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
|
|---|---|---|---|---|---|---|---|
Everyone who is not strong or not humble is both not generous and patient.
Everyone who is not happy is not old and vice versa.
If alice is wise then fred is not curious or not funny and vice versa.
If someone is creative then someone is both quiet and not wise.
If lucy is strong then fred is funny.
If mary is both curious and calm then lucy is both patient and not patient.
Everyone who is not wise or not humble is rich or not wise and vice versa.
If someone is not funny then fred is both humble and not creative.
Everyone who is old or generous is both not funny and not patient.
Everyone who is either not creative or not strong is funny or not generous and vice versa.
If susan is not calm then mary is both not generous and funny and vice versa.
If fred is not strong or not generous then someone is calm or wise.
If someone is happy then someone is tall or not curious.
If paul is both humble and brave then lucy is either not rich or not curious.
If lucy is tall then someone is not wise.
Everyone who is not patient or not funny is either generous or not old.
Paul is old.
Susan is humble.
Paul is not old or kind.
Mary is both kind and not humble.
Someone is both old and not kind.
Lucy is either creative or not curious.
Paul is tall or not old.
Someone is not quiet. | Paul is generous. | entailment | (![X]:((~strong(X)|~humble(X))=>(~generous(X)&patient(X))))&
(![X]:(~happy(X)<=>~old(X)))&
((wise(alice))<=>((~curious(fred)|~funny(fred))))&
((?[X]:(creative(X)))=>(?[X]:((quiet(X)&~wise(X)))))&
((strong(lucy))=>(funny(fred)))&
(((curious(mary)&calm(mary)))=>((patient(lucy)&~patient(lucy))))&
(![X]:((~wise(X)|~humble(X))<=>(rich(X)|~wise(X))))&
((?[X]:(~funny(X)))=>((humble(fred)&~creative(fred))))&
(![X]:((old(X)|generous(X))=>(~funny(X)&~patient(X))))&
(![X]:((~creative(X)<~>~strong(X))<=>(funny(X)|~generous(X))))&
((~calm(susan))<=>((~generous(mary)&funny(mary))))&
(((~strong(fred)|~generous(fred)))=>(?[X]:((calm(X)|wise(X)))))&
((?[X]:(happy(X)))=>(?[X]:((tall(X)|~curious(X)))))&
(((humble(paul)&brave(paul)))=>((~rich(lucy)<~>~curious(lucy))))&
((tall(lucy))=>(?[X]:(~wise(X))))&
(![X]:((~patient(X)|~funny(X))=>(generous(X)<~>~old(X))))&
(old(paul))&
(humble(susan))&
((~old(paul)|kind(paul)))&
((kind(mary)&~humble(mary)))&
(?[X]:((old(X)&~kind(X))))&
((creative(lucy)<~>~curious(lucy)))&
((tall(paul)|~old(paul)))&
(?[X]:(~quiet(X))) | generous(paul) | [
"p8",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3016882590031329667703305
% SZS output start Proof for 3016882590031329667703305
9. ! [X0] : ((generous(X0) | old(X0)) => (~patient(X0) & ~funny(X0))) [input p8]
16. ! [X0] : ((~funny(X0) | ~patient(X0)) => (generous(X0) <~> ~old(X0))) [input p15]
17. old(paul) [input p16]
25. ~generous(paul) [input hypothesis]
37. ! [X0] : ((~patient(X0) & ~funny(X0)) | (~generous(X0) & ~old(X0))) [ennf transformation 9]
41. ! [X0] : ((generous(X0) <~> ~old(X0)) | (funny(X0) & patient(X0))) [ennf transformation 16]
60. ! [X0] : (((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | (funny(X0) & patient(X0))) [nnf transformation 41]
85. ~funny(X0) | ~old(X0) [cnf transformation 37]
103. ~old(X0) | generous(X0) | funny(X0) [cnf transformation 60]
106. old(paul) [cnf transformation 17]
117. ~generous(paul) [cnf transformation 25]
237. ~old(X0) | generous(X0) [subsumption resolution 103,85]
276. generous(paul) [resolution 237,106]
278. $false [subsumption resolution 276,117]
% SZS output end Proof for 3016882590031329667703305
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or tall then someone is both rich and quiet and vice versa.
Everyone who is not patient or not old is either not old or not rich.
Everyone who is tall is both not generous and generous and vice versa.
Everyone who is either curious or calm is either not old or not curious and vice versa.
If someone is both not quiet and wise then someone is not quiet or old and vice versa.
Everyone who is either funny or not generous is not tall and vice versa.
Everyone who is not tall is both calm and not quiet and vice versa.
If alice is not creative then susan is quiet or not kind and vice versa.
If susan is both rich and not quiet then paul is not calm and vice versa.
Everyone who is not creative or not quiet is wise and vice versa.
If someone is either not tall or not curious then lucy is both not brave and not humble.
If susan is not rich or generous then fred is brave or not generous.
If someone is both generous and not creative then someone is happy or not happy and vice versa.
If someone is calm then paul is either tall or not tall and vice versa.
If lucy is either not curious or calm then someone is not creative.
Everyone who is either not generous or not curious is not wise.
Someone is creative.
Someone is both not tall and patient.
Someone is either humble or brave.
Someone is not funny.
Mary is not quiet.
Someone is both generous and curious.
Lucy is both not funny and not generous. | Mary is wise. | entailment | ((?[X]:((rich(X)|tall(X))))<=>(?[X]:((rich(X)&quiet(X)))))&
(![X]:((~patient(X)|~old(X))=>(~old(X)<~>~rich(X))))&
(![X]:(tall(X)<=>(~generous(X)&generous(X))))&
(![X]:((curious(X)<~>calm(X))<=>(~old(X)<~>~curious(X))))&
((?[X]:((~quiet(X)&wise(X))))<=>(?[X]:((~quiet(X)|old(X)))))&
(![X]:((funny(X)<~>~generous(X))<=>~tall(X)))&
(![X]:(~tall(X)<=>(calm(X)&~quiet(X))))&
((~creative(alice))<=>((quiet(susan)|~kind(susan))))&
(((rich(susan)&~quiet(susan)))<=>(~calm(paul)))&
(![X]:((~creative(X)|~quiet(X))<=>wise(X)))&
((?[X]:((~tall(X)<~>~curious(X))))=>((~brave(lucy)&~humble(lucy))))&
(((~rich(susan)|generous(susan)))=>((brave(fred)|~generous(fred))))&
((?[X]:((generous(X)&~creative(X))))<=>(?[X]:((happy(X)|~happy(X)))))&
((?[X]:(calm(X)))<=>((tall(paul)<~>~tall(paul))))&
(((~curious(lucy)<~>calm(lucy)))=>(?[X]:(~creative(X))))&
(![X]:((~generous(X)<~>~curious(X))=>~wise(X)))&
(?[X]:(creative(X)))&
(?[X]:((~tall(X)&patient(X))))&
(?[X]:((humble(X)<~>brave(X))))&
(?[X]:(~funny(X)))&
(~quiet(mary))&
(?[X]:((generous(X)&curious(X))))&
((~funny(lucy)&~generous(lucy))) | wise(mary) | [
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7773017433043639702765809
% SZS output start Proof for 7773017433043639702765809
10. ! [X0] : ((~quiet(X0) | ~creative(X0)) <=> wise(X0)) [input p9]
21. ~quiet(mary) [input p20]
24. ~wise(mary) [input hypothesis]
57. ! [X0] : (((~quiet(X0) | ~creative(X0)) | ~wise(X0)) & (wise(X0) | (quiet(X0) & creative(X0)))) [nnf transformation 10]
58. ! [X0] : ((~quiet(X0) | ~creative(X0) | ~wise(X0)) & (wise(X0) | (quiet(X0) & creative(X0)))) [flattening 57]
121. wise(X0) | quiet(X0) [cnf transformation 58]
147. ~quiet(mary) [cnf transformation 21]
152. ~wise(mary) [cnf transformation 24]
343. quiet(mary) [resolution 121,152]
344. $false [subsumption resolution 343,147]
% SZS output end Proof for 7773017433043639702765809
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is tall or not patient then alice is either not humble or curious.
Everyone who is not calm is either generous or not strong and vice versa.
Everyone who is old or not tall is curious or wise and vice versa.
If susan is not kind or quiet then someone is not patient and vice versa.
Everyone who is not quiet is strong or not tall and vice versa.
If paul is either tall or happy then someone is not generous and vice versa.
Everyone who is either not generous or not strong is not old.
Everyone who is not kind is funny or not rich.
Everyone who is happy or rich is not happy and vice versa.
If fred is humble or funny then someone is rich.
If someone is not creative or funny then someone is wise or not wise and vice versa.
If someone is both not generous and not calm then john is funny.
Everyone who is either creative or humble is either not kind or not brave and vice versa.
Everyone who is both calm and humble is not calm and vice versa.
If alice is both generous and not generous then someone is not patient or generous and vice versa.
If mary is both not strong and not rich then john is either rich or not happy and vice versa.
Susan is either wise or curious.
Someone is either quiet or not happy.
John is patient or calm.
Alice is kind.
Someone is not kind.
Someone is strong.
Someone is not brave. | Alice is happy. | contradiction | (((tall(mary)|~patient(mary)))=>((~humble(alice)<~>curious(alice))))&
(![X]:(~calm(X)<=>(generous(X)<~>~strong(X))))&
(![X]:((old(X)|~tall(X))<=>(curious(X)|wise(X))))&
(((~kind(susan)|quiet(susan)))<=>(?[X]:(~patient(X))))&
(![X]:(~quiet(X)<=>(strong(X)|~tall(X))))&
(((tall(paul)<~>happy(paul)))<=>(?[X]:(~generous(X))))&
(![X]:((~generous(X)<~>~strong(X))=>~old(X)))&
(![X]:(~kind(X)=>(funny(X)|~rich(X))))&
(![X]:((happy(X)|rich(X))<=>~happy(X)))&
(((humble(fred)|funny(fred)))=>(?[X]:(rich(X))))&
((?[X]:((~creative(X)|funny(X))))<=>(?[X]:((wise(X)|~wise(X)))))&
((?[X]:((~generous(X)&~calm(X))))=>(funny(john)))&
(![X]:((creative(X)<~>humble(X))<=>(~kind(X)<~>~brave(X))))&
(![X]:((calm(X)&humble(X))<=>~calm(X)))&
(((generous(alice)&~generous(alice)))<=>(?[X]:((~patient(X)|generous(X)))))&
(((~strong(mary)&~rich(mary)))<=>((rich(john)<~>~happy(john))))&
((wise(susan)<~>curious(susan)))&
(?[X]:((quiet(X)<~>~happy(X))))&
((patient(john)|calm(john)))&
(kind(alice))&
(?[X]:(~kind(X)))&
(?[X]:(strong(X)))&
(?[X]:(~brave(X))) | happy(alice) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2093798837994680484662145
% SZS output start Proof for 2093798837994680484662145
9. ! [X0] : ((rich(X0) | happy(X0)) <=> ~happy(X0)) [input p8]
24. happy(alice) [input hypothesis]
48. ! [X0] : (((rich(X0) | happy(X0)) | happy(X0)) & (~happy(X0) | (~rich(X0) & ~happy(X0)))) [nnf transformation 9]
49. ! [X0] : ((rich(X0) | happy(X0) | happy(X0)) & (~happy(X0) | (~rich(X0) & ~happy(X0)))) [flattening 48]
102. ~happy(X0) | ~happy(X0) [cnf transformation 49]
143. happy(alice) [cnf transformation 24]
146. ~happy(X0) [duplicate literal removal 102]
280. $false [subsumption resolution 143,146]
% SZS output end Proof for 2093798837994680484662145
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not kind then someone is either not creative or creative and vice versa. Everyone who is either not rich or not humble is both happy and patient and vice versa. If someone is tall then someone is both not kind and kind. Everyone who is humble or calm is not quiet and vice versa. If someone is either curious or not generous then john is either not humble or old. If lucy is either not old or not funny then john is not tall or not patient and vice versa. If susan is both not creative and calm then lucy is either not humble or not funny. If someone is both not funny and not calm then someone is either not generous or wise and vice versa. If someone is not creative then john is rich. If lucy is both not strong and not rich then someone is either not generous or not humble. Everyone who is not strong is brave or generous and vice versa. If alice is not calm or rich then someone is not brave and vice versa. If someone is not quiet then someone is quiet and vice versa. If paul is rich or not brave then paul is either not kind or not generous and vice versa. Everyone who is not humble or brave is both strong and not old and vice versa. Paul is either curious or calm. Someone is not curious. Someone is not creative or curious. Mary is calm or tall. John is not funny. Someone is not humble or not generous. Lucy is both not generous and not happy. Mary is patient. | Paul is tall. | contradiction | (((brave(susan)|~kind(susan)))<=>(?[X]:((~creative(X)<~>creative(X)))))&
(![X]:((~rich(X)<~>~humble(X))<=>(happy(X)&patient(X))))&
((?[X]:(tall(X)))=>(?[X]:((~kind(X)&kind(X)))))&
(![X]:((humble(X)|calm(X))<=>~quiet(X)))&
((?[X]:((curious(X)<~>~generous(X))))=>((~humble(john)<~>old(john))))&
(((~old(lucy)<~>~funny(lucy)))<=>((~tall(john)|~patient(john))))&
(((~creative(susan)&calm(susan)))=>((~humble(lucy)<~>~funny(lucy))))&
((?[X]:((~funny(X)&~calm(X))))<=>(?[X]:((~generous(X)<~>wise(X)))))&
((?[X]:(~creative(X)))=>(rich(john)))&
(((~strong(lucy)&~rich(lucy)))=>(?[X]:((~generous(X)<~>~humble(X)))))&
(![X]:(~strong(X)<=>(brave(X)|generous(X))))&
(((~calm(alice)|rich(alice)))<=>(?[X]:(~brave(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:(quiet(X))))&
(((rich(paul)|~brave(paul)))<=>((~kind(paul)<~>~generous(paul))))&
(![X]:((~humble(X)|brave(X))<=>(strong(X)&~old(X))))&
((curious(paul)<~>calm(paul)))&
(?[X]:(~curious(X)))&
(?[X]:((~creative(X)|curious(X))))&
((calm(mary)|tall(mary)))&
(~funny(john))&
(?[X]:((~humble(X)|~generous(X))))&
((~generous(lucy)&~happy(lucy)))&
(patient(mary)) | tall(paul) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 411542544448318276984187
% SZS output start Proof for 411542544448318276984187
3. ? [X0] : tall(X0) => ? [X0] : (kind(X0) & ~kind(X0)) [input p2]
24. tall(paul) [input hypothesis]
25. ? [X0] : tall(X0) => ? [X1] : (kind(X1) & ~kind(X1)) [rectify 3]
28. ? [X1] : (kind(X1) & ~kind(X1)) | ! [X0] : ~tall(X0) [ennf transformation 25]
42. ? [X0] : (kind(X0) & ~kind(X0)) | ! [X1] : ~tall(X1) [rectify 28]
43. ? [X0] : (kind(X0) & ~kind(X0)) => (kind(sK1) & ~kind(sK1)) [choice axiom]
44. (kind(sK1) & ~kind(sK1)) | ! [X1] : ~tall(X1) [skolemisation 42,43]
94. ~kind(sK1) | ~tall(X1) [cnf transformation 44]
95. kind(sK1) | ~tall(X1) [cnf transformation 44]
149. tall(paul) [cnf transformation 24]
169. 5 <=> ! [X1] : ~tall(X1) [avatar definition]
170. ~tall(X1) <- (5) [avatar component clause 169]
172. 6 <=> kind(sK1) [avatar definition]
175. 5 | 6 [avatar split clause 95,172,169]
176. 5 | ~6 [avatar split clause 94,172,169]
384. $false <- (5) [resolution 170,149]
385. ~5 [avatar contradiction clause 384]
386. $false [avatar sat refutation 175,176,385]
% SZS output end Proof for 411542544448318276984187
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet is both not patient and kind.
Everyone who is not wise or not calm is either calm or humble and vice versa.
Everyone who is not tall or not calm is either quiet or not creative.
Everyone who is not calm or calm is not creative or curious.
Everyone who is not quiet or rich is both patient and kind.
Everyone who is strong or funny is generous and vice versa.
If paul is strong or not happy then john is not brave or not wise.
Everyone who is not happy is generous or not brave.
If someone is either not brave or patient then susan is either wise or not brave.
Everyone who is not funny or creative is both not strong and not calm and vice versa.
If susan is not strong then someone is rich and vice versa.
If john is both not kind and not rich then someone is either not curious or humble and vice versa.
Everyone who is either brave or old is both not quiet and not brave.
If someone is both quiet and tall then someone is not quiet or strong and vice versa.
Everyone who is both not happy and not quiet is both creative and kind and vice versa.
Everyone who is not kind or not generous is both not generous and strong.
Susan is not generous or not wise.
Someone is not curious.
Susan is either tall or not rich. | John is calm. | entailment | (![X]:((~patient(X)<~>~quiet(X))=>(~patient(X)&kind(X))))&
(![X]:((~wise(X)|~calm(X))<=>(calm(X)<~>humble(X))))&
(![X]:((~tall(X)|~calm(X))=>(quiet(X)<~>~creative(X))))&
(![X]:((~calm(X)|calm(X))=>(~creative(X)|curious(X))))&
(![X]:((~quiet(X)|rich(X))=>(patient(X)&kind(X))))&
(![X]:((strong(X)|funny(X))<=>generous(X)))&
(((strong(paul)|~happy(paul)))=>((~brave(john)|~wise(john))))&
(![X]:(~happy(X)=>(generous(X)|~brave(X))))&
((?[X]:((~brave(X)<~>patient(X))))=>((wise(susan)<~>~brave(susan))))&
(![X]:((~funny(X)|creative(X))<=>(~strong(X)&~calm(X))))&
((~strong(susan))<=>(?[X]:(rich(X))))&
(((~kind(john)&~rich(john)))<=>(?[X]:((~curious(X)<~>humble(X)))))&
(![X]:((brave(X)<~>old(X))=>(~quiet(X)&~brave(X))))&
((?[X]:((quiet(X)&tall(X))))<=>(?[X]:((~quiet(X)|strong(X)))))&
(![X]:((~happy(X)&~quiet(X))<=>(creative(X)&kind(X))))&
(![X]:((~kind(X)|~generous(X))=>(~generous(X)&strong(X))))&
((~generous(susan)|~wise(susan)))&
(?[X]:(~curious(X)))&
((tall(susan)<~>~rich(susan))) | calm(john) | [
"p0",
"p2",
"p4",
"p5",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1784898662740615840305334
% SZS output start Proof for 1784898662740615840305334
1. ! [X0] : ((~patient(X0) <~> ~quiet(X0)) => (kind(X0) & ~patient(X0))) [input p0]
3. ! [X0] : ((~calm(X0) | ~tall(X0)) => (quiet(X0) <~> ~creative(X0))) [input p2]
5. ! [X0] : ((rich(X0) | ~quiet(X0)) => (kind(X0) & patient(X0))) [input p4]
6. ! [X0] : ((funny(X0) | strong(X0)) <=> generous(X0)) [input p5]
15. ! [X0] : ((~quiet(X0) & ~happy(X0)) <=> (kind(X0) & creative(X0))) [input p14]
16. ! [X0] : ((~generous(X0) | ~kind(X0)) => (strong(X0) & ~generous(X0))) [input p15]
20. ~calm(john) [input hypothesis]
22. ! [X0] : ((kind(X0) & ~patient(X0)) | (~patient(X0) <=> ~quiet(X0))) [ennf transformation 1]
23. ! [X0] : ((quiet(X0) <~> ~creative(X0)) | (calm(X0) & tall(X0))) [ennf transformation 3]
26. ! [X0] : ((kind(X0) & patient(X0)) | (~rich(X0) & quiet(X0))) [ennf transformation 5]
33. ! [X0] : ((strong(X0) & ~generous(X0)) | (generous(X0) & kind(X0))) [ennf transformation 16]
34. ! [X0] : ((kind(X0) & ~patient(X0)) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0)))) [nnf transformation 22]
37. ! [X0] : (((creative(X0) | ~quiet(X0)) & (~creative(X0) | quiet(X0))) | (calm(X0) & tall(X0))) [nnf transformation 23]
38. ! [X0] : (((funny(X0) | strong(X0)) | ~generous(X0)) & (generous(X0) | (~funny(X0) & ~strong(X0)))) [nnf transformation 6]
39. ! [X0] : ((funny(X0) | strong(X0) | ~generous(X0)) & (generous(X0) | (~funny(X0) & ~strong(X0)))) [flattening 38]
58. ! [X0] : (((~quiet(X0) & ~happy(X0)) | (~kind(X0) | ~creative(X0))) & ((kind(X0) & creative(X0)) | (quiet(X0) | happy(X0)))) [nnf transformation 15]
59. ! [X0] : (((~quiet(X0) & ~happy(X0)) | ~kind(X0) | ~creative(X0)) & ((kind(X0) & creative(X0)) | quiet(X0) | happy(X0))) [flattening 58]
64. ~patient(X0) | ~patient(X0) | quiet(X0) [cnf transformation 34]
76. ~quiet(X0) | creative(X0) | calm(X0) [cnf transformation 37]
79. patient(X0) | quiet(X0) [cnf transformation 26]
83. ~strong(X0) | generous(X0) [cnf transformation 39]
118. ~quiet(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 59]
119. ~generous(X0) | kind(X0) [cnf transformation 33]
122. strong(X0) | generous(X0) [cnf transformation 33]
127. ~calm(john) [cnf transformation 20]
131. ~patient(X0) | quiet(X0) [duplicate literal removal 64]
133. quiet(X0) [subsumption resolution 79,131]
232. ~creative(X0) | ~kind(X0) [subsumption resolution 118,133]
233. generous(X0) [subsumption resolution 122,83]
234. kind(X0) [subsumption resolution 119,233]
297. creative(X0) | calm(X0) [resolution 76,133]
325. calm(X3) | ~kind(X3) [resolution 297,232]
330. calm(X3) [subsumption resolution 325,234]
331. $false [resolution 330,127]
% SZS output end Proof for 1784898662740615840305334
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not rich and tall then john is both wise and not patient.
Everyone who is quiet or creative is not patient and vice versa.
If someone is either generous or curious then mary is both not brave and not patient and vice versa.
If someone is kind then john is both wise and not wise and vice versa.
Everyone who is both patient and not wise is either not rich or curious and vice versa.
If someone is either brave or not brave then someone is quiet.
If paul is either brave or not humble then alice is either happy or brave and vice versa.
If someone is funny or not tall then john is both generous and not generous and vice versa.
If paul is not calm then mary is both not tall and not humble and vice versa.
Everyone who is creative or happy is kind or not funny.
If paul is either wise or happy then paul is not funny or happy and vice versa.
Everyone who is humble or quiet is not old or not generous.
If someone is both generous and not wise then someone is either patient or brave.
Everyone who is patient is both brave and not wise.
Everyone who is either not calm or wise is either brave or calm.
Fred is not curious.
Alice is both not old and not strong.
Lucy is either not old or old.
Alice is not creative or wise.
John is not happy or patient.
Someone is not quiet or not rich.
Someone is not tall or strong. | John is not funny. | entailment | (((~rich(paul)&tall(paul)))=>((wise(john)&~patient(john))))&
(![X]:((quiet(X)|creative(X))<=>~patient(X)))&
((?[X]:((generous(X)<~>curious(X))))<=>((~brave(mary)&~patient(mary))))&
((?[X]:(kind(X)))<=>((wise(john)&~wise(john))))&
(![X]:((patient(X)&~wise(X))<=>(~rich(X)<~>curious(X))))&
((?[X]:((brave(X)<~>~brave(X))))=>(?[X]:(quiet(X))))&
(((brave(paul)<~>~humble(paul)))<=>((happy(alice)<~>brave(alice))))&
((?[X]:((funny(X)|~tall(X))))<=>((generous(john)&~generous(john))))&
((~calm(paul))<=>((~tall(mary)&~humble(mary))))&
(![X]:((creative(X)|happy(X))=>(kind(X)|~funny(X))))&
(((wise(paul)<~>happy(paul)))<=>((~funny(paul)|happy(paul))))&
(![X]:((humble(X)|quiet(X))=>(~old(X)|~generous(X))))&
((?[X]:((generous(X)&~wise(X))))=>(?[X]:((patient(X)<~>brave(X)))))&
(![X]:(patient(X)=>(brave(X)&~wise(X))))&
(![X]:((~calm(X)<~>wise(X))=>(brave(X)<~>calm(X))))&
(~curious(fred))&
((~old(alice)&~strong(alice)))&
((~old(lucy)<~>old(lucy)))&
((~creative(alice)|wise(alice)))&
((~happy(john)|patient(john)))&
(?[X]:((~quiet(X)|~rich(X))))&
(?[X]:((~tall(X)|strong(X)))) | ~funny(john) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3037364274348275262316562
% SZS output start Proof for 3037364274348275262316562
8. ? [X0] : (~tall(X0) | funny(X0)) <=> (~generous(john) & generous(john)) [input p7]
23. funny(john) [input hypothesis]
55. (? [X0] : (~tall(X0) | funny(X0)) | (generous(john) | ~generous(john))) & ((~generous(john) & generous(john)) | ! [X0] : (tall(X0) & ~funny(X0))) [nnf transformation 8]
56. (? [X0] : (~tall(X0) | funny(X0)) | generous(john) | ~generous(john)) & ((~generous(john) & generous(john)) | ! [X0] : (tall(X0) & ~funny(X0))) [flattening 55]
57. (? [X0] : (~tall(X0) | funny(X0)) | generous(john) | ~generous(john)) & ((~generous(john) & generous(john)) | ! [X1] : (tall(X1) & ~funny(X1))) [rectify 56]
58. ? [X0] : (~tall(X0) | funny(X0)) => (~tall(sK3) | funny(sK3)) [choice axiom]
59. ((~tall(sK3) | funny(sK3)) | generous(john) | ~generous(john)) & ((~generous(john) & generous(john)) | ! [X1] : (tall(X1) & ~funny(X1))) [skolemisation 57,58]
104. generous(john) | ~funny(X1) [cnf transformation 59]
106. ~generous(john) | ~funny(X1) [cnf transformation 59]
139. funny(john) [cnf transformation 23]
237. 20 <=> generous(john) [avatar definition]
242. 21 <=> ! [X1] : ~funny(X1) [avatar definition]
243. ~funny(X1) <- (21) [avatar component clause 242]
244. 21 | ~20 [avatar split clause 106,237,242]
246. 21 | 20 [avatar split clause 104,237,242]
325. $false <- (21) [resolution 243,139]
326. ~21 [avatar contradiction clause 325]
327. $false [avatar sat refutation 244,246,326]
% SZS output end Proof for 3037364274348275262316562
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or generous is either creative or not calm and vice versa.
If someone is either creative or strong then mary is not brave.
Everyone who is both humble and happy is either not kind or funny and vice versa.
Everyone who is not quiet is not brave or not rich and vice versa.
Everyone who is old is generous or not old and vice versa.
Everyone who is not rich is both strong and quiet.
Everyone who is both not rich and not tall is both patient and happy.
Everyone who is quiet or not funny is curious or generous.
If someone is humble or not kind then someone is not brave or not old and vice versa.
If someone is either tall or not happy then susan is not happy or strong and vice versa.
If someone is not quiet then someone is strong and vice versa.
If someone is either not brave or curious then someone is both happy and not creative.
If john is both tall and not patient then someone is either not funny or not generous.
If someone is wise or not wise then someone is happy or not kind.
If someone is both not quiet and not funny then someone is not happy or not humble.
Everyone who is calm is either calm or patient and vice versa.
Someone is not funny or generous.
Paul is not happy or not brave.
Someone is quiet or brave.
Alice is both not creative and not tall.
Mary is either not brave or not patient.
John is both happy and not wise. | Susan is happy. | neutral | (![X]:((old(X)|generous(X))<=>(creative(X)<~>~calm(X))))&
((?[X]:((creative(X)<~>strong(X))))=>(~brave(mary)))&
(![X]:((humble(X)&happy(X))<=>(~kind(X)<~>funny(X))))&
(![X]:(~quiet(X)<=>(~brave(X)|~rich(X))))&
(![X]:(old(X)<=>(generous(X)|~old(X))))&
(![X]:(~rich(X)=>(strong(X)&quiet(X))))&
(![X]:((~rich(X)&~tall(X))=>(patient(X)&happy(X))))&
(![X]:((quiet(X)|~funny(X))=>(curious(X)|generous(X))))&
((?[X]:((humble(X)|~kind(X))))<=>(?[X]:((~brave(X)|~old(X)))))&
((?[X]:((tall(X)<~>~happy(X))))<=>((~happy(susan)|strong(susan))))&
((?[X]:(~quiet(X)))<=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)<~>curious(X))))=>(?[X]:((happy(X)&~creative(X)))))&
(((tall(john)&~patient(john)))=>(?[X]:((~funny(X)<~>~generous(X)))))&
((?[X]:((wise(X)|~wise(X))))=>(?[X]:((happy(X)|~kind(X)))))&
((?[X]:((~quiet(X)&~funny(X))))=>(?[X]:((~happy(X)|~humble(X)))))&
(![X]:(calm(X)<=>(calm(X)<~>patient(X))))&
(?[X]:((~funny(X)|generous(X))))&
((~happy(paul)|~brave(paul)))&
(?[X]:((quiet(X)|brave(X))))&
((~creative(alice)&~tall(alice)))&
((~brave(mary)<~>~patient(mary)))&
((happy(john)&~wise(john))) | happy(susan) | [] | null | 0 |
If someone is not quiet then someone is both not curious and tall and vice versa.
Everyone who is both brave and not kind is not creative and vice versa.
If alice is curious or not creative then someone is kind.
Everyone who is both curious and not humble is quiet and vice versa.
Everyone who is both wise and creative is not quiet.
If paul is both not quiet and not humble then someone is either strong or brave and vice versa.
Everyone who is both happy and curious is wise.
Everyone who is both rich and not wise is not curious and vice versa.
If someone is either happy or strong then someone is old.
If someone is not rich or not tall then mary is not old.
If someone is both generous and not old then lucy is either not curious or not generous.
Everyone who is either tall or kind is either kind or not kind and vice versa.
Everyone who is either patient or not strong is not patient or old and vice versa.
Everyone who is either calm or not strong is either kind or not brave and vice versa.
Everyone who is both not patient and not funny is both old and not quiet.
Everyone who is not quiet or wise is not strong or funny and vice versa.
Someone is either curious or creative.
Someone is either not old or rich.
Fred is both curious and brave.
Someone is either not curious or creative.
Someone is creative.
Someone is either creative or humble.
John is not patient or calm. | Mary is wise. | neutral | ((?[X]:(~quiet(X)))<=>(?[X]:((~curious(X)&tall(X)))))&
(![X]:((brave(X)&~kind(X))<=>~creative(X)))&
(((curious(alice)|~creative(alice)))=>(?[X]:(kind(X))))&
(![X]:((curious(X)&~humble(X))<=>quiet(X)))&
(![X]:((wise(X)&creative(X))=>~quiet(X)))&
(((~quiet(paul)&~humble(paul)))<=>(?[X]:((strong(X)<~>brave(X)))))&
(![X]:((happy(X)&curious(X))=>wise(X)))&
(![X]:((rich(X)&~wise(X))<=>~curious(X)))&
((?[X]:((happy(X)<~>strong(X))))=>(?[X]:(old(X))))&
((?[X]:((~rich(X)|~tall(X))))=>(~old(mary)))&
((?[X]:((generous(X)&~old(X))))=>((~curious(lucy)<~>~generous(lucy))))&
(![X]:((tall(X)<~>kind(X))<=>(kind(X)<~>~kind(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(~patient(X)|old(X))))&
(![X]:((calm(X)<~>~strong(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((~patient(X)&~funny(X))=>(old(X)&~quiet(X))))&
(![X]:((~quiet(X)|wise(X))<=>(~strong(X)|funny(X))))&
(?[X]:((curious(X)<~>creative(X))))&
(?[X]:((~old(X)<~>rich(X))))&
((curious(fred)&brave(fred)))&
(?[X]:((~curious(X)<~>creative(X))))&
(?[X]:(creative(X)))&
(?[X]:((creative(X)<~>humble(X))))&
((~patient(john)|calm(john))) | wise(mary) | [] | null | 0 |
Everyone who is humble or brave is not creative.
Everyone who is either brave or humble is rich.
Everyone who is not happy or not old is either not curious or brave.
Everyone who is both not generous and calm is humble and vice versa.
If someone is either patient or not patient then susan is not quiet or not old.
Everyone who is calm or rich is either not rich or not brave.
Everyone who is either not happy or not calm is either kind or calm.
Everyone who is both not creative and humble is both quiet and humble and vice versa.
If someone is either wise or not quiet then alice is both creative and humble and vice versa.
If paul is either generous or not generous then someone is both tall and creative.
If someone is not kind or not rich then mary is both not rich and patient.
Everyone who is both not strong and quiet is not generous or calm and vice versa.
If someone is both not funny and happy then john is both not happy and tall and vice versa.
If someone is both funny and creative then someone is not humble.
Everyone who is both kind and brave is not calm and vice versa.
Everyone who is not patient is either not strong or not tall and vice versa.
Someone is wise or creative.
Fred is not curious or curious.
John is both not strong and not kind.
Paul is not happy or not patient.
Someone is old or creative.
John is old.
Alice is either wise or patient. | Susan is not wise. | entailment | (![X]:((humble(X)|brave(X))=>~creative(X)))&
(![X]:((brave(X)<~>humble(X))=>rich(X)))&
(![X]:((~happy(X)|~old(X))=>(~curious(X)<~>brave(X))))&
(![X]:((~generous(X)&calm(X))<=>humble(X)))&
((?[X]:((patient(X)<~>~patient(X))))=>((~quiet(susan)|~old(susan))))&
(![X]:((calm(X)|rich(X))=>(~rich(X)<~>~brave(X))))&
(![X]:((~happy(X)<~>~calm(X))=>(kind(X)<~>calm(X))))&
(![X]:((~creative(X)&humble(X))<=>(quiet(X)&humble(X))))&
((?[X]:((wise(X)<~>~quiet(X))))<=>((creative(alice)&humble(alice))))&
(((generous(paul)<~>~generous(paul)))=>(?[X]:((tall(X)&creative(X)))))&
((?[X]:((~kind(X)|~rich(X))))=>((~rich(mary)&patient(mary))))&
(![X]:((~strong(X)&quiet(X))<=>(~generous(X)|calm(X))))&
((?[X]:((~funny(X)&happy(X))))<=>((~happy(john)&tall(john))))&
((?[X]:((funny(X)&creative(X))))=>(?[X]:(~humble(X))))&
(![X]:((kind(X)&brave(X))<=>~calm(X)))&
(![X]:(~patient(X)<=>(~strong(X)<~>~tall(X))))&
(?[X]:((wise(X)|creative(X))))&
((~curious(fred)|curious(fred)))&
((~strong(john)&~kind(john)))&
((~happy(paul)|~patient(paul)))&
(?[X]:((old(X)|creative(X))))&
(old(john))&
((wise(alice)<~>patient(alice))) | ~wise(susan) | [
"p0",
"p1",
"p3",
"p5",
"p8",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2067965295720654804265857
% SZS output start Proof for 2067965295720654804265857
1. ! [X0] : ((brave(X0) | humble(X0)) => ~creative(X0)) [input p0]
2. ! [X0] : ((brave(X0) <~> humble(X0)) => rich(X0)) [input p1]
4. ! [X0] : ((calm(X0) & ~generous(X0)) <=> humble(X0)) [input p3]
6. ! [X0] : ((rich(X0) | calm(X0)) => (~rich(X0) <~> ~brave(X0))) [input p5]
9. ? [X0] : (wise(X0) <~> ~quiet(X0)) <=> (humble(alice) & creative(alice)) [input p8]
12. ! [X0] : ((quiet(X0) & ~strong(X0)) <=> (calm(X0) | ~generous(X0))) [input p11]
15. ! [X0] : ((brave(X0) & kind(X0)) <=> ~calm(X0)) [input p14]
24. wise(susan) [input hypothesis]
26. ! [X0] : (~creative(X0) | (~brave(X0) & ~humble(X0))) [ennf transformation 1]
27. ! [X0] : (rich(X0) | (brave(X0) <=> humble(X0))) [ennf transformation 2]
31. ! [X0] : ((~rich(X0) <~> ~brave(X0)) | (~rich(X0) & ~calm(X0))) [ennf transformation 6]
36. ! [X0] : (rich(X0) | ((brave(X0) | ~humble(X0)) & (humble(X0) | ~brave(X0)))) [nnf transformation 27]
38. ! [X0] : (((calm(X0) & ~generous(X0)) | ~humble(X0)) & (humble(X0) | (~calm(X0) | generous(X0)))) [nnf transformation 4]
39. ! [X0] : (((calm(X0) & ~generous(X0)) | ~humble(X0)) & (humble(X0) | ~calm(X0) | generous(X0))) [flattening 38]
41. ! [X0] : (((brave(X0) | rich(X0)) & (~brave(X0) | ~rich(X0))) | (~rich(X0) & ~calm(X0))) [nnf transformation 31]
45. (? [X0] : ((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | (~humble(alice) | ~creative(alice))) & ((humble(alice) & creative(alice)) | ! [X0] : ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) [nnf transformation 9]
46. (? [X0] : ((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | ~humble(alice) | ~creative(alice)) & ((humble(alice) & creative(alice)) | ! [X0] : ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) [flattening 45]
47. (? [X0] : ((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | ~humble(alice) | ~creative(alice)) & ((humble(alice) & creative(alice)) | ! [X1] : ((wise(X1) | quiet(X1)) & (~quiet(X1) | ~wise(X1)))) [rectify 46]
48. ? [X0] : ((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) => ((quiet(sK0) | ~wise(sK0)) & (~quiet(sK0) | wise(sK0))) [choice axiom]
49. (((quiet(sK0) | ~wise(sK0)) & (~quiet(sK0) | wise(sK0))) | ~humble(alice) | ~creative(alice)) & ((humble(alice) & creative(alice)) | ! [X1] : ((wise(X1) | quiet(X1)) & (~quiet(X1) | ~wise(X1)))) [skolemisation 47,48]
53. ! [X0] : (((quiet(X0) & ~strong(X0)) | (~calm(X0) & generous(X0))) & ((calm(X0) | ~generous(X0)) | (~quiet(X0) | strong(X0)))) [nnf transformation 12]
54. ! [X0] : (((quiet(X0) & ~strong(X0)) | (~calm(X0) & generous(X0))) & (calm(X0) | ~generous(X0) | ~quiet(X0) | strong(X0))) [flattening 53]
63. ! [X0] : (((brave(X0) & kind(X0)) | calm(X0)) & (~calm(X0) | (~brave(X0) | ~kind(X0)))) [nnf transformation 15]
64. ! [X0] : (((brave(X0) & kind(X0)) | calm(X0)) & (~calm(X0) | ~brave(X0) | ~kind(X0))) [flattening 63]
71. ~creative(X0) | ~humble(X0) [cnf transformation 26]
73. ~brave(X0) | humble(X0) | rich(X0) [cnf transformation 36]
80. ~generous(X0) | ~humble(X0) [cnf transformation 39]
85. ~brave(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 41]
96. creative(alice) | ~quiet(X1) | ~wise(X1) [cnf transformation 49]
98. humble(alice) | ~quiet(X1) | ~wise(X1) [cnf transformation 49]
113. quiet(X0) | generous(X0) [cnf transformation 54]
114. ~calm(X0) | quiet(X0) [cnf transformation 54]
122. calm(X0) | brave(X0) [cnf transformation 64]
136. wise(susan) [cnf transformation 24]
143. ~rich(X0) | ~brave(X0) [duplicate literal removal 85]
150. 2 <=> quiet(susan) [avatar definition]
152. ~quiet(susan) <- (~2) [avatar component clause 150]
167. 6 <=> humble(alice) [avatar definition]
169. humble(alice) <- (6) [avatar component clause 167]
172. 7 <=> ! [X1] : (~quiet(X1) | ~wise(X1)) [avatar definition]
173. ~wise(X1) | ~quiet(X1) <- (7) [avatar component clause 172]
174. 7 | 6 [avatar split clause 98,167,172]
176. 8 <=> creative(alice) [avatar definition]
178. creative(alice) <- (8) [avatar component clause 176]
180. 7 | 8 [avatar split clause 96,176,172]
283. ~humble(alice) <- (8) [resolution 71,178]
285. $false <- (6, 8) [subsumption resolution 283,169]
286. ~6 | ~8 [avatar contradiction clause 285]
294. quiet(X0) | brave(X0) [resolution 122,114]
297. ~quiet(susan) <- (7) [resolution 173,136]
334. ~2 | ~7 [avatar split clause 297,172,150]
335. brave(susan) <- (~2) [resolution 152,294]
336. generous(susan) <- (~2) [resolution 152,113]
341. ~humble(susan) <- (~2) [resolution 336,80]
386. humble(susan) | rich(susan) <- (~2) [resolution 335,73]
387. rich(susan) <- (~2) [subsumption resolution 386,341]
510. ~brave(susan) <- (~2) [resolution 387,143]
511. $false <- (~2) [subsumption resolution 510,335]
512. 2 [avatar contradiction clause 511]
513. $false [avatar sat refutation 174,180,286,334,512]
% SZS output end Proof for 2067965295720654804265857
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either happy or not tall then john is either not creative or not old and vice versa. Everyone who is not patient is both not quiet and strong and vice versa. If someone is not old then john is either not brave or calm. If someone is both not brave and not happy then someone is either not creative or curious and vice versa. If paul is not old or not patient then alice is either not wise or funny. If someone is tall then john is both not curious and calm. If john is kind or patient then mary is either old or funny. Everyone who is either not calm or not funny is not brave and vice versa. Everyone who is either not old or not funny is old and vice versa. Everyone who is not generous or creative is both wise and curious and vice versa. Everyone who is both kind and funny is not curious or not calm. If alice is either tall or not old then someone is both not tall and patient and vice versa. If mary is generous then alice is not calm or generous and vice versa. If someone is not curious then someone is not tall. Everyone who is wise or not curious is both not tall and not old and vice versa. If lucy is not quiet or humble then someone is not funny. Paul is old or not creative. Alice is either kind or strong. Someone is either quiet or not creative. John is both rich and old. Someone is quiet or not wise. | Lucy is not wise. | entailment | (((happy(fred)<~>~tall(fred)))<=>((~creative(john)<~>~old(john))))&
(![X]:(~patient(X)<=>(~quiet(X)&strong(X))))&
((?[X]:(~old(X)))=>((~brave(john)<~>calm(john))))&
((?[X]:((~brave(X)&~happy(X))))<=>(?[X]:((~creative(X)<~>curious(X)))))&
(((~old(paul)|~patient(paul)))=>((~wise(alice)<~>funny(alice))))&
((?[X]:(tall(X)))=>((~curious(john)&calm(john))))&
(((kind(john)|patient(john)))=>((old(mary)<~>funny(mary))))&
(![X]:((~calm(X)<~>~funny(X))<=>~brave(X)))&
(![X]:((~old(X)<~>~funny(X))<=>old(X)))&
(![X]:((~generous(X)|creative(X))<=>(wise(X)&curious(X))))&
(![X]:((kind(X)&funny(X))=>(~curious(X)|~calm(X))))&
(((tall(alice)<~>~old(alice)))<=>(?[X]:((~tall(X)&patient(X)))))&
((generous(mary))<=>((~calm(alice)|generous(alice))))&
((?[X]:(~curious(X)))=>(?[X]:(~tall(X))))&
(![X]:((wise(X)|~curious(X))<=>(~tall(X)&~old(X))))&
(((~quiet(lucy)|humble(lucy)))=>(?[X]:(~funny(X))))&
((old(paul)|~creative(paul)))&
((kind(alice)<~>strong(alice)))&
(?[X]:((quiet(X)<~>~creative(X))))&
((rich(john)&old(john)))&
(?[X]:((quiet(X)|~wise(X)))) | ~wise(lucy) | [
"p2",
"p7",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6375282234567825932155
% SZS output start Proof for 6375282234567825932155
3. ? [X0] : ~old(X0) => (~brave(john) <~> calm(john)) [input p2]
8. ! [X0] : ((~calm(X0) <~> ~funny(X0)) <=> ~brave(X0)) [input p7]
9. ! [X0] : ((~old(X0) <~> ~funny(X0)) <=> old(X0)) [input p8]
15. ! [X0] : ((~curious(X0) | wise(X0)) <=> (~old(X0) & ~tall(X0))) [input p14]
22. wise(lucy) [input hypothesis]
27. (~brave(john) <~> calm(john)) | ! [X0] : old(X0) [ennf transformation 3]
38. ((~calm(john) | brave(john)) & (calm(john) | ~brave(john))) | ! [X0] : old(X0) [nnf transformation 27]
46. ! [X0] : ((((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) | brave(X0)) & (~brave(X0) | ((~calm(X0) | funny(X0)) & (~funny(X0) | calm(X0))))) [nnf transformation 8]
47. ! [X0] : ((((funny(X0) | old(X0)) & (~funny(X0) | ~old(X0))) | ~old(X0)) & (old(X0) | ((~old(X0) | funny(X0)) & (~funny(X0) | old(X0))))) [nnf transformation 9]
59. ! [X0] : (((~curious(X0) | wise(X0)) | (old(X0) | tall(X0))) & ((~old(X0) & ~tall(X0)) | (curious(X0) & ~wise(X0)))) [nnf transformation 15]
60. ! [X0] : ((~curious(X0) | wise(X0) | old(X0) | tall(X0)) & ((~old(X0) & ~tall(X0)) | (curious(X0) & ~wise(X0)))) [flattening 59]
80. calm(john) | ~brave(john) | old(X0) [cnf transformation 38]
81. ~calm(john) | brave(john) | old(X0) [cnf transformation 38]
99. ~calm(X0) | ~brave(X0) | funny(X0) [cnf transformation 46]
101. funny(X0) | calm(X0) | brave(X0) [cnf transformation 46]
102. old(X0) | ~funny(X0) | old(X0) [cnf transformation 47]
104. ~funny(X0) | ~old(X0) | ~old(X0) [cnf transformation 47]
124. ~wise(X0) | ~old(X0) [cnf transformation 60]
135. wise(lucy) [cnf transformation 22]
136. old(X0) | ~funny(X0) [duplicate literal removal 102]
137. ~funny(X0) | ~old(X0) [duplicate literal removal 104]
163. 5 <=> ! [X0] : old(X0) [avatar definition]
164. old(X0) <- (5) [avatar component clause 163]
166. 6 <=> brave(john) [avatar definition]
167. ~brave(john) <- (~6) [avatar component clause 166]
168. brave(john) <- (6) [avatar component clause 166]
170. 7 <=> calm(john) [avatar definition]
171. calm(john) <- (7) [avatar component clause 170]
172. ~calm(john) <- (~7) [avatar component clause 170]
173. 5 | 6 | ~7 [avatar split clause 81,170,166,163]
174. 5 | ~6 | 7 [avatar split clause 80,170,166,163]
255. ~funny(X0) [subsumption resolution 136,137]
344. ~old(lucy) [resolution 124,135]
356. ~brave(john) | funny(john) <- (7) [resolution 99,171]
357. funny(john) <- (6, 7) [subsumption resolution 356,168]
358. $false <- (6, 7) [subsumption resolution 357,255]
359. ~6 | ~7 [avatar contradiction clause 358]
363. calm(X3) | brave(X3) [resolution 101,255]
385. brave(john) <- (~7) [resolution 363,172]
386. $false <- (~6, ~7) [subsumption resolution 385,167]
387. 6 | 7 [avatar contradiction clause 386]
390. $false <- (5) [resolution 164,344]
391. ~5 [avatar contradiction clause 390]
393. $false [avatar sat refutation 173,174,359,387,391]
% SZS output end Proof for 6375282234567825932155
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall is quiet and vice versa. If someone is not strong or not kind then someone is not wise. Everyone who is both not humble and not strong is both not calm and not strong. If someone is both wise and not humble then mary is humble. If alice is both old and rich then someone is both not funny and quiet. If paul is not calm then susan is either old or not rich. Everyone who is both funny and not patient is rich and vice versa. Everyone who is both not brave and humble is kind or not calm. If john is happy then fred is either not old or not happy and vice versa. If someone is either brave or creative then someone is not brave and vice versa. Everyone who is curious is funny. If lucy is funny then fred is not quiet and vice versa. Everyone who is calm is either funny or not rich and vice versa. If john is not kind then someone is either quiet or old. Everyone who is not strong is both generous and old and vice versa. If someone is either patient or kind then fred is both curious and not rich and vice versa. Someone is either creative or not strong. Someone is calm or not creative. Paul is not brave. Susan is not tall. Fred is not funny or not creative. Susan is happy. Someone is either not generous or strong. | Mary is calm. | neutral | (![X]:(tall(X)<=>quiet(X)))&
((?[X]:((~strong(X)|~kind(X))))=>(?[X]:(~wise(X))))&
(![X]:((~humble(X)&~strong(X))=>(~calm(X)&~strong(X))))&
((?[X]:((wise(X)&~humble(X))))=>(humble(mary)))&
(((old(alice)&rich(alice)))=>(?[X]:((~funny(X)&quiet(X)))))&
((~calm(paul))=>((old(susan)<~>~rich(susan))))&
(![X]:((funny(X)&~patient(X))<=>rich(X)))&
(![X]:((~brave(X)&humble(X))=>(kind(X)|~calm(X))))&
((happy(john))<=>((~old(fred)<~>~happy(fred))))&
((?[X]:((brave(X)<~>creative(X))))<=>(?[X]:(~brave(X))))&
(![X]:(curious(X)=>funny(X)))&
((funny(lucy))<=>(~quiet(fred)))&
(![X]:(calm(X)<=>(funny(X)<~>~rich(X))))&
((~kind(john))=>(?[X]:((quiet(X)<~>old(X)))))&
(![X]:(~strong(X)<=>(generous(X)&old(X))))&
((?[X]:((patient(X)<~>kind(X))))<=>((curious(fred)&~rich(fred))))&
(?[X]:((creative(X)<~>~strong(X))))&
(?[X]:((calm(X)|~creative(X))))&
(~brave(paul))&
(~tall(susan))&
((~funny(fred)|~creative(fred)))&
(happy(susan))&
(?[X]:((~generous(X)<~>strong(X)))) | calm(mary) | [] | null | 0 |
Everyone who is kind is either not generous or brave and vice versa.
If paul is both not curious and not kind then paul is not generous and vice versa.
If paul is both tall and not kind then someone is either tall or not strong and vice versa.
If fred is not wise or happy then mary is not creative and vice versa.
If someone is either not quiet or patient then someone is wise or not quiet.
If fred is not curious then someone is not creative or not old and vice versa.
If someone is either not patient or humble then someone is funny or not old.
If mary is both generous and rich then alice is both curious and humble.
Everyone who is either not brave or not old is brave or not creative.
Everyone who is not patient is brave or creative and vice versa.
If someone is not strong then someone is either old or not old.
Everyone who is either not brave or humble is patient.
Everyone who is wise or not happy is strong and vice versa.
Everyone who is not funny is both not happy and not generous.
Everyone who is wise is old and vice versa.
Everyone who is quiet or old is both happy and curious.
Lucy is both funny and humble.
Fred is both not rich and generous.
Alice is either not patient or curious.
Someone is either creative or wise.
Someone is either not humble or not old.
Someone is both quiet and not calm.
Someone is not strong or creative.
John is quiet. | Paul is not generous. | neutral | (![X]:(kind(X)<=>(~generous(X)<~>brave(X))))&
(((~curious(paul)&~kind(paul)))<=>(~generous(paul)))&
(((tall(paul)&~kind(paul)))<=>(?[X]:((tall(X)<~>~strong(X)))))&
(((~wise(fred)|happy(fred)))<=>(~creative(mary)))&
((?[X]:((~quiet(X)<~>patient(X))))=>(?[X]:((wise(X)|~quiet(X)))))&
((~curious(fred))<=>(?[X]:((~creative(X)|~old(X)))))&
((?[X]:((~patient(X)<~>humble(X))))=>(?[X]:((funny(X)|~old(X)))))&
(((generous(mary)&rich(mary)))=>((curious(alice)&humble(alice))))&
(![X]:((~brave(X)<~>~old(X))=>(brave(X)|~creative(X))))&
(![X]:(~patient(X)<=>(brave(X)|creative(X))))&
((?[X]:(~strong(X)))=>(?[X]:((old(X)<~>~old(X)))))&
(![X]:((~brave(X)<~>humble(X))=>patient(X)))&
(![X]:((wise(X)|~happy(X))<=>strong(X)))&
(![X]:(~funny(X)=>(~happy(X)&~generous(X))))&
(![X]:(wise(X)<=>old(X)))&
(![X]:((quiet(X)|old(X))=>(happy(X)&curious(X))))&
((funny(lucy)&humble(lucy)))&
((~rich(fred)&generous(fred)))&
((~patient(alice)<~>curious(alice)))&
(?[X]:((creative(X)<~>wise(X))))&
(?[X]:((~humble(X)<~>~old(X))))&
(?[X]:((quiet(X)&~calm(X))))&
(?[X]:((~strong(X)|creative(X))))&
(quiet(john)) | ~generous(paul) | [] | null | 0 |
Everyone who is both strong and tall is both tall and not rich. Everyone who is either not calm or not kind is happy or not calm and vice versa. If someone is not wise then lucy is both patient and not calm and vice versa. If someone is either not happy or not humble then fred is patient and vice versa. Everyone who is both not curious and kind is rich and vice versa. Everyone who is both not generous and not creative is both strong and patient. If susan is humble or happy then someone is brave or not wise and vice versa. Everyone who is either creative or old is both not happy and not old. If someone is not creative or strong then lucy is both not quiet and creative and vice versa. Everyone who is not calm or not brave is both not curious and calm and vice versa. If susan is both not strong and not kind then fred is not brave or kind. If someone is not quiet then susan is rich or not old and vice versa. Everyone who is not funny or not generous is both not strong and not brave and vice versa. If mary is creative or not old then paul is not quiet or not brave. Everyone who is either not happy or not rich is not kind or curious. Everyone who is both not generous and not calm is old and vice versa. Someone is brave. Susan is not strong or kind. Someone is wise or brave. Susan is calm or not rich. Paul is both not strong and not quiet. Someone is not strong or not humble. Mary is kind or quiet. | Susan is not old. | entailment | (![X]:((strong(X)&tall(X))=>(tall(X)&~rich(X))))&
(![X]:((~calm(X)<~>~kind(X))<=>(happy(X)|~calm(X))))&
((?[X]:(~wise(X)))<=>((patient(lucy)&~calm(lucy))))&
((?[X]:((~happy(X)<~>~humble(X))))<=>(patient(fred)))&
(![X]:((~curious(X)&kind(X))<=>rich(X)))&
(![X]:((~generous(X)&~creative(X))=>(strong(X)&patient(X))))&
(((humble(susan)|happy(susan)))<=>(?[X]:((brave(X)|~wise(X)))))&
(![X]:((creative(X)<~>old(X))=>(~happy(X)&~old(X))))&
((?[X]:((~creative(X)|strong(X))))<=>((~quiet(lucy)&creative(lucy))))&
(![X]:((~calm(X)|~brave(X))<=>(~curious(X)&calm(X))))&
(((~strong(susan)&~kind(susan)))=>((~brave(fred)|kind(fred))))&
((?[X]:(~quiet(X)))<=>((rich(susan)|~old(susan))))&
(![X]:((~funny(X)|~generous(X))<=>(~strong(X)&~brave(X))))&
(((creative(mary)|~old(mary)))=>((~quiet(paul)|~brave(paul))))&
(![X]:((~happy(X)<~>~rich(X))=>(~kind(X)|curious(X))))&
(![X]:((~generous(X)&~calm(X))<=>old(X)))&
(?[X]:(brave(X)))&
((~strong(susan)|kind(susan)))&
(?[X]:((wise(X)|brave(X))))&
((calm(susan)|~rich(susan)))&
((~strong(paul)&~quiet(paul)))&
(?[X]:((~strong(X)|~humble(X))))&
((kind(mary)|quiet(mary))) | ~old(susan) | [
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2056797605480724154246920
% SZS output start Proof for 2056797605480724154246920
10. ! [X0] : ((~brave(X0) | ~calm(X0)) <=> (calm(X0) & ~curious(X0))) [input p9]
16. ! [X0] : ((~calm(X0) & ~generous(X0)) <=> old(X0)) [input p15]
24. old(susan) [input hypothesis]
60. ! [X0] : (((~brave(X0) | ~calm(X0)) | (~calm(X0) | curious(X0))) & ((calm(X0) & ~curious(X0)) | (brave(X0) & calm(X0)))) [nnf transformation 10]
61. ! [X0] : ((~brave(X0) | ~calm(X0) | ~calm(X0) | curious(X0)) & ((calm(X0) & ~curious(X0)) | (brave(X0) & calm(X0)))) [flattening 60]
70. ! [X0] : (((~calm(X0) & ~generous(X0)) | ~old(X0)) & (old(X0) | (calm(X0) | generous(X0)))) [nnf transformation 16]
71. ! [X0] : (((~calm(X0) & ~generous(X0)) | ~old(X0)) & (old(X0) | calm(X0) | generous(X0))) [flattening 70]
113. calm(X0) | calm(X0) [cnf transformation 61]
131. ~calm(X0) | ~old(X0) [cnf transformation 71]
140. old(susan) [cnf transformation 24]
141. calm(X0) [duplicate literal removal 113]
292. ~old(X0) [subsumption resolution 131,141]
322. $false [subsumption resolution 140,292]
% SZS output end Proof for 2056797605480724154246920
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not quiet or patient then someone is tall and vice versa. Everyone who is both curious and not happy is either happy or not patient. If alice is either not generous or patient then someone is not happy or not strong and vice versa. Everyone who is patient is not curious or wise and vice versa. Everyone who is funny is either not kind or not brave and vice versa. Everyone who is brave is both not curious and not patient and vice versa. If someone is either not generous or strong then mary is not wise and vice versa. If lucy is quiet or not brave then someone is either not strong or wise and vice versa. If alice is either humble or not tall then someone is both not generous and strong. Everyone who is not wise is either wise or not quiet and vice versa. If someone is quiet then susan is not old. If mary is not patient or not creative then lucy is either generous or not creative and vice versa. Everyone who is both not strong and brave is tall or wise and vice versa. Everyone who is not rich is both generous and not calm and vice versa. If someone is either not brave or humble then susan is both calm and not generous. Everyone who is not patient or generous is either not quiet or not rich. Susan is either kind or not kind. Susan is either not happy or not funny. Alice is not generous or not quiet. Lucy is not tall. Someone is both not calm and not humble. Susan is either not creative or happy. John is either not creative or calm. Someone is not old or wise. | Susan is not calm. | contradiction | ((?[X]:((~quiet(X)<~>patient(X))))<=>(?[X]:(tall(X))))&
(![X]:((curious(X)&~happy(X))=>(happy(X)<~>~patient(X))))&
(((~generous(alice)<~>patient(alice)))<=>(?[X]:((~happy(X)|~strong(X)))))&
(![X]:(patient(X)<=>(~curious(X)|wise(X))))&
(![X]:(funny(X)<=>(~kind(X)<~>~brave(X))))&
(![X]:(brave(X)<=>(~curious(X)&~patient(X))))&
((?[X]:((~generous(X)<~>strong(X))))<=>(~wise(mary)))&
(((quiet(lucy)|~brave(lucy)))<=>(?[X]:((~strong(X)<~>wise(X)))))&
(((humble(alice)<~>~tall(alice)))=>(?[X]:((~generous(X)&strong(X)))))&
(![X]:(~wise(X)<=>(wise(X)<~>~quiet(X))))&
((?[X]:(quiet(X)))=>(~old(susan)))&
(((~patient(mary)|~creative(mary)))<=>((generous(lucy)<~>~creative(lucy))))&
(![X]:((~strong(X)&brave(X))<=>(tall(X)|wise(X))))&
(![X]:(~rich(X)<=>(generous(X)&~calm(X))))&
((?[X]:((~brave(X)<~>humble(X))))=>((calm(susan)&~generous(susan))))&
(![X]:((~patient(X)|generous(X))=>(~quiet(X)<~>~rich(X))))&
((kind(susan)<~>~kind(susan)))&
((~happy(susan)<~>~funny(susan)))&
((~generous(alice)|~quiet(alice)))&
(~tall(lucy))&
(?[X]:((~calm(X)&~humble(X))))&
((~creative(susan)<~>happy(susan)))&
((~creative(john)<~>calm(john)))&
(?[X]:((~old(X)|wise(X)))) | ~calm(susan) | [
"p0",
"p3",
"p5",
"p9",
"p12",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7831477499141326389478148
% SZS output start Proof for 7831477499141326389478148
1. ? [X0] : (~quiet(X0) <~> patient(X0)) <=> ? [X0] : tall(X0) [input p0]
4. ! [X0] : (patient(X0) <=> (wise(X0) | ~curious(X0))) [input p3]
6. ! [X0] : (brave(X0) <=> (~patient(X0) & ~curious(X0))) [input p5]
10. ! [X0] : (~wise(X0) <=> (wise(X0) <~> ~quiet(X0))) [input p9]
13. ! [X0] : ((brave(X0) & ~strong(X0)) <=> (wise(X0) | tall(X0))) [input p12]
15. ? [X0] : (~brave(X0) <~> humble(X0)) => (~generous(susan) & calm(susan)) [input p14]
21. ? [X0] : (~humble(X0) & ~calm(X0)) [input p20]
25. ~calm(susan) [input hypothesis]
26. ? [X0] : (~quiet(X0) <~> patient(X0)) <=> ? [X1] : tall(X1) [rectify 1]
32. (~generous(susan) & calm(susan)) | ! [X0] : (~brave(X0) <=> humble(X0)) [ennf transformation 15]
34. (? [X0] : ((~patient(X0) | quiet(X0)) & (patient(X0) | ~quiet(X0))) | ! [X1] : ~tall(X1)) & (? [X1] : tall(X1) | ! [X0] : ((~quiet(X0) | ~patient(X0)) & (patient(X0) | quiet(X0)))) [nnf transformation 26]
35. (? [X0] : ((~patient(X0) | quiet(X0)) & (patient(X0) | ~quiet(X0))) | ! [X1] : ~tall(X1)) & (? [X2] : tall(X2) | ! [X3] : ((~quiet(X3) | ~patient(X3)) & (patient(X3) | quiet(X3)))) [rectify 34]
36. ? [X0] : ((~patient(X0) | quiet(X0)) & (patient(X0) | ~quiet(X0))) => ((~patient(sK0) | quiet(sK0)) & (patient(sK0) | ~quiet(sK0))) [choice axiom]
37. ? [X2] : tall(X2) => tall(sK1) [choice axiom]
38. (((~patient(sK0) | quiet(sK0)) & (patient(sK0) | ~quiet(sK0))) | ! [X1] : ~tall(X1)) & (tall(sK1) | ! [X3] : ((~quiet(X3) | ~patient(X3)) & (patient(X3) | quiet(X3)))) [skolemisation 35,37,36]
44. ! [X0] : ((patient(X0) | (~wise(X0) & curious(X0))) & ((wise(X0) | ~curious(X0)) | ~patient(X0))) [nnf transformation 4]
45. ! [X0] : ((patient(X0) | (~wise(X0) & curious(X0))) & (wise(X0) | ~curious(X0) | ~patient(X0))) [flattening 44]
47. ! [X0] : ((brave(X0) | (patient(X0) | curious(X0))) & ((~patient(X0) & ~curious(X0)) | ~brave(X0))) [nnf transformation 6]
48. ! [X0] : ((brave(X0) | patient(X0) | curious(X0)) & ((~patient(X0) & ~curious(X0)) | ~brave(X0))) [flattening 47]
61. ! [X0] : ((~wise(X0) | ((wise(X0) | quiet(X0)) & (~quiet(X0) | ~wise(X0)))) & (((quiet(X0) | ~wise(X0)) & (~quiet(X0) | wise(X0))) | wise(X0))) [nnf transformation 10]
64. ! [X0] : (((brave(X0) & ~strong(X0)) | (~wise(X0) & ~tall(X0))) & ((wise(X0) | tall(X0)) | (~brave(X0) | strong(X0)))) [nnf transformation 13]
65. ! [X0] : (((brave(X0) & ~strong(X0)) | (~wise(X0) & ~tall(X0))) & (wise(X0) | tall(X0) | ~brave(X0) | strong(X0))) [flattening 64]
68. (~generous(susan) & calm(susan)) | ! [X0] : ((~brave(X0) | ~humble(X0)) & (humble(X0) | brave(X0))) [nnf transformation 32]
72. ? [X0] : (~humble(X0) & ~calm(X0)) => (~humble(sK6) & ~calm(sK6)) [choice axiom]
73. ~humble(sK6) & ~calm(sK6) [skolemisation 21,72]
76. tall(sK1) | patient(X3) | quiet(X3) [cnf transformation 38]
89. curious(X0) | patient(X0) [cnf transformation 45]
95. ~brave(X0) | ~curious(X0) [cnf transformation 48]
96. ~brave(X0) | ~patient(X0) [cnf transformation 48]
112. ~quiet(X0) | wise(X0) | wise(X0) [cnf transformation 61]
114. ~wise(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 61]
125. ~tall(X0) | brave(X0) [cnf transformation 65]
130. calm(susan) | humble(X0) | brave(X0) [cnf transformation 68]
145. ~humble(sK6) [cnf transformation 73]
150. ~calm(susan) [cnf transformation 25]
151. ~quiet(X0) | wise(X0) [duplicate literal removal 112]
152. ~wise(X0) | ~quiet(X0) [duplicate literal removal 114]
171. 5 <=> tall(sK1) [avatar definition]
173. tall(sK1) <- (5) [avatar component clause 171]
176. 6 <=> ! [X3] : (patient(X3) | quiet(X3)) [avatar definition]
177. patient(X3) | quiet(X3) <- (6) [avatar component clause 176]
178. 6 | 5 [avatar split clause 76,171,176]
277. ~quiet(X0) [subsumption resolution 151,152]
310. 34 <=> ! [X0] : (humble(X0) | brave(X0)) [avatar definition]
311. humble(X0) | brave(X0) <- (34) [avatar component clause 310]
314. 35 <=> calm(susan) [avatar definition]
318. 34 | 35 [avatar split clause 130,314,310]
347. ~35 [avatar split clause 150,314]
348. brave(sK1) <- (5) [resolution 125,173]
350. ~patient(sK1) <- (5) [resolution 348,96]
351. ~curious(sK1) <- (5) [resolution 348,95]
354. patient(sK1) <- (5) [resolution 351,89]
355. $false <- (5) [subsumption resolution 354,350]
356. ~5 [avatar contradiction clause 355]
357. patient(X3) <- (6) [subsumption resolution 177,277]
367. brave(sK6) <- (34) [resolution 311,145]
370. ~patient(sK6) <- (34) [resolution 367,96]
372. $false <- (6, 34) [subsumption resolution 370,357]
373. ~6 | ~34 [avatar contradiction clause 372]
374. $false [avatar sat refutation 178,318,347,356,373]
% SZS output end Proof for 7831477499141326389478148
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and strong then someone is both creative and tall.
