16) [subsumption resolution 511,410]
513. ~9 | 16 [avatar contradiction clause 512]
519. $false <- (~12) [subsumption resolution 231,509]
520. 12 [avatar contradiction clause 519]
531. $false <- (21) [resolution 270,152]
536. ~21 [avatar contradiction clause 531]
537. $false [avatar sat refutation 233,273,513,520,536]
% SZS output end Proof for 2231297891318661366856144
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not humble or not brave then fred is brave and vice versa.
Everyone who is either not patient or not generous is not strong or not funny and vice versa.
If someone is generous then paul is both not generous and not kind and vice versa.
If someone is either not tall or happy then fred is not patient and vice versa.
Everyone who is wise or kind is brave.
Everyone who is brave is either not generous or humble and vice versa.
Everyone who is either not calm or not curious is generous or not strong and vice versa.
Everyone who is either quiet or curious is both curious and happy and vice versa.
Everyone who is creative or not wise is brave.
Everyone who is not strong or not generous is strong and vice versa.
If someone is both not wise and not generous then susan is either not rich or not kind and vice versa.
Everyone who is patient is not generous or not wise.
If someone is both generous and not funny then someone is curious and vice versa.
If someone is both not old and curious then fred is either not kind or quiet.
If paul is both not generous and not humble then john is funny.
Everyone who is either not humble or not wise is either not old or generous and vice versa.
Alice is strong or curious.
Susan is not happy or happy.
Someone is not patient or not generous.
Lucy is not curious or not calm.
Someone is both not calm and creative.
Susan is not kind or curious. | Paul is not brave. | contradiction | ((?[X]:((~humble(X)<~>~brave(X))))<=>(brave(fred)))&
(![X]:((~patient(X)<~>~generous(X))<=>(~strong(X)|~funny(X))))&
((?[X]:(generous(X)))<=>((~generous(paul)&~kind(paul))))&
((?[X]:((~tall(X)<~>happy(X))))<=>(~patient(fred)))&
(![X]:((wise(X)|kind(X))=>brave(X)))&
(![X]:(brave(X)<=>(~generous(X)<~>humble(X))))&
(![X]:((~calm(X)<~>~curious(X))<=>(generous(X)|~strong(X))))&
(![X]:((quiet(X)<~>curious(X))<=>(curious(X)&happy(X))))&
(![X]:((creative(X)|~wise(X))=>brave(X)))&
(![X]:((~strong(X)|~generous(X))<=>strong(X)))&
((?[X]:((~wise(X)&~generous(X))))<=>((~rich(susan)<~>~kind(susan))))&
(![X]:(patient(X)=>(~generous(X)|~wise(X))))&
((?[X]:((generous(X)&~funny(X))))<=>(?[X]:(curious(X))))&
((?[X]:((~old(X)&curious(X))))=>((~kind(fred)<~>quiet(fred))))&
(((~generous(paul)&~humble(paul)))=>(funny(john)))&
(![X]:((~humble(X)<~>~wise(X))<=>(~old(X)<~>generous(X))))&
((strong(alice)|curious(alice)))&
((~happy(susan)|happy(susan)))&
(?[X]:((~patient(X)|~generous(X))))&
((~curious(lucy)|~calm(lucy)))&
(?[X]:((~calm(X)&creative(X))))&
((~kind(susan)|curious(susan))) | ~brave(paul) | [
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2109310206601564142759876
% SZS output start Proof for 2109310206601564142759876
5. ! [X0] : ((kind(X0) | wise(X0)) => brave(X0)) [input p4]
9. ! [X0] : ((~wise(X0) | creative(X0)) => brave(X0)) [input p8]
23. ~brave(paul) [input hypothesis]
25. ! [X0] : (brave(X0) | (~kind(X0) & ~wise(X0))) [ennf transformation 5]
26. ! [X0] : (brave(X0) | (wise(X0) & ~creative(X0))) [ennf transformation 9]
86. brave(X0) | ~wise(X0) [cnf transformation 25]
105. brave(X0) | wise(X0) [cnf transformation 26]
137. ~brave(paul) [cnf transformation 23]
204. brave(X0) [subsumption resolution 105,86]
296. $false [subsumption resolution 137,204]
% SZS output end Proof for 2109310206601564142759876
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either funny or quiet is both not rich and curious.
If susan is old then someone is both not patient and not rich and vice versa.
Everyone who is not happy or not strong is either not funny or quiet and vice versa.
Everyone who is either generous or not old is both not calm and generous and vice versa.
Everyone who is not tall is tall.
If fred is both old and not strong then alice is either wise or not kind.
Everyone who is wise or not wise is not tall or old.
If someone is both calm and happy then john is both not happy and not kind and vice versa.
If mary is either curious or not patient then someone is not rich or strong and vice versa.
Everyone who is not brave is either wise or creative and vice versa.
If someone is not generous or strong then paul is patient and vice versa.
If someone is either not strong or not rich then someone is both brave and curious and vice versa.
If someone is both not generous and happy then someone is both quiet and old.
Everyone who is both not old and not calm is old or not kind.
If someone is either not old or not curious then john is both humble and not wise and vice versa.
Everyone who is calm or curious is either happy or not brave.
Someone is tall.
Alice is strong or not calm.
Someone is both curious and not wise.
Fred is either not patient or funny.
Someone is both not patient and not kind.
Mary is either strong or humble.
Someone is both not brave and kind. | Paul is not humble. | neutral | (![X]:((funny(X)<~>quiet(X))=>(~rich(X)&curious(X))))&
((old(susan))<=>(?[X]:((~patient(X)&~rich(X)))))&
(![X]:((~happy(X)|~strong(X))<=>(~funny(X)<~>quiet(X))))&
(![X]:((generous(X)<~>~old(X))<=>(~calm(X)&generous(X))))&
(![X]:(~tall(X)=>tall(X)))&
(((old(fred)&~strong(fred)))=>((wise(alice)<~>~kind(alice))))&
(![X]:((wise(X)|~wise(X))=>(~tall(X)|old(X))))&
((?[X]:((calm(X)&happy(X))))<=>((~happy(john)&~kind(john))))&
(((curious(mary)<~>~patient(mary)))<=>(?[X]:((~rich(X)|strong(X)))))&
(![X]:(~brave(X)<=>(wise(X)<~>creative(X))))&
((?[X]:((~generous(X)|strong(X))))<=>(patient(paul)))&
((?[X]:((~strong(X)<~>~rich(X))))<=>(?[X]:((brave(X)&curious(X)))))&
((?[X]:((~generous(X)&happy(X))))=>(?[X]:((quiet(X)&old(X)))))&
(![X]:((~old(X)&~calm(X))=>(old(X)|~kind(X))))&
((?[X]:((~old(X)<~>~curious(X))))<=>((humble(john)&~wise(john))))&
(![X]:((calm(X)|curious(X))=>(happy(X)<~>~brave(X))))&
(?[X]:(tall(X)))&
((strong(alice)|~calm(alice)))&
(?[X]:((curious(X)&~wise(X))))&
((~patient(fred)<~>funny(fred)))&
(?[X]:((~patient(X)&~kind(X))))&
((strong(mary)<~>humble(mary)))&
(?[X]:((~brave(X)&kind(X)))) | ~humble(paul) | [] | null | 0 |
If mary is funny then someone is not kind and vice versa.
Everyone who is kind or not quiet is both tall and creative and vice versa.
Everyone who is either calm or not funny is both generous and not wise and vice versa.
Everyone who is quiet or happy is both wise and generous and vice versa.
Everyone who is both generous and not quiet is either not kind or generous.
If someone is not patient or not strong then mary is either happy or not wise.
Everyone who is either strong or rich is both not brave and strong.
If lucy is either funny or not brave then fred is not funny or not creative and vice versa.
Everyone who is strong is both brave and not tall and vice versa.
If someone is curious or not old then someone is either not funny or rich and vice versa.
If someone is either patient or generous then lucy is brave and vice versa.
If susan is creative or not quiet then john is not kind and vice versa.
If mary is not creative then someone is not patient.
Everyone who is either strong or not brave is not patient.
Everyone who is either patient or not brave is rich and vice versa.
Everyone who is both not quiet and not happy is not happy and vice versa.
Fred is generous.
Lucy is not kind or creative.
Lucy is not strong or creative.
Someone is either not happy or old.
John is either not generous or old.
Someone is either kind or not happy.
Someone is calm or rich.
Fred is not patient or not strong. | Mary is happy. | neutral | ((funny(mary))<=>(?[X]:(~kind(X))))&
(![X]:((kind(X)|~quiet(X))<=>(tall(X)&creative(X))))&
(![X]:((calm(X)<~>~funny(X))<=>(generous(X)&~wise(X))))&
(![X]:((quiet(X)|happy(X))<=>(wise(X)&generous(X))))&
(![X]:((generous(X)&~quiet(X))=>(~kind(X)<~>generous(X))))&
((?[X]:((~patient(X)|~strong(X))))=>((happy(mary)<~>~wise(mary))))&
(![X]:((strong(X)<~>rich(X))=>(~brave(X)&strong(X))))&
(((funny(lucy)<~>~brave(lucy)))<=>((~funny(fred)|~creative(fred))))&
(![X]:(strong(X)<=>(brave(X)&~tall(X))))&
((?[X]:((curious(X)|~old(X))))<=>(?[X]:((~funny(X)<~>rich(X)))))&
((?[X]:((patient(X)<~>generous(X))))<=>(brave(lucy)))&
(((creative(susan)|~quiet(susan)))<=>(~kind(john)))&
((~creative(mary))=>(?[X]:(~patient(X))))&
(![X]:((strong(X)<~>~brave(X))=>~patient(X)))&
(![X]:((patient(X)<~>~brave(X))<=>rich(X)))&
(![X]:((~quiet(X)&~happy(X))<=>~happy(X)))&
(generous(fred))&
((~kind(lucy)|creative(lucy)))&
((~strong(lucy)|creative(lucy)))&
(?[X]:((~happy(X)<~>old(X))))&
((~generous(john)<~>old(john)))&
(?[X]:((kind(X)<~>~happy(X))))&
(?[X]:((calm(X)|rich(X))))&
((~patient(fred)|~strong(fred))) | happy(mary) | [] | null | 0 |
If fred is either rich or not tall then mary is generous. If someone is not kind or not creative then susan is not brave or curious. Everyone who is not patient is not humble or not creative and vice versa. Everyone who is not rich or quiet is not old or not strong and vice versa. If susan is calm then mary is both strong and not curious and vice versa. If alice is not tall or calm then someone is quiet. If someone is not happy then someone is not wise or patient. Everyone who is both not brave and not wise is either happy or not wise and vice versa. If someone is not creative or quiet then someone is either not patient or not creative. Everyone who is old is both not old and tall. If someone is not happy then someone is not wise. If someone is either calm or not generous then someone is not wise and vice versa. Everyone who is funny or not patient is either tall or wise. Everyone who is both old and not creative is curious or calm and vice versa. If susan is either calm or old then mary is either not funny or not patient. Everyone who is not brave or not patient is both calm and not patient. Someone is humble. Alice is either creative or not generous. Mary is both not tall and not calm. Someone is kind. Someone is either not rich or not brave. | Mary is not patient. | contradiction | (((rich(fred)<~>~tall(fred)))=>(generous(mary)))&
((?[X]:((~kind(X)|~creative(X))))=>((~brave(susan)|curious(susan))))&
(![X]:(~patient(X)<=>(~humble(X)|~creative(X))))&
(![X]:((~rich(X)|quiet(X))<=>(~old(X)|~strong(X))))&
((calm(susan))<=>((strong(mary)&~curious(mary))))&
(((~tall(alice)|calm(alice)))=>(?[X]:(quiet(X))))&
((?[X]:(~happy(X)))=>(?[X]:((~wise(X)|patient(X)))))&
(![X]:((~brave(X)&~wise(X))<=>(happy(X)<~>~wise(X))))&
((?[X]:((~creative(X)|quiet(X))))=>(?[X]:((~patient(X)<~>~creative(X)))))&
(![X]:(old(X)=>(~old(X)&tall(X))))&
((?[X]:(~happy(X)))=>(?[X]:(~wise(X))))&
((?[X]:((calm(X)<~>~generous(X))))<=>(?[X]:(~wise(X))))&
(![X]:((funny(X)|~patient(X))=>(tall(X)<~>wise(X))))&
(![X]:((old(X)&~creative(X))<=>(curious(X)|calm(X))))&
(((calm(susan)<~>old(susan)))=>((~funny(mary)<~>~patient(mary))))&
(![X]:((~brave(X)|~patient(X))=>(calm(X)&~patient(X))))&
(?[X]:(humble(X)))&
((creative(alice)<~>~generous(alice)))&
((~tall(mary)&~calm(mary)))&
(?[X]:(kind(X)))&
(?[X]:((~rich(X)<~>~brave(X)))) | ~patient(mary) | [
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8693034675996129744595781
% SZS output start Proof for 8693034675996129744595781
10. ! [X0] : (old(X0) => (tall(X0) & ~old(X0))) [input p9]
14. ! [X0] : ((~creative(X0) & old(X0)) <=> (calm(X0) | curious(X0))) [input p13]
16. ! [X0] : ((~patient(X0) | ~brave(X0)) => (~patient(X0) & calm(X0))) [input p15]
22. ~patient(mary) [input hypothesis]
35. ! [X0] : ((tall(X0) & ~old(X0)) | ~old(X0)) [ennf transformation 10]
39. ! [X0] : ((~patient(X0) & calm(X0)) | (patient(X0) & brave(X0))) [ennf transformation 16]
67. ! [X0] : (((~creative(X0) & old(X0)) | (~calm(X0) & ~curious(X0))) & ((calm(X0) | curious(X0)) | (creative(X0) | ~old(X0)))) [nnf transformation 14]
68. ! [X0] : (((~creative(X0) & old(X0)) | (~calm(X0) & ~curious(X0))) & (calm(X0) | curious(X0) | creative(X0) | ~old(X0))) [flattening 67]
102. ~old(X0) | ~old(X0) [cnf transformation 35]
115. old(X0) | ~calm(X0) [cnf transformation 68]
123. calm(X0) | patient(X0) [cnf transformation 39]
133. ~patient(mary) [cnf transformation 22]
134. ~old(X0) [duplicate literal removal 102]
254. ~calm(X0) [subsumption resolution 115,134]
256. patient(X0) [subsumption resolution 123,254]
269. $false [subsumption resolution 133,256]
% SZS output end Proof for 8693034675996129744595781
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is not curious.
If someone is not kind or rich then lucy is not quiet.
Everyone who is humble or curious is both not strong and happy and vice versa.
If someone is both not generous and not quiet then someone is happy and vice versa.
Everyone who is not happy or not tall is wise and vice versa.
If someone is either not strong or not generous then someone is not curious or not happy and vice versa.
If mary is tall then lucy is not humble and vice versa.
If someone is both calm and not patient then paul is both not funny and brave.
Everyone who is either not quiet or not humble is not generous or funny.
Everyone who is either quiet or not old is both not brave and brave.
Everyone who is both generous and not rich is creative or funny.
If someone is either not old or not quiet then someone is either wise or humble.
If someone is both old and not patient then someone is not wise or not old and vice versa.
Everyone who is either wise or patient is either calm or humble.
Everyone who is both calm and tall is either not quiet or not old.
Everyone who is not quiet is both generous and not curious.
Mary is not calm.
Someone is both quiet and patient.
John is not humble.
Someone is either patient or calm.
Alice is both funny and not old.
John is curious or not happy.
Paul is both generous and not quiet. | John is not curious. | entailment | (![X]:(~kind(X)=>~curious(X)))&
((?[X]:((~kind(X)|rich(X))))=>(~quiet(lucy)))&
(![X]:((humble(X)|curious(X))<=>(~strong(X)&happy(X))))&
((?[X]:((~generous(X)&~quiet(X))))<=>(?[X]:(happy(X))))&
(![X]:((~happy(X)|~tall(X))<=>wise(X)))&
((?[X]:((~strong(X)<~>~generous(X))))<=>(?[X]:((~curious(X)|~happy(X)))))&
((tall(mary))<=>(~humble(lucy)))&
((?[X]:((calm(X)&~patient(X))))=>((~funny(paul)&brave(paul))))&
(![X]:((~quiet(X)<~>~humble(X))=>(~generous(X)|funny(X))))&
(![X]:((quiet(X)<~>~old(X))=>(~brave(X)&brave(X))))&
(![X]:((generous(X)&~rich(X))=>(creative(X)|funny(X))))&
((?[X]:((~old(X)<~>~quiet(X))))=>(?[X]:((wise(X)<~>humble(X)))))&
((?[X]:((old(X)&~patient(X))))<=>(?[X]:((~wise(X)|~old(X)))))&
(![X]:((wise(X)<~>patient(X))=>(calm(X)<~>humble(X))))&
(![X]:((calm(X)&tall(X))=>(~quiet(X)<~>~old(X))))&
(![X]:(~quiet(X)=>(generous(X)&~curious(X))))&
(~calm(mary))&
(?[X]:((quiet(X)&patient(X))))&
(~humble(john))&
(?[X]:((patient(X)<~>calm(X))))&
((funny(alice)&~old(alice)))&
((curious(john)|~happy(john)))&
((generous(paul)&~quiet(paul))) | ~curious(john) | [
"p2",
"p3",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4121372534299739658989538
% SZS output start Proof for 4121372534299739658989538
3. ! [X0] : ((curious(X0) | humble(X0)) <=> (happy(X0) & ~strong(X0))) [input p2]
4. ? [X0] : (~quiet(X0) & ~generous(X0)) <=> ? [X0] : happy(X0) [input p3]
16. ! [X0] : (~quiet(X0) => (~curious(X0) & generous(X0))) [input p15]
24. curious(john) [input hypothesis]
25. ? [X0] : (~quiet(X0) & ~generous(X0)) <=> ? [X1] : happy(X1) [rectify 4]
41. ! [X0] : ((~curious(X0) & generous(X0)) | quiet(X0)) [ennf transformation 16]
42. ! [X0] : (((curious(X0) | humble(X0)) | (~happy(X0) | strong(X0))) & ((happy(X0) & ~strong(X0)) | (~curious(X0) & ~humble(X0)))) [nnf transformation 3]
43. ! [X0] : ((curious(X0) | humble(X0) | ~happy(X0) | strong(X0)) & ((happy(X0) & ~strong(X0)) | (~curious(X0) & ~humble(X0)))) [flattening 42]
44. (? [X0] : (~quiet(X0) & ~generous(X0)) | ! [X1] : ~happy(X1)) & (? [X1] : happy(X1) | ! [X0] : (quiet(X0) | generous(X0))) [nnf transformation 25]
45. (? [X0] : (~quiet(X0) & ~generous(X0)) | ! [X1] : ~happy(X1)) & (? [X2] : happy(X2) | ! [X3] : (quiet(X3) | generous(X3))) [rectify 44]
46. ? [X0] : (~quiet(X0) & ~generous(X0)) => (~quiet(sK0) & ~generous(sK0)) [choice axiom]
47. ? [X2] : happy(X2) => happy(sK1) [choice axiom]
48. ((~quiet(sK0) & ~generous(sK0)) | ! [X1] : ~happy(X1)) & (happy(sK1) | ! [X3] : (quiet(X3) | generous(X3))) [skolemisation 45,47,46]
78. ~curious(X0) | happy(X0) [cnf transformation 43]
81. ~generous(sK0) | ~happy(X1) [cnf transformation 48]
82. ~quiet(sK0) | ~happy(X1) [cnf transformation 48]
117. generous(X0) | quiet(X0) [cnf transformation 41]
130. curious(john) [cnf transformation 24]
132. 1 <=> ! [X1] : ~happy(X1) [avatar definition]
133. ~happy(X1) <- (1) [avatar component clause 132]
135. 2 <=> quiet(sK0) [avatar definition]
138. 1 | ~2 [avatar split clause 82,135,132]
140. 3 <=> generous(sK0) [avatar definition]
142. ~generous(sK0) <- (~3) [avatar component clause 140]
143. 1 | ~3 [avatar split clause 81,140,132]
145. 4 <=> ! [X3] : (quiet(X3) | generous(X3)) [avatar definition]
146. generous(X3) | quiet(X3) <- (4) [avatar component clause 145]
258. 4 [avatar split clause 117,145]
270. 30 <=> curious(john) [avatar definition]
272. curious(john) <- (30) [avatar component clause 270]
274. 31 <=> happy(john) [avatar definition]
275. happy(john) <- (31) [avatar component clause 274]
278. 30 [avatar split clause 130,270]
288. happy(john) <- (30) [resolution 78,272]
289. 31 | ~30 [avatar split clause 288,270,274]
293. quiet(sK0) <- (~3, 4) [resolution 146,142]
297. 2 | 3 | ~4 [avatar split clause 293,145,140,135]
299. $false <- (1, 31) [resolution 133,275]
302. ~1 | ~31 [avatar contradiction clause 299]
304. $false [avatar sat refutation 138,143,258,278,289,297,302]
% SZS output end Proof for 4121372534299739658989538
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is both not brave and not tall then someone is quiet or kind and vice versa. If lucy is not kind then someone is not strong or curious. If someone is strong then someone is old or not quiet and vice versa. If alice is either patient or happy then someone is either creative or not funny. If john is either not generous or tall then fred is not kind or strong. Everyone who is both curious and happy is either not tall or not kind. If lucy is either not tall or not wise then paul is either calm or patient and vice versa. Everyone who is curious or wise is both quiet and not curious and vice versa. If lucy is either not calm or happy then mary is not humble and vice versa. Everyone who is tall or not brave is both kind and not creative. If someone is tall then john is not curious or quiet and vice versa. If someone is calm or generous then someone is both not happy and old and vice versa. Everyone who is not calm is both not quiet and not funny. Everyone who is not strong is both not creative and quiet and vice versa. If someone is curious then lucy is strong or kind and vice versa. Everyone who is rich is both curious and not rich and vice versa. Someone is not old or not curious. Someone is either not wise or not rich. Susan is both patient and kind. Someone is not funny. Paul is both not funny and not kind. Someone is either brave or funny. Someone is either patient or not curious. Someone is not quiet or not funny. | Lucy is curious. | contradiction | (((~brave(susan)&~tall(susan)))<=>(?[X]:((quiet(X)|kind(X)))))&
((~kind(lucy))=>(?[X]:((~strong(X)|curious(X)))))&
((?[X]:(strong(X)))<=>(?[X]:((old(X)|~quiet(X)))))&
(((patient(alice)<~>happy(alice)))=>(?[X]:((creative(X)<~>~funny(X)))))&
(((~generous(john)<~>tall(john)))=>((~kind(fred)|strong(fred))))&
(![X]:((curious(X)&happy(X))=>(~tall(X)<~>~kind(X))))&
(((~tall(lucy)<~>~wise(lucy)))<=>((calm(paul)<~>patient(paul))))&
(![X]:((curious(X)|wise(X))<=>(quiet(X)&~curious(X))))&
(((~calm(lucy)<~>happy(lucy)))<=>(~humble(mary)))&
(![X]:((tall(X)|~brave(X))=>(kind(X)&~creative(X))))&
((?[X]:(tall(X)))<=>((~curious(john)|quiet(john))))&
((?[X]:((calm(X)|generous(X))))<=>(?[X]:((~happy(X)&old(X)))))&
(![X]:(~calm(X)=>(~quiet(X)&~funny(X))))&
(![X]:(~strong(X)<=>(~creative(X)&quiet(X))))&
((?[X]:(curious(X)))<=>((strong(lucy)|kind(lucy))))&
(![X]:(rich(X)<=>(curious(X)&~rich(X))))&
(?[X]:((~old(X)|~curious(X))))&
(?[X]:((~wise(X)<~>~rich(X))))&
((patient(susan)&kind(susan)))&
(?[X]:(~funny(X)))&
((~funny(paul)&~kind(paul)))&
(?[X]:((brave(X)<~>funny(X))))&
(?[X]:((patient(X)<~>~curious(X))))&
(?[X]:((~quiet(X)|~funny(X)))) | curious(lucy) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1441321713199546427561825
% SZS output start Proof for 1441321713199546427561825
8. ! [X0] : ((wise(X0) | curious(X0)) <=> (~curious(X0) & quiet(X0))) [input p7]
25. curious(lucy) [input hypothesis]
54. ! [X0] : (((wise(X0) | curious(X0)) | (curious(X0) | ~quiet(X0))) & ((~curious(X0) & quiet(X0)) | (~wise(X0) & ~curious(X0)))) [nnf transformation 8]
55. ! [X0] : ((wise(X0) | curious(X0) | curious(X0) | ~quiet(X0)) & ((~curious(X0) & quiet(X0)) | (~wise(X0) & ~curious(X0)))) [flattening 54]
118. ~curious(X0) | ~curious(X0) [cnf transformation 55]
161. curious(lucy) [cnf transformation 25]
164. ~curious(X0) [duplicate literal removal 118]
373. $false [subsumption resolution 161,164]
% SZS output end Proof for 1441321713199546427561825
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either strong or generous then paul is wise and vice versa.
Everyone who is tall or old is old and vice versa.
If mary is both not generous and not patient then paul is wise or generous.
Everyone who is funny is either tall or strong and vice versa.
Everyone who is not calm is not patient or happy.
If john is not calm or quiet then someone is either old or not old.
Everyone who is patient is both brave and quiet and vice versa.
Everyone who is quiet is funny or rich and vice versa.
Everyone who is both not kind and old is either patient or not brave and vice versa.
If someone is both not brave and not patient then lucy is both patient and kind and vice versa.
Everyone who is not wise or not kind is not patient and vice versa.
If someone is not humble or not strong then someone is both brave and not old and vice versa.
If someone is either not generous or calm then paul is curious or old and vice versa.
If someone is humble then someone is either creative or patient and vice versa.
Everyone who is either kind or creative is rich or not curious and vice versa.
Everyone who is not quiet is not happy.
Susan is either not tall or not calm.
Someone is either patient or old.
Someone is not humble.
Someone is not tall or humble.
Someone is not strong or not old.
John is not old. | Paul is not humble. | neutral | ((?[X]:((strong(X)<~>generous(X))))<=>(wise(paul)))&
(![X]:((tall(X)|old(X))<=>old(X)))&
(((~generous(mary)&~patient(mary)))=>((wise(paul)|generous(paul))))&
(![X]:(funny(X)<=>(tall(X)<~>strong(X))))&
(![X]:(~calm(X)=>(~patient(X)|happy(X))))&
(((~calm(john)|quiet(john)))=>(?[X]:((old(X)<~>~old(X)))))&
(![X]:(patient(X)<=>(brave(X)&quiet(X))))&
(![X]:(quiet(X)<=>(funny(X)|rich(X))))&
(![X]:((~kind(X)&old(X))<=>(patient(X)<~>~brave(X))))&
((?[X]:((~brave(X)&~patient(X))))<=>((patient(lucy)&kind(lucy))))&
(![X]:((~wise(X)|~kind(X))<=>~patient(X)))&
((?[X]:((~humble(X)|~strong(X))))<=>(?[X]:((brave(X)&~old(X)))))&
((?[X]:((~generous(X)<~>calm(X))))<=>((curious(paul)|old(paul))))&
((?[X]:(humble(X)))<=>(?[X]:((creative(X)<~>patient(X)))))&
(![X]:((kind(X)<~>creative(X))<=>(rich(X)|~curious(X))))&
(![X]:(~quiet(X)=>~happy(X)))&
((~tall(susan)<~>~calm(susan)))&
(?[X]:((patient(X)<~>old(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~tall(X)|humble(X))))&
(?[X]:((~strong(X)|~old(X))))&
(~old(john)) | ~humble(paul) | [] | null | 0 |
If someone is either not generous or not patient then someone is either not wise or wise.
Everyone who is both wise and brave is either not wise or not patient.
Everyone who is kind is either not humble or creative and vice versa.
Everyone who is strong or not creative is not rich and vice versa.
If paul is rich or kind then paul is not brave or not kind.
Everyone who is either not wise or not generous is either not humble or quiet.
Everyone who is quiet is kind.
If mary is not wise then susan is happy or not happy and vice versa.
If john is funny then paul is not creative and vice versa.
Everyone who is not happy is not patient or happy and vice versa.
Everyone who is either not strong or not tall is humble and vice versa.
If fred is not strong then someone is either tall or creative and vice versa.
If lucy is both not tall and not kind then john is not strong or curious and vice versa.
Everyone who is either old or not quiet is humble and vice versa.
Everyone who is both not wise and not quiet is not rich or not curious and vice versa.
Everyone who is not funny or not tall is both not kind and rich.
Someone is happy or rich.
Fred is not patient or old.
Mary is both strong and brave.
Lucy is both not kind and tall.
Paul is either generous or not tall.
Mary is both generous and not calm.
Someone is not old. | Paul is not kind. | contradiction | ((?[X]:((~generous(X)<~>~patient(X))))=>(?[X]:((~wise(X)<~>wise(X)))))&
(![X]:((wise(X)&brave(X))=>(~wise(X)<~>~patient(X))))&
(![X]:(kind(X)<=>(~humble(X)<~>creative(X))))&
(![X]:((strong(X)|~creative(X))<=>~rich(X)))&
(((rich(paul)|kind(paul)))=>((~brave(paul)|~kind(paul))))&
(![X]:((~wise(X)<~>~generous(X))=>(~humble(X)<~>quiet(X))))&
(![X]:(quiet(X)=>kind(X)))&
((~wise(mary))<=>((happy(susan)|~happy(susan))))&
((funny(john))<=>(~creative(paul)))&
(![X]:(~happy(X)<=>(~patient(X)|happy(X))))&
(![X]:((~strong(X)<~>~tall(X))<=>humble(X)))&
((~strong(fred))<=>(?[X]:((tall(X)<~>creative(X)))))&
(((~tall(lucy)&~kind(lucy)))<=>((~strong(john)|curious(john))))&
(![X]:((old(X)<~>~quiet(X))<=>humble(X)))&
(![X]:((~wise(X)&~quiet(X))<=>(~rich(X)|~curious(X))))&
(![X]:((~funny(X)|~tall(X))=>(~kind(X)&rich(X))))&
(?[X]:((happy(X)|rich(X))))&
((~patient(fred)|old(fred)))&
((strong(mary)&brave(mary)))&
((~kind(lucy)&tall(lucy)))&
((generous(paul)<~>~tall(paul)))&
((generous(mary)&~calm(mary)))&
(?[X]:(~old(X))) | ~kind(paul) | [
"p2",
"p3",
"p5",
"p6",
"p8",
"p12",
"p14",
"p15",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6583268258351143066838127
% SZS output start Proof for 6583268258351143066838127
3. ! [X0] : (kind(X0) <=> (~humble(X0) <~> creative(X0))) [input p2]
4. ! [X0] : ((~creative(X0) | strong(X0)) <=> ~rich(X0)) [input p3]
6. ! [X0] : ((~wise(X0) <~> ~generous(X0)) => (~humble(X0) <~> quiet(X0))) [input p5]
7. ! [X0] : (quiet(X0) => kind(X0)) [input p6]
9. funny(john) <=> ~creative(paul) [input p8]
13. (~kind(lucy) & ~tall(lucy)) <=> (curious(john) | ~strong(john)) [input p12]
15. ! [X0] : ((~quiet(X0) & ~wise(X0)) <=> (~curious(X0) | ~rich(X0))) [input p14]
16. ! [X0] : ((~tall(X0) | ~funny(X0)) => (rich(X0) & ~kind(X0))) [input p15]
20. tall(lucy) & ~kind(lucy) [input p19]
21. generous(paul) <~> ~tall(paul) [input p20]
24. ~kind(paul) [input hypothesis]
32. ! [X0] : ((~humble(X0) <~> quiet(X0)) | (~wise(X0) <=> ~generous(X0))) [ennf transformation 6]
33. ! [X0] : (kind(X0) | ~quiet(X0)) [ennf transformation 7]
34. ! [X0] : ((rich(X0) & ~kind(X0)) | (tall(X0) & funny(X0))) [ennf transformation 16]
40. ! [X0] : ((kind(X0) | ((~humble(X0) | ~creative(X0)) & (creative(X0) | humble(X0)))) & (((~creative(X0) | humble(X0)) & (creative(X0) | ~humble(X0))) | ~kind(X0))) [nnf transformation 3]
41. ! [X0] : (((~creative(X0) | strong(X0)) | rich(X0)) & (~rich(X0) | (creative(X0) & ~strong(X0)))) [nnf transformation 4]
42. ! [X0] : ((~creative(X0) | strong(X0) | rich(X0)) & (~rich(X0) | (creative(X0) & ~strong(X0)))) [flattening 41]
43. ! [X0] : (((~quiet(X0) | humble(X0)) & (quiet(X0) | ~humble(X0))) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0)))) [nnf transformation 32]
46. (funny(john) | creative(paul)) & (~creative(paul) | ~funny(john)) [nnf transformation 9]
54. ((~kind(lucy) & ~tall(lucy)) | (~curious(john) & strong(john))) & ((curious(john) | ~strong(john)) | (kind(lucy) | tall(lucy))) [nnf transformation 13]
55. ((~kind(lucy) & ~tall(lucy)) | (~curious(john) & strong(john))) & (curious(john) | ~strong(john) | kind(lucy) | tall(lucy)) [flattening 54]
57. ! [X0] : (((~quiet(X0) & ~wise(X0)) | (curious(X0) & rich(X0))) & ((~curious(X0) | ~rich(X0)) | (quiet(X0) | wise(X0)))) [nnf transformation 15]
58. ! [X0] : (((~quiet(X0) & ~wise(X0)) | (curious(X0) & rich(X0))) & (~curious(X0) | ~rich(X0) | quiet(X0) | wise(X0))) [flattening 57]
61. (tall(paul) | ~generous(paul)) & (~tall(paul) | generous(paul)) [nnf transformation 21]
72. creative(X0) | kind(X0) | humble(X0) [cnf transformation 40]
74. ~rich(X0) | ~strong(X0) [cnf transformation 42]
75. ~rich(X0) | creative(X0) [cnf transformation 42]
79. ~humble(X0) | quiet(X0) | ~generous(X0) | wise(X0) [cnf transformation 43]
83. ~quiet(X0) | kind(X0) [cnf transformation 33]
87. ~creative(paul) | ~funny(john) [cnf transformation 46]
101. ~tall(lucy) | strong(john) [cnf transformation 55]
110. ~wise(X0) | rich(X0) [cnf transformation 58]
116. funny(X0) | rich(X0) [cnf transformation 34]
117. tall(X0) | rich(X0) [cnf transformation 34]
123. tall(lucy) [cnf transformation 20]
124. ~tall(paul) | generous(paul) [cnf transformation 61]
128. ~kind(paul) [cnf transformation 24]
138. 2 <=> kind(paul) [avatar definition]
140. ~kind(paul) <- (~2) [avatar component clause 138]
143. 3 <=> rich(paul) [avatar definition]
144. rich(paul) <- (3) [avatar component clause 143]
145. ~rich(paul) <- (~3) [avatar component clause 143]
158. 6 <=> creative(paul) [avatar definition]
159. ~creative(paul) <- (~6) [avatar component clause 158]
162. 7 <=> funny(john) [avatar definition]
163. ~funny(john) <- (~7) [avatar component clause 162]
166. ~7 | ~6 [avatar split clause 87,158,162]
200. 15 <=> strong(john) [avatar definition]
202. strong(john) <- (15) [avatar component clause 200]
205. 16 <=> tall(lucy) [avatar definition]
209. 15 | ~16 [avatar split clause 101,205,200]
212. 16 [avatar split clause 123,205]
215. 17 <=> generous(paul) [avatar definition]
216. generous(paul) <- (17) [avatar component clause 215]
219. 18 <=> tall(paul) [avatar definition]
220. ~tall(paul) <- (~18) [avatar component clause 219]
223. 17 | ~18 [avatar split clause 124,219,215]
224. ~2 [avatar split clause 128,138]
227. rich(john) <- (~7) [resolution 116,163]
229. ~strong(john) <- (~7) [resolution 227,74]
230. $false <- (~7, 15) [subsumption resolution 229,202]
231. 7 | ~15 [avatar contradiction clause 230]
232. rich(paul) <- (~18) [resolution 117,220]
233. 3 | 18 [avatar split clause 232,219,143]
234. creative(paul) <- (3) [resolution 144,75]
236. $false <- (3, ~6) [subsumption resolution 234,159]
237. ~3 | 6 [avatar contradiction clause 236]
257. kind(paul) | humble(paul) <- (~6) [resolution 72,159]
262. humble(paul) <- (~2, ~6) [subsumption resolution 257,140]
354. quiet(paul) | ~generous(paul) | wise(paul) <- (~2, ~6) [resolution 79,262]
357. quiet(paul) | wise(paul) <- (~2, ~6, 17) [subsumption resolution 354,216]
359. 28 <=> wise(paul) [avatar definition]
361. wise(paul) <- (28) [avatar component clause 359]
363. 29 <=> quiet(paul) [avatar definition]
365. quiet(paul) <- (29) [avatar component clause 363]
366. 28 | 29 | 2 | 6 | ~17 [avatar split clause 357,215,158,138,363,359]
403. rich(paul) <- (28) [resolution 361,110]
404. $false <- (~3, 28) [subsumption resolution 403,145]
405. 3 | ~28 [avatar contradiction clause 404]
426. kind(paul) <- (29) [resolution 365,83]
430. $false <- (~2, 29) [subsumption resolution 426,140]
431. 2 | ~29 [avatar contradiction clause 430]
432. $false [avatar sat refutation 166,209,212,223,224,231,233,237,366,405,431]
% SZS output end Proof for 6583268258351143066838127
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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 not funny. | contradiction | ((?[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 2093573542838981733435981
% SZS output start Proof for 2093573542838981733435981
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 2093573542838981733435981
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or humble is both not creative and happy and vice versa.
