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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|---|---|---|---|---|---|---|---|
If someone is either not creative or humble then someone is either not rich or not wise.
If alice is creative then lucy is brave or not patient.
Everyone who is both old and not quiet is either brave or not old.
Everyone who is not kind is not curious.
Everyone who is either not curious or brave is creative.
If someone is both not rich and not generous then someone is not calm.
If john is both creative and curious then lucy is both kind and wise and vice versa.
Everyone who is both old and not strong is brave or funny and vice versa.
Everyone who is happy or creative is not generous and vice versa.
Everyone who is generous is not humble and vice versa.
Everyone who is brave or not calm is strong and vice versa.
Everyone who is both happy and patient is either strong or patient and vice versa.
If someone is both rich and not curious then fred is not brave.
Everyone who is both funny and wise is not tall or not happy and vice versa.
Everyone who is either humble or not rich is both not strong and not funny and vice versa.
Everyone who is both not creative and not strong is not patient.
Someone is either not humble or not old.
John is humble or not rich.
Someone is both not happy and funny.
Someone is wise.
Someone is both curious and creative.
Mary is either wise or not generous. | Lucy is not strong. | entailment | ((?[X]:((~creative(X)<~>humble(X))))=>(?[X]:((~rich(X)<~>~wise(X)))))&
((creative(alice))=>((brave(lucy)|~patient(lucy))))&
(![X]:((old(X)&~quiet(X))=>(brave(X)<~>~old(X))))&
(![X]:(~kind(X)=>~curious(X)))&
(![X]:((~curious(X)<~>brave(X))=>creative(X)))&
((?[X]:((~rich(X)&~generous(X))))=>(?[X]:(~calm(X))))&
(((creative(john)&curious(john)))<=>((kind(lucy)&wise(lucy))))&
(![X]:((old(X)&~strong(X))<=>(brave(X)|funny(X))))&
(![X]:((happy(X)|creative(X))<=>~generous(X)))&
(![X]:(generous(X)<=>~humble(X)))&
(![X]:((brave(X)|~calm(X))<=>strong(X)))&
(![X]:((happy(X)&patient(X))<=>(strong(X)<~>patient(X))))&
((?[X]:((rich(X)&~curious(X))))=>(~brave(fred)))&
(![X]:((funny(X)&wise(X))<=>(~tall(X)|~happy(X))))&
(![X]:((humble(X)<~>~rich(X))<=>(~strong(X)&~funny(X))))&
(![X]:((~creative(X)&~strong(X))=>~patient(X)))&
(?[X]:((~humble(X)<~>~old(X))))&
((humble(john)|~rich(john)))&
(?[X]:((~happy(X)&funny(X))))&
(?[X]:(wise(X)))&
(?[X]:((curious(X)&creative(X))))&
((wise(mary)<~>~generous(mary))) | ~strong(lucy) | [
"p7",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 554939129367263497539297
% SZS output start Proof for 554939129367263497539297
8. ! [X0] : ((~strong(X0) & old(X0)) <=> (funny(X0) | brave(X0))) [input p7]
12. ! [X0] : ((patient(X0) & happy(X0)) <=> (strong(X0) <~> patient(X0))) [input p11]
14. ! [X0] : ((wise(X0) & funny(X0)) <=> (~happy(X0) | ~tall(X0))) [input p13]
23. strong(lucy) [input hypothesis]
46. ! [X0] : (((~strong(X0) & old(X0)) | (~funny(X0) & ~brave(X0))) & ((funny(X0) | brave(X0)) | (strong(X0) | ~old(X0)))) [nnf transformation 8]
47. ! [X0] : (((~strong(X0) & old(X0)) | (~funny(X0) & ~brave(X0))) & (funny(X0) | brave(X0) | strong(X0) | ~old(X0))) [flattening 46]
53. ! [X0] : (((patient(X0) & happy(X0)) | ((strong(X0) | ~patient(X0)) & (patient(X0) | ~strong(X0)))) & (((~patient(X0) | ~strong(X0)) & (patient(X0) | strong(X0))) | (~patient(X0) | ~happy(X0)))) [nnf transformation 12]
54. ! [X0] : (((patient(X0) & happy(X0)) | ((strong(X0) | ~patient(X0)) & (patient(X0) | ~strong(X0)))) & (((~patient(X0) | ~strong(X0)) & (patient(X0) | strong(X0))) | ~patient(X0) | ~happy(X0))) [flattening 53]
55. ! [X0] : (((wise(X0) & funny(X0)) | (happy(X0) & tall(X0))) & ((~happy(X0) | ~tall(X0)) | (~wise(X0) | ~funny(X0)))) [nnf transformation 14]
56. ! [X0] : (((wise(X0) & funny(X0)) | (happy(X0) & tall(X0))) & (~happy(X0) | ~tall(X0) | ~wise(X0) | ~funny(X0))) [flattening 55]
86. ~funny(X0) | ~strong(X0) [cnf transformation 47]
96. ~patient(X0) | ~strong(X0) | ~patient(X0) | ~happy(X0) [cnf transformation 54]
99. patient(X0) | patient(X0) | ~strong(X0) [cnf transformation 54]
104. happy(X0) | funny(X0) [cnf transformation 56]
124. strong(lucy) [cnf transformation 23]
125. ~patient(X0) | ~strong(X0) | ~happy(X0) [duplicate literal removal 96]
126. ~strong(X0) | patient(X0) [duplicate literal removal 99]
188. ~happy(X0) | ~strong(X0) [subsumption resolution 125,126]
239. ~strong(X1) | funny(X1) [resolution 188,104]
240. ~strong(X1) [subsumption resolution 239,86]
241. $false [resolution 240,124]
% SZS output end Proof for 554939129367263497539297
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not brave is both calm and brave and vice versa. Everyone who is brave or creative is not patient and vice versa. Everyone who is funny is both old and wise. Everyone who is either not calm or not old is both old and patient and vice versa. If susan is either not humble or not rich then susan is not patient. If susan is both not calm and not creative then someone is not creative or not generous and vice versa. Everyone who is humble or not humble is not calm and vice versa. Everyone who is not quiet or rich is not creative or not calm and vice versa. Everyone who is both not wise and humble is not wise or creative and vice versa. If fred is quiet or not tall then paul is brave or not wise and vice versa. If john is both kind and quiet then susan is not humble or not quiet. If susan is curious then someone is both not brave and not generous and vice versa. If mary is both strong and kind then lucy is not patient. If someone is humble or wise then someone is not tall and vice versa. Everyone who is calm or not old is calm. If someone is either not brave or not tall then fred is not wise. Lucy is not happy. Someone is either quiet or wise. Someone is both not wise and old. Fred is both happy and rich. Someone is strong. Someone is both tall and not generous. Someone is either not quiet or not happy. Fred is not strong or not kind. | Mary is not rich. | contradiction | (![X]:((~rich(X)&~brave(X))<=>(calm(X)&brave(X))))&
(![X]:((brave(X)|creative(X))<=>~patient(X)))&
(![X]:(funny(X)=>(old(X)&wise(X))))&
(![X]:((~calm(X)<~>~old(X))<=>(old(X)&patient(X))))&
(((~humble(susan)<~>~rich(susan)))=>(~patient(susan)))&
(((~calm(susan)&~creative(susan)))<=>(?[X]:((~creative(X)|~generous(X)))))&
(![X]:((humble(X)|~humble(X))<=>~calm(X)))&
(![X]:((~quiet(X)|rich(X))<=>(~creative(X)|~calm(X))))&
(![X]:((~wise(X)&humble(X))<=>(~wise(X)|creative(X))))&
(((quiet(fred)|~tall(fred)))<=>((brave(paul)|~wise(paul))))&
(((kind(john)&quiet(john)))=>((~humble(susan)|~quiet(susan))))&
((curious(susan))<=>(?[X]:((~brave(X)&~generous(X)))))&
(((strong(mary)&kind(mary)))=>(~patient(lucy)))&
((?[X]:((humble(X)|wise(X))))<=>(?[X]:(~tall(X))))&
(![X]:((calm(X)|~old(X))=>calm(X)))&
((?[X]:((~brave(X)<~>~tall(X))))=>(~wise(fred)))&
(~happy(lucy))&
(?[X]:((quiet(X)<~>wise(X))))&
(?[X]:((~wise(X)&old(X))))&
((happy(fred)&rich(fred)))&
(?[X]:(strong(X)))&
(?[X]:((tall(X)&~generous(X))))&
(?[X]:((~quiet(X)<~>~happy(X))))&
((~strong(fred)|~kind(fred))) | ~rich(mary) | [
"p0",
"p1",
"p3",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1785072702762139814551576
% SZS output start Proof for 1785072702762139814551576
1. ! [X0] : ((~brave(X0) & ~rich(X0)) <=> (brave(X0) & calm(X0))) [input p0]
2. ! [X0] : ((creative(X0) | brave(X0)) <=> ~patient(X0)) [input p1]
4. ! [X0] : ((~calm(X0) <~> ~old(X0)) <=> (patient(X0) & old(X0))) [input p3]
7. ! [X0] : ((~humble(X0) | humble(X0)) <=> ~calm(X0)) [input p6]
15. ! [X0] : ((~old(X0) | calm(X0)) => calm(X0)) [input p14]
25. ~rich(mary) [input hypothesis]
33. ! [X0] : (calm(X0) | (old(X0) & ~calm(X0))) [ennf transformation 15]
35. ! [X0] : (((~brave(X0) & ~rich(X0)) | (~brave(X0) | ~calm(X0))) & ((brave(X0) & calm(X0)) | (brave(X0) | rich(X0)))) [nnf transformation 1]
36. ! [X0] : (((~brave(X0) & ~rich(X0)) | ~brave(X0) | ~calm(X0)) & ((brave(X0) & calm(X0)) | brave(X0) | rich(X0))) [flattening 35]
37. ! [X0] : (((creative(X0) | brave(X0)) | patient(X0)) & (~patient(X0) | (~creative(X0) & ~brave(X0)))) [nnf transformation 2]
38. ! [X0] : ((creative(X0) | brave(X0) | patient(X0)) & (~patient(X0) | (~creative(X0) & ~brave(X0)))) [flattening 37]
39. ! [X0] : ((((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | (~patient(X0) | ~old(X0))) & ((patient(X0) & old(X0)) | ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0))))) [nnf transformation 4]
40. ! [X0] : ((((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | ~patient(X0) | ~old(X0)) & ((patient(X0) & old(X0)) | ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0))))) [flattening 39]
47. ! [X0] : (((~humble(X0) | humble(X0)) | calm(X0)) & (~calm(X0) | (humble(X0) & ~humble(X0)))) [nnf transformation 7]
48. ! [X0] : ((~humble(X0) | humble(X0) | calm(X0)) & (~calm(X0) | (humble(X0) & ~humble(X0)))) [flattening 47]
76. brave(X0) | brave(X0) | rich(X0) [cnf transformation 36]
79. ~patient(X0) | ~brave(X0) [cnf transformation 38]
84. ~old(X0) | patient(X0) | calm(X0) [cnf transformation 40]
95. ~calm(X0) | ~humble(X0) [cnf transformation 48]
96. ~calm(X0) | humble(X0) [cnf transformation 48]
118. calm(X0) | old(X0) [cnf transformation 33]
132. ~rich(mary) [cnf transformation 25]
135. brave(X0) | rich(X0) [duplicate literal removal 76]
178. ~calm(X0) [subsumption resolution 95,96]
230. old(X0) [subsumption resolution 118,178]
270. patient(X0) | calm(X0) [resolution 84,230]
271. patient(X0) [subsumption resolution 270,178]
275. ~brave(X1) [resolution 271,79]
279. rich(X0) [resolution 275,135]
282. $false [resolution 279,132]
% SZS output end Proof for 1785072702762139814551576
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or not generous is not calm.
If fred is rich or not generous then mary is both patient and curious and vice versa.
Everyone who is both tall and brave is either not calm or not rich.
Everyone who is not generous is either wise or tall and vice versa.
Everyone who is either not curious or curious is brave.
If someone is generous or wise then someone is not creative.
If fred is both calm and not quiet then john is quiet and vice versa.
If john is not tall then someone is either curious or not calm and vice versa.
Everyone who is wise or not wise is both old and calm.
If someone is not creative or not tall then fred is both tall and strong and vice versa.
If john is happy then someone is either wise or old.
Everyone who is humble or kind is not patient or not wise and vice versa.
Everyone who is either not curious or humble is both curious and not kind and vice versa.
Everyone who is either not patient or not tall is brave or not quiet.
Everyone who is either not happy or old is not humble or curious and vice versa.
If mary is both brave and funny then lucy is either generous or strong and vice versa.
Alice is not tall.
Someone is either kind or not patient.
Someone is either not wise or strong.
Someone is both old and rich.
Someone is not happy or not kind.
Fred is either not curious or wise. | Fred is rich. | contradiction | (![X]:((~strong(X)|~generous(X))=>~calm(X)))&
(((rich(fred)|~generous(fred)))<=>((patient(mary)&curious(mary))))&
(![X]:((tall(X)&brave(X))=>(~calm(X)<~>~rich(X))))&
(![X]:(~generous(X)<=>(wise(X)<~>tall(X))))&
(![X]:((~curious(X)<~>curious(X))=>brave(X)))&
((?[X]:((generous(X)|wise(X))))=>(?[X]:(~creative(X))))&
(((calm(fred)&~quiet(fred)))<=>(quiet(john)))&
((~tall(john))<=>(?[X]:((curious(X)<~>~calm(X)))))&
(![X]:((wise(X)|~wise(X))=>(old(X)&calm(X))))&
((?[X]:((~creative(X)|~tall(X))))<=>((tall(fred)&strong(fred))))&
((happy(john))=>(?[X]:((wise(X)<~>old(X)))))&
(![X]:((humble(X)|kind(X))<=>(~patient(X)|~wise(X))))&
(![X]:((~curious(X)<~>humble(X))<=>(curious(X)&~kind(X))))&
(![X]:((~patient(X)<~>~tall(X))=>(brave(X)|~quiet(X))))&
(![X]:((~happy(X)<~>old(X))<=>(~humble(X)|curious(X))))&
(((brave(mary)&funny(mary)))<=>((generous(lucy)<~>strong(lucy))))&
(~tall(alice))&
(?[X]:((kind(X)<~>~patient(X))))&
(?[X]:((~wise(X)<~>strong(X))))&
(?[X]:((old(X)&rich(X))))&
(?[X]:((~happy(X)|~kind(X))))&
((~curious(fred)<~>wise(fred))) | rich(fred) | [
"p2",
"p4",
"p8",
"p9",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7829885126337224581376816
% SZS output start Proof for 7829885126337224581376816
3. ! [X0] : ((brave(X0) & tall(X0)) => (~calm(X0) <~> ~rich(X0))) [input p2]
5. ! [X0] : ((~curious(X0) <~> curious(X0)) => brave(X0)) [input p4]
9. ! [X0] : ((~wise(X0) | wise(X0)) => (calm(X0) & old(X0))) [input p8]
10. ? [X0] : (~tall(X0) | ~creative(X0)) <=> (strong(fred) & tall(fred)) [input p9]
17. ~tall(alice) [input p16]
23. rich(fred) [input hypothesis]
26. ! [X0] : ((~calm(X0) <~> ~rich(X0)) | (~brave(X0) | ~tall(X0))) [ennf transformation 3]
27. ! [X0] : ((~calm(X0) <~> ~rich(X0)) | ~brave(X0) | ~tall(X0)) [flattening 26]
28. ! [X0] : (brave(X0) | (~curious(X0) <=> curious(X0))) [ennf transformation 5]
30. ! [X0] : ((calm(X0) & old(X0)) | (wise(X0) & ~wise(X0))) [ennf transformation 9]
36. ! [X0] : (((rich(X0) | calm(X0)) & (~rich(X0) | ~calm(X0))) | ~brave(X0) | ~tall(X0)) [nnf transformation 27]
38. ! [X0] : (brave(X0) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0)))) [nnf transformation 28]
48. (? [X0] : (~tall(X0) | ~creative(X0)) | (~strong(fred) | ~tall(fred))) & ((strong(fred) & tall(fred)) | ! [X0] : (tall(X0) & creative(X0))) [nnf transformation 10]
49. (? [X0] : (~tall(X0) | ~creative(X0)) | ~strong(fred) | ~tall(fred)) & ((strong(fred) & tall(fred)) | ! [X0] : (tall(X0) & creative(X0))) [flattening 48]
50. (? [X0] : (~tall(X0) | ~creative(X0)) | ~strong(fred) | ~tall(fred)) & ((strong(fred) & tall(fred)) | ! [X1] : (tall(X1) & creative(X1))) [rectify 49]
51. ? [X0] : (~tall(X0) | ~creative(X0)) => (~tall(sK2) | ~creative(sK2)) [choice axiom]
52. ((~tall(sK2) | ~creative(sK2)) | ~strong(fred) | ~tall(fred)) & ((strong(fred) & tall(fred)) | ! [X1] : (tall(X1) & creative(X1))) [skolemisation 50,51]
83. ~brave(X0) | ~calm(X0) | ~rich(X0) | ~tall(X0) [cnf transformation 36]
89. brave(X0) | curious(X0) | curious(X0) [cnf transformation 38]
90. brave(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 38]
102. calm(X0) | ~wise(X0) [cnf transformation 30]
103. wise(X0) | calm(X0) [cnf transformation 30]
105. tall(fred) | tall(X1) [cnf transformation 52]
135. ~tall(alice) [cnf transformation 17]
145. rich(fred) [cnf transformation 23]
148. brave(X0) | curious(X0) [duplicate literal removal 89]
149. ~curious(X0) | brave(X0) [duplicate literal removal 90]
159. 3 <=> rich(fred) [avatar definition]
161. rich(fred) <- (3) [avatar component clause 159]
171. brave(X0) [subsumption resolution 148,149]
221. calm(X0) [subsumption resolution 102,103]
224. 16 <=> tall(fred) [avatar definition]
225. tall(fred) <- (16) [avatar component clause 224]
241. 20 <=> ! [X1] : tall(X1) [avatar definition]
242. tall(X1) <- (20) [avatar component clause 241]
248. 20 | 16 [avatar split clause 105,224,241]
321. 3 [avatar split clause 145,159]
362. $false <- (20) [resolution 242,135]
365. ~20 [avatar contradiction clause 362]
449. ~calm(X0) | ~rich(X0) | ~tall(X0) [resolution 83,171]
450. ~tall(X0) | ~rich(X0) [subsumption resolution 449,221]
485. ~rich(fred) <- (16) [resolution 450,225]
487. $false <- (3, 16) [subsumption resolution 485,161]
488. ~3 | ~16 [avatar contradiction clause 487]
489. $false [avatar sat refutation 248,321,365,488]
% SZS output end Proof for 7829885126337224581376816
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not generous is either not quiet or calm and vice versa.
If paul is not strong then someone is either curious or not generous.
If mary is rich or not strong then mary is generous and vice versa.
If someone is not humble or not creative then someone is not generous or rich and vice versa.
If someone is rich or strong then someone is either patient or tall.
Everyone who is both rich and happy is both not creative and not quiet and vice versa.
If someone is not rich then someone is both not wise and not calm and vice versa.
Everyone who is not creative or quiet is not funny or funny.
Everyone who is both creative and not creative is brave or not wise and vice versa.
Everyone who is either not calm or creative is funny and vice versa.
Everyone who is not wise or wise is humble or curious.
Everyone who is both quiet and not patient is strong and vice versa.
If someone is both not calm and not old then someone is curious and vice versa.
If alice is both funny and calm then someone is not calm.
Everyone who is not tall is either not curious or not creative and vice versa.
If john is both not funny and rich then mary is both not rich and not strong.
Lucy is creative.
Lucy is not patient or quiet.
Lucy is generous.
John is both not brave and not strong.
Mary is not patient or wise.
Paul is old.
Someone is not strong or wise.
Someone is both wise and kind. | Paul is not wise. | contradiction | (![X]:((humble(X)|~generous(X))<=>(~quiet(X)<~>calm(X))))&
((~strong(paul))=>(?[X]:((curious(X)<~>~generous(X)))))&
(((rich(mary)|~strong(mary)))<=>(generous(mary)))&
((?[X]:((~humble(X)|~creative(X))))<=>(?[X]:((~generous(X)|rich(X)))))&
((?[X]:((rich(X)|strong(X))))=>(?[X]:((patient(X)<~>tall(X)))))&
(![X]:((rich(X)&happy(X))<=>(~creative(X)&~quiet(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~wise(X)&~calm(X)))))&
(![X]:((~creative(X)|quiet(X))=>(~funny(X)|funny(X))))&
(![X]:((creative(X)&~creative(X))<=>(brave(X)|~wise(X))))&
(![X]:((~calm(X)<~>creative(X))<=>funny(X)))&
(![X]:((~wise(X)|wise(X))=>(humble(X)|curious(X))))&
(![X]:((quiet(X)&~patient(X))<=>strong(X)))&
((?[X]:((~calm(X)&~old(X))))<=>(?[X]:(curious(X))))&
(((funny(alice)&calm(alice)))=>(?[X]:(~calm(X))))&
(![X]:(~tall(X)<=>(~curious(X)<~>~creative(X))))&
(((~funny(john)&rich(john)))=>((~rich(mary)&~strong(mary))))&
(creative(lucy))&
((~patient(lucy)|quiet(lucy)))&
(generous(lucy))&
((~brave(john)&~strong(john)))&
((~patient(mary)|wise(mary)))&
(old(paul))&
(?[X]:((~strong(X)|wise(X))))&
(?[X]:((wise(X)&kind(X)))) | ~wise(paul) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8121920027898178863938904
% SZS output start Proof for 8121920027898178863938904
9. ! [X0] : ((~creative(X0) & creative(X0)) <=> (~wise(X0) | brave(X0))) [input p8]
25. ~wise(paul) [input hypothesis]
64. ! [X0] : (((~creative(X0) & creative(X0)) | (wise(X0) & ~brave(X0))) & ((~wise(X0) | brave(X0)) | (creative(X0) | ~creative(X0)))) [nnf transformation 9]
65. ! [X0] : (((~creative(X0) & creative(X0)) | (wise(X0) & ~brave(X0))) & (~wise(X0) | brave(X0) | creative(X0) | ~creative(X0))) [flattening 64]
111. creative(X0) | wise(X0) [cnf transformation 65]
113. ~creative(X0) | wise(X0) [cnf transformation 65]
142. ~wise(paul) [cnf transformation 25]
240. wise(X0) [subsumption resolution 111,113]
296. $false [subsumption resolution 142,240]
% SZS output end Proof for 8121920027898178863938904
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not rich or not strong then someone is generous or not funny and vice versa.
Everyone who is either brave or quiet is both not funny and not quiet.
Everyone who is not creative or not kind is either not creative or not brave and vice versa.
Everyone who is either not calm or not quiet is not wise or rich.
Everyone who is not generous or not wise is happy.
If someone is either wise or not tall then someone is either not calm or not quiet and vice versa.
Everyone who is both quiet and not calm is rich or not quiet and vice versa.
Everyone who is not tall is both not creative and not humble.
Everyone who is both patient and wise is generous or creative and vice versa.
If lucy is not kind or not funny then someone is either not calm or humble.
Everyone who is either old or happy is not old.
If someone is not tall or funny then someone is not generous.
If someone is either curious or not rich then someone is either old or humble and vice versa.
If someone is not kind or funny then paul is both generous and brave.
Everyone who is not quiet or not tall is either funny or old.
Everyone who is not wise is not strong or not humble and vice versa.
Someone is not old or not tall.
Someone is not patient or not strong.
Susan is quiet or not curious.
Paul is both not strong and brave.
Paul is funny or not rich.
John is either not patient or creative.
John is either calm or not wise. | Paul is creative. | contradiction | ((?[X]:((~rich(X)<~>~strong(X))))<=>(?[X]:((generous(X)|~funny(X)))))&
(![X]:((brave(X)<~>quiet(X))=>(~funny(X)&~quiet(X))))&
(![X]:((~creative(X)|~kind(X))<=>(~creative(X)<~>~brave(X))))&
(![X]:((~calm(X)<~>~quiet(X))=>(~wise(X)|rich(X))))&
(![X]:((~generous(X)|~wise(X))=>happy(X)))&
((?[X]:((wise(X)<~>~tall(X))))<=>(?[X]:((~calm(X)<~>~quiet(X)))))&
(![X]:((quiet(X)&~calm(X))<=>(rich(X)|~quiet(X))))&
(![X]:(~tall(X)=>(~creative(X)&~humble(X))))&
(![X]:((patient(X)&wise(X))<=>(generous(X)|creative(X))))&
(((~kind(lucy)|~funny(lucy)))=>(?[X]:((~calm(X)<~>humble(X)))))&
(![X]:((old(X)<~>happy(X))=>~old(X)))&
((?[X]:((~tall(X)|funny(X))))=>(?[X]:(~generous(X))))&
((?[X]:((curious(X)<~>~rich(X))))<=>(?[X]:((old(X)<~>humble(X)))))&
((?[X]:((~kind(X)|funny(X))))=>((generous(paul)&brave(paul))))&
(![X]:((~quiet(X)|~tall(X))=>(funny(X)<~>old(X))))&
(![X]:(~wise(X)<=>(~strong(X)|~humble(X))))&
(?[X]:((~old(X)|~tall(X))))&
(?[X]:((~patient(X)|~strong(X))))&
((quiet(susan)|~curious(susan)))&
((~strong(paul)&brave(paul)))&
((funny(paul)|~rich(paul)))&
((~patient(john)<~>creative(john)))&
((calm(john)<~>~wise(john))) | creative(paul) | [
"p8",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2610092434114007178501937
% SZS output start Proof for 2610092434114007178501937
9. ! [X0] : ((wise(X0) & patient(X0)) <=> (creative(X0) | generous(X0))) [input p8]
16. ! [X0] : (~wise(X0) <=> (~humble(X0) | ~strong(X0))) [input p15]
20. brave(paul) & ~strong(paul) [input p19]
24. creative(paul) [input hypothesis]
55. ! [X0] : (((wise(X0) & patient(X0)) | (~creative(X0) & ~generous(X0))) & ((creative(X0) | generous(X0)) | (~wise(X0) | ~patient(X0)))) [nnf transformation 9]
56. ! [X0] : (((wise(X0) & patient(X0)) | (~creative(X0) & ~generous(X0))) & (creative(X0) | generous(X0) | ~wise(X0) | ~patient(X0))) [flattening 55]
70. ! [X0] : ((~wise(X0) | (humble(X0) & strong(X0))) & ((~humble(X0) | ~strong(X0)) | wise(X0))) [nnf transformation 16]
71. ! [X0] : ((~wise(X0) | (humble(X0) & strong(X0))) & (~humble(X0) | ~strong(X0) | wise(X0))) [flattening 70]
117. ~creative(X0) | wise(X0) [cnf transformation 56]
143. ~wise(X0) | strong(X0) [cnf transformation 71]
148. ~strong(paul) [cnf transformation 20]
155. creative(paul) [cnf transformation 24]
368. wise(paul) [resolution 117,155]
369. strong(paul) [resolution 368,143]
370. $false [subsumption resolution 369,148]
% SZS output end Proof for 2610092434114007178501937
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and patient is not kind or patient.
Everyone who is generous or not generous is either not happy or kind.
Everyone who is both rich and brave is either creative or not curious and vice versa.
Everyone who is either not curious or brave is both brave and strong.
Everyone who is strong or rich is not brave.
Everyone who is either curious or not strong is either humble or not rich and vice versa.
Everyone who is both rich and old is either rich or strong and vice versa.
If lucy is either happy or kind then someone is both rich and not humble and vice versa.
If someone is both old and not funny then someone is tall or not strong.
Everyone who is either brave or not calm is not generous and vice versa.
If lucy is both not calm and not humble then fred is both not creative and strong.
If paul is old then fred is kind or not calm and vice versa.
If someone is not rich or funny then mary is either calm or not curious and vice versa.
If mary is strong or not happy then someone is either not curious or kind.
Everyone who is not calm or not happy is strong or wise.
Everyone who is not old or not wise is both not brave and not old and vice versa.
John is either not old or not humble.
Mary is both not patient and not happy.
Someone is tall.
John is generous.
Someone is strong.
Someone is either creative or wise.
John is brave. | John is humble. | contradiction | (![X]:((tall(X)&patient(X))=>(~kind(X)|patient(X))))&
(![X]:((generous(X)|~generous(X))=>(~happy(X)<~>kind(X))))&
(![X]:((rich(X)&brave(X))<=>(creative(X)<~>~curious(X))))&
(![X]:((~curious(X)<~>brave(X))=>(brave(X)&strong(X))))&
(![X]:((strong(X)|rich(X))=>~brave(X)))&
(![X]:((curious(X)<~>~strong(X))<=>(humble(X)<~>~rich(X))))&
(![X]:((rich(X)&old(X))<=>(rich(X)<~>strong(X))))&
(((happy(lucy)<~>kind(lucy)))<=>(?[X]:((rich(X)&~humble(X)))))&
((?[X]:((old(X)&~funny(X))))=>(?[X]:((tall(X)|~strong(X)))))&
(![X]:((brave(X)<~>~calm(X))<=>~generous(X)))&
(((~calm(lucy)&~humble(lucy)))=>((~creative(fred)&strong(fred))))&
((old(paul))<=>((kind(fred)|~calm(fred))))&
((?[X]:((~rich(X)|funny(X))))<=>((calm(mary)<~>~curious(mary))))&
(((strong(mary)|~happy(mary)))=>(?[X]:((~curious(X)<~>kind(X)))))&
(![X]:((~calm(X)|~happy(X))=>(strong(X)|wise(X))))&
(![X]:((~old(X)|~wise(X))<=>(~brave(X)&~old(X))))&
((~old(john)<~>~humble(john)))&
((~patient(mary)&~happy(mary)))&
(?[X]:(tall(X)))&
(generous(john))&
(?[X]:(strong(X)))&
(?[X]:((creative(X)<~>wise(X))))&
(brave(john)) | humble(john) | [
"p15",
"p16",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8739331894064893893903566
% SZS output start Proof for 8739331894064893893903566
16. ! [X0] : ((~wise(X0) | ~old(X0)) <=> (~old(X0) & ~brave(X0))) [input p15]
17. ~old(john) <~> ~humble(john) [input p16]
23. brave(john) [input p22]
24. humble(john) [input hypothesis]
61. ! [X0] : (((~wise(X0) | ~old(X0)) | (old(X0) | brave(X0))) & ((~old(X0) & ~brave(X0)) | (wise(X0) & old(X0)))) [nnf transformation 16]
62. ! [X0] : ((~wise(X0) | ~old(X0) | old(X0) | brave(X0)) & ((~old(X0) & ~brave(X0)) | (wise(X0) & old(X0)))) [flattening 61]
63. (humble(john) | old(john)) & (~humble(john) | ~old(john)) [nnf transformation 17]
130. ~brave(X0) | old(X0) [cnf transformation 62]
135. ~humble(john) | ~old(john) [cnf transformation 63]
144. brave(john) [cnf transformation 23]
145. humble(john) [cnf transformation 24]
257. 23 <=> old(john) [avatar definition]
258. ~old(john) <- (~23) [avatar component clause 257]
261. 24 <=> humble(john) [avatar definition]
265. ~23 | ~24 [avatar split clause 135,261,257]
277. 24 [avatar split clause 145,261]
280. old(john) [resolution 130,144]
281. $false <- (~23) [subsumption resolution 280,258]
282. 23 [avatar contradiction clause 281]
283. $false [avatar sat refutation 265,277,282]
% SZS output end Proof for 8739331894064893893903566
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is not generous or quiet.
Everyone who is both not wise and funny is either strong or not tall and vice versa.
Everyone who is old is both not strong and brave and vice versa.
Everyone who is either calm or not rich is either kind or not calm and vice versa.
If susan is not generous or brave then mary is happy or not old.
Everyone who is not generous or generous is either not generous or not old and vice versa.
Everyone who is either not wise or brave is not creative.
Everyone who is rich or humble is both not funny and not creative.
If fred is not patient then fred is not brave or not wise and vice versa.
Everyone who is either kind or humble is kind or not old.
Everyone who is not curious is tall.
If someone is either not quiet or quiet then someone is not creative and vice versa.
Everyone who is not strong is either not rich or kind and vice versa.
If someone is not curious then lucy is both not patient and not brave and vice versa.
Everyone who is both patient and not calm is not patient.
If someone is both quiet and calm then someone is brave or old.
Susan is humble or not creative.
Lucy is either calm or not creative.
Someone is not brave.
John is either not old or tall.
Alice is either not patient or not wise.
Mary is both not funny and brave.
Paul is either not tall or quiet. | John is strong. | contradiction | (![X]:(brave(X)=>(~generous(X)|quiet(X))))&
(![X]:((~wise(X)&funny(X))<=>(strong(X)<~>~tall(X))))&
(![X]:(old(X)<=>(~strong(X)&brave(X))))&
(![X]:((calm(X)<~>~rich(X))<=>(kind(X)<~>~calm(X))))&
(((~generous(susan)|brave(susan)))=>((happy(mary)|~old(mary))))&
(![X]:((~generous(X)|generous(X))<=>(~generous(X)<~>~old(X))))&
(![X]:((~wise(X)<~>brave(X))=>~creative(X)))&
(![X]:((rich(X)|humble(X))=>(~funny(X)&~creative(X))))&
((~patient(fred))<=>((~brave(fred)|~wise(fred))))&
(![X]:((kind(X)<~>humble(X))=>(kind(X)|~old(X))))&
(![X]:(~curious(X)=>tall(X)))&
((?[X]:((~quiet(X)<~>quiet(X))))<=>(?[X]:(~creative(X))))&
(![X]:(~strong(X)<=>(~rich(X)<~>kind(X))))&
((?[X]:(~curious(X)))<=>((~patient(lucy)&~brave(lucy))))&
(![X]:((patient(X)&~calm(X))=>~patient(X)))&
((?[X]:((quiet(X)&calm(X))))=>(?[X]:((brave(X)|old(X)))))&
((humble(susan)|~creative(susan)))&
((calm(lucy)<~>~creative(lucy)))&
(?[X]:(~brave(X)))&
((~old(john)<~>tall(john)))&
((~patient(alice)<~>~wise(alice)))&
((~funny(mary)&brave(mary)))&
((~tall(paul)<~>quiet(paul))) | strong(john) | [
"p3",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 620065392442297393945759
% SZS output start Proof for 620065392442297393945759
4. ! [X0] : ((calm(X0) <~> ~rich(X0)) <=> (kind(X0) <~> ~calm(X0))) [input p3]
13. ! [X0] : (~strong(X0) <=> (~rich(X0) <~> kind(X0))) [input p12]
24. strong(john) [input hypothesis]
42. ! [X0] : ((((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | ((kind(X0) | calm(X0)) & (~calm(X0) | ~kind(X0)))) & (((calm(X0) | ~kind(X0)) & (~calm(X0) | kind(X0))) | ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0))))) [nnf transformation 4]
54. ! [X0] : ((~strong(X0) | ((~rich(X0) | ~kind(X0)) & (kind(X0) | rich(X0)))) & (((~kind(X0) | rich(X0)) & (kind(X0) | ~rich(X0))) | strong(X0))) [nnf transformation 13]
79. ~calm(X0) | kind(X0) | ~rich(X0) | ~calm(X0) [cnf transformation 42]
82. calm(X0) | ~kind(X0) | calm(X0) | rich(X0) [cnf transformation 42]
84. ~rich(X0) | calm(X0) | kind(X0) | calm(X0) [cnf transformation 42]
85. rich(X0) | ~calm(X0) | ~calm(X0) | ~kind(X0) [cnf transformation 42]
111. ~strong(X0) | kind(X0) | rich(X0) [cnf transformation 54]
112. ~strong(X0) | ~rich(X0) | ~kind(X0) [cnf transformation 54]
130. strong(john) [cnf transformation 24]
139. ~calm(X0) | kind(X0) | ~rich(X0) [duplicate literal removal 79]
140. calm(X0) | ~kind(X0) | rich(X0) [duplicate literal removal 82]
141. ~rich(X0) | calm(X0) | kind(X0) [duplicate literal removal 84]
142. rich(X0) | ~calm(X0) | ~kind(X0) [duplicate literal removal 85]
143. ~kind(X0) | rich(X0) [subsumption resolution 140,142]
144. kind(X0) | ~rich(X0) [subsumption resolution 139,141]
172. ~strong(X0) | ~kind(X0) [subsumption resolution 112,143]
173. ~strong(X0) | kind(X0) [subsumption resolution 111,144]
174. ~strong(X0) [subsumption resolution 173,172]
243. $false [subsumption resolution 130,174]
% SZS output end Proof for 620065392442297393945759
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not wise and strong then fred is both not generous and calm.
Everyone who is not quiet is either not humble or not generous.
Everyone who is either not old or not quiet is both quiet and patient.
Everyone who is rich or not humble is both wise and old and vice versa.
If mary is either strong or happy then someone is both not rich and curious.
If someone is old then someone is quiet.
Everyone who is both not humble and curious is both not curious and wise and vice versa.
Everyone who is both not generous and not brave is either brave or not rich.
Everyone who is either humble or not tall is both patient and old.
If lucy is not tall or funny then someone is happy.
Everyone who is rich or not strong is tall or creative and vice versa.
Everyone who is not quiet or not generous is not tall.
If someone is wise then paul is brave.
If someone is not wise then someone is rich and vice versa.
If susan is not wise then fred is not wise or calm.
Everyone who is not quiet or not generous is not old or quiet.
Someone is either not happy or not patient.
Someone is rich.
Paul is not rich or not happy.
Someone is both funny and not curious.
Someone is not tall.
Mary is not creative.
John is either not curious or brave.
Mary is either humble or not funny. | Susan is humble. | entailment | ((?[X]:((~wise(X)&strong(X))))=>((~generous(fred)&calm(fred))))&
(![X]:(~quiet(X)=>(~humble(X)<~>~generous(X))))&
(![X]:((~old(X)<~>~quiet(X))=>(quiet(X)&patient(X))))&
(![X]:((rich(X)|~humble(X))<=>(wise(X)&old(X))))&
(((strong(mary)<~>happy(mary)))=>(?[X]:((~rich(X)&curious(X)))))&
((?[X]:(old(X)))=>(?[X]:(quiet(X))))&
(![X]:((~humble(X)&curious(X))<=>(~curious(X)&wise(X))))&
(![X]:((~generous(X)&~brave(X))=>(brave(X)<~>~rich(X))))&
(![X]:((humble(X)<~>~tall(X))=>(patient(X)&old(X))))&
(((~tall(lucy)|funny(lucy)))=>(?[X]:(happy(X))))&
(![X]:((rich(X)|~strong(X))<=>(tall(X)|creative(X))))&
(![X]:((~quiet(X)|~generous(X))=>~tall(X)))&
((?[X]:(wise(X)))=>(brave(paul)))&
((?[X]:(~wise(X)))<=>(?[X]:(rich(X))))&
((~wise(susan))=>((~wise(fred)|calm(fred))))&
(![X]:((~quiet(X)|~generous(X))=>(~old(X)|quiet(X))))&
(?[X]:((~happy(X)<~>~patient(X))))&
(?[X]:(rich(X)))&
((~rich(paul)|~happy(paul)))&
(?[X]:((funny(X)&~curious(X))))&
(?[X]:(~tall(X)))&
(~creative(mary))&
((~curious(john)<~>brave(john)))&
((humble(mary)<~>~funny(mary))) | humble(susan) | [
"p3",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 7169348257576412946712972
% SZS output start Proof for 7169348257576412946712972
4. ! [X0] : ((~humble(X0) | rich(X0)) <=> (old(X0) & wise(X0))) [input p3]
7. ! [X0] : ((curious(X0) & ~humble(X0)) <=> (wise(X0) & ~curious(X0))) [input p6]
25. ~humble(susan) [input hypothesis]
45. ! [X0] : (((~humble(X0) | rich(X0)) | (~old(X0) | ~wise(X0))) & ((old(X0) & wise(X0)) | (humble(X0) & ~rich(X0)))) [nnf transformation 4]
46. ! [X0] : ((~humble(X0) | rich(X0) | ~old(X0) | ~wise(X0)) & ((old(X0) & wise(X0)) | (humble(X0) & ~rich(X0)))) [flattening 45]
53. ! [X0] : (((curious(X0) & ~humble(X0)) | (~wise(X0) | curious(X0))) & ((wise(X0) & ~curious(X0)) | (~curious(X0) | humble(X0)))) [nnf transformation 7]
54. ! [X0] : (((curious(X0) & ~humble(X0)) | ~wise(X0) | curious(X0)) & ((wise(X0) & ~curious(X0)) | ~curious(X0) | humble(X0))) [flattening 53]
85. humble(X0) | wise(X0) [cnf transformation 46]
94. ~curious(X0) | ~curious(X0) | humble(X0) [cnf transformation 54]
97. curious(X0) | ~wise(X0) | curious(X0) [cnf transformation 54]
129. ~humble(susan) [cnf transformation 25]
132. ~curious(X0) | humble(X0) [duplicate literal removal 94]
133. ~wise(X0) | curious(X0) [duplicate literal removal 97]
257. wise(susan) [resolution 85,129]
266. curious(susan) [resolution 133,257]
275. humble(susan) [resolution 266,132]
276. $false [subsumption resolution 275,129]
% SZS output end Proof for 7169348257576412946712972
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not kind or not curious then someone is generous.
If someone is either not funny or not calm then someone is either not creative or generous and vice versa.
Everyone who is both happy and calm is not humble.
If someone is old then someone is wise and vice versa.
If lucy is either curious or not kind then paul is quiet or not generous and vice versa.
If fred is not quiet or not brave then someone is both happy and not humble and vice versa.
Everyone who is either not kind or wise is both not curious and old and vice versa.
Everyone who is not brave or not funny is brave.
If someone is not kind or humble then paul is creative.
If someone is either kind or not funny then john is both kind and not calm and vice versa.
If someone is either not brave or not creative then mary is not humble.
Everyone who is not quiet or patient is creative.
If fred is quiet then fred is not humble or wise.
If someone is not kind or not curious then someone is either not kind or not tall and vice versa.
Everyone who is either not happy or not curious is both tall and happy and vice versa.
If someone is either not happy or patient then someone is generous or old and vice versa.
Someone is not calm.
Someone is not patient or not old.
Fred is either not wise or not humble.
Mary is wise or old.
Susan is generous or rich.
Mary is not rich or not wise.
Mary is generous or wise. | Mary is not brave. | contradiction | ((?[X]:((~kind(X)<~>~curious(X))))=>(?[X]:(generous(X))))&
((?[X]:((~funny(X)<~>~calm(X))))<=>(?[X]:((~creative(X)<~>generous(X)))))&
(![X]:((happy(X)&calm(X))=>~humble(X)))&
((?[X]:(old(X)))<=>(?[X]:(wise(X))))&
(((curious(lucy)<~>~kind(lucy)))<=>((quiet(paul)|~generous(paul))))&
(((~quiet(fred)|~brave(fred)))<=>(?[X]:((happy(X)&~humble(X)))))&
(![X]:((~kind(X)<~>wise(X))<=>(~curious(X)&old(X))))&
(![X]:((~brave(X)|~funny(X))=>brave(X)))&
((?[X]:((~kind(X)|humble(X))))=>(creative(paul)))&
((?[X]:((kind(X)<~>~funny(X))))<=>((kind(john)&~calm(john))))&
((?[X]:((~brave(X)<~>~creative(X))))=>(~humble(mary)))&
(![X]:((~quiet(X)|patient(X))=>creative(X)))&
((quiet(fred))=>((~humble(fred)|wise(fred))))&
((?[X]:((~kind(X)|~curious(X))))<=>(?[X]:((~kind(X)<~>~tall(X)))))&
(![X]:((~happy(X)<~>~curious(X))<=>(tall(X)&happy(X))))&
((?[X]:((~happy(X)<~>patient(X))))<=>(?[X]:((generous(X)|old(X)))))&
(?[X]:(~calm(X)))&
(?[X]:((~patient(X)|~old(X))))&
((~wise(fred)<~>~humble(fred)))&
((wise(mary)|old(mary)))&
((generous(susan)|rich(susan)))&
((~rich(mary)|~wise(mary)))&
((generous(mary)|wise(mary))) | ~brave(mary) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 7560031456552166091173609
% SZS output start Proof for 7560031456552166091173609
8. ! [X0] : ((~funny(X0) | ~brave(X0)) => brave(X0)) [input p7]
24. ~brave(mary) [input hypothesis]
33. ! [X0] : (brave(X0) | (funny(X0) & brave(X0))) [ennf transformation 8]
115. brave(X0) | brave(X0) [cnf transformation 33]
156. ~brave(mary) [cnf transformation 24]
159. brave(X0) [duplicate literal removal 115]
429. $false [subsumption resolution 156,159]
% SZS output end Proof for 7560031456552166091173609
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or brave is either not generous or rich.
Everyone who is both brave and not humble is both not rich and kind.
Everyone who is either not strong or humble is brave or not kind.
Everyone who is not strong is not creative.
Everyone who is either patient or brave is either patient or not kind and vice versa.
If mary is generous then someone is tall or strong.
Everyone who is not calm is not humble and vice versa.
If alice is not generous or not happy then someone is old.
If fred is curious or not humble then john is either strong or not generous and vice versa.
Everyone who is both happy and humble is both calm and not curious and vice versa.
Everyone who is brave or kind is either not funny or generous.
If someone is both not humble and humble then someone is humble or not tall and vice versa.
If someone is both not quiet and curious then someone is either calm or quiet and vice versa.
Everyone who is both old and curious is not brave or patient and vice versa.
If john is strong then someone is creative or not quiet and vice versa.
Everyone who is either not curious or not wise is not generous and vice versa.
Someone is both quiet and kind.
Mary is either creative or brave.
Someone is either not tall or not quiet.
Someone is both not patient and not funny.
Someone is either not wise or generous. | John is kind. | entailment | (![X]:((happy(X)|brave(X))=>(~generous(X)<~>rich(X))))&
(![X]:((brave(X)&~humble(X))=>(~rich(X)&kind(X))))&
(![X]:((~strong(X)<~>humble(X))=>(brave(X)|~kind(X))))&
(![X]:(~strong(X)=>~creative(X)))&
(![X]:((patient(X)<~>brave(X))<=>(patient(X)<~>~kind(X))))&
((generous(mary))=>(?[X]:((tall(X)|strong(X)))))&
(![X]:(~calm(X)<=>~humble(X)))&
(((~generous(alice)|~happy(alice)))=>(?[X]:(old(X))))&
(((curious(fred)|~humble(fred)))<=>((strong(john)<~>~generous(john))))&
(![X]:((happy(X)&humble(X))<=>(calm(X)&~curious(X))))&
(![X]:((brave(X)|kind(X))=>(~funny(X)<~>generous(X))))&
((?[X]:((~humble(X)&humble(X))))<=>(?[X]:((humble(X)|~tall(X)))))&
((?[X]:((~quiet(X)&curious(X))))<=>(?[X]:((calm(X)<~>quiet(X)))))&
(![X]:((old(X)&curious(X))<=>(~brave(X)|patient(X))))&
((strong(john))<=>(?[X]:((creative(X)|~quiet(X)))))&
(![X]:((~curious(X)<~>~wise(X))<=>~generous(X)))&
(?[X]:((quiet(X)&kind(X))))&
((creative(mary)<~>brave(mary)))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(?[X]:((~patient(X)&~funny(X))))&
(?[X]:((~wise(X)<~>generous(X)))) | kind(john) | [
"p0",
"p1",
"p4",
"p6",
"p8",
"p11",
"p12",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5968274732170402316678718
% SZS output start Proof for 5968274732170402316678718
1. ! [X0] : ((brave(X0) | happy(X0)) => (~generous(X0) <~> rich(X0))) [input p0]
2. ! [X0] : ((~humble(X0) & brave(X0)) => (kind(X0) & ~rich(X0))) [input p1]
5. ! [X0] : ((patient(X0) <~> brave(X0)) <=> (patient(X0) <~> ~kind(X0))) [input p4]
7. ! [X0] : (~calm(X0) <=> ~humble(X0)) [input p6]
9. (~humble(fred) | curious(fred)) <=> (strong(john) <~> ~generous(john)) [input p8]
12. ? [X0] : (humble(X0) & ~humble(X0)) <=> ? [X0] : (~tall(X0) | humble(X0)) [input p11]
13. ? [X0] : (curious(X0) & ~quiet(X0)) <=> ? [X0] : (calm(X0) <~> quiet(X0)) [input p12]
15. strong(john) <=> ? [X0] : (~quiet(X0) | creative(X0)) [input p14]
17. ? [X0] : (kind(X0) & quiet(X0)) [input p16]
22. ~kind(john) [input hypothesis]
23. ? [X0] : (humble(X0) & ~humble(X0)) <=> ? [X1] : (~tall(X1) | humble(X1)) [rectify 12]
24. ? [X0] : (curious(X0) & ~quiet(X0)) <=> ? [X1] : (calm(X1) <~> quiet(X1)) [rectify 13]
25. ! [X0] : ((~generous(X0) <~> rich(X0)) | (~brave(X0) & ~happy(X0))) [ennf transformation 1]
26. ! [X0] : ((kind(X0) & ~rich(X0)) | (humble(X0) | ~brave(X0))) [ennf transformation 2]
27. ! [X0] : ((kind(X0) & ~rich(X0)) | humble(X0) | ~brave(X0)) [flattening 26]
34. ! [X0] : (((~rich(X0) | generous(X0)) & (rich(X0) | ~generous(X0))) | (~brave(X0) & ~happy(X0))) [nnf transformation 25]
36. ! [X0] : ((((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0))))) [nnf transformation 5]
39. ! [X0] : ((~calm(X0) | humble(X0)) & (~humble(X0) | calm(X0))) [nnf transformation 7]
42. ((~humble(fred) | curious(fred)) | ((strong(john) | generous(john)) & (~generous(john) | ~strong(john)))) & (((generous(john) | ~strong(john)) & (~generous(john) | strong(john))) | (humble(fred) & ~curious(fred))) [nnf transformation 9]
43. (~humble(fred) | curious(fred) | ((strong(john) | generous(john)) & (~generous(john) | ~strong(john)))) & (((generous(john) | ~strong(john)) & (~generous(john) | strong(john))) | (humble(fred) & ~curious(fred))) [flattening 42]
47. (? [X0] : (humble(X0) & ~humble(X0)) | ! [X1] : (tall(X1) & ~humble(X1))) & (? [X1] : (~tall(X1) | humble(X1)) | ! [X0] : (~humble(X0) | humble(X0))) [nnf transformation 23]
48. (? [X0] : (humble(X0) & ~humble(X0)) | ! [X1] : (tall(X1) & ~humble(X1))) & (? [X2] : (~tall(X2) | humble(X2)) | ! [X3] : (~humble(X3) | humble(X3))) [rectify 47]
49. ? [X0] : (humble(X0) & ~humble(X0)) => (humble(sK2) & ~humble(sK2)) [choice axiom]
50. ? [X2] : (~tall(X2) | humble(X2)) => (~tall(sK3) | humble(sK3)) [choice axiom]
51. ((humble(sK2) & ~humble(sK2)) | ! [X1] : (tall(X1) & ~humble(X1))) & ((~tall(sK3) | humble(sK3)) | ! [X3] : (~humble(X3) | humble(X3))) [skolemisation 48,50,49]
52. (? [X0] : (curious(X0) & ~quiet(X0)) | ! [X1] : ((calm(X1) | ~quiet(X1)) & (quiet(X1) | ~calm(X1)))) & (? [X1] : ((~quiet(X1) | ~calm(X1)) & (quiet(X1) | calm(X1))) | ! [X0] : (~curious(X0) | quiet(X0))) [nnf transformation 24]
53. (? [X0] : (curious(X0) & ~quiet(X0)) | ! [X1] : ((calm(X1) | ~quiet(X1)) & (quiet(X1) | ~calm(X1)))) & (? [X2] : ((~quiet(X2) | ~calm(X2)) & (quiet(X2) | calm(X2))) | ! [X3] : (~curious(X3) | quiet(X3))) [rectify 52]
54. ? [X0] : (curious(X0) & ~quiet(X0)) => (curious(sK4) & ~quiet(sK4)) [choice axiom]
55. ? [X2] : ((~quiet(X2) | ~calm(X2)) & (quiet(X2) | calm(X2))) => ((~quiet(sK5) | ~calm(sK5)) & (quiet(sK5) | calm(sK5))) [choice axiom]
56. ((curious(sK4) & ~quiet(sK4)) | ! [X1] : ((calm(X1) | ~quiet(X1)) & (quiet(X1) | ~calm(X1)))) & (((~quiet(sK5) | ~calm(sK5)) & (quiet(sK5) | calm(sK5))) | ! [X3] : (~curious(X3) | quiet(X3))) [skolemisation 53,55,54]
59. (strong(john) | ! [X0] : (quiet(X0) & ~creative(X0))) & (? [X0] : (~quiet(X0) | creative(X0)) | ~strong(john)) [nnf transformation 15]
60. (strong(john) | ! [X0] : (quiet(X0) & ~creative(X0))) & (? [X1] : (~quiet(X1) | creative(X1)) | ~strong(john)) [rectify 59]
61. ? [X1] : (~quiet(X1) | creative(X1)) => (~quiet(sK6) | creative(sK6)) [choice axiom]
62. (strong(john) | ! [X0] : (quiet(X0) & ~creative(X0))) & ((~quiet(sK6) | creative(sK6)) | ~strong(john)) [skolemisation 60,61]
64. ? [X0] : (kind(X0) & quiet(X0)) => (kind(sK7) & quiet(sK7)) [choice axiom]
65. kind(sK7) & quiet(sK7) [skolemisation 17,64]
76. ~generous(X0) | rich(X0) | ~brave(X0) [cnf transformation 34]
79. ~rich(X0) | humble(X0) | ~brave(X0) [cnf transformation 27]
86. kind(X0) | ~patient(X0) | brave(X0) | ~patient(X0) [cnf transformation 36]
89. brave(X0) | patient(X0) | patient(X0) | kind(X0) [cnf transformation 36]
94. ~calm(X0) | humble(X0) [cnf transformation 39]
100. generous(john) | ~strong(john) | humble(fred) [cnf transformation 43]
112. ~humble(sK2) | ~humble(X1) [cnf transformation 51]
114. humble(sK2) | ~humble(X1) [cnf transformation 51]
119. ~quiet(sK4) | calm(X1) | ~quiet(X1) [cnf transformation 56]
129. strong(john) | quiet(X0) [cnf transformation 62]
134. quiet(sK7) [cnf transformation 65]
144. ~kind(john) [cnf transformation 22]
146. kind(X0) | ~patient(X0) | brave(X0) [duplicate literal removal 86]
147. brave(X0) | patient(X0) | kind(X0) [duplicate literal removal 89]
149. kind(X0) | brave(X0) [subsumption resolution 146,147]
179. 7 <=> generous(john) [avatar definition]
181. generous(john) <- (7) [avatar component clause 179]
183. 8 <=> strong(john) [avatar definition]
191. 10 <=> humble(fred) [avatar definition]
192. humble(fred) <- (10) [avatar component clause 191]
196. 10 | ~8 | 7 [avatar split clause 100,179,183,191]
204. 12 <=> humble(sK2) [avatar definition]
209. 13 <=> ! [X1] : ~humble(X1) [avatar definition]
210. ~humble(X1) <- (13) [avatar component clause 209]
211. 13 | 12 [avatar split clause 114,204,209]
213. 13 | ~12 [avatar split clause 112,204,209]
215. 14 <=> ! [X1] : (calm(X1) | ~quiet(X1)) [avatar definition]
216. ~quiet(X1) | calm(X1) <- (14) [avatar component clause 215]
227. 17 <=> quiet(sK4) [avatar definition]
229. ~quiet(sK4) <- (~17) [avatar component clause 227]
230. 14 | ~17 [avatar split clause 119,227,215]
246. 21 <=> ! [X0] : quiet(X0) [avatar definition]
247. quiet(X0) <- (21) [avatar component clause 246]
248. 21 | 8 [avatar split clause 129,183,246]
293. brave(john) [resolution 149,144]
301. calm(sK7) <- (14) [resolution 216,134]
308. 32 <=> rich(john) [avatar definition]
310. rich(john) <- (32) [avatar component clause 308]
313. humble(sK7) <- (14) [resolution 301,94]
314. $false <- (13, 14) [subsumption resolution 313,210]
315. ~13 | ~14 [avatar contradiction clause 314]
316. rich(john) | ~brave(john) <- (7) [resolution 76,181]
317. rich(john) <- (7) [subsumption resolution 316,293]
318. 32 | ~7 [avatar split clause 317,179,308]
319. $false <- (10, 13) [subsumption resolution 192,210]
320. ~10 | ~13 [avatar contradiction clause 319]
322. $false <- (~17, 21) [resolution 247,229]
327. 17 | ~21 [avatar contradiction clause 322]
334. humble(john) | ~brave(john) <- (32) [resolution 79,310]
335. ~brave(john) <- (13, 32) [subsumption resolution 334,210]
336. $false <- (13, 32) [subsumption resolution 335,293]
337. ~13 | ~32 [avatar contradiction clause 336]
338. $false [avatar sat refutation 196,211,213,230,248,315,318,320,327,337]
% SZS output end Proof for 5968274732170402316678718
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not happy or happy then lucy is either not humble or not wise.
Everyone who is either rich or not kind is both rich and wise.
Everyone who is wise is tall and vice versa.
If someone is either not old or curious then alice is either not rich or quiet.
If someone is either not old or quiet then someone is not happy or not creative and vice versa.
If lucy is either quiet or not humble then someone is both tall and strong.
Everyone who is either old or calm is both old and kind.
Everyone who is old or not quiet is either not strong or tall.
Everyone who is not creative or generous is either brave or happy and vice versa.
Everyone who is both not calm and wise is quiet or not quiet.
Everyone who is not happy or strong is both not funny and not kind.
Everyone who is either old or not strong is not calm.
Everyone who is curious is both patient and not curious and vice versa.
If mary is both not creative and tall then someone is both happy and quiet.
If lucy is both not old and strong then someone is both not old and patient.
Everyone who is not strong is not curious.
Someone is brave or quiet.
Someone is not curious or wise.
Someone is creative or tall.
Paul is wise or quiet.
Mary is not wise.
Someone is both not curious and not patient.
Someone is both old and quiet.
Mary is either kind or not funny. | Lucy is not patient. | entailment | (((~happy(susan)|happy(susan)))=>((~humble(lucy)<~>~wise(lucy))))&
(![X]:((rich(X)<~>~kind(X))=>(rich(X)&wise(X))))&
(![X]:(wise(X)<=>tall(X)))&
((?[X]:((~old(X)<~>curious(X))))=>((~rich(alice)<~>quiet(alice))))&
((?[X]:((~old(X)<~>quiet(X))))<=>(?[X]:((~happy(X)|~creative(X)))))&
(((quiet(lucy)<~>~humble(lucy)))=>(?[X]:((tall(X)&strong(X)))))&
(![X]:((old(X)<~>calm(X))=>(old(X)&kind(X))))&
(![X]:((old(X)|~quiet(X))=>(~strong(X)<~>tall(X))))&
(![X]:((~creative(X)|generous(X))<=>(brave(X)<~>happy(X))))&
(![X]:((~calm(X)&wise(X))=>(quiet(X)|~quiet(X))))&
(![X]:((~happy(X)|strong(X))=>(~funny(X)&~kind(X))))&
(![X]:((old(X)<~>~strong(X))=>~calm(X)))&
(![X]:(curious(X)<=>(patient(X)&~curious(X))))&
(((~creative(mary)&tall(mary)))=>(?[X]:((happy(X)&quiet(X)))))&
(((~old(lucy)&strong(lucy)))=>(?[X]:((~old(X)&patient(X)))))&
(![X]:(~strong(X)=>~curious(X)))&
(?[X]:((brave(X)|quiet(X))))&
(?[X]:((~curious(X)|wise(X))))&
(?[X]:((creative(X)|tall(X))))&
((wise(paul)|quiet(paul)))&
(~wise(mary))&
(?[X]:((~curious(X)&~patient(X))))&
(?[X]:((old(X)&quiet(X))))&
((kind(mary)<~>~funny(mary))) | ~patient(lucy) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 176259438936523370656733
% SZS output start Proof for 176259438936523370656733
13. ! [X0] : (curious(X0) <=> (~curious(X0) & patient(X0))) [input p12]
25. patient(lucy) [input hypothesis]
59. ! [X0] : ((curious(X0) | (curious(X0) | ~patient(X0))) & ((~curious(X0) & patient(X0)) | ~curious(X0))) [nnf transformation 13]
60. ! [X0] : ((curious(X0) | curious(X0) | ~patient(X0)) & ((~curious(X0) & patient(X0)) | ~curious(X0))) [flattening 59]
122. ~curious(X0) | ~curious(X0) [cnf transformation 60]
123. curious(X0) | curious(X0) | ~patient(X0) [cnf transformation 60]
140. patient(lucy) [cnf transformation 25]
141. ~curious(X0) [duplicate literal removal 122]
142. ~patient(X0) | curious(X0) [duplicate literal removal 123]
305. curious(lucy) [resolution 142,140]
306. $false [subsumption resolution 305,141]
% SZS output end Proof for 176259438936523370656733
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either humble or quiet then someone is not kind.
Everyone who is both not wise and not funny is not wise.
If someone is either not tall or not kind then someone is either humble or not kind and vice versa.
If someone is both not brave and not generous then paul is brave or not strong.
Everyone who is strong or creative is either patient or not brave.
If paul is either not happy or not rich then paul is either creative or humble and vice versa.
Everyone who is either not wise or wise is both not happy and rich and vice versa.
If someone is either calm or not funny then john is not humble or not tall and vice versa.
Everyone who is not kind or quiet is both strong and patient and vice versa.
Everyone who is both funny and calm is tall or not funny.
Everyone who is not kind or creative is both wise and curious.
If lucy is happy then john is tall and vice versa.
If susan is not wise or patient then lucy is not tall and vice versa.
Everyone who is not rich or patient is both not generous and not tall and vice versa.
If mary is both not curious and not strong then someone is both not calm and tall and vice versa.
Everyone who is happy is either rich or wise.
Fred is quiet.
Lucy is both funny and wise.
Paul is either generous or not funny.
Someone is not quiet or not curious.
Someone is either not kind or not old.
Paul is not rich or strong.
Someone is not happy or not tall. | Lucy is not wise. | contradiction | ((?[X]:((humble(X)<~>quiet(X))))=>(?[X]:(~kind(X))))&
(![X]:((~wise(X)&~funny(X))=>~wise(X)))&
((?[X]:((~tall(X)<~>~kind(X))))<=>(?[X]:((humble(X)<~>~kind(X)))))&
((?[X]:((~brave(X)&~generous(X))))=>((brave(paul)|~strong(paul))))&
(![X]:((strong(X)|creative(X))=>(patient(X)<~>~brave(X))))&
(((~happy(paul)<~>~rich(paul)))<=>((creative(paul)<~>humble(paul))))&
(![X]:((~wise(X)<~>wise(X))<=>(~happy(X)&rich(X))))&
((?[X]:((calm(X)<~>~funny(X))))<=>((~humble(john)|~tall(john))))&
(![X]:((~kind(X)|quiet(X))<=>(strong(X)&patient(X))))&
(![X]:((funny(X)&calm(X))=>(tall(X)|~funny(X))))&
(![X]:((~kind(X)|creative(X))=>(wise(X)&curious(X))))&
((happy(lucy))<=>(tall(john)))&
(((~wise(susan)|patient(susan)))<=>(~tall(lucy)))&
(![X]:((~rich(X)|patient(X))<=>(~generous(X)&~tall(X))))&
(((~curious(mary)&~strong(mary)))<=>(?[X]:((~calm(X)&tall(X)))))&
(![X]:(happy(X)=>(rich(X)<~>wise(X))))&
(quiet(fred))&
((funny(lucy)&wise(lucy)))&
((generous(paul)<~>~funny(paul)))&
(?[X]:((~quiet(X)|~curious(X))))&
(?[X]:((~kind(X)<~>~old(X))))&
((~rich(paul)|strong(paul)))&
(?[X]:((~happy(X)|~tall(X)))) | ~wise(lucy) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2602473586858740084778875
% SZS output start Proof for 2602473586858740084778875
18. wise(lucy) & funny(lucy) [input p17]
24. ~wise(lucy) [input hypothesis]
140. wise(lucy) [cnf transformation 18]
148. ~wise(lucy) [cnf transformation 24]
340. $false [subsumption resolution 148,140]
% SZS output end Proof for 2602473586858740084778875
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise is either not funny or not quiet and vice versa.
Everyone who is not happy or not quiet is calm.
If someone is tall then someone is both curious and calm.
Everyone who is both wise and patient is not happy and vice versa.
If mary is creative then someone is either tall or not strong and vice versa.
If someone is kind then someone is either wise or rich.
If someone is generous then someone is wise or humble and vice versa.
Everyone who is both happy and not rich is either old or not happy and vice versa.
Everyone who is quiet is creative and vice versa.
If fred is happy or not quiet then someone is either strong or patient and vice versa.
Everyone who is funny is either not curious or happy and vice versa.
Everyone who is calm is both strong and generous and vice versa.
Everyone who is not patient is both humble and not funny.
If lucy is happy then someone is funny or patient.
Everyone who is old or not kind is both old and not curious.
Everyone who is not calm or tall is both creative and not kind and vice versa.
Paul is either strong or quiet.
Mary is either not funny or not calm.
Lucy is either patient or funny.
Someone is tall or old.
Paul is either generous or humble.
Paul is not quiet.
