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
|
|---|---|---|---|---|---|---|---|
If alice is both curious and old then someone is both not calm and old and vice versa.
Everyone who is funny or not creative is either not quiet or calm.
Everyone who is wise or not tall is not calm or humble.
If lucy is calm then lucy is either funny or not quiet.
If someone is not curious or happy then someone is either not wise or patient and vice versa.
Everyone who is tall or not funny is both strong and not creative and vice versa.
Everyone who is either tall or not kind is both not strong and rich.
Everyone who is both not creative and not rich is either not funny or not patient and vice versa.
If john is funny then alice is either old or not old.
Everyone who is both not old and curious is both not creative and not tall and vice versa.
Everyone who is either strong or generous is both rich and strong.
Everyone who is not tall is not patient and vice versa.
If someone is both tall and funny then someone is not calm or not strong and vice versa.
Everyone who is not humble is calm or brave and vice versa.
Everyone who is rich or not wise is either old or not rich.
Everyone who is not creative or not rich is curious.
Someone is not patient.
Lucy is either not humble or tall.
Someone is happy or not humble.
Someone is not creative.
Someone is not curious or not funny.
Mary is kind or not happy.
Alice is curious or not wise. | Lucy is not creative. | entailment | (((curious(alice)&old(alice)))<=>(?[X]:((~calm(X)&old(X)))))&
(![X]:((funny(X)|~creative(X))=>(~quiet(X)<~>calm(X))))&
(![X]:((wise(X)|~tall(X))=>(~calm(X)|humble(X))))&
((calm(lucy))=>((funny(lucy)<~>~quiet(lucy))))&
((?[X]:((~curious(X)|happy(X))))<=>(?[X]:((~wise(X)<~>patient(X)))))&
(![X]:((tall(X)|~funny(X))<=>(strong(X)&~creative(X))))&
(![X]:((tall(X)<~>~kind(X))=>(~strong(X)&rich(X))))&
(![X]:((~creative(X)&~rich(X))<=>(~funny(X)<~>~patient(X))))&
((funny(john))=>((old(alice)<~>~old(alice))))&
(![X]:((~old(X)&curious(X))<=>(~creative(X)&~tall(X))))&
(![X]:((strong(X)<~>generous(X))=>(rich(X)&strong(X))))&
(![X]:(~tall(X)<=>~patient(X)))&
((?[X]:((tall(X)&funny(X))))<=>(?[X]:((~calm(X)|~strong(X)))))&
(![X]:(~humble(X)<=>(calm(X)|brave(X))))&
(![X]:((rich(X)|~wise(X))=>(old(X)<~>~rich(X))))&
(![X]:((~creative(X)|~rich(X))=>curious(X)))&
(?[X]:(~patient(X)))&
((~humble(lucy)<~>tall(lucy)))&
(?[X]:((happy(X)|~humble(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~curious(X)|~funny(X))))&
((kind(mary)|~happy(mary)))&
((curious(alice)|~wise(alice))) | ~creative(lucy) | [
"p5",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7037427194655628406522499
% SZS output start Proof for 7037427194655628406522499
6. ! [X0] : ((~funny(X0) | tall(X0)) <=> (~creative(X0) & strong(X0))) [input p5]
8. ! [X0] : ((~rich(X0) & ~creative(X0)) <=> (~funny(X0) <~> ~patient(X0))) [input p7]
12. ! [X0] : (~tall(X0) <=> ~patient(X0)) [input p11]
24. creative(lucy) [input hypothesis]
48. ! [X0] : (((~funny(X0) | tall(X0)) | (creative(X0) | ~strong(X0))) & ((~creative(X0) & strong(X0)) | (funny(X0) & ~tall(X0)))) [nnf transformation 6]
49. ! [X0] : ((~funny(X0) | tall(X0) | creative(X0) | ~strong(X0)) & ((~creative(X0) & strong(X0)) | (funny(X0) & ~tall(X0)))) [flattening 48]
51. ! [X0] : (((~rich(X0) & ~creative(X0)) | ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) & (((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) | (rich(X0) | creative(X0)))) [nnf transformation 8]
52. ! [X0] : (((~rich(X0) & ~creative(X0)) | ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) & (((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) | rich(X0) | creative(X0))) [flattening 51]
57. ! [X0] : ((~tall(X0) | patient(X0)) & (~patient(X0) | tall(X0))) [nnf transformation 12]
95. ~tall(X0) | ~creative(X0) [cnf transformation 49]
96. ~creative(X0) | funny(X0) [cnf transformation 49]
105. ~creative(X0) | ~funny(X0) | patient(X0) [cnf transformation 52]
118. ~patient(X0) | tall(X0) [cnf transformation 57]
142. creative(lucy) [cnf transformation 24]
216. ~creative(X0) | patient(X0) [subsumption resolution 105,96]
253. 25 <=> tall(lucy) [avatar definition]
254. tall(lucy) <- (25) [avatar component clause 253]
307. patient(lucy) [resolution 216,142]
309. tall(lucy) [resolution 307,118]
312. 25 [avatar split clause 309,253]
315. ~creative(lucy) <- (25) [resolution 254,95]
317. $false <- (25) [subsumption resolution 315,142]
318. ~25 [avatar contradiction clause 317]
319. $false [avatar sat refutation 312,318]
% SZS output end Proof for 7037427194655628406522499
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not rich or not happy then someone is either kind or not curious and vice versa.
If someone is strong or humble then someone is either not wise or tall and vice versa.
If someone is not patient then someone is curious.
Everyone who is both not tall and not rich is either kind or not old.
Everyone who is either not calm or not quiet is kind or not funny and vice versa.
If someone is both old and happy then fred is not old and vice versa.
Everyone who is strong or not tall is either creative or tall and vice versa.
Everyone who is either not happy or funny is both not humble and not old.
If john is either not humble or wise then someone is not wise or not generous.
If alice is either not creative or kind then someone is either not brave or not strong and vice versa.
If someone is either not curious or not wise then mary is both wise and not wise.
Everyone who is tall or humble is patient or old and vice versa.
Everyone who is not humble or not brave is not curious or not happy.
If paul is not brave or not patient then john is both tall and not quiet and vice versa.
Everyone who is not quiet or not strong is patient or not humble and vice versa.
If someone is either quiet or calm then someone is both not creative and generous.
Someone is both not generous and calm.
Someone is both not humble and patient.
Someone is not strong.
Someone is both not calm and not patient.
John is both not humble and kind.
Paul is either happy or not kind.
Alice is curious.
Someone is calm. | Alice is wise. | entailment | (((~rich(paul)<~>~happy(paul)))<=>(?[X]:((kind(X)<~>~curious(X)))))&
((?[X]:((strong(X)|humble(X))))<=>(?[X]:((~wise(X)<~>tall(X)))))&
((?[X]:(~patient(X)))=>(?[X]:(curious(X))))&
(![X]:((~tall(X)&~rich(X))=>(kind(X)<~>~old(X))))&
(![X]:((~calm(X)<~>~quiet(X))<=>(kind(X)|~funny(X))))&
((?[X]:((old(X)&happy(X))))<=>(~old(fred)))&
(![X]:((strong(X)|~tall(X))<=>(creative(X)<~>tall(X))))&
(![X]:((~happy(X)<~>funny(X))=>(~humble(X)&~old(X))))&
(((~humble(john)<~>wise(john)))=>(?[X]:((~wise(X)|~generous(X)))))&
(((~creative(alice)<~>kind(alice)))<=>(?[X]:((~brave(X)<~>~strong(X)))))&
((?[X]:((~curious(X)<~>~wise(X))))=>((wise(mary)&~wise(mary))))&
(![X]:((tall(X)|humble(X))<=>(patient(X)|old(X))))&
(![X]:((~humble(X)|~brave(X))=>(~curious(X)|~happy(X))))&
(((~brave(paul)|~patient(paul)))<=>((tall(john)&~quiet(john))))&
(![X]:((~quiet(X)|~strong(X))<=>(patient(X)|~humble(X))))&
((?[X]:((quiet(X)<~>calm(X))))=>(?[X]:((~creative(X)&generous(X)))))&
(?[X]:((~generous(X)&calm(X))))&
(?[X]:((~humble(X)&patient(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~calm(X)&~patient(X))))&
((~humble(john)&kind(john)))&
((happy(paul)<~>~kind(paul)))&
(curious(alice))&
(?[X]:(calm(X))) | wise(alice) | [
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3730828488386697353481743
% SZS output start Proof for 3730828488386697353481743
11. ? [X0] : (~curious(X0) <~> ~wise(X0)) => (~wise(mary) & wise(mary)) [input p10]
23. curious(alice) [input p22]
25. ~wise(alice) [input hypothesis]
34. (~wise(mary) & wise(mary)) | ! [X0] : (~curious(X0) <=> ~wise(X0)) [ennf transformation 11]
67. (~wise(mary) & wise(mary)) | ! [X0] : ((~curious(X0) | wise(X0)) & (~wise(X0) | curious(X0))) [nnf transformation 34]
136. wise(mary) | ~curious(X0) | wise(X0) [cnf transformation 67]
138. ~wise(mary) | ~curious(X0) | wise(X0) [cnf transformation 67]
169. curious(alice) [cnf transformation 23]
171. ~wise(alice) [cnf transformation 25]
313. 31 <=> ! [X0] : (~curious(X0) | wise(X0)) [avatar definition]
314. ~curious(X0) | wise(X0) <- (31) [avatar component clause 313]
316. 32 <=> wise(mary) [avatar definition]
319. 31 | ~32 [avatar split clause 138,316,313]
324. 31 | 32 [avatar split clause 136,316,313]
375. wise(alice) <- (31) [resolution 314,169]
377. $false <- (31) [subsumption resolution 375,171]
378. ~31 [avatar contradiction clause 377]
379. $false [avatar sat refutation 319,324,378]
% SZS output end Proof for 3730828488386697353481743
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is humble then someone is either not humble or curious. Everyone who is both not old and funny is either not funny or old and vice versa. Everyone who is not wise or not funny is kind and vice versa. If mary is either not curious or not humble then john is either not curious or humble and vice versa. If john is both curious and not brave then someone is both funny and humble and vice versa. Everyone who is not creative or not generous is curious or rich and vice versa. Everyone who is either rich or brave is both patient and not calm and vice versa. If fred is either not calm or not strong then fred is brave or not generous. If someone is not humble then someone is both rich and tall and vice versa. Everyone who is curious is not wise and vice versa. Everyone who is either wise or humble is either strong or not tall and vice versa. Everyone who is not curious or curious is both creative and not curious and vice versa. Everyone who is either not creative or patient is either humble or calm and vice versa. If someone is both not tall and humble then someone is either quiet or not strong and vice versa. If mary is both not old and not rich then someone is old or patient. Everyone who is both curious and not calm is not quiet. Someone is both not strong and not quiet. Someone is either humble or not calm. Mary is both old and tall. Paul is either kind or not calm. Susan is either not funny or rich. | Fred is not kind. | contradiction | ((humble(paul))=>(?[X]:((~humble(X)<~>curious(X)))))&
(![X]:((~old(X)&funny(X))<=>(~funny(X)<~>old(X))))&
(![X]:((~wise(X)|~funny(X))<=>kind(X)))&
(((~curious(mary)<~>~humble(mary)))<=>((~curious(john)<~>humble(john))))&
(((curious(john)&~brave(john)))<=>(?[X]:((funny(X)&humble(X)))))&
(![X]:((~creative(X)|~generous(X))<=>(curious(X)|rich(X))))&
(![X]:((rich(X)<~>brave(X))<=>(patient(X)&~calm(X))))&
(((~calm(fred)<~>~strong(fred)))=>((brave(fred)|~generous(fred))))&
((?[X]:(~humble(X)))<=>(?[X]:((rich(X)&tall(X)))))&
(![X]:(curious(X)<=>~wise(X)))&
(![X]:((wise(X)<~>humble(X))<=>(strong(X)<~>~tall(X))))&
(![X]:((~curious(X)|curious(X))<=>(creative(X)&~curious(X))))&
(![X]:((~creative(X)<~>patient(X))<=>(humble(X)<~>calm(X))))&
((?[X]:((~tall(X)&humble(X))))<=>(?[X]:((quiet(X)<~>~strong(X)))))&
(((~old(mary)&~rich(mary)))=>(?[X]:((old(X)|patient(X)))))&
(![X]:((curious(X)&~calm(X))=>~quiet(X)))&
(?[X]:((~strong(X)&~quiet(X))))&
(?[X]:((humble(X)<~>~calm(X))))&
((old(mary)&tall(mary)))&
((kind(paul)<~>~calm(paul)))&
((~funny(susan)<~>rich(susan))) | ~kind(fred) | [
"p1",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 4908830548956031399387009
% SZS output start Proof for 4908830548956031399387009
2. ! [X0] : ((funny(X0) & ~old(X0)) <=> (~funny(X0) <~> old(X0))) [input p1]
3. ! [X0] : ((~funny(X0) | ~wise(X0)) <=> kind(X0)) [input p2]
22. ~kind(fred) [input hypothesis]
35. ! [X0] : (((funny(X0) & ~old(X0)) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0)))) & (((~old(X0) | funny(X0)) & (old(X0) | ~funny(X0))) | (~funny(X0) | old(X0)))) [nnf transformation 2]
36. ! [X0] : (((funny(X0) & ~old(X0)) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0)))) & (((~old(X0) | funny(X0)) & (old(X0) | ~funny(X0))) | ~funny(X0) | old(X0))) [flattening 35]
37. ! [X0] : (((~funny(X0) | ~wise(X0)) | ~kind(X0)) & (kind(X0) | (funny(X0) & wise(X0)))) [nnf transformation 3]
38. ! [X0] : ((~funny(X0) | ~wise(X0) | ~kind(X0)) & (kind(X0) | (funny(X0) & wise(X0)))) [flattening 37]
76. old(X0) | ~funny(X0) | ~funny(X0) | old(X0) [cnf transformation 36]
79. ~old(X0) | ~funny(X0) | ~old(X0) [cnf transformation 36]
83. kind(X0) | funny(X0) [cnf transformation 38]
153. ~kind(fred) [cnf transformation 22]
156. old(X0) | ~funny(X0) [duplicate literal removal 76]
157. ~old(X0) | ~funny(X0) [duplicate literal removal 79]
173. ~funny(X0) [subsumption resolution 156,157]
174. kind(X0) [subsumption resolution 83,173]
315. $false [subsumption resolution 153,174]
% SZS output end Proof for 4908830548956031399387009
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or not humble is either brave or curious and vice versa.
Everyone who is both tall and not wise is either not brave or not patient.
If paul is both not funny and strong then someone is either old or patient and vice versa.
If someone is either not curious or humble then fred is both not curious and not strong and vice versa.
Everyone who is tall or not tall is not humble and vice versa.
If fred is not calm or not rich then someone is kind.
Everyone who is not strong or not happy is either tall or humble and vice versa.
Everyone who is happy is strong.
If mary is humble then someone is either wise or generous.
Everyone who is both creative and rich is both creative and funny.
If john is both strong and funny then someone is not creative.
If someone is happy or curious then someone is either quiet or generous and vice versa.
If alice is wise or old then someone is either old or not tall.
Everyone who is both generous and patient is not happy and vice versa.
Everyone who is both quiet and not wise is not tall or not happy and vice versa.
If someone is either not generous or curious then john is both not brave and not quiet and vice versa.
Paul is creative.
Someone is either curious or not curious.
Someone is not brave.
Paul is either not tall or not humble.
John is not humble.
Someone is not humble.
Alice is quiet. | Paul is rich. | contradiction | (![X]:((~rich(X)<~>~humble(X))<=>(brave(X)<~>curious(X))))&
(![X]:((tall(X)&~wise(X))=>(~brave(X)<~>~patient(X))))&
(((~funny(paul)&strong(paul)))<=>(?[X]:((old(X)<~>patient(X)))))&
((?[X]:((~curious(X)<~>humble(X))))<=>((~curious(fred)&~strong(fred))))&
(![X]:((tall(X)|~tall(X))<=>~humble(X)))&
(((~calm(fred)|~rich(fred)))=>(?[X]:(kind(X))))&
(![X]:((~strong(X)|~happy(X))<=>(tall(X)<~>humble(X))))&
(![X]:(happy(X)=>strong(X)))&
((humble(mary))=>(?[X]:((wise(X)<~>generous(X)))))&
(![X]:((creative(X)&rich(X))=>(creative(X)&funny(X))))&
(((strong(john)&funny(john)))=>(?[X]:(~creative(X))))&
((?[X]:((happy(X)|curious(X))))<=>(?[X]:((quiet(X)<~>generous(X)))))&
(((wise(alice)|old(alice)))=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:((generous(X)&patient(X))<=>~happy(X)))&
(![X]:((quiet(X)&~wise(X))<=>(~tall(X)|~happy(X))))&
((?[X]:((~generous(X)<~>curious(X))))<=>((~brave(john)&~quiet(john))))&
(creative(paul))&
(?[X]:((curious(X)<~>~curious(X))))&
(?[X]:(~brave(X)))&
((~tall(paul)<~>~humble(paul)))&
(~humble(john))&
(?[X]:(~humble(X)))&
(quiet(alice)) | rich(paul) | [
"p0",
"p1",
"p4",
"p6",
"p7",
"p13",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8655870204857432092568088
% SZS output start Proof for 8655870204857432092568088
1. ! [X0] : ((~rich(X0) <~> ~humble(X0)) <=> (brave(X0) <~> curious(X0))) [input p0]
2. ! [X0] : ((~wise(X0) & tall(X0)) => (~brave(X0) <~> ~patient(X0))) [input p1]
5. ! [X0] : ((~tall(X0) | tall(X0)) <=> ~humble(X0)) [input p4]
7. ! [X0] : ((~happy(X0) | ~strong(X0)) <=> (tall(X0) <~> humble(X0))) [input p6]
8. ! [X0] : (happy(X0) => strong(X0)) [input p7]
14. ! [X0] : ((patient(X0) & generous(X0)) <=> ~happy(X0)) [input p13]
15. ! [X0] : ((~wise(X0) & quiet(X0)) <=> (~happy(X0) | ~tall(X0))) [input p14]
16. ? [X0] : (~generous(X0) <~> curious(X0)) <=> (~quiet(john) & ~brave(john)) [input p15]
20. ~tall(paul) <~> ~humble(paul) [input p19]
24. rich(paul) [input hypothesis]
27. ! [X0] : ((~brave(X0) <~> ~patient(X0)) | (wise(X0) | ~tall(X0))) [ennf transformation 2]
28. ! [X0] : ((~brave(X0) <~> ~patient(X0)) | wise(X0) | ~tall(X0)) [flattening 27]
29. ! [X0] : (strong(X0) | ~happy(X0)) [ennf transformation 8]
36. ! [X0] : ((((humble(X0) | rich(X0)) & (~humble(X0) | ~rich(X0))) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0)))) & (((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | ((~rich(X0) | humble(X0)) & (~humble(X0) | rich(X0))))) [nnf transformation 1]
37. ! [X0] : (((patient(X0) | brave(X0)) & (~patient(X0) | ~brave(X0))) | wise(X0) | ~tall(X0)) [nnf transformation 28]
48. ! [X0] : (((~tall(X0) | tall(X0)) | humble(X0)) & (~humble(X0) | (tall(X0) & ~tall(X0)))) [nnf transformation 5]
49. ! [X0] : ((~tall(X0) | tall(X0) | humble(X0)) & (~humble(X0) | (tall(X0) & ~tall(X0)))) [flattening 48]
50. ! [X0] : (((~happy(X0) | ~strong(X0)) | ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0)))) & (((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | (happy(X0) & strong(X0)))) [nnf transformation 7]
51. ! [X0] : ((~happy(X0) | ~strong(X0) | ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0)))) & (((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | (happy(X0) & strong(X0)))) [flattening 50]
65. ! [X0] : (((patient(X0) & generous(X0)) | happy(X0)) & (~happy(X0) | (~patient(X0) | ~generous(X0)))) [nnf transformation 14]
66. ! [X0] : (((patient(X0) & generous(X0)) | happy(X0)) & (~happy(X0) | ~patient(X0) | ~generous(X0))) [flattening 65]
67. ! [X0] : (((~wise(X0) & quiet(X0)) | (happy(X0) & tall(X0))) & ((~happy(X0) | ~tall(X0)) | (wise(X0) | ~quiet(X0)))) [nnf transformation 15]
68. ! [X0] : (((~wise(X0) & quiet(X0)) | (happy(X0) & tall(X0))) & (~happy(X0) | ~tall(X0) | wise(X0) | ~quiet(X0))) [flattening 67]
69. (? [X0] : ((~curious(X0) | generous(X0)) & (curious(X0) | ~generous(X0))) | (quiet(john) | brave(john))) & ((~quiet(john) & ~brave(john)) | ! [X0] : ((~generous(X0) | ~curious(X0)) & (curious(X0) | generous(X0)))) [nnf transformation 16]
70. (? [X0] : ((~curious(X0) | generous(X0)) & (curious(X0) | ~generous(X0))) | quiet(john) | brave(john)) & ((~quiet(john) & ~brave(john)) | ! [X0] : ((~generous(X0) | ~curious(X0)) & (curious(X0) | generous(X0)))) [flattening 69]
71. (? [X0] : ((~curious(X0) | generous(X0)) & (curious(X0) | ~generous(X0))) | quiet(john) | brave(john)) & ((~quiet(john) & ~brave(john)) | ! [X1] : ((~generous(X1) | ~curious(X1)) & (curious(X1) | generous(X1)))) [rectify 70]
72. ? [X0] : ((~curious(X0) | generous(X0)) & (curious(X0) | ~generous(X0))) => ((~curious(sK7) | generous(sK7)) & (curious(sK7) | ~generous(sK7))) [choice axiom]
73. (((~curious(sK7) | generous(sK7)) & (curious(sK7) | ~generous(sK7))) | quiet(john) | brave(john)) & ((~quiet(john) & ~brave(john)) | ! [X1] : ((~generous(X1) | ~curious(X1)) & (curious(X1) | generous(X1)))) [skolemisation 71,72]
79. (humble(paul) | tall(paul)) & (~humble(paul) | ~tall(paul)) [nnf transformation 20]
83. ~rich(X0) | brave(X0) | curious(X0) | humble(X0) [cnf transformation 36]
90. ~patient(X0) | ~brave(X0) | wise(X0) | ~tall(X0) [cnf transformation 37]
104. ~humble(X0) | ~tall(X0) [cnf transformation 49]
105. ~humble(X0) | tall(X0) [cnf transformation 49]
111. ~happy(X0) | ~strong(X0) | humble(X0) | ~tall(X0) [cnf transformation 51]
113. ~happy(X0) | strong(X0) [cnf transformation 29]
129. ~generous(X0) | ~patient(X0) | ~happy(X0) [cnf transformation 66]
130. generous(X0) | happy(X0) [cnf transformation 66]
131. happy(X0) | patient(X0) [cnf transformation 66]
133. quiet(X0) | tall(X0) [cnf transformation 68]
134. quiet(X0) | happy(X0) [cnf transformation 68]
136. ~wise(X0) | happy(X0) [cnf transformation 68]
139. ~quiet(john) | curious(X1) | generous(X1) [cnf transformation 73]
140. ~quiet(john) | ~generous(X1) | ~curious(X1) [cnf transformation 73]
148. humble(paul) | tall(paul) [cnf transformation 79]
152. rich(paul) [cnf transformation 24]
157. 2 <=> strong(paul) [avatar definition]
209. ~humble(X0) [subsumption resolution 104,105]
210. ~happy(X0) | ~strong(X0) | ~tall(X0) [subsumption resolution 111,209]
214. 13 <=> strong(john) [avatar definition]
215. strong(john) <- (13) [avatar component clause 214]
285. 29 <=> quiet(john) [avatar definition]
286. ~quiet(john) <- (~29) [avatar component clause 285]
299. 32 <=> ! [X1] : (~generous(X1) | ~curious(X1)) [avatar definition]
300. ~generous(X1) | ~curious(X1) <- (32) [avatar component clause 299]
301. 32 | ~29 [avatar split clause 140,285,299]
303. 33 <=> ! [X1] : (curious(X1) | generous(X1)) [avatar definition]
304. generous(X1) | curious(X1) <- (33) [avatar component clause 303]
305. 33 | ~29 [avatar split clause 139,285,303]
308. tall(paul) [subsumption resolution 148,209]
312. strong(X0) | patient(X0) [resolution 131,113]
314. tall(john) <- (~29) [resolution 133,286]
316. happy(john) <- (~29) [resolution 134,286]
317. strong(john) <- (~29) [resolution 316,113]
318. 13 | 29 [avatar split clause 317,285,214]
334. ~strong(X1) | ~tall(X1) | patient(X1) [resolution 210,131]
335. ~strong(john) | ~tall(john) <- (~29) [resolution 210,316]
339. ~tall(X1) | patient(X1) [subsumption resolution 334,312]
340. ~tall(john) <- (13, ~29) [subsumption resolution 335,215]
341. $false <- (13, ~29) [subsumption resolution 340,314]
342. ~13 | 29 [avatar contradiction clause 341]
346. ~curious(X0) | happy(X0) <- (32) [resolution 300,130]
350. ~happy(X1) | ~patient(X1) | curious(X1) <- (33) [resolution 304,129]
364. brave(paul) | curious(paul) | humble(paul) [resolution 83,152]
365. brave(paul) | curious(paul) [subsumption resolution 364,209]
367. 36 <=> curious(paul) [avatar definition]
368. ~curious(paul) <- (~36) [avatar component clause 367]
369. curious(paul) <- (36) [avatar component clause 367]
371. 37 <=> brave(paul) [avatar definition]
373. brave(paul) <- (37) [avatar component clause 371]
374. 36 | 37 [avatar split clause 365,371,367]
500. patient(paul) [resolution 339,308]
635. ~brave(paul) | wise(paul) | ~tall(paul) [resolution 500,90]
637. wise(paul) | ~tall(paul) <- (37) [subsumption resolution 635,373]
638. wise(paul) <- (37) [subsumption resolution 637,308]
688. happy(paul) <- (37) [resolution 638,136]
693. ~patient(paul) | curious(paul) <- (33, 37) [resolution 688,350]
696. curious(paul) <- (33, 37) [subsumption resolution 693,500]
697. $false <- (33, ~36, 37) [subsumption resolution 696,368]
698. ~33 | 36 | ~37 [avatar contradiction clause 697]
708. happy(paul) <- (32, 36) [resolution 369,346]
715. ~strong(paul) | ~tall(paul) <- (32, 36) [resolution 708,210]
716. strong(paul) <- (32, 36) [resolution 708,113]
720. 2 | ~32 | ~36 [avatar split clause 716,367,299,157]
721. ~strong(paul) <- (32, 36) [subsumption resolution 715,308]
722. ~2 | ~32 | ~36 [avatar split clause 721,367,299,157]
723. $false [avatar sat refutation 301,305,318,342,374,698,720,722]
% SZS output end Proof for 8655870204857432092568088
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not wise or happy then someone is either not wise or not funny and vice versa.
Everyone who is both not strong and not old is both generous and kind and vice versa.
If someone is not generous then john is both not tall and creative and vice versa.
If someone is either not wise or rich then someone is either not calm or generous and vice versa.
Everyone who is either not generous or not humble is patient or not tall.
Everyone who is not tall is both old and not generous.
If someone is rich or not tall then someone is not generous or not old and vice versa.
If someone is either not calm or calm then john is not happy.
Everyone who is calm or humble is either creative or generous and vice versa.
Everyone who is either not kind or old is curious or generous.
If alice is not happy or curious then alice is not old or tall and vice versa.
If someone is creative or not funny then someone is wise or humble.
Everyone who is either not quiet or not kind is both tall and not old and vice versa.
Everyone who is both not funny and not rich is both not curious and not rich.
Everyone who is tall or patient is not tall or calm and vice versa.
Everyone who is either not rich or humble is either calm or humble.
Alice is either funny or not happy.
Someone is either not curious or not quiet.
Susan is calm or kind.
Someone is either not calm or not generous.
Fred is not creative.
Fred is not strong or rich.
Mary is either not patient or curious. | Alice is tall. | neutral | ((?[X]:((~wise(X)<~>happy(X))))<=>(?[X]:((~wise(X)<~>~funny(X)))))&
(![X]:((~strong(X)&~old(X))<=>(generous(X)&kind(X))))&
((?[X]:(~generous(X)))<=>((~tall(john)&creative(john))))&
((?[X]:((~wise(X)<~>rich(X))))<=>(?[X]:((~calm(X)<~>generous(X)))))&
(![X]:((~generous(X)<~>~humble(X))=>(patient(X)|~tall(X))))&
(![X]:(~tall(X)=>(old(X)&~generous(X))))&
((?[X]:((rich(X)|~tall(X))))<=>(?[X]:((~generous(X)|~old(X)))))&
((?[X]:((~calm(X)<~>calm(X))))=>(~happy(john)))&
(![X]:((calm(X)|humble(X))<=>(creative(X)<~>generous(X))))&
(![X]:((~kind(X)<~>old(X))=>(curious(X)|generous(X))))&
(((~happy(alice)|curious(alice)))<=>((~old(alice)|tall(alice))))&
((?[X]:((creative(X)|~funny(X))))=>(?[X]:((wise(X)|humble(X)))))&
(![X]:((~quiet(X)<~>~kind(X))<=>(tall(X)&~old(X))))&
(![X]:((~funny(X)&~rich(X))=>(~curious(X)&~rich(X))))&
(![X]:((tall(X)|patient(X))<=>(~tall(X)|calm(X))))&
(![X]:((~rich(X)<~>humble(X))=>(calm(X)<~>humble(X))))&
((funny(alice)<~>~happy(alice)))&
(?[X]:((~curious(X)<~>~quiet(X))))&
((calm(susan)|kind(susan)))&
(?[X]:((~calm(X)<~>~generous(X))))&
(~creative(fred))&
((~strong(fred)|rich(fred)))&
((~patient(mary)<~>curious(mary))) | tall(alice) | [] | null | 0 |
Everyone who is calm is both not generous and not curious. Everyone who is either not old or creative is both not curious and not wise. Everyone who is quiet or rich is both not strong and not creative and vice versa. Everyone who is either not tall or old is either kind or patient. If susan is both calm and tall then paul is both not patient and not generous. Everyone who is both happy and not old is either creative or calm. If someone is not kind then alice is both not brave and not funny and vice versa. If fred is not kind then someone is either not generous or not rich and vice versa. If someone is either not quiet or creative then someone is not patient and vice versa. Everyone who is not brave is both funny and brave and vice versa. Everyone who is either humble or calm is both tall and not patient and vice versa. If fred is either humble or not kind then lucy is either rich or not patient and vice versa. Everyone who is not creative is funny and vice versa. Everyone who is either not brave or not tall is quiet. If someone is both not rich and not quiet then fred is either not funny or not curious and vice versa. Everyone who is both not brave and happy is both happy and calm. Fred is curious. Someone is generous or kind. Alice is either not humble or patient. Susan is not quiet or not kind. Fred is both kind and wise. Someone is both not rich and patient. Someone is kind. | Fred is humble. | contradiction | (![X]:(calm(X)=>(~generous(X)&~curious(X))))&
(![X]:((~old(X)<~>creative(X))=>(~curious(X)&~wise(X))))&
(![X]:((quiet(X)|rich(X))<=>(~strong(X)&~creative(X))))&
(![X]:((~tall(X)<~>old(X))=>(kind(X)<~>patient(X))))&
(((calm(susan)&tall(susan)))=>((~patient(paul)&~generous(paul))))&
(![X]:((happy(X)&~old(X))=>(creative(X)<~>calm(X))))&
((?[X]:(~kind(X)))<=>((~brave(alice)&~funny(alice))))&
((~kind(fred))<=>(?[X]:((~generous(X)<~>~rich(X)))))&
((?[X]:((~quiet(X)<~>creative(X))))<=>(?[X]:(~patient(X))))&
(![X]:(~brave(X)<=>(funny(X)&brave(X))))&
(![X]:((humble(X)<~>calm(X))<=>(tall(X)&~patient(X))))&
(((humble(fred)<~>~kind(fred)))<=>((rich(lucy)<~>~patient(lucy))))&
(![X]:(~creative(X)<=>funny(X)))&
(![X]:((~brave(X)<~>~tall(X))=>quiet(X)))&
((?[X]:((~rich(X)&~quiet(X))))<=>((~funny(fred)<~>~curious(fred))))&
(![X]:((~brave(X)&happy(X))=>(happy(X)&calm(X))))&
(curious(fred))&
(?[X]:((generous(X)|kind(X))))&
((~humble(alice)<~>patient(alice)))&
((~quiet(susan)|~kind(susan)))&
((kind(fred)&wise(fred)))&
(?[X]:((~rich(X)&patient(X))))&
(?[X]:(kind(X))) | humble(fred) | [
"p2",
"p8",
"p9",
"p11",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7652433862190716327548845
% SZS output start Proof for 7652433862190716327548845
3. ! [X0] : ((rich(X0) | quiet(X0)) <=> (~creative(X0) & ~strong(X0))) [input p2]
9. ? [X0] : (~quiet(X0) <~> creative(X0)) <=> ? [X0] : ~patient(X0) [input p8]
10. ! [X0] : (~brave(X0) <=> (brave(X0) & funny(X0))) [input p9]
12. (humble(fred) <~> ~kind(fred)) <=> (rich(lucy) <~> ~patient(lucy)) [input p11]
13. ! [X0] : (~creative(X0) <=> funny(X0)) [input p12]
21. wise(fred) & kind(fred) [input p20]
24. humble(fred) [input hypothesis]
25. ? [X0] : (~quiet(X0) <~> creative(X0)) <=> ? [X1] : ~patient(X1) [rectify 9]
37. ! [X0] : (((rich(X0) | quiet(X0)) | (creative(X0) | strong(X0))) & ((~creative(X0) & ~strong(X0)) | (~rich(X0) & ~quiet(X0)))) [nnf transformation 3]
38. ! [X0] : ((rich(X0) | quiet(X0) | creative(X0) | strong(X0)) & ((~creative(X0) & ~strong(X0)) | (~rich(X0) & ~quiet(X0)))) [flattening 37]
50. (? [X0] : ((~creative(X0) | quiet(X0)) & (creative(X0) | ~quiet(X0))) | ! [X1] : patient(X1)) & (? [X1] : ~patient(X1) | ! [X0] : ((~quiet(X0) | ~creative(X0)) & (creative(X0) | quiet(X0)))) [nnf transformation 25]
51. (? [X0] : ((~creative(X0) | quiet(X0)) & (creative(X0) | ~quiet(X0))) | ! [X1] : patient(X1)) & (? [X2] : ~patient(X2) | ! [X3] : ((~quiet(X3) | ~creative(X3)) & (creative(X3) | quiet(X3)))) [rectify 50]
52. ? [X0] : ((~creative(X0) | quiet(X0)) & (creative(X0) | ~quiet(X0))) => ((~creative(sK2) | quiet(sK2)) & (creative(sK2) | ~quiet(sK2))) [choice axiom]
53. ? [X2] : ~patient(X2) => ~patient(sK3) [choice axiom]
54. (((~creative(sK2) | quiet(sK2)) & (creative(sK2) | ~quiet(sK2))) | ! [X1] : patient(X1)) & (~patient(sK3) | ! [X3] : ((~quiet(X3) | ~creative(X3)) & (creative(X3) | quiet(X3)))) [skolemisation 51,53,52]
55. ! [X0] : ((~brave(X0) | (~brave(X0) | ~funny(X0))) & ((brave(X0) & funny(X0)) | brave(X0))) [nnf transformation 10]
56. ! [X0] : ((~brave(X0) | ~brave(X0) | ~funny(X0)) & ((brave(X0) & funny(X0)) | brave(X0))) [flattening 55]
59. (((kind(fred) | ~humble(fred)) & (~kind(fred) | humble(fred))) | ((rich(lucy) | patient(lucy)) & (~patient(lucy) | ~rich(lucy)))) & (((patient(lucy) | ~rich(lucy)) & (~patient(lucy) | rich(lucy))) | ((humble(fred) | kind(fred)) & (~kind(fred) | ~humble(fred)))) [nnf transformation 12]
60. ! [X0] : ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0))) [nnf transformation 13]
81. ~quiet(X0) | ~creative(X0) [cnf transformation 38]
82. ~rich(X0) | ~creative(X0) [cnf transformation 38]
102. ~creative(sK2) | quiet(sK2) | patient(X1) [cnf transformation 54]
104. brave(X0) | brave(X0) [cnf transformation 56]
105. ~brave(X0) | ~brave(X0) | ~funny(X0) [cnf transformation 56]
112. ~patient(lucy) | rich(lucy) | ~kind(fred) | ~humble(fred) [cnf transformation 59]
120. funny(X0) | creative(X0) [cnf transformation 60]
137. kind(fred) [cnf transformation 21]
142. humble(fred) [cnf transformation 24]
143. brave(X0) [duplicate literal removal 104]
144. ~funny(X0) | ~brave(X0) [duplicate literal removal 105]
185. 10 <=> kind(fred) [avatar definition]
203. ~creative(sK2) | patient(X1) [subsumption resolution 102,81]
205. 14 <=> ! [X1] : patient(X1) [avatar definition]
206. patient(X1) <- (14) [avatar component clause 205]
208. 15 <=> creative(sK2) [avatar definition]
210. ~creative(sK2) <- (~15) [avatar component clause 208]
211. 14 | ~15 [avatar split clause 203,208,205]
227. 19 <=> patient(lucy) [avatar definition]
228. ~patient(lucy) <- (~19) [avatar component clause 227]
231. 20 <=> rich(lucy) [avatar definition]
233. rich(lucy) <- (20) [avatar component clause 231]
235. 21 <=> humble(fred) [avatar definition]
245. ~21 | ~10 | 20 | ~19 [avatar split clause 112,227,231,185,235]
301. 10 [avatar split clause 137,185]
302. 21 [avatar split clause 142,235]
314. ~brave(X0) | creative(X0) [resolution 144,120]
315. creative(X0) [subsumption resolution 314,143]
316. $false <- (~15) [resolution 315,210]
317. 15 [avatar contradiction clause 316]
319. $false <- (14, ~19) [resolution 206,228]
322. ~14 | 19 [avatar contradiction clause 319]
324. ~creative(lucy) <- (20) [resolution 233,82]
325. $false <- (20) [subsumption resolution 324,315]
326. ~20 [avatar contradiction clause 325]
327. $false [avatar sat refutation 211,245,301,302,317,322,326]
% SZS output end Proof for 7652433862190716327548845
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either not old or not quiet then paul is either not happy or patient and vice versa.
If fred is both not tall and not kind then someone is not humble or not wise and vice versa.
Everyone who is rich or old is not wise.
If mary is not old or not strong then someone is not funny.
Everyone who is funny is not rich or not funny and vice versa.
Everyone who is not curious is humble or not humble.
If someone is not old or funny then someone is either not old or not wise and vice versa.
If someone is patient or funny then john is both wise and not tall and vice versa.
Everyone who is either not curious or happy is either curious or old and vice versa.
Everyone who is both curious and not funny is either generous or humble and vice versa.
If someone is both patient and quiet then someone is brave and vice versa.
If someone is not rich or creative then paul is tall.
Everyone who is either not generous or not calm is either creative or not calm.
If someone is both not kind and strong then fred is either tall or not generous and vice versa.
Mary is tall or not generous.
John is both calm and not old.
Someone is both not kind and humble.
Susan is rich or happy. | Susan is not wise. | neutral | (((~old(fred)<~>~quiet(fred)))<=>((~happy(paul)<~>patient(paul))))&
(((~tall(fred)&~kind(fred)))<=>(?[X]:((~humble(X)|~wise(X)))))&
(![X]:((rich(X)|old(X))=>~wise(X)))&
(((~old(mary)|~strong(mary)))=>(?[X]:(~funny(X))))&
(![X]:(funny(X)<=>(~rich(X)|~funny(X))))&
(![X]:(~curious(X)=>(humble(X)|~humble(X))))&
((?[X]:((~old(X)|funny(X))))<=>(?[X]:((~old(X)<~>~wise(X)))))&
((?[X]:((patient(X)|funny(X))))<=>((wise(john)&~tall(john))))&
(![X]:((~curious(X)<~>happy(X))<=>(curious(X)<~>old(X))))&
(![X]:((curious(X)&~funny(X))<=>(generous(X)<~>humble(X))))&
((?[X]:((patient(X)&quiet(X))))<=>(?[X]:(brave(X))))&
((?[X]:((~rich(X)|creative(X))))=>(tall(paul)))&
(![X]:((~generous(X)<~>~calm(X))=>(creative(X)<~>~calm(X))))&
((?[X]:((~kind(X)&strong(X))))<=>((tall(fred)<~>~generous(fred))))&
((tall(mary)|~generous(mary)))&
((calm(john)&~old(john)))&
(?[X]:((~kind(X)&humble(X))))&
((rich(susan)|happy(susan))) | ~wise(susan) | [] | null | 0 |
Everyone who is both not tall and not kind is funny or brave and vice versa.
If john is quiet then john is either humble or curious and vice versa.
Everyone who is generous is either tall or quiet.
If someone is either not wise or kind then john is both brave and not strong.
Everyone who is not brave is both brave and not brave.
Everyone who is both calm and not quiet is not brave.
If someone is not old or curious then mary is both calm and humble.
Everyone who is either patient or not old is both happy and curious and vice versa.
Everyone who is both not curious and not happy is not happy and vice versa.
Everyone who is either quiet or not kind is not kind and vice versa.
Everyone who is not quiet or not brave is either humble or happy and vice versa.
Everyone who is not happy or not curious is either not calm or humble.
If someone is curious or not wise then someone is not strong or not generous and vice versa.
Everyone who is not generous or not funny is not generous.
Someone is not funny or happy.
Lucy is not old or brave.
Paul is not quiet or rich. | Paul is not patient. | entailment | (![X]:((~tall(X)&~kind(X))<=>(funny(X)|brave(X))))&
((quiet(john))<=>((humble(john)<~>curious(john))))&
(![X]:(generous(X)=>(tall(X)<~>quiet(X))))&
((?[X]:((~wise(X)<~>kind(X))))=>((brave(john)&~strong(john))))&
(![X]:(~brave(X)=>(brave(X)&~brave(X))))&
(![X]:((calm(X)&~quiet(X))=>~brave(X)))&
((?[X]:((~old(X)|curious(X))))=>((calm(mary)&humble(mary))))&
(![X]:((patient(X)<~>~old(X))<=>(happy(X)&curious(X))))&
(![X]:((~curious(X)&~happy(X))<=>~happy(X)))&
(![X]:((quiet(X)<~>~kind(X))<=>~kind(X)))&
(![X]:((~quiet(X)|~brave(X))<=>(humble(X)<~>happy(X))))&
(![X]:((~happy(X)|~curious(X))=>(~calm(X)<~>humble(X))))&
((?[X]:((curious(X)|~wise(X))))<=>(?[X]:((~strong(X)|~generous(X)))))&
(![X]:((~generous(X)|~funny(X))=>~generous(X)))&
(?[X]:((~funny(X)|happy(X))))&
((~old(lucy)|brave(lucy)))&
((~quiet(paul)|rich(paul))) | ~patient(paul) | [
"p4",
"p5",
"p6",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3710334694450824528467759
% SZS output start Proof for 3710334694450824528467759
5. ! [X0] : (~brave(X0) => (~brave(X0) & brave(X0))) [input p4]
6. ! [X0] : ((~quiet(X0) & calm(X0)) => ~brave(X0)) [input p5]
7. ? [X0] : (curious(X0) | ~old(X0)) => (humble(mary) & calm(mary)) [input p6]
8. ! [X0] : ((patient(X0) <~> ~old(X0)) <=> (curious(X0) & happy(X0))) [input p7]
10. ! [X0] : ((quiet(X0) <~> ~kind(X0)) <=> ~kind(X0)) [input p9]
18. patient(paul) [input hypothesis]
23. ! [X0] : ((~brave(X0) & brave(X0)) | brave(X0)) [ennf transformation 5]
24. ! [X0] : (~brave(X0) | (quiet(X0) | ~calm(X0))) [ennf transformation 6]
25. ! [X0] : (~brave(X0) | quiet(X0) | ~calm(X0)) [flattening 24]
26. (humble(mary) & calm(mary)) | ! [X0] : (~curious(X0) & old(X0)) [ennf transformation 7]
34. ! [X0] : ((((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | (~curious(X0) | ~happy(X0))) & ((curious(X0) & happy(X0)) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0))))) [nnf transformation 8]
35. ! [X0] : ((((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | ~curious(X0) | ~happy(X0)) & ((curious(X0) & happy(X0)) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0))))) [flattening 34]
38. ! [X0] : ((((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | kind(X0)) & (~kind(X0) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0))))) [nnf transformation 10]
64. brave(X0) | brave(X0) [cnf transformation 23]
66. ~brave(X0) | quiet(X0) | ~calm(X0) [cnf transformation 25]
67. calm(mary) | old(X0) [cnf transformation 26]
68. calm(mary) | ~curious(X0) [cnf transformation 26]
73. ~patient(X0) | ~old(X0) | curious(X0) [cnf transformation 35]
80. ~kind(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 38]
83. kind(X0) | ~quiet(X0) | kind(X0) [cnf transformation 38]
102. patient(paul) [cnf transformation 18]
103. ~kind(X0) | ~quiet(X0) [duplicate literal removal 80]
104. ~quiet(X0) | kind(X0) [duplicate literal removal 83]
105. brave(X0) [duplicate literal removal 64]
140. ~calm(X0) | quiet(X0) [subsumption resolution 66,105]
142. 8 <=> ! [X0] : ~curious(X0) [avatar definition]
143. ~curious(X0) <- (8) [avatar component clause 142]
150. 10 <=> ! [X0] : old(X0) [avatar definition]
151. old(X0) <- (10) [avatar component clause 150]
154. 11 <=> calm(mary) [avatar definition]
156. calm(mary) <- (11) [avatar component clause 154]
157. 8 | 11 [avatar split clause 68,154,142]
158. 10 | 11 [avatar split clause 67,154,150]
159. ~quiet(X0) [subsumption resolution 103,104]
212. ~old(paul) | curious(paul) [resolution 73,102]
213. curious(paul) <- (10) [subsumption resolution 212,151]
214. $false <- (8, 10) [subsumption resolution 213,143]
215. ~8 | ~10 [avatar contradiction clause 214]
218. quiet(mary) <- (11) [resolution 156,140]
219. $false <- (11) [subsumption resolution 218,159]
220. ~11 [avatar contradiction clause 219]
221. $false [avatar sat refutation 157,158,215,220]
% SZS output end Proof for 3710334694450824528467759
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or not brave is either creative or funny and vice versa.
If alice is creative then susan is not strong or not wise and vice versa.
If someone is both brave and strong then fred is both kind and not curious and vice versa.
Everyone who is not happy is happy or kind.
Everyone who is not rich is brave or not happy and vice versa.
If someone is both not brave and not generous then mary is not old or patient and vice versa.
Everyone who is both not rich and not humble is either brave or not creative and vice versa.
If someone is not creative then alice is patient or kind.
Everyone who is either brave or tall is both not brave and not patient.
Everyone who is not humble is either creative or not kind.
Everyone who is not wise or not patient is both wise and not patient and vice versa.
Everyone who is not brave is both kind and old and vice versa.
If fred is not generous then someone is both not creative and funny.
If lucy is not wise or humble then john is not humble.
Everyone who is quiet or not generous is both funny and not quiet.
If mary is strong or not quiet then john is either not old or not calm.
Alice is both not patient and wise.
Someone is not rich or not happy.
Someone is kind.
Paul is creative.
Someone is not calm.
Someone is either wise or not curious.
Someone is not old or creative. | Alice is not kind. | contradiction | (![X]:((~patient(X)|~brave(X))<=>(creative(X)<~>funny(X))))&
((creative(alice))<=>((~strong(susan)|~wise(susan))))&
((?[X]:((brave(X)&strong(X))))<=>((kind(fred)&~curious(fred))))&
(![X]:(~happy(X)=>(happy(X)|kind(X))))&
(![X]:(~rich(X)<=>(brave(X)|~happy(X))))&
((?[X]:((~brave(X)&~generous(X))))<=>((~old(mary)|patient(mary))))&
(![X]:((~rich(X)&~humble(X))<=>(brave(X)<~>~creative(X))))&
((?[X]:(~creative(X)))=>((patient(alice)|kind(alice))))&
(![X]:((brave(X)<~>tall(X))=>(~brave(X)&~patient(X))))&
(![X]:(~humble(X)=>(creative(X)<~>~kind(X))))&
(![X]:((~wise(X)|~patient(X))<=>(wise(X)&~patient(X))))&
(![X]:(~brave(X)<=>(kind(X)&old(X))))&
((~generous(fred))=>(?[X]:((~creative(X)&funny(X)))))&
(((~wise(lucy)|humble(lucy)))=>(~humble(john)))&
(![X]:((quiet(X)|~generous(X))=>(funny(X)&~quiet(X))))&
(((strong(mary)|~quiet(mary)))=>((~old(john)<~>~calm(john))))&
((~patient(alice)&wise(alice)))&
(?[X]:((~rich(X)|~happy(X))))&
(?[X]:(kind(X)))&
(creative(paul))&
(?[X]:(~calm(X)))&
(?[X]:((wise(X)<~>~curious(X))))&
(?[X]:((~old(X)|creative(X)))) | ~kind(alice) | [
"p6",
"p7",
"p9",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 141753600215592163956856
% SZS output start Proof for 141753600215592163956856
7. ! [X0] : ((~humble(X0) & ~rich(X0)) <=> (brave(X0) <~> ~creative(X0))) [input p6]
8. ? [X0] : ~creative(X0) => (kind(alice) | patient(alice)) [input p7]
10. ! [X0] : (~humble(X0) => (creative(X0) <~> ~kind(X0))) [input p9]
12. ! [X0] : (~brave(X0) <=> (old(X0) & kind(X0))) [input p11]
17. wise(alice) & ~patient(alice) [input p16]
24. ~kind(alice) [input hypothesis]
27. (kind(alice) | patient(alice)) | ! [X0] : creative(X0) [ennf transformation 8]
28. kind(alice) | patient(alice) | ! [X0] : creative(X0) [flattening 27]
30. ! [X0] : ((creative(X0) <~> ~kind(X0)) | humble(X0)) [ennf transformation 10]
51. ! [X0] : (((~humble(X0) & ~rich(X0)) | ((brave(X0) | creative(X0)) & (~creative(X0) | ~brave(X0)))) & (((creative(X0) | ~brave(X0)) & (~creative(X0) | brave(X0))) | (humble(X0) | rich(X0)))) [nnf transformation 7]
52. ! [X0] : (((~humble(X0) & ~rich(X0)) | ((brave(X0) | creative(X0)) & (~creative(X0) | ~brave(X0)))) & (((creative(X0) | ~brave(X0)) & (~creative(X0) | brave(X0))) | humble(X0) | rich(X0))) [flattening 51]
54. ! [X0] : (((kind(X0) | ~creative(X0)) & (~kind(X0) | creative(X0))) | humble(X0)) [nnf transformation 30]
57. ! [X0] : ((~brave(X0) | (~old(X0) | ~kind(X0))) & ((old(X0) & kind(X0)) | brave(X0))) [nnf transformation 12]
58. ! [X0] : ((~brave(X0) | ~old(X0) | ~kind(X0)) & ((old(X0) & kind(X0)) | brave(X0))) [flattening 57]
99. ~humble(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 52]
101. kind(alice) | patient(alice) | creative(X0) [cnf transformation 28]
107. ~creative(X0) | kind(X0) | humble(X0) [cnf transformation 54]
113. kind(X0) | brave(X0) [cnf transformation 58]
128. ~patient(alice) [cnf transformation 17]
137. ~kind(alice) [cnf transformation 24]
208. 14 <=> ! [X0] : creative(X0) [avatar definition]
209. creative(X0) <- (14) [avatar component clause 208]
211. 15 <=> patient(alice) [avatar definition]
215. 16 <=> kind(alice) [avatar definition]
216. ~kind(alice) <- (~16) [avatar component clause 215]
218. 14 | 15 | 16 [avatar split clause 101,215,211,208]
261. ~15 [avatar split clause 128,211]
273. ~16 [avatar split clause 137,215]
313. humble(X0) | kind(X0) <- (14) [resolution 107,209]
377. kind(X1) | ~creative(X1) | ~brave(X1) <- (14) [resolution 313,99]
380. kind(X1) | ~brave(X1) <- (14) [subsumption resolution 377,209]
381. kind(X1) <- (14) [subsumption resolution 380,113]
427. $false <- (14, ~16) [resolution 381,216]
429. ~14 | 16 [avatar contradiction clause 427]
430. $false [avatar sat refutation 218,261,273,429]
% SZS output end Proof for 141753600215592163956856
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is both not kind and humble and vice versa. If alice is either not funny or curious then someone is either not quiet or quiet and vice versa. Everyone who is either strong or not wise is either not quiet or patient. Everyone who is either not curious or not happy is not rich. If someone is both happy and not tall then susan is both funny and not strong. If susan is both not happy and not calm then susan is either not brave or not happy. If someone is creative or not patient then mary is either wise or strong. Everyone who is not brave or not happy is calm or not calm and vice versa. If someone is either not strong or not rich then someone is not old. Everyone who is tall or curious is both tall and brave. Everyone who is patient is either happy or not generous. Everyone who is both rich and patient is generous or not curious and vice versa. If someone is not funny then lucy is not wise or quiet and vice versa. Everyone who is old or curious is either not curious or strong and vice versa. Everyone who is not patient or not calm is either not humble or not old. Everyone who is either not old or tall is either not wise or calm and vice versa. Fred is humble or not happy. Someone is not curious or not patient. Lucy is either brave or generous. Someone is not curious or not calm. Someone is both brave and not old. Someone is either not wise or happy. Someone is brave or quiet. | Susan is not wise. | neutral | (![X]:(~happy(X)<=>(~kind(X)&humble(X))))&
(((~funny(alice)<~>curious(alice)))<=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:((strong(X)<~>~wise(X))=>(~quiet(X)<~>patient(X))))&
(![X]:((~curious(X)<~>~happy(X))=>~rich(X)))&
((?[X]:((happy(X)&~tall(X))))=>((funny(susan)&~strong(susan))))&
(((~happy(susan)&~calm(susan)))=>((~brave(susan)<~>~happy(susan))))&
((?[X]:((creative(X)|~patient(X))))=>((wise(mary)<~>strong(mary))))&
(![X]:((~brave(X)|~happy(X))<=>(calm(X)|~calm(X))))&
((?[X]:((~strong(X)<~>~rich(X))))=>(?[X]:(~old(X))))&
(![X]:((tall(X)|curious(X))=>(tall(X)&brave(X))))&
(![X]:(patient(X)=>(happy(X)<~>~generous(X))))&
(![X]:((rich(X)&patient(X))<=>(generous(X)|~curious(X))))&
((?[X]:(~funny(X)))<=>((~wise(lucy)|quiet(lucy))))&
(![X]:((old(X)|curious(X))<=>(~curious(X)<~>strong(X))))&
(![X]:((~patient(X)|~calm(X))=>(~humble(X)<~>~old(X))))&
(![X]:((~old(X)<~>tall(X))<=>(~wise(X)<~>calm(X))))&
((humble(fred)|~happy(fred)))&
(?[X]:((~curious(X)|~patient(X))))&
((brave(lucy)<~>generous(lucy)))&
(?[X]:((~curious(X)|~calm(X))))&
(?[X]:((brave(X)&~old(X))))&
(?[X]:((~wise(X)<~>happy(X))))&
(?[X]:((brave(X)|quiet(X)))) | ~wise(susan) | [] | null | 0 |
If paul is either kind or strong then lucy is both quiet and not happy. If someone is calm then someone is strong or humble and vice versa. If someone is both calm and humble then someone is either rich or not quiet. If someone is both kind and not patient then someone is both tall and not old. If someone is not generous or generous then fred is either rich or not patient and vice versa. Everyone who is both not old and not strong is not rich or strong and vice versa. If someone is wise then john is not tall or not strong and vice versa. Everyone who is not humble is both not old and wise and vice versa. Everyone who is either not rich or creative is both calm and kind and vice versa. If susan is both calm and not humble then fred is either not old or tall and vice versa. Everyone who is not funny or happy is both funny and humble. Everyone who is curious is either not old or old. Everyone who is not brave is both not calm and not brave. Everyone who is calm or not humble is either not brave or not calm. Everyone who is both rich and not rich is either curious or happy and vice versa. If someone is not calm or calm then someone is both brave and not patient. Someone is wise. Alice is either wise or quiet. Lucy is quiet or not kind. Susan is creative or not creative. John is either not curious or generous. Fred is tall. | John is creative. | entailment | (((kind(paul)<~>strong(paul)))=>((quiet(lucy)&~happy(lucy))))&
((?[X]:(calm(X)))<=>(?[X]:((strong(X)|humble(X)))))&
((?[X]:((calm(X)&humble(X))))=>(?[X]:((rich(X)<~>~quiet(X)))))&
((?[X]:((kind(X)&~patient(X))))=>(?[X]:((tall(X)&~old(X)))))&
((?[X]:((~generous(X)|generous(X))))<=>((rich(fred)<~>~patient(fred))))&
(![X]:((~old(X)&~strong(X))<=>(~rich(X)|strong(X))))&
((?[X]:(wise(X)))<=>((~tall(john)|~strong(john))))&
(![X]:(~humble(X)<=>(~old(X)&wise(X))))&
(![X]:((~rich(X)<~>creative(X))<=>(calm(X)&kind(X))))&
(((calm(susan)&~humble(susan)))<=>((~old(fred)<~>tall(fred))))&
(![X]:((~funny(X)|happy(X))=>(funny(X)&humble(X))))&
(![X]:(curious(X)=>(~old(X)<~>old(X))))&
(![X]:(~brave(X)=>(~calm(X)&~brave(X))))&
(![X]:((calm(X)|~humble(X))=>(~brave(X)<~>~calm(X))))&
(![X]:((rich(X)&~rich(X))<=>(curious(X)<~>happy(X))))&
((?[X]:((~calm(X)|calm(X))))=>(?[X]:((brave(X)&~patient(X)))))&
(?[X]:(wise(X)))&
((wise(alice)<~>quiet(alice)))&
((quiet(lucy)|~kind(lucy)))&
((creative(susan)|~creative(susan)))&
((~curious(john)<~>generous(john)))&
(tall(fred)) | creative(john) | [
"p1",
"p5",
"p7",
"p8",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5192330697048709442526506
% SZS output start Proof for 5192330697048709442526506
2. ? [X0] : calm(X0) <=> ? [X0] : (humble(X0) | strong(X0)) [input p1]
6. ! [X0] : ((~strong(X0) & ~old(X0)) <=> (strong(X0) | ~rich(X0))) [input p5]
8. ! [X0] : (~humble(X0) <=> (wise(X0) & ~old(X0))) [input p7]
9. ! [X0] : ((~rich(X0) <~> creative(X0)) <=> (kind(X0) & calm(X0))) [input p8]
13. ! [X0] : (~brave(X0) => (~brave(X0) & ~calm(X0))) [input p12]
14. ! [X0] : ((~humble(X0) | calm(X0)) => (~brave(X0) <~> ~calm(X0))) [input p13]
23. ~creative(john) [input hypothesis]
24. ? [X0] : calm(X0) <=> ? [X1] : (humble(X1) | strong(X1)) [rectify 2]
34. ! [X0] : ((~brave(X0) & ~calm(X0)) | brave(X0)) [ennf transformation 13]
35. ! [X0] : ((~brave(X0) <~> ~calm(X0)) | (humble(X0) & ~calm(X0))) [ennf transformation 14]
38. (? [X0] : calm(X0) | ! [X1] : (~humble(X1) & ~strong(X1))) & (? [X1] : (humble(X1) | strong(X1)) | ! [X0] : ~calm(X0)) [nnf transformation 24]
39. (? [X0] : calm(X0) | ! [X1] : (~humble(X1) & ~strong(X1))) & (? [X2] : (humble(X2) | strong(X2)) | ! [X3] : ~calm(X3)) [rectify 38]
40. ? [X0] : calm(X0) => calm(sK0) [choice axiom]
41. ? [X2] : (humble(X2) | strong(X2)) => (humble(sK1) | strong(sK1)) [choice axiom]
42. (calm(sK0) | ! [X1] : (~humble(X1) & ~strong(X1))) & ((humble(sK1) | strong(sK1)) | ! [X3] : ~calm(X3)) [skolemisation 39,41,40]
54. ! [X0] : (((~strong(X0) & ~old(X0)) | (~strong(X0) & rich(X0))) & ((strong(X0) | ~rich(X0)) | (strong(X0) | old(X0)))) [nnf transformation 6]
55. ! [X0] : (((~strong(X0) & ~old(X0)) | (~strong(X0) & rich(X0))) & (strong(X0) | ~rich(X0) | strong(X0) | old(X0))) [flattening 54]
61. ! [X0] : ((~humble(X0) | (~wise(X0) | old(X0))) & ((wise(X0) & ~old(X0)) | humble(X0))) [nnf transformation 8]
62. ! [X0] : ((~humble(X0) | ~wise(X0) | old(X0)) & ((wise(X0) & ~old(X0)) | humble(X0))) [flattening 61]
63. ! [X0] : ((((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | (~kind(X0) | ~calm(X0))) & ((kind(X0) & calm(X0)) | ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0))))) [nnf transformation 9]
64. ! [X0] : ((((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | ~kind(X0) | ~calm(X0)) & ((kind(X0) & calm(X0)) | ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0))))) [flattening 63]
68. ! [X0] : (((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | (humble(X0) & ~calm(X0))) [nnf transformation 35]
84. calm(sK0) | ~humble(X1) [cnf transformation 42]
95. strong(X0) | ~rich(X0) | strong(X0) | old(X0) [cnf transformation 55]
99. ~strong(X0) | ~strong(X0) [cnf transformation 55]
103. ~old(X0) | humble(X0) [cnf transformation 62]
106. creative(X0) | calm(X0) | rich(X0) [cnf transformation 64]
121. ~calm(X0) | brave(X0) [cnf transformation 34]
123. ~calm(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 68]
145. ~creative(john) [cnf transformation 23]
146. ~calm(X0) | ~brave(X0) [duplicate literal removal 123]
147. ~rich(X0) | strong(X0) | old(X0) [duplicate literal removal 95]
148. ~strong(X0) [duplicate literal removal 99]
170. 5 <=> ! [X1] : ~humble(X1) [avatar definition]
171. ~humble(X1) <- (5) [avatar component clause 170]
173. 6 <=> calm(sK0) [avatar definition]
175. calm(sK0) <- (6) [avatar component clause 173]
176. 5 | 6 [avatar split clause 84,173,170]
178. 7 <=> ! [X1] : ~strong(X1) [avatar definition]
179. ~strong(X1) <- (7) [avatar component clause 178]
182. 8 <=> ! [X3] : ~calm(X3) [avatar definition]
183. ~calm(X3) <- (8) [avatar component clause 182]
237. 7 [avatar split clause 148,178]
239. 21 <=> strong(john) [avatar definition]
240. ~strong(john) <- (~21) [avatar component clause 239]
241. strong(john) <- (21) [avatar component clause 239]
280. ~calm(X0) [subsumption resolution 146,121]
281. 8 [avatar split clause 280,182]
333. calm(john) | rich(john) [resolution 106,145]
334. rich(john) <- (8) [subsumption resolution 333,183]
343. strong(john) | old(john) <- (8) [resolution 147,334]
344. old(john) <- (8, ~21) [subsumption resolution 343,240]
345. humble(john) <- (8, ~21) [resolution 344,103]
348. $false <- (5, 8, ~21) [subsumption resolution 345,171]
349. ~5 | ~8 | 21 [avatar contradiction clause 348]
377. $false <- (6, 8) [subsumption resolution 175,183]
378. ~6 | ~8 [avatar contradiction clause 377]
380. $false <- (7, 21) [subsumption resolution 241,179]
381. ~7 | ~21 [avatar contradiction clause 380]
382. $false [avatar sat refutation 176,237,281,349,378,381]
% SZS output end Proof for 5192330697048709442526506
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and not curious then mary is tall and vice versa. If someone is both kind and generous then john is both patient and funny. If alice is both happy and funny then someone is generous. If paul is not happy or not kind then someone is both funny and not humble and vice versa. If mary is both not old and not funny then someone is both quiet and strong. Everyone who is either kind or not strong is both brave and not quiet. Everyone who is not wise or not tall is both strong and creative and vice versa. If lucy is not generous or not calm then john is both funny and not rich. If john is tall or not happy then mary is both not happy and kind and vice versa. Everyone who is not creative is both not old and not patient. If john is either tall or old then someone is both not curious and brave and vice versa. Everyone who is both not creative and not brave is both not patient and funny and vice versa. Everyone who is not quiet is quiet or not kind and vice versa. Everyone who is either wise or not tall is not generous and vice versa. If someone is not generous then susan is both not curious and not strong and vice versa. Lucy is not patient or patient. Someone is either tall or quiet. Someone is patient. Someone is both not old and happy. Someone is old. Someone is not creative or curious. | Mary is quiet. | contradiction | (((~quiet(mary)&~curious(mary)))<=>(tall(mary)))&
((?[X]:((kind(X)&generous(X))))=>((patient(john)&funny(john))))&
(((happy(alice)&funny(alice)))=>(?[X]:(generous(X))))&
(((~happy(paul)|~kind(paul)))<=>(?[X]:((funny(X)&~humble(X)))))&
(((~old(mary)&~funny(mary)))=>(?[X]:((quiet(X)&strong(X)))))&
(![X]:((kind(X)<~>~strong(X))=>(brave(X)&~quiet(X))))&
(![X]:((~wise(X)|~tall(X))<=>(strong(X)&creative(X))))&
(((~generous(lucy)|~calm(lucy)))=>((funny(john)&~rich(john))))&
(((tall(john)|~happy(john)))<=>((~happy(mary)&kind(mary))))&
(![X]:(~creative(X)=>(~old(X)&~patient(X))))&
(((tall(john)<~>old(john)))<=>(?[X]:((~curious(X)&brave(X)))))&
(![X]:((~creative(X)&~brave(X))<=>(~patient(X)&funny(X))))&
(![X]:(~quiet(X)<=>(quiet(X)|~kind(X))))&
(![X]:((wise(X)<~>~tall(X))<=>~generous(X)))&
((?[X]:(~generous(X)))<=>((~curious(susan)&~strong(susan))))&
((~patient(lucy)|patient(lucy)))&
(?[X]:((tall(X)<~>quiet(X))))&
(?[X]:(patient(X)))&
(?[X]:((~old(X)&happy(X))))&
(?[X]:(old(X)))&
(?[X]:((~creative(X)|curious(X)))) | quiet(mary) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4437121319839766348178814
% SZS output start Proof for 4437121319839766348178814
13. ! [X0] : (~quiet(X0) <=> (~kind(X0) | quiet(X0))) [input p12]
22. quiet(mary) [input hypothesis]
55. ! [X0] : ((~quiet(X0) | (kind(X0) & ~quiet(X0))) & ((~kind(X0) | quiet(X0)) | quiet(X0))) [nnf transformation 13]
56. ! [X0] : ((~quiet(X0) | (kind(X0) & ~quiet(X0))) & (~kind(X0) | quiet(X0) | quiet(X0))) [flattening 55]
115. ~quiet(X0) | ~quiet(X0) [cnf transformation 56]
132. quiet(mary) [cnf transformation 22]
134. ~quiet(X0) [duplicate literal removal 115]
294. $false [subsumption resolution 132,134]
% SZS output end Proof for 4437121319839766348178814
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and not calm is not curious or not funny and vice versa.