Everyone who is either not rich or happy is kind or not generous and vice versa.
Everyone who is not funny or calm is old or not old.
If someone is both not humble and not funny then someone is not funny.
Everyone who is wise is old or tall.
If someone is creative then susan is not calm and vice versa.
Everyone who is either rich or not wise is not generous and vice versa.
Everyone who is not generous or happy is either not creative or rich.
Everyone who is not brave or old is both humble and not humble and vice versa.
Everyone who is both not wise and not curious is not strong or humble.
Everyone who is either curious or not quiet is not quiet or calm.
If mary is either rich or not brave then someone is brave and vice versa.
Everyone who is both not tall and tall is kind.
If mary is not funny or patient then someone is not creative and vice versa.
Everyone who is both kind and not old is humble or strong.
If mary is humble or not curious then someone is not calm.
John is either not curious or curious.
Lucy is not calm or calm.
Paul is both strong and not funny.
Someone is either kind or not humble.
Susan is either strong or brave.
Someone is not old.
Someone is either curious or generous. | Lucy is brave. | entailment | (![X]:((wise(X)|humble(X))<=>(~creative(X)&happy(X))))&
(![X]:((~rich(X)<~>happy(X))<=>(kind(X)|~generous(X))))&
(![X]:((~funny(X)|calm(X))=>(old(X)|~old(X))))&
((?[X]:((~humble(X)&~funny(X))))=>(?[X]:(~funny(X))))&
(![X]:(wise(X)=>(old(X)|tall(X))))&
((?[X]:(creative(X)))<=>(~calm(susan)))&
(![X]:((rich(X)<~>~wise(X))<=>~generous(X)))&
(![X]:((~generous(X)|happy(X))=>(~creative(X)<~>rich(X))))&
(![X]:((~brave(X)|old(X))<=>(humble(X)&~humble(X))))&
(![X]:((~wise(X)&~curious(X))=>(~strong(X)|humble(X))))&
(![X]:((curious(X)<~>~quiet(X))=>(~quiet(X)|calm(X))))&
(((rich(mary)<~>~brave(mary)))<=>(?[X]:(brave(X))))&
(![X]:((~tall(X)&tall(X))=>kind(X)))&
(((~funny(mary)|patient(mary)))<=>(?[X]:(~creative(X))))&
(![X]:((kind(X)&~old(X))=>(humble(X)|strong(X))))&
(((humble(mary)|~curious(mary)))=>(?[X]:(~calm(X))))&
((~curious(john)<~>curious(john)))&
((~calm(lucy)|calm(lucy)))&
((strong(paul)&~funny(paul)))&
(?[X]:((kind(X)<~>~humble(X))))&
((strong(susan)<~>brave(susan)))&
(?[X]:(~old(X)))&
(?[X]:((curious(X)<~>generous(X)))) | brave(lucy) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6822058242005570809138595
% SZS output start Proof for 6822058242005570809138595
9. ! [X0] : ((old(X0) | ~brave(X0)) <=> (~humble(X0) & humble(X0))) [input p8]
24. ~brave(lucy) [input hypothesis]
54. ! [X0] : (((old(X0) | ~brave(X0)) | (humble(X0) | ~humble(X0))) & ((~humble(X0) & humble(X0)) | (~old(X0) & brave(X0)))) [nnf transformation 9]
55. ! [X0] : ((old(X0) | ~brave(X0) | humble(X0) | ~humble(X0)) & ((~humble(X0) & humble(X0)) | (~old(X0) & brave(X0)))) [flattening 54]
103. humble(X0) | brave(X0) [cnf transformation 55]
105. ~humble(X0) | brave(X0) [cnf transformation 55]
134. ~brave(lucy) [cnf transformation 24]
158. brave(X0) [subsumption resolution 103,105]
215. $false [subsumption resolution 134,158]
% SZS output end Proof for 6822058242005570809138595
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or happy is both quiet and patient.
If john is both not creative and not curious then someone is not brave or not wise and vice versa.
Everyone who is not curious or calm is either strong or brave.
If someone is happy then someone is either happy or not old.
Everyone who is either funny or creative is not quiet.
If someone is tall then someone is not calm or not quiet and vice versa.
If alice is not humble then someone is not calm and vice versa.
Everyone who is both not strong and funny is both not old and not funny and vice versa.
Everyone who is both generous and not strong is both not wise and not old.
If fred is either not creative or not wise then someone is both rich and old.
Everyone who is either not brave or not curious is not brave and vice versa.
Everyone who is not generous or patient is either happy or generous and vice versa.
Everyone who is both not humble and not generous is not kind or not creative and vice versa.
If susan is both generous and not quiet then someone is either not calm or strong and vice versa.
Everyone who is both kind and not happy is patient or not kind.
Everyone who is either curious or not humble is either quiet or happy and vice versa.
Alice is both tall and strong.
Someone is either not tall or humble.
Susan is humble or not generous.
Someone is generous or not patient.
Susan is either not kind or tall.
Someone is not quiet or calm.
Fred is either happy or not rich. | Alice is not creative. | neutral | (![X]:((~brave(X)|happy(X))=>(quiet(X)&patient(X))))&
(((~creative(john)&~curious(john)))<=>(?[X]:((~brave(X)|~wise(X)))))&
(![X]:((~curious(X)|calm(X))=>(strong(X)<~>brave(X))))&
((?[X]:(happy(X)))=>(?[X]:((happy(X)<~>~old(X)))))&
(![X]:((funny(X)<~>creative(X))=>~quiet(X)))&
((?[X]:(tall(X)))<=>(?[X]:((~calm(X)|~quiet(X)))))&
((~humble(alice))<=>(?[X]:(~calm(X))))&
(![X]:((~strong(X)&funny(X))<=>(~old(X)&~funny(X))))&
(![X]:((generous(X)&~strong(X))=>(~wise(X)&~old(X))))&
(((~creative(fred)<~>~wise(fred)))=>(?[X]:((rich(X)&old(X)))))&
(![X]:((~brave(X)<~>~curious(X))<=>~brave(X)))&
(![X]:((~generous(X)|patient(X))<=>(happy(X)<~>generous(X))))&
(![X]:((~humble(X)&~generous(X))<=>(~kind(X)|~creative(X))))&
(((generous(susan)&~quiet(susan)))<=>(?[X]:((~calm(X)<~>strong(X)))))&
(![X]:((kind(X)&~happy(X))=>(patient(X)|~kind(X))))&
(![X]:((curious(X)<~>~humble(X))<=>(quiet(X)<~>happy(X))))&
((tall(alice)&strong(alice)))&
(?[X]:((~tall(X)<~>humble(X))))&
((humble(susan)|~generous(susan)))&
(?[X]:((generous(X)|~patient(X))))&
((~kind(susan)<~>tall(susan)))&
(?[X]:((~quiet(X)|calm(X))))&
((happy(fred)<~>~rich(fred))) | ~creative(alice) | [] | null | 0 |
Everyone who is not humble or not funny is both strong and brave and vice versa.
If someone is strong or not tall then fred is either rich or not curious.
Everyone who is both funny and not patient is either kind or not creative.
If alice is both funny and not generous then lucy is brave.
Everyone who is either humble or not old is both wise and not strong and vice versa.
Everyone who is not calm or not rich is not old and vice versa.
If someone is either not rich or not patient then someone is wise.
Everyone who is curious or quiet is not creative or wise.
Everyone who is not kind or not old is both not old and kind.
If someone is calm or tall then someone is curious or kind.
If fred is not quiet then paul is humble or strong and vice versa.
If someone is not wise then paul is either generous or not curious.
If susan is brave then fred is not rich or brave.
If susan is generous then john is either rich or patient and vice versa.
Everyone who is either not humble or not old is patient or not creative and vice versa.
If someone is not patient or kind then someone is quiet or creative and vice versa.
Susan is both humble and not patient.
Someone is not tall or creative.
Fred is strong or creative.
Lucy is both not strong and brave.
Someone is either not old or calm.
John is both happy and not calm.
Someone is quiet or kind.
Someone is wise or not quiet. | Lucy is funny. | entailment | (![X]:((~humble(X)|~funny(X))<=>(strong(X)&brave(X))))&
((?[X]:((strong(X)|~tall(X))))=>((rich(fred)<~>~curious(fred))))&
(![X]:((funny(X)&~patient(X))=>(kind(X)<~>~creative(X))))&
(((funny(alice)&~generous(alice)))=>(brave(lucy)))&
(![X]:((humble(X)<~>~old(X))<=>(wise(X)&~strong(X))))&
(![X]:((~calm(X)|~rich(X))<=>~old(X)))&
((?[X]:((~rich(X)<~>~patient(X))))=>(?[X]:(wise(X))))&
(![X]:((curious(X)|quiet(X))=>(~creative(X)|wise(X))))&
(![X]:((~kind(X)|~old(X))=>(~old(X)&kind(X))))&
((?[X]:((calm(X)|tall(X))))=>(?[X]:((curious(X)|kind(X)))))&
((~quiet(fred))<=>((humble(paul)|strong(paul))))&
((?[X]:(~wise(X)))=>((generous(paul)<~>~curious(paul))))&
((brave(susan))=>((~rich(fred)|brave(fred))))&
((generous(susan))<=>((rich(john)<~>patient(john))))&
(![X]:((~humble(X)<~>~old(X))<=>(patient(X)|~creative(X))))&
((?[X]:((~patient(X)|kind(X))))<=>(?[X]:((quiet(X)|creative(X)))))&
((humble(susan)&~patient(susan)))&
(?[X]:((~tall(X)|creative(X))))&
((strong(fred)|creative(fred)))&
((~strong(lucy)&brave(lucy)))&
(?[X]:((~old(X)<~>calm(X))))&
((happy(john)&~calm(john)))&
(?[X]:((quiet(X)|kind(X))))&
(?[X]:((wise(X)|~quiet(X)))) | funny(lucy) | [
"p0",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7325830113926008680348961
% SZS output start Proof for 7325830113926008680348961
1. ! [X0] : ((~funny(X0) | ~humble(X0)) <=> (brave(X0) & strong(X0))) [input p0]
20. brave(lucy) & ~strong(lucy) [input p19]
25. ~funny(lucy) [input hypothesis]
43. ! [X0] : (((~funny(X0) | ~humble(X0)) | (~brave(X0) | ~strong(X0))) & ((brave(X0) & strong(X0)) | (funny(X0) & humble(X0)))) [nnf transformation 1]
44. ! [X0] : ((~funny(X0) | ~humble(X0) | ~brave(X0) | ~strong(X0)) & ((brave(X0) & strong(X0)) | (funny(X0) & humble(X0)))) [flattening 43]
79. strong(X0) | funny(X0) [cnf transformation 44]
133. ~strong(lucy) [cnf transformation 20]
140. ~funny(lucy) [cnf transformation 25]
293. funny(lucy) [resolution 79,133]
294. $false [subsumption resolution 293,140]
% SZS output end Proof for 7325830113926008680348961
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or patient is not humble.
Everyone who is patient or not old is creative or curious.
If someone is funny or strong then lucy is humble.
If john is either not creative or calm then someone is not funny or not generous and vice versa.
Everyone who is either not strong or not tall is both not generous and rich and vice versa.
Everyone who is not kind or not curious is curious and vice versa.
If someone is tall then fred is not rich or not humble and vice versa.
Everyone who is not creative is both not strong and generous.
Everyone who is not creative or not happy is not strong.
If lucy is creative then someone is both wise and happy and vice versa.
Everyone who is not tall is not kind or curious.
If paul is both not quiet and rich then someone is either happy or not generous.
If paul is both humble and brave then someone is either brave or creative and vice versa.
If john is both not quiet and not kind then susan is curious or not rich and vice versa.
If susan is either quiet or not tall then someone is funny and vice versa.
If alice is either tall or calm then susan is not humble.
Paul is not creative.
Someone is patient or creative.
Alice is both not brave and wise.
Someone is calm.
Someone is wise or not patient.
Someone is not quiet.
Someone is either humble or not quiet.
Someone is not humble or not quiet. | Fred is rich. | neutral | (![X]:((strong(X)|patient(X))=>~humble(X)))&
(![X]:((patient(X)|~old(X))=>(creative(X)|curious(X))))&
((?[X]:((funny(X)|strong(X))))=>(humble(lucy)))&
(((~creative(john)<~>calm(john)))<=>(?[X]:((~funny(X)|~generous(X)))))&
(![X]:((~strong(X)<~>~tall(X))<=>(~generous(X)&rich(X))))&
(![X]:((~kind(X)|~curious(X))<=>curious(X)))&
((?[X]:(tall(X)))<=>((~rich(fred)|~humble(fred))))&
(![X]:(~creative(X)=>(~strong(X)&generous(X))))&
(![X]:((~creative(X)|~happy(X))=>~strong(X)))&
((creative(lucy))<=>(?[X]:((wise(X)&happy(X)))))&
(![X]:(~tall(X)=>(~kind(X)|curious(X))))&
(((~quiet(paul)&rich(paul)))=>(?[X]:((happy(X)<~>~generous(X)))))&
(((humble(paul)&brave(paul)))<=>(?[X]:((brave(X)<~>creative(X)))))&
(((~quiet(john)&~kind(john)))<=>((curious(susan)|~rich(susan))))&
(((quiet(susan)<~>~tall(susan)))<=>(?[X]:(funny(X))))&
(((tall(alice)<~>calm(alice)))=>(~humble(susan)))&
(~creative(paul))&
(?[X]:((patient(X)|creative(X))))&
((~brave(alice)&wise(alice)))&
(?[X]:(calm(X)))&
(?[X]:((wise(X)|~patient(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((humble(X)<~>~quiet(X))))&
(?[X]:((~humble(X)|~quiet(X)))) | rich(fred) | [] | null | 0 |
If someone is both not tall and not curious then someone is either wise or not tall and vice versa.
Everyone who is both not generous and not wise is curious.
Everyone who is either wise or not funny is either not brave or not strong and vice versa.
Everyone who is either not strong or not quiet is rich or not creative and vice versa.
Everyone who is either wise or tall is both not brave and not calm and vice versa.
Everyone who is both generous and strong is both not brave and calm and vice versa.
Everyone who is not calm or tall is both old and not curious.
If fred is either not funny or old then someone is either patient or not tall.
If paul is both happy and not calm then someone is kind or rich.
If john is either funny or generous then alice is humble or not tall and vice versa.
Everyone who is not kind is both not humble and not old.
If someone is both not humble and tall then alice is humble or not creative and vice versa.
If paul is both not patient and kind then lucy is both not strong and calm and vice versa.
Everyone who is not kind or not curious is either not happy or not curious.
Everyone who is either not quiet or not patient is happy or not strong.
Everyone who is both humble and not kind is funny and vice versa.
John is both not calm and wise.
Someone is not generous or not tall.
Someone is funny or not humble.
Someone is old or wise.
Fred is generous or not creative.
Someone is both not patient and not curious.
Mary is both not calm and not wise. | Fred is not happy. | neutral | ((?[X]:((~tall(X)&~curious(X))))<=>(?[X]:((wise(X)<~>~tall(X)))))&
(![X]:((~generous(X)&~wise(X))=>curious(X)))&
(![X]:((wise(X)<~>~funny(X))<=>(~brave(X)<~>~strong(X))))&
(![X]:((~strong(X)<~>~quiet(X))<=>(rich(X)|~creative(X))))&
(![X]:((wise(X)<~>tall(X))<=>(~brave(X)&~calm(X))))&
(![X]:((generous(X)&strong(X))<=>(~brave(X)&calm(X))))&
(![X]:((~calm(X)|tall(X))=>(old(X)&~curious(X))))&
(((~funny(fred)<~>old(fred)))=>(?[X]:((patient(X)<~>~tall(X)))))&
(((happy(paul)&~calm(paul)))=>(?[X]:((kind(X)|rich(X)))))&
(((funny(john)<~>generous(john)))<=>((humble(alice)|~tall(alice))))&
(![X]:(~kind(X)=>(~humble(X)&~old(X))))&
((?[X]:((~humble(X)&tall(X))))<=>((humble(alice)|~creative(alice))))&
(((~patient(paul)&kind(paul)))<=>((~strong(lucy)&calm(lucy))))&
(![X]:((~kind(X)|~curious(X))=>(~happy(X)<~>~curious(X))))&
(![X]:((~quiet(X)<~>~patient(X))=>(happy(X)|~strong(X))))&
(![X]:((humble(X)&~kind(X))<=>funny(X)))&
((~calm(john)&wise(john)))&
(?[X]:((~generous(X)|~tall(X))))&
(?[X]:((funny(X)|~humble(X))))&
(?[X]:((old(X)|wise(X))))&
((generous(fred)|~creative(fred)))&
(?[X]:((~patient(X)&~curious(X))))&
((~calm(mary)&~wise(mary))) | ~happy(fred) | [] | null | 0 |
Everyone who is either not rich or brave is either humble or not patient and vice versa.
Everyone who is either not funny or calm is tall and vice versa.
If mary is either kind or happy then someone is kind or not patient and vice versa.
If someone is both tall and funny then john is not rich or not brave.
Everyone who is either happy or patient is both happy and not tall and vice versa.
Everyone who is patient is wise and vice versa.
If john is both not strong and brave then someone is curious or not calm.
Everyone who is either curious or not tall is both not generous and not strong and vice versa.
Everyone who is old is patient and vice versa.
If someone is either not happy or not curious then someone is not old.
If someone is not old or not patient then susan is strong or not brave and vice versa.
Everyone who is old or creative is both not rich and not tall and vice versa.
Everyone who is either not calm or kind is not brave or not quiet and vice versa.
Everyone who is either not creative or not old is not curious or happy and vice versa.
If someone is happy or humble then alice is either curious or not happy and vice versa.
If someone is both not generous and not quiet then someone is not creative or not tall and vice versa.
Fred is either wise or creative.
Mary is either not patient or not curious.
Paul is either curious or not calm.
Alice is either not wise or not generous.
Susan is not strong.
Someone is both not calm and rich.
Mary is not brave or tall.
Someone is both generous and strong. | Fred is creative. | entailment | (![X]:((~rich(X)<~>brave(X))<=>(humble(X)<~>~patient(X))))&
(![X]:((~funny(X)<~>calm(X))<=>tall(X)))&
(((kind(mary)<~>happy(mary)))<=>(?[X]:((kind(X)|~patient(X)))))&
((?[X]:((tall(X)&funny(X))))=>((~rich(john)|~brave(john))))&
(![X]:((happy(X)<~>patient(X))<=>(happy(X)&~tall(X))))&
(![X]:(patient(X)<=>wise(X)))&
(((~strong(john)&brave(john)))=>(?[X]:((curious(X)|~calm(X)))))&
(![X]:((curious(X)<~>~tall(X))<=>(~generous(X)&~strong(X))))&
(![X]:(old(X)<=>patient(X)))&
((?[X]:((~happy(X)<~>~curious(X))))=>(?[X]:(~old(X))))&
((?[X]:((~old(X)|~patient(X))))<=>((strong(susan)|~brave(susan))))&
(![X]:((old(X)|creative(X))<=>(~rich(X)&~tall(X))))&
(![X]:((~calm(X)<~>kind(X))<=>(~brave(X)|~quiet(X))))&
(![X]:((~creative(X)<~>~old(X))<=>(~curious(X)|happy(X))))&
((?[X]:((happy(X)|humble(X))))<=>((curious(alice)<~>~happy(alice))))&
((?[X]:((~generous(X)&~quiet(X))))<=>(?[X]:((~creative(X)|~tall(X)))))&
((wise(fred)<~>creative(fred)))&
((~patient(mary)<~>~curious(mary)))&
((curious(paul)<~>~calm(paul)))&
((~wise(alice)<~>~generous(alice)))&
(~strong(susan))&
(?[X]:((~calm(X)&rich(X))))&
((~brave(mary)|tall(mary)))&
(?[X]:((generous(X)&strong(X)))) | creative(fred) | [
"p4",
"p5",
"p8",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 712838105875305224639499
% SZS output start Proof for 712838105875305224639499
5. ! [X0] : ((happy(X0) <~> patient(X0)) <=> (~tall(X0) & happy(X0))) [input p4]
6. ! [X0] : (patient(X0) <=> wise(X0)) [input p5]
9. ! [X0] : (old(X0) <=> patient(X0)) [input p8]
12. ! [X0] : ((creative(X0) | old(X0)) <=> (~tall(X0) & ~rich(X0))) [input p11]
17. wise(fred) <~> creative(fred) [input p16]
25. ~creative(fred) [input hypothesis]
39. ! [X0] : ((((~patient(X0) | ~happy(X0)) & (patient(X0) | happy(X0))) | (tall(X0) | ~happy(X0))) & ((~tall(X0) & happy(X0)) | ((happy(X0) | ~patient(X0)) & (patient(X0) | ~happy(X0))))) [nnf transformation 5]
40. ! [X0] : ((((~patient(X0) | ~happy(X0)) & (patient(X0) | happy(X0))) | tall(X0) | ~happy(X0)) & ((~tall(X0) & happy(X0)) | ((happy(X0) | ~patient(X0)) & (patient(X0) | ~happy(X0))))) [flattening 39]
41. ! [X0] : ((patient(X0) | ~wise(X0)) & (wise(X0) | ~patient(X0))) [nnf transformation 6]
46. ! [X0] : ((old(X0) | ~patient(X0)) & (patient(X0) | ~old(X0))) [nnf transformation 9]
56. ! [X0] : (((creative(X0) | old(X0)) | (tall(X0) | rich(X0))) & ((~tall(X0) & ~rich(X0)) | (~creative(X0) & ~old(X0)))) [nnf transformation 12]
57. ! [X0] : ((creative(X0) | old(X0) | tall(X0) | rich(X0)) & ((~tall(X0) & ~rich(X0)) | (~creative(X0) & ~old(X0)))) [flattening 56]
71. (~creative(fred) | ~wise(fred)) & (creative(fred) | wise(fred)) [nnf transformation 17]
99. happy(X0) | happy(X0) | ~patient(X0) [cnf transformation 40]
103. ~patient(X0) | ~happy(X0) | tall(X0) | ~happy(X0) [cnf transformation 40]
105. ~wise(X0) | patient(X0) [cnf transformation 41]
114. ~patient(X0) | old(X0) [cnf transformation 46]
123. ~old(X0) | ~tall(X0) [cnf transformation 57]
149. creative(fred) | wise(fred) [cnf transformation 71]
163. ~creative(fred) [cnf transformation 25]
164. ~patient(X0) | happy(X0) [duplicate literal removal 99]
165. ~happy(X0) | ~patient(X0) | tall(X0) [duplicate literal removal 103]
299. 30 <=> wise(fred) [avatar definition]
300. wise(fred) <- (30) [avatar component clause 299]
303. 31 <=> creative(fred) [avatar definition]
307. 30 | 31 [avatar split clause 149,303,299]
348. ~31 [avatar split clause 163,303]
350. patient(fred) <- (30) [resolution 105,300]
355. old(fred) <- (30) [resolution 114,350]
363. ~tall(fred) <- (30) [resolution 123,355]
369. happy(fred) <- (30) [resolution 164,350]
526. ~patient(fred) | tall(fred) <- (30) [resolution 165,369]
528. tall(fred) <- (30) [subsumption resolution 526,350]
529. $false <- (30) [subsumption resolution 528,363]
530. ~30 [avatar contradiction clause 529]
534. $false [avatar sat refutation 307,348,530]
% SZS output end Proof for 712838105875305224639499
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both strong and not happy then susan is not brave. Everyone who is either brave or not creative is kind and vice versa. Everyone who is both not old and quiet is happy. If lucy is both quiet and not wise then mary is both wise and not patient. Everyone who is creative or humble is either not patient or rich. Everyone who is either not creative or generous is not brave. Everyone who is brave is not calm or humble and vice versa. If fred is either not strong or not wise then paul is both strong and old. Everyone who is old is either not funny or not brave. Everyone who is both not brave and patient is both not wise and brave and vice versa. If someone is not quiet or not brave then someone is both not kind and humble. Everyone who is patient or not tall is either not humble or wise. Everyone who is both kind and not funny is not patient and vice versa. If someone is not calm or patient then paul is generous. Everyone who is either not wise or not strong is either not rich or strong and vice versa. Someone is brave. Mary is either funny or curious. Someone is creative. Someone is not patient or wise. Someone is either happy or not old. Mary is not tall or not kind. | Susan is humble. | entailment | ((?[X]:((strong(X)&~happy(X))))=>(~brave(susan)))&
(![X]:((brave(X)<~>~creative(X))<=>kind(X)))&
(![X]:((~old(X)&quiet(X))=>happy(X)))&
(((quiet(lucy)&~wise(lucy)))=>((wise(mary)&~patient(mary))))&
(![X]:((creative(X)|humble(X))=>(~patient(X)<~>rich(X))))&
(![X]:((~creative(X)<~>generous(X))=>~brave(X)))&
(![X]:(brave(X)<=>(~calm(X)|humble(X))))&
(((~strong(fred)<~>~wise(fred)))=>((strong(paul)&old(paul))))&
(![X]:(old(X)=>(~funny(X)<~>~brave(X))))&
(![X]:((~brave(X)&patient(X))<=>(~wise(X)&brave(X))))&
((?[X]:((~quiet(X)|~brave(X))))=>(?[X]:((~kind(X)&humble(X)))))&
(![X]:((patient(X)|~tall(X))=>(~humble(X)<~>wise(X))))&
(![X]:((kind(X)&~funny(X))<=>~patient(X)))&
((?[X]:((~calm(X)|patient(X))))=>(generous(paul)))&
(![X]:((~wise(X)<~>~strong(X))<=>(~rich(X)<~>strong(X))))&
(?[X]:(brave(X)))&
((funny(mary)<~>curious(mary)))&
(?[X]:(creative(X)))&
(?[X]:((~patient(X)|wise(X))))&
(?[X]:((happy(X)<~>~old(X))))&
((~tall(mary)|~kind(mary))) | humble(susan) | [
"p1",
"p4",
"p5",
"p6",
"p9",
"p10",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2773570873289664213621219
% SZS output start Proof for 2773570873289664213621219
2. ! [X0] : ((brave(X0) <~> ~creative(X0)) <=> kind(X0)) [input p1]
5. ! [X0] : ((humble(X0) | creative(X0)) => (~patient(X0) <~> rich(X0))) [input p4]
6. ! [X0] : ((~creative(X0) <~> generous(X0)) => ~brave(X0)) [input p5]
7. ! [X0] : (brave(X0) <=> (humble(X0) | ~calm(X0))) [input p6]
10. ! [X0] : ((patient(X0) & ~brave(X0)) <=> (brave(X0) & ~wise(X0))) [input p9]
11. ? [X0] : (~brave(X0) | ~quiet(X0)) => ? [X0] : (humble(X0) & ~kind(X0)) [input p10]
12. ! [X0] : ((~tall(X0) | patient(X0)) => (~humble(X0) <~> wise(X0))) [input p11]
13. ! [X0] : ((~funny(X0) & kind(X0)) <=> ~patient(X0)) [input p12]
14. ? [X0] : (patient(X0) | ~calm(X0)) => generous(paul) [input p13]
15. ! [X0] : ((~wise(X0) <~> ~strong(X0)) <=> (~rich(X0) <~> strong(X0))) [input p14]
22. ~humble(susan) [input hypothesis]
23. ? [X0] : (~brave(X0) | ~quiet(X0)) => ? [X1] : (humble(X1) & ~kind(X1)) [rectify 11]
29. ! [X0] : ((~patient(X0) <~> rich(X0)) | (~humble(X0) & ~creative(X0))) [ennf transformation 5]
30. ! [X0] : (~brave(X0) | (~creative(X0) <=> generous(X0))) [ennf transformation 6]
33. ? [X1] : (humble(X1) & ~kind(X1)) | ! [X0] : (brave(X0) & quiet(X0)) [ennf transformation 23]
34. ! [X0] : ((~humble(X0) <~> wise(X0)) | (tall(X0) & ~patient(X0))) [ennf transformation 12]
35. generous(paul) | ! [X0] : (~patient(X0) & calm(X0)) [ennf transformation 14]
36. ! [X0] : ((((creative(X0) | ~brave(X0)) & (~creative(X0) | brave(X0))) | ~kind(X0)) & (kind(X0) | ((brave(X0) | creative(X0)) & (~creative(X0) | ~brave(X0))))) [nnf transformation 2]
37. ! [X0] : (((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | (~humble(X0) & ~creative(X0))) [nnf transformation 29]
38. ! [X0] : (~brave(X0) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0)))) [nnf transformation 30]
39. ! [X0] : ((brave(X0) | (~humble(X0) & calm(X0))) & ((humble(X0) | ~calm(X0)) | ~brave(X0))) [nnf transformation 7]
40. ! [X0] : ((brave(X0) | (~humble(X0) & calm(X0))) & (humble(X0) | ~calm(X0) | ~brave(X0))) [flattening 39]
43. ! [X0] : (((patient(X0) & ~brave(X0)) | (~brave(X0) | wise(X0))) & ((brave(X0) & ~wise(X0)) | (~patient(X0) | brave(X0)))) [nnf transformation 10]
44. ! [X0] : (((patient(X0) & ~brave(X0)) | ~brave(X0) | wise(X0)) & ((brave(X0) & ~wise(X0)) | ~patient(X0) | brave(X0))) [flattening 43]
45. ? [X0] : (humble(X0) & ~kind(X0)) | ! [X1] : (brave(X1) & quiet(X1)) [rectify 33]
46. ? [X0] : (humble(X0) & ~kind(X0)) => (humble(sK0) & ~kind(sK0)) [choice axiom]
47. (humble(sK0) & ~kind(sK0)) | ! [X1] : (brave(X1) & quiet(X1)) [skolemisation 45,46]
48. ! [X0] : (((~wise(X0) | humble(X0)) & (wise(X0) | ~humble(X0))) | (tall(X0) & ~patient(X0))) [nnf transformation 34]
49. ! [X0] : (((~funny(X0) & kind(X0)) | patient(X0)) & (~patient(X0) | (funny(X0) | ~kind(X0)))) [nnf transformation 13]
50. ! [X0] : (((~funny(X0) & kind(X0)) | patient(X0)) & (~patient(X0) | funny(X0) | ~kind(X0))) [flattening 49]
51. ! [X0] : ((((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0))))) [nnf transformation 15]
66. ~kind(X0) | ~brave(X0) | creative(X0) [cnf transformation 36]
71. ~humble(X0) | ~patient(X0) | rich(X0) [cnf transformation 37]
75. ~generous(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 38]
76. ~calm(X0) | humble(X0) | ~brave(X0) [cnf transformation 40]
78. ~humble(X0) | brave(X0) [cnf transformation 40]
87. ~brave(X0) | ~brave(X0) | wise(X0) [cnf transformation 44]
90. ~kind(sK0) | brave(X1) [cnf transformation 47]
92. humble(sK0) | brave(X1) [cnf transformation 47]
95. ~patient(X0) | humble(X0) | ~wise(X0) [cnf transformation 48]
98. patient(X0) | kind(X0) [cnf transformation 50]
100. generous(paul) | calm(X0) [cnf transformation 35]
103. strong(X0) | ~rich(X0) | ~wise(X0) | strong(X0) [cnf transformation 51]
107. ~strong(X0) | ~wise(X0) | ~rich(X0) | ~strong(X0) [cnf transformation 51]
118. ~humble(susan) [cnf transformation 22]
119. strong(X0) | ~rich(X0) | ~wise(X0) [duplicate literal removal 103]
121. ~rich(X0) | ~wise(X0) | ~strong(X0) [duplicate literal removal 107]
124. ~brave(X0) | wise(X0) [duplicate literal removal 87]
172. 11 <=> ! [X1] : brave(X1) [avatar definition]
173. brave(X1) <- (11) [avatar component clause 172]
175. 12 <=> humble(sK0) [avatar definition]
177. humble(sK0) <- (12) [avatar component clause 175]
178. 11 | 12 [avatar split clause 92,175,172]
184. 14 <=> kind(sK0) [avatar definition]
186. ~kind(sK0) <- (~14) [avatar component clause 184]
187. 11 | ~14 [avatar split clause 90,184,172]
193. 16 <=> generous(paul) [avatar definition]
195. generous(paul) <- (16) [avatar component clause 193]
198. 17 <=> ! [X0] : calm(X0) [avatar definition]
199. calm(X0) <- (17) [avatar component clause 198]
200. 17 | 16 [avatar split clause 100,193,198]
202. ~rich(X0) | ~wise(X0) [subsumption resolution 119,121]
241. brave(sK0) <- (12) [resolution 78,177]
248. wise(sK0) <- (12) [resolution 124,241]
291. ~patient(sK0) | rich(sK0) <- (12) [resolution 71,177]
293. 30 <=> rich(sK0) [avatar definition]
295. rich(sK0) <- (30) [avatar component clause 293]
297. 31 <=> patient(sK0) [avatar definition]
299. ~patient(sK0) <- (~31) [avatar component clause 297]
300. 30 | ~31 | ~12 [avatar split clause 291,175,297,293]
301. kind(sK0) <- (~31) [resolution 299,98]
302. $false <- (~14, ~31) [subsumption resolution 301,186]
303. 14 | 31 [avatar contradiction clause 302]
306. ~wise(sK0) <- (30) [resolution 295,202]
307. $false <- (12, 30) [subsumption resolution 306,248]
308. ~12 | ~30 [avatar contradiction clause 307]
310. wise(X0) <- (11) [resolution 173,124]
334. ~creative(paul) | ~brave(paul) <- (16) [resolution 75,195]
335. ~creative(paul) <- (11, 16) [subsumption resolution 334,173]
353. humble(X0) | ~wise(X0) | kind(X0) [resolution 95,98]
356. humble(X0) | kind(X0) <- (11) [subsumption resolution 353,310]
426. kind(X2) | ~patient(X2) | rich(X2) <- (11) [resolution 356,71]
428. rich(X2) | kind(X2) <- (11) [subsumption resolution 426,98]
453. kind(X3) | ~wise(X3) <- (11) [resolution 428,202]
457. kind(X3) <- (11) [subsumption resolution 453,310]
462. ~brave(X0) | creative(X0) <- (11) [resolution 457,66]
464. creative(X0) <- (11) [subsumption resolution 462,173]
469. $false <- (11, 16) [resolution 464,335]
470. ~11 | ~16 [avatar contradiction clause 469]
473. humble(X0) | ~brave(X0) <- (17) [resolution 199,76]
474. humble(X0) <- (11, 17) [subsumption resolution 473,173]
475. $false <- (11, 17) [resolution 474,118]
480. ~11 | ~17 [avatar contradiction clause 475]
481. $false [avatar sat refutation 178,187,200,300,303,308,470,480]
% SZS output end Proof for 2773570873289664213621219
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and quiet is not humble or patient and vice versa.
