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 both humble and brave is not patient or old and vice versa.
If someone is both tall and generous then someone is either humble or not funny and vice versa.
If mary is both funny and not patient then mary is both patient and not brave.
If someone is patient then alice is both not brave and kind and vice versa.
If susan is not generous then someone is either not calm or strong.
Everyone who is not kind is either not brave or not kind and vice versa.
Everyone who is either humble or kind is either not quiet or brave.
If someone is quiet or not brave then alice is both not curious and happy.
Everyone who is calm is both strong and not generous.
Everyone who is happy or quiet is either humble or quiet.
If john is not humble or not curious then mary is kind or not generous.
Everyone who is both not strong and old is calm or not kind.
Everyone who is humble or strong is both wise and not curious and vice versa.
If someone is rich or not curious then john is not funny and vice versa.
Everyone who is not tall is not wise and vice versa.
Everyone who is either humble or not generous is rich.
Fred is either brave or quiet.
Someone is not brave or tall.
Someone is not old or kind.
Someone is either curious or not creative.
Alice is both not funny and not quiet. | Alice is happy. | neutral | (![X]:((humble(X)&brave(X))<=>(~patient(X)|old(X))))&
((?[X]:((tall(X)&generous(X))))<=>(?[X]:((humble(X)<~>~funny(X)))))&
(((funny(mary)&~patient(mary)))=>((patient(mary)&~brave(mary))))&
((?[X]:(patient(X)))<=>((~brave(alice)&kind(alice))))&
((~generous(susan))=>(?[X]:((~calm(X)<~>strong(X)))))&
(![X]:(~kind(X)<=>(~brave(X)<~>~kind(X))))&
(![X]:((humble(X)<~>kind(X))=>(~quiet(X)<~>brave(X))))&
((?[X]:((quiet(X)|~brave(X))))=>((~curious(alice)&happy(alice))))&
(![X]:(calm(X)=>(strong(X)&~generous(X))))&
(![X]:((happy(X)|quiet(X))=>(humble(X)<~>quiet(X))))&
(((~humble(john)|~curious(john)))=>((kind(mary)|~generous(mary))))&
(![X]:((~strong(X)&old(X))=>(calm(X)|~kind(X))))&
(![X]:((humble(X)|strong(X))<=>(wise(X)&~curious(X))))&
((?[X]:((rich(X)|~curious(X))))<=>(~funny(john)))&
(![X]:(~tall(X)<=>~wise(X)))&
(![X]:((humble(X)<~>~generous(X))=>rich(X)))&
((brave(fred)<~>quiet(fred)))&
(?[X]:((~brave(X)|tall(X))))&
(?[X]:((~old(X)|kind(X))))&
(?[X]:((curious(X)<~>~creative(X))))&
((~funny(alice)&~quiet(alice))) | happy(alice) | [] | null | 0 |
Everyone who is not wise is both humble and not curious and vice versa.
If someone is both happy and curious then someone is either not patient or not generous.
If lucy is old then fred is either calm or not strong and vice versa.
If paul is both not generous and not tall then someone is either not tall or not strong and vice versa.
If john is either not curious or not wise then someone is both not calm and curious and vice versa.
If susan is not brave or creative then john is both curious and kind and vice versa.
Everyone who is not curious or not happy is both kind and calm.
If susan is either patient or not tall then someone is both wise and tall and vice versa.
Everyone who is both brave and not old is either generous or not quiet.
If susan is not rich then susan is both calm and not creative.
Everyone who is either rich or wise is either not brave or not generous.
If john is not humble then john is not calm and vice versa.
Everyone who is not kind or not quiet is wise or not tall.
If someone is not tall or not wise then lucy is either not strong or rich.
If john is not rich then paul is either funny or patient.
If someone is both not curious and not wise then susan is not quiet and vice versa.
Someone is either not rich or not kind.
Lucy is either not strong or not happy.
Fred is not patient or happy.
Mary is wise.
Fred is not happy or not rich.
Lucy is both not kind and not funny.
Someone is either not strong or wise.
Mary is both not brave and kind. | John is rich. | neutral | (![X]:(~wise(X)<=>(humble(X)&~curious(X))))&
((?[X]:((happy(X)&curious(X))))=>(?[X]:((~patient(X)<~>~generous(X)))))&
((old(lucy))<=>((calm(fred)<~>~strong(fred))))&
(((~generous(paul)&~tall(paul)))<=>(?[X]:((~tall(X)<~>~strong(X)))))&
(((~curious(john)<~>~wise(john)))<=>(?[X]:((~calm(X)&curious(X)))))&
(((~brave(susan)|creative(susan)))<=>((curious(john)&kind(john))))&
(![X]:((~curious(X)|~happy(X))=>(kind(X)&calm(X))))&
(((patient(susan)<~>~tall(susan)))<=>(?[X]:((wise(X)&tall(X)))))&
(![X]:((brave(X)&~old(X))=>(generous(X)<~>~quiet(X))))&
((~rich(susan))=>((calm(susan)&~creative(susan))))&
(![X]:((rich(X)<~>wise(X))=>(~brave(X)<~>~generous(X))))&
((~humble(john))<=>(~calm(john)))&
(![X]:((~kind(X)|~quiet(X))=>(wise(X)|~tall(X))))&
((?[X]:((~tall(X)|~wise(X))))=>((~strong(lucy)<~>rich(lucy))))&
((~rich(john))=>((funny(paul)<~>patient(paul))))&
((?[X]:((~curious(X)&~wise(X))))<=>(~quiet(susan)))&
(?[X]:((~rich(X)<~>~kind(X))))&
((~strong(lucy)<~>~happy(lucy)))&
((~patient(fred)|happy(fred)))&
(wise(mary))&
((~happy(fred)|~rich(fred)))&
((~kind(lucy)&~funny(lucy)))&
(?[X]:((~strong(X)<~>wise(X))))&
((~brave(mary)&kind(mary))) | rich(john) | [] | null | 0 |
Everyone who is both not happy and wise is both strong and rich and vice versa.
Everyone who is not old is kind or not generous and vice versa.
If someone is old then alice is both not brave and funny and vice versa.
Everyone who is both funny and calm is either tall or not tall and vice versa.
If someone is kind or not generous then someone is both not curious and curious and vice versa.
Everyone who is generous or calm is not patient or brave and vice versa.
Everyone who is not old or strong is both not humble and not generous and vice versa.
If mary is not kind then fred is either strong or old and vice versa.
If fred is both brave and rich then someone is either not old or not humble and vice versa.
Everyone who is not humble or tall is either calm or patient.
Everyone who is strong is wise and vice versa.
If someone is both not curious and not creative then john is both old and not strong and vice versa.
Everyone who is either curious or generous is not quiet.
Everyone who is both not brave and not funny is not funny or brave.
If someone is both strong and wise then alice is both patient and not happy and vice versa.
Someone is not strong.
Someone is either not rich or not generous.
Paul is creative.
Someone is either happy or not humble.
Paul is humble or not happy. | Alice is kind. | contradiction | (![X]:((~happy(X)&wise(X))<=>(strong(X)&rich(X))))&
(![X]:(~old(X)<=>(kind(X)|~generous(X))))&
((?[X]:(old(X)))<=>((~brave(alice)&funny(alice))))&
(![X]:((funny(X)&calm(X))<=>(tall(X)<~>~tall(X))))&
((?[X]:((kind(X)|~generous(X))))<=>(?[X]:((~curious(X)&curious(X)))))&
(![X]:((generous(X)|calm(X))<=>(~patient(X)|brave(X))))&
(![X]:((~old(X)|strong(X))<=>(~humble(X)&~generous(X))))&
((~kind(mary))<=>((strong(fred)<~>old(fred))))&
(((brave(fred)&rich(fred)))<=>(?[X]:((~old(X)<~>~humble(X)))))&
(![X]:((~humble(X)|tall(X))=>(calm(X)<~>patient(X))))&
(![X]:(strong(X)<=>wise(X)))&
((?[X]:((~curious(X)&~creative(X))))<=>((old(john)&~strong(john))))&
(![X]:((curious(X)<~>generous(X))=>~quiet(X)))&
(![X]:((~brave(X)&~funny(X))=>(~funny(X)|brave(X))))&
((?[X]:((strong(X)&wise(X))))<=>((patient(alice)&~happy(alice))))&
(?[X]:(~strong(X)))&
(?[X]:((~rich(X)<~>~generous(X))))&
(creative(paul))&
(?[X]:((happy(X)<~>~humble(X))))&
((humble(paul)|~happy(paul))) | kind(alice) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 4005101233808178866585571
% SZS output start Proof for 4005101233808178866585571
5. ? [X0] : (~generous(X0) | kind(X0)) <=> ? [X0] : (curious(X0) & ~curious(X0)) [input p4]
21. kind(alice) [input hypothesis]
22. ? [X0] : (~generous(X0) | kind(X0)) <=> ? [X1] : (curious(X1) & ~curious(X1)) [rectify 5]
38. (? [X0] : (~generous(X0) | kind(X0)) | ! [X1] : (~curious(X1) | curious(X1))) & (? [X1] : (curious(X1) & ~curious(X1)) | ! [X0] : (generous(X0) & ~kind(X0))) [nnf transformation 22]
39. (? [X0] : (~generous(X0) | kind(X0)) | ! [X1] : (~curious(X1) | curious(X1))) & (? [X2] : (curious(X2) & ~curious(X2)) | ! [X3] : (generous(X3) & ~kind(X3))) [rectify 38]
40. ? [X0] : (~generous(X0) | kind(X0)) => (~generous(sK1) | kind(sK1)) [choice axiom]
41. ? [X2] : (curious(X2) & ~curious(X2)) => (curious(sK2) & ~curious(sK2)) [choice axiom]
42. ((~generous(sK1) | kind(sK1)) | ! [X1] : (~curious(X1) | curious(X1))) & ((curious(sK2) & ~curious(sK2)) | ! [X3] : (generous(X3) & ~kind(X3))) [skolemisation 39,41,40]
89. ~curious(sK2) | ~kind(X3) [cnf transformation 42]
91. curious(sK2) | ~kind(X3) [cnf transformation 42]
135. kind(alice) [cnf transformation 21]
165. 6 <=> curious(sK2) [avatar definition]
170. 7 <=> ! [X3] : ~kind(X3) [avatar definition]
171. ~kind(X3) <- (7) [avatar component clause 170]
172. 7 | 6 [avatar split clause 91,165,170]
174. 7 | ~6 [avatar split clause 89,165,170]
300. $false <- (7) [resolution 171,135]
301. ~7 [avatar contradiction clause 300]
302. $false [avatar sat refutation 172,174,301]
% SZS output end Proof for 4005101233808178866585571
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or not brave is not patient and vice versa. Everyone who is not strong is not wise or not brave. If someone is either rich or happy then someone is either brave or not patient and vice versa. If someone is not happy then someone is both generous and not brave and vice versa. If someone is either brave or curious then someone is not tall. If mary is not brave or wise then paul is both kind and not wise. If lucy is funny or humble then someone is either strong or not brave and vice versa. Everyone who is both generous and not calm is both quiet and old. Everyone who is calm is both not calm and not funny. Everyone who is either brave or not funny is either not creative or not wise. Everyone who is curious or patient is both calm and not wise and vice versa. Everyone who is either not calm or not generous is not happy or not old. If lucy is funny or not tall then mary is old and vice versa. Everyone who is either rich or not patient is patient. If someone is both humble and rich then paul is both kind and not brave and vice versa. Everyone who is humble is not creative. John is patient or humble. Alice is both not creative and not old. Lucy is not creative. Fred is both kind and not funny. | John is not brave. | entailment | (![X]:((~rich(X)|~brave(X))<=>~patient(X)))&
(![X]:(~strong(X)=>(~wise(X)|~brave(X))))&
((?[X]:((rich(X)<~>happy(X))))<=>(?[X]:((brave(X)<~>~patient(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:((generous(X)&~brave(X)))))&
((?[X]:((brave(X)<~>curious(X))))=>(?[X]:(~tall(X))))&
(((~brave(mary)|wise(mary)))=>((kind(paul)&~wise(paul))))&
(((funny(lucy)|humble(lucy)))<=>(?[X]:((strong(X)<~>~brave(X)))))&
(![X]:((generous(X)&~calm(X))=>(quiet(X)&old(X))))&
(![X]:(calm(X)=>(~calm(X)&~funny(X))))&
(![X]:((brave(X)<~>~funny(X))=>(~creative(X)<~>~wise(X))))&
(![X]:((curious(X)|patient(X))<=>(calm(X)&~wise(X))))&
(![X]:((~calm(X)<~>~generous(X))=>(~happy(X)|~old(X))))&
(((funny(lucy)|~tall(lucy)))<=>(old(mary)))&
(![X]:((rich(X)<~>~patient(X))=>patient(X)))&
((?[X]:((humble(X)&rich(X))))<=>((kind(paul)&~brave(paul))))&
(![X]:(humble(X)=>~creative(X)))&
((patient(john)|humble(john)))&
((~creative(alice)&~old(alice)))&
(~creative(lucy))&
((kind(fred)&~funny(fred))) | ~brave(john) | [
"p0",
"p8",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 472253698320113572730238
% SZS output start Proof for 472253698320113572730238
1. ! [X0] : ((~brave(X0) | ~rich(X0)) <=> ~patient(X0)) [input p0]
9. ! [X0] : (calm(X0) => (~funny(X0) & ~calm(X0))) [input p8]
11. ! [X0] : ((patient(X0) | curious(X0)) <=> (~wise(X0) & calm(X0))) [input p10]
14. ! [X0] : ((rich(X0) <~> ~patient(X0)) => patient(X0)) [input p13]
21. brave(john) [input hypothesis]
32. ! [X0] : ((~funny(X0) & ~calm(X0)) | ~calm(X0)) [ennf transformation 9]
36. ! [X0] : (patient(X0) | (rich(X0) <=> ~patient(X0))) [ennf transformation 14]
38. ! [X0] : (((~brave(X0) | ~rich(X0)) | patient(X0)) & (~patient(X0) | (brave(X0) & rich(X0)))) [nnf transformation 1]
39. ! [X0] : ((~brave(X0) | ~rich(X0) | patient(X0)) & (~patient(X0) | (brave(X0) & rich(X0)))) [flattening 38]
60. ! [X0] : (((patient(X0) | curious(X0)) | (wise(X0) | ~calm(X0))) & ((~wise(X0) & calm(X0)) | (~patient(X0) & ~curious(X0)))) [nnf transformation 11]
61. ! [X0] : ((patient(X0) | curious(X0) | wise(X0) | ~calm(X0)) & ((~wise(X0) & calm(X0)) | (~patient(X0) & ~curious(X0)))) [flattening 60]
65. ! [X0] : (patient(X0) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0)))) [nnf transformation 36]
71. ~patient(X0) | rich(X0) [cnf transformation 39]
73. ~brave(X0) | ~rich(X0) | patient(X0) [cnf transformation 39]
99. ~calm(X0) | ~calm(X0) [cnf transformation 32]
106. calm(X0) | ~patient(X0) [cnf transformation 61]
116. patient(X0) | rich(X0) | patient(X0) [cnf transformation 65]
128. brave(john) [cnf transformation 21]
129. patient(X0) | rich(X0) [duplicate literal removal 116]
130. ~calm(X0) [duplicate literal removal 99]
146. 4 <=> ! [X1] : ~patient(X1) [avatar definition]
147. ~patient(X1) <- (4) [avatar component clause 146]
250. ~patient(X0) [subsumption resolution 106,130]
251. 4 [avatar split clause 250,146]
265. rich(X0) [subsumption resolution 129,71]
297. ~rich(john) | patient(john) [resolution 73,128]
298. patient(john) [subsumption resolution 297,265]
299. $false <- (4) [subsumption resolution 298,147]
300. ~4 [avatar contradiction clause 299]
301. $false [avatar sat refutation 251,300]
% SZS output end Proof for 472253698320113572730238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and not rich then susan is strong.
If susan is not brave then lucy is both not patient and patient.
Everyone who is either humble or rich is either humble or not creative and vice versa.
If mary is old then someone is not quiet.
If someone is either quiet or generous then john is happy.
If someone is not generous then someone is funny or kind and vice versa.
If paul is calm then susan is not brave and vice versa.
Everyone who is both calm and not brave is both not kind and creative and vice versa.
Everyone who is both not patient and calm is rich.
If someone is either not curious or happy then someone is either humble or quiet.
If mary is curious then paul is not kind and vice versa.
Everyone who is not brave is not humble and vice versa.
Everyone who is either calm or curious is either not patient or patient and vice versa.
Everyone who is either humble or not kind is both not curious and kind.
Everyone who is not humble is either calm or not kind.
Susan is brave or wise.
Someone is creative.
John is either not brave or happy.
Someone is either generous or kind.
Someone is either not wise or quiet.
Someone is wise.
Paul is either kind or quiet. | Mary is not curious. | contradiction | ((?[X]:((generous(X)&~rich(X))))=>(strong(susan)))&
((~brave(susan))=>((~patient(lucy)&patient(lucy))))&
(![X]:((humble(X)<~>rich(X))<=>(humble(X)<~>~creative(X))))&
((old(mary))=>(?[X]:(~quiet(X))))&
((?[X]:((quiet(X)<~>generous(X))))=>(happy(john)))&
((?[X]:(~generous(X)))<=>(?[X]:((funny(X)|kind(X)))))&
((calm(paul))<=>(~brave(susan)))&
(![X]:((calm(X)&~brave(X))<=>(~kind(X)&creative(X))))&
(![X]:((~patient(X)&calm(X))=>rich(X)))&
((?[X]:((~curious(X)<~>happy(X))))=>(?[X]:((humble(X)<~>quiet(X)))))&
((curious(mary))<=>(~kind(paul)))&
(![X]:(~brave(X)<=>~humble(X)))&
(![X]:((calm(X)<~>curious(X))<=>(~patient(X)<~>patient(X))))&
(![X]:((humble(X)<~>~kind(X))=>(~curious(X)&kind(X))))&
(![X]:(~humble(X)=>(calm(X)<~>~kind(X))))&
((brave(susan)|wise(susan)))&
(?[X]:(creative(X)))&
((~brave(john)<~>happy(john)))&
(?[X]:((generous(X)<~>kind(X))))&
(?[X]:((~wise(X)<~>quiet(X))))&
(?[X]:(wise(X)))&
((kind(paul)<~>quiet(paul))) | ~curious(mary) | [
"p1",
"p6",
"p7",
"p10",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9215890069812186994600640
% SZS output start Proof for 9215890069812186994600640
2. ~brave(susan) => (patient(lucy) & ~patient(lucy)) [input p1]
7. calm(paul) <=> ~brave(susan) [input p6]
8. ! [X0] : ((~brave(X0) & calm(X0)) <=> (creative(X0) & ~kind(X0))) [input p7]
11. curious(mary) <=> ~kind(paul) [input p10]
12. ! [X0] : (~brave(X0) <=> ~humble(X0)) [input p11]
13. ! [X0] : ((calm(X0) <~> curious(X0)) <=> (~patient(X0) <~> patient(X0))) [input p12]
14. ! [X0] : ((humble(X0) <~> ~kind(X0)) => (kind(X0) & ~curious(X0))) [input p13]
15. ! [X0] : (~humble(X0) => (calm(X0) <~> ~kind(X0))) [input p14]
23. ~curious(mary) [input hypothesis]
28. (patient(lucy) & ~patient(lucy)) | brave(susan) [ennf transformation 2]
33. ! [X0] : ((kind(X0) & ~curious(X0)) | (humble(X0) <=> ~kind(X0))) [ennf transformation 14]
34. ! [X0] : ((calm(X0) <~> ~kind(X0)) | humble(X0)) [ennf transformation 15]
42. (calm(paul) | brave(susan)) & (~brave(susan) | ~calm(paul)) [nnf transformation 7]
43. ! [X0] : (((~brave(X0) & calm(X0)) | (~creative(X0) | kind(X0))) & ((creative(X0) & ~kind(X0)) | (brave(X0) | ~calm(X0)))) [nnf transformation 8]
44. ! [X0] : (((~brave(X0) & calm(X0)) | ~creative(X0) | kind(X0)) & ((creative(X0) & ~kind(X0)) | brave(X0) | ~calm(X0))) [flattening 43]
49. (curious(mary) | kind(paul)) & (~kind(paul) | ~curious(mary)) [nnf transformation 11]
50. ! [X0] : ((~brave(X0) | humble(X0)) & (~humble(X0) | brave(X0))) [nnf transformation 12]
51. ! [X0] : ((((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) & (((~patient(X0) | patient(X0)) & (patient(X0) | ~patient(X0))) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0))))) [nnf transformation 13]
52. ! [X0] : ((kind(X0) & ~curious(X0)) | ((humble(X0) | kind(X0)) & (~kind(X0) | ~humble(X0)))) [nnf transformation 33]
53. ! [X0] : (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | humble(X0)) [nnf transformation 34]
66. ~patient(lucy) | brave(susan) [cnf transformation 28]
67. patient(lucy) | brave(susan) [cnf transformation 28]
81. ~brave(susan) | ~calm(paul) [cnf transformation 42]
83. ~calm(X0) | brave(X0) | ~kind(X0) [cnf transformation 44]
93. curious(mary) | kind(paul) [cnf transformation 49]
95. ~brave(X0) | humble(X0) [cnf transformation 50]
100. curious(X0) | calm(X0) | patient(X0) | patient(X0) [cnf transformation 51]
101. curious(X0) | calm(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 51]
104. ~curious(X0) | ~kind(X0) | ~humble(X0) [cnf transformation 52]
107. kind(X0) | humble(X0) | kind(X0) [cnf transformation 52]
108. ~kind(X0) | calm(X0) | humble(X0) [cnf transformation 53]
121. ~curious(mary) [cnf transformation 23]
122. kind(X0) | humble(X0) [duplicate literal removal 107]
123. curious(X0) | calm(X0) | patient(X0) [duplicate literal removal 100]
124. ~patient(X0) | calm(X0) | curious(X0) [duplicate literal removal 101]
132. 1 <=> brave(susan) [avatar definition]
136. 2 <=> patient(lucy) [avatar definition]
139. 1 | 2 [avatar split clause 67,136,132]
140. 1 | ~2 [avatar split clause 66,136,132]
180. 12 <=> calm(paul) [avatar definition]
181. ~calm(paul) <- (~12) [avatar component clause 180]
184. ~12 | ~1 [avatar split clause 81,132,180]
204. 17 <=> kind(paul) [avatar definition]
206. kind(paul) <- (17) [avatar component clause 204]
208. 18 <=> curious(mary) [avatar definition]
211. 17 | 18 [avatar split clause 93,208,204]
214. curious(X0) | calm(X0) [subsumption resolution 123,124]
215. calm(X0) | humble(X0) [subsumption resolution 108,122]
253. ~18 [avatar split clause 121,208]
270. brave(X0) | ~kind(X0) | humble(X0) [resolution 83,215]
280. ~kind(X0) | humble(X0) [subsumption resolution 270,95]
281. humble(X0) [subsumption resolution 280,122]
315. ~kind(X0) | ~humble(X0) | calm(X0) [resolution 104,214]
316. ~kind(X0) | calm(X0) [subsumption resolution 315,281]
328. calm(paul) <- (17) [resolution 316,206]
331. $false <- (~12, 17) [subsumption resolution 328,181]
332. 12 | ~17 [avatar contradiction clause 331]
334. $false [avatar sat refutation 139,140,184,211,253,332]
% SZS output end Proof for 9215890069812186994600640
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not wise is both old and strong and vice versa.
If someone is wise or not brave then paul is both not quiet and not brave and vice versa.
If mary is either creative or not funny then someone is strong or not patient.
Everyone who is both not calm and humble is kind or humble.
Everyone who is rich or not rich is strong or not wise.
Everyone who is both old and strong is either creative or patient and vice versa.
If someone is either not wise or rich then paul is quiet.
If someone is curious or patient then john is not strong and vice versa.
Everyone who is either tall or patient is either not humble or generous.
If john is both tall and patient then someone is rich or not patient and vice versa.
Everyone who is strong or not patient is either not funny or patient and vice versa.
Everyone who is wise or generous is either rich or funny.
Everyone who is either not rich or happy is both not calm and creative.
If paul is either not quiet or kind then paul is both brave and wise.
Everyone who is not brave is either not tall or strong.
If someone is both calm and wise then someone is funny or not strong.
Someone is humble or brave.
Someone is happy or not calm.
Someone is not kind or calm.
Someone is tall or happy.
Someone is either rich or not patient.
Fred is both not happy and old.
Alice is either not old or funny. | Paul is wise. | contradiction | (![X]:((creative(X)<~>~wise(X))<=>(old(X)&strong(X))))&
((?[X]:((wise(X)|~brave(X))))<=>((~quiet(paul)&~brave(paul))))&
(((creative(mary)<~>~funny(mary)))=>(?[X]:((strong(X)|~patient(X)))))&
(![X]:((~calm(X)&humble(X))=>(kind(X)|humble(X))))&
(![X]:((rich(X)|~rich(X))=>(strong(X)|~wise(X))))&
(![X]:((old(X)&strong(X))<=>(creative(X)<~>patient(X))))&
((?[X]:((~wise(X)<~>rich(X))))=>(quiet(paul)))&
((?[X]:((curious(X)|patient(X))))<=>(~strong(john)))&
(![X]:((tall(X)<~>patient(X))=>(~humble(X)<~>generous(X))))&
(((tall(john)&patient(john)))<=>(?[X]:((rich(X)|~patient(X)))))&
(![X]:((strong(X)|~patient(X))<=>(~funny(X)<~>patient(X))))&
(![X]:((wise(X)|generous(X))=>(rich(X)<~>funny(X))))&
(![X]:((~rich(X)<~>happy(X))=>(~calm(X)&creative(X))))&
(((~quiet(paul)<~>kind(paul)))=>((brave(paul)&wise(paul))))&
(![X]:(~brave(X)=>(~tall(X)<~>strong(X))))&
((?[X]:((calm(X)&wise(X))))=>(?[X]:((funny(X)|~strong(X)))))&
(?[X]:((humble(X)|brave(X))))&
(?[X]:((happy(X)|~calm(X))))&
(?[X]:((~kind(X)|calm(X))))&
(?[X]:((tall(X)|happy(X))))&
(?[X]:((rich(X)<~>~patient(X))))&
((~happy(fred)&old(fred)))&
((~old(alice)<~>funny(alice))) | wise(paul) | [
"p0",
"p1",
"p4",
"p5",
"p6",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8780882882260583668140406
% SZS output start Proof for 8780882882260583668140406
1. ! [X0] : ((creative(X0) <~> ~wise(X0)) <=> (strong(X0) & old(X0))) [input p0]
2. ? [X0] : (~brave(X0) | wise(X0)) <=> (~brave(paul) & ~quiet(paul)) [input p1]
5. ! [X0] : ((~rich(X0) | rich(X0)) => (~wise(X0) | strong(X0))) [input p4]
6. ! [X0] : ((strong(X0) & old(X0)) <=> (creative(X0) <~> patient(X0))) [input p5]
7. ? [X0] : (~wise(X0) <~> rich(X0)) => quiet(paul) [input p6]
11. ! [X0] : ((~patient(X0) | strong(X0)) <=> (~funny(X0) <~> patient(X0))) [input p10]
12. ! [X0] : ((generous(X0) | wise(X0)) => (rich(X0) <~> funny(X0))) [input p11]
24. wise(paul) [input hypothesis]
29. ! [X0] : ((~wise(X0) | strong(X0)) | (rich(X0) & ~rich(X0))) [ennf transformation 5]
30. ! [X0] : (~wise(X0) | strong(X0) | (rich(X0) & ~rich(X0))) [flattening 29]
31. quiet(paul) | ! [X0] : (~wise(X0) <=> rich(X0)) [ennf transformation 7]
33. ! [X0] : ((rich(X0) <~> funny(X0)) | (~generous(X0) & ~wise(X0))) [ennf transformation 12]
38. ! [X0] : ((((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | (~strong(X0) | ~old(X0))) & ((strong(X0) & old(X0)) | ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0))))) [nnf transformation 1]
39. ! [X0] : ((((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | ~strong(X0) | ~old(X0)) & ((strong(X0) & old(X0)) | ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0))))) [flattening 38]
40. (? [X0] : (~brave(X0) | wise(X0)) | (brave(paul) | quiet(paul))) & ((~brave(paul) & ~quiet(paul)) | ! [X0] : (brave(X0) & ~wise(X0))) [nnf transformation 2]
41. (? [X0] : (~brave(X0) | wise(X0)) | brave(paul) | quiet(paul)) & ((~brave(paul) & ~quiet(paul)) | ! [X0] : (brave(X0) & ~wise(X0))) [flattening 40]
42. (? [X0] : (~brave(X0) | wise(X0)) | brave(paul) | quiet(paul)) & ((~brave(paul) & ~quiet(paul)) | ! [X1] : (brave(X1) & ~wise(X1))) [rectify 41]
43. ? [X0] : (~brave(X0) | wise(X0)) => (~brave(sK0) | wise(sK0)) [choice axiom]
44. ((~brave(sK0) | wise(sK0)) | brave(paul) | quiet(paul)) & ((~brave(paul) & ~quiet(paul)) | ! [X1] : (brave(X1) & ~wise(X1))) [skolemisation 42,43]
48. ! [X0] : (((strong(X0) & old(X0)) | ((creative(X0) | ~patient(X0)) & (patient(X0) | ~creative(X0)))) & (((~patient(X0) | ~creative(X0)) & (patient(X0) | creative(X0))) | (~strong(X0) | ~old(X0)))) [nnf transformation 6]
49. ! [X0] : (((strong(X0) & old(X0)) | ((creative(X0) | ~patient(X0)) & (patient(X0) | ~creative(X0)))) & (((~patient(X0) | ~creative(X0)) & (patient(X0) | creative(X0))) | ~strong(X0) | ~old(X0))) [flattening 48]
50. quiet(paul) | ! [X0] : ((~wise(X0) | ~rich(X0)) & (rich(X0) | wise(X0))) [nnf transformation 31]
61. ! [X0] : (((~patient(X0) | strong(X0)) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0)))) & (((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | (patient(X0) & ~strong(X0)))) [nnf transformation 11]
62. ! [X0] : ((~patient(X0) | strong(X0) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0)))) & (((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | (patient(X0) & ~strong(X0)))) [flattening 61]
63. ! [X0] : (((~funny(X0) | ~rich(X0)) & (funny(X0) | rich(X0))) | (~generous(X0) & ~wise(X0))) [nnf transformation 33]
82. ~wise(X0) | old(X0) | ~creative(X0) [cnf transformation 39]
86. ~strong(X0) | creative(X0) | ~wise(X0) | ~old(X0) [cnf transformation 39]
88. ~quiet(paul) | ~wise(X1) [cnf transformation 44]
96. ~wise(X0) | strong(X0) | ~rich(X0) [cnf transformation 30]
97. ~wise(X0) | strong(X0) | rich(X0) [cnf transformation 30]
99. ~patient(X0) | ~creative(X0) | ~strong(X0) | ~old(X0) [cnf transformation 49]
101. ~patient(X0) | creative(X0) | old(X0) [cnf transformation 49]
105. quiet(paul) | ~wise(X0) | ~rich(X0) [cnf transformation 50]
119. patient(X0) | ~funny(X0) | patient(X0) [cnf transformation 62]
124. ~wise(X0) | rich(X0) | funny(X0) [cnf transformation 63]
149. wise(paul) [cnf transformation 24]
150. ~funny(X0) | patient(X0) [duplicate literal removal 119]
153. 1 <=> quiet(paul) [avatar definition]
174. 6 <=> ! [X1] : ~wise(X1) [avatar definition]
175. ~wise(X1) <- (6) [avatar component clause 174]
178. 6 | ~1 [avatar split clause 88,153,174]
197. ~wise(X0) | strong(X0) [subsumption resolution 96,97]
199. 11 <=> ! [X0] : (~wise(X0) | ~rich(X0)) [avatar definition]
200. ~rich(X0) | ~wise(X0) <- (11) [avatar component clause 199]
201. 11 | 1 [avatar split clause 105,153,199]
259. 25 <=> wise(paul) [avatar definition]
261. wise(paul) <- (25) [avatar component clause 259]
334. 25 [avatar split clause 149,259]
343. $false <- (6, 25) [resolution 261,175]
344. ~6 | ~25 [avatar contradiction clause 343]
350. strong(paul) <- (25) [resolution 197,261]
353. old(paul) | ~creative(paul) <- (25) [resolution 82,261]
355. 41 <=> creative(paul) [avatar definition]
359. 42 <=> old(paul) [avatar definition]
362. ~41 | 42 | ~25 [avatar split clause 353,259,359,355]
475. rich(paul) | funny(paul) <- (25) [resolution 124,261]
478. 56 <=> funny(paul) [avatar definition]
480. funny(paul) <- (56) [avatar component clause 478]
482. 57 <=> rich(paul) [avatar definition]
484. rich(paul) <- (57) [avatar component clause 482]
485. 56 | 57 | ~25 [avatar split clause 475,259,482,478]
494. ~wise(paul) <- (11, 57) [resolution 484,200]
497. $false <- (11, 25, 57) [subsumption resolution 494,261]
498. ~11 | ~25 | ~57 [avatar contradiction clause 497]
499. patient(paul) <- (56) [resolution 480,150]
575. creative(paul) | ~wise(paul) | ~old(paul) <- (25) [resolution 86,350]
752. ~creative(paul) | ~strong(paul) | ~old(paul) <- (56) [resolution 499,99]
756. creative(paul) | old(paul) <- (56) [resolution 499,101]
760. 42 | 41 | ~56 [avatar split clause 756,478,355,359]
761. ~creative(paul) | ~old(paul) <- (25, 56) [subsumption resolution 752,350]
762. ~42 | ~41 | ~25 | ~56 [avatar split clause 761,478,259,355,359]
763. creative(paul) | ~old(paul) <- (25) [subsumption resolution 575,261]
764. ~42 | 41 | ~25 [avatar split clause 763,259,355,359]
765. $false [avatar sat refutation 178,201,334,344,362,485,498,760,762,764]
% SZS output end Proof for 8780882882260583668140406
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not old and not patient then someone is quiet and vice versa.
If someone is either humble or kind then fred is either generous or not old and vice versa.
If someone is either generous or old then someone is either funny or humble and vice versa.
If someone is not brave then someone is either humble or rich and vice versa.
If lucy is either not funny or not old then someone is both not quiet and strong and vice versa.
Everyone who is either not wise or humble is both not curious and not patient.
If alice is either not kind or tall then john is both not brave and not curious and vice versa.
If susan is both old and not generous then lucy is not strong.
Everyone who is creative or not wise is not strong and vice versa.
If paul is not calm or not happy then someone is both old and not creative and vice versa.
If someone is both not tall and not funny then lucy is both old and not quiet.
If paul is not old then alice is not curious and vice versa.
If someone is not funny then mary is either curious or not humble and vice versa.
Everyone who is humble is brave or happy.
Everyone who is either strong or not funny is not tall.
Everyone who is both tall and wise is not happy and vice versa.
Lucy is both strong and curious.
Someone is either not brave or not old.
Mary is not curious.
John is not creative.
Fred is both calm and quiet.
Someone is rich.
Fred is not curious or not happy.
Someone is brave. | Lucy is humble. | contradiction | ((?[X]:((~old(X)&~patient(X))))<=>(?[X]:(quiet(X))))&
((?[X]:((humble(X)<~>kind(X))))<=>((generous(fred)<~>~old(fred))))&
((?[X]:((generous(X)<~>old(X))))<=>(?[X]:((funny(X)<~>humble(X)))))&
((?[X]:(~brave(X)))<=>(?[X]:((humble(X)<~>rich(X)))))&
(((~funny(lucy)<~>~old(lucy)))<=>(?[X]:((~quiet(X)&strong(X)))))&
(![X]:((~wise(X)<~>humble(X))=>(~curious(X)&~patient(X))))&
(((~kind(alice)<~>tall(alice)))<=>((~brave(john)&~curious(john))))&
(((old(susan)&~generous(susan)))=>(~strong(lucy)))&
(![X]:((creative(X)|~wise(X))<=>~strong(X)))&
(((~calm(paul)|~happy(paul)))<=>(?[X]:((old(X)&~creative(X)))))&
((?[X]:((~tall(X)&~funny(X))))=>((old(lucy)&~quiet(lucy))))&
((~old(paul))<=>(~curious(alice)))&
((?[X]:(~funny(X)))<=>((curious(mary)<~>~humble(mary))))&
(![X]:(humble(X)=>(brave(X)|happy(X))))&
(![X]:((strong(X)<~>~funny(X))=>~tall(X)))&
(![X]:((tall(X)&wise(X))<=>~happy(X)))&
((strong(lucy)&curious(lucy)))&
(?[X]:((~brave(X)<~>~old(X))))&
(~curious(mary))&
(~creative(john))&
((calm(fred)&quiet(fred)))&
(?[X]:(rich(X)))&
((~curious(fred)|~happy(fred)))&
(?[X]:(brave(X))) | humble(lucy) | [
"p5",
"p8",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8081821823649945376745248
% SZS output start Proof for 8081821823649945376745248
6. ! [X0] : ((~wise(X0) <~> humble(X0)) => (~patient(X0) & ~curious(X0))) [input p5]
9. ! [X0] : ((~wise(X0) | creative(X0)) <=> ~strong(X0)) [input p8]
17. curious(lucy) & strong(lucy) [input p16]
25. humble(lucy) [input hypothesis]
29. ! [X0] : ((~patient(X0) & ~curious(X0)) | (~wise(X0) <=> humble(X0))) [ennf transformation 6]
59. ! [X0] : ((~patient(X0) & ~curious(X0)) | ((~wise(X0) | ~humble(X0)) & (humble(X0) | wise(X0)))) [nnf transformation 29]
62. ! [X0] : (((~wise(X0) | creative(X0)) | strong(X0)) & (~strong(X0) | (wise(X0) & ~creative(X0)))) [nnf transformation 9]
63. ! [X0] : ((~wise(X0) | creative(X0) | strong(X0)) & (~strong(X0) | (wise(X0) & ~creative(X0)))) [flattening 62]
114. ~curious(X0) | ~wise(X0) | ~humble(X0) [cnf transformation 59]
125. ~strong(X0) | wise(X0) [cnf transformation 63]
146. strong(lucy) [cnf transformation 17]
147. curious(lucy) [cnf transformation 17]
157. humble(lucy) [cnf transformation 25]
326. 37 <=> strong(lucy) [avatar definition]
327. strong(lucy) <- (37) [avatar component clause 326]
392. 37 [avatar split clause 146,326]
417. wise(lucy) <- (37) [resolution 125,327]
438. ~wise(lucy) | ~humble(lucy) [resolution 114,147]
439. ~humble(lucy) <- (37) [subsumption resolution 438,417]
440. $false <- (37) [subsumption resolution 439,157]
441. ~37 [avatar contradiction clause 440]
442. $false [avatar sat refutation 392,441]
% SZS output end Proof for 8081821823649945376745248
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or strong is both wise and rich and vice versa.
If alice is not creative then someone is generous and vice versa.
Everyone who is both curious and not strong is not wise.
If someone is either not patient or old then someone is not rich and vice versa.
Everyone who is either not brave or kind is either patient or generous and vice versa.
If someone is either brave or not brave then fred is either not patient or rich and vice versa.
If susan is either not brave or not wise then john is both not humble and humble.
Everyone who is both old and calm is either not rich or strong.
If someone is not tall or not creative then someone is both not patient and not old and vice versa.
If john is both strong and patient then someone is not calm or not wise.
Everyone who is both quiet and curious is not creative and vice versa.
If lucy is either not old or not generous then mary is both wise and calm and vice versa.
If fred is brave then someone is either tall or quiet and vice versa.
If someone is not calm then susan is both not brave and not patient and vice versa.
Everyone who is either humble or not happy is rich or not funny.
Everyone who is not tall or not quiet is not old or generous.
John is not funny.
John is not old.
Someone is patient.
Someone is either not strong or not wise. | John is not generous. | entailment | (![X]:((~strong(X)|strong(X))<=>(wise(X)&rich(X))))&
((~creative(alice))<=>(?[X]:(generous(X))))&
(![X]:((curious(X)&~strong(X))=>~wise(X)))&
((?[X]:((~patient(X)<~>old(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~brave(X)<~>kind(X))<=>(patient(X)<~>generous(X))))&
((?[X]:((brave(X)<~>~brave(X))))<=>((~patient(fred)<~>rich(fred))))&
(((~brave(susan)<~>~wise(susan)))=>((~humble(john)&humble(john))))&
(![X]:((old(X)&calm(X))=>(~rich(X)<~>strong(X))))&
((?[X]:((~tall(X)|~creative(X))))<=>(?[X]:((~patient(X)&~old(X)))))&
(((strong(john)&patient(john)))=>(?[X]:((~calm(X)|~wise(X)))))&
(![X]:((quiet(X)&curious(X))<=>~creative(X)))&
(((~old(lucy)<~>~generous(lucy)))<=>((wise(mary)&calm(mary))))&
((brave(fred))<=>(?[X]:((tall(X)<~>quiet(X)))))&
((?[X]:(~calm(X)))<=>((~brave(susan)&~patient(susan))))&
(![X]:((humble(X)<~>~happy(X))=>(rich(X)|~funny(X))))&
(![X]:((~tall(X)|~quiet(X))=>(~old(X)|generous(X))))&
(~funny(john))&
(~old(john))&
(?[X]:(patient(X)))&
(?[X]:((~strong(X)<~>~wise(X)))) | ~generous(john) | [
"p0",
"p1",
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5469520392781884795784797
% SZS output start Proof for 5469520392781884795784797
1. ! [X0] : ((strong(X0) | ~strong(X0)) <=> (rich(X0) & wise(X0))) [input p0]
2. ~creative(alice) <=> ? [X0] : generous(X0) [input p1]
4. ? [X0] : (~patient(X0) <~> old(X0)) <=> ? [X0] : ~rich(X0) [input p3]
9. ? [X0] : (~creative(X0) | ~tall(X0)) <=> ? [X0] : (~old(X0) & ~patient(X0)) [input p8]
21. generous(john) [input hypothesis]
22. ? [X0] : (~patient(X0) <~> old(X0)) <=> ? [X1] : ~rich(X1) [rectify 4]
23. ? [X0] : (~creative(X0) | ~tall(X0)) <=> ? [X1] : (~old(X1) & ~patient(X1)) [rectify 9]
35. ! [X0] : (((strong(X0) | ~strong(X0)) | (~rich(X0) | ~wise(X0))) & ((rich(X0) & wise(X0)) | (~strong(X0) & strong(X0)))) [nnf transformation 1]
36. ! [X0] : ((strong(X0) | ~strong(X0) | ~rich(X0) | ~wise(X0)) & ((rich(X0) & wise(X0)) | (~strong(X0) & strong(X0)))) [flattening 35]
37. (~creative(alice) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | creative(alice)) [nnf transformation 2]
38. (~creative(alice) | ! [X0] : ~generous(X0)) & (? [X1] : generous(X1) | creative(alice)) [rectify 37]
39. ? [X1] : generous(X1) => generous(sK0) [choice axiom]
40. (~creative(alice) | ! [X0] : ~generous(X0)) & (generous(sK0) | creative(alice)) [skolemisation 38,39]
41. (? [X0] : ((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | ! [X1] : rich(X1)) & (? [X1] : ~rich(X1) | ! [X0] : ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0)))) [nnf transformation 22]
42. (? [X0] : ((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) | ! [X1] : rich(X1)) & (? [X2] : ~rich(X2) | ! [X3] : ((~patient(X3) | ~old(X3)) & (old(X3) | patient(X3)))) [rectify 41]
43. ? [X0] : ((~old(X0) | patient(X0)) & (old(X0) | ~patient(X0))) => ((~old(sK1) | patient(sK1)) & (old(sK1) | ~patient(sK1))) [choice axiom]
44. ? [X2] : ~rich(X2) => ~rich(sK2) [choice axiom]
45. (((~old(sK1) | patient(sK1)) & (old(sK1) | ~patient(sK1))) | ! [X1] : rich(X1)) & (~rich(sK2) | ! [X3] : ((~patient(X3) | ~old(X3)) & (old(X3) | patient(X3)))) [skolemisation 42,44,43]
53. (? [X0] : (~creative(X0) | ~tall(X0)) | ! [X1] : (old(X1) | patient(X1))) & (? [X1] : (~old(X1) & ~patient(X1)) | ! [X0] : (creative(X0) & tall(X0))) [nnf transformation 23]
54. (? [X0] : (~creative(X0) | ~tall(X0)) | ! [X1] : (old(X1) | patient(X1))) & (? [X2] : (~old(X2) & ~patient(X2)) | ! [X3] : (creative(X3) & tall(X3))) [rectify 53]
55. ? [X0] : (~creative(X0) | ~tall(X0)) => (~creative(sK4) | ~tall(sK4)) [choice axiom]
56. ? [X2] : (~old(X2) & ~patient(X2)) => (~old(sK5) & ~patient(sK5)) [choice axiom]
57. ((~creative(sK4) | ~tall(sK4)) | ! [X1] : (old(X1) | patient(X1))) & ((~old(sK5) & ~patient(sK5)) | ! [X3] : (creative(X3) & tall(X3))) [skolemisation 54,56,55]
80. rich(X0) | strong(X0) [cnf transformation 36]
81. ~strong(X0) | rich(X0) [cnf transformation 36]
84. ~creative(alice) | ~generous(X0) [cnf transformation 40]
86. ~rich(sK2) | old(X3) | patient(X3) [cnf transformation 45]
113. ~patient(sK5) | creative(X3) [cnf transformation 57]
115. ~old(sK5) | creative(X3) [cnf transformation 57]
140. generous(john) [cnf transformation 21]
145. rich(X0) [subsumption resolution 80,81]
148. 1 <=> ! [X0] : ~generous(X0) [avatar definition]
149. ~generous(X0) <- (1) [avatar component clause 148]
151. 2 <=> creative(alice) [avatar definition]
153. ~creative(alice) <- (~2) [avatar component clause 151]
154. 1 | ~2 [avatar split clause 84,151,148]
162. old(X3) | patient(X3) [subsumption resolution 86,145]
191. 9 <=> ! [X3] : creative(X3) [avatar definition]
192. creative(X3) <- (9) [avatar component clause 191]
194. 10 <=> old(sK5) [avatar definition]
196. ~old(sK5) <- (~10) [avatar component clause 194]
197. 9 | ~10 [avatar split clause 115,194,191]
203. 12 <=> patient(sK5) [avatar definition]
205. ~patient(sK5) <- (~12) [avatar component clause 203]
206. 9 | ~12 [avatar split clause 113,203,191]
284. patient(sK5) <- (~10) [resolution 162,196]
287. $false <- (~10, ~12) [subsumption resolution 284,205]
288. 10 | 12 [avatar contradiction clause 287]
289. $false <- (~2, 9) [resolution 192,153]
290. 2 | ~9 [avatar contradiction clause 289]
291. $false <- (1) [resolution 149,140]
294. ~1 [avatar contradiction clause 291]
295. $false [avatar sat refutation 154,197,206,288,290,294]
% SZS output end Proof for 5469520392781884795784797
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong is not rich.
Everyone who is patient or kind is humble or not tall.
Everyone who is either not humble or not wise is both calm and curious and vice versa.
Everyone who is both not tall and creative is creative or wise and vice versa.
Everyone who is calm or creative is not brave and vice versa.
Everyone who is not patient is funny.
Everyone who is either not patient or not generous is not funny or funny.
If someone is not funny then someone is both funny and brave.
Everyone who is old is wise.
If someone is either brave or kind then someone is not kind or patient.
If mary is either not quiet or humble then fred is wise.
Everyone who is not happy or happy is both brave and rich.
Everyone who is both not brave and patient is not tall and vice versa.
Everyone who is either brave or not humble is quiet or calm.
If someone is either not curious or generous then susan is either not strong or not generous and vice versa.
If someone is quiet or not happy then someone is not generous and vice versa.
Lucy is both not creative and not kind.
John is kind or not old.
Mary is not happy or happy.
Someone is not humble.
Susan is either not humble or not curious. | Fred is not old. | entailment | (![X]:(~strong(X)=>~rich(X)))&
(![X]:((patient(X)|kind(X))=>(humble(X)|~tall(X))))&
(![X]:((~humble(X)<~>~wise(X))<=>(calm(X)&curious(X))))&
(![X]:((~tall(X)&creative(X))<=>(creative(X)|wise(X))))&
(![X]:((calm(X)|creative(X))<=>~brave(X)))&
(![X]:(~patient(X)=>funny(X)))&
(![X]:((~patient(X)<~>~generous(X))=>(~funny(X)|funny(X))))&
((?[X]:(~funny(X)))=>(?[X]:((funny(X)&brave(X)))))&
(![X]:(old(X)=>wise(X)))&
((?[X]:((brave(X)<~>kind(X))))=>(?[X]:((~kind(X)|patient(X)))))&
(((~quiet(mary)<~>humble(mary)))=>(wise(fred)))&
(![X]:((~happy(X)|happy(X))=>(brave(X)&rich(X))))&
(![X]:((~brave(X)&patient(X))<=>~tall(X)))&
(![X]:((brave(X)<~>~humble(X))=>(quiet(X)|calm(X))))&
((?[X]:((~curious(X)<~>generous(X))))<=>((~strong(susan)<~>~generous(susan))))&
((?[X]:((quiet(X)|~happy(X))))<=>(?[X]:(~generous(X))))&
((~creative(lucy)&~kind(lucy)))&
((kind(john)|~old(john)))&
((~happy(mary)|happy(mary)))&
(?[X]:(~humble(X)))&
((~humble(susan)<~>~curious(susan))) | ~old(fred) | [
"p3",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 850654470248874552418288
% SZS output start Proof for 850654470248874552418288
4. ! [X0] : ((creative(X0) & ~tall(X0)) <=> (wise(X0) | creative(X0))) [input p3]
9. ! [X0] : (old(X0) => wise(X0)) [input p8]
12. ! [X0] : ((happy(X0) | ~happy(X0)) => (rich(X0) & brave(X0))) [input p11]
13. ! [X0] : ((patient(X0) & ~brave(X0)) <=> ~tall(X0)) [input p12]
22. old(fred) [input hypothesis]
33. ! [X0] : (wise(X0) | ~old(X0)) [ennf transformation 9]
36. ! [X0] : ((rich(X0) & brave(X0)) | (~happy(X0) & happy(X0))) [ennf transformation 12]
41. ! [X0] : (((creative(X0) & ~tall(X0)) | (~wise(X0) & ~creative(X0))) & ((wise(X0) | creative(X0)) | (~creative(X0) | tall(X0)))) [nnf transformation 4]
42. ! [X0] : (((creative(X0) & ~tall(X0)) | (~wise(X0) & ~creative(X0))) & (wise(X0) | creative(X0) | ~creative(X0) | tall(X0))) [flattening 41]
54. ! [X0] : (((patient(X0) & ~brave(X0)) | tall(X0)) & (~tall(X0) | (~patient(X0) | brave(X0)))) [nnf transformation 13]
55. ! [X0] : (((patient(X0) & ~brave(X0)) | tall(X0)) & (~tall(X0) | ~patient(X0) | brave(X0))) [flattening 54]
80. ~wise(X0) | ~tall(X0) [cnf transformation 42]
91. ~old(X0) | wise(X0) [cnf transformation 33]
96. brave(X0) | happy(X0) [cnf transformation 36]
97. brave(X0) | ~happy(X0) [cnf transformation 36]
101. ~brave(X0) | tall(X0) [cnf transformation 55]
123. old(fred) [cnf transformation 22]
162. 10 <=> wise(fred) [avatar definition]
164. wise(fred) <- (10) [avatar component clause 162]
168. brave(X0) [subsumption resolution 96,97]
169. tall(X0) [subsumption resolution 101,168]
249. wise(fred) [resolution 91,123]
250. 10 [avatar split clause 249,162]
252. ~tall(fred) <- (10) [resolution 164,80]
255. $false <- (10) [subsumption resolution 252,169]
256. ~10 [avatar contradiction clause 255]
257. $false [avatar sat refutation 250,256]
% SZS output end Proof for 850654470248874552418288
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative or not curious then lucy is not brave and vice versa.
If paul is either brave or happy then someone is both not creative and curious and vice versa.
Everyone who is either patient or not humble is not curious.
Everyone who is not strong is both quiet and not happy.
If someone is either not generous or humble then mary is happy or quiet.
If paul is both not humble and humble then someone is not happy.
Everyone who is not quiet is tall or funny and vice versa.
If someone is not calm or not wise then someone is creative or generous and vice versa.
If someone is curious then someone is either curious or not old.
Everyone who is both old and kind is tall or calm.
Everyone who is not humble is not humble or not brave and vice versa.
If john is both not calm and wise then someone is either tall or old.
Everyone who is either funny or brave is generous or not happy and vice versa.
If mary is either not humble or not rich then mary is either old or brave.
Everyone who is curious is generous or humble.
Someone is both not kind and not rich.
Someone is either quiet or tall.
Someone is both not kind and calm.
Someone is either not tall or not creative.
John is humble or not calm.
John is both happy and calm.
Someone is patient.
Mary is either tall or not curious. | John is creative. | neutral | ((?[X]:((creative(X)|~curious(X))))<=>(~brave(lucy)))&
(((brave(paul)<~>happy(paul)))<=>(?[X]:((~creative(X)&curious(X)))))&
(![X]:((patient(X)<~>~humble(X))=>~curious(X)))&
(![X]:(~strong(X)=>(quiet(X)&~happy(X))))&
((?[X]:((~generous(X)<~>humble(X))))=>((happy(mary)|quiet(mary))))&
(((~humble(paul)&humble(paul)))=>(?[X]:(~happy(X))))&
(![X]:(~quiet(X)<=>(tall(X)|funny(X))))&
((?[X]:((~calm(X)|~wise(X))))<=>(?[X]:((creative(X)|generous(X)))))&
((?[X]:(curious(X)))=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:((old(X)&kind(X))=>(tall(X)|calm(X))))&
(![X]:(~humble(X)<=>(~humble(X)|~brave(X))))&
(((~calm(john)&wise(john)))=>(?[X]:((tall(X)<~>old(X)))))&
(![X]:((funny(X)<~>brave(X))<=>(generous(X)|~happy(X))))&
(((~humble(mary)<~>~rich(mary)))=>((old(mary)<~>brave(mary))))&
(![X]:(curious(X)=>(generous(X)|humble(X))))&
(?[X]:((~kind(X)&~rich(X))))&
(?[X]:((quiet(X)<~>tall(X))))&
(?[X]:((~kind(X)&calm(X))))&
(?[X]:((~tall(X)<~>~creative(X))))&
((humble(john)|~calm(john)))&
((happy(john)&calm(john)))&
(?[X]:(patient(X)))&
((tall(mary)<~>~curious(mary))) | creative(john) | [] | null | 0 |
Everyone who is either not rich or not happy is both not brave and not rich. Everyone who is not kind or wise is both not calm and wise. Everyone who is humble is both quiet and not patient. If alice is both not patient and brave then lucy is humble and vice versa. If someone is creative or not happy then mary is not quiet or patient and vice versa. Everyone who is both strong and generous is not tall. If paul is not creative or humble then someone is not happy or wise. If lucy is either not old or wise then paul is either not brave or calm and vice versa. Everyone who is either not happy or not wise is not patient or not funny and vice versa. If john is brave or strong then mary is old or not rich and vice versa. If someone is either tall or old then lucy is wise. If lucy is funny or not funny then someone is not wise or not old and vice versa. Everyone who is both not happy and wise is not calm or not patient and vice versa. If someone is brave then mary is both generous and not kind. Everyone who is tall or strong is both rich and generous and vice versa. Everyone who is both not humble and rich is either not kind or not rich and vice versa. Someone is patient or strong. Paul is not old or creative. Someone is not calm or happy. Someone is either kind or not humble. Paul is either old or humble. Susan is calm or generous. Someone is either not kind or patient. Lucy is not humble. | Mary is wise. | entailment | (![X]:((~rich(X)<~>~happy(X))=>(~brave(X)&~rich(X))))&
(![X]:((~kind(X)|wise(X))=>(~calm(X)&wise(X))))&
(![X]:(humble(X)=>(quiet(X)&~patient(X))))&
(((~patient(alice)&brave(alice)))<=>(humble(lucy)))&
((?[X]:((creative(X)|~happy(X))))<=>((~quiet(mary)|patient(mary))))&
(![X]:((strong(X)&generous(X))=>~tall(X)))&
(((~creative(paul)|humble(paul)))=>(?[X]:((~happy(X)|wise(X)))))&
(((~old(lucy)<~>wise(lucy)))<=>((~brave(paul)<~>calm(paul))))&
(![X]:((~happy(X)<~>~wise(X))<=>(~patient(X)|~funny(X))))&
(((brave(john)|strong(john)))<=>((old(mary)|~rich(mary))))&
((?[X]:((tall(X)<~>old(X))))=>(wise(lucy)))&
(((funny(lucy)|~funny(lucy)))<=>(?[X]:((~wise(X)|~old(X)))))&
(![X]:((~happy(X)&wise(X))<=>(~calm(X)|~patient(X))))&
((?[X]:(brave(X)))=>((generous(mary)&~kind(mary))))&
(![X]:((tall(X)|strong(X))<=>(rich(X)&generous(X))))&
(![X]:((~humble(X)&rich(X))<=>(~kind(X)<~>~rich(X))))&
(?[X]:((patient(X)|strong(X))))&
((~old(paul)|creative(paul)))&
(?[X]:((~calm(X)|happy(X))))&
(?[X]:((kind(X)<~>~humble(X))))&
((old(paul)<~>humble(paul)))&
((calm(susan)|generous(susan)))&
(?[X]:((~kind(X)<~>patient(X))))&
(~humble(lucy)) | wise(mary) | [
"p0",
"p1",
"p2",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8020562077320717234238123
% SZS output start Proof for 8020562077320717234238123
1. ! [X0] : ((~rich(X0) <~> ~happy(X0)) => (~rich(X0) & ~brave(X0))) [input p0]
2. ! [X0] : ((wise(X0) | ~kind(X0)) => (wise(X0) & ~calm(X0))) [input p1]
3. ! [X0] : (humble(X0) => (~patient(X0) & quiet(X0))) [input p2]
13. ! [X0] : ((wise(X0) & ~happy(X0)) <=> (~patient(X0) | ~calm(X0))) [input p12]
16. ! [X0] : ((rich(X0) & ~humble(X0)) <=> (~kind(X0) <~> ~rich(X0))) [input p15]
25. ~wise(mary) [input hypothesis]
26. ! [X0] : ((~rich(X0) & ~brave(X0)) | (~rich(X0) <=> ~happy(X0))) [ennf transformation 1]
27. ! [X0] : ((wise(X0) & ~calm(X0)) | (~wise(X0) & kind(X0))) [ennf transformation 2]
28. ! [X0] : ((~patient(X0) & quiet(X0)) | ~humble(X0)) [ennf transformation 3]
34. ! [X0] : ((~rich(X0) & ~brave(X0)) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0)))) [nnf transformation 26]
55. ! [X0] : (((wise(X0) & ~happy(X0)) | (patient(X0) & calm(X0))) & ((~patient(X0) | ~calm(X0)) | (~wise(X0) | happy(X0)))) [nnf transformation 13]
56. ! [X0] : (((wise(X0) & ~happy(X0)) | (patient(X0) & calm(X0))) & (~patient(X0) | ~calm(X0) | ~wise(X0) | happy(X0))) [flattening 55]
59. ! [X0] : (((rich(X0) & ~humble(X0)) | ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0)))) & (((rich(X0) | kind(X0)) & (~rich(X0) | ~kind(X0))) | (~rich(X0) | humble(X0)))) [nnf transformation 16]
60. ! [X0] : (((rich(X0) & ~humble(X0)) | ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0)))) & (((rich(X0) | kind(X0)) & (~rich(X0) | ~kind(X0))) | ~rich(X0) | humble(X0))) [flattening 59]
75. ~rich(X0) | ~rich(X0) | happy(X0) [cnf transformation 34]
78. wise(X0) | kind(X0) [cnf transformation 27]
81. ~patient(X0) | ~humble(X0) [cnf transformation 28]
118. ~happy(X0) | patient(X0) [cnf transformation 56]
128. ~rich(X0) | ~kind(X0) | ~rich(X0) | humble(X0) [cnf transformation 60]
133. rich(X0) | ~kind(X0) | rich(X0) [cnf transformation 60]
145. ~wise(mary) [cnf transformation 25]
146. ~rich(X0) | ~kind(X0) | humble(X0) [duplicate literal removal 128]
147. ~kind(X0) | rich(X0) [duplicate literal removal 133]
148. ~rich(X0) | happy(X0) [duplicate literal removal 75]
165. 4 <=> patient(mary) [avatar definition]
166. patient(mary) <- (4) [avatar component clause 165]
233. 18 <=> rich(mary) [avatar definition]
235. rich(mary) <- (18) [avatar component clause 233]
278. 28 <=> kind(mary) [avatar definition]
279. kind(mary) <- (28) [avatar component clause 278]
287. ~kind(X0) | humble(X0) [subsumption resolution 146,147]
346. kind(mary) [resolution 78,145]
348. 28 [avatar split clause 346,278]
358. rich(mary) <- (28) [resolution 147,279]
362. happy(mary) <- (18) [resolution 148,235]
363. patient(mary) <- (18) [resolution 362,118]
365. 4 | ~18 [avatar split clause 363,233,165]
366. 18 | ~28 [avatar split clause 358,278,233]
369. ~humble(mary) <- (4) [resolution 166,81]
371. humble(mary) <- (28) [resolution 287,279]
375. $false <- (4, 28) [subsumption resolution 371,369]
376. ~4 | ~28 [avatar contradiction clause 375]
377. $false [avatar sat refutation 348,365,366,376]
% SZS output end Proof for 8020562077320717234238123
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is brave or old and vice versa. Everyone who is both not generous and generous is not kind and vice versa. Everyone who is not brave is both happy and not calm. If someone is creative then alice is generous and vice versa. If someone is both not brave and not quiet then someone is not generous or not happy. Everyone who is both tall and funny is both patient and not kind and vice versa. Everyone who is not funny is either funny or not quiet. Everyone who is either not generous or wise is not tall or not generous and vice versa. If fred is not kind or rich then someone is both creative and humble. If alice is rich or generous then lucy is not humble and vice versa. If john is not tall then mary is both brave and not patient and vice versa. Everyone who is either humble or not old is curious. Everyone who is both happy and not curious is old or not wise. Everyone who is not brave is both strong and curious and vice versa. If mary is both curious and happy then someone is humble or not strong. If someone is not brave then someone is both kind and calm and vice versa. Fred is quiet. John is tall. Someone is not curious or generous. Someone is either happy or not generous. Someone is not humble or not generous. Mary is happy or generous. Someone is kind or not generous. | Alice is creative. | neutral | (![X]:(rich(X)<=>(brave(X)|old(X))))&
(![X]:((~generous(X)&generous(X))<=>~kind(X)))&
(![X]:(~brave(X)=>(happy(X)&~calm(X))))&
((?[X]:(creative(X)))<=>(generous(alice)))&
((?[X]:((~brave(X)&~quiet(X))))=>(?[X]:((~generous(X)|~happy(X)))))&
(![X]:((tall(X)&funny(X))<=>(patient(X)&~kind(X))))&
(![X]:(~funny(X)=>(funny(X)<~>~quiet(X))))&
(![X]:((~generous(X)<~>wise(X))<=>(~tall(X)|~generous(X))))&
(((~kind(fred)|rich(fred)))=>(?[X]:((creative(X)&humble(X)))))&
(((rich(alice)|generous(alice)))<=>(~humble(lucy)))&
((~tall(john))<=>((brave(mary)&~patient(mary))))&
(![X]:((humble(X)<~>~old(X))=>curious(X)))&
(![X]:((happy(X)&~curious(X))=>(old(X)|~wise(X))))&
(![X]:(~brave(X)<=>(strong(X)&curious(X))))&
(((curious(mary)&happy(mary)))=>(?[X]:((humble(X)|~strong(X)))))&
((?[X]:(~brave(X)))<=>(?[X]:((kind(X)&calm(X)))))&
(quiet(fred))&
(tall(john))&
(?[X]:((~curious(X)|generous(X))))&
(?[X]:((happy(X)<~>~generous(X))))&
(?[X]:((~humble(X)|~generous(X))))&
((happy(mary)|generous(mary)))&
(?[X]:((kind(X)|~generous(X)))) | creative(alice) | [] | null | 0 |
If someone is either not quiet or happy then fred is funny.