If someone is kind or old then susan is either funny or not calm.
If mary is strong or not tall then someone is not quiet.
If someone is not patient or patient then paul is not rich or not tall.
Everyone who is not generous or not strong is both not happy and humble and vice versa.
If someone is both not old and humble then alice is not generous.
Everyone who is calm is either not wise or old and vice versa.
If paul is both not kind and curious then paul is curious.
If paul is both not happy and wise then someone is either curious or not calm.
Everyone who is not wise is humble or not kind and vice versa.
Everyone who is not creative is either not brave or quiet and vice versa.
If someone is both not rich and not creative then mary is either patient or humble.
Everyone who is generous or strong is generous.
Everyone who is both creative and not generous is not humble and vice versa.
Everyone who is both not creative and patient is patient or not brave.
If someone is wise or strong then someone is quiet or old.
Fred is not rich or not humble.
Someone is both generous and kind.
Someone is calm.
Susan is not funny or wise.
Fred is both not brave and kind.
John is brave or not rich.
Someone is either funny or not rich.
Mary is both not curious and not patient. | Mary is calm. | contradiction | (![X]:((~curious(X)&~calm(X))<=>(~curious(X)|~funny(X))))&
((?[X]:((kind(X)|old(X))))=>((funny(susan)<~>~calm(susan))))&
(((strong(mary)|~tall(mary)))=>(?[X]:(~quiet(X))))&
((?[X]:((~patient(X)|patient(X))))=>((~rich(paul)|~tall(paul))))&
(![X]:((~generous(X)|~strong(X))<=>(~happy(X)&humble(X))))&
((?[X]:((~old(X)&humble(X))))=>(~generous(alice)))&
(![X]:(calm(X)<=>(~wise(X)<~>old(X))))&
(((~kind(paul)&curious(paul)))=>(curious(paul)))&
(((~happy(paul)&wise(paul)))=>(?[X]:((curious(X)<~>~calm(X)))))&
(![X]:(~wise(X)<=>(humble(X)|~kind(X))))&
(![X]:(~creative(X)<=>(~brave(X)<~>quiet(X))))&
((?[X]:((~rich(X)&~creative(X))))=>((patient(mary)<~>humble(mary))))&
(![X]:((generous(X)|strong(X))=>generous(X)))&
(![X]:((creative(X)&~generous(X))<=>~humble(X)))&
(![X]:((~creative(X)&patient(X))=>(patient(X)|~brave(X))))&
((?[X]:((wise(X)|strong(X))))=>(?[X]:((quiet(X)|old(X)))))&
((~rich(fred)|~humble(fred)))&
(?[X]:((generous(X)&kind(X))))&
(?[X]:(calm(X)))&
((~funny(susan)|wise(susan)))&
((~brave(fred)&kind(fred)))&
((brave(john)|~rich(john)))&
(?[X]:((funny(X)<~>~rich(X))))&
((~curious(mary)&~patient(mary))) | calm(mary) | [
"p0",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 610412316212613764175704
% SZS output start Proof for 610412316212613764175704
1. ! [X0] : ((~calm(X0) & ~curious(X0)) <=> (~funny(X0) | ~curious(X0))) [input p0]
24. ~patient(mary) & ~curious(mary) [input p23]
25. calm(mary) [input hypothesis]
41. ! [X0] : (((~calm(X0) & ~curious(X0)) | (funny(X0) & curious(X0))) & ((~funny(X0) | ~curious(X0)) | (calm(X0) | curious(X0)))) [nnf transformation 1]
42. ! [X0] : (((~calm(X0) & ~curious(X0)) | (funny(X0) & curious(X0))) & (~funny(X0) | ~curious(X0) | calm(X0) | curious(X0))) [flattening 41]
71. ~calm(X0) | curious(X0) [cnf transformation 42]
121. ~curious(mary) [cnf transformation 24]
123. calm(mary) [cnf transformation 25]
253. curious(mary) [resolution 71,123]
254. $false [subsumption resolution 253,121]
% SZS output end Proof for 610412316212613764175704
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not happy is not calm. Everyone who is not old or wise is either rich or strong. If someone is both wise and not humble then someone is not generous or happy. Everyone who is not rich or not kind is either happy or not funny and vice versa. If someone is old then alice is not funny or old. Everyone who is both not rich and not curious is both not kind and generous and vice versa. Everyone who is either not funny or not patient is both kind and old. If someone is either not happy or not old then someone is not curious or rich. If someone is not tall then alice is not curious or not patient. If lucy is both strong and not creative then someone is not rich or funny and vice versa. Everyone who is old or creative is either not quiet or not rich. Everyone who is funny or creative is either not creative or strong. Everyone who is both not wise and patient is both not calm and not old. Everyone who is both funny and old is funny or wise. If john is both funny and calm then fred is funny or not rich and vice versa. Everyone who is kind is wise. Someone is not wise. John is both not quiet and funny. Lucy is both rich and not kind. Someone is both not patient and not funny. Someone is either curious or not wise. Paul is generous. John is either not quiet or patient. Someone is either not curious or curious. | Lucy is generous. | contradiction | (![X]:((~patient(X)<~>~happy(X))=>~calm(X)))&
(![X]:((~old(X)|wise(X))=>(rich(X)<~>strong(X))))&
((?[X]:((wise(X)&~humble(X))))=>(?[X]:((~generous(X)|happy(X)))))&
(![X]:((~rich(X)|~kind(X))<=>(happy(X)<~>~funny(X))))&
((?[X]:(old(X)))=>((~funny(alice)|old(alice))))&
(![X]:((~rich(X)&~curious(X))<=>(~kind(X)&generous(X))))&
(![X]:((~funny(X)<~>~patient(X))=>(kind(X)&old(X))))&
((?[X]:((~happy(X)<~>~old(X))))=>(?[X]:((~curious(X)|rich(X)))))&
((?[X]:(~tall(X)))=>((~curious(alice)|~patient(alice))))&
(((strong(lucy)&~creative(lucy)))<=>(?[X]:((~rich(X)|funny(X)))))&
(![X]:((old(X)|creative(X))=>(~quiet(X)<~>~rich(X))))&
(![X]:((funny(X)|creative(X))=>(~creative(X)<~>strong(X))))&
(![X]:((~wise(X)&patient(X))=>(~calm(X)&~old(X))))&
(![X]:((funny(X)&old(X))=>(funny(X)|wise(X))))&
(((funny(john)&calm(john)))<=>((funny(fred)|~rich(fred))))&
(![X]:(kind(X)=>wise(X)))&
(?[X]:(~wise(X)))&
((~quiet(john)&funny(john)))&
((rich(lucy)&~kind(lucy)))&
(?[X]:((~patient(X)&~funny(X))))&
(?[X]:((curious(X)<~>~wise(X))))&
(generous(paul))&
((~quiet(john)<~>patient(john)))&
(?[X]:((~curious(X)<~>curious(X)))) | generous(lucy) | [
"p5",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7553537415072827946421246
% SZS output start Proof for 7553537415072827946421246
6. ! [X0] : ((~curious(X0) & ~rich(X0)) <=> (generous(X0) & ~kind(X0))) [input p5]
19. ~kind(lucy) & rich(lucy) [input p18]
25. generous(lucy) [input hypothesis]
47. ! [X0] : (((~curious(X0) & ~rich(X0)) | (~generous(X0) | kind(X0))) & ((generous(X0) & ~kind(X0)) | (curious(X0) | rich(X0)))) [nnf transformation 6]
48. ! [X0] : (((~curious(X0) & ~rich(X0)) | ~generous(X0) | kind(X0)) & ((generous(X0) & ~kind(X0)) | curious(X0) | rich(X0))) [flattening 47]
89. ~generous(X0) | ~rich(X0) | kind(X0) [cnf transformation 48]
122. rich(lucy) [cnf transformation 19]
123. ~kind(lucy) [cnf transformation 19]
133. generous(lucy) [cnf transformation 25]
275. ~rich(lucy) | kind(lucy) [resolution 89,133]
285. kind(lucy) [subsumption resolution 275,122]
286. $false [subsumption resolution 285,123]
% SZS output end Proof for 7553537415072827946421246
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is either not old or funny and vice versa.
If someone is either not wise or funny then someone is either calm or happy.
Everyone who is either creative or curious is not brave.
Everyone who is both not generous and happy is happy or not calm and vice versa.
If someone is not funny then lucy is rich or not tall.
Everyone who is not funny is both not funny and funny and vice versa.
Everyone who is not wise or not strong is both generous and not quiet.
If someone is not old or patient then someone is both humble and strong and vice versa.
Everyone who is generous or not patient is both funny and creative and vice versa.
Everyone who is both creative and rich is both strong and not creative and vice versa.
Everyone who is tall or not generous is generous.
Everyone who is either not rich or kind is not kind and vice versa.
If mary is both not creative and funny then fred is not wise or not happy.
Everyone who is either rich or old is not happy or quiet.
Everyone who is not quiet or generous is both not quiet and creative and vice versa.
Everyone who is tall is both calm and not rich.
Fred is both tall and not quiet.
Someone is brave.
Someone is both old and not kind.
Susan is humble or funny.
Paul is both creative and calm.
Alice is either not calm or calm. | Alice is not rich. | entailment | (![X]:(~humble(X)<=>(~old(X)<~>funny(X))))&
((?[X]:((~wise(X)<~>funny(X))))=>(?[X]:((calm(X)<~>happy(X)))))&
(![X]:((creative(X)<~>curious(X))=>~brave(X)))&
(![X]:((~generous(X)&happy(X))<=>(happy(X)|~calm(X))))&
((?[X]:(~funny(X)))=>((rich(lucy)|~tall(lucy))))&
(![X]:(~funny(X)<=>(~funny(X)&funny(X))))&
(![X]:((~wise(X)|~strong(X))=>(generous(X)&~quiet(X))))&
((?[X]:((~old(X)|patient(X))))<=>(?[X]:((humble(X)&strong(X)))))&
(![X]:((generous(X)|~patient(X))<=>(funny(X)&creative(X))))&
(![X]:((creative(X)&rich(X))<=>(strong(X)&~creative(X))))&
(![X]:((tall(X)|~generous(X))=>generous(X)))&
(![X]:((~rich(X)<~>kind(X))<=>~kind(X)))&
(((~creative(mary)&funny(mary)))=>((~wise(fred)|~happy(fred))))&
(![X]:((rich(X)<~>old(X))=>(~happy(X)|quiet(X))))&
(![X]:((~quiet(X)|generous(X))<=>(~quiet(X)&creative(X))))&
(![X]:(tall(X)=>(calm(X)&~rich(X))))&
((tall(fred)&~quiet(fred)))&
(?[X]:(brave(X)))&
(?[X]:((old(X)&~kind(X))))&
((humble(susan)|funny(susan)))&
((creative(paul)&calm(paul)))&
((~calm(alice)<~>calm(alice))) | ~rich(alice) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6903181067606726707734674
% SZS output start Proof for 6903181067606726707734674
12. ! [X0] : ((~rich(X0) <~> kind(X0)) <=> ~kind(X0)) [input p11]
23. rich(alice) [input hypothesis]
56. ! [X0] : ((((~kind(X0) | rich(X0)) & (kind(X0) | ~rich(X0))) | kind(X0)) & (~kind(X0) | ((~rich(X0) | ~kind(X0)) & (kind(X0) | rich(X0))))) [nnf transformation 12]
105. ~kind(X0) | ~rich(X0) | ~kind(X0) [cnf transformation 56]
106. kind(X0) | ~rich(X0) | kind(X0) [cnf transformation 56]
128. rich(alice) [cnf transformation 23]
129. ~kind(X0) | ~rich(X0) [duplicate literal removal 105]
130. kind(X0) | ~rich(X0) [duplicate literal removal 106]
197. ~rich(X0) [subsumption resolution 129,130]
226. $false [subsumption resolution 128,197]
% SZS output end Proof for 6903181067606726707734674
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not creative is kind and vice versa.
Everyone who is not patient is either old or curious and vice versa.
Everyone who is not creative is patient and vice versa.
If someone is either happy or tall then someone is both curious and not generous and vice versa.
Everyone who is both patient and not tall is not patient.
Everyone who is both happy and not happy is not calm or happy.
Everyone who is both not creative and creative is generous or calm and vice versa.
Everyone who is either not tall or calm is happy and vice versa.
Everyone who is both happy and rich is brave and vice versa.
If alice is not happy or not humble then someone is either wise or calm and vice versa.
If someone is both happy and not humble then someone is both tall and not humble and vice versa.
If someone is both calm and not funny then someone is either rich or quiet and vice versa.
Everyone who is either not calm or not brave is not funny or curious.
Everyone who is creative or not kind is not calm and vice versa.
Everyone who is either not funny or wise is both wise and not rich and vice versa.
Everyone who is not creative or not humble is rich and vice versa.
Paul is either not happy or not wise.
Someone is rich or creative.
Mary is both tall and wise.
Someone is either not creative or curious.
Someone is not rich or humble.
John is not creative or tall.
Fred is not wise or wise. | John is happy. | contradiction | (![X]:((happy(X)|~creative(X))<=>kind(X)))&
(![X]:(~patient(X)<=>(old(X)<~>curious(X))))&
(![X]:(~creative(X)<=>patient(X)))&
((?[X]:((happy(X)<~>tall(X))))<=>(?[X]:((curious(X)&~generous(X)))))&
(![X]:((patient(X)&~tall(X))=>~patient(X)))&
(![X]:((happy(X)&~happy(X))=>(~calm(X)|happy(X))))&
(![X]:((~creative(X)&creative(X))<=>(generous(X)|calm(X))))&
(![X]:((~tall(X)<~>calm(X))<=>happy(X)))&
(![X]:((happy(X)&rich(X))<=>brave(X)))&
(((~happy(alice)|~humble(alice)))<=>(?[X]:((wise(X)<~>calm(X)))))&
((?[X]:((happy(X)&~humble(X))))<=>(?[X]:((tall(X)&~humble(X)))))&
((?[X]:((calm(X)&~funny(X))))<=>(?[X]:((rich(X)<~>quiet(X)))))&
(![X]:((~calm(X)<~>~brave(X))=>(~funny(X)|curious(X))))&
(![X]:((creative(X)|~kind(X))<=>~calm(X)))&
(![X]:((~funny(X)<~>wise(X))<=>(wise(X)&~rich(X))))&
(![X]:((~creative(X)|~humble(X))<=>rich(X)))&
((~happy(paul)<~>~wise(paul)))&
(?[X]:((rich(X)|creative(X))))&
((tall(mary)&wise(mary)))&
(?[X]:((~creative(X)<~>curious(X))))&
(?[X]:((~rich(X)|humble(X))))&
((~creative(john)|tall(john)))&
((~wise(fred)|wise(fred))) | happy(john) | [
"p0",
"p6",
"p7",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2071446903745882228408684
% SZS output start Proof for 2071446903745882228408684
1. ! [X0] : ((~creative(X0) | happy(X0)) <=> kind(X0)) [input p0]
7. ! [X0] : ((creative(X0) & ~creative(X0)) <=> (calm(X0) | generous(X0))) [input p6]
8. ! [X0] : ((~tall(X0) <~> calm(X0)) <=> happy(X0)) [input p7]
14. ! [X0] : ((~kind(X0) | creative(X0)) <=> ~calm(X0)) [input p13]
22. tall(john) | ~creative(john) [input p21]
24. happy(john) [input hypothesis]
34. ! [X0] : (((~creative(X0) | happy(X0)) | ~kind(X0)) & (kind(X0) | (creative(X0) & ~happy(X0)))) [nnf transformation 1]
35. ! [X0] : ((~creative(X0) | happy(X0) | ~kind(X0)) & (kind(X0) | (creative(X0) & ~happy(X0)))) [flattening 34]
43. ! [X0] : (((creative(X0) & ~creative(X0)) | (~calm(X0) & ~generous(X0))) & ((calm(X0) | generous(X0)) | (~creative(X0) | creative(X0)))) [nnf transformation 7]
44. ! [X0] : (((creative(X0) & ~creative(X0)) | (~calm(X0) & ~generous(X0))) & (calm(X0) | generous(X0) | ~creative(X0) | creative(X0))) [flattening 43]
45. ! [X0] : ((((~calm(X0) | tall(X0)) & (calm(X0) | ~tall(X0))) | ~happy(X0)) & (happy(X0) | ((~tall(X0) | ~calm(X0)) & (calm(X0) | tall(X0))))) [nnf transformation 8]
64. ! [X0] : (((~kind(X0) | creative(X0)) | calm(X0)) & (~calm(X0) | (kind(X0) & ~creative(X0)))) [nnf transformation 14]
65. ! [X0] : ((~kind(X0) | creative(X0) | calm(X0)) & (~calm(X0) | (kind(X0) & ~creative(X0)))) [flattening 64]
79. kind(X0) | creative(X0) [cnf transformation 35]
97. ~creative(X0) | ~calm(X0) [cnf transformation 44]
99. ~calm(X0) | creative(X0) [cnf transformation 44]
102. calm(X0) | ~tall(X0) | ~happy(X0) [cnf transformation 45]
127. ~kind(X0) | creative(X0) | calm(X0) [cnf transformation 65]
145. tall(john) | ~creative(john) [cnf transformation 22]
147. happy(john) [cnf transformation 24]
183. ~calm(X0) [subsumption resolution 97,99]
185. ~tall(X0) | ~happy(X0) [subsumption resolution 102,183]
251. ~kind(X0) | creative(X0) [subsumption resolution 127,183]
252. creative(X0) [subsumption resolution 251,79]
266. tall(john) [subsumption resolution 145,252]
286. ~happy(john) [resolution 185,266]
287. $false [subsumption resolution 286,147]
% SZS output end Proof for 2071446903745882228408684
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not kind is both not kind and not strong and vice versa.
Everyone who is rich is wise.
Everyone who is brave is both funny and humble and vice versa.
Everyone who is either not humble or brave is not happy or curious.
If fred is both rich and not calm then someone is either generous or not humble.
Everyone who is either not quiet or not creative is either kind or not rich and vice versa.
If lucy is either not brave or not strong then someone is both wise and humble and vice versa.
If someone is not tall then someone is calm and vice versa.
Everyone who is both patient and tall is generous.
Everyone who is either creative or strong is either funny or not humble.
If lucy is both humble and creative then fred is patient.
Everyone who is both tall and not strong is both wise and not humble and vice versa.
Everyone who is either brave or not wise is rich.
If someone is either tall or not old then lucy is not humble.
Everyone who is curious or not old is not calm or generous and vice versa.
Everyone who is not strong or brave is tall or not kind and vice versa.
Mary is happy.
Alice is both old and not strong.
Someone is either humble or not kind.
John is either not strong or happy.
Fred is both generous and not patient.
Fred is both wise and humble.
Someone is brave.
Mary is tall. | Alice is tall. | contradiction | (![X]:((~calm(X)<~>~kind(X))<=>(~kind(X)&~strong(X))))&
(![X]:(rich(X)=>wise(X)))&
(![X]:(brave(X)<=>(funny(X)&humble(X))))&
(![X]:((~humble(X)<~>brave(X))=>(~happy(X)|curious(X))))&
(((rich(fred)&~calm(fred)))=>(?[X]:((generous(X)<~>~humble(X)))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(kind(X)<~>~rich(X))))&
(((~brave(lucy)<~>~strong(lucy)))<=>(?[X]:((wise(X)&humble(X)))))&
((?[X]:(~tall(X)))<=>(?[X]:(calm(X))))&
(![X]:((patient(X)&tall(X))=>generous(X)))&
(![X]:((creative(X)<~>strong(X))=>(funny(X)<~>~humble(X))))&
(((humble(lucy)&creative(lucy)))=>(patient(fred)))&
(![X]:((tall(X)&~strong(X))<=>(wise(X)&~humble(X))))&
(![X]:((brave(X)<~>~wise(X))=>rich(X)))&
((?[X]:((tall(X)<~>~old(X))))=>(~humble(lucy)))&
(![X]:((curious(X)|~old(X))<=>(~calm(X)|generous(X))))&
(![X]:((~strong(X)|brave(X))<=>(tall(X)|~kind(X))))&
(happy(mary))&
((old(alice)&~strong(alice)))&
(?[X]:((humble(X)<~>~kind(X))))&
((~strong(john)<~>happy(john)))&
((generous(fred)&~patient(fred)))&
((wise(fred)&humble(fred)))&
(?[X]:(brave(X)))&
(tall(mary)) | tall(alice) | [
"p1",
"p2",
"p6",
"p11",
"p12",
"p13",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8442935211477084411969793
% SZS output start Proof for 8442935211477084411969793
2. ! [X0] : (rich(X0) => wise(X0)) [input p1]
3. ! [X0] : (brave(X0) <=> (humble(X0) & funny(X0))) [input p2]
7. (~brave(lucy) <~> ~strong(lucy)) <=> ? [X0] : (humble(X0) & wise(X0)) [input p6]
12. ! [X0] : ((~strong(X0) & tall(X0)) <=> (~humble(X0) & wise(X0))) [input p11]
13. ! [X0] : ((brave(X0) <~> ~wise(X0)) => rich(X0)) [input p12]
14. ? [X0] : (tall(X0) <~> ~old(X0)) => ~humble(lucy) [input p13]
18. ~strong(alice) & old(alice) [input p17]
22. humble(fred) & wise(fred) [input p21]
25. tall(alice) [input hypothesis]
27. ! [X0] : (wise(X0) | ~rich(X0)) [ennf transformation 2]
37. ! [X0] : (rich(X0) | (brave(X0) <=> ~wise(X0))) [ennf transformation 13]
38. ~humble(lucy) | ! [X0] : (tall(X0) <=> ~old(X0)) [ennf transformation 14]
41. ! [X0] : ((brave(X0) | (~humble(X0) | ~funny(X0))) & ((humble(X0) & funny(X0)) | ~brave(X0))) [nnf transformation 3]
42. ! [X0] : ((brave(X0) | ~humble(X0) | ~funny(X0)) & ((humble(X0) & funny(X0)) | ~brave(X0))) [flattening 41]
48. (((strong(lucy) | brave(lucy)) & (~strong(lucy) | ~brave(lucy))) | ! [X0] : (~humble(X0) | ~wise(X0))) & (? [X0] : (humble(X0) & wise(X0)) | ((~brave(lucy) | strong(lucy)) & (~strong(lucy) | brave(lucy)))) [nnf transformation 7]
49. (((strong(lucy) | brave(lucy)) & (~strong(lucy) | ~brave(lucy))) | ! [X0] : (~humble(X0) | ~wise(X0))) & (? [X1] : (humble(X1) & wise(X1)) | ((~brave(lucy) | strong(lucy)) & (~strong(lucy) | brave(lucy)))) [rectify 48]
50. ? [X1] : (humble(X1) & wise(X1)) => (humble(sK1) & wise(sK1)) [choice axiom]
51. (((strong(lucy) | brave(lucy)) & (~strong(lucy) | ~brave(lucy))) | ! [X0] : (~humble(X0) | ~wise(X0))) & ((humble(sK1) & wise(sK1)) | ((~brave(lucy) | strong(lucy)) & (~strong(lucy) | brave(lucy)))) [skolemisation 49,50]
58. ! [X0] : (((~strong(X0) & tall(X0)) | (humble(X0) | ~wise(X0))) & ((~humble(X0) & wise(X0)) | (strong(X0) | ~tall(X0)))) [nnf transformation 12]
59. ! [X0] : (((~strong(X0) & tall(X0)) | humble(X0) | ~wise(X0)) & ((~humble(X0) & wise(X0)) | strong(X0) | ~tall(X0))) [flattening 58]
60. ! [X0] : (rich(X0) | ((brave(X0) | wise(X0)) & (~wise(X0) | ~brave(X0)))) [nnf transformation 37]
61. ~humble(lucy) | ! [X0] : ((tall(X0) | old(X0)) & (~old(X0) | ~tall(X0))) [nnf transformation 38]
78. ~rich(X0) | wise(X0) [cnf transformation 27]
80. ~brave(X0) | humble(X0) [cnf transformation 42]
99. strong(lucy) | brave(lucy) | ~humble(X0) | ~wise(X0) [cnf transformation 51]
111. ~wise(X0) | humble(X0) | ~strong(X0) [cnf transformation 59]
113. rich(X0) | brave(X0) | wise(X0) [cnf transformation 60]
114. ~humble(lucy) | ~old(X0) | ~tall(X0) [cnf transformation 61]
125. old(alice) [cnf transformation 18]
133. wise(fred) [cnf transformation 22]
134. humble(fred) [cnf transformation 22]
137. tall(alice) [cnf transformation 25]
161. 5 <=> ! [X0] : (~humble(X0) | ~wise(X0)) [avatar definition]
162. ~humble(X0) | ~wise(X0) <- (5) [avatar component clause 161]
164. 6 <=> brave(lucy) [avatar definition]
165. ~brave(lucy) <- (~6) [avatar component clause 164]
166. brave(lucy) <- (6) [avatar component clause 164]
168. 7 <=> strong(lucy) [avatar definition]
170. strong(lucy) <- (7) [avatar component clause 168]
171. 5 | 6 | 7 [avatar split clause 99,168,164,161]
202. 14 <=> humble(lucy) [avatar definition]
204. ~humble(lucy) <- (~14) [avatar component clause 202]
214. brave(X0) | wise(X0) [subsumption resolution 113,78]
220. 18 <=> ! [X0] : (~old(X0) | ~tall(X0)) [avatar definition]
221. ~old(X0) | ~tall(X0) <- (18) [avatar component clause 220]
222. 18 | ~14 [avatar split clause 114,202,220]
248. ~wise(fred) <- (5) [resolution 162,134]
250. $false <- (5) [subsumption resolution 248,133]
251. ~5 [avatar contradiction clause 250]
252. humble(lucy) <- (6) [resolution 166,80]
256. 14 | ~6 [avatar split clause 252,164,202]
264. ~tall(alice) <- (18) [resolution 221,125]
266. $false <- (18) [subsumption resolution 264,137]
267. ~18 [avatar contradiction clause 266]
268. wise(lucy) <- (~6) [resolution 165,214]
332. humble(lucy) | ~strong(lucy) <- (~6) [resolution 111,268]
336. ~strong(lucy) <- (~6, ~14) [subsumption resolution 332,204]
337. $false <- (~6, 7, ~14) [subsumption resolution 336,170]
338. 6 | ~7 | 14 [avatar contradiction clause 337]
341. $false [avatar sat refutation 171,222,251,256,267,338]
% SZS output end Proof for 8442935211477084411969793
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either kind or not calm then lucy is either not brave or not calm and vice versa.
If mary is not calm or wise then alice is strong or tall and vice versa.
Everyone who is quiet is not strong.
Everyone who is both not creative and curious is humble or curious and vice versa.
If john is not patient or not quiet then someone is not patient or funny and vice versa.
If susan is both calm and kind then alice is kind or tall.
If someone is either not brave or not humble then someone is either tall or generous and vice versa.
If someone is old or rich then someone is not calm or happy.
If susan is curious then lucy is either patient or old.
If someone is both not quiet and kind then someone is tall or not strong.
Everyone who is not brave is not calm or not kind.
Everyone who is not generous is either old or tall and vice versa.
If someone is creative then alice is either happy or not old and vice versa.
Everyone who is not curious or generous is either happy or tall and vice versa.
Everyone who is generous is both strong and not strong.
Everyone who is not rich is both not old and not calm and vice versa.
Someone is either curious or strong.
Susan is both not wise and curious.
Lucy is not wise.
Someone is not humble or not patient.
Mary is either not creative or tall.
Susan is curious or strong.
Someone is not kind or generous.
Fred is not generous or not patient. | Lucy is generous. | contradiction | (((kind(mary)<~>~calm(mary)))<=>((~brave(lucy)<~>~calm(lucy))))&
(((~calm(mary)|wise(mary)))<=>((strong(alice)|tall(alice))))&
(![X]:(quiet(X)=>~strong(X)))&
(![X]:((~creative(X)&curious(X))<=>(humble(X)|curious(X))))&
(((~patient(john)|~quiet(john)))<=>(?[X]:((~patient(X)|funny(X)))))&
(((calm(susan)&kind(susan)))=>((kind(alice)|tall(alice))))&
((?[X]:((~brave(X)<~>~humble(X))))<=>(?[X]:((tall(X)<~>generous(X)))))&
((?[X]:((old(X)|rich(X))))=>(?[X]:((~calm(X)|happy(X)))))&
((curious(susan))=>((patient(lucy)<~>old(lucy))))&
((?[X]:((~quiet(X)&kind(X))))=>(?[X]:((tall(X)|~strong(X)))))&
(![X]:(~brave(X)=>(~calm(X)|~kind(X))))&
(![X]:(~generous(X)<=>(old(X)<~>tall(X))))&
((?[X]:(creative(X)))<=>((happy(alice)<~>~old(alice))))&
(![X]:((~curious(X)|generous(X))<=>(happy(X)<~>tall(X))))&
(![X]:(generous(X)=>(strong(X)&~strong(X))))&
(![X]:(~rich(X)<=>(~old(X)&~calm(X))))&
(?[X]:((curious(X)<~>strong(X))))&
((~wise(susan)&curious(susan)))&
(~wise(lucy))&
(?[X]:((~humble(X)|~patient(X))))&
((~creative(mary)<~>tall(mary)))&
((curious(susan)|strong(susan)))&
(?[X]:((~kind(X)|generous(X))))&
((~generous(fred)|~patient(fred))) | generous(lucy) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2586949701471169207525639
% SZS output start Proof for 2586949701471169207525639
15. ! [X0] : (generous(X0) => (~strong(X0) & strong(X0))) [input p14]
25. generous(lucy) [input hypothesis]
38. ! [X0] : ((~strong(X0) & strong(X0)) | ~generous(X0)) [ennf transformation 15]
128. strong(X0) | ~generous(X0) [cnf transformation 38]
129. ~strong(X0) | ~generous(X0) [cnf transformation 38]
143. generous(lucy) [cnf transformation 25]
320. ~generous(X0) [subsumption resolution 128,129]
357. $false [subsumption resolution 143,320]
% SZS output end Proof for 2586949701471169207525639
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and funny then lucy is either not quiet or not old.
If lucy is not kind or brave then someone is funny or patient.
Everyone who is both old and not old is either kind or generous and vice versa.
If mary is both not happy and not generous then lucy is not calm.
Everyone who is patient or not kind is happy and vice versa.
If someone is either kind or curious then someone is both curious and calm.
Everyone who is not patient is both patient and not curious.
Everyone who is both tall and patient is curious and vice versa.
Everyone who is both not strong and not generous is not tall.
If someone is not wise or wise then fred is not quiet and vice versa.
Everyone who is creative is not creative or not calm.
If fred is both not kind and not happy then someone is both not quiet and curious.
Everyone who is either not happy or not patient is either not quiet or not calm.
Everyone who is old is both happy and old.
If someone is either not funny or not tall then someone is both not patient and calm and vice versa.
If paul is not calm or not generous then someone is not brave and vice versa.
Someone is happy.
Someone is strong.
Susan is strong.
Mary is creative.
Someone is either not kind or rich.
Someone is old.
Someone is brave.
Someone is both rich and brave. | Lucy is calm. | neutral | ((?[X]:((brave(X)&funny(X))))=>((~quiet(lucy)<~>~old(lucy))))&
(((~kind(lucy)|brave(lucy)))=>(?[X]:((funny(X)|patient(X)))))&
(![X]:((old(X)&~old(X))<=>(kind(X)<~>generous(X))))&
(((~happy(mary)&~generous(mary)))=>(~calm(lucy)))&
(![X]:((patient(X)|~kind(X))<=>happy(X)))&
((?[X]:((kind(X)<~>curious(X))))=>(?[X]:((curious(X)&calm(X)))))&
(![X]:(~patient(X)=>(patient(X)&~curious(X))))&
(![X]:((tall(X)&patient(X))<=>curious(X)))&
(![X]:((~strong(X)&~generous(X))=>~tall(X)))&
((?[X]:((~wise(X)|wise(X))))<=>(~quiet(fred)))&
(![X]:(creative(X)=>(~creative(X)|~calm(X))))&
(((~kind(fred)&~happy(fred)))=>(?[X]:((~quiet(X)&curious(X)))))&
(![X]:((~happy(X)<~>~patient(X))=>(~quiet(X)<~>~calm(X))))&
(![X]:(old(X)=>(happy(X)&old(X))))&
((?[X]:((~funny(X)<~>~tall(X))))<=>(?[X]:((~patient(X)&calm(X)))))&
(((~calm(paul)|~generous(paul)))<=>(?[X]:(~brave(X))))&
(?[X]:(happy(X)))&
(?[X]:(strong(X)))&
(strong(susan))&
(creative(mary))&
(?[X]:((~kind(X)<~>rich(X))))&
(?[X]:(old(X)))&
(?[X]:(brave(X)))&
(?[X]:((rich(X)&brave(X)))) | calm(lucy) | [] | null | 0 |
Everyone who is either not strong or not patient is not calm or not quiet and vice versa.
If paul is both strong and generous then someone is patient and vice versa.
Everyone who is creative is either not rich or tall and vice versa.
If someone is wise or calm then fred is old or not tall.
If someone is creative or not quiet then someone is both quiet and rich.
If paul is both curious and generous then someone is humble or funny.
If someone is curious or not patient then someone is both not tall and not wise.
If john is not curious or happy then susan is tall or curious and vice versa.
Everyone who is creative is both humble and not creative.
Everyone who is either creative or not generous is not funny.
Everyone who is not calm is either tall or not quiet and vice versa.
Everyone who is both kind and rich is not calm and vice versa.
If someone is either rich or calm then susan is not curious and vice versa.
If alice is not funny then paul is humble and vice versa.
Everyone who is either creative or rich is patient and vice versa.
Everyone who is both wise and not patient is both generous and not tall.
Paul is either creative or not rich.
Fred is not tall.
Fred is not kind or not rich.
Someone is either not brave or not humble.
Someone is not strong or not humble.
Susan is brave or not strong.
Someone is either not wise or not kind. | Susan is strong. | neutral | (![X]:((~strong(X)<~>~patient(X))<=>(~calm(X)|~quiet(X))))&
(((strong(paul)&generous(paul)))<=>(?[X]:(patient(X))))&
(![X]:(creative(X)<=>(~rich(X)<~>tall(X))))&
((?[X]:((wise(X)|calm(X))))=>((old(fred)|~tall(fred))))&
((?[X]:((creative(X)|~quiet(X))))=>(?[X]:((quiet(X)&rich(X)))))&
(((curious(paul)&generous(paul)))=>(?[X]:((humble(X)|funny(X)))))&
((?[X]:((curious(X)|~patient(X))))=>(?[X]:((~tall(X)&~wise(X)))))&
(((~curious(john)|happy(john)))<=>((tall(susan)|curious(susan))))&
(![X]:(creative(X)=>(humble(X)&~creative(X))))&
(![X]:((creative(X)<~>~generous(X))=>~funny(X)))&
(![X]:(~calm(X)<=>(tall(X)<~>~quiet(X))))&
(![X]:((kind(X)&rich(X))<=>~calm(X)))&
((?[X]:((rich(X)<~>calm(X))))<=>(~curious(susan)))&
((~funny(alice))<=>(humble(paul)))&
(![X]:((creative(X)<~>rich(X))<=>patient(X)))&
(![X]:((wise(X)&~patient(X))=>(generous(X)&~tall(X))))&
((creative(paul)<~>~rich(paul)))&
(~tall(fred))&
((~kind(fred)|~rich(fred)))&
(?[X]:((~brave(X)<~>~humble(X))))&
(?[X]:((~strong(X)|~humble(X))))&
((brave(susan)|~strong(susan)))&
(?[X]:((~wise(X)<~>~kind(X)))) | strong(susan) | [] | null | 0 |
Everyone who is not tall or not creative is both not strong and generous and vice versa.
Everyone who is either quiet or not quiet is rich or not quiet.
Everyone who is both kind and not old is both not kind and not rich.
If lucy is both quiet and wise then someone is either not funny or not creative.
Everyone who is both not strong and funny is both not curious and not calm and vice versa.
Everyone who is either not calm or strong is patient or rich and vice versa.
If john is not patient then john is tall or not patient.
Everyone who is not quiet or humble is both not funny and patient.
Everyone who is both not creative and not quiet is either generous or humble and vice versa.
Everyone who is either strong or not patient is patient.
Everyone who is either not strong or not brave is either not kind or not rich and vice versa.
Everyone who is both curious and kind is either not funny or not wise.
Everyone who is not kind or wise is either not humble or not curious and vice versa.
Everyone who is not old or kind is generous or tall and vice versa.
If someone is not patient or creative then mary is not tall or not wise.
Everyone who is either not strong or not rich is not strong or tall.
John is both quiet and brave.
Fred is strong or patient.
Someone is either patient or tall.
Mary is both tall and funny.
Fred is not patient or not old.
Someone is patient or not generous.
Someone is wise. | John is strong. | neutral | (![X]:((~tall(X)|~creative(X))<=>(~strong(X)&generous(X))))&
(![X]:((quiet(X)<~>~quiet(X))=>(rich(X)|~quiet(X))))&
(![X]:((kind(X)&~old(X))=>(~kind(X)&~rich(X))))&
(((quiet(lucy)&wise(lucy)))=>(?[X]:((~funny(X)<~>~creative(X)))))&
(![X]:((~strong(X)&funny(X))<=>(~curious(X)&~calm(X))))&
(![X]:((~calm(X)<~>strong(X))<=>(patient(X)|rich(X))))&
((~patient(john))=>((tall(john)|~patient(john))))&
(![X]:((~quiet(X)|humble(X))=>(~funny(X)&patient(X))))&
(![X]:((~creative(X)&~quiet(X))<=>(generous(X)<~>humble(X))))&
(![X]:((strong(X)<~>~patient(X))=>patient(X)))&
(![X]:((~strong(X)<~>~brave(X))<=>(~kind(X)<~>~rich(X))))&
(![X]:((curious(X)&kind(X))=>(~funny(X)<~>~wise(X))))&
(![X]:((~kind(X)|wise(X))<=>(~humble(X)<~>~curious(X))))&
(![X]:((~old(X)|kind(X))<=>(generous(X)|tall(X))))&
((?[X]:((~patient(X)|creative(X))))=>((~tall(mary)|~wise(mary))))&
(![X]:((~strong(X)<~>~rich(X))=>(~strong(X)|tall(X))))&
((quiet(john)&brave(john)))&
((strong(fred)|patient(fred)))&
(?[X]:((patient(X)<~>tall(X))))&
((tall(mary)&funny(mary)))&
((~patient(fred)|~old(fred)))&
(?[X]:((patient(X)|~generous(X))))&
(?[X]:(wise(X))) | strong(john) | [] | null | 0 |
Everyone who is either not patient or not humble is either wise or rich and vice versa. If fred is not brave then alice is either quiet or not curious. Everyone who is either not creative or not happy is either happy or not calm. If lucy is not creative then susan is not happy. Everyone who is not strong or happy is not happy and vice versa. Everyone who is brave or not patient is old and vice versa. Everyone who is not happy is both not curious and not happy and vice versa. If someone is both funny and not happy then fred is kind or strong and vice versa. If fred is funny or wise then someone is both not humble and strong. Everyone who is not brave or rich is not quiet or brave and vice versa. If mary is either not creative or not brave then someone is generous. Everyone who is either not wise or generous is either not old or patient and vice versa. Everyone who is not humble is creative and vice versa. Everyone who is either wise or funny is quiet and vice versa. Everyone who is both strong and not humble is both not happy and not wise. If someone is both rich and quiet then john is either creative or not calm. Someone is either not quiet or old. Someone is patient. Someone is both kind and generous. Mary is either old or tall. Alice is either funny or kind. Mary is both calm and not old. | Lucy is not quiet. | neutral | (![X]:((~patient(X)<~>~humble(X))<=>(wise(X)<~>rich(X))))&
((~brave(fred))=>((quiet(alice)<~>~curious(alice))))&
(![X]:((~creative(X)<~>~happy(X))=>(happy(X)<~>~calm(X))))&
((~creative(lucy))=>(~happy(susan)))&
(![X]:((~strong(X)|happy(X))<=>~happy(X)))&
(![X]:((brave(X)|~patient(X))<=>old(X)))&
(![X]:(~happy(X)<=>(~curious(X)&~happy(X))))&
((?[X]:((funny(X)&~happy(X))))<=>((kind(fred)|strong(fred))))&
(((funny(fred)|wise(fred)))=>(?[X]:((~humble(X)&strong(X)))))&
(![X]:((~brave(X)|rich(X))<=>(~quiet(X)|brave(X))))&
(((~creative(mary)<~>~brave(mary)))=>(?[X]:(generous(X))))&
(![X]:((~wise(X)<~>generous(X))<=>(~old(X)<~>patient(X))))&
(![X]:(~humble(X)<=>creative(X)))&
(![X]:((wise(X)<~>funny(X))<=>quiet(X)))&
(![X]:((strong(X)&~humble(X))=>(~happy(X)&~wise(X))))&
((?[X]:((rich(X)&quiet(X))))=>((creative(john)<~>~calm(john))))&
(?[X]:((~quiet(X)<~>old(X))))&
(?[X]:(patient(X)))&
(?[X]:((kind(X)&generous(X))))&
((old(mary)<~>tall(mary)))&
((funny(alice)<~>kind(alice)))&
((calm(mary)&~old(mary))) | ~quiet(lucy) | [] | null | 0 |
If someone is both humble and quiet then someone is not humble. Everyone who is not strong is kind and vice versa. If paul is tall then someone is either old or funny. Everyone who is creative or generous is both not quiet and tall and vice versa. Everyone who is creative is curious or not generous. Everyone who is both patient and not happy is either not calm or calm. If lucy is both not funny and not rich then someone is humble. If paul is either not old or old then alice is not tall or not quiet and vice versa. If someone is old or not patient then fred is brave or tall. If someone is both old and not calm then lucy is not kind. Everyone who is both old and not funny is either creative or kind and vice versa. If lucy is not creative then john is kind. Everyone who is either patient or not generous is not humble. If john is strong then lucy is patient or not strong. Everyone who is calm is rich and vice versa. Everyone who is either not funny or strong is not happy or humble and vice versa. Lucy is both curious and generous. Lucy is both not funny and not brave. Fred is wise. Alice is kind. Someone is either not calm or quiet. Someone is not humble. Someone is both not calm and not happy. Someone is both not rich and kind. | Alice is not tall. | neutral | ((?[X]:((humble(X)&quiet(X))))=>(?[X]:(~humble(X))))&
(![X]:(~strong(X)<=>kind(X)))&
((tall(paul))=>(?[X]:((old(X)<~>funny(X)))))&
(![X]:((creative(X)|generous(X))<=>(~quiet(X)&tall(X))))&
(![X]:(creative(X)=>(curious(X)|~generous(X))))&
(![X]:((patient(X)&~happy(X))=>(~calm(X)<~>calm(X))))&
(((~funny(lucy)&~rich(lucy)))=>(?[X]:(humble(X))))&
(((~old(paul)<~>old(paul)))<=>((~tall(alice)|~quiet(alice))))&
((?[X]:((old(X)|~patient(X))))=>((brave(fred)|tall(fred))))&
((?[X]:((old(X)&~calm(X))))=>(~kind(lucy)))&
(![X]:((old(X)&~funny(X))<=>(creative(X)<~>kind(X))))&
((~creative(lucy))=>(kind(john)))&
(![X]:((patient(X)<~>~generous(X))=>~humble(X)))&
((strong(john))=>((patient(lucy)|~strong(lucy))))&
(![X]:(calm(X)<=>rich(X)))&
(![X]:((~funny(X)<~>strong(X))<=>(~happy(X)|humble(X))))&
((curious(lucy)&generous(lucy)))&
((~funny(lucy)&~brave(lucy)))&
(wise(fred))&
(kind(alice))&
(?[X]:((~calm(X)<~>quiet(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~calm(X)&~happy(X))))&
(?[X]:((~rich(X)&kind(X)))) | ~tall(alice) | [] | null | 0 |
Everyone who is both kind and not old is both not funny and not brave.
Everyone who is curious is brave or not brave.
If alice is not rich then susan is not happy or happy.
Everyone who is curious is kind or not strong and vice versa.
Everyone who is either creative or not wise is not brave or strong and vice versa.
Everyone who is both not quiet and not curious is strong or not kind.
If alice is either generous or not strong then susan is both humble and tall and vice versa.
If mary is either not brave or quiet then someone is not tall.
Everyone who is both not curious and not old is kind or not tall and vice versa.
Everyone who is not happy is not old or calm and vice versa.
If someone is happy then lucy is both not funny and not brave.
Everyone who is either not curious or creative is not humble and vice versa.
If mary is both not curious and tall then paul is not patient.
If someone is both not tall and quiet then someone is either not brave or patient.
Everyone who is not brave or kind is old.
If someone is calm or not quiet then fred is both not generous and happy and vice versa.
Someone is either old or not happy.
John is creative.
Mary is creative or not patient.
Someone is patient.
Someone is not funny or not humble.
Lucy is not strong.
John is not patient or brave.
Mary is old or wise. | Lucy is curious. | entailment | (![X]:((kind(X)&~old(X))=>(~funny(X)&~brave(X))))&
(![X]:(curious(X)=>(brave(X)|~brave(X))))&
((~rich(alice))=>((~happy(susan)|happy(susan))))&
(![X]:(curious(X)<=>(kind(X)|~strong(X))))&
(![X]:((creative(X)<~>~wise(X))<=>(~brave(X)|strong(X))))&
(![X]:((~quiet(X)&~curious(X))=>(strong(X)|~kind(X))))&
(((generous(alice)<~>~strong(alice)))<=>((humble(susan)&tall(susan))))&
(((~brave(mary)<~>quiet(mary)))=>(?[X]:(~tall(X))))&
(![X]:((~curious(X)&~old(X))<=>(kind(X)|~tall(X))))&
(![X]:(~happy(X)<=>(~old(X)|calm(X))))&
((?[X]:(happy(X)))=>((~funny(lucy)&~brave(lucy))))&
(![X]:((~curious(X)<~>creative(X))<=>~humble(X)))&
(((~curious(mary)&tall(mary)))=>(~patient(paul)))&
((?[X]:((~tall(X)&quiet(X))))=>(?[X]:((~brave(X)<~>patient(X)))))&
(![X]:((~brave(X)|kind(X))=>old(X)))&
((?[X]:((calm(X)|~quiet(X))))<=>((~generous(fred)&happy(fred))))&
(?[X]:((old(X)<~>~happy(X))))&
(creative(john))&
((creative(mary)|~patient(mary)))&
(?[X]:(patient(X)))&
(?[X]:((~funny(X)|~humble(X))))&
(~strong(lucy))&
((~patient(john)|brave(john)))&
((old(mary)|wise(mary))) | curious(lucy) | [
"p3",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 598911391974796711453321
% SZS output start Proof for 598911391974796711453321
4. ! [X0] : (curious(X0) <=> (~strong(X0) | kind(X0))) [input p3]
22. ~strong(lucy) [input p21]
25. ~curious(lucy) [input hypothesis]
43. ! [X0] : ((curious(X0) | (strong(X0) & ~kind(X0))) & ((~strong(X0) | kind(X0)) | ~curious(X0))) [nnf transformation 4]
44. ! [X0] : ((curious(X0) | (strong(X0) & ~kind(X0))) & (~strong(X0) | kind(X0) | ~curious(X0))) [flattening 43]
75. strong(X0) | curious(X0) [cnf transformation 44]
119. ~strong(lucy) [cnf transformation 22]
122. ~curious(lucy) [cnf transformation 25]
258. curious(lucy) [resolution 75,119]
260. $false [subsumption resolution 258,122]
% SZS output end Proof for 598911391974796711453321
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and patient is both not creative and not happy.
Everyone who is tall or not generous is curious and vice versa.
Everyone who is not strong or not wise is old.
If paul is both curious and not patient then fred is strong.
Everyone who is either funny or quiet is old or not tall and vice versa.
Everyone who is both tall and not happy is both not humble and not happy and vice versa.
Everyone who is funny is not calm or old and vice versa.
Everyone who is not calm or kind is strong and vice versa.
Everyone who is not funny is both humble and not wise and vice versa.
Everyone who is not kind or generous is old or not old.
Everyone who is patient or tall is not strong and vice versa.
If fred is both not creative and not quiet then susan is either not kind or wise and vice versa.
If someone is either not humble or not tall then someone is either not creative or funny.
Everyone who is humble is not wise and vice versa.
Everyone who is patient or generous is rich or not creative.
Everyone who is quiet or funny is either quiet or not quiet.
Someone is both not kind and funny.
Alice is not patient.
John is curious or wise.
Mary is either not brave or not happy.
Someone is either not kind or not patient.
Fred is both brave and not calm.
Mary is tall. | Alice is not calm. | neutral | (![X]:((curious(X)&patient(X))=>(~creative(X)&~happy(X))))&
(![X]:((tall(X)|~generous(X))<=>curious(X)))&
(![X]:((~strong(X)|~wise(X))=>old(X)))&
(((curious(paul)&~patient(paul)))=>(strong(fred)))&
(![X]:((funny(X)<~>quiet(X))<=>(old(X)|~tall(X))))&
(![X]:((tall(X)&~happy(X))<=>(~humble(X)&~happy(X))))&
(![X]:(funny(X)<=>(~calm(X)|old(X))))&
(![X]:((~calm(X)|kind(X))<=>strong(X)))&
(![X]:(~funny(X)<=>(humble(X)&~wise(X))))&
(![X]:((~kind(X)|generous(X))=>(old(X)|~old(X))))&
(![X]:((patient(X)|tall(X))<=>~strong(X)))&
(((~creative(fred)&~quiet(fred)))<=>((~kind(susan)<~>wise(susan))))&
((?[X]:((~humble(X)<~>~tall(X))))=>(?[X]:((~creative(X)<~>funny(X)))))&
(![X]:(humble(X)<=>~wise(X)))&
(![X]:((patient(X)|generous(X))=>(rich(X)|~creative(X))))&
(![X]:((quiet(X)|funny(X))=>(quiet(X)<~>~quiet(X))))&
(?[X]:((~kind(X)&funny(X))))&
(~patient(alice))&
((curious(john)|wise(john)))&
((~brave(mary)<~>~happy(mary)))&
(?[X]:((~kind(X)<~>~patient(X))))&
((brave(fred)&~calm(fred)))&
(tall(mary)) | ~calm(alice) | [] | null | 0 |
If fred is not patient then alice is not rich.
Everyone who is both not curious and not creative is not humble and vice versa.
Everyone who is both not strong and not humble is rich and vice versa.
Everyone who is brave is both not calm and not funny.
Everyone who is both quiet and not generous is not calm or not wise.
Everyone who is both funny and tall is curious or generous.
If john is either tall or not strong then john is both happy and creative.
Everyone who is creative or not curious is both brave and patient.
If someone is kind or not old then someone is either not tall or quiet and vice versa.
Everyone who is both funny and wise is quiet or not rich and vice versa.
If someone is either not kind or not tall then fred is both not curious and not calm.
Everyone who is either calm or generous is either funny or not rich.
If someone is not rich then someone is not brave or strong.
Everyone who is both not happy and curious is both patient and not kind and vice versa.
If paul is either funny or not patient then someone is strong or old.
If someone is both not generous and old then susan is not calm or kind and vice versa.
Someone is not kind or not wise.
Mary is funny or not calm.
Alice is either funny or calm.
Someone is both not brave and not strong.
Susan is either patient or brave.