If someone is not quiet or old then someone is not brave or wise and vice versa.
Everyone who is either not happy or not wise is both kind and happy and vice versa.
If someone is funny then someone is not kind or wise and vice versa.
If mary is rich then john is not funny and vice versa.
Everyone who is creative is strong.
If someone is not kind or generous then someone is both not patient and not old and vice versa.
Everyone who is happy or not brave is both happy and funny and vice versa.
Everyone who is both not curious and patient is not tall or tall.
If someone is calm or not generous then someone is generous and vice versa.
Everyone who is generous or not old is either not strong or old.
Everyone who is not happy or humble is patient.
If fred is quiet then john is quiet or not funny.
If alice is both not calm and kind then alice is strong or not creative and vice versa.
If someone is humble or creative then susan is not calm or not wise and vice versa.
If paul is tall or creative then paul is old or not humble.
Fred is both not patient and not calm.
Someone is both not generous and creative.
Someone is not generous.
John is creative.
Lucy is wise.
Alice is not brave or strong. | Mary is curious. | neutral | (![X]:((~brave(X)&quiet(X))<=>(~humble(X)|patient(X))))&
((?[X]:((~quiet(X)|old(X))))<=>(?[X]:((~brave(X)|wise(X)))))&
(![X]:((~happy(X)<~>~wise(X))<=>(kind(X)&happy(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~kind(X)|wise(X)))))&
((rich(mary))<=>(~funny(john)))&
(![X]:(creative(X)=>strong(X)))&
((?[X]:((~kind(X)|generous(X))))<=>(?[X]:((~patient(X)&~old(X)))))&
(![X]:((happy(X)|~brave(X))<=>(happy(X)&funny(X))))&
(![X]:((~curious(X)&patient(X))=>(~tall(X)|tall(X))))&
((?[X]:((calm(X)|~generous(X))))<=>(?[X]:(generous(X))))&
(![X]:((generous(X)|~old(X))=>(~strong(X)<~>old(X))))&
(![X]:((~happy(X)|humble(X))=>patient(X)))&
((quiet(fred))=>((quiet(john)|~funny(john))))&
(((~calm(alice)&kind(alice)))<=>((strong(alice)|~creative(alice))))&
((?[X]:((humble(X)|creative(X))))<=>((~calm(susan)|~wise(susan))))&
(((tall(paul)|creative(paul)))=>((old(paul)|~humble(paul))))&
((~patient(fred)&~calm(fred)))&
(?[X]:((~generous(X)&creative(X))))&
(?[X]:(~generous(X)))&
(creative(john))&
(wise(lucy))&
((~brave(alice)|strong(alice))) | curious(mary) | [] | null | 0 |
If fred is not creative or not old then someone is not calm or quiet.
Everyone who is creative or not happy is not strong.
Everyone who is not creative or brave is both not humble and rich.
Everyone who is either not generous or creative is both not generous and funny.
Everyone who is kind or patient is generous or tall and vice versa.
If mary is not brave or generous then someone is not funny.
Everyone who is either tall or humble is either wise or not calm and vice versa.
If someone is both not quiet and quiet then fred is either funny or not calm and vice versa.
If susan is either not happy or calm then someone is curious or not happy.
If john is both happy and not brave then someone is not funny.
Everyone who is both calm and tall is rich.
Everyone who is not rich is generous and vice versa.
If john is either not calm or not strong then someone is not rich.
If susan is both not old and curious then someone is humble and vice versa.
Everyone who is both not brave and calm is both humble and not happy and vice versa.
If someone is either funny or not quiet then someone is either generous or not brave.
Alice is either tall or strong.
Lucy is either not strong or not old.
Someone is calm.
Fred is patient.
Alice is not old or not patient.
Someone is not generous or not old.
Someone is both quiet and creative.
Someone is strong. | Alice is strong. | neutral | (((~creative(fred)|~old(fred)))=>(?[X]:((~calm(X)|quiet(X)))))&
(![X]:((creative(X)|~happy(X))=>~strong(X)))&
(![X]:((~creative(X)|brave(X))=>(~humble(X)&rich(X))))&
(![X]:((~generous(X)<~>creative(X))=>(~generous(X)&funny(X))))&
(![X]:((kind(X)|patient(X))<=>(generous(X)|tall(X))))&
(((~brave(mary)|generous(mary)))=>(?[X]:(~funny(X))))&
(![X]:((tall(X)<~>humble(X))<=>(wise(X)<~>~calm(X))))&
((?[X]:((~quiet(X)&quiet(X))))<=>((funny(fred)<~>~calm(fred))))&
(((~happy(susan)<~>calm(susan)))=>(?[X]:((curious(X)|~happy(X)))))&
(((happy(john)&~brave(john)))=>(?[X]:(~funny(X))))&
(![X]:((calm(X)&tall(X))=>rich(X)))&
(![X]:(~rich(X)<=>generous(X)))&
(((~calm(john)<~>~strong(john)))=>(?[X]:(~rich(X))))&
(((~old(susan)&curious(susan)))<=>(?[X]:(humble(X))))&
(![X]:((~brave(X)&calm(X))<=>(humble(X)&~happy(X))))&
((?[X]:((funny(X)<~>~quiet(X))))=>(?[X]:((generous(X)<~>~brave(X)))))&
((tall(alice)<~>strong(alice)))&
((~strong(lucy)<~>~old(lucy)))&
(?[X]:(calm(X)))&
(patient(fred))&
((~old(alice)|~patient(alice)))&
(?[X]:((~generous(X)|~old(X))))&
(?[X]:((quiet(X)&creative(X))))&
(?[X]:(strong(X))) | strong(alice) | [] | null | 0 |
If someone is either strong or not happy then susan is either not rich or not happy. Everyone who is both rich and not quiet is both calm and not calm and vice versa. If alice is both kind and quiet then fred is either happy or not patient and vice versa. If someone is either not wise or not patient then someone is not patient and vice versa. Everyone who is not brave is patient or not quiet and vice versa. Everyone who is both not old and kind is not calm or humble. If fred is tall or not rich then someone is humble and vice versa. Everyone who is not kind is either quiet or not happy and vice versa. If someone is either old or curious then paul is quiet or curious and vice versa. Everyone who is tall is quiet or not funny. Everyone who is not happy or humble is both tall and not kind and vice versa. If paul is either funny or not happy then someone is either not patient or funny. Everyone who is not humble or humble is either wise or creative and vice versa. Everyone who is either happy or not calm is either wise or brave and vice versa. Everyone who is not calm or old is patient and vice versa. If mary is either funny or not patient then lucy is not humble. Someone is both quiet and not tall. Lucy is both patient and calm. Lucy is either brave or creative. John is not brave or creative. Susan is not kind. Lucy is creative. John is brave. Mary is both patient and calm. | Fred is not kind. | entailment | ((?[X]:((strong(X)<~>~happy(X))))=>((~rich(susan)<~>~happy(susan))))&
(![X]:((rich(X)&~quiet(X))<=>(calm(X)&~calm(X))))&
(((kind(alice)&quiet(alice)))<=>((happy(fred)<~>~patient(fred))))&
((?[X]:((~wise(X)<~>~patient(X))))<=>(?[X]:(~patient(X))))&
(![X]:(~brave(X)<=>(patient(X)|~quiet(X))))&
(![X]:((~old(X)&kind(X))=>(~calm(X)|humble(X))))&
(((tall(fred)|~rich(fred)))<=>(?[X]:(humble(X))))&
(![X]:(~kind(X)<=>(quiet(X)<~>~happy(X))))&
((?[X]:((old(X)<~>curious(X))))<=>((quiet(paul)|curious(paul))))&
(![X]:(tall(X)=>(quiet(X)|~funny(X))))&
(![X]:((~happy(X)|humble(X))<=>(tall(X)&~kind(X))))&
(((funny(paul)<~>~happy(paul)))=>(?[X]:((~patient(X)<~>funny(X)))))&
(![X]:((~humble(X)|humble(X))<=>(wise(X)<~>creative(X))))&
(![X]:((happy(X)<~>~calm(X))<=>(wise(X)<~>brave(X))))&
(![X]:((~calm(X)|old(X))<=>patient(X)))&
(((funny(mary)<~>~patient(mary)))=>(~humble(lucy)))&
(?[X]:((quiet(X)&~tall(X))))&
((patient(lucy)&calm(lucy)))&
((brave(lucy)<~>creative(lucy)))&
((~brave(john)|creative(john)))&
(~kind(susan))&
(creative(lucy))&
(brave(john))&
((patient(mary)&calm(mary))) | ~kind(fred) | [
"p2",
"p5",
"p7",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8841914935954850409255767
% SZS output start Proof for 8841914935954850409255767
3. (quiet(alice) & kind(alice)) <=> (happy(fred) <~> ~patient(fred)) [input p2]
6. ! [X0] : ((kind(X0) & ~old(X0)) => (humble(X0) | ~calm(X0))) [input p5]
8. ! [X0] : (~kind(X0) <=> (quiet(X0) <~> ~happy(X0))) [input p7]
11. ! [X0] : ((humble(X0) | ~happy(X0)) <=> (~kind(X0) & tall(X0))) [input p10]
15. ! [X0] : ((old(X0) | ~calm(X0)) <=> patient(X0)) [input p14]
25. kind(fred) [input hypothesis]
28. ! [X0] : ((humble(X0) | ~calm(X0)) | (~kind(X0) | old(X0))) [ennf transformation 6]
29. ! [X0] : (humble(X0) | ~calm(X0) | ~kind(X0) | old(X0)) [flattening 28]
37. ((quiet(alice) & kind(alice)) | ((happy(fred) | patient(fred)) & (~patient(fred) | ~happy(fred)))) & (((patient(fred) | ~happy(fred)) & (~patient(fred) | happy(fred))) | (~quiet(alice) | ~kind(alice))) [nnf transformation 3]
38. ((quiet(alice) & kind(alice)) | ((happy(fred) | patient(fred)) & (~patient(fred) | ~happy(fred)))) & (((patient(fred) | ~happy(fred)) & (~patient(fred) | happy(fred))) | ~quiet(alice) | ~kind(alice)) [flattening 37]
51. ! [X0] : ((~kind(X0) | ((quiet(X0) | happy(X0)) & (~happy(X0) | ~quiet(X0)))) & (((happy(X0) | ~quiet(X0)) & (~happy(X0) | quiet(X0))) | kind(X0))) [nnf transformation 8]
57. ! [X0] : (((humble(X0) | ~happy(X0)) | (kind(X0) | ~tall(X0))) & ((~kind(X0) & tall(X0)) | (~humble(X0) & happy(X0)))) [nnf transformation 11]
58. ! [X0] : ((humble(X0) | ~happy(X0) | kind(X0) | ~tall(X0)) & ((~kind(X0) & tall(X0)) | (~humble(X0) & happy(X0)))) [flattening 57]
65. ! [X0] : (((old(X0) | ~calm(X0)) | ~patient(X0)) & (patient(X0) | (~old(X0) & calm(X0)))) [nnf transformation 15]
66. ! [X0] : ((old(X0) | ~calm(X0) | ~patient(X0)) & (patient(X0) | (~old(X0) & calm(X0)))) [flattening 65]
81. kind(alice) | ~patient(fred) | ~happy(fred) [cnf transformation 38]
83. quiet(alice) | ~patient(fred) | ~happy(fred) [cnf transformation 38]
92. ~kind(X0) | ~calm(X0) | humble(X0) | old(X0) [cnf transformation 29]
98. ~kind(X0) | ~happy(X0) | ~quiet(X0) [cnf transformation 51]
109. ~kind(X0) | happy(X0) [cnf transformation 58]
110. ~humble(X0) | ~kind(X0) [cnf transformation 58]
130. patient(X0) | calm(X0) [cnf transformation 66]
131. ~old(X0) | patient(X0) [cnf transformation 66]
147. kind(fred) [cnf transformation 25]
168. 5 <=> patient(fred) [avatar definition]
169. ~patient(fred) <- (~5) [avatar component clause 168]
172. 6 <=> happy(fred) [avatar definition]
176. 7 <=> quiet(alice) [avatar definition]
180. ~6 | ~5 | 7 [avatar split clause 83,176,168,172]
182. 8 <=> kind(alice) [avatar definition]
184. kind(alice) <- (8) [avatar component clause 182]
186. ~6 | ~5 | 8 [avatar split clause 81,182,168,172]
327. happy(fred) [resolution 109,147]
328. calm(fred) <- (~5) [resolution 130,169]
402. ~calm(fred) | humble(fred) | old(fred) [resolution 92,147]
403. humble(fred) | old(fred) <- (~5) [subsumption resolution 402,328]
405. 40 <=> old(fred) [avatar definition]
407. old(fred) <- (40) [avatar component clause 405]
409. 41 <=> humble(fred) [avatar definition]
411. humble(fred) <- (41) [avatar component clause 409]
412. 40 | 41 | 5 [avatar split clause 403,168,409,405]
493. ~happy(alice) | ~quiet(alice) <- (8) [resolution 184,98]
494. happy(alice) <- (8) [resolution 184,109]
511. ~quiet(alice) <- (8) [subsumption resolution 493,494]
512. ~7 | ~8 [avatar split clause 511,182,176]
522. ~kind(fred) <- (41) [resolution 411,110]
524. $false <- (41) [subsumption resolution 522,147]
525. ~41 [avatar contradiction clause 524]
535. patient(fred) <- (40) [resolution 407,131]
538. 5 | ~40 [avatar split clause 535,405,168]
545. 6 [avatar split clause 327,172]
546. $false [avatar sat refutation 180,186,412,512,525,538,545]
% SZS output end Proof for 8841914935954850409255767
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not rich and not kind then someone is funny or not quiet.
If alice is humble then someone is either not curious or not happy and vice versa.
Everyone who is both not generous and not patient is either not happy or generous.
If mary is either not funny or not generous then someone is quiet and vice versa.
Everyone who is either generous or not strong is quiet.
If someone is either rich or calm then someone is not happy.
If lucy is not tall then someone is rich or brave.
Everyone who is humble or strong is both not quiet and not tall.
If someone is not kind or old then paul is either creative or generous and vice versa.
Everyone who is tall is quiet or patient and vice versa.
Everyone who is either old or rich is either quiet or not quiet.
Everyone who is not kind or humble is either calm or funny and vice versa.
If someone is not generous or tall then john is either kind or not creative and vice versa.
If susan is both tall and rich then someone is old or not funny.
If susan is not patient then someone is both tall and not strong.
If fred is either not rich or funny then someone is quiet or not funny.
Someone is patient or curious.
Fred is either not old or brave.
John is both not creative and not rich.
Mary is both not old and strong.
Someone is both tall and not quiet.
Paul is either humble or not old.
Someone is both not patient and not brave.
Fred is calm. | Mary is happy. | contradiction | ((?[X]:((~rich(X)&~kind(X))))=>(?[X]:((funny(X)|~quiet(X)))))&
((humble(alice))<=>(?[X]:((~curious(X)<~>~happy(X)))))&
(![X]:((~generous(X)&~patient(X))=>(~happy(X)<~>generous(X))))&
(((~funny(mary)<~>~generous(mary)))<=>(?[X]:(quiet(X))))&
(![X]:((generous(X)<~>~strong(X))=>quiet(X)))&
((?[X]:((rich(X)<~>calm(X))))=>(?[X]:(~happy(X))))&
((~tall(lucy))=>(?[X]:((rich(X)|brave(X)))))&
(![X]:((humble(X)|strong(X))=>(~quiet(X)&~tall(X))))&
((?[X]:((~kind(X)|old(X))))<=>((creative(paul)<~>generous(paul))))&
(![X]:(tall(X)<=>(quiet(X)|patient(X))))&
(![X]:((old(X)<~>rich(X))=>(quiet(X)<~>~quiet(X))))&
(![X]:((~kind(X)|humble(X))<=>(calm(X)<~>funny(X))))&
((?[X]:((~generous(X)|tall(X))))<=>((kind(john)<~>~creative(john))))&
(((tall(susan)&rich(susan)))=>(?[X]:((old(X)|~funny(X)))))&
((~patient(susan))=>(?[X]:((tall(X)&~strong(X)))))&
(((~rich(fred)<~>funny(fred)))=>(?[X]:((quiet(X)|~funny(X)))))&
(?[X]:((patient(X)|curious(X))))&
((~old(fred)<~>brave(fred)))&
((~creative(john)&~rich(john)))&
((~old(mary)&strong(mary)))&
(?[X]:((tall(X)&~quiet(X))))&
((humble(paul)<~>~old(paul)))&
(?[X]:((~patient(X)&~brave(X))))&
(calm(fred)) | happy(mary) | [
"p2",
"p4",
"p7",
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8925038473663941706932445
% SZS output start Proof for 8925038473663941706932445
3. ! [X0] : ((~patient(X0) & ~generous(X0)) => (~happy(X0) <~> generous(X0))) [input p2]
5. ! [X0] : ((generous(X0) <~> ~strong(X0)) => quiet(X0)) [input p4]
8. ! [X0] : ((strong(X0) | humble(X0)) => (~tall(X0) & ~quiet(X0))) [input p7]
10. ! [X0] : (tall(X0) <=> (patient(X0) | quiet(X0))) [input p9]
20. strong(mary) & ~old(mary) [input p19]
25. happy(mary) [input hypothesis]
29. ! [X0] : ((~happy(X0) <~> generous(X0)) | (patient(X0) | generous(X0))) [ennf transformation 3]
30. ! [X0] : ((~happy(X0) <~> generous(X0)) | patient(X0) | generous(X0)) [flattening 29]
31. ! [X0] : (quiet(X0) | (generous(X0) <=> ~strong(X0))) [ennf transformation 5]
34. ! [X0] : ((~tall(X0) & ~quiet(X0)) | (~strong(X0) & ~humble(X0))) [ennf transformation 8]
47. ! [X0] : (((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | patient(X0) | generous(X0)) [nnf transformation 30]
52. ! [X0] : (quiet(X0) | ((generous(X0) | strong(X0)) & (~strong(X0) | ~generous(X0)))) [nnf transformation 31]
63. ! [X0] : ((tall(X0) | (~patient(X0) & ~quiet(X0))) & ((patient(X0) | quiet(X0)) | ~tall(X0))) [nnf transformation 10]
64. ! [X0] : ((tall(X0) | (~patient(X0) & ~quiet(X0))) & (patient(X0) | quiet(X0) | ~tall(X0))) [flattening 63]
92. generous(X0) | ~happy(X0) | patient(X0) | generous(X0) [cnf transformation 47]
98. ~strong(X0) | quiet(X0) | ~generous(X0) [cnf transformation 52]
104. ~strong(X0) | ~quiet(X0) [cnf transformation 34]
106. ~tall(X0) | ~strong(X0) [cnf transformation 34]
115. ~patient(X0) | tall(X0) [cnf transformation 64]
143. strong(mary) [cnf transformation 20]
151. happy(mary) [cnf transformation 25]
152. ~happy(X0) | generous(X0) | patient(X0) [duplicate literal removal 92]
195. 11 <=> generous(mary) [avatar definition]
196. ~generous(mary) <- (~11) [avatar component clause 195]
197. generous(mary) <- (11) [avatar component clause 195]
366. ~quiet(mary) [resolution 104,143]
379. quiet(mary) | ~generous(mary) [resolution 98,143]
410. generous(mary) | patient(mary) [resolution 152,151]
411. patient(mary) <- (~11) [subsumption resolution 410,196]
412. tall(mary) <- (~11) [resolution 411,115]
423. ~strong(mary) <- (~11) [resolution 412,106]
425. $false <- (~11) [subsumption resolution 423,143]
426. 11 [avatar contradiction clause 425]
434. quiet(mary) <- (11) [subsumption resolution 379,197]
467. $false <- (11) [subsumption resolution 366,434]
468. ~11 [avatar contradiction clause 467]
469. $false [avatar sat refutation 426,468]
% SZS output end Proof for 8925038473663941706932445
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or old is either not generous or not old. Everyone who is either not humble or wise is either not rich or not kind. Everyone who is not calm or rich is humble or kind. If someone is both not wise and not rich then susan is both kind and strong. Everyone who is quiet or wise is either not kind or not brave. If someone is both wise and humble then someone is tall or not patient. If someone is not curious or strong then someone is old. Everyone who is not rich is either not patient or not funny and vice versa. Everyone who is not tall is either not kind or brave. Everyone who is either old or not brave is happy or strong and vice versa. If fred is both not brave and calm then someone is either humble or not patient and vice versa. If mary is either not wise or not strong then someone is either patient or not rich. Everyone who is both not tall and tall is strong and vice versa. If fred is not humble then someone is not curious or old and vice versa. Everyone who is either not calm or strong is both brave and patient. Everyone who is creative or not curious is not calm and vice versa. Someone is both not patient and not brave. Fred is both humble and kind. Someone is either not patient or generous. Someone is not funny or generous. Someone is generous. Someone is either strong or not kind. | Fred is not creative. | entailment | (![X]:((brave(X)|old(X))=>(~generous(X)<~>~old(X))))&
(![X]:((~humble(X)<~>wise(X))=>(~rich(X)<~>~kind(X))))&
(![X]:((~calm(X)|rich(X))=>(humble(X)|kind(X))))&
((?[X]:((~wise(X)&~rich(X))))=>((kind(susan)&strong(susan))))&
(![X]:((quiet(X)|wise(X))=>(~kind(X)<~>~brave(X))))&
((?[X]:((wise(X)&humble(X))))=>(?[X]:((tall(X)|~patient(X)))))&
((?[X]:((~curious(X)|strong(X))))=>(?[X]:(old(X))))&
(![X]:(~rich(X)<=>(~patient(X)<~>~funny(X))))&
(![X]:(~tall(X)=>(~kind(X)<~>brave(X))))&
(![X]:((old(X)<~>~brave(X))<=>(happy(X)|strong(X))))&
(((~brave(fred)&calm(fred)))<=>(?[X]:((humble(X)<~>~patient(X)))))&
(((~wise(mary)<~>~strong(mary)))=>(?[X]:((patient(X)<~>~rich(X)))))&
(![X]:((~tall(X)&tall(X))<=>strong(X)))&
((~humble(fred))<=>(?[X]:((~curious(X)|old(X)))))&
(![X]:((~calm(X)<~>strong(X))=>(brave(X)&patient(X))))&
(![X]:((creative(X)|~curious(X))<=>~calm(X)))&
(?[X]:((~patient(X)&~brave(X))))&
((humble(fred)&kind(fred)))&
(?[X]:((~patient(X)<~>generous(X))))&
(?[X]:((~funny(X)|generous(X))))&
(?[X]:(generous(X)))&
(?[X]:((strong(X)<~>~kind(X)))) | ~creative(fred) | [
"p10",
"p12",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6629649446921927851896225
% SZS output start Proof for 6629649446921927851896225
11. (calm(fred) & ~brave(fred)) <=> ? [X0] : (humble(X0) <~> ~patient(X0)) [input p10]
13. ! [X0] : ((tall(X0) & ~tall(X0)) <=> strong(X0)) [input p12]
15. ! [X0] : ((~calm(X0) <~> strong(X0)) => (patient(X0) & brave(X0))) [input p14]
16. ! [X0] : ((~curious(X0) | creative(X0)) <=> ~calm(X0)) [input p15]
18. kind(fred) & humble(fred) [input p17]
23. creative(fred) [input hypothesis]
37. ! [X0] : ((patient(X0) & brave(X0)) | (~calm(X0) <=> strong(X0))) [ennf transformation 15]
51. ((calm(fred) & ~brave(fred)) | ! [X0] : ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0)))) & (? [X0] : ((patient(X0) | ~humble(X0)) & (~patient(X0) | humble(X0))) | (~calm(fred) | brave(fred))) [nnf transformation 11]
52. ((calm(fred) & ~brave(fred)) | ! [X0] : ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0)))) & (? [X0] : ((patient(X0) | ~humble(X0)) & (~patient(X0) | humble(X0))) | ~calm(fred) | brave(fred)) [flattening 51]
53. ((calm(fred) & ~brave(fred)) | ! [X0] : ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0)))) & (? [X1] : ((patient(X1) | ~humble(X1)) & (~patient(X1) | humble(X1))) | ~calm(fred) | brave(fred)) [rectify 52]
54. ? [X1] : ((patient(X1) | ~humble(X1)) & (~patient(X1) | humble(X1))) => ((patient(sK2) | ~humble(sK2)) & (~patient(sK2) | humble(sK2))) [choice axiom]
55. ((calm(fred) & ~brave(fred)) | ! [X0] : ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0)))) & (((patient(sK2) | ~humble(sK2)) & (~patient(sK2) | humble(sK2))) | ~calm(fred) | brave(fred)) [skolemisation 53,54]
59. ! [X0] : (((tall(X0) & ~tall(X0)) | ~strong(X0)) & (strong(X0) | (~tall(X0) | tall(X0)))) [nnf transformation 13]
60. ! [X0] : (((tall(X0) & ~tall(X0)) | ~strong(X0)) & (strong(X0) | ~tall(X0) | tall(X0))) [flattening 59]
65. ! [X0] : ((patient(X0) & brave(X0)) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0)))) [nnf transformation 37]
66. ! [X0] : (((~curious(X0) | creative(X0)) | calm(X0)) & (~calm(X0) | (curious(X0) & ~creative(X0)))) [nnf transformation 16]
67. ! [X0] : ((~curious(X0) | creative(X0) | calm(X0)) & (~calm(X0) | (curious(X0) & ~creative(X0)))) [flattening 66]
111. ~brave(fred) | ~patient(X0) | ~humble(X0) [cnf transformation 55]
120. ~tall(X0) | ~strong(X0) [cnf transformation 60]
121. ~strong(X0) | tall(X0) [cnf transformation 60]
125. strong(X0) | brave(X0) | calm(X0) [cnf transformation 65]
127. patient(X0) | strong(X0) | calm(X0) [cnf transformation 65]
129. ~creative(X0) | ~calm(X0) [cnf transformation 67]
134. humble(fred) [cnf transformation 18]
142. creative(fred) [cnf transformation 23]
170. 7 <=> ! [X1] : ~strong(X1) [avatar definition]
171. ~strong(X1) <- (7) [avatar component clause 170]
185. 11 <=> calm(fred) [avatar definition]
186. ~calm(fred) <- (~11) [avatar component clause 185]
190. 12 <=> ! [X0] : (~patient(X0) | ~humble(X0)) [avatar definition]
191. ~patient(X0) | ~humble(X0) <- (12) [avatar component clause 190]
194. 13 <=> brave(fred) [avatar definition]
198. 12 | ~13 [avatar split clause 111,194,190]
229. ~strong(X0) [subsumption resolution 120,121]
230. 7 [avatar split clause 229,170]
235. 21 <=> humble(fred) [avatar definition]
236. humble(fred) <- (21) [avatar component clause 235]
249. 21 [avatar split clause 134,235]
281. ~calm(fred) [resolution 129,142]
284. ~11 [avatar split clause 281,185]
354. calm(X3) | brave(X3) <- (7) [resolution 125,171]
360. brave(fred) <- (7, ~11) [resolution 354,186]
364. 13 | ~7 | 11 [avatar split clause 360,185,170,194]
379. strong(X1) | calm(X1) | ~humble(X1) <- (12) [resolution 127,191]
386. ~humble(X1) | calm(X1) <- (7, 12) [subsumption resolution 379,171]
409. calm(fred) <- (7, 12, 21) [resolution 386,236]
415. $false <- (7, ~11, 12, 21) [subsumption resolution 409,186]
416. ~7 | 11 | ~12 | ~21 [avatar contradiction clause 415]
417. $false [avatar sat refutation 198,230,249,284,364,416]
% SZS output end Proof for 6629649446921927851896225
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and strong is rich or old. Everyone who is both not brave and not funny is either quiet or curious. If someone is both humble and generous then someone is either strong or happy and vice versa. Everyone who is both not strong and not creative is wise and vice versa. If someone is not tall then someone is kind and vice versa. If someone is both not patient and not curious then someone is not wise. If mary is wise then alice is both not creative and not happy. Everyone who is both old and not old is wise and vice versa. Everyone who is happy is wise and vice versa. If someone is not happy or tall then fred is either not generous or funny and vice versa. Everyone who is creative or patient is either not old or curious and vice versa. If someone is old then lucy is not humble. Everyone who is not patient is not curious or not humble. If fred is not curious or creative then paul is both old and kind. If mary is either curious or not humble then john is happy or patient and vice versa. Everyone who is tall is both curious and not creative and vice versa. Someone is not rich. Someone is both not curious and not wise. John is either not strong or not quiet. John is either not humble or creative. John is either curious or not funny. Alice is not quiet or not brave. John is not quiet or wise. Someone is curious. | Fred is not wise. | entailment | (![X]:((generous(X)&strong(X))=>(rich(X)|old(X))))&
(![X]:((~brave(X)&~funny(X))=>(quiet(X)<~>curious(X))))&
((?[X]:((humble(X)&generous(X))))<=>(?[X]:((strong(X)<~>happy(X)))))&
(![X]:((~strong(X)&~creative(X))<=>wise(X)))&
((?[X]:(~tall(X)))<=>(?[X]:(kind(X))))&
((?[X]:((~patient(X)&~curious(X))))=>(?[X]:(~wise(X))))&
((wise(mary))=>((~creative(alice)&~happy(alice))))&
(![X]:((old(X)&~old(X))<=>wise(X)))&
(![X]:(happy(X)<=>wise(X)))&
((?[X]:((~happy(X)|tall(X))))<=>((~generous(fred)<~>funny(fred))))&
(![X]:((creative(X)|patient(X))<=>(~old(X)<~>curious(X))))&
((?[X]:(old(X)))=>(~humble(lucy)))&
(![X]:(~patient(X)=>(~curious(X)|~humble(X))))&
(((~curious(fred)|creative(fred)))=>((old(paul)&kind(paul))))&
(((curious(mary)<~>~humble(mary)))<=>((happy(john)|patient(john))))&
(![X]:(tall(X)<=>(curious(X)&~creative(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~curious(X)&~wise(X))))&
((~strong(john)<~>~quiet(john)))&
((~humble(john)<~>creative(john)))&
((curious(john)<~>~funny(john)))&
((~quiet(alice)|~brave(alice)))&
((~quiet(john)|wise(john)))&
(?[X]:(curious(X))) | ~wise(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5017566157919534708622871
% SZS output start Proof for 5017566157919534708622871
8. ! [X0] : ((~old(X0) & old(X0)) <=> wise(X0)) [input p7]
25. wise(fred) [input hypothesis]
55. ! [X0] : (((~old(X0) & old(X0)) | ~wise(X0)) & (wise(X0) | (old(X0) | ~old(X0)))) [nnf transformation 8]
56. ! [X0] : (((~old(X0) & old(X0)) | ~wise(X0)) & (wise(X0) | old(X0) | ~old(X0))) [flattening 55]
95. old(X0) | ~wise(X0) [cnf transformation 56]
96. ~old(X0) | ~wise(X0) [cnf transformation 56]
138. wise(fred) [cnf transformation 25]
208. ~wise(X0) [subsumption resolution 95,96]
314. $false [subsumption resolution 138,208]
% SZS output end Proof for 5017566157919534708622871
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or funny is not humble or wise and vice versa.
Everyone who is not tall or not brave is both rich and old and vice versa.
If lucy is not humble then alice is not brave and vice versa.
Everyone who is humble or curious is funny and vice versa.
Everyone who is either not humble or not wise is kind and vice versa.
Everyone who is both not brave and not kind is either not creative or not brave.
Everyone who is not kind or humble is both old and not calm.