If fred is not strong or not calm then paul is either not humble or strong and vice versa.
Everyone who is either not generous or old is both happy and not funny and vice versa.
Everyone who is not curious is both not generous and not quiet and vice versa.
If someone is both funny and wise then someone is either wise or rich.
Everyone who is both not rich and patient is either not kind or strong.
If someone is both not kind and not rich then someone is strong or curious and vice versa.
If someone is not generous or old then someone is either kind or not brave.
If someone is both not happy and not generous then someone is brave or not creative and vice versa.
Everyone who is both funny and happy is both not humble and calm and vice versa.
If susan is generous or kind then paul is not creative or not generous.
Everyone who is humble is either rich or not happy and vice versa.
Everyone who is wise or calm is both brave and not wise.
Everyone who is not strong is patient or not tall.
Someone is rich or not happy.
Someone is either happy or not tall.
Susan is calm or kind.
Someone is generous or brave.
Susan is either not rich or not kind. | Fred is brave. | neutral | ((?[X]:((~tall(X)&strong(X))))=>(?[X]:((creative(X)&tall(X)))))&
(((~strong(fred)|~calm(fred)))<=>((~humble(paul)<~>strong(paul))))&
(![X]:((~generous(X)<~>old(X))<=>(happy(X)&~funny(X))))&
(![X]:(~curious(X)<=>(~generous(X)&~quiet(X))))&
((?[X]:((funny(X)&wise(X))))=>(?[X]:((wise(X)<~>rich(X)))))&
(![X]:((~rich(X)&patient(X))=>(~kind(X)<~>strong(X))))&
((?[X]:((~kind(X)&~rich(X))))<=>(?[X]:((strong(X)|curious(X)))))&
((?[X]:((~generous(X)|old(X))))=>(?[X]:((kind(X)<~>~brave(X)))))&
((?[X]:((~happy(X)&~generous(X))))<=>(?[X]:((brave(X)|~creative(X)))))&
(![X]:((funny(X)&happy(X))<=>(~humble(X)&calm(X))))&
(((generous(susan)|kind(susan)))=>((~creative(paul)|~generous(paul))))&
(![X]:(humble(X)<=>(rich(X)<~>~happy(X))))&
(![X]:((wise(X)|calm(X))=>(brave(X)&~wise(X))))&
(![X]:(~strong(X)=>(patient(X)|~tall(X))))&
(?[X]:((rich(X)|~happy(X))))&
(?[X]:((happy(X)<~>~tall(X))))&
((calm(susan)|kind(susan)))&
(?[X]:((generous(X)|brave(X))))&
((~rich(susan)<~>~kind(susan))) | brave(fred) | [] | null | 0 |
Everyone who is not tall is funny or not brave and vice versa. Everyone who is not creative or not tall is both strong and not generous. Everyone who is both generous and not quiet is calm. If susan is brave or not kind then someone is either not calm or patient and vice versa. Everyone who is both old and generous is old. Everyone who is curious is either not creative or funny and vice versa. Everyone who is either not happy or not creative is either not calm or strong and vice versa. Everyone who is brave or not brave is not patient. If someone is either funny or not old then someone is both patient and kind. If mary is not calm then someone is patient. Everyone who is both not patient and creative is either not happy or rich. If susan is both not creative and not rich then someone is both happy and curious and vice versa. Everyone who is not funny is happy or curious and vice versa. If someone is both quiet and not funny then susan is not humble or not patient and vice versa. Everyone who is funny or creative is both not calm and kind and vice versa. If someone is not strong then paul is not patient or funny. Alice is both not rich and not funny. Someone is both not humble and not funny. John is either not quiet or curious. Someone is wise or humble. Someone is either rich or not old. Someone is either patient or curious. Someone is not quiet or not calm. Someone is either funny or creative. | Mary is not strong. | contradiction | (![X]:(~tall(X)<=>(funny(X)|~brave(X))))&
(![X]:((~creative(X)|~tall(X))=>(strong(X)&~generous(X))))&
(![X]:((generous(X)&~quiet(X))=>calm(X)))&
(((brave(susan)|~kind(susan)))<=>(?[X]:((~calm(X)<~>patient(X)))))&
(![X]:((old(X)&generous(X))=>old(X)))&
(![X]:(curious(X)<=>(~creative(X)<~>funny(X))))&
(![X]:((~happy(X)<~>~creative(X))<=>(~calm(X)<~>strong(X))))&
(![X]:((brave(X)|~brave(X))=>~patient(X)))&
((?[X]:((funny(X)<~>~old(X))))=>(?[X]:((patient(X)&kind(X)))))&
((~calm(mary))=>(?[X]:(patient(X))))&
(![X]:((~patient(X)&creative(X))=>(~happy(X)<~>rich(X))))&
(((~creative(susan)&~rich(susan)))<=>(?[X]:((happy(X)&curious(X)))))&
(![X]:(~funny(X)<=>(happy(X)|curious(X))))&
((?[X]:((quiet(X)&~funny(X))))<=>((~humble(susan)|~patient(susan))))&
(![X]:((funny(X)|creative(X))<=>(~calm(X)&kind(X))))&
((?[X]:(~strong(X)))=>((~patient(paul)|funny(paul))))&
((~rich(alice)&~funny(alice)))&
(?[X]:((~humble(X)&~funny(X))))&
((~quiet(john)<~>curious(john)))&
(?[X]:((wise(X)|humble(X))))&
(?[X]:((rich(X)<~>~old(X))))&
(?[X]:((patient(X)<~>curious(X))))&
(?[X]:((~quiet(X)|~calm(X))))&
(?[X]:((funny(X)<~>creative(X)))) | ~strong(mary) | [
"p1",
"p7",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2041828093023237363831406
% SZS output start Proof for 2041828093023237363831406
2. ! [X0] : ((~tall(X0) | ~creative(X0)) => (~generous(X0) & strong(X0))) [input p1]
8. ! [X0] : ((~brave(X0) | brave(X0)) => ~patient(X0)) [input p7]
10. ~calm(mary) => ? [X0] : patient(X0) [input p9]
15. ! [X0] : ((creative(X0) | funny(X0)) <=> (kind(X0) & ~calm(X0))) [input p14]
25. ~strong(mary) [input hypothesis]
29. ! [X0] : ((~tall(X0) | ~creative(X0)) => strong(X0)) [pure predicate removal 2]
33. ! [X0] : (strong(X0) | (tall(X0) & creative(X0))) [ennf transformation 29]
34. ! [X0] : (~patient(X0) | (brave(X0) & ~brave(X0))) [ennf transformation 8]
36. ? [X0] : patient(X0) | calm(mary) [ennf transformation 10]
52. ? [X0] : patient(X0) => patient(sK2) [choice axiom]
53. patient(sK2) | calm(mary) [skolemisation 36,52]
67. ! [X0] : (((creative(X0) | funny(X0)) | (~kind(X0) | calm(X0))) & ((kind(X0) & ~calm(X0)) | (~creative(X0) & ~funny(X0)))) [nnf transformation 15]
68. ! [X0] : ((creative(X0) | funny(X0) | ~kind(X0) | calm(X0)) & ((kind(X0) & ~calm(X0)) | (~creative(X0) & ~funny(X0)))) [flattening 67]
85. strong(X0) | creative(X0) [cnf transformation 33]
105. ~patient(X0) | ~brave(X0) [cnf transformation 34]
106. ~patient(X0) | brave(X0) [cnf transformation 34]
111. patient(sK2) | calm(mary) [cnf transformation 53]
127. ~calm(X0) | ~creative(X0) [cnf transformation 68]
145. ~strong(mary) [cnf transformation 25]
178. ~patient(X0) [subsumption resolution 105,106]
195. calm(mary) [subsumption resolution 111,178]
264. creative(mary) [resolution 85,145]
269. ~creative(mary) [resolution 127,195]
270. $false [subsumption resolution 269,264]
% SZS output end Proof for 2041828093023237363831406
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not quiet is generous or not funny and vice versa.
If susan is both not curious and humble then mary is either not curious or happy.
Everyone who is wise or not generous is both brave and not wise and vice versa.
Everyone who is either rich or not strong is both not generous and not wise and vice versa.
Everyone who is both funny and kind is not calm and vice versa.
Everyone who is strong is either calm or generous and vice versa.
If someone is curious then john is patient.
If alice is not happy or not tall then paul is tall or strong and vice versa.
Everyone who is not quiet or patient is not rich.
Everyone who is rich or not rich is not funny and vice versa.
Everyone who is quiet is both humble and generous and vice versa.
If lucy is not happy then fred is either not creative or rich and vice versa.
Everyone who is creative is kind or patient and vice versa.
Everyone who is both wise and generous is both rich and not happy.
If someone is rich then paul is kind.
Everyone who is not happy is rich and vice versa.
Someone is either not old or not kind.
Susan is not wise.
Someone is either funny or not funny.
Fred is not strong or not creative.
Someone is generous or not kind. | John is quiet. | entailment | (![X]:((calm(X)|~quiet(X))<=>(generous(X)|~funny(X))))&
(((~curious(susan)&humble(susan)))=>((~curious(mary)<~>happy(mary))))&
(![X]:((wise(X)|~generous(X))<=>(brave(X)&~wise(X))))&
(![X]:((rich(X)<~>~strong(X))<=>(~generous(X)&~wise(X))))&
(![X]:((funny(X)&kind(X))<=>~calm(X)))&
(![X]:(strong(X)<=>(calm(X)<~>generous(X))))&
((?[X]:(curious(X)))=>(patient(john)))&
(((~happy(alice)|~tall(alice)))<=>((tall(paul)|strong(paul))))&
(![X]:((~quiet(X)|patient(X))=>~rich(X)))&
(![X]:((rich(X)|~rich(X))<=>~funny(X)))&
(![X]:(quiet(X)<=>(humble(X)&generous(X))))&
((~happy(lucy))<=>((~creative(fred)<~>rich(fred))))&
(![X]:(creative(X)<=>(kind(X)|patient(X))))&
(![X]:((wise(X)&generous(X))=>(rich(X)&~happy(X))))&
((?[X]:(rich(X)))=>(kind(paul)))&
(![X]:(~happy(X)<=>rich(X)))&
(?[X]:((~old(X)<~>~kind(X))))&
(~wise(susan))&
(?[X]:((funny(X)<~>~funny(X))))&
((~strong(fred)|~creative(fred)))&
(?[X]:((generous(X)|~kind(X)))) | quiet(john) | [
"p2",
"p3",
"p4",
"p5",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1664914065748479580826632
% SZS output start Proof for 1664914065748479580826632
3. ! [X0] : ((~generous(X0) | wise(X0)) <=> (~wise(X0) & brave(X0))) [input p2]
4. ! [X0] : ((rich(X0) <~> ~strong(X0)) <=> (~wise(X0) & ~generous(X0))) [input p3]
5. ! [X0] : ((kind(X0) & funny(X0)) <=> ~calm(X0)) [input p4]
6. ! [X0] : (strong(X0) <=> (calm(X0) <~> generous(X0))) [input p5]
9. ! [X0] : ((patient(X0) | ~quiet(X0)) => ~rich(X0)) [input p8]
10. ! [X0] : ((~rich(X0) | rich(X0)) <=> ~funny(X0)) [input p9]
11. ! [X0] : (quiet(X0) <=> (generous(X0) & humble(X0))) [input p10]
22. ~quiet(john) [input hypothesis]
26. ! [X0] : (~rich(X0) | (~patient(X0) & quiet(X0))) [ennf transformation 9]
33. ! [X0] : (((~generous(X0) | wise(X0)) | (wise(X0) | ~brave(X0))) & ((~wise(X0) & brave(X0)) | (generous(X0) & ~wise(X0)))) [nnf transformation 3]
34. ! [X0] : ((~generous(X0) | wise(X0) | wise(X0) | ~brave(X0)) & ((~wise(X0) & brave(X0)) | (generous(X0) & ~wise(X0)))) [flattening 33]
35. ! [X0] : ((((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | (wise(X0) | generous(X0))) & ((~wise(X0) & ~generous(X0)) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0))))) [nnf transformation 4]
36. ! [X0] : ((((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | wise(X0) | generous(X0)) & ((~wise(X0) & ~generous(X0)) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0))))) [flattening 35]
37. ! [X0] : (((kind(X0) & funny(X0)) | calm(X0)) & (~calm(X0) | (~kind(X0) | ~funny(X0)))) [nnf transformation 5]
38. ! [X0] : (((kind(X0) & funny(X0)) | calm(X0)) & (~calm(X0) | ~kind(X0) | ~funny(X0))) [flattening 37]
39. ! [X0] : ((strong(X0) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0)))) & (((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | ~strong(X0))) [nnf transformation 6]
42. ! [X0] : (((~rich(X0) | rich(X0)) | funny(X0)) & (~funny(X0) | (rich(X0) & ~rich(X0)))) [nnf transformation 10]
43. ! [X0] : ((~rich(X0) | rich(X0) | funny(X0)) & (~funny(X0) | (rich(X0) & ~rich(X0)))) [flattening 42]
44. ! [X0] : ((quiet(X0) | (~generous(X0) | ~humble(X0))) & ((generous(X0) & humble(X0)) | ~quiet(X0))) [nnf transformation 11]
45. ! [X0] : ((quiet(X0) | ~generous(X0) | ~humble(X0)) & ((generous(X0) & humble(X0)) | ~quiet(X0))) [flattening 44]
66. ~wise(X0) | ~wise(X0) [cnf transformation 34]
70. ~generous(X0) | rich(X0) | strong(X0) [cnf transformation 36]
73. ~strong(X0) | rich(X0) | wise(X0) | generous(X0) [cnf transformation 36]
76. funny(X0) | calm(X0) [cnf transformation 38]
79. ~strong(X0) | ~calm(X0) | ~generous(X0) [cnf transformation 39]
80. ~calm(X0) | generous(X0) | strong(X0) [cnf transformation 39]
87. ~rich(X0) | quiet(X0) [cnf transformation 26]
89. ~funny(X0) | ~rich(X0) [cnf transformation 43]
90. ~funny(X0) | rich(X0) [cnf transformation 43]
93. ~quiet(X0) | generous(X0) [cnf transformation 45]
114. ~quiet(john) [cnf transformation 22]
115. ~wise(X0) [duplicate literal removal 66]
136. ~strong(X0) | rich(X0) | generous(X0) [subsumption resolution 73,115]
165. ~funny(X0) [subsumption resolution 89,90]
214. calm(X0) [resolution 76,165]
235. strong(X0) | generous(X0) [resolution 80,214]
263. rich(X0) | generous(X0) | generous(X0) [resolution 136,235]
264. rich(X0) | generous(X0) [duplicate literal removal 263]
282. generous(X2) | quiet(X2) [resolution 264,87]
284. generous(X2) [subsumption resolution 282,93]
289. strong(X1) | rich(X1) [resolution 284,70]
300. rich(X1) | ~calm(X1) | ~generous(X1) [resolution 289,79]
305. rich(X1) | ~generous(X1) [subsumption resolution 300,214]
306. rich(X1) [subsumption resolution 305,284]
310. quiet(X2) [resolution 306,87]
338. $false [resolution 310,114]
% SZS output end Proof for 1664914065748479580826632
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or wise is both patient and generous and vice versa.
If fred is either quiet or generous then someone is happy or not humble.
If mary is either not brave or not tall then someone is funny.
If susan is not tall then someone is rich and vice versa.
If alice is both brave and not curious then mary is both not calm and quiet and vice versa.
Everyone who is happy or patient is happy.
If mary is both not humble and not old then someone is not happy.
Everyone who is not tall is both old and brave.
Everyone who is brave or not curious is both tall and brave and vice versa.
Everyone who is either curious or strong is both humble and not generous.
If someone is not wise then someone is patient and vice versa.
If someone is not rich or not humble then someone is generous or not creative and vice versa.
Everyone who is curious or patient is either not curious or not wise and vice versa.
Everyone who is wise is both wise and quiet.
Everyone who is not tall is strong or funny and vice versa.
If someone is not generous then someone is either curious or not generous and vice versa.
Someone is wise.
Someone is not wise or not creative.
Someone is not humble or kind.
Lucy is creative or curious.
Someone is both creative and not wise.
Alice is not wise.
Someone is either not patient or patient. | Lucy is not tall. | contradiction | (![X]:((~calm(X)<~>wise(X))<=>(patient(X)&generous(X))))&
(((quiet(fred)<~>generous(fred)))=>(?[X]:((happy(X)|~humble(X)))))&
(((~brave(mary)<~>~tall(mary)))=>(?[X]:(funny(X))))&
((~tall(susan))<=>(?[X]:(rich(X))))&
(((brave(alice)&~curious(alice)))<=>((~calm(mary)&quiet(mary))))&
(![X]:((happy(X)|patient(X))=>happy(X)))&
(((~humble(mary)&~old(mary)))=>(?[X]:(~happy(X))))&
(![X]:(~tall(X)=>(old(X)&brave(X))))&
(![X]:((brave(X)|~curious(X))<=>(tall(X)&brave(X))))&
(![X]:((curious(X)<~>strong(X))=>(humble(X)&~generous(X))))&
((?[X]:(~wise(X)))<=>(?[X]:(patient(X))))&
((?[X]:((~rich(X)|~humble(X))))<=>(?[X]:((generous(X)|~creative(X)))))&
(![X]:((curious(X)|patient(X))<=>(~curious(X)<~>~wise(X))))&
(![X]:(wise(X)=>(wise(X)&quiet(X))))&
(![X]:(~tall(X)<=>(strong(X)|funny(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((curious(X)<~>~generous(X)))))&
(?[X]:(wise(X)))&
(?[X]:((~wise(X)|~creative(X))))&
(?[X]:((~humble(X)|kind(X))))&
((creative(lucy)|curious(lucy)))&
(?[X]:((creative(X)&~wise(X))))&
(~wise(alice))&
(?[X]:((~patient(X)<~>patient(X)))) | ~tall(lucy) | [
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 149875271535146137447595
% SZS output start Proof for 149875271535146137447595
8. ! [X0] : (~tall(X0) => (brave(X0) & old(X0))) [input p7]
9. ! [X0] : ((~curious(X0) | brave(X0)) <=> (brave(X0) & tall(X0))) [input p8]
24. ~tall(lucy) [input hypothesis]
29. ! [X0] : (~tall(X0) => brave(X0)) [pure predicate removal 8]
34. ! [X0] : (brave(X0) | tall(X0)) [ennf transformation 29]
51. ! [X0] : (((~curious(X0) | brave(X0)) | (~brave(X0) | ~tall(X0))) & ((brave(X0) & tall(X0)) | (curious(X0) & ~brave(X0)))) [nnf transformation 9]
52. ! [X0] : ((~curious(X0) | brave(X0) | ~brave(X0) | ~tall(X0)) & ((brave(X0) & tall(X0)) | (curious(X0) & ~brave(X0)))) [flattening 51]
100. brave(X0) | tall(X0) [cnf transformation 34]
101. tall(X0) | ~brave(X0) [cnf transformation 52]
139. ~tall(lucy) [cnf transformation 24]
207. tall(X0) [subsumption resolution 101,100]
301. $false [subsumption resolution 139,207]
% SZS output end Proof for 149875271535146137447595
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind or old then someone is either not happy or happy and vice versa.
Everyone who is both generous and rich is not calm and vice versa.
If someone is both not generous and brave then someone is both not creative and not generous.
Everyone who is both not tall and not calm is not patient and vice versa.
Everyone who is either not wise or not generous is wise or not calm and vice versa.
Everyone who is patient or funny is calm.
Everyone who is humble or not humble is strong.
Everyone who is tall or not tall is not patient and vice versa.
If someone is not strong or not generous then someone is either patient or humble and vice versa.
Everyone who is either not rich or kind is funny and vice versa.
If someone is either not curious or strong then someone is quiet or not funny.
If someone is not calm or not curious then susan is either happy or curious and vice versa.
Everyone who is both generous and old is not quiet and vice versa.
Everyone who is either not rich or not generous is kind.
If paul is wise or generous then lucy is both quiet and not patient and vice versa.
Mary is old or not rich.
Someone is not generous or brave.
Lucy is either quiet or not curious. | Susan is wise. | contradiction | ((?[X]:((~kind(X)|old(X))))<=>(?[X]:((~happy(X)<~>happy(X)))))&
(![X]:((generous(X)&rich(X))<=>~calm(X)))&
((?[X]:((~generous(X)&brave(X))))=>(?[X]:((~creative(X)&~generous(X)))))&
(![X]:((~tall(X)&~calm(X))<=>~patient(X)))&
(![X]:((~wise(X)<~>~generous(X))<=>(wise(X)|~calm(X))))&
(![X]:((patient(X)|funny(X))=>calm(X)))&
(![X]:((humble(X)|~humble(X))=>strong(X)))&
(![X]:((tall(X)|~tall(X))<=>~patient(X)))&
((?[X]:((~strong(X)|~generous(X))))<=>(?[X]:((patient(X)<~>humble(X)))))&
(![X]:((~rich(X)<~>kind(X))<=>funny(X)))&
((?[X]:((~curious(X)<~>strong(X))))=>(?[X]:((quiet(X)|~funny(X)))))&
((?[X]:((~calm(X)|~curious(X))))<=>((happy(susan)<~>curious(susan))))&
(![X]:((generous(X)&old(X))<=>~quiet(X)))&
(![X]:((~rich(X)<~>~generous(X))=>kind(X)))&
(((wise(paul)|generous(paul)))<=>((quiet(lucy)&~patient(lucy))))&
((old(mary)|~rich(mary)))&
(?[X]:((~generous(X)|brave(X))))&
((quiet(lucy)<~>~curious(lucy))) | wise(susan) | [
"p1",
"p3",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5914208647069644349439707
% SZS output start Proof for 5914208647069644349439707
2. ! [X0] : ((rich(X0) & generous(X0)) <=> ~calm(X0)) [input p1]
4. ! [X0] : ((~calm(X0) & ~tall(X0)) <=> ~patient(X0)) [input p3]
5. ! [X0] : ((~wise(X0) <~> ~generous(X0)) <=> (~calm(X0) | wise(X0))) [input p4]
8. ! [X0] : ((~tall(X0) | tall(X0)) <=> ~patient(X0)) [input p7]
19. wise(susan) [input hypothesis]
37. ! [X0] : (((rich(X0) & generous(X0)) | calm(X0)) & (~calm(X0) | (~rich(X0) | ~generous(X0)))) [nnf transformation 2]
38. ! [X0] : (((rich(X0) & generous(X0)) | calm(X0)) & (~calm(X0) | ~rich(X0) | ~generous(X0))) [flattening 37]
42. ! [X0] : (((~calm(X0) & ~tall(X0)) | patient(X0)) & (~patient(X0) | (calm(X0) | tall(X0)))) [nnf transformation 4]
43. ! [X0] : (((~calm(X0) & ~tall(X0)) | patient(X0)) & (~patient(X0) | calm(X0) | tall(X0))) [flattening 42]
44. ! [X0] : ((((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | (calm(X0) & ~wise(X0))) & ((~calm(X0) | wise(X0)) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0))))) [nnf transformation 5]
45. ! [X0] : ((((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | (calm(X0) & ~wise(X0))) & (~calm(X0) | wise(X0) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0))))) [flattening 44]
46. ! [X0] : (((~tall(X0) | tall(X0)) | patient(X0)) & (~patient(X0) | (tall(X0) & ~tall(X0)))) [nnf transformation 8]
47. ! [X0] : ((~tall(X0) | tall(X0) | patient(X0)) & (~patient(X0) | (tall(X0) & ~tall(X0)))) [flattening 46]
77. calm(X0) | generous(X0) [cnf transformation 38]
82. ~calm(X0) | patient(X0) [cnf transformation 43]
85. ~generous(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 45]
93. ~patient(X0) | ~tall(X0) [cnf transformation 47]
94. ~patient(X0) | tall(X0) [cnf transformation 47]
126. wise(susan) [cnf transformation 19]
128. ~wise(X0) | ~generous(X0) [duplicate literal removal 85]
158. ~patient(X0) [subsumption resolution 93,94]
171. 9 <=> ! [X3] : generous(X3) [avatar definition]
172. generous(X3) <- (9) [avatar component clause 171]
270. patient(X1) | generous(X1) [resolution 82,77]
272. generous(X1) [subsumption resolution 270,158]
273. 9 [avatar split clause 272,171]
278. ~generous(susan) [resolution 128,126]
279. $false <- (9) [subsumption resolution 278,172]
280. ~9 [avatar contradiction clause 279]
281. $false [avatar sat refutation 273,280]
% SZS output end Proof for 5914208647069644349439707
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both tall and rich is kind. Everyone who is old or brave is quiet and vice versa. Everyone who is both rich and brave is not calm and vice versa. Everyone who is not brave or patient is both not creative and not funny. If someone is not quiet or not curious then lucy is both curious and not rich. If someone is humble then fred is either not creative or not happy. If someone is not quiet then someone is either old or not generous. If fred is not funny then someone is either old or creative and vice versa. Everyone who is not strong is curious and vice versa. If someone is not old or happy then someone is either not tall or not generous. Everyone who is calm or not brave is not brave and vice versa. If alice is not calm then someone is both not old and not happy. If someone is both funny and brave then someone is not strong and vice versa. Everyone who is both tall and calm is either not humble or quiet. If someone is either not strong or not old then someone is either curious or quiet. If john is both not funny and not tall then mary is funny or not curious and vice versa. Mary is happy. Lucy is both creative and not funny. Someone is creative. Someone is not humble or not patient. Paul is kind. Someone is tall. Susan is patient. | Mary is brave. | entailment | (![X]:((tall(X)&rich(X))=>kind(X)))&
(![X]:((old(X)|brave(X))<=>quiet(X)))&
(![X]:((rich(X)&brave(X))<=>~calm(X)))&
(![X]:((~brave(X)|patient(X))=>(~creative(X)&~funny(X))))&
((?[X]:((~quiet(X)|~curious(X))))=>((curious(lucy)&~rich(lucy))))&
((?[X]:(humble(X)))=>((~creative(fred)<~>~happy(fred))))&
((?[X]:(~quiet(X)))=>(?[X]:((old(X)<~>~generous(X)))))&
((~funny(fred))<=>(?[X]:((old(X)<~>creative(X)))))&
(![X]:(~strong(X)<=>curious(X)))&
((?[X]:((~old(X)|happy(X))))=>(?[X]:((~tall(X)<~>~generous(X)))))&
(![X]:((calm(X)|~brave(X))<=>~brave(X)))&
((~calm(alice))=>(?[X]:((~old(X)&~happy(X)))))&
((?[X]:((funny(X)&brave(X))))<=>(?[X]:(~strong(X))))&
(![X]:((tall(X)&calm(X))=>(~humble(X)<~>quiet(X))))&
((?[X]:((~strong(X)<~>~old(X))))=>(?[X]:((curious(X)<~>quiet(X)))))&
(((~funny(john)&~tall(john)))<=>((funny(mary)|~curious(mary))))&
(happy(mary))&
((creative(lucy)&~funny(lucy)))&
(?[X]:(creative(X)))&
(?[X]:((~humble(X)|~patient(X))))&
(kind(paul))&
(?[X]:(tall(X)))&
(patient(susan)) | brave(mary) | [
"p1",
"p2",
"p3",
"p4",
"p8",
"p10",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2769980187424355466355451
% SZS output start Proof for 2769980187424355466355451
2. ! [X0] : ((brave(X0) | old(X0)) <=> quiet(X0)) [input p1]
3. ! [X0] : ((brave(X0) & rich(X0)) <=> ~calm(X0)) [input p2]
4. ! [X0] : ((patient(X0) | ~brave(X0)) => (~funny(X0) & ~creative(X0))) [input p3]
5. ? [X0] : (~curious(X0) | ~quiet(X0)) => (~rich(lucy) & curious(lucy)) [input p4]
9. ! [X0] : (~strong(X0) <=> curious(X0)) [input p8]
11. ! [X0] : ((~brave(X0) | calm(X0)) <=> ~brave(X0)) [input p10]
15. ? [X0] : (~strong(X0) <~> ~old(X0)) => ? [X0] : (curious(X0) <~> quiet(X0)) [input p14]
18. ~funny(lucy) & creative(lucy) [input p17]
24. ~brave(mary) [input hypothesis]
28. ? [X0] : (~strong(X0) <~> ~old(X0)) => ? [X1] : (curious(X1) <~> quiet(X1)) [rectify 15]
31. ! [X0] : ((~funny(X0) & ~creative(X0)) | (~patient(X0) & brave(X0))) [ennf transformation 4]
32. (~rich(lucy) & curious(lucy)) | ! [X0] : (curious(X0) & quiet(X0)) [ennf transformation 5]
39. ? [X1] : (curious(X1) <~> quiet(X1)) | ! [X0] : (~strong(X0) <=> ~old(X0)) [ennf transformation 28]
40. ! [X0] : (((brave(X0) | old(X0)) | ~quiet(X0)) & (quiet(X0) | (~brave(X0) & ~old(X0)))) [nnf transformation 2]
41. ! [X0] : ((brave(X0) | old(X0) | ~quiet(X0)) & (quiet(X0) | (~brave(X0) & ~old(X0)))) [flattening 40]
42. ! [X0] : (((brave(X0) & rich(X0)) | calm(X0)) & (~calm(X0) | (~brave(X0) | ~rich(X0)))) [nnf transformation 3]
43. ! [X0] : (((brave(X0) & rich(X0)) | calm(X0)) & (~calm(X0) | ~brave(X0) | ~rich(X0))) [flattening 42]
53. ! [X0] : ((~strong(X0) | ~curious(X0)) & (curious(X0) | strong(X0))) [nnf transformation 9]
58. ! [X0] : (((~brave(X0) | calm(X0)) | brave(X0)) & (~brave(X0) | (brave(X0) & ~calm(X0)))) [nnf transformation 11]
59. ! [X0] : ((~brave(X0) | calm(X0) | brave(X0)) & (~brave(X0) | (brave(X0) & ~calm(X0)))) [flattening 58]
68. ? [X1] : ((~quiet(X1) | ~curious(X1)) & (quiet(X1) | curious(X1))) | ! [X0] : ((~strong(X0) | old(X0)) & (~old(X0) | strong(X0))) [nnf transformation 39]
69. ? [X0] : ((~quiet(X0) | ~curious(X0)) & (quiet(X0) | curious(X0))) | ! [X1] : ((~strong(X1) | old(X1)) & (~old(X1) | strong(X1))) [rectify 68]
70. ? [X0] : ((~quiet(X0) | ~curious(X0)) & (quiet(X0) | curious(X0))) => ((~quiet(sK6) | ~curious(sK6)) & (quiet(sK6) | curious(sK6))) [choice axiom]
71. ((~quiet(sK6) | ~curious(sK6)) & (quiet(sK6) | curious(sK6))) | ! [X1] : ((~strong(X1) | old(X1)) & (~old(X1) | strong(X1))) [skolemisation 69,70]
82. ~quiet(X0) | old(X0) | brave(X0) [cnf transformation 41]
84. calm(X0) | rich(X0) [cnf transformation 43]
86. ~creative(X0) | brave(X0) [cnf transformation 31]
92. ~rich(lucy) | quiet(X0) [cnf transformation 32]
93. ~rich(lucy) | curious(X0) [cnf transformation 32]
103. ~strong(X0) | ~curious(X0) [cnf transformation 53]
108. ~calm(X0) | ~brave(X0) [cnf transformation 59]
120. ~quiet(sK6) | ~curious(sK6) | ~old(X1) | strong(X1) [cnf transformation 71]
128. creative(lucy) [cnf transformation 18]
134. ~brave(mary) [cnf transformation 24]
136. 1 <=> ! [X0] : curious(X0) [avatar definition]
137. curious(X0) <- (1) [avatar component clause 136]
139. 2 <=> rich(lucy) [avatar definition]
142. 1 | ~2 [avatar split clause 93,139,136]
144. 3 <=> ! [X0] : quiet(X0) [avatar definition]
145. quiet(X0) <- (3) [avatar component clause 144]
146. 3 | ~2 [avatar split clause 92,139,144]
256. 28 <=> curious(sK6) [avatar definition]
258. ~curious(sK6) <- (~28) [avatar component clause 256]
260. 29 <=> quiet(sK6) [avatar definition]
262. ~quiet(sK6) <- (~29) [avatar component clause 260]
265. 30 <=> ! [X1] : (~old(X1) | strong(X1)) [avatar definition]
266. ~old(X1) | strong(X1) <- (30) [avatar component clause 265]
267. 30 | ~28 | ~29 [avatar split clause 120,260,256,265]
303. brave(lucy) [resolution 86,128]
317. ~brave(X1) | rich(X1) [resolution 108,84]
334. rich(lucy) [resolution 317,303]
340. 2 [avatar split clause 334,139]
343. $false <- (3, ~29) [resolution 145,262]
344. brave(X0) | old(X0) <- (3) [resolution 145,82]
345. ~3 | 29 [avatar contradiction clause 343]
346. $false <- (1, ~28) [subsumption resolution 258,137]
347. ~1 | 28 [avatar contradiction clause 346]
351. old(mary) <- (3) [resolution 344,134]
375. strong(mary) <- (3, 30) [resolution 351,266]
387. ~curious(mary) <- (3, 30) [resolution 375,103]
388. $false <- (1, 3, 30) [subsumption resolution 387,137]
389. ~1 | ~3 | ~30 [avatar contradiction clause 388]
390. $false [avatar sat refutation 142,146,267,340,345,347,389]
% SZS output end Proof for 2769980187424355466355451
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or rich is both not wise and not brave and vice versa.
Everyone who is both old and generous is not tall or calm.
Everyone who is either not humble or calm is not happy or not kind and vice versa.
If someone is wise then susan is both rich and quiet.
Everyone who is not rich or not quiet is not calm or not brave and vice versa.
Everyone who is not calm is not old or not happy and vice versa.
Everyone who is both strong and humble is old or not brave and vice versa.
If someone is both not quiet and not curious then someone is not curious.
If mary is tall or calm then fred is either tall or not quiet and vice versa.
If someone is kind then someone is both not humble and not brave and vice versa.
Everyone who is not generous is either strong or not kind.
Everyone who is not patient is not curious or quiet and vice versa.
If fred is both wise and funny then fred is both not curious and not kind and vice versa.
If mary is not brave or not quiet then lucy is wise or curious and vice versa.
Alice is not funny or not generous.
Mary is either funny or calm.
Paul is either old or not funny.
Someone is either creative or not wise. | Alice is old. | entailment | (![X]:((brave(X)|rich(X))<=>(~wise(X)&~brave(X))))&
(![X]:((old(X)&generous(X))=>(~tall(X)|calm(X))))&
(![X]:((~humble(X)<~>calm(X))<=>(~happy(X)|~kind(X))))&
((?[X]:(wise(X)))=>((rich(susan)&quiet(susan))))&
(![X]:((~rich(X)|~quiet(X))<=>(~calm(X)|~brave(X))))&
(![X]:(~calm(X)<=>(~old(X)|~happy(X))))&
(![X]:((strong(X)&humble(X))<=>(old(X)|~brave(X))))&
((?[X]:((~quiet(X)&~curious(X))))=>(?[X]:(~curious(X))))&
(((tall(mary)|calm(mary)))<=>((tall(fred)<~>~quiet(fred))))&
((?[X]:(kind(X)))<=>(?[X]:((~humble(X)&~brave(X)))))&
(![X]:(~generous(X)=>(strong(X)<~>~kind(X))))&
(![X]:(~patient(X)<=>(~curious(X)|quiet(X))))&
(((wise(fred)&funny(fred)))<=>((~curious(fred)&~kind(fred))))&
(((~brave(mary)|~quiet(mary)))<=>((wise(lucy)|curious(lucy))))&
((~funny(alice)|~generous(alice)))&
((funny(mary)<~>calm(mary)))&
((old(paul)<~>~funny(paul)))&
(?[X]:((creative(X)<~>~wise(X)))) | old(alice) | [
"p0",
"p2",
"p5",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2938622441985281940244838
% SZS output start Proof for 2938622441985281940244838
1. ! [X0] : ((rich(X0) | brave(X0)) <=> (~brave(X0) & ~wise(X0))) [input p0]
3. ! [X0] : ((~humble(X0) <~> calm(X0)) <=> (~kind(X0) | ~happy(X0))) [input p2]
6. ! [X0] : (~calm(X0) <=> (~happy(X0) | ~old(X0))) [input p5]
7. ! [X0] : ((humble(X0) & strong(X0)) <=> (~brave(X0) | old(X0))) [input p6]
10. ? [X0] : kind(X0) <=> ? [X0] : (~brave(X0) & ~humble(X0)) [input p9]
19. ~old(alice) [input hypothesis]
21. ? [X0] : kind(X0) <=> ? [X1] : (~brave(X1) & ~humble(X1)) [rectify 10]
27. ! [X0] : (((rich(X0) | brave(X0)) | (brave(X0) | wise(X0))) & ((~brave(X0) & ~wise(X0)) | (~rich(X0) & ~brave(X0)))) [nnf transformation 1]
28. ! [X0] : ((rich(X0) | brave(X0) | brave(X0) | wise(X0)) & ((~brave(X0) & ~wise(X0)) | (~rich(X0) & ~brave(X0)))) [flattening 27]
29. ! [X0] : ((((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0))))) [nnf transformation 3]
30. ! [X0] : ((((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0))))) [flattening 29]
33. ! [X0] : ((~calm(X0) | (happy(X0) & old(X0))) & ((~happy(X0) | ~old(X0)) | calm(X0))) [nnf transformation 6]
34. ! [X0] : ((~calm(X0) | (happy(X0) & old(X0))) & (~happy(X0) | ~old(X0) | calm(X0))) [flattening 33]
35. ! [X0] : (((humble(X0) & strong(X0)) | (brave(X0) & ~old(X0))) & ((~brave(X0) | old(X0)) | (~humble(X0) | ~strong(X0)))) [nnf transformation 7]
36. ! [X0] : (((humble(X0) & strong(X0)) | (brave(X0) & ~old(X0))) & (~brave(X0) | old(X0) | ~humble(X0) | ~strong(X0))) [flattening 35]
42. (? [X0] : kind(X0) | ! [X1] : (brave(X1) | humble(X1))) & (? [X1] : (~brave(X1) & ~humble(X1)) | ! [X0] : ~kind(X0)) [nnf transformation 21]
43. (? [X0] : kind(X0) | ! [X1] : (brave(X1) | humble(X1))) & (? [X2] : (~brave(X2) & ~humble(X2)) | ! [X3] : ~kind(X3)) [rectify 42]
44. ? [X0] : kind(X0) => kind(sK1) [choice axiom]
45. ? [X2] : (~brave(X2) & ~humble(X2)) => (~brave(sK2) & ~humble(sK2)) [choice axiom]
46. (kind(sK1) | ! [X1] : (brave(X1) | humble(X1))) & ((~brave(sK2) & ~humble(sK2)) | ! [X3] : ~kind(X3)) [skolemisation 43,45,44]
59. ~brave(X0) | ~brave(X0) [cnf transformation 28]
66. ~humble(X0) | calm(X0) | kind(X0) [cnf transformation 30]
76. ~calm(X0) | old(X0) [cnf transformation 34]
82. humble(X0) | brave(X0) [cnf transformation 36]
90. ~humble(sK2) | ~kind(X3) [cnf transformation 46]
110. ~old(alice) [cnf transformation 19]
111. ~brave(X0) [duplicate literal removal 59]
127. humble(X0) [subsumption resolution 82,111]
159. ~kind(X3) [subsumption resolution 90,127]
232. calm(X0) | kind(X0) [resolution 66,127]
233. calm(X0) [subsumption resolution 232,159]
237. old(X2) [resolution 233,76]
240. $false [resolution 237,110]
% SZS output end Proof for 2938622441985281940244838
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is both tall and not wise. If someone is both not humble and brave then someone is not funny or not calm and vice versa. Everyone who is funny is both calm and strong and vice versa. Everyone who is either not calm or old is not generous and vice versa. Everyone who is both wise and not quiet is not strong or not quiet. If someone is both humble and not funny then someone is either humble or brave and vice versa. If paul is brave or curious then john is funny and vice versa. Everyone who is either not calm or creative is both tall and not calm and vice versa. Everyone who is not tall or patient is not calm or not strong and vice versa. If someone is both not rich and funny then someone is both not brave and quiet. If fred is both funny and wise then mary is either funny or calm and vice versa. Everyone who is either kind or generous is not rich or wise and vice versa. Everyone who is both quiet and not wise is both not happy and not strong. Everyone who is both not quiet and not generous is happy. Everyone who is both not rich and strong is both not humble and not quiet. Everyone who is either kind or not kind is happy and vice versa. Someone is either not funny or not kind. Susan is not kind or funny. John is not tall. Someone is either generous or not wise. Lucy is patient or humble. Someone is rich. John is both strong and happy. Mary is either not humble or not rich. | Susan is curious. | neutral | (![X]:(~patient(X)=>(tall(X)&~wise(X))))&
((?[X]:((~humble(X)&brave(X))))<=>(?[X]:((~funny(X)|~calm(X)))))&
(![X]:(funny(X)<=>(calm(X)&strong(X))))&
(![X]:((~calm(X)<~>old(X))<=>~generous(X)))&
(![X]:((wise(X)&~quiet(X))=>(~strong(X)|~quiet(X))))&
((?[X]:((humble(X)&~funny(X))))<=>(?[X]:((humble(X)<~>brave(X)))))&
(((brave(paul)|curious(paul)))<=>(funny(john)))&
(![X]:((~calm(X)<~>creative(X))<=>(tall(X)&~calm(X))))&
(![X]:((~tall(X)|patient(X))<=>(~calm(X)|~strong(X))))&
((?[X]:((~rich(X)&funny(X))))=>(?[X]:((~brave(X)&quiet(X)))))&
(((funny(fred)&wise(fred)))<=>((funny(mary)<~>calm(mary))))&
(![X]:((kind(X)<~>generous(X))<=>(~rich(X)|wise(X))))&
(![X]:((quiet(X)&~wise(X))=>(~happy(X)&~strong(X))))&
(![X]:((~quiet(X)&~generous(X))=>happy(X)))&
(![X]:((~rich(X)&strong(X))=>(~humble(X)&~quiet(X))))&
(![X]:((kind(X)<~>~kind(X))<=>happy(X)))&
(?[X]:((~funny(X)<~>~kind(X))))&
((~kind(susan)|funny(susan)))&
(~tall(john))&
(?[X]:((generous(X)<~>~wise(X))))&
((patient(lucy)|humble(lucy)))&
(?[X]:(rich(X)))&
((strong(john)&happy(john)))&
((~humble(mary)<~>~rich(mary))) | curious(susan) | [] | null | 0 |
If someone is both not humble and not old then someone is either not rich or not old. If someone is kind or creative then mary is either strong or not funny and vice versa. Everyone who is patient or humble is strong or not strong and vice versa. Everyone who is both not generous and wise is either humble or patient and vice versa. Everyone who is patient is either funny or not quiet. If someone is either wise or not humble then someone is funny or kind and vice versa. If susan is either quiet or not brave then someone is not happy or not calm and vice versa. Everyone who is either not calm or quiet is not curious and vice versa. Everyone who is not quiet is either brave or kind and vice versa. Everyone who is either generous or not funny is not brave or not generous and vice versa. Everyone who is not curious or tall is either humble or not curious. Everyone who is curious is both patient and not quiet. Everyone who is not wise is both kind and creative and vice versa. If john is creative then someone is either not kind or tall and vice versa. If someone is both old and rich then someone is both not rich and not wise. Everyone who is either curious or happy is both generous and not wise. Someone is not old or not patient. Someone is either happy or not creative. Someone is not kind or not humble. Someone is not curious or not quiet. John is either not kind or happy. Someone is not creative or generous. John is rich. Alice is either not strong or happy. | Susan is quiet. | contradiction | ((?[X]:((~humble(X)&~old(X))))=>(?[X]:((~rich(X)<~>~old(X)))))&
((?[X]:((kind(X)|creative(X))))<=>((strong(mary)<~>~funny(mary))))&
(![X]:((patient(X)|humble(X))<=>(strong(X)|~strong(X))))&
(![X]:((~generous(X)&wise(X))<=>(humble(X)<~>patient(X))))&
(![X]:(patient(X)=>(funny(X)<~>~quiet(X))))&
((?[X]:((wise(X)<~>~humble(X))))<=>(?[X]:((funny(X)|kind(X)))))&
(((quiet(susan)<~>~brave(susan)))<=>(?[X]:((~happy(X)|~calm(X)))))&
(![X]:((~calm(X)<~>quiet(X))<=>~curious(X)))&
(![X]:(~quiet(X)<=>(brave(X)<~>kind(X))))&
(![X]:((generous(X)<~>~funny(X))<=>(~brave(X)|~generous(X))))&
(![X]:((~curious(X)|tall(X))=>(humble(X)<~>~curious(X))))&
(![X]:(curious(X)=>(patient(X)&~quiet(X))))&
(![X]:(~wise(X)<=>(kind(X)&creative(X))))&
((creative(john))<=>(?[X]:((~kind(X)<~>tall(X)))))&
((?[X]:((old(X)&rich(X))))=>(?[X]:((~rich(X)&~wise(X)))))&
(![X]:((curious(X)<~>happy(X))=>(generous(X)&~wise(X))))&
(?[X]:((~old(X)|~patient(X))))&
(?[X]:((happy(X)<~>~creative(X))))&
(?[X]:((~kind(X)|~humble(X))))&
(?[X]:((~curious(X)|~quiet(X))))&
((~kind(john)<~>happy(john)))&
(?[X]:((~creative(X)|generous(X))))&
(rich(john))&
((~strong(alice)<~>happy(alice))) | quiet(susan) | [
"p2",
"p3",
"p4",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4194706046732266254841714
% SZS output start Proof for 4194706046732266254841714
3. ! [X0] : ((humble(X0) | patient(X0)) <=> (~strong(X0) | strong(X0))) [input p2]
4. ! [X0] : ((wise(X0) & ~generous(X0)) <=> (humble(X0) <~> patient(X0))) [input p3]
5. ! [X0] : (patient(X0) => (funny(X0) <~> ~quiet(X0))) [input p4]
10. ! [X0] : ((generous(X0) <~> ~funny(X0)) <=> (~generous(X0) | ~brave(X0))) [input p9]
11. ! [X0] : ((tall(X0) | ~curious(X0)) => (humble(X0) <~> ~curious(X0))) [input p10]
12. ! [X0] : (curious(X0) => (~quiet(X0) & patient(X0))) [input p11]
25. quiet(susan) [input hypothesis]
30. ! [X0] : ((funny(X0) <~> ~quiet(X0)) | ~patient(X0)) [ennf transformation 5]
31. ! [X0] : ((humble(X0) <~> ~curious(X0)) | (~tall(X0) & curious(X0))) [ennf transformation 11]
32. ! [X0] : ((~quiet(X0) & patient(X0)) | ~curious(X0)) [ennf transformation 12]
43. ! [X0] : (((humble(X0) | patient(X0)) | (strong(X0) & ~strong(X0))) & ((~strong(X0) | strong(X0)) | (~humble(X0) & ~patient(X0)))) [nnf transformation 3]
44. ! [X0] : ((humble(X0) | patient(X0) | (strong(X0) & ~strong(X0))) & (~strong(X0) | strong(X0) | (~humble(X0) & ~patient(X0)))) [flattening 43]
45. ! [X0] : (((wise(X0) & ~generous(X0)) | ((humble(X0) | ~patient(X0)) & (patient(X0) | ~humble(X0)))) & (((~patient(X0) | ~humble(X0)) & (patient(X0) | humble(X0))) | (~wise(X0) | generous(X0)))) [nnf transformation 4]
46. ! [X0] : (((wise(X0) & ~generous(X0)) | ((humble(X0) | ~patient(X0)) & (patient(X0) | ~humble(X0)))) & (((~patient(X0) | ~humble(X0)) & (patient(X0) | humble(X0))) | ~wise(X0) | generous(X0))) [flattening 45]
47. ! [X0] : (((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | ~patient(X0)) [nnf transformation 30]
59. ! [X0] : ((((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | (generous(X0) & brave(X0))) & ((~generous(X0) | ~brave(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0))))) [nnf transformation 10]
60. ! [X0] : ((((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | (generous(X0) & brave(X0))) & (~generous(X0) | ~brave(X0) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0))))) [flattening 59]
61. ! [X0] : (((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | (~tall(X0) & curious(X0))) [nnf transformation 31]
95. humble(X0) | patient(X0) | ~strong(X0) [cnf transformation 44]
96. patient(X0) | humble(X0) | strong(X0) [cnf transformation 44]
100. ~generous(X0) | humble(X0) | ~patient(X0) [cnf transformation 46]
103. ~quiet(X0) | funny(X0) | ~patient(X0) [cnf transformation 47]
128. ~funny(X0) | generous(X0) | generous(X0) [cnf transformation 60]
133. curious(X0) | ~humble(X0) | curious(X0) [cnf transformation 61]
136. ~curious(X0) | ~quiet(X0) [cnf transformation 32]
161. quiet(susan) [cnf transformation 25]
162. ~humble(X0) | curious(X0) [duplicate literal removal 133]
164. ~funny(X0) | generous(X0) [duplicate literal removal 128]
206. patient(X0) | humble(X0) [subsumption resolution 95,96]
209. ~generous(X0) | humble(X0) [subsumption resolution 100,206]
246. 17 <=> quiet(susan) [avatar definition]
247. quiet(susan) <- (17) [avatar component clause 246]
363. 17 [avatar split clause 161,246]
396. funny(susan) | ~patient(susan) <- (17) [resolution 103,247]
405. 43 <=> humble(susan) [avatar definition]
406. ~humble(susan) <- (~43) [avatar component clause 405]
407. humble(susan) <- (43) [avatar component clause 405]
411. 44 <=> patient(susan) [avatar definition]
413. ~patient(susan) <- (~44) [avatar component clause 411]
415. 45 <=> funny(susan) [avatar definition]
417. funny(susan) <- (45) [avatar component clause 415]
418. ~44 | 45 | ~17 [avatar split clause 396,246,415,411]
430. humble(susan) <- (~44) [resolution 413,206]
456. curious(susan) <- (43) [resolution 407,162]
486. ~quiet(susan) <- (43) [resolution 456,136]
491. $false <- (17, 43) [subsumption resolution 486,247]
492. ~17 | ~43 [avatar contradiction clause 491]
500. 43 | 44 [avatar split clause 430,411,405]
520. generous(susan) <- (45) [resolution 417,164]
535. humble(susan) <- (45) [resolution 520,209]
536. $false <- (~43, 45) [subsumption resolution 535,406]
537. 43 | ~45 [avatar contradiction clause 536]
538. $false [avatar sat refutation 363,418,492,500,537]
% SZS output end Proof for 4194706046732266254841714
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either creative or not humble then someone is not rich or strong.
If john is curious then paul is rich or not strong and vice versa.
If someone is not brave then someone is either not humble or happy.
Everyone who is happy is wise and vice versa.
Everyone who is either not creative or old is both not rich and tall.
Everyone who is not kind is quiet or not old and vice versa.
If susan is both not patient and not creative then john is old and vice versa.
Everyone who is both not wise and wise is both not funny and generous and vice versa.
If susan is not old then someone is either happy or not happy and vice versa.
If someone is humble then paul is strong or patient.
If john is both rich and not old then susan is either not funny or happy and vice versa.
Everyone who is not creative is kind and vice versa.
If someone is creative then someone is not quiet or happy.
Everyone who is not creative is not happy or kind.
Everyone who is not generous or not happy is not creative.
If someone is rich then someone is both not quiet and rich and vice versa.
Mary is both old and not kind.
Mary is happy.
Someone is humble.
Someone is both not rich and patient.
Lucy is both not generous and not creative.