Someone is not kind or not strong. | John is happy. | neutral | ((~patient(fred))=>(~rich(alice)))&
(![X]:((~curious(X)&~creative(X))<=>~humble(X)))&
(![X]:((~strong(X)&~humble(X))<=>rich(X)))&
(![X]:(brave(X)=>(~calm(X)&~funny(X))))&
(![X]:((quiet(X)&~generous(X))=>(~calm(X)|~wise(X))))&
(![X]:((funny(X)&tall(X))=>(curious(X)|generous(X))))&
(((tall(john)<~>~strong(john)))=>((happy(john)&creative(john))))&
(![X]:((creative(X)|~curious(X))=>(brave(X)&patient(X))))&
((?[X]:((kind(X)|~old(X))))<=>(?[X]:((~tall(X)<~>quiet(X)))))&
(![X]:((funny(X)&wise(X))<=>(quiet(X)|~rich(X))))&
((?[X]:((~kind(X)<~>~tall(X))))=>((~curious(fred)&~calm(fred))))&
(![X]:((calm(X)<~>generous(X))=>(funny(X)<~>~rich(X))))&
((?[X]:(~rich(X)))=>(?[X]:((~brave(X)|strong(X)))))&
(![X]:((~happy(X)&curious(X))<=>(patient(X)&~kind(X))))&
(((funny(paul)<~>~patient(paul)))=>(?[X]:((strong(X)|old(X)))))&
((?[X]:((~generous(X)&old(X))))<=>((~calm(susan)|kind(susan))))&
(?[X]:((~kind(X)|~wise(X))))&
((funny(mary)|~calm(mary)))&
((funny(alice)<~>calm(alice)))&
(?[X]:((~brave(X)&~strong(X))))&
((patient(susan)<~>brave(susan)))&
(?[X]:((~kind(X)|~strong(X)))) | happy(john) | [] | null | 0 |
Everyone who is either happy or wise is both happy and not old.
Everyone who is happy or rich is not patient.
Everyone who is either humble or patient is rich or kind and vice versa.
Everyone who is brave is both kind and patient.
Everyone who is either brave or funny is kind or patient and vice versa.
Everyone who is kind or brave is both patient and not brave.
If someone is both patient and not calm then mary is both not generous and not kind.
Everyone who is either not funny or not wise is either not patient or brave.
Everyone who is both curious and not old is either not quiet or brave and vice versa.
If susan is both old and not happy then someone is not generous or not kind and vice versa.
Everyone who is not humble or not calm is not humble or generous and vice versa.
Everyone who is either not funny or not happy is either creative or not funny.
If paul is both humble and wise then john is both happy and not calm.
Everyone who is both quiet and calm is both not creative and brave and vice versa.
Someone is not curious or not brave.
Lucy is not quiet or not humble.
Someone is both not old and not rich.
Someone is not rich or not funny.
Someone is not humble.
Someone is creative or funny. | Mary is patient. | contradiction | (![X]:((happy(X)<~>wise(X))=>(happy(X)&~old(X))))&
(![X]:((happy(X)|rich(X))=>~patient(X)))&
(![X]:((humble(X)<~>patient(X))<=>(rich(X)|kind(X))))&
(![X]:(brave(X)=>(kind(X)&patient(X))))&
(![X]:((brave(X)<~>funny(X))<=>(kind(X)|patient(X))))&
(![X]:((kind(X)|brave(X))=>(patient(X)&~brave(X))))&
((?[X]:((patient(X)&~calm(X))))=>((~generous(mary)&~kind(mary))))&
(![X]:((~funny(X)<~>~wise(X))=>(~patient(X)<~>brave(X))))&
(![X]:((curious(X)&~old(X))<=>(~quiet(X)<~>brave(X))))&
(((old(susan)&~happy(susan)))<=>(?[X]:((~generous(X)|~kind(X)))))&
(![X]:((~humble(X)|~calm(X))<=>(~humble(X)|generous(X))))&
(![X]:((~funny(X)<~>~happy(X))=>(creative(X)<~>~funny(X))))&
(((humble(paul)&wise(paul)))=>((happy(john)&~calm(john))))&
(![X]:((quiet(X)&calm(X))<=>(~creative(X)&brave(X))))&
(?[X]:((~curious(X)|~brave(X))))&
((~quiet(lucy)|~humble(lucy)))&
(?[X]:((~old(X)&~rich(X))))&
(?[X]:((~rich(X)|~funny(X))))&
(?[X]:(~humble(X)))&
(?[X]:((creative(X)|funny(X)))) | patient(mary) | [
"p0",
"p1",
"p4",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6178123322337889120986772
% SZS output start Proof for 6178123322337889120986772
1. ! [X0] : ((happy(X0) <~> wise(X0)) => (~old(X0) & happy(X0))) [input p0]
2. ! [X0] : ((rich(X0) | happy(X0)) => ~patient(X0)) [input p1]
5. ! [X0] : ((brave(X0) <~> funny(X0)) <=> (patient(X0) | kind(X0))) [input p4]
6. ! [X0] : ((brave(X0) | kind(X0)) => (~brave(X0) & patient(X0))) [input p5]
8. ! [X0] : ((~funny(X0) <~> ~wise(X0)) => (~patient(X0) <~> brave(X0))) [input p7]
21. patient(mary) [input hypothesis]
22. ! [X0] : ((~old(X0) & happy(X0)) | (happy(X0) <=> wise(X0))) [ennf transformation 1]
23. ! [X0] : (~patient(X0) | (~rich(X0) & ~happy(X0))) [ennf transformation 2]
25. ! [X0] : ((~brave(X0) & patient(X0)) | (~brave(X0) & ~kind(X0))) [ennf transformation 6]
27. ! [X0] : ((~patient(X0) <~> brave(X0)) | (~funny(X0) <=> ~wise(X0))) [ennf transformation 8]
31. ! [X0] : ((~old(X0) & happy(X0)) | ((happy(X0) | ~wise(X0)) & (wise(X0) | ~happy(X0)))) [nnf transformation 22]
34. ! [X0] : ((((~funny(X0) | ~brave(X0)) & (funny(X0) | brave(X0))) | (~patient(X0) & ~kind(X0))) & ((patient(X0) | kind(X0)) | ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0))))) [nnf transformation 5]
35. ! [X0] : ((((~funny(X0) | ~brave(X0)) & (funny(X0) | brave(X0))) | (~patient(X0) & ~kind(X0))) & (patient(X0) | kind(X0) | ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0))))) [flattening 34]
36. ! [X0] : (((~brave(X0) | patient(X0)) & (brave(X0) | ~patient(X0))) | ((~funny(X0) | wise(X0)) & (~wise(X0) | funny(X0)))) [nnf transformation 27]
60. happy(X0) | happy(X0) | ~wise(X0) [cnf transformation 31]
63. ~patient(X0) | ~happy(X0) [cnf transformation 23]
76. ~patient(X0) | brave(X0) | funny(X0) [cnf transformation 35]
82. ~brave(X0) | ~brave(X0) [cnf transformation 25]
86. brave(X0) | ~patient(X0) | ~funny(X0) | wise(X0) [cnf transformation 36]
121. patient(mary) [cnf transformation 21]
124. ~brave(X0) [duplicate literal removal 82]
125. ~wise(X0) | happy(X0) [duplicate literal removal 60]
143. ~funny(X0) | ~patient(X0) | wise(X0) [subsumption resolution 86,124]
224. ~happy(mary) [resolution 63,121]
231. brave(mary) | funny(mary) [resolution 76,121]
232. funny(mary) [subsumption resolution 231,124]
249. ~patient(mary) | wise(mary) [resolution 143,232]
250. wise(mary) [subsumption resolution 249,121]
251. happy(mary) [resolution 250,125]
252. $false [subsumption resolution 251,224]
% SZS output end Proof for 6178123322337889120986772
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either calm or not strong then someone is calm or creative and vice versa. If fred is not rich then susan is both old and not wise and vice versa. Everyone who is both not creative and quiet is both not old and not tall. If mary is not curious or generous then someone is either not rich or patient. If susan is both strong and not curious then paul is not funny or funny. Everyone who is not curious is rich. If paul is either not creative or not strong then someone is old or not generous and vice versa. Everyone who is not generous or creative is either curious or not brave and vice versa. Everyone who is kind is curious or wise. If someone is either not creative or not patient then fred is generous or tall and vice versa. If someone is not quiet or curious then mary is both not curious and generous. Everyone who is not creative is both old and not patient and vice versa. Everyone who is either curious or calm is both rich and not rich. If mary is not creative or not quiet then someone is both not old and not generous and vice versa. Everyone who is either not kind or not patient is either humble or wise. Everyone who is either rich or not curious is not kind or not old and vice versa. Someone is not wise or not kind. Susan is both rich and strong. John is either quiet or not funny. Paul is both kind and rich. Someone is both not humble and not quiet. Paul is either curious or rich. John is either kind or not humble. Someone is not creative or rich. | Paul is creative. | neutral | (((calm(john)<~>~strong(john)))<=>(?[X]:((calm(X)|creative(X)))))&
((~rich(fred))<=>((old(susan)&~wise(susan))))&
(![X]:((~creative(X)&quiet(X))=>(~old(X)&~tall(X))))&
(((~curious(mary)|generous(mary)))=>(?[X]:((~rich(X)<~>patient(X)))))&
(((strong(susan)&~curious(susan)))=>((~funny(paul)|funny(paul))))&
(![X]:(~curious(X)=>rich(X)))&
(((~creative(paul)<~>~strong(paul)))<=>(?[X]:((old(X)|~generous(X)))))&
(![X]:((~generous(X)|creative(X))<=>(curious(X)<~>~brave(X))))&
(![X]:(kind(X)=>(curious(X)|wise(X))))&
((?[X]:((~creative(X)<~>~patient(X))))<=>((generous(fred)|tall(fred))))&
((?[X]:((~quiet(X)|curious(X))))=>((~curious(mary)&generous(mary))))&
(![X]:(~creative(X)<=>(old(X)&~patient(X))))&
(![X]:((curious(X)<~>calm(X))=>(rich(X)&~rich(X))))&
(((~creative(mary)|~quiet(mary)))<=>(?[X]:((~old(X)&~generous(X)))))&
(![X]:((~kind(X)<~>~patient(X))=>(humble(X)<~>wise(X))))&
(![X]:((rich(X)<~>~curious(X))<=>(~kind(X)|~old(X))))&
(?[X]:((~wise(X)|~kind(X))))&
((rich(susan)&strong(susan)))&
((quiet(john)<~>~funny(john)))&
((kind(paul)&rich(paul)))&
(?[X]:((~humble(X)&~quiet(X))))&
((curious(paul)<~>rich(paul)))&
((kind(john)<~>~humble(john)))&
(?[X]:((~creative(X)|rich(X)))) | creative(paul) | [] | null | 0 |
Everyone who is not brave or funny is not happy.
If susan is curious then john is both creative and rich and vice versa.
Everyone who is not rich is not patient or not kind.
Everyone who is both quiet and old is either not creative or wise.
Everyone who is both not curious and not kind is patient or not strong.
Everyone who is either creative or strong is either patient or not creative and vice versa.
If john is both kind and not creative then someone is curious or funny and vice versa.
If john is not quiet or brave then mary is kind.
Everyone who is both curious and tall is either not creative or not calm and vice versa.
If mary is not quiet then mary is creative or happy and vice versa.
Everyone who is funny is both strong and calm and vice versa.
Everyone who is either not strong or happy is both not brave and not creative.
Everyone who is not patient is not old or strong.
Everyone who is quiet or not happy is strong and vice versa.
Everyone who is not calm is old and vice versa.
Everyone who is not generous or not kind is not curious or not humble.
Lucy is either tall or wise.
Someone is wise.
Someone is either rich or tall.
Someone is creative.
Someone is both brave and quiet.
Someone is both rich and not strong.
Lucy is both not tall and curious.
Someone is not creative. | Lucy is not strong. | neutral | (![X]:((~brave(X)|funny(X))=>~happy(X)))&
((curious(susan))<=>((creative(john)&rich(john))))&
(![X]:(~rich(X)=>(~patient(X)|~kind(X))))&
(![X]:((quiet(X)&old(X))=>(~creative(X)<~>wise(X))))&
(![X]:((~curious(X)&~kind(X))=>(patient(X)|~strong(X))))&
(![X]:((creative(X)<~>strong(X))<=>(patient(X)<~>~creative(X))))&
(((kind(john)&~creative(john)))<=>(?[X]:((curious(X)|funny(X)))))&
(((~quiet(john)|brave(john)))=>(kind(mary)))&
(![X]:((curious(X)&tall(X))<=>(~creative(X)<~>~calm(X))))&
((~quiet(mary))<=>((creative(mary)|happy(mary))))&
(![X]:(funny(X)<=>(strong(X)&calm(X))))&
(![X]:((~strong(X)<~>happy(X))=>(~brave(X)&~creative(X))))&
(![X]:(~patient(X)=>(~old(X)|strong(X))))&
(![X]:((quiet(X)|~happy(X))<=>strong(X)))&
(![X]:(~calm(X)<=>old(X)))&
(![X]:((~generous(X)|~kind(X))=>(~curious(X)|~humble(X))))&
((tall(lucy)<~>wise(lucy)))&
(?[X]:(wise(X)))&
(?[X]:((rich(X)<~>tall(X))))&
(?[X]:(creative(X)))&
(?[X]:((brave(X)&quiet(X))))&
(?[X]:((rich(X)&~strong(X))))&
((~tall(lucy)&curious(lucy)))&
(?[X]:(~creative(X))) | ~strong(lucy) | [] | null | 0 |
Everyone who is either not funny or kind is either happy or curious and vice versa.
Everyone who is not old is not funny or not calm and vice versa.
Everyone who is either not quiet or not calm is either not humble or not rich and vice versa.
If someone is either not curious or not old then someone is not funny.
If someone is humble then someone is not calm and vice versa.
If someone is not quiet then someone is either not generous or rich and vice versa.
If john is both brave and kind then paul is patient or not curious.
If someone is not tall or not strong then john is humble and vice versa.
Everyone who is either patient or creative is not calm or not generous and vice versa.
If someone is either not calm or not creative then someone is either not quiet or brave and vice versa.
If someone is quiet or not old then john is both not creative and not humble.
If alice is not patient then alice is tall or not wise and vice versa.
If someone is humble then john is not humble.
Everyone who is strong is both calm and not funny and vice versa.
Everyone who is old is tall or curious.
Lucy is wise.
Fred is strong or not quiet.
Someone is not humble.
Someone is both not kind and tall.
Someone is either curious or rich.
Someone is not quiet or brave. | Fred is not rich. | neutral | (![X]:((~funny(X)<~>kind(X))<=>(happy(X)<~>curious(X))))&
(![X]:(~old(X)<=>(~funny(X)|~calm(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~humble(X)<~>~rich(X))))&
((?[X]:((~curious(X)<~>~old(X))))=>(?[X]:(~funny(X))))&
((?[X]:(humble(X)))<=>(?[X]:(~calm(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~generous(X)<~>rich(X)))))&
(((brave(john)&kind(john)))=>((patient(paul)|~curious(paul))))&
((?[X]:((~tall(X)|~strong(X))))<=>(humble(john)))&
(![X]:((patient(X)<~>creative(X))<=>(~calm(X)|~generous(X))))&
((?[X]:((~calm(X)<~>~creative(X))))<=>(?[X]:((~quiet(X)<~>brave(X)))))&
((?[X]:((quiet(X)|~old(X))))=>((~creative(john)&~humble(john))))&
((~patient(alice))<=>((tall(alice)|~wise(alice))))&
((?[X]:(humble(X)))=>(~humble(john)))&
(![X]:(strong(X)<=>(calm(X)&~funny(X))))&
(![X]:(old(X)=>(tall(X)|curious(X))))&
(wise(lucy))&
((strong(fred)|~quiet(fred)))&
(?[X]:(~humble(X)))&
(?[X]:((~kind(X)&tall(X))))&
(?[X]:((curious(X)<~>rich(X))))&
(?[X]:((~quiet(X)|brave(X)))) | ~rich(fred) | [] | null | 0 |
If someone is not old or creative then someone is either not rich or not humble.
Everyone who is not old or not brave is both not brave and not old.
If john is both calm and not strong then someone is both not humble and quiet.
Everyone who is either not kind or funny is not quiet or not old.
Everyone who is patient or funny is not strong.
Everyone who is either old or patient is both not rich and not happy.
If lucy is not old then mary is patient and vice versa.
If lucy is funny then alice is either not generous or calm.
If john is wise or not old then someone is both not humble and not generous.
Everyone who is calm or generous is old and vice versa.
Everyone who is patient or not rich is not humble and vice versa.
If someone is happy or not patient then someone is kind or not kind and vice versa.
Everyone who is calm or funny is not curious or funny and vice versa.
If mary is strong or not curious then someone is not generous and vice versa.
If john is both not quiet and not patient then someone is either not creative or wise.
If lucy is either old or not strong then susan is patient or not humble.
Someone is either not happy or old.
Someone is either rich or not rich.
Someone is not happy or not brave.
Someone is either not happy or creative.
Alice is happy or not patient.
Someone is not kind or generous.
Fred is both humble and quiet.
Someone is kind. | Alice is generous. | neutral | ((?[X]:((~old(X)|creative(X))))=>(?[X]:((~rich(X)<~>~humble(X)))))&
(![X]:((~old(X)|~brave(X))=>(~brave(X)&~old(X))))&
(((calm(john)&~strong(john)))=>(?[X]:((~humble(X)&quiet(X)))))&
(![X]:((~kind(X)<~>funny(X))=>(~quiet(X)|~old(X))))&
(![X]:((patient(X)|funny(X))=>~strong(X)))&
(![X]:((old(X)<~>patient(X))=>(~rich(X)&~happy(X))))&
((~old(lucy))<=>(patient(mary)))&
((funny(lucy))=>((~generous(alice)<~>calm(alice))))&
(((wise(john)|~old(john)))=>(?[X]:((~humble(X)&~generous(X)))))&
(![X]:((calm(X)|generous(X))<=>old(X)))&
(![X]:((patient(X)|~rich(X))<=>~humble(X)))&
((?[X]:((happy(X)|~patient(X))))<=>(?[X]:((kind(X)|~kind(X)))))&
(![X]:((calm(X)|funny(X))<=>(~curious(X)|funny(X))))&
(((strong(mary)|~curious(mary)))<=>(?[X]:(~generous(X))))&
(((~quiet(john)&~patient(john)))=>(?[X]:((~creative(X)<~>wise(X)))))&
(((old(lucy)<~>~strong(lucy)))=>((patient(susan)|~humble(susan))))&
(?[X]:((~happy(X)<~>old(X))))&
(?[X]:((rich(X)<~>~rich(X))))&
(?[X]:((~happy(X)|~brave(X))))&
(?[X]:((~happy(X)<~>creative(X))))&
((happy(alice)|~patient(alice)))&
(?[X]:((~kind(X)|generous(X))))&
((humble(fred)&quiet(fred)))&
(?[X]:(kind(X))) | generous(alice) | [] | null | 0 |
If fred is kind or brave then alice is either not wise or not patient. Everyone who is wise is not strong and vice versa. Everyone who is both creative and rich is both not tall and kind and vice versa. If john is calm then fred is strong. Everyone who is not quiet is both quiet and not wise and vice versa. Everyone who is either not kind or happy is either rich or happy. Everyone who is rich is not calm or strong. Everyone who is both wise and generous is not humble or not curious and vice versa. If paul is either tall or not quiet then someone is either not kind or wise. Everyone who is not old is not quiet and vice versa. Everyone who is both funny and not strong is either patient or tall. If someone is not tall then someone is tall or not calm. If someone is quiet or not calm then alice is not calm and vice versa. If susan is not curious or quiet then someone is either not happy or strong and vice versa. Everyone who is curious or happy is not funny or not brave and vice versa. Everyone who is both strong and patient is both not creative and funny and vice versa. Someone is both not patient and kind. Fred is rich or not old. Someone is kind or generous. John is curious or not strong. Paul is not happy. John is generous or tall. Susan is generous. | Paul is brave. | neutral | (((kind(fred)|brave(fred)))=>((~wise(alice)<~>~patient(alice))))&
(![X]:(wise(X)<=>~strong(X)))&
(![X]:((creative(X)&rich(X))<=>(~tall(X)&kind(X))))&
((calm(john))=>(strong(fred)))&
(![X]:(~quiet(X)<=>(quiet(X)&~wise(X))))&
(![X]:((~kind(X)<~>happy(X))=>(rich(X)<~>happy(X))))&
(![X]:(rich(X)=>(~calm(X)|strong(X))))&
(![X]:((wise(X)&generous(X))<=>(~humble(X)|~curious(X))))&
(((tall(paul)<~>~quiet(paul)))=>(?[X]:((~kind(X)<~>wise(X)))))&
(![X]:(~old(X)<=>~quiet(X)))&
(![X]:((funny(X)&~strong(X))=>(patient(X)<~>tall(X))))&
((?[X]:(~tall(X)))=>(?[X]:((tall(X)|~calm(X)))))&
((?[X]:((quiet(X)|~calm(X))))<=>(~calm(alice)))&
(((~curious(susan)|quiet(susan)))<=>(?[X]:((~happy(X)<~>strong(X)))))&
(![X]:((curious(X)|happy(X))<=>(~funny(X)|~brave(X))))&
(![X]:((strong(X)&patient(X))<=>(~creative(X)&funny(X))))&
(?[X]:((~patient(X)&kind(X))))&
((rich(fred)|~old(fred)))&
(?[X]:((kind(X)|generous(X))))&
((curious(john)|~strong(john)))&
(~happy(paul))&
((generous(john)|tall(john)))&
(generous(susan)) | brave(paul) | [] | null | 0 |
Everyone who is patient is both not curious and not rich and vice versa.
If someone is not happy or not calm then fred is brave or not patient and vice versa.
If someone is not old then lucy is both not quiet and not strong and vice versa.
If someone is either rich or not happy then paul is humble or not generous and vice versa.
If john is not creative or quiet then mary is either tall or creative and vice versa.
Everyone who is patient is either not kind or not strong and vice versa.
Everyone who is not wise is calm or not curious and vice versa.
If fred is wise then someone is funny and vice versa.
If someone is not humble then someone is not curious and vice versa.
If susan is either quiet or funny then someone is not kind and vice versa.
Everyone who is tall or generous is tall.
Everyone who is strong or funny is wise or humble and vice versa.
If susan is either not rich or wise then someone is either rich or not rich and vice versa.
Everyone who is curious or not humble is happy or not generous.
Everyone who is not wise or not creative is either curious or not strong.
Everyone who is both not wise and quiet is either rich or creative and vice versa.
Someone is not creative.
Susan is either old or not kind.
Someone is both not humble and kind.
Someone is both not humble and not rich.
Fred is kind.
Mary is creative.
Someone is both not patient and generous. | John is not kind. | neutral | (![X]:(patient(X)<=>(~curious(X)&~rich(X))))&
((?[X]:((~happy(X)|~calm(X))))<=>((brave(fred)|~patient(fred))))&
((?[X]:(~old(X)))<=>((~quiet(lucy)&~strong(lucy))))&
((?[X]:((rich(X)<~>~happy(X))))<=>((humble(paul)|~generous(paul))))&
(((~creative(john)|quiet(john)))<=>((tall(mary)<~>creative(mary))))&
(![X]:(patient(X)<=>(~kind(X)<~>~strong(X))))&
(![X]:(~wise(X)<=>(calm(X)|~curious(X))))&
((wise(fred))<=>(?[X]:(funny(X))))&
((?[X]:(~humble(X)))<=>(?[X]:(~curious(X))))&
(((quiet(susan)<~>funny(susan)))<=>(?[X]:(~kind(X))))&
(![X]:((tall(X)|generous(X))=>tall(X)))&
(![X]:((strong(X)|funny(X))<=>(wise(X)|humble(X))))&
(((~rich(susan)<~>wise(susan)))<=>(?[X]:((rich(X)<~>~rich(X)))))&
(![X]:((curious(X)|~humble(X))=>(happy(X)|~generous(X))))&
(![X]:((~wise(X)|~creative(X))=>(curious(X)<~>~strong(X))))&
(![X]:((~wise(X)&quiet(X))<=>(rich(X)<~>creative(X))))&
(?[X]:(~creative(X)))&
((old(susan)<~>~kind(susan)))&
(?[X]:((~humble(X)&kind(X))))&
(?[X]:((~humble(X)&~rich(X))))&
(kind(fred))&
(creative(mary))&
(?[X]:((~patient(X)&generous(X)))) | ~kind(john) | [] | null | 0 |
If someone is calm or tall then someone is humble or wise. Everyone who is kind or calm is not curious or not kind and vice versa. If mary is not tall or not wise then someone is both creative and not wise. If someone is both not generous and wise then someone is either tall or not patient and vice versa. Everyone who is kind or rich is both not strong and not rich and vice versa. Everyone who is both not brave and not happy is not creative or not strong and vice versa. If john is not strong or not quiet then paul is both not tall and patient. Everyone who is both not kind and not curious is either not happy or funny and vice versa. Everyone who is both not generous and not humble is both generous and not humble and vice versa. If susan is both not happy and rich then fred is calm or old and vice versa. If someone is funny then lucy is humble and vice versa. Everyone who is either not calm or not happy is creative and vice versa. If mary is both tall and not kind then someone is either not tall or quiet and vice versa. Everyone who is either not patient or not tall is either not happy or not kind and vice versa. If someone is calm then someone is not patient and vice versa. If someone is not rich then susan is not creative or tall and vice versa. John is both not tall and quiet. Lucy is either brave or not strong. Someone is humble. Susan is either not tall or not creative. Lucy is not rich or brave. Someone is either not kind or old. Someone is either old or not humble. | Susan is not strong. | entailment | ((?[X]:((calm(X)|tall(X))))=>(?[X]:((humble(X)|wise(X)))))&
(![X]:((kind(X)|calm(X))<=>(~curious(X)|~kind(X))))&
(((~tall(mary)|~wise(mary)))=>(?[X]:((creative(X)&~wise(X)))))&
((?[X]:((~generous(X)&wise(X))))<=>(?[X]:((tall(X)<~>~patient(X)))))&
(![X]:((kind(X)|rich(X))<=>(~strong(X)&~rich(X))))&
(![X]:((~brave(X)&~happy(X))<=>(~creative(X)|~strong(X))))&
(((~strong(john)|~quiet(john)))=>((~tall(paul)&patient(paul))))&
(![X]:((~kind(X)&~curious(X))<=>(~happy(X)<~>funny(X))))&
(![X]:((~generous(X)&~humble(X))<=>(generous(X)&~humble(X))))&
(((~happy(susan)&rich(susan)))<=>((calm(fred)|old(fred))))&
((?[X]:(funny(X)))<=>(humble(lucy)))&
(![X]:((~calm(X)<~>~happy(X))<=>creative(X)))&
(((tall(mary)&~kind(mary)))<=>(?[X]:((~tall(X)<~>quiet(X)))))&
(![X]:((~patient(X)<~>~tall(X))<=>(~happy(X)<~>~kind(X))))&
((?[X]:(calm(X)))<=>(?[X]:(~patient(X))))&
((?[X]:(~rich(X)))<=>((~creative(susan)|tall(susan))))&
((~tall(john)&quiet(john)))&
((brave(lucy)<~>~strong(lucy)))&
(?[X]:(humble(X)))&
((~tall(susan)<~>~creative(susan)))&
((~rich(lucy)|brave(lucy)))&
(?[X]:((~kind(X)<~>old(X))))&
(?[X]:((old(X)<~>~humble(X)))) | ~strong(susan) | [
"p1",
"p4",
"p5",
"p11",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2888550470025290081293299
% SZS output start Proof for 2888550470025290081293299
2. ! [X0] : ((calm(X0) | kind(X0)) <=> (~kind(X0) | ~curious(X0))) [input p1]
5. ! [X0] : ((rich(X0) | kind(X0)) <=> (~rich(X0) & ~strong(X0))) [input p4]
6. ! [X0] : ((~happy(X0) & ~brave(X0)) <=> (~strong(X0) | ~creative(X0))) [input p5]
12. ! [X0] : ((~calm(X0) <~> ~happy(X0)) <=> creative(X0)) [input p11]
16. ? [X0] : ~rich(X0) <=> (tall(susan) | ~creative(susan)) [input p15]
20. ~tall(susan) <~> ~creative(susan) [input p19]
24. strong(susan) [input hypothesis]
34. ! [X0] : (((calm(X0) | kind(X0)) | (kind(X0) & curious(X0))) & ((~kind(X0) | ~curious(X0)) | (~calm(X0) & ~kind(X0)))) [nnf transformation 2]
35. ! [X0] : ((calm(X0) | kind(X0) | (kind(X0) & curious(X0))) & (~kind(X0) | ~curious(X0) | (~calm(X0) & ~kind(X0)))) [flattening 34]
43. ! [X0] : (((rich(X0) | kind(X0)) | (rich(X0) | strong(X0))) & ((~rich(X0) & ~strong(X0)) | (~rich(X0) & ~kind(X0)))) [nnf transformation 5]
44. ! [X0] : ((rich(X0) | kind(X0) | rich(X0) | strong(X0)) & ((~rich(X0) & ~strong(X0)) | (~rich(X0) & ~kind(X0)))) [flattening 43]
45. ! [X0] : (((~happy(X0) & ~brave(X0)) | (strong(X0) & creative(X0))) & ((~strong(X0) | ~creative(X0)) | (happy(X0) | brave(X0)))) [nnf transformation 6]
46. ! [X0] : (((~happy(X0) & ~brave(X0)) | (strong(X0) & creative(X0))) & (~strong(X0) | ~creative(X0) | happy(X0) | brave(X0))) [flattening 45]
57. ! [X0] : ((((happy(X0) | calm(X0)) & (~happy(X0) | ~calm(X0))) | ~creative(X0)) & (creative(X0) | ((~calm(X0) | happy(X0)) & (~happy(X0) | calm(X0))))) [nnf transformation 12]
69. (? [X0] : ~rich(X0) | (~tall(susan) & creative(susan))) & ((tall(susan) | ~creative(susan)) | ! [X0] : rich(X0)) [nnf transformation 16]
70. (? [X0] : ~rich(X0) | (~tall(susan) & creative(susan))) & (tall(susan) | ~creative(susan) | ! [X0] : rich(X0)) [flattening 69]
71. (? [X0] : ~rich(X0) | (~tall(susan) & creative(susan))) & (tall(susan) | ~creative(susan) | ! [X1] : rich(X1)) [rectify 70]
72. ? [X0] : ~rich(X0) => ~rich(sK8) [choice axiom]
73. (~rich(sK8) | (~tall(susan) & creative(susan))) & (tall(susan) | ~creative(susan) | ! [X1] : rich(X1)) [skolemisation 71,72]
77. (creative(susan) | tall(susan)) & (~creative(susan) | ~tall(susan)) [nnf transformation 20]
89. calm(X0) | kind(X0) | kind(X0) [cnf transformation 35]
100. ~strong(X0) | ~kind(X0) [cnf transformation 44]
103. ~rich(X0) | ~rich(X0) [cnf transformation 44]
108. ~happy(X0) | creative(X0) [cnf transformation 46]
132. creative(X0) | ~calm(X0) | happy(X0) [cnf transformation 57]
133. ~happy(X0) | ~calm(X0) | ~creative(X0) [cnf transformation 57]
151. tall(susan) | ~creative(susan) | rich(X1) [cnf transformation 73]
159. ~creative(susan) | ~tall(susan) [cnf transformation 77]
166. strong(susan) [cnf transformation 24]
169. ~rich(X0) [duplicate literal removal 103]
172. kind(X0) | calm(X0) [duplicate literal removal 89]
264. ~happy(X0) | ~calm(X0) [subsumption resolution 133,108]
265. ~calm(X0) | creative(X0) [subsumption resolution 132,264]
303. tall(susan) | ~creative(susan) [subsumption resolution 151,169]
305. 28 <=> creative(susan) [avatar definition]
307. ~creative(susan) <- (~28) [avatar component clause 305]
309. 29 <=> tall(susan) [avatar definition]
312. ~28 | 29 [avatar split clause 303,309,305]
324. ~29 | ~28 [avatar split clause 159,305,309]
340. ~kind(susan) [resolution 100,166]
343. calm(susan) [resolution 172,340]
348. creative(susan) [resolution 343,265]
349. $false <- (~28) [subsumption resolution 348,307]
350. 28 [avatar contradiction clause 349]
351. $false [avatar sat refutation 312,324,350]
% SZS output end Proof for 2888550470025290081293299
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise or not kind then someone is both quiet and calm.
If fred is not generous or quiet then someone is either not strong or calm and vice versa.
If someone is not generous then someone is both not curious and calm and vice versa.
Everyone who is generous is not curious and vice versa.
Everyone who is not old or not rich is old or not generous.
Everyone who is not calm or curious is calm.
If someone is creative then someone is either calm or not generous and vice versa.
Everyone who is tall or not generous is not calm or brave.
Everyone who is both curious and kind is both tall and not wise and vice versa.
If mary is not curious or brave then alice is either curious or creative and vice versa.
Everyone who is either quiet or not funny is both not patient and strong and vice versa.
Everyone who is strong is either not quiet or not curious.
Everyone who is not patient or not tall is patient and vice versa.
If someone is not strong then someone is both patient and not calm and vice versa.
Everyone who is either funny or quiet is both not rich and wise and vice versa.
If someone is both wise and not curious then someone is patient.
Someone is not rich.
Alice is funny or not creative.
Someone is not generous.
Paul is both strong and old.
Lucy is quiet. | Lucy is not tall. | entailment | ((?[X]:((~wise(X)|~kind(X))))=>(?[X]:((quiet(X)&calm(X)))))&
(((~generous(fred)|quiet(fred)))<=>(?[X]:((~strong(X)<~>calm(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((~curious(X)&calm(X)))))&
(![X]:(generous(X)<=>~curious(X)))&
(![X]:((~old(X)|~rich(X))=>(old(X)|~generous(X))))&
(![X]:((~calm(X)|curious(X))=>calm(X)))&
((?[X]:(creative(X)))<=>(?[X]:((calm(X)<~>~generous(X)))))&
(![X]:((tall(X)|~generous(X))=>(~calm(X)|brave(X))))&
(![X]:((curious(X)&kind(X))<=>(tall(X)&~wise(X))))&
(((~curious(mary)|brave(mary)))<=>((curious(alice)<~>creative(alice))))&
(![X]:((quiet(X)<~>~funny(X))<=>(~patient(X)&strong(X))))&
(![X]:(strong(X)=>(~quiet(X)<~>~curious(X))))&
(![X]:((~patient(X)|~tall(X))<=>patient(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((patient(X)&~calm(X)))))&
(![X]:((funny(X)<~>quiet(X))<=>(~rich(X)&wise(X))))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:(patient(X))))&
(?[X]:(~rich(X)))&
((funny(alice)|~creative(alice)))&
(?[X]:(~generous(X)))&
((strong(paul)&old(paul)))&
(quiet(lucy)) | ~tall(lucy) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2288920560552966088622807
% SZS output start Proof for 2288920560552966088622807
13. ! [X0] : ((~tall(X0) | ~patient(X0)) <=> patient(X0)) [input p12]
22. tall(lucy) [input hypothesis]
62. ! [X0] : (((~tall(X0) | ~patient(X0)) | ~patient(X0)) & (patient(X0) | (tall(X0) & patient(X0)))) [nnf transformation 13]
63. ! [X0] : ((~tall(X0) | ~patient(X0) | ~patient(X0)) & (patient(X0) | (tall(X0) & patient(X0)))) [flattening 62]
119. patient(X0) | patient(X0) [cnf transformation 63]
121. ~tall(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 63]
137. tall(lucy) [cnf transformation 22]
138. patient(X0) [duplicate literal removal 119]
139. ~patient(X0) | ~tall(X0) [duplicate literal removal 121]
275. ~tall(X1) [resolution 139,138]
276. $false [resolution 275,137]
% SZS output end Proof for 2288920560552966088622807
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is patient then someone is either not funny or old.
Everyone who is happy or tall is either not curious or creative.
Everyone who is both tall and creative is not humble.
Everyone who is old or not wise is either not funny or patient.
If someone is creative or not curious then someone is both old and wise and vice versa.
If paul is rich then john is both not wise and old.
Everyone who is either strong or not tall is strong.
If paul is both not rich and not humble then mary is both not funny and not curious.
Everyone who is both creative and tall is wise and vice versa.
If someone is either not tall or calm then mary is quiet and vice versa.
If someone is either not strong or brave then fred is either not humble or not brave and vice versa.
Everyone who is not quiet or old is happy or calm.
If susan is not patient or generous then someone is either kind or not curious.
Everyone who is both calm and humble is not funny or wise and vice versa.
Everyone who is either creative or kind is curious and vice versa.
Everyone who is both old and not humble is either brave or not wise.
Someone is both patient and calm.
Paul is both funny and not old.
Someone is curious or not calm.
Someone is either curious or not strong.
Someone is not tall or patient.
Someone is either funny or not wise. | Fred is kind. | entailment | ((?[X]:(patient(X)))=>(?[X]:((~funny(X)<~>old(X)))))&
(![X]:((happy(X)|tall(X))=>(~curious(X)<~>creative(X))))&
(![X]:((tall(X)&creative(X))=>~humble(X)))&
(![X]:((old(X)|~wise(X))=>(~funny(X)<~>patient(X))))&
((?[X]:((creative(X)|~curious(X))))<=>(?[X]:((old(X)&wise(X)))))&
((rich(paul))=>((~wise(john)&old(john))))&
(![X]:((strong(X)<~>~tall(X))=>strong(X)))&
(((~rich(paul)&~humble(paul)))=>((~funny(mary)&~curious(mary))))&
(![X]:((creative(X)&tall(X))<=>wise(X)))&
((?[X]:((~tall(X)<~>calm(X))))<=>(quiet(mary)))&
((?[X]:((~strong(X)<~>brave(X))))<=>((~humble(fred)<~>~brave(fred))))&
(![X]:((~quiet(X)|old(X))=>(happy(X)|calm(X))))&
(((~patient(susan)|generous(susan)))=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((calm(X)&humble(X))<=>(~funny(X)|wise(X))))&
(![X]:((creative(X)<~>kind(X))<=>curious(X)))&
(![X]:((old(X)&~humble(X))=>(brave(X)<~>~wise(X))))&
(?[X]:((patient(X)&calm(X))))&
((funny(paul)&~old(paul)))&
(?[X]:((curious(X)|~calm(X))))&
(?[X]:((curious(X)<~>~strong(X))))&
(?[X]:((~tall(X)|patient(X))))&
(?[X]:((funny(X)<~>~wise(X)))) | kind(fred) | [
"p2",
"p4",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5622843438739736215885628
% SZS output start Proof for 5622843438739736215885628
3. ! [X0] : ((creative(X0) & tall(X0)) => ~humble(X0)) [input p2]
5. ? [X0] : (~curious(X0) | creative(X0)) <=> ? [X0] : (wise(X0) & old(X0)) [input p4]
9. ! [X0] : ((tall(X0) & creative(X0)) <=> wise(X0)) [input p8]
14. ! [X0] : ((humble(X0) & calm(X0)) <=> (wise(X0) | ~funny(X0))) [input p13]
15. ! [X0] : ((creative(X0) <~> kind(X0)) <=> curious(X0)) [input p14]
23. ~kind(fred) [input hypothesis]
25. ? [X0] : (~curious(X0) | creative(X0)) <=> ? [X1] : (wise(X1) & old(X1)) [rectify 5]
29. ! [X0] : (~humble(X0) | (~creative(X0) | ~tall(X0))) [ennf transformation 3]
30. ! [X0] : (~humble(X0) | ~creative(X0) | ~tall(X0)) [flattening 29]
47. (? [X0] : (~curious(X0) | creative(X0)) | ! [X1] : (~wise(X1) | ~old(X1))) & (? [X1] : (wise(X1) & old(X1)) | ! [X0] : (curious(X0) & ~creative(X0))) [nnf transformation 25]
48. (? [X0] : (~curious(X0) | creative(X0)) | ! [X1] : (~wise(X1) | ~old(X1))) & (? [X2] : (wise(X2) & old(X2)) | ! [X3] : (curious(X3) & ~creative(X3))) [rectify 47]
49. ? [X0] : (~curious(X0) | creative(X0)) => (~curious(sK1) | creative(sK1)) [choice axiom]
50. ? [X2] : (wise(X2) & old(X2)) => (wise(sK2) & old(sK2)) [choice axiom]
51. ((~curious(sK1) | creative(sK1)) | ! [X1] : (~wise(X1) | ~old(X1))) & ((wise(sK2) & old(sK2)) | ! [X3] : (curious(X3) & ~creative(X3))) [skolemisation 48,50,49]
53. ! [X0] : (((tall(X0) & creative(X0)) | ~wise(X0)) & (wise(X0) | (~tall(X0) | ~creative(X0)))) [nnf transformation 9]
54. ! [X0] : (((tall(X0) & creative(X0)) | ~wise(X0)) & (wise(X0) | ~tall(X0) | ~creative(X0))) [flattening 53]
66. ! [X0] : (((humble(X0) & calm(X0)) | (~wise(X0) & funny(X0))) & ((wise(X0) | ~funny(X0)) | (~humble(X0) | ~calm(X0)))) [nnf transformation 14]
67. ! [X0] : (((humble(X0) & calm(X0)) | (~wise(X0) & funny(X0))) & (wise(X0) | ~funny(X0) | ~humble(X0) | ~calm(X0))) [flattening 66]
68. ! [X0] : ((((~kind(X0) | ~creative(X0)) & (kind(X0) | creative(X0))) | ~curious(X0)) & (curious(X0) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0))))) [nnf transformation 15]
88. ~humble(X0) | ~creative(X0) | ~tall(X0) [cnf transformation 30]
95. wise(sK2) | ~creative(X3) [cnf transformation 51]
96. wise(sK2) | curious(X3) [cnf transformation 51]
105. ~wise(X0) | creative(X0) [cnf transformation 54]
106. ~wise(X0) | tall(X0) [cnf transformation 54]
127. ~wise(X0) | humble(X0) [cnf transformation 67]
130. ~curious(X0) | creative(X0) | kind(X0) [cnf transformation 68]
144. ~kind(fred) [cnf transformation 23]
172. 7 <=> ! [X3] : curious(X3) [avatar definition]
173. curious(X3) <- (7) [avatar component clause 172]
175. 8 <=> wise(sK2) [avatar definition]
177. wise(sK2) <- (8) [avatar component clause 175]
178. 7 | 8 [avatar split clause 96,175,172]
180. 9 <=> ! [X3] : ~creative(X3) [avatar definition]
181. ~creative(X3) <- (9) [avatar component clause 180]
182. 9 | 8 [avatar split clause 95,175,180]
454. creative(X0) | kind(X0) <- (7) [resolution 130,173]
457. kind(X0) <- (7, 9) [subsumption resolution 454,181]
497. $false <- (7, 9) [resolution 457,144]
502. ~7 | ~9 [avatar contradiction clause 497]
553. humble(sK2) <- (8) [resolution 177,127]
555. tall(sK2) <- (8) [resolution 177,106]
556. creative(sK2) <- (8) [resolution 177,105]
568. ~creative(sK2) | ~tall(sK2) <- (8) [resolution 553,88]
569. ~tall(sK2) <- (8) [subsumption resolution 568,556]
570. $false <- (8) [subsumption resolution 569,555]
571. ~8 [avatar contradiction clause 570]
572. $false [avatar sat refutation 178,182,502,571]
% SZS output end Proof for 5622843438739736215885628
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is funny or not old then alice is not funny and vice versa. Everyone who is both quiet and happy is both not calm and not brave and vice versa. Everyone who is generous is either not quiet or not kind. Everyone who is tall or not happy is either not patient or not brave. Everyone who is either not brave or not wise is not patient or not funny and vice versa. Everyone who is either patient or not happy is calm or not calm and vice versa. Everyone who is both rich and not happy is generous or not calm and vice versa. If someone is creative then paul is curious and vice versa. If someone is both quiet and not happy then paul is not creative. Everyone who is both tall and not kind is not quiet and vice versa. If susan is strong then someone is either quiet or generous and vice versa. If someone is either calm or not creative then someone is not old and vice versa. If alice is funny then paul is not rich and vice versa. Everyone who is not rich or not creative is either happy or strong and vice versa. If someone is not quiet or not patient then mary is both strong and not generous and vice versa. Everyone who is both calm and not strong is either not patient or not creative. Someone is either tall or patient. Fred is either not creative or not wise. Susan is both not quiet and patient. Someone is both tall and funny. Someone is not humble. Mary is either not funny or not generous. Someone is not quiet or not old. | Mary is wise. | contradiction | (((funny(john)|~old(john)))<=>(~funny(alice)))&
(![X]:((quiet(X)&happy(X))<=>(~calm(X)&~brave(X))))&
(![X]:(generous(X)=>(~quiet(X)<~>~kind(X))))&
(![X]:((tall(X)|~happy(X))=>(~patient(X)<~>~brave(X))))&
(![X]:((~brave(X)<~>~wise(X))<=>(~patient(X)|~funny(X))))&
(![X]:((patient(X)<~>~happy(X))<=>(calm(X)|~calm(X))))&
(![X]:((rich(X)&~happy(X))<=>(generous(X)|~calm(X))))&
((?[X]:(creative(X)))<=>(curious(paul)))&
((?[X]:((quiet(X)&~happy(X))))=>(~creative(paul)))&
(![X]:((tall(X)&~kind(X))<=>~quiet(X)))&
((strong(susan))<=>(?[X]:((quiet(X)<~>generous(X)))))&
((?[X]:((calm(X)<~>~creative(X))))<=>(?[X]:(~old(X))))&
((funny(alice))<=>(~rich(paul)))&
(![X]:((~rich(X)|~creative(X))<=>(happy(X)<~>strong(X))))&
((?[X]:((~quiet(X)|~patient(X))))<=>((strong(mary)&~generous(mary))))&
(![X]:((calm(X)&~strong(X))=>(~patient(X)<~>~creative(X))))&
(?[X]:((tall(X)<~>patient(X))))&
((~creative(fred)<~>~wise(fred)))&
((~quiet(susan)&patient(susan)))&
(?[X]:((tall(X)&funny(X))))&
(?[X]:(~humble(X)))&
((~funny(mary)<~>~generous(mary)))&
(?[X]:((~quiet(X)|~old(X)))) | wise(mary) | [
"p1",
"p3",
"p4",
"p5",
"p6",
"p9",
"p14",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4011227875023722069255583
% SZS output start Proof for 4011227875023722069255583
2. ! [X0] : ((happy(X0) & quiet(X0)) <=> (~brave(X0) & ~calm(X0))) [input p1]
4. ! [X0] : ((~happy(X0) | tall(X0)) => (~patient(X0) <~> ~brave(X0))) [input p3]
5. ! [X0] : ((~brave(X0) <~> ~wise(X0)) <=> (~funny(X0) | ~patient(X0))) [input p4]
6. ! [X0] : ((patient(X0) <~> ~happy(X0)) <=> (~calm(X0) | calm(X0))) [input p5]
7. ! [X0] : ((~happy(X0) & rich(X0)) <=> (~calm(X0) | generous(X0))) [input p6]
10. ! [X0] : ((~kind(X0) & tall(X0)) <=> ~quiet(X0)) [input p9]
15. ? [X0] : (~patient(X0) | ~quiet(X0)) <=> (~generous(mary) & strong(mary)) [input p14]
19. patient(susan) & ~quiet(susan) [input p18]
22. ~funny(mary) <~> ~generous(mary) [input p21]
24. wise(mary) [input hypothesis]
28. ! [X0] : ((~patient(X0) <~> ~brave(X0)) | (happy(X0) & ~tall(X0))) [ennf transformation 4]
34. ! [X0] : (((happy(X0) & quiet(X0)) | (brave(X0) | calm(X0))) & ((~brave(X0) & ~calm(X0)) | (~happy(X0) | ~quiet(X0)))) [nnf transformation 2]
35. ! [X0] : (((happy(X0) & quiet(X0)) | brave(X0) | calm(X0)) & ((~brave(X0) & ~calm(X0)) | ~happy(X0) | ~quiet(X0))) [flattening 34]
37. ! [X0] : (((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | (happy(X0) & ~tall(X0))) [nnf transformation 28]
38. ! [X0] : ((((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | (funny(X0) & patient(X0))) & ((~funny(X0) | ~patient(X0)) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0))))) [nnf transformation 5]
39. ! [X0] : ((((wise(X0) | brave(X0)) & (~wise(X0) | ~brave(X0))) | (funny(X0) & patient(X0))) & (~funny(X0) | ~patient(X0) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0))))) [flattening 38]
40. ! [X0] : ((((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | (calm(X0) & ~calm(X0))) & ((~calm(X0) | calm(X0)) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0))))) [nnf transformation 6]
41. ! [X0] : ((((happy(X0) | ~patient(X0)) & (~happy(X0) | patient(X0))) | (calm(X0) & ~calm(X0))) & (~calm(X0) | calm(X0) | ((patient(X0) | happy(X0)) & (~happy(X0) | ~patient(X0))))) [flattening 40]
42. ! [X0] : (((~happy(X0) & rich(X0)) | (calm(X0) & ~generous(X0))) & ((~calm(X0) | generous(X0)) | (happy(X0) | ~rich(X0)))) [nnf transformation 7]
43. ! [X0] : (((~happy(X0) & rich(X0)) | (calm(X0) & ~generous(X0))) & (~calm(X0) | generous(X0) | happy(X0) | ~rich(X0))) [flattening 42]
48. ! [X0] : (((~kind(X0) & tall(X0)) | quiet(X0)) & (~quiet(X0) | (kind(X0) | ~tall(X0)))) [nnf transformation 10]
49. ! [X0] : (((~kind(X0) & tall(X0)) | quiet(X0)) & (~quiet(X0) | kind(X0) | ~tall(X0))) [flattening 48]
62. (? [X0] : (~patient(X0) | ~quiet(X0)) | (generous(mary) | ~strong(mary))) & ((~generous(mary) & strong(mary)) | ! [X0] : (patient(X0) & quiet(X0))) [nnf transformation 15]
63. (? [X0] : (~patient(X0) | ~quiet(X0)) | generous(mary) | ~strong(mary)) & ((~generous(mary) & strong(mary)) | ! [X0] : (patient(X0) & quiet(X0))) [flattening 62]
64. (? [X0] : (~patient(X0) | ~quiet(X0)) | generous(mary) | ~strong(mary)) & ((~generous(mary) & strong(mary)) | ! [X1] : (patient(X1) & quiet(X1))) [rectify 63]
65. ? [X0] : (~patient(X0) | ~quiet(X0)) => (~patient(sK4) | ~quiet(sK4)) [choice axiom]
66. ((~patient(sK4) | ~quiet(sK4)) | generous(mary) | ~strong(mary)) & ((~generous(mary) & strong(mary)) | ! [X1] : (patient(X1) & quiet(X1))) [skolemisation 64,65]
74. (generous(mary) | funny(mary)) & (~generous(mary) | ~funny(mary)) [nnf transformation 22]
80. ~calm(X0) | ~happy(X0) | ~quiet(X0) [cnf transformation 35]
81. ~brave(X0) | ~happy(X0) | ~quiet(X0) [cnf transformation 35]
83. brave(X0) | happy(X0) | calm(X0) [cnf transformation 35]
86. ~patient(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 37]
88. ~tall(X0) | patient(X0) | brave(X0) [cnf transformation 37]
89. patient(X0) | brave(X0) | happy(X0) [cnf transformation 37]
90. ~wise(X0) | ~patient(X0) | ~funny(X0) | brave(X0) [cnf transformation 39]
92. ~wise(X0) | ~brave(X0) | patient(X0) [cnf transformation 39]
100. happy(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 41]
101. ~patient(X0) | happy(X0) | calm(X0) [cnf transformation 41]
106. ~happy(X0) | calm(X0) [cnf transformation 43]
111. tall(X0) | quiet(X0) [cnf transformation 49]
131. ~generous(mary) | quiet(X1) [cnf transformation 66]
140. ~quiet(susan) [cnf transformation 19]
145. generous(mary) | funny(mary) [cnf transformation 74]
147. wise(mary) [cnf transformation 24]
163. ~patient(X0) | happy(X0) [subsumption resolution 100,101]
244. 22 <=> generous(mary) [avatar definition]
261. 26 <=> ! [X1] : quiet(X1) [avatar definition]
262. quiet(X1) <- (26) [avatar component clause 261]
263. 26 | ~22 [avatar split clause 131,244,261]
287. 31 <=> funny(mary) [avatar definition]
289. funny(mary) <- (31) [avatar component clause 287]
290. 31 | 22 [avatar split clause 145,244,287]
302. $false <- (26) [resolution 262,140]
303. ~26 [avatar contradiction clause 302]
326. patient(X0) | brave(X0) | quiet(X0) [resolution 88,111]
345. brave(X2) | happy(X2) | happy(X2) [resolution 89,163]
346. brave(X2) | happy(X2) [duplicate literal removal 345]
358. ~brave(mary) | patient(mary) [resolution 92,147]
360. 40 <=> patient(mary) [avatar definition]
361. ~patient(mary) <- (~40) [avatar component clause 360]
362. patient(mary) <- (40) [avatar component clause 360]
364. 41 <=> brave(mary) [avatar definition]
365. brave(mary) <- (41) [avatar component clause 364]
366. ~brave(mary) <- (~41) [avatar component clause 364]
367. 40 | ~41 [avatar split clause 358,364,360]
379. happy(mary) | calm(mary) <- (~41) [resolution 366,83]
381. calm(mary) <- (~41) [subsumption resolution 379,106]
413. ~happy(mary) | ~quiet(mary) <- (~41) [resolution 381,80]
415. 47 <=> quiet(mary) [avatar definition]
417. ~quiet(mary) <- (~47) [avatar component clause 415]
419. 48 <=> happy(mary) [avatar definition]
420. happy(mary) <- (48) [avatar component clause 419]
421. ~happy(mary) <- (~48) [avatar component clause 419]
422. ~47 | ~48 | 41 [avatar split clause 413,364,419,415]
454. happy(mary) <- (~41) [resolution 346,366]
456. $false <- (~41, ~48) [subsumption resolution 454,421]
457. 41 | 48 [avatar contradiction clause 456]
461. ~patient(mary) | ~funny(mary) | brave(mary) [resolution 90,147]
469. happy(mary) <- (40) [resolution 362,163]
475. $false <- (40, ~48) [subsumption resolution 469,421]
476. ~40 | 48 [avatar contradiction clause 475]
477. ~patient(mary) | brave(mary) <- (31) [subsumption resolution 461,289]
478. 41 | ~40 | ~31 [avatar split clause 477,287,360,364]
564. brave(mary) | quiet(mary) <- (~40) [resolution 326,361]
567. quiet(mary) <- (~40, ~41) [subsumption resolution 564,366]
568. $false <- (~40, ~41, ~47) [subsumption resolution 567,417]
569. 40 | 41 | 47 [avatar contradiction clause 568]
573. ~brave(mary) | ~tall(mary) <- (40) [resolution 362,86]
575. ~tall(mary) <- (40, 41) [subsumption resolution 573,365]
576. ~happy(mary) | ~quiet(mary) <- (41) [resolution 365,81]
577. quiet(mary) <- (40, 41) [resolution 575,111]
580. 47 | ~40 | ~41 [avatar split clause 577,364,360,415]
581. ~quiet(mary) <- (41, 48) [subsumption resolution 576,420]
582. ~47 | ~41 | ~48 [avatar split clause 581,419,364,415]
583. $false [avatar sat refutation 263,290,303,367,422,457,476,478,569,580,582]
% SZS output end Proof for 4011227875023722069255583
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then someone is strong or quiet and vice versa. Everyone who is not rich or not strong is happy. If paul is patient then john is kind and vice versa. Everyone who is either not humble or rich is not old or not humble and vice versa. If someone is either kind or not kind then alice is curious or not happy and vice versa. Everyone who is either not humble or brave is either rich or strong. If alice is rich then someone is curious. If someone is either funny or not rich then paul is either humble or brave. If someone is either old or not brave then someone is both not patient and not wise and vice versa. If paul is either not patient or not strong then someone is kind and vice versa. Everyone who is either happy or quiet is calm and vice versa. If someone is either strong or generous then someone is both not strong and not curious. Everyone who is not calm is either not creative or rich and vice versa. If someone is not old or not rich then someone is both not tall and not patient. Everyone who is not humble is either not strong or not old. If someone is not tall then lucy is both old and creative and vice versa. Someone is both kind and not rich. Paul is not happy or rich. Someone is funny. Someone is either not old or not rich. Someone is both quiet and brave. Someone is old. Someone is both not funny and strong. Susan is not happy or happy. | Lucy is rich. | contradiction | ((?[X]:(~old(X)))<=>(?[X]:((strong(X)|quiet(X)))))&
(![X]:((~rich(X)|~strong(X))=>happy(X)))&
((patient(paul))<=>(kind(john)))&
(![X]:((~humble(X)<~>rich(X))<=>(~old(X)|~humble(X))))&
((?[X]:((kind(X)<~>~kind(X))))<=>((curious(alice)|~happy(alice))))&
(![X]:((~humble(X)<~>brave(X))=>(rich(X)<~>strong(X))))&
((rich(alice))=>(?[X]:(curious(X))))&
((?[X]:((funny(X)<~>~rich(X))))=>((humble(paul)<~>brave(paul))))&
((?[X]:((old(X)<~>~brave(X))))<=>(?[X]:((~patient(X)&~wise(X)))))&
(((~patient(paul)<~>~strong(paul)))<=>(?[X]:(kind(X))))&
(![X]:((happy(X)<~>quiet(X))<=>calm(X)))&
((?[X]:((strong(X)<~>generous(X))))=>(?[X]:((~strong(X)&~curious(X)))))&
(![X]:(~calm(X)<=>(~creative(X)<~>rich(X))))&
((?[X]:((~old(X)|~rich(X))))=>(?[X]:((~tall(X)&~patient(X)))))&
(![X]:(~humble(X)=>(~strong(X)<~>~old(X))))&
((?[X]:(~tall(X)))<=>((old(lucy)&creative(lucy))))&
(?[X]:((kind(X)&~rich(X))))&
((~happy(paul)|rich(paul)))&
(?[X]:(funny(X)))&
(?[X]:((~old(X)<~>~rich(X))))&
(?[X]:((quiet(X)&brave(X))))&
(?[X]:(old(X)))&
(?[X]:((~funny(X)&strong(X))))&
((~happy(susan)|happy(susan))) | rich(lucy) | [
"p0",
"p3",
"p13",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6171742876528218114444332
% SZS output start Proof for 6171742876528218114444332
1. ? [X0] : ~old(X0) <=> ? [X0] : (quiet(X0) | strong(X0)) [input p0]
4. ! [X0] : ((~humble(X0) <~> rich(X0)) <=> (~humble(X0) | ~old(X0))) [input p3]
14. ? [X0] : (~rich(X0) | ~old(X0)) => ? [X0] : (~patient(X0) & ~tall(X0)) [input p13]
16. ? [X0] : ~tall(X0) <=> (creative(lucy) & old(lucy)) [input p15]
21. ? [X0] : (brave(X0) & quiet(X0)) [input p20]
25. rich(lucy) [input hypothesis]
26. ? [X0] : ~old(X0) <=> ? [X1] : (quiet(X1) | strong(X1)) [rectify 1]
29. ? [X0] : (~rich(X0) | ~old(X0)) => ? [X1] : (~patient(X1) & ~tall(X1)) [rectify 14]
35. ? [X1] : (~patient(X1) & ~tall(X1)) | ! [X0] : (rich(X0) & old(X0)) [ennf transformation 29]
37. (? [X0] : ~old(X0) | ! [X1] : (~quiet(X1) & ~strong(X1))) & (? [X1] : (quiet(X1) | strong(X1)) | ! [X0] : old(X0)) [nnf transformation 26]
38. (? [X0] : ~old(X0) | ! [X1] : (~quiet(X1) & ~strong(X1))) & (? [X2] : (quiet(X2) | strong(X2)) | ! [X3] : old(X3)) [rectify 37]
39. ? [X0] : ~old(X0) => ~old(sK0) [choice axiom]
40. ? [X2] : (quiet(X2) | strong(X2)) => (quiet(sK1) | strong(sK1)) [choice axiom]
41. (~old(sK0) | ! [X1] : (~quiet(X1) & ~strong(X1))) & ((quiet(sK1) | strong(sK1)) | ! [X3] : old(X3)) [skolemisation 38,40,39]
43. ! [X0] : ((((~rich(X0) | humble(X0)) & (rich(X0) | ~humble(X0))) | (humble(X0) & old(X0))) & ((~humble(X0) | ~old(X0)) | ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0))))) [nnf transformation 4]
44. ! [X0] : ((((~rich(X0) | humble(X0)) & (rich(X0) | ~humble(X0))) | (humble(X0) & old(X0))) & (~humble(X0) | ~old(X0) | ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0))))) [flattening 43]
69. ? [X0] : (~patient(X0) & ~tall(X0)) | ! [X1] : (rich(X1) & old(X1)) [rectify 35]
70. ? [X0] : (~patient(X0) & ~tall(X0)) => (~patient(sK8) & ~tall(sK8)) [choice axiom]
71. (~patient(sK8) & ~tall(sK8)) | ! [X1] : (rich(X1) & old(X1)) [skolemisation 69,70]
73. (? [X0] : ~tall(X0) | (~creative(lucy) | ~old(lucy))) & ((creative(lucy) & old(lucy)) | ! [X0] : tall(X0)) [nnf transformation 16]
74. (? [X0] : ~tall(X0) | ~creative(lucy) | ~old(lucy)) & ((creative(lucy) & old(lucy)) | ! [X0] : tall(X0)) [flattening 73]
75. (? [X0] : ~tall(X0) | ~creative(lucy) | ~old(lucy)) & ((creative(lucy) & old(lucy)) | ! [X1] : tall(X1)) [rectify 74]
76. ? [X0] : ~tall(X0) => ~tall(sK9) [choice axiom]
77. (~tall(sK9) | ~creative(lucy) | ~old(lucy)) & ((creative(lucy) & old(lucy)) | ! [X1] : tall(X1)) [skolemisation 75,76]
85. ? [X0] : (brave(X0) & quiet(X0)) => (brave(sK13) & quiet(sK13)) [choice axiom]
86. brave(sK13) & quiet(sK13) [skolemisation 21,85]
93. ~old(sK0) | ~quiet(X1) [cnf transformation 41]
99. ~humble(X0) | ~old(X0) | ~humble(X0) | ~rich(X0) [cnf transformation 44]
103. ~rich(X0) | humble(X0) | humble(X0) [cnf transformation 44]
141. ~tall(sK8) | old(X1) [cnf transformation 71]
147. old(lucy) | tall(X1) [cnf transformation 77]
156. quiet(sK13) [cnf transformation 86]
162. rich(lucy) [cnf transformation 25]
165. ~humble(X0) | ~old(X0) | ~rich(X0) [duplicate literal removal 99]
166. ~rich(X0) | humble(X0) [duplicate literal removal 103]
168. 1 <=> ! [X1] : ~quiet(X1) [avatar definition]
169. ~quiet(X1) <- (1) [avatar component clause 168]
171. 2 <=> old(sK0) [avatar definition]
173. ~old(sK0) <- (~2) [avatar component clause 171]
174. 1 | ~2 [avatar split clause 93,171,168]
180. 4 <=> ! [X3] : old(X3) [avatar definition]
181. old(X3) <- (4) [avatar component clause 180]
201. ~rich(X0) | ~old(X0) [subsumption resolution 165,166]
318. 34 <=> tall(sK8) [avatar definition]
320. ~tall(sK8) <- (~34) [avatar component clause 318]
322. 4 | ~34 [avatar split clause 141,318,180]
324. 35 <=> old(lucy) [avatar definition]
337. 38 <=> ! [X1] : tall(X1) [avatar definition]
338. tall(X1) <- (38) [avatar component clause 337]
340. 38 | 35 [avatar split clause 147,324,337]
351. $false <- (~2, 4) [subsumption resolution 173,181]
352. 2 | ~4 [avatar contradiction clause 351]
360. ~old(lucy) [resolution 201,162]
364. ~35 [avatar split clause 360,324]
365. $false <- (~34, 38) [resolution 338,320]
368. 34 | ~38 [avatar contradiction clause 365]
369. $false <- (1) [resolution 169,156]
370. ~1 [avatar contradiction clause 369]
371. $false [avatar sat refutation 174,322,340,352,364,368,370]
% SZS output end Proof for 6171742876528218114444332
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not creative is patient and vice versa.