If fred is not strong then john is both brave and calm and vice versa.
If someone is calm then someone is creative.
If someone is either not tall or not curious then someone is either humble or not happy and vice versa.
If someone is either wise or strong then john is not happy and vice versa.
Everyone who is either happy or not wise is not creative or not strong and vice versa.
Everyone who is both not rich and tall is curious or rich and vice versa.
If susan is not curious or not old then someone is either not strong or generous.
Everyone who is not patient is not curious or quiet and vice versa.
If fred is both wise and funny then fred is both not curious and not kind and vice versa.
Someone is both not generous and patient.
Alice is not funny or not generous.
Mary is either funny or calm.
Paul is either old or not funny. | Lucy is happy. | contradiction | (![X]:((kind(X)<~>funny(X))<=>(~humble(X)|wise(X))))&
(![X]:((~tall(X)|~brave(X))<=>(rich(X)&old(X))))&
((~humble(lucy))<=>(~brave(alice)))&
(![X]:((humble(X)|curious(X))<=>funny(X)))&
(![X]:((~humble(X)<~>~wise(X))<=>kind(X)))&
(![X]:((~brave(X)&~kind(X))=>(~creative(X)<~>~brave(X))))&
(![X]:((~kind(X)|humble(X))=>(old(X)&~calm(X))))&
((~strong(fred))<=>((brave(john)&calm(john))))&
((?[X]:(calm(X)))=>(?[X]:(creative(X))))&
((?[X]:((~tall(X)<~>~curious(X))))<=>(?[X]:((humble(X)<~>~happy(X)))))&
((?[X]:((wise(X)<~>strong(X))))<=>(~happy(john)))&
(![X]:((happy(X)<~>~wise(X))<=>(~creative(X)|~strong(X))))&
(![X]:((~rich(X)&tall(X))<=>(curious(X)|rich(X))))&
(((~curious(susan)|~old(susan)))=>(?[X]:((~strong(X)<~>generous(X)))))&
(![X]:(~patient(X)<=>(~curious(X)|quiet(X))))&
(((wise(fred)&funny(fred)))<=>((~curious(fred)&~kind(fred))))&
(?[X]:((~generous(X)&patient(X))))&
((~funny(alice)|~generous(alice)))&
((funny(mary)<~>calm(mary)))&
((old(paul)<~>~funny(paul))) | happy(lucy) | [
"p1",
"p2",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3558632356885360613186917
% SZS output start Proof for 3558632356885360613186917
2. ! [X0] : ((~brave(X0) | ~tall(X0)) <=> (old(X0) & rich(X0))) [input p1]
3. ~humble(lucy) <=> ~brave(alice) [input p2]
10. ? [X0] : (~tall(X0) <~> ~curious(X0)) <=> ? [X0] : (humble(X0) <~> ~happy(X0)) [input p9]
13. ! [X0] : ((tall(X0) & ~rich(X0)) <=> (rich(X0) | curious(X0))) [input p12]
21. happy(lucy) [input hypothesis]
23. ? [X0] : (~tall(X0) <~> ~curious(X0)) <=> ? [X1] : (humble(X1) <~> ~happy(X1)) [rectify 10]
34. ! [X0] : (((~brave(X0) | ~tall(X0)) | (~old(X0) | ~rich(X0))) & ((old(X0) & rich(X0)) | (brave(X0) & tall(X0)))) [nnf transformation 2]
35. ! [X0] : ((~brave(X0) | ~tall(X0) | ~old(X0) | ~rich(X0)) & ((old(X0) & rich(X0)) | (brave(X0) & tall(X0)))) [flattening 34]
36. (~humble(lucy) | brave(alice)) & (~brave(alice) | humble(lucy)) [nnf transformation 3]
46. (? [X0] : ((curious(X0) | tall(X0)) & (~curious(X0) | ~tall(X0))) | ! [X1] : ((humble(X1) | happy(X1)) & (~happy(X1) | ~humble(X1)))) & (? [X1] : ((happy(X1) | ~humble(X1)) & (~happy(X1) | humble(X1))) | ! [X0] : ((~tall(X0) | curious(X0)) & (~curious(X0) | tall(X0)))) [nnf transformation 23]
47. (? [X0] : ((curious(X0) | tall(X0)) & (~curious(X0) | ~tall(X0))) | ! [X1] : ((humble(X1) | happy(X1)) & (~happy(X1) | ~humble(X1)))) & (? [X2] : ((happy(X2) | ~humble(X2)) & (~happy(X2) | humble(X2))) | ! [X3] : ((~tall(X3) | curious(X3)) & (~curious(X3) | tall(X3)))) [rectify 46]
48. ? [X0] : ((curious(X0) | tall(X0)) & (~curious(X0) | ~tall(X0))) => ((curious(sK1) | tall(sK1)) & (~curious(sK1) | ~tall(sK1))) [choice axiom]
49. ? [X2] : ((happy(X2) | ~humble(X2)) & (~happy(X2) | humble(X2))) => ((happy(sK2) | ~humble(sK2)) & (~happy(sK2) | humble(sK2))) [choice axiom]
50. (((curious(sK1) | tall(sK1)) & (~curious(sK1) | ~tall(sK1))) | ! [X1] : ((humble(X1) | happy(X1)) & (~happy(X1) | ~humble(X1)))) & (((happy(sK2) | ~humble(sK2)) & (~happy(sK2) | humble(sK2))) | ! [X3] : ((~tall(X3) | curious(X3)) & (~curious(X3) | tall(X3)))) [skolemisation 47,49,48]
57. ! [X0] : (((tall(X0) & ~rich(X0)) | (~rich(X0) & ~curious(X0))) & ((rich(X0) | curious(X0)) | (~tall(X0) | rich(X0)))) [nnf transformation 13]
58. ! [X0] : (((tall(X0) & ~rich(X0)) | (~rich(X0) & ~curious(X0))) & (rich(X0) | curious(X0) | ~tall(X0) | rich(X0))) [flattening 57]
74. rich(X0) | tall(X0) [cnf transformation 35]
75. rich(X0) | brave(X0) [cnf transformation 35]
79. ~brave(alice) | humble(lucy) [cnf transformation 36]
102. ~curious(sK1) | ~tall(sK1) | ~happy(X1) | ~humble(X1) [cnf transformation 50]
116. rich(X0) | curious(X0) | ~tall(X0) | rich(X0) [cnf transformation 58]
118. ~rich(X0) | ~rich(X0) [cnf transformation 58]
120. tall(X0) | ~rich(X0) [cnf transformation 58]
137. happy(lucy) [cnf transformation 21]
138. rich(X0) | curious(X0) | ~tall(X0) [duplicate literal removal 116]
139. ~rich(X0) [duplicate literal removal 118]
142. 1 <=> brave(alice) [avatar definition]
143. ~brave(alice) <- (~1) [avatar component clause 142]
146. 2 <=> humble(lucy) [avatar definition]
147. humble(lucy) <- (2) [avatar component clause 146]
150. 2 | ~1 [avatar split clause 79,142,146]
178. 9 <=> tall(sK1) [avatar definition]
179. ~tall(sK1) <- (~9) [avatar component clause 178]
182. 10 <=> curious(sK1) [avatar definition]
183. ~curious(sK1) <- (~10) [avatar component clause 182]
187. 11 <=> ! [X1] : (~happy(X1) | ~humble(X1)) [avatar definition]
188. ~happy(X1) | ~humble(X1) <- (11) [avatar component clause 187]
191. 11 | ~9 | ~10 [avatar split clause 102,182,178,187]
232. tall(X0) [subsumption resolution 120,74]
233. curious(X0) | ~tall(X0) [subsumption resolution 138,139]
234. curious(X0) [subsumption resolution 233,232]
288. $false <- (~10) [subsumption resolution 183,234]
289. 10 [avatar contradiction clause 288]
292. $false <- (~9) [subsumption resolution 179,232]
293. 9 [avatar contradiction clause 292]
295. brave(X0) [resolution 75,139]
296. $false <- (~1) [resolution 295,143]
297. 1 [avatar contradiction clause 296]
316. ~humble(lucy) <- (11) [resolution 188,137]
319. $false <- (2, 11) [subsumption resolution 316,147]
320. ~2 | ~11 [avatar contradiction clause 319]
323. $false [avatar sat refutation 150,191,289,293,297,320]
% SZS output end Proof for 3558632356885360613186917
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not creative or rich then john is calm and vice versa.
Everyone who is rich is not quiet.
If john is either old or not wise then someone is not rich and vice versa.
If someone is rich then fred is not funny or not creative and vice versa.
Everyone who is not generous or curious is not funny.
Everyone who is not brave or wise is tall and vice versa.
Everyone who is not funny is either humble or funny.
Everyone who is both humble and not old is not curious.
Everyone who is both patient and generous is both not generous and not curious.
If someone is both rich and old then someone is not calm or patient.
If mary is rich then someone is funny or not calm.
If fred is brave then fred is both not patient and humble.
Everyone who is either not strong or quiet is both generous and not strong and vice versa.
If fred is both not generous and tall then someone is wise and vice versa.
If fred is either wise or not happy then alice is not wise or not patient and vice versa.
If someone is either generous or not quiet then someone is both curious and not curious.
Alice is not tall or generous.
John is either patient or creative.
Someone is both not quiet and generous.
Alice is either humble or quiet.
Someone is both strong and not curious.
Someone is either not kind or generous.
Someone is both not old and not wise.
Someone is not rich. | Alice is patient. | contradiction | (((~creative(alice)|rich(alice)))<=>(calm(john)))&
(![X]:(rich(X)=>~quiet(X)))&
(((old(john)<~>~wise(john)))<=>(?[X]:(~rich(X))))&
((?[X]:(rich(X)))<=>((~funny(fred)|~creative(fred))))&
(![X]:((~generous(X)|curious(X))=>~funny(X)))&
(![X]:((~brave(X)|wise(X))<=>tall(X)))&
(![X]:(~funny(X)=>(humble(X)<~>funny(X))))&
(![X]:((humble(X)&~old(X))=>~curious(X)))&
(![X]:((patient(X)&generous(X))=>(~generous(X)&~curious(X))))&
((?[X]:((rich(X)&old(X))))=>(?[X]:((~calm(X)|patient(X)))))&
((rich(mary))=>(?[X]:((funny(X)|~calm(X)))))&
((brave(fred))=>((~patient(fred)&humble(fred))))&
(![X]:((~strong(X)<~>quiet(X))<=>(generous(X)&~strong(X))))&
(((~generous(fred)&tall(fred)))<=>(?[X]:(wise(X))))&
(((wise(fred)<~>~happy(fred)))<=>((~wise(alice)|~patient(alice))))&
((?[X]:((generous(X)<~>~quiet(X))))=>(?[X]:((curious(X)&~curious(X)))))&
((~tall(alice)|generous(alice)))&
((patient(john)<~>creative(john)))&
(?[X]:((~quiet(X)&generous(X))))&
((humble(alice)<~>quiet(alice)))&
(?[X]:((strong(X)&~curious(X))))&
(?[X]:((~kind(X)<~>generous(X))))&
(?[X]:((~old(X)&~wise(X))))&
(?[X]:(~rich(X))) | patient(alice) | [
"p4",
"p6",
"p8",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 9129485661828975017722012
% SZS output start Proof for 9129485661828975017722012
5. ! [X0] : ((curious(X0) | ~generous(X0)) => ~funny(X0)) [input p4]
7. ! [X0] : (~funny(X0) => (humble(X0) <~> funny(X0))) [input p6]
9. ! [X0] : ((generous(X0) & patient(X0)) => (~curious(X0) & ~generous(X0))) [input p8]
16. ? [X0] : (generous(X0) <~> ~quiet(X0)) => ? [X0] : (~curious(X0) & curious(X0)) [input p15]
20. humble(alice) <~> quiet(alice) [input p19]
25. patient(alice) [input hypothesis]
27. ? [X0] : (generous(X0) <~> ~quiet(X0)) => ? [X1] : (~curious(X1) & curious(X1)) [rectify 16]
29. ! [X0] : (~funny(X0) | (~curious(X0) & generous(X0))) [ennf transformation 5]
30. ! [X0] : ((humble(X0) <~> funny(X0)) | funny(X0)) [ennf transformation 7]
33. ! [X0] : ((~curious(X0) & ~generous(X0)) | (~generous(X0) | ~patient(X0))) [ennf transformation 9]
34. ! [X0] : ((~curious(X0) & ~generous(X0)) | ~generous(X0) | ~patient(X0)) [flattening 33]
38. ? [X1] : (~curious(X1) & curious(X1)) | ! [X0] : (generous(X0) <=> ~quiet(X0)) [ennf transformation 27]
52. ! [X0] : (((~funny(X0) | ~humble(X0)) & (funny(X0) | humble(X0))) | funny(X0)) [nnf transformation 30]
67. ? [X1] : (~curious(X1) & curious(X1)) | ! [X0] : ((generous(X0) | quiet(X0)) & (~quiet(X0) | ~generous(X0))) [nnf transformation 38]
68. ? [X0] : (~curious(X0) & curious(X0)) | ! [X1] : ((generous(X1) | quiet(X1)) & (~quiet(X1) | ~generous(X1))) [rectify 67]
69. ? [X0] : (~curious(X0) & curious(X0)) => (~curious(sK5) & curious(sK5)) [choice axiom]
70. (~curious(sK5) & curious(sK5)) | ! [X1] : ((generous(X1) | quiet(X1)) & (~quiet(X1) | ~generous(X1))) [skolemisation 68,69]
74. (~quiet(alice) | ~humble(alice)) & (quiet(alice) | humble(alice)) [nnf transformation 20]
95. ~funny(X0) | generous(X0) [cnf transformation 29]
100. funny(X0) | humble(X0) | funny(X0) [cnf transformation 52]
103. ~generous(X0) | ~generous(X0) | ~patient(X0) [cnf transformation 34]
125. curious(sK5) | generous(X1) | quiet(X1) [cnf transformation 70]
127. ~curious(sK5) | generous(X1) | quiet(X1) [cnf transformation 70]
134. ~quiet(alice) | ~humble(alice) [cnf transformation 74]
142. patient(alice) [cnf transformation 25]
145. ~patient(X0) | ~generous(X0) [duplicate literal removal 103]
146. humble(X0) | funny(X0) [duplicate literal removal 100]
257. 25 <=> patient(alice) [avatar definition]
259. patient(alice) <- (25) [avatar component clause 257]
279. 29 <=> ! [X1] : (generous(X1) | quiet(X1)) [avatar definition]
280. generous(X1) | quiet(X1) <- (29) [avatar component clause 279]
282. 30 <=> curious(sK5) [avatar definition]
285. 29 | ~30 [avatar split clause 127,282,279]
290. 29 | 30 [avatar split clause 125,282,279]
297. 33 <=> generous(alice) [avatar definition]
298. ~generous(alice) <- (~33) [avatar component clause 297]
312. 36 <=> humble(alice) [avatar definition]
314. ~humble(alice) <- (~36) [avatar component clause 312]
316. 37 <=> quiet(alice) [avatar definition]
319. ~36 | ~37 [avatar split clause 134,316,312]
331. 25 [avatar split clause 142,257]
337. ~generous(alice) <- (25) [resolution 145,259]
339. ~33 | ~25 [avatar split clause 337,257,297]
341. quiet(alice) <- (29, ~33) [resolution 280,298]
344. 37 | ~29 | 33 [avatar split clause 341,297,279,316]
345. funny(alice) <- (~36) [resolution 314,146]
354. generous(alice) <- (~36) [resolution 345,95]
355. $false <- (~33, ~36) [subsumption resolution 354,298]
356. 33 | 36 [avatar contradiction clause 355]
357. $false [avatar sat refutation 285,290,319,331,339,344,356]
% SZS output end Proof for 9129485661828975017722012
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both patient and not curious then fred is both not creative and old.
Everyone who is either not wise or creative is not curious or not kind and vice versa.
Everyone who is not brave is either not wise or not generous.
Everyone who is either not rich or tall is funny and vice versa.
Everyone who is not calm is creative or happy and vice versa.
Everyone who is not tall or not calm is not creative and vice versa.
Everyone who is either not brave or creative is not humble.
If someone is curious or not quiet then someone is both not generous and not calm and vice versa.
Everyone who is either not humble or not creative is both not calm and funny.
If someone is not curious then alice is not funny or creative and vice versa.
If lucy is either patient or not strong then paul is both not wise and not brave.
If someone is calm or not old then lucy is not calm or not wise.
If john is both not rich and not strong then lucy is not strong.
If john is either patient or not rich then someone is both tall and old and vice versa.
Everyone who is either rich or not quiet is either not kind or not quiet.
If susan is tall then someone is calm or not old.
Someone is either not quiet or not funny.
Lucy is not wise.
Someone is not funny or tall.
Someone is either not rich or quiet.
Lucy is either not curious or not calm.
Someone is funny or not quiet.
Someone is both not calm and wise. | Fred is not wise. | neutral | (((patient(lucy)&~curious(lucy)))=>((~creative(fred)&old(fred))))&
(![X]:((~wise(X)<~>creative(X))<=>(~curious(X)|~kind(X))))&
(![X]:(~brave(X)=>(~wise(X)<~>~generous(X))))&
(![X]:((~rich(X)<~>tall(X))<=>funny(X)))&
(![X]:(~calm(X)<=>(creative(X)|happy(X))))&
(![X]:((~tall(X)|~calm(X))<=>~creative(X)))&
(![X]:((~brave(X)<~>creative(X))=>~humble(X)))&
((?[X]:((curious(X)|~quiet(X))))<=>(?[X]:((~generous(X)&~calm(X)))))&
(![X]:((~humble(X)<~>~creative(X))=>(~calm(X)&funny(X))))&
((?[X]:(~curious(X)))<=>((~funny(alice)|creative(alice))))&
(((patient(lucy)<~>~strong(lucy)))=>((~wise(paul)&~brave(paul))))&
((?[X]:((calm(X)|~old(X))))=>((~calm(lucy)|~wise(lucy))))&
(((~rich(john)&~strong(john)))=>(~strong(lucy)))&
(((patient(john)<~>~rich(john)))<=>(?[X]:((tall(X)&old(X)))))&
(![X]:((rich(X)<~>~quiet(X))=>(~kind(X)<~>~quiet(X))))&
((tall(susan))=>(?[X]:((calm(X)|~old(X)))))&
(?[X]:((~quiet(X)<~>~funny(X))))&
(~wise(lucy))&
(?[X]:((~funny(X)|tall(X))))&
(?[X]:((~rich(X)<~>quiet(X))))&
((~curious(lucy)<~>~calm(lucy)))&
(?[X]:((funny(X)|~quiet(X))))&
(?[X]:((~calm(X)&wise(X)))) | ~wise(fred) | [] | null | 0 |
If someone is either rich or not creative then fred is not tall or not happy and vice versa. If someone is brave then someone is calm and vice versa. If alice is both not wise and not quiet then someone is both calm and not old and vice versa. Everyone who is wise or not patient is either not happy or rich and vice versa. Everyone who is not kind is either wise or creative. Everyone who is calm is not old and vice versa. Everyone who is both wise and not humble is not quiet or not kind. Everyone who is quiet or humble is not funny or not old. If paul is not strong then someone is either not happy or old. If susan is not brave or wise then someone is not calm and vice versa. Everyone who is both rich and not humble is not funny. If susan is either kind or wise then someone is not curious. Everyone who is not rich is not old or curious and vice versa. Everyone who is not wise or creative is both not curious and quiet. If lucy is kind or not kind then mary is not funny and vice versa. Everyone who is both kind and funny is both funny and not happy. Someone is both not quiet and not happy. John is not calm. Lucy is either creative or not tall. Someone is not calm. Someone is not rich or not funny. John is both not tall and not creative. Someone is either wise or funny. | Paul is not old. | contradiction | ((?[X]:((rich(X)<~>~creative(X))))<=>((~tall(fred)|~happy(fred))))&
((?[X]:(brave(X)))<=>(?[X]:(calm(X))))&
(((~wise(alice)&~quiet(alice)))<=>(?[X]:((calm(X)&~old(X)))))&
(![X]:((wise(X)|~patient(X))<=>(~happy(X)<~>rich(X))))&
(![X]:(~kind(X)=>(wise(X)<~>creative(X))))&
(![X]:(calm(X)<=>~old(X)))&
(![X]:((wise(X)&~humble(X))=>(~quiet(X)|~kind(X))))&
(![X]:((quiet(X)|humble(X))=>(~funny(X)|~old(X))))&
((~strong(paul))=>(?[X]:((~happy(X)<~>old(X)))))&
(((~brave(susan)|wise(susan)))<=>(?[X]:(~calm(X))))&
(![X]:((rich(X)&~humble(X))=>~funny(X)))&
(((kind(susan)<~>wise(susan)))=>(?[X]:(~curious(X))))&
(![X]:(~rich(X)<=>(~old(X)|curious(X))))&
(![X]:((~wise(X)|creative(X))=>(~curious(X)&quiet(X))))&
(((kind(lucy)|~kind(lucy)))<=>(~funny(mary)))&
(![X]:((kind(X)&funny(X))=>(funny(X)&~happy(X))))&
(?[X]:((~quiet(X)&~happy(X))))&
(~calm(john))&
((creative(lucy)<~>~tall(lucy)))&
(?[X]:(~calm(X)))&
(?[X]:((~rich(X)|~funny(X))))&
((~tall(john)&~creative(john)))&
(?[X]:((wise(X)<~>funny(X)))) | ~old(paul) | [
"p2",
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1595234995923042868563920
% SZS output start Proof for 1595234995923042868563920
3. (~quiet(alice) & ~wise(alice)) <=> ? [X0] : (~old(X0) & calm(X0)) [input p2]
6. ! [X0] : (calm(X0) <=> ~old(X0)) [input p5]
14. ! [X0] : ((creative(X0) | ~wise(X0)) => (quiet(X0) & ~curious(X0))) [input p13]
24. ~old(paul) [input hypothesis]
35. ! [X0] : ((quiet(X0) & ~curious(X0)) | (~creative(X0) & wise(X0))) [ennf transformation 14]
48. ((~quiet(alice) & ~wise(alice)) | ! [X0] : (old(X0) | ~calm(X0))) & (? [X0] : (~old(X0) & calm(X0)) | (quiet(alice) | wise(alice))) [nnf transformation 3]
49. ((~quiet(alice) & ~wise(alice)) | ! [X0] : (old(X0) | ~calm(X0))) & (? [X0] : (~old(X0) & calm(X0)) | quiet(alice) | wise(alice)) [flattening 48]
50. ((~quiet(alice) & ~wise(alice)) | ! [X0] : (old(X0) | ~calm(X0))) & (? [X1] : (~old(X1) & calm(X1)) | quiet(alice) | wise(alice)) [rectify 49]
51. ? [X1] : (~old(X1) & calm(X1)) => (~old(sK3) & calm(sK3)) [choice axiom]
52. ((~quiet(alice) & ~wise(alice)) | ! [X0] : (old(X0) | ~calm(X0))) & ((~old(sK3) & calm(sK3)) | quiet(alice) | wise(alice)) [skolemisation 50,51]
56. ! [X0] : ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0))) [nnf transformation 6]
89. ~wise(alice) | old(X0) | ~calm(X0) [cnf transformation 52]
90. ~quiet(alice) | old(X0) | ~calm(X0) [cnf transformation 52]
99. ~old(X0) | ~calm(X0) [cnf transformation 56]
100. old(X0) | calm(X0) [cnf transformation 56]
115. quiet(X0) | wise(X0) [cnf transformation 35]
133. ~old(paul) [cnf transformation 24]
163. 7 <=> ! [X1] : ~calm(X1) [avatar definition]
164. ~calm(X1) <- (7) [avatar component clause 163]
179. 11 <=> ! [X0] : (old(X0) | ~calm(X0)) [avatar definition]
180. old(X0) | ~calm(X0) <- (11) [avatar component clause 179]
182. 12 <=> quiet(alice) [avatar definition]
184. ~quiet(alice) <- (~12) [avatar component clause 182]
185. 11 | ~12 [avatar split clause 90,182,179]
187. 13 <=> wise(alice) [avatar definition]
189. ~wise(alice) <- (~13) [avatar component clause 187]
190. 11 | ~13 [avatar split clause 89,187,179]
268. ~calm(X0) <- (11) [subsumption resolution 180,99]
269. 7 | ~11 [avatar split clause 268,179,163]
270. calm(paul) [resolution 100,133]
272. $false <- (7) [subsumption resolution 270,164]
273. ~7 [avatar contradiction clause 272]
278. wise(alice) <- (~12) [resolution 115,184]
279. $false <- (~12, ~13) [subsumption resolution 278,189]
280. 12 | 13 [avatar contradiction clause 279]
281. $false [avatar sat refutation 185,190,269,273,280]
% SZS output end Proof for 1595234995923042868563920
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not curious and happy then john is either brave or not old. If someone is patient then someone is happy and vice versa. If mary is either not happy or not old then paul is not wise or not happy. If susan is either not curious or curious then alice is tall. If someone is quiet or creative then someone is wise. If susan is curious or old then someone is either not generous or not funny and vice versa. Everyone who is not quiet is both creative and funny. Everyone who is both not strong and calm is either happy or not funny and vice versa. Everyone who is happy or old is not wise. Everyone who is either not strong or not wise is not happy or quiet. Everyone who is funny or not calm is not kind. Everyone who is both not patient and not brave is quiet or strong. Everyone who is both not wise and not patient is rich and vice versa. Everyone who is both not brave and brave is either generous or not curious. If fred is not tall then susan is both not kind and not calm. Everyone who is both not kind and not brave is either quiet or brave and vice versa. Someone is either not brave or not calm. Someone is not curious or humble. Someone is humble or rich. Lucy is not kind. Paul is either not happy or patient. Mary is both brave and not calm. Paul is not quiet or humble. Someone is calm or kind. | Paul is humble. | entailment | ((?[X]:((~curious(X)&happy(X))))=>((brave(john)<~>~old(john))))&
((?[X]:(patient(X)))<=>(?[X]:(happy(X))))&
(((~happy(mary)<~>~old(mary)))=>((~wise(paul)|~happy(paul))))&
(((~curious(susan)<~>curious(susan)))=>(tall(alice)))&
((?[X]:((quiet(X)|creative(X))))=>(?[X]:(wise(X))))&
(((curious(susan)|old(susan)))<=>(?[X]:((~generous(X)<~>~funny(X)))))&
(![X]:(~quiet(X)=>(creative(X)&funny(X))))&
(![X]:((~strong(X)&calm(X))<=>(happy(X)<~>~funny(X))))&
(![X]:((happy(X)|old(X))=>~wise(X)))&
(![X]:((~strong(X)<~>~wise(X))=>(~happy(X)|quiet(X))))&
(![X]:((funny(X)|~calm(X))=>~kind(X)))&
(![X]:((~patient(X)&~brave(X))=>(quiet(X)|strong(X))))&
(![X]:((~wise(X)&~patient(X))<=>rich(X)))&
(![X]:((~brave(X)&brave(X))=>(generous(X)<~>~curious(X))))&
((~tall(fred))=>((~kind(susan)&~calm(susan))))&
(![X]:((~kind(X)&~brave(X))<=>(quiet(X)<~>brave(X))))&
(?[X]:((~brave(X)<~>~calm(X))))&
(?[X]:((~curious(X)|humble(X))))&
(?[X]:((humble(X)|rich(X))))&
(~kind(lucy))&
((~happy(paul)<~>patient(paul)))&
((brave(mary)&~calm(mary)))&
((~quiet(paul)|humble(paul)))&
(?[X]:((calm(X)|kind(X)))) | humble(paul) | [
"p6",
"p10",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1352955238975000887437320
% SZS output start Proof for 1352955238975000887437320
7. ! [X0] : (~quiet(X0) => (funny(X0) & creative(X0))) [input p6]
11. ! [X0] : ((~calm(X0) | funny(X0)) => ~kind(X0)) [input p10]
16. ! [X0] : ((~brave(X0) & ~kind(X0)) <=> (quiet(X0) <~> brave(X0))) [input p15]
23. humble(paul) | ~quiet(paul) [input p22]
25. ~humble(paul) [input hypothesis]
35. ! [X0] : ((funny(X0) & creative(X0)) | quiet(X0)) [ennf transformation 7]
39. ! [X0] : (~kind(X0) | (calm(X0) & ~funny(X0))) [ennf transformation 11]
64. ! [X0] : (((~brave(X0) & ~kind(X0)) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0)))) & (((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | (brave(X0) | kind(X0)))) [nnf transformation 16]
65. ! [X0] : (((~brave(X0) & ~kind(X0)) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0)))) & (((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | brave(X0) | kind(X0))) [flattening 64]
91. funny(X0) | quiet(X0) [cnf transformation 35]
102. ~kind(X0) | ~funny(X0) [cnf transformation 39]
109. brave(X0) | quiet(X0) | brave(X0) | kind(X0) [cnf transformation 65]
114. ~brave(X0) | quiet(X0) | ~brave(X0) [cnf transformation 65]
124. humble(paul) | ~quiet(paul) [cnf transformation 23]
126. ~humble(paul) [cnf transformation 25]
127. brave(X0) | quiet(X0) | kind(X0) [duplicate literal removal 109]
128. ~brave(X0) | quiet(X0) [duplicate literal removal 114]
217. kind(X0) | quiet(X0) [subsumption resolution 127,128]
253. 28 <=> quiet(paul) [avatar definition]
255. ~quiet(paul) <- (~28) [avatar component clause 253]
257. 29 <=> humble(paul) [avatar definition]
260. ~28 | 29 [avatar split clause 124,257,253]
262. ~29 [avatar split clause 126,257]
270. quiet(X1) | ~funny(X1) [resolution 217,102]
271. quiet(X1) [subsumption resolution 270,91]
272. $false <- (~28) [resolution 271,255]
273. 28 [avatar contradiction clause 272]
274. $false [avatar sat refutation 260,262,273]
% SZS output end Proof for 1352955238975000887437320
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is wise then fred is either kind or brave and vice versa.
Everyone who is both humble and not creative is strong and vice versa.
If someone is not strong or not quiet then paul is tall and vice versa.
If someone is rich then alice is both not patient and not kind.
Everyone who is brave or tall is not funny or not creative.
Everyone who is both strong and not creative is not rich and vice versa.
If paul is funny or kind then someone is old or not curious.
Everyone who is not brave or not humble is either not happy or not humble.
Everyone who is either not strong or wise is both not kind and generous.
If someone is both funny and quiet then lucy is not rich.
Everyone who is not kind is either not happy or not old.
If paul is not curious or wise then fred is either not strong or not funny.
Everyone who is both tall and not strong is either not rich or not strong.
If mary is not wise then alice is creative.
If paul is either not wise or not creative then someone is either happy or generous and vice versa.
Everyone who is strong is both rich and patient and vice versa.
Fred is both rich and calm.
Someone is either not kind or old.
Someone is calm or quiet.
Susan is both not generous and funny.
Lucy is not kind or not wise.
Paul is either patient or not strong.
John is patient or not patient.
Someone is calm or kind. | Susan is wise. | entailment | ((wise(lucy))<=>((kind(fred)<~>brave(fred))))&
(![X]:((humble(X)&~creative(X))<=>strong(X)))&
((?[X]:((~strong(X)|~quiet(X))))<=>(tall(paul)))&
((?[X]:(rich(X)))=>((~patient(alice)&~kind(alice))))&
(![X]:((brave(X)|tall(X))=>(~funny(X)|~creative(X))))&
(![X]:((strong(X)&~creative(X))<=>~rich(X)))&
(((funny(paul)|kind(paul)))=>(?[X]:((old(X)|~curious(X)))))&
(![X]:((~brave(X)|~humble(X))=>(~happy(X)<~>~humble(X))))&
(![X]:((~strong(X)<~>wise(X))=>(~kind(X)&generous(X))))&
((?[X]:((funny(X)&quiet(X))))=>(~rich(lucy)))&
(![X]:(~kind(X)=>(~happy(X)<~>~old(X))))&
(((~curious(paul)|wise(paul)))=>((~strong(fred)<~>~funny(fred))))&
(![X]:((tall(X)&~strong(X))=>(~rich(X)<~>~strong(X))))&
((~wise(mary))=>(creative(alice)))&
(((~wise(paul)<~>~creative(paul)))<=>(?[X]:((happy(X)<~>generous(X)))))&
(![X]:(strong(X)<=>(rich(X)&patient(X))))&
((rich(fred)&calm(fred)))&
(?[X]:((~kind(X)<~>old(X))))&
(?[X]:((calm(X)|quiet(X))))&
((~generous(susan)&funny(susan)))&
((~kind(lucy)|~wise(lucy)))&
((patient(paul)<~>~strong(paul)))&
((patient(john)|~patient(john)))&
(?[X]:((calm(X)|kind(X)))) | wise(susan) | [
"p1",
"p5",
"p8",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5165499497899454262108494
% SZS output start Proof for 5165499497899454262108494
2. ! [X0] : ((~creative(X0) & humble(X0)) <=> strong(X0)) [input p1]
6. ! [X0] : ((~creative(X0) & strong(X0)) <=> ~rich(X0)) [input p5]
9. ! [X0] : ((~strong(X0) <~> wise(X0)) => (generous(X0) & ~kind(X0))) [input p8]
16. ! [X0] : (strong(X0) <=> (patient(X0) & rich(X0))) [input p15]
20. funny(susan) & ~generous(susan) [input p19]
25. ~wise(susan) [input hypothesis]
34. ! [X0] : ((generous(X0) & ~kind(X0)) | (~strong(X0) <=> wise(X0))) [ennf transformation 9]
42. ! [X0] : (((~creative(X0) & humble(X0)) | ~strong(X0)) & (strong(X0) | (creative(X0) | ~humble(X0)))) [nnf transformation 2]
43. ! [X0] : (((~creative(X0) & humble(X0)) | ~strong(X0)) & (strong(X0) | creative(X0) | ~humble(X0))) [flattening 42]
48. ! [X0] : (((~creative(X0) & strong(X0)) | rich(X0)) & (~rich(X0) | (creative(X0) | ~strong(X0)))) [nnf transformation 6]
49. ! [X0] : (((~creative(X0) & strong(X0)) | rich(X0)) & (~rich(X0) | creative(X0) | ~strong(X0))) [flattening 48]
53. ! [X0] : ((generous(X0) & ~kind(X0)) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0)))) [nnf transformation 34]
61. ! [X0] : ((strong(X0) | (~patient(X0) | ~rich(X0))) & ((patient(X0) & rich(X0)) | ~strong(X0))) [nnf transformation 16]
62. ! [X0] : ((strong(X0) | ~patient(X0) | ~rich(X0)) & ((patient(X0) & rich(X0)) | ~strong(X0))) [flattening 61]
73. ~strong(X0) | ~creative(X0) [cnf transformation 43]
81. ~rich(X0) | creative(X0) | ~strong(X0) [cnf transformation 49]
82. rich(X0) | strong(X0) [cnf transformation 49]
92. generous(X0) | wise(X0) | strong(X0) [cnf transformation 53]
112. rich(X0) | ~strong(X0) [cnf transformation 62]
118. ~generous(susan) [cnf transformation 20]
124. ~wise(susan) [cnf transformation 25]
177. ~rich(X0) | ~strong(X0) [subsumption resolution 81,73]
260. rich(X0) [subsumption resolution 112,82]
306. ~strong(X1) [resolution 177,260]
344. wise(susan) | strong(susan) [resolution 92,118]
346. strong(susan) [subsumption resolution 344,124]
347. $false [subsumption resolution 346,306]
% SZS output end Proof for 5165499497899454262108494
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not tall or not strong then someone is not old and vice versa.