If someone is brave then paul is calm and vice versa.
Everyone who is either patient or not funny is both not generous and curious.
If john is either brave or funny then paul is not calm.
If susan is both strong and not tall then paul is either not curious or not brave.
If someone is either not strong or generous then paul is happy or curious.
Everyone who is happy or not wise is both not rich and not curious.
Everyone who is both not curious and not quiet is not creative or not quiet and vice versa.
Everyone who is both happy and humble is not wise or strong and vice versa.
Everyone who is not happy or humble is either kind or not brave and vice versa.
Everyone who is both calm and not calm is not curious and vice versa.
If susan is old or not wise then fred is not wise or rich.
Everyone who is calm or curious is either not creative or not rich and vice versa.
Everyone who is not humble is not curious and vice versa.
If alice is not calm or brave then someone is either funny or creative and vice versa.
Susan is either tall or not strong.
Someone is old.
Fred is either not patient or brave.
Paul is not creative or curious.
Paul is happy or old. | Fred is not curious. | contradiction | ((?[X]:((~quiet(X)<~>happy(X))))=>(funny(fred)))&
((?[X]:(brave(X)))<=>(calm(paul)))&
(![X]:((patient(X)<~>~funny(X))=>(~generous(X)&curious(X))))&
(((brave(john)<~>funny(john)))=>(~calm(paul)))&
(((strong(susan)&~tall(susan)))=>((~curious(paul)<~>~brave(paul))))&
((?[X]:((~strong(X)<~>generous(X))))=>((happy(paul)|curious(paul))))&
(![X]:((happy(X)|~wise(X))=>(~rich(X)&~curious(X))))&
(![X]:((~curious(X)&~quiet(X))<=>(~creative(X)|~quiet(X))))&
(![X]:((happy(X)&humble(X))<=>(~wise(X)|strong(X))))&
(![X]:((~happy(X)|humble(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((calm(X)&~calm(X))<=>~curious(X)))&
(((old(susan)|~wise(susan)))=>((~wise(fred)|rich(fred))))&
(![X]:((calm(X)|curious(X))<=>(~creative(X)<~>~rich(X))))&
(![X]:(~humble(X)<=>~curious(X)))&
(((~calm(alice)|brave(alice)))<=>(?[X]:((funny(X)<~>creative(X)))))&
((tall(susan)<~>~strong(susan)))&
(?[X]:(old(X)))&
((~patient(fred)<~>brave(fred)))&
((~creative(paul)|curious(paul)))&
((happy(paul)|old(paul))) | ~curious(fred) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1678588376920548425451333
% SZS output start Proof for 1678588376920548425451333
11. ! [X0] : ((~calm(X0) & calm(X0)) <=> ~curious(X0)) [input p10]
21. ~curious(fred) [input hypothesis]
47. ! [X0] : (((~calm(X0) & calm(X0)) | curious(X0)) & (~curious(X0) | (calm(X0) | ~calm(X0)))) [nnf transformation 11]
48. ! [X0] : (((~calm(X0) & calm(X0)) | curious(X0)) & (~curious(X0) | calm(X0) | ~calm(X0))) [flattening 47]
96. calm(X0) | curious(X0) [cnf transformation 48]
97. ~calm(X0) | curious(X0) [cnf transformation 48]
121. ~curious(fred) [cnf transformation 21]
187. curious(X0) [subsumption resolution 96,97]
253. $false [subsumption resolution 121,187]
% SZS output end Proof for 1678588376920548425451333
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall or not tall is both quiet and not wise and vice versa.
Everyone who is either not kind or not curious is old.
If someone is not old or not brave then alice is either creative or tall.
Everyone who is not old is not brave or kind and vice versa.
If susan is either creative or not happy then someone is both happy and generous.
Everyone who is not old is both humble and not happy.
If someone is quiet then mary is either brave or not tall.
If mary is humble then someone is not rich or wise.
Everyone who is not rich or not creative is calm or wise and vice versa.
Everyone who is either not rich or not strong is both not funny and creative.
Everyone who is not calm is both not calm and humble and vice versa.
If someone is not old then someone is brave.
Everyone who is both not patient and humble is not happy or tall and vice versa.
Everyone who is either calm or creative is either strong or tall.
Everyone who is rich is either not wise or creative.
Mary is either happy or not calm.
Someone is either not wise or not tall.
Susan is either not funny or not generous.
Susan is not funny or humble.
Someone is either generous or not rich.
John is either patient or wise.
Someone is either not happy or not generous.
Mary is both not generous and funny. | Susan is not generous. | neutral | (![X]:((tall(X)|~tall(X))<=>(quiet(X)&~wise(X))))&
(![X]:((~kind(X)<~>~curious(X))=>old(X)))&
((?[X]:((~old(X)|~brave(X))))=>((creative(alice)<~>tall(alice))))&
(![X]:(~old(X)<=>(~brave(X)|kind(X))))&
(((creative(susan)<~>~happy(susan)))=>(?[X]:((happy(X)&generous(X)))))&
(![X]:(~old(X)=>(humble(X)&~happy(X))))&
((?[X]:(quiet(X)))=>((brave(mary)<~>~tall(mary))))&
((humble(mary))=>(?[X]:((~rich(X)|wise(X)))))&
(![X]:((~rich(X)|~creative(X))<=>(calm(X)|wise(X))))&
(![X]:((~rich(X)<~>~strong(X))=>(~funny(X)&creative(X))))&
(![X]:(~calm(X)<=>(~calm(X)&humble(X))))&
((?[X]:(~old(X)))=>(?[X]:(brave(X))))&
(![X]:((~patient(X)&humble(X))<=>(~happy(X)|tall(X))))&
(![X]:((calm(X)<~>creative(X))=>(strong(X)<~>tall(X))))&
(![X]:(rich(X)=>(~wise(X)<~>creative(X))))&
((happy(mary)<~>~calm(mary)))&
(?[X]:((~wise(X)<~>~tall(X))))&
((~funny(susan)<~>~generous(susan)))&
((~funny(susan)|humble(susan)))&
(?[X]:((generous(X)<~>~rich(X))))&
((patient(john)<~>wise(john)))&
(?[X]:((~happy(X)<~>~generous(X))))&
((~generous(mary)&funny(mary))) | ~generous(susan) | [] | null | 0 |
Everyone who is either kind or happy is not kind or calm and vice versa.
Everyone who is both patient and funny is either not creative or not generous.
If someone is both quiet and funny then someone is not strong.
If alice is both not calm and not curious then john is creative.
If someone is generous then someone is both old and not curious and vice versa.
Everyone who is tall or not generous is both strong and not happy.
If someone is patient then someone is not brave or patient and vice versa.
If someone is creative or not kind then someone is not patient.
Everyone who is not calm is brave.
If john is both quiet and strong then someone is both quiet and not tall and vice versa.
Everyone who is both not rich and not kind is curious.
Everyone who is not curious is rich or not curious.
Everyone who is not kind or not wise is both not quiet and tall.
If someone is brave then someone is both humble and old and vice versa.
Everyone who is both not humble and not tall is either not humble or kind and vice versa.
Everyone who is not funny is not quiet or not rich.
Alice is not rich or quiet.
Alice is patient or curious.
Fred is wise or not brave.
Paul is either wise or not patient.
Someone is strong or tall.
Someone is both old and patient.
John is either not wise or patient. | John is not creative. | neutral | (![X]:((kind(X)<~>happy(X))<=>(~kind(X)|calm(X))))&
(![X]:((patient(X)&funny(X))=>(~creative(X)<~>~generous(X))))&
((?[X]:((quiet(X)&funny(X))))=>(?[X]:(~strong(X))))&
(((~calm(alice)&~curious(alice)))=>(creative(john)))&
((?[X]:(generous(X)))<=>(?[X]:((old(X)&~curious(X)))))&
(![X]:((tall(X)|~generous(X))=>(strong(X)&~happy(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~brave(X)|patient(X)))))&
((?[X]:((creative(X)|~kind(X))))=>(?[X]:(~patient(X))))&
(![X]:(~calm(X)=>brave(X)))&
(((quiet(john)&strong(john)))<=>(?[X]:((quiet(X)&~tall(X)))))&
(![X]:((~rich(X)&~kind(X))=>curious(X)))&
(![X]:(~curious(X)=>(rich(X)|~curious(X))))&
(![X]:((~kind(X)|~wise(X))=>(~quiet(X)&tall(X))))&
((?[X]:(brave(X)))<=>(?[X]:((humble(X)&old(X)))))&
(![X]:((~humble(X)&~tall(X))<=>(~humble(X)<~>kind(X))))&
(![X]:(~funny(X)=>(~quiet(X)|~rich(X))))&
((~rich(alice)|quiet(alice)))&
((patient(alice)|curious(alice)))&
((wise(fred)|~brave(fred)))&
((wise(paul)<~>~patient(paul)))&
(?[X]:((strong(X)|tall(X))))&
(?[X]:((old(X)&patient(X))))&
((~wise(john)<~>patient(john))) | ~creative(john) | [] | null | 0 |
If someone is both not generous and not happy then mary is both happy and not brave and vice versa.
If mary is either not creative or quiet then someone is not tall and vice versa.
If someone is both not rich and not kind then lucy is calm or not strong.
If someone is not happy then susan is happy and vice versa.
If john is both not quiet and rich then someone is brave and vice versa.
Everyone who is both brave and not brave is both kind and not generous and vice versa.
Everyone who is not strong or old is both not kind and not tall and vice versa.
Everyone who is both not strong and curious is kind or not generous.
Everyone who is either not wise or strong is patient.
Everyone who is not rich or not calm is both not tall and quiet.
If paul is either wise or not quiet then paul is either generous or not curious.
If alice is curious then someone is either kind or funny and vice versa.
If fred is not patient or creative then someone is both not wise and not quiet and vice versa.
Everyone who is not tall is generous or not funny and vice versa.
Everyone who is both not tall and not generous is both curious and wise and vice versa.
If someone is not curious then alice is strong or calm and vice versa.
Someone is not old.
Someone is both happy and tall.
John is either kind or not humble.
Paul is either strong or brave.
Someone is either tall or not generous.
Someone is curious or brave.
Someone is either old or brave. | Susan is strong. | neutral | ((?[X]:((~generous(X)&~happy(X))))<=>((happy(mary)&~brave(mary))))&
(((~creative(mary)<~>quiet(mary)))<=>(?[X]:(~tall(X))))&
((?[X]:((~rich(X)&~kind(X))))=>((calm(lucy)|~strong(lucy))))&
((?[X]:(~happy(X)))<=>(happy(susan)))&
(((~quiet(john)&rich(john)))<=>(?[X]:(brave(X))))&
(![X]:((brave(X)&~brave(X))<=>(kind(X)&~generous(X))))&
(![X]:((~strong(X)|old(X))<=>(~kind(X)&~tall(X))))&
(![X]:((~strong(X)&curious(X))=>(kind(X)|~generous(X))))&
(![X]:((~wise(X)<~>strong(X))=>patient(X)))&
(![X]:((~rich(X)|~calm(X))=>(~tall(X)&quiet(X))))&
(((wise(paul)<~>~quiet(paul)))=>((generous(paul)<~>~curious(paul))))&
((curious(alice))<=>(?[X]:((kind(X)<~>funny(X)))))&
(((~patient(fred)|creative(fred)))<=>(?[X]:((~wise(X)&~quiet(X)))))&
(![X]:(~tall(X)<=>(generous(X)|~funny(X))))&
(![X]:((~tall(X)&~generous(X))<=>(curious(X)&wise(X))))&
((?[X]:(~curious(X)))<=>((strong(alice)|calm(alice))))&
(?[X]:(~old(X)))&
(?[X]:((happy(X)&tall(X))))&
((kind(john)<~>~humble(john)))&
((strong(paul)<~>brave(paul)))&
(?[X]:((tall(X)<~>~generous(X))))&
(?[X]:((curious(X)|brave(X))))&
(?[X]:((old(X)<~>brave(X)))) | strong(susan) | [] | null | 0 |
Everyone who is not quiet is brave or wise. Everyone who is both curious and happy is not brave. Everyone who is tall or creative is funny. Everyone who is either creative or not funny is either not generous or not calm. Everyone who is not creative is humble and vice versa. Everyone who is not creative is rich or funny and vice versa. Everyone who is not humble or not funny is both tall and not funny and vice versa. Everyone who is either not generous or humble is both not kind and not tall and vice versa. If someone is kind or not creative then fred is both humble and not rich. Everyone who is wise is generous or not calm and vice versa. If someone is not kind or strong then susan is not rich. If lucy is both not calm and patient then susan is not brave or patient. Everyone who is both not brave and not rich is not curious or not creative and vice versa. Everyone who is not quiet is not funny or old and vice versa. Everyone who is both not wise and kind is tall. Everyone who is both not patient and old is either funny or strong and vice versa. Someone is either humble or not funny. Someone is both humble and not old. Someone is quiet or not wise. Someone is both kind and not rich. John is not generous. Someone is kind or not calm. | Lucy is strong. | neutral | (![X]:(~quiet(X)=>(brave(X)|wise(X))))&
(![X]:((curious(X)&happy(X))=>~brave(X)))&
(![X]:((tall(X)|creative(X))=>funny(X)))&
(![X]:((creative(X)<~>~funny(X))=>(~generous(X)<~>~calm(X))))&
(![X]:(~creative(X)<=>humble(X)))&
(![X]:(~creative(X)<=>(rich(X)|funny(X))))&
(![X]:((~humble(X)|~funny(X))<=>(tall(X)&~funny(X))))&
(![X]:((~generous(X)<~>humble(X))<=>(~kind(X)&~tall(X))))&
((?[X]:((kind(X)|~creative(X))))=>((humble(fred)&~rich(fred))))&
(![X]:(wise(X)<=>(generous(X)|~calm(X))))&
((?[X]:((~kind(X)|strong(X))))=>(~rich(susan)))&
(((~calm(lucy)&patient(lucy)))=>((~brave(susan)|patient(susan))))&
(![X]:((~brave(X)&~rich(X))<=>(~curious(X)|~creative(X))))&
(![X]:(~quiet(X)<=>(~funny(X)|old(X))))&
(![X]:((~wise(X)&kind(X))=>tall(X)))&
(![X]:((~patient(X)&old(X))<=>(funny(X)<~>strong(X))))&
(?[X]:((humble(X)<~>~funny(X))))&
(?[X]:((humble(X)&~old(X))))&
(?[X]:((quiet(X)|~wise(X))))&
(?[X]:((kind(X)&~rich(X))))&
(~generous(john))&
(?[X]:((kind(X)|~calm(X)))) | strong(lucy) | [] | null | 0 |
Everyone who is either not rich or not humble is either patient or not creative. Everyone who is both not strong and rich is not humble. Everyone who is calm is not patient or not strong. If someone is quiet or brave then susan is tall. Everyone who is patient or not patient is happy or humble and vice versa. Everyone who is both not strong and patient is strong or not strong and vice versa. Everyone who is either not calm or not humble is wise and vice versa. Everyone who is both not strong and generous is quiet or not brave and vice versa. If fred is either patient or generous then fred is either not patient or not tall. Everyone who is not calm is both calm and not creative. Everyone who is generous is strong or wise and vice versa. Everyone who is either generous or not calm is both patient and funny. Everyone who is not brave is not wise or rich and vice versa. If susan is funny or humble then paul is either curious or strong. If fred is either strong or happy then fred is either tall or not quiet and vice versa. Everyone who is rich is both humble and brave. Someone is both not old and not tall. Someone is not humble or not creative. Someone is either not curious or old. Someone is either not brave or calm. Someone is not funny or not rich. Mary is either not generous or curious. Alice is either not tall or not wise. Someone is either not funny or calm. | Mary is not quiet. | contradiction | (![X]:((~rich(X)<~>~humble(X))=>(patient(X)<~>~creative(X))))&
(![X]:((~strong(X)&rich(X))=>~humble(X)))&
(![X]:(calm(X)=>(~patient(X)|~strong(X))))&
((?[X]:((quiet(X)|brave(X))))=>(tall(susan)))&
(![X]:((patient(X)|~patient(X))<=>(happy(X)|humble(X))))&
(![X]:((~strong(X)&patient(X))<=>(strong(X)|~strong(X))))&
(![X]:((~calm(X)<~>~humble(X))<=>wise(X)))&
(![X]:((~strong(X)&generous(X))<=>(quiet(X)|~brave(X))))&
(((patient(fred)<~>generous(fred)))=>((~patient(fred)<~>~tall(fred))))&
(![X]:(~calm(X)=>(calm(X)&~creative(X))))&
(![X]:(generous(X)<=>(strong(X)|wise(X))))&
(![X]:((generous(X)<~>~calm(X))=>(patient(X)&funny(X))))&
(![X]:(~brave(X)<=>(~wise(X)|rich(X))))&
(((funny(susan)|humble(susan)))=>((curious(paul)<~>strong(paul))))&
(((strong(fred)<~>happy(fred)))<=>((tall(fred)<~>~quiet(fred))))&
(![X]:(rich(X)=>(humble(X)&brave(X))))&
(?[X]:((~old(X)&~tall(X))))&
(?[X]:((~humble(X)|~creative(X))))&
(?[X]:((~curious(X)<~>old(X))))&
(?[X]:((~brave(X)<~>calm(X))))&
(?[X]:((~funny(X)|~rich(X))))&
((~generous(mary)<~>curious(mary)))&
((~tall(alice)<~>~wise(alice)))&
(?[X]:((~funny(X)<~>calm(X)))) | ~quiet(mary) | [
"p5",
"p7",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1791116999434181196742715
% SZS output start Proof for 1791116999434181196742715
6. ! [X0] : ((patient(X0) & ~strong(X0)) <=> (~strong(X0) | strong(X0))) [input p5]
8. ! [X0] : ((generous(X0) & ~strong(X0)) <=> (~brave(X0) | quiet(X0))) [input p7]
11. ! [X0] : (generous(X0) <=> (wise(X0) | strong(X0))) [input p10]
13. ! [X0] : (~brave(X0) <=> (rich(X0) | ~wise(X0))) [input p12]
16. ! [X0] : (rich(X0) => (brave(X0) & humble(X0))) [input p15]
25. ~quiet(mary) [input hypothesis]
36. ! [X0] : ((brave(X0) & humble(X0)) | ~rich(X0)) [ennf transformation 16]
40. ! [X0] : (((patient(X0) & ~strong(X0)) | (strong(X0) & ~strong(X0))) & ((~strong(X0) | strong(X0)) | (~patient(X0) | strong(X0)))) [nnf transformation 6]
41. ! [X0] : (((patient(X0) & ~strong(X0)) | (strong(X0) & ~strong(X0))) & (~strong(X0) | strong(X0) | ~patient(X0) | strong(X0))) [flattening 40]
43. ! [X0] : (((generous(X0) & ~strong(X0)) | (brave(X0) & ~quiet(X0))) & ((~brave(X0) | quiet(X0)) | (~generous(X0) | strong(X0)))) [nnf transformation 8]
44. ! [X0] : (((generous(X0) & ~strong(X0)) | (brave(X0) & ~quiet(X0))) & (~brave(X0) | quiet(X0) | ~generous(X0) | strong(X0))) [flattening 43]
46. ! [X0] : ((generous(X0) | (~wise(X0) & ~strong(X0))) & ((wise(X0) | strong(X0)) | ~generous(X0))) [nnf transformation 11]
47. ! [X0] : ((generous(X0) | (~wise(X0) & ~strong(X0))) & (wise(X0) | strong(X0) | ~generous(X0))) [flattening 46]
49. ! [X0] : ((~brave(X0) | (~rich(X0) & wise(X0))) & ((rich(X0) | ~wise(X0)) | brave(X0))) [nnf transformation 13]
50. ! [X0] : ((~brave(X0) | (~rich(X0) & wise(X0))) & (rich(X0) | ~wise(X0) | brave(X0))) [flattening 49]
83. ~strong(X0) | ~strong(X0) [cnf transformation 41]
91. ~brave(X0) | quiet(X0) | ~generous(X0) | strong(X0) [cnf transformation 44]
95. generous(X0) | brave(X0) [cnf transformation 44]
102. wise(X0) | strong(X0) | ~generous(X0) [cnf transformation 47]
104. ~wise(X0) | generous(X0) [cnf transformation 47]
109. ~wise(X0) | rich(X0) | brave(X0) [cnf transformation 50]
110. ~brave(X0) | wise(X0) [cnf transformation 50]
111. ~brave(X0) | ~rich(X0) [cnf transformation 50]
125. brave(X0) | ~rich(X0) [cnf transformation 36]
140. ~quiet(mary) [cnf transformation 25]
145. ~strong(X0) [duplicate literal removal 83]
160. ~generous(X0) | quiet(X0) | ~brave(X0) [subsumption resolution 91,145]
171. ~generous(X0) | wise(X0) [subsumption resolution 102,145]
205. ~rich(X0) [subsumption resolution 125,111]
259. wise(X0) | brave(X0) [resolution 171,95]
261. wise(X0) [subsumption resolution 259,110]
267. generous(X0) [resolution 261,104]
293. rich(X0) | brave(X0) [resolution 109,261]
294. brave(X0) [subsumption resolution 293,205]
295. quiet(X0) | ~brave(X0) [resolution 160,267]
299. quiet(X0) [subsumption resolution 295,294]
302. $false [resolution 299,140]
% SZS output end Proof for 1791116999434181196742715
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not old then susan is not calm and vice versa.
If someone is not humble then someone is both not wise and not happy and vice versa.
If someone is tall then someone is not rich or curious and vice versa.
Everyone who is both wise and not brave is both not strong and happy.
Everyone who is either not kind or strong is both rich and old.
If someone is both not rich and not patient then mary is either not kind or not old and vice versa.
Everyone who is humble is both not creative and tall.
If lucy is either not strong or creative then someone is either not old or wise.
If john is both patient and happy then lucy is not tall or not quiet.
Everyone who is patient is both not creative and wise.
If alice is happy then someone is either not patient or brave and vice versa.
Everyone who is rich is quiet or humble and vice versa.
Everyone who is either not kind or not strong is both wise and happy.
Everyone who is either calm or not generous is not generous.
Everyone who is patient is old or not patient and vice versa.
Everyone who is either not creative or creative is either not funny or kind and vice versa.
Someone is curious or creative.
Alice is either not calm or not rich.
Someone is rich.
Someone is either not quiet or kind.
Someone is not brave or not wise.
Someone is not creative.
Lucy is old. | Alice is old. | entailment | ((?[X]:((wise(X)|~old(X))))<=>(~calm(susan)))&
((?[X]:(~humble(X)))<=>(?[X]:((~wise(X)&~happy(X)))))&
((?[X]:(tall(X)))<=>(?[X]:((~rich(X)|curious(X)))))&
(![X]:((wise(X)&~brave(X))=>(~strong(X)&happy(X))))&
(![X]:((~kind(X)<~>strong(X))=>(rich(X)&old(X))))&
((?[X]:((~rich(X)&~patient(X))))<=>((~kind(mary)<~>~old(mary))))&
(![X]:(humble(X)=>(~creative(X)&tall(X))))&
(((~strong(lucy)<~>creative(lucy)))=>(?[X]:((~old(X)<~>wise(X)))))&
(((patient(john)&happy(john)))=>((~tall(lucy)|~quiet(lucy))))&
(![X]:(patient(X)=>(~creative(X)&wise(X))))&
((happy(alice))<=>(?[X]:((~patient(X)<~>brave(X)))))&
(![X]:(rich(X)<=>(quiet(X)|humble(X))))&
(![X]:((~kind(X)<~>~strong(X))=>(wise(X)&happy(X))))&
(![X]:((calm(X)<~>~generous(X))=>~generous(X)))&
(![X]:(patient(X)<=>(old(X)|~patient(X))))&
(![X]:((~creative(X)<~>creative(X))<=>(~funny(X)<~>kind(X))))&
(?[X]:((curious(X)|creative(X))))&
((~calm(alice)<~>~rich(alice)))&
(?[X]:(rich(X)))&
(?[X]:((~quiet(X)<~>kind(X))))&
(?[X]:((~brave(X)|~wise(X))))&
(?[X]:(~creative(X)))&
(old(lucy)) | old(alice) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 831152544031957829843252
% SZS output start Proof for 831152544031957829843252
15. ! [X0] : (patient(X0) <=> (~patient(X0) | old(X0))) [input p14]
24. ~old(alice) [input hypothesis]
67. ! [X0] : ((patient(X0) | (patient(X0) & ~old(X0))) & ((~patient(X0) | old(X0)) | ~patient(X0))) [nnf transformation 15]
68. ! [X0] : ((patient(X0) | (patient(X0) & ~old(X0))) & (~patient(X0) | old(X0) | ~patient(X0))) [flattening 67]
125. ~patient(X0) | old(X0) | ~patient(X0) [cnf transformation 68]
127. patient(X0) | patient(X0) [cnf transformation 68]
145. ~old(alice) [cnf transformation 24]
150. ~patient(X0) | old(X0) [duplicate literal removal 125]
151. patient(X0) [duplicate literal removal 127]
167. 4 <=> ! [X1] : old(X1) [avatar definition]
168. old(X1) <- (4) [avatar component clause 167]
303. old(X0) [subsumption resolution 150,151]
304. 4 [avatar split clause 303,167]
352. $false <- (4) [resolution 168,145]
353. ~4 [avatar contradiction clause 352]
354. $false [avatar sat refutation 304,353]
% SZS output end Proof for 831152544031957829843252
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or not tall is either kind or wise.
Everyone who is either not calm or not happy is either not kind or happy and vice versa.
Everyone who is old or not generous is not strong or not brave and vice versa.
Everyone who is either tall or not curious is old or tall and vice versa.
Everyone who is kind or not happy is both not wise and funny.
If someone is not quiet then mary is creative or not calm and vice versa.
Everyone who is both calm and tall is brave.
If lucy is generous then someone is curious.
Everyone who is patient or creative is generous or not kind.
Everyone who is wise or not generous is calm.
Everyone who is happy or humble is both creative and not strong and vice versa.
If lucy is kind or humble then someone is both kind and patient and vice versa.
Everyone who is patient is not creative and vice versa.
If someone is either not strong or funny then someone is either creative or patient and vice versa.
If someone is tall or funny then someone is either curious or patient and vice versa.
If someone is not generous or not happy then someone is both rich and patient.
Someone is calm or humble.
Fred is generous or tall.
Someone is either brave or not wise.
Someone is either generous or not strong.
Alice is either wise or old.
Alice is either not generous or not tall. | Fred is brave. | neutral | (![X]:((old(X)|~tall(X))=>(kind(X)<~>wise(X))))&
(![X]:((~calm(X)<~>~happy(X))<=>(~kind(X)<~>happy(X))))&
(![X]:((old(X)|~generous(X))<=>(~strong(X)|~brave(X))))&
(![X]:((tall(X)<~>~curious(X))<=>(old(X)|tall(X))))&
(![X]:((kind(X)|~happy(X))=>(~wise(X)&funny(X))))&
((?[X]:(~quiet(X)))<=>((creative(mary)|~calm(mary))))&
(![X]:((calm(X)&tall(X))=>brave(X)))&
((generous(lucy))=>(?[X]:(curious(X))))&
(![X]:((patient(X)|creative(X))=>(generous(X)|~kind(X))))&
(![X]:((wise(X)|~generous(X))=>calm(X)))&
(![X]:((happy(X)|humble(X))<=>(creative(X)&~strong(X))))&
(((kind(lucy)|humble(lucy)))<=>(?[X]:((kind(X)&patient(X)))))&
(![X]:(patient(X)<=>~creative(X)))&
((?[X]:((~strong(X)<~>funny(X))))<=>(?[X]:((creative(X)<~>patient(X)))))&
((?[X]:((tall(X)|funny(X))))<=>(?[X]:((curious(X)<~>patient(X)))))&
((?[X]:((~generous(X)|~happy(X))))=>(?[X]:((rich(X)&patient(X)))))&
(?[X]:((calm(X)|humble(X))))&
((generous(fred)|tall(fred)))&
(?[X]:((brave(X)<~>~wise(X))))&
(?[X]:((generous(X)<~>~strong(X))))&
((wise(alice)<~>old(alice)))&
((~generous(alice)<~>~tall(alice))) | brave(fred) | [] | null | 0 |
Everyone who is tall or not wise is tall.
If paul is either not wise or not funny then fred is not curious or not funny and vice versa.
If susan is either not strong or not wise then paul is funny and vice versa.
Everyone who is not patient or patient is either not calm or curious.
If someone is patient then mary is both funny and curious.
Everyone who is either not wise or brave is both patient and not patient.
If fred is not patient or not strong then someone is both not generous and not happy and vice versa.
Everyone who is creative is either rich or funny and vice versa.
Everyone who is not funny or wise is either not wise or not brave and vice versa.
Everyone who is not calm or happy is either not old or not patient.
Everyone who is either strong or old is both not humble and tall and vice versa.
Everyone who is both not kind and not quiet is not curious or not kind and vice versa.
Everyone who is either funny or brave is both happy and not brave.
Everyone who is either wise or not patient is not patient or curious and vice versa.
If someone is both quiet and not creative then someone is not curious or not old and vice versa.
If susan is either not curious or not patient then lucy is both not calm and not strong and vice versa.
Alice is either tall or not wise.
Susan is patient.
Alice is not humble.
Someone is either quiet or patient.
Someone is either not patient or not kind.
Someone is brave or not strong.
Paul is funny. | Lucy is not funny. | neutral | (![X]:((tall(X)|~wise(X))=>tall(X)))&
(((~wise(paul)<~>~funny(paul)))<=>((~curious(fred)|~funny(fred))))&
(((~strong(susan)<~>~wise(susan)))<=>(funny(paul)))&
(![X]:((~patient(X)|patient(X))=>(~calm(X)<~>curious(X))))&
((?[X]:(patient(X)))=>((funny(mary)&curious(mary))))&
(![X]:((~wise(X)<~>brave(X))=>(patient(X)&~patient(X))))&
(((~patient(fred)|~strong(fred)))<=>(?[X]:((~generous(X)&~happy(X)))))&
(![X]:(creative(X)<=>(rich(X)<~>funny(X))))&
(![X]:((~funny(X)|wise(X))<=>(~wise(X)<~>~brave(X))))&
(![X]:((~calm(X)|happy(X))=>(~old(X)<~>~patient(X))))&
(![X]:((strong(X)<~>old(X))<=>(~humble(X)&tall(X))))&
(![X]:((~kind(X)&~quiet(X))<=>(~curious(X)|~kind(X))))&
(![X]:((funny(X)<~>brave(X))=>(happy(X)&~brave(X))))&
(![X]:((wise(X)<~>~patient(X))<=>(~patient(X)|curious(X))))&
((?[X]:((quiet(X)&~creative(X))))<=>(?[X]:((~curious(X)|~old(X)))))&
(((~curious(susan)<~>~patient(susan)))<=>((~calm(lucy)&~strong(lucy))))&
((tall(alice)<~>~wise(alice)))&
(patient(susan))&
(~humble(alice))&
(?[X]:((quiet(X)<~>patient(X))))&
(?[X]:((~patient(X)<~>~kind(X))))&
(?[X]:((brave(X)|~strong(X))))&
(funny(paul)) | ~funny(lucy) | [] | null | 0 |
If someone is not calm then someone is both not happy and curious and vice versa. Everyone who is generous or not generous is either rich or patient and vice versa. Everyone who is both calm and funny is both strong and humble. Everyone who is kind is either calm or humble and vice versa. Everyone who is either calm or tall is wise or rich and vice versa. If lucy is both not kind and not strong then mary is both not tall and brave. If mary is not curious then someone is both not old and funny and vice versa. If someone is both happy and not generous then lucy is both tall and not wise. Everyone who is strong or old is both not funny and calm. Everyone who is either curious or not calm is creative and vice versa. If alice is both not patient and brave then someone is both not patient and not brave and vice versa. If john is curious then someone is either not kind or not strong. If someone is not brave then mary is either not happy or not humble. If mary is not tall then alice is not tall or rich and vice versa. If susan is not wise then someone is funny or not tall. Everyone who is both not creative and tall is either kind or not old and vice versa. John is both not old and not quiet. Mary is rich. Someone is not old or calm. Alice is not calm or creative. Someone is creative or calm. Someone is both not curious and funny. Someone is not happy. Someone is either not happy or not old. | Susan is not generous. | neutral | ((?[X]:(~calm(X)))<=>(?[X]:((~happy(X)&curious(X)))))&
(![X]:((generous(X)|~generous(X))<=>(rich(X)<~>patient(X))))&
(![X]:((calm(X)&funny(X))=>(strong(X)&humble(X))))&
(![X]:(kind(X)<=>(calm(X)<~>humble(X))))&
(![X]:((calm(X)<~>tall(X))<=>(wise(X)|rich(X))))&
(((~kind(lucy)&~strong(lucy)))=>((~tall(mary)&brave(mary))))&
((~curious(mary))<=>(?[X]:((~old(X)&funny(X)))))&
((?[X]:((happy(X)&~generous(X))))=>((tall(lucy)&~wise(lucy))))&
(![X]:((strong(X)|old(X))=>(~funny(X)&calm(X))))&
(![X]:((curious(X)<~>~calm(X))<=>creative(X)))&
(((~patient(alice)&brave(alice)))<=>(?[X]:((~patient(X)&~brave(X)))))&
((curious(john))=>(?[X]:((~kind(X)<~>~strong(X)))))&
((?[X]:(~brave(X)))=>((~happy(mary)<~>~humble(mary))))&
((~tall(mary))<=>((~tall(alice)|rich(alice))))&
((~wise(susan))=>(?[X]:((funny(X)|~tall(X)))))&
(![X]:((~creative(X)&tall(X))<=>(kind(X)<~>~old(X))))&
((~old(john)&~quiet(john)))&
(rich(mary))&
(?[X]:((~old(X)|calm(X))))&
((~calm(alice)|creative(alice)))&
(?[X]:((creative(X)|calm(X))))&
(?[X]:((~curious(X)&funny(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~happy(X)<~>~old(X)))) | ~generous(susan) | [] | null | 0 |
Everyone who is either not funny or tall is both calm and not calm and vice versa.
Everyone who is either not humble or rich is wise or not tall.
Everyone who is not quiet is either quiet or strong.
Everyone who is either not wise or funny is generous and vice versa.
Everyone who is either not generous or brave is either tall or not kind.
If someone is not old or not wise then lucy is both not patient and not funny.
If someone is not happy or curious then someone is both not brave and not creative.
Everyone who is either not generous or not humble is either not brave or not generous and vice versa.
Everyone who is either not wise or funny is both not brave and not curious and vice versa.
If lucy is either funny or not happy then alice is both patient and strong and vice versa.
If someone is both not patient and not kind then mary is not happy or strong and vice versa.
If someone is not curious then susan is brave and vice versa.
Everyone who is either generous or brave is either curious or rich.
Everyone who is wise is both not humble and not tall and vice versa.
If someone is creative or not quiet then alice is both tall and not calm.
Everyone who is both not old and calm is not wise.
Alice is not curious.
Someone is either tall or humble.
Mary is not tall.
Someone is not wise.
Mary is rich or creative.
Alice is both wise and not strong.
Someone is generous or happy.
John is not funny. | Susan is not funny. | contradiction | (![X]:((~funny(X)<~>tall(X))<=>(calm(X)&~calm(X))))&
(![X]:((~humble(X)<~>rich(X))=>(wise(X)|~tall(X))))&
(![X]:(~quiet(X)=>(quiet(X)<~>strong(X))))&
(![X]:((~wise(X)<~>funny(X))<=>generous(X)))&
(![X]:((~generous(X)<~>brave(X))=>(tall(X)<~>~kind(X))))&
((?[X]:((~old(X)|~wise(X))))=>((~patient(lucy)&~funny(lucy))))&
((?[X]:((~happy(X)|curious(X))))=>(?[X]:((~brave(X)&~creative(X)))))&
(![X]:((~generous(X)<~>~humble(X))<=>(~brave(X)<~>~generous(X))))&
(![X]:((~wise(X)<~>funny(X))<=>(~brave(X)&~curious(X))))&
(((funny(lucy)<~>~happy(lucy)))<=>((patient(alice)&strong(alice))))&
((?[X]:((~patient(X)&~kind(X))))<=>((~happy(mary)|strong(mary))))&
((?[X]:(~curious(X)))<=>(brave(susan)))&
(![X]:((generous(X)<~>brave(X))=>(curious(X)<~>rich(X))))&
(![X]:(wise(X)<=>(~humble(X)&~tall(X))))&
((?[X]:((creative(X)|~quiet(X))))=>((tall(alice)&~calm(alice))))&
(![X]:((~old(X)&calm(X))=>~wise(X)))&
(~curious(alice))&
(?[X]:((tall(X)<~>humble(X))))&
(~tall(mary))&
(?[X]:(~wise(X)))&
((rich(mary)|creative(mary)))&
((wise(alice)&~strong(alice)))&
(?[X]:((generous(X)|happy(X))))&
(~funny(john)) | ~funny(susan) | [
"p7",
"p8",
"p11",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 211928745855288726554672
% SZS output start Proof for 211928745855288726554672
8. ! [X0] : ((~generous(X0) <~> ~humble(X0)) <=> (~brave(X0) <~> ~generous(X0))) [input p7]
9. ! [X0] : ((~wise(X0) <~> funny(X0)) <=> (~curious(X0) & ~brave(X0))) [input p8]
12. ? [X0] : ~curious(X0) <=> brave(susan) [input p11]
14. ! [X0] : (wise(X0) <=> (~tall(X0) & ~humble(X0))) [input p13]
17. ~curious(alice) [input p16]
25. ~funny(susan) [input hypothesis]
46. ! [X0] : ((((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0)))) & (((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | ((~generous(X0) | humble(X0)) & (~humble(X0) | generous(X0))))) [nnf transformation 8]
47. ! [X0] : ((((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | (curious(X0) | brave(X0))) & ((~curious(X0) & ~brave(X0)) | ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0))))) [nnf transformation 9]
48. ! [X0] : ((((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | curious(X0) | brave(X0)) & ((~curious(X0) & ~brave(X0)) | ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0))))) [flattening 47]
56. (? [X0] : ~curious(X0) | ~brave(susan)) & (brave(susan) | ! [X0] : curious(X0)) [nnf transformation 12]
57. (? [X0] : ~curious(X0) | ~brave(susan)) & (brave(susan) | ! [X1] : curious(X1)) [rectify 56]
58. ? [X0] : ~curious(X0) => ~curious(sK2) [choice axiom]
59. (~curious(sK2) | ~brave(susan)) & (brave(susan) | ! [X1] : curious(X1)) [skolemisation 57,58]
61. ! [X0] : ((wise(X0) | (tall(X0) | humble(X0))) & ((~tall(X0) & ~humble(X0)) | ~wise(X0))) [nnf transformation 14]
62. ! [X0] : ((wise(X0) | tall(X0) | humble(X0)) & ((~tall(X0) & ~humble(X0)) | ~wise(X0))) [flattening 61]
95. ~generous(X0) | ~brave(X0) | ~generous(X0) | humble(X0) [cnf transformation 46]
101. humble(X0) | generous(X0) | ~brave(X0) | generous(X0) [cnf transformation 46]
102. ~brave(X0) | funny(X0) | wise(X0) [cnf transformation 48]
119. brave(susan) | curious(X1) [cnf transformation 59]
125. ~wise(X0) | ~humble(X0) [cnf transformation 62]
132. ~curious(alice) [cnf transformation 17]
142. ~funny(susan) [cnf transformation 25]
143. ~generous(X0) | ~brave(X0) | humble(X0) [duplicate literal removal 95]
146. humble(X0) | generous(X0) | ~brave(X0) [duplicate literal removal 101]
182. ~brave(X0) | humble(X0) [subsumption resolution 143,146]
226. 16 <=> brave(susan) [avatar definition]
227. brave(susan) <- (16) [avatar component clause 226]
235. 18 <=> ! [X1] : curious(X1) [avatar definition]
236. curious(X1) <- (18) [avatar component clause 235]
237. 18 | 16 [avatar split clause 119,226,235]
293. humble(susan) <- (16) [resolution 182,227]
316. funny(susan) | wise(susan) <- (16) [resolution 102,227]
317. wise(susan) <- (16) [subsumption resolution 316,142]
321. ~humble(susan) <- (16) [resolution 317,125]
322. $false <- (16) [subsumption resolution 321,293]
323. ~16 [avatar contradiction clause 322]
324. $false <- (18) [resolution 236,132]
327. ~18 [avatar contradiction clause 324]
328. $false [avatar sat refutation 237,323,327]
% SZS output end Proof for 211928745855288726554672
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is brave then someone is not funny or not happy. Everyone who is brave is either rich or generous. If mary is not patient then someone is both wise and not strong and vice versa. If someone is strong then someone is either not generous or calm. If susan is either not brave or kind then mary is not brave or not creative and vice versa. If someone is not patient then someone is not quiet or not humble and vice versa. If someone is kind or not brave then fred is not wise or not tall and vice versa. If someone is calm or not quiet then someone is not creative and vice versa. If paul is brave then lucy is not creative or strong and vice versa. If someone is brave then someone is both strong and not strong and vice versa. If susan is humble or not happy then alice is either quiet or tall and vice versa. Everyone who is either not kind or old is not patient. If someone is both not happy and rich then paul is not wise. If lucy is either not brave or tall then alice is either not strong or not patient and vice versa. Everyone who is both curious and funny is not curious. If alice is either not happy or not kind then susan is happy. Mary is strong or tall. Someone is rich or kind. Someone is either generous or happy. Susan is patient or strong. Susan is both not brave and quiet. Susan is either rich or not funny. Someone is both humble and not quiet. Fred is either not tall or not wise. | Susan is kind. | contradiction | ((?[X]:(brave(X)))=>(?[X]:((~funny(X)|~happy(X)))))&
(![X]:(brave(X)=>(rich(X)<~>generous(X))))&
((~patient(mary))<=>(?[X]:((wise(X)&~strong(X)))))&
((?[X]:(strong(X)))=>(?[X]:((~generous(X)<~>calm(X)))))&
(((~brave(susan)<~>kind(susan)))<=>((~brave(mary)|~creative(mary))))&
((?[X]:(~patient(X)))<=>(?[X]:((~quiet(X)|~humble(X)))))&
((?[X]:((kind(X)|~brave(X))))<=>((~wise(fred)|~tall(fred))))&
((?[X]:((calm(X)|~quiet(X))))<=>(?[X]:(~creative(X))))&
((brave(paul))<=>((~creative(lucy)|strong(lucy))))&
((?[X]:(brave(X)))<=>(?[X]:((strong(X)&~strong(X)))))&
(((humble(susan)|~happy(susan)))<=>((quiet(alice)<~>tall(alice))))&
(![X]:((~kind(X)<~>old(X))=>~patient(X)))&
((?[X]:((~happy(X)&rich(X))))=>(~wise(paul)))&
(((~brave(lucy)<~>tall(lucy)))<=>((~strong(alice)<~>~patient(alice))))&
(![X]:((curious(X)&funny(X))=>~curious(X)))&
(((~happy(alice)<~>~kind(alice)))=>(happy(susan)))&
((strong(mary)|tall(mary)))&
(?[X]:((rich(X)|kind(X))))&
(?[X]:((generous(X)<~>happy(X))))&
((patient(susan)|strong(susan)))&
((~brave(susan)&quiet(susan)))&
((rich(susan)<~>~funny(susan)))&
(?[X]:((humble(X)&~quiet(X))))&
((~tall(fred)<~>~wise(fred))) | kind(susan) | [
"p4",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4826227604172933848536849
% SZS output start Proof for 4826227604172933848536849
5. (~brave(susan) <~> kind(susan)) <=> (~creative(mary) | ~brave(mary)) [input p4]
10. ? [X0] : brave(X0) <=> ? [X0] : (~strong(X0) & strong(X0)) [input p9]
21. quiet(susan) & ~brave(susan) [input p20]
25. kind(susan) [input hypothesis]
30. ? [X0] : brave(X0) <=> ? [X1] : (~strong(X1) & strong(X1)) [rectify 10]
50. (((~kind(susan) | brave(susan)) & (kind(susan) | ~brave(susan))) | (creative(mary) & brave(mary))) & ((~creative(mary) | ~brave(mary)) | ((~brave(susan) | ~kind(susan)) & (kind(susan) | brave(susan)))) [nnf transformation 5]
51. (((~kind(susan) | brave(susan)) & (kind(susan) | ~brave(susan))) | (creative(mary) & brave(mary))) & (~creative(mary) | ~brave(mary) | ((~brave(susan) | ~kind(susan)) & (kind(susan) | brave(susan)))) [flattening 50]
69. (? [X0] : brave(X0) | ! [X1] : (strong(X1) | ~strong(X1))) & (? [X1] : (~strong(X1) & strong(X1)) | ! [X0] : ~brave(X0)) [nnf transformation 30]
70. (? [X0] : brave(X0) | ! [X1] : (strong(X1) | ~strong(X1))) & (? [X2] : (~strong(X2) & strong(X2)) | ! [X3] : ~brave(X3)) [rectify 69]
71. ? [X0] : brave(X0) => brave(sK8) [choice axiom]
72. ? [X2] : (~strong(X2) & strong(X2)) => (~strong(sK9) & strong(sK9)) [choice axiom]
73. (brave(sK8) | ! [X1] : (strong(X1) | ~strong(X1))) & ((~strong(sK9) & strong(sK9)) | ! [X3] : ~brave(X3)) [skolemisation 70,72,71]
100. ~kind(susan) | brave(susan) | brave(mary) [cnf transformation 51]
115. strong(sK9) | ~brave(X3) [cnf transformation 73]
116. ~strong(sK9) | ~brave(X3) [cnf transformation 73]
142. ~brave(susan) [cnf transformation 21]
150. kind(susan) [cnf transformation 25]
152. 1 <=> ! [X1] : ~brave(X1) [avatar definition]
153. ~brave(X1) <- (1) [avatar component clause 152]
199. 12 <=> brave(susan) [avatar definition]
203. 13 <=> kind(susan) [avatar definition]
208. 14 <=> brave(mary) [avatar definition]
210. brave(mary) <- (14) [avatar component clause 208]
211. 14 | 12 | ~13 [avatar split clause 100,203,199,208]
303. 35 <=> strong(sK9) [avatar definition]
306. 1 | ~35 [avatar split clause 116,303,152]
307. 1 | 35 [avatar split clause 115,303,152]
409. ~12 [avatar split clause 142,199]
422. 13 [avatar split clause 150,203]
423. $false <- (1, 14) [resolution 210,153]
424. ~1 | ~14 [avatar contradiction clause 423]
425. $false [avatar sat refutation 211,306,307,409,422,424]
% SZS output end Proof for 4826227604172933848536849
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or not patient is calm or tall.
Everyone who is both not rich and not humble is both generous and wise and vice versa.
Everyone who is not quiet or not old is calm and vice versa.
If john is not wise or curious then someone is not patient.
If paul is strong or old then paul is not tall and vice versa.
If someone is wise or kind then someone is both quiet and calm and vice versa.
If lucy is both happy and wise then susan is quiet and vice versa.
If alice is curious or brave then someone is tall or not humble.
Everyone who is not old or not humble is funny and vice versa.
If someone is either funny or not humble then someone is either brave or not calm and vice versa.
Everyone who is funny or not old is both wise and not strong and vice versa.
Everyone who is either strong or not funny is either not tall or tall and vice versa.
If fred is not tall or tall then someone is not curious and vice versa.
If someone is both not curious and happy then someone is both not humble and not wise.
If mary is not quiet or not strong then alice is kind or not tall.
If fred is either calm or not curious then lucy is not rich or brave.
Alice is both not tall and creative.
Someone is wise or not wise.
Someone is not funny.
Someone is both creative and happy.
Lucy is not old or not happy.
Lucy is wise or creative. | Susan is humble. | entailment | (![X]:((patient(X)|~patient(X))=>(calm(X)|tall(X))))&
(![X]:((~rich(X)&~humble(X))<=>(generous(X)&wise(X))))&
(![X]:((~quiet(X)|~old(X))<=>calm(X)))&
(((~wise(john)|curious(john)))=>(?[X]:(~patient(X))))&
(((strong(paul)|old(paul)))<=>(~tall(paul)))&
((?[X]:((wise(X)|kind(X))))<=>(?[X]:((quiet(X)&calm(X)))))&
(((happy(lucy)&wise(lucy)))<=>(quiet(susan)))&
(((curious(alice)|brave(alice)))=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((~old(X)|~humble(X))<=>funny(X)))&
((?[X]:((funny(X)<~>~humble(X))))<=>(?[X]:((brave(X)<~>~calm(X)))))&
(![X]:((funny(X)|~old(X))<=>(wise(X)&~strong(X))))&
(![X]:((strong(X)<~>~funny(X))<=>(~tall(X)<~>tall(X))))&
(((~tall(fred)|tall(fred)))<=>(?[X]:(~curious(X))))&
((?[X]:((~curious(X)&happy(X))))=>(?[X]:((~humble(X)&~wise(X)))))&
(((~quiet(mary)|~strong(mary)))=>((kind(alice)|~tall(alice))))&
(((calm(fred)<~>~curious(fred)))=>((~rich(lucy)|brave(lucy))))&
((~tall(alice)&creative(alice)))&
(?[X]:((wise(X)|~wise(X))))&
(?[X]:(~funny(X)))&
(?[X]:((creative(X)&happy(X))))&
((~old(lucy)|~happy(lucy)))&
((wise(lucy)|creative(lucy))) | humble(susan) | [
"p8",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8698367874228280171885583
% SZS output start Proof for 8698367874228280171885583
9. ! [X0] : ((~humble(X0) | ~old(X0)) <=> funny(X0)) [input p8]
11. ! [X0] : ((~old(X0) | funny(X0)) <=> (~strong(X0) & wise(X0))) [input p10]
12. ! [X0] : ((strong(X0) <~> ~funny(X0)) <=> (~tall(X0) <~> tall(X0))) [input p11]
23. ~humble(susan) [input hypothesis]
56. ! [X0] : (((~humble(X0) | ~old(X0)) | ~funny(X0)) & (funny(X0) | (humble(X0) & old(X0)))) [nnf transformation 9]
57. ! [X0] : ((~humble(X0) | ~old(X0) | ~funny(X0)) & (funny(X0) | (humble(X0) & old(X0)))) [flattening 56]
63. ! [X0] : (((~old(X0) | funny(X0)) | (strong(X0) | ~wise(X0))) & ((~strong(X0) & wise(X0)) | (old(X0) & ~funny(X0)))) [nnf transformation 11]
64. ! [X0] : ((~old(X0) | funny(X0) | strong(X0) | ~wise(X0)) & ((~strong(X0) & wise(X0)) | (old(X0) & ~funny(X0)))) [flattening 63]
65. ! [X0] : ((((funny(X0) | ~strong(X0)) & (~funny(X0) | strong(X0))) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) & (((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0))))) [nnf transformation 12]
106. funny(X0) | humble(X0) [cnf transformation 57]
118. ~strong(X0) | ~funny(X0) [cnf transformation 64]
125. ~funny(X0) | strong(X0) | tall(X0) | tall(X0) [cnf transformation 65]
126. ~funny(X0) | strong(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 65]
127. funny(X0) | ~strong(X0) | tall(X0) | tall(X0) [cnf transformation 65]
128. funny(X0) | ~strong(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 65]
143. ~humble(susan) [cnf transformation 23]
144. ~funny(X0) | strong(X0) | tall(X0) [duplicate literal removal 125]
145. ~funny(X0) | strong(X0) | ~tall(X0) [duplicate literal removal 126]
146. funny(X0) | ~strong(X0) | tall(X0) [duplicate literal removal 127]
147. funny(X0) | ~strong(X0) | ~tall(X0) [duplicate literal removal 128]
277. ~strong(X0) | ~tall(X0) [subsumption resolution 147,118]
278. ~strong(X0) | tall(X0) [subsumption resolution 146,118]
279. ~strong(X0) [subsumption resolution 278,277]
280. ~funny(X0) | ~tall(X0) [subsumption resolution 145,279]
281. ~funny(X0) | tall(X0) [subsumption resolution 144,279]
282. ~funny(X0) [subsumption resolution 281,280]
350. humble(X0) [resolution 106,282]
353. $false [resolution 350,143]
% SZS output end Proof for 8698367874228280171885583
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is happy. Everyone who is brave or not kind is not kind or rich and vice versa. Everyone who is either not old or wise is calm or brave and vice versa. Everyone who is not quiet or not strong is either funny or wise and vice versa. Everyone who is either curious or not strong is tall or not patient. Everyone who is calm or not old is not curious or not brave and vice versa. Everyone who is not brave is both not brave and not tall. Everyone who is not humble or humble is not rich or not creative. Everyone who is old is both not tall and generous and vice versa. Everyone who is either calm or curious is generous. Everyone who is not kind or strong is patient or not kind. Everyone who is either not humble or humble is both not curious and not creative. Everyone who is generous is not wise and vice versa. Everyone who is both rich and brave is both happy and not wise and vice versa. If someone is both not creative and happy then mary is both not brave and generous. If lucy is either not happy or rich then paul is either generous or calm. Someone is funny. Someone is either kind or not rich. Someone is brave or kind. | Paul is brave. | entailment | (![X]:(~tall(X)=>happy(X)))&
(![X]:((brave(X)|~kind(X))<=>(~kind(X)|rich(X))))&
(![X]:((~old(X)<~>wise(X))<=>(calm(X)|brave(X))))&
(![X]:((~quiet(X)|~strong(X))<=>(funny(X)<~>wise(X))))&
(![X]:((curious(X)<~>~strong(X))=>(tall(X)|~patient(X))))&
(![X]:((calm(X)|~old(X))<=>(~curious(X)|~brave(X))))&
(![X]:(~brave(X)=>(~brave(X)&~tall(X))))&
(![X]:((~humble(X)|humble(X))=>(~rich(X)|~creative(X))))&
(![X]:(old(X)<=>(~tall(X)&generous(X))))&
(![X]:((calm(X)<~>curious(X))=>generous(X)))&
(![X]:((~kind(X)|strong(X))=>(patient(X)|~kind(X))))&
(![X]:((~humble(X)<~>humble(X))=>(~curious(X)&~creative(X))))&
(![X]:(generous(X)<=>~wise(X)))&
(![X]:((rich(X)&brave(X))<=>(happy(X)&~wise(X))))&
((?[X]:((~creative(X)&happy(X))))=>((~brave(mary)&generous(mary))))&
(((~happy(lucy)<~>rich(lucy)))=>((generous(paul)<~>calm(paul))))&
(?[X]:(funny(X)))&
(?[X]:((kind(X)<~>~rich(X))))&
(?[X]:((brave(X)|kind(X)))) | brave(paul) | [
"p0",
"p2",
"p5",
"p6",
"p8",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7945455779515856266716009
% SZS output start Proof for 7945455779515856266716009
1. ! [X0] : (~tall(X0) => happy(X0)) [input p0]
3. ! [X0] : ((~old(X0) <~> wise(X0)) <=> (brave(X0) | calm(X0))) [input p2]
6. ! [X0] : ((~old(X0) | calm(X0)) <=> (~brave(X0) | ~curious(X0))) [input p5]
7. ! [X0] : (~brave(X0) => (~tall(X0) & ~brave(X0))) [input p6]
9. ! [X0] : (old(X0) <=> (generous(X0) & ~tall(X0))) [input p8]
12. ! [X0] : ((~humble(X0) <~> humble(X0)) => (~creative(X0) & ~curious(X0))) [input p11]
13. ! [X0] : (generous(X0) <=> ~wise(X0)) [input p12]
15. ? [X0] : (happy(X0) & ~creative(X0)) => (generous(mary) & ~brave(mary)) [input p14]
20. ~brave(paul) [input hypothesis]
21. ! [X0] : (happy(X0) | tall(X0)) [ennf transformation 1]
24. ! [X0] : ((~tall(X0) & ~brave(X0)) | brave(X0)) [ennf transformation 7]
30. ! [X0] : ((~creative(X0) & ~curious(X0)) | (~humble(X0) <=> humble(X0))) [ennf transformation 12]
31. (generous(mary) & ~brave(mary)) | ! [X0] : (~happy(X0) | creative(X0)) [ennf transformation 15]
35. ! [X0] : ((((~wise(X0) | old(X0)) & (wise(X0) | ~old(X0))) | (~brave(X0) & ~calm(X0))) & ((brave(X0) | calm(X0)) | ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0))))) [nnf transformation 3]
36. ! [X0] : ((((~wise(X0) | old(X0)) & (wise(X0) | ~old(X0))) | (~brave(X0) & ~calm(X0))) & (brave(X0) | calm(X0) | ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0))))) [flattening 35]
40. ! [X0] : (((~old(X0) | calm(X0)) | (brave(X0) & curious(X0))) & ((~brave(X0) | ~curious(X0)) | (old(X0) & ~calm(X0)))) [nnf transformation 6]
41. ! [X0] : ((~old(X0) | calm(X0) | (brave(X0) & curious(X0))) & (~brave(X0) | ~curious(X0) | (old(X0) & ~calm(X0)))) [flattening 40]
42. ! [X0] : ((old(X0) | (~generous(X0) | tall(X0))) & ((generous(X0) & ~tall(X0)) | ~old(X0))) [nnf transformation 9]
43. ! [X0] : ((old(X0) | ~generous(X0) | tall(X0)) & ((generous(X0) & ~tall(X0)) | ~old(X0))) [flattening 42]
45. ! [X0] : ((~creative(X0) & ~curious(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) [nnf transformation 30]
46. ! [X0] : ((generous(X0) | wise(X0)) & (~wise(X0) | ~generous(X0))) [nnf transformation 13]
57. happy(X0) | tall(X0) [cnf transformation 21]
64. ~calm(X0) | ~old(X0) | wise(X0) [cnf transformation 36]
79. ~old(X0) | calm(X0) | brave(X0) [cnf transformation 41]
81. ~tall(X0) | brave(X0) [cnf transformation 24]
86. ~generous(X0) | old(X0) | tall(X0) [cnf transformation 43]
93. ~creative(X0) | humble(X0) | humble(X0) [cnf transformation 45]
94. ~creative(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 45]
95. ~generous(X0) | ~wise(X0) [cnf transformation 46]
101. ~brave(mary) | ~happy(X0) | creative(X0) [cnf transformation 31]
102. generous(mary) | ~happy(X0) | creative(X0) [cnf transformation 31]
111. ~brave(paul) [cnf transformation 20]
114. ~creative(X0) | humble(X0) [duplicate literal removal 93]
115. ~creative(X0) | ~humble(X0) [duplicate literal removal 94]
117. ~creative(X0) [subsumption resolution 114,115]
119. generous(mary) | ~happy(X0) [subsumption resolution 102,117]
121. 1 <=> ! [X0] : ~happy(X0) [avatar definition]
122. ~happy(X0) <- (1) [avatar component clause 121]
124. 2 <=> generous(mary) [avatar definition]
126. generous(mary) <- (2) [avatar component clause 124]
127. 1 | 2 [avatar split clause 119,124,121]
128. ~brave(mary) | ~happy(X0) [subsumption resolution 101,117]
130. 3 <=> brave(mary) [avatar definition]
132. ~brave(mary) <- (~3) [avatar component clause 130]
133. 1 | ~3 [avatar split clause 128,130,121]
198. 14 <=> tall(mary) [avatar definition]
200. tall(mary) <- (14) [avatar component clause 198]
202. 15 <=> old(mary) [avatar definition]
204. old(mary) <- (15) [avatar component clause 202]
206. tall(X0) <- (1) [resolution 122,57]
208. brave(X0) <- (1) [resolution 206,81]
210. $false <- (1) [resolution 208,111]
213. ~1 [avatar contradiction clause 210]
214. old(mary) | tall(mary) <- (2) [resolution 126,86]
215. ~wise(mary) <- (2) [resolution 126,95]
216. brave(mary) <- (14) [resolution 200,81]
217. $false <- (~3, 14) [subsumption resolution 216,132]
218. 3 | ~14 [avatar contradiction clause 217]
219. 14 | 15 | ~2 [avatar split clause 214,124,202,198]
254. calm(mary) | brave(mary) <- (15) [resolution 204,79]
259. calm(mary) <- (~3, 15) [subsumption resolution 254,132]
296. ~old(mary) | wise(mary) <- (~3, 15) [resolution 259,64]
297. wise(mary) <- (~3, 15) [subsumption resolution 296,204]
298. $false <- (2, ~3, 15) [subsumption resolution 297,215]
299. ~2 | 3 | ~15 [avatar contradiction clause 298]
300. $false [avatar sat refutation 127,133,213,218,219,299]
% SZS output end Proof for 7945455779515856266716009
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is not creative or creative.