Susan is humble or brave. | John is not creative. | contradiction | ((?[X]:((creative(X)<~>~humble(X))))=>(?[X]:((~rich(X)|strong(X)))))&
((curious(john))<=>((rich(paul)|~strong(paul))))&
((?[X]:(~brave(X)))=>(?[X]:((~humble(X)<~>happy(X)))))&
(![X]:(happy(X)<=>wise(X)))&
(![X]:((~creative(X)<~>old(X))=>(~rich(X)&tall(X))))&
(![X]:(~kind(X)<=>(quiet(X)|~old(X))))&
(((~patient(susan)&~creative(susan)))<=>(old(john)))&
(![X]:((~wise(X)&wise(X))<=>(~funny(X)&generous(X))))&
((~old(susan))<=>(?[X]:((happy(X)<~>~happy(X)))))&
((?[X]:(humble(X)))=>((strong(paul)|patient(paul))))&
(((rich(john)&~old(john)))<=>((~funny(susan)<~>happy(susan))))&
(![X]:(~creative(X)<=>kind(X)))&
((?[X]:(creative(X)))=>(?[X]:((~quiet(X)|happy(X)))))&
(![X]:(~creative(X)=>(~happy(X)|kind(X))))&
(![X]:((~generous(X)|~happy(X))=>~creative(X)))&
((?[X]:(rich(X)))<=>(?[X]:((~quiet(X)&rich(X)))))&
((old(mary)&~kind(mary)))&
(happy(mary))&
(?[X]:(humble(X)))&
(?[X]:((~rich(X)&patient(X))))&
((~generous(lucy)&~creative(lucy)))&
((humble(susan)|brave(susan))) | ~creative(john) | [
"p5",
"p6",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8796732425133953672709614
% SZS output start Proof for 8796732425133953672709614
6. ! [X0] : (~kind(X0) <=> (~old(X0) | quiet(X0))) [input p5]
7. (~creative(susan) & ~patient(susan)) <=> old(john) [input p6]
9. ~old(susan) <=> ? [X0] : (happy(X0) <~> ~happy(X0)) [input p8]
12. ! [X0] : (~creative(X0) <=> kind(X0)) [input p11]
23. ~creative(john) [input hypothesis]
47. ! [X0] : ((~kind(X0) | (old(X0) & ~quiet(X0))) & ((~old(X0) | quiet(X0)) | kind(X0))) [nnf transformation 6]
48. ! [X0] : ((~kind(X0) | (old(X0) & ~quiet(X0))) & (~old(X0) | quiet(X0) | kind(X0))) [flattening 47]
49. ((~creative(susan) & ~patient(susan)) | ~old(john)) & (old(john) | (creative(susan) | patient(susan))) [nnf transformation 7]
50. ((~creative(susan) & ~patient(susan)) | ~old(john)) & (old(john) | creative(susan) | patient(susan)) [flattening 49]
53. (~old(susan) | ! [X0] : ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) & (? [X0] : ((happy(X0) | ~happy(X0)) & (~happy(X0) | happy(X0))) | old(susan)) [nnf transformation 9]
54. (~old(susan) | ! [X0] : ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) & (? [X1] : ((happy(X1) | ~happy(X1)) & (~happy(X1) | happy(X1))) | old(susan)) [rectify 53]
55. ? [X1] : ((happy(X1) | ~happy(X1)) & (~happy(X1) | happy(X1))) => ((happy(sK1) | ~happy(sK1)) & (~happy(sK1) | happy(sK1))) [choice axiom]
56. (~old(susan) | ! [X0] : ((happy(X0) | happy(X0)) & (~happy(X0) | ~happy(X0)))) & (((happy(sK1) | ~happy(sK1)) & (~happy(sK1) | happy(sK1))) | old(susan)) [skolemisation 54,55]
59. ! [X0] : ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0))) [nnf transformation 12]
83. ~kind(X0) | old(X0) [cnf transformation 48]
86. ~creative(susan) | ~old(john) [cnf transformation 50]
93. ~old(susan) | ~happy(X0) | ~happy(X0) [cnf transformation 56]
94. ~old(susan) | happy(X0) | happy(X0) [cnf transformation 56]
102. kind(X0) | creative(X0) [cnf transformation 59]
119. ~creative(john) [cnf transformation 23]
120. ~old(susan) | ~happy(X0) [duplicate literal removal 93]
121. ~old(susan) | happy(X0) [duplicate literal removal 94]
154. 8 <=> old(john) [avatar definition]
156. ~old(john) <- (~8) [avatar component clause 154]
158. 9 <=> creative(susan) [avatar definition]
161. ~8 | ~9 [avatar split clause 86,158,154]
170. 11 <=> ! [X0] : happy(X0) [avatar definition]
171. happy(X0) <- (11) [avatar component clause 170]
173. 12 <=> old(susan) [avatar definition]
175. ~old(susan) <- (~12) [avatar component clause 173]
176. 11 | ~12 [avatar split clause 121,173,170]
178. 13 <=> ! [X0] : ~happy(X0) [avatar definition]
179. ~happy(X0) <- (13) [avatar component clause 178]
180. 13 | ~12 [avatar split clause 120,173,178]
245. old(X0) | creative(X0) [resolution 102,83]
250. creative(susan) <- (~12) [resolution 245,175]
253. 9 | 12 [avatar split clause 250,173,158]
254. creative(john) <- (~8) [resolution 156,245]
255. $false <- (~8) [subsumption resolution 254,119]
256. 8 [avatar contradiction clause 255]
257. $false <- (11, 13) [subsumption resolution 171,179]
258. ~11 | ~13 [avatar contradiction clause 257]
259. $false [avatar sat refutation 161,176,180,253,256,258]
% SZS output end Proof for 8796732425133953672709614
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is either not wise or calm and vice versa. If someone is kind or not strong then paul is either not quiet or not strong. Everyone who is both quiet and kind is both not strong and curious. If someone is either funny or not tall then susan is not wise. Everyone who is not patient or calm is either wise or humble and vice versa. If lucy is not wise then susan is brave or creative. Everyone who is both not wise and not brave is quiet or not rich and vice versa. If someone is tall then someone is both not wise and generous and vice versa. If someone is either not wise or not humble then someone is wise. If someone is not wise then someone is not rich or humble and vice versa. Everyone who is patient is either brave or not patient and vice versa. If paul is funny then fred is strong and vice versa. Everyone who is either not humble or not rich is not strong or not humble and vice versa. Everyone who is rich or not old is both tall and old. Everyone who is both patient and calm is humble or not happy. If someone is not creative then susan is not rich or happy. John is kind. Mary is not kind. Someone is both not kind and patient. Someone is not kind. Someone is both not wise and not creative. John is either tall or generous. Someone is quiet or not kind. | Fred is not brave. | contradiction | (![X]:(funny(X)<=>(~wise(X)<~>calm(X))))&
((?[X]:((kind(X)|~strong(X))))=>((~quiet(paul)<~>~strong(paul))))&
(![X]:((quiet(X)&kind(X))=>(~strong(X)&curious(X))))&
((?[X]:((funny(X)<~>~tall(X))))=>(~wise(susan)))&
(![X]:((~patient(X)|calm(X))<=>(wise(X)<~>humble(X))))&
((~wise(lucy))=>((brave(susan)|creative(susan))))&
(![X]:((~wise(X)&~brave(X))<=>(quiet(X)|~rich(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~wise(X)&generous(X)))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(?[X]:(wise(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((~rich(X)|humble(X)))))&
(![X]:(patient(X)<=>(brave(X)<~>~patient(X))))&
((funny(paul))<=>(strong(fred)))&
(![X]:((~humble(X)<~>~rich(X))<=>(~strong(X)|~humble(X))))&
(![X]:((rich(X)|~old(X))=>(tall(X)&old(X))))&
(![X]:((patient(X)&calm(X))=>(humble(X)|~happy(X))))&
((?[X]:(~creative(X)))=>((~rich(susan)|happy(susan))))&
(kind(john))&
(~kind(mary))&
(?[X]:((~kind(X)&patient(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~wise(X)&~creative(X))))&
((tall(john)<~>generous(john)))&
(?[X]:((quiet(X)|~kind(X)))) | ~brave(fred) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4475548452003702839944501
% SZS output start Proof for 4475548452003702839944501
11. ! [X0] : (patient(X0) <=> (brave(X0) <~> ~patient(X0))) [input p10]
24. ~brave(fred) [input hypothesis]
63. ! [X0] : ((patient(X0) | ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0)))) & (((patient(X0) | ~brave(X0)) & (~patient(X0) | brave(X0))) | ~patient(X0))) [nnf transformation 11]
107. ~patient(X0) | brave(X0) | ~patient(X0) [cnf transformation 63]
110. patient(X0) | brave(X0) | patient(X0) [cnf transformation 63]
132. ~brave(fred) [cnf transformation 24]
135. ~patient(X0) | brave(X0) [duplicate literal removal 107]
136. patient(X0) | brave(X0) [duplicate literal removal 110]
237. brave(X0) [subsumption resolution 135,136]
280. $false [subsumption resolution 132,237]
% SZS output end Proof for 4475548452003702839944501
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is both wise and funny.
If someone is not happy or tall then mary is not kind or not curious.
If fred is brave then someone is both not generous and funny.
Everyone who is both not strong and kind is generous or funny.
If someone is either happy or creative then someone is not funny and vice versa.
Everyone who is either not generous or kind is happy or not humble.
If john is either not kind or not patient then someone is wise.
If someone is tall or calm then someone is either not happy or generous and vice versa.
Everyone who is humble is not creative or calm and vice versa.
Everyone who is strong is not creative and vice versa.
Everyone who is not quiet or not kind is either not tall or happy.
If lucy is both not tall and not humble then someone is either curious or funny and vice versa.
If susan is both not curious and not quiet then someone is not brave or funny and vice versa.
If mary is brave then alice is either not curious or not brave.
Everyone who is not rich or tall is patient.
Everyone who is both creative and not kind is either not wise or not strong and vice versa.
Mary is either kind or not brave.
Someone is patient or happy.
Someone is calm or not curious.
Fred is both humble and funny.
Fred is either humble or not happy.
Someone is not old. | Susan is generous. | neutral | (![X]:(~creative(X)=>(wise(X)&funny(X))))&
((?[X]:((~happy(X)|tall(X))))=>((~kind(mary)|~curious(mary))))&
((brave(fred))=>(?[X]:((~generous(X)&funny(X)))))&
(![X]:((~strong(X)&kind(X))=>(generous(X)|funny(X))))&
((?[X]:((happy(X)<~>creative(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~generous(X)<~>kind(X))=>(happy(X)|~humble(X))))&
(((~kind(john)<~>~patient(john)))=>(?[X]:(wise(X))))&
((?[X]:((tall(X)|calm(X))))<=>(?[X]:((~happy(X)<~>generous(X)))))&
(![X]:(humble(X)<=>(~creative(X)|calm(X))))&
(![X]:(strong(X)<=>~creative(X)))&
(![X]:((~quiet(X)|~kind(X))=>(~tall(X)<~>happy(X))))&
(((~tall(lucy)&~humble(lucy)))<=>(?[X]:((curious(X)<~>funny(X)))))&
(((~curious(susan)&~quiet(susan)))<=>(?[X]:((~brave(X)|funny(X)))))&
((brave(mary))=>((~curious(alice)<~>~brave(alice))))&
(![X]:((~rich(X)|tall(X))=>patient(X)))&
(![X]:((creative(X)&~kind(X))<=>(~wise(X)<~>~strong(X))))&
((kind(mary)<~>~brave(mary)))&
(?[X]:((patient(X)|happy(X))))&
(?[X]:((calm(X)|~curious(X))))&
((humble(fred)&funny(fred)))&
((humble(fred)<~>~happy(fred)))&
(?[X]:(~old(X))) | generous(susan) | [] | null | 0 |
Everyone who is creative is tall or not generous and vice versa.
Everyone who is not humble or not old is not calm or not strong.
If alice is either not strong or old then someone is both not funny and not wise and vice versa.
Everyone who is not kind or not wise is not tall or not old and vice versa.
Everyone who is both humble and generous is not generous or creative and vice versa.
Everyone who is either old or creative is both not generous and quiet.
If someone is not curious then paul is either not happy or funny and vice versa.
If someone is both old and not curious then someone is both humble and not funny.
Everyone who is either quiet or calm is either not funny or curious and vice versa.
Everyone who is either not brave or creative is tall.
Everyone who is not creative is both not rich and not wise and vice versa.
If john is both generous and curious then someone is not calm or not creative and vice versa.
Everyone who is either not funny or brave is either wise or not creative and vice versa.
Everyone who is not old or not generous is happy or brave and vice versa.
If someone is not old then susan is either not old or not strong.
If someone is either happy or wise then mary is both funny and not brave.
Someone is strong or curious.
Someone is rich or not tall.
Alice is either brave or not strong.
Someone is either calm or not calm.
Someone is either not wise or not curious. | Paul is not funny. | contradiction | (![X]:(creative(X)<=>(tall(X)|~generous(X))))&
(![X]:((~humble(X)|~old(X))=>(~calm(X)|~strong(X))))&
(((~strong(alice)<~>old(alice)))<=>(?[X]:((~funny(X)&~wise(X)))))&
(![X]:((~kind(X)|~wise(X))<=>(~tall(X)|~old(X))))&
(![X]:((humble(X)&generous(X))<=>(~generous(X)|creative(X))))&
(![X]:((old(X)<~>creative(X))=>(~generous(X)&quiet(X))))&
((?[X]:(~curious(X)))<=>((~happy(paul)<~>funny(paul))))&
((?[X]:((old(X)&~curious(X))))=>(?[X]:((humble(X)&~funny(X)))))&
(![X]:((quiet(X)<~>calm(X))<=>(~funny(X)<~>curious(X))))&
(![X]:((~brave(X)<~>creative(X))=>tall(X)))&
(![X]:(~creative(X)<=>(~rich(X)&~wise(X))))&
(((generous(john)&curious(john)))<=>(?[X]:((~calm(X)|~creative(X)))))&
(![X]:((~funny(X)<~>brave(X))<=>(wise(X)<~>~creative(X))))&
(![X]:((~old(X)|~generous(X))<=>(happy(X)|brave(X))))&
((?[X]:(~old(X)))=>((~old(susan)<~>~strong(susan))))&
((?[X]:((happy(X)<~>wise(X))))=>((funny(mary)&~brave(mary))))&
(?[X]:((strong(X)|curious(X))))&
(?[X]:((rich(X)|~tall(X))))&
((brave(alice)<~>~strong(alice)))&
(?[X]:((calm(X)<~>~calm(X))))&
(?[X]:((~wise(X)<~>~curious(X)))) | ~funny(paul) | [
"p0",
"p2",
"p3",
"p4",
"p5",
"p9",
"p10",
"p12",
"p13",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7445488900872898962646854
% SZS output start Proof for 7445488900872898962646854
1. ! [X0] : (creative(X0) <=> (~generous(X0) | tall(X0))) [input p0]
3. (~strong(alice) <~> old(alice)) <=> ? [X0] : (~wise(X0) & ~funny(X0)) [input p2]
4. ! [X0] : ((~wise(X0) | ~kind(X0)) <=> (~old(X0) | ~tall(X0))) [input p3]
5. ! [X0] : ((generous(X0) & humble(X0)) <=> (creative(X0) | ~generous(X0))) [input p4]
6. ! [X0] : ((old(X0) <~> creative(X0)) => (quiet(X0) & ~generous(X0))) [input p5]
10. ! [X0] : ((~brave(X0) <~> creative(X0)) => tall(X0)) [input p9]
11. ! [X0] : (~creative(X0) <=> (~wise(X0) & ~rich(X0))) [input p10]
13. ! [X0] : ((~funny(X0) <~> brave(X0)) <=> (wise(X0) <~> ~creative(X0))) [input p12]
14. ! [X0] : ((~generous(X0) | ~old(X0)) <=> (brave(X0) | happy(X0))) [input p13]
16. ? [X0] : (happy(X0) <~> wise(X0)) => (~brave(mary) & funny(mary)) [input p15]
19. brave(alice) <~> ~strong(alice) [input p18]
22. ~funny(paul) [input hypothesis]
26. ! [X0] : ((quiet(X0) & ~generous(X0)) | (old(X0) <=> creative(X0))) [ennf transformation 6]
28. ! [X0] : (tall(X0) | (~brave(X0) <=> creative(X0))) [ennf transformation 10]
30. (~brave(mary) & funny(mary)) | ! [X0] : (happy(X0) <=> wise(X0)) [ennf transformation 16]
31. ! [X0] : ((creative(X0) | (generous(X0) & ~tall(X0))) & ((~generous(X0) | tall(X0)) | ~creative(X0))) [nnf transformation 1]
32. ! [X0] : ((creative(X0) | (generous(X0) & ~tall(X0))) & (~generous(X0) | tall(X0) | ~creative(X0))) [flattening 31]
33. (((~old(alice) | strong(alice)) & (old(alice) | ~strong(alice))) | ! [X0] : (wise(X0) | funny(X0))) & (? [X0] : (~wise(X0) & ~funny(X0)) | ((~strong(alice) | ~old(alice)) & (old(alice) | strong(alice)))) [nnf transformation 3]
34. (((~old(alice) | strong(alice)) & (old(alice) | ~strong(alice))) | ! [X0] : (wise(X0) | funny(X0))) & (? [X1] : (~wise(X1) & ~funny(X1)) | ((~strong(alice) | ~old(alice)) & (old(alice) | strong(alice)))) [rectify 33]
35. ? [X1] : (~wise(X1) & ~funny(X1)) => (~wise(sK0) & ~funny(sK0)) [choice axiom]
36. (((~old(alice) | strong(alice)) & (old(alice) | ~strong(alice))) | ! [X0] : (wise(X0) | funny(X0))) & ((~wise(sK0) & ~funny(sK0)) | ((~strong(alice) | ~old(alice)) & (old(alice) | strong(alice)))) [skolemisation 34,35]
37. ! [X0] : (((~wise(X0) | ~kind(X0)) | (old(X0) & tall(X0))) & ((~old(X0) | ~tall(X0)) | (wise(X0) & kind(X0)))) [nnf transformation 4]
38. ! [X0] : ((~wise(X0) | ~kind(X0) | (old(X0) & tall(X0))) & (~old(X0) | ~tall(X0) | (wise(X0) & kind(X0)))) [flattening 37]
39. ! [X0] : (((generous(X0) & humble(X0)) | (~creative(X0) & generous(X0))) & ((creative(X0) | ~generous(X0)) | (~generous(X0) | ~humble(X0)))) [nnf transformation 5]
40. ! [X0] : (((generous(X0) & humble(X0)) | (~creative(X0) & generous(X0))) & (creative(X0) | ~generous(X0) | ~generous(X0) | ~humble(X0))) [flattening 39]
41. ! [X0] : ((quiet(X0) & ~generous(X0)) | ((old(X0) | ~creative(X0)) & (creative(X0) | ~old(X0)))) [nnf transformation 26]
50. ! [X0] : (tall(X0) | ((~brave(X0) | ~creative(X0)) & (creative(X0) | brave(X0)))) [nnf transformation 28]
51. ! [X0] : ((~creative(X0) | (wise(X0) | rich(X0))) & ((~wise(X0) & ~rich(X0)) | creative(X0))) [nnf transformation 11]
52. ! [X0] : ((~creative(X0) | wise(X0) | rich(X0)) & ((~wise(X0) & ~rich(X0)) | creative(X0))) [flattening 51]
58. ! [X0] : ((((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | ((wise(X0) | creative(X0)) & (~creative(X0) | ~wise(X0)))) & (((creative(X0) | ~wise(X0)) & (~creative(X0) | wise(X0))) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0))))) [nnf transformation 13]
59. ! [X0] : (((~generous(X0) | ~old(X0)) | (~brave(X0) & ~happy(X0))) & ((brave(X0) | happy(X0)) | (generous(X0) & old(X0)))) [nnf transformation 14]
60. ! [X0] : ((~generous(X0) | ~old(X0) | (~brave(X0) & ~happy(X0))) & (brave(X0) | happy(X0) | (generous(X0) & old(X0)))) [flattening 59]
62. (~brave(mary) & funny(mary)) | ! [X0] : ((happy(X0) | ~wise(X0)) & (wise(X0) | ~happy(X0))) [nnf transformation 30]
67. (strong(alice) | ~brave(alice)) & (~strong(alice) | brave(alice)) [nnf transformation 19]
74. ~generous(X0) | tall(X0) | ~creative(X0) [cnf transformation 32]
75. ~tall(X0) | creative(X0) [cnf transformation 32]
76. generous(X0) | creative(X0) [cnf transformation 32]
83. old(alice) | ~strong(alice) | wise(X0) | funny(X0) [cnf transformation 36]
84. ~old(alice) | strong(alice) | wise(X0) | funny(X0) [cnf transformation 36]
86. ~old(X0) | ~tall(X0) | wise(X0) [cnf transformation 38]
93. generous(X0) | ~creative(X0) [cnf transformation 40]
95. ~generous(X0) | old(X0) | ~creative(X0) [cnf transformation 41]
112. tall(X0) | creative(X0) | brave(X0) [cnf transformation 50]
115. ~wise(X0) | creative(X0) [cnf transformation 52]
126. brave(X0) | ~funny(X0) | ~creative(X0) | ~wise(X0) [cnf transformation 58]
129. ~brave(X0) | funny(X0) | wise(X0) | creative(X0) [cnf transformation 58]
132. ~generous(X0) | ~old(X0) | ~happy(X0) [cnf transformation 60]
133. ~generous(X0) | ~old(X0) | ~brave(X0) [cnf transformation 60]
137. funny(mary) | happy(X0) | ~wise(X0) [cnf transformation 62]
139. ~brave(mary) | happy(X0) | ~wise(X0) [cnf transformation 62]
142. ~strong(alice) | brave(alice) [cnf transformation 67]
143. strong(alice) | ~brave(alice) [cnf transformation 67]
148. ~funny(paul) [cnf transformation 22]
152. 1 <=> ! [X0] : (wise(X0) | funny(X0)) [avatar definition]
153. wise(X0) | funny(X0) <- (1) [avatar component clause 152]
155. 2 <=> strong(alice) [avatar definition]
159. 3 <=> old(alice) [avatar definition]
160. old(alice) <- (3) [avatar component clause 159]
161. ~old(alice) <- (~3) [avatar component clause 159]
162. 1 | 2 | ~3 [avatar split clause 84,159,155,152]
163. 1 | ~2 | 3 [avatar split clause 83,159,155,152]
176. generous(X0) [subsumption resolution 93,76]
178. ~creative(X0) | old(X0) [subsumption resolution 95,176]
181. 6 <=> funny(paul) [avatar definition]
183. ~funny(paul) <- (~6) [avatar component clause 181]
185. 7 <=> happy(paul) [avatar definition]
186. happy(paul) <- (7) [avatar component clause 185]
187. ~happy(paul) <- (~7) [avatar component clause 185]
212. brave(X0) | creative(X0) [subsumption resolution 112,75]
235. funny(X0) | wise(X0) | creative(X0) [subsumption resolution 129,212]
236. funny(X0) | creative(X0) [subsumption resolution 235,115]
238. ~wise(X0) | ~funny(X0) | brave(X0) [subsumption resolution 126,115]
240. ~brave(X0) | ~old(X0) [subsumption resolution 133,176]
241. ~happy(X0) | ~old(X0) [subsumption resolution 132,176]
256. 21 <=> ! [X0] : (happy(X0) | ~wise(X0)) [avatar definition]
257. ~wise(X0) | happy(X0) <- (21) [avatar component clause 256]
259. 22 <=> brave(mary) [avatar definition]
261. ~brave(mary) <- (~22) [avatar component clause 259]
262. 21 | ~22 [avatar split clause 139,259,256]
268. 24 <=> funny(mary) [avatar definition]
270. funny(mary) <- (24) [avatar component clause 268]
271. 21 | 24 [avatar split clause 137,268,256]
292. 29 <=> brave(alice) [avatar definition]
293. brave(alice) <- (29) [avatar component clause 292]
294. ~brave(alice) <- (~29) [avatar component clause 292]
295. ~29 | 2 [avatar split clause 143,155,292]
296. 29 | ~2 [avatar split clause 142,155,292]
307. ~6 [avatar split clause 148,181]
320. creative(mary) <- (~22) [resolution 212,261]
321. creative(alice) <- (~29) [resolution 212,294]
322. old(mary) <- (~22) [resolution 320,178]
325. creative(paul) <- (~6) [resolution 236,183]
326. old(alice) <- (~29) [resolution 321,178]
328. $false <- (~3, ~29) [subsumption resolution 326,161]
329. 3 | 29 [avatar contradiction clause 328]
335. ~old(alice) <- (29) [resolution 240,293]
336. $false <- (3, 29) [subsumption resolution 335,160]
337. ~3 | ~29 [avatar contradiction clause 336]
339. old(paul) <- (~6) [resolution 325,178]
347. happy(X0) | funny(X0) <- (1, 21) [resolution 257,153]
356. ~creative(X1) | tall(X1) [resolution 74,176]
391. ~tall(mary) | wise(mary) <- (~22) [resolution 322,86]
396. 38 <=> wise(mary) [avatar definition]
398. wise(mary) <- (38) [avatar component clause 396]
400. 39 <=> tall(mary) [avatar definition]
403. 38 | ~39 | 22 [avatar split clause 391,259,400,396]
656. funny(paul) <- (1, ~7, 21) [resolution 347,187]
659. $false <- (1, ~6, ~7, 21) [subsumption resolution 656,183]
660. ~1 | 6 | 7 | ~21 [avatar contradiction clause 659]
662. ~old(paul) <- (7) [resolution 186,241]
663. $false <- (~6, 7) [subsumption resolution 662,339]
664. 6 | ~7 [avatar contradiction clause 663]
701. tall(mary) <- (~22) [resolution 356,320]
713. 39 | 22 [avatar split clause 701,259,400]
770. ~funny(mary) | brave(mary) <- (38) [resolution 398,238]
772. brave(mary) <- (24, 38) [subsumption resolution 770,270]
773. $false <- (~22, 24, 38) [subsumption resolution 772,261]
774. 22 | ~24 | ~38 [avatar contradiction clause 773]
775. $false [avatar sat refutation 162,163,262,271,295,296,307,329,337,403,660,664,713,774]
% SZS output end Proof for 7445488900872898962646854
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or calm is both not tall and not rich and vice versa.
Everyone who is either not old or not rich is calm or funny and vice versa.
Everyone who is either brave or humble is either patient or old and vice versa.
Everyone who is both creative and not tall is both not old and patient.
If someone is not generous then someone is both not generous and not rich and vice versa.
If someone is humble then alice is curious and vice versa.
If mary is not old then someone is humble and vice versa.
If someone is both funny and not generous then alice is either rich or funny.
Everyone who is not rich or curious is tall or not rich and vice versa.
Everyone who is either rich or old is not humble.
Everyone who is tall or not creative is quiet.
Everyone who is both generous and not patient is not calm or funny.
Everyone who is either humble or strong is both creative and funny.
Everyone who is not humble or not funny is both strong and not funny and vice versa.
Everyone who is old is not strong or tall and vice versa.
If someone is either old or curious then someone is kind or not rich and vice versa.
Someone is not wise.
Lucy is not tall or not strong.
Someone is either not kind or not generous.
Fred is both not rich and not brave.
Someone is both patient and not rich.
Someone is either generous or not funny. | Alice is not tall. | entailment | (![X]:((strong(X)|calm(X))<=>(~tall(X)&~rich(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(calm(X)|funny(X))))&
(![X]:((brave(X)<~>humble(X))<=>(patient(X)<~>old(X))))&
(![X]:((creative(X)&~tall(X))=>(~old(X)&patient(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~generous(X)&~rich(X)))))&
((?[X]:(humble(X)))<=>(curious(alice)))&
((~old(mary))<=>(?[X]:(humble(X))))&
((?[X]:((funny(X)&~generous(X))))=>((rich(alice)<~>funny(alice))))&
(![X]:((~rich(X)|curious(X))<=>(tall(X)|~rich(X))))&
(![X]:((rich(X)<~>old(X))=>~humble(X)))&
(![X]:((tall(X)|~creative(X))=>quiet(X)))&
(![X]:((generous(X)&~patient(X))=>(~calm(X)|funny(X))))&
(![X]:((humble(X)<~>strong(X))=>(creative(X)&funny(X))))&
(![X]:((~humble(X)|~funny(X))<=>(strong(X)&~funny(X))))&
(![X]:(old(X)<=>(~strong(X)|tall(X))))&
((?[X]:((old(X)<~>curious(X))))<=>(?[X]:((kind(X)|~rich(X)))))&
(?[X]:(~wise(X)))&
((~tall(lucy)|~strong(lucy)))&
(?[X]:((~kind(X)<~>~generous(X))))&
((~rich(fred)&~brave(fred)))&
(?[X]:((patient(X)&~rich(X))))&
(?[X]:((generous(X)<~>~funny(X)))) | ~tall(alice) | [
"p0",
"p1",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2985225308997584630563204
% SZS output start Proof for 2985225308997584630563204
1. ! [X0] : ((calm(X0) | strong(X0)) <=> (~rich(X0) & ~tall(X0))) [input p0]
2. ! [X0] : ((~old(X0) <~> ~rich(X0)) <=> (funny(X0) | calm(X0))) [input p1]
10. ! [X0] : ((rich(X0) <~> old(X0)) => ~humble(X0)) [input p9]
14. ! [X0] : ((~funny(X0) | ~humble(X0)) <=> (~funny(X0) & strong(X0))) [input p13]
15. ! [X0] : (old(X0) <=> (tall(X0) | ~strong(X0))) [input p14]
23. tall(alice) [input hypothesis]
31. ! [X0] : (~humble(X0) | (rich(X0) <=> old(X0))) [ennf transformation 10]
35. ! [X0] : (((calm(X0) | strong(X0)) | (rich(X0) | tall(X0))) & ((~rich(X0) & ~tall(X0)) | (~calm(X0) & ~strong(X0)))) [nnf transformation 1]
36. ! [X0] : ((calm(X0) | strong(X0) | rich(X0) | tall(X0)) & ((~rich(X0) & ~tall(X0)) | (~calm(X0) & ~strong(X0)))) [flattening 35]
37. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (~funny(X0) & ~calm(X0))) & ((funny(X0) | calm(X0)) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [nnf transformation 2]
38. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (~funny(X0) & ~calm(X0))) & (funny(X0) | calm(X0) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [flattening 37]
56. ! [X0] : (~humble(X0) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0)))) [nnf transformation 31]
58. ! [X0] : (((~funny(X0) | ~humble(X0)) | (funny(X0) | ~strong(X0))) & ((~funny(X0) & strong(X0)) | (funny(X0) & humble(X0)))) [nnf transformation 14]
59. ! [X0] : ((~funny(X0) | ~humble(X0) | funny(X0) | ~strong(X0)) & ((~funny(X0) & strong(X0)) | (funny(X0) & humble(X0)))) [flattening 58]
60. ! [X0] : ((old(X0) | (~tall(X0) & strong(X0))) & ((tall(X0) | ~strong(X0)) | ~old(X0))) [nnf transformation 15]
61. ! [X0] : ((old(X0) | (~tall(X0) & strong(X0))) & (tall(X0) | ~strong(X0) | ~old(X0))) [flattening 60]
75. ~tall(X0) | ~strong(X0) [cnf transformation 36]
77. ~rich(X0) | ~strong(X0) [cnf transformation 36]
83. ~funny(X0) | ~old(X0) | ~rich(X0) [cnf transformation 38]
110. ~humble(X0) | rich(X0) | ~old(X0) [cnf transformation 56]
116. humble(X0) | strong(X0) [cnf transformation 59]
117. funny(X0) | strong(X0) [cnf transformation 59]
122. old(X0) | strong(X0) [cnf transformation 61]
139. tall(alice) [cnf transformation 23]
254. ~strong(alice) [resolution 75,139]
267. ~old(X0) | ~rich(X0) | strong(X0) [resolution 83,117]
268. ~rich(X0) | strong(X0) [subsumption resolution 267,122]
269. ~rich(X0) [subsumption resolution 268,77]
279. rich(X0) | ~old(X0) | strong(X0) [resolution 110,116]
282. ~old(X0) | strong(X0) [subsumption resolution 279,269]
283. strong(X0) [subsumption resolution 282,122]
286. $false [resolution 283,254]
% SZS output end Proof for 2985225308997584630563204
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious or not old is calm.
Everyone who is brave or old is not rich or calm and vice versa.
Everyone who is wise is old or not wise.
If someone is not calm then alice is rich or kind.
If someone is either not rich or brave then john is both not strong and funny.
Everyone who is rich is either not calm or curious and vice versa.
Everyone who is either kind or funny is humble or not kind and vice versa.
If susan is quiet then alice is wise.
Everyone who is not funny or not old is either not creative or not quiet.
Everyone who is both rich and not rich is not calm or rich and vice versa.
Everyone who is either creative or wise is brave or not humble and vice versa.
Everyone who is either humble or not quiet is quiet or wise and vice versa.
If someone is either curious or not curious then someone is either not funny or brave.
Everyone who is both quiet and wise is both not creative and not rich and vice versa.
If paul is strong or quiet then fred is not wise or kind.
Everyone who is brave is either tall or generous.
Mary is not curious or not quiet.
Lucy is not funny or not calm.
Someone is creative.
Lucy is either brave or creative. | John is not quiet. | neutral | (![X]:((curious(X)|~old(X))=>calm(X)))&
(![X]:((brave(X)|old(X))<=>(~rich(X)|calm(X))))&
(![X]:(wise(X)=>(old(X)|~wise(X))))&
((?[X]:(~calm(X)))=>((rich(alice)|kind(alice))))&
((?[X]:((~rich(X)<~>brave(X))))=>((~strong(john)&funny(john))))&
(![X]:(rich(X)<=>(~calm(X)<~>curious(X))))&
(![X]:((kind(X)<~>funny(X))<=>(humble(X)|~kind(X))))&
((quiet(susan))=>(wise(alice)))&
(![X]:((~funny(X)|~old(X))=>(~creative(X)<~>~quiet(X))))&
(![X]:((rich(X)&~rich(X))<=>(~calm(X)|rich(X))))&
(![X]:((creative(X)<~>wise(X))<=>(brave(X)|~humble(X))))&
(![X]:((humble(X)<~>~quiet(X))<=>(quiet(X)|wise(X))))&
((?[X]:((curious(X)<~>~curious(X))))=>(?[X]:((~funny(X)<~>brave(X)))))&
(![X]:((quiet(X)&wise(X))<=>(~creative(X)&~rich(X))))&
(((strong(paul)|quiet(paul)))=>((~wise(fred)|kind(fred))))&
(![X]:(brave(X)=>(tall(X)<~>generous(X))))&
((~curious(mary)|~quiet(mary)))&
((~funny(lucy)|~calm(lucy)))&
(?[X]:(creative(X)))&
((brave(lucy)<~>creative(lucy))) | ~quiet(john) | [] | null | 0 |
Everyone who is either not rich or not curious is not wise or not happy.
If someone is patient then alice is generous.
If someone is either tall or not strong then someone is not brave or tall and vice versa.
Everyone who is creative or not quiet is either not kind or rich and vice versa.
Everyone who is either not strong or kind is either not strong or rich and vice versa.
If john is not rich then paul is either funny or patient.
If someone is both not curious and not wise then susan is not quiet and vice versa.
Everyone who is both not rich and not kind is not wise and vice versa.
Everyone who is both not wise and not kind is happy and vice versa.
Everyone who is not tall or not wise is generous and vice versa.
Everyone who is either not happy or kind is humble or not quiet and vice versa.
Everyone who is brave is humble or not curious.
Everyone who is not rich or not curious is wise or not tall.
If mary is either not happy or not creative then lucy is not calm and vice versa.
If john is brave or not old then someone is not creative or tall.
Everyone who is not generous is either rich or creative.
Alice is either curious or kind.
Someone is patient or creative.
Lucy is not brave or not calm.
John is either not rich or not calm.
Lucy is happy.
Someone is kind or patient.
Fred is both not calm and quiet. | Fred is not humble. | entailment | (![X]:((~rich(X)<~>~curious(X))=>(~wise(X)|~happy(X))))&
((?[X]:(patient(X)))=>(generous(alice)))&
((?[X]:((tall(X)<~>~strong(X))))<=>(?[X]:((~brave(X)|tall(X)))))&
(![X]:((creative(X)|~quiet(X))<=>(~kind(X)<~>rich(X))))&
(![X]:((~strong(X)<~>kind(X))<=>(~strong(X)<~>rich(X))))&
((~rich(john))=>((funny(paul)<~>patient(paul))))&
((?[X]:((~curious(X)&~wise(X))))<=>(~quiet(susan)))&
(![X]:((~rich(X)&~kind(X))<=>~wise(X)))&
(![X]:((~wise(X)&~kind(X))<=>happy(X)))&
(![X]:((~tall(X)|~wise(X))<=>generous(X)))&
(![X]:((~happy(X)<~>kind(X))<=>(humble(X)|~quiet(X))))&
(![X]:(brave(X)=>(humble(X)|~curious(X))))&
(![X]:((~rich(X)|~curious(X))=>(wise(X)|~tall(X))))&
(((~happy(mary)<~>~creative(mary)))<=>(~calm(lucy)))&
(((brave(john)|~old(john)))=>(?[X]:((~creative(X)|tall(X)))))&
(![X]:(~generous(X)=>(rich(X)<~>creative(X))))&
((curious(alice)<~>kind(alice)))&
(?[X]:((patient(X)|creative(X))))&
((~brave(lucy)|~calm(lucy)))&
((~rich(john)<~>~calm(john)))&
(happy(lucy))&
(?[X]:((kind(X)|patient(X))))&
((~calm(fred)&quiet(fred))) | ~humble(fred) | [
"p4",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7713397300771454183662545
% SZS output start Proof for 7713397300771454183662545
5. ! [X0] : ((~strong(X0) <~> kind(X0)) <=> (~strong(X0) <~> rich(X0))) [input p4]
8. ! [X0] : ((~kind(X0) & ~rich(X0)) <=> ~wise(X0)) [input p7]
9. ! [X0] : ((~kind(X0) & ~wise(X0)) <=> happy(X0)) [input p8]
11. ! [X0] : ((~happy(X0) <~> kind(X0)) <=> (~quiet(X0) | humble(X0))) [input p10]
24. humble(fred) [input hypothesis]
48. ! [X0] : ((((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | ((~strong(X0) | ~rich(X0)) & (rich(X0) | strong(X0)))) & (((~rich(X0) | strong(X0)) & (rich(X0) | ~strong(X0))) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))))) [nnf transformation 5]
54. ! [X0] : (((~kind(X0) & ~rich(X0)) | wise(X0)) & (~wise(X0) | (kind(X0) | rich(X0)))) [nnf transformation 8]
55. ! [X0] : (((~kind(X0) & ~rich(X0)) | wise(X0)) & (~wise(X0) | kind(X0) | rich(X0))) [flattening 54]
56. ! [X0] : (((~kind(X0) & ~wise(X0)) | ~happy(X0)) & (happy(X0) | (kind(X0) | wise(X0)))) [nnf transformation 9]
57. ! [X0] : (((~kind(X0) & ~wise(X0)) | ~happy(X0)) & (happy(X0) | kind(X0) | wise(X0))) [flattening 56]
58. ! [X0] : ((((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) | (quiet(X0) & ~humble(X0))) & ((~quiet(X0) | humble(X0)) | ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0))))) [nnf transformation 11]
59. ! [X0] : ((((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) | (quiet(X0) & ~humble(X0))) & (~quiet(X0) | humble(X0) | ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0))))) [flattening 58]
87. ~rich(X0) | strong(X0) | kind(X0) | strong(X0) [cnf transformation 48]
90. kind(X0) | ~strong(X0) | ~strong(X0) | ~rich(X0) [cnf transformation 48]
98. ~wise(X0) | kind(X0) | rich(X0) [cnf transformation 55]
101. happy(X0) | kind(X0) | wise(X0) [cnf transformation 57]
103. ~kind(X0) | ~happy(X0) [cnf transformation 57]
107. kind(X0) | ~happy(X0) | ~humble(X0) [cnf transformation 59]
109. ~kind(X0) | happy(X0) | ~humble(X0) [cnf transformation 59]
131. humble(fred) [cnf transformation 24]
133. ~rich(X0) | strong(X0) | kind(X0) [duplicate literal removal 87]
134. kind(X0) | ~strong(X0) | ~rich(X0) [duplicate literal removal 90]
178. ~rich(X0) | kind(X0) [subsumption resolution 133,134]
212. ~wise(X0) | kind(X0) [subsumption resolution 98,178]
213. kind(X0) | happy(X0) [subsumption resolution 101,212]
215. ~humble(X0) | ~kind(X0) [subsumption resolution 109,103]
218. ~humble(X0) | ~happy(X0) [subsumption resolution 107,215]
321. ~kind(fred) [resolution 215,131]
322. happy(fred) [resolution 321,213]
323. ~happy(fred) [resolution 218,131]
324. $false [subsumption resolution 323,322]
% SZS output end Proof for 7713397300771454183662545
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either not curious or tall then lucy is either not rich or quiet and vice versa.
If john is not calm then alice is not calm and vice versa.
If mary is either brave or not rich then susan is wise and vice versa.
Everyone who is not kind is funny or not quiet and vice versa.
Everyone who is both not quiet and quiet is strong.
Everyone who is both not strong and wise is either patient or not humble.
Everyone who is old is not happy or not calm.
If someone is happy or tall then mary is both not patient and not tall.
Everyone who is curious is both not creative and rich and vice versa.
If alice is not curious then alice is both strong and creative and vice versa.
If someone is tall then lucy is kind or not creative.
Everyone who is funny or creative is either not tall or happy.
If someone is both quiet and humble then mary is either not rich or not creative.
Everyone who is not creative or not brave is either not patient or not rich and vice versa.
If susan is kind then fred is either funny or not brave and vice versa.
Everyone who is strong is not tall.
Someone is not curious.
Lucy is both creative and not tall.
Someone is not quiet.
Someone is either not generous or brave.
John is not strong or not rich.
Someone is happy.
Someone is brave.
Susan is creative or curious. | Mary is patient. | contradiction | (((~curious(mary)<~>tall(mary)))<=>((~rich(lucy)<~>quiet(lucy))))&
((~calm(john))<=>(~calm(alice)))&
(((brave(mary)<~>~rich(mary)))<=>(wise(susan)))&
(![X]:(~kind(X)<=>(funny(X)|~quiet(X))))&
(![X]:((~quiet(X)&quiet(X))=>strong(X)))&
(![X]:((~strong(X)&wise(X))=>(patient(X)<~>~humble(X))))&
(![X]:(old(X)=>(~happy(X)|~calm(X))))&
((?[X]:((happy(X)|tall(X))))=>((~patient(mary)&~tall(mary))))&
(![X]:(curious(X)<=>(~creative(X)&rich(X))))&
((~curious(alice))<=>((strong(alice)&creative(alice))))&
((?[X]:(tall(X)))=>((kind(lucy)|~creative(lucy))))&
(![X]:((funny(X)|creative(X))=>(~tall(X)<~>happy(X))))&
((?[X]:((quiet(X)&humble(X))))=>((~rich(mary)<~>~creative(mary))))&
(![X]:((~creative(X)|~brave(X))<=>(~patient(X)<~>~rich(X))))&
((kind(susan))<=>((funny(fred)<~>~brave(fred))))&
(![X]:(strong(X)=>~tall(X)))&
(?[X]:(~curious(X)))&
((creative(lucy)&~tall(lucy)))&
(?[X]:(~quiet(X)))&
(?[X]:((~generous(X)<~>brave(X))))&
((~strong(john)|~rich(john)))&
(?[X]:(happy(X)))&
(?[X]:(brave(X)))&
((creative(susan)|curious(susan))) | patient(mary) | [
"p7",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5660437499023583418196087
% SZS output start Proof for 5660437499023583418196087
8. ? [X0] : (tall(X0) | happy(X0)) => (~tall(mary) & ~patient(mary)) [input p7]
22. ? [X0] : happy(X0) [input p21]
25. patient(mary) [input hypothesis]
31. (~tall(mary) & ~patient(mary)) | ! [X0] : (~tall(X0) & ~happy(X0)) [ennf transformation 8]
59. ? [X0] : happy(X0) => happy(sK3) [choice axiom]
60. happy(sK3) [skolemisation 22,59]
83. ~patient(mary) | ~happy(X0) [cnf transformation 31]
118. happy(sK3) [cnf transformation 60]
121. patient(mary) [cnf transformation 25]
177. 11 <=> ! [X0] : ~happy(X0) [avatar definition]
178. ~happy(X0) <- (11) [avatar component clause 177]
181. 12 <=> patient(mary) [avatar definition]
185. 11 | ~12 [avatar split clause 83,181,177]
263. 12 [avatar split clause 121,181]
264. $false <- (11) [resolution 178,118]
265. ~11 [avatar contradiction clause 264]
266. $false [avatar sat refutation 185,263,265]
% SZS output end Proof for 5660437499023583418196087
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is not kind and vice versa.
Everyone who is not calm is not happy or strong and vice versa.
Everyone who is both not rich and not kind is either not wise or not brave.
Everyone who is either strong or not wise is happy and vice versa.
Everyone who is curious is calm.
Everyone who is either curious or not brave is strong and vice versa.
Everyone who is either not wise or not kind is both quiet and brave and vice versa.
Everyone who is both curious and not creative is not funny or calm and vice versa.
Everyone who is not brave or quiet is quiet and vice versa.
If mary is not wise then someone is either not old or brave.
Everyone who is not calm or not old is either not generous or calm and vice versa.
If fred is calm or not kind then alice is old and vice versa.
If someone is either generous or curious then someone is brave.
Susan is not curious.
Someone is not curious.
Someone is either not tall or not strong.
Alice is not generous or calm.
Someone is not old. | Susan is quiet. | entailment | (![X]:(~curious(X)<=>~kind(X)))&
(![X]:(~calm(X)<=>(~happy(X)|strong(X))))&
(![X]:((~rich(X)&~kind(X))=>(~wise(X)<~>~brave(X))))&
(![X]:((strong(X)<~>~wise(X))<=>happy(X)))&
(![X]:(curious(X)=>calm(X)))&
(![X]:((curious(X)<~>~brave(X))<=>strong(X)))&
(![X]:((~wise(X)<~>~kind(X))<=>(quiet(X)&brave(X))))&
(![X]:((curious(X)&~creative(X))<=>(~funny(X)|calm(X))))&
(![X]:((~brave(X)|quiet(X))<=>quiet(X)))&
((~wise(mary))=>(?[X]:((~old(X)<~>brave(X)))))&
(![X]:((~calm(X)|~old(X))<=>(~generous(X)<~>calm(X))))&
(((calm(fred)|~kind(fred)))<=>(old(alice)))&
((?[X]:((generous(X)<~>curious(X))))=>(?[X]:(brave(X))))&
(~curious(susan))&
(?[X]:(~curious(X)))&
(?[X]:((~tall(X)<~>~strong(X))))&
((~generous(alice)|calm(alice)))&
(?[X]:(~old(X))) | quiet(susan) | [
"p0",
"p1",
"p3",
"p5",
"p6",
"p7",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3181720690763594925661915
% SZS output start Proof for 3181720690763594925661915
1. ! [X0] : (~curious(X0) <=> ~kind(X0)) [input p0]
2. ! [X0] : (~calm(X0) <=> (strong(X0) | ~happy(X0))) [input p1]
4. ! [X0] : ((strong(X0) <~> ~wise(X0)) <=> happy(X0)) [input p3]
6. ! [X0] : ((curious(X0) <~> ~brave(X0)) <=> strong(X0)) [input p5]
7. ! [X0] : ((~wise(X0) <~> ~kind(X0)) <=> (brave(X0) & quiet(X0))) [input p6]
8. ! [X0] : ((~creative(X0) & curious(X0)) <=> (calm(X0) | ~funny(X0))) [input p7]
9. ! [X0] : ((quiet(X0) | ~brave(X0)) <=> quiet(X0)) [input p8]
14. ~curious(susan) [input p13]
19. ~quiet(susan) [input hypothesis]
25. ! [X0] : ((~curious(X0) | kind(X0)) & (~kind(X0) | curious(X0))) [nnf transformation 1]
26. ! [X0] : ((~calm(X0) | (~strong(X0) & happy(X0))) & ((strong(X0) | ~happy(X0)) | calm(X0))) [nnf transformation 2]
27. ! [X0] : ((~calm(X0) | (~strong(X0) & happy(X0))) & (strong(X0) | ~happy(X0) | calm(X0))) [flattening 26]
28. ! [X0] : ((((wise(X0) | ~strong(X0)) & (~wise(X0) | strong(X0))) | ~happy(X0)) & (happy(X0) | ((strong(X0) | wise(X0)) & (~wise(X0) | ~strong(X0))))) [nnf transformation 4]
29. ! [X0] : ((((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | ~strong(X0)) & (strong(X0) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0))))) [nnf transformation 6]
30. ! [X0] : ((((kind(X0) | wise(X0)) & (~kind(X0) | ~wise(X0))) | (~brave(X0) | ~quiet(X0))) & ((brave(X0) & quiet(X0)) | ((~wise(X0) | kind(X0)) & (~kind(X0) | wise(X0))))) [nnf transformation 7]
31. ! [X0] : ((((kind(X0) | wise(X0)) & (~kind(X0) | ~wise(X0))) | ~brave(X0) | ~quiet(X0)) & ((brave(X0) & quiet(X0)) | ((~wise(X0) | kind(X0)) & (~kind(X0) | wise(X0))))) [flattening 30]
32. ! [X0] : (((~creative(X0) & curious(X0)) | (~calm(X0) & funny(X0))) & ((calm(X0) | ~funny(X0)) | (creative(X0) | ~curious(X0)))) [nnf transformation 8]
33. ! [X0] : (((~creative(X0) & curious(X0)) | (~calm(X0) & funny(X0))) & (calm(X0) | ~funny(X0) | creative(X0) | ~curious(X0))) [flattening 32]
34. ! [X0] : (((quiet(X0) | ~brave(X0)) | ~quiet(X0)) & (quiet(X0) | (~quiet(X0) & brave(X0)))) [nnf transformation 9]
35. ! [X0] : ((quiet(X0) | ~brave(X0) | ~quiet(X0)) & (quiet(X0) | (~quiet(X0) & brave(X0)))) [flattening 34]
54. ~kind(X0) | curious(X0) [cnf transformation 25]
56. ~happy(X0) | strong(X0) | calm(X0) [cnf transformation 27]
60. wise(X0) | strong(X0) | happy(X0) [cnf transformation 28]
66. ~brave(X0) | curious(X0) | ~strong(X0) [cnf transformation 29]
69. ~wise(X0) | quiet(X0) | kind(X0) [cnf transformation 31]
76. ~calm(X0) | curious(X0) [cnf transformation 33]
79. quiet(X0) | brave(X0) [cnf transformation 35]
95. ~curious(susan) [cnf transformation 14]
101. ~quiet(susan) [cnf transformation 19]
155. brave(susan) [resolution 79,101]
198. curious(susan) | ~strong(susan) [resolution 66,155]
202. ~strong(susan) [subsumption resolution 198,95]
207. quiet(X0) | kind(X0) | strong(X0) | happy(X0) [resolution 69,60]
262. kind(susan) | strong(susan) | happy(susan) [resolution 207,101]
266. kind(susan) | happy(susan) [subsumption resolution 262,202]
268. 25 <=> happy(susan) [avatar definition]
270. happy(susan) <- (25) [avatar component clause 268]
272. 26 <=> kind(susan) [avatar definition]
274. kind(susan) <- (26) [avatar component clause 272]
275. 25 | 26 [avatar split clause 266,272,268]
276. strong(susan) | calm(susan) <- (25) [resolution 270,56]
277. calm(susan) <- (25) [subsumption resolution 276,202]
282. curious(susan) <- (25) [resolution 277,76]
293. $false <- (25) [subsumption resolution 282,95]
294. ~25 [avatar contradiction clause 293]
297. curious(susan) <- (26) [resolution 274,54]
299. $false <- (26) [subsumption resolution 297,95]
300. ~26 [avatar contradiction clause 299]
301. $false [avatar sat refutation 275,294,300]
% SZS output end Proof for 3181720690763594925661915
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or curious is both not kind and not happy and vice versa.
If paul is humble then someone is not strong or not quiet.
If paul is not kind or not creative then susan is calm or not calm.
Everyone who is both curious and not funny is not kind and vice versa.
If someone is not strong then susan is either not humble or not brave and vice versa.
If someone is either happy or not strong then someone is either not tall or not funny and vice versa.
Everyone who is not generous is both old and rich and vice versa.
If lucy is both not wise and curious then fred is not humble and vice versa.
Everyone who is not strong is not quiet.
Everyone who is both rich and humble is either strong or not kind and vice versa.
Everyone who is curious or not old is either creative or not patient and vice versa.
If john is either not happy or old then someone is creative or happy and vice versa.
If someone is kind then paul is both generous and funny.
Everyone who is both not tall and not old is not patient or tall.
Everyone who is not brave or tall is both not curious and not old and vice versa.
If someone is both not tall and not old then someone is both rich and not humble and vice versa.
Alice is both patient and not rich.
Someone is both happy and not wise.
Someone is not brave or not tall.
Someone is either not generous or kind.
Alice is happy.
Fred is either not brave or generous.
Someone is both not funny and not wise.
Someone is either brave or not kind. | Alice is not creative. | contradiction | (![X]:((~quiet(X)<~>curious(X))<=>(~kind(X)&~happy(X))))&
((humble(paul))=>(?[X]:((~strong(X)|~quiet(X)))))&
(((~kind(paul)|~creative(paul)))=>((calm(susan)|~calm(susan))))&
(![X]:((curious(X)&~funny(X))<=>~kind(X)))&
((?[X]:(~strong(X)))<=>((~humble(susan)<~>~brave(susan))))&
((?[X]:((happy(X)<~>~strong(X))))<=>(?[X]:((~tall(X)<~>~funny(X)))))&
(![X]:(~generous(X)<=>(old(X)&rich(X))))&
(((~wise(lucy)&curious(lucy)))<=>(~humble(fred)))&
(![X]:(~strong(X)=>~quiet(X)))&
(![X]:((rich(X)&humble(X))<=>(strong(X)<~>~kind(X))))&
(![X]:((curious(X)|~old(X))<=>(creative(X)<~>~patient(X))))&
(((~happy(john)<~>old(john)))<=>(?[X]:((creative(X)|happy(X)))))&
((?[X]:(kind(X)))=>((generous(paul)&funny(paul))))&
(![X]:((~tall(X)&~old(X))=>(~patient(X)|tall(X))))&
(![X]:((~brave(X)|tall(X))<=>(~curious(X)&~old(X))))&
((?[X]:((~tall(X)&~old(X))))<=>(?[X]:((rich(X)&~humble(X)))))&
((patient(alice)&~rich(alice)))&
(?[X]:((happy(X)&~wise(X))))&
(?[X]:((~brave(X)|~tall(X))))&
(?[X]:((~generous(X)<~>kind(X))))&
(happy(alice))&
((~brave(fred)<~>generous(fred)))&
(?[X]:((~funny(X)&~wise(X))))&
(?[X]:((brave(X)<~>~kind(X)))) | ~creative(alice) | [
"p0",
"p3",
"p8",
"p9",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2712057096470598476925612
% SZS output start Proof for 2712057096470598476925612
1. ! [X0] : ((~quiet(X0) <~> curious(X0)) <=> (~happy(X0) & ~kind(X0))) [input p0]
4. ! [X0] : ((~funny(X0) & curious(X0)) <=> ~kind(X0)) [input p3]
9. ! [X0] : (~strong(X0) => ~quiet(X0)) [input p8]
10. ! [X0] : ((humble(X0) & rich(X0)) <=> (strong(X0) <~> ~kind(X0))) [input p9]
11. ! [X0] : ((~old(X0) | curious(X0)) <=> (creative(X0) <~> ~patient(X0))) [input p10]
17. ~rich(alice) & patient(alice) [input p16]
25. ~creative(alice) [input hypothesis]
31. ! [X0] : (~quiet(X0) | strong(X0)) [ennf transformation 9]
35. ! [X0] : ((((~curious(X0) | quiet(X0)) & (curious(X0) | ~quiet(X0))) | (happy(X0) | kind(X0))) & ((~happy(X0) & ~kind(X0)) | ((~quiet(X0) | ~curious(X0)) & (curious(X0) | quiet(X0))))) [nnf transformation 1]
36. ! [X0] : ((((~curious(X0) | quiet(X0)) & (curious(X0) | ~quiet(X0))) | happy(X0) | kind(X0)) & ((~happy(X0) & ~kind(X0)) | ((~quiet(X0) | ~curious(X0)) & (curious(X0) | quiet(X0))))) [flattening 35]
39. ! [X0] : (((~funny(X0) & curious(X0)) | kind(X0)) & (~kind(X0) | (funny(X0) | ~curious(X0)))) [nnf transformation 4]
40. ! [X0] : (((~funny(X0) & curious(X0)) | kind(X0)) & (~kind(X0) | funny(X0) | ~curious(X0))) [flattening 39]
54. ! [X0] : (((humble(X0) & rich(X0)) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0)))) & (((kind(X0) | ~strong(X0)) & (~kind(X0) | strong(X0))) | (~humble(X0) | ~rich(X0)))) [nnf transformation 10]
55. ! [X0] : (((humble(X0) & rich(X0)) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0)))) & (((kind(X0) | ~strong(X0)) & (~kind(X0) | strong(X0))) | ~humble(X0) | ~rich(X0))) [flattening 54]
56. ! [X0] : (((~old(X0) | curious(X0)) | ((creative(X0) | patient(X0)) & (~patient(X0) | ~creative(X0)))) & (((patient(X0) | ~creative(X0)) & (~patient(X0) | creative(X0))) | (old(X0) & ~curious(X0)))) [nnf transformation 11]
57. ! [X0] : ((~old(X0) | curious(X0) | ((creative(X0) | patient(X0)) & (~patient(X0) | ~creative(X0)))) & (((patient(X0) | ~creative(X0)) & (~patient(X0) | creative(X0))) | (old(X0) & ~curious(X0)))) [flattening 56]
82. ~kind(X0) | curious(X0) | quiet(X0) [cnf transformation 36]
92. kind(X0) | curious(X0) [cnf transformation 40]
112. ~quiet(X0) | strong(X0) [cnf transformation 31]
115. ~strong(X0) | ~kind(X0) | rich(X0) [cnf transformation 55]
119. ~patient(X0) | creative(X0) | ~curious(X0) [cnf transformation 57]
143. patient(alice) [cnf transformation 17]
144. ~rich(alice) [cnf transformation 17]
157. ~creative(alice) [cnf transformation 25]
393. curious(X0) | quiet(X0) | curious(X0) [resolution 82,92]
396. curious(X0) | quiet(X0) [duplicate literal removal 393]
440. 48 <=> curious(alice) [avatar definition]
442. ~curious(alice) <- (~48) [avatar component clause 440]
444. 49 <=> quiet(alice) [avatar definition]
445. quiet(alice) <- (49) [avatar component clause 444]
518. 63 <=> kind(alice) [avatar definition]
519. ~kind(alice) <- (~63) [avatar component clause 518]
520. kind(alice) <- (63) [avatar component clause 518]
522. 64 <=> strong(alice) [avatar definition]
524. strong(alice) <- (64) [avatar component clause 522]
545. creative(alice) | ~curious(alice) [resolution 119,143]
694. quiet(alice) <- (~48) [resolution 396,442]
698. 49 | 48 [avatar split clause 694,440,444]
705. strong(alice) <- (49) [resolution 445,112]
706. 64 | ~49 [avatar split clause 705,444,522]
708. ~kind(alice) | rich(alice) <- (64) [resolution 524,115]
710. rich(alice) <- (63, 64) [subsumption resolution 708,520]
711. $false <- (63, 64) [subsumption resolution 710,144]
712. ~63 | ~64 [avatar contradiction clause 711]
719. ~curious(alice) [subsumption resolution 545,157]
720. ~48 [avatar split clause 719,440]
724. curious(alice) <- (~63) [resolution 519,92]
725. $false <- (~48, ~63) [subsumption resolution 724,442]
726. 48 | 63 [avatar contradiction clause 725]
727. $false [avatar sat refutation 698,706,712,720,726]
% SZS output end Proof for 2712057096470598476925612
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny then someone is both not patient and funny. Everyone who is both brave and happy is both not quiet and not curious and vice versa. Everyone who is funny is both not kind and not old and vice versa. If lucy is both strong and not old then someone is both funny and not funny and vice versa. If mary is rich or not tall then fred is brave and vice versa. Everyone who is brave or not humble is curious. Everyone who is either not kind or patient is tall or brave and vice versa. If someone is not funny or patient then fred is both not calm and strong. Everyone who is generous or not funny is either quiet or not kind. If someone is either not happy or not strong then someone is not generous. Everyone who is either not tall or patient is patient and vice versa. If someone is both not funny and not calm then alice is not humble and vice versa. Everyone who is either generous or happy is not wise or happy and vice versa. Everyone who is both not calm and funny is both not old and generous. Alice is not kind or calm. Someone is not happy. Someone is either calm or old. Someone is not old or calm. Someone is not quiet. Alice is both not creative and not wise. | Fred is not funny. | neutral | ((?[X]:(~funny(X)))=>(?[X]:((~patient(X)&funny(X)))))&
(![X]:((brave(X)&happy(X))<=>(~quiet(X)&~curious(X))))&
(![X]:(funny(X)<=>(~kind(X)&~old(X))))&
(((strong(lucy)&~old(lucy)))<=>(?[X]:((funny(X)&~funny(X)))))&
(((rich(mary)|~tall(mary)))<=>(brave(fred)))&
(![X]:((brave(X)|~humble(X))=>curious(X)))&
(![X]:((~kind(X)<~>patient(X))<=>(tall(X)|brave(X))))&
((?[X]:((~funny(X)|patient(X))))=>((~calm(fred)&strong(fred))))&
(![X]:((generous(X)|~funny(X))=>(quiet(X)<~>~kind(X))))&
((?[X]:((~happy(X)<~>~strong(X))))=>(?[X]:(~generous(X))))&
(![X]:((~tall(X)<~>patient(X))<=>patient(X)))&
((?[X]:((~funny(X)&~calm(X))))<=>(~humble(alice)))&
(![X]:((generous(X)<~>happy(X))<=>(~wise(X)|happy(X))))&
(![X]:((~calm(X)&funny(X))=>(~old(X)&generous(X))))&
((~kind(alice)|calm(alice)))&
(?[X]:(~happy(X)))&
(?[X]:((calm(X)<~>old(X))))&
(?[X]:((~old(X)|calm(X))))&
(?[X]:(~quiet(X)))&
((~creative(alice)&~wise(alice))) | ~funny(fred) | [] | null | 0 |
If someone is not humble or funny then john is brave and vice versa.
If lucy is calm then someone is both quiet and not patient.
Everyone who is either kind or not tall is not tall or not creative.
Everyone who is not quiet or kind is both humble and quiet and vice versa.
Everyone who is not happy is generous.
Everyone who is creative or not patient is kind.
Everyone who is both curious and not funny is both not generous and brave.
If lucy is not happy or humble then paul is wise.
If someone is not rich or not brave then fred is both not creative and not happy and vice versa.
If susan is curious then someone is either curious or humble and vice versa.
Everyone who is either not patient or not old is not happy or not humble.
Everyone who is happy or tall is either creative or not kind and vice versa.
Everyone who is both calm and not curious is not happy or not generous and vice versa.
If paul is strong or brave then lucy is tall and vice versa.
Everyone who is wise or not strong is not calm or not humble.
If someone is not rich or not creative then lucy is either not tall or patient and vice versa.
Someone is both not happy and not curious.
Someone is both not patient and quiet.
Someone is patient or not quiet.