Everyone who is both not tall and rich is both strong and not curious and vice versa.
Everyone who is both patient and not wise is kind.
Everyone who is either not strong or generous is either not creative or not happy and vice versa.
If someone is strong or not tall then fred is not quiet or tall and vice versa.
If someone is both not funny and generous then fred is both funny and humble and vice versa.
If someone is both tall and not strong then susan is either not wise or not curious.
If someone is either not calm or not curious then susan is both not calm and not old and vice versa.
Everyone who is old or tall is not humble.
Everyone who is both kind and not patient is not humble and vice versa.
If susan is not calm then paul is strong or calm.
Everyone who is strong or quiet is not humble or old.
If mary is both not strong and generous then someone is either not calm or not generous.
If alice is both not happy and not tall then someone is not strong and vice versa.
Everyone who is creative or not tall is not creative or creative and vice versa.
Everyone who is either not curious or not patient is not patient or curious and vice versa.
Someone is either patient or old.
Someone is not generous or curious.
Someone is either not strong or not creative.
Fred is not humble.
Alice is both not quiet and not humble.
Someone is either humble or not happy.
Someone is happy or curious. | Mary is not generous. | neutral | (((~tall(alice)<~>~strong(alice)))<=>(?[X]:(~old(X))))&
(![X]:((~tall(X)&rich(X))<=>(strong(X)&~curious(X))))&
(![X]:((patient(X)&~wise(X))=>kind(X)))&
(![X]:((~strong(X)<~>generous(X))<=>(~creative(X)<~>~happy(X))))&
((?[X]:((strong(X)|~tall(X))))<=>((~quiet(fred)|tall(fred))))&
((?[X]:((~funny(X)&generous(X))))<=>((funny(fred)&humble(fred))))&
((?[X]:((tall(X)&~strong(X))))=>((~wise(susan)<~>~curious(susan))))&
((?[X]:((~calm(X)<~>~curious(X))))<=>((~calm(susan)&~old(susan))))&
(![X]:((old(X)|tall(X))=>~humble(X)))&
(![X]:((kind(X)&~patient(X))<=>~humble(X)))&
((~calm(susan))=>((strong(paul)|calm(paul))))&
(![X]:((strong(X)|quiet(X))=>(~humble(X)|old(X))))&
(((~strong(mary)&generous(mary)))=>(?[X]:((~calm(X)<~>~generous(X)))))&
(((~happy(alice)&~tall(alice)))<=>(?[X]:(~strong(X))))&
(![X]:((creative(X)|~tall(X))<=>(~creative(X)|creative(X))))&
(![X]:((~curious(X)<~>~patient(X))<=>(~patient(X)|curious(X))))&
(?[X]:((patient(X)<~>old(X))))&
(?[X]:((~generous(X)|curious(X))))&
(?[X]:((~strong(X)<~>~creative(X))))&
(~humble(fred))&
((~quiet(alice)&~humble(alice)))&
(?[X]:((humble(X)<~>~happy(X))))&
(?[X]:((happy(X)|curious(X)))) | ~generous(mary) | [] | null | 0 |
Everyone who is happy or strong is both not kind and happy and vice versa. If someone is curious or not rich then mary is either brave or not quiet. Everyone who is either not rich or curious is not calm. Everyone who is not wise or not strong is creative or curious. Everyone who is both not patient and calm is both brave and not funny and vice versa. If someone is either not generous or not happy then paul is generous or creative and vice versa. If someone is not strong then mary is both calm and creative and vice versa. Everyone who is wise is not happy and vice versa. Everyone who is not strong or old is strong or not brave and vice versa. If someone is not kind or calm then mary is both not kind and not rich. If john is not rich then someone is either not patient or wise and vice versa. If someone is both calm and not creative then alice is quiet and vice versa. Everyone who is both tall and humble is tall or not humble. Everyone who is both rich and not generous is both not old and generous. If paul is not brave or humble then susan is old or happy and vice versa. Everyone who is either not quiet or not humble is quiet or not humble. Paul is kind or not creative. Paul is kind. Alice is either wise or not strong. Someone is not curious. Fred is not funny. Someone is both generous and quiet. Alice is creative or not funny. Fred is creative or not creative. | Mary is kind. | contradiction | (![X]:((happy(X)|strong(X))<=>(~kind(X)&happy(X))))&
((?[X]:((curious(X)|~rich(X))))=>((brave(mary)<~>~quiet(mary))))&
(![X]:((~rich(X)<~>curious(X))=>~calm(X)))&
(![X]:((~wise(X)|~strong(X))=>(creative(X)|curious(X))))&
(![X]:((~patient(X)&calm(X))<=>(brave(X)&~funny(X))))&
((?[X]:((~generous(X)<~>~happy(X))))<=>((generous(paul)|creative(paul))))&
((?[X]:(~strong(X)))<=>((calm(mary)&creative(mary))))&
(![X]:(wise(X)<=>~happy(X)))&
(![X]:((~strong(X)|old(X))<=>(strong(X)|~brave(X))))&
((?[X]:((~kind(X)|calm(X))))=>((~kind(mary)&~rich(mary))))&
((~rich(john))<=>(?[X]:((~patient(X)<~>wise(X)))))&
((?[X]:((calm(X)&~creative(X))))<=>(quiet(alice)))&
(![X]:((tall(X)&humble(X))=>(tall(X)|~humble(X))))&
(![X]:((rich(X)&~generous(X))=>(~old(X)&generous(X))))&
(((~brave(paul)|humble(paul)))<=>((old(susan)|happy(susan))))&
(![X]:((~quiet(X)<~>~humble(X))=>(quiet(X)|~humble(X))))&
((kind(paul)|~creative(paul)))&
(kind(paul))&
((wise(alice)<~>~strong(alice)))&
(?[X]:(~curious(X)))&
(~funny(fred))&
(?[X]:((generous(X)&quiet(X))))&
((creative(alice)|~funny(alice)))&
((creative(fred)|~creative(fred))) | kind(mary) | [
"p0",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7289036045969267629839277
% SZS output start Proof for 7289036045969267629839277
1. ! [X0] : ((strong(X0) | happy(X0)) <=> (happy(X0) & ~kind(X0))) [input p0]
7. ? [X0] : ~strong(X0) <=> (creative(mary) & calm(mary)) [input p6]
10. ? [X0] : (calm(X0) | ~kind(X0)) => (~rich(mary) & ~kind(mary)) [input p9]
25. kind(mary) [input hypothesis]
30. (~rich(mary) & ~kind(mary)) | ! [X0] : (~calm(X0) & kind(X0)) [ennf transformation 10]
37. ! [X0] : (((strong(X0) | happy(X0)) | (~happy(X0) | kind(X0))) & ((happy(X0) & ~kind(X0)) | (~strong(X0) & ~happy(X0)))) [nnf transformation 1]
38. ! [X0] : ((strong(X0) | happy(X0) | ~happy(X0) | kind(X0)) & ((happy(X0) & ~kind(X0)) | (~strong(X0) & ~happy(X0)))) [flattening 37]
48. (? [X0] : ~strong(X0) | (~creative(mary) | ~calm(mary))) & ((creative(mary) & calm(mary)) | ! [X0] : strong(X0)) [nnf transformation 7]
49. (? [X0] : ~strong(X0) | ~creative(mary) | ~calm(mary)) & ((creative(mary) & calm(mary)) | ! [X0] : strong(X0)) [flattening 48]
50. (? [X0] : ~strong(X0) | ~creative(mary) | ~calm(mary)) & ((creative(mary) & calm(mary)) | ! [X1] : strong(X1)) [rectify 49]
51. ? [X0] : ~strong(X0) => ~strong(sK1) [choice axiom]
52. (~strong(sK1) | ~creative(mary) | ~calm(mary)) & ((creative(mary) & calm(mary)) | ! [X1] : strong(X1)) [skolemisation 50,51]
73. ~kind(X0) | ~strong(X0) [cnf transformation 38]
95. calm(mary) | strong(X1) [cnf transformation 52]
105. ~kind(mary) | ~calm(X0) [cnf transformation 30]
134. kind(mary) [cnf transformation 25]
187. 11 <=> calm(mary) [avatar definition]
188. calm(mary) <- (11) [avatar component clause 187]
200. 14 <=> ! [X1] : strong(X1) [avatar definition]
201. strong(X1) <- (14) [avatar component clause 200]
203. 14 | 11 [avatar split clause 95,187,200]
205. 15 <=> ! [X0] : ~calm(X0) [avatar definition]
206. ~calm(X0) <- (15) [avatar component clause 205]
217. 18 <=> kind(mary) [avatar definition]
218. kind(mary) <- (18) [avatar component clause 217]
220. 15 | ~18 [avatar split clause 105,217,205]
307. 18 [avatar split clause 134,217]
308. $false <- (11, 15) [subsumption resolution 188,206]
309. ~11 | ~15 [avatar contradiction clause 308]
322. ~strong(mary) <- (18) [resolution 73,218]
326. $false <- (14, 18) [subsumption resolution 322,201]
327. ~14 | ~18 [avatar contradiction clause 326]
330. $false [avatar sat refutation 203,220,307,309,327]
% SZS output end Proof for 7289036045969267629839277
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If paul is generous then someone is not brave or not curious and vice versa.
If someone is either kind or not strong then lucy is tall or not creative.
Everyone who is either not patient or not rich is brave or generous.
If someone is funny or not creative then someone is both not creative and not funny and vice versa.
If paul is not funny then someone is calm and vice versa.
Everyone who is strong is not happy or humble and vice versa.
Everyone who is not quiet or not humble is tall or patient and vice versa.
If someone is not wise or brave then fred is either not humble or not brave and vice versa.
Everyone who is either not generous or creative is both humble and not funny and vice versa.
If someone is both generous and not wise then mary is wise or curious and vice versa.
Everyone who is either not patient or humble is not brave.
Everyone who is curious is not wise and vice versa.
Everyone who is either not wise or not happy is both humble and kind and vice versa.
Everyone who is old or kind is both not creative and strong and vice versa.
Everyone who is either creative or kind is both curious and not generous and vice versa.
Everyone who is either tall or not humble is either brave or not calm and vice versa.
Someone is both strong and funny.
Mary is happy.
Someone is rich.
Someone is both creative and not patient.
John is either not kind or happy.
Fred is not patient or not creative.
Susan is both not happy and not wise. | John is not wise. | entailment | ((generous(paul))<=>(?[X]:((~brave(X)|~curious(X)))))&
((?[X]:((kind(X)<~>~strong(X))))=>((tall(lucy)|~creative(lucy))))&
(![X]:((~patient(X)<~>~rich(X))=>(brave(X)|generous(X))))&
((?[X]:((funny(X)|~creative(X))))<=>(?[X]:((~creative(X)&~funny(X)))))&
((~funny(paul))<=>(?[X]:(calm(X))))&
(![X]:(strong(X)<=>(~happy(X)|humble(X))))&
(![X]:((~quiet(X)|~humble(X))<=>(tall(X)|patient(X))))&
((?[X]:((~wise(X)|brave(X))))<=>((~humble(fred)<~>~brave(fred))))&
(![X]:((~generous(X)<~>creative(X))<=>(humble(X)&~funny(X))))&
((?[X]:((generous(X)&~wise(X))))<=>((wise(mary)|curious(mary))))&
(![X]:((~patient(X)<~>humble(X))=>~brave(X)))&
(![X]:(curious(X)<=>~wise(X)))&
(![X]:((~wise(X)<~>~happy(X))<=>(humble(X)&kind(X))))&
(![X]:((old(X)|kind(X))<=>(~creative(X)&strong(X))))&
(![X]:((creative(X)<~>kind(X))<=>(curious(X)&~generous(X))))&
(![X]:((tall(X)<~>~humble(X))<=>(brave(X)<~>~calm(X))))&
(?[X]:((strong(X)&funny(X))))&
(happy(mary))&
(?[X]:(rich(X)))&
(?[X]:((creative(X)&~patient(X))))&
((~kind(john)<~>happy(john)))&
((~patient(fred)|~creative(fred)))&
((~happy(susan)&~wise(susan))) | ~wise(john) | [
"p11",
"p12",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 542695525562972489050138
% SZS output start Proof for 542695525562972489050138
12. ! [X0] : (curious(X0) <=> ~wise(X0)) [input p11]
13. ! [X0] : ((~wise(X0) <~> ~happy(X0)) <=> (kind(X0) & humble(X0))) [input p12]
14. ! [X0] : ((kind(X0) | old(X0)) <=> (strong(X0) & ~creative(X0))) [input p13]
15. ! [X0] : ((creative(X0) <~> kind(X0)) <=> (~generous(X0) & curious(X0))) [input p14]
21. ~kind(john) <~> happy(john) [input p20]
24. wise(john) [input hypothesis]
62. ! [X0] : ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0))) [nnf transformation 12]
63. ! [X0] : ((((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | (~kind(X0) | ~humble(X0))) & ((kind(X0) & humble(X0)) | ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0))))) [nnf transformation 13]
64. ! [X0] : ((((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | ~kind(X0) | ~humble(X0)) & ((kind(X0) & humble(X0)) | ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0))))) [flattening 63]
65. ! [X0] : (((kind(X0) | old(X0)) | (~strong(X0) | creative(X0))) & ((strong(X0) & ~creative(X0)) | (~kind(X0) & ~old(X0)))) [nnf transformation 14]
66. ! [X0] : ((kind(X0) | old(X0) | ~strong(X0) | creative(X0)) & ((strong(X0) & ~creative(X0)) | (~kind(X0) & ~old(X0)))) [flattening 65]
67. ! [X0] : ((((~kind(X0) | ~creative(X0)) & (kind(X0) | creative(X0))) | (generous(X0) | ~curious(X0))) & ((~generous(X0) & curious(X0)) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0))))) [nnf transformation 15]
68. ! [X0] : ((((~kind(X0) | ~creative(X0)) & (kind(X0) | creative(X0))) | generous(X0) | ~curious(X0)) & ((~generous(X0) & curious(X0)) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0))))) [flattening 67]
76. (~happy(john) | kind(john)) & (happy(john) | ~kind(john)) [nnf transformation 21]
117. ~wise(X0) | ~curious(X0) [cnf transformation 62]
122. ~wise(X0) | kind(X0) | happy(X0) [cnf transformation 64]
126. ~creative(X0) | ~kind(X0) [cnf transformation 66]
131. curious(X0) | creative(X0) | ~kind(X0) [cnf transformation 68]
151. ~happy(john) | kind(john) [cnf transformation 76]
155. wise(john) [cnf transformation 24]
290. ~kind(X0) | curious(X0) [subsumption resolution 131,126]
293. 31 <=> kind(john) [avatar definition]
295. kind(john) <- (31) [avatar component clause 293]
297. 32 <=> happy(john) [avatar definition]
300. 31 | ~32 [avatar split clause 151,297,293]
313. ~curious(john) [resolution 117,155]
405. kind(john) | happy(john) [resolution 122,155]
411. 32 | 31 [avatar split clause 405,293,297]
417. curious(john) <- (31) [resolution 295,290]
420. $false <- (31) [subsumption resolution 417,313]
421. ~31 [avatar contradiction clause 420]
422. $false [avatar sat refutation 300,411,421]
% SZS output end Proof for 542695525562972489050138
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or tall is either humble or not happy and vice versa. If someone is either not strong or not funny then someone is wise. If lucy is not rich or not brave then john is either not generous or not funny. Everyone who is either patient or not happy is both wise and not kind. If someone is either quiet or strong then someone is either not kind or not strong. If someone is not funny or curious then someone is either not calm or not humble and vice versa. If john is both not funny and happy then alice is not patient and vice versa. Everyone who is either not humble or not curious is not curious and vice versa. Everyone who is creative or not curious is humble. If someone is both not generous and old then someone is generous or not calm. If paul is patient or not patient then someone is either tall or happy and vice versa. If someone is either not brave or happy then someone is either not quiet or happy. Everyone who is either funny or not funny is either not creative or quiet. If paul is both generous and not kind then susan is not quiet and vice versa. Everyone who is creative is either not calm or strong. Everyone who is not quiet or not tall is curious or funny and vice versa. Someone is not tall. Paul is not happy or not calm. Alice is either not wise or not quiet. Someone is not patient or humble. Someone is either not creative or strong. Someone is not quiet. Someone is not strong or happy. | Lucy is brave. | neutral | (![X]:((patient(X)<~>tall(X))<=>(humble(X)<~>~happy(X))))&
((?[X]:((~strong(X)<~>~funny(X))))=>(?[X]:(wise(X))))&
(((~rich(lucy)|~brave(lucy)))=>((~generous(john)<~>~funny(john))))&
(![X]:((patient(X)<~>~happy(X))=>(wise(X)&~kind(X))))&
((?[X]:((quiet(X)<~>strong(X))))=>(?[X]:((~kind(X)<~>~strong(X)))))&
((?[X]:((~funny(X)|curious(X))))<=>(?[X]:((~calm(X)<~>~humble(X)))))&
(((~funny(john)&happy(john)))<=>(~patient(alice)))&
(![X]:((~humble(X)<~>~curious(X))<=>~curious(X)))&
(![X]:((creative(X)|~curious(X))=>humble(X)))&
((?[X]:((~generous(X)&old(X))))=>(?[X]:((generous(X)|~calm(X)))))&
(((patient(paul)|~patient(paul)))<=>(?[X]:((tall(X)<~>happy(X)))))&
((?[X]:((~brave(X)<~>happy(X))))=>(?[X]:((~quiet(X)<~>happy(X)))))&
(![X]:((funny(X)<~>~funny(X))=>(~creative(X)<~>quiet(X))))&
(((generous(paul)&~kind(paul)))<=>(~quiet(susan)))&
(![X]:(creative(X)=>(~calm(X)<~>strong(X))))&
(![X]:((~quiet(X)|~tall(X))<=>(curious(X)|funny(X))))&
(?[X]:(~tall(X)))&
((~happy(paul)|~calm(paul)))&
((~wise(alice)<~>~quiet(alice)))&
(?[X]:((~patient(X)|humble(X))))&
(?[X]:((~creative(X)<~>strong(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~strong(X)|happy(X)))) | brave(lucy) | [] | null | 0 |
Everyone who is not tall or not kind is not tall or not generous.
Everyone who is both not creative and patient is not generous and vice versa.
Everyone who is both patient and not rich is both not strong and not rich.
If paul is either happy or not strong then susan is not generous.
If fred is both not generous and calm then someone is both not strong and not rich.
If alice is not patient or kind then paul is old and vice versa.
If someone is not curious or not patient then someone is quiet or patient.
Everyone who is not creative is either not happy or quiet.
Everyone who is not rich or not brave is strong.
If paul is not curious then paul is either not curious or not creative and vice versa.
If alice is either not patient or creative then someone is either not creative or wise and vice versa.
Everyone who is both calm and humble is both not happy and not kind.
Everyone who is strong or not funny is not patient and vice versa.
If someone is both not generous and not tall then fred is quiet or not funny and vice versa.
Everyone who is either rich or strong is either not generous or generous and vice versa.
If susan is creative or generous then someone is not kind and vice versa.
Someone is not quiet or not strong.
Susan is not happy.
Someone is both not tall and strong.
Fred is both tall and not quiet.
Someone is not patient.
Someone is either not patient or creative.
Alice is both rich and old.
Someone is both not funny and creative. | Alice is creative. | neutral | (![X]:((~tall(X)|~kind(X))=>(~tall(X)|~generous(X))))&
(![X]:((~creative(X)&patient(X))<=>~generous(X)))&
(![X]:((patient(X)&~rich(X))=>(~strong(X)&~rich(X))))&
(((happy(paul)<~>~strong(paul)))=>(~generous(susan)))&
(((~generous(fred)&calm(fred)))=>(?[X]:((~strong(X)&~rich(X)))))&
(((~patient(alice)|kind(alice)))<=>(old(paul)))&
((?[X]:((~curious(X)|~patient(X))))=>(?[X]:((quiet(X)|patient(X)))))&
(![X]:(~creative(X)=>(~happy(X)<~>quiet(X))))&
(![X]:((~rich(X)|~brave(X))=>strong(X)))&
((~curious(paul))<=>((~curious(paul)<~>~creative(paul))))&
(((~patient(alice)<~>creative(alice)))<=>(?[X]:((~creative(X)<~>wise(X)))))&
(![X]:((calm(X)&humble(X))=>(~happy(X)&~kind(X))))&
(![X]:((strong(X)|~funny(X))<=>~patient(X)))&
((?[X]:((~generous(X)&~tall(X))))<=>((quiet(fred)|~funny(fred))))&
(![X]:((rich(X)<~>strong(X))<=>(~generous(X)<~>generous(X))))&
(((creative(susan)|generous(susan)))<=>(?[X]:(~kind(X))))&
(?[X]:((~quiet(X)|~strong(X))))&
(~happy(susan))&
(?[X]:((~tall(X)&strong(X))))&
((tall(fred)&~quiet(fred)))&
(?[X]:(~patient(X)))&
(?[X]:((~patient(X)<~>creative(X))))&
((rich(alice)&old(alice)))&
(?[X]:((~funny(X)&creative(X)))) | creative(alice) | [] | null | 0 |
Everyone who is either not brave or kind is not curious. Everyone who is both not funny and not old is curious or not kind. Everyone who is either not happy or not calm is happy or not strong and vice versa. Everyone who is calm is either happy or strong and vice versa. If paul is generous or old then someone is patient or not old and vice versa. Everyone who is both not strong and kind is both not brave and not kind and vice versa. Everyone who is kind or generous is not curious or happy and vice versa. Everyone who is not happy is both not strong and patient and vice versa. Everyone who is both strong and not patient is both wise and not funny. If fred is both not humble and rich then fred is not quiet. If susan is not patient or not creative then john is creative and vice versa. Everyone who is either not creative or humble is not old. If paul is both not calm and patient then lucy is not patient. Everyone who is rich is either not kind or brave. If someone is both not patient and not curious then someone is calm or strong and vice versa. If alice is either rich or not creative then alice is both curious and funny and vice versa. John is either generous or old. John is funny. Susan is either not creative or not rich. Alice is not wise. Lucy is not humble or not wise. Alice is quiet. | Alice is not humble. | neutral | (![X]:((~brave(X)<~>kind(X))=>~curious(X)))&
(![X]:((~funny(X)&~old(X))=>(curious(X)|~kind(X))))&
(![X]:((~happy(X)<~>~calm(X))<=>(happy(X)|~strong(X))))&
(![X]:(calm(X)<=>(happy(X)<~>strong(X))))&
(((generous(paul)|old(paul)))<=>(?[X]:((patient(X)|~old(X)))))&
(![X]:((~strong(X)&kind(X))<=>(~brave(X)&~kind(X))))&
(![X]:((kind(X)|generous(X))<=>(~curious(X)|happy(X))))&
(![X]:(~happy(X)<=>(~strong(X)&patient(X))))&
(![X]:((strong(X)&~patient(X))=>(wise(X)&~funny(X))))&
(((~humble(fred)&rich(fred)))=>(~quiet(fred)))&
(((~patient(susan)|~creative(susan)))<=>(creative(john)))&
(![X]:((~creative(X)<~>humble(X))=>~old(X)))&
(((~calm(paul)&patient(paul)))=>(~patient(lucy)))&
(![X]:(rich(X)=>(~kind(X)<~>brave(X))))&
((?[X]:((~patient(X)&~curious(X))))<=>(?[X]:((calm(X)|strong(X)))))&
(((rich(alice)<~>~creative(alice)))<=>((curious(alice)&funny(alice))))&
((generous(john)<~>old(john)))&
(funny(john))&
((~creative(susan)<~>~rich(susan)))&
(~wise(alice))&
((~humble(lucy)|~wise(lucy)))&
(quiet(alice)) | ~humble(alice) | [] | null | 0 |
If someone is wise or old then alice is rich or not calm and vice versa.
If alice is wise then someone is both not rich and not generous and vice versa.
If someone is tall or creative then someone is either brave or not calm and vice versa.
Everyone who is both not wise and funny is tall or not patient and vice versa.
If paul is either calm or quiet then someone is funny or not brave.
Everyone who is both funny and not tall is brave.
Everyone who is either strong or tall is either not happy or not curious.
Everyone who is not funny is not calm or not funny.
Everyone who is either not generous or kind is both not happy and curious and vice versa.
If fred is both not kind and rich then fred is both creative and rich.
If someone is not old then alice is both not tall and funny and vice versa.
If someone is humble then someone is not patient or wise.
If someone is either funny or old then someone is not creative and vice versa.
If fred is not funny then someone is not generous or generous and vice versa.
Everyone who is either not strong or not creative is either curious or creative and vice versa.
If fred is quiet then someone is both not creative and brave and vice versa.
Fred is both not humble and not rich.
Someone is both not wise and patient.
Someone is strong.
Someone is not generous.
Someone is generous.
Someone is not tall.
Someone is both funny and not patient.
Fred is both not brave and creative. | Alice is not tall. | neutral | ((?[X]:((wise(X)|old(X))))<=>((rich(alice)|~calm(alice))))&
((wise(alice))<=>(?[X]:((~rich(X)&~generous(X)))))&
((?[X]:((tall(X)|creative(X))))<=>(?[X]:((brave(X)<~>~calm(X)))))&
(![X]:((~wise(X)&funny(X))<=>(tall(X)|~patient(X))))&
(((calm(paul)<~>quiet(paul)))=>(?[X]:((funny(X)|~brave(X)))))&
(![X]:((funny(X)&~tall(X))=>brave(X)))&
(![X]:((strong(X)<~>tall(X))=>(~happy(X)<~>~curious(X))))&
(![X]:(~funny(X)=>(~calm(X)|~funny(X))))&
(![X]:((~generous(X)<~>kind(X))<=>(~happy(X)&curious(X))))&
(((~kind(fred)&rich(fred)))=>((creative(fred)&rich(fred))))&
((?[X]:(~old(X)))<=>((~tall(alice)&funny(alice))))&
((?[X]:(humble(X)))=>(?[X]:((~patient(X)|wise(X)))))&
((?[X]:((funny(X)<~>old(X))))<=>(?[X]:(~creative(X))))&
((~funny(fred))<=>(?[X]:((~generous(X)|generous(X)))))&
(![X]:((~strong(X)<~>~creative(X))<=>(curious(X)<~>creative(X))))&
((quiet(fred))<=>(?[X]:((~creative(X)&brave(X)))))&
((~humble(fred)&~rich(fred)))&
(?[X]:((~wise(X)&patient(X))))&
(?[X]:(strong(X)))&
(?[X]:(~generous(X)))&
(?[X]:(generous(X)))&
(?[X]:(~tall(X)))&
(?[X]:((funny(X)&~patient(X))))&
((~brave(fred)&creative(fred))) | ~tall(alice) | [] | null | 0 |
Everyone who is either not old or rich is both not calm and not old.
If paul is either not strong or not brave then someone is either not wise or brave.
Everyone who is not quiet is happy.
If john is either rich or not wise then paul is humble.
If someone is tall then someone is either old or wise.
If someone is old or not happy then fred is both curious and not brave.
Everyone who is either not happy or humble is not tall or kind and vice versa.
If someone is both not generous and generous then someone is kind and vice versa.
Everyone who is humble is either not tall or happy.
Everyone who is either kind or not happy is either tall or not rich and vice versa.
Everyone who is both not patient and rich is not funny.
Everyone who is both not tall and not rich is either calm or rich and vice versa.
If paul is patient then john is either not kind or kind.
If mary is either not quiet or calm then someone is both old and rich and vice versa.
Everyone who is both not happy and not calm is either quiet or strong and vice versa.
If someone is patient then someone is not generous.
Susan is not kind.
Susan is calm.
Someone is not humble or not wise.
Someone is either tall or not happy.
Someone is either patient or kind.
Someone is both quiet and patient. | Susan is strong. | entailment | (![X]:((~old(X)<~>rich(X))=>(~calm(X)&~old(X))))&
(((~strong(paul)<~>~brave(paul)))=>(?[X]:((~wise(X)<~>brave(X)))))&
(![X]:(~quiet(X)=>happy(X)))&
(((rich(john)<~>~wise(john)))=>(humble(paul)))&
((?[X]:(tall(X)))=>(?[X]:((old(X)<~>wise(X)))))&
((?[X]:((old(X)|~happy(X))))=>((curious(fred)&~brave(fred))))&
(![X]:((~happy(X)<~>humble(X))<=>(~tall(X)|kind(X))))&
((?[X]:((~generous(X)&generous(X))))<=>(?[X]:(kind(X))))&
(![X]:(humble(X)=>(~tall(X)<~>happy(X))))&
(![X]:((kind(X)<~>~happy(X))<=>(tall(X)<~>~rich(X))))&
(![X]:((~patient(X)&rich(X))=>~funny(X)))&
(![X]:((~tall(X)&~rich(X))<=>(calm(X)<~>rich(X))))&
((patient(paul))=>((~kind(john)<~>kind(john))))&
(((~quiet(mary)<~>calm(mary)))<=>(?[X]:((old(X)&rich(X)))))&
(![X]:((~happy(X)&~calm(X))<=>(quiet(X)<~>strong(X))))&
((?[X]:(patient(X)))=>(?[X]:(~generous(X))))&
(~kind(susan))&
(calm(susan))&
(?[X]:((~humble(X)|~wise(X))))&
(?[X]:((tall(X)<~>~happy(X))))&
(?[X]:((patient(X)<~>kind(X))))&
(?[X]:((quiet(X)&patient(X)))) | strong(susan) | [
"p2",
"p6",
"p7",
"p8",
"p9",
"p11",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 502065550652948638371233
% SZS output start Proof for 502065550652948638371233
3. ! [X0] : (~quiet(X0) => happy(X0)) [input p2]
7. ! [X0] : ((~happy(X0) <~> humble(X0)) <=> (kind(X0) | ~tall(X0))) [input p6]
8. ? [X0] : (generous(X0) & ~generous(X0)) <=> ? [X0] : kind(X0) [input p7]
9. ! [X0] : (humble(X0) => (~tall(X0) <~> happy(X0))) [input p8]
10. ! [X0] : ((kind(X0) <~> ~happy(X0)) <=> (tall(X0) <~> ~rich(X0))) [input p9]
12. ! [X0] : ((~rich(X0) & ~tall(X0)) <=> (calm(X0) <~> rich(X0))) [input p11]
15. ! [X0] : ((~calm(X0) & ~happy(X0)) <=> (quiet(X0) <~> strong(X0))) [input p14]
18. calm(susan) [input p17]
23. ~strong(susan) [input hypothesis]
25. ? [X0] : (generous(X0) & ~generous(X0)) <=> ? [X1] : kind(X1) [rectify 8]
31. ! [X0] : (happy(X0) | quiet(X0)) [ennf transformation 3]
35. ! [X0] : ((~tall(X0) <~> happy(X0)) | ~humble(X0)) [ennf transformation 9]
47. ! [X0] : ((((~humble(X0) | happy(X0)) & (humble(X0) | ~happy(X0))) | (~kind(X0) & tall(X0))) & ((kind(X0) | ~tall(X0)) | ((~happy(X0) | ~humble(X0)) & (humble(X0) | happy(X0))))) [nnf transformation 7]
48. ! [X0] : ((((~humble(X0) | happy(X0)) & (humble(X0) | ~happy(X0))) | (~kind(X0) & tall(X0))) & (kind(X0) | ~tall(X0) | ((~happy(X0) | ~humble(X0)) & (humble(X0) | happy(X0))))) [flattening 47]
49. (? [X0] : (generous(X0) & ~generous(X0)) | ! [X1] : ~kind(X1)) & (? [X1] : kind(X1) | ! [X0] : (~generous(X0) | generous(X0))) [nnf transformation 25]
50. (? [X0] : (generous(X0) & ~generous(X0)) | ! [X1] : ~kind(X1)) & (? [X2] : kind(X2) | ! [X3] : (~generous(X3) | generous(X3))) [rectify 49]
51. ? [X0] : (generous(X0) & ~generous(X0)) => (generous(sK2) & ~generous(sK2)) [choice axiom]
52. ? [X2] : kind(X2) => kind(sK3) [choice axiom]
53. ((generous(sK2) & ~generous(sK2)) | ! [X1] : ~kind(X1)) & (kind(sK3) | ! [X3] : (~generous(X3) | generous(X3))) [skolemisation 50,52,51]
54. ! [X0] : (((~happy(X0) | tall(X0)) & (happy(X0) | ~tall(X0))) | ~humble(X0)) [nnf transformation 35]
55. ! [X0] : ((((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0)))) & (((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))))) [nnf transformation 10]
56. ! [X0] : (((~rich(X0) & ~tall(X0)) | ((calm(X0) | ~rich(X0)) & (rich(X0) | ~calm(X0)))) & (((~rich(X0) | ~calm(X0)) & (rich(X0) | calm(X0))) | (rich(X0) | tall(X0)))) [nnf transformation 12]
57. ! [X0] : (((~rich(X0) & ~tall(X0)) | ((calm(X0) | ~rich(X0)) & (rich(X0) | ~calm(X0)))) & (((~rich(X0) | ~calm(X0)) & (rich(X0) | calm(X0))) | rich(X0) | tall(X0))) [flattening 56]
63. ! [X0] : (((~calm(X0) & ~happy(X0)) | ((quiet(X0) | ~strong(X0)) & (strong(X0) | ~quiet(X0)))) & (((~strong(X0) | ~quiet(X0)) & (strong(X0) | quiet(X0))) | (calm(X0) | happy(X0)))) [nnf transformation 15]
64. ! [X0] : (((~calm(X0) & ~happy(X0)) | ((quiet(X0) | ~strong(X0)) & (strong(X0) | ~quiet(X0)))) & (((~strong(X0) | ~quiet(X0)) & (strong(X0) | quiet(X0))) | calm(X0) | happy(X0))) [flattening 63]
86. happy(X0) | quiet(X0) [cnf transformation 31]
95. ~happy(X0) | humble(X0) | tall(X0) [cnf transformation 48]
97. ~humble(X0) | happy(X0) | tall(X0) [cnf transformation 48]
100. ~generous(sK2) | ~kind(X1) [cnf transformation 53]
101. generous(sK2) | ~kind(X1) [cnf transformation 53]
103. ~happy(X0) | tall(X0) | ~humble(X0) [cnf transformation 54]
108. ~tall(X0) | kind(X0) | ~rich(X0) | ~happy(X0) [cnf transformation 55]
114. ~tall(X0) | rich(X0) | ~calm(X0) [cnf transformation 57]
130. ~quiet(X0) | strong(X0) | ~calm(X0) [cnf transformation 64]
134. calm(susan) [cnf transformation 18]
142. ~strong(susan) [cnf transformation 23]
206. 14 <=> ! [X1] : ~kind(X1) [avatar definition]
207. ~kind(X1) <- (14) [avatar component clause 206]
209. 15 <=> generous(sK2) [avatar definition]
212. 14 | 15 [avatar split clause 101,209,206]
213. 14 | ~15 [avatar split clause 100,209,206]
214. ~humble(X0) | tall(X0) [subsumption resolution 103,97]
312. humble(X0) | tall(X0) | quiet(X0) [resolution 95,86]
314. tall(X0) | quiet(X0) [subsumption resolution 312,214]
315. ~calm(X0) | rich(X0) | quiet(X0) [resolution 114,314]
374. kind(X0) | ~rich(X0) | ~happy(X0) | quiet(X0) [resolution 108,314]
377. ~rich(X0) | ~happy(X0) | quiet(X0) <- (14) [subsumption resolution 374,207]
378. ~rich(X0) | quiet(X0) <- (14) [subsumption resolution 377,86]
385. rich(susan) | quiet(susan) [resolution 315,134]
386. quiet(susan) <- (14) [subsumption resolution 385,378]
388. strong(susan) | ~calm(susan) <- (14) [resolution 386,130]
391. ~calm(susan) <- (14) [subsumption resolution 388,142]
392. $false <- (14) [subsumption resolution 391,134]
393. ~14 [avatar contradiction clause 392]
394. $false [avatar sat refutation 212,213,393]
% SZS output end Proof for 502065550652948638371233
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is rich and vice versa.