Everyone who is either not wise or quiet is either old or not generous.
Everyone who is either brave or strong is both not happy and old and vice versa.
Everyone who is both happy and not patient is both calm and not calm.
If someone is kind or patient then someone is funny or not wise and vice versa.
If someone is both calm and not calm then someone is generous.
If someone is either not quiet or not humble then someone is quiet or not kind and vice versa.
Everyone who is old is humble or brave and vice versa.
Everyone who is wise is both not wise and kind and vice versa.
If susan is curious or not brave then fred is either creative or not generous.
If susan is both tall and not brave then someone is funny.
Everyone who is both not generous and not quiet is not brave or not generous.
Everyone who is not generous or rich is not funny.
If mary is both not funny and not generous then someone is both not curious and not wise.
If someone is either not wise or not curious then someone is rich and vice versa.
If someone is not calm then someone is not calm or funny and vice versa.
Susan is not patient.
Fred is funny or brave.
Susan is not wise.
Someone is both not calm and strong.
Someone is not generous or not quiet.
Someone is not happy.
Someone is strong or not patient.
Lucy is either quiet or not curious. | Mary is not tall. | neutral | (![X]:(calm(X)=>(~creative(X)|creative(X))))&
(![X]:((~wise(X)<~>quiet(X))=>(old(X)<~>~generous(X))))&
(![X]:((brave(X)<~>strong(X))<=>(~happy(X)&old(X))))&
(![X]:((happy(X)&~patient(X))=>(calm(X)&~calm(X))))&
((?[X]:((kind(X)|patient(X))))<=>(?[X]:((funny(X)|~wise(X)))))&
((?[X]:((calm(X)&~calm(X))))=>(?[X]:(generous(X))))&
((?[X]:((~quiet(X)<~>~humble(X))))<=>(?[X]:((quiet(X)|~kind(X)))))&
(![X]:(old(X)<=>(humble(X)|brave(X))))&
(![X]:(wise(X)<=>(~wise(X)&kind(X))))&
(((curious(susan)|~brave(susan)))=>((creative(fred)<~>~generous(fred))))&
(((tall(susan)&~brave(susan)))=>(?[X]:(funny(X))))&
(![X]:((~generous(X)&~quiet(X))=>(~brave(X)|~generous(X))))&
(![X]:((~generous(X)|rich(X))=>~funny(X)))&
(((~funny(mary)&~generous(mary)))=>(?[X]:((~curious(X)&~wise(X)))))&
((?[X]:((~wise(X)<~>~curious(X))))<=>(?[X]:(rich(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~calm(X)|funny(X)))))&
(~patient(susan))&
((funny(fred)|brave(fred)))&
(~wise(susan))&
(?[X]:((~calm(X)&strong(X))))&
(?[X]:((~generous(X)|~quiet(X))))&
(?[X]:(~happy(X)))&
(?[X]:((strong(X)|~patient(X))))&
((quiet(lucy)<~>~curious(lucy))) | ~tall(mary) | [] | null | 0 |
Everyone who is rich is generous.
If susan is not kind then someone is not generous or not funny.
If lucy is either kind or not quiet then someone is both not curious and tall.
Everyone who is both old and not strong is both generous and creative and vice versa.
Everyone who is not generous or strong is either happy or not brave and vice versa.
Everyone who is calm or old is calm or not old and vice versa.
If someone is either not funny or patient then someone is both not quiet and not funny.
Everyone who is both tall and not kind is rich or curious and vice versa.
If john is not wise then paul is not generous.
Everyone who is either wise or kind is not brave and vice versa.
If someone is curious or not rich then someone is wise.
Everyone who is either not funny or not generous is not happy or brave.
Everyone who is not funny is creative and vice versa.
If lucy is happy or not quiet then someone is both not funny and not rich.
If john is not old then paul is either not happy or not creative.
Someone is both not creative and not kind.
Someone is not humble.
Fred is either not brave or not kind.
Alice is both patient and happy.
Fred is quiet or brave.
John is both happy and not tall.
Mary is calm or not tall.
Someone is not quiet or not happy. | John is happy. | entailment | (![X]:(rich(X)=>generous(X)))&
((~kind(susan))=>(?[X]:((~generous(X)|~funny(X)))))&
(((kind(lucy)<~>~quiet(lucy)))=>(?[X]:((~curious(X)&tall(X)))))&
(![X]:((old(X)&~strong(X))<=>(generous(X)&creative(X))))&
(![X]:((~generous(X)|strong(X))<=>(happy(X)<~>~brave(X))))&
(![X]:((calm(X)|old(X))<=>(calm(X)|~old(X))))&
((?[X]:((~funny(X)<~>patient(X))))=>(?[X]:((~quiet(X)&~funny(X)))))&
(![X]:((tall(X)&~kind(X))<=>(rich(X)|curious(X))))&
((~wise(john))=>(~generous(paul)))&
(![X]:((wise(X)<~>kind(X))<=>~brave(X)))&
((?[X]:((curious(X)|~rich(X))))=>(?[X]:(wise(X))))&
(![X]:((~funny(X)<~>~generous(X))=>(~happy(X)|brave(X))))&
(![X]:(~funny(X)<=>creative(X)))&
(((happy(lucy)|~quiet(lucy)))=>(?[X]:((~funny(X)&~rich(X)))))&
((~old(john))=>((~happy(paul)<~>~creative(paul))))&
(?[X]:((~creative(X)&~kind(X))))&
(?[X]:(~humble(X)))&
((~brave(fred)<~>~kind(fred)))&
((patient(alice)&happy(alice)))&
((quiet(fred)|brave(fred)))&
((happy(john)&~tall(john)))&
((calm(mary)|~tall(mary)))&
(?[X]:((~quiet(X)|~happy(X)))) | happy(john) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5920552281559182026172102
% SZS output start Proof for 5920552281559182026172102
21. ~tall(john) & happy(john) [input p20]
24. ~happy(john) [input hypothesis]
122. happy(john) [cnf transformation 21]
126. ~happy(john) [cnf transformation 24]
257. $false [subsumption resolution 126,122]
% SZS output end Proof for 5920552281559182026172102
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is wise or patient then alice is not calm or strong.
Everyone who is both happy and not humble is old.
If someone is either rich or not generous then paul is not quiet.
Everyone who is wise is both curious and not wise.
If someone is either generous or funny then someone is strong and vice versa.
If someone is either humble or not funny then someone is both strong and calm and vice versa.
If alice is not wise then someone is either patient or old and vice versa.
If john is not funny then fred is both not brave and wise.
Everyone who is both kind and not funny is not old.
Everyone who is either humble or not old is creative and vice versa.
Everyone who is either brave or not funny is brave and vice versa.
Everyone who is not happy is either quiet or not rich.
If john is either tall or strong then paul is brave or rich.
Everyone who is either patient or not rich is either old or happy and vice versa.
Everyone who is generous or not generous is not curious.
If someone is rich then someone is either strong or patient and vice versa.
Alice is both generous and not creative.
Someone is quiet or not tall.
Someone is either calm or wise.
Paul is both not quiet and not patient.
Someone is not quiet or wise.
Someone is both not curious and generous.
Lucy is either tall or not wise.
Fred is either strong or not calm. | Lucy is curious. | contradiction | ((?[X]:((wise(X)|patient(X))))=>((~calm(alice)|strong(alice))))&
(![X]:((happy(X)&~humble(X))=>old(X)))&
((?[X]:((rich(X)<~>~generous(X))))=>(~quiet(paul)))&
(![X]:(wise(X)=>(curious(X)&~wise(X))))&
((?[X]:((generous(X)<~>funny(X))))<=>(?[X]:(strong(X))))&
((?[X]:((humble(X)<~>~funny(X))))<=>(?[X]:((strong(X)&calm(X)))))&
((~wise(alice))<=>(?[X]:((patient(X)<~>old(X)))))&
((~funny(john))=>((~brave(fred)&wise(fred))))&
(![X]:((kind(X)&~funny(X))=>~old(X)))&
(![X]:((humble(X)<~>~old(X))<=>creative(X)))&
(![X]:((brave(X)<~>~funny(X))<=>brave(X)))&
(![X]:(~happy(X)=>(quiet(X)<~>~rich(X))))&
(((tall(john)<~>strong(john)))=>((brave(paul)|rich(paul))))&
(![X]:((patient(X)<~>~rich(X))<=>(old(X)<~>happy(X))))&
(![X]:((generous(X)|~generous(X))=>~curious(X)))&
((?[X]:(rich(X)))<=>(?[X]:((strong(X)<~>patient(X)))))&
((generous(alice)&~creative(alice)))&
(?[X]:((quiet(X)|~tall(X))))&
(?[X]:((calm(X)<~>wise(X))))&
((~quiet(paul)&~patient(paul)))&
(?[X]:((~quiet(X)|wise(X))))&
(?[X]:((~curious(X)&generous(X))))&
((tall(lucy)<~>~wise(lucy)))&
((strong(fred)<~>~calm(fred))) | curious(lucy) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8730148297094620918142157
% SZS output start Proof for 8730148297094620918142157
15. ! [X0] : ((~generous(X0) | generous(X0)) => ~curious(X0)) [input p14]
25. curious(lucy) [input hypothesis]
42. ! [X0] : (~curious(X0) | (generous(X0) & ~generous(X0))) [ennf transformation 15]
120. ~curious(X0) | ~generous(X0) [cnf transformation 42]
121. ~curious(X0) | generous(X0) [cnf transformation 42]
140. curious(lucy) [cnf transformation 25]
284. ~curious(X0) [subsumption resolution 120,121]
359. $false [subsumption resolution 140,284]
% SZS output end Proof for 8730148297094620918142157
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and brave is either rich or patient.
If someone is both rich and creative then susan is kind and vice versa.
Everyone who is rich or curious is both kind and patient and vice versa.
If susan is generous or creative then someone is either not happy or not humble.
Everyone who is either tall or quiet is both not tall and not funny and vice versa.
If someone is both not wise and not strong then paul is not humble or old.
If susan is either humble or not brave then paul is kind or tall and vice versa.
Everyone who is either not brave or tall is not happy or not tall.
Everyone who is patient or rich is either not brave or not rich.
Everyone who is not rich or generous is both not rich and not tall.
Everyone who is both calm and not tall is either patient or brave and vice versa.
If fred is wise or not funny then someone is either not quiet or not tall.
Everyone who is either not kind or not wise is both not tall and generous and vice versa.
If someone is either not wise or wise then alice is rich or not happy.
Everyone who is both not kind and curious is either curious or quiet.
If someone is rich or not old then john is both patient and not curious.
Lucy is both not strong and calm.
Someone is strong or rich.
Alice is either quiet or not kind.
Lucy is either not tall or curious.
Someone is quiet.
John is both humble and funny.
Someone is either quiet or not strong. | John is patient. | entailment | (![X]:((~rich(X)&brave(X))=>(rich(X)<~>patient(X))))&
((?[X]:((rich(X)&creative(X))))<=>(kind(susan)))&
(![X]:((rich(X)|curious(X))<=>(kind(X)&patient(X))))&
(((generous(susan)|creative(susan)))=>(?[X]:((~happy(X)<~>~humble(X)))))&
(![X]:((tall(X)<~>quiet(X))<=>(~tall(X)&~funny(X))))&
((?[X]:((~wise(X)&~strong(X))))=>((~humble(paul)|old(paul))))&
(((humble(susan)<~>~brave(susan)))<=>((kind(paul)|tall(paul))))&
(![X]:((~brave(X)<~>tall(X))=>(~happy(X)|~tall(X))))&
(![X]:((patient(X)|rich(X))=>(~brave(X)<~>~rich(X))))&
(![X]:((~rich(X)|generous(X))=>(~rich(X)&~tall(X))))&
(![X]:((calm(X)&~tall(X))<=>(patient(X)<~>brave(X))))&
(((wise(fred)|~funny(fred)))=>(?[X]:((~quiet(X)<~>~tall(X)))))&
(![X]:((~kind(X)<~>~wise(X))<=>(~tall(X)&generous(X))))&
((?[X]:((~wise(X)<~>wise(X))))=>((rich(alice)|~happy(alice))))&
(![X]:((~kind(X)&curious(X))=>(curious(X)<~>quiet(X))))&
((?[X]:((rich(X)|~old(X))))=>((patient(john)&~curious(john))))&
((~strong(lucy)&calm(lucy)))&
(?[X]:((strong(X)|rich(X))))&
((quiet(alice)<~>~kind(alice)))&
((~tall(lucy)<~>curious(lucy)))&
(?[X]:(quiet(X)))&
((humble(john)&funny(john)))&
(?[X]:((quiet(X)<~>~strong(X)))) | patient(john) | [
"p0",
"p8",
"p9",
"p10",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4103101385584588740513928
% SZS output start Proof for 4103101385584588740513928
1. ! [X0] : ((brave(X0) & ~rich(X0)) => (rich(X0) <~> patient(X0))) [input p0]
9. ! [X0] : ((rich(X0) | patient(X0)) => (~brave(X0) <~> ~rich(X0))) [input p8]
10. ! [X0] : ((generous(X0) | ~rich(X0)) => (~tall(X0) & ~rich(X0))) [input p9]
11. ! [X0] : ((~tall(X0) & calm(X0)) <=> (patient(X0) <~> brave(X0))) [input p10]
16. ? [X0] : (~old(X0) | rich(X0)) => (~curious(john) & patient(john)) [input p15]
17. calm(lucy) & ~strong(lucy) [input p16]
24. ~patient(john) [input hypothesis]
26. ? [X0] : rich(X0) => (~curious(john) & patient(john)) [pure predicate removal 16]
27. ! [X0] : ((rich(X0) <~> patient(X0)) | (~brave(X0) | rich(X0))) [ennf transformation 1]
28. ! [X0] : ((rich(X0) <~> patient(X0)) | ~brave(X0) | rich(X0)) [flattening 27]
32. ! [X0] : ((~brave(X0) <~> ~rich(X0)) | (~rich(X0) & ~patient(X0))) [ennf transformation 9]
33. ! [X0] : ((~tall(X0) & ~rich(X0)) | (~generous(X0) & rich(X0))) [ennf transformation 10]
39. (~curious(john) & patient(john)) | ! [X0] : ~rich(X0) [ennf transformation 26]
40. ! [X0] : (((~patient(X0) | ~rich(X0)) & (patient(X0) | rich(X0))) | ~brave(X0) | rich(X0)) [nnf transformation 28]
55. ! [X0] : (((rich(X0) | brave(X0)) & (~rich(X0) | ~brave(X0))) | (~rich(X0) & ~patient(X0))) [nnf transformation 32]
56. ! [X0] : (((~tall(X0) & calm(X0)) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0)))) & (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | (tall(X0) | ~calm(X0)))) [nnf transformation 11]
57. ! [X0] : (((~tall(X0) & calm(X0)) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0)))) & (((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | tall(X0) | ~calm(X0))) [flattening 56]
74. patient(X0) | rich(X0) | ~brave(X0) | rich(X0) [cnf transformation 40]
104. ~patient(X0) | brave(X0) | rich(X0) [cnf transformation 55]
108. ~tall(X0) | rich(X0) [cnf transformation 33]
110. ~calm(X0) | patient(X0) | tall(X0) | brave(X0) [cnf transformation 57]
111. ~calm(X0) | ~patient(X0) | tall(X0) | ~brave(X0) [cnf transformation 57]
130. patient(john) | ~rich(X0) [cnf transformation 39]
133. calm(lucy) [cnf transformation 17]
144. ~patient(john) [cnf transformation 24]
152. ~brave(X0) | rich(X0) | patient(X0) [duplicate literal removal 74]
256. 21 <=> ! [X0] : ~rich(X0) [avatar definition]
257. ~rich(X0) <- (21) [avatar component clause 256]
264. 23 <=> patient(john) [avatar definition]
267. 21 | 23 [avatar split clause 130,264,256]
288. 28 <=> tall(lucy) [avatar definition]
289. ~tall(lucy) <- (~28) [avatar component clause 288]
290. tall(lucy) <- (28) [avatar component clause 288]
307. ~23 [avatar split clause 144,264]
337. patient(lucy) | tall(lucy) | brave(lucy) [resolution 110,133]
340. 36 <=> brave(lucy) [avatar definition]
341. ~brave(lucy) <- (~36) [avatar component clause 340]
342. brave(lucy) <- (36) [avatar component clause 340]
344. 37 <=> patient(lucy) [avatar definition]
345. ~patient(lucy) <- (~37) [avatar component clause 344]
346. patient(lucy) <- (37) [avatar component clause 344]
348. 36 | 28 | 37 [avatar split clause 337,344,288,340]
349. rich(lucy) <- (28) [resolution 290,108]
356. $false <- (21, 28) [subsumption resolution 349,257]
357. ~21 | ~28 [avatar contradiction clause 356]
374. ~patient(lucy) | tall(lucy) | ~brave(lucy) [resolution 111,133]
375. ~patient(lucy) | ~brave(lucy) <- (~28) [subsumption resolution 374,289]
378. rich(lucy) | patient(lucy) <- (36) [resolution 342,152]
381. patient(lucy) <- (21, 36) [subsumption resolution 378,257]
382. $false <- (21, 36, ~37) [subsumption resolution 381,345]
383. ~21 | ~36 | 37 [avatar contradiction clause 382]
384. ~36 | ~37 | 28 [avatar split clause 375,288,344,340]
386. brave(lucy) | rich(lucy) <- (37) [resolution 346,104]
387. rich(lucy) <- (~36, 37) [subsumption resolution 386,341]
388. $false <- (21, ~36, 37) [subsumption resolution 387,257]
389. ~21 | 36 | ~37 [avatar contradiction clause 388]
390. $false [avatar sat refutation 267,307,348,357,383,384,389]
% SZS output end Proof for 4103101385584588740513928
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or humble is not calm and vice versa. Everyone who is calm or funny is either not generous or generous. If someone is both creative and happy then fred is not wise. Everyone who is both not funny and tall is both old and not patient. Everyone who is both creative and quiet is both not tall and not humble. If someone is not generous or not quiet then someone is both calm and happy and vice versa. Everyone who is both not wise and not curious is either not tall or tall and vice versa. Everyone who is curious or tall is not rich or happy and vice versa. If someone is not rich or humble then paul is not humble or strong and vice versa. If someone is not rich then fred is not curious or funny. Everyone who is funny is both calm and curious. Everyone who is not generous or tall is either not wise or not funny. Everyone who is not happy or not curious is kind or happy and vice versa. If alice is either strong or tall then someone is either wise or old. Everyone who is either not curious or creative is not funny and vice versa. John is not kind or not wise. Someone is funny or not wise. Susan is not creative. Someone is either creative or not humble. Someone is not strong or not generous. | Susan is wise. | contradiction | (![X]:((funny(X)<~>humble(X))<=>~calm(X)))&
(![X]:((calm(X)|funny(X))=>(~generous(X)<~>generous(X))))&
((?[X]:((creative(X)&happy(X))))=>(~wise(fred)))&
(![X]:((~funny(X)&tall(X))=>(old(X)&~patient(X))))&
(![X]:((creative(X)&quiet(X))=>(~tall(X)&~humble(X))))&
((?[X]:((~generous(X)|~quiet(X))))<=>(?[X]:((calm(X)&happy(X)))))&
(![X]:((~wise(X)&~curious(X))<=>(~tall(X)<~>tall(X))))&
(![X]:((curious(X)|tall(X))<=>(~rich(X)|happy(X))))&
((?[X]:((~rich(X)|humble(X))))<=>((~humble(paul)|strong(paul))))&
((?[X]:(~rich(X)))=>((~curious(fred)|funny(fred))))&
(![X]:(funny(X)=>(calm(X)&curious(X))))&
(![X]:((~generous(X)|tall(X))=>(~wise(X)<~>~funny(X))))&
(![X]:((~happy(X)|~curious(X))<=>(kind(X)|happy(X))))&
(((strong(alice)<~>tall(alice)))=>(?[X]:((wise(X)<~>old(X)))))&
(![X]:((~curious(X)<~>creative(X))<=>~funny(X)))&
((~kind(john)|~wise(john)))&
(?[X]:((funny(X)|~wise(X))))&
(~creative(susan))&
(?[X]:((creative(X)<~>~humble(X))))&
(?[X]:((~strong(X)|~generous(X)))) | wise(susan) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 5228874043733103035586517
% SZS output start Proof for 5228874043733103035586517
7. ! [X0] : ((~curious(X0) & ~wise(X0)) <=> (~tall(X0) <~> tall(X0))) [input p6]
21. wise(susan) [input hypothesis]
42. ! [X0] : (((~curious(X0) & ~wise(X0)) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) & (((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | (curious(X0) | wise(X0)))) [nnf transformation 7]
43. ! [X0] : (((~curious(X0) & ~wise(X0)) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) & (((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | curious(X0) | wise(X0))) [flattening 42]
84. ~wise(X0) | tall(X0) | tall(X0) [cnf transformation 43]
85. ~wise(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 43]
121. wise(susan) [cnf transformation 21]
124. ~wise(X0) | tall(X0) [duplicate literal removal 84]
125. ~wise(X0) | ~tall(X0) [duplicate literal removal 85]
167. ~wise(X0) [subsumption resolution 124,125]
226. $false [subsumption resolution 121,167]
% SZS output end Proof for 5228874043733103035586517
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious or not generous is either not funny or not patient and vice versa.
Everyone who is not tall is funny or not tall and vice versa.
If someone is kind or not rich then fred is not funny or brave.
If alice is curious or not tall then mary is not old and vice versa.
If someone is not old or generous then someone is either not rich or strong.
If alice is not funny then someone is quiet or not funny.
If fred is not strong or not brave then mary is either funny or quiet.
Everyone who is not rich or not creative is creative or strong and vice versa.
Everyone who is both not generous and curious is both not funny and strong and vice versa.
Everyone who is either humble or not humble is either funny or not happy and vice versa.
Everyone who is brave or not curious is rich.
Everyone who is wise is generous or not wise and vice versa.
If someone is both wise and humble then someone is not brave or not strong.
If someone is not curious then someone is either tall or not tall and vice versa.
Everyone who is happy is either not calm or not tall and vice versa.
Everyone who is either kind or creative is not calm.
Paul is patient.
Someone is either not happy or quiet.
Someone is either not tall or not brave.
Someone is not curious.
Fred is either rich or not rich.
Mary is both calm and kind.
Someone is not calm or funny. | Paul is curious. | neutral | (![X]:((curious(X)|~generous(X))<=>(~funny(X)<~>~patient(X))))&
(![X]:(~tall(X)<=>(funny(X)|~tall(X))))&
((?[X]:((kind(X)|~rich(X))))=>((~funny(fred)|brave(fred))))&
(((curious(alice)|~tall(alice)))<=>(~old(mary)))&
((?[X]:((~old(X)|generous(X))))=>(?[X]:((~rich(X)<~>strong(X)))))&
((~funny(alice))=>(?[X]:((quiet(X)|~funny(X)))))&
(((~strong(fred)|~brave(fred)))=>((funny(mary)<~>quiet(mary))))&
(![X]:((~rich(X)|~creative(X))<=>(creative(X)|strong(X))))&
(![X]:((~generous(X)&curious(X))<=>(~funny(X)&strong(X))))&
(![X]:((humble(X)<~>~humble(X))<=>(funny(X)<~>~happy(X))))&
(![X]:((brave(X)|~curious(X))=>rich(X)))&
(![X]:(wise(X)<=>(generous(X)|~wise(X))))&
((?[X]:((wise(X)&humble(X))))=>(?[X]:((~brave(X)|~strong(X)))))&
((?[X]:(~curious(X)))<=>(?[X]:((tall(X)<~>~tall(X)))))&
(![X]:(happy(X)<=>(~calm(X)<~>~tall(X))))&
(![X]:((kind(X)<~>creative(X))=>~calm(X)))&
(patient(paul))&
(?[X]:((~happy(X)<~>quiet(X))))&
(?[X]:((~tall(X)<~>~brave(X))))&
(?[X]:(~curious(X)))&
((rich(fred)<~>~rich(fred)))&
((calm(mary)&kind(mary)))&
(?[X]:((~calm(X)|funny(X)))) | curious(paul) | [] | null | 0 |
If alice is not funny then lucy is strong and vice versa. If john is not wise or humble then fred is both wise and creative and vice versa. If fred is generous then mary is not wise or not funny. If fred is both wise and not funny then paul is both not humble and old. Everyone who is either patient or not patient is both creative and funny and vice versa. If susan is both not kind and old then susan is not old. Everyone who is not kind is not wise or funny and vice versa. Everyone who is not kind or rich is either not quiet or calm. If lucy is humble then alice is curious and vice versa. Everyone who is not generous or patient is not creative and vice versa. Everyone who is both rich and strong is both generous and not curious. Everyone who is humble is not patient or not humble. Everyone who is not humble or tall is both funny and wise. If someone is patient or not quiet then paul is not patient or strong and vice versa. Everyone who is not happy or not patient is not strong and vice versa. Someone is both curious and not old. Fred is not strong. Alice is either not generous or calm. Fred is tall. Alice is generous. Someone is funny or not patient. Someone is not patient. | Lucy is not kind. | entailment | ((~funny(alice))<=>(strong(lucy)))&
(((~wise(john)|humble(john)))<=>((wise(fred)&creative(fred))))&
((generous(fred))=>((~wise(mary)|~funny(mary))))&
(((wise(fred)&~funny(fred)))=>((~humble(paul)&old(paul))))&
(![X]:((patient(X)<~>~patient(X))<=>(creative(X)&funny(X))))&
(((~kind(susan)&old(susan)))=>(~old(susan)))&
(![X]:(~kind(X)<=>(~wise(X)|funny(X))))&
(![X]:((~kind(X)|rich(X))=>(~quiet(X)<~>calm(X))))&
((humble(lucy))<=>(curious(alice)))&
(![X]:((~generous(X)|patient(X))<=>~creative(X)))&
(![X]:((rich(X)&strong(X))=>(generous(X)&~curious(X))))&
(![X]:(humble(X)=>(~patient(X)|~humble(X))))&
(![X]:((~humble(X)|tall(X))=>(funny(X)&wise(X))))&
((?[X]:((patient(X)|~quiet(X))))<=>((~patient(paul)|strong(paul))))&
(![X]:((~happy(X)|~patient(X))<=>~strong(X)))&
(?[X]:((curious(X)&~old(X))))&
(~strong(fred))&
((~generous(alice)<~>calm(alice)))&
(tall(fred))&
(generous(alice))&
(?[X]:((funny(X)|~patient(X))))&
(?[X]:(~patient(X))) | ~kind(lucy) | [
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 1301128823968192868196490
% SZS output start Proof for 1301128823968192868196490
5. ! [X0] : ((patient(X0) <~> ~patient(X0)) <=> (funny(X0) & creative(X0))) [input p4]
7. ! [X0] : (~kind(X0) <=> (funny(X0) | ~wise(X0))) [input p6]
23. kind(lucy) [input hypothesis]
24. ! [X0] : ((funny(X0) | ~wise(X0)) => ~kind(X0)) [unused predicate definition removal 7]
33. ! [X0] : (~kind(X0) | (~funny(X0) & wise(X0))) [ennf transformation 24]
41. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | (~funny(X0) | ~creative(X0))) & ((funny(X0) & creative(X0)) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [nnf transformation 5]
42. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | ~funny(X0) | ~creative(X0)) & ((funny(X0) & creative(X0)) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [flattening 41]
73. funny(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 42]
74. funny(X0) | patient(X0) | patient(X0) [cnf transformation 42]
79. ~kind(X0) | ~funny(X0) [cnf transformation 33]
108. kind(lucy) [cnf transformation 23]
113. funny(X0) | ~patient(X0) [duplicate literal removal 73]
114. funny(X0) | patient(X0) [duplicate literal removal 74]
173. funny(X0) [subsumption resolution 113,114]
184. ~kind(X0) [subsumption resolution 79,173]
214. $false [subsumption resolution 108,184]
% SZS output end Proof for 1301128823968192868196490
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet then lucy is generous or not patient and vice versa.
If someone is calm or not tall then someone is either strong or patient.
Everyone who is either not patient or rich is not humble and vice versa.
Everyone who is not tall or funny is not funny.
Everyone who is strong is not funny or not brave.
Everyone who is not old is happy or kind.
Everyone who is both humble and not strong is both rich and tall.
If paul is not funny then someone is rich or wise.
If alice is not old or calm then mary is quiet.
If lucy is not quiet then susan is either not kind or not happy and vice versa.
If someone is happy or not old then someone is both not strong and patient.
Everyone who is not creative or happy is either tall or not quiet and vice versa.
If someone is both not funny and old then someone is not brave or not kind.
Everyone who is both not strong and old is not humble or not wise and vice versa.
If mary is both not creative and old then someone is not kind or creative and vice versa.
Everyone who is not strong or calm is both old and funny and vice versa.
Paul is either not creative or rich.
Someone is either not happy or patient.
Someone is calm or not kind.
Lucy is strong.
Someone is not humble or patient. | Lucy is not happy. | entailment | ((?[X]:(quiet(X)))<=>((generous(lucy)|~patient(lucy))))&
((?[X]:((calm(X)|~tall(X))))=>(?[X]:((strong(X)<~>patient(X)))))&
(![X]:((~patient(X)<~>rich(X))<=>~humble(X)))&
(![X]:((~tall(X)|funny(X))=>~funny(X)))&
(![X]:(strong(X)=>(~funny(X)|~brave(X))))&
(![X]:(~old(X)=>(happy(X)|kind(X))))&
(![X]:((humble(X)&~strong(X))=>(rich(X)&tall(X))))&
((~funny(paul))=>(?[X]:((rich(X)|wise(X)))))&
(((~old(alice)|calm(alice)))=>(quiet(mary)))&
((~quiet(lucy))<=>((~kind(susan)<~>~happy(susan))))&
((?[X]:((happy(X)|~old(X))))=>(?[X]:((~strong(X)&patient(X)))))&
(![X]:((~creative(X)|happy(X))<=>(tall(X)<~>~quiet(X))))&
((?[X]:((~funny(X)&old(X))))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((~strong(X)&old(X))<=>(~humble(X)|~wise(X))))&
(((~creative(mary)&old(mary)))<=>(?[X]:((~kind(X)|creative(X)))))&
(![X]:((~strong(X)|calm(X))<=>(old(X)&funny(X))))&
((~creative(paul)<~>rich(paul)))&
(?[X]:((~happy(X)<~>patient(X))))&
(?[X]:((calm(X)|~kind(X))))&
(strong(lucy))&
(?[X]:((~humble(X)|patient(X)))) | ~happy(lucy) | [
"p3",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4914604003293830711708823
% SZS output start Proof for 4914604003293830711708823
4. ! [X0] : ((funny(X0) | ~tall(X0)) => ~funny(X0)) [input p3]
11. ? [X0] : (~old(X0) | happy(X0)) => ? [X0] : (patient(X0) & ~strong(X0)) [input p10]
16. ! [X0] : ((calm(X0) | ~strong(X0)) <=> (funny(X0) & old(X0))) [input p15]
22. happy(lucy) [input hypothesis]
24. ? [X0] : (~old(X0) | happy(X0)) => ? [X1] : (patient(X1) & ~strong(X1)) [rectify 11]
29. ! [X0] : (~funny(X0) | (~funny(X0) & tall(X0))) [ennf transformation 4]
36. ? [X1] : (patient(X1) & ~strong(X1)) | ! [X0] : (old(X0) & ~happy(X0)) [ennf transformation 24]
50. ? [X0] : (patient(X0) & ~strong(X0)) | ! [X1] : (old(X1) & ~happy(X1)) [rectify 36]
51. ? [X0] : (patient(X0) & ~strong(X0)) => (patient(sK3) & ~strong(sK3)) [choice axiom]
52. (patient(sK3) & ~strong(sK3)) | ! [X1] : (old(X1) & ~happy(X1)) [skolemisation 50,51]
62. ! [X0] : (((calm(X0) | ~strong(X0)) | (~funny(X0) | ~old(X0))) & ((funny(X0) & old(X0)) | (~calm(X0) & strong(X0)))) [nnf transformation 16]
63. ! [X0] : ((calm(X0) | ~strong(X0) | ~funny(X0) | ~old(X0)) & ((funny(X0) & old(X0)) | (~calm(X0) & strong(X0)))) [flattening 62]
84. ~funny(X0) | ~funny(X0) [cnf transformation 29]
95. ~strong(sK3) | ~happy(X1) [cnf transformation 52]
117. funny(X0) | strong(X0) [cnf transformation 63]
127. happy(lucy) [cnf transformation 22]
128. ~funny(X0) [duplicate literal removal 84]
214. 19 <=> ! [X1] : ~happy(X1) [avatar definition]
215. ~happy(X1) <- (19) [avatar component clause 214]
218. 20 <=> strong(sK3) [avatar definition]
220. ~strong(sK3) <- (~20) [avatar component clause 218]
222. 19 | ~20 [avatar split clause 95,218,214]
252. strong(X0) [subsumption resolution 117,128]
291. $false <- (~20) [subsumption resolution 220,252]
292. 20 [avatar contradiction clause 291]
293. $false <- (19) [resolution 215,127]
296. ~19 [avatar contradiction clause 293]
297. $false [avatar sat refutation 222,292,296]
% SZS output end Proof for 4914604003293830711708823
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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 not strong. | entailment | (![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 1024485937966112206841710
% SZS output start Proof for 1024485937966112206841710
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 1024485937966112206841710
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or quiet is not brave.
If alice is humble then someone is both rich and not old.
If susan is not funny or not quiet then paul is either rich or not funny and vice versa.
Everyone who is either not old or old is brave and vice versa.
Everyone who is old or not old is not creative or not wise and vice versa.
Everyone who is not creative is not creative or rich.
If someone is old or not old then susan is strong or tall and vice versa.
Everyone who is not kind or not curious is both generous and wise and vice versa.
If someone is both old and calm then someone is both wise and generous and vice versa.
Everyone who is not kind or creative is funny or patient.
Everyone who is both generous and not tall is either generous or not funny and vice versa.
If fred is old then fred is both calm and old and vice versa.
Everyone who is not quiet is both not humble and not happy.
Everyone who is either not humble or curious is both not humble and not brave and vice versa.
If someone is either creative or not curious then john is funny or generous and vice versa.
Everyone who is rich is either tall or not patient.
Someone is not wise.
Someone is both generous and funny.
Alice is wise or patient.
Someone is either curious or calm.
Someone is both funny and curious. | John is not brave. | contradiction | (![X]:((~rich(X)|quiet(X))=>~brave(X)))&
((humble(alice))=>(?[X]:((rich(X)&~old(X)))))&
(((~funny(susan)|~quiet(susan)))<=>((rich(paul)<~>~funny(paul))))&
(![X]:((~old(X)<~>old(X))<=>brave(X)))&
(![X]:((old(X)|~old(X))<=>(~creative(X)|~wise(X))))&
(![X]:(~creative(X)=>(~creative(X)|rich(X))))&
((?[X]:((old(X)|~old(X))))<=>((strong(susan)|tall(susan))))&
(![X]:((~kind(X)|~curious(X))<=>(generous(X)&wise(X))))&
((?[X]:((old(X)&calm(X))))<=>(?[X]:((wise(X)&generous(X)))))&
(![X]:((~kind(X)|creative(X))=>(funny(X)|patient(X))))&
(![X]:((generous(X)&~tall(X))<=>(generous(X)<~>~funny(X))))&
((old(fred))<=>((calm(fred)&old(fred))))&
(![X]:(~quiet(X)=>(~humble(X)&~happy(X))))&
(![X]:((~humble(X)<~>curious(X))<=>(~humble(X)&~brave(X))))&
((?[X]:((creative(X)<~>~curious(X))))<=>((funny(john)|generous(john))))&
(![X]:(rich(X)=>(tall(X)<~>~patient(X))))&
(?[X]:(~wise(X)))&
(?[X]:((generous(X)&funny(X))))&
((wise(alice)|patient(alice)))&
(?[X]:((curious(X)<~>calm(X))))&
(?[X]:((funny(X)&curious(X)))) | ~brave(john) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 639278504697575424434300
% SZS output start Proof for 639278504697575424434300
4. ! [X0] : ((~old(X0) <~> old(X0)) <=> brave(X0)) [input p3]
22. ~brave(john) [input hypothesis]
37. ! [X0] : ((((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | ~brave(X0)) & (brave(X0) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0))))) [nnf transformation 4]
83. brave(X0) | old(X0) | old(X0) [cnf transformation 37]
84. brave(X0) | ~old(X0) | ~old(X0) [cnf transformation 37]
139. ~brave(john) [cnf transformation 22]
144. brave(X0) | old(X0) [duplicate literal removal 83]
145. brave(X0) | ~old(X0) [duplicate literal removal 84]
182. brave(X0) [subsumption resolution 144,145]
277. $false [subsumption resolution 139,182]
% SZS output end Proof for 639278504697575424434300
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or not creative is both not old and not tall.
If susan is not quiet then someone is brave or not humble.
If someone is both funny and not curious then mary is either patient or tall.
Everyone who is old is not patient or tall and vice versa.
Everyone who is happy is not generous and vice versa.
Everyone who is either not old or not rich is either not wise or wise.
Everyone who is rich is either not creative or not patient.
If someone is both tall and not patient then susan is either not tall or patient.
If someone is not kind or not happy then someone is humble.
If someone is not strong then susan is both not tall and not humble and vice versa.
Everyone who is both not quiet and quiet is both not quiet and not generous and vice versa.
If alice is either not generous or not wise then lucy is both not rich and funny.
Everyone who is not quiet or not old is not strong and vice versa.
Everyone who is not brave or not curious is brave or not humble.
If fred is either strong or not rich then someone is not strong or not creative.
Mary is either old or quiet.
Susan is both not creative and calm.
Fred is strong or not kind.
Alice is tall.
John is either calm or generous.
Someone is both wise and not old.
Lucy is either not wise or rich.
Fred is strong or not funny. | Susan is not curious. | neutral | (![X]:((~happy(X)|~creative(X))=>(~old(X)&~tall(X))))&
((~quiet(susan))=>(?[X]:((brave(X)|~humble(X)))))&
((?[X]:((funny(X)&~curious(X))))=>((patient(mary)<~>tall(mary))))&
(![X]:(old(X)<=>(~patient(X)|tall(X))))&
(![X]:(happy(X)<=>~generous(X)))&
(![X]:((~old(X)<~>~rich(X))=>(~wise(X)<~>wise(X))))&
(![X]:(rich(X)=>(~creative(X)<~>~patient(X))))&
((?[X]:((tall(X)&~patient(X))))=>((~tall(susan)<~>patient(susan))))&
((?[X]:((~kind(X)|~happy(X))))=>(?[X]:(humble(X))))&
((?[X]:(~strong(X)))<=>((~tall(susan)&~humble(susan))))&
(![X]:((~quiet(X)&quiet(X))<=>(~quiet(X)&~generous(X))))&
(((~generous(alice)<~>~wise(alice)))=>((~rich(lucy)&funny(lucy))))&
(![X]:((~quiet(X)|~old(X))<=>~strong(X)))&
(![X]:((~brave(X)|~curious(X))=>(brave(X)|~humble(X))))&
(((strong(fred)<~>~rich(fred)))=>(?[X]:((~strong(X)|~creative(X)))))&
((old(mary)<~>quiet(mary)))&
((~creative(susan)&calm(susan)))&
((strong(fred)|~kind(fred)))&
(tall(alice))&
((calm(john)<~>generous(john)))&
(?[X]:((wise(X)&~old(X))))&
((~wise(lucy)<~>rich(lucy)))&
((strong(fred)|~funny(fred))) | ~curious(susan) | [] | null | 0 |
If someone is not calm or not happy then mary is strong and vice versa.
If someone is not curious or not quiet then fred is kind or creative.
If lucy is not rich or patient then lucy is wise.
Everyone who is either calm or humble is both rich and tall and vice versa.
Everyone who is both rich and calm is not wise and vice versa.
Everyone who is both quiet and creative is either not tall or not generous.
If someone is curious then someone is either not kind or not happy and vice versa.
If paul is not wise or not old then someone is either generous or brave.
Everyone who is kind or generous is both rich and brave.
Everyone who is not quiet is funny or strong.
Everyone who is not patient is not old and vice versa.
If someone is funny then mary is not quiet.
Everyone who is either happy or patient is either not wise or kind and vice versa.
Everyone who is funny or not curious is not wise.
If someone is both patient and brave then lucy is not brave or not curious and vice versa.
If someone is not old then fred is either wise or rich and vice versa.
Someone is quiet.
Paul is both not brave and not humble.
John is not rich.
Someone is not old or not wise.
Alice is not quiet.
Someone is strong.
Someone is not old or generous. | Alice is not creative. | neutral | ((?[X]:((~calm(X)|~happy(X))))<=>(strong(mary)))&
((?[X]:((~curious(X)|~quiet(X))))=>((kind(fred)|creative(fred))))&
(((~rich(lucy)|patient(lucy)))=>(wise(lucy)))&
(![X]:((calm(X)<~>humble(X))<=>(rich(X)&tall(X))))&
(![X]:((rich(X)&calm(X))<=>~wise(X)))&
(![X]:((quiet(X)&creative(X))=>(~tall(X)<~>~generous(X))))&
((?[X]:(curious(X)))<=>(?[X]:((~kind(X)<~>~happy(X)))))&
(((~wise(paul)|~old(paul)))=>(?[X]:((generous(X)<~>brave(X)))))&
(![X]:((kind(X)|generous(X))=>(rich(X)&brave(X))))&
(![X]:(~quiet(X)=>(funny(X)|strong(X))))&
(![X]:(~patient(X)<=>~old(X)))&
((?[X]:(funny(X)))=>(~quiet(mary)))&
(![X]:((happy(X)<~>patient(X))<=>(~wise(X)<~>kind(X))))&
(![X]:((funny(X)|~curious(X))=>~wise(X)))&
((?[X]:((patient(X)&brave(X))))<=>((~brave(lucy)|~curious(lucy))))&
((?[X]:(~old(X)))<=>((wise(fred)<~>rich(fred))))&
(?[X]:(quiet(X)))&
((~brave(paul)&~humble(paul)))&
(~rich(john))&
(?[X]:((~old(X)|~wise(X))))&
(~quiet(alice))&
(?[X]:(strong(X)))&
(?[X]:((~old(X)|generous(X)))) | ~creative(alice) | [] | null | 0 |
Everyone who is not tall is not old or not happy and vice versa.
Everyone who is quiet is brave or not happy.
Everyone who is both strong and wise is patient.
Everyone who is strong or not generous is curious and vice versa.
Everyone who is tall is not wise or not calm and vice versa.
Everyone who is both quiet and not rich is both not humble and old and vice versa.
If someone is humble or old then lucy is both not wise and funny.
Everyone who is both humble and old is not funny or not quiet.
If mary is both not brave and not funny then someone is both not strong and humble and vice versa.
Everyone who is either strong or old is not humble or not wise and vice versa.
If someone is funny then paul is not brave and vice versa.
If paul is not tall or not generous then someone is both not patient and funny.
If fred is both not kind and not calm then someone is either funny or brave.
If someone is both funny and creative then mary is both not creative and not strong and vice versa.
Everyone who is either quiet or creative is wise.
Someone is kind or not generous.
Susan is both not old and wise.
Fred is not brave.
Alice is not patient.
Someone is either creative or not generous.
Someone is not strong or not tall.
Someone is both strong and quiet.
Mary is both not strong and not curious. | Paul is not brave. | entailment | (![X]:(~tall(X)<=>(~old(X)|~happy(X))))&
(![X]:(quiet(X)=>(brave(X)|~happy(X))))&
(![X]:((strong(X)&wise(X))=>patient(X)))&
(![X]:((strong(X)|~generous(X))<=>curious(X)))&
(![X]:(tall(X)<=>(~wise(X)|~calm(X))))&
(![X]:((quiet(X)&~rich(X))<=>(~humble(X)&old(X))))&
((?[X]:((humble(X)|old(X))))=>((~wise(lucy)&funny(lucy))))&
(![X]:((humble(X)&old(X))=>(~funny(X)|~quiet(X))))&
(((~brave(mary)&~funny(mary)))<=>(?[X]:((~strong(X)&humble(X)))))&
(![X]:((strong(X)<~>old(X))<=>(~humble(X)|~wise(X))))&
((?[X]:(funny(X)))<=>(~brave(paul)))&
(((~tall(paul)|~generous(paul)))=>(?[X]:((~patient(X)&funny(X)))))&
(((~kind(fred)&~calm(fred)))=>(?[X]:((funny(X)<~>brave(X)))))&
((?[X]:((funny(X)&creative(X))))<=>((~creative(mary)&~strong(mary))))&
(![X]:((quiet(X)<~>creative(X))=>wise(X)))&
(?[X]:((kind(X)|~generous(X))))&
((~old(susan)&wise(susan)))&
(~brave(fred))&
(~patient(alice))&
(?[X]:((creative(X)<~>~generous(X))))&
(?[X]:((~strong(X)|~tall(X))))&
(?[X]:((strong(X)&quiet(X))))&
((~strong(mary)&~curious(mary))) | ~brave(paul) | [
"p0",
"p6",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7406282855036319528791201
% SZS output start Proof for 7406282855036319528791201
1. ! [X0] : (~tall(X0) <=> (~happy(X0) | ~old(X0))) [input p0]
7. ? [X0] : (old(X0) | humble(X0)) => (funny(lucy) & ~wise(lucy)) [input p6]
11. ? [X0] : funny(X0) <=> ~brave(paul) [input p10]
12. (~generous(paul) | ~tall(paul)) => ? [X0] : (funny(X0) & ~patient(X0)) [input p11]
24. brave(paul) [input hypothesis]
33. (funny(lucy) & ~wise(lucy)) | ! [X0] : (~old(X0) & ~humble(X0)) [ennf transformation 7]
36. ? [X0] : (funny(X0) & ~patient(X0)) | (generous(paul) & tall(paul)) [ennf transformation 12]
38. ! [X0] : ((~tall(X0) | (happy(X0) & old(X0))) & ((~happy(X0) | ~old(X0)) | tall(X0))) [nnf transformation 1]
39. ! [X0] : ((~tall(X0) | (happy(X0) & old(X0))) & (~happy(X0) | ~old(X0) | tall(X0))) [flattening 38]
51. (? [X0] : funny(X0) | brave(paul)) & (~brave(paul) | ! [X0] : ~funny(X0)) [nnf transformation 11]
52. (? [X0] : funny(X0) | brave(paul)) & (~brave(paul) | ! [X1] : ~funny(X1)) [rectify 51]
53. ? [X0] : funny(X0) => funny(sK1) [choice axiom]
54. (funny(sK1) | brave(paul)) & (~brave(paul) | ! [X1] : ~funny(X1)) [skolemisation 52,53]
55. ? [X0] : (funny(X0) & ~patient(X0)) => (funny(sK2) & ~patient(sK2)) [choice axiom]
56. (funny(sK2) & ~patient(sK2)) | (generous(paul) & tall(paul)) [skolemisation 36,55]
71. ~tall(X0) | old(X0) [cnf transformation 39]
87. funny(lucy) | ~old(X0) [cnf transformation 33]
99. ~brave(paul) | ~funny(X1) [cnf transformation 54]
103. funny(sK2) | tall(paul) [cnf transformation 56]
122. brave(paul) [cnf transformation 24]
124. 1 <=> ! [X0] : ~old(X0) [avatar definition]
125. ~old(X0) <- (1) [avatar component clause 124]
127. 2 <=> funny(lucy) [avatar definition]
129. funny(lucy) <- (2) [avatar component clause 127]
130. 1 | 2 [avatar split clause 87,127,124]
165. 10 <=> brave(paul) [avatar definition]
174. 12 <=> ! [X1] : ~funny(X1) [avatar definition]
175. ~funny(X1) <- (12) [avatar component clause 174]
176. 12 | ~10 [avatar split clause 99,165,174]
182. 14 <=> funny(sK2) [avatar definition]
184. funny(sK2) <- (14) [avatar component clause 182]
187. 15 <=> tall(paul) [avatar definition]
189. tall(paul) <- (15) [avatar component clause 187]
190. 15 | 14 [avatar split clause 103,182,187]
240. 10 [avatar split clause 122,165]
243. $false <- (2, 12) [subsumption resolution 129,175]
244. ~2 | ~12 [avatar contradiction clause 243]
245. $false <- (12, 14) [resolution 184,175]
246. ~12 | ~14 [avatar contradiction clause 245]
249. old(paul) <- (15) [resolution 71,189]
250. $false <- (1, 15) [subsumption resolution 249,125]
251. ~1 | ~15 [avatar contradiction clause 250]
252. $false [avatar sat refutation 130,176,190,240,244,246,251]
% SZS output end Proof for 7406282855036319528791201
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is wise or not rich then susan is not patient or curious. Everyone who is not creative or not strong is both not brave and not strong and vice versa. If someone is not tall or curious then someone is both not happy and generous and vice versa. Everyone who is wise or not quiet is either not brave or strong. Everyone who is either not curious or tall is both not patient and not calm and vice versa. If paul is curious or not humble then someone is not brave or funny and vice versa. If someone is not calm then fred is both wise and happy. If someone is not rich then paul is old and vice versa. Everyone who is not kind is not patient or not generous. If someone is kind or not creative then someone is either not happy or not patient and vice versa. Everyone who is not quiet or generous is either patient or curious and vice versa. Everyone who is quiet or humble is either not humble or not brave and vice versa. If someone is not brave then paul is either quiet or curious and vice versa. If someone is either not curious or not calm then someone is both not strong and not brave. Everyone who is not kind or not curious is either not happy or not tall. If mary is generous or not brave then someone is either not strong or not rich and vice versa. Paul is wise or not generous. Someone is both wise and patient. Lucy is happy or kind. Lucy is strong. John is either not kind or rich. Paul is either not calm or not strong. John is either kind or not humble. | Mary is happy. | neutral | ((?[X]:((wise(X)|~rich(X))))=>((~patient(susan)|curious(susan))))&
(![X]:((~creative(X)|~strong(X))<=>(~brave(X)&~strong(X))))&
((?[X]:((~tall(X)|curious(X))))<=>(?[X]:((~happy(X)&generous(X)))))&
(![X]:((wise(X)|~quiet(X))=>(~brave(X)<~>strong(X))))&
(![X]:((~curious(X)<~>tall(X))<=>(~patient(X)&~calm(X))))&
(((curious(paul)|~humble(paul)))<=>(?[X]:((~brave(X)|funny(X)))))&
((?[X]:(~calm(X)))=>((wise(fred)&happy(fred))))&
((?[X]:(~rich(X)))<=>(old(paul)))&
(![X]:(~kind(X)=>(~patient(X)|~generous(X))))&
((?[X]:((kind(X)|~creative(X))))<=>(?[X]:((~happy(X)<~>~patient(X)))))&
(![X]:((~quiet(X)|generous(X))<=>(patient(X)<~>curious(X))))&
(![X]:((quiet(X)|humble(X))<=>(~humble(X)<~>~brave(X))))&
((?[X]:(~brave(X)))<=>((quiet(paul)<~>curious(paul))))&
((?[X]:((~curious(X)<~>~calm(X))))=>(?[X]:((~strong(X)&~brave(X)))))&
(![X]:((~kind(X)|~curious(X))=>(~happy(X)<~>~tall(X))))&
(((generous(mary)|~brave(mary)))<=>(?[X]:((~strong(X)<~>~rich(X)))))&
((wise(paul)|~generous(paul)))&
(?[X]:((wise(X)&patient(X))))&
((happy(lucy)|kind(lucy)))&
(strong(lucy))&
((~kind(john)<~>rich(john)))&
((~calm(paul)<~>~strong(paul)))&
((kind(john)<~>~humble(john))) | happy(mary) | [] | null | 0 |
Everyone who is not kind is both strong and tall and vice versa.
If someone is rich then alice is either not quiet or not curious and vice versa.
If mary is both not brave and not curious then alice is calm or brave.
If someone is not generous then someone is not happy or calm and vice versa.
If john is happy then susan is generous and vice versa.
If someone is either patient or kind then someone is kind or not kind and vice versa.
Everyone who is both not rich and rich is old or tall.
Everyone who is not funny is both curious and not patient and vice versa.
Everyone who is not humble or patient is wise and vice versa.
Everyone who is not kind is both wise and patient and vice versa.
Everyone who is not funny is either not brave or brave and vice versa.
If someone is both kind and wise then fred is both not humble and not wise.
If someone is both not rich and generous then someone is happy or old and vice versa.
If someone is not old then alice is not kind or quiet and vice versa.
Everyone who is funny is both humble and creative.
Everyone who is kind is not quiet and vice versa.
Lucy is not tall or not strong.
Susan is both humble and creative.
Susan is creative or not calm.
Alice is both not rich and not happy.
Someone is creative or not old.
Someone is not rich or wise. | Lucy is funny. | contradiction | (![X]:(~kind(X)<=>(strong(X)&tall(X))))&
((?[X]:(rich(X)))<=>((~quiet(alice)<~>~curious(alice))))&
(((~brave(mary)&~curious(mary)))=>((calm(alice)|brave(alice))))&
((?[X]:(~generous(X)))<=>(?[X]:((~happy(X)|calm(X)))))&
((happy(john))<=>(generous(susan)))&
((?[X]:((patient(X)<~>kind(X))))<=>(?[X]:((kind(X)|~kind(X)))))&
(![X]:((~rich(X)&rich(X))=>(old(X)|tall(X))))&
(![X]:(~funny(X)<=>(curious(X)&~patient(X))))&
(![X]:((~humble(X)|patient(X))<=>wise(X)))&
(![X]:(~kind(X)<=>(wise(X)&patient(X))))&
(![X]:(~funny(X)<=>(~brave(X)<~>brave(X))))&
((?[X]:((kind(X)&wise(X))))=>((~humble(fred)&~wise(fred))))&
((?[X]:((~rich(X)&generous(X))))<=>(?[X]:((happy(X)|old(X)))))&
((?[X]:(~old(X)))<=>((~kind(alice)|quiet(alice))))&
(![X]:(funny(X)=>(humble(X)&creative(X))))&
(![X]:(kind(X)<=>~quiet(X)))&
((~tall(lucy)|~strong(lucy)))&
((humble(susan)&creative(susan)))&
((creative(susan)|~calm(susan)))&
((~rich(alice)&~happy(alice)))&
(?[X]:((creative(X)|~old(X))))&
(?[X]:((~rich(X)|wise(X)))) | funny(lucy) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 519955480806041126015162
% SZS output start Proof for 519955480806041126015162
11. ! [X0] : (~funny(X0) <=> (~brave(X0) <~> brave(X0))) [input p10]
23. funny(lucy) [input hypothesis]
60. ! [X0] : ((~funny(X0) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) & (((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | funny(X0))) [nnf transformation 11]
105. ~funny(X0) | brave(X0) | brave(X0) [cnf transformation 60]
106. ~funny(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 60]
125. funny(lucy) [cnf transformation 23]
126. ~funny(X0) | brave(X0) [duplicate literal removal 105]
127. ~funny(X0) | ~brave(X0) [duplicate literal removal 106]
217. ~funny(X0) [subsumption resolution 126,127]
293. $false [subsumption resolution 125,217]
% SZS output end Proof for 519955480806041126015162
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and not calm is either wise or not brave.
If fred is not rich or not creative then someone is rich.
Everyone who is either not old or not curious is not old or curious.
Everyone who is funny is not calm or not strong.
Everyone who is not generous is quiet and vice versa.
Everyone who is not rich or happy is both not patient and not wise and vice versa.
If someone is either not funny or not rich then alice is both brave and not tall and vice versa.
If someone is funny or generous then someone is both strong and generous and vice versa.
If paul is either strong or old then someone is either not brave or not rich and vice versa.
If susan is either not wise or not kind then someone is either generous or not brave.
Everyone who is both creative and strong is either not kind or not old.
If someone is kind or not strong then paul is both generous and not rich.
If susan is both happy and calm then someone is both not brave and happy.
Everyone who is tall is rich or kind and vice versa.
If john is either not calm or patient then someone is either funny or not curious.
If mary is humble then john is not strong and vice versa.
Paul is either creative or not generous.
Alice is strong or humble.
Paul is both happy and quiet.
Susan is not humble or not strong.
Lucy is generous.
Fred is both not curious and not rich.
Someone is humble.
Someone is calm or curious. | Fred is rich. | contradiction | (![X]:((funny(X)&~calm(X))=>(wise(X)<~>~brave(X))))&
(((~rich(fred)|~creative(fred)))=>(?[X]:(rich(X))))&
(![X]:((~old(X)<~>~curious(X))=>(~old(X)|curious(X))))&
(![X]:(funny(X)=>(~calm(X)|~strong(X))))&
(![X]:(~generous(X)<=>quiet(X)))&
(![X]:((~rich(X)|happy(X))<=>(~patient(X)&~wise(X))))&
((?[X]:((~funny(X)<~>~rich(X))))<=>((brave(alice)&~tall(alice))))&
((?[X]:((funny(X)|generous(X))))<=>(?[X]:((strong(X)&generous(X)))))&
(((strong(paul)<~>old(paul)))<=>(?[X]:((~brave(X)<~>~rich(X)))))&
(((~wise(susan)<~>~kind(susan)))=>(?[X]:((generous(X)<~>~brave(X)))))&
(![X]:((creative(X)&strong(X))=>(~kind(X)<~>~old(X))))&
((?[X]:((kind(X)|~strong(X))))=>((generous(paul)&~rich(paul))))&
(((happy(susan)&calm(susan)))=>(?[X]:((~brave(X)&happy(X)))))&
(![X]:(tall(X)<=>(rich(X)|kind(X))))&
(((~calm(john)<~>patient(john)))=>(?[X]:((funny(X)<~>~curious(X)))))&
((humble(mary))<=>(~strong(john)))&
((creative(paul)<~>~generous(paul)))&
((strong(alice)|humble(alice)))&
((happy(paul)&quiet(paul)))&
((~humble(susan)|~strong(susan)))&
(generous(lucy))&
((~curious(fred)&~rich(fred)))&
(?[X]:(humble(X)))&
(?[X]:((calm(X)|curious(X)))) | rich(fred) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3315272301461287119342180
% SZS output start Proof for 3315272301461287119342180
22. ~rich(fred) & ~curious(fred) [input p21]
25. rich(fred) [input hypothesis]
141. ~rich(fred) [cnf transformation 22]
144. rich(fred) [cnf transformation 25]
156. 3 <=> rich(fred) [avatar definition]
358. ~3 [avatar split clause 141,156]
368. 3 [avatar split clause 144,156]
369. $false [avatar sat refutation 358,368]
% SZS output end Proof for 3315272301461287119342180
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and not brave is both not kind and kind and vice versa.