Everyone who is not generous is either not strong or happy.
Everyone who is either quiet or not tall is not quiet or strong.
Everyone who is not rich or not old is both not funny and not rich.
Everyone who is brave is either not calm or not wise.
If lucy is both not happy and not kind then someone is patient and vice versa.
Everyone who is both brave and rich is both not quiet and strong and vice versa.
If john is both funny and wise then alice is both old and calm.
Everyone who is either old or calm is either curious or not quiet.
Everyone who is curious or brave is patient or humble and vice versa.
If alice is either not generous or not rich then someone is either calm or strong and vice versa.
If someone is calm then susan is funny and vice versa.
If someone is tall or not calm then someone is either old or not creative and vice versa.
If susan is rich or not humble then someone is either not creative or kind.
Everyone who is both not quiet and not patient is happy and vice versa.
Everyone who is either quiet or not quiet is both not creative and not old.
Someone is not happy.
Someone is both not kind and not strong.
Someone is not funny or rich.
Paul is not strong.
Fred is not tall or not patient.
Susan is both tall and not old.
Susan is not rich. | Fred is not creative. | entailment | (![X]:((creative(X)|~creative(X))<=>patient(X)))&
(![X]:(~generous(X)=>(~strong(X)<~>happy(X))))&
(![X]:((quiet(X)<~>~tall(X))=>(~quiet(X)|strong(X))))&
(![X]:((~rich(X)|~old(X))=>(~funny(X)&~rich(X))))&
(![X]:(brave(X)=>(~calm(X)<~>~wise(X))))&
(((~happy(lucy)&~kind(lucy)))<=>(?[X]:(patient(X))))&
(![X]:((brave(X)&rich(X))<=>(~quiet(X)&strong(X))))&
(((funny(john)&wise(john)))=>((old(alice)&calm(alice))))&
(![X]:((old(X)<~>calm(X))=>(curious(X)<~>~quiet(X))))&
(![X]:((curious(X)|brave(X))<=>(patient(X)|humble(X))))&
(((~generous(alice)<~>~rich(alice)))<=>(?[X]:((calm(X)<~>strong(X)))))&
((?[X]:(calm(X)))<=>(funny(susan)))&
((?[X]:((tall(X)|~calm(X))))<=>(?[X]:((old(X)<~>~creative(X)))))&
(((rich(susan)|~humble(susan)))=>(?[X]:((~creative(X)<~>kind(X)))))&
(![X]:((~quiet(X)&~patient(X))<=>happy(X)))&
(![X]:((quiet(X)<~>~quiet(X))=>(~creative(X)&~old(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~kind(X)&~strong(X))))&
(?[X]:((~funny(X)|rich(X))))&
(~strong(paul))&
((~tall(fred)|~patient(fred)))&
((tall(susan)&~old(susan)))&
(~rich(susan)) | ~creative(fred) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2628313940786856492682897
% SZS output start Proof for 2628313940786856492682897
16. ! [X0] : ((quiet(X0) <~> ~quiet(X0)) => (~old(X0) & ~creative(X0))) [input p15]
24. creative(fred) [input hypothesis]
35. ! [X0] : ((~old(X0) & ~creative(X0)) | (quiet(X0) <=> ~quiet(X0))) [ennf transformation 16]
69. ! [X0] : ((~old(X0) & ~creative(X0)) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0)))) [nnf transformation 35]
129. ~creative(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 69]
130. ~creative(X0) | quiet(X0) | quiet(X0) [cnf transformation 69]
142. creative(fred) [cnf transformation 24]
143. ~creative(X0) | ~quiet(X0) [duplicate literal removal 129]
144. ~creative(X0) | quiet(X0) [duplicate literal removal 130]
269. ~creative(X0) [subsumption resolution 143,144]
272. $false [subsumption resolution 142,269]
% SZS output end Proof for 2628313940786856492682897
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not wise then susan is patient or not humble.
Everyone who is either curious or not curious is not calm or old and vice versa.
If john is tall then someone is patient.
Everyone who is not rich or not patient is either patient or not calm.
If susan is generous or not tall then alice is not tall.
If paul is either not happy or happy then paul is happy or quiet and vice versa.
Everyone who is old or kind is funny.
Everyone who is both not wise and not kind is not old and vice versa.
If someone is brave then alice is rich or not rich and vice versa.
If someone is either not happy or happy then paul is both not rich and funny.
If mary is either quiet or wise then lucy is not curious and vice versa.
Everyone who is wise is not quiet or happy and vice versa.
Everyone who is not happy or quiet is both brave and not curious.
Everyone who is not creative or patient is either generous or patient and vice versa.
If fred is either tall or calm then alice is both calm and not generous.
If paul is quiet then someone is curious and vice versa.
Lucy is either not old or not quiet.
Lucy is creative or humble.
Paul is not funny or not calm.
Someone is either generous or creative.
John is not brave or not patient.
Mary is creative.
Paul is calm or not old. | Paul is not curious. | entailment | ((?[X]:((old(X)|~wise(X))))=>((patient(susan)|~humble(susan))))&
(![X]:((curious(X)<~>~curious(X))<=>(~calm(X)|old(X))))&
((tall(john))=>(?[X]:(patient(X))))&
(![X]:((~rich(X)|~patient(X))=>(patient(X)<~>~calm(X))))&
(((generous(susan)|~tall(susan)))=>(~tall(alice)))&
(((~happy(paul)<~>happy(paul)))<=>((happy(paul)|quiet(paul))))&
(![X]:((old(X)|kind(X))=>funny(X)))&
(![X]:((~wise(X)&~kind(X))<=>~old(X)))&
((?[X]:(brave(X)))<=>((rich(alice)|~rich(alice))))&
((?[X]:((~happy(X)<~>happy(X))))=>((~rich(paul)&funny(paul))))&
(((quiet(mary)<~>wise(mary)))<=>(~curious(lucy)))&
(![X]:(wise(X)<=>(~quiet(X)|happy(X))))&
(![X]:((~happy(X)|quiet(X))=>(brave(X)&~curious(X))))&
(![X]:((~creative(X)|patient(X))<=>(generous(X)<~>patient(X))))&
(((tall(fred)<~>calm(fred)))=>((calm(alice)&~generous(alice))))&
((quiet(paul))<=>(?[X]:(curious(X))))&
((~old(lucy)<~>~quiet(lucy)))&
((creative(lucy)|humble(lucy)))&
((~funny(paul)|~calm(paul)))&
(?[X]:((generous(X)<~>creative(X))))&
((~brave(john)|~patient(john)))&
(creative(mary))&
((calm(paul)|~old(paul))) | ~curious(paul) | [
"p7",
"p9",
"p11",
"p12",
"p18",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 727814332280202249669310
% SZS output start Proof for 727814332280202249669310
8. ! [X0] : ((~kind(X0) & ~wise(X0)) <=> ~old(X0)) [input p7]
10. ? [X0] : (~happy(X0) <~> happy(X0)) => (funny(paul) & ~rich(paul)) [input p9]
12. ! [X0] : (wise(X0) <=> (happy(X0) | ~quiet(X0))) [input p11]
13. ! [X0] : ((quiet(X0) | ~happy(X0)) => (~curious(X0) & brave(X0))) [input p12]
19. ~calm(paul) | ~funny(paul) [input p18]
23. ~old(paul) | calm(paul) [input p22]
24. curious(paul) [input hypothesis]
31. (funny(paul) & ~rich(paul)) | ! [X0] : (~happy(X0) <=> happy(X0)) [ennf transformation 10]
32. ! [X0] : ((~curious(X0) & brave(X0)) | (~quiet(X0) & happy(X0))) [ennf transformation 13]
41. ! [X0] : (((~kind(X0) & ~wise(X0)) | old(X0)) & (~old(X0) | (kind(X0) | wise(X0)))) [nnf transformation 8]
42. ! [X0] : (((~kind(X0) & ~wise(X0)) | old(X0)) & (~old(X0) | kind(X0) | wise(X0))) [flattening 41]
48. (funny(paul) & ~rich(paul)) | ! [X0] : ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0))) [nnf transformation 31]
50. ! [X0] : ((wise(X0) | (~happy(X0) & quiet(X0))) & ((happy(X0) | ~quiet(X0)) | ~wise(X0))) [nnf transformation 12]
51. ! [X0] : ((wise(X0) | (~happy(X0) & quiet(X0))) & (happy(X0) | ~quiet(X0) | ~wise(X0))) [flattening 50]
87. ~wise(X0) | old(X0) [cnf transformation 42]
94. funny(paul) | happy(X0) | happy(X0) [cnf transformation 48]
95. funny(paul) | ~happy(X0) | ~happy(X0) [cnf transformation 48]
102. ~happy(X0) | wise(X0) [cnf transformation 51]
105. ~curious(X0) | happy(X0) [cnf transformation 32]
122. ~calm(paul) | ~funny(paul) [cnf transformation 19]
127. ~old(paul) | calm(paul) [cnf transformation 23]
128. curious(paul) [cnf transformation 24]
133. funny(paul) | happy(X0) [duplicate literal removal 94]
134. funny(paul) | ~happy(X0) [duplicate literal removal 95]
183. 10 <=> happy(paul) [avatar definition]
185. happy(paul) <- (10) [avatar component clause 183]
202. 14 <=> ! [X0] : ~happy(X0) [avatar definition]
203. ~happy(X0) <- (14) [avatar component clause 202]
205. 15 <=> funny(paul) [avatar definition]
208. 14 | 15 [avatar split clause 134,205,202]
210. 16 <=> ! [X0] : happy(X0) [avatar definition]
211. happy(X0) <- (16) [avatar component clause 210]
212. 16 | 15 [avatar split clause 133,205,210]
284. 31 <=> calm(paul) [avatar definition]
287. ~15 | ~31 [avatar split clause 122,284,205]
308. 36 <=> old(paul) [avatar definition]
310. ~old(paul) <- (~36) [avatar component clause 308]
311. 31 | ~36 [avatar split clause 127,308,284]
319. wise(paul) <- (10) [resolution 102,185]
320. old(paul) <- (10) [resolution 319,87]
321. $false <- (10, ~36) [subsumption resolution 320,310]
322. ~10 | 36 [avatar contradiction clause 321]
326. happy(paul) [resolution 105,128]
330. 10 [avatar split clause 326,183]
331. $false <- (14, 16) [subsumption resolution 203,211]
332. ~14 | ~16 [avatar contradiction clause 331]
333. $false [avatar sat refutation 208,212,287,311,322,330,332]
% SZS output end Proof for 727814332280202249669310
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is both not creative and old then alice is humble and vice versa. If someone is not brave then paul is not brave or not wise and vice versa. If susan is generous then paul is old or curious. If someone is both quiet and not strong then paul is either old or not humble. Everyone who is either not funny or not happy is not brave or not strong and vice versa. If someone is not brave then mary is either not tall or calm and vice versa. If susan is strong or not generous then someone is not wise or not happy. Everyone who is both not wise and generous is either patient or not kind and vice versa. Everyone who is either kind or not kind is either not funny or not tall and vice versa. If someone is strong or not curious then john is not kind. Everyone who is either not patient or not rich is brave and vice versa. Everyone who is not strong is not old or funny. Everyone who is both not creative and not funny is quiet or not rich and vice versa. If alice is not quiet then someone is both humble and kind. If someone is either tall or rich then lucy is both not strong and patient. Everyone who is either curious or not happy is both funny and old and vice versa. Someone is humble. Someone is kind. Susan is not patient or not brave. Someone is rich or not curious. Someone is either not funny or not curious. Paul is strong or not happy. Someone is not curious. Paul is both not strong and wise. | Paul is not happy. | entailment | (((~creative(alice)&old(alice)))<=>(humble(alice)))&
((?[X]:(~brave(X)))<=>((~brave(paul)|~wise(paul))))&
((generous(susan))=>((old(paul)|curious(paul))))&
((?[X]:((quiet(X)&~strong(X))))=>((old(paul)<~>~humble(paul))))&
(![X]:((~funny(X)<~>~happy(X))<=>(~brave(X)|~strong(X))))&
((?[X]:(~brave(X)))<=>((~tall(mary)<~>calm(mary))))&
(((strong(susan)|~generous(susan)))=>(?[X]:((~wise(X)|~happy(X)))))&
(![X]:((~wise(X)&generous(X))<=>(patient(X)<~>~kind(X))))&
(![X]:((kind(X)<~>~kind(X))<=>(~funny(X)<~>~tall(X))))&
((?[X]:((strong(X)|~curious(X))))=>(~kind(john)))&
(![X]:((~patient(X)<~>~rich(X))<=>brave(X)))&
(![X]:(~strong(X)=>(~old(X)|funny(X))))&
(![X]:((~creative(X)&~funny(X))<=>(quiet(X)|~rich(X))))&
((~quiet(alice))=>(?[X]:((humble(X)&kind(X)))))&
((?[X]:((tall(X)<~>rich(X))))=>((~strong(lucy)&patient(lucy))))&
(![X]:((curious(X)<~>~happy(X))<=>(funny(X)&old(X))))&
(?[X]:(humble(X)))&
(?[X]:(kind(X)))&
((~patient(susan)|~brave(susan)))&
(?[X]:((rich(X)|~curious(X))))&
(?[X]:((~funny(X)<~>~curious(X))))&
((strong(paul)|~happy(paul)))&
(?[X]:(~curious(X)))&
((~strong(paul)&wise(paul))) | ~happy(paul) | [
"p21",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 657191189761721036279133
% SZS output start Proof for 657191189761721036279133
22. ~happy(paul) | strong(paul) [input p21]
24. wise(paul) & ~strong(paul) [input p23]
25. happy(paul) [input hypothesis]
138. ~happy(paul) | strong(paul) [cnf transformation 22]
140. ~strong(paul) [cnf transformation 24]
142. happy(paul) [cnf transformation 25]
307. 35 <=> strong(paul) [avatar definition]
311. 36 <=> happy(paul) [avatar definition]
314. 35 | ~36 [avatar split clause 138,311,307]
316. ~35 [avatar split clause 140,307]
317. 36 [avatar split clause 142,311]
318. $false [avatar sat refutation 314,316,317]
% SZS output end Proof for 657191189761721036279133
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not calm is either not calm or rich and vice versa.
If alice is quiet or not humble then someone is not tall.
If mary is both not funny and tall then john is not rich and vice versa.
Everyone who is either patient or kind is both not quiet and curious and vice versa.
Everyone who is either not patient or funny is not humble or not brave.
If someone is not wise then someone is either brave or creative and vice versa.
Everyone who is patient is happy or generous and vice versa.
If someone is either not curious or rich then alice is either not old or kind and vice versa.
Everyone who is kind or not calm is not patient and vice versa.
If someone is both funny and generous then someone is either not kind or not brave.
If john is not rich or not happy then alice is not patient or creative and vice versa.
Everyone who is either wise or not kind is patient.
Everyone who is happy is either rich or funny and vice versa.
Everyone who is both patient and humble is either rich or happy.
If alice is both quiet and funny then mary is not quiet or generous and vice versa.
If someone is curious then someone is not old.
John is both wise and not rich.
Someone is not humble or not calm.
Someone is either curious or not calm.
Someone is both not rich and not quiet.
Paul is not humble.
Someone is either happy or curious.
Someone is not funny or not wise.
Fred is either curious or brave. | Mary is humble. | contradiction | (![X]:((tall(X)<~>~calm(X))<=>(~calm(X)<~>rich(X))))&
(((quiet(alice)|~humble(alice)))=>(?[X]:(~tall(X))))&
(((~funny(mary)&tall(mary)))<=>(~rich(john)))&
(![X]:((patient(X)<~>kind(X))<=>(~quiet(X)&curious(X))))&
(![X]:((~patient(X)<~>funny(X))=>(~humble(X)|~brave(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((brave(X)<~>creative(X)))))&
(![X]:(patient(X)<=>(happy(X)|generous(X))))&
((?[X]:((~curious(X)<~>rich(X))))<=>((~old(alice)<~>kind(alice))))&
(![X]:((kind(X)|~calm(X))<=>~patient(X)))&
((?[X]:((funny(X)&generous(X))))=>(?[X]:((~kind(X)<~>~brave(X)))))&
(((~rich(john)|~happy(john)))<=>((~patient(alice)|creative(alice))))&
(![X]:((wise(X)<~>~kind(X))=>patient(X)))&
(![X]:(happy(X)<=>(rich(X)<~>funny(X))))&
(![X]:((patient(X)&humble(X))=>(rich(X)<~>happy(X))))&
(((quiet(alice)&funny(alice)))<=>((~quiet(mary)|generous(mary))))&
((?[X]:(curious(X)))=>(?[X]:(~old(X))))&
((wise(john)&~rich(john)))&
(?[X]:((~humble(X)|~calm(X))))&
(?[X]:((curious(X)<~>~calm(X))))&
(?[X]:((~rich(X)&~quiet(X))))&
(~humble(paul))&
(?[X]:((happy(X)<~>curious(X))))&
(?[X]:((~funny(X)|~wise(X))))&
((curious(fred)<~>brave(fred))) | humble(mary) | [
"p0",
"p2",
"p6",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7554712342680148629434340
% SZS output start Proof for 7554712342680148629434340
1. ! [X0] : ((tall(X0) <~> ~calm(X0)) <=> (~calm(X0) <~> rich(X0))) [input p0]
3. (tall(mary) & ~funny(mary)) <=> ~rich(john) [input p2]
7. ! [X0] : (patient(X0) <=> (generous(X0) | happy(X0))) [input p6]
13. ! [X0] : (happy(X0) <=> (rich(X0) <~> funny(X0))) [input p12]
14. ! [X0] : ((humble(X0) & patient(X0)) => (rich(X0) <~> happy(X0))) [input p13]
17. ~rich(john) & wise(john) [input p16]
25. humble(mary) [input hypothesis]
34. ! [X0] : ((rich(X0) <~> happy(X0)) | (~humble(X0) | ~patient(X0))) [ennf transformation 14]
35. ! [X0] : ((rich(X0) <~> happy(X0)) | ~humble(X0) | ~patient(X0)) [flattening 34]
37. ! [X0] : ((((calm(X0) | ~tall(X0)) & (~calm(X0) | tall(X0))) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0)))) & (((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | ((tall(X0) | calm(X0)) & (~calm(X0) | ~tall(X0))))) [nnf transformation 1]
40. ((tall(mary) & ~funny(mary)) | rich(john)) & (~rich(john) | (~tall(mary) | funny(mary))) [nnf transformation 3]
41. ((tall(mary) & ~funny(mary)) | rich(john)) & (~rich(john) | ~tall(mary) | funny(mary)) [flattening 40]
50. ! [X0] : ((patient(X0) | (~generous(X0) & ~happy(X0))) & ((generous(X0) | happy(X0)) | ~patient(X0))) [nnf transformation 7]
51. ! [X0] : ((patient(X0) | (~generous(X0) & ~happy(X0))) & (generous(X0) | happy(X0) | ~patient(X0))) [flattening 50]
65. ! [X0] : ((happy(X0) | ((rich(X0) | ~funny(X0)) & (funny(X0) | ~rich(X0)))) & (((~funny(X0) | ~rich(X0)) & (funny(X0) | rich(X0))) | ~happy(X0))) [nnf transformation 13]
66. ! [X0] : (((~happy(X0) | ~rich(X0)) & (happy(X0) | rich(X0))) | ~humble(X0) | ~patient(X0)) [nnf transformation 35]
85. rich(X0) | ~calm(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 37]
91. calm(X0) | ~tall(X0) | rich(X0) | calm(X0) [cnf transformation 37]
96. ~funny(mary) | rich(john) [cnf transformation 41]
97. tall(mary) | rich(john) [cnf transformation 41]
111. ~happy(X0) | patient(X0) [cnf transformation 51]
134. ~rich(X0) | funny(X0) | happy(X0) [cnf transformation 65]
137. ~happy(X0) | ~rich(X0) | ~humble(X0) | ~patient(X0) [cnf transformation 66]
145. ~rich(john) [cnf transformation 17]
157. humble(mary) [cnf transformation 25]
158. rich(X0) | ~calm(X0) | ~tall(X0) [duplicate literal removal 85]
161. ~tall(X0) | calm(X0) | rich(X0) [duplicate literal removal 91]
163. ~tall(X0) | rich(X0) [subsumption resolution 158,161]
179. 4 <=> rich(john) [avatar definition]
183. 5 <=> tall(mary) [avatar definition]
185. tall(mary) <- (5) [avatar component clause 183]
186. 4 | 5 [avatar split clause 97,183,179]
188. 6 <=> funny(mary) [avatar definition]
190. ~funny(mary) <- (~6) [avatar component clause 188]
191. 4 | ~6 [avatar split clause 96,188,179]
278. ~happy(X0) | ~rich(X0) | ~humble(X0) [subsumption resolution 137,111]
304. ~4 [avatar split clause 145,179]
357. rich(mary) <- (5) [resolution 163,185]
398. funny(mary) | happy(mary) <- (5) [resolution 134,357]
399. happy(mary) <- (5, ~6) [subsumption resolution 398,190]
512. ~rich(mary) | ~humble(mary) <- (5, ~6) [resolution 399,278]
516. ~humble(mary) <- (5, ~6) [subsumption resolution 512,357]
517. $false <- (5, ~6) [subsumption resolution 516,157]
518. ~5 | 6 [avatar contradiction clause 517]
519. $false [avatar sat refutation 186,191,304,518]
% SZS output end Proof for 7554712342680148629434340
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and humble is not happy or strong.
If paul is brave then lucy is both creative and patient.
Everyone who is humble or generous is either funny or not old.
Everyone who is both tall and happy is not happy and vice versa.
If someone is creative or not quiet then someone is either quiet or tall.
If alice is either patient or not humble then someone is both kind and not happy.
If fred is tall or brave then john is humble and vice versa.
Everyone who is brave is both not old and not happy and vice versa.
If susan is both not brave and not quiet then someone is both not creative and not humble.
If alice is either creative or curious then susan is either not old or humble.
If alice is generous or kind then alice is both not generous and not kind.
If someone is either not wise or wise then someone is not happy or not wise and vice versa.
If someone is not patient then someone is not calm or not humble.
If someone is both humble and not kind then paul is both tall and not rich and vice versa.
If alice is both not tall and generous then susan is not humble.
If paul is either not wise or humble then mary is either not creative or not strong and vice versa.
Susan is not tall or not curious.
Someone is either not patient or not funny.
John is happy.
Mary is not wise or strong.
Someone is both not strong and not calm.
Someone is not old.
Someone is kind. | Fred is not happy. | contradiction | (![X]:((~generous(X)&humble(X))=>(~happy(X)|strong(X))))&
((brave(paul))=>((creative(lucy)&patient(lucy))))&
(![X]:((humble(X)|generous(X))=>(funny(X)<~>~old(X))))&
(![X]:((tall(X)&happy(X))<=>~happy(X)))&
((?[X]:((creative(X)|~quiet(X))))=>(?[X]:((quiet(X)<~>tall(X)))))&
(((patient(alice)<~>~humble(alice)))=>(?[X]:((kind(X)&~happy(X)))))&
(((tall(fred)|brave(fred)))<=>(humble(john)))&
(![X]:(brave(X)<=>(~old(X)&~happy(X))))&
(((~brave(susan)&~quiet(susan)))=>(?[X]:((~creative(X)&~humble(X)))))&
(((creative(alice)<~>curious(alice)))=>((~old(susan)<~>humble(susan))))&
(((generous(alice)|kind(alice)))=>((~generous(alice)&~kind(alice))))&
((?[X]:((~wise(X)<~>wise(X))))<=>(?[X]:((~happy(X)|~wise(X)))))&
((?[X]:(~patient(X)))=>(?[X]:((~calm(X)|~humble(X)))))&
((?[X]:((humble(X)&~kind(X))))<=>((tall(paul)&~rich(paul))))&
(((~tall(alice)&generous(alice)))=>(~humble(susan)))&
(((~wise(paul)<~>humble(paul)))<=>((~creative(mary)<~>~strong(mary))))&
((~tall(susan)|~curious(susan)))&
(?[X]:((~patient(X)<~>~funny(X))))&
(happy(john))&
((~wise(mary)|strong(mary)))&
(?[X]:((~strong(X)&~calm(X))))&
(?[X]:(~old(X)))&
(?[X]:(kind(X))) | ~happy(fred) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3236813371469250126303919
% SZS output start Proof for 3236813371469250126303919
4. ! [X0] : ((happy(X0) & tall(X0)) <=> ~happy(X0)) [input p3]
24. ~happy(fred) [input hypothesis]
43. ! [X0] : (((happy(X0) & tall(X0)) | happy(X0)) & (~happy(X0) | (~happy(X0) | ~tall(X0)))) [nnf transformation 4]
44. ! [X0] : (((happy(X0) & tall(X0)) | happy(X0)) & (~happy(X0) | ~happy(X0) | ~tall(X0))) [flattening 43]
88. happy(X0) | happy(X0) [cnf transformation 44]
140. ~happy(fred) [cnf transformation 24]
146. happy(X0) [duplicate literal removal 88]
305. $false [subsumption resolution 140,146]
% SZS output end Proof for 3236813371469250126303919
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or kind is funny and vice versa. If susan is either curious or kind then paul is both not creative and not brave. If someone is both strong and rich then someone is both kind and not old. Everyone who is either curious or not old is either quiet or not humble. Everyone who is both not happy and rich is both not kind and not brave. Everyone who is not happy is old. Everyone who is creative is either not wise or wise. If mary is either tall or not brave then someone is either strong or not rich and vice versa. Everyone who is kind or happy is either not strong or patient. Everyone who is either quiet or not funny is not strong or not rich. Everyone who is both not wise and patient is brave or not calm and vice versa. Everyone who is not calm or not kind is not happy. Everyone who is both not curious and happy is not calm. If john is not creative or tall then susan is not curious or quiet. Everyone who is either brave or happy is not funny or not tall and vice versa. If someone is both not humble and not calm then john is both not curious and old. Mary is either tall or generous. Someone is either not happy or creative. Someone is either happy or not happy. Someone is both brave and not quiet. Fred is creative or not strong. Lucy is either not funny or generous. Someone is either not old or not calm. Someone is either patient or not generous. | Fred is not funny. | contradiction | (![X]:((patient(X)|kind(X))<=>funny(X)))&
(((curious(susan)<~>kind(susan)))=>((~creative(paul)&~brave(paul))))&
((?[X]:((strong(X)&rich(X))))=>(?[X]:((kind(X)&~old(X)))))&
(![X]:((curious(X)<~>~old(X))=>(quiet(X)<~>~humble(X))))&
(![X]:((~happy(X)&rich(X))=>(~kind(X)&~brave(X))))&
(![X]:(~happy(X)=>old(X)))&
(![X]:(creative(X)=>(~wise(X)<~>wise(X))))&
(((tall(mary)<~>~brave(mary)))<=>(?[X]:((strong(X)<~>~rich(X)))))&
(![X]:((kind(X)|happy(X))=>(~strong(X)<~>patient(X))))&
(![X]:((quiet(X)<~>~funny(X))=>(~strong(X)|~rich(X))))&
(![X]:((~wise(X)&patient(X))<=>(brave(X)|~calm(X))))&
(![X]:((~calm(X)|~kind(X))=>~happy(X)))&
(![X]:((~curious(X)&happy(X))=>~calm(X)))&
(((~creative(john)|tall(john)))=>((~curious(susan)|quiet(susan))))&
(![X]:((brave(X)<~>happy(X))<=>(~funny(X)|~tall(X))))&
((?[X]:((~humble(X)&~calm(X))))=>((~curious(john)&old(john))))&
((tall(mary)<~>generous(mary)))&
(?[X]:((~happy(X)<~>creative(X))))&
(?[X]:((happy(X)<~>~happy(X))))&
(?[X]:((brave(X)&~quiet(X))))&
((creative(fred)|~strong(fred)))&
((~funny(lucy)<~>generous(lucy)))&
(?[X]:((~old(X)<~>~calm(X))))&
(?[X]:((patient(X)<~>~generous(X)))) | ~funny(fred) | [
"p0",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3136337485957137877514105
% SZS output start Proof for 3136337485957137877514105
1. ! [X0] : ((kind(X0) | patient(X0)) <=> funny(X0)) [input p0]
11. ! [X0] : ((patient(X0) & ~wise(X0)) <=> (~calm(X0) | brave(X0))) [input p10]
12. ! [X0] : ((~kind(X0) | ~calm(X0)) => ~happy(X0)) [input p11]
15. ! [X0] : ((brave(X0) <~> happy(X0)) <=> (~tall(X0) | ~funny(X0))) [input p14]
25. ~funny(fred) [input hypothesis]
37. ! [X0] : (~happy(X0) | (kind(X0) & calm(X0))) [ennf transformation 12]
43. ! [X0] : (((kind(X0) | patient(X0)) | ~funny(X0)) & (funny(X0) | (~kind(X0) & ~patient(X0)))) [nnf transformation 1]
44. ! [X0] : ((kind(X0) | patient(X0) | ~funny(X0)) & (funny(X0) | (~kind(X0) & ~patient(X0)))) [flattening 43]
57. ! [X0] : (((patient(X0) & ~wise(X0)) | (calm(X0) & ~brave(X0))) & ((~calm(X0) | brave(X0)) | (~patient(X0) | wise(X0)))) [nnf transformation 11]
58. ! [X0] : (((patient(X0) & ~wise(X0)) | (calm(X0) & ~brave(X0))) & (~calm(X0) | brave(X0) | ~patient(X0) | wise(X0))) [flattening 57]
59. ! [X0] : ((((~happy(X0) | ~brave(X0)) & (happy(X0) | brave(X0))) | (tall(X0) & funny(X0))) & ((~tall(X0) | ~funny(X0)) | ((brave(X0) | ~happy(X0)) & (happy(X0) | ~brave(X0))))) [nnf transformation 15]
60. ! [X0] : ((((~happy(X0) | ~brave(X0)) & (happy(X0) | brave(X0))) | (tall(X0) & funny(X0))) & (~tall(X0) | ~funny(X0) | ((brave(X0) | ~happy(X0)) & (happy(X0) | ~brave(X0))))) [flattening 59]
77. ~patient(X0) | funny(X0) [cnf transformation 44]
78. ~kind(X0) | funny(X0) [cnf transformation 44]
112. ~brave(X0) | patient(X0) [cnf transformation 58]
115. ~happy(X0) | kind(X0) [cnf transformation 37]
121. happy(X0) | brave(X0) | funny(X0) [cnf transformation 60]
142. ~funny(fred) [cnf transformation 25]
307. brave(X3) | funny(X3) | kind(X3) [resolution 121,115]
320. brave(X3) | funny(X3) [subsumption resolution 307,78]
372. funny(X0) | patient(X0) [resolution 320,112]
374. funny(X0) [subsumption resolution 372,77]
395. $false [resolution 374,142]
% SZS output end Proof for 3136337485957137877514105
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not calm or happy then john is not old or calm.
Everyone who is tall is not kind and vice versa.
If mary is patient then fred is not happy and vice versa.
Everyone who is not happy is not kind or creative and vice versa.
Everyone who is both strong and happy is either strong or not brave.
Everyone who is not rich is not tall.
Everyone who is kind or not curious is humble.
Everyone who is not curious or rich is both funny and tall and vice versa.
Everyone who is both not kind and not brave is either happy or wise.
If paul is calm or not tall then susan is not creative or funny and vice versa.
Everyone who is kind or happy is brave and vice versa.
If mary is both not humble and not funny then alice is both not rich and not patient and vice versa.
If someone is either not happy or creative then someone is both not curious and patient and vice versa.
If susan is not tall or patient then someone is not humble and vice versa.
Everyone who is both rich and generous is both not kind and not patient and vice versa.
If someone is both brave and not quiet then someone is either not curious or not generous and vice versa.
Fred is not tall or creative.
Mary is kind.
Someone is not quiet.
Someone is quiet.
Alice is wise.
John is quiet.
Susan is not generous. | Alice is old. | neutral | ((?[X]:((~calm(X)<~>happy(X))))=>((~old(john)|calm(john))))&
(![X]:(tall(X)<=>~kind(X)))&
((patient(mary))<=>(~happy(fred)))&
(![X]:(~happy(X)<=>(~kind(X)|creative(X))))&
(![X]:((strong(X)&happy(X))=>(strong(X)<~>~brave(X))))&
(![X]:(~rich(X)=>~tall(X)))&
(![X]:((kind(X)|~curious(X))=>humble(X)))&
(![X]:((~curious(X)|rich(X))<=>(funny(X)&tall(X))))&
(![X]:((~kind(X)&~brave(X))=>(happy(X)<~>wise(X))))&
(((calm(paul)|~tall(paul)))<=>((~creative(susan)|funny(susan))))&
(![X]:((kind(X)|happy(X))<=>brave(X)))&
(((~humble(mary)&~funny(mary)))<=>((~rich(alice)&~patient(alice))))&
((?[X]:((~happy(X)<~>creative(X))))<=>(?[X]:((~curious(X)&patient(X)))))&
(((~tall(susan)|patient(susan)))<=>(?[X]:(~humble(X))))&
(![X]:((rich(X)&generous(X))<=>(~kind(X)&~patient(X))))&
((?[X]:((brave(X)&~quiet(X))))<=>(?[X]:((~curious(X)<~>~generous(X)))))&
((~tall(fred)|creative(fred)))&
(kind(mary))&
(?[X]:(~quiet(X)))&
(?[X]:(quiet(X)))&
(wise(alice))&
(quiet(john))&
(~generous(susan)) | old(alice) | [] | null | 0 |
If someone is either happy or not brave then susan is wise or not creative. If someone is either not funny or strong then someone is both tall and creative and vice versa. If someone is both not happy and wise then someone is both not curious and not creative. If someone is both strong and quiet then someone is not generous or not happy and vice versa. Everyone who is not humble is either not funny or not quiet. If someone is not patient or not generous then someone is either not generous or wise and vice versa. Everyone who is either not happy or creative is either not old or not generous. Everyone who is either not strong or not funny is either patient or generous and vice versa. Everyone who is both not curious and happy is funny or not creative. If someone is brave then someone is either patient or creative and vice versa. Everyone who is either not wise or quiet is not funny and vice versa. Everyone who is not calm or not quiet is creative or funny. Everyone who is generous is both not wise and calm. Everyone who is quiet is not strong. Everyone who is not happy or wise is both not creative and not strong and vice versa. If paul is either not old or not tall then someone is not calm. Someone is not quiet or not old. Fred is generous. Paul is humble or patient. Lucy is rich. Someone is either quiet or not strong. | Lucy is calm. | entailment | ((?[X]:((happy(X)<~>~brave(X))))=>((wise(susan)|~creative(susan))))&
((?[X]:((~funny(X)<~>strong(X))))<=>(?[X]:((tall(X)&creative(X)))))&
((?[X]:((~happy(X)&wise(X))))=>(?[X]:((~curious(X)&~creative(X)))))&
((?[X]:((strong(X)&quiet(X))))<=>(?[X]:((~generous(X)|~happy(X)))))&
(![X]:(~humble(X)=>(~funny(X)<~>~quiet(X))))&
((?[X]:((~patient(X)|~generous(X))))<=>(?[X]:((~generous(X)<~>wise(X)))))&
(![X]:((~happy(X)<~>creative(X))=>(~old(X)<~>~generous(X))))&
(![X]:((~strong(X)<~>~funny(X))<=>(patient(X)<~>generous(X))))&
(![X]:((~curious(X)&happy(X))=>(funny(X)|~creative(X))))&
((?[X]:(brave(X)))<=>(?[X]:((patient(X)<~>creative(X)))))&
(![X]:((~wise(X)<~>quiet(X))<=>~funny(X)))&
(![X]:((~calm(X)|~quiet(X))=>(creative(X)|funny(X))))&
(![X]:(generous(X)=>(~wise(X)&calm(X))))&
(![X]:(quiet(X)=>~strong(X)))&
(![X]:((~happy(X)|wise(X))<=>(~creative(X)&~strong(X))))&
(((~old(paul)<~>~tall(paul)))=>(?[X]:(~calm(X))))&
(?[X]:((~quiet(X)|~old(X))))&
(generous(fred))&
((humble(paul)|patient(paul)))&
(rich(lucy))&
(?[X]:((quiet(X)<~>~strong(X)))) | calm(lucy) | [
"p3",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 513879159834906990533027
% SZS output start Proof for 513879159834906990533027
4. ? [X0] : (quiet(X0) & strong(X0)) <=> ? [X0] : (~happy(X0) | ~generous(X0)) [input p3]
13. ! [X0] : (generous(X0) => (calm(X0) & ~wise(X0))) [input p12]
14. ! [X0] : (quiet(X0) => ~strong(X0)) [input p13]
22. ~calm(lucy) [input hypothesis]
25. ? [X0] : (quiet(X0) & strong(X0)) <=> ? [X1] : (~happy(X1) | ~generous(X1)) [rectify 4]
39. ! [X0] : ((calm(X0) & ~wise(X0)) | ~generous(X0)) [ennf transformation 13]
40. ! [X0] : (~strong(X0) | ~quiet(X0)) [ennf transformation 14]
51. (? [X0] : (quiet(X0) & strong(X0)) | ! [X1] : (happy(X1) & generous(X1))) & (? [X1] : (~happy(X1) | ~generous(X1)) | ! [X0] : (~quiet(X0) | ~strong(X0))) [nnf transformation 25]
52. (? [X0] : (quiet(X0) & strong(X0)) | ! [X1] : (happy(X1) & generous(X1))) & (? [X2] : (~happy(X2) | ~generous(X2)) | ! [X3] : (~quiet(X3) | ~strong(X3))) [rectify 51]
53. ? [X0] : (quiet(X0) & strong(X0)) => (quiet(sK3) & strong(sK3)) [choice axiom]
54. ? [X2] : (~happy(X2) | ~generous(X2)) => (~happy(sK4) | ~generous(sK4)) [choice axiom]
55. ((quiet(sK3) & strong(sK3)) | ! [X1] : (happy(X1) & generous(X1))) & ((~happy(sK4) | ~generous(sK4)) | ! [X3] : (~quiet(X3) | ~strong(X3))) [skolemisation 52,54,53]
90. strong(sK3) | generous(X1) [cnf transformation 55]
92. quiet(sK3) | generous(X1) [cnf transformation 55]
124. ~generous(X0) | calm(X0) [cnf transformation 39]
125. ~strong(X0) | ~quiet(X0) [cnf transformation 40]
137. ~calm(lucy) [cnf transformation 22]
202. 16 <=> quiet(sK3) [avatar definition]
204. quiet(sK3) <- (16) [avatar component clause 202]
207. 17 <=> ! [X1] : generous(X1) [avatar definition]
208. generous(X1) <- (17) [avatar component clause 207]
209. 17 | 16 [avatar split clause 92,202,207]
211. 18 <=> strong(sK3) [avatar definition]
215. 17 | 18 [avatar split clause 90,211,207]
217. 19 <=> ! [X3] : (~quiet(X3) | ~strong(X3)) [avatar definition]
218. ~quiet(X3) | ~strong(X3) <- (19) [avatar component clause 217]
285. 19 [avatar split clause 125,217]
341. ~strong(sK3) <- (16, 19) [resolution 218,204]
344. ~18 | ~16 | ~19 [avatar split clause 341,217,202,211]
345. calm(X0) <- (17) [resolution 208,124]
352. $false <- (17) [resolution 345,137]
355. ~17 [avatar contradiction clause 352]
356. $false [avatar sat refutation 209,215,285,344,355]
% SZS output end Proof for 513879159834906990533027
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and not patient is either not humble or not creative and vice versa.
If someone is rich then john is not wise.
If someone is not creative then mary is quiet and vice versa.
Everyone who is both not wise and not calm is not old or patient and vice versa.
Everyone who is both rich and not brave is patient and vice versa.
If someone is not old then paul is not kind and vice versa.
Everyone who is humble or not generous is either not kind or not funny.
Everyone who is quiet is happy or not wise and vice versa.
Everyone who is patient or not kind is wise or not quiet.
If john is either kind or curious then someone is not happy or happy and vice versa.
Everyone who is calm or not rich is both not strong and humble.
Everyone who is both funny and rich is not wise or not happy and vice versa.
If someone is both not rich and tall then someone is both tall and quiet and vice versa.
Everyone who is both not strong and not wise is both strong and old and vice versa.
Everyone who is not patient or not calm is not rich and vice versa.
If someone is either generous or not brave then someone is rich.
Someone is either not funny or not wise.
Someone is either brave or not kind.
Paul is both not generous and humble.
Lucy is calm or not curious.
Paul is either not curious or not brave.
Lucy is either not tall or not creative. | Lucy is generous. | neutral | (![X]:((calm(X)&~patient(X))<=>(~humble(X)<~>~creative(X))))&
((?[X]:(rich(X)))=>(~wise(john)))&
((?[X]:(~creative(X)))<=>(quiet(mary)))&
(![X]:((~wise(X)&~calm(X))<=>(~old(X)|patient(X))))&
(![X]:((rich(X)&~brave(X))<=>patient(X)))&
((?[X]:(~old(X)))<=>(~kind(paul)))&
(![X]:((humble(X)|~generous(X))=>(~kind(X)<~>~funny(X))))&
(![X]:(quiet(X)<=>(happy(X)|~wise(X))))&
(![X]:((patient(X)|~kind(X))=>(wise(X)|~quiet(X))))&
(((kind(john)<~>curious(john)))<=>(?[X]:((~happy(X)|happy(X)))))&
(![X]:((calm(X)|~rich(X))=>(~strong(X)&humble(X))))&
(![X]:((funny(X)&rich(X))<=>(~wise(X)|~happy(X))))&
((?[X]:((~rich(X)&tall(X))))<=>(?[X]:((tall(X)&quiet(X)))))&
(![X]:((~strong(X)&~wise(X))<=>(strong(X)&old(X))))&
(![X]:((~patient(X)|~calm(X))<=>~rich(X)))&
((?[X]:((generous(X)<~>~brave(X))))=>(?[X]:(rich(X))))&
(?[X]:((~funny(X)<~>~wise(X))))&
(?[X]:((brave(X)<~>~kind(X))))&
((~generous(paul)&humble(paul)))&
((calm(lucy)|~curious(lucy)))&
((~curious(paul)<~>~brave(paul)))&
((~tall(lucy)<~>~creative(lucy))) | generous(lucy) | [] | null | 0 |
Everyone who is both humble and not quiet is old or wise and vice versa.
Everyone who is calm or quiet is both brave and tall and vice versa.
Everyone who is not strong is not happy.
Everyone who is not wise is both curious and not humble.
Everyone who is wise is either humble or wise.
Everyone who is happy is patient.
Everyone who is both patient and funny is either not strong or calm and vice versa.
Everyone who is creative is not curious or not tall.
Everyone who is not humble or old is both not generous and calm.
If john is both not calm and tall then someone is both not funny and brave and vice versa.
If someone is kind then mary is not patient and vice versa.
If lucy is either curious or funny then someone is not creative.
Everyone who is not strong is either curious or generous.
Everyone who is either generous or not tall is happy or not tall and vice versa.
Someone is either not strong or not humble.
Susan is not strong or calm.
Someone is either not strong or not quiet.
Susan is not wise or brave.
Someone is either not rich or not curious. | Lucy is not creative. | entailment | (![X]:((humble(X)&~quiet(X))<=>(old(X)|wise(X))))&
(![X]:((calm(X)|quiet(X))<=>(brave(X)&tall(X))))&
(![X]:(~strong(X)=>~happy(X)))&
(![X]:(~wise(X)=>(curious(X)&~humble(X))))&
(![X]:(wise(X)=>(humble(X)<~>wise(X))))&
(![X]:(happy(X)=>patient(X)))&
(![X]:((patient(X)&funny(X))<=>(~strong(X)<~>calm(X))))&
(![X]:(creative(X)=>(~curious(X)|~tall(X))))&
(![X]:((~humble(X)|old(X))=>(~generous(X)&calm(X))))&
(((~calm(john)&tall(john)))<=>(?[X]:((~funny(X)&brave(X)))))&
((?[X]:(kind(X)))<=>(~patient(mary)))&
(((curious(lucy)<~>funny(lucy)))=>(?[X]:(~creative(X))))&
(![X]:(~strong(X)=>(curious(X)<~>generous(X))))&
(![X]:((generous(X)<~>~tall(X))<=>(happy(X)|~tall(X))))&
(?[X]:((~strong(X)<~>~humble(X))))&
((~strong(susan)|calm(susan)))&
(?[X]:((~strong(X)<~>~quiet(X))))&
((~wise(susan)|brave(susan)))&
(?[X]:((~rich(X)<~>~curious(X)))) | ~creative(lucy) | [
"p0",
"p1",
"p3",
"p4",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 431109106655496294113534
% SZS output start Proof for 431109106655496294113534
1. ! [X0] : ((~quiet(X0) & humble(X0)) <=> (wise(X0) | old(X0))) [input p0]
2. ! [X0] : ((quiet(X0) | calm(X0)) <=> (tall(X0) & brave(X0))) [input p1]
4. ! [X0] : (~wise(X0) => (~humble(X0) & curious(X0))) [input p3]
5. ! [X0] : (wise(X0) => (humble(X0) <~> wise(X0))) [input p4]
8. ! [X0] : (creative(X0) => (~tall(X0) | ~curious(X0))) [input p7]
9. ! [X0] : ((old(X0) | ~humble(X0)) => (calm(X0) & ~generous(X0))) [input p8]
20. creative(lucy) [input hypothesis]
22. ! [X0] : ((~humble(X0) & curious(X0)) | wise(X0)) [ennf transformation 4]
23. ! [X0] : ((humble(X0) <~> wise(X0)) | ~wise(X0)) [ennf transformation 5]
25. ! [X0] : ((~tall(X0) | ~curious(X0)) | ~creative(X0)) [ennf transformation 8]
26. ! [X0] : (~tall(X0) | ~curious(X0) | ~creative(X0)) [flattening 25]
27. ! [X0] : ((calm(X0) & ~generous(X0)) | (~old(X0) & humble(X0))) [ennf transformation 9]
30. ! [X0] : (((~quiet(X0) & humble(X0)) | (~wise(X0) & ~old(X0))) & ((wise(X0) | old(X0)) | (quiet(X0) | ~humble(X0)))) [nnf transformation 1]
31. ! [X0] : (((~quiet(X0) & humble(X0)) | (~wise(X0) & ~old(X0))) & (wise(X0) | old(X0) | quiet(X0) | ~humble(X0))) [flattening 30]
32. ! [X0] : (((quiet(X0) | calm(X0)) | (~tall(X0) | ~brave(X0))) & ((tall(X0) & brave(X0)) | (~quiet(X0) & ~calm(X0)))) [nnf transformation 2]
33. ! [X0] : ((quiet(X0) | calm(X0) | ~tall(X0) | ~brave(X0)) & ((tall(X0) & brave(X0)) | (~quiet(X0) & ~calm(X0)))) [flattening 32]
34. ! [X0] : (((~wise(X0) | ~humble(X0)) & (wise(X0) | humble(X0))) | ~wise(X0)) [nnf transformation 23]
63. ~wise(X0) | humble(X0) [cnf transformation 31]
68. ~calm(X0) | tall(X0) [cnf transformation 33]
72. curious(X0) | wise(X0) [cnf transformation 22]
73. ~humble(X0) | wise(X0) [cnf transformation 22]
75. ~wise(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 34]
83. ~creative(X0) | ~curious(X0) | ~tall(X0) [cnf transformation 26]
86. calm(X0) | humble(X0) [cnf transformation 27]
112. creative(lucy) [cnf transformation 20]
115. ~wise(X0) | ~humble(X0) [duplicate literal removal 75]
116. ~humble(X0) [subsumption resolution 115,73]
117. calm(X0) [subsumption resolution 86,116]
147. 7 <=> curious(lucy) [avatar definition]
148. ~curious(lucy) <- (~7) [avatar component clause 147]
189. tall(X0) [resolution 68,117]
203. ~curious(lucy) | ~tall(lucy) [resolution 83,112]
204. ~curious(lucy) [subsumption resolution 203,189]
205. ~7 [avatar split clause 204,147]
207. wise(lucy) <- (~7) [resolution 148,72]
212. humble(lucy) <- (~7) [resolution 207,63]
213. $false <- (~7) [subsumption resolution 212,116]
214. 7 [avatar contradiction clause 213]
215. $false [avatar sat refutation 205,214]
% SZS output end Proof for 431109106655496294113534
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet and vice versa.
Everyone who is either not humble or strong is both not tall and not creative and vice versa.
Everyone who is not generous or not funny is not old and vice versa.
Everyone who is both patient and not funny is either tall or not funny and vice versa.
If someone is both calm and not tall then someone is not humble or rich and vice versa.
Everyone who is either strong or kind is not tall and vice versa.
If someone is either old or tall then john is either calm or kind.
If alice is both not curious and strong then someone is both wise and not strong.
Everyone who is wise or not quiet is calm and vice versa.
If paul is happy or not creative then someone is both not happy and strong and vice versa.
If alice is humble or not quiet then someone is curious or not kind.
Everyone who is either not brave or quiet is both funny and generous and vice versa.
Everyone who is either not strong or generous is both humble and not calm.
If john is both funny and not generous then someone is either not quiet or generous and vice versa.
If someone is curious or calm then fred is either creative or calm and vice versa.
Everyone who is rich or kind is wise and vice versa.
Lucy is quiet or not strong.
Someone is calm.
Someone is not curious.
Someone is kind or humble.
Fred is either not generous or strong.
Someone is either patient or not wise.
Lucy is not humble.
Someone is either not tall or not humble. | Fred is kind. | contradiction | (![X]:(generous(X)<=>~quiet(X)))&
(![X]:((~humble(X)<~>strong(X))<=>(~tall(X)&~creative(X))))&
(![X]:((~generous(X)|~funny(X))<=>~old(X)))&
(![X]:((patient(X)&~funny(X))<=>(tall(X)<~>~funny(X))))&
((?[X]:((calm(X)&~tall(X))))<=>(?[X]:((~humble(X)|rich(X)))))&
(![X]:((strong(X)<~>kind(X))<=>~tall(X)))&
((?[X]:((old(X)<~>tall(X))))=>((calm(john)<~>kind(john))))&
(((~curious(alice)&strong(alice)))=>(?[X]:((wise(X)&~strong(X)))))&
(![X]:((wise(X)|~quiet(X))<=>calm(X)))&
(((happy(paul)|~creative(paul)))<=>(?[X]:((~happy(X)&strong(X)))))&
(((humble(alice)|~quiet(alice)))=>(?[X]:((curious(X)|~kind(X)))))&
(![X]:((~brave(X)<~>quiet(X))<=>(funny(X)&generous(X))))&
(![X]:((~strong(X)<~>generous(X))=>(humble(X)&~calm(X))))&
(((funny(john)&~generous(john)))<=>(?[X]:((~quiet(X)<~>generous(X)))))&
((?[X]:((curious(X)|calm(X))))<=>((creative(fred)<~>calm(fred))))&
(![X]:((rich(X)|kind(X))<=>wise(X)))&
((quiet(lucy)|~strong(lucy)))&
(?[X]:(calm(X)))&
(?[X]:(~curious(X)))&
(?[X]:((kind(X)|humble(X))))&
((~generous(fred)<~>strong(fred)))&
(?[X]:((patient(X)<~>~wise(X))))&
(~humble(lucy))&
(?[X]:((~tall(X)<~>~humble(X)))) | kind(fred) | [
"p8",
"p12",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7330018524929922096213368
% SZS output start Proof for 7330018524929922096213368
9. ! [X0] : ((~quiet(X0) | wise(X0)) <=> calm(X0)) [input p8]
13. ! [X0] : ((~strong(X0) <~> generous(X0)) => (~calm(X0) & humble(X0))) [input p12]
16. ! [X0] : ((kind(X0) | rich(X0)) <=> wise(X0)) [input p15]
21. ~generous(fred) <~> strong(fred) [input p20]
25. kind(fred) [input hypothesis]
31. ! [X0] : ((~calm(X0) & humble(X0)) | (~strong(X0) <=> generous(X0))) [ennf transformation 13]
48. ! [X0] : (((~quiet(X0) | wise(X0)) | ~calm(X0)) & (calm(X0) | (quiet(X0) & ~wise(X0)))) [nnf transformation 9]
49. ! [X0] : ((~quiet(X0) | wise(X0) | ~calm(X0)) & (calm(X0) | (quiet(X0) & ~wise(X0)))) [flattening 48]
59. ! [X0] : ((~calm(X0) & humble(X0)) | ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0)))) [nnf transformation 31]
69. ! [X0] : (((kind(X0) | rich(X0)) | ~wise(X0)) & (wise(X0) | (~kind(X0) & ~rich(X0)))) [nnf transformation 16]
70. ! [X0] : ((kind(X0) | rich(X0) | ~wise(X0)) & (wise(X0) | (~kind(X0) & ~rich(X0)))) [flattening 69]
77. (~strong(fred) | generous(fred)) & (strong(fred) | ~generous(fred)) [nnf transformation 21]
116. ~wise(X0) | calm(X0) [cnf transformation 49]
134. ~calm(X0) | generous(X0) | strong(X0) [cnf transformation 59]
135. ~calm(X0) | ~strong(X0) | ~generous(X0) [cnf transformation 59]
149. ~kind(X0) | wise(X0) [cnf transformation 70]
155. strong(fred) | ~generous(fred) [cnf transformation 77]
156. ~strong(fred) | generous(fred) [cnf transformation 77]
162. kind(fred) [cnf transformation 25]
293. 28 <=> calm(fred) [avatar definition]
294. calm(fred) <- (28) [avatar component clause 293]
339. 38 <=> generous(fred) [avatar definition]
341. generous(fred) <- (38) [avatar component clause 339]
343. 39 <=> strong(fred) [avatar definition]
344. strong(fred) <- (39) [avatar component clause 343]
346. 38 | ~39 [avatar split clause 156,343,339]
347. ~38 | 39 [avatar split clause 155,343,339]
369. wise(fred) [resolution 149,162]
371. calm(fred) [resolution 369,116]
540. generous(fred) | strong(fred) <- (28) [resolution 134,294]
565. 39 | 38 | ~28 [avatar split clause 540,293,339,343]
588. ~strong(fred) | ~generous(fred) <- (28) [resolution 135,294]
593. ~generous(fred) <- (28, 39) [subsumption resolution 588,344]
594. $false <- (28, 38, 39) [subsumption resolution 593,341]
595. ~28 | ~38 | ~39 [avatar contradiction clause 594]
600. 28 [avatar split clause 371,293]
601. $false [avatar sat refutation 346,347,565,595,600]
% SZS output end Proof for 7330018524929922096213368
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both patient and strong then someone is not calm and vice versa.
If alice is either brave or not rich then susan is both not tall and not funny.
If someone is not humble or wise then paul is both tall and creative.
Everyone who is either happy or not old is creative.
If paul is either not calm or not humble then someone is not quiet.
Everyone who is not patient or not strong is not quiet.
Everyone who is not happy is not strong or not happy and vice versa.
If someone is happy then someone is funny.
If someone is either calm or generous then someone is quiet.
If fred is rich then alice is not wise.
Everyone who is calm or not happy is happy or quiet and vice versa.
Everyone who is not kind or not generous is both not tall and not old and vice versa.
If someone is both funny and patient then lucy is not rich and vice versa.
Everyone who is creative is quiet or tall and vice versa.
Everyone who is wise or humble is not kind or not happy.
Everyone who is not happy is generous or patient and vice versa.
Someone is either quiet or not kind.
Paul is happy.
Susan is either humble or not humble.
Someone is not calm.