If someone is either not kind or not quiet then paul is not rich and vice versa.
Everyone who is either happy or not curious is both not wise and not strong and vice versa.
Everyone who is tall or not generous is not brave or generous and vice versa.
If someone is quiet or calm then someone is patient or not quiet.
Everyone who is kind is not old or not curious.
Everyone who is both quiet and not old is both old and not happy.
If fred is either kind or not happy then mary is both not humble and not calm and vice versa.
Everyone who is both tall and old is both curious and kind and vice versa.
If mary is not funny then fred is both not rich and kind.
If alice is funny then alice is not quiet and vice versa.
If paul is not creative then someone is either creative or not patient.
Everyone who is either not wise or not generous is either not quiet or tall.
If alice is quiet or not generous then someone is strong or not tall.
Everyone who is rich is brave or not rich and vice versa.
If someone is old then lucy is either rich or not happy and vice versa.
Lucy is not kind.
Someone is not curious or not kind.
Someone is both humble and wise.
Someone is curious or not tall.
John is not quiet. | Fred is not generous. | contradiction | (![X]:(humble(X)<=>rich(X)))&
((?[X]:((~kind(X)<~>~quiet(X))))<=>(~rich(paul)))&
(![X]:((happy(X)<~>~curious(X))<=>(~wise(X)&~strong(X))))&
(![X]:((tall(X)|~generous(X))<=>(~brave(X)|generous(X))))&
((?[X]:((quiet(X)|calm(X))))=>(?[X]:((patient(X)|~quiet(X)))))&
(![X]:(kind(X)=>(~old(X)|~curious(X))))&
(![X]:((quiet(X)&~old(X))=>(old(X)&~happy(X))))&
(((kind(fred)<~>~happy(fred)))<=>((~humble(mary)&~calm(mary))))&
(![X]:((tall(X)&old(X))<=>(curious(X)&kind(X))))&
((~funny(mary))=>((~rich(fred)&kind(fred))))&
((funny(alice))<=>(~quiet(alice)))&
((~creative(paul))=>(?[X]:((creative(X)<~>~patient(X)))))&
(![X]:((~wise(X)<~>~generous(X))=>(~quiet(X)<~>tall(X))))&
(((quiet(alice)|~generous(alice)))=>(?[X]:((strong(X)|~tall(X)))))&
(![X]:(rich(X)<=>(brave(X)|~rich(X))))&
((?[X]:(old(X)))<=>((rich(lucy)<~>~happy(lucy))))&
(~kind(lucy))&
(?[X]:((~curious(X)|~kind(X))))&
(?[X]:((humble(X)&wise(X))))&
(?[X]:((curious(X)|~tall(X))))&
(~quiet(john)) | ~generous(fred) | [
"p3",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6340589355808910365358300
% SZS output start Proof for 6340589355808910365358300
4. ! [X0] : ((~generous(X0) | tall(X0)) <=> (generous(X0) | ~brave(X0))) [input p3]
15. ! [X0] : (rich(X0) <=> (~rich(X0) | brave(X0))) [input p14]
22. ~generous(fred) [input hypothesis]
40. ! [X0] : (((~generous(X0) | tall(X0)) | (~generous(X0) & brave(X0))) & ((generous(X0) | ~brave(X0)) | (generous(X0) & ~tall(X0)))) [nnf transformation 4]
41. ! [X0] : ((~generous(X0) | tall(X0) | (~generous(X0) & brave(X0))) & (generous(X0) | ~brave(X0) | (generous(X0) & ~tall(X0)))) [flattening 40]
56. ! [X0] : ((rich(X0) | (rich(X0) & ~brave(X0))) & ((~rich(X0) | brave(X0)) | ~rich(X0))) [nnf transformation 15]
57. ! [X0] : ((rich(X0) | (rich(X0) & ~brave(X0))) & (~rich(X0) | brave(X0) | ~rich(X0))) [flattening 56]
81. generous(X0) | ~brave(X0) | generous(X0) [cnf transformation 41]
111. ~rich(X0) | brave(X0) | ~rich(X0) [cnf transformation 57]
113. rich(X0) | rich(X0) [cnf transformation 57]
124. ~generous(fred) [cnf transformation 22]
125. ~rich(X0) | brave(X0) [duplicate literal removal 111]
126. rich(X0) [duplicate literal removal 113]
128. ~brave(X0) | generous(X0) [duplicate literal removal 81]
241. brave(X0) [subsumption resolution 125,126]
275. generous(X0) [resolution 128,241]
276. $false [resolution 275,124]
% SZS output end Proof for 6340589355808910365358300
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or wise then someone is both funny and not kind and vice versa.
If john is tall then john is curious.
Everyone who is both not kind and patient is either not patient or quiet.
Everyone who is both quiet and strong is generous.
Everyone who is not calm is not kind and vice versa.
If alice is both wise and not quiet then paul is old.
Everyone who is not funny or not curious is funny or not humble and vice versa.
Everyone who is either not calm or not wise is strong.
Everyone who is quiet or humble is either not calm or tall and vice versa.
If someone is funny then someone is either not creative or not kind.
If someone is either not wise or quiet then john is both not strong and curious and vice versa.
If someone is brave then someone is not rich or not calm.
If someone is both curious and not patient then someone is both not happy and not strong.
If susan is either brave or not old then alice is either creative or wise.
If someone is both happy and not rich then someone is rich or curious and vice versa.
If someone is generous then someone is either generous or not patient and vice versa.
Someone is not calm or strong.
Susan is rich or wise.
Someone is both not kind and curious.
Someone is either not creative or humble.
John is either generous or not creative.
Lucy is not generous or not rich.
John is not generous.
Someone is both patient and brave. | John is not creative. | entailment | ((?[X]:((~quiet(X)|wise(X))))<=>(?[X]:((funny(X)&~kind(X)))))&
((tall(john))=>(curious(john)))&
(![X]:((~kind(X)&patient(X))=>(~patient(X)<~>quiet(X))))&
(![X]:((quiet(X)&strong(X))=>generous(X)))&
(![X]:(~calm(X)<=>~kind(X)))&
(((wise(alice)&~quiet(alice)))=>(old(paul)))&
(![X]:((~funny(X)|~curious(X))<=>(funny(X)|~humble(X))))&
(![X]:((~calm(X)<~>~wise(X))=>strong(X)))&
(![X]:((quiet(X)|humble(X))<=>(~calm(X)<~>tall(X))))&
((?[X]:(funny(X)))=>(?[X]:((~creative(X)<~>~kind(X)))))&
((?[X]:((~wise(X)<~>quiet(X))))<=>((~strong(john)&curious(john))))&
((?[X]:(brave(X)))=>(?[X]:((~rich(X)|~calm(X)))))&
((?[X]:((curious(X)&~patient(X))))=>(?[X]:((~happy(X)&~strong(X)))))&
(((brave(susan)<~>~old(susan)))=>((creative(alice)<~>wise(alice))))&
((?[X]:((happy(X)&~rich(X))))<=>(?[X]:((rich(X)|curious(X)))))&
((?[X]:(generous(X)))<=>(?[X]:((generous(X)<~>~patient(X)))))&
(?[X]:((~calm(X)|strong(X))))&
((rich(susan)|wise(susan)))&
(?[X]:((~kind(X)&curious(X))))&
(?[X]:((~creative(X)<~>humble(X))))&
((generous(john)<~>~creative(john)))&
((~generous(lucy)|~rich(lucy)))&
(~generous(john))&
(?[X]:((patient(X)&brave(X)))) | ~creative(john) | [
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5936971485874499468220347
% SZS output start Proof for 5936971485874499468220347
21. generous(john) <~> ~creative(john) [input p20]
23. ~generous(john) [input p22]
25. creative(john) [input hypothesis]
89. (creative(john) | ~generous(john)) & (~creative(john) | generous(john)) [nnf transformation 21]
146. ~creative(john) | generous(john) [cnf transformation 89]
149. ~generous(john) [cnf transformation 23]
152. creative(john) [cnf transformation 25]
370. 49 <=> generous(john) [avatar definition]
374. 50 <=> creative(john) [avatar definition]
378. 49 | ~50 [avatar split clause 146,374,370]
388. ~49 [avatar split clause 149,370]
389. 50 [avatar split clause 152,374]
390. $false [avatar sat refutation 378,388,389]
% SZS output end Proof for 5936971485874499468220347
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or kind is either not humble or not strong and vice versa.
If someone is quiet then lucy is rich.
If someone is not humble or not curious then someone is humble and vice versa.
If someone is both not brave and not creative then susan is quiet and vice versa.
Everyone who is both not calm and humble is calm.
If someone is not patient or creative then fred is either not brave or humble.
If someone is either brave or tall then someone is humble and vice versa.
Everyone who is not humble or kind is either curious or not wise.
Everyone who is funny or humble is not tall.
Everyone who is old is both not rich and generous and vice versa.
Everyone who is kind or not old is not humble or curious.
Everyone who is not rich is not happy.
If mary is either not rich or old then someone is both calm and strong and vice versa.
Everyone who is either humble or not quiet is wise or calm.
Everyone who is not generous is both humble and tall.
If john is both not brave and creative then fred is curious or generous and vice versa.
Someone is tall.
John is both rich and not kind.
Lucy is not quiet.
Someone is both wise and not creative.
Someone is wise or not calm.
Someone is not curious.
Someone is curious or rich.
Someone is both wise and brave. | John is brave. | contradiction | (![X]:((~wise(X)<~>kind(X))<=>(~humble(X)<~>~strong(X))))&
((?[X]:(quiet(X)))=>(rich(lucy)))&
((?[X]:((~humble(X)|~curious(X))))<=>(?[X]:(humble(X))))&
((?[X]:((~brave(X)&~creative(X))))<=>(quiet(susan)))&
(![X]:((~calm(X)&humble(X))=>calm(X)))&
((?[X]:((~patient(X)|creative(X))))=>((~brave(fred)<~>humble(fred))))&
((?[X]:((brave(X)<~>tall(X))))<=>(?[X]:(humble(X))))&
(![X]:((~humble(X)|kind(X))=>(curious(X)<~>~wise(X))))&
(![X]:((funny(X)|humble(X))=>~tall(X)))&
(![X]:(old(X)<=>(~rich(X)&generous(X))))&
(![X]:((kind(X)|~old(X))=>(~humble(X)|curious(X))))&
(![X]:(~rich(X)=>~happy(X)))&
(((~rich(mary)<~>old(mary)))<=>(?[X]:((calm(X)&strong(X)))))&
(![X]:((humble(X)<~>~quiet(X))=>(wise(X)|calm(X))))&
(![X]:(~generous(X)=>(humble(X)&tall(X))))&
(((~brave(john)&creative(john)))<=>((curious(fred)|generous(fred))))&
(?[X]:(tall(X)))&
((rich(john)&~kind(john)))&
(~quiet(lucy))&
(?[X]:((wise(X)&~creative(X))))&
(?[X]:((wise(X)|~calm(X))))&
(?[X]:(~curious(X)))&
(?[X]:((curious(X)|rich(X))))&
(?[X]:((wise(X)&brave(X)))) | brave(john) | [
"p8",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3902074028788278052501764
% SZS output start Proof for 3902074028788278052501764
9. ! [X0] : ((humble(X0) | funny(X0)) => ~tall(X0)) [input p8]
15. ! [X0] : (~generous(X0) => (tall(X0) & humble(X0))) [input p14]
16. (creative(john) & ~brave(john)) <=> (generous(fred) | curious(fred)) [input p15]
25. brave(john) [input hypothesis]
29. ! [X0] : (humble(X0) => ~tall(X0)) [pure predicate removal 9]
36. ! [X0] : (~tall(X0) | ~humble(X0)) [ennf transformation 29]
41. ! [X0] : ((tall(X0) & humble(X0)) | generous(X0)) [ennf transformation 15]
66. ((creative(john) & ~brave(john)) | (~generous(fred) & ~curious(fred))) & ((generous(fred) | curious(fred)) | (~creative(john) | brave(john))) [nnf transformation 16]
67. ((creative(john) & ~brave(john)) | (~generous(fred) & ~curious(fred))) & (generous(fred) | curious(fred) | ~creative(john) | brave(john)) [flattening 66]
106. ~tall(X0) | ~humble(X0) [cnf transformation 36]
120. generous(X0) | humble(X0) [cnf transformation 41]
121. generous(X0) | tall(X0) [cnf transformation 41]
124. ~brave(john) | ~generous(fred) [cnf transformation 67]
138. brave(john) [cnf transformation 25]
198. 15 <=> humble(fred) [avatar definition]
252. 26 <=> generous(fred) [avatar definition]
254. ~generous(fred) <- (~26) [avatar component clause 252]
266. 29 <=> brave(john) [avatar definition]
269. ~26 | ~29 [avatar split clause 124,266,252]
290. 29 [avatar split clause 138,266]
307. humble(fred) <- (~26) [resolution 120,254]
308. tall(fred) <- (~26) [resolution 121,254]
309. ~humble(fred) <- (~26) [resolution 308,106]
312. ~15 | 26 [avatar split clause 309,252,198]
313. 15 | 26 [avatar split clause 307,252,198]
314. $false [avatar sat refutation 269,290,312,313]
% SZS output end Proof for 3902074028788278052501764
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall then someone is either not funny or creative and vice versa.
Everyone who is both not humble and wise is either not curious or not old.
If someone is not happy then someone is not patient or not generous and vice versa.
Everyone who is both not calm and strong is not patient and vice versa.
If mary is patient or not humble then mary is both not generous and calm.
Everyone who is generous is both calm and not wise.
If john is either not quiet or wise then paul is not happy and vice versa.
If someone is not creative then lucy is not patient.
If someone is not calm or not wise then fred is generous.
Everyone who is both happy and quiet is calm or rich.
If paul is happy or not funny then someone is not humble or not tall.
If someone is not curious then someone is not creative.
Everyone who is humble or brave is not rich.
If john is both rich and not quiet then someone is creative or not curious.
Everyone who is either not patient or calm is not generous.
Everyone who is both wise and funny is both not wise and not humble and vice versa.
Someone is either old or not humble.
Someone is both calm and rich.
Someone is either not old or strong.
Someone is not tall.
Someone is either not wise or not rich.
Alice is not happy. | Lucy is wise. | entailment | ((?[X]:(tall(X)))<=>(?[X]:((~funny(X)<~>creative(X)))))&
(![X]:((~humble(X)&wise(X))=>(~curious(X)<~>~old(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~patient(X)|~generous(X)))))&
(![X]:((~calm(X)&strong(X))<=>~patient(X)))&
(((patient(mary)|~humble(mary)))=>((~generous(mary)&calm(mary))))&
(![X]:(generous(X)=>(calm(X)&~wise(X))))&
(((~quiet(john)<~>wise(john)))<=>(~happy(paul)))&
((?[X]:(~creative(X)))=>(~patient(lucy)))&
((?[X]:((~calm(X)|~wise(X))))=>(generous(fred)))&
(![X]:((happy(X)&quiet(X))=>(calm(X)|rich(X))))&
(((happy(paul)|~funny(paul)))=>(?[X]:((~humble(X)|~tall(X)))))&
((?[X]:(~curious(X)))=>(?[X]:(~creative(X))))&
(![X]:((humble(X)|brave(X))=>~rich(X)))&
(((rich(john)&~quiet(john)))=>(?[X]:((creative(X)|~curious(X)))))&
(![X]:((~patient(X)<~>calm(X))=>~generous(X)))&
(![X]:((wise(X)&funny(X))<=>(~wise(X)&~humble(X))))&
(?[X]:((old(X)<~>~humble(X))))&
(?[X]:((calm(X)&rich(X))))&
(?[X]:((~old(X)<~>strong(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~wise(X)<~>~rich(X))))&
(~happy(alice)) | wise(lucy) | [
"p3",
"p5",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 127507747041557482443842
% SZS output start Proof for 127507747041557482443842
4. ! [X0] : ((strong(X0) & ~calm(X0)) <=> ~patient(X0)) [input p3]
6. ! [X0] : (generous(X0) => (~wise(X0) & calm(X0))) [input p5]
9. ? [X0] : (~wise(X0) | ~calm(X0)) => generous(fred) [input p8]
15. ! [X0] : ((~patient(X0) <~> calm(X0)) => ~generous(X0)) [input p14]
23. ~wise(lucy) [input hypothesis]
31. ! [X0] : ((~wise(X0) & calm(X0)) | ~generous(X0)) [ennf transformation 6]
33. generous(fred) | ! [X0] : (wise(X0) & calm(X0)) [ennf transformation 9]
41. ! [X0] : (~generous(X0) | (~patient(X0) <=> calm(X0))) [ennf transformation 15]
53. ! [X0] : (((strong(X0) & ~calm(X0)) | patient(X0)) & (~patient(X0) | (~strong(X0) | calm(X0)))) [nnf transformation 4]
54. ! [X0] : (((strong(X0) & ~calm(X0)) | patient(X0)) & (~patient(X0) | ~strong(X0) | calm(X0))) [flattening 53]
63. ! [X0] : (~generous(X0) | ((~patient(X0) | ~calm(X0)) & (calm(X0) | patient(X0)))) [nnf transformation 41]
89. ~calm(X0) | patient(X0) [cnf transformation 54]
95. calm(X0) | ~generous(X0) [cnf transformation 31]
103. generous(fred) | wise(X0) [cnf transformation 33]
111. ~generous(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 63]
126. ~wise(lucy) [cnf transformation 23]
223. 22 <=> ! [X0] : wise(X0) [avatar definition]
224. wise(X0) <- (22) [avatar component clause 223]
226. 23 <=> generous(fred) [avatar definition]
228. generous(fred) <- (23) [avatar component clause 226]
229. 22 | 23 [avatar split clause 103,226,223]
269. ~generous(X0) | ~calm(X0) [subsumption resolution 111,89]
270. ~generous(X0) [subsumption resolution 269,95]
301. $false <- (23) [subsumption resolution 228,270]
302. ~23 [avatar contradiction clause 301]
303. $false <- (22) [resolution 224,126]
306. ~22 [avatar contradiction clause 303]
307. $false [avatar sat refutation 229,302,306]
% SZS output end Proof for 127507747041557482443842
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either patient or tall then fred is either not old or not funny and vice versa.
Everyone who is both brave and not wise is not creative or curious and vice versa.
If mary is either tall or not generous then lucy is both happy and not strong and vice versa.
Everyone who is not quiet or tall is both quiet and not kind.
Everyone who is not tall or generous is not kind or not wise.
If susan is not kind then someone is old or not old and vice versa.
Everyone who is both strong and kind is not quiet and vice versa.
If someone is both curious and not patient then susan is both brave and not brave and vice versa.
Everyone who is strong is old or not calm.
If someone is either not wise or not generous then someone is happy or strong and vice versa.
If someone is brave then someone is either not creative or calm and vice versa.
If lucy is both not wise and not rich then susan is either happy or brave and vice versa.
Everyone who is either wise or strong is both patient and brave.
If paul is not generous or not brave then mary is not brave.
Everyone who is both not curious and not old is calm and vice versa.
Everyone who is rich is either curious or not strong.
Someone is either not rich or happy.
Someone is both not rich and not wise.
Alice is not patient or not humble.
Someone is both kind and funny.
Someone is either not old or curious.
Alice is both old and humble.
Alice is not tall. | Lucy is not rich. | neutral | ((?[X]:((patient(X)<~>tall(X))))<=>((~old(fred)<~>~funny(fred))))&
(![X]:((brave(X)&~wise(X))<=>(~creative(X)|curious(X))))&
(((tall(mary)<~>~generous(mary)))<=>((happy(lucy)&~strong(lucy))))&
(![X]:((~quiet(X)|tall(X))=>(quiet(X)&~kind(X))))&
(![X]:((~tall(X)|generous(X))=>(~kind(X)|~wise(X))))&
((~kind(susan))<=>(?[X]:((old(X)|~old(X)))))&
(![X]:((strong(X)&kind(X))<=>~quiet(X)))&
((?[X]:((curious(X)&~patient(X))))<=>((brave(susan)&~brave(susan))))&
(![X]:(strong(X)=>(old(X)|~calm(X))))&
((?[X]:((~wise(X)<~>~generous(X))))<=>(?[X]:((happy(X)|strong(X)))))&
((?[X]:(brave(X)))<=>(?[X]:((~creative(X)<~>calm(X)))))&
(((~wise(lucy)&~rich(lucy)))<=>((happy(susan)<~>brave(susan))))&
(![X]:((wise(X)<~>strong(X))=>(patient(X)&brave(X))))&
(((~generous(paul)|~brave(paul)))=>(~brave(mary)))&
(![X]:((~curious(X)&~old(X))<=>calm(X)))&
(![X]:(rich(X)=>(curious(X)<~>~strong(X))))&
(?[X]:((~rich(X)<~>happy(X))))&
(?[X]:((~rich(X)&~wise(X))))&
((~patient(alice)|~humble(alice)))&
(?[X]:((kind(X)&funny(X))))&
(?[X]:((~old(X)<~>curious(X))))&
((old(alice)&humble(alice)))&
(~tall(alice)) | ~rich(lucy) | [] | null | 0 |
Everyone who is either curious or not calm is curious and vice versa. Everyone who is both funny and not calm is not wise or not curious and vice versa. Everyone who is calm or old is both not humble and quiet. Everyone who is both not rich and not wise is not creative. If someone is either not kind or not tall then paul is tall or generous and vice versa. Everyone who is rich or humble is not patient. Everyone who is either calm or not strong is not old. Everyone who is not brave or rich is happy or not kind and vice versa. If alice is either not wise or strong then someone is not quiet and vice versa. Everyone who is quiet is curious or strong. If someone is happy or not creative then someone is both not creative and funny. Everyone who is either old or not strong is not wise or quiet. Everyone who is calm or funny is funny or humble and vice versa. Everyone who is both not quiet and not old is either calm or not brave and vice versa. If mary is either not patient or strong then someone is either brave or humble and vice versa. If someone is either rich or tall then someone is not quiet or humble. Someone is not rich or not patient. John is both not old and not kind. Someone is either rich or curious. Paul is not brave or not patient. Alice is both calm and not creative. Someone is not brave. | Alice is not tall. | neutral | (![X]:((curious(X)<~>~calm(X))<=>curious(X)))&
(![X]:((funny(X)&~calm(X))<=>(~wise(X)|~curious(X))))&
(![X]:((calm(X)|old(X))=>(~humble(X)&quiet(X))))&
(![X]:((~rich(X)&~wise(X))=>~creative(X)))&
((?[X]:((~kind(X)<~>~tall(X))))<=>((tall(paul)|generous(paul))))&
(![X]:((rich(X)|humble(X))=>~patient(X)))&
(![X]:((calm(X)<~>~strong(X))=>~old(X)))&
(![X]:((~brave(X)|rich(X))<=>(happy(X)|~kind(X))))&
(((~wise(alice)<~>strong(alice)))<=>(?[X]:(~quiet(X))))&
(![X]:(quiet(X)=>(curious(X)|strong(X))))&
((?[X]:((happy(X)|~creative(X))))=>(?[X]:((~creative(X)&funny(X)))))&
(![X]:((old(X)<~>~strong(X))=>(~wise(X)|quiet(X))))&
(![X]:((calm(X)|funny(X))<=>(funny(X)|humble(X))))&
(![X]:((~quiet(X)&~old(X))<=>(calm(X)<~>~brave(X))))&
(((~patient(mary)<~>strong(mary)))<=>(?[X]:((brave(X)<~>humble(X)))))&
((?[X]:((rich(X)<~>tall(X))))=>(?[X]:((~quiet(X)|humble(X)))))&
(?[X]:((~rich(X)|~patient(X))))&
((~old(john)&~kind(john)))&
(?[X]:((rich(X)<~>curious(X))))&
((~brave(paul)|~patient(paul)))&
((calm(alice)&~creative(alice)))&
(?[X]:(~brave(X))) | ~tall(alice) | [] | null | 0 |
If lucy is not creative or not rich then someone is not creative or not funny and vice versa.
Everyone who is both humble and creative is generous and vice versa.
Everyone who is both quiet and funny is both not happy and tall.
Everyone who is both not tall and not strong is not creative.
Everyone who is not strong or rich is either generous or quiet.
Everyone who is not patient or not old is both calm and not happy.
If someone is not curious or not old then susan is old or not quiet.
If alice is both generous and not brave then susan is humble.
Everyone who is patient is brave or not patient and vice versa.
If someone is both not patient and not brave then someone is either old or not patient and vice versa.
If someone is both not kind and not quiet then someone is not creative.
If someone is both not creative and not funny then fred is not happy or not old.
If someone is either wise or tall then fred is not kind.
Everyone who is both not rich and creative is not wise or not kind.
Everyone who is either not calm or old is not wise and vice versa.
If someone is humble then someone is not wise or patient and vice versa.
Someone is not old.
Fred is rich.
Someone is not humble.
Someone is tall or not kind.
Someone is old or quiet. | Alice is not creative. | neutral | (((~creative(lucy)|~rich(lucy)))<=>(?[X]:((~creative(X)|~funny(X)))))&
(![X]:((humble(X)&creative(X))<=>generous(X)))&
(![X]:((quiet(X)&funny(X))=>(~happy(X)&tall(X))))&
(![X]:((~tall(X)&~strong(X))=>~creative(X)))&
(![X]:((~strong(X)|rich(X))=>(generous(X)<~>quiet(X))))&
(![X]:((~patient(X)|~old(X))=>(calm(X)&~happy(X))))&
((?[X]:((~curious(X)|~old(X))))=>((old(susan)|~quiet(susan))))&
(((generous(alice)&~brave(alice)))=>(humble(susan)))&
(![X]:(patient(X)<=>(brave(X)|~patient(X))))&
((?[X]:((~patient(X)&~brave(X))))<=>(?[X]:((old(X)<~>~patient(X)))))&
((?[X]:((~kind(X)&~quiet(X))))=>(?[X]:(~creative(X))))&
((?[X]:((~creative(X)&~funny(X))))=>((~happy(fred)|~old(fred))))&
((?[X]:((wise(X)<~>tall(X))))=>(~kind(fred)))&
(![X]:((~rich(X)&creative(X))=>(~wise(X)|~kind(X))))&
(![X]:((~calm(X)<~>old(X))<=>~wise(X)))&
((?[X]:(humble(X)))<=>(?[X]:((~wise(X)|patient(X)))))&
(?[X]:(~old(X)))&
(rich(fred))&
(?[X]:(~humble(X)))&
(?[X]:((tall(X)|~kind(X))))&
(?[X]:((old(X)|quiet(X)))) | ~creative(alice) | [] | null | 0 |
Everyone who is old or rich is not wise and vice versa.
Everyone who is either strong or not calm is not generous or quiet and vice versa.
Everyone who is funny or tall is patient or quiet.
Everyone who is both not tall and wise is either quiet or generous.
Everyone who is calm is brave or not wise.
If someone is either not wise or not funny then paul is either not calm or brave and vice versa.
If someone is both not kind and not tall then john is funny.
If someone is either humble or strong then someone is patient and vice versa.
Everyone who is not generous or not patient is either not brave or not happy and vice versa.
Everyone who is not patient or not wise is not curious and vice versa.
Everyone who is not kind or not wise is tall and vice versa.
If someone is old then someone is either not humble or generous.
Everyone who is wise or happy is tall.
If lucy is creative then susan is not humble.
Everyone who is either not creative or humble is either happy or strong.
Everyone who is not strong or not generous is not quiet or not brave and vice versa.
John is patient or not creative.
Someone is both happy and generous.
Fred is either quiet or generous.
Someone is old.
Someone is both kind and not strong.
Someone is either not funny or rich.
Someone is both not generous and happy. | John is funny. | neutral | (![X]:((old(X)|rich(X))<=>~wise(X)))&
(![X]:((strong(X)<~>~calm(X))<=>(~generous(X)|quiet(X))))&
(![X]:((funny(X)|tall(X))=>(patient(X)|quiet(X))))&
(![X]:((~tall(X)&wise(X))=>(quiet(X)<~>generous(X))))&
(![X]:(calm(X)=>(brave(X)|~wise(X))))&
((?[X]:((~wise(X)<~>~funny(X))))<=>((~calm(paul)<~>brave(paul))))&
((?[X]:((~kind(X)&~tall(X))))=>(funny(john)))&
((?[X]:((humble(X)<~>strong(X))))<=>(?[X]:(patient(X))))&
(![X]:((~generous(X)|~patient(X))<=>(~brave(X)<~>~happy(X))))&
(![X]:((~patient(X)|~wise(X))<=>~curious(X)))&
(![X]:((~kind(X)|~wise(X))<=>tall(X)))&
((?[X]:(old(X)))=>(?[X]:((~humble(X)<~>generous(X)))))&
(![X]:((wise(X)|happy(X))=>tall(X)))&
((creative(lucy))=>(~humble(susan)))&
(![X]:((~creative(X)<~>humble(X))=>(happy(X)<~>strong(X))))&
(![X]:((~strong(X)|~generous(X))<=>(~quiet(X)|~brave(X))))&
((patient(john)|~creative(john)))&
(?[X]:((happy(X)&generous(X))))&
((quiet(fred)<~>generous(fred)))&
(?[X]:(old(X)))&
(?[X]:((kind(X)&~strong(X))))&
(?[X]:((~funny(X)<~>rich(X))))&
(?[X]:((~generous(X)&happy(X)))) | funny(john) | [] | null | 0 |
Everyone who is both not tall and strong is funny and vice versa.
Everyone who is both curious and kind is not quiet or happy and vice versa.
Everyone who is not patient is not curious.
Everyone who is not patient or strong is either not quiet or humble.
Everyone who is not tall or not creative is humble and vice versa.
Everyone who is quiet is both not generous and rich and vice versa.
Everyone who is both not humble and creative is patient.
Everyone who is either not patient or not kind is generous and vice versa.
If fred is not tall then mary is not curious.
If someone is strong then mary is either humble or happy.
Everyone who is both not kind and wise is not funny and vice versa.
Everyone who is not old or not patient is both kind and rich.
If someone is both not patient and humble then paul is not curious.
If someone is either not rich or strong then someone is not curious and vice versa.
If someone is not calm or quiet then susan is not humble or not curious.
Everyone who is not calm or not patient is both generous and strong and vice versa.
Mary is quiet or not brave.
Susan is both not brave and not old.
Someone is either generous or funny.
Lucy is not wise.