Someone is not patient or not humble. | Lucy is not patient. | contradiction | (![X]:(wise(X)<=>(~funny(X)<~>~quiet(X))))&
(![X]:((~happy(X)|~quiet(X))=>calm(X)))&
((?[X]:(tall(X)))=>(?[X]:((curious(X)&calm(X)))))&
(![X]:((wise(X)&patient(X))<=>~happy(X)))&
((creative(mary))<=>(?[X]:((tall(X)<~>~strong(X)))))&
((?[X]:(kind(X)))=>(?[X]:((wise(X)<~>rich(X)))))&
((?[X]:(generous(X)))<=>(?[X]:((wise(X)|humble(X)))))&
(![X]:((happy(X)&~rich(X))<=>(old(X)<~>~happy(X))))&
(![X]:(quiet(X)<=>creative(X)))&
(((happy(fred)|~quiet(fred)))<=>(?[X]:((strong(X)<~>patient(X)))))&
(![X]:(funny(X)<=>(~curious(X)<~>happy(X))))&
(![X]:(calm(X)<=>(strong(X)&generous(X))))&
(![X]:(~patient(X)=>(humble(X)&~funny(X))))&
((happy(lucy))=>(?[X]:((funny(X)|patient(X)))))&
(![X]:((old(X)|~kind(X))=>(old(X)&~curious(X))))&
(![X]:((~calm(X)|tall(X))<=>(creative(X)&~kind(X))))&
((strong(paul)<~>quiet(paul)))&
((~funny(mary)<~>~calm(mary)))&
((patient(lucy)<~>funny(lucy)))&
(?[X]:((tall(X)|old(X))))&
((generous(paul)<~>humble(paul)))&
(~quiet(paul))&
(?[X]:((~patient(X)|~humble(X)))) | ~patient(lucy) | [
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7207321652704636075331620
% SZS output start Proof for 7207321652704636075331620
13. ! [X0] : (~patient(X0) => (~funny(X0) & humble(X0))) [input p12]
19. patient(lucy) <~> funny(lucy) [input p18]
24. ~patient(lucy) [input hypothesis]
31. ! [X0] : ((~funny(X0) & humble(X0)) | patient(X0)) [ennf transformation 13]
70. (~funny(lucy) | ~patient(lucy)) & (funny(lucy) | patient(lucy)) [nnf transformation 19]
118. ~funny(X0) | patient(X0) [cnf transformation 31]
133. funny(lucy) | patient(lucy) [cnf transformation 70]
134. ~funny(lucy) | ~patient(lucy) [cnf transformation 70]
140. ~patient(lucy) [cnf transformation 24]
274. ~funny(lucy) [subsumption resolution 134,118]
275. patient(lucy) [subsumption resolution 133,274]
305. $false [subsumption resolution 140,275]
% SZS output end Proof for 7207321652704636075331620
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or not funny is both old and not rich and vice versa.
Everyone who is both not wise and not creative is either not creative or calm.
Everyone who is either not old or not funny is both brave and creative and vice versa.
Everyone who is both not calm and not creative is either funny or not creative.
Everyone who is either not rich or not brave is either not tall or brave.
If alice is happy or not brave then fred is either wise or creative.
Everyone who is both not creative and not patient is tall and vice versa.
Everyone who is either not happy or not patient is both not calm and not brave.
Everyone who is either not generous or humble is patient and vice versa.
If fred is both kind and curious then someone is not humble.
Everyone who is not tall is both not funny and not humble and vice versa.
Everyone who is both curious and not funny is not humble or humble.
If alice is either curious or generous then someone is not patient and vice versa.
If someone is either not generous or not calm then someone is not patient or not brave.
Everyone who is either kind or humble is either tall or not funny.
If alice is both not calm and creative then someone is not calm or not generous.
Someone is both kind and not patient.
Someone is either not curious or not humble.
Someone is not wise or calm.
Alice is either not wise or strong.
Fred is either not rich or not creative.
Fred is generous or tall. | Fred is rich. | entailment | (![X]:((~humble(X)|~funny(X))<=>(old(X)&~rich(X))))&
(![X]:((~wise(X)&~creative(X))=>(~creative(X)<~>calm(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(brave(X)&creative(X))))&
(![X]:((~calm(X)&~creative(X))=>(funny(X)<~>~creative(X))))&
(![X]:((~rich(X)<~>~brave(X))=>(~tall(X)<~>brave(X))))&
(((happy(alice)|~brave(alice)))=>((wise(fred)<~>creative(fred))))&
(![X]:((~creative(X)&~patient(X))<=>tall(X)))&
(![X]:((~happy(X)<~>~patient(X))=>(~calm(X)&~brave(X))))&
(![X]:((~generous(X)<~>humble(X))<=>patient(X)))&
(((kind(fred)&curious(fred)))=>(?[X]:(~humble(X))))&
(![X]:(~tall(X)<=>(~funny(X)&~humble(X))))&
(![X]:((curious(X)&~funny(X))=>(~humble(X)|humble(X))))&
(((curious(alice)<~>generous(alice)))<=>(?[X]:(~patient(X))))&
((?[X]:((~generous(X)<~>~calm(X))))=>(?[X]:((~patient(X)|~brave(X)))))&
(![X]:((kind(X)<~>humble(X))=>(tall(X)<~>~funny(X))))&
(((~calm(alice)&creative(alice)))=>(?[X]:((~calm(X)|~generous(X)))))&
(?[X]:((kind(X)&~patient(X))))&
(?[X]:((~curious(X)<~>~humble(X))))&
(?[X]:((~wise(X)|calm(X))))&
((~wise(alice)<~>strong(alice)))&
((~rich(fred)<~>~creative(fred)))&
((generous(fred)|tall(fred))) | rich(fred) | [
"p0",
"p2",
"p4",
"p6",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2254636195619405088145835
% SZS output start Proof for 2254636195619405088145835
1. ! [X0] : ((~funny(X0) | ~humble(X0)) <=> (~rich(X0) & old(X0))) [input p0]
3. ! [X0] : ((~old(X0) <~> ~funny(X0)) <=> (creative(X0) & brave(X0))) [input p2]
5. ! [X0] : ((~rich(X0) <~> ~brave(X0)) => (~tall(X0) <~> brave(X0))) [input p4]
7. ! [X0] : ((~patient(X0) & ~creative(X0)) <=> tall(X0)) [input p6]
11. ! [X0] : (~tall(X0) <=> (~humble(X0) & ~funny(X0))) [input p10]
21. ~rich(fred) <~> ~creative(fred) [input p20]
23. ~rich(fred) [input hypothesis]
29. ! [X0] : ((~tall(X0) <~> brave(X0)) | (~rich(X0) <=> ~brave(X0))) [ennf transformation 5]
40. ! [X0] : (((~funny(X0) | ~humble(X0)) | (rich(X0) | ~old(X0))) & ((~rich(X0) & old(X0)) | (funny(X0) & humble(X0)))) [nnf transformation 1]
41. ! [X0] : ((~funny(X0) | ~humble(X0) | rich(X0) | ~old(X0)) & ((~rich(X0) & old(X0)) | (funny(X0) & humble(X0)))) [flattening 40]
43. ! [X0] : ((((funny(X0) | old(X0)) & (~funny(X0) | ~old(X0))) | (~creative(X0) | ~brave(X0))) & ((creative(X0) & brave(X0)) | ((~old(X0) | funny(X0)) & (~funny(X0) | old(X0))))) [nnf transformation 3]
44. ! [X0] : ((((funny(X0) | old(X0)) & (~funny(X0) | ~old(X0))) | ~creative(X0) | ~brave(X0)) & ((creative(X0) & brave(X0)) | ((~old(X0) | funny(X0)) & (~funny(X0) | old(X0))))) [flattening 43]
46. ! [X0] : (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | ((~rich(X0) | brave(X0)) & (~brave(X0) | rich(X0)))) [nnf transformation 29]
48. ! [X0] : (((~patient(X0) & ~creative(X0)) | ~tall(X0)) & (tall(X0) | (patient(X0) | creative(X0)))) [nnf transformation 7]
49. ! [X0] : (((~patient(X0) & ~creative(X0)) | ~tall(X0)) & (tall(X0) | patient(X0) | creative(X0))) [flattening 48]
54. ! [X0] : ((~tall(X0) | (humble(X0) | funny(X0))) & ((~humble(X0) & ~funny(X0)) | tall(X0))) [nnf transformation 11]
55. ! [X0] : ((~tall(X0) | humble(X0) | funny(X0)) & ((~humble(X0) & ~funny(X0)) | tall(X0))) [flattening 54]
75. (creative(fred) | rich(fred)) & (~creative(fred) | ~rich(fred)) [nnf transformation 21]
77. old(X0) | funny(X0) [cnf transformation 41]
84. brave(X0) | ~old(X0) | funny(X0) [cnf transformation 44]
93. ~brave(X0) | tall(X0) | ~brave(X0) | rich(X0) [cnf transformation 46]
100. ~tall(X0) | ~creative(X0) [cnf transformation 49]
111. ~funny(X0) | tall(X0) [cnf transformation 55]
134. creative(fred) | rich(fred) [cnf transformation 75]
136. ~rich(fred) [cnf transformation 23]
138. ~brave(X0) | tall(X0) | rich(X0) [duplicate literal removal 93]
143. brave(X0) | funny(X0) [subsumption resolution 84,77]
155. 3 <=> creative(fred) [avatar definition]
156. creative(fred) <- (3) [avatar component clause 155]
259. 25 <=> rich(fred) [avatar definition]
260. ~rich(fred) <- (~25) [avatar component clause 259]
262. 25 | 3 [avatar split clause 134,155,259]
273. ~25 [avatar split clause 136,259]
391. tall(X1) | rich(X1) | funny(X1) [resolution 138,143]
393. tall(X1) | rich(X1) [subsumption resolution 391,111]
445. ~creative(X3) | rich(X3) [resolution 393,100]
650. rich(fred) <- (3) [resolution 445,156]
653. $false <- (3, ~25) [subsumption resolution 650,260]
654. ~3 | 25 [avatar contradiction clause 653]
655. $false [avatar sat refutation 262,273,654]
% SZS output end Proof for 2254636195619405088145835
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not calm or not tall then someone is either quiet or old and vice versa. Everyone who is either not kind or strong is not strong and vice versa. Everyone who is both not curious and not patient is either not strong or wise and vice versa. Everyone who is both patient and not strong is both not wise and not strong and vice versa. Everyone who is not rich or rich is not quiet and vice versa. If someone is curious then someone is either not brave or not quiet and vice versa. If susan is not wise then someone is calm or old. Everyone who is either not tall or not strong is curious and vice versa. Everyone who is both not calm and funny is either generous or funny. Everyone who is old or creative is rich or kind and vice versa. If someone is either humble or not calm then someone is either not tall or strong and vice versa. Everyone who is not tall is happy or generous. Everyone who is creative or patient is both not strong and not quiet. Everyone who is humble or not quiet is brave. Everyone who is creative or not brave is curious or kind and vice versa. Everyone who is calm is funny. Someone is not kind or curious. Someone is either not calm or not creative. Paul is not calm. Someone is strong. Susan is not tall or wise. Lucy is either not patient or not brave. | Susan is wise. | entailment | ((?[X]:((~calm(X)<~>~tall(X))))<=>(?[X]:((quiet(X)<~>old(X)))))&
(![X]:((~kind(X)<~>strong(X))<=>~strong(X)))&
(![X]:((~curious(X)&~patient(X))<=>(~strong(X)<~>wise(X))))&
(![X]:((patient(X)&~strong(X))<=>(~wise(X)&~strong(X))))&
(![X]:((~rich(X)|rich(X))<=>~quiet(X)))&
((?[X]:(curious(X)))<=>(?[X]:((~brave(X)<~>~quiet(X)))))&
((~wise(susan))=>(?[X]:((calm(X)|old(X)))))&
(![X]:((~tall(X)<~>~strong(X))<=>curious(X)))&
(![X]:((~calm(X)&funny(X))=>(generous(X)<~>funny(X))))&
(![X]:((old(X)|creative(X))<=>(rich(X)|kind(X))))&
((?[X]:((humble(X)<~>~calm(X))))<=>(?[X]:((~tall(X)<~>strong(X)))))&
(![X]:(~tall(X)=>(happy(X)|generous(X))))&
(![X]:((creative(X)|patient(X))=>(~strong(X)&~quiet(X))))&
(![X]:((humble(X)|~quiet(X))=>brave(X)))&
(![X]:((creative(X)|~brave(X))<=>(curious(X)|kind(X))))&
(![X]:(calm(X)=>funny(X)))&
(?[X]:((~kind(X)|curious(X))))&
(?[X]:((~calm(X)<~>~creative(X))))&
(~calm(paul))&
(?[X]:(strong(X)))&
((~tall(susan)|wise(susan)))&
((~patient(lucy)<~>~brave(lucy))) | wise(susan) | [
"p2",
"p3",
"p4",
"p7",
"p12",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4874058624973197367582605
% SZS output start Proof for 4874058624973197367582605
3. ! [X0] : ((~patient(X0) & ~curious(X0)) <=> (~strong(X0) <~> wise(X0))) [input p2]
4. ! [X0] : ((~strong(X0) & patient(X0)) <=> (~strong(X0) & ~wise(X0))) [input p3]
5. ! [X0] : ((rich(X0) | ~rich(X0)) <=> ~quiet(X0)) [input p4]
8. ! [X0] : ((~tall(X0) <~> ~strong(X0)) <=> curious(X0)) [input p7]
13. ! [X0] : ((patient(X0) | creative(X0)) => (~quiet(X0) & ~strong(X0))) [input p12]
14. ! [X0] : ((~quiet(X0) | humble(X0)) => brave(X0)) [input p13]
15. ! [X0] : ((~brave(X0) | creative(X0)) <=> (kind(X0) | curious(X0))) [input p14]
21. wise(susan) | ~tall(susan) [input p20]
23. ~wise(susan) [input hypothesis]
31. ! [X0] : ((~quiet(X0) & ~strong(X0)) | (~patient(X0) & ~creative(X0))) [ennf transformation 13]
32. ! [X0] : (brave(X0) | (quiet(X0) & ~humble(X0))) [ennf transformation 14]
40. ! [X0] : (((~patient(X0) & ~curious(X0)) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0)))) & (((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | (patient(X0) | curious(X0)))) [nnf transformation 3]
41. ! [X0] : (((~patient(X0) & ~curious(X0)) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0)))) & (((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | patient(X0) | curious(X0))) [flattening 40]
42. ! [X0] : (((~strong(X0) & patient(X0)) | (strong(X0) | wise(X0))) & ((~strong(X0) & ~wise(X0)) | (strong(X0) | ~patient(X0)))) [nnf transformation 4]
43. ! [X0] : (((~strong(X0) & patient(X0)) | strong(X0) | wise(X0)) & ((~strong(X0) & ~wise(X0)) | strong(X0) | ~patient(X0))) [flattening 42]
44. ! [X0] : (((rich(X0) | ~rich(X0)) | quiet(X0)) & (~quiet(X0) | (~rich(X0) & rich(X0)))) [nnf transformation 5]
45. ! [X0] : ((rich(X0) | ~rich(X0) | quiet(X0)) & (~quiet(X0) | (~rich(X0) & rich(X0)))) [flattening 44]
53. ! [X0] : ((((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) | ~curious(X0)) & (curious(X0) | ((~tall(X0) | strong(X0)) & (~strong(X0) | tall(X0))))) [nnf transformation 8]
62. ! [X0] : (((~brave(X0) | creative(X0)) | (~kind(X0) & ~curious(X0))) & ((kind(X0) | curious(X0)) | (brave(X0) & ~creative(X0)))) [nnf transformation 15]
63. ! [X0] : ((~brave(X0) | creative(X0) | (~kind(X0) & ~curious(X0))) & (kind(X0) | curious(X0) | (brave(X0) & ~creative(X0)))) [flattening 62]
88. ~patient(X0) | wise(X0) | strong(X0) [cnf transformation 41]
92. patient(X0) | strong(X0) | wise(X0) [cnf transformation 43]
94. ~quiet(X0) | rich(X0) [cnf transformation 45]
95. ~rich(X0) | ~quiet(X0) [cnf transformation 45]
102. ~strong(X0) | curious(X0) | tall(X0) [cnf transformation 53]
120. ~creative(X0) | ~strong(X0) [cnf transformation 31]
125. brave(X0) | quiet(X0) [cnf transformation 32]
128. ~brave(X0) | creative(X0) | ~curious(X0) [cnf transformation 63]
136. wise(susan) | ~tall(susan) [cnf transformation 21]
139. ~wise(susan) [cnf transformation 23]
180. wise(X0) | strong(X0) [subsumption resolution 92,88]
182. ~quiet(X0) [subsumption resolution 94,95]
202. 13 <=> wise(susan) [avatar definition]
203. ~wise(susan) <- (~13) [avatar component clause 202]
252. brave(X0) [subsumption resolution 125,182]
253. ~curious(X0) | creative(X0) [subsumption resolution 128,252]
266. 26 <=> tall(susan) [avatar definition]
268. ~tall(susan) <- (~26) [avatar component clause 266]
269. ~26 | 13 [avatar split clause 136,202,266]
271. ~13 [avatar split clause 139,202]
281. strong(susan) <- (~13) [resolution 180,203]
295. curious(susan) | tall(susan) <- (~13) [resolution 102,281]
305. curious(susan) <- (~13, ~26) [subsumption resolution 295,268]
308. creative(susan) <- (~13, ~26) [resolution 305,253]
313. ~strong(susan) <- (~13, ~26) [resolution 308,120]
314. $false <- (~13, ~26) [subsumption resolution 313,281]
315. 13 | 26 [avatar contradiction clause 314]
316. $false [avatar sat refutation 269,271,315]
% SZS output end Proof for 4874058624973197367582605
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both calm and not humble then susan is either calm or patient and vice versa.
Everyone who is not old or not brave is both patient and not happy.
If paul is either calm or not curious then someone is either wise or not generous.
Everyone who is both happy and not rich is both generous and quiet.
Everyone who is either not rich or tall is either not quiet or rich and vice versa.
If paul is either not calm or happy then someone is not quiet and vice versa.
Everyone who is not quiet is both not generous and not tall.
Everyone who is both happy and old is either not humble or not rich.
Everyone who is rich is both calm and not tall and vice versa.
Everyone who is brave is not strong and vice versa.
If someone is brave then someone is both not wise and funny and vice versa.
Everyone who is both patient and kind is both rich and wise and vice versa.
Everyone who is not brave or brave is brave or not creative and vice versa.
Everyone who is not strong or patient is both rich and funny.
Everyone who is both calm and not rich is both not old and wise and vice versa.
If someone is both not old and old then someone is not funny and vice versa.
Susan is patient or not kind.
Someone is not kind.
Someone is both not kind and not strong.
John is both not patient and not humble.
Lucy is either not wise or curious.
Paul is either quiet or brave.
Someone is either not creative or old. | Lucy is not generous. | entailment | (((calm(fred)&~humble(fred)))<=>((calm(susan)<~>patient(susan))))&
(![X]:((~old(X)|~brave(X))=>(patient(X)&~happy(X))))&
(((calm(paul)<~>~curious(paul)))=>(?[X]:((wise(X)<~>~generous(X)))))&
(![X]:((happy(X)&~rich(X))=>(generous(X)&quiet(X))))&
(![X]:((~rich(X)<~>tall(X))<=>(~quiet(X)<~>rich(X))))&
(((~calm(paul)<~>happy(paul)))<=>(?[X]:(~quiet(X))))&
(![X]:(~quiet(X)=>(~generous(X)&~tall(X))))&
(![X]:((happy(X)&old(X))=>(~humble(X)<~>~rich(X))))&
(![X]:(rich(X)<=>(calm(X)&~tall(X))))&
(![X]:(brave(X)<=>~strong(X)))&
((?[X]:(brave(X)))<=>(?[X]:((~wise(X)&funny(X)))))&
(![X]:((patient(X)&kind(X))<=>(rich(X)&wise(X))))&
(![X]:((~brave(X)|brave(X))<=>(brave(X)|~creative(X))))&
(![X]:((~strong(X)|patient(X))=>(rich(X)&funny(X))))&
(![X]:((calm(X)&~rich(X))<=>(~old(X)&wise(X))))&
((?[X]:((~old(X)&old(X))))<=>(?[X]:(~funny(X))))&
((patient(susan)|~kind(susan)))&
(?[X]:(~kind(X)))&
(?[X]:((~kind(X)&~strong(X))))&
((~patient(john)&~humble(john)))&
((~wise(lucy)<~>curious(lucy)))&
((quiet(paul)<~>brave(paul)))&
(?[X]:((~creative(X)<~>old(X)))) | ~generous(lucy) | [
"p1",
"p4",
"p6",
"p8",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6042716105279039346309255
% SZS output start Proof for 6042716105279039346309255
2. ! [X0] : ((~brave(X0) | ~old(X0)) => (~happy(X0) & patient(X0))) [input p1]
5. ! [X0] : ((~rich(X0) <~> tall(X0)) <=> (~quiet(X0) <~> rich(X0))) [input p4]
7. ! [X0] : (~quiet(X0) => (~tall(X0) & ~generous(X0))) [input p6]
9. ! [X0] : (rich(X0) <=> (~tall(X0) & calm(X0))) [input p8]
10. ! [X0] : (brave(X0) <=> ~strong(X0)) [input p9]
14. ! [X0] : ((patient(X0) | ~strong(X0)) => (funny(X0) & rich(X0))) [input p13]
24. generous(lucy) [input hypothesis]
27. ! [X0] : ((~happy(X0) & patient(X0)) | (brave(X0) & old(X0))) [ennf transformation 2]
31. ! [X0] : ((~tall(X0) & ~generous(X0)) | quiet(X0)) [ennf transformation 7]
34. ! [X0] : ((funny(X0) & rich(X0)) | (~patient(X0) & strong(X0))) [ennf transformation 14]
40. ! [X0] : ((((~tall(X0) | rich(X0)) & (tall(X0) | ~rich(X0))) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0)))) & (((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | ((~rich(X0) | ~tall(X0)) & (tall(X0) | rich(X0))))) [nnf transformation 5]
46. ! [X0] : ((rich(X0) | (tall(X0) | ~calm(X0))) & ((~tall(X0) & calm(X0)) | ~rich(X0))) [nnf transformation 9]
47. ! [X0] : ((rich(X0) | tall(X0) | ~calm(X0)) & ((~tall(X0) & calm(X0)) | ~rich(X0))) [flattening 46]
48. ! [X0] : ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))) [nnf transformation 10]
81. brave(X0) | patient(X0) [cnf transformation 27]
90. rich(X0) | ~quiet(X0) | tall(X0) | rich(X0) [cnf transformation 40]
95. tall(X0) | ~rich(X0) | ~quiet(X0) | ~rich(X0) [cnf transformation 40]
102. ~generous(X0) | quiet(X0) [cnf transformation 31]
107. ~tall(X0) | ~rich(X0) [cnf transformation 47]
109. ~strong(X0) | ~brave(X0) [cnf transformation 48]
122. strong(X0) | rich(X0) [cnf transformation 34]
123. ~patient(X0) | rich(X0) [cnf transformation 34]
145. generous(lucy) [cnf transformation 24]
148. rich(X0) | ~quiet(X0) | tall(X0) [duplicate literal removal 90]
150. tall(X0) | ~rich(X0) | ~quiet(X0) [duplicate literal removal 95]
195. ~quiet(X0) | tall(X0) [subsumption resolution 148,150]
287. quiet(lucy) [resolution 102,145]
291. ~brave(X0) | rich(X0) [resolution 122,109]
305. tall(lucy) [resolution 195,287]
314. ~rich(lucy) [resolution 305,107]
317. rich(X0) | patient(X0) [resolution 291,81]
321. rich(X0) [subsumption resolution 317,123]
323. $false [resolution 321,314]
% SZS output end Proof for 6042716105279039346309255
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either humble or not strong then someone is creative or tall.
Everyone who is both tall and not old is kind.
Everyone who is generous is both not calm and happy and vice versa.
If lucy is creative then someone is funny or not humble.
If alice is strong or calm then someone is both old and not rich.
If someone is both not happy and creative then paul is not brave or not kind and vice versa.
If lucy is wise then susan is not brave.
Everyone who is both not tall and humble is not quiet.
Everyone who is either happy or quiet is both funny and not kind.
If susan is not happy then lucy is not old or brave.
If paul is both quiet and not quiet then someone is rich and vice versa.
Everyone who is not calm is not generous and vice versa.
Everyone who is not old is curious and vice versa.
Everyone who is happy is either funny or kind.
If someone is happy or strong then someone is quiet or not wise and vice versa.
If paul is either not kind or not rich then someone is not creative or calm and vice versa.
Someone is both strong and patient.
Someone is either not funny or generous.
Alice is either creative or not patient.
Fred is not calm or happy.
John is not humble or generous.
Mary is either funny or calm.
Lucy is both old and not rich. | John is happy. | contradiction | (((humble(john)<~>~strong(john)))=>(?[X]:((creative(X)|tall(X)))))&
(![X]:((tall(X)&~old(X))=>kind(X)))&
(![X]:(generous(X)<=>(~calm(X)&happy(X))))&
((creative(lucy))=>(?[X]:((funny(X)|~humble(X)))))&
(((strong(alice)|calm(alice)))=>(?[X]:((old(X)&~rich(X)))))&
((?[X]:((~happy(X)&creative(X))))<=>((~brave(paul)|~kind(paul))))&
((wise(lucy))=>(~brave(susan)))&
(![X]:((~tall(X)&humble(X))=>~quiet(X)))&
(![X]:((happy(X)<~>quiet(X))=>(funny(X)&~kind(X))))&
((~happy(susan))=>((~old(lucy)|brave(lucy))))&
(((quiet(paul)&~quiet(paul)))<=>(?[X]:(rich(X))))&
(![X]:(~calm(X)<=>~generous(X)))&
(![X]:(~old(X)<=>curious(X)))&
(![X]:(happy(X)=>(funny(X)<~>kind(X))))&
((?[X]:((happy(X)|strong(X))))<=>(?[X]:((quiet(X)|~wise(X)))))&
(((~kind(paul)<~>~rich(paul)))<=>(?[X]:((~creative(X)|calm(X)))))&
(?[X]:((strong(X)&patient(X))))&
(?[X]:((~funny(X)<~>generous(X))))&
((creative(alice)<~>~patient(alice)))&
((~calm(fred)|happy(fred)))&
((~humble(john)|generous(john)))&
((funny(mary)<~>calm(mary)))&
((old(lucy)&~rich(lucy))) | happy(john) | [
"p2",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3344879252070552342677836
% SZS output start Proof for 3344879252070552342677836
3. ! [X0] : (generous(X0) <=> (happy(X0) & ~calm(X0))) [input p2]
12. ! [X0] : (~calm(X0) <=> ~generous(X0)) [input p11]
24. happy(john) [input hypothesis]
41. ! [X0] : ((generous(X0) | (~happy(X0) | calm(X0))) & ((happy(X0) & ~calm(X0)) | ~generous(X0))) [nnf transformation 3]
42. ! [X0] : ((generous(X0) | ~happy(X0) | calm(X0)) & ((happy(X0) & ~calm(X0)) | ~generous(X0))) [flattening 41]
58. ! [X0] : ((~calm(X0) | generous(X0)) & (~generous(X0) | calm(X0))) [nnf transformation 12]
80. ~calm(X0) | ~generous(X0) [cnf transformation 42]
82. ~happy(X0) | generous(X0) | calm(X0) [cnf transformation 42]
103. ~generous(X0) | calm(X0) [cnf transformation 58]
104. ~calm(X0) | generous(X0) [cnf transformation 58]
131. happy(john) [cnf transformation 24]
238. ~calm(X0) [subsumption resolution 104,80]
239. ~generous(X0) [subsumption resolution 103,238]
305. generous(john) | calm(john) [resolution 82,131]
308. calm(john) [subsumption resolution 305,239]
309. $false [subsumption resolution 308,238]
% SZS output end Proof for 3344879252070552342677836
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is either not curious or calm.
If someone is rich or patient then susan is either kind or not tall and vice versa.
Everyone who is brave or not strong is not brave and vice versa.
If mary is either not kind or kind then someone is not strong and vice versa.
Everyone who is not curious or rich is not calm or not curious and vice versa.
If lucy is either not creative or generous then lucy is rich and vice versa.
Everyone who is both humble and creative is funny and vice versa.
Everyone who is both happy and creative is either strong or not funny.
Everyone who is not quiet or curious is both generous and not happy and vice versa.
If alice is either happy or not funny then fred is both not wise and kind and vice versa.
Everyone who is not curious or not tall is strong or patient.
Everyone who is either not happy or strong is tall or not generous and vice versa.
If paul is not creative or not curious then someone is either not calm or not creative.
If john is not tall or not strong then someone is not funny or not tall.
If someone is both rich and brave then someone is brave or not funny.
If someone is both patient and not curious then someone is both not funny and brave and vice versa.
Alice is humble.
John is both patient and not old.
Susan is not patient.
John is quiet or not quiet.
Someone is not kind.
Mary is either not happy or not curious. | John is not funny. | neutral | (![X]:(humble(X)=>(~curious(X)<~>calm(X))))&
((?[X]:((rich(X)|patient(X))))<=>((kind(susan)<~>~tall(susan))))&
(![X]:((brave(X)|~strong(X))<=>~brave(X)))&
(((~kind(mary)<~>kind(mary)))<=>(?[X]:(~strong(X))))&
(![X]:((~curious(X)|rich(X))<=>(~calm(X)|~curious(X))))&
(((~creative(lucy)<~>generous(lucy)))<=>(rich(lucy)))&
(![X]:((humble(X)&creative(X))<=>funny(X)))&
(![X]:((happy(X)&creative(X))=>(strong(X)<~>~funny(X))))&
(![X]:((~quiet(X)|curious(X))<=>(generous(X)&~happy(X))))&
(((happy(alice)<~>~funny(alice)))<=>((~wise(fred)&kind(fred))))&
(![X]:((~curious(X)|~tall(X))=>(strong(X)|patient(X))))&
(![X]:((~happy(X)<~>strong(X))<=>(tall(X)|~generous(X))))&
(((~creative(paul)|~curious(paul)))=>(?[X]:((~calm(X)<~>~creative(X)))))&
(((~tall(john)|~strong(john)))=>(?[X]:((~funny(X)|~tall(X)))))&
((?[X]:((rich(X)&brave(X))))=>(?[X]:((brave(X)|~funny(X)))))&
((?[X]:((patient(X)&~curious(X))))<=>(?[X]:((~funny(X)&brave(X)))))&
(humble(alice))&
((patient(john)&~old(john)))&
(~patient(susan))&
((quiet(john)|~quiet(john)))&
(?[X]:(~kind(X)))&
((~happy(mary)<~>~curious(mary))) | ~funny(john) | [] | null | 0 |
Everyone who is both not kind and rich is not funny and vice versa.
If someone is both brave and not patient then alice is both not humble and creative and vice versa.
Everyone who is curious is not tall or happy and vice versa.
If someone is generous then someone is rich or funny and vice versa.
Everyone who is not humble is both not calm and not strong.
Everyone who is rich is kind or not rich and vice versa.
Everyone who is generous is both not old and curious and vice versa.
Everyone who is not quiet or not curious is either not strong or rich.
If someone is not tall then susan is not quiet or strong and vice versa.
If someone is not funny then someone is either generous or happy.
If someone is happy then lucy is not old or rich and vice versa.
Everyone who is quiet or not brave is both not quiet and wise and vice versa.
Everyone who is both not kind and not generous is not quiet or wise.
Everyone who is both not kind and brave is generous.
Everyone who is either not patient or not wise is both rich and generous.
Mary is not creative.
Lucy is not calm.
Mary is calm or humble.
Someone is either humble or happy.
Paul is strong or rich.
John is not humble or not patient.
Alice is both not happy and not creative. | Lucy is not kind. | contradiction | (![X]:((~kind(X)&rich(X))<=>~funny(X)))&
((?[X]:((brave(X)&~patient(X))))<=>((~humble(alice)&creative(alice))))&
(![X]:(curious(X)<=>(~tall(X)|happy(X))))&
((?[X]:(generous(X)))<=>(?[X]:((rich(X)|funny(X)))))&
(![X]:(~humble(X)=>(~calm(X)&~strong(X))))&
(![X]:(rich(X)<=>(kind(X)|~rich(X))))&
(![X]:(generous(X)<=>(~old(X)&curious(X))))&
(![X]:((~quiet(X)|~curious(X))=>(~strong(X)<~>rich(X))))&
((?[X]:(~tall(X)))<=>((~quiet(susan)|strong(susan))))&
((?[X]:(~funny(X)))=>(?[X]:((generous(X)<~>happy(X)))))&
((?[X]:(happy(X)))<=>((~old(lucy)|rich(lucy))))&
(![X]:((quiet(X)|~brave(X))<=>(~quiet(X)&wise(X))))&
(![X]:((~kind(X)&~generous(X))=>(~quiet(X)|wise(X))))&
(![X]:((~kind(X)&brave(X))=>generous(X)))&
(![X]:((~patient(X)<~>~wise(X))=>(rich(X)&generous(X))))&
(~creative(mary))&
(~calm(lucy))&
((calm(mary)|humble(mary)))&
(?[X]:((humble(X)<~>happy(X))))&
((strong(paul)|rich(paul)))&
((~humble(john)|~patient(john)))&
((~happy(alice)&~creative(alice))) | ~kind(lucy) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 3634177303466550037634350
% SZS output start Proof for 3634177303466550037634350
6. ! [X0] : (rich(X0) <=> (~rich(X0) | kind(X0))) [input p5]
23. ~kind(lucy) [input hypothesis]
48. ! [X0] : ((rich(X0) | (rich(X0) & ~kind(X0))) & ((~rich(X0) | kind(X0)) | ~rich(X0))) [nnf transformation 6]
49. ! [X0] : ((rich(X0) | (rich(X0) & ~kind(X0))) & (~rich(X0) | kind(X0) | ~rich(X0))) [flattening 48]
88. ~rich(X0) | kind(X0) | ~rich(X0) [cnf transformation 49]
90. rich(X0) | rich(X0) [cnf transformation 49]
126. ~kind(lucy) [cnf transformation 23]
129. ~rich(X0) | kind(X0) [duplicate literal removal 88]
130. rich(X0) [duplicate literal removal 90]
166. kind(X0) [subsumption resolution 129,130]
223. $false [subsumption resolution 126,166]
% SZS output end Proof for 3634177303466550037634350
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not rich then someone is either tall or not humble. Everyone who is either generous or patient is not happy. If mary is both not tall and not generous then someone is not wise. Everyone who is rich or not generous is not funny or not happy and vice versa. Everyone who is not wise is both not quiet and not brave and vice versa. If someone is both strong and funny then someone is both wise and not kind and vice versa. Everyone who is generous or patient is not strong or happy and vice versa. If mary is not humble then someone is not brave and vice versa. If susan is not old then alice is both not humble and strong. Everyone who is both not strong and happy is both tall and humble and vice versa. If someone is either creative or generous then someone is humble. Everyone who is not kind is old or humble and vice versa. Everyone who is not brave or wise is both not calm and not funny. If someone is either kind or not curious then someone is both creative and not happy. If alice is either not calm or not patient then someone is both not happy and brave. If paul is both creative and humble then alice is kind. Fred is both not calm and happy. Someone is happy. Someone is kind. Someone is calm or not patient. Lucy is either not brave or old. Someone is not generous. Someone is either curious or not old. | Lucy is not brave. | entailment | ((~rich(susan))=>(?[X]:((tall(X)<~>~humble(X)))))&
(![X]:((generous(X)<~>patient(X))=>~happy(X)))&
(((~tall(mary)&~generous(mary)))=>(?[X]:(~wise(X))))&
(![X]:((rich(X)|~generous(X))<=>(~funny(X)|~happy(X))))&
(![X]:(~wise(X)<=>(~quiet(X)&~brave(X))))&
((?[X]:((strong(X)&funny(X))))<=>(?[X]:((wise(X)&~kind(X)))))&
(![X]:((generous(X)|patient(X))<=>(~strong(X)|happy(X))))&
((~humble(mary))<=>(?[X]:(~brave(X))))&
((~old(susan))=>((~humble(alice)&strong(alice))))&
(![X]:((~strong(X)&happy(X))<=>(tall(X)&humble(X))))&
((?[X]:((creative(X)<~>generous(X))))=>(?[X]:(humble(X))))&
(![X]:(~kind(X)<=>(old(X)|humble(X))))&
(![X]:((~brave(X)|wise(X))=>(~calm(X)&~funny(X))))&
((?[X]:((kind(X)<~>~curious(X))))=>(?[X]:((creative(X)&~happy(X)))))&
(((~calm(alice)<~>~patient(alice)))=>(?[X]:((~happy(X)&brave(X)))))&
(((creative(paul)&humble(paul)))=>(kind(alice)))&
((~calm(fred)&happy(fred)))&
(?[X]:(happy(X)))&
(?[X]:(kind(X)))&
(?[X]:((calm(X)|~patient(X))))&
((~brave(lucy)<~>old(lucy)))&
(?[X]:(~generous(X)))&
(?[X]:((curious(X)<~>~old(X)))) | ~brave(lucy) | [
"p4",
"p5",
"p11",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7280692801441100954653386
% SZS output start Proof for 7280692801441100954653386
5. ! [X0] : (~wise(X0) <=> (~brave(X0) & ~quiet(X0))) [input p4]
6. ? [X0] : (funny(X0) & strong(X0)) <=> ? [X0] : (~kind(X0) & wise(X0)) [input p5]
12. ! [X0] : (~kind(X0) <=> (humble(X0) | old(X0))) [input p11]
13. ! [X0] : ((wise(X0) | ~brave(X0)) => (~funny(X0) & ~calm(X0))) [input p12]
21. ~brave(lucy) <~> old(lucy) [input p20]
24. brave(lucy) [input hypothesis]
25. ? [X0] : (funny(X0) & strong(X0)) <=> ? [X1] : (~kind(X1) & wise(X1)) [rectify 6]
34. ! [X0] : ((~funny(X0) & ~calm(X0)) | (~wise(X0) & brave(X0))) [ennf transformation 13]
47. ! [X0] : ((~wise(X0) | (brave(X0) | quiet(X0))) & ((~brave(X0) & ~quiet(X0)) | wise(X0))) [nnf transformation 5]
48. ! [X0] : ((~wise(X0) | brave(X0) | quiet(X0)) & ((~brave(X0) & ~quiet(X0)) | wise(X0))) [flattening 47]
49. (? [X0] : (funny(X0) & strong(X0)) | ! [X1] : (kind(X1) | ~wise(X1))) & (? [X1] : (~kind(X1) & wise(X1)) | ! [X0] : (~funny(X0) | ~strong(X0))) [nnf transformation 25]
50. (? [X0] : (funny(X0) & strong(X0)) | ! [X1] : (kind(X1) | ~wise(X1))) & (? [X2] : (~kind(X2) & wise(X2)) | ! [X3] : (~funny(X3) | ~strong(X3))) [rectify 49]
51. ? [X0] : (funny(X0) & strong(X0)) => (funny(sK2) & strong(sK2)) [choice axiom]
52. ? [X2] : (~kind(X2) & wise(X2)) => (~kind(sK3) & wise(sK3)) [choice axiom]
53. ((funny(sK2) & strong(sK2)) | ! [X1] : (kind(X1) | ~wise(X1))) & ((~kind(sK3) & wise(sK3)) | ! [X3] : (~funny(X3) | ~strong(X3))) [skolemisation 50,52,51]
66. ! [X0] : ((~kind(X0) | (~humble(X0) & ~old(X0))) & ((humble(X0) | old(X0)) | kind(X0))) [nnf transformation 12]
67. ! [X0] : ((~kind(X0) | (~humble(X0) & ~old(X0))) & (humble(X0) | old(X0) | kind(X0))) [flattening 66]
81. (~old(lucy) | brave(lucy)) & (old(lucy) | ~brave(lucy)) [nnf transformation 21]
97. ~brave(X0) | wise(X0) [cnf transformation 48]
102. funny(sK2) | kind(X1) | ~wise(X1) [cnf transformation 53]
118. ~old(X0) | ~kind(X0) [cnf transformation 67]
122. ~funny(X0) | brave(X0) [cnf transformation 34]
123. ~funny(X0) | ~wise(X0) [cnf transformation 34]
138. old(lucy) | ~brave(lucy) [cnf transformation 81]
143. brave(lucy) [cnf transformation 24]
172. 7 <=> ! [X1] : (kind(X1) | ~wise(X1)) [avatar definition]
173. ~wise(X1) | kind(X1) <- (7) [avatar component clause 172]
175. 8 <=> funny(sK2) [avatar definition]
177. funny(sK2) <- (8) [avatar component clause 175]
178. 7 | 8 [avatar split clause 102,175,172]
298. 35 <=> brave(lucy) [avatar definition]
300. brave(lucy) <- (35) [avatar component clause 298]
302. 36 <=> old(lucy) [avatar definition]
303. old(lucy) <- (36) [avatar component clause 302]
306. ~35 | 36 [avatar split clause 138,302,298]
317. 35 [avatar split clause 143,298]
318. wise(lucy) <- (35) [resolution 97,300]
320. ~kind(lucy) <- (36) [resolution 118,303]
322. kind(lucy) <- (7, 35) [resolution 173,318]
323. $false <- (7, 35, 36) [subsumption resolution 322,320]
324. ~7 | ~35 | ~36 [avatar contradiction clause 323]
325. ~wise(sK2) <- (8) [resolution 177,123]
326. brave(sK2) <- (8) [resolution 177,122]
332. wise(sK2) <- (8) [resolution 326,97]
333. $false <- (8) [subsumption resolution 332,325]
334. ~8 [avatar contradiction clause 333]
335. $false [avatar sat refutation 178,306,317,324,334]
% SZS output end Proof for 7280692801441100954653386
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not creative or old then john is both old and not wise and vice versa.
Everyone who is either patient or not brave is funny and vice versa.
Everyone who is patient is not humble and vice versa.
Everyone who is curious or old is rich or curious.
If someone is strong then john is both not generous and not brave.
If someone is both not generous and not kind then someone is either funny or not happy and vice versa.
Everyone who is not generous is both not curious and not happy and vice versa.
Everyone who is either rich or not creative is both not wise and not brave and vice versa.
If paul is not kind or generous then someone is not kind and vice versa.
Everyone who is not creative or tall is not happy or not funny.
Everyone who is both patient and creative is old and vice versa.
If someone is both not funny and not quiet then paul is either happy or not rich and vice versa.
Everyone who is not rich or not happy is either funny or old and vice versa.
Everyone who is calm is either patient or humble.
If someone is rich then john is tall.
If paul is not rich then someone is either not curious or not generous and vice versa.
Someone is not patient.
Someone is either not wise or not brave.
Someone is both curious and quiet.
Fred is either not humble or calm.
John is not tall or old.
Someone is both not humble and funny.
Lucy is not brave.
Someone is generous or not strong. | John is rich. | entailment | ((?[X]:((~creative(X)<~>old(X))))<=>((old(john)&~wise(john))))&
(![X]:((patient(X)<~>~brave(X))<=>funny(X)))&
(![X]:(patient(X)<=>~humble(X)))&
(![X]:((curious(X)|old(X))=>(rich(X)|curious(X))))&
((?[X]:(strong(X)))=>((~generous(john)&~brave(john))))&
((?[X]:((~generous(X)&~kind(X))))<=>(?[X]:((funny(X)<~>~happy(X)))))&
(![X]:(~generous(X)<=>(~curious(X)&~happy(X))))&
(![X]:((rich(X)<~>~creative(X))<=>(~wise(X)&~brave(X))))&
(((~kind(paul)|generous(paul)))<=>(?[X]:(~kind(X))))&
(![X]:((~creative(X)|tall(X))=>(~happy(X)|~funny(X))))&
(![X]:((patient(X)&creative(X))<=>old(X)))&
((?[X]:((~funny(X)&~quiet(X))))<=>((happy(paul)<~>~rich(paul))))&
(![X]:((~rich(X)|~happy(X))<=>(funny(X)<~>old(X))))&
(![X]:(calm(X)=>(patient(X)<~>humble(X))))&
((?[X]:(rich(X)))=>(tall(john)))&
((~rich(paul))<=>(?[X]:((~curious(X)<~>~generous(X)))))&
(?[X]:(~patient(X)))&
(?[X]:((~wise(X)<~>~brave(X))))&
(?[X]:((curious(X)&quiet(X))))&
((~humble(fred)<~>calm(fred)))&
((~tall(john)|old(john)))&
(?[X]:((~humble(X)&funny(X))))&
(~brave(lucy))&
(?[X]:((generous(X)|~strong(X)))) | rich(john) | [
"p0",
"p1",
"p2",
"p7",
"p10",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7651457452385893955786446
% SZS output start Proof for 7651457452385893955786446
1. ? [X0] : (~creative(X0) <~> old(X0)) <=> (~wise(john) & old(john)) [input p0]
2. ! [X0] : ((patient(X0) <~> ~brave(X0)) <=> funny(X0)) [input p1]
3. ! [X0] : (patient(X0) <=> ~humble(X0)) [input p2]
8. ! [X0] : ((rich(X0) <~> ~creative(X0)) <=> (~brave(X0) & ~wise(X0))) [input p7]
11. ! [X0] : ((creative(X0) & patient(X0)) <=> old(X0)) [input p10]
13. ! [X0] : ((~happy(X0) | ~rich(X0)) <=> (funny(X0) <~> old(X0))) [input p12]
22. ? [X0] : (funny(X0) & ~humble(X0)) [input p21]
25. ~rich(john) [input hypothesis]
35. (? [X0] : ((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | (wise(john) | ~old(john))) & ((~wise(john) & old(john)) | ! [X0] : ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0)))) [nnf transformation 1]
36. (? [X0] : ((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | wise(john) | ~old(john)) & ((~wise(john) & old(john)) | ! [X0] : ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0)))) [flattening 35]
37. (? [X0] : ((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | wise(john) | ~old(john)) & ((~wise(john) & old(john)) | ! [X1] : ((~creative(X1) | ~old(X1)) & (old(X1) | creative(X1)))) [rectify 36]
38. ? [X0] : ((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) => ((~old(sK0) | creative(sK0)) & (old(sK0) | ~creative(sK0))) [choice axiom]
39. (((~old(sK0) | creative(sK0)) & (old(sK0) | ~creative(sK0))) | wise(john) | ~old(john)) & ((~wise(john) & old(john)) | ! [X1] : ((~creative(X1) | ~old(X1)) & (old(X1) | creative(X1)))) [skolemisation 37,38]
40. ! [X0] : ((((brave(X0) | ~patient(X0)) & (~brave(X0) | patient(X0))) | ~funny(X0)) & (funny(X0) | ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0))))) [nnf transformation 2]
41. ! [X0] : ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0))) [nnf transformation 3]
49. ! [X0] : ((((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | (brave(X0) | wise(X0))) & ((~brave(X0) & ~wise(X0)) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0))))) [nnf transformation 8]
50. ! [X0] : ((((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | brave(X0) | wise(X0)) & ((~brave(X0) & ~wise(X0)) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0))))) [flattening 49]
56. ! [X0] : (((creative(X0) & patient(X0)) | ~old(X0)) & (old(X0) | (~creative(X0) | ~patient(X0)))) [nnf transformation 11]
57. ! [X0] : (((creative(X0) & patient(X0)) | ~old(X0)) & (old(X0) | ~creative(X0) | ~patient(X0))) [flattening 56]
62. ! [X0] : (((~happy(X0) | ~rich(X0)) | ((funny(X0) | ~old(X0)) & (old(X0) | ~funny(X0)))) & (((~old(X0) | ~funny(X0)) & (old(X0) | funny(X0))) | (happy(X0) & rich(X0)))) [nnf transformation 13]
63. ! [X0] : ((~happy(X0) | ~rich(X0) | ((funny(X0) | ~old(X0)) & (old(X0) | ~funny(X0)))) & (((~old(X0) | ~funny(X0)) & (old(X0) | funny(X0))) | (happy(X0) & rich(X0)))) [flattening 62]
77. ? [X0] : (funny(X0) & ~humble(X0)) => (funny(sK9) & ~humble(sK9)) [choice axiom]
78. funny(sK9) & ~humble(sK9) [skolemisation 22,77]
79. old(john) | old(X1) | creative(X1) [cnf transformation 39]
80. old(john) | ~creative(X1) | ~old(X1) [cnf transformation 39]
82. ~wise(john) | ~creative(X1) | ~old(X1) [cnf transformation 39]
85. ~brave(X0) | funny(X0) | ~patient(X0) [cnf transformation 40]
90. humble(X0) | patient(X0) [cnf transformation 41]
106. ~creative(X0) | rich(X0) | brave(X0) | wise(X0) [cnf transformation 50]
113. ~patient(X0) | ~creative(X0) | old(X0) [cnf transformation 57]
114. ~old(X0) | patient(X0) [cnf transformation 57]
115. ~old(X0) | creative(X0) [cnf transformation 57]
124. ~funny(X0) | ~old(X0) | rich(X0) [cnf transformation 63]
143. ~humble(sK9) [cnf transformation 78]
146. ~rich(john) [cnf transformation 25]
148. 1 <=> old(john) [avatar definition]
149. old(john) <- (1) [avatar component clause 148]
152. 2 <=> wise(john) [avatar definition]
153. ~wise(john) <- (~2) [avatar component clause 152]
166. 5 <=> ! [X1] : (~creative(X1) | ~old(X1)) [avatar definition]
167. ~creative(X1) | ~old(X1) <- (5) [avatar component clause 166]
168. 5 | ~2 [avatar split clause 82,152,166]
170. 6 <=> ! [X1] : (old(X1) | creative(X1)) [avatar definition]
171. old(X1) | creative(X1) <- (6) [avatar component clause 170]
173. 5 | 1 [avatar split clause 80,148,166]
174. 6 | 1 [avatar split clause 79,148,170]
296. creative(X1) <- (6) [subsumption resolution 171,115]
297. ~old(X1) <- (5, 6) [subsumption resolution 167,296]
298. patient(sK9) [resolution 90,143]
364. ~creative(sK9) | old(sK9) [resolution 113,298]
366. old(sK9) <- (6) [subsumption resolution 364,296]
367. $false <- (5, 6) [subsumption resolution 366,297]
368. ~5 | ~6 [avatar contradiction clause 367]
412. ~old(X1) <- (5) [subsumption resolution 167,115]
413. $false <- (1, 5) [subsumption resolution 149,412]
414. ~1 | ~5 [avatar contradiction clause 413]
430. creative(john) <- (1) [resolution 149,115]
431. patient(john) <- (1) [resolution 149,114]
435. 47 <=> funny(john) [avatar definition]
436. funny(john) <- (47) [avatar component clause 435]
509. rich(john) | brave(john) | wise(john) <- (1) [resolution 106,430]
516. brave(john) | wise(john) <- (1) [subsumption resolution 509,146]
517. brave(john) <- (1, ~2) [subsumption resolution 516,153]
652. funny(john) | ~patient(john) <- (1, ~2) [resolution 517,85]
656. funny(john) <- (1, ~2) [subsumption resolution 652,431]
657. 47 | ~1 | 2 [avatar split clause 656,152,148,435]
659. ~old(john) | rich(john) <- (47) [resolution 436,124]
665. rich(john) <- (1, 47) [subsumption resolution 659,149]
666. $false <- (1, 47) [subsumption resolution 665,146]
667. ~1 | ~47 [avatar contradiction clause 666]
668. $false [avatar sat refutation 168,173,174,368,414,657,667]
% SZS output end Proof for 7651457452385893955786446
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative is either funny or quiet and vice versa.
Everyone who is not brave or wise is both not calm and calm.
Everyone who is funny is either quiet or not kind and vice versa.
If someone is both not old and not calm then someone is both not wise and not brave.
If someone is happy then someone is not brave and vice versa.
Everyone who is both not generous and curious is both not tall and patient.
Everyone who is not generous is both brave and not rich and vice versa.
If someone is either not curious or curious then someone is calm.
If someone is not funny or funny then someone is either not rich or strong and vice versa.
Everyone who is both not wise and old is both not tall and happy and vice versa.
If someone is either not old or not wise then mary is rich or not brave.
Everyone who is either tall or not brave is kind or not funny and vice versa.
If fred is either not tall or wise then fred is kind and vice versa.
Everyone who is not calm or not funny is brave.
If lucy is either not funny or old then someone is quiet or generous and vice versa.
If someone is both rich and brave then someone is tall or calm and vice versa.
Someone is patient.
Mary is both not funny and not generous.
John is rich.
Someone is both not strong and not old.
Someone is not humble. | John is old. | contradiction | (![X]:(~creative(X)<=>(funny(X)<~>quiet(X))))&
(![X]:((~brave(X)|wise(X))=>(~calm(X)&calm(X))))&
(![X]:(funny(X)<=>(quiet(X)<~>~kind(X))))&
((?[X]:((~old(X)&~calm(X))))=>(?[X]:((~wise(X)&~brave(X)))))&
((?[X]:(happy(X)))<=>(?[X]:(~brave(X))))&
(![X]:((~generous(X)&curious(X))=>(~tall(X)&patient(X))))&
(![X]:(~generous(X)<=>(brave(X)&~rich(X))))&
((?[X]:((~curious(X)<~>curious(X))))=>(?[X]:(calm(X))))&
((?[X]:((~funny(X)|funny(X))))<=>(?[X]:((~rich(X)<~>strong(X)))))&
(![X]:((~wise(X)&old(X))<=>(~tall(X)&happy(X))))&
((?[X]:((~old(X)<~>~wise(X))))=>((rich(mary)|~brave(mary))))&
(![X]:((tall(X)<~>~brave(X))<=>(kind(X)|~funny(X))))&
(((~tall(fred)<~>wise(fred)))<=>(kind(fred)))&
(![X]:((~calm(X)|~funny(X))=>brave(X)))&
(((~funny(lucy)<~>old(lucy)))<=>(?[X]:((quiet(X)|generous(X)))))&
((?[X]:((rich(X)&brave(X))))<=>(?[X]:((tall(X)|calm(X)))))&
(?[X]:(patient(X)))&
((~funny(mary)&~generous(mary)))&
(rich(john))&
(?[X]:((~strong(X)&~old(X))))&
(?[X]:(~humble(X))) | old(john) | [
"p1",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6360535934700034755173898
% SZS output start Proof for 6360535934700034755173898
2. ! [X0] : ((wise(X0) | ~brave(X0)) => (calm(X0) & ~calm(X0))) [input p1]
5. ? [X0] : happy(X0) <=> ? [X0] : ~brave(X0) [input p4]
10. ! [X0] : ((old(X0) & ~wise(X0)) <=> (happy(X0) & ~tall(X0))) [input p9]
22. old(john) [input hypothesis]
24. ? [X0] : happy(X0) <=> ? [X1] : ~brave(X1) [rectify 5]
31. ! [X0] : ((calm(X0) & ~calm(X0)) | (~wise(X0) & brave(X0))) [ennf transformation 2]
43. (? [X0] : happy(X0) | ! [X1] : brave(X1)) & (? [X1] : ~brave(X1) | ! [X0] : ~happy(X0)) [nnf transformation 24]
44. (? [X0] : happy(X0) | ! [X1] : brave(X1)) & (? [X2] : ~brave(X2) | ! [X3] : ~happy(X3)) [rectify 43]
45. ? [X0] : happy(X0) => happy(sK1) [choice axiom]
46. ? [X2] : ~brave(X2) => ~brave(sK2) [choice axiom]
47. (happy(sK1) | ! [X1] : brave(X1)) & (~brave(sK2) | ! [X3] : ~happy(X3)) [skolemisation 44,46,45]
59. ! [X0] : (((old(X0) & ~wise(X0)) | (~happy(X0) | tall(X0))) & ((happy(X0) & ~tall(X0)) | (~old(X0) | wise(X0)))) [nnf transformation 10]
60. ! [X0] : (((old(X0) & ~wise(X0)) | ~happy(X0) | tall(X0)) & ((happy(X0) & ~tall(X0)) | ~old(X0) | wise(X0))) [flattening 59]
76. ~calm(X0) | brave(X0) [cnf transformation 31]
77. ~calm(X0) | ~wise(X0) [cnf transformation 31]
78. calm(X0) | brave(X0) [cnf transformation 31]
79. calm(X0) | ~wise(X0) [cnf transformation 31]
86. ~brave(sK2) | ~happy(X3) [cnf transformation 47]
101. happy(X0) | ~old(X0) | wise(X0) [cnf transformation 60]
134. old(john) [cnf transformation 22]
137. ~wise(X0) [subsumption resolution 77,79]
138. brave(X0) [subsumption resolution 76,78]
140. ~happy(X3) [subsumption resolution 86,138]
172. ~old(X0) | wise(X0) [subsumption resolution 101,140]
173. ~old(X0) [subsumption resolution 172,137]
230. $false [subsumption resolution 134,173]
% SZS output end Proof for 6360535934700034755173898
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is not curious.
If someone is both not brave and happy then fred is not kind and vice versa.
Everyone who is either not tall or not rich is not old.
Everyone who is either rich or not rich is either creative or strong and vice versa.
If someone is both not quiet and rich then lucy is humble or not patient.
Everyone who is generous or not brave is both curious and not tall.
If someone is both not old and not patient then fred is generous or funny.
Everyone who is either strong or quiet is not funny or rich and vice versa.
If paul is curious then someone is creative or not generous.
Everyone who is not calm or not curious is quiet or strong and vice versa.
If lucy is not humble then susan is either strong or happy and vice versa.
Everyone who is quiet or tall is not brave.
Everyone who is not patient or strong is kind and vice versa.
If someone is funny or not creative then john is not patient or funny and vice versa.
If lucy is old or not kind then someone is happy.
If someone is both not humble and not patient then someone is both not kind and not old and vice versa.
Someone is both not happy and brave.
Lucy is either not calm or creative.
Paul is both calm and not quiet.
Someone is both curious and creative.
Someone is creative.
Susan is both humble and not patient.
John is not tall.
Paul is not patient or tall. | Fred is not rich. | neutral | (![X]:((funny(X)&~happy(X))=>~curious(X)))&
((?[X]:((~brave(X)&happy(X))))<=>(~kind(fred)))&
(![X]:((~tall(X)<~>~rich(X))=>~old(X)))&
(![X]:((rich(X)<~>~rich(X))<=>(creative(X)<~>strong(X))))&
((?[X]:((~quiet(X)&rich(X))))=>((humble(lucy)|~patient(lucy))))&
(![X]:((generous(X)|~brave(X))=>(curious(X)&~tall(X))))&
((?[X]:((~old(X)&~patient(X))))=>((generous(fred)|funny(fred))))&
(![X]:((strong(X)<~>quiet(X))<=>(~funny(X)|rich(X))))&
((curious(paul))=>(?[X]:((creative(X)|~generous(X)))))&
(![X]:((~calm(X)|~curious(X))<=>(quiet(X)|strong(X))))&
((~humble(lucy))<=>((strong(susan)<~>happy(susan))))&
(![X]:((quiet(X)|tall(X))=>~brave(X)))&
(![X]:((~patient(X)|strong(X))<=>kind(X)))&
((?[X]:((funny(X)|~creative(X))))<=>((~patient(john)|funny(john))))&
(((old(lucy)|~kind(lucy)))=>(?[X]:(happy(X))))&
((?[X]:((~humble(X)&~patient(X))))<=>(?[X]:((~kind(X)&~old(X)))))&
(?[X]:((~happy(X)&brave(X))))&
((~calm(lucy)<~>creative(lucy)))&
((calm(paul)&~quiet(paul)))&
(?[X]:((curious(X)&creative(X))))&
(?[X]:(creative(X)))&
((humble(susan)&~patient(susan)))&
(~tall(john))&
((~patient(paul)|tall(paul))) | ~rich(fred) | [] | null | 0 |
Everyone who is either not tall or calm is curious and vice versa.
Everyone who is both not curious and curious is either kind or calm and vice versa.
If paul is happy or calm then someone is wise.
Everyone who is both not wise and humble is old or not generous.
If someone is either humble or creative then john is both not generous and old and vice versa.
Everyone who is not patient or not curious is both brave and not rich and vice versa.
If john is both strong and not tall then someone is both quiet and old and vice versa.
Everyone who is not creative is either not humble or not calm and vice versa.
If someone is old then someone is generous.
If someone is either creative or not creative then lucy is either not wise or calm.
Everyone who is both generous and happy is either not kind or old and vice versa.
Everyone who is generous or not happy is either not funny or rich and vice versa.
Everyone who is not generous or not rich is both not curious and not patient and vice versa.
If someone is not happy or not humble then mary is both not brave and old.
If someone is either strong or patient then someone is not creative or not quiet.
Everyone who is both wise and not quiet is not patient or tall.
Paul is both generous and not tall.
Someone is brave or tall.
Alice is quiet.
Someone is either not strong or generous.
Susan is both not old and not funny.
Someone is both not old and not funny.
Susan is not calm or humble.
Paul is not kind or brave. | Susan is patient. | contradiction | (![X]:((~tall(X)<~>calm(X))<=>curious(X)))&
(![X]:((~curious(X)&curious(X))<=>(kind(X)<~>calm(X))))&
(((happy(paul)|calm(paul)))=>(?[X]:(wise(X))))&
(![X]:((~wise(X)&humble(X))=>(old(X)|~generous(X))))&
((?[X]:((humble(X)<~>creative(X))))<=>((~generous(john)&old(john))))&
(![X]:((~patient(X)|~curious(X))<=>(brave(X)&~rich(X))))&
(((strong(john)&~tall(john)))<=>(?[X]:((quiet(X)&old(X)))))&
(![X]:(~creative(X)<=>(~humble(X)<~>~calm(X))))&
((?[X]:(old(X)))=>(?[X]:(generous(X))))&
((?[X]:((creative(X)<~>~creative(X))))=>((~wise(lucy)<~>calm(lucy))))&
(![X]:((generous(X)&happy(X))<=>(~kind(X)<~>old(X))))&
(![X]:((generous(X)|~happy(X))<=>(~funny(X)<~>rich(X))))&
(![X]:((~generous(X)|~rich(X))<=>(~curious(X)&~patient(X))))&
((?[X]:((~happy(X)|~humble(X))))=>((~brave(mary)&old(mary))))&
((?[X]:((strong(X)<~>patient(X))))=>(?[X]:((~creative(X)|~quiet(X)))))&
(![X]:((wise(X)&~quiet(X))=>(~patient(X)|tall(X))))&
((generous(paul)&~tall(paul)))&
(?[X]:((brave(X)|tall(X))))&
(quiet(alice))&
(?[X]:((~strong(X)<~>generous(X))))&
((~old(susan)&~funny(susan)))&
(?[X]:((~old(X)&~funny(X))))&
((~calm(susan)|humble(susan)))&
((~kind(paul)|brave(paul))) | patient(susan) | [
"p11",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3170714234262327814564321
% SZS output start Proof for 3170714234262327814564321
12. ! [X0] : ((~happy(X0) | generous(X0)) <=> (~funny(X0) <~> rich(X0))) [input p11]
13. ! [X0] : ((~rich(X0) | ~generous(X0)) <=> (~patient(X0) & ~curious(X0))) [input p12]
21. ~funny(susan) & ~old(susan) [input p20]
25. patient(susan) [input hypothesis]
61. ! [X0] : (((~happy(X0) | generous(X0)) | ((~funny(X0) | ~rich(X0)) & (rich(X0) | funny(X0)))) & (((~rich(X0) | funny(X0)) & (rich(X0) | ~funny(X0))) | (happy(X0) & ~generous(X0)))) [nnf transformation 12]
62. ! [X0] : ((~happy(X0) | generous(X0) | ((~funny(X0) | ~rich(X0)) & (rich(X0) | funny(X0)))) & (((~rich(X0) | funny(X0)) & (rich(X0) | ~funny(X0))) | (happy(X0) & ~generous(X0)))) [flattening 61]
63. ! [X0] : (((~rich(X0) | ~generous(X0)) | (patient(X0) | curious(X0))) & ((~patient(X0) & ~curious(X0)) | (rich(X0) & generous(X0)))) [nnf transformation 13]
64. ! [X0] : ((~rich(X0) | ~generous(X0) | patient(X0) | curious(X0)) & ((~patient(X0) & ~curious(X0)) | (rich(X0) & generous(X0)))) [flattening 63]
121. ~rich(X0) | funny(X0) | ~generous(X0) [cnf transformation 62]
127. ~patient(X0) | generous(X0) [cnf transformation 64]
128. ~patient(X0) | rich(X0) [cnf transformation 64]
144. ~funny(susan) [cnf transformation 21]
149. patient(susan) [cnf transformation 25]
328. generous(susan) [resolution 127,149]
330. rich(susan) [resolution 128,149]
466. funny(susan) | ~generous(susan) [resolution 121,330]
468. ~generous(susan) [subsumption resolution 466,144]
469. $false [subsumption resolution 468,328]
% SZS output end Proof for 3170714234262327814564321
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is happy then someone is tall or humble.
Everyone who is quiet is either not rich or creative.
Everyone who is either funny or wise is either tall or not rich.
If mary is not strong then someone is not old or not funny and vice versa.
Everyone who is old or not humble is both patient and curious and vice versa.
If someone is kind then someone is both strong and not generous and vice versa.
Everyone who is curious is wise or not strong and vice versa.
If lucy is both not generous and not calm then fred is either generous or not curious.
If lucy is both kind and not brave then someone is both kind and patient and vice versa.
Everyone who is funny is old.
Everyone who is both not tall and not creative is either strong or not happy.
Everyone who is strong or funny is not patient or patient and vice versa.
Everyone who is either brave or tall is rich or wise.
If mary is not curious then someone is either not kind or not funny and vice versa.
If someone is generous or kind then someone is not kind or wise and vice versa.
If someone is either not tall or creative then alice is either kind or not tall.
John is happy or strong.
Lucy is kind.
Someone is either not generous or rich.
Fred is not patient or not old.
Alice is either not wise or not happy.
Paul is either not kind or happy.
Someone is not creative.