Fred is both not tall and kind. | Paul is strong. | entailment | (((patient(mary)&strong(mary)))<=>(?[X]:(~calm(X))))&
(((brave(alice)<~>~rich(alice)))=>((~tall(susan)&~funny(susan))))&
((?[X]:((~humble(X)|wise(X))))=>((tall(paul)&creative(paul))))&
(![X]:((happy(X)<~>~old(X))=>creative(X)))&
(((~calm(paul)<~>~humble(paul)))=>(?[X]:(~quiet(X))))&
(![X]:((~patient(X)|~strong(X))=>~quiet(X)))&
(![X]:(~happy(X)<=>(~strong(X)|~happy(X))))&
((?[X]:(happy(X)))=>(?[X]:(funny(X))))&
((?[X]:((calm(X)<~>generous(X))))=>(?[X]:(quiet(X))))&
((rich(fred))=>(~wise(alice)))&
(![X]:((calm(X)|~happy(X))<=>(happy(X)|quiet(X))))&
(![X]:((~kind(X)|~generous(X))<=>(~tall(X)&~old(X))))&
((?[X]:((funny(X)&patient(X))))<=>(~rich(lucy)))&
(![X]:(creative(X)<=>(quiet(X)|tall(X))))&
(![X]:((wise(X)|humble(X))=>(~kind(X)|~happy(X))))&
(![X]:(~happy(X)<=>(generous(X)|patient(X))))&
(?[X]:((quiet(X)<~>~kind(X))))&
(happy(paul))&
((humble(susan)<~>~humble(susan)))&
(?[X]:(~calm(X)))&
((~tall(fred)&kind(fred))) | strong(paul) | [
"p6",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8744269750938428207946918
% SZS output start Proof for 8744269750938428207946918
7. ! [X0] : (~happy(X0) <=> (~happy(X0) | ~strong(X0))) [input p6]
18. happy(paul) [input p17]
22. ~strong(paul) [input hypothesis]
50. ! [X0] : ((~happy(X0) | (happy(X0) & strong(X0))) & ((~happy(X0) | ~strong(X0)) | happy(X0))) [nnf transformation 7]
51. ! [X0] : ((~happy(X0) | (happy(X0) & strong(X0))) & (~happy(X0) | ~strong(X0) | happy(X0))) [flattening 50]
91. ~happy(X0) | strong(X0) [cnf transformation 51]
115. happy(paul) [cnf transformation 18]
121. ~strong(paul) [cnf transformation 22]
241. strong(paul) [resolution 91,115]
242. $false [subsumption resolution 241,121]
% SZS output end Proof for 8744269750938428207946918
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not funny then alice is not calm or not brave and vice versa.
Everyone who is brave is patient.
Everyone who is both not wise and quiet is either humble or not generous and vice versa.
Everyone who is both not wise and not rich is curious.
Everyone who is either strong or not happy is both not brave and not generous.
Everyone who is either not kind or not calm is either tall or not rich and vice versa.
Everyone who is both not quiet and humble is both generous and funny and vice versa.
If susan is either not humble or brave then someone is both brave and tall and vice versa.
Everyone who is generous or patient is both not kind and not curious.
Everyone who is not happy is both not generous and brave.
If someone is either not wise or not humble then paul is not tall or not calm and vice versa.
If susan is not patient or not happy then paul is both not patient and rich.
Everyone who is both not creative and patient is not strong and vice versa.
Everyone who is not tall is both not patient and curious and vice versa.
If someone is either humble or kind then someone is both not rich and not generous and vice versa.
If someone is not creative then lucy is either not kind or not patient.
Someone is both not wise and not generous.
Someone is not kind or not old.
Mary is either kind or not rich.
Lucy is either not rich or patient.
Someone is not old.
Someone is brave.
Mary is either old or not wise. | Lucy is not curious. | neutral | ((~funny(john))<=>((~calm(alice)|~brave(alice))))&
(![X]:(brave(X)=>patient(X)))&
(![X]:((~wise(X)&quiet(X))<=>(humble(X)<~>~generous(X))))&
(![X]:((~wise(X)&~rich(X))=>curious(X)))&
(![X]:((strong(X)<~>~happy(X))=>(~brave(X)&~generous(X))))&
(![X]:((~kind(X)<~>~calm(X))<=>(tall(X)<~>~rich(X))))&
(![X]:((~quiet(X)&humble(X))<=>(generous(X)&funny(X))))&
(((~humble(susan)<~>brave(susan)))<=>(?[X]:((brave(X)&tall(X)))))&
(![X]:((generous(X)|patient(X))=>(~kind(X)&~curious(X))))&
(![X]:(~happy(X)=>(~generous(X)&brave(X))))&
((?[X]:((~wise(X)<~>~humble(X))))<=>((~tall(paul)|~calm(paul))))&
(((~patient(susan)|~happy(susan)))=>((~patient(paul)&rich(paul))))&
(![X]:((~creative(X)&patient(X))<=>~strong(X)))&
(![X]:(~tall(X)<=>(~patient(X)&curious(X))))&
((?[X]:((humble(X)<~>kind(X))))<=>(?[X]:((~rich(X)&~generous(X)))))&
((?[X]:(~creative(X)))=>((~kind(lucy)<~>~patient(lucy))))&
(?[X]:((~wise(X)&~generous(X))))&
(?[X]:((~kind(X)|~old(X))))&
((kind(mary)<~>~rich(mary)))&
((~rich(lucy)<~>patient(lucy)))&
(?[X]:(~old(X)))&
(?[X]:(brave(X)))&
((old(mary)<~>~wise(mary))) | ~curious(lucy) | [] | null | 0 |
Everyone who is both not patient and curious is patient and vice versa. Everyone who is both tall and not calm is both not rich and not wise and vice versa. If someone is either not generous or not funny then paul is strong or generous. If someone is strong or funny then someone is both curious and brave. If mary is not kind then paul is either not happy or brave. If someone is either wise or kind then mary is calm. Everyone who is not humble is either not brave or humble. Everyone who is curious is either tall or funny. Everyone who is either curious or not brave is either not quiet or not humble and vice versa. If paul is both not happy and not generous then mary is either kind or not funny and vice versa. Everyone who is not wise or not strong is either not generous or humble. If someone is curious then someone is both creative and patient and vice versa. Everyone who is either not patient or old is either creative or patient and vice versa. Everyone who is either brave or not strong is both not kind and brave and vice versa. Everyone who is wise is kind. Paul is not patient. Paul is either not humble or happy. Mary is both not old and quiet. Someone is not creative or not curious. | Paul is happy. | entailment | (![X]:((~patient(X)&curious(X))<=>patient(X)))&
(![X]:((tall(X)&~calm(X))<=>(~rich(X)&~wise(X))))&
((?[X]:((~generous(X)<~>~funny(X))))=>((strong(paul)|generous(paul))))&
((?[X]:((strong(X)|funny(X))))=>(?[X]:((curious(X)&brave(X)))))&
((~kind(mary))=>((~happy(paul)<~>brave(paul))))&
((?[X]:((wise(X)<~>kind(X))))=>(calm(mary)))&
(![X]:(~humble(X)=>(~brave(X)<~>humble(X))))&
(![X]:(curious(X)=>(tall(X)<~>funny(X))))&
(![X]:((curious(X)<~>~brave(X))<=>(~quiet(X)<~>~humble(X))))&
(((~happy(paul)&~generous(paul)))<=>((kind(mary)<~>~funny(mary))))&
(![X]:((~wise(X)|~strong(X))=>(~generous(X)<~>humble(X))))&
((?[X]:(curious(X)))<=>(?[X]:((creative(X)&patient(X)))))&
(![X]:((~patient(X)<~>old(X))<=>(creative(X)<~>patient(X))))&
(![X]:((brave(X)<~>~strong(X))<=>(~kind(X)&brave(X))))&
(![X]:(wise(X)=>kind(X)))&
(~patient(paul))&
((~humble(paul)<~>happy(paul)))&
((~old(mary)&quiet(mary)))&
(?[X]:((~creative(X)|~curious(X)))) | happy(paul) | [
"p0",
"p3",
"p6",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5878825846912854532681131
% SZS output start Proof for 5878825846912854532681131
1. ! [X0] : ((curious(X0) & ~patient(X0)) <=> patient(X0)) [input p0]
4. ? [X0] : (funny(X0) | strong(X0)) => ? [X0] : (brave(X0) & curious(X0)) [input p3]
7. ! [X0] : (~humble(X0) => (~brave(X0) <~> humble(X0))) [input p6]
14. ! [X0] : ((brave(X0) <~> ~strong(X0)) <=> (brave(X0) & ~kind(X0))) [input p13]
17. ~humble(paul) <~> happy(paul) [input p16]
20. ~happy(paul) [input hypothesis]
21. ? [X0] : (funny(X0) | strong(X0)) => ? [X1] : (brave(X1) & curious(X1)) [rectify 4]
25. ? [X1] : (brave(X1) & curious(X1)) | ! [X0] : (~funny(X0) & ~strong(X0)) [ennf transformation 21]
28. ! [X0] : ((~brave(X0) <~> humble(X0)) | humble(X0)) [ennf transformation 7]
32. ! [X0] : (((curious(X0) & ~patient(X0)) | ~patient(X0)) & (patient(X0) | (~curious(X0) | patient(X0)))) [nnf transformation 1]
33. ! [X0] : (((curious(X0) & ~patient(X0)) | ~patient(X0)) & (patient(X0) | ~curious(X0) | patient(X0))) [flattening 32]
37. ? [X0] : (brave(X0) & curious(X0)) | ! [X1] : (~funny(X1) & ~strong(X1)) [rectify 25]
38. ? [X0] : (brave(X0) & curious(X0)) => (brave(sK0) & curious(sK0)) [choice axiom]
39. (brave(sK0) & curious(sK0)) | ! [X1] : (~funny(X1) & ~strong(X1)) [skolemisation 37,38]
42. ! [X0] : (((~humble(X0) | brave(X0)) & (humble(X0) | ~brave(X0))) | humble(X0)) [nnf transformation 28]
54. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | (~brave(X0) | kind(X0))) & ((brave(X0) & ~kind(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [nnf transformation 14]
55. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | ~brave(X0) | kind(X0)) & ((brave(X0) & ~kind(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [flattening 54]
56. (~happy(paul) | humble(paul)) & (happy(paul) | ~humble(paul)) [nnf transformation 17]
59. patient(X0) | ~curious(X0) | patient(X0) [cnf transformation 33]
60. ~patient(X0) | ~patient(X0) [cnf transformation 33]
68. curious(sK0) | ~strong(X1) [cnf transformation 39]
76. humble(X0) | ~brave(X0) | humble(X0) [cnf transformation 42]
112. brave(X0) | brave(X0) | strong(X0) [cnf transformation 55]
117. happy(paul) | ~humble(paul) [cnf transformation 56]
122. ~happy(paul) [cnf transformation 20]
123. brave(X0) | strong(X0) [duplicate literal removal 112]
129. ~brave(X0) | humble(X0) [duplicate literal removal 76]
130. patient(X0) | ~curious(X0) [duplicate literal removal 59]
131. ~patient(X0) [duplicate literal removal 60]
132. ~curious(X0) [subsumption resolution 130,131]
158. 7 <=> ! [X1] : ~strong(X1) [avatar definition]
159. ~strong(X1) <- (7) [avatar component clause 158]
163. ~strong(X1) [subsumption resolution 68,132]
164. 7 [avatar split clause 163,158]
170. 9 <=> happy(paul) [avatar definition]
210. 15 <=> humble(paul) [avatar definition]
211. ~humble(paul) <- (~15) [avatar component clause 210]
214. ~15 | 9 [avatar split clause 117,170,210]
215. ~9 [avatar split clause 122,170]
221. humble(X0) | strong(X0) [resolution 129,123]
223. humble(X0) <- (7) [subsumption resolution 221,159]
224. $false <- (7, ~15) [resolution 223,211]
225. ~7 | 15 [avatar contradiction clause 224]
226. $false [avatar sat refutation 164,214,215,225]
% SZS output end Proof for 5878825846912854532681131
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is both not tall and not quiet and vice versa. If someone is quiet then paul is funny and vice versa. Everyone who is creative or strong is both not kind and not curious. If paul is not quiet then paul is either not wise or old and vice versa. Everyone who is patient is either brave or not humble and vice versa. If john is both brave and humble then someone is not strong or not creative. If fred is not kind then mary is funny or not funny and vice versa. Everyone who is both not old and not kind is not patient or tall and vice versa. If someone is humble or not happy then someone is rich. If someone is not generous then someone is not funny and vice versa. If someone is either not brave or not old then someone is not strong or kind and vice versa. Everyone who is strong is tall or humble. Everyone who is both not generous and tall is generous or quiet and vice versa. Everyone who is not humble is happy or not funny and vice versa. Everyone who is both not kind and rich is not calm and vice versa. Everyone who is humble is humble or happy. Someone is either creative or not strong. Someone is either funny or kind. Someone is not old. Someone is both not rich and tall. Someone is creative. | John is curious. | neutral | (![X]:(~humble(X)<=>(~tall(X)&~quiet(X))))&
((?[X]:(quiet(X)))<=>(funny(paul)))&
(![X]:((creative(X)|strong(X))=>(~kind(X)&~curious(X))))&
((~quiet(paul))<=>((~wise(paul)<~>old(paul))))&
(![X]:(patient(X)<=>(brave(X)<~>~humble(X))))&
(((brave(john)&humble(john)))=>(?[X]:((~strong(X)|~creative(X)))))&
((~kind(fred))<=>((funny(mary)|~funny(mary))))&
(![X]:((~old(X)&~kind(X))<=>(~patient(X)|tall(X))))&
((?[X]:((humble(X)|~happy(X))))=>(?[X]:(rich(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(~funny(X))))&
((?[X]:((~brave(X)<~>~old(X))))<=>(?[X]:((~strong(X)|kind(X)))))&
(![X]:(strong(X)=>(tall(X)|humble(X))))&
(![X]:((~generous(X)&tall(X))<=>(generous(X)|quiet(X))))&
(![X]:(~humble(X)<=>(happy(X)|~funny(X))))&
(![X]:((~kind(X)&rich(X))<=>~calm(X)))&
(![X]:(humble(X)=>(humble(X)|happy(X))))&
(?[X]:((creative(X)<~>~strong(X))))&
(?[X]:((funny(X)<~>kind(X))))&
(?[X]:(~old(X)))&
(?[X]:((~rich(X)&tall(X))))&
(?[X]:(creative(X))) | curious(john) | [] | null | 0 |
If alice is both not brave and not kind then fred is generous or strong and vice versa.
Everyone who is either not humble or not patient is either not creative or not humble.
Everyone who is not tall is curious or quiet.
Everyone who is not creative or humble is kind or not humble.
If someone is generous or brave then john is calm or not funny and vice versa.
Everyone who is both not wise and happy is creative.
Everyone who is both wise and happy is both humble and not rich and vice versa.
Everyone who is either rich or calm is either patient or not kind.
If susan is both funny and generous then alice is both not patient and not creative.
Everyone who is either humble or curious is both generous and not funny.
Everyone who is happy is both strong and happy.
Everyone who is quiet is not rich or humble and vice versa.
If john is not kind then someone is not calm and vice versa.
If john is rich or strong then john is brave or not strong and vice versa.
If someone is wise or rich then fred is kind and vice versa.
If susan is both wise and generous then someone is quiet or funny and vice versa.
Alice is not brave.
Paul is rich.
Susan is quiet or not kind.
Alice is not kind or humble.
John is both patient and not happy.
Fred is not curious or curious.
Alice is not calm or tall. | Alice is not quiet. | neutral | (((~brave(alice)&~kind(alice)))<=>((generous(fred)|strong(fred))))&
(![X]:((~humble(X)<~>~patient(X))=>(~creative(X)<~>~humble(X))))&
(![X]:(~tall(X)=>(curious(X)|quiet(X))))&
(![X]:((~creative(X)|humble(X))=>(kind(X)|~humble(X))))&
((?[X]:((generous(X)|brave(X))))<=>((calm(john)|~funny(john))))&
(![X]:((~wise(X)&happy(X))=>creative(X)))&
(![X]:((wise(X)&happy(X))<=>(humble(X)&~rich(X))))&
(![X]:((rich(X)<~>calm(X))=>(patient(X)<~>~kind(X))))&
(((funny(susan)&generous(susan)))=>((~patient(alice)&~creative(alice))))&
(![X]:((humble(X)<~>curious(X))=>(generous(X)&~funny(X))))&
(![X]:(happy(X)=>(strong(X)&happy(X))))&
(![X]:(quiet(X)<=>(~rich(X)|humble(X))))&
((~kind(john))<=>(?[X]:(~calm(X))))&
(((rich(john)|strong(john)))<=>((brave(john)|~strong(john))))&
((?[X]:((wise(X)|rich(X))))<=>(kind(fred)))&
(((wise(susan)&generous(susan)))<=>(?[X]:((quiet(X)|funny(X)))))&
(~brave(alice))&
(rich(paul))&
((quiet(susan)|~kind(susan)))&
((~kind(alice)|humble(alice)))&
((patient(john)&~happy(john)))&
((~curious(fred)|curious(fred)))&
((~calm(alice)|tall(alice))) | ~quiet(alice) | [] | null | 0 |
Everyone who is both creative and rich is creative or strong and vice versa.
If someone is either rich or happy then someone is both not funny and not curious and vice versa.
If someone is either not humble or not generous then someone is either brave or strong.
Everyone who is not rich or brave is both not tall and strong.
If mary is both brave and not creative then someone is funny or not quiet and vice versa.
Everyone who is either creative or old is both not patient and not kind and vice versa.
Everyone who is either not curious or generous is not rich or humble.
Everyone who is either not strong or not patient is humble.
Everyone who is not brave is not rich.
If mary is both not wise and curious then someone is either calm or not tall and vice versa.
If someone is not old or not quiet then lucy is both not rich and creative and vice versa.
Everyone who is both not humble and wise is not generous.
Everyone who is both not funny and not kind is curious or patient and vice versa.
Everyone who is either not wise or calm is not curious or not brave.
Everyone who is either not old or not quiet is both humble and strong and vice versa.
Paul is both not funny and not kind.
Someone is either kind or not wise.
Someone is not calm. | Lucy is not kind. | entailment | (![X]:((creative(X)&rich(X))<=>(creative(X)|strong(X))))&
((?[X]:((rich(X)<~>happy(X))))<=>(?[X]:((~funny(X)&~curious(X)))))&
((?[X]:((~humble(X)<~>~generous(X))))=>(?[X]:((brave(X)<~>strong(X)))))&
(![X]:((~rich(X)|brave(X))=>(~tall(X)&strong(X))))&
(((brave(mary)&~creative(mary)))<=>(?[X]:((funny(X)|~quiet(X)))))&
(![X]:((creative(X)<~>old(X))<=>(~patient(X)&~kind(X))))&
(![X]:((~curious(X)<~>generous(X))=>(~rich(X)|humble(X))))&
(![X]:((~strong(X)<~>~patient(X))=>humble(X)))&
(![X]:(~brave(X)=>~rich(X)))&
(((~wise(mary)&curious(mary)))<=>(?[X]:((calm(X)<~>~tall(X)))))&
((?[X]:((~old(X)|~quiet(X))))<=>((~rich(lucy)&creative(lucy))))&
(![X]:((~humble(X)&wise(X))=>~generous(X)))&
(![X]:((~funny(X)&~kind(X))<=>(curious(X)|patient(X))))&
(![X]:((~wise(X)<~>calm(X))=>(~curious(X)|~brave(X))))&
(![X]:((~old(X)<~>~quiet(X))<=>(humble(X)&strong(X))))&
((~funny(paul)&~kind(paul)))&
(?[X]:((kind(X)<~>~wise(X))))&
(?[X]:(~calm(X))) | ~kind(lucy) | [
"p0",
"p3",
"p7",
"p8",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1348839424811647926866504
% SZS output start Proof for 1348839424811647926866504
1. ! [X0] : ((rich(X0) & creative(X0)) <=> (strong(X0) | creative(X0))) [input p0]
4. ! [X0] : ((brave(X0) | ~rich(X0)) => (strong(X0) & ~tall(X0))) [input p3]
8. ! [X0] : ((~strong(X0) <~> ~patient(X0)) => humble(X0)) [input p7]
9. ! [X0] : (~brave(X0) => ~rich(X0)) [input p8]
11. ? [X0] : (~quiet(X0) | ~old(X0)) <=> (creative(lucy) & ~rich(lucy)) [input p10]
13. ! [X0] : ((~kind(X0) & ~funny(X0)) <=> (patient(X0) | curious(X0))) [input p12]
15. ! [X0] : ((~old(X0) <~> ~quiet(X0)) <=> (strong(X0) & humble(X0))) [input p14]
19. kind(lucy) [input hypothesis]
23. ! [X0] : ((strong(X0) & ~tall(X0)) | (~brave(X0) & rich(X0))) [ennf transformation 4]
26. ! [X0] : (humble(X0) | (~strong(X0) <=> ~patient(X0))) [ennf transformation 8]
27. ! [X0] : (~rich(X0) | brave(X0)) [ennf transformation 9]
32. ! [X0] : (((rich(X0) & creative(X0)) | (~strong(X0) & ~creative(X0))) & ((strong(X0) | creative(X0)) | (~rich(X0) | ~creative(X0)))) [nnf transformation 1]
33. ! [X0] : (((rich(X0) & creative(X0)) | (~strong(X0) & ~creative(X0))) & (strong(X0) | creative(X0) | ~rich(X0) | ~creative(X0))) [flattening 32]
51. ! [X0] : (humble(X0) | ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) [nnf transformation 26]
57. (? [X0] : (~quiet(X0) | ~old(X0)) | (~creative(lucy) | rich(lucy))) & ((creative(lucy) & ~rich(lucy)) | ! [X0] : (quiet(X0) & old(X0))) [nnf transformation 11]
58. (? [X0] : (~quiet(X0) | ~old(X0)) | ~creative(lucy) | rich(lucy)) & ((creative(lucy) & ~rich(lucy)) | ! [X0] : (quiet(X0) & old(X0))) [flattening 57]
59. (? [X0] : (~quiet(X0) | ~old(X0)) | ~creative(lucy) | rich(lucy)) & ((creative(lucy) & ~rich(lucy)) | ! [X1] : (quiet(X1) & old(X1))) [rectify 58]
60. ? [X0] : (~quiet(X0) | ~old(X0)) => (~quiet(sK5) | ~old(sK5)) [choice axiom]
61. ((~quiet(sK5) | ~old(sK5)) | ~creative(lucy) | rich(lucy)) & ((creative(lucy) & ~rich(lucy)) | ! [X1] : (quiet(X1) & old(X1))) [skolemisation 59,60]
62. ! [X0] : (((~kind(X0) & ~funny(X0)) | (~patient(X0) & ~curious(X0))) & ((patient(X0) | curious(X0)) | (kind(X0) | funny(X0)))) [nnf transformation 13]
63. ! [X0] : (((~kind(X0) & ~funny(X0)) | (~patient(X0) & ~curious(X0))) & (patient(X0) | curious(X0) | kind(X0) | funny(X0))) [flattening 62]
65. ! [X0] : ((((quiet(X0) | old(X0)) & (~quiet(X0) | ~old(X0))) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | ((~old(X0) | quiet(X0)) & (~quiet(X0) | old(X0))))) [nnf transformation 15]
66. ! [X0] : ((((quiet(X0) | old(X0)) & (~quiet(X0) | ~old(X0))) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | ((~old(X0) | quiet(X0)) & (~quiet(X0) | old(X0))))) [flattening 65]
76. ~strong(X0) | rich(X0) [cnf transformation 33]
89. strong(X0) | rich(X0) [cnf transformation 23]
90. ~brave(X0) | strong(X0) [cnf transformation 23]
105. ~strong(X0) | humble(X0) | patient(X0) [cnf transformation 51]
106. ~rich(X0) | brave(X0) [cnf transformation 27]
113. ~rich(lucy) | old(X1) [cnf transformation 61]
114. ~rich(lucy) | quiet(X1) [cnf transformation 61]
123. ~kind(X0) | ~patient(X0) [cnf transformation 63]
130. ~old(X0) | ~quiet(X0) | ~strong(X0) | ~humble(X0) [cnf transformation 66]
137. kind(lucy) [cnf transformation 19]
187. rich(X0) [subsumption resolution 89,76]
189. 12 <=> ! [X0] : quiet(X0) [avatar definition]
190. quiet(X0) <- (12) [avatar component clause 189]
217. brave(X0) [subsumption resolution 106,187]
252. 25 <=> ! [X1] : old(X1) [avatar definition]
253. old(X1) <- (25) [avatar component clause 252]
255. quiet(X1) [subsumption resolution 114,187]
256. 12 [avatar split clause 255,189]
257. old(X1) [subsumption resolution 113,187]
258. 25 [avatar split clause 257,252]
276. strong(X0) [resolution 90,217]
286. ~patient(lucy) [resolution 123,137]
289. patient(X0) | humble(X0) [resolution 105,276]
294. humble(lucy) [resolution 289,286]
339. ~quiet(X0) | ~strong(X0) | ~humble(X0) <- (25) [resolution 130,253]
340. ~strong(X0) | ~humble(X0) <- (12, 25) [subsumption resolution 339,190]
341. ~humble(X0) <- (12, 25) [subsumption resolution 340,276]
342. $false <- (12, 25) [resolution 341,294]
344. ~12 | ~25 [avatar contradiction clause 342]
345. $false [avatar sat refutation 256,258,344]
% SZS output end Proof for 1348839424811647926866504
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is either not wise or not rich.
Everyone who is not kind is generous.
Everyone who is either old or rich is tall and vice versa.
If paul is either brave or funny then someone is either old or not kind.
Everyone who is not kind or humble is both rich and not creative and vice versa.
Everyone who is either not tall or not creative is brave and vice versa.
Everyone who is not tall or wise is not quiet or generous and vice versa.
If john is funny then someone is not quiet.
If alice is not calm or patient then paul is old.
Everyone who is not wise is not funny.
Everyone who is not calm or not tall is both not wise and tall and vice versa.
Everyone who is kind or generous is not patient or humble and vice versa.
If someone is wise then someone is wise or quiet.
If someone is either rich or not rich then someone is both patient and rich.
Everyone who is both quiet and strong is not brave.
If someone is not old then paul is either not old or not patient and vice versa.
Alice is not patient or not wise.
Alice is either funny or not kind.
John is not patient or not happy.
Paul is funny.
Someone is either not rich or not calm.
Someone is either not brave or curious.
Alice is not rich. | Alice is not wise. | contradiction | (![X]:(~quiet(X)=>(~wise(X)<~>~rich(X))))&
(![X]:(~kind(X)=>generous(X)))&
(![X]:((old(X)<~>rich(X))<=>tall(X)))&
(((brave(paul)<~>funny(paul)))=>(?[X]:((old(X)<~>~kind(X)))))&
(![X]:((~kind(X)|humble(X))<=>(rich(X)&~creative(X))))&
(![X]:((~tall(X)<~>~creative(X))<=>brave(X)))&
(![X]:((~tall(X)|wise(X))<=>(~quiet(X)|generous(X))))&
((funny(john))=>(?[X]:(~quiet(X))))&
(((~calm(alice)|patient(alice)))=>(old(paul)))&
(![X]:(~wise(X)=>~funny(X)))&
(![X]:((~calm(X)|~tall(X))<=>(~wise(X)&tall(X))))&
(![X]:((kind(X)|generous(X))<=>(~patient(X)|humble(X))))&
((?[X]:(wise(X)))=>(?[X]:((wise(X)|quiet(X)))))&
((?[X]:((rich(X)<~>~rich(X))))=>(?[X]:((patient(X)&rich(X)))))&
(![X]:((quiet(X)&strong(X))=>~brave(X)))&
((?[X]:(~old(X)))<=>((~old(paul)<~>~patient(paul))))&
((~patient(alice)|~wise(alice)))&
((funny(alice)<~>~kind(alice)))&
((~patient(john)|~happy(john)))&
(funny(paul))&
(?[X]:((~rich(X)<~>~calm(X))))&
(?[X]:((~brave(X)<~>curious(X))))&
(~rich(alice)) | ~wise(alice) | [
"p4",
"p9",
"p17",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8719131924960572212401380
% SZS output start Proof for 8719131924960572212401380
5. ! [X0] : ((humble(X0) | ~kind(X0)) <=> (~creative(X0) & rich(X0))) [input p4]
10. ! [X0] : (~wise(X0) => ~funny(X0)) [input p9]
18. funny(alice) <~> ~kind(alice) [input p17]
23. ~rich(alice) [input p22]
24. ~wise(alice) [input hypothesis]
34. ! [X0] : (~funny(X0) | wise(X0)) [ennf transformation 10]
42. ! [X0] : (((humble(X0) | ~kind(X0)) | (creative(X0) | ~rich(X0))) & ((~creative(X0) & rich(X0)) | (~humble(X0) & kind(X0)))) [nnf transformation 5]
43. ! [X0] : ((humble(X0) | ~kind(X0) | creative(X0) | ~rich(X0)) & ((~creative(X0) & rich(X0)) | (~humble(X0) & kind(X0)))) [flattening 42]
64. (kind(alice) | ~funny(alice)) & (~kind(alice) | funny(alice)) [nnf transformation 18]
82. kind(X0) | rich(X0) [cnf transformation 43]
98. ~funny(X0) | wise(X0) [cnf transformation 34]
118. ~kind(alice) | funny(alice) [cnf transformation 64]
125. ~rich(alice) [cnf transformation 23]
126. ~wise(alice) [cnf transformation 24]
222. 20 <=> wise(alice) [avatar definition]
224. ~wise(alice) <- (~20) [avatar component clause 222]
227. 21 <=> funny(alice) [avatar definition]
228. funny(alice) <- (21) [avatar component clause 227]
231. 22 <=> kind(alice) [avatar definition]
232. ~kind(alice) <- (~22) [avatar component clause 231]
235. 21 | ~22 [avatar split clause 118,231,227]
257. ~20 [avatar split clause 126,222]
263. rich(alice) <- (~22) [resolution 82,232]
264. $false <- (~22) [subsumption resolution 263,125]
265. 22 [avatar contradiction clause 264]
267. wise(alice) <- (21) [resolution 98,228]
270. $false <- (~20, 21) [subsumption resolution 267,224]
271. 20 | ~21 [avatar contradiction clause 270]
272. $false [avatar sat refutation 235,257,265,271]
% SZS output end Proof for 8719131924960572212401380
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or kind is both creative and kind and vice versa.
Everyone who is both not curious and old is either not creative or creative and vice versa.
Everyone who is wise is either kind or not rich.
If someone is either not strong or old then paul is either not old or not wise.
If alice is both not rich and tall then someone is not humble.
Everyone who is brave is patient and vice versa.
Everyone who is either patient or not strong is both not calm and brave and vice versa.
Everyone who is not strong is kind or not calm and vice versa.
If susan is old or not tall then someone is quiet.
If someone is both quiet and happy then fred is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
If someone is both brave and curious then susan is not humble or curious and vice versa.
Everyone who is generous is generous or not kind and vice versa.
John is kind.
Susan is not funny or funny.
Susan is either not generous or rich.
Someone is either not calm or not quiet.
Fred is either rich or curious. | John is not happy. | neutral | (![X]:((~wise(X)<~>kind(X))<=>(creative(X)&kind(X))))&
(![X]:((~curious(X)&old(X))<=>(~creative(X)<~>creative(X))))&
(![X]:(wise(X)=>(kind(X)<~>~rich(X))))&
((?[X]:((~strong(X)<~>old(X))))=>((~old(paul)<~>~wise(paul))))&
(((~rich(alice)&tall(alice)))=>(?[X]:(~humble(X))))&
(![X]:(brave(X)<=>patient(X)))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
((?[X]:((brave(X)&curious(X))))<=>((~humble(susan)|curious(susan))))&
(![X]:(generous(X)<=>(generous(X)|~kind(X))))&
(kind(john))&
((~funny(susan)|funny(susan)))&
((~generous(susan)<~>rich(susan)))&
(?[X]:((~calm(X)<~>~quiet(X))))&
((rich(fred)<~>curious(fred))) | ~happy(john) | [] | null | 0 |
Everyone who is not rich or funny is both not patient and not calm.
Everyone who is either strong or calm is not brave.
If someone is both quiet and old then someone is either humble or wise and vice versa.
Everyone who is not kind or not humble is not funny or not wise and vice versa.
If someone is generous or not humble then someone is brave.
If someone is either funny or generous then fred is both wise and not strong and vice versa.
Everyone who is both strong and not quiet is tall and vice versa.
Everyone who is not patient is either happy or not rich and vice versa.
If alice is not generous or funny then someone is either not curious or not rich and vice versa.
Everyone who is not generous is not curious.
If someone is rich then someone is either strong or patient and vice versa.
Everyone who is both not generous and not creative is quiet or not tall and vice versa.
If lucy is old or wise then someone is brave or funny.
Everyone who is strong is not tall or not strong and vice versa.
If someone is funny or old then fred is either not wise or not funny.
Everyone who is both not old and happy is patient.
Susan is humble.
Someone is either rich or quiet.
Someone is not tall or calm.
John is patient or happy. | Fred is not old. | neutral | (![X]:((~rich(X)|funny(X))=>(~patient(X)&~calm(X))))&
(![X]:((strong(X)<~>calm(X))=>~brave(X)))&
((?[X]:((quiet(X)&old(X))))<=>(?[X]:((humble(X)<~>wise(X)))))&
(![X]:((~kind(X)|~humble(X))<=>(~funny(X)|~wise(X))))&
((?[X]:((generous(X)|~humble(X))))=>(?[X]:(brave(X))))&
((?[X]:((funny(X)<~>generous(X))))<=>((wise(fred)&~strong(fred))))&
(![X]:((strong(X)&~quiet(X))<=>tall(X)))&
(![X]:(~patient(X)<=>(happy(X)<~>~rich(X))))&
(((~generous(alice)|funny(alice)))<=>(?[X]:((~curious(X)<~>~rich(X)))))&
(![X]:(~generous(X)=>~curious(X)))&
((?[X]:(rich(X)))<=>(?[X]:((strong(X)<~>patient(X)))))&
(![X]:((~generous(X)&~creative(X))<=>(quiet(X)|~tall(X))))&
(((old(lucy)|wise(lucy)))=>(?[X]:((brave(X)|funny(X)))))&
(![X]:(strong(X)<=>(~tall(X)|~strong(X))))&
((?[X]:((funny(X)|old(X))))=>((~wise(fred)<~>~funny(fred))))&
(![X]:((~old(X)&happy(X))=>patient(X)))&
(humble(susan))&
(?[X]:((rich(X)<~>quiet(X))))&
(?[X]:((~tall(X)|calm(X))))&
((patient(john)|happy(john))) | ~old(fred) | [] | null | 0 |
Everyone who is brave is both kind and not patient and vice versa.
If paul is either wise or curious then mary is brave or not calm.
Everyone who is either old or funny is not happy or not generous and vice versa.
Everyone who is kind or not calm is either wise or not humble and vice versa.
Everyone who is both brave and humble is not patient or curious.
Everyone who is both not patient and creative is either humble or rich.
Everyone who is not wise or kind is happy or brave.
Everyone who is not curious is kind.
Everyone who is brave or not rich is both not patient and funny.
Everyone who is kind is either not strong or tall and vice versa.
Everyone who is either not humble or not rich is both not funny and old and vice versa.
Everyone who is not quiet or kind is both old and humble and vice versa.
If someone is either wise or not strong then someone is happy and vice versa.
Everyone who is not creative or kind is either not brave or not calm.
Everyone who is both not brave and quiet is not quiet or curious.
Everyone who is not curious or calm is not brave.
Someone is funny or not strong.
Someone is patient or brave.
Fred is both funny and humble.
Someone is both quiet and strong.
Fred is kind or not kind.
John is kind.
Someone is happy or not brave.
Mary is quiet. | John is not happy. | contradiction | (![X]:(brave(X)<=>(kind(X)&~patient(X))))&
(((wise(paul)<~>curious(paul)))=>((brave(mary)|~calm(mary))))&
(![X]:((old(X)<~>funny(X))<=>(~happy(X)|~generous(X))))&
(![X]:((kind(X)|~calm(X))<=>(wise(X)<~>~humble(X))))&
(![X]:((brave(X)&humble(X))=>(~patient(X)|curious(X))))&
(![X]:((~patient(X)&creative(X))=>(humble(X)<~>rich(X))))&
(![X]:((~wise(X)|kind(X))=>(happy(X)|brave(X))))&
(![X]:(~curious(X)=>kind(X)))&
(![X]:((brave(X)|~rich(X))=>(~patient(X)&funny(X))))&
(![X]:(kind(X)<=>(~strong(X)<~>tall(X))))&
(![X]:((~humble(X)<~>~rich(X))<=>(~funny(X)&old(X))))&
(![X]:((~quiet(X)|kind(X))<=>(old(X)&humble(X))))&
((?[X]:((wise(X)<~>~strong(X))))<=>(?[X]:(happy(X))))&
(![X]:((~creative(X)|kind(X))=>(~brave(X)<~>~calm(X))))&
(![X]:((~brave(X)&quiet(X))=>(~quiet(X)|curious(X))))&
(![X]:((~curious(X)|calm(X))=>~brave(X)))&
(?[X]:((funny(X)|~strong(X))))&
(?[X]:((patient(X)|brave(X))))&
((funny(fred)&humble(fred)))&
(?[X]:((quiet(X)&strong(X))))&
((kind(fred)|~kind(fred)))&
(kind(john))&
(?[X]:((happy(X)|~brave(X))))&
(quiet(mary)) | ~happy(john) | [
"p2",
"p6",
"p8",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1774990343150961770327856
% SZS output start Proof for 1774990343150961770327856
3. ! [X0] : ((old(X0) <~> funny(X0)) <=> (~generous(X0) | ~happy(X0))) [input p2]
7. ! [X0] : ((kind(X0) | ~wise(X0)) => (brave(X0) | happy(X0))) [input p6]
9. ! [X0] : ((~rich(X0) | brave(X0)) => (funny(X0) & ~patient(X0))) [input p8]
12. ! [X0] : ((kind(X0) | ~quiet(X0)) <=> (humble(X0) & old(X0))) [input p11]
22. kind(john) [input p21]
25. ~happy(john) [input hypothesis]
33. ! [X0] : ((brave(X0) | happy(X0)) | (~kind(X0) & wise(X0))) [ennf transformation 7]
34. ! [X0] : (brave(X0) | happy(X0) | (~kind(X0) & wise(X0))) [flattening 33]
36. ! [X0] : ((funny(X0) & ~patient(X0)) | (rich(X0) & ~brave(X0))) [ennf transformation 9]
44. ! [X0] : ((((~funny(X0) | ~old(X0)) & (funny(X0) | old(X0))) | (generous(X0) & happy(X0))) & ((~generous(X0) | ~happy(X0)) | ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0))))) [nnf transformation 3]
45. ! [X0] : ((((~funny(X0) | ~old(X0)) & (funny(X0) | old(X0))) | (generous(X0) & happy(X0))) & (~generous(X0) | ~happy(X0) | ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0))))) [flattening 44]
52. ! [X0] : (((kind(X0) | ~quiet(X0)) | (~humble(X0) | ~old(X0))) & ((humble(X0) & old(X0)) | (~kind(X0) & quiet(X0)))) [nnf transformation 12]
53. ! [X0] : ((kind(X0) | ~quiet(X0) | ~humble(X0) | ~old(X0)) & ((humble(X0) & old(X0)) | (~kind(X0) & quiet(X0)))) [flattening 52]
77. ~funny(X0) | ~old(X0) | happy(X0) [cnf transformation 45]
89. ~kind(X0) | happy(X0) | brave(X0) [cnf transformation 34]
93. ~brave(X0) | funny(X0) [cnf transformation 36]
106. ~kind(X0) | old(X0) [cnf transformation 53]
128. kind(john) [cnf transformation 22]
131. ~happy(john) [cnf transformation 25]
209. old(john) [resolution 106,128]
215. 17 <=> brave(john) [avatar definition]
216. ~brave(john) <- (~17) [avatar component clause 215]
217. brave(john) <- (17) [avatar component clause 215]
224. funny(john) <- (17) [resolution 217,93]
228. ~old(john) | happy(john) <- (17) [resolution 77,224]
238. happy(john) <- (17) [subsumption resolution 228,209]
239. $false <- (17) [subsumption resolution 238,131]
240. ~17 [avatar contradiction clause 239]
268. happy(john) | brave(john) [resolution 89,128]
269. brave(john) [subsumption resolution 268,131]
270. $false <- (~17) [subsumption resolution 269,216]
271. 17 [avatar contradiction clause 270]
272. $false [avatar sat refutation 240,271]
% SZS output end Proof for 1774990343150961770327856
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If paul is brave then lucy is not rich or not old and vice versa.
If alice is both not patient and not brave then someone is both happy and curious and vice versa.
If someone is not kind then lucy is either humble or not curious and vice versa.
Everyone who is not happy is rich and vice versa.
If someone is either funny or not wise then someone is either generous or not funny and vice versa.
Everyone who is either generous or not strong is rich.
If paul is happy or tall then someone is kind or quiet.
Everyone who is tall or not rich is both not old and not curious.
Everyone who is either brave or not patient is either not old or not humble and vice versa.
Everyone who is not generous is not creative or wise and vice versa.
If someone is generous or not brave then lucy is not rich.
Everyone who is funny or not old is either curious or not creative.
If mary is either patient or not happy then mary is not rich or tall.
If fred is brave then someone is either kind or not happy and vice versa.
If someone is not curious or not generous then lucy is both not old and funny and vice versa.
Everyone who is humble is both not patient and not humble and vice versa.
Paul is either humble or rich.
John is funny.
Susan is both not old and curious.
John is creative.
Someone is not patient or not curious.
Paul is not funny. | Paul is not happy. | entailment | ((brave(paul))<=>((~rich(lucy)|~old(lucy))))&
(((~patient(alice)&~brave(alice)))<=>(?[X]:((happy(X)&curious(X)))))&
((?[X]:(~kind(X)))<=>((humble(lucy)<~>~curious(lucy))))&
(![X]:(~happy(X)<=>rich(X)))&
((?[X]:((funny(X)<~>~wise(X))))<=>(?[X]:((generous(X)<~>~funny(X)))))&
(![X]:((generous(X)<~>~strong(X))=>rich(X)))&
(((happy(paul)|tall(paul)))=>(?[X]:((kind(X)|quiet(X)))))&
(![X]:((tall(X)|~rich(X))=>(~old(X)&~curious(X))))&
(![X]:((brave(X)<~>~patient(X))<=>(~old(X)<~>~humble(X))))&
(![X]:(~generous(X)<=>(~creative(X)|wise(X))))&
((?[X]:((generous(X)|~brave(X))))=>(~rich(lucy)))&
(![X]:((funny(X)|~old(X))=>(curious(X)<~>~creative(X))))&
(((patient(mary)<~>~happy(mary)))=>((~rich(mary)|tall(mary))))&
((brave(fred))<=>(?[X]:((kind(X)<~>~happy(X)))))&
((?[X]:((~curious(X)|~generous(X))))<=>((~old(lucy)&funny(lucy))))&
(![X]:(humble(X)<=>(~patient(X)&~humble(X))))&
((humble(paul)<~>rich(paul)))&
(funny(john))&
((~old(susan)&curious(susan)))&
(creative(john))&
(?[X]:((~patient(X)|~curious(X))))&
(~funny(paul)) | ~happy(paul) | [
"p3",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4904200960396972528619591
% SZS output start Proof for 4904200960396972528619591
4. ! [X0] : (~happy(X0) <=> rich(X0)) [input p3]
16. ! [X0] : (humble(X0) <=> (~humble(X0) & ~patient(X0))) [input p15]
17. humble(paul) <~> rich(paul) [input p16]
23. happy(paul) [input hypothesis]
43. ! [X0] : ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))) [nnf transformation 4]
64. ! [X0] : ((humble(X0) | (humble(X0) | patient(X0))) & ((~humble(X0) & ~patient(X0)) | ~humble(X0))) [nnf transformation 16]
65. ! [X0] : ((humble(X0) | humble(X0) | patient(X0)) & ((~humble(X0) & ~patient(X0)) | ~humble(X0))) [flattening 64]
66. (~rich(paul) | ~humble(paul)) & (rich(paul) | humble(paul)) [nnf transformation 17]
81. ~happy(X0) | ~rich(X0) [cnf transformation 43]
125. ~humble(X0) | ~humble(X0) [cnf transformation 65]
127. rich(paul) | humble(paul) [cnf transformation 66]
135. happy(paul) [cnf transformation 23]
136. ~humble(X0) [duplicate literal removal 125]
298. rich(paul) [subsumption resolution 127,136]
309. ~rich(paul) [resolution 81,135]
311. $false [subsumption resolution 309,298]
% SZS output end Proof for 4904200960396972528619591
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old and not strong then someone is either curious or not tall and vice versa. Everyone who is not kind or creative is either not calm or old and vice versa. If john is tall or not rich then fred is rich. Everyone who is either wise or brave is both not curious and rich and vice versa. Everyone who is funny or not wise is quiet or creative. Everyone who is kind is either not old or calm and vice versa. Everyone who is either not patient or brave is funny. If fred is not strong then someone is either not quiet or curious and vice versa. Everyone who is both not rich and not old is kind or not humble. If susan is either funny or happy then alice is not creative or not strong. Everyone who is either not generous or funny is either not wise or old and vice versa. If someone is both tall and not curious then someone is both not wise and not creative. Everyone who is either not wise or humble is not funny. If alice is rich or not rich then lucy is not brave or old. If lucy is both not creative and calm then lucy is either not kind or not funny. If someone is kind then john is not patient or patient and vice versa. Someone is both not tall and kind. Lucy is both wise and quiet. Someone is not curious or patient. Someone is either not generous or wise. Mary is either not generous or not quiet. Someone is both patient and kind. John is both rich and not happy. | Mary is generous. | neutral | ((?[X]:((~old(X)&~strong(X))))<=>(?[X]:((curious(X)<~>~tall(X)))))&
(![X]:((~kind(X)|creative(X))<=>(~calm(X)<~>old(X))))&
(((tall(john)|~rich(john)))=>(rich(fred)))&
(![X]:((wise(X)<~>brave(X))<=>(~curious(X)&rich(X))))&
(![X]:((funny(X)|~wise(X))=>(quiet(X)|creative(X))))&
(![X]:(kind(X)<=>(~old(X)<~>calm(X))))&
(![X]:((~patient(X)<~>brave(X))=>funny(X)))&
((~strong(fred))<=>(?[X]:((~quiet(X)<~>curious(X)))))&
(![X]:((~rich(X)&~old(X))=>(kind(X)|~humble(X))))&
(((funny(susan)<~>happy(susan)))=>((~creative(alice)|~strong(alice))))&
(![X]:((~generous(X)<~>funny(X))<=>(~wise(X)<~>old(X))))&
((?[X]:((tall(X)&~curious(X))))=>(?[X]:((~wise(X)&~creative(X)))))&
(![X]:((~wise(X)<~>humble(X))=>~funny(X)))&
(((rich(alice)|~rich(alice)))=>((~brave(lucy)|old(lucy))))&
(((~creative(lucy)&calm(lucy)))=>((~kind(lucy)<~>~funny(lucy))))&
((?[X]:(kind(X)))<=>((~patient(john)|patient(john))))&
(?[X]:((~tall(X)&kind(X))))&
((wise(lucy)&quiet(lucy)))&
(?[X]:((~curious(X)|patient(X))))&
(?[X]:((~generous(X)<~>wise(X))))&
((~generous(mary)<~>~quiet(mary)))&
(?[X]:((patient(X)&kind(X))))&
((rich(john)&~happy(john))) | generous(mary) | [] | null | 0 |
Everyone who is both curious and patient is both not creative and happy.
If someone is happy or not curious then susan is both kind and not humble and vice versa.
Everyone who is both not happy and not funny is either not generous or not happy.
Everyone who is both quiet and kind is not brave or funny and vice versa.
If alice is curious or creative then someone is both creative and quiet.
Everyone who is not curious or tall is both not old and funny and vice versa.
If someone is not rich or not strong then someone is both not calm and not old.
If alice is either wise or funny then someone is strong and vice versa.
Everyone who is both not calm and not quiet is either not patient or not creative and vice versa.
If someone is either not tall or not funny then someone is either strong or not calm and vice versa.
Everyone who is wise or happy is not kind.
Everyone who is not kind or funny is either not happy or not tall.
Everyone who is either not strong or not kind is both not old and not patient.
If alice is either not rich or not tall then lucy is both brave and not rich.
If someone is both kind and not rich then someone is both old and not strong and vice versa.
If someone is either generous or not wise then paul is not curious.
Paul is strong.
Lucy is not humble.
Mary is not strong.
Someone is either happy or brave.
Someone is both funny and not rich.
Someone is either not happy or humble.
Paul is not strong or tall. | Alice is not tall. | neutral | (![X]:((curious(X)&patient(X))=>(~creative(X)&happy(X))))&
((?[X]:((happy(X)|~curious(X))))<=>((kind(susan)&~humble(susan))))&
(![X]:((~happy(X)&~funny(X))=>(~generous(X)<~>~happy(X))))&
(![X]:((quiet(X)&kind(X))<=>(~brave(X)|funny(X))))&
(((curious(alice)|creative(alice)))=>(?[X]:((creative(X)&quiet(X)))))&
(![X]:((~curious(X)|tall(X))<=>(~old(X)&funny(X))))&
((?[X]:((~rich(X)|~strong(X))))=>(?[X]:((~calm(X)&~old(X)))))&
(((wise(alice)<~>funny(alice)))<=>(?[X]:(strong(X))))&
(![X]:((~calm(X)&~quiet(X))<=>(~patient(X)<~>~creative(X))))&
((?[X]:((~tall(X)<~>~funny(X))))<=>(?[X]:((strong(X)<~>~calm(X)))))&
(![X]:((wise(X)|happy(X))=>~kind(X)))&
(![X]:((~kind(X)|funny(X))=>(~happy(X)<~>~tall(X))))&
(![X]:((~strong(X)<~>~kind(X))=>(~old(X)&~patient(X))))&
(((~rich(alice)<~>~tall(alice)))=>((brave(lucy)&~rich(lucy))))&
((?[X]:((kind(X)&~rich(X))))<=>(?[X]:((old(X)&~strong(X)))))&
((?[X]:((generous(X)<~>~wise(X))))=>(~curious(paul)))&
(strong(paul))&
(~humble(lucy))&
(~strong(mary))&
(?[X]:((happy(X)<~>brave(X))))&
(?[X]:((funny(X)&~rich(X))))&
(?[X]:((~happy(X)<~>humble(X))))&
((~strong(paul)|tall(paul))) | ~tall(alice) | [] | null | 0 |
Everyone who is either strong or not generous is funny or not strong and vice versa.
Everyone who is kind is both not quiet and not tall.
Everyone who is both old and not wise is not calm or not humble.
Everyone who is either tall or not generous is not generous and vice versa.
If susan is both not humble and not wise then someone is humble or rich and vice versa.
If someone is not generous then someone is both generous and not curious.
If someone is both happy and tall then someone is both creative and not curious.
Everyone who is not calm is either brave or not humble.
If someone is both curious and not creative then someone is either happy or not brave.
Everyone who is old or tall is both not quiet and not humble.
If mary is curious or old then someone is not brave or not kind.
Everyone who is not curious or calm is not quiet.
If someone is either humble or not patient then someone is not wise or curious and vice versa.
If mary is strong then paul is rich or brave.
If fred is both not funny and old then someone is funny and vice versa.
Everyone who is either not quiet or not brave is not quiet and vice versa.
Someone is happy or tall.
Susan is calm or not generous.
Someone is both not happy and calm.
Fred is not happy.
Someone is not kind.
Someone is both wise and not quiet. | Fred is quiet. | contradiction | (![X]:((strong(X)<~>~generous(X))<=>(funny(X)|~strong(X))))&
(![X]:(kind(X)=>(~quiet(X)&~tall(X))))&
(![X]:((old(X)&~wise(X))=>(~calm(X)|~humble(X))))&
(![X]:((tall(X)<~>~generous(X))<=>~generous(X)))&
(((~humble(susan)&~wise(susan)))<=>(?[X]:((humble(X)|rich(X)))))&
((?[X]:(~generous(X)))=>(?[X]:((generous(X)&~curious(X)))))&
((?[X]:((happy(X)&tall(X))))=>(?[X]:((creative(X)&~curious(X)))))&
(![X]:(~calm(X)=>(brave(X)<~>~humble(X))))&
((?[X]:((curious(X)&~creative(X))))=>(?[X]:((happy(X)<~>~brave(X)))))&
(![X]:((old(X)|tall(X))=>(~quiet(X)&~humble(X))))&
(((curious(mary)|old(mary)))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((~curious(X)|calm(X))=>~quiet(X)))&
((?[X]:((humble(X)<~>~patient(X))))<=>(?[X]:((~wise(X)|curious(X)))))&
((strong(mary))=>((rich(paul)|brave(paul))))&
(((~funny(fred)&old(fred)))<=>(?[X]:(funny(X))))&
(![X]:((~quiet(X)<~>~brave(X))<=>~quiet(X)))&
(?[X]:((happy(X)|tall(X))))&
((calm(susan)|~generous(susan)))&
(?[X]:((~happy(X)&calm(X))))&
(~happy(fred))&
(?[X]:(~kind(X)))&
(?[X]:((wise(X)&~quiet(X)))) | quiet(fred) | [
"p0",
"p5",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5254365031789247887566196
% SZS output start Proof for 5254365031789247887566196
1. ! [X0] : ((strong(X0) <~> ~generous(X0)) <=> (~strong(X0) | funny(X0))) [input p0]
6. ? [X0] : ~generous(X0) => ? [X0] : (~curious(X0) & generous(X0)) [input p5]
10. ! [X0] : ((tall(X0) | old(X0)) => (~humble(X0) & ~quiet(X0))) [input p9]
15. (old(fred) & ~funny(fred)) <=> ? [X0] : funny(X0) [input p14]
23. quiet(fred) [input hypothesis]
24. ? [X0] : ~generous(X0) => ? [X1] : (~curious(X1) & generous(X1)) [rectify 6]
35. ? [X1] : (~curious(X1) & generous(X1)) | ! [X0] : generous(X0) [ennf transformation 24]
38. ! [X0] : ((~humble(X0) & ~quiet(X0)) | (~tall(X0) & ~old(X0))) [ennf transformation 10]
42. ! [X0] : ((((generous(X0) | ~strong(X0)) & (~generous(X0) | strong(X0))) | (strong(X0) & ~funny(X0))) & ((~strong(X0) | funny(X0)) | ((strong(X0) | generous(X0)) & (~generous(X0) | ~strong(X0))))) [nnf transformation 1]
43. ! [X0] : ((((generous(X0) | ~strong(X0)) & (~generous(X0) | strong(X0))) | (strong(X0) & ~funny(X0))) & (~strong(X0) | funny(X0) | ((strong(X0) | generous(X0)) & (~generous(X0) | ~strong(X0))))) [flattening 42]
50. ? [X0] : (~curious(X0) & generous(X0)) | ! [X1] : generous(X1) [rectify 35]
51. ? [X0] : (~curious(X0) & generous(X0)) => (~curious(sK1) & generous(sK1)) [choice axiom]
52. (~curious(sK1) & generous(sK1)) | ! [X1] : generous(X1) [skolemisation 50,51]
62. ((old(fred) & ~funny(fred)) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | (~old(fred) | funny(fred))) [nnf transformation 15]
63. ((old(fred) & ~funny(fred)) | ! [X0] : ~funny(X0)) & (? [X0] : funny(X0) | ~old(fred) | funny(fred)) [flattening 62]
64. ((old(fred) & ~funny(fred)) | ! [X0] : ~funny(X0)) & (? [X1] : funny(X1) | ~old(fred) | funny(fred)) [rectify 63]
65. ? [X1] : funny(X1) => funny(sK5) [choice axiom]
66. ((old(fred) & ~funny(fred)) | ! [X0] : ~funny(X0)) & (funny(sK5) | ~old(fred) | funny(fred)) [skolemisation 64,65]
74. ~strong(X0) | funny(X0) | ~generous(X0) | ~strong(X0) [cnf transformation 43]
77. ~generous(X0) | strong(X0) | strong(X0) [cnf transformation 43]
90. generous(sK1) | generous(X1) [cnf transformation 52]
95. ~old(X0) | ~quiet(X0) [cnf transformation 38]
110. old(fred) | ~funny(X0) [cnf transformation 66]
122. quiet(fred) [cnf transformation 23]
127. ~strong(X0) | funny(X0) | ~generous(X0) [duplicate literal removal 74]
128. ~generous(X0) | strong(X0) [duplicate literal removal 77]
129. ~generous(X0) | funny(X0) [subsumption resolution 127,128]
159. 7 <=> ! [X1] : generous(X1) [avatar definition]
160. generous(X1) <- (7) [avatar component clause 159]
167. 9 <=> generous(sK1) [avatar definition]
169. generous(sK1) <- (9) [avatar component clause 167]
170. 7 | 9 [avatar split clause 90,167,159]
219. 21 <=> ! [X0] : ~funny(X0) [avatar definition]
220. ~funny(X0) <- (21) [avatar component clause 219]
222. 22 <=> old(fred) [avatar definition]
224. old(fred) <- (22) [avatar component clause 222]
225. 21 | 22 [avatar split clause 110,222,219]
253. funny(sK1) <- (9) [resolution 129,169]
254. $false <- (9, 21) [subsumption resolution 253,220]
255. ~9 | ~21 [avatar contradiction clause 254]
256. ~quiet(fred) <- (22) [resolution 224,95]
257. $false <- (22) [subsumption resolution 256,122]
258. ~22 [avatar contradiction clause 257]
259. funny(X0) <- (7) [resolution 160,129]
261. $false <- (7, 21) [subsumption resolution 259,220]
262. ~7 | ~21 [avatar contradiction clause 261]
263. $false [avatar sat refutation 170,225,255,258,262]
% SZS output end Proof for 5254365031789247887566196
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not wise is either not calm or not generous and vice versa. If mary is old or not calm then lucy is not funny. Everyone who is either funny or tall is either not wise or not kind and vice versa. Everyone who is either not kind or not brave is either creative or not old. Everyone who is both calm and not funny is both not quiet and not generous. If someone is not wise then john is not patient and vice versa. Everyone who is not wise is either patient or not rich and vice versa. Everyone who is quiet or happy is creative or not brave. If alice is quiet or old then someone is either curious or not generous. Everyone who is not tall is both creative and not tall and vice versa. Everyone who is generous or not curious is creative or not quiet and vice versa. Everyone who is either not funny or not humble is either not funny or calm and vice versa. If someone is not kind or not humble then paul is rich or not strong and vice versa. Everyone who is either not creative or not calm is not brave or not wise and vice versa. Everyone who is either not generous or strong is creative. If someone is either not patient or not old then mary is not brave or not wise. Someone is both not calm and not quiet. Someone is strong. Someone is not calm. Lucy is kind or not strong. Someone is either generous or tall. Someone is brave or not rich. Mary is kind or not happy. | John is funny. | neutral | (![X]:((~creative(X)<~>~wise(X))<=>(~calm(X)<~>~generous(X))))&
(((old(mary)|~calm(mary)))=>(~funny(lucy)))&
(![X]:((funny(X)<~>tall(X))<=>(~wise(X)<~>~kind(X))))&
(![X]:((~kind(X)<~>~brave(X))=>(creative(X)<~>~old(X))))&
(![X]:((calm(X)&~funny(X))=>(~quiet(X)&~generous(X))))&
((?[X]:(~wise(X)))<=>(~patient(john)))&
(![X]:(~wise(X)<=>(patient(X)<~>~rich(X))))&
(![X]:((quiet(X)|happy(X))=>(creative(X)|~brave(X))))&
(((quiet(alice)|old(alice)))=>(?[X]:((curious(X)<~>~generous(X)))))&
(![X]:(~tall(X)<=>(creative(X)&~tall(X))))&
(![X]:((generous(X)|~curious(X))<=>(creative(X)|~quiet(X))))&
(![X]:((~funny(X)<~>~humble(X))<=>(~funny(X)<~>calm(X))))&
((?[X]:((~kind(X)|~humble(X))))<=>((rich(paul)|~strong(paul))))&
(![X]:((~creative(X)<~>~calm(X))<=>(~brave(X)|~wise(X))))&
(![X]:((~generous(X)<~>strong(X))=>creative(X)))&
((?[X]:((~patient(X)<~>~old(X))))=>((~brave(mary)|~wise(mary))))&
(?[X]:((~calm(X)&~quiet(X))))&
(?[X]:(strong(X)))&
(?[X]:(~calm(X)))&
((kind(lucy)|~strong(lucy)))&
(?[X]:((generous(X)<~>tall(X))))&
(?[X]:((brave(X)|~rich(X))))&
((kind(mary)|~happy(mary))) | funny(john) | [] | null | 0 |
Everyone who is not happy or not patient is kind and vice versa. If lucy is not kind then someone is either not creative or not curious. If susan is not kind then mary is both not funny and not quiet and vice versa. Everyone who is both humble and not creative is either generous or not generous and vice versa. Everyone who is not quiet or calm is either wise or quiet. Everyone who is either happy or creative is not brave or not wise. If alice is either old or not old then someone is both not patient and generous and vice versa. Everyone who is both quiet and not quiet is either not kind or patient. If someone is either humble or not rich then paul is both old and not generous and vice versa. Everyone who is either not old or not humble is not calm or not humble. If mary is wise or not kind then john is quiet or patient and vice versa. If someone is not old or kind then susan is funny or not happy. Everyone who is either not tall or brave is rich. If mary is either not old or creative then someone is either strong or not kind. Everyone who is both not rich and rich is either not rich or generous and vice versa. Someone is both not happy and tall. Lucy is either not patient or not humble. Someone is either calm or curious. Lucy is either creative or humble. Susan is either not quiet or not calm. Someone is not tall or not humble. | John is creative. | contradiction | (![X]:((~happy(X)|~patient(X))<=>kind(X)))&
((~kind(lucy))=>(?[X]:((~creative(X)<~>~curious(X)))))&
((~kind(susan))<=>((~funny(mary)&~quiet(mary))))&
(![X]:((humble(X)&~creative(X))<=>(generous(X)<~>~generous(X))))&
(![X]:((~quiet(X)|calm(X))=>(wise(X)<~>quiet(X))))&
(![X]:((happy(X)<~>creative(X))=>(~brave(X)|~wise(X))))&
(((old(alice)<~>~old(alice)))<=>(?[X]:((~patient(X)&generous(X)))))&
(![X]:((quiet(X)&~quiet(X))=>(~kind(X)<~>patient(X))))&
((?[X]:((humble(X)<~>~rich(X))))<=>((old(paul)&~generous(paul))))&
(![X]:((~old(X)<~>~humble(X))=>(~calm(X)|~humble(X))))&
(((wise(mary)|~kind(mary)))<=>((quiet(john)|patient(john))))&
((?[X]:((~old(X)|kind(X))))=>((funny(susan)|~happy(susan))))&
(![X]:((~tall(X)<~>brave(X))=>rich(X)))&
(((~old(mary)<~>creative(mary)))=>(?[X]:((strong(X)<~>~kind(X)))))&
(![X]:((~rich(X)&rich(X))<=>(~rich(X)<~>generous(X))))&
(?[X]:((~happy(X)&tall(X))))&
((~patient(lucy)<~>~humble(lucy)))&
(?[X]:((calm(X)<~>curious(X))))&
((creative(lucy)<~>humble(lucy)))&
((~quiet(susan)<~>~calm(susan)))&
(?[X]:((~tall(X)|~humble(X)))) | creative(john) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3945858957102282886658446
% SZS output start Proof for 3945858957102282886658446
4. ! [X0] : ((~creative(X0) & humble(X0)) <=> (generous(X0) <~> ~generous(X0))) [input p3]
22. creative(john) [input hypothesis]
42. ! [X0] : (((~creative(X0) & humble(X0)) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0)))) & (((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | (creative(X0) | ~humble(X0)))) [nnf transformation 4]
43. ! [X0] : (((~creative(X0) & humble(X0)) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0)))) & (((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | creative(X0) | ~humble(X0))) [flattening 42]
87. ~creative(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 43]
88. ~creative(X0) | generous(X0) | generous(X0) [cnf transformation 43]
140. creative(john) [cnf transformation 22]
153. ~creative(X0) | ~generous(X0) [duplicate literal removal 87]
154. ~creative(X0) | generous(X0) [duplicate literal removal 88]
184. ~creative(X0) [subsumption resolution 153,154]
299. $false [subsumption resolution 140,184]
% SZS output end Proof for 3945858957102282886658446
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both wise and not brave then someone is both not funny and not kind.