Someone is either not curious or not quiet.
Someone is not wise or rich.
Lucy is both creative and not curious.
Alice is both not rich and curious.
Someone is not patient. | Lucy is not old. | entailment | ((?[X]:((~humble(X)|funny(X))))<=>(brave(john)))&
((calm(lucy))=>(?[X]:((quiet(X)&~patient(X)))))&
(![X]:((kind(X)<~>~tall(X))=>(~tall(X)|~creative(X))))&
(![X]:((~quiet(X)|kind(X))<=>(humble(X)&quiet(X))))&
(![X]:(~happy(X)=>generous(X)))&
(![X]:((creative(X)|~patient(X))=>kind(X)))&
(![X]:((curious(X)&~funny(X))=>(~generous(X)&brave(X))))&
(((~happy(lucy)|humble(lucy)))=>(wise(paul)))&
((?[X]:((~rich(X)|~brave(X))))<=>((~creative(fred)&~happy(fred))))&
((curious(susan))<=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((~patient(X)<~>~old(X))=>(~happy(X)|~humble(X))))&
(![X]:((happy(X)|tall(X))<=>(creative(X)<~>~kind(X))))&
(![X]:((calm(X)&~curious(X))<=>(~happy(X)|~generous(X))))&
(((strong(paul)|brave(paul)))<=>(tall(lucy)))&
(![X]:((wise(X)|~strong(X))=>(~calm(X)|~humble(X))))&
((?[X]:((~rich(X)|~creative(X))))<=>((~tall(lucy)<~>patient(lucy))))&
(?[X]:((~happy(X)&~curious(X))))&
(?[X]:((~patient(X)&quiet(X))))&
(?[X]:((patient(X)|~quiet(X))))&
(?[X]:((~curious(X)<~>~quiet(X))))&
(?[X]:((~wise(X)|rich(X))))&
((creative(lucy)&~curious(lucy)))&
((~rich(alice)&curious(alice)))&
(?[X]:(~patient(X))) | ~old(lucy) | [
"p2",
"p3",
"p5",
"p10",
"p11",
"p15",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1289424496116341452445887
% SZS output start Proof for 1289424496116341452445887
3. ! [X0] : ((kind(X0) <~> ~tall(X0)) => (~creative(X0) | ~tall(X0))) [input p2]
4. ! [X0] : ((kind(X0) | ~quiet(X0)) <=> (quiet(X0) & humble(X0))) [input p3]
6. ! [X0] : ((~patient(X0) | creative(X0)) => kind(X0)) [input p5]
11. ! [X0] : ((~patient(X0) <~> ~old(X0)) => (~humble(X0) | ~happy(X0))) [input p10]
12. ! [X0] : ((tall(X0) | happy(X0)) <=> (creative(X0) <~> ~kind(X0))) [input p11]
16. ? [X0] : (~creative(X0) | ~rich(X0)) <=> (~tall(lucy) <~> patient(lucy)) [input p15]
22. ~curious(lucy) & creative(lucy) [input p21]
23. curious(alice) & ~rich(alice) [input p22]
25. old(lucy) [input hypothesis]
27. ! [X0] : ((~creative(X0) | ~tall(X0)) | (kind(X0) <=> ~tall(X0))) [ennf transformation 3]
28. ! [X0] : (~creative(X0) | ~tall(X0) | (kind(X0) <=> ~tall(X0))) [flattening 27]
30. ! [X0] : (kind(X0) | (patient(X0) & ~creative(X0))) [ennf transformation 6]
34. ! [X0] : ((~humble(X0) | ~happy(X0)) | (~patient(X0) <=> ~old(X0))) [ennf transformation 11]
35. ! [X0] : (~humble(X0) | ~happy(X0) | (~patient(X0) <=> ~old(X0))) [flattening 34]
44. ! [X0] : (~creative(X0) | ~tall(X0) | ((kind(X0) | tall(X0)) & (~tall(X0) | ~kind(X0)))) [nnf transformation 28]
45. ! [X0] : (((kind(X0) | ~quiet(X0)) | (~quiet(X0) | ~humble(X0))) & ((quiet(X0) & humble(X0)) | (~kind(X0) & quiet(X0)))) [nnf transformation 4]
46. ! [X0] : ((kind(X0) | ~quiet(X0) | ~quiet(X0) | ~humble(X0)) & ((quiet(X0) & humble(X0)) | (~kind(X0) & quiet(X0)))) [flattening 45]
56. ! [X0] : (~humble(X0) | ~happy(X0) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0)))) [nnf transformation 35]
57. ! [X0] : (((tall(X0) | happy(X0)) | ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0)))) & (((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | (~tall(X0) & ~happy(X0)))) [nnf transformation 12]
58. ! [X0] : ((tall(X0) | happy(X0) | ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0)))) & (((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | (~tall(X0) & ~happy(X0)))) [flattening 57]
63. (? [X0] : (~creative(X0) | ~rich(X0)) | ((~tall(lucy) | ~patient(lucy)) & (patient(lucy) | tall(lucy)))) & (((~patient(lucy) | tall(lucy)) & (patient(lucy) | ~tall(lucy))) | ! [X0] : (creative(X0) & rich(X0))) [nnf transformation 16]
64. (? [X0] : (~creative(X0) | ~rich(X0)) | ((~tall(lucy) | ~patient(lucy)) & (patient(lucy) | tall(lucy)))) & (((~patient(lucy) | tall(lucy)) & (patient(lucy) | ~tall(lucy))) | ! [X1] : (creative(X1) & rich(X1))) [rectify 63]
65. ? [X0] : (~creative(X0) | ~rich(X0)) => (~creative(sK4) | ~rich(sK4)) [choice axiom]
66. ((~creative(sK4) | ~rich(sK4)) | ((~tall(lucy) | ~patient(lucy)) & (patient(lucy) | tall(lucy)))) & (((~patient(lucy) | tall(lucy)) & (patient(lucy) | ~tall(lucy))) | ! [X1] : (creative(X1) & rich(X1))) [skolemisation 64,65]
85. ~creative(X0) | ~tall(X0) | ~tall(X0) | ~kind(X0) [cnf transformation 44]
88. ~kind(X0) | humble(X0) [cnf transformation 46]
93. ~creative(X0) | kind(X0) [cnf transformation 30]
108. ~old(X0) | ~happy(X0) | ~humble(X0) | patient(X0) [cnf transformation 56]
111. ~kind(X0) | creative(X0) | ~tall(X0) [cnf transformation 58]
114. tall(X0) | happy(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 58]
128. ~patient(lucy) | tall(lucy) | rich(X1) [cnf transformation 66]
140. creative(lucy) [cnf transformation 22]
142. ~rich(alice) [cnf transformation 23]
145. old(lucy) [cnf transformation 25]
148. ~creative(X0) | ~tall(X0) | ~kind(X0) [duplicate literal removal 85]
185. 9 <=> humble(lucy) [avatar definition]
186. humble(lucy) <- (9) [avatar component clause 185]
194. 11 <=> happy(lucy) [avatar definition]
196. happy(lucy) <- (11) [avatar component clause 194]
220. 17 <=> ! [X1] : rich(X1) [avatar definition]
221. rich(X1) <- (17) [avatar component clause 220]
248. ~creative(X0) | happy(X0) | tall(X0) [subsumption resolution 114,93]
249. ~tall(X0) | ~kind(X0) [subsumption resolution 111,148]
251. 23 <=> tall(lucy) [avatar definition]
252. tall(lucy) <- (23) [avatar component clause 251]
253. ~tall(lucy) <- (~23) [avatar component clause 251]
266. 26 <=> patient(lucy) [avatar definition]
268. ~patient(lucy) <- (~26) [avatar component clause 266]
283. 17 | 23 | ~26 [avatar split clause 128,266,251,220]
299. kind(lucy) [resolution 93,140]
303. humble(lucy) [resolution 299,88]
304. 9 [avatar split clause 303,185]
428. $false <- (17) [resolution 221,142]
431. ~17 [avatar contradiction clause 428]
434. ~kind(lucy) <- (23) [resolution 252,249]
435. $false <- (23) [subsumption resolution 434,299]
436. ~23 [avatar contradiction clause 435]
442. happy(lucy) | tall(lucy) [resolution 248,140]
443. happy(lucy) <- (~23) [subsumption resolution 442,253]
444. 11 | 23 [avatar split clause 443,251,194]
446. ~happy(lucy) | ~humble(lucy) | patient(lucy) [resolution 108,145]
447. ~humble(lucy) | patient(lucy) <- (11) [subsumption resolution 446,196]
448. patient(lucy) <- (9, 11) [subsumption resolution 447,186]
449. $false <- (9, 11, ~26) [subsumption resolution 448,268]
450. ~9 | ~11 | 26 [avatar contradiction clause 449]
451. $false [avatar sat refutation 283,304,431,436,444,450]
% SZS output end Proof for 1289424496116341452445887
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both rich and humble then susan is curious or happy.
Everyone who is either not old or tall is either not rich or generous.
Everyone who is not brave is brave or not creative and vice versa.
Everyone who is either wise or generous is quiet.
Everyone who is not curious is either happy or tall and vice versa.
Everyone who is tall is not brave or tall and vice versa.
If alice is both not curious and generous then someone is both not quiet and not funny.
Everyone who is either funny or not kind is not old or curious.
If mary is both curious and not calm then someone is humble.
Everyone who is not humble is either not wise or brave.
Everyone who is either not old or rich is not kind.
If lucy is not funny then fred is both old and wise.
If someone is either generous or funny then someone is not kind or not wise.
If someone is not curious then paul is generous.
If someone is both not wise and not brave then someone is both not tall and old.
If someone is not quiet or rich then susan is tall.
Alice is not rich or not funny.
Fred is either not quiet or not strong.
Someone is either generous or wise.
Alice is funny.
Lucy is not happy.
Mary is both wise and humble.
Someone is wise. | Susan is wise. | entailment | ((?[X]:((rich(X)&humble(X))))=>((curious(susan)|happy(susan))))&
(![X]:((~old(X)<~>tall(X))=>(~rich(X)<~>generous(X))))&
(![X]:(~brave(X)<=>(brave(X)|~creative(X))))&
(![X]:((wise(X)<~>generous(X))=>quiet(X)))&
(![X]:(~curious(X)<=>(happy(X)<~>tall(X))))&
(![X]:(tall(X)<=>(~brave(X)|tall(X))))&
(((~curious(alice)&generous(alice)))=>(?[X]:((~quiet(X)&~funny(X)))))&
(![X]:((funny(X)<~>~kind(X))=>(~old(X)|curious(X))))&
(((curious(mary)&~calm(mary)))=>(?[X]:(humble(X))))&
(![X]:(~humble(X)=>(~wise(X)<~>brave(X))))&
(![X]:((~old(X)<~>rich(X))=>~kind(X)))&
((~funny(lucy))=>((old(fred)&wise(fred))))&
((?[X]:((generous(X)<~>funny(X))))=>(?[X]:((~kind(X)|~wise(X)))))&
((?[X]:(~curious(X)))=>(generous(paul)))&
((?[X]:((~wise(X)&~brave(X))))=>(?[X]:((~tall(X)&old(X)))))&
((?[X]:((~quiet(X)|rich(X))))=>(tall(susan)))&
((~rich(alice)|~funny(alice)))&
((~quiet(fred)<~>~strong(fred)))&
(?[X]:((generous(X)<~>wise(X))))&
(funny(alice))&
(~happy(lucy))&
((wise(mary)&humble(mary)))&
(?[X]:(wise(X))) | wise(susan) | [
"p2",
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5385751751484491899769207
% SZS output start Proof for 5385751751484491899769207
3. ! [X0] : (~brave(X0) <=> (~creative(X0) | brave(X0))) [input p2]
6. ! [X0] : (tall(X0) <=> (tall(X0) | ~brave(X0))) [input p5]
15. ? [X0] : (~brave(X0) & ~wise(X0)) => ? [X0] : (old(X0) & ~tall(X0)) [input p14]
24. ~wise(susan) [input hypothesis]
26. ? [X0] : (~brave(X0) & ~wise(X0)) => ? [X1] : (old(X1) & ~tall(X1)) [rectify 15]
43. ? [X1] : (old(X1) & ~tall(X1)) | ! [X0] : (brave(X0) | wise(X0)) [ennf transformation 26]
46. ! [X0] : ((~brave(X0) | (creative(X0) & ~brave(X0))) & ((~creative(X0) | brave(X0)) | brave(X0))) [nnf transformation 3]
47. ! [X0] : ((~brave(X0) | (creative(X0) & ~brave(X0))) & (~creative(X0) | brave(X0) | brave(X0))) [flattening 46]
50. ! [X0] : ((tall(X0) | (~tall(X0) & brave(X0))) & ((tall(X0) | ~brave(X0)) | ~tall(X0))) [nnf transformation 6]
51. ! [X0] : ((tall(X0) | (~tall(X0) & brave(X0))) & (tall(X0) | ~brave(X0) | ~tall(X0))) [flattening 50]
61. ? [X0] : (old(X0) & ~tall(X0)) | ! [X1] : (brave(X1) | wise(X1)) [rectify 43]
62. ? [X0] : (old(X0) & ~tall(X0)) => (old(sK2) & ~tall(sK2)) [choice axiom]
63. (old(sK2) & ~tall(sK2)) | ! [X1] : (brave(X1) | wise(X1)) [skolemisation 61,62]
76. ~brave(X0) | ~brave(X0) [cnf transformation 47]
83. tall(X0) | brave(X0) [cnf transformation 51]
98. ~tall(sK2) | brave(X1) | wise(X1) [cnf transformation 63]
112. ~wise(susan) [cnf transformation 24]
114. ~brave(X0) [duplicate literal removal 76]
128. tall(X0) [subsumption resolution 83,114]
188. 17 <=> ! [X1] : wise(X1) [avatar definition]
189. wise(X1) <- (17) [avatar component clause 188]
195. brave(X1) | wise(X1) [subsumption resolution 98,128]
196. wise(X1) [subsumption resolution 195,114]
197. 17 [avatar split clause 196,188]
228. $false <- (17) [resolution 189,112]
229. ~17 [avatar contradiction clause 228]
230. $false [avatar sat refutation 197,229]
% SZS output end Proof for 5385751751484491899769207
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and not rich is either kind or not patient.
If someone is either not strong or calm then someone is both not wise and not rich.
Everyone who is either old or not old is both not wise and brave.
Everyone who is wise or kind is both not creative and not generous and vice versa.
If someone is both brave and not patient then someone is old or not wise and vice versa.
Everyone who is wise or kind is wise and vice versa.
Everyone who is either creative or quiet is either strong or quiet and vice versa.
Everyone who is not generous or strong is humble or happy.
Everyone who is not funny or curious is both creative and tall and vice versa.
If fred is kind or not wise then lucy is either not kind or not patient.
If someone is not happy then someone is both not quiet and not creative.
Everyone who is brave or not curious is not humble.
Everyone who is not kind or not generous is happy and vice versa.
If lucy is both not old and creative then john is both not generous and not patient and vice versa.
If alice is humble or old then lucy is patient and vice versa.
If someone is both not old and happy then someone is not generous or not kind.
Someone is either not old or not curious.
Someone is both not creative and happy.
Someone is either rich or not generous.
Someone is either happy or patient.
Mary is not calm or generous.
Paul is either calm or kind.
Someone is tall. | Paul is not patient. | neutral | (![X]:((~curious(X)&~rich(X))=>(kind(X)<~>~patient(X))))&
((?[X]:((~strong(X)<~>calm(X))))=>(?[X]:((~wise(X)&~rich(X)))))&
(![X]:((old(X)<~>~old(X))=>(~wise(X)&brave(X))))&
(![X]:((wise(X)|kind(X))<=>(~creative(X)&~generous(X))))&
((?[X]:((brave(X)&~patient(X))))<=>(?[X]:((old(X)|~wise(X)))))&
(![X]:((wise(X)|kind(X))<=>wise(X)))&
(![X]:((creative(X)<~>quiet(X))<=>(strong(X)<~>quiet(X))))&
(![X]:((~generous(X)|strong(X))=>(humble(X)|happy(X))))&
(![X]:((~funny(X)|curious(X))<=>(creative(X)&tall(X))))&
(((kind(fred)|~wise(fred)))=>((~kind(lucy)<~>~patient(lucy))))&
((?[X]:(~happy(X)))=>(?[X]:((~quiet(X)&~creative(X)))))&
(![X]:((brave(X)|~curious(X))=>~humble(X)))&
(![X]:((~kind(X)|~generous(X))<=>happy(X)))&
(((~old(lucy)&creative(lucy)))<=>((~generous(john)&~patient(john))))&
(((humble(alice)|old(alice)))<=>(patient(lucy)))&
((?[X]:((~old(X)&happy(X))))=>(?[X]:((~generous(X)|~kind(X)))))&
(?[X]:((~old(X)<~>~curious(X))))&
(?[X]:((~creative(X)&happy(X))))&
(?[X]:((rich(X)<~>~generous(X))))&
(?[X]:((happy(X)<~>patient(X))))&
((~calm(mary)|generous(mary)))&
((calm(paul)<~>kind(paul)))&
(?[X]:(tall(X))) | ~patient(paul) | [] | null | 0 |
If someone is happy then john is either not calm or kind and vice versa.
If alice is not funny or happy then john is wise.
If susan is both funny and quiet then someone is either brave or not tall and vice versa.
Everyone who is not calm is either not wise or not brave and vice versa.
If lucy is either humble or happy then susan is not rich or creative.
If susan is not calm or not generous then someone is both generous and quiet and vice versa.
Everyone who is not rich is not generous or creative and vice versa.
If susan is humble or creative then someone is creative and vice versa.
Everyone who is both brave and generous is not calm and vice versa.
Everyone who is not patient is both funny and strong.
If fred is generous then john is funny and vice versa.
Everyone who is not strong is creative or not generous and vice versa.
If someone is either kind or not old then mary is both tall and not calm.
Everyone who is both strong and not old is not happy or not generous and vice versa.
Everyone who is calm is not quiet.
Someone is quiet.
Someone is not funny.
Alice is both kind and not quiet.
John is either calm or patient.
Someone is either wise or not humble.
Someone is old.
Fred is not curious. | John is not funny. | contradiction | ((?[X]:(happy(X)))<=>((~calm(john)<~>kind(john))))&
(((~funny(alice)|happy(alice)))=>(wise(john)))&
(((funny(susan)&quiet(susan)))<=>(?[X]:((brave(X)<~>~tall(X)))))&
(![X]:(~calm(X)<=>(~wise(X)<~>~brave(X))))&
(((humble(lucy)<~>happy(lucy)))=>((~rich(susan)|creative(susan))))&
(((~calm(susan)|~generous(susan)))<=>(?[X]:((generous(X)&quiet(X)))))&
(![X]:(~rich(X)<=>(~generous(X)|creative(X))))&
(((humble(susan)|creative(susan)))<=>(?[X]:(creative(X))))&
(![X]:((brave(X)&generous(X))<=>~calm(X)))&
(![X]:(~patient(X)=>(funny(X)&strong(X))))&
((generous(fred))<=>(funny(john)))&
(![X]:(~strong(X)<=>(creative(X)|~generous(X))))&
((?[X]:((kind(X)<~>~old(X))))=>((tall(mary)&~calm(mary))))&
(![X]:((strong(X)&~old(X))<=>(~happy(X)|~generous(X))))&
(![X]:(calm(X)=>~quiet(X)))&
(?[X]:(quiet(X)))&
(?[X]:(~funny(X)))&
((kind(alice)&~quiet(alice)))&
((calm(john)<~>patient(john)))&
(?[X]:((wise(X)<~>~humble(X))))&
(?[X]:(old(X)))&
(~curious(fred)) | ~funny(john) | [
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3329919253144861677242969
% SZS output start Proof for 3329919253144861677242969
11. generous(fred) <=> funny(john) [input p10]
12. ! [X0] : (~strong(X0) <=> (~generous(X0) | creative(X0))) [input p11]
14. ! [X0] : ((~old(X0) & strong(X0)) <=> (~generous(X0) | ~happy(X0))) [input p13]
23. ~funny(john) [input hypothesis]
57. (generous(fred) | ~funny(john)) & (funny(john) | ~generous(fred)) [nnf transformation 11]
58. ! [X0] : ((~strong(X0) | (generous(X0) & ~creative(X0))) & ((~generous(X0) | creative(X0)) | strong(X0))) [nnf transformation 12]
59. ! [X0] : ((~strong(X0) | (generous(X0) & ~creative(X0))) & (~generous(X0) | creative(X0) | strong(X0))) [flattening 58]
61. ! [X0] : (((~old(X0) & strong(X0)) | (generous(X0) & happy(X0))) & ((~generous(X0) | ~happy(X0)) | (old(X0) | ~strong(X0)))) [nnf transformation 14]
62. ! [X0] : (((~old(X0) & strong(X0)) | (generous(X0) & happy(X0))) & (~generous(X0) | ~happy(X0) | old(X0) | ~strong(X0))) [flattening 61]
105. funny(john) | ~generous(fred) [cnf transformation 57]
109. ~strong(X0) | generous(X0) [cnf transformation 59]
116. strong(X0) | generous(X0) [cnf transformation 62]
129. ~funny(john) [cnf transformation 23]
248. 26 <=> funny(john) [avatar definition]
252. 27 <=> generous(fred) [avatar definition]
253. ~generous(fred) <- (~27) [avatar component clause 252]
256. ~27 | 26 [avatar split clause 105,248,252]
275. generous(X0) [subsumption resolution 116,109]
293. ~26 [avatar split clause 129,248]
294. $false <- (~27) [subsumption resolution 253,275]
295. 27 [avatar contradiction clause 294]
297. $false [avatar sat refutation 256,293,295]
% SZS output end Proof for 3329919253144861677242969
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is wise.
If someone is not kind then paul is either not brave or not happy and vice versa.
If someone is either quiet or not curious then someone is either quiet or not tall.
Everyone who is not kind is both not kind and not curious.
Everyone who is either not old or not strong is happy.
Everyone who is either not happy or generous is either not brave or funny.
If susan is both not kind and happy then paul is either not funny or brave and vice versa.
Everyone who is both not happy and quiet is either not curious or curious and vice versa.
Everyone who is funny or not kind is either not rich or not humble.
If someone is both not kind and not rich then susan is either happy or funny and vice versa.
If someone is not old or not funny then alice is not tall or not strong and vice versa.
If fred is tall then someone is not happy and vice versa.
If someone is kind or humble then fred is generous.
If someone is strong or old then lucy is both not patient and not tall.
If fred is humble then alice is patient or not humble.
Everyone who is not generous or brave is not strong and vice versa.
Lucy is both not kind and not patient.
Mary is either quiet or not kind.
Paul is not old.
Someone is not kind or not rich.
Someone is either strong or not kind.
Someone is rich. | Lucy is not generous. | neutral | (![X]:(generous(X)=>wise(X)))&
((?[X]:(~kind(X)))<=>((~brave(paul)<~>~happy(paul))))&
((?[X]:((quiet(X)<~>~curious(X))))=>(?[X]:((quiet(X)<~>~tall(X)))))&
(![X]:(~kind(X)=>(~kind(X)&~curious(X))))&
(![X]:((~old(X)<~>~strong(X))=>happy(X)))&
(![X]:((~happy(X)<~>generous(X))=>(~brave(X)<~>funny(X))))&
(((~kind(susan)&happy(susan)))<=>((~funny(paul)<~>brave(paul))))&
(![X]:((~happy(X)&quiet(X))<=>(~curious(X)<~>curious(X))))&
(![X]:((funny(X)|~kind(X))=>(~rich(X)<~>~humble(X))))&
((?[X]:((~kind(X)&~rich(X))))<=>((happy(susan)<~>funny(susan))))&
((?[X]:((~old(X)|~funny(X))))<=>((~tall(alice)|~strong(alice))))&
((tall(fred))<=>(?[X]:(~happy(X))))&
((?[X]:((kind(X)|humble(X))))=>(generous(fred)))&
((?[X]:((strong(X)|old(X))))=>((~patient(lucy)&~tall(lucy))))&
((humble(fred))=>((patient(alice)|~humble(alice))))&
(![X]:((~generous(X)|brave(X))<=>~strong(X)))&
((~kind(lucy)&~patient(lucy)))&
((quiet(mary)<~>~kind(mary)))&
(~old(paul))&
(?[X]:((~kind(X)|~rich(X))))&
(?[X]:((strong(X)<~>~kind(X))))&
(?[X]:(rich(X))) | ~generous(lucy) | [] | null | 0 |
If john is not patient or not strong then paul is rich.
Everyone who is not rich is generous.
If someone is curious or quiet then fred is both not tall and not wise and vice versa.
Everyone who is not happy is not patient or brave and vice versa.
If susan is not wise or not generous then someone is not funny or not creative and vice versa.
If lucy is not creative or not humble then someone is both rich and old and vice versa.
If susan is both not rich and rich then someone is either kind or brave and vice versa.
Everyone who is both not creative and calm is wise or not rich.
If susan is both strong and not creative then mary is both strong and tall.
Everyone who is both strong and creative is either brave or old and vice versa.
Everyone who is both not generous and not strong is both old and happy.
Everyone who is quiet is both not curious and not old and vice versa.
If someone is brave then someone is not humble or not brave and vice versa.
If someone is not happy or not calm then paul is either rich or tall and vice versa.
If someone is not creative then john is either tall or curious.
Someone is old.
Someone is either generous or not wise.
Alice is not humble.
Someone is creative.
Someone is either old or not generous.
Someone is not creative or kind.
Someone is not happy or not humble. | Susan is not rich. | neutral | (((~patient(john)|~strong(john)))=>(rich(paul)))&
(![X]:(~rich(X)=>generous(X)))&
((?[X]:((curious(X)|quiet(X))))<=>((~tall(fred)&~wise(fred))))&
(![X]:(~happy(X)<=>(~patient(X)|brave(X))))&
(((~wise(susan)|~generous(susan)))<=>(?[X]:((~funny(X)|~creative(X)))))&
(((~creative(lucy)|~humble(lucy)))<=>(?[X]:((rich(X)&old(X)))))&
(((~rich(susan)&rich(susan)))<=>(?[X]:((kind(X)<~>brave(X)))))&
(![X]:((~creative(X)&calm(X))=>(wise(X)|~rich(X))))&
(((strong(susan)&~creative(susan)))=>((strong(mary)&tall(mary))))&
(![X]:((strong(X)&creative(X))<=>(brave(X)<~>old(X))))&
(![X]:((~generous(X)&~strong(X))=>(old(X)&happy(X))))&
(![X]:(quiet(X)<=>(~curious(X)&~old(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~humble(X)|~brave(X)))))&
((?[X]:((~happy(X)|~calm(X))))<=>((rich(paul)<~>tall(paul))))&
((?[X]:(~creative(X)))=>((tall(john)<~>curious(john))))&
(?[X]:(old(X)))&
(?[X]:((generous(X)<~>~wise(X))))&
(~humble(alice))&
(?[X]:(creative(X)))&
(?[X]:((old(X)<~>~generous(X))))&
(?[X]:((~creative(X)|kind(X))))&
(?[X]:((~happy(X)|~humble(X)))) | ~rich(susan) | [] | null | 0 |
If someone is either brave or not curious then someone is strong or not curious. If john is quiet or curious then mary is not quiet. If paul is humble or strong then susan is either not quiet or tall and vice versa. Everyone who is both wise and not patient is not funny or strong and vice versa. Everyone who is either not tall or curious is not tall. If susan is generous then mary is quiet or not funny and vice versa. Everyone who is patient is strong and vice versa. Everyone who is either rich or calm is not quiet. Everyone who is both not creative and patient is not brave and vice versa. Everyone who is quiet is kind or strong and vice versa. If someone is either quiet or not tall then someone is both not creative and not curious and vice versa. If someone is either wise or not old then someone is either not tall or not happy and vice versa. Everyone who is not brave or not old is both kind and not generous. Everyone who is both not generous and tall is both not patient and brave. If someone is either quiet or not tall then fred is not old and vice versa. Susan is both not quiet and happy. Someone is kind or brave. Someone is both not curious and not strong. Someone is not happy or not brave. Someone is funny. Someone is either not brave or kind. Someone is both not quiet and not tall. Paul is either not curious or tall. | Susan is not strong. | entailment | ((?[X]:((brave(X)<~>~curious(X))))=>(?[X]:((strong(X)|~curious(X)))))&
(((quiet(john)|curious(john)))=>(~quiet(mary)))&
(((humble(paul)|strong(paul)))<=>((~quiet(susan)<~>tall(susan))))&
(![X]:((wise(X)&~patient(X))<=>(~funny(X)|strong(X))))&
(![X]:((~tall(X)<~>curious(X))=>~tall(X)))&
((generous(susan))<=>((quiet(mary)|~funny(mary))))&
(![X]:(patient(X)<=>strong(X)))&
(![X]:((rich(X)<~>calm(X))=>~quiet(X)))&
(![X]:((~creative(X)&patient(X))<=>~brave(X)))&
(![X]:(quiet(X)<=>(kind(X)|strong(X))))&
((?[X]:((quiet(X)<~>~tall(X))))<=>(?[X]:((~creative(X)&~curious(X)))))&
((?[X]:((wise(X)<~>~old(X))))<=>(?[X]:((~tall(X)<~>~happy(X)))))&
(![X]:((~brave(X)|~old(X))=>(kind(X)&~generous(X))))&
(![X]:((~generous(X)&tall(X))=>(~patient(X)&brave(X))))&
((?[X]:((quiet(X)<~>~tall(X))))<=>(~old(fred)))&
((~quiet(susan)&happy(susan)))&
(?[X]:((kind(X)|brave(X))))&
(?[X]:((~curious(X)&~strong(X))))&
(?[X]:((~happy(X)|~brave(X))))&
(?[X]:(funny(X)))&
(?[X]:((~brave(X)<~>kind(X))))&
(?[X]:((~quiet(X)&~tall(X))))&
((~curious(paul)<~>tall(paul))) | ~strong(susan) | [
"p3",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6354261088548446934914103
% SZS output start Proof for 6354261088548446934914103
4. ! [X0] : ((~patient(X0) & wise(X0)) <=> (strong(X0) | ~funny(X0))) [input p3]
7. ! [X0] : (patient(X0) <=> strong(X0)) [input p6]
24. strong(susan) [input hypothesis]
41. ! [X0] : (((~patient(X0) & wise(X0)) | (~strong(X0) & funny(X0))) & ((strong(X0) | ~funny(X0)) | (patient(X0) | ~wise(X0)))) [nnf transformation 4]
42. ! [X0] : (((~patient(X0) & wise(X0)) | (~strong(X0) & funny(X0))) & (strong(X0) | ~funny(X0) | patient(X0) | ~wise(X0))) [flattening 41]
46. ! [X0] : ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0))) [nnf transformation 7]
94. ~patient(X0) | ~strong(X0) [cnf transformation 42]
101. patient(X0) | ~strong(X0) [cnf transformation 46]
147. strong(susan) [cnf transformation 24]
212. ~strong(X0) [subsumption resolution 101,94]
304. $false [subsumption resolution 147,212]
% SZS output end Proof for 6354261088548446934914103
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both funny and curious then paul is either not curious or wise and vice versa.
If someone is either not rich or generous then john is old and vice versa.
If someone is either generous or funny then lucy is not kind or not strong.
Everyone who is not wise or rich is wise and vice versa.
If someone is both quiet and not quiet then someone is both not tall and not calm.
If mary is both not quiet and happy then paul is either rich or not brave and vice versa.
If someone is both not happy and tall then alice is either brave or tall.
Everyone who is not strong or not curious is either generous or not patient.
If mary is not humble then lucy is either not creative or wise and vice versa.
If paul is creative then alice is both humble and funny.
If susan is either kind or patient then alice is not brave.
Everyone who is creative is tall or quiet.
Everyone who is both not curious and humble is either creative or calm.
Everyone who is not humble or not kind is not brave or curious.
If fred is either quiet or not curious then someone is both creative and happy.
If mary is both not strong and strong then lucy is either not kind or quiet.
Mary is not quiet or happy.
Someone is either not creative or rich.
Someone is both happy and not generous.
Someone is either strong or creative.
Someone is patient or rich.
Someone is not tall or not brave.
Someone is wise.
Someone is humble. | Mary is wise. | entailment | ((?[X]:((funny(X)&curious(X))))<=>((~curious(paul)<~>wise(paul))))&
((?[X]:((~rich(X)<~>generous(X))))<=>(old(john)))&
((?[X]:((generous(X)<~>funny(X))))=>((~kind(lucy)|~strong(lucy))))&
(![X]:((~wise(X)|rich(X))<=>wise(X)))&
((?[X]:((quiet(X)&~quiet(X))))=>(?[X]:((~tall(X)&~calm(X)))))&
(((~quiet(mary)&happy(mary)))<=>((rich(paul)<~>~brave(paul))))&
((?[X]:((~happy(X)&tall(X))))=>((brave(alice)<~>tall(alice))))&
(![X]:((~strong(X)|~curious(X))=>(generous(X)<~>~patient(X))))&
((~humble(mary))<=>((~creative(lucy)<~>wise(lucy))))&
((creative(paul))=>((humble(alice)&funny(alice))))&
(((kind(susan)<~>patient(susan)))=>(~brave(alice)))&
(![X]:(creative(X)=>(tall(X)|quiet(X))))&
(![X]:((~curious(X)&humble(X))=>(creative(X)<~>calm(X))))&
(![X]:((~humble(X)|~kind(X))=>(~brave(X)|curious(X))))&
(((quiet(fred)<~>~curious(fred)))=>(?[X]:((creative(X)&happy(X)))))&
(((~strong(mary)&strong(mary)))=>((~kind(lucy)<~>quiet(lucy))))&
((~quiet(mary)|happy(mary)))&
(?[X]:((~creative(X)<~>rich(X))))&
(?[X]:((happy(X)&~generous(X))))&
(?[X]:((strong(X)<~>creative(X))))&
(?[X]:((patient(X)|rich(X))))&
(?[X]:((~tall(X)|~brave(X))))&
(?[X]:(wise(X)))&
(?[X]:(humble(X))) | wise(mary) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 5662578831919885431651162
% SZS output start Proof for 5662578831919885431651162
4. ! [X0] : ((rich(X0) | ~wise(X0)) <=> wise(X0)) [input p3]
25. ~wise(mary) [input hypothesis]
52. ! [X0] : (((rich(X0) | ~wise(X0)) | ~wise(X0)) & (wise(X0) | (~rich(X0) & wise(X0)))) [nnf transformation 4]
53. ! [X0] : ((rich(X0) | ~wise(X0) | ~wise(X0)) & (wise(X0) | (~rich(X0) & wise(X0)))) [flattening 52]
96. wise(X0) | wise(X0) [cnf transformation 53]
143. ~wise(mary) [cnf transformation 25]
144. wise(X0) [duplicate literal removal 96]
339. $false [subsumption resolution 143,144]
% SZS output end Proof for 5662578831919885431651162
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or calm is both humble and wise and vice versa.
Everyone who is not brave is both strong and not tall and vice versa.
If alice is both creative and not quiet then lucy is strong and vice versa.
Everyone who is both old and humble is rich or brave and vice versa.
If alice is either curious or not brave then someone is both not creative and curious.
If john is either happy or patient then someone is brave and vice versa.
If fred is funny then john is both not quiet and rich and vice versa.
If someone is both not curious and strong then someone is not quiet and vice versa.
If someone is creative then john is quiet or old.
Everyone who is not creative or strong is either not quiet or humble and vice versa.
Everyone who is not brave is creative and vice versa.
Everyone who is not funny or humble is both calm and rich.
If john is either not quiet or not generous then john is creative.
If someone is both not brave and patient then fred is both kind and not humble and vice versa.
If someone is either not funny or not rich then fred is both humble and rich.
Everyone who is not wise is not creative.
Someone is either humble or curious.
Someone is rich or not kind.
Someone is not happy or generous.
Paul is either not generous or not old.
Someone is not patient or patient.
Alice is either humble or not creative.
Mary is not wise. | Paul is not humble. | neutral | (![X]:((~kind(X)<~>calm(X))<=>(humble(X)&wise(X))))&
(![X]:(~brave(X)<=>(strong(X)&~tall(X))))&
(((creative(alice)&~quiet(alice)))<=>(strong(lucy)))&
(![X]:((old(X)&humble(X))<=>(rich(X)|brave(X))))&
(((curious(alice)<~>~brave(alice)))=>(?[X]:((~creative(X)&curious(X)))))&
(((happy(john)<~>patient(john)))<=>(?[X]:(brave(X))))&
((funny(fred))<=>((~quiet(john)&rich(john))))&
((?[X]:((~curious(X)&strong(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:(creative(X)))=>((quiet(john)|old(john))))&
(![X]:((~creative(X)|strong(X))<=>(~quiet(X)<~>humble(X))))&
(![X]:(~brave(X)<=>creative(X)))&
(![X]:((~funny(X)|humble(X))=>(calm(X)&rich(X))))&
(((~quiet(john)<~>~generous(john)))=>(creative(john)))&
((?[X]:((~brave(X)&patient(X))))<=>((kind(fred)&~humble(fred))))&
((?[X]:((~funny(X)<~>~rich(X))))=>((humble(fred)&rich(fred))))&
(![X]:(~wise(X)=>~creative(X)))&
(?[X]:((humble(X)<~>curious(X))))&
(?[X]:((rich(X)|~kind(X))))&
(?[X]:((~happy(X)|generous(X))))&
((~generous(paul)<~>~old(paul)))&
(?[X]:((~patient(X)|patient(X))))&
((humble(alice)<~>~creative(alice)))&
(~wise(mary)) | ~humble(paul) | [] | null | 0 |
Everyone who is both not brave and calm is both not tall and not happy.
Everyone who is funny is not kind.
Everyone who is tall is kind.
Everyone who is either not creative or not happy is quiet or rich and vice versa.
Everyone who is not happy or quiet is not creative or quiet.
Everyone who is not humble is both not strong and generous.
If someone is happy then someone is both curious and not patient.
If someone is both curious and calm then paul is happy and vice versa.
If john is not tall or not quiet then paul is either not wise or calm and vice versa.
If alice is either calm or not wise then someone is either creative or not quiet.
Everyone who is quiet or not humble is not patient or happy.
Everyone who is not wise or not old is both not tall and funny and vice versa.
If alice is either rich or humble then someone is brave.
Everyone who is not strong or tall is strong.
If someone is both not old and humble then someone is calm.
Everyone who is not wise or creative is quiet or not old and vice versa.
Lucy is not creative or rich.
Paul is both not old and not brave.
Someone is both strong and tall.
Someone is both brave and curious.
Alice is calm.
Someone is funny or brave.
Someone is creative or funny.
Fred is brave. | Paul is wise. | neutral | (![X]:((~brave(X)&calm(X))=>(~tall(X)&~happy(X))))&
(![X]:(funny(X)=>~kind(X)))&
(![X]:(tall(X)=>kind(X)))&
(![X]:((~creative(X)<~>~happy(X))<=>(quiet(X)|rich(X))))&
(![X]:((~happy(X)|quiet(X))=>(~creative(X)|quiet(X))))&
(![X]:(~humble(X)=>(~strong(X)&generous(X))))&
((?[X]:(happy(X)))=>(?[X]:((curious(X)&~patient(X)))))&
((?[X]:((curious(X)&calm(X))))<=>(happy(paul)))&
(((~tall(john)|~quiet(john)))<=>((~wise(paul)<~>calm(paul))))&
(((calm(alice)<~>~wise(alice)))=>(?[X]:((creative(X)<~>~quiet(X)))))&
(![X]:((quiet(X)|~humble(X))=>(~patient(X)|happy(X))))&
(![X]:((~wise(X)|~old(X))<=>(~tall(X)&funny(X))))&
(((rich(alice)<~>humble(alice)))=>(?[X]:(brave(X))))&
(![X]:((~strong(X)|tall(X))=>strong(X)))&
((?[X]:((~old(X)&humble(X))))=>(?[X]:(calm(X))))&
(![X]:((~wise(X)|creative(X))<=>(quiet(X)|~old(X))))&
((~creative(lucy)|rich(lucy)))&
((~old(paul)&~brave(paul)))&
(?[X]:((strong(X)&tall(X))))&
(?[X]:((brave(X)&curious(X))))&
(calm(alice))&
(?[X]:((funny(X)|brave(X))))&
(?[X]:((creative(X)|funny(X))))&
(brave(fred)) | wise(paul) | [] | null | 0 |
Everyone who is either not generous or creative is both not calm and kind.
Everyone who is not humble or not generous is not rich or not kind.
Everyone who is either not curious or not wise is not old and vice versa.
If someone is rich then alice is brave or not curious.
Everyone who is either wise or old is kind or not old.
If paul is not happy or not curious then mary is quiet and vice versa.
If someone is curious then mary is calm.
If mary is either not happy or not creative then fred is not rich.
Everyone who is both not wise and not rich is either not funny or happy.
If lucy is either not wise or strong then mary is kind or not old.
If someone is both calm and wise then fred is either not funny or humble.
If paul is wise or not wise then fred is both not strong and not generous.
Everyone who is not wise or creative is not quiet and vice versa.
If alice is not generous or not quiet then paul is not brave or patient and vice versa.
If lucy is both not happy and not funny then paul is not rich or not funny and vice versa.
Everyone who is either not wise or rich is not happy.
Mary is not tall or not old.
Someone is creative.
Susan is curious or tall.
Someone is strong.
Someone is happy or humble.
Someone is not generous or not curious.
Someone is wise.
Lucy is both not wise and patient. | Lucy is quiet. | contradiction | (![X]:((~generous(X)<~>creative(X))=>(~calm(X)&kind(X))))&
(![X]:((~humble(X)|~generous(X))=>(~rich(X)|~kind(X))))&
(![X]:((~curious(X)<~>~wise(X))<=>~old(X)))&
((?[X]:(rich(X)))=>((brave(alice)|~curious(alice))))&
(![X]:((wise(X)<~>old(X))=>(kind(X)|~old(X))))&
(((~happy(paul)|~curious(paul)))<=>(quiet(mary)))&
((?[X]:(curious(X)))=>(calm(mary)))&
(((~happy(mary)<~>~creative(mary)))=>(~rich(fred)))&
(![X]:((~wise(X)&~rich(X))=>(~funny(X)<~>happy(X))))&
(((~wise(lucy)<~>strong(lucy)))=>((kind(mary)|~old(mary))))&
((?[X]:((calm(X)&wise(X))))=>((~funny(fred)<~>humble(fred))))&
(((wise(paul)|~wise(paul)))=>((~strong(fred)&~generous(fred))))&
(![X]:((~wise(X)|creative(X))<=>~quiet(X)))&
(((~generous(alice)|~quiet(alice)))<=>((~brave(paul)|patient(paul))))&
(((~happy(lucy)&~funny(lucy)))<=>((~rich(paul)|~funny(paul))))&
(![X]:((~wise(X)<~>rich(X))=>~happy(X)))&
((~tall(mary)|~old(mary)))&
(?[X]:(creative(X)))&
((curious(susan)|tall(susan)))&
(?[X]:(strong(X)))&
(?[X]:((happy(X)|humble(X))))&
(?[X]:((~generous(X)|~curious(X))))&
(?[X]:(wise(X)))&
((~wise(lucy)&patient(lucy))) | quiet(lucy) | [
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7790572760435490974531260
% SZS output start Proof for 7790572760435490974531260
13. ! [X0] : ((creative(X0) | ~wise(X0)) <=> ~quiet(X0)) [input p12]
24. patient(lucy) & ~wise(lucy) [input p23]
25. quiet(lucy) [input hypothesis]
51. ! [X0] : (((creative(X0) | ~wise(X0)) | quiet(X0)) & (~quiet(X0) | (~creative(X0) & wise(X0)))) [nnf transformation 13]
52. ! [X0] : ((creative(X0) | ~wise(X0) | quiet(X0)) & (~quiet(X0) | (~creative(X0) & wise(X0)))) [flattening 51]
97. ~quiet(X0) | wise(X0) [cnf transformation 52]
118. ~wise(lucy) [cnf transformation 24]
120. quiet(lucy) [cnf transformation 25]
176. 13 <=> wise(lucy) [avatar definition]
178. ~wise(lucy) <- (~13) [avatar component clause 176]
291. ~13 [avatar split clause 118,176]
294. wise(lucy) [resolution 97,120]
296. $false <- (~13) [subsumption resolution 294,178]
297. 13 [avatar contradiction clause 296]
298. $false [avatar sat refutation 291,297]
% SZS output end Proof for 7790572760435490974531260
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or not generous is strong and vice versa. Everyone who is creative is funny or not curious. Everyone who is either strong or not strong is funny and vice versa. Everyone who is not generous or tall is strong. If someone is both rich and calm then someone is either funny or generous and vice versa. If someone is either old or curious then mary is either wise or rich. Everyone who is humble is both kind and strong and vice versa. Everyone who is both not curious and not kind is either calm or not generous and vice versa. Everyone who is both generous and strong is not calm. If someone is either humble or not happy then someone is not creative or not tall and vice versa. If mary is strong or not curious then someone is not rich and vice versa. Everyone who is brave is old and vice versa. If someone is not wise or not strong then paul is both humble and creative and vice versa. Everyone who is wise or not quiet is either not wise or not curious. Everyone who is not generous is either not generous or generous. If fred is either humble or happy then lucy is generous and vice versa. Someone is not generous or not creative. Mary is either not generous or not funny. Someone is either not tall or not creative. John is happy. Someone is either strong or not funny. Someone is patient. Someone is curious. | John is old. | neutral | (![X]:((~curious(X)<~>~generous(X))<=>strong(X)))&
(![X]:(creative(X)=>(funny(X)|~curious(X))))&
(![X]:((strong(X)<~>~strong(X))<=>funny(X)))&
(![X]:((~generous(X)|tall(X))=>strong(X)))&
((?[X]:((rich(X)&calm(X))))<=>(?[X]:((funny(X)<~>generous(X)))))&
((?[X]:((old(X)<~>curious(X))))=>((wise(mary)<~>rich(mary))))&
(![X]:(humble(X)<=>(kind(X)&strong(X))))&
(![X]:((~curious(X)&~kind(X))<=>(calm(X)<~>~generous(X))))&
(![X]:((generous(X)&strong(X))=>~calm(X)))&
((?[X]:((humble(X)<~>~happy(X))))<=>(?[X]:((~creative(X)|~tall(X)))))&
(((strong(mary)|~curious(mary)))<=>(?[X]:(~rich(X))))&
(![X]:(brave(X)<=>old(X)))&
((?[X]:((~wise(X)|~strong(X))))<=>((humble(paul)&creative(paul))))&
(![X]:((wise(X)|~quiet(X))=>(~wise(X)<~>~curious(X))))&
(![X]:(~generous(X)=>(~generous(X)<~>generous(X))))&
(((humble(fred)<~>happy(fred)))<=>(generous(lucy)))&
(?[X]:((~generous(X)|~creative(X))))&
((~generous(mary)<~>~funny(mary)))&
(?[X]:((~tall(X)<~>~creative(X))))&
(happy(john))&
(?[X]:((strong(X)<~>~funny(X))))&
(?[X]:(patient(X)))&
(?[X]:(curious(X))) | old(john) | [] | null | 0 |
Everyone who is not funny is kind.
If john is creative or not creative then someone is curious or not kind.
Everyone who is not tall is not creative or not funny.
Everyone who is curious or not funny is not happy or wise.
Everyone who is either not curious or not humble is either happy or rich and vice versa.
If someone is both not funny and not generous then john is either rich or not brave and vice versa.
If someone is rich or not funny then lucy is both not wise and not tall and vice versa.
If someone is patient or not old then someone is strong or tall.
Everyone who is either not patient or patient is not calm.
If someone is humble then someone is either old or patient and vice versa.
Everyone who is not calm is rich or not happy and vice versa.
If someone is funny then someone is not creative and vice versa.
If lucy is both generous and not funny then susan is both not curious and not calm and vice versa.
If fred is not generous or quiet then alice is generous and vice versa.
If lucy is either happy or brave then alice is both not patient and quiet and vice versa.
If mary is not rich or not patient then mary is both calm and humble.
Someone is not old.
Lucy is patient or not wise.
Someone is either brave or not creative.
Someone is either generous or strong.
Someone is strong or not wise.
Someone is both not patient and creative.
Susan is not tall.
Paul is not wise. | Paul is not calm. | entailment | (![X]:(~funny(X)=>kind(X)))&
(((creative(john)|~creative(john)))=>(?[X]:((curious(X)|~kind(X)))))&
(![X]:(~tall(X)=>(~creative(X)|~funny(X))))&
(![X]:((curious(X)|~funny(X))=>(~happy(X)|wise(X))))&
(![X]:((~curious(X)<~>~humble(X))<=>(happy(X)<~>rich(X))))&
((?[X]:((~funny(X)&~generous(X))))<=>((rich(john)<~>~brave(john))))&
((?[X]:((rich(X)|~funny(X))))<=>((~wise(lucy)&~tall(lucy))))&
((?[X]:((patient(X)|~old(X))))=>(?[X]:((strong(X)|tall(X)))))&
(![X]:((~patient(X)<~>patient(X))=>~calm(X)))&
((?[X]:(humble(X)))<=>(?[X]:((old(X)<~>patient(X)))))&
(![X]:(~calm(X)<=>(rich(X)|~happy(X))))&
((?[X]:(funny(X)))<=>(?[X]:(~creative(X))))&
(((generous(lucy)&~funny(lucy)))<=>((~curious(susan)&~calm(susan))))&
(((~generous(fred)|quiet(fred)))<=>(generous(alice)))&
(((happy(lucy)<~>brave(lucy)))<=>((~patient(alice)&quiet(alice))))&
(((~rich(mary)|~patient(mary)))=>((calm(mary)&humble(mary))))&
(?[X]:(~old(X)))&
((patient(lucy)|~wise(lucy)))&
(?[X]:((brave(X)<~>~creative(X))))&
(?[X]:((generous(X)<~>strong(X))))&
(?[X]:((strong(X)|~wise(X))))&
(?[X]:((~patient(X)&creative(X))))&
(~tall(susan))&
(~wise(paul)) | ~calm(paul) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1725366338201099595768209
% SZS output start Proof for 1725366338201099595768209
9. ! [X0] : ((~patient(X0) <~> patient(X0)) => ~calm(X0)) [input p8]
25. calm(paul) [input hypothesis]
36. ! [X0] : (~calm(X0) | (~patient(X0) <=> patient(X0))) [ennf transformation 9]
53. ! [X0] : (~calm(X0) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) [nnf transformation 36]
111. ~calm(X0) | patient(X0) | patient(X0) [cnf transformation 53]
112. ~calm(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 53]
150. calm(paul) [cnf transformation 25]
151. ~calm(X0) | patient(X0) [duplicate literal removal 111]
152. ~calm(X0) | ~patient(X0) [duplicate literal removal 112]
235. ~calm(X0) [subsumption resolution 151,152]
384. $false [subsumption resolution 150,235]
% SZS output end Proof for 1725366338201099595768209
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either not patient or humble then someone is either not humble or rich and vice versa.
Everyone who is not kind or quiet is either not kind or tall.
Everyone who is not calm is quiet.
Everyone who is kind is not old.
Everyone who is not funny is not rich or not tall.
Everyone who is not rich or not happy is not calm or brave.
Everyone who is creative is funny or kind.
Everyone who is both not funny and tall is quiet or brave and vice versa.
Everyone who is both patient and kind is either not happy or not quiet.
Everyone who is creative or rich is not rich.
Everyone who is generous is both calm and not creative.
If someone is either not funny or not humble then susan is not patient.
Everyone who is either not funny or not old is calm or not kind.
If someone is not creative then john is both strong and not tall and vice versa.
Everyone who is patient or not calm is both not wise and old.
If john is funny or curious then lucy is either generous or tall.
Someone is either humble or curious.
John is calm.
Fred is wise or rich.
Someone is not tall or not quiet.
Susan is both curious and not rich. | Fred is creative. | entailment | (((~patient(mary)<~>humble(mary)))<=>(?[X]:((~humble(X)<~>rich(X)))))&
(![X]:((~kind(X)|quiet(X))=>(~kind(X)<~>tall(X))))&
(![X]:(~calm(X)=>quiet(X)))&
(![X]:(kind(X)=>~old(X)))&
(![X]:(~funny(X)=>(~rich(X)|~tall(X))))&
(![X]:((~rich(X)|~happy(X))=>(~calm(X)|brave(X))))&
(![X]:(creative(X)=>(funny(X)|kind(X))))&
(![X]:((~funny(X)&tall(X))<=>(quiet(X)|brave(X))))&
(![X]:((patient(X)&kind(X))=>(~happy(X)<~>~quiet(X))))&
(![X]:((creative(X)|rich(X))=>~rich(X)))&
(![X]:(generous(X)=>(calm(X)&~creative(X))))&
((?[X]:((~funny(X)<~>~humble(X))))=>(~patient(susan)))&
(![X]:((~funny(X)<~>~old(X))=>(calm(X)|~kind(X))))&
((?[X]:(~creative(X)))<=>((strong(john)&~tall(john))))&
(![X]:((patient(X)|~calm(X))=>(~wise(X)&old(X))))&
(((funny(john)|curious(john)))=>((generous(lucy)<~>tall(lucy))))&
(?[X]:((humble(X)<~>curious(X))))&
(calm(john))&
((wise(fred)|rich(fred)))&
(?[X]:((~tall(X)|~quiet(X))))&
((curious(susan)&~rich(susan))) | creative(fred) | [
"p5",
"p7",
"p9",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4047808984281470945238190
% SZS output start Proof for 4047808984281470945238190
6. ! [X0] : ((~happy(X0) | ~rich(X0)) => (brave(X0) | ~calm(X0))) [input p5]
8. ! [X0] : ((tall(X0) & ~funny(X0)) <=> (brave(X0) | quiet(X0))) [input p7]
10. ! [X0] : ((rich(X0) | creative(X0)) => ~rich(X0)) [input p9]
14. ? [X0] : ~creative(X0) <=> (~tall(john) & strong(john)) [input p13]
18. calm(john) [input p17]
22. ~creative(fred) [input hypothesis]
28. ! [X0] : ((brave(X0) | ~calm(X0)) | (happy(X0) & rich(X0))) [ennf transformation 6]
29. ! [X0] : (brave(X0) | ~calm(X0) | (happy(X0) & rich(X0))) [flattening 28]
34. ! [X0] : (~rich(X0) | (~rich(X0) & ~creative(X0))) [ennf transformation 10]
46. ! [X0] : (((tall(X0) & ~funny(X0)) | (~brave(X0) & ~quiet(X0))) & ((brave(X0) | quiet(X0)) | (~tall(X0) | funny(X0)))) [nnf transformation 8]
47. ! [X0] : (((tall(X0) & ~funny(X0)) | (~brave(X0) & ~quiet(X0))) & (brave(X0) | quiet(X0) | ~tall(X0) | funny(X0))) [flattening 46]
51. (? [X0] : ~creative(X0) | (tall(john) | ~strong(john))) & ((~tall(john) & strong(john)) | ! [X0] : creative(X0)) [nnf transformation 14]
52. (? [X0] : ~creative(X0) | tall(john) | ~strong(john)) & ((~tall(john) & strong(john)) | ! [X0] : creative(X0)) [flattening 51]
53. (? [X0] : ~creative(X0) | tall(john) | ~strong(john)) & ((~tall(john) & strong(john)) | ! [X1] : creative(X1)) [rectify 52]
54. ? [X0] : ~creative(X0) => ~creative(sK1) [choice axiom]
55. (~creative(sK1) | tall(john) | ~strong(john)) & ((~tall(john) & strong(john)) | ! [X1] : creative(X1)) [skolemisation 53,54]
77. ~calm(X0) | brave(X0) | rich(X0) [cnf transformation 29]
84. ~brave(X0) | tall(X0) [cnf transformation 47]
88. ~rich(X0) | ~rich(X0) [cnf transformation 34]
96. ~tall(john) | creative(X1) [cnf transformation 55]
108. calm(john) [cnf transformation 18]
113. ~creative(fred) [cnf transformation 22]
114. ~rich(X0) [duplicate literal removal 88]
164. 11 <=> tall(john) [avatar definition]
173. 13 <=> ! [X1] : creative(X1) [avatar definition]
174. creative(X1) <- (13) [avatar component clause 173]
175. 13 | ~11 [avatar split clause 96,164,173]
212. brave(john) | rich(john) [resolution 77,108]
215. brave(john) [subsumption resolution 212,114]
221. tall(john) [resolution 215,84]
225. 11 [avatar split clause 221,164]
239. $false <- (13) [resolution 174,113]
242. ~13 [avatar contradiction clause 239]
243. $false [avatar sat refutation 175,225,242]
% SZS output end Proof for 4047808984281470945238190
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative or not calm is not generous or tall and vice versa. If alice is either not kind or creative then someone is both curious and not creative and vice versa. Everyone who is not calm or old is either creative or not old and vice versa. Everyone who is both rich and tall is either old or not old and vice versa. Everyone who is both not creative and brave is not patient and vice versa. If someone is either strong or curious then paul is either not brave or not strong and vice versa. Everyone who is not tall is either not humble or not quiet. Everyone who is not brave or strong is brave and vice versa. Everyone who is not patient is generous or not tall. If someone is happy or brave then someone is either quiet or not old. Everyone who is not rich is not brave and vice versa. Everyone who is either funny or not generous is not old. If someone is not creative or not old then someone is both calm and not rich and vice versa. If john is both not wise and not old then susan is tall or not curious. Everyone who is not strong is brave. Everyone who is creative or not calm is not wise or old. Someone is either rich or not quiet. Mary is tall. Mary is generous. Someone is either brave or not rich. Someone is not humble or not tall. Susan is both not humble and not funny. Fred is humble. | John is not patient. | contradiction | (![X]:((creative(X)|~calm(X))<=>(~generous(X)|tall(X))))&
(((~kind(alice)<~>creative(alice)))<=>(?[X]:((curious(X)&~creative(X)))))&
(![X]:((~calm(X)|old(X))<=>(creative(X)<~>~old(X))))&
(![X]:((rich(X)&tall(X))<=>(old(X)<~>~old(X))))&
(![X]:((~creative(X)&brave(X))<=>~patient(X)))&
((?[X]:((strong(X)<~>curious(X))))<=>((~brave(paul)<~>~strong(paul))))&
(![X]:(~tall(X)=>(~humble(X)<~>~quiet(X))))&
(![X]:((~brave(X)|strong(X))<=>brave(X)))&
(![X]:(~patient(X)=>(generous(X)|~tall(X))))&
((?[X]:((happy(X)|brave(X))))=>(?[X]:((quiet(X)<~>~old(X)))))&
(![X]:(~rich(X)<=>~brave(X)))&
(![X]:((funny(X)<~>~generous(X))=>~old(X)))&
((?[X]:((~creative(X)|~old(X))))<=>(?[X]:((calm(X)&~rich(X)))))&
(((~wise(john)&~old(john)))=>((tall(susan)|~curious(susan))))&
(![X]:(~strong(X)=>brave(X)))&
(![X]:((creative(X)|~calm(X))=>(~wise(X)|old(X))))&
(?[X]:((rich(X)<~>~quiet(X))))&
(tall(mary))&
(generous(mary))&
(?[X]:((brave(X)<~>~rich(X))))&
(?[X]:((~humble(X)|~tall(X))))&
((~humble(susan)&~funny(susan)))&
(humble(fred)) | ~patient(john) | [
"p3",
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2232617179281673956145178
% SZS output start Proof for 2232617179281673956145178
4. ! [X0] : ((tall(X0) & rich(X0)) <=> (old(X0) <~> ~old(X0))) [input p3]
5. ! [X0] : ((brave(X0) & ~creative(X0)) <=> ~patient(X0)) [input p4]
13. ? [X0] : (~old(X0) | ~creative(X0)) <=> ? [X0] : (~rich(X0) & calm(X0)) [input p12]
24. ~patient(john) [input hypothesis]
26. ? [X0] : (~old(X0) | ~creative(X0)) <=> ? [X1] : (~rich(X1) & calm(X1)) [rectify 13]
46. ! [X0] : (((tall(X0) & rich(X0)) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) & (((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) | (~tall(X0) | ~rich(X0)))) [nnf transformation 4]
47. ! [X0] : (((tall(X0) & rich(X0)) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) & (((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) | ~tall(X0) | ~rich(X0))) [flattening 46]
48. ! [X0] : (((brave(X0) & ~creative(X0)) | patient(X0)) & (~patient(X0) | (~brave(X0) | creative(X0)))) [nnf transformation 5]
49. ! [X0] : (((brave(X0) & ~creative(X0)) | patient(X0)) & (~patient(X0) | ~brave(X0) | creative(X0))) [flattening 48]
63. (? [X0] : (~old(X0) | ~creative(X0)) | ! [X1] : (rich(X1) | ~calm(X1))) & (? [X1] : (~rich(X1) & calm(X1)) | ! [X0] : (old(X0) & creative(X0))) [nnf transformation 26]
64. (? [X0] : (~old(X0) | ~creative(X0)) | ! [X1] : (rich(X1) | ~calm(X1))) & (? [X2] : (~rich(X2) & calm(X2)) | ! [X3] : (old(X3) & creative(X3))) [rectify 63]
65. ? [X0] : (~old(X0) | ~creative(X0)) => (~old(sK3) | ~creative(sK3)) [choice axiom]
66. ? [X2] : (~rich(X2) & calm(X2)) => (~rich(sK4) & calm(sK4)) [choice axiom]
67. ((~old(sK3) | ~creative(sK3)) | ! [X1] : (rich(X1) | ~calm(X1))) & ((~rich(sK4) & calm(sK4)) | ! [X3] : (old(X3) & creative(X3))) [skolemisation 64,66,65]
94. rich(X0) | ~old(X0) | ~old(X0) [cnf transformation 47]
95. rich(X0) | old(X0) | old(X0) [cnf transformation 47]
99. ~creative(X0) | patient(X0) [cnf transformation 49]
123. ~rich(sK4) | creative(X3) [cnf transformation 67]
140. ~patient(john) [cnf transformation 24]
143. rich(X0) | ~old(X0) [duplicate literal removal 94]
144. rich(X0) | old(X0) [duplicate literal removal 95]
175. rich(X0) [subsumption resolution 143,144]
220. creative(X3) [subsumption resolution 123,175]
231. patient(X0) [resolution 99,220]
233. $false [resolution 231,140]
% SZS output end Proof for 2232617179281673956145178
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either curious or not funny then someone is not brave or wise and vice versa.