Someone is creative or not old. | Fred is not strong. | contradiction | ((?[X]:(happy(X)))=>(?[X]:((tall(X)|humble(X)))))&
(![X]:(quiet(X)=>(~rich(X)<~>creative(X))))&
(![X]:((funny(X)<~>wise(X))=>(tall(X)<~>~rich(X))))&
((~strong(mary))<=>(?[X]:((~old(X)|~funny(X)))))&
(![X]:((old(X)|~humble(X))<=>(patient(X)&curious(X))))&
((?[X]:(kind(X)))<=>(?[X]:((strong(X)&~generous(X)))))&
(![X]:(curious(X)<=>(wise(X)|~strong(X))))&
(((~generous(lucy)&~calm(lucy)))=>((generous(fred)<~>~curious(fred))))&
(((kind(lucy)&~brave(lucy)))<=>(?[X]:((kind(X)&patient(X)))))&
(![X]:(funny(X)=>old(X)))&
(![X]:((~tall(X)&~creative(X))=>(strong(X)<~>~happy(X))))&
(![X]:((strong(X)|funny(X))<=>(~patient(X)|patient(X))))&
(![X]:((brave(X)<~>tall(X))=>(rich(X)|wise(X))))&
((~curious(mary))<=>(?[X]:((~kind(X)<~>~funny(X)))))&
((?[X]:((generous(X)|kind(X))))<=>(?[X]:((~kind(X)|wise(X)))))&
((?[X]:((~tall(X)<~>creative(X))))=>((kind(alice)<~>~tall(alice))))&
((happy(john)|strong(john)))&
(kind(lucy))&
(?[X]:((~generous(X)<~>rich(X))))&
((~patient(fred)|~old(fred)))&
((~wise(alice)<~>~happy(alice)))&
((~kind(paul)<~>happy(paul)))&
(?[X]:(~creative(X)))&
(?[X]:((creative(X)|~old(X)))) | ~strong(fred) | [
"p4",
"p9",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7782867202737070373251768
% SZS output start Proof for 7782867202737070373251768
5. ! [X0] : ((~humble(X0) | old(X0)) <=> (curious(X0) & patient(X0))) [input p4]
10. ! [X0] : (funny(X0) => old(X0)) [input p9]
12. ! [X0] : ((funny(X0) | strong(X0)) <=> (patient(X0) | ~patient(X0))) [input p11]
20. ~old(fred) | ~patient(fred) [input p19]
25. ~strong(fred) [input hypothesis]
33. ! [X0] : (old(X0) | ~funny(X0)) [ennf transformation 10]
47. ! [X0] : (((~humble(X0) | old(X0)) | (~curious(X0) | ~patient(X0))) & ((curious(X0) & patient(X0)) | (humble(X0) & ~old(X0)))) [nnf transformation 5]
48. ! [X0] : ((~humble(X0) | old(X0) | ~curious(X0) | ~patient(X0)) & ((curious(X0) & patient(X0)) | (humble(X0) & ~old(X0)))) [flattening 47]
62. ! [X0] : (((funny(X0) | strong(X0)) | (~patient(X0) & patient(X0))) & ((patient(X0) | ~patient(X0)) | (~funny(X0) & ~strong(X0)))) [nnf transformation 12]
63. ! [X0] : ((funny(X0) | strong(X0) | (~patient(X0) & patient(X0))) & (patient(X0) | ~patient(X0) | (~funny(X0) & ~strong(X0)))) [flattening 62]
92. ~old(X0) | patient(X0) [cnf transformation 48]
107. ~funny(X0) | old(X0) [cnf transformation 33]
112. funny(X0) | strong(X0) | patient(X0) [cnf transformation 63]
113. funny(X0) | strong(X0) | ~patient(X0) [cnf transformation 63]
132. ~old(fred) | ~patient(fred) [cnf transformation 20]
139. ~strong(fred) [cnf transformation 25]
217. strong(X0) | funny(X0) [subsumption resolution 112,113]
307. ~old(fred) [subsumption resolution 132,92]
345. funny(fred) [resolution 217,139]
352. old(fred) [resolution 345,107]
353. $false [subsumption resolution 352,307]
% SZS output end Proof for 7782867202737070373251768
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either tall or not patient then lucy is either not strong or not creative.
If susan is both not tall and not rich then someone is both curious and generous.
Everyone who is not funny is strong or not wise and vice versa.
Everyone who is old is both patient and not curious and vice versa.
If someone is happy or wise then someone is either calm or not strong.
Everyone who is either calm or tall is either strong or patient.
Everyone who is either not generous or quiet is tall or not old and vice versa.
Everyone who is strong is either not wise or curious.
Everyone who is funny or not generous is quiet or not curious.
If fred is both curious and creative then someone is not tall.
If someone is either curious or humble then susan is both creative and not funny.
Everyone who is not generous or happy is both not brave and curious and vice versa.
If someone is either tall or quiet then someone is both wise and not brave.
If someone is either not brave or rich then paul is kind or not curious and vice versa.
Everyone who is strong or quiet is not quiet.
Everyone who is not happy or brave is either not curious or not rich.
Someone is brave or not brave.
Someone is either not humble or strong.
Alice is wise.
Someone is patient. | Alice is funny. | entailment | (((tall(fred)<~>~patient(fred)))=>((~strong(lucy)<~>~creative(lucy))))&
(((~tall(susan)&~rich(susan)))=>(?[X]:((curious(X)&generous(X)))))&
(![X]:(~funny(X)<=>(strong(X)|~wise(X))))&
(![X]:(old(X)<=>(patient(X)&~curious(X))))&
((?[X]:((happy(X)|wise(X))))=>(?[X]:((calm(X)<~>~strong(X)))))&
(![X]:((calm(X)<~>tall(X))=>(strong(X)<~>patient(X))))&
(![X]:((~generous(X)<~>quiet(X))<=>(tall(X)|~old(X))))&
(![X]:(strong(X)=>(~wise(X)<~>curious(X))))&
(![X]:((funny(X)|~generous(X))=>(quiet(X)|~curious(X))))&
(((curious(fred)&creative(fred)))=>(?[X]:(~tall(X))))&
((?[X]:((curious(X)<~>humble(X))))=>((creative(susan)&~funny(susan))))&
(![X]:((~generous(X)|happy(X))<=>(~brave(X)&curious(X))))&
((?[X]:((tall(X)<~>quiet(X))))=>(?[X]:((wise(X)&~brave(X)))))&
((?[X]:((~brave(X)<~>rich(X))))<=>((kind(paul)|~curious(paul))))&
(![X]:((strong(X)|quiet(X))=>~quiet(X)))&
(![X]:((~happy(X)|brave(X))=>(~curious(X)<~>~rich(X))))&
(?[X]:((brave(X)|~brave(X))))&
(?[X]:((~humble(X)<~>strong(X))))&
(wise(alice))&
(?[X]:(patient(X))) | funny(alice) | [
"p2",
"p3",
"p6",
"p7",
"p8",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 542843051616442919435950
% SZS output start Proof for 542843051616442919435950
3. ! [X0] : (~funny(X0) <=> (~wise(X0) | strong(X0))) [input p2]
4. ! [X0] : (old(X0) <=> (~curious(X0) & patient(X0))) [input p3]
7. ! [X0] : ((~generous(X0) <~> quiet(X0)) <=> (~old(X0) | tall(X0))) [input p6]
8. ! [X0] : (strong(X0) => (~wise(X0) <~> curious(X0))) [input p7]
9. ! [X0] : ((~generous(X0) | funny(X0)) => (~curious(X0) | quiet(X0))) [input p8]
15. ! [X0] : ((quiet(X0) | strong(X0)) => ~quiet(X0)) [input p14]
19. wise(alice) [input p18]
21. ~funny(alice) [input hypothesis]
24. ! [X0] : (~funny(X0) => (~wise(X0) | strong(X0))) [unused predicate definition removal 3]
28. ! [X0] : ((~wise(X0) | strong(X0)) | funny(X0)) [ennf transformation 24]
29. ! [X0] : (~wise(X0) | strong(X0) | funny(X0)) [flattening 28]
32. ! [X0] : ((~wise(X0) <~> curious(X0)) | ~strong(X0)) [ennf transformation 8]
33. ! [X0] : ((~curious(X0) | quiet(X0)) | (generous(X0) & ~funny(X0))) [ennf transformation 9]
34. ! [X0] : (~curious(X0) | quiet(X0) | (generous(X0) & ~funny(X0))) [flattening 33]
39. ! [X0] : (~quiet(X0) | (~quiet(X0) & ~strong(X0))) [ennf transformation 15]
44. ! [X0] : ((old(X0) | (curious(X0) | ~patient(X0))) & ((~curious(X0) & patient(X0)) | ~old(X0))) [nnf transformation 4]
45. ! [X0] : ((old(X0) | curious(X0) | ~patient(X0)) & ((~curious(X0) & patient(X0)) | ~old(X0))) [flattening 44]
51. ! [X0] : ((((~quiet(X0) | generous(X0)) & (quiet(X0) | ~generous(X0))) | (old(X0) & ~tall(X0))) & ((~old(X0) | tall(X0)) | ((~generous(X0) | ~quiet(X0)) & (quiet(X0) | generous(X0))))) [nnf transformation 7]
52. ! [X0] : ((((~quiet(X0) | generous(X0)) & (quiet(X0) | ~generous(X0))) | (old(X0) & ~tall(X0))) & (~old(X0) | tall(X0) | ((~generous(X0) | ~quiet(X0)) & (quiet(X0) | generous(X0))))) [flattening 51]
53. ! [X0] : (((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | ~strong(X0)) [nnf transformation 32]
82. ~wise(X0) | strong(X0) | funny(X0) [cnf transformation 29]
84. ~old(X0) | ~curious(X0) [cnf transformation 45]
97. ~generous(X0) | quiet(X0) | old(X0) [cnf transformation 52]
100. ~wise(X0) | curious(X0) | ~strong(X0) [cnf transformation 53]
103. ~curious(X0) | quiet(X0) | generous(X0) [cnf transformation 34]
125. ~quiet(X0) | ~quiet(X0) [cnf transformation 39]
133. wise(alice) [cnf transformation 19]
135. ~funny(alice) [cnf transformation 21]
136. ~quiet(X0) [duplicate literal removal 125]
288. strong(alice) | funny(alice) [resolution 82,133]
290. strong(alice) [subsumption resolution 288,135]
320. curious(alice) | ~strong(alice) [resolution 100,133]
321. curious(alice) [subsumption resolution 320,290]
327. quiet(alice) | generous(alice) [resolution 103,321]
329. generous(alice) [subsumption resolution 327,136]
330. quiet(alice) | old(alice) [resolution 329,97]
332. old(alice) [subsumption resolution 330,136]
344. ~curious(alice) [resolution 332,84]
346. $false [subsumption resolution 344,321]
% SZS output end Proof for 542843051616442919435950
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both not happy and not quiet then someone is both wise and patient.
If someone is either not strong or not wise then someone is both curious and patient and vice versa.
If fred is both old and not happy then someone is kind or calm.
If someone is kind then someone is either humble or not happy.
Everyone who is either not old or not generous is not happy or rich.
Everyone who is strong is generous.
If john is not rich or not wise then paul is not quiet or not happy.
Everyone who is patient or curious is either not kind or not patient.
If paul is not patient or patient then someone is strong or not rich and vice versa.
Everyone who is either brave or not wise is generous and vice versa.
If susan is not brave then someone is either creative or humble and vice versa.
Everyone who is both happy and humble is not patient.
Everyone who is not brave or not patient is both not quiet and not calm.
Everyone who is not generous is either quiet or brave.
If someone is either not rich or not calm then someone is patient and vice versa.
If someone is brave or not tall then paul is kind or wise.
John is either not wise or wise.
Someone is both not generous and not curious.
Someone is either not wise or brave.
Susan is both not calm and quiet.
Someone is either not rich or not curious.
Fred is not calm.
Someone is rich. | John is rich. | neutral | (((~happy(mary)&~quiet(mary)))=>(?[X]:((wise(X)&patient(X)))))&
((?[X]:((~strong(X)<~>~wise(X))))<=>(?[X]:((curious(X)&patient(X)))))&
(((old(fred)&~happy(fred)))=>(?[X]:((kind(X)|calm(X)))))&
((?[X]:(kind(X)))=>(?[X]:((humble(X)<~>~happy(X)))))&
(![X]:((~old(X)<~>~generous(X))=>(~happy(X)|rich(X))))&
(![X]:(strong(X)=>generous(X)))&
(((~rich(john)|~wise(john)))=>((~quiet(paul)|~happy(paul))))&
(![X]:((patient(X)|curious(X))=>(~kind(X)<~>~patient(X))))&
(((~patient(paul)|patient(paul)))<=>(?[X]:((strong(X)|~rich(X)))))&
(![X]:((brave(X)<~>~wise(X))<=>generous(X)))&
((~brave(susan))<=>(?[X]:((creative(X)<~>humble(X)))))&
(![X]:((happy(X)&humble(X))=>~patient(X)))&
(![X]:((~brave(X)|~patient(X))=>(~quiet(X)&~calm(X))))&
(![X]:(~generous(X)=>(quiet(X)<~>brave(X))))&
((?[X]:((~rich(X)<~>~calm(X))))<=>(?[X]:(patient(X))))&
((?[X]:((brave(X)|~tall(X))))=>((kind(paul)|wise(paul))))&
((~wise(john)<~>wise(john)))&
(?[X]:((~generous(X)&~curious(X))))&
(?[X]:((~wise(X)<~>brave(X))))&
((~calm(susan)&quiet(susan)))&
(?[X]:((~rich(X)<~>~curious(X))))&
(~calm(fred))&
(?[X]:(rich(X))) | rich(john) | [] | null | 0 |
If john is humble or funny then someone is patient and vice versa.
If fred is funny or not old then someone is old and vice versa.
Everyone who is not calm is happy or not humble.
Everyone who is either rich or not tall is not funny and vice versa.
Everyone who is either not rich or old is not calm or not happy and vice versa.
Everyone who is either not calm or not old is both not kind and curious.
Everyone who is both not generous and not kind is generous.
Everyone who is both not strong and not brave is either not tall or not brave.
Everyone who is both not creative and not calm is funny or not patient and vice versa.
If someone is both not generous and not funny then someone is either generous or not funny.
If john is not calm then someone is either generous or happy.
Everyone who is both patient and not humble is strong or not kind and vice versa.
If john is generous or not quiet then mary is both not kind and quiet.
Everyone who is both not brave and generous is funny or not generous and vice versa.
Everyone who is both not wise and not tall is tall or not wise and vice versa.
Everyone who is both strong and not calm is not quiet.
Someone is not tall or old.
Someone is wise or not strong.
Fred is humble or wise.
Mary is not kind or not curious.
John is both not humble and old. | Fred is not generous. | contradiction | (((humble(john)|funny(john)))<=>(?[X]:(patient(X))))&
(((funny(fred)|~old(fred)))<=>(?[X]:(old(X))))&
(![X]:(~calm(X)=>(happy(X)|~humble(X))))&
(![X]:((rich(X)<~>~tall(X))<=>~funny(X)))&
(![X]:((~rich(X)<~>old(X))<=>(~calm(X)|~happy(X))))&
(![X]:((~calm(X)<~>~old(X))=>(~kind(X)&curious(X))))&
(![X]:((~generous(X)&~kind(X))=>generous(X)))&
(![X]:((~strong(X)&~brave(X))=>(~tall(X)<~>~brave(X))))&
(![X]:((~creative(X)&~calm(X))<=>(funny(X)|~patient(X))))&
((?[X]:((~generous(X)&~funny(X))))=>(?[X]:((generous(X)<~>~funny(X)))))&
((~calm(john))=>(?[X]:((generous(X)<~>happy(X)))))&
(![X]:((patient(X)&~humble(X))<=>(strong(X)|~kind(X))))&
(((generous(john)|~quiet(john)))=>((~kind(mary)&quiet(mary))))&
(![X]:((~brave(X)&generous(X))<=>(funny(X)|~generous(X))))&
(![X]:((~wise(X)&~tall(X))<=>(tall(X)|~wise(X))))&
(![X]:((strong(X)&~calm(X))=>~quiet(X)))&
(?[X]:((~tall(X)|old(X))))&
(?[X]:((wise(X)|~strong(X))))&
((humble(fred)|wise(fred)))&
((~kind(mary)|~curious(mary)))&
((~humble(john)&old(john))) | ~generous(fred) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6843359600442156160108221
% SZS output start Proof for 6843359600442156160108221
14. ! [X0] : ((generous(X0) & ~brave(X0)) <=> (~generous(X0) | funny(X0))) [input p13]
22. ~generous(fred) [input hypothesis]
62. ! [X0] : (((generous(X0) & ~brave(X0)) | (generous(X0) & ~funny(X0))) & ((~generous(X0) | funny(X0)) | (~generous(X0) | brave(X0)))) [nnf transformation 14]
63. ! [X0] : (((generous(X0) & ~brave(X0)) | (generous(X0) & ~funny(X0))) & (~generous(X0) | funny(X0) | ~generous(X0) | brave(X0))) [flattening 62]
116. generous(X0) | generous(X0) [cnf transformation 63]
129. ~generous(fred) [cnf transformation 22]
133. generous(X0) [duplicate literal removal 116]
244. $false [subsumption resolution 129,133]
% SZS output end Proof for 6843359600442156160108221
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both strong and patient then john is both funny and patient.
Everyone who is not creative or not generous is calm and vice versa.
Everyone who is not funny is either not calm or generous.
Everyone who is not quiet or wise is either not quiet or patient.
If susan is old then someone is both not tall and strong and vice versa.
If someone is quiet or not old then someone is both not wise and wise.
If someone is both patient and not quiet then fred is calm.
Everyone who is either not tall or not calm is both creative and not wise and vice versa.
If someone is not creative or not generous then someone is both wise and not kind.
If fred is both happy and old then john is funny and vice versa.
Everyone who is both not happy and funny is not funny and vice versa.
Everyone who is both not patient and not curious is funny.
If someone is not tall or not patient then paul is both not generous and not humble.
Everyone who is either funny or not creative is not kind or not old.
If susan is both not tall and not happy then someone is kind or curious.
Everyone who is either old or patient is brave and vice versa.
Fred is kind or not creative.
Someone is not tall or generous.
Someone is not patient.
Alice is funny or happy.
Mary is humble. | Susan is not old. | contradiction | (((strong(paul)&patient(paul)))=>((funny(john)&patient(john))))&
(![X]:((~creative(X)|~generous(X))<=>calm(X)))&
(![X]:(~funny(X)=>(~calm(X)<~>generous(X))))&
(![X]:((~quiet(X)|wise(X))=>(~quiet(X)<~>patient(X))))&
((old(susan))<=>(?[X]:((~tall(X)&strong(X)))))&
((?[X]:((quiet(X)|~old(X))))=>(?[X]:((~wise(X)&wise(X)))))&
((?[X]:((patient(X)&~quiet(X))))=>(calm(fred)))&
(![X]:((~tall(X)<~>~calm(X))<=>(creative(X)&~wise(X))))&
((?[X]:((~creative(X)|~generous(X))))=>(?[X]:((wise(X)&~kind(X)))))&
(((happy(fred)&old(fred)))<=>(funny(john)))&
(![X]:((~happy(X)&funny(X))<=>~funny(X)))&
(![X]:((~patient(X)&~curious(X))=>funny(X)))&
((?[X]:((~tall(X)|~patient(X))))=>((~generous(paul)&~humble(paul))))&
(![X]:((funny(X)<~>~creative(X))=>(~kind(X)|~old(X))))&
(((~tall(susan)&~happy(susan)))=>(?[X]:((kind(X)|curious(X)))))&
(![X]:((old(X)<~>patient(X))<=>brave(X)))&
((kind(fred)|~creative(fred)))&
(?[X]:((~tall(X)|generous(X))))&
(?[X]:(~patient(X)))&
((funny(alice)|happy(alice)))&
(humble(mary)) | ~old(susan) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 8766668191752020855808144
% SZS output start Proof for 8766668191752020855808144
6. ? [X0] : (~old(X0) | quiet(X0)) => ? [X0] : (wise(X0) & ~wise(X0)) [input p5]
22. ~old(susan) [input hypothesis]
23. ? [X0] : (~old(X0) | quiet(X0)) => ? [X1] : (wise(X1) & ~wise(X1)) [rectify 6]
31. ? [X1] : (wise(X1) & ~wise(X1)) | ! [X0] : (old(X0) & ~quiet(X0)) [ennf transformation 23]
45. ? [X0] : (wise(X0) & ~wise(X0)) | ! [X1] : (old(X1) & ~quiet(X1)) [rectify 31]
46. ? [X0] : (wise(X0) & ~wise(X0)) => (wise(sK1) & ~wise(sK1)) [choice axiom]
47. (wise(sK1) & ~wise(sK1)) | ! [X1] : (old(X1) & ~quiet(X1)) [skolemisation 45,46]
77. ~wise(sK1) | old(X1) [cnf transformation 47]
79. wise(sK1) | old(X1) [cnf transformation 47]
108. ~old(susan) [cnf transformation 22]
136. 6 <=> old(susan) [avatar definition]
137. ~old(susan) <- (~6) [avatar component clause 136]
151. 9 <=> ! [X1] : old(X1) [avatar definition]
152. old(X1) <- (9) [avatar component clause 151]
154. 10 <=> wise(sK1) [avatar definition]
157. 9 | 10 [avatar split clause 79,154,151]
162. 9 | ~10 [avatar split clause 77,154,151]
233. ~6 [avatar split clause 108,136]
234. $false <- (~6, 9) [subsumption resolution 137,152]
235. 6 | ~9 [avatar contradiction clause 234]
238. $false [avatar sat refutation 157,162,233,235]
% SZS output end Proof for 8766668191752020855808144
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old or not calm then mary is both not curious and quiet.
Everyone who is not generous or creative is either not kind or humble.
If paul is calm then someone is either strong or funny.
Everyone who is not calm or rich is either wise or patient.
Everyone who is either funny or not humble is both curious and happy.
Everyone who is not calm is both not generous and rich.
If alice is both not old and calm then someone is not strong and vice versa.
If someone is either generous or not patient then mary is brave or not funny.
Everyone who is either not patient or wise is curious.
If someone is tall then paul is not curious or not kind and vice versa.
If fred is old then john is not brave.
If someone is not humble then someone is not old and vice versa.
If someone is not funny or rich then lucy is both not brave and not calm and vice versa.
Everyone who is either happy or not curious is tall.
Everyone who is both brave and not brave is not generous and vice versa.
Everyone who is both not calm and not curious is both rich and quiet.
Paul is curious.
Someone is not patient or strong.
Someone is either not funny or calm.
Someone is not old or not happy. | Paul is quiet. | neutral | ((?[X]:((~old(X)|~calm(X))))=>((~curious(mary)&quiet(mary))))&
(![X]:((~generous(X)|creative(X))=>(~kind(X)<~>humble(X))))&
((calm(paul))=>(?[X]:((strong(X)<~>funny(X)))))&
(![X]:((~calm(X)|rich(X))=>(wise(X)<~>patient(X))))&
(![X]:((funny(X)<~>~humble(X))=>(curious(X)&happy(X))))&
(![X]:(~calm(X)=>(~generous(X)&rich(X))))&
(((~old(alice)&calm(alice)))<=>(?[X]:(~strong(X))))&
((?[X]:((generous(X)<~>~patient(X))))=>((brave(mary)|~funny(mary))))&
(![X]:((~patient(X)<~>wise(X))=>curious(X)))&
((?[X]:(tall(X)))<=>((~curious(paul)|~kind(paul))))&
((old(fred))=>(~brave(john)))&
((?[X]:(~humble(X)))<=>(?[X]:(~old(X))))&
((?[X]:((~funny(X)|rich(X))))<=>((~brave(lucy)&~calm(lucy))))&
(![X]:((happy(X)<~>~curious(X))=>tall(X)))&
(![X]:((brave(X)&~brave(X))<=>~generous(X)))&
(![X]:((~calm(X)&~curious(X))=>(rich(X)&quiet(X))))&
(curious(paul))&
(?[X]:((~patient(X)|strong(X))))&
(?[X]:((~funny(X)<~>calm(X))))&
(?[X]:((~old(X)|~happy(X)))) | quiet(paul) | [] | null | 0 |
If paul is brave then someone is brave and vice versa. Everyone who is both curious and happy is both not creative and not happy and vice versa. If someone is both funny and humble then alice is not funny or patient. If lucy is not rich or not curious then alice is brave or funny and vice versa. Everyone who is either not strong or not humble is tall or generous and vice versa. Everyone who is either not generous or generous is either tall or not brave. If paul is both not old and not tall then someone is either not rich or not wise. Everyone who is either not wise or quiet is creative. Everyone who is either not humble or patient is both kind and not happy. Everyone who is curious or creative is both happy and not wise and vice versa. Everyone who is either not tall or generous is not brave or kind. Everyone who is both not tall and humble is not humble or quiet and vice versa. Everyone who is old is not funny or tall and vice versa. Everyone who is creative or kind is not kind or not rich. Everyone who is either curious or kind is either not happy or calm and vice versa. If someone is both not calm and curious then fred is both not tall and calm and vice versa. John is either not creative or generous. Someone is not happy or old. John is not strong or humble. Fred is quiet. Paul is calm. Someone is funny. | Alice is funny. | contradiction | ((brave(paul))<=>(?[X]:(brave(X))))&
(![X]:((curious(X)&happy(X))<=>(~creative(X)&~happy(X))))&
((?[X]:((funny(X)&humble(X))))=>((~funny(alice)|patient(alice))))&
(((~rich(lucy)|~curious(lucy)))<=>((brave(alice)|funny(alice))))&
(![X]:((~strong(X)<~>~humble(X))<=>(tall(X)|generous(X))))&
(![X]:((~generous(X)<~>generous(X))=>(tall(X)<~>~brave(X))))&
(((~old(paul)&~tall(paul)))=>(?[X]:((~rich(X)<~>~wise(X)))))&
(![X]:((~wise(X)<~>quiet(X))=>creative(X)))&
(![X]:((~humble(X)<~>patient(X))=>(kind(X)&~happy(X))))&
(![X]:((curious(X)|creative(X))<=>(happy(X)&~wise(X))))&
(![X]:((~tall(X)<~>generous(X))=>(~brave(X)|kind(X))))&
(![X]:((~tall(X)&humble(X))<=>(~humble(X)|quiet(X))))&
(![X]:(old(X)<=>(~funny(X)|tall(X))))&
(![X]:((creative(X)|kind(X))=>(~kind(X)|~rich(X))))&
(![X]:((curious(X)<~>kind(X))<=>(~happy(X)<~>calm(X))))&
((?[X]:((~calm(X)&curious(X))))<=>((~tall(fred)&calm(fred))))&
((~creative(john)<~>generous(john)))&
(?[X]:((~happy(X)|old(X))))&
((~strong(john)|humble(john)))&
(quiet(fred))&
(calm(paul))&
(?[X]:(funny(X))) | funny(alice) | [
"p1",
"p2",
"p8",
"p9",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4357221517087355837126772
% SZS output start Proof for 4357221517087355837126772
2. ! [X0] : ((happy(X0) & curious(X0)) <=> (~happy(X0) & ~creative(X0))) [input p1]
3. ? [X0] : (humble(X0) & funny(X0)) => (patient(alice) | ~funny(alice)) [input p2]
9. ! [X0] : ((~humble(X0) <~> patient(X0)) => (~happy(X0) & kind(X0))) [input p8]
10. ! [X0] : ((creative(X0) | curious(X0)) <=> (~wise(X0) & happy(X0))) [input p9]
12. ! [X0] : ((humble(X0) & ~tall(X0)) <=> (quiet(X0) | ~humble(X0))) [input p11]
22. ? [X0] : funny(X0) [input p21]
23. funny(alice) [input hypothesis]
25. (patient(alice) | ~funny(alice)) | ! [X0] : (~humble(X0) | ~funny(X0)) [ennf transformation 3]
26. patient(alice) | ~funny(alice) | ! [X0] : (~humble(X0) | ~funny(X0)) [flattening 25]
31. ! [X0] : ((~happy(X0) & kind(X0)) | (~humble(X0) <=> patient(X0))) [ennf transformation 9]
42. ! [X0] : (((happy(X0) & curious(X0)) | (happy(X0) | creative(X0))) & ((~happy(X0) & ~creative(X0)) | (~happy(X0) | ~curious(X0)))) [nnf transformation 2]
43. ! [X0] : (((happy(X0) & curious(X0)) | happy(X0) | creative(X0)) & ((~happy(X0) & ~creative(X0)) | ~happy(X0) | ~curious(X0))) [flattening 42]
53. ! [X0] : ((~happy(X0) & kind(X0)) | ((~humble(X0) | ~patient(X0)) & (patient(X0) | humble(X0)))) [nnf transformation 31]
54. ! [X0] : (((creative(X0) | curious(X0)) | (wise(X0) | ~happy(X0))) & ((~wise(X0) & happy(X0)) | (~creative(X0) & ~curious(X0)))) [nnf transformation 10]
55. ! [X0] : ((creative(X0) | curious(X0) | wise(X0) | ~happy(X0)) & ((~wise(X0) & happy(X0)) | (~creative(X0) & ~curious(X0)))) [flattening 54]
57. ! [X0] : (((humble(X0) & ~tall(X0)) | (~quiet(X0) & humble(X0))) & ((quiet(X0) | ~humble(X0)) | (~humble(X0) | tall(X0)))) [nnf transformation 12]
58. ! [X0] : (((humble(X0) & ~tall(X0)) | (~quiet(X0) & humble(X0))) & (quiet(X0) | ~humble(X0) | ~humble(X0) | tall(X0))) [flattening 57]
68. ? [X0] : funny(X0) => funny(sK4) [choice axiom]
69. funny(sK4) [skolemisation 22,68]
75. happy(X0) | happy(X0) | creative(X0) [cnf transformation 43]
76. patient(alice) | ~funny(alice) | ~humble(X0) | ~funny(X0) [cnf transformation 26]
98. ~patient(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 53]
100. happy(X0) | ~creative(X0) [cnf transformation 55]
109. humble(X0) | humble(X0) [cnf transformation 58]
132. funny(sK4) [cnf transformation 69]
133. funny(alice) [cnf transformation 23]
136. humble(X0) [duplicate literal removal 109]
142. creative(X0) | happy(X0) [duplicate literal removal 75]
157. 4 <=> ! [X0] : (~humble(X0) | ~funny(X0)) [avatar definition]
158. ~humble(X0) | ~funny(X0) <- (4) [avatar component clause 157]
160. 5 <=> funny(alice) [avatar definition]
164. 6 <=> patient(alice) [avatar definition]
166. patient(alice) <- (6) [avatar component clause 164]
167. 4 | ~5 | 6 [avatar split clause 76,164,160,157]
205. happy(X0) [subsumption resolution 100,142]
244. 5 [avatar split clause 133,160]
245. ~funny(X0) <- (4) [subsumption resolution 158,136]
246. $false <- (4) [resolution 245,132]
249. ~4 [avatar contradiction clause 246]
276. ~humble(alice) | ~happy(alice) <- (6) [resolution 98,166]
277. ~happy(alice) <- (6) [subsumption resolution 276,136]
278. $false <- (6) [subsumption resolution 277,205]
279. ~6 [avatar contradiction clause 278]
280. $false [avatar sat refutation 167,244,249,279]
% SZS output end Proof for 4357221517087355837126772
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy then paul is funny or not tall.
Everyone who is both wise and not generous is both strong and kind.
If lucy is not curious then lucy is rich or patient and vice versa.
Everyone who is not funny is kind.
If lucy is both wise and humble then someone is both funny and calm.
Everyone who is not brave is not quiet or not strong.
If susan is either old or not creative then someone is not quiet.
Everyone who is both creative and not wise is not wise.
If someone is both not patient and not quiet then someone is both creative and not old.
Everyone who is humble or not humble is both not funny and not generous and vice versa.
Everyone who is quiet is either not kind or brave and vice versa.
Everyone who is not quiet or not kind is either not brave or quiet and vice versa.
If someone is both not tall and not wise then fred is not rich and vice versa.
If john is not wise then someone is curious or tall.
Everyone who is both wise and happy is wise or not strong and vice versa.
If susan is not quiet then someone is not tall or not kind.
Someone is curious.
Someone is not generous or tall.
Fred is both rich and tall.
Someone is not humble or old.
Someone is both not patient and not happy.
Someone is not funny. | Lucy is brave. | contradiction | ((?[X]:(~happy(X)))=>((funny(paul)|~tall(paul))))&
(![X]:((wise(X)&~generous(X))=>(strong(X)&kind(X))))&
((~curious(lucy))<=>((rich(lucy)|patient(lucy))))&
(![X]:(~funny(X)=>kind(X)))&
(((wise(lucy)&humble(lucy)))=>(?[X]:((funny(X)&calm(X)))))&
(![X]:(~brave(X)=>(~quiet(X)|~strong(X))))&
(((old(susan)<~>~creative(susan)))=>(?[X]:(~quiet(X))))&
(![X]:((creative(X)&~wise(X))=>~wise(X)))&
((?[X]:((~patient(X)&~quiet(X))))=>(?[X]:((creative(X)&~old(X)))))&
(![X]:((humble(X)|~humble(X))<=>(~funny(X)&~generous(X))))&
(![X]:(quiet(X)<=>(~kind(X)<~>brave(X))))&
(![X]:((~quiet(X)|~kind(X))<=>(~brave(X)<~>quiet(X))))&
((?[X]:((~tall(X)&~wise(X))))<=>(~rich(fred)))&
((~wise(john))=>(?[X]:((curious(X)|tall(X)))))&
(![X]:((wise(X)&happy(X))<=>(wise(X)|~strong(X))))&
((~quiet(susan))=>(?[X]:((~tall(X)|~kind(X)))))&
(?[X]:(curious(X)))&
(?[X]:((~generous(X)|tall(X))))&
((rich(fred)&tall(fred)))&
(?[X]:((~humble(X)|old(X))))&
(?[X]:((~patient(X)&~happy(X))))&
(?[X]:(~funny(X))) | brave(lucy) | [
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3831236134360242760973673
% SZS output start Proof for 3831236134360242760973673
11. ! [X0] : (quiet(X0) <=> (~kind(X0) <~> brave(X0))) [input p10]
12. ! [X0] : ((~kind(X0) | ~quiet(X0)) <=> (~brave(X0) <~> quiet(X0))) [input p11]
23. brave(lucy) [input hypothesis]
53. ! [X0] : ((quiet(X0) | ((~kind(X0) | ~brave(X0)) & (brave(X0) | kind(X0)))) & (((~brave(X0) | kind(X0)) & (brave(X0) | ~kind(X0))) | ~quiet(X0))) [nnf transformation 11]
54. ! [X0] : (((~kind(X0) | ~quiet(X0)) | ((~brave(X0) | ~quiet(X0)) & (quiet(X0) | brave(X0)))) & (((~quiet(X0) | brave(X0)) & (quiet(X0) | ~brave(X0))) | (kind(X0) & quiet(X0)))) [nnf transformation 12]
55. ! [X0] : ((~kind(X0) | ~quiet(X0) | ((~brave(X0) | ~quiet(X0)) & (quiet(X0) | brave(X0)))) & (((~quiet(X0) | brave(X0)) & (quiet(X0) | ~brave(X0))) | (kind(X0) & quiet(X0)))) [flattening 54]
96. ~brave(X0) | kind(X0) | ~quiet(X0) [cnf transformation 53]
99. quiet(X0) | ~brave(X0) | quiet(X0) [cnf transformation 55]
104. ~kind(X0) | ~quiet(X0) | ~brave(X0) | ~quiet(X0) [cnf transformation 55]
123. brave(lucy) [cnf transformation 23]
124. quiet(X0) | ~brave(X0) [duplicate literal removal 99]
125. ~kind(X0) | ~quiet(X0) | ~brave(X0) [duplicate literal removal 104]
195. ~quiet(X0) | ~brave(X0) [subsumption resolution 125,96]
199. ~brave(X0) [subsumption resolution 124,195]
251. $false [subsumption resolution 123,199]
% SZS output end Proof for 3831236134360242760973673
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise then paul is both not creative and not humble. If lucy is either not curious or brave then mary is kind or happy and vice versa. Everyone who is both not curious and not patient is wise. Everyone who is rich is generous or not generous and vice versa. If susan is creative or curious then someone is either funny or not strong. Everyone who is kind is not tall and vice versa. If someone is creative or rich then someone is either patient or not rich. Everyone who is not brave or not quiet is brave and vice versa. Everyone who is either happy or strong is not tall and vice versa. Everyone who is both calm and generous is both happy and not wise and vice versa. Everyone who is not humble is curious or rich and vice versa. If someone is either humble or not calm then paul is either generous or not kind and vice versa. If alice is either not quiet or not patient then someone is both not strong and old and vice versa. Everyone who is not kind or not calm is both creative and wise and vice versa. Everyone who is not curious or curious is generous and vice versa. Everyone who is not generous is either not quiet or rich. Paul is either not happy or not quiet. Lucy is both patient and funny. Someone is both patient and strong. Susan is not strong. Someone is either old or not patient. John is not creative or happy. Someone is happy or not old. Someone is funny or not kind. | Lucy is not humble. | entailment | ((?[X]:(~wise(X)))=>((~creative(paul)&~humble(paul))))&
(((~curious(lucy)<~>brave(lucy)))<=>((kind(mary)|happy(mary))))&
(![X]:((~curious(X)&~patient(X))=>wise(X)))&
(![X]:(rich(X)<=>(generous(X)|~generous(X))))&
(((creative(susan)|curious(susan)))=>(?[X]:((funny(X)<~>~strong(X)))))&
(![X]:(kind(X)<=>~tall(X)))&
((?[X]:((creative(X)|rich(X))))=>(?[X]:((patient(X)<~>~rich(X)))))&
(![X]:((~brave(X)|~quiet(X))<=>brave(X)))&
(![X]:((happy(X)<~>strong(X))<=>~tall(X)))&
(![X]:((calm(X)&generous(X))<=>(happy(X)&~wise(X))))&
(![X]:(~humble(X)<=>(curious(X)|rich(X))))&
((?[X]:((humble(X)<~>~calm(X))))<=>((generous(paul)<~>~kind(paul))))&
(((~quiet(alice)<~>~patient(alice)))<=>(?[X]:((~strong(X)&old(X)))))&
(![X]:((~kind(X)|~calm(X))<=>(creative(X)&wise(X))))&
(![X]:((~curious(X)|curious(X))<=>generous(X)))&
(![X]:(~generous(X)=>(~quiet(X)<~>rich(X))))&
((~happy(paul)<~>~quiet(paul)))&
((patient(lucy)&funny(lucy)))&
(?[X]:((patient(X)&strong(X))))&
(~strong(susan))&
(?[X]:((old(X)<~>~patient(X))))&
((~creative(john)|happy(john)))&
(?[X]:((happy(X)|~old(X))))&
(?[X]:((funny(X)|~kind(X)))) | ~humble(lucy) | [
"p3",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5568999754776552627226392
% SZS output start Proof for 5568999754776552627226392
4. ! [X0] : (rich(X0) <=> (~generous(X0) | generous(X0))) [input p3]
11. ! [X0] : (~humble(X0) <=> (rich(X0) | curious(X0))) [input p10]
25. humble(lucy) [input hypothesis]
35. ! [X0] : ((rich(X0) | (generous(X0) & ~generous(X0))) & ((~generous(X0) | generous(X0)) | ~rich(X0))) [nnf transformation 4]
36. ! [X0] : ((rich(X0) | (generous(X0) & ~generous(X0))) & (~generous(X0) | generous(X0) | ~rich(X0))) [flattening 35]
50. ! [X0] : ((~humble(X0) | (~rich(X0) & ~curious(X0))) & ((rich(X0) | curious(X0)) | humble(X0))) [nnf transformation 11]
51. ! [X0] : ((~humble(X0) | (~rich(X0) & ~curious(X0))) & (rich(X0) | curious(X0) | humble(X0))) [flattening 50]
85. rich(X0) | ~generous(X0) [cnf transformation 36]
86. rich(X0) | generous(X0) [cnf transformation 36]
110. ~humble(X0) | ~rich(X0) [cnf transformation 51]
147. humble(lucy) [cnf transformation 25]
185. rich(X0) [subsumption resolution 85,86]
208. ~humble(X0) [subsumption resolution 110,185]
305. $false [subsumption resolution 147,208]
% SZS output end Proof for 5568999754776552627226392
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not happy or not generous then someone is either not rich or quiet and vice versa.
Everyone who is humble is either not rich or happy.
If someone is not rich then someone is rich or not creative.
Everyone who is not creative or rich is not quiet and vice versa.
Everyone who is tall is both not rich and patient and vice versa.
If someone is kind then someone is both not creative and strong and vice versa.
If lucy is not curious or happy then someone is happy or funny and vice versa.
Everyone who is both not tall and humble is both curious and funny.
Everyone who is either brave or wise is both creative and rich.
Everyone who is not patient or curious is old and vice versa.
Everyone who is both strong and not quiet is both creative and calm and vice versa.
If someone is not happy then lucy is either not patient or rich and vice versa.
If someone is funny then someone is either not tall or strong and vice versa.
Everyone who is either not happy or patient is both not calm and brave and vice versa.
If someone is either generous or not creative then someone is patient or not calm.
If someone is not old then someone is not patient.
Mary is not kind.
Someone is either generous or not brave.
Someone is both tall and calm.
Someone is curious or not tall.
Someone is not kind or not creative.
Someone is not wise or not quiet.
Someone is not strong or not happy.
Mary is either not generous or not curious. | Mary is not funny. | neutral | (((~happy(lucy)|~generous(lucy)))<=>(?[X]:((~rich(X)<~>quiet(X)))))&
(![X]:(humble(X)=>(~rich(X)<~>happy(X))))&
((?[X]:(~rich(X)))=>(?[X]:((rich(X)|~creative(X)))))&
(![X]:((~creative(X)|rich(X))<=>~quiet(X)))&
(![X]:(tall(X)<=>(~rich(X)&patient(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~creative(X)&strong(X)))))&
(((~curious(lucy)|happy(lucy)))<=>(?[X]:((happy(X)|funny(X)))))&
(![X]:((~tall(X)&humble(X))=>(curious(X)&funny(X))))&
(![X]:((brave(X)<~>wise(X))=>(creative(X)&rich(X))))&
(![X]:((~patient(X)|curious(X))<=>old(X)))&
(![X]:((strong(X)&~quiet(X))<=>(creative(X)&calm(X))))&
((?[X]:(~happy(X)))<=>((~patient(lucy)<~>rich(lucy))))&
((?[X]:(funny(X)))<=>(?[X]:((~tall(X)<~>strong(X)))))&
(![X]:((~happy(X)<~>patient(X))<=>(~calm(X)&brave(X))))&
((?[X]:((generous(X)<~>~creative(X))))=>(?[X]:((patient(X)|~calm(X)))))&
((?[X]:(~old(X)))=>(?[X]:(~patient(X))))&
(~kind(mary))&
(?[X]:((generous(X)<~>~brave(X))))&
(?[X]:((tall(X)&calm(X))))&
(?[X]:((curious(X)|~tall(X))))&
(?[X]:((~kind(X)|~creative(X))))&
(?[X]:((~wise(X)|~quiet(X))))&
(?[X]:((~strong(X)|~happy(X))))&
((~generous(mary)<~>~curious(mary))) | ~funny(mary) | [] | null | 0 |
Everyone who is either happy or tall is both not wise and curious.
Everyone who is either brave or happy is not patient or not funny and vice versa.
Everyone who is old or not creative is patient or creative.
If someone is wise then someone is both not humble and brave.
If susan is old or creative then someone is not generous or happy and vice versa.
Everyone who is both not patient and kind is either curious or brave.
Everyone who is not kind or not generous is not humble and vice versa.
Everyone who is both quiet and not patient is either not happy or tall and vice versa.
If alice is not curious then lucy is either wise or patient.
Everyone who is either funny or tall is curious or tall and vice versa.
If lucy is not wise or not old then someone is not strong or funny.
Everyone who is either not happy or brave is not old or quiet and vice versa.
If someone is wise or patient then alice is funny or not old and vice versa.
Everyone who is both not humble and tall is not humble or patient.
Everyone who is either rich or not happy is humble and vice versa.
Everyone who is either kind or not curious is not strong.
Someone is creative.
John is humble or not old.
Someone is kind or not patient.
Lucy is either not curious or not brave.
Alice is rich.
Someone is either old or happy.
John is not creative or brave.
Someone is both not tall and quiet. | Alice is not kind. | contradiction | (![X]:((happy(X)<~>tall(X))=>(~wise(X)&curious(X))))&
(![X]:((brave(X)<~>happy(X))<=>(~patient(X)|~funny(X))))&
(![X]:((old(X)|~creative(X))=>(patient(X)|creative(X))))&
((?[X]:(wise(X)))=>(?[X]:((~humble(X)&brave(X)))))&
(((old(susan)|creative(susan)))<=>(?[X]:((~generous(X)|happy(X)))))&
(![X]:((~patient(X)&kind(X))=>(curious(X)<~>brave(X))))&
(![X]:((~kind(X)|~generous(X))<=>~humble(X)))&
(![X]:((quiet(X)&~patient(X))<=>(~happy(X)<~>tall(X))))&
((~curious(alice))=>((wise(lucy)<~>patient(lucy))))&
(![X]:((funny(X)<~>tall(X))<=>(curious(X)|tall(X))))&
(((~wise(lucy)|~old(lucy)))=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:((~happy(X)<~>brave(X))<=>(~old(X)|quiet(X))))&
((?[X]:((wise(X)|patient(X))))<=>((funny(alice)|~old(alice))))&
(![X]:((~humble(X)&tall(X))=>(~humble(X)|patient(X))))&
(![X]:((rich(X)<~>~happy(X))<=>humble(X)))&
(![X]:((kind(X)<~>~curious(X))=>~strong(X)))&
(?[X]:(creative(X)))&
((humble(john)|~old(john)))&
(?[X]:((kind(X)|~patient(X))))&
((~curious(lucy)<~>~brave(lucy)))&
(rich(alice))&
(?[X]:((old(X)<~>happy(X))))&
((~creative(john)|brave(john)))&
(?[X]:((~tall(X)&quiet(X)))) | ~kind(alice) | [
"p1",
"p6",
"p7",
"p9",
"p11",
"p12",
"p14",
"p20",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1549577016606848442886584
% SZS output start Proof for 1549577016606848442886584
2. ! [X0] : ((brave(X0) <~> happy(X0)) <=> (~funny(X0) | ~patient(X0))) [input p1]
7. ! [X0] : ((~generous(X0) | ~kind(X0)) <=> ~humble(X0)) [input p6]
8. ! [X0] : ((~patient(X0) & quiet(X0)) <=> (~happy(X0) <~> tall(X0))) [input p7]
10. ! [X0] : ((funny(X0) <~> tall(X0)) <=> (tall(X0) | curious(X0))) [input p9]
12. ! [X0] : ((~happy(X0) <~> brave(X0)) <=> (quiet(X0) | ~old(X0))) [input p11]
13. ? [X0] : (patient(X0) | wise(X0)) <=> (~old(alice) | funny(alice)) [input p12]
15. ! [X0] : ((rich(X0) <~> ~happy(X0)) <=> humble(X0)) [input p14]
21. rich(alice) [input p20]
24. ? [X0] : (quiet(X0) & ~tall(X0)) [input p23]
25. ~kind(alice) [input hypothesis]
39. ! [X0] : ((((~happy(X0) | ~brave(X0)) & (happy(X0) | brave(X0))) | (funny(X0) & patient(X0))) & ((~funny(X0) | ~patient(X0)) | ((brave(X0) | ~happy(X0)) & (happy(X0) | ~brave(X0))))) [nnf transformation 2]
40. ! [X0] : ((((~happy(X0) | ~brave(X0)) & (happy(X0) | brave(X0))) | (funny(X0) & patient(X0))) & (~funny(X0) | ~patient(X0) | ((brave(X0) | ~happy(X0)) & (happy(X0) | ~brave(X0))))) [flattening 39]
50. ! [X0] : (((~generous(X0) | ~kind(X0)) | humble(X0)) & (~humble(X0) | (generous(X0) & kind(X0)))) [nnf transformation 7]
51. ! [X0] : ((~generous(X0) | ~kind(X0) | humble(X0)) & (~humble(X0) | (generous(X0) & kind(X0)))) [flattening 50]
52. ! [X0] : (((~patient(X0) & quiet(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0)))) & (((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | (patient(X0) | ~quiet(X0)))) [nnf transformation 8]
53. ! [X0] : (((~patient(X0) & quiet(X0)) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0)))) & (((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | patient(X0) | ~quiet(X0))) [flattening 52]
55. ! [X0] : ((((~tall(X0) | ~funny(X0)) & (tall(X0) | funny(X0))) | (~tall(X0) & ~curious(X0))) & ((tall(X0) | curious(X0)) | ((funny(X0) | ~tall(X0)) & (tall(X0) | ~funny(X0))))) [nnf transformation 10]
56. ! [X0] : ((((~tall(X0) | ~funny(X0)) & (tall(X0) | funny(X0))) | (~tall(X0) & ~curious(X0))) & (tall(X0) | curious(X0) | ((funny(X0) | ~tall(X0)) & (tall(X0) | ~funny(X0))))) [flattening 55]
57. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~quiet(X0) & old(X0))) & ((quiet(X0) | ~old(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [nnf transformation 12]
58. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~quiet(X0) & old(X0))) & (quiet(X0) | ~old(X0) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [flattening 57]
59. (? [X0] : (patient(X0) | wise(X0)) | (old(alice) & ~funny(alice))) & ((~old(alice) | funny(alice)) | ! [X0] : (~patient(X0) & ~wise(X0))) [nnf transformation 13]
60. (? [X0] : (patient(X0) | wise(X0)) | (old(alice) & ~funny(alice))) & (~old(alice) | funny(alice) | ! [X0] : (~patient(X0) & ~wise(X0))) [flattening 59]
61. (? [X0] : (patient(X0) | wise(X0)) | (old(alice) & ~funny(alice))) & (~old(alice) | funny(alice) | ! [X1] : (~patient(X1) & ~wise(X1))) [rectify 60]
62. ? [X0] : (patient(X0) | wise(X0)) => (patient(sK2) | wise(sK2)) [choice axiom]
63. ((patient(sK2) | wise(sK2)) | (old(alice) & ~funny(alice))) & (~old(alice) | funny(alice) | ! [X1] : (~patient(X1) & ~wise(X1))) [skolemisation 61,62]
64. ! [X0] : ((((happy(X0) | ~rich(X0)) & (~happy(X0) | rich(X0))) | ~humble(X0)) & (humble(X0) | ((rich(X0) | happy(X0)) & (~happy(X0) | ~rich(X0))))) [nnf transformation 15]
73. ? [X0] : (quiet(X0) & ~tall(X0)) => (quiet(sK6) & ~tall(sK6)) [choice axiom]
74. quiet(sK6) & ~tall(sK6) [skolemisation 24,73]
81. patient(X0) | brave(X0) | happy(X0) [cnf transformation 40]
82. funny(X0) | brave(X0) | happy(X0) [cnf transformation 40]
83. ~brave(X0) | ~happy(X0) | patient(X0) [cnf transformation 40]
95. ~humble(X0) | kind(X0) [cnf transformation 51]
100. quiet(X0) | tall(X0) | happy(X0) [cnf transformation 53]
102. ~patient(X0) | tall(X0) | happy(X0) [cnf transformation 53]
111. ~tall(X0) | ~funny(X0) | ~tall(X0) [cnf transformation 56]
115. ~quiet(X0) | ~happy(X0) | brave(X0) [cnf transformation 58]
116. ~brave(X0) | happy(X0) | old(X0) [cnf transformation 58]
117. ~quiet(X0) | happy(X0) | ~brave(X0) [cnf transformation 58]
119. ~old(alice) | funny(alice) | ~patient(X1) [cnf transformation 63]
123. ~rich(X0) | ~happy(X0) | humble(X0) [cnf transformation 64]
132. rich(alice) [cnf transformation 21]
137. quiet(sK6) [cnf transformation 74]
138. ~kind(alice) [cnf transformation 25]
140. ~funny(X0) | ~tall(X0) [duplicate literal removal 111]
197. 13 <=> old(alice) [avatar definition]
198. ~old(alice) <- (~13) [avatar component clause 197]
210. 16 <=> funny(alice) [avatar definition]
211. funny(alice) <- (16) [avatar component clause 210]
215. 17 <=> ! [X1] : ~patient(X1) [avatar definition]
216. ~patient(X1) <- (17) [avatar component clause 215]
217. 17 | 16 | ~13 [avatar split clause 119,197,210,215]
291. ~tall(X1) | happy(X1) | brave(X1) [resolution 82,140]
314. tall(X0) | happy(X0) | brave(X0) | happy(X0) [resolution 102,81]
316. tall(X0) | happy(X0) | brave(X0) [duplicate literal removal 314]
326. brave(X0) | happy(X0) [subsumption resolution 316,291]
353. 41 <=> tall(alice) [avatar definition]
354. ~tall(alice) <- (~41) [avatar component clause 353]
355. tall(alice) <- (41) [avatar component clause 353]
379. 46 <=> happy(alice) [avatar definition]
383. ~happy(sK6) | brave(sK6) [resolution 115,137]
385. brave(sK6) [subsumption resolution 383,326]
398. happy(sK6) | ~brave(sK6) [resolution 117,137]
399. happy(X0) | ~brave(X0) | tall(X0) | happy(X0) [resolution 117,100]
400. happy(X0) | ~brave(X0) | tall(X0) [duplicate literal removal 399]
401. happy(sK6) [subsumption resolution 398,385]
402. tall(X0) | happy(X0) [subsumption resolution 400,326]
405. ~happy(sK6) | patient(sK6) [resolution 385,83]
407. patient(sK6) [subsumption resolution 405,401]
408. ~happy(alice) | humble(alice) [resolution 123,132]
487. happy(X0) | happy(X0) | old(X0) [resolution 326,116]
491. old(X0) | happy(X0) [duplicate literal removal 487]
508. $false <- (17) [resolution 216,407]
509. ~17 [avatar contradiction clause 508]
590. happy(alice) <- (~13) [resolution 491,198]
594. 46 | 13 [avatar split clause 590,197,379]
596. 56 <=> humble(alice) [avatar definition]
597. humble(alice) <- (56) [avatar component clause 596]
600. 56 | ~46 [avatar split clause 408,379,596]
608. happy(alice) <- (~41) [resolution 354,402]
616. kind(alice) <- (56) [resolution 597,95]
617. $false <- (56) [subsumption resolution 616,138]
618. ~56 [avatar contradiction clause 617]
619. 46 | 41 [avatar split clause 608,353,379]
625. ~tall(alice) <- (16) [resolution 211,140]
638. $false <- (16, 41) [subsumption resolution 625,355]
639. ~16 | ~41 [avatar contradiction clause 638]
640. $false [avatar sat refutation 217,509,594,600,618,619,639]
% SZS output end Proof for 1549577016606848442886584
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or quiet is not old and vice versa.
If someone is both not humble and creative then fred is both not calm and not rich.
If paul is either generous or patient then alice is strong.
Everyone who is either not creative or not generous is not quiet.
Everyone who is both not old and old is not quiet.
If someone is both calm and not brave then someone is either not quiet or happy.
If someone is both curious and not generous then someone is quiet and vice versa.
Everyone who is either funny or brave is funny or not brave and vice versa.
Everyone who is both not generous and curious is both not creative and not generous and vice versa.
Everyone who is both not quiet and tall is either curious or generous.
If paul is both not happy and not rich then paul is quiet.
If susan is rich then lucy is either not quiet or kind and vice versa.
Everyone who is creative is calm and vice versa.
If someone is happy or not curious then mary is either patient or kind and vice versa.
Everyone who is not funny is either rich or old.
Alice is both not rich and not tall.
John is either not tall or happy.
John is not kind.
Someone is not curious.
Paul is happy or not wise. | Paul is not happy. | neutral | (![X]:((~kind(X)|quiet(X))<=>~old(X)))&
((?[X]:((~humble(X)&creative(X))))=>((~calm(fred)&~rich(fred))))&
(((generous(paul)<~>patient(paul)))=>(strong(alice)))&
(![X]:((~creative(X)<~>~generous(X))=>~quiet(X)))&
(![X]:((~old(X)&old(X))=>~quiet(X)))&
((?[X]:((calm(X)&~brave(X))))=>(?[X]:((~quiet(X)<~>happy(X)))))&
((?[X]:((curious(X)&~generous(X))))<=>(?[X]:(quiet(X))))&
(![X]:((funny(X)<~>brave(X))<=>(funny(X)|~brave(X))))&
(![X]:((~generous(X)&curious(X))<=>(~creative(X)&~generous(X))))&
(![X]:((~quiet(X)&tall(X))=>(curious(X)<~>generous(X))))&
(((~happy(paul)&~rich(paul)))=>(quiet(paul)))&
((rich(susan))<=>((~quiet(lucy)<~>kind(lucy))))&
(![X]:(creative(X)<=>calm(X)))&
((?[X]:((happy(X)|~curious(X))))<=>((patient(mary)<~>kind(mary))))&
(![X]:(~funny(X)=>(rich(X)<~>old(X))))&
((~rich(alice)&~tall(alice)))&
((~tall(john)<~>happy(john)))&
(~kind(john))&
(?[X]:(~curious(X)))&
((happy(paul)|~wise(paul))) | ~happy(paul) | [] | null | 0 |
If someone is either not rich or not funny then paul is patient or not wise. Everyone who is both not rich and curious is humble or quiet and vice versa. If fred is not patient or old then someone is old and vice versa. Everyone who is not quiet is either not curious or not patient and vice versa. If someone is both old and not curious then someone is not old and vice versa. 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. Someone is not patient or old. Fred is creative or not creative. Someone is funny or not happy. Susan is not tall or not creative. Someone is not rich or generous. Someone is either not brave or not curious. John is patient. | Alice is not humble. | entailment | ((?[X]:((~rich(X)<~>~funny(X))))=>((patient(paul)|~wise(paul))))&
(![X]:((~rich(X)&curious(X))<=>(humble(X)|quiet(X))))&
(((~patient(fred)|old(fred)))<=>(?[X]:(old(X))))&
(![X]:(~quiet(X)<=>(~curious(X)<~>~patient(X))))&
((?[X]:((old(X)&~curious(X))))<=>(?[X]:(~old(X))))&
(![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]:((~patient(X)|old(X))))&
((creative(fred)|~creative(fred)))&
(?[X]:((funny(X)|~happy(X))))&
((~tall(susan)|~creative(susan)))&
(?[X]:((~rich(X)|generous(X))))&
(?[X]:((~brave(X)<~>~curious(X))))&
(patient(john)) | ~humble(alice) | [
"p7",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4417650005428350002852930
% SZS output start Proof for 4417650005428350002852930
8. ! [X0] : ((kind(X0) | ~kind(X0)) <=> (strong(X0) & kind(X0))) [input p7]
11. ! [X0] : ((~strong(X0) & ~brave(X0)) <=> ~quiet(X0)) [input p10]
13. ! [X0] : (~quiet(X0) <=> (~curious(X0) | humble(X0))) [input p12]
24. humble(alice) [input hypothesis]
52. ! [X0] : (((kind(X0) | ~kind(X0)) | (~strong(X0) | ~kind(X0))) & ((strong(X0) & kind(X0)) | (~kind(X0) & kind(X0)))) [nnf transformation 8]
53. ! [X0] : ((kind(X0) | ~kind(X0) | ~strong(X0) | ~kind(X0)) & ((strong(X0) & kind(X0)) | (~kind(X0) & kind(X0)))) [flattening 52]
55. ! [X0] : (((~strong(X0) & ~brave(X0)) | quiet(X0)) & (~quiet(X0) | (strong(X0) | brave(X0)))) [nnf transformation 11]
56. ! [X0] : (((~strong(X0) & ~brave(X0)) | quiet(X0)) & (~quiet(X0) | strong(X0) | brave(X0))) [flattening 55]
61. ! [X0] : ((~quiet(X0) | (curious(X0) & ~humble(X0))) & ((~curious(X0) | humble(X0)) | quiet(X0))) [nnf transformation 13]
62. ! [X0] : ((~quiet(X0) | (curious(X0) & ~humble(X0))) & (~curious(X0) | humble(X0) | quiet(X0))) [flattening 61]
102. strong(X0) | kind(X0) [cnf transformation 53]
103. strong(X0) | ~kind(X0) [cnf transformation 53]
112. ~strong(X0) | quiet(X0) [cnf transformation 56]
118. ~quiet(X0) | ~humble(X0) [cnf transformation 62]
141. humble(alice) [cnf transformation 24]
201. strong(X0) [subsumption resolution 102,103]
217. quiet(X0) [subsumption resolution 112,201]
233. ~humble(X0) [subsumption resolution 118,217]
318. $false [subsumption resolution 141,233]
% SZS output end Proof for 4417650005428350002852930
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or happy is both quiet and not patient. If john is not happy then someone is both not creative and tall. If lucy is generous then mary is tall. If someone is humble then alice is calm or funny. Everyone who is humble or calm is rich and vice versa. If someone is either humble or not funny then someone is not generous or not wise and vice versa. Everyone who is not generous or old is rich or wise. If someone is brave or not old then someone is not curious. Everyone who is either quiet or not generous is generous. If someone is either not generous or not old then someone is calm and vice versa. Everyone who is either humble or not curious is kind or calm. If someone is either not happy or not wise then someone is either not happy or not calm. Everyone who is calm or not humble is not kind and vice versa. Everyone who is not calm is quiet or not quiet and vice versa. If lucy is not strong or not curious then fred is both not generous and patient and vice versa. If someone is not creative then lucy is patient or strong and vice versa. Paul is not happy or strong. Someone is either quiet or not rich. Lucy is both funny and not old. Lucy is not patient. Someone is not kind. Someone is not strong or not brave. Someone is not patient or not calm. | Lucy is not calm. | entailment | (![X]:((~tall(X)|happy(X))=>(quiet(X)&~patient(X))))&
((~happy(john))=>(?[X]:((~creative(X)&tall(X)))))&
((generous(lucy))=>(tall(mary)))&
((?[X]:(humble(X)))=>((calm(alice)|funny(alice))))&
(![X]:((humble(X)|calm(X))<=>rich(X)))&
((?[X]:((humble(X)<~>~funny(X))))<=>(?[X]:((~generous(X)|~wise(X)))))&
(![X]:((~generous(X)|old(X))=>(rich(X)|wise(X))))&
((?[X]:((brave(X)|~old(X))))=>(?[X]:(~curious(X))))&
(![X]:((quiet(X)<~>~generous(X))=>generous(X)))&
((?[X]:((~generous(X)<~>~old(X))))<=>(?[X]:(calm(X))))&
(![X]:((humble(X)<~>~curious(X))=>(kind(X)|calm(X))))&
((?[X]:((~happy(X)<~>~wise(X))))=>(?[X]:((~happy(X)<~>~calm(X)))))&
(![X]:((calm(X)|~humble(X))<=>~kind(X)))&
(![X]:(~calm(X)<=>(quiet(X)|~quiet(X))))&
(((~strong(lucy)|~curious(lucy)))<=>((~generous(fred)&patient(fred))))&
((?[X]:(~creative(X)))<=>((patient(lucy)|strong(lucy))))&
((~happy(paul)|strong(paul)))&
(?[X]:((quiet(X)<~>~rich(X))))&
((funny(lucy)&~old(lucy)))&
(~patient(lucy))&
(?[X]:(~kind(X)))&
(?[X]:((~strong(X)|~brave(X))))&
(?[X]:((~patient(X)|~calm(X)))) | ~calm(lucy) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4932331640679361331303795
% SZS output start Proof for 4932331640679361331303795
14. ! [X0] : (~calm(X0) <=> (~quiet(X0) | quiet(X0))) [input p13]
24. calm(lucy) [input hypothesis]
70. ! [X0] : ((~calm(X0) | (quiet(X0) & ~quiet(X0))) & ((~quiet(X0) | quiet(X0)) | calm(X0))) [nnf transformation 14]
71. ! [X0] : ((~calm(X0) | (quiet(X0) & ~quiet(X0))) & (~quiet(X0) | quiet(X0) | calm(X0))) [flattening 70]
118. ~calm(X0) | ~quiet(X0) [cnf transformation 71]
119. ~calm(X0) | quiet(X0) [cnf transformation 71]
136. calm(lucy) [cnf transformation 24]
202. 16 <=> ! [X1] : ~calm(X1) [avatar definition]
203. ~calm(X1) <- (16) [avatar component clause 202]
244. ~calm(X0) [subsumption resolution 118,119]
245. 16 [avatar split clause 244,202]
310. $false <- (16) [resolution 203,136]
311. ~16 [avatar contradiction clause 310]
312. $false [avatar sat refutation 245,311]
% SZS output end Proof for 4932331640679361331303795
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not brave or strong then susan is both not generous and wise and vice versa.
Everyone who is either not humble or strong is happy.
If someone is funny or curious then someone is not humble or not generous and vice versa.
Everyone who is either not wise or not brave is not quiet.
Everyone who is both happy and old is not happy or quiet.
If someone is both not kind and not tall then someone is either curious or not creative.
Everyone who is both not happy and rich is rich or curious and vice versa.
If someone is either humble or old then paul is either patient or happy.
If someone is calm or generous then someone is not old.
Everyone who is quiet or funny is either not patient or not calm.
If someone is kind then paul is curious and vice versa.
If someone is both not curious and brave then someone is not old or not funny.
Everyone who is old or not humble is not humble or not patient and vice versa.
Everyone who is both humble and not calm is both happy and kind.
Everyone who is tall is either kind or not brave and vice versa.
Everyone who is not old or quiet is both brave and patient and vice versa.
Someone is both not wise and kind.
Someone is either not old or not funny.
Someone is funny.
Someone is both patient and not curious.
Someone is either calm or kind.
Someone is not brave or happy.
Someone is not strong.