If someone is either calm or tall then someone is funny and vice versa.
Everyone who is not calm or quiet is both not wise and not generous.
If susan is not calm then someone is both not humble and not rich.
Everyone who is both not patient and not humble is not old or curious.
Everyone who is either patient or not strong is both not calm and brave and vice versa.
Everyone who is not strong is kind or not calm and vice versa.
If susan is old or not tall then someone is quiet.
If someone is both quiet and happy then fred is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is not curious or not calm is not calm and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
If someone is both brave and curious then susan is not humble or curious and vice versa.
If someone is both kind and quiet then someone is strong or not old.
Someone is not rich or not funny.
Mary is not quiet.
Mary is both tall and not humble.
Someone is either not quiet or not creative. | Fred is kind. | contradiction | (![X]:((kind(X)&~brave(X))<=>(~kind(X)&kind(X))))&
((?[X]:((calm(X)<~>tall(X))))<=>(?[X]:(funny(X))))&
(![X]:((~calm(X)|quiet(X))=>(~wise(X)&~generous(X))))&
((~calm(susan))=>(?[X]:((~humble(X)&~rich(X)))))&
(![X]:((~patient(X)&~humble(X))=>(~old(X)|curious(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
((?[X]:((brave(X)&curious(X))))<=>((~humble(susan)|curious(susan))))&
((?[X]:((kind(X)&quiet(X))))=>(?[X]:((strong(X)|~old(X)))))&
(?[X]:((~rich(X)|~funny(X))))&
(~quiet(mary))&
((tall(mary)&~humble(mary)))&
(?[X]:((~quiet(X)<~>~creative(X)))) | kind(fred) | [
"p0",
"p2",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8499185506581253010208752
% SZS output start Proof for 8499185506581253010208752
1. ! [X0] : ((~brave(X0) & kind(X0)) <=> (kind(X0) & ~kind(X0))) [input p0]
3. ! [X0] : ((quiet(X0) | ~calm(X0)) => (~generous(X0) & ~wise(X0))) [input p2]
10. ! [X0] : ((~rich(X0) | ~wise(X0)) => (~brave(X0) & ~happy(X0))) [input p9]
12. ! [X0] : ((~calm(X0) | ~curious(X0)) <=> ~calm(X0)) [input p11]
13. ! [X0] : ((rich(X0) <~> curious(X0)) <=> (~quiet(X0) | brave(X0))) [input p12]
20. kind(fred) [input hypothesis]
26. ! [X0] : ((~generous(X0) & ~wise(X0)) | (~quiet(X0) & calm(X0))) [ennf transformation 3]
29. ! [X0] : ((~brave(X0) & ~happy(X0)) | (rich(X0) & wise(X0))) [ennf transformation 10]
30. ! [X0] : (((~brave(X0) & kind(X0)) | (~kind(X0) | kind(X0))) & ((kind(X0) & ~kind(X0)) | (brave(X0) | ~kind(X0)))) [nnf transformation 1]
31. ! [X0] : (((~brave(X0) & kind(X0)) | ~kind(X0) | kind(X0)) & ((kind(X0) & ~kind(X0)) | brave(X0) | ~kind(X0))) [flattening 30]
52. ! [X0] : (((~calm(X0) | ~curious(X0)) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [nnf transformation 12]
53. ! [X0] : ((~calm(X0) | ~curious(X0) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [flattening 52]
54. ! [X0] : ((((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | (quiet(X0) & ~brave(X0))) & ((~quiet(X0) | brave(X0)) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0))))) [nnf transformation 13]
55. ! [X0] : ((((~curious(X0) | ~rich(X0)) & (curious(X0) | rich(X0))) | (quiet(X0) & ~brave(X0))) & (~quiet(X0) | brave(X0) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0))))) [flattening 54]
66. ~kind(X0) | brave(X0) | ~kind(X0) [cnf transformation 31]
74. ~wise(X0) | calm(X0) [cnf transformation 26]
75. ~wise(X0) | ~quiet(X0) [cnf transformation 26]
97. ~brave(X0) | wise(X0) [cnf transformation 29]
98. ~brave(X0) | rich(X0) [cnf transformation 29]
105. ~calm(X0) | curious(X0) [cnf transformation 53]
113. ~curious(X0) | ~rich(X0) | quiet(X0) [cnf transformation 55]
125. kind(fred) [cnf transformation 20]
128. ~kind(X0) | brave(X0) [duplicate literal removal 66]
253. brave(fred) [resolution 128,125]
254. rich(fred) [resolution 253,98]
255. wise(fred) [resolution 253,97]
257. ~quiet(fred) [resolution 255,75]
258. calm(fred) [resolution 255,74]
292. curious(fred) [resolution 258,105]
445. ~rich(fred) | quiet(fred) [resolution 292,113]
448. quiet(fred) [subsumption resolution 445,254]
449. $false [subsumption resolution 448,257]
% SZS output end Proof for 8499185506581253010208752
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is either not old or quiet.
Everyone who is not old or not wise is kind and vice versa.
If alice is either not funny or not strong then paul is either not funny or wise and vice versa.
If someone is rich then someone is old.
Everyone who is both happy and patient is both strong and quiet and vice versa.
If lucy is both old and not rich then someone is calm.
If lucy is both strong and wise then mary is happy or not old.
Everyone who is funny or generous is curious or not brave and vice versa.
Everyone who is not happy is rich or not rich and vice versa.
Everyone who is both not happy and kind is either creative or not rich and vice versa.
If someone is not humble or not creative then someone is either curious or kind.
Everyone who is either creative or brave is old and vice versa.
If alice is both patient and not calm then someone is both not calm and old.
If someone is both not curious and rich then paul is both tall and funny.
If someone is not happy then someone is strong or not creative and vice versa.
Everyone who is not funny or humble is either not strong or brave and vice versa.
Alice is calm.
Paul is either kind or not happy.
Someone is funny.
Fred is not quiet.
Someone is not calm or not rich.
Lucy is either not brave or not rich.
Someone is both not wise and not calm.
Lucy is either not curious or happy. | Lucy is creative. | entailment | (![X]:(kind(X)=>(~old(X)<~>quiet(X))))&
(![X]:((~old(X)|~wise(X))<=>kind(X)))&
(((~funny(alice)<~>~strong(alice)))<=>((~funny(paul)<~>wise(paul))))&
((?[X]:(rich(X)))=>(?[X]:(old(X))))&
(![X]:((happy(X)&patient(X))<=>(strong(X)&quiet(X))))&
(((old(lucy)&~rich(lucy)))=>(?[X]:(calm(X))))&
(((strong(lucy)&wise(lucy)))=>((happy(mary)|~old(mary))))&
(![X]:((funny(X)|generous(X))<=>(curious(X)|~brave(X))))&
(![X]:(~happy(X)<=>(rich(X)|~rich(X))))&
(![X]:((~happy(X)&kind(X))<=>(creative(X)<~>~rich(X))))&
((?[X]:((~humble(X)|~creative(X))))=>(?[X]:((curious(X)<~>kind(X)))))&
(![X]:((creative(X)<~>brave(X))<=>old(X)))&
(((patient(alice)&~calm(alice)))=>(?[X]:((~calm(X)&old(X)))))&
((?[X]:((~curious(X)&rich(X))))=>((tall(paul)&funny(paul))))&
((?[X]:(~happy(X)))<=>(?[X]:((strong(X)|~creative(X)))))&
(![X]:((~funny(X)|humble(X))<=>(~strong(X)<~>brave(X))))&
(calm(alice))&
((kind(paul)<~>~happy(paul)))&
(?[X]:(funny(X)))&
(~quiet(fred))&
(?[X]:((~calm(X)|~rich(X))))&
((~brave(lucy)<~>~rich(lucy)))&
(?[X]:((~wise(X)&~calm(X))))&
((~curious(lucy)<~>happy(lucy))) | creative(lucy) | [
"p0",
"p1",
"p4",
"p7",
"p8",
"p9",
"p11",
"p15",
"p21",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 716845864533870733297714
% SZS output start Proof for 716845864533870733297714
1. ! [X0] : (kind(X0) => (~old(X0) <~> quiet(X0))) [input p0]
2. ! [X0] : ((~wise(X0) | ~old(X0)) <=> kind(X0)) [input p1]
5. ! [X0] : ((patient(X0) & happy(X0)) <=> (quiet(X0) & strong(X0))) [input p4]
8. ! [X0] : ((generous(X0) | funny(X0)) <=> (~brave(X0) | curious(X0))) [input p7]
9. ! [X0] : (~happy(X0) <=> (~rich(X0) | rich(X0))) [input p8]
10. ! [X0] : ((kind(X0) & ~happy(X0)) <=> (creative(X0) <~> ~rich(X0))) [input p9]
12. ! [X0] : ((creative(X0) <~> brave(X0)) <=> old(X0)) [input p11]
16. ! [X0] : ((humble(X0) | ~funny(X0)) <=> (~strong(X0) <~> brave(X0))) [input p15]
22. ~brave(lucy) <~> ~rich(lucy) [input p21]
24. ~curious(lucy) <~> happy(lucy) [input p23]
25. ~creative(lucy) [input hypothesis]
30. ! [X0] : ((~old(X0) <~> quiet(X0)) | ~kind(X0)) [ennf transformation 1]
40. ! [X0] : (((~quiet(X0) | old(X0)) & (quiet(X0) | ~old(X0))) | ~kind(X0)) [nnf transformation 30]
41. ! [X0] : (((~wise(X0) | ~old(X0)) | ~kind(X0)) & (kind(X0) | (wise(X0) & old(X0)))) [nnf transformation 2]
42. ! [X0] : ((~wise(X0) | ~old(X0) | ~kind(X0)) & (kind(X0) | (wise(X0) & old(X0)))) [flattening 41]
47. ! [X0] : (((patient(X0) & happy(X0)) | (~quiet(X0) | ~strong(X0))) & ((quiet(X0) & strong(X0)) | (~patient(X0) | ~happy(X0)))) [nnf transformation 5]
48. ! [X0] : (((patient(X0) & happy(X0)) | ~quiet(X0) | ~strong(X0)) & ((quiet(X0) & strong(X0)) | ~patient(X0) | ~happy(X0))) [flattening 47]
51. ! [X0] : (((generous(X0) | funny(X0)) | (brave(X0) & ~curious(X0))) & ((~brave(X0) | curious(X0)) | (~generous(X0) & ~funny(X0)))) [nnf transformation 8]
52. ! [X0] : ((generous(X0) | funny(X0) | (brave(X0) & ~curious(X0))) & (~brave(X0) | curious(X0) | (~generous(X0) & ~funny(X0)))) [flattening 51]
53. ! [X0] : ((~happy(X0) | (rich(X0) & ~rich(X0))) & ((~rich(X0) | rich(X0)) | happy(X0))) [nnf transformation 9]
54. ! [X0] : ((~happy(X0) | (rich(X0) & ~rich(X0))) & (~rich(X0) | rich(X0) | happy(X0))) [flattening 53]
55. ! [X0] : (((kind(X0) & ~happy(X0)) | ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) & (((rich(X0) | ~creative(X0)) & (~rich(X0) | creative(X0))) | (~kind(X0) | happy(X0)))) [nnf transformation 10]
56. ! [X0] : (((kind(X0) & ~happy(X0)) | ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) & (((rich(X0) | ~creative(X0)) & (~rich(X0) | creative(X0))) | ~kind(X0) | happy(X0))) [flattening 55]
61. ! [X0] : ((((~brave(X0) | ~creative(X0)) & (brave(X0) | creative(X0))) | ~old(X0)) & (old(X0) | ((creative(X0) | ~brave(X0)) & (brave(X0) | ~creative(X0))))) [nnf transformation 12]
69. ! [X0] : (((humble(X0) | ~funny(X0)) | ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0)))) & (((~brave(X0) | strong(X0)) & (brave(X0) | ~strong(X0))) | (~humble(X0) & funny(X0)))) [nnf transformation 16]
70. ! [X0] : ((humble(X0) | ~funny(X0) | ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0)))) & (((~brave(X0) | strong(X0)) & (brave(X0) | ~strong(X0))) | (~humble(X0) & funny(X0)))) [flattening 69]
76. (rich(lucy) | brave(lucy)) & (~rich(lucy) | ~brave(lucy)) [nnf transformation 22]
79. (~happy(lucy) | curious(lucy)) & (happy(lucy) | ~curious(lucy)) [nnf transformation 24]
80. ~old(X0) | quiet(X0) | ~kind(X0) [cnf transformation 40]
82. old(X0) | kind(X0) [cnf transformation 42]
96. ~strong(X0) | ~quiet(X0) | happy(X0) [cnf transformation 48]
100. ~brave(X0) | curious(X0) | ~funny(X0) [cnf transformation 52]
105. ~happy(X0) | ~rich(X0) [cnf transformation 54]
106. ~happy(X0) | rich(X0) [cnf transformation 54]
107. ~rich(X0) | creative(X0) | ~kind(X0) | happy(X0) [cnf transformation 56]
112. creative(X0) | kind(X0) | rich(X0) [cnf transformation 56]
118. ~brave(X0) | creative(X0) | old(X0) [cnf transformation 61]
119. ~old(X0) | creative(X0) | brave(X0) [cnf transformation 61]
129. ~brave(X0) | strong(X0) | funny(X0) [cnf transformation 70]
139. ~rich(lucy) | ~brave(lucy) [cnf transformation 76]
140. rich(lucy) | brave(lucy) [cnf transformation 76]
143. happy(lucy) | ~curious(lucy) [cnf transformation 79]
145. ~creative(lucy) [cnf transformation 25]
179. 7 <=> old(lucy) [avatar definition]
180. old(lucy) <- (7) [avatar component clause 179]
181. ~old(lucy) <- (~7) [avatar component clause 179]
183. 8 <=> rich(lucy) [avatar definition]
185. rich(lucy) <- (8) [avatar component clause 183]
192. 10 <=> strong(lucy) [avatar definition]
193. strong(lucy) <- (10) [avatar component clause 192]
208. ~happy(X0) [subsumption resolution 105,106]
210. ~rich(X0) | creative(X0) | ~kind(X0) [subsumption resolution 107,208]
273. 27 <=> brave(lucy) [avatar definition]
274. ~brave(lucy) <- (~27) [avatar component clause 273]
275. brave(lucy) <- (27) [avatar component clause 273]
276. 27 | 8 [avatar split clause 140,183,273]
277. ~27 | ~8 [avatar split clause 139,183,273]
278. ~curious(lucy) [subsumption resolution 143,208]
320. 33 <=> funny(lucy) [avatar definition]
321. ~funny(lucy) <- (~33) [avatar component clause 320]
326. curious(lucy) | ~funny(lucy) <- (27) [resolution 275,100]
329. ~funny(lucy) <- (27) [subsumption resolution 326,278]
330. ~33 | ~27 [avatar split clause 329,273,320]
331. kind(lucy) | rich(lucy) [resolution 112,145]
372. creative(lucy) | old(lucy) <- (27) [resolution 118,275]
373. old(lucy) <- (27) [subsumption resolution 372,145]
374. $false <- (~7, 27) [subsumption resolution 373,181]
375. 7 | ~27 [avatar contradiction clause 374]
389. 42 <=> kind(lucy) [avatar definition]
391. kind(lucy) <- (42) [avatar component clause 389]
392. 8 | 42 [avatar split clause 331,389,183]
395. creative(lucy) | brave(lucy) <- (7) [resolution 180,119]
396. quiet(lucy) | ~kind(lucy) <- (7) [resolution 180,80]
397. brave(lucy) <- (7) [subsumption resolution 395,145]
398. $false <- (7, ~27) [subsumption resolution 397,274]
399. ~7 | 27 [avatar contradiction clause 398]
401. 43 <=> quiet(lucy) [avatar definition]
403. quiet(lucy) <- (43) [avatar component clause 401]
404. ~42 | 43 | ~7 [avatar split clause 396,179,401,389]
405. kind(lucy) <- (~7) [resolution 181,82]
406. 42 | 7 [avatar split clause 405,179,389]
423. strong(lucy) | funny(lucy) <- (27) [resolution 129,275]
425. strong(lucy) <- (27, ~33) [subsumption resolution 423,321]
426. 10 | ~27 | 33 [avatar split clause 425,320,273,192]
429. ~quiet(lucy) | happy(lucy) <- (10) [resolution 193,96]
431. happy(lucy) <- (10, 43) [subsumption resolution 429,403]
432. $false <- (10, 43) [subsumption resolution 431,208]
433. ~10 | ~43 [avatar contradiction clause 432]
439. creative(lucy) | ~kind(lucy) <- (8) [resolution 210,185]
442. ~kind(lucy) <- (8) [subsumption resolution 439,145]
443. $false <- (8, 42) [subsumption resolution 442,391]
444. ~8 | ~42 [avatar contradiction clause 443]
445. $false [avatar sat refutation 276,277,330,375,392,399,404,406,426,433,444]
% SZS output end Proof for 716845864533870733297714
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not generous is not patient or kind.
Everyone who is either kind or not humble is not creative.
Everyone who is not curious or old is not generous or wise.
Everyone who is either not calm or not creative is brave or funny and vice versa.
If someone is either happy or not curious then someone is both not brave and strong.
Everyone who is both not creative and quiet is not tall and vice versa.
If lucy is not patient then susan is both quiet and creative.
Everyone who is not humble or calm is not tall and vice versa.
Everyone who is not curious is quiet or generous and vice versa.
If fred is wise or not happy then lucy is humble or funny.
If lucy is both not creative and not happy then lucy is not brave and vice versa.
If someone is not strong then lucy is not tall.
Everyone who is either not patient or calm is both humble and not old and vice versa.
Everyone who is calm is strong.
Everyone who is not happy or not curious is both wise and kind and vice versa.
If fred is generous or quiet then someone is happy or patient.
Someone is not creative or not calm.
Someone is creative or curious.
Someone is not humble or not calm.
Someone is either strong or not creative.
Fred is generous or strong.
Someone is either not quiet or not old.
Fred is both not strong and not funny.
John is not wise or calm. | Lucy is not patient. | contradiction | (![X]:((~wise(X)|~generous(X))=>(~patient(X)|kind(X))))&
(![X]:((kind(X)<~>~humble(X))=>~creative(X)))&
(![X]:((~curious(X)|old(X))=>(~generous(X)|wise(X))))&
(![X]:((~calm(X)<~>~creative(X))<=>(brave(X)|funny(X))))&
((?[X]:((happy(X)<~>~curious(X))))=>(?[X]:((~brave(X)&strong(X)))))&
(![X]:((~creative(X)&quiet(X))<=>~tall(X)))&
((~patient(lucy))=>((quiet(susan)&creative(susan))))&
(![X]:((~humble(X)|calm(X))<=>~tall(X)))&
(![X]:(~curious(X)<=>(quiet(X)|generous(X))))&
(((wise(fred)|~happy(fred)))=>((humble(lucy)|funny(lucy))))&
(((~creative(lucy)&~happy(lucy)))<=>(~brave(lucy)))&
((?[X]:(~strong(X)))=>(~tall(lucy)))&
(![X]:((~patient(X)<~>calm(X))<=>(humble(X)&~old(X))))&
(![X]:(calm(X)=>strong(X)))&
(![X]:((~happy(X)|~curious(X))<=>(wise(X)&kind(X))))&
(((generous(fred)|quiet(fred)))=>(?[X]:((happy(X)|patient(X)))))&
(?[X]:((~creative(X)|~calm(X))))&
(?[X]:((creative(X)|curious(X))))&
(?[X]:((~humble(X)|~calm(X))))&
(?[X]:((strong(X)<~>~creative(X))))&
((generous(fred)|strong(fred)))&
(?[X]:((~quiet(X)<~>~old(X))))&
((~strong(fred)&~funny(fred)))&
((~wise(john)|calm(john))) | ~patient(lucy) | [
"p1",
"p5",
"p6",
"p7",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 825084100224340143211851
% SZS output start Proof for 825084100224340143211851
2. ! [X0] : ((kind(X0) <~> ~humble(X0)) => ~creative(X0)) [input p1]
6. ! [X0] : ((quiet(X0) & ~creative(X0)) <=> ~tall(X0)) [input p5]
7. ~patient(lucy) => (creative(susan) & quiet(susan)) [input p6]
8. ! [X0] : ((calm(X0) | ~humble(X0)) <=> ~tall(X0)) [input p7]
9. ! [X0] : (~curious(X0) <=> (generous(X0) | quiet(X0))) [input p8]
15. ! [X0] : ((~curious(X0) | ~happy(X0)) <=> (kind(X0) & wise(X0))) [input p14]
25. ~patient(lucy) [input hypothesis]
29. ! [X0] : (~creative(X0) | (kind(X0) <=> ~humble(X0))) [ennf transformation 2]
33. (creative(susan) & quiet(susan)) | patient(lucy) [ennf transformation 7]
39. ! [X0] : (~creative(X0) | ((kind(X0) | humble(X0)) & (~humble(X0) | ~kind(X0)))) [nnf transformation 29]
46. ! [X0] : (((quiet(X0) & ~creative(X0)) | tall(X0)) & (~tall(X0) | (~quiet(X0) | creative(X0)))) [nnf transformation 6]
47. ! [X0] : (((quiet(X0) & ~creative(X0)) | tall(X0)) & (~tall(X0) | ~quiet(X0) | creative(X0))) [flattening 46]
48. ! [X0] : (((calm(X0) | ~humble(X0)) | tall(X0)) & (~tall(X0) | (~calm(X0) & humble(X0)))) [nnf transformation 8]
49. ! [X0] : ((calm(X0) | ~humble(X0) | tall(X0)) & (~tall(X0) | (~calm(X0) & humble(X0)))) [flattening 48]
50. ! [X0] : ((~curious(X0) | (~generous(X0) & ~quiet(X0))) & ((generous(X0) | quiet(X0)) | curious(X0))) [nnf transformation 9]
51. ! [X0] : ((~curious(X0) | (~generous(X0) & ~quiet(X0))) & (generous(X0) | quiet(X0) | curious(X0))) [flattening 50]
56. ! [X0] : (((~curious(X0) | ~happy(X0)) | (~kind(X0) | ~wise(X0))) & ((kind(X0) & wise(X0)) | (curious(X0) & happy(X0)))) [nnf transformation 15]
57. ! [X0] : ((~curious(X0) | ~happy(X0) | ~kind(X0) | ~wise(X0)) & ((kind(X0) & wise(X0)) | (curious(X0) & happy(X0)))) [flattening 56]
74. ~creative(X0) | ~humble(X0) | ~kind(X0) [cnf transformation 39]
89. ~creative(X0) | tall(X0) [cnf transformation 47]
91. quiet(susan) | patient(lucy) [cnf transformation 33]
92. creative(susan) | patient(lucy) [cnf transformation 33]
93. ~tall(X0) | humble(X0) [cnf transformation 49]
97. ~quiet(X0) | ~curious(X0) [cnf transformation 51]
115. curious(X0) | kind(X0) [cnf transformation 57]
130. ~patient(lucy) [cnf transformation 25]
150. 5 <=> patient(lucy) [avatar definition]
154. 6 <=> creative(susan) [avatar definition]
156. creative(susan) <- (6) [avatar component clause 154]
157. 5 | 6 [avatar split clause 92,154,150]
159. 7 <=> quiet(susan) [avatar definition]
161. quiet(susan) <- (7) [avatar component clause 159]
162. 5 | 7 [avatar split clause 91,159,150]
284. ~5 [avatar split clause 130,150]
285. tall(susan) <- (6) [resolution 89,156]
288. humble(susan) <- (6) [resolution 93,285]
294. ~curious(susan) <- (7) [resolution 97,161]
302. kind(susan) <- (7) [resolution 115,294]
307. ~humble(susan) | ~kind(susan) <- (6) [resolution 74,156]
309. ~kind(susan) <- (6) [subsumption resolution 307,288]
310. $false <- (6, 7) [subsumption resolution 309,302]
311. ~6 | ~7 [avatar contradiction clause 310]
313. $false [avatar sat refutation 157,162,284,311]
% SZS output end Proof for 825084100224340143211851
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or happy is creative and vice versa.
If susan is patient then someone is both not curious and not rich and vice versa.
If someone is both not rich and old then someone is wise and vice versa.
If paul is patient or not generous then paul is not patient or not wise.
Everyone who is not generous or not quiet is either not wise or not kind.
Everyone who is either curious or quiet is not strong and vice versa.
Everyone who is both not strong and wise is both not old and not kind.
If someone is not old then lucy is not generous or kind and vice versa.
Everyone who is either tall or old is either not generous or old.
Everyone who is both not calm and not strong is not generous or strong.
Everyone who is both generous and happy is both not strong and curious.
Everyone who is funny or wise is both strong and not calm and vice versa.
If someone is either strong or rich then someone is either not calm or creative and vice versa.
Everyone who is both not funny and humble is funny or rich and vice versa.
Everyone who is not curious or not tall is funny or not quiet and vice versa.
Everyone who is wise is both not old and not kind and vice versa.
Fred is either funny or tall.
Someone is happy or tall.
Someone is both rich and not happy.
Someone is strong.
Someone is patient or not kind.
Susan is not generous.
Paul is both not funny and not strong. | Lucy is not creative. | neutral | (![X]:((strong(X)|happy(X))<=>creative(X)))&
((patient(susan))<=>(?[X]:((~curious(X)&~rich(X)))))&
((?[X]:((~rich(X)&old(X))))<=>(?[X]:(wise(X))))&
(((patient(paul)|~generous(paul)))=>((~patient(paul)|~wise(paul))))&
(![X]:((~generous(X)|~quiet(X))=>(~wise(X)<~>~kind(X))))&
(![X]:((curious(X)<~>quiet(X))<=>~strong(X)))&
(![X]:((~strong(X)&wise(X))=>(~old(X)&~kind(X))))&
((?[X]:(~old(X)))<=>((~generous(lucy)|kind(lucy))))&
(![X]:((tall(X)<~>old(X))=>(~generous(X)<~>old(X))))&
(![X]:((~calm(X)&~strong(X))=>(~generous(X)|strong(X))))&
(![X]:((generous(X)&happy(X))=>(~strong(X)&curious(X))))&
(![X]:((funny(X)|wise(X))<=>(strong(X)&~calm(X))))&
((?[X]:((strong(X)<~>rich(X))))<=>(?[X]:((~calm(X)<~>creative(X)))))&
(![X]:((~funny(X)&humble(X))<=>(funny(X)|rich(X))))&
(![X]:((~curious(X)|~tall(X))<=>(funny(X)|~quiet(X))))&
(![X]:(wise(X)<=>(~old(X)&~kind(X))))&
((funny(fred)<~>tall(fred)))&
(?[X]:((happy(X)|tall(X))))&
(?[X]:((rich(X)&~happy(X))))&
(?[X]:(strong(X)))&
(?[X]:((patient(X)|~kind(X))))&
(~generous(susan))&
((~funny(paul)&~strong(paul))) | ~creative(lucy) | [] | null | 0 |
If alice is wise or quiet then mary is rich and vice versa.
Everyone who is either curious or not curious is both not old and not brave and vice versa.
Everyone who is both wise and brave is not kind and vice versa.
Everyone who is wise or creative is both not quiet and brave and vice versa.
Everyone who is both funny and not strong is either happy or quiet and vice versa.
If someone is either wise or old then someone is not rich.
If lucy is both happy and not brave then someone is not rich or not calm and vice versa.
If someone is either not old or not brave then someone is not brave.
Everyone who is old is not rich and vice versa.
If susan is both not happy and curious then alice is not calm or wise and vice versa.
Everyone who is both generous and not happy is old or not funny and vice versa.
If fred is old or not strong then someone is happy or kind and vice versa.
If someone is brave or not creative then lucy is either tall or funny and vice versa.
If alice is quiet or not patient then someone is both tall and strong and vice versa.
Everyone who is both not curious and not kind is calm.
Someone is either calm or not wise.
Someone is either not happy or not old.
Someone is not curious.
Someone is rich.
Someone is not quiet or not generous.
Someone is not curious or funny. | Susan is not strong. | neutral | (((wise(alice)|quiet(alice)))<=>(rich(mary)))&
(![X]:((curious(X)<~>~curious(X))<=>(~old(X)&~brave(X))))&
(![X]:((wise(X)&brave(X))<=>~kind(X)))&
(![X]:((wise(X)|creative(X))<=>(~quiet(X)&brave(X))))&
(![X]:((funny(X)&~strong(X))<=>(happy(X)<~>quiet(X))))&
((?[X]:((wise(X)<~>old(X))))=>(?[X]:(~rich(X))))&
(((happy(lucy)&~brave(lucy)))<=>(?[X]:((~rich(X)|~calm(X)))))&
((?[X]:((~old(X)<~>~brave(X))))=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>~rich(X)))&
(((~happy(susan)&curious(susan)))<=>((~calm(alice)|wise(alice))))&
(![X]:((generous(X)&~happy(X))<=>(old(X)|~funny(X))))&
(((old(fred)|~strong(fred)))<=>(?[X]:((happy(X)|kind(X)))))&
((?[X]:((brave(X)|~creative(X))))<=>((tall(lucy)<~>funny(lucy))))&
(((quiet(alice)|~patient(alice)))<=>(?[X]:((tall(X)&strong(X)))))&
(![X]:((~curious(X)&~kind(X))=>calm(X)))&
(?[X]:((calm(X)<~>~wise(X))))&
(?[X]:((~happy(X)<~>~old(X))))&
(?[X]:(~curious(X)))&
(?[X]:(rich(X)))&
(?[X]:((~quiet(X)|~generous(X))))&
(?[X]:((~curious(X)|funny(X)))) | ~strong(susan) | [] | null | 0 |
If someone is either not rich or not quiet then lucy is either not creative or not strong.
If someone is kind or calm then lucy is both not calm and rich.
Everyone who is not rich or rich is generous or humble.
Everyone who is either rich or not quiet is kind or happy.
Everyone who is both brave and old is either happy or not kind.
If someone is strong then someone is both not humble and curious and vice versa.
If paul is either generous or humble then alice is calm or brave.
Everyone who is either not curious or not wise is either not wise or funny.
If susan is not humble or not strong then someone is both generous and not humble and vice versa.
If lucy is not tall or quiet then paul is either calm or not funny.
Everyone who is either happy or not patient is creative and vice versa.
If someone is both not kind and not tall then someone is either not humble or brave.
Everyone who is both tall and humble is calm or not quiet and vice versa.
Everyone who is not calm or calm is both not rich and patient.
Everyone who is both not wise and not humble is either not patient or not wise.
If susan is not calm then someone is funny or not creative and vice versa.
Someone is calm or happy.
Someone is either not rich or brave.
Someone is either funny or brave.
Lucy is both quiet and generous.
Lucy is humble or curious.
Someone is not generous or not brave. | Susan is not kind. | entailment | ((?[X]:((~rich(X)<~>~quiet(X))))=>((~creative(lucy)<~>~strong(lucy))))&
((?[X]:((kind(X)|calm(X))))=>((~calm(lucy)&rich(lucy))))&
(![X]:((~rich(X)|rich(X))=>(generous(X)|humble(X))))&
(![X]:((rich(X)<~>~quiet(X))=>(kind(X)|happy(X))))&
(![X]:((brave(X)&old(X))=>(happy(X)<~>~kind(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~humble(X)&curious(X)))))&
(((generous(paul)<~>humble(paul)))=>((calm(alice)|brave(alice))))&
(![X]:((~curious(X)<~>~wise(X))=>(~wise(X)<~>funny(X))))&
(((~humble(susan)|~strong(susan)))<=>(?[X]:((generous(X)&~humble(X)))))&
(((~tall(lucy)|quiet(lucy)))=>((calm(paul)<~>~funny(paul))))&
(![X]:((happy(X)<~>~patient(X))<=>creative(X)))&
((?[X]:((~kind(X)&~tall(X))))=>(?[X]:((~humble(X)<~>brave(X)))))&
(![X]:((tall(X)&humble(X))<=>(calm(X)|~quiet(X))))&
(![X]:((~calm(X)|calm(X))=>(~rich(X)&patient(X))))&
(![X]:((~wise(X)&~humble(X))=>(~patient(X)<~>~wise(X))))&
((~calm(susan))<=>(?[X]:((funny(X)|~creative(X)))))&
(?[X]:((calm(X)|happy(X))))&
(?[X]:((~rich(X)<~>brave(X))))&
(?[X]:((funny(X)<~>brave(X))))&
((quiet(lucy)&generous(lucy)))&
((humble(lucy)|curious(lucy)))&
(?[X]:((~generous(X)|~brave(X)))) | ~kind(susan) | [
"p1",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1586228220592607777342659
% SZS output start Proof for 1586228220592607777342659
2. ? [X0] : (calm(X0) | kind(X0)) => (rich(lucy) & ~calm(lucy)) [input p1]
14. ! [X0] : ((calm(X0) | ~calm(X0)) => (patient(X0) & ~rich(X0))) [input p13]
23. kind(susan) [input hypothesis]
28. (rich(lucy) & ~calm(lucy)) | ! [X0] : (~calm(X0) & ~kind(X0)) [ennf transformation 2]
38. ! [X0] : ((patient(X0) & ~rich(X0)) | (~calm(X0) & calm(X0))) [ennf transformation 14]
84. rich(lucy) | ~kind(X0) [cnf transformation 28]
119. ~rich(X0) | calm(X0) [cnf transformation 38]
120. ~rich(X0) | ~calm(X0) [cnf transformation 38]
137. kind(susan) [cnf transformation 23]
163. 6 <=> rich(lucy) [avatar definition]
165. rich(lucy) <- (6) [avatar component clause 163]
168. 7 <=> ! [X0] : ~kind(X0) [avatar definition]
169. ~kind(X0) <- (7) [avatar component clause 168]
170. 7 | 6 [avatar split clause 84,163,168]
278. ~rich(X0) [subsumption resolution 119,120]
339. $false <- (6) [subsumption resolution 165,278]
340. ~6 [avatar contradiction clause 339]
341. $false <- (7) [resolution 169,137]
342. ~7 [avatar contradiction clause 341]
343. $false [avatar sat refutation 170,340,342]
% SZS output end Proof for 1586228220592607777342659
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or quiet then susan is strong and vice versa.
Everyone who is both wise and quiet is both creative and kind.
Everyone who is both not creative and quiet is either not kind or not generous and vice versa.
Everyone who is either not creative or calm is wise.
If someone is not funny or strong then someone is strong.
If someone is tall then someone is both creative and not wise.
If someone is both not tall and not calm then susan is not calm or not kind and vice versa.
If john is either not tall or not quiet then susan is both not creative and not generous and vice versa.
If someone is both not kind and quiet then someone is either happy or not creative and vice versa.
If fred is either old or rich then someone is either not rich or brave.
Everyone who is both calm and quiet is either not happy or not funny.
Everyone who is brave or not happy is both brave and not creative.
Everyone who is tall is not wise and vice versa.
If mary is either not creative or creative then fred is calm or not rich and vice versa.
Everyone who is both not tall and wise is brave or calm and vice versa.
Everyone who is brave is tall or not curious and vice versa.
Someone is either not generous or not patient.
Alice is both not old and brave.
Someone is calm.
Paul is brave.
John is not generous.
Someone is either not rich or not happy.
Paul is humble. | Mary is wise. | entailment | ((?[X]:((happy(X)|quiet(X))))<=>(strong(susan)))&
(![X]:((wise(X)&quiet(X))=>(creative(X)&kind(X))))&
(![X]:((~creative(X)&quiet(X))<=>(~kind(X)<~>~generous(X))))&
(![X]:((~creative(X)<~>calm(X))=>wise(X)))&
((?[X]:((~funny(X)|strong(X))))=>(?[X]:(strong(X))))&
((?[X]:(tall(X)))=>(?[X]:((creative(X)&~wise(X)))))&
((?[X]:((~tall(X)&~calm(X))))<=>((~calm(susan)|~kind(susan))))&
(((~tall(john)<~>~quiet(john)))<=>((~creative(susan)&~generous(susan))))&
((?[X]:((~kind(X)&quiet(X))))<=>(?[X]:((happy(X)<~>~creative(X)))))&
(((old(fred)<~>rich(fred)))=>(?[X]:((~rich(X)<~>brave(X)))))&
(![X]:((calm(X)&quiet(X))=>(~happy(X)<~>~funny(X))))&
(![X]:((brave(X)|~happy(X))=>(brave(X)&~creative(X))))&
(![X]:(tall(X)<=>~wise(X)))&
(((~creative(mary)<~>creative(mary)))<=>((calm(fred)|~rich(fred))))&
(![X]:((~tall(X)&wise(X))<=>(brave(X)|calm(X))))&
(![X]:(brave(X)<=>(tall(X)|~curious(X))))&
(?[X]:((~generous(X)<~>~patient(X))))&
((~old(alice)&brave(alice)))&
(?[X]:(calm(X)))&
(brave(paul))&
(~generous(john))&
(?[X]:((~rich(X)<~>~happy(X))))&
(humble(paul)) | wise(mary) | [
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2267117163212610991686210
% SZS output start Proof for 2267117163212610991686210
13. ! [X0] : (tall(X0) <=> ~wise(X0)) [input p12]
15. ! [X0] : ((wise(X0) & ~tall(X0)) <=> (calm(X0) | brave(X0))) [input p14]
16. ! [X0] : (brave(X0) <=> (~curious(X0) | tall(X0))) [input p15]
24. ~wise(mary) [input hypothesis]
67. ! [X0] : ((tall(X0) | wise(X0)) & (~wise(X0) | ~tall(X0))) [nnf transformation 13]
70. ! [X0] : (((wise(X0) & ~tall(X0)) | (~calm(X0) & ~brave(X0))) & ((calm(X0) | brave(X0)) | (~wise(X0) | tall(X0)))) [nnf transformation 15]
71. ! [X0] : (((wise(X0) & ~tall(X0)) | (~calm(X0) & ~brave(X0))) & (calm(X0) | brave(X0) | ~wise(X0) | tall(X0))) [flattening 70]
72. ! [X0] : ((brave(X0) | (curious(X0) & ~tall(X0))) & ((~curious(X0) | tall(X0)) | ~brave(X0))) [nnf transformation 16]
73. ! [X0] : ((brave(X0) | (curious(X0) & ~tall(X0))) & (~curious(X0) | tall(X0) | ~brave(X0))) [flattening 72]
127. tall(X0) | wise(X0) [cnf transformation 67]
135. ~tall(X0) | ~brave(X0) [cnf transformation 71]
140. brave(X0) | ~tall(X0) [cnf transformation 73]
151. ~wise(mary) [cnf transformation 24]
188. 9 <=> ! [X1] : ~tall(X1) [avatar definition]
189. ~tall(X1) <- (9) [avatar component clause 188]
308. ~tall(X0) [subsumption resolution 140,135]
309. 9 [avatar split clause 308,188]
356. wise(X1) <- (9) [resolution 127,189]
359. $false <- (9) [resolution 356,151]
360. ~9 [avatar contradiction clause 359]
361. $false [avatar sat refutation 309,360]
% SZS output end Proof for 2267117163212610991686210
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not curious or not creative then paul is not tall or not happy.
If john is both brave and not curious then paul is old or not funny and vice versa.
Everyone who is not calm is not quiet and vice versa.
If alice is either not happy or not old then someone is both not rich and not patient.
Everyone who is not rich is curious or not curious and vice versa.
Everyone who is not happy or funny is either generous or rich.
If john is tall then someone is not curious or not old and vice versa.
If someone is either not wise or patient then susan is rich and vice versa.
If susan is either not tall or calm then mary is either not curious or not funny.
If someone is calm then someone is either tall or not patient.
Everyone who is kind is either not happy or strong and vice versa.
If fred is not old or not rich then susan is both not curious and wise and vice versa.
If someone is old then fred is both not wise and curious and vice versa.
Everyone who is both not curious and brave is either rich or strong and vice versa.
If john is either not generous or not old then someone is either wise or happy and vice versa.
Everyone who is not brave is both humble and calm.
Paul is both creative and not generous.
Fred is both not kind and generous.
Someone is tall or patient.
Lucy is both funny and happy.
Alice is not calm.
Paul is not wise or not humble.
Someone is either wise or creative. | Mary is not rich. | entailment | (((~curious(lucy)<~>~creative(lucy)))=>((~tall(paul)|~happy(paul))))&
(((brave(john)&~curious(john)))<=>((old(paul)|~funny(paul))))&
(![X]:(~calm(X)<=>~quiet(X)))&
(((~happy(alice)<~>~old(alice)))=>(?[X]:((~rich(X)&~patient(X)))))&
(![X]:(~rich(X)<=>(curious(X)|~curious(X))))&
(![X]:((~happy(X)|funny(X))=>(generous(X)<~>rich(X))))&
((tall(john))<=>(?[X]:((~curious(X)|~old(X)))))&
((?[X]:((~wise(X)<~>patient(X))))<=>(rich(susan)))&
(((~tall(susan)<~>calm(susan)))=>((~curious(mary)<~>~funny(mary))))&
((?[X]:(calm(X)))=>(?[X]:((tall(X)<~>~patient(X)))))&
(![X]:(kind(X)<=>(~happy(X)<~>strong(X))))&
(((~old(fred)|~rich(fred)))<=>((~curious(susan)&wise(susan))))&
((?[X]:(old(X)))<=>((~wise(fred)&curious(fred))))&
(![X]:((~curious(X)&brave(X))<=>(rich(X)<~>strong(X))))&
(((~generous(john)<~>~old(john)))<=>(?[X]:((wise(X)<~>happy(X)))))&
(![X]:(~brave(X)=>(humble(X)&calm(X))))&
((creative(paul)&~generous(paul)))&
((~kind(fred)&generous(fred)))&
(?[X]:((tall(X)|patient(X))))&
((funny(lucy)&happy(lucy)))&
(~calm(alice))&
((~wise(paul)|~humble(paul)))&
(?[X]:((wise(X)<~>creative(X)))) | ~rich(mary) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 2591158079836473484575918
% SZS output start Proof for 2591158079836473484575918
5. ! [X0] : (~rich(X0) <=> (~curious(X0) | curious(X0))) [input p4]
24. rich(mary) [input hypothesis]
42. ! [X0] : ((~rich(X0) | (curious(X0) & ~curious(X0))) & ((~curious(X0) | curious(X0)) | rich(X0))) [nnf transformation 5]
43. ! [X0] : ((~rich(X0) | (curious(X0) & ~curious(X0))) & (~curious(X0) | curious(X0) | rich(X0))) [flattening 42]
91. ~rich(X0) | ~curious(X0) [cnf transformation 43]
92. ~rich(X0) | curious(X0) [cnf transformation 43]
147. rich(mary) [cnf transformation 24]
207. ~rich(X0) [subsumption resolution 91,92]
347. $false [subsumption resolution 147,207]
% SZS output end Proof for 2591158079836473484575918
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy or creative is both not strong and humble. If susan is not tall or funny then john is both happy and funny and vice versa. Everyone who is not rich or not funny is both kind and wise and vice versa. If lucy is both not funny and not strong then someone is rich and vice versa. Everyone who is patient or not strong is either not quiet or not rich. Everyone who is creative is either tall or not generous and vice versa. Everyone who is not calm is tall or not calm. Everyone who is not quiet is not brave. Everyone who is quiet is both not calm and not curious and vice versa. Everyone who is curious is either not kind or not generous. Everyone who is not funny or tall is either not calm or quiet. Everyone who is not calm is not wise or brave. If alice is either not wise or happy then mary is calm. Everyone who is either curious or calm is not kind. If mary is both not tall and calm then john is either quiet or funny. Everyone who is not quiet is both old and kind. Someone is both not patient and not creative. Someone is either happy or brave. Someone is calm or not humble. Susan is either not wise or happy. Someone is patient. Someone is both not curious and generous. | Alice is not wise. | contradiction | (![X]:((~happy(X)<~>creative(X))=>(~strong(X)&humble(X))))&
(((~tall(susan)|funny(susan)))<=>((happy(john)&funny(john))))&
(![X]:((~rich(X)|~funny(X))<=>(kind(X)&wise(X))))&
(((~funny(lucy)&~strong(lucy)))<=>(?[X]:(rich(X))))&
(![X]:((patient(X)|~strong(X))=>(~quiet(X)<~>~rich(X))))&
(![X]:(creative(X)<=>(tall(X)<~>~generous(X))))&
(![X]:(~calm(X)=>(tall(X)|~calm(X))))&
(![X]:(~quiet(X)=>~brave(X)))&
(![X]:(quiet(X)<=>(~calm(X)&~curious(X))))&
(![X]:(curious(X)=>(~kind(X)<~>~generous(X))))&
(![X]:((~funny(X)|tall(X))=>(~calm(X)<~>quiet(X))))&
(![X]:(~calm(X)=>(~wise(X)|brave(X))))&
(((~wise(alice)<~>happy(alice)))=>(calm(mary)))&
(![X]:((curious(X)<~>calm(X))=>~kind(X)))&
(((~tall(mary)&calm(mary)))=>((quiet(john)<~>funny(john))))&
(![X]:(~quiet(X)=>(old(X)&kind(X))))&
(?[X]:((~patient(X)&~creative(X))))&
(?[X]:((happy(X)<~>brave(X))))&
(?[X]:((calm(X)|~humble(X))))&
((~wise(susan)<~>happy(susan)))&
(?[X]:(patient(X)))&
(?[X]:((~curious(X)&generous(X)))) | ~wise(alice) | [
"p2",
"p3",
"p7",
"p8",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2092885432814961024152302
% SZS output start Proof for 2092885432814961024152302
3. ! [X0] : ((~funny(X0) | ~rich(X0)) <=> (wise(X0) & kind(X0))) [input p2]
4. (~strong(lucy) & ~funny(lucy)) <=> ? [X0] : rich(X0) [input p3]
8. ! [X0] : (~quiet(X0) => ~brave(X0)) [input p7]
9. ! [X0] : (quiet(X0) <=> (~curious(X0) & ~calm(X0))) [input p8]
11. ! [X0] : ((tall(X0) | ~funny(X0)) => (~calm(X0) <~> quiet(X0))) [input p10]
12. ! [X0] : (~calm(X0) => (brave(X0) | ~wise(X0))) [input p11]
23. ~wise(alice) [input hypothesis]
29. ! [X0] : (~brave(X0) | quiet(X0)) [ennf transformation 8]
31. ! [X0] : ((~calm(X0) <~> quiet(X0)) | (~tall(X0) & funny(X0))) [ennf transformation 11]
32. ! [X0] : ((brave(X0) | ~wise(X0)) | calm(X0)) [ennf transformation 12]
33. ! [X0] : (brave(X0) | ~wise(X0) | calm(X0)) [flattening 32]
42. ! [X0] : (((~funny(X0) | ~rich(X0)) | (~wise(X0) | ~kind(X0))) & ((wise(X0) & kind(X0)) | (funny(X0) & rich(X0)))) [nnf transformation 3]
43. ! [X0] : ((~funny(X0) | ~rich(X0) | ~wise(X0) | ~kind(X0)) & ((wise(X0) & kind(X0)) | (funny(X0) & rich(X0)))) [flattening 42]
44. ((~strong(lucy) & ~funny(lucy)) | ! [X0] : ~rich(X0)) & (? [X0] : rich(X0) | (strong(lucy) | funny(lucy))) [nnf transformation 4]
45. ((~strong(lucy) & ~funny(lucy)) | ! [X0] : ~rich(X0)) & (? [X0] : rich(X0) | strong(lucy) | funny(lucy)) [flattening 44]
46. ((~strong(lucy) & ~funny(lucy)) | ! [X0] : ~rich(X0)) & (? [X1] : rich(X1) | strong(lucy) | funny(lucy)) [rectify 45]
47. ? [X1] : rich(X1) => rich(sK0) [choice axiom]
48. ((~strong(lucy) & ~funny(lucy)) | ! [X0] : ~rich(X0)) & (rich(sK0) | strong(lucy) | funny(lucy)) [skolemisation 46,47]
51. ! [X0] : ((quiet(X0) | (curious(X0) | calm(X0))) & ((~curious(X0) & ~calm(X0)) | ~quiet(X0))) [nnf transformation 9]
52. ! [X0] : ((quiet(X0) | curious(X0) | calm(X0)) & ((~curious(X0) & ~calm(X0)) | ~quiet(X0))) [flattening 51]
54. ! [X0] : (((~quiet(X0) | calm(X0)) & (quiet(X0) | ~calm(X0))) | (~tall(X0) & funny(X0))) [nnf transformation 31]
81. wise(X0) | rich(X0) [cnf transformation 43]
82. wise(X0) | funny(X0) [cnf transformation 43]
85. ~funny(lucy) | ~rich(X0) [cnf transformation 48]
96. ~brave(X0) | quiet(X0) [cnf transformation 29]
97. ~calm(X0) | ~quiet(X0) [cnf transformation 52]
102. quiet(X0) | ~calm(X0) | funny(X0) [cnf transformation 54]
104. ~quiet(X0) | calm(X0) | funny(X0) [cnf transformation 54]
106. ~wise(X0) | brave(X0) | calm(X0) [cnf transformation 33]
124. ~wise(alice) [cnf transformation 23]
147. 5 <=> ! [X0] : ~rich(X0) [avatar definition]
148. ~rich(X0) <- (5) [avatar component clause 147]
155. 7 <=> funny(lucy) [avatar definition]
157. ~funny(lucy) <- (~7) [avatar component clause 155]
158. 5 | ~7 [avatar split clause 85,155,147]
165. ~quiet(X0) | funny(X0) [subsumption resolution 104,97]
167. ~calm(X0) | funny(X0) [subsumption resolution 102,97]
173. 10 <=> wise(alice) [avatar definition]
175. ~wise(alice) <- (~10) [avatar component clause 173]
221. ~10 [avatar split clause 124,173]
222. rich(alice) <- (~10) [resolution 81,175]
224. $false <- (5, ~10) [subsumption resolution 222,148]
225. ~5 | 10 [avatar contradiction clause 224]
336. brave(X0) | calm(X0) | funny(X0) [resolution 106,82]
339. brave(X0) | funny(X0) [subsumption resolution 336,167]
367. funny(X0) | quiet(X0) [resolution 339,96]
368. funny(X0) [subsumption resolution 367,165]
379. $false <- (~7) [resolution 368,157]
380. 7 [avatar contradiction clause 379]
381. $false [avatar sat refutation 158,221,225,380]
% SZS output end Proof for 2092885432814961024152302
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is both brave and not patient then someone is not tall or not wise and vice versa.
If someone is either creative or not old then someone is either curious or old.
Everyone who is curious or happy is not tall and vice versa.
Everyone who is either not kind or humble is both happy and brave and vice versa.
If lucy is both not creative and kind then someone is either brave or not old and vice versa.
Everyone who is tall is not generous.
If someone is not rich or not patient then someone is not brave or wise.
Everyone who is both strong and rich is not tall and vice versa.
Everyone who is both quiet and rich is generous.
If john is both not creative and not wise then someone is both not generous and not kind and vice versa.
If someone is either not curious or strong then someone is either not curious or old and vice versa.
Everyone who is either not tall or not kind is either tall or curious.
Everyone who is either not calm or brave is not patient or strong and vice versa.
If someone is calm or patient then susan is both not tall and not calm and vice versa.
Everyone who is either not generous or wise is funny or kind.
Everyone who is either happy or funny is quiet or not curious.
Someone is either not happy or not kind.
John is kind or not generous.
Someone is humble or not rich.
Someone is funny.
Paul is funny.
Someone is not humble or strong.
Lucy is either tall or not funny.
Someone is wise. | Susan is not brave. | entailment | ((?[X]:((brave(X)&~patient(X))))<=>(?[X]:((~tall(X)|~wise(X)))))&
((?[X]:((creative(X)<~>~old(X))))=>(?[X]:((curious(X)<~>old(X)))))&
(![X]:((curious(X)|happy(X))<=>~tall(X)))&
(![X]:((~kind(X)<~>humble(X))<=>(happy(X)&brave(X))))&
(((~creative(lucy)&kind(lucy)))<=>(?[X]:((brave(X)<~>~old(X)))))&
(![X]:(tall(X)=>~generous(X)))&
((?[X]:((~rich(X)|~patient(X))))=>(?[X]:((~brave(X)|wise(X)))))&
(![X]:((strong(X)&rich(X))<=>~tall(X)))&
(![X]:((quiet(X)&rich(X))=>generous(X)))&
(((~creative(john)&~wise(john)))<=>(?[X]:((~generous(X)&~kind(X)))))&
((?[X]:((~curious(X)<~>strong(X))))<=>(?[X]:((~curious(X)<~>old(X)))))&
(![X]:((~tall(X)<~>~kind(X))=>(tall(X)<~>curious(X))))&
(![X]:((~calm(X)<~>brave(X))<=>(~patient(X)|strong(X))))&
((?[X]:((calm(X)|patient(X))))<=>((~tall(susan)&~calm(susan))))&
(![X]:((~generous(X)<~>wise(X))=>(funny(X)|kind(X))))&
(![X]:((happy(X)<~>funny(X))=>(quiet(X)|~curious(X))))&
(?[X]:((~happy(X)<~>~kind(X))))&
((kind(john)|~generous(john)))&
(?[X]:((humble(X)|~rich(X))))&
(?[X]:(funny(X)))&
(funny(paul))&
(?[X]:((~humble(X)|strong(X))))&
((tall(lucy)<~>~funny(lucy)))&
(?[X]:(wise(X))) | ~brave(susan) | [
"p7",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1400184977008080454518180
% SZS output start Proof for 1400184977008080454518180
8. ! [X0] : ((rich(X0) & strong(X0)) <=> ~tall(X0)) [input p7]
13. ! [X0] : ((~calm(X0) <~> brave(X0)) <=> (strong(X0) | ~patient(X0))) [input p12]
14. ? [X0] : (patient(X0) | calm(X0)) <=> (~calm(susan) & ~tall(susan)) [input p13]
25. brave(susan) [input hypothesis]
61. ! [X0] : (((rich(X0) & strong(X0)) | tall(X0)) & (~tall(X0) | (~rich(X0) | ~strong(X0)))) [nnf transformation 8]
62. ! [X0] : (((rich(X0) & strong(X0)) | tall(X0)) & (~tall(X0) | ~rich(X0) | ~strong(X0))) [flattening 61]
74. ! [X0] : ((((~brave(X0) | calm(X0)) & (brave(X0) | ~calm(X0))) | (~strong(X0) & patient(X0))) & ((strong(X0) | ~patient(X0)) | ((~calm(X0) | ~brave(X0)) & (brave(X0) | calm(X0))))) [nnf transformation 13]
75. ! [X0] : ((((~brave(X0) | calm(X0)) & (brave(X0) | ~calm(X0))) | (~strong(X0) & patient(X0))) & (strong(X0) | ~patient(X0) | ((~calm(X0) | ~brave(X0)) & (brave(X0) | calm(X0))))) [flattening 74]
76. (? [X0] : (patient(X0) | calm(X0)) | (calm(susan) | tall(susan))) & ((~calm(susan) & ~tall(susan)) | ! [X0] : (~patient(X0) & ~calm(X0))) [nnf transformation 14]
77. (? [X0] : (patient(X0) | calm(X0)) | calm(susan) | tall(susan)) & ((~calm(susan) & ~tall(susan)) | ! [X0] : (~patient(X0) & ~calm(X0))) [flattening 76]
78. (? [X0] : (patient(X0) | calm(X0)) | calm(susan) | tall(susan)) & ((~calm(susan) & ~tall(susan)) | ! [X1] : (~patient(X1) & ~calm(X1))) [rectify 77]
79. ? [X0] : (patient(X0) | calm(X0)) => (patient(sK8) | calm(sK8)) [choice axiom]
80. ((patient(sK8) | calm(sK8)) | calm(susan) | tall(susan)) & ((~calm(susan) & ~tall(susan)) | ! [X1] : (~patient(X1) & ~calm(X1))) [skolemisation 78,79]
123. strong(X0) | tall(X0) [cnf transformation 62]
146. ~brave(X0) | calm(X0) | patient(X0) [cnf transformation 75]
147. ~strong(X0) | calm(X0) | ~brave(X0) [cnf transformation 75]
148. ~tall(susan) | ~calm(X1) [cnf transformation 80]
149. ~tall(susan) | ~patient(X1) [cnf transformation 80]
150. ~calm(susan) | ~calm(X1) [cnf transformation 80]
167. brave(susan) [cnf transformation 25]
322. 35 <=> tall(susan) [avatar definition]
326. 36 <=> calm(susan) [avatar definition]
327. ~calm(susan) <- (~36) [avatar component clause 326]
328. calm(susan) <- (36) [avatar component clause 326]
339. 39 <=> ! [X1] : ~patient(X1) [avatar definition]
340. ~patient(X1) <- (39) [avatar component clause 339]
343. 40 <=> ! [X1] : ~calm(X1) [avatar definition]
344. ~calm(X1) <- (40) [avatar component clause 343]
345. 40 | ~36 [avatar split clause 150,326,343]
346. 39 | ~35 [avatar split clause 149,322,339]
347. 40 | ~35 [avatar split clause 148,322,343]
442. calm(susan) | patient(susan) [resolution 146,167]
447. ~brave(X0) | calm(X0) | tall(X0) [resolution 147,123]
491. calm(susan) | tall(susan) [resolution 447,167]
493. tall(susan) <- (~36) [subsumption resolution 491,327]
496. 35 | 36 [avatar split clause 493,326,322]
501. patient(susan) <- (40) [subsumption resolution 442,344]
502. $false <- (39, 40) [subsumption resolution 501,340]
503. ~39 | ~40 [avatar contradiction clause 502]
504. $false <- (36, 40) [subsumption resolution 328,344]
505. ~36 | ~40 [avatar contradiction clause 504]
506. $false [avatar sat refutation 345,346,347,496,503,505]
% SZS output end Proof for 1400184977008080454518180
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not tall then someone is either not humble or tall.
Everyone who is either calm or not strong is both not tall and tall and vice versa.
If mary is either old or funny then mary is either not calm or quiet and vice versa.
If someone is funny then someone is both not wise and strong.
If someone is patient then john is not calm and vice versa.
If someone is both not brave and not curious then someone is both rich and not patient and vice versa.
Everyone who is creative is either old or tall.
If paul is both curious and happy then susan is not happy.
Everyone who is not wise is either funny or not wise and vice versa.
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.
Paul is not calm or not quiet.
Someone is both tall and calm.
Mary is either funny or not kind.
Someone is not old. | Susan is not brave. | neutral | ((~tall(paul))=>(?[X]:((~humble(X)<~>tall(X)))))&
(![X]:((calm(X)<~>~strong(X))<=>(~tall(X)&tall(X))))&
(((old(mary)<~>funny(mary)))<=>((~calm(mary)<~>quiet(mary))))&
((?[X]:(funny(X)))=>(?[X]:((~wise(X)&strong(X)))))&
((?[X]:(patient(X)))<=>(~calm(john)))&
((?[X]:((~brave(X)&~curious(X))))<=>(?[X]:((rich(X)&~patient(X)))))&
(![X]:(creative(X)=>(old(X)<~>tall(X))))&
(((curious(paul)&happy(paul)))=>(~happy(susan)))&
(![X]:(~wise(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))))&
((~calm(paul)|~quiet(paul)))&
(?[X]:((tall(X)&calm(X))))&
((funny(mary)<~>~kind(mary)))&
(?[X]:(~old(X))) | ~brave(susan) | [] | null | 0 |
If someone is calm then someone is strong or humble and vice versa.
If someone is both calm and humble then someone is either rich or not quiet.
If someone is both kind and not patient then someone is both tall and not old.
If someone is not generous or generous then fred is either rich or not patient and vice versa.
Everyone who is both not old and not strong is not rich or strong and vice versa.
If someone is wise then john is not tall or not strong and vice versa.
Everyone who is not humble is both not old and wise and vice versa.
Everyone who is either not rich or creative is both calm and kind and vice versa.
If susan is both calm and not humble then fred is either not old or tall and vice versa.
Everyone who is not funny or happy is both funny and humble.
Everyone who is curious is either not old or old.
Everyone who is not brave is both not calm and not brave.
Everyone who is calm or not humble is either not brave or not calm.
Everyone who is both rich and not rich is either curious or happy and vice versa.
If someone is not calm or calm then someone is both brave and not patient.
If fred is both curious and not happy then someone is either not wise or not tall and vice versa.
Someone is either quiet or not strong.
Mary is either funny or quiet.
Someone is quiet or not old. | Fred is old. | contradiction | ((?[X]:(calm(X)))<=>(?[X]:((strong(X)|humble(X)))))&
((?[X]:((calm(X)&humble(X))))=>(?[X]:((rich(X)<~>~quiet(X)))))&
((?[X]:((kind(X)&~patient(X))))=>(?[X]:((tall(X)&~old(X)))))&
((?[X]:((~generous(X)|generous(X))))<=>((rich(fred)<~>~patient(fred))))&
(![X]:((~old(X)&~strong(X))<=>(~rich(X)|strong(X))))&
((?[X]:(wise(X)))<=>((~tall(john)|~strong(john))))&
(![X]:(~humble(X)<=>(~old(X)&wise(X))))&
(![X]:((~rich(X)<~>creative(X))<=>(calm(X)&kind(X))))&
(((calm(susan)&~humble(susan)))<=>((~old(fred)<~>tall(fred))))&
(![X]:((~funny(X)|happy(X))=>(funny(X)&humble(X))))&
(![X]:(curious(X)=>(~old(X)<~>old(X))))&
(![X]:(~brave(X)=>(~calm(X)&~brave(X))))&
(![X]:((calm(X)|~humble(X))=>(~brave(X)<~>~calm(X))))&
(![X]:((rich(X)&~rich(X))<=>(curious(X)<~>happy(X))))&
((?[X]:((~calm(X)|calm(X))))=>(?[X]:((brave(X)&~patient(X)))))&
(((curious(fred)&~happy(fred)))<=>(?[X]:((~wise(X)<~>~tall(X)))))&
(?[X]:((quiet(X)<~>~strong(X))))&
((funny(mary)<~>quiet(mary)))&
(?[X]:((quiet(X)|~old(X)))) | old(fred) | [
"p0",
"p6",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7634069837606347548622985
% SZS output start Proof for 7634069837606347548622985
1. ? [X0] : calm(X0) <=> ? [X0] : (humble(X0) | strong(X0)) [input p0]
7. ! [X0] : (~humble(X0) <=> (wise(X0) & ~old(X0))) [input p6]
12. ! [X0] : (~brave(X0) => (~brave(X0) & ~calm(X0))) [input p11]
13. ! [X0] : ((~humble(X0) | calm(X0)) => (~brave(X0) <~> ~calm(X0))) [input p12]
20. old(fred) [input hypothesis]
21. ? [X0] : calm(X0) <=> ? [X1] : (humble(X1) | strong(X1)) [rectify 1]
29. ! [X0] : ((~brave(X0) & ~calm(X0)) | brave(X0)) [ennf transformation 12]
30. ! [X0] : ((~brave(X0) <~> ~calm(X0)) | (humble(X0) & ~calm(X0))) [ennf transformation 13]
32. (? [X0] : calm(X0) | ! [X1] : (~humble(X1) & ~strong(X1))) & (? [X1] : (humble(X1) | strong(X1)) | ! [X0] : ~calm(X0)) [nnf transformation 21]
33. (? [X0] : calm(X0) | ! [X1] : (~humble(X1) & ~strong(X1))) & (? [X2] : (humble(X2) | strong(X2)) | ! [X3] : ~calm(X3)) [rectify 32]
34. ? [X0] : calm(X0) => calm(sK0) [choice axiom]
35. ? [X2] : (humble(X2) | strong(X2)) => (humble(sK1) | strong(sK1)) [choice axiom]
36. (calm(sK0) | ! [X1] : (~humble(X1) & ~strong(X1))) & ((humble(sK1) | strong(sK1)) | ! [X3] : ~calm(X3)) [skolemisation 33,35,34]
55. ! [X0] : ((~humble(X0) | (~wise(X0) | old(X0))) & ((wise(X0) & ~old(X0)) | humble(X0))) [nnf transformation 7]
56. ! [X0] : ((~humble(X0) | ~wise(X0) | old(X0)) & ((wise(X0) & ~old(X0)) | humble(X0))) [flattening 55]
62. ! [X0] : (((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | (humble(X0) & ~calm(X0))) [nnf transformation 30]
81. calm(sK0) | ~humble(X1) [cnf transformation 36]
100. ~old(X0) | humble(X0) [cnf transformation 56]
121. ~calm(X0) | brave(X0) [cnf transformation 29]
123. ~calm(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 62]
148. old(fred) [cnf transformation 20]
149. ~calm(X0) | ~brave(X0) [duplicate literal removal 123]
154. 1 <=> ! [X1] : ~humble(X1) [avatar definition]
155. ~humble(X1) <- (1) [avatar component clause 154]
157. 2 <=> calm(sK0) [avatar definition]
159. calm(sK0) <- (2) [avatar component clause 157]
160. 1 | 2 [avatar split clause 81,157,154]
166. 4 <=> ! [X3] : ~calm(X3) [avatar definition]
167. ~calm(X3) <- (4) [avatar component clause 166]
245. 22 <=> old(fred) [avatar definition]
246. old(fred) <- (22) [avatar component clause 245]
264. ~calm(X0) [subsumption resolution 149,121]
265. 4 [avatar split clause 264,166]
321. 22 [avatar split clause 148,245]
326. $false <- (2, 4) [resolution 167,159]
327. ~2 | ~4 [avatar contradiction clause 326]
333. humble(fred) <- (22) [resolution 100,246]
334. $false <- (1, 22) [subsumption resolution 333,155]
335. ~1 | ~22 [avatar contradiction clause 334]
336. $false [avatar sat refutation 160,265,321,327,335]
% SZS output end Proof for 7634069837606347548622985
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is either not humble or not old and vice versa.
If john is either not tall or not humble then someone is not humble.
Everyone who is rich or not old is both strong and calm and vice versa.
If paul is not brave or humble then someone is calm or not patient.
Everyone who is both not generous and kind is both patient and not kind and vice versa.
Everyone who is patient or not curious is both not funny and not happy and vice versa.
If someone is both not calm and not creative then someone is both creative and old and vice versa.
Everyone who is both patient and funny is creative or brave.
If someone is either not kind or generous then someone is both happy and brave.
If someone is tall then someone is either funny or brave and vice versa.
Everyone who is happy is both not brave and patient and vice versa.
Everyone who is not patient or happy is either not creative or not quiet.
If fred is either not brave or not kind then fred is either not patient or not tall.
Everyone who is not kind or creative is not calm.
Everyone who is not funny or not strong is both not kind and not curious.
Someone is not happy or wise.
Someone is both curious and strong.
Fred is not kind or happy.
Someone is funny. | John is calm. | contradiction | (![X]:(generous(X)<=>(~humble(X)<~>~old(X))))&
(((~tall(john)<~>~humble(john)))=>(?[X]:(~humble(X))))&
(![X]:((rich(X)|~old(X))<=>(strong(X)&calm(X))))&
(((~brave(paul)|humble(paul)))=>(?[X]:((calm(X)|~patient(X)))))&
(![X]:((~generous(X)&kind(X))<=>(patient(X)&~kind(X))))&
(![X]:((patient(X)|~curious(X))<=>(~funny(X)&~happy(X))))&
((?[X]:((~calm(X)&~creative(X))))<=>(?[X]:((creative(X)&old(X)))))&
(![X]:((patient(X)&funny(X))=>(creative(X)|brave(X))))&
((?[X]:((~kind(X)<~>generous(X))))=>(?[X]:((happy(X)&brave(X)))))&
((?[X]:(tall(X)))<=>(?[X]:((funny(X)<~>brave(X)))))&
(![X]:(happy(X)<=>(~brave(X)&patient(X))))&
(![X]:((~patient(X)|happy(X))=>(~creative(X)<~>~quiet(X))))&
(((~brave(fred)<~>~kind(fred)))=>((~patient(fred)<~>~tall(fred))))&
(![X]:((~kind(X)|creative(X))=>~calm(X)))&
(![X]:((~funny(X)|~strong(X))=>(~kind(X)&~curious(X))))&
(?[X]:((~happy(X)|wise(X))))&
(?[X]:((curious(X)&strong(X))))&
((~kind(fred)|happy(fred)))&
(?[X]:(funny(X))) | calm(john) | [
"p4",
"p5",
"p8",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5999743054245028792840796
% SZS output start Proof for 5999743054245028792840796
5. ! [X0] : ((kind(X0) & ~generous(X0)) <=> (~kind(X0) & patient(X0))) [input p4]
6. ! [X0] : ((~curious(X0) | patient(X0)) <=> (~happy(X0) & ~funny(X0))) [input p5]
9. ? [X0] : (~kind(X0) <~> generous(X0)) => ? [X0] : (brave(X0) & happy(X0)) [input p8]
11. ! [X0] : (happy(X0) <=> (patient(X0) & ~brave(X0))) [input p10]
14. ! [X0] : ((creative(X0) | ~kind(X0)) => ~calm(X0)) [input p13]
20. calm(john) [input hypothesis]
22. ? [X0] : (~kind(X0) <~> generous(X0)) => ? [X1] : (brave(X1) & happy(X1)) [rectify 9]
29. ? [X1] : (brave(X1) & happy(X1)) | ! [X0] : (~kind(X0) <=> generous(X0)) [ennf transformation 22]
32. ! [X0] : (~calm(X0) | (~creative(X0) & kind(X0))) [ennf transformation 14]
42. ! [X0] : (((kind(X0) & ~generous(X0)) | (kind(X0) | ~patient(X0))) & ((~kind(X0) & patient(X0)) | (~kind(X0) | generous(X0)))) [nnf transformation 5]
43. ! [X0] : (((kind(X0) & ~generous(X0)) | kind(X0) | ~patient(X0)) & ((~kind(X0) & patient(X0)) | ~kind(X0) | generous(X0))) [flattening 42]
44. ! [X0] : (((~curious(X0) | patient(X0)) | (happy(X0) | funny(X0))) & ((~happy(X0) & ~funny(X0)) | (curious(X0) & ~patient(X0)))) [nnf transformation 6]
45. ! [X0] : ((~curious(X0) | patient(X0) | happy(X0) | funny(X0)) & ((~happy(X0) & ~funny(X0)) | (curious(X0) & ~patient(X0)))) [flattening 44]
51. ? [X1] : (brave(X1) & happy(X1)) | ! [X0] : ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0))) [nnf transformation 29]
52. ? [X0] : (brave(X0) & happy(X0)) | ! [X1] : ((~kind(X1) | ~generous(X1)) & (generous(X1) | kind(X1))) [rectify 51]
53. ? [X0] : (brave(X0) & happy(X0)) => (brave(sK4) & happy(sK4)) [choice axiom]
54. (brave(sK4) & happy(sK4)) | ! [X1] : ((~kind(X1) | ~generous(X1)) & (generous(X1) | kind(X1))) [skolemisation 52,53]
60. ! [X0] : ((happy(X0) | (~patient(X0) | brave(X0))) & ((patient(X0) & ~brave(X0)) | ~happy(X0))) [nnf transformation 11]
61. ! [X0] : ((happy(X0) | ~patient(X0) | brave(X0)) & ((patient(X0) & ~brave(X0)) | ~happy(X0))) [flattening 60]
82. ~kind(X0) | ~kind(X0) | generous(X0) [cnf transformation 43]
87. ~happy(X0) | ~patient(X0) [cnf transformation 45]
96. happy(sK4) | ~kind(X1) | ~generous(X1) [cnf transformation 54]
104. patient(X0) | ~happy(X0) [cnf transformation 61]
114. ~calm(X0) | kind(X0) [cnf transformation 32]
124. calm(john) [cnf transformation 20]
125. ~kind(X0) | generous(X0) [duplicate literal removal 82]
187. 14 <=> ! [X1] : ~kind(X1) [avatar definition]
188. ~kind(X1) <- (14) [avatar component clause 187]
199. happy(sK4) | ~kind(X1) [subsumption resolution 96,125]
201. 17 <=> happy(sK4) [avatar definition]
203. happy(sK4) <- (17) [avatar component clause 201]
204. 14 | 17 [avatar split clause 199,201,187]
233. ~happy(X0) [subsumption resolution 104,87]
257. kind(john) [resolution 114,124]
259. $false <- (14) [subsumption resolution 257,188]
260. ~14 [avatar contradiction clause 259]
262. $false <- (17) [subsumption resolution 203,233]
263. ~17 [avatar contradiction clause 262]
264. $false [avatar sat refutation 204,260,263]
% SZS output end Proof for 5999743054245028792840796
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and generous is both not patient and not strong and vice versa.
If someone is either not brave or not patient then paul is not funny or not quiet.
Everyone who is both not happy and curious is patient and vice versa.
If mary is tall then someone is either not kind or not generous and vice versa.
If mary is not generous or not patient then someone is patient or not humble and vice versa.
Everyone who is both brave and not rich is either kind or not calm.
Everyone who is either not happy or not curious is old.
Everyone who is old is old or not strong and vice versa.
Everyone who is not kind is not patient and vice versa.
Everyone who is not patient is both not humble and brave.
Everyone who is both not happy and curious is happy and vice versa.
Everyone who is funny or patient is not happy.
If paul is wise then someone is not kind and vice versa.
If someone is curious or not wise then john is calm or patient and vice versa.
Everyone who is quiet is either curious or rich.
Someone is not tall or humble.
Someone is either funny or strong.
Someone is not tall or quiet.
Someone is either curious or generous.
Paul is either generous or not quiet. | John is not old. | neutral | (![X]:((wise(X)&generous(X))<=>(~patient(X)&~strong(X))))&
((?[X]:((~brave(X)<~>~patient(X))))=>((~funny(paul)|~quiet(paul))))&
(![X]:((~happy(X)&curious(X))<=>patient(X)))&
((tall(mary))<=>(?[X]:((~kind(X)<~>~generous(X)))))&
(((~generous(mary)|~patient(mary)))<=>(?[X]:((patient(X)|~humble(X)))))&
(![X]:((brave(X)&~rich(X))=>(kind(X)<~>~calm(X))))&
(![X]:((~happy(X)<~>~curious(X))=>old(X)))&
(![X]:(old(X)<=>(old(X)|~strong(X))))&
(![X]:(~kind(X)<=>~patient(X)))&
(![X]:(~patient(X)=>(~humble(X)&brave(X))))&
(![X]:((~happy(X)&curious(X))<=>happy(X)))&
(![X]:((funny(X)|patient(X))=>~happy(X)))&
((wise(paul))<=>(?[X]:(~kind(X))))&
((?[X]:((curious(X)|~wise(X))))<=>((calm(john)|patient(john))))&
(![X]:(quiet(X)=>(curious(X)<~>rich(X))))&
(?[X]:((~tall(X)|humble(X))))&
(?[X]:((funny(X)<~>strong(X))))&
(?[X]:((~tall(X)|quiet(X))))&
(?[X]:((curious(X)<~>generous(X))))&
((generous(paul)<~>~quiet(paul))) | ~old(john) | [] | null | 0 |
If someone is brave or rich then john is both not funny and not happy.
Everyone who is tall is not brave and vice versa.
Everyone who is generous is not happy and vice versa.
Everyone who is either not strong or funny is both generous and humble and vice versa.
If paul is both not kind and not brave then mary is either not wise or not curious and vice versa.
Everyone who is not curious is both old and not kind and vice versa.
Everyone who is humble is both happy and not wise.
Everyone who is either not happy or brave is either happy or not wise and vice versa.
If someone is tall then mary is both strong and not calm and vice versa.
Everyone who is old is strong or quiet.
Everyone who is either not curious or not happy is not kind and vice versa.
Everyone who is both not humble and not kind is both funny and not brave.
If mary is rich or brave then paul is quiet or not funny and vice versa.
If someone is quiet or not generous then lucy is either curious or not happy and vice versa.
If someone is creative then paul is either humble or not humble and vice versa.
Susan is creative or not wise.
Someone is brave or happy.
Alice is creative or funny.
Susan is curious or not brave.
Paul is either brave or not rich.
Alice is not funny or kind. | Lucy is not kind. | contradiction | ((?[X]:((brave(X)|rich(X))))=>((~funny(john)&~happy(john))))&
(![X]:(tall(X)<=>~brave(X)))&
(![X]:(generous(X)<=>~happy(X)))&
(![X]:((~strong(X)<~>funny(X))<=>(generous(X)&humble(X))))&
(((~kind(paul)&~brave(paul)))<=>((~wise(mary)<~>~curious(mary))))&
(![X]:(~curious(X)<=>(old(X)&~kind(X))))&
(![X]:(humble(X)=>(happy(X)&~wise(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(happy(X)<~>~wise(X))))&
((?[X]:(tall(X)))<=>((strong(mary)&~calm(mary))))&
(![X]:(old(X)=>(strong(X)|quiet(X))))&
(![X]:((~curious(X)<~>~happy(X))<=>~kind(X)))&
(![X]:((~humble(X)&~kind(X))=>(funny(X)&~brave(X))))&
(((rich(mary)|brave(mary)))<=>((quiet(paul)|~funny(paul))))&
((?[X]:((quiet(X)|~generous(X))))<=>((curious(lucy)<~>~happy(lucy))))&
((?[X]:(creative(X)))<=>((humble(paul)<~>~humble(paul))))&
((creative(susan)|~wise(susan)))&
(?[X]:((brave(X)|happy(X))))&
((creative(alice)|funny(alice)))&
((curious(susan)|~brave(susan)))&
((brave(paul)<~>~rich(paul)))&
((~funny(alice)|kind(alice))) | ~kind(lucy) | [
"p1",
"p2",
"p3",
"p5",
"p6",
"p7",
"p8",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2133647736186884763750903
% SZS output start Proof for 2133647736186884763750903
2. ! [X0] : (tall(X0) <=> ~brave(X0)) [input p1]
3. ! [X0] : (generous(X0) <=> ~happy(X0)) [input p2]
4. ! [X0] : ((~strong(X0) <~> funny(X0)) <=> (humble(X0) & generous(X0))) [input p3]
6. ! [X0] : (~curious(X0) <=> (~kind(X0) & old(X0))) [input p5]
7. ! [X0] : (humble(X0) => (~wise(X0) & happy(X0))) [input p6]
8. ! [X0] : ((~happy(X0) <~> brave(X0)) <=> (happy(X0) <~> ~wise(X0))) [input p7]
9. ? [X0] : tall(X0) <=> (~calm(mary) & strong(mary)) [input p8]
11. ! [X0] : ((~curious(X0) <~> ~happy(X0)) <=> ~kind(X0)) [input p10]
12. ! [X0] : ((~kind(X0) & ~humble(X0)) => (~brave(X0) & funny(X0))) [input p11]
14. ? [X0] : (~generous(X0) | quiet(X0)) <=> (curious(lucy) <~> ~happy(lucy)) [input p13]
22. ~kind(lucy) [input hypothesis]
24. ! [X0] : ((~wise(X0) & happy(X0)) | ~humble(X0)) [ennf transformation 7]
27. ! [X0] : ((~brave(X0) & funny(X0)) | (kind(X0) | humble(X0))) [ennf transformation 12]
28. ! [X0] : ((~brave(X0) & funny(X0)) | kind(X0) | humble(X0)) [flattening 27]
29. ! [X0] : ((tall(X0) | brave(X0)) & (~brave(X0) | ~tall(X0))) [nnf transformation 2]
30. ! [X0] : ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0))) [nnf transformation 3]
31. ! [X0] : ((((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | (~humble(X0) | ~generous(X0))) & ((humble(X0) & generous(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0))))) [nnf transformation 4]
32. ! [X0] : ((((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | ~humble(X0) | ~generous(X0)) & ((humble(X0) & generous(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0))))) [flattening 31]
35. ! [X0] : ((~curious(X0) | (kind(X0) | ~old(X0))) & ((~kind(X0) & old(X0)) | curious(X0))) [nnf transformation 6]
36. ! [X0] : ((~curious(X0) | kind(X0) | ~old(X0)) & ((~kind(X0) & old(X0)) | curious(X0))) [flattening 35]
37. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | ((happy(X0) | wise(X0)) & (~wise(X0) | ~happy(X0)))) & (((wise(X0) | ~happy(X0)) & (~wise(X0) | happy(X0))) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [nnf transformation 8]
38. (? [X0] : tall(X0) | (calm(mary) | ~strong(mary))) & ((~calm(mary) & strong(mary)) | ! [X0] : ~tall(X0)) [nnf transformation 9]
39. (? [X0] : tall(X0) | calm(mary) | ~strong(mary)) & ((~calm(mary) & strong(mary)) | ! [X0] : ~tall(X0)) [flattening 38]
40. (? [X0] : tall(X0) | calm(mary) | ~strong(mary)) & ((~calm(mary) & strong(mary)) | ! [X1] : ~tall(X1)) [rectify 39]
41. ? [X0] : tall(X0) => tall(sK0) [choice axiom]
42. (tall(sK0) | calm(mary) | ~strong(mary)) & ((~calm(mary) & strong(mary)) | ! [X1] : ~tall(X1)) [skolemisation 40,41]
43. ! [X0] : ((((happy(X0) | curious(X0)) & (~happy(X0) | ~curious(X0))) | kind(X0)) & (~kind(X0) | ((~curious(X0) | happy(X0)) & (~happy(X0) | curious(X0))))) [nnf transformation 11]
46. (? [X0] : (~generous(X0) | quiet(X0)) | ((curious(lucy) | happy(lucy)) & (~happy(lucy) | ~curious(lucy)))) & (((happy(lucy) | ~curious(lucy)) & (~happy(lucy) | curious(lucy))) | ! [X0] : (generous(X0) & ~quiet(X0))) [nnf transformation 14]
47. (? [X0] : (~generous(X0) | quiet(X0)) | ((curious(lucy) | happy(lucy)) & (~happy(lucy) | ~curious(lucy)))) & (((happy(lucy) | ~curious(lucy)) & (~happy(lucy) | curious(lucy))) | ! [X1] : (generous(X1) & ~quiet(X1))) [rectify 46]
48. ? [X0] : (~generous(X0) | quiet(X0)) => (~generous(sK1) | quiet(sK1)) [choice axiom]
49. ((~generous(sK1) | quiet(sK1)) | ((curious(lucy) | happy(lucy)) & (~happy(lucy) | ~curious(lucy)))) & (((happy(lucy) | ~curious(lucy)) & (~happy(lucy) | curious(lucy))) | ! [X1] : (generous(X1) & ~quiet(X1))) [skolemisation 47,48]
62. tall(X0) | brave(X0) [cnf transformation 29]
63. ~generous(X0) | ~happy(X0) [cnf transformation 30]
68. ~strong(X0) | humble(X0) | ~funny(X0) [cnf transformation 32]
78. ~kind(X0) | curious(X0) [cnf transformation 36]
80. ~humble(X0) | happy(X0) [cnf transformation 24]
81. ~wise(X0) | ~humble(X0) [cnf transformation 24]
85. wise(X0) | ~happy(X0) | ~happy(X0) | ~brave(X0) [cnf transformation 37]
89. ~brave(X0) | happy(X0) | happy(X0) | wise(X0) [cnf transformation 37]
90. strong(mary) | ~tall(X1) [cnf transformation 42]
95. ~kind(X0) | ~curious(X0) | happy(X0) [cnf transformation 43]
96. ~curious(X0) | ~happy(X0) | kind(X0) [cnf transformation 43]
97. happy(X0) | curious(X0) | kind(X0) [cnf transformation 43]
98. kind(X0) | funny(X0) | humble(X0) [cnf transformation 28]
99. ~brave(X0) | kind(X0) | humble(X0) [cnf transformation 28]
105. ~happy(lucy) | curious(lucy) | generous(X1) [cnf transformation 49]
107. happy(lucy) | ~curious(lucy) | generous(X1) [cnf transformation 49]
121. ~kind(lucy) [cnf transformation 22]
125. wise(X0) | ~happy(X0) | ~brave(X0) [duplicate literal removal 85]
127. ~brave(X0) | happy(X0) | wise(X0) [duplicate literal removal 89]
168. ~brave(X0) | wise(X0) [subsumption resolution 125,127]
171. 9 <=> strong(mary) [avatar definition]
172. strong(mary) <- (9) [avatar component clause 171]
184. 12 <=> ! [X1] : ~tall(X1) [avatar definition]
185. ~tall(X1) <- (12) [avatar component clause 184]
187. 12 | 9 [avatar split clause 90,171,184]
188. curious(X0) | happy(X0) [subsumption resolution 97,78]
189. ~kind(X0) | happy(X0) [subsumption resolution 95,78]
211. 17 <=> curious(lucy) [avatar definition]
212. curious(lucy) <- (17) [avatar component clause 211]
215. 18 <=> happy(lucy) [avatar definition]
227. happy(lucy) | generous(X1) [subsumption resolution 107,188]
229. 21 <=> ! [X1] : generous(X1) [avatar definition]
230. generous(X1) <- (21) [avatar component clause 229]
231. 21 | 18 [avatar split clause 227,215,229]
237. curious(lucy) | generous(X1) [subsumption resolution 105,188]
238. 21 | 17 [avatar split clause 237,211,229]
256. 26 <=> wise(susan) [avatar definition]
257. wise(susan) <- (26) [avatar component clause 256]
258. ~wise(susan) <- (~26) [avatar component clause 256]
283. 32 <=> brave(susan) [avatar definition]
284. brave(susan) <- (32) [avatar component clause 283]
285. ~brave(susan) <- (~32) [avatar component clause 283]
299. brave(X1) <- (12) [resolution 62,185]
302. $false <- (12, ~32) [resolution 299,285]
303. ~12 | 32 [avatar contradiction clause 302]
310. wise(X0) <- (12) [resolution 168,299]
314. $false <- (12, ~26) [resolution 310,258]
317. ~12 | 26 [avatar contradiction clause 314]
331. ~happy(lucy) | kind(lucy) <- (17) [resolution 96,212]
346. 37 <=> kind(susan) [avatar definition]
348. kind(susan) <- (37) [avatar component clause 346]
354. ~happy(lucy) <- (17) [subsumption resolution 331,121]
355. ~18 | ~17 [avatar split clause 354,211,215]
357. ~happy(X0) <- (21) [resolution 230,63]
363. funny(X0) | humble(X0) | happy(X0) [resolution 98,189]
375. funny(X0) | humble(X0) <- (21) [subsumption resolution 363,357]
401. humble(mary) | ~funny(mary) <- (9) [resolution 172,68]
403. humble(mary) <- (9, 21) [subsumption resolution 401,375]
406. ~humble(susan) <- (26) [resolution 257,81]
409. kind(susan) | humble(susan) <- (32) [resolution 99,284]
411. kind(susan) <- (26, 32) [subsumption resolution 409,406]
412. 37 | ~26 | ~32 [avatar split clause 411,283,256,346]
418. happy(susan) <- (37) [resolution 348,189]
422. $false <- (21, 37) [subsumption resolution 418,357]
423. ~21 | ~37 [avatar contradiction clause 422]
440. happy(mary) <- (9, 21) [resolution 403,80]
444. $false <- (9, 21) [subsumption resolution 440,357]
445. ~9 | ~21 [avatar contradiction clause 444]
446. $false [avatar sat refutation 187,231,238,303,317,355,412,423,445]
% SZS output end Proof for 2133647736186884763750903
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is either kind or generous and vice versa. Everyone who is both not brave and kind is both old and not kind. Everyone who is either not creative or not happy is old. Everyone who is both not humble and not rich is either generous or creative and vice versa. Everyone who is either not happy or strong is either not kind or not wise. Everyone who is both funny and not generous is not happy or not tall and vice versa. Everyone who is brave or not patient is both not creative and not tall and vice versa. If susan is not curious or not kind then someone is kind and vice versa. Everyone who is not tall is either wise or not quiet and vice versa. Everyone who is both not old and generous is both not creative and quiet. Everyone who is both not old and creative is either not quiet or not tall and vice versa. Everyone who is both not humble and not creative is strong or not kind and vice versa. If mary is both creative and not quiet then someone is both not happy and funny. If john is both not calm and not quiet then fred is creative or calm and vice versa. Everyone who is both rich and not wise is both tall and not curious and vice versa. If fred is either not patient or not creative then someone is both wise and creative. Someone is not curious or not quiet. Susan is both not brave and not humble. Mary is either not brave or rich. Someone is rich. Susan is not calm or not strong. | Susan is not quiet. | contradiction | (![X]:(~calm(X)<=>(kind(X)<~>generous(X))))&
(![X]:((~brave(X)&kind(X))=>(old(X)&~kind(X))))&
(![X]:((~creative(X)<~>~happy(X))=>old(X)))&
(![X]:((~humble(X)&~rich(X))<=>(generous(X)<~>creative(X))))&
(![X]:((~happy(X)<~>strong(X))=>(~kind(X)<~>~wise(X))))&
(![X]:((funny(X)&~generous(X))<=>(~happy(X)|~tall(X))))&
(![X]:((brave(X)|~patient(X))<=>(~creative(X)&~tall(X))))&
(((~curious(susan)|~kind(susan)))<=>(?[X]:(kind(X))))&
(![X]:(~tall(X)<=>(wise(X)<~>~quiet(X))))&
(![X]:((~old(X)&generous(X))=>(~creative(X)&quiet(X))))&
(![X]:((~old(X)&creative(X))<=>(~quiet(X)<~>~tall(X))))&
(![X]:((~humble(X)&~creative(X))<=>(strong(X)|~kind(X))))&
(((creative(mary)&~quiet(mary)))=>(?[X]:((~happy(X)&funny(X)))))&
(((~calm(john)&~quiet(john)))<=>((creative(fred)|calm(fred))))&
(![X]:((rich(X)&~wise(X))<=>(tall(X)&~curious(X))))&
(((~patient(fred)<~>~creative(fred)))=>(?[X]:((wise(X)&creative(X)))))&
(?[X]:((~curious(X)|~quiet(X))))&
((~brave(susan)&~humble(susan)))&
((~brave(mary)<~>rich(mary)))&
(?[X]:(rich(X)))&
((~calm(susan)|~strong(susan))) | ~quiet(susan) | [
"p1",
"p3",
"p5",
"p8",
"p10",
"p11",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2854669006584489781688674
% SZS output start Proof for 2854669006584489781688674
2. ! [X0] : ((kind(X0) & ~brave(X0)) => (~kind(X0) & old(X0))) [input p1]
4. ! [X0] : ((~rich(X0) & ~humble(X0)) <=> (generous(X0) <~> creative(X0))) [input p3]
6. ! [X0] : ((~generous(X0) & funny(X0)) <=> (~tall(X0) | ~happy(X0))) [input p5]
9. ! [X0] : (~tall(X0) <=> (wise(X0) <~> ~quiet(X0))) [input p8]
11. ! [X0] : ((creative(X0) & ~old(X0)) <=> (~quiet(X0) <~> ~tall(X0))) [input p10]
12. ! [X0] : ((~creative(X0) & ~humble(X0)) <=> (~kind(X0) | strong(X0))) [input p11]
15. ! [X0] : ((~wise(X0) & rich(X0)) <=> (~curious(X0) & tall(X0))) [input p14]
18. ~humble(susan) & ~brave(susan) [input p17]
22. ~quiet(susan) [input hypothesis]
23. ! [X0] : ((~kind(X0) & old(X0)) | (~kind(X0) | brave(X0))) [ennf transformation 2]
24. ! [X0] : ((~kind(X0) & old(X0)) | ~kind(X0) | brave(X0)) [flattening 23]
34. ! [X0] : (((~rich(X0) & ~humble(X0)) | ((generous(X0) | ~creative(X0)) & (creative(X0) | ~generous(X0)))) & (((~creative(X0) | ~generous(X0)) & (creative(X0) | generous(X0))) | (rich(X0) | humble(X0)))) [nnf transformation 4]
35. ! [X0] : (((~rich(X0) & ~humble(X0)) | ((generous(X0) | ~creative(X0)) & (creative(X0) | ~generous(X0)))) & (((~creative(X0) | ~generous(X0)) & (creative(X0) | generous(X0))) | rich(X0) | humble(X0))) [flattening 34]
37. ! [X0] : (((~generous(X0) & funny(X0)) | (tall(X0) & happy(X0))) & ((~tall(X0) | ~happy(X0)) | (generous(X0) | ~funny(X0)))) [nnf transformation 6]
38. ! [X0] : (((~generous(X0) & funny(X0)) | (tall(X0) & happy(X0))) & (~tall(X0) | ~happy(X0) | generous(X0) | ~funny(X0))) [flattening 37]
46. ! [X0] : ((~tall(X0) | ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) & (((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | tall(X0))) [nnf transformation 9]
47. ! [X0] : (((creative(X0) & ~old(X0)) | ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0)))) & (((tall(X0) | quiet(X0)) & (~tall(X0) | ~quiet(X0))) | (~creative(X0) | old(X0)))) [nnf transformation 11]
48. ! [X0] : (((creative(X0) & ~old(X0)) | ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0)))) & (((tall(X0) | quiet(X0)) & (~tall(X0) | ~quiet(X0))) | ~creative(X0) | old(X0))) [flattening 47]
49. ! [X0] : (((~creative(X0) & ~humble(X0)) | (kind(X0) & ~strong(X0))) & ((~kind(X0) | strong(X0)) | (creative(X0) | humble(X0)))) [nnf transformation 12]
50. ! [X0] : (((~creative(X0) & ~humble(X0)) | (kind(X0) & ~strong(X0))) & (~kind(X0) | strong(X0) | creative(X0) | humble(X0))) [flattening 49]
55. ! [X0] : (((~wise(X0) & rich(X0)) | (curious(X0) | ~tall(X0))) & ((~curious(X0) & tall(X0)) | (wise(X0) | ~rich(X0)))) [nnf transformation 15]
56. ! [X0] : (((~wise(X0) & rich(X0)) | curious(X0) | ~tall(X0)) & ((~curious(X0) & tall(X0)) | wise(X0) | ~rich(X0))) [flattening 55]
70. ~kind(X0) | ~kind(X0) | brave(X0) [cnf transformation 24]
73. rich(X0) | generous(X0) | creative(X0) | humble(X0) [cnf transformation 35]
87. ~generous(X0) | tall(X0) [cnf transformation 38]
97. ~wise(X0) | quiet(X0) | tall(X0) [cnf transformation 46]
99. ~tall(X0) | wise(X0) | quiet(X0) [cnf transformation 46]
106. ~tall(X0) | creative(X0) | quiet(X0) [cnf transformation 48]
112. ~creative(X0) | kind(X0) [cnf transformation 50]
120. ~rich(X0) | wise(X0) | tall(X0) [cnf transformation 56]
129. ~brave(susan) [cnf transformation 18]
130. ~humble(susan) [cnf transformation 18]
135. ~quiet(susan) [cnf transformation 22]
136. ~kind(X0) | brave(X0) [duplicate literal removal 70]
145. 3 <=> kind(susan) [avatar definition]
146. kind(susan) <- (3) [avatar component clause 145]
147. ~kind(susan) <- (~3) [avatar component clause 145]
326. generous(X0) | creative(X0) | humble(X0) | wise(X0) | tall(X0) [resolution 73,120]
341. tall(X0) | humble(X0) | wise(X0) | creative(X0) [subsumption resolution 326,87]
472. 41 <=> wise(susan) [avatar definition]
474. wise(susan) <- (41) [avatar component clause 472]
637. humble(X3) | wise(X3) | creative(X3) | wise(X3) | quiet(X3) [resolution 341,99]
643. quiet(X3) | wise(X3) | creative(X3) | humble(X3) [duplicate literal removal 637]
904. wise(susan) | creative(susan) | humble(susan) [resolution 643,135]
909. wise(susan) | creative(susan) [subsumption resolution 904,130]
911. 75 <=> creative(susan) [avatar definition]
912. ~creative(susan) <- (~75) [avatar component clause 911]
913. creative(susan) <- (75) [avatar component clause 911]
914. 75 | 41 [avatar split clause 909,472,911]
935. kind(susan) <- (75) [resolution 913,112]
959. 80 <=> tall(susan) [avatar definition]
961. tall(susan) <- (80) [avatar component clause 959]
963. $false <- (~3, 75) [subsumption resolution 935,147]
964. 3 | ~75 [avatar contradiction clause 963]
970. quiet(susan) | tall(susan) <- (41) [resolution 474,97]
971. tall(susan) <- (41) [subsumption resolution 970,135]
972. 80 | ~41 [avatar split clause 971,472,959]
1479. creative(susan) | quiet(susan) <- (80) [resolution 961,106]
1488. quiet(susan) <- (~75, 80) [subsumption resolution 1479,912]
1489. $false <- (~75, 80) [subsumption resolution 1488,135]
1490. 75 | ~80 [avatar contradiction clause 1489]
1503. brave(susan) <- (3) [resolution 146,136]
1507. $false <- (3) [subsumption resolution 1503,129]
1508. ~3 [avatar contradiction clause 1507]
1509. $false [avatar sat refutation 914,964,972,1490,1508]
% SZS output end Proof for 2854669006584489781688674
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5756
% Time elapsed: 0.045 s
% ------------------------------
% ------------------------------
| 0 |
If someone is happy then john is either calm or brave.
If someone is both not rich and generous then someone is not old or rich.
If john is strong or not curious then someone is both not kind and not curious and vice versa.
If alice is wise or not strong then someone is both creative and calm.
Everyone who is both calm and not rich is not rich or tall and vice versa.
If susan is both not quiet and tall then paul is either kind or curious.
If someone is rich or humble then someone is either creative or happy and vice versa.
If someone is both kind and not wise then someone is curious or generous and vice versa.
If lucy is creative or strong then someone is not humble and vice versa.
If paul is either patient or kind then someone is not creative or calm and vice versa.
If someone is brave then someone is both not kind and not rich and vice versa.
Everyone who is not strong or patient is not strong.
If someone is old then someone is not funny or not kind.
If mary is either patient or not generous then someone is patient or old and vice versa.
Everyone who is either tall or funny is not happy and vice versa.
If someone is not wise or funny then susan is not calm.
Someone is either not rich or not curious.
Someone is either not patient or not calm.
Someone is both happy and not patient.
Someone is both not rich and not humble.
Lucy is either funny or not strong.
Someone is either not calm or strong. | Paul is curious. | neutral | ((?[X]:(happy(X)))=>((calm(john)<~>brave(john))))&
((?[X]:((~rich(X)&generous(X))))=>(?[X]:((~old(X)|rich(X)))))&
(((strong(john)|~curious(john)))<=>(?[X]:((~kind(X)&~curious(X)))))&
(((wise(alice)|~strong(alice)))=>(?[X]:((creative(X)&calm(X)))))&
(![X]:((calm(X)&~rich(X))<=>(~rich(X)|tall(X))))&
(((~quiet(susan)&tall(susan)))=>((kind(paul)<~>curious(paul))))&
((?[X]:((rich(X)|humble(X))))<=>(?[X]:((creative(X)<~>happy(X)))))&
((?[X]:((kind(X)&~wise(X))))<=>(?[X]:((curious(X)|generous(X)))))&
(((creative(lucy)|strong(lucy)))<=>(?[X]:(~humble(X))))&
(((patient(paul)<~>kind(paul)))<=>(?[X]:((~creative(X)|calm(X)))))&
((?[X]:(brave(X)))<=>(?[X]:((~kind(X)&~rich(X)))))&
(![X]:((~strong(X)|patient(X))=>~strong(X)))&
((?[X]:(old(X)))=>(?[X]:((~funny(X)|~kind(X)))))&
(((patient(mary)<~>~generous(mary)))<=>(?[X]:((patient(X)|old(X)))))&
(![X]:((tall(X)<~>funny(X))<=>~happy(X)))&
((?[X]:((~wise(X)|funny(X))))=>(~calm(susan)))&
(?[X]:((~rich(X)<~>~curious(X))))&
(?[X]:((~patient(X)<~>~calm(X))))&
(?[X]:((happy(X)&~patient(X))))&
(?[X]:((~rich(X)&~humble(X))))&
((funny(lucy)<~>~strong(lucy)))&
(?[X]:((~calm(X)<~>strong(X)))) | curious(paul) | [] | null | 0 |
Everyone who is not strong is both happy and not happy.
If susan is both curious and patient then someone is either calm or not rich.
Everyone who is both not happy and curious is both not tall and rich.
Everyone who is brave or not patient is not funny and vice versa.
Everyone who is tall is both not generous and not quiet.
Everyone who is not creative is either kind or creative.
Everyone who is either not calm or not tall is either not strong or not tall and vice versa.
Everyone who is not brave or not patient is humble and vice versa.
Everyone who is not brave or patient is creative or humble.
Everyone who is either tall or not funny is either brave or funny and vice versa.
Everyone who is either kind or quiet is quiet and vice versa.
Everyone who is quiet or funny is not creative and vice versa.
Everyone who is both not wise and tall is both not curious and not patient and vice versa.
Everyone who is tall or not old is not quiet or not old.
Everyone who is both not kind and not old is either not humble or not rich and vice versa.
If someone is kind or humble then alice is quiet.
Someone is either curious or not brave.
Susan is happy.
Someone is both not rich and not curious.
Someone is not happy or tall.
Susan is both happy and calm.
Someone is not calm or patient. | Susan is not funny. | entailment | (![X]:(~strong(X)=>(happy(X)&~happy(X))))&
(((curious(susan)&patient(susan)))=>(?[X]:((calm(X)<~>~rich(X)))))&
(![X]:((~happy(X)&curious(X))=>(~tall(X)&rich(X))))&
(![X]:((brave(X)|~patient(X))<=>~funny(X)))&
(![X]:(tall(X)=>(~generous(X)&~quiet(X))))&
(![X]:(~creative(X)=>(kind(X)<~>creative(X))))&
(![X]:((~calm(X)<~>~tall(X))<=>(~strong(X)<~>~tall(X))))&
(![X]:((~brave(X)|~patient(X))<=>humble(X)))&
(![X]:((~brave(X)|patient(X))=>(creative(X)|humble(X))))&
(![X]:((tall(X)<~>~funny(X))<=>(brave(X)<~>funny(X))))&
(![X]:((kind(X)<~>quiet(X))<=>quiet(X)))&
(![X]:((quiet(X)|funny(X))<=>~creative(X)))&
(![X]:((~wise(X)&tall(X))<=>(~curious(X)&~patient(X))))&
(![X]:((tall(X)|~old(X))=>(~quiet(X)|~old(X))))&
(![X]:((~kind(X)&~old(X))<=>(~humble(X)<~>~rich(X))))&
((?[X]:((kind(X)|humble(X))))=>(quiet(alice)))&
(?[X]:((curious(X)<~>~brave(X))))&
(happy(susan))&
(?[X]:((~rich(X)&~curious(X))))&
(?[X]:((~happy(X)|tall(X))))&
((happy(susan)&calm(susan)))&
(?[X]:((~calm(X)|patient(X)))) | ~funny(susan) | [
"p3",
"p5",
"p7",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 54612088101067598603497
% SZS output start Proof for 54612088101067598603497
4. ! [X0] : ((~patient(X0) | brave(X0)) <=> ~funny(X0)) [input p3]
6. ! [X0] : (~creative(X0) => (kind(X0) <~> creative(X0))) [input p5]
8. ! [X0] : ((~patient(X0) | ~brave(X0)) <=> humble(X0)) [input p7]
11. ! [X0] : ((kind(X0) <~> quiet(X0)) <=> quiet(X0)) [input p10]
12. ! [X0] : ((funny(X0) | quiet(X0)) <=> ~creative(X0)) [input p11]
16. ? [X0] : (humble(X0) | kind(X0)) => quiet(alice) [input p15]
23. funny(susan) [input hypothesis]
31. ! [X0] : ((kind(X0) <~> creative(X0)) | creative(X0)) [ennf transformation 6]
36. quiet(alice) | ! [X0] : (~humble(X0) & ~kind(X0)) [ennf transformation 16]
40. ! [X0] : (((~patient(X0) | brave(X0)) | funny(X0)) & (~funny(X0) | (patient(X0) & ~brave(X0)))) [nnf transformation 4]
41. ! [X0] : ((~patient(X0) | brave(X0) | funny(X0)) & (~funny(X0) | (patient(X0) & ~brave(X0)))) [flattening 40]
42. ! [X0] : (((~creative(X0) | ~kind(X0)) & (creative(X0) | kind(X0))) | creative(X0)) [nnf transformation 31]
44. ! [X0] : (((~patient(X0) | ~brave(X0)) | ~humble(X0)) & (humble(X0) | (patient(X0) & brave(X0)))) [nnf transformation 8]
45. ! [X0] : ((~patient(X0) | ~brave(X0) | ~humble(X0)) & (humble(X0) | (patient(X0) & brave(X0)))) [flattening 44]
47. ! [X0] : ((((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | ~quiet(X0)) & (quiet(X0) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0))))) [nnf transformation 11]
48. ! [X0] : (((funny(X0) | quiet(X0)) | creative(X0)) & (~creative(X0) | (~funny(X0) & ~quiet(X0)))) [nnf transformation 12]
49. ! [X0] : ((funny(X0) | quiet(X0) | creative(X0)) & (~creative(X0) | (~funny(X0) & ~quiet(X0)))) [flattening 48]
69. ~funny(X0) | ~brave(X0) [cnf transformation 41]
73. creative(X0) | kind(X0) | creative(X0) [cnf transformation 42]
83. humble(X0) | brave(X0) [cnf transformation 45]
99. ~quiet(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 47]
100. ~creative(X0) | ~quiet(X0) [cnf transformation 49]
116. quiet(alice) | ~humble(X0) [cnf transformation 36]
126. funny(susan) [cnf transformation 23]
128. ~kind(X0) | ~quiet(X0) [duplicate literal removal 99]
137. kind(X0) | creative(X0) [duplicate literal removal 73]
168. 5 <=> ! [X0] : ~humble(X0) [avatar definition]
169. ~humble(X0) <- (5) [avatar component clause 168]
171. 6 <=> quiet(alice) [avatar definition]
173. quiet(alice) <- (6) [avatar component clause 171]
174. 5 | 6 [avatar split clause 116,171,168]
196. ~brave(susan) [resolution 69,126]
199. brave(X0) <- (5) [resolution 83,169]
201. $false <- (5) [resolution 199,196]
202. ~5 [avatar contradiction clause 201]
205. creative(X0) | ~quiet(X0) [resolution 137,128]
207. ~quiet(X0) [subsumption resolution 205,100]
211. $false <- (6) [resolution 207,173]
212. ~6 [avatar contradiction clause 211]
213. $false [avatar sat refutation 174,202,212]
% SZS output end Proof for 54612088101067598603497
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either calm or not patient then fred is both humble and strong.
If someone is both rich and old then someone is both brave and quiet and vice versa.
Everyone who is either kind or not tall is either generous or old and vice versa.
Everyone who is either funny or not rich is both not wise and not calm.
Everyone who is creative or old is both not creative and not brave.
Everyone who is both patient and kind is either strong or wise.
Everyone who is rich is both not rich and not brave.
Everyone who is both kind and curious is tall or not wise.
If mary is not generous then someone is either kind or not rich.
If fred is both kind and not patient then someone is curious and vice versa.
Everyone who is tall or not curious is not strong.
Everyone who is both rich and creative is both wise and kind and vice versa.
Everyone who is both not humble and not wise is both not curious and happy.
Everyone who is either not wise or not generous is either not patient or not old and vice versa.
Everyone who is either funny or not generous is both not creative and rich and vice versa.
Everyone who is not rich is generous and vice versa.
Someone is quiet.
Someone is strong.
Someone is not calm.
Susan is either kind or not kind.
Lucy is curious.
Susan is old or generous. | Susan is creative. | contradiction | (((calm(lucy)<~>~patient(lucy)))=>((humble(fred)&strong(fred))))&
((?[X]:((rich(X)&old(X))))<=>(?[X]:((brave(X)&quiet(X)))))&
(![X]:((kind(X)<~>~tall(X))<=>(generous(X)<~>old(X))))&
(![X]:((funny(X)<~>~rich(X))=>(~wise(X)&~calm(X))))&
(![X]:((creative(X)|old(X))=>(~creative(X)&~brave(X))))&
(![X]:((patient(X)&kind(X))=>(strong(X)<~>wise(X))))&
(![X]:(rich(X)=>(~rich(X)&~brave(X))))&
(![X]:((kind(X)&curious(X))=>(tall(X)|~wise(X))))&
((~generous(mary))=>(?[X]:((kind(X)<~>~rich(X)))))&
(((kind(fred)&~patient(fred)))<=>(?[X]:(curious(X))))&
(![X]:((tall(X)|~curious(X))=>~strong(X)))&
(![X]:((rich(X)&creative(X))<=>(wise(X)&kind(X))))&
(![X]:((~humble(X)&~wise(X))=>(~curious(X)&happy(X))))&
(![X]:((~wise(X)<~>~generous(X))<=>(~patient(X)<~>~old(X))))&
(![X]:((funny(X)<~>~generous(X))<=>(~creative(X)&rich(X))))&
(![X]:(~rich(X)<=>generous(X)))&
(?[X]:(quiet(X)))&
(?[X]:(strong(X)))&
(?[X]:(~calm(X)))&
((kind(susan)<~>~kind(susan)))&
(curious(lucy))&
((old(susan)|generous(susan))) | creative(susan) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 7551338962068418987842069
% SZS output start Proof for 7551338962068418987842069
5. ! [X0] : ((old(X0) | creative(X0)) => (~brave(X0) & ~creative(X0))) [input p4]
23. creative(susan) [input hypothesis]
30. ! [X0] : ((~brave(X0) & ~creative(X0)) | (~old(X0) & ~creative(X0))) [ennf transformation 5]
86. ~creative(X0) | ~creative(X0) [cnf transformation 30]
129. creative(susan) [cnf transformation 23]
131. ~creative(X0) [duplicate literal removal 86]
204. $false [subsumption resolution 129,131]
% SZS output end Proof for 7551338962068418987842069
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not 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. | Fred is not old. | neutral | (![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)))) | ~old(fred) | [] | null | 0 |
Everyone who is rich or patient is both not tall and strong. If someone is not wise or calm then mary is either curious or not curious. If lucy is kind or not rich then someone is either tall or kind and vice versa. Everyone who is either not curious or humble is both funny and curious. Everyone who is not generous or funny is both not creative and not quiet. Everyone who is brave or curious is not humble or not tall and vice versa. Everyone who is not patient is old or happy. If john is strong or not brave then someone is either not happy or not strong. Everyone who is not quiet is patient. If someone is curious then alice is both creative and generous. Everyone who is not funny is both not wise and patient and vice versa. If someone is either calm or quiet then mary is curious or not creative. Everyone who is both not patient and not rich is both tall and creative. If john is not happy then someone is happy and vice versa. Alice is either not calm or brave. Someone is rich or not happy. Paul is either not strong or not generous. Someone is not brave. Someone is brave. Susan is happy or brave. | Alice is not patient. | contradiction | (![X]:((rich(X)|patient(X))=>(~tall(X)&strong(X))))&
((?[X]:((~wise(X)|calm(X))))=>((curious(mary)<~>~curious(mary))))&
(((kind(lucy)|~rich(lucy)))<=>(?[X]:((tall(X)<~>kind(X)))))&
(![X]:((~curious(X)<~>humble(X))=>(funny(X)&curious(X))))&
(![X]:((~generous(X)|funny(X))=>(~creative(X)&~quiet(X))))&
(![X]:((brave(X)|curious(X))<=>(~humble(X)|~tall(X))))&
(![X]:(~patient(X)=>(old(X)|happy(X))))&
(((strong(john)|~brave(john)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:(~quiet(X)=>patient(X)))&
((?[X]:(curious(X)))=>((creative(alice)&generous(alice))))&
(![X]:(~funny(X)<=>(~wise(X)&patient(X))))&
((?[X]:((calm(X)<~>quiet(X))))=>((curious(mary)|~creative(mary))))&
(![X]:((~patient(X)&~rich(X))=>(tall(X)&creative(X))))&
((~happy(john))<=>(?[X]:(happy(X))))&
((~calm(alice)<~>brave(alice)))&
(?[X]:((rich(X)|~happy(X))))&
((~strong(paul)<~>~generous(paul)))&
(?[X]:(~brave(X)))&
(?[X]:(brave(X)))&
((happy(susan)|brave(susan))) | ~patient(alice) | [
"p4",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6055800750741648648263029
% SZS output start Proof for 6055800750741648648263029
5. ! [X0] : ((funny(X0) | ~generous(X0)) => (~quiet(X0) & ~creative(X0))) [input p4]
9. ! [X0] : (~quiet(X0) => patient(X0)) [input p8]
11. ! [X0] : (~funny(X0) <=> (patient(X0) & ~wise(X0))) [input p10]
21. ~patient(alice) [input hypothesis]
26. ! [X0] : ((~quiet(X0) & ~creative(X0)) | (~funny(X0) & generous(X0))) [ennf transformation 5]
28. ! [X0] : (patient(X0) | quiet(X0)) [ennf transformation 9]
46. ! [X0] : ((~funny(X0) | (~patient(X0) | wise(X0))) & ((patient(X0) & ~wise(X0)) | funny(X0))) [nnf transformation 11]
47. ! [X0] : ((~funny(X0) | ~patient(X0) | wise(X0)) & ((patient(X0) & ~wise(X0)) | funny(X0))) [flattening 46]
82. ~quiet(X0) | ~funny(X0) [cnf transformation 26]
91. quiet(X0) | patient(X0) [cnf transformation 28]
95. patient(X0) | funny(X0) [cnf transformation 47]
111. ~patient(alice) [cnf transformation 21]
247. patient(X0) | ~funny(X0) [resolution 91,82]
249. patient(X0) [subsumption resolution 247,95]
250. $false [resolution 249,111]
% SZS output end Proof for 6055800750741648648263029
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or not happy is either not brave or kind.
If someone is not tall or not old then alice is both not happy and not calm and vice versa.
If lucy is both not calm and not tall then alice is either not wise or generous and vice versa.
Everyone who is old or not funny is not strong or patient and vice versa.
If someone is both old and strong then someone is either creative or calm and vice versa.
Everyone who is either kind or wise is not funny and vice versa.
Everyone who is both curious and not funny is both not patient and old and vice versa.
Everyone who is creative or old is both calm and not funny.
If fred is both humble and tall then someone is tall and vice versa.
Everyone who is either not brave or funny is both not funny and kind and vice versa.
Everyone who is both calm and quiet is either not creative or not wise.
Everyone who is generous or patient is not tall and vice versa.
Everyone who is not rich is both not humble and not happy.
Everyone who is both not rich and not old is strong or quiet.
Everyone who is either strong or not brave is either not patient or not strong and vice versa.
Everyone who is not generous or old is either not calm or humble.
Alice is tall or funny.
Susan is either patient or rich.
Mary is either not humble or not funny. | Susan is rich. | entailment | (![X]:((patient(X)<~>~happy(X))=>(~brave(X)<~>kind(X))))&
((?[X]:((~tall(X)|~old(X))))<=>((~happy(alice)&~calm(alice))))&
(((~calm(lucy)&~tall(lucy)))<=>((~wise(alice)<~>generous(alice))))&
(![X]:((old(X)|~funny(X))<=>(~strong(X)|patient(X))))&
((?[X]:((old(X)&strong(X))))<=>(?[X]:((creative(X)<~>calm(X)))))&
(![X]:((kind(X)<~>wise(X))<=>~funny(X)))&
(![X]:((curious(X)&~funny(X))<=>(~patient(X)&old(X))))&
(![X]:((creative(X)|old(X))=>(calm(X)&~funny(X))))&
(((humble(fred)&tall(fred)))<=>(?[X]:(tall(X))))&
(![X]:((~brave(X)<~>funny(X))<=>(~funny(X)&kind(X))))&
(![X]:((calm(X)&quiet(X))=>(~creative(X)<~>~wise(X))))&
(![X]:((generous(X)|patient(X))<=>~tall(X)))&
(![X]:(~rich(X)=>(~humble(X)&~happy(X))))&
(![X]:((~rich(X)&~old(X))=>(strong(X)|quiet(X))))&
(![X]:((strong(X)<~>~brave(X))<=>(~patient(X)<~>~strong(X))))&
(![X]:((~generous(X)|old(X))=>(~calm(X)<~>humble(X))))&
((tall(alice)|funny(alice)))&
((patient(susan)<~>rich(susan)))&
((~humble(mary)<~>~funny(mary))) | rich(susan) | [
"p0",
"p1",
"p3",
"p7",
"p9",
"p11",
"p14",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 936565259967694961739105
% SZS output start Proof for 936565259967694961739105
1. ! [X0] : ((patient(X0) <~> ~happy(X0)) => (~brave(X0) <~> kind(X0))) [input p0]
2. ? [X0] : (~old(X0) | ~tall(X0)) <=> (~calm(alice) & ~happy(alice)) [input p1]
4. ! [X0] : ((~funny(X0) | old(X0)) <=> (patient(X0) | ~strong(X0))) [input p3]
8. ! [X0] : ((old(X0) | creative(X0)) => (~funny(X0) & calm(X0))) [input p7]
10. ! [X0] : ((~brave(X0) <~> funny(X0)) <=> (kind(X0) & ~funny(X0))) [input p9]
12. ! [X0] : ((patient(X0) | generous(X0)) <=> ~tall(X0)) [input p11]
15. ! [X0] : ((strong(X0) <~> ~brave(X0)) <=> (~patient(X0) <~> ~strong(X0))) [input p14]
17. funny(alice) | tall(alice) [input p16]
18. patient(susan) <~> rich(susan) [input p17]
20. ~rich(susan) [input hypothesis]
22. ! [X0] : ((~brave(X0) <~> kind(X0)) | (patient(X0) <=> ~happy(X0))) [ennf transformation 1]
23. ! [X0] : ((~funny(X0) & calm(X0)) | (~old(X0) & ~creative(X0))) [ennf transformation 8]
30. ! [X0] : (((~kind(X0) | brave(X0)) & (kind(X0) | ~brave(X0))) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0)))) [nnf transformation 22]
31. (? [X0] : (~old(X0) | ~tall(X0)) | (calm(alice) | happy(alice))) & ((~calm(alice) & ~happy(alice)) | ! [X0] : (old(X0) & tall(X0))) [nnf transformation 2]
32. (? [X0] : (~old(X0) | ~tall(X0)) | calm(alice) | happy(alice)) & ((~calm(alice) & ~happy(alice)) | ! [X0] : (old(X0) & tall(X0))) [flattening 31]
33. (? [X0] : (~old(X0) | ~tall(X0)) | calm(alice) | happy(alice)) & ((~calm(alice) & ~happy(alice)) | ! [X1] : (old(X1) & tall(X1))) [rectify 32]
34. ? [X0] : (~old(X0) | ~tall(X0)) => (~old(sK0) | ~tall(sK0)) [choice axiom]
35. ((~old(sK0) | ~tall(sK0)) | calm(alice) | happy(alice)) & ((~calm(alice) & ~happy(alice)) | ! [X1] : (old(X1) & tall(X1))) [skolemisation 33,34]
38. ! [X0] : (((~funny(X0) | old(X0)) | (~patient(X0) & strong(X0))) & ((patient(X0) | ~strong(X0)) | (funny(X0) & ~old(X0)))) [nnf transformation 4]
39. ! [X0] : ((~funny(X0) | old(X0) | (~patient(X0) & strong(X0))) & (patient(X0) | ~strong(X0) | (funny(X0) & ~old(X0)))) [flattening 38]
53. ! [X0] : ((((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | (~kind(X0) | funny(X0))) & ((kind(X0) & ~funny(X0)) | ((~brave(X0) | ~funny(X0)) & (funny(X0) | brave(X0))))) [nnf transformation 10]
54. ! [X0] : ((((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | ~kind(X0) | funny(X0)) & ((kind(X0) & ~funny(X0)) | ((~brave(X0) | ~funny(X0)) & (funny(X0) | brave(X0))))) [flattening 53]
56. ! [X0] : (((patient(X0) | generous(X0)) | tall(X0)) & (~tall(X0) | (~patient(X0) & ~generous(X0)))) [nnf transformation 12]
57. ! [X0] : ((patient(X0) | generous(X0) | tall(X0)) & (~tall(X0) | (~patient(X0) & ~generous(X0)))) [flattening 56]
58. ! [X0] : ((((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) & (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0))))) [nnf transformation 15]
60. (~rich(susan) | ~patient(susan)) & (rich(susan) | patient(susan)) [nnf transformation 18]
63. ~brave(X0) | kind(X0) | patient(X0) | happy(X0) [cnf transformation 30]
66. ~happy(alice) | tall(X1) [cnf transformation 35]
80. ~funny(X0) | old(X0) | ~patient(X0) [cnf transformation 39]
98. ~funny(X0) | ~old(X0) [cnf transformation 23]
103. ~funny(X0) | ~brave(X0) | ~funny(X0) [cnf transformation 54]
106. funny(X0) | ~brave(X0) | ~kind(X0) | funny(X0) [cnf transformation 54]
111. ~tall(X0) | ~patient(X0) [cnf transformation 57]
119. strong(X0) | patient(X0) | strong(X0) | brave(X0) [cnf transformation 58]
122. brave(X0) | ~strong(X0) | ~strong(X0) | patient(X0) [cnf transformation 58]
128. funny(alice) | tall(alice) [cnf transformation 17]
129. rich(susan) | patient(susan) [cnf transformation 60]
133. ~rich(susan) [cnf transformation 20]
135. strong(X0) | patient(X0) | brave(X0) [duplicate literal removal 119]
137. ~strong(X0) | brave(X0) | patient(X0) [duplicate literal removal 122]
138. ~funny(X0) | ~brave(X0) [duplicate literal removal 103]
139. ~kind(X0) | ~brave(X0) | funny(X0) [duplicate literal removal 106]
141. 1 <=> happy(alice) [avatar definition]
162. 6 <=> ! [X1] : tall(X1) [avatar definition]
163. tall(X1) <- (6) [avatar component clause 162]
166. 6 | ~1 [avatar split clause 66,141,162]
239. brave(X0) | patient(X0) [subsumption resolution 135,137]
243. 22 <=> tall(alice) [avatar definition]
245. tall(alice) <- (22) [avatar component clause 243]
247. 23 <=> funny(alice) [avatar definition]
248. ~funny(alice) <- (~23) [avatar component clause 247]
249. funny(alice) <- (23) [avatar component clause 247]
250. 22 | 23 [avatar split clause 128,247,243]
252. 24 <=> patient(susan) [avatar definition]
253. patient(susan) <- (24) [avatar component clause 252]
256. 25 <=> rich(susan) [avatar definition]
260. 24 | 25 [avatar split clause 129,256,252]
271. ~25 [avatar split clause 133,256]
367. 37 <=> patient(alice) [avatar definition]
368. ~patient(alice) <- (~37) [avatar component clause 367]
389. old(alice) | ~patient(alice) <- (23) [resolution 249,80]
393. ~old(alice) <- (23) [resolution 249,98]
395. ~brave(alice) <- (23) [resolution 249,138]
401. 41 <=> old(alice) [avatar definition]
405. ~37 | 41 | ~23 [avatar split clause 389,247,401,367]
408. ~41 | ~23 [avatar split clause 393,247,401]
429. kind(X0) | patient(X0) | happy(X0) | patient(X0) [resolution 63,239]
430. kind(X0) | patient(X0) | happy(X0) [duplicate literal removal 429]
456. 45 <=> kind(alice) [avatar definition]
457. ~kind(alice) <- (~45) [avatar component clause 456]
458. kind(alice) <- (45) [avatar component clause 456]
463. ~patient(alice) <- (22) [resolution 245,111]
464. patient(alice) <- (23) [resolution 395,239]
465. $false <- (23, ~37) [subsumption resolution 464,368]
466. ~23 | 37 [avatar contradiction clause 465]
556. patient(alice) | happy(alice) <- (~45) [resolution 430,457]
576. ~patient(X0) <- (6) [resolution 163,111]
595. $false <- (6, 24) [resolution 576,253]
596. ~6 | ~24 [avatar contradiction clause 595]
600. 1 | 37 | 45 [avatar split clause 556,456,367,141]
604. ~37 | ~22 [avatar split clause 463,243,367]
612. 55 <=> brave(alice) [avatar definition]
613. ~brave(alice) <- (~55) [avatar component clause 612]
634. ~brave(alice) | funny(alice) <- (45) [resolution 458,139]
635. ~brave(alice) <- (~23, 45) [subsumption resolution 634,248]
636. ~55 | 23 | ~45 [avatar split clause 635,456,247,612]
637. patient(alice) <- (~55) [resolution 613,239]
638. $false <- (~37, ~55) [subsumption resolution 637,368]
639. 37 | 55 [avatar contradiction clause 638]
640. $false [avatar sat refutation 166,250,260,271,405,408,466,596,600,604,636,639]
% SZS output end Proof for 936565259967694961739105
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not creative is both curious and not strong and vice versa.