If someone is tall or calm then alice is not curious and vice versa.
Everyone who is not wise or not creative is either curious or not tall.
Everyone who is either brave or not generous is not curious or rich.
Everyone who is either not tall or not strong is generous or not generous and vice versa.
Everyone who is both quiet and humble is old.
If mary is calm then someone is not generous and vice versa.
Everyone who is both not calm and strong is strong and vice versa.
If fred is not patient or not curious then someone is both quiet and curious and vice versa.
Everyone who is both kind and humble is both not brave and humble and vice versa.
Everyone who is either not tall or rich is generous and vice versa.
If fred is either not calm or curious then someone is rich or not funny.
Everyone who is either not brave or not kind is not funny or quiet.
If someone is not funny or kind then someone is rich and vice versa.
If someone is funny then mary is either not wise or creative.
Everyone who is either funny or not tall is either strong or patient.
Alice is both patient and not tall.
Someone is both not calm and not humble.
Lucy is either brave or not strong.
Lucy is both wise and quiet.
Someone is either patient or calm.
Mary is strong or not happy. | Lucy is not curious. | entailment | (((curious(alice)<~>~funny(alice)))<=>(?[X]:((~brave(X)|wise(X)))))&
((?[X]:((tall(X)|calm(X))))<=>(~curious(alice)))&
(![X]:((~wise(X)|~creative(X))=>(curious(X)<~>~tall(X))))&
(![X]:((brave(X)<~>~generous(X))=>(~curious(X)|rich(X))))&
(![X]:((~tall(X)<~>~strong(X))<=>(generous(X)|~generous(X))))&
(![X]:((quiet(X)&humble(X))=>old(X)))&
((calm(mary))<=>(?[X]:(~generous(X))))&
(![X]:((~calm(X)&strong(X))<=>strong(X)))&
(((~patient(fred)|~curious(fred)))<=>(?[X]:((quiet(X)&curious(X)))))&
(![X]:((kind(X)&humble(X))<=>(~brave(X)&humble(X))))&
(![X]:((~tall(X)<~>rich(X))<=>generous(X)))&
(((~calm(fred)<~>curious(fred)))=>(?[X]:((rich(X)|~funny(X)))))&
(![X]:((~brave(X)<~>~kind(X))=>(~funny(X)|quiet(X))))&
((?[X]:((~funny(X)|kind(X))))<=>(?[X]:(rich(X))))&
((?[X]:(funny(X)))=>((~wise(mary)<~>creative(mary))))&
(![X]:((funny(X)<~>~tall(X))=>(strong(X)<~>patient(X))))&
((patient(alice)&~tall(alice)))&
(?[X]:((~calm(X)&~humble(X))))&
((brave(lucy)<~>~strong(lucy)))&
((wise(lucy)&quiet(lucy)))&
(?[X]:((patient(X)<~>calm(X))))&
((strong(mary)|~happy(mary))) | ~curious(lucy) | [
"p0",
"p1",
"p3",
"p4",
"p6",
"p10",
"p13",
"p15",
"p16",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4838735648933144063554814
% SZS output start Proof for 4838735648933144063554814
1. (curious(alice) <~> ~funny(alice)) <=> ? [X0] : (wise(X0) | ~brave(X0)) [input p0]
2. ? [X0] : (calm(X0) | tall(X0)) <=> ~curious(alice) [input p1]
4. ! [X0] : ((brave(X0) <~> ~generous(X0)) => (rich(X0) | ~curious(X0))) [input p3]
5. ! [X0] : ((~tall(X0) <~> ~strong(X0)) <=> (~generous(X0) | generous(X0))) [input p4]
7. calm(mary) <=> ? [X0] : ~generous(X0) [input p6]
11. ! [X0] : ((~tall(X0) <~> rich(X0)) <=> generous(X0)) [input p10]
14. ? [X0] : (kind(X0) | ~funny(X0)) <=> ? [X0] : rich(X0) [input p13]
16. ! [X0] : ((funny(X0) <~> ~tall(X0)) => (strong(X0) <~> patient(X0))) [input p15]
17. ~tall(alice) & patient(alice) [input p16]
19. brave(lucy) <~> ~strong(lucy) [input p18]
20. quiet(lucy) & wise(lucy) [input p19]
23. curious(lucy) [input hypothesis]
24. ? [X0] : (kind(X0) | ~funny(X0)) <=> ? [X1] : rich(X1) [rectify 14]
28. ! [X0] : ((rich(X0) | ~curious(X0)) | (brave(X0) <=> ~generous(X0))) [ennf transformation 4]
29. ! [X0] : (rich(X0) | ~curious(X0) | (brave(X0) <=> ~generous(X0))) [flattening 28]
34. ! [X0] : ((strong(X0) <~> patient(X0)) | (funny(X0) <=> ~tall(X0))) [ennf transformation 16]
35. (((funny(alice) | ~curious(alice)) & (~funny(alice) | curious(alice))) | ! [X0] : (~wise(X0) & brave(X0))) & (? [X0] : (wise(X0) | ~brave(X0)) | ((curious(alice) | funny(alice)) & (~funny(alice) | ~curious(alice)))) [nnf transformation 1]
36. (((funny(alice) | ~curious(alice)) & (~funny(alice) | curious(alice))) | ! [X0] : (~wise(X0) & brave(X0))) & (? [X1] : (wise(X1) | ~brave(X1)) | ((curious(alice) | funny(alice)) & (~funny(alice) | ~curious(alice)))) [rectify 35]
37. ? [X1] : (wise(X1) | ~brave(X1)) => (wise(sK0) | ~brave(sK0)) [choice axiom]
38. (((funny(alice) | ~curious(alice)) & (~funny(alice) | curious(alice))) | ! [X0] : (~wise(X0) & brave(X0))) & ((wise(sK0) | ~brave(sK0)) | ((curious(alice) | funny(alice)) & (~funny(alice) | ~curious(alice)))) [skolemisation 36,37]
39. (? [X0] : (calm(X0) | tall(X0)) | curious(alice)) & (~curious(alice) | ! [X0] : (~calm(X0) & ~tall(X0))) [nnf transformation 2]
40. (? [X0] : (calm(X0) | tall(X0)) | curious(alice)) & (~curious(alice) | ! [X1] : (~calm(X1) & ~tall(X1))) [rectify 39]
41. ? [X0] : (calm(X0) | tall(X0)) => (calm(sK1) | tall(sK1)) [choice axiom]
42. ((calm(sK1) | tall(sK1)) | curious(alice)) & (~curious(alice) | ! [X1] : (~calm(X1) & ~tall(X1))) [skolemisation 40,41]
44. ! [X0] : (rich(X0) | ~curious(X0) | ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0)))) [nnf transformation 29]
45. ! [X0] : ((((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) | (generous(X0) & ~generous(X0))) & ((~generous(X0) | generous(X0)) | ((~tall(X0) | strong(X0)) & (~strong(X0) | tall(X0))))) [nnf transformation 5]
46. ! [X0] : ((((strong(X0) | tall(X0)) & (~strong(X0) | ~tall(X0))) | (generous(X0) & ~generous(X0))) & (~generous(X0) | generous(X0) | ((~tall(X0) | strong(X0)) & (~strong(X0) | tall(X0))))) [flattening 45]
47. (calm(mary) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | ~calm(mary)) [nnf transformation 7]
48. (calm(mary) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | ~calm(mary)) [rectify 47]
49. ? [X1] : ~generous(X1) => ~generous(sK2) [choice axiom]
50. (calm(mary) | ! [X0] : generous(X0)) & (~generous(sK2) | ~calm(mary)) [skolemisation 48,49]
60. ! [X0] : ((((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | ~generous(X0)) & (generous(X0) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0))))) [nnf transformation 11]
65. (? [X0] : (kind(X0) | ~funny(X0)) | ! [X1] : ~rich(X1)) & (? [X1] : rich(X1) | ! [X0] : (~kind(X0) & funny(X0))) [nnf transformation 24]
66. (? [X0] : (kind(X0) | ~funny(X0)) | ! [X1] : ~rich(X1)) & (? [X2] : rich(X2) | ! [X3] : (~kind(X3) & funny(X3))) [rectify 65]
67. ? [X0] : (kind(X0) | ~funny(X0)) => (kind(sK5) | ~funny(sK5)) [choice axiom]
68. ? [X2] : rich(X2) => rich(sK6) [choice axiom]
69. ((kind(sK5) | ~funny(sK5)) | ! [X1] : ~rich(X1)) & (rich(sK6) | ! [X3] : (~kind(X3) & funny(X3))) [skolemisation 66,68,67]
71. ! [X0] : (((~patient(X0) | ~strong(X0)) & (patient(X0) | strong(X0))) | ((funny(X0) | tall(X0)) & (~tall(X0) | ~funny(X0)))) [nnf transformation 34]
74. (strong(lucy) | ~brave(lucy)) & (~strong(lucy) | brave(lucy)) [nnf transformation 19]
81. ~funny(alice) | curious(alice) | ~wise(X0) [cnf transformation 38]
84. ~curious(alice) | ~tall(X1) [cnf transformation 42]
85. ~curious(alice) | ~calm(X1) [cnf transformation 42]
91. ~generous(X0) | ~curious(X0) | rich(X0) | ~brave(X0) [cnf transformation 44]
95. ~strong(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 46]
96. ~strong(X0) | ~tall(X0) | generous(X0) [cnf transformation 46]
97. strong(X0) | tall(X0) | ~generous(X0) [cnf transformation 46]
98. strong(X0) | tall(X0) | generous(X0) [cnf transformation 46]
100. calm(mary) | generous(X0) [cnf transformation 50]
116. ~rich(X0) | tall(X0) | ~generous(X0) [cnf transformation 60]
121. rich(sK6) | funny(X3) [cnf transformation 69]
122. rich(sK6) | ~kind(X3) [cnf transformation 69]
123. kind(sK5) | ~funny(sK5) | ~rich(X1) [cnf transformation 69]
129. ~patient(X0) | ~strong(X0) | funny(X0) | tall(X0) [cnf transformation 71]
130. patient(alice) [cnf transformation 17]
131. ~tall(alice) [cnf transformation 17]
134. ~strong(lucy) | brave(lucy) [cnf transformation 74]
136. wise(lucy) [cnf transformation 20]
140. curious(lucy) [cnf transformation 23]
142. 1 <=> ! [X0] : ~wise(X0) [avatar definition]
143. ~wise(X0) <- (1) [avatar component clause 142]
145. 2 <=> curious(alice) [avatar definition]
149. 3 <=> funny(alice) [avatar definition]
150. ~funny(alice) <- (~3) [avatar component clause 149]
157. 1 | 2 | ~3 [avatar split clause 81,149,145,142]
179. 9 <=> ! [X1] : ~calm(X1) [avatar definition]
180. ~calm(X1) <- (9) [avatar component clause 179]
181. 9 | ~2 [avatar split clause 85,145,179]
183. 10 <=> ! [X1] : ~tall(X1) [avatar definition]
184. ~tall(X1) <- (10) [avatar component clause 183]
185. 10 | ~2 [avatar split clause 84,145,183]
186. strong(X0) | tall(X0) [subsumption resolution 97,98]
187. ~strong(X0) | ~tall(X0) [subsumption resolution 95,96]
189. 11 <=> ! [X0] : generous(X0) [avatar definition]
190. generous(X0) <- (11) [avatar component clause 189]
192. 12 <=> calm(mary) [avatar definition]
194. calm(mary) <- (12) [avatar component clause 192]
195. 11 | 12 [avatar split clause 100,192,189]
240. 22 <=> ! [X1] : ~rich(X1) [avatar definition]
241. ~rich(X1) <- (22) [avatar component clause 240]
243. 23 <=> funny(sK5) [avatar definition]
245. ~funny(sK5) <- (~23) [avatar component clause 243]
247. 24 <=> kind(sK5) [avatar definition]
249. kind(sK5) <- (24) [avatar component clause 247]
250. 22 | ~23 | 24 [avatar split clause 123,247,243,240]
252. 25 <=> ! [X3] : ~kind(X3) [avatar definition]
253. ~kind(X3) <- (25) [avatar component clause 252]
255. 26 <=> rich(sK6) [avatar definition]
257. rich(sK6) <- (26) [avatar component clause 255]
258. 25 | 26 [avatar split clause 122,255,252]
260. 27 <=> ! [X3] : funny(X3) [avatar definition]
261. funny(X3) <- (27) [avatar component clause 260]
262. 27 | 26 [avatar split clause 121,255,260]
276. ~patient(X0) | ~strong(X0) | funny(X0) [subsumption resolution 129,187]
279. 31 <=> brave(lucy) [avatar definition]
280. brave(lucy) <- (31) [avatar component clause 279]
283. 32 <=> strong(lucy) [avatar definition]
284. ~strong(lucy) <- (~32) [avatar component clause 283]
287. 31 | ~32 [avatar split clause 134,283,279]
300. tall(lucy) <- (~32) [resolution 186,284]
352. 39 <=> generous(sK6) [avatar definition]
353. ~generous(sK6) <- (~39) [avatar component clause 352]
356. 40 <=> tall(sK6) [avatar definition]
357. tall(sK6) <- (40) [avatar component clause 356]
358. ~tall(sK6) <- (~40) [avatar component clause 356]
360. tall(sK6) | ~generous(sK6) <- (26) [resolution 116,257]
363. ~generous(sK6) <- (26, ~40) [subsumption resolution 360,358]
364. ~39 | ~26 | 40 [avatar split clause 363,356,255,352]
365. ~strong(alice) | funny(alice) [resolution 276,130]
368. ~strong(alice) <- (~3) [subsumption resolution 365,150]
388. tall(alice) <- (~3) [resolution 368,186]
390. $false <- (~3) [subsumption resolution 388,131]
391. 3 [avatar contradiction clause 390]
397. $false <- (1) [resolution 143,136]
398. ~1 [avatar contradiction clause 397]
407. $false <- (9, 12) [resolution 180,194]
408. ~9 | ~12 [avatar contradiction clause 407]
409. $false <- (10, ~32) [resolution 184,300]
414. ~10 | 32 [avatar contradiction clause 409]
420. $false <- (11, ~39) [resolution 190,353]
422. ~11 | 39 [avatar contradiction clause 420]
426. $false <- (~23, 27) [resolution 261,245]
427. 23 | ~27 [avatar contradiction clause 426]
433. $false <- (24, 25) [subsumption resolution 249,253]
434. ~24 | ~25 [avatar contradiction clause 433]
435. $false <- (10, 40) [subsumption resolution 357,184]
436. ~10 | ~40 [avatar contradiction clause 435]
448. ~curious(X0) | rich(X0) | ~brave(X0) <- (11) [resolution 91,190]
450. ~brave(X0) | ~curious(X0) <- (11, 22) [subsumption resolution 448,241]
476. ~curious(lucy) <- (11, 22, 31) [resolution 450,280]
477. $false <- (11, 22, 31) [subsumption resolution 476,140]
478. ~11 | ~22 | ~31 [avatar contradiction clause 477]
479. $false [avatar sat refutation 157,181,185,195,250,258,262,287,364,391,398,408,414,422,427,434,436,478]
% SZS output end Proof for 4838735648933144063554814
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is either patient or rich and vice versa. If fred is humble then someone is either old or patient. If someone is wise or patient then someone is generous. Everyone who is both not happy and generous is both brave and not old and vice versa. If someone is both calm and not funny then someone is not old or not creative. Everyone who is either not calm or not quiet is both not calm and old. If someone is patient or not strong then mary is either kind or happy. If someone is either strong or not funny then fred is not quiet or brave and vice versa. Everyone who is not curious is not patient or creative and vice versa. If someone is not patient or quiet then someone is both patient and not kind. Everyone who is either quiet or brave is not quiet and vice versa. Everyone who is both strong and old is both not humble and not happy. Everyone who is not strong or not happy is both happy and curious and vice versa. Everyone who is happy is either funny or kind. If lucy is either brave or tall then lucy is tall or not kind. Someone is either generous or happy. Someone is either not generous or not funny. Lucy is not rich or tall. John is strong or not funny. Someone is humble. | Lucy is not curious. | contradiction | (![X]:(~curious(X)<=>(patient(X)<~>rich(X))))&
((humble(fred))=>(?[X]:((old(X)<~>patient(X)))))&
((?[X]:((wise(X)|patient(X))))=>(?[X]:(generous(X))))&
(![X]:((~happy(X)&generous(X))<=>(brave(X)&~old(X))))&
((?[X]:((calm(X)&~funny(X))))=>(?[X]:((~old(X)|~creative(X)))))&
(![X]:((~calm(X)<~>~quiet(X))=>(~calm(X)&old(X))))&
((?[X]:((patient(X)|~strong(X))))=>((kind(mary)<~>happy(mary))))&
((?[X]:((strong(X)<~>~funny(X))))<=>((~quiet(fred)|brave(fred))))&
(![X]:(~curious(X)<=>(~patient(X)|creative(X))))&
((?[X]:((~patient(X)|quiet(X))))=>(?[X]:((patient(X)&~kind(X)))))&
(![X]:((quiet(X)<~>brave(X))<=>~quiet(X)))&
(![X]:((strong(X)&old(X))=>(~humble(X)&~happy(X))))&
(![X]:((~strong(X)|~happy(X))<=>(happy(X)&curious(X))))&
(![X]:(happy(X)=>(funny(X)<~>kind(X))))&
(((brave(lucy)<~>tall(lucy)))=>((tall(lucy)|~kind(lucy))))&
(?[X]:((generous(X)<~>happy(X))))&
(?[X]:((~generous(X)<~>~funny(X))))&
((~rich(lucy)|tall(lucy)))&
((strong(john)|~funny(john)))&
(?[X]:(humble(X))) | ~curious(lucy) | [
"p3",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4571161263857278845920147
% SZS output start Proof for 4571161263857278845920147
4. ! [X0] : ((generous(X0) & ~happy(X0)) <=> (~old(X0) & brave(X0))) [input p3]
11. ! [X0] : ((quiet(X0) <~> brave(X0)) <=> ~quiet(X0)) [input p10]
12. ! [X0] : ((old(X0) & strong(X0)) => (~happy(X0) & ~humble(X0))) [input p11]
13. ! [X0] : ((~happy(X0) | ~strong(X0)) <=> (curious(X0) & happy(X0))) [input p12]
21. ~curious(lucy) [input hypothesis]
32. ! [X0] : ((~happy(X0) & ~humble(X0)) | (~old(X0) | ~strong(X0))) [ennf transformation 12]
33. ! [X0] : ((~happy(X0) & ~humble(X0)) | ~old(X0) | ~strong(X0)) [flattening 32]
44. ! [X0] : (((generous(X0) & ~happy(X0)) | (old(X0) | ~brave(X0))) & ((~old(X0) & brave(X0)) | (~generous(X0) | happy(X0)))) [nnf transformation 4]
45. ! [X0] : (((generous(X0) & ~happy(X0)) | old(X0) | ~brave(X0)) & ((~old(X0) & brave(X0)) | ~generous(X0) | happy(X0))) [flattening 44]
61. ! [X0] : ((((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | quiet(X0)) & (~quiet(X0) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0))))) [nnf transformation 11]
62. ! [X0] : (((~happy(X0) | ~strong(X0)) | (~curious(X0) | ~happy(X0))) & ((curious(X0) & happy(X0)) | (happy(X0) & strong(X0)))) [nnf transformation 13]
63. ! [X0] : ((~happy(X0) | ~strong(X0) | ~curious(X0) | ~happy(X0)) & ((curious(X0) & happy(X0)) | (happy(X0) & strong(X0)))) [flattening 62]
83. ~brave(X0) | old(X0) | ~happy(X0) [cnf transformation 45]
107. ~quiet(X0) | brave(X0) | ~quiet(X0) [cnf transformation 61]
109. brave(X0) | quiet(X0) | quiet(X0) [cnf transformation 61]
112. ~strong(X0) | ~old(X0) | ~happy(X0) [cnf transformation 33]
114. happy(X0) | happy(X0) [cnf transformation 63]
115. strong(X0) | curious(X0) [cnf transformation 63]
129. ~curious(lucy) [cnf transformation 21]
131. happy(X0) [duplicate literal removal 114]
133. ~quiet(X0) | brave(X0) [duplicate literal removal 107]
134. quiet(X0) | brave(X0) [duplicate literal removal 109]
231. brave(X0) [subsumption resolution 133,134]
296. old(X0) | ~happy(X0) [resolution 83,231]
297. old(X0) [subsumption resolution 296,131]
307. ~old(X0) | ~happy(X0) | curious(X0) [resolution 112,115]
308. ~happy(X0) | curious(X0) [subsumption resolution 307,297]
309. curious(X0) [subsumption resolution 308,131]
310. $false [resolution 309,129]
% SZS output end Proof for 4571161263857278845920147
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or humble is curious.
If someone is not quiet or not generous then someone is either tall or patient.
Everyone who is both quiet and not strong is both brave and happy.
Everyone who is not kind or funny is either not strong or not rich and vice versa.
If john is both happy and not strong then someone is either not strong or not generous and vice versa.
Everyone who is not strong or wise is not calm or humble.
If alice is not humble then someone is either brave or humble and vice versa.
If mary is generous or patient then someone is either not strong or calm.
Everyone who is both not curious and not quiet is either calm or not calm and vice versa.
Everyone who is strong or wise is both not quiet and not generous and vice versa.
If someone is either not quiet or not generous then susan is both quiet and humble.
If susan is both not kind and not creative then fred is not generous or creative.
If someone is both not quiet and not tall then mary is both rich and not humble and vice versa.
If susan is both not happy and not humble then someone is both not humble and not calm and vice versa.
If someone is both patient and happy then someone is both not tall and quiet.
Fred is humble or happy.
Susan is rich or not creative.
Susan is both happy and brave.
Lucy is either not quiet or not wise.
Alice is both not quiet and rich. | Fred is not happy. | neutral | (![X]:((wise(X)<~>humble(X))=>curious(X)))&
((?[X]:((~quiet(X)|~generous(X))))=>(?[X]:((tall(X)<~>patient(X)))))&
(![X]:((quiet(X)&~strong(X))=>(brave(X)&happy(X))))&
(![X]:((~kind(X)|funny(X))<=>(~strong(X)<~>~rich(X))))&
(((happy(john)&~strong(john)))<=>(?[X]:((~strong(X)<~>~generous(X)))))&
(![X]:((~strong(X)|wise(X))=>(~calm(X)|humble(X))))&
((~humble(alice))<=>(?[X]:((brave(X)<~>humble(X)))))&
(((generous(mary)|patient(mary)))=>(?[X]:((~strong(X)<~>calm(X)))))&
(![X]:((~curious(X)&~quiet(X))<=>(calm(X)<~>~calm(X))))&
(![X]:((strong(X)|wise(X))<=>(~quiet(X)&~generous(X))))&
((?[X]:((~quiet(X)<~>~generous(X))))=>((quiet(susan)&humble(susan))))&
(((~kind(susan)&~creative(susan)))=>((~generous(fred)|creative(fred))))&
((?[X]:((~quiet(X)&~tall(X))))<=>((rich(mary)&~humble(mary))))&
(((~happy(susan)&~humble(susan)))<=>(?[X]:((~humble(X)&~calm(X)))))&
((?[X]:((patient(X)&happy(X))))=>(?[X]:((~tall(X)&quiet(X)))))&
((humble(fred)|happy(fred)))&
((rich(susan)|~creative(susan)))&
((happy(susan)&brave(susan)))&
((~quiet(lucy)<~>~wise(lucy)))&
((~quiet(alice)&rich(alice))) | ~happy(fred) | [] | null | 0 |
If susan is either happy or not happy then alice is not tall and vice versa.
Everyone who is not wise is not quiet or generous and vice versa.
Everyone who is either not rich or not calm is not creative or creative and vice versa.
Everyone who is rich or not rich is both creative and not strong and vice versa.
If someone is both not generous and happy then susan is not generous or creative and vice versa.
Everyone who is either not brave or not happy is not humble and vice versa.
If someone is both calm and not patient then john is both not kind and strong.
Everyone who is not wise or not quiet is not patient or creative and vice versa.
Everyone who is humble or not wise is either not rich or not quiet.
If susan is not old then someone is both rich and funny.
If john is calm or brave then someone is either not rich or not creative and vice versa.
Everyone who is curious is not humble.
If someone is both not tall and patient then john is either not generous or generous and vice versa.
Everyone who is strong is patient.
If paul is not brave or not quiet then someone is tall and vice versa.
Everyone who is either generous or not strong is either not creative or not humble.
John is quiet.
Someone is both quiet and funny.
Someone is not calm.
Susan is patient or not kind.
Someone is both not brave and not humble.
Someone is both not curious and not quiet.
Mary is both not humble and not quiet. | Susan is funny. | neutral | (((happy(susan)<~>~happy(susan)))<=>(~tall(alice)))&
(![X]:(~wise(X)<=>(~quiet(X)|generous(X))))&
(![X]:((~rich(X)<~>~calm(X))<=>(~creative(X)|creative(X))))&
(![X]:((rich(X)|~rich(X))<=>(creative(X)&~strong(X))))&
((?[X]:((~generous(X)&happy(X))))<=>((~generous(susan)|creative(susan))))&
(![X]:((~brave(X)<~>~happy(X))<=>~humble(X)))&
((?[X]:((calm(X)&~patient(X))))=>((~kind(john)&strong(john))))&
(![X]:((~wise(X)|~quiet(X))<=>(~patient(X)|creative(X))))&
(![X]:((humble(X)|~wise(X))=>(~rich(X)<~>~quiet(X))))&
((~old(susan))=>(?[X]:((rich(X)&funny(X)))))&
(((calm(john)|brave(john)))<=>(?[X]:((~rich(X)<~>~creative(X)))))&
(![X]:(curious(X)=>~humble(X)))&
((?[X]:((~tall(X)&patient(X))))<=>((~generous(john)<~>generous(john))))&
(![X]:(strong(X)=>patient(X)))&
(((~brave(paul)|~quiet(paul)))<=>(?[X]:(tall(X))))&
(![X]:((generous(X)<~>~strong(X))=>(~creative(X)<~>~humble(X))))&
(quiet(john))&
(?[X]:((quiet(X)&funny(X))))&
(?[X]:(~calm(X)))&
((patient(susan)|~kind(susan)))&
(?[X]:((~brave(X)&~humble(X))))&
(?[X]:((~curious(X)&~quiet(X))))&
((~humble(mary)&~quiet(mary))) | funny(susan) | [] | null | 0 |
Everyone who is both not humble and quiet is old and vice versa.
If fred is not calm then someone is rich or quiet and vice versa.
If someone is humble or patient then susan is curious.
If someone is either not calm or not patient then susan is either kind or not quiet.
If paul is both rich and calm then fred is both not old and not funny.
Everyone who is either kind or brave is not funny or calm.
Everyone who is not brave or humble is not kind and vice versa.
Everyone who is generous is either patient or humble and vice versa.
If paul is both happy and not creative then mary is either funny or rich and vice versa.
If someone is not funny or not tall then someone is both happy and brave.
Everyone who is generous is either not quiet or generous.
If someone is either quiet or not curious then lucy is wise.
If john is both quiet and not humble then john is either generous or not happy.
Everyone who is either not wise or kind is not wise or not calm and vice versa.
Everyone who is either not humble or wise is generous or not kind.
Everyone who is both not calm and funny is not rich or not creative.
Mary is either quiet or not happy.
Mary is either patient or not patient.
Someone is not brave or generous.
Someone is old or not quiet.
Someone is both not funny and not curious.
Someone is either generous or not humble.
Lucy is kind.
Someone is creative. | Lucy is humble. | contradiction | (![X]:((~humble(X)&quiet(X))<=>old(X)))&
((~calm(fred))<=>(?[X]:((rich(X)|quiet(X)))))&
((?[X]:((humble(X)|patient(X))))=>(curious(susan)))&
((?[X]:((~calm(X)<~>~patient(X))))=>((kind(susan)<~>~quiet(susan))))&
(((rich(paul)&calm(paul)))=>((~old(fred)&~funny(fred))))&
(![X]:((kind(X)<~>brave(X))=>(~funny(X)|calm(X))))&
(![X]:((~brave(X)|humble(X))<=>~kind(X)))&
(![X]:(generous(X)<=>(patient(X)<~>humble(X))))&
(((happy(paul)&~creative(paul)))<=>((funny(mary)<~>rich(mary))))&
((?[X]:((~funny(X)|~tall(X))))=>(?[X]:((happy(X)&brave(X)))))&
(![X]:(generous(X)=>(~quiet(X)<~>generous(X))))&
((?[X]:((quiet(X)<~>~curious(X))))=>(wise(lucy)))&
(((quiet(john)&~humble(john)))=>((generous(john)<~>~happy(john))))&
(![X]:((~wise(X)<~>kind(X))<=>(~wise(X)|~calm(X))))&
(![X]:((~humble(X)<~>wise(X))=>(generous(X)|~kind(X))))&
(![X]:((~calm(X)&funny(X))=>(~rich(X)|~creative(X))))&
((quiet(mary)<~>~happy(mary)))&
((patient(mary)<~>~patient(mary)))&
(?[X]:((~brave(X)|generous(X))))&
(?[X]:((old(X)|~quiet(X))))&
(?[X]:((~funny(X)&~curious(X))))&
(?[X]:((generous(X)<~>~humble(X))))&
(kind(lucy))&
(?[X]:(creative(X))) | humble(lucy) | [
"p6",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1321003587645488853272095
% SZS output start Proof for 1321003587645488853272095
7. ! [X0] : ((humble(X0) | ~brave(X0)) <=> ~kind(X0)) [input p6]
23. kind(lucy) [input p22]
25. humble(lucy) [input hypothesis]
51. ! [X0] : (((humble(X0) | ~brave(X0)) | kind(X0)) & (~kind(X0) | (~humble(X0) & brave(X0)))) [nnf transformation 7]
52. ! [X0] : ((humble(X0) | ~brave(X0) | kind(X0)) & (~kind(X0) | (~humble(X0) & brave(X0)))) [flattening 51]
95. ~kind(X0) | ~humble(X0) [cnf transformation 52]
134. kind(lucy) [cnf transformation 23]
136. humble(lucy) [cnf transformation 25]
319. ~humble(lucy) [resolution 95,134]
320. $false [subsumption resolution 319,136]
% SZS output end Proof for 1321003587645488853272095
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise then paul is not quiet.
Everyone who is both calm and not rich is both quiet and not curious and vice versa.
If someone is both old and not creative then someone is not curious.
Everyone who is either not wise or not kind is humble or patient.
If someone is tall then someone is either kind or not tall and vice versa.
If paul is not old or not patient then someone is not tall or not calm and vice versa.
Everyone who is either not rich or not strong is wise or calm.
If mary is old or brave then john is either not calm or generous and vice versa.
Everyone who is either not calm or not kind is either not happy or strong.
Everyone who is not creative or generous is quiet.
Everyone who is not generous is both not tall and not creative and vice versa.
If someone is funny or not patient then john is both tall and not generous.
If someone is both calm and not tall then paul is both wise and quiet.
Everyone who is both not calm and not wise is both kind and not creative and vice versa.
If someone is either not brave or calm then someone is not rich or not brave and vice versa.
Someone is calm or not humble.
John is curious.
Paul is wise or happy.
Someone is either generous or creative.
Someone is either strong or not patient.
Alice is either quiet or not strong. | Alice is not strong. | contradiction | ((?[X]:(~wise(X)))=>(~quiet(paul)))&
(![X]:((calm(X)&~rich(X))<=>(quiet(X)&~curious(X))))&
((?[X]:((old(X)&~creative(X))))=>(?[X]:(~curious(X))))&
(![X]:((~wise(X)<~>~kind(X))=>(humble(X)|patient(X))))&
((?[X]:(tall(X)))<=>(?[X]:((kind(X)<~>~tall(X)))))&
(((~old(paul)|~patient(paul)))<=>(?[X]:((~tall(X)|~calm(X)))))&
(![X]:((~rich(X)<~>~strong(X))=>(wise(X)|calm(X))))&
(((old(mary)|brave(mary)))<=>((~calm(john)<~>generous(john))))&
(![X]:((~calm(X)<~>~kind(X))=>(~happy(X)<~>strong(X))))&
(![X]:((~creative(X)|generous(X))=>quiet(X)))&
(![X]:(~generous(X)<=>(~tall(X)&~creative(X))))&
((?[X]:((funny(X)|~patient(X))))=>((tall(john)&~generous(john))))&
((?[X]:((calm(X)&~tall(X))))=>((wise(paul)&quiet(paul))))&
(![X]:((~calm(X)&~wise(X))<=>(kind(X)&~creative(X))))&
((?[X]:((~brave(X)<~>calm(X))))<=>(?[X]:((~rich(X)|~brave(X)))))&
(?[X]:((calm(X)|~humble(X))))&
(curious(john))&
((wise(paul)|happy(paul)))&
(?[X]:((generous(X)<~>creative(X))))&
(?[X]:((strong(X)<~>~patient(X))))&
((quiet(alice)<~>~strong(alice))) | ~strong(alice) | [
"p9",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1576833876017213562377959
% SZS output start Proof for 1576833876017213562377959
10. ! [X0] : ((generous(X0) | ~creative(X0)) => quiet(X0)) [input p9]
11. ! [X0] : (~generous(X0) <=> (~creative(X0) & ~tall(X0))) [input p10]
21. quiet(alice) <~> ~strong(alice) [input p20]
22. ~strong(alice) [input hypothesis]
34. ! [X0] : (quiet(X0) | (~generous(X0) & creative(X0))) [ennf transformation 10]
57. ! [X0] : ((~generous(X0) | (creative(X0) | tall(X0))) & ((~creative(X0) & ~tall(X0)) | generous(X0))) [nnf transformation 11]
58. ! [X0] : ((~generous(X0) | creative(X0) | tall(X0)) & ((~creative(X0) & ~tall(X0)) | generous(X0))) [flattening 57]
74. (strong(alice) | ~quiet(alice)) & (~strong(alice) | quiet(alice)) [nnf transformation 21]
103. creative(X0) | quiet(X0) [cnf transformation 34]
104. ~generous(X0) | quiet(X0) [cnf transformation 34]
106. ~creative(X0) | generous(X0) [cnf transformation 58]
130. strong(alice) | ~quiet(alice) [cnf transformation 74]
131. ~strong(alice) [cnf transformation 22]
300. 38 <=> quiet(alice) [avatar definition]
302. ~quiet(alice) <- (~38) [avatar component clause 300]
304. 39 <=> strong(alice) [avatar definition]
307. ~38 | 39 [avatar split clause 130,304,300]
309. ~39 [avatar split clause 131,304]
318. generous(X0) | quiet(X0) [resolution 106,103]
319. quiet(X0) [subsumption resolution 318,104]
325. $false <- (~38) [resolution 319,302]
326. 38 [avatar contradiction clause 325]
328. $false [avatar sat refutation 307,309,326]
% SZS output end Proof for 1576833876017213562377959
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or curious is kind or generous.
If someone is both not brave and not humble then someone is both quiet and happy and vice versa.
Everyone who is calm or not rich is either creative or strong and vice versa.
Everyone who is either curious or not old is either not curious or rich and vice versa.
Everyone who is kind or generous is both quiet and old.
If lucy is not quiet then paul is not humble.
If someone is quiet then mary is not wise or old and vice versa.
Everyone who is funny or not curious is both not strong and not generous.
If someone is calm or tall then someone is patient and vice versa.
If fred is creative or not happy then someone is not brave and vice versa.
If someone is not strong or patient then someone is not curious or humble.
Everyone who is both rich and humble is both not happy and not creative and vice versa.
Everyone who is not wise or happy is either not curious or not old and vice versa.
If someone is not quiet or quiet then someone is both funny and not creative.
Someone is either wise or not generous.
Someone is not happy.
Someone is not strong.
Someone is either not kind or old.
John is not patient.
Someone is both quiet and not generous.
Someone is both not happy and tall.
Paul is not kind or humble. | Mary is not rich. | contradiction | (![X]:((~humble(X)|curious(X))=>(kind(X)|generous(X))))&
((?[X]:((~brave(X)&~humble(X))))<=>(?[X]:((quiet(X)&happy(X)))))&
(![X]:((calm(X)|~rich(X))<=>(creative(X)<~>strong(X))))&
(![X]:((curious(X)<~>~old(X))<=>(~curious(X)<~>rich(X))))&
(![X]:((kind(X)|generous(X))=>(quiet(X)&old(X))))&
((~quiet(lucy))=>(~humble(paul)))&
((?[X]:(quiet(X)))<=>((~wise(mary)|old(mary))))&
(![X]:((funny(X)|~curious(X))=>(~strong(X)&~generous(X))))&
((?[X]:((calm(X)|tall(X))))<=>(?[X]:(patient(X))))&
(((creative(fred)|~happy(fred)))<=>(?[X]:(~brave(X))))&
((?[X]:((~strong(X)|patient(X))))=>(?[X]:((~curious(X)|humble(X)))))&
(![X]:((rich(X)&humble(X))<=>(~happy(X)&~creative(X))))&
(![X]:((~wise(X)|happy(X))<=>(~curious(X)<~>~old(X))))&
((?[X]:((~quiet(X)|quiet(X))))=>(?[X]:((funny(X)&~creative(X)))))&
(?[X]:((wise(X)<~>~generous(X))))&
(?[X]:(~happy(X)))&
(?[X]:(~strong(X)))&
(?[X]:((~kind(X)<~>old(X))))&
(~patient(john))&
(?[X]:((quiet(X)&~generous(X))))&
(?[X]:((~happy(X)&tall(X))))&
((~kind(paul)|humble(paul))) | ~rich(mary) | [
"p0",
"p3",
"p4",
"p6",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8702677478624939313304188
% SZS output start Proof for 8702677478624939313304188
1. ! [X0] : ((curious(X0) | ~humble(X0)) => (generous(X0) | kind(X0))) [input p0]
4. ! [X0] : ((curious(X0) <~> ~old(X0)) <=> (~curious(X0) <~> rich(X0))) [input p3]
5. ! [X0] : ((generous(X0) | kind(X0)) => (old(X0) & quiet(X0))) [input p4]
7. ? [X0] : quiet(X0) <=> (old(mary) | ~wise(mary)) [input p6]
13. ! [X0] : ((happy(X0) | ~wise(X0)) <=> (~curious(X0) <~> ~old(X0))) [input p12]
20. ? [X0] : (~generous(X0) & quiet(X0)) [input p19]
23. ~rich(mary) [input hypothesis]
28. ! [X0] : ((generous(X0) | kind(X0)) | (~curious(X0) & humble(X0))) [ennf transformation 1]
29. ! [X0] : (generous(X0) | kind(X0) | (~curious(X0) & humble(X0))) [flattening 28]
30. ! [X0] : ((old(X0) & quiet(X0)) | (~generous(X0) & ~kind(X0))) [ennf transformation 5]
42. ! [X0] : ((((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | ((~curious(X0) | ~rich(X0)) & (rich(X0) | curious(X0)))) & (((~rich(X0) | curious(X0)) & (rich(X0) | ~curious(X0))) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0))))) [nnf transformation 4]
43. (? [X0] : quiet(X0) | (~old(mary) & wise(mary))) & ((old(mary) | ~wise(mary)) | ! [X0] : ~quiet(X0)) [nnf transformation 7]
44. (? [X0] : quiet(X0) | (~old(mary) & wise(mary))) & (old(mary) | ~wise(mary) | ! [X0] : ~quiet(X0)) [flattening 43]
45. (? [X0] : quiet(X0) | (~old(mary) & wise(mary))) & (old(mary) | ~wise(mary) | ! [X1] : ~quiet(X1)) [rectify 44]
46. ? [X0] : quiet(X0) => quiet(sK2) [choice axiom]
47. (quiet(sK2) | (~old(mary) & wise(mary))) & (old(mary) | ~wise(mary) | ! [X1] : ~quiet(X1)) [skolemisation 45,46]
63. ! [X0] : (((happy(X0) | ~wise(X0)) | ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0)))) & (((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | (~happy(X0) & wise(X0)))) [nnf transformation 13]
64. ! [X0] : ((happy(X0) | ~wise(X0) | ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0)))) & (((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | (~happy(X0) & wise(X0)))) [flattening 63]
78. ? [X0] : (~generous(X0) & quiet(X0)) => (~generous(sK12) & quiet(sK12)) [choice axiom]
79. ~generous(sK12) & quiet(sK12) [skolemisation 20,78]
83. ~curious(X0) | kind(X0) | generous(X0) [cnf transformation 29]
94. rich(X0) | ~curious(X0) | ~old(X0) | ~curious(X0) [cnf transformation 42]
98. ~old(X0) | curious(X0) | rich(X0) | curious(X0) [cnf transformation 42]
104. ~kind(X0) | old(X0) [cnf transformation 30]
105. ~generous(X0) | old(X0) [cnf transformation 30]
107. old(mary) | ~wise(mary) | ~quiet(X1) [cnf transformation 47]
128. wise(X0) | curious(X0) | old(X0) [cnf transformation 64]
143. quiet(sK12) [cnf transformation 79]
148. ~rich(mary) [cnf transformation 23]
149. rich(X0) | ~curious(X0) | ~old(X0) [duplicate literal removal 94]
151. ~old(X0) | curious(X0) | rich(X0) [duplicate literal removal 98]
180. ~old(X0) | rich(X0) [subsumption resolution 149,151]
191. 9 <=> old(mary) [avatar definition]
192. old(mary) <- (9) [avatar component clause 191]
193. ~old(mary) <- (~9) [avatar component clause 191]
200. 11 <=> wise(mary) [avatar definition]
201. ~wise(mary) <- (~11) [avatar component clause 200]
205. 12 <=> ! [X1] : ~quiet(X1) [avatar definition]
206. ~quiet(X1) <- (12) [avatar component clause 205]
207. 12 | ~11 | 9 [avatar split clause 107,191,200,205]
417. curious(mary) | old(mary) <- (~11) [resolution 128,201]
419. 47 <=> curious(mary) [avatar definition]
421. curious(mary) <- (47) [avatar component clause 419]
422. 9 | 47 | 11 [avatar split clause 417,200,419,191]
423. kind(mary) | generous(mary) <- (47) [resolution 421,83]
425. 48 <=> generous(mary) [avatar definition]
427. generous(mary) <- (48) [avatar component clause 425]
429. 49 <=> kind(mary) [avatar definition]
431. kind(mary) <- (49) [avatar component clause 429]
432. 48 | 49 | ~47 [avatar split clause 423,419,429,425]
433. old(mary) <- (49) [resolution 431,104]
435. 9 | ~49 [avatar split clause 433,429,191]
438. rich(mary) <- (9) [resolution 192,180]
442. $false <- (9) [subsumption resolution 438,148]
443. ~9 [avatar contradiction clause 442]
448. old(mary) <- (48) [resolution 427,105]
450. $false <- (~9, 48) [subsumption resolution 448,193]
451. 9 | ~48 [avatar contradiction clause 450]
460. $false <- (12) [resolution 206,143]
463. ~12 [avatar contradiction clause 460]
464. $false [avatar sat refutation 207,422,432,435,443,451,463]
% SZS output end Proof for 8702677478624939313304188
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not strong or not curious then someone is either not wise or creative and vice versa.
If lucy is not generous then someone is quiet or rich and vice versa.
If mary is both not happy and not generous then alice is either strong or happy and vice versa.
If someone is either happy or not humble then lucy is brave or not rich.
Everyone who is both not curious and calm is either not generous or not brave and vice versa.
Everyone who is kind is not calm and vice versa.
Everyone who is both happy and calm is both happy and not rich.
Everyone who is both brave and not humble is not brave.
Everyone who is both not rich and kind is not creative or not happy and vice versa.
If someone is either not brave or creative then someone is brave.
Everyone who is funny is quiet or not curious and vice versa.
Everyone who is funny is not creative and vice versa.
If someone is quiet then paul is not curious or kind and vice versa.
Everyone who is not kind or not brave is rich.
If lucy is tall then someone is creative.
Everyone who is either not creative or not old is both funny and creative and vice versa.
Alice is not curious.
Lucy is quiet or not funny.
Fred is both not funny and not calm.
Someone is patient or generous.
Lucy is either not wise or happy.
Alice is both humble and not curious.
Mary is tall.
Paul is not happy or not curious. | Alice is not calm. | entailment | (((~strong(alice)|~curious(alice)))<=>(?[X]:((~wise(X)<~>creative(X)))))&
((~generous(lucy))<=>(?[X]:((quiet(X)|rich(X)))))&
(((~happy(mary)&~generous(mary)))<=>((strong(alice)<~>happy(alice))))&
((?[X]:((happy(X)<~>~humble(X))))=>((brave(lucy)|~rich(lucy))))&
(![X]:((~curious(X)&calm(X))<=>(~generous(X)<~>~brave(X))))&
(![X]:(kind(X)<=>~calm(X)))&
(![X]:((happy(X)&calm(X))=>(happy(X)&~rich(X))))&
(![X]:((brave(X)&~humble(X))=>~brave(X)))&
(![X]:((~rich(X)&kind(X))<=>(~creative(X)|~happy(X))))&
((?[X]:((~brave(X)<~>creative(X))))=>(?[X]:(brave(X))))&
(![X]:(funny(X)<=>(quiet(X)|~curious(X))))&
(![X]:(funny(X)<=>~creative(X)))&
((?[X]:(quiet(X)))<=>((~curious(paul)|kind(paul))))&
(![X]:((~kind(X)|~brave(X))=>rich(X)))&
((tall(lucy))=>(?[X]:(creative(X))))&
(![X]:((~creative(X)<~>~old(X))<=>(funny(X)&creative(X))))&
(~curious(alice))&
((quiet(lucy)|~funny(lucy)))&
((~funny(fred)&~calm(fred)))&
(?[X]:((patient(X)|generous(X))))&
((~wise(lucy)<~>happy(lucy)))&
((humble(alice)&~curious(alice)))&
(tall(mary))&
((~happy(paul)|~curious(paul))) | ~calm(alice) | [
"p5",
"p8",
"p10",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2923381098465931829235096
% SZS output start Proof for 2923381098465931829235096
6. ! [X0] : (kind(X0) <=> ~calm(X0)) [input p5]
9. ! [X0] : ((kind(X0) & ~rich(X0)) <=> (~happy(X0) | ~creative(X0))) [input p8]
11. ! [X0] : (funny(X0) <=> (~curious(X0) | quiet(X0))) [input p10]
12. ! [X0] : (funny(X0) <=> ~creative(X0)) [input p11]
22. ~curious(alice) & humble(alice) [input p21]
25. calm(alice) [input hypothesis]
51. ! [X0] : ((kind(X0) | calm(X0)) & (~calm(X0) | ~kind(X0))) [nnf transformation 6]
52. ! [X0] : (((kind(X0) & ~rich(X0)) | (happy(X0) & creative(X0))) & ((~happy(X0) | ~creative(X0)) | (~kind(X0) | rich(X0)))) [nnf transformation 9]
53. ! [X0] : (((kind(X0) & ~rich(X0)) | (happy(X0) & creative(X0))) & (~happy(X0) | ~creative(X0) | ~kind(X0) | rich(X0))) [flattening 52]
58. ! [X0] : ((funny(X0) | (curious(X0) & ~quiet(X0))) & ((~curious(X0) | quiet(X0)) | ~funny(X0))) [nnf transformation 11]
59. ! [X0] : ((funny(X0) | (curious(X0) & ~quiet(X0))) & (~curious(X0) | quiet(X0) | ~funny(X0))) [flattening 58]
60. ! [X0] : ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0))) [nnf transformation 12]
94. ~kind(X0) | ~calm(X0) [cnf transformation 51]
102. kind(X0) | creative(X0) [cnf transformation 53]
108. funny(X0) | curious(X0) [cnf transformation 59]
109. ~funny(X0) | ~creative(X0) [cnf transformation 60]
130. ~curious(alice) [cnf transformation 22]
133. calm(alice) [cnf transformation 25]
145. 3 <=> curious(alice) [avatar definition]
147. ~curious(alice) <- (~3) [avatar component clause 145]
277. ~3 [avatar split clause 130,145]
286. ~calm(X0) | creative(X0) [resolution 102,94]
292. ~creative(X0) | curious(X0) [resolution 109,108]
340. creative(alice) [resolution 286,133]
383. curious(alice) [resolution 292,340]
384. $false <- (~3) [subsumption resolution 383,147]
385. 3 [avatar contradiction clause 384]
386. $false [avatar sat refutation 277,385]
% SZS output end Proof for 2923381098465931829235096
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not generous then lucy is old or calm and vice versa.
If someone is old or quiet then lucy is either patient or not creative.
Everyone who is old or patient is old and vice versa.
Everyone who is not curious or wise is happy and vice versa.
Everyone who is not brave or rich is both kind and brave.
Everyone who is either funny or creative is both calm and not kind.
Everyone who is not patient or not kind is both not old and quiet and vice versa.
Everyone who is both not rich and not wise is kind and vice versa.
If someone is either generous or brave then someone is either kind or tall and vice versa.
If someone is not quiet or not brave then someone is generous and vice versa.
If someone is creative then someone is either quiet or strong.
Everyone who is either not quiet or brave is both not old and not quiet.
If someone is not kind then susan is not patient.
Everyone who is either tall or not kind is not patient and vice versa.
If fred is curious then fred is calm.
Everyone who is either not curious or old is not old or kind and vice versa.
Paul is strong.
Someone is not old or patient.
Someone is either not curious or not calm.
Susan is either wise or brave.
Lucy is either not humble or not brave.
Mary is both old and not tall. | Paul is brave. | entailment | ((~generous(lucy))<=>((old(lucy)|calm(lucy))))&
((?[X]:((old(X)|quiet(X))))=>((patient(lucy)<~>~creative(lucy))))&
(![X]:((old(X)|patient(X))<=>old(X)))&
(![X]:((~curious(X)|wise(X))<=>happy(X)))&
(![X]:((~brave(X)|rich(X))=>(kind(X)&brave(X))))&
(![X]:((funny(X)<~>creative(X))=>(calm(X)&~kind(X))))&
(![X]:((~patient(X)|~kind(X))<=>(~old(X)&quiet(X))))&
(![X]:((~rich(X)&~wise(X))<=>kind(X)))&
((?[X]:((generous(X)<~>brave(X))))<=>(?[X]:((kind(X)<~>tall(X)))))&
((?[X]:((~quiet(X)|~brave(X))))<=>(?[X]:(generous(X))))&
((?[X]:(creative(X)))=>(?[X]:((quiet(X)<~>strong(X)))))&
(![X]:((~quiet(X)<~>brave(X))=>(~old(X)&~quiet(X))))&
((?[X]:(~kind(X)))=>(~patient(susan)))&
(![X]:((tall(X)<~>~kind(X))<=>~patient(X)))&
((curious(fred))=>(calm(fred)))&
(![X]:((~curious(X)<~>old(X))<=>(~old(X)|kind(X))))&
(strong(paul))&
(?[X]:((~old(X)|patient(X))))&
(?[X]:((~curious(X)<~>~calm(X))))&
((wise(susan)<~>brave(susan)))&
((~humble(lucy)<~>~brave(lucy)))&
((old(mary)&~tall(mary))) | brave(paul) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 437537999962261324371127
% SZS output start Proof for 437537999962261324371127
5. ! [X0] : ((rich(X0) | ~brave(X0)) => (brave(X0) & kind(X0))) [input p4]
23. ~brave(paul) [input hypothesis]
28. ! [X0] : ((brave(X0) & kind(X0)) | (~rich(X0) & brave(X0))) [ennf transformation 5]
81. brave(X0) | brave(X0) [cnf transformation 28]
134. ~brave(paul) [cnf transformation 23]
138. brave(X0) [duplicate literal removal 81]
266. $false [subsumption resolution 134,138]
% SZS output end Proof for 437537999962261324371127
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or not wise is either generous or not generous.
If john is either not old or not strong then alice is either not calm or tall and vice versa.
If someone is either not calm or wise then someone is either rich or kind.
If susan is either old or patient then someone is not curious or not patient.
If someone is both strong and not calm then mary is rich or not quiet and vice versa.
If someone is not kind then lucy is not rich or not tall and vice versa.
Everyone who is both generous and creative is not humble and vice versa.
Everyone who is not patient or strong is both creative and rich.
Everyone who is strong is both not funny and not rich.
If alice is humble or quiet then someone is creative and vice versa.
Everyone who is both not old and old is generous or curious.
If alice is either not rich or quiet then someone is both not quiet and humble and vice versa.
Everyone who is both calm and not patient is calm and vice versa.
Everyone who is not kind or generous is both wise and not curious.
Everyone who is not old or humble is not kind or happy and vice versa.
Everyone who is not humble is rich or not kind.
Someone is wise or not patient.
Someone is not happy.
Alice is either strong or not quiet.
Someone is either not wise or tall.
Someone is not old or not strong.
Someone is both not wise and rich. | Susan is calm. | neutral | (![X]:((~rich(X)<~>~wise(X))=>(generous(X)<~>~generous(X))))&
(((~old(john)<~>~strong(john)))<=>((~calm(alice)<~>tall(alice))))&
((?[X]:((~calm(X)<~>wise(X))))=>(?[X]:((rich(X)<~>kind(X)))))&
(((old(susan)<~>patient(susan)))=>(?[X]:((~curious(X)|~patient(X)))))&
((?[X]:((strong(X)&~calm(X))))<=>((rich(mary)|~quiet(mary))))&
((?[X]:(~kind(X)))<=>((~rich(lucy)|~tall(lucy))))&
(![X]:((generous(X)&creative(X))<=>~humble(X)))&
(![X]:((~patient(X)|strong(X))=>(creative(X)&rich(X))))&
(![X]:(strong(X)=>(~funny(X)&~rich(X))))&
(((humble(alice)|quiet(alice)))<=>(?[X]:(creative(X))))&
(![X]:((~old(X)&old(X))=>(generous(X)|curious(X))))&
(((~rich(alice)<~>quiet(alice)))<=>(?[X]:((~quiet(X)&humble(X)))))&
(![X]:((calm(X)&~patient(X))<=>calm(X)))&
(![X]:((~kind(X)|generous(X))=>(wise(X)&~curious(X))))&
(![X]:((~old(X)|humble(X))<=>(~kind(X)|happy(X))))&
(![X]:(~humble(X)=>(rich(X)|~kind(X))))&
(?[X]:((wise(X)|~patient(X))))&
(?[X]:(~happy(X)))&
((strong(alice)<~>~quiet(alice)))&
(?[X]:((~wise(X)<~>tall(X))))&
(?[X]:((~old(X)|~strong(X))))&
(?[X]:((~wise(X)&rich(X)))) | calm(susan) | [] | null | 0 |
Everyone who is not patient is both happy and quiet and vice versa.
Everyone who is funny or not quiet is either creative or not generous and vice versa.
Everyone who is creative is both kind and patient.
If paul is either not calm or wise then someone is creative or wise and vice versa.
If alice is happy or not patient then someone is humble.
If susan is not creative or wise then someone is either brave or tall.
Everyone who is not calm or not funny is humble or not tall.
Everyone who is both not calm and strong is not patient and vice versa.
Everyone who is both not brave and kind is not strong and vice versa.
If someone is both patient and not generous then alice is patient.
Everyone who is not wise or not quiet is both patient and happy and vice versa.
Everyone who is either not creative or not rich is both not creative and not old and vice versa.
If someone is either not patient or curious then fred is not funny and vice versa.
If someone is not wise or old then someone is either kind or not calm.
Everyone who is not calm is brave or not happy and vice versa.
If someone is either not old or patient then susan is both creative and strong and vice versa.
Someone is both not kind and brave.
Someone is both not creative and not rich.
Susan is tall.
Someone is either not strong or patient.
Someone is calm or not humble.
Paul is either quiet or rich.
Someone is both not creative and not patient. | Paul is calm. | entailment | (![X]:(~patient(X)<=>(happy(X)&quiet(X))))&
(![X]:((funny(X)|~quiet(X))<=>(creative(X)<~>~generous(X))))&
(![X]:(creative(X)=>(kind(X)&patient(X))))&
(((~calm(paul)<~>wise(paul)))<=>(?[X]:((creative(X)|wise(X)))))&
(((happy(alice)|~patient(alice)))=>(?[X]:(humble(X))))&
(((~creative(susan)|wise(susan)))=>(?[X]:((brave(X)<~>tall(X)))))&
(![X]:((~calm(X)|~funny(X))=>(humble(X)|~tall(X))))&
(![X]:((~calm(X)&strong(X))<=>~patient(X)))&
(![X]:((~brave(X)&kind(X))<=>~strong(X)))&
((?[X]:((patient(X)&~generous(X))))=>(patient(alice)))&
(![X]:((~wise(X)|~quiet(X))<=>(patient(X)&happy(X))))&
(![X]:((~creative(X)<~>~rich(X))<=>(~creative(X)&~old(X))))&
((?[X]:((~patient(X)<~>curious(X))))<=>(~funny(fred)))&
((?[X]:((~wise(X)|old(X))))=>(?[X]:((kind(X)<~>~calm(X)))))&
(![X]:(~calm(X)<=>(brave(X)|~happy(X))))&
((?[X]:((~old(X)<~>patient(X))))<=>((creative(susan)&strong(susan))))&
(?[X]:((~kind(X)&brave(X))))&
(?[X]:((~creative(X)&~rich(X))))&
(tall(susan))&
(?[X]:((~strong(X)<~>patient(X))))&
(?[X]:((calm(X)|~humble(X))))&
((quiet(paul)<~>rich(paul)))&
(?[X]:((~creative(X)&~patient(X)))) | calm(paul) | [
"p3",
"p7",
"p8",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 644303366088806154762116
% SZS output start Proof for 644303366088806154762116
4. (~calm(paul) <~> wise(paul)) <=> ? [X0] : (wise(X0) | creative(X0)) [input p3]
8. ! [X0] : ((strong(X0) & ~calm(X0)) <=> ~patient(X0)) [input p7]
9. ! [X0] : ((kind(X0) & ~brave(X0)) <=> ~strong(X0)) [input p8]
11. ! [X0] : ((~quiet(X0) | ~wise(X0)) <=> (happy(X0) & patient(X0))) [input p10]
15. ! [X0] : (~calm(X0) <=> (~happy(X0) | brave(X0))) [input p14]
24. ~calm(paul) [input hypothesis]
37. (((~wise(paul) | calm(paul)) & (wise(paul) | ~calm(paul))) | ! [X0] : (~wise(X0) & ~creative(X0))) & (? [X0] : (wise(X0) | creative(X0)) | ((~calm(paul) | ~wise(paul)) & (wise(paul) | calm(paul)))) [nnf transformation 4]
38. (((~wise(paul) | calm(paul)) & (wise(paul) | ~calm(paul))) | ! [X0] : (~wise(X0) & ~creative(X0))) & (? [X1] : (wise(X1) | creative(X1)) | ((~calm(paul) | ~wise(paul)) & (wise(paul) | calm(paul)))) [rectify 37]
39. ? [X1] : (wise(X1) | creative(X1)) => (wise(sK0) | creative(sK0)) [choice axiom]
40. (((~wise(paul) | calm(paul)) & (wise(paul) | ~calm(paul))) | ! [X0] : (~wise(X0) & ~creative(X0))) & ((wise(sK0) | creative(sK0)) | ((~calm(paul) | ~wise(paul)) & (wise(paul) | calm(paul)))) [skolemisation 38,39]
46. ! [X0] : (((strong(X0) & ~calm(X0)) | patient(X0)) & (~patient(X0) | (~strong(X0) | calm(X0)))) [nnf transformation 8]
47. ! [X0] : (((strong(X0) & ~calm(X0)) | patient(X0)) & (~patient(X0) | ~strong(X0) | calm(X0))) [flattening 46]
48. ! [X0] : (((kind(X0) & ~brave(X0)) | strong(X0)) & (~strong(X0) | (~kind(X0) | brave(X0)))) [nnf transformation 9]
49. ! [X0] : (((kind(X0) & ~brave(X0)) | strong(X0)) & (~strong(X0) | ~kind(X0) | brave(X0))) [flattening 48]
50. ! [X0] : (((~quiet(X0) | ~wise(X0)) | (~happy(X0) | ~patient(X0))) & ((happy(X0) & patient(X0)) | (quiet(X0) & wise(X0)))) [nnf transformation 11]
51. ! [X0] : ((~quiet(X0) | ~wise(X0) | ~happy(X0) | ~patient(X0)) & ((happy(X0) & patient(X0)) | (quiet(X0) & wise(X0)))) [flattening 50]
62. ! [X0] : ((~calm(X0) | (happy(X0) & ~brave(X0))) & ((~happy(X0) | brave(X0)) | calm(X0))) [nnf transformation 15]
63. ! [X0] : ((~calm(X0) | (happy(X0) & ~brave(X0))) & (~happy(X0) | brave(X0) | calm(X0))) [flattening 62]
97. ~wise(paul) | calm(paul) | ~wise(X0) [cnf transformation 40]
106. ~strong(X0) | ~patient(X0) | calm(X0) [cnf transformation 47]
110. ~brave(X0) | strong(X0) [cnf transformation 49]
113. wise(X0) | patient(X0) [cnf transformation 51]
115. wise(X0) | happy(X0) [cnf transformation 51]
132. ~happy(X0) | brave(X0) | calm(X0) [cnf transformation 63]
153. ~calm(paul) [cnf transformation 24]
157. 1 <=> ! [X0] : ~wise(X0) [avatar definition]
158. ~wise(X0) <- (1) [avatar component clause 157]
160. 2 <=> calm(paul) [avatar definition]
161. ~calm(paul) <- (~2) [avatar component clause 160]
164. 3 <=> wise(paul) [avatar definition]
165. wise(paul) <- (3) [avatar component clause 164]
166. ~wise(paul) <- (~3) [avatar component clause 164]
167. 1 | 2 | ~3 [avatar split clause 97,164,160,157]
307. ~2 [avatar split clause 153,160]
314. patient(paul) <- (~3) [resolution 113,166]
316. happy(paul) <- (~3) [resolution 115,166]
436. brave(paul) | calm(paul) <- (~3) [resolution 132,316]
439. brave(paul) <- (~2, ~3) [subsumption resolution 436,161]
593. strong(paul) <- (~2, ~3) [resolution 439,110]
643. ~patient(paul) | calm(paul) <- (~2, ~3) [resolution 593,106]
644. calm(paul) <- (~2, ~3) [subsumption resolution 643,314]
645. $false <- (~2, ~3) [subsumption resolution 644,161]
646. 2 | 3 [avatar contradiction clause 645]
651. $false <- (1, 3) [resolution 165,158]
652. ~1 | ~3 [avatar contradiction clause 651]
653. $false [avatar sat refutation 167,307,646,652]
% SZS output end Proof for 644303366088806154762116
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is either old or not tall is not tall or not humble and vice versa.