Someone is both not wise and strong. | Paul is not funny. | contradiction | (![X]:((~tall(X)&strong(X))<=>funny(X)))&
(![X]:((curious(X)&kind(X))<=>(~quiet(X)|happy(X))))&
(![X]:(~patient(X)=>~curious(X)))&
(![X]:((~patient(X)|strong(X))=>(~quiet(X)<~>humble(X))))&
(![X]:((~tall(X)|~creative(X))<=>humble(X)))&
(![X]:(quiet(X)<=>(~generous(X)&rich(X))))&
(![X]:((~humble(X)&creative(X))=>patient(X)))&
(![X]:((~patient(X)<~>~kind(X))<=>generous(X)))&
((~tall(fred))=>(~curious(mary)))&
((?[X]:(strong(X)))=>((humble(mary)<~>happy(mary))))&
(![X]:((~kind(X)&wise(X))<=>~funny(X)))&
(![X]:((~old(X)|~patient(X))=>(kind(X)&rich(X))))&
((?[X]:((~patient(X)&humble(X))))=>(~curious(paul)))&
((?[X]:((~rich(X)<~>strong(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((~calm(X)|quiet(X))))=>((~humble(susan)|~curious(susan))))&
(![X]:((~calm(X)|~patient(X))<=>(generous(X)&strong(X))))&
((quiet(mary)|~brave(mary)))&
((~brave(susan)&~old(susan)))&
(?[X]:((generous(X)<~>funny(X))))&
(~wise(lucy))&
(?[X]:((~wise(X)&strong(X)))) | ~funny(paul) | [
"p1",
"p3",
"p4",
"p5",
"p6",
"p7",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 230521535748604460622740
% SZS output start Proof for 230521535748604460622740
2. ! [X0] : ((kind(X0) & curious(X0)) <=> (happy(X0) | ~quiet(X0))) [input p1]
4. ! [X0] : ((strong(X0) | ~patient(X0)) => (~quiet(X0) <~> humble(X0))) [input p3]
5. ! [X0] : ((~creative(X0) | ~tall(X0)) <=> humble(X0)) [input p4]
6. ! [X0] : (quiet(X0) <=> (rich(X0) & ~generous(X0))) [input p5]
7. ! [X0] : ((creative(X0) & ~humble(X0)) => patient(X0)) [input p6]
8. ! [X0] : ((~patient(X0) <~> ~kind(X0)) <=> generous(X0)) [input p7]
11. ! [X0] : ((wise(X0) & ~kind(X0)) <=> ~funny(X0)) [input p10]
16. ! [X0] : ((~patient(X0) | ~calm(X0)) <=> (strong(X0) & generous(X0))) [input p15]
22. ~funny(paul) [input hypothesis]
27. ! [X0] : ((~quiet(X0) <~> humble(X0)) | (~strong(X0) & patient(X0))) [ennf transformation 4]
28. ! [X0] : (patient(X0) | (~creative(X0) | humble(X0))) [ennf transformation 7]
29. ! [X0] : (patient(X0) | ~creative(X0) | humble(X0)) [flattening 28]
38. ! [X0] : (((kind(X0) & curious(X0)) | (~happy(X0) & quiet(X0))) & ((happy(X0) | ~quiet(X0)) | (~kind(X0) | ~curious(X0)))) [nnf transformation 2]
39. ! [X0] : (((kind(X0) & curious(X0)) | (~happy(X0) & quiet(X0))) & (happy(X0) | ~quiet(X0) | ~kind(X0) | ~curious(X0))) [flattening 38]
40. ! [X0] : (((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | (~strong(X0) & patient(X0))) [nnf transformation 27]
41. ! [X0] : (((~creative(X0) | ~tall(X0)) | ~humble(X0)) & (humble(X0) | (creative(X0) & tall(X0)))) [nnf transformation 5]
42. ! [X0] : ((~creative(X0) | ~tall(X0) | ~humble(X0)) & (humble(X0) | (creative(X0) & tall(X0)))) [flattening 41]
43. ! [X0] : ((quiet(X0) | (~rich(X0) | generous(X0))) & ((rich(X0) & ~generous(X0)) | ~quiet(X0))) [nnf transformation 6]
44. ! [X0] : ((quiet(X0) | ~rich(X0) | generous(X0)) & ((rich(X0) & ~generous(X0)) | ~quiet(X0))) [flattening 43]
45. ! [X0] : ((((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | ~generous(X0)) & (generous(X0) | ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0))))) [nnf transformation 8]
47. ! [X0] : (((wise(X0) & ~kind(X0)) | funny(X0)) & (~funny(X0) | (~wise(X0) | kind(X0)))) [nnf transformation 11]
48. ! [X0] : (((wise(X0) & ~kind(X0)) | funny(X0)) & (~funny(X0) | ~wise(X0) | kind(X0))) [flattening 47]
54. ! [X0] : (((~patient(X0) | ~calm(X0)) | (~strong(X0) | ~generous(X0))) & ((strong(X0) & generous(X0)) | (patient(X0) & calm(X0)))) [nnf transformation 16]
55. ! [X0] : ((~patient(X0) | ~calm(X0) | ~strong(X0) | ~generous(X0)) & ((strong(X0) & generous(X0)) | (patient(X0) & calm(X0)))) [flattening 54]
67. quiet(X0) | kind(X0) [cnf transformation 39]
72. ~humble(X0) | quiet(X0) | patient(X0) [cnf transformation 40]
75. creative(X0) | humble(X0) [cnf transformation 42]
77. ~generous(X0) | ~quiet(X0) [cnf transformation 44]
80. patient(X0) | ~creative(X0) | humble(X0) [cnf transformation 29]
82. ~patient(X0) | generous(X0) | kind(X0) [cnf transformation 45]
89. ~kind(X0) | funny(X0) [cnf transformation 48]
103. generous(X0) | patient(X0) [cnf transformation 55]
113. ~funny(paul) [cnf transformation 22]
114. humble(X0) | patient(X0) [subsumption resolution 80,75]
139. 6 <=> ! [X0] : patient(X0) [avatar definition]
140. patient(X0) <- (6) [avatar component clause 139]
220. ~quiet(X0) | patient(X0) [resolution 103,77]
235. quiet(X0) | patient(X0) | patient(X0) [resolution 72,114]
238. quiet(X0) | patient(X0) [duplicate literal removal 235]
240. patient(X0) [subsumption resolution 238,220]
241. 6 [avatar split clause 240,139]
265. generous(X0) | kind(X0) <- (6) [resolution 82,140]
384. kind(X2) | ~quiet(X2) <- (6) [resolution 265,77]
388. kind(X2) <- (6) [subsumption resolution 384,67]
390. funny(X1) <- (6) [resolution 388,89]
393. $false <- (6) [resolution 390,113]
396. ~6 [avatar contradiction clause 393]
397. $false [avatar sat refutation 241,396]
% SZS output end Proof for 230521535748604460622740
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind and not creative then lucy is generous or tall. If someone is brave then someone is not strong. If someone is wise or not happy then alice is not humble or not funny. If someone is brave or not quiet then someone is not quiet. If someone is both not wise and not brave then alice is not rich or not curious. Everyone who is either creative or rich is either not tall or not funny. Everyone who is not kind or tall is not humble or brave and vice versa. Everyone who is not wise or brave is either humble or not patient and vice versa. Everyone who is not quiet is not strong and vice versa. Everyone who is quiet is not calm or not creative. Everyone who is not generous or not humble is both quiet and not generous and vice versa. Everyone who is both not wise and not rich is not calm or funny and vice versa. If john is not tall then john is either not wise or tall and vice versa. If someone is both not creative and not curious then someone is both not rich and kind. Everyone who is not funny is not rich or not quiet. Everyone who is not old or brave is not rich. Someone is kind or wise. Someone is not curious or creative. Mary is both not curious and brave. Alice is brave or happy. John is not calm or not funny. Lucy is both not generous and not happy. Fred is calm. Someone is either quiet or not tall. | Lucy is not rich. | entailment | ((?[X]:((kind(X)&~creative(X))))=>((generous(lucy)|tall(lucy))))&
((?[X]:(brave(X)))=>(?[X]:(~strong(X))))&
((?[X]:((wise(X)|~happy(X))))=>((~humble(alice)|~funny(alice))))&
((?[X]:((brave(X)|~quiet(X))))=>(?[X]:(~quiet(X))))&
((?[X]:((~wise(X)&~brave(X))))=>((~rich(alice)|~curious(alice))))&
(![X]:((creative(X)<~>rich(X))=>(~tall(X)<~>~funny(X))))&
(![X]:((~kind(X)|tall(X))<=>(~humble(X)|brave(X))))&
(![X]:((~wise(X)|brave(X))<=>(humble(X)<~>~patient(X))))&
(![X]:(~quiet(X)<=>~strong(X)))&
(![X]:(quiet(X)=>(~calm(X)|~creative(X))))&
(![X]:((~generous(X)|~humble(X))<=>(quiet(X)&~generous(X))))&
(![X]:((~wise(X)&~rich(X))<=>(~calm(X)|funny(X))))&
((~tall(john))<=>((~wise(john)<~>tall(john))))&
((?[X]:((~creative(X)&~curious(X))))=>(?[X]:((~rich(X)&kind(X)))))&
(![X]:(~funny(X)=>(~rich(X)|~quiet(X))))&
(![X]:((~old(X)|brave(X))=>~rich(X)))&
(?[X]:((kind(X)|wise(X))))&
(?[X]:((~curious(X)|creative(X))))&
((~curious(mary)&brave(mary)))&
((brave(alice)|happy(alice)))&
((~calm(john)|~funny(john)))&
((~generous(lucy)&~happy(lucy)))&
(calm(fred))&
(?[X]:((quiet(X)<~>~tall(X)))) | ~rich(lucy) | [
"p10",
"p11",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4785418432385536381499356
% SZS output start Proof for 4785418432385536381499356
11. ! [X0] : ((~humble(X0) | ~generous(X0)) <=> (~generous(X0) & quiet(X0))) [input p10]
12. ! [X0] : ((~rich(X0) & ~wise(X0)) <=> (funny(X0) | ~calm(X0))) [input p11]
15. ! [X0] : (~funny(X0) => (~quiet(X0) | ~rich(X0))) [input p14]
22. ~happy(lucy) & ~generous(lucy) [input p21]
25. rich(lucy) [input hypothesis]
42. ! [X0] : ((~quiet(X0) | ~rich(X0)) | funny(X0)) [ennf transformation 15]
43. ! [X0] : (~quiet(X0) | ~rich(X0) | funny(X0)) [flattening 42]
57. ! [X0] : (((~humble(X0) | ~generous(X0)) | (generous(X0) | ~quiet(X0))) & ((~generous(X0) & quiet(X0)) | (humble(X0) & generous(X0)))) [nnf transformation 11]
58. ! [X0] : ((~humble(X0) | ~generous(X0) | generous(X0) | ~quiet(X0)) & ((~generous(X0) & quiet(X0)) | (humble(X0) & generous(X0)))) [flattening 57]
59. ! [X0] : (((~rich(X0) & ~wise(X0)) | (~funny(X0) & calm(X0))) & ((funny(X0) | ~calm(X0)) | (rich(X0) | wise(X0)))) [nnf transformation 12]
60. ! [X0] : (((~rich(X0) & ~wise(X0)) | (~funny(X0) & calm(X0))) & (funny(X0) | ~calm(X0) | rich(X0) | wise(X0))) [flattening 59]
96. quiet(X0) | generous(X0) [cnf transformation 58]
105. ~rich(X0) | ~funny(X0) [cnf transformation 60]
112. ~quiet(X0) | ~rich(X0) | funny(X0) [cnf transformation 43]
120. ~generous(lucy) [cnf transformation 22]
125. rich(lucy) [cnf transformation 25]
132. 2 <=> generous(lucy) [avatar definition]
133. ~generous(lucy) <- (~2) [avatar component clause 132]
208. ~rich(X0) | ~quiet(X0) [subsumption resolution 112,105]
245. ~2 [avatar split clause 120,132]
270. ~quiet(lucy) [resolution 208,125]
301. generous(lucy) [resolution 270,96]
302. $false <- (~2) [subsumption resolution 301,133]
303. 2 [avatar contradiction clause 302]
304. $false [avatar sat refutation 245,303]
% SZS output end Proof for 4785418432385536381499356
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or patient and vice versa. Everyone who is either not kind or not creative is old or calm. If mary is both not brave and quiet then someone is either old or not happy. Everyone who is not brave is not kind or strong. If someone is either generous or not tall then someone is curious or not patient. Everyone who is funny or not calm is both not brave and curious and vice versa. If susan is rich then someone is old or kind. If fred is both not old and rich then someone is both not kind and wise and vice versa. If someone is not curious then someone is creative or rich and vice versa. Everyone who is not rich or not curious is tall. If susan is either wise or generous then lucy is either not funny or tall and vice versa. Everyone who is not patient or not humble is either creative or tall and vice versa. Everyone who is both humble and strong is both humble and not patient and vice versa. Everyone who is either humble or quiet is both not funny and not kind. Everyone who is tall or rich is both not patient and not happy. If someone is either not brave or calm then susan is not generous and vice versa. Alice is both not happy and funny. Someone is funny. Someone is not wise. Susan is not patient or kind. Paul is either brave or not generous. Someone is not humble or not curious. Someone is either brave or tall. | Paul is patient. | contradiction | (![X]:((wise(X)<~>~patient(X))<=>(~curious(X)<~>patient(X))))&
(![X]:((~kind(X)<~>~creative(X))=>(old(X)|calm(X))))&
(((~brave(mary)&quiet(mary)))=>(?[X]:((old(X)<~>~happy(X)))))&
(![X]:(~brave(X)=>(~kind(X)|strong(X))))&
((?[X]:((generous(X)<~>~tall(X))))=>(?[X]:((curious(X)|~patient(X)))))&
(![X]:((funny(X)|~calm(X))<=>(~brave(X)&curious(X))))&
((rich(susan))=>(?[X]:((old(X)|kind(X)))))&
(((~old(fred)&rich(fred)))<=>(?[X]:((~kind(X)&wise(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:((creative(X)|rich(X)))))&
(![X]:((~rich(X)|~curious(X))=>tall(X)))&
(((wise(susan)<~>generous(susan)))<=>((~funny(lucy)<~>tall(lucy))))&
(![X]:((~patient(X)|~humble(X))<=>(creative(X)<~>tall(X))))&
(![X]:((humble(X)&strong(X))<=>(humble(X)&~patient(X))))&
(![X]:((humble(X)<~>quiet(X))=>(~funny(X)&~kind(X))))&
(![X]:((tall(X)|rich(X))=>(~patient(X)&~happy(X))))&
((?[X]:((~brave(X)<~>calm(X))))<=>(~generous(susan)))&
((~happy(alice)&funny(alice)))&
(?[X]:(funny(X)))&
(?[X]:(~wise(X)))&
((~patient(susan)|kind(susan)))&
((brave(paul)<~>~generous(paul)))&
(?[X]:((~humble(X)|~curious(X))))&
(?[X]:((brave(X)<~>tall(X)))) | patient(paul) | [
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 27905853428383758793835
% SZS output start Proof for 27905853428383758793835
10. ! [X0] : ((~curious(X0) | ~rich(X0)) => tall(X0)) [input p9]
15. ! [X0] : ((rich(X0) | tall(X0)) => (~happy(X0) & ~patient(X0))) [input p14]
24. patient(paul) [input hypothesis]
35. ! [X0] : (tall(X0) | (curious(X0) & rich(X0))) [ennf transformation 10]
37. ! [X0] : ((~happy(X0) & ~patient(X0)) | (~rich(X0) & ~tall(X0))) [ennf transformation 15]
109. rich(X0) | tall(X0) [cnf transformation 35]
133. ~tall(X0) | ~patient(X0) [cnf transformation 37]
134. ~rich(X0) | ~patient(X0) [cnf transformation 37]
151. patient(paul) [cnf transformation 24]
352. ~patient(X0) | tall(X0) [resolution 134,109]
362. ~patient(X0) [subsumption resolution 352,133]
369. $false [resolution 362,151]
% SZS output end Proof for 27905853428383758793835
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is not strong or strong then lucy is both not brave and not tall and vice versa.
Everyone who is not patient or brave is quiet and vice versa.
Everyone who is both humble and rich is both not generous and not calm and vice versa.
Everyone who is either brave or not calm is brave.
Everyone who is either not humble or not calm is both wise and humble.
Everyone who is either not humble or not old is kind or calm and vice versa.
Everyone who is not rich or not happy is quiet and vice versa.
If someone is either not old or not brave then someone is both rich and not curious.
If alice is creative then someone is either not funny or not happy.
Everyone who is not rich or not calm is either not creative or wise and vice versa.
If someone is happy then someone is not creative and vice versa.
If someone is either not funny or creative then fred is not quiet or not patient and vice versa.
If someone is old then someone is both not calm and not quiet.
If alice is wise then john is not patient.
Everyone who is not calm or not rich is happy and vice versa.
Everyone who is quiet is not funny.
Alice is tall or not creative.
Alice is not creative or not strong.
Someone is both not strong and tall.
Mary is either not patient or tall.
Paul is not creative or not wise.
John is not wise.
Someone is kind or not generous.
Someone is curious or not wise. | Paul is wise. | contradiction | (((~strong(mary)|strong(mary)))<=>((~brave(lucy)&~tall(lucy))))&
(![X]:((~patient(X)|brave(X))<=>quiet(X)))&
(![X]:((humble(X)&rich(X))<=>(~generous(X)&~calm(X))))&
(![X]:((brave(X)<~>~calm(X))=>brave(X)))&
(![X]:((~humble(X)<~>~calm(X))=>(wise(X)&humble(X))))&
(![X]:((~humble(X)<~>~old(X))<=>(kind(X)|calm(X))))&
(![X]:((~rich(X)|~happy(X))<=>quiet(X)))&
((?[X]:((~old(X)<~>~brave(X))))=>(?[X]:((rich(X)&~curious(X)))))&
((creative(alice))=>(?[X]:((~funny(X)<~>~happy(X)))))&
(![X]:((~rich(X)|~calm(X))<=>(~creative(X)<~>wise(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~creative(X))))&
((?[X]:((~funny(X)<~>creative(X))))<=>((~quiet(fred)|~patient(fred))))&
((?[X]:(old(X)))=>(?[X]:((~calm(X)&~quiet(X)))))&
((wise(alice))=>(~patient(john)))&
(![X]:((~calm(X)|~rich(X))<=>happy(X)))&
(![X]:(quiet(X)=>~funny(X)))&
((tall(alice)|~creative(alice)))&
((~creative(alice)|~strong(alice)))&
(?[X]:((~strong(X)&tall(X))))&
((~patient(mary)<~>tall(mary)))&
((~creative(paul)|~wise(paul)))&
(~wise(john))&
(?[X]:((kind(X)|~generous(X))))&
(?[X]:((curious(X)|~wise(X)))) | wise(paul) | [
"p2",
"p4",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 170571587949292320715775
% SZS output start Proof for 170571587949292320715775
3. ! [X0] : ((rich(X0) & humble(X0)) <=> (~calm(X0) & ~generous(X0))) [input p2]
5. ! [X0] : ((~humble(X0) <~> ~calm(X0)) => (humble(X0) & wise(X0))) [input p4]
10. ! [X0] : ((~calm(X0) | ~rich(X0)) <=> (~creative(X0) <~> wise(X0))) [input p9]
21. ~wise(paul) | ~creative(paul) [input p20]
25. wise(paul) [input hypothesis]
30. ! [X0] : ((humble(X0) & wise(X0)) | (~humble(X0) <=> ~calm(X0))) [ennf transformation 5]
40. ! [X0] : (((rich(X0) & humble(X0)) | (calm(X0) | generous(X0))) & ((~calm(X0) & ~generous(X0)) | (~rich(X0) | ~humble(X0)))) [nnf transformation 3]
41. ! [X0] : (((rich(X0) & humble(X0)) | calm(X0) | generous(X0)) & ((~calm(X0) & ~generous(X0)) | ~rich(X0) | ~humble(X0))) [flattening 40]
43. ! [X0] : ((humble(X0) & wise(X0)) | ((~humble(X0) | calm(X0)) & (~calm(X0) | humble(X0)))) [nnf transformation 30]
55. ! [X0] : (((~calm(X0) | ~rich(X0)) | ((~creative(X0) | ~wise(X0)) & (wise(X0) | creative(X0)))) & (((~wise(X0) | creative(X0)) & (wise(X0) | ~creative(X0))) | (calm(X0) & rich(X0)))) [nnf transformation 10]
56. ! [X0] : ((~calm(X0) | ~rich(X0) | ((~creative(X0) | ~wise(X0)) & (wise(X0) | creative(X0)))) & (((~wise(X0) | creative(X0)) & (wise(X0) | ~creative(X0))) | (calm(X0) & rich(X0)))) [flattening 55]
88. ~calm(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 41]
95. humble(X0) | ~calm(X0) | humble(X0) [cnf transformation 43]
114. ~wise(X0) | creative(X0) | rich(X0) [cnf transformation 56]
115. ~wise(X0) | creative(X0) | calm(X0) [cnf transformation 56]
139. ~wise(paul) | ~creative(paul) [cnf transformation 21]
143. wise(paul) [cnf transformation 25]
144. ~calm(X0) | humble(X0) [duplicate literal removal 95]
283. 30 <=> creative(paul) [avatar definition]
285. ~creative(paul) <- (~30) [avatar component clause 283]
287. 31 <=> wise(paul) [avatar definition]
288. wise(paul) <- (31) [avatar component clause 287]
290. ~30 | ~31 [avatar split clause 139,287,283]
309. 31 [avatar split clause 143,287]
372. creative(paul) | rich(paul) <- (31) [resolution 114,288]
373. rich(paul) <- (~30, 31) [subsumption resolution 372,285]
375. creative(paul) | calm(paul) <- (31) [resolution 115,288]
376. calm(paul) <- (~30, 31) [subsumption resolution 375,285]
377. ~rich(paul) | ~humble(paul) <- (~30, 31) [resolution 376,88]
378. humble(paul) <- (~30, 31) [resolution 376,144]
379. ~humble(paul) <- (~30, 31) [subsumption resolution 377,373]
380. $false <- (~30, 31) [subsumption resolution 378,379]
381. 30 | ~31 [avatar contradiction clause 380]
382. $false [avatar sat refutation 290,309,381]
% SZS output end Proof for 170571587949292320715775
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is both wise and not humble and vice versa. If someone is both tall and brave then mary is either humble or patient and vice versa. Everyone who is either not quiet or not patient is either curious or not calm. Everyone who is both not creative and wise is either generous or rich. If someone is quiet then someone is not curious. Everyone who is wise is tall. If paul is not kind or not brave then lucy is either funny or strong. Everyone who is both not funny and patient is not calm or calm and vice versa. If lucy is both creative and rich then fred is either not kind or old and vice versa. If someone is quiet or kind then susan is kind or funny. If someone is both not brave and kind then someone is both brave and kind and vice versa. Everyone who is quiet or humble is not tall or rich. If someone is not kind then someone is not humble or not tall and vice versa. If someone is curious or not strong then fred is either calm or tall and vice versa. Everyone who is either not brave or not patient is brave. Someone is both not happy and not old. John is generous or not funny. Someone is tall. Paul is not creative or humble. Someone is patient or calm. Someone is wise. | Lucy is quiet. | contradiction | (![X]:(~creative(X)<=>(wise(X)&~humble(X))))&
((?[X]:((tall(X)&brave(X))))<=>((humble(mary)<~>patient(mary))))&
(![X]:((~quiet(X)<~>~patient(X))=>(curious(X)<~>~calm(X))))&
(![X]:((~creative(X)&wise(X))=>(generous(X)<~>rich(X))))&
((?[X]:(quiet(X)))=>(?[X]:(~curious(X))))&
(![X]:(wise(X)=>tall(X)))&
(((~kind(paul)|~brave(paul)))=>((funny(lucy)<~>strong(lucy))))&
(![X]:((~funny(X)&patient(X))<=>(~calm(X)|calm(X))))&
(((creative(lucy)&rich(lucy)))<=>((~kind(fred)<~>old(fred))))&
((?[X]:((quiet(X)|kind(X))))=>((kind(susan)|funny(susan))))&
((?[X]:((~brave(X)&kind(X))))<=>(?[X]:((brave(X)&kind(X)))))&
(![X]:((quiet(X)|humble(X))=>(~tall(X)|rich(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((~humble(X)|~tall(X)))))&
((?[X]:((curious(X)|~strong(X))))<=>((calm(fred)<~>tall(fred))))&
(![X]:((~brave(X)<~>~patient(X))=>brave(X)))&
(?[X]:((~happy(X)&~old(X))))&
((generous(john)|~funny(john)))&
(?[X]:(tall(X)))&
((~creative(paul)|humble(paul)))&
(?[X]:((patient(X)|calm(X))))&
(?[X]:(wise(X))) | quiet(lucy) | [
"p7",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 415657445443983510198642
% SZS output start Proof for 415657445443983510198642
8. ! [X0] : ((patient(X0) & ~funny(X0)) <=> (calm(X0) | ~calm(X0))) [input p7]
10. ? [X0] : (kind(X0) | quiet(X0)) => (funny(susan) | kind(susan)) [input p9]
11. ? [X0] : (kind(X0) & ~brave(X0)) <=> ? [X0] : (kind(X0) & brave(X0)) [input p10]
15. ! [X0] : ((~brave(X0) <~> ~patient(X0)) => brave(X0)) [input p14]
22. quiet(lucy) [input hypothesis]
24. ? [X0] : (kind(X0) & ~brave(X0)) <=> ? [X1] : (kind(X1) & brave(X1)) [rectify 11]
33. (funny(susan) | kind(susan)) | ! [X0] : (~kind(X0) & ~quiet(X0)) [ennf transformation 10]
34. funny(susan) | kind(susan) | ! [X0] : (~kind(X0) & ~quiet(X0)) [flattening 33]
37. ! [X0] : (brave(X0) | (~brave(X0) <=> ~patient(X0))) [ennf transformation 15]
50. ! [X0] : (((patient(X0) & ~funny(X0)) | (~calm(X0) & calm(X0))) & ((calm(X0) | ~calm(X0)) | (~patient(X0) | funny(X0)))) [nnf transformation 8]
51. ! [X0] : (((patient(X0) & ~funny(X0)) | (~calm(X0) & calm(X0))) & (calm(X0) | ~calm(X0) | ~patient(X0) | funny(X0))) [flattening 50]
54. (? [X0] : (kind(X0) & ~brave(X0)) | ! [X1] : (~kind(X1) | ~brave(X1))) & (? [X1] : (kind(X1) & brave(X1)) | ! [X0] : (~kind(X0) | brave(X0))) [nnf transformation 24]
55. (? [X0] : (kind(X0) & ~brave(X0)) | ! [X1] : (~kind(X1) | ~brave(X1))) & (? [X2] : (kind(X2) & brave(X2)) | ! [X3] : (~kind(X3) | brave(X3))) [rectify 54]
56. ? [X0] : (kind(X0) & ~brave(X0)) => (kind(sK2) & ~brave(sK2)) [choice axiom]
57. ? [X2] : (kind(X2) & brave(X2)) => (kind(sK3) & brave(sK3)) [choice axiom]
58. ((kind(sK2) & ~brave(sK2)) | ! [X1] : (~kind(X1) | ~brave(X1))) & ((kind(sK3) & brave(sK3)) | ! [X3] : (~kind(X3) | brave(X3))) [skolemisation 55,57,56]
68. ! [X0] : (brave(X0) | ((~brave(X0) | patient(X0)) & (~patient(X0) | brave(X0)))) [nnf transformation 37]
99. ~funny(X0) | calm(X0) [cnf transformation 51]
100. ~funny(X0) | ~calm(X0) [cnf transformation 51]
101. patient(X0) | calm(X0) [cnf transformation 51]
102. patient(X0) | ~calm(X0) [cnf transformation 51]
109. funny(susan) | kind(susan) | ~quiet(X0) [cnf transformation 34]
113. ~brave(sK2) | ~kind(X1) | ~brave(X1) [cnf transformation 58]
126. brave(X0) | ~patient(X0) | brave(X0) [cnf transformation 68]
134. quiet(lucy) [cnf transformation 22]
135. brave(X0) | ~patient(X0) [duplicate literal removal 126]
164. 6 <=> ! [X1] : ~quiet(X1) [avatar definition]
165. ~quiet(X1) <- (6) [avatar component clause 164]
191. patient(X0) [subsumption resolution 101,102]
192. ~funny(X0) [subsumption resolution 99,100]
217. 16 <=> ! [X0] : ~kind(X0) [avatar definition]
218. ~kind(X0) <- (16) [avatar component clause 217]
220. 17 <=> kind(susan) [avatar definition]
222. kind(susan) <- (17) [avatar component clause 220]
224. kind(susan) | ~quiet(X0) [subsumption resolution 109,192]
225. 6 | 17 [avatar split clause 224,220,164]
227. 18 <=> ! [X1] : (~kind(X1) | ~brave(X1)) [avatar definition]
228. ~kind(X1) | ~brave(X1) <- (18) [avatar component clause 227]
235. 20 <=> brave(sK2) [avatar definition]
237. ~brave(sK2) <- (~20) [avatar component clause 235]
238. 18 | ~20 [avatar split clause 113,235,227]
304. brave(X0) [subsumption resolution 135,191]
314. ~kind(X1) <- (18) [subsumption resolution 228,304]
315. 16 | ~18 [avatar split clause 314,227,217]
320. $false <- (6) [resolution 165,134]
321. ~6 [avatar contradiction clause 320]
322. $false <- (16, 17) [subsumption resolution 222,218]
323. ~16 | ~17 [avatar contradiction clause 322]
324. $false <- (~20) [subsumption resolution 237,304]
325. 20 [avatar contradiction clause 324]
326. $false [avatar sat refutation 225,238,315,321,323,325]
% SZS output end Proof for 415657445443983510198642
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not wise then someone is not calm or not humble.
If someone is either not creative or not happy then someone is either not tall or not calm and vice versa.
If someone is not strong or strong then someone is both happy and not tall and vice versa.
If someone is generous or not humble then john is both not creative and not quiet and vice versa.
If alice is either not old or not humble then lucy is funny or not quiet and vice versa.
Everyone who is both not patient and rich is curious or quiet and vice versa.
If someone is both not generous and not quiet then someone is tall or patient.
If someone is either old or not patient then alice is either rich or brave and vice versa.
Everyone who is both not kind and not calm is either funny or not wise.
Everyone who is strong or not creative is not creative.
If susan is either happy or not calm then someone is tall and vice versa.
If someone is either happy or creative then fred is either creative or not calm.
Everyone who is either not strong or not patient is either not tall or kind.
Everyone who is patient is both not patient and creative and vice versa.
Everyone who is creative is creative or not curious and vice versa.
If susan is funny or humble then susan is not humble and vice versa.
Susan is both not humble and not old.
Paul is not calm or not quiet.
Someone is both tall and calm.
John is not calm.
Mary is either funny or not kind.
Someone is not old. | Susan is tall. | neutral | ((~wise(paul))=>(?[X]:((~calm(X)|~humble(X)))))&
((?[X]:((~creative(X)<~>~happy(X))))<=>(?[X]:((~tall(X)<~>~calm(X)))))&
((?[X]:((~strong(X)|strong(X))))<=>(?[X]:((happy(X)&~tall(X)))))&
((?[X]:((generous(X)|~humble(X))))<=>((~creative(john)&~quiet(john))))&
(((~old(alice)<~>~humble(alice)))<=>((funny(lucy)|~quiet(lucy))))&
(![X]:((~patient(X)&rich(X))<=>(curious(X)|quiet(X))))&
((?[X]:((~generous(X)&~quiet(X))))=>(?[X]:((tall(X)|patient(X)))))&
((?[X]:((old(X)<~>~patient(X))))<=>((rich(alice)<~>brave(alice))))&
(![X]:((~kind(X)&~calm(X))=>(funny(X)<~>~wise(X))))&
(![X]:((strong(X)|~creative(X))=>~creative(X)))&
(((happy(susan)<~>~calm(susan)))<=>(?[X]:(tall(X))))&
((?[X]:((happy(X)<~>creative(X))))=>((creative(fred)<~>~calm(fred))))&
(![X]:((~strong(X)<~>~patient(X))=>(~tall(X)<~>kind(X))))&
(![X]:(patient(X)<=>(~patient(X)&creative(X))))&
(![X]:(creative(X)<=>(creative(X)|~curious(X))))&
(((funny(susan)|humble(susan)))<=>(~humble(susan)))&
((~humble(susan)&~old(susan)))&
((~calm(paul)|~quiet(paul)))&
(?[X]:((tall(X)&calm(X))))&
(~calm(john))&
((funny(mary)<~>~kind(mary)))&
(?[X]:(~old(X))) | tall(susan) | [] | null | 0 |
Everyone who is not old is not calm and vice versa.
If someone is not curious then someone is not brave or not happy and vice versa.
Everyone who is not strong or kind is either old or not generous.
Everyone who is wise is either not rich or old and vice versa.
Everyone who is either brave or patient is either not kind or not patient and vice versa.
Everyone who is wise or not brave is not strong or funny and vice versa.
If fred is not old then paul is both kind and rich and vice versa.
Everyone who is calm or not happy is happy or generous.
Everyone who is quiet or not curious is not happy and vice versa.
Everyone who is either not patient or happy is either tall or strong and vice versa.
If someone is not funny or not patient then someone is not creative.
Everyone who is tall or not rich is both not funny and funny and vice versa.
If lucy is not creative then fred is not old and vice versa.
If susan is both not patient and patient then someone is either not wise or generous and vice versa.
If lucy is not quiet then someone is quiet.
If fred is either not rich or old then someone is both not happy and rich and vice versa.
Someone is not kind.
Paul is either kind or not humble.
Someone is either funny or wise.
Someone is either not quiet or brave.
Paul is either not wise or funny.
Paul is not tall.
Susan is curious or not happy.