Someone is funny or not creative. | Susan is not generous. | neutral | (((~brave(lucy)|strong(lucy)))<=>((~generous(susan)&wise(susan))))&
(![X]:((~humble(X)<~>strong(X))=>happy(X)))&
((?[X]:((funny(X)|curious(X))))<=>(?[X]:((~humble(X)|~generous(X)))))&
(![X]:((~wise(X)<~>~brave(X))=>~quiet(X)))&
(![X]:((happy(X)&old(X))=>(~happy(X)|quiet(X))))&
((?[X]:((~kind(X)&~tall(X))))=>(?[X]:((curious(X)<~>~creative(X)))))&
(![X]:((~happy(X)&rich(X))<=>(rich(X)|curious(X))))&
((?[X]:((humble(X)<~>old(X))))=>((patient(paul)<~>happy(paul))))&
((?[X]:((calm(X)|generous(X))))=>(?[X]:(~old(X))))&
(![X]:((quiet(X)|funny(X))=>(~patient(X)<~>~calm(X))))&
((?[X]:(kind(X)))<=>(curious(paul)))&
((?[X]:((~curious(X)&brave(X))))=>(?[X]:((~old(X)|~funny(X)))))&
(![X]:((old(X)|~humble(X))<=>(~humble(X)|~patient(X))))&
(![X]:((humble(X)&~calm(X))=>(happy(X)&kind(X))))&
(![X]:(tall(X)<=>(kind(X)<~>~brave(X))))&
(![X]:((~old(X)|quiet(X))<=>(brave(X)&patient(X))))&
(?[X]:((~wise(X)&kind(X))))&
(?[X]:((~old(X)<~>~funny(X))))&
(?[X]:(funny(X)))&
(?[X]:((patient(X)&~curious(X))))&
(?[X]:((calm(X)<~>kind(X))))&
(?[X]:((~brave(X)|happy(X))))&
(?[X]:(~strong(X)))&
(?[X]:((funny(X)|~creative(X)))) | ~generous(susan) | [] | null | 0 |
If someone is wise or not kind then fred is tall or strong and vice versa.
Everyone who is creative or wise is either not kind or calm.
Everyone who is either kind or tall is either creative or not kind.
Everyone who is not wise is not calm or patient and vice versa.
If lucy is either not patient or not funny then mary is not happy and vice versa.
If someone is both not old and not kind then alice is rich or not brave and vice versa.
If lucy is both not humble and tall then mary is both not rich and not kind.
Everyone who is either humble or not rich is not old or not brave.
If someone is both not wise and rich then paul is either not generous or quiet.
If alice is not happy then someone is either curious or not brave and vice versa.
If someone is both old and not kind then someone is not curious or generous and vice versa.
If someone is either creative or quiet then someone is not old and vice versa.
Everyone who is not wise is quiet or not creative and vice versa.
Everyone who is not patient is either not calm or not quiet.
Everyone who is either not rich or brave is both kind and rich and vice versa.
Everyone who is wise is either wise or not wise and vice versa.
Lucy is either funny or not brave.
Mary is either tall or not happy.
Alice is not humble.
Someone is either not happy or curious.
Someone is both humble and not quiet.
Someone is either curious or not funny.
Lucy is not curious or not generous. | Fred is not kind. | contradiction | ((?[X]:((wise(X)|~kind(X))))<=>((tall(fred)|strong(fred))))&
(![X]:((creative(X)|wise(X))=>(~kind(X)<~>calm(X))))&
(![X]:((kind(X)<~>tall(X))=>(creative(X)<~>~kind(X))))&
(![X]:(~wise(X)<=>(~calm(X)|patient(X))))&
(((~patient(lucy)<~>~funny(lucy)))<=>(~happy(mary)))&
((?[X]:((~old(X)&~kind(X))))<=>((rich(alice)|~brave(alice))))&
(((~humble(lucy)&tall(lucy)))=>((~rich(mary)&~kind(mary))))&
(![X]:((humble(X)<~>~rich(X))=>(~old(X)|~brave(X))))&
((?[X]:((~wise(X)&rich(X))))=>((~generous(paul)<~>quiet(paul))))&
((~happy(alice))<=>(?[X]:((curious(X)<~>~brave(X)))))&
((?[X]:((old(X)&~kind(X))))<=>(?[X]:((~curious(X)|generous(X)))))&
((?[X]:((creative(X)<~>quiet(X))))<=>(?[X]:(~old(X))))&
(![X]:(~wise(X)<=>(quiet(X)|~creative(X))))&
(![X]:(~patient(X)=>(~calm(X)<~>~quiet(X))))&
(![X]:((~rich(X)<~>brave(X))<=>(kind(X)&rich(X))))&
(![X]:(wise(X)<=>(wise(X)<~>~wise(X))))&
((funny(lucy)<~>~brave(lucy)))&
((tall(mary)<~>~happy(mary)))&
(~humble(alice))&
(?[X]:((~happy(X)<~>curious(X))))&
(?[X]:((humble(X)&~quiet(X))))&
(?[X]:((curious(X)<~>~funny(X))))&
((~curious(lucy)|~generous(lucy))) | ~kind(fred) | [
"p1",
"p3",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2292951300412720270254783
% SZS output start Proof for 2292951300412720270254783
2. ! [X0] : ((wise(X0) | creative(X0)) => (~kind(X0) <~> calm(X0))) [input p1]
4. ! [X0] : (~wise(X0) <=> (patient(X0) | ~calm(X0))) [input p3]
13. ! [X0] : (~wise(X0) <=> (~creative(X0) | quiet(X0))) [input p12]
16. ! [X0] : (wise(X0) <=> (wise(X0) <~> ~wise(X0))) [input p15]
24. ~kind(fred) [input hypothesis]
27. ! [X0] : ((~kind(X0) <~> calm(X0)) | (~wise(X0) & ~creative(X0))) [ennf transformation 2]
40. ! [X0] : (((~calm(X0) | kind(X0)) & (calm(X0) | ~kind(X0))) | (~wise(X0) & ~creative(X0))) [nnf transformation 27]
42. ! [X0] : ((~wise(X0) | (~patient(X0) & calm(X0))) & ((patient(X0) | ~calm(X0)) | wise(X0))) [nnf transformation 4]
43. ! [X0] : ((~wise(X0) | (~patient(X0) & calm(X0))) & (patient(X0) | ~calm(X0) | wise(X0))) [flattening 42]
66. ! [X0] : ((~wise(X0) | (creative(X0) & ~quiet(X0))) & ((~creative(X0) | quiet(X0)) | wise(X0))) [nnf transformation 13]
67. ! [X0] : ((~wise(X0) | (creative(X0) & ~quiet(X0))) & (~creative(X0) | quiet(X0) | wise(X0))) [flattening 66]
71. ! [X0] : ((wise(X0) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | ~wise(X0))) [nnf transformation 16]
88. ~calm(X0) | kind(X0) | ~creative(X0) [cnf transformation 40]
95. ~wise(X0) | calm(X0) [cnf transformation 43]
127. ~wise(X0) | creative(X0) [cnf transformation 67]
139. wise(X0) | wise(X0) | wise(X0) [cnf transformation 71]
152. ~kind(fred) [cnf transformation 24]
156. wise(X0) [duplicate literal removal 139]
180. 5 <=> ! [X1] : kind(X1) [avatar definition]
181. kind(X1) <- (5) [avatar component clause 180]
387. calm(X0) [resolution 95,156]
391. creative(X0) [resolution 127,156]
400. kind(X0) | ~creative(X0) [resolution 88,387]
401. kind(X0) [subsumption resolution 400,391]
402. 5 [avatar split clause 401,180]
404. $false <- (5) [resolution 181,152]
411. ~5 [avatar contradiction clause 404]
412. $false [avatar sat refutation 402,411]
% SZS output end Proof for 2292951300412720270254783
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If alice is old or not creative then someone is calm and vice versa. If alice is not patient or not old then fred is not wise or not humble and vice versa. If someone is not brave then fred is not old or kind and vice versa. If john is not calm then someone is not wise or rich. Everyone who is not creative is both not wise and wise and vice versa. Everyone who is either not old or patient is either wise or funny and vice versa. If lucy is strong or kind then someone is either happy or not brave and vice versa. Everyone who is not patient or generous is not brave. If someone is not funny or not strong then someone is both not curious and brave and vice versa. Everyone who is not tall or not humble is not old or not rich. Everyone who is not rich is happy and vice versa. Everyone who is either not creative or patient is both not brave and not old. If susan is curious or happy then someone is not quiet and vice versa. If susan is curious or not wise then someone is strong or not wise. Everyone who is not curious is not happy and vice versa. If john is not tall then mary is not rich or brave. Someone is happy or not rich. Someone is either brave or wise. Susan is both curious and not rich. Lucy is both not calm and wise. Someone is wise or rich. Someone is both creative and wise. Someone is either not kind or not wise. | Mary is strong. | entailment | (((old(alice)|~creative(alice)))<=>(?[X]:(calm(X))))&
(((~patient(alice)|~old(alice)))<=>((~wise(fred)|~humble(fred))))&
((?[X]:(~brave(X)))<=>((~old(fred)|kind(fred))))&
((~calm(john))=>(?[X]:((~wise(X)|rich(X)))))&
(![X]:(~creative(X)<=>(~wise(X)&wise(X))))&
(![X]:((~old(X)<~>patient(X))<=>(wise(X)<~>funny(X))))&
(((strong(lucy)|kind(lucy)))<=>(?[X]:((happy(X)<~>~brave(X)))))&
(![X]:((~patient(X)|generous(X))=>~brave(X)))&
((?[X]:((~funny(X)|~strong(X))))<=>(?[X]:((~curious(X)&brave(X)))))&
(![X]:((~tall(X)|~humble(X))=>(~old(X)|~rich(X))))&
(![X]:(~rich(X)<=>happy(X)))&
(![X]:((~creative(X)<~>patient(X))=>(~brave(X)&~old(X))))&
(((curious(susan)|happy(susan)))<=>(?[X]:(~quiet(X))))&
(((curious(susan)|~wise(susan)))=>(?[X]:((strong(X)|~wise(X)))))&
(![X]:(~curious(X)<=>~happy(X)))&
((~tall(john))=>((~rich(mary)|brave(mary))))&
(?[X]:((happy(X)|~rich(X))))&
(?[X]:((brave(X)<~>wise(X))))&
((curious(susan)&~rich(susan)))&
((~calm(lucy)&wise(lucy)))&
(?[X]:((wise(X)|rich(X))))&
(?[X]:((creative(X)&wise(X))))&
(?[X]:((~kind(X)<~>~wise(X)))) | strong(mary) | [
"p4",
"p7",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2325918217667777593988800
% SZS output start Proof for 2325918217667777593988800
5. ! [X0] : (~creative(X0) <=> (wise(X0) & ~wise(X0))) [input p4]
8. ! [X0] : ((generous(X0) | ~patient(X0)) => ~brave(X0)) [input p7]
9. ? [X0] : (~strong(X0) | ~funny(X0)) <=> ? [X0] : (brave(X0) & ~curious(X0)) [input p8]
12. ! [X0] : ((~creative(X0) <~> patient(X0)) => (~old(X0) & ~brave(X0))) [input p11]
24. ~strong(mary) [input hypothesis]
25. ? [X0] : (~strong(X0) | ~funny(X0)) <=> ? [X1] : (brave(X1) & ~curious(X1)) [rectify 9]
28. ! [X0] : (~patient(X0) => ~brave(X0)) [pure predicate removal 8]
30. ! [X0] : (~brave(X0) | patient(X0)) [ennf transformation 28]
33. ! [X0] : ((~old(X0) & ~brave(X0)) | (~creative(X0) <=> patient(X0))) [ennf transformation 12]
49. ! [X0] : ((~creative(X0) | (~wise(X0) | wise(X0))) & ((wise(X0) & ~wise(X0)) | creative(X0))) [nnf transformation 5]
50. ! [X0] : ((~creative(X0) | ~wise(X0) | wise(X0)) & ((wise(X0) & ~wise(X0)) | creative(X0))) [flattening 49]
57. (? [X0] : (~strong(X0) | ~funny(X0)) | ! [X1] : (~brave(X1) | curious(X1))) & (? [X1] : (brave(X1) & ~curious(X1)) | ! [X0] : (strong(X0) & funny(X0))) [nnf transformation 25]
58. (? [X0] : (~strong(X0) | ~funny(X0)) | ! [X1] : (~brave(X1) | curious(X1))) & (? [X2] : (brave(X2) & ~curious(X2)) | ! [X3] : (strong(X3) & funny(X3))) [rectify 57]
59. ? [X0] : (~strong(X0) | ~funny(X0)) => (~strong(sK4) | ~funny(sK4)) [choice axiom]
60. ? [X2] : (brave(X2) & ~curious(X2)) => (brave(sK5) & ~curious(sK5)) [choice axiom]
61. ((~strong(sK4) | ~funny(sK4)) | ! [X1] : (~brave(X1) | curious(X1))) & ((brave(sK5) & ~curious(sK5)) | ! [X3] : (strong(X3) & funny(X3))) [skolemisation 58,60,59]
63. ! [X0] : ((~old(X0) & ~brave(X0)) | ((~creative(X0) | ~patient(X0)) & (patient(X0) | creative(X0)))) [nnf transformation 33]
95. ~wise(X0) | creative(X0) [cnf transformation 50]
96. wise(X0) | creative(X0) [cnf transformation 50]
112. ~brave(X0) | patient(X0) [cnf transformation 30]
116. brave(sK5) | strong(X3) [cnf transformation 61]
122. ~brave(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 63]
144. ~strong(mary) [cnf transformation 24]
210. creative(X0) [subsumption resolution 95,96]
252. 24 <=> ! [X3] : strong(X3) [avatar definition]
253. strong(X3) <- (24) [avatar component clause 252]
255. 25 <=> brave(sK5) [avatar definition]
257. brave(sK5) <- (25) [avatar component clause 255]
258. 24 | 25 [avatar split clause 116,255,252]
270. ~brave(X0) | ~patient(X0) [subsumption resolution 122,210]
271. ~brave(X0) [subsumption resolution 270,112]
326. $false <- (25) [subsumption resolution 257,271]
327. ~25 [avatar contradiction clause 326]
330. $false <- (24) [resolution 253,144]
331. ~24 [avatar contradiction clause 330]
332. $false [avatar sat refutation 258,327,331]
% SZS output end Proof for 2325918217667777593988800
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is either rich or creative.
If someone is generous then someone is patient.
Everyone who is either tall or not rich is both patient and not wise.
If john is not humble then someone is either wise or brave and vice versa.
Everyone who is not rich or not curious is both not generous and not happy.
Everyone who is kind or not tall is happy and vice versa.
If alice is not brave or generous then paul is both quiet and humble and vice versa.
Everyone who is both funny and not quiet is both not funny and not happy and vice versa.
If someone is not old then fred is both quiet and not old and vice versa.
Everyone who is happy is either not wise or not old.
Everyone who is not kind is both generous and wise.
If someone is either not quiet or kind then fred is either not tall or not humble.
If someone is patient then lucy is both wise and not rich and vice versa.
If mary is both quiet and not funny then alice is not quiet and vice versa.
If paul is not creative then someone is either creative or not patient.
Everyone who is either not wise or not generous is either not quiet or tall.
Mary is quiet.
Someone is strong.
Someone is kind.
Someone is both humble and rich.
John is not strong.
Someone is either creative or old.
Lucy is either rich or not happy. | Fred is not rich. | contradiction | (![X]:(old(X)=>(rich(X)<~>creative(X))))&
((?[X]:(generous(X)))=>(?[X]:(patient(X))))&
(![X]:((tall(X)<~>~rich(X))=>(patient(X)&~wise(X))))&
((~humble(john))<=>(?[X]:((wise(X)<~>brave(X)))))&
(![X]:((~rich(X)|~curious(X))=>(~generous(X)&~happy(X))))&
(![X]:((kind(X)|~tall(X))<=>happy(X)))&
(((~brave(alice)|generous(alice)))<=>((quiet(paul)&humble(paul))))&
(![X]:((funny(X)&~quiet(X))<=>(~funny(X)&~happy(X))))&
((?[X]:(~old(X)))<=>((quiet(fred)&~old(fred))))&
(![X]:(happy(X)=>(~wise(X)<~>~old(X))))&
(![X]:(~kind(X)=>(generous(X)&wise(X))))&
((?[X]:((~quiet(X)<~>kind(X))))=>((~tall(fred)<~>~humble(fred))))&
((?[X]:(patient(X)))<=>((wise(lucy)&~rich(lucy))))&
(((quiet(mary)&~funny(mary)))<=>(~quiet(alice)))&
((~creative(paul))=>(?[X]:((creative(X)<~>~patient(X)))))&
(![X]:((~wise(X)<~>~generous(X))=>(~quiet(X)<~>tall(X))))&
(quiet(mary))&
(?[X]:(strong(X)))&
(?[X]:(kind(X)))&
(?[X]:((humble(X)&rich(X))))&
(~strong(john))&
(?[X]:((creative(X)<~>old(X))))&
((rich(lucy)<~>~happy(lucy))) | ~rich(fred) | [
"p4",
"p5",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 364638107375120505267806
% SZS output start Proof for 364638107375120505267806
5. ! [X0] : ((~curious(X0) | ~rich(X0)) => (~happy(X0) & ~generous(X0))) [input p4]
6. ! [X0] : ((~tall(X0) | kind(X0)) <=> happy(X0)) [input p5]
11. ! [X0] : (~kind(X0) => (wise(X0) & generous(X0))) [input p10]
24. ~rich(fred) [input hypothesis]
26. ! [X0] : (~rich(X0) => (~happy(X0) & ~generous(X0))) [pure predicate removal 5]
30. ! [X0] : ((~happy(X0) & ~generous(X0)) | rich(X0)) [ennf transformation 26]
32. ! [X0] : ((wise(X0) & generous(X0)) | kind(X0)) [ennf transformation 11]
45. ! [X0] : (((~tall(X0) | kind(X0)) | ~happy(X0)) & (happy(X0) | (tall(X0) & ~kind(X0)))) [nnf transformation 6]
46. ! [X0] : ((~tall(X0) | kind(X0) | ~happy(X0)) & (happy(X0) | (tall(X0) & ~kind(X0)))) [flattening 45]
90. ~generous(X0) | rich(X0) [cnf transformation 30]
91. ~happy(X0) | rich(X0) [cnf transformation 30]
92. ~kind(X0) | happy(X0) [cnf transformation 46]
109. kind(X0) | generous(X0) [cnf transformation 32]
137. ~rich(fred) [cnf transformation 24]
293. happy(X0) | generous(X0) [resolution 109,92]
301. generous(X0) | rich(X0) [resolution 293,91]
302. rich(X0) [subsumption resolution 301,90]
305. $false [resolution 302,137]
% SZS output end Proof for 364638107375120505267806
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not generous and generous then someone is kind.
Everyone who is humble is either not tall or happy.
Everyone who is either kind or not happy is either tall or not rich and vice versa.
Everyone who is both not patient and rich is not funny.
Everyone who is both not tall and not rich is either calm or rich and vice versa.
If paul is patient then john is either not kind or kind.
If mary is either not quiet or calm then someone is both old and rich and vice versa.
Everyone who is both not happy and not calm is either quiet or strong and vice versa.
If someone is patient then someone is not generous.
Everyone who is not creative is either not patient or not generous and vice versa.
If mary is wise then someone is either not wise or tall and vice versa.
If susan is not creative or not wise then john is both funny and kind.
If susan is either not funny or happy then someone is either not generous or generous.
If fred is wise then john is either happy or not happy and vice versa.
Everyone who is either wise or not brave is humble or generous.
Everyone who is strong is happy.
Someone is brave or not old.
Someone is not generous.
Someone is old.
Someone is not brave.
Lucy is both wise and kind.
Someone is not tall or wise.
Someone is not wise.
Paul is either not kind or not generous. | John is kind. | neutral | ((?[X]:((~generous(X)&generous(X))))=>(?[X]:(kind(X))))&
(![X]:(humble(X)=>(~tall(X)<~>happy(X))))&
(![X]:((kind(X)<~>~happy(X))<=>(tall(X)<~>~rich(X))))&
(![X]:((~patient(X)&rich(X))=>~funny(X)))&
(![X]:((~tall(X)&~rich(X))<=>(calm(X)<~>rich(X))))&
((patient(paul))=>((~kind(john)<~>kind(john))))&
(((~quiet(mary)<~>calm(mary)))<=>(?[X]:((old(X)&rich(X)))))&
(![X]:((~happy(X)&~calm(X))<=>(quiet(X)<~>strong(X))))&
((?[X]:(patient(X)))=>(?[X]:(~generous(X))))&
(![X]:(~creative(X)<=>(~patient(X)<~>~generous(X))))&
((wise(mary))<=>(?[X]:((~wise(X)<~>tall(X)))))&
(((~creative(susan)|~wise(susan)))=>((funny(john)&kind(john))))&
(((~funny(susan)<~>happy(susan)))=>(?[X]:((~generous(X)<~>generous(X)))))&
((wise(fred))<=>((happy(john)<~>~happy(john))))&
(![X]:((wise(X)<~>~brave(X))=>(humble(X)|generous(X))))&
(![X]:(strong(X)=>happy(X)))&
(?[X]:((brave(X)|~old(X))))&
(?[X]:(~generous(X)))&
(?[X]:(old(X)))&
(?[X]:(~brave(X)))&
((wise(lucy)&kind(lucy)))&
(?[X]:((~tall(X)|wise(X))))&
(?[X]:(~wise(X)))&
((~kind(paul)<~>~generous(paul))) | kind(john) | [] | null | 0 |
Everyone who is either not quiet or kind is both not humble and not happy. Everyone who is either not creative or funny is either rich or brave and vice versa. If mary is either quiet or not brave then john is either happy or kind and vice versa. If someone is not calm or brave then lucy is generous or not rich and vice versa. If fred is both not wise and patient then paul is calm and vice versa. If alice is patient or generous then someone is not generous and vice versa. Everyone who is patient is either not wise or generous and vice versa. Everyone who is not rich or humble is not old or not brave. Everyone who is not generous is both strong and creative and vice versa. If mary is either not happy or wise then fred is humble. Everyone who is either wise or strong is either not rich or not old and vice versa. If susan is either old or not wise then someone is either not brave or not rich. If someone is not tall or quiet then someone is either not rich or patient and vice versa. Everyone who is either not happy or not quiet is kind and vice versa. Everyone who is quiet or not humble is not kind. John is quiet. Someone is either patient or not old. Lucy is either not strong or patient. Fred is not brave or patient. Mary is not rich or not calm. Someone is not patient or not kind. Someone is not patient or not tall. Someone is either rich or brave. | Fred is not tall. | neutral | (![X]:((~quiet(X)<~>kind(X))=>(~humble(X)&~happy(X))))&
(![X]:((~creative(X)<~>funny(X))<=>(rich(X)<~>brave(X))))&
(((quiet(mary)<~>~brave(mary)))<=>((happy(john)<~>kind(john))))&
((?[X]:((~calm(X)|brave(X))))<=>((generous(lucy)|~rich(lucy))))&
(((~wise(fred)&patient(fred)))<=>(calm(paul)))&
(((patient(alice)|generous(alice)))<=>(?[X]:(~generous(X))))&
(![X]:(patient(X)<=>(~wise(X)<~>generous(X))))&
(![X]:((~rich(X)|humble(X))=>(~old(X)|~brave(X))))&
(![X]:(~generous(X)<=>(strong(X)&creative(X))))&
(((~happy(mary)<~>wise(mary)))=>(humble(fred)))&
(![X]:((wise(X)<~>strong(X))<=>(~rich(X)<~>~old(X))))&
(((old(susan)<~>~wise(susan)))=>(?[X]:((~brave(X)<~>~rich(X)))))&
((?[X]:((~tall(X)|quiet(X))))<=>(?[X]:((~rich(X)<~>patient(X)))))&
(![X]:((~happy(X)<~>~quiet(X))<=>kind(X)))&
(![X]:((quiet(X)|~humble(X))=>~kind(X)))&
(quiet(john))&
(?[X]:((patient(X)<~>~old(X))))&
((~strong(lucy)<~>patient(lucy)))&
((~brave(fred)|patient(fred)))&
((~rich(mary)|~calm(mary)))&
(?[X]:((~patient(X)|~kind(X))))&
(?[X]:((~patient(X)|~tall(X))))&
(?[X]:((rich(X)<~>brave(X)))) | ~tall(fred) | [] | null | 0 |
Everyone who is both calm and curious is wise or happy. If someone is both not calm and quiet then someone is not brave or not tall and vice versa. Everyone who is both not generous and kind is either not kind or not funny and vice versa. Everyone who is wise or quiet is both not curious and brave and vice versa. If someone is either creative or old then someone is both calm and kind. Everyone who is both not curious and not old is brave or rich. Everyone who is either not creative or funny is either not curious or not rich. Everyone who is either not generous or generous is either not wise or happy. Everyone who is both brave and calm is not quiet and vice versa. If someone is either generous or not old then someone is both not curious and happy and vice versa. Everyone who is humble is either not quiet or not calm. Everyone who is not kind or not old is not patient. Everyone who is tall or not calm is both not humble and old and vice versa. If john is humble then someone is either not humble or not calm and vice versa. If someone is not generous then someone is either not old or not calm and vice versa. If someone is funny or not patient then john is either wise or happy and vice versa. Alice is either tall or rich. Fred is either old or not creative. Someone is rich. Mary is not humble. John is funny or tall. | Alice is calm. | contradiction | (![X]:((calm(X)&curious(X))=>(wise(X)|happy(X))))&
((?[X]:((~calm(X)&quiet(X))))<=>(?[X]:((~brave(X)|~tall(X)))))&
(![X]:((~generous(X)&kind(X))<=>(~kind(X)<~>~funny(X))))&
(![X]:((wise(X)|quiet(X))<=>(~curious(X)&brave(X))))&
((?[X]:((creative(X)<~>old(X))))=>(?[X]:((calm(X)&kind(X)))))&
(![X]:((~curious(X)&~old(X))=>(brave(X)|rich(X))))&
(![X]:((~creative(X)<~>funny(X))=>(~curious(X)<~>~rich(X))))&
(![X]:((~generous(X)<~>generous(X))=>(~wise(X)<~>happy(X))))&
(![X]:((brave(X)&calm(X))<=>~quiet(X)))&
((?[X]:((generous(X)<~>~old(X))))<=>(?[X]:((~curious(X)&happy(X)))))&
(![X]:(humble(X)=>(~quiet(X)<~>~calm(X))))&
(![X]:((~kind(X)|~old(X))=>~patient(X)))&
(![X]:((tall(X)|~calm(X))<=>(~humble(X)&old(X))))&
((humble(john))<=>(?[X]:((~humble(X)<~>~calm(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((~old(X)<~>~calm(X)))))&
((?[X]:((funny(X)|~patient(X))))<=>((wise(john)<~>happy(john))))&
((tall(alice)<~>rich(alice)))&
((old(fred)<~>~creative(fred)))&
(?[X]:(rich(X)))&
(~humble(mary))&
((funny(john)|tall(john))) | calm(alice) | [
"p0",
"p2",
"p3",
"p7",
"p8",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5517564933529127759210134
% SZS output start Proof for 5517564933529127759210134
1. ! [X0] : ((curious(X0) & calm(X0)) => (happy(X0) | wise(X0))) [input p0]
3. ! [X0] : ((kind(X0) & ~generous(X0)) <=> (~kind(X0) <~> ~funny(X0))) [input p2]
4. ! [X0] : ((quiet(X0) | wise(X0)) <=> (brave(X0) & ~curious(X0))) [input p3]
8. ! [X0] : ((~generous(X0) <~> generous(X0)) => (~wise(X0) <~> happy(X0))) [input p7]
9. ! [X0] : ((calm(X0) & brave(X0)) <=> ~quiet(X0)) [input p8]
10. ? [X0] : (generous(X0) <~> ~old(X0)) <=> ? [X0] : (happy(X0) & ~curious(X0)) [input p9]
12. ! [X0] : ((~old(X0) | ~kind(X0)) => ~patient(X0)) [input p11]
16. ? [X0] : (~patient(X0) | funny(X0)) <=> (wise(john) <~> happy(john)) [input p15]
22. calm(alice) [input hypothesis]
25. ? [X0] : (generous(X0) <~> ~old(X0)) <=> ? [X1] : (happy(X1) & ~curious(X1)) [rectify 10]
27. ! [X0] : ((happy(X0) | wise(X0)) | (~curious(X0) | ~calm(X0))) [ennf transformation 1]
28. ! [X0] : (happy(X0) | wise(X0) | ~curious(X0) | ~calm(X0)) [flattening 27]
33. ! [X0] : ((~wise(X0) <~> happy(X0)) | (~generous(X0) <=> generous(X0))) [ennf transformation 8]
35. ! [X0] : (~patient(X0) | (old(X0) & kind(X0))) [ennf transformation 12]
41. ! [X0] : (((kind(X0) & ~generous(X0)) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0)))) & (((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | (~kind(X0) | generous(X0)))) [nnf transformation 3]
42. ! [X0] : (((kind(X0) & ~generous(X0)) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0)))) & (((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | ~kind(X0) | generous(X0))) [flattening 41]
43. ! [X0] : (((quiet(X0) | wise(X0)) | (~brave(X0) | curious(X0))) & ((brave(X0) & ~curious(X0)) | (~quiet(X0) & ~wise(X0)))) [nnf transformation 4]
44. ! [X0] : ((quiet(X0) | wise(X0) | ~brave(X0) | curious(X0)) & ((brave(X0) & ~curious(X0)) | (~quiet(X0) & ~wise(X0)))) [flattening 43]
50. ! [X0] : (((~happy(X0) | wise(X0)) & (happy(X0) | ~wise(X0))) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) [nnf transformation 33]
51. ! [X0] : (((calm(X0) & brave(X0)) | quiet(X0)) & (~quiet(X0) | (~calm(X0) | ~brave(X0)))) [nnf transformation 9]
52. ! [X0] : (((calm(X0) & brave(X0)) | quiet(X0)) & (~quiet(X0) | ~calm(X0) | ~brave(X0))) [flattening 51]
53. (? [X0] : ((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | ! [X1] : (~happy(X1) | curious(X1))) & (? [X1] : (happy(X1) & ~curious(X1)) | ! [X0] : ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0)))) [nnf transformation 25]
54. (? [X0] : ((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | ! [X1] : (~happy(X1) | curious(X1))) & (? [X2] : (happy(X2) & ~curious(X2)) | ! [X3] : ((generous(X3) | old(X3)) & (~old(X3) | ~generous(X3)))) [rectify 53]
55. ? [X0] : ((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) => ((old(sK3) | ~generous(sK3)) & (~old(sK3) | generous(sK3))) [choice axiom]
56. ? [X2] : (happy(X2) & ~curious(X2)) => (happy(sK4) & ~curious(sK4)) [choice axiom]
57. (((old(sK3) | ~generous(sK3)) & (~old(sK3) | generous(sK3))) | ! [X1] : (~happy(X1) | curious(X1))) & ((happy(sK4) & ~curious(sK4)) | ! [X3] : ((generous(X3) | old(X3)) & (~old(X3) | ~generous(X3)))) [skolemisation 54,56,55]
70. (? [X0] : (~patient(X0) | funny(X0)) | ((wise(john) | ~happy(john)) & (happy(john) | ~wise(john)))) & (((~happy(john) | ~wise(john)) & (happy(john) | wise(john))) | ! [X0] : (patient(X0) & ~funny(X0))) [nnf transformation 16]
71. (? [X0] : (~patient(X0) | funny(X0)) | ((wise(john) | ~happy(john)) & (happy(john) | ~wise(john)))) & (((~happy(john) | ~wise(john)) & (happy(john) | wise(john))) | ! [X1] : (patient(X1) & ~funny(X1))) [rectify 70]
72. ? [X0] : (~patient(X0) | funny(X0)) => (~patient(sK8) | funny(sK8)) [choice axiom]
73. ((~patient(sK8) | funny(sK8)) | ((wise(john) | ~happy(john)) & (happy(john) | ~wise(john)))) & (((~happy(john) | ~wise(john)) & (happy(john) | wise(john))) | ! [X1] : (patient(X1) & ~funny(X1))) [skolemisation 71,72]
78. ~curious(X0) | wise(X0) | happy(X0) | ~calm(X0) [cnf transformation 28]
87. ~kind(X0) | ~generous(X0) | funny(X0) [cnf transformation 42]
90. ~wise(X0) | ~curious(X0) [cnf transformation 44]
93. ~quiet(X0) | brave(X0) [cnf transformation 44]
94. ~brave(X0) | wise(X0) | quiet(X0) | curious(X0) [cnf transformation 44]
104. happy(X0) | ~wise(X0) | generous(X0) | generous(X0) [cnf transformation 50]
105. happy(X0) | ~wise(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 50]
106. ~happy(X0) | wise(X0) | generous(X0) | generous(X0) [cnf transformation 50]
107. ~happy(X0) | wise(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 50]
108. ~quiet(X0) | ~calm(X0) | ~brave(X0) [cnf transformation 52]
109. brave(X0) | quiet(X0) [cnf transformation 52]
115. ~old(sK3) | generous(sK3) | ~happy(X1) | curious(X1) [cnf transformation 57]
119. ~patient(X0) | kind(X0) [cnf transformation 35]
120. ~patient(X0) | old(X0) [cnf transformation 35]
134. happy(john) | wise(john) | ~funny(X1) [cnf transformation 73]
135. happy(john) | wise(john) | patient(X1) [cnf transformation 73]
136. ~happy(john) | ~wise(john) | ~funny(X1) [cnf transformation 73]
137. ~happy(john) | ~wise(john) | patient(X1) [cnf transformation 73]
147. calm(alice) [cnf transformation 22]
148. happy(X0) | ~wise(X0) | generous(X0) [duplicate literal removal 104]
149. ~generous(X0) | ~wise(X0) | happy(X0) [duplicate literal removal 105]
150. ~happy(X0) | wise(X0) | generous(X0) [duplicate literal removal 106]
151. ~generous(X0) | wise(X0) | ~happy(X0) [duplicate literal removal 107]
163. 3 <=> ! [X1] : brave(X1) [avatar definition]
164. brave(X1) <- (3) [avatar component clause 163]
203. ~happy(X0) | wise(X0) [subsumption resolution 150,151]
204. ~wise(X0) | happy(X0) [subsumption resolution 148,149]
205. brave(X0) [subsumption resolution 109,93]
206. 3 [avatar split clause 205,163]
207. ~quiet(X0) | ~calm(X0) [subsumption resolution 108,93]
209. 12 <=> ! [X1] : (~happy(X1) | curious(X1)) [avatar definition]
210. ~happy(X1) | curious(X1) <- (12) [avatar component clause 209]
212. 13 <=> generous(sK3) [avatar definition]
213. generous(sK3) <- (13) [avatar component clause 212]
216. 14 <=> old(sK3) [avatar definition]
217. ~old(sK3) <- (~14) [avatar component clause 216]
220. 12 | 13 | ~14 [avatar split clause 115,216,212,209]
270. 25 <=> ! [X1] : old(X1) [avatar definition]
271. old(X1) <- (25) [avatar component clause 270]
285. ~wise(john) | patient(X1) [subsumption resolution 137,204]
287. 29 <=> ! [X1] : patient(X1) [avatar definition]
288. patient(X1) <- (29) [avatar component clause 287]
290. 30 <=> wise(john) [avatar definition]
293. 29 | ~30 [avatar split clause 285,290,287]
294. ~wise(john) | ~funny(X1) [subsumption resolution 136,204]
296. 31 <=> ! [X1] : ~funny(X1) [avatar definition]
297. ~funny(X1) <- (31) [avatar component clause 296]
298. 31 | ~30 [avatar split clause 294,290,296]
299. wise(john) | patient(X1) [subsumption resolution 135,203]
300. 29 | 30 [avatar split clause 299,290,287]
301. wise(john) | ~funny(X1) [subsumption resolution 134,203]
302. 31 | 30 [avatar split clause 301,290,296]
338. kind(X0) <- (29) [resolution 119,288]
339. old(X0) <- (29) [resolution 120,288]
340. 25 | ~29 [avatar split clause 339,287,270]
341. $false <- (~14, 25) [resolution 271,217]
344. 14 | ~25 [avatar contradiction clause 341]
356. ~generous(X0) | funny(X0) <- (29) [resolution 87,338]
358. ~generous(X0) <- (29, 31) [subsumption resolution 356,297]
368. $false <- (13, 29, 31) [resolution 358,213]
369. ~13 | ~29 | ~31 [avatar contradiction clause 368]
386. quiet(X0) | wise(X0) | curious(X0) <- (3) [resolution 94,164]
410. 43 <=> curious(alice) [avatar definition]
411. curious(alice) <- (43) [avatar component clause 410]
412. ~curious(alice) <- (~43) [avatar component clause 410]
433. ~calm(X0) | curious(X0) | wise(X0) <- (3) [resolution 386,207]
436. curious(alice) | wise(alice) <- (3) [resolution 433,147]
439. wise(alice) <- (3, ~43) [subsumption resolution 436,412]
452. happy(alice) <- (3, ~43) [resolution 439,204]
459. curious(alice) <- (3, 12, ~43) [resolution 452,210]
461. $false <- (3, 12, ~43) [subsumption resolution 459,412]
462. ~3 | ~12 | 43 [avatar contradiction clause 461]
464. 46 <=> wise(alice) [avatar definition]
466. wise(alice) <- (46) [avatar component clause 464]
467. 46 | 43 | ~3 [avatar split clause 436,163,410,464]
470. wise(alice) | happy(alice) | ~calm(alice) <- (43) [resolution 411,78]
471. wise(alice) | happy(alice) <- (43) [subsumption resolution 470,147]
472. happy(alice) <- (43) [subsumption resolution 471,204]
474. wise(alice) <- (43) [resolution 472,203]
475. 46 | ~43 [avatar split clause 474,410,464]
478. ~curious(alice) <- (46) [resolution 466,90]
479. $false <- (43, 46) [subsumption resolution 478,411]
480. ~43 | ~46 [avatar contradiction clause 479]
481. $false [avatar sat refutation 206,220,293,298,300,302,340,344,369,462,467,475,480]
% SZS output end Proof for 5517564933529127759210134
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both rich and funny then someone is not funny.
Everyone who is not kind is either rich or humble and vice versa.
Everyone who is kind is not wise or not tall and vice versa.
Everyone who is humble is not rich or old.
If john is not rich then someone is either not old or patient and vice versa.
If mary is not rich or curious then alice is either not patient or not funny.
Everyone who is either funny or strong is not patient or curious and vice versa.
If fred is tall or not creative then mary is patient or strong.
Everyone who is both not generous and tall is either quiet or calm and vice versa.
Everyone who is either not funny or tall is both funny and kind.
If someone is wise or not happy then alice is both not quiet and not wise.
Everyone who is not kind is both not humble and happy and vice versa.
If fred is both curious and happy then someone is both wise and patient and vice versa.
If someone is either not old or happy then john is not calm.
Everyone who is kind or calm is creative and vice versa.
Everyone who is either not funny or not happy is both kind and patient and vice versa.
John is both not strong and not quiet.
Alice is not generous or wise.
Mary is either creative or not brave.
Someone is either not humble or kind.
Someone is not tall.
Someone is not wise or not old. | Mary is creative. | entailment | ((?[X]:((rich(X)&funny(X))))=>(?[X]:(~funny(X))))&
(![X]:(~kind(X)<=>(rich(X)<~>humble(X))))&
(![X]:(kind(X)<=>(~wise(X)|~tall(X))))&
(![X]:(humble(X)=>(~rich(X)|old(X))))&
((~rich(john))<=>(?[X]:((~old(X)<~>patient(X)))))&
(((~rich(mary)|curious(mary)))=>((~patient(alice)<~>~funny(alice))))&
(![X]:((funny(X)<~>strong(X))<=>(~patient(X)|curious(X))))&
(((tall(fred)|~creative(fred)))=>((patient(mary)|strong(mary))))&
(![X]:((~generous(X)&tall(X))<=>(quiet(X)<~>calm(X))))&
(![X]:((~funny(X)<~>tall(X))=>(funny(X)&kind(X))))&
((?[X]:((wise(X)|~happy(X))))=>((~quiet(alice)&~wise(alice))))&
(![X]:(~kind(X)<=>(~humble(X)&happy(X))))&
(((curious(fred)&happy(fred)))<=>(?[X]:((wise(X)&patient(X)))))&
((?[X]:((~old(X)<~>happy(X))))=>(~calm(john)))&
(![X]:((kind(X)|calm(X))<=>creative(X)))&
(![X]:((~funny(X)<~>~happy(X))<=>(kind(X)&patient(X))))&
((~strong(john)&~quiet(john)))&
((~generous(alice)|wise(alice)))&
((creative(mary)<~>~brave(mary)))&
(?[X]:((~humble(X)<~>kind(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~wise(X)|~old(X)))) | creative(mary) | [
"p2",
"p9",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8411255090877880672436493
% SZS output start Proof for 8411255090877880672436493
3. ! [X0] : (kind(X0) <=> (~tall(X0) | ~wise(X0))) [input p2]
10. ! [X0] : ((~funny(X0) <~> tall(X0)) => (kind(X0) & funny(X0))) [input p9]
12. ! [X0] : (~kind(X0) <=> (happy(X0) & ~humble(X0))) [input p11]
15. ! [X0] : ((calm(X0) | kind(X0)) <=> creative(X0)) [input p14]
16. ! [X0] : ((~funny(X0) <~> ~happy(X0)) <=> (patient(X0) & kind(X0))) [input p15]
23. ~creative(mary) [input hypothesis]
31. ! [X0] : ((kind(X0) & funny(X0)) | (~funny(X0) <=> tall(X0))) [ennf transformation 10]
38. ! [X0] : ((kind(X0) | (tall(X0) & wise(X0))) & ((~tall(X0) | ~wise(X0)) | ~kind(X0))) [nnf transformation 3]
39. ! [X0] : ((kind(X0) | (tall(X0) & wise(X0))) & (~tall(X0) | ~wise(X0) | ~kind(X0))) [flattening 38]
49. ! [X0] : ((kind(X0) & funny(X0)) | ((~funny(X0) | ~tall(X0)) & (tall(X0) | funny(X0)))) [nnf transformation 31]
50. ! [X0] : ((~kind(X0) | (~happy(X0) | humble(X0))) & ((happy(X0) & ~humble(X0)) | kind(X0))) [nnf transformation 12]
51. ! [X0] : ((~kind(X0) | ~happy(X0) | humble(X0)) & ((happy(X0) & ~humble(X0)) | kind(X0))) [flattening 50]
58. ! [X0] : (((calm(X0) | kind(X0)) | ~creative(X0)) & (creative(X0) | (~calm(X0) & ~kind(X0)))) [nnf transformation 15]
59. ! [X0] : ((calm(X0) | kind(X0) | ~creative(X0)) & (creative(X0) | (~calm(X0) & ~kind(X0)))) [flattening 58]
60. ! [X0] : ((((happy(X0) | funny(X0)) & (~happy(X0) | ~funny(X0))) | (~patient(X0) | ~kind(X0))) & ((patient(X0) & kind(X0)) | ((~funny(X0) | happy(X0)) & (~happy(X0) | funny(X0))))) [nnf transformation 16]
61. ! [X0] : ((((happy(X0) | funny(X0)) & (~happy(X0) | ~funny(X0))) | ~patient(X0) | ~kind(X0)) & ((patient(X0) & kind(X0)) | ((~funny(X0) | happy(X0)) & (~happy(X0) | funny(X0))))) [flattening 60]
77. tall(X0) | kind(X0) [cnf transformation 39]
104. kind(X0) | ~funny(X0) | ~tall(X0) [cnf transformation 49]
110. happy(X0) | kind(X0) [cnf transformation 51]
118. ~kind(X0) | creative(X0) [cnf transformation 59]
121. kind(X0) | ~happy(X0) | funny(X0) [cnf transformation 61]
136. ~creative(mary) [cnf transformation 23]
206. kind(X0) | ~funny(X0) [subsumption resolution 104,77]
262. kind(X0) | ~happy(X0) [subsumption resolution 121,206]
263. kind(X0) [subsumption resolution 262,110]
270. 29 <=> creative(mary) [avatar definition]
272. ~creative(mary) <- (~29) [avatar component clause 270]
289. ~29 [avatar split clause 136,270]
295. creative(X0) [resolution 118,263]
296. $false <- (~29) [resolution 295,272]
297. 29 [avatar contradiction clause 296]
298. $false [avatar sat refutation 289,297]
% SZS output end Proof for 8411255090877880672436493
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and not creative is either not tall or curious and vice versa.
If someone is generous then someone is either not generous or not rich.
If someone is not rich then lucy is both happy and not creative and vice versa.
If someone is either not rich or calm then paul is wise or calm.
If paul is not patient or not kind then someone is not generous and vice versa.
Everyone who is wise or rich is either not tall or curious.
Everyone who is both tall and not funny is not old or curious.
Everyone who is both not creative and wise is either not curious or not patient.
Everyone who is not curious or happy is both humble and brave and vice versa.
Everyone who is not rich is both not wise and curious and vice versa.
If mary is both generous and old then mary is both not humble and quiet.
If someone is funny then someone is not patient and vice versa.
If someone is either patient or humble then someone is not tall or curious and vice versa.
If someone is brave then someone is either not creative or creative and vice versa.
Everyone who is kind is both strong and not funny and vice versa.
Everyone who is both not patient and calm is both not brave and not old and vice versa.
Someone is humble.
Lucy is not generous or not kind.
Someone is both not humble and brave.
Fred is either calm or creative.
Someone is either strong or happy.
Someone is not rich.
Lucy is both old and not calm. | Mary is not humble. | neutral | (![X]:((creative(X)&~creative(X))<=>(~tall(X)<~>curious(X))))&
((?[X]:(generous(X)))=>(?[X]:((~generous(X)<~>~rich(X)))))&
((?[X]:(~rich(X)))<=>((happy(lucy)&~creative(lucy))))&
((?[X]:((~rich(X)<~>calm(X))))=>((wise(paul)|calm(paul))))&
(((~patient(paul)|~kind(paul)))<=>(?[X]:(~generous(X))))&
(![X]:((wise(X)|rich(X))=>(~tall(X)<~>curious(X))))&
(![X]:((tall(X)&~funny(X))=>(~old(X)|curious(X))))&
(![X]:((~creative(X)&wise(X))=>(~curious(X)<~>~patient(X))))&
(![X]:((~curious(X)|happy(X))<=>(humble(X)&brave(X))))&
(![X]:(~rich(X)<=>(~wise(X)&curious(X))))&
(((generous(mary)&old(mary)))=>((~humble(mary)&quiet(mary))))&
((?[X]:(funny(X)))<=>(?[X]:(~patient(X))))&
((?[X]:((patient(X)<~>humble(X))))<=>(?[X]:((~tall(X)|curious(X)))))&
((?[X]:(brave(X)))<=>(?[X]:((~creative(X)<~>creative(X)))))&
(![X]:(kind(X)<=>(strong(X)&~funny(X))))&
(![X]:((~patient(X)&calm(X))<=>(~brave(X)&~old(X))))&
(?[X]:(humble(X)))&
((~generous(lucy)|~kind(lucy)))&
(?[X]:((~humble(X)&brave(X))))&
((calm(fred)<~>creative(fred)))&
(?[X]:((strong(X)<~>happy(X))))&
(?[X]:(~rich(X)))&
((old(lucy)&~calm(lucy))) | ~humble(mary) | [] | null | 0 |
Everyone who is both creative and not tall is rich and vice versa.
Everyone who is wise is creative or strong.
If fred is quiet or wise then alice is both not curious and not wise.
If paul is both not quiet and strong then mary is humble or happy and vice versa.
Everyone who is patient is either humble or happy.
Everyone who is strong is not old or not tall.
Everyone who is not humble or not generous is curious or not wise and vice versa.
If someone is both quiet and not quiet then someone is strong or brave and vice versa.
Everyone who is both quiet and humble is either kind or quiet and vice versa.
Everyone who is kind is not funny.
Everyone who is either not funny or not wise is not humble or not strong.
If paul is both funny and not patient then susan is both tall and not humble.
Everyone who is either kind or not tall is both old and not tall and vice versa.
Everyone who is both strong and old is either quiet or creative and vice versa.
If mary is not tall then mary is both calm and funny.
Everyone who is tall or kind is tall.
Fred is both humble and not strong.
Someone is not strong or humble.
Someone is either old or not strong.
John is either generous or not funny.
Someone is not calm or not old.
John is either not rich or humble.
Lucy is old. | Susan is strong. | contradiction | (![X]:((creative(X)&~tall(X))<=>rich(X)))&
(![X]:(wise(X)=>(creative(X)|strong(X))))&
(((quiet(fred)|wise(fred)))=>((~curious(alice)&~wise(alice))))&
(((~quiet(paul)&strong(paul)))<=>((humble(mary)|happy(mary))))&
(![X]:(patient(X)=>(humble(X)<~>happy(X))))&
(![X]:(strong(X)=>(~old(X)|~tall(X))))&
(![X]:((~humble(X)|~generous(X))<=>(curious(X)|~wise(X))))&
((?[X]:((quiet(X)&~quiet(X))))<=>(?[X]:((strong(X)|brave(X)))))&
(![X]:((quiet(X)&humble(X))<=>(kind(X)<~>quiet(X))))&
(![X]:(kind(X)=>~funny(X)))&
(![X]:((~funny(X)<~>~wise(X))=>(~humble(X)|~strong(X))))&
(((funny(paul)&~patient(paul)))=>((tall(susan)&~humble(susan))))&
(![X]:((kind(X)<~>~tall(X))<=>(old(X)&~tall(X))))&
(![X]:((strong(X)&old(X))<=>(quiet(X)<~>creative(X))))&
((~tall(mary))=>((calm(mary)&funny(mary))))&
(![X]:((tall(X)|kind(X))=>tall(X)))&
((humble(fred)&~strong(fred)))&
(?[X]:((~strong(X)|humble(X))))&
(?[X]:((old(X)<~>~strong(X))))&
((generous(john)<~>~funny(john)))&
(?[X]:((~calm(X)|~old(X))))&
((~rich(john)<~>humble(john)))&
(old(lucy)) | strong(susan) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 621328727229407104360133
% SZS output start Proof for 621328727229407104360133
8. ? [X0] : (~quiet(X0) & quiet(X0)) <=> ? [X0] : (brave(X0) | strong(X0)) [input p7]
24. strong(susan) [input hypothesis]
25. ? [X0] : (~quiet(X0) & quiet(X0)) <=> ? [X1] : (brave(X1) | strong(X1)) [rectify 8]
46. (? [X0] : (~quiet(X0) & quiet(X0)) | ! [X1] : (~brave(X1) & ~strong(X1))) & (? [X1] : (brave(X1) | strong(X1)) | ! [X0] : (quiet(X0) | ~quiet(X0))) [nnf transformation 25]
47. (? [X0] : (~quiet(X0) & quiet(X0)) | ! [X1] : (~brave(X1) & ~strong(X1))) & (? [X2] : (brave(X2) | strong(X2)) | ! [X3] : (quiet(X3) | ~quiet(X3))) [rectify 46]
48. ? [X0] : (~quiet(X0) & quiet(X0)) => (~quiet(sK0) & quiet(sK0)) [choice axiom]
49. ? [X2] : (brave(X2) | strong(X2)) => (brave(sK1) | strong(sK1)) [choice axiom]
50. ((~quiet(sK0) & quiet(sK0)) | ! [X1] : (~brave(X1) & ~strong(X1))) & ((brave(sK1) | strong(sK1)) | ! [X3] : (quiet(X3) | ~quiet(X3))) [skolemisation 47,49,48]
88. quiet(sK0) | ~strong(X1) [cnf transformation 50]
90. ~quiet(sK0) | ~strong(X1) [cnf transformation 50]
130. strong(susan) [cnf transformation 24]
180. 10 <=> quiet(sK0) [avatar definition]
185. 11 <=> ! [X1] : ~strong(X1) [avatar definition]
186. ~strong(X1) <- (11) [avatar component clause 185]
187. 11 | ~10 [avatar split clause 90,180,185]
189. 11 | 10 [avatar split clause 88,180,185]
272. $false <- (11) [resolution 186,130]
273. ~11 [avatar contradiction clause 272]
274. $false [avatar sat refutation 187,189,273]
% SZS output end Proof for 621328727229407104360133
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is not rich or not quiet then someone is curious or not quiet and vice versa.
Everyone who is either curious or not wise is either not kind or not old.
If paul is either not happy or not calm then john is both not curious and happy and vice versa.
If someone is generous then mary is both not quiet and kind.
If lucy is not rich or not patient then mary is not humble and vice versa.
Everyone who is either not curious or old is not calm or not creative.
If someone is both not brave and strong then someone is either kind or curious.
Everyone who is both not kind and not wise is either tall or not rich.
Everyone who is both brave and creative is either not curious or creative and vice versa.
Everyone who is both not calm and not rich is not funny.
Everyone who is either brave or patient is humble.
If mary is not rich or quiet then someone is either rich or not brave.
Everyone who is either brave or not curious is quiet.
If someone is either humble or not creative then john is not rich or happy and vice versa.
If john is kind or not kind then someone is both not old and not brave and vice versa.
If alice is either not strong or not quiet then someone is quiet or not old.
John is either tall or not curious.
Mary is both not happy and patient.
Paul is generous or old.
Someone is either not happy or not strong.
Someone is brave or not humble.
Alice is both calm and not kind.
Paul is both not rich and not old. | John is not curious. | neutral | (((~rich(john)|~quiet(john)))<=>(?[X]:((curious(X)|~quiet(X)))))&
(![X]:((curious(X)<~>~wise(X))=>(~kind(X)<~>~old(X))))&
(((~happy(paul)<~>~calm(paul)))<=>((~curious(john)&happy(john))))&
((?[X]:(generous(X)))=>((~quiet(mary)&kind(mary))))&
(((~rich(lucy)|~patient(lucy)))<=>(~humble(mary)))&
(![X]:((~curious(X)<~>old(X))=>(~calm(X)|~creative(X))))&
((?[X]:((~brave(X)&strong(X))))=>(?[X]:((kind(X)<~>curious(X)))))&
(![X]:((~kind(X)&~wise(X))=>(tall(X)<~>~rich(X))))&
(![X]:((brave(X)&creative(X))<=>(~curious(X)<~>creative(X))))&
(![X]:((~calm(X)&~rich(X))=>~funny(X)))&
(![X]:((brave(X)<~>patient(X))=>humble(X)))&
(((~rich(mary)|quiet(mary)))=>(?[X]:((rich(X)<~>~brave(X)))))&
(![X]:((brave(X)<~>~curious(X))=>quiet(X)))&
((?[X]:((humble(X)<~>~creative(X))))<=>((~rich(john)|happy(john))))&
(((kind(john)|~kind(john)))<=>(?[X]:((~old(X)&~brave(X)))))&
(((~strong(alice)<~>~quiet(alice)))=>(?[X]:((quiet(X)|~old(X)))))&
((tall(john)<~>~curious(john)))&
((~happy(mary)&patient(mary)))&
((generous(paul)|old(paul)))&
(?[X]:((~happy(X)<~>~strong(X))))&
(?[X]:((brave(X)|~humble(X))))&
((calm(alice)&~kind(alice)))&
((~rich(paul)&~old(paul))) | ~curious(john) | [] | null | 0 |
Everyone who is not creative or quiet is both not creative and quiet and vice versa. Everyone who is brave or not wise is both not rich and creative and vice versa. Everyone who is curious is either curious or humble and vice versa. If alice is either not creative or curious then mary is quiet. If someone is either not humble or not kind then lucy is both generous and not quiet and vice versa. Everyone who is both calm and strong is both quiet and wise. If lucy is both rich and not generous then paul is either creative or not tall and vice versa. If someone is rich then paul is both not old and strong. If someone is not creative or wise then fred is humble. Everyone who is not kind or funny is either patient or tall and vice versa. If alice is not patient then someone is brave. Everyone who is either not funny or funny is either not kind or quiet and vice versa. If lucy is both funny and tall then someone is either quiet or kind. If fred is humble then john is both brave and happy and vice versa. If lucy is either rich or brave then john is both not strong and humble and vice versa. If mary is calm then fred is either kind or rich. Someone is both brave and not rich. Someone is happy or not humble. Someone is not generous. Susan is not old or generous. Someone is either strong or funny. Susan is either not calm or funny. | John is old. | neutral | (![X]:((~creative(X)|quiet(X))<=>(~creative(X)&quiet(X))))&
(![X]:((brave(X)|~wise(X))<=>(~rich(X)&creative(X))))&
(![X]:(curious(X)<=>(curious(X)<~>humble(X))))&
(((~creative(alice)<~>curious(alice)))=>(quiet(mary)))&
((?[X]:((~humble(X)<~>~kind(X))))<=>((generous(lucy)&~quiet(lucy))))&
(![X]:((calm(X)&strong(X))=>(quiet(X)&wise(X))))&
(((rich(lucy)&~generous(lucy)))<=>((creative(paul)<~>~tall(paul))))&
((?[X]:(rich(X)))=>((~old(paul)&strong(paul))))&
((?[X]:((~creative(X)|wise(X))))=>(humble(fred)))&
(![X]:((~kind(X)|funny(X))<=>(patient(X)<~>tall(X))))&
((~patient(alice))=>(?[X]:(brave(X))))&
(![X]:((~funny(X)<~>funny(X))<=>(~kind(X)<~>quiet(X))))&
(((funny(lucy)&tall(lucy)))=>(?[X]:((quiet(X)<~>kind(X)))))&
((humble(fred))<=>((brave(john)&happy(john))))&
(((rich(lucy)<~>brave(lucy)))<=>((~strong(john)&humble(john))))&
((calm(mary))=>((kind(fred)<~>rich(fred))))&
(?[X]:((brave(X)&~rich(X))))&
(?[X]:((happy(X)|~humble(X))))&
(?[X]:(~generous(X)))&
((~old(susan)|generous(susan)))&
(?[X]:((strong(X)<~>funny(X))))&
((~calm(susan)<~>funny(susan))) | old(john) | [] | null | 0 |
If someone is wise or not patient then mary is not curious or patient. Everyone who is both humble and creative is not brave or patient and vice versa. If someone is both not tall and generous then fred is both not happy and old and vice versa. If someone is not kind then someone is creative or happy and vice versa. If paul is either not rich or not tall then someone is both not wise and tall. If someone is both not old and old then someone is brave and vice versa. Everyone who is patient or tall is both tall and strong and vice versa. If someone is both funny and calm then someone is not strong or quiet. Everyone who is either not kind or tall is not rich or not quiet and vice versa. If mary is not funny or not strong then someone is not curious or curious and vice versa. Everyone who is either not humble or not brave is not tall or not creative. Everyone who is both not humble and old is both tall and not calm. Everyone who is generous is both not brave and not creative. If someone is both not generous and not wise then fred is both rich and creative. Everyone who is either not curious or wise is not quiet and vice versa. Someone is both strong and not old. Fred is not generous. Someone is not kind. John is either wise or brave. Someone is either not rich or not happy. Someone is curious or brave. Paul is creative. | Fred is patient. | contradiction | ((?[X]:((wise(X)|~patient(X))))=>((~curious(mary)|patient(mary))))&
(![X]:((humble(X)&creative(X))<=>(~brave(X)|patient(X))))&
((?[X]:((~tall(X)&generous(X))))<=>((~happy(fred)&old(fred))))&
((?[X]:(~kind(X)))<=>(?[X]:((creative(X)|happy(X)))))&
(((~rich(paul)<~>~tall(paul)))=>(?[X]:((~wise(X)&tall(X)))))&
((?[X]:((~old(X)&old(X))))<=>(?[X]:(brave(X))))&
(![X]:((patient(X)|tall(X))<=>(tall(X)&strong(X))))&
((?[X]:((funny(X)&calm(X))))=>(?[X]:((~strong(X)|quiet(X)))))&
(![X]:((~kind(X)<~>tall(X))<=>(~rich(X)|~quiet(X))))&
(((~funny(mary)|~strong(mary)))<=>(?[X]:((~curious(X)|curious(X)))))&
(![X]:((~humble(X)<~>~brave(X))=>(~tall(X)|~creative(X))))&
(![X]:((~humble(X)&old(X))=>(tall(X)&~calm(X))))&
(![X]:(generous(X)=>(~brave(X)&~creative(X))))&
((?[X]:((~generous(X)&~wise(X))))=>((rich(fred)&creative(fred))))&
(![X]:((~curious(X)<~>wise(X))<=>~quiet(X)))&
(?[X]:((strong(X)&~old(X))))&
(~generous(fred))&
(?[X]:(~kind(X)))&
((wise(john)<~>brave(john)))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:((curious(X)|brave(X))))&
(creative(paul)) | patient(fred) | [
"p1",
"p5",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5982022166420487904429701
% SZS output start Proof for 5982022166420487904429701
2. ! [X0] : ((creative(X0) & humble(X0)) <=> (patient(X0) | ~brave(X0))) [input p1]
6. ? [X0] : (old(X0) & ~old(X0)) <=> ? [X0] : brave(X0) [input p5]
7. ! [X0] : ((tall(X0) | patient(X0)) <=> (strong(X0) & tall(X0))) [input p6]
11. ! [X0] : ((~humble(X0) <~> ~brave(X0)) => (~creative(X0) | ~tall(X0))) [input p10]
23. patient(fred) [input hypothesis]
25. ? [X0] : (old(X0) & ~old(X0)) <=> ? [X1] : brave(X1) [rectify 6]
32. ! [X0] : ((~creative(X0) | ~tall(X0)) | (~humble(X0) <=> ~brave(X0))) [ennf transformation 11]
33. ! [X0] : (~creative(X0) | ~tall(X0) | (~humble(X0) <=> ~brave(X0))) [flattening 32]
38. ! [X0] : (((creative(X0) & humble(X0)) | (~patient(X0) & brave(X0))) & ((patient(X0) | ~brave(X0)) | (~creative(X0) | ~humble(X0)))) [nnf transformation 2]
39. ! [X0] : (((creative(X0) & humble(X0)) | (~patient(X0) & brave(X0))) & (patient(X0) | ~brave(X0) | ~creative(X0) | ~humble(X0))) [flattening 38]
53. (? [X0] : (old(X0) & ~old(X0)) | ! [X1] : ~brave(X1)) & (? [X1] : brave(X1) | ! [X0] : (~old(X0) | old(X0))) [nnf transformation 25]
54. (? [X0] : (old(X0) & ~old(X0)) | ! [X1] : ~brave(X1)) & (? [X2] : brave(X2) | ! [X3] : (~old(X3) | old(X3))) [rectify 53]
55. ? [X0] : (old(X0) & ~old(X0)) => (old(sK4) & ~old(sK4)) [choice axiom]
56. ? [X2] : brave(X2) => brave(sK5) [choice axiom]
57. ((old(sK4) & ~old(sK4)) | ! [X1] : ~brave(X1)) & (brave(sK5) | ! [X3] : (~old(X3) | old(X3))) [skolemisation 54,56,55]
58. ! [X0] : (((tall(X0) | patient(X0)) | (~strong(X0) | ~tall(X0))) & ((strong(X0) & tall(X0)) | (~tall(X0) & ~patient(X0)))) [nnf transformation 7]
59. ! [X0] : ((tall(X0) | patient(X0) | ~strong(X0) | ~tall(X0)) & ((strong(X0) & tall(X0)) | (~tall(X0) & ~patient(X0)))) [flattening 58]
67. ! [X0] : (~creative(X0) | ~tall(X0) | ((~humble(X0) | brave(X0)) & (~brave(X0) | humble(X0)))) [nnf transformation 33]
82. brave(X0) | humble(X0) [cnf transformation 39]
84. brave(X0) | creative(X0) [cnf transformation 39]
98. ~old(sK4) | ~brave(X1) [cnf transformation 57]
99. old(sK4) | ~brave(X1) [cnf transformation 57]
100. ~patient(X0) | tall(X0) [cnf transformation 59]
116. ~creative(X0) | ~tall(X0) | ~humble(X0) | brave(X0) [cnf transformation 67]
136. patient(fred) [cnf transformation 23]
221. 20 <=> ! [X1] : ~brave(X1) [avatar definition]
222. ~brave(X1) <- (20) [avatar component clause 221]
224. 21 <=> old(sK4) [avatar definition]
227. 20 | 21 [avatar split clause 99,224,221]
228. 20 | ~21 [avatar split clause 98,224,221]
245. ~tall(X0) | ~humble(X0) | brave(X0) [subsumption resolution 116,84]
246. ~tall(X0) | brave(X0) [subsumption resolution 245,82]
300. tall(fred) [resolution 100,136]
307. brave(fred) [resolution 246,300]
308. $false <- (20) [subsumption resolution 307,222]
309. ~20 [avatar contradiction clause 308]
310. $false [avatar sat refutation 227,228,309]
% SZS output end Proof for 5982022166420487904429701
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and not happy is old or kind and vice versa. Everyone who is rich or tall is either not curious or kind and vice versa. Everyone who is either calm or patient is either not calm or humble. Everyone who is funny or not happy is not creative and vice versa. Everyone who is happy or not creative is either patient or not funny. Everyone who is patient is curious or not quiet and vice versa. If lucy is both not humble and not funny then lucy is both quiet and not rich and vice versa. Everyone who is either brave or not rich is curious and vice versa. Everyone who is not old or creative is either not quiet or curious. Everyone who is both not happy and not creative is curious and vice versa. If john is either not happy or not generous then someone is not quiet. Everyone who is either not happy or quiet is calm or humble and vice versa. If someone is old or wise then alice is old. If someone is funny or not kind then someone is not humble or not strong. Everyone who is either not generous or rich is both not quiet and not rich. Everyone who is old or not brave is not patient. Susan is either rich or not creative. Someone is either not kind or not creative. Mary is both funny and not strong. Someone is not rich or not funny. Alice is tall or not brave. Mary is not wise. | Lucy is not rich. | neutral | (![X]:((~creative(X)&~happy(X))<=>(old(X)|kind(X))))&
(![X]:((rich(X)|tall(X))<=>(~curious(X)<~>kind(X))))&
(![X]:((calm(X)<~>patient(X))=>(~calm(X)<~>humble(X))))&
(![X]:((funny(X)|~happy(X))<=>~creative(X)))&
(![X]:((happy(X)|~creative(X))=>(patient(X)<~>~funny(X))))&
(![X]:(patient(X)<=>(curious(X)|~quiet(X))))&
(((~humble(lucy)&~funny(lucy)))<=>((quiet(lucy)&~rich(lucy))))&
(![X]:((brave(X)<~>~rich(X))<=>curious(X)))&
(![X]:((~old(X)|creative(X))=>(~quiet(X)<~>curious(X))))&
(![X]:((~happy(X)&~creative(X))<=>curious(X)))&
(((~happy(john)<~>~generous(john)))=>(?[X]:(~quiet(X))))&
(![X]:((~happy(X)<~>quiet(X))<=>(calm(X)|humble(X))))&
((?[X]:((old(X)|wise(X))))=>(old(alice)))&
((?[X]:((funny(X)|~kind(X))))=>(?[X]:((~humble(X)|~strong(X)))))&
(![X]:((~generous(X)<~>rich(X))=>(~quiet(X)&~rich(X))))&
(![X]:((old(X)|~brave(X))=>~patient(X)))&
((rich(susan)<~>~creative(susan)))&
(?[X]:((~kind(X)<~>~creative(X))))&
((funny(mary)&~strong(mary)))&
(?[X]:((~rich(X)|~funny(X))))&
((tall(alice)|~brave(alice)))&
(~wise(mary)) | ~rich(lucy) | [] | null | 0 |
Everyone who is strong or not calm is either curious or old and vice versa.