Everyone who is either not patient or curious is not old or creative and vice versa.
Everyone who is either not generous or not strong is old and vice versa.
If susan is both not funny and strong then someone is either quiet or not old and vice versa.
Everyone who is not patient or not old is not old or not tall.
If someone is not generous or generous then someone is not strong and vice versa.
Everyone who is kind is not happy.
Everyone who is not wise is both kind and not tall and vice versa.
Everyone who is not kind is either calm or patient.
If lucy is not happy or quiet then lucy is both kind and generous and vice versa.
If someone is not kind or patient then fred is both funny and not generous.
If someone is funny or not kind then someone is both not humble and not rich and vice versa.
Everyone who is either patient or humble is both not strong and curious.
Everyone who is either not funny or quiet is not humble.
Everyone who is either not old or happy is old and vice versa.
Everyone who is both wise and humble is not strong or wise.
Someone is old.
Someone is both not rich and curious.
Lucy is tall.
Someone is not creative.
Someone is either not wise or quiet.
Mary is brave or not humble.
Someone is not kind or not strong.
Someone is both not funny and wise. | Lucy is not kind. | entailment | (![X]:((old(X)<~>~tall(X))<=>(~tall(X)|~humble(X))))&
(![X]:((~patient(X)<~>curious(X))<=>(~old(X)|creative(X))))&
(![X]:((~generous(X)<~>~strong(X))<=>old(X)))&
(((~funny(susan)&strong(susan)))<=>(?[X]:((quiet(X)<~>~old(X)))))&
(![X]:((~patient(X)|~old(X))=>(~old(X)|~tall(X))))&
((?[X]:((~generous(X)|generous(X))))<=>(?[X]:(~strong(X))))&
(![X]:(kind(X)=>~happy(X)))&
(![X]:(~wise(X)<=>(kind(X)&~tall(X))))&
(![X]:(~kind(X)=>(calm(X)<~>patient(X))))&
(((~happy(lucy)|quiet(lucy)))<=>((kind(lucy)&generous(lucy))))&
((?[X]:((~kind(X)|patient(X))))=>((funny(fred)&~generous(fred))))&
((?[X]:((funny(X)|~kind(X))))<=>(?[X]:((~humble(X)&~rich(X)))))&
(![X]:((patient(X)<~>humble(X))=>(~strong(X)&curious(X))))&
(![X]:((~funny(X)<~>quiet(X))=>~humble(X)))&
(![X]:((~old(X)<~>happy(X))<=>old(X)))&
(![X]:((wise(X)&humble(X))=>(~strong(X)|wise(X))))&
(?[X]:(old(X)))&
(?[X]:((~rich(X)&curious(X))))&
(tall(lucy))&
(?[X]:(~creative(X)))&
(?[X]:((~wise(X)<~>quiet(X))))&
((brave(mary)|~humble(mary)))&
(?[X]:((~kind(X)|~strong(X))))&
(?[X]:((~funny(X)&wise(X)))) | ~kind(lucy) | [
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8246063402789199873897691
% SZS output start Proof for 8246063402789199873897691
7. ! [X0] : (kind(X0) => ~happy(X0)) [input p6]
15. ! [X0] : ((~old(X0) <~> happy(X0)) <=> old(X0)) [input p14]
25. kind(lucy) [input hypothesis]
31. ! [X0] : (~happy(X0) | ~kind(X0)) [ennf transformation 7]
65. ! [X0] : ((((~happy(X0) | old(X0)) & (happy(X0) | ~old(X0))) | ~old(X0)) & (old(X0) | ((~old(X0) | ~happy(X0)) & (happy(X0) | old(X0))))) [nnf transformation 15]
106. ~happy(X0) | ~kind(X0) [cnf transformation 31]
132. old(X0) | happy(X0) | old(X0) [cnf transformation 65]
134. happy(X0) | ~old(X0) | ~old(X0) [cnf transformation 65]
147. kind(lucy) [cnf transformation 25]
148. old(X0) | happy(X0) [duplicate literal removal 132]
149. happy(X0) | ~old(X0) [duplicate literal removal 134]
209. 13 <=> kind(lucy) [avatar definition]
211. kind(lucy) <- (13) [avatar component clause 209]
259. happy(X0) [subsumption resolution 148,149]
279. 13 [avatar split clause 147,209]
282. ~kind(X0) [resolution 106,259]
283. $false <- (13) [resolution 282,211]
284. ~13 [avatar contradiction clause 283]
285. $false [avatar sat refutation 279,284]
% SZS output end Proof for 8246063402789199873897691
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or calm is both humble and rich and vice versa.
If paul is not generous then alice is calm or not quiet.
Everyone who is funny or curious is not creative or calm.
If someone is curious or patient then fred is either not happy or not generous and vice versa.
Everyone who is happy is not tall or happy and vice versa.
If someone is either strong or generous then fred is not calm and vice versa.
Everyone who is not wise or wise is either not patient or not calm and vice versa.
If alice is wise or not strong then fred is both not tall and rich.
If someone is either calm or not quiet then someone is not old and vice versa.
Everyone who is patient or curious is generous or humble and vice versa.
Everyone who is not patient is generous or not rich.
If someone is both not creative and not brave then alice is not humble.
Everyone who is both not quiet and humble is brave or generous.
Everyone who is either brave or not wise is old.
Everyone who is both not patient and calm is both not generous and tall and vice versa.
If alice is either not wise or rich then someone is both not rich and not brave.
Fred is not calm or not patient.
Mary is both happy and humble.
John is either rich or generous.
Someone is creative.
Mary is calm or funny.
Mary is not wise.
Someone is both not rich and not old.
Someone is both not tall and strong. | Fred is not calm. | entailment | (![X]:((quiet(X)|calm(X))<=>(humble(X)&rich(X))))&
((~generous(paul))=>((calm(alice)|~quiet(alice))))&
(![X]:((funny(X)|curious(X))=>(~creative(X)|calm(X))))&
((?[X]:((curious(X)|patient(X))))<=>((~happy(fred)<~>~generous(fred))))&
(![X]:(happy(X)<=>(~tall(X)|happy(X))))&
((?[X]:((strong(X)<~>generous(X))))<=>(~calm(fred)))&
(![X]:((~wise(X)|wise(X))<=>(~patient(X)<~>~calm(X))))&
(((wise(alice)|~strong(alice)))=>((~tall(fred)&rich(fred))))&
((?[X]:((calm(X)<~>~quiet(X))))<=>(?[X]:(~old(X))))&
(![X]:((patient(X)|curious(X))<=>(generous(X)|humble(X))))&
(![X]:(~patient(X)=>(generous(X)|~rich(X))))&
((?[X]:((~creative(X)&~brave(X))))=>(~humble(alice)))&
(![X]:((~quiet(X)&humble(X))=>(brave(X)|generous(X))))&
(![X]:((brave(X)<~>~wise(X))=>old(X)))&
(![X]:((~patient(X)&calm(X))<=>(~generous(X)&tall(X))))&
(((~wise(alice)<~>rich(alice)))=>(?[X]:((~rich(X)&~brave(X)))))&
((~calm(fred)|~patient(fred)))&
((happy(mary)&humble(mary)))&
((rich(john)<~>generous(john)))&
(?[X]:(creative(X)))&
((calm(mary)|funny(mary)))&
(~wise(mary))&
(?[X]:((~rich(X)&~old(X))))&
(?[X]:((~tall(X)&strong(X)))) | ~calm(fred) | [
"p0",
"p6",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3380075091064554881498411
% SZS output start Proof for 3380075091064554881498411
1. ! [X0] : ((calm(X0) | quiet(X0)) <=> (rich(X0) & humble(X0))) [input p0]
7. ! [X0] : ((wise(X0) | ~wise(X0)) <=> (~patient(X0) <~> ~calm(X0))) [input p6]
11. ! [X0] : (~patient(X0) => (~rich(X0) | generous(X0))) [input p10]
15. ! [X0] : ((calm(X0) & ~patient(X0)) <=> (tall(X0) & ~generous(X0))) [input p14]
25. calm(fred) [input hypothesis]
32. ! [X0] : ((~rich(X0) | generous(X0)) | patient(X0)) [ennf transformation 11]
33. ! [X0] : (~rich(X0) | generous(X0) | patient(X0)) [flattening 32]
39. ! [X0] : (((calm(X0) | quiet(X0)) | (~rich(X0) | ~humble(X0))) & ((rich(X0) & humble(X0)) | (~calm(X0) & ~quiet(X0)))) [nnf transformation 1]
40. ! [X0] : ((calm(X0) | quiet(X0) | ~rich(X0) | ~humble(X0)) & ((rich(X0) & humble(X0)) | (~calm(X0) & ~quiet(X0)))) [flattening 39]
51. ! [X0] : (((wise(X0) | ~wise(X0)) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) & (((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | (~wise(X0) & wise(X0)))) [nnf transformation 7]
52. ! [X0] : ((wise(X0) | ~wise(X0) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) & (((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | (~wise(X0) & wise(X0)))) [flattening 51]
61. ! [X0] : (((calm(X0) & ~patient(X0)) | (~tall(X0) | generous(X0))) & ((tall(X0) & ~generous(X0)) | (~calm(X0) | patient(X0)))) [nnf transformation 15]
62. ! [X0] : (((calm(X0) & ~patient(X0)) | ~tall(X0) | generous(X0)) & ((tall(X0) & ~generous(X0)) | ~calm(X0) | patient(X0))) [flattening 61]
76. ~calm(X0) | rich(X0) [cnf transformation 40]
94. ~calm(X0) | ~patient(X0) | wise(X0) [cnf transformation 52]
95. ~wise(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 52]
96. calm(X0) | patient(X0) | wise(X0) [cnf transformation 52]
97. ~wise(X0) | patient(X0) | calm(X0) [cnf transformation 52]
112. ~rich(X0) | generous(X0) | patient(X0) [cnf transformation 33]
117. ~generous(X0) | ~calm(X0) | patient(X0) [cnf transformation 62]
137. calm(fred) [cnf transformation 25]
152. 4 <=> generous(fred) [avatar definition]
153. ~generous(fred) <- (~4) [avatar component clause 152]
154. generous(fred) <- (4) [avatar component clause 152]
180. 10 <=> calm(fred) [avatar definition]
182. calm(fred) <- (10) [avatar component clause 180]
201. patient(X0) | calm(X0) [subsumption resolution 96,97]
202. ~patient(X0) | ~calm(X0) [subsumption resolution 94,95]
208. 16 <=> rich(fred) [avatar definition]
210. rich(fred) <- (16) [avatar component clause 208]
257. ~generous(X0) | patient(X0) [subsumption resolution 117,201]
293. 10 [avatar split clause 137,180]
296. rich(fred) <- (10) [resolution 76,182]
298. 16 | ~10 [avatar split clause 296,180,208]
308. patient(fred) <- (4) [resolution 257,154]
322. ~calm(fred) <- (4) [resolution 308,202]
323. $false <- (4, 10) [subsumption resolution 322,182]
324. ~4 | ~10 [avatar contradiction clause 323]
370. 40 <=> patient(fred) [avatar definition]
372. patient(fred) <- (40) [avatar component clause 370]
385. generous(fred) | patient(fred) <- (16) [resolution 112,210]
387. patient(fred) <- (~4, 16) [subsumption resolution 385,153]
388. 40 | 4 | ~16 [avatar split clause 387,208,152,370]
393. ~calm(fred) <- (40) [resolution 372,202]
394. $false <- (10, 40) [subsumption resolution 393,182]
395. ~10 | ~40 [avatar contradiction clause 394]
396. $false [avatar sat refutation 293,298,324,388,395]
% SZS output end Proof for 3380075091064554881498411
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is happy or patient.
Everyone who is not funny or calm is wise and vice versa.
Everyone who is not rich or not generous is not brave and vice versa.
If paul is not humble then someone is either not humble or not rich.
If someone is not kind or rich then someone is either rich or kind and vice versa.
Everyone who is both not brave and strong is either not wise or not curious and vice versa.
Everyone who is both calm and rich is not brave or old and vice versa.
If mary is either old or not tall then john is happy and vice versa.
Everyone who is generous or not old is not brave and vice versa.
If someone is creative or not old then lucy is not creative or strong.
Everyone who is either old or not patient is not generous.
If someone is not creative then someone is either humble or not creative and vice versa.
If paul is rich or calm then paul is not strong.
Everyone who is strong or kind is either not creative or not rich.
Everyone who is both wise and not brave is not creative and vice versa.
Paul is both not tall and kind.
Susan is calm or patient.
Paul is happy or not curious.
Fred is either not rich or not curious.
Mary is either not old or curious.
Alice is kind or strong. | Alice is not kind. | neutral | (![X]:(patient(X)=>(happy(X)|patient(X))))&
(![X]:((~funny(X)|calm(X))<=>wise(X)))&
(![X]:((~rich(X)|~generous(X))<=>~brave(X)))&
((~humble(paul))=>(?[X]:((~humble(X)<~>~rich(X)))))&
((?[X]:((~kind(X)|rich(X))))<=>(?[X]:((rich(X)<~>kind(X)))))&
(![X]:((~brave(X)&strong(X))<=>(~wise(X)<~>~curious(X))))&
(![X]:((calm(X)&rich(X))<=>(~brave(X)|old(X))))&
(((old(mary)<~>~tall(mary)))<=>(happy(john)))&
(![X]:((generous(X)|~old(X))<=>~brave(X)))&
((?[X]:((creative(X)|~old(X))))=>((~creative(lucy)|strong(lucy))))&
(![X]:((old(X)<~>~patient(X))=>~generous(X)))&
((?[X]:(~creative(X)))<=>(?[X]:((humble(X)<~>~creative(X)))))&
(((rich(paul)|calm(paul)))=>(~strong(paul)))&
(![X]:((strong(X)|kind(X))=>(~creative(X)<~>~rich(X))))&
(![X]:((wise(X)&~brave(X))<=>~creative(X)))&
((~tall(paul)&kind(paul)))&
((calm(susan)|patient(susan)))&
((happy(paul)|~curious(paul)))&
((~rich(fred)<~>~curious(fred)))&
((~old(mary)<~>curious(mary)))&
((kind(alice)|strong(alice))) | ~kind(alice) | [] | null | 0 |
Everyone who is both not tall and not kind is both old and not old and vice versa.
Everyone who is either not kind or old is either not happy or not quiet.
Everyone who is either not brave or old is either tall or not generous and vice versa.
Everyone who is strong is either not generous or not funny.
Everyone who is both not strong and not patient is both not happy and rich and vice versa.
If someone is both not creative and wise then someone is either rich or curious and vice versa.
If someone is not tall or not rich then someone is not kind or not tall and vice versa.
If susan is either generous or strong then john is both not wise and not quiet and vice versa.
Everyone who is strong or curious is both calm and rich.
If paul is either not rich or not happy then someone is both old and not creative.
Everyone who is either not humble or tall is both quiet and not wise and vice versa.
If someone is not humble then susan is both not curious and happy.
If someone is patient then someone is rich or calm and vice versa.
If someone is either wise or not creative then someone is patient and vice versa.
Everyone who is either not kind or not tall is both brave and not tall.
If paul is not generous or funny then someone is both not brave and not wise.
John is either not rich or not wise.
Alice is rich.
Mary is not patient.
Someone is brave or wise.
Susan is both creative and curious.
John is either not generous or not humble.
Someone is brave or not old.
Someone is not happy or generous. | Paul is kind. | entailment | (![X]:((~tall(X)&~kind(X))<=>(old(X)&~old(X))))&
(![X]:((~kind(X)<~>old(X))=>(~happy(X)<~>~quiet(X))))&
(![X]:((~brave(X)<~>old(X))<=>(tall(X)<~>~generous(X))))&
(![X]:(strong(X)=>(~generous(X)<~>~funny(X))))&
(![X]:((~strong(X)&~patient(X))<=>(~happy(X)&rich(X))))&
((?[X]:((~creative(X)&wise(X))))<=>(?[X]:((rich(X)<~>curious(X)))))&
((?[X]:((~tall(X)|~rich(X))))<=>(?[X]:((~kind(X)|~tall(X)))))&
(((generous(susan)<~>strong(susan)))<=>((~wise(john)&~quiet(john))))&
(![X]:((strong(X)|curious(X))=>(calm(X)&rich(X))))&
(((~rich(paul)<~>~happy(paul)))=>(?[X]:((old(X)&~creative(X)))))&
(![X]:((~humble(X)<~>tall(X))<=>(quiet(X)&~wise(X))))&
((?[X]:(~humble(X)))=>((~curious(susan)&happy(susan))))&
((?[X]:(patient(X)))<=>(?[X]:((rich(X)|calm(X)))))&
((?[X]:((wise(X)<~>~creative(X))))<=>(?[X]:(patient(X))))&
(![X]:((~kind(X)<~>~tall(X))=>(brave(X)&~tall(X))))&
(((~generous(paul)|funny(paul)))=>(?[X]:((~brave(X)&~wise(X)))))&
((~rich(john)<~>~wise(john)))&
(rich(alice))&
(~patient(mary))&
(?[X]:((brave(X)|wise(X))))&
((creative(susan)&curious(susan)))&
((~generous(john)<~>~humble(john)))&
(?[X]:((brave(X)|~old(X))))&
(?[X]:((~happy(X)|generous(X)))) | kind(paul) | [
"p0",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8092427351395208991559219
% SZS output start Proof for 8092427351395208991559219
1. ! [X0] : ((~kind(X0) & ~tall(X0)) <=> (~old(X0) & old(X0))) [input p0]
15. ! [X0] : ((~kind(X0) <~> ~tall(X0)) => (~tall(X0) & brave(X0))) [input p14]
25. ~kind(paul) [input hypothesis]
35. ! [X0] : ((~tall(X0) & brave(X0)) | (~kind(X0) <=> ~tall(X0))) [ennf transformation 15]
37. ! [X0] : (((~kind(X0) & ~tall(X0)) | (old(X0) | ~old(X0))) & ((~old(X0) & old(X0)) | (kind(X0) | tall(X0)))) [nnf transformation 1]
38. ! [X0] : (((~kind(X0) & ~tall(X0)) | old(X0) | ~old(X0)) & ((~old(X0) & old(X0)) | kind(X0) | tall(X0))) [flattening 37]
71. ! [X0] : ((~tall(X0) & brave(X0)) | ((~kind(X0) | tall(X0)) & (~tall(X0) | kind(X0)))) [nnf transformation 35]
82. old(X0) | kind(X0) | tall(X0) [cnf transformation 38]
83. ~old(X0) | kind(X0) | tall(X0) [cnf transformation 38]
145. ~tall(X0) | ~tall(X0) | kind(X0) [cnf transformation 71]
162. ~kind(paul) [cnf transformation 25]
163. ~tall(X0) | kind(X0) [duplicate literal removal 145]
164. kind(X0) | tall(X0) [subsumption resolution 82,83]
209. 11 <=> ! [X1] : kind(X1) [avatar definition]
210. kind(X1) <- (11) [avatar component clause 209]
327. kind(X0) [subsumption resolution 163,164]
328. 11 [avatar split clause 327,209]
397. $false <- (11) [resolution 210,162]
398. ~11 [avatar contradiction clause 397]
399. $false [avatar sat refutation 328,398]
% SZS output end Proof for 8092427351395208991559219
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or curious is either humble or rich.
Everyone who is not tall is not generous and vice versa.
If john is not wise or not generous then someone is both not rich and not humble.
Everyone who is not old is both strong and funny and vice versa.
Everyone who is not calm or kind is not happy or not wise.
If someone is not strong then someone is either humble or not strong.
Everyone who is wise or kind is either wise or not tall.
Everyone who is either not tall or old is tall and vice versa.
If fred is brave then someone is both generous and not funny.
If someone is either patient or not kind then john is both not kind and not funny.
Everyone who is both calm and not rich is not brave and vice versa.
If someone is not quiet or brave then mary is both curious and not quiet.
Everyone who is both brave and not creative is quiet.
Everyone who is humble is not calm and vice versa.
Everyone who is both brave and not funny is either not quiet or not rich.
If someone is happy then someone is not curious or not happy and vice versa.
Someone is not brave or quiet.
Alice is either kind or not brave.
Someone is humble or not funny.
Someone is both not patient and wise.
Alice is calm or not wise.
Alice is tall.
Someone is either funny or patient.
Mary is not patient. | Fred is humble. | neutral | (![X]:((~calm(X)|curious(X))=>(humble(X)<~>rich(X))))&
(![X]:(~tall(X)<=>~generous(X)))&
(((~wise(john)|~generous(john)))=>(?[X]:((~rich(X)&~humble(X)))))&
(![X]:(~old(X)<=>(strong(X)&funny(X))))&
(![X]:((~calm(X)|kind(X))=>(~happy(X)|~wise(X))))&
((?[X]:(~strong(X)))=>(?[X]:((humble(X)<~>~strong(X)))))&
(![X]:((wise(X)|kind(X))=>(wise(X)<~>~tall(X))))&
(![X]:((~tall(X)<~>old(X))<=>tall(X)))&
((brave(fred))=>(?[X]:((generous(X)&~funny(X)))))&
((?[X]:((patient(X)<~>~kind(X))))=>((~kind(john)&~funny(john))))&
(![X]:((calm(X)&~rich(X))<=>~brave(X)))&
((?[X]:((~quiet(X)|brave(X))))=>((curious(mary)&~quiet(mary))))&
(![X]:((brave(X)&~creative(X))=>quiet(X)))&
(![X]:(humble(X)<=>~calm(X)))&
(![X]:((brave(X)&~funny(X))=>(~quiet(X)<~>~rich(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~curious(X)|~happy(X)))))&
(?[X]:((~brave(X)|quiet(X))))&
((kind(alice)<~>~brave(alice)))&
(?[X]:((humble(X)|~funny(X))))&
(?[X]:((~patient(X)&wise(X))))&
((calm(alice)|~wise(alice)))&
(tall(alice))&
(?[X]:((funny(X)<~>patient(X))))&
(~patient(mary)) | humble(fred) | [] | null | 0 |
If someone is funny then paul is creative or not humble.
Everyone who is either kind or not patient is either creative or not rich and vice versa.
Everyone who is quiet is not curious or not happy and vice versa.
Everyone who is either tall or not tall is both patient and not generous and vice versa.
Everyone who is either not quiet or not tall is both not humble and not generous and vice versa.
Everyone who is not humble is both not patient and not wise and vice versa.
Everyone who is both strong and not strong is both wise and not curious.
If someone is either generous or not tall then lucy is either not calm or not funny.
If someone is not wise then someone is both patient and not creative and vice versa.
If alice is either strong or rich then someone is humble or quiet and vice versa.
Everyone who is either patient or brave is both not quiet and humble.
If lucy is both not strong and not quiet then someone is both tall and funny and vice versa.
Everyone who is either not happy or not wise is both not funny and not creative.
If someone is patient then someone is either not patient or not rich and vice versa.
If someone is not happy or calm then susan is either not kind or not rich and vice versa.
Everyone who is either not old or wise is both rich and generous.
Someone is either quiet or happy.
Paul is rich.
Someone is not kind.
Someone is not brave.
Alice is either not patient or rich.
Susan is not funny or brave. | Paul is humble. | entailment | ((?[X]:(funny(X)))=>((creative(paul)|~humble(paul))))&
(![X]:((kind(X)<~>~patient(X))<=>(creative(X)<~>~rich(X))))&
(![X]:(quiet(X)<=>(~curious(X)|~happy(X))))&
(![X]:((tall(X)<~>~tall(X))<=>(patient(X)&~generous(X))))&
(![X]:((~quiet(X)<~>~tall(X))<=>(~humble(X)&~generous(X))))&
(![X]:(~humble(X)<=>(~patient(X)&~wise(X))))&
(![X]:((strong(X)&~strong(X))=>(wise(X)&~curious(X))))&
((?[X]:((generous(X)<~>~tall(X))))=>((~calm(lucy)<~>~funny(lucy))))&
((?[X]:(~wise(X)))<=>(?[X]:((patient(X)&~creative(X)))))&
(((strong(alice)<~>rich(alice)))<=>(?[X]:((humble(X)|quiet(X)))))&
(![X]:((patient(X)<~>brave(X))=>(~quiet(X)&humble(X))))&
(((~strong(lucy)&~quiet(lucy)))<=>(?[X]:((tall(X)&funny(X)))))&
(![X]:((~happy(X)<~>~wise(X))=>(~funny(X)&~creative(X))))&
((?[X]:(patient(X)))<=>(?[X]:((~patient(X)<~>~rich(X)))))&
((?[X]:((~happy(X)|calm(X))))<=>((~kind(susan)<~>~rich(susan))))&
(![X]:((~old(X)<~>wise(X))=>(rich(X)&generous(X))))&
(?[X]:((quiet(X)<~>happy(X))))&
(rich(paul))&
(?[X]:(~kind(X)))&
(?[X]:(~brave(X)))&
((~patient(alice)<~>rich(alice)))&
((~funny(susan)|brave(susan))) | humble(paul) | [
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1311292781680901556687775
% SZS output start Proof for 1311292781680901556687775
4. ! [X0] : ((tall(X0) <~> ~tall(X0)) <=> (~generous(X0) & patient(X0))) [input p3]
6. ! [X0] : (~humble(X0) <=> (~wise(X0) & ~patient(X0))) [input p5]
23. ~humble(paul) [input hypothesis]
37. ! [X0] : ((((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | (generous(X0) | ~patient(X0))) & ((~generous(X0) & patient(X0)) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0))))) [nnf transformation 4]
38. ! [X0] : ((((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | generous(X0) | ~patient(X0)) & ((~generous(X0) & patient(X0)) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0))))) [flattening 37]
41. ! [X0] : ((~humble(X0) | (wise(X0) | patient(X0))) & ((~wise(X0) & ~patient(X0)) | humble(X0))) [nnf transformation 6]
42. ! [X0] : ((~humble(X0) | wise(X0) | patient(X0)) & ((~wise(X0) & ~patient(X0)) | humble(X0))) [flattening 41]
90. patient(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 38]
91. patient(X0) | tall(X0) | tall(X0) [cnf transformation 38]
102. ~patient(X0) | humble(X0) [cnf transformation 42]
154. ~humble(paul) [cnf transformation 23]
155. patient(X0) | ~tall(X0) [duplicate literal removal 90]
156. patient(X0) | tall(X0) [duplicate literal removal 91]
172. patient(X0) [subsumption resolution 155,156]
175. humble(X0) [subsumption resolution 102,172]
301. $false [subsumption resolution 154,175]
% SZS output end Proof for 1311292781680901556687775
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is happy or strong.
If someone is curious or not tall then mary is kind or not patient.
If mary is creative or not quiet then lucy is humble or generous.
Everyone who is either strong or wise is wise or not calm.
Everyone who is not funny or brave is both brave and not calm.
If fred is both not old and tall then someone is creative or funny and vice versa.
Everyone who is either rich or not wise is either not tall or wise and vice versa.
Everyone who is not curious or not funny is kind or not curious.
Everyone who is both happy and not tall is humble or not wise and vice versa.
Everyone who is both curious and quiet is brave.
Everyone who is either calm or curious is generous or not rich and vice versa.
If someone is both not creative and curious then mary is not strong or creative.
If fred is wise or not calm then fred is both not rich and strong and vice versa.
If someone is generous or not old then alice is not rich or funny.
Everyone who is not brave is either not tall or strong and vice versa.
Susan is either brave or strong.
John is not creative.
Susan is not calm.
Someone is both old and generous.
Someone is not wise or tall.
Someone is either not patient or tall.
Someone is not humble. | Mary is happy. | entailment | (![X]:(brave(X)=>(happy(X)|strong(X))))&
((?[X]:((curious(X)|~tall(X))))=>((kind(mary)|~patient(mary))))&
(((creative(mary)|~quiet(mary)))=>((humble(lucy)|generous(lucy))))&
(![X]:((strong(X)<~>wise(X))=>(wise(X)|~calm(X))))&
(![X]:((~funny(X)|brave(X))=>(brave(X)&~calm(X))))&
(((~old(fred)&tall(fred)))<=>(?[X]:((creative(X)|funny(X)))))&
(![X]:((rich(X)<~>~wise(X))<=>(~tall(X)<~>wise(X))))&
(![X]:((~curious(X)|~funny(X))=>(kind(X)|~curious(X))))&
(![X]:((happy(X)&~tall(X))<=>(humble(X)|~wise(X))))&
(![X]:((curious(X)&quiet(X))=>brave(X)))&
(![X]:((calm(X)<~>curious(X))<=>(generous(X)|~rich(X))))&
((?[X]:((~creative(X)&curious(X))))=>((~strong(mary)|creative(mary))))&
(((wise(fred)|~calm(fred)))<=>((~rich(fred)&strong(fred))))&
((?[X]:((generous(X)|~old(X))))=>((~rich(alice)|funny(alice))))&
(![X]:(~brave(X)<=>(~tall(X)<~>strong(X))))&
((brave(susan)<~>strong(susan)))&
(~creative(john))&
(~calm(susan))&
(?[X]:((old(X)&generous(X))))&
(?[X]:((~wise(X)|tall(X))))&
(?[X]:((~patient(X)<~>tall(X))))&
(?[X]:(~humble(X))) | happy(mary) | [
"p0",
"p4",
"p5",
"p6",
"p8",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4783442436031580706210849
% SZS output start Proof for 4783442436031580706210849
1. ! [X0] : (brave(X0) => (strong(X0) | happy(X0))) [input p0]
5. ! [X0] : ((brave(X0) | ~funny(X0)) => (~calm(X0) & brave(X0))) [input p4]
6. (tall(fred) & ~old(fred)) <=> ? [X0] : (funny(X0) | creative(X0)) [input p5]
7. ! [X0] : ((rich(X0) <~> ~wise(X0)) <=> (~tall(X0) <~> wise(X0))) [input p6]
9. ! [X0] : ((~tall(X0) & happy(X0)) <=> (~wise(X0) | humble(X0))) [input p8]
11. ! [X0] : ((calm(X0) <~> curious(X0)) <=> (~rich(X0) | generous(X0))) [input p10]
12. ? [X0] : (curious(X0) & ~creative(X0)) => (creative(mary) | ~strong(mary)) [input p11]
13. (~calm(fred) | wise(fred)) <=> (strong(fred) & ~rich(fred)) [input p12]
23. ~happy(mary) [input hypothesis]
26. ! [X0] : ((strong(X0) | happy(X0)) | ~brave(X0)) [ennf transformation 1]
27. ! [X0] : (strong(X0) | happy(X0) | ~brave(X0)) [flattening 26]
32. ! [X0] : ((~calm(X0) & brave(X0)) | (~brave(X0) & funny(X0))) [ennf transformation 5]
35. (creative(mary) | ~strong(mary)) | ! [X0] : (~curious(X0) | creative(X0)) [ennf transformation 12]
36. creative(mary) | ~strong(mary) | ! [X0] : (~curious(X0) | creative(X0)) [flattening 35]
40. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & (? [X0] : (funny(X0) | creative(X0)) | (~tall(fred) | old(fred))) [nnf transformation 6]
41. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & (? [X0] : (funny(X0) | creative(X0)) | ~tall(fred) | old(fred)) [flattening 40]
42. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & (? [X1] : (funny(X1) | creative(X1)) | ~tall(fred) | old(fred)) [rectify 41]
43. ? [X1] : (funny(X1) | creative(X1)) => (funny(sK0) | creative(sK0)) [choice axiom]
44. ((tall(fred) & ~old(fred)) | ! [X0] : (~funny(X0) & ~creative(X0))) & ((funny(sK0) | creative(sK0)) | ~tall(fred) | old(fred)) [skolemisation 42,43]
45. ! [X0] : ((((wise(X0) | ~rich(X0)) & (~wise(X0) | rich(X0))) | ((~tall(X0) | ~wise(X0)) & (wise(X0) | tall(X0)))) & (((~wise(X0) | tall(X0)) & (wise(X0) | ~tall(X0))) | ((rich(X0) | wise(X0)) & (~wise(X0) | ~rich(X0))))) [nnf transformation 7]
46. ! [X0] : (((~tall(X0) & happy(X0)) | (wise(X0) & ~humble(X0))) & ((~wise(X0) | humble(X0)) | (tall(X0) | ~happy(X0)))) [nnf transformation 9]
47. ! [X0] : (((~tall(X0) & happy(X0)) | (wise(X0) & ~humble(X0))) & (~wise(X0) | humble(X0) | tall(X0) | ~happy(X0))) [flattening 46]
48. ! [X0] : ((((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | (rich(X0) & ~generous(X0))) & ((~rich(X0) | generous(X0)) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0))))) [nnf transformation 11]
49. ! [X0] : ((((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | (rich(X0) & ~generous(X0))) & (~rich(X0) | generous(X0) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0))))) [flattening 48]
50. ((~calm(fred) | wise(fred)) | (~strong(fred) | rich(fred))) & ((strong(fred) & ~rich(fred)) | (calm(fred) & ~wise(fred))) [nnf transformation 13]
51. (~calm(fred) | wise(fred) | ~strong(fred) | rich(fred)) & ((strong(fred) & ~rich(fred)) | (calm(fred) & ~wise(fred))) [flattening 50]
63. ~brave(X0) | happy(X0) | strong(X0) [cnf transformation 27]
68. funny(X0) | brave(X0) [cnf transformation 32]
70. ~calm(X0) | funny(X0) [cnf transformation 32]
75. tall(fred) | ~creative(X0) [cnf transformation 44]
76. tall(fred) | ~funny(X0) [cnf transformation 44]
78. wise(X0) | ~tall(X0) | rich(X0) | wise(X0) [cnf transformation 45]
82. ~wise(X0) | rich(X0) | ~tall(X0) | ~wise(X0) [cnf transformation 45]
89. ~tall(X0) | wise(X0) [cnf transformation 47]
94. rich(X0) | calm(X0) | curious(X0) [cnf transformation 49]
97. creative(mary) | ~strong(mary) | ~curious(X0) | creative(X0) [cnf transformation 36]
98. ~rich(fred) | ~wise(fred) [cnf transformation 51]
99. ~rich(fred) | calm(fred) [cnf transformation 51]
119. ~happy(mary) [cnf transformation 23]
120. wise(X0) | ~tall(X0) | rich(X0) [duplicate literal removal 78]
122. ~wise(X0) | rich(X0) | ~tall(X0) [duplicate literal removal 82]
139. 4 <=> creative(mary) [avatar definition]
140. creative(mary) <- (4) [avatar component clause 139]
144. 5 <=> ! [X0] : ~funny(X0) [avatar definition]
145. ~funny(X0) <- (5) [avatar component clause 144]
147. 6 <=> tall(fred) [avatar definition]
149. tall(fred) <- (6) [avatar component clause 147]
150. 5 | 6 [avatar split clause 76,147,144]
152. 7 <=> ! [X0] : ~creative(X0) [avatar definition]
153. ~creative(X0) <- (7) [avatar component clause 152]
154. 7 | 6 [avatar split clause 75,147,152]
171. ~tall(X0) | rich(X0) [subsumption resolution 120,122]
173. 11 <=> ! [X0] : (~curious(X0) | creative(X0)) [avatar definition]
174. ~curious(X0) | creative(X0) <- (11) [avatar component clause 173]
176. 12 <=> strong(mary) [avatar definition]
178. ~strong(mary) <- (~12) [avatar component clause 176]
179. 11 | ~12 | 4 [avatar split clause 97,139,176,173]
181. 13 <=> calm(fred) [avatar definition]
182. ~calm(fred) <- (~13) [avatar component clause 181]
183. calm(fred) <- (13) [avatar component clause 181]
190. 15 <=> wise(fred) [avatar definition]
192. ~wise(fred) <- (~15) [avatar component clause 190]
195. 16 <=> rich(fred) [avatar definition]
197. ~rich(fred) <- (~16) [avatar component clause 195]
198. 13 | ~16 [avatar split clause 99,195,181]
199. ~15 | ~16 [avatar split clause 98,195,190]
246. funny(fred) <- (13) [resolution 70,183]
247. $false <- (5, 13) [subsumption resolution 246,145]
248. ~5 | ~13 [avatar contradiction clause 247]
256. wise(fred) <- (6) [resolution 89,149]
257. $false <- (6, ~15) [subsumption resolution 256,192]
258. ~6 | 15 [avatar contradiction clause 257]
274. calm(fred) | curious(fred) <- (~16) [resolution 94,197]
285. curious(fred) <- (~13, ~16) [subsumption resolution 274,182]
288. rich(fred) <- (6) [resolution 149,171]
290. $false <- (6, ~16) [subsumption resolution 288,197]
291. ~6 | 16 [avatar contradiction clause 290]
292. brave(X0) <- (5) [resolution 145,68]
299. strong(X0) | happy(X0) <- (5) [resolution 292,63]
300. happy(mary) <- (5, ~12) [resolution 299,178]
302. $false <- (5, ~12) [subsumption resolution 300,119]
303. ~5 | 12 [avatar contradiction clause 302]
304. $false <- (4, 7) [subsumption resolution 140,153]
305. ~4 | ~7 [avatar contradiction clause 304]
306. ~curious(X0) <- (7, 11) [subsumption resolution 174,153]
309. $false <- (7, 11, ~13, ~16) [resolution 306,285]
310. ~7 | ~11 | 13 | 16 [avatar contradiction clause 309]
313. $false [avatar sat refutation 150,154,179,198,199,248,258,291,303,305,310]
% SZS output end Proof for 4783442436031580706210849
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either rich or generous then someone is both not brave and not strong and vice versa. If susan is funny or brave then someone is not patient. Everyone who is not strong is both tall and not calm and vice versa. If alice is not happy or tall then someone is not kind or not calm. Everyone who is not rich is either patient or old. If lucy is calm then john is not strong or strong and vice versa. Everyone who is happy or creative is either not humble or not generous. Everyone who is either tall or not strong is both not funny and quiet and vice versa. Everyone who is both quiet and brave is not tall and vice versa. If fred is not curious or not tall then someone is patient and vice versa. If susan is either not kind or quiet then someone is both not quiet and patient. Everyone who is either not curious or not wise is both strong and not quiet and vice versa. If lucy is both not calm and not kind then someone is happy or not rich and vice versa. If someone is patient then paul is not wise and vice versa. If mary is rich then someone is either not funny or patient and vice versa. Everyone who is not strong or not humble is not brave and vice versa. Mary is either not humble or brave. Fred is curious. Someone is both not old and calm. Someone is not wise. Someone is calm. Someone is kind or not strong. Lucy is quiet or humble. | Alice is happy. | contradiction | ((?[X]:((rich(X)<~>generous(X))))<=>(?[X]:((~brave(X)&~strong(X)))))&
(((funny(susan)|brave(susan)))=>(?[X]:(~patient(X))))&
(![X]:(~strong(X)<=>(tall(X)&~calm(X))))&
(((~happy(alice)|tall(alice)))=>(?[X]:((~kind(X)|~calm(X)))))&
(![X]:(~rich(X)=>(patient(X)<~>old(X))))&
((calm(lucy))<=>((~strong(john)|strong(john))))&
(![X]:((happy(X)|creative(X))=>(~humble(X)<~>~generous(X))))&
(![X]:((tall(X)<~>~strong(X))<=>(~funny(X)&quiet(X))))&
(![X]:((quiet(X)&brave(X))<=>~tall(X)))&
(((~curious(fred)|~tall(fred)))<=>(?[X]:(patient(X))))&
(((~kind(susan)<~>quiet(susan)))=>(?[X]:((~quiet(X)&patient(X)))))&
(![X]:((~curious(X)<~>~wise(X))<=>(strong(X)&~quiet(X))))&
(((~calm(lucy)&~kind(lucy)))<=>(?[X]:((happy(X)|~rich(X)))))&
((?[X]:(patient(X)))<=>(~wise(paul)))&
((rich(mary))<=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:((~strong(X)|~humble(X))<=>~brave(X)))&
((~humble(mary)<~>brave(mary)))&
(curious(fred))&
(?[X]:((~old(X)&calm(X))))&
(?[X]:(~wise(X)))&
(?[X]:(calm(X)))&
(?[X]:((kind(X)|~strong(X))))&
((quiet(lucy)|humble(lucy))) | happy(alice) | [
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5866552762509070878275871
% SZS output start Proof for 5866552762509070878275871
6. calm(lucy) <=> (strong(john) | ~strong(john)) [input p5]
13. (~kind(lucy) & ~calm(lucy)) <=> ? [X0] : (~rich(X0) | happy(X0)) [input p12]
24. happy(alice) [input hypothesis]
44. (calm(lucy) | (~strong(john) & strong(john))) & ((strong(john) | ~strong(john)) | ~calm(lucy)) [nnf transformation 6]
45. (calm(lucy) | (~strong(john) & strong(john))) & (strong(john) | ~strong(john) | ~calm(lucy)) [flattening 44]
61. ((~kind(lucy) & ~calm(lucy)) | ! [X0] : (rich(X0) & ~happy(X0))) & (? [X0] : (~rich(X0) | happy(X0)) | (kind(lucy) | calm(lucy))) [nnf transformation 13]
62. ((~kind(lucy) & ~calm(lucy)) | ! [X0] : (rich(X0) & ~happy(X0))) & (? [X0] : (~rich(X0) | happy(X0)) | kind(lucy) | calm(lucy)) [flattening 61]
63. ((~kind(lucy) & ~calm(lucy)) | ! [X0] : (rich(X0) & ~happy(X0))) & (? [X1] : (~rich(X1) | happy(X1)) | kind(lucy) | calm(lucy)) [rectify 62]
64. ? [X1] : (~rich(X1) | happy(X1)) => (~rich(sK6) | happy(sK6)) [choice axiom]
65. ((~kind(lucy) & ~calm(lucy)) | ! [X0] : (rich(X0) & ~happy(X0))) & ((~rich(sK6) | happy(sK6)) | kind(lucy) | calm(lucy)) [skolemisation 63,64]
101. calm(lucy) | strong(john) [cnf transformation 45]
102. calm(lucy) | ~strong(john) [cnf transformation 45]
128. ~calm(lucy) | ~happy(X0) [cnf transformation 65]
150. happy(alice) [cnf transformation 24]
210. 14 <=> happy(alice) [avatar definition]
212. happy(alice) <- (14) [avatar component clause 210]
215. 15 <=> strong(john) [avatar definition]
219. 16 <=> calm(lucy) [avatar definition]
222. ~15 | 16 [avatar split clause 102,219,215]
223. 15 | 16 [avatar split clause 101,219,215]
273. 27 <=> ! [X0] : ~happy(X0) [avatar definition]
274. ~happy(X0) <- (27) [avatar component clause 273]
277. 27 | ~16 [avatar split clause 128,219,273]
347. 14 [avatar split clause 150,210]
348. $false <- (14, 27) [subsumption resolution 212,274]
349. ~14 | ~27 [avatar contradiction clause 348]
350. $false [avatar sat refutation 222,223,277,347,349]
% SZS output end Proof for 5866552762509070878275871
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or curious is both not kind and calm and vice versa.
If fred is both not wise and wise then someone is either not humble or not calm and vice versa.
Everyone who is happy is either funny or not patient and vice versa.
Everyone who is not calm is both kind and patient.
Everyone who is both wise and not generous is tall and vice versa.
Everyone who is either not funny or not patient is either old or not rich and vice versa.
If someone is both not creative and quiet then someone is both funny and not rich.
Everyone who is not creative is either not wise or quiet and vice versa.
If paul is kind or funny then susan is either funny or not quiet and vice versa.
If someone is either not old or not brave then alice is not wise or not humble and vice versa.
Everyone who is not kind or rich is both humble and not humble.
Everyone who is either not generous or not happy is either calm or not calm.
Everyone who is quiet is either rich or old.
If john is both rich and not tall then someone is humble.
Everyone who is not brave is not quiet or not curious and vice versa.
If someone is either not happy or not old then someone is not brave.
John is not happy or not rich.
Someone is either not humble or not old.
Mary is not calm.
Someone is either old or wise.
Lucy is both not funny and not strong.
Someone is quiet. | Lucy is wise. | neutral | (![X]:((calm(X)|curious(X))<=>(~kind(X)&calm(X))))&
(((~wise(fred)&wise(fred)))<=>(?[X]:((~humble(X)<~>~calm(X)))))&
(![X]:(happy(X)<=>(funny(X)<~>~patient(X))))&
(![X]:(~calm(X)=>(kind(X)&patient(X))))&
(![X]:((wise(X)&~generous(X))<=>tall(X)))&
(![X]:((~funny(X)<~>~patient(X))<=>(old(X)<~>~rich(X))))&
((?[X]:((~creative(X)&quiet(X))))=>(?[X]:((funny(X)&~rich(X)))))&
(![X]:(~creative(X)<=>(~wise(X)<~>quiet(X))))&
(((kind(paul)|funny(paul)))<=>((funny(susan)<~>~quiet(susan))))&
((?[X]:((~old(X)<~>~brave(X))))<=>((~wise(alice)|~humble(alice))))&
(![X]:((~kind(X)|rich(X))=>(humble(X)&~humble(X))))&
(![X]:((~generous(X)<~>~happy(X))=>(calm(X)<~>~calm(X))))&
(![X]:(quiet(X)=>(rich(X)<~>old(X))))&
(((rich(john)&~tall(john)))=>(?[X]:(humble(X))))&
(![X]:(~brave(X)<=>(~quiet(X)|~curious(X))))&
((?[X]:((~happy(X)<~>~old(X))))=>(?[X]:(~brave(X))))&
((~happy(john)|~rich(john)))&
(?[X]:((~humble(X)<~>~old(X))))&
(~calm(mary))&
(?[X]:((old(X)<~>wise(X))))&
((~funny(lucy)&~strong(lucy)))&
(?[X]:(quiet(X))) | wise(lucy) | [] | null | 0 |
If someone is either not curious or rich then lucy is both rich and quiet and vice versa.
Everyone who is both not strong and creative is either not curious or not brave.
Everyone who is not brave or not tall is both not old and rich and vice versa.
Everyone who is both creative and kind is not tall and vice versa.
Everyone who is either not quiet or not happy is not funny or generous and vice versa.
If lucy is both not tall and not curious then someone is both not strong and old.
If someone is both not quiet and not curious then susan is either not patient or brave.
Everyone who is not rich or not quiet is not tall and vice versa.
Everyone who is not happy is either patient or tall.
Everyone who is not funny is both not wise and quiet and vice versa.
Everyone who is not funny is both not strong and wise.
If someone is strong then susan is patient.
Everyone who is both kind and funny is both not happy and not brave.
Everyone who is not humble or patient is both kind and not quiet and vice versa.
Everyone who is not rich or not wise is wise or curious.
If susan is quiet then someone is not calm.
John is either calm or not tall.
John is both not quiet and not wise.
Someone is either not curious or not strong.
Lucy is not patient.
Mary is either brave or not quiet.
Susan is either strong or not quiet.
Alice is not humble or curious. | Susan is funny. | entailment | ((?[X]:((~curious(X)<~>rich(X))))<=>((rich(lucy)&quiet(lucy))))&
(![X]:((~strong(X)&creative(X))=>(~curious(X)<~>~brave(X))))&
(![X]:((~brave(X)|~tall(X))<=>(~old(X)&rich(X))))&
(![X]:((creative(X)&kind(X))<=>~tall(X)))&
(![X]:((~quiet(X)<~>~happy(X))<=>(~funny(X)|generous(X))))&
(((~tall(lucy)&~curious(lucy)))=>(?[X]:((~strong(X)&old(X)))))&
((?[X]:((~quiet(X)&~curious(X))))=>((~patient(susan)<~>brave(susan))))&
(![X]:((~rich(X)|~quiet(X))<=>~tall(X)))&
(![X]:(~happy(X)=>(patient(X)<~>tall(X))))&
(![X]:(~funny(X)<=>(~wise(X)&quiet(X))))&
(![X]:(~funny(X)=>(~strong(X)&wise(X))))&
((?[X]:(strong(X)))=>(patient(susan)))&
(![X]:((kind(X)&funny(X))=>(~happy(X)&~brave(X))))&
(![X]:((~humble(X)|patient(X))<=>(kind(X)&~quiet(X))))&
(![X]:((~rich(X)|~wise(X))=>(wise(X)|curious(X))))&
((quiet(susan))=>(?[X]:(~calm(X))))&
((calm(john)<~>~tall(john)))&
((~quiet(john)&~wise(john)))&
(?[X]:((~curious(X)<~>~strong(X))))&
(~patient(lucy))&
((brave(mary)<~>~quiet(mary)))&
((strong(susan)<~>~quiet(susan)))&
((~humble(alice)|curious(alice))) | funny(susan) | [
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2918562200286392023293112
% SZS output start Proof for 2918562200286392023293112
10. ! [X0] : (~funny(X0) <=> (quiet(X0) & ~wise(X0))) [input p9]
11. ! [X0] : (~funny(X0) => (wise(X0) & ~strong(X0))) [input p10]
24. ~funny(susan) [input hypothesis]
31. ! [X0] : ((wise(X0) & ~strong(X0)) | funny(X0)) [ennf transformation 11]
56. ! [X0] : ((~funny(X0) | (~quiet(X0) | wise(X0))) & ((quiet(X0) & ~wise(X0)) | funny(X0))) [nnf transformation 10]
57. ! [X0] : ((~funny(X0) | ~quiet(X0) | wise(X0)) & ((quiet(X0) & ~wise(X0)) | funny(X0))) [flattening 56]
99. ~wise(X0) | funny(X0) [cnf transformation 57]
103. wise(X0) | funny(X0) [cnf transformation 31]
127. ~funny(susan) [cnf transformation 24]
190. funny(X0) [subsumption resolution 103,99]
251. $false [subsumption resolution 127,190]
% SZS output end Proof for 2918562200286392023293112
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both kind and old then lucy is both wise and not strong and vice versa. If john is either not calm or not humble then lucy is not generous or not calm. If someone is both kind and not kind then paul is either not quiet or happy and vice versa. Everyone who is either not rich or not happy is not generous. Everyone who is either strong or calm is strong or not wise and vice versa. If fred is both not funny and happy then paul is not quiet or kind. If someone is both rich and not patient then susan is either not generous or not funny. Everyone who is rich is either not calm or rich and vice versa. If someone is both not curious and not calm then someone is not brave and vice versa. If someone is both kind and happy then fred is rich or creative and vice versa. If someone is both not rich and not calm then someone is both rich and creative. Everyone who is both not kind and not happy is either patient or not generous and vice versa. Everyone who is either wise or not tall is either patient or not generous and vice versa. Everyone who is either humble or quiet is not brave or not creative and vice versa. Everyone who is humble is not quiet. If lucy is both tall and rich then someone is either not funny or patient. Someone is both happy and not patient. Someone is both not funny and not old. Someone is not quiet. Paul is both not creative and humble. Susan is either funny or quiet. | Fred is not calm. | contradiction | ((?[X]:((kind(X)&old(X))))<=>((wise(lucy)&~strong(lucy))))&
(((~calm(john)<~>~humble(john)))=>((~generous(lucy)|~calm(lucy))))&
((?[X]:((kind(X)&~kind(X))))<=>((~quiet(paul)<~>happy(paul))))&
(![X]:((~rich(X)<~>~happy(X))=>~generous(X)))&
(![X]:((strong(X)<~>calm(X))<=>(strong(X)|~wise(X))))&
(((~funny(fred)&happy(fred)))=>((~quiet(paul)|kind(paul))))&
((?[X]:((rich(X)&~patient(X))))=>((~generous(susan)<~>~funny(susan))))&
(![X]:(rich(X)<=>(~calm(X)<~>rich(X))))&
((?[X]:((~curious(X)&~calm(X))))<=>(?[X]:(~brave(X))))&
((?[X]:((kind(X)&happy(X))))<=>((rich(fred)|creative(fred))))&
((?[X]:((~rich(X)&~calm(X))))=>(?[X]:((rich(X)&creative(X)))))&
(![X]:((~kind(X)&~happy(X))<=>(patient(X)<~>~generous(X))))&
(![X]:((wise(X)<~>~tall(X))<=>(patient(X)<~>~generous(X))))&
(![X]:((humble(X)<~>quiet(X))<=>(~brave(X)|~creative(X))))&
(![X]:(humble(X)=>~quiet(X)))&
(((tall(lucy)&rich(lucy)))=>(?[X]:((~funny(X)<~>patient(X)))))&
(?[X]:((happy(X)&~patient(X))))&
(?[X]:((~funny(X)&~old(X))))&
(?[X]:(~quiet(X)))&
((~creative(paul)&humble(paul)))&
((funny(susan)<~>quiet(susan))) | ~calm(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6977377104188032383248929
% SZS output start Proof for 6977377104188032383248929
8. ! [X0] : (rich(X0) <=> (~calm(X0) <~> rich(X0))) [input p7]
22. ~calm(fred) [input hypothesis]
49. ! [X0] : ((rich(X0) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0)))) & (((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | ~rich(X0))) [nnf transformation 8]
102. ~rich(X0) | calm(X0) | ~rich(X0) [cnf transformation 49]
103. rich(X0) | rich(X0) | calm(X0) [cnf transformation 49]
147. ~calm(fred) [cnf transformation 22]
148. ~rich(X0) | calm(X0) [duplicate literal removal 102]
149. rich(X0) | calm(X0) [duplicate literal removal 103]
236. calm(X0) [subsumption resolution 148,149]
288. $false [subsumption resolution 147,236]
% SZS output end Proof for 6977377104188032383248929
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or not strong is rich or funny and vice versa.
If someone is old or happy then paul is wise or brave.
Everyone who is either not old or not tall is generous or old and vice versa.
Everyone who is old is both not curious and quiet.
If someone is either quiet or not happy then someone is wise and vice versa.
Everyone who is both not humble and not tall is either not rich or tall.
Everyone who is rich or not quiet is both calm and happy.
Everyone who is calm is quiet and vice versa.
Everyone who is not strong is not funny and vice versa.
If someone is not strong then paul is humble.
Everyone who is either rich or not brave is either not old or creative and vice versa.
Everyone who is kind is both curious and not kind and vice versa.
If someone is either tall or quiet then someone is old.
Everyone who is either creative or not patient is both old and kind and vice versa.
Someone is not kind.
Someone is patient or funny.
Fred is not calm or patient.
Someone is either not curious or not creative.
Fred is not funny or generous. | Fred is not wise. | neutral | (![X]:((~quiet(X)|~strong(X))<=>(rich(X)|funny(X))))&
((?[X]:((old(X)|happy(X))))=>((wise(paul)|brave(paul))))&
(![X]:((~old(X)<~>~tall(X))<=>(generous(X)|old(X))))&
(![X]:(old(X)=>(~curious(X)&quiet(X))))&
((?[X]:((quiet(X)<~>~happy(X))))<=>(?[X]:(wise(X))))&
(![X]:((~humble(X)&~tall(X))=>(~rich(X)<~>tall(X))))&
(![X]:((rich(X)|~quiet(X))=>(calm(X)&happy(X))))&
(![X]:(calm(X)<=>quiet(X)))&
(![X]:(~strong(X)<=>~funny(X)))&
((?[X]:(~strong(X)))=>(humble(paul)))&
(![X]:((rich(X)<~>~brave(X))<=>(~old(X)<~>creative(X))))&
(![X]:(kind(X)<=>(curious(X)&~kind(X))))&
((?[X]:((tall(X)<~>quiet(X))))=>(?[X]:(old(X))))&
(![X]:((creative(X)<~>~patient(X))<=>(old(X)&kind(X))))&
(?[X]:(~kind(X)))&
(?[X]:((patient(X)|funny(X))))&
((~calm(fred)|patient(fred)))&
(?[X]:((~curious(X)<~>~creative(X))))&
((~funny(fred)|generous(fred))) | ~wise(fred) | [] | null | 0 |
Everyone who is either tall or generous is old and vice versa.
If someone is both not creative and brave then alice is both not old and not strong and vice versa.
If lucy is either strong or not funny then fred is kind or patient and vice versa.
If alice is both tall and not calm then someone is both happy and not quiet.
Everyone who is not tall is both wise and tall.
Everyone who is not generous is not wise or tall and vice versa.
Everyone who is either not calm or not wise is happy or calm.
Everyone who is old is not generous and vice versa.
Everyone who is quiet or old is either rich or not brave and vice versa.
Everyone who is not calm or patient is either not funny or not humble and vice versa.
Everyone who is either not rich or not quiet is wise or patient and vice versa.
Everyone who is curious is not wise and vice versa.
Everyone who is both generous and patient is not quiet or not strong.
Everyone who is calm or happy is either not tall or not happy and vice versa.
Everyone who is not old is either not brave or kind.
Everyone who is both not curious and strong is not quiet or patient and vice versa.
Alice is not rich or creative.
Someone is curious or kind.
Someone is either curious or not creative.
Someone is old.
Mary is happy or patient.