Someone is not generous or not humble. | Fred is old. | entailment | (![X]:(~old(X)<=>~calm(X)))&
((?[X]:(~curious(X)))<=>(?[X]:((~brave(X)|~happy(X)))))&
(![X]:((~strong(X)|kind(X))=>(old(X)<~>~generous(X))))&
(![X]:(wise(X)<=>(~rich(X)<~>old(X))))&
(![X]:((brave(X)<~>patient(X))<=>(~kind(X)<~>~patient(X))))&
(![X]:((wise(X)|~brave(X))<=>(~strong(X)|funny(X))))&
((~old(fred))<=>((kind(paul)&rich(paul))))&
(![X]:((calm(X)|~happy(X))=>(happy(X)|generous(X))))&
(![X]:((quiet(X)|~curious(X))<=>~happy(X)))&
(![X]:((~patient(X)<~>happy(X))<=>(tall(X)<~>strong(X))))&
((?[X]:((~funny(X)|~patient(X))))=>(?[X]:(~creative(X))))&
(![X]:((tall(X)|~rich(X))<=>(~funny(X)&funny(X))))&
((~creative(lucy))<=>(~old(fred)))&
(((~patient(susan)&patient(susan)))<=>(?[X]:((~wise(X)<~>generous(X)))))&
((~quiet(lucy))=>(?[X]:(quiet(X))))&
(((~rich(fred)<~>old(fred)))<=>(?[X]:((~happy(X)&rich(X)))))&
(?[X]:(~kind(X)))&
((kind(paul)<~>~humble(paul)))&
(?[X]:((funny(X)<~>wise(X))))&
(?[X]:((~quiet(X)<~>brave(X))))&
((~wise(paul)<~>funny(paul)))&
(~tall(paul))&
((curious(susan)|~happy(susan)))&
(?[X]:((~generous(X)|~humble(X)))) | old(fred) | [
"p8",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1687900559141382274177513
% SZS output start Proof for 1687900559141382274177513
9. ! [X0] : ((~curious(X0) | quiet(X0)) <=> ~happy(X0)) [input p8]
12. ! [X0] : ((~rich(X0) | tall(X0)) <=> (funny(X0) & ~funny(X0))) [input p11]
15. ~quiet(lucy) => ? [X0] : quiet(X0) [input p14]
16. (~rich(fred) <~> old(fred)) <=> ? [X0] : (rich(X0) & ~happy(X0)) [input p15]
25. ~old(fred) [input hypothesis]
32. ? [X0] : quiet(X0) | quiet(lucy) [ennf transformation 15]
46. ! [X0] : (((~curious(X0) | quiet(X0)) | happy(X0)) & (~happy(X0) | (curious(X0) & ~quiet(X0)))) [nnf transformation 9]
47. ! [X0] : ((~curious(X0) | quiet(X0) | happy(X0)) & (~happy(X0) | (curious(X0) & ~quiet(X0)))) [flattening 46]
52. ! [X0] : (((~rich(X0) | tall(X0)) | (~funny(X0) | funny(X0))) & ((funny(X0) & ~funny(X0)) | (rich(X0) & ~tall(X0)))) [nnf transformation 12]
53. ! [X0] : ((~rich(X0) | tall(X0) | ~funny(X0) | funny(X0)) & ((funny(X0) & ~funny(X0)) | (rich(X0) & ~tall(X0)))) [flattening 52]
60. ? [X0] : quiet(X0) => quiet(sK4) [choice axiom]
61. quiet(sK4) | quiet(lucy) [skolemisation 32,60]
62. (((~old(fred) | rich(fred)) & (old(fred) | ~rich(fred))) | ! [X0] : (~rich(X0) | happy(X0))) & (? [X0] : (rich(X0) & ~happy(X0)) | ((~rich(fred) | ~old(fred)) & (old(fred) | rich(fred)))) [nnf transformation 16]
63. (((~old(fred) | rich(fred)) & (old(fred) | ~rich(fred))) | ! [X0] : (~rich(X0) | happy(X0))) & (? [X1] : (rich(X1) & ~happy(X1)) | ((~rich(fred) | ~old(fred)) & (old(fred) | rich(fred)))) [rectify 62]
64. ? [X1] : (rich(X1) & ~happy(X1)) => (rich(sK5) & ~happy(sK5)) [choice axiom]
65. (((~old(fred) | rich(fred)) & (old(fred) | ~rich(fred))) | ! [X0] : (~rich(X0) | happy(X0))) & ((rich(sK5) & ~happy(sK5)) | ((~rich(fred) | ~old(fred)) & (old(fred) | rich(fred)))) [skolemisation 63,64]
108. ~quiet(X0) | ~happy(X0) [cnf transformation 47]
122. ~funny(X0) | rich(X0) [cnf transformation 53]
124. funny(X0) | rich(X0) [cnf transformation 53]
134. quiet(sK4) | quiet(lucy) [cnf transformation 61]
139. old(fred) | ~rich(fred) | ~rich(X0) | happy(X0) [cnf transformation 65]
153. ~old(fred) [cnf transformation 25]
160. 1 <=> ! [X1] : happy(X1) [avatar definition]
161. happy(X1) <- (1) [avatar component clause 160]
194. 9 <=> old(fred) [avatar definition]
212. rich(X0) [subsumption resolution 122,124]
235. 17 <=> quiet(lucy) [avatar definition]
237. quiet(lucy) <- (17) [avatar component clause 235]
239. 18 <=> quiet(sK4) [avatar definition]
241. quiet(sK4) <- (18) [avatar component clause 239]
242. 17 | 18 [avatar split clause 134,239,235]
243. old(fred) | ~rich(X0) | happy(X0) [subsumption resolution 139,212]
244. old(fred) | happy(X0) [subsumption resolution 243,212]
245. 1 | 9 [avatar split clause 244,194,160]
297. ~9 [avatar split clause 153,194]
298. ~happy(lucy) <- (17) [resolution 108,237]
299. $false <- (1, 17) [subsumption resolution 298,161]
300. ~1 | ~17 [avatar contradiction clause 299]
301. ~happy(sK4) <- (18) [resolution 241,108]
302. $false <- (1, 18) [subsumption resolution 301,161]
303. ~1 | ~18 [avatar contradiction clause 302]
304. $false [avatar sat refutation 242,245,297,300,303]
% SZS output end Proof for 1687900559141382274177513
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not kind or creative then someone is both not wise and not funny. Everyone who is both rich and not rich is funny and vice versa. Everyone who is not rich is brave or not rich and vice versa. If someone is tall then someone is rich or not creative. If alice is both funny and kind then mary is calm or brave and vice versa. If alice is tall or humble then susan is not quiet or strong and vice versa. Everyone who is not rich or not generous is either not funny or not strong and vice versa. If susan is not humble then someone is not brave. If susan is not tall or not humble then someone is not funny. If someone is not tall or humble then someone is either funny or creative and vice versa. If fred is brave then john is not wise or not rich. If lucy is calm then someone is not old. Everyone who is creative or humble is quiet or strong. If someone is not calm then fred is either not quiet or brave and vice versa. Everyone who is curious or calm is not creative. If someone is curious then someone is not happy. Someone is both calm and not generous. Lucy is not tall. Someone is not tall or old. Someone is either not brave or rich. Someone is either not tall or not quiet. Susan is not wise. Someone is either rich or not quiet. Someone is patient. | Fred is not funny. | entailment | ((?[X]:((~kind(X)|creative(X))))=>(?[X]:((~wise(X)&~funny(X)))))&
(![X]:((rich(X)&~rich(X))<=>funny(X)))&
(![X]:(~rich(X)<=>(brave(X)|~rich(X))))&
((?[X]:(tall(X)))=>(?[X]:((rich(X)|~creative(X)))))&
(((funny(alice)&kind(alice)))<=>((calm(mary)|brave(mary))))&
(((tall(alice)|humble(alice)))<=>((~quiet(susan)|strong(susan))))&
(![X]:((~rich(X)|~generous(X))<=>(~funny(X)<~>~strong(X))))&
((~humble(susan))=>(?[X]:(~brave(X))))&
(((~tall(susan)|~humble(susan)))=>(?[X]:(~funny(X))))&
((?[X]:((~tall(X)|humble(X))))<=>(?[X]:((funny(X)<~>creative(X)))))&
((brave(fred))=>((~wise(john)|~rich(john))))&
((calm(lucy))=>(?[X]:(~old(X))))&
(![X]:((creative(X)|humble(X))=>(quiet(X)|strong(X))))&
((?[X]:(~calm(X)))<=>((~quiet(fred)<~>brave(fred))))&
(![X]:((curious(X)|calm(X))=>~creative(X)))&
((?[X]:(curious(X)))=>(?[X]:(~happy(X))))&
(?[X]:((calm(X)&~generous(X))))&
(~tall(lucy))&
(?[X]:((~tall(X)|old(X))))&
(?[X]:((~brave(X)<~>rich(X))))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(~wise(susan))&
(?[X]:((rich(X)<~>~quiet(X))))&
(?[X]:(patient(X))) | ~funny(fred) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 1201839801764126465736833
% SZS output start Proof for 1201839801764126465736833
2. ! [X0] : ((~rich(X0) & rich(X0)) <=> funny(X0)) [input p1]
25. funny(fred) [input hypothesis]
47. ! [X0] : (((~rich(X0) & rich(X0)) | ~funny(X0)) & (funny(X0) | (rich(X0) | ~rich(X0)))) [nnf transformation 2]
48. ! [X0] : (((~rich(X0) & rich(X0)) | ~funny(X0)) & (funny(X0) | rich(X0) | ~rich(X0))) [flattening 47]
91. rich(X0) | ~funny(X0) [cnf transformation 48]
92. ~rich(X0) | ~funny(X0) [cnf transformation 48]
139. funny(fred) [cnf transformation 25]
152. ~funny(X0) [subsumption resolution 91,92]
298. $false [subsumption resolution 139,152]
% SZS output end Proof for 1201839801764126465736833
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not calm or happy then paul is not curious or not quiet and vice versa. Everyone who is either not calm or not kind is not curious or rich and vice versa. Everyone who is not wise or not tall is both not old and not tall. If someone is not old or not quiet then john is generous or not creative and vice versa. If someone is not kind or not patient then someone is not humble and vice versa. Everyone who is kind is both patient and not wise. Everyone who is either kind or calm is curious or wise and vice versa. If lucy is rich then someone is either tall or not happy. If lucy is both not brave and kind then john is both tall and old and vice versa. Everyone who is strong or not generous is not happy or not calm and vice versa. If lucy is curious then mary is both not old and not funny and vice versa. Everyone who is either not funny or old is either not tall or not humble and vice versa. Everyone who is wise is not strong or not happy and vice versa. Everyone who is not strong is both not creative and patient and vice versa. Everyone who is either not calm or kind is quiet or rich and vice versa. If paul is not happy or not funny then susan is both happy and rich. Someone is both not rich and not kind. Someone is not generous. Lucy is creative. Fred is funny or not generous. Mary is either not creative or humble. Someone is not generous or not happy. | Mary is not kind. | entailment | ((?[X]:((~calm(X)<~>happy(X))))<=>((~curious(paul)|~quiet(paul))))&
(![X]:((~calm(X)<~>~kind(X))<=>(~curious(X)|rich(X))))&
(![X]:((~wise(X)|~tall(X))=>(~old(X)&~tall(X))))&
((?[X]:((~old(X)|~quiet(X))))<=>((generous(john)|~creative(john))))&
((?[X]:((~kind(X)|~patient(X))))<=>(?[X]:(~humble(X))))&
(![X]:(kind(X)=>(patient(X)&~wise(X))))&
(![X]:((kind(X)<~>calm(X))<=>(curious(X)|wise(X))))&
((rich(lucy))=>(?[X]:((tall(X)<~>~happy(X)))))&
(((~brave(lucy)&kind(lucy)))<=>((tall(john)&old(john))))&
(![X]:((strong(X)|~generous(X))<=>(~happy(X)|~calm(X))))&
((curious(lucy))<=>((~old(mary)&~funny(mary))))&
(![X]:((~funny(X)<~>old(X))<=>(~tall(X)<~>~humble(X))))&
(![X]:(wise(X)<=>(~strong(X)|~happy(X))))&
(![X]:(~strong(X)<=>(~creative(X)&patient(X))))&
(![X]:((~calm(X)<~>kind(X))<=>(quiet(X)|rich(X))))&
(((~happy(paul)|~funny(paul)))=>((happy(susan)&rich(susan))))&
(?[X]:((~rich(X)&~kind(X))))&
(?[X]:(~generous(X)))&
(creative(lucy))&
((funny(fred)|~generous(fred)))&
((~creative(mary)<~>humble(mary)))&
(?[X]:((~generous(X)|~happy(X)))) | ~kind(mary) | [
"p1",
"p5",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6172787438333230360527835
% SZS output start Proof for 6172787438333230360527835
2. ! [X0] : ((~calm(X0) <~> ~kind(X0)) <=> (rich(X0) | ~curious(X0))) [input p1]
6. ! [X0] : (kind(X0) => (~wise(X0) & patient(X0))) [input p5]
7. ! [X0] : ((kind(X0) <~> calm(X0)) <=> (wise(X0) | curious(X0))) [input p6]
15. ! [X0] : ((~calm(X0) <~> kind(X0)) <=> (rich(X0) | quiet(X0))) [input p14]
23. kind(mary) [input hypothesis]
26. ! [X0] : ((~wise(X0) & patient(X0)) | ~kind(X0)) [ennf transformation 6]
34. ! [X0] : ((((kind(X0) | calm(X0)) & (~kind(X0) | ~calm(X0))) | (~rich(X0) & curious(X0))) & ((rich(X0) | ~curious(X0)) | ((~calm(X0) | kind(X0)) & (~kind(X0) | calm(X0))))) [nnf transformation 2]
35. ! [X0] : ((((kind(X0) | calm(X0)) & (~kind(X0) | ~calm(X0))) | (~rich(X0) & curious(X0))) & (rich(X0) | ~curious(X0) | ((~calm(X0) | kind(X0)) & (~kind(X0) | calm(X0))))) [flattening 34]
46. ! [X0] : ((((~calm(X0) | ~kind(X0)) & (calm(X0) | kind(X0))) | (~wise(X0) & ~curious(X0))) & ((wise(X0) | curious(X0)) | ((kind(X0) | ~calm(X0)) & (calm(X0) | ~kind(X0))))) [nnf transformation 7]
47. ! [X0] : ((((~calm(X0) | ~kind(X0)) & (calm(X0) | kind(X0))) | (~wise(X0) & ~curious(X0))) & (wise(X0) | curious(X0) | ((kind(X0) | ~calm(X0)) & (calm(X0) | ~kind(X0))))) [flattening 46]
62. ! [X0] : ((((~kind(X0) | calm(X0)) & (kind(X0) | ~calm(X0))) | (~rich(X0) & ~quiet(X0))) & ((rich(X0) | quiet(X0)) | ((~calm(X0) | ~kind(X0)) & (kind(X0) | calm(X0))))) [nnf transformation 15]
63. ! [X0] : ((((~kind(X0) | calm(X0)) & (kind(X0) | ~calm(X0))) | (~rich(X0) & ~quiet(X0))) & (rich(X0) | quiet(X0) | ((~calm(X0) | ~kind(X0)) & (kind(X0) | calm(X0))))) [flattening 62]
77. ~kind(X0) | ~curious(X0) | rich(X0) | calm(X0) [cnf transformation 35]
79. ~kind(X0) | ~calm(X0) | curious(X0) [cnf transformation 35]
81. kind(X0) | calm(X0) | curious(X0) [cnf transformation 35]
82. ~rich(X0) | calm(X0) | kind(X0) [cnf transformation 35]
95. ~wise(X0) | ~kind(X0) [cnf transformation 26]
96. wise(X0) | curious(X0) | calm(X0) | ~kind(X0) [cnf transformation 47]
97. wise(X0) | curious(X0) | kind(X0) | ~calm(X0) [cnf transformation 47]
98. calm(X0) | kind(X0) | ~curious(X0) [cnf transformation 47]
99. calm(X0) | kind(X0) | ~wise(X0) [cnf transformation 47]
100. ~calm(X0) | ~kind(X0) | ~curious(X0) [cnf transformation 47]
134. ~kind(X0) | calm(X0) | ~rich(X0) [cnf transformation 63]
147. kind(mary) [cnf transformation 23]
226. ~kind(X0) | ~calm(X0) [subsumption resolution 100,79]
227. ~wise(X0) | calm(X0) [subsumption resolution 99,95]
228. kind(X0) | calm(X0) [subsumption resolution 98,81]
229. wise(X0) | curious(X0) | kind(X0) [subsumption resolution 97,228]
230. wise(X0) | curious(X0) | ~kind(X0) [subsumption resolution 96,226]
231. wise(X0) | curious(X0) [subsumption resolution 230,229]
287. ~rich(X0) | calm(X0) [subsumption resolution 134,82]
348. ~calm(mary) [resolution 226,147]
362. curious(X0) | calm(X0) [resolution 231,227]
447. ~curious(X1) | rich(X1) | calm(X1) | calm(X1) [resolution 77,228]
448. ~curious(X1) | rich(X1) | calm(X1) [duplicate literal removal 447]
452. rich(X1) | calm(X1) [subsumption resolution 448,362]
453. calm(X1) [subsumption resolution 452,287]
461. $false [resolution 453,348]
% SZS output end Proof for 6172787438333230360527835
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not curious is not patient.
Everyone who is both not rich and not happy is both not brave and not rich.
If someone is both not funny and not creative then someone is not creative and vice versa.
If paul is not generous or not wise then susan is both not generous and not strong and vice versa.
If paul is not wise then someone is not rich or brave and vice versa.
If someone is not tall then fred is either funny or not generous and vice versa.
If someone is not old or kind then susan is both not curious and not creative and vice versa.
If someone is not patient then someone is both not brave and wise and vice versa.
Everyone who is both not funny and generous is both old and not generous and vice versa.
Everyone who is either not brave or creative is both not quiet and not old and vice versa.
If someone is not curious or funny then someone is either patient or humble and vice versa.
Everyone who is both wise and not wise is happy or humble and vice versa.
Everyone who is not quiet or quiet is both not humble and not curious and vice versa.
Everyone who is both kind and humble is either patient or brave and vice versa.
Someone is either happy or not brave.
Lucy is both rich and not generous.
Fred is either funny or not quiet.
Paul is either strong or kind.
John is either old or not patient.
Someone is not happy or not rich.
Someone is not brave or not humble. | Susan is generous. | contradiction | (![X]:((creative(X)&~curious(X))=>~patient(X)))&
(![X]:((~rich(X)&~happy(X))=>(~brave(X)&~rich(X))))&
((?[X]:((~funny(X)&~creative(X))))<=>(?[X]:(~creative(X))))&
(((~generous(paul)|~wise(paul)))<=>((~generous(susan)&~strong(susan))))&
((~wise(paul))<=>(?[X]:((~rich(X)|brave(X)))))&
((?[X]:(~tall(X)))<=>((funny(fred)<~>~generous(fred))))&
((?[X]:((~old(X)|kind(X))))<=>((~curious(susan)&~creative(susan))))&
((?[X]:(~patient(X)))<=>(?[X]:((~brave(X)&wise(X)))))&
(![X]:((~funny(X)&generous(X))<=>(old(X)&~generous(X))))&
(![X]:((~brave(X)<~>creative(X))<=>(~quiet(X)&~old(X))))&
((?[X]:((~curious(X)|funny(X))))<=>(?[X]:((patient(X)<~>humble(X)))))&
(![X]:((wise(X)&~wise(X))<=>(happy(X)|humble(X))))&
(![X]:((~quiet(X)|quiet(X))<=>(~humble(X)&~curious(X))))&
(![X]:((kind(X)&humble(X))<=>(patient(X)<~>brave(X))))&
(?[X]:((happy(X)<~>~brave(X))))&
((rich(lucy)&~generous(lucy)))&
((funny(fred)<~>~quiet(fred)))&
((strong(paul)<~>kind(paul)))&
((old(john)<~>~patient(john)))&
(?[X]:((~happy(X)|~rich(X))))&
(?[X]:((~brave(X)|~humble(X)))) | generous(susan) | [
"p3",
"p4",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 175708196655389819867690
% SZS output start Proof for 175708196655389819867690
4. (~wise(paul) | ~generous(paul)) <=> (~strong(susan) & ~generous(susan)) [input p3]
5. ~wise(paul) <=> ? [X0] : (brave(X0) | ~rich(X0)) [input p4]
11. ? [X0] : (funny(X0) | ~curious(X0)) <=> ? [X0] : (patient(X0) <~> humble(X0)) [input p10]
12. ! [X0] : ((~wise(X0) & wise(X0)) <=> (humble(X0) | happy(X0))) [input p11]
13. ! [X0] : ((quiet(X0) | ~quiet(X0)) <=> (~curious(X0) & ~humble(X0))) [input p12]
14. ! [X0] : ((humble(X0) & kind(X0)) <=> (patient(X0) <~> brave(X0))) [input p13]
22. generous(susan) [input hypothesis]
25. ? [X0] : (funny(X0) | ~curious(X0)) <=> ? [X1] : (patient(X1) <~> humble(X1)) [rectify 11]
35. ((~wise(paul) | ~generous(paul)) | (strong(susan) | generous(susan))) & ((~strong(susan) & ~generous(susan)) | (wise(paul) & generous(paul))) [nnf transformation 4]
36. (~wise(paul) | ~generous(paul) | strong(susan) | generous(susan)) & ((~strong(susan) & ~generous(susan)) | (wise(paul) & generous(paul))) [flattening 35]
37. (~wise(paul) | ! [X0] : (~brave(X0) & rich(X0))) & (? [X0] : (brave(X0) | ~rich(X0)) | wise(paul)) [nnf transformation 5]
38. (~wise(paul) | ! [X0] : (~brave(X0) & rich(X0))) & (? [X1] : (brave(X1) | ~rich(X1)) | wise(paul)) [rectify 37]
39. ? [X1] : (brave(X1) | ~rich(X1)) => (brave(sK2) | ~rich(sK2)) [choice axiom]
40. (~wise(paul) | ! [X0] : (~brave(X0) & rich(X0))) & ((brave(sK2) | ~rich(sK2)) | wise(paul)) [skolemisation 38,39]
59. (? [X0] : (funny(X0) | ~curious(X0)) | ! [X1] : ((patient(X1) | ~humble(X1)) & (humble(X1) | ~patient(X1)))) & (? [X1] : ((~humble(X1) | ~patient(X1)) & (humble(X1) | patient(X1))) | ! [X0] : (~funny(X0) & curious(X0))) [nnf transformation 25]
60. (? [X0] : (funny(X0) | ~curious(X0)) | ! [X1] : ((patient(X1) | ~humble(X1)) & (humble(X1) | ~patient(X1)))) & (? [X2] : ((~humble(X2) | ~patient(X2)) & (humble(X2) | patient(X2))) | ! [X3] : (~funny(X3) & curious(X3))) [rectify 59]
61. ? [X0] : (funny(X0) | ~curious(X0)) => (funny(sK7) | ~curious(sK7)) [choice axiom]
62. ? [X2] : ((~humble(X2) | ~patient(X2)) & (humble(X2) | patient(X2))) => ((~humble(sK8) | ~patient(sK8)) & (humble(sK8) | patient(sK8))) [choice axiom]
63. ((funny(sK7) | ~curious(sK7)) | ! [X1] : ((patient(X1) | ~humble(X1)) & (humble(X1) | ~patient(X1)))) & (((~humble(sK8) | ~patient(sK8)) & (humble(sK8) | patient(sK8))) | ! [X3] : (~funny(X3) & curious(X3))) [skolemisation 60,62,61]
64. ! [X0] : (((~wise(X0) & wise(X0)) | (~humble(X0) & ~happy(X0))) & ((humble(X0) | happy(X0)) | (wise(X0) | ~wise(X0)))) [nnf transformation 12]
65. ! [X0] : (((~wise(X0) & wise(X0)) | (~humble(X0) & ~happy(X0))) & (humble(X0) | happy(X0) | wise(X0) | ~wise(X0))) [flattening 64]
66. ! [X0] : (((quiet(X0) | ~quiet(X0)) | (curious(X0) | humble(X0))) & ((~curious(X0) & ~humble(X0)) | (~quiet(X0) & quiet(X0)))) [nnf transformation 13]
67. ! [X0] : ((quiet(X0) | ~quiet(X0) | curious(X0) | humble(X0)) & ((~curious(X0) & ~humble(X0)) | (~quiet(X0) & quiet(X0)))) [flattening 66]
68. ! [X0] : (((humble(X0) & kind(X0)) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0)))) & (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | (~humble(X0) | ~kind(X0)))) [nnf transformation 14]
69. ! [X0] : (((humble(X0) & kind(X0)) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0)))) & (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | ~humble(X0) | ~kind(X0))) [flattening 68]
87. ~generous(susan) | wise(paul) [cnf transformation 36]
93. ~wise(paul) | ~brave(X0) [cnf transformation 40]
116. humble(sK8) | patient(sK8) | curious(X3) [cnf transformation 63]
124. wise(X0) | ~humble(X0) [cnf transformation 65]
126. ~humble(X0) | ~wise(X0) [cnf transformation 65]
129. ~curious(X0) | quiet(X0) [cnf transformation 67]
130. ~quiet(X0) | ~curious(X0) [cnf transformation 67]
136. humble(X0) | brave(X0) | ~patient(X0) [cnf transformation 69]
150. generous(susan) [cnf transformation 22]
175. 6 <=> generous(susan) [avatar definition]
187. 9 <=> wise(paul) [avatar definition]
193. 9 | ~6 [avatar split clause 87,175,187]
196. 10 <=> ! [X0] : ~brave(X0) [avatar definition]
197. ~brave(X0) <- (10) [avatar component clause 196]
198. 10 | ~9 [avatar split clause 93,187,196]
299. 34 <=> patient(sK8) [avatar definition]
300. patient(sK8) <- (34) [avatar component clause 299]
303. 35 <=> humble(sK8) [avatar definition]
304. humble(sK8) <- (35) [avatar component clause 303]
308. 36 <=> ! [X3] : curious(X3) [avatar definition]
309. curious(X3) <- (36) [avatar component clause 308]
312. 36 | 34 | 35 [avatar split clause 116,303,299,308]
313. ~humble(X0) [subsumption resolution 124,126]
315. ~curious(X0) [subsumption resolution 129,130]
317. ~patient(X0) | brave(X0) [subsumption resolution 136,313]
345. 6 [avatar split clause 150,175]
357. brave(sK8) <- (34) [resolution 317,300]
358. $false <- (10, 34) [subsumption resolution 357,197]
359. ~10 | ~34 [avatar contradiction clause 358]
360. $false <- (35) [subsumption resolution 304,313]
361. ~35 [avatar contradiction clause 360]
362. $false <- (36) [subsumption resolution 309,315]
363. ~36 [avatar contradiction clause 362]
364. $false [avatar sat refutation 193,198,312,345,359,361,363]
% SZS output end Proof for 175708196655389819867690
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not old is strong and vice versa.
Everyone who is not quiet or generous is either kind or curious and vice versa.
If someone is curious then mary is both not humble and not wise.
Everyone who is either strong or not curious is both not humble and wise and vice versa.
Everyone who is both curious and patient is strong or happy and vice versa.
If susan is either not quiet or not funny then someone is both kind and quiet.
If john is not rich then fred is not old.
Everyone who is not curious is both not quiet and wise and vice versa.
If mary is both not funny and not happy then paul is not curious or brave.
Everyone who is not happy or tall is either not generous or not funny and vice versa.
If susan is not curious then mary is both not quiet and not creative and vice versa.
Everyone who is humble is both quiet and generous and vice versa.
Everyone who is both not wise and not quiet is either brave or patient and vice versa.
Everyone who is wise is not humble or wise and vice versa.
Everyone who is both not old and tall is both happy and generous and vice versa.
Someone is funny.
Someone is either not patient or not calm.
Susan is both creative and rich.
Someone is either not tall or not happy.
Susan is tall.
Someone is both creative and not calm. | Susan is wise. | entailment | (![X]:((strong(X)<~>~old(X))<=>strong(X)))&
(![X]:((~quiet(X)|generous(X))<=>(kind(X)<~>curious(X))))&
((?[X]:(curious(X)))=>((~humble(mary)&~wise(mary))))&
(![X]:((strong(X)<~>~curious(X))<=>(~humble(X)&wise(X))))&
(![X]:((curious(X)&patient(X))<=>(strong(X)|happy(X))))&
(((~quiet(susan)<~>~funny(susan)))=>(?[X]:((kind(X)&quiet(X)))))&
((~rich(john))=>(~old(fred)))&
(![X]:(~curious(X)<=>(~quiet(X)&wise(X))))&
(((~funny(mary)&~happy(mary)))=>((~curious(paul)|brave(paul))))&
(![X]:((~happy(X)|tall(X))<=>(~generous(X)<~>~funny(X))))&
((~curious(susan))<=>((~quiet(mary)&~creative(mary))))&
(![X]:(humble(X)<=>(quiet(X)&generous(X))))&
(![X]:((~wise(X)&~quiet(X))<=>(brave(X)<~>patient(X))))&
(![X]:(wise(X)<=>(~humble(X)|wise(X))))&
(![X]:((~old(X)&tall(X))<=>(happy(X)&generous(X))))&
(?[X]:(funny(X)))&
(?[X]:((~patient(X)<~>~calm(X))))&
((creative(susan)&rich(susan)))&
(?[X]:((~tall(X)<~>~happy(X))))&
(tall(susan))&
(?[X]:((creative(X)&~calm(X)))) | wise(susan) | [
"p2",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8786604109904391649948470
% SZS output start Proof for 8786604109904391649948470
3. ? [X0] : curious(X0) => (~wise(mary) & ~humble(mary)) [input p2]
8. ! [X0] : (~curious(X0) <=> (wise(X0) & ~quiet(X0))) [input p7]
14. ! [X0] : (wise(X0) <=> (wise(X0) | ~humble(X0))) [input p13]
22. ~wise(susan) [input hypothesis]
25. (~wise(mary) & ~humble(mary)) | ! [X0] : ~curious(X0) [ennf transformation 3]
39. ! [X0] : ((~curious(X0) | (~wise(X0) | quiet(X0))) & ((wise(X0) & ~quiet(X0)) | curious(X0))) [nnf transformation 8]
40. ! [X0] : ((~curious(X0) | ~wise(X0) | quiet(X0)) & ((wise(X0) & ~quiet(X0)) | curious(X0))) [flattening 39]
49. ! [X0] : ((wise(X0) | (~wise(X0) & humble(X0))) & ((wise(X0) | ~humble(X0)) | ~wise(X0))) [nnf transformation 14]
50. ! [X0] : ((wise(X0) | (~wise(X0) & humble(X0))) & (wise(X0) | ~humble(X0) | ~wise(X0))) [flattening 49]
73. ~humble(mary) | ~curious(X0) [cnf transformation 25]
74. ~wise(mary) | ~curious(X0) [cnf transformation 25]
91. wise(X0) | curious(X0) [cnf transformation 40]
113. wise(X0) | humble(X0) [cnf transformation 50]
128. ~wise(susan) [cnf transformation 22]
133. 1 <=> ! [X0] : ~curious(X0) [avatar definition]
134. ~curious(X0) <- (1) [avatar component clause 133]
136. 2 <=> wise(mary) [avatar definition]
138. ~wise(mary) <- (~2) [avatar component clause 136]
139. 1 | ~2 [avatar split clause 74,136,133]
141. 3 <=> humble(mary) [avatar definition]
143. ~humble(mary) <- (~3) [avatar component clause 141]
144. 1 | ~3 [avatar split clause 73,141,133]
191. 14 <=> curious(susan) [avatar definition]
192. curious(susan) <- (14) [avatar component clause 191]
218. curious(susan) [resolution 91,128]
222. 14 [avatar split clause 218,191]
225. humble(mary) <- (~2) [resolution 113,138]
226. $false <- (~2, ~3) [subsumption resolution 225,143]
227. 2 | 3 [avatar contradiction clause 226]
228. $false <- (1, 14) [resolution 134,192]
229. ~1 | ~14 [avatar contradiction clause 228]
230. $false [avatar sat refutation 139,144,222,227,229]
% SZS output end Proof for 8786604109904391649948470
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is not kind or quiet and vice versa.
Everyone who is old or happy is either not patient or quiet.
Everyone who is either not wise or wise is both funny and not patient.
Everyone who is either quiet or tall is rich or quiet.
If mary is both not humble and calm then someone is not calm or patient.
If lucy is either not patient or not generous then lucy is both not kind and wise and vice versa.
Everyone who is either funny or not generous is not quiet or old and vice versa.
If lucy is calm or rich then paul is either creative or funny.
Everyone who is not generous is either not curious or not funny and vice versa.
If someone is brave then lucy is either not quiet or strong and vice versa.
Everyone who is generous is tall.
Everyone who is not humble or not generous is wise.
Everyone who is both not humble and not calm is either humble or not rich.
Everyone who is both not old and not quiet is both brave and not old.
If susan is either not generous or not kind then susan is creative or calm and vice versa.
Paul is either happy or funny.
Paul is either funny or quiet.
Fred is either kind or not patient.
Fred is either not humble or generous.
Fred is not funny or tall.
Someone is either not curious or humble. | Paul is generous. | entailment | (![X]:(~quiet(X)<=>(~kind(X)|quiet(X))))&
(![X]:((old(X)|happy(X))=>(~patient(X)<~>quiet(X))))&
(![X]:((~wise(X)<~>wise(X))=>(funny(X)&~patient(X))))&
(![X]:((quiet(X)<~>tall(X))=>(rich(X)|quiet(X))))&
(((~humble(mary)&calm(mary)))=>(?[X]:((~calm(X)|patient(X)))))&
(((~patient(lucy)<~>~generous(lucy)))<=>((~kind(lucy)&wise(lucy))))&
(![X]:((funny(X)<~>~generous(X))<=>(~quiet(X)|old(X))))&
(((calm(lucy)|rich(lucy)))=>((creative(paul)<~>funny(paul))))&
(![X]:(~generous(X)<=>(~curious(X)<~>~funny(X))))&
((?[X]:(brave(X)))<=>((~quiet(lucy)<~>strong(lucy))))&
(![X]:(generous(X)=>tall(X)))&
(![X]:((~humble(X)|~generous(X))=>wise(X)))&
(![X]:((~humble(X)&~calm(X))=>(humble(X)<~>~rich(X))))&
(![X]:((~old(X)&~quiet(X))=>(brave(X)&~old(X))))&
(((~generous(susan)<~>~kind(susan)))<=>((creative(susan)|calm(susan))))&
((happy(paul)<~>funny(paul)))&
((funny(paul)<~>quiet(paul)))&
((kind(fred)<~>~patient(fred)))&
((~humble(fred)<~>generous(fred)))&
((~funny(fred)|tall(fred)))&
(?[X]:((~curious(X)<~>humble(X)))) | generous(paul) | [
"p0",
"p2",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2087573319040469796910878
% SZS output start Proof for 2087573319040469796910878
1. ! [X0] : (~quiet(X0) <=> (quiet(X0) | ~kind(X0))) [input p0]
3. ! [X0] : ((~wise(X0) <~> wise(X0)) => (~patient(X0) & funny(X0))) [input p2]
7. ! [X0] : ((funny(X0) <~> ~generous(X0)) <=> (old(X0) | ~quiet(X0))) [input p6]
22. ~generous(paul) [input hypothesis]
24. ! [X0] : ((~patient(X0) & funny(X0)) | (~wise(X0) <=> wise(X0))) [ennf transformation 3]
36. ! [X0] : ((~quiet(X0) | (~quiet(X0) & kind(X0))) & ((quiet(X0) | ~kind(X0)) | quiet(X0))) [nnf transformation 1]
37. ! [X0] : ((~quiet(X0) | (~quiet(X0) & kind(X0))) & (quiet(X0) | ~kind(X0) | quiet(X0))) [flattening 36]
39. ! [X0] : ((~patient(X0) & funny(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) [nnf transformation 24]
45. ! [X0] : ((((generous(X0) | ~funny(X0)) & (~generous(X0) | funny(X0))) | (~old(X0) & quiet(X0))) & ((old(X0) | ~quiet(X0)) | ((funny(X0) | generous(X0)) & (~generous(X0) | ~funny(X0))))) [nnf transformation 7]
46. ! [X0] : ((((generous(X0) | ~funny(X0)) & (~generous(X0) | funny(X0))) | (~old(X0) & quiet(X0))) & (old(X0) | ~quiet(X0) | ((funny(X0) | generous(X0)) & (~generous(X0) | ~funny(X0))))) [flattening 45]
65. ~quiet(X0) | ~quiet(X0) [cnf transformation 37]
70. funny(X0) | wise(X0) | wise(X0) [cnf transformation 39]
71. funny(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 39]
87. generous(X0) | ~funny(X0) | quiet(X0) [cnf transformation 46]
125. ~generous(paul) [cnf transformation 22]
128. funny(X0) | wise(X0) [duplicate literal removal 70]
129. funny(X0) | ~wise(X0) [duplicate literal removal 71]
133. ~quiet(X0) [duplicate literal removal 65]
138. funny(X0) [subsumption resolution 128,129]
168. generous(X0) | quiet(X0) [subsumption resolution 87,138]
169. generous(X0) [subsumption resolution 168,133]
219. $false [subsumption resolution 125,169]
% SZS output end Proof for 2087573319040469796910878
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
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