If paul is curious then paul is both not generous and curious.
If someone is either not tall or quiet then someone is not curious or not generous.
Everyone who is both not brave and old is either strong or not humble and vice versa.
If fred is both not strong and strong then someone is either not old or not brave and vice versa.
If someone is both not tall and not quiet then fred is not strong and vice versa.
If someone is not kind then someone is not rich and vice versa.
Everyone who is either happy or patient is both not curious and humble and vice versa.
Everyone who is either not old or creative is both not creative and strong.
Everyone who is either not curious or patient is both not wise and not rich and vice versa.
Everyone who is either not funny or humble is not humble or not wise.
Everyone who is strong or happy is happy.
Everyone who is either creative or not tall is not tall or old and vice versa.
If someone is not rich or kind then mary is both funny and not kind and vice versa.
If someone is either tall or not wise then someone is either not generous or curious.
If mary is rich then john is not creative.
Susan is either old or funny.
Paul is both not wise and not brave.
Mary is not patient or not rich.
Someone is either funny or not creative.
Lucy is either humble or not quiet.
Fred is either generous or strong.
Mary is either not happy or wise.
Someone is either not generous or humble. | Susan is not creative. | entailment | (((wise(susan)&~brave(susan)))=>(?[X]:((~funny(X)&~kind(X)))))&
((curious(paul))=>((~generous(paul)&curious(paul))))&
((?[X]:((~tall(X)<~>quiet(X))))=>(?[X]:((~curious(X)|~generous(X)))))&
(![X]:((~brave(X)&old(X))<=>(strong(X)<~>~humble(X))))&
(((~strong(fred)&strong(fred)))<=>(?[X]:((~old(X)<~>~brave(X)))))&
((?[X]:((~tall(X)&~quiet(X))))<=>(~strong(fred)))&
((?[X]:(~kind(X)))<=>(?[X]:(~rich(X))))&
(![X]:((happy(X)<~>patient(X))<=>(~curious(X)&humble(X))))&
(![X]:((~old(X)<~>creative(X))=>(~creative(X)&strong(X))))&
(![X]:((~curious(X)<~>patient(X))<=>(~wise(X)&~rich(X))))&
(![X]:((~funny(X)<~>humble(X))=>(~humble(X)|~wise(X))))&
(![X]:((strong(X)|happy(X))=>happy(X)))&
(![X]:((creative(X)<~>~tall(X))<=>(~tall(X)|old(X))))&
((?[X]:((~rich(X)|kind(X))))<=>((funny(mary)&~kind(mary))))&
((?[X]:((tall(X)<~>~wise(X))))=>(?[X]:((~generous(X)<~>curious(X)))))&
((rich(mary))=>(~creative(john)))&
((old(susan)<~>funny(susan)))&
((~wise(paul)&~brave(paul)))&
((~patient(mary)|~rich(mary)))&
(?[X]:((funny(X)<~>~creative(X))))&
((humble(lucy)<~>~quiet(lucy)))&
((generous(fred)<~>strong(fred)))&
((~happy(mary)<~>wise(mary)))&
(?[X]:((~generous(X)<~>humble(X)))) | ~creative(susan) | [
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7033739244257713301380933
% SZS output start Proof for 7033739244257713301380933
9. ! [X0] : ((~old(X0) <~> creative(X0)) => (strong(X0) & ~creative(X0))) [input p8]
13. ! [X0] : ((creative(X0) <~> ~tall(X0)) <=> (old(X0) | ~tall(X0))) [input p12]
25. creative(susan) [input hypothesis]
33. ! [X0] : ((strong(X0) & ~creative(X0)) | (~old(X0) <=> creative(X0))) [ennf transformation 9]
63. ! [X0] : ((strong(X0) & ~creative(X0)) | ((~old(X0) | ~creative(X0)) & (creative(X0) | old(X0)))) [nnf transformation 33]
67. ! [X0] : ((((tall(X0) | ~creative(X0)) & (~tall(X0) | creative(X0))) | (~old(X0) & tall(X0))) & ((old(X0) | ~tall(X0)) | ((creative(X0) | tall(X0)) & (~tall(X0) | ~creative(X0))))) [nnf transformation 13]
68. ! [X0] : ((((tall(X0) | ~creative(X0)) & (~tall(X0) | creative(X0))) | (~old(X0) & tall(X0))) & (old(X0) | ~tall(X0) | ((creative(X0) | tall(X0)) & (~tall(X0) | ~creative(X0))))) [flattening 67]
118. ~creative(X0) | ~old(X0) | ~creative(X0) [cnf transformation 63]
131. old(X0) | ~tall(X0) | ~tall(X0) | ~creative(X0) [cnf transformation 68]
135. tall(X0) | ~creative(X0) | tall(X0) [cnf transformation 68]
162. creative(susan) [cnf transformation 25]
163. old(X0) | ~tall(X0) | ~creative(X0) [duplicate literal removal 131]
164. tall(X0) | ~creative(X0) [duplicate literal removal 135]
166. ~creative(X0) | ~old(X0) [duplicate literal removal 118]
252. ~tall(X0) | ~creative(X0) [subsumption resolution 163,166]
253. ~creative(X0) [subsumption resolution 252,164]
352. $false [subsumption resolution 162,253]
% SZS output end Proof for 7033739244257713301380933
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either not old or strong then fred is either not funny or not humble and vice versa.
Everyone who is either not patient or not wise is kind or not strong.
If someone is not happy then john is both not happy and funny.
Everyone who is not quiet or not calm is both not creative and not wise.
Everyone who is not brave or old is either not humble or tall and vice versa.
Everyone who is either not brave or not old is both not kind and not old and vice versa.
Everyone who is strong is not creative or not generous and vice versa.
If someone is generous or not quiet then someone is either not old or patient.
Everyone who is either not wise or curious is not old or patient and vice versa.
If lucy is generous or not calm then paul is not rich.
If fred is curious or not kind then lucy is both old and quiet.
Everyone who is strong or not happy is not rich or not quiet.
Everyone who is calm is not strong.
Everyone who is brave is either happy or old and vice versa.
Everyone who is generous is kind and vice versa.
If alice is both not rich and calm then someone is not brave or quiet and vice versa.
Someone is both not creative and not happy.
John is either not generous or kind.
Fred is both old and not kind.
Mary is quiet.
Someone is either not humble or not patient.
Someone is not brave or not creative.
Lucy is both not tall and old.
Susan is not humble. | Alice is not strong. | entailment | (((~old(fred)<~>strong(fred)))<=>((~funny(fred)<~>~humble(fred))))&
(![X]:((~patient(X)<~>~wise(X))=>(kind(X)|~strong(X))))&
((?[X]:(~happy(X)))=>((~happy(john)&funny(john))))&
(![X]:((~quiet(X)|~calm(X))=>(~creative(X)&~wise(X))))&
(![X]:((~brave(X)|old(X))<=>(~humble(X)<~>tall(X))))&
(![X]:((~brave(X)<~>~old(X))<=>(~kind(X)&~old(X))))&
(![X]:(strong(X)<=>(~creative(X)|~generous(X))))&
((?[X]:((generous(X)|~quiet(X))))=>(?[X]:((~old(X)<~>patient(X)))))&
(![X]:((~wise(X)<~>curious(X))<=>(~old(X)|patient(X))))&
(((generous(lucy)|~calm(lucy)))=>(~rich(paul)))&
(((curious(fred)|~kind(fred)))=>((old(lucy)&quiet(lucy))))&
(![X]:((strong(X)|~happy(X))=>(~rich(X)|~quiet(X))))&
(![X]:(calm(X)=>~strong(X)))&
(![X]:(brave(X)<=>(happy(X)<~>old(X))))&
(![X]:(generous(X)<=>kind(X)))&
(((~rich(alice)&calm(alice)))<=>(?[X]:((~brave(X)|quiet(X)))))&
(?[X]:((~creative(X)&~happy(X))))&
((~generous(john)<~>kind(john)))&
((old(fred)&~kind(fred)))&
(quiet(mary))&
(?[X]:((~humble(X)<~>~patient(X))))&
(?[X]:((~brave(X)|~creative(X))))&
((~tall(lucy)&old(lucy)))&
(~humble(susan)) | ~strong(alice) | [
"p12",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8716174474958273741898257
% SZS output start Proof for 8716174474958273741898257
13. ! [X0] : (calm(X0) => ~strong(X0)) [input p12]
16. (calm(alice) & ~rich(alice)) <=> ? [X0] : (quiet(X0) | ~brave(X0)) [input p15]
20. quiet(mary) [input p19]
25. strong(alice) [input hypothesis]
36. ! [X0] : (~strong(X0) | ~calm(X0)) [ennf transformation 13]
53. ((calm(alice) & ~rich(alice)) | ! [X0] : (~quiet(X0) & brave(X0))) & (? [X0] : (quiet(X0) | ~brave(X0)) | (~calm(alice) | rich(alice))) [nnf transformation 16]
54. ((calm(alice) & ~rich(alice)) | ! [X0] : (~quiet(X0) & brave(X0))) & (? [X0] : (quiet(X0) | ~brave(X0)) | ~calm(alice) | rich(alice)) [flattening 53]
55. ((calm(alice) & ~rich(alice)) | ! [X0] : (~quiet(X0) & brave(X0))) & (? [X1] : (quiet(X1) | ~brave(X1)) | ~calm(alice) | rich(alice)) [rectify 54]
56. ? [X1] : (quiet(X1) | ~brave(X1)) => (quiet(sK1) | ~brave(sK1)) [choice axiom]
57. ((calm(alice) & ~rich(alice)) | ! [X0] : (~quiet(X0) & brave(X0))) & ((quiet(sK1) | ~brave(sK1)) | ~calm(alice) | rich(alice)) [skolemisation 55,56]
115. ~calm(X0) | ~strong(X0) [cnf transformation 36]
126. calm(alice) | ~quiet(X0) [cnf transformation 57]
133. quiet(mary) [cnf transformation 20]
140. strong(alice) [cnf transformation 25]
235. 19 <=> ! [X0] : ~quiet(X0) [avatar definition]
236. ~quiet(X0) <- (19) [avatar component clause 235]
238. 20 <=> calm(alice) [avatar definition]
240. calm(alice) <- (20) [avatar component clause 238]
241. 19 | 20 [avatar split clause 126,238,235]
289. ~strong(alice) <- (20) [resolution 115,240]
290. $false <- (20) [subsumption resolution 289,140]
291. ~20 [avatar contradiction clause 290]
292. $false <- (19) [resolution 236,133]
295. ~19 [avatar contradiction clause 292]
296. $false [avatar sat refutation 241,291,295]
% SZS output end Proof for 8716174474958273741898257
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both kind and not wise is both not creative and strong. Everyone who is both not rich and brave is not creative and vice versa. Everyone who is rich is not generous or not humble. Everyone who is both creative and not happy is either quiet or not quiet. Everyone who is not brave is not happy. If someone is both not wise and happy then susan is funny and vice versa. Everyone who is humble is not happy and vice versa. If mary is patient or curious then mary is not brave and vice versa. Everyone who is calm is not kind or wise. Everyone who is both kind and not patient is not old and vice versa. If paul is not happy then someone is either not strong or not creative. Everyone who is strong or old is both not brave and not old and vice versa. If lucy is not humble then someone is not generous or not patient. If someone is both tall and funny then someone is either not patient or not quiet and vice versa. Everyone who is both calm and not rich is either not tall or not old. If someone is old then someone is quiet and vice versa. Someone is either quiet or generous. Mary is calm or kind. Someone is both not calm and happy. Lucy is either not kind or not creative. Susan is either wise or not humble. Someone is kind or not rich. Mary is either not kind or rich. | Susan is not funny. | entailment | (![X]:((kind(X)&~wise(X))=>(~creative(X)&strong(X))))&
(![X]:((~rich(X)&brave(X))<=>~creative(X)))&
(![X]:(rich(X)=>(~generous(X)|~humble(X))))&
(![X]:((creative(X)&~happy(X))=>(quiet(X)<~>~quiet(X))))&
(![X]:(~brave(X)=>~happy(X)))&
((?[X]:((~wise(X)&happy(X))))<=>(funny(susan)))&
(![X]:(humble(X)<=>~happy(X)))&
(((patient(mary)|curious(mary)))<=>(~brave(mary)))&
(![X]:(calm(X)=>(~kind(X)|wise(X))))&
(![X]:((kind(X)&~patient(X))<=>~old(X)))&
((~happy(paul))=>(?[X]:((~strong(X)<~>~creative(X)))))&
(![X]:((strong(X)|old(X))<=>(~brave(X)&~old(X))))&
((~humble(lucy))=>(?[X]:((~generous(X)|~patient(X)))))&
((?[X]:((tall(X)&funny(X))))<=>(?[X]:((~patient(X)<~>~quiet(X)))))&
(![X]:((calm(X)&~rich(X))=>(~tall(X)<~>~old(X))))&
((?[X]:(old(X)))<=>(?[X]:(quiet(X))))&
(?[X]:((quiet(X)<~>generous(X))))&
((calm(mary)|kind(mary)))&
(?[X]:((~calm(X)&happy(X))))&
((~kind(lucy)<~>~creative(lucy)))&
((wise(susan)<~>~humble(susan)))&
(?[X]:((kind(X)|~rich(X))))&
((~kind(mary)<~>rich(mary))) | ~funny(susan) | [
"p0",
"p4",
"p5",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6978089713718997038109619
% SZS output start Proof for 6978089713718997038109619
1. ! [X0] : ((~wise(X0) & kind(X0)) => (strong(X0) & ~creative(X0))) [input p0]
5. ! [X0] : (~brave(X0) => ~happy(X0)) [input p4]
6. ? [X0] : (happy(X0) & ~wise(X0)) <=> funny(susan) [input p5]
10. ! [X0] : ((~patient(X0) & kind(X0)) <=> ~old(X0)) [input p9]
12. ! [X0] : ((old(X0) | strong(X0)) <=> (~old(X0) & ~brave(X0))) [input p11]
24. funny(susan) [input hypothesis]
27. ! [X0] : ((strong(X0) & ~creative(X0)) | (wise(X0) | ~kind(X0))) [ennf transformation 1]
28. ! [X0] : ((strong(X0) & ~creative(X0)) | wise(X0) | ~kind(X0)) [flattening 27]
33. ! [X0] : (~happy(X0) | brave(X0)) [ennf transformation 5]
43. (? [X0] : (happy(X0) & ~wise(X0)) | ~funny(susan)) & (funny(susan) | ! [X0] : (~happy(X0) | wise(X0))) [nnf transformation 6]
44. (? [X0] : (happy(X0) & ~wise(X0)) | ~funny(susan)) & (funny(susan) | ! [X1] : (~happy(X1) | wise(X1))) [rectify 43]
45. ? [X0] : (happy(X0) & ~wise(X0)) => (happy(sK0) & ~wise(sK0)) [choice axiom]
46. ((happy(sK0) & ~wise(sK0)) | ~funny(susan)) & (funny(susan) | ! [X1] : (~happy(X1) | wise(X1))) [skolemisation 44,45]
50. ! [X0] : (((~patient(X0) & kind(X0)) | old(X0)) & (~old(X0) | (patient(X0) | ~kind(X0)))) [nnf transformation 10]
51. ! [X0] : (((~patient(X0) & kind(X0)) | old(X0)) & (~old(X0) | patient(X0) | ~kind(X0))) [flattening 50]
55. ! [X0] : (((old(X0) | strong(X0)) | (old(X0) | brave(X0))) & ((~old(X0) & ~brave(X0)) | (~old(X0) & ~strong(X0)))) [nnf transformation 12]
56. ! [X0] : ((old(X0) | strong(X0) | old(X0) | brave(X0)) & ((~old(X0) & ~brave(X0)) | (~old(X0) & ~strong(X0)))) [flattening 55]
81. ~kind(X0) | wise(X0) | strong(X0) [cnf transformation 28]
88. ~happy(X0) | brave(X0) [cnf transformation 33]
90. ~wise(sK0) | ~funny(susan) [cnf transformation 46]
91. happy(sK0) | ~funny(susan) [cnf transformation 46]
99. old(X0) | kind(X0) [cnf transformation 51]
103. ~brave(X0) | ~strong(X0) [cnf transformation 56]
106. ~old(X0) | ~old(X0) [cnf transformation 56]
131. funny(susan) [cnf transformation 24]
132. ~old(X0) [duplicate literal removal 106]
135. 1 <=> funny(susan) [avatar definition]
139. 2 <=> happy(sK0) [avatar definition]
141. happy(sK0) <- (2) [avatar component clause 139]
142. ~1 | 2 [avatar split clause 91,139,135]
144. 3 <=> wise(sK0) [avatar definition]
146. ~wise(sK0) <- (~3) [avatar component clause 144]
147. ~1 | ~3 [avatar split clause 90,144,135]
272. 1 [avatar split clause 131,135]
275. brave(sK0) <- (2) [resolution 88,141]
282. kind(X0) [resolution 99,132]
286. ~strong(sK0) <- (2) [resolution 103,275]
292. strong(X0) | wise(X0) [resolution 81,282]
371. wise(sK0) <- (2) [resolution 292,286]
375. $false <- (2, ~3) [subsumption resolution 371,146]
376. ~2 | 3 [avatar contradiction clause 375]
377. $false [avatar sat refutation 142,147,272,376]
% SZS output end Proof for 6978089713718997038109619
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is either kind or happy and vice versa.
Everyone who is both calm and not brave is not funny or not brave.
Everyone who is not creative is not patient.
Everyone who is both funny and not tall is both kind and not brave.
If someone is both rich and not creative then paul is both not calm and wise and vice versa.
If paul is not funny or old then fred is not rich and vice versa.
If someone is quiet then susan is both funny and not old and vice versa.
If susan is both not funny and humble then alice is both not tall and wise.
Everyone who is humble or not patient is funny.
Everyone who is both funny and calm is either strong or creative and vice versa.
If susan is generous or not kind then someone is either strong or not curious.
If alice is both not kind and quiet then someone is patient or old and vice versa.
Everyone who is not funny is either not rich or quiet and vice versa.
If someone is either not old or quiet then someone is not happy or not creative and vice versa.
If lucy is either quiet or not humble then someone is both tall and strong.
Everyone who is either old or calm is both old and kind.
Someone is both old and not quiet.
John is both humble and kind.
Someone is both brave and not funny.
Someone is either brave or happy.
Fred is tall or wise.
Someone is quiet or not quiet.
Someone is strong.
Someone is both rich and not funny. | Susan is not calm. | entailment | (![X]:(strong(X)<=>(kind(X)<~>happy(X))))&
(![X]:((calm(X)&~brave(X))=>(~funny(X)|~brave(X))))&
(![X]:(~creative(X)=>~patient(X)))&
(![X]:((funny(X)&~tall(X))=>(kind(X)&~brave(X))))&
((?[X]:((rich(X)&~creative(X))))<=>((~calm(paul)&wise(paul))))&
(((~funny(paul)|old(paul)))<=>(~rich(fred)))&
((?[X]:(quiet(X)))<=>((funny(susan)&~old(susan))))&
(((~funny(susan)&humble(susan)))=>((~tall(alice)&wise(alice))))&
(![X]:((humble(X)|~patient(X))=>funny(X)))&
(![X]:((funny(X)&calm(X))<=>(strong(X)<~>creative(X))))&
(((generous(susan)|~kind(susan)))=>(?[X]:((strong(X)<~>~curious(X)))))&
(((~kind(alice)&quiet(alice)))<=>(?[X]:((patient(X)|old(X)))))&
(![X]:(~funny(X)<=>(~rich(X)<~>quiet(X))))&
((?[X]:((~old(X)<~>quiet(X))))<=>(?[X]:((~happy(X)|~creative(X)))))&
(((quiet(lucy)<~>~humble(lucy)))=>(?[X]:((tall(X)&strong(X)))))&
(![X]:((old(X)<~>calm(X))=>(old(X)&kind(X))))&
(?[X]:((old(X)&~quiet(X))))&
((humble(john)&kind(john)))&
(?[X]:((brave(X)&~funny(X))))&
(?[X]:((brave(X)<~>happy(X))))&
((tall(fred)|wise(fred)))&
(?[X]:((quiet(X)|~quiet(X))))&
(?[X]:(strong(X)))&
(?[X]:((rich(X)&~funny(X)))) | ~calm(susan) | [
"p6",
"p11",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2687880749363727995102044
% SZS output start Proof for 2687880749363727995102044
7. ? [X0] : quiet(X0) <=> (~old(susan) & funny(susan)) [input p6]
12. (quiet(alice) & ~kind(alice)) <=> ? [X0] : (old(X0) | patient(X0)) [input p11]
16. ! [X0] : ((old(X0) <~> calm(X0)) => (kind(X0) & old(X0))) [input p15]
17. ? [X0] : (~quiet(X0) & old(X0)) [input p16]
25. calm(susan) [input hypothesis]
38. ! [X0] : ((kind(X0) & old(X0)) | (old(X0) <=> calm(X0))) [ennf transformation 16]
47. (? [X0] : quiet(X0) | (old(susan) | ~funny(susan))) & ((~old(susan) & funny(susan)) | ! [X0] : ~quiet(X0)) [nnf transformation 7]
48. (? [X0] : quiet(X0) | old(susan) | ~funny(susan)) & ((~old(susan) & funny(susan)) | ! [X0] : ~quiet(X0)) [flattening 47]
49. (? [X0] : quiet(X0) | old(susan) | ~funny(susan)) & ((~old(susan) & funny(susan)) | ! [X1] : ~quiet(X1)) [rectify 48]
50. ? [X0] : quiet(X0) => quiet(sK1) [choice axiom]
51. (quiet(sK1) | old(susan) | ~funny(susan)) & ((~old(susan) & funny(susan)) | ! [X1] : ~quiet(X1)) [skolemisation 49,50]
57. ((quiet(alice) & ~kind(alice)) | ! [X0] : (~old(X0) & ~patient(X0))) & (? [X0] : (old(X0) | patient(X0)) | (~quiet(alice) | kind(alice))) [nnf transformation 12]
58. ((quiet(alice) & ~kind(alice)) | ! [X0] : (~old(X0) & ~patient(X0))) & (? [X0] : (old(X0) | patient(X0)) | ~quiet(alice) | kind(alice)) [flattening 57]
59. ((quiet(alice) & ~kind(alice)) | ! [X0] : (~old(X0) & ~patient(X0))) & (? [X1] : (old(X1) | patient(X1)) | ~quiet(alice) | kind(alice)) [rectify 58]
60. ? [X1] : (old(X1) | patient(X1)) => (old(sK3) | patient(sK3)) [choice axiom]
61. ((quiet(alice) & ~kind(alice)) | ! [X0] : (~old(X0) & ~patient(X0))) & ((old(sK3) | patient(sK3)) | ~quiet(alice) | kind(alice)) [skolemisation 59,60]
71. ! [X0] : ((kind(X0) & old(X0)) | ((old(X0) | ~calm(X0)) & (calm(X0) | ~old(X0)))) [nnf transformation 38]
72. ? [X0] : (~quiet(X0) & old(X0)) => (~quiet(sK7) & old(sK7)) [choice axiom]
73. ~quiet(sK7) & old(sK7) [skolemisation 17,72]
101. ~old(susan) | ~quiet(X1) [cnf transformation 51]
119. quiet(alice) | ~old(X0) [cnf transformation 61]
135. old(X0) | old(X0) | ~calm(X0) [cnf transformation 71]
138. old(sK7) [cnf transformation 73]
151. calm(susan) [cnf transformation 25]
152. ~calm(X0) | old(X0) [duplicate literal removal 135]
196. 10 <=> old(susan) [avatar definition]
205. 12 <=> ! [X1] : ~quiet(X1) [avatar definition]
206. ~quiet(X1) <- (12) [avatar component clause 205]
207. 12 | ~10 [avatar split clause 101,196,205]
238. 19 <=> ! [X0] : ~old(X0) [avatar definition]
239. ~old(X0) <- (19) [avatar component clause 238]
241. 20 <=> quiet(alice) [avatar definition]
243. quiet(alice) <- (20) [avatar component clause 241]
244. 19 | 20 [avatar split clause 119,241,238]
337. $false <- (19) [resolution 239,138]
338. ~19 [avatar contradiction clause 337]
345. old(susan) [resolution 152,151]
348. 10 [avatar split clause 345,196]
350. $false <- (12, 20) [resolution 206,243]
351. ~12 | ~20 [avatar contradiction clause 350]
353. $false [avatar sat refutation 207,244,338,348,351]
% SZS output end Proof for 2687880749363727995102044
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or funny is both not funny and rich.
Everyone who is either funny or creative is not rich and vice versa.
If mary is strong then someone is both not calm and creative.
If fred is rich or not funny then someone is either not kind or not tall.
If someone is either tall or not kind then someone is generous.
If susan is not generous then susan is either not strong or not patient and vice versa.
If fred is not curious then lucy is both not funny and kind.
Everyone who is both happy and strong is kind or not wise.
Everyone who is both not strong and creative is funny or calm and vice versa.
Everyone who is rich is either not patient or not wise and vice versa.
If someone is either not calm or not humble then someone is both funny and rich.
Everyone who is both happy and not old is not generous.
If fred is both happy and not kind then susan is either generous or wise.
Everyone who is either funny or not strong is not rich or not happy and vice versa.
Everyone who is not funny or tall is both creative and not curious and vice versa.
If john is tall then fred is wise or not strong and vice versa.
Paul is either not happy or not humble.
Paul is not tall or strong.
Someone is either not tall or strong.
Someone is not calm or not generous.
Fred is kind. | Fred is not humble. | contradiction | (![X]:((~calm(X)|funny(X))=>(~funny(X)&rich(X))))&
(![X]:((funny(X)<~>creative(X))<=>~rich(X)))&
((strong(mary))=>(?[X]:((~calm(X)&creative(X)))))&
(((rich(fred)|~funny(fred)))=>(?[X]:((~kind(X)<~>~tall(X)))))&
((?[X]:((tall(X)<~>~kind(X))))=>(?[X]:(generous(X))))&
((~generous(susan))<=>((~strong(susan)<~>~patient(susan))))&
((~curious(fred))=>((~funny(lucy)&kind(lucy))))&
(![X]:((happy(X)&strong(X))=>(kind(X)|~wise(X))))&
(![X]:((~strong(X)&creative(X))<=>(funny(X)|calm(X))))&
(![X]:(rich(X)<=>(~patient(X)<~>~wise(X))))&
((?[X]:((~calm(X)<~>~humble(X))))=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((happy(X)&~old(X))=>~generous(X)))&
(((happy(fred)&~kind(fred)))=>((generous(susan)<~>wise(susan))))&
(![X]:((funny(X)<~>~strong(X))<=>(~rich(X)|~happy(X))))&
(![X]:((~funny(X)|tall(X))<=>(creative(X)&~curious(X))))&
((tall(john))<=>((wise(fred)|~strong(fred))))&
((~happy(paul)<~>~humble(paul)))&
((~tall(paul)|strong(paul)))&
(?[X]:((~tall(X)<~>strong(X))))&
(?[X]:((~calm(X)|~generous(X))))&
(kind(fred)) | ~humble(fred) | [
"p0",
"p1",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1500483481380941950311513
% SZS output start Proof for 1500483481380941950311513
1. ! [X0] : ((funny(X0) | ~calm(X0)) => (rich(X0) & ~funny(X0))) [input p0]
2. ! [X0] : ((funny(X0) <~> creative(X0)) <=> ~rich(X0)) [input p1]
11. ? [X0] : (~calm(X0) <~> ~humble(X0)) => ? [X0] : (rich(X0) & funny(X0)) [input p10]
15. ! [X0] : ((tall(X0) | ~funny(X0)) <=> (~curious(X0) & creative(X0))) [input p14]
22. ~humble(fred) [input hypothesis]
24. ? [X0] : (~calm(X0) <~> ~humble(X0)) => ? [X1] : (rich(X1) & funny(X1)) [rectify 11]
26. ! [X0] : ((rich(X0) & ~funny(X0)) | (~funny(X0) & calm(X0))) [ennf transformation 1]
33. ? [X1] : (rich(X1) & funny(X1)) | ! [X0] : (~calm(X0) <=> ~humble(X0)) [ennf transformation 24]
36. ! [X0] : ((((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | rich(X0)) & (~rich(X0) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0))))) [nnf transformation 2]
50. ? [X1] : (rich(X1) & funny(X1)) | ! [X0] : ((~calm(X0) | humble(X0)) & (~humble(X0) | calm(X0))) [nnf transformation 33]
51. ? [X0] : (rich(X0) & funny(X0)) | ! [X1] : ((~calm(X1) | humble(X1)) & (~humble(X1) | calm(X1))) [rectify 50]
52. ? [X0] : (rich(X0) & funny(X0)) => (rich(sK3) & funny(sK3)) [choice axiom]
53. (rich(sK3) & funny(sK3)) | ! [X1] : ((~calm(X1) | humble(X1)) & (~humble(X1) | calm(X1))) [skolemisation 51,52]
57. ! [X0] : (((tall(X0) | ~funny(X0)) | (curious(X0) | ~creative(X0))) & ((~curious(X0) & creative(X0)) | (~tall(X0) & funny(X0)))) [nnf transformation 15]
58. ! [X0] : ((tall(X0) | ~funny(X0) | curious(X0) | ~creative(X0)) & ((~curious(X0) & creative(X0)) | (~tall(X0) & funny(X0)))) [flattening 57]
68. ~funny(X0) | ~funny(X0) [cnf transformation 26]
69. rich(X0) | calm(X0) [cnf transformation 26]
72. ~rich(X0) | funny(X0) | ~creative(X0) [cnf transformation 36]
100. funny(sK3) | ~calm(X1) | humble(X1) [cnf transformation 53]
111. creative(X0) | funny(X0) [cnf transformation 58]
126. ~humble(fred) [cnf transformation 22]
127. ~funny(X0) [duplicate literal removal 68]
129. ~creative(X0) | ~rich(X0) [subsumption resolution 72,127]
201. 15 <=> ! [X1] : (~calm(X1) | humble(X1)) [avatar definition]
202. ~calm(X1) | humble(X1) <- (15) [avatar component clause 201]
212. ~calm(X1) | humble(X1) [subsumption resolution 100,127]
213. 15 [avatar split clause 212,201]
234. creative(X0) [subsumption resolution 111,127]
293. ~rich(X1) [resolution 129,234]
294. calm(X0) [resolution 293,69]
296. humble(X0) <- (15) [resolution 294,202]
302. $false <- (15) [resolution 296,126]
306. ~15 [avatar contradiction clause 302]
307. $false [avatar sat refutation 213,306]
% SZS output end Proof for 1500483481380941950311513
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not funny or generous is either not happy or old and vice versa.
If paul is both not curious and not wise then fred is either tall or kind and vice versa.
If someone is both rich and not wise then fred is both not generous and not humble and vice versa.
Everyone who is humble or not kind is not quiet.
If someone is not quiet then paul is either not creative or not wise.
If paul is not humble or not old then someone is not funny.
Everyone who is strong or wise is both not quiet and not creative and vice versa.
Everyone who is strong or creative is either calm or creative and vice versa.
If someone is patient then john is both not wise and not funny and vice versa.
Everyone who is brave is both strong and not tall and vice versa.
If someone is either tall or wise then someone is generous or not happy.
Everyone who is not rich is not patient and vice versa.
If paul is both not funny and quiet then paul is not tall or wise.
Everyone who is brave is not curious.
If someone is either calm or creative then someone is either not wise or not calm.
Everyone who is tall is both not patient and tall and vice versa.
Someone is both not funny and not brave.
Paul is either happy or not kind.
John is both not calm and kind.
Lucy is not generous or creative.
Alice is patient.
Someone is strong.
Fred is both generous and not curious.
John is both tall and not creative. | Paul is not curious. | neutral | (![X]:((~funny(X)<~>generous(X))<=>(~happy(X)<~>old(X))))&
(((~curious(paul)&~wise(paul)))<=>((tall(fred)<~>kind(fred))))&
((?[X]:((rich(X)&~wise(X))))<=>((~generous(fred)&~humble(fred))))&
(![X]:((humble(X)|~kind(X))=>~quiet(X)))&
((?[X]:(~quiet(X)))=>((~creative(paul)<~>~wise(paul))))&
(((~humble(paul)|~old(paul)))=>(?[X]:(~funny(X))))&
(![X]:((strong(X)|wise(X))<=>(~quiet(X)&~creative(X))))&
(![X]:((strong(X)|creative(X))<=>(calm(X)<~>creative(X))))&
((?[X]:(patient(X)))<=>((~wise(john)&~funny(john))))&
(![X]:(brave(X)<=>(strong(X)&~tall(X))))&
((?[X]:((tall(X)<~>wise(X))))=>(?[X]:((generous(X)|~happy(X)))))&
(![X]:(~rich(X)<=>~patient(X)))&
(((~funny(paul)&quiet(paul)))=>((~tall(paul)|wise(paul))))&
(![X]:(brave(X)=>~curious(X)))&
((?[X]:((calm(X)<~>creative(X))))=>(?[X]:((~wise(X)<~>~calm(X)))))&
(![X]:(tall(X)<=>(~patient(X)&tall(X))))&
(?[X]:((~funny(X)&~brave(X))))&
((happy(paul)<~>~kind(paul)))&
((~calm(john)&kind(john)))&
((~generous(lucy)|creative(lucy)))&
(patient(alice))&
(?[X]:(strong(X)))&
((generous(fred)&~curious(fred)))&
((tall(john)&~creative(john))) | ~curious(paul) | [] | null | 0 |
Everyone who is either not patient or wise is either happy or not creative. If fred is not curious then someone is both brave and not old and vice versa. Everyone who is strong or not funny is both not humble and not quiet and vice versa. Everyone who is both not kind and tall is both calm and not wise. Everyone who is not patient or not funny is both patient and not rich and vice versa. Everyone who is brave is creative or patient and vice versa. If fred is tall then someone is not funny or not calm and vice versa. Everyone who is either not strong or happy is not tall or calm. If fred is old or not brave then john is not strong or curious and vice versa. If susan is either not kind or tall then someone is not brave or patient. Everyone who is not quiet or humble is strong. If alice is both not humble and old then someone is not funny and vice versa. Everyone who is both not patient and strong is both generous and not strong. Everyone who is either not rich or old is brave or not curious and vice versa. If paul is either not wise or not generous then fred is not curious or kind. Everyone who is both not strong and strong is both not happy and rich and vice versa. Someone is either not tall or tall. Someone is not curious or not patient. Susan is strong. Paul is either happy or rich. Alice is not kind. Mary is not creative. John is humble or not quiet. Susan is humble or wise. | Mary is patient. | entailment | (![X]:((~patient(X)<~>wise(X))=>(happy(X)<~>~creative(X))))&
((~curious(fred))<=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((strong(X)|~funny(X))<=>(~humble(X)&~quiet(X))))&
(![X]:((~kind(X)&tall(X))=>(calm(X)&~wise(X))))&
(![X]:((~patient(X)|~funny(X))<=>(patient(X)&~rich(X))))&
(![X]:(brave(X)<=>(creative(X)|patient(X))))&
((tall(fred))<=>(?[X]:((~funny(X)|~calm(X)))))&
(![X]:((~strong(X)<~>happy(X))=>(~tall(X)|calm(X))))&
(((old(fred)|~brave(fred)))<=>((~strong(john)|curious(john))))&
(((~kind(susan)<~>tall(susan)))=>(?[X]:((~brave(X)|patient(X)))))&
(![X]:((~quiet(X)|humble(X))=>strong(X)))&
(((~humble(alice)&old(alice)))<=>(?[X]:(~funny(X))))&
(![X]:((~patient(X)&strong(X))=>(generous(X)&~strong(X))))&
(![X]:((~rich(X)<~>old(X))<=>(brave(X)|~curious(X))))&
(((~wise(paul)<~>~generous(paul)))=>((~curious(fred)|kind(fred))))&
(![X]:((~strong(X)&strong(X))<=>(~happy(X)&rich(X))))&
(?[X]:((~tall(X)<~>tall(X))))&
(?[X]:((~curious(X)|~patient(X))))&
(strong(susan))&
((happy(paul)<~>rich(paul)))&
(~kind(alice))&
(~creative(mary))&
((humble(john)|~quiet(john)))&
((humble(susan)|wise(susan))) | patient(mary) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 7743838775784109884958334
% SZS output start Proof for 7743838775784109884958334
5. ! [X0] : ((~funny(X0) | ~patient(X0)) <=> (~rich(X0) & patient(X0))) [input p4]
25. ~patient(mary) [input hypothesis]
44. ! [X0] : (((~funny(X0) | ~patient(X0)) | (rich(X0) | ~patient(X0))) & ((~rich(X0) & patient(X0)) | (funny(X0) & patient(X0)))) [nnf transformation 5]
45. ! [X0] : ((~funny(X0) | ~patient(X0) | rich(X0) | ~patient(X0)) & ((~rich(X0) & patient(X0)) | (funny(X0) & patient(X0)))) [flattening 44]
88. patient(X0) | patient(X0) [cnf transformation 45]
136. ~patient(mary) [cnf transformation 25]
138. patient(X0) [duplicate literal removal 88]
231. $false [subsumption resolution 136,138]
% SZS output end Proof for 7743838775784109884958334
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and not rich is both quiet and calm.
If someone is both not old and not rich then paul is strong.
If alice is kind then someone is both not curious and not humble.
If susan is wise or creative then paul is funny or not creative.
If someone is either generous or not humble then mary is both not creative and not kind.
If someone is both not curious and not tall then john is not wise or not generous and vice versa.
Everyone who is not funny or not rich is either not curious or patient and vice versa.
Everyone who is both not curious and not old is not funny and vice versa.
If someone is not kind or curious then john is not rich and vice versa.
Everyone who is not curious is quiet and vice versa.
Everyone who is both not quiet and happy is funny and vice versa.
If mary is brave or rich then someone is both old and curious.
Everyone who is both not kind and not rich is quiet or curious and vice versa.
Everyone who is brave is funny or not generous and vice versa.
Everyone who is either old or not creative is not rich and vice versa.
Everyone who is not creative is not brave and vice versa.
Mary is either tall or not quiet.
Someone is not brave.
Alice is happy or tall.
Someone is patient or not brave.
Alice is not old.
Alice is both quiet and not creative. | Mary is not patient. | entailment | (![X]:((happy(X)&~rich(X))=>(quiet(X)&calm(X))))&
((?[X]:((~old(X)&~rich(X))))=>(strong(paul)))&
((kind(alice))=>(?[X]:((~curious(X)&~humble(X)))))&
(((wise(susan)|creative(susan)))=>((funny(paul)|~creative(paul))))&
((?[X]:((generous(X)<~>~humble(X))))=>((~creative(mary)&~kind(mary))))&
((?[X]:((~curious(X)&~tall(X))))<=>((~wise(john)|~generous(john))))&
(![X]:((~funny(X)|~rich(X))<=>(~curious(X)<~>patient(X))))&
(![X]:((~curious(X)&~old(X))<=>~funny(X)))&
((?[X]:((~kind(X)|curious(X))))<=>(~rich(john)))&
(![X]:(~curious(X)<=>quiet(X)))&
(![X]:((~quiet(X)&happy(X))<=>funny(X)))&
(((brave(mary)|rich(mary)))=>(?[X]:((old(X)&curious(X)))))&
(![X]:((~kind(X)&~rich(X))<=>(quiet(X)|curious(X))))&
(![X]:(brave(X)<=>(funny(X)|~generous(X))))&
(![X]:((old(X)<~>~creative(X))<=>~rich(X)))&
(![X]:(~creative(X)<=>~brave(X)))&
((tall(mary)<~>~quiet(mary)))&
(?[X]:(~brave(X)))&
((happy(alice)|tall(alice)))&
(?[X]:((patient(X)|~brave(X))))&
(~old(alice))&
((quiet(alice)&~creative(alice))) | ~patient(mary) | [
"p0",
"p6",
"p7",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 891122283066731267621220
% SZS output start Proof for 891122283066731267621220
1. ! [X0] : ((~rich(X0) & happy(X0)) => (calm(X0) & quiet(X0))) [input p0]
7. ! [X0] : ((~rich(X0) | ~funny(X0)) <=> (~curious(X0) <~> patient(X0))) [input p6]
8. ! [X0] : ((~old(X0) & ~curious(X0)) <=> ~funny(X0)) [input p7]
10. ! [X0] : (~curious(X0) <=> quiet(X0)) [input p9]
11. ! [X0] : ((happy(X0) & ~quiet(X0)) <=> funny(X0)) [input p10]
13. ! [X0] : ((~rich(X0) & ~kind(X0)) <=> (curious(X0) | quiet(X0))) [input p12]
23. patient(mary) [input hypothesis]
25. ! [X0] : ((~rich(X0) & happy(X0)) => quiet(X0)) [pure predicate removal 1]
26. ! [X0] : (quiet(X0) | (rich(X0) | ~happy(X0))) [ennf transformation 25]
27. ! [X0] : (quiet(X0) | rich(X0) | ~happy(X0)) [flattening 26]
41. ! [X0] : (((~rich(X0) | ~funny(X0)) | ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0)))) & (((~patient(X0) | curious(X0)) & (patient(X0) | ~curious(X0))) | (rich(X0) & funny(X0)))) [nnf transformation 7]
42. ! [X0] : ((~rich(X0) | ~funny(X0) | ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0)))) & (((~patient(X0) | curious(X0)) & (patient(X0) | ~curious(X0))) | (rich(X0) & funny(X0)))) [flattening 41]
43. ! [X0] : (((~old(X0) & ~curious(X0)) | funny(X0)) & (~funny(X0) | (old(X0) | curious(X0)))) [nnf transformation 8]
44. ! [X0] : (((~old(X0) & ~curious(X0)) | funny(X0)) & (~funny(X0) | old(X0) | curious(X0))) [flattening 43]
49. ! [X0] : ((~curious(X0) | ~quiet(X0)) & (quiet(X0) | curious(X0))) [nnf transformation 10]
50. ! [X0] : (((happy(X0) & ~quiet(X0)) | ~funny(X0)) & (funny(X0) | (~happy(X0) | quiet(X0)))) [nnf transformation 11]
51. ! [X0] : (((happy(X0) & ~quiet(X0)) | ~funny(X0)) & (funny(X0) | ~happy(X0) | quiet(X0))) [flattening 50]
54. ! [X0] : (((~rich(X0) & ~kind(X0)) | (~curious(X0) & ~quiet(X0))) & ((curious(X0) | quiet(X0)) | (rich(X0) | kind(X0)))) [nnf transformation 13]
55. ! [X0] : (((~rich(X0) & ~kind(X0)) | (~curious(X0) & ~quiet(X0))) & (curious(X0) | quiet(X0) | rich(X0) | kind(X0))) [flattening 54]
65. ~happy(X0) | rich(X0) | quiet(X0) [cnf transformation 27]
81. ~patient(X0) | curious(X0) | funny(X0) [cnf transformation 42]
86. ~curious(X0) | funny(X0) [cnf transformation 44]
91. curious(X0) | quiet(X0) [cnf transformation 49]
94. ~funny(X0) | ~quiet(X0) [cnf transformation 51]
95. ~funny(X0) | happy(X0) [cnf transformation 51]
103. ~quiet(X0) | ~rich(X0) [cnf transformation 55]
104. ~curious(X0) | ~rich(X0) [cnf transformation 55]
122. patient(mary) [cnf transformation 23]
243. 27 <=> quiet(mary) [avatar definition]
273. ~rich(X0) | quiet(X0) [resolution 104,91]
274. ~rich(X0) [subsumption resolution 273,103]
286. curious(mary) | funny(mary) [resolution 81,122]
287. funny(mary) [subsumption resolution 286,86]
289. happy(mary) [resolution 287,95]
290. ~quiet(mary) [resolution 287,94]
329. rich(mary) | quiet(mary) [resolution 289,65]
333. quiet(mary) [subsumption resolution 329,274]
349. 27 [avatar split clause 333,243]
350. ~27 [avatar split clause 290,243]
351. $false [avatar sat refutation 349,350]
% SZS output end Proof for 891122283066731267621220
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both curious and wise then someone is both strong and not funny.
Everyone who is curious is both creative and not funny and vice versa.
If someone is patient then someone is not tall or not funny.
Everyone who is brave or not calm is not generous or not funny and vice versa.
If mary is either not curious or not calm then someone is both not generous and patient and vice versa.
Everyone who is funny or not rich is both curious and not quiet and vice versa.
If someone is not kind then paul is not strong or not curious and vice versa.
If someone is both not curious and quiet then someone is both not quiet and not tall.
If john is not rich or not calm then john is either not quiet or not curious.
Everyone who is curious is either creative or funny.
Everyone who is either not happy or happy is either not happy or not wise and vice versa.
If fred is both generous and not old then john is both not strong and not wise.
If paul is both humble and not curious then someone is not brave and vice versa.
Everyone who is both not patient and kind is either creative or strong.
Everyone who is both curious and brave is rich or not calm and vice versa.
Everyone who is both rich and not patient is either tall or kind and vice versa.
Someone is either not wise or rich.
Someone is both rich and not strong.
Susan is either calm or not strong.
Someone is either old or kind.
Paul is wise or not funny.
John is rich.
Alice is both not calm and not funny.
John is tall or not wise. | Mary is funny. | contradiction | (((curious(john)&wise(john)))=>(?[X]:((strong(X)&~funny(X)))))&
(![X]:(curious(X)<=>(creative(X)&~funny(X))))&
((?[X]:(patient(X)))=>(?[X]:((~tall(X)|~funny(X)))))&
(![X]:((brave(X)|~calm(X))<=>(~generous(X)|~funny(X))))&
(((~curious(mary)<~>~calm(mary)))<=>(?[X]:((~generous(X)&patient(X)))))&
(![X]:((funny(X)|~rich(X))<=>(curious(X)&~quiet(X))))&
((?[X]:(~kind(X)))<=>((~strong(paul)|~curious(paul))))&
((?[X]:((~curious(X)&quiet(X))))=>(?[X]:((~quiet(X)&~tall(X)))))&
(((~rich(john)|~calm(john)))=>((~quiet(john)<~>~curious(john))))&
(![X]:(curious(X)=>(creative(X)<~>funny(X))))&
(![X]:((~happy(X)<~>happy(X))<=>(~happy(X)<~>~wise(X))))&
(((generous(fred)&~old(fred)))=>((~strong(john)&~wise(john))))&
(((humble(paul)&~curious(paul)))<=>(?[X]:(~brave(X))))&
(![X]:((~patient(X)&kind(X))=>(creative(X)<~>strong(X))))&
(![X]:((curious(X)&brave(X))<=>(rich(X)|~calm(X))))&
(![X]:((rich(X)&~patient(X))<=>(tall(X)<~>kind(X))))&
(?[X]:((~wise(X)<~>rich(X))))&
(?[X]:((rich(X)&~strong(X))))&
((calm(susan)<~>~strong(susan)))&
(?[X]:((old(X)<~>kind(X))))&
((wise(paul)|~funny(paul)))&
(rich(john))&
((~calm(alice)&~funny(alice)))&
((tall(john)|~wise(john))) | funny(mary) | [
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6114529707350229665652768
% SZS output start Proof for 6114529707350229665652768
2. ! [X0] : (curious(X0) <=> (~funny(X0) & creative(X0))) [input p1]
6. ! [X0] : ((~rich(X0) | funny(X0)) <=> (~quiet(X0) & curious(X0))) [input p5]
25. funny(mary) [input hypothesis]
40. ! [X0] : ((curious(X0) | (funny(X0) | ~creative(X0))) & ((~funny(X0) & creative(X0)) | ~curious(X0))) [nnf transformation 2]
41. ! [X0] : ((curious(X0) | funny(X0) | ~creative(X0)) & ((~funny(X0) & creative(X0)) | ~curious(X0))) [flattening 40]
51. ! [X0] : (((~rich(X0) | funny(X0)) | (quiet(X0) | ~curious(X0))) & ((~quiet(X0) & curious(X0)) | (rich(X0) & ~funny(X0)))) [nnf transformation 6]
52. ! [X0] : ((~rich(X0) | funny(X0) | quiet(X0) | ~curious(X0)) & ((~quiet(X0) & curious(X0)) | (rich(X0) & ~funny(X0)))) [flattening 51]
86. ~funny(X0) | ~curious(X0) [cnf transformation 41]
99. curious(X0) | ~funny(X0) [cnf transformation 52]
154. funny(mary) [cnf transformation 25]
219. ~funny(X0) [subsumption resolution 99,86]
326. $false [subsumption resolution 154,219]
% SZS output end Proof for 6114529707350229665652768
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not rich is either brave or tall and vice versa. Everyone who is both not calm and not humble is kind and vice versa. If someone is not old or not curious then mary is not old or patient. If someone is not brave then susan is either not curious or not tall. Everyone who is both not curious and funny is not quiet and vice versa. Everyone who is not creative is kind or not patient and vice versa. Everyone who is both tall and kind is not brave or rich and vice versa. Everyone who is both not calm and kind is either not calm or not creative. If someone is both brave and old then someone is either patient or not generous. If mary is happy then susan is either funny or not funny. If someone is happy or funny then alice is either not old or strong and vice versa. Everyone who is tall is strong or not generous. Everyone who is funny is both kind and not calm. If someone is strong or quiet then john is not rich or not patient and vice versa. If lucy is both brave and not humble then john is rich or curious. If someone is not tall or not curious then someone is wise or generous. Someone is not tall. Someone is brave. John is both not curious and humble. John is both old and not funny. Someone is either not quiet or not curious. Someone is not generous or not patient. Alice is either not quiet or not tall. | Alice is quiet. | entailment | (![X]:((strong(X)<~>~rich(X))<=>(brave(X)<~>tall(X))))&
(![X]:((~calm(X)&~humble(X))<=>kind(X)))&
((?[X]:((~old(X)|~curious(X))))=>((~old(mary)|patient(mary))))&
((?[X]:(~brave(X)))=>((~curious(susan)<~>~tall(susan))))&
(![X]:((~curious(X)&funny(X))<=>~quiet(X)))&
(![X]:(~creative(X)<=>(kind(X)|~patient(X))))&
(![X]:((tall(X)&kind(X))<=>(~brave(X)|rich(X))))&
(![X]:((~calm(X)&kind(X))=>(~calm(X)<~>~creative(X))))&
((?[X]:((brave(X)&old(X))))=>(?[X]:((patient(X)<~>~generous(X)))))&
((happy(mary))=>((funny(susan)<~>~funny(susan))))&
((?[X]:((happy(X)|funny(X))))<=>((~old(alice)<~>strong(alice))))&
(![X]:(tall(X)=>(strong(X)|~generous(X))))&
(![X]:(funny(X)=>(kind(X)&~calm(X))))&
((?[X]:((strong(X)|quiet(X))))<=>((~rich(john)|~patient(john))))&
(((brave(lucy)&~humble(lucy)))=>((rich(john)|curious(john))))&
((?[X]:((~tall(X)|~curious(X))))=>(?[X]:((wise(X)|generous(X)))))&
(?[X]:(~tall(X)))&
(?[X]:(brave(X)))&
((~curious(john)&humble(john)))&
((old(john)&~funny(john)))&
(?[X]:((~quiet(X)<~>~curious(X))))&
(?[X]:((~generous(X)|~patient(X))))&
((~quiet(alice)<~>~tall(alice))) | quiet(alice) | [
"p1",
"p4",
"p5",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2671491170824982900513216
% SZS output start Proof for 2671491170824982900513216
2. ! [X0] : ((~humble(X0) & ~calm(X0)) <=> kind(X0)) [input p1]
5. ! [X0] : ((funny(X0) & ~curious(X0)) <=> ~quiet(X0)) [input p4]
6. ! [X0] : (~creative(X0) <=> (~patient(X0) | kind(X0))) [input p5]
8. ! [X0] : ((kind(X0) & ~calm(X0)) => (~calm(X0) <~> ~creative(X0))) [input p7]
13. ! [X0] : (funny(X0) => (~calm(X0) & kind(X0))) [input p12]
24. ~quiet(alice) [input hypothesis]
31. ! [X0] : ((~calm(X0) <~> ~creative(X0)) | (~kind(X0) | calm(X0))) [ennf transformation 8]
32. ! [X0] : ((~calm(X0) <~> ~creative(X0)) | ~kind(X0) | calm(X0)) [flattening 31]
37. ! [X0] : ((~calm(X0) & kind(X0)) | ~funny(X0)) [ennf transformation 13]
41. ! [X0] : (((~humble(X0) & ~calm(X0)) | ~kind(X0)) & (kind(X0) | (humble(X0) | calm(X0)))) [nnf transformation 2]
42. ! [X0] : (((~humble(X0) & ~calm(X0)) | ~kind(X0)) & (kind(X0) | humble(X0) | calm(X0))) [flattening 41]
44. ! [X0] : (((funny(X0) & ~curious(X0)) | quiet(X0)) & (~quiet(X0) | (~funny(X0) | curious(X0)))) [nnf transformation 5]
45. ! [X0] : (((funny(X0) & ~curious(X0)) | quiet(X0)) & (~quiet(X0) | ~funny(X0) | curious(X0))) [flattening 44]
46. ! [X0] : ((~creative(X0) | (patient(X0) & ~kind(X0))) & ((~patient(X0) | kind(X0)) | creative(X0))) [nnf transformation 6]
47. ! [X0] : ((~creative(X0) | (patient(X0) & ~kind(X0))) & (~patient(X0) | kind(X0) | creative(X0))) [flattening 46]
50. ! [X0] : (((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | ~kind(X0) | calm(X0)) [nnf transformation 32]
84. ~kind(X0) | ~calm(X0) [cnf transformation 42]
92. quiet(X0) | funny(X0) [cnf transformation 45]
94. ~creative(X0) | ~kind(X0) [cnf transformation 47]
102. creative(X0) | calm(X0) | ~kind(X0) | calm(X0) [cnf transformation 50]
114. kind(X0) | ~funny(X0) [cnf transformation 37]
132. ~quiet(alice) [cnf transformation 24]
133. creative(X0) | calm(X0) | ~kind(X0) [duplicate literal removal 102]
163. creative(X0) | ~kind(X0) [subsumption resolution 133,84]
164. ~kind(X0) [subsumption resolution 163,94]
197. 15 <=> ! [X1] : ~funny(X1) [avatar definition]
198. ~funny(X1) <- (15) [avatar component clause 197]
206. ~funny(X0) [subsumption resolution 114,164]
207. 15 [avatar split clause 206,197]
260. 28 <=> quiet(alice) [avatar definition]
261. ~quiet(alice) <- (~28) [avatar component clause 260]
269. ~28 [avatar split clause 132,260]
271. funny(alice) <- (~28) [resolution 92,261]
272. $false <- (15, ~28) [subsumption resolution 271,198]
273. ~15 | 28 [avatar contradiction clause 272]
274. $false [avatar sat refutation 207,269,273]
% SZS output end Proof for 2671491170824982900513216
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both generous and calm then susan is either not kind or not strong.
Everyone who is both not brave and strong is both not patient and wise and vice versa.