Everyone who is both old and not patient is both happy and patient and vice versa.
Everyone who is either not calm or not strong is either kind or quiet and vice versa.
If lucy is either quiet or not creative then someone is both humble and not generous and vice versa.
Everyone who is both kind and not curious is either not calm or not wise and vice versa.
Everyone who is both old and not creative is both not happy and strong.
Everyone who is either not quiet or old is not happy or not humble and vice versa.
If fred is curious then someone is quiet and vice versa.
If paul is wise or patient then someone is not wise or not creative and vice versa.
Everyone who is both curious and brave is not brave.
Everyone who is not patient is old and vice versa.
Everyone who is not humble or brave is either not creative or not patient.
Everyone who is tall is either patient or wise and vice versa.
If paul is both strong and humble then someone is not strong and vice versa.
If lucy is patient or not generous then someone is either old or not calm and vice versa.
Someone is not humble.
Someone is not funny or not patient.
Someone is either tall or not rich.
Paul is either not calm or not humble.
Someone is old or not tall.
Someone is creative. | Lucy is curious. | neutral | (![X]:((strong(X)|~calm(X))<=>(curious(X)<~>old(X))))&
(![X]:((old(X)&~patient(X))<=>(happy(X)&patient(X))))&
(![X]:((~calm(X)<~>~strong(X))<=>(kind(X)<~>quiet(X))))&
(((quiet(lucy)<~>~creative(lucy)))<=>(?[X]:((humble(X)&~generous(X)))))&
(![X]:((kind(X)&~curious(X))<=>(~calm(X)<~>~wise(X))))&
(![X]:((old(X)&~creative(X))=>(~happy(X)&strong(X))))&
(![X]:((~quiet(X)<~>old(X))<=>(~happy(X)|~humble(X))))&
((curious(fred))<=>(?[X]:(quiet(X))))&
(((wise(paul)|patient(paul)))<=>(?[X]:((~wise(X)|~creative(X)))))&
(![X]:((curious(X)&brave(X))=>~brave(X)))&
(![X]:(~patient(X)<=>old(X)))&
(![X]:((~humble(X)|brave(X))=>(~creative(X)<~>~patient(X))))&
(![X]:(tall(X)<=>(patient(X)<~>wise(X))))&
(((strong(paul)&humble(paul)))<=>(?[X]:(~strong(X))))&
(((patient(lucy)|~generous(lucy)))<=>(?[X]:((old(X)<~>~calm(X)))))&
(?[X]:(~humble(X)))&
(?[X]:((~funny(X)|~patient(X))))&
(?[X]:((tall(X)<~>~rich(X))))&
((~calm(paul)<~>~humble(paul)))&
(?[X]:((old(X)|~tall(X))))&
(?[X]:(creative(X))) | curious(lucy) | [] | null | 0 |
Everyone who is either not curious or generous is humble and vice versa. Everyone who is old is either happy or not creative. Everyone who is both wise and rich is not curious and vice versa. Everyone who is both not strong and rich is not patient or not humble and vice versa. Everyone who is kind or not patient is not creative or wise and vice versa. Everyone who is not old is either not calm or not wise and vice versa. Everyone who is wise is happy or brave and vice versa. Everyone who is both not generous and not quiet is not tall or not old. If someone is not wise then fred is both creative and not funny and vice versa. If alice is rich or not creative then fred is both not patient and brave and vice versa. If mary is both tall and not patient then someone is either not strong or not funny. If john is not patient or not rich then someone is both not kind and kind and vice versa. If someone is not wise then someone is either not calm or not quiet and vice versa. Everyone who is creative is both strong and not creative. If paul is either patient or not kind then someone is both tall and not creative. Everyone who is either not happy or rich is not calm or rich and vice versa. Fred is both not tall and not humble. Someone is wise. Someone is not brave or patient. Susan is not generous. | Fred is not old. | entailment | (![X]:((~curious(X)<~>generous(X))<=>humble(X)))&
(![X]:(old(X)=>(happy(X)<~>~creative(X))))&
(![X]:((wise(X)&rich(X))<=>~curious(X)))&
(![X]:((~strong(X)&rich(X))<=>(~patient(X)|~humble(X))))&
(![X]:((kind(X)|~patient(X))<=>(~creative(X)|wise(X))))&
(![X]:(~old(X)<=>(~calm(X)<~>~wise(X))))&
(![X]:(wise(X)<=>(happy(X)|brave(X))))&
(![X]:((~generous(X)&~quiet(X))=>(~tall(X)|~old(X))))&
((?[X]:(~wise(X)))<=>((creative(fred)&~funny(fred))))&
(((rich(alice)|~creative(alice)))<=>((~patient(fred)&brave(fred))))&
(((tall(mary)&~patient(mary)))=>(?[X]:((~strong(X)<~>~funny(X)))))&
(((~patient(john)|~rich(john)))<=>(?[X]:((~kind(X)&kind(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)<~>~quiet(X)))))&
(![X]:(creative(X)=>(strong(X)&~creative(X))))&
(((patient(paul)<~>~kind(paul)))=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:((~happy(X)<~>rich(X))<=>(~calm(X)|rich(X))))&
((~tall(fred)&~humble(fred)))&
(?[X]:(wise(X)))&
(?[X]:((~brave(X)|patient(X))))&
(~generous(susan)) | ~old(fred) | [
"p1",
"p3",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8885757730948228453425892
% SZS output start Proof for 8885757730948228453425892
2. ! [X0] : (old(X0) => (happy(X0) <~> ~creative(X0))) [input p1]
4. ! [X0] : ((rich(X0) & ~strong(X0)) <=> (~humble(X0) | ~patient(X0))) [input p3]
10. (~creative(alice) | rich(alice)) <=> (brave(fred) & ~patient(fred)) [input p9]
14. ! [X0] : (creative(X0) => (~creative(X0) & strong(X0))) [input p13]
16. ! [X0] : ((~happy(X0) <~> rich(X0)) <=> (rich(X0) | ~calm(X0))) [input p15]
21. old(fred) [input hypothesis]
23. ! [X0] : ((happy(X0) <~> ~creative(X0)) | ~old(X0)) [ennf transformation 2]
28. ! [X0] : ((~creative(X0) & strong(X0)) | ~creative(X0)) [ennf transformation 14]
31. ! [X0] : (((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | ~old(X0)) [nnf transformation 23]
34. ! [X0] : (((rich(X0) & ~strong(X0)) | (humble(X0) & patient(X0))) & ((~humble(X0) | ~patient(X0)) | (~rich(X0) | strong(X0)))) [nnf transformation 4]
35. ! [X0] : (((rich(X0) & ~strong(X0)) | (humble(X0) & patient(X0))) & (~humble(X0) | ~patient(X0) | ~rich(X0) | strong(X0))) [flattening 34]
46. ((~creative(alice) | rich(alice)) | (~brave(fred) | patient(fred))) & ((brave(fred) & ~patient(fred)) | (creative(alice) & ~rich(alice))) [nnf transformation 10]
47. (~creative(alice) | rich(alice) | ~brave(fred) | patient(fred)) & ((brave(fred) & ~patient(fred)) | (creative(alice) & ~rich(alice))) [flattening 46]
64. ! [X0] : ((((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))))) [nnf transformation 16]
65. ! [X0] : ((((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))))) [flattening 64]
75. ~happy(X0) | creative(X0) | ~old(X0) [cnf transformation 31]
82. patient(X0) | rich(X0) [cnf transformation 35]
100. ~patient(fred) | creative(alice) [cnf transformation 47]
116. ~creative(X0) | ~creative(X0) [cnf transformation 28]
126. ~rich(X0) | happy(X0) | ~rich(X0) [cnf transformation 65]
132. old(fred) [cnf transformation 21]
134. ~rich(X0) | happy(X0) [duplicate literal removal 126]
135. ~creative(X0) [duplicate literal removal 116]
155. 5 <=> patient(fred) [avatar definition]
156. ~patient(fred) <- (~5) [avatar component clause 155]
167. 8 <=> creative(alice) [avatar definition]
168. creative(alice) <- (8) [avatar component clause 167]
173. 8 | ~5 [avatar split clause 100,155,167]
261. rich(fred) <- (~5) [resolution 82,156]
266. happy(fred) <- (~5) [resolution 134,261]
293. creative(fred) | ~old(fred) <- (~5) [resolution 75,266]
298. ~old(fred) <- (~5) [subsumption resolution 293,135]
299. $false <- (~5) [subsumption resolution 298,132]
300. 5 [avatar contradiction clause 299]
303. $false <- (8) [subsumption resolution 168,135]
304. ~8 [avatar contradiction clause 303]
305. $false [avatar sat refutation 173,300,304]
% SZS output end Proof for 8885757730948228453425892
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall.
If someone is tall then susan is both not quiet and curious.
If someone is kind then susan is generous and vice versa.
Everyone who is generous is not funny or not rich and vice versa.
Everyone who is both not kind and not calm is both not old and not rich and vice versa.
Everyone who is either not quiet or kind is happy or brave and vice versa.
Everyone who is kind is not old.
If fred is both quiet and not strong then someone is both not old and not humble and vice versa.
Everyone who is not humble is both not calm and not funny and vice versa.
Everyone who is quiet or not wise is both quiet and brave and vice versa.
If someone is not strong or kind then susan is either strong or not creative and vice versa.
If someone is both strong and quiet then paul is humble.
Everyone who is both not tall and not generous is either not humble or not funny.
Everyone who is either calm or rich is kind.
If paul is either not rich or curious then someone is both not kind and happy.
If susan is not tall or creative then someone is old or not generous and vice versa.
Someone is either not wise or generous.
Someone is both not curious and not strong.
Someone is not generous.
Alice is both not tall and not patient.
Fred is either creative or brave.
Someone is funny.
Someone is either funny or not funny.
Lucy is not curious or wise. | Susan is not wise. | contradiction | (![X]:(happy(X)=>~tall(X)))&
((?[X]:(tall(X)))=>((~quiet(susan)&curious(susan))))&
((?[X]:(kind(X)))<=>(generous(susan)))&
(![X]:(generous(X)<=>(~funny(X)|~rich(X))))&
(![X]:((~kind(X)&~calm(X))<=>(~old(X)&~rich(X))))&
(![X]:((~quiet(X)<~>kind(X))<=>(happy(X)|brave(X))))&
(![X]:(kind(X)=>~old(X)))&
(((quiet(fred)&~strong(fred)))<=>(?[X]:((~old(X)&~humble(X)))))&
(![X]:(~humble(X)<=>(~calm(X)&~funny(X))))&
(![X]:((quiet(X)|~wise(X))<=>(quiet(X)&brave(X))))&
((?[X]:((~strong(X)|kind(X))))<=>((strong(susan)<~>~creative(susan))))&
((?[X]:((strong(X)&quiet(X))))=>(humble(paul)))&
(![X]:((~tall(X)&~generous(X))=>(~humble(X)<~>~funny(X))))&
(![X]:((calm(X)<~>rich(X))=>kind(X)))&
(((~rich(paul)<~>curious(paul)))=>(?[X]:((~kind(X)&happy(X)))))&
(((~tall(susan)|creative(susan)))<=>(?[X]:((old(X)|~generous(X)))))&
(?[X]:((~wise(X)<~>generous(X))))&
(?[X]:((~curious(X)&~strong(X))))&
(?[X]:(~generous(X)))&
((~tall(alice)&~patient(alice)))&
((creative(fred)<~>brave(fred)))&
(?[X]:(funny(X)))&
(?[X]:((funny(X)<~>~funny(X))))&
((~curious(lucy)|wise(lucy))) | ~wise(susan) | [
"p1",
"p3",
"p8",
"p9",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7382968692312496107790122
% SZS output start Proof for 7382968692312496107790122
2. ? [X0] : tall(X0) => (curious(susan) & ~quiet(susan)) [input p1]
4. ! [X0] : (generous(X0) <=> (~rich(X0) | ~funny(X0))) [input p3]
9. ! [X0] : (~humble(X0) <=> (~funny(X0) & ~calm(X0))) [input p8]
10. ! [X0] : ((~wise(X0) | quiet(X0)) <=> (brave(X0) & quiet(X0))) [input p9]
13. ! [X0] : ((~generous(X0) & ~tall(X0)) => (~humble(X0) <~> ~funny(X0))) [input p12]
19. ? [X0] : ~generous(X0) [input p18]
25. ~wise(susan) [input hypothesis]
28. (curious(susan) & ~quiet(susan)) | ! [X0] : ~tall(X0) [ennf transformation 2]
31. ! [X0] : ((~humble(X0) <~> ~funny(X0)) | (generous(X0) | tall(X0))) [ennf transformation 13]
32. ! [X0] : ((~humble(X0) <~> ~funny(X0)) | generous(X0) | tall(X0)) [flattening 31]
39. ! [X0] : ((generous(X0) | (rich(X0) & funny(X0))) & ((~rich(X0) | ~funny(X0)) | ~generous(X0))) [nnf transformation 4]
40. ! [X0] : ((generous(X0) | (rich(X0) & funny(X0))) & (~rich(X0) | ~funny(X0) | ~generous(X0))) [flattening 39]
50. ! [X0] : ((~humble(X0) | (funny(X0) | calm(X0))) & ((~funny(X0) & ~calm(X0)) | humble(X0))) [nnf transformation 9]
51. ! [X0] : ((~humble(X0) | funny(X0) | calm(X0)) & ((~funny(X0) & ~calm(X0)) | humble(X0))) [flattening 50]
52. ! [X0] : (((~wise(X0) | quiet(X0)) | (~brave(X0) | ~quiet(X0))) & ((brave(X0) & quiet(X0)) | (wise(X0) & ~quiet(X0)))) [nnf transformation 10]
53. ! [X0] : ((~wise(X0) | quiet(X0) | ~brave(X0) | ~quiet(X0)) & ((brave(X0) & quiet(X0)) | (wise(X0) & ~quiet(X0)))) [flattening 52]
58. ! [X0] : (((funny(X0) | humble(X0)) & (~funny(X0) | ~humble(X0))) | generous(X0) | tall(X0)) [nnf transformation 32]
73. ? [X0] : ~generous(X0) => ~generous(sK7) [choice axiom]
74. ~generous(sK7) [skolemisation 19,73]
82. ~quiet(susan) | ~tall(X0) [cnf transformation 28]
87. funny(X0) | generous(X0) [cnf transformation 40]
105. ~funny(X0) | humble(X0) [cnf transformation 51]
108. wise(X0) | quiet(X0) [cnf transformation 53]
119. ~funny(X0) | ~humble(X0) | generous(X0) | tall(X0) [cnf transformation 58]
135. ~generous(sK7) [cnf transformation 74]
143. ~wise(susan) [cnf transformation 25]
145. 1 <=> ! [X0] : ~tall(X0) [avatar definition]
146. ~tall(X0) <- (1) [avatar component clause 145]
153. 3 <=> quiet(susan) [avatar definition]
156. 1 | ~3 [avatar split clause 82,153,145]
226. ~humble(X0) | generous(X0) | tall(X0) [subsumption resolution 119,87]
248. 23 <=> ! [X0] : generous(X0) [avatar definition]
249. generous(X0) <- (23) [avatar component clause 248]
300. humble(X0) | generous(X0) [resolution 105,87]
301. quiet(susan) [resolution 108,143]
305. 3 [avatar split clause 301,153]
378. generous(X0) | tall(X0) | generous(X0) [resolution 226,300]
380. generous(X0) | tall(X0) [duplicate literal removal 378]
382. generous(X0) <- (1) [subsumption resolution 380,146]
383. 23 | ~1 [avatar split clause 382,145,248]
387. $false <- (23) [resolution 249,135]
388. ~23 [avatar contradiction clause 387]
391. $false [avatar sat refutation 156,305,383,388]
% SZS output end Proof for 7382968692312496107790122
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong or not rich then paul is both quiet and kind.
If someone is rich then lucy is either not generous or kind.
If someone is tall then fred is patient and vice versa.
If someone is both humble and not patient then someone is both not brave and kind.
If someone is either brave or creative then mary is not brave or not patient and vice versa.
If someone is both not curious and not quiet then someone is calm or not brave and vice versa.
Everyone who is either not patient or not generous is not wise and vice versa.
Everyone who is creative or funny is either humble or creative.
Everyone who is patient or funny is either not quiet or not old and vice versa.
Everyone who is either curious or not quiet is not wise or not creative.
If someone is both generous and quiet then someone is not wise and vice versa.
Everyone who is either patient or old is both wise and not calm.
Everyone who is rich is either not rich or strong and vice versa.
Everyone who is calm or not creative is not strong or happy.
Everyone who is brave or patient is either not wise or not old.
Everyone who is either happy or humble is patient.
Someone is both not creative and not humble.
Fred is not curious or not quiet.
Fred is curious or wise.
Paul is either not humble or not happy.
Someone is either not strong or brave.
Susan is either humble or rich.
Someone is both generous and not patient.
Someone is not quiet or quiet. | Fred is not strong. | contradiction | ((?[X]:((strong(X)|~rich(X))))=>((quiet(paul)&kind(paul))))&
((?[X]:(rich(X)))=>((~generous(lucy)<~>kind(lucy))))&
((?[X]:(tall(X)))<=>(patient(fred)))&
((?[X]:((humble(X)&~patient(X))))=>(?[X]:((~brave(X)&kind(X)))))&
((?[X]:((brave(X)<~>creative(X))))<=>((~brave(mary)|~patient(mary))))&
((?[X]:((~curious(X)&~quiet(X))))<=>(?[X]:((calm(X)|~brave(X)))))&
(![X]:((~patient(X)<~>~generous(X))<=>~wise(X)))&
(![X]:((creative(X)|funny(X))=>(humble(X)<~>creative(X))))&
(![X]:((patient(X)|funny(X))<=>(~quiet(X)<~>~old(X))))&
(![X]:((curious(X)<~>~quiet(X))=>(~wise(X)|~creative(X))))&
((?[X]:((generous(X)&quiet(X))))<=>(?[X]:(~wise(X))))&
(![X]:((patient(X)<~>old(X))=>(wise(X)&~calm(X))))&
(![X]:(rich(X)<=>(~rich(X)<~>strong(X))))&
(![X]:((calm(X)|~creative(X))=>(~strong(X)|happy(X))))&
(![X]:((brave(X)|patient(X))=>(~wise(X)<~>~old(X))))&
(![X]:((happy(X)<~>humble(X))=>patient(X)))&
(?[X]:((~creative(X)&~humble(X))))&
((~curious(fred)|~quiet(fred)))&
((curious(fred)|wise(fred)))&
((~humble(paul)<~>~happy(paul)))&
(?[X]:((~strong(X)<~>brave(X))))&
((humble(susan)<~>rich(susan)))&
(?[X]:((generous(X)&~patient(X))))&
(?[X]:((~quiet(X)|quiet(X)))) | ~strong(fred) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 184072773664699642829573
% SZS output start Proof for 184072773664699642829573
13. ! [X0] : (rich(X0) <=> (~rich(X0) <~> strong(X0))) [input p12]
25. ~strong(fred) [input hypothesis]
69. ! [X0] : ((rich(X0) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | ~rich(X0))) [nnf transformation 13]
127. strong(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 69]
129. rich(X0) | strong(X0) | rich(X0) [cnf transformation 69]
152. ~strong(fred) [cnf transformation 25]
153. strong(X0) | ~rich(X0) [duplicate literal removal 127]
154. rich(X0) | strong(X0) [duplicate literal removal 129]
292. strong(X0) [subsumption resolution 153,154]
330. $false [subsumption resolution 152,292]
% SZS output end Proof for 184072773664699642829573
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and strong is either rich or not wise.
Everyone who is strong or not humble is both humble and calm.
If someone is both generous and funny then someone is either funny or quiet and vice versa.
Everyone who is both not funny and not quiet is calm and vice versa.
If lucy is not rich or strong then paul is either not creative or kind and vice versa.
If someone is either not tall or rich then someone is patient or kind and vice versa.
Everyone who is creative or not funny is both patient and not old and vice versa.
Everyone who is curious or funny is either rich or quiet.
If someone is either rich or not happy then john is not patient.
Everyone who is either brave or patient is both quiet and not old.
Everyone who is generous or not strong is either old or strong.
If someone is not curious or not quiet then fred is rich.
Everyone who is not brave or generous is either tall or curious and vice versa.
If fred is not brave or calm then someone is not funny.
Everyone who is funny is either brave or patient.
If susan is either tall or curious then someone is either strong or not funny and vice versa.
Mary is creative or not creative.
Someone is not quiet or wise.
Mary is generous.
Someone is either not humble or kind.
Alice is both tall and not old.
Alice is both not wise and not old. | Fred is old. | contradiction | (![X]:((~generous(X)&strong(X))=>(rich(X)<~>~wise(X))))&
(![X]:((strong(X)|~humble(X))=>(humble(X)&calm(X))))&
((?[X]:((generous(X)&funny(X))))<=>(?[X]:((funny(X)<~>quiet(X)))))&
(![X]:((~funny(X)&~quiet(X))<=>calm(X)))&
(((~rich(lucy)|strong(lucy)))<=>((~creative(paul)<~>kind(paul))))&
((?[X]:((~tall(X)<~>rich(X))))<=>(?[X]:((patient(X)|kind(X)))))&
(![X]:((creative(X)|~funny(X))<=>(patient(X)&~old(X))))&
(![X]:((curious(X)|funny(X))=>(rich(X)<~>quiet(X))))&
((?[X]:((rich(X)<~>~happy(X))))=>(~patient(john)))&
(![X]:((brave(X)<~>patient(X))=>(quiet(X)&~old(X))))&
(![X]:((generous(X)|~strong(X))=>(old(X)<~>strong(X))))&
((?[X]:((~curious(X)|~quiet(X))))=>(rich(fred)))&
(![X]:((~brave(X)|generous(X))<=>(tall(X)<~>curious(X))))&
(((~brave(fred)|calm(fred)))=>(?[X]:(~funny(X))))&
(![X]:(funny(X)=>(brave(X)<~>patient(X))))&
(((tall(susan)<~>curious(susan)))<=>(?[X]:((strong(X)<~>~funny(X)))))&
((creative(mary)|~creative(mary)))&
(?[X]:((~quiet(X)|wise(X))))&
(generous(mary))&
(?[X]:((~humble(X)<~>kind(X))))&
((tall(alice)&~old(alice)))&
((~wise(alice)&~old(alice))) | old(fred) | [
"p6",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1944388176231556503664337
% SZS output start Proof for 1944388176231556503664337
7. ! [X0] : ((~funny(X0) | creative(X0)) <=> (~old(X0) & patient(X0))) [input p6]
10. ! [X0] : ((brave(X0) <~> patient(X0)) => (~old(X0) & quiet(X0))) [input p9]
15. ! [X0] : (funny(X0) => (brave(X0) <~> patient(X0))) [input p14]
23. old(fred) [input hypothesis]
31. ! [X0] : ((~old(X0) & quiet(X0)) | (brave(X0) <=> patient(X0))) [ennf transformation 10]
35. ! [X0] : ((brave(X0) <~> patient(X0)) | ~funny(X0)) [ennf transformation 15]
51. ! [X0] : (((~funny(X0) | creative(X0)) | (old(X0) | ~patient(X0))) & ((~old(X0) & patient(X0)) | (funny(X0) & ~creative(X0)))) [nnf transformation 7]
52. ! [X0] : ((~funny(X0) | creative(X0) | old(X0) | ~patient(X0)) & ((~old(X0) & patient(X0)) | (funny(X0) & ~creative(X0)))) [flattening 51]
55. ! [X0] : ((~old(X0) & quiet(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) [nnf transformation 31]
61. ! [X0] : (((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | ~funny(X0)) [nnf transformation 35]
99. patient(X0) | funny(X0) [cnf transformation 52]
101. ~old(X0) | funny(X0) [cnf transformation 52]
111. ~brave(X0) | patient(X0) | ~old(X0) [cnf transformation 55]
112. ~old(X0) | brave(X0) | ~patient(X0) [cnf transformation 55]
127. patient(X0) | brave(X0) | ~funny(X0) [cnf transformation 61]
128. ~brave(X0) | ~patient(X0) | ~funny(X0) [cnf transformation 61]
146. old(fred) [cnf transformation 23]
270. 28 <=> brave(fred) [avatar definition]
272. brave(fred) <- (28) [avatar component clause 270]
274. brave(X0) | patient(X0) [subsumption resolution 127,99]
320. funny(fred) [resolution 101,146]
417. patient(X0) | ~old(X0) | patient(X0) [resolution 111,274]
418. ~old(X0) | patient(X0) [duplicate literal removal 417]
419. brave(fred) | ~patient(fred) [resolution 112,146]
421. brave(fred) [subsumption resolution 419,274]
422. 28 [avatar split clause 421,270]
464. ~patient(fred) | ~funny(fred) <- (28) [resolution 128,272]
465. ~patient(fred) <- (28) [subsumption resolution 464,320]
522. patient(fred) [resolution 418,146]
524. $false <- (28) [subsumption resolution 522,465]
525. ~28 [avatar contradiction clause 524]
526. $false [avatar sat refutation 422,525]
% SZS output end Proof for 1944388176231556503664337
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either tall or not kind then someone is both happy and calm and vice versa. Everyone who is strong or rich is not kind or not rich. Everyone who is not rich or funny is either not curious or kind. If alice is both patient and not happy then someone is either not curious or not old. Everyone who is not wise or not old is both rich and not wise and vice versa. If john is not brave or not kind then alice is either not humble or not kind. Everyone who is humble or creative is either not humble or brave. Everyone who is not creative or creative is funny. If someone is patient then someone is both not curious and not generous and vice versa. If someone is both brave and not old then someone is kind or not strong. If someone is both old and not funny then someone is rich and vice versa. Everyone who is both not strong and not wise is both not wise and not calm. Everyone who is not calm is not quiet or old and vice versa. Everyone who is patient is either not old or not wise and vice versa. If lucy is both old and not tall then alice is either not curious or curious and vice versa. Everyone who is rich or quiet is not generous. Someone is rich or not happy. Someone is not happy. Alice is not wise or tall. Lucy is either not kind or not tall. Alice is both tall and not happy. | Alice is curious. | contradiction | ((?[X]:((tall(X)<~>~kind(X))))<=>(?[X]:((happy(X)&calm(X)))))&
(![X]:((strong(X)|rich(X))=>(~kind(X)|~rich(X))))&
(![X]:((~rich(X)|funny(X))=>(~curious(X)<~>kind(X))))&
(((patient(alice)&~happy(alice)))=>(?[X]:((~curious(X)<~>~old(X)))))&
(![X]:((~wise(X)|~old(X))<=>(rich(X)&~wise(X))))&
(((~brave(john)|~kind(john)))=>((~humble(alice)<~>~kind(alice))))&
(![X]:((humble(X)|creative(X))=>(~humble(X)<~>brave(X))))&
(![X]:((~creative(X)|creative(X))=>funny(X)))&
((?[X]:(patient(X)))<=>(?[X]:((~curious(X)&~generous(X)))))&
((?[X]:((brave(X)&~old(X))))=>(?[X]:((kind(X)|~strong(X)))))&
((?[X]:((old(X)&~funny(X))))<=>(?[X]:(rich(X))))&
(![X]:((~strong(X)&~wise(X))=>(~wise(X)&~calm(X))))&
(![X]:(~calm(X)<=>(~quiet(X)|old(X))))&
(![X]:(patient(X)<=>(~old(X)<~>~wise(X))))&
(((old(lucy)&~tall(lucy)))<=>((~curious(alice)<~>curious(alice))))&
(![X]:((rich(X)|quiet(X))=>~generous(X)))&
(?[X]:((rich(X)|~happy(X))))&
(?[X]:(~happy(X)))&
((~wise(alice)|tall(alice)))&
((~kind(lucy)<~>~tall(lucy)))&
((tall(alice)&~happy(alice))) | curious(alice) | [
"p0",
"p2",
"p4",
"p7",
"p10",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2048757367742972605753720
% SZS output start Proof for 2048757367742972605753720
1. ? [X0] : (tall(X0) <~> ~kind(X0)) <=> ? [X0] : (calm(X0) & happy(X0)) [input p0]
3. ! [X0] : ((funny(X0) | ~rich(X0)) => (~curious(X0) <~> kind(X0))) [input p2]
5. ! [X0] : ((~old(X0) | ~wise(X0)) <=> (~wise(X0) & rich(X0))) [input p4]
8. ! [X0] : ((creative(X0) | ~creative(X0)) => funny(X0)) [input p7]
11. ? [X0] : (~funny(X0) & old(X0)) <=> ? [X0] : rich(X0) [input p10]
13. ! [X0] : (~calm(X0) <=> (old(X0) | ~quiet(X0))) [input p12]
21. ~happy(alice) & tall(alice) [input p20]
22. curious(alice) [input hypothesis]
23. ? [X0] : (tall(X0) <~> ~kind(X0)) <=> ? [X1] : (calm(X1) & happy(X1)) [rectify 1]
26. ? [X0] : (~funny(X0) & old(X0)) <=> ? [X1] : rich(X1) [rectify 11]
29. ! [X0] : ((~curious(X0) <~> kind(X0)) | (~funny(X0) & rich(X0))) [ennf transformation 3]
34. ! [X0] : (funny(X0) | (~creative(X0) & creative(X0))) [ennf transformation 8]
39. (? [X0] : ((kind(X0) | ~tall(X0)) & (~kind(X0) | tall(X0))) | ! [X1] : (~calm(X1) | ~happy(X1))) & (? [X1] : (calm(X1) & happy(X1)) | ! [X0] : ((tall(X0) | kind(X0)) & (~kind(X0) | ~tall(X0)))) [nnf transformation 23]
40. (? [X0] : ((kind(X0) | ~tall(X0)) & (~kind(X0) | tall(X0))) | ! [X1] : (~calm(X1) | ~happy(X1))) & (? [X2] : (calm(X2) & happy(X2)) | ! [X3] : ((tall(X3) | kind(X3)) & (~kind(X3) | ~tall(X3)))) [rectify 39]
41. ? [X0] : ((kind(X0) | ~tall(X0)) & (~kind(X0) | tall(X0))) => ((kind(sK0) | ~tall(sK0)) & (~kind(sK0) | tall(sK0))) [choice axiom]
42. ? [X2] : (calm(X2) & happy(X2)) => (calm(sK1) & happy(sK1)) [choice axiom]
43. (((kind(sK0) | ~tall(sK0)) & (~kind(sK0) | tall(sK0))) | ! [X1] : (~calm(X1) | ~happy(X1))) & ((calm(sK1) & happy(sK1)) | ! [X3] : ((tall(X3) | kind(X3)) & (~kind(X3) | ~tall(X3)))) [skolemisation 40,42,41]
44. ! [X0] : (((~kind(X0) | curious(X0)) & (kind(X0) | ~curious(X0))) | (~funny(X0) & rich(X0))) [nnf transformation 29]
48. ! [X0] : (((~old(X0) | ~wise(X0)) | (wise(X0) | ~rich(X0))) & ((~wise(X0) & rich(X0)) | (old(X0) & wise(X0)))) [nnf transformation 5]
49. ! [X0] : ((~old(X0) | ~wise(X0) | wise(X0) | ~rich(X0)) & ((~wise(X0) & rich(X0)) | (old(X0) & wise(X0)))) [flattening 48]
60. (? [X0] : (~funny(X0) & old(X0)) | ! [X1] : ~rich(X1)) & (? [X1] : rich(X1) | ! [X0] : (funny(X0) | ~old(X0))) [nnf transformation 26]
61. (? [X0] : (~funny(X0) & old(X0)) | ! [X1] : ~rich(X1)) & (? [X2] : rich(X2) | ! [X3] : (funny(X3) | ~old(X3))) [rectify 60]
62. ? [X0] : (~funny(X0) & old(X0)) => (~funny(sK6) & old(sK6)) [choice axiom]
63. ? [X2] : rich(X2) => rich(sK7) [choice axiom]
64. ((~funny(sK6) & old(sK6)) | ! [X1] : ~rich(X1)) & (rich(sK7) | ! [X3] : (funny(X3) | ~old(X3))) [skolemisation 61,63,62]
65. ! [X0] : ((~calm(X0) | (~old(X0) & quiet(X0))) & ((old(X0) | ~quiet(X0)) | calm(X0))) [nnf transformation 13]
66. ! [X0] : ((~calm(X0) | (~old(X0) & quiet(X0))) & (old(X0) | ~quiet(X0) | calm(X0))) [flattening 65]
77. calm(sK1) | ~kind(X3) | ~tall(X3) [cnf transformation 43]
83. ~curious(X0) | kind(X0) | rich(X0) [cnf transformation 44]
90. old(X0) | rich(X0) [cnf transformation 49]
102. funny(X0) | creative(X0) [cnf transformation 34]
103. ~creative(X0) | funny(X0) [cnf transformation 34]
110. ~funny(sK6) | ~rich(X1) [cnf transformation 64]
115. ~old(X0) | ~calm(X0) [cnf transformation 66]
133. tall(alice) [cnf transformation 21]
135. curious(alice) [cnf transformation 22]
159. 5 <=> calm(sK1) [avatar definition]
161. calm(sK1) <- (5) [avatar component clause 159]
164. 6 <=> ! [X3] : (~kind(X3) | ~tall(X3)) [avatar definition]
165. ~kind(X3) | ~tall(X3) <- (6) [avatar component clause 164]
166. 6 | 5 [avatar split clause 77,159,164]
201. 14 <=> kind(alice) [avatar definition]
203. kind(alice) <- (14) [avatar component clause 201]
212. funny(X0) [subsumption resolution 102,103]
246. ~rich(X1) [subsumption resolution 110,212]
250. 24 <=> curious(alice) [avatar definition]
251. curious(alice) <- (24) [avatar component clause 250]
271. 28 <=> tall(alice) [avatar definition]
273. tall(alice) <- (28) [avatar component clause 271]
282. 28 [avatar split clause 133,271]
283. 24 [avatar split clause 135,250]
286. ~calm(X0) | rich(X0) [resolution 115,90]
287. ~calm(X0) [subsumption resolution 286,246]
293. $false <- (5) [subsumption resolution 161,287]
294. ~5 [avatar contradiction clause 293]
309. kind(alice) | rich(alice) <- (24) [resolution 83,251]
315. kind(alice) <- (24) [subsumption resolution 309,246]
316. 14 | ~24 [avatar split clause 315,250,201]
318. ~tall(alice) <- (6, 14) [resolution 203,165]
319. $false <- (6, 14, 28) [subsumption resolution 318,273]
320. ~6 | ~14 | ~28 [avatar contradiction clause 319]
321. $false [avatar sat refutation 166,282,283,294,316,320]
% SZS output end Proof for 2048757367742972605753720
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative then someone is patient. Everyone who is both tall and not brave is brave or humble and vice versa. If someone is both not wise and not calm then lucy is not calm or not funny. If someone is both not generous and happy then someone is generous or not funny and vice versa. Everyone who is rich is not old and vice versa. If fred is generous then someone is either not generous or brave. If someone is not humble then someone is both rich and tall and vice versa. Everyone who is not funny is quiet or not wise and vice versa. If someone is humble or not generous then lucy is not curious. Everyone who is both rich and not funny is not wise or not brave and vice versa. If someone is creative or not calm then susan is either quiet or brave. If someone is not generous or humble then someone is either not quiet or not strong. If someone is both creative and quiet then susan is not brave and vice versa. If paul is creative then fred is funny or not tall. If paul is either creative or curious then someone is not humble and vice versa. Someone is either not brave or not creative. Someone is not funny or funny. Someone is both strong and not funny. Lucy is either not patient or not rich. John is rich. | Lucy is not patient. | entailment | ((?[X]:(creative(X)))=>(?[X]:(patient(X))))&
(![X]:((tall(X)&~brave(X))<=>(brave(X)|humble(X))))&
((?[X]:((~wise(X)&~calm(X))))=>((~calm(lucy)|~funny(lucy))))&
((?[X]:((~generous(X)&happy(X))))<=>(?[X]:((generous(X)|~funny(X)))))&
(![X]:(rich(X)<=>~old(X)))&
((generous(fred))=>(?[X]:((~generous(X)<~>brave(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((rich(X)&tall(X)))))&
(![X]:(~funny(X)<=>(quiet(X)|~wise(X))))&
((?[X]:((humble(X)|~generous(X))))=>(~curious(lucy)))&
(![X]:((rich(X)&~funny(X))<=>(~wise(X)|~brave(X))))&
((?[X]:((creative(X)|~calm(X))))=>((quiet(susan)<~>brave(susan))))&
((?[X]:((~generous(X)|humble(X))))=>(?[X]:((~quiet(X)<~>~strong(X)))))&
((?[X]:((creative(X)&quiet(X))))<=>(~brave(susan)))&
((creative(paul))=>((funny(fred)|~tall(fred))))&
(((creative(paul)<~>curious(paul)))<=>(?[X]:(~humble(X))))&
(?[X]:((~brave(X)<~>~creative(X))))&
(?[X]:((~funny(X)|funny(X))))&
(?[X]:((strong(X)&~funny(X))))&
((~patient(lucy)<~>~rich(lucy)))&
(rich(john)) | ~patient(lucy) | [
"p1",
"p9",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2798340667783509206973364
% SZS output start Proof for 2798340667783509206973364
2. ! [X0] : ((~brave(X0) & tall(X0)) <=> (humble(X0) | brave(X0))) [input p1]
10. ! [X0] : ((~funny(X0) & rich(X0)) <=> (~brave(X0) | ~wise(X0))) [input p9]
19. ~patient(lucy) <~> ~rich(lucy) [input p18]
21. patient(lucy) [input hypothesis]
38. ! [X0] : (((~brave(X0) & tall(X0)) | (~humble(X0) & ~brave(X0))) & ((humble(X0) | brave(X0)) | (brave(X0) | ~tall(X0)))) [nnf transformation 2]
39. ! [X0] : (((~brave(X0) & tall(X0)) | (~humble(X0) & ~brave(X0))) & (humble(X0) | brave(X0) | brave(X0) | ~tall(X0))) [flattening 38]
56. ! [X0] : (((~funny(X0) & rich(X0)) | (brave(X0) & wise(X0))) & ((~brave(X0) | ~wise(X0)) | (funny(X0) | ~rich(X0)))) [nnf transformation 10]
57. ! [X0] : (((~funny(X0) & rich(X0)) | (brave(X0) & wise(X0))) & (~brave(X0) | ~wise(X0) | funny(X0) | ~rich(X0))) [flattening 56]
78. (rich(lucy) | patient(lucy)) & (~rich(lucy) | ~patient(lucy)) [nnf transformation 19]
83. ~brave(X0) | ~brave(X0) [cnf transformation 39]
105. rich(X0) | brave(X0) [cnf transformation 57]
129. ~rich(lucy) | ~patient(lucy) [cnf transformation 78]
132. patient(lucy) [cnf transformation 21]
134. ~brave(X0) [duplicate literal removal 83]
230. rich(X0) [subsumption resolution 105,134]
279. ~patient(lucy) [subsumption resolution 129,230]
280. $false [subsumption resolution 132,279]
% SZS output end Proof for 2798340667783509206973364
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative or not wise then paul is humble or not quiet and vice versa.
Everyone who is wise or kind is brave and vice versa.
If someone is either not generous or not strong then alice is either not old or not rich.
Everyone who is not quiet is quiet.
If lucy is not brave or funny then john is both not tall and not humble and vice versa.
If someone is brave then mary is either not rich or not happy and vice versa.
Everyone who is both not funny and quiet is either not brave or not humble.
Everyone who is not curious or not old is patient.
If susan is either funny or kind then mary is either not patient or not happy and vice versa.
If someone is both not kind and generous then someone is wise.
If someone is happy then alice is either brave or not humble.
Everyone who is wise or patient is kind.
Everyone who is creative is strong or not strong and vice versa.
If alice is not quiet then alice is not strong or not calm and vice versa.
Everyone who is either kind or not old is either funny or not happy.
If someone is both quiet and not patient then alice is both not strong and not rich and vice versa.
Lucy is kind or not rich.
Someone is not strong or creative.
Someone is both brave and strong.
Susan is humble.
Someone is both strong and wise.
Susan is either not old or not patient. | Paul is brave. | entailment | ((?[X]:((~creative(X)|~wise(X))))<=>((humble(paul)|~quiet(paul))))&
(![X]:((wise(X)|kind(X))<=>brave(X)))&
((?[X]:((~generous(X)<~>~strong(X))))=>((~old(alice)<~>~rich(alice))))&
(![X]:(~quiet(X)=>quiet(X)))&
(((~brave(lucy)|funny(lucy)))<=>((~tall(john)&~humble(john))))&
((?[X]:(brave(X)))<=>((~rich(mary)<~>~happy(mary))))&
(![X]:((~funny(X)&quiet(X))=>(~brave(X)<~>~humble(X))))&
(![X]:((~curious(X)|~old(X))=>patient(X)))&
(((funny(susan)<~>kind(susan)))<=>((~patient(mary)<~>~happy(mary))))&
((?[X]:((~kind(X)&generous(X))))=>(?[X]:(wise(X))))&
((?[X]:(happy(X)))=>((brave(alice)<~>~humble(alice))))&
(![X]:((wise(X)|patient(X))=>kind(X)))&
(![X]:(creative(X)<=>(strong(X)|~strong(X))))&
((~quiet(alice))<=>((~strong(alice)|~calm(alice))))&
(![X]:((kind(X)<~>~old(X))=>(funny(X)<~>~happy(X))))&
((?[X]:((quiet(X)&~patient(X))))<=>((~strong(alice)&~rich(alice))))&
((kind(lucy)|~rich(lucy)))&
(?[X]:((~strong(X)|creative(X))))&
(?[X]:((brave(X)&strong(X))))&
(humble(susan))&
(?[X]:((strong(X)&wise(X))))&
((~old(susan)<~>~patient(susan))) | brave(paul) | [
"p1",
"p3",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7276981249521037195735649
% SZS output start Proof for 7276981249521037195735649
2. ! [X0] : ((kind(X0) | wise(X0)) <=> brave(X0)) [input p1]
4. ! [X0] : (~quiet(X0) => quiet(X0)) [input p3]
12. ! [X0] : ((patient(X0) | wise(X0)) => kind(X0)) [input p11]
14. ~quiet(alice) <=> (~calm(alice) | ~strong(alice)) [input p13]
16. ? [X0] : (~patient(X0) & quiet(X0)) <=> (~rich(alice) & ~strong(alice)) [input p15]
23. ~brave(paul) [input hypothesis]
27. ! [X0] : (quiet(X0) | quiet(X0)) [ennf transformation 4]
33. ! [X0] : (kind(X0) | (~patient(X0) & ~wise(X0))) [ennf transformation 12]
40. ! [X0] : (((kind(X0) | wise(X0)) | ~brave(X0)) & (brave(X0) | (~kind(X0) & ~wise(X0)))) [nnf transformation 2]
41. ! [X0] : ((kind(X0) | wise(X0) | ~brave(X0)) & (brave(X0) | (~kind(X0) & ~wise(X0)))) [flattening 40]
57. (~quiet(alice) | (calm(alice) & strong(alice))) & ((~calm(alice) | ~strong(alice)) | quiet(alice)) [nnf transformation 14]
58. (~quiet(alice) | (calm(alice) & strong(alice))) & (~calm(alice) | ~strong(alice) | quiet(alice)) [flattening 57]
60. (? [X0] : (~patient(X0) & quiet(X0)) | (rich(alice) | strong(alice))) & ((~rich(alice) & ~strong(alice)) | ! [X0] : (patient(X0) | ~quiet(X0))) [nnf transformation 16]
61. (? [X0] : (~patient(X0) & quiet(X0)) | rich(alice) | strong(alice)) & ((~rich(alice) & ~strong(alice)) | ! [X0] : (patient(X0) | ~quiet(X0))) [flattening 60]
62. (? [X0] : (~patient(X0) & quiet(X0)) | rich(alice) | strong(alice)) & ((~rich(alice) & ~strong(alice)) | ! [X1] : (patient(X1) | ~quiet(X1))) [rectify 61]
63. ? [X0] : (~patient(X0) & quiet(X0)) => (~patient(sK3) & quiet(sK3)) [choice axiom]
64. ((~patient(sK3) & quiet(sK3)) | rich(alice) | strong(alice)) & ((~rich(alice) & ~strong(alice)) | ! [X1] : (patient(X1) | ~quiet(X1))) [skolemisation 62,63]
77. ~kind(X0) | brave(X0) [cnf transformation 41]
83. quiet(X0) | quiet(X0) [cnf transformation 27]
108. ~patient(X0) | kind(X0) [cnf transformation 33]
113. ~quiet(alice) | strong(alice) [cnf transformation 58]
119. ~strong(alice) | patient(X1) | ~quiet(X1) [cnf transformation 64]
132. ~brave(paul) [cnf transformation 23]
133. quiet(X0) [duplicate literal removal 83]
264. strong(alice) [subsumption resolution 113,133]
267. 27 <=> ! [X1] : patient(X1) [avatar definition]
268. patient(X1) <- (27) [avatar component clause 267]
270. patient(X1) | ~quiet(X1) [subsumption resolution 119,264]
271. patient(X1) [subsumption resolution 270,133]
272. 27 [avatar split clause 271,267]
304. kind(X1) <- (27) [resolution 108,268]
306. brave(X0) <- (27) [resolution 304,77]
308. $false <- (27) [resolution 306,132]
313. ~27 [avatar contradiction clause 308]
314. $false [avatar sat refutation 272,313]
% SZS output end Proof for 7276981249521037195735649
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious then someone is not wise or not kind and vice versa. If someone is not generous then susan is old and vice versa. Everyone who is either tall or not creative is not quiet and vice versa. If alice is both not calm and not generous then susan is either generous or not strong and vice versa. Everyone who is either rich or not rich is either patient or rich and vice versa. Everyone who is either happy or wise is patient and vice versa. Everyone who is quiet or happy is not curious. If lucy is both not brave and calm then mary is either not patient or not quiet. If someone is either curious or not strong then someone is not funny or not brave and vice versa. If susan is either not old or not calm then someone is not kind or curious. Everyone who is both not quiet and not old is both generous and wise and vice versa. Everyone who is either patient or tall is not rich or not curious and vice versa. Everyone who is not tall is not quiet. If fred is either not rich or tall then someone is not funny or generous. If someone is not generous or not humble then paul is not creative. Everyone who is either funny or not wise is not rich or not calm. Someone is both not tall and not kind. Paul is calm or patient. Mary is brave. John is either old or tall. Someone is not wise or quiet. Paul is not creative. Mary is not wise or not curious. | John is rich. | neutral | ((?[X]:(~curious(X)))<=>(?[X]:((~wise(X)|~kind(X)))))&
((?[X]:(~generous(X)))<=>(old(susan)))&
(![X]:((tall(X)<~>~creative(X))<=>~quiet(X)))&
(((~calm(alice)&~generous(alice)))<=>((generous(susan)<~>~strong(susan))))&
(![X]:((rich(X)<~>~rich(X))<=>(patient(X)<~>rich(X))))&
(![X]:((happy(X)<~>wise(X))<=>patient(X)))&
(![X]:((quiet(X)|happy(X))=>~curious(X)))&
(((~brave(lucy)&calm(lucy)))=>((~patient(mary)<~>~quiet(mary))))&
((?[X]:((curious(X)<~>~strong(X))))<=>(?[X]:((~funny(X)|~brave(X)))))&
(((~old(susan)<~>~calm(susan)))=>(?[X]:((~kind(X)|curious(X)))))&
(![X]:((~quiet(X)&~old(X))<=>(generous(X)&wise(X))))&
(![X]:((patient(X)<~>tall(X))<=>(~rich(X)|~curious(X))))&
(![X]:(~tall(X)=>~quiet(X)))&
(((~rich(fred)<~>tall(fred)))=>(?[X]:((~funny(X)|generous(X)))))&
((?[X]:((~generous(X)|~humble(X))))=>(~creative(paul)))&
(![X]:((funny(X)<~>~wise(X))=>(~rich(X)|~calm(X))))&
(?[X]:((~tall(X)&~kind(X))))&
((calm(paul)|patient(paul)))&
(brave(mary))&
((old(john)<~>tall(john)))&
(?[X]:((~wise(X)|quiet(X))))&
(~creative(paul))&
((~wise(mary)|~curious(mary))) | rich(john) | [] | null | 0 |
If mary is not curious or not calm then paul is either not brave or wise.
If someone is either patient or quiet then someone is not happy.
Everyone who is strong or not happy is humble or not strong and vice versa.
Everyone who is creative is either curious or humble.
Everyone who is not wise or tall is both humble and creative and vice versa.
If mary is both not wise and not patient then someone is strong.
Everyone who is not quiet or not humble is both not curious and kind.
If someone is either not patient or generous then lucy is either rich or not patient.
If john is not generous or not rich then someone is not creative or creative.
If susan is happy then lucy is not curious or curious and vice versa.
Everyone who is old or not funny is both not creative and not humble and vice versa.
Everyone who is either not creative or not old is happy.
Everyone who is both not strong and not patient is not funny and vice versa.
Everyone who is either not generous or not happy is not quiet or curious.
Everyone who is strong is not strong or not quiet and vice versa.
Everyone who is not creative or not quiet is either humble or not funny.
Someone is both calm and not happy.
Alice is either creative or quiet.
Someone is both creative and kind.
Someone is brave.
Someone is strong or brave.
Someone is either not tall or quiet.
Susan is both not rich and not curious.
Susan is both brave and not calm. | Alice is quiet. | contradiction | (((~curious(mary)|~calm(mary)))=>((~brave(paul)<~>wise(paul))))&
((?[X]:((patient(X)<~>quiet(X))))=>(?[X]:(~happy(X))))&
(![X]:((strong(X)|~happy(X))<=>(humble(X)|~strong(X))))&
(![X]:(creative(X)=>(curious(X)<~>humble(X))))&
(![X]:((~wise(X)|tall(X))<=>(humble(X)&creative(X))))&
(((~wise(mary)&~patient(mary)))=>(?[X]:(strong(X))))&
(![X]:((~quiet(X)|~humble(X))=>(~curious(X)&kind(X))))&
((?[X]:((~patient(X)<~>generous(X))))=>((rich(lucy)<~>~patient(lucy))))&
(((~generous(john)|~rich(john)))=>(?[X]:((~creative(X)|creative(X)))))&
((happy(susan))<=>((~curious(lucy)|curious(lucy))))&
(![X]:((old(X)|~funny(X))<=>(~creative(X)&~humble(X))))&
(![X]:((~creative(X)<~>~old(X))=>happy(X)))&
(![X]:((~strong(X)&~patient(X))<=>~funny(X)))&
(![X]:((~generous(X)<~>~happy(X))=>(~quiet(X)|curious(X))))&
(![X]:(strong(X)<=>(~strong(X)|~quiet(X))))&
(![X]:((~creative(X)|~quiet(X))=>(humble(X)<~>~funny(X))))&
(?[X]:((calm(X)&~happy(X))))&
((creative(alice)<~>quiet(alice)))&
(?[X]:((creative(X)&kind(X))))&
(?[X]:(brave(X)))&
(?[X]:((strong(X)|brave(X))))&
(?[X]:((~tall(X)<~>quiet(X))))&
((~rich(susan)&~curious(susan)))&
((brave(susan)&~calm(susan))) | quiet(alice) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6076607090319104565103853
% SZS output start Proof for 6076607090319104565103853
15. ! [X0] : (strong(X0) <=> (~quiet(X0) | ~strong(X0))) [input p14]
25. quiet(alice) [input hypothesis]
64. ! [X0] : ((strong(X0) | (quiet(X0) & strong(X0))) & ((~quiet(X0) | ~strong(X0)) | ~strong(X0))) [nnf transformation 15]
65. ! [X0] : ((strong(X0) | (quiet(X0) & strong(X0))) & (~quiet(X0) | ~strong(X0) | ~strong(X0))) [flattening 64]
120. ~quiet(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 65]
121. strong(X0) | strong(X0) [cnf transformation 65]
140. quiet(alice) [cnf transformation 25]
141. ~quiet(X0) | ~strong(X0) [duplicate literal removal 120]
142. strong(X0) [duplicate literal removal 121]
220. ~quiet(X0) [subsumption resolution 141,142]
224. $false [subsumption resolution 140,220]
% SZS output end Proof for 6076607090319104565103853
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind then mary is calm or not tall.
If someone is not generous then someone is not kind and vice versa.
Everyone who is not calm is not tall.
Everyone who is not tall is not tall or strong and vice versa.
Everyone who is not wise or tall is calm or not brave and vice versa.
Everyone who is not strong or curious is both creative and brave and vice versa.
Everyone who is patient is not strong or not brave.
Everyone who is humble is both wise and not humble and vice versa.
If someone is either not happy or not calm then john is either generous or not humble.
If alice is both kind and quiet then someone is creative or not patient.
Everyone who is funny is kind or not kind and vice versa.
If paul is either curious or not brave then someone is both not kind and not funny and vice versa.
Everyone who is either patient or brave is funny or calm and vice versa.
If lucy is either generous or not patient then someone is both humble and tall and vice versa.
Everyone who is patient or wise is quiet and vice versa.
Everyone who is wise is either creative or not funny.
Alice is not curious or wise.
Someone is not funny or happy.
Someone is either not wise or not kind.
John is rich or not curious.
John is both not patient and not quiet.
Someone is both not curious and brave.
John is either not happy or not creative.
John is either patient or strong. | Paul is not quiet. | entailment | ((?[X]:(~kind(X)))=>((calm(mary)|~tall(mary))))&
((?[X]:(~generous(X)))<=>(?[X]:(~kind(X))))&
(![X]:(~calm(X)=>~tall(X)))&
(![X]:(~tall(X)<=>(~tall(X)|strong(X))))&
(![X]:((~wise(X)|tall(X))<=>(calm(X)|~brave(X))))&
(![X]:((~strong(X)|curious(X))<=>(creative(X)&brave(X))))&
(![X]:(patient(X)=>(~strong(X)|~brave(X))))&
(![X]:(humble(X)<=>(wise(X)&~humble(X))))&
((?[X]:((~happy(X)<~>~calm(X))))=>((generous(john)<~>~humble(john))))&
(((kind(alice)&quiet(alice)))=>(?[X]:((creative(X)|~patient(X)))))&
(![X]:(funny(X)<=>(kind(X)|~kind(X))))&
(((curious(paul)<~>~brave(paul)))<=>(?[X]:((~kind(X)&~funny(X)))))&
(![X]:((patient(X)<~>brave(X))<=>(funny(X)|calm(X))))&
(((generous(lucy)<~>~patient(lucy)))<=>(?[X]:((humble(X)&tall(X)))))&
(![X]:((patient(X)|wise(X))<=>quiet(X)))&
(![X]:(wise(X)=>(creative(X)<~>~funny(X))))&
((~curious(alice)|wise(alice)))&
(?[X]:((~funny(X)|happy(X))))&
(?[X]:((~wise(X)<~>~kind(X))))&
((rich(john)|~curious(john)))&
((~patient(john)&~quiet(john)))&
(?[X]:((~curious(X)&brave(X))))&
((~happy(john)<~>~creative(john)))&
((patient(john)<~>strong(john))) | ~quiet(paul) | [
"p5",
"p7",
"p10",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4728545880642911897573324
% SZS output start Proof for 4728545880642911897573324
6. ! [X0] : ((curious(X0) | ~strong(X0)) <=> (brave(X0) & creative(X0))) [input p5]
8. ! [X0] : (humble(X0) <=> (~humble(X0) & wise(X0))) [input p7]
11. ! [X0] : (funny(X0) <=> (~kind(X0) | kind(X0))) [input p10]
12. (curious(paul) <~> ~brave(paul)) <=> ? [X0] : (~funny(X0) & ~kind(X0)) [input p11]
13. ! [X0] : ((patient(X0) <~> brave(X0)) <=> (calm(X0) | funny(X0))) [input p12]
15. ! [X0] : ((wise(X0) | patient(X0)) <=> quiet(X0)) [input p14]
25. quiet(paul) [input hypothesis]
46. ! [X0] : (((curious(X0) | ~strong(X0)) | (~brave(X0) | ~creative(X0))) & ((brave(X0) & creative(X0)) | (~curious(X0) & strong(X0)))) [nnf transformation 6]
47. ! [X0] : ((curious(X0) | ~strong(X0) | ~brave(X0) | ~creative(X0)) & ((brave(X0) & creative(X0)) | (~curious(X0) & strong(X0)))) [flattening 46]
48. ! [X0] : ((humble(X0) | (humble(X0) | ~wise(X0))) & ((~humble(X0) & wise(X0)) | ~humble(X0))) [nnf transformation 8]
49. ! [X0] : ((humble(X0) | humble(X0) | ~wise(X0)) & ((~humble(X0) & wise(X0)) | ~humble(X0))) [flattening 48]
53. ! [X0] : ((funny(X0) | (kind(X0) & ~kind(X0))) & ((~kind(X0) | kind(X0)) | ~funny(X0))) [nnf transformation 11]
54. ! [X0] : ((funny(X0) | (kind(X0) & ~kind(X0))) & (~kind(X0) | kind(X0) | ~funny(X0))) [flattening 53]
55. (((brave(paul) | ~curious(paul)) & (~brave(paul) | curious(paul))) | ! [X0] : (funny(X0) | kind(X0))) & (? [X0] : (~funny(X0) & ~kind(X0)) | ((curious(paul) | brave(paul)) & (~brave(paul) | ~curious(paul)))) [nnf transformation 12]
56. (((brave(paul) | ~curious(paul)) & (~brave(paul) | curious(paul))) | ! [X0] : (funny(X0) | kind(X0))) & (? [X1] : (~funny(X1) & ~kind(X1)) | ((curious(paul) | brave(paul)) & (~brave(paul) | ~curious(paul)))) [rectify 55]
57. ? [X1] : (~funny(X1) & ~kind(X1)) => (~funny(sK3) & ~kind(sK3)) [choice axiom]
58. (((brave(paul) | ~curious(paul)) & (~brave(paul) | curious(paul))) | ! [X0] : (funny(X0) | kind(X0))) & ((~funny(sK3) & ~kind(sK3)) | ((curious(paul) | brave(paul)) & (~brave(paul) | ~curious(paul)))) [skolemisation 56,57]
59. ! [X0] : ((((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | (~calm(X0) & ~funny(X0))) & ((calm(X0) | funny(X0)) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0))))) [nnf transformation 13]
60. ! [X0] : ((((~brave(X0) | ~patient(X0)) & (brave(X0) | patient(X0))) | (~calm(X0) & ~funny(X0))) & (calm(X0) | funny(X0) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0))))) [flattening 59]
65. ! [X0] : (((wise(X0) | patient(X0)) | ~quiet(X0)) & (quiet(X0) | (~wise(X0) & ~patient(X0)))) [nnf transformation 15]
66. ! [X0] : ((wise(X0) | patient(X0) | ~quiet(X0)) & (quiet(X0) | (~wise(X0) & ~patient(X0)))) [flattening 65]
91. ~curious(X0) | brave(X0) [cnf transformation 47]
95. ~humble(X0) | ~humble(X0) [cnf transformation 49]
96. humble(X0) | humble(X0) | ~wise(X0) [cnf transformation 49]
103. funny(X0) | ~kind(X0) [cnf transformation 54]
104. funny(X0) | kind(X0) [cnf transformation 54]
108. ~funny(sK3) | curious(paul) | brave(paul) [cnf transformation 58]
115. ~brave(X0) | ~patient(X0) | ~funny(X0) [cnf transformation 60]
125. ~quiet(X0) | patient(X0) | wise(X0) [cnf transformation 66]
140. quiet(paul) [cnf transformation 25]
141. ~humble(X0) [duplicate literal removal 95]
142. ~wise(X0) | humble(X0) [duplicate literal removal 96]
199. funny(X0) [subsumption resolution 103,104]
200. curious(paul) | brave(paul) [subsumption resolution 108,199]
201. brave(paul) [subsumption resolution 200,91]
204. ~patient(X0) | ~brave(X0) [subsumption resolution 115,199]
283. 25 <=> wise(paul) [avatar definition]
284. ~wise(paul) <- (~25) [avatar component clause 283]
285. wise(paul) <- (25) [avatar component clause 283]
314. humble(paul) <- (25) [resolution 285,142]
321. $false <- (25) [subsumption resolution 314,141]
322. ~25 [avatar contradiction clause 321]
342. patient(paul) | wise(paul) [resolution 125,140]
344. patient(paul) <- (~25) [subsumption resolution 342,284]
351. ~brave(paul) <- (~25) [resolution 344,204]
357. $false <- (~25) [subsumption resolution 351,201]
358. 25 [avatar contradiction clause 357]
359. $false [avatar sat refutation 322,358]
% SZS output end Proof for 4728545880642911897573324
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not wise then someone is either not tall or not calm and vice versa.
If alice is both kind and calm then paul is either curious or kind and vice versa.
If someone is either patient or not old then mary is not kind.
If someone is not funny or not wise then someone is both old and not old.
If someone is not quiet then someone is patient.
Everyone who is brave is both not patient and not tall.
If john is patient or not wise then someone is both generous and tall.
Everyone who is old is not quiet.
If someone is curious then fred is not happy.
If someone is both not old and old then someone is both not creative and tall and vice versa.
Everyone who is patient is both old and not funny.
If someone is not funny then someone is either curious or brave and vice versa.
Everyone who is happy or not generous is both humble and patient.
Everyone who is both not humble and not patient is kind or not old and vice versa.
Everyone who is not rich is either wise or not curious and vice versa.
Mary is generous.
Alice is both not calm and not kind.
Someone is tall.
Susan is not quiet or creative.
Someone is both not old and rich.
Someone is either not kind or funny. | John is humble. | contradiction | ((?[X]:((strong(X)|~wise(X))))<=>(?[X]:((~tall(X)<~>~calm(X)))))&
(((kind(alice)&calm(alice)))<=>((curious(paul)<~>kind(paul))))&
((?[X]:((patient(X)<~>~old(X))))=>(~kind(mary)))&
((?[X]:((~funny(X)|~wise(X))))=>(?[X]:((old(X)&~old(X)))))&
((?[X]:(~quiet(X)))=>(?[X]:(patient(X))))&
(![X]:(brave(X)=>(~patient(X)&~tall(X))))&
(((patient(john)|~wise(john)))=>(?[X]:((generous(X)&tall(X)))))&
(![X]:(old(X)=>~quiet(X)))&
((?[X]:(curious(X)))=>(~happy(fred)))&
((?[X]:((~old(X)&old(X))))<=>(?[X]:((~creative(X)&tall(X)))))&
(![X]:(patient(X)=>(old(X)&~funny(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((curious(X)<~>brave(X)))))&
(![X]:((happy(X)|~generous(X))=>(humble(X)&patient(X))))&
(![X]:((~humble(X)&~patient(X))<=>(kind(X)|~old(X))))&
(![X]:(~rich(X)<=>(wise(X)<~>~curious(X))))&
(generous(mary))&
((~calm(alice)&~kind(alice)))&
(?[X]:(tall(X)))&
((~quiet(susan)|creative(susan)))&
(?[X]:((~old(X)&rich(X))))&
(?[X]:((~kind(X)<~>funny(X)))) | humble(john) | [
"p3",
"p4",
"p7",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2801614003019675837928571
% SZS output start Proof for 2801614003019675837928571
4. ? [X0] : (~wise(X0) | ~funny(X0)) => ? [X0] : (~old(X0) & old(X0)) [input p3]
5. ? [X0] : ~quiet(X0) => ? [X0] : patient(X0) [input p4]
8. ! [X0] : (old(X0) => ~quiet(X0)) [input p7]
11. ! [X0] : (patient(X0) => (~funny(X0) & old(X0))) [input p10]
14. ! [X0] : ((~patient(X0) & ~humble(X0)) <=> (~old(X0) | kind(X0))) [input p13]
22. humble(john) [input hypothesis]
24. ? [X0] : (~wise(X0) | ~funny(X0)) => ? [X1] : (~old(X1) & old(X1)) [rectify 4]
25. ? [X0] : ~quiet(X0) => ? [X1] : patient(X1) [rectify 5]
35. ? [X1] : (~old(X1) & old(X1)) | ! [X0] : (wise(X0) & funny(X0)) [ennf transformation 24]
36. ? [X1] : patient(X1) | ! [X0] : quiet(X0) [ennf transformation 25]
39. ! [X0] : (~quiet(X0) | ~old(X0)) [ennf transformation 8]
40. ! [X0] : ((~funny(X0) & old(X0)) | ~patient(X0)) [ennf transformation 11]
50. ? [X0] : (~old(X0) & old(X0)) | ! [X1] : (wise(X1) & funny(X1)) [rectify 35]
51. ? [X0] : (~old(X0) & old(X0)) => (~old(sK2) & old(sK2)) [choice axiom]
52. (~old(sK2) & old(sK2)) | ! [X1] : (wise(X1) & funny(X1)) [skolemisation 50,51]
53. ? [X0] : patient(X0) | ! [X1] : quiet(X1) [rectify 36]
54. ? [X0] : patient(X0) => patient(sK3) [choice axiom]
55. patient(sK3) | ! [X1] : quiet(X1) [skolemisation 53,54]
68. ! [X0] : (((~patient(X0) & ~humble(X0)) | (old(X0) & ~kind(X0))) & ((~old(X0) | kind(X0)) | (patient(X0) | humble(X0)))) [nnf transformation 14]
69. ! [X0] : (((~patient(X0) & ~humble(X0)) | (old(X0) & ~kind(X0))) & (~old(X0) | kind(X0) | patient(X0) | humble(X0))) [flattening 68]
92. old(sK2) | funny(X1) [cnf transformation 52]
94. ~old(sK2) | funny(X1) [cnf transformation 52]
96. patient(sK3) | quiet(X1) [cnf transformation 55]
101. ~quiet(X0) | ~old(X0) [cnf transformation 39]
107. ~funny(X0) | ~patient(X0) [cnf transformation 40]
114. ~humble(X0) | old(X0) [cnf transformation 69]
127. humble(john) [cnf transformation 22]
197. 16 <=> old(sK2) [avatar definition]
202. 17 <=> ! [X1] : funny(X1) [avatar definition]
203. funny(X1) <- (17) [avatar component clause 202]
204. 17 | ~16 [avatar split clause 94,197,202]
206. 17 | 16 [avatar split clause 92,197,202]
208. 18 <=> ! [X1] : quiet(X1) [avatar definition]
209. quiet(X1) <- (18) [avatar component clause 208]
211. 19 <=> patient(sK3) [avatar definition]
213. patient(sK3) <- (19) [avatar component clause 211]
214. 18 | 19 [avatar split clause 96,211,208]
290. ~patient(X0) <- (17) [resolution 107,203]
292. $false <- (17, 19) [resolution 290,213]
293. ~17 | ~19 [avatar contradiction clause 292]
294. ~old(X0) <- (18) [resolution 209,101]
296. old(john) [resolution 114,127]
297. $false <- (18) [subsumption resolution 296,294]
298. ~18 [avatar contradiction clause 297]
299. $false [avatar sat refutation 204,206,214,293,298]
% SZS output end Proof for 2801614003019675837928571
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both strong and happy then paul is either not funny or kind and vice versa.