Lucy is not wise or strong. | Alice is patient. | neutral | (![X]:((tall(X)<~>generous(X))<=>old(X)))&
((?[X]:((~creative(X)&brave(X))))<=>((~old(alice)&~strong(alice))))&
(((strong(lucy)<~>~funny(lucy)))<=>((kind(fred)|patient(fred))))&
(((tall(alice)&~calm(alice)))=>(?[X]:((happy(X)&~quiet(X)))))&
(![X]:(~tall(X)=>(wise(X)&tall(X))))&
(![X]:(~generous(X)<=>(~wise(X)|tall(X))))&
(![X]:((~calm(X)<~>~wise(X))=>(happy(X)|calm(X))))&
(![X]:(old(X)<=>~generous(X)))&
(![X]:((quiet(X)|old(X))<=>(rich(X)<~>~brave(X))))&
(![X]:((~calm(X)|patient(X))<=>(~funny(X)<~>~humble(X))))&
(![X]:((~rich(X)<~>~quiet(X))<=>(wise(X)|patient(X))))&
(![X]:(curious(X)<=>~wise(X)))&
(![X]:((generous(X)&patient(X))=>(~quiet(X)|~strong(X))))&
(![X]:((calm(X)|happy(X))<=>(~tall(X)<~>~happy(X))))&
(![X]:(~old(X)=>(~brave(X)<~>kind(X))))&
(![X]:((~curious(X)&strong(X))<=>(~quiet(X)|patient(X))))&
((~rich(alice)|creative(alice)))&
(?[X]:((curious(X)|kind(X))))&
(?[X]:((curious(X)<~>~creative(X))))&
(?[X]:(old(X)))&
((happy(mary)|patient(mary)))&
((~wise(lucy)|strong(lucy))) | patient(alice) | [] | null | 0 |
Everyone who is either not kind or strong is either happy or brave and vice versa. Everyone who is happy or generous is both not humble and curious and vice versa. If susan is either not calm or not wise then susan is both quiet and rich. If paul is either calm or not tall then lucy is brave. If someone is either not wise or not brave then someone is both not generous and curious and vice versa. If someone is both not tall and humble then mary is either not patient or tall and vice versa. Everyone who is both generous and calm is funny and vice versa. Everyone who is either curious or old is both not kind and brave and vice versa. If mary is either funny or strong then someone is both humble and not wise. If someone is not rich then fred is either not creative or tall and vice versa. If someone is either quiet or not quiet then someone is not wise or creative. If mary is both patient and wise then lucy is either not kind or not humble and vice versa. Everyone who is both wise and patient is both calm and brave. Everyone who is both old and not tall is both tall and curious and vice versa. Everyone who is both brave and not wise is both old and patient. If someone is both not creative and not quiet then someone is not happy. Paul is either not curious or not funny. Mary is not funny or wise. Paul is both not humble and not happy. Someone is not humble. Someone is either tall or not curious. Someone is not funny or calm. Alice is humble. | Paul is not kind. | entailment | (![X]:((~kind(X)<~>strong(X))<=>(happy(X)<~>brave(X))))&
(![X]:((happy(X)|generous(X))<=>(~humble(X)&curious(X))))&
(((~calm(susan)<~>~wise(susan)))=>((quiet(susan)&rich(susan))))&
(((calm(paul)<~>~tall(paul)))=>(brave(lucy)))&
((?[X]:((~wise(X)<~>~brave(X))))<=>(?[X]:((~generous(X)&curious(X)))))&
((?[X]:((~tall(X)&humble(X))))<=>((~patient(mary)<~>tall(mary))))&
(![X]:((generous(X)&calm(X))<=>funny(X)))&
(![X]:((curious(X)<~>old(X))<=>(~kind(X)&brave(X))))&
(((funny(mary)<~>strong(mary)))=>(?[X]:((humble(X)&~wise(X)))))&
((?[X]:(~rich(X)))<=>((~creative(fred)<~>tall(fred))))&
((?[X]:((quiet(X)<~>~quiet(X))))=>(?[X]:((~wise(X)|creative(X)))))&
(((patient(mary)&wise(mary)))<=>((~kind(lucy)<~>~humble(lucy))))&
(![X]:((wise(X)&patient(X))=>(calm(X)&brave(X))))&
(![X]:((old(X)&~tall(X))<=>(tall(X)&curious(X))))&
(![X]:((brave(X)&~wise(X))=>(old(X)&patient(X))))&
((?[X]:((~creative(X)&~quiet(X))))=>(?[X]:(~happy(X))))&
((~curious(paul)<~>~funny(paul)))&
((~funny(mary)|wise(mary)))&
((~humble(paul)&~happy(paul)))&
(?[X]:(~humble(X)))&
(?[X]:((tall(X)<~>~curious(X))))&
(?[X]:((~funny(X)|calm(X))))&
(humble(alice)) | ~kind(paul) | [
"p1",
"p6",
"p7",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4602495362121810759977662
% SZS output start Proof for 4602495362121810759977662
2. ! [X0] : ((generous(X0) | happy(X0)) <=> (curious(X0) & ~humble(X0))) [input p1]
7. ! [X0] : ((calm(X0) & generous(X0)) <=> funny(X0)) [input p6]
8. ! [X0] : ((curious(X0) <~> old(X0)) <=> (brave(X0) & ~kind(X0))) [input p7]
14. ! [X0] : ((~tall(X0) & old(X0)) <=> (curious(X0) & tall(X0))) [input p13]
17. ~curious(paul) <~> ~funny(paul) [input p16]
24. kind(paul) [input hypothesis]
38. ! [X0] : (((generous(X0) | happy(X0)) | (~curious(X0) | humble(X0))) & ((curious(X0) & ~humble(X0)) | (~generous(X0) & ~happy(X0)))) [nnf transformation 2]
39. ! [X0] : ((generous(X0) | happy(X0) | ~curious(X0) | humble(X0)) & ((curious(X0) & ~humble(X0)) | (~generous(X0) & ~happy(X0)))) [flattening 38]
51. ! [X0] : (((calm(X0) & generous(X0)) | ~funny(X0)) & (funny(X0) | (~calm(X0) | ~generous(X0)))) [nnf transformation 7]
52. ! [X0] : (((calm(X0) & generous(X0)) | ~funny(X0)) & (funny(X0) | ~calm(X0) | ~generous(X0))) [flattening 51]
53. ! [X0] : ((((~old(X0) | ~curious(X0)) & (old(X0) | curious(X0))) | (~brave(X0) | kind(X0))) & ((brave(X0) & ~kind(X0)) | ((curious(X0) | ~old(X0)) & (old(X0) | ~curious(X0))))) [nnf transformation 8]
54. ! [X0] : ((((~old(X0) | ~curious(X0)) & (old(X0) | curious(X0))) | ~brave(X0) | kind(X0)) & ((brave(X0) & ~kind(X0)) | ((curious(X0) | ~old(X0)) & (old(X0) | ~curious(X0))))) [flattening 53]
68. ! [X0] : (((~tall(X0) & old(X0)) | (~curious(X0) | ~tall(X0))) & ((curious(X0) & tall(X0)) | (tall(X0) | ~old(X0)))) [nnf transformation 14]
69. ! [X0] : (((~tall(X0) & old(X0)) | ~curious(X0) | ~tall(X0)) & ((curious(X0) & tall(X0)) | tall(X0) | ~old(X0))) [flattening 68]
73. (funny(paul) | curious(paul)) & (~funny(paul) | ~curious(paul)) [nnf transformation 17]
92. ~generous(X0) | curious(X0) [cnf transformation 39]
113. ~funny(X0) | generous(X0) [cnf transformation 52]
115. ~curious(X0) | old(X0) | ~kind(X0) [cnf transformation 54]
139. tall(X0) | tall(X0) | ~old(X0) [cnf transformation 69]
142. ~tall(X0) | ~curious(X0) | ~tall(X0) [cnf transformation 69]
147. funny(paul) | curious(paul) [cnf transformation 73]
156. kind(paul) [cnf transformation 24]
157. ~old(X0) | tall(X0) [duplicate literal removal 139]
158. ~tall(X0) | ~curious(X0) [duplicate literal removal 142]
182. 5 <=> tall(paul) [avatar definition]
183. ~tall(paul) <- (~5) [avatar component clause 182]
184. tall(paul) <- (5) [avatar component clause 182]
333. 37 <=> curious(paul) [avatar definition]
334. ~curious(paul) <- (~37) [avatar component clause 333]
335. curious(paul) <- (37) [avatar component clause 333]
337. 38 <=> funny(paul) [avatar definition]
339. funny(paul) <- (38) [avatar component clause 337]
340. 37 | 38 [avatar split clause 147,337,333]
349. ~curious(paul) <- (5) [resolution 158,184]
352. ~37 | ~5 [avatar split clause 349,182,333]
364. old(paul) | ~kind(paul) <- (37) [resolution 115,335]
374. old(paul) <- (37) [subsumption resolution 364,156]
376. tall(paul) <- (37) [resolution 374,157]
377. $false <- (~5, 37) [subsumption resolution 376,183]
378. 5 | ~37 [avatar contradiction clause 377]
380. 41 <=> generous(paul) [avatar definition]
381. generous(paul) <- (41) [avatar component clause 380]
385. generous(paul) <- (38) [resolution 339,113]
386. 41 | ~38 [avatar split clause 385,337,380]
393. curious(paul) <- (41) [resolution 381,92]
394. $false <- (~37, 41) [subsumption resolution 393,334]
395. 37 | ~41 [avatar contradiction clause 394]
396. $false [avatar sat refutation 340,352,378,386,395]
% SZS output end Proof for 4602495362121810759977662
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both not curious and not old then someone is both calm and not old and vice versa. Everyone who is quiet or wise is both not rich and not old and vice versa. Everyone who is either humble or not happy is not strong. Everyone who is not rich or not quiet is either not kind or not generous. If lucy is creative or kind then john is both not calm and not creative and vice versa. Everyone who is not patient is strong or brave and vice versa. If fred is either not generous or not patient then someone is both kind and calm and vice versa. If someone is tall then mary is creative or not old and vice versa. If someone is rich or not brave then fred is not wise and vice versa. If lucy is either not patient or strong then someone is not patient or quiet. Everyone who is happy is both not funny and creative and vice versa. Everyone who is not brave is both not old and not strong. If lucy is not quiet or brave then someone is not kind or not brave and vice versa. If someone is both old and not happy then someone is both not creative and not rich. Everyone who is either curious or not tall is either not happy or kind and vice versa. Everyone who is both strong and not creative is both wise and generous and vice versa. Susan is not tall. Someone is either not curious or not kind. Someone is humble. Alice is both tall and not strong. Susan is strong. Someone is either not humble or strong. Susan is both not tall and kind. Paul is not generous or creative. | Susan is not creative. | contradiction | (((~curious(mary)&~old(mary)))<=>(?[X]:((calm(X)&~old(X)))))&
(![X]:((quiet(X)|wise(X))<=>(~rich(X)&~old(X))))&
(![X]:((humble(X)<~>~happy(X))=>~strong(X)))&
(![X]:((~rich(X)|~quiet(X))=>(~kind(X)<~>~generous(X))))&
(((creative(lucy)|kind(lucy)))<=>((~calm(john)&~creative(john))))&
(![X]:(~patient(X)<=>(strong(X)|brave(X))))&
(((~generous(fred)<~>~patient(fred)))<=>(?[X]:((kind(X)&calm(X)))))&
((?[X]:(tall(X)))<=>((creative(mary)|~old(mary))))&
((?[X]:((rich(X)|~brave(X))))<=>(~wise(fred)))&
(((~patient(lucy)<~>strong(lucy)))=>(?[X]:((~patient(X)|quiet(X)))))&
(![X]:(happy(X)<=>(~funny(X)&creative(X))))&
(![X]:(~brave(X)=>(~old(X)&~strong(X))))&
(((~quiet(lucy)|brave(lucy)))<=>(?[X]:((~kind(X)|~brave(X)))))&
((?[X]:((old(X)&~happy(X))))=>(?[X]:((~creative(X)&~rich(X)))))&
(![X]:((curious(X)<~>~tall(X))<=>(~happy(X)<~>kind(X))))&
(![X]:((strong(X)&~creative(X))<=>(wise(X)&generous(X))))&
(~tall(susan))&
(?[X]:((~curious(X)<~>~kind(X))))&
(?[X]:(humble(X)))&
((tall(alice)&~strong(alice)))&
(strong(susan))&
(?[X]:((~humble(X)<~>strong(X))))&
((~tall(susan)&kind(susan)))&
((~generous(paul)|creative(paul))) | ~creative(susan) | [
"p1",
"p3",
"p15",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8284504835386725020577841
% SZS output start Proof for 8284504835386725020577841
2. ! [X0] : ((wise(X0) | quiet(X0)) <=> (~old(X0) & ~rich(X0))) [input p1]
4. ! [X0] : ((~quiet(X0) | ~rich(X0)) => (~kind(X0) <~> ~generous(X0))) [input p3]
16. ! [X0] : ((~creative(X0) & strong(X0)) <=> (generous(X0) & wise(X0))) [input p15]
21. strong(susan) [input p20]
23. kind(susan) & ~tall(susan) [input p22]
25. ~creative(susan) [input hypothesis]
28. ! [X0] : ((~kind(X0) <~> ~generous(X0)) | (quiet(X0) & rich(X0))) [ennf transformation 4]
37. ! [X0] : (((wise(X0) | quiet(X0)) | (old(X0) | rich(X0))) & ((~old(X0) & ~rich(X0)) | (~wise(X0) & ~quiet(X0)))) [nnf transformation 2]
38. ! [X0] : ((wise(X0) | quiet(X0) | old(X0) | rich(X0)) & ((~old(X0) & ~rich(X0)) | (~wise(X0) & ~quiet(X0)))) [flattening 37]
40. ! [X0] : (((generous(X0) | kind(X0)) & (~generous(X0) | ~kind(X0))) | (quiet(X0) & rich(X0))) [nnf transformation 28]
72. ! [X0] : (((~creative(X0) & strong(X0)) | (~generous(X0) | ~wise(X0))) & ((generous(X0) & wise(X0)) | (creative(X0) | ~strong(X0)))) [nnf transformation 16]
73. ! [X0] : (((~creative(X0) & strong(X0)) | ~generous(X0) | ~wise(X0)) & ((generous(X0) & wise(X0)) | creative(X0) | ~strong(X0))) [flattening 72]
87. ~rich(X0) | ~wise(X0) [cnf transformation 38]
93. ~generous(X0) | ~kind(X0) | rich(X0) [cnf transformation 40]
138. ~strong(X0) | creative(X0) | wise(X0) [cnf transformation 73]
139. ~strong(X0) | creative(X0) | generous(X0) [cnf transformation 73]
148. strong(susan) [cnf transformation 21]
152. kind(susan) [cnf transformation 23]
154. ~creative(susan) [cnf transformation 25]
421. creative(susan) | wise(susan) [resolution 138,148]
422. wise(susan) [subsumption resolution 421,154]
423. creative(susan) | generous(susan) [resolution 139,148]
424. generous(susan) [subsumption resolution 423,154]
460. ~kind(susan) | rich(susan) [resolution 424,93]
462. rich(susan) [subsumption resolution 460,152]
552. ~wise(susan) [resolution 462,87]
554. $false [subsumption resolution 552,422]
% SZS output end Proof for 8284504835386725020577841
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is calm or not calm and vice versa.
Everyone who is both rich and not brave is not tall or brave and vice versa.
If someone is not wise then john is either not humble or brave and vice versa.
Everyone who is funny or not curious is either not funny or patient and vice versa.
If someone is both not quiet and happy then someone is not strong or generous.
Everyone who is creative is either not curious or curious and vice versa.
Everyone who is not wise is either happy or kind and vice versa.
If someone is old or not patient then someone is either not wise or rich and vice versa.
If susan is both not quiet and patient then susan is not old and vice versa.
If someone is either tall or not humble then susan is both not wise and humble and vice versa.
Everyone who is happy is not quiet or not generous.
If paul is both calm and not quiet then someone is not creative.
If alice is either patient or not calm then someone is curious.
If someone is both rich and not wise then mary is kind or not wise.
Everyone who is funny or not old is either calm or not humble and vice versa.
Everyone who is both humble and not humble is either not quiet or not strong and vice versa.
Someone is both tall and not quiet.
Fred is not humble.
Someone is kind.
Someone is not strong or wise.
Lucy is not generous or not humble.
John is either creative or funny.
Someone is strong. | Fred is not tall. | neutral | (![X]:(patient(X)<=>(calm(X)|~calm(X))))&
(![X]:((rich(X)&~brave(X))<=>(~tall(X)|brave(X))))&
((?[X]:(~wise(X)))<=>((~humble(john)<~>brave(john))))&
(![X]:((funny(X)|~curious(X))<=>(~funny(X)<~>patient(X))))&
((?[X]:((~quiet(X)&happy(X))))=>(?[X]:((~strong(X)|generous(X)))))&
(![X]:(creative(X)<=>(~curious(X)<~>curious(X))))&
(![X]:(~wise(X)<=>(happy(X)<~>kind(X))))&
((?[X]:((old(X)|~patient(X))))<=>(?[X]:((~wise(X)<~>rich(X)))))&
(((~quiet(susan)&patient(susan)))<=>(~old(susan)))&
((?[X]:((tall(X)<~>~humble(X))))<=>((~wise(susan)&humble(susan))))&
(![X]:(happy(X)=>(~quiet(X)|~generous(X))))&
(((calm(paul)&~quiet(paul)))=>(?[X]:(~creative(X))))&
(((patient(alice)<~>~calm(alice)))=>(?[X]:(curious(X))))&
((?[X]:((rich(X)&~wise(X))))=>((kind(mary)|~wise(mary))))&
(![X]:((funny(X)|~old(X))<=>(calm(X)<~>~humble(X))))&
(![X]:((humble(X)&~humble(X))<=>(~quiet(X)<~>~strong(X))))&
(?[X]:((tall(X)&~quiet(X))))&
(~humble(fred))&
(?[X]:(kind(X)))&
(?[X]:((~strong(X)|wise(X))))&
((~generous(lucy)|~humble(lucy)))&
((creative(john)<~>funny(john)))&
(?[X]:(strong(X))) | ~tall(fred) | [] | null | 0 |
Everyone who is either old or patient is not strong or not creative and vice versa.
Everyone who is kind or not rich is either not curious or curious.
If susan is both calm and not creative then paul is creative.
Everyone who is both not curious and curious is quiet.
If someone is quiet or funny then someone is rich and vice versa.
Everyone who is either funny or tall is rich or brave and vice versa.
Everyone who is either wise or not calm is not quiet and vice versa.
Everyone who is either not quiet or not creative is generous.
Everyone who is creative is either funny or old and vice versa.
If someone is not old or creative then someone is either tall or not kind and vice versa.
Everyone who is both creative and calm is old.
If someone is both not quiet and not calm then fred is not old or calm and vice versa.
Everyone who is both not creative and kind is not calm or rich and vice versa.
If alice is both old and not calm then someone is quiet or happy and vice versa.
Everyone who is kind is both quiet and generous.
If someone is both not kind and not calm then someone is both not curious and not tall and vice versa.
Paul is both quiet and funny.
Lucy is strong or not patient.
Someone is strong or not humble.
Fred is both brave and not calm.
John is both curious and not kind.
John is not quiet.
Someone is generous.
Paul is not brave or not tall. | Alice is not generous. | contradiction | (![X]:((old(X)<~>patient(X))<=>(~strong(X)|~creative(X))))&
(![X]:((kind(X)|~rich(X))=>(~curious(X)<~>curious(X))))&
(((calm(susan)&~creative(susan)))=>(creative(paul)))&
(![X]:((~curious(X)&curious(X))=>quiet(X)))&
((?[X]:((quiet(X)|funny(X))))<=>(?[X]:(rich(X))))&
(![X]:((funny(X)<~>tall(X))<=>(rich(X)|brave(X))))&
(![X]:((wise(X)<~>~calm(X))<=>~quiet(X)))&
(![X]:((~quiet(X)<~>~creative(X))=>generous(X)))&
(![X]:(creative(X)<=>(funny(X)<~>old(X))))&
((?[X]:((~old(X)|creative(X))))<=>(?[X]:((tall(X)<~>~kind(X)))))&
(![X]:((creative(X)&calm(X))=>old(X)))&
((?[X]:((~quiet(X)&~calm(X))))<=>((~old(fred)|calm(fred))))&
(![X]:((~creative(X)&kind(X))<=>(~calm(X)|rich(X))))&
(((old(alice)&~calm(alice)))<=>(?[X]:((quiet(X)|happy(X)))))&
(![X]:(kind(X)=>(quiet(X)&generous(X))))&
((?[X]:((~kind(X)&~calm(X))))<=>(?[X]:((~curious(X)&~tall(X)))))&
((quiet(paul)&funny(paul)))&
((strong(lucy)|~patient(lucy)))&
(?[X]:((strong(X)|~humble(X))))&
((brave(fred)&~calm(fred)))&
((curious(john)&~kind(john)))&
(~quiet(john))&
(?[X]:(generous(X)))&
((~brave(paul)|~tall(paul))) | ~generous(alice) | [
"p12",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8794258556997501370236007
% SZS output start Proof for 8794258556997501370236007
13. ! [X0] : ((kind(X0) & ~creative(X0)) <=> (rich(X0) | ~calm(X0))) [input p12]
14. (~calm(alice) & old(alice)) <=> ? [X0] : (happy(X0) | quiet(X0)) [input p13]
15. ! [X0] : (kind(X0) => (generous(X0) & quiet(X0))) [input p14]
17. funny(paul) & quiet(paul) [input p16]
25. ~generous(alice) [input hypothesis]
38. ! [X0] : ((generous(X0) & quiet(X0)) | ~kind(X0)) [ennf transformation 15]
62. ! [X0] : (((kind(X0) & ~creative(X0)) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | (~kind(X0) | creative(X0)))) [nnf transformation 13]
63. ! [X0] : (((kind(X0) & ~creative(X0)) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ~kind(X0) | creative(X0))) [flattening 62]
64. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & (? [X0] : (happy(X0) | quiet(X0)) | (calm(alice) | ~old(alice))) [nnf transformation 14]
65. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & (? [X0] : (happy(X0) | quiet(X0)) | calm(alice) | ~old(alice)) [flattening 64]
66. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & (? [X1] : (happy(X1) | quiet(X1)) | calm(alice) | ~old(alice)) [rectify 65]
67. ? [X1] : (happy(X1) | quiet(X1)) => (happy(sK5) | quiet(sK5)) [choice axiom]
68. ((~calm(alice) & old(alice)) | ! [X0] : (~happy(X0) & ~quiet(X0))) & ((happy(sK5) | quiet(sK5)) | calm(alice) | ~old(alice)) [skolemisation 66,67]
122. calm(X0) | kind(X0) [cnf transformation 63]
127. ~calm(alice) | ~quiet(X0) [cnf transformation 68]
130. ~kind(X0) | generous(X0) [cnf transformation 38]
135. quiet(paul) [cnf transformation 17]
145. ~generous(alice) [cnf transformation 25]
180. 9 <=> ! [X3] : ~quiet(X3) [avatar definition]
181. ~quiet(X3) <- (9) [avatar component clause 180]
245. 24 <=> calm(alice) [avatar definition]
247. ~calm(alice) <- (~24) [avatar component clause 245]
249. 9 | ~24 [avatar split clause 127,245,180]
303. $false <- (9) [resolution 181,135]
304. ~9 [avatar contradiction clause 303]
308. kind(alice) <- (~24) [resolution 122,247]
318. generous(alice) <- (~24) [resolution 308,130]
320. $false <- (~24) [subsumption resolution 318,145]
321. 24 [avatar contradiction clause 320]
322. $false [avatar sat refutation 249,304,321]
% SZS output end Proof for 8794258556997501370236007
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both generous and patient is both old and not kind and vice versa.
Everyone who is not funny is either not old or not curious and vice versa.
If someone is creative then fred is either happy or kind and vice versa.
If fred is curious or strong then someone is humble.
If fred is not tall or not kind then mary is not tall and vice versa.
Everyone who is not generous or not kind is both quiet and brave and vice versa.
Everyone who is both wise and not strong is either not old or not humble and vice versa.
If someone is either curious or quiet then mary is not happy or not quiet and vice versa.
If john is not happy then someone is either happy or not strong.
If fred is strong or not rich then someone is either calm or tall and vice versa.
If paul is either not brave or creative then someone is not kind or not strong.
Everyone who is both not patient and not old is brave or not creative and vice versa.
If mary is not wise then susan is either not brave or not humble.
Everyone who is both kind and not tall is either humble or not strong.
Everyone who is either funny or not patient is not brave or humble.
Everyone who is old or not happy is both not curious and not generous.
Someone is not strong or not wise.
Someone is both not tall and not kind.
Lucy is not humble.
John is kind.
Paul is humble.
Someone is quiet.
Alice is both not kind and strong.
Paul is not kind. | Fred is old. | contradiction | (![X]:((generous(X)&patient(X))<=>(old(X)&~kind(X))))&
(![X]:(~funny(X)<=>(~old(X)<~>~curious(X))))&
((?[X]:(creative(X)))<=>((happy(fred)<~>kind(fred))))&
(((curious(fred)|strong(fred)))=>(?[X]:(humble(X))))&
(((~tall(fred)|~kind(fred)))<=>(~tall(mary)))&
(![X]:((~generous(X)|~kind(X))<=>(quiet(X)&brave(X))))&
(![X]:((wise(X)&~strong(X))<=>(~old(X)<~>~humble(X))))&
((?[X]:((curious(X)<~>quiet(X))))<=>((~happy(mary)|~quiet(mary))))&
((~happy(john))=>(?[X]:((happy(X)<~>~strong(X)))))&
(((strong(fred)|~rich(fred)))<=>(?[X]:((calm(X)<~>tall(X)))))&
(((~brave(paul)<~>creative(paul)))=>(?[X]:((~kind(X)|~strong(X)))))&
(![X]:((~patient(X)&~old(X))<=>(brave(X)|~creative(X))))&
((~wise(mary))=>((~brave(susan)<~>~humble(susan))))&
(![X]:((kind(X)&~tall(X))=>(humble(X)<~>~strong(X))))&
(![X]:((funny(X)<~>~patient(X))=>(~brave(X)|humble(X))))&
(![X]:((old(X)|~happy(X))=>(~curious(X)&~generous(X))))&
(?[X]:((~strong(X)|~wise(X))))&
(?[X]:((~tall(X)&~kind(X))))&
(~humble(lucy))&
(kind(john))&
(humble(paul))&
(?[X]:(quiet(X)))&
((~kind(alice)&strong(alice)))&
(~kind(paul)) | old(fred) | [
"p5",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2216950061054562269547387
% SZS output start Proof for 2216950061054562269547387
6. ! [X0] : ((~kind(X0) | ~generous(X0)) <=> (brave(X0) & quiet(X0))) [input p5]
12. ! [X0] : ((~old(X0) & ~patient(X0)) <=> (~creative(X0) | brave(X0))) [input p11]
16. ! [X0] : ((~happy(X0) | old(X0)) => (~generous(X0) & ~curious(X0))) [input p15]
25. old(fred) [input hypothesis]
34. ! [X0] : ((~generous(X0) & ~curious(X0)) | (happy(X0) & ~old(X0))) [ennf transformation 16]
46. ! [X0] : (((~kind(X0) | ~generous(X0)) | (~brave(X0) | ~quiet(X0))) & ((brave(X0) & quiet(X0)) | (kind(X0) & generous(X0)))) [nnf transformation 6]
47. ! [X0] : ((~kind(X0) | ~generous(X0) | ~brave(X0) | ~quiet(X0)) & ((brave(X0) & quiet(X0)) | (kind(X0) & generous(X0)))) [flattening 46]
66. ! [X0] : (((~old(X0) & ~patient(X0)) | (creative(X0) & ~brave(X0))) & ((~creative(X0) | brave(X0)) | (old(X0) | patient(X0)))) [nnf transformation 12]
67. ! [X0] : (((~old(X0) & ~patient(X0)) | (creative(X0) & ~brave(X0))) & (~creative(X0) | brave(X0) | old(X0) | patient(X0))) [flattening 66]
96. brave(X0) | generous(X0) [cnf transformation 47]
124. ~brave(X0) | ~old(X0) [cnf transformation 67]
134. ~generous(X0) | ~old(X0) [cnf transformation 34]
146. old(fred) [cnf transformation 25]
306. ~old(X1) | generous(X1) [resolution 124,96]
307. ~old(X1) [subsumption resolution 306,134]
308. $false [resolution 307,146]
% SZS output end Proof for 2216950061054562269547387
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not old is both not tall and not curious and vice versa.
If someone is both patient and happy then someone is either not happy or not calm.
If lucy is not funny then fred is either not strong or not quiet and vice versa.
Everyone who is calm is brave and vice versa.
If someone is tall or happy then someone is either tall or not funny and vice versa.
Everyone who is both kind and not funny is not tall and vice versa.
If john is patient or not tall then someone is not generous or not quiet and vice versa.
Everyone who is both kind and happy is not kind or happy and vice versa.
Everyone who is both not patient and not brave is both not curious and not creative.
If mary is both patient and curious then someone is either not humble or not generous and vice versa.
If someone is old then susan is both funny and not brave.
If someone is not old or not humble then john is not generous and vice versa.
If someone is funny then someone is both not creative and not old.
If alice is both kind and not creative then lucy is both not generous and kind.
If john is not kind or not brave then john is both not quiet and not happy and vice versa.
Everyone who is brave is both not old and not strong and vice versa.
Mary is either not kind or funny.
Someone is both not calm and rich.
John is either not calm or curious.
Someone is both calm and kind.
Someone is either strong or quiet.
Fred is rich. | Susan is wise. | contradiction | (![X]:((wise(X)|~old(X))<=>(~tall(X)&~curious(X))))&
((?[X]:((patient(X)&happy(X))))=>(?[X]:((~happy(X)<~>~calm(X)))))&
((~funny(lucy))<=>((~strong(fred)<~>~quiet(fred))))&
(![X]:(calm(X)<=>brave(X)))&
((?[X]:((tall(X)|happy(X))))<=>(?[X]:((tall(X)<~>~funny(X)))))&
(![X]:((kind(X)&~funny(X))<=>~tall(X)))&
(((patient(john)|~tall(john)))<=>(?[X]:((~generous(X)|~quiet(X)))))&
(![X]:((kind(X)&happy(X))<=>(~kind(X)|happy(X))))&
(![X]:((~patient(X)&~brave(X))=>(~curious(X)&~creative(X))))&
(((patient(mary)&curious(mary)))<=>(?[X]:((~humble(X)<~>~generous(X)))))&
((?[X]:(old(X)))=>((funny(susan)&~brave(susan))))&
((?[X]:((~old(X)|~humble(X))))<=>(~generous(john)))&
((?[X]:(funny(X)))=>(?[X]:((~creative(X)&~old(X)))))&
(((kind(alice)&~creative(alice)))=>((~generous(lucy)&kind(lucy))))&
(((~kind(john)|~brave(john)))<=>((~quiet(john)&~happy(john))))&
(![X]:(brave(X)<=>(~old(X)&~strong(X))))&
((~kind(mary)<~>funny(mary)))&
(?[X]:((~calm(X)&rich(X))))&
((~calm(john)<~>curious(john)))&
(?[X]:((calm(X)&kind(X))))&
(?[X]:((strong(X)<~>quiet(X))))&
(rich(fred)) | wise(susan) | [
"p0",
"p5",
"p7",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1894681468501396904424077
% SZS output start Proof for 1894681468501396904424077
1. ! [X0] : ((~old(X0) | wise(X0)) <=> (~curious(X0) & ~tall(X0))) [input p0]
6. ! [X0] : ((~funny(X0) & kind(X0)) <=> ~tall(X0)) [input p5]
8. ! [X0] : ((happy(X0) & kind(X0)) <=> (happy(X0) | ~kind(X0))) [input p7]
11. ? [X0] : old(X0) => (~brave(susan) & funny(susan)) [input p10]
17. ~kind(mary) <~> funny(mary) [input p16]
23. wise(susan) [input hypothesis]
32. (~brave(susan) & funny(susan)) | ! [X0] : ~old(X0) [ennf transformation 11]
36. ! [X0] : (((~old(X0) | wise(X0)) | (curious(X0) | tall(X0))) & ((~curious(X0) & ~tall(X0)) | (old(X0) & ~wise(X0)))) [nnf transformation 1]
37. ! [X0] : ((~old(X0) | wise(X0) | curious(X0) | tall(X0)) & ((~curious(X0) & ~tall(X0)) | (old(X0) & ~wise(X0)))) [flattening 36]
49. ! [X0] : (((~funny(X0) & kind(X0)) | tall(X0)) & (~tall(X0) | (funny(X0) | ~kind(X0)))) [nnf transformation 6]
50. ! [X0] : (((~funny(X0) & kind(X0)) | tall(X0)) & (~tall(X0) | funny(X0) | ~kind(X0))) [flattening 49]
56. ! [X0] : (((happy(X0) & kind(X0)) | (~happy(X0) & kind(X0))) & ((happy(X0) | ~kind(X0)) | (~happy(X0) | ~kind(X0)))) [nnf transformation 8]
57. ! [X0] : (((happy(X0) & kind(X0)) | (~happy(X0) & kind(X0))) & (happy(X0) | ~kind(X0) | ~happy(X0) | ~kind(X0))) [flattening 56]
74. (~funny(mary) | kind(mary)) & (funny(mary) | ~kind(mary)) [nnf transformation 17]
83. ~tall(X0) | ~wise(X0) [cnf transformation 37]
84. ~tall(X0) | old(X0) [cnf transformation 37]
104. ~funny(X0) | tall(X0) [cnf transformation 50]
111. kind(X0) | ~happy(X0) [cnf transformation 57]
112. kind(X0) | happy(X0) [cnf transformation 57]
122. funny(susan) | ~old(X0) [cnf transformation 32]
139. funny(mary) | ~kind(mary) [cnf transformation 74]
148. wise(susan) [cnf transformation 23]
240. kind(X0) [subsumption resolution 111,112]
270. 27 <=> ! [X0] : ~old(X0) [avatar definition]
271. ~old(X0) <- (27) [avatar component clause 270]
278. 29 <=> funny(susan) [avatar definition]
280. funny(susan) <- (29) [avatar component clause 278]
281. 27 | 29 [avatar split clause 122,278,270]
342. funny(mary) [subsumption resolution 139,240]
369. tall(mary) [resolution 104,342]
370. old(mary) [resolution 369,84]
372. $false <- (27) [subsumption resolution 370,271]
373. ~27 [avatar contradiction clause 372]
374. tall(susan) <- (29) [resolution 280,104]
377. ~wise(susan) <- (29) [resolution 374,83]
378. $false <- (29) [subsumption resolution 377,148]
379. ~29 [avatar contradiction clause 378]
380. $false [avatar sat refutation 281,373,379]
% SZS output end Proof for 1894681468501396904424077
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not calm then john is both humble and tall.
If someone is both not brave and happy then alice is both not strong and quiet.
If alice is humble then someone is patient or rich and vice versa.
Everyone who is either not kind or calm is both not tall and not rich and vice versa.
If someone is not tall then someone is either not rich or not brave.
If someone is not generous then someone is not old.
Everyone who is both quiet and not tall is not quiet and vice versa.
Everyone who is both not rich and curious is either tall or not quiet and vice versa.
If lucy is both not kind and not old then someone is either not kind or wise.
If alice is either not old or not wise then alice is quiet or patient and vice versa.
If alice is brave or strong then paul is not patient and vice versa.
Everyone who is either not generous or kind is not strong.
If someone is patient then someone is calm or not generous.
Everyone who is both generous and not wise is either old or happy.
Everyone who is not funny is both funny and not patient and vice versa.
Everyone who is generous or not calm is both not quiet and funny and vice versa.
Fred is either not strong or not brave.
John is tall or not curious.
Someone is not wise.
Someone is either brave or not brave.
Someone is quiet. | John is not generous. | entailment | ((~calm(lucy))=>((humble(john)&tall(john))))&
((?[X]:((~brave(X)&happy(X))))=>((~strong(alice)&quiet(alice))))&
((humble(alice))<=>(?[X]:((patient(X)|rich(X)))))&
(![X]:((~kind(X)<~>calm(X))<=>(~tall(X)&~rich(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~rich(X)<~>~brave(X)))))&
((?[X]:(~generous(X)))=>(?[X]:(~old(X))))&
(![X]:((quiet(X)&~tall(X))<=>~quiet(X)))&
(![X]:((~rich(X)&curious(X))<=>(tall(X)<~>~quiet(X))))&
(((~kind(lucy)&~old(lucy)))=>(?[X]:((~kind(X)<~>wise(X)))))&
(((~old(alice)<~>~wise(alice)))<=>((quiet(alice)|patient(alice))))&
(((brave(alice)|strong(alice)))<=>(~patient(paul)))&
(![X]:((~generous(X)<~>kind(X))=>~strong(X)))&
((?[X]:(patient(X)))=>(?[X]:((calm(X)|~generous(X)))))&
(![X]:((generous(X)&~wise(X))=>(old(X)<~>happy(X))))&
(![X]:(~funny(X)<=>(funny(X)&~patient(X))))&
(![X]:((generous(X)|~calm(X))<=>(~quiet(X)&funny(X))))&
((~strong(fred)<~>~brave(fred)))&
((tall(john)|~curious(john)))&
(?[X]:(~wise(X)))&
(?[X]:((brave(X)<~>~brave(X))))&
(?[X]:(quiet(X))) | ~generous(john) | [
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 93828512409772725452786
% SZS output start Proof for 93828512409772725452786
7. ! [X0] : ((~tall(X0) & quiet(X0)) <=> ~quiet(X0)) [input p6]
16. ! [X0] : ((~calm(X0) | generous(X0)) <=> (funny(X0) & ~quiet(X0))) [input p15]
22. generous(john) [input hypothesis]
49. ! [X0] : (((~tall(X0) & quiet(X0)) | quiet(X0)) & (~quiet(X0) | (tall(X0) | ~quiet(X0)))) [nnf transformation 7]
50. ! [X0] : (((~tall(X0) & quiet(X0)) | quiet(X0)) & (~quiet(X0) | tall(X0) | ~quiet(X0))) [flattening 49]
67. ! [X0] : (((~calm(X0) | generous(X0)) | (~funny(X0) | quiet(X0))) & ((funny(X0) & ~quiet(X0)) | (calm(X0) & ~generous(X0)))) [nnf transformation 16]
68. ! [X0] : ((~calm(X0) | generous(X0) | ~funny(X0) | quiet(X0)) & ((funny(X0) & ~quiet(X0)) | (calm(X0) & ~generous(X0)))) [flattening 67]
94. quiet(X0) | quiet(X0) [cnf transformation 50]
121. ~quiet(X0) | ~generous(X0) [cnf transformation 68]
133. generous(john) [cnf transformation 22]
137. quiet(X0) [duplicate literal removal 94]
269. ~generous(X0) [subsumption resolution 121,137]
285. $false [subsumption resolution 133,269]
% SZS output end Proof for 93828512409772725452786
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not calm and curious then fred is both not tall and not generous.
Everyone who is tall or not wise is both quiet and not happy.
If paul is both not creative and generous then someone is curious or not rich.
Everyone who is not calm or not wise is not happy or patient.
Everyone who is both happy and not wise is either not curious or not patient and vice versa.
If fred is not funny then paul is both not funny and quiet.
Everyone who is both not patient and wise is either not rich or humble and vice versa.
Everyone who is strong or tall is either not strong or happy and vice versa.
Everyone who is not patient is both generous and strong.
Everyone who is either kind or brave is both not rich and not funny and vice versa.
Everyone who is either not wise or rich is not happy.
If someone is both tall and strong then someone is generous or tall and vice versa.
If someone is both not quiet and humble then alice is not strong or not patient.
Everyone who is both creative and tall is either old or not old.
Everyone who is not rich is either not calm or kind and vice versa.
Everyone who is strong or not funny is quiet or not tall and vice versa.
Someone is not brave or not quiet.
Fred is not quiet or generous.
Someone is both quiet and curious.
Someone is not strong or quiet.
Susan is not rich or patient.
Someone is both strong and not kind.
Someone is either quiet or not quiet. | Paul is not curious. | contradiction | (((~calm(fred)&curious(fred)))=>((~tall(fred)&~generous(fred))))&
(![X]:((tall(X)|~wise(X))=>(quiet(X)&~happy(X))))&
(((~creative(paul)&generous(paul)))=>(?[X]:((curious(X)|~rich(X)))))&
(![X]:((~calm(X)|~wise(X))=>(~happy(X)|patient(X))))&
(![X]:((happy(X)&~wise(X))<=>(~curious(X)<~>~patient(X))))&
((~funny(fred))=>((~funny(paul)&quiet(paul))))&
(![X]:((~patient(X)&wise(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((strong(X)|tall(X))<=>(~strong(X)<~>happy(X))))&
(![X]:(~patient(X)=>(generous(X)&strong(X))))&
(![X]:((kind(X)<~>brave(X))<=>(~rich(X)&~funny(X))))&
(![X]:((~wise(X)<~>rich(X))=>~happy(X)))&
((?[X]:((tall(X)&strong(X))))<=>(?[X]:((generous(X)|tall(X)))))&
((?[X]:((~quiet(X)&humble(X))))=>((~strong(alice)|~patient(alice))))&
(![X]:((creative(X)&tall(X))=>(old(X)<~>~old(X))))&
(![X]:(~rich(X)<=>(~calm(X)<~>kind(X))))&
(![X]:((strong(X)|~funny(X))<=>(quiet(X)|~tall(X))))&
(?[X]:((~brave(X)|~quiet(X))))&
((~quiet(fred)|generous(fred)))&
(?[X]:((quiet(X)&curious(X))))&
(?[X]:((~strong(X)|quiet(X))))&
((~rich(susan)|patient(susan)))&
(?[X]:((strong(X)&~kind(X))))&
(?[X]:((quiet(X)<~>~quiet(X)))) | ~curious(paul) | [
"p1",
"p4",
"p7",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6251008488639189198433063
% SZS output start Proof for 6251008488639189198433063
2. ! [X0] : ((~wise(X0) | tall(X0)) => (~happy(X0) & quiet(X0))) [input p1]
5. ! [X0] : ((~wise(X0) & happy(X0)) <=> (~curious(X0) <~> ~patient(X0))) [input p4]
8. ! [X0] : ((tall(X0) | strong(X0)) <=> (~strong(X0) <~> happy(X0))) [input p7]
9. ! [X0] : (~patient(X0) => (strong(X0) & generous(X0))) [input p8]
12. ? [X0] : (strong(X0) & tall(X0)) <=> ? [X0] : (tall(X0) | generous(X0)) [input p11]
24. ~curious(paul) [input hypothesis]
25. ? [X0] : (strong(X0) & tall(X0)) <=> ? [X1] : (tall(X1) | generous(X1)) [rectify 12]
28. ! [X0] : ((~happy(X0) & quiet(X0)) | (wise(X0) & ~tall(X0))) [ennf transformation 2]
34. ! [X0] : ((strong(X0) & generous(X0)) | patient(X0)) [ennf transformation 9]
42. ! [X0] : (((~wise(X0) & happy(X0)) | ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0)))) & (((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | (wise(X0) | ~happy(X0)))) [nnf transformation 5]
43. ! [X0] : (((~wise(X0) & happy(X0)) | ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0)))) & (((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | wise(X0) | ~happy(X0))) [flattening 42]
46. ! [X0] : (((tall(X0) | strong(X0)) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0)))) & (((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | (~tall(X0) & ~strong(X0)))) [nnf transformation 8]
47. ! [X0] : ((tall(X0) | strong(X0) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0)))) & (((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | (~tall(X0) & ~strong(X0)))) [flattening 46]
51. (? [X0] : (strong(X0) & tall(X0)) | ! [X1] : (~tall(X1) & ~generous(X1))) & (? [X1] : (tall(X1) | generous(X1)) | ! [X0] : (~strong(X0) | ~tall(X0))) [nnf transformation 25]
52. (? [X0] : (strong(X0) & tall(X0)) | ! [X1] : (~tall(X1) & ~generous(X1))) & (? [X2] : (tall(X2) | generous(X2)) | ! [X3] : (~strong(X3) | ~tall(X3))) [rectify 51]
53. ? [X0] : (strong(X0) & tall(X0)) => (strong(sK1) & tall(sK1)) [choice axiom]
54. ? [X2] : (tall(X2) | generous(X2)) => (tall(sK2) | generous(sK2)) [choice axiom]
55. ((strong(sK1) & tall(sK1)) | ! [X1] : (~tall(X1) & ~generous(X1))) & ((tall(sK2) | generous(sK2)) | ! [X3] : (~strong(X3) | ~tall(X3))) [skolemisation 52,54,53]
75. ~happy(X0) | ~tall(X0) [cnf transformation 28]
76. ~happy(X0) | wise(X0) [cnf transformation 28]
82. ~patient(X0) | happy(X0) | curious(X0) [cnf transformation 43]
84. ~patient(X0) | ~wise(X0) | curious(X0) [cnf transformation 43]
95. happy(X0) | ~strong(X0) | ~tall(X0) [cnf transformation 47]
100. patient(X0) | generous(X0) [cnf transformation 34]
111. tall(sK1) | ~generous(X1) [cnf transformation 55]
113. strong(sK1) | ~generous(X1) [cnf transformation 55]
136. ~curious(paul) [cnf transformation 24]
188. ~strong(X0) | ~tall(X0) [subsumption resolution 95,75]
194. 13 <=> strong(sK1) [avatar definition]
196. strong(sK1) <- (13) [avatar component clause 194]
199. 14 <=> ! [X1] : ~generous(X1) [avatar definition]
200. ~generous(X1) <- (14) [avatar component clause 199]
201. 14 | 13 [avatar split clause 113,194,199]
203. 15 <=> tall(sK1) [avatar definition]
207. 14 | 15 [avatar split clause 111,203,199]
265. ~tall(sK1) <- (13) [resolution 188,196]
269. ~15 | ~13 [avatar split clause 265,194,203]
295. happy(X0) | curious(X0) | generous(X0) [resolution 82,100]
298. happy(X0) | curious(X0) <- (14) [subsumption resolution 295,200]
300. ~wise(X0) | curious(X0) | generous(X0) [resolution 84,100]
303. ~wise(X0) | curious(X0) <- (14) [subsumption resolution 300,200]
335. curious(X1) | wise(X1) <- (14) [resolution 298,76]
337. curious(X1) <- (14) [subsumption resolution 335,303]
340. $false <- (14) [resolution 337,136]
343. ~14 [avatar contradiction clause 340]
345. $false [avatar sat refutation 201,207,269,343]
% SZS output end Proof for 6251008488639189198433063
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is not happy or not humble and vice versa.
Everyone who is either not strong or not generous is both happy and rich.
Everyone who is not strong or patient is both not old and not quiet and vice versa.
If someone is either patient or not quiet then someone is either generous or creative and vice versa.
If someone is either calm or not rich then lucy is curious or not curious.
Everyone who is both creative and tall is both not patient and tall.
Everyone who is patient or not humble is both not curious and funny and vice versa.
Everyone who is both old and not quiet is both happy and tall.
If mary is quiet or not rich then someone is tall and vice versa.
Everyone who is either not old or not funny is both not tall and wise and vice versa.
Everyone who is not curious is not humble.
Everyone who is not rich or not creative is both not patient and generous.
Everyone who is not humble is funny and vice versa.
Everyone who is either not curious or not rich is both not rich and generous.
If john is not generous then someone is not funny or not calm.
Everyone who is either not generous or tall is humble or wise.
Someone is either curious or old.
Someone is both not old and not calm.
Someone is either old or not humble.
Alice is not old or quiet.
Fred is tall or not patient.
Fred is either not humble or old.
Fred is either not patient or kind.
Someone is either not rich or not kind. | Mary is patient. | contradiction | (![X]:(generous(X)<=>(~happy(X)|~humble(X))))&
(![X]:((~strong(X)<~>~generous(X))=>(happy(X)&rich(X))))&
(![X]:((~strong(X)|patient(X))<=>(~old(X)&~quiet(X))))&
((?[X]:((patient(X)<~>~quiet(X))))<=>(?[X]:((generous(X)<~>creative(X)))))&
((?[X]:((calm(X)<~>~rich(X))))=>((curious(lucy)|~curious(lucy))))&
(![X]:((creative(X)&tall(X))=>(~patient(X)&tall(X))))&
(![X]:((patient(X)|~humble(X))<=>(~curious(X)&funny(X))))&
(![X]:((old(X)&~quiet(X))=>(happy(X)&tall(X))))&
(((quiet(mary)|~rich(mary)))<=>(?[X]:(tall(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(~tall(X)&wise(X))))&
(![X]:(~curious(X)=>~humble(X)))&
(![X]:((~rich(X)|~creative(X))=>(~patient(X)&generous(X))))&
(![X]:(~humble(X)<=>funny(X)))&
(![X]:((~curious(X)<~>~rich(X))=>(~rich(X)&generous(X))))&
((~generous(john))=>(?[X]:((~funny(X)|~calm(X)))))&
(![X]:((~generous(X)<~>tall(X))=>(humble(X)|wise(X))))&
(?[X]:((curious(X)<~>old(X))))&
(?[X]:((~old(X)&~calm(X))))&
(?[X]:((old(X)<~>~humble(X))))&
((~old(alice)|quiet(alice)))&
((tall(fred)|~patient(fred)))&
((~humble(fred)<~>old(fred)))&
((~patient(fred)<~>kind(fred)))&
(?[X]:((~rich(X)<~>~kind(X)))) | patient(mary) | [
"p6",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7130080331166450394911023
% SZS output start Proof for 7130080331166450394911023
7. ! [X0] : ((~humble(X0) | patient(X0)) <=> (funny(X0) & ~curious(X0))) [input p6]
12. ! [X0] : ((~creative(X0) | ~rich(X0)) => (generous(X0) & ~patient(X0))) [input p11]
14. ! [X0] : ((~curious(X0) <~> ~rich(X0)) => (generous(X0) & ~rich(X0))) [input p13]
25. patient(mary) [input hypothesis]
35. ! [X0] : ((generous(X0) & ~patient(X0)) | (creative(X0) & rich(X0))) [ennf transformation 12]
36. ! [X0] : ((generous(X0) & ~rich(X0)) | (~curious(X0) <=> ~rich(X0))) [ennf transformation 14]
51. ! [X0] : (((~humble(X0) | patient(X0)) | (~funny(X0) | curious(X0))) & ((funny(X0) & ~curious(X0)) | (humble(X0) & ~patient(X0)))) [nnf transformation 7]
52. ! [X0] : ((~humble(X0) | patient(X0) | ~funny(X0) | curious(X0)) & ((funny(X0) & ~curious(X0)) | (humble(X0) & ~patient(X0)))) [flattening 51]
61. ! [X0] : ((generous(X0) & ~rich(X0)) | ((~curious(X0) | rich(X0)) & (~rich(X0) | curious(X0)))) [nnf transformation 36]
102. ~curious(X0) | ~patient(X0) [cnf transformation 52]
119. ~patient(X0) | rich(X0) [cnf transformation 35]
125. ~rich(X0) | ~rich(X0) | curious(X0) [cnf transformation 61]
146. patient(mary) [cnf transformation 25]
147. ~rich(X0) | curious(X0) [duplicate literal removal 125]
192. 10 <=> rich(mary) [avatar definition]
193. rich(mary) <- (10) [avatar component clause 192]
290. rich(mary) [resolution 119,146]
296. curious(mary) <- (10) [resolution 147,193]
300. ~patient(mary) <- (10) [resolution 296,102]
303. $false <- (10) [subsumption resolution 300,146]
304. ~10 [avatar contradiction clause 303]
305. 10 [avatar split clause 290,192]
308. $false [avatar sat refutation 304,305]
% SZS output end Proof for 7130080331166450394911023
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or happy is happy or wise. If someone is not generous or brave then susan is not old or quiet and vice versa. If someone is not rich or patient then alice is both not humble and not patient. If susan is not quiet then someone is not calm and vice versa. Everyone who is either not creative or not funny is both not happy and brave. If someone is not strong or tall then john is not rich or not humble. If lucy is either not happy or not humble then someone is either humble or not brave and vice versa. Everyone who is both funny and humble is strong and vice versa. If john is both not rich and curious then someone is not happy and vice versa. Everyone who is strong or not creative is not funny. Everyone who is not calm is both happy and funny. Everyone who is funny or not creative is either not patient or strong and vice versa. Everyone who is both generous and not creative is either not creative or creative and vice versa. Everyone who is either not funny or not generous is either humble or tall. Everyone who is quiet is either not patient or happy. Everyone who is patient or not creative is either not old or not tall and vice versa. Someone is either not humble or creative. Someone is both not rich and not old. Someone is strong or not rich. Someone is either strong or rich. | John is not strong. | entailment | (![X]:((humble(X)<~>happy(X))=>(happy(X)|wise(X))))&
((?[X]:((~generous(X)|brave(X))))<=>((~old(susan)|quiet(susan))))&
((?[X]:((~rich(X)|patient(X))))=>((~humble(alice)&~patient(alice))))&
((~quiet(susan))<=>(?[X]:(~calm(X))))&
(![X]:((~creative(X)<~>~funny(X))=>(~happy(X)&brave(X))))&
((?[X]:((~strong(X)|tall(X))))=>((~rich(john)|~humble(john))))&
(((~happy(lucy)<~>~humble(lucy)))<=>(?[X]:((humble(X)<~>~brave(X)))))&
(![X]:((funny(X)&humble(X))<=>strong(X)))&
(((~rich(john)&curious(john)))<=>(?[X]:(~happy(X))))&
(![X]:((strong(X)|~creative(X))=>~funny(X)))&
(![X]:(~calm(X)=>(happy(X)&funny(X))))&
(![X]:((funny(X)|~creative(X))<=>(~patient(X)<~>strong(X))))&
(![X]:((generous(X)&~creative(X))<=>(~creative(X)<~>creative(X))))&
(![X]:((~funny(X)<~>~generous(X))=>(humble(X)<~>tall(X))))&
(![X]:(quiet(X)=>(~patient(X)<~>happy(X))))&
(![X]:((patient(X)|~creative(X))<=>(~old(X)<~>~tall(X))))&
(?[X]:((~humble(X)<~>creative(X))))&
(?[X]:((~rich(X)&~old(X))))&
(?[X]:((strong(X)|~rich(X))))&
(?[X]:((strong(X)<~>rich(X)))) | ~strong(john) | [
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 955302172141143055885925
% SZS output start Proof for 955302172141143055885925
8. ! [X0] : ((humble(X0) & funny(X0)) <=> strong(X0)) [input p7]
10. ! [X0] : ((~creative(X0) | strong(X0)) => ~funny(X0)) [input p9]
21. strong(john) [input hypothesis]
27. ! [X0] : (~funny(X0) | (creative(X0) & ~strong(X0))) [ennf transformation 10]
45. ! [X0] : (((humble(X0) & funny(X0)) | ~strong(X0)) & (strong(X0) | (~humble(X0) | ~funny(X0)))) [nnf transformation 8]
46. ! [X0] : (((humble(X0) & funny(X0)) | ~strong(X0)) & (strong(X0) | ~humble(X0) | ~funny(X0))) [flattening 45]
95. funny(X0) | ~strong(X0) [cnf transformation 46]
100. ~funny(X0) | ~strong(X0) [cnf transformation 27]
135. strong(john) [cnf transformation 21]
255. ~strong(X0) [subsumption resolution 100,95]
266. $false [subsumption resolution 135,255]
% SZS output end Proof for 955302172141143055885925
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not tall is either strong or not humble.
Everyone who is strong is not quiet or not tall.
Everyone who is either rich or creative is not kind and vice versa.
If john is not creative or not rich then susan is both not funny and tall.
Everyone who is not humble is not generous or kind.
If john is not brave or old then fred is humble and vice versa.
If someone is both not wise and old then alice is old or creative and vice versa.
Everyone who is not generous or not old is either humble or not patient.
If john is not kind then lucy is both not happy and old and vice versa.
Everyone who is either not humble or not creative is both patient and creative and vice versa.
Everyone who is both not brave and old is either not brave or rich and vice versa.
If someone is not quiet or not patient then someone is not creative or humble.
Everyone who is either not quiet or not strong is either not strong or not patient.
If someone is not strong then john is either tall or calm.
If someone is calm then lucy is either not creative or not kind.
John is creative or funny.
Paul is both calm and not funny.
Someone is both old and not humble.
Someone is either tall or not calm.
Alice is both calm and generous.
John is creative.