Everyone who is patient is not patient.
Everyone who is both kind and tall is both brave and not kind.
If someone is either not calm or funny then someone is not tall or creative.
If paul is not quiet or not rich then someone is either happy or curious and vice versa.
If fred is either not brave or not tall then someone is either not curious or not tall and vice versa.
Everyone who is happy is kind.
If someone is not funny then alice is either not old or curious.
Everyone who is not wise or old is either not calm or not old.
If someone is both quiet and not quiet then someone is calm or not tall and vice versa.
Everyone who is not old or not wise is both not wise and not strong.
Everyone who is either not generous or humble is both patient and not happy.
If mary is either curious or not patient then someone is not patient.
Everyone who is not strong is creative and vice versa.
If lucy is both not patient and strong then someone is creative and vice versa.
Someone is not generous or not calm.
Paul is either not funny or brave.
Someone is both strong and not patient.
Someone is old.
Mary is both not rich and creative.
Lucy is both not generous and not creative.
Susan is either not quiet or tall. | Fred is calm. | contradiction | (((generous(susan)&calm(susan)))=>((~kind(susan)<~>~strong(susan))))&
(![X]:((~brave(X)&strong(X))<=>(~patient(X)&wise(X))))&
(![X]:(patient(X)=>~patient(X)))&
(![X]:((kind(X)&tall(X))=>(brave(X)&~kind(X))))&
((?[X]:((~calm(X)<~>funny(X))))=>(?[X]:((~tall(X)|creative(X)))))&
(((~quiet(paul)|~rich(paul)))<=>(?[X]:((happy(X)<~>curious(X)))))&
(((~brave(fred)<~>~tall(fred)))<=>(?[X]:((~curious(X)<~>~tall(X)))))&
(![X]:(happy(X)=>kind(X)))&
((?[X]:(~funny(X)))=>((~old(alice)<~>curious(alice))))&
(![X]:((~wise(X)|old(X))=>(~calm(X)<~>~old(X))))&
((?[X]:((quiet(X)&~quiet(X))))<=>(?[X]:((calm(X)|~tall(X)))))&
(![X]:((~old(X)|~wise(X))=>(~wise(X)&~strong(X))))&
(![X]:((~generous(X)<~>humble(X))=>(patient(X)&~happy(X))))&
(((curious(mary)<~>~patient(mary)))=>(?[X]:(~patient(X))))&
(![X]:(~strong(X)<=>creative(X)))&
(((~patient(lucy)&strong(lucy)))<=>(?[X]:(creative(X))))&
(?[X]:((~generous(X)|~calm(X))))&
((~funny(paul)<~>brave(paul)))&
(?[X]:((strong(X)&~patient(X))))&
(?[X]:(old(X)))&
((~rich(mary)&creative(mary)))&
((~generous(lucy)&~creative(lucy)))&
((~quiet(susan)<~>tall(susan))) | calm(fred) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4519086721618489078396711
% SZS output start Proof for 4519086721618489078396711
11. ? [X0] : (~quiet(X0) & quiet(X0)) <=> ? [X0] : (~tall(X0) | calm(X0)) [input p10]
24. calm(fred) [input hypothesis]
26. ? [X0] : (~quiet(X0) & quiet(X0)) <=> ? [X1] : (~tall(X1) | calm(X1)) [rectify 11]
57. (? [X0] : (~quiet(X0) & quiet(X0)) | ! [X1] : (tall(X1) & ~calm(X1))) & (? [X1] : (~tall(X1) | calm(X1)) | ! [X0] : (quiet(X0) | ~quiet(X0))) [nnf transformation 26]
58. (? [X0] : (~quiet(X0) & quiet(X0)) | ! [X1] : (tall(X1) & ~calm(X1))) & (? [X2] : (~tall(X2) | calm(X2)) | ! [X3] : (quiet(X3) | ~quiet(X3))) [rectify 57]
59. ? [X0] : (~quiet(X0) & quiet(X0)) => (~quiet(sK3) & quiet(sK3)) [choice axiom]
60. ? [X2] : (~tall(X2) | calm(X2)) => (~tall(sK4) | calm(sK4)) [choice axiom]
61. ((~quiet(sK3) & quiet(sK3)) | ! [X1] : (tall(X1) & ~calm(X1))) & ((~tall(sK4) | calm(sK4)) | ! [X3] : (quiet(X3) | ~quiet(X3))) [skolemisation 58,60,59]
113. quiet(sK3) | ~calm(X1) [cnf transformation 61]
115. ~quiet(sK3) | ~calm(X1) [cnf transformation 61]
144. calm(fred) [cnf transformation 24]
257. 25 <=> quiet(sK3) [avatar definition]
262. 26 <=> ! [X1] : ~calm(X1) [avatar definition]
263. ~calm(X1) <- (26) [avatar component clause 262]
264. 26 | ~25 [avatar split clause 115,257,262]
266. 26 | 25 [avatar split clause 113,257,262]
323. $false <- (26) [resolution 263,144]
324. ~26 [avatar contradiction clause 323]
325. $false [avatar sat refutation 264,266,324]
% SZS output end Proof for 4519086721618489078396711
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is either not funny or kind and vice versa. Everyone who is both not calm and creative is both not rich and strong and vice versa. Everyone who is either not old or creative is both not kind and not curious and vice versa. If john is either not quiet or not happy then fred is both not strong and not wise. Everyone who is both curious and not humble is either brave or happy. Everyone who is kind is either kind or not happy and vice versa. If someone is both funny and happy then john is creative. Everyone who is patient or calm is either quiet or not rich. Everyone who is both not tall and not rich is either happy or not calm and vice versa. Everyone who is old is brave. If lucy is not creative or wise then paul is calm or not rich. Everyone who is not calm or not curious is old or not happy and vice versa. If someone is humble then john is both happy and not humble and vice versa. If someone is not tall then john is not funny and vice versa. Someone is not creative or quiet. Someone is happy or rich. Susan is old or tall. Someone is either not calm or not tall. Fred is not strong or not rich. | Susan is brave. | entailment | (![X]:((~curious(X)<~>wise(X))<=>(~funny(X)<~>kind(X))))&
(![X]:((~calm(X)&creative(X))<=>(~rich(X)&strong(X))))&
(![X]:((~old(X)<~>creative(X))<=>(~kind(X)&~curious(X))))&
(((~quiet(john)<~>~happy(john)))=>((~strong(fred)&~wise(fred))))&
(![X]:((curious(X)&~humble(X))=>(brave(X)<~>happy(X))))&
(![X]:(kind(X)<=>(kind(X)<~>~happy(X))))&
((?[X]:((funny(X)&happy(X))))=>(creative(john)))&
(![X]:((patient(X)|calm(X))=>(quiet(X)<~>~rich(X))))&
(![X]:((~tall(X)&~rich(X))<=>(happy(X)<~>~calm(X))))&
(![X]:(old(X)=>brave(X)))&
(((~creative(lucy)|wise(lucy)))=>((calm(paul)|~rich(paul))))&
(![X]:((~calm(X)|~curious(X))<=>(old(X)|~happy(X))))&
((?[X]:(humble(X)))<=>((happy(john)&~humble(john))))&
((?[X]:(~tall(X)))<=>(~funny(john)))&
(?[X]:((~creative(X)|quiet(X))))&
(?[X]:((happy(X)|rich(X))))&
((old(susan)|tall(susan)))&
(?[X]:((~calm(X)<~>~tall(X))))&
((~strong(fred)|~rich(fred))) | brave(susan) | [
"p5",
"p8",
"p9",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7904959459874228601666091
% SZS output start Proof for 7904959459874228601666091
6. ! [X0] : (kind(X0) <=> (kind(X0) <~> ~happy(X0))) [input p5]
9. ! [X0] : ((~rich(X0) & ~tall(X0)) <=> (happy(X0) <~> ~calm(X0))) [input p8]
10. ! [X0] : (old(X0) => brave(X0)) [input p9]
12. ! [X0] : ((~curious(X0) | ~calm(X0)) <=> (~happy(X0) | old(X0))) [input p11]
17. tall(susan) | old(susan) [input p16]
20. ~brave(susan) [input hypothesis]
27. ! [X0] : (brave(X0) | ~old(X0)) [ennf transformation 10]
37. ! [X0] : ((kind(X0) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0)))) & (((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | ~kind(X0))) [nnf transformation 6]
39. ! [X0] : (((~rich(X0) & ~tall(X0)) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) & (((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | (rich(X0) | tall(X0)))) [nnf transformation 9]
40. ! [X0] : (((~rich(X0) & ~tall(X0)) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) & (((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | rich(X0) | tall(X0))) [flattening 39]
41. ! [X0] : (((~curious(X0) | ~calm(X0)) | (happy(X0) & ~old(X0))) & ((~happy(X0) | old(X0)) | (curious(X0) & calm(X0)))) [nnf transformation 12]
42. ! [X0] : ((~curious(X0) | ~calm(X0) | (happy(X0) & ~old(X0))) & (~happy(X0) | old(X0) | (curious(X0) & calm(X0)))) [flattening 41]
84. happy(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 37]
86. kind(X0) | kind(X0) | happy(X0) [cnf transformation 37]
92. ~tall(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 40]
96. ~old(X0) | brave(X0) [cnf transformation 27]
99. ~happy(X0) | old(X0) | calm(X0) [cnf transformation 42]
110. tall(susan) | old(susan) [cnf transformation 17]
114. ~brave(susan) [cnf transformation 20]
115. happy(X0) | ~kind(X0) [duplicate literal removal 84]
116. happy(X0) | kind(X0) [duplicate literal removal 86]
137. happy(X0) [subsumption resolution 115,116]
148. ~tall(X0) | ~calm(X0) [subsumption resolution 92,137]
167. old(X0) | calm(X0) [subsumption resolution 99,137]
205. 18 <=> old(susan) [avatar definition]
206. ~old(susan) <- (~18) [avatar component clause 205]
207. old(susan) <- (18) [avatar component clause 205]
209. 19 <=> tall(susan) [avatar definition]
211. tall(susan) <- (19) [avatar component clause 209]
212. 18 | 19 [avatar split clause 110,209,205]
227. brave(susan) <- (18) [resolution 96,207]
228. $false <- (18) [subsumption resolution 227,114]
229. ~18 [avatar contradiction clause 228]
230. ~calm(susan) <- (19) [resolution 148,211]
234. calm(susan) <- (~18) [resolution 167,206]
235. $false <- (~18, 19) [subsumption resolution 234,230]
236. 18 | ~19 [avatar contradiction clause 235]
237. $false [avatar sat refutation 212,229,236]
% SZS output end Proof for 7904959459874228601666091
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then fred is either not patient or not kind and vice versa.
If someone is not generous then paul is both calm and not tall.
Everyone who is not old is calm or not rich and vice versa.
If someone is not patient then alice is creative or not funny and vice versa.
If someone is either old or creative then fred is old.
Everyone who is both humble and wise is curious or creative and vice versa.
Everyone who is funny is not tall or not rich and vice versa.
Everyone who is not wise or not patient is both generous and kind.
If susan is either happy or not creative then someone is generous.
If paul is creative then someone is patient or not wise.
If someone is kind then someone is brave.
If someone is brave then someone is either not strong or not kind.
Everyone who is not patient or not wise is not generous.
If paul is both not strong and not curious then john is not rich or rich and vice versa.
Everyone who is either generous or brave is either calm or not generous and vice versa.
If susan is generous then someone is both old and not wise and vice versa.
Fred is not happy or kind.
Someone is both funny and not rich.
John is either creative or not happy.
Someone is either not quiet or not brave.
Someone is both rich and not brave.
Mary is both not humble and not kind.
Someone is not calm or not old.
Lucy is either funny or not strong. | Paul is not funny. | contradiction | ((?[X]:(~generous(X)))<=>((~patient(fred)<~>~kind(fred))))&
((?[X]:(~generous(X)))=>((calm(paul)&~tall(paul))))&
(![X]:(~old(X)<=>(calm(X)|~rich(X))))&
((?[X]:(~patient(X)))<=>((creative(alice)|~funny(alice))))&
((?[X]:((old(X)<~>creative(X))))=>(old(fred)))&
(![X]:((humble(X)&wise(X))<=>(curious(X)|creative(X))))&
(![X]:(funny(X)<=>(~tall(X)|~rich(X))))&
(![X]:((~wise(X)|~patient(X))=>(generous(X)&kind(X))))&
(((happy(susan)<~>~creative(susan)))=>(?[X]:(generous(X))))&
((creative(paul))=>(?[X]:((patient(X)|~wise(X)))))&
((?[X]:(kind(X)))=>(?[X]:(brave(X))))&
((?[X]:(brave(X)))=>(?[X]:((~strong(X)<~>~kind(X)))))&
(![X]:((~patient(X)|~wise(X))=>~generous(X)))&
(((~strong(paul)&~curious(paul)))<=>((~rich(john)|rich(john))))&
(![X]:((generous(X)<~>brave(X))<=>(calm(X)<~>~generous(X))))&
((generous(susan))<=>(?[X]:((old(X)&~wise(X)))))&
((~happy(fred)|kind(fred)))&
(?[X]:((funny(X)&~rich(X))))&
((creative(john)<~>~happy(john)))&
(?[X]:((~quiet(X)<~>~brave(X))))&
(?[X]:((rich(X)&~brave(X))))&
((~humble(mary)&~kind(mary)))&
(?[X]:((~calm(X)|~old(X))))&
((funny(lucy)<~>~strong(lucy))) | ~funny(paul) | [
"p1",
"p6",
"p7",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 731237214740682990678022
% SZS output start Proof for 731237214740682990678022
2. ? [X0] : ~generous(X0) => (~tall(paul) & calm(paul)) [input p1]
7. ! [X0] : (funny(X0) <=> (~rich(X0) | ~tall(X0))) [input p6]
8. ! [X0] : ((~patient(X0) | ~wise(X0)) => (kind(X0) & generous(X0))) [input p7]
13. ! [X0] : ((~wise(X0) | ~patient(X0)) => ~generous(X0)) [input p12]
16. generous(susan) <=> ? [X0] : (~wise(X0) & old(X0)) [input p15]
25. ~funny(paul) [input hypothesis]
28. (~tall(paul) & calm(paul)) | ! [X0] : generous(X0) [ennf transformation 2]
30. ! [X0] : ((kind(X0) & generous(X0)) | (patient(X0) & wise(X0))) [ennf transformation 8]
35. ! [X0] : (~generous(X0) | (wise(X0) & patient(X0))) [ennf transformation 13]
50. ! [X0] : ((funny(X0) | (rich(X0) & tall(X0))) & ((~rich(X0) | ~tall(X0)) | ~funny(X0))) [nnf transformation 7]
51. ! [X0] : ((funny(X0) | (rich(X0) & tall(X0))) & (~rich(X0) | ~tall(X0) | ~funny(X0))) [flattening 50]
67. (generous(susan) | ! [X0] : (wise(X0) | ~old(X0))) & (? [X0] : (~wise(X0) & old(X0)) | ~generous(susan)) [nnf transformation 16]
68. (generous(susan) | ! [X0] : (wise(X0) | ~old(X0))) & (? [X1] : (~wise(X1) & old(X1)) | ~generous(susan)) [rectify 67]
69. ? [X1] : (~wise(X1) & old(X1)) => (~wise(sK6) & old(sK6)) [choice axiom]
70. (generous(susan) | ! [X0] : (wise(X0) | ~old(X0))) & ((~wise(sK6) & old(sK6)) | ~generous(susan)) [skolemisation 68,69]
87. ~tall(paul) | generous(X0) [cnf transformation 28]
102. funny(X0) | tall(X0) [cnf transformation 51]
104. generous(X0) | wise(X0) [cnf transformation 30]
115. ~generous(X0) | wise(X0) [cnf transformation 35]
130. ~wise(sK6) | ~generous(susan) [cnf transformation 70]
146. ~funny(paul) [cnf transformation 25]
166. 4 <=> ! [X1] : generous(X1) [avatar definition]
167. generous(X1) <- (4) [avatar component clause 166]
171. 5 <=> tall(paul) [avatar definition]
174. 4 | ~5 [avatar split clause 87,171,166]
258. wise(X0) [subsumption resolution 115,104]
279. ~generous(susan) [subsumption resolution 130,258]
327. tall(paul) [resolution 102,146]
331. 5 [avatar split clause 327,171]
336. $false <- (4) [resolution 167,279]
337. ~4 [avatar contradiction clause 336]
338. $false [avatar sat refutation 174,331,337]
% SZS output end Proof for 731237214740682990678022
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either tall or strong then someone is either happy or patient. If lucy is not generous then someone is either not kind or kind and vice versa. Everyone who is generous is both not wise and not calm and vice versa. If someone is not strong then someone is either not strong or wise and vice versa. Everyone who is either not wise or not rich is either not quiet or curious and vice versa. If someone is not kind then someone is both not humble and happy. If someone is both not quiet and old then alice is either not kind or creative. Everyone who is happy or quiet is both old and humble. If someone is not kind or not calm then lucy is not tall or strong and vice versa. If someone is funny then susan is either patient or not curious and vice versa. If fred is either happy or not funny then john is both not rich and not old and vice versa. Everyone who is quiet is both calm and not rich. Everyone who is both not generous and quiet is both not tall and not quiet and vice versa. If alice is either old or not calm then someone is not creative. Everyone who is not tall or kind is both humble and not calm and vice versa. If someone is both not kind and generous then susan is either humble or not calm and vice versa. Paul is not quiet. Someone is tall or not strong. Someone is both humble and funny. Someone is funny. Someone is generous. Lucy is tall or funny. Someone is not strong or humble. | Lucy is quiet. | contradiction | (((tall(alice)<~>strong(alice)))=>(?[X]:((happy(X)<~>patient(X)))))&
((~generous(lucy))<=>(?[X]:((~kind(X)<~>kind(X)))))&
(![X]:(generous(X)<=>(~wise(X)&~calm(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~strong(X)<~>wise(X)))))&
(![X]:((~wise(X)<~>~rich(X))<=>(~quiet(X)<~>curious(X))))&
((?[X]:(~kind(X)))=>(?[X]:((~humble(X)&happy(X)))))&
((?[X]:((~quiet(X)&old(X))))=>((~kind(alice)<~>creative(alice))))&
(![X]:((happy(X)|quiet(X))=>(old(X)&humble(X))))&
((?[X]:((~kind(X)|~calm(X))))<=>((~tall(lucy)|strong(lucy))))&
((?[X]:(funny(X)))<=>((patient(susan)<~>~curious(susan))))&
(((happy(fred)<~>~funny(fred)))<=>((~rich(john)&~old(john))))&
(![X]:(quiet(X)=>(calm(X)&~rich(X))))&
(![X]:((~generous(X)&quiet(X))<=>(~tall(X)&~quiet(X))))&
(((old(alice)<~>~calm(alice)))=>(?[X]:(~creative(X))))&
(![X]:((~tall(X)|kind(X))<=>(humble(X)&~calm(X))))&
((?[X]:((~kind(X)&generous(X))))<=>((humble(susan)<~>~calm(susan))))&
(~quiet(paul))&
(?[X]:((tall(X)|~strong(X))))&
(?[X]:((humble(X)&funny(X))))&
(?[X]:(funny(X)))&
(?[X]:(generous(X)))&
((tall(lucy)|funny(lucy)))&
(?[X]:((~strong(X)|humble(X)))) | quiet(lucy) | [
"p5",
"p7",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8566151082746181314533520
% SZS output start Proof for 8566151082746181314533520
6. ? [X0] : ~kind(X0) => ? [X0] : (happy(X0) & ~humble(X0)) [input p5]
8. ! [X0] : ((quiet(X0) | happy(X0)) => (humble(X0) & old(X0))) [input p7]
12. ! [X0] : (quiet(X0) => (~rich(X0) & calm(X0))) [input p11]
15. ! [X0] : ((kind(X0) | ~tall(X0)) <=> (~calm(X0) & humble(X0))) [input p14]
24. quiet(lucy) [input hypothesis]
26. ? [X0] : ~kind(X0) => ? [X1] : (happy(X1) & ~humble(X1)) [rectify 6]
28. ? [X1] : (happy(X1) & ~humble(X1)) | ! [X0] : kind(X0) [ennf transformation 26]
30. ! [X0] : ((humble(X0) & old(X0)) | (~quiet(X0) & ~happy(X0))) [ennf transformation 8]
31. ! [X0] : ((~rich(X0) & calm(X0)) | ~quiet(X0)) [ennf transformation 12]
48. ? [X0] : (happy(X0) & ~humble(X0)) | ! [X1] : kind(X1) [rectify 28]
49. ? [X0] : (happy(X0) & ~humble(X0)) => (happy(sK4) & ~humble(sK4)) [choice axiom]
50. (happy(sK4) & ~humble(sK4)) | ! [X1] : kind(X1) [skolemisation 48,49]
68. ! [X0] : (((kind(X0) | ~tall(X0)) | (calm(X0) | ~humble(X0))) & ((~calm(X0) & humble(X0)) | (~kind(X0) & tall(X0)))) [nnf transformation 15]
69. ! [X0] : ((kind(X0) | ~tall(X0) | calm(X0) | ~humble(X0)) & ((~calm(X0) & humble(X0)) | (~kind(X0) & tall(X0)))) [flattening 68]
107. ~humble(sK4) | kind(X1) [cnf transformation 50]
108. happy(sK4) | kind(X1) [cnf transformation 50]
113. ~happy(X0) | humble(X0) [cnf transformation 30]
129. ~quiet(X0) | calm(X0) [cnf transformation 31]
140. ~calm(X0) | ~kind(X0) [cnf transformation 69]
156. quiet(lucy) [cnf transformation 24]
190. 7 <=> ! [X0] : kind(X0) [avatar definition]
191. kind(X0) <- (7) [avatar component clause 190]
219. 14 <=> happy(sK4) [avatar definition]
221. happy(sK4) <- (14) [avatar component clause 219]
222. 7 | 14 [avatar split clause 108,219,190]
224. 15 <=> humble(sK4) [avatar definition]
227. 7 | ~15 [avatar split clause 107,224,190]
371. humble(sK4) <- (14) [resolution 113,221]
374. 15 | ~14 [avatar split clause 371,219,224]
378. calm(lucy) [resolution 129,156]
384. ~kind(lucy) [resolution 140,378]
385. $false <- (7) [subsumption resolution 384,191]
386. ~7 [avatar contradiction clause 385]
387. $false [avatar sat refutation 222,227,374,386]
% SZS output end Proof for 8566151082746181314533520
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy or not funny then someone is both not kind and wise.
Everyone who is not curious is tall or strong and vice versa.
Everyone who is not funny or not generous is not strong and vice versa.
Everyone who is not quiet is either not humble or curious.
Everyone who is both humble and happy is either not tall or funny and vice versa.
If someone is not funny then fred is either not tall or not old.
If john is curious then john is not curious or calm.
If someone is either quiet or kind then lucy is both not generous and not wise.
Everyone who is humble is not happy or old.
Everyone who is tall or old is not tall or strong and vice versa.
If someone is quiet or not old then someone is both not wise and wise.
If someone is both patient and not quiet then fred is calm.
Everyone who is either not tall or not calm is both creative and not wise and vice versa.
If someone is not creative or not generous then someone is both wise and not kind.
If fred is both happy and old then john is funny and vice versa.
Everyone who is both not happy and funny is not funny and vice versa.
Mary is both not curious and patient.
Alice is happy or funny.
Mary is not creative.
Someone is not calm or strong.
Alice is not old or funny.
Alice is both not quiet and creative.
Someone is not calm.
Someone is happy. | Alice is not strong. | contradiction | ((?[X]:((~happy(X)|~funny(X))))=>(?[X]:((~kind(X)&wise(X)))))&
(![X]:(~curious(X)<=>(tall(X)|strong(X))))&
(![X]:((~funny(X)|~generous(X))<=>~strong(X)))&
(![X]:(~quiet(X)=>(~humble(X)<~>curious(X))))&
(![X]:((humble(X)&happy(X))<=>(~tall(X)<~>funny(X))))&
((?[X]:(~funny(X)))=>((~tall(fred)<~>~old(fred))))&
((curious(john))=>((~curious(john)|calm(john))))&
((?[X]:((quiet(X)<~>kind(X))))=>((~generous(lucy)&~wise(lucy))))&
(![X]:(humble(X)=>(~happy(X)|old(X))))&
(![X]:((tall(X)|old(X))<=>(~tall(X)|strong(X))))&
((?[X]:((quiet(X)|~old(X))))=>(?[X]:((~wise(X)&wise(X)))))&
((?[X]:((patient(X)&~quiet(X))))=>(calm(fred)))&
(![X]:((~tall(X)<~>~calm(X))<=>(creative(X)&~wise(X))))&
((?[X]:((~creative(X)|~generous(X))))=>(?[X]:((wise(X)&~kind(X)))))&
(((happy(fred)&old(fred)))<=>(funny(john)))&
(![X]:((~happy(X)&funny(X))<=>~funny(X)))&
((~curious(mary)&patient(mary)))&
((happy(alice)|funny(alice)))&
(~creative(mary))&
(?[X]:((~calm(X)|strong(X))))&
((~old(alice)|funny(alice)))&
((~quiet(alice)&creative(alice)))&
(?[X]:(~calm(X)))&
(?[X]:(happy(X))) | ~strong(alice) | [
"p1",
"p3",
"p4",
"p9",
"p15",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 886677304501728955510709
% SZS output start Proof for 886677304501728955510709
2. ! [X0] : (~curious(X0) <=> (strong(X0) | tall(X0))) [input p1]
4. ! [X0] : (~quiet(X0) => (~humble(X0) <~> curious(X0))) [input p3]
5. ! [X0] : ((happy(X0) & humble(X0)) <=> (~tall(X0) <~> funny(X0))) [input p4]
10. ! [X0] : ((old(X0) | tall(X0)) <=> (strong(X0) | ~tall(X0))) [input p9]
16. ! [X0] : ((funny(X0) & ~happy(X0)) <=> ~funny(X0)) [input p15]
18. funny(alice) | happy(alice) [input p17]
22. creative(alice) & ~quiet(alice) [input p21]
25. ~strong(alice) [input hypothesis]
30. ! [X0] : ((~humble(X0) <~> curious(X0)) | quiet(X0)) [ennf transformation 4]
43. ! [X0] : ((~curious(X0) | (~strong(X0) & ~tall(X0))) & ((strong(X0) | tall(X0)) | curious(X0))) [nnf transformation 2]
44. ! [X0] : ((~curious(X0) | (~strong(X0) & ~tall(X0))) & (strong(X0) | tall(X0) | curious(X0))) [flattening 43]
47. ! [X0] : (((~curious(X0) | humble(X0)) & (curious(X0) | ~humble(X0))) | quiet(X0)) [nnf transformation 30]
48. ! [X0] : (((happy(X0) & humble(X0)) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0)))) & (((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | (~happy(X0) | ~humble(X0)))) [nnf transformation 5]
49. ! [X0] : (((happy(X0) & humble(X0)) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0)))) & (((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | ~happy(X0) | ~humble(X0))) [flattening 48]
52. ! [X0] : (((old(X0) | tall(X0)) | (~strong(X0) & tall(X0))) & ((strong(X0) | ~tall(X0)) | (~old(X0) & ~tall(X0)))) [nnf transformation 10]
53. ! [X0] : ((old(X0) | tall(X0) | (~strong(X0) & tall(X0))) & (strong(X0) | ~tall(X0) | (~old(X0) & ~tall(X0)))) [flattening 52]
64. ! [X0] : (((funny(X0) & ~happy(X0)) | funny(X0)) & (~funny(X0) | (~funny(X0) | happy(X0)))) [nnf transformation 16]
65. ! [X0] : (((funny(X0) & ~happy(X0)) | funny(X0)) & (~funny(X0) | ~funny(X0) | happy(X0))) [flattening 64]
76. strong(X0) | tall(X0) | curious(X0) [cnf transformation 44]
83. ~curious(X0) | humble(X0) | quiet(X0) [cnf transformation 47]
85. ~humble(X0) | tall(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 49]
98. strong(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 53]
120. ~funny(X0) | ~funny(X0) | happy(X0) [cnf transformation 65]
121. ~happy(X0) | funny(X0) [cnf transformation 65]
125. funny(alice) | happy(alice) [cnf transformation 18]
129. ~quiet(alice) [cnf transformation 22]
133. ~strong(alice) [cnf transformation 25]
134. ~funny(X0) | happy(X0) [duplicate literal removal 120]
136. ~tall(X0) | strong(X0) [duplicate literal removal 98]
246. funny(alice) [subsumption resolution 125,121]
266. happy(alice) [resolution 134,246]
270. tall(alice) | curious(alice) [resolution 76,133]
275. 26 <=> curious(alice) [avatar definition]
277. curious(alice) <- (26) [avatar component clause 275]
279. 27 <=> tall(alice) [avatar definition]
281. tall(alice) <- (27) [avatar component clause 279]
282. 26 | 27 [avatar split clause 270,279,275]
295. humble(alice) | quiet(alice) <- (26) [resolution 83,277]
296. humble(alice) <- (26) [subsumption resolution 295,129]
345. tall(alice) | ~happy(alice) | ~funny(alice) <- (26) [resolution 85,296]
351. tall(alice) | ~happy(alice) <- (26) [subsumption resolution 345,246]
353. 30 <=> happy(alice) [avatar definition]
356. ~30 | 27 | ~26 [avatar split clause 351,275,279,353]
357. 30 [avatar split clause 266,353]
377. strong(alice) <- (27) [resolution 281,136]
381. $false <- (27) [subsumption resolution 377,133]
382. ~27 [avatar contradiction clause 381]
385. $false [avatar sat refutation 282,356,357,382]
% SZS output end Proof for 886677304501728955510709
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not tall or not creative then lucy is either kind or brave and vice versa.
If john is both not old and wise then paul is both strong and creative and vice versa.
If lucy is both kind and not brave then fred is quiet and vice versa.
If someone is not generous or not wise then alice is not creative or not kind and vice versa.
If lucy is not curious or wise then someone is either old or not kind and vice versa.
If lucy is not wise or not creative then mary is either curious or not tall and vice versa.
Everyone who is both not quiet and not creative is not tall.
Everyone who is both creative and wise is calm or not patient and vice versa.
If john is not tall or not wise then mary is either happy or not rich.
Everyone who is both patient and humble is both not kind and not happy.
If lucy is either not funny or generous then fred is patient or not old.
If someone is strong or funny then mary is not creative and vice versa.
If susan is both not wise and curious then someone is both old and not rich and vice versa.
If someone is not curious or calm then john is both kind and not kind and vice versa.
If paul is wise or rich then someone is not kind or not old and vice versa.
Everyone who is either quiet or not kind is either not generous or not patient and vice versa.
Paul is either humble or tall.
Someone is not tall or brave.
John is both quiet and funny.
Someone is not wise or not quiet.
Mary is either happy or not generous.
Someone is both tall and strong.
Someone is both brave and not strong. | Lucy is not calm. | entailment | (((~tall(susan)|~creative(susan)))<=>((kind(lucy)<~>brave(lucy))))&
(((~old(john)&wise(john)))<=>((strong(paul)&creative(paul))))&
(((kind(lucy)&~brave(lucy)))<=>(quiet(fred)))&
((?[X]:((~generous(X)|~wise(X))))<=>((~creative(alice)|~kind(alice))))&
(((~curious(lucy)|wise(lucy)))<=>(?[X]:((old(X)<~>~kind(X)))))&
(((~wise(lucy)|~creative(lucy)))<=>((curious(mary)<~>~tall(mary))))&
(![X]:((~quiet(X)&~creative(X))=>~tall(X)))&
(![X]:((creative(X)&wise(X))<=>(calm(X)|~patient(X))))&
(((~tall(john)|~wise(john)))=>((happy(mary)<~>~rich(mary))))&
(![X]:((patient(X)&humble(X))=>(~kind(X)&~happy(X))))&
(((~funny(lucy)<~>generous(lucy)))=>((patient(fred)|~old(fred))))&
((?[X]:((strong(X)|funny(X))))<=>(~creative(mary)))&
(((~wise(susan)&curious(susan)))<=>(?[X]:((old(X)&~rich(X)))))&
((?[X]:((~curious(X)|calm(X))))<=>((kind(john)&~kind(john))))&
(((wise(paul)|rich(paul)))<=>(?[X]:((~kind(X)|~old(X)))))&
(![X]:((quiet(X)<~>~kind(X))<=>(~generous(X)<~>~patient(X))))&
((humble(paul)<~>tall(paul)))&
(?[X]:((~tall(X)|brave(X))))&
((quiet(john)&funny(john)))&
(?[X]:((~wise(X)|~quiet(X))))&
((happy(mary)<~>~generous(mary)))&
(?[X]:((tall(X)&strong(X))))&
(?[X]:((brave(X)&~strong(X)))) | ~calm(lucy) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7913043932896328885116463
% SZS output start Proof for 7913043932896328885116463
14. ? [X0] : (calm(X0) | ~curious(X0)) <=> (~kind(john) & kind(john)) [input p13]
24. calm(lucy) [input hypothesis]
63. (? [X0] : (calm(X0) | ~curious(X0)) | (kind(john) | ~kind(john))) & ((~kind(john) & kind(john)) | ! [X0] : (~calm(X0) & curious(X0))) [nnf transformation 14]
64. (? [X0] : (calm(X0) | ~curious(X0)) | kind(john) | ~kind(john)) & ((~kind(john) & kind(john)) | ! [X0] : (~calm(X0) & curious(X0))) [flattening 63]
65. (? [X0] : (calm(X0) | ~curious(X0)) | kind(john) | ~kind(john)) & ((~kind(john) & kind(john)) | ! [X1] : (~calm(X1) & curious(X1))) [rectify 64]
66. ? [X0] : (calm(X0) | ~curious(X0)) => (calm(sK4) | ~curious(sK4)) [choice axiom]
67. ((calm(sK4) | ~curious(sK4)) | kind(john) | ~kind(john)) & ((~kind(john) & kind(john)) | ! [X1] : (~calm(X1) & curious(X1))) [skolemisation 65,66]
135. kind(john) | ~calm(X1) [cnf transformation 67]
137. ~kind(john) | ~calm(X1) [cnf transformation 67]
163. calm(lucy) [cnf transformation 24]
364. 42 <=> ! [X1] : ~calm(X1) [avatar definition]
365. ~calm(X1) <- (42) [avatar component clause 364]
367. 43 <=> kind(john) [avatar definition]
370. 42 | ~43 [avatar split clause 137,367,364]
375. 42 | 43 [avatar split clause 135,367,364]
443. $false <- (42) [resolution 365,163]
444. ~42 [avatar contradiction clause 443]
445. $false [avatar sat refutation 370,375,444]
% SZS output end Proof for 7913043932896328885116463
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or not wise is both funny and patient. Everyone who is both funny and not creative is not wise or not old and vice versa. If mary is creative then someone is not brave and vice versa. Everyone who is tall is both not happy and happy and vice versa. Everyone who is quiet is either not creative or patient. Everyone who is not old is either not strong or not happy. Everyone who is not old is either happy or humble. Everyone who is not generous or not rich is quiet and vice versa. Everyone who is quiet or not creative is either not creative or happy and vice versa. If someone is not patient or not creative then someone is not rich or not kind. Everyone who is quiet or not brave is either brave or patient and vice versa. If lucy is either kind or not kind then someone is either quiet or funny. Everyone who is either not happy or not strong is patient and vice versa. Everyone who is happy or old is either calm or not curious and vice versa. Everyone who is kind is not old or rich and vice versa. Lucy is either creative or calm. Paul is funny. Mary is both funny and patient. Susan is strong. Someone is both kind and not brave. Someone is either strong or not kind. Lucy is curious. | Susan is not wise. | neutral | (![X]:((~strong(X)|~wise(X))=>(funny(X)&patient(X))))&
(![X]:((funny(X)&~creative(X))<=>(~wise(X)|~old(X))))&
((creative(mary))<=>(?[X]:(~brave(X))))&
(![X]:(tall(X)<=>(~happy(X)&happy(X))))&
(![X]:(quiet(X)=>(~creative(X)<~>patient(X))))&
(![X]:(~old(X)=>(~strong(X)<~>~happy(X))))&
(![X]:(~old(X)=>(happy(X)<~>humble(X))))&
(![X]:((~generous(X)|~rich(X))<=>quiet(X)))&
(![X]:((quiet(X)|~creative(X))<=>(~creative(X)<~>happy(X))))&
((?[X]:((~patient(X)|~creative(X))))=>(?[X]:((~rich(X)|~kind(X)))))&
(![X]:((quiet(X)|~brave(X))<=>(brave(X)<~>patient(X))))&
(((kind(lucy)<~>~kind(lucy)))=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:((~happy(X)<~>~strong(X))<=>patient(X)))&
(![X]:((happy(X)|old(X))<=>(calm(X)<~>~curious(X))))&
(![X]:(kind(X)<=>(~old(X)|rich(X))))&
((creative(lucy)<~>calm(lucy)))&
(funny(paul))&
((funny(mary)&patient(mary)))&
(strong(susan))&
(?[X]:((kind(X)&~brave(X))))&
(?[X]:((strong(X)<~>~kind(X))))&
(curious(lucy)) | ~wise(susan) | [] | null | 0 |
Everyone who is either not curious or not wise is both not rich and not old and vice versa. Everyone who is both strong and kind is either not calm or brave and vice versa. If mary is both not patient and curious then someone is either not old or not rich. If alice is not creative then susan is curious or not calm. If someone is both not kind and creative then john is calm and vice versa. If mary is not rich or creative then alice is not funny. If paul is patient or strong then someone is both happy and kind. Everyone who is funny or not strong is both not rich and not funny and vice versa. If someone is both not quiet and not patient then mary is either not humble or not strong and vice versa. Everyone who is brave or not patient is either creative or not humble. If fred is either kind or not strong then someone is not happy and vice versa. If alice is both generous and not funny then susan is curious or not creative. If someone is not tall or old then someone is either not strong or not kind. Everyone who is either not rich or not happy is not funny or rich. If fred is quiet then someone is not rich or not quiet. Everyone who is both happy and not happy is not rich or curious and vice versa. John is happy or not old. Someone is tall. Alice is either patient or not happy. Someone is either humble or not kind. Someone is both not quiet and calm. Someone is not wise or not old. | John is not quiet. | neutral | (![X]:((~curious(X)<~>~wise(X))<=>(~rich(X)&~old(X))))&
(![X]:((strong(X)&kind(X))<=>(~calm(X)<~>brave(X))))&
(((~patient(mary)&curious(mary)))=>(?[X]:((~old(X)<~>~rich(X)))))&
((~creative(alice))=>((curious(susan)|~calm(susan))))&
((?[X]:((~kind(X)&creative(X))))<=>(calm(john)))&
(((~rich(mary)|creative(mary)))=>(~funny(alice)))&
(((patient(paul)|strong(paul)))=>(?[X]:((happy(X)&kind(X)))))&
(![X]:((funny(X)|~strong(X))<=>(~rich(X)&~funny(X))))&
((?[X]:((~quiet(X)&~patient(X))))<=>((~humble(mary)<~>~strong(mary))))&
(![X]:((brave(X)|~patient(X))=>(creative(X)<~>~humble(X))))&
(((kind(fred)<~>~strong(fred)))<=>(?[X]:(~happy(X))))&
(((generous(alice)&~funny(alice)))=>((curious(susan)|~creative(susan))))&
((?[X]:((~tall(X)|old(X))))=>(?[X]:((~strong(X)<~>~kind(X)))))&
(![X]:((~rich(X)<~>~happy(X))=>(~funny(X)|rich(X))))&
((quiet(fred))=>(?[X]:((~rich(X)|~quiet(X)))))&
(![X]:((happy(X)&~happy(X))<=>(~rich(X)|curious(X))))&
((happy(john)|~old(john)))&
(?[X]:(tall(X)))&
((patient(alice)<~>~happy(alice)))&
(?[X]:((humble(X)<~>~kind(X))))&
(?[X]:((~quiet(X)&calm(X))))&
(?[X]:((~wise(X)|~old(X)))) | ~quiet(john) | [] | null | 0 |
If fred is curious or not strong then susan is patient or happy.
Everyone who is both not strong and old is both quiet and not wise.
Everyone who is both creative and not generous is both quiet and creative.
Everyone who is both not calm and not tall is not wise or quiet.
If someone is both not calm and generous then someone is funny or curious.
Everyone who is either kind or tall is not kind or not strong and vice versa.
If someone is both quiet and not rich then someone is not generous or old and vice versa.
If fred is either not patient or old then mary is not generous and vice versa.
If someone is both not strong and not quiet then someone is both not happy and calm and vice versa.
If fred is rich or not generous then someone is either not happy or not generous.
Everyone who is not patient or not funny is not old or not creative.
If someone is both not kind and not humble then someone is rich.
Everyone who is not rich or not quiet is both not tall and rich.
If someone is curious or not happy then someone is generous or not generous and vice versa.
Everyone who is not tall is not funny or not old and vice versa.
Everyone who is creative or rich is not quiet and vice versa.
John is not generous or not creative.
Someone is either not curious or generous.
Alice is either not humble or not creative.
Alice is patient or not tall.
Someone is either brave or not wise.
Alice is not happy. | Mary is not quiet. | entailment | (((curious(fred)|~strong(fred)))=>((patient(susan)|happy(susan))))&
(![X]:((~strong(X)&old(X))=>(quiet(X)&~wise(X))))&
(![X]:((creative(X)&~generous(X))=>(quiet(X)&creative(X))))&
(![X]:((~calm(X)&~tall(X))=>(~wise(X)|quiet(X))))&
((?[X]:((~calm(X)&generous(X))))=>(?[X]:((funny(X)|curious(X)))))&
(![X]:((kind(X)<~>tall(X))<=>(~kind(X)|~strong(X))))&
((?[X]:((quiet(X)&~rich(X))))<=>(?[X]:((~generous(X)|old(X)))))&
(((~patient(fred)<~>old(fred)))<=>(~generous(mary)))&
((?[X]:((~strong(X)&~quiet(X))))<=>(?[X]:((~happy(X)&calm(X)))))&
(((rich(fred)|~generous(fred)))=>(?[X]:((~happy(X)<~>~generous(X)))))&
(![X]:((~patient(X)|~funny(X))=>(~old(X)|~creative(X))))&
((?[X]:((~kind(X)&~humble(X))))=>(?[X]:(rich(X))))&
(![X]:((~rich(X)|~quiet(X))=>(~tall(X)&rich(X))))&
((?[X]:((curious(X)|~happy(X))))<=>(?[X]:((generous(X)|~generous(X)))))&
(![X]:(~tall(X)<=>(~funny(X)|~old(X))))&
(![X]:((creative(X)|rich(X))<=>~quiet(X)))&
((~generous(john)|~creative(john)))&
(?[X]:((~curious(X)<~>generous(X))))&
((~humble(alice)<~>~creative(alice)))&
((patient(alice)|~tall(alice)))&
(?[X]:((brave(X)<~>~wise(X))))&
(~happy(alice)) | ~quiet(mary) | [
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7350434260465395396555611
% SZS output start Proof for 7350434260465395396555611
13. ! [X0] : ((~quiet(X0) | ~rich(X0)) => (rich(X0) & ~tall(X0))) [input p12]
16. ! [X0] : ((rich(X0) | creative(X0)) <=> ~quiet(X0)) [input p15]
23. quiet(mary) [input hypothesis]
42. ! [X0] : ((rich(X0) & ~tall(X0)) | (quiet(X0) & rich(X0))) [ennf transformation 13]
72. ! [X0] : (((rich(X0) | creative(X0)) | quiet(X0)) & (~quiet(X0) | (~rich(X0) & ~creative(X0)))) [nnf transformation 16]
73. ! [X0] : ((rich(X0) | creative(X0) | quiet(X0)) & (~quiet(X0) | (~rich(X0) & ~creative(X0)))) [flattening 72]
117. rich(X0) | rich(X0) [cnf transformation 42]
127. ~quiet(X0) | ~rich(X0) [cnf transformation 73]
138. quiet(mary) [cnf transformation 23]
139. rich(X0) [duplicate literal removal 117]
286. ~quiet(X0) [subsumption resolution 127,139]
335. $false [subsumption resolution 138,286]
% SZS output end Proof for 7350434260465395396555611
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not generous or not patient then someone is either not calm or calm.
If someone is either calm or funny then alice is tall and vice versa.
If fred is both not curious and not quiet then someone is strong or not rich.
Everyone who is both not brave and creative is both kind and not wise.
If alice is not happy then someone is not calm and vice versa.
Everyone who is both not happy and brave is both happy and kind.
Everyone who is both not calm and strong is generous and vice versa.
Everyone who is funny is either not curious or happy and vice versa.
Everyone who is calm is both strong and generous and vice versa.
Everyone who is not patient is both humble and not funny.
If lucy is happy then someone is funny or patient.
Everyone who is old or not kind is both old and not curious.
Everyone who is not calm or strong is either not wise or old and vice versa.
If fred is both not kind and kind then lucy is either creative or humble.
If fred is strong then paul is both not rich and not wise.
Paul is tall.
Someone is not rich or strong. | Paul is not creative. | neutral | ((?[X]:((~generous(X)<~>~patient(X))))=>(?[X]:((~calm(X)<~>calm(X)))))&
((?[X]:((calm(X)<~>funny(X))))<=>(tall(alice)))&
(((~curious(fred)&~quiet(fred)))=>(?[X]:((strong(X)|~rich(X)))))&
(![X]:((~brave(X)&creative(X))=>(kind(X)&~wise(X))))&
((~happy(alice))<=>(?[X]:(~calm(X))))&
(![X]:((~happy(X)&brave(X))=>(happy(X)&kind(X))))&
(![X]:((~calm(X)&strong(X))<=>generous(X)))&
(![X]:(funny(X)<=>(~curious(X)<~>happy(X))))&
(![X]:(calm(X)<=>(strong(X)&generous(X))))&
(![X]:(~patient(X)=>(humble(X)&~funny(X))))&
((happy(lucy))=>(?[X]:((funny(X)|patient(X)))))&
(![X]:((old(X)|~kind(X))=>(old(X)&~curious(X))))&
(![X]:((~calm(X)|strong(X))<=>(~wise(X)<~>old(X))))&
(((~kind(fred)&kind(fred)))=>((creative(lucy)<~>humble(lucy))))&
((strong(fred))=>((~rich(paul)&~wise(paul))))&
(tall(paul))&
(?[X]:((~rich(X)|strong(X)))) | ~creative(paul) | [] | null | 0 |
If alice is not funny then someone is either not happy or not funny.
If mary is rich or not rich then paul is not kind or not rich.
If someone is not wise or not tall then someone is either not patient or not humble.
Everyone who is not strong or not wise is both calm and not generous.
Everyone who is either not kind or old is both funny and generous and vice versa.
Everyone who is wise or not quiet is kind.
Everyone who is either not curious or rich is either not funny or creative and vice versa.
If paul is quiet or not wise then lucy is either old or not old.
If alice is happy then paul is not old and vice versa.
Everyone who is happy or patient is either not tall or brave.
Everyone who is either not strong or calm is not kind or creative.
If someone is not quiet or not strong then susan is both not creative and generous and vice versa.
Everyone who is not happy or creative is both not old and not brave.
If lucy is not wise or not brave then john is either not funny or not quiet.
Everyone who is both not curious and not humble is generous.
Someone is not patient.
Someone is both not rich and not patient.
Someone is not old or brave.
Fred is either not quiet or calm.
Mary is either not funny or patient.
Fred is either kind or curious.
Someone is not wise or not happy.
Alice is either not curious or kind. | Paul is not quiet. | neutral | ((~funny(alice))=>(?[X]:((~happy(X)<~>~funny(X)))))&
(((rich(mary)|~rich(mary)))=>((~kind(paul)|~rich(paul))))&
((?[X]:((~wise(X)|~tall(X))))=>(?[X]:((~patient(X)<~>~humble(X)))))&
(![X]:((~strong(X)|~wise(X))=>(calm(X)&~generous(X))))&
(![X]:((~kind(X)<~>old(X))<=>(funny(X)&generous(X))))&
(![X]:((wise(X)|~quiet(X))=>kind(X)))&
(![X]:((~curious(X)<~>rich(X))<=>(~funny(X)<~>creative(X))))&
(((quiet(paul)|~wise(paul)))=>((old(lucy)<~>~old(lucy))))&
((happy(alice))<=>(~old(paul)))&
(![X]:((happy(X)|patient(X))=>(~tall(X)<~>brave(X))))&
(![X]:((~strong(X)<~>calm(X))=>(~kind(X)|creative(X))))&
((?[X]:((~quiet(X)|~strong(X))))<=>((~creative(susan)&generous(susan))))&
(![X]:((~happy(X)|creative(X))=>(~old(X)&~brave(X))))&
(((~wise(lucy)|~brave(lucy)))=>((~funny(john)<~>~quiet(john))))&
(![X]:((~curious(X)&~humble(X))=>generous(X)))&
(?[X]:(~patient(X)))&
(?[X]:((~rich(X)&~patient(X))))&
(?[X]:((~old(X)|brave(X))))&
((~quiet(fred)<~>calm(fred)))&
((~funny(mary)<~>patient(mary)))&
((kind(fred)<~>curious(fred)))&
(?[X]:((~wise(X)|~happy(X))))&
((~curious(alice)<~>kind(alice))) | ~quiet(paul) | [] | null | 0 |
If someone is either patient or not kind then paul is either not tall or not funny and vice versa. Everyone who is not strong or happy is wise. If someone is not creative then someone is not rich or not strong and vice versa. If susan is both quiet and generous then alice is quiet or not curious and vice versa. Everyone who is both not brave and not happy is not kind or not tall and vice versa. Everyone who is either not creative or not rich is both not generous and not tall. Everyone who is tall or brave is either not generous or tall and vice versa. Everyone who is rich is either curious or not tall. Everyone who is both curious and funny is both not tall and creative. If lucy is either not humble or brave then mary is quiet or old and vice versa. If someone is tall then mary is both not rich and quiet. Everyone who is either not quiet or not strong is not rich and vice versa. Everyone who is not kind is both tall and humble. If someone is rich then someone is tall or funny. Everyone who is happy is humble or wise. If someone is both wise and funny then john is not kind or not humble. Fred is not quiet. John is both not wise and not curious. Someone is either brave or not calm. Someone is either not curious or wise. Fred is not generous or not rich. Someone is not funny. Mary is both wise and not patient. | Fred is not strong. | contradiction | ((?[X]:((patient(X)<~>~kind(X))))<=>((~tall(paul)<~>~funny(paul))))&
(![X]:((~strong(X)|happy(X))=>wise(X)))&
((?[X]:(~creative(X)))<=>(?[X]:((~rich(X)|~strong(X)))))&
(((quiet(susan)&generous(susan)))<=>((quiet(alice)|~curious(alice))))&
(![X]:((~brave(X)&~happy(X))<=>(~kind(X)|~tall(X))))&
(![X]:((~creative(X)<~>~rich(X))=>(~generous(X)&~tall(X))))&
(![X]:((tall(X)|brave(X))<=>(~generous(X)<~>tall(X))))&
(![X]:(rich(X)=>(curious(X)<~>~tall(X))))&
(![X]:((curious(X)&funny(X))=>(~tall(X)&creative(X))))&
(((~humble(lucy)<~>brave(lucy)))<=>((quiet(mary)|old(mary))))&
((?[X]:(tall(X)))=>((~rich(mary)&quiet(mary))))&
(![X]:((~quiet(X)<~>~strong(X))<=>~rich(X)))&
(![X]:(~kind(X)=>(tall(X)&humble(X))))&
((?[X]:(rich(X)))=>(?[X]:((tall(X)|funny(X)))))&
(![X]:(happy(X)=>(humble(X)|wise(X))))&
((?[X]:((wise(X)&funny(X))))=>((~kind(john)|~humble(john))))&
(~quiet(fred))&
((~wise(john)&~curious(john)))&
(?[X]:((brave(X)<~>~calm(X))))&
(?[X]:((~curious(X)<~>wise(X))))&
((~generous(fred)|~rich(fred)))&
(?[X]:(~funny(X)))&
((wise(mary)&~patient(mary))) | ~strong(fred) | [
"p4",
"p6",
"p11",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5638753641483322191108631
% SZS output start Proof for 5638753641483322191108631
5. ! [X0] : ((~happy(X0) & ~brave(X0)) <=> (~tall(X0) | ~kind(X0))) [input p4]
7. ! [X0] : ((brave(X0) | tall(X0)) <=> (~generous(X0) <~> tall(X0))) [input p6]
12. ! [X0] : ((~quiet(X0) <~> ~strong(X0)) <=> ~rich(X0)) [input p11]
17. ~quiet(fred) [input p16]
21. ~rich(fred) | ~generous(fred) [input p20]
24. ~strong(fred) [input hypothesis]
50. ! [X0] : (((~happy(X0) & ~brave(X0)) | (tall(X0) & kind(X0))) & ((~tall(X0) | ~kind(X0)) | (happy(X0) | brave(X0)))) [nnf transformation 5]
51. ! [X0] : (((~happy(X0) & ~brave(X0)) | (tall(X0) & kind(X0))) & (~tall(X0) | ~kind(X0) | happy(X0) | brave(X0))) [flattening 50]
53. ! [X0] : (((brave(X0) | tall(X0)) | ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0)))) & (((~tall(X0) | generous(X0)) & (tall(X0) | ~generous(X0))) | (~brave(X0) & ~tall(X0)))) [nnf transformation 7]
54. ! [X0] : ((brave(X0) | tall(X0) | ((~generous(X0) | ~tall(X0)) & (tall(X0) | generous(X0)))) & (((~tall(X0) | generous(X0)) & (tall(X0) | ~generous(X0))) | (~brave(X0) & ~tall(X0)))) [flattening 53]
58. ! [X0] : ((((strong(X0) | quiet(X0)) & (~strong(X0) | ~quiet(X0))) | rich(X0)) & (~rich(X0) | ((~quiet(X0) | strong(X0)) & (~strong(X0) | quiet(X0))))) [nnf transformation 12]
90. ~brave(X0) | tall(X0) [cnf transformation 51]
99. ~tall(X0) | generous(X0) | ~tall(X0) [cnf transformation 54]
101. brave(X0) | tall(X0) | tall(X0) | generous(X0) [cnf transformation 54]
118. quiet(X0) | strong(X0) | rich(X0) [cnf transformation 58]
124. ~quiet(fred) [cnf transformation 17]
131. ~rich(fred) | ~generous(fred) [cnf transformation 21]
135. ~strong(fred) [cnf transformation 24]
136. ~tall(X0) | generous(X0) [duplicate literal removal 99]
137. brave(X0) | tall(X0) | generous(X0) [duplicate literal removal 101]
213. generous(X0) | tall(X0) [subsumption resolution 137,90]
215. generous(X0) [subsumption resolution 136,213]
291. ~rich(fred) [subsumption resolution 131,215]
325. strong(fred) | rich(fred) [resolution 118,124]
330. rich(fred) [subsumption resolution 325,135]
331. $false [subsumption resolution 330,291]
% SZS output end Proof for 5638753641483322191108631
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not funny and quiet then someone is either brave or curious.
Everyone who is creative or rich is both curious and old and vice versa.
If someone is not old or generous then someone is either not old or strong and vice versa.
If lucy is either curious or generous then someone is not tall.
If paul is quiet or not kind then someone is either wise or not kind and vice versa.
Everyone who is both patient and not wise is strong.
Everyone who is both rich and not quiet is not old or creative and vice versa.
Everyone who is both happy and not kind is not humble or not tall and vice versa.
Everyone who is both calm and tall is humble or old and vice versa.
Everyone who is not funny is rich and vice versa.
Everyone who is both not kind and not quiet is both strong and not rich and vice versa.
Everyone who is curious is both rich and not curious.
If someone is both not quiet and wise then fred is not strong or kind and vice versa.
Everyone who is both kind and not humble is not curious or not tall.
Everyone who is either not brave or curious is not happy or strong.
Everyone who is either calm or not funny is either not strong or funny.
Mary is either funny or wise.
Someone is either not humble or not patient.
Someone is not quiet.
Someone is calm or not curious.
Mary is both not kind and humble.
Someone is either wise or not kind. | Mary is creative. | contradiction | ((?[X]:((~funny(X)&quiet(X))))=>(?[X]:((brave(X)<~>curious(X)))))&
(![X]:((creative(X)|rich(X))<=>(curious(X)&old(X))))&
((?[X]:((~old(X)|generous(X))))<=>(?[X]:((~old(X)<~>strong(X)))))&
(((curious(lucy)<~>generous(lucy)))=>(?[X]:(~tall(X))))&
(((quiet(paul)|~kind(paul)))<=>(?[X]:((wise(X)<~>~kind(X)))))&
(![X]:((patient(X)&~wise(X))=>strong(X)))&
(![X]:((rich(X)&~quiet(X))<=>(~old(X)|creative(X))))&
(![X]:((happy(X)&~kind(X))<=>(~humble(X)|~tall(X))))&
(![X]:((calm(X)&tall(X))<=>(humble(X)|old(X))))&
(![X]:(~funny(X)<=>rich(X)))&
(![X]:((~kind(X)&~quiet(X))<=>(strong(X)&~rich(X))))&
(![X]:(curious(X)=>(rich(X)&~curious(X))))&
((?[X]:((~quiet(X)&wise(X))))<=>((~strong(fred)|kind(fred))))&
(![X]:((kind(X)&~humble(X))=>(~curious(X)|~tall(X))))&
(![X]:((~brave(X)<~>curious(X))=>(~happy(X)|strong(X))))&
(![X]:((calm(X)<~>~funny(X))=>(~strong(X)<~>funny(X))))&
((funny(mary)<~>wise(mary)))&
(?[X]:((~humble(X)<~>~patient(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((calm(X)|~curious(X))))&
((~kind(mary)&humble(mary)))&
(?[X]:((wise(X)<~>~kind(X)))) | creative(mary) | [
"p1",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5503756099725934134167831
% SZS output start Proof for 5503756099725934134167831
2. ! [X0] : ((rich(X0) | creative(X0)) <=> (old(X0) & curious(X0))) [input p1]
12. ! [X0] : (curious(X0) => (~curious(X0) & rich(X0))) [input p11]
23. creative(mary) [input hypothesis]
30. ! [X0] : ((~curious(X0) & rich(X0)) | ~curious(X0)) [ennf transformation 12]
40. ! [X0] : (((rich(X0) | creative(X0)) | (~old(X0) | ~curious(X0))) & ((old(X0) & curious(X0)) | (~rich(X0) & ~creative(X0)))) [nnf transformation 2]
41. ! [X0] : ((rich(X0) | creative(X0) | ~old(X0) | ~curious(X0)) & ((old(X0) & curious(X0)) | (~rich(X0) & ~creative(X0)))) [flattening 40]
84. ~creative(X0) | curious(X0) [cnf transformation 41]
126. ~curious(X0) | ~curious(X0) [cnf transformation 30]
149. creative(mary) [cnf transformation 23]
152. ~curious(X0) [duplicate literal removal 126]
306. curious(mary) [resolution 84,149]
307. $false [subsumption resolution 306,152]
% SZS output end Proof for 5503756099725934134167831
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and old is both not quiet and generous and vice versa.
Everyone who is brave or calm is either not calm or not old.
If fred is either not happy or kind then someone is not rich or patient.
Everyone who is both humble and happy is curious.
Everyone who is either generous or funny is both not tall and not patient.
If someone is both not rich and not tall then mary is tall.
Everyone who is not strong is either quiet or not old and vice versa.
If someone is not curious then someone is creative or patient and vice versa.
If susan is either not curious or not creative then someone is not strong.
Everyone who is either funny or not quiet is either not old or happy and vice versa.
Everyone who is funny or not calm is either creative or generous and vice versa.
Everyone who is either patient or not happy is creative.
If fred is brave then someone is humble.
Everyone who is not wise or old is either strong or brave and vice versa.
Everyone who is both not old and not generous is not generous or brave and vice versa.
Everyone who is both funny and not curious is either tall or not brave.
Fred is not kind or not wise.
Someone is brave or not calm.
Lucy is not strong.
John is either not humble or happy.
Someone is both calm and quiet.
Someone is rich.
Someone is not brave.
Mary is both kind and not strong. | Mary is not generous. | entailment | (![X]:((brave(X)&old(X))<=>(~quiet(X)&generous(X))))&
(![X]:((brave(X)|calm(X))=>(~calm(X)<~>~old(X))))&
(((~happy(fred)<~>kind(fred)))=>(?[X]:((~rich(X)|patient(X)))))&
(![X]:((humble(X)&happy(X))=>curious(X)))&
(![X]:((generous(X)<~>funny(X))=>(~tall(X)&~patient(X))))&
((?[X]:((~rich(X)&~tall(X))))=>(tall(mary)))&
(![X]:(~strong(X)<=>(quiet(X)<~>~old(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((creative(X)|patient(X)))))&
(((~curious(susan)<~>~creative(susan)))=>(?[X]:(~strong(X))))&
(![X]:((funny(X)<~>~quiet(X))<=>(~old(X)<~>happy(X))))&
(![X]:((funny(X)|~calm(X))<=>(creative(X)<~>generous(X))))&
(![X]:((patient(X)<~>~happy(X))=>creative(X)))&
((brave(fred))=>(?[X]:(humble(X))))&
(![X]:((~wise(X)|old(X))<=>(strong(X)<~>brave(X))))&
(![X]:((~old(X)&~generous(X))<=>(~generous(X)|brave(X))))&
(![X]:((funny(X)&~curious(X))=>(tall(X)<~>~brave(X))))&
((~kind(fred)|~wise(fred)))&
(?[X]:((brave(X)|~calm(X))))&
(~strong(lucy))&
((~humble(john)<~>happy(john)))&
(?[X]:((calm(X)&quiet(X))))&
(?[X]:(rich(X)))&
(?[X]:(~brave(X)))&
((kind(mary)&~strong(mary))) | ~generous(mary) | [
"p0",
"p6",
"p13",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 315517564656532318639074
% SZS output start Proof for 315517564656532318639074
1. ! [X0] : ((old(X0) & brave(X0)) <=> (generous(X0) & ~quiet(X0))) [input p0]
7. ! [X0] : (~strong(X0) <=> (quiet(X0) <~> ~old(X0))) [input p6]
14. ! [X0] : ((old(X0) | ~wise(X0)) <=> (strong(X0) <~> brave(X0))) [input p13]
15. ! [X0] : ((~generous(X0) & ~old(X0)) <=> (brave(X0) | ~generous(X0))) [input p14]
24. ~strong(mary) & kind(mary) [input p23]
25. generous(mary) [input hypothesis]
38. ! [X0] : (((old(X0) & brave(X0)) | (~generous(X0) | quiet(X0))) & ((generous(X0) & ~quiet(X0)) | (~old(X0) | ~brave(X0)))) [nnf transformation 1]
39. ! [X0] : (((old(X0) & brave(X0)) | ~generous(X0) | quiet(X0)) & ((generous(X0) & ~quiet(X0)) | ~old(X0) | ~brave(X0))) [flattening 38]
45. ! [X0] : ((~strong(X0) | ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0)))) & (((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | strong(X0))) [nnf transformation 7]
60. ! [X0] : (((old(X0) | ~wise(X0)) | ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0)))) & (((~brave(X0) | ~strong(X0)) & (brave(X0) | strong(X0))) | (~old(X0) & wise(X0)))) [nnf transformation 14]
61. ! [X0] : ((old(X0) | ~wise(X0) | ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0)))) & (((~brave(X0) | ~strong(X0)) & (brave(X0) | strong(X0))) | (~old(X0) & wise(X0)))) [flattening 60]
62. ! [X0] : (((~generous(X0) & ~old(X0)) | (~brave(X0) & generous(X0))) & ((brave(X0) | ~generous(X0)) | (generous(X0) | old(X0)))) [nnf transformation 15]
63. ! [X0] : (((~generous(X0) & ~old(X0)) | (~brave(X0) & generous(X0))) & (brave(X0) | ~generous(X0) | generous(X0) | old(X0))) [flattening 62]
76. ~generous(X0) | brave(X0) | quiet(X0) [cnf transformation 39]
91. ~quiet(X0) | old(X0) | strong(X0) [cnf transformation 45]
117. ~old(X0) | strong(X0) | brave(X0) [cnf transformation 61]
126. ~generous(X0) | ~brave(X0) [cnf transformation 63]
139. ~strong(mary) [cnf transformation 24]
140. generous(mary) [cnf transformation 25]
241. ~brave(mary) [resolution 126,140]
244. brave(mary) | quiet(mary) [resolution 76,140]
245. quiet(mary) [subsumption resolution 244,241]
251. old(mary) | strong(mary) [resolution 91,245]
253. old(mary) [subsumption resolution 251,139]
300. strong(mary) | brave(mary) [resolution 117,253]
301. brave(mary) [subsumption resolution 300,139]
302. $false [subsumption resolution 301,241]
% SZS output end Proof for 315517564656532318639074
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is both not tall and not creative and vice versa. If someone is not kind or not happy then john is both calm and happy and vice versa. If someone is not strong or curious then someone is either not tall or curious and vice versa. If alice is both not kind and not rich then someone is either not wise or tall. If fred is both not curious and not quiet then someone is strong or not rich. Everyone who is both not brave and creative is both kind and not wise. If alice is not happy then someone is not calm and vice versa. Everyone who is both not happy and brave is both happy and kind. Everyone who is both not calm and strong is generous and vice versa. Everyone who is funny is either not curious or happy and vice versa. Everyone who is not patient is both humble and not funny. If lucy is happy then someone is funny or patient. Everyone who is old or not kind is both old and not curious. Everyone who is not calm or strong is either not wise or old and vice versa. Mary is either strong or not calm. John is tall or old. Paul is either generous or humble. Paul is not quiet. Someone is not patient or not humble. Fred is either not humble or not rich. | Alice is brave. | neutral | (![X]:(tall(X)<=>(~tall(X)&~creative(X))))&
((?[X]:((~kind(X)|~happy(X))))<=>((calm(john)&happy(john))))&
((?[X]:((~strong(X)|curious(X))))<=>(?[X]:((~tall(X)<~>curious(X)))))&
(((~kind(alice)&~rich(alice)))=>(?[X]:((~wise(X)<~>tall(X)))))&
(((~curious(fred)&~quiet(fred)))=>(?[X]:((strong(X)|~rich(X)))))&
(![X]:((~brave(X)&creative(X))=>(kind(X)&~wise(X))))&
((~happy(alice))<=>(?[X]:(~calm(X))))&
(![X]:((~happy(X)&brave(X))=>(happy(X)&kind(X))))&
(![X]:((~calm(X)&strong(X))<=>generous(X)))&
(![X]:(funny(X)<=>(~curious(X)<~>happy(X))))&
(![X]:(~patient(X)=>(humble(X)&~funny(X))))&
((happy(lucy))=>(?[X]:((funny(X)|patient(X)))))&
(![X]:((old(X)|~kind(X))=>(old(X)&~curious(X))))&
(![X]:((~calm(X)|strong(X))<=>(~wise(X)<~>old(X))))&
((strong(mary)<~>~calm(mary)))&
((tall(john)|old(john)))&
((generous(paul)<~>humble(paul)))&
(~quiet(paul))&
(?[X]:((~patient(X)|~humble(X))))&
((~humble(fred)<~>~rich(fred))) | brave(alice) | [] | null | 0 |
If john is either quiet or not quiet then john is either not kind or humble and vice versa. If someone is not brave then someone is either not patient or funny. Everyone who is not patient is not kind. Everyone who is both patient and calm is either not happy or old. Everyone who is both old and brave is either not humble or curious. If fred is kind then someone is both brave and not creative and vice versa. Everyone who is not creative or not rich is not tall and vice versa. If someone is old or happy then john is patient or not patient and vice versa. If someone is not strong then john is either not curious or tall and vice versa. If someone is either not tall or funny then someone is either quiet or strong and vice versa. Everyone who is curious or patient is both happy and not creative and vice versa. Everyone who is not humble or not wise is not humble. If mary is either not kind or not wise then someone is patient. Everyone who is either wise or curious is calm or rich and vice versa. If susan is not tall then alice is not curious or not creative and vice versa. Everyone who is not brave or brave is both old and rich. Fred is both not wise and not kind. Someone is not patient or not tall. Alice is quiet. Someone is either curious or not old. Someone is either not humble or kind. Susan is either calm or strong. | Alice is wise. | neutral | (((quiet(john)<~>~quiet(john)))<=>((~kind(john)<~>humble(john))))&
((?[X]:(~brave(X)))=>(?[X]:((~patient(X)<~>funny(X)))))&
(![X]:(~patient(X)=>~kind(X)))&
(![X]:((patient(X)&calm(X))=>(~happy(X)<~>old(X))))&
(![X]:((old(X)&brave(X))=>(~humble(X)<~>curious(X))))&
((kind(fred))<=>(?[X]:((brave(X)&~creative(X)))))&
(![X]:((~creative(X)|~rich(X))<=>~tall(X)))&
((?[X]:((old(X)|happy(X))))<=>((patient(john)|~patient(john))))&
((?[X]:(~strong(X)))<=>((~curious(john)<~>tall(john))))&
((?[X]:((~tall(X)<~>funny(X))))<=>(?[X]:((quiet(X)<~>strong(X)))))&
(![X]:((curious(X)|patient(X))<=>(happy(X)&~creative(X))))&
(![X]:((~humble(X)|~wise(X))=>~humble(X)))&
(((~kind(mary)<~>~wise(mary)))=>(?[X]:(patient(X))))&
(![X]:((wise(X)<~>curious(X))<=>(calm(X)|rich(X))))&
((~tall(susan))<=>((~curious(alice)|~creative(alice))))&
(![X]:((~brave(X)|brave(X))=>(old(X)&rich(X))))&
((~wise(fred)&~kind(fred)))&
(?[X]:((~patient(X)|~tall(X))))&
(quiet(alice))&
(?[X]:((curious(X)<~>~old(X))))&
(?[X]:((~humble(X)<~>kind(X))))&
((calm(susan)<~>strong(susan))) | wise(alice) | [] | null | 0 |
If someone is rich then someone is both not funny and quiet. If fred is both brave and kind then someone is not tall or not brave and vice versa. Everyone who is either calm or not generous is either not rich or funny. Everyone who is either not rich or curious is either creative or humble. If someone is either not rich or not creative then fred is not humble or not generous and vice versa. Everyone who is both strong and curious is either strong or quiet. Everyone who is not generous is wise and vice versa. If someone is curious or funny then paul is kind. If someone is not happy or kind then susan is both kind and curious. If someone is not brave then someone is brave or old. Everyone who is not strong or not brave is either wise or happy. Everyone who is not wise or old is not wise or generous and vice versa. If mary is not humble then someone is quiet. If susan is kind then paul is kind and vice versa. Everyone who is both not curious and rich is both old and not old and vice versa. Everyone who is not brave or not kind is not wise or not rich. Susan is curious. Lucy is both rich and not happy. Mary is not kind. Someone is not tall or generous. Fred is both not curious and quiet. Fred is not calm. Someone is either not old or not wise. Someone is either not old or patient. | Lucy is not happy. | entailment | ((?[X]:(rich(X)))=>(?[X]:((~funny(X)&quiet(X)))))&
(((brave(fred)&kind(fred)))<=>(?[X]:((~tall(X)|~brave(X)))))&
(![X]:((calm(X)<~>~generous(X))=>(~rich(X)<~>funny(X))))&
(![X]:((~rich(X)<~>curious(X))=>(creative(X)<~>humble(X))))&
((?[X]:((~rich(X)<~>~creative(X))))<=>((~humble(fred)|~generous(fred))))&
(![X]:((strong(X)&curious(X))=>(strong(X)<~>quiet(X))))&
(![X]:(~generous(X)<=>wise(X)))&
((?[X]:((curious(X)|funny(X))))=>(kind(paul)))&
((?[X]:((~happy(X)|kind(X))))=>((kind(susan)&curious(susan))))&
((?[X]:(~brave(X)))=>(?[X]:((brave(X)|old(X)))))&
(![X]:((~strong(X)|~brave(X))=>(wise(X)<~>happy(X))))&
(![X]:((~wise(X)|old(X))<=>(~wise(X)|generous(X))))&
((~humble(mary))=>(?[X]:(quiet(X))))&
((kind(susan))<=>(kind(paul)))&
(![X]:((~curious(X)&rich(X))<=>(old(X)&~old(X))))&
(![X]:((~brave(X)|~kind(X))=>(~wise(X)|~rich(X))))&
(curious(susan))&
((rich(lucy)&~happy(lucy)))&
(~kind(mary))&
(?[X]:((~tall(X)|generous(X))))&
((~curious(fred)&quiet(fred)))&
(~calm(fred))&
(?[X]:((~old(X)<~>~wise(X))))&
(?[X]:((~old(X)<~>patient(X)))) | ~happy(lucy) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 67484782594191449815897
% SZS output start Proof for 67484782594191449815897
18. ~happy(lucy) & rich(lucy) [input p17]
25. happy(lucy) [input hypothesis]
127. ~happy(lucy) [cnf transformation 18]
137. happy(lucy) [cnf transformation 25]
288. $false [subsumption resolution 137,127]
% SZS output end Proof for 67484782594191449815897
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both not brave and not curious then someone is patient and vice versa.
Everyone who is not curious or not quiet is both patient and not old and vice versa.
If fred is both curious and generous then someone is generous or wise.
Everyone who is either wise or strong is tall and vice versa.
Everyone who is calm or not brave is generous or kind and vice versa.
If john is happy or kind then lucy is not curious or not patient and vice versa.
Everyone who is not brave or not wise is not humble or not wise and vice versa.
If someone is both old and not generous then alice is not wise or calm.
If paul is wise or humble then someone is not wise or generous and vice versa.
If mary is patient then john is not old or funny and vice versa.
If someone is curious or not tall then lucy is both creative and not generous.
Everyone who is not patient is both calm and brave and vice versa.
Everyone who is both not funny and strong is both patient and generous.
Everyone who is both not funny and not rich is either not strong or not kind and vice versa.
Everyone who is humble is either calm or funny.
Everyone who is both curious and rich is generous or not funny and vice versa.
Mary is either not strong or rich.
Someone is not quiet or not old.
John is tall or not humble.
Someone is both humble and tall.
Paul is either not curious or brave.
Mary is both not tall and strong.
Fred is either not funny or brave.
Someone is creative. | Alice is kind. | entailment | (((~brave(alice)&~curious(alice)))<=>(?[X]:(patient(X))))&
(![X]:((~curious(X)|~quiet(X))<=>(patient(X)&~old(X))))&
(((curious(fred)&generous(fred)))=>(?[X]:((generous(X)|wise(X)))))&
(![X]:((wise(X)<~>strong(X))<=>tall(X)))&
(![X]:((calm(X)|~brave(X))<=>(generous(X)|kind(X))))&
(((happy(john)|kind(john)))<=>((~curious(lucy)|~patient(lucy))))&
(![X]:((~brave(X)|~wise(X))<=>(~humble(X)|~wise(X))))&
((?[X]:((old(X)&~generous(X))))=>((~wise(alice)|calm(alice))))&
(((wise(paul)|humble(paul)))<=>(?[X]:((~wise(X)|generous(X)))))&
((patient(mary))<=>((~old(john)|funny(john))))&
((?[X]:((curious(X)|~tall(X))))=>((creative(lucy)&~generous(lucy))))&
(![X]:(~patient(X)<=>(calm(X)&brave(X))))&
(![X]:((~funny(X)&strong(X))=>(patient(X)&generous(X))))&
(![X]:((~funny(X)&~rich(X))<=>(~strong(X)<~>~kind(X))))&
(![X]:(humble(X)=>(calm(X)<~>funny(X))))&
(![X]:((curious(X)&rich(X))<=>(generous(X)|~funny(X))))&
((~strong(mary)<~>rich(mary)))&
(?[X]:((~quiet(X)|~old(X))))&
((tall(john)|~humble(john)))&
(?[X]:((humble(X)&tall(X))))&
((~curious(paul)<~>brave(paul)))&
((~tall(mary)&strong(mary)))&
((~funny(fred)<~>brave(fred)))&
(?[X]:(creative(X))) | kind(alice) | [
"p0",
"p3",
"p4",
"p6",
"p11",
"p12",
"p13",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3364901431540678381230684
% SZS output start Proof for 3364901431540678381230684
1. (~curious(alice) & ~brave(alice)) <=> ? [X0] : patient(X0) [input p0]
4. ! [X0] : ((wise(X0) <~> strong(X0)) <=> tall(X0)) [input p3]
5. ! [X0] : ((~brave(X0) | calm(X0)) <=> (kind(X0) | generous(X0))) [input p4]
7. ! [X0] : ((~wise(X0) | ~brave(X0)) <=> (~wise(X0) | ~humble(X0))) [input p6]
12. ! [X0] : (~patient(X0) <=> (brave(X0) & calm(X0))) [input p11]
13. ! [X0] : ((strong(X0) & ~funny(X0)) => (generous(X0) & patient(X0))) [input p12]
14. ! [X0] : ((~rich(X0) & ~funny(X0)) <=> (~strong(X0) <~> ~kind(X0))) [input p13]
15. ! [X0] : (humble(X0) => (calm(X0) <~> funny(X0))) [input p14]
16. ! [X0] : ((rich(X0) & curious(X0)) <=> (~funny(X0) | generous(X0))) [input p15]
22. strong(mary) & ~tall(mary) [input p21]
25. ~kind(alice) [input hypothesis]
33. ! [X0] : ((generous(X0) & patient(X0)) | (~strong(X0) | funny(X0))) [ennf transformation 13]
34. ! [X0] : ((generous(X0) & patient(X0)) | ~strong(X0) | funny(X0)) [flattening 33]
35. ! [X0] : ((calm(X0) <~> funny(X0)) | ~humble(X0)) [ennf transformation 15]
36. ((~curious(alice) & ~brave(alice)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | (curious(alice) | brave(alice))) [nnf transformation 1]
37. ((~curious(alice) & ~brave(alice)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | curious(alice) | brave(alice)) [flattening 36]
38. ((~curious(alice) & ~brave(alice)) | ! [X0] : ~patient(X0)) & (? [X1] : patient(X1) | curious(alice) | brave(alice)) [rectify 37]
39. ? [X1] : patient(X1) => patient(sK0) [choice axiom]
40. ((~curious(alice) & ~brave(alice)) | ! [X0] : ~patient(X0)) & (patient(sK0) | curious(alice) | brave(alice)) [skolemisation 38,39]
45. ! [X0] : ((((~strong(X0) | ~wise(X0)) & (strong(X0) | wise(X0))) | ~tall(X0)) & (tall(X0) | ((wise(X0) | ~strong(X0)) & (strong(X0) | ~wise(X0))))) [nnf transformation 4]
46. ! [X0] : (((~brave(X0) | calm(X0)) | (~kind(X0) & ~generous(X0))) & ((kind(X0) | generous(X0)) | (brave(X0) & ~calm(X0)))) [nnf transformation 5]
47. ! [X0] : ((~brave(X0) | calm(X0) | (~kind(X0) & ~generous(X0))) & (kind(X0) | generous(X0) | (brave(X0) & ~calm(X0)))) [flattening 46]
50. ! [X0] : (((~wise(X0) | ~brave(X0)) | (wise(X0) & humble(X0))) & ((~wise(X0) | ~humble(X0)) | (wise(X0) & brave(X0)))) [nnf transformation 7]
51. ! [X0] : ((~wise(X0) | ~brave(X0) | (wise(X0) & humble(X0))) & (~wise(X0) | ~humble(X0) | (wise(X0) & brave(X0)))) [flattening 50]
59. ! [X0] : ((~patient(X0) | (~brave(X0) | ~calm(X0))) & ((brave(X0) & calm(X0)) | patient(X0))) [nnf transformation 12]
60. ! [X0] : ((~patient(X0) | ~brave(X0) | ~calm(X0)) & ((brave(X0) & calm(X0)) | patient(X0))) [flattening 59]
61. ! [X0] : (((~rich(X0) & ~funny(X0)) | ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0)))) & (((kind(X0) | strong(X0)) & (~kind(X0) | ~strong(X0))) | (rich(X0) | funny(X0)))) [nnf transformation 14]
62. ! [X0] : (((~rich(X0) & ~funny(X0)) | ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0)))) & (((kind(X0) | strong(X0)) & (~kind(X0) | ~strong(X0))) | rich(X0) | funny(X0))) [flattening 61]
63. ! [X0] : (((~funny(X0) | ~calm(X0)) & (funny(X0) | calm(X0))) | ~humble(X0)) [nnf transformation 35]
64. ! [X0] : (((rich(X0) & curious(X0)) | (funny(X0) & ~generous(X0))) & ((~funny(X0) | generous(X0)) | (~rich(X0) | ~curious(X0)))) [nnf transformation 16]
65. ! [X0] : (((rich(X0) & curious(X0)) | (funny(X0) & ~generous(X0))) & (~funny(X0) | generous(X0) | ~rich(X0) | ~curious(X0))) [flattening 64]
74. ~brave(alice) | ~patient(X0) [cnf transformation 40]
75. ~curious(alice) | ~patient(X0) [cnf transformation 40]
83. ~strong(X0) | wise(X0) | tall(X0) [cnf transformation 45]
87. kind(X0) | generous(X0) | brave(X0) [cnf transformation 47]
89. ~kind(X0) | calm(X0) | ~brave(X0) [cnf transformation 47]
96. ~wise(X0) | ~brave(X0) | humble(X0) [cnf transformation 51]
109. patient(X0) | brave(X0) [cnf transformation 60]
111. ~strong(X0) | patient(X0) | funny(X0) [cnf transformation 34]
116. ~funny(X0) | ~strong(X0) | kind(X0) [cnf transformation 62]
120. ~funny(X0) | ~calm(X0) | ~humble(X0) [cnf transformation 63]
122. ~generous(X0) | curious(X0) [cnf transformation 65]
134. ~tall(mary) [cnf transformation 22]
135. strong(mary) [cnf transformation 22]
138. ~kind(alice) [cnf transformation 25]
140. 1 <=> ! [X0] : ~patient(X0) [avatar definition]
141. ~patient(X0) <- (1) [avatar component clause 140]
143. 2 <=> curious(alice) [avatar definition]
145. ~curious(alice) <- (~2) [avatar component clause 143]
146. 1 | ~2 [avatar split clause 75,143,140]
148. 3 <=> brave(alice) [avatar definition]
150. ~brave(alice) <- (~3) [avatar component clause 148]
151. 1 | ~3 [avatar split clause 74,148,140]
260. 28 <=> strong(mary) [avatar definition]
262. strong(mary) <- (28) [avatar component clause 260]
289. 28 [avatar split clause 135,260]
313. wise(mary) | tall(mary) <- (28) [resolution 83,262]
314. wise(mary) <- (28) [subsumption resolution 313,134]
331. generous(alice) | brave(alice) [resolution 87,138]
332. generous(alice) <- (~3) [subsumption resolution 331,150]
335. curious(alice) <- (~3) [resolution 332,122]
336. $false <- (~2, ~3) [subsumption resolution 335,145]
337. 2 | 3 [avatar contradiction clause 336]
345. brave(X0) <- (1) [resolution 141,109]
363. ~brave(mary) | humble(mary) <- (28) [resolution 96,314]
364. humble(mary) <- (1, 28) [subsumption resolution 363,345]
367. patient(mary) | funny(mary) <- (28) [resolution 111,262]
369. funny(mary) <- (1, 28) [subsumption resolution 367,141]
388. ~strong(mary) | kind(mary) <- (1, 28) [resolution 116,369]
391. kind(mary) <- (1, 28) [subsumption resolution 388,262]
401. calm(mary) | ~brave(mary) <- (1, 28) [resolution 391,89]
402. calm(mary) <- (1, 28) [subsumption resolution 401,345]
435. ~calm(mary) | ~humble(mary) <- (1, 28) [resolution 120,369]
446. ~humble(mary) <- (1, 28) [subsumption resolution 435,402]
447. $false <- (1, 28) [subsumption resolution 446,364]
448. ~1 | ~28 [avatar contradiction clause 447]
450. $false [avatar sat refutation 146,151,289,337,448]
% SZS output end Proof for 3364901431540678381230684
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm then someone is both not happy and curious and vice versa. Everyone who is generous or not generous is either rich or patient and vice versa. Everyone who is both calm and funny is both strong and humble. Everyone who is kind is either calm or humble and vice versa. Everyone who is either calm or tall is wise or rich and vice versa. If lucy is both not kind and not strong then mary is both not tall and brave. If mary is not curious then someone is both not old and funny and vice versa. If someone is both happy and not generous then lucy is both tall and not wise. Everyone who is strong or old is both not funny and calm. Everyone who is either curious or not calm is creative and vice versa. If alice is both not patient and brave then someone is both not patient and not brave and vice versa. If john is curious then someone is either not kind or not strong. If someone is not brave then mary is either not happy or not humble. If mary is not tall then alice is not tall or rich and vice versa. If susan is not wise then someone is funny or not tall. Everyone who is both not creative and tall is either kind or not old and vice versa. John is both not old and not quiet. Mary is rich. Someone is not old or calm. Alice is not calm or creative. Someone is creative or calm. Someone is both not curious and funny. Someone is not happy. Someone is either not happy or not old. | Lucy is not creative. | neutral | ((?[X]:(~calm(X)))<=>(?[X]:((~happy(X)&curious(X)))))&
(![X]:((generous(X)|~generous(X))<=>(rich(X)<~>patient(X))))&
(![X]:((calm(X)&funny(X))=>(strong(X)&humble(X))))&
(![X]:(kind(X)<=>(calm(X)<~>humble(X))))&
(![X]:((calm(X)<~>tall(X))<=>(wise(X)|rich(X))))&
(((~kind(lucy)&~strong(lucy)))=>((~tall(mary)&brave(mary))))&
((~curious(mary))<=>(?[X]:((~old(X)&funny(X)))))&
((?[X]:((happy(X)&~generous(X))))=>((tall(lucy)&~wise(lucy))))&
(![X]:((strong(X)|old(X))=>(~funny(X)&calm(X))))&
(![X]:((curious(X)<~>~calm(X))<=>creative(X)))&
(((~patient(alice)&brave(alice)))<=>(?[X]:((~patient(X)&~brave(X)))))&
((curious(john))=>(?[X]:((~kind(X)<~>~strong(X)))))&
((?[X]:(~brave(X)))=>((~happy(mary)<~>~humble(mary))))&
((~tall(mary))<=>((~tall(alice)|rich(alice))))&
((~wise(susan))=>(?[X]:((funny(X)|~tall(X)))))&
(![X]:((~creative(X)&tall(X))<=>(kind(X)<~>~old(X))))&
((~old(john)&~quiet(john)))&
(rich(mary))&
(?[X]:((~old(X)|calm(X))))&
((~calm(alice)|creative(alice)))&
(?[X]:((creative(X)|calm(X))))&
(?[X]:((~curious(X)&funny(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~happy(X)<~>~old(X)))) | ~creative(lucy) | [] | null | 0 |
Everyone who is either not generous or not funny is either not kind or happy and vice versa.
Everyone who is either not tall or not calm is old or not old.
Everyone who is strong or not funny is not funny or not humble.
If someone is both not humble and not calm then someone is wise or generous and vice versa.
Everyone who is old is both old and not creative and vice versa.
Everyone who is funny is not funny or wise.
Everyone who is either curious or not humble is not calm.
Everyone who is either humble or quiet is either not strong or not tall.
If john is strong then someone is both not patient and not wise and vice versa.
If john is both patient and not happy then lucy is both old and not old.
If someone is rich or funny then someone is wise or not quiet.
If someone is both old and not calm then someone is brave or not rich and vice versa.
If someone is not generous or creative then someone is both not rich and happy and vice versa.
If someone is either generous or not calm then alice is not strong or not brave.
Everyone who is both rich and not creative is not happy or humble and vice versa.
If mary is both not quiet and not generous then someone is tall or generous and vice versa.
Fred is either not kind or not calm.
Someone is either not creative or not quiet.
Fred is both brave and not happy.
Someone is either not old or old.
Someone is not quiet.
Someone is either humble or not strong.
Fred is not old.
Lucy is not strong or creative. | Fred is not creative. | entailment | (![X]:((~generous(X)<~>~funny(X))<=>(~kind(X)<~>happy(X))))&
(![X]:((~tall(X)<~>~calm(X))=>(old(X)|~old(X))))&
(![X]:((strong(X)|~funny(X))=>(~funny(X)|~humble(X))))&
((?[X]:((~humble(X)&~calm(X))))<=>(?[X]:((wise(X)|generous(X)))))&
(![X]:(old(X)<=>(old(X)&~creative(X))))&
(![X]:(funny(X)=>(~funny(X)|wise(X))))&
(![X]:((curious(X)<~>~humble(X))=>~calm(X)))&
(![X]:((humble(X)<~>quiet(X))=>(~strong(X)<~>~tall(X))))&
((strong(john))<=>(?[X]:((~patient(X)&~wise(X)))))&
(((patient(john)&~happy(john)))=>((old(lucy)&~old(lucy))))&
((?[X]:((rich(X)|funny(X))))=>(?[X]:((wise(X)|~quiet(X)))))&
((?[X]:((old(X)&~calm(X))))<=>(?[X]:((brave(X)|~rich(X)))))&
((?[X]:((~generous(X)|creative(X))))<=>(?[X]:((~rich(X)&happy(X)))))&
((?[X]:((generous(X)<~>~calm(X))))=>((~strong(alice)|~brave(alice))))&
(![X]:((rich(X)&~creative(X))<=>(~happy(X)|humble(X))))&
(((~quiet(mary)&~generous(mary)))<=>(?[X]:((tall(X)|generous(X)))))&
((~kind(fred)<~>~calm(fred)))&
(?[X]:((~creative(X)<~>~quiet(X))))&
((brave(fred)&~happy(fred)))&
(?[X]:((~old(X)<~>old(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((humble(X)<~>~strong(X))))&
(~old(fred))&
((~strong(lucy)|creative(lucy))) | ~creative(fred) | [
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1803990474672007693975760
% SZS output start Proof for 1803990474672007693975760
15. ! [X0] : ((~creative(X0) & rich(X0)) <=> (humble(X0) | ~happy(X0))) [input p14]
19. ~happy(fred) & brave(fred) [input p18]
25. creative(fred) [input hypothesis]
72. ! [X0] : (((~creative(X0) & rich(X0)) | (~humble(X0) & happy(X0))) & ((humble(X0) | ~happy(X0)) | (creative(X0) | ~rich(X0)))) [nnf transformation 15]
73. ! [X0] : (((~creative(X0) & rich(X0)) | (~humble(X0) & happy(X0))) & (humble(X0) | ~happy(X0) | creative(X0) | ~rich(X0))) [flattening 72]
140. ~creative(X0) | happy(X0) [cnf transformation 73]
152. ~happy(fred) [cnf transformation 19]
160. creative(fred) [cnf transformation 25]
387. happy(fred) [resolution 140,160]
389. $false [subsumption resolution 387,152]
% SZS output end Proof for 1803990474672007693975760
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not brave or generous then someone is either not creative or tall.
If someone is kind or creative then susan is wise and vice versa.
Everyone who is not creative or creative is either not patient or not strong.
Everyone who is creative or not strong is either not brave or not happy.
Everyone who is brave is happy and vice versa.
Everyone who is both not tall and not curious is humble or wise and vice versa.
If john is rich or not old then someone is both strong and not creative and vice versa.
Everyone who is either not calm or not quiet is either not wise or not old.
If lucy is either old or not rich then someone is tall.
Everyone who is either kind or wise is not humble or not generous.
Everyone who is humble or funny is both quiet and humble and vice versa.
Everyone who is humble is both not rich and not funny and vice versa.
Everyone who is not quiet or not curious is not rich or not kind and vice versa.
If someone is either wise or not happy then susan is both not happy and generous.
If john is both not old and funny then someone is not funny.
Everyone who is both not brave and old is not humble and vice versa.
Susan is both humble and not patient.
Someone is either quiet or not strong.
Someone is either not wise or curious.
Alice is either not brave or creative.
Alice is not curious. | John is not old. | neutral | ((?[X]:((~brave(X)<~>generous(X))))=>(?[X]:((~creative(X)<~>tall(X)))))&
((?[X]:((kind(X)|creative(X))))<=>(wise(susan)))&
(![X]:((~creative(X)|creative(X))=>(~patient(X)<~>~strong(X))))&
(![X]:((creative(X)|~strong(X))=>(~brave(X)<~>~happy(X))))&
(![X]:(brave(X)<=>happy(X)))&
(![X]:((~tall(X)&~curious(X))<=>(humble(X)|wise(X))))&
(((rich(john)|~old(john)))<=>(?[X]:((strong(X)&~creative(X)))))&
(![X]:((~calm(X)<~>~quiet(X))=>(~wise(X)<~>~old(X))))&
(((old(lucy)<~>~rich(lucy)))=>(?[X]:(tall(X))))&
(![X]:((kind(X)<~>wise(X))=>(~humble(X)|~generous(X))))&
(![X]:((humble(X)|funny(X))<=>(quiet(X)&humble(X))))&
(![X]:(humble(X)<=>(~rich(X)&~funny(X))))&
(![X]:((~quiet(X)|~curious(X))<=>(~rich(X)|~kind(X))))&
((?[X]:((wise(X)<~>~happy(X))))=>((~happy(susan)&generous(susan))))&
(((~old(john)&funny(john)))=>(?[X]:(~funny(X))))&
(![X]:((~brave(X)&old(X))<=>~humble(X)))&
((humble(susan)&~patient(susan)))&
(?[X]:((quiet(X)<~>~strong(X))))&
(?[X]:((~wise(X)<~>curious(X))))&
((~brave(alice)<~>creative(alice)))&
(~curious(alice)) | ~old(john) | [] | null | 0 |
Everyone who is not kind is both creative and wise.
Everyone who is not curious or curious is generous and vice versa.
Everyone who is not generous is either not quiet or rich.
Everyone who is not happy or not quiet is both wise and not curious.
Everyone who is both not patient and not funny is both not curious and generous and vice versa.
If paul is not humble then someone is either wise or brave and vice versa.
Everyone who is happy or not old is funny or not kind and vice versa.
If someone is quiet then paul is generous and vice versa.
If lucy is both not brave and not quiet then someone is rich and vice versa.
Everyone who is both not patient and wise is wise or not old and vice versa.
Everyone who is both not brave and funny is either not happy or kind.
Everyone who is either not quiet or not curious is not creative or wise and vice versa.
Everyone who is either not tall or funny is strong or humble and vice versa.
Everyone who is not quiet or funny is wise or not generous.
If lucy is generous then susan is not curious.
If someone is both not kind and curious then someone is kind or humble and vice versa.
Lucy is not calm.
Mary is either tall or quiet.
Someone is either brave or not curious.
Paul is either not calm or not kind.
Paul is either not wise or not kind.
Someone is not patient or brave. | Lucy is not humble. | entailment | (![X]:(~kind(X)=>(creative(X)&wise(X))))&
(![X]:((~curious(X)|curious(X))<=>generous(X)))&
(![X]:(~generous(X)=>(~quiet(X)<~>rich(X))))&
(![X]:((~happy(X)|~quiet(X))=>(wise(X)&~curious(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~curious(X)&generous(X))))&
((~humble(paul))<=>(?[X]:((wise(X)<~>brave(X)))))&
(![X]:((happy(X)|~old(X))<=>(funny(X)|~kind(X))))&
((?[X]:(quiet(X)))<=>(generous(paul)))&
(((~brave(lucy)&~quiet(lucy)))<=>(?[X]:(rich(X))))&
(![X]:((~patient(X)&wise(X))<=>(wise(X)|~old(X))))&
(![X]:((~brave(X)&funny(X))=>(~happy(X)<~>kind(X))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~creative(X)|wise(X))))&
(![X]:((~tall(X)<~>funny(X))<=>(strong(X)|humble(X))))&
(![X]:((~quiet(X)|funny(X))=>(wise(X)|~generous(X))))&
((generous(lucy))=>(~curious(susan)))&
((?[X]:((~kind(X)&curious(X))))<=>(?[X]:((kind(X)|humble(X)))))&
(~calm(lucy))&
((tall(mary)<~>quiet(mary)))&
(?[X]:((brave(X)<~>~curious(X))))&
((~calm(paul)<~>~kind(paul)))&
((~wise(paul)<~>~kind(paul)))&
(?[X]:((~patient(X)|brave(X)))) | ~humble(lucy) | [
"p0",
"p3",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7282544432571824859821810
% SZS output start Proof for 7282544432571824859821810
1. ! [X0] : (~kind(X0) => (wise(X0) & creative(X0))) [input p0]
4. ! [X0] : ((~quiet(X0) | ~happy(X0)) => (~curious(X0) & wise(X0))) [input p3]
12. ! [X0] : ((~quiet(X0) <~> ~curious(X0)) <=> (wise(X0) | ~creative(X0))) [input p11]
16. ? [X0] : (curious(X0) & ~kind(X0)) <=> ? [X0] : (humble(X0) | kind(X0)) [input p15]
23. humble(lucy) [input hypothesis]
24. ? [X0] : (curious(X0) & ~kind(X0)) <=> ? [X1] : (humble(X1) | kind(X1)) [rectify 16]
25. ! [X0] : ((wise(X0) & creative(X0)) | kind(X0)) [ennf transformation 1]
27. ! [X0] : ((~curious(X0) & wise(X0)) | (quiet(X0) & happy(X0))) [ennf transformation 4]
56. ! [X0] : ((((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | (~wise(X0) & creative(X0))) & ((wise(X0) | ~creative(X0)) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0))))) [nnf transformation 12]
57. ! [X0] : ((((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | (~wise(X0) & creative(X0))) & (wise(X0) | ~creative(X0) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0))))) [flattening 56]
60. (? [X0] : (curious(X0) & ~kind(X0)) | ! [X1] : (~humble(X1) & ~kind(X1))) & (? [X1] : (humble(X1) | kind(X1)) | ! [X0] : (~curious(X0) | kind(X0))) [nnf transformation 24]
61. (? [X0] : (curious(X0) & ~kind(X0)) | ! [X1] : (~humble(X1) & ~kind(X1))) & (? [X2] : (humble(X2) | kind(X2)) | ! [X3] : (~curious(X3) | kind(X3))) [rectify 60]
62. ? [X0] : (curious(X0) & ~kind(X0)) => (curious(sK3) & ~kind(sK3)) [choice axiom]
63. ? [X2] : (humble(X2) | kind(X2)) => (humble(sK4) | kind(sK4)) [choice axiom]
64. ((curious(sK3) & ~kind(sK3)) | ! [X1] : (~humble(X1) & ~kind(X1))) & ((humble(sK4) | kind(sK4)) | ! [X3] : (~curious(X3) | kind(X3))) [skolemisation 61,63,62]
74. wise(X0) | kind(X0) [cnf transformation 25]
81. quiet(X0) | wise(X0) [cnf transformation 27]
83. ~curious(X0) | quiet(X0) [cnf transformation 27]
111. ~curious(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 57]
113. curious(X0) | quiet(X0) | ~wise(X0) [cnf transformation 57]
125. ~kind(sK3) | ~humble(X1) [cnf transformation 64]
127. curious(sK3) | ~humble(X1) [cnf transformation 64]
138. humble(lucy) [cnf transformation 23]
183. quiet(X0) | ~wise(X0) [subsumption resolution 113,83]
184. quiet(X0) [subsumption resolution 183,81]
185. ~curious(X0) | ~wise(X0) [subsumption resolution 111,184]
191. 10 <=> ! [X1] : ~humble(X1) [avatar definition]
192. ~humble(X1) <- (10) [avatar component clause 191]
194. 11 <=> curious(sK3) [avatar definition]
196. curious(sK3) <- (11) [avatar component clause 194]
197. 10 | 11 [avatar split clause 127,194,191]
203. 13 <=> kind(sK3) [avatar definition]
205. ~kind(sK3) <- (~13) [avatar component clause 203]
206. 10 | ~13 [avatar split clause 125,203,191]
258. ~wise(sK3) <- (11) [resolution 185,196]
259. kind(sK3) <- (11) [resolution 258,74]
260. $false <- (11, ~13) [subsumption resolution 259,205]
261. ~11 | 13 [avatar contradiction clause 260]
262. $false <- (10) [resolution 192,138]
263. ~10 [avatar contradiction clause 262]
264. $false [avatar sat refutation 197,206,261,263]
% SZS output end Proof for 7282544432571824859821810
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is both not quiet and not brave and vice versa.
If someone is both strong and funny then someone is both wise and not kind and vice versa.
Everyone who is generous or patient is not strong or happy and vice versa.
If mary is not humble then someone is not brave and vice versa.
If susan is not old then alice is both not humble and strong.
Everyone who is both not strong and happy is both tall and humble and vice versa.
If someone is either creative or generous then someone is humble.
Everyone who is not kind is old or humble and vice versa.
Everyone who is not brave or wise is both not calm and not funny.
If someone is either kind or not curious then someone is both creative and not happy.
If alice is either not calm or not patient then someone is both not happy and brave.
If paul is both creative and humble then alice is kind.
Everyone who is either happy or quiet is either quiet or not kind.
If lucy is either happy or calm then mary is funny and vice versa.
Everyone who is both not generous and wise is either strong or not wise.
Someone is either not humble or calm.
Susan is not strong or not rich.
Mary is both not tall and not calm.
Fred is either wise or tall.
Someone is either not calm or calm.
Someone is either not quiet or not rich.
Someone is either generous or kind. | Fred is generous. | neutral | (![X]:(~wise(X)<=>(~quiet(X)&~brave(X))))&
((?[X]:((strong(X)&funny(X))))<=>(?[X]:((wise(X)&~kind(X)))))&
(![X]:((generous(X)|patient(X))<=>(~strong(X)|happy(X))))&
((~humble(mary))<=>(?[X]:(~brave(X))))&
((~old(susan))=>((~humble(alice)&strong(alice))))&
(![X]:((~strong(X)&happy(X))<=>(tall(X)&humble(X))))&
((?[X]:((creative(X)<~>generous(X))))=>(?[X]:(humble(X))))&
(![X]:(~kind(X)<=>(old(X)|humble(X))))&
(![X]:((~brave(X)|wise(X))=>(~calm(X)&~funny(X))))&
((?[X]:((kind(X)<~>~curious(X))))=>(?[X]:((creative(X)&~happy(X)))))&
(((~calm(alice)<~>~patient(alice)))=>(?[X]:((~happy(X)&brave(X)))))&
(((creative(paul)&humble(paul)))=>(kind(alice)))&
(![X]:((happy(X)<~>quiet(X))=>(quiet(X)<~>~kind(X))))&
(((happy(lucy)<~>calm(lucy)))<=>(funny(mary)))&
(![X]:((~generous(X)&wise(X))=>(strong(X)<~>~wise(X))))&
(?[X]:((~humble(X)<~>calm(X))))&
((~strong(susan)|~rich(susan)))&
((~tall(mary)&~calm(mary)))&
((wise(fred)<~>tall(fred)))&
(?[X]:((~calm(X)<~>calm(X))))&
(?[X]:((~quiet(X)<~>~rich(X))))&
(?[X]:((generous(X)<~>kind(X)))) | generous(fred) | [] | null | 0 |
Everyone who is strong or not rich is not generous and vice versa.
Everyone who is calm is either not strong or humble and vice versa.
Everyone who is either generous or not rich is both old and kind and vice versa.
Everyone who is generous or kind is strong and vice versa.
Everyone who is not patient or humble is funny and vice versa.
If someone is both creative and old then someone is both old and creative.
Everyone who is generous or happy is either not tall or rich and vice versa.
Everyone who is either not generous or happy is creative.
Everyone who is either not wise or quiet is not rich or creative.
Everyone who is both not patient and creative is wise and vice versa.
Everyone who is either happy or not old is creative and vice versa.
Everyone who is both rich and not kind is wise or quiet and vice versa.
Everyone who is not curious or strong is either humble or kind.
If someone is patient or brave then susan is not old and vice versa.
If someone is either not happy or not humble then fred is both old and creative and vice versa.
Susan is quiet or not humble.
John is either wise or not rich.
Someone is either brave or tall.
Lucy is either wise or not quiet.
Someone is either not patient or not funny. | Susan is not patient. | contradiction | (![X]:((strong(X)|~rich(X))<=>~generous(X)))&
(![X]:(calm(X)<=>(~strong(X)<~>humble(X))))&
(![X]:((generous(X)<~>~rich(X))<=>(old(X)&kind(X))))&
(![X]:((generous(X)|kind(X))<=>strong(X)))&
(![X]:((~patient(X)|humble(X))<=>funny(X)))&
((?[X]:((creative(X)&old(X))))=>(?[X]:((old(X)&creative(X)))))&
(![X]:((generous(X)|happy(X))<=>(~tall(X)<~>rich(X))))&
(![X]:((~generous(X)<~>happy(X))=>creative(X)))&
(![X]:((~wise(X)<~>quiet(X))=>(~rich(X)|creative(X))))&
(![X]:((~patient(X)&creative(X))<=>wise(X)))&
(![X]:((happy(X)<~>~old(X))<=>creative(X)))&
(![X]:((rich(X)&~kind(X))<=>(wise(X)|quiet(X))))&
(![X]:((~curious(X)|strong(X))=>(humble(X)<~>kind(X))))&
((?[X]:((patient(X)|brave(X))))<=>(~old(susan)))&
((?[X]:((~happy(X)<~>~humble(X))))<=>((old(fred)&creative(fred))))&
((quiet(susan)|~humble(susan)))&
((wise(john)<~>~rich(john)))&
(?[X]:((brave(X)<~>tall(X))))&
((wise(lucy)<~>~quiet(lucy)))&
(?[X]:((~patient(X)<~>~funny(X)))) | ~patient(susan) | [
"p0",
"p2",
"p3",
"p7",
"p8",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6154002479641761111326405
% SZS output start Proof for 6154002479641761111326405
1. ! [X0] : ((~rich(X0) | strong(X0)) <=> ~generous(X0)) [input p0]
3. ! [X0] : ((generous(X0) <~> ~rich(X0)) <=> (kind(X0) & old(X0))) [input p2]
4. ! [X0] : ((kind(X0) | generous(X0)) <=> strong(X0)) [input p3]
8. ! [X0] : ((~generous(X0) <~> happy(X0)) => creative(X0)) [input p7]
9. ! [X0] : ((~wise(X0) <~> quiet(X0)) => (creative(X0) | ~rich(X0))) [input p8]
10. ! [X0] : ((creative(X0) & ~patient(X0)) <=> wise(X0)) [input p9]
11. ! [X0] : ((happy(X0) <~> ~old(X0)) <=> creative(X0)) [input p10]
12. ! [X0] : ((~kind(X0) & rich(X0)) <=> (quiet(X0) | wise(X0))) [input p11]
21. ~patient(susan) [input hypothesis]
25. ! [X0] : (creative(X0) | (~generous(X0) <=> happy(X0))) [ennf transformation 8]
26. ! [X0] : ((creative(X0) | ~rich(X0)) | (~wise(X0) <=> quiet(X0))) [ennf transformation 9]
27. ! [X0] : (creative(X0) | ~rich(X0) | (~wise(X0) <=> quiet(X0))) [flattening 26]
29. ! [X0] : (((~rich(X0) | strong(X0)) | generous(X0)) & (~generous(X0) | (rich(X0) & ~strong(X0)))) [nnf transformation 1]
30. ! [X0] : ((~rich(X0) | strong(X0) | generous(X0)) & (~generous(X0) | (rich(X0) & ~strong(X0)))) [flattening 29]
31. ! [X0] : ((((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | (~kind(X0) | ~old(X0))) & ((kind(X0) & old(X0)) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0))))) [nnf transformation 3]
32. ! [X0] : ((((rich(X0) | ~generous(X0)) & (~rich(X0) | generous(X0))) | ~kind(X0) | ~old(X0)) & ((kind(X0) & old(X0)) | ((generous(X0) | rich(X0)) & (~rich(X0) | ~generous(X0))))) [flattening 31]
33. ! [X0] : (((kind(X0) | generous(X0)) | ~strong(X0)) & (strong(X0) | (~kind(X0) & ~generous(X0)))) [nnf transformation 4]
34. ! [X0] : ((kind(X0) | generous(X0) | ~strong(X0)) & (strong(X0) | (~kind(X0) & ~generous(X0)))) [flattening 33]
42. ! [X0] : (creative(X0) | ((~generous(X0) | ~happy(X0)) & (happy(X0) | generous(X0)))) [nnf transformation 25]
43. ! [X0] : (creative(X0) | ~rich(X0) | ((~wise(X0) | ~quiet(X0)) & (quiet(X0) | wise(X0)))) [nnf transformation 27]
44. ! [X0] : (((creative(X0) & ~patient(X0)) | ~wise(X0)) & (wise(X0) | (~creative(X0) | patient(X0)))) [nnf transformation 10]
45. ! [X0] : (((creative(X0) & ~patient(X0)) | ~wise(X0)) & (wise(X0) | ~creative(X0) | patient(X0))) [flattening 44]
46. ! [X0] : ((((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | ~creative(X0)) & (creative(X0) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0))))) [nnf transformation 11]
47. ! [X0] : (((~kind(X0) & rich(X0)) | (~quiet(X0) & ~wise(X0))) & ((quiet(X0) | wise(X0)) | (kind(X0) | ~rich(X0)))) [nnf transformation 12]
48. ! [X0] : (((~kind(X0) & rich(X0)) | (~quiet(X0) & ~wise(X0))) & (quiet(X0) | wise(X0) | kind(X0) | ~rich(X0))) [flattening 47]
67. ~generous(X0) | ~strong(X0) [cnf transformation 30]
68. ~generous(X0) | rich(X0) [cnf transformation 30]
69. ~rich(X0) | strong(X0) | generous(X0) [cnf transformation 30]
71. old(X0) | generous(X0) | rich(X0) [cnf transformation 32]
73. kind(X0) | generous(X0) | rich(X0) [cnf transformation 32]
76. strong(X0) | ~generous(X0) [cnf transformation 34]
77. ~kind(X0) | strong(X0) [cnf transformation 34]
78. kind(X0) | generous(X0) | ~strong(X0) [cnf transformation 34]
90. creative(X0) | happy(X0) | generous(X0) [cnf transformation 42]
92. ~rich(X0) | creative(X0) | quiet(X0) | wise(X0) [cnf transformation 43]
94. ~creative(X0) | wise(X0) | patient(X0) [cnf transformation 45]
96. ~wise(X0) | creative(X0) [cnf transformation 45]
97. creative(X0) | ~old(X0) | ~happy(X0) [cnf transformation 46]
99. ~old(X0) | happy(X0) | ~creative(X0) [cnf transformation 46]
104. ~wise(X0) | ~kind(X0) [cnf transformation 48]
105. ~quiet(X0) | ~kind(X0) [cnf transformation 48]
126. ~patient(susan) [cnf transformation 21]
127. kind(X0) | rich(X0) [subsumption resolution 73,68]
129. old(X0) | rich(X0) [subsumption resolution 71,68]
131. ~strong(X0) | kind(X0) [subsumption resolution 78,67]
132. ~generous(X0) [subsumption resolution 76,67]
148. happy(X0) | creative(X0) [subsumption resolution 90,132]
149. ~old(X0) | happy(X0) [subsumption resolution 99,148]
150. ~old(X0) | creative(X0) [subsumption resolution 97,149]
154. 4 <=> old(susan) [avatar definition]
155. ~old(susan) <- (~4) [avatar component clause 154]
156. old(susan) <- (4) [avatar component clause 154]
205. 15 <=> quiet(susan) [avatar definition]
207. quiet(susan) <- (15) [avatar component clause 205]
251. rich(X0) | strong(X0) [resolution 127,77]
262. strong(X0) | generous(X0) | strong(X0) [resolution 69,251]
263. strong(X0) | generous(X0) [duplicate literal removal 262]
265. strong(X0) [subsumption resolution 263,132]
269. kind(X0) [resolution 265,131]
394. 39 <=> creative(susan) [avatar definition]
396. creative(susan) <- (39) [avatar component clause 394]
398. creative(susan) <- (4) [resolution 156,150]
400. 39 | ~4 [avatar split clause 398,154,394]
422. rich(susan) <- (~4) [resolution 155,129]
449. creative(susan) | quiet(susan) | wise(susan) <- (~4) [resolution 422,92]
473. wise(susan) | patient(susan) <- (39) [resolution 396,94]
474. wise(susan) <- (39) [subsumption resolution 473,126]
541. ~kind(susan) <- (39) [resolution 474,104]
545. $false <- (39) [subsumption resolution 541,269]
546. ~39 [avatar contradiction clause 545]
547. creative(susan) | quiet(susan) <- (~4) [subsumption resolution 449,96]
548. 15 | 39 | 4 [avatar split clause 547,154,394,205]
550. ~kind(susan) <- (15) [resolution 207,105]
552. $false <- (15) [subsumption resolution 550,269]
553. ~15 [avatar contradiction clause 552]
554. $false [avatar sat refutation 400,546,548,553]
% SZS output end Proof for 6154002479641761111326405
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is both brave and not funny then someone is not quiet or not humble and vice versa.
If someone is kind or not brave then fred is not wise or not tall and vice versa.
If someone is calm or not quiet then someone is not creative and vice versa.
If paul is brave then lucy is not creative or strong and vice versa.
If someone is brave then someone is both strong and not strong and vice versa.
If susan is humble or not happy then alice is either quiet or tall and vice versa.
Everyone who is either not kind or old is not patient.
If someone is both not happy and rich then paul is not wise.
If lucy is either not brave or tall then alice is either not strong or not patient and vice versa.
Everyone who is both curious and funny is not curious.
If alice is either not happy or not kind then susan is happy.
Everyone who is either kind or curious is not brave.
Everyone who is both funny and not old is not creative.
Everyone who is curious is either old or curious and vice versa.
If someone is either creative or brave then susan is not generous.
Someone is both not funny and generous.
Fred is rich.
John is not wise or not curious.
Mary is not rich or not quiet.
Someone is either curious or not old.
John is not brave.
Someone is creative.
John is either not quiet or quiet. | Alice is humble. | entailment | ((?[X]:((brave(X)&~funny(X))))<=>(?[X]:((~quiet(X)|~humble(X)))))&
((?[X]:((kind(X)|~brave(X))))<=>((~wise(fred)|~tall(fred))))&
((?[X]:((calm(X)|~quiet(X))))<=>(?[X]:(~creative(X))))&
((brave(paul))<=>((~creative(lucy)|strong(lucy))))&
((?[X]:(brave(X)))<=>(?[X]:((strong(X)&~strong(X)))))&
(((humble(susan)|~happy(susan)))<=>((quiet(alice)<~>tall(alice))))&
(![X]:((~kind(X)<~>old(X))=>~patient(X)))&
((?[X]:((~happy(X)&rich(X))))=>(~wise(paul)))&
(((~brave(lucy)<~>tall(lucy)))<=>((~strong(alice)<~>~patient(alice))))&
(![X]:((curious(X)&funny(X))=>~curious(X)))&
(((~happy(alice)<~>~kind(alice)))=>(happy(susan)))&
(![X]:((kind(X)<~>curious(X))=>~brave(X)))&
(![X]:((funny(X)&~old(X))=>~creative(X)))&
(![X]:(curious(X)<=>(old(X)<~>curious(X))))&
((?[X]:((creative(X)<~>brave(X))))=>(~generous(susan)))&
(?[X]:((~funny(X)&generous(X))))&
(rich(fred))&
((~wise(john)|~curious(john)))&
((~rich(mary)|~quiet(mary)))&
(?[X]:((curious(X)<~>~old(X))))&
(~brave(john))&
(?[X]:(creative(X)))&
((~quiet(john)<~>quiet(john))) | humble(alice) | [
"p0",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 6020563730226999239316375
% SZS output start Proof for 6020563730226999239316375
1. ? [X0] : (~funny(X0) & brave(X0)) <=> ? [X0] : (~humble(X0) | ~quiet(X0)) [input p0]
5. ? [X0] : brave(X0) <=> ? [X0] : (~strong(X0) & strong(X0)) [input p4]
24. ~humble(alice) [input hypothesis]
25. ? [X0] : (~funny(X0) & brave(X0)) <=> ? [X1] : (~humble(X1) | ~quiet(X1)) [rectify 1]
27. ? [X0] : brave(X0) <=> ? [X1] : (~strong(X1) & strong(X1)) [rectify 5]
37. (? [X0] : (~funny(X0) & brave(X0)) | ! [X1] : (humble(X1) & quiet(X1))) & (? [X1] : (~humble(X1) | ~quiet(X1)) | ! [X0] : (funny(X0) | ~brave(X0))) [nnf transformation 25]
38. (? [X0] : (~funny(X0) & brave(X0)) | ! [X1] : (humble(X1) & quiet(X1))) & (? [X2] : (~humble(X2) | ~quiet(X2)) | ! [X3] : (funny(X3) | ~brave(X3))) [rectify 37]
39. ? [X0] : (~funny(X0) & brave(X0)) => (~funny(sK0) & brave(sK0)) [choice axiom]
40. ? [X2] : (~humble(X2) | ~quiet(X2)) => (~humble(sK1) | ~quiet(sK1)) [choice axiom]
41. ((~funny(sK0) & brave(sK0)) | ! [X1] : (humble(X1) & quiet(X1))) & ((~humble(sK1) | ~quiet(sK1)) | ! [X3] : (funny(X3) | ~brave(X3))) [skolemisation 38,40,39]
54. (? [X0] : brave(X0) | ! [X1] : (strong(X1) | ~strong(X1))) & (? [X1] : (~strong(X1) & strong(X1)) | ! [X0] : ~brave(X0)) [nnf transformation 27]
55. (? [X0] : brave(X0) | ! [X1] : (strong(X1) | ~strong(X1))) & (? [X2] : (~strong(X2) & strong(X2)) | ! [X3] : ~brave(X3)) [rectify 54]
56. ? [X0] : brave(X0) => brave(sK5) [choice axiom]
57. ? [X2] : (~strong(X2) & strong(X2)) => (~strong(sK6) & strong(sK6)) [choice axiom]
58. (brave(sK5) | ! [X1] : (strong(X1) | ~strong(X1))) & ((~strong(sK6) & strong(sK6)) | ! [X3] : ~brave(X3)) [skolemisation 55,57,56]
77. brave(sK0) | humble(X1) [cnf transformation 41]
90. strong(sK6) | ~brave(X3) [cnf transformation 58]
91. ~strong(sK6) | ~brave(X3) [cnf transformation 58]
133. ~humble(alice) [cnf transformation 24]
138. 1 <=> ! [X1] : humble(X1) [avatar definition]
139. humble(X1) <- (1) [avatar component clause 138]
150. 4 <=> brave(sK0) [avatar definition]
152. brave(sK0) <- (4) [avatar component clause 150]
153. 1 | 4 [avatar split clause 77,150,138]
230. 22 <=> ! [X3] : ~brave(X3) [avatar definition]
231. ~brave(X3) <- (22) [avatar component clause 230]
233. 23 <=> strong(sK6) [avatar definition]
236. 22 | ~23 [avatar split clause 91,233,230]
237. 22 | 23 [avatar split clause 90,233,230]
336. $false <- (4, 22) [subsumption resolution 152,231]
337. ~4 | ~22 [avatar contradiction clause 336]
338. $false <- (1) [resolution 139,133]
339. ~1 [avatar contradiction clause 338]
340. $false [avatar sat refutation 153,236,237,337,339]
% SZS output end Proof for 6020563730226999239316375
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.