If someone is both patient and not happy then lucy is curious or humble and vice versa.
Everyone who is not quiet or happy is either not rich or brave.
Everyone who is both not happy and not generous is generous or not generous and vice versa.
If someone is either not generous or not tall then alice is either creative or not quiet.
Everyone who is not quiet or humble is either not quiet or calm and vice versa.
Everyone who is either wise or not humble is either not generous or wise and vice versa.
Everyone who is not old or generous is either tall or wise and vice versa.
Everyone who is not generous or generous is not old and vice versa.
Everyone who is either patient or not kind is either quiet or not wise and vice versa.
Everyone who is either generous or calm is either not kind or quiet and vice versa.
If paul is either not rich or happy then someone is both not quiet and quiet.
Everyone who is either not patient or patient is both not old and not quiet.
Everyone who is not patient is either not creative or funny and vice versa.
If susan is either not happy or kind then susan is either not tall or not old and vice versa.
Susan is brave or strong.
Susan is both funny and not old.
Someone is not quiet or not calm.
Fred is both not creative and not rich.
Paul is both not tall and not quiet.
Someone is not wise. | Alice is not creative. | entailment | ((?[X]:((strong(X)&happy(X))))<=>((~funny(paul)<~>kind(paul))))&
((?[X]:((patient(X)&~happy(X))))<=>((curious(lucy)|humble(lucy))))&
(![X]:((~quiet(X)|happy(X))=>(~rich(X)<~>brave(X))))&
(![X]:((~happy(X)&~generous(X))<=>(generous(X)|~generous(X))))&
((?[X]:((~generous(X)<~>~tall(X))))=>((creative(alice)<~>~quiet(alice))))&
(![X]:((~quiet(X)|humble(X))<=>(~quiet(X)<~>calm(X))))&
(![X]:((wise(X)<~>~humble(X))<=>(~generous(X)<~>wise(X))))&
(![X]:((~old(X)|generous(X))<=>(tall(X)<~>wise(X))))&
(![X]:((~generous(X)|generous(X))<=>~old(X)))&
(![X]:((patient(X)<~>~kind(X))<=>(quiet(X)<~>~wise(X))))&
(![X]:((generous(X)<~>calm(X))<=>(~kind(X)<~>quiet(X))))&
(((~rich(paul)<~>happy(paul)))=>(?[X]:((~quiet(X)&quiet(X)))))&
(![X]:((~patient(X)<~>patient(X))=>(~old(X)&~quiet(X))))&
(![X]:(~patient(X)<=>(~creative(X)<~>funny(X))))&
(((~happy(susan)<~>kind(susan)))<=>((~tall(susan)<~>~old(susan))))&
((brave(susan)|strong(susan)))&
((funny(susan)&~old(susan)))&
(?[X]:((~quiet(X)|~calm(X))))&
((~creative(fred)&~rich(fred)))&
((~tall(paul)&~quiet(paul)))&
(?[X]:(~wise(X))) | ~creative(alice) | [
"p3",
"p4",
"p7",
"p8",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7220871305029698912518969
% SZS output start Proof for 7220871305029698912518969
4. ! [X0] : ((~generous(X0) & ~happy(X0)) <=> (~generous(X0) | generous(X0))) [input p3]
5. ? [X0] : (~generous(X0) <~> ~tall(X0)) => (creative(alice) <~> ~quiet(alice)) [input p4]
8. ! [X0] : ((generous(X0) | ~old(X0)) <=> (tall(X0) <~> wise(X0))) [input p7]
9. ! [X0] : ((generous(X0) | ~generous(X0)) <=> ~old(X0)) [input p8]
13. ! [X0] : ((~patient(X0) <~> patient(X0)) => (~quiet(X0) & ~old(X0))) [input p12]
21. ? [X0] : ~wise(X0) [input p20]
22. creative(alice) [input hypothesis]
24. (creative(alice) <~> ~quiet(alice)) | ! [X0] : (~generous(X0) <=> ~tall(X0)) [ennf transformation 5]
26. ! [X0] : ((~quiet(X0) & ~old(X0)) | (~patient(X0) <=> patient(X0))) [ennf transformation 13]
37. ! [X0] : (((~generous(X0) & ~happy(X0)) | (generous(X0) & ~generous(X0))) & ((~generous(X0) | generous(X0)) | (generous(X0) | happy(X0)))) [nnf transformation 4]
38. ! [X0] : (((~generous(X0) & ~happy(X0)) | (generous(X0) & ~generous(X0))) & (~generous(X0) | generous(X0) | generous(X0) | happy(X0))) [flattening 37]
39. ((quiet(alice) | ~creative(alice)) & (~quiet(alice) | creative(alice))) | ! [X0] : ((~generous(X0) | tall(X0)) & (~tall(X0) | generous(X0))) [nnf transformation 24]
43. ! [X0] : (((generous(X0) | ~old(X0)) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0)))) & (((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | (~generous(X0) & old(X0)))) [nnf transformation 8]
44. ! [X0] : ((generous(X0) | ~old(X0) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0)))) & (((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | (~generous(X0) & old(X0)))) [flattening 43]
45. ! [X0] : (((generous(X0) | ~generous(X0)) | old(X0)) & (~old(X0) | (~generous(X0) & generous(X0)))) [nnf transformation 9]
46. ! [X0] : ((generous(X0) | ~generous(X0) | old(X0)) & (~old(X0) | (~generous(X0) & generous(X0)))) [flattening 45]
52. ! [X0] : ((~quiet(X0) & ~old(X0)) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) [nnf transformation 26]
57. ? [X0] : ~wise(X0) => ~wise(sK4) [choice axiom]
58. ~wise(sK4) [skolemisation 21,57]
77. ~generous(X0) | ~generous(X0) [cnf transformation 38]
81. quiet(alice) | ~creative(alice) | ~tall(X0) | generous(X0) [cnf transformation 39]
97. old(X0) | tall(X0) | wise(X0) [cnf transformation 44]
103. ~old(X0) | generous(X0) [cnf transformation 46]
128. ~quiet(X0) | patient(X0) | patient(X0) [cnf transformation 52]
129. ~quiet(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 52]
150. ~wise(sK4) [cnf transformation 58]
151. creative(alice) [cnf transformation 22]
154. ~quiet(X0) | patient(X0) [duplicate literal removal 128]
155. ~quiet(X0) | ~patient(X0) [duplicate literal removal 129]
163. ~generous(X0) [duplicate literal removal 77]
214. quiet(alice) | ~creative(alice) | ~tall(X0) [subsumption resolution 81,163]
216. 11 <=> ! [X0] : ~tall(X0) [avatar definition]
217. ~tall(X0) <- (11) [avatar component clause 216]
219. 12 <=> creative(alice) [avatar definition]
223. 13 <=> quiet(alice) [avatar definition]
225. quiet(alice) <- (13) [avatar component clause 223]
226. 11 | ~12 | 13 [avatar split clause 214,223,219,216]
234. ~old(X0) [subsumption resolution 103,163]
252. ~quiet(X0) [subsumption resolution 154,155]
276. 12 [avatar split clause 151,219]
281. $false <- (13) [subsumption resolution 225,252]
282. ~13 [avatar contradiction clause 281]
301. tall(X0) | wise(X0) [resolution 97,234]
302. wise(X0) <- (11) [subsumption resolution 301,217]
303. $false <- (11) [resolution 302,150]
304. ~11 [avatar contradiction clause 303]
305. $false [avatar sat refutation 226,276,282,304]
% SZS output end Proof for 7220871305029698912518969
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny then someone is either rich or tall.
Everyone who is not funny is both funny and old and vice versa.
If paul is not patient or not generous then someone is both not generous and creative.
If john is creative then alice is either wise or not quiet and vice versa.
If susan is strong or not kind then mary is either creative or patient.
Everyone who is both not happy and funny is either funny or curious and vice versa.
Everyone who is tall or generous is not brave or not wise.
If someone is either not creative or calm then fred is not funny and vice versa.
Everyone who is either tall or calm is either wise or not brave.
Everyone who is either wise or humble is either creative or kind and vice versa.
Everyone who is old or not brave is either not rich or creative and vice versa.
Everyone who is either not old or wise is both brave and not calm.
Everyone who is either not patient or brave is not calm or not wise.
If fred is not patient then alice is happy and vice versa.
If fred is not funny or not curious then john is humble.
If susan is both not curious and not creative then fred is either creative or not happy.
Someone is wise.
Fred is wise or calm.
John is not quiet.
Someone is either humble or quiet.
Someone is rich.
Fred is rich.
John is not humble or not old.
Someone is not curious. | Fred is funny. | entailment | ((?[X]:(funny(X)))=>(?[X]:((rich(X)<~>tall(X)))))&
(![X]:(~funny(X)<=>(funny(X)&old(X))))&
(((~patient(paul)|~generous(paul)))=>(?[X]:((~generous(X)&creative(X)))))&
((creative(john))<=>((wise(alice)<~>~quiet(alice))))&
(((strong(susan)|~kind(susan)))=>((creative(mary)<~>patient(mary))))&
(![X]:((~happy(X)&funny(X))<=>(funny(X)<~>curious(X))))&
(![X]:((tall(X)|generous(X))=>(~brave(X)|~wise(X))))&
((?[X]:((~creative(X)<~>calm(X))))<=>(~funny(fred)))&
(![X]:((tall(X)<~>calm(X))=>(wise(X)<~>~brave(X))))&
(![X]:((wise(X)<~>humble(X))<=>(creative(X)<~>kind(X))))&
(![X]:((old(X)|~brave(X))<=>(~rich(X)<~>creative(X))))&
(![X]:((~old(X)<~>wise(X))=>(brave(X)&~calm(X))))&
(![X]:((~patient(X)<~>brave(X))=>(~calm(X)|~wise(X))))&
((~patient(fred))<=>(happy(alice)))&
(((~funny(fred)|~curious(fred)))=>(humble(john)))&
(((~curious(susan)&~creative(susan)))=>((creative(fred)<~>~happy(fred))))&
(?[X]:(wise(X)))&
((wise(fred)|calm(fred)))&
(~quiet(john))&
(?[X]:((humble(X)<~>quiet(X))))&
(?[X]:(rich(X)))&
(rich(fred))&
((~humble(john)|~old(john)))&
(?[X]:(~curious(X))) | funny(fred) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 85607755672817153047233
% SZS output start Proof for 85607755672817153047233
2. ! [X0] : (~funny(X0) <=> (old(X0) & funny(X0))) [input p1]
25. ~funny(fred) [input hypothesis]
44. ! [X0] : ((~funny(X0) | (~old(X0) | ~funny(X0))) & ((old(X0) & funny(X0)) | funny(X0))) [nnf transformation 2]
45. ! [X0] : ((~funny(X0) | ~old(X0) | ~funny(X0)) & ((old(X0) & funny(X0)) | funny(X0))) [flattening 44]
75. funny(X0) | funny(X0) [cnf transformation 45]
139. ~funny(fred) [cnf transformation 25]
142. funny(X0) [duplicate literal removal 75]
274. $false [subsumption resolution 139,142]
% SZS output end Proof for 85607755672817153047233
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall or not quiet is not old or not rich and vice versa.
If someone is not kind then paul is either old or not curious and vice versa.
Everyone who is both rich and kind is both not creative and calm and vice versa.
If someone is either funny or curious then paul is both not rich and not old and vice versa.
Everyone who is either tall or generous is either not wise or calm and vice versa.
Everyone who is not tall or not creative is either old or not tall.
If someone is not humble then john is not happy and vice versa.
If lucy is either humble or not curious then susan is either strong or not kind.
Everyone who is either not tall or not kind is both creative and brave and vice versa.
If someone is not generous then someone is old and vice versa.
If lucy is not tall then someone is either not calm or humble and vice versa.
If someone is either not kind or brave then someone is either calm or not funny.
If john is not funny or brave then john is both not funny and rich and vice versa.
Everyone who is humble or not tall is both tall and wise and vice versa.
If someone is curious then someone is patient.
If someone is both patient and funny then mary is either not patient or tall.
Someone is both not quiet and not old.
Someone is either calm or tall.
Someone is not patient.
Susan is not tall or happy.
Someone is not funny or wise.
Alice is not strong. | Alice is quiet. | contradiction | (![X]:((~tall(X)|~quiet(X))<=>(~old(X)|~rich(X))))&
((?[X]:(~kind(X)))<=>((old(paul)<~>~curious(paul))))&
(![X]:((rich(X)&kind(X))<=>(~creative(X)&calm(X))))&
((?[X]:((funny(X)<~>curious(X))))<=>((~rich(paul)&~old(paul))))&
(![X]:((tall(X)<~>generous(X))<=>(~wise(X)<~>calm(X))))&
(![X]:((~tall(X)|~creative(X))=>(old(X)<~>~tall(X))))&
((?[X]:(~humble(X)))<=>(~happy(john)))&
(((humble(lucy)<~>~curious(lucy)))=>((strong(susan)<~>~kind(susan))))&
(![X]:((~tall(X)<~>~kind(X))<=>(creative(X)&brave(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(old(X))))&
((~tall(lucy))<=>(?[X]:((~calm(X)<~>humble(X)))))&
((?[X]:((~kind(X)<~>brave(X))))=>(?[X]:((calm(X)<~>~funny(X)))))&
(((~funny(john)|brave(john)))<=>((~funny(john)&rich(john))))&
(![X]:((humble(X)|~tall(X))<=>(tall(X)&wise(X))))&
((?[X]:(curious(X)))=>(?[X]:(patient(X))))&
((?[X]:((patient(X)&funny(X))))=>((~patient(mary)<~>tall(mary))))&
(?[X]:((~quiet(X)&~old(X))))&
(?[X]:((calm(X)<~>tall(X))))&
(?[X]:(~patient(X)))&
((~tall(susan)|happy(susan)))&
(?[X]:((~funny(X)|wise(X))))&
(~strong(alice)) | quiet(alice) | [
"p0",
"p4",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1609272311557176873669864
% SZS output start Proof for 1609272311557176873669864
1. ! [X0] : ((~quiet(X0) | ~tall(X0)) <=> (~rich(X0) | ~old(X0))) [input p0]
5. ! [X0] : ((tall(X0) <~> generous(X0)) <=> (~wise(X0) <~> calm(X0))) [input p4]
10. ? [X0] : ~generous(X0) <=> ? [X0] : old(X0) [input p9]
11. ~tall(lucy) <=> ? [X0] : (~calm(X0) <~> humble(X0)) [input p10]
14. ! [X0] : ((~tall(X0) | humble(X0)) <=> (wise(X0) & tall(X0))) [input p13]
23. quiet(alice) [input hypothesis]
24. ? [X0] : ~generous(X0) <=> ? [X1] : old(X1) [rectify 10]
32. ! [X0] : (((~quiet(X0) | ~tall(X0)) | (rich(X0) & old(X0))) & ((~rich(X0) | ~old(X0)) | (quiet(X0) & tall(X0)))) [nnf transformation 1]
33. ! [X0] : ((~quiet(X0) | ~tall(X0) | (rich(X0) & old(X0))) & (~rich(X0) | ~old(X0) | (quiet(X0) & tall(X0)))) [flattening 32]
45. ! [X0] : ((((~generous(X0) | ~tall(X0)) & (generous(X0) | tall(X0))) | ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0)))) & (((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0))))) [nnf transformation 5]
54. (? [X0] : ~generous(X0) | ! [X1] : ~old(X1)) & (? [X1] : old(X1) | ! [X0] : generous(X0)) [nnf transformation 24]
55. (? [X0] : ~generous(X0) | ! [X1] : ~old(X1)) & (? [X2] : old(X2) | ! [X3] : generous(X3)) [rectify 54]
56. ? [X0] : ~generous(X0) => ~generous(sK3) [choice axiom]
57. ? [X2] : old(X2) => old(sK4) [choice axiom]
58. (~generous(sK3) | ! [X1] : ~old(X1)) & (old(sK4) | ! [X3] : generous(X3)) [skolemisation 55,57,56]
59. (~tall(lucy) | ! [X0] : ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0)))) & (? [X0] : ((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | tall(lucy)) [nnf transformation 11]
60. (~tall(lucy) | ! [X0] : ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0)))) & (? [X1] : ((~humble(X1) | calm(X1)) & (humble(X1) | ~calm(X1))) | tall(lucy)) [rectify 59]
61. ? [X1] : ((~humble(X1) | calm(X1)) & (humble(X1) | ~calm(X1))) => ((~humble(sK5) | calm(sK5)) & (humble(sK5) | ~calm(sK5))) [choice axiom]
62. (~tall(lucy) | ! [X0] : ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0)))) & (((~humble(sK5) | calm(sK5)) & (humble(sK5) | ~calm(sK5))) | tall(lucy)) [skolemisation 60,61]
69. ! [X0] : (((~tall(X0) | humble(X0)) | (~wise(X0) | ~tall(X0))) & ((wise(X0) & tall(X0)) | (tall(X0) & ~humble(X0)))) [nnf transformation 14]
70. ! [X0] : ((~tall(X0) | humble(X0) | ~wise(X0) | ~tall(X0)) & ((wise(X0) & tall(X0)) | (tall(X0) & ~humble(X0)))) [flattening 69]
86. ~quiet(X0) | ~tall(X0) | old(X0) [cnf transformation 33]
102. ~wise(X0) | calm(X0) | generous(X0) | ~tall(X0) [cnf transformation 45]
104. ~calm(X0) | wise(X0) | generous(X0) | ~tall(X0) [cnf transformation 45]
127. ~generous(sK3) | ~old(X1) [cnf transformation 58]
130. ~tall(lucy) | humble(X0) | calm(X0) [cnf transformation 62]
131. ~tall(lucy) | ~calm(X0) | ~humble(X0) [cnf transformation 62]
142. tall(X0) | tall(X0) [cnf transformation 70]
143. ~humble(X0) | wise(X0) [cnf transformation 70]
145. ~tall(X0) | humble(X0) | ~wise(X0) | ~tall(X0) [cnf transformation 70]
157. quiet(alice) [cnf transformation 23]
158. tall(X0) [duplicate literal removal 142]
159. ~wise(X0) | humble(X0) | ~tall(X0) [duplicate literal removal 145]
238. 17 <=> ! [X1] : ~old(X1) [avatar definition]
239. ~old(X1) <- (17) [avatar component clause 238]
241. 18 <=> generous(sK3) [avatar definition]
243. ~generous(sK3) <- (~18) [avatar component clause 241]
244. 17 | ~18 [avatar split clause 127,241,238]
254. 21 <=> ! [X0] : (~calm(X0) | ~humble(X0)) [avatar definition]
255. ~humble(X0) | ~calm(X0) <- (21) [avatar component clause 254]
257. 22 <=> tall(lucy) [avatar definition]
259. ~tall(lucy) <- (~22) [avatar component clause 257]
260. 21 | ~22 [avatar split clause 131,257,254]
262. 23 <=> ! [X0] : (humble(X0) | calm(X0)) [avatar definition]
263. humble(X0) | calm(X0) <- (23) [avatar component clause 262]
264. 23 | ~22 [avatar split clause 130,257,262]
336. $false <- (~22) [subsumption resolution 259,158]
337. 22 [avatar contradiction clause 336]
343. wise(X1) | calm(X1) <- (23) [resolution 263,143]
349. ~tall(alice) | old(alice) [resolution 86,157]
350. old(alice) [subsumption resolution 349,158]
351. $false <- (17) [subsumption resolution 350,239]
352. ~17 [avatar contradiction clause 351]
411. calm(X1) | generous(X1) | ~tall(X1) | calm(X1) <- (23) [resolution 102,343]
413. calm(X1) | generous(X1) | ~tall(X1) <- (23) [duplicate literal removal 411]
420. generous(X1) | calm(X1) <- (23) [subsumption resolution 413,158]
460. calm(sK3) <- (~18, 23) [resolution 420,243]
465. wise(sK3) | generous(sK3) | ~tall(sK3) <- (~18, 23) [resolution 460,104]
468. wise(sK3) | ~tall(sK3) <- (~18, 23) [subsumption resolution 465,243]
469. wise(sK3) <- (~18, 23) [subsumption resolution 468,158]
487. humble(sK3) | ~tall(sK3) <- (~18, 23) [resolution 469,159]
488. humble(sK3) <- (~18, 23) [subsumption resolution 487,158]
516. ~calm(sK3) <- (~18, 21, 23) [resolution 488,255]
518. $false <- (~18, 21, 23) [subsumption resolution 516,460]
519. 18 | ~21 | ~23 [avatar contradiction clause 518]
520. $false [avatar sat refutation 244,260,264,337,352,519]
% SZS output end Proof for 1609272311557176873669864
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not creative is not calm. If alice is both funny and not happy then john is either not tall or not humble. If someone is not rich then someone is strong or not wise. Everyone who is both curious and generous is not generous or not old and vice versa. If someone is not happy or not calm then fred is both not calm and wise and vice versa. Everyone who is generous is not wise. Everyone who is not creative is either not humble or rich. If mary is not wise or curious then mary is not wise. If alice is happy or not patient then mary is either not kind or curious and vice versa. Everyone who is either happy or not humble is strong. Everyone who is not funny is not rich. Everyone who is both not patient and not quiet is both not brave and not wise and vice versa. If someone is either not funny or not humble then paul is not old or not calm and vice versa. If someone is either not curious or rich then someone is generous or not patient. If someone is strong or wise then someone is both not tall and not brave and vice versa. Everyone who is not creative or wise is wise and vice versa. Someone is either not brave or not curious. Someone is both funny and brave. Someone is either not wise or strong. Someone is both not wise and happy. Paul is not quiet or curious. Susan is either not funny or kind. | John is not humble. | entailment | (![X]:((~patient(X)<~>~creative(X))=>~calm(X)))&
(((funny(alice)&~happy(alice)))=>((~tall(john)<~>~humble(john))))&
((?[X]:(~rich(X)))=>(?[X]:((strong(X)|~wise(X)))))&
(![X]:((curious(X)&generous(X))<=>(~generous(X)|~old(X))))&
((?[X]:((~happy(X)|~calm(X))))<=>((~calm(fred)&wise(fred))))&
(![X]:(generous(X)=>~wise(X)))&
(![X]:(~creative(X)=>(~humble(X)<~>rich(X))))&
(((~wise(mary)|curious(mary)))=>(~wise(mary)))&
(((happy(alice)|~patient(alice)))<=>((~kind(mary)<~>curious(mary))))&
(![X]:((happy(X)<~>~humble(X))=>strong(X)))&
(![X]:(~funny(X)=>~rich(X)))&
(![X]:((~patient(X)&~quiet(X))<=>(~brave(X)&~wise(X))))&
((?[X]:((~funny(X)<~>~humble(X))))<=>((~old(paul)|~calm(paul))))&
((?[X]:((~curious(X)<~>rich(X))))=>(?[X]:((generous(X)|~patient(X)))))&
((?[X]:((strong(X)|wise(X))))<=>(?[X]:((~tall(X)&~brave(X)))))&
(![X]:((~creative(X)|wise(X))<=>wise(X)))&
(?[X]:((~brave(X)<~>~curious(X))))&
(?[X]:((funny(X)&brave(X))))&
(?[X]:((~wise(X)<~>strong(X))))&
(?[X]:((~wise(X)&happy(X))))&
((~quiet(paul)|curious(paul)))&
((~funny(susan)<~>kind(susan))) | ~humble(john) | [
"p0",
"p3",
"p4",
"p5",
"p9",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 965419473547238959800578
% SZS output start Proof for 965419473547238959800578
1. ! [X0] : ((~patient(X0) <~> ~creative(X0)) => ~calm(X0)) [input p0]
4. ! [X0] : ((generous(X0) & curious(X0)) <=> (~old(X0) | ~generous(X0))) [input p3]
5. ? [X0] : (~calm(X0) | ~happy(X0)) <=> (wise(fred) & ~calm(fred)) [input p4]
6. ! [X0] : (generous(X0) => ~wise(X0)) [input p5]
10. ! [X0] : ((happy(X0) <~> ~humble(X0)) => strong(X0)) [input p9]
12. ! [X0] : ((~quiet(X0) & ~patient(X0)) <=> (~wise(X0) & ~brave(X0))) [input p11]
15. ? [X0] : (wise(X0) | strong(X0)) <=> ? [X0] : (~brave(X0) & ~tall(X0)) [input p14]
16. ! [X0] : ((wise(X0) | ~creative(X0)) <=> wise(X0)) [input p15]
23. humble(john) [input hypothesis]
26. ? [X0] : (wise(X0) | strong(X0)) <=> ? [X1] : (~brave(X1) & ~tall(X1)) [rectify 15]
27. ! [X0] : (~calm(X0) | (~patient(X0) <=> ~creative(X0))) [ennf transformation 1]
31. ! [X0] : (~wise(X0) | ~generous(X0)) [ennf transformation 6]
34. ! [X0] : (strong(X0) | (happy(X0) <=> ~humble(X0))) [ennf transformation 10]
37. ! [X0] : (~calm(X0) | ((~patient(X0) | creative(X0)) & (~creative(X0) | patient(X0)))) [nnf transformation 27]
42. ! [X0] : (((generous(X0) & curious(X0)) | (old(X0) & generous(X0))) & ((~old(X0) | ~generous(X0)) | (~generous(X0) | ~curious(X0)))) [nnf transformation 4]
43. ! [X0] : (((generous(X0) & curious(X0)) | (old(X0) & generous(X0))) & (~old(X0) | ~generous(X0) | ~generous(X0) | ~curious(X0))) [flattening 42]
44. (? [X0] : (~calm(X0) | ~happy(X0)) | (~wise(fred) | calm(fred))) & ((wise(fred) & ~calm(fred)) | ! [X0] : (calm(X0) & happy(X0))) [nnf transformation 5]
45. (? [X0] : (~calm(X0) | ~happy(X0)) | ~wise(fred) | calm(fred)) & ((wise(fred) & ~calm(fred)) | ! [X0] : (calm(X0) & happy(X0))) [flattening 44]
46. (? [X0] : (~calm(X0) | ~happy(X0)) | ~wise(fred) | calm(fred)) & ((wise(fred) & ~calm(fred)) | ! [X1] : (calm(X1) & happy(X1))) [rectify 45]
47. ? [X0] : (~calm(X0) | ~happy(X0)) => (~calm(sK1) | ~happy(sK1)) [choice axiom]
48. ((~calm(sK1) | ~happy(sK1)) | ~wise(fred) | calm(fred)) & ((wise(fred) & ~calm(fred)) | ! [X1] : (calm(X1) & happy(X1))) [skolemisation 46,47]
52. ! [X0] : (strong(X0) | ((happy(X0) | humble(X0)) & (~humble(X0) | ~happy(X0)))) [nnf transformation 34]
53. ! [X0] : (((~quiet(X0) & ~patient(X0)) | (wise(X0) | brave(X0))) & ((~wise(X0) & ~brave(X0)) | (quiet(X0) | patient(X0)))) [nnf transformation 12]
54. ! [X0] : (((~quiet(X0) & ~patient(X0)) | wise(X0) | brave(X0)) & ((~wise(X0) & ~brave(X0)) | quiet(X0) | patient(X0))) [flattening 53]
64. (? [X0] : (wise(X0) | strong(X0)) | ! [X1] : (brave(X1) | tall(X1))) & (? [X1] : (~brave(X1) & ~tall(X1)) | ! [X0] : (~wise(X0) & ~strong(X0))) [nnf transformation 26]
65. (? [X0] : (wise(X0) | strong(X0)) | ! [X1] : (brave(X1) | tall(X1))) & (? [X2] : (~brave(X2) & ~tall(X2)) | ! [X3] : (~wise(X3) & ~strong(X3))) [rectify 64]
66. ? [X0] : (wise(X0) | strong(X0)) => (wise(sK4) | strong(sK4)) [choice axiom]
67. ? [X2] : (~brave(X2) & ~tall(X2)) => (~brave(sK5) & ~tall(sK5)) [choice axiom]
68. ((wise(sK4) | strong(sK4)) | ! [X1] : (brave(X1) | tall(X1))) & ((~brave(sK5) & ~tall(sK5)) | ! [X3] : (~wise(X3) & ~strong(X3))) [skolemisation 65,67,66]
69. ! [X0] : (((wise(X0) | ~creative(X0)) | ~wise(X0)) & (wise(X0) | (~wise(X0) & creative(X0)))) [nnf transformation 16]
70. ! [X0] : ((wise(X0) | ~creative(X0) | ~wise(X0)) & (wise(X0) | (~wise(X0) & creative(X0)))) [flattening 69]
82. ~calm(X0) | ~creative(X0) | patient(X0) [cnf transformation 37]
90. generous(X0) | generous(X0) [cnf transformation 43]
94. wise(fred) | happy(X1) [cnf transformation 48]
95. wise(fred) | calm(X1) [cnf transformation 48]
97. ~wise(X0) | ~generous(X0) [cnf transformation 31]
108. ~humble(X0) | strong(X0) | ~happy(X0) [cnf transformation 52]
113. ~patient(X0) | wise(X0) | brave(X0) [cnf transformation 54]
125. ~brave(sK5) | ~strong(X3) [cnf transformation 68]
128. wise(X0) | creative(X0) [cnf transformation 70]
142. humble(john) [cnf transformation 23]
144. generous(X0) [duplicate literal removal 90]
158. 4 <=> humble(john) [avatar definition]
160. humble(john) <- (4) [avatar component clause 158]
181. 9 <=> wise(fred) [avatar definition]
182. wise(fred) <- (9) [avatar component clause 181]
194. 12 <=> ! [X1] : calm(X1) [avatar definition]
195. calm(X1) <- (12) [avatar component clause 194]
196. 12 | 9 [avatar split clause 95,181,194]
198. 13 <=> ! [X1] : happy(X1) [avatar definition]
199. happy(X1) <- (13) [avatar component clause 198]
200. 13 | 9 [avatar split clause 94,181,198]
203. ~wise(X0) [subsumption resolution 97,144]
223. ~patient(X0) | brave(X0) [subsumption resolution 113,203]
262. 25 <=> ! [X3] : ~strong(X3) [avatar definition]
263. ~strong(X3) <- (25) [avatar component clause 262]
265. 26 <=> brave(sK5) [avatar definition]
267. ~brave(sK5) <- (~26) [avatar component clause 265]
268. 25 | ~26 [avatar split clause 125,265,262]
274. creative(X0) [subsumption resolution 128,203]
305. 4 [avatar split clause 142,158]
306. $false <- (9) [subsumption resolution 182,203]
307. ~9 [avatar contradiction clause 306]
329. ~creative(X0) | patient(X0) <- (12) [resolution 82,195]
330. patient(X0) <- (12) [subsumption resolution 329,274]
334. brave(X0) <- (12) [resolution 330,223]
338. $false <- (12, ~26) [resolution 334,267]
339. ~12 | 26 [avatar contradiction clause 338]
342. strong(john) | ~happy(john) <- (4) [resolution 108,160]
344. ~happy(john) <- (4, 25) [subsumption resolution 342,263]
345. $false <- (4, 13, 25) [subsumption resolution 344,199]
346. ~4 | ~13 | ~25 [avatar contradiction clause 345]
350. $false [avatar sat refutation 196,200,268,305,307,339,346]
% SZS output end Proof for 965419473547238959800578
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or strong is both curious and not old and vice versa. Everyone who is not kind or kind is not patient or not old and vice versa. Everyone who is both tall and not generous is both not rich and not quiet and vice versa. Everyone who is either not creative or not old is not brave or tall. If someone is patient then someone is kind or not happy and vice versa. If someone is not rich or wise then fred is strong or tall. Everyone who is both creative and old is not creative or creative and vice versa. Everyone who is both not curious and not humble is both patient and not happy. If someone is both generous and brave then john is either not quiet or curious. If mary is both funny and not rich then lucy is creative or not rich and vice versa. If someone is tall then someone is not calm or not rich. If alice is either not brave or not wise then paul is not happy or humble. Everyone who is quiet is either not creative or calm. If paul is either not generous or not creative then someone is either not generous or rich. Everyone who is tall or not funny is both not kind and generous and vice versa. If paul is wise or not strong then john is not generous and vice versa. Someone is not rich. Someone is either wise or not old. John is both calm and not brave. Someone is not brave. Alice is either not quiet or not happy. Lucy is both happy and generous. John is not strong or patient. | John is not happy. | contradiction | (![X]:((~calm(X)|strong(X))<=>(curious(X)&~old(X))))&
(![X]:((~kind(X)|kind(X))<=>(~patient(X)|~old(X))))&
(![X]:((tall(X)&~generous(X))<=>(~rich(X)&~quiet(X))))&
(![X]:((~creative(X)<~>~old(X))=>(~brave(X)|tall(X))))&
((?[X]:(patient(X)))<=>(?[X]:((kind(X)|~happy(X)))))&
((?[X]:((~rich(X)|wise(X))))=>((strong(fred)|tall(fred))))&
(![X]:((creative(X)&old(X))<=>(~creative(X)|creative(X))))&
(![X]:((~curious(X)&~humble(X))=>(patient(X)&~happy(X))))&
((?[X]:((generous(X)&brave(X))))=>((~quiet(john)<~>curious(john))))&
(((funny(mary)&~rich(mary)))<=>((creative(lucy)|~rich(lucy))))&
((?[X]:(tall(X)))=>(?[X]:((~calm(X)|~rich(X)))))&
(((~brave(alice)<~>~wise(alice)))=>((~happy(paul)|humble(paul))))&
(![X]:(quiet(X)=>(~creative(X)<~>calm(X))))&
(((~generous(paul)<~>~creative(paul)))=>(?[X]:((~generous(X)<~>rich(X)))))&
(![X]:((tall(X)|~funny(X))<=>(~kind(X)&generous(X))))&
(((wise(paul)|~strong(paul)))<=>(~generous(john)))&
(?[X]:(~rich(X)))&
(?[X]:((wise(X)<~>~old(X))))&
((calm(john)&~brave(john)))&
(?[X]:(~brave(X)))&
((~quiet(alice)<~>~happy(alice)))&
((happy(lucy)&generous(lucy)))&
((~strong(john)|patient(john))) | ~happy(john) | [
"p1",
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2129239274191582785952091
% SZS output start Proof for 2129239274191582785952091
2. ! [X0] : ((kind(X0) | ~kind(X0)) <=> (~old(X0) | ~patient(X0))) [input p1]
5. ? [X0] : patient(X0) <=> ? [X0] : (~happy(X0) | kind(X0)) [input p4]
7. ! [X0] : ((old(X0) & creative(X0)) <=> (creative(X0) | ~creative(X0))) [input p6]
24. ~happy(john) [input hypothesis]
25. ? [X0] : patient(X0) <=> ? [X1] : (~happy(X1) | kind(X1)) [rectify 5]
40. ! [X0] : (((kind(X0) | ~kind(X0)) | (old(X0) & patient(X0))) & ((~old(X0) | ~patient(X0)) | (~kind(X0) & kind(X0)))) [nnf transformation 2]
41. ! [X0] : ((kind(X0) | ~kind(X0) | (old(X0) & patient(X0))) & (~old(X0) | ~patient(X0) | (~kind(X0) & kind(X0)))) [flattening 40]
44. (? [X0] : patient(X0) | ! [X1] : (happy(X1) & ~kind(X1))) & (? [X1] : (~happy(X1) | kind(X1)) | ! [X0] : ~patient(X0)) [nnf transformation 25]
45. (? [X0] : patient(X0) | ! [X1] : (happy(X1) & ~kind(X1))) & (? [X2] : (~happy(X2) | kind(X2)) | ! [X3] : ~patient(X3)) [rectify 44]
46. ? [X0] : patient(X0) => patient(sK0) [choice axiom]
47. ? [X2] : (~happy(X2) | kind(X2)) => (~happy(sK1) | kind(sK1)) [choice axiom]
48. (patient(sK0) | ! [X1] : (happy(X1) & ~kind(X1))) & ((~happy(sK1) | kind(sK1)) | ! [X3] : ~patient(X3)) [skolemisation 45,47,46]
49. ! [X0] : (((old(X0) & creative(X0)) | (~creative(X0) & creative(X0))) & ((creative(X0) | ~creative(X0)) | (~old(X0) | ~creative(X0)))) [nnf transformation 7]
50. ! [X0] : (((old(X0) & creative(X0)) | (~creative(X0) & creative(X0))) & (creative(X0) | ~creative(X0) | ~old(X0) | ~creative(X0))) [flattening 49]
75. ~old(X0) | ~patient(X0) | kind(X0) [cnf transformation 41]
76. ~old(X0) | ~patient(X0) | ~kind(X0) [cnf transformation 41]
85. patient(sK0) | happy(X1) [cnf transformation 48]
91. old(X0) | creative(X0) [cnf transformation 50]
92. ~creative(X0) | old(X0) [cnf transformation 50]
122. ~happy(john) [cnf transformation 24]
125. ~patient(X0) | ~old(X0) [subsumption resolution 75,76]
127. 1 <=> ! [X1] : happy(X1) [avatar definition]
128. happy(X1) <- (1) [avatar component clause 127]
130. 2 <=> patient(sK0) [avatar definition]
132. patient(sK0) <- (2) [avatar component clause 130]
133. 1 | 2 [avatar split clause 85,130,127]
166. old(X0) [subsumption resolution 91,92]
257. ~old(sK0) <- (2) [resolution 125,132]
258. $false <- (2) [subsumption resolution 257,166]
259. ~2 [avatar contradiction clause 258]
260. $false <- (1) [resolution 128,122]
265. ~1 [avatar contradiction clause 260]
266. $false [avatar sat refutation 133,259,265]
% SZS output end Proof for 2129239274191582785952091
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or humble is either not funny or not kind and vice versa.
If mary is kind then someone is strong.
If fred is not humble then lucy is humble and vice versa.
If someone is not happy or not quiet then someone is both happy and not funny and vice versa.
If someone is creative or rich then someone is not rich or kind and vice versa.
Everyone who is either not strong or not humble is both curious and not quiet and vice versa.
Everyone who is not happy is either rich or humble.
If susan is not brave or not rich then someone is not happy and vice versa.
If someone is not generous then fred is both wise and strong.
Everyone who is wise is both not happy and tall and vice versa.
Everyone who is strong is both not tall and creative.
Everyone who is curious or not generous is not patient or not kind.
Everyone who is both not happy and generous is not strong.
If someone is not curious then mary is tall or not brave and vice versa.
If someone is both not patient and quiet then someone is either not generous or not curious and vice versa.
Everyone who is not strong is both not quiet and not tall.
Someone is humble or not brave.
Paul is not calm or curious.
Someone is funny or patient.
Someone is either not funny or not patient.
Someone is creative or not rich.
Susan is not calm or not kind.
Someone is either not brave or humble. | Mary is not brave. | neutral | (![X]:((kind(X)|humble(X))<=>(~funny(X)<~>~kind(X))))&
((kind(mary))=>(?[X]:(strong(X))))&
((~humble(fred))<=>(humble(lucy)))&
((?[X]:((~happy(X)|~quiet(X))))<=>(?[X]:((happy(X)&~funny(X)))))&
((?[X]:((creative(X)|rich(X))))<=>(?[X]:((~rich(X)|kind(X)))))&
(![X]:((~strong(X)<~>~humble(X))<=>(curious(X)&~quiet(X))))&
(![X]:(~happy(X)=>(rich(X)<~>humble(X))))&
(((~brave(susan)|~rich(susan)))<=>(?[X]:(~happy(X))))&
((?[X]:(~generous(X)))=>((wise(fred)&strong(fred))))&
(![X]:(wise(X)<=>(~happy(X)&tall(X))))&
(![X]:(strong(X)=>(~tall(X)&creative(X))))&
(![X]:((curious(X)|~generous(X))=>(~patient(X)|~kind(X))))&
(![X]:((~happy(X)&generous(X))=>~strong(X)))&
((?[X]:(~curious(X)))<=>((tall(mary)|~brave(mary))))&
((?[X]:((~patient(X)&quiet(X))))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
(![X]:(~strong(X)=>(~quiet(X)&~tall(X))))&
(?[X]:((humble(X)|~brave(X))))&
((~calm(paul)|curious(paul)))&
(?[X]:((funny(X)|patient(X))))&
(?[X]:((~funny(X)<~>~patient(X))))&
(?[X]:((creative(X)|~rich(X))))&
((~calm(susan)|~kind(susan)))&
(?[X]:((~brave(X)<~>humble(X)))) | ~brave(mary) | [] | null | 0 |
Everyone who is both not brave and patient is not happy or humble and vice versa.
Everyone who is both happy and tall is not calm and vice versa.
Everyone who is funny is humble and vice versa.
Everyone who is humble or quiet is either old or not happy and vice versa.
Everyone who is quiet is either calm or tall.
If mary is old then someone is either not kind or not strong and vice versa.
Everyone who is both not patient and generous is either not old or not calm.
Everyone who is either not happy or old is calm or not wise and vice versa.
Everyone who is both patient and not tall is wise or funny.
If someone is either not brave or not happy then john is not funny or calm.
If alice is tall or kind then someone is not kind and vice versa.
If lucy is both quiet and not curious then paul is either not quiet or tall and vice versa.
If mary is either not quiet or not humble then someone is either not happy or kind.
Everyone who is both not brave and curious is both not happy and not generous.
If fred is brave then paul is either old or not old.
Everyone who is not creative is both wise and not humble and vice versa.
Someone is tall.
Fred is either not tall or not brave.
Someone is not generous or not tall.
Susan is humble.
Mary is both rich and not patient.
Alice is both not creative and strong. | Paul is not humble. | neutral | (![X]:((~brave(X)&patient(X))<=>(~happy(X)|humble(X))))&
(![X]:((happy(X)&tall(X))<=>~calm(X)))&
(![X]:(funny(X)<=>humble(X)))&
(![X]:((humble(X)|quiet(X))<=>(old(X)<~>~happy(X))))&
(![X]:(quiet(X)=>(calm(X)<~>tall(X))))&
((old(mary))<=>(?[X]:((~kind(X)<~>~strong(X)))))&
(![X]:((~patient(X)&generous(X))=>(~old(X)<~>~calm(X))))&
(![X]:((~happy(X)<~>old(X))<=>(calm(X)|~wise(X))))&
(![X]:((patient(X)&~tall(X))=>(wise(X)|funny(X))))&
((?[X]:((~brave(X)<~>~happy(X))))=>((~funny(john)|calm(john))))&
(((tall(alice)|kind(alice)))<=>(?[X]:(~kind(X))))&
(((quiet(lucy)&~curious(lucy)))<=>((~quiet(paul)<~>tall(paul))))&
(((~quiet(mary)<~>~humble(mary)))=>(?[X]:((~happy(X)<~>kind(X)))))&
(![X]:((~brave(X)&curious(X))=>(~happy(X)&~generous(X))))&
((brave(fred))=>((old(paul)<~>~old(paul))))&
(![X]:(~creative(X)<=>(wise(X)&~humble(X))))&
(?[X]:(tall(X)))&
((~tall(fred)<~>~brave(fred)))&
(?[X]:((~generous(X)|~tall(X))))&
(humble(susan))&
((rich(mary)&~patient(mary)))&
((~creative(alice)&strong(alice))) | ~humble(paul) | [] | null | 0 |
If someone is either not strong or not generous then someone is both quiet and not tall and vice versa.
Everyone who is both not rich and brave is calm or wise and vice versa.
Everyone who is either not rich or not patient is both not happy and strong.
If alice is tall then fred is not funny or creative and vice versa.
Everyone who is either not tall or not kind is quiet and vice versa.
Everyone who is strong is both patient and kind and vice versa.
If someone is both not creative and old then someone is quiet or not rich.
Everyone who is either not kind or not wise is either rich or curious and vice versa.
If someone is either rich or not humble then fred is old or not brave and vice versa.
If alice is either quiet or not calm then someone is rich or generous and vice versa.
If someone is both kind and not funny then someone is happy or not calm and vice versa.
If john is either quiet or not patient then someone is either kind or not old and vice versa.
If someone is not brave or brave then someone is not happy.
If someone is humble or not creative then fred is either not old or brave and vice versa.
Everyone who is both not tall and strong is either not wise or not tall.
Everyone who is not strong or funny is not brave and vice versa.
Alice is patient.
Lucy is not strong or not rich.
Someone is not calm.
Someone is both not curious and not old.
Susan is not patient or not creative.
Paul is quiet or creative.
John is quiet or humble.
Lucy is funny. | Alice is wise. | neutral | ((?[X]:((~strong(X)<~>~generous(X))))<=>(?[X]:((quiet(X)&~tall(X)))))&
(![X]:((~rich(X)&brave(X))<=>(calm(X)|wise(X))))&
(![X]:((~rich(X)<~>~patient(X))=>(~happy(X)&strong(X))))&
((tall(alice))<=>((~funny(fred)|creative(fred))))&
(![X]:((~tall(X)<~>~kind(X))<=>quiet(X)))&
(![X]:(strong(X)<=>(patient(X)&kind(X))))&
((?[X]:((~creative(X)&old(X))))=>(?[X]:((quiet(X)|~rich(X)))))&
(![X]:((~kind(X)<~>~wise(X))<=>(rich(X)<~>curious(X))))&
((?[X]:((rich(X)<~>~humble(X))))<=>((old(fred)|~brave(fred))))&
(((quiet(alice)<~>~calm(alice)))<=>(?[X]:((rich(X)|generous(X)))))&
((?[X]:((kind(X)&~funny(X))))<=>(?[X]:((happy(X)|~calm(X)))))&
(((quiet(john)<~>~patient(john)))<=>(?[X]:((kind(X)<~>~old(X)))))&
((?[X]:((~brave(X)|brave(X))))=>(?[X]:(~happy(X))))&
((?[X]:((humble(X)|~creative(X))))<=>((~old(fred)<~>brave(fred))))&
(![X]:((~tall(X)&strong(X))=>(~wise(X)<~>~tall(X))))&
(![X]:((~strong(X)|funny(X))<=>~brave(X)))&
(patient(alice))&
((~strong(lucy)|~rich(lucy)))&
(?[X]:(~calm(X)))&
(?[X]:((~curious(X)&~old(X))))&
((~patient(susan)|~creative(susan)))&
((quiet(paul)|creative(paul)))&
((quiet(john)|humble(john)))&
(funny(lucy)) | wise(alice) | [] | null | 0 |
Everyone who is not strong or quiet is rich or strong and vice versa.
If fred is brave or generous then susan is either kind or rich.
Everyone who is old or tall is kind and vice versa.
Everyone who is both wise and not humble is kind and vice versa.
If john is funny or not curious then someone is both not calm and not patient.
Everyone who is not quiet or generous is either creative or tall and vice versa.
Everyone who is both kind and not happy is generous or happy and vice versa.
If lucy is either not creative or not happy then someone is quiet and vice versa.
Everyone who is funny is not humble and vice versa.
If someone is either not tall or funny then someone is not brave and vice versa.
Everyone who is either not kind or happy is not brave.
If someone is both curious and not quiet then someone is not strong and vice versa.
Everyone who is not quiet is both not tall and not kind.
Everyone who is tall is not curious or generous and vice versa.
Everyone who is not quiet or not creative is not tall.
If alice is not patient then someone is either kind or not tall.
Paul is not happy.
Susan is not funny or generous.
Someone is humble or not patient.
Someone is either not humble or quiet.
Someone is not tall or brave. | Alice is old. | contradiction | (![X]:((~strong(X)|quiet(X))<=>(rich(X)|strong(X))))&
(((brave(fred)|generous(fred)))=>((kind(susan)<~>rich(susan))))&
(![X]:((old(X)|tall(X))<=>kind(X)))&
(![X]:((wise(X)&~humble(X))<=>kind(X)))&
(((funny(john)|~curious(john)))=>(?[X]:((~calm(X)&~patient(X)))))&
(![X]:((~quiet(X)|generous(X))<=>(creative(X)<~>tall(X))))&
(![X]:((kind(X)&~happy(X))<=>(generous(X)|happy(X))))&
(((~creative(lucy)<~>~happy(lucy)))<=>(?[X]:(quiet(X))))&
(![X]:(funny(X)<=>~humble(X)))&
((?[X]:((~tall(X)<~>funny(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~kind(X)<~>happy(X))=>~brave(X)))&
((?[X]:((curious(X)&~quiet(X))))<=>(?[X]:(~strong(X))))&
(![X]:(~quiet(X)=>(~tall(X)&~kind(X))))&
(![X]:(tall(X)<=>(~curious(X)|generous(X))))&
(![X]:((~quiet(X)|~creative(X))=>~tall(X)))&
((~patient(alice))=>(?[X]:((kind(X)<~>~tall(X)))))&
(~happy(paul))&
((~funny(susan)|generous(susan)))&
(?[X]:((humble(X)|~patient(X))))&
(?[X]:((~humble(X)<~>quiet(X))))&
(?[X]:((~tall(X)|brave(X)))) | old(alice) | [
"p2",
"p5",
"p6",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 12834397412393289277392
% SZS output start Proof for 12834397412393289277392
3. ! [X0] : ((tall(X0) | old(X0)) <=> kind(X0)) [input p2]
6. ! [X0] : ((generous(X0) | ~quiet(X0)) <=> (creative(X0) <~> tall(X0))) [input p5]
7. ! [X0] : ((~happy(X0) & kind(X0)) <=> (happy(X0) | generous(X0))) [input p6]
14. ! [X0] : (tall(X0) <=> (generous(X0) | ~curious(X0))) [input p13]
15. ! [X0] : ((~creative(X0) | ~quiet(X0)) => ~tall(X0)) [input p14]
22. old(alice) [input hypothesis]
30. ! [X0] : (~tall(X0) | (creative(X0) & quiet(X0))) [ennf transformation 15]
35. ! [X0] : (((tall(X0) | old(X0)) | ~kind(X0)) & (kind(X0) | (~tall(X0) & ~old(X0)))) [nnf transformation 3]
36. ! [X0] : ((tall(X0) | old(X0) | ~kind(X0)) & (kind(X0) | (~tall(X0) & ~old(X0)))) [flattening 35]
41. ! [X0] : (((generous(X0) | ~quiet(X0)) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) & (((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (~generous(X0) & quiet(X0)))) [nnf transformation 6]
42. ! [X0] : ((generous(X0) | ~quiet(X0) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) & (((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (~generous(X0) & quiet(X0)))) [flattening 41]
43. ! [X0] : (((~happy(X0) & kind(X0)) | (~happy(X0) & ~generous(X0))) & ((happy(X0) | generous(X0)) | (happy(X0) | ~kind(X0)))) [nnf transformation 7]
44. ! [X0] : (((~happy(X0) & kind(X0)) | (~happy(X0) & ~generous(X0))) & (happy(X0) | generous(X0) | happy(X0) | ~kind(X0))) [flattening 43]
61. ! [X0] : ((tall(X0) | (~generous(X0) & curious(X0))) & ((generous(X0) | ~curious(X0)) | ~tall(X0))) [nnf transformation 14]
62. ! [X0] : ((tall(X0) | (~generous(X0) & curious(X0))) & (generous(X0) | ~curious(X0) | ~tall(X0))) [flattening 61]
81. ~old(X0) | kind(X0) [cnf transformation 36]
92. ~creative(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 42]
95. happy(X0) | generous(X0) | happy(X0) | ~kind(X0) [cnf transformation 44]
99. ~happy(X0) | ~happy(X0) [cnf transformation 44]
119. ~generous(X0) | tall(X0) [cnf transformation 62]
121. ~tall(X0) | creative(X0) [cnf transformation 30]
130. old(alice) [cnf transformation 22]
131. happy(X0) | generous(X0) | ~kind(X0) [duplicate literal removal 95]
132. ~happy(X0) [duplicate literal removal 99]
169. ~kind(X0) | generous(X0) [subsumption resolution 131,132]
284. kind(alice) [resolution 81,130]
295. generous(alice) [resolution 169,284]
296. tall(alice) [resolution 295,119]
298. creative(alice) [resolution 296,121]
311. ~tall(alice) | ~generous(alice) [resolution 92,298]
314. ~generous(alice) [subsumption resolution 311,296]
315. $false [subsumption resolution 314,295]
% SZS output end Proof for 12834397412393289277392
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or calm is calm.
Everyone who is both strong and generous is both not strong and not happy.
Everyone who is not curious or not generous is either old or patient.
Everyone who is both not brave and not strong is both not strong and not tall and vice versa.
Everyone who is brave or generous is old and vice versa.
Everyone who is wise is creative or old and vice versa.
Everyone who is both not wise and not happy is creative or rich and vice versa.
Everyone who is both quiet and not quiet is brave.
If someone is kind then mary is both not patient and generous.
Everyone who is brave is funny.
If someone is not patient then someone is rich and vice versa.
If someone is either not old or not funny then someone is both curious and old.
If someone is strong or not wise then mary is either not patient or happy.
If john is both not creative and creative then someone is kind or not kind.
If alice is both old and not quiet then lucy is curious.
Someone is either kind or not generous.
Someone is tall or brave.
Someone is both calm and wise.
Mary is funny.
Someone is both tall and funny.
Lucy is either patient or not quiet.
Susan is not funny.
John is kind or not wise. | Mary is not rich. | entailment | (![X]:((rich(X)<~>calm(X))=>calm(X)))&
(![X]:((strong(X)&generous(X))=>(~strong(X)&~happy(X))))&
(![X]:((~curious(X)|~generous(X))=>(old(X)<~>patient(X))))&
(![X]:((~brave(X)&~strong(X))<=>(~strong(X)&~tall(X))))&
(![X]:((brave(X)|generous(X))<=>old(X)))&
(![X]:(wise(X)<=>(creative(X)|old(X))))&
(![X]:((~wise(X)&~happy(X))<=>(creative(X)|rich(X))))&
(![X]:((quiet(X)&~quiet(X))=>brave(X)))&
((?[X]:(kind(X)))=>((~patient(mary)&generous(mary))))&
(![X]:(brave(X)=>funny(X)))&
((?[X]:(~patient(X)))<=>(?[X]:(rich(X))))&
((?[X]:((~old(X)<~>~funny(X))))=>(?[X]:((curious(X)&old(X)))))&
((?[X]:((strong(X)|~wise(X))))=>((~patient(mary)<~>happy(mary))))&
(((~creative(john)&creative(john)))=>(?[X]:((kind(X)|~kind(X)))))&
(((old(alice)&~quiet(alice)))=>(curious(lucy)))&
(?[X]:((kind(X)<~>~generous(X))))&
(?[X]:((tall(X)|brave(X))))&
(?[X]:((calm(X)&wise(X))))&
(funny(mary))&
(?[X]:((tall(X)&funny(X))))&
((patient(lucy)<~>~quiet(lucy)))&
(~funny(susan))&
((kind(john)|~wise(john))) | ~rich(mary) | [
"p2",
"p4",
"p5",
"p6",
"p8",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4497631536637121242828849
% SZS output start Proof for 4497631536637121242828849
3. ! [X0] : ((~generous(X0) | ~curious(X0)) => (old(X0) <~> patient(X0))) [input p2]
5. ! [X0] : ((generous(X0) | brave(X0)) <=> old(X0)) [input p4]
6. ! [X0] : (wise(X0) <=> (old(X0) | creative(X0))) [input p5]
7. ! [X0] : ((~happy(X0) & ~wise(X0)) <=> (rich(X0) | creative(X0))) [input p6]
9. ? [X0] : kind(X0) => (generous(mary) & ~patient(mary)) [input p8]
13. ? [X0] : (~wise(X0) | strong(X0)) => (~patient(mary) <~> happy(mary)) [input p12]
23. ~wise(john) | kind(john) [input p22]
24. rich(mary) [input hypothesis]
27. ! [X0] : (~generous(X0) => (old(X0) <~> patient(X0))) [pure predicate removal 3]
33. ! [X0] : ((old(X0) <~> patient(X0)) | generous(X0)) [ennf transformation 27]
36. (generous(mary) & ~patient(mary)) | ! [X0] : ~kind(X0) [ennf transformation 9]
39. (~patient(mary) <~> happy(mary)) | ! [X0] : (wise(X0) & ~strong(X0)) [ennf transformation 13]
43. ! [X0] : (((~patient(X0) | ~old(X0)) & (patient(X0) | old(X0))) | generous(X0)) [nnf transformation 33]
46. ! [X0] : (((generous(X0) | brave(X0)) | ~old(X0)) & (old(X0) | (~generous(X0) & ~brave(X0)))) [nnf transformation 5]
47. ! [X0] : ((generous(X0) | brave(X0) | ~old(X0)) & (old(X0) | (~generous(X0) & ~brave(X0)))) [flattening 46]
48. ! [X0] : ((wise(X0) | (~old(X0) & ~creative(X0))) & ((old(X0) | creative(X0)) | ~wise(X0))) [nnf transformation 6]
49. ! [X0] : ((wise(X0) | (~old(X0) & ~creative(X0))) & (old(X0) | creative(X0) | ~wise(X0))) [flattening 48]
50. ! [X0] : (((~happy(X0) & ~wise(X0)) | (~rich(X0) & ~creative(X0))) & ((rich(X0) | creative(X0)) | (happy(X0) | wise(X0)))) [nnf transformation 7]
51. ! [X0] : (((~happy(X0) & ~wise(X0)) | (~rich(X0) & ~creative(X0))) & (rich(X0) | creative(X0) | happy(X0) | wise(X0))) [flattening 50]
61. ((~happy(mary) | patient(mary)) & (happy(mary) | ~patient(mary))) | ! [X0] : (wise(X0) & ~strong(X0)) [nnf transformation 39]
78. patient(X0) | old(X0) | generous(X0) [cnf transformation 43]
85. ~generous(X0) | old(X0) [cnf transformation 47]
89. ~old(X0) | wise(X0) [cnf transformation 49]
92. ~wise(X0) | ~rich(X0) [cnf transformation 51]
94. ~happy(X0) | ~rich(X0) [cnf transformation 51]
96. ~patient(mary) | ~kind(X0) [cnf transformation 36]
104. happy(mary) | ~patient(mary) | wise(X0) [cnf transformation 61]
119. ~wise(john) | kind(john) [cnf transformation 23]
120. rich(mary) [cnf transformation 24]
126. 1 <=> ! [X0] : ~kind(X0) [avatar definition]
127. ~kind(X0) <- (1) [avatar component clause 126]
129. 2 <=> generous(mary) [avatar definition]
130. ~generous(mary) <- (~2) [avatar component clause 129]
131. generous(mary) <- (2) [avatar component clause 129]
134. 3 <=> patient(mary) [avatar definition]
136. ~patient(mary) <- (~3) [avatar component clause 134]
137. 1 | ~3 [avatar split clause 96,134,126]
167. 11 <=> ! [X0] : wise(X0) [avatar definition]
168. wise(X0) <- (11) [avatar component clause 167]
170. 12 <=> happy(mary) [avatar definition]
171. happy(mary) <- (12) [avatar component clause 170]
178. 11 | ~3 | 12 [avatar split clause 104,170,134,167]
210. 20 <=> kind(john) [avatar definition]
212. kind(john) <- (20) [avatar component clause 210]
214. 21 <=> wise(john) [avatar definition]
216. ~wise(john) <- (~21) [avatar component clause 214]
217. 20 | ~21 [avatar split clause 119,214,210]
222. old(mary) <- (2) [resolution 85,131]
224. wise(mary) <- (2) [resolution 89,222]
227. ~rich(mary) <- (2) [resolution 224,92]
228. $false <- (2) [subsumption resolution 227,120]
229. ~2 [avatar contradiction clause 228]
232. old(mary) | generous(mary) <- (~3) [resolution 78,136]
235. old(mary) <- (~2, ~3) [subsumption resolution 232,130]
240. wise(mary) <- (~2, ~3) [resolution 235,89]
338. ~rich(mary) <- (~2, ~3) [resolution 240,92]
339. $false <- (~2, ~3) [subsumption resolution 338,120]
340. 2 | 3 [avatar contradiction clause 339]
350. ~rich(mary) <- (12) [resolution 171,94]
351. $false <- (12) [subsumption resolution 350,120]
352. ~12 [avatar contradiction clause 351]
353. $false <- (11, ~21) [resolution 168,216]
356. ~11 | 21 [avatar contradiction clause 353]
359. $false <- (1, 20) [subsumption resolution 212,127]
360. ~1 | ~20 [avatar contradiction clause 359]
361. $false [avatar sat refutation 137,178,217,229,340,352,356,360]
% SZS output end Proof for 4497631536637121242828849
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not generous then someone is quiet and vice versa.
If alice is kind or strong then someone is patient or not humble.
If paul is both humble and patient then someone is both rich and old.
If susan is not generous or brave then someone is not wise or not calm and vice versa.
If someone is either not tall or old then someone is both strong and tall and vice versa.
If fred is both not creative and old then lucy is either not brave or brave.
If fred is either curious or not kind then john is brave.
If someone is both brave and happy then mary is both old and not patient.
If paul is not patient or not funny then someone is not tall or not humble.
Everyone who is old is both creative and not humble and vice versa.
If someone is humble then mary is kind or wise and vice versa.
Everyone who is wise or tall is both not funny and funny and vice versa.
If lucy is both not creative and not happy then someone is both not quiet and happy.
If someone is old then paul is either not brave or not happy.
Everyone who is either not old or not brave is creative or strong and vice versa.
Everyone who is either curious or not humble is not humble.
Someone is either not tall or brave.
Someone is either quiet or strong.
Someone is either rich or curious.
Someone is kind.
Alice is either curious or wise.
Someone is both curious and not patient.