If someone is not creative or not tall then someone is both calm and patient.
If someone is either curious or not wise then someone is both not rich and funny.
If paul is either not creative or not happy then paul is not wise or not kind and vice versa.
Everyone who is either not happy or not brave is not kind and vice versa.
If someone is happy or kind then someone is not curious and vice versa.
Everyone who is not funny is either not patient or not rich.
If someone is old or not calm then lucy is both generous and not kind.
If someone is not kind then paul is curious or not quiet and vice versa.
Everyone who is not curious or kind is not funny and vice versa.
Everyone who is happy is both quiet and humble and vice versa.
If susan is either old or curious then someone is both not rich and creative and vice versa.
Everyone who is not tall is both not calm and creative and vice versa.
If lucy is either humble or kind then someone is either rich or strong and vice versa.
Everyone who is not strong is not tall.
If alice is either creative or happy then paul is both strong and curious and vice versa.
Someone is either not happy or calm.
Susan is brave.
Susan is both wise and kind.
Paul is not humble.
Paul is not kind or happy.
Someone is kind or old.
Someone is either wise or quiet.
Lucy is both tall and not wise. | Paul is kind. | contradiction | (![X]:((strong(X)<~>~creative(X))<=>(curious(X)&~strong(X))))&
((?[X]:((~creative(X)|~tall(X))))=>(?[X]:((calm(X)&patient(X)))))&
((?[X]:((curious(X)<~>~wise(X))))=>(?[X]:((~rich(X)&funny(X)))))&
(((~creative(paul)<~>~happy(paul)))<=>((~wise(paul)|~kind(paul))))&
(![X]:((~happy(X)<~>~brave(X))<=>~kind(X)))&
((?[X]:((happy(X)|kind(X))))<=>(?[X]:(~curious(X))))&
(![X]:(~funny(X)=>(~patient(X)<~>~rich(X))))&
((?[X]:((old(X)|~calm(X))))=>((generous(lucy)&~kind(lucy))))&
((?[X]:(~kind(X)))<=>((curious(paul)|~quiet(paul))))&
(![X]:((~curious(X)|kind(X))<=>~funny(X)))&
(![X]:(happy(X)<=>(quiet(X)&humble(X))))&
(((old(susan)<~>curious(susan)))<=>(?[X]:((~rich(X)&creative(X)))))&
(![X]:(~tall(X)<=>(~calm(X)&creative(X))))&
(((humble(lucy)<~>kind(lucy)))<=>(?[X]:((rich(X)<~>strong(X)))))&
(![X]:(~strong(X)=>~tall(X)))&
(((creative(alice)<~>happy(alice)))<=>((strong(paul)&curious(paul))))&
(?[X]:((~happy(X)<~>calm(X))))&
(brave(susan))&
((wise(susan)&kind(susan)))&
(~humble(paul))&
((~kind(paul)|happy(paul)))&
(?[X]:((kind(X)|old(X))))&
(?[X]:((wise(X)<~>quiet(X))))&
((tall(lucy)&~wise(lucy))) | kind(paul) | [
"p10",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 253181259325962162654156
% SZS output start Proof for 253181259325962162654156
11. ! [X0] : (happy(X0) <=> (humble(X0) & quiet(X0))) [input p10]
20. ~humble(paul) [input p19]
21. happy(paul) | ~kind(paul) [input p20]
25. kind(paul) [input hypothesis]
60. ! [X0] : ((happy(X0) | (~humble(X0) | ~quiet(X0))) & ((humble(X0) & quiet(X0)) | ~happy(X0))) [nnf transformation 11]
61. ! [X0] : ((happy(X0) | ~humble(X0) | ~quiet(X0)) & ((humble(X0) & quiet(X0)) | ~happy(X0))) [flattening 60]
119. ~happy(X0) | humble(X0) [cnf transformation 61]
150. ~humble(paul) [cnf transformation 20]
151. happy(paul) | ~kind(paul) [cnf transformation 21]
157. kind(paul) [cnf transformation 25]
197. 9 <=> kind(paul) [avatar definition]
205. 11 <=> happy(paul) [avatar definition]
207. happy(paul) <- (11) [avatar component clause 205]
351. ~9 | 11 [avatar split clause 151,205,197]
371. 9 [avatar split clause 157,197]
389. humble(paul) <- (11) [resolution 119,207]
390. $false <- (11) [subsumption resolution 389,150]
391. ~11 [avatar contradiction clause 390]
392. $false [avatar sat refutation 351,371,391]
% SZS output end Proof for 253181259325962162654156
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or not kind is not humble or not old. If someone is not humble then lucy is either brave or not wise and vice versa. Everyone who is both strong and not tall is calm or old. Everyone who is wise is both not curious and not humble. Everyone who is not quiet is both not creative and not happy and vice versa. If lucy is not old or funny then john is not old and vice versa. Everyone who is both humble and calm is not calm. If mary is both old and brave then susan is rich. Everyone who is both not curious and not wise is patient or not happy. If someone is either curious or not funny then someone is both strong and not funny. Everyone who is not quiet or not brave is either kind or not wise and vice versa. If paul is either not old or strong then someone is not calm. If mary is quiet then john is both not kind and patient. Everyone who is both not tall and not kind is not brave or curious. Everyone who is both tall and not curious is humble. If john is generous or kind then someone is not kind. Someone is quiet or not curious. Fred is patient. Fred is both not wise and not funny. Alice is both not wise and patient. Someone is both calm and not strong. Mary is both not kind and not tall. Susan is both not tall and not brave. Fred is old or quiet. | John is kind. | neutral | (![X]:((old(X)<~>~kind(X))=>(~humble(X)|~old(X))))&
((?[X]:(~humble(X)))<=>((brave(lucy)<~>~wise(lucy))))&
(![X]:((strong(X)&~tall(X))=>(calm(X)|old(X))))&
(![X]:(wise(X)=>(~curious(X)&~humble(X))))&
(![X]:(~quiet(X)<=>(~creative(X)&~happy(X))))&
(((~old(lucy)|funny(lucy)))<=>(~old(john)))&
(![X]:((humble(X)&calm(X))=>~calm(X)))&
(((old(mary)&brave(mary)))=>(rich(susan)))&
(![X]:((~curious(X)&~wise(X))=>(patient(X)|~happy(X))))&
((?[X]:((curious(X)<~>~funny(X))))=>(?[X]:((strong(X)&~funny(X)))))&
(![X]:((~quiet(X)|~brave(X))<=>(kind(X)<~>~wise(X))))&
(((~old(paul)<~>strong(paul)))=>(?[X]:(~calm(X))))&
((quiet(mary))=>((~kind(john)&patient(john))))&
(![X]:((~tall(X)&~kind(X))=>(~brave(X)|curious(X))))&
(![X]:((tall(X)&~curious(X))=>humble(X)))&
(((generous(john)|kind(john)))=>(?[X]:(~kind(X))))&
(?[X]:((quiet(X)|~curious(X))))&
(patient(fred))&
((~wise(fred)&~funny(fred)))&
((~wise(alice)&patient(alice)))&
(?[X]:((calm(X)&~strong(X))))&
((~kind(mary)&~tall(mary)))&
((~tall(susan)&~brave(susan)))&
((old(fred)|quiet(fred))) | kind(john) | [] | null | 0 |
Everyone who is not wise or funny is either not wise or not curious. If john is not curious or tall then someone is either not generous or humble and vice versa. If someone is tall or not funny then lucy is strong. If someone is both not quiet and not happy then someone is creative or not patient. Everyone who is either not quiet or not calm is either not patient or calm and vice versa. Everyone who is not happy or not curious is both not brave and generous. Everyone who is both not creative and not happy is both not kind and funny and vice versa. Everyone who is both funny and not brave is either not old or not strong. If someone is not curious then someone is both quiet and patient. If alice is both happy and funny then someone is patient. Everyone who is either kind or not tall is rich and vice versa. Everyone who is either not funny or brave is both not curious and not generous. If someone is both happy and calm then alice is either not brave or curious and vice versa. If someone is either not brave or generous then fred is quiet and vice versa. If someone is both curious and not funny then someone is wise. If someone is both not tall and not patient then someone is both quiet and not creative. Susan is not brave. Someone is humble or calm. Someone is creative. Someone is not humble or not patient. Paul is either not patient or strong. Fred is either not kind or funny. Fred is calm or tall. Paul is either not generous or creative. | Susan is wise. | contradiction | (![X]:((~wise(X)|funny(X))=>(~wise(X)<~>~curious(X))))&
(((~curious(john)|tall(john)))<=>(?[X]:((~generous(X)<~>humble(X)))))&
((?[X]:((tall(X)|~funny(X))))=>(strong(lucy)))&
((?[X]:((~quiet(X)&~happy(X))))=>(?[X]:((creative(X)|~patient(X)))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~patient(X)<~>calm(X))))&
(![X]:((~happy(X)|~curious(X))=>(~brave(X)&generous(X))))&
(![X]:((~creative(X)&~happy(X))<=>(~kind(X)&funny(X))))&
(![X]:((funny(X)&~brave(X))=>(~old(X)<~>~strong(X))))&
((?[X]:(~curious(X)))=>(?[X]:((quiet(X)&patient(X)))))&
(((happy(alice)&funny(alice)))=>(?[X]:(patient(X))))&
(![X]:((kind(X)<~>~tall(X))<=>rich(X)))&
(![X]:((~funny(X)<~>brave(X))=>(~curious(X)&~generous(X))))&
((?[X]:((happy(X)&calm(X))))<=>((~brave(alice)<~>curious(alice))))&
((?[X]:((~brave(X)<~>generous(X))))<=>(quiet(fred)))&
((?[X]:((curious(X)&~funny(X))))=>(?[X]:(wise(X))))&
((?[X]:((~tall(X)&~patient(X))))=>(?[X]:((quiet(X)&~creative(X)))))&
(~brave(susan))&
(?[X]:((humble(X)|calm(X))))&
(?[X]:(creative(X)))&
(?[X]:((~humble(X)|~patient(X))))&
((~patient(paul)<~>strong(paul)))&
((~kind(fred)<~>funny(fred)))&
((calm(fred)|tall(fred)))&
((~generous(paul)<~>creative(paul))) | wise(susan) | [
"p0",
"p4",
"p8",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8194500830070233266310465
% SZS output start Proof for 8194500830070233266310465
1. ! [X0] : ((funny(X0) | ~wise(X0)) => (~wise(X0) <~> ~curious(X0))) [input p0]
5. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) <=> (~patient(X0) <~> calm(X0))) [input p4]
9. ? [X0] : ~curious(X0) => ? [X0] : (patient(X0) & quiet(X0)) [input p8]
12. ! [X0] : ((~funny(X0) <~> brave(X0)) => (~generous(X0) & ~curious(X0))) [input p11]
17. ~brave(susan) [input p16]
25. wise(susan) [input hypothesis]
27. ? [X0] : ~curious(X0) => ? [X1] : (patient(X1) & quiet(X1)) [rectify 9]
30. ! [X0] : ((~wise(X0) <~> ~curious(X0)) | (~funny(X0) & wise(X0))) [ennf transformation 1]
36. ? [X1] : (patient(X1) & quiet(X1)) | ! [X0] : curious(X0) [ennf transformation 27]
39. ! [X0] : ((~generous(X0) & ~curious(X0)) | (~funny(X0) <=> brave(X0))) [ennf transformation 12]
42. ! [X0] : (((curious(X0) | wise(X0)) & (~curious(X0) | ~wise(X0))) | (~funny(X0) & wise(X0))) [nnf transformation 30]
51. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ((~patient(X0) | ~calm(X0)) & (calm(X0) | patient(X0)))) & (((~calm(X0) | patient(X0)) & (calm(X0) | ~patient(X0))) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [nnf transformation 5]
55. ? [X0] : (patient(X0) & quiet(X0)) | ! [X1] : curious(X1) [rectify 36]
56. ? [X0] : (patient(X0) & quiet(X0)) => (patient(sK2) & quiet(sK2)) [choice axiom]
57. (patient(sK2) & quiet(sK2)) | ! [X1] : curious(X1) [skolemisation 55,56]
60. ! [X0] : ((~generous(X0) & ~curious(X0)) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0)))) [nnf transformation 39]
85. ~curious(X0) | ~wise(X0) | ~funny(X0) [cnf transformation 42]
98. calm(X0) | ~patient(X0) | ~quiet(X0) | calm(X0) [cnf transformation 51]
102. ~calm(X0) | ~quiet(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 51]
115. quiet(sK2) | curious(X1) [cnf transformation 57]
116. patient(sK2) | curious(X1) [cnf transformation 57]
118. ~curious(X0) | brave(X0) | funny(X0) [cnf transformation 60]
135. ~brave(susan) [cnf transformation 17]
146. wise(susan) [cnf transformation 25]
147. calm(X0) | ~patient(X0) | ~quiet(X0) [duplicate literal removal 98]
149. ~calm(X0) | ~quiet(X0) | ~patient(X0) [duplicate literal removal 102]
205. ~patient(X0) | ~quiet(X0) [subsumption resolution 147,149]
207. 13 <=> ! [X1] : curious(X1) [avatar definition]
208. curious(X1) <- (13) [avatar component clause 207]
210. 14 <=> patient(sK2) [avatar definition]
212. patient(sK2) <- (14) [avatar component clause 210]
213. 13 | 14 [avatar split clause 116,210,207]
215. 15 <=> quiet(sK2) [avatar definition]
217. quiet(sK2) <- (15) [avatar component clause 215]
218. 13 | 15 [avatar split clause 115,215,207]
392. ~funny(X1) | ~wise(X1) <- (13) [resolution 85,208]
440. brave(X1) | funny(X1) <- (13) [resolution 118,208]
507. funny(susan) <- (13) [resolution 440,135]
527. ~wise(susan) <- (13) [resolution 507,392]
548. $false <- (13) [subsumption resolution 527,146]
549. ~13 [avatar contradiction clause 548]
563. ~quiet(sK2) <- (14) [resolution 212,205]
564. $false <- (14, 15) [subsumption resolution 563,217]
565. ~14 | ~15 [avatar contradiction clause 564]
566. $false [avatar sat refutation 213,218,549,565]
% SZS output end Proof for 8194500830070233266310465
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and not creative is either generous or brave and vice versa.
Everyone who is either curious or old is both not brave and not strong and vice versa.
If susan is not old or not happy then someone is either old or not old.
Everyone who is both not old and not generous is not curious and vice versa.
If someone is both strong and not calm then someone is not quiet or not humble and vice versa.
Everyone who is either not quiet or not curious is either not funny or old and vice versa.
Everyone who is not curious or funny is either curious or strong.
If alice is wise or strong then someone is not creative or curious and vice versa.
If lucy is both not wise and not quiet then someone is both strong and not quiet and vice versa.
Everyone who is either strong or rich is either not strong or tall.
If someone is calm then lucy is curious and vice versa.
If mary is either old or not generous then someone is either not kind or generous and vice versa.
Everyone who is not strong or tall is tall and vice versa.
If paul is either patient or rich then someone is either not funny or not happy and vice versa.
If fred is either not wise or humble then someone is not generous or quiet.
If lucy is rich then someone is either strong or not curious.
Someone is either brave or not curious.
Someone is old.
John is not happy.
Alice is not quiet or patient.
John is both brave and not quiet.
Fred is both wise and not calm.
Someone is either funny or not wise. | Fred is brave. | neutral | (![X]:((kind(X)&~creative(X))<=>(generous(X)<~>brave(X))))&
(![X]:((curious(X)<~>old(X))<=>(~brave(X)&~strong(X))))&
(((~old(susan)|~happy(susan)))=>(?[X]:((old(X)<~>~old(X)))))&
(![X]:((~old(X)&~generous(X))<=>~curious(X)))&
((?[X]:((strong(X)&~calm(X))))<=>(?[X]:((~quiet(X)|~humble(X)))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~funny(X)<~>old(X))))&
(![X]:((~curious(X)|funny(X))=>(curious(X)<~>strong(X))))&
(((wise(alice)|strong(alice)))<=>(?[X]:((~creative(X)|curious(X)))))&
(((~wise(lucy)&~quiet(lucy)))<=>(?[X]:((strong(X)&~quiet(X)))))&
(![X]:((strong(X)<~>rich(X))=>(~strong(X)<~>tall(X))))&
((?[X]:(calm(X)))<=>(curious(lucy)))&
(((old(mary)<~>~generous(mary)))<=>(?[X]:((~kind(X)<~>generous(X)))))&
(![X]:((~strong(X)|tall(X))<=>tall(X)))&
(((patient(paul)<~>rich(paul)))<=>(?[X]:((~funny(X)<~>~happy(X)))))&
(((~wise(fred)<~>humble(fred)))=>(?[X]:((~generous(X)|quiet(X)))))&
((rich(lucy))=>(?[X]:((strong(X)<~>~curious(X)))))&
(?[X]:((brave(X)<~>~curious(X))))&
(?[X]:(old(X)))&
(~happy(john))&
((~quiet(alice)|patient(alice)))&
((brave(john)&~quiet(john)))&
((wise(fred)&~calm(fred)))&
(?[X]:((funny(X)<~>~wise(X)))) | brave(fred) | [] | null | 0 |
If paul is not wise then mary is humble and vice versa. Everyone who is not quiet or not tall is either creative or happy and vice versa. Everyone who is both generous and not creative is not patient or not funny. Everyone who is either old or wise is not wise and vice versa. Everyone who is both not curious and old is old or strong and vice versa. Everyone who is old is both funny and not brave. Everyone who is either not old or not generous is either not quiet or happy and vice versa. If someone is either humble or not generous then susan is both not old and not humble. If susan is either not patient or not happy then someone is generous or not strong and vice versa. If alice is either not brave or not wise then someone is either not old or patient and vice versa. Everyone who is both not wise and not patient is both strong and generous and vice versa. If someone is not rich or not funny then john is either not old or creative. If someone is both calm and patient then someone is strong. If someone is both not funny and not strong then someone is either creative or generous and vice versa. Everyone who is either happy or brave is both rich and not curious and vice versa. If someone is not patient or happy then someone is either calm or not creative. Someone is both calm and rich. Someone is both calm and not tall. Someone is both strong and not patient. Someone is not humble. Lucy is both old and not wise. Someone is either tall or not rich. | Mary is old. | entailment | ((~wise(paul))<=>(humble(mary)))&
(![X]:((~quiet(X)|~tall(X))<=>(creative(X)<~>happy(X))))&
(![X]:((generous(X)&~creative(X))=>(~patient(X)|~funny(X))))&
(![X]:((old(X)<~>wise(X))<=>~wise(X)))&
(![X]:((~curious(X)&old(X))<=>(old(X)|strong(X))))&
(![X]:(old(X)=>(funny(X)&~brave(X))))&
(![X]:((~old(X)<~>~generous(X))<=>(~quiet(X)<~>happy(X))))&
((?[X]:((humble(X)<~>~generous(X))))=>((~old(susan)&~humble(susan))))&
(((~patient(susan)<~>~happy(susan)))<=>(?[X]:((generous(X)|~strong(X)))))&
(((~brave(alice)<~>~wise(alice)))<=>(?[X]:((~old(X)<~>patient(X)))))&
(![X]:((~wise(X)&~patient(X))<=>(strong(X)&generous(X))))&
((?[X]:((~rich(X)|~funny(X))))=>((~old(john)<~>creative(john))))&
((?[X]:((calm(X)&patient(X))))=>(?[X]:(strong(X))))&
((?[X]:((~funny(X)&~strong(X))))<=>(?[X]:((creative(X)<~>generous(X)))))&
(![X]:((happy(X)<~>brave(X))<=>(rich(X)&~curious(X))))&
((?[X]:((~patient(X)|happy(X))))=>(?[X]:((calm(X)<~>~creative(X)))))&
(?[X]:((calm(X)&rich(X))))&
(?[X]:((calm(X)&~tall(X))))&
(?[X]:((strong(X)&~patient(X))))&
(?[X]:(~humble(X)))&
((old(lucy)&~wise(lucy)))&
(?[X]:((tall(X)<~>~rich(X)))) | old(mary) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 6097248811797519477373767
% SZS output start Proof for 6097248811797519477373767
4. ! [X0] : ((old(X0) <~> wise(X0)) <=> ~wise(X0)) [input p3]
23. ~old(mary) [input hypothesis]
37. ! [X0] : ((((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) | wise(X0)) & (~wise(X0) | ((old(X0) | ~wise(X0)) & (wise(X0) | ~old(X0))))) [nnf transformation 4]
88. ~wise(X0) | old(X0) | ~wise(X0) [cnf transformation 37]
89. wise(X0) | old(X0) | wise(X0) [cnf transformation 37]
160. ~old(mary) [cnf transformation 23]
161. ~wise(X0) | old(X0) [duplicate literal removal 88]
162. wise(X0) | old(X0) [duplicate literal removal 89]
173. old(X0) [subsumption resolution 161,162]
306. $false [subsumption resolution 160,173]
% SZS output end Proof for 6097248811797519477373767
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not strong or not calm is not kind.
If someone is generous then fred is patient or humble and vice versa.
If john is either old or funny then alice is old and vice versa.
If someone is brave or patient then someone is either not strong or not patient.
If susan is brave then mary is calm.
Everyone who is patient is either not wise or curious.
If someone is both rich and not quiet then lucy is both not happy and not patient and vice versa.
Everyone who is either not wise or not generous is either not strong or not funny.
If fred is either humble or not strong then someone is both humble and not rich.
Everyone who is happy or calm is not creative and vice versa.
If john is either not generous or kind then someone is either happy or not kind and vice versa.
Everyone who is either not humble or strong is either not strong or not curious.
If lucy is both not curious and not strong then someone is either not brave or not patient and vice versa.
Everyone who is either not tall or quiet is brave or not calm.
Everyone who is either not kind or not rich is either not quiet or generous.
Everyone who is tall or not funny is not wise or wise and vice versa.
Susan is brave or rich.
Someone is both not wise and not rich.
Mary is not creative or not strong.
John is both wise and brave.
Lucy is both not creative and not old.
Someone is not quiet or quiet.
Someone is not tall or not curious. | Fred is not strong. | neutral | (![X]:((~strong(X)<~>~calm(X))=>~kind(X)))&
((?[X]:(generous(X)))<=>((patient(fred)|humble(fred))))&
(((old(john)<~>funny(john)))<=>(old(alice)))&
((?[X]:((brave(X)|patient(X))))=>(?[X]:((~strong(X)<~>~patient(X)))))&
((brave(susan))=>(calm(mary)))&
(![X]:(patient(X)=>(~wise(X)<~>curious(X))))&
((?[X]:((rich(X)&~quiet(X))))<=>((~happy(lucy)&~patient(lucy))))&
(![X]:((~wise(X)<~>~generous(X))=>(~strong(X)<~>~funny(X))))&
(((humble(fred)<~>~strong(fred)))=>(?[X]:((humble(X)&~rich(X)))))&
(![X]:((happy(X)|calm(X))<=>~creative(X)))&
(((~generous(john)<~>kind(john)))<=>(?[X]:((happy(X)<~>~kind(X)))))&
(![X]:((~humble(X)<~>strong(X))=>(~strong(X)<~>~curious(X))))&
(((~curious(lucy)&~strong(lucy)))<=>(?[X]:((~brave(X)<~>~patient(X)))))&
(![X]:((~tall(X)<~>quiet(X))=>(brave(X)|~calm(X))))&
(![X]:((~kind(X)<~>~rich(X))=>(~quiet(X)<~>generous(X))))&
(![X]:((tall(X)|~funny(X))<=>(~wise(X)|wise(X))))&
((brave(susan)|rich(susan)))&
(?[X]:((~wise(X)&~rich(X))))&
((~creative(mary)|~strong(mary)))&
((wise(john)&brave(john)))&
((~creative(lucy)&~old(lucy)))&
(?[X]:((~quiet(X)|quiet(X))))&
(?[X]:((~tall(X)|~curious(X)))) | ~strong(fred) | [] | null | 0 |
Everyone who is not strong is wise or not patient and vice versa.
Everyone who is both kind and not strong is not generous and vice versa.
Everyone who is not kind or kind is both kind and strong and vice versa.
Everyone who is both not rich and kind is funny or creative.
If someone is curious or calm then alice is either kind or brave.
Everyone who is both not brave and not strong is not quiet and vice versa.
If someone is creative then lucy is either calm or quiet and vice versa.
Everyone who is not quiet is humble or not curious and vice versa.
If someone is happy or not happy then mary is creative.
If lucy is not strong then fred is both humble and quiet and vice versa.
If someone is either brave or not tall then someone is either not creative or not humble and vice versa.
Everyone who is not strong or old is generous and vice versa.
Everyone who is either happy or generous is patient and vice versa.
If mary is not tall then paul is creative or not old and vice versa.
If mary is either not calm or strong then someone is not kind and vice versa.
If john is both creative and not quiet then someone is not quiet.
Someone is not tall.
Someone is either not humble or not kind.
John is calm.
Someone is both not wise and not tall.
Fred is not calm.
Susan is either funny or old.
Lucy is not humble or creative. | Susan is not kind. | contradiction | (![X]:(~strong(X)<=>(wise(X)|~patient(X))))&
(![X]:((kind(X)&~strong(X))<=>~generous(X)))&
(![X]:((~kind(X)|kind(X))<=>(kind(X)&strong(X))))&
(![X]:((~rich(X)&kind(X))=>(funny(X)|creative(X))))&
((?[X]:((curious(X)|calm(X))))=>((kind(alice)<~>brave(alice))))&
(![X]:((~brave(X)&~strong(X))<=>~quiet(X)))&
((?[X]:(creative(X)))<=>((calm(lucy)<~>quiet(lucy))))&
(![X]:(~quiet(X)<=>(humble(X)|~curious(X))))&
((?[X]:((happy(X)|~happy(X))))=>(creative(mary)))&
((~strong(lucy))<=>((humble(fred)&quiet(fred))))&
((?[X]:((brave(X)<~>~tall(X))))<=>(?[X]:((~creative(X)<~>~humble(X)))))&
(![X]:((~strong(X)|old(X))<=>generous(X)))&
(![X]:((happy(X)<~>generous(X))<=>patient(X)))&
((~tall(mary))<=>((creative(paul)|~old(paul))))&
(((~calm(mary)<~>strong(mary)))<=>(?[X]:(~kind(X))))&
(((creative(john)&~quiet(john)))=>(?[X]:(~quiet(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~humble(X)<~>~kind(X))))&
(calm(john))&
(?[X]:((~wise(X)&~tall(X))))&
(~calm(fred))&
((funny(susan)<~>old(susan)))&
((~humble(lucy)|creative(lucy))) | ~kind(susan) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 6305177341942225445856429
% SZS output start Proof for 6305177341942225445856429
3. ! [X0] : ((kind(X0) | ~kind(X0)) <=> (strong(X0) & kind(X0))) [input p2]
24. ~kind(susan) [input hypothesis]
35. ! [X0] : (((kind(X0) | ~kind(X0)) | (~strong(X0) | ~kind(X0))) & ((strong(X0) & kind(X0)) | (~kind(X0) & kind(X0)))) [nnf transformation 3]
36. ! [X0] : ((kind(X0) | ~kind(X0) | ~strong(X0) | ~kind(X0)) & ((strong(X0) & kind(X0)) | (~kind(X0) & kind(X0)))) [flattening 35]
78. kind(X0) | kind(X0) [cnf transformation 36]
135. ~kind(susan) [cnf transformation 24]
136. kind(X0) [duplicate literal removal 78]
237. $false [subsumption resolution 135,136]
% SZS output end Proof for 6305177341942225445856429
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is kind or creative and vice versa.
If john is not rich then someone is kind or wise.
If someone is not generous then someone is both strong and curious and vice versa.
Everyone who is tall or strong is either patient or curious.
If someone is patient then lucy is rich or not patient.
Everyone who is not patient is curious or wise and vice versa.
Everyone who is both not kind and old is both happy and not patient.
Everyone who is both tall and not generous is either not curious or rich and vice versa.
If someone is not creative then mary is not curious and vice versa.
If mary is either strong or tall then paul is rich and vice versa.
Everyone who is both humble and brave is strong and vice versa.
Everyone who is quiet or not wise is both strong and old.
Everyone who is not tall is tall or not curious.
Everyone who is not wise or not quiet is either not brave or strong and vice versa.
Everyone who is calm is not rich or not happy and vice versa.
Everyone who is quiet or not generous is not brave.
Lucy is either not humble or wise.
Mary is both not old and rich.
Someone is both funny and not patient.
Susan is either not creative or not kind.
Fred is rich or kind.
Lucy is not wise or not funny.
Paul is both not wise and strong.
Lucy is both tall and curious. | Lucy is not quiet. | entailment | (![X]:(wise(X)<=>(kind(X)|creative(X))))&
((~rich(john))=>(?[X]:((kind(X)|wise(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((strong(X)&curious(X)))))&
(![X]:((tall(X)|strong(X))=>(patient(X)<~>curious(X))))&
((?[X]:(patient(X)))=>((rich(lucy)|~patient(lucy))))&
(![X]:(~patient(X)<=>(curious(X)|wise(X))))&
(![X]:((~kind(X)&old(X))=>(happy(X)&~patient(X))))&
(![X]:((tall(X)&~generous(X))<=>(~curious(X)<~>rich(X))))&
((?[X]:(~creative(X)))<=>(~curious(mary)))&
(((strong(mary)<~>tall(mary)))<=>(rich(paul)))&
(![X]:((humble(X)&brave(X))<=>strong(X)))&
(![X]:((quiet(X)|~wise(X))=>(strong(X)&old(X))))&
(![X]:(~tall(X)=>(tall(X)|~curious(X))))&
(![X]:((~wise(X)|~quiet(X))<=>(~brave(X)<~>strong(X))))&
(![X]:(calm(X)<=>(~rich(X)|~happy(X))))&
(![X]:((quiet(X)|~generous(X))=>~brave(X)))&
((~humble(lucy)<~>wise(lucy)))&
((~old(mary)&rich(mary)))&
(?[X]:((funny(X)&~patient(X))))&
((~creative(susan)<~>~kind(susan)))&
((rich(fred)|kind(fred)))&
((~wise(lucy)|~funny(lucy)))&
((~wise(paul)&strong(paul)))&
((tall(lucy)&curious(lucy))) | ~quiet(lucy) | [
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1993568085694712202573337
% SZS output start Proof for 1993568085694712202573337
11. ! [X0] : ((brave(X0) & humble(X0)) <=> strong(X0)) [input p10]
12. ! [X0] : ((~wise(X0) | quiet(X0)) => (old(X0) & strong(X0))) [input p11]
16. ! [X0] : ((~generous(X0) | quiet(X0)) => ~brave(X0)) [input p15]
25. quiet(lucy) [input hypothesis]
34. ! [X0] : ((old(X0) & strong(X0)) | (wise(X0) & ~quiet(X0))) [ennf transformation 12]
37. ! [X0] : (~brave(X0) | (generous(X0) & ~quiet(X0))) [ennf transformation 16]
57. ! [X0] : (((brave(X0) & humble(X0)) | ~strong(X0)) & (strong(X0) | (~brave(X0) | ~humble(X0)))) [nnf transformation 11]
58. ! [X0] : (((brave(X0) & humble(X0)) | ~strong(X0)) & (strong(X0) | ~brave(X0) | ~humble(X0))) [flattening 57]
95. ~strong(X0) | brave(X0) [cnf transformation 58]
96. ~quiet(X0) | strong(X0) [cnf transformation 34]
107. ~quiet(X0) | ~brave(X0) [cnf transformation 37]
123. quiet(lucy) [cnf transformation 25]
241. strong(lucy) [resolution 96,123]
246. brave(lucy) [resolution 241,95]
252. ~brave(lucy) [resolution 107,123]
253. $false [subsumption resolution 252,246]
% SZS output end Proof for 1993568085694712202573337
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is either creative or happy is both not humble and not happy and vice versa.
If someone is both not wise and not happy then someone is creative or rich.
Everyone who is both not humble and creative is not generous or happy.
Everyone who is both old and not brave is not creative or strong and vice versa.
If someone is patient or quiet then someone is happy and vice versa.
Everyone who is kind is both calm and brave and vice versa.
If paul is either not wise or tall then someone is both not creative and patient.
Everyone who is not quiet or strong is not strong.
Everyone who is strong or not old is rich or not old.
Everyone who is either not calm or old is not happy.
If fred is both generous and not curious then someone is humble.
If john is either brave or generous then susan is both tall and not rich and vice versa.
Everyone who is either not rich or not happy is curious or not rich and vice versa.
Everyone who is either not strong or generous is wise.
Everyone who is both humble and wise is either not rich or not old.
Everyone who is either not generous or quiet is either rich or curious and vice versa.
Susan is not funny or quiet.
Lucy is both not quiet and not creative.
Someone is tall or wise.
Someone is not strong or rich.
Someone is not creative.
Lucy is not brave.
Lucy is both calm and not funny.
Someone is both not kind and not happy. | Lucy is not wise. | entailment | (![X]:((creative(X)<~>happy(X))<=>(~humble(X)&~happy(X))))&
((?[X]:((~wise(X)&~happy(X))))=>(?[X]:((creative(X)|rich(X)))))&
(![X]:((~humble(X)&creative(X))=>(~generous(X)|happy(X))))&
(![X]:((old(X)&~brave(X))<=>(~creative(X)|strong(X))))&
((?[X]:((patient(X)|quiet(X))))<=>(?[X]:(happy(X))))&
(![X]:(kind(X)<=>(calm(X)&brave(X))))&
(((~wise(paul)<~>tall(paul)))=>(?[X]:((~creative(X)&patient(X)))))&
(![X]:((~quiet(X)|strong(X))=>~strong(X)))&
(![X]:((strong(X)|~old(X))=>(rich(X)|~old(X))))&
(![X]:((~calm(X)<~>old(X))=>~happy(X)))&
(((generous(fred)&~curious(fred)))=>(?[X]:(humble(X))))&
(((brave(john)<~>generous(john)))<=>((tall(susan)&~rich(susan))))&
(![X]:((~rich(X)<~>~happy(X))<=>(curious(X)|~rich(X))))&
(![X]:((~strong(X)<~>generous(X))=>wise(X)))&
(![X]:((humble(X)&wise(X))=>(~rich(X)<~>~old(X))))&
(![X]:((~generous(X)<~>quiet(X))<=>(rich(X)<~>curious(X))))&
((~funny(susan)|quiet(susan)))&
((~quiet(lucy)&~creative(lucy)))&
(?[X]:((tall(X)|wise(X))))&
(?[X]:((~strong(X)|rich(X))))&
(?[X]:(~creative(X)))&
(~brave(lucy))&
((calm(lucy)&~funny(lucy)))&
(?[X]:((~kind(X)&~happy(X)))) | ~wise(lucy) | [
"p0",
"p3",
"p9",
"p12",
"p14",
"p17",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4360815796057576085868264
% SZS output start Proof for 4360815796057576085868264
1. ! [X0] : ((creative(X0) <~> happy(X0)) <=> (~happy(X0) & ~humble(X0))) [input p0]
4. ! [X0] : ((~brave(X0) & old(X0)) <=> (strong(X0) | ~creative(X0))) [input p3]
10. ! [X0] : ((~calm(X0) <~> old(X0)) => ~happy(X0)) [input p9]
13. ! [X0] : ((~rich(X0) <~> ~happy(X0)) <=> (~rich(X0) | curious(X0))) [input p12]
15. ! [X0] : ((wise(X0) & humble(X0)) => (~rich(X0) <~> ~old(X0))) [input p14]
18. ~creative(lucy) & ~quiet(lucy) [input p17]
23. ~funny(lucy) & calm(lucy) [input p22]
25. wise(lucy) [input hypothesis]
30. calm(lucy) [pure predicate removal 23]
40. ! [X0] : (~happy(X0) | (~calm(X0) <=> old(X0))) [ennf transformation 10]
44. ! [X0] : ((~rich(X0) <~> ~old(X0)) | (~wise(X0) | ~humble(X0))) [ennf transformation 15]
45. ! [X0] : ((~rich(X0) <~> ~old(X0)) | ~wise(X0) | ~humble(X0)) [flattening 44]
46. ! [X0] : ((((~happy(X0) | ~creative(X0)) & (happy(X0) | creative(X0))) | (happy(X0) | humble(X0))) & ((~happy(X0) & ~humble(X0)) | ((creative(X0) | ~happy(X0)) & (happy(X0) | ~creative(X0))))) [nnf transformation 1]
47. ! [X0] : ((((~happy(X0) | ~creative(X0)) & (happy(X0) | creative(X0))) | happy(X0) | humble(X0)) & ((~happy(X0) & ~humble(X0)) | ((creative(X0) | ~happy(X0)) & (happy(X0) | ~creative(X0))))) [flattening 46]
51. ! [X0] : (((~brave(X0) & old(X0)) | (~strong(X0) & creative(X0))) & ((strong(X0) | ~creative(X0)) | (brave(X0) | ~old(X0)))) [nnf transformation 4]
52. ! [X0] : (((~brave(X0) & old(X0)) | (~strong(X0) & creative(X0))) & (strong(X0) | ~creative(X0) | brave(X0) | ~old(X0))) [flattening 51]
61. ! [X0] : (~happy(X0) | ((~calm(X0) | ~old(X0)) & (old(X0) | calm(X0)))) [nnf transformation 40]
66. ! [X0] : ((((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | (rich(X0) & ~curious(X0))) & ((~rich(X0) | curious(X0)) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0))))) [nnf transformation 13]
67. ! [X0] : ((((happy(X0) | rich(X0)) & (~happy(X0) | ~rich(X0))) | (rich(X0) & ~curious(X0))) & (~rich(X0) | curious(X0) | ((~rich(X0) | happy(X0)) & (~happy(X0) | rich(X0))))) [flattening 66]
69. ! [X0] : (((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | ~wise(X0) | ~humble(X0)) [nnf transformation 45]
83. happy(X0) | creative(X0) | happy(X0) | humble(X0) [cnf transformation 47]
88. old(X0) | creative(X0) [cnf transformation 52]
105. ~calm(X0) | ~happy(X0) | ~old(X0) [cnf transformation 61]
118. happy(X0) | rich(X0) | rich(X0) [cnf transformation 67]
121. ~old(X0) | ~rich(X0) | ~wise(X0) | ~humble(X0) [cnf transformation 69]
132. ~creative(lucy) [cnf transformation 18]
137. calm(lucy) [cnf transformation 30]
140. wise(lucy) [cnf transformation 25]
142. rich(X0) | happy(X0) [duplicate literal removal 118]
145. humble(X0) | creative(X0) | happy(X0) [duplicate literal removal 83]
279. ~happy(lucy) | ~old(lucy) [resolution 105,137]
282. 27 <=> old(lucy) [avatar definition]
283. old(lucy) <- (27) [avatar component clause 282]
284. ~old(lucy) <- (~27) [avatar component clause 282]
286. 28 <=> happy(lucy) [avatar definition]
288. ~happy(lucy) <- (~28) [avatar component clause 286]
289. ~27 | ~28 [avatar split clause 279,286,282]
351. 39 <=> humble(lucy) [avatar definition]
352. humble(lucy) <- (39) [avatar component clause 351]
353. ~humble(lucy) <- (~39) [avatar component clause 351]
355. 40 <=> rich(lucy) [avatar definition]
356. ~rich(lucy) <- (~40) [avatar component clause 355]
359. creative(lucy) | happy(lucy) <- (~39) [resolution 353,145]
360. happy(lucy) <- (~39) [subsumption resolution 359,132]
363. 28 | 39 [avatar split clause 360,351,286]
365. creative(lucy) <- (~27) [resolution 284,88]
366. $false <- (~27) [subsumption resolution 365,132]
367. 27 [avatar contradiction clause 366]
368. ~rich(lucy) | ~wise(lucy) | ~humble(lucy) <- (27) [resolution 283,121]
370. ~rich(lucy) | ~humble(lucy) <- (27) [subsumption resolution 368,140]
371. ~rich(lucy) <- (27, 39) [subsumption resolution 370,352]
372. ~40 | ~27 | ~39 [avatar split clause 371,351,282,355]
383. happy(lucy) <- (~40) [resolution 356,142]
384. $false <- (~28, ~40) [subsumption resolution 383,288]
385. 28 | 40 [avatar contradiction clause 384]
386. $false [avatar sat refutation 289,363,367,372,385]
% SZS output end Proof for 4360815796057576085868264
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is not creative or patient and vice versa.
If alice is not generous or not humble then someone is not brave.
Everyone who is brave or not quiet is both generous and curious and vice versa.
If someone is not wise or not happy then someone is not creative and vice versa.
Everyone who is not happy or old is either curious or not kind and vice versa.
If someone is either not wise or calm then someone is curious or calm.
Everyone who is both curious and old is either not humble or happy.
Everyone who is wise is both not funny and not strong.
If someone is either patient or kind then fred is either old or not wise and vice versa.
If someone is not generous then someone is wise or strong and vice versa.
Everyone who is either humble or not generous is either funny or not calm.
Everyone who is either creative or not creative is brave and vice versa.
If john is either not quiet or creative then someone is tall and vice versa.
If susan is not brave then someone is both not funny and generous.
Everyone who is both not tall and not curious is either creative or not wise.
Everyone who is both rich and wise is not humble.
Alice is not strong.
Someone is either not funny or not curious.
Someone is either not rich or not curious.
Someone is both not strong and generous.
Paul is both funny and not calm.
Someone is humble or funny.
Paul is not generous or old. | Paul is wise. | contradiction | (![X]:(~rich(X)<=>(~creative(X)|patient(X))))&
(((~generous(alice)|~humble(alice)))=>(?[X]:(~brave(X))))&
(![X]:((brave(X)|~quiet(X))<=>(generous(X)&curious(X))))&
((?[X]:((~wise(X)|~happy(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~happy(X)|old(X))<=>(curious(X)<~>~kind(X))))&
((?[X]:((~wise(X)<~>calm(X))))=>(?[X]:((curious(X)|calm(X)))))&
(![X]:((curious(X)&old(X))=>(~humble(X)<~>happy(X))))&
(![X]:(wise(X)=>(~funny(X)&~strong(X))))&
((?[X]:((patient(X)<~>kind(X))))<=>((old(fred)<~>~wise(fred))))&
((?[X]:(~generous(X)))<=>(?[X]:((wise(X)|strong(X)))))&
(![X]:((humble(X)<~>~generous(X))=>(funny(X)<~>~calm(X))))&
(![X]:((creative(X)<~>~creative(X))<=>brave(X)))&
(((~quiet(john)<~>creative(john)))<=>(?[X]:(tall(X))))&
((~brave(susan))=>(?[X]:((~funny(X)&generous(X)))))&
(![X]:((~tall(X)&~curious(X))=>(creative(X)<~>~wise(X))))&
(![X]:((rich(X)&wise(X))=>~humble(X)))&
(~strong(alice))&
(?[X]:((~funny(X)<~>~curious(X))))&
(?[X]:((~rich(X)<~>~curious(X))))&
(?[X]:((~strong(X)&generous(X))))&
((funny(paul)&~calm(paul)))&
(?[X]:((humble(X)|funny(X))))&
((~generous(paul)|old(paul))) | wise(paul) | [
"p2",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 781612167339594315936622
% SZS output start Proof for 781612167339594315936622
3. ! [X0] : ((~quiet(X0) | brave(X0)) <=> (curious(X0) & generous(X0))) [input p2]
10. ? [X0] : ~generous(X0) <=> ? [X0] : (strong(X0) | wise(X0)) [input p9]
12. ! [X0] : ((creative(X0) <~> ~creative(X0)) <=> brave(X0)) [input p11]
24. wise(paul) [input hypothesis]
27. ? [X0] : ~generous(X0) <=> ? [X1] : (strong(X1) | wise(X1)) [rectify 10]
43. ! [X0] : (((~quiet(X0) | brave(X0)) | (~curious(X0) | ~generous(X0))) & ((curious(X0) & generous(X0)) | (quiet(X0) & ~brave(X0)))) [nnf transformation 3]
44. ! [X0] : ((~quiet(X0) | brave(X0) | ~curious(X0) | ~generous(X0)) & ((curious(X0) & generous(X0)) | (quiet(X0) & ~brave(X0)))) [flattening 43]
61. (? [X0] : ~generous(X0) | ! [X1] : (~strong(X1) & ~wise(X1))) & (? [X1] : (strong(X1) | wise(X1)) | ! [X0] : generous(X0)) [nnf transformation 27]
62. (? [X0] : ~generous(X0) | ! [X1] : (~strong(X1) & ~wise(X1))) & (? [X2] : (strong(X2) | wise(X2)) | ! [X3] : generous(X3)) [rectify 61]
63. ? [X0] : ~generous(X0) => ~generous(sK5) [choice axiom]
64. ? [X2] : (strong(X2) | wise(X2)) => (strong(sK6) | wise(sK6)) [choice axiom]
65. (~generous(sK5) | ! [X1] : (~strong(X1) & ~wise(X1))) & ((strong(sK6) | wise(sK6)) | ! [X3] : generous(X3)) [skolemisation 62,64,63]
67. ! [X0] : ((((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | ~brave(X0)) & (brave(X0) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0))))) [nnf transformation 12]
90. ~brave(X0) | generous(X0) [cnf transformation 44]
119. ~generous(sK5) | ~wise(X1) [cnf transformation 65]
125. brave(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 67]
126. brave(X0) | creative(X0) | creative(X0) [cnf transformation 67]
149. wise(paul) [cnf transformation 24]
150. brave(X0) | ~creative(X0) [duplicate literal removal 125]
151. brave(X0) | creative(X0) [duplicate literal removal 126]
240. 21 <=> generous(sK5) [avatar definition]
242. ~generous(sK5) <- (~21) [avatar component clause 240]
245. 22 <=> ! [X1] : ~wise(X1) [avatar definition]
246. ~wise(X1) <- (22) [avatar component clause 245]
247. 22 | ~21 [avatar split clause 119,240,245]
249. 23 <=> ! [X3] : generous(X3) [avatar definition]
250. generous(X3) <- (23) [avatar component clause 249]
260. brave(X0) [subsumption resolution 150,151]
318. $false <- (~21, 23) [subsumption resolution 242,250]
319. 21 | ~23 [avatar contradiction clause 318]
322. $false <- (22) [resolution 246,149]
323. ~22 [avatar contradiction clause 322]
326. generous(X0) [resolution 90,260]
327. 23 [avatar split clause 326,249]
328. $false [avatar sat refutation 247,319,323,327]
% SZS output end Proof for 781612167339594315936622
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either kind or not generous is not patient or funny and vice versa. Everyone who is not brave is happy and vice versa. Everyone who is tall or strong is curious. Everyone who is either calm or not humble is either not wise or rich and vice versa. If someone is either tall or curious then lucy is humble and vice versa. Everyone who is both brave and not wise is both not generous and creative and vice versa. If someone is funny then lucy is either kind or not rich. Everyone who is either happy or not patient is curious or not wise. Everyone who is both creative and quiet is not calm or wise and vice versa. If john is humble or not tall then someone is not humble or generous and vice versa. Everyone who is either strong or not creative is either not calm or strong and vice versa. Everyone who is not brave is not humble. Everyone who is happy or not humble is both brave and generous and vice versa. If susan is wise then someone is both brave and tall. If mary is either not patient or tall then fred is curious or tall. Everyone who is either creative or not patient is not wise. Susan is either not rich or not kind. Paul is both old and not humble. Someone is both not kind and tall. Lucy is both tall and not patient. Susan is generous or not happy. Someone is patient or not calm. Paul is old or generous. | Fred is not quiet. | neutral | (![X]:((kind(X)<~>~generous(X))<=>(~patient(X)|funny(X))))&
(![X]:(~brave(X)<=>happy(X)))&
(![X]:((tall(X)|strong(X))=>curious(X)))&
(![X]:((calm(X)<~>~humble(X))<=>(~wise(X)<~>rich(X))))&
((?[X]:((tall(X)<~>curious(X))))<=>(humble(lucy)))&
(![X]:((brave(X)&~wise(X))<=>(~generous(X)&creative(X))))&
((?[X]:(funny(X)))=>((kind(lucy)<~>~rich(lucy))))&
(![X]:((happy(X)<~>~patient(X))=>(curious(X)|~wise(X))))&
(![X]:((creative(X)&quiet(X))<=>(~calm(X)|wise(X))))&
(((humble(john)|~tall(john)))<=>(?[X]:((~humble(X)|generous(X)))))&
(![X]:((strong(X)<~>~creative(X))<=>(~calm(X)<~>strong(X))))&
(![X]:(~brave(X)=>~humble(X)))&
(![X]:((happy(X)|~humble(X))<=>(brave(X)&generous(X))))&
((wise(susan))=>(?[X]:((brave(X)&tall(X)))))&
(((~patient(mary)<~>tall(mary)))=>((curious(fred)|tall(fred))))&
(![X]:((creative(X)<~>~patient(X))=>~wise(X)))&
((~rich(susan)<~>~kind(susan)))&
((old(paul)&~humble(paul)))&
(?[X]:((~kind(X)&tall(X))))&
((tall(lucy)&~patient(lucy)))&
((generous(susan)|~happy(susan)))&
(?[X]:((patient(X)|~calm(X))))&
((old(paul)|generous(paul))) | ~quiet(fred) | [] | null | 0 |
If susan is either funny or patient then lucy is generous. Everyone who is both rich and not humble is rich and vice versa. Everyone who is both kind and wise is either not calm or not tall. Everyone who is not wise is either not patient or strong and vice versa. If paul is both kind and not tall then lucy is both not strong and rich and vice versa. Everyone who is either old or not wise is either patient or rich and vice versa. If someone is not funny or kind then john is both not quiet and calm and vice versa. If paul is both not quiet and old then someone is not creative. Everyone who is not wise or patient is both not brave and tall and vice versa. If someone is not generous or not strong then john is either strong or tall. If paul is not kind then someone is not happy or patient. If someone is both quiet and not brave then someone is either calm or not calm and vice versa. If someone is both not tall and not happy then someone is both strong and not brave. Everyone who is both not tall and humble is not generous or not kind and vice versa. If mary is not brave or tall then lucy is both not kind and not quiet and vice versa. Everyone who is either wise or not strong is not calm or calm and vice versa. Susan is not wise. Alice is strong or creative. Someone is not old. Susan is both not calm and creative. Someone is not curious. Someone is both not creative and not rich. Someone is strong. Someone is not calm. | John is patient. | contradiction | (((funny(susan)<~>patient(susan)))=>(generous(lucy)))&
(![X]:((rich(X)&~humble(X))<=>rich(X)))&
(![X]:((kind(X)&wise(X))=>(~calm(X)<~>~tall(X))))&
(![X]:(~wise(X)<=>(~patient(X)<~>strong(X))))&
(((kind(paul)&~tall(paul)))<=>((~strong(lucy)&rich(lucy))))&
(![X]:((old(X)<~>~wise(X))<=>(patient(X)<~>rich(X))))&
((?[X]:((~funny(X)|kind(X))))<=>((~quiet(john)&calm(john))))&
(((~quiet(paul)&old(paul)))=>(?[X]:(~creative(X))))&
(![X]:((~wise(X)|patient(X))<=>(~brave(X)&tall(X))))&
((?[X]:((~generous(X)|~strong(X))))=>((strong(john)<~>tall(john))))&
((~kind(paul))=>(?[X]:((~happy(X)|patient(X)))))&
((?[X]:((quiet(X)&~brave(X))))<=>(?[X]:((calm(X)<~>~calm(X)))))&
((?[X]:((~tall(X)&~happy(X))))=>(?[X]:((strong(X)&~brave(X)))))&
(![X]:((~tall(X)&humble(X))<=>(~generous(X)|~kind(X))))&
(((~brave(mary)|tall(mary)))<=>((~kind(lucy)&~quiet(lucy))))&
(![X]:((wise(X)<~>~strong(X))<=>(~calm(X)|calm(X))))&
(~wise(susan))&
((strong(alice)|creative(alice)))&
(?[X]:(~old(X)))&
((~calm(susan)&creative(susan)))&
(?[X]:(~curious(X)))&
(?[X]:((~creative(X)&~rich(X))))&
(?[X]:(strong(X)))&
(?[X]:(~calm(X))) | patient(john) | [
"p3",
"p8",
"p9",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6025277176437657553399970
% SZS output start Proof for 6025277176437657553399970
4. ! [X0] : (~wise(X0) <=> (~patient(X0) <~> strong(X0))) [input p3]
9. ! [X0] : ((patient(X0) | ~wise(X0)) <=> (tall(X0) & ~brave(X0))) [input p8]
10. ? [X0] : (~strong(X0) | ~generous(X0)) => (strong(john) <~> tall(john)) [input p9]
16. ! [X0] : ((wise(X0) <~> ~strong(X0)) <=> (calm(X0) | ~calm(X0))) [input p15]
17. ~wise(susan) [input p16]
25. patient(john) [input hypothesis]
34. (strong(john) <~> tall(john)) | ! [X0] : (strong(X0) & generous(X0)) [ennf transformation 10]
41. ! [X0] : ((~wise(X0) | ((~patient(X0) | ~strong(X0)) & (strong(X0) | patient(X0)))) & (((~strong(X0) | patient(X0)) & (strong(X0) | ~patient(X0))) | wise(X0))) [nnf transformation 4]
52. ! [X0] : (((patient(X0) | ~wise(X0)) | (~tall(X0) | brave(X0))) & ((tall(X0) & ~brave(X0)) | (~patient(X0) & wise(X0)))) [nnf transformation 9]
53. ! [X0] : ((patient(X0) | ~wise(X0) | ~tall(X0) | brave(X0)) & ((tall(X0) & ~brave(X0)) | (~patient(X0) & wise(X0)))) [flattening 52]
54. ((~tall(john) | ~strong(john)) & (tall(john) | strong(john))) | ! [X0] : (strong(X0) & generous(X0)) [nnf transformation 34]
69. ! [X0] : ((((strong(X0) | ~wise(X0)) & (~strong(X0) | wise(X0))) | (~calm(X0) & calm(X0))) & ((calm(X0) | ~calm(X0)) | ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0))))) [nnf transformation 16]
70. ! [X0] : ((((strong(X0) | ~wise(X0)) & (~strong(X0) | wise(X0))) | (~calm(X0) & calm(X0))) & (calm(X0) | ~calm(X0) | ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0))))) [flattening 69]
86. ~patient(X0) | strong(X0) | wise(X0) [cnf transformation 41]
111. ~patient(X0) | tall(X0) [cnf transformation 53]
116. ~tall(john) | ~strong(john) | strong(X0) [cnf transformation 54]
138. ~strong(X0) | wise(X0) | calm(X0) [cnf transformation 70]
139. ~strong(X0) | wise(X0) | ~calm(X0) [cnf transformation 70]
140. strong(X0) | ~wise(X0) | calm(X0) [cnf transformation 70]
141. strong(X0) | ~wise(X0) | ~calm(X0) [cnf transformation 70]
142. ~wise(susan) [cnf transformation 17]
151. patient(john) [cnf transformation 25]
231. 17 <=> ! [X0] : strong(X0) [avatar definition]
232. strong(X0) <- (17) [avatar component clause 231]
234. 18 <=> strong(john) [avatar definition]
238. 19 <=> tall(john) [avatar definition]
241. 17 | ~18 | ~19 [avatar split clause 116,238,234,231]
309. ~wise(X0) | strong(X0) [subsumption resolution 140,141]
310. ~strong(X0) | wise(X0) [subsumption resolution 138,139]
329. tall(john) [resolution 111,151]
333. 19 [avatar split clause 329,238]
356. strong(john) | wise(john) [resolution 86,151]
366. strong(john) [subsumption resolution 356,309]
367. 18 [avatar split clause 366,234]
369. wise(X1) <- (17) [resolution 232,310]
376. $false <- (17) [resolution 369,142]
379. ~17 [avatar contradiction clause 376]
380. $false [avatar sat refutation 241,333,367,379]
% SZS output end Proof for 6025277176437657553399970
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or brave is both kind and strong. Everyone who is calm or not old is either brave or rich and vice versa. Everyone who is either curious or not old is both brave and strong. If someone is not quiet or not old then someone is strong or not calm and vice versa. If someone is tall or not curious then someone is tall or not kind. If paul is not rich then someone is not patient or rich and vice versa. Everyone who is rich is brave. If someone is either tall or not generous then susan is both not rich and not funny and vice versa. Everyone who is humble or patient is funny and vice versa. Everyone who is not generous or not happy is not rich or not funny. If alice is quiet or tall then mary is either not generous or calm. If someone is either not old or happy then someone is either not kind or not brave and vice versa. If someone is either creative or rich then susan is either kind or tall and vice versa. If lucy is both generous and brave then someone is either not wise or kind and vice versa. Someone is either not humble or patient. Paul is not curious. Someone is either not humble or quiet. Someone is quiet or happy. Someone is both not curious and humble. | Lucy is not patient. | neutral | (![X]:((~calm(X)|brave(X))=>(kind(X)&strong(X))))&
(![X]:((calm(X)|~old(X))<=>(brave(X)<~>rich(X))))&
(![X]:((curious(X)<~>~old(X))=>(brave(X)&strong(X))))&
((?[X]:((~quiet(X)|~old(X))))<=>(?[X]:((strong(X)|~calm(X)))))&
((?[X]:((tall(X)|~curious(X))))=>(?[X]:((tall(X)|~kind(X)))))&
((~rich(paul))<=>(?[X]:((~patient(X)|rich(X)))))&
(![X]:(rich(X)=>brave(X)))&
((?[X]:((tall(X)<~>~generous(X))))<=>((~rich(susan)&~funny(susan))))&
(![X]:((humble(X)|patient(X))<=>funny(X)))&
(![X]:((~generous(X)|~happy(X))=>(~rich(X)|~funny(X))))&
(((quiet(alice)|tall(alice)))=>((~generous(mary)<~>calm(mary))))&
((?[X]:((~old(X)<~>happy(X))))<=>(?[X]:((~kind(X)<~>~brave(X)))))&
((?[X]:((creative(X)<~>rich(X))))<=>((kind(susan)<~>tall(susan))))&
(((generous(lucy)&brave(lucy)))<=>(?[X]:((~wise(X)<~>kind(X)))))&
(?[X]:((~humble(X)<~>patient(X))))&
(~curious(paul))&
(?[X]:((~humble(X)<~>quiet(X))))&
(?[X]:((quiet(X)|happy(X))))&
(?[X]:((~curious(X)&humble(X)))) | ~patient(lucy) | [] | null | 0 |
Everyone who is both not strong and not rich is not happy or creative.
Everyone who is not strong is either not calm or not patient.
If someone is either not patient or not happy then alice is not curious.
Everyone who is rich is both rich and brave and vice versa.
If someone is not calm or old then susan is either not creative or not calm and vice versa.
If alice is both not tall and wise then john is either not humble or not strong.
If someone is kind then mary is either happy or strong.
If susan is not tall then someone is strong or not patient and vice versa.
If someone is curious or old then lucy is both not old and rich and vice versa.
Everyone who is not rich or not brave is funny and vice versa.
If someone is not generous then mary is both curious and not happy and vice versa.
Everyone who is either not strong or strong is creative or calm.
Everyone who is both not quiet and funny is not brave or generous.
Everyone who is not tall or not generous is strong or not rich and vice versa.
If someone is not calm then someone is rich or kind.
If alice is either not humble or patient then someone is calm or not happy.
Paul is not kind or not tall.
Someone is old or not humble.
Someone is brave or not curious.
Someone is either funny or tall.
Lucy is funny.
Someone is happy or not tall.
Susan is not strong or not old. | Lucy is not generous. | contradiction | (![X]:((~strong(X)&~rich(X))=>(~happy(X)|creative(X))))&
(![X]:(~strong(X)=>(~calm(X)<~>~patient(X))))&
((?[X]:((~patient(X)<~>~happy(X))))=>(~curious(alice)))&
(![X]:(rich(X)<=>(rich(X)&brave(X))))&
((?[X]:((~calm(X)|old(X))))<=>((~creative(susan)<~>~calm(susan))))&
(((~tall(alice)&wise(alice)))=>((~humble(john)<~>~strong(john))))&
((?[X]:(kind(X)))=>((happy(mary)<~>strong(mary))))&
((~tall(susan))<=>(?[X]:((strong(X)|~patient(X)))))&
((?[X]:((curious(X)|old(X))))<=>((~old(lucy)&rich(lucy))))&
(![X]:((~rich(X)|~brave(X))<=>funny(X)))&
((?[X]:(~generous(X)))<=>((curious(mary)&~happy(mary))))&
(![X]:((~strong(X)<~>strong(X))=>(creative(X)|calm(X))))&
(![X]:((~quiet(X)&funny(X))=>(~brave(X)|generous(X))))&
(![X]:((~tall(X)|~generous(X))<=>(strong(X)|~rich(X))))&
((?[X]:(~calm(X)))=>(?[X]:((rich(X)|kind(X)))))&
(((~humble(alice)<~>patient(alice)))=>(?[X]:((calm(X)|~happy(X)))))&
((~kind(paul)|~tall(paul)))&
(?[X]:((old(X)|~humble(X))))&
(?[X]:((brave(X)|~curious(X))))&
(?[X]:((funny(X)<~>tall(X))))&
(funny(lucy))&
(?[X]:((happy(X)|~tall(X))))&
((~strong(susan)|~old(susan))) | ~generous(lucy) | [
"p3",
"p8",
"p9",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5567001810362788414694928
% SZS output start Proof for 5567001810362788414694928
4. ! [X0] : (rich(X0) <=> (brave(X0) & rich(X0))) [input p3]
9. ? [X0] : (old(X0) | curious(X0)) <=> (rich(lucy) & ~old(lucy)) [input p8]
10. ! [X0] : ((~brave(X0) | ~rich(X0)) <=> funny(X0)) [input p9]
11. ? [X0] : ~generous(X0) <=> (~happy(mary) & curious(mary)) [input p10]
21. funny(lucy) [input p20]
24. ~generous(lucy) [input hypothesis]
39. ! [X0] : ((rich(X0) | (~brave(X0) | ~rich(X0))) & ((brave(X0) & rich(X0)) | ~rich(X0))) [nnf transformation 4]
40. ! [X0] : ((rich(X0) | ~brave(X0) | ~rich(X0)) & ((brave(X0) & rich(X0)) | ~rich(X0))) [flattening 39]
50. (? [X0] : (old(X0) | curious(X0)) | (~rich(lucy) | old(lucy))) & ((rich(lucy) & ~old(lucy)) | ! [X0] : (~old(X0) & ~curious(X0))) [nnf transformation 9]
51. (? [X0] : (old(X0) | curious(X0)) | ~rich(lucy) | old(lucy)) & ((rich(lucy) & ~old(lucy)) | ! [X0] : (~old(X0) & ~curious(X0))) [flattening 50]
52. (? [X0] : (old(X0) | curious(X0)) | ~rich(lucy) | old(lucy)) & ((rich(lucy) & ~old(lucy)) | ! [X1] : (~old(X1) & ~curious(X1))) [rectify 51]
53. ? [X0] : (old(X0) | curious(X0)) => (old(sK2) | curious(sK2)) [choice axiom]
54. ((old(sK2) | curious(sK2)) | ~rich(lucy) | old(lucy)) & ((rich(lucy) & ~old(lucy)) | ! [X1] : (~old(X1) & ~curious(X1))) [skolemisation 52,53]
55. ! [X0] : (((~brave(X0) | ~rich(X0)) | ~funny(X0)) & (funny(X0) | (brave(X0) & rich(X0)))) [nnf transformation 10]
56. ! [X0] : ((~brave(X0) | ~rich(X0) | ~funny(X0)) & (funny(X0) | (brave(X0) & rich(X0)))) [flattening 55]
57. (? [X0] : ~generous(X0) | (happy(mary) | ~curious(mary))) & ((~happy(mary) & curious(mary)) | ! [X0] : generous(X0)) [nnf transformation 11]
58. (? [X0] : ~generous(X0) | happy(mary) | ~curious(mary)) & ((~happy(mary) & curious(mary)) | ! [X0] : generous(X0)) [flattening 57]
59. (? [X0] : ~generous(X0) | happy(mary) | ~curious(mary)) & ((~happy(mary) & curious(mary)) | ! [X1] : generous(X1)) [rectify 58]
60. ? [X0] : ~generous(X0) => ~generous(sK3) [choice axiom]
61. (~generous(sK3) | happy(mary) | ~curious(mary)) & ((~happy(mary) & curious(mary)) | ! [X1] : generous(X1)) [skolemisation 59,60]
86. ~rich(X0) | brave(X0) [cnf transformation 40]
101. rich(lucy) | ~curious(X1) [cnf transformation 54]
106. ~brave(X0) | ~rich(X0) | ~funny(X0) [cnf transformation 56]
107. curious(mary) | generous(X1) [cnf transformation 61]
124. funny(lucy) [cnf transformation 21]
127. ~generous(lucy) [cnf transformation 24]
209. 19 <=> rich(lucy) [avatar definition]
223. 22 <=> ! [X1] : ~curious(X1) [avatar definition]
224. ~curious(X1) <- (22) [avatar component clause 223]
225. 22 | 19 [avatar split clause 101,209,223]
228. ~funny(X0) | ~rich(X0) [subsumption resolution 106,86]
230. 23 <=> curious(mary) [avatar definition]
231. curious(mary) <- (23) [avatar component clause 230]
239. 25 <=> ! [X1] : generous(X1) [avatar definition]
240. generous(X1) <- (25) [avatar component clause 239]
242. 25 | 23 [avatar split clause 107,230,239]
329. ~rich(lucy) [resolution 228,124]
335. ~19 [avatar split clause 329,209]
339. $false <- (22, 23) [resolution 224,231]
340. ~22 | ~23 [avatar contradiction clause 339]
342. $false <- (25) [resolution 240,127]
345. ~25 [avatar contradiction clause 342]
346. $false [avatar sat refutation 225,242,335,340,345]
% SZS output end Proof for 5567001810362788414694928
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not calm is either not creative or not calm and vice versa.
If paul is both strong and calm then someone is patient.
If john is both not curious and not calm then someone is tall or funny.
Everyone who is funny or not humble is either not strong or not creative and vice versa.
If someone is both not kind and not humble then lucy is both not brave and curious.
Everyone who is both generous and not generous is either not happy or rich and vice versa.
Everyone who is both not creative and patient is old or funny and vice versa.
Everyone who is either not tall or not kind is either not tall or rich.
Everyone who is not kind is happy and vice versa.
Everyone who is not old is both not humble and not tall.
If someone is either not old or creative then paul is both funny and brave.
If someone is calm or humble then someone is not creative and vice versa.
If someone is not brave then someone is both kind and quiet.
Everyone who is not happy is both not calm and humble.
Everyone who is not creative or not calm is both not rich and quiet.
Everyone who is either creative or not old is either not kind or not creative and vice versa.
Susan is curious or strong.
Mary is not kind.
Someone is both strong and not generous.
Susan is both funny and not curious.
Fred is both old and quiet.
Fred is either not humble or not funny. | Paul is not patient. | contradiction | (![X]:((~wise(X)<~>~calm(X))<=>(~creative(X)<~>~calm(X))))&
(((strong(paul)&calm(paul)))=>(?[X]:(patient(X))))&
(((~curious(john)&~calm(john)))=>(?[X]:((tall(X)|funny(X)))))&
(![X]:((funny(X)|~humble(X))<=>(~strong(X)<~>~creative(X))))&
((?[X]:((~kind(X)&~humble(X))))=>((~brave(lucy)&curious(lucy))))&
(![X]:((generous(X)&~generous(X))<=>(~happy(X)<~>rich(X))))&
(![X]:((~creative(X)&patient(X))<=>(old(X)|funny(X))))&
(![X]:((~tall(X)<~>~kind(X))=>(~tall(X)<~>rich(X))))&
(![X]:(~kind(X)<=>happy(X)))&
(![X]:(~old(X)=>(~humble(X)&~tall(X))))&
((?[X]:((~old(X)<~>creative(X))))=>((funny(paul)&brave(paul))))&
((?[X]:((calm(X)|humble(X))))<=>(?[X]:(~creative(X))))&
((?[X]:(~brave(X)))=>(?[X]:((kind(X)&quiet(X)))))&
(![X]:(~happy(X)=>(~calm(X)&humble(X))))&
(![X]:((~creative(X)|~calm(X))=>(~rich(X)&quiet(X))))&
(![X]:((creative(X)<~>~old(X))<=>(~kind(X)<~>~creative(X))))&
((curious(susan)|strong(susan)))&
(~kind(mary))&
(?[X]:((strong(X)&~generous(X))))&
((funny(susan)&~curious(susan)))&
((old(fred)&quiet(fred)))&
((~humble(fred)<~>~funny(fred))) | ~patient(paul) | [
"p4",
"p5",
"p6",
"p8",
"p9",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7699350337121942377870752
% SZS output start Proof for 7699350337121942377870752
5. ? [X0] : (~humble(X0) & ~kind(X0)) => (curious(lucy) & ~brave(lucy)) [input p4]
6. ! [X0] : ((~generous(X0) & generous(X0)) <=> (~happy(X0) <~> rich(X0))) [input p5]
7. ! [X0] : ((patient(X0) & ~creative(X0)) <=> (funny(X0) | old(X0))) [input p6]
9. ! [X0] : (~kind(X0) <=> happy(X0)) [input p8]
10. ! [X0] : (~old(X0) => (~tall(X0) & ~humble(X0))) [input p9]
13. ? [X0] : ~brave(X0) => ? [X0] : (quiet(X0) & kind(X0)) [input p12]
14. ! [X0] : (~happy(X0) => (humble(X0) & ~calm(X0))) [input p13]
15. ! [X0] : ((~calm(X0) | ~creative(X0)) => (quiet(X0) & ~rich(X0))) [input p14]
23. ~patient(paul) [input hypothesis]
25. ? [X0] : ~brave(X0) => ? [X1] : (quiet(X1) & kind(X1)) [rectify 13]
27. ! [X0] : ((~calm(X0) | ~creative(X0)) => ~rich(X0)) [pure predicate removal 15]
28. ? [X0] : ~brave(X0) => ? [X1] : kind(X1) [pure predicate removal 25]
33. (curious(lucy) & ~brave(lucy)) | ! [X0] : (humble(X0) | kind(X0)) [ennf transformation 5]
35. ! [X0] : ((~tall(X0) & ~humble(X0)) | old(X0)) [ennf transformation 10]
37. ? [X1] : kind(X1) | ! [X0] : brave(X0) [ennf transformation 28]
38. ! [X0] : ((humble(X0) & ~calm(X0)) | happy(X0)) [ennf transformation 14]
39. ! [X0] : (~rich(X0) | (calm(X0) & creative(X0))) [ennf transformation 27]
47. ! [X0] : (((~generous(X0) & generous(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0)))) & (((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (generous(X0) | ~generous(X0)))) [nnf transformation 6]
48. ! [X0] : (((~generous(X0) & generous(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0)))) & (((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | generous(X0) | ~generous(X0))) [flattening 47]
49. ! [X0] : (((patient(X0) & ~creative(X0)) | (~funny(X0) & ~old(X0))) & ((funny(X0) | old(X0)) | (~patient(X0) | creative(X0)))) [nnf transformation 7]
50. ! [X0] : (((patient(X0) & ~creative(X0)) | (~funny(X0) & ~old(X0))) & (funny(X0) | old(X0) | ~patient(X0) | creative(X0))) [flattening 49]
52. ! [X0] : ((~kind(X0) | ~happy(X0)) & (happy(X0) | kind(X0))) [nnf transformation 9]
59. ? [X0] : kind(X0) | ! [X1] : brave(X1) [rectify 37]
60. ? [X0] : kind(X0) => kind(sK4) [choice axiom]
61. kind(sK4) | ! [X1] : brave(X1) [skolemisation 59,60]
82. ~brave(lucy) | humble(X0) | kind(X0) [cnf transformation 33]
86. generous(X0) | rich(X0) | happy(X0) [cnf transformation 48]
88. ~generous(X0) | rich(X0) | happy(X0) [cnf transformation 48]
93. ~old(X0) | patient(X0) [cnf transformation 50]
100. ~happy(X0) | ~kind(X0) [cnf transformation 52]
101. ~humble(X0) | old(X0) [cnf transformation 35]
110. kind(sK4) | brave(X1) [cnf transformation 61]
111. ~calm(X0) | happy(X0) [cnf transformation 38]
112. happy(X0) | humble(X0) [cnf transformation 38]
114. ~rich(X0) | calm(X0) [cnf transformation 39]
132. ~patient(paul) [cnf transformation 23]
176. 8 <=> ! [X0] : (humble(X0) | kind(X0)) [avatar definition]
177. humble(X0) | kind(X0) <- (8) [avatar component clause 176]
184. 10 <=> brave(lucy) [avatar definition]
186. ~brave(lucy) <- (~10) [avatar component clause 184]
187. 8 | ~10 [avatar split clause 82,184,176]
189. rich(X0) | happy(X0) [subsumption resolution 86,88]
228. 20 <=> ! [X1] : brave(X1) [avatar definition]
229. brave(X1) <- (20) [avatar component clause 228]
231. 21 <=> kind(sK4) [avatar definition]
233. kind(sK4) <- (21) [avatar component clause 231]
234. 20 | 21 [avatar split clause 110,231,228]
267. humble(X0) | ~kind(X0) [resolution 112,100]
268. humble(X0) <- (8) [subsumption resolution 267,177]
270. old(X0) <- (8) [resolution 268,101]
271. patient(X0) <- (8) [resolution 270,93]
273. $false <- (8) [resolution 271,132]
274. ~8 [avatar contradiction clause 273]
275. $false <- (~10, 20) [subsumption resolution 186,229]
276. 10 | ~20 [avatar contradiction clause 275]
278. happy(X1) | calm(X1) [resolution 189,114]
280. happy(X1) [subsumption resolution 278,111]
281. ~kind(X0) [resolution 280,100]
284. $false <- (21) [resolution 281,233]
285. ~21 [avatar contradiction clause 284]
286. $false [avatar sat refutation 187,234,274,276,285]
% SZS output end Proof for 7699350337121942377870752
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is quiet then someone is both quiet and tall and vice versa.
If someone is both not patient and brave then someone is not creative or not funny and vice versa.
Everyone who is either brave or happy is kind.
If paul is both not strong and curious then someone is curious or calm and vice versa.
If someone is happy then susan is either not tall or funny and vice versa.
If someone is not kind then someone is not rich.
If someone is either not happy or brave then someone is either patient or not calm.
Everyone who is not calm or not brave is creative and vice versa.
Everyone who is not happy or brave is not funny or rich.
Everyone who is not happy or not calm is either not funny or not quiet.
Everyone who is either not wise or curious is either happy or patient and vice versa.
Everyone who is not wise is happy or quiet and vice versa.
Everyone who is not wise or wise is both not patient and curious.
If lucy is not creative then susan is either not kind or strong.
If someone is kind or quiet then susan is either curious or wise and vice versa.
If someone is either not brave or humble then someone is both not strong and strong.
Susan is both not patient and curious.
John is either not curious or strong.
Alice is quiet or funny.
Lucy is either funny or not creative.
Someone is either patient or kind.
Paul is both tall and humble. | Susan is tall. | entailment | ((quiet(lucy))<=>(?[X]:((quiet(X)&tall(X)))))&
((?[X]:((~patient(X)&brave(X))))<=>(?[X]:((~creative(X)|~funny(X)))))&
(![X]:((brave(X)<~>happy(X))=>kind(X)))&
(((~strong(paul)&curious(paul)))<=>(?[X]:((curious(X)|calm(X)))))&
((?[X]:(happy(X)))<=>((~tall(susan)<~>funny(susan))))&
((?[X]:(~kind(X)))=>(?[X]:(~rich(X))))&
((?[X]:((~happy(X)<~>brave(X))))=>(?[X]:((patient(X)<~>~calm(X)))))&
(![X]:((~calm(X)|~brave(X))<=>creative(X)))&
(![X]:((~happy(X)|brave(X))=>(~funny(X)|rich(X))))&
(![X]:((~happy(X)|~calm(X))=>(~funny(X)<~>~quiet(X))))&
(![X]:((~wise(X)<~>curious(X))<=>(happy(X)<~>patient(X))))&
(![X]:(~wise(X)<=>(happy(X)|quiet(X))))&
(![X]:((~wise(X)|wise(X))=>(~patient(X)&curious(X))))&
((~creative(lucy))=>((~kind(susan)<~>strong(susan))))&
((?[X]:((kind(X)|quiet(X))))<=>((curious(susan)<~>wise(susan))))&
((?[X]:((~brave(X)<~>humble(X))))=>(?[X]:((~strong(X)&strong(X)))))&
((~patient(susan)&curious(susan)))&
((~curious(john)<~>strong(john)))&
((quiet(alice)|funny(alice)))&
((funny(lucy)<~>~creative(lucy)))&
(?[X]:((patient(X)<~>kind(X))))&
((tall(paul)&humble(paul))) | tall(susan) | [
"p4",
"p9",
"p10",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1465142765963365934926291
% SZS output start Proof for 1465142765963365934926291
5. ? [X0] : happy(X0) <=> (~tall(susan) <~> funny(susan)) [input p4]
10. ! [X0] : ((~calm(X0) | ~happy(X0)) => (~funny(X0) <~> ~quiet(X0))) [input p9]
11. ! [X0] : ((~wise(X0) <~> curious(X0)) <=> (happy(X0) <~> patient(X0))) [input p10]
12. ! [X0] : (~wise(X0) <=> (quiet(X0) | happy(X0))) [input p11]
13. ! [X0] : ((wise(X0) | ~wise(X0)) => (curious(X0) & ~patient(X0))) [input p12]
15. ? [X0] : (quiet(X0) | kind(X0)) <=> (curious(susan) <~> wise(susan)) [input p14]
23. ~tall(susan) [input hypothesis]
33. ! [X0] : ((~funny(X0) <~> ~quiet(X0)) | (calm(X0) & happy(X0))) [ennf transformation 10]
34. ! [X0] : ((curious(X0) & ~patient(X0)) | (~wise(X0) & wise(X0))) [ennf transformation 13]
52. (? [X0] : happy(X0) | ((~tall(susan) | ~funny(susan)) & (funny(susan) | tall(susan)))) & (((~funny(susan) | tall(susan)) & (funny(susan) | ~tall(susan))) | ! [X0] : ~happy(X0)) [nnf transformation 5]
53. (? [X0] : happy(X0) | ((~tall(susan) | ~funny(susan)) & (funny(susan) | tall(susan)))) & (((~funny(susan) | tall(susan)) & (funny(susan) | ~tall(susan))) | ! [X1] : ~happy(X1)) [rectify 52]
54. ? [X0] : happy(X0) => happy(sK4) [choice axiom]
55. (happy(sK4) | ((~tall(susan) | ~funny(susan)) & (funny(susan) | tall(susan)))) & (((~funny(susan) | tall(susan)) & (funny(susan) | ~tall(susan))) | ! [X1] : ~happy(X1)) [skolemisation 53,54]
65. ! [X0] : (((quiet(X0) | funny(X0)) & (~quiet(X0) | ~funny(X0))) | (calm(X0) & happy(X0))) [nnf transformation 33]
66. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | ((happy(X0) | ~patient(X0)) & (patient(X0) | ~happy(X0)))) & (((~patient(X0) | ~happy(X0)) & (patient(X0) | happy(X0))) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [nnf transformation 11]
67. ! [X0] : ((~wise(X0) | (~quiet(X0) & ~happy(X0))) & ((quiet(X0) | happy(X0)) | wise(X0))) [nnf transformation 12]
68. ! [X0] : ((~wise(X0) | (~quiet(X0) & ~happy(X0))) & (quiet(X0) | happy(X0) | wise(X0))) [flattening 67]
70. (? [X0] : (quiet(X0) | kind(X0)) | ((curious(susan) | ~wise(susan)) & (wise(susan) | ~curious(susan)))) & (((~wise(susan) | ~curious(susan)) & (wise(susan) | curious(susan))) | ! [X0] : (~quiet(X0) & ~kind(X0))) [nnf transformation 15]
71. (? [X0] : (quiet(X0) | kind(X0)) | ((curious(susan) | ~wise(susan)) & (wise(susan) | ~curious(susan)))) & (((~wise(susan) | ~curious(susan)) & (wise(susan) | curious(susan))) | ! [X1] : (~quiet(X1) & ~kind(X1))) [rectify 70]
72. ? [X0] : (quiet(X0) | kind(X0)) => (quiet(sK7) | kind(sK7)) [choice axiom]
73. ((quiet(sK7) | kind(sK7)) | ((curious(susan) | ~wise(susan)) & (wise(susan) | ~curious(susan)))) & (((~wise(susan) | ~curious(susan)) & (wise(susan) | curious(susan))) | ! [X1] : (~quiet(X1) & ~kind(X1))) [skolemisation 71,72]
100. happy(sK4) | funny(susan) | tall(susan) [cnf transformation 55]
112. ~funny(X0) | ~quiet(X0) | happy(X0) [cnf transformation 65]
117. ~wise(X0) | happy(X0) | patient(X0) | ~curious(X0) [cnf transformation 66]
122. ~curious(X0) | wise(X0) | patient(X0) | ~happy(X0) [cnf transformation 66]
124. wise(X0) | happy(X0) | quiet(X0) [cnf transformation 68]
125. ~wise(X0) | ~happy(X0) [cnf transformation 68]
127. ~patient(X0) | wise(X0) [cnf transformation 34]
128. ~wise(X0) | ~patient(X0) [cnf transformation 34]
129. curious(X0) | wise(X0) [cnf transformation 34]
130. ~wise(X0) | curious(X0) [cnf transformation 34]
136. ~wise(susan) | ~curious(susan) | ~quiet(X1) [cnf transformation 73]
154. ~tall(susan) [cnf transformation 23]
231. 18 <=> funny(susan) [avatar definition]
232. funny(susan) <- (18) [avatar component clause 231]
235. 19 <=> tall(susan) [avatar definition]
239. 20 <=> happy(sK4) [avatar definition]
241. happy(sK4) <- (20) [avatar component clause 239]
243. 19 | 18 | 20 [avatar split clause 100,239,231,235]
245. 21 <=> ! [X1] : ~happy(X1) [avatar definition]
246. ~happy(X1) <- (21) [avatar component clause 245]
275. curious(X0) [subsumption resolution 129,130]
276. ~patient(X0) [subsumption resolution 127,128]
293. 31 <=> wise(susan) [avatar definition]
294. ~wise(susan) <- (~31) [avatar component clause 293]
305. ~wise(susan) | ~quiet(X1) [subsumption resolution 136,275]
307. 34 <=> ! [X1] : ~quiet(X1) [avatar definition]
308. ~quiet(X1) <- (34) [avatar component clause 307]
309. 34 | ~31 [avatar split clause 305,293,307]
346. ~19 [avatar split clause 154,235]
386. $false <- (20, 21) [resolution 246,241]
387. ~20 | ~21 [avatar contradiction clause 386]
462. happy(susan) | quiet(susan) <- (~31) [resolution 124,294]
468. 52 <=> quiet(susan) [avatar definition]
472. 53 <=> happy(susan) [avatar definition]
474. happy(susan) <- (53) [avatar component clause 472]
475. 52 | 53 | 31 [avatar split clause 462,293,472,468]
493. happy(X1) | patient(X1) | ~curious(X1) | happy(X1) | quiet(X1) [resolution 117,124]
494. happy(X1) | patient(X1) | ~curious(X1) | quiet(X1) [duplicate literal removal 493]
496. happy(X1) | ~curious(X1) | quiet(X1) [subsumption resolution 494,276]
497. happy(X1) | quiet(X1) [subsumption resolution 496,275]
523. wise(X0) | patient(X0) | ~happy(X0) [resolution 122,275]
524. wise(X0) | ~happy(X0) [subsumption resolution 523,276]
525. ~happy(X0) [subsumption resolution 524,125]
526. 21 [avatar split clause 525,245]
528. ~quiet(susan) | happy(susan) <- (18) [resolution 232,112]
535. ~quiet(susan) <- (18, 21) [subsumption resolution 528,246]
536. ~52 | ~18 | ~21 [avatar split clause 535,245,231,468]
542. $false <- (21, 53) [subsumption resolution 474,246]
543. ~21 | ~53 [avatar contradiction clause 542]
548. quiet(X0) <- (21) [resolution 246,497]
550. $false <- (21, 34) [subsumption resolution 548,308]
551. ~21 | ~34 [avatar contradiction clause 550]
554. $false [avatar sat refutation 243,309,346,387,475,526,536,543,551]
% SZS output end Proof for 1465142765963365934926291
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either humble or not humble then john is kind.
Everyone who is either strong or not rich is funny or curious and vice versa.
Everyone who is brave is generous.
If alice is wise then fred is not patient and vice versa.
If john is patient then paul is kind or not humble and vice versa.
Everyone who is both not quiet and creative is both not rich and wise.
Everyone who is either not happy or not curious is either humble or generous and vice versa.
Everyone who is not quiet or happy is strong and vice versa.
If someone is either not curious or not generous then someone is either kind or not curious and vice versa.
Everyone who is both not wise and kind is both not old and not kind and vice versa.
Everyone who is both not calm and not happy is not kind or not quiet.
Everyone who is either not calm or funny is either kind or not wise and vice versa.
If someone is both not old and wise then fred is both not old and curious and vice versa.
If someone is calm then susan is either not happy or not wise and vice versa.
Everyone who is kind or creative is both not calm and not generous and vice versa.
Alice is both calm and not curious.
Mary is either wise or not wise.
Paul is creative or quiet.
Lucy is not quiet or patient.
Alice is both not happy and humble.
Someone is either curious or not creative. | Fred is not quiet. | neutral | (((humble(susan)<~>~humble(susan)))=>(kind(john)))&
(![X]:((strong(X)<~>~rich(X))<=>(funny(X)|curious(X))))&
(![X]:(brave(X)=>generous(X)))&
((wise(alice))<=>(~patient(fred)))&
((patient(john))<=>((kind(paul)|~humble(paul))))&
(![X]:((~quiet(X)&creative(X))=>(~rich(X)&wise(X))))&
(![X]:((~happy(X)<~>~curious(X))<=>(humble(X)<~>generous(X))))&
(![X]:((~quiet(X)|happy(X))<=>strong(X)))&
((?[X]:((~curious(X)<~>~generous(X))))<=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((~wise(X)&kind(X))<=>(~old(X)&~kind(X))))&
(![X]:((~calm(X)&~happy(X))=>(~kind(X)|~quiet(X))))&
(![X]:((~calm(X)<~>funny(X))<=>(kind(X)<~>~wise(X))))&
((?[X]:((~old(X)&wise(X))))<=>((~old(fred)&curious(fred))))&
((?[X]:(calm(X)))<=>((~happy(susan)<~>~wise(susan))))&
(![X]:((kind(X)|creative(X))<=>(~calm(X)&~generous(X))))&
((calm(alice)&~curious(alice)))&
((wise(mary)<~>~wise(mary)))&
((creative(paul)|quiet(paul)))&
((~quiet(lucy)|patient(lucy)))&
((~happy(alice)&humble(alice)))&
(?[X]:((curious(X)<~>~creative(X)))) | ~quiet(fred) | [] | null | 0 |
Everyone who is happy is old and vice versa.
Everyone who is not brave is funny and vice versa.
If susan is both humble and patient then someone is not rich.
Everyone who is humble or not creative is both not brave and tall and vice versa.
If someone is tall then mary is either calm or strong.
Everyone who is curious is happy and vice versa.
Everyone who is both brave and not kind is quiet and vice versa.
Everyone who is kind or old is brave or not quiet and vice versa.
Everyone who is not kind or calm is not brave or not funny.
Everyone who is wise is not humble.
Everyone who is humble or wise is both not generous and not creative.
Everyone who is humble is rich or brave and vice versa.
If someone is brave then lucy is not patient or not generous and vice versa.
If someone is not quiet or calm then someone is not happy and vice versa.
If alice is either wise or not generous then someone is both not brave and old and vice versa.
Someone is either not tall or rich.
Someone is strong or rich.
Someone is not quiet or quiet.
John is either not calm or happy.
Fred is both tall and not patient.
Someone is not humble.
Susan is not rich or creative. | Alice is not tall. | neutral | (![X]:(happy(X)<=>old(X)))&
(![X]:(~brave(X)<=>funny(X)))&
(((humble(susan)&patient(susan)))=>(?[X]:(~rich(X))))&
(![X]:((humble(X)|~creative(X))<=>(~brave(X)&tall(X))))&
((?[X]:(tall(X)))=>((calm(mary)<~>strong(mary))))&
(![X]:(curious(X)<=>happy(X)))&
(![X]:((brave(X)&~kind(X))<=>quiet(X)))&
(![X]:((kind(X)|old(X))<=>(brave(X)|~quiet(X))))&
(![X]:((~kind(X)|calm(X))=>(~brave(X)|~funny(X))))&
(![X]:(wise(X)=>~humble(X)))&
(![X]:((humble(X)|wise(X))=>(~generous(X)&~creative(X))))&
(![X]:(humble(X)<=>(rich(X)|brave(X))))&
((?[X]:(brave(X)))<=>((~patient(lucy)|~generous(lucy))))&
((?[X]:((~quiet(X)|calm(X))))<=>(?[X]:(~happy(X))))&
(((wise(alice)<~>~generous(alice)))<=>(?[X]:((~brave(X)&old(X)))))&
(?[X]:((~tall(X)<~>rich(X))))&
(?[X]:((strong(X)|rich(X))))&
(?[X]:((~quiet(X)|quiet(X))))&
((~calm(john)<~>happy(john)))&
((tall(fred)&~patient(fred)))&
(?[X]:(~humble(X)))&
((~rich(susan)|creative(susan))) | ~tall(alice) | [] | null | 0 |
If someone is not kind then susan is not wise or strong. Everyone who is either not wise or calm is funny or not patient and vice versa. Everyone who is either not creative or generous is both not old and patient and vice versa. Everyone who is creative is not funny and vice versa. Everyone who is kind or creative is both creative and calm and vice versa. If alice is wise or not humble then john is either not wise or not curious. Everyone who is calm is brave or happy and vice versa. If someone is not wise then alice is wise and vice versa. Everyone who is both funny and tall is both strong and quiet. If susan is wise or not quiet then someone is both patient and old. Everyone who is either kind or not quiet is not quiet or not happy. If alice is both creative and strong then someone is both kind and humble and vice versa. If someone is either wise or not happy then fred is both patient and kind. If someone is funny or not creative then someone is not patient. Everyone who is both not calm and not rich is either creative or generous and vice versa. If mary is not wise then paul is both not generous and not brave and vice versa. Someone is either not calm or calm. Someone is calm or patient. Mary is either wise or not old. Someone is either quiet or tall. Someone is both creative and not brave. Alice is not curious or calm. Someone is not brave or quiet. John is either happy or wise. | Fred is not patient. | contradiction | ((?[X]:(~kind(X)))=>((~wise(susan)|strong(susan))))&
(![X]:((~wise(X)<~>calm(X))<=>(funny(X)|~patient(X))))&
(![X]:((~creative(X)<~>generous(X))<=>(~old(X)&patient(X))))&
(![X]:(creative(X)<=>~funny(X)))&
(![X]:((kind(X)|creative(X))<=>(creative(X)&calm(X))))&
(((wise(alice)|~humble(alice)))=>((~wise(john)<~>~curious(john))))&
(![X]:(calm(X)<=>(brave(X)|happy(X))))&
((?[X]:(~wise(X)))<=>(wise(alice)))&
(![X]:((funny(X)&tall(X))=>(strong(X)&quiet(X))))&
(((wise(susan)|~quiet(susan)))=>(?[X]:((patient(X)&old(X)))))&
(![X]:((kind(X)<~>~quiet(X))=>(~quiet(X)|~happy(X))))&
(((creative(alice)&strong(alice)))<=>(?[X]:((kind(X)&humble(X)))))&
((?[X]:((wise(X)<~>~happy(X))))=>((patient(fred)&kind(fred))))&
((?[X]:((funny(X)|~creative(X))))=>(?[X]:(~patient(X))))&
(![X]:((~calm(X)&~rich(X))<=>(creative(X)<~>generous(X))))&
((~wise(mary))<=>((~generous(paul)&~brave(paul))))&
(?[X]:((~calm(X)<~>calm(X))))&
(?[X]:((calm(X)|patient(X))))&
((wise(mary)<~>~old(mary)))&
(?[X]:((quiet(X)<~>tall(X))))&
(?[X]:((creative(X)&~brave(X))))&
((~curious(alice)|calm(alice)))&
(?[X]:((~brave(X)|quiet(X))))&
((happy(john)<~>wise(john))) | ~patient(fred) | [
"p1",
"p2",
"p3",
"p4",
"p6",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5847051898298520237946823
% SZS output start Proof for 5847051898298520237946823
2. ! [X0] : ((~wise(X0) <~> calm(X0)) <=> (~patient(X0) | funny(X0))) [input p1]
3. ! [X0] : ((~creative(X0) <~> generous(X0)) <=> (patient(X0) & ~old(X0))) [input p2]
4. ! [X0] : (creative(X0) <=> ~funny(X0)) [input p3]
5. ! [X0] : ((creative(X0) | kind(X0)) <=> (calm(X0) & creative(X0))) [input p4]
7. ! [X0] : (calm(X0) <=> (happy(X0) | brave(X0))) [input p6]
13. ? [X0] : (wise(X0) <~> ~happy(X0)) => (kind(fred) & patient(fred)) [input p12]
15. ! [X0] : ((~rich(X0) & ~calm(X0)) <=> (creative(X0) <~> generous(X0))) [input p14]
25. ~patient(fred) [input hypothesis]
35. (kind(fred) & patient(fred)) | ! [X0] : (wise(X0) <=> ~happy(X0)) [ennf transformation 13]
37. ! [X0] : ((((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | (patient(X0) & ~funny(X0))) & ((~patient(X0) | funny(X0)) | ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0))))) [nnf transformation 2]
38. ! [X0] : ((((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | (patient(X0) & ~funny(X0))) & (~patient(X0) | funny(X0) | ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0))))) [flattening 37]
39. ! [X0] : ((((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | (~patient(X0) | old(X0))) & ((patient(X0) & ~old(X0)) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0))))) [nnf transformation 3]
40. ! [X0] : ((((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | ~patient(X0) | old(X0)) & ((patient(X0) & ~old(X0)) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0))))) [flattening 39]
41. ! [X0] : ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0))) [nnf transformation 4]
42. ! [X0] : (((creative(X0) | kind(X0)) | (~calm(X0) | ~creative(X0))) & ((calm(X0) & creative(X0)) | (~creative(X0) & ~kind(X0)))) [nnf transformation 5]
43. ! [X0] : ((creative(X0) | kind(X0) | ~calm(X0) | ~creative(X0)) & ((calm(X0) & creative(X0)) | (~creative(X0) & ~kind(X0)))) [flattening 42]
45. ! [X0] : ((calm(X0) | (~happy(X0) & ~brave(X0))) & ((happy(X0) | brave(X0)) | ~calm(X0))) [nnf transformation 7]
46. ! [X0] : ((calm(X0) | (~happy(X0) & ~brave(X0))) & (happy(X0) | brave(X0) | ~calm(X0))) [flattening 45]
59. (kind(fred) & patient(fred)) | ! [X0] : ((wise(X0) | happy(X0)) & (~happy(X0) | ~wise(X0))) [nnf transformation 35]
63. ! [X0] : (((~rich(X0) & ~calm(X0)) | ((creative(X0) | ~generous(X0)) & (generous(X0) | ~creative(X0)))) & (((~generous(X0) | ~creative(X0)) & (generous(X0) | creative(X0))) | (rich(X0) | calm(X0)))) [nnf transformation 15]
64. ! [X0] : (((~rich(X0) & ~calm(X0)) | ((creative(X0) | ~generous(X0)) & (generous(X0) | ~creative(X0)))) & (((~generous(X0) | ~creative(X0)) & (generous(X0) | creative(X0))) | rich(X0) | calm(X0))) [flattening 63]
84. ~funny(X0) | ~wise(X0) | calm(X0) [cnf transformation 38]
90. generous(X0) | patient(X0) | creative(X0) [cnf transformation 40]
91. ~generous(X0) | ~creative(X0) | patient(X0) [cnf transformation 40]
94. ~creative(X0) | ~funny(X0) [cnf transformation 41]
95. creative(X0) | funny(X0) [cnf transformation 41]
99. ~creative(X0) | calm(X0) [cnf transformation 43]
107. ~happy(X0) | calm(X0) [cnf transformation 46]
123. patient(fred) | wise(X0) | happy(X0) [cnf transformation 59]
130. ~calm(X0) | generous(X0) | ~creative(X0) [cnf transformation 64]
131. ~generous(X0) | creative(X0) | ~calm(X0) [cnf transformation 64]
150. ~patient(fred) [cnf transformation 25]
233. 18 <=> ! [X0] : (wise(X0) | happy(X0)) [avatar definition]
234. happy(X0) | wise(X0) <- (18) [avatar component clause 233]
245. 21 <=> patient(fred) [avatar definition]
246. ~patient(fred) <- (~21) [avatar component clause 245]
248. 18 | 21 [avatar split clause 123,245,233]
262. ~creative(X0) | generous(X0) [subsumption resolution 130,99]
328. ~21 [avatar split clause 150,245]
332. funny(X0) | calm(X0) [resolution 99,95]
334. calm(X0) | wise(X0) <- (18) [resolution 234,107]
337. generous(X0) | funny(X0) [resolution 262,95]
339. calm(X0) | ~wise(X0) | calm(X0) [resolution 332,84]
340. calm(X0) | ~wise(X0) [duplicate literal removal 339]
341. calm(X0) <- (18) [subsumption resolution 340,334]
384. ~creative(X1) | patient(X1) | funny(X1) [resolution 91,337]
386. patient(X1) | funny(X1) [subsumption resolution 384,95]
406. creative(X0) | ~calm(X0) | patient(X0) | creative(X0) [resolution 131,90]
408. creative(X0) | ~calm(X0) | patient(X0) [duplicate literal removal 406]
409. creative(X0) | patient(X0) <- (18) [subsumption resolution 408,341]
453. patient(X3) | ~funny(X3) <- (18) [resolution 409,94]
455. patient(X3) <- (18) [subsumption resolution 453,386]
460. $false <- (18, ~21) [resolution 455,246]
465. ~18 | 21 [avatar contradiction clause 460]
467. $false [avatar sat refutation 248,328,465]
% SZS output end Proof for 5847051898298520237946823
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or not wise is creative.
Everyone who is both humble and not brave is either not happy or wise.
If someone is not brave then lucy is tall.
Everyone who is either not happy or not brave is either not rich or not tall and vice versa.
Everyone who is patient is both not kind and humble and vice versa.
Everyone who is tall or not rich is strong.
If someone is not patient then someone is either creative or not generous.
Everyone who is not generous is not wise.
Everyone who is both not rich and tall is not generous.
Everyone who is either not funny or rich is patient.
Everyone who is both kind and not generous is either not calm or rich and vice versa.
Everyone who is not generous is patient and vice versa.
Everyone who is creative is either rich or not quiet and vice versa.
If someone is kind or not happy then someone is both not generous and not humble and vice versa.
Everyone who is either generous or strong is both not wise and not brave and vice versa.
Everyone who is both curious and not wise is not generous and vice versa.
Someone is funny.
John is creative.
Someone is quiet or generous.
Someone is not happy or not quiet.
Someone is creative.
Susan is not patient.
Alice is humble or funny.
Someone is not wise or quiet. | Alice is not generous. | contradiction | (![X]:((funny(X)|~wise(X))=>creative(X)))&
(![X]:((humble(X)&~brave(X))=>(~happy(X)<~>wise(X))))&
((?[X]:(~brave(X)))=>(tall(lucy)))&
(![X]:((~happy(X)<~>~brave(X))<=>(~rich(X)<~>~tall(X))))&
(![X]:(patient(X)<=>(~kind(X)&humble(X))))&
(![X]:((tall(X)|~rich(X))=>strong(X)))&
((?[X]:(~patient(X)))=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:(~generous(X)=>~wise(X)))&
(![X]:((~rich(X)&tall(X))=>~generous(X)))&
(![X]:((~funny(X)<~>rich(X))=>patient(X)))&
(![X]:((kind(X)&~generous(X))<=>(~calm(X)<~>rich(X))))&
(![X]:(~generous(X)<=>patient(X)))&
(![X]:(creative(X)<=>(rich(X)<~>~quiet(X))))&
((?[X]:((kind(X)|~happy(X))))<=>(?[X]:((~generous(X)&~humble(X)))))&
(![X]:((generous(X)<~>strong(X))<=>(~wise(X)&~brave(X))))&
(![X]:((curious(X)&~wise(X))<=>~generous(X)))&
(?[X]:(funny(X)))&
(creative(john))&
(?[X]:((quiet(X)|generous(X))))&
(?[X]:((~happy(X)|~quiet(X))))&
(?[X]:(creative(X)))&
(~patient(susan))&
((humble(alice)|funny(alice)))&
(?[X]:((~wise(X)|quiet(X)))) | ~generous(alice) | [
"p1",
"p3",
"p4",
"p5",
"p7",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 620391363682438499598602
% SZS output start Proof for 620391363682438499598602
2. ! [X0] : ((~brave(X0) & humble(X0)) => (~happy(X0) <~> wise(X0))) [input p1]
4. ! [X0] : ((~happy(X0) <~> ~brave(X0)) <=> (~rich(X0) <~> ~tall(X0))) [input p3]
5. ! [X0] : (patient(X0) <=> (humble(X0) & ~kind(X0))) [input p4]
6. ! [X0] : ((~rich(X0) | tall(X0)) => strong(X0)) [input p5]
8. ! [X0] : (~generous(X0) => ~wise(X0)) [input p7]
12. ! [X0] : (~generous(X0) <=> patient(X0)) [input p11]
14. ? [X0] : (~happy(X0) | kind(X0)) <=> ? [X0] : (~humble(X0) & ~generous(X0)) [input p13]
15. ! [X0] : ((generous(X0) <~> strong(X0)) <=> (~brave(X0) & ~wise(X0))) [input p14]
25. ~generous(alice) [input hypothesis]
27. ? [X0] : (~happy(X0) | kind(X0)) <=> ? [X1] : (~humble(X1) & ~generous(X1)) [rectify 14]
29. ! [X0] : ((~happy(X0) <~> wise(X0)) | (brave(X0) | ~humble(X0))) [ennf transformation 2]
30. ! [X0] : ((~happy(X0) <~> wise(X0)) | brave(X0) | ~humble(X0)) [flattening 29]
32. ! [X0] : (strong(X0) | (rich(X0) & ~tall(X0))) [ennf transformation 6]
34. ! [X0] : (~wise(X0) | generous(X0)) [ennf transformation 8]
38. ! [X0] : (((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | brave(X0) | ~humble(X0)) [nnf transformation 30]
39. ! [X0] : ((((brave(X0) | happy(X0)) & (~brave(X0) | ~happy(X0))) | ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0)))) & (((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | ((~happy(X0) | brave(X0)) & (~brave(X0) | happy(X0))))) [nnf transformation 4]
40. ! [X0] : ((patient(X0) | (~humble(X0) | kind(X0))) & ((humble(X0) & ~kind(X0)) | ~patient(X0))) [nnf transformation 5]
41. ! [X0] : ((patient(X0) | ~humble(X0) | kind(X0)) & ((humble(X0) & ~kind(X0)) | ~patient(X0))) [flattening 40]
49. ! [X0] : ((~generous(X0) | ~patient(X0)) & (patient(X0) | generous(X0))) [nnf transformation 12]
51. (? [X0] : (~happy(X0) | kind(X0)) | ! [X1] : (humble(X1) | generous(X1))) & (? [X1] : (~humble(X1) & ~generous(X1)) | ! [X0] : (happy(X0) & ~kind(X0))) [nnf transformation 27]
52. (? [X0] : (~happy(X0) | kind(X0)) | ! [X1] : (humble(X1) | generous(X1))) & (? [X2] : (~humble(X2) & ~generous(X2)) | ! [X3] : (happy(X3) & ~kind(X3))) [rectify 51]
53. ? [X0] : (~happy(X0) | kind(X0)) => (~happy(sK1) | kind(sK1)) [choice axiom]
54. ? [X2] : (~humble(X2) & ~generous(X2)) => (~humble(sK2) & ~generous(sK2)) [choice axiom]
55. ((~happy(sK1) | kind(sK1)) | ! [X1] : (humble(X1) | generous(X1))) & ((~humble(sK2) & ~generous(sK2)) | ! [X3] : (happy(X3) & ~kind(X3))) [skolemisation 52,54,53]
56. ! [X0] : ((((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | (brave(X0) | wise(X0))) & ((~brave(X0) & ~wise(X0)) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0))))) [nnf transformation 15]
57. ! [X0] : ((((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | brave(X0) | wise(X0)) & ((~brave(X0) & ~wise(X0)) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0))))) [flattening 56]
72. ~happy(X0) | wise(X0) | brave(X0) | ~humble(X0) [cnf transformation 38]
80. ~rich(X0) | ~happy(X0) | ~brave(X0) | tall(X0) [cnf transformation 39]
84. ~patient(X0) | humble(X0) [cnf transformation 41]
86. ~tall(X0) | strong(X0) [cnf transformation 32]
87. strong(X0) | rich(X0) [cnf transformation 32]
90. ~wise(X0) | generous(X0) [cnf transformation 34]
100. generous(X0) | patient(X0) [cnf transformation 49]
107. ~generous(sK2) | happy(X3) [cnf transformation 55]
109. ~humble(sK2) | happy(X3) [cnf transformation 55]
114. ~strong(X0) | generous(X0) | ~brave(X0) [cnf transformation 57]
128. ~generous(alice) [cnf transformation 25]
163. 9 <=> ! [X3] : happy(X3) [avatar definition]
164. happy(X3) <- (9) [avatar component clause 163]
166. 10 <=> humble(sK2) [avatar definition]
168. ~humble(sK2) <- (~10) [avatar component clause 166]
169. 9 | ~10 [avatar split clause 109,166,163]
175. 12 <=> generous(sK2) [avatar definition]
177. ~generous(sK2) <- (~12) [avatar component clause 175]
178. 9 | ~12 [avatar split clause 107,175,163]
201. 17 <=> humble(alice) [avatar definition]
203. humble(alice) <- (17) [avatar component clause 201]
224. patient(alice) [resolution 100,128]
225. patient(sK2) <- (~12) [resolution 100,177]
226. humble(alice) [resolution 224,84]
229. humble(sK2) <- (~12) [resolution 225,84]
230. $false <- (~10, ~12) [subsumption resolution 229,168]
231. 10 | 12 [avatar contradiction clause 230]
366. ~brave(X0) | generous(X0) | rich(X0) [resolution 114,87]
398. 43 <=> brave(alice) [avatar definition]
400. brave(alice) <- (43) [avatar component clause 398]
402. 44 <=> strong(alice) [avatar definition]
404. strong(alice) <- (44) [avatar component clause 402]
406. ~humble(X0) | brave(X0) | wise(X0) <- (9) [resolution 72,164]
540. generous(alice) | rich(alice) <- (43) [resolution 366,400]
541. rich(alice) <- (43) [subsumption resolution 540,128]
547. ~happy(alice) | ~brave(alice) | tall(alice) <- (43) [resolution 541,80]
552. ~brave(alice) | tall(alice) <- (9, 43) [subsumption resolution 547,164]
553. tall(alice) <- (9, 43) [subsumption resolution 552,400]
563. brave(alice) | wise(alice) <- (9, 17) [resolution 406,203]
570. strong(alice) <- (9, 43) [resolution 553,86]
571. 44 | ~9 | ~43 [avatar split clause 570,398,163,402]
572. generous(alice) | ~brave(alice) <- (44) [resolution 404,114]
573. ~brave(alice) <- (44) [subsumption resolution 572,128]
576. ~43 | ~44 [avatar split clause 573,402,398]
578. 56 <=> wise(alice) [avatar definition]
580. wise(alice) <- (56) [avatar component clause 578]
581. 56 | 43 | ~9 | ~17 [avatar split clause 563,201,163,398,578]
627. generous(alice) <- (56) [resolution 580,90]
628. $false <- (56) [subsumption resolution 627,128]
629. ~56 [avatar contradiction clause 628]
631. 17 [avatar split clause 226,201]
634. $false [avatar sat refutation 169,178,231,571,576,581,629,631]
% SZS output end Proof for 620391363682438499598602
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or not generous is not calm and vice versa.
Everyone who is not wise or not calm is both not brave and brave and vice versa.
If fred is either not calm or creative then someone is either happy or curious and vice versa.
Everyone who is rich or strong is kind or not quiet.
Everyone who is not quiet is patient or not calm.
If john is either not quiet or not funny then alice is either happy or wise.
If someone is either happy or not humble then someone is both wise and strong and vice versa.
If alice is either not kind or strong then mary is either generous or not patient and vice versa.
If fred is not kind then john is not quiet and vice versa.
If someone is both patient and generous then someone is creative or generous and vice versa.
Everyone who is either not calm or not strong is both not generous and wise.
If fred is either not wise or humble then paul is both tall and curious and vice versa.
Everyone who is funny or wise is either not old or not patient.
If john is not wise or wise then susan is both strong and wise.
If someone is either not humble or not curious then paul is either happy or patient and vice versa.
John is either not wise or not kind.
Fred is either not kind or not curious.
Someone is rich or wise.
Lucy is either not creative or rich.
Someone is creative.
John is creative or not patient.
Lucy is creative.
Paul is kind. | Paul is strong. | entailment | (![X]:((brave(X)|~generous(X))<=>~calm(X)))&
(![X]:((~wise(X)|~calm(X))<=>(~brave(X)&brave(X))))&
(((~calm(fred)<~>creative(fred)))<=>(?[X]:((happy(X)<~>curious(X)))))&
(![X]:((rich(X)|strong(X))=>(kind(X)|~quiet(X))))&
(![X]:(~quiet(X)=>(patient(X)|~calm(X))))&
(((~quiet(john)<~>~funny(john)))=>((happy(alice)<~>wise(alice))))&
((?[X]:((happy(X)<~>~humble(X))))<=>(?[X]:((wise(X)&strong(X)))))&
(((~kind(alice)<~>strong(alice)))<=>((generous(mary)<~>~patient(mary))))&
((~kind(fred))<=>(~quiet(john)))&
((?[X]:((patient(X)&generous(X))))<=>(?[X]:((creative(X)|generous(X)))))&
(![X]:((~calm(X)<~>~strong(X))=>(~generous(X)&wise(X))))&
(((~wise(fred)<~>humble(fred)))<=>((tall(paul)&curious(paul))))&
(![X]:((funny(X)|wise(X))=>(~old(X)<~>~patient(X))))&
(((~wise(john)|wise(john)))=>((strong(susan)&wise(susan))))&
((?[X]:((~humble(X)<~>~curious(X))))<=>((happy(paul)<~>patient(paul))))&
((~wise(john)<~>~kind(john)))&
((~kind(fred)<~>~curious(fred)))&
(?[X]:((rich(X)|wise(X))))&
((~creative(lucy)<~>rich(lucy)))&
(?[X]:(creative(X)))&
((creative(john)|~patient(john)))&
(creative(lucy))&
(kind(paul)) | strong(paul) | [
"p0",
"p1",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 275722303175421455336820
% SZS output start Proof for 275722303175421455336820
1. ! [X0] : ((~generous(X0) | brave(X0)) <=> ~calm(X0)) [input p0]
2. ! [X0] : ((~calm(X0) | ~wise(X0)) <=> (brave(X0) & ~brave(X0))) [input p1]
11. ! [X0] : ((~calm(X0) <~> ~strong(X0)) => (wise(X0) & ~generous(X0))) [input p10]
24. ~strong(paul) [input hypothesis]
32. ! [X0] : ((wise(X0) & ~generous(X0)) | (~calm(X0) <=> ~strong(X0))) [ennf transformation 11]
35. ! [X0] : (((~generous(X0) | brave(X0)) | calm(X0)) & (~calm(X0) | (generous(X0) & ~brave(X0)))) [nnf transformation 1]
36. ! [X0] : ((~generous(X0) | brave(X0) | calm(X0)) & (~calm(X0) | (generous(X0) & ~brave(X0)))) [flattening 35]
37. ! [X0] : (((~calm(X0) | ~wise(X0)) | (~brave(X0) | brave(X0))) & ((brave(X0) & ~brave(X0)) | (calm(X0) & wise(X0)))) [nnf transformation 2]
38. ! [X0] : ((~calm(X0) | ~wise(X0) | ~brave(X0) | brave(X0)) & ((brave(X0) & ~brave(X0)) | (calm(X0) & wise(X0)))) [flattening 37]
56. ! [X0] : ((wise(X0) & ~generous(X0)) | ((~calm(X0) | strong(X0)) & (~strong(X0) | calm(X0)))) [nnf transformation 32]
72. ~calm(X0) | generous(X0) [cnf transformation 36]
75. ~brave(X0) | calm(X0) [cnf transformation 38]
77. calm(X0) | brave(X0) [cnf transformation 38]
116. ~generous(X0) | ~calm(X0) | strong(X0) [cnf transformation 56]
152. ~strong(paul) [cnf transformation 24]
153. calm(X0) [subsumption resolution 75,77]
285. ~generous(X0) | strong(X0) [subsumption resolution 116,153]
371. generous(X0) [resolution 72,153]
390. strong(X0) [resolution 285,371]
391. $false [resolution 390,152]
% SZS output end Proof for 275722303175421455336820
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If someone is patient then someone is not kind and vice versa. If fred is generous then fred is not brave. Everyone who is not brave or brave is either creative or curious. Everyone who is both brave and rich is both rich and not funny and vice versa. Everyone who is both tall and not kind is both not generous and creative and vice versa. Everyone who is either curious or generous is either tall or wise. If someone is not calm or happy then someone is brave or not curious and vice versa. Everyone who is both not calm and funny is either curious or not curious and vice versa. Everyone who is not brave or generous is either calm or not brave and vice versa. Everyone who is generous or not creative is not quiet or brave and vice versa. Everyone who is either rich or strong is kind and vice versa. Everyone who is funny or calm is either not generous or not creative. If alice is not creative or not funny then someone is either generous or happy. Everyone who is curious is either tall or not patient. If someone is both not kind and not wise then someone is both not curious and not rich and vice versa. If john is either not brave or tall then someone is either tall or not old. Susan is curious. Lucy is rich or not tall. Someone is happy or not calm. Fred is generous or funny. John is both not patient and not happy. Lucy is old or curious. Lucy is either quiet or not funny. | Susan is quiet. | contradiction | ((?[X]:(patient(X)))<=>(?[X]:(~kind(X))))&
((generous(fred))=>(~brave(fred)))&
(![X]:((~brave(X)|brave(X))=>(creative(X)<~>curious(X))))&
(![X]:((brave(X)&rich(X))<=>(rich(X)&~funny(X))))&
(![X]:((tall(X)&~kind(X))<=>(~generous(X)&creative(X))))&
(![X]:((curious(X)<~>generous(X))=>(tall(X)<~>wise(X))))&
((?[X]:((~calm(X)|happy(X))))<=>(?[X]:((brave(X)|~curious(X)))))&
(![X]:((~calm(X)&funny(X))<=>(curious(X)<~>~curious(X))))&
(![X]:((~brave(X)|generous(X))<=>(calm(X)<~>~brave(X))))&
(![X]:((generous(X)|~creative(X))<=>(~quiet(X)|brave(X))))&
(![X]:((rich(X)<~>strong(X))<=>kind(X)))&
(![X]:((funny(X)|calm(X))=>(~generous(X)<~>~creative(X))))&
(((~creative(alice)|~funny(alice)))=>(?[X]:((generous(X)<~>happy(X)))))&
(![X]:(curious(X)=>(tall(X)<~>~patient(X))))&
((?[X]:((~kind(X)&~wise(X))))<=>(?[X]:((~curious(X)&~rich(X)))))&
(((~brave(john)<~>tall(john)))=>(?[X]:((tall(X)<~>~old(X)))))&
(curious(susan))&
((rich(lucy)|~tall(lucy)))&
(?[X]:((happy(X)|~calm(X))))&
((generous(fred)|funny(fred)))&
((~patient(john)&~happy(john)))&
((old(lucy)|curious(lucy)))&
((quiet(lucy)<~>~funny(lucy))) | quiet(susan) | [
"p2",
"p7",
"p8",
"p9",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4614749460790254422672844
% SZS output start Proof for 4614749460790254422672844
3. ! [X0] : ((brave(X0) | ~brave(X0)) => (creative(X0) <~> curious(X0))) [input p2]
8. ! [X0] : ((funny(X0) & ~calm(X0)) <=> (curious(X0) <~> ~curious(X0))) [input p7]
9. ! [X0] : ((generous(X0) | ~brave(X0)) <=> (calm(X0) <~> ~brave(X0))) [input p8]
10. ! [X0] : ((~creative(X0) | generous(X0)) <=> (brave(X0) | ~quiet(X0))) [input p9]
12. ! [X0] : ((calm(X0) | funny(X0)) => (~generous(X0) <~> ~creative(X0))) [input p11]
17. curious(susan) [input p16]
24. quiet(susan) [input hypothesis]
29. ! [X0] : ((creative(X0) <~> curious(X0)) | (~brave(X0) & brave(X0))) [ennf transformation 3]
31. ! [X0] : ((~generous(X0) <~> ~creative(X0)) | (~calm(X0) & ~funny(X0))) [ennf transformation 12]
40. ! [X0] : (((~curious(X0) | ~creative(X0)) & (curious(X0) | creative(X0))) | (~brave(X0) & brave(X0))) [nnf transformation 29]
51. ! [X0] : (((funny(X0) & ~calm(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | (~funny(X0) | calm(X0)))) [nnf transformation 8]
52. ! [X0] : (((funny(X0) & ~calm(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | ~funny(X0) | calm(X0))) [flattening 51]
53. ! [X0] : (((generous(X0) | ~brave(X0)) | ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0)))) & (((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | (~generous(X0) & brave(X0)))) [nnf transformation 9]
54. ! [X0] : ((generous(X0) | ~brave(X0) | ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0)))) & (((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | (~generous(X0) & brave(X0)))) [flattening 53]
55. ! [X0] : (((~creative(X0) | generous(X0)) | (~brave(X0) & quiet(X0))) & ((brave(X0) | ~quiet(X0)) | (creative(X0) & ~generous(X0)))) [nnf transformation 10]
56. ! [X0] : ((~creative(X0) | generous(X0) | (~brave(X0) & quiet(X0))) & (brave(X0) | ~quiet(X0) | (creative(X0) & ~generous(X0)))) [flattening 55]
58. ! [X0] : (((creative(X0) | generous(X0)) & (~creative(X0) | ~generous(X0))) | (~calm(X0) & ~funny(X0))) [nnf transformation 31]
79. ~curious(X0) | ~creative(X0) | brave(X0) [cnf transformation 40]
80. ~curious(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 40]
99. ~calm(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 52]
100. ~calm(X0) | curious(X0) | curious(X0) [cnf transformation 52]
101. funny(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 52]
102. funny(X0) | curious(X0) | curious(X0) [cnf transformation 52]
104. ~brave(X0) | calm(X0) | ~generous(X0) [cnf transformation 54]
109. brave(X0) | ~quiet(X0) | ~generous(X0) [cnf transformation 56]
119. creative(X0) | generous(X0) | ~funny(X0) [cnf transformation 58]
135. curious(susan) [cnf transformation 17]
144. quiet(susan) [cnf transformation 24]
147. ~calm(X0) | ~curious(X0) [duplicate literal removal 99]
148. ~calm(X0) | curious(X0) [duplicate literal removal 100]
149. funny(X0) | ~curious(X0) [duplicate literal removal 101]
150. funny(X0) | curious(X0) [duplicate literal removal 102]
176. ~curious(X0) | ~creative(X0) [subsumption resolution 79,80]
210. funny(X0) [subsumption resolution 149,150]
211. ~calm(X0) [subsumption resolution 147,148]
212. ~brave(X0) | ~generous(X0) [subsumption resolution 104,211]
214. ~quiet(X0) | ~generous(X0) [subsumption resolution 109,212]
215. creative(X0) | generous(X0) [subsumption resolution 119,210]
296. ~creative(susan) [resolution 176,135]
303. ~generous(susan) [resolution 214,144]
306. generous(susan) [resolution 215,296]
308. $false [subsumption resolution 306,303]
% SZS output end Proof for 4614749460790254422672844
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both brave and not old then fred is not happy and vice versa. If someone is wise or old then someone is not happy or not patient and vice versa. Everyone who is either wise or calm is both tall and humble and vice versa. Everyone who is curious is both funny and calm and vice versa. Everyone who is not happy or kind is both not patient and not happy and vice versa. Everyone who is both not calm and not rich is not calm or calm and vice versa. Everyone who is both not brave and not funny is both not generous and not patient. Everyone who is both strong and not funny is not generous and vice versa. If someone is not creative or strong then someone is both funny and quiet and vice versa. Everyone who is not kind is not creative. If someone is curious then john is either not rich or humble and vice versa. Everyone who is either tall or not kind is either brave or humble and vice versa. Everyone who is kind or not strong is both not kind and wise and vice versa. Everyone who is both rich and not curious is either not old or not creative and vice versa. If someone is both not curious and quiet then susan is quiet and vice versa. Alice is not curious. Susan is either not old or creative. Paul is both not strong and not creative. Someone is not humble. Paul is either not tall or not happy. Someone is not calm. | Alice is calm. | contradiction | (((brave(fred)&~old(fred)))<=>(~happy(fred)))&
((?[X]:((wise(X)|old(X))))<=>(?[X]:((~happy(X)|~patient(X)))))&
(![X]:((wise(X)<~>calm(X))<=>(tall(X)&humble(X))))&
(![X]:(curious(X)<=>(funny(X)&calm(X))))&
(![X]:((~happy(X)|kind(X))<=>(~patient(X)&~happy(X))))&
(![X]:((~calm(X)&~rich(X))<=>(~calm(X)|calm(X))))&
(![X]:((~brave(X)&~funny(X))=>(~generous(X)&~patient(X))))&
(![X]:((strong(X)&~funny(X))<=>~generous(X)))&
((?[X]:((~creative(X)|strong(X))))<=>(?[X]:((funny(X)&quiet(X)))))&
(![X]:(~kind(X)=>~creative(X)))&
((?[X]:(curious(X)))<=>((~rich(john)<~>humble(john))))&
(![X]:((tall(X)<~>~kind(X))<=>(brave(X)<~>humble(X))))&
(![X]:((kind(X)|~strong(X))<=>(~kind(X)&wise(X))))&
(![X]:((rich(X)&~curious(X))<=>(~old(X)<~>~creative(X))))&
((?[X]:((~curious(X)&quiet(X))))<=>(quiet(susan)))&
(~curious(alice))&
((~old(susan)<~>creative(susan)))&
((~strong(paul)&~creative(paul)))&
(?[X]:(~humble(X)))&
((~tall(paul)<~>~happy(paul)))&
(?[X]:(~calm(X))) | calm(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 750863517655270158864422
% SZS output start Proof for 750863517655270158864422
6. ! [X0] : ((~rich(X0) & ~calm(X0)) <=> (calm(X0) | ~calm(X0))) [input p5]
22. calm(alice) [input hypothesis]
43. ! [X0] : (((~rich(X0) & ~calm(X0)) | (~calm(X0) & calm(X0))) & ((calm(X0) | ~calm(X0)) | (rich(X0) | calm(X0)))) [nnf transformation 6]
44. ! [X0] : (((~rich(X0) & ~calm(X0)) | (~calm(X0) & calm(X0))) & (calm(X0) | ~calm(X0) | rich(X0) | calm(X0))) [flattening 43]
92. ~calm(X0) | ~calm(X0) [cnf transformation 44]
140. calm(alice) [cnf transformation 22]
144. ~calm(X0) [duplicate literal removal 92]
268. $false [subsumption resolution 140,144]
% SZS output end Proof for 750863517655270158864422
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not wise and not tall then someone is either not wise or humble. Everyone who is not calm or tall is either curious or humble and vice versa. If susan is not generous or generous then mary is both not old and not kind and vice versa. If mary is curious then paul is either not curious or not patient. If someone is either not funny or not generous then mary is not brave and vice versa. Everyone who is either happy or rich is both creative and generous and vice versa. Everyone who is kind or not happy is creative or not calm and vice versa. If someone is not quiet then mary is rich and vice versa. Everyone who is not old is either strong or not brave. Everyone who is rich is calm and vice versa. Everyone who is both wise and not creative is brave and vice versa. Everyone who is both not patient and not funny is either old or patient. Everyone who is either not tall or happy is both creative and not happy and vice versa. Everyone who is both not funny and not generous is both not rich and curious. If someone is not generous or brave then someone is not calm or happy. Everyone who is not calm is not curious and vice versa. Mary is either kind or not generous. Someone is both not creative and not funny. Someone is both quiet and curious. Fred is not calm. Paul is both not generous and curious. John is not quiet. John is not rich. Someone is either humble or generous. | Mary is creative. | contradiction | (((~wise(susan)&~tall(susan)))=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:((~calm(X)|tall(X))<=>(curious(X)<~>humble(X))))&
(((~generous(susan)|generous(susan)))<=>((~old(mary)&~kind(mary))))&
((curious(mary))=>((~curious(paul)<~>~patient(paul))))&
((?[X]:((~funny(X)<~>~generous(X))))<=>(~brave(mary)))&
(![X]:((happy(X)<~>rich(X))<=>(creative(X)&generous(X))))&
(![X]:((kind(X)|~happy(X))<=>(creative(X)|~calm(X))))&
((?[X]:(~quiet(X)))<=>(rich(mary)))&
(![X]:(~old(X)=>(strong(X)<~>~brave(X))))&
(![X]:(rich(X)<=>calm(X)))&
(![X]:((wise(X)&~creative(X))<=>brave(X)))&
(![X]:((~patient(X)&~funny(X))=>(old(X)<~>patient(X))))&
(![X]:((~tall(X)<~>happy(X))<=>(creative(X)&~happy(X))))&
(![X]:((~funny(X)&~generous(X))=>(~rich(X)&curious(X))))&
((?[X]:((~generous(X)|brave(X))))=>(?[X]:((~calm(X)|happy(X)))))&
(![X]:(~calm(X)<=>~curious(X)))&
((kind(mary)<~>~generous(mary)))&
(?[X]:((~creative(X)&~funny(X))))&
(?[X]:((quiet(X)&curious(X))))&
(~calm(fred))&
((~generous(paul)&curious(paul)))&
(~quiet(john))&
(~rich(john))&
(?[X]:((humble(X)<~>generous(X)))) | creative(mary) | [
"p2",
"p5",
"p6",
"p7",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3317658349415921288143266
% SZS output start Proof for 3317658349415921288143266
3. (generous(susan) | ~generous(susan)) <=> (~kind(mary) & ~old(mary)) [input p2]
6. ! [X0] : ((happy(X0) <~> rich(X0)) <=> (generous(X0) & creative(X0))) [input p5]
7. ! [X0] : ((~happy(X0) | kind(X0)) <=> (~calm(X0) | creative(X0))) [input p6]
8. ? [X0] : ~quiet(X0) <=> rich(mary) [input p7]
17. kind(mary) <~> ~generous(mary) [input p16]
22. ~quiet(john) [input p21]
25. creative(mary) [input hypothesis]
41. ((generous(susan) | ~generous(susan)) | (kind(mary) | old(mary))) & ((~kind(mary) & ~old(mary)) | (~generous(susan) & generous(susan))) [nnf transformation 3]
42. (generous(susan) | ~generous(susan) | kind(mary) | old(mary)) & ((~kind(mary) & ~old(mary)) | (~generous(susan) & generous(susan))) [flattening 41]
48. ! [X0] : ((((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | (~generous(X0) | ~creative(X0))) & ((generous(X0) & creative(X0)) | ((happy(X0) | ~rich(X0)) & (rich(X0) | ~happy(X0))))) [nnf transformation 6]
49. ! [X0] : ((((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | ~generous(X0) | ~creative(X0)) & ((generous(X0) & creative(X0)) | ((happy(X0) | ~rich(X0)) & (rich(X0) | ~happy(X0))))) [flattening 48]
50. ! [X0] : (((~happy(X0) | kind(X0)) | (calm(X0) & ~creative(X0))) & ((~calm(X0) | creative(X0)) | (happy(X0) & ~kind(X0)))) [nnf transformation 7]
51. ! [X0] : ((~happy(X0) | kind(X0) | (calm(X0) & ~creative(X0))) & (~calm(X0) | creative(X0) | (happy(X0) & ~kind(X0)))) [flattening 50]
52. (? [X0] : ~quiet(X0) | ~rich(mary)) & (rich(mary) | ! [X0] : quiet(X0)) [nnf transformation 8]
53. (? [X0] : ~quiet(X0) | ~rich(mary)) & (rich(mary) | ! [X1] : quiet(X1)) [rectify 52]
54. ? [X0] : ~quiet(X0) => ~quiet(sK2) [choice axiom]
55. (~quiet(sK2) | ~rich(mary)) & (rich(mary) | ! [X1] : quiet(X1)) [skolemisation 53,54]
67. (generous(mary) | ~kind(mary)) & (~generous(mary) | kind(mary)) [nnf transformation 17]
85. ~kind(mary) | generous(susan) [cnf transformation 42]
86. ~kind(mary) | ~generous(susan) [cnf transformation 42]
97. ~rich(X0) | happy(X0) | generous(X0) [cnf transformation 49]
102. ~creative(X0) | kind(X0) | ~happy(X0) [cnf transformation 51]
104. rich(mary) | quiet(X1) [cnf transformation 55]
127. ~generous(mary) | kind(mary) [cnf transformation 67]
128. generous(mary) | ~kind(mary) [cnf transformation 67]
136. ~quiet(john) [cnf transformation 22]
140. creative(mary) [cnf transformation 25]
163. 5 <=> generous(susan) [avatar definition]
167. 6 <=> kind(mary) [avatar definition]
169. ~kind(mary) <- (~6) [avatar component clause 167]
170. ~5 | ~6 [avatar split clause 86,167,163]
171. 5 | ~6 [avatar split clause 85,167,163]
215. 16 <=> rich(mary) [avatar definition]
216. rich(mary) <- (16) [avatar component clause 215]
224. 18 <=> ! [X1] : quiet(X1) [avatar definition]
225. quiet(X1) <- (18) [avatar component clause 224]
226. 18 | 16 [avatar split clause 104,215,224]
244. 23 <=> generous(mary) [avatar definition]
245. ~generous(mary) <- (~23) [avatar component clause 244]
247. ~6 | 23 [avatar split clause 128,244,167]
248. 6 | ~23 [avatar split clause 127,244,167]
339. happy(mary) | generous(mary) <- (16) [resolution 97,216]
342. happy(mary) <- (16, ~23) [subsumption resolution 339,245]
362. kind(mary) | ~happy(mary) [resolution 102,140]
364. ~happy(mary) <- (~6) [subsumption resolution 362,169]
365. $false <- (~6, 16, ~23) [subsumption resolution 364,342]
366. 6 | ~16 | 23 [avatar contradiction clause 365]
369. $false <- (18) [resolution 225,136]
372. ~18 [avatar contradiction clause 369]
373. $false [avatar sat refutation 170,171,226,247,248,366,372]
% SZS output end Proof for 3317658349415921288143266
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not patient is calm or tall.
Everyone who is not quiet or not old is calm and vice versa.
If john is not wise or curious then someone is not patient.
If paul is strong or old then paul is not tall and vice versa.
If someone is wise or kind then someone is both quiet and calm and vice versa.
If lucy is both happy and wise then susan is quiet and vice versa.
If alice is curious or brave then someone is tall or not humble.
Everyone who is not old or not humble is funny and vice versa.
If someone is either funny or not humble then someone is either brave or not calm and vice versa.
Everyone who is funny or not old is both wise and not strong and vice versa.
Everyone who is either strong or not funny is either not tall or tall and vice versa.
If fred is not tall or tall then someone is not curious and vice versa.
If someone is both not curious and happy then someone is both not humble and not wise.
If mary is not quiet or not strong then alice is kind or not tall.
If fred is either calm or not curious then lucy is not rich or brave.
If someone is wise then someone is kind.
Someone is wise or not wise.
Someone is not funny.
Someone is both creative and happy.
Lucy is not old or not happy.
Lucy is wise or creative. | Lucy is not patient. | neutral | (![X]:((patient(X)|~patient(X))=>(calm(X)|tall(X))))&
(![X]:((~quiet(X)|~old(X))<=>calm(X)))&
(((~wise(john)|curious(john)))=>(?[X]:(~patient(X))))&
(((strong(paul)|old(paul)))<=>(~tall(paul)))&
((?[X]:((wise(X)|kind(X))))<=>(?[X]:((quiet(X)&calm(X)))))&
(((happy(lucy)&wise(lucy)))<=>(quiet(susan)))&
(((curious(alice)|brave(alice)))=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((~old(X)|~humble(X))<=>funny(X)))&
((?[X]:((funny(X)<~>~humble(X))))<=>(?[X]:((brave(X)<~>~calm(X)))))&
(![X]:((funny(X)|~old(X))<=>(wise(X)&~strong(X))))&
(![X]:((strong(X)<~>~funny(X))<=>(~tall(X)<~>tall(X))))&
(((~tall(fred)|tall(fred)))<=>(?[X]:(~curious(X))))&
((?[X]:((~curious(X)&happy(X))))=>(?[X]:((~humble(X)&~wise(X)))))&
(((~quiet(mary)|~strong(mary)))=>((kind(alice)|~tall(alice))))&
(((calm(fred)<~>~curious(fred)))=>((~rich(lucy)|brave(lucy))))&
((?[X]:(wise(X)))=>(?[X]:(kind(X))))&
(?[X]:((wise(X)|~wise(X))))&
(?[X]:(~funny(X)))&
(?[X]:((creative(X)&happy(X))))&
((~old(lucy)|~happy(lucy)))&
((wise(lucy)|creative(lucy))) | ~patient(lucy) | [] | null | 0 |
Everyone who is both not humble and not wise is not generous and vice versa. If susan is rich or humble then lucy is both funny and not strong and vice versa. Everyone who is not tall is either not humble or kind. Everyone who is both creative and not rich is either creative or funny and vice versa. Everyone who is quiet or happy is both patient and rich. Everyone who is not generous is either not tall or not funny and vice versa. If someone is not calm then someone is not funny and vice versa. Everyone who is both creative and not old is both not kind and not generous and vice versa. Everyone who is not generous or patient is wise and vice versa. Everyone who is both not quiet and calm is both not generous and not humble and vice versa. If fred is not strong or generous then fred is both not old and not funny and vice versa. Everyone who is both creative and not curious is not quiet or funny and vice versa. If john is not patient then someone is either quiet or humble and vice versa. Everyone who is either kind or curious is both not calm and kind. If someone is old or patient then alice is wise or calm and vice versa. Someone is both patient and not kind. Someone is either happy or curious. | John is tall. | neutral | (![X]:((~humble(X)&~wise(X))<=>~generous(X)))&
(((rich(susan)|humble(susan)))<=>((funny(lucy)&~strong(lucy))))&
(![X]:(~tall(X)=>(~humble(X)<~>kind(X))))&
(![X]:((creative(X)&~rich(X))<=>(creative(X)<~>funny(X))))&
(![X]:((quiet(X)|happy(X))=>(patient(X)&rich(X))))&
(![X]:(~generous(X)<=>(~tall(X)<~>~funny(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(~funny(X))))&
(![X]:((creative(X)&~old(X))<=>(~kind(X)&~generous(X))))&
(![X]:((~generous(X)|patient(X))<=>wise(X)))&
(![X]:((~quiet(X)&calm(X))<=>(~generous(X)&~humble(X))))&
(((~strong(fred)|generous(fred)))<=>((~old(fred)&~funny(fred))))&
(![X]:((creative(X)&~curious(X))<=>(~quiet(X)|funny(X))))&
((~patient(john))<=>(?[X]:((quiet(X)<~>humble(X)))))&
(![X]:((kind(X)<~>curious(X))=>(~calm(X)&kind(X))))&
((?[X]:((old(X)|patient(X))))<=>((wise(alice)|calm(alice))))&
(?[X]:((patient(X)&~kind(X))))&
(?[X]:((happy(X)<~>curious(X)))) | tall(john) | [] | null | 0 |
If someone is not curious or curious then someone is not brave or not creative.
If lucy is either happy or creative then alice is kind.
If mary is both not quiet and tall then someone is not creative or not happy and vice versa.
If lucy is both not creative and kind then someone is either patient or not old.
If someone is tall or patient then alice is either funny or quiet and vice versa.
If someone is old or patient then someone is not calm or happy and vice versa.
Everyone who is either not patient or not funny is kind.
Everyone who is either not patient or calm is wise or not wise.
If someone is either not rich or not generous then someone is not strong and vice versa.
If fred is both not happy and not curious then someone is both not humble and not funny and vice versa.
Everyone who is not old or calm is not curious or not creative and vice versa.
If john is both not rich and not strong then someone is both rich and not funny.
Everyone who is both not old and not strong is either not kind or not curious.
If someone is not rich then susan is both happy and not quiet and vice versa.
If lucy is generous or not kind then someone is either brave or kind.
If someone is both not kind and not rich then someone is either not strong or not wise.
Paul is both calm and quiet.
John is either not funny or not generous.
Lucy is happy or not funny.
Someone is rich.
Someone is not happy or not calm.
Someone is both old and not tall.
Lucy is either patient or not patient.
Fred is happy or funny. | Fred is happy. | neutral | ((?[X]:((~curious(X)|curious(X))))=>(?[X]:((~brave(X)|~creative(X)))))&
(((happy(lucy)<~>creative(lucy)))=>(kind(alice)))&
(((~quiet(mary)&tall(mary)))<=>(?[X]:((~creative(X)|~happy(X)))))&
(((~creative(lucy)&kind(lucy)))=>(?[X]:((patient(X)<~>~old(X)))))&
((?[X]:((tall(X)|patient(X))))<=>((funny(alice)<~>quiet(alice))))&
((?[X]:((old(X)|patient(X))))<=>(?[X]:((~calm(X)|happy(X)))))&
(![X]:((~patient(X)<~>~funny(X))=>kind(X)))&
(![X]:((~patient(X)<~>calm(X))=>(wise(X)|~wise(X))))&
((?[X]:((~rich(X)<~>~generous(X))))<=>(?[X]:(~strong(X))))&
(((~happy(fred)&~curious(fred)))<=>(?[X]:((~humble(X)&~funny(X)))))&
(![X]:((~old(X)|calm(X))<=>(~curious(X)|~creative(X))))&
(((~rich(john)&~strong(john)))=>(?[X]:((rich(X)&~funny(X)))))&
(![X]:((~old(X)&~strong(X))=>(~kind(X)<~>~curious(X))))&
((?[X]:(~rich(X)))<=>((happy(susan)&~quiet(susan))))&
(((generous(lucy)|~kind(lucy)))=>(?[X]:((brave(X)<~>kind(X)))))&
((?[X]:((~kind(X)&~rich(X))))=>(?[X]:((~strong(X)<~>~wise(X)))))&
((calm(paul)&quiet(paul)))&
((~funny(john)<~>~generous(john)))&
((happy(lucy)|~funny(lucy)))&
(?[X]:(rich(X)))&
(?[X]:((~happy(X)|~calm(X))))&
(?[X]:((old(X)&~tall(X))))&
((patient(lucy)<~>~patient(lucy)))&
((happy(fred)|funny(fred))) | happy(fred) | [] | null | 0 |
Everyone who is not generous or not strong is both not rich and kind.
Everyone who is not funny is funny or not strong and vice versa.
Everyone who is both patient and creative is both not kind and funny and vice versa.
Everyone who is rich or tall is either generous or brave.
Everyone who is not creative is not tall and vice versa.
If susan is both not old and not rich then someone is both funny and patient and vice versa.
Everyone who is both not humble and not tall is happy and vice versa.
If someone is both generous and not tall then someone is happy.
If paul is both brave and not funny then someone is both rich and not curious and vice versa.
If mary is both not strong and not generous then someone is both wise and not rich.
If someone is not humble then someone is both generous and not brave and vice versa.
If someone is either humble or not wise then alice is both not tall and not patient.
If someone is both humble and not curious then fred is old and vice versa.
If someone is either not funny or not calm then someone is brave or not quiet and vice versa.
Everyone who is both wise and rich is not wise or not kind and vice versa.
Everyone who is either strong or not patient is quiet.
Someone is either creative or not calm.
Someone is both not humble and not creative.
Someone is humble.
John is brave.
Someone is not rich.
Someone is happy or not happy. | Paul is not brave. | entailment | (![X]:((~generous(X)|~strong(X))=>(~rich(X)&kind(X))))&
(![X]:(~funny(X)<=>(funny(X)|~strong(X))))&
(![X]:((patient(X)&creative(X))<=>(~kind(X)&funny(X))))&
(![X]:((rich(X)|tall(X))=>(generous(X)<~>brave(X))))&
(![X]:(~creative(X)<=>~tall(X)))&
(((~old(susan)&~rich(susan)))<=>(?[X]:((funny(X)&patient(X)))))&
(![X]:((~humble(X)&~tall(X))<=>happy(X)))&
((?[X]:((generous(X)&~tall(X))))=>(?[X]:(happy(X))))&
(((brave(paul)&~funny(paul)))<=>(?[X]:((rich(X)&~curious(X)))))&
(((~strong(mary)&~generous(mary)))=>(?[X]:((wise(X)&~rich(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((generous(X)&~brave(X)))))&
((?[X]:((humble(X)<~>~wise(X))))=>((~tall(alice)&~patient(alice))))&
((?[X]:((humble(X)&~curious(X))))<=>(old(fred)))&
((?[X]:((~funny(X)<~>~calm(X))))<=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:((wise(X)&rich(X))<=>(~wise(X)|~kind(X))))&
(![X]:((strong(X)<~>~patient(X))=>quiet(X)))&
(?[X]:((creative(X)<~>~calm(X))))&
(?[X]:((~humble(X)&~creative(X))))&
(?[X]:(humble(X)))&
(brave(john))&
(?[X]:(~rich(X)))&
(?[X]:((happy(X)|~happy(X)))) | ~brave(paul) | [
"p0",
"p1",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2745484456857547528887529
% SZS output start Proof for 2745484456857547528887529
1. ! [X0] : ((~strong(X0) | ~generous(X0)) => (kind(X0) & ~rich(X0))) [input p0]
2. ! [X0] : (~funny(X0) <=> (~strong(X0) | funny(X0))) [input p1]
9. (~funny(paul) & brave(paul)) <=> ? [X0] : (~curious(X0) & rich(X0)) [input p8]
23. brave(paul) [input hypothesis]
27. ! [X0] : ((kind(X0) & ~rich(X0)) | (strong(X0) & generous(X0))) [ennf transformation 1]
34. ! [X0] : ((~funny(X0) | (strong(X0) & ~funny(X0))) & ((~strong(X0) | funny(X0)) | funny(X0))) [nnf transformation 2]
35. ! [X0] : ((~funny(X0) | (strong(X0) & ~funny(X0))) & (~strong(X0) | funny(X0) | funny(X0))) [flattening 34]
50. ((~funny(paul) & brave(paul)) | ! [X0] : (curious(X0) | ~rich(X0))) & (? [X0] : (~curious(X0) & rich(X0)) | (funny(paul) | ~brave(paul))) [nnf transformation 9]
51. ((~funny(paul) & brave(paul)) | ! [X0] : (curious(X0) | ~rich(X0))) & (? [X0] : (~curious(X0) & rich(X0)) | funny(paul) | ~brave(paul)) [flattening 50]
52. ((~funny(paul) & brave(paul)) | ! [X0] : (curious(X0) | ~rich(X0))) & (? [X1] : (~curious(X1) & rich(X1)) | funny(paul) | ~brave(paul)) [rectify 51]
53. ? [X1] : (~curious(X1) & rich(X1)) => (~curious(sK2) & rich(sK2)) [choice axiom]
54. ((~funny(paul) & brave(paul)) | ! [X0] : (curious(X0) | ~rich(X0))) & ((~curious(sK2) & rich(sK2)) | funny(paul) | ~brave(paul)) [skolemisation 52,53]
87. ~rich(X0) | strong(X0) [cnf transformation 27]
90. ~strong(X0) | funny(X0) | funny(X0) [cnf transformation 35]
91. ~funny(X0) | ~funny(X0) [cnf transformation 35]
111. rich(sK2) | funny(paul) | ~brave(paul) [cnf transformation 54]
148. brave(paul) [cnf transformation 23]
151. ~strong(X0) | funny(X0) [duplicate literal removal 90]
152. ~funny(X0) [duplicate literal removal 91]
153. ~strong(X0) [subsumption resolution 151,152]
183. 7 <=> brave(paul) [avatar definition]
193. rich(sK2) | ~brave(paul) [subsumption resolution 111,152]
195. 9 <=> rich(sK2) [avatar definition]
197. rich(sK2) <- (9) [avatar component clause 195]
198. ~7 | 9 [avatar split clause 193,195,183]
311. 7 [avatar split clause 148,183]
319. strong(sK2) <- (9) [resolution 87,197]
322. $false <- (9) [subsumption resolution 319,153]
323. ~9 [avatar contradiction clause 322]
324. $false [avatar sat refutation 198,311,323]
% SZS output end Proof for 2745484456857547528887529
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and not generous is either generous or not funny.
If alice is either not patient or not brave then lucy is both patient and not kind.
Everyone who is rich is either funny or not strong.
If fred is creative then someone is either wise or old and vice versa.
Everyone who is either not old or patient is not wise.
Everyone who is either generous or not generous is curious or not funny.
If someone is not kind or not patient then john is either not curious or not brave and vice versa.
If alice is both not tall and happy then someone is either humble or kind and vice versa.
Everyone who is both not brave and not curious is not happy and vice versa.
Everyone who is either not kind or not old is not kind and vice versa.
If someone is both funny and not happy then someone is patient or quiet.
Everyone who is either not brave or not calm is not happy.
If someone is not rich or not curious then someone is rich.
If someone is happy or not calm then alice is curious or not brave and vice versa.
If someone is either funny or not creative then susan is either calm or strong.
If mary is both strong and not old then someone is tall and vice versa.
Lucy is brave.
Someone is both not wise and quiet.
John is not happy.
Someone is curious or not humble.
Someone is tall or not humble.
Lucy is either not funny or not old.
Lucy is both not rich and not tall.
Someone is not brave or rich. | John is curious. | contradiction | (![X]:((~wise(X)&~generous(X))=>(generous(X)<~>~funny(X))))&
(((~patient(alice)<~>~brave(alice)))=>((patient(lucy)&~kind(lucy))))&
(![X]:(rich(X)=>(funny(X)<~>~strong(X))))&
((creative(fred))<=>(?[X]:((wise(X)<~>old(X)))))&
(![X]:((~old(X)<~>patient(X))=>~wise(X)))&
(![X]:((generous(X)<~>~generous(X))=>(curious(X)|~funny(X))))&
((?[X]:((~kind(X)|~patient(X))))<=>((~curious(john)<~>~brave(john))))&
(((~tall(alice)&happy(alice)))<=>(?[X]:((humble(X)<~>kind(X)))))&
(![X]:((~brave(X)&~curious(X))<=>~happy(X)))&
(![X]:((~kind(X)<~>~old(X))<=>~kind(X)))&
((?[X]:((funny(X)&~happy(X))))=>(?[X]:((patient(X)|quiet(X)))))&
(![X]:((~brave(X)<~>~calm(X))=>~happy(X)))&
((?[X]:((~rich(X)|~curious(X))))=>(?[X]:(rich(X))))&
((?[X]:((happy(X)|~calm(X))))<=>((curious(alice)|~brave(alice))))&
((?[X]:((funny(X)<~>~creative(X))))=>((calm(susan)<~>strong(susan))))&
(((strong(mary)&~old(mary)))<=>(?[X]:(tall(X))))&
(brave(lucy))&
(?[X]:((~wise(X)&quiet(X))))&
(~happy(john))&
(?[X]:((curious(X)|~humble(X))))&
(?[X]:((tall(X)|~humble(X))))&
((~funny(lucy)<~>~old(lucy)))&
((~rich(lucy)&~tall(lucy)))&
(?[X]:((~brave(X)|rich(X)))) | curious(john) | [
"p8",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1622378992012055875495873
% SZS output start Proof for 1622378992012055875495873
9. ! [X0] : ((~curious(X0) & ~brave(X0)) <=> ~happy(X0)) [input p8]
19. ~happy(john) [input p18]
25. curious(john) [input hypothesis]
58. ! [X0] : (((~curious(X0) & ~brave(X0)) | happy(X0)) & (~happy(X0) | (curious(X0) | brave(X0)))) [nnf transformation 9]
59. ! [X0] : (((~curious(X0) & ~brave(X0)) | happy(X0)) & (~happy(X0) | curious(X0) | brave(X0))) [flattening 58]
115. ~curious(X0) | happy(X0) [cnf transformation 59]
137. ~happy(john) [cnf transformation 19]
145. curious(john) [cnf transformation 25]
199. 11 <=> curious(john) [avatar definition]
200. curious(john) <- (11) [avatar component clause 199]
325. 11 [avatar split clause 145,199]
332. happy(john) <- (11) [resolution 115,200]
333. $false <- (11) [subsumption resolution 332,137]
334. ~11 [avatar contradiction clause 333]
335. $false [avatar sat refutation 325,334]
% SZS output end Proof for 1622378992012055875495873
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is both funny and generous and vice versa. Everyone who is not brave is not wise or generous and vice versa. Everyone who is curious is either not patient or tall. Everyone who is not strong is either rich or not old and vice versa. If john is both not curious and not humble then someone is not humble and vice versa. Everyone who is not patient or not creative is either not calm or not happy. If someone is patient then someone is either not happy or not calm and vice versa. Everyone who is not calm or kind is either not calm or not wise and vice versa. Everyone who is both strong and not generous is both rich and generous. Everyone who is not rich or not generous is both not calm and generous. Everyone who is not humble is both kind and tall. If someone is both kind and not old then someone is rich or tall. Everyone who is not brave or generous is both not wise and not funny and vice versa. Everyone who is not funny is not strong or not humble and vice versa. Everyone who is calm is old and vice versa. If someone is not quiet then someone is happy. Someone is humble. Lucy is not humble. Someone is either not strong or brave. Someone is both not wise and humble. Someone is not creative or strong. | Lucy is old. | entailment | (![X]:(happy(X)<=>(funny(X)&generous(X))))&
(![X]:(~brave(X)<=>(~wise(X)|generous(X))))&
(![X]:(curious(X)=>(~patient(X)<~>tall(X))))&
(![X]:(~strong(X)<=>(rich(X)<~>~old(X))))&
(((~curious(john)&~humble(john)))<=>(?[X]:(~humble(X))))&
(![X]:((~patient(X)|~creative(X))=>(~calm(X)<~>~happy(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~happy(X)<~>~calm(X)))))&
(![X]:((~calm(X)|kind(X))<=>(~calm(X)<~>~wise(X))))&
(![X]:((strong(X)&~generous(X))=>(rich(X)&generous(X))))&
(![X]:((~rich(X)|~generous(X))=>(~calm(X)&generous(X))))&
(![X]:(~humble(X)=>(kind(X)&tall(X))))&
((?[X]:((kind(X)&~old(X))))=>(?[X]:((rich(X)|tall(X)))))&
(![X]:((~brave(X)|generous(X))<=>(~wise(X)&~funny(X))))&
(![X]:(~funny(X)<=>(~strong(X)|~humble(X))))&
(![X]:(calm(X)<=>old(X)))&
((?[X]:(~quiet(X)))=>(?[X]:(happy(X))))&
(?[X]:(humble(X)))&
(~humble(lucy))&
(?[X]:((~strong(X)<~>brave(X))))&
(?[X]:((~wise(X)&humble(X))))&
(?[X]:((~creative(X)|strong(X)))) | old(lucy) | [
"p7",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5712627393427146878191897
% SZS output start Proof for 5712627393427146878191897
8. ! [X0] : ((kind(X0) | ~calm(X0)) <=> (~calm(X0) <~> ~wise(X0))) [input p7]
10. ! [X0] : ((~generous(X0) | ~rich(X0)) => (generous(X0) & ~calm(X0))) [input p9]
13. ! [X0] : ((generous(X0) | ~brave(X0)) <=> (~funny(X0) & ~wise(X0))) [input p12]
15. ! [X0] : (calm(X0) <=> old(X0)) [input p14]
22. ~old(lucy) [input hypothesis]
31. ! [X0] : ((generous(X0) & ~calm(X0)) | (generous(X0) & rich(X0))) [ennf transformation 10]
51. ! [X0] : (((kind(X0) | ~calm(X0)) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) & (((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | (~kind(X0) & calm(X0)))) [nnf transformation 8]
52. ! [X0] : ((kind(X0) | ~calm(X0) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0)))) & (((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | (~kind(X0) & calm(X0)))) [flattening 51]
56. ! [X0] : (((generous(X0) | ~brave(X0)) | (funny(X0) | wise(X0))) & ((~funny(X0) & ~wise(X0)) | (~generous(X0) & brave(X0)))) [nnf transformation 13]
57. ! [X0] : ((generous(X0) | ~brave(X0) | funny(X0) | wise(X0)) & ((~funny(X0) & ~wise(X0)) | (~generous(X0) & brave(X0)))) [flattening 56]
60. ! [X0] : ((calm(X0) | ~old(X0)) & (old(X0) | ~calm(X0))) [nnf transformation 15]
95. wise(X0) | calm(X0) | calm(X0) [cnf transformation 52]
104. generous(X0) | generous(X0) [cnf transformation 31]
109. ~wise(X0) | ~generous(X0) [cnf transformation 57]
116. ~calm(X0) | old(X0) [cnf transformation 60]
125. ~old(lucy) [cnf transformation 22]
126. generous(X0) [duplicate literal removal 104]
128. calm(X0) | wise(X0) [duplicate literal removal 95]
186. ~wise(X0) [subsumption resolution 109,126]
216. wise(X0) | old(X0) [resolution 128,116]
220. old(X0) [subsumption resolution 216,186]
224. $false [resolution 220,125]
% SZS output end Proof for 5712627393427146878191897
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny or not rich then fred is both patient and not strong.
If someone is quiet then someone is either not calm or quiet and vice versa.
Everyone who is not tall is either funny or not happy and vice versa.
Everyone who is tall or not calm is not calm or not strong.
Everyone who is either strong or not brave is not brave.
If susan is either humble or generous then john is not calm or brave.
If someone is both kind and not creative then someone is kind or quiet.
If someone is either wise or not tall then someone is either wise or not quiet.
Everyone who is both rich and not rich is both not quiet and humble.
If alice is not strong then someone is either not calm or humble and vice versa.
Everyone who is rich is both not happy and patient and vice versa.
If someone is either generous or wise then someone is either wise or not rich.
If someone is either tall or not humble then someone is either not rich or tall and vice versa.
If lucy is both wise and not funny then someone is not curious and vice versa.
Everyone who is either not happy or strong is either not funny or funny.
If someone is not creative or wise then susan is not humble or humble.
Someone is either happy or not wise.
Fred is both old and happy.
Lucy is both not humble and patient.
Someone is both patient and quiet.
Someone is old.
Mary is either rich or not calm.
Someone is either not happy or brave. | Fred is strong. | contradiction | ((?[X]:((funny(X)|~rich(X))))=>((patient(fred)&~strong(fred))))&
((?[X]:(quiet(X)))<=>(?[X]:((~calm(X)<~>quiet(X)))))&
(![X]:(~tall(X)<=>(funny(X)<~>~happy(X))))&
(![X]:((tall(X)|~calm(X))=>(~calm(X)|~strong(X))))&
(![X]:((strong(X)<~>~brave(X))=>~brave(X)))&
(((humble(susan)<~>generous(susan)))=>((~calm(john)|brave(john))))&
((?[X]:((kind(X)&~creative(X))))=>(?[X]:((kind(X)|quiet(X)))))&
((?[X]:((wise(X)<~>~tall(X))))=>(?[X]:((wise(X)<~>~quiet(X)))))&
(![X]:((rich(X)&~rich(X))=>(~quiet(X)&humble(X))))&
((~strong(alice))<=>(?[X]:((~calm(X)<~>humble(X)))))&
(![X]:(rich(X)<=>(~happy(X)&patient(X))))&
((?[X]:((generous(X)<~>wise(X))))=>(?[X]:((wise(X)<~>~rich(X)))))&
((?[X]:((tall(X)<~>~humble(X))))<=>(?[X]:((~rich(X)<~>tall(X)))))&
(((wise(lucy)&~funny(lucy)))<=>(?[X]:(~curious(X))))&
(![X]:((~happy(X)<~>strong(X))=>(~funny(X)<~>funny(X))))&
((?[X]:((~creative(X)|wise(X))))=>((~humble(susan)|humble(susan))))&
(?[X]:((happy(X)<~>~wise(X))))&
((old(fred)&happy(fred)))&
((~humble(lucy)&patient(lucy)))&
(?[X]:((patient(X)&quiet(X))))&
(?[X]:(old(X)))&
((rich(mary)<~>~calm(mary)))&
(?[X]:((~happy(X)<~>brave(X)))) | strong(fred) | [
"p0",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1223261026587286350619287
% SZS output start Proof for 1223261026587286350619287
1. ? [X0] : (~rich(X0) | funny(X0)) => (~strong(fred) & patient(fred)) [input p0]
11. ! [X0] : (rich(X0) <=> (patient(X0) & ~happy(X0))) [input p10]
18. happy(fred) & old(fred) [input p17]
24. strong(fred) [input hypothesis]
31. happy(fred) [pure predicate removal 18]
34. (~strong(fred) & patient(fred)) | ! [X0] : (rich(X0) & ~funny(X0)) [ennf transformation 1]
63. ! [X0] : ((rich(X0) | (~patient(X0) | happy(X0))) & ((patient(X0) & ~happy(X0)) | ~rich(X0))) [nnf transformation 11]
64. ! [X0] : ((rich(X0) | ~patient(X0) | happy(X0)) & ((patient(X0) & ~happy(X0)) | ~rich(X0))) [flattening 63]
92. ~strong(fred) | rich(X0) [cnf transformation 34]
117. ~happy(X0) | ~rich(X0) [cnf transformation 64]
142. happy(fred) [cnf transformation 31]
151. strong(fred) [cnf transformation 24]
154. 1 <=> ! [X0] : rich(X0) [avatar definition]
155. rich(X0) <- (1) [avatar component clause 154]
157. 2 <=> strong(fred) [avatar definition]
160. 1 | ~2 [avatar split clause 92,157,154]
356. 2 [avatar split clause 151,157]
363. ~rich(fred) [resolution 117,142]
364. $false <- (1) [subsumption resolution 363,155]
365. ~1 [avatar contradiction clause 364]
366. $false [avatar sat refutation 160,356,365]
% SZS output end Proof for 1223261026587286350619287
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not generous then alice is not humble or wise and vice versa.
Everyone who is not tall is not curious and vice versa.
Everyone who is not happy or not generous is patient or not tall and vice versa.
If someone is not wise then alice is both tall and not strong and vice versa.
Everyone who is kind is not generous and vice versa.
Everyone who is both not generous and not tall is either not strong or not humble and vice versa.
Everyone who is patient or not old is either not generous or not funny and vice versa.
If someone is either not tall or creative then fred is either not curious or curious.
If someone is not generous then paul is not kind and vice versa.
Everyone who is calm is both not humble and creative and vice versa.
If alice is either not curious or not quiet then someone is either not strong or funny and vice versa.
Everyone who is either patient or not strong is either brave or not funny.
Everyone who is both not calm and tall is either wise or strong.
Everyone who is not funny or not tall is not happy or quiet.
If someone is not kind then paul is both not rich and brave.
If someone is either humble or not quiet then someone is curious or quiet.
Someone is humble or not wise.
Someone is old.
Susan is either not tall or wise.
Someone is generous or not wise.
Someone is not generous or not happy.
Someone is strong.
Someone is not patient or not humble. | Fred is not brave. | neutral | ((~generous(john))<=>((~humble(alice)|wise(alice))))&
(![X]:(~tall(X)<=>~curious(X)))&
(![X]:((~happy(X)|~generous(X))<=>(patient(X)|~tall(X))))&
((?[X]:(~wise(X)))<=>((tall(alice)&~strong(alice))))&
(![X]:(kind(X)<=>~generous(X)))&
(![X]:((~generous(X)&~tall(X))<=>(~strong(X)<~>~humble(X))))&
(![X]:((patient(X)|~old(X))<=>(~generous(X)<~>~funny(X))))&
((?[X]:((~tall(X)<~>creative(X))))=>((~curious(fred)<~>curious(fred))))&
((?[X]:(~generous(X)))<=>(~kind(paul)))&
(![X]:(calm(X)<=>(~humble(X)&creative(X))))&
(((~curious(alice)<~>~quiet(alice)))<=>(?[X]:((~strong(X)<~>funny(X)))))&
(![X]:((patient(X)<~>~strong(X))=>(brave(X)<~>~funny(X))))&
(![X]:((~calm(X)&tall(X))=>(wise(X)<~>strong(X))))&
(![X]:((~funny(X)|~tall(X))=>(~happy(X)|quiet(X))))&
((?[X]:(~kind(X)))=>((~rich(paul)&brave(paul))))&
((?[X]:((humble(X)<~>~quiet(X))))=>(?[X]:((curious(X)|quiet(X)))))&
(?[X]:((humble(X)|~wise(X))))&
(?[X]:(old(X)))&
((~tall(susan)<~>wise(susan)))&
(?[X]:((generous(X)|~wise(X))))&
(?[X]:((~generous(X)|~happy(X))))&
(?[X]:(strong(X)))&
(?[X]:((~patient(X)|~humble(X)))) | ~brave(fred) | [] | null | 0 |
If susan is either not wise or not strong then someone is both not patient and rich and vice versa. If someone is curious then susan is not brave or rich and vice versa. If alice is kind then someone is not strong or not curious and vice versa. Everyone who is both brave and not strong is patient or not quiet and vice versa. If mary is both funny and not tall then mary is patient and vice versa. If paul is both not quiet and not rich then someone is rich or not funny and vice versa. Everyone who is generous is either not kind or not humble. Everyone who is rich or not rich is not kind. If susan is either not creative or old then someone is generous or calm and vice versa. Everyone who is both not funny and not happy is curious or kind. Everyone who is not generous is not quiet or old and vice versa. If someone is not old then paul is not curious or old and vice versa. Everyone who is either wise or not tall is both not wise and not happy and vice versa. Everyone who is rich or wise is creative and vice versa. Someone is not funny or not patient. John is both not happy and old. Mary is not humble. Someone is tall or not patient. Someone is either not quiet or calm. Alice is strong or not patient. Someone is both strong and calm. John is not humble. | Susan is not kind. | entailment | (((~wise(susan)<~>~strong(susan)))<=>(?[X]:((~patient(X)&rich(X)))))&
((?[X]:(curious(X)))<=>((~brave(susan)|rich(susan))))&
((kind(alice))<=>(?[X]:((~strong(X)|~curious(X)))))&
(![X]:((brave(X)&~strong(X))<=>(patient(X)|~quiet(X))))&
(((funny(mary)&~tall(mary)))<=>(patient(mary)))&
(((~quiet(paul)&~rich(paul)))<=>(?[X]:((rich(X)|~funny(X)))))&
(![X]:(generous(X)=>(~kind(X)<~>~humble(X))))&
(![X]:((rich(X)|~rich(X))=>~kind(X)))&
(((~creative(susan)<~>old(susan)))<=>(?[X]:((generous(X)|calm(X)))))&
(![X]:((~funny(X)&~happy(X))=>(curious(X)|kind(X))))&
(![X]:(~generous(X)<=>(~quiet(X)|old(X))))&
((?[X]:(~old(X)))<=>((~curious(paul)|old(paul))))&
(![X]:((wise(X)<~>~tall(X))<=>(~wise(X)&~happy(X))))&
(![X]:((rich(X)|wise(X))<=>creative(X)))&
(?[X]:((~funny(X)|~patient(X))))&
((~happy(john)&old(john)))&
(~humble(mary))&
(?[X]:((tall(X)|~patient(X))))&
(?[X]:((~quiet(X)<~>calm(X))))&
((strong(alice)|~patient(alice)))&
(?[X]:((strong(X)&calm(X))))&
(~humble(john)) | ~kind(susan) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7805950530532243285783450
% SZS output start Proof for 7805950530532243285783450
8. ! [X0] : ((~rich(X0) | rich(X0)) => ~kind(X0)) [input p7]
23. kind(susan) [input hypothesis]
25. ! [X0] : (~kind(X0) | (rich(X0) & ~rich(X0))) [ennf transformation 8]
102. ~kind(X0) | ~rich(X0) [cnf transformation 25]
103. ~kind(X0) | rich(X0) [cnf transformation 25]
137. kind(susan) [cnf transformation 23]
246. ~kind(X0) [subsumption resolution 102,103]
323. $false [subsumption resolution 137,246]
% SZS output end Proof for 7805950530532243285783450
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich then someone is both not old and old. If someone is not wise then mary is either not brave or curious and vice versa. Everyone who is either brave or not brave is not patient and vice versa. If someone is either creative or not wise then john is wise or not happy and vice versa. Everyone who is quiet or tall is both not quiet and happy and vice versa. Everyone who is generous is either tall or not humble. If someone is both kind and curious then susan is not strong and vice versa. Everyone who is calm or not humble is humble or not wise and vice versa. Everyone who is either not calm or not old is either tall or old and vice versa. If someone is not strong or not patient then someone is both strong and humble and vice versa. Everyone who is generous or rich is not brave and vice versa. Everyone who is not strong or happy is either not rich or not funny and vice versa. Everyone who is either calm or not wise is funny and vice versa. Everyone who is both not funny and funny is not generous. Everyone who is both old and not creative is either not brave or generous and vice versa. John is not rich or wise. Someone is both not funny and creative. Paul is not patient. Lucy is either humble or not generous. Fred is either calm or kind. Someone is not calm or not tall. Someone is curious or not strong. | Susan is not quiet. | entailment | ((~rich(alice))=>(?[X]:((~old(X)&old(X)))))&
((?[X]:(~wise(X)))<=>((~brave(mary)<~>curious(mary))))&
(![X]:((brave(X)<~>~brave(X))<=>~patient(X)))&
((?[X]:((creative(X)<~>~wise(X))))<=>((wise(john)|~happy(john))))&
(![X]:((quiet(X)|tall(X))<=>(~quiet(X)&happy(X))))&
(![X]:(generous(X)=>(tall(X)<~>~humble(X))))&
((?[X]:((kind(X)&curious(X))))<=>(~strong(susan)))&
(![X]:((calm(X)|~humble(X))<=>(humble(X)|~wise(X))))&
(![X]:((~calm(X)<~>~old(X))<=>(tall(X)<~>old(X))))&
((?[X]:((~strong(X)|~patient(X))))<=>(?[X]:((strong(X)&humble(X)))))&
(![X]:((generous(X)|rich(X))<=>~brave(X)))&
(![X]:((~strong(X)|happy(X))<=>(~rich(X)<~>~funny(X))))&
(![X]:((calm(X)<~>~wise(X))<=>funny(X)))&
(![X]:((~funny(X)&funny(X))=>~generous(X)))&
(![X]:((old(X)&~creative(X))<=>(~brave(X)<~>generous(X))))&
((~rich(john)|wise(john)))&
(?[X]:((~funny(X)&creative(X))))&
(~patient(paul))&
((humble(lucy)<~>~generous(lucy)))&
((calm(fred)<~>kind(fred)))&
(?[X]:((~calm(X)|~tall(X))))&
(?[X]:((curious(X)|~strong(X)))) | ~quiet(susan) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 4087293426779887863518032
% SZS output start Proof for 4087293426779887863518032
5. ! [X0] : ((tall(X0) | quiet(X0)) <=> (happy(X0) & ~quiet(X0))) [input p4]
23. quiet(susan) [input hypothesis]
41. ! [X0] : (((tall(X0) | quiet(X0)) | (~happy(X0) | quiet(X0))) & ((happy(X0) & ~quiet(X0)) | (~tall(X0) & ~quiet(X0)))) [nnf transformation 5]
42. ! [X0] : ((tall(X0) | quiet(X0) | ~happy(X0) | quiet(X0)) & ((happy(X0) & ~quiet(X0)) | (~tall(X0) & ~quiet(X0)))) [flattening 41]
87. ~quiet(X0) | ~quiet(X0) [cnf transformation 42]
144. quiet(susan) [cnf transformation 23]
151. ~quiet(X0) [duplicate literal removal 87]
272. $false [subsumption resolution 144,151]
% SZS output end Proof for 4087293426779887863518032
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or happy then lucy is either not calm or curious and vice versa.
Everyone who is either rich or patient is either not patient or not funny.
If paul is either not patient or not rich then fred is both not curious and not funny.
Everyone who is not quiet is not brave or happy and vice versa.
Everyone who is either not curious or happy is either humble or not happy.
If someone is tall or curious then alice is either not quiet or calm.
Everyone who is both patient and not happy is either kind or humble and vice versa.
Everyone who is both not funny and not strong is not kind and vice versa.
Everyone who is both not old and not kind is generous or not wise and vice versa.
If someone is not calm or not kind then paul is both humble and generous.
If someone is either funny or not tall then paul is strong.
If someone is old then alice is either not funny or wise and vice versa.
Everyone who is both not curious and not brave is calm or not quiet.
If someone is calm then susan is happy or tall and vice versa.
Everyone who is curious is both not strong and tall.
Everyone who is rich is both wise and strong and vice versa.
Someone is strong or not wise.
John is either not humble or happy.
Someone is quiet.
Fred is not humble or not generous.
Susan is not wise.
Someone is not generous.
Someone is not old.
Someone is either generous or tall. | Paul is curious. | entailment | ((?[X]:((kind(X)|happy(X))))<=>((~calm(lucy)<~>curious(lucy))))&
(![X]:((rich(X)<~>patient(X))=>(~patient(X)<~>~funny(X))))&
(((~patient(paul)<~>~rich(paul)))=>((~curious(fred)&~funny(fred))))&
(![X]:(~quiet(X)<=>(~brave(X)|happy(X))))&
(![X]:((~curious(X)<~>happy(X))=>(humble(X)<~>~happy(X))))&
((?[X]:((tall(X)|curious(X))))=>((~quiet(alice)<~>calm(alice))))&
(![X]:((patient(X)&~happy(X))<=>(kind(X)<~>humble(X))))&
(![X]:((~funny(X)&~strong(X))<=>~kind(X)))&
(![X]:((~old(X)&~kind(X))<=>(generous(X)|~wise(X))))&
((?[X]:((~calm(X)|~kind(X))))=>((humble(paul)&generous(paul))))&
((?[X]:((funny(X)<~>~tall(X))))=>(strong(paul)))&
((?[X]:(old(X)))<=>((~funny(alice)<~>wise(alice))))&
(![X]:((~curious(X)&~brave(X))=>(calm(X)|~quiet(X))))&
((?[X]:(calm(X)))<=>((happy(susan)|tall(susan))))&
(![X]:(curious(X)=>(~strong(X)&tall(X))))&
(![X]:(rich(X)<=>(wise(X)&strong(X))))&
(?[X]:((strong(X)|~wise(X))))&
((~humble(john)<~>happy(john)))&
(?[X]:(quiet(X)))&
((~humble(fred)|~generous(fred)))&
(~wise(susan))&
(?[X]:(~generous(X)))&
(?[X]:(~old(X)))&
(?[X]:((generous(X)<~>tall(X)))) | curious(paul) | [
"p4",
"p6",
"p8",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2492133301860458077525777
% SZS output start Proof for 2492133301860458077525777
5. ! [X0] : ((~curious(X0) <~> happy(X0)) => (humble(X0) <~> ~happy(X0))) [input p4]
7. ! [X0] : ((~happy(X0) & patient(X0)) <=> (kind(X0) <~> humble(X0))) [input p6]
9. ! [X0] : ((~kind(X0) & ~old(X0)) <=> (~wise(X0) | generous(X0))) [input p8]
10. ? [X0] : (~kind(X0) | ~calm(X0)) => (generous(paul) & humble(paul)) [input p9]
21. ~wise(susan) [input p20]
25. ~curious(paul) [input hypothesis]
28. ! [X0] : ((humble(X0) <~> ~happy(X0)) | (~curious(X0) <=> happy(X0))) [ennf transformation 5]
30. (generous(paul) & humble(paul)) | ! [X0] : (kind(X0) & calm(X0)) [ennf transformation 10]
43. ! [X0] : (((happy(X0) | ~humble(X0)) & (~happy(X0) | humble(X0))) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0)))) [nnf transformation 28]
45. ! [X0] : (((~happy(X0) & patient(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | (happy(X0) | ~patient(X0)))) [nnf transformation 7]
46. ! [X0] : (((~happy(X0) & patient(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | happy(X0) | ~patient(X0))) [flattening 45]
49. ! [X0] : (((~kind(X0) & ~old(X0)) | (wise(X0) & ~generous(X0))) & ((~wise(X0) | generous(X0)) | (kind(X0) | old(X0)))) [nnf transformation 9]
50. ! [X0] : (((~kind(X0) & ~old(X0)) | (wise(X0) & ~generous(X0))) & (~wise(X0) | generous(X0) | kind(X0) | old(X0))) [flattening 49]
94. happy(X0) | ~humble(X0) | happy(X0) | curious(X0) [cnf transformation 43]
105. ~humble(X0) | kind(X0) | ~happy(X0) [cnf transformation 46]
112. ~generous(X0) | ~kind(X0) [cnf transformation 50]
113. ~kind(X0) | wise(X0) [cnf transformation 50]
115. humble(paul) | kind(X0) [cnf transformation 30]
117. generous(paul) | kind(X0) [cnf transformation 30]
138. ~wise(susan) [cnf transformation 21]
143. ~curious(paul) [cnf transformation 25]
145. ~humble(X0) | happy(X0) | curious(X0) [duplicate literal removal 94]
215. 15 <=> ! [X0] : kind(X0) [avatar definition]
216. kind(X0) <- (15) [avatar component clause 215]
218. 16 <=> generous(paul) [avatar definition]
220. generous(paul) <- (16) [avatar component clause 218]
221. 15 | 16 [avatar split clause 117,218,215]
227. 18 <=> humble(paul) [avatar definition]
229. humble(paul) <- (18) [avatar component clause 227]
230. 15 | 18 [avatar split clause 115,227,215]
329. ~kind(paul) <- (16) [resolution 112,220]
361. kind(paul) | ~happy(paul) <- (18) [resolution 105,229]
362. ~happy(paul) <- (16, 18) [subsumption resolution 361,329]
387. happy(paul) | curious(paul) <- (18) [resolution 145,229]
388. curious(paul) <- (16, 18) [subsumption resolution 387,362]
389. $false <- (16, 18) [subsumption resolution 388,143]
390. ~16 | ~18 [avatar contradiction clause 389]
403. wise(X2) <- (15) [resolution 216,113]
408. $false <- (15) [resolution 403,138]
411. ~15 [avatar contradiction clause 408]
413. $false [avatar sat refutation 221,230,390,411]
% SZS output end Proof for 2492133301860458077525777
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both not patient and not creative then someone is not creative or not funny.
If john is not calm or not creative then paul is either funny or not generous.
Everyone who is old is old or generous and vice versa.
If john is funny then lucy is not happy or wise and vice versa.
If someone is not kind or not happy then someone is quiet and vice versa.
If someone is both patient and not quiet then someone is calm.
If lucy is not rich then someone is not humble and vice versa.
Everyone who is either not generous or not tall is either humble or creative and vice versa.
If john is quiet then susan is kind and vice versa.
Everyone who is both not calm and not old is either funny or curious.
Everyone who is either wise or not humble is either not tall or kind and vice versa.
Everyone who is both wise and generous is not calm or not brave and vice versa.
Everyone who is not creative is not generous and vice versa.
If someone is both kind and tall then someone is both not wise and not curious.
Everyone who is both not funny and not kind is either funny or generous and vice versa.
Everyone who is either old or not wise is both not funny and happy.
John is either kind or not patient.
Someone is both not quiet and brave.
Someone is patient or not tall.
Someone is not old or wise.
Someone is not patient or not kind.
John is brave or not strong.
Fred is not quiet.
Fred is funny or quiet. | Fred is brave. | entailment | (((~patient(lucy)&~creative(lucy)))=>(?[X]:((~creative(X)|~funny(X)))))&
(((~calm(john)|~creative(john)))=>((funny(paul)<~>~generous(paul))))&
(![X]:(old(X)<=>(old(X)|generous(X))))&
((funny(john))<=>((~happy(lucy)|wise(lucy))))&
((?[X]:((~kind(X)|~happy(X))))<=>(?[X]:(quiet(X))))&
((?[X]:((patient(X)&~quiet(X))))=>(?[X]:(calm(X))))&
((~rich(lucy))<=>(?[X]:(~humble(X))))&
(![X]:((~generous(X)<~>~tall(X))<=>(humble(X)<~>creative(X))))&
((quiet(john))<=>(kind(susan)))&
(![X]:((~calm(X)&~old(X))=>(funny(X)<~>curious(X))))&
(![X]:((wise(X)<~>~humble(X))<=>(~tall(X)<~>kind(X))))&
(![X]:((wise(X)&generous(X))<=>(~calm(X)|~brave(X))))&
(![X]:(~creative(X)<=>~generous(X)))&
((?[X]:((kind(X)&tall(X))))=>(?[X]:((~wise(X)&~curious(X)))))&
(![X]:((~funny(X)&~kind(X))<=>(funny(X)<~>generous(X))))&
(![X]:((old(X)<~>~wise(X))=>(~funny(X)&happy(X))))&
((kind(john)<~>~patient(john)))&
(?[X]:((~quiet(X)&brave(X))))&
(?[X]:((patient(X)|~tall(X))))&
(?[X]:((~old(X)|wise(X))))&
(?[X]:((~patient(X)|~kind(X))))&
((brave(john)|~strong(john)))&
(~quiet(fred))&
((funny(fred)|quiet(fred))) | brave(fred) | [
"p2",
"p11",
"p15",
"p22",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7869753121090558109403314
% SZS output start Proof for 7869753121090558109403314
3. ! [X0] : (old(X0) <=> (generous(X0) | old(X0))) [input p2]
12. ! [X0] : ((generous(X0) & wise(X0)) <=> (~brave(X0) | ~calm(X0))) [input p11]
16. ! [X0] : ((old(X0) <~> ~wise(X0)) => (happy(X0) & ~funny(X0))) [input p15]
23. ~quiet(fred) [input p22]
24. quiet(fred) | funny(fred) [input p23]
25. ~brave(fred) [input hypothesis]
37. ! [X0] : ((happy(X0) & ~funny(X0)) | (old(X0) <=> ~wise(X0))) [ennf transformation 16]
41. ! [X0] : ((old(X0) | (~generous(X0) & ~old(X0))) & ((generous(X0) | old(X0)) | ~old(X0))) [nnf transformation 3]
42. ! [X0] : ((old(X0) | (~generous(X0) & ~old(X0))) & (generous(X0) | old(X0) | ~old(X0))) [flattening 41]
61. ! [X0] : (((generous(X0) & wise(X0)) | (brave(X0) & calm(X0))) & ((~brave(X0) | ~calm(X0)) | (~generous(X0) | ~wise(X0)))) [nnf transformation 12]
62. ! [X0] : (((generous(X0) & wise(X0)) | (brave(X0) & calm(X0))) & (~brave(X0) | ~calm(X0) | ~generous(X0) | ~wise(X0))) [flattening 61]
69. ! [X0] : ((happy(X0) & ~funny(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0)))) [nnf transformation 37]
86. ~generous(X0) | old(X0) [cnf transformation 42]
118. brave(X0) | wise(X0) [cnf transformation 62]
120. brave(X0) | generous(X0) [cnf transformation 62]
131. ~wise(X0) | ~funny(X0) | ~old(X0) [cnf transformation 69]
142. ~quiet(fred) [cnf transformation 23]
143. quiet(fred) | funny(fred) [cnf transformation 24]
144. ~brave(fred) [cnf transformation 25]
305. funny(fred) [subsumption resolution 143,142]
307. wise(fred) [resolution 118,144]
310. generous(fred) [resolution 120,144]
313. old(fred) [resolution 310,86]
333. ~funny(fred) | ~old(fred) [resolution 131,307]
335. ~old(fred) [subsumption resolution 333,305]
336. $false [subsumption resolution 335,313]
% SZS output end Proof for 7869753121090558109403314
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
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