Someone is not old or calm. | Alice is rich. | contradiction | (![X]:((~curious(X)|~tall(X))=>(strong(X)<~>~humble(X))))&
(![X]:(strong(X)=>(~quiet(X)|~tall(X))))&
(![X]:((rich(X)<~>creative(X))<=>~kind(X)))&
(((~creative(john)|~rich(john)))=>((~funny(susan)&tall(susan))))&
(![X]:(~humble(X)=>(~generous(X)|kind(X))))&
(((~brave(john)|old(john)))<=>(humble(fred)))&
((?[X]:((~wise(X)&old(X))))<=>((old(alice)|creative(alice))))&
(![X]:((~generous(X)|~old(X))=>(humble(X)<~>~patient(X))))&
((~kind(john))<=>((~happy(lucy)&old(lucy))))&
(![X]:((~humble(X)<~>~creative(X))<=>(patient(X)&creative(X))))&
(![X]:((~brave(X)&old(X))<=>(~brave(X)<~>rich(X))))&
((?[X]:((~quiet(X)|~patient(X))))=>(?[X]:((~creative(X)|humble(X)))))&
(![X]:((~quiet(X)<~>~strong(X))=>(~strong(X)<~>~patient(X))))&
((?[X]:(~strong(X)))=>((tall(john)<~>calm(john))))&
((?[X]:(calm(X)))=>((~creative(lucy)<~>~kind(lucy))))&
((creative(john)|funny(john)))&
((calm(paul)&~funny(paul)))&
(?[X]:((old(X)&~humble(X))))&
(?[X]:((tall(X)<~>~calm(X))))&
((calm(alice)&generous(alice)))&
(creative(john))&
(?[X]:((~old(X)|calm(X)))) | rich(alice) | [
"p2",
"p4",
"p7",
"p9",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6455276816440512444255903
% SZS output start Proof for 6455276816440512444255903
3. ! [X0] : ((rich(X0) <~> creative(X0)) <=> ~kind(X0)) [input p2]
5. ! [X0] : (~humble(X0) => (kind(X0) | ~generous(X0))) [input p4]
8. ! [X0] : ((~old(X0) | ~generous(X0)) => (humble(X0) <~> ~patient(X0))) [input p7]
10. ! [X0] : ((~humble(X0) <~> ~creative(X0)) <=> (creative(X0) & patient(X0))) [input p9]
11. ! [X0] : ((old(X0) & ~brave(X0)) <=> (~brave(X0) <~> rich(X0))) [input p10]
20. generous(alice) & calm(alice) [input p19]
23. rich(alice) [input hypothesis]
30. ! [X0] : ((kind(X0) | ~generous(X0)) | humble(X0)) [ennf transformation 5]
31. ! [X0] : (kind(X0) | ~generous(X0) | humble(X0)) [flattening 30]
32. ! [X0] : ((humble(X0) <~> ~patient(X0)) | (old(X0) & generous(X0))) [ennf transformation 8]
38. ! [X0] : ((((~creative(X0) | ~rich(X0)) & (creative(X0) | rich(X0))) | kind(X0)) & (~kind(X0) | ((rich(X0) | ~creative(X0)) & (creative(X0) | ~rich(X0))))) [nnf transformation 3]
46. ! [X0] : (((patient(X0) | ~humble(X0)) & (~patient(X0) | humble(X0))) | (old(X0) & generous(X0))) [nnf transformation 32]
49. ! [X0] : ((((creative(X0) | humble(X0)) & (~creative(X0) | ~humble(X0))) | (~creative(X0) | ~patient(X0))) & ((creative(X0) & patient(X0)) | ((~humble(X0) | creative(X0)) & (~creative(X0) | humble(X0))))) [nnf transformation 10]
50. ! [X0] : ((((creative(X0) | humble(X0)) & (~creative(X0) | ~humble(X0))) | ~creative(X0) | ~patient(X0)) & ((creative(X0) & patient(X0)) | ((~humble(X0) | creative(X0)) & (~creative(X0) | humble(X0))))) [flattening 49]
51. ! [X0] : (((old(X0) & ~brave(X0)) | ((~brave(X0) | ~rich(X0)) & (rich(X0) | brave(X0)))) & (((~rich(X0) | brave(X0)) & (rich(X0) | ~brave(X0))) | (~old(X0) | brave(X0)))) [nnf transformation 11]
52. ! [X0] : (((old(X0) & ~brave(X0)) | ((~brave(X0) | ~rich(X0)) & (rich(X0) | brave(X0)))) & (((~rich(X0) | brave(X0)) & (rich(X0) | ~brave(X0))) | ~old(X0) | brave(X0))) [flattening 51]
69. ~kind(X0) | creative(X0) | ~rich(X0) [cnf transformation 38]
72. ~creative(X0) | ~rich(X0) | kind(X0) [cnf transformation 38]
77. ~generous(X0) | kind(X0) | humble(X0) [cnf transformation 31]
87. ~patient(X0) | humble(X0) | old(X0) [cnf transformation 46]
89. ~humble(X0) | patient(X0) | old(X0) [cnf transformation 46]
93. ~creative(X0) | patient(X0) | humble(X0) [cnf transformation 50]
96. creative(X0) | ~humble(X0) | creative(X0) [cnf transformation 50]
97. ~creative(X0) | ~humble(X0) | ~creative(X0) | ~patient(X0) [cnf transformation 50]
100. ~rich(X0) | brave(X0) | ~old(X0) | brave(X0) [cnf transformation 52]
102. ~brave(X0) | ~brave(X0) | ~rich(X0) [cnf transformation 52]
123. generous(alice) [cnf transformation 20]
126. rich(alice) [cnf transformation 23]
129. ~rich(X0) | brave(X0) | ~old(X0) [duplicate literal removal 100]
130. ~brave(X0) | ~rich(X0) [duplicate literal removal 102]
131. ~humble(X0) | creative(X0) [duplicate literal removal 96]
132. ~patient(X0) | ~humble(X0) | ~creative(X0) [duplicate literal removal 97]
169. 8 <=> creative(alice) [avatar definition]
170. creative(alice) <- (8) [avatar component clause 169]
171. ~creative(alice) <- (~8) [avatar component clause 169]
178. 10 <=> old(alice) [avatar definition]
179. old(alice) <- (10) [avatar component clause 178]
180. ~old(alice) <- (~10) [avatar component clause 178]
207. ~old(X0) | ~rich(X0) [subsumption resolution 129,130]
313. kind(alice) | humble(alice) [resolution 77,123]
340. patient(alice) | humble(alice) <- (8) [resolution 93,170]
352. 38 <=> humble(alice) [avatar definition]
354. humble(alice) <- (38) [avatar component clause 352]
356. 39 <=> patient(alice) [avatar definition]
358. patient(alice) <- (39) [avatar component clause 356]
359. 38 | 39 | ~8 [avatar split clause 340,169,356,352]
370. 42 <=> kind(alice) [avatar definition]
372. kind(alice) <- (42) [avatar component clause 370]
373. 38 | 42 [avatar split clause 313,370,352]
375. ~rich(alice) <- (10) [resolution 179,207]
376. $false <- (10) [subsumption resolution 375,126]
377. ~10 [avatar contradiction clause 376]
379. ~rich(alice) | kind(alice) <- (8) [resolution 170,72]
380. kind(alice) <- (8) [subsumption resolution 379,126]
381. 42 | ~8 [avatar split clause 380,169,370]
424. patient(alice) | old(alice) <- (38) [resolution 354,89]
427. creative(alice) <- (38) [resolution 354,131]
428. patient(alice) <- (~10, 38) [subsumption resolution 424,180]
429. 39 | 10 | ~38 [avatar split clause 428,352,178,356]
430. $false <- (~8, 38) [subsumption resolution 427,171]
431. 8 | ~38 [avatar contradiction clause 430]
452. creative(alice) | ~rich(alice) <- (42) [resolution 372,69]
456. creative(alice) <- (42) [subsumption resolution 452,126]
457. 8 | ~42 [avatar split clause 456,370,169]
460. ~humble(alice) | ~creative(alice) <- (39) [resolution 358,132]
462. humble(alice) | old(alice) <- (39) [resolution 358,87]
468. humble(alice) <- (~10, 39) [subsumption resolution 462,180]
469. 38 | 10 | ~39 [avatar split clause 468,356,178,352]
470. ~humble(alice) <- (8, 39) [subsumption resolution 460,170]
471. ~38 | ~8 | ~39 [avatar split clause 470,356,169,352]
472. $false [avatar sat refutation 359,373,377,381,429,431,457,469,471]
% SZS output end Proof for 6455276816440512444255903
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or generous is patient. Everyone who is both wise and generous is either not quiet or not generous and vice versa. If paul is not old or not curious then fred is not kind or wise. Everyone who is not quiet or not kind is both creative and not old and vice versa. If someone is either not curious or not brave then someone is not happy or calm. Everyone who is both generous and curious is humble or not quiet and vice versa. If someone is not funny then someone is tall and vice versa. If someone is both generous and quiet then someone is not curious or calm and vice versa. Everyone who is both not generous and not funny is old or not happy and vice versa. Everyone who is curious or not patient is generous and vice versa. If someone is creative then someone is not funny and vice versa. If someone is not brave then fred is either wise or not calm. If someone is either happy or wise then paul is both not brave and humble and vice versa. If someone is both rich and wise then mary is brave. Everyone who is either not old or creative is either not wise or patient and vice versa. Everyone who is both not strong and not kind is either not happy or not quiet. Someone is both tall and curious. Someone is tall. Someone is happy. Fred is either not quiet or generous. Someone is not brave or not wise. | Fred is rich. | neutral | (![X]:((~old(X)|generous(X))=>patient(X)))&
(![X]:((wise(X)&generous(X))<=>(~quiet(X)<~>~generous(X))))&
(((~old(paul)|~curious(paul)))=>((~kind(fred)|wise(fred))))&
(![X]:((~quiet(X)|~kind(X))<=>(creative(X)&~old(X))))&
((?[X]:((~curious(X)<~>~brave(X))))=>(?[X]:((~happy(X)|calm(X)))))&
(![X]:((generous(X)&curious(X))<=>(humble(X)|~quiet(X))))&
((?[X]:(~funny(X)))<=>(?[X]:(tall(X))))&
((?[X]:((generous(X)&quiet(X))))<=>(?[X]:((~curious(X)|calm(X)))))&
(![X]:((~generous(X)&~funny(X))<=>(old(X)|~happy(X))))&
(![X]:((curious(X)|~patient(X))<=>generous(X)))&
((?[X]:(creative(X)))<=>(?[X]:(~funny(X))))&
((?[X]:(~brave(X)))=>((wise(fred)<~>~calm(fred))))&
((?[X]:((happy(X)<~>wise(X))))<=>((~brave(paul)&humble(paul))))&
((?[X]:((rich(X)&wise(X))))=>(brave(mary)))&
(![X]:((~old(X)<~>creative(X))<=>(~wise(X)<~>patient(X))))&
(![X]:((~strong(X)&~kind(X))=>(~happy(X)<~>~quiet(X))))&
(?[X]:((tall(X)&curious(X))))&
(?[X]:(tall(X)))&
(?[X]:(happy(X)))&
((~quiet(fred)<~>generous(fred)))&
(?[X]:((~brave(X)|~wise(X)))) | rich(fred) | [] | null | 0 |
If mary is either kind or old then someone is both rich and not funny.
Everyone who is kind is both quiet and creative and vice versa.
Everyone who is both not old and wise is both calm and kind.
Everyone who is not calm or brave is both not calm and not tall.
Everyone who is calm is not funny and vice versa.
Everyone who is both tall and quiet is brave or kind and vice versa.
Everyone who is either wise or not funny is both not calm and brave.
Everyone who is either rich or not rich is both creative and curious.
If someone is not tall then someone is either not generous or not humble and vice versa.
If alice is both generous and not humble then paul is not happy and vice versa.
Everyone who is calm or not kind is happy and vice versa.
If alice is both humble and not tall then someone is patient or not calm and vice versa.
Everyone who is either calm or tall is both not patient and creative.
If lucy is quiet or not wise then john is creative.
Everyone who is either quiet or not brave is either not brave or not happy.
If paul is either not funny or not brave then someone is either old or funny.
Someone is strong.
Lucy is both curious and creative.
Someone is either not rich or not generous.
Fred is both rich and kind.
Someone is both kind and curious.
Someone is not quiet.
Mary is either not wise or curious.
Someone is either not happy or strong. | Fred is creative. | entailment | (((kind(mary)<~>old(mary)))=>(?[X]:((rich(X)&~funny(X)))))&
(![X]:(kind(X)<=>(quiet(X)&creative(X))))&
(![X]:((~old(X)&wise(X))=>(calm(X)&kind(X))))&
(![X]:((~calm(X)|brave(X))=>(~calm(X)&~tall(X))))&
(![X]:(calm(X)<=>~funny(X)))&
(![X]:((tall(X)&quiet(X))<=>(brave(X)|kind(X))))&
(![X]:((wise(X)<~>~funny(X))=>(~calm(X)&brave(X))))&
(![X]:((rich(X)<~>~rich(X))=>(creative(X)&curious(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~generous(X)<~>~humble(X)))))&
(((generous(alice)&~humble(alice)))<=>(~happy(paul)))&
(![X]:((calm(X)|~kind(X))<=>happy(X)))&
(((humble(alice)&~tall(alice)))<=>(?[X]:((patient(X)|~calm(X)))))&
(![X]:((calm(X)<~>tall(X))=>(~patient(X)&creative(X))))&
(((quiet(lucy)|~wise(lucy)))=>(creative(john)))&
(![X]:((quiet(X)<~>~brave(X))=>(~brave(X)<~>~happy(X))))&
(((~funny(paul)<~>~brave(paul)))=>(?[X]:((old(X)<~>funny(X)))))&
(?[X]:(strong(X)))&
((curious(lucy)&creative(lucy)))&
(?[X]:((~rich(X)<~>~generous(X))))&
((rich(fred)&kind(fred)))&
(?[X]:((kind(X)&curious(X))))&
(?[X]:(~quiet(X)))&
((~wise(mary)<~>curious(mary)))&
(?[X]:((~happy(X)<~>strong(X)))) | creative(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4354139780362585107914011
% SZS output start Proof for 4354139780362585107914011
8. ! [X0] : ((rich(X0) <~> ~rich(X0)) => (curious(X0) & creative(X0))) [input p7]
25. ~creative(fred) [input hypothesis]
32. ! [X0] : ((curious(X0) & creative(X0)) | (rich(X0) <=> ~rich(X0))) [ennf transformation 8]
46. ! [X0] : ((curious(X0) & creative(X0)) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0)))) [nnf transformation 32]
103. creative(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 46]
104. creative(X0) | rich(X0) | rich(X0) [cnf transformation 46]
150. ~creative(fred) [cnf transformation 25]
153. creative(X0) | ~rich(X0) [duplicate literal removal 103]
154. creative(X0) | rich(X0) [duplicate literal removal 104]
182. creative(X0) [subsumption resolution 153,154]
284. $false [subsumption resolution 150,182]
% SZS output end Proof for 4354139780362585107914011
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is not strong or patient and vice versa.
If paul is kind or not curious then someone is either curious or not rich.
Everyone who is both calm and not funny is either creative or not wise.
If someone is either not brave or not patient then someone is calm or happy.
Everyone who is either not wise or not patient is humble or patient.
Everyone who is patient or not strong is not curious and vice versa.
If someone is either calm or not happy then someone is not tall.
If susan is either generous or brave then someone is either not generous or brave and vice versa.
If someone is either calm or kind then lucy is both humble and not rich.
Everyone who is both brave and quiet is both not generous and not brave and vice versa.
Everyone who is strong or funny is both rich and not brave.
Everyone who is either funny or curious is both not happy and creative and vice versa.
Everyone who is calm or brave is both not wise and not calm.
If susan is both wise and tall then someone is both brave and not tall.
If someone is calm or patient then paul is either not generous or not rich and vice versa.
Everyone who is not brave or not quiet is kind or not tall and vice versa.
Someone is kind.
Someone is either not happy or not curious.
Fred is either not happy or wise.
Someone is tall or not calm.
Alice is both not kind and happy.
Someone is generous or not creative. | Fred is not brave. | neutral | (![X]:(~kind(X)<=>(~strong(X)|patient(X))))&
(((kind(paul)|~curious(paul)))=>(?[X]:((curious(X)<~>~rich(X)))))&
(![X]:((calm(X)&~funny(X))=>(creative(X)<~>~wise(X))))&
((?[X]:((~brave(X)<~>~patient(X))))=>(?[X]:((calm(X)|happy(X)))))&
(![X]:((~wise(X)<~>~patient(X))=>(humble(X)|patient(X))))&
(![X]:((patient(X)|~strong(X))<=>~curious(X)))&
((?[X]:((calm(X)<~>~happy(X))))=>(?[X]:(~tall(X))))&
(((generous(susan)<~>brave(susan)))<=>(?[X]:((~generous(X)<~>brave(X)))))&
((?[X]:((calm(X)<~>kind(X))))=>((humble(lucy)&~rich(lucy))))&
(![X]:((brave(X)&quiet(X))<=>(~generous(X)&~brave(X))))&
(![X]:((strong(X)|funny(X))=>(rich(X)&~brave(X))))&
(![X]:((funny(X)<~>curious(X))<=>(~happy(X)&creative(X))))&
(![X]:((calm(X)|brave(X))=>(~wise(X)&~calm(X))))&
(((wise(susan)&tall(susan)))=>(?[X]:((brave(X)&~tall(X)))))&
((?[X]:((calm(X)|patient(X))))<=>((~generous(paul)<~>~rich(paul))))&
(![X]:((~brave(X)|~quiet(X))<=>(kind(X)|~tall(X))))&
(?[X]:(kind(X)))&
(?[X]:((~happy(X)<~>~curious(X))))&
((~happy(fred)<~>wise(fred)))&
(?[X]:((tall(X)|~calm(X))))&
((~kind(alice)&happy(alice)))&
(?[X]:((generous(X)|~creative(X)))) | ~brave(fred) | [] | null | 0 |
If alice is either not rich or patient then someone is either not patient or wise and vice versa.
Everyone who is happy or tall is curious or not patient.
Everyone who is not brave or brave is rich.
If alice is either quiet or not generous then someone is not rich and vice versa.
Everyone who is rich is calm or not strong and vice versa.
If lucy is not happy then mary is either calm or not tall and vice versa.
If someone is both not tall and tall then someone is humble or patient and vice versa.
If lucy is not wise or creative then susan is both wise and curious.
Everyone who is strong or not brave is both happy and calm.
If lucy is both not strong and calm then mary is either tall or strong.
Everyone who is quiet is either not creative or not curious.
If someone is quiet then someone is wise or rich.
If someone is generous then someone is either not old or not quiet and vice versa.
Everyone who is quiet is kind or not funny.
Everyone who is either not wise or creative is both tall and generous and vice versa.
If john is either not rich or not calm then someone is either not curious or not funny and vice versa.
Lucy is old or not calm.
Alice is kind or old.
Fred is not calm.
Fred is wise or not rich.
Someone is either tall or not patient.
Susan is both old and not happy.
John is not strong or not old.
Someone is wise or not funny. | Susan is wise. | entailment | (((~rich(alice)<~>patient(alice)))<=>(?[X]:((~patient(X)<~>wise(X)))))&
(![X]:((happy(X)|tall(X))=>(curious(X)|~patient(X))))&
(![X]:((~brave(X)|brave(X))=>rich(X)))&
(((quiet(alice)<~>~generous(alice)))<=>(?[X]:(~rich(X))))&
(![X]:(rich(X)<=>(calm(X)|~strong(X))))&
((~happy(lucy))<=>((calm(mary)<~>~tall(mary))))&
((?[X]:((~tall(X)&tall(X))))<=>(?[X]:((humble(X)|patient(X)))))&
(((~wise(lucy)|creative(lucy)))=>((wise(susan)&curious(susan))))&
(![X]:((strong(X)|~brave(X))=>(happy(X)&calm(X))))&
(((~strong(lucy)&calm(lucy)))=>((tall(mary)<~>strong(mary))))&
(![X]:(quiet(X)=>(~creative(X)<~>~curious(X))))&
((?[X]:(quiet(X)))=>(?[X]:((wise(X)|rich(X)))))&
((?[X]:(generous(X)))<=>(?[X]:((~old(X)<~>~quiet(X)))))&
(![X]:(quiet(X)=>(kind(X)|~funny(X))))&
(![X]:((~wise(X)<~>creative(X))<=>(tall(X)&generous(X))))&
(((~rich(john)<~>~calm(john)))<=>(?[X]:((~curious(X)<~>~funny(X)))))&
((old(lucy)|~calm(lucy)))&
((kind(alice)|old(alice)))&
(~calm(fred))&
((wise(fred)|~rich(fred)))&
(?[X]:((tall(X)<~>~patient(X))))&
((old(susan)&~happy(susan)))&
((~strong(john)|~old(john)))&
(?[X]:((wise(X)|~funny(X)))) | wise(susan) | [
"p0",
"p2",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2809804268078758766139279
% SZS output start Proof for 2809804268078758766139279
1. (~rich(alice) <~> patient(alice)) <=> ? [X0] : (~patient(X0) <~> wise(X0)) [input p0]
3. ! [X0] : ((brave(X0) | ~brave(X0)) => rich(X0)) [input p2]
7. ? [X0] : (tall(X0) & ~tall(X0)) <=> ? [X0] : (patient(X0) | humble(X0)) [input p6]
25. ~wise(susan) [input hypothesis]
26. ? [X0] : (tall(X0) & ~tall(X0)) <=> ? [X1] : (patient(X1) | humble(X1)) [rectify 7]
33. ! [X0] : (rich(X0) | (~brave(X0) & brave(X0))) [ennf transformation 3]
40. (((~patient(alice) | rich(alice)) & (patient(alice) | ~rich(alice))) | ! [X0] : ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) & (? [X0] : ((~wise(X0) | patient(X0)) & (wise(X0) | ~patient(X0))) | ((~rich(alice) | ~patient(alice)) & (patient(alice) | rich(alice)))) [nnf transformation 1]
41. (((~patient(alice) | rich(alice)) & (patient(alice) | ~rich(alice))) | ! [X0] : ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) & (? [X1] : ((~wise(X1) | patient(X1)) & (wise(X1) | ~patient(X1))) | ((~rich(alice) | ~patient(alice)) & (patient(alice) | rich(alice)))) [rectify 40]
42. ? [X1] : ((~wise(X1) | patient(X1)) & (wise(X1) | ~patient(X1))) => ((~wise(sK0) | patient(sK0)) & (wise(sK0) | ~patient(sK0))) [choice axiom]
43. (((~patient(alice) | rich(alice)) & (patient(alice) | ~rich(alice))) | ! [X0] : ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) & (((~wise(sK0) | patient(sK0)) & (wise(sK0) | ~patient(sK0))) | ((~rich(alice) | ~patient(alice)) & (patient(alice) | rich(alice)))) [skolemisation 41,42]
51. (? [X0] : (tall(X0) & ~tall(X0)) | ! [X1] : (~patient(X1) & ~humble(X1))) & (? [X1] : (patient(X1) | humble(X1)) | ! [X0] : (~tall(X0) | tall(X0))) [nnf transformation 26]
52. (? [X0] : (tall(X0) & ~tall(X0)) | ! [X1] : (~patient(X1) & ~humble(X1))) & (? [X2] : (patient(X2) | humble(X2)) | ! [X3] : (~tall(X3) | tall(X3))) [rectify 51]
53. ? [X0] : (tall(X0) & ~tall(X0)) => (tall(sK2) & ~tall(sK2)) [choice axiom]
54. ? [X2] : (patient(X2) | humble(X2)) => (patient(sK3) | humble(sK3)) [choice axiom]
55. ((tall(sK2) & ~tall(sK2)) | ! [X1] : (~patient(X1) & ~humble(X1))) & ((patient(sK3) | humble(sK3)) | ! [X3] : (~tall(X3) | tall(X3))) [skolemisation 52,54,53]
81. patient(alice) | ~rich(alice) | wise(X0) | patient(X0) [cnf transformation 43]
87. rich(X0) | brave(X0) [cnf transformation 33]
88. rich(X0) | ~brave(X0) [cnf transformation 33]
102. ~tall(sK2) | ~patient(X1) [cnf transformation 55]
104. tall(sK2) | ~patient(X1) [cnf transformation 55]
145. ~wise(susan) [cnf transformation 25]
150. 2 <=> rich(alice) [avatar definition]
151. ~rich(alice) <- (~2) [avatar component clause 150]
154. 3 <=> patient(alice) [avatar definition]
155. patient(alice) <- (3) [avatar component clause 154]
159. 4 <=> ! [X0] : (wise(X0) | patient(X0)) [avatar definition]
160. wise(X0) | patient(X0) <- (4) [avatar component clause 159]
163. 4 | ~2 | 3 [avatar split clause 81,154,150,159]
176. rich(X0) [subsumption resolution 87,88]
207. 12 <=> ! [X1] : ~patient(X1) [avatar definition]
208. ~patient(X1) <- (12) [avatar component clause 207]
210. 13 <=> tall(sK2) [avatar definition]
213. 12 | 13 [avatar split clause 104,210,207]
218. 12 | ~13 [avatar split clause 102,210,207]
235. 18 <=> wise(susan) [avatar definition]
236. ~wise(susan) <- (~18) [avatar component clause 235]
339. ~18 [avatar split clause 145,235]
344. $false <- (~2) [subsumption resolution 151,176]
345. 2 [avatar contradiction clause 344]
346. wise(X0) <- (4, 12) [subsumption resolution 160,208]
348. $false <- (4, 12, ~18) [resolution 346,236]
349. ~4 | ~12 | 18 [avatar contradiction clause 348]
351. $false <- (3, 12) [subsumption resolution 155,208]
352. ~3 | ~12 [avatar contradiction clause 351]
353. $false [avatar sat refutation 163,213,218,339,345,349,352]
% SZS output end Proof for 2809804268078758766139279
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and not funny is patient and vice versa.
Everyone who is quiet or patient is both not calm and old and vice versa.
If someone is not curious then paul is not curious or rich.
If someone is not tall or not patient then someone is both not calm and not rich and vice versa.
If mary is both not generous and calm then someone is strong or not rich.
Everyone who is wise or rich is either strong or generous.
Everyone who is both kind and old is both generous and not old.
Everyone who is old or humble is calm.
Everyone who is rich or not generous is either not creative or not humble.
If fred is either not brave or not wise then someone is either not kind or humble and vice versa.
Everyone who is both funny and not quiet is not generous or not calm.
Everyone who is both wise and not patient is both patient and brave.
Everyone who is either strong or not patient is either humble or kind.
Everyone who is creative or generous is not calm.
Everyone who is curious or strong is both not wise and not humble and vice versa.
If someone is both not generous and not humble then susan is not generous.
Paul is brave or not brave.
Someone is tall or curious.
Someone is either rich or not brave.
Someone is brave.
Lucy is not wise or not curious.
Someone is either funny or creative.
Mary is not curious.
Someone is both kind and not strong. | Susan is curious. | neutral | (![X]:((wise(X)&~funny(X))<=>patient(X)))&
(![X]:((quiet(X)|patient(X))<=>(~calm(X)&old(X))))&
((?[X]:(~curious(X)))=>((~curious(paul)|rich(paul))))&
((?[X]:((~tall(X)|~patient(X))))<=>(?[X]:((~calm(X)&~rich(X)))))&
(((~generous(mary)&calm(mary)))=>(?[X]:((strong(X)|~rich(X)))))&
(![X]:((wise(X)|rich(X))=>(strong(X)<~>generous(X))))&
(![X]:((kind(X)&old(X))=>(generous(X)&~old(X))))&
(![X]:((old(X)|humble(X))=>calm(X)))&
(![X]:((rich(X)|~generous(X))=>(~creative(X)<~>~humble(X))))&
(((~brave(fred)<~>~wise(fred)))<=>(?[X]:((~kind(X)<~>humble(X)))))&
(![X]:((funny(X)&~quiet(X))=>(~generous(X)|~calm(X))))&
(![X]:((wise(X)&~patient(X))=>(patient(X)&brave(X))))&
(![X]:((strong(X)<~>~patient(X))=>(humble(X)<~>kind(X))))&
(![X]:((creative(X)|generous(X))=>~calm(X)))&
(![X]:((curious(X)|strong(X))<=>(~wise(X)&~humble(X))))&
((?[X]:((~generous(X)&~humble(X))))=>(~generous(susan)))&
((brave(paul)|~brave(paul)))&
(?[X]:((tall(X)|curious(X))))&
(?[X]:((rich(X)<~>~brave(X))))&
(?[X]:(brave(X)))&
((~wise(lucy)|~curious(lucy)))&
(?[X]:((funny(X)<~>creative(X))))&
(~curious(mary))&
(?[X]:((kind(X)&~strong(X)))) | curious(susan) | [] | null | 0 |
If someone is either strong or generous then paul is wise and vice versa.
Everyone who is tall or old is old and vice versa.
If mary is both not generous and not patient then paul is wise or generous.
Everyone who is funny is either tall or strong and vice versa.
Everyone who is not calm is not patient or happy.
If john is not calm or quiet then someone is either old or not old.
Everyone who is patient is both brave and quiet and vice versa.
Everyone who is quiet is funny or rich and vice versa.
Everyone who is both not kind and old is either patient or not brave and vice versa.
If someone is both not brave and not patient then lucy is both patient and kind and vice versa.
Everyone who is not wise or not kind is not patient and vice versa.
If someone is not humble or not strong then someone is both brave and not old and vice versa.
If someone is either not generous or calm then paul is curious or old and vice versa.
If someone is humble then someone is either creative or patient and vice versa.
Everyone who is either kind or creative is rich or not curious and vice versa.
Everyone who is not quiet is not happy.
Susan is either not tall or not calm.
Someone is either patient or old.
Someone is not humble.
Someone is not tall or humble.
Someone is not strong or not old.
John is not old. | Paul is humble. | neutral | ((?[X]:((strong(X)<~>generous(X))))<=>(wise(paul)))&
(![X]:((tall(X)|old(X))<=>old(X)))&
(((~generous(mary)&~patient(mary)))=>((wise(paul)|generous(paul))))&
(![X]:(funny(X)<=>(tall(X)<~>strong(X))))&
(![X]:(~calm(X)=>(~patient(X)|happy(X))))&
(((~calm(john)|quiet(john)))=>(?[X]:((old(X)<~>~old(X)))))&
(![X]:(patient(X)<=>(brave(X)&quiet(X))))&
(![X]:(quiet(X)<=>(funny(X)|rich(X))))&
(![X]:((~kind(X)&old(X))<=>(patient(X)<~>~brave(X))))&
((?[X]:((~brave(X)&~patient(X))))<=>((patient(lucy)&kind(lucy))))&
(![X]:((~wise(X)|~kind(X))<=>~patient(X)))&
((?[X]:((~humble(X)|~strong(X))))<=>(?[X]:((brave(X)&~old(X)))))&
((?[X]:((~generous(X)<~>calm(X))))<=>((curious(paul)|old(paul))))&
((?[X]:(humble(X)))<=>(?[X]:((creative(X)<~>patient(X)))))&
(![X]:((kind(X)<~>creative(X))<=>(rich(X)|~curious(X))))&
(![X]:(~quiet(X)=>~happy(X)))&
((~tall(susan)<~>~calm(susan)))&
(?[X]:((patient(X)<~>old(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~tall(X)|humble(X))))&
(?[X]:((~strong(X)|~old(X))))&
(~old(john)) | humble(paul) | [] | null | 0 |
If john is either strong or not old then mary is happy or not quiet.
If alice is tall then lucy is rich or funny and vice versa.
Everyone who is not humble or curious is not kind and vice versa.
Everyone who is both not humble and funny is not calm or calm and vice versa.
Everyone who is both not generous and brave is not creative and vice versa.
Everyone who is tall or not curious is not wise or not happy.
If someone is both not humble and not rich then someone is both tall and not calm and vice versa.
If fred is not generous or old then someone is either not creative or not happy and vice versa.
If someone is not happy then someone is not kind or not humble and vice versa.
Everyone who is strong is tall or not happy and vice versa.
If someone is old or not creative then someone is either not rich or wise and vice versa.
Everyone who is either wise or not old is strong and vice versa.
If mary is wise then someone is not calm.
If fred is either rich or brave then someone is humble and vice versa.
If susan is generous then lucy is both not rich and kind.
If someone is either generous or not strong then someone is both generous and not happy.
Someone is patient.
John is not old.
Mary is curious.
Paul is generous or not kind.
Someone is not curious. | Susan is tall. | neutral | (((strong(john)<~>~old(john)))=>((happy(mary)|~quiet(mary))))&
((tall(alice))<=>((rich(lucy)|funny(lucy))))&
(![X]:((~humble(X)|curious(X))<=>~kind(X)))&
(![X]:((~humble(X)&funny(X))<=>(~calm(X)|calm(X))))&
(![X]:((~generous(X)&brave(X))<=>~creative(X)))&
(![X]:((tall(X)|~curious(X))=>(~wise(X)|~happy(X))))&
((?[X]:((~humble(X)&~rich(X))))<=>(?[X]:((tall(X)&~calm(X)))))&
(((~generous(fred)|old(fred)))<=>(?[X]:((~creative(X)<~>~happy(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:((~kind(X)|~humble(X)))))&
(![X]:(strong(X)<=>(tall(X)|~happy(X))))&
((?[X]:((old(X)|~creative(X))))<=>(?[X]:((~rich(X)<~>wise(X)))))&
(![X]:((wise(X)<~>~old(X))<=>strong(X)))&
((wise(mary))=>(?[X]:(~calm(X))))&
(((rich(fred)<~>brave(fred)))<=>(?[X]:(humble(X))))&
((generous(susan))=>((~rich(lucy)&kind(lucy))))&
((?[X]:((generous(X)<~>~strong(X))))=>(?[X]:((generous(X)&~happy(X)))))&
(?[X]:(patient(X)))&
(~old(john))&
(curious(mary))&
((generous(paul)|~kind(paul)))&
(?[X]:(~curious(X))) | tall(susan) | [] | null | 0 |
If lucy is wise then paul is not tall and vice versa.
Everyone who is not kind is old.
If mary is both calm and strong then alice is either not calm or old and vice versa.
Everyone who is not generous or tall is not wise or curious.
If someone is both not kind and wise then someone is wise or not generous and vice versa.
Everyone who is not kind is both not generous and strong.
If fred is both funny and not brave then someone is either not happy or creative.
Everyone who is both quiet and not curious is either humble or calm and vice versa.
If mary is not curious then alice is old or quiet and vice versa.
Everyone who is both kind and creative is kind and vice versa.
If fred is either not old or not happy then someone is either not calm or kind.
Everyone who is both quiet and strong is not happy or quiet and vice versa.
Everyone who is either not old or not funny is either strong or humble and vice versa.
If paul is both not humble and not old then lucy is patient or not tall and vice versa.
Everyone who is either kind or creative is either old or not tall and vice versa.
Alice is happy.
Someone is either not curious or brave.
Someone is either not generous or not calm.
Someone is not brave or wise.
Someone is brave or not quiet.
Alice is generous or patient. | Mary is not humble. | neutral | ((wise(lucy))<=>(~tall(paul)))&
(![X]:(~kind(X)=>old(X)))&
(((calm(mary)&strong(mary)))<=>((~calm(alice)<~>old(alice))))&
(![X]:((~generous(X)|tall(X))=>(~wise(X)|curious(X))))&
((?[X]:((~kind(X)&wise(X))))<=>(?[X]:((wise(X)|~generous(X)))))&
(![X]:(~kind(X)=>(~generous(X)&strong(X))))&
(((funny(fred)&~brave(fred)))=>(?[X]:((~happy(X)<~>creative(X)))))&
(![X]:((quiet(X)&~curious(X))<=>(humble(X)<~>calm(X))))&
((~curious(mary))<=>((old(alice)|quiet(alice))))&
(![X]:((kind(X)&creative(X))<=>kind(X)))&
(((~old(fred)<~>~happy(fred)))=>(?[X]:((~calm(X)<~>kind(X)))))&
(![X]:((quiet(X)&strong(X))<=>(~happy(X)|quiet(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(strong(X)<~>humble(X))))&
(((~humble(paul)&~old(paul)))<=>((patient(lucy)|~tall(lucy))))&
(![X]:((kind(X)<~>creative(X))<=>(old(X)<~>~tall(X))))&
(happy(alice))&
(?[X]:((~curious(X)<~>brave(X))))&
(?[X]:((~generous(X)<~>~calm(X))))&
(?[X]:((~brave(X)|wise(X))))&
(?[X]:((brave(X)|~quiet(X))))&
((generous(alice)|patient(alice))) | ~humble(mary) | [] | null | 0 |
Everyone who is both not happy and curious is either not old or not patient. If someone is kind or not humble then susan is generous. If someone is not rich then john is wise. Everyone who is both tall and not funny is funny. Everyone who is both not wise and kind is either not rich or not calm and vice versa. Everyone who is not kind or not curious is either not generous or not strong and vice versa. Everyone who is kind is not wise or brave. If someone is either not happy or curious then susan is not strong. Everyone who is curious or not happy is strong. Everyone who is either funny or not kind is not generous and vice versa. If susan is not humble then paul is not wise. Everyone who is not generous or curious is not wise and vice versa. If someone is either kind or patient then someone is either not kind or tall. Everyone who is both old and curious is both not patient and not funny. Everyone who is not happy is both wise and kind and vice versa. If lucy is happy or brave then lucy is rich and vice versa. Someone is brave or calm. Someone is happy or not humble. Paul is either not rich or not funny. John is brave or not funny. Lucy is either not rich or curious. Mary is not brave or not calm. Someone is either creative or kind. | Lucy is strong. | entailment | (![X]:((~happy(X)&curious(X))=>(~old(X)<~>~patient(X))))&
((?[X]:((kind(X)|~humble(X))))=>(generous(susan)))&
((?[X]:(~rich(X)))=>(wise(john)))&
(![X]:((tall(X)&~funny(X))=>funny(X)))&
(![X]:((~wise(X)&kind(X))<=>(~rich(X)<~>~calm(X))))&
(![X]:((~kind(X)|~curious(X))<=>(~generous(X)<~>~strong(X))))&
(![X]:(kind(X)=>(~wise(X)|brave(X))))&
((?[X]:((~happy(X)<~>curious(X))))=>(~strong(susan)))&
(![X]:((curious(X)|~happy(X))=>strong(X)))&
(![X]:((funny(X)<~>~kind(X))<=>~generous(X)))&
((~humble(susan))=>(~wise(paul)))&
(![X]:((~generous(X)|curious(X))<=>~wise(X)))&
((?[X]:((kind(X)<~>patient(X))))=>(?[X]:((~kind(X)<~>tall(X)))))&
(![X]:((old(X)&curious(X))=>(~patient(X)&~funny(X))))&
(![X]:(~happy(X)<=>(wise(X)&kind(X))))&
(((happy(lucy)|brave(lucy)))<=>(rich(lucy)))&
(?[X]:((brave(X)|calm(X))))&
(?[X]:((happy(X)|~humble(X))))&
((~rich(paul)<~>~funny(paul)))&
((brave(john)|~funny(john)))&
((~rich(lucy)<~>curious(lucy)))&
((~brave(mary)|~calm(mary)))&
(?[X]:((creative(X)<~>kind(X)))) | strong(lucy) | [
"p8",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5703029762011546420417584
% SZS output start Proof for 5703029762011546420417584
9. ! [X0] : ((~happy(X0) | curious(X0)) => strong(X0)) [input p8]
16. (brave(lucy) | happy(lucy)) <=> rich(lucy) [input p15]
21. ~rich(lucy) <~> curious(lucy) [input p20]
24. ~strong(lucy) [input hypothesis]
35. ! [X0] : (strong(X0) | (happy(X0) & ~curious(X0))) [ennf transformation 9]
55. ((brave(lucy) | happy(lucy)) | ~rich(lucy)) & (rich(lucy) | (~brave(lucy) & ~happy(lucy))) [nnf transformation 16]
56. (brave(lucy) | happy(lucy) | ~rich(lucy)) & (rich(lucy) | (~brave(lucy) & ~happy(lucy))) [flattening 55]
62. (~curious(lucy) | rich(lucy)) & (curious(lucy) | ~rich(lucy)) [nnf transformation 21]
87. ~curious(X0) | strong(X0) [cnf transformation 35]
88. strong(X0) | happy(X0) [cnf transformation 35]
106. rich(lucy) | ~happy(lucy) [cnf transformation 56]
114. curious(lucy) | ~rich(lucy) [cnf transformation 62]
119. ~strong(lucy) [cnf transformation 24]
181. 15 <=> rich(lucy) [avatar definition]
185. 16 <=> happy(lucy) [avatar definition]
194. ~16 | 15 [avatar split clause 106,181,185]
233. 26 <=> curious(lucy) [avatar definition]
234. curious(lucy) <- (26) [avatar component clause 233]
237. ~15 | 26 [avatar split clause 114,233,181]
259. happy(lucy) [resolution 88,119]
263. 16 [avatar split clause 259,185]
264. strong(lucy) <- (26) [resolution 234,87]
265. $false <- (26) [subsumption resolution 264,119]
266. ~26 [avatar contradiction clause 265]
267. $false [avatar sat refutation 194,237,263,266]
% SZS output end Proof for 5703029762011546420417584
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both patient and strong is either humble or creative.
Everyone who is not strong or kind is calm or rich and vice versa.
Everyone who is both not calm and kind is both old and wise and vice versa.
If john is not brave or funny then someone is wise and vice versa.
If susan is not funny then john is either quiet or old.
If lucy is not patient then someone is old or creative.
If mary is not strong then mary is both happy and not tall.
Everyone who is both not generous and quiet is quiet or kind.
Everyone who is not wise is both not funny and generous.
If someone is either not old or wise then someone is calm.
If alice is patient then someone is not calm or generous and vice versa.
Everyone who is both not humble and tall is creative or humble and vice versa.
If someone is either old or humble then alice is both quiet and kind.
Everyone who is either kind or not patient is either not humble or rich.
If someone is either not generous or not kind then someone is both not brave and not generous and vice versa.
If john is either not funny or patient then someone is either humble or not old and vice versa.
Someone is both funny and not kind.
John is either not humble or happy.
Fred is either not strong or tall.
Someone is both not strong and creative.
Someone is both not curious and not happy.
Paul is not kind or happy.
Someone is both not creative and happy.
Someone is not happy. | Alice is quiet. | neutral | (![X]:((patient(X)&strong(X))=>(humble(X)<~>creative(X))))&
(![X]:((~strong(X)|kind(X))<=>(calm(X)|rich(X))))&
(![X]:((~calm(X)&kind(X))<=>(old(X)&wise(X))))&
(((~brave(john)|funny(john)))<=>(?[X]:(wise(X))))&
((~funny(susan))=>((quiet(john)<~>old(john))))&
((~patient(lucy))=>(?[X]:((old(X)|creative(X)))))&
((~strong(mary))=>((happy(mary)&~tall(mary))))&
(![X]:((~generous(X)&quiet(X))=>(quiet(X)|kind(X))))&
(![X]:(~wise(X)=>(~funny(X)&generous(X))))&
((?[X]:((~old(X)<~>wise(X))))=>(?[X]:(calm(X))))&
((patient(alice))<=>(?[X]:((~calm(X)|generous(X)))))&
(![X]:((~humble(X)&tall(X))<=>(creative(X)|humble(X))))&
((?[X]:((old(X)<~>humble(X))))=>((quiet(alice)&kind(alice))))&
(![X]:((kind(X)<~>~patient(X))=>(~humble(X)<~>rich(X))))&
((?[X]:((~generous(X)<~>~kind(X))))<=>(?[X]:((~brave(X)&~generous(X)))))&
(((~funny(john)<~>patient(john)))<=>(?[X]:((humble(X)<~>~old(X)))))&
(?[X]:((funny(X)&~kind(X))))&
((~humble(john)<~>happy(john)))&
((~strong(fred)<~>tall(fred)))&
(?[X]:((~strong(X)&creative(X))))&
(?[X]:((~curious(X)&~happy(X))))&
((~kind(paul)|happy(paul)))&
(?[X]:((~creative(X)&happy(X))))&
(?[X]:(~happy(X))) | quiet(alice) | [] | null | 0 |
Everyone who is both not kind and not happy is both old and quiet.
Everyone who is kind is not wise and vice versa.
If fred is either funny or not brave then lucy is not tall and vice versa.
If mary is either not calm or quiet then john is either not creative or happy and vice versa.
If someone is both not calm and calm then susan is strong.
Everyone who is either not creative or patient is kind and vice versa.
Everyone who is not rich is both not rich and not creative and vice versa.
If lucy is either not humble or not quiet then fred is both not funny and not rich and vice versa.
Everyone who is both not humble and not happy is not creative.
If john is both quiet and not rich then someone is not quiet and vice versa.
Everyone who is not tall is either brave or patient.
Everyone who is humble or wise is not patient.
Everyone who is both not patient and not kind is either not rich or funny.
If alice is both strong and not generous then someone is either not quiet or tall.
If fred is both happy and funny then someone is funny or not wise.
If lucy is wise or patient then john is both humble and happy.
Mary is both rich and not patient.
Susan is old.
Fred is not creative or not brave.
Lucy is rich or not tall.
Alice is both wise and not kind.
Paul is either not rich or not creative.
Paul is both happy and not brave.
Alice is old. | Lucy is patient. | neutral | (![X]:((~kind(X)&~happy(X))=>(old(X)&quiet(X))))&
(![X]:(kind(X)<=>~wise(X)))&
(((funny(fred)<~>~brave(fred)))<=>(~tall(lucy)))&
(((~calm(mary)<~>quiet(mary)))<=>((~creative(john)<~>happy(john))))&
((?[X]:((~calm(X)&calm(X))))=>(strong(susan)))&
(![X]:((~creative(X)<~>patient(X))<=>kind(X)))&
(![X]:(~rich(X)<=>(~rich(X)&~creative(X))))&
(((~humble(lucy)<~>~quiet(lucy)))<=>((~funny(fred)&~rich(fred))))&
(![X]:((~humble(X)&~happy(X))=>~creative(X)))&
(((quiet(john)&~rich(john)))<=>(?[X]:(~quiet(X))))&
(![X]:(~tall(X)=>(brave(X)<~>patient(X))))&
(![X]:((humble(X)|wise(X))=>~patient(X)))&
(![X]:((~patient(X)&~kind(X))=>(~rich(X)<~>funny(X))))&
(((strong(alice)&~generous(alice)))=>(?[X]:((~quiet(X)<~>tall(X)))))&
(((happy(fred)&funny(fred)))=>(?[X]:((funny(X)|~wise(X)))))&
(((wise(lucy)|patient(lucy)))=>((humble(john)&happy(john))))&
((rich(mary)&~patient(mary)))&
(old(susan))&
((~creative(fred)|~brave(fred)))&
((rich(lucy)|~tall(lucy)))&
((wise(alice)&~kind(alice)))&
((~rich(paul)<~>~creative(paul)))&
((happy(paul)&~brave(paul)))&
(old(alice)) | patient(lucy) | [] | null | 0 |
Everyone who is either strong or not strong is both not funny and creative.
Everyone who is strong or wise is happy or patient and vice versa.
If mary is not strong or not generous then fred is not curious or humble and vice versa.
Everyone who is both rich and not quiet is not strong or humble.
Everyone who is not tall is not brave and vice versa.
Everyone who is both not brave and calm is either not calm or humble.
Everyone who is both not kind and happy is both kind and quiet.
If someone is wise or old then mary is both not funny and funny and vice versa.
If someone is both not curious and generous then someone is not creative and vice versa.
Everyone who is both old and happy is both funny and not wise.
If someone is either not kind or not happy then someone is not curious.
Everyone who is not wise or humble is either curious or not wise.
If someone is either not generous or not tall then susan is humble and vice versa.
Everyone who is both not patient and old is happy or not rich and vice versa.
If someone is happy then someone is not brave and vice versa.
Someone is not happy or funny.
John is either not generous or wise.
Someone is both not old and not wise.
Someone is both not wise and humble.
Someone is not funny or tall.
Fred is either quiet or not curious. | John is not wise. | entailment | (![X]:((strong(X)<~>~strong(X))=>(~funny(X)&creative(X))))&
(![X]:((strong(X)|wise(X))<=>(happy(X)|patient(X))))&
(((~strong(mary)|~generous(mary)))<=>((~curious(fred)|humble(fred))))&
(![X]:((rich(X)&~quiet(X))=>(~strong(X)|humble(X))))&
(![X]:(~tall(X)<=>~brave(X)))&
(![X]:((~brave(X)&calm(X))=>(~calm(X)<~>humble(X))))&
(![X]:((~kind(X)&happy(X))=>(kind(X)&quiet(X))))&
((?[X]:((wise(X)|old(X))))<=>((~funny(mary)&funny(mary))))&
((?[X]:((~curious(X)&generous(X))))<=>(?[X]:(~creative(X))))&
(![X]:((old(X)&happy(X))=>(funny(X)&~wise(X))))&
((?[X]:((~kind(X)<~>~happy(X))))=>(?[X]:(~curious(X))))&
(![X]:((~wise(X)|humble(X))=>(curious(X)<~>~wise(X))))&
((?[X]:((~generous(X)<~>~tall(X))))<=>(humble(susan)))&
(![X]:((~patient(X)&old(X))<=>(happy(X)|~rich(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~brave(X))))&
(?[X]:((~happy(X)|funny(X))))&
((~generous(john)<~>wise(john)))&
(?[X]:((~old(X)&~wise(X))))&
(?[X]:((~wise(X)&humble(X))))&
(?[X]:((~funny(X)|tall(X))))&
((quiet(fred)<~>~curious(fred))) | ~wise(john) | [
"p0",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4749851387709390585404347
% SZS output start Proof for 4749851387709390585404347
1. ! [X0] : ((strong(X0) <~> ~strong(X0)) => (creative(X0) & ~funny(X0))) [input p0]
8. ? [X0] : (old(X0) | wise(X0)) <=> (funny(mary) & ~funny(mary)) [input p7]
22. wise(john) [input hypothesis]
26. ! [X0] : ((creative(X0) & ~funny(X0)) | (strong(X0) <=> ~strong(X0))) [ennf transformation 1]
37. ! [X0] : ((creative(X0) & ~funny(X0)) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) [nnf transformation 26]
44. (? [X0] : (old(X0) | wise(X0)) | (~funny(mary) | funny(mary))) & ((funny(mary) & ~funny(mary)) | ! [X0] : (~old(X0) & ~wise(X0))) [nnf transformation 8]
45. (? [X0] : (old(X0) | wise(X0)) | ~funny(mary) | funny(mary)) & ((funny(mary) & ~funny(mary)) | ! [X0] : (~old(X0) & ~wise(X0))) [flattening 44]
46. (? [X0] : (old(X0) | wise(X0)) | ~funny(mary) | funny(mary)) & ((funny(mary) & ~funny(mary)) | ! [X1] : (~old(X1) & ~wise(X1))) [rectify 45]
47. ? [X0] : (old(X0) | wise(X0)) => (old(sK0) | wise(sK0)) [choice axiom]
48. ((old(sK0) | wise(sK0)) | ~funny(mary) | funny(mary)) & ((funny(mary) & ~funny(mary)) | ! [X1] : (~old(X1) & ~wise(X1))) [skolemisation 46,47]
80. ~funny(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 37]
81. ~funny(X0) | strong(X0) | strong(X0) [cnf transformation 37]
101. funny(mary) | ~wise(X1) [cnf transformation 48]
136. wise(john) [cnf transformation 22]
140. ~funny(X0) | ~strong(X0) [duplicate literal removal 80]
141. ~funny(X0) | strong(X0) [duplicate literal removal 81]
145. ~funny(X0) [subsumption resolution 140,141]
167. ~wise(X1) [subsumption resolution 101,145]
206. $false [subsumption resolution 136,167]
% SZS output end Proof for 4749851387709390585404347
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and not creative is not calm. If someone is either not old or not patient then someone is rich. If someone is not quiet or wise then someone is both funny and not kind and vice versa. If john is tall then john is curious. Everyone who is both not kind and patient is either not patient or quiet. Everyone who is both quiet and strong is generous. Everyone who is not calm is not kind and vice versa. If alice is both wise and not quiet then paul is old. Everyone who is not funny or not curious is funny or not humble and vice versa. Everyone who is either not calm or not wise is strong. Everyone who is quiet or humble is either not calm or tall and vice versa. If someone is funny then someone is either not creative or not kind. If someone is either not wise or quiet then john is both not strong and curious and vice versa. If someone is brave then someone is not rich or not calm. If someone is both curious and not patient then someone is both not happy and not strong. If susan is either brave or not old then alice is either creative or wise. John is either humble or not rich. Alice is kind or strong. Someone is either not strong or quiet. Susan is not happy or not rich. Fred is both not wise and not old. Paul is both brave and not curious. Mary is not creative. Lucy is creative. | Fred is not old. | entailment | (![X]:((kind(X)&~creative(X))=>~calm(X)))&
((?[X]:((~old(X)<~>~patient(X))))=>(?[X]:(rich(X))))&
((?[X]:((~quiet(X)|wise(X))))<=>(?[X]:((funny(X)&~kind(X)))))&
((tall(john))=>(curious(john)))&
(![X]:((~kind(X)&patient(X))=>(~patient(X)<~>quiet(X))))&
(![X]:((quiet(X)&strong(X))=>generous(X)))&
(![X]:(~calm(X)<=>~kind(X)))&
(((wise(alice)&~quiet(alice)))=>(old(paul)))&
(![X]:((~funny(X)|~curious(X))<=>(funny(X)|~humble(X))))&
(![X]:((~calm(X)<~>~wise(X))=>strong(X)))&
(![X]:((quiet(X)|humble(X))<=>(~calm(X)<~>tall(X))))&
((?[X]:(funny(X)))=>(?[X]:((~creative(X)<~>~kind(X)))))&
((?[X]:((~wise(X)<~>quiet(X))))<=>((~strong(john)&curious(john))))&
((?[X]:(brave(X)))=>(?[X]:((~rich(X)|~calm(X)))))&
((?[X]:((curious(X)&~patient(X))))=>(?[X]:((~happy(X)&~strong(X)))))&
(((brave(susan)<~>~old(susan)))=>((creative(alice)<~>wise(alice))))&
((humble(john)<~>~rich(john)))&
((kind(alice)|strong(alice)))&
(?[X]:((~strong(X)<~>quiet(X))))&
((~happy(susan)|~rich(susan)))&
((~wise(fred)&~old(fred)))&
((brave(paul)&~curious(paul)))&
(~creative(mary))&
(creative(lucy)) | ~old(fred) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 506445305972353014557874
% SZS output start Proof for 506445305972353014557874
21. ~old(fred) & ~wise(fred) [input p20]
25. old(fred) [input hypothesis]
129. ~old(fred) [cnf transformation 21]
134. old(fred) [cnf transformation 25]
304. $false [subsumption resolution 134,129]
% SZS output end Proof for 506445305972353014557874
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then someone is kind and vice versa.
Everyone who is either not old or old is both curious and not generous.
If someone is not brave or humble then someone is either not creative or not old.
If someone is not brave or not kind then susan is not creative or funny and vice versa.
Everyone who is both funny and generous is patient and vice versa.
Everyone who is either calm or not tall is not curious and vice versa.
If paul is kind or old then mary is brave or not strong.
If someone is both old and not happy then someone is either not strong or not calm.
Everyone who is humble or old is not generous.
If someone is both not brave and not patient then someone is either not brave or tall.
If someone is rich then alice is both tall and kind and vice versa.
If susan is both happy and generous then someone is both not funny and not rich.
Everyone who is either generous or not tall is both not patient and old.
Everyone who is both happy and brave is both not wise and tall.
Everyone who is quiet or tall is both not old and not curious and vice versa.
Everyone who is either curious or calm is generous or tall.
Someone is not brave or not generous.
Susan is either not calm or humble.
Lucy is not rich or quiet.
Mary is not strong or not quiet.
Fred is either not quiet or not curious.
Alice is both humble and curious. | Mary is not quiet. | entailment | ((generous(john))<=>(?[X]:(kind(X))))&
(![X]:((~old(X)<~>old(X))=>(curious(X)&~generous(X))))&
((?[X]:((~brave(X)|humble(X))))=>(?[X]:((~creative(X)<~>~old(X)))))&
((?[X]:((~brave(X)|~kind(X))))<=>((~creative(susan)|funny(susan))))&
(![X]:((funny(X)&generous(X))<=>patient(X)))&
(![X]:((calm(X)<~>~tall(X))<=>~curious(X)))&
(((kind(paul)|old(paul)))=>((brave(mary)|~strong(mary))))&
((?[X]:((old(X)&~happy(X))))=>(?[X]:((~strong(X)<~>~calm(X)))))&
(![X]:((humble(X)|old(X))=>~generous(X)))&
((?[X]:((~brave(X)&~patient(X))))=>(?[X]:((~brave(X)<~>tall(X)))))&
((?[X]:(rich(X)))<=>((tall(alice)&kind(alice))))&
(((happy(susan)&generous(susan)))=>(?[X]:((~funny(X)&~rich(X)))))&
(![X]:((generous(X)<~>~tall(X))=>(~patient(X)&old(X))))&
(![X]:((happy(X)&brave(X))=>(~wise(X)&tall(X))))&
(![X]:((quiet(X)|tall(X))<=>(~old(X)&~curious(X))))&
(![X]:((curious(X)<~>calm(X))=>(generous(X)|tall(X))))&
(?[X]:((~brave(X)|~generous(X))))&
((~calm(susan)<~>humble(susan)))&
((~rich(lucy)|quiet(lucy)))&
((~strong(mary)|~quiet(mary)))&
((~quiet(fred)<~>~curious(fred)))&
((humble(alice)&curious(alice))) | ~quiet(mary) | [
"p1",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 414004562645233862053199
% SZS output start Proof for 414004562645233862053199
2. ! [X0] : ((~old(X0) <~> old(X0)) => (~generous(X0) & curious(X0))) [input p1]
15. ! [X0] : ((tall(X0) | quiet(X0)) <=> (~curious(X0) & ~old(X0))) [input p14]
23. quiet(mary) [input hypothesis]
28. ! [X0] : ((~generous(X0) & curious(X0)) | (~old(X0) <=> old(X0))) [ennf transformation 2]
46. ! [X0] : ((~generous(X0) & curious(X0)) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) [nnf transformation 28]
75. ! [X0] : (((tall(X0) | quiet(X0)) | (curious(X0) | old(X0))) & ((~curious(X0) & ~old(X0)) | (~tall(X0) & ~quiet(X0)))) [nnf transformation 15]
76. ! [X0] : ((tall(X0) | quiet(X0) | curious(X0) | old(X0)) & ((~curious(X0) & ~old(X0)) | (~tall(X0) & ~quiet(X0)))) [flattening 75]
84. curious(X0) | old(X0) | old(X0) [cnf transformation 46]
85. curious(X0) | ~old(X0) | ~old(X0) [cnf transformation 46]
123. ~curious(X0) | ~quiet(X0) [cnf transformation 76]
137. quiet(mary) [cnf transformation 23]
138. curious(X0) | old(X0) [duplicate literal removal 84]
139. curious(X0) | ~old(X0) [duplicate literal removal 85]
156. curious(X0) [subsumption resolution 138,139]
264. ~quiet(X0) [subsumption resolution 123,156]
276. $false [subsumption resolution 137,264]
% SZS output end Proof for 414004562645233862053199
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and happy then lucy is not brave or creative. If someone is humble or not generous then someone is both strong and not wise and vice versa. Everyone who is generous is calm or not old and vice versa. Everyone who is both not wise and not curious is quiet and vice versa. Everyone who is both rich and happy is wise or old. Everyone who is either not tall or not old is either not wise or humble. If someone is either not rich or rich then someone is not happy or not old and vice versa. If someone is not humble or not funny then someone is brave or not strong. If susan is either not funny or quiet then alice is either strong or rich and vice versa. Everyone who is calm or not creative is both not generous and creative and vice versa. If mary is not curious then someone is either old or brave. If someone is both old and rich then alice is not brave or quiet. Everyone who is not creative is not quiet and vice versa. Everyone who is both not patient and generous is either not happy or not curious. Everyone who is either not tall or curious is either patient or kind and vice versa. Someone is either humble or not tall. Someone is not rich or not brave. Lucy is wise or happy. Someone is both creative and strong. Paul is brave. | Lucy is not curious. | entailment | ((?[X]:((~strong(X)&happy(X))))=>((~brave(lucy)|creative(lucy))))&
((?[X]:((humble(X)|~generous(X))))<=>(?[X]:((strong(X)&~wise(X)))))&
(![X]:(generous(X)<=>(calm(X)|~old(X))))&
(![X]:((~wise(X)&~curious(X))<=>quiet(X)))&
(![X]:((rich(X)&happy(X))=>(wise(X)|old(X))))&
(![X]:((~tall(X)<~>~old(X))=>(~wise(X)<~>humble(X))))&
((?[X]:((~rich(X)<~>rich(X))))<=>(?[X]:((~happy(X)|~old(X)))))&
((?[X]:((~humble(X)|~funny(X))))=>(?[X]:((brave(X)|~strong(X)))))&
(((~funny(susan)<~>quiet(susan)))<=>((strong(alice)<~>rich(alice))))&
(![X]:((calm(X)|~creative(X))<=>(~generous(X)&creative(X))))&
((~curious(mary))=>(?[X]:((old(X)<~>brave(X)))))&
((?[X]:((old(X)&rich(X))))=>((~brave(alice)|quiet(alice))))&
(![X]:(~creative(X)<=>~quiet(X)))&
(![X]:((~patient(X)&generous(X))=>(~happy(X)<~>~curious(X))))&
(![X]:((~tall(X)<~>curious(X))<=>(patient(X)<~>kind(X))))&
(?[X]:((humble(X)<~>~tall(X))))&
(?[X]:((~rich(X)|~brave(X))))&
((wise(lucy)|happy(lucy)))&
(?[X]:((creative(X)&strong(X))))&
(brave(paul)) | ~curious(lucy) | [
"p3",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5996919510094219693884686
% SZS output start Proof for 5996919510094219693884686
4. ! [X0] : ((~curious(X0) & ~wise(X0)) <=> quiet(X0)) [input p3]
10. ! [X0] : ((~creative(X0) | calm(X0)) <=> (creative(X0) & ~generous(X0))) [input p9]
13. ! [X0] : (~creative(X0) <=> ~quiet(X0)) [input p12]
21. curious(lucy) [input hypothesis]
43. ! [X0] : (((~curious(X0) & ~wise(X0)) | ~quiet(X0)) & (quiet(X0) | (curious(X0) | wise(X0)))) [nnf transformation 4]
44. ! [X0] : (((~curious(X0) & ~wise(X0)) | ~quiet(X0)) & (quiet(X0) | curious(X0) | wise(X0))) [flattening 43]
55. ! [X0] : (((~creative(X0) | calm(X0)) | (~creative(X0) | generous(X0))) & ((creative(X0) & ~generous(X0)) | (creative(X0) & ~calm(X0)))) [nnf transformation 10]
56. ! [X0] : ((~creative(X0) | calm(X0) | ~creative(X0) | generous(X0)) & ((creative(X0) & ~generous(X0)) | (creative(X0) & ~calm(X0)))) [flattening 55]
60. ! [X0] : ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0))) [nnf transformation 13]
81. ~quiet(X0) | ~curious(X0) [cnf transformation 44]
106. creative(X0) | creative(X0) [cnf transformation 56]
112. ~creative(X0) | quiet(X0) [cnf transformation 60]
130. curious(lucy) [cnf transformation 21]
131. creative(X0) [duplicate literal removal 106]
261. quiet(X0) [subsumption resolution 112,131]
297. ~curious(X0) [resolution 81,261]
303. $false [resolution 297,130]
% SZS output end Proof for 5996919510094219693884686
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or funny is both old and not creative. Everyone who is old or humble is creative. If someone is not curious then lucy is either brave or generous and vice versa. Everyone who is both not old and not strong is both calm and tall. Everyone who is either not wise or happy is either quiet or not curious. Everyone who is both tall and calm is not calm and vice versa. If someone is either funny or tall then alice is either happy or kind. Everyone who is not tall is either wise or not rich. Everyone who is not generous is not strong or not humble. Everyone who is not curious or calm is both not humble and kind and vice versa. If john is humble then alice is either not rich or not quiet. If john is both creative and funny then susan is either not quiet or brave and vice versa. If mary is kind then paul is creative or curious and vice versa. Everyone who is both not generous and not kind is both not happy and not creative. If fred is both old and not humble then someone is either old or not tall and vice versa. Everyone who is quiet is both humble and not creative and vice versa. Someone is both not creative and not humble. Someone is brave or not funny. Someone is not old. Lucy is both not old and not rich. | Alice is rich. | neutral | (![X]:((~curious(X)<~>funny(X))=>(old(X)&~creative(X))))&
(![X]:((old(X)|humble(X))=>creative(X)))&
((?[X]:(~curious(X)))<=>((brave(lucy)<~>generous(lucy))))&
(![X]:((~old(X)&~strong(X))=>(calm(X)&tall(X))))&
(![X]:((~wise(X)<~>happy(X))=>(quiet(X)<~>~curious(X))))&
(![X]:((tall(X)&calm(X))<=>~calm(X)))&
((?[X]:((funny(X)<~>tall(X))))=>((happy(alice)<~>kind(alice))))&
(![X]:(~tall(X)=>(wise(X)<~>~rich(X))))&
(![X]:(~generous(X)=>(~strong(X)|~humble(X))))&
(![X]:((~curious(X)|calm(X))<=>(~humble(X)&kind(X))))&
((humble(john))=>((~rich(alice)<~>~quiet(alice))))&
(((creative(john)&funny(john)))<=>((~quiet(susan)<~>brave(susan))))&
((kind(mary))<=>((creative(paul)|curious(paul))))&
(![X]:((~generous(X)&~kind(X))=>(~happy(X)&~creative(X))))&
(((old(fred)&~humble(fred)))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:(quiet(X)<=>(humble(X)&~creative(X))))&
(?[X]:((~creative(X)&~humble(X))))&
(?[X]:((brave(X)|~funny(X))))&
(?[X]:(~old(X)))&
((~old(lucy)&~rich(lucy))) | rich(alice) | [] | null | 0 |
Subsets and Splits