John is either not funny or old. | Susan is not creative. | contradiction | ((~generous(lucy))<=>(?[X]:(quiet(X))))&
(((kind(alice)|strong(alice)))=>(?[X]:((patient(X)|~humble(X)))))&
(((humble(paul)&patient(paul)))=>(?[X]:((rich(X)&old(X)))))&
(((~generous(susan)|brave(susan)))<=>(?[X]:((~wise(X)|~calm(X)))))&
((?[X]:((~tall(X)<~>old(X))))<=>(?[X]:((strong(X)&tall(X)))))&
(((~creative(fred)&old(fred)))=>((~brave(lucy)<~>brave(lucy))))&
(((curious(fred)<~>~kind(fred)))=>(brave(john)))&
((?[X]:((brave(X)&happy(X))))=>((old(mary)&~patient(mary))))&
(((~patient(paul)|~funny(paul)))=>(?[X]:((~tall(X)|~humble(X)))))&
(![X]:(old(X)<=>(creative(X)&~humble(X))))&
((?[X]:(humble(X)))<=>((kind(mary)|wise(mary))))&
(![X]:((wise(X)|tall(X))<=>(~funny(X)&funny(X))))&
(((~creative(lucy)&~happy(lucy)))=>(?[X]:((~quiet(X)&happy(X)))))&
((?[X]:(old(X)))=>((~brave(paul)<~>~happy(paul))))&
(![X]:((~old(X)<~>~brave(X))<=>(creative(X)|strong(X))))&
(![X]:((curious(X)<~>~humble(X))=>~humble(X)))&
(?[X]:((~tall(X)<~>brave(X))))&
(?[X]:((quiet(X)<~>strong(X))))&
(?[X]:((rich(X)<~>curious(X))))&
(?[X]:(kind(X)))&
((curious(alice)<~>wise(alice)))&
(?[X]:((curious(X)&~patient(X))))&
((~funny(john)<~>old(john))) | ~creative(susan) | [
"p4",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4228162439329734394246135
% SZS output start Proof for 4228162439329734394246135
5. ? [X0] : (~tall(X0) <~> old(X0)) <=> ? [X0] : (tall(X0) & strong(X0)) [input p4]
10. ! [X0] : (old(X0) <=> (~humble(X0) & creative(X0))) [input p9]
12. ! [X0] : ((tall(X0) | wise(X0)) <=> (funny(X0) & ~funny(X0))) [input p11]
24. ~creative(susan) [input hypothesis]
25. ? [X0] : (~tall(X0) <~> old(X0)) <=> ? [X1] : (tall(X1) & strong(X1)) [rectify 5]
51. (? [X0] : ((~old(X0) | tall(X0)) & (old(X0) | ~tall(X0))) | ! [X1] : (~tall(X1) | ~strong(X1))) & (? [X1] : (tall(X1) & strong(X1)) | ! [X0] : ((~tall(X0) | ~old(X0)) & (old(X0) | tall(X0)))) [nnf transformation 25]
52. (? [X0] : ((~old(X0) | tall(X0)) & (old(X0) | ~tall(X0))) | ! [X1] : (~tall(X1) | ~strong(X1))) & (? [X2] : (tall(X2) & strong(X2)) | ! [X3] : ((~tall(X3) | ~old(X3)) & (old(X3) | tall(X3)))) [rectify 51]
53. ? [X0] : ((~old(X0) | tall(X0)) & (old(X0) | ~tall(X0))) => ((~old(sK4) | tall(sK4)) & (old(sK4) | ~tall(sK4))) [choice axiom]
54. ? [X2] : (tall(X2) & strong(X2)) => (tall(sK5) & strong(sK5)) [choice axiom]
55. (((~old(sK4) | tall(sK4)) & (old(sK4) | ~tall(sK4))) | ! [X1] : (~tall(X1) | ~strong(X1))) & ((tall(sK5) & strong(sK5)) | ! [X3] : ((~tall(X3) | ~old(X3)) & (old(X3) | tall(X3)))) [skolemisation 52,54,53]
60. ! [X0] : ((old(X0) | (humble(X0) | ~creative(X0))) & ((~humble(X0) & creative(X0)) | ~old(X0))) [nnf transformation 10]
61. ! [X0] : ((old(X0) | humble(X0) | ~creative(X0)) & ((~humble(X0) & creative(X0)) | ~old(X0))) [flattening 60]
67. ! [X0] : (((tall(X0) | wise(X0)) | (~funny(X0) | funny(X0))) & ((funny(X0) & ~funny(X0)) | (~tall(X0) & ~wise(X0)))) [nnf transformation 12]
68. ! [X0] : ((tall(X0) | wise(X0) | ~funny(X0) | funny(X0)) & ((funny(X0) & ~funny(X0)) | (~tall(X0) & ~wise(X0)))) [flattening 67]
102. tall(sK5) | old(X3) | tall(X3) [cnf transformation 55]
114. ~old(X0) | creative(X0) [cnf transformation 61]
121. ~funny(X0) | ~tall(X0) [cnf transformation 68]
123. funny(X0) | ~tall(X0) [cnf transformation 68]
150. ~creative(susan) [cnf transformation 24]
244. 22 <=> tall(sK5) [avatar definition]
246. tall(sK5) <- (22) [avatar component clause 244]
249. 23 <=> ! [X3] : (old(X3) | tall(X3)) [avatar definition]
250. old(X3) | tall(X3) <- (23) [avatar component clause 249]
251. 23 | 22 [avatar split clause 102,244,249]
317. ~tall(X0) [subsumption resolution 121,123]
389. $false <- (22) [subsumption resolution 246,317]
390. ~22 [avatar contradiction clause 389]
391. old(X3) <- (23) [subsumption resolution 250,317]
396. creative(X0) <- (23) [resolution 114,391]
401. $false <- (23) [resolution 396,150]
402. ~23 [avatar contradiction clause 401]
403. $false [avatar sat refutation 251,390,402]
% SZS output end Proof for 4228162439329734394246135
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or not brave is either not humble or calm and vice versa.
Everyone who is rich or creative is humble and vice versa.
If susan is both not brave and patient then mary is not humble or not calm.
If someone is both not quiet and old then someone is not quiet and vice versa.
Everyone who is brave is not funny.
If lucy is both happy and not tall then someone is both not humble and not patient.
Everyone who is not calm is either rich or humble.
If someone is not funny or happy then mary is not tall or not strong and vice versa.
If mary is creative then someone is either not funny or patient.
Everyone who is kind is either not creative or funny and vice versa.
Everyone who is generous or not humble is not generous or generous and vice versa.
If mary is both patient and rich then someone is not patient or happy.
If john is not strong or brave then someone is not tall or not generous.
If john is both not wise and not humble then john is both happy and old and vice versa.
Everyone who is not curious or not patient is both quiet and curious and vice versa.
Everyone who is not tall is not rich.
Someone is both happy and quiet.
John is not rich or generous.
Someone is quiet.
Mary is either patient or tall.
Lucy is either not generous or strong.
Someone is either not old or not humble.
Susan is either creative or not brave.
Paul is not wise or tall. | John is strong. | neutral | (![X]:((~patient(X)|~brave(X))<=>(~humble(X)<~>calm(X))))&
(![X]:((rich(X)|creative(X))<=>humble(X)))&
(((~brave(susan)&patient(susan)))=>((~humble(mary)|~calm(mary))))&
((?[X]:((~quiet(X)&old(X))))<=>(?[X]:(~quiet(X))))&
(![X]:(brave(X)=>~funny(X)))&
(((happy(lucy)&~tall(lucy)))=>(?[X]:((~humble(X)&~patient(X)))))&
(![X]:(~calm(X)=>(rich(X)<~>humble(X))))&
((?[X]:((~funny(X)|happy(X))))<=>((~tall(mary)|~strong(mary))))&
((creative(mary))=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:(kind(X)<=>(~creative(X)<~>funny(X))))&
(![X]:((generous(X)|~humble(X))<=>(~generous(X)|generous(X))))&
(((patient(mary)&rich(mary)))=>(?[X]:((~patient(X)|happy(X)))))&
(((~strong(john)|brave(john)))=>(?[X]:((~tall(X)|~generous(X)))))&
(((~wise(john)&~humble(john)))<=>((happy(john)&old(john))))&
(![X]:((~curious(X)|~patient(X))<=>(quiet(X)&curious(X))))&
(![X]:(~tall(X)=>~rich(X)))&
(?[X]:((happy(X)&quiet(X))))&
((~rich(john)|generous(john)))&
(?[X]:(quiet(X)))&
((patient(mary)<~>tall(mary)))&
((~generous(lucy)<~>strong(lucy)))&
(?[X]:((~old(X)<~>~humble(X))))&
((creative(susan)<~>~brave(susan)))&
((~wise(paul)|tall(paul))) | strong(john) | [] | null | 0 |
Everyone who is both not funny and rich is either not humble or kind and vice versa.
Everyone who is not creative is not strong and vice versa.
Everyone who is old or not generous is both strong and not happy.
Everyone who is both not quiet and wise is happy and vice versa.
Everyone who is both patient and not creative is not generous or kind and vice versa.
Everyone who is not funny or brave is not humble or not patient and vice versa.
Everyone who is either patient or generous is calm or not generous and vice versa.
If someone is patient then susan is kind.
Everyone who is not strong is old or calm and vice versa.
If someone is either not creative or not humble then fred is curious or not wise.
If someone is not creative or not strong then someone is both quiet and brave.
If alice is not quiet then john is not brave.
Everyone who is either not creative or happy is both not creative and not wise.
Everyone who is either not curious or funny is not wise and vice versa.
Someone is not tall or not wise.
John is either patient or wise.
John is curious or funny.
Someone is both not rich and not tall.
John is humble or quiet.
Someone is both rich and curious.
Lucy is either not humble or creative. | Lucy is patient. | contradiction | (![X]:((~funny(X)&rich(X))<=>(~humble(X)<~>kind(X))))&
(![X]:(~creative(X)<=>~strong(X)))&
(![X]:((old(X)|~generous(X))=>(strong(X)&~happy(X))))&
(![X]:((~quiet(X)&wise(X))<=>happy(X)))&
(![X]:((patient(X)&~creative(X))<=>(~generous(X)|kind(X))))&
(![X]:((~funny(X)|brave(X))<=>(~humble(X)|~patient(X))))&
(![X]:((patient(X)<~>generous(X))<=>(calm(X)|~generous(X))))&
((?[X]:(patient(X)))=>(kind(susan)))&
(![X]:(~strong(X)<=>(old(X)|calm(X))))&
((?[X]:((~creative(X)<~>~humble(X))))=>((curious(fred)|~wise(fred))))&
((?[X]:((~creative(X)|~strong(X))))=>(?[X]:((quiet(X)&brave(X)))))&
((~quiet(alice))=>(~brave(john)))&
(![X]:((~creative(X)<~>happy(X))=>(~creative(X)&~wise(X))))&
(![X]:((~curious(X)<~>funny(X))<=>~wise(X)))&
(?[X]:((~tall(X)|~wise(X))))&
((patient(john)<~>wise(john)))&
((curious(john)|funny(john)))&
(?[X]:((~rich(X)&~tall(X))))&
((humble(john)|quiet(john)))&
(?[X]:((rich(X)&curious(X))))&
((~humble(lucy)<~>creative(lucy))) | patient(lucy) | [
"p1",
"p2",
"p4",
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2463096298459235306791924
% SZS output start Proof for 2463096298459235306791924
2. ! [X0] : (~creative(X0) <=> ~strong(X0)) [input p1]
3. ! [X0] : ((~generous(X0) | old(X0)) => (~happy(X0) & strong(X0))) [input p2]
5. ! [X0] : ((~creative(X0) & patient(X0)) <=> (kind(X0) | ~generous(X0))) [input p4]
7. ! [X0] : ((patient(X0) <~> generous(X0)) <=> (~generous(X0) | calm(X0))) [input p6]
8. ? [X0] : patient(X0) => kind(susan) [input p7]
9. ! [X0] : (~strong(X0) <=> (calm(X0) | old(X0))) [input p8]
22. patient(lucy) [input hypothesis]
26. ! [X0] : ((~happy(X0) & strong(X0)) | (generous(X0) & ~old(X0))) [ennf transformation 3]
27. kind(susan) | ! [X0] : ~patient(X0) [ennf transformation 8]
35. ! [X0] : ((~creative(X0) | strong(X0)) & (~strong(X0) | creative(X0))) [nnf transformation 2]
38. ! [X0] : (((~creative(X0) & patient(X0)) | (~kind(X0) & generous(X0))) & ((kind(X0) | ~generous(X0)) | (creative(X0) | ~patient(X0)))) [nnf transformation 5]
39. ! [X0] : (((~creative(X0) & patient(X0)) | (~kind(X0) & generous(X0))) & (kind(X0) | ~generous(X0) | creative(X0) | ~patient(X0))) [flattening 38]
42. ! [X0] : ((((~generous(X0) | ~patient(X0)) & (generous(X0) | patient(X0))) | (generous(X0) & ~calm(X0))) & ((~generous(X0) | calm(X0)) | ((patient(X0) | ~generous(X0)) & (generous(X0) | ~patient(X0))))) [nnf transformation 7]
43. ! [X0] : ((((~generous(X0) | ~patient(X0)) & (generous(X0) | patient(X0))) | (generous(X0) & ~calm(X0))) & (~generous(X0) | calm(X0) | ((patient(X0) | ~generous(X0)) & (generous(X0) | ~patient(X0))))) [flattening 42]
44. ! [X0] : ((~strong(X0) | (~calm(X0) & ~old(X0))) & ((calm(X0) | old(X0)) | strong(X0))) [nnf transformation 9]
45. ! [X0] : ((~strong(X0) | (~calm(X0) & ~old(X0))) & (calm(X0) | old(X0) | strong(X0))) [flattening 44]
64. ~strong(X0) | creative(X0) [cnf transformation 35]
66. ~old(X0) | strong(X0) [cnf transformation 26]
67. generous(X0) | strong(X0) [cnf transformation 26]
75. ~kind(X0) | patient(X0) [cnf transformation 39]
77. ~creative(X0) | ~kind(X0) [cnf transformation 39]
86. ~calm(X0) | ~patient(X0) | ~generous(X0) [cnf transformation 43]
88. kind(susan) | ~patient(X0) [cnf transformation 27]
89. calm(X0) | old(X0) | strong(X0) [cnf transformation 45]
90. ~strong(X0) | ~old(X0) [cnf transformation 45]
116. patient(lucy) [cnf transformation 22]
122. 1 <=> ! [X0] : ~patient(X0) [avatar definition]
123. ~patient(X0) <- (1) [avatar component clause 122]
125. 2 <=> kind(susan) [avatar definition]
127. kind(susan) <- (2) [avatar component clause 125]
128. 1 | 2 [avatar split clause 88,125,122]
129. ~old(X0) [subsumption resolution 90,66]
130. calm(X0) | strong(X0) [subsumption resolution 89,129]
218. patient(susan) <- (2) [resolution 75,127]
261. ~patient(X0) | ~generous(X0) | strong(X0) [resolution 86,130]
263. ~patient(X0) | strong(X0) [subsumption resolution 261,67]
265. strong(susan) <- (2) [resolution 263,218]
269. creative(susan) <- (2) [resolution 265,64]
460. ~kind(susan) <- (2) [resolution 269,77]
463. $false <- (2) [subsumption resolution 460,127]
464. ~2 [avatar contradiction clause 463]
468. $false <- (1) [resolution 123,116]
471. ~1 [avatar contradiction clause 468]
473. $false [avatar sat refutation 128,464,471]
% SZS output end Proof for 2463096298459235306791924
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or humble then someone is both not quiet and not strong.
If john is not generous or creative then john is either not rich or generous.
Everyone who is not patient is rich.
Everyone who is calm is either not brave or not kind and vice versa.
Everyone who is either not old or quiet is tall and vice versa.
If mary is quiet or tall then lucy is not quiet and vice versa.
If john is both not brave and not old then paul is either not humble or wise and vice versa.
Everyone who is generous is not creative or not tall and vice versa.
If susan is both not rich and rich then someone is either rich or generous and vice versa.
Everyone who is either not wise or not generous is rich or not calm and vice versa.
Everyone who is not strong is not wise or not curious.
Everyone who is not wise or not curious is both curious and not patient.
Everyone who is either happy or generous is either patient or creative and vice versa.
If paul is not generous or not curious then john is both not funny and calm.
If mary is either old or not generous then alice is not tall or humble and vice versa.
If lucy is not brave then someone is strong and vice versa.
Someone is funny or kind.
Paul is both not calm and brave.
Fred is rich or not wise.
Someone is tall.
Mary is not curious or not generous.
Someone is either not tall or old.
Someone is either tall or kind.
Someone is not generous. | Fred is patient. | contradiction | ((?[X]:((~humble(X)|humble(X))))=>(?[X]:((~quiet(X)&~strong(X)))))&
(((~generous(john)|creative(john)))=>((~rich(john)<~>generous(john))))&
(![X]:(~patient(X)=>rich(X)))&
(![X]:(calm(X)<=>(~brave(X)<~>~kind(X))))&
(![X]:((~old(X)<~>quiet(X))<=>tall(X)))&
(((quiet(mary)|tall(mary)))<=>(~quiet(lucy)))&
(((~brave(john)&~old(john)))<=>((~humble(paul)<~>wise(paul))))&
(![X]:(generous(X)<=>(~creative(X)|~tall(X))))&
(((~rich(susan)&rich(susan)))<=>(?[X]:((rich(X)<~>generous(X)))))&
(![X]:((~wise(X)<~>~generous(X))<=>(rich(X)|~calm(X))))&
(![X]:(~strong(X)=>(~wise(X)|~curious(X))))&
(![X]:((~wise(X)|~curious(X))=>(curious(X)&~patient(X))))&
(![X]:((happy(X)<~>generous(X))<=>(patient(X)<~>creative(X))))&
(((~generous(paul)|~curious(paul)))=>((~funny(john)&calm(john))))&
(((old(mary)<~>~generous(mary)))<=>((~tall(alice)|humble(alice))))&
((~brave(lucy))<=>(?[X]:(strong(X))))&
(?[X]:((funny(X)|kind(X))))&
((~calm(paul)&brave(paul)))&
((rich(fred)|~wise(fred)))&
(?[X]:(tall(X)))&
((~curious(mary)|~generous(mary)))&
(?[X]:((~tall(X)<~>old(X))))&
(?[X]:((tall(X)<~>kind(X))))&
(?[X]:(~generous(X))) | patient(fred) | [
"p8",
"p9",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1272433301743102558924687
% SZS output start Proof for 1272433301743102558924687
9. (rich(susan) & ~rich(susan)) <=> ? [X0] : (rich(X0) <~> generous(X0)) [input p8]
10. ! [X0] : ((~wise(X0) <~> ~generous(X0)) <=> (~calm(X0) | rich(X0))) [input p9]
12. ! [X0] : ((~curious(X0) | ~wise(X0)) => (~patient(X0) & curious(X0))) [input p11]
19. ~wise(fred) | rich(fred) [input p18]
25. patient(fred) [input hypothesis]
32. ! [X0] : ((~patient(X0) & curious(X0)) | (curious(X0) & wise(X0))) [ennf transformation 12]
46. ((rich(susan) & ~rich(susan)) | ! [X0] : ((rich(X0) | ~generous(X0)) & (generous(X0) | ~rich(X0)))) & (? [X0] : ((~generous(X0) | ~rich(X0)) & (generous(X0) | rich(X0))) | (~rich(susan) | rich(susan))) [nnf transformation 9]
47. ((rich(susan) & ~rich(susan)) | ! [X0] : ((rich(X0) | ~generous(X0)) & (generous(X0) | ~rich(X0)))) & (? [X0] : ((~generous(X0) | ~rich(X0)) & (generous(X0) | rich(X0))) | ~rich(susan) | rich(susan)) [flattening 46]
48. ((rich(susan) & ~rich(susan)) | ! [X0] : ((rich(X0) | ~generous(X0)) & (generous(X0) | ~rich(X0)))) & (? [X1] : ((~generous(X1) | ~rich(X1)) & (generous(X1) | rich(X1))) | ~rich(susan) | rich(susan)) [rectify 47]
49. ? [X1] : ((~generous(X1) | ~rich(X1)) & (generous(X1) | rich(X1))) => ((~generous(sK1) | ~rich(sK1)) & (generous(sK1) | rich(sK1))) [choice axiom]
50. ((rich(susan) & ~rich(susan)) | ! [X0] : ((rich(X0) | ~generous(X0)) & (generous(X0) | ~rich(X0)))) & (((~generous(sK1) | ~rich(sK1)) & (generous(sK1) | rich(sK1))) | ~rich(susan) | rich(susan)) [skolemisation 48,49]
51. ! [X0] : ((((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | (calm(X0) & ~rich(X0))) & ((~calm(X0) | rich(X0)) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0))))) [nnf transformation 10]
52. ! [X0] : ((((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | (calm(X0) & ~rich(X0))) & (~calm(X0) | rich(X0) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0))))) [flattening 51]
103. ~rich(susan) | generous(X0) | ~rich(X0) [cnf transformation 50]
105. rich(susan) | generous(X0) | ~rich(X0) [cnf transformation 50]
109. ~wise(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 52]
116. ~patient(X0) | wise(X0) [cnf transformation 32]
141. ~wise(fred) | rich(fred) [cnf transformation 19]
149. patient(fred) [cnf transformation 25]
226. 16 <=> rich(susan) [avatar definition]
231. 17 <=> ! [X0] : (generous(X0) | ~rich(X0)) [avatar definition]
232. ~rich(X0) | generous(X0) <- (17) [avatar component clause 231]
233. 17 | 16 [avatar split clause 105,226,231]
235. 17 | ~16 [avatar split clause 103,226,231]
299. 30 <=> rich(fred) [avatar definition]
301. rich(fred) <- (30) [avatar component clause 299]
303. 31 <=> wise(fred) [avatar definition]
304. wise(fred) <- (31) [avatar component clause 303]
306. 30 | ~31 [avatar split clause 141,303,299]
333. wise(fred) [resolution 116,149]
337. 31 [avatar split clause 333,303]
347. generous(fred) <- (17, 30) [resolution 232,301]
450. ~generous(fred) | ~rich(fred) <- (31) [resolution 109,304]
451. ~rich(fred) <- (17, 30, 31) [subsumption resolution 450,347]
452. $false <- (17, 30, 31) [subsumption resolution 451,301]
453. ~17 | ~30 | ~31 [avatar contradiction clause 452]
454. $false [avatar sat refutation 233,235,306,337,453]
% SZS output end Proof for 1272433301743102558924687
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is 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. | Alice is quiet. | contradiction | ((?[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)) | quiet(alice) | [
"p1",
"p11",
"p12",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4576438929538901399803586
% SZS output start Proof for 4576438929538901399803586
2. ! [X0] : ((quiet(X0) & wise(X0)) => (kind(X0) & creative(X0))) [input p1]
12. ! [X0] : ((~happy(X0) | brave(X0)) => (~creative(X0) & brave(X0))) [input p11]
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]
18. brave(alice) & ~old(alice) [input p17]
24. quiet(alice) [input hypothesis]
29. ! [X0] : ((kind(X0) & creative(X0)) | (~quiet(X0) | ~wise(X0))) [ennf transformation 2]
30. ! [X0] : ((kind(X0) & creative(X0)) | ~quiet(X0) | ~wise(X0)) [flattening 29]
37. ! [X0] : ((~creative(X0) & brave(X0)) | (happy(X0) & ~brave(X0))) [ennf transformation 12]
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]
85. ~wise(X0) | ~quiet(X0) | creative(X0) [cnf transformation 30]
124. ~brave(X0) | ~creative(X0) [cnf transformation 37]
127. tall(X0) | wise(X0) [cnf transformation 67]
135. ~brave(X0) | ~tall(X0) [cnf transformation 71]
140. brave(X0) | ~tall(X0) [cnf transformation 73]
145. brave(alice) [cnf transformation 18]
151. quiet(alice) [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]
333. ~creative(alice) [resolution 124,145]
340. wise(X1) <- (9) [resolution 127,189]
352. ~quiet(X0) | creative(X0) <- (9) [resolution 85,340]
353. creative(alice) <- (9) [resolution 352,151]
356. $false <- (9) [subsumption resolution 353,333]
357. ~9 [avatar contradiction clause 356]
358. $false [avatar sat refutation 309,357]
% SZS output end Proof for 4576438929538901399803586
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either curious or happy. Everyone who is not patient is tall or quiet and vice versa. If someone is not brave then someone is not calm or creative. If lucy is humble or strong then someone is both curious and not strong and vice versa. Everyone who is rich or not funny is either funny or strong. If someone is either happy or not patient then someone is brave or creative. If someone is both funny and not rich then lucy is both not patient and wise. If alice is creative or not creative then someone is not tall or tall and vice versa. Everyone who is not kind or creative is either not kind or not tall and vice versa. If lucy is both not humble and not curious then someone is not humble. Everyone who is not funny is either not generous or brave. Everyone who is not funny or not rich is both not wise and not generous. If someone is both humble and calm then someone is both not brave and tall. Everyone who is patient or wise is creative or old and vice versa. If john is both curious and not happy then mary is not brave and vice versa. If alice is not patient then someone is not wise and vice versa. John is not funny. Someone is generous or not rich. Susan is either not creative or not generous. Someone is quiet or not wise. Paul is both not patient and not brave. John is both not wise and tall. Lucy is not rich. Someone is either not funny or not patient. | John is creative. | contradiction | (![X]:(~tall(X)=>(curious(X)<~>happy(X))))&
(![X]:(~patient(X)<=>(tall(X)|quiet(X))))&
((?[X]:(~brave(X)))=>(?[X]:((~calm(X)|creative(X)))))&
(((humble(lucy)|strong(lucy)))<=>(?[X]:((curious(X)&~strong(X)))))&
(![X]:((rich(X)|~funny(X))=>(funny(X)<~>strong(X))))&
((?[X]:((happy(X)<~>~patient(X))))=>(?[X]:((brave(X)|creative(X)))))&
((?[X]:((funny(X)&~rich(X))))=>((~patient(lucy)&wise(lucy))))&
(((creative(alice)|~creative(alice)))<=>(?[X]:((~tall(X)|tall(X)))))&
(![X]:((~kind(X)|creative(X))<=>(~kind(X)<~>~tall(X))))&
(((~humble(lucy)&~curious(lucy)))=>(?[X]:(~humble(X))))&
(![X]:(~funny(X)=>(~generous(X)<~>brave(X))))&
(![X]:((~funny(X)|~rich(X))=>(~wise(X)&~generous(X))))&
((?[X]:((humble(X)&calm(X))))=>(?[X]:((~brave(X)&tall(X)))))&
(![X]:((patient(X)|wise(X))<=>(creative(X)|old(X))))&
(((curious(john)&~happy(john)))<=>(~brave(mary)))&
((~patient(alice))<=>(?[X]:(~wise(X))))&
(~funny(john))&
(?[X]:((generous(X)|~rich(X))))&
((~creative(susan)<~>~generous(susan)))&
(?[X]:((quiet(X)|~wise(X))))&
((~patient(paul)&~brave(paul)))&
((~wise(john)&tall(john)))&
(~rich(lucy))&
(?[X]:((~funny(X)<~>~patient(X)))) | creative(john) | [
"p1",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 397290648241053049454119
% SZS output start Proof for 397290648241053049454119
2. ! [X0] : (~patient(X0) <=> (quiet(X0) | tall(X0))) [input p1]
14. ! [X0] : ((wise(X0) | patient(X0)) <=> (old(X0) | creative(X0))) [input p13]
22. tall(john) & ~wise(john) [input p21]
25. creative(john) [input hypothesis]
40. ! [X0] : ((~patient(X0) | (~quiet(X0) & ~tall(X0))) & ((quiet(X0) | tall(X0)) | patient(X0))) [nnf transformation 2]
41. ! [X0] : ((~patient(X0) | (~quiet(X0) & ~tall(X0))) & (quiet(X0) | tall(X0) | patient(X0))) [flattening 40]
62. ! [X0] : (((wise(X0) | patient(X0)) | (~old(X0) & ~creative(X0))) & ((old(X0) | creative(X0)) | (~wise(X0) & ~patient(X0)))) [nnf transformation 14]
63. ! [X0] : ((wise(X0) | patient(X0) | (~old(X0) & ~creative(X0))) & (old(X0) | creative(X0) | (~wise(X0) & ~patient(X0)))) [flattening 62]
81. ~patient(X0) | ~tall(X0) [cnf transformation 41]
115. ~creative(X0) | patient(X0) | wise(X0) [cnf transformation 63]
129. ~wise(john) [cnf transformation 22]
130. tall(john) [cnf transformation 22]
134. creative(john) [cnf transformation 25]
309. patient(john) | wise(john) [resolution 115,134]
312. patient(john) [subsumption resolution 309,129]
332. ~tall(john) [resolution 312,81]
333. $false [subsumption resolution 332,130]
% SZS output end Proof for 397290648241053049454119
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or curious is calm and vice versa.
Everyone who is generous is not brave and vice versa.
Everyone who is both calm and tall is both wise and not curious and vice versa.
Everyone who is not strong or not funny is not quiet and vice versa.
If someone is both calm and creative then paul is humble or not quiet and vice versa.
If someone is both not strong and not patient then susan is either funny or patient.
If someone is strong then someone is both creative and funny.
Everyone who is either not tall or not humble is either quiet or not generous and vice versa.
Everyone who is not strong or not brave is old or curious and vice versa.
If someone is both humble and not funny then alice is not wise or not generous and vice versa.
Everyone who is both brave and not humble is both calm and happy and vice versa.
Everyone who is either patient or not generous is either creative or not kind and vice versa.
Everyone who is generous or tall is funny or old.
Everyone who is both not funny and kind is curious.
If someone is either not funny or curious then someone is either not brave or not quiet.
John is strong.
Someone is either not curious or not happy.
Someone is rich or not happy.
Lucy is not calm.
Paul is both happy and not kind.
Someone is either generous or not curious.
John is both not creative and not wise. | Alice is curious. | neutral | (![X]:((~happy(X)<~>curious(X))<=>calm(X)))&
(![X]:(generous(X)<=>~brave(X)))&
(![X]:((calm(X)&tall(X))<=>(wise(X)&~curious(X))))&
(![X]:((~strong(X)|~funny(X))<=>~quiet(X)))&
((?[X]:((calm(X)&creative(X))))<=>((humble(paul)|~quiet(paul))))&
((?[X]:((~strong(X)&~patient(X))))=>((funny(susan)<~>patient(susan))))&
((?[X]:(strong(X)))=>(?[X]:((creative(X)&funny(X)))))&
(![X]:((~tall(X)<~>~humble(X))<=>(quiet(X)<~>~generous(X))))&
(![X]:((~strong(X)|~brave(X))<=>(old(X)|curious(X))))&
((?[X]:((humble(X)&~funny(X))))<=>((~wise(alice)|~generous(alice))))&
(![X]:((brave(X)&~humble(X))<=>(calm(X)&happy(X))))&
(![X]:((patient(X)<~>~generous(X))<=>(creative(X)<~>~kind(X))))&
(![X]:((generous(X)|tall(X))=>(funny(X)|old(X))))&
(![X]:((~funny(X)&kind(X))=>curious(X)))&
((?[X]:((~funny(X)<~>curious(X))))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(strong(john))&
(?[X]:((~curious(X)<~>~happy(X))))&
(?[X]:((rich(X)|~happy(X))))&
(~calm(lucy))&
((happy(paul)&~kind(paul)))&
(?[X]:((generous(X)<~>~curious(X))))&
((~creative(john)&~wise(john))) | curious(alice) | [] | null | 0 |
If someone is not patient or happy then someone is both not strong and old.
Everyone who is both quiet and not wise is both curious and not creative.
Everyone who is both quiet and creative is both happy and not tall.
Everyone who is both funny and generous is both not calm and generous and vice versa.
Everyone who is patient or curious is kind or tall and vice versa.
Everyone who is either not kind or not strong is humble and vice versa.
If someone is both not rich and not old then john is old.
If fred is either not patient or old then mary is not generous and vice versa.
If someone is both not strong and not quiet then someone is both not happy and calm and vice versa.
If fred is rich or not generous then someone is either not happy or not generous.
Everyone who is not patient or not funny is not old or not creative.
If someone is both not kind and not humble then someone is rich.
Everyone who is not rich or not quiet is both not tall and rich.
If someone is curious or not happy then someone is generous or not generous and vice versa.
Everyone who is not tall is not funny or not old and vice versa.
Everyone who is creative or rich is not quiet and vice versa.
John is not generous or not creative.
Someone is either not curious or generous.
Alice is either not humble or not creative.
Alice is patient or not tall.
Someone is either brave or not wise.
Alice is not happy. | Alice is not quiet. | entailment | ((?[X]:((~patient(X)|happy(X))))=>(?[X]:((~strong(X)&old(X)))))&
(![X]:((quiet(X)&~wise(X))=>(curious(X)&~creative(X))))&
(![X]:((quiet(X)&creative(X))=>(happy(X)&~tall(X))))&
(![X]:((funny(X)&generous(X))<=>(~calm(X)&generous(X))))&
(![X]:((patient(X)|curious(X))<=>(kind(X)|tall(X))))&
(![X]:((~kind(X)<~>~strong(X))<=>humble(X)))&
((?[X]:((~rich(X)&~old(X))))=>(old(john)))&
(((~patient(fred)<~>old(fred)))<=>(~generous(mary)))&
((?[X]:((~strong(X)&~quiet(X))))<=>(?[X]:((~happy(X)&calm(X)))))&
(((rich(fred)|~generous(fred)))=>(?[X]:((~happy(X)<~>~generous(X)))))&
(![X]:((~patient(X)|~funny(X))=>(~old(X)|~creative(X))))&
((?[X]:((~kind(X)&~humble(X))))=>(?[X]:(rich(X))))&
(![X]:((~rich(X)|~quiet(X))=>(~tall(X)&rich(X))))&
((?[X]:((curious(X)|~happy(X))))<=>(?[X]:((generous(X)|~generous(X)))))&
(![X]:(~tall(X)<=>(~funny(X)|~old(X))))&
(![X]:((creative(X)|rich(X))<=>~quiet(X)))&
((~generous(john)|~creative(john)))&
(?[X]:((~curious(X)<~>generous(X))))&
((~humble(alice)<~>~creative(alice)))&
((patient(alice)|~tall(alice)))&
(?[X]:((brave(X)<~>~wise(X))))&
(~happy(alice)) | ~quiet(alice) | [
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3919997084462793934756573
% SZS output start Proof for 3919997084462793934756573
13. ! [X0] : ((~quiet(X0) | ~rich(X0)) => (rich(X0) & ~tall(X0))) [input p12]
16. ! [X0] : ((rich(X0) | creative(X0)) <=> ~quiet(X0)) [input p15]
23. quiet(alice) [input hypothesis]
38. ! [X0] : ((rich(X0) & ~tall(X0)) | (quiet(X0) & rich(X0))) [ennf transformation 13]
66. ! [X0] : (((rich(X0) | creative(X0)) | quiet(X0)) & (~quiet(X0) | (~rich(X0) & ~creative(X0)))) [nnf transformation 16]
67. ! [X0] : ((rich(X0) | creative(X0) | quiet(X0)) & (~quiet(X0) | (~rich(X0) & ~creative(X0)))) [flattening 66]
113. rich(X0) | rich(X0) [cnf transformation 38]
123. ~quiet(X0) | ~rich(X0) [cnf transformation 67]
134. quiet(alice) [cnf transformation 23]
135. rich(X0) [duplicate literal removal 113]
248. ~quiet(X0) [subsumption resolution 123,135]
297. $false [subsumption resolution 134,248]
% SZS output end Proof for 3919997084462793934756573
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is rich or quiet then someone is quiet or tall and vice versa. Everyone who is both curious and brave is not wise. If someone is both not brave and not old then john is both happy and not happy. Everyone who is not wise is both not tall and not funny and vice versa. Everyone who is not humble is either calm or happy. Everyone who is not funny or kind is both tall and not kind and vice versa. Everyone who is not humble is curious and vice versa. Everyone who is both not kind and not generous is both kind and not calm and vice versa. Everyone who is not strong or not rich is either generous or brave and vice versa. Everyone who is generous is either not humble or generous. Everyone who is both not old and not generous is not old or tall. If someone is either not old or happy then fred is not patient and vice versa. If john is not patient then someone is not quiet or patient and vice versa. If someone is both not tall and not humble then someone is either funny or not quiet and vice versa. If fred is either calm or not wise then someone is both not old and tall. If someone is not wise then susan is both strong and old and vice versa. John is either not calm or curious. Someone is not quiet. Someone is not rich or tall. Paul is either strong or generous. Alice is both brave and not old. Paul is either not patient or not strong. | Fred is not generous. | contradiction | (((rich(john)|quiet(john)))<=>(?[X]:((quiet(X)|tall(X)))))&
(![X]:((curious(X)&brave(X))=>~wise(X)))&
((?[X]:((~brave(X)&~old(X))))=>((happy(john)&~happy(john))))&
(![X]:(~wise(X)<=>(~tall(X)&~funny(X))))&
(![X]:(~humble(X)=>(calm(X)<~>happy(X))))&
(![X]:((~funny(X)|kind(X))<=>(tall(X)&~kind(X))))&
(![X]:(~humble(X)<=>curious(X)))&
(![X]:((~kind(X)&~generous(X))<=>(kind(X)&~calm(X))))&
(![X]:((~strong(X)|~rich(X))<=>(generous(X)<~>brave(X))))&
(![X]:(generous(X)=>(~humble(X)<~>generous(X))))&
(![X]:((~old(X)&~generous(X))=>(~old(X)|tall(X))))&
((?[X]:((~old(X)<~>happy(X))))<=>(~patient(fred)))&
((~patient(john))<=>(?[X]:((~quiet(X)|patient(X)))))&
((?[X]:((~tall(X)&~humble(X))))<=>(?[X]:((funny(X)<~>~quiet(X)))))&
(((calm(fred)<~>~wise(fred)))=>(?[X]:((~old(X)&tall(X)))))&
((?[X]:(~wise(X)))<=>((strong(susan)&old(susan))))&
((~calm(john)<~>curious(john)))&
(?[X]:(~quiet(X)))&
(?[X]:((~rich(X)|tall(X))))&
((strong(paul)<~>generous(paul)))&
((brave(alice)&~old(alice)))&
((~patient(paul)<~>~strong(paul))) | ~generous(fred) | [
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 598663440417687661410806
% SZS output start Proof for 598663440417687661410806
6. ! [X0] : ((kind(X0) | ~funny(X0)) <=> (~kind(X0) & tall(X0))) [input p5]
8. ! [X0] : ((~generous(X0) & ~kind(X0)) <=> (~calm(X0) & kind(X0))) [input p7]
23. ~generous(fred) [input hypothesis]
41. ! [X0] : (((kind(X0) | ~funny(X0)) | (kind(X0) | ~tall(X0))) & ((~kind(X0) & tall(X0)) | (~kind(X0) & funny(X0)))) [nnf transformation 6]
42. ! [X0] : ((kind(X0) | ~funny(X0) | kind(X0) | ~tall(X0)) & ((~kind(X0) & tall(X0)) | (~kind(X0) & funny(X0)))) [flattening 41]
44. ! [X0] : (((~generous(X0) & ~kind(X0)) | (calm(X0) | ~kind(X0))) & ((~calm(X0) & kind(X0)) | (generous(X0) | kind(X0)))) [nnf transformation 8]
45. ! [X0] : (((~generous(X0) & ~kind(X0)) | calm(X0) | ~kind(X0)) & ((~calm(X0) & kind(X0)) | generous(X0) | kind(X0))) [flattening 44]
92. ~kind(X0) | ~kind(X0) [cnf transformation 42]
96. kind(X0) | generous(X0) | kind(X0) [cnf transformation 45]
139. ~generous(fred) [cnf transformation 23]
141. kind(X0) | generous(X0) [duplicate literal removal 96]
143. ~kind(X0) [duplicate literal removal 92]
181. generous(X0) [subsumption resolution 141,143]
290. $false [subsumption resolution 139,181]
% SZS output end Proof for 598663440417687661410806
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both generous and quiet then susan is quiet. Everyone who is either calm or not humble is not strong or not quiet. Everyone who is humble is tall and vice versa. If susan is creative or not creative then someone is either not quiet or calm and vice versa. If someone is calm then someone is both old and tall and vice versa. If someone is either patient or quiet then fred is not quiet or not strong and vice versa. Everyone who is either not brave or humble is both not calm and not humble and vice versa. If john is both not quiet and creative then someone is kind or patient and vice versa. If fred is generous then someone is not old or not kind and vice versa. If lucy is either not humble or not quiet then fred is not happy or not rich. If someone is both curious and not quiet then someone is strong and vice versa. Everyone who is either not funny or generous is generous or brave and vice versa. Everyone who is both not quiet and creative is rich. Everyone who is not old or not curious is both not tall and not calm. Everyone who is either not rich or tall is both strong and kind and vice versa. Everyone who is either not creative or creative is not quiet and vice versa. Someone is both creative and not calm. Someone is both not quiet and not patient. Fred is not strong or not creative. Mary is generous. Someone is both not tall and not brave. Lucy is either wise or not kind. Someone is both generous and humble. Someone is either wise or not kind. | Lucy is generous. | neutral | (((generous(susan)&quiet(susan)))=>(quiet(susan)))&
(![X]:((calm(X)<~>~humble(X))=>(~strong(X)|~quiet(X))))&
(![X]:(humble(X)<=>tall(X)))&
(((creative(susan)|~creative(susan)))<=>(?[X]:((~quiet(X)<~>calm(X)))))&
((?[X]:(calm(X)))<=>(?[X]:((old(X)&tall(X)))))&
((?[X]:((patient(X)<~>quiet(X))))<=>((~quiet(fred)|~strong(fred))))&
(![X]:((~brave(X)<~>humble(X))<=>(~calm(X)&~humble(X))))&
(((~quiet(john)&creative(john)))<=>(?[X]:((kind(X)|patient(X)))))&
((generous(fred))<=>(?[X]:((~old(X)|~kind(X)))))&
(((~humble(lucy)<~>~quiet(lucy)))=>((~happy(fred)|~rich(fred))))&
((?[X]:((curious(X)&~quiet(X))))<=>(?[X]:(strong(X))))&
(![X]:((~funny(X)<~>generous(X))<=>(generous(X)|brave(X))))&
(![X]:((~quiet(X)&creative(X))=>rich(X)))&
(![X]:((~old(X)|~curious(X))=>(~tall(X)&~calm(X))))&
(![X]:((~rich(X)<~>tall(X))<=>(strong(X)&kind(X))))&
(![X]:((~creative(X)<~>creative(X))<=>~quiet(X)))&
(?[X]:((creative(X)&~calm(X))))&
(?[X]:((~quiet(X)&~patient(X))))&
((~strong(fred)|~creative(fred)))&
(generous(mary))&
(?[X]:((~tall(X)&~brave(X))))&
((wise(lucy)<~>~kind(lucy)))&
(?[X]:((generous(X)&humble(X))))&
(?[X]:((wise(X)<~>~kind(X)))) | generous(lucy) | [] | null | 0 |
If paul is not calm then someone is both not funny and generous and vice versa.
If someone is both kind and rich then someone is either happy or not wise and vice versa.
Everyone who is kind or not happy is both quiet and not calm.
Everyone who is not happy or humble is both not happy and not creative and vice versa.
If someone is both tall and happy then someone is not humble or generous and vice versa.
Everyone who is rich or tall is both not creative and not funny and vice versa.
If someone is both not rich and generous then someone is old or generous.
If someone is not patient then mary is old.
If someone is either humble or not calm then john is either brave or old.
Everyone who is kind or not happy is both curious and not wise.
If someone is not humble or not creative then fred is both curious and happy and vice versa.
Everyone who is not happy is generous.
Everyone who is either creative or calm is wise.
If fred is either brave or generous then someone is strong.
If someone is both not rich and calm then susan is not rich or not patient and vice versa.
Everyone who is funny is both not curious and not brave and vice versa.
Someone is brave or not calm.
Someone is not kind.
Someone is either rich or funny.
Someone is either not generous or generous.
Someone is not tall or not generous.
Mary is either quiet or old.
Susan is either humble or not strong.
Mary is both not humble and creative. | Fred is not funny. | entailment | ((~calm(paul))<=>(?[X]:((~funny(X)&generous(X)))))&
((?[X]:((kind(X)&rich(X))))<=>(?[X]:((happy(X)<~>~wise(X)))))&
(![X]:((kind(X)|~happy(X))=>(quiet(X)&~calm(X))))&
(![X]:((~happy(X)|humble(X))<=>(~happy(X)&~creative(X))))&
((?[X]:((tall(X)&happy(X))))<=>(?[X]:((~humble(X)|generous(X)))))&
(![X]:((rich(X)|tall(X))<=>(~creative(X)&~funny(X))))&
((?[X]:((~rich(X)&generous(X))))=>(?[X]:((old(X)|generous(X)))))&
((?[X]:(~patient(X)))=>(old(mary)))&
((?[X]:((humble(X)<~>~calm(X))))=>((brave(john)<~>old(john))))&
(![X]:((kind(X)|~happy(X))=>(curious(X)&~wise(X))))&
((?[X]:((~humble(X)|~creative(X))))<=>((curious(fred)&happy(fred))))&
(![X]:(~happy(X)=>generous(X)))&
(![X]:((creative(X)<~>calm(X))=>wise(X)))&
(((brave(fred)<~>generous(fred)))=>(?[X]:(strong(X))))&
((?[X]:((~rich(X)&calm(X))))<=>((~rich(susan)|~patient(susan))))&
(![X]:(funny(X)<=>(~curious(X)&~brave(X))))&
(?[X]:((brave(X)|~calm(X))))&
(?[X]:(~kind(X)))&
(?[X]:((rich(X)<~>funny(X))))&
(?[X]:((~generous(X)<~>generous(X))))&
(?[X]:((~tall(X)|~generous(X))))&
((quiet(mary)<~>old(mary)))&
((humble(susan)<~>~strong(susan)))&
((~humble(mary)&creative(mary))) | ~funny(fred) | [
"p10",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7665618853900895792484853
% SZS output start Proof for 7665618853900895792484853
11. ? [X0] : (~creative(X0) | ~humble(X0)) <=> (happy(fred) & curious(fred)) [input p10]
16. ! [X0] : (funny(X0) <=> (~brave(X0) & ~curious(X0))) [input p15]
24. creative(mary) & ~humble(mary) [input p23]
25. funny(fred) [input hypothesis]
59. (? [X0] : (~creative(X0) | ~humble(X0)) | (~happy(fred) | ~curious(fred))) & ((happy(fred) & curious(fred)) | ! [X0] : (creative(X0) & humble(X0))) [nnf transformation 11]
60. (? [X0] : (~creative(X0) | ~humble(X0)) | ~happy(fred) | ~curious(fred)) & ((happy(fred) & curious(fred)) | ! [X0] : (creative(X0) & humble(X0))) [flattening 59]
61. (? [X0] : (~creative(X0) | ~humble(X0)) | ~happy(fred) | ~curious(fred)) & ((happy(fred) & curious(fred)) | ! [X1] : (creative(X1) & humble(X1))) [rectify 60]
62. ? [X0] : (~creative(X0) | ~humble(X0)) => (~creative(sK6) | ~humble(sK6)) [choice axiom]
63. ((~creative(sK6) | ~humble(sK6)) | ~happy(fred) | ~curious(fred)) & ((happy(fred) & curious(fred)) | ! [X1] : (creative(X1) & humble(X1))) [skolemisation 61,62]
73. ! [X0] : ((funny(X0) | (brave(X0) | curious(X0))) & ((~brave(X0) & ~curious(X0)) | ~funny(X0))) [nnf transformation 16]
74. ! [X0] : ((funny(X0) | brave(X0) | curious(X0)) & ((~brave(X0) & ~curious(X0)) | ~funny(X0))) [flattening 73]
127. curious(fred) | humble(X1) [cnf transformation 63]
142. ~curious(X0) | ~funny(X0) [cnf transformation 74]
156. ~humble(mary) [cnf transformation 24]
158. funny(fred) [cnf transformation 25]
217. 14 <=> ! [X1] : humble(X1) [avatar definition]
218. humble(X1) <- (14) [avatar component clause 217]
286. 30 <=> curious(fred) [avatar definition]
288. curious(fred) <- (30) [avatar component clause 286]
290. 14 | 30 [avatar split clause 127,286,217]
376. $false <- (14) [resolution 218,156]
377. ~14 [avatar contradiction clause 376]
394. ~funny(fred) <- (30) [resolution 142,288]
396. $false <- (30) [subsumption resolution 394,158]
397. ~30 [avatar contradiction clause 396]
398. $false [avatar sat refutation 290,377,397]
% SZS output end Proof for 7665618853900895792484853
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and rich is either brave or not wise. If someone is not tall or patient then susan is both not patient and not happy. Everyone who is not quiet is not patient and vice versa. If someone is both not curious and not patient then someone is not old and vice versa. Everyone who is either kind or not brave is either creative or not creative and vice versa. If susan is both not old and not rich then lucy is either quiet or not calm and vice versa. If someone is not rich or brave then someone is both strong and happy and vice versa. If alice is quiet then someone is both kind and strong. Everyone who is not calm or not happy is not creative or tall. Everyone who is not curious is both patient and not strong and vice versa. If fred is funny then someone is either patient or humble. If lucy is both happy and not quiet then someone is both happy and calm. If someone is both rich and old then lucy is either kind or curious. Everyone who is both rich and not generous is happy. Everyone who is either not kind or happy is both calm and not kind and vice versa. Everyone who is not rich or wise is both curious and not tall and vice versa. Someone is wise or strong. John is wise or not strong. John is both brave and not creative. Someone is either humble or patient. Fred is not calm or not old. Lucy is both not creative and kind. Someone is wise or not old. | Susan is not old. | contradiction | (![X]:((tall(X)&rich(X))=>(brave(X)<~>~wise(X))))&
((?[X]:((~tall(X)|patient(X))))=>((~patient(susan)&~happy(susan))))&
(![X]:(~quiet(X)<=>~patient(X)))&
((?[X]:((~curious(X)&~patient(X))))<=>(?[X]:(~old(X))))&
(![X]:((kind(X)<~>~brave(X))<=>(creative(X)<~>~creative(X))))&
(((~old(susan)&~rich(susan)))<=>((quiet(lucy)<~>~calm(lucy))))&
((?[X]:((~rich(X)|brave(X))))<=>(?[X]:((strong(X)&happy(X)))))&
((quiet(alice))=>(?[X]:((kind(X)&strong(X)))))&
(![X]:((~calm(X)|~happy(X))=>(~creative(X)|tall(X))))&
(![X]:(~curious(X)<=>(patient(X)&~strong(X))))&
((funny(fred))=>(?[X]:((patient(X)<~>humble(X)))))&
(((happy(lucy)&~quiet(lucy)))=>(?[X]:((happy(X)&calm(X)))))&
((?[X]:((rich(X)&old(X))))=>((kind(lucy)<~>curious(lucy))))&
(![X]:((rich(X)&~generous(X))=>happy(X)))&
(![X]:((~kind(X)<~>happy(X))<=>(calm(X)&~kind(X))))&
(![X]:((~rich(X)|wise(X))<=>(curious(X)&~tall(X))))&
(?[X]:((wise(X)|strong(X))))&
((wise(john)|~strong(john)))&
((brave(john)&~creative(john)))&
(?[X]:((humble(X)<~>patient(X))))&
((~calm(fred)|~old(fred)))&
((~creative(lucy)&kind(lucy)))&
(?[X]:((wise(X)|~old(X)))) | ~old(susan) | [
"p3",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8082779762285831971295514
% SZS output start Proof for 8082779762285831971295514
4. ? [X0] : (~patient(X0) & ~curious(X0)) <=> ? [X0] : ~old(X0) [input p3]
10. ! [X0] : (~curious(X0) <=> (~strong(X0) & patient(X0))) [input p9]
24. ~old(susan) [input hypothesis]
25. ? [X0] : (~patient(X0) & ~curious(X0)) <=> ? [X1] : ~old(X1) [rectify 4]
40. (? [X0] : (~patient(X0) & ~curious(X0)) | ! [X1] : old(X1)) & (? [X1] : ~old(X1) | ! [X0] : (patient(X0) | curious(X0))) [nnf transformation 25]
41. (? [X0] : (~patient(X0) & ~curious(X0)) | ! [X1] : old(X1)) & (? [X2] : ~old(X2) | ! [X3] : (patient(X3) | curious(X3))) [rectify 40]
42. ? [X0] : (~patient(X0) & ~curious(X0)) => (~patient(sK0) & ~curious(sK0)) [choice axiom]
43. ? [X2] : ~old(X2) => ~old(sK1) [choice axiom]
44. ((~patient(sK0) & ~curious(sK0)) | ! [X1] : old(X1)) & (~old(sK1) | ! [X3] : (patient(X3) | curious(X3))) [skolemisation 41,43,42]
55. ! [X0] : ((~curious(X0) | (strong(X0) | ~patient(X0))) & ((~strong(X0) & patient(X0)) | curious(X0))) [nnf transformation 10]
56. ! [X0] : ((~curious(X0) | strong(X0) | ~patient(X0)) & ((~strong(X0) & patient(X0)) | curious(X0))) [flattening 55]
80. ~curious(sK0) | old(X1) [cnf transformation 44]
81. ~patient(sK0) | old(X1) [cnf transformation 44]
105. patient(X0) | curious(X0) [cnf transformation 56]
133. ~old(susan) [cnf transformation 24]
159. 5 <=> ! [X1] : old(X1) [avatar definition]
160. old(X1) <- (5) [avatar component clause 159]
162. 6 <=> patient(sK0) [avatar definition]
165. 5 | ~6 [avatar split clause 81,162,159]
167. 7 <=> curious(sK0) [avatar definition]
169. ~curious(sK0) <- (~7) [avatar component clause 167]
170. 5 | ~7 [avatar split clause 80,167,159]
172. 8 <=> ! [X3] : (patient(X3) | curious(X3)) [avatar definition]
173. curious(X3) | patient(X3) <- (8) [avatar component clause 172]
196. 13 <=> old(susan) [avatar definition]
198. ~old(susan) <- (~13) [avatar component clause 196]
247. 8 [avatar split clause 105,172]
322. ~13 [avatar split clause 133,196]
335. patient(sK0) <- (~7, 8) [resolution 173,169]
339. 6 | 7 | ~8 [avatar split clause 335,172,167,162]
340. $false <- (5, ~13) [resolution 160,198]
343. ~5 | 13 [avatar contradiction clause 340]
344. $false [avatar sat refutation 165,170,247,322,339,343]
% SZS output end Proof for 8082779762285831971295514
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both not tall and not patient then someone is either wise or not wise and vice versa.
If paul is both strong and rich then someone is both curious and not kind and vice versa.
If lucy is both curious and not funny then susan is either not generous or happy.
Everyone who is not tall or kind is both not calm and quiet.
If someone is both old and creative then someone is both not calm and strong and vice versa.
Everyone who is tall is not quiet.
Everyone who is not patient or funny is brave or not patient and vice versa.
Everyone who is either not rich or not strong is not tall or quiet.
Everyone who is old or creative is not tall.
Everyone who is not patient or not curious is either not rich or not humble and vice versa.
Everyone who is either rich or not calm is not wise and vice versa.
Everyone who is not old is both not happy and not funny and vice versa.
Everyone who is both not rich and not quiet is rich and vice versa.
Everyone who is kind or not curious is either not generous or not patient.
If someone is not funny or old then someone is either generous or not curious.
Everyone who is curious or not quiet is not calm or not happy and vice versa.
Fred is both brave and not strong.
Someone is either old or calm.
Someone is both not calm and old.
Paul is funny.
Paul is not calm.
Someone is strong.
Fred is either creative or strong. | Fred is curious. | entailment | (((~tall(fred)&~patient(fred)))<=>(?[X]:((wise(X)<~>~wise(X)))))&
(((strong(paul)&rich(paul)))<=>(?[X]:((curious(X)&~kind(X)))))&
(((curious(lucy)&~funny(lucy)))=>((~generous(susan)<~>happy(susan))))&
(![X]:((~tall(X)|kind(X))=>(~calm(X)&quiet(X))))&
((?[X]:((old(X)&creative(X))))<=>(?[X]:((~calm(X)&strong(X)))))&
(![X]:(tall(X)=>~quiet(X)))&
(![X]:((~patient(X)|funny(X))<=>(brave(X)|~patient(X))))&
(![X]:((~rich(X)<~>~strong(X))=>(~tall(X)|quiet(X))))&
(![X]:((old(X)|creative(X))=>~tall(X)))&
(![X]:((~patient(X)|~curious(X))<=>(~rich(X)<~>~humble(X))))&
(![X]:((rich(X)<~>~calm(X))<=>~wise(X)))&
(![X]:(~old(X)<=>(~happy(X)&~funny(X))))&
(![X]:((~rich(X)&~quiet(X))<=>rich(X)))&
(![X]:((kind(X)|~curious(X))=>(~generous(X)<~>~patient(X))))&
((?[X]:((~funny(X)|old(X))))=>(?[X]:((generous(X)<~>~curious(X)))))&
(![X]:((curious(X)|~quiet(X))<=>(~calm(X)|~happy(X))))&
((brave(fred)&~strong(fred)))&
(?[X]:((old(X)<~>calm(X))))&
(?[X]:((~calm(X)&old(X))))&
(funny(paul))&
(~calm(paul))&
(?[X]:(strong(X)))&
((creative(fred)<~>strong(fred))) | curious(fred) | [
"p3",
"p5",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 950559188571057736500350
% SZS output start Proof for 950559188571057736500350
4. ! [X0] : ((kind(X0) | ~tall(X0)) => (quiet(X0) & ~calm(X0))) [input p3]
6. ! [X0] : (tall(X0) => ~quiet(X0)) [input p5]
13. ! [X0] : ((~quiet(X0) & ~rich(X0)) <=> rich(X0)) [input p12]
16. ! [X0] : ((~quiet(X0) | curious(X0)) <=> (~happy(X0) | ~calm(X0))) [input p15]
24. ~curious(fred) [input hypothesis]
29. ! [X0] : ((quiet(X0) & ~calm(X0)) | (~kind(X0) & tall(X0))) [ennf transformation 4]
30. ! [X0] : (~quiet(X0) | ~tall(X0)) [ennf transformation 6]
60. ! [X0] : (((~quiet(X0) & ~rich(X0)) | ~rich(X0)) & (rich(X0) | (quiet(X0) | rich(X0)))) [nnf transformation 13]
61. ! [X0] : (((~quiet(X0) & ~rich(X0)) | ~rich(X0)) & (rich(X0) | quiet(X0) | rich(X0))) [flattening 60]
67. ! [X0] : (((~quiet(X0) | curious(X0)) | (happy(X0) & calm(X0))) & ((~happy(X0) | ~calm(X0)) | (quiet(X0) & ~curious(X0)))) [nnf transformation 16]
68. ! [X0] : ((~quiet(X0) | curious(X0) | (happy(X0) & calm(X0))) & (~happy(X0) | ~calm(X0) | (quiet(X0) & ~curious(X0)))) [flattening 67]
89. ~calm(X0) | tall(X0) [cnf transformation 29]
97. ~quiet(X0) | ~tall(X0) [cnf transformation 30]
119. rich(X0) | quiet(X0) | rich(X0) [cnf transformation 61]
120. ~rich(X0) | ~rich(X0) [cnf transformation 61]
132. ~quiet(X0) | curious(X0) | calm(X0) [cnf transformation 68]
145. ~curious(fred) [cnf transformation 24]
146. rich(X0) | quiet(X0) [duplicate literal removal 119]
147. ~rich(X0) [duplicate literal removal 120]
239. quiet(X0) [subsumption resolution 146,147]
259. calm(X0) | curious(X0) [subsumption resolution 132,239]
272. ~tall(X1) [resolution 97,239]
293. curious(X1) | tall(X1) [resolution 259,89]
298. curious(X1) [subsumption resolution 293,272]
300. $false [resolution 298,145]
% SZS output end Proof for 950559188571057736500350
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and not strong then someone is either wise or calm.
Everyone who is either not humble or brave is not old and vice versa.
Everyone who is not humble or not funny is both patient and not wise.
If someone is patient or strong then someone is patient.
Everyone who is both patient and not humble is either not curious or humble and vice versa.
If lucy is both funny and not wise then alice is either not quiet or wise and vice versa.
Everyone who is either not funny or rich is both patient and funny and vice versa.
Everyone who is both wise and not patient is not calm or wise and vice versa.
Everyone who is strong is not rich or not strong.
Everyone who is generous is not patient and vice versa.
Everyone who is generous or not curious is generous or rich.
If mary is either strong or generous then mary is not funny or not tall.
If mary is not calm then alice is both happy and wise and vice versa.
Everyone who is both not wise and humble is kind or not kind.
If someone is tall then lucy is not wise and vice versa.
If someone is tall then lucy is kind or humble.
Lucy is humble or funny.
Someone is both wise and not tall.
Susan is both not curious and quiet.
Alice is both not kind and not calm.
Someone is either not rich or not old.
Mary is both not calm and not old.
Someone is old or not tall.
Someone is not curious or not patient. | Susan is not humble. | neutral | (((~funny(susan)&~strong(susan)))=>(?[X]:((wise(X)<~>calm(X)))))&
(![X]:((~humble(X)<~>brave(X))<=>~old(X)))&
(![X]:((~humble(X)|~funny(X))=>(patient(X)&~wise(X))))&
((?[X]:((patient(X)|strong(X))))=>(?[X]:(patient(X))))&
(![X]:((patient(X)&~humble(X))<=>(~curious(X)<~>humble(X))))&
(((funny(lucy)&~wise(lucy)))<=>((~quiet(alice)<~>wise(alice))))&
(![X]:((~funny(X)<~>rich(X))<=>(patient(X)&funny(X))))&
(![X]:((wise(X)&~patient(X))<=>(~calm(X)|wise(X))))&
(![X]:(strong(X)=>(~rich(X)|~strong(X))))&
(![X]:(generous(X)<=>~patient(X)))&
(![X]:((generous(X)|~curious(X))=>(generous(X)|rich(X))))&
(((strong(mary)<~>generous(mary)))=>((~funny(mary)|~tall(mary))))&
((~calm(mary))<=>((happy(alice)&wise(alice))))&
(![X]:((~wise(X)&humble(X))=>(kind(X)|~kind(X))))&
((?[X]:(tall(X)))<=>(~wise(lucy)))&
((?[X]:(tall(X)))=>((kind(lucy)|humble(lucy))))&
((humble(lucy)|funny(lucy)))&
(?[X]:((wise(X)&~tall(X))))&
((~curious(susan)&quiet(susan)))&
((~kind(alice)&~calm(alice)))&
(?[X]:((~rich(X)<~>~old(X))))&
((~calm(mary)&~old(mary)))&
(?[X]:((old(X)|~tall(X))))&
(?[X]:((~curious(X)|~patient(X)))) | ~humble(susan) | [] | null | 0 |
If john is not patient then someone is not brave or not humble and vice versa.
If someone is either not calm or rich then someone is not kind.
Everyone who is not generous is not funny or not creative.
Everyone who is either not creative or not patient is either curious or not calm and vice versa.
Everyone who is either not strong or humble is patient.
If someone is kind or happy then lucy is both funny and not humble.
If paul is funny or quiet then alice is both funny and not generous.
If someone is old or creative then fred is not brave and vice versa.
If someone is not wise then someone is both not patient and not funny.
Everyone who is not generous is either not old or not wise.
If lucy is not brave then lucy is patient and vice versa.
Everyone who is not humble or not rich is not happy or quiet.
Everyone who is either patient or not rich is both not tall and not old.
Everyone who is either rich or not rich is funny or patient and vice versa.
Everyone who is curious is not generous.
Someone is kind or generous.
Alice is not calm or not humble.
Someone is either not creative or not kind.
Someone is both not quiet and not old.
Someone is patient or not wise.
Someone is wise or happy. | John is not patient. | entailment | ((~patient(john))<=>(?[X]:((~brave(X)|~humble(X)))))&
((?[X]:((~calm(X)<~>rich(X))))=>(?[X]:(~kind(X))))&
(![X]:(~generous(X)=>(~funny(X)|~creative(X))))&
(![X]:((~creative(X)<~>~patient(X))<=>(curious(X)<~>~calm(X))))&
(![X]:((~strong(X)<~>humble(X))=>patient(X)))&
((?[X]:((kind(X)|happy(X))))=>((funny(lucy)&~humble(lucy))))&
(((funny(paul)|quiet(paul)))=>((funny(alice)&~generous(alice))))&
((?[X]:((old(X)|creative(X))))<=>(~brave(fred)))&
((?[X]:(~wise(X)))=>(?[X]:((~patient(X)&~funny(X)))))&
(![X]:(~generous(X)=>(~old(X)<~>~wise(X))))&
((~brave(lucy))<=>(patient(lucy)))&
(![X]:((~humble(X)|~rich(X))=>(~happy(X)|quiet(X))))&
(![X]:((patient(X)<~>~rich(X))=>(~tall(X)&~old(X))))&
(![X]:((rich(X)<~>~rich(X))<=>(funny(X)|patient(X))))&
(![X]:(curious(X)=>~generous(X)))&
(?[X]:((kind(X)|generous(X))))&
((~calm(alice)|~humble(alice)))&
(?[X]:((~creative(X)<~>~kind(X))))&
(?[X]:((~quiet(X)&~old(X))))&
(?[X]:((patient(X)|~wise(X))))&
(?[X]:((wise(X)|happy(X)))) | ~patient(john) | [
"p0",
"p5",
"p7",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3387199121025471705606634
% SZS output start Proof for 3387199121025471705606634
1. ~patient(john) <=> ? [X0] : (~humble(X0) | ~brave(X0)) [input p0]
6. ? [X0] : (happy(X0) | kind(X0)) => (~humble(lucy) & funny(lucy)) [input p5]
8. ? [X0] : (creative(X0) | old(X0)) <=> ~brave(fred) [input p7]
18. ? [X0] : (~creative(X0) <~> ~kind(X0)) [input p17]
22. patient(john) [input hypothesis]
30. (~humble(lucy) & funny(lucy)) | ! [X0] : (~happy(X0) & ~kind(X0)) [ennf transformation 6]
38. (~patient(john) | ! [X0] : (humble(X0) & brave(X0))) & (? [X0] : (~humble(X0) | ~brave(X0)) | patient(john)) [nnf transformation 1]
39. (~patient(john) | ! [X0] : (humble(X0) & brave(X0))) & (? [X1] : (~humble(X1) | ~brave(X1)) | patient(john)) [rectify 38]
40. ? [X1] : (~humble(X1) | ~brave(X1)) => (~humble(sK0) | ~brave(sK0)) [choice axiom]
41. (~patient(john) | ! [X0] : (humble(X0) & brave(X0))) & ((~humble(sK0) | ~brave(sK0)) | patient(john)) [skolemisation 39,40]
48. (? [X0] : (creative(X0) | old(X0)) | brave(fred)) & (~brave(fred) | ! [X0] : (~creative(X0) & ~old(X0))) [nnf transformation 8]
49. (? [X0] : (creative(X0) | old(X0)) | brave(fred)) & (~brave(fred) | ! [X1] : (~creative(X1) & ~old(X1))) [rectify 48]
50. ? [X0] : (creative(X0) | old(X0)) => (creative(sK2) | old(sK2)) [choice axiom]
51. ((creative(sK2) | old(sK2)) | brave(fred)) & (~brave(fred) | ! [X1] : (~creative(X1) & ~old(X1))) [skolemisation 49,50]
62. ? [X0] : ((kind(X0) | creative(X0)) & (~kind(X0) | ~creative(X0))) [nnf transformation 18]
63. ? [X0] : ((kind(X0) | creative(X0)) & (~kind(X0) | ~creative(X0))) => ((kind(sK5) | creative(sK5)) & (~kind(sK5) | ~creative(sK5))) [choice axiom]
64. (kind(sK5) | creative(sK5)) & (~kind(sK5) | ~creative(sK5)) [skolemisation 62,63]
72. ~patient(john) | brave(X0) [cnf transformation 41]
73. ~patient(john) | humble(X0) [cnf transformation 41]
89. ~humble(lucy) | ~kind(X0) [cnf transformation 30]
96. ~brave(fred) | ~creative(X1) [cnf transformation 51]
118. kind(sK5) | creative(sK5) [cnf transformation 64]
123. patient(john) [cnf transformation 22]
127. 1 <=> ! [X0] : humble(X0) [avatar definition]
128. humble(X0) <- (1) [avatar component clause 127]
130. 2 <=> patient(john) [avatar definition]
133. 1 | ~2 [avatar split clause 73,130,127]
135. 3 <=> ! [X0] : brave(X0) [avatar definition]
136. brave(X0) <- (3) [avatar component clause 135]
137. 3 | ~2 [avatar split clause 72,130,135]
163. 10 <=> humble(lucy) [avatar definition]
165. ~humble(lucy) <- (~10) [avatar component clause 163]
168. 11 <=> ! [X0] : ~kind(X0) [avatar definition]
169. ~kind(X0) <- (11) [avatar component clause 168]
170. 11 | ~10 [avatar split clause 89,163,168]
198. 17 <=> brave(fred) [avatar definition]
199. ~brave(fred) <- (~17) [avatar component clause 198]
211. 20 <=> ! [X1] : ~creative(X1) [avatar definition]
212. ~creative(X1) <- (20) [avatar component clause 211]
213. 20 | ~17 [avatar split clause 96,198,211]
261. 31 <=> creative(sK5) [avatar definition]
263. creative(sK5) <- (31) [avatar component clause 261]
265. 32 <=> kind(sK5) [avatar definition]
267. kind(sK5) <- (32) [avatar component clause 265]
268. 31 | 32 [avatar split clause 118,265,261]
288. 2 [avatar split clause 123,130]
289. $false <- (3, ~17) [resolution 199,136]
290. ~3 | 17 [avatar contradiction clause 289]
297. $false <- (1, ~10) [subsumption resolution 165,128]
298. ~1 | 10 [avatar contradiction clause 297]
299. $false <- (20, 31) [resolution 263,212]
300. ~20 | ~31 [avatar contradiction clause 299]
301. $false <- (11, 32) [subsumption resolution 267,169]
302. ~11 | ~32 [avatar contradiction clause 301]
303. $false [avatar sat refutation 133,137,170,213,268,288,290,298,300,302]
% SZS output end Proof for 3387199121025471705606634
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or not humble is generous or not patient and vice versa. Everyone who is either not wise or kind is both kind and not strong. Everyone who is not calm or not funny is creative or tall and vice versa. Everyone who is patient or humble is either funny or tall. Everyone who is both old and not rich is kind. Everyone who is both kind and quiet is not old or strong. Everyone who is humble is either not patient or funny. If lucy is happy or funny then someone is either not funny or humble. If someone is not humble or not kind then alice is happy or rich and vice versa. Everyone who is both rich and not patient is either kind or rich and vice versa. If alice is both calm and not tall then someone is not humble or rich and vice versa. Everyone who is creative is not strong and vice versa. If someone is both rich and curious then someone is calm or creative and vice versa. If alice is either not strong or not tall then someone is either not rich or not funny and vice versa. If mary is creative or not tall then susan is either calm or not curious. Someone is strong or not tall. Someone is either patient or not patient. Someone is either patient or tall. Someone is either not brave or happy. Someone is funny. Someone is either kind or wise. Someone is not tall. Someone is either not old or wise. | Susan is quiet. | neutral | (![X]:((calm(X)<~>~humble(X))<=>(generous(X)|~patient(X))))&
(![X]:((~wise(X)<~>kind(X))=>(kind(X)&~strong(X))))&
(![X]:((~calm(X)|~funny(X))<=>(creative(X)|tall(X))))&
(![X]:((patient(X)|humble(X))=>(funny(X)<~>tall(X))))&
(![X]:((old(X)&~rich(X))=>kind(X)))&
(![X]:((kind(X)&quiet(X))=>(~old(X)|strong(X))))&
(![X]:(humble(X)=>(~patient(X)<~>funny(X))))&
(((happy(lucy)|funny(lucy)))=>(?[X]:((~funny(X)<~>humble(X)))))&
((?[X]:((~humble(X)|~kind(X))))<=>((happy(alice)|rich(alice))))&
(![X]:((rich(X)&~patient(X))<=>(kind(X)<~>rich(X))))&
(((calm(alice)&~tall(alice)))<=>(?[X]:((~humble(X)|rich(X)))))&
(![X]:(creative(X)<=>~strong(X)))&
((?[X]:((rich(X)&curious(X))))<=>(?[X]:((calm(X)|creative(X)))))&
(((~strong(alice)<~>~tall(alice)))<=>(?[X]:((~rich(X)<~>~funny(X)))))&
(((creative(mary)|~tall(mary)))=>((calm(susan)<~>~curious(susan))))&
(?[X]:((strong(X)|~tall(X))))&
(?[X]:((patient(X)<~>~patient(X))))&
(?[X]:((patient(X)<~>tall(X))))&
(?[X]:((~brave(X)<~>happy(X))))&
(?[X]:(funny(X)))&
(?[X]:((kind(X)<~>wise(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~old(X)<~>wise(X)))) | quiet(susan) | [] | null | 0 |
Everyone who is either brave or not rich is not calm.
Everyone who is brave or not tall is brave or strong and vice versa.
If someone is creative then someone is both calm and not calm and vice versa.
Everyone who is quiet is funny or patient.
Everyone who is not happy is either not rich or brave and vice versa.
If someone is either quiet or brave then susan is not patient or not brave.
If someone is both curious and not tall then paul is either not curious or not brave and vice versa.
Everyone who is both not rich and kind is either not funny or creative.
If paul is both not old and quiet then someone is both not quiet and patient.
Everyone who is quiet is creative and vice versa.
Everyone who is not quiet is both not wise and not quiet.
Everyone who is not patient is not quiet.
If someone is both strong and not rich then john is both not tall and not happy.
Everyone who is not brave or not quiet is either strong or happy and vice versa.
If someone is patient or brave then someone is either not patient or not old and vice versa.
Everyone who is quiet or old is patient and vice versa.
Alice is either wise or curious.
Someone is not creative or not strong.
Susan is both not tall and not generous.
Alice is either not funny or strong.
Someone is both not kind and not humble.
Someone is either tall or quiet.
Someone is not humble. | Alice is patient. | contradiction | (![X]:((brave(X)<~>~rich(X))=>~calm(X)))&
(![X]:((brave(X)|~tall(X))<=>(brave(X)|strong(X))))&
((?[X]:(creative(X)))<=>(?[X]:((calm(X)&~calm(X)))))&
(![X]:(quiet(X)=>(funny(X)|patient(X))))&
(![X]:(~happy(X)<=>(~rich(X)<~>brave(X))))&
((?[X]:((quiet(X)<~>brave(X))))=>((~patient(susan)|~brave(susan))))&
((?[X]:((curious(X)&~tall(X))))<=>((~curious(paul)<~>~brave(paul))))&
(![X]:((~rich(X)&kind(X))=>(~funny(X)<~>creative(X))))&
(((~old(paul)&quiet(paul)))=>(?[X]:((~quiet(X)&patient(X)))))&
(![X]:(quiet(X)<=>creative(X)))&
(![X]:(~quiet(X)=>(~wise(X)&~quiet(X))))&
(![X]:(~patient(X)=>~quiet(X)))&
((?[X]:((strong(X)&~rich(X))))=>((~tall(john)&~happy(john))))&
(![X]:((~brave(X)|~quiet(X))<=>(strong(X)<~>happy(X))))&
((?[X]:((patient(X)|brave(X))))<=>(?[X]:((~patient(X)<~>~old(X)))))&
(![X]:((quiet(X)|old(X))<=>patient(X)))&
((wise(alice)<~>curious(alice)))&
(?[X]:((~creative(X)|~strong(X))))&
((~tall(susan)&~generous(susan)))&
((~funny(alice)<~>strong(alice)))&
(?[X]:((~kind(X)&~humble(X))))&
(?[X]:((tall(X)<~>quiet(X))))&
(?[X]:(~humble(X))) | patient(alice) | [
"p2",
"p9",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3862840317056926698533966
% SZS output start Proof for 3862840317056926698533966
3. ? [X0] : creative(X0) <=> ? [X0] : (~calm(X0) & calm(X0)) [input p2]
10. ! [X0] : (quiet(X0) <=> creative(X0)) [input p9]
15. ? [X0] : (brave(X0) | patient(X0)) <=> ? [X0] : (~patient(X0) <~> ~old(X0)) [input p14]
16. ! [X0] : ((old(X0) | quiet(X0)) <=> patient(X0)) [input p15]
24. patient(alice) [input hypothesis]
25. ? [X0] : creative(X0) <=> ? [X1] : (~calm(X1) & calm(X1)) [rectify 3]
26. ? [X0] : (brave(X0) | patient(X0)) <=> ? [X1] : (~patient(X1) <~> ~old(X1)) [rectify 15]
45. (? [X0] : creative(X0) | ! [X1] : (calm(X1) | ~calm(X1))) & (? [X1] : (~calm(X1) & calm(X1)) | ! [X0] : ~creative(X0)) [nnf transformation 25]
46. (? [X0] : creative(X0) | ! [X1] : (calm(X1) | ~calm(X1))) & (? [X2] : (~calm(X2) & calm(X2)) | ! [X3] : ~creative(X3)) [rectify 45]
47. ? [X0] : creative(X0) => creative(sK0) [choice axiom]
48. ? [X2] : (~calm(X2) & calm(X2)) => (~calm(sK1) & calm(sK1)) [choice axiom]
49. (creative(sK0) | ! [X1] : (calm(X1) | ~calm(X1))) & ((~calm(sK1) & calm(sK1)) | ! [X3] : ~creative(X3)) [skolemisation 46,48,47]
58. ! [X0] : ((quiet(X0) | ~creative(X0)) & (creative(X0) | ~quiet(X0))) [nnf transformation 10]
61. (? [X0] : (brave(X0) | patient(X0)) | ! [X1] : ((~patient(X1) | old(X1)) & (~old(X1) | patient(X1)))) & (? [X1] : ((old(X1) | patient(X1)) & (~old(X1) | ~patient(X1))) | ! [X0] : (~brave(X0) & ~patient(X0))) [nnf transformation 26]
62. (? [X0] : (brave(X0) | patient(X0)) | ! [X1] : ((~patient(X1) | old(X1)) & (~old(X1) | patient(X1)))) & (? [X2] : ((old(X2) | patient(X2)) & (~old(X2) | ~patient(X2))) | ! [X3] : (~brave(X3) & ~patient(X3))) [rectify 61]
63. ? [X0] : (brave(X0) | patient(X0)) => (brave(sK4) | patient(sK4)) [choice axiom]
64. ? [X2] : ((old(X2) | patient(X2)) & (~old(X2) | ~patient(X2))) => ((old(sK5) | patient(sK5)) & (~old(sK5) | ~patient(sK5))) [choice axiom]
65. ((brave(sK4) | patient(sK4)) | ! [X1] : ((~patient(X1) | old(X1)) & (~old(X1) | patient(X1)))) & (((old(sK5) | patient(sK5)) & (~old(sK5) | ~patient(sK5))) | ! [X3] : (~brave(X3) & ~patient(X3))) [skolemisation 62,64,63]
66. ! [X0] : (((old(X0) | quiet(X0)) | ~patient(X0)) & (patient(X0) | (~old(X0) & ~quiet(X0)))) [nnf transformation 16]
67. ! [X0] : ((old(X0) | quiet(X0) | ~patient(X0)) & (patient(X0) | (~old(X0) & ~quiet(X0)))) [flattening 66]
81. calm(sK1) | ~creative(X3) [cnf transformation 49]
82. ~calm(sK1) | ~creative(X3) [cnf transformation 49]
99. ~quiet(X0) | creative(X0) [cnf transformation 58]
112. ~old(sK5) | ~patient(sK5) | ~patient(X3) [cnf transformation 65]
114. old(sK5) | patient(sK5) | ~patient(X3) [cnf transformation 65]
119. patient(X0) | ~old(X0) [cnf transformation 67]
120. ~patient(X0) | quiet(X0) | old(X0) [cnf transformation 67]
129. patient(alice) [cnf transformation 24]
131. 1 <=> ! [X3] : ~creative(X3) [avatar definition]
132. ~creative(X3) <- (1) [avatar component clause 131]
134. 2 <=> calm(sK1) [avatar definition]
137. 1 | ~2 [avatar split clause 82,134,131]
138. 1 | 2 [avatar split clause 81,134,131]
224. 22 <=> ! [X1] : (~old(X1) | patient(X1)) [avatar definition]
225. ~old(X1) | patient(X1) <- (22) [avatar component clause 224]
231. 24 <=> patient(sK5) [avatar definition]
233. patient(sK5) <- (24) [avatar component clause 231]
235. 25 <=> old(sK5) [avatar definition]
236. ~old(sK5) <- (~25) [avatar component clause 235]
237. old(sK5) <- (25) [avatar component clause 235]
240. 26 <=> ! [X3] : ~patient(X3) [avatar definition]
241. ~patient(X3) <- (26) [avatar component clause 240]
242. 26 | 24 | 25 [avatar split clause 114,235,231,240]
244. 26 | ~24 | ~25 [avatar split clause 112,235,231,240]
245. 22 [avatar split clause 119,224]
387. quiet(sK5) | old(sK5) <- (24) [resolution 120,233]
398. quiet(sK5) <- (24, ~25) [subsumption resolution 387,236]
438. creative(sK5) <- (24, ~25) [resolution 398,99]
452. $false <- (1, 24, ~25) [subsumption resolution 438,132]
453. ~1 | ~24 | 25 [avatar contradiction clause 452]
454. patient(sK5) <- (22, 25) [resolution 237,225]
457. 24 | ~22 | ~25 [avatar split clause 454,235,224,231]
468. $false <- (26) [resolution 241,129]
471. ~26 [avatar contradiction clause 468]
472. $false [avatar sat refutation 137,138,242,244,245,453,457,471]
% SZS output end Proof for 3862840317056926698533966
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not brave or not wise then mary is strong or brave. Everyone who is not calm or not funny is not happy or not calm. Everyone who is rich or humble is creative or generous and vice versa. Everyone who is both not strong and not patient is not strong or funny and vice versa. Everyone who is patient or not curious is both curious and not calm and vice versa. If someone is either rich or not old then lucy is either not kind or not strong and vice versa. If fred is both not quiet and not brave then fred is both not tall and quiet. If someone is not tall then mary is either calm or not generous and vice versa. Everyone who is both not generous and creative is not curious and vice versa. If fred is either not happy or not humble then paul is not rich. Everyone who is not patient is quiet or not strong and vice versa. Everyone who is both not curious and not quiet is either not brave or kind and vice versa. If someone is both not generous and not calm then lucy is not curious or not humble. Everyone who is either not tall or not quiet is either creative or not humble and vice versa. Everyone who is either not patient or creative is not kind or not generous. If someone is rich then someone is either not calm or not wise and vice versa. Someone is curious or not brave. Someone is not humble. John is generous or quiet. Someone is either funny or not curious. Fred is not old. Someone is not happy or generous. Susan is both not patient and strong. | Lucy is old. | neutral | (((~brave(john)<~>~wise(john)))=>((strong(mary)|brave(mary))))&
(![X]:((~calm(X)|~funny(X))=>(~happy(X)|~calm(X))))&
(![X]:((rich(X)|humble(X))<=>(creative(X)|generous(X))))&
(![X]:((~strong(X)&~patient(X))<=>(~strong(X)|funny(X))))&
(![X]:((patient(X)|~curious(X))<=>(curious(X)&~calm(X))))&
((?[X]:((rich(X)<~>~old(X))))<=>((~kind(lucy)<~>~strong(lucy))))&
(((~quiet(fred)&~brave(fred)))=>((~tall(fred)&quiet(fred))))&
((?[X]:(~tall(X)))<=>((calm(mary)<~>~generous(mary))))&
(![X]:((~generous(X)&creative(X))<=>~curious(X)))&
(((~happy(fred)<~>~humble(fred)))=>(~rich(paul)))&
(![X]:(~patient(X)<=>(quiet(X)|~strong(X))))&
(![X]:((~curious(X)&~quiet(X))<=>(~brave(X)<~>kind(X))))&
((?[X]:((~generous(X)&~calm(X))))=>((~curious(lucy)|~humble(lucy))))&
(![X]:((~tall(X)<~>~quiet(X))<=>(creative(X)<~>~humble(X))))&
(![X]:((~patient(X)<~>creative(X))=>(~kind(X)|~generous(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~calm(X)<~>~wise(X)))))&
(?[X]:((curious(X)|~brave(X))))&
(?[X]:(~humble(X)))&
((generous(john)|quiet(john)))&
(?[X]:((funny(X)<~>~curious(X))))&
(~old(fred))&
(?[X]:((~happy(X)|generous(X))))&
((~patient(susan)&strong(susan))) | old(lucy) | [] | null | 0 |
Everyone who is both rich and happy is quiet.
If someone is not happy or not calm then someone is patient or tall.
Everyone who is funny is rich or strong and vice versa.
If lucy is not wise or generous then paul is not patient or not happy and vice versa.
Everyone who is calm is either patient or not strong.
If someone is not kind or not calm then someone is not tall or quiet.
If paul is patient or tall then susan is both not generous and patient and vice versa.
Everyone who is not generous is humble or kind and vice versa.
Everyone who is both not curious and not patient is either not generous or not strong and vice versa.
If fred is either generous or not funny then someone is both calm and not funny and vice versa.
If susan is both not rich and not brave then someone is both brave and rich and vice versa.
Everyone who is quiet is not curious.
If someone is either not strong or rich then fred is both old and wise.
If lucy is both not quiet and not happy then someone is either not brave or rich and vice versa.
Everyone who is both wise and not brave is both not humble and quiet.
If someone is generous or calm then mary is both generous and old and vice versa.
Mary is not creative.
Someone is rich or not tall.
Alice is either brave or not strong.
Someone is either calm or not calm.
Alice is both not humble and not curious.
Susan is either not happy or not calm.
Someone is either not wise or not curious. | Lucy is not happy. | neutral | (![X]:((rich(X)&happy(X))=>quiet(X)))&
((?[X]:((~happy(X)|~calm(X))))=>(?[X]:((patient(X)|tall(X)))))&
(![X]:(funny(X)<=>(rich(X)|strong(X))))&
(((~wise(lucy)|generous(lucy)))<=>((~patient(paul)|~happy(paul))))&
(![X]:(calm(X)=>(patient(X)<~>~strong(X))))&
((?[X]:((~kind(X)|~calm(X))))=>(?[X]:((~tall(X)|quiet(X)))))&
(((patient(paul)|tall(paul)))<=>((~generous(susan)&patient(susan))))&
(![X]:(~generous(X)<=>(humble(X)|kind(X))))&
(![X]:((~curious(X)&~patient(X))<=>(~generous(X)<~>~strong(X))))&
(((generous(fred)<~>~funny(fred)))<=>(?[X]:((calm(X)&~funny(X)))))&
(((~rich(susan)&~brave(susan)))<=>(?[X]:((brave(X)&rich(X)))))&
(![X]:(quiet(X)=>~curious(X)))&
((?[X]:((~strong(X)<~>rich(X))))=>((old(fred)&wise(fred))))&
(((~quiet(lucy)&~happy(lucy)))<=>(?[X]:((~brave(X)<~>rich(X)))))&
(![X]:((wise(X)&~brave(X))=>(~humble(X)&quiet(X))))&
((?[X]:((generous(X)|calm(X))))<=>((generous(mary)&old(mary))))&
(~creative(mary))&
(?[X]:((rich(X)|~tall(X))))&
((brave(alice)<~>~strong(alice)))&
(?[X]:((calm(X)<~>~calm(X))))&
((~humble(alice)&~curious(alice)))&
((~happy(susan)<~>~calm(susan)))&
(?[X]:((~wise(X)<~>~curious(X)))) | ~happy(lucy) | [] | null | 0 |
Everyone who is both patient and wise is not creative or not generous and vice versa. If someone is happy or creative then someone is generous. If fred is either tall or strong then john is not rich. Everyone who is both not quiet and quiet is not creative or not rich and vice versa. Everyone who is both not wise and rich is either not tall or not generous and vice versa. If john is either kind or brave then paul is generous. If susan is both not brave and not kind then someone is either not brave or not calm and vice versa. If someone is funny then alice is both not rich and generous and vice versa. If paul is both generous and not curious then someone is not tall or not curious and vice versa. Everyone who is happy is strong and vice versa. Everyone who is not patient or curious is quiet. If fred is both curious and generous then someone is either not humble or not brave. Everyone who is both not generous and curious is not calm or old and vice versa. Everyone who is either not curious or rich is happy or generous and vice versa. Everyone who is humble or wise is either strong or not calm and vice versa. If alice is not wise or wise then someone is not kind or not tall and vice versa. Paul is kind or not funny. Susan is not old. Someone is quiet or strong. | Alice is not happy. | contradiction | (![X]:((patient(X)&wise(X))<=>(~creative(X)|~generous(X))))&
((?[X]:((happy(X)|creative(X))))=>(?[X]:(generous(X))))&
(((tall(fred)<~>strong(fred)))=>(~rich(john)))&
(![X]:((~quiet(X)&quiet(X))<=>(~creative(X)|~rich(X))))&
(![X]:((~wise(X)&rich(X))<=>(~tall(X)<~>~generous(X))))&
(((kind(john)<~>brave(john)))=>(generous(paul)))&
(((~brave(susan)&~kind(susan)))<=>(?[X]:((~brave(X)<~>~calm(X)))))&
((?[X]:(funny(X)))<=>((~rich(alice)&generous(alice))))&
(((generous(paul)&~curious(paul)))<=>(?[X]:((~tall(X)|~curious(X)))))&
(![X]:(happy(X)<=>strong(X)))&
(![X]:((~patient(X)|curious(X))=>quiet(X)))&
(((curious(fred)&generous(fred)))=>(?[X]:((~humble(X)<~>~brave(X)))))&
(![X]:((~generous(X)&curious(X))<=>(~calm(X)|old(X))))&
(![X]:((~curious(X)<~>rich(X))<=>(happy(X)|generous(X))))&
(![X]:((humble(X)|wise(X))<=>(strong(X)<~>~calm(X))))&
(((~wise(alice)|wise(alice)))<=>(?[X]:((~kind(X)|~tall(X)))))&
((kind(paul)|~funny(paul)))&
(~old(susan))&
(?[X]:((quiet(X)|strong(X)))) | ~happy(alice) | [
"p0",
"p3",
"p4",
"p8",
"p9",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1888976298587966491589690
% SZS output start Proof for 1888976298587966491589690
1. ! [X0] : ((wise(X0) & patient(X0)) <=> (~generous(X0) | ~creative(X0))) [input p0]
4. ! [X0] : ((quiet(X0) & ~quiet(X0)) <=> (~rich(X0) | ~creative(X0))) [input p3]
5. ! [X0] : ((rich(X0) & ~wise(X0)) <=> (~tall(X0) <~> ~generous(X0))) [input p4]
9. (~curious(paul) & generous(paul)) <=> ? [X0] : (~curious(X0) | ~tall(X0)) [input p8]
10. ! [X0] : (happy(X0) <=> strong(X0)) [input p9]
13. ! [X0] : ((curious(X0) & ~generous(X0)) <=> (old(X0) | ~calm(X0))) [input p12]
14. ! [X0] : ((~curious(X0) <~> rich(X0)) <=> (generous(X0) | happy(X0))) [input p13]
15. ! [X0] : ((wise(X0) | humble(X0)) <=> (strong(X0) <~> ~calm(X0))) [input p14]
20. ~happy(alice) [input hypothesis]
28. ! [X0] : (((wise(X0) & patient(X0)) | (generous(X0) & creative(X0))) & ((~generous(X0) | ~creative(X0)) | (~wise(X0) | ~patient(X0)))) [nnf transformation 1]
29. ! [X0] : (((wise(X0) & patient(X0)) | (generous(X0) & creative(X0))) & (~generous(X0) | ~creative(X0) | ~wise(X0) | ~patient(X0))) [flattening 28]
34. ! [X0] : (((quiet(X0) & ~quiet(X0)) | (rich(X0) & creative(X0))) & ((~rich(X0) | ~creative(X0)) | (~quiet(X0) | quiet(X0)))) [nnf transformation 4]
35. ! [X0] : (((quiet(X0) & ~quiet(X0)) | (rich(X0) & creative(X0))) & (~rich(X0) | ~creative(X0) | ~quiet(X0) | quiet(X0))) [flattening 34]
36. ! [X0] : (((rich(X0) & ~wise(X0)) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0)))) & (((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | (~rich(X0) | wise(X0)))) [nnf transformation 5]
37. ! [X0] : (((rich(X0) & ~wise(X0)) | ((~tall(X0) | generous(X0)) & (~generous(X0) | tall(X0)))) & (((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | ~rich(X0) | wise(X0))) [flattening 36]
49. ((~curious(paul) & generous(paul)) | ! [X0] : (curious(X0) & tall(X0))) & (? [X0] : (~curious(X0) | ~tall(X0)) | (curious(paul) | ~generous(paul))) [nnf transformation 9]
50. ((~curious(paul) & generous(paul)) | ! [X0] : (curious(X0) & tall(X0))) & (? [X0] : (~curious(X0) | ~tall(X0)) | curious(paul) | ~generous(paul)) [flattening 49]
51. ((~curious(paul) & generous(paul)) | ! [X0] : (curious(X0) & tall(X0))) & (? [X1] : (~curious(X1) | ~tall(X1)) | curious(paul) | ~generous(paul)) [rectify 50]
52. ? [X1] : (~curious(X1) | ~tall(X1)) => (~curious(sK3) | ~tall(sK3)) [choice axiom]
53. ((~curious(paul) & generous(paul)) | ! [X0] : (curious(X0) & tall(X0))) & ((~curious(sK3) | ~tall(sK3)) | curious(paul) | ~generous(paul)) [skolemisation 51,52]
54. ! [X0] : ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0))) [nnf transformation 10]
58. ! [X0] : (((curious(X0) & ~generous(X0)) | (~old(X0) & calm(X0))) & ((old(X0) | ~calm(X0)) | (~curious(X0) | generous(X0)))) [nnf transformation 13]
59. ! [X0] : (((curious(X0) & ~generous(X0)) | (~old(X0) & calm(X0))) & (old(X0) | ~calm(X0) | ~curious(X0) | generous(X0))) [flattening 58]
60. ! [X0] : ((((~rich(X0) | curious(X0)) & (rich(X0) | ~curious(X0))) | (~generous(X0) & ~happy(X0))) & ((generous(X0) | happy(X0)) | ((~curious(X0) | ~rich(X0)) & (rich(X0) | curious(X0))))) [nnf transformation 14]
61. ! [X0] : ((((~rich(X0) | curious(X0)) & (rich(X0) | ~curious(X0))) | (~generous(X0) & ~happy(X0))) & (generous(X0) | happy(X0) | ((~curious(X0) | ~rich(X0)) & (rich(X0) | curious(X0))))) [flattening 60]
62. ! [X0] : (((wise(X0) | humble(X0)) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0)))) & (((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | (~wise(X0) & ~humble(X0)))) [nnf transformation 15]
63. ! [X0] : ((wise(X0) | humble(X0) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0)))) & (((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | (~wise(X0) & ~humble(X0)))) [flattening 62]
75. generous(X0) | wise(X0) [cnf transformation 29]
82. ~quiet(X0) | rich(X0) [cnf transformation 35]
84. quiet(X0) | rich(X0) [cnf transformation 35]
85. ~generous(X0) | ~tall(X0) | ~rich(X0) | wise(X0) [cnf transformation 37]
88. ~wise(X0) | ~tall(X0) | generous(X0) [cnf transformation 37]
103. generous(paul) | tall(X0) [cnf transformation 53]
105. ~curious(paul) | tall(X0) [cnf transformation 53]
108. ~strong(X0) | happy(X0) [cnf transformation 54]
114. ~generous(X0) | calm(X0) [cnf transformation 59]
123. ~rich(X0) | curious(X0) | ~generous(X0) [cnf transformation 61]
125. ~calm(X0) | strong(X0) | ~wise(X0) [cnf transformation 63]
137. ~happy(alice) [cnf transformation 20]
164. rich(X0) [subsumption resolution 82,84]
166. ~tall(X0) | generous(X0) [subsumption resolution 88,75]
167. ~generous(X0) | ~tall(X0) | wise(X0) [subsumption resolution 85,164]
168. ~tall(X0) | wise(X0) [subsumption resolution 167,166]
178. 9 <=> generous(paul) [avatar definition]
180. generous(paul) <- (9) [avatar component clause 178]
225. 19 <=> curious(paul) [avatar definition]
230. 20 <=> ! [X0] : tall(X0) [avatar definition]
231. tall(X0) <- (20) [avatar component clause 230]
232. 20 | ~19 [avatar split clause 105,225,230]
234. 20 | 9 [avatar split clause 103,178,230]
262. ~generous(X0) | curious(X0) [subsumption resolution 123,164]
313. curious(paul) <- (9) [resolution 262,180]
318. 19 | ~9 [avatar split clause 313,178,225]
327. wise(X0) <- (20) [resolution 231,168]
328. generous(X1) <- (20) [resolution 231,166]
341. calm(X2) <- (20) [resolution 328,114]
380. strong(X1) | ~wise(X1) <- (20) [resolution 341,125]
382. strong(X1) <- (20) [subsumption resolution 380,327]
412. happy(X1) <- (20) [resolution 382,108]
420. $false <- (20) [resolution 412,137]
423. ~20 [avatar contradiction clause 420]
424. $false [avatar sat refutation 232,234,318,423]
% SZS output end Proof for 1888976298587966491589690
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not wise or not rich then john is both calm and not patient. Everyone who is not creative is both not calm and rich. Everyone who is strong or funny is both wise and creative and vice versa. Everyone who is not patient or not strong is either kind or rich. Everyone who is not quiet or curious is both humble and not funny. If someone is both rich and tall then someone is not wise and vice versa. Everyone who is creative is either not creative or not old. Everyone who is either not calm or not rich is not tall or old. Everyone who is both creative and not old is either not creative or not old and vice versa. If someone is either not tall or tall then fred is both not patient and not creative. If susan is either not funny or creative then someone is both not brave and kind. If lucy is both not creative and rich then paul is not tall or kind. If someone is not old then john is not old. If someone is not curious or not humble then someone is either not curious or generous and vice versa. If lucy is either funny or not old then mary is not generous or creative and vice versa. If someone is not strong or old then paul is either not patient or not wise and vice versa. Mary is either not humble or not calm. Alice is generous or not curious. Someone is not calm or not creative. Alice is calm. Susan is either quiet or not quiet. Fred is not quiet or patient. Susan is both not humble and calm. Someone is old or humble. | Fred is funny. | contradiction | (((~wise(john)<~>~rich(john)))=>((calm(john)&~patient(john))))&
(![X]:(~creative(X)=>(~calm(X)&rich(X))))&
(![X]:((strong(X)|funny(X))<=>(wise(X)&creative(X))))&
(![X]:((~patient(X)|~strong(X))=>(kind(X)<~>rich(X))))&
(![X]:((~quiet(X)|curious(X))=>(humble(X)&~funny(X))))&
((?[X]:((rich(X)&tall(X))))<=>(?[X]:(~wise(X))))&
(![X]:(creative(X)=>(~creative(X)<~>~old(X))))&
(![X]:((~calm(X)<~>~rich(X))=>(~tall(X)|old(X))))&
(![X]:((creative(X)&~old(X))<=>(~creative(X)<~>~old(X))))&
((?[X]:((~tall(X)<~>tall(X))))=>((~patient(fred)&~creative(fred))))&
(((~funny(susan)<~>creative(susan)))=>(?[X]:((~brave(X)&kind(X)))))&
(((~creative(lucy)&rich(lucy)))=>((~tall(paul)|kind(paul))))&
((?[X]:(~old(X)))=>(~old(john)))&
((?[X]:((~curious(X)|~humble(X))))<=>(?[X]:((~curious(X)<~>generous(X)))))&
(((funny(lucy)<~>~old(lucy)))<=>((~generous(mary)|creative(mary))))&
((?[X]:((~strong(X)|old(X))))<=>((~patient(paul)<~>~wise(paul))))&
((~humble(mary)<~>~calm(mary)))&
((generous(alice)|~curious(alice)))&
(?[X]:((~calm(X)|~creative(X))))&
(calm(alice))&
((quiet(susan)<~>~quiet(susan)))&
((~quiet(fred)|patient(fred)))&
((~humble(susan)&calm(susan)))&
(?[X]:((old(X)|humble(X)))) | funny(fred) | [
"p2",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3207895301190783711155101
% SZS output start Proof for 3207895301190783711155101
3. ! [X0] : ((funny(X0) | strong(X0)) <=> (creative(X0) & wise(X0))) [input p2]
10. ? [X0] : (~tall(X0) <~> tall(X0)) => (~creative(fred) & ~patient(fred)) [input p9]
25. funny(fred) [input hypothesis]
36. (~creative(fred) & ~patient(fred)) | ! [X0] : (~tall(X0) <=> tall(X0)) [ennf transformation 10]
42. ! [X0] : (((funny(X0) | strong(X0)) | (~creative(X0) | ~wise(X0))) & ((creative(X0) & wise(X0)) | (~funny(X0) & ~strong(X0)))) [nnf transformation 3]
43. ! [X0] : ((funny(X0) | strong(X0) | ~creative(X0) | ~wise(X0)) & ((creative(X0) & wise(X0)) | (~funny(X0) & ~strong(X0)))) [flattening 42]
54. (~creative(fred) & ~patient(fred)) | ! [X0] : ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0))) [nnf transformation 36]
84. ~funny(X0) | creative(X0) [cnf transformation 43]
109. ~creative(fred) | tall(X0) | tall(X0) [cnf transformation 54]
110. ~creative(fred) | ~tall(X0) | ~tall(X0) [cnf transformation 54]
144. funny(fred) [cnf transformation 25]
147. ~creative(fred) | tall(X0) [duplicate literal removal 109]
148. ~creative(fred) | ~tall(X0) [duplicate literal removal 110]
197. 10 <=> ! [X0] : ~tall(X0) [avatar definition]
198. ~tall(X0) <- (10) [avatar component clause 197]
200. 11 <=> creative(fred) [avatar definition]
203. 10 | ~11 [avatar split clause 148,200,197]
205. 12 <=> ! [X0] : tall(X0) [avatar definition]
206. tall(X0) <- (12) [avatar component clause 205]
207. 12 | ~11 [avatar split clause 147,200,205]
351. creative(fred) [resolution 84,144]
354. 11 [avatar split clause 351,200]
355. $false <- (10, 12) [subsumption resolution 198,206]
356. ~10 | ~12 [avatar contradiction clause 355]
357. $false [avatar sat refutation 203,207,354,356]
% SZS output end Proof for 3207895301190783711155101
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is patient or not brave and vice versa. Everyone who is brave is either not curious or not patient and vice versa. Everyone who is either not kind or rich is not wise and vice versa. If john is both generous and not strong then someone is not funny or strong and vice versa. If john is rich or not strong then mary is either kind or quiet. If someone is either curious or not happy then someone is either humble or quiet. If someone is both quiet and not old then susan is not old. If someone is not quiet or not old then fred is either tall or curious and vice versa. Everyone who is funny or not funny is either not humble or not calm. If fred is not humble then paul is both curious and not generous. If someone is both happy and not patient then someone is not calm or not tall and vice versa. Everyone who is strong or brave is old or not funny and vice versa. Everyone who is not strong or old is not kind and vice versa. Everyone who is either not brave or wise is not quiet or not kind and vice versa. Everyone who is not old is not old or wise. Everyone who is not creative is both happy and kind. Someone is not creative or humble. Alice is either funny or not funny. John is both not kind and not wise. Someone is quiet. Someone is both old and wise. John is happy or not strong. Someone is both curious and generous. | Alice is not strong. | entailment | (![X]:(~generous(X)<=>(patient(X)|~brave(X))))&
(![X]:(brave(X)<=>(~curious(X)<~>~patient(X))))&
(![X]:((~kind(X)<~>rich(X))<=>~wise(X)))&
(((generous(john)&~strong(john)))<=>(?[X]:((~funny(X)|strong(X)))))&
(((rich(john)|~strong(john)))=>((kind(mary)<~>quiet(mary))))&
((?[X]:((curious(X)<~>~happy(X))))=>(?[X]:((humble(X)<~>quiet(X)))))&
((?[X]:((quiet(X)&~old(X))))=>(~old(susan)))&
((?[X]:((~quiet(X)|~old(X))))<=>((tall(fred)<~>curious(fred))))&
(![X]:((funny(X)|~funny(X))=>(~humble(X)<~>~calm(X))))&
((~humble(fred))=>((curious(paul)&~generous(paul))))&
((?[X]:((happy(X)&~patient(X))))<=>(?[X]:((~calm(X)|~tall(X)))))&
(![X]:((strong(X)|brave(X))<=>(old(X)|~funny(X))))&
(![X]:((~strong(X)|old(X))<=>~kind(X)))&
(![X]:((~brave(X)<~>wise(X))<=>(~quiet(X)|~kind(X))))&
(![X]:(~old(X)=>(~old(X)|wise(X))))&
(![X]:(~creative(X)=>(happy(X)&kind(X))))&
(?[X]:((~creative(X)|humble(X))))&
((funny(alice)<~>~funny(alice)))&
((~kind(john)&~wise(john)))&
(?[X]:(quiet(X)))&
(?[X]:((old(X)&wise(X))))&
((happy(john)|~strong(john)))&
(?[X]:((curious(X)&generous(X)))) | ~strong(alice) | [
"p0",
"p3",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5066070870453203283322889
% SZS output start Proof for 5066070870453203283322889
1. ! [X0] : (~generous(X0) <=> (~brave(X0) | patient(X0))) [input p0]
4. (~strong(john) & generous(john)) <=> ? [X0] : (strong(X0) | ~funny(X0)) [input p3]
14. ! [X0] : ((~brave(X0) <~> wise(X0)) <=> (~kind(X0) | ~quiet(X0))) [input p13]
19. ~wise(john) & ~kind(john) [input p18]
24. strong(alice) [input hypothesis]
35. ! [X0] : ((~generous(X0) | (brave(X0) & ~patient(X0))) & ((~brave(X0) | patient(X0)) | generous(X0))) [nnf transformation 1]
36. ! [X0] : ((~generous(X0) | (brave(X0) & ~patient(X0))) & (~brave(X0) | patient(X0) | generous(X0))) [flattening 35]
39. ((~strong(john) & generous(john)) | ! [X0] : (~strong(X0) & funny(X0))) & (? [X0] : (strong(X0) | ~funny(X0)) | (strong(john) | ~generous(john))) [nnf transformation 4]
40. ((~strong(john) & generous(john)) | ! [X0] : (~strong(X0) & funny(X0))) & (? [X0] : (strong(X0) | ~funny(X0)) | strong(john) | ~generous(john)) [flattening 39]
41. ((~strong(john) & generous(john)) | ! [X0] : (~strong(X0) & funny(X0))) & (? [X1] : (strong(X1) | ~funny(X1)) | strong(john) | ~generous(john)) [rectify 40]
42. ? [X1] : (strong(X1) | ~funny(X1)) => (strong(sK0) | ~funny(sK0)) [choice axiom]
43. ((~strong(john) & generous(john)) | ! [X0] : (~strong(X0) & funny(X0))) & ((strong(sK0) | ~funny(sK0)) | strong(john) | ~generous(john)) [skolemisation 41,42]
63. ! [X0] : ((((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | (kind(X0) & quiet(X0))) & ((~kind(X0) | ~quiet(X0)) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0))))) [nnf transformation 14]
64. ! [X0] : ((((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | (kind(X0) & quiet(X0))) & (~kind(X0) | ~quiet(X0) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0))))) [flattening 63]
76. ~generous(X0) | brave(X0) [cnf transformation 36]
87. generous(john) | ~strong(X0) [cnf transformation 43]
126. ~brave(X0) | wise(X0) | kind(X0) [cnf transformation 64]
135. ~kind(john) [cnf transformation 19]
136. ~wise(john) [cnf transformation 19]
143. strong(alice) [cnf transformation 24]
145. 1 <=> ! [X0] : ~strong(X0) [avatar definition]
146. ~strong(X0) <- (1) [avatar component clause 145]
157. 4 <=> generous(john) [avatar definition]
159. generous(john) <- (4) [avatar component clause 157]
160. 1 | 4 [avatar split clause 87,157,145]
343. $false <- (1) [resolution 146,143]
348. ~1 [avatar contradiction clause 343]
351. brave(john) <- (4) [resolution 159,76]
466. wise(john) | kind(john) <- (4) [resolution 126,351]
472. kind(john) <- (4) [subsumption resolution 466,136]
473. $false <- (4) [subsumption resolution 472,135]
474. ~4 [avatar contradiction clause 473]
475. $false [avatar sat refutation 160,348,474]
% SZS output end Proof for 5066070870453203283322889
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is either brave or wise.
If fred is not creative or brave then someone is rich and vice versa.
If someone is not tall then someone is funny and vice versa.
Everyone who is brave is both curious and not generous and vice versa.
Everyone who is both not curious and not strong is either not brave or not wise and vice versa.
If someone is kind then someone is either not strong or kind and vice versa.
Everyone who is both not brave and funny is either not strong or not old.
Everyone who is both not creative and tall is not patient or not funny.
Everyone who is either not brave or curious is both curious and not kind and vice versa.
If someone is both not brave and funny then someone is brave or not humble and vice versa.
If paul is quiet then someone is either not wise or not creative.
If someone is either not patient or generous then lucy is either tall or creative and vice versa.
Everyone who is both creative and happy is either funny or rich and vice versa.
Everyone who is patient or quiet is both not brave and brave and vice versa.
Everyone who is both patient and not creative is not calm and vice versa.
If someone is either not strong or not funny then someone is not old.
Fred is either not brave or brave.
Lucy is not creative or not wise.
Someone is curious.
Someone is creative or not strong.
Someone is generous.
John is kind or not wise.
Someone is either calm or not tall.
Someone is humble or strong. | John is not generous. | contradiction | (![X]:(funny(X)=>(brave(X)<~>wise(X))))&
(((~creative(fred)|brave(fred)))<=>(?[X]:(rich(X))))&
((?[X]:(~tall(X)))<=>(?[X]:(funny(X))))&
(![X]:(brave(X)<=>(curious(X)&~generous(X))))&
(![X]:((~curious(X)&~strong(X))<=>(~brave(X)<~>~wise(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~strong(X)<~>kind(X)))))&
(![X]:((~brave(X)&funny(X))=>(~strong(X)<~>~old(X))))&
(![X]:((~creative(X)&tall(X))=>(~patient(X)|~funny(X))))&
(![X]:((~brave(X)<~>curious(X))<=>(curious(X)&~kind(X))))&
((?[X]:((~brave(X)&funny(X))))<=>(?[X]:((brave(X)|~humble(X)))))&
((quiet(paul))=>(?[X]:((~wise(X)<~>~creative(X)))))&
((?[X]:((~patient(X)<~>generous(X))))<=>((tall(lucy)<~>creative(lucy))))&
(![X]:((creative(X)&happy(X))<=>(funny(X)<~>rich(X))))&
(![X]:((patient(X)|quiet(X))<=>(~brave(X)&brave(X))))&
(![X]:((patient(X)&~creative(X))<=>~calm(X)))&
((?[X]:((~strong(X)<~>~funny(X))))=>(?[X]:(~old(X))))&
((~brave(fred)<~>brave(fred)))&
((~creative(lucy)|~wise(lucy)))&
(?[X]:(curious(X)))&
(?[X]:((creative(X)|~strong(X))))&
(?[X]:(generous(X)))&
((kind(john)|~wise(john)))&
(?[X]:((calm(X)<~>~tall(X))))&
(?[X]:((humble(X)|strong(X)))) | ~generous(john) | [
"p3",
"p4",
"p8",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 826887456894000210618135
% SZS output start Proof for 826887456894000210618135
4. ! [X0] : (brave(X0) <=> (~generous(X0) & curious(X0))) [input p3]
5. ! [X0] : ((~strong(X0) & ~curious(X0)) <=> (~brave(X0) <~> ~wise(X0))) [input p4]
9. ! [X0] : ((~brave(X0) <~> curious(X0)) <=> (~kind(X0) & curious(X0))) [input p8]
22. ~wise(john) | kind(john) [input p21]
25. ~generous(john) [input hypothesis]
48. ! [X0] : ((brave(X0) | (generous(X0) | ~curious(X0))) & ((~generous(X0) & curious(X0)) | ~brave(X0))) [nnf transformation 4]
49. ! [X0] : ((brave(X0) | generous(X0) | ~curious(X0)) & ((~generous(X0) & curious(X0)) | ~brave(X0))) [flattening 48]
50. ! [X0] : (((~strong(X0) & ~curious(X0)) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0)))) & (((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | (strong(X0) | curious(X0)))) [nnf transformation 5]
51. ! [X0] : (((~strong(X0) & ~curious(X0)) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0)))) & (((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | strong(X0) | curious(X0))) [flattening 50]
58. ! [X0] : ((((~curious(X0) | brave(X0)) & (curious(X0) | ~brave(X0))) | (kind(X0) | ~curious(X0))) & ((~kind(X0) & curious(X0)) | ((~brave(X0) | ~curious(X0)) & (curious(X0) | brave(X0))))) [nnf transformation 9]
59. ! [X0] : ((((~curious(X0) | brave(X0)) & (curious(X0) | ~brave(X0))) | kind(X0) | ~curious(X0)) & ((~kind(X0) & curious(X0)) | ((~brave(X0) | ~curious(X0)) & (curious(X0) | brave(X0))))) [flattening 58]
101. ~brave(X0) | curious(X0) [cnf transformation 49]
103. ~curious(X0) | generous(X0) | brave(X0) [cnf transformation 49]
107. ~curious(X0) | ~brave(X0) | wise(X0) [cnf transformation 51]
117. curious(X0) | curious(X0) | brave(X0) [cnf transformation 59]
120. ~kind(X0) | ~brave(X0) | ~curious(X0) [cnf transformation 59]
160. ~wise(john) | kind(john) [cnf transformation 22]
164. ~generous(john) [cnf transformation 25]
165. curious(X0) | brave(X0) [duplicate literal removal 117]
201. ~brave(X0) | wise(X0) [subsumption resolution 107,101]
228. ~kind(X0) | ~brave(X0) [subsumption resolution 120,101]
230. curious(X0) [subsumption resolution 165,101]
335. 37 <=> kind(john) [avatar definition]
337. kind(john) <- (37) [avatar component clause 335]
339. 38 <=> wise(john) [avatar definition]
342. 37 | ~38 [avatar split clause 160,339,335]
370. generous(X0) | brave(X0) [resolution 103,230]
374. brave(john) [resolution 370,164]
425. wise(john) [resolution 374,201]
429. 38 [avatar split clause 425,339]
431. ~brave(john) <- (37) [resolution 337,228]
432. $false <- (37) [subsumption resolution 431,374]
433. ~37 [avatar contradiction clause 432]
434. $false [avatar sat refutation 342,429,433]
% SZS output end Proof for 826887456894000210618135
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is happy or not strong then someone is both not creative and calm and vice versa.
Everyone who is not calm is not quiet and vice versa.
If someone is either curious or not humble then someone is either not humble or not happy.
Everyone who is not quiet is either generous or happy and vice versa.
If lucy is not rich or curious then mary is not patient or old.
If someone is calm or not calm then someone is both tall and not patient and vice versa.
Everyone who is funny or not patient is quiet.
If paul is both not strong and not happy then paul is either not quiet or calm and vice versa.
Everyone who is both patient and not creative is not funny.
If someone is not calm then someone is either not old or kind and vice versa.
If someone is both generous and funny then someone is either wise or curious.
Everyone who is not happy or not generous is both old and patient.
If someone is not rich or not brave then someone is both creative and rich and vice versa.
Everyone who is either not tall or not quiet is old and vice versa.
Everyone who is humble or not kind is either tall or happy.
Everyone who is either not kind or strong is not generous and vice versa.
Someone is both quiet and not tall.
Someone is not curious.
Alice is not brave or not curious.
Fred is not strong or happy.
Lucy is not curious or happy.
Someone is strong.
Lucy is either humble or generous. | Paul is kind. | entailment | (((happy(alice)|~strong(alice)))<=>(?[X]:((~creative(X)&calm(X)))))&
(![X]:(~calm(X)<=>~quiet(X)))&
((?[X]:((curious(X)<~>~humble(X))))=>(?[X]:((~humble(X)<~>~happy(X)))))&
(![X]:(~quiet(X)<=>(generous(X)<~>happy(X))))&
(((~rich(lucy)|curious(lucy)))=>((~patient(mary)|old(mary))))&
((?[X]:((calm(X)|~calm(X))))<=>(?[X]:((tall(X)&~patient(X)))))&
(![X]:((funny(X)|~patient(X))=>quiet(X)))&
(((~strong(paul)&~happy(paul)))<=>((~quiet(paul)<~>calm(paul))))&
(![X]:((patient(X)&~creative(X))=>~funny(X)))&
((?[X]:(~calm(X)))<=>(?[X]:((~old(X)<~>kind(X)))))&
((?[X]:((generous(X)&funny(X))))=>(?[X]:((wise(X)<~>curious(X)))))&
(![X]:((~happy(X)|~generous(X))=>(old(X)&patient(X))))&
((?[X]:((~rich(X)|~brave(X))))<=>(?[X]:((creative(X)&rich(X)))))&
(![X]:((~tall(X)<~>~quiet(X))<=>old(X)))&
(![X]:((humble(X)|~kind(X))=>(tall(X)<~>happy(X))))&
(![X]:((~kind(X)<~>strong(X))<=>~generous(X)))&
(?[X]:((quiet(X)&~tall(X))))&
(?[X]:(~curious(X)))&
((~brave(alice)|~curious(alice)))&
((~strong(fred)|happy(fred)))&
((~curious(lucy)|happy(lucy)))&
(?[X]:(strong(X)))&
((humble(lucy)<~>generous(lucy))) | kind(paul) | [
"p1",
"p3",
"p7",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 16641206064306003517733
% SZS output start Proof for 16641206064306003517733
2. ! [X0] : (~calm(X0) <=> ~quiet(X0)) [input p1]
4. ! [X0] : (~quiet(X0) <=> (generous(X0) <~> happy(X0))) [input p3]
8. (~happy(paul) & ~strong(paul)) <=> (~quiet(paul) <~> calm(paul)) [input p7]
12. ! [X0] : ((~generous(X0) | ~happy(X0)) => (patient(X0) & old(X0))) [input p11]
14. ! [X0] : ((~tall(X0) <~> ~quiet(X0)) <=> old(X0)) [input p13]
15. ! [X0] : ((~kind(X0) | humble(X0)) => (tall(X0) <~> happy(X0))) [input p14]
16. ! [X0] : ((~kind(X0) <~> strong(X0)) <=> ~generous(X0)) [input p15]
24. ~kind(paul) [input hypothesis]
37. ! [X0] : ((patient(X0) & old(X0)) | (generous(X0) & happy(X0))) [ennf transformation 12]
38. ! [X0] : ((tall(X0) <~> happy(X0)) | (kind(X0) & ~humble(X0))) [ennf transformation 15]
44. ! [X0] : ((~calm(X0) | quiet(X0)) & (~quiet(X0) | calm(X0))) [nnf transformation 2]
49. ! [X0] : ((~quiet(X0) | ((generous(X0) | ~happy(X0)) & (happy(X0) | ~generous(X0)))) & (((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | quiet(X0))) [nnf transformation 4]
55. ((~happy(paul) & ~strong(paul)) | ((~quiet(paul) | ~calm(paul)) & (calm(paul) | quiet(paul)))) & (((~calm(paul) | quiet(paul)) & (calm(paul) | ~quiet(paul))) | (happy(paul) | strong(paul))) [nnf transformation 8]
56. ((~happy(paul) & ~strong(paul)) | ((~quiet(paul) | ~calm(paul)) & (calm(paul) | quiet(paul)))) & (((~calm(paul) | quiet(paul)) & (calm(paul) | ~quiet(paul))) | happy(paul) | strong(paul)) [flattening 55]
67. ! [X0] : ((((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | ~old(X0)) & (old(X0) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0))))) [nnf transformation 14]
68. ! [X0] : (((~happy(X0) | ~tall(X0)) & (happy(X0) | tall(X0))) | (kind(X0) & ~humble(X0))) [nnf transformation 38]
69. ! [X0] : ((((~strong(X0) | kind(X0)) & (strong(X0) | ~kind(X0))) | generous(X0)) & (~generous(X0) | ((~kind(X0) | ~strong(X0)) & (strong(X0) | kind(X0))))) [nnf transformation 16]
82. ~quiet(X0) | calm(X0) [cnf transformation 44]
83. ~calm(X0) | quiet(X0) [cnf transformation 44]
88. generous(X0) | happy(X0) | quiet(X0) [cnf transformation 49]
102. ~strong(paul) | calm(paul) | quiet(paul) [cnf transformation 56]
104. ~happy(paul) | calm(paul) | quiet(paul) [cnf transformation 56]
105. ~happy(paul) | ~quiet(paul) | ~calm(paul) [cnf transformation 56]
110. old(X0) | happy(X0) [cnf transformation 37]
121. ~tall(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 67]
124. kind(X0) | tall(X0) | happy(X0) [cnf transformation 68]
127. ~generous(X0) | strong(X0) | kind(X0) [cnf transformation 69]
140. ~kind(paul) [cnf transformation 24]
219. ~happy(paul) | ~quiet(paul) [subsumption resolution 105,82]
221. 18 <=> quiet(paul) [avatar definition]
222. quiet(paul) <- (18) [avatar component clause 221]
225. 19 <=> happy(paul) [avatar definition]
227. ~happy(paul) <- (~19) [avatar component clause 225]
228. ~18 | ~19 [avatar split clause 219,225,221]
229. ~happy(paul) | quiet(paul) [subsumption resolution 104,83]
230. 18 | ~19 [avatar split clause 229,225,221]
233. 20 <=> strong(paul) [avatar definition]
235. ~strong(paul) <- (~20) [avatar component clause 233]
237. ~strong(paul) | quiet(paul) [subsumption resolution 102,83]
238. 18 | ~20 [avatar split clause 237,233,221]
413. tall(paul) | happy(paul) [resolution 124,140]
415. tall(paul) <- (~19) [subsumption resolution 413,227]
432. ~quiet(paul) | ~old(paul) <- (~19) [resolution 415,121]
476. ~old(paul) <- (18, ~19) [subsumption resolution 432,222]
484. kind(X0) | strong(X0) | happy(X0) | quiet(X0) [resolution 127,88]
588. strong(paul) | happy(paul) | quiet(paul) [resolution 484,140]
690. happy(paul) <- (18, ~19) [resolution 476,110]
691. $false <- (18, ~19) [subsumption resolution 690,227]
692. ~18 | 19 [avatar contradiction clause 691]
693. happy(paul) | quiet(paul) <- (~20) [subsumption resolution 588,235]
694. quiet(paul) <- (~19, ~20) [subsumption resolution 693,227]
695. 18 | 19 | 20 [avatar split clause 694,233,225,221]
702. $false [avatar sat refutation 228,230,238,692,695]
% SZS output end Proof for 16641206064306003517733
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If fred is tall then someone is not old or not wise.
If someone is rich or not funny then paul is funny.
Everyone who is either not brave or not tall is both not creative and happy.
If someone is curious or not creative then someone is both not tall and strong.
If john is curious then fred is either not happy or not wise and vice versa.
Everyone who is rich or not old is both not calm and not tall and vice versa.
If alice is both creative and humble then someone is either kind or not wise.
Everyone who is calm or funny is not curious.
Everyone who is not funny is both curious and happy.
Everyone who is not curious or not generous is both not generous and rich and vice versa.
Everyone who is either rich or not kind is kind and vice versa.
If someone is either quiet or brave then someone is not brave or not tall.
Everyone who is funny is not creative or rich.
Everyone who is both not quiet and not calm is not patient or not funny.
Everyone who is either happy or not kind is funny or creative.
Everyone who is not generous is creative or tall.
Someone is not kind.
Someone is both funny and not humble.
Susan is either patient or not funny.
Someone is either not curious or not brave.
Fred is not tall or calm.
Susan is calm or not happy. | Alice is rich. | entailment | ((tall(fred))=>(?[X]:((~old(X)|~wise(X)))))&
((?[X]:((rich(X)|~funny(X))))=>(funny(paul)))&
(![X]:((~brave(X)<~>~tall(X))=>(~creative(X)&happy(X))))&
((?[X]:((curious(X)|~creative(X))))=>(?[X]:((~tall(X)&strong(X)))))&
((curious(john))<=>((~happy(fred)<~>~wise(fred))))&
(![X]:((rich(X)|~old(X))<=>(~calm(X)&~tall(X))))&
(((creative(alice)&humble(alice)))=>(?[X]:((kind(X)<~>~wise(X)))))&
(![X]:((calm(X)|funny(X))=>~curious(X)))&
(![X]:(~funny(X)=>(curious(X)&happy(X))))&
(![X]:((~curious(X)|~generous(X))<=>(~generous(X)&rich(X))))&
(![X]:((rich(X)<~>~kind(X))<=>kind(X)))&
((?[X]:((quiet(X)<~>brave(X))))=>(?[X]:((~brave(X)|~tall(X)))))&
(![X]:(funny(X)=>(~creative(X)|rich(X))))&
(![X]:((~quiet(X)&~calm(X))=>(~patient(X)|~funny(X))))&
(![X]:((happy(X)<~>~kind(X))=>(funny(X)|creative(X))))&
(![X]:(~generous(X)=>(creative(X)|tall(X))))&
(?[X]:(~kind(X)))&
(?[X]:((funny(X)&~humble(X))))&
((patient(susan)<~>~funny(susan)))&
(?[X]:((~curious(X)<~>~brave(X))))&
((~tall(fred)|calm(fred)))&
((calm(susan)|~happy(susan))) | rich(alice) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2398740286511381304923584
% SZS output start Proof for 2398740286511381304923584
11. ! [X0] : ((rich(X0) <~> ~kind(X0)) <=> kind(X0)) [input p10]
23. ~rich(alice) [input hypothesis]
55. ! [X0] : ((((kind(X0) | ~rich(X0)) & (~kind(X0) | rich(X0))) | ~kind(X0)) & (kind(X0) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0))))) [nnf transformation 11]
97. kind(X0) | rich(X0) | kind(X0) [cnf transformation 55]
98. ~kind(X0) | rich(X0) | ~kind(X0) [cnf transformation 55]
115. ~rich(alice) [cnf transformation 23]
116. kind(X0) | rich(X0) [duplicate literal removal 97]
117. ~kind(X0) | rich(X0) [duplicate literal removal 98]
171. rich(X0) [subsumption resolution 116,117]
223. $false [subsumption resolution 115,171]
% SZS output end Proof for 2398740286511381304923584
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or wise then someone is both not old and curious and vice versa.
Everyone who is either brave or not funny is not rich or curious and vice versa.
Everyone who is brave or calm is old or rich and vice versa.
Everyone who is both calm and not humble is not generous or creative.
Everyone who is generous or not strong is patient or humble.
If someone is either not humble or not patient then someone is brave or not funny.
Everyone who is either generous or not old is not old or brave.
Everyone who is not quiet or not patient is either not kind or generous and vice versa.
Everyone who is happy or not quiet is not kind and vice versa.
Everyone who is both not happy and creative is either not patient or not happy.
If someone is curious or quiet then mary is calm or funny and vice versa.
Everyone who is not brave is either brave or not happy and vice versa.
Everyone who is not old is either generous or not patient.
If lucy is both patient and not happy then paul is either quiet or not humble.
Everyone who is rich is patient and vice versa.
Everyone who is both not wise and not generous is both happy and generous.
Susan is either quiet or not quiet.
Someone is curious or not tall.
Someone is both creative and not quiet.
Someone is both wise and strong.
Fred is both not funny and quiet.
Paul is either strong or not calm.
Someone is both brave and calm. | Fred is old. | entailment | ((?[X]:((kind(X)<~>wise(X))))<=>(?[X]:((~old(X)&curious(X)))))&
(![X]:((brave(X)<~>~funny(X))<=>(~rich(X)|curious(X))))&
(![X]:((brave(X)|calm(X))<=>(old(X)|rich(X))))&
(![X]:((calm(X)&~humble(X))=>(~generous(X)|creative(X))))&
(![X]:((generous(X)|~strong(X))=>(patient(X)|humble(X))))&
((?[X]:((~humble(X)<~>~patient(X))))=>(?[X]:((brave(X)|~funny(X)))))&
(![X]:((generous(X)<~>~old(X))=>(~old(X)|brave(X))))&
(![X]:((~quiet(X)|~patient(X))<=>(~kind(X)<~>generous(X))))&
(![X]:((happy(X)|~quiet(X))<=>~kind(X)))&
(![X]:((~happy(X)&creative(X))=>(~patient(X)<~>~happy(X))))&
((?[X]:((curious(X)|quiet(X))))<=>((calm(mary)|funny(mary))))&
(![X]:(~brave(X)<=>(brave(X)<~>~happy(X))))&
(![X]:(~old(X)=>(generous(X)<~>~patient(X))))&
(((patient(lucy)&~happy(lucy)))=>((quiet(paul)<~>~humble(paul))))&
(![X]:(rich(X)<=>patient(X)))&
(![X]:((~wise(X)&~generous(X))=>(happy(X)&generous(X))))&
((quiet(susan)<~>~quiet(susan)))&
(?[X]:((curious(X)|~tall(X))))&
(?[X]:((creative(X)&~quiet(X))))&
(?[X]:((wise(X)&strong(X))))&
((~funny(fred)&quiet(fred)))&
((strong(paul)<~>~calm(paul)))&
(?[X]:((brave(X)&calm(X)))) | old(fred) | [
"p7",
"p8",
"p11",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1823865893553530529588822
% SZS output start Proof for 1823865893553530529588822
8. ! [X0] : ((~patient(X0) | ~quiet(X0)) <=> (~kind(X0) <~> generous(X0))) [input p7]
9. ! [X0] : ((~quiet(X0) | happy(X0)) <=> ~kind(X0)) [input p8]
12. ! [X0] : (~brave(X0) <=> (brave(X0) <~> ~happy(X0))) [input p11]
13. ! [X0] : (~old(X0) => (generous(X0) <~> ~patient(X0))) [input p12]
21. quiet(fred) & ~funny(fred) [input p20]
24. ~old(fred) [input hypothesis]
37. ! [X0] : ((generous(X0) <~> ~patient(X0)) | old(X0)) [ennf transformation 13]
56. ! [X0] : (((~patient(X0) | ~quiet(X0)) | ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0)))) & (((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | (patient(X0) & quiet(X0)))) [nnf transformation 8]
57. ! [X0] : ((~patient(X0) | ~quiet(X0) | ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0)))) & (((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | (patient(X0) & quiet(X0)))) [flattening 56]
58. ! [X0] : (((~quiet(X0) | happy(X0)) | kind(X0)) & (~kind(X0) | (quiet(X0) & ~happy(X0)))) [nnf transformation 9]
59. ! [X0] : ((~quiet(X0) | happy(X0) | kind(X0)) & (~kind(X0) | (quiet(X0) & ~happy(X0)))) [flattening 58]
66. ! [X0] : ((~brave(X0) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0)))) & (((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | brave(X0))) [nnf transformation 12]
67. ! [X0] : (((patient(X0) | ~generous(X0)) & (~patient(X0) | generous(X0))) | old(X0)) [nnf transformation 37]
102. ~kind(X0) | generous(X0) | patient(X0) [cnf transformation 57]
106. ~quiet(X0) | ~patient(X0) | ~kind(X0) | ~generous(X0) [cnf transformation 57]
109. ~quiet(X0) | happy(X0) | kind(X0) [cnf transformation 59]
116. ~happy(X0) | brave(X0) | brave(X0) [cnf transformation 66]
118. ~brave(X0) | ~happy(X0) | ~brave(X0) [cnf transformation 66]
120. ~patient(X0) | generous(X0) | old(X0) [cnf transformation 67]
121. ~generous(X0) | patient(X0) | old(X0) [cnf transformation 67]
135. quiet(fred) [cnf transformation 21]
140. ~old(fred) [cnf transformation 24]
142. ~happy(X0) | brave(X0) [duplicate literal removal 116]
143. ~happy(X0) | ~brave(X0) [duplicate literal removal 118]
219. ~happy(X0) [subsumption resolution 142,143]
341. happy(fred) | kind(fred) [resolution 109,135]
343. kind(fred) [subsumption resolution 341,219]
344. generous(fred) | patient(fred) [resolution 343,102]
348. 35 <=> patient(fred) [avatar definition]
350. patient(fred) <- (35) [avatar component clause 348]
352. 36 <=> generous(fred) [avatar definition]
354. generous(fred) <- (36) [avatar component clause 352]
355. 35 | 36 [avatar split clause 344,352,348]
373. generous(fred) | old(fred) <- (35) [resolution 350,120]
375. generous(fred) <- (35) [subsumption resolution 373,140]
376. 36 | ~35 [avatar split clause 375,348,352]
384. patient(fred) | old(fred) <- (36) [resolution 354,121]
470. ~patient(fred) | ~kind(fred) | ~generous(fred) [resolution 106,135]
479. ~patient(fred) | ~generous(fred) [subsumption resolution 470,343]
480. ~patient(fred) <- (36) [subsumption resolution 479,354]
481. ~35 | ~36 [avatar split clause 480,352,348]
483. patient(fred) <- (36) [subsumption resolution 384,140]
484. 35 | ~36 [avatar split clause 483,352,348]
485. $false [avatar sat refutation 355,376,481,484]
% SZS output end Proof for 1823865893553530529588822
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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