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 someone is not creative then someone is either creative or not funny.
Everyone who is humble is both brave and curious and vice versa.
If paul is brave then someone is kind.
Everyone who is both curious and humble is not generous or wise.
Everyone who is not rich is generous or rich.
If john is tall then mary is kind.
If someone is both not kind and patient then mary is funny.
If mary is not funny or not old then someone is funny or not tall and vice versa.
If alice is either not creative or strong then alice is quiet or not brave.
Everyone who is both not quiet and tall is old or patient and vice versa.
If someone is either not quiet or not kind then someone is either not creative or happy.
If mary is either old or not creative then fred is not brave.
If someone is funny or creative then someone is funny or happy.
Everyone who is both brave and kind is either humble or not strong.
Everyone who is either not strong or patient is either kind or not quiet.
If john is curious then lucy is both strong and wise and vice versa.
John is not creative.
Someone is both patient and not old.
Someone is generous.
Mary is either not patient or wise.
Someone is kind or not kind.
Someone is either not wise or not quiet.
Someone is either not brave or not old. | Fred is not brave. | neutral | ((?[X]:(~creative(X)))=>(?[X]:((creative(X)<~>~funny(X)))))&
(![X]:(humble(X)<=>(brave(X)&curious(X))))&
((brave(paul))=>(?[X]:(kind(X))))&
(![X]:((curious(X)&humble(X))=>(~generous(X)|wise(X))))&
(![X]:(~rich(X)=>(generous(X)|rich(X))))&
((tall(john))=>(kind(mary)))&
((?[X]:((~kind(X)&patient(X))))=>(funny(mary)))&
(((~funny(mary)|~old(mary)))<=>(?[X]:((funny(X)|~tall(X)))))&
(((~creative(alice)<~>strong(alice)))=>((quiet(alice)|~brave(alice))))&
(![X]:((~quiet(X)&tall(X))<=>(old(X)|patient(X))))&
((?[X]:((~quiet(X)<~>~kind(X))))=>(?[X]:((~creative(X)<~>happy(X)))))&
(((old(mary)<~>~creative(mary)))=>(~brave(fred)))&
((?[X]:((funny(X)|creative(X))))=>(?[X]:((funny(X)|happy(X)))))&
(![X]:((brave(X)&kind(X))=>(humble(X)<~>~strong(X))))&
(![X]:((~strong(X)<~>patient(X))=>(kind(X)<~>~quiet(X))))&
((curious(john))<=>((strong(lucy)&wise(lucy))))&
(~creative(john))&
(?[X]:((patient(X)&~old(X))))&
(?[X]:(generous(X)))&
((~patient(mary)<~>wise(mary)))&
(?[X]:((kind(X)|~kind(X))))&
(?[X]:((~wise(X)<~>~quiet(X))))&
(?[X]:((~brave(X)<~>~old(X)))) | ~brave(fred) | [] | null | 0 |
Everyone who is funny or not generous is not happy or curious.
Everyone who is not curious is either not curious or not strong.
If someone is either funny or not brave then someone is not creative or not old and vice versa.
Everyone who is both wise and not creative is strong or creative.
Everyone who is not funny or funny is both happy and humble and vice versa.
If someone is not calm or quiet then someone is curious or not curious.
Everyone who is either brave or calm is calm or humble and vice versa.
If john is not patient or creative then paul is humble or not calm.
If mary is not old or not happy then someone is not funny and vice versa.
Everyone who is both old and not strong is either kind or not funny.
Everyone who is not strong is both tall and quiet and vice versa.
Everyone who is both wise and quiet is both wise and curious and vice versa.
Everyone who is either happy or not patient is both tall and not funny and vice versa.
If someone is not generous then paul is either not rich or generous.
Everyone who is not tall or quiet is both funny and curious and vice versa.
Everyone who is either quiet or strong is both happy and not calm.
Mary is not creative or calm.
Someone is either happy or not strong.
Someone is either not curious or not quiet.
Someone is both not kind and not generous.
Susan is not creative or generous.
Susan is both not wise and not calm.
Mary is both not strong and curious. | Susan is not patient. | neutral | (![X]:((funny(X)|~generous(X))=>(~happy(X)|curious(X))))&
(![X]:(~curious(X)=>(~curious(X)<~>~strong(X))))&
((?[X]:((funny(X)<~>~brave(X))))<=>(?[X]:((~creative(X)|~old(X)))))&
(![X]:((wise(X)&~creative(X))=>(strong(X)|creative(X))))&
(![X]:((~funny(X)|funny(X))<=>(happy(X)&humble(X))))&
((?[X]:((~calm(X)|quiet(X))))=>(?[X]:((curious(X)|~curious(X)))))&
(![X]:((brave(X)<~>calm(X))<=>(calm(X)|humble(X))))&
(((~patient(john)|creative(john)))=>((humble(paul)|~calm(paul))))&
(((~old(mary)|~happy(mary)))<=>(?[X]:(~funny(X))))&
(![X]:((old(X)&~strong(X))=>(kind(X)<~>~funny(X))))&
(![X]:(~strong(X)<=>(tall(X)&quiet(X))))&
(![X]:((wise(X)&quiet(X))<=>(wise(X)&curious(X))))&
(![X]:((happy(X)<~>~patient(X))<=>(tall(X)&~funny(X))))&
((?[X]:(~generous(X)))=>((~rich(paul)<~>generous(paul))))&
(![X]:((~tall(X)|quiet(X))<=>(funny(X)&curious(X))))&
(![X]:((quiet(X)<~>strong(X))=>(happy(X)&~calm(X))))&
((~creative(mary)|calm(mary)))&
(?[X]:((happy(X)<~>~strong(X))))&
(?[X]:((~curious(X)<~>~quiet(X))))&
(?[X]:((~kind(X)&~generous(X))))&
((~creative(susan)|generous(susan)))&
((~wise(susan)&~calm(susan)))&
((~strong(mary)&curious(mary))) | ~patient(susan) | [] | null | 0 |
Everyone who is both humble and patient is brave and vice versa.
If someone is not creative then lucy is both not generous and generous.
If john is not wise or generous then someone is not creative or not brave.
Everyone who is humble or wise is not wise or brave and vice versa.
If fred is both happy and humble then someone is both happy and wise and vice versa.
Everyone who is either old or tall is either not happy or tall and vice versa.
If someone is either not patient or creative then lucy is not wise and vice versa.
If someone is kind then someone is not brave or happy.
Everyone who is not rich or tall is creative.
Everyone who is both not quiet and creative is either not calm or humble and vice versa.
Everyone who is not funny or happy is old or not humble and vice versa.
If john is either not curious or not generous then paul is either curious or rich and vice versa.
Everyone who is patient or not wise is either quiet or not humble.
If alice is brave then someone is either kind or not patient.
Everyone who is not tall is kind and vice versa.
If mary is both tall and old then someone is not brave or not rich.
Someone is both not kind and old.
Fred is not patient or not happy.
Susan is brave.
Susan is either quiet or not wise.
Someone is quiet.
Someone is either generous or happy.
Fred is brave or not generous.
John is not kind. | John is tall. | entailment | (![X]:((humble(X)&patient(X))<=>brave(X)))&
((?[X]:(~creative(X)))=>((~generous(lucy)&generous(lucy))))&
(((~wise(john)|generous(john)))=>(?[X]:((~creative(X)|~brave(X)))))&
(![X]:((humble(X)|wise(X))<=>(~wise(X)|brave(X))))&
(((happy(fred)&humble(fred)))<=>(?[X]:((happy(X)&wise(X)))))&
(![X]:((old(X)<~>tall(X))<=>(~happy(X)<~>tall(X))))&
((?[X]:((~patient(X)<~>creative(X))))<=>(~wise(lucy)))&
((?[X]:(kind(X)))=>(?[X]:((~brave(X)|happy(X)))))&
(![X]:((~rich(X)|tall(X))=>creative(X)))&
(![X]:((~quiet(X)&creative(X))<=>(~calm(X)<~>humble(X))))&
(![X]:((~funny(X)|happy(X))<=>(old(X)|~humble(X))))&
(((~curious(john)<~>~generous(john)))<=>((curious(paul)<~>rich(paul))))&
(![X]:((patient(X)|~wise(X))=>(quiet(X)<~>~humble(X))))&
((brave(alice))=>(?[X]:((kind(X)<~>~patient(X)))))&
(![X]:(~tall(X)<=>kind(X)))&
(((tall(mary)&old(mary)))=>(?[X]:((~brave(X)|~rich(X)))))&
(?[X]:((~kind(X)&old(X))))&
((~patient(fred)|~happy(fred)))&
(brave(susan))&
((quiet(susan)<~>~wise(susan)))&
(?[X]:(quiet(X)))&
(?[X]:((generous(X)<~>happy(X))))&
((brave(fred)|~generous(fred)))&
(~kind(john)) | tall(john) | [
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1978199290031421521816276
% SZS output start Proof for 1978199290031421521816276
15. ! [X0] : (~tall(X0) <=> kind(X0)) [input p14]
24. ~kind(john) [input p23]
25. ~tall(john) [input hypothesis]
63. ! [X0] : ((~tall(X0) | ~kind(X0)) & (kind(X0) | tall(X0))) [nnf transformation 15]
128. kind(X0) | tall(X0) [cnf transformation 63]
141. ~kind(john) [cnf transformation 24]
142. ~tall(john) [cnf transformation 25]
326. tall(john) [resolution 128,141]
327. $false [subsumption resolution 326,142]
% SZS output end Proof for 1978199290031421521816276
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then mary is both happy and strong.
If someone is either patient or rich then someone is calm or happy and vice versa.
Everyone who is not happy or calm is either humble or wise and vice versa.
Everyone who is not happy is not old or not quiet and vice versa.
Everyone who is kind or not curious is happy or not funny and vice versa.
If mary is brave then mary is wise or not tall and vice versa.
If someone is both tall and not funny then paul is both patient and calm and vice versa.
If someone is not curious or not generous then alice is both brave and happy.
If susan is either not funny or not strong then fred is both not funny and funny and vice versa.
If lucy is humble or not old then someone is funny and vice versa.
Everyone who is funny or not quiet is both not patient and rich and vice versa.
Everyone who is rich is either humble or funny and vice versa.
Everyone who is generous or not humble is both not brave and not old.
Everyone who is either not funny or not old is patient or not strong and vice versa.
If someone is quiet or funny then someone is both not brave and creative and vice versa.
Lucy is either kind or not quiet.
Paul is generous or quiet.
Someone is not wise or rich.
John is curious.
Mary is both patient and brave.
Someone is creative or not wise.
Someone is both quiet and brave. | Alice is patient. | entailment | ((?[X]:(~generous(X)))=>((happy(mary)&strong(mary))))&
((?[X]:((patient(X)<~>rich(X))))<=>(?[X]:((calm(X)|happy(X)))))&
(![X]:((~happy(X)|calm(X))<=>(humble(X)<~>wise(X))))&
(![X]:(~happy(X)<=>(~old(X)|~quiet(X))))&
(![X]:((kind(X)|~curious(X))<=>(happy(X)|~funny(X))))&
((brave(mary))<=>((wise(mary)|~tall(mary))))&
((?[X]:((tall(X)&~funny(X))))<=>((patient(paul)&calm(paul))))&
((?[X]:((~curious(X)|~generous(X))))=>((brave(alice)&happy(alice))))&
(((~funny(susan)<~>~strong(susan)))<=>((~funny(fred)&funny(fred))))&
(((humble(lucy)|~old(lucy)))<=>(?[X]:(funny(X))))&
(![X]:((funny(X)|~quiet(X))<=>(~patient(X)&rich(X))))&
(![X]:(rich(X)<=>(humble(X)<~>funny(X))))&
(![X]:((generous(X)|~humble(X))=>(~brave(X)&~old(X))))&
(![X]:((~funny(X)<~>~old(X))<=>(patient(X)|~strong(X))))&
((?[X]:((quiet(X)|funny(X))))<=>(?[X]:((~brave(X)&creative(X)))))&
((kind(lucy)<~>~quiet(lucy)))&
((generous(paul)|quiet(paul)))&
(?[X]:((~wise(X)|rich(X))))&
(curious(john))&
((patient(mary)&brave(mary)))&
(?[X]:((creative(X)|~wise(X))))&
(?[X]:((quiet(X)&brave(X)))) | patient(alice) | [
"p3",
"p7",
"p10",
"p11",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 9033797905629571069653324
% SZS output start Proof for 9033797905629571069653324
4. ! [X0] : (~happy(X0) <=> (~quiet(X0) | ~old(X0))) [input p3]
8. ? [X0] : (~generous(X0) | ~curious(X0)) => (happy(alice) & brave(alice)) [input p7]
11. ! [X0] : ((~quiet(X0) | funny(X0)) <=> (rich(X0) & ~patient(X0))) [input p10]
12. ! [X0] : (rich(X0) <=> (humble(X0) <~> funny(X0))) [input p11]
13. ! [X0] : ((~humble(X0) | generous(X0)) => (~old(X0) & ~brave(X0))) [input p12]
22. ? [X0] : (brave(X0) & quiet(X0)) [input p21]
23. ~patient(alice) [input hypothesis]
27. (happy(alice) & brave(alice)) | ! [X0] : (generous(X0) & curious(X0)) [ennf transformation 8]
28. ! [X0] : ((~old(X0) & ~brave(X0)) | (humble(X0) & ~generous(X0))) [ennf transformation 13]
36. ! [X0] : ((~happy(X0) | (quiet(X0) & old(X0))) & ((~quiet(X0) | ~old(X0)) | happy(X0))) [nnf transformation 4]
37. ! [X0] : ((~happy(X0) | (quiet(X0) & old(X0))) & (~quiet(X0) | ~old(X0) | happy(X0))) [flattening 36]
54. ! [X0] : (((~quiet(X0) | funny(X0)) | (~rich(X0) | patient(X0))) & ((rich(X0) & ~patient(X0)) | (quiet(X0) & ~funny(X0)))) [nnf transformation 11]
55. ! [X0] : ((~quiet(X0) | funny(X0) | ~rich(X0) | patient(X0)) & ((rich(X0) & ~patient(X0)) | (quiet(X0) & ~funny(X0)))) [flattening 54]
56. ! [X0] : ((rich(X0) | ((humble(X0) | ~funny(X0)) & (funny(X0) | ~humble(X0)))) & (((~funny(X0) | ~humble(X0)) & (funny(X0) | humble(X0))) | ~rich(X0))) [nnf transformation 12]
69. ? [X0] : (brave(X0) & quiet(X0)) => (brave(sK8) & quiet(sK8)) [choice axiom]
70. brave(sK8) & quiet(sK8) [skolemisation 22,69]
87. ~happy(X0) | quiet(X0) [cnf transformation 37]
100. brave(alice) | generous(X0) [cnf transformation 27]
102. happy(alice) | generous(X0) [cnf transformation 27]
114. ~funny(X0) | rich(X0) [cnf transformation 55]
116. ~quiet(X0) | funny(X0) | ~rich(X0) | patient(X0) [cnf transformation 55]
118. ~funny(X0) | ~humble(X0) | ~rich(X0) [cnf transformation 56]
119. rich(X0) | funny(X0) | ~humble(X0) [cnf transformation 56]
121. ~brave(X0) | ~generous(X0) [cnf transformation 28]
122. ~brave(X0) | humble(X0) [cnf transformation 28]
145. brave(sK8) [cnf transformation 70]
146. ~patient(alice) [cnf transformation 23]
148. 1 <=> ! [X0] : generous(X0) [avatar definition]
149. generous(X0) <- (1) [avatar component clause 148]
233. 20 <=> happy(alice) [avatar definition]
235. happy(alice) <- (20) [avatar component clause 233]
236. 1 | 20 [avatar split clause 102,233,148]
242. 22 <=> brave(alice) [avatar definition]
244. brave(alice) <- (22) [avatar component clause 242]
245. 1 | 22 [avatar split clause 100,242,148]
281. ~humble(X0) | rich(X0) [subsumption resolution 119,114]
282. ~funny(X0) | ~humble(X0) [subsumption resolution 118,281]
362. ~generous(sK8) [resolution 121,145]
367. humble(alice) <- (22) [resolution 122,244]
385. rich(alice) <- (22) [resolution 367,281]
600. $false <- (1) [resolution 149,362]
605. ~1 [avatar contradiction clause 600]
606. quiet(alice) <- (20) [resolution 235,87]
676. funny(alice) | ~rich(alice) | patient(alice) <- (20) [resolution 606,116]
678. funny(alice) | patient(alice) <- (20, 22) [subsumption resolution 676,385]
679. funny(alice) <- (20, 22) [subsumption resolution 678,146]
888. ~humble(alice) <- (20, 22) [resolution 679,282]
891. $false <- (20, 22) [subsumption resolution 888,367]
892. ~20 | ~22 [avatar contradiction clause 891]
893. $false [avatar sat refutation 236,245,605,892]
% SZS output end Proof for 9033797905629571069653324
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not brave is either not rich or not quiet and vice versa.
Everyone who is either quiet or kind is not strong or not creative and vice versa.
If lucy is not patient or not funny then someone is both tall and not quiet.
Everyone who is not calm or not patient is not kind or wise.
Everyone who is not wise or humble is not wise or tall and vice versa.
Everyone who is not kind is happy or old and vice versa.
If mary is not calm or rich then someone is either not kind or not calm.
If alice is either curious or not old then someone is either not rich or not strong.
Everyone who is curious or wise is either calm or humble.
If someone is both not quiet and not rich then alice is both patient and old and vice versa.
Everyone who is not old or creative is both not calm and not tall and vice versa.
Everyone who is either not rich or brave is both not brave and not happy and vice versa.
If john is not creative or humble then mary is not calm.
Everyone who is both rich and humble is both not kind and funny and vice versa.
If someone is either strong or tall then john is tall or kind.
Everyone who is both not creative and not calm is both happy and not quiet and vice versa.
Susan is not old.
Someone is quiet.
Someone is both not strong and not patient.
Someone is both not generous and tall.
Someone is both strong and happy.
Paul is both tall and not kind.
Someone is both not brave and not funny. | John is not strong. | neutral | (![X]:((generous(X)&~brave(X))<=>(~rich(X)<~>~quiet(X))))&
(![X]:((quiet(X)<~>kind(X))<=>(~strong(X)|~creative(X))))&
(((~patient(lucy)|~funny(lucy)))=>(?[X]:((tall(X)&~quiet(X)))))&
(![X]:((~calm(X)|~patient(X))=>(~kind(X)|wise(X))))&
(![X]:((~wise(X)|humble(X))<=>(~wise(X)|tall(X))))&
(![X]:(~kind(X)<=>(happy(X)|old(X))))&
(((~calm(mary)|rich(mary)))=>(?[X]:((~kind(X)<~>~calm(X)))))&
(((curious(alice)<~>~old(alice)))=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((curious(X)|wise(X))=>(calm(X)<~>humble(X))))&
((?[X]:((~quiet(X)&~rich(X))))<=>((patient(alice)&old(alice))))&
(![X]:((~old(X)|creative(X))<=>(~calm(X)&~tall(X))))&
(![X]:((~rich(X)<~>brave(X))<=>(~brave(X)&~happy(X))))&
(((~creative(john)|humble(john)))=>(~calm(mary)))&
(![X]:((rich(X)&humble(X))<=>(~kind(X)&funny(X))))&
((?[X]:((strong(X)<~>tall(X))))=>((tall(john)|kind(john))))&
(![X]:((~creative(X)&~calm(X))<=>(happy(X)&~quiet(X))))&
(~old(susan))&
(?[X]:(quiet(X)))&
(?[X]:((~strong(X)&~patient(X))))&
(?[X]:((~generous(X)&tall(X))))&
(?[X]:((strong(X)&happy(X))))&
((tall(paul)&~kind(paul)))&
(?[X]:((~brave(X)&~funny(X)))) | ~strong(john) | [] | null | 0 |
If someone is either not kind or quiet then lucy is either not wise or curious.
Everyone who is both not curious and curious is both not happy and funny.
If someone is either calm or not generous then alice is not humble and vice versa.
Everyone who is brave is both not rich and not happy and vice versa.
If john is both generous and not strong then someone is not patient or not rich and vice versa.
If someone is both generous and not calm then lucy is not curious or funny and vice versa.
If someone is not kind or generous then someone is both funny and not funny and vice versa.
Everyone who is either not rich or quiet is calm or tall and vice versa.
Everyone who is not strong is either creative or not old and vice versa.
Everyone who is wise or curious is rich or funny and vice versa.
If someone is both not old and not tall then lucy is humble and vice versa.
Everyone who is either calm or not brave is not kind.
Everyone who is both not kind and generous is both happy and not patient.
If lucy is either not patient or not brave then someone is not humble and vice versa.
Everyone who is not old is not wise or rich and vice versa.
Mary is strong or not patient.
Alice is either not brave or wise.
Mary is humble.
Someone is quiet or strong.
Mary is both not wise and rich.
Fred is both not wise and calm. | Lucy is quiet. | entailment | ((?[X]:((~kind(X)<~>quiet(X))))=>((~wise(lucy)<~>curious(lucy))))&
(![X]:((~curious(X)&curious(X))=>(~happy(X)&funny(X))))&
((?[X]:((calm(X)<~>~generous(X))))<=>(~humble(alice)))&
(![X]:(brave(X)<=>(~rich(X)&~happy(X))))&
(((generous(john)&~strong(john)))<=>(?[X]:((~patient(X)|~rich(X)))))&
((?[X]:((generous(X)&~calm(X))))<=>((~curious(lucy)|funny(lucy))))&
((?[X]:((~kind(X)|generous(X))))<=>(?[X]:((funny(X)&~funny(X)))))&
(![X]:((~rich(X)<~>quiet(X))<=>(calm(X)|tall(X))))&
(![X]:(~strong(X)<=>(creative(X)<~>~old(X))))&
(![X]:((wise(X)|curious(X))<=>(rich(X)|funny(X))))&
((?[X]:((~old(X)&~tall(X))))<=>(humble(lucy)))&
(![X]:((calm(X)<~>~brave(X))=>~kind(X)))&
(![X]:((~kind(X)&generous(X))=>(happy(X)&~patient(X))))&
(((~patient(lucy)<~>~brave(lucy)))<=>(?[X]:(~humble(X))))&
(![X]:(~old(X)<=>(~wise(X)|rich(X))))&
((strong(mary)|~patient(mary)))&
((~brave(alice)<~>wise(alice)))&
(humble(mary))&
(?[X]:((quiet(X)|strong(X))))&
((~wise(mary)&rich(mary)))&
((~wise(fred)&calm(fred))) | quiet(lucy) | [
"p2",
"p3",
"p4",
"p6",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2664635631201279498813697
% SZS output start Proof for 2664635631201279498813697
3. ? [X0] : (calm(X0) <~> ~generous(X0)) <=> ~humble(alice) [input p2]
4. ! [X0] : (brave(X0) <=> (~happy(X0) & ~rich(X0))) [input p3]
5. (~strong(john) & generous(john)) <=> ? [X0] : (~rich(X0) | ~patient(X0)) [input p4]
7. ? [X0] : (generous(X0) | ~kind(X0)) <=> ? [X0] : (~funny(X0) & funny(X0)) [input p6]
8. ! [X0] : ((~rich(X0) <~> quiet(X0)) <=> (tall(X0) | calm(X0))) [input p7]
12. ! [X0] : ((calm(X0) <~> ~brave(X0)) => ~kind(X0)) [input p11]
22. ~quiet(lucy) [input hypothesis]
23. ? [X0] : (generous(X0) | ~kind(X0)) <=> ? [X1] : (~funny(X1) & funny(X1)) [rectify 7]
27. ! [X0] : (~kind(X0) | (calm(X0) <=> ~brave(X0))) [ennf transformation 12]
31. (? [X0] : ((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) | humble(alice)) & (~humble(alice) | ! [X0] : ((calm(X0) | generous(X0)) & (~generous(X0) | ~calm(X0)))) [nnf transformation 3]
32. (? [X0] : ((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) | humble(alice)) & (~humble(alice) | ! [X1] : ((calm(X1) | generous(X1)) & (~generous(X1) | ~calm(X1)))) [rectify 31]
33. ? [X0] : ((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) => ((generous(sK0) | ~calm(sK0)) & (~generous(sK0) | calm(sK0))) [choice axiom]
34. (((generous(sK0) | ~calm(sK0)) & (~generous(sK0) | calm(sK0))) | humble(alice)) & (~humble(alice) | ! [X1] : ((calm(X1) | generous(X1)) & (~generous(X1) | ~calm(X1)))) [skolemisation 32,33]
35. ! [X0] : ((brave(X0) | (happy(X0) | rich(X0))) & ((~happy(X0) & ~rich(X0)) | ~brave(X0))) [nnf transformation 4]
36. ! [X0] : ((brave(X0) | happy(X0) | rich(X0)) & ((~happy(X0) & ~rich(X0)) | ~brave(X0))) [flattening 35]
37. ((~strong(john) & generous(john)) | ! [X0] : (rich(X0) & patient(X0))) & (? [X0] : (~rich(X0) | ~patient(X0)) | (strong(john) | ~generous(john))) [nnf transformation 5]
38. ((~strong(john) & generous(john)) | ! [X0] : (rich(X0) & patient(X0))) & (? [X0] : (~rich(X0) | ~patient(X0)) | strong(john) | ~generous(john)) [flattening 37]
39. ((~strong(john) & generous(john)) | ! [X0] : (rich(X0) & patient(X0))) & (? [X1] : (~rich(X1) | ~patient(X1)) | strong(john) | ~generous(john)) [rectify 38]
40. ? [X1] : (~rich(X1) | ~patient(X1)) => (~rich(sK1) | ~patient(sK1)) [choice axiom]
41. ((~strong(john) & generous(john)) | ! [X0] : (rich(X0) & patient(X0))) & ((~rich(sK1) | ~patient(sK1)) | strong(john) | ~generous(john)) [skolemisation 39,40]
47. (? [X0] : (generous(X0) | ~kind(X0)) | ! [X1] : (funny(X1) | ~funny(X1))) & (? [X1] : (~funny(X1) & funny(X1)) | ! [X0] : (~generous(X0) & kind(X0))) [nnf transformation 23]
48. (? [X0] : (generous(X0) | ~kind(X0)) | ! [X1] : (funny(X1) | ~funny(X1))) & (? [X2] : (~funny(X2) & funny(X2)) | ! [X3] : (~generous(X3) & kind(X3))) [rectify 47]
49. ? [X0] : (generous(X0) | ~kind(X0)) => (generous(sK3) | ~kind(sK3)) [choice axiom]
50. ? [X2] : (~funny(X2) & funny(X2)) => (~funny(sK4) & funny(sK4)) [choice axiom]
51. ((generous(sK3) | ~kind(sK3)) | ! [X1] : (funny(X1) | ~funny(X1))) & ((~funny(sK4) & funny(sK4)) | ! [X3] : (~generous(X3) & kind(X3))) [skolemisation 48,50,49]
52. ! [X0] : ((((~quiet(X0) | rich(X0)) & (quiet(X0) | ~rich(X0))) | (~tall(X0) & ~calm(X0))) & ((tall(X0) | calm(X0)) | ((~rich(X0) | ~quiet(X0)) & (quiet(X0) | rich(X0))))) [nnf transformation 8]
53. ! [X0] : ((((~quiet(X0) | rich(X0)) & (quiet(X0) | ~rich(X0))) | (~tall(X0) & ~calm(X0))) & (tall(X0) | calm(X0) | ((~rich(X0) | ~quiet(X0)) & (quiet(X0) | rich(X0))))) [flattening 52]
61. ! [X0] : (~kind(X0) | ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0)))) [nnf transformation 27]
78. ~humble(alice) | calm(X1) | generous(X1) [cnf transformation 34]
80. generous(sK0) | ~calm(sK0) | humble(alice) [cnf transformation 34]
81. ~rich(X0) | ~brave(X0) [cnf transformation 36]
86. generous(john) | rich(X0) [cnf transformation 41]
94. funny(sK4) | kind(X3) [cnf transformation 51]
95. funny(sK4) | ~generous(X3) [cnf transformation 51]
96. ~funny(sK4) | kind(X3) [cnf transformation 51]
97. ~funny(sK4) | ~generous(X3) [cnf transformation 51]
101. ~rich(X0) | quiet(X0) | ~calm(X0) [cnf transformation 53]
117. ~kind(X0) | calm(X0) | brave(X0) [cnf transformation 61]
136. ~quiet(lucy) [cnf transformation 22]
156. 5 <=> humble(alice) [avatar definition]
160. 6 <=> calm(sK0) [avatar definition]
162. ~calm(sK0) <- (~6) [avatar component clause 160]
164. 7 <=> generous(sK0) [avatar definition]
166. generous(sK0) <- (7) [avatar component clause 164]
167. 5 | ~6 | 7 [avatar split clause 80,164,160,156]
170. 8 <=> ! [X1] : (calm(X1) | generous(X1)) [avatar definition]
171. calm(X1) | generous(X1) <- (8) [avatar component clause 170]
172. 8 | ~5 [avatar split clause 78,156,170]
178. 10 <=> ! [X0] : rich(X0) [avatar definition]
179. rich(X0) <- (10) [avatar component clause 178]
190. 13 <=> generous(john) [avatar definition]
192. generous(john) <- (13) [avatar component clause 190]
193. 10 | 13 [avatar split clause 86,190,178]
225. 20 <=> ! [X3] : ~generous(X3) [avatar definition]
226. ~generous(X3) <- (20) [avatar component clause 225]
228. 21 <=> funny(sK4) [avatar definition]
231. 20 | ~21 [avatar split clause 97,228,225]
233. 22 <=> ! [X3] : kind(X3) [avatar definition]
234. kind(X3) <- (22) [avatar component clause 233]
235. 22 | ~21 [avatar split clause 96,228,233]
236. 20 | 21 [avatar split clause 95,228,225]
237. 22 | 21 [avatar split clause 94,228,233]
305. $false <- (13, 20) [subsumption resolution 192,226]
306. ~13 | ~20 [avatar contradiction clause 305]
309. calm(X1) <- (8, 20) [subsumption resolution 171,226]
321. ~brave(X0) <- (10) [resolution 81,179]
325. ~calm(X1) | quiet(X1) <- (10) [resolution 101,179]
329. quiet(X1) <- (8, 10, 20) [subsumption resolution 325,309]
330. $false <- (8, 10, 20) [resolution 329,136]
331. ~8 | ~10 | ~20 [avatar contradiction clause 330]
366. calm(X0) | brave(X0) <- (22) [resolution 117,234]
367. calm(X0) <- (10, 22) [subsumption resolution 366,321]
368. $false <- (~6, 10, 22) [resolution 367,162]
371. 6 | ~10 | ~22 [avatar contradiction clause 368]
372. $false <- (7, 20) [subsumption resolution 166,226]
373. ~7 | ~20 [avatar contradiction clause 372]
374. $false [avatar sat refutation 167,172,193,231,235,236,237,306,331,371,373]
% SZS output end Proof for 2664635631201279498813697
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or not funny is either generous or wise. If someone is funny or not brave then lucy is rich and vice versa. Everyone who is either not creative or not happy is rich and vice versa. Everyone who is either patient or not old is both generous and humble and vice versa. Everyone who is not rich is either patient or not happy and vice versa. If someone is not happy then someone is not calm and vice versa. Everyone who is either funny or old is either not old or rich and vice versa. Everyone who is not strong or calm is funny or not calm. If someone is not patient then fred is funny. Everyone who is quiet or kind is tall. Everyone who is either quiet or funny is not curious or creative and vice versa. Everyone who is not curious is curious. If someone is patient or rich then lucy is both not patient and not tall and vice versa. If susan is wise or strong then someone is not tall or not strong and vice versa. Everyone who is either not strong or old is not brave. If someone is both curious and not creative then lucy is not curious or old. Lucy is both wise and not funny. Susan is not calm or strong. Someone is old. Someone is not creative or not rich. Someone is both humble and generous. Someone is not patient or not rich. Susan is both not calm and not rich. | Fred is funny. | entailment | (![X]:((~strong(X)<~>~funny(X))=>(generous(X)<~>wise(X))))&
((?[X]:((funny(X)|~brave(X))))<=>(rich(lucy)))&
(![X]:((~creative(X)<~>~happy(X))<=>rich(X)))&
(![X]:((patient(X)<~>~old(X))<=>(generous(X)&humble(X))))&
(![X]:(~rich(X)<=>(patient(X)<~>~happy(X))))&
((?[X]:(~happy(X)))<=>(?[X]:(~calm(X))))&
(![X]:((funny(X)<~>old(X))<=>(~old(X)<~>rich(X))))&
(![X]:((~strong(X)|calm(X))=>(funny(X)|~calm(X))))&
((?[X]:(~patient(X)))=>(funny(fred)))&
(![X]:((quiet(X)|kind(X))=>tall(X)))&
(![X]:((quiet(X)<~>funny(X))<=>(~curious(X)|creative(X))))&
(![X]:(~curious(X)=>curious(X)))&
((?[X]:((patient(X)|rich(X))))<=>((~patient(lucy)&~tall(lucy))))&
(((wise(susan)|strong(susan)))<=>(?[X]:((~tall(X)|~strong(X)))))&
(![X]:((~strong(X)<~>old(X))=>~brave(X)))&
((?[X]:((curious(X)&~creative(X))))=>((~curious(lucy)|old(lucy))))&
((wise(lucy)&~funny(lucy)))&
((~calm(susan)|strong(susan)))&
(?[X]:(old(X)))&
(?[X]:((~creative(X)|~rich(X))))&
(?[X]:((humble(X)&generous(X))))&
(?[X]:((~patient(X)|~rich(X))))&
((~calm(susan)&~rich(susan))) | funny(fred) | [
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7129639717902652432186502
% SZS output start Proof for 7129639717902652432186502
9. ? [X0] : ~patient(X0) => funny(fred) [input p8]
13. ? [X0] : (rich(X0) | patient(X0)) <=> (~tall(lucy) & ~patient(lucy)) [input p12]
24. ~funny(fred) [input hypothesis]
30. funny(fred) | ! [X0] : patient(X0) [ennf transformation 9]
53. (? [X0] : (rich(X0) | patient(X0)) | (tall(lucy) | patient(lucy))) & ((~tall(lucy) & ~patient(lucy)) | ! [X0] : (~rich(X0) & ~patient(X0))) [nnf transformation 13]
54. (? [X0] : (rich(X0) | patient(X0)) | tall(lucy) | patient(lucy)) & ((~tall(lucy) & ~patient(lucy)) | ! [X0] : (~rich(X0) & ~patient(X0))) [flattening 53]
55. (? [X0] : (rich(X0) | patient(X0)) | tall(lucy) | patient(lucy)) & ((~tall(lucy) & ~patient(lucy)) | ! [X1] : (~rich(X1) & ~patient(X1))) [rectify 54]
56. ? [X0] : (rich(X0) | patient(X0)) => (rich(sK3) | patient(sK3)) [choice axiom]
57. ((rich(sK3) | patient(sK3)) | tall(lucy) | patient(lucy)) & ((~tall(lucy) & ~patient(lucy)) | ! [X1] : (~rich(X1) & ~patient(X1))) [skolemisation 55,56]
105. funny(fred) | patient(X0) [cnf transformation 30]
114. ~patient(lucy) | ~patient(X1) [cnf transformation 57]
136. ~funny(fred) [cnf transformation 24]
183. 10 <=> ! [X0] : patient(X0) [avatar definition]
184. patient(X0) <- (10) [avatar component clause 183]
186. 11 <=> funny(fred) [avatar definition]
189. 10 | 11 [avatar split clause 105,186,183]
191. 12 <=> patient(lucy) [avatar definition]
192. ~patient(lucy) <- (~12) [avatar component clause 191]
212. 17 <=> ! [X1] : ~patient(X1) [avatar definition]
213. ~patient(X1) <- (17) [avatar component clause 212]
216. 17 | ~12 [avatar split clause 114,191,212]
277. ~11 [avatar split clause 136,186]
280. $false <- (10, ~12) [resolution 192,184]
281. ~10 | 12 [avatar contradiction clause 280]
282. $false <- (10, 17) [subsumption resolution 213,184]
283. ~10 | ~17 [avatar contradiction clause 282]
284. $false [avatar sat refutation 189,216,277,281,283]
% SZS output end Proof for 7129639717902652432186502
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy then fred is both not rich and brave. If alice is either not patient or not old then someone is not tall. Everyone who is not rich or old is both kind and tall and vice versa. Everyone who is not wise or generous is wise. If someone is either patient or not tall then someone is both curious and not happy and vice versa. Everyone who is not old or wise is either wise or curious. If paul is creative or calm then paul is either not quiet or tall and vice versa. If lucy is not brave or wise then fred is quiet. If alice is either not rich or wise then someone is both not old and funny. If someone is both tall and patient then paul is not brave or rich. Everyone who is both happy and not strong is both not creative and not wise and vice versa. If alice is not old or tall then someone is not brave or not quiet. Everyone who is kind or not humble is brave or not curious and vice versa. Everyone who is not funny is tall or rich and vice versa. Everyone who is not kind or not generous is creative or not happy and vice versa. Everyone who is not creative is brave or happy. Someone is both not kind and strong. Someone is strong or calm. Someone is either humble or not rich. Someone is kind or not strong. Someone is either not wise or quiet. Someone is not creative or not humble. Someone is not funny. Susan is brave or not calm. | Fred is quiet. | entailment | ((?[X]:(~happy(X)))=>((~rich(fred)&brave(fred))))&
(((~patient(alice)<~>~old(alice)))=>(?[X]:(~tall(X))))&
(![X]:((~rich(X)|old(X))<=>(kind(X)&tall(X))))&
(![X]:((~wise(X)|generous(X))=>wise(X)))&
((?[X]:((patient(X)<~>~tall(X))))<=>(?[X]:((curious(X)&~happy(X)))))&
(![X]:((~old(X)|wise(X))=>(wise(X)<~>curious(X))))&
(((creative(paul)|calm(paul)))<=>((~quiet(paul)<~>tall(paul))))&
(((~brave(lucy)|wise(lucy)))=>(quiet(fred)))&
(((~rich(alice)<~>wise(alice)))=>(?[X]:((~old(X)&funny(X)))))&
((?[X]:((tall(X)&patient(X))))=>((~brave(paul)|rich(paul))))&
(![X]:((happy(X)&~strong(X))<=>(~creative(X)&~wise(X))))&
(((~old(alice)|tall(alice)))=>(?[X]:((~brave(X)|~quiet(X)))))&
(![X]:((kind(X)|~humble(X))<=>(brave(X)|~curious(X))))&
(![X]:(~funny(X)<=>(tall(X)|rich(X))))&
(![X]:((~kind(X)|~generous(X))<=>(creative(X)|~happy(X))))&
(![X]:(~creative(X)=>(brave(X)|happy(X))))&
(?[X]:((~kind(X)&strong(X))))&
(?[X]:((strong(X)|calm(X))))&
(?[X]:((humble(X)<~>~rich(X))))&
(?[X]:((kind(X)|~strong(X))))&
(?[X]:((~wise(X)<~>quiet(X))))&
(?[X]:((~creative(X)|~humble(X))))&
(?[X]:(~funny(X)))&
((brave(susan)|~calm(susan))) | quiet(fred) | [
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4902402873230241811452531
% SZS output start Proof for 4902402873230241811452531
4. ! [X0] : ((generous(X0) | ~wise(X0)) => wise(X0)) [input p3]
8. (wise(lucy) | ~brave(lucy)) => quiet(fred) [input p7]
25. ~quiet(fred) [input hypothesis]
29. ! [X0] : (wise(X0) | (~generous(X0) & wise(X0))) [ennf transformation 4]
31. quiet(fred) | (~wise(lucy) & brave(lucy)) [ennf transformation 8]
89. wise(X0) | wise(X0) [cnf transformation 29]
108. quiet(fred) | ~wise(lucy) [cnf transformation 31]
143. ~quiet(fred) [cnf transformation 25]
145. wise(X0) [duplicate literal removal 89]
227. quiet(fred) [subsumption resolution 108,145]
316. $false [subsumption resolution 143,227]
% SZS output end Proof for 4902402873230241811452531
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is both not quiet and old.
Everyone who is generous or curious is not curious.
If someone is funny then someone is old or strong.
Everyone who is either rich or creative is either not quiet or calm and vice versa.
Everyone who is both not tall and not humble is not kind or humble.
If someone is both not rich and curious then someone is tall and vice versa.
If someone is either not brave or not humble then alice is both not wise and not happy.
Everyone who is either curious or calm is wise or tall.
If someone is both humble and happy then someone is either not old or creative.
If john is kind or not kind then fred is not humble or happy.
If john is not humble then someone is not curious and vice versa.
Everyone who is not curious is both not humble and not quiet and vice versa.
If john is either tall or not tall then mary is curious or not kind and vice versa.
Everyone who is not humble or not happy is either funny or not creative and vice versa.
If mary is not wise or wise then susan is not rich or not happy and vice versa.
Everyone who is kind or not rich is either brave or not old.
Someone is not patient or not creative.
Paul is funny or not calm.
Someone is either calm or quiet.
Lucy is both calm and happy.
Mary is not tall or brave. | Mary is humble. | contradiction | (![X]:(~humble(X)=>(~quiet(X)&old(X))))&
(![X]:((generous(X)|curious(X))=>~curious(X)))&
((?[X]:(funny(X)))=>(?[X]:((old(X)|strong(X)))))&
(![X]:((rich(X)<~>creative(X))<=>(~quiet(X)<~>calm(X))))&
(![X]:((~tall(X)&~humble(X))=>(~kind(X)|humble(X))))&
((?[X]:((~rich(X)&curious(X))))<=>(?[X]:(tall(X))))&
((?[X]:((~brave(X)<~>~humble(X))))=>((~wise(alice)&~happy(alice))))&
(![X]:((curious(X)<~>calm(X))=>(wise(X)|tall(X))))&
((?[X]:((humble(X)&happy(X))))=>(?[X]:((~old(X)<~>creative(X)))))&
(((kind(john)|~kind(john)))=>((~humble(fred)|happy(fred))))&
((~humble(john))<=>(?[X]:(~curious(X))))&
(![X]:(~curious(X)<=>(~humble(X)&~quiet(X))))&
(((tall(john)<~>~tall(john)))<=>((curious(mary)|~kind(mary))))&
(![X]:((~humble(X)|~happy(X))<=>(funny(X)<~>~creative(X))))&
(((~wise(mary)|wise(mary)))<=>((~rich(susan)|~happy(susan))))&
(![X]:((kind(X)|~rich(X))=>(brave(X)<~>~old(X))))&
(?[X]:((~patient(X)|~creative(X))))&
((funny(paul)|~calm(paul)))&
(?[X]:((calm(X)<~>quiet(X))))&
((calm(lucy)&happy(lucy)))&
((~tall(mary)|brave(mary))) | humble(mary) | [
"p1",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7320079725299976218580559
% SZS output start Proof for 7320079725299976218580559
2. ! [X0] : ((curious(X0) | generous(X0)) => ~curious(X0)) [input p1]
12. ! [X0] : (~curious(X0) <=> (~quiet(X0) & ~humble(X0))) [input p11]
22. humble(mary) [input hypothesis]
28. ! [X0] : (curious(X0) => ~curious(X0)) [pure predicate removal 2]
30. ! [X0] : (~curious(X0) | ~curious(X0)) [ennf transformation 28]
56. ! [X0] : ((~curious(X0) | (quiet(X0) | humble(X0))) & ((~quiet(X0) & ~humble(X0)) | curious(X0))) [nnf transformation 12]
57. ! [X0] : ((~curious(X0) | quiet(X0) | humble(X0)) & ((~quiet(X0) & ~humble(X0)) | curious(X0))) [flattening 56]
70. ~curious(X0) | ~curious(X0) [cnf transformation 30]
95. ~humble(X0) | curious(X0) [cnf transformation 57]
124. humble(mary) [cnf transformation 22]
128. ~curious(X0) [duplicate literal removal 70]
179. ~humble(X0) [subsumption resolution 95,128]
208. $false [subsumption resolution 124,179]
% SZS output end Proof for 7320079725299976218580559
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or not creative then someone is creative or not strong.
Everyone who is wise or not happy is not generous.
If susan is either funny or not creative then lucy is not wise or not strong.
If john is both not happy and humble then paul is not rich.
If john is both tall and not old then someone is both not funny and calm and vice versa.
If someone is generous or not happy then someone is both not creative and not humble and vice versa.
Everyone who is curious or not rich is either brave or kind and vice versa.
Everyone who is either rich or quiet is quiet.
Everyone who is both not brave and not humble is not generous or tall and vice versa.
If susan is both patient and happy then someone is either creative or not generous and vice versa.
If lucy is both generous and patient then susan is not kind or funny and vice versa.
If someone is either not old or not generous then someone is not strong.
If someone is either not wise or tall then fred is either not strong or wise and vice versa.
If alice is either not curious or not creative then susan is either old or not curious.
Everyone who is either brave or wise is both not humble and not funny and vice versa.
If someone is either curious or creative then someone is not quiet or old.
Someone is either brave or wise.
Someone is both not kind and not strong.
Someone is both not wise and not kind.
Mary is either generous or not brave.
Someone is not tall or creative.
Alice is either not quiet or not happy.
Someone is either tall or calm.
Someone is not funny or quiet. | Mary is strong. | neutral | ((?[X]:((kind(X)<~>~creative(X))))=>(?[X]:((creative(X)|~strong(X)))))&
(![X]:((wise(X)|~happy(X))=>~generous(X)))&
(((funny(susan)<~>~creative(susan)))=>((~wise(lucy)|~strong(lucy))))&
(((~happy(john)&humble(john)))=>(~rich(paul)))&
(((tall(john)&~old(john)))<=>(?[X]:((~funny(X)&calm(X)))))&
((?[X]:((generous(X)|~happy(X))))<=>(?[X]:((~creative(X)&~humble(X)))))&
(![X]:((curious(X)|~rich(X))<=>(brave(X)<~>kind(X))))&
(![X]:((rich(X)<~>quiet(X))=>quiet(X)))&
(![X]:((~brave(X)&~humble(X))<=>(~generous(X)|tall(X))))&
(((patient(susan)&happy(susan)))<=>(?[X]:((creative(X)<~>~generous(X)))))&
(((generous(lucy)&patient(lucy)))<=>((~kind(susan)|funny(susan))))&
((?[X]:((~old(X)<~>~generous(X))))=>(?[X]:(~strong(X))))&
((?[X]:((~wise(X)<~>tall(X))))<=>((~strong(fred)<~>wise(fred))))&
(((~curious(alice)<~>~creative(alice)))=>((old(susan)<~>~curious(susan))))&
(![X]:((brave(X)<~>wise(X))<=>(~humble(X)&~funny(X))))&
((?[X]:((curious(X)<~>creative(X))))=>(?[X]:((~quiet(X)|old(X)))))&
(?[X]:((brave(X)<~>wise(X))))&
(?[X]:((~kind(X)&~strong(X))))&
(?[X]:((~wise(X)&~kind(X))))&
((generous(mary)<~>~brave(mary)))&
(?[X]:((~tall(X)|creative(X))))&
((~quiet(alice)<~>~happy(alice)))&
(?[X]:((tall(X)<~>calm(X))))&
(?[X]:((~funny(X)|quiet(X)))) | strong(mary) | [] | null | 0 |
Everyone who is both not old and rich is both not rich and generous and vice versa.
Everyone who is brave or rich is not tall.
If someone is quiet or kind then fred is wise or quiet and vice versa.
Everyone who is quiet is both creative and strong and vice versa.
Everyone who is both humble and generous is creative and vice versa.
If lucy is both not patient and not old then lucy is kind or quiet.
Everyone who is both tall and old is curious.
Everyone who is either not quiet or funny is not wise or humble.
If fred is patient or not kind then paul is not brave or calm and vice versa.
Everyone who is both tall and not brave is generous.
If someone is both not kind and happy then someone is both old and not curious.
Everyone who is both not humble and quiet is both not curious and not tall.
If susan is either not curious or rich then someone is not funny.
If someone is either kind or strong then mary is not brave.
If mary is funny then someone is tall.
If john is old then alice is both rich and brave and vice versa.
Fred is either quiet or not kind.
Someone is happy.
Paul is not strong.
Alice is either rich or not creative.
Someone is funny.
Someone is humble or quiet.
Someone is both not kind and brave.
Someone is both not curious and old. | Mary is calm. | neutral | (![X]:((~old(X)&rich(X))<=>(~rich(X)&generous(X))))&
(![X]:((brave(X)|rich(X))=>~tall(X)))&
((?[X]:((quiet(X)|kind(X))))<=>((wise(fred)|quiet(fred))))&
(![X]:(quiet(X)<=>(creative(X)&strong(X))))&
(![X]:((humble(X)&generous(X))<=>creative(X)))&
(((~patient(lucy)&~old(lucy)))=>((kind(lucy)|quiet(lucy))))&
(![X]:((tall(X)&old(X))=>curious(X)))&
(![X]:((~quiet(X)<~>funny(X))=>(~wise(X)|humble(X))))&
(((patient(fred)|~kind(fred)))<=>((~brave(paul)|calm(paul))))&
(![X]:((tall(X)&~brave(X))=>generous(X)))&
((?[X]:((~kind(X)&happy(X))))=>(?[X]:((old(X)&~curious(X)))))&
(![X]:((~humble(X)&quiet(X))=>(~curious(X)&~tall(X))))&
(((~curious(susan)<~>rich(susan)))=>(?[X]:(~funny(X))))&
((?[X]:((kind(X)<~>strong(X))))=>(~brave(mary)))&
((funny(mary))=>(?[X]:(tall(X))))&
((old(john))<=>((rich(alice)&brave(alice))))&
((quiet(fred)<~>~kind(fred)))&
(?[X]:(happy(X)))&
(~strong(paul))&
((rich(alice)<~>~creative(alice)))&
(?[X]:(funny(X)))&
(?[X]:((humble(X)|quiet(X))))&
(?[X]:((~kind(X)&brave(X))))&
(?[X]:((~curious(X)&old(X)))) | calm(mary) | [] | null | 0 |
Everyone who is both creative and generous is not kind or not generous and vice versa.
If someone is not generous or not kind then susan is curious and vice versa.
If someone is quiet or not humble then john is either funny or not brave and vice versa.
If lucy is not humble then fred is humble or not tall and vice versa.
Everyone who is both not old and funny is both not curious and not funny and vice versa.
If mary is either strong or generous then lucy is either curious or not quiet and vice versa.
Everyone who is kind or not old is both not tall and not generous and vice versa.
Everyone who is curious is humble or happy and vice versa.
Everyone who is either not humble or strong is both not quiet and not strong.
If someone is both funny and not patient then john is curious and vice versa.
If someone is kind then someone is either not patient or not old.
If someone is not rich then someone is both not humble and generous and vice versa.
If someone is not quiet then susan is not strong and vice versa.
If someone is not strong or not humble then alice is quiet or happy and vice versa.
Everyone who is both generous and not rich is both generous and happy.
If mary is not wise or not calm then susan is either not brave or not old and vice versa.
Someone is either not rich or strong.
Someone is not rich.
Susan is both not kind and old.
Someone is not curious.
Someone is curious.
Someone is both not strong and not quiet.
Mary is patient. | Mary is not generous. | contradiction | (![X]:((creative(X)&generous(X))<=>(~kind(X)|~generous(X))))&
((?[X]:((~generous(X)|~kind(X))))<=>(curious(susan)))&
((?[X]:((quiet(X)|~humble(X))))<=>((funny(john)<~>~brave(john))))&
((~humble(lucy))<=>((humble(fred)|~tall(fred))))&
(![X]:((~old(X)&funny(X))<=>(~curious(X)&~funny(X))))&
(((strong(mary)<~>generous(mary)))<=>((curious(lucy)<~>~quiet(lucy))))&
(![X]:((kind(X)|~old(X))<=>(~tall(X)&~generous(X))))&
(![X]:(curious(X)<=>(humble(X)|happy(X))))&
(![X]:((~humble(X)<~>strong(X))=>(~quiet(X)&~strong(X))))&
((?[X]:((funny(X)&~patient(X))))<=>(curious(john)))&
((?[X]:(kind(X)))=>(?[X]:((~patient(X)<~>~old(X)))))&
((?[X]:(~rich(X)))<=>(?[X]:((~humble(X)&generous(X)))))&
((?[X]:(~quiet(X)))<=>(~strong(susan)))&
((?[X]:((~strong(X)|~humble(X))))<=>((quiet(alice)|happy(alice))))&
(![X]:((generous(X)&~rich(X))=>(generous(X)&happy(X))))&
(((~wise(mary)|~calm(mary)))<=>((~brave(susan)<~>~old(susan))))&
(?[X]:((~rich(X)<~>strong(X))))&
(?[X]:(~rich(X)))&
((~kind(susan)&old(susan)))&
(?[X]:(~curious(X)))&
(?[X]:(curious(X)))&
(?[X]:((~strong(X)&~quiet(X))))&
(patient(mary)) | ~generous(mary) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 3140583211957493594594928
% SZS output start Proof for 3140583211957493594594928
1. ! [X0] : ((generous(X0) & creative(X0)) <=> (~generous(X0) | ~kind(X0))) [input p0]
24. ~generous(mary) [input hypothesis]
31. ! [X0] : (((generous(X0) & creative(X0)) | (generous(X0) & kind(X0))) & ((~generous(X0) | ~kind(X0)) | (~generous(X0) | ~creative(X0)))) [nnf transformation 1]
32. ! [X0] : (((generous(X0) & creative(X0)) | (generous(X0) & kind(X0))) & (~generous(X0) | ~kind(X0) | ~generous(X0) | ~creative(X0))) [flattening 31]
90. generous(X0) | generous(X0) [cnf transformation 32]
159. ~generous(mary) [cnf transformation 24]
164. generous(X0) [duplicate literal removal 90]
332. $false [subsumption resolution 159,164]
% SZS output end Proof for 3140583211957493594594928
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and creative is patient and vice versa.
If someone is not curious or not kind then someone is generous or calm and vice versa.
Everyone who is not old or patient is not patient or not humble.
If susan is not happy then fred is both humble and patient.
Everyone who is not happy or old is not happy or not generous.
If someone is either not strong or wise then someone is either funny or not brave.
Everyone who is not curious is either not calm or strong and vice versa.
If someone is both not kind and generous then someone is not rich and vice versa.
If mary is not wise then john is humble or curious.
If someone is not calm or quiet then someone is curious or not curious.
Everyone who is either brave or calm is calm or humble and vice versa.
If john is not patient or creative then paul is humble or not calm.
If mary is not old or not happy then someone is not funny and vice versa.
Everyone who is both old and not strong is either kind or not funny.
Everyone who is not strong is both tall and quiet and vice versa.
Everyone who is both wise and quiet is both wise and curious and vice versa.
Someone is both happy and not patient.
Someone is both tall and not funny.
Alice is not calm or calm.
Someone is generous.
Paul is both not tall and quiet.
Mary is not old.
Susan is either not funny or not humble.
Someone is kind or generous. | Susan is not funny. | neutral | (![X]:((calm(X)&creative(X))<=>patient(X)))&
((?[X]:((~curious(X)|~kind(X))))<=>(?[X]:((generous(X)|calm(X)))))&
(![X]:((~old(X)|patient(X))=>(~patient(X)|~humble(X))))&
((~happy(susan))=>((humble(fred)&patient(fred))))&
(![X]:((~happy(X)|old(X))=>(~happy(X)|~generous(X))))&
((?[X]:((~strong(X)<~>wise(X))))=>(?[X]:((funny(X)<~>~brave(X)))))&
(![X]:(~curious(X)<=>(~calm(X)<~>strong(X))))&
((?[X]:((~kind(X)&generous(X))))<=>(?[X]:(~rich(X))))&
((~wise(mary))=>((humble(john)|curious(john))))&
((?[X]:((~calm(X)|quiet(X))))=>(?[X]:((curious(X)|~curious(X)))))&
(![X]:((brave(X)<~>calm(X))<=>(calm(X)|humble(X))))&
(((~patient(john)|creative(john)))=>((humble(paul)|~calm(paul))))&
(((~old(mary)|~happy(mary)))<=>(?[X]:(~funny(X))))&
(![X]:((old(X)&~strong(X))=>(kind(X)<~>~funny(X))))&
(![X]:(~strong(X)<=>(tall(X)&quiet(X))))&
(![X]:((wise(X)&quiet(X))<=>(wise(X)&curious(X))))&
(?[X]:((happy(X)&~patient(X))))&
(?[X]:((tall(X)&~funny(X))))&
((~calm(alice)|calm(alice)))&
(?[X]:(generous(X)))&
((~tall(paul)&quiet(paul)))&
(~old(mary))&
((~funny(susan)<~>~humble(susan)))&
(?[X]:((kind(X)|generous(X)))) | ~funny(susan) | [] | null | 0 |
Everyone who is rich is brave. Everyone who is both curious and not kind is not rich or happy. Everyone who is generous is not rich. Everyone who is strong is both not humble and not brave and vice versa. Everyone who is both creative and not curious is both funny and not calm and vice versa. If fred is not happy then someone is calm or curious and vice versa. If john is not creative or humble then someone is wise or patient and vice versa. Everyone who is both not quiet and not creative is happy and vice versa. Everyone who is both not old and not strong is curious or not patient. If someone is not happy or not curious then someone is both kind and quiet. If fred is either wise or quiet then someone is brave or not humble. If susan is either not quiet or old then someone is kind or curious and vice versa. Everyone who is either generous or old is either brave or not generous and vice versa. Everyone who is both not tall and not kind is strong and vice versa. Everyone who is not curious or wise is rich or not old and vice versa. Everyone who is not quiet is not creative or strong and vice versa. Someone is either tall or creative. Alice is rich or not brave. Someone is both not calm and not generous. Paul is either rich or kind. Someone is either creative or not wise. Someone is not humble or not quiet. Someone is not creative. | Paul is generous. | neutral | (![X]:(rich(X)=>brave(X)))&
(![X]:((curious(X)&~kind(X))=>(~rich(X)|happy(X))))&
(![X]:(generous(X)=>~rich(X)))&
(![X]:(strong(X)<=>(~humble(X)&~brave(X))))&
(![X]:((creative(X)&~curious(X))<=>(funny(X)&~calm(X))))&
((~happy(fred))<=>(?[X]:((calm(X)|curious(X)))))&
(((~creative(john)|humble(john)))<=>(?[X]:((wise(X)|patient(X)))))&
(![X]:((~quiet(X)&~creative(X))<=>happy(X)))&
(![X]:((~old(X)&~strong(X))=>(curious(X)|~patient(X))))&
((?[X]:((~happy(X)|~curious(X))))=>(?[X]:((kind(X)&quiet(X)))))&
(((wise(fred)<~>quiet(fred)))=>(?[X]:((brave(X)|~humble(X)))))&
(((~quiet(susan)<~>old(susan)))<=>(?[X]:((kind(X)|curious(X)))))&
(![X]:((generous(X)<~>old(X))<=>(brave(X)<~>~generous(X))))&
(![X]:((~tall(X)&~kind(X))<=>strong(X)))&
(![X]:((~curious(X)|wise(X))<=>(rich(X)|~old(X))))&
(![X]:(~quiet(X)<=>(~creative(X)|strong(X))))&
(?[X]:((tall(X)<~>creative(X))))&
((rich(alice)|~brave(alice)))&
(?[X]:((~calm(X)&~generous(X))))&
((rich(paul)<~>kind(paul)))&
(?[X]:((creative(X)<~>~wise(X))))&
(?[X]:((~humble(X)|~quiet(X))))&
(?[X]:(~creative(X))) | generous(paul) | [] | null | 0 |
Everyone who is not wise is not calm. Everyone who is both not rich and patient is either kind or not patient. If someone is either not kind or not happy then someone is creative. If someone is not kind or not tall then paul is calm and vice versa. If lucy is both brave and not strong then someone is either not humble or patient and vice versa. Everyone who is either not tall or not humble is either not quiet or not humble and vice versa. If fred is wise then fred is both not rich and happy and vice versa. If lucy is both not funny and wise then someone is both not creative and not brave. Everyone who is either not happy or creative is curious or not calm. If john is tall or rich then someone is wise. Everyone who is quiet or creative is both not generous and not quiet. Everyone who is either not curious or creative is either wise or patient. Everyone who is both calm and strong is either not tall or not generous and vice versa. If paul is calm or not tall then someone is not creative or not funny and vice versa. Everyone who is either not funny or quiet is either not calm or not tall. Everyone who is both not wise and wise is both happy and funny and vice versa. Someone is old or brave. Someone is either not funny or generous. Fred is either brave or funny. Susan is not generous or calm. Someone is not old or not calm. Fred is not calm. Someone is either not old or not strong. Mary is brave or not tall. | Fred is not brave. | entailment | (![X]:(~wise(X)=>~calm(X)))&
(![X]:((~rich(X)&patient(X))=>(kind(X)<~>~patient(X))))&
((?[X]:((~kind(X)<~>~happy(X))))=>(?[X]:(creative(X))))&
((?[X]:((~kind(X)|~tall(X))))<=>(calm(paul)))&
(((brave(lucy)&~strong(lucy)))<=>(?[X]:((~humble(X)<~>patient(X)))))&
(![X]:((~tall(X)<~>~humble(X))<=>(~quiet(X)<~>~humble(X))))&
((wise(fred))<=>((~rich(fred)&happy(fred))))&
(((~funny(lucy)&wise(lucy)))=>(?[X]:((~creative(X)&~brave(X)))))&
(![X]:((~happy(X)<~>creative(X))=>(curious(X)|~calm(X))))&
(((tall(john)|rich(john)))=>(?[X]:(wise(X))))&
(![X]:((quiet(X)|creative(X))=>(~generous(X)&~quiet(X))))&
(![X]:((~curious(X)<~>creative(X))=>(wise(X)<~>patient(X))))&
(![X]:((calm(X)&strong(X))<=>(~tall(X)<~>~generous(X))))&
(((calm(paul)|~tall(paul)))<=>(?[X]:((~creative(X)|~funny(X)))))&
(![X]:((~funny(X)<~>quiet(X))=>(~calm(X)<~>~tall(X))))&
(![X]:((~wise(X)&wise(X))<=>(happy(X)&funny(X))))&
(?[X]:((old(X)|brave(X))))&
(?[X]:((~funny(X)<~>generous(X))))&
((brave(fred)<~>funny(fred)))&
((~generous(susan)|calm(susan)))&
(?[X]:((~old(X)|~calm(X))))&
(~calm(fred))&
(?[X]:((~old(X)<~>~strong(X))))&
((brave(mary)|~tall(mary))) | ~brave(fred) | [
"p5",
"p10",
"p14",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3342116418202088444559245
% SZS output start Proof for 3342116418202088444559245
6. ! [X0] : ((~tall(X0) <~> ~humble(X0)) <=> (~quiet(X0) <~> ~humble(X0))) [input p5]
11. ! [X0] : ((creative(X0) | quiet(X0)) => (~quiet(X0) & ~generous(X0))) [input p10]
15. ! [X0] : ((~funny(X0) <~> quiet(X0)) => (~calm(X0) <~> ~tall(X0))) [input p14]
19. brave(fred) <~> funny(fred) [input p18]
22. ~calm(fred) [input p21]
25. brave(fred) [input hypothesis]
36. ! [X0] : ((~quiet(X0) & ~generous(X0)) | (~creative(X0) & ~quiet(X0))) [ennf transformation 11]
38. ! [X0] : ((~calm(X0) <~> ~tall(X0)) | (~funny(X0) <=> quiet(X0))) [ennf transformation 15]
53. ! [X0] : ((((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | ((~quiet(X0) | humble(X0)) & (~humble(X0) | quiet(X0)))) & (((humble(X0) | quiet(X0)) & (~humble(X0) | ~quiet(X0))) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0))))) [nnf transformation 6]
69. ! [X0] : (((tall(X0) | calm(X0)) & (~tall(X0) | ~calm(X0))) | ((~funny(X0) | ~quiet(X0)) & (quiet(X0) | funny(X0)))) [nnf transformation 38]
77. (~funny(fred) | ~brave(fred)) & (funny(fred) | brave(fred)) [nnf transformation 19]
100. humble(X0) | quiet(X0) | ~tall(X0) | humble(X0) [cnf transformation 53]
101. ~humble(X0) | ~tall(X0) | ~humble(X0) | quiet(X0) [cnf transformation 53]
116. ~quiet(X0) | ~quiet(X0) [cnf transformation 36]
134. tall(X0) | calm(X0) | quiet(X0) | funny(X0) [cnf transformation 69]
144. ~funny(fred) | ~brave(fred) [cnf transformation 77]
147. ~calm(fred) [cnf transformation 22]
151. brave(fred) [cnf transformation 25]
152. ~quiet(X0) [duplicate literal removal 116]
154. humble(X0) | quiet(X0) | ~tall(X0) [duplicate literal removal 100]
155. ~humble(X0) | ~tall(X0) | quiet(X0) [duplicate literal removal 101]
219. ~tall(X0) | quiet(X0) [subsumption resolution 154,155]
290. funny(X0) | calm(X0) | tall(X0) [subsumption resolution 134,152]
312. 34 <=> brave(fred) [avatar definition]
316. 35 <=> funny(fred) [avatar definition]
318. ~funny(fred) <- (~35) [avatar component clause 316]
319. ~34 | ~35 [avatar split clause 144,316,312]
358. 34 [avatar split clause 151,312]
363. calm(fred) | tall(fred) <- (~35) [resolution 290,318]
375. tall(fred) <- (~35) [subsumption resolution 363,147]
452. quiet(fred) <- (~35) [resolution 375,219]
464. $false <- (~35) [subsumption resolution 452,152]
465. 35 [avatar contradiction clause 464]
466. $false [avatar sat refutation 319,358,465]
% SZS output end Proof for 3342116418202088444559245
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is patient and vice versa.
Everyone who is either not tall or not kind is not funny or humble.
Everyone who is rich is both wise and not curious and vice versa.
If someone is rich or tall then someone is either not creative or not tall and vice versa.
Everyone who is either happy or not patient is not happy or creative and vice versa.
If john is funny then someone is either not rich or rich and vice versa.
If fred is not brave then john is calm or wise and vice versa.
If lucy is patient or calm then paul is either quiet or calm.
If someone is not quiet or creative then alice is not humble.
Everyone who is either humble or kind is either not calm or not rich.
Everyone who is either not strong or curious is not creative and vice versa.
Everyone who is rich is either old or tall and vice versa.
Everyone who is either not happy or not quiet is not humble or funny and vice versa.
Everyone who is not curious or generous is generous or wise.
Everyone who is either creative or not quiet is not tall.
Everyone who is not quiet is either not creative or brave.
Lucy is old or not humble.
Someone is either not brave or patient.
Someone is either not humble or wise.
Someone is both not happy and not tall.
Someone is happy.
Someone is calm.
Susan is either humble or not patient.
Someone is humble. | Alice is not patient. | entailment | (![X]:(humble(X)<=>patient(X)))&
(![X]:((~tall(X)<~>~kind(X))=>(~funny(X)|humble(X))))&
(![X]:(rich(X)<=>(wise(X)&~curious(X))))&
((?[X]:((rich(X)|tall(X))))<=>(?[X]:((~creative(X)<~>~tall(X)))))&
(![X]:((happy(X)<~>~patient(X))<=>(~happy(X)|creative(X))))&
((funny(john))<=>(?[X]:((~rich(X)<~>rich(X)))))&
((~brave(fred))<=>((calm(john)|wise(john))))&
(((patient(lucy)|calm(lucy)))=>((quiet(paul)<~>calm(paul))))&
((?[X]:((~quiet(X)|creative(X))))=>(~humble(alice)))&
(![X]:((humble(X)<~>kind(X))=>(~calm(X)<~>~rich(X))))&
(![X]:((~strong(X)<~>curious(X))<=>~creative(X)))&
(![X]:(rich(X)<=>(old(X)<~>tall(X))))&
(![X]:((~happy(X)<~>~quiet(X))<=>(~humble(X)|funny(X))))&
(![X]:((~curious(X)|generous(X))=>(generous(X)|wise(X))))&
(![X]:((creative(X)<~>~quiet(X))=>~tall(X)))&
(![X]:(~quiet(X)=>(~creative(X)<~>brave(X))))&
((old(lucy)|~humble(lucy)))&
(?[X]:((~brave(X)<~>patient(X))))&
(?[X]:((~humble(X)<~>wise(X))))&
(?[X]:((~happy(X)&~tall(X))))&
(?[X]:(happy(X)))&
(?[X]:(calm(X)))&
((humble(susan)<~>~patient(susan)))&
(?[X]:(humble(X))) | ~patient(alice) | [
"p0",
"p4",
"p8",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4206901619720000134384210
% SZS output start Proof for 4206901619720000134384210
1. ! [X0] : (humble(X0) <=> patient(X0)) [input p0]
5. ! [X0] : ((happy(X0) <~> ~patient(X0)) <=> (creative(X0) | ~happy(X0))) [input p4]
9. ? [X0] : (creative(X0) | ~quiet(X0)) => ~humble(alice) [input p8]
24. ? [X0] : humble(X0) [input p23]
25. patient(alice) [input hypothesis]
30. ~humble(alice) | ! [X0] : (~creative(X0) & quiet(X0)) [ennf transformation 9]
36. ! [X0] : ((humble(X0) | ~patient(X0)) & (patient(X0) | ~humble(X0))) [nnf transformation 1]
45. ! [X0] : ((((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | (~creative(X0) & happy(X0))) & ((creative(X0) | ~happy(X0)) | ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0))))) [nnf transformation 5]
46. ! [X0] : ((((patient(X0) | ~happy(X0)) & (~patient(X0) | happy(X0))) | (~creative(X0) & happy(X0))) & (creative(X0) | ~happy(X0) | ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0))))) [flattening 45]
74. ? [X0] : humble(X0) => humble(sK8) [choice axiom]
75. humble(sK8) [skolemisation 24,74]
76. ~humble(X0) | patient(X0) [cnf transformation 36]
77. ~patient(X0) | humble(X0) [cnf transformation 36]
89. creative(X0) | ~happy(X0) | ~patient(X0) | ~happy(X0) [cnf transformation 46]
91. ~patient(X0) | happy(X0) | happy(X0) [cnf transformation 46]
107. ~humble(alice) | ~creative(X0) [cnf transformation 30]
143. humble(sK8) [cnf transformation 75]
144. patient(alice) [cnf transformation 25]
147. creative(X0) | ~happy(X0) | ~patient(X0) [duplicate literal removal 89]
148. ~patient(X0) | happy(X0) [duplicate literal removal 91]
183. ~patient(X0) | creative(X0) [subsumption resolution 147,148]
229. 18 <=> ! [X0] : ~creative(X0) [avatar definition]
230. ~creative(X0) <- (18) [avatar component clause 229]
232. 19 <=> humble(alice) [avatar definition]
235. 18 | ~19 [avatar split clause 107,232,229]
269. patient(sK8) [resolution 76,143]
270. humble(alice) [resolution 77,144]
273. 19 [avatar split clause 270,232]
282. creative(sK8) [resolution 183,269]
285. $false <- (18) [subsumption resolution 282,230]
286. ~18 [avatar contradiction clause 285]
287. $false [avatar sat refutation 235,273,286]
% SZS output end Proof for 4206901619720000134384210
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is not patient.
If someone is wise or rich then someone is both rich and not quiet.
If alice is not wise or quiet then someone is both generous and not brave and vice versa.
Everyone who is not brave or not old is both creative and patient.
Everyone who is generous or brave is not rich and vice versa.
Everyone who is both not funny and not generous is rich or not curious.
If someone is not old then someone is both not strong and not creative.
If paul is humble then someone is brave.
Everyone who is either not patient or not brave is both quiet and not kind.
If someone is either not tall or kind then lucy is generous and vice versa.
If someone is both not tall and rich then john is either tall or old.
Everyone who is both not happy and wise is both rich and not rich.
Everyone who is not brave or not happy is both happy and not wise and vice versa.
Everyone who is creative or curious is happy and vice versa.
If john is calm or not brave then john is creative.
Paul is either generous or funny.
Someone is either not quiet or not tall.
Lucy is either not strong or creative.
Someone is either not quiet or not humble.
Someone is quiet or curious.
Mary is not strong. | Mary is not humble. | neutral | (![X]:(calm(X)=>~patient(X)))&
((?[X]:((wise(X)|rich(X))))=>(?[X]:((rich(X)&~quiet(X)))))&
(((~wise(alice)|quiet(alice)))<=>(?[X]:((generous(X)&~brave(X)))))&
(![X]:((~brave(X)|~old(X))=>(creative(X)&patient(X))))&
(![X]:((generous(X)|brave(X))<=>~rich(X)))&
(![X]:((~funny(X)&~generous(X))=>(rich(X)|~curious(X))))&
((?[X]:(~old(X)))=>(?[X]:((~strong(X)&~creative(X)))))&
((humble(paul))=>(?[X]:(brave(X))))&
(![X]:((~patient(X)<~>~brave(X))=>(quiet(X)&~kind(X))))&
((?[X]:((~tall(X)<~>kind(X))))<=>(generous(lucy)))&
((?[X]:((~tall(X)&rich(X))))=>((tall(john)<~>old(john))))&
(![X]:((~happy(X)&wise(X))=>(rich(X)&~rich(X))))&
(![X]:((~brave(X)|~happy(X))<=>(happy(X)&~wise(X))))&
(![X]:((creative(X)|curious(X))<=>happy(X)))&
(((calm(john)|~brave(john)))=>(creative(john)))&
((generous(paul)<~>funny(paul)))&
(?[X]:((~quiet(X)<~>~tall(X))))&
((~strong(lucy)<~>creative(lucy)))&
(?[X]:((~quiet(X)<~>~humble(X))))&
(?[X]:((quiet(X)|curious(X))))&
(~strong(mary)) | ~humble(mary) | [] | null | 0 |
Everyone who is either old or not quiet is both curious and not kind.
Everyone who is creative or patient is not quiet.
Everyone who is not happy or humble is both not brave and not funny.
Everyone who is not quiet is strong.
If someone is either brave or not curious then someone is funny and vice versa.
Everyone who is both happy and not kind is not wise or not patient and vice versa.
Everyone who is either not brave or funny is both tall and patient.
Everyone who is both not kind and not quiet is either rich or tall.
Everyone who is not wise is not generous.
If mary is either quiet or humble then someone is both not wise and patient and vice versa.
If alice is brave then someone is both not old and not funny and vice versa.
Everyone who is rich is not calm or not humble and vice versa.
Everyone who is either not humble or quiet is not old.
If someone is not strong then paul is both calm and not old.
Someone is either curious or not happy.
Fred is not old or calm.
John is brave or wise.
Alice is both not wise and happy.
Fred is not old or brave. | Paul is not tall. | neutral | (![X]:((old(X)<~>~quiet(X))=>(curious(X)&~kind(X))))&
(![X]:((creative(X)|patient(X))=>~quiet(X)))&
(![X]:((~happy(X)|humble(X))=>(~brave(X)&~funny(X))))&
(![X]:(~quiet(X)=>strong(X)))&
((?[X]:((brave(X)<~>~curious(X))))<=>(?[X]:(funny(X))))&
(![X]:((happy(X)&~kind(X))<=>(~wise(X)|~patient(X))))&
(![X]:((~brave(X)<~>funny(X))=>(tall(X)&patient(X))))&
(![X]:((~kind(X)&~quiet(X))=>(rich(X)<~>tall(X))))&
(![X]:(~wise(X)=>~generous(X)))&
(((quiet(mary)<~>humble(mary)))<=>(?[X]:((~wise(X)&patient(X)))))&
((brave(alice))<=>(?[X]:((~old(X)&~funny(X)))))&
(![X]:(rich(X)<=>(~calm(X)|~humble(X))))&
(![X]:((~humble(X)<~>quiet(X))=>~old(X)))&
((?[X]:(~strong(X)))=>((calm(paul)&~old(paul))))&
(?[X]:((curious(X)<~>~happy(X))))&
((~old(fred)|calm(fred)))&
((brave(john)|wise(john)))&
((~wise(alice)&happy(alice)))&
((~old(fred)|brave(fred))) | ~tall(paul) | [] | null | 0 |
Everyone who is both wise and not kind is either not generous or kind and vice versa.
If someone is both happy and creative then susan is both not humble and brave.
Everyone who is both not strong and curious is either strong or not generous and vice versa.
If alice is both not kind and not curious then someone is either not old or not funny.
If susan is either patient or not funny then someone is calm and vice versa.
Everyone who is funny or happy is either patient or not kind.
If someone is patient or not strong then someone is both not kind and not tall.
Everyone who is not creative is wise and vice versa.
Everyone who is either old or not kind is not funny and vice versa.
If someone is generous then someone is both curious and not strong and vice versa.
If someone is both not happy and not creative then paul is both creative and not rich and vice versa.
Everyone who is both strong and funny is either not tall or not calm and vice versa.
Everyone who is both tall and old is either brave or calm and vice versa.
Everyone who is not creative or humble is both kind and happy and vice versa.
Everyone who is both not funny and not brave is both not rich and calm.
If john is old or quiet then lucy is both quiet and humble and vice versa.
Someone is not calm or happy.
Susan is either happy or not creative.
Paul is curious.
Fred is not patient or kind.
Someone is both not tall and creative.
Fred is either kind or patient.
Someone is either rich or not wise.
Someone is both patient and humble. | Susan is not old. | entailment | (![X]:((wise(X)&~kind(X))<=>(~generous(X)<~>kind(X))))&
((?[X]:((happy(X)&creative(X))))=>((~humble(susan)&brave(susan))))&
(![X]:((~strong(X)&curious(X))<=>(strong(X)<~>~generous(X))))&
(((~kind(alice)&~curious(alice)))=>(?[X]:((~old(X)<~>~funny(X)))))&
(((patient(susan)<~>~funny(susan)))<=>(?[X]:(calm(X))))&
(![X]:((funny(X)|happy(X))=>(patient(X)<~>~kind(X))))&
((?[X]:((patient(X)|~strong(X))))=>(?[X]:((~kind(X)&~tall(X)))))&
(![X]:(~creative(X)<=>wise(X)))&
(![X]:((old(X)<~>~kind(X))<=>~funny(X)))&
((?[X]:(generous(X)))<=>(?[X]:((curious(X)&~strong(X)))))&
((?[X]:((~happy(X)&~creative(X))))<=>((creative(paul)&~rich(paul))))&
(![X]:((strong(X)&funny(X))<=>(~tall(X)<~>~calm(X))))&
(![X]:((tall(X)&old(X))<=>(brave(X)<~>calm(X))))&
(![X]:((~creative(X)|humble(X))<=>(kind(X)&happy(X))))&
(![X]:((~funny(X)&~brave(X))=>(~rich(X)&calm(X))))&
(((old(john)|quiet(john)))<=>((quiet(lucy)&humble(lucy))))&
(?[X]:((~calm(X)|happy(X))))&
((happy(susan)<~>~creative(susan)))&
(curious(paul))&
((~patient(fred)|kind(fred)))&
(?[X]:((~tall(X)&creative(X))))&
((kind(fred)<~>patient(fred)))&
(?[X]:((rich(X)<~>~wise(X))))&
(?[X]:((patient(X)&humble(X)))) | ~old(susan) | [
"p0",
"p1",
"p2",
"p4",
"p5",
"p7",
"p8",
"p11",
"p12",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 9033531556104393177931935
% SZS output start Proof for 9033531556104393177931935
1. ! [X0] : ((~kind(X0) & wise(X0)) <=> (~generous(X0) <~> kind(X0))) [input p0]
2. ? [X0] : (creative(X0) & happy(X0)) => (brave(susan) & ~humble(susan)) [input p1]
3. ! [X0] : ((curious(X0) & ~strong(X0)) <=> (strong(X0) <~> ~generous(X0))) [input p2]
5. (patient(susan) <~> ~funny(susan)) <=> ? [X0] : calm(X0) [input p4]
6. ! [X0] : ((happy(X0) | funny(X0)) => (patient(X0) <~> ~kind(X0))) [input p5]
8. ! [X0] : (~creative(X0) <=> wise(X0)) [input p7]
9. ! [X0] : ((old(X0) <~> ~kind(X0)) <=> ~funny(X0)) [input p8]
12. ! [X0] : ((funny(X0) & strong(X0)) <=> (~tall(X0) <~> ~calm(X0))) [input p11]
13. ! [X0] : ((old(X0) & tall(X0)) <=> (brave(X0) <~> calm(X0))) [input p12]
14. ! [X0] : ((humble(X0) | ~creative(X0)) <=> (happy(X0) & kind(X0))) [input p13]
18. happy(susan) <~> ~creative(susan) [input p17]
25. old(susan) [input hypothesis]
28. (brave(susan) & ~humble(susan)) | ! [X0] : (~creative(X0) | ~happy(X0)) [ennf transformation 2]
31. ! [X0] : ((patient(X0) <~> ~kind(X0)) | (~happy(X0) & ~funny(X0))) [ennf transformation 6]
35. ! [X0] : (((~kind(X0) & wise(X0)) | ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0)))) & (((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | (kind(X0) | ~wise(X0)))) [nnf transformation 1]
36. ! [X0] : (((~kind(X0) & wise(X0)) | ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0)))) & (((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | kind(X0) | ~wise(X0))) [flattening 35]
37. ! [X0] : (((curious(X0) & ~strong(X0)) | ((strong(X0) | generous(X0)) & (~generous(X0) | ~strong(X0)))) & (((generous(X0) | ~strong(X0)) & (~generous(X0) | strong(X0))) | (~curious(X0) | strong(X0)))) [nnf transformation 3]
38. ! [X0] : (((curious(X0) & ~strong(X0)) | ((strong(X0) | generous(X0)) & (~generous(X0) | ~strong(X0)))) & (((generous(X0) | ~strong(X0)) & (~generous(X0) | strong(X0))) | ~curious(X0) | strong(X0))) [flattening 37]
42. (((funny(susan) | ~patient(susan)) & (~funny(susan) | patient(susan))) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | ((patient(susan) | funny(susan)) & (~funny(susan) | ~patient(susan)))) [nnf transformation 5]
43. (((funny(susan) | ~patient(susan)) & (~funny(susan) | patient(susan))) | ! [X0] : ~calm(X0)) & (? [X1] : calm(X1) | ((patient(susan) | funny(susan)) & (~funny(susan) | ~patient(susan)))) [rectify 42]
44. ? [X1] : calm(X1) => calm(sK1) [choice axiom]
45. (((funny(susan) | ~patient(susan)) & (~funny(susan) | patient(susan))) | ! [X0] : ~calm(X0)) & (calm(sK1) | ((patient(susan) | funny(susan)) & (~funny(susan) | ~patient(susan)))) [skolemisation 43,44]
46. ! [X0] : (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | (~happy(X0) & ~funny(X0))) [nnf transformation 31]
50. ! [X0] : ((~creative(X0) | ~wise(X0)) & (wise(X0) | creative(X0))) [nnf transformation 8]
51. ! [X0] : ((((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | funny(X0)) & (~funny(X0) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0))))) [nnf transformation 9]
62. ! [X0] : (((funny(X0) & strong(X0)) | ((~tall(X0) | calm(X0)) & (~calm(X0) | tall(X0)))) & (((calm(X0) | tall(X0)) & (~calm(X0) | ~tall(X0))) | (~funny(X0) | ~strong(X0)))) [nnf transformation 12]
63. ! [X0] : (((funny(X0) & strong(X0)) | ((~tall(X0) | calm(X0)) & (~calm(X0) | tall(X0)))) & (((calm(X0) | tall(X0)) & (~calm(X0) | ~tall(X0))) | ~funny(X0) | ~strong(X0))) [flattening 62]
64. ! [X0] : (((old(X0) & tall(X0)) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0)))) & (((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | (~old(X0) | ~tall(X0)))) [nnf transformation 13]
65. ! [X0] : (((old(X0) & tall(X0)) | ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0)))) & (((~calm(X0) | ~brave(X0)) & (calm(X0) | brave(X0))) | ~old(X0) | ~tall(X0))) [flattening 64]
66. ! [X0] : (((humble(X0) | ~creative(X0)) | (~happy(X0) | ~kind(X0))) & ((happy(X0) & kind(X0)) | (~humble(X0) & creative(X0)))) [nnf transformation 14]
67. ! [X0] : ((humble(X0) | ~creative(X0) | ~happy(X0) | ~kind(X0)) & ((happy(X0) & kind(X0)) | (~humble(X0) & creative(X0)))) [flattening 66]
72. (creative(susan) | ~happy(susan)) & (~creative(susan) | happy(susan)) [nnf transformation 18]
83. generous(X0) | kind(X0) | wise(X0) [cnf transformation 36]
87. ~humble(susan) | ~creative(X0) | ~happy(X0) [cnf transformation 28]
88. brave(susan) | ~creative(X0) | ~happy(X0) [cnf transformation 28]
89. ~generous(X0) | strong(X0) | ~curious(X0) | strong(X0) [cnf transformation 38]
91. ~strong(X0) | ~generous(X0) | ~strong(X0) [cnf transformation 38]
93. ~strong(X0) | ~generous(X0) | curious(X0) [cnf transformation 38]
99. ~funny(susan) | patient(susan) | ~calm(X0) [cnf transformation 45]
104. ~patient(X0) | kind(X0) | ~happy(X0) [cnf transformation 46]
110. ~creative(X0) | ~wise(X0) [cnf transformation 50]
114. ~old(X0) | kind(X0) | funny(X0) [cnf transformation 51]
125. ~tall(X0) | strong(X0) | calm(X0) [cnf transformation 63]
130. ~brave(X0) | calm(X0) | tall(X0) [cnf transformation 65]
136. happy(X0) | creative(X0) [cnf transformation 67]
138. ~creative(X0) | humble(X0) | ~happy(X0) | ~kind(X0) [cnf transformation 67]
147. ~creative(susan) | happy(susan) [cnf transformation 72]
148. creative(susan) | ~happy(susan) [cnf transformation 72]
159. old(susan) [cnf transformation 25]
160. ~generous(X0) | strong(X0) | ~curious(X0) [duplicate literal removal 89]
161. ~strong(X0) | ~generous(X0) [duplicate literal removal 91]
166. 1 <=> ! [X0] : (~creative(X0) | ~happy(X0)) [avatar definition]
167. ~creative(X0) | ~happy(X0) <- (1) [avatar component clause 166]
169. 2 <=> brave(susan) [avatar definition]
171. brave(susan) <- (2) [avatar component clause 169]
172. 1 | 2 [avatar split clause 88,169,166]
174. 3 <=> humble(susan) [avatar definition]
176. ~humble(susan) <- (~3) [avatar component clause 174]
177. 1 | ~3 [avatar split clause 87,174,166]
178. ~curious(X0) | ~generous(X0) [subsumption resolution 160,161]
198. 8 <=> ! [X0] : ~calm(X0) [avatar definition]
199. ~calm(X0) <- (8) [avatar component clause 198]
201. 9 <=> patient(susan) [avatar definition]
202. patient(susan) <- (9) [avatar component clause 201]
205. 10 <=> funny(susan) [avatar definition]
209. 8 | 9 | ~10 [avatar split clause 99,205,201,198]
274. 25 <=> ! [X1] : (creative(X1) | happy(X1)) [avatar definition]
275. creative(X1) | happy(X1) <- (25) [avatar component clause 274]
278. 25 [avatar split clause 136,274]
310. 32 <=> happy(susan) [avatar definition]
311. happy(susan) <- (32) [avatar component clause 310]
312. ~happy(susan) <- (~32) [avatar component clause 310]
314. 33 <=> creative(susan) [avatar definition]
315. ~creative(susan) <- (~33) [avatar component clause 314]
316. creative(susan) <- (33) [avatar component clause 314]
317. ~32 | 33 [avatar split clause 148,314,310]
318. 32 | ~33 [avatar split clause 147,314,310]
356. happy(susan) <- (25, ~33) [resolution 275,315]
358. $false <- (25, ~32, ~33) [subsumption resolution 356,312]
359. ~25 | 32 | 33 [avatar contradiction clause 358]
360. ~wise(susan) <- (33) [resolution 316,110]
434. kind(susan) | funny(susan) [resolution 114,159]
441. 46 <=> kind(susan) [avatar definition]
442. ~kind(susan) <- (~46) [avatar component clause 441]
444. 10 | 46 [avatar split clause 434,441,205]
446. kind(susan) | ~happy(susan) <- (9) [resolution 202,104]
448. kind(susan) <- (9, 32) [subsumption resolution 446,311]
449. 46 | ~9 | ~32 [avatar split clause 448,310,201,441]
465. calm(susan) | tall(susan) <- (2) [resolution 130,171]
466. tall(susan) <- (2, 8) [subsumption resolution 465,199]
468. strong(susan) | calm(susan) <- (2, 8) [resolution 466,125]
469. strong(susan) <- (2, 8) [subsumption resolution 468,199]
541. ~generous(susan) | curious(susan) <- (2, 8) [resolution 469,93]
543. ~generous(susan) <- (2, 8) [subsumption resolution 541,178]
550. humble(susan) | ~happy(susan) | ~kind(susan) <- (33) [resolution 138,316]
634. kind(susan) | wise(susan) <- (2, 8) [resolution 543,83]
635. wise(susan) <- (2, 8, ~46) [subsumption resolution 634,442]
636. $false <- (2, 8, 33, ~46) [subsumption resolution 635,360]
637. ~2 | ~8 | ~33 | 46 [avatar contradiction clause 636]
651. ~happy(susan) <- (1, 33) [resolution 167,316]
655. $false <- (1, 32, 33) [subsumption resolution 651,311]
656. ~1 | ~32 | ~33 [avatar contradiction clause 655]
661. ~happy(susan) | ~kind(susan) <- (~3, 33) [subsumption resolution 550,176]
662. ~kind(susan) <- (~3, 32, 33) [subsumption resolution 661,311]
663. ~46 | 3 | ~32 | ~33 [avatar split clause 662,314,310,174,441]
664. $false [avatar sat refutation 172,177,209,278,317,318,359,444,449,637,656,663]
% SZS output end Proof for 9033531556104393177931935
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is brave then lucy is not kind or not tall and vice versa. Everyone who is both brave and wise is either rich or not curious. Everyone who is either rich or strong is either not rich or quiet and vice versa. If someone is both creative and not rich then alice is either not funny or strong and vice versa. Everyone who is both tall and happy is both funny and tall and vice versa. If someone is either not old or not quiet then susan is both generous and not humble and vice versa. If someone is old or funny then john is both old and not rich and vice versa. If someone is creative or strong then someone is not curious and vice versa. If someone is kind or funny then someone is not curious. Everyone who is not patient is both not tall and curious and vice versa. Everyone who is not wise is old. If someone is curious then mary is generous and vice versa. If someone is either not tall or not kind then mary is not old and vice versa. Everyone who is not quiet or not patient is either curious or creative and vice versa. If mary is funny then someone is either not kind or curious. Everyone who is either generous or not curious is humble or not wise. Alice is either quiet or not curious. Paul is not rich. Alice is not rich or strong. Someone is either humble or brave. Someone is not funny. Someone is happy or not funny. Someone is either kind or not tall. Alice is not curious or patient. | Alice is patient. | entailment | ((?[X]:(brave(X)))<=>((~kind(lucy)|~tall(lucy))))&
(![X]:((brave(X)&wise(X))=>(rich(X)<~>~curious(X))))&
(![X]:((rich(X)<~>strong(X))<=>(~rich(X)<~>quiet(X))))&
((?[X]:((creative(X)&~rich(X))))<=>((~funny(alice)<~>strong(alice))))&
(![X]:((tall(X)&happy(X))<=>(funny(X)&tall(X))))&
((?[X]:((~old(X)<~>~quiet(X))))<=>((generous(susan)&~humble(susan))))&
((?[X]:((old(X)|funny(X))))<=>((old(john)&~rich(john))))&
((?[X]:((creative(X)|strong(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((kind(X)|funny(X))))=>(?[X]:(~curious(X))))&
(![X]:(~patient(X)<=>(~tall(X)&curious(X))))&
(![X]:(~wise(X)=>old(X)))&
((?[X]:(curious(X)))<=>(generous(mary)))&
((?[X]:((~tall(X)<~>~kind(X))))<=>(~old(mary)))&
(![X]:((~quiet(X)|~patient(X))<=>(curious(X)<~>creative(X))))&
((funny(mary))=>(?[X]:((~kind(X)<~>curious(X)))))&
(![X]:((generous(X)<~>~curious(X))=>(humble(X)|~wise(X))))&
((quiet(alice)<~>~curious(alice)))&
(~rich(paul))&
((~rich(alice)|strong(alice)))&
(?[X]:((humble(X)<~>brave(X))))&
(?[X]:(~funny(X)))&
(?[X]:((happy(X)|~funny(X))))&
(?[X]:((kind(X)<~>~tall(X))))&
((~curious(alice)|patient(alice))) | patient(alice) | [
"p9",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2601246587632787570732941
% SZS output start Proof for 2601246587632787570732941
10. ! [X0] : (~patient(X0) <=> (curious(X0) & ~tall(X0))) [input p9]
24. patient(alice) | ~curious(alice) [input p23]
25. ~patient(alice) [input hypothesis]
66. ! [X0] : ((~patient(X0) | (~curious(X0) | tall(X0))) & ((curious(X0) & ~tall(X0)) | patient(X0))) [nnf transformation 10]
67. ! [X0] : ((~patient(X0) | ~curious(X0) | tall(X0)) & ((curious(X0) & ~tall(X0)) | patient(X0))) [flattening 66]
133. curious(X0) | patient(X0) [cnf transformation 67]
162. patient(alice) | ~curious(alice) [cnf transformation 24]
163. ~patient(alice) [cnf transformation 25]
396. patient(alice) [subsumption resolution 162,133]
397. $false [subsumption resolution 163,396]
% SZS output end Proof for 2601246587632787570732941
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or calm is both not rich and not strong. If fred is not quiet then paul is calm or not quiet. Everyone who is both patient and not tall is brave or rich. Everyone who is either not happy or humble is generous or old and vice versa. Everyone who is not creative or patient is both happy and not tall. If fred is not quiet then fred is either not humble or not rich. If someone is humble then someone is funny. Everyone who is wise or tall is both not creative and not funny. Everyone who is either wise or not curious is both kind and not old. If john is not brave or patient then lucy is not curious. Everyone who is either not curious or not old is either not creative or strong and vice versa. If alice is both not happy and patient then mary is calm. If someone is calm or strong then mary is both funny and kind. If someone is not kind or happy then alice is patient. Everyone who is either not humble or humble is both not calm and not curious and vice versa. Everyone who is not happy is brave or not strong and vice versa. Alice is either tall or funny. Someone is both not calm and not happy. Mary is both quiet and creative. Alice is either humble or not kind. Lucy is either wise or not wise. Alice is not wise. | Alice is not calm. | entailment | (![X]:((wise(X)|calm(X))=>(~rich(X)&~strong(X))))&
((~quiet(fred))=>((calm(paul)|~quiet(paul))))&
(![X]:((patient(X)&~tall(X))=>(brave(X)|rich(X))))&
(![X]:((~happy(X)<~>humble(X))<=>(generous(X)|old(X))))&
(![X]:((~creative(X)|patient(X))=>(happy(X)&~tall(X))))&
((~quiet(fred))=>((~humble(fred)<~>~rich(fred))))&
((?[X]:(humble(X)))=>(?[X]:(funny(X))))&
(![X]:((wise(X)|tall(X))=>(~creative(X)&~funny(X))))&
(![X]:((wise(X)<~>~curious(X))=>(kind(X)&~old(X))))&
(((~brave(john)|patient(john)))=>(~curious(lucy)))&
(![X]:((~curious(X)<~>~old(X))<=>(~creative(X)<~>strong(X))))&
(((~happy(alice)&patient(alice)))=>(calm(mary)))&
((?[X]:((calm(X)|strong(X))))=>((funny(mary)&kind(mary))))&
((?[X]:((~kind(X)|happy(X))))=>(patient(alice)))&
(![X]:((~humble(X)<~>humble(X))<=>(~calm(X)&~curious(X))))&
(![X]:(~happy(X)<=>(brave(X)|~strong(X))))&
((tall(alice)<~>funny(alice)))&
(?[X]:((~calm(X)&~happy(X))))&
((quiet(mary)&creative(mary)))&
((humble(alice)<~>~kind(alice)))&
((wise(lucy)<~>~wise(lucy)))&
(~wise(alice)) | ~calm(alice) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3511138593980934614196214
% SZS output start Proof for 3511138593980934614196214
15. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> (~curious(X0) & ~calm(X0))) [input p14]
23. calm(alice) [input hypothesis]
48. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (curious(X0) | calm(X0))) & ((~curious(X0) & ~calm(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 15]
49. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | curious(X0) | calm(X0)) & ((~curious(X0) & ~calm(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [flattening 48]
101. ~calm(X0) | humble(X0) | humble(X0) [cnf transformation 49]
102. ~calm(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 49]
121. calm(alice) [cnf transformation 23]
122. ~calm(X0) | humble(X0) [duplicate literal removal 101]
123. ~calm(X0) | ~humble(X0) [duplicate literal removal 102]
181. 13 <=> ! [X0] : ~calm(X0) [avatar definition]
182. ~calm(X0) <- (13) [avatar component clause 181]
203. ~calm(X0) [subsumption resolution 122,123]
204. 13 [avatar split clause 203,181]
218. $false <- (13) [resolution 182,121]
219. ~13 [avatar contradiction clause 218]
220. $false [avatar sat refutation 204,219]
% SZS output end Proof for 3511138593980934614196214
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or not old is both not generous and not calm. Everyone who is either quiet or generous is not calm. If someone is both not rich and not happy then someone is not rich or humble. Everyone who is both patient and funny is both funny and old and vice versa. Everyone who is both not wise and curious is not quiet. Everyone who is tall or not happy is both curious and happy and vice versa. Everyone who is strong is tall. If someone is calm then lucy is not patient or not calm. Everyone who is calm is curious and vice versa. If alice is not rich then lucy is not generous. If someone is both not curious and creative then someone is not happy or funny. Everyone who is not creative is funny or not humble and vice versa. If someone is happy or brave then someone is both not generous and funny. If susan is either creative or not humble then paul is not patient and vice versa. Everyone who is either wise or patient is either not generous or not humble. If susan is generous then susan is happy and vice versa. Susan is both kind and not humble. Fred is either not funny or creative. Susan is not strong. Susan is not brave. Paul is humble. Someone is either not tall or not rich. Someone is not creative or creative. Someone is either wise or not humble. | Paul is not curious. | entailment | (![X]:((~generous(X)|~old(X))=>(~generous(X)&~calm(X))))&
(![X]:((quiet(X)<~>generous(X))=>~calm(X)))&
((?[X]:((~rich(X)&~happy(X))))=>(?[X]:((~rich(X)|humble(X)))))&
(![X]:((patient(X)&funny(X))<=>(funny(X)&old(X))))&
(![X]:((~wise(X)&curious(X))=>~quiet(X)))&
(![X]:((tall(X)|~happy(X))<=>(curious(X)&happy(X))))&
(![X]:(strong(X)=>tall(X)))&
((?[X]:(calm(X)))=>((~patient(lucy)|~calm(lucy))))&
(![X]:(calm(X)<=>curious(X)))&
((~rich(alice))=>(~generous(lucy)))&
((?[X]:((~curious(X)&creative(X))))=>(?[X]:((~happy(X)|funny(X)))))&
(![X]:(~creative(X)<=>(funny(X)|~humble(X))))&
((?[X]:((happy(X)|brave(X))))=>(?[X]:((~generous(X)&funny(X)))))&
(((creative(susan)<~>~humble(susan)))<=>(~patient(paul)))&
(![X]:((wise(X)<~>patient(X))=>(~generous(X)<~>~humble(X))))&
((generous(susan))<=>(happy(susan)))&
((kind(susan)&~humble(susan)))&
((~funny(fred)<~>creative(fred)))&
(~strong(susan))&
(~brave(susan))&
(humble(paul))&
(?[X]:((~tall(X)<~>~rich(X))))&
(?[X]:((~creative(X)|creative(X))))&
(?[X]:((wise(X)<~>~humble(X)))) | ~curious(paul) | [
"p0",
"p1",
"p4",
"p8",
"p11",
"p13",
"p14",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6914218330525353555783828
% SZS output start Proof for 6914218330525353555783828
1. ! [X0] : ((~old(X0) | ~generous(X0)) => (~calm(X0) & ~generous(X0))) [input p0]
2. ! [X0] : ((quiet(X0) <~> generous(X0)) => ~calm(X0)) [input p1]
5. ! [X0] : ((curious(X0) & ~wise(X0)) => ~quiet(X0)) [input p4]
9. ! [X0] : (calm(X0) <=> curious(X0)) [input p8]
12. ! [X0] : (~creative(X0) <=> (~humble(X0) | funny(X0))) [input p11]
14. (creative(susan) <~> ~humble(susan)) <=> ~patient(paul) [input p13]
15. ! [X0] : ((wise(X0) <~> patient(X0)) => (~generous(X0) <~> ~humble(X0))) [input p14]
17. ~humble(susan) & kind(susan) [input p16]
21. humble(paul) [input p20]
25. curious(paul) [input hypothesis]
29. ! [X0] : (curious(X0) => calm(X0)) [unused predicate definition removal 9]
30. ~humble(susan) [pure predicate removal 17]
35. ! [X0] : ((~calm(X0) & ~generous(X0)) | (old(X0) & generous(X0))) [ennf transformation 1]
36. ! [X0] : (~calm(X0) | (quiet(X0) <=> generous(X0))) [ennf transformation 2]
38. ! [X0] : (~quiet(X0) | (~curious(X0) | wise(X0))) [ennf transformation 5]
39. ! [X0] : (~quiet(X0) | ~curious(X0) | wise(X0)) [flattening 38]
42. ! [X0] : (calm(X0) | ~curious(X0)) [ennf transformation 29]
46. ! [X0] : ((~generous(X0) <~> ~humble(X0)) | (wise(X0) <=> patient(X0))) [ennf transformation 15]
47. ! [X0] : (~calm(X0) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0)))) [nnf transformation 36]
58. ! [X0] : ((~creative(X0) | (humble(X0) & ~funny(X0))) & ((~humble(X0) | funny(X0)) | creative(X0))) [nnf transformation 12]
59. ! [X0] : ((~creative(X0) | (humble(X0) & ~funny(X0))) & (~humble(X0) | funny(X0) | creative(X0))) [flattening 58]
63. (((humble(susan) | ~creative(susan)) & (~humble(susan) | creative(susan))) | patient(paul)) & (~patient(paul) | ((creative(susan) | humble(susan)) & (~humble(susan) | ~creative(susan)))) [nnf transformation 14]
64. ! [X0] : (((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | ((wise(X0) | ~patient(X0)) & (patient(X0) | ~wise(X0)))) [nnf transformation 46]
77. ~calm(X0) | generous(X0) [cnf transformation 35]
80. ~calm(X0) | quiet(X0) | ~generous(X0) [cnf transformation 47]
86. ~curious(X0) | ~quiet(X0) | wise(X0) [cnf transformation 39]
93. ~curious(X0) | calm(X0) [cnf transformation 42]
98. ~creative(X0) | humble(X0) [cnf transformation 59]
102. ~patient(paul) | creative(susan) | humble(susan) [cnf transformation 63]
105. ~wise(X0) | ~generous(X0) | patient(X0) | ~humble(X0) [cnf transformation 64]
111. ~humble(susan) [cnf transformation 30]
114. humble(paul) [cnf transformation 21]
120. curious(paul) [cnf transformation 25]
123. ~calm(X0) | quiet(X0) [subsumption resolution 80,77]
169. 11 <=> patient(paul) [avatar definition]
170. ~patient(paul) <- (~11) [avatar component clause 169]
177. 13 <=> humble(susan) [avatar definition]
181. ~patient(paul) | humble(susan) [subsumption resolution 102,98]
182. 13 | ~11 [avatar split clause 181,169,177]
186. ~13 [avatar split clause 111,177]
211. calm(paul) [resolution 93,120]
214. generous(paul) [resolution 211,77]
217. quiet(paul) [resolution 123,211]
233. ~quiet(paul) | wise(paul) [resolution 86,120]
235. wise(paul) [subsumption resolution 233,217]
254. ~generous(paul) | patient(paul) | ~humble(paul) [resolution 105,235]
255. patient(paul) | ~humble(paul) [subsumption resolution 254,214]
256. ~humble(paul) <- (~11) [subsumption resolution 255,170]
257. $false <- (~11) [subsumption resolution 256,114]
258. 11 [avatar contradiction clause 257]
259. $false [avatar sat refutation 182,186,258]
% SZS output end Proof for 6914218330525353555783828
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious or creative then someone is both calm and not rich and vice versa. If paul is rich or happy then lucy is not curious or tall. Everyone who is wise is strong and vice versa. Everyone who is either creative or rich is either not kind or quiet. Everyone who is brave or humble is not generous and vice versa. If susan is either old or funny then someone is kind. If fred is old then someone is either generous or humble and vice versa. If mary is not creative then mary is either calm or brave and vice versa. Everyone who is old is funny and vice versa. If someone is not old then fred is either not humble or not tall and vice versa. Everyone who is either strong or not wise is brave and vice versa. If alice is not wise then someone is curious. Everyone who is quiet or not rich is patient or not generous. Everyone who is either not humble or kind is both kind and curious and vice versa. Everyone who is not strong is strong. If john is not tall then mary is both not curious and not old. Someone is tall. Mary is both patient and not curious. Susan is not rich or tall. John is either curious or not old. Mary is quiet. Lucy is not creative. | Alice is not rich. | neutral | ((?[X]:((~curious(X)|creative(X))))<=>(?[X]:((calm(X)&~rich(X)))))&
(((rich(paul)|happy(paul)))=>((~curious(lucy)|tall(lucy))))&
(![X]:(wise(X)<=>strong(X)))&
(![X]:((creative(X)<~>rich(X))=>(~kind(X)<~>quiet(X))))&
(![X]:((brave(X)|humble(X))<=>~generous(X)))&
(((old(susan)<~>funny(susan)))=>(?[X]:(kind(X))))&
((old(fred))<=>(?[X]:((generous(X)<~>humble(X)))))&
((~creative(mary))<=>((calm(mary)<~>brave(mary))))&
(![X]:(old(X)<=>funny(X)))&
((?[X]:(~old(X)))<=>((~humble(fred)<~>~tall(fred))))&
(![X]:((strong(X)<~>~wise(X))<=>brave(X)))&
((~wise(alice))=>(?[X]:(curious(X))))&
(![X]:((quiet(X)|~rich(X))=>(patient(X)|~generous(X))))&
(![X]:((~humble(X)<~>kind(X))<=>(kind(X)&curious(X))))&
(![X]:(~strong(X)=>strong(X)))&
((~tall(john))=>((~curious(mary)&~old(mary))))&
(?[X]:(tall(X)))&
((patient(mary)&~curious(mary)))&
((~rich(susan)|tall(susan)))&
((curious(john)<~>~old(john)))&
(quiet(mary))&
(~creative(lucy)) | ~rich(alice) | [] | null | 0 |
Everyone who is both generous and not funny is old and vice versa. Everyone who is quiet or not brave is both not calm and happy. If fred is both rich and patient then someone is both creative and not creative and vice versa. If someone is either not tall or generous then someone is not humble. Everyone who is not curious is creative and vice versa. Everyone who is either not humble or calm is creative and vice versa. If mary is both not old and happy then someone is patient or not tall. Everyone who is both not quiet and brave is both not wise and not generous and vice versa. Everyone who is both strong and not tall is both curious and not patient. Everyone who is both curious and not brave is both creative and wise and vice versa. If fred is either not funny or humble then someone is both kind and not generous. Everyone who is either tall or not generous is rich or not curious and vice versa. Everyone who is either not brave or funny is both not brave and generous and vice versa. If someone is strong then someone is either not brave or generous and vice versa. If alice is both not tall and humble then someone is curious and vice versa. Everyone who is either tall or not calm is both patient and not rich and vice versa. John is both calm and not rich. Paul is both patient and brave. John is both not humble and tall. Paul is old or not brave. Fred is both rich and not kind. Fred is either not funny or not rich. Alice is either generous or not rich. Fred is not happy or wise. | John is not creative. | entailment | (![X]:((generous(X)&~funny(X))<=>old(X)))&
(![X]:((quiet(X)|~brave(X))=>(~calm(X)&happy(X))))&
(((rich(fred)&patient(fred)))<=>(?[X]:((creative(X)&~creative(X)))))&
((?[X]:((~tall(X)<~>generous(X))))=>(?[X]:(~humble(X))))&
(![X]:(~curious(X)<=>creative(X)))&
(![X]:((~humble(X)<~>calm(X))<=>creative(X)))&
(((~old(mary)&happy(mary)))=>(?[X]:((patient(X)|~tall(X)))))&
(![X]:((~quiet(X)&brave(X))<=>(~wise(X)&~generous(X))))&
(![X]:((strong(X)&~tall(X))=>(curious(X)&~patient(X))))&
(![X]:((curious(X)&~brave(X))<=>(creative(X)&wise(X))))&
(((~funny(fred)<~>humble(fred)))=>(?[X]:((kind(X)&~generous(X)))))&
(![X]:((tall(X)<~>~generous(X))<=>(rich(X)|~curious(X))))&
(![X]:((~brave(X)<~>funny(X))<=>(~brave(X)&generous(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~brave(X)<~>generous(X)))))&
(((~tall(alice)&humble(alice)))<=>(?[X]:(curious(X))))&
(![X]:((tall(X)<~>~calm(X))<=>(patient(X)&~rich(X))))&
((calm(john)&~rich(john)))&
((patient(paul)&brave(paul)))&
((~humble(john)&tall(john)))&
((old(paul)|~brave(paul)))&
((rich(fred)&~kind(fred)))&
((~funny(fred)<~>~rich(fred)))&
((generous(alice)<~>~rich(alice)))&
((~happy(fred)|wise(fred))) | ~creative(john) | [
"p5",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7072501257719079288907558
% SZS output start Proof for 7072501257719079288907558
6. ! [X0] : ((~humble(X0) <~> calm(X0)) <=> creative(X0)) [input p5]
17. ~rich(john) & calm(john) [input p16]
19. tall(john) & ~humble(john) [input p18]
25. creative(john) [input hypothesis]
47. ! [X0] : ((((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | ~creative(X0)) & (creative(X0) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0))))) [nnf transformation 6]
92. ~creative(X0) | humble(X0) | ~calm(X0) [cnf transformation 47]
133. calm(john) [cnf transformation 17]
137. ~humble(john) [cnf transformation 19]
147. creative(john) [cnf transformation 25]
304. humble(john) | ~calm(john) [resolution 92,147]
306. ~calm(john) [subsumption resolution 304,137]
307. $false [subsumption resolution 306,133]
% SZS output end Proof for 7072501257719079288907558
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and strong is calm or curious and vice versa.
If alice is not strong then someone is wise or not quiet.
Everyone who is not patient is wise.
If fred is both old and kind then someone is either old or not creative and vice versa.
Everyone who is not rich or tall is happy.
If someone is quiet or wise then paul is both wise and strong and vice versa.
If john is kind or not old then susan is calm or creative and vice versa.
Everyone who is curious or not calm is either not creative or kind and vice versa.
Everyone who is humble is both not old and not generous.
If someone is rich then someone is both not calm and humble and vice versa.
Everyone who is either kind or patient is not wise and vice versa.
If someone is not curious then mary is both calm and not funny.
If someone is either rich or funny then john is both not tall and not quiet and vice versa.
Everyone who is either not quiet or not generous is quiet.
If lucy is not rich or not patient then paul is either not wise or not curious.
If someone is either not calm or not patient then someone is both not curious and not funny.
Someone is humble.
Someone is either wise or not quiet.
Mary is quiet or not calm.
Alice is not creative or not patient.
John is both creative and brave.
Someone is either not strong or creative.
Someone is not funny or old.
Mary is funny. | Lucy is not calm. | contradiction | (![X]:((funny(X)&strong(X))<=>(calm(X)|curious(X))))&
((~strong(alice))=>(?[X]:((wise(X)|~quiet(X)))))&
(![X]:(~patient(X)=>wise(X)))&
(((old(fred)&kind(fred)))<=>(?[X]:((old(X)<~>~creative(X)))))&
(![X]:((~rich(X)|tall(X))=>happy(X)))&
((?[X]:((quiet(X)|wise(X))))<=>((wise(paul)&strong(paul))))&
(((kind(john)|~old(john)))<=>((calm(susan)|creative(susan))))&
(![X]:((curious(X)|~calm(X))<=>(~creative(X)<~>kind(X))))&
(![X]:(humble(X)=>(~old(X)&~generous(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~calm(X)&humble(X)))))&
(![X]:((kind(X)<~>patient(X))<=>~wise(X)))&
((?[X]:(~curious(X)))=>((calm(mary)&~funny(mary))))&
((?[X]:((rich(X)<~>funny(X))))<=>((~tall(john)&~quiet(john))))&
(![X]:((~quiet(X)<~>~generous(X))=>quiet(X)))&
(((~rich(lucy)|~patient(lucy)))=>((~wise(paul)<~>~curious(paul))))&
((?[X]:((~calm(X)<~>~patient(X))))=>(?[X]:((~curious(X)&~funny(X)))))&
(?[X]:(humble(X)))&
(?[X]:((wise(X)<~>~quiet(X))))&
((quiet(mary)|~calm(mary)))&
((~creative(alice)|~patient(alice)))&
((creative(john)&brave(john)))&
(?[X]:((~strong(X)<~>creative(X))))&
(?[X]:((~funny(X)|old(X))))&
(funny(mary)) | ~calm(lucy) | [
"p0",
"p2",
"p5",
"p11",
"p14",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4614110415640932530482639
% SZS output start Proof for 4614110415640932530482639
1. ! [X0] : ((strong(X0) & funny(X0)) <=> (curious(X0) | calm(X0))) [input p0]
3. ! [X0] : (~patient(X0) => wise(X0)) [input p2]
6. ? [X0] : (wise(X0) | quiet(X0)) <=> (strong(paul) & wise(paul)) [input p5]
12. ? [X0] : ~curious(X0) => (~funny(mary) & calm(mary)) [input p11]
15. (~patient(lucy) | ~rich(lucy)) => (~wise(paul) <~> ~curious(paul)) [input p14]
16. ? [X0] : (~calm(X0) <~> ~patient(X0)) => ? [X0] : (~funny(X0) & ~curious(X0)) [input p15]
24. funny(mary) [input p23]
25. ~calm(lucy) [input hypothesis]
27. ? [X0] : (~calm(X0) <~> ~patient(X0)) => ? [X1] : (~funny(X1) & ~curious(X1)) [rectify 16]
31. ! [X0] : (wise(X0) | patient(X0)) [ennf transformation 3]
33. (~funny(mary) & calm(mary)) | ! [X0] : curious(X0) [ennf transformation 12]
35. (~wise(paul) <~> ~curious(paul)) | (patient(lucy) & rich(lucy)) [ennf transformation 15]
36. ? [X1] : (~funny(X1) & ~curious(X1)) | ! [X0] : (~calm(X0) <=> ~patient(X0)) [ennf transformation 27]
37. ! [X0] : (((strong(X0) & funny(X0)) | (~curious(X0) & ~calm(X0))) & ((curious(X0) | calm(X0)) | (~strong(X0) | ~funny(X0)))) [nnf transformation 1]
38. ! [X0] : (((strong(X0) & funny(X0)) | (~curious(X0) & ~calm(X0))) & (curious(X0) | calm(X0) | ~strong(X0) | ~funny(X0))) [flattening 37]
46. (? [X0] : (wise(X0) | quiet(X0)) | (~strong(paul) | ~wise(paul))) & ((strong(paul) & wise(paul)) | ! [X0] : (~wise(X0) & ~quiet(X0))) [nnf transformation 6]
47. (? [X0] : (wise(X0) | quiet(X0)) | ~strong(paul) | ~wise(paul)) & ((strong(paul) & wise(paul)) | ! [X0] : (~wise(X0) & ~quiet(X0))) [flattening 46]
48. (? [X0] : (wise(X0) | quiet(X0)) | ~strong(paul) | ~wise(paul)) & ((strong(paul) & wise(paul)) | ! [X1] : (~wise(X1) & ~quiet(X1))) [rectify 47]
49. ? [X0] : (wise(X0) | quiet(X0)) => (wise(sK2) | quiet(sK2)) [choice axiom]
50. ((wise(sK2) | quiet(sK2)) | ~strong(paul) | ~wise(paul)) & ((strong(paul) & wise(paul)) | ! [X1] : (~wise(X1) & ~quiet(X1))) [skolemisation 48,49]
67. ((curious(paul) | wise(paul)) & (~curious(paul) | ~wise(paul))) | (patient(lucy) & rich(lucy)) [nnf transformation 35]
68. ? [X1] : (~funny(X1) & ~curious(X1)) | ! [X0] : ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0))) [nnf transformation 36]
69. ? [X0] : (~funny(X0) & ~curious(X0)) | ! [X1] : ((~calm(X1) | patient(X1)) & (~patient(X1) | calm(X1))) [rectify 68]
70. ? [X0] : (~funny(X0) & ~curious(X0)) => (~funny(sK6) & ~curious(sK6)) [choice axiom]
71. (~funny(sK6) & ~curious(sK6)) | ! [X1] : ((~calm(X1) | patient(X1)) & (~patient(X1) | calm(X1))) [skolemisation 69,70]
84. ~curious(X0) | funny(X0) [cnf transformation 38]
88. patient(X0) | wise(X0) [cnf transformation 31]
96. wise(paul) | ~wise(X1) [cnf transformation 50]
120. ~funny(mary) | curious(X0) [cnf transformation 33]
130. ~curious(paul) | ~wise(paul) | patient(lucy) [cnf transformation 67]
135. ~funny(sK6) | ~patient(X1) | calm(X1) [cnf transformation 71]
146. funny(mary) [cnf transformation 24]
147. ~calm(lucy) [cnf transformation 25]
191. 10 <=> wise(paul) [avatar definition]
208. 14 <=> ! [X1] : ~wise(X1) [avatar definition]
209. ~wise(X1) <- (14) [avatar component clause 208]
215. 14 | 10 [avatar split clause 96,191,208]
261. 25 <=> ! [X0] : curious(X0) [avatar definition]
262. curious(X0) <- (25) [avatar component clause 261]
264. 26 <=> funny(mary) [avatar definition]
267. 25 | ~26 [avatar split clause 120,264,261]
302. 34 <=> patient(lucy) [avatar definition]
303. ~patient(lucy) <- (~34) [avatar component clause 302]
304. patient(lucy) <- (34) [avatar component clause 302]
306. 35 <=> curious(paul) [avatar definition]
307. ~curious(paul) <- (~35) [avatar component clause 306]
315. 34 | ~10 | ~35 [avatar split clause 130,306,191,302]
321. 38 <=> funny(sK6) [avatar definition]
323. ~funny(sK6) <- (~38) [avatar component clause 321]
326. 39 <=> ! [X1] : (~patient(X1) | calm(X1)) [avatar definition]
327. ~patient(X1) | calm(X1) <- (39) [avatar component clause 326]
328. 39 | ~38 [avatar split clause 135,321,326]
378. 26 [avatar split clause 146,264]
381. $false <- (25, ~35) [resolution 307,262]
382. ~25 | 35 [avatar contradiction clause 381]
387. funny(X0) <- (25) [resolution 84,262]
389. $false <- (25, ~38) [resolution 387,323]
392. ~25 | 38 [avatar contradiction clause 389]
411. calm(lucy) <- (34, 39) [resolution 327,304]
412. $false <- (34, 39) [subsumption resolution 411,147]
413. ~34 | ~39 [avatar contradiction clause 412]
416. wise(lucy) <- (~34) [resolution 303,88]
417. $false <- (14, ~34) [subsumption resolution 416,209]
418. ~14 | 34 [avatar contradiction clause 417]
419. $false [avatar sat refutation 215,267,315,328,378,382,392,413,418]
% SZS output end Proof for 4614110415640932530482639
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or not wise then susan is both kind and not creative.
Everyone who is not humble is strong or generous and vice versa.
Everyone who is strong is not patient and vice versa.
Everyone who is not funny is both not quiet and tall.
Everyone who is kind is both not generous and not happy.
Everyone who is quiet or not quiet is both not rich and not kind and vice versa.
If someone is both not generous and funny then someone is both not kind and humble and vice versa.
Everyone who is both not calm and funny is patient and vice versa.
If lucy is happy then paul is not creative.
Everyone who is both not creative and not kind is both strong and humble and vice versa.
Everyone who is either quiet or not wise is both not quiet and not curious.
If mary is either not kind or humble then lucy is not calm.
If someone is either not happy or not old then lucy is either not calm or calm and vice versa.
Everyone who is either old or wise is not generous or wise and vice versa.
Someone is either brave or not brave.
Susan is not strong or curious.
Someone is not calm.
Fred is not patient or not calm.
Someone is both not kind and wise.
John is happy. | Paul is creative. | entailment | ((?[X]:((~humble(X)|~wise(X))))=>((kind(susan)&~creative(susan))))&
(![X]:(~humble(X)<=>(strong(X)|generous(X))))&
(![X]:(strong(X)<=>~patient(X)))&
(![X]:(~funny(X)=>(~quiet(X)&tall(X))))&
(![X]:(kind(X)=>(~generous(X)&~happy(X))))&
(![X]:((quiet(X)|~quiet(X))<=>(~rich(X)&~kind(X))))&
((?[X]:((~generous(X)&funny(X))))<=>(?[X]:((~kind(X)&humble(X)))))&
(![X]:((~calm(X)&funny(X))<=>patient(X)))&
((happy(lucy))=>(~creative(paul)))&
(![X]:((~creative(X)&~kind(X))<=>(strong(X)&humble(X))))&
(![X]:((quiet(X)<~>~wise(X))=>(~quiet(X)&~curious(X))))&
(((~kind(mary)<~>humble(mary)))=>(~calm(lucy)))&
((?[X]:((~happy(X)<~>~old(X))))<=>((~calm(lucy)<~>calm(lucy))))&
(![X]:((old(X)<~>wise(X))<=>(~generous(X)|wise(X))))&
(?[X]:((brave(X)<~>~brave(X))))&
((~strong(susan)|curious(susan)))&
(?[X]:(~calm(X)))&
((~patient(fred)|~calm(fred)))&
(?[X]:((~kind(X)&wise(X))))&
(happy(john)) | creative(paul) | [
"p0",
"p1",
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5277703189253553906497261
% SZS output start Proof for 5277703189253553906497261
1. ? [X0] : (~wise(X0) | ~humble(X0)) => (~creative(susan) & kind(susan)) [input p0]
2. ! [X0] : (~humble(X0) <=> (generous(X0) | strong(X0))) [input p1]
6. ! [X0] : ((~quiet(X0) | quiet(X0)) <=> (~kind(X0) & ~rich(X0))) [input p5]
10. ! [X0] : ((~kind(X0) & ~creative(X0)) <=> (humble(X0) & strong(X0))) [input p9]
21. ~creative(paul) [input hypothesis]
24. (~creative(susan) & kind(susan)) | ! [X0] : (wise(X0) & humble(X0)) [ennf transformation 1]
30. ! [X0] : ((~humble(X0) | (~generous(X0) & ~strong(X0))) & ((generous(X0) | strong(X0)) | humble(X0))) [nnf transformation 2]
31. ! [X0] : ((~humble(X0) | (~generous(X0) & ~strong(X0))) & (generous(X0) | strong(X0) | humble(X0))) [flattening 30]
33. ! [X0] : (((~quiet(X0) | quiet(X0)) | (kind(X0) | rich(X0))) & ((~kind(X0) & ~rich(X0)) | (quiet(X0) & ~quiet(X0)))) [nnf transformation 6]
34. ! [X0] : ((~quiet(X0) | quiet(X0) | kind(X0) | rich(X0)) & ((~kind(X0) & ~rich(X0)) | (quiet(X0) & ~quiet(X0)))) [flattening 33]
42. ! [X0] : (((~kind(X0) & ~creative(X0)) | (~humble(X0) | ~strong(X0))) & ((humble(X0) & strong(X0)) | (kind(X0) | creative(X0)))) [nnf transformation 10]
43. ! [X0] : (((~kind(X0) & ~creative(X0)) | ~humble(X0) | ~strong(X0)) & ((humble(X0) & strong(X0)) | kind(X0) | creative(X0))) [flattening 42]
59. kind(susan) | humble(X0) [cnf transformation 24]
64. ~strong(X0) | ~humble(X0) [cnf transformation 31]
73. ~kind(X0) | ~quiet(X0) [cnf transformation 34]
74. ~kind(X0) | quiet(X0) [cnf transformation 34]
84. strong(X0) | kind(X0) | creative(X0) [cnf transformation 43]
116. ~creative(paul) [cnf transformation 21]
133. 3 <=> ! [X0] : humble(X0) [avatar definition]
134. humble(X0) <- (3) [avatar component clause 133]
137. 4 <=> kind(susan) [avatar definition]
139. kind(susan) <- (4) [avatar component clause 137]
141. 3 | 4 [avatar split clause 59,137,133]
142. ~kind(X0) [subsumption resolution 73,74]
172. 11 <=> creative(paul) [avatar definition]
174. ~creative(paul) <- (~11) [avatar component clause 172]
177. strong(X0) | creative(X0) [subsumption resolution 84,142]
210. ~11 [avatar split clause 116,172]
211. $false <- (4) [subsumption resolution 139,142]
212. ~4 [avatar contradiction clause 211]
225. creative(X0) | ~humble(X0) [resolution 177,64]
228. creative(X0) <- (3) [subsumption resolution 225,134]
229. $false <- (3, ~11) [resolution 228,174]
230. ~3 | 11 [avatar contradiction clause 229]
231. $false [avatar sat refutation 141,210,212,230]
% SZS output end Proof for 5277703189253553906497261
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not creative or not strong then susan is not quiet.
Everyone who is either not old or funny is not funny or not wise.
Everyone who is either not curious or not quiet is calm.
If lucy is both funny and not rich then mary is patient.
Everyone who is not wise is rich or brave.
Everyone who is brave is both not quiet and not generous.
If someone is kind then lucy is not wise or funny.
If someone is curious then paul is both funny and kind and vice versa.
If susan is both not strong and not kind then lucy is not brave and vice versa.
Everyone who is either old or not humble is both quiet and not happy and vice versa.
Everyone who is either not generous or not calm is either strong or humble and vice versa.
If someone is either funny or not funny then susan is both not calm and old.
Everyone who is both not kind and generous is not funny or quiet.
Everyone who is kind is either not creative or strong.
Everyone who is not brave is kind and vice versa.
Everyone who is either not curious or funny is either wise or not happy and vice versa.
Someone is both kind and quiet.
Paul is either not old or kind.
Someone is not creative.
Someone is kind.
Someone is funny.
Someone is not happy.
Fred is both generous and not wise.
Someone is both creative and generous. | Paul is not happy. | neutral | ((?[X]:((~creative(X)<~>~strong(X))))=>(~quiet(susan)))&
(![X]:((~old(X)<~>funny(X))=>(~funny(X)|~wise(X))))&
(![X]:((~curious(X)<~>~quiet(X))=>calm(X)))&
(((funny(lucy)&~rich(lucy)))=>(patient(mary)))&
(![X]:(~wise(X)=>(rich(X)|brave(X))))&
(![X]:(brave(X)=>(~quiet(X)&~generous(X))))&
((?[X]:(kind(X)))=>((~wise(lucy)|funny(lucy))))&
((?[X]:(curious(X)))<=>((funny(paul)&kind(paul))))&
(((~strong(susan)&~kind(susan)))<=>(~brave(lucy)))&
(![X]:((old(X)<~>~humble(X))<=>(quiet(X)&~happy(X))))&
(![X]:((~generous(X)<~>~calm(X))<=>(strong(X)<~>humble(X))))&
((?[X]:((funny(X)<~>~funny(X))))=>((~calm(susan)&old(susan))))&
(![X]:((~kind(X)&generous(X))=>(~funny(X)|quiet(X))))&
(![X]:(kind(X)=>(~creative(X)<~>strong(X))))&
(![X]:(~brave(X)<=>kind(X)))&
(![X]:((~curious(X)<~>funny(X))<=>(wise(X)<~>~happy(X))))&
(?[X]:((kind(X)&quiet(X))))&
((~old(paul)<~>kind(paul)))&
(?[X]:(~creative(X)))&
(?[X]:(kind(X)))&
(?[X]:(funny(X)))&
(?[X]:(~happy(X)))&
((generous(fred)&~wise(fred)))&
(?[X]:((creative(X)&generous(X)))) | ~happy(paul) | [] | null | 0 |
If someone is rich then paul is tall and vice versa. If mary is either not happy or humble then someone is either not strong or calm. If alice is not happy then someone is either brave or calm. Everyone who is either not tall or not creative is creative. If mary is either strong or not quiet then lucy is either wise or curious and vice versa. Everyone who is either wise or brave is not wise or not strong and vice versa. If someone is either quiet or creative then john is either rich or not curious and vice versa. Everyone who is not rich or brave is both calm and not calm. If lucy is either not brave or not creative then someone is old or happy. If lucy is both brave and not curious then someone is not happy and vice versa. Everyone who is either not strong or patient is not rich and vice versa. Everyone who is either not humble or not creative is either not generous or not happy and vice versa. If paul is brave then someone is not strong. Everyone who is either not brave or rich is not happy or happy. Everyone who is not kind or curious is not humble. Someone is strong or funny. Fred is either calm or not kind. Fred is either not humble or not curious. Someone is either generous or not curious. Alice is kind or happy. | John is brave. | contradiction | ((?[X]:(rich(X)))<=>(tall(paul)))&
(((~happy(mary)<~>humble(mary)))=>(?[X]:((~strong(X)<~>calm(X)))))&
((~happy(alice))=>(?[X]:((brave(X)<~>calm(X)))))&
(![X]:((~tall(X)<~>~creative(X))=>creative(X)))&
(((strong(mary)<~>~quiet(mary)))<=>((wise(lucy)<~>curious(lucy))))&
(![X]:((wise(X)<~>brave(X))<=>(~wise(X)|~strong(X))))&
((?[X]:((quiet(X)<~>creative(X))))<=>((rich(john)<~>~curious(john))))&
(![X]:((~rich(X)|brave(X))=>(calm(X)&~calm(X))))&
(((~brave(lucy)<~>~creative(lucy)))=>(?[X]:((old(X)|happy(X)))))&
(((brave(lucy)&~curious(lucy)))<=>(?[X]:(~happy(X))))&
(![X]:((~strong(X)<~>patient(X))<=>~rich(X)))&
(![X]:((~humble(X)<~>~creative(X))<=>(~generous(X)<~>~happy(X))))&
((brave(paul))=>(?[X]:(~strong(X))))&
(![X]:((~brave(X)<~>rich(X))=>(~happy(X)|happy(X))))&
(![X]:((~kind(X)|curious(X))=>~humble(X)))&
(?[X]:((strong(X)|funny(X))))&
((calm(fred)<~>~kind(fred)))&
((~humble(fred)<~>~curious(fred)))&
(?[X]:((generous(X)<~>~curious(X))))&
((kind(alice)|happy(alice))) | brave(john) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4323826239067940526307742
% SZS output start Proof for 4323826239067940526307742
8. ! [X0] : ((brave(X0) | ~rich(X0)) => (~calm(X0) & calm(X0))) [input p7]
21. brave(john) [input hypothesis]
27. ! [X0] : ((~calm(X0) & calm(X0)) | (~brave(X0) & rich(X0))) [ennf transformation 8]
98. calm(X0) | ~brave(X0) [cnf transformation 27]
100. ~calm(X0) | ~brave(X0) [cnf transformation 27]
128. brave(john) [cnf transformation 21]
234. ~brave(X0) [subsumption resolution 98,100]
278. $false [subsumption resolution 128,234]
% SZS output end Proof for 4323826239067940526307742
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not strong is not creative.
Everyone who is not tall is not funny or quiet and vice versa.
If susan is both rich and not old then paul is both not happy and not strong and vice versa.
Everyone who is both kind and not kind is creative and vice versa.
Everyone who is either kind or not creative is creative or not creative and vice versa.
If mary is brave then mary is not calm or curious and vice versa.
Everyone who is not happy is not patient or not creative and vice versa.
Everyone who is not old or funny is either not humble or strong and vice versa.
If someone is not wise then john is either not funny or not wise.
Everyone who is both not funny and funny is not old and vice versa.
Everyone who is either kind or not funny is either not generous or not humble.
If fred is brave then someone is not humble or not patient.
If john is not funny or not calm then someone is happy.
Everyone who is both calm and humble is happy.
If paul is either not quiet or funny then someone is both curious and wise and vice versa.
Paul is both not patient and calm.
Susan is funny.
Fred is not strong.
Mary is either creative or not humble.
Lucy is both not generous and patient. | Mary is not quiet. | neutral | (![X]:((~wise(X)|~strong(X))=>~creative(X)))&
(![X]:(~tall(X)<=>(~funny(X)|quiet(X))))&
(((rich(susan)&~old(susan)))<=>((~happy(paul)&~strong(paul))))&
(![X]:((kind(X)&~kind(X))<=>creative(X)))&
(![X]:((kind(X)<~>~creative(X))<=>(creative(X)|~creative(X))))&
((brave(mary))<=>((~calm(mary)|curious(mary))))&
(![X]:(~happy(X)<=>(~patient(X)|~creative(X))))&
(![X]:((~old(X)|funny(X))<=>(~humble(X)<~>strong(X))))&
((?[X]:(~wise(X)))=>((~funny(john)<~>~wise(john))))&
(![X]:((~funny(X)&funny(X))<=>~old(X)))&
(![X]:((kind(X)<~>~funny(X))=>(~generous(X)<~>~humble(X))))&
((brave(fred))=>(?[X]:((~humble(X)|~patient(X)))))&
(((~funny(john)|~calm(john)))=>(?[X]:(happy(X))))&
(![X]:((calm(X)&humble(X))=>happy(X)))&
(((~quiet(paul)<~>funny(paul)))<=>(?[X]:((curious(X)&wise(X)))))&
((~patient(paul)&calm(paul)))&
(funny(susan))&
(~strong(fred))&
((creative(mary)<~>~humble(mary)))&
((~generous(lucy)&patient(lucy))) | ~quiet(mary) | [] | null | 0 |
Everyone who is not funny is both quiet and not funny. Everyone who is either not humble or funny is old and vice versa. Everyone who is strong or not generous is happy or creative. Everyone who is either not creative or not generous is not brave. If someone is not generous or tall then mary is both not curious and patient. Everyone who is either happy or not tall is both not patient and not quiet. Everyone who is both not kind and humble is either old or humble and vice versa. Everyone who is patient is both not funny and brave and vice versa. Everyone who is not quiet is funny and vice versa. Everyone who is either not calm or not rich is humble or not quiet. Everyone who is strong or not old is patient or not old and vice versa. Everyone who is both not brave and old is both not old and kind and vice versa. If fred is both not old and not kind then someone is either not rich or not tall. If someone is not tall then john is not happy or brave and vice versa. Everyone who is either creative or not funny is either not brave or not old and vice versa. Everyone who is either not generous or curious is either not curious or happy. Someone is tall or not strong. Lucy is either kind or not funny. Paul is not brave. Someone is not wise or not patient. Someone is both not creative and not old. Someone is happy. | Lucy is quiet. | entailment | (![X]:(~funny(X)=>(quiet(X)&~funny(X))))&
(![X]:((~humble(X)<~>funny(X))<=>old(X)))&
(![X]:((strong(X)|~generous(X))=>(happy(X)|creative(X))))&
(![X]:((~creative(X)<~>~generous(X))=>~brave(X)))&
((?[X]:((~generous(X)|tall(X))))=>((~curious(mary)&patient(mary))))&
(![X]:((happy(X)<~>~tall(X))=>(~patient(X)&~quiet(X))))&
(![X]:((~kind(X)&humble(X))<=>(old(X)<~>humble(X))))&
(![X]:(patient(X)<=>(~funny(X)&brave(X))))&
(![X]:(~quiet(X)<=>funny(X)))&
(![X]:((~calm(X)<~>~rich(X))=>(humble(X)|~quiet(X))))&
(![X]:((strong(X)|~old(X))<=>(patient(X)|~old(X))))&
(![X]:((~brave(X)&old(X))<=>(~old(X)&kind(X))))&
(((~old(fred)&~kind(fred)))=>(?[X]:((~rich(X)<~>~tall(X)))))&
((?[X]:(~tall(X)))<=>((~happy(john)|brave(john))))&
(![X]:((creative(X)<~>~funny(X))<=>(~brave(X)<~>~old(X))))&
(![X]:((~generous(X)<~>curious(X))=>(~curious(X)<~>happy(X))))&
(?[X]:((tall(X)|~strong(X))))&
((kind(lucy)<~>~funny(lucy)))&
(~brave(paul))&
(?[X]:((~wise(X)|~patient(X))))&
(?[X]:((~creative(X)&~old(X))))&
(?[X]:(happy(X))) | quiet(lucy) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p6",
"p7",
"p11",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 651273373133122018479262
% SZS output start Proof for 651273373133122018479262
1. ! [X0] : (~funny(X0) => (~funny(X0) & quiet(X0))) [input p0]
2. ! [X0] : ((~humble(X0) <~> funny(X0)) <=> old(X0)) [input p1]
3. ! [X0] : ((~generous(X0) | strong(X0)) => (creative(X0) | happy(X0))) [input p2]
4. ! [X0] : ((~creative(X0) <~> ~generous(X0)) => ~brave(X0)) [input p3]
5. ? [X0] : (tall(X0) | ~generous(X0)) => (patient(mary) & ~curious(mary)) [input p4]
7. ! [X0] : ((humble(X0) & ~kind(X0)) <=> (old(X0) <~> humble(X0))) [input p6]
8. ! [X0] : (patient(X0) <=> (brave(X0) & ~funny(X0))) [input p7]
12. ! [X0] : ((old(X0) & ~brave(X0)) <=> (kind(X0) & ~old(X0))) [input p11]
15. ! [X0] : ((creative(X0) <~> ~funny(X0)) <=> (~brave(X0) <~> ~old(X0))) [input p14]
16. ! [X0] : ((~generous(X0) <~> curious(X0)) => (~curious(X0) <~> happy(X0))) [input p15]
18. kind(lucy) <~> ~funny(lucy) [input p17]
23. ~quiet(lucy) [input hypothesis]
25. ! [X0] : ((~funny(X0) & quiet(X0)) | funny(X0)) [ennf transformation 1]
26. ! [X0] : ((creative(X0) | happy(X0)) | (generous(X0) & ~strong(X0))) [ennf transformation 3]
27. ! [X0] : (creative(X0) | happy(X0) | (generous(X0) & ~strong(X0))) [flattening 26]
28. ! [X0] : (~brave(X0) | (~creative(X0) <=> ~generous(X0))) [ennf transformation 4]
29. (patient(mary) & ~curious(mary)) | ! [X0] : (~tall(X0) & generous(X0)) [ennf transformation 5]
35. ! [X0] : ((~curious(X0) <~> happy(X0)) | (~generous(X0) <=> curious(X0))) [ennf transformation 16]
36. ! [X0] : ((((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | ~old(X0)) & (old(X0) | ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0))))) [nnf transformation 2]
37. ! [X0] : (~brave(X0) | ((~creative(X0) | generous(X0)) & (~generous(X0) | creative(X0)))) [nnf transformation 28]
39. ! [X0] : (((humble(X0) & ~kind(X0)) | ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0)))) & (((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | (~humble(X0) | kind(X0)))) [nnf transformation 7]
40. ! [X0] : (((humble(X0) & ~kind(X0)) | ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0)))) & (((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | ~humble(X0) | kind(X0))) [flattening 39]
41. ! [X0] : ((patient(X0) | (~brave(X0) | funny(X0))) & ((brave(X0) & ~funny(X0)) | ~patient(X0))) [nnf transformation 8]
42. ! [X0] : ((patient(X0) | ~brave(X0) | funny(X0)) & ((brave(X0) & ~funny(X0)) | ~patient(X0))) [flattening 41]
47. ! [X0] : (((old(X0) & ~brave(X0)) | (~kind(X0) | old(X0))) & ((kind(X0) & ~old(X0)) | (~old(X0) | brave(X0)))) [nnf transformation 12]
48. ! [X0] : (((old(X0) & ~brave(X0)) | ~kind(X0) | old(X0)) & ((kind(X0) & ~old(X0)) | ~old(X0) | brave(X0))) [flattening 47]
57. ! [X0] : ((((funny(X0) | ~creative(X0)) & (~funny(X0) | creative(X0))) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0)))) & (((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0))))) [nnf transformation 15]
58. ! [X0] : (((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | ((~generous(X0) | ~curious(X0)) & (curious(X0) | generous(X0)))) [nnf transformation 35]
61. (funny(lucy) | ~kind(lucy)) & (~funny(lucy) | kind(lucy)) [nnf transformation 18]
66. quiet(X0) | funny(X0) [cnf transformation 25]
70. ~old(X0) | ~humble(X0) | funny(X0) [cnf transformation 36]
73. creative(X0) | happy(X0) | generous(X0) [cnf transformation 27]
74. ~brave(X0) | ~generous(X0) | creative(X0) [cnf transformation 37]
76. ~curious(mary) | generous(X0) [cnf transformation 29]
78. patient(mary) | generous(X0) [cnf transformation 29]
88. humble(X0) | humble(X0) | ~old(X0) [cnf transformation 40]
90. ~patient(X0) | ~funny(X0) [cnf transformation 42]
91. ~patient(X0) | brave(X0) [cnf transformation 42]
101. ~old(X0) | ~old(X0) | brave(X0) [cnf transformation 48]
104. old(X0) | ~kind(X0) | old(X0) [cnf transformation 48]
110. ~old(X0) | ~brave(X0) | ~funny(X0) | ~creative(X0) [cnf transformation 57]
117. ~brave(X0) | ~creative(X0) | funny(X0) | old(X0) [cnf transformation 57]
120. ~happy(X0) | curious(X0) | curious(X0) | generous(X0) [cnf transformation 58]
123. ~funny(lucy) | kind(lucy) [cnf transformation 61]
129. ~quiet(lucy) [cnf transformation 23]
131. ~happy(X0) | curious(X0) | generous(X0) [duplicate literal removal 120]
132. ~old(X0) | brave(X0) [duplicate literal removal 101]
133. ~kind(X0) | old(X0) [duplicate literal removal 104]
135. ~old(X0) | humble(X0) [duplicate literal removal 88]
140. 2 <=> patient(mary) [avatar definition]
142. patient(mary) <- (2) [avatar component clause 140]
145. 3 <=> ! [X0] : generous(X0) [avatar definition]
146. generous(X0) <- (3) [avatar component clause 145]
147. 3 | 2 [avatar split clause 78,140,145]
149. 4 <=> curious(mary) [avatar definition]
153. 3 | ~4 [avatar split clause 76,149,145]
192. ~creative(X0) | ~funny(X0) | ~old(X0) [subsumption resolution 110,132]
203. 14 <=> kind(lucy) [avatar definition]
204. kind(lucy) <- (14) [avatar component clause 203]
207. 15 <=> funny(lucy) [avatar definition]
209. funny(lucy) <- (15) [avatar component clause 207]
211. 14 | ~15 [avatar split clause 123,207,203]
212. funny(lucy) [resolution 66,129]
215. 15 [avatar split clause 212,207]
216. ~funny(mary) <- (2) [resolution 90,142]
217. brave(mary) <- (2) [resolution 91,142]
220. old(lucy) <- (14) [resolution 133,204]
221. brave(lucy) <- (14) [resolution 220,132]
265. ~generous(mary) | creative(mary) <- (2) [resolution 74,217]
267. ~generous(lucy) | creative(lucy) <- (14) [resolution 74,221]
269. 20 <=> creative(mary) [avatar definition]
270. ~creative(mary) <- (~20) [avatar component clause 269]
271. creative(mary) <- (20) [avatar component clause 269]
273. 21 <=> generous(mary) [avatar definition]
275. ~generous(mary) <- (~21) [avatar component clause 273]
276. 20 | ~21 | ~2 [avatar split clause 265,140,273,269]
287. 24 <=> creative(lucy) [avatar definition]
289. creative(lucy) <- (24) [avatar component clause 287]
291. 25 <=> generous(lucy) [avatar definition]
293. ~generous(lucy) <- (~25) [avatar component clause 291]
294. 24 | ~25 | ~14 [avatar split clause 267,203,291,287]
304. happy(mary) | generous(mary) <- (~20) [resolution 270,73]
305. happy(mary) <- (~20, ~21) [subsumption resolution 304,275]
321. 26 <=> old(mary) [avatar definition]
322. old(mary) <- (26) [avatar component clause 321]
330. curious(mary) | generous(mary) <- (~20, ~21) [resolution 131,305]
348. curious(mary) <- (~20, ~21) [subsumption resolution 330,275]
349. 4 | 20 | 21 [avatar split clause 348,273,269,149]
352. $false <- (3, ~25) [resolution 146,293]
353. ~3 | 25 [avatar contradiction clause 352]
390. ~creative(mary) | funny(mary) | old(mary) <- (2) [resolution 117,217]
394. funny(mary) | old(mary) <- (2, 20) [subsumption resolution 390,271]
395. old(mary) <- (2, 20) [subsumption resolution 394,216]
398. 26 | ~2 | ~20 [avatar split clause 395,269,140,321]
401. ~humble(mary) | funny(mary) <- (26) [resolution 322,70]
403. humble(mary) <- (26) [resolution 322,135]
405. ~humble(mary) <- (2, 26) [subsumption resolution 401,216]
406. $false <- (2, 26) [subsumption resolution 403,405]
407. ~2 | ~26 [avatar contradiction clause 406]
476. ~funny(lucy) | ~old(lucy) <- (24) [resolution 289,192]
478. ~old(lucy) <- (15, 24) [subsumption resolution 476,209]
479. $false <- (14, 15, 24) [subsumption resolution 478,220]
480. ~14 | ~15 | ~24 [avatar contradiction clause 479]
481. $false [avatar sat refutation 147,153,211,215,276,294,349,353,398,407,480]
% SZS output end Proof for 651273373133122018479262
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or funny then mary is not creative or not strong and vice versa.
If susan is either not quiet or generous then paul is either happy or not patient and vice versa.
If alice is not kind then fred is not kind.
If someone is not curious then lucy is either not patient or humble.
Everyone who is not quiet or not tall is happy.
If someone is not wise or generous then paul is either tall or patient and vice versa.
If someone is both not wise and rich then susan is generous.
Everyone who is quiet is humble or not rich and vice versa.
If paul is both brave and tall then susan is funny or calm.
Everyone who is not curious or not rich is both rich and not rich and vice versa.
If alice is both not brave and not calm then paul is not quiet or not humble.
Everyone who is happy or not old is both not kind and kind.
If someone is both not calm and old then mary is both not kind and not creative and vice versa.
If someone is both not quiet and not funny then someone is not brave or not kind.
Everyone who is patient is both not generous and not tall.
Everyone who is both not strong and tall is both not funny and not rich.
Someone is humble.
Someone is both not brave and kind.
Someone is either not kind or patient.
John is both quiet and generous. | Lucy is creative. | neutral | ((?[X]:((~tall(X)|funny(X))))<=>((~creative(mary)|~strong(mary))))&
(((~quiet(susan)<~>generous(susan)))<=>((happy(paul)<~>~patient(paul))))&
((~kind(alice))=>(~kind(fred)))&
((?[X]:(~curious(X)))=>((~patient(lucy)<~>humble(lucy))))&
(![X]:((~quiet(X)|~tall(X))=>happy(X)))&
((?[X]:((~wise(X)|generous(X))))<=>((tall(paul)<~>patient(paul))))&
((?[X]:((~wise(X)&rich(X))))=>(generous(susan)))&
(![X]:(quiet(X)<=>(humble(X)|~rich(X))))&
(((brave(paul)&tall(paul)))=>((funny(susan)|calm(susan))))&
(![X]:((~curious(X)|~rich(X))<=>(rich(X)&~rich(X))))&
(((~brave(alice)&~calm(alice)))=>((~quiet(paul)|~humble(paul))))&
(![X]:((happy(X)|~old(X))=>(~kind(X)&kind(X))))&
((?[X]:((~calm(X)&old(X))))<=>((~kind(mary)&~creative(mary))))&
((?[X]:((~quiet(X)&~funny(X))))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:(patient(X)=>(~generous(X)&~tall(X))))&
(![X]:((~strong(X)&tall(X))=>(~funny(X)&~rich(X))))&
(?[X]:(humble(X)))&
(?[X]:((~brave(X)&kind(X))))&
(?[X]:((~kind(X)<~>patient(X))))&
((quiet(john)&generous(john))) | creative(lucy) | [] | null | 0 |
If paul is either happy or wise then someone is brave or happy and vice versa.
Everyone who is both not rich and kind is wise and vice versa.
Everyone who is both brave and curious is either strong or not wise and vice versa.
Everyone who is happy is generous.
Everyone who is both funny and not old is quiet or not curious and vice versa.
If susan is either generous or not wise then fred is not kind.
If alice is either not funny or not strong then fred is either not funny or not kind and vice versa.
Everyone who is either not patient or humble is not funny or not strong and vice versa.
If alice is curious then susan is not strong and vice versa.
Everyone who is either brave or not happy is not brave or rich and vice versa.
If fred is both not patient and not happy then alice is both creative and not quiet and vice versa.
If someone is both not generous and not wise then someone is not curious.
Everyone who is funny or strong is not old or humble and vice versa.
Everyone who is old or not rich is both not tall and kind and vice versa.
If someone is not creative then lucy is either not creative or not rich.
Everyone who is brave or not wise is rich and vice versa.
Someone is wise.
Fred is both not quiet and brave.
Someone is not funny.
Someone is not patient or brave.
Susan is funny or not curious.
Someone is both creative and not happy.
Susan is not creative or brave.
Lucy is either happy or not brave. | Fred is not strong. | neutral | (((happy(paul)<~>wise(paul)))<=>(?[X]:((brave(X)|happy(X)))))&
(![X]:((~rich(X)&kind(X))<=>wise(X)))&
(![X]:((brave(X)&curious(X))<=>(strong(X)<~>~wise(X))))&
(![X]:(happy(X)=>generous(X)))&
(![X]:((funny(X)&~old(X))<=>(quiet(X)|~curious(X))))&
(((generous(susan)<~>~wise(susan)))=>(~kind(fred)))&
(((~funny(alice)<~>~strong(alice)))<=>((~funny(fred)<~>~kind(fred))))&
(![X]:((~patient(X)<~>humble(X))<=>(~funny(X)|~strong(X))))&
((curious(alice))<=>(~strong(susan)))&
(![X]:((brave(X)<~>~happy(X))<=>(~brave(X)|rich(X))))&
(((~patient(fred)&~happy(fred)))<=>((creative(alice)&~quiet(alice))))&
((?[X]:((~generous(X)&~wise(X))))=>(?[X]:(~curious(X))))&
(![X]:((funny(X)|strong(X))<=>(~old(X)|humble(X))))&
(![X]:((old(X)|~rich(X))<=>(~tall(X)&kind(X))))&
((?[X]:(~creative(X)))=>((~creative(lucy)<~>~rich(lucy))))&
(![X]:((brave(X)|~wise(X))<=>rich(X)))&
(?[X]:(wise(X)))&
((~quiet(fred)&brave(fred)))&
(?[X]:(~funny(X)))&
(?[X]:((~patient(X)|brave(X))))&
((funny(susan)|~curious(susan)))&
(?[X]:((creative(X)&~happy(X))))&
((~creative(susan)|brave(susan)))&
((happy(lucy)<~>~brave(lucy))) | ~strong(fred) | [] | null | 0 |
Everyone who is not quiet is both old and generous. Everyone who is not old or kind is either not rich or not strong. If someone is both brave and not generous then someone is brave. If fred is either wise or tall then someone is either not old or creative and vice versa. Everyone who is not generous is rich and vice versa. Everyone who is either not strong or generous is both not old and wise. Everyone who is tall or not wise is either not tall or not strong. Everyone who is either brave or not wise is not humble and vice versa. If alice is humble then someone is both not happy and not strong and vice versa. Everyone who is either not calm or not creative is either rich or not humble. If mary is either not brave or not funny then someone is wise and vice versa. If lucy is generous then someone is generous. If alice is not quiet then susan is both not old and creative and vice versa. If someone is either old or not wise then someone is both not generous and not calm and vice versa. Everyone who is funny is rich or generous. Everyone who is both old and not patient is not old and vice versa. John is either calm or rich. Someone is both tall and not brave. Fred is either not creative or funny. Fred is either old or not tall. Someone is either humble or wise. John is humble. | Alice is tall. | neutral | (![X]:(~quiet(X)=>(old(X)&generous(X))))&
(![X]:((~old(X)|kind(X))=>(~rich(X)<~>~strong(X))))&
((?[X]:((brave(X)&~generous(X))))=>(?[X]:(brave(X))))&
(((wise(fred)<~>tall(fred)))<=>(?[X]:((~old(X)<~>creative(X)))))&
(![X]:(~generous(X)<=>rich(X)))&
(![X]:((~strong(X)<~>generous(X))=>(~old(X)&wise(X))))&
(![X]:((tall(X)|~wise(X))=>(~tall(X)<~>~strong(X))))&
(![X]:((brave(X)<~>~wise(X))<=>~humble(X)))&
((humble(alice))<=>(?[X]:((~happy(X)&~strong(X)))))&
(![X]:((~calm(X)<~>~creative(X))=>(rich(X)<~>~humble(X))))&
(((~brave(mary)<~>~funny(mary)))<=>(?[X]:(wise(X))))&
((generous(lucy))=>(?[X]:(generous(X))))&
((~quiet(alice))<=>((~old(susan)&creative(susan))))&
((?[X]:((old(X)<~>~wise(X))))<=>(?[X]:((~generous(X)&~calm(X)))))&
(![X]:(funny(X)=>(rich(X)|generous(X))))&
(![X]:((old(X)&~patient(X))<=>~old(X)))&
((calm(john)<~>rich(john)))&
(?[X]:((tall(X)&~brave(X))))&
((~creative(fred)<~>funny(fred)))&
((old(fred)<~>~tall(fred)))&
(?[X]:((humble(X)<~>wise(X))))&
(humble(john)) | tall(alice) | [] | null | 0 |
If susan is not calm then someone is either generous or not calm.
Everyone who is either wise or not old is either not wise or strong and vice versa.
If paul is humble then mary is not wise or not old.
Everyone who is not brave is curious or wise.
Everyone who is not brave or kind is quiet and vice versa.
If fred is funny or not humble then someone is both not rich and humble.
Everyone who is not calm or happy is not calm and vice versa.
If fred is both not quiet and not rich then someone is either not happy or strong.
If paul is not funny or brave then lucy is both strong and not quiet and vice versa.
If someone is either not old or tall then alice is both wise and calm and vice versa.
If someone is either brave or old then someone is not tall and vice versa.
If mary is either humble or brave then someone is either not quiet or wise.
Everyone who is humble is either humble or not wise and vice versa.
Everyone who is either not happy or not quiet is either creative or not curious and vice versa.
If someone is not calm or brave then fred is either strong or not kind and vice versa.
Everyone who is not patient or kind is either wise or old.
Someone is either wise or not calm.
Mary is funny.
Fred is patient.
Someone is generous.
Paul is curious or wise.
Someone is both tall and quiet.
Someone is generous or not generous. | Fred is not quiet. | neutral | ((~calm(susan))=>(?[X]:((generous(X)<~>~calm(X)))))&
(![X]:((wise(X)<~>~old(X))<=>(~wise(X)<~>strong(X))))&
((humble(paul))=>((~wise(mary)|~old(mary))))&
(![X]:(~brave(X)=>(curious(X)|wise(X))))&
(![X]:((~brave(X)|kind(X))<=>quiet(X)))&
(((funny(fred)|~humble(fred)))=>(?[X]:((~rich(X)&humble(X)))))&
(![X]:((~calm(X)|happy(X))<=>~calm(X)))&
(((~quiet(fred)&~rich(fred)))=>(?[X]:((~happy(X)<~>strong(X)))))&
(((~funny(paul)|brave(paul)))<=>((strong(lucy)&~quiet(lucy))))&
((?[X]:((~old(X)<~>tall(X))))<=>((wise(alice)&calm(alice))))&
((?[X]:((brave(X)<~>old(X))))<=>(?[X]:(~tall(X))))&
(((humble(mary)<~>brave(mary)))=>(?[X]:((~quiet(X)<~>wise(X)))))&
(![X]:(humble(X)<=>(humble(X)<~>~wise(X))))&
(![X]:((~happy(X)<~>~quiet(X))<=>(creative(X)<~>~curious(X))))&
((?[X]:((~calm(X)|brave(X))))<=>((strong(fred)<~>~kind(fred))))&
(![X]:((~patient(X)|kind(X))=>(wise(X)<~>old(X))))&
(?[X]:((wise(X)<~>~calm(X))))&
(funny(mary))&
(patient(fred))&
(?[X]:(generous(X)))&
((curious(paul)|wise(paul)))&
(?[X]:((tall(X)&quiet(X))))&
(?[X]:((generous(X)|~generous(X)))) | ~quiet(fred) | [] | null | 0 |
If paul is humble then lucy is either not rich or not curious and vice versa.
If someone is creative then someone is not old or not calm and vice versa.
If someone is not kind or not patient then someone is not rich.
If someone is not tall or quiet then someone is either not rich or patient and vice versa.
Everyone who is rich or not rich is both curious and generous.
Everyone who is either not happy or not quiet is kind and vice versa.
Everyone who is quiet or not humble is not kind.
If someone is both tall and rich then susan is either not tall or generous.
Everyone who is either strong or not quiet is not curious.
Everyone who is both generous and not kind is rich.
If john is rich or brave then someone is patient or quiet and vice versa.
If mary is either not brave or brave then someone is both not kind and not funny and vice versa.
If fred is both not curious and not humble then mary is either kind or not calm and vice versa.
If someone is both not patient and not quiet then fred is either funny or not funny.
Everyone who is kind is both curious and brave and vice versa.
John is either not kind or humble.
Mary is either happy or not happy.
Paul is tall.
Alice is not calm.
Lucy is tall.
Susan is patient. | Fred is curious. | entailment | ((humble(paul))<=>((~rich(lucy)<~>~curious(lucy))))&
((?[X]:(creative(X)))<=>(?[X]:((~old(X)|~calm(X)))))&
((?[X]:((~kind(X)|~patient(X))))=>(?[X]:(~rich(X))))&
((?[X]:((~tall(X)|quiet(X))))<=>(?[X]:((~rich(X)<~>patient(X)))))&
(![X]:((rich(X)|~rich(X))=>(curious(X)&generous(X))))&
(![X]:((~happy(X)<~>~quiet(X))<=>kind(X)))&
(![X]:((quiet(X)|~humble(X))=>~kind(X)))&
((?[X]:((tall(X)&rich(X))))=>((~tall(susan)<~>generous(susan))))&
(![X]:((strong(X)<~>~quiet(X))=>~curious(X)))&
(![X]:((generous(X)&~kind(X))=>rich(X)))&
(((rich(john)|brave(john)))<=>(?[X]:((patient(X)|quiet(X)))))&
(((~brave(mary)<~>brave(mary)))<=>(?[X]:((~kind(X)&~funny(X)))))&
(((~curious(fred)&~humble(fred)))<=>((kind(mary)<~>~calm(mary))))&
((?[X]:((~patient(X)&~quiet(X))))=>((funny(fred)<~>~funny(fred))))&
(![X]:(kind(X)<=>(curious(X)&brave(X))))&
((~kind(john)<~>humble(john)))&
((happy(mary)<~>~happy(mary)))&
(tall(paul))&
(~calm(alice))&
(tall(lucy))&
(patient(susan)) | curious(fred) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 5523707880512920324170417
% SZS output start Proof for 5523707880512920324170417
5. ! [X0] : ((~rich(X0) | rich(X0)) => (generous(X0) & curious(X0))) [input p4]
22. ~curious(fred) [input hypothesis]
27. ! [X0] : ((generous(X0) & curious(X0)) | (rich(X0) & ~rich(X0))) [ennf transformation 5]
82. curious(X0) | ~rich(X0) [cnf transformation 27]
83. curious(X0) | rich(X0) [cnf transformation 27]
126. ~curious(fred) [cnf transformation 22]
218. curious(X0) [subsumption resolution 82,83]
298. $false [subsumption resolution 126,218]
% SZS output end Proof for 5523707880512920324170417
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or quiet is not brave. If lucy is not curious then someone is both not old and not funny and vice versa. If alice is either not humble or tall then paul is both strong and not tall and vice versa. Everyone who is calm is old and vice versa. If susan is not creative then someone is kind and vice versa. Everyone who is either not tall or not quiet is brave and vice versa. Everyone who is either not wise or creative is either patient or creative. Everyone who is either not strong or not old is both not calm and not patient. If someone is both humble and not creative then someone is not old or not humble. Everyone who is either not humble or not kind is both not wise and not patient and vice versa. Everyone who is not kind or curious is either humble or not brave and vice versa. If someone is both strong and tall then paul is funny and vice versa. If paul is both generous and quiet then someone is wise and vice versa. If someone is not calm or quiet then someone is not tall or generous and vice versa. Everyone who is both patient and not funny is both not patient and not happy and vice versa. Everyone who is not curious or tall is both not quiet and not tall. Fred is either curious or not wise. Fred is generous. Someone is either patient or creative. Someone is either not kind or not quiet. Someone is quiet or generous. John is both not kind and funny. | Paul is brave. | contradiction | (![X]:((tall(X)<~>quiet(X))=>~brave(X)))&
((~curious(lucy))<=>(?[X]:((~old(X)&~funny(X)))))&
(((~humble(alice)<~>tall(alice)))<=>((strong(paul)&~tall(paul))))&
(![X]:(calm(X)<=>old(X)))&
((~creative(susan))<=>(?[X]:(kind(X))))&
(![X]:((~tall(X)<~>~quiet(X))<=>brave(X)))&
(![X]:((~wise(X)<~>creative(X))=>(patient(X)<~>creative(X))))&
(![X]:((~strong(X)<~>~old(X))=>(~calm(X)&~patient(X))))&
((?[X]:((humble(X)&~creative(X))))=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:((~humble(X)<~>~kind(X))<=>(~wise(X)&~patient(X))))&
(![X]:((~kind(X)|curious(X))<=>(humble(X)<~>~brave(X))))&
((?[X]:((strong(X)&tall(X))))<=>(funny(paul)))&
(((generous(paul)&quiet(paul)))<=>(?[X]:(wise(X))))&
((?[X]:((~calm(X)|quiet(X))))<=>(?[X]:((~tall(X)|generous(X)))))&
(![X]:((patient(X)&~funny(X))<=>(~patient(X)&~happy(X))))&
(![X]:((~curious(X)|tall(X))=>(~quiet(X)&~tall(X))))&
((curious(fred)<~>~wise(fred)))&
(generous(fred))&
(?[X]:((patient(X)<~>creative(X))))&
(?[X]:((~kind(X)<~>~quiet(X))))&
(?[X]:((quiet(X)|generous(X))))&
((~kind(john)&funny(john))) | brave(paul) | [
"p0",
"p5",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4755099646953195386360187
% SZS output start Proof for 4755099646953195386360187
1. ! [X0] : ((tall(X0) <~> quiet(X0)) => ~brave(X0)) [input p0]
6. ! [X0] : ((~tall(X0) <~> ~quiet(X0)) <=> brave(X0)) [input p5]
16. ! [X0] : ((tall(X0) | ~curious(X0)) => (~tall(X0) & ~quiet(X0))) [input p15]
23. brave(paul) [input hypothesis]
26. ! [X0] : (~brave(X0) | (tall(X0) <=> quiet(X0))) [ennf transformation 1]
30. ! [X0] : ((~tall(X0) & ~quiet(X0)) | (~tall(X0) & curious(X0))) [ennf transformation 16]
31. ! [X0] : (~brave(X0) | ((tall(X0) | ~quiet(X0)) & (quiet(X0) | ~tall(X0)))) [nnf transformation 26]
43. ! [X0] : ((((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | ~brave(X0)) & (brave(X0) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0))))) [nnf transformation 6]
79. ~brave(X0) | tall(X0) | ~quiet(X0) [cnf transformation 31]
96. quiet(X0) | tall(X0) | ~brave(X0) [cnf transformation 43]
135. ~tall(X0) | ~tall(X0) [cnf transformation 30]
146. brave(paul) [cnf transformation 23]
147. ~tall(X0) [duplicate literal removal 135]
205. ~brave(X0) | tall(X0) [subsumption resolution 96,79]
335. tall(paul) [resolution 205,146]
336. $false [subsumption resolution 335,147]
% SZS output end Proof for 4755099646953195386360187
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is either curious or not creative then someone is not wise and vice versa. Everyone who is old is kind or not quiet. If mary is old then someone is wise or rich and vice versa. Everyone who is wise is both curious and quiet and vice versa. If lucy is either funny or not strong then someone is both kind and strong and vice versa. If someone is both wise and not brave then someone is both not brave and not wise. If someone is not wise then someone is both tall and quiet. If someone is tall then susan is both calm and not generous. Everyone who is humble is not calm and vice versa. If someone is rich or old then john is both not humble and not calm and vice versa. Everyone who is both not strong and not tall is humble or not quiet. Everyone who is both strong and not calm is either quiet or kind and vice versa. If someone is both not creative and not rich then someone is both not kind and funny and vice versa. Everyone who is humble or not tall is either not brave or not curious. Everyone who is either not quiet or not wise is either happy or not curious and vice versa. If someone is not happy or not strong then someone is not patient and vice versa. Someone is both generous and not curious. Someone is either not generous or not creative. Someone is rich or curious. Someone is both not curious and not creative. Someone is not happy. Mary is both not kind and not curious. | John is wise. | contradiction | (((curious(susan)<~>~creative(susan)))<=>(?[X]:(~wise(X))))&
(![X]:(old(X)=>(kind(X)|~quiet(X))))&
((old(mary))<=>(?[X]:((wise(X)|rich(X)))))&
(![X]:(wise(X)<=>(curious(X)&quiet(X))))&
(((funny(lucy)<~>~strong(lucy)))<=>(?[X]:((kind(X)&strong(X)))))&
((?[X]:((wise(X)&~brave(X))))=>(?[X]:((~brave(X)&~wise(X)))))&
((?[X]:(~wise(X)))=>(?[X]:((tall(X)&quiet(X)))))&
((?[X]:(tall(X)))=>((calm(susan)&~generous(susan))))&
(![X]:(humble(X)<=>~calm(X)))&
((?[X]:((rich(X)|old(X))))<=>((~humble(john)&~calm(john))))&
(![X]:((~strong(X)&~tall(X))=>(humble(X)|~quiet(X))))&
(![X]:((strong(X)&~calm(X))<=>(quiet(X)<~>kind(X))))&
((?[X]:((~creative(X)&~rich(X))))<=>(?[X]:((~kind(X)&funny(X)))))&
(![X]:((humble(X)|~tall(X))=>(~brave(X)<~>~curious(X))))&
(![X]:((~quiet(X)<~>~wise(X))<=>(happy(X)<~>~curious(X))))&
((?[X]:((~happy(X)|~strong(X))))<=>(?[X]:(~patient(X))))&
(?[X]:((generous(X)&~curious(X))))&
(?[X]:((~generous(X)<~>~creative(X))))&
(?[X]:((rich(X)|curious(X))))&
(?[X]:((~curious(X)&~creative(X))))&
(?[X]:(~happy(X)))&
((~kind(mary)&~curious(mary))) | wise(john) | [
"p2",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5496732054862092661632251
% SZS output start Proof for 5496732054862092661632251
3. old(mary) <=> ? [X0] : (rich(X0) | wise(X0)) [input p2]
9. ! [X0] : (humble(X0) <=> ~calm(X0)) [input p8]
10. ? [X0] : (old(X0) | rich(X0)) <=> (~calm(john) & ~humble(john)) [input p9]
23. wise(john) [input hypothesis]
40. (old(mary) | ! [X0] : (~rich(X0) & ~wise(X0))) & (? [X0] : (rich(X0) | wise(X0)) | ~old(mary)) [nnf transformation 3]
41. (old(mary) | ! [X0] : (~rich(X0) & ~wise(X0))) & (? [X1] : (rich(X1) | wise(X1)) | ~old(mary)) [rectify 40]
42. ? [X1] : (rich(X1) | wise(X1)) => (rich(sK1) | wise(sK1)) [choice axiom]
43. (old(mary) | ! [X0] : (~rich(X0) & ~wise(X0))) & ((rich(sK1) | wise(sK1)) | ~old(mary)) [skolemisation 41,42]
56. ! [X0] : ((humble(X0) | calm(X0)) & (~calm(X0) | ~humble(X0))) [nnf transformation 9]
57. (? [X0] : (old(X0) | rich(X0)) | (calm(john) | humble(john))) & ((~calm(john) & ~humble(john)) | ! [X0] : (~old(X0) & ~rich(X0))) [nnf transformation 10]
58. (? [X0] : (old(X0) | rich(X0)) | calm(john) | humble(john)) & ((~calm(john) & ~humble(john)) | ! [X0] : (~old(X0) & ~rich(X0))) [flattening 57]
59. (? [X0] : (old(X0) | rich(X0)) | calm(john) | humble(john)) & ((~calm(john) & ~humble(john)) | ! [X1] : (~old(X1) & ~rich(X1))) [rectify 58]
60. ? [X0] : (old(X0) | rich(X0)) => (old(sK5) | rich(sK5)) [choice axiom]
61. ((old(sK5) | rich(sK5)) | calm(john) | humble(john)) & ((~calm(john) & ~humble(john)) | ! [X1] : (~old(X1) & ~rich(X1))) [skolemisation 59,60]
93. old(mary) | ~wise(X0) [cnf transformation 43]
111. humble(X0) | calm(X0) [cnf transformation 56]
113. ~humble(john) | ~old(X1) [cnf transformation 61]
115. ~calm(john) | ~old(X1) [cnf transformation 61]
153. wise(john) [cnf transformation 23]
177. 6 <=> old(mary) [avatar definition]
179. old(mary) <- (6) [avatar component clause 177]
182. 7 <=> ! [X0] : ~wise(X0) [avatar definition]
183. ~wise(X0) <- (7) [avatar component clause 182]
184. 7 | 6 [avatar split clause 93,177,182]
256. 23 <=> ! [X1] : ~old(X1) [avatar definition]
257. ~old(X1) <- (23) [avatar component clause 256]
259. 24 <=> calm(john) [avatar definition]
261. ~calm(john) <- (~24) [avatar component clause 259]
262. 23 | ~24 [avatar split clause 115,259,256]
265. 25 <=> humble(john) [avatar definition]
267. ~humble(john) <- (~25) [avatar component clause 265]
268. 23 | ~25 [avatar split clause 113,265,256]
345. $false <- (7) [resolution 183,153]
346. ~7 [avatar contradiction clause 345]
353. calm(john) <- (~25) [resolution 111,267]
355. $false <- (~24, ~25) [subsumption resolution 353,261]
356. 24 | 25 [avatar contradiction clause 355]
357. $false <- (6, 23) [resolution 257,179]
358. ~6 | ~23 [avatar contradiction clause 357]
359. $false [avatar sat refutation 184,262,268,346,356,358]
% SZS output end Proof for 5496732054862092661632251
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is funny. Everyone who is not patient or calm is not tall and vice versa. If mary is either quiet or not curious then someone is both not kind and not strong. If someone is either not patient or not strong then someone is creative or humble. Everyone who is both quiet and not kind is both calm and happy and vice versa. Everyone who is not happy or happy is both not wise and not brave and vice versa. Everyone who is both not strong and kind is both not kind and rich. Everyone who is either happy or not old is both quiet and not humble and vice versa. Everyone who is either rich or quiet is both not rich and curious. Everyone who is both not curious and kind is both not wise and not creative. Everyone who is happy or curious is either kind or not brave. If someone is not quiet or not rich then someone is both quiet and creative and vice versa. Everyone who is not creative is either funny or calm. If alice is not tall or old then someone is either brave or not creative. Everyone who is kind is both funny and not happy. If mary is brave or quiet then john is calm or not generous and vice versa. Someone is not happy or not calm. Someone is not calm or not strong. Someone is not happy. Someone is both not wise and not brave. Mary is either not patient or creative. Someone is both curious and not humble. Someone is both quiet and not happy. Susan is either not happy or not calm. | Mary is not brave. | entailment | (![X]:(~generous(X)=>funny(X)))&
(![X]:((~patient(X)|calm(X))<=>~tall(X)))&
(((quiet(mary)<~>~curious(mary)))=>(?[X]:((~kind(X)&~strong(X)))))&
((?[X]:((~patient(X)<~>~strong(X))))=>(?[X]:((creative(X)|humble(X)))))&
(![X]:((quiet(X)&~kind(X))<=>(calm(X)&happy(X))))&
(![X]:((~happy(X)|happy(X))<=>(~wise(X)&~brave(X))))&
(![X]:((~strong(X)&kind(X))=>(~kind(X)&rich(X))))&
(![X]:((happy(X)<~>~old(X))<=>(quiet(X)&~humble(X))))&
(![X]:((rich(X)<~>quiet(X))=>(~rich(X)&curious(X))))&
(![X]:((~curious(X)&kind(X))=>(~wise(X)&~creative(X))))&
(![X]:((happy(X)|curious(X))=>(kind(X)<~>~brave(X))))&
((?[X]:((~quiet(X)|~rich(X))))<=>(?[X]:((quiet(X)&creative(X)))))&
(![X]:(~creative(X)=>(funny(X)<~>calm(X))))&
(((~tall(alice)|old(alice)))=>(?[X]:((brave(X)<~>~creative(X)))))&
(![X]:(kind(X)=>(funny(X)&~happy(X))))&
(((brave(mary)|quiet(mary)))<=>((calm(john)|~generous(john))))&
(?[X]:((~happy(X)|~calm(X))))&
(?[X]:((~calm(X)|~strong(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~wise(X)&~brave(X))))&
((~patient(mary)<~>creative(mary)))&
(?[X]:((curious(X)&~humble(X))))&
(?[X]:((quiet(X)&~happy(X))))&
((~happy(susan)<~>~calm(susan))) | ~brave(mary) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 8763036771421377264615299
% SZS output start Proof for 8763036771421377264615299
6. ! [X0] : ((happy(X0) | ~happy(X0)) <=> (~brave(X0) & ~wise(X0))) [input p5]
25. brave(mary) [input hypothesis]
51. ! [X0] : (((happy(X0) | ~happy(X0)) | (brave(X0) | wise(X0))) & ((~brave(X0) & ~wise(X0)) | (~happy(X0) & happy(X0)))) [nnf transformation 6]
52. ! [X0] : ((happy(X0) | ~happy(X0) | brave(X0) | wise(X0)) & ((~brave(X0) & ~wise(X0)) | (~happy(X0) & happy(X0)))) [flattening 51]
97. ~brave(X0) | happy(X0) [cnf transformation 52]
98. ~brave(X0) | ~happy(X0) [cnf transformation 52]
148. brave(mary) [cnf transformation 25]
187. ~brave(X0) [subsumption resolution 97,98]
285. $false [subsumption resolution 148,187]
% SZS output end Proof for 8763036771421377264615299
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or calm is not patient or not old and vice versa. Everyone who is either not strong or not creative is not brave and vice versa. Everyone who is both not rich and not tall is either happy or brave. If someone is both not humble and calm then someone is either not strong or not brave and vice versa. If someone is both funny and not patient then someone is both not calm and brave. Everyone who is either not patient or not tall is either strong or not patient and vice versa. If lucy is not quiet or wise then someone is either not rich or not tall and vice versa. Everyone who is curious is either not wise or not curious and vice versa. If someone is tall or calm then someone is calm. Everyone who is not tall or not generous is either rich or not patient and vice versa. If john is either not quiet or rich then susan is funny and vice versa. If someone is not tall or rich then someone is wise. If someone is not generous or calm then alice is both not strong and patient. Everyone who is not wise is both not happy and not humble. If someone is either patient or calm then someone is either happy or brave and vice versa. Everyone who is either not curious or not rich is not humble or not brave. Someone is not happy. John is either not calm or not humble. Paul is either not creative or not wise. Paul is quiet. John is not generous or not brave. Paul is both not strong and not funny. Lucy is both calm and curious. | Lucy is brave. | neutral | (![X]:((brave(X)|calm(X))<=>(~patient(X)|~old(X))))&
(![X]:((~strong(X)<~>~creative(X))<=>~brave(X)))&
(![X]:((~rich(X)&~tall(X))=>(happy(X)<~>brave(X))))&
((?[X]:((~humble(X)&calm(X))))<=>(?[X]:((~strong(X)<~>~brave(X)))))&
((?[X]:((funny(X)&~patient(X))))=>(?[X]:((~calm(X)&brave(X)))))&
(![X]:((~patient(X)<~>~tall(X))<=>(strong(X)<~>~patient(X))))&
(((~quiet(lucy)|wise(lucy)))<=>(?[X]:((~rich(X)<~>~tall(X)))))&
(![X]:(curious(X)<=>(~wise(X)<~>~curious(X))))&
((?[X]:((tall(X)|calm(X))))=>(?[X]:(calm(X))))&
(![X]:((~tall(X)|~generous(X))<=>(rich(X)<~>~patient(X))))&
(((~quiet(john)<~>rich(john)))<=>(funny(susan)))&
((?[X]:((~tall(X)|rich(X))))=>(?[X]:(wise(X))))&
((?[X]:((~generous(X)|calm(X))))=>((~strong(alice)&patient(alice))))&
(![X]:(~wise(X)=>(~happy(X)&~humble(X))))&
((?[X]:((patient(X)<~>calm(X))))<=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:((~curious(X)<~>~rich(X))=>(~humble(X)|~brave(X))))&
(?[X]:(~happy(X)))&
((~calm(john)<~>~humble(john)))&
((~creative(paul)<~>~wise(paul)))&
(quiet(paul))&
((~generous(john)|~brave(john)))&
((~strong(paul)&~funny(paul)))&
((calm(lucy)&curious(lucy))) | brave(lucy) | [] | null | 0 |
Everyone who is creative or tall is both funny and not funny. Everyone who is not strong or not generous is rich. Everyone who is not humble is both brave and not tall and vice versa. Everyone who is either happy or not quiet is not brave or calm and vice versa. Everyone who is not calm is both not curious and patient and vice versa. Everyone who is both curious and not generous is both not wise and not kind and vice versa. If someone is both not calm and wise then someone is not brave. Everyone who is not quiet is kind and vice versa. If susan is both not kind and calm then john is both tall and funny. If alice is strong then alice is both not old and not curious and vice versa. If alice is not curious then alice is either curious or not quiet and vice versa. If alice is either not happy or humble then mary is either rich or not strong. If someone is calm then someone is creative. Everyone who is both not brave and not rich is both not creative and not old and vice versa. Everyone who is both creative and not calm is not old or not happy and vice versa. Someone is generous. Someone is generous or not happy. Someone is either not curious or wise. Someone is quiet or not rich. Susan is not brave or not rich. | Alice is humble. | contradiction | (![X]:((creative(X)|tall(X))=>(funny(X)&~funny(X))))&
(![X]:((~strong(X)|~generous(X))=>rich(X)))&
(![X]:(~humble(X)<=>(brave(X)&~tall(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>(~brave(X)|calm(X))))&
(![X]:(~calm(X)<=>(~curious(X)&patient(X))))&
(![X]:((curious(X)&~generous(X))<=>(~wise(X)&~kind(X))))&
((?[X]:((~calm(X)&wise(X))))=>(?[X]:(~brave(X))))&
(![X]:(~quiet(X)<=>kind(X)))&
(((~kind(susan)&calm(susan)))=>((tall(john)&funny(john))))&
((strong(alice))<=>((~old(alice)&~curious(alice))))&
((~curious(alice))<=>((curious(alice)<~>~quiet(alice))))&
(((~happy(alice)<~>humble(alice)))=>((rich(mary)<~>~strong(mary))))&
((?[X]:(calm(X)))=>(?[X]:(creative(X))))&
(![X]:((~brave(X)&~rich(X))<=>(~creative(X)&~old(X))))&
(![X]:((creative(X)&~calm(X))<=>(~old(X)|~happy(X))))&
(?[X]:(generous(X)))&
(?[X]:((generous(X)|~happy(X))))&
(?[X]:((~curious(X)<~>wise(X))))&
(?[X]:((quiet(X)|~rich(X))))&
((~brave(susan)|~rich(susan))) | humble(alice) | [
"p0",
"p2",
"p3",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1916204309401519908613238
% SZS output start Proof for 1916204309401519908613238
1. ! [X0] : ((tall(X0) | creative(X0)) => (~funny(X0) & funny(X0))) [input p0]
3. ! [X0] : (~humble(X0) <=> (~tall(X0) & brave(X0))) [input p2]
4. ! [X0] : ((happy(X0) <~> ~quiet(X0)) <=> (calm(X0) | ~brave(X0))) [input p3]
11. ~curious(alice) <=> (curious(alice) <~> ~quiet(alice)) [input p10]
15. ! [X0] : ((~calm(X0) & creative(X0)) <=> (~happy(X0) | ~old(X0))) [input p14]
21. humble(alice) [input hypothesis]
24. ! [X0] : ((~funny(X0) & funny(X0)) | (~tall(X0) & ~creative(X0))) [ennf transformation 1]
31. ! [X0] : ((~humble(X0) | (tall(X0) | ~brave(X0))) & ((~tall(X0) & brave(X0)) | humble(X0))) [nnf transformation 3]
32. ! [X0] : ((~humble(X0) | tall(X0) | ~brave(X0)) & ((~tall(X0) & brave(X0)) | humble(X0))) [flattening 31]
33. ! [X0] : ((((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | (~calm(X0) & brave(X0))) & ((calm(X0) | ~brave(X0)) | ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0))))) [nnf transformation 4]
34. ! [X0] : ((((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | (~calm(X0) & brave(X0))) & (calm(X0) | ~brave(X0) | ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0))))) [flattening 33]
45. (~curious(alice) | ((curious(alice) | quiet(alice)) & (~quiet(alice) | ~curious(alice)))) & (((quiet(alice) | ~curious(alice)) & (~quiet(alice) | curious(alice))) | curious(alice)) [nnf transformation 11]
52. ! [X0] : (((~calm(X0) & creative(X0)) | (happy(X0) & old(X0))) & ((~happy(X0) | ~old(X0)) | (calm(X0) | ~creative(X0)))) [nnf transformation 15]
53. ! [X0] : (((~calm(X0) & creative(X0)) | (happy(X0) & old(X0))) & (~happy(X0) | ~old(X0) | calm(X0) | ~creative(X0))) [flattening 52]
63. funny(X0) | ~creative(X0) [cnf transformation 24]
64. funny(X0) | ~tall(X0) [cnf transformation 24]
65. ~funny(X0) | ~creative(X0) [cnf transformation 24]
66. ~funny(X0) | ~tall(X0) [cnf transformation 24]
71. ~humble(X0) | tall(X0) | ~brave(X0) [cnf transformation 32]
76. ~happy(X0) | quiet(X0) | brave(X0) [cnf transformation 34]
93. ~quiet(alice) | curious(alice) | curious(alice) [cnf transformation 45]
95. ~curious(alice) | ~quiet(alice) | ~curious(alice) [cnf transformation 45]
108. creative(X0) | happy(X0) [cnf transformation 53]
117. humble(alice) [cnf transformation 21]
118. ~quiet(alice) | curious(alice) [duplicate literal removal 93]
119. ~curious(alice) | ~quiet(alice) [duplicate literal removal 95]
120. ~tall(X0) [subsumption resolution 64,66]
121. ~creative(X0) [subsumption resolution 63,65]
122. ~brave(X0) | ~humble(X0) [subsumption resolution 71,120]
151. 7 <=> curious(alice) [avatar definition]
162. 9 <=> quiet(alice) [avatar definition]
164. ~quiet(alice) <- (~9) [avatar component clause 162]
165. ~9 | ~7 [avatar split clause 119,151,162]
166. 7 | ~9 [avatar split clause 118,162,151]
169. 10 <=> humble(alice) [avatar definition]
170. humble(alice) <- (10) [avatar component clause 169]
194. happy(X0) [subsumption resolution 108,121]
225. 10 [avatar split clause 117,169]
239. quiet(X0) | brave(X0) [resolution 76,194]
240. brave(alice) <- (~9) [resolution 239,164]
244. ~humble(alice) <- (~9) [resolution 240,122]
245. $false <- (~9, 10) [subsumption resolution 244,170]
246. 9 | ~10 [avatar contradiction clause 245]
247. $false [avatar sat refutation 165,166,225,246]
% SZS output end Proof for 1916204309401519908613238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is wise.
Everyone who is not humble is both not humble and happy and vice versa.
If susan is strong or happy then someone is calm.
Everyone who is brave or funny is either kind or not old and vice versa.
Everyone who is not strong or rich is not calm and vice versa.
If someone is either strong or not curious then someone is either not creative or strong and vice versa.
If john is either brave or rich then someone is not humble and vice versa.
If someone is not humble then mary is not funny and vice versa.
Everyone who is either not old or quiet is generous or rich.
If someone is not patient then mary is not wise.
Everyone who is not funny is both calm and wise.
Everyone who is either funny or old is both not curious and not creative.
Everyone who is either curious or not happy is either not tall or not patient.
If lucy is not curious then someone is either generous or not generous.
If someone is either rich or not rich then susan is not patient and vice versa.
Everyone who is not rich or not creative is either not patient or not curious and vice versa.
Mary is both generous and funny.
Someone is both funny and old.
Lucy is not kind or tall.
Paul is kind or not old.
Lucy is both creative and not funny.
Lucy is not rich.
Someone is not patient. | Mary is generous. | entailment | (![X]:(~tall(X)=>wise(X)))&
(![X]:(~humble(X)<=>(~humble(X)&happy(X))))&
(((strong(susan)|happy(susan)))=>(?[X]:(calm(X))))&
(![X]:((brave(X)|funny(X))<=>(kind(X)<~>~old(X))))&
(![X]:((~strong(X)|rich(X))<=>~calm(X)))&
((?[X]:((strong(X)<~>~curious(X))))<=>(?[X]:((~creative(X)<~>strong(X)))))&
(((brave(john)<~>rich(john)))<=>(?[X]:(~humble(X))))&
((?[X]:(~humble(X)))<=>(~funny(mary)))&
(![X]:((~old(X)<~>quiet(X))=>(generous(X)|rich(X))))&
((?[X]:(~patient(X)))=>(~wise(mary)))&
(![X]:(~funny(X)=>(calm(X)&wise(X))))&
(![X]:((funny(X)<~>old(X))=>(~curious(X)&~creative(X))))&
(![X]:((curious(X)<~>~happy(X))=>(~tall(X)<~>~patient(X))))&
((~curious(lucy))=>(?[X]:((generous(X)<~>~generous(X)))))&
((?[X]:((rich(X)<~>~rich(X))))<=>(~patient(susan)))&
(![X]:((~rich(X)|~creative(X))<=>(~patient(X)<~>~curious(X))))&
((generous(mary)&funny(mary)))&
(?[X]:((funny(X)&old(X))))&
((~kind(lucy)|tall(lucy)))&
((kind(paul)|~old(paul)))&
((creative(lucy)&~funny(lucy)))&
(~rich(lucy))&
(?[X]:(~patient(X))) | generous(mary) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 22676622647534663087317
% SZS output start Proof for 22676622647534663087317
17. funny(mary) & generous(mary) [input p16]
24. ~generous(mary) [input hypothesis]
125. generous(mary) [cnf transformation 17]
135. ~generous(mary) [cnf transformation 24]
256. $false [subsumption resolution 135,125]
% SZS output end Proof for 22676622647534663087317
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind or strong then someone is not happy. Everyone who is happy is either not patient or not kind. Everyone who is either happy or not creative is not strong and vice versa. Everyone who is not wise is humble and vice versa. Everyone who is either generous or wise is either not strong or not kind. Everyone who is both kind and rich is either not old or kind and vice versa. If someone is either not strong or generous then someone is both not brave and humble and vice versa. Everyone who is either not happy or not humble is either not generous or not old and vice versa. If mary is both not strong and humble then someone is either not quiet or not happy. If susan is wise or patient then lucy is not tall or humble and vice versa. If someone is funny or old then someone is both patient and quiet and vice versa. If someone is either not rich or not wise then susan is not humble or not generous. Everyone who is creative or not tall is old or curious and vice versa. If someone is either funny or not brave then mary is either funny or not brave. If someone is patient then someone is happy and vice versa. If someone is both strong and old then susan is calm and vice versa. Mary is either not creative or curious. John is both not strong and old. Someone is tall or not happy. John is both tall and not strong. Someone is either not strong or not funny. Paul is tall or not kind. Susan is creative or not calm. Someone is generous or curious. | John is not kind. | contradiction | ((?[X]:((kind(X)|strong(X))))=>(?[X]:(~happy(X))))&
(![X]:(happy(X)=>(~patient(X)<~>~kind(X))))&
(![X]:((happy(X)<~>~creative(X))<=>~strong(X)))&
(![X]:(~wise(X)<=>humble(X)))&
(![X]:((generous(X)<~>wise(X))=>(~strong(X)<~>~kind(X))))&
(![X]:((kind(X)&rich(X))<=>(~old(X)<~>kind(X))))&
((?[X]:((~strong(X)<~>generous(X))))<=>(?[X]:((~brave(X)&humble(X)))))&
(![X]:((~happy(X)<~>~humble(X))<=>(~generous(X)<~>~old(X))))&
(((~strong(mary)&humble(mary)))=>(?[X]:((~quiet(X)<~>~happy(X)))))&
(((wise(susan)|patient(susan)))<=>((~tall(lucy)|humble(lucy))))&
((?[X]:((funny(X)|old(X))))<=>(?[X]:((patient(X)&quiet(X)))))&
((?[X]:((~rich(X)<~>~wise(X))))=>((~humble(susan)|~generous(susan))))&
(![X]:((creative(X)|~tall(X))<=>(old(X)|curious(X))))&
((?[X]:((funny(X)<~>~brave(X))))=>((funny(mary)<~>~brave(mary))))&
((?[X]:(patient(X)))<=>(?[X]:(happy(X))))&
((?[X]:((strong(X)&old(X))))<=>(calm(susan)))&
((~creative(mary)<~>curious(mary)))&
((~strong(john)&old(john)))&
(?[X]:((tall(X)|~happy(X))))&
((tall(john)&~strong(john)))&
(?[X]:((~strong(X)<~>~funny(X))))&
((tall(paul)|~kind(paul)))&
((creative(susan)|~calm(susan)))&
(?[X]:((generous(X)|curious(X)))) | ~kind(john) | [
"p2",
"p3",
"p4",
"p7",
"p12",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 50880502233013950308535
% SZS output start Proof for 50880502233013950308535
3. ! [X0] : ((happy(X0) <~> ~creative(X0)) <=> ~strong(X0)) [input p2]
4. ! [X0] : (~wise(X0) <=> humble(X0)) [input p3]
5. ! [X0] : ((generous(X0) <~> wise(X0)) => (~strong(X0) <~> ~kind(X0))) [input p4]
8. ! [X0] : ((~happy(X0) <~> ~humble(X0)) <=> (~generous(X0) <~> ~old(X0))) [input p7]
13. ! [X0] : ((~tall(X0) | creative(X0)) <=> (curious(X0) | old(X0))) [input p12]
18. old(john) & ~strong(john) [input p17]
20. ~strong(john) & tall(john) [input p19]
25. ~kind(john) [input hypothesis]
32. ! [X0] : ((~strong(X0) <~> ~kind(X0)) | (generous(X0) <=> wise(X0))) [ennf transformation 5]
42. ! [X0] : ((((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | strong(X0)) & (~strong(X0) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0))))) [nnf transformation 3]
43. ! [X0] : ((~wise(X0) | ~humble(X0)) & (humble(X0) | wise(X0))) [nnf transformation 4]
44. ! [X0] : (((kind(X0) | strong(X0)) & (~kind(X0) | ~strong(X0))) | ((generous(X0) | ~wise(X0)) & (wise(X0) | ~generous(X0)))) [nnf transformation 32]
52. ! [X0] : ((((humble(X0) | happy(X0)) & (~humble(X0) | ~happy(X0))) | ((~generous(X0) | old(X0)) & (~old(X0) | generous(X0)))) & (((old(X0) | generous(X0)) & (~old(X0) | ~generous(X0))) | ((~happy(X0) | humble(X0)) & (~humble(X0) | happy(X0))))) [nnf transformation 8]
64. ! [X0] : (((~tall(X0) | creative(X0)) | (~curious(X0) & ~old(X0))) & ((curious(X0) | old(X0)) | (tall(X0) & ~creative(X0)))) [nnf transformation 13]
65. ! [X0] : ((~tall(X0) | creative(X0) | (~curious(X0) & ~old(X0))) & (curious(X0) | old(X0) | (tall(X0) & ~creative(X0)))) [flattening 64]
90. ~creative(X0) | happy(X0) | strong(X0) [cnf transformation 42]
92. humble(X0) | wise(X0) [cnf transformation 43]
93. ~humble(X0) | ~wise(X0) [cnf transformation 43]
96. ~generous(X0) | strong(X0) | wise(X0) | kind(X0) [cnf transformation 44]
97. ~wise(X0) | strong(X0) | generous(X0) | kind(X0) [cnf transformation 44]
111. ~old(X0) | ~generous(X0) | ~happy(X0) | humble(X0) [cnf transformation 52]
114. ~old(X0) | ~happy(X0) | ~humble(X0) | generous(X0) [cnf transformation 52]
133. ~tall(X0) | creative(X0) | ~old(X0) [cnf transformation 65]
146. ~strong(john) [cnf transformation 18]
147. old(john) [cnf transformation 18]
149. tall(john) [cnf transformation 20]
156. ~kind(john) [cnf transformation 25]
499. creative(john) | ~old(john) [resolution 133,149]
500. creative(john) [subsumption resolution 499,147]
504. happy(john) | strong(john) [resolution 500,90]
506. happy(john) [subsumption resolution 504,146]
573. ~generous(john) | ~happy(john) | humble(john) [resolution 111,147]
577. ~generous(john) | humble(john) [subsumption resolution 573,506]
579. 78 <=> humble(john) [avatar definition]
580. ~humble(john) <- (~78) [avatar component clause 579]
581. humble(john) <- (78) [avatar component clause 579]
583. 79 <=> generous(john) [avatar definition]
584. generous(john) <- (79) [avatar component clause 583]
585. ~generous(john) <- (~79) [avatar component clause 583]
586. 78 | ~79 [avatar split clause 577,583,579]
631. ~wise(john) <- (78) [resolution 581,93]
647. strong(john) | wise(john) | kind(john) <- (79) [resolution 584,96]
649. ~happy(john) | ~humble(john) | generous(john) [resolution 114,147]
1001. wise(john) | kind(john) <- (79) [subsumption resolution 647,146]
1002. kind(john) <- (78, 79) [subsumption resolution 1001,631]
1003. $false <- (78, 79) [subsumption resolution 1002,156]
1004. ~78 | ~79 [avatar contradiction clause 1003]
1014. ~humble(john) | generous(john) [subsumption resolution 649,506]
1017. ~humble(john) <- (~79) [subsumption resolution 1014,585]
1018. ~78 | 79 [avatar split clause 1017,583,579]
1081. wise(john) <- (~78) [resolution 580,92]
1196. strong(john) | generous(john) | kind(john) <- (~78) [resolution 1081,97]
1198. generous(john) | kind(john) <- (~78) [subsumption resolution 1196,146]
1199. kind(john) <- (~78, ~79) [subsumption resolution 1198,585]
1200. $false <- (~78, ~79) [subsumption resolution 1199,156]
1201. 78 | 79 [avatar contradiction clause 1200]
1202. $false [avatar sat refutation 586,1004,1018,1201]
% SZS output end Proof for 50880502233013950308535
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5628
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not tall or not quiet then mary is either not patient or not creative.
Everyone who is both not funny and not strong is not calm and vice versa.
Everyone who is either rich or not happy is not patient or not humble and vice versa.
If susan is quiet or wise then susan is either quiet or rich and vice versa.
If someone is not calm then someone is not brave.
Everyone who is both creative and not humble is not old.
If paul is both kind and not humble then someone is not patient.
If lucy is both not generous and funny then someone is either not happy or curious and vice versa.
If someone is either not calm or not patient then lucy is both strong and funny and vice versa.
If someone is not brave then lucy is either not old or not tall and vice versa.
If someone is not kind or old then someone is humble or not old and vice versa.
Everyone who is either not curious or humble is not happy or not quiet.
Everyone who is not patient is patient or not patient.
Everyone who is not happy or not rich is both not happy and not calm.
Everyone who is either generous or happy is both not wise and not humble.
Everyone who is not curious is either not quiet or not humble.
Fred is both not funny and kind.
Mary is either not humble or calm.
Someone is not funny.
Mary is either curious or kind.
Lucy is not generous or kind.
Mary is not wise or kind.
Someone is quiet or not wise. | Susan is funny. | neutral | (((~tall(alice)|~quiet(alice)))=>((~patient(mary)<~>~creative(mary))))&
(![X]:((~funny(X)&~strong(X))<=>~calm(X)))&
(![X]:((rich(X)<~>~happy(X))<=>(~patient(X)|~humble(X))))&
(((quiet(susan)|wise(susan)))<=>((quiet(susan)<~>rich(susan))))&
((?[X]:(~calm(X)))=>(?[X]:(~brave(X))))&
(![X]:((creative(X)&~humble(X))=>~old(X)))&
(((kind(paul)&~humble(paul)))=>(?[X]:(~patient(X))))&
(((~generous(lucy)&funny(lucy)))<=>(?[X]:((~happy(X)<~>curious(X)))))&
((?[X]:((~calm(X)<~>~patient(X))))<=>((strong(lucy)&funny(lucy))))&
((?[X]:(~brave(X)))<=>((~old(lucy)<~>~tall(lucy))))&
((?[X]:((~kind(X)|old(X))))<=>(?[X]:((humble(X)|~old(X)))))&
(![X]:((~curious(X)<~>humble(X))=>(~happy(X)|~quiet(X))))&
(![X]:(~patient(X)=>(patient(X)|~patient(X))))&
(![X]:((~happy(X)|~rich(X))=>(~happy(X)&~calm(X))))&
(![X]:((generous(X)<~>happy(X))=>(~wise(X)&~humble(X))))&
(![X]:(~curious(X)=>(~quiet(X)<~>~humble(X))))&
((~funny(fred)&kind(fred)))&
((~humble(mary)<~>calm(mary)))&
(?[X]:(~funny(X)))&
((curious(mary)<~>kind(mary)))&
((~generous(lucy)|kind(lucy)))&
((~wise(mary)|kind(mary)))&
(?[X]:((quiet(X)|~wise(X)))) | funny(susan) | [] | null | 0 |
If someone is patient or not old then someone is creative. If someone is either not tall or not brave then john is not funny or funny and vice versa. If someone is both curious and not wise then john is not kind or not generous and vice versa. Everyone who is not curious or curious is brave or not creative and vice versa. If susan is either old or not generous then fred is either not old or tall. If susan is tall then someone is either not wise or not generous. Everyone who is both tall and strong is either tall or not creative. Everyone who is not kind or brave is both brave and humble and vice versa. If paul is not funny or funny then alice is both not strong and curious and vice versa. Everyone who is either not humble or not quiet is both kind and not wise and vice versa. If fred is kind or quiet then someone is happy. Everyone who is both not tall and not generous is either curious or not curious and vice versa. If susan is tall then someone is humble. Everyone who is not strong is tall or not strong. Everyone who is not patient is funny or quiet. Everyone who is old or not happy is creative or calm. Someone is either patient or not calm. Fred is both happy and brave. Lucy is both not creative and curious. Fred is not generous or not kind. Someone is not calm or not strong. John is both rich and not patient. Paul is not rich or not creative. Someone is both funny and not brave. | Lucy is not tall. | entailment | ((?[X]:((patient(X)|~old(X))))=>(?[X]:(creative(X))))&
((?[X]:((~tall(X)<~>~brave(X))))<=>((~funny(john)|funny(john))))&
((?[X]:((curious(X)&~wise(X))))<=>((~kind(john)|~generous(john))))&
(![X]:((~curious(X)|curious(X))<=>(brave(X)|~creative(X))))&
(((old(susan)<~>~generous(susan)))=>((~old(fred)<~>tall(fred))))&
((tall(susan))=>(?[X]:((~wise(X)<~>~generous(X)))))&
(![X]:((tall(X)&strong(X))=>(tall(X)<~>~creative(X))))&
(![X]:((~kind(X)|brave(X))<=>(brave(X)&humble(X))))&
(((~funny(paul)|funny(paul)))<=>((~strong(alice)&curious(alice))))&
(![X]:((~humble(X)<~>~quiet(X))<=>(kind(X)&~wise(X))))&
(((kind(fred)|quiet(fred)))=>(?[X]:(happy(X))))&
(![X]:((~tall(X)&~generous(X))<=>(curious(X)<~>~curious(X))))&
((tall(susan))=>(?[X]:(humble(X))))&
(![X]:(~strong(X)=>(tall(X)|~strong(X))))&
(![X]:(~patient(X)=>(funny(X)|quiet(X))))&
(![X]:((old(X)|~happy(X))=>(creative(X)|calm(X))))&
(?[X]:((patient(X)<~>~calm(X))))&
((happy(fred)&brave(fred)))&
((~creative(lucy)&curious(lucy)))&
((~generous(fred)|~kind(fred)))&
(?[X]:((~calm(X)|~strong(X))))&
((rich(john)&~patient(john)))&
((~rich(paul)|~creative(paul)))&
(?[X]:((funny(X)&~brave(X)))) | ~tall(lucy) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 650074687010391355945355
% SZS output start Proof for 650074687010391355945355
12. ! [X0] : ((~generous(X0) & ~tall(X0)) <=> (curious(X0) <~> ~curious(X0))) [input p11]
25. tall(lucy) [input hypothesis]
68. ! [X0] : (((~generous(X0) & ~tall(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | (generous(X0) | tall(X0)))) [nnf transformation 12]
69. ! [X0] : (((~generous(X0) & ~tall(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | generous(X0) | tall(X0))) [flattening 68]
122. ~tall(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 69]
123. ~tall(X0) | curious(X0) | curious(X0) [cnf transformation 69]
142. tall(lucy) [cnf transformation 25]
143. ~tall(X0) | ~curious(X0) [duplicate literal removal 122]
144. ~tall(X0) | curious(X0) [duplicate literal removal 123]
254. ~tall(X0) [subsumption resolution 143,144]
283. $false [subsumption resolution 142,254]
% SZS output end Proof for 650074687010391355945355
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and not quiet is tall. If lucy is both quiet and not wise then someone is not generous. If someone is both humble and calm then someone is not curious and vice versa. If someone is either calm or strong then mary is rich. If john is rich or not funny then someone is either not patient or not old. Everyone who is both happy and not curious is both not generous and patient. If someone is not tall or not generous then someone is not rich and vice versa. Everyone who is either not humble or curious is both creative and happy. If lucy is both calm and not kind then paul is not old or strong. Everyone who is either quiet or not tall is both patient and not tall. Everyone who is not patient or not strong is both tall and not kind and vice versa. Everyone who is not calm or patient is strong. If john is not rich or old then alice is not calm or not creative and vice versa. Everyone who is both not creative and calm is not wise. Everyone who is generous is not tall or humble and vice versa. If mary is happy then someone is both not rich and brave and vice versa. Someone is either generous or wise. Paul is both not tall and quiet. Someone is either brave or not rich. Susan is both calm and not funny. Alice is not strong or curious. Fred is not creative. Mary is not tall or not rich. Someone is both funny and not rich. | John is not generous. | neutral | (![X]:((kind(X)&~quiet(X))=>tall(X)))&
(((quiet(lucy)&~wise(lucy)))=>(?[X]:(~generous(X))))&
((?[X]:((humble(X)&calm(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((calm(X)<~>strong(X))))=>(rich(mary)))&
(((rich(john)|~funny(john)))=>(?[X]:((~patient(X)<~>~old(X)))))&
(![X]:((happy(X)&~curious(X))=>(~generous(X)&patient(X))))&
((?[X]:((~tall(X)|~generous(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~humble(X)<~>curious(X))=>(creative(X)&happy(X))))&
(((calm(lucy)&~kind(lucy)))=>((~old(paul)|strong(paul))))&
(![X]:((quiet(X)<~>~tall(X))=>(patient(X)&~tall(X))))&
(![X]:((~patient(X)|~strong(X))<=>(tall(X)&~kind(X))))&
(![X]:((~calm(X)|patient(X))=>strong(X)))&
(((~rich(john)|old(john)))<=>((~calm(alice)|~creative(alice))))&
(![X]:((~creative(X)&calm(X))=>~wise(X)))&
(![X]:(generous(X)<=>(~tall(X)|humble(X))))&
((happy(mary))<=>(?[X]:((~rich(X)&brave(X)))))&
(?[X]:((generous(X)<~>wise(X))))&
((~tall(paul)&quiet(paul)))&
(?[X]:((brave(X)<~>~rich(X))))&
((calm(susan)&~funny(susan)))&
((~strong(alice)|curious(alice)))&
(~creative(fred))&
((~tall(mary)|~rich(mary)))&
(?[X]:((funny(X)&~rich(X)))) | ~generous(john) | [] | null | 0 |
Everyone who is either wise or brave is either creative or not patient and vice versa.
Everyone who is either not creative or not brave is not creative or happy.
If someone is both creative and not brave then paul is not tall or quiet.
If someone is both kind and quiet then someone is happy.
Everyone who is both not kind and generous is either creative or not humble and vice versa.
Everyone who is both quiet and not humble is patient or not old and vice versa.
Everyone who is calm is either brave or creative.
Everyone who is not wise is both not calm and not curious and vice versa.
Everyone who is funny or not wise is either curious or quiet and vice versa.
If fred is either not rich or old then fred is either strong or rich and vice versa.
Everyone who is funny or not creative is brave.
If mary is both not funny and tall then alice is not patient and vice versa.
If someone is both not brave and not generous then john is not funny or generous.
If susan is not generous or not creative then someone is quiet and vice versa.
Everyone who is quiet or funny is either calm or brave.
If fred is not calm or not tall then susan is not rich and vice versa.
Someone is both not curious and not strong.
Lucy is either not tall or not old.
Lucy is both not patient and happy.
Someone is either humble or not wise.
John is not wise.
Someone is not wise or not strong.
Someone is either not tall or not old.
Lucy is both not quiet and not generous. | Lucy is not brave. | contradiction | (![X]:((wise(X)<~>brave(X))<=>(creative(X)<~>~patient(X))))&
(![X]:((~creative(X)<~>~brave(X))=>(~creative(X)|happy(X))))&
((?[X]:((creative(X)&~brave(X))))=>((~tall(paul)|quiet(paul))))&
((?[X]:((kind(X)&quiet(X))))=>(?[X]:(happy(X))))&
(![X]:((~kind(X)&generous(X))<=>(creative(X)<~>~humble(X))))&
(![X]:((quiet(X)&~humble(X))<=>(patient(X)|~old(X))))&
(![X]:(calm(X)=>(brave(X)<~>creative(X))))&
(![X]:(~wise(X)<=>(~calm(X)&~curious(X))))&
(![X]:((funny(X)|~wise(X))<=>(curious(X)<~>quiet(X))))&
(((~rich(fred)<~>old(fred)))<=>((strong(fred)<~>rich(fred))))&
(![X]:((funny(X)|~creative(X))=>brave(X)))&
(((~funny(mary)&tall(mary)))<=>(~patient(alice)))&
((?[X]:((~brave(X)&~generous(X))))=>((~funny(john)|generous(john))))&
(((~generous(susan)|~creative(susan)))<=>(?[X]:(quiet(X))))&
(![X]:((quiet(X)|funny(X))=>(calm(X)<~>brave(X))))&
(((~calm(fred)|~tall(fred)))<=>(~rich(susan)))&
(?[X]:((~curious(X)&~strong(X))))&
((~tall(lucy)<~>~old(lucy)))&
((~patient(lucy)&happy(lucy)))&
(?[X]:((humble(X)<~>~wise(X))))&
(~wise(john))&
(?[X]:((~wise(X)|~strong(X))))&
(?[X]:((~tall(X)<~>~old(X))))&
((~quiet(lucy)&~generous(lucy))) | ~brave(lucy) | [
"p0",
"p7",
"p8",
"p10",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6711144995048862517554270
% SZS output start Proof for 6711144995048862517554270
1. ! [X0] : ((wise(X0) <~> brave(X0)) <=> (creative(X0) <~> ~patient(X0))) [input p0]
8. ! [X0] : (~wise(X0) <=> (~curious(X0) & ~calm(X0))) [input p7]
9. ! [X0] : ((~wise(X0) | funny(X0)) <=> (curious(X0) <~> quiet(X0))) [input p8]
11. ! [X0] : ((~creative(X0) | funny(X0)) => brave(X0)) [input p10]
15. ! [X0] : ((funny(X0) | quiet(X0)) => (calm(X0) <~> brave(X0))) [input p14]
19. happy(lucy) & ~patient(lucy) [input p18]
25. ~brave(lucy) [input hypothesis]
28. ~patient(lucy) [pure predicate removal 19]
33. ! [X0] : (brave(X0) | (creative(X0) & ~funny(X0))) [ennf transformation 11]
36. ! [X0] : ((calm(X0) <~> brave(X0)) | (~funny(X0) & ~quiet(X0))) [ennf transformation 15]
37. ! [X0] : ((((~brave(X0) | ~wise(X0)) & (brave(X0) | wise(X0))) | ((creative(X0) | patient(X0)) & (~patient(X0) | ~creative(X0)))) & (((patient(X0) | ~creative(X0)) & (~patient(X0) | creative(X0))) | ((wise(X0) | ~brave(X0)) & (brave(X0) | ~wise(X0))))) [nnf transformation 1]
43. ! [X0] : ((~wise(X0) | (curious(X0) | calm(X0))) & ((~curious(X0) & ~calm(X0)) | wise(X0))) [nnf transformation 8]
44. ! [X0] : ((~wise(X0) | curious(X0) | calm(X0)) & ((~curious(X0) & ~calm(X0)) | wise(X0))) [flattening 43]
45. ! [X0] : (((~wise(X0) | funny(X0)) | ((curious(X0) | ~quiet(X0)) & (quiet(X0) | ~curious(X0)))) & (((~quiet(X0) | ~curious(X0)) & (quiet(X0) | curious(X0))) | (wise(X0) & ~funny(X0)))) [nnf transformation 9]
46. ! [X0] : ((~wise(X0) | funny(X0) | ((curious(X0) | ~quiet(X0)) & (quiet(X0) | ~curious(X0)))) & (((~quiet(X0) | ~curious(X0)) & (quiet(X0) | curious(X0))) | (wise(X0) & ~funny(X0)))) [flattening 45]
55. ! [X0] : (((~brave(X0) | ~calm(X0)) & (brave(X0) | calm(X0))) | (~funny(X0) & ~quiet(X0))) [nnf transformation 36]
71. ~creative(X0) | patient(X0) | brave(X0) | ~wise(X0) [cnf transformation 37]
91. ~calm(X0) | wise(X0) [cnf transformation 44]
92. ~curious(X0) | wise(X0) [cnf transformation 44]
95. quiet(X0) | curious(X0) | wise(X0) [cnf transformation 46]
109. creative(X0) | brave(X0) [cnf transformation 33]
117. ~quiet(X0) | calm(X0) | brave(X0) [cnf transformation 55]
128. ~patient(lucy) [cnf transformation 28]
137. ~brave(lucy) [cnf transformation 25]
155. quiet(X0) | wise(X0) [subsumption resolution 95,92]
314. calm(X0) | brave(X0) | wise(X0) [resolution 117,155]
318. brave(X0) | wise(X0) [subsumption resolution 314,91]
355. patient(X0) | brave(X0) | ~wise(X0) | brave(X0) [resolution 71,109]
356. patient(X0) | brave(X0) | ~wise(X0) [duplicate literal removal 355]
357. patient(X0) | brave(X0) [subsumption resolution 356,318]
358. brave(lucy) [resolution 357,128]
364. $false [subsumption resolution 358,137]
% SZS output end Proof for 6711144995048862517554270
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich is both happy and not brave. If alice is both not calm and not strong then someone is wise or patient and vice versa. Everyone who is both not curious and calm is not curious or not wise and vice versa. Everyone who is not brave is either tall or not strong and vice versa. Everyone who is quiet or not patient is creative or tall and vice versa. Everyone who is happy or not quiet is not quiet or old and vice versa. If mary is funny then lucy is either generous or not old and vice versa. If someone is curious or not rich then john is not old or brave. If mary is both not old and curious then john is both tall and not brave. If someone is happy then someone is generous. Everyone who is both not happy and not tall is rich. Everyone who is both calm and not kind is either not brave or not happy. If someone is both not rich and not calm then susan is both old and not curious and vice versa. Everyone who is not funny or wise is rich or calm and vice versa. If john is not brave then someone is both curious and not creative. If someone is both generous and not quiet then john is either old or brave and vice versa. Paul is either not generous or not creative. Susan is calm or not calm. Someone is either curious or not generous. Lucy is not kind. Someone is quiet. Lucy is creative or not quiet. Someone is both not funny and generous. Mary is not happy or patient. | Susan is calm. | neutral | (![X]:(rich(X)=>(happy(X)&~brave(X))))&
(((~calm(alice)&~strong(alice)))<=>(?[X]:((wise(X)|patient(X)))))&
(![X]:((~curious(X)&calm(X))<=>(~curious(X)|~wise(X))))&
(![X]:(~brave(X)<=>(tall(X)<~>~strong(X))))&
(![X]:((quiet(X)|~patient(X))<=>(creative(X)|tall(X))))&
(![X]:((happy(X)|~quiet(X))<=>(~quiet(X)|old(X))))&
((funny(mary))<=>((generous(lucy)<~>~old(lucy))))&
((?[X]:((curious(X)|~rich(X))))=>((~old(john)|brave(john))))&
(((~old(mary)&curious(mary)))=>((tall(john)&~brave(john))))&
((?[X]:(happy(X)))=>(?[X]:(generous(X))))&
(![X]:((~happy(X)&~tall(X))=>rich(X)))&
(![X]:((calm(X)&~kind(X))=>(~brave(X)<~>~happy(X))))&
((?[X]:((~rich(X)&~calm(X))))<=>((old(susan)&~curious(susan))))&
(![X]:((~funny(X)|wise(X))<=>(rich(X)|calm(X))))&
((~brave(john))=>(?[X]:((curious(X)&~creative(X)))))&
((?[X]:((generous(X)&~quiet(X))))<=>((old(john)<~>brave(john))))&
((~generous(paul)<~>~creative(paul)))&
((calm(susan)|~calm(susan)))&
(?[X]:((curious(X)<~>~generous(X))))&
(~kind(lucy))&
(?[X]:(quiet(X)))&
((creative(lucy)|~quiet(lucy)))&
(?[X]:((~funny(X)&generous(X))))&
((~happy(mary)|patient(mary))) | calm(susan) | [] | null | 0 |
Everyone who is strong is generous and vice versa.
If susan is both kind and not wise then someone is not kind and vice versa.
Everyone who is not tall is not quiet and vice versa.
Everyone who is both not funny and not creative is not rich and vice versa.
If someone is both not humble and not strong then someone is either kind or not happy and vice versa.
Everyone who is either creative or not old is both happy and tall.
Everyone who is not strong is kind.
Everyone who is both not creative and humble is either humble or not generous and vice versa.
Everyone who is curious or not rich is old or brave.
Everyone who is wise or not brave is old or not rich and vice versa.
If someone is both not brave and brave then someone is not wise.
If susan is both wise and not funny then fred is brave and vice versa.
Everyone who is both not happy and strong is either wise or tall and vice versa.
If someone is creative then lucy is either happy or not kind and vice versa.
Everyone who is either not tall or funny is either brave or not wise.
If someone is both not happy and not tall then someone is either not happy or strong.
Someone is both not kind and not rich.
Someone is both wise and humble.
Someone is quiet.
Susan is both not rich and not creative.
John is either not brave or happy.
Paul is wise. | Lucy is curious. | neutral | (![X]:(strong(X)<=>generous(X)))&
(((kind(susan)&~wise(susan)))<=>(?[X]:(~kind(X))))&
(![X]:(~tall(X)<=>~quiet(X)))&
(![X]:((~funny(X)&~creative(X))<=>~rich(X)))&
((?[X]:((~humble(X)&~strong(X))))<=>(?[X]:((kind(X)<~>~happy(X)))))&
(![X]:((creative(X)<~>~old(X))=>(happy(X)&tall(X))))&
(![X]:(~strong(X)=>kind(X)))&
(![X]:((~creative(X)&humble(X))<=>(humble(X)<~>~generous(X))))&
(![X]:((curious(X)|~rich(X))=>(old(X)|brave(X))))&
(![X]:((wise(X)|~brave(X))<=>(old(X)|~rich(X))))&
((?[X]:((~brave(X)&brave(X))))=>(?[X]:(~wise(X))))&
(((wise(susan)&~funny(susan)))<=>(brave(fred)))&
(![X]:((~happy(X)&strong(X))<=>(wise(X)<~>tall(X))))&
((?[X]:(creative(X)))<=>((happy(lucy)<~>~kind(lucy))))&
(![X]:((~tall(X)<~>funny(X))=>(brave(X)<~>~wise(X))))&
((?[X]:((~happy(X)&~tall(X))))=>(?[X]:((~happy(X)<~>strong(X)))))&
(?[X]:((~kind(X)&~rich(X))))&
(?[X]:((wise(X)&humble(X))))&
(?[X]:(quiet(X)))&
((~rich(susan)&~creative(susan)))&
((~brave(john)<~>happy(john)))&
(wise(paul)) | curious(lucy) | [] | null | 0 |
Everyone who is either strong or brave is brave or calm. Everyone who is strong is calm. If someone is either not old or wise then mary is both not funny and not humble. If susan is both humble and rich then someone is not curious or generous. Everyone who is both not generous and not humble is brave or not patient. If john is both not humble and not wise then fred is either tall or not old. If fred is either not wise or not rich then someone is either old or not kind. If someone is creative or not humble then mary is rich. Everyone who is either humble or wise is both patient and wise and vice versa. Everyone who is not tall is both not generous and old. If alice is patient or not curious then someone is not kind and vice versa. If lucy is not generous or wise then mary is not curious. If someone is happy or not quiet then someone is not rich. Everyone who is not funny is both not strong and rich and vice versa. Everyone who is both not generous and rich is not funny or not rich and vice versa. Everyone who is not calm or not brave is creative and vice versa. Someone is quiet or wise. Someone is not kind or not curious. Mary is patient. Someone is not brave or not rich. John is either not wise or happy. Mary is both not curious and not old. | Alice is not wise. | neutral | (![X]:((strong(X)<~>brave(X))=>(brave(X)|calm(X))))&
(![X]:(strong(X)=>calm(X)))&
((?[X]:((~old(X)<~>wise(X))))=>((~funny(mary)&~humble(mary))))&
(((humble(susan)&rich(susan)))=>(?[X]:((~curious(X)|generous(X)))))&
(![X]:((~generous(X)&~humble(X))=>(brave(X)|~patient(X))))&
(((~humble(john)&~wise(john)))=>((tall(fred)<~>~old(fred))))&
(((~wise(fred)<~>~rich(fred)))=>(?[X]:((old(X)<~>~kind(X)))))&
((?[X]:((creative(X)|~humble(X))))=>(rich(mary)))&
(![X]:((humble(X)<~>wise(X))<=>(patient(X)&wise(X))))&
(![X]:(~tall(X)=>(~generous(X)&old(X))))&
(((patient(alice)|~curious(alice)))<=>(?[X]:(~kind(X))))&
(((~generous(lucy)|wise(lucy)))=>(~curious(mary)))&
((?[X]:((happy(X)|~quiet(X))))=>(?[X]:(~rich(X))))&
(![X]:(~funny(X)<=>(~strong(X)&rich(X))))&
(![X]:((~generous(X)&rich(X))<=>(~funny(X)|~rich(X))))&
(![X]:((~calm(X)|~brave(X))<=>creative(X)))&
(?[X]:((quiet(X)|wise(X))))&
(?[X]:((~kind(X)|~curious(X))))&
(patient(mary))&
(?[X]:((~brave(X)|~rich(X))))&
((~wise(john)<~>happy(john)))&
((~curious(mary)&~old(mary))) | ~wise(alice) | [] | null | 0 |
Everyone who is not wise or brave is not kind.
Everyone who is either happy or tall is both rich and curious.
Everyone who is not calm or not humble is both happy and wise.
Everyone who is either not tall or not happy is both generous and creative and vice versa.
If someone is both quiet and creative then alice is not patient.
Everyone who is rich or not strong is both happy and brave and vice versa.
Everyone who is rich is patient or not brave.
Everyone who is strong is not patient or happy and vice versa.
Everyone who is old or not wise is either generous or funny.
If someone is either brave or not calm then john is not old or not quiet.
If alice is both creative and patient then someone is either not wise or not quiet and vice versa.
Everyone who is not kind or not old is either not kind or generous.
Everyone who is either not rich or not creative is brave.
If someone is not strong then someone is kind or not wise and vice versa.
If lucy is not happy then mary is creative and vice versa.
Everyone who is either not patient or not strong is either strong or rich and vice versa.
Susan is quiet or not calm.
Someone is not curious or strong.
Fred is brave.
Someone is both not tall and brave. | Mary is not wise. | contradiction | (![X]:((~wise(X)|brave(X))=>~kind(X)))&
(![X]:((happy(X)<~>tall(X))=>(rich(X)&curious(X))))&
(![X]:((~calm(X)|~humble(X))=>(happy(X)&wise(X))))&
(![X]:((~tall(X)<~>~happy(X))<=>(generous(X)&creative(X))))&
((?[X]:((quiet(X)&creative(X))))=>(~patient(alice)))&
(![X]:((rich(X)|~strong(X))<=>(happy(X)&brave(X))))&
(![X]:(rich(X)=>(patient(X)|~brave(X))))&
(![X]:(strong(X)<=>(~patient(X)|happy(X))))&
(![X]:((old(X)|~wise(X))=>(generous(X)<~>funny(X))))&
((?[X]:((brave(X)<~>~calm(X))))=>((~old(john)|~quiet(john))))&
(((creative(alice)&patient(alice)))<=>(?[X]:((~wise(X)<~>~quiet(X)))))&
(![X]:((~kind(X)|~old(X))=>(~kind(X)<~>generous(X))))&
(![X]:((~rich(X)<~>~creative(X))=>brave(X)))&
((?[X]:(~strong(X)))<=>(?[X]:((kind(X)|~wise(X)))))&
((~happy(lucy))<=>(creative(mary)))&
(![X]:((~patient(X)<~>~strong(X))<=>(strong(X)<~>rich(X))))&
((quiet(susan)|~calm(susan)))&
(?[X]:((~curious(X)|strong(X))))&
(brave(fred))&
(?[X]:((~tall(X)&brave(X)))) | ~wise(mary) | [
"p5",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 850385448842528405652630
% SZS output start Proof for 850385448842528405652630
6. ! [X0] : ((~strong(X0) | rich(X0)) <=> (brave(X0) & happy(X0))) [input p5]
8. ! [X0] : (strong(X0) <=> (happy(X0) | ~patient(X0))) [input p7]
14. ? [X0] : ~strong(X0) <=> ? [X0] : (~wise(X0) | kind(X0)) [input p13]
21. ~wise(mary) [input hypothesis]
22. ? [X0] : ~strong(X0) <=> ? [X1] : (~wise(X1) | kind(X1)) [rectify 14]
38. ! [X0] : (((~strong(X0) | rich(X0)) | (~brave(X0) | ~happy(X0))) & ((brave(X0) & happy(X0)) | (strong(X0) & ~rich(X0)))) [nnf transformation 6]
39. ! [X0] : ((~strong(X0) | rich(X0) | ~brave(X0) | ~happy(X0)) & ((brave(X0) & happy(X0)) | (strong(X0) & ~rich(X0)))) [flattening 38]
40. ! [X0] : ((strong(X0) | (~happy(X0) & patient(X0))) & ((happy(X0) | ~patient(X0)) | ~strong(X0))) [nnf transformation 8]
41. ! [X0] : ((strong(X0) | (~happy(X0) & patient(X0))) & (happy(X0) | ~patient(X0) | ~strong(X0))) [flattening 40]
51. (? [X0] : ~strong(X0) | ! [X1] : (wise(X1) & ~kind(X1))) & (? [X1] : (~wise(X1) | kind(X1)) | ! [X0] : strong(X0)) [nnf transformation 22]
52. (? [X0] : ~strong(X0) | ! [X1] : (wise(X1) & ~kind(X1))) & (? [X2] : (~wise(X2) | kind(X2)) | ! [X3] : strong(X3)) [rectify 51]
53. ? [X0] : ~strong(X0) => ~strong(sK1) [choice axiom]
54. ? [X2] : (~wise(X2) | kind(X2)) => (~wise(sK2) | kind(sK2)) [choice axiom]
55. (~strong(sK1) | ! [X1] : (wise(X1) & ~kind(X1))) & ((~wise(sK2) | kind(sK2)) | ! [X3] : strong(X3)) [skolemisation 52,54,53]
78. happy(X0) | strong(X0) [cnf transformation 39]
85. strong(X0) | ~happy(X0) [cnf transformation 41]
106. ~strong(sK1) | wise(X1) [cnf transformation 55]
122. ~wise(mary) [cnf transformation 21]
137. strong(X0) [subsumption resolution 85,78]
180. wise(X1) [subsumption resolution 106,137]
202. $false [subsumption resolution 122,180]
% SZS output end Proof for 850385448842528405652630
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble then mary is not humble. Everyone who is not creative is either kind or not wise. Everyone who is not wise or not quiet is strong. If someone is not curious or humble then mary is strong and vice versa. Everyone who is generous or strong is not kind and vice versa. If someone is generous then paul is either not funny or calm and vice versa. Everyone who is either old or not happy is creative or not kind and vice versa. If someone is curious or not wise then fred is generous or not wise and vice versa. If someone is both not old and old then someone is funny or not curious and vice versa. Everyone who is calm is not wise and vice versa. Everyone who is old or happy is either wise or not quiet and vice versa. Everyone who is both not rich and wise is funny. Everyone who is either humble or happy is creative or not calm. If john is both not calm and not old then someone is calm. Everyone who is both curious and not old is both not tall and not quiet. Everyone who is not old or not curious is not humble or happy. Someone is either generous or curious. Someone is both strong and wise. Paul is either curious or not old. Fred is not old. Someone is brave. Someone is both not funny and strong. | Paul is not generous. | neutral | ((?[X]:(humble(X)))=>(~humble(mary)))&
(![X]:(~creative(X)=>(kind(X)<~>~wise(X))))&
(![X]:((~wise(X)|~quiet(X))=>strong(X)))&
((?[X]:((~curious(X)|humble(X))))<=>(strong(mary)))&
(![X]:((generous(X)|strong(X))<=>~kind(X)))&
((?[X]:(generous(X)))<=>((~funny(paul)<~>calm(paul))))&
(![X]:((old(X)<~>~happy(X))<=>(creative(X)|~kind(X))))&
((?[X]:((curious(X)|~wise(X))))<=>((generous(fred)|~wise(fred))))&
((?[X]:((~old(X)&old(X))))<=>(?[X]:((funny(X)|~curious(X)))))&
(![X]:(calm(X)<=>~wise(X)))&
(![X]:((old(X)|happy(X))<=>(wise(X)<~>~quiet(X))))&
(![X]:((~rich(X)&wise(X))=>funny(X)))&
(![X]:((humble(X)<~>happy(X))=>(creative(X)|~calm(X))))&
(((~calm(john)&~old(john)))=>(?[X]:(calm(X))))&
(![X]:((curious(X)&~old(X))=>(~tall(X)&~quiet(X))))&
(![X]:((~old(X)|~curious(X))=>(~humble(X)|happy(X))))&
(?[X]:((generous(X)<~>curious(X))))&
(?[X]:((strong(X)&wise(X))))&
((curious(paul)<~>~old(paul)))&
(~old(fred))&
(?[X]:(brave(X)))&
(?[X]:((~funny(X)&strong(X)))) | ~generous(paul) | [] | null | 0 |
Everyone who is either curious or not curious is not patient or generous.
If lucy is both not humble and not rich then someone is funny or not creative and vice versa.
If alice is not generous or calm then susan is not brave and vice versa.
Everyone who is wise is either humble or not strong.
If paul is either not old or kind then lucy is both quiet and not quiet.
Everyone who is generous or not strong is both not funny and funny and vice versa.
If someone is either kind or happy then john is either not generous or not wise.
Everyone who is both not rich and not tall is not quiet or not old and vice versa.
If someone is rich then john is not tall.
If paul is both not curious and not calm then someone is not brave or not strong.
Everyone who is either patient or not wise is both not rich and creative and vice versa.
If someone is not tall or creative then someone is either generous or not funny.
Everyone who is both not kind and calm is not quiet or not rich.
Everyone who is both generous and tall is both not strong and not rich and vice versa.
If lucy is tall then lucy is patient or not brave.
If mary is both generous and old then alice is kind.
Fred is either not calm or not kind.
Someone is not kind.
Someone is not kind or humble.
Alice is either calm or happy.
Someone is old or not generous.
Susan is not patient.
Someone is both not creative and not happy. | Susan is not strong. | contradiction | (![X]:((curious(X)<~>~curious(X))=>(~patient(X)|generous(X))))&
(((~humble(lucy)&~rich(lucy)))<=>(?[X]:((funny(X)|~creative(X)))))&
(((~generous(alice)|calm(alice)))<=>(~brave(susan)))&
(![X]:(wise(X)=>(humble(X)<~>~strong(X))))&
(((~old(paul)<~>kind(paul)))=>((quiet(lucy)&~quiet(lucy))))&
(![X]:((generous(X)|~strong(X))<=>(~funny(X)&funny(X))))&
((?[X]:((kind(X)<~>happy(X))))=>((~generous(john)<~>~wise(john))))&
(![X]:((~rich(X)&~tall(X))<=>(~quiet(X)|~old(X))))&
((?[X]:(rich(X)))=>(~tall(john)))&
(((~curious(paul)&~calm(paul)))=>(?[X]:((~brave(X)|~strong(X)))))&
(![X]:((patient(X)<~>~wise(X))<=>(~rich(X)&creative(X))))&
((?[X]:((~tall(X)|creative(X))))=>(?[X]:((generous(X)<~>~funny(X)))))&
(![X]:((~kind(X)&calm(X))=>(~quiet(X)|~rich(X))))&
(![X]:((generous(X)&tall(X))<=>(~strong(X)&~rich(X))))&
((tall(lucy))=>((patient(lucy)|~brave(lucy))))&
(((generous(mary)&old(mary)))=>(kind(alice)))&
((~calm(fred)<~>~kind(fred)))&
(?[X]:(~kind(X)))&
(?[X]:((~kind(X)|humble(X))))&
((calm(alice)<~>happy(alice)))&
(?[X]:((old(X)|~generous(X))))&
(~patient(susan))&
(?[X]:((~creative(X)&~happy(X)))) | ~strong(susan) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 2080861780122916536807952
% SZS output start Proof for 2080861780122916536807952
6. ! [X0] : ((~strong(X0) | generous(X0)) <=> (funny(X0) & ~funny(X0))) [input p5]
24. ~strong(susan) [input hypothesis]
51. ! [X0] : (((~strong(X0) | generous(X0)) | (~funny(X0) | funny(X0))) & ((funny(X0) & ~funny(X0)) | (strong(X0) & ~generous(X0)))) [nnf transformation 6]
52. ! [X0] : ((~strong(X0) | generous(X0) | ~funny(X0) | funny(X0)) & ((funny(X0) & ~funny(X0)) | (strong(X0) & ~generous(X0)))) [flattening 51]
93. ~funny(X0) | strong(X0) [cnf transformation 52]
95. funny(X0) | strong(X0) [cnf transformation 52]
135. ~strong(susan) [cnf transformation 24]
197. strong(X0) [subsumption resolution 93,95]
288. $false [subsumption resolution 135,197]
% SZS output end Proof for 2080861780122916536807952
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either not patient or not wise then mary is either not happy or not wise. Everyone who is both creative and not quiet is either rich or not happy and vice versa. If someone is not funny then mary is not old. If susan is both funny and creative then someone is both not quiet and not generous and vice versa. If mary is either not patient or curious then someone is strong or rich and vice versa. Everyone who is both generous and strong is not patient. If fred is not patient or not humble then someone is not patient or not strong and vice versa. Everyone who is both brave and not rich is funny or not patient. If someone is not quiet then someone is calm and vice versa. Everyone who is either not rich or quiet is not wise. If someone is either happy or not humble then someone is either funny or calm. If someone is humble then alice is both strong and not rich and vice versa. If alice is either not brave or curious then someone is happy or not curious and vice versa. If someone is humble or happy then someone is not happy or not rich and vice versa. If someone is either creative or kind then someone is both not happy and strong. If someone is brave or not wise then john is patient or not quiet and vice versa. Someone is either quiet or happy. Someone is not tall or wise. Someone is not generous or not brave. Someone is either curious or not brave. Someone is both not happy and not calm. John is not old or generous. Mary is not wise. Alice is creative. | Mary is not wise. | entailment | (((~patient(lucy)<~>~wise(lucy)))=>((~happy(mary)<~>~wise(mary))))&
(![X]:((creative(X)&~quiet(X))<=>(rich(X)<~>~happy(X))))&
((?[X]:(~funny(X)))=>(~old(mary)))&
(((funny(susan)&creative(susan)))<=>(?[X]:((~quiet(X)&~generous(X)))))&
(((~patient(mary)<~>curious(mary)))<=>(?[X]:((strong(X)|rich(X)))))&
(![X]:((generous(X)&strong(X))=>~patient(X)))&
(((~patient(fred)|~humble(fred)))<=>(?[X]:((~patient(X)|~strong(X)))))&
(![X]:((brave(X)&~rich(X))=>(funny(X)|~patient(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:(calm(X))))&
(![X]:((~rich(X)<~>quiet(X))=>~wise(X)))&
((?[X]:((happy(X)<~>~humble(X))))=>(?[X]:((funny(X)<~>calm(X)))))&
((?[X]:(humble(X)))<=>((strong(alice)&~rich(alice))))&
(((~brave(alice)<~>curious(alice)))<=>(?[X]:((happy(X)|~curious(X)))))&
((?[X]:((humble(X)|happy(X))))<=>(?[X]:((~happy(X)|~rich(X)))))&
((?[X]:((creative(X)<~>kind(X))))=>(?[X]:((~happy(X)&strong(X)))))&
((?[X]:((brave(X)|~wise(X))))<=>((patient(john)|~quiet(john))))&
(?[X]:((quiet(X)<~>happy(X))))&
(?[X]:((~tall(X)|wise(X))))&
(?[X]:((~generous(X)|~brave(X))))&
(?[X]:((curious(X)<~>~brave(X))))&
(?[X]:((~happy(X)&~calm(X))))&
((~old(john)|generous(john)))&
(~wise(mary))&
(creative(alice)) | ~wise(mary) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6699887011280521126756831
% SZS output start Proof for 6699887011280521126756831
23. ~wise(mary) [input p22]
25. wise(mary) [input hypothesis]
163. ~wise(mary) [cnf transformation 23]
165. wise(mary) [cnf transformation 25]
179. 4 <=> wise(mary) [avatar definition]
442. ~4 [avatar split clause 163,179]
443. 4 [avatar split clause 165,179]
444. $false [avatar sat refutation 442,443]
% SZS output end Proof for 6699887011280521126756831
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not rich or not curious then mary is both happy and not patient and vice versa. Everyone who is not curious is calm. If alice is creative then john is either tall or not humble. If someone is both not old and curious then fred is both not wise and not tall and vice versa. Everyone who is either not happy or not curious is generous or patient and vice versa. Everyone who is either not kind or not humble is humble or not happy. Everyone who is both strong and happy is both wise and not brave. Everyone who is not calm is either not happy or kind and vice versa. Everyone who is both tall and creative is kind or not humble. Everyone who is either happy or not calm is quiet or not humble and vice versa. If alice is not happy then john is either not wise or strong and vice versa. If john is both quiet and not strong then alice is patient. Everyone who is both quiet and not old is either not calm or not happy. If someone is tall or not old then someone is either not patient or humble and vice versa. Everyone who is quiet or not curious is not kind. If someone is not tall or not quiet then susan is not kind or generous. Susan is not humble. Alice is either not wise or old. Someone is both not quiet and brave. Someone is happy or not quiet. Someone is both not happy and wise. Susan is wise or not kind. Susan is either not tall or not strong. Someone is both not wise and not calm. | Susan is kind. | contradiction | (((~rich(john)<~>~curious(john)))<=>((happy(mary)&~patient(mary))))&
(![X]:(~curious(X)=>calm(X)))&
((creative(alice))=>((tall(john)<~>~humble(john))))&
((?[X]:((~old(X)&curious(X))))<=>((~wise(fred)&~tall(fred))))&
(![X]:((~happy(X)<~>~curious(X))<=>(generous(X)|patient(X))))&
(![X]:((~kind(X)<~>~humble(X))=>(humble(X)|~happy(X))))&
(![X]:((strong(X)&happy(X))=>(wise(X)&~brave(X))))&
(![X]:(~calm(X)<=>(~happy(X)<~>kind(X))))&
(![X]:((tall(X)&creative(X))=>(kind(X)|~humble(X))))&
(![X]:((happy(X)<~>~calm(X))<=>(quiet(X)|~humble(X))))&
((~happy(alice))<=>((~wise(john)<~>strong(john))))&
(((quiet(john)&~strong(john)))=>(patient(alice)))&
(![X]:((quiet(X)&~old(X))=>(~calm(X)<~>~happy(X))))&
((?[X]:((tall(X)|~old(X))))<=>(?[X]:((~patient(X)<~>humble(X)))))&
(![X]:((quiet(X)|~curious(X))=>~kind(X)))&
((?[X]:((~tall(X)|~quiet(X))))=>((~kind(susan)|generous(susan))))&
(~humble(susan))&
((~wise(alice)<~>old(alice)))&
(?[X]:((~quiet(X)&brave(X))))&
(?[X]:((happy(X)|~quiet(X))))&
(?[X]:((~happy(X)&wise(X))))&
((wise(susan)|~kind(susan)))&
((~tall(susan)<~>~strong(susan)))&
(?[X]:((~wise(X)&~calm(X)))) | kind(susan) | [
"p4",
"p7",
"p9",
"p14",
"p15",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8752084601910693122807068
% SZS output start Proof for 8752084601910693122807068
5. ! [X0] : ((~happy(X0) <~> ~curious(X0)) <=> (patient(X0) | generous(X0))) [input p4]
8. ! [X0] : (~calm(X0) <=> (~happy(X0) <~> kind(X0))) [input p7]
10. ! [X0] : ((happy(X0) <~> ~calm(X0)) <=> (~humble(X0) | quiet(X0))) [input p9]
15. ! [X0] : ((~curious(X0) | quiet(X0)) => ~kind(X0)) [input p14]
16. ? [X0] : (~quiet(X0) | ~tall(X0)) => (generous(susan) | ~kind(susan)) [input p15]
17. ~humble(susan) [input p16]
19. ? [X0] : (brave(X0) & ~quiet(X0)) [input p18]
25. kind(susan) [input hypothesis]
38. ! [X0] : (~kind(X0) | (curious(X0) & ~quiet(X0))) [ennf transformation 15]
39. (generous(susan) | ~kind(susan)) | ! [X0] : (quiet(X0) & tall(X0)) [ennf transformation 16]
40. generous(susan) | ~kind(susan) | ! [X0] : (quiet(X0) & tall(X0)) [flattening 39]
48. ! [X0] : ((((curious(X0) | happy(X0)) & (~curious(X0) | ~happy(X0))) | (~patient(X0) & ~generous(X0))) & ((patient(X0) | generous(X0)) | ((~happy(X0) | curious(X0)) & (~curious(X0) | happy(X0))))) [nnf transformation 5]
49. ! [X0] : ((((curious(X0) | happy(X0)) & (~curious(X0) | ~happy(X0))) | (~patient(X0) & ~generous(X0))) & (patient(X0) | generous(X0) | ((~happy(X0) | curious(X0)) & (~curious(X0) | happy(X0))))) [flattening 48]
51. ! [X0] : ((~calm(X0) | ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0)))) & (((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) | calm(X0))) [nnf transformation 8]
52. ! [X0] : ((((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | (humble(X0) & ~quiet(X0))) & ((~humble(X0) | quiet(X0)) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0))))) [nnf transformation 10]
53. ! [X0] : ((((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | (humble(X0) & ~quiet(X0))) & (~humble(X0) | quiet(X0) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0))))) [flattening 52]
62. ? [X0] : (brave(X0) & ~quiet(X0)) => (brave(sK3) & ~quiet(sK3)) [choice axiom]
63. brave(sK3) & ~quiet(sK3) [skolemisation 19,62]
84. ~generous(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 49]
93. ~kind(X0) | happy(X0) | calm(X0) [cnf transformation 51]
99. ~calm(X0) | happy(X0) | humble(X0) [cnf transformation 53]
116. ~kind(X0) | curious(X0) [cnf transformation 38]
118. generous(susan) | ~kind(susan) | quiet(X0) [cnf transformation 40]
119. ~humble(susan) [cnf transformation 17]
122. ~quiet(sK3) [cnf transformation 63]
132. kind(susan) [cnf transformation 25]
241. 23 <=> ! [X0] : quiet(X0) [avatar definition]
242. quiet(X0) <- (23) [avatar component clause 241]
244. 24 <=> kind(susan) [avatar definition]
245. kind(susan) <- (24) [avatar component clause 244]
248. 25 <=> generous(susan) [avatar definition]
250. generous(susan) <- (25) [avatar component clause 248]
251. 23 | ~24 | 25 [avatar split clause 118,248,244,241]
290. 24 [avatar split clause 132,244]
292. curious(susan) <- (24) [resolution 116,245]
293. ~happy(susan) | ~curious(susan) <- (25) [resolution 84,250]
294. ~happy(susan) <- (24, 25) [subsumption resolution 293,292]
306. happy(susan) | calm(susan) <- (24) [resolution 93,245]
307. calm(susan) <- (24, 25) [subsumption resolution 306,294]
318. happy(susan) | humble(susan) <- (24, 25) [resolution 99,307]
319. humble(susan) <- (24, 25) [subsumption resolution 318,294]
320. $false <- (24, 25) [subsumption resolution 319,119]
321. ~24 | ~25 [avatar contradiction clause 320]
335. $false <- (23) [resolution 242,122]
338. ~23 [avatar contradiction clause 335]
340. $false [avatar sat refutation 251,290,321,338]
% SZS output end Proof for 8752084601910693122807068
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is either not humble or not strong. Everyone who is creative or wise is both not generous and not curious and vice versa. Everyone who is both not rich and funny is wise or curious. If someone is either funny or creative then someone is either not kind or rich and vice versa. If mary is either brave or not creative then alice is both not tall and tall. If someone is both not strong and not humble then alice is tall. If someone is both old and not kind then someone is either not creative or not rich. Everyone who is both not calm and not wise is both funny and not quiet. If mary is both not calm and happy then someone is creative or not old. Everyone who is not rich or not quiet is not curious. Everyone who is calm is funny and vice versa. If someone is either not generous or not brave then mary is patient or not generous. Everyone who is either curious or patient is both not rich and not humble. If lucy is not generous or generous then someone is either quiet or not rich and vice versa. If someone is either not tall or old then fred is not funny or strong. If alice is both not funny and not quiet then someone is both old and quiet and vice versa. Paul is not funny. Lucy is not funny. Someone is not creative. Someone is both not rich and strong. Someone is old or not strong. Lucy is either tall or curious. Someone is happy. Alice is not funny or not old. | Lucy is not tall. | contradiction | (![X]:(old(X)=>(~humble(X)<~>~strong(X))))&
(![X]:((creative(X)|wise(X))<=>(~generous(X)&~curious(X))))&
(![X]:((~rich(X)&funny(X))=>(wise(X)|curious(X))))&
((?[X]:((funny(X)<~>creative(X))))<=>(?[X]:((~kind(X)<~>rich(X)))))&
(((brave(mary)<~>~creative(mary)))=>((~tall(alice)&tall(alice))))&
((?[X]:((~strong(X)&~humble(X))))=>(tall(alice)))&
((?[X]:((old(X)&~kind(X))))=>(?[X]:((~creative(X)<~>~rich(X)))))&
(![X]:((~calm(X)&~wise(X))=>(funny(X)&~quiet(X))))&
(((~calm(mary)&happy(mary)))=>(?[X]:((creative(X)|~old(X)))))&
(![X]:((~rich(X)|~quiet(X))=>~curious(X)))&
(![X]:(calm(X)<=>funny(X)))&
((?[X]:((~generous(X)<~>~brave(X))))=>((patient(mary)|~generous(mary))))&
(![X]:((curious(X)<~>patient(X))=>(~rich(X)&~humble(X))))&
(((~generous(lucy)|generous(lucy)))<=>(?[X]:((quiet(X)<~>~rich(X)))))&
((?[X]:((~tall(X)<~>old(X))))=>((~funny(fred)|strong(fred))))&
(((~funny(alice)&~quiet(alice)))<=>(?[X]:((old(X)&quiet(X)))))&
(~funny(paul))&
(~funny(lucy))&
(?[X]:(~creative(X)))&
(?[X]:((~rich(X)&strong(X))))&
(?[X]:((old(X)|~strong(X))))&
((tall(lucy)<~>curious(lucy)))&
(?[X]:(happy(X)))&
((~funny(alice)|~old(alice))) | ~tall(lucy) | [
"p1",
"p7",
"p10",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5544223523629718694266418
% SZS output start Proof for 5544223523629718694266418
2. ! [X0] : ((wise(X0) | creative(X0)) <=> (~curious(X0) & ~generous(X0))) [input p1]
8. ! [X0] : ((~wise(X0) & ~calm(X0)) => (~quiet(X0) & funny(X0))) [input p7]
11. ! [X0] : (calm(X0) <=> funny(X0)) [input p10]
18. ~funny(lucy) [input p17]
22. tall(lucy) <~> curious(lucy) [input p21]
25. ~tall(lucy) [input hypothesis]
28. ! [X0] : (calm(X0) => funny(X0)) [unused predicate definition removal 11]
35. ! [X0] : ((~quiet(X0) & funny(X0)) | (wise(X0) | calm(X0))) [ennf transformation 8]
36. ! [X0] : ((~quiet(X0) & funny(X0)) | wise(X0) | calm(X0)) [flattening 35]
40. ! [X0] : (funny(X0) | ~calm(X0)) [ennf transformation 28]
47. ! [X0] : (((wise(X0) | creative(X0)) | (curious(X0) | generous(X0))) & ((~curious(X0) & ~generous(X0)) | (~wise(X0) & ~creative(X0)))) [nnf transformation 2]
48. ! [X0] : ((wise(X0) | creative(X0) | curious(X0) | generous(X0)) & ((~curious(X0) & ~generous(X0)) | (~wise(X0) & ~creative(X0)))) [flattening 47]
80. (~curious(lucy) | ~tall(lucy)) & (curious(lucy) | tall(lucy)) [nnf transformation 22]
88. ~curious(X0) | ~wise(X0) [cnf transformation 48]
106. calm(X0) | wise(X0) | funny(X0) [cnf transformation 36]
111. ~calm(X0) | funny(X0) [cnf transformation 40]
131. ~funny(lucy) [cnf transformation 18]
136. curious(lucy) | tall(lucy) [cnf transformation 80]
140. ~tall(lucy) [cnf transformation 25]
309. 38 <=> tall(lucy) [avatar definition]
313. 39 <=> curious(lucy) [avatar definition]
314. curious(lucy) <- (39) [avatar component clause 313]
317. 38 | 39 [avatar split clause 136,313,309]
323. ~38 [avatar split clause 140,309]
325. ~wise(lucy) <- (39) [resolution 88,314]
342. wise(X0) | funny(X0) | funny(X0) [resolution 106,111]
343. funny(X0) | wise(X0) [duplicate literal removal 342]
345. wise(lucy) [resolution 343,131]
348. $false <- (39) [subsumption resolution 345,325]
349. ~39 [avatar contradiction clause 348]
350. $false [avatar sat refutation 317,323,349]
% SZS output end Proof for 5544223523629718694266418
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old or funny then mary is either not quiet or not wise and vice versa. Everyone who is either not strong or not tall is curious. If someone is not wise then someone is either not kind or quiet. Everyone who is both not patient and not humble is quiet. Everyone who is not kind is rich. Everyone who is either not patient or not strong is either not wise or not curious and vice versa. If paul is both calm and not creative then lucy is either not funny or not creative and vice versa. Everyone who is either tall or not quiet is funny or kind. Everyone who is tall or not curious is tall and vice versa. Everyone who is creative or not tall is old. Everyone who is both not tall and not calm is either not brave or not strong. Everyone who is humble or not calm is either not humble or not tall and vice versa. Everyone who is quiet or not strong is both happy and not happy and vice versa. Everyone who is both quiet and not kind is both not happy and calm and vice versa. If fred is not rich then lucy is old or creative and vice versa. Everyone who is either creative or not wise is both not funny and not wise. Someone is rich or not humble. Someone is either not old or curious. Fred is not generous. Someone is either quiet or not happy. Paul is either old or not creative. Mary is not curious. | Mary is wise. | contradiction | ((?[X]:((old(X)|funny(X))))<=>((~quiet(mary)<~>~wise(mary))))&
(![X]:((~strong(X)<~>~tall(X))=>curious(X)))&
((?[X]:(~wise(X)))=>(?[X]:((~kind(X)<~>quiet(X)))))&
(![X]:((~patient(X)&~humble(X))=>quiet(X)))&
(![X]:(~kind(X)=>rich(X)))&
(![X]:((~patient(X)<~>~strong(X))<=>(~wise(X)<~>~curious(X))))&
(((calm(paul)&~creative(paul)))<=>((~funny(lucy)<~>~creative(lucy))))&
(![X]:((tall(X)<~>~quiet(X))=>(funny(X)|kind(X))))&
(![X]:((tall(X)|~curious(X))<=>tall(X)))&
(![X]:((creative(X)|~tall(X))=>old(X)))&
(![X]:((~tall(X)&~calm(X))=>(~brave(X)<~>~strong(X))))&
(![X]:((humble(X)|~calm(X))<=>(~humble(X)<~>~tall(X))))&
(![X]:((quiet(X)|~strong(X))<=>(happy(X)&~happy(X))))&
(![X]:((quiet(X)&~kind(X))<=>(~happy(X)&calm(X))))&
((~rich(fred))<=>((old(lucy)|creative(lucy))))&
(![X]:((creative(X)<~>~wise(X))=>(~funny(X)&~wise(X))))&
(?[X]:((rich(X)|~humble(X))))&
(?[X]:((~old(X)<~>curious(X))))&
(~generous(fred))&
(?[X]:((quiet(X)<~>~happy(X))))&
((old(paul)<~>~creative(paul)))&
(~curious(mary)) | wise(mary) | [
"p3",
"p5",
"p8",
"p11",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 739324893111139493872991
% SZS output start Proof for 739324893111139493872991
4. ! [X0] : ((~humble(X0) & ~patient(X0)) => quiet(X0)) [input p3]
6. ! [X0] : ((~patient(X0) <~> ~strong(X0)) <=> (~wise(X0) <~> ~curious(X0))) [input p5]
9. ! [X0] : ((~curious(X0) | tall(X0)) <=> tall(X0)) [input p8]
12. ! [X0] : ((~calm(X0) | humble(X0)) <=> (~humble(X0) <~> ~tall(X0))) [input p11]
13. ! [X0] : ((~strong(X0) | quiet(X0)) <=> (~happy(X0) & happy(X0))) [input p12]
22. ~curious(mary) [input p21]
23. wise(mary) [input hypothesis]
28. ! [X0] : (quiet(X0) | (humble(X0) | patient(X0))) [ennf transformation 4]
29. ! [X0] : (quiet(X0) | humble(X0) | patient(X0)) [flattening 28]
46. ! [X0] : ((((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | ((~wise(X0) | curious(X0)) & (~curious(X0) | wise(X0)))) & (((curious(X0) | wise(X0)) & (~curious(X0) | ~wise(X0))) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0))))) [nnf transformation 6]
50. ! [X0] : (((~curious(X0) | tall(X0)) | ~tall(X0)) & (tall(X0) | (curious(X0) & ~tall(X0)))) [nnf transformation 9]
51. ! [X0] : ((~curious(X0) | tall(X0) | ~tall(X0)) & (tall(X0) | (curious(X0) & ~tall(X0)))) [flattening 50]
53. ! [X0] : (((~calm(X0) | humble(X0)) | ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) & (((tall(X0) | humble(X0)) & (~tall(X0) | ~humble(X0))) | (calm(X0) & ~humble(X0)))) [nnf transformation 12]
54. ! [X0] : ((~calm(X0) | humble(X0) | ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) & (((tall(X0) | humble(X0)) & (~tall(X0) | ~humble(X0))) | (calm(X0) & ~humble(X0)))) [flattening 53]
55. ! [X0] : (((~strong(X0) | quiet(X0)) | (happy(X0) | ~happy(X0))) & ((~happy(X0) & happy(X0)) | (strong(X0) & ~quiet(X0)))) [nnf transformation 13]
56. ! [X0] : ((~strong(X0) | quiet(X0) | happy(X0) | ~happy(X0)) & ((~happy(X0) & happy(X0)) | (strong(X0) & ~quiet(X0)))) [flattening 55]
81. humble(X0) | quiet(X0) | patient(X0) [cnf transformation 29]
83. ~curious(X0) | ~wise(X0) | ~strong(X0) | patient(X0) [cnf transformation 46]
85. ~strong(X0) | wise(X0) | curious(X0) | patient(X0) [cnf transformation 46]
88. ~patient(X0) | ~strong(X0) | ~wise(X0) | curious(X0) [cnf transformation 46]
100. curious(X0) | tall(X0) [cnf transformation 51]
106. ~tall(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 54]
112. happy(X0) | ~quiet(X0) [cnf transformation 56]
113. happy(X0) | strong(X0) [cnf transformation 56]
114. ~happy(X0) | ~quiet(X0) [cnf transformation 56]
115. ~happy(X0) | strong(X0) [cnf transformation 56]
135. ~curious(mary) [cnf transformation 22]
136. wise(mary) [cnf transformation 23]
138. ~humble(X0) | ~tall(X0) [duplicate literal removal 106]
141. 1 <=> wise(mary) [avatar definition]
143. wise(mary) <- (1) [avatar component clause 141]
203. strong(X0) [subsumption resolution 113,115]
204. ~quiet(X0) [subsumption resolution 112,114]
243. 1 [avatar split clause 136,141]
251. quiet(X0) | patient(X0) | ~tall(X0) [resolution 81,138]
253. ~tall(X0) | patient(X0) [subsumption resolution 251,204]
291. ~wise(X0) | ~strong(X0) | patient(X0) | tall(X0) [resolution 83,100]
292. ~wise(X0) | patient(X0) | tall(X0) [subsumption resolution 291,203]
293. ~wise(X0) | patient(X0) [subsumption resolution 292,253]
298. wise(X0) | curious(X0) | patient(X0) [resolution 85,203]
299. patient(X0) | curious(X0) [subsumption resolution 298,293]
326. ~strong(X1) | ~wise(X1) | curious(X1) | curious(X1) [resolution 88,299]
330. ~strong(X1) | ~wise(X1) | curious(X1) [duplicate literal removal 326]
332. ~wise(X1) | curious(X1) [subsumption resolution 330,203]
336. curious(mary) <- (1) [resolution 332,143]
337. $false <- (1) [subsumption resolution 336,135]
338. ~1 [avatar contradiction clause 337]
339. $false [avatar sat refutation 243,338]
% SZS output end Proof for 739324893111139493872991
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either happy or not tall then john is either not creative or not old and vice versa. Everyone who is not patient is both not quiet and strong and vice versa. If someone is not old then john is either not brave or calm. If someone is both not brave and not happy then someone is either not creative or curious and vice versa. If paul is not old or not patient then alice is either not wise or funny. If someone is tall then john is both not curious and calm. If john is kind or patient then mary is either old or funny. Everyone who is either not calm or not funny is not brave and vice versa. Everyone who is either not old or not funny is old and vice versa. Everyone who is not generous or creative is both wise and curious and vice versa. Everyone who is both kind and funny is not curious or not calm. If alice is either tall or not old then someone is both not tall and patient and vice versa. If mary is generous then alice is not calm or generous and vice versa. If someone is not curious then someone is not tall. Everyone who is wise or not curious is both not tall and not old and vice versa. If lucy is not quiet or humble then someone is not funny. Paul is old or not creative. Alice is either kind or strong. Someone is either quiet or not creative. John is both rich and old. Someone is quiet or not wise. | Mary is not old. | contradiction | (((happy(fred)<~>~tall(fred)))<=>((~creative(john)<~>~old(john))))&
(![X]:(~patient(X)<=>(~quiet(X)&strong(X))))&
((?[X]:(~old(X)))=>((~brave(john)<~>calm(john))))&
((?[X]:((~brave(X)&~happy(X))))<=>(?[X]:((~creative(X)<~>curious(X)))))&
(((~old(paul)|~patient(paul)))=>((~wise(alice)<~>funny(alice))))&
((?[X]:(tall(X)))=>((~curious(john)&calm(john))))&
(((kind(john)|patient(john)))=>((old(mary)<~>funny(mary))))&
(![X]:((~calm(X)<~>~funny(X))<=>~brave(X)))&
(![X]:((~old(X)<~>~funny(X))<=>old(X)))&
(![X]:((~generous(X)|creative(X))<=>(wise(X)&curious(X))))&
(![X]:((kind(X)&funny(X))=>(~curious(X)|~calm(X))))&
(((tall(alice)<~>~old(alice)))<=>(?[X]:((~tall(X)&patient(X)))))&
((generous(mary))<=>((~calm(alice)|generous(alice))))&
((?[X]:(~curious(X)))=>(?[X]:(~tall(X))))&
(![X]:((wise(X)|~curious(X))<=>(~tall(X)&~old(X))))&
(((~quiet(lucy)|humble(lucy)))=>(?[X]:(~funny(X))))&
((old(paul)|~creative(paul)))&
((kind(alice)<~>strong(alice)))&
(?[X]:((quiet(X)<~>~creative(X))))&
((rich(john)&old(john)))&
(?[X]:((quiet(X)|~wise(X)))) | ~old(mary) | [
"p2",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7765295597118781395830919
% SZS output start Proof for 7765295597118781395830919
3. ? [X0] : ~old(X0) => (~brave(john) <~> calm(john)) [input p2]
8. ! [X0] : ((~calm(X0) <~> ~funny(X0)) <=> ~brave(X0)) [input p7]
9. ! [X0] : ((~old(X0) <~> ~funny(X0)) <=> old(X0)) [input p8]
22. ~old(mary) [input hypothesis]
27. (~brave(john) <~> calm(john)) | ! [X0] : old(X0) [ennf transformation 3]
38. ((~calm(john) | brave(john)) & (calm(john) | ~brave(john))) | ! [X0] : old(X0) [nnf transformation 27]
46. ! [X0] : ((((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) | brave(X0)) & (~brave(X0) | ((~calm(X0) | funny(X0)) & (~funny(X0) | calm(X0))))) [nnf transformation 8]
47. ! [X0] : ((((funny(X0) | old(X0)) & (~funny(X0) | ~old(X0))) | ~old(X0)) & (old(X0) | ((~old(X0) | funny(X0)) & (~funny(X0) | old(X0))))) [nnf transformation 9]
80. calm(john) | ~brave(john) | old(X0) [cnf transformation 38]
81. ~calm(john) | brave(john) | old(X0) [cnf transformation 38]
99. ~calm(X0) | ~brave(X0) | funny(X0) [cnf transformation 46]
101. funny(X0) | calm(X0) | brave(X0) [cnf transformation 46]
102. old(X0) | ~funny(X0) | old(X0) [cnf transformation 47]
104. ~funny(X0) | ~old(X0) | ~old(X0) [cnf transformation 47]
135. ~old(mary) [cnf transformation 22]
136. old(X0) | ~funny(X0) [duplicate literal removal 102]
137. ~funny(X0) | ~old(X0) [duplicate literal removal 104]
163. 5 <=> ! [X0] : old(X0) [avatar definition]
164. old(X0) <- (5) [avatar component clause 163]
166. 6 <=> brave(john) [avatar definition]
167. ~brave(john) <- (~6) [avatar component clause 166]
168. brave(john) <- (6) [avatar component clause 166]
170. 7 <=> calm(john) [avatar definition]
171. calm(john) <- (7) [avatar component clause 170]
172. ~calm(john) <- (~7) [avatar component clause 170]
173. 5 | 6 | ~7 [avatar split clause 81,170,166,163]
174. 5 | ~6 | 7 [avatar split clause 80,170,166,163]
240. 22 <=> old(mary) [avatar definition]
242. ~old(mary) <- (~22) [avatar component clause 240]
255. ~funny(X0) [subsumption resolution 136,137]
339. ~22 [avatar split clause 135,240]
340. $false <- (5, ~22) [resolution 242,164]
341. ~5 | 22 [avatar contradiction clause 340]
355. ~brave(john) | funny(john) <- (7) [resolution 99,171]
356. funny(john) <- (6, 7) [subsumption resolution 355,168]
357. $false <- (6, 7) [subsumption resolution 356,255]
358. ~6 | ~7 [avatar contradiction clause 357]
362. calm(X3) | brave(X3) [resolution 101,255]
384. brave(john) <- (~7) [resolution 362,172]
385. $false <- (~6, ~7) [subsumption resolution 384,167]
386. 6 | 7 [avatar contradiction clause 385]
387. $false [avatar sat refutation 173,174,339,341,358,386]
% SZS output end Proof for 7765295597118781395830919
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or not patient is either not tall or not brave. If someone is tall then fred is either not tall or brave. Everyone who is both not strong and funny is either not kind or not wise and vice versa. If mary is not funny or brave then paul is not curious and vice versa. Everyone who is kind is not patient. Everyone who is brave or not generous is both not humble and kind. If lucy is creative then someone is both not creative and not quiet and vice versa. If someone is both not kind and tall then paul is both not patient and not happy. If lucy is brave then someone is not generous and vice versa. Everyone who is not happy or generous is not strong. If lucy is not patient or quiet then alice is rich or humble and vice versa. Everyone who is not happy or curious is patient and vice versa. Everyone who is not curious is happy and vice versa. If john is happy then someone is both not calm and not quiet and vice versa. Everyone who is quiet or curious is tall. Lucy is generous. Someone is old. Someone is either not patient or not strong. Someone is either quiet or not wise. Fred is not wise. | Mary is humble. | contradiction | (![X]:((patient(X)<~>~patient(X))=>(~tall(X)<~>~brave(X))))&
((?[X]:(tall(X)))=>((~tall(fred)<~>brave(fred))))&
(![X]:((~strong(X)&funny(X))<=>(~kind(X)<~>~wise(X))))&
(((~funny(mary)|brave(mary)))<=>(~curious(paul)))&
(![X]:(kind(X)=>~patient(X)))&
(![X]:((brave(X)|~generous(X))=>(~humble(X)&kind(X))))&
((creative(lucy))<=>(?[X]:((~creative(X)&~quiet(X)))))&
((?[X]:((~kind(X)&tall(X))))=>((~patient(paul)&~happy(paul))))&
((brave(lucy))<=>(?[X]:(~generous(X))))&
(![X]:((~happy(X)|generous(X))=>~strong(X)))&
(((~patient(lucy)|quiet(lucy)))<=>((rich(alice)|humble(alice))))&
(![X]:((~happy(X)|curious(X))<=>patient(X)))&
(![X]:(~curious(X)<=>happy(X)))&
((happy(john))<=>(?[X]:((~calm(X)&~quiet(X)))))&
(![X]:((quiet(X)|curious(X))=>tall(X)))&
(generous(lucy))&
(?[X]:(old(X)))&
(?[X]:((~patient(X)<~>~strong(X))))&
(?[X]:((quiet(X)<~>~wise(X))))&
(~wise(fred)) | humble(mary) | [
"p0",
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 5832807597623296582623881
% SZS output start Proof for 5832807597623296582623881
1. ! [X0] : ((patient(X0) <~> ~patient(X0)) => (~tall(X0) <~> ~brave(X0))) [input p0]
2. ? [X0] : tall(X0) => (~tall(fred) <~> brave(fred)) [input p1]
6. ! [X0] : ((~generous(X0) | brave(X0)) => (kind(X0) & ~humble(X0))) [input p5]
21. humble(mary) [input hypothesis]
23. ! [X0] : ((~tall(X0) <~> ~brave(X0)) | (patient(X0) <=> ~patient(X0))) [ennf transformation 1]
24. (~tall(fred) <~> brave(fred)) | ! [X0] : ~tall(X0) [ennf transformation 2]
26. ! [X0] : ((kind(X0) & ~humble(X0)) | (generous(X0) & ~brave(X0))) [ennf transformation 6]
30. ! [X0] : (((brave(X0) | tall(X0)) & (~brave(X0) | ~tall(X0))) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0)))) [nnf transformation 23]
31. ((~brave(fred) | tall(fred)) & (brave(fred) | ~tall(fred))) | ! [X0] : ~tall(X0) [nnf transformation 24]
59. ~brave(X0) | ~tall(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 30]
60. ~brave(X0) | ~tall(X0) | patient(X0) | patient(X0) [cnf transformation 30]
61. brave(X0) | tall(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 30]
62. brave(X0) | tall(X0) | patient(X0) | patient(X0) [cnf transformation 30]
63. brave(fred) | ~tall(fred) | ~tall(X0) [cnf transformation 31]
64. ~brave(fred) | tall(fred) | ~tall(X0) [cnf transformation 31]
75. ~humble(X0) | ~brave(X0) [cnf transformation 26]
108. humble(mary) [cnf transformation 21]
109. ~brave(X0) | ~tall(X0) | ~patient(X0) [duplicate literal removal 59]
110. ~brave(X0) | ~tall(X0) | patient(X0) [duplicate literal removal 60]
111. brave(X0) | tall(X0) | ~patient(X0) [duplicate literal removal 61]
112. brave(X0) | tall(X0) | patient(X0) [duplicate literal removal 62]
113. brave(X0) | tall(X0) [subsumption resolution 111,112]
114. ~brave(X0) | ~tall(X0) [subsumption resolution 109,110]
115. ~brave(fred) | ~tall(X0) [subsumption resolution 64,114]
117. 1 <=> ! [X0] : ~tall(X0) [avatar definition]
118. ~tall(X0) <- (1) [avatar component clause 117]
120. 2 <=> brave(fred) [avatar definition]
123. 1 | ~2 [avatar split clause 115,120,117]
124. brave(fred) | ~tall(X0) [subsumption resolution 63,113]
125. 1 | 2 [avatar split clause 124,120,117]
135. 5 <=> brave(mary) [avatar definition]
136. ~brave(mary) <- (~5) [avatar component clause 135]
243. ~brave(mary) [resolution 75,108]
245. ~5 [avatar split clause 243,135]
265. tall(mary) <- (~5) [resolution 113,136]
269. $false <- (1, ~5) [subsumption resolution 265,118]
270. ~1 | 5 [avatar contradiction clause 269]
275. $false [avatar sat refutation 123,125,245,270]
% SZS output end Proof for 5832807597623296582623881
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or not kind is old.
If mary is not humble then john is not quiet or not curious.
If susan is either not quiet or not rich then alice is either brave or not strong.
If someone is either not calm or not patient then someone is calm or rich and vice versa.
Everyone who is not wise or not kind is tall and vice versa.
Everyone who is not quiet is either not generous or not quiet.
If susan is both not wise and rich then mary is both calm and rich and vice versa.
If someone is old then someone is not funny or not generous.
If susan is not calm then someone is not creative and vice versa.
Everyone who is not old is either old or not quiet and vice versa.
Everyone who is both not generous and not funny is wise or strong and vice versa.
Everyone who is both generous and funny is happy and vice versa.
If lucy is either not patient or generous then lucy is old or not rich and vice versa.
Everyone who is both not brave and not curious is not kind.
Everyone who is not wise is either not tall or not wise.
Paul is not happy.
Someone is either not strong or not happy.
Someone is either not strong or not calm.
Someone is curious.
Someone is patient.
Susan is not strong or not generous.
Alice is not creative or strong. | Alice is not wise. | entailment | (![X]:((kind(X)<~>~kind(X))=>old(X)))&
((~humble(mary))=>((~quiet(john)|~curious(john))))&
(((~quiet(susan)<~>~rich(susan)))=>((brave(alice)<~>~strong(alice))))&
((?[X]:((~calm(X)<~>~patient(X))))<=>(?[X]:((calm(X)|rich(X)))))&
(![X]:((~wise(X)|~kind(X))<=>tall(X)))&
(![X]:(~quiet(X)=>(~generous(X)<~>~quiet(X))))&
(((~wise(susan)&rich(susan)))<=>((calm(mary)&rich(mary))))&
((?[X]:(old(X)))=>(?[X]:((~funny(X)|~generous(X)))))&
((~calm(susan))<=>(?[X]:(~creative(X))))&
(![X]:(~old(X)<=>(old(X)<~>~quiet(X))))&
(![X]:((~generous(X)&~funny(X))<=>(wise(X)|strong(X))))&
(![X]:((generous(X)&funny(X))<=>happy(X)))&
(((~patient(lucy)<~>generous(lucy)))<=>((old(lucy)|~rich(lucy))))&
(![X]:((~brave(X)&~curious(X))=>~kind(X)))&
(![X]:(~wise(X)=>(~tall(X)<~>~wise(X))))&
(~happy(paul))&
(?[X]:((~strong(X)<~>~happy(X))))&
(?[X]:((~strong(X)<~>~calm(X))))&
(?[X]:(curious(X)))&
(?[X]:(patient(X)))&
((~strong(susan)|~generous(susan)))&
((~creative(alice)|strong(alice))) | ~wise(alice) | [
"p0",
"p5",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7649306407119764679249704
% SZS output start Proof for 7649306407119764679249704
1. ! [X0] : ((kind(X0) <~> ~kind(X0)) => old(X0)) [input p0]
6. ! [X0] : (~quiet(X0) => (~generous(X0) <~> ~quiet(X0))) [input p5]
10. ! [X0] : (~old(X0) <=> (old(X0) <~> ~quiet(X0))) [input p9]
11. ! [X0] : ((~funny(X0) & ~generous(X0)) <=> (strong(X0) | wise(X0))) [input p10]
23. wise(alice) [input hypothesis]
29. ! [X0] : (old(X0) | (kind(X0) <=> ~kind(X0))) [ennf transformation 1]
31. ! [X0] : ((~generous(X0) <~> ~quiet(X0)) | quiet(X0)) [ennf transformation 6]
34. ! [X0] : (old(X0) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) [nnf transformation 29]
43. ! [X0] : (((quiet(X0) | generous(X0)) & (~quiet(X0) | ~generous(X0))) | quiet(X0)) [nnf transformation 31]
53. ! [X0] : ((~old(X0) | ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0)))) & (((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | old(X0))) [nnf transformation 10]
54. ! [X0] : (((~funny(X0) & ~generous(X0)) | (~strong(X0) & ~wise(X0))) & ((strong(X0) | wise(X0)) | (funny(X0) | generous(X0)))) [nnf transformation 11]
55. ! [X0] : (((~funny(X0) & ~generous(X0)) | (~strong(X0) & ~wise(X0))) & (strong(X0) | wise(X0) | funny(X0) | generous(X0))) [flattening 54]
69. old(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 34]
70. old(X0) | kind(X0) | kind(X0) [cnf transformation 34]
85. quiet(X0) | generous(X0) | quiet(X0) [cnf transformation 43]
95. ~old(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 53]
98. ~generous(X0) | ~wise(X0) [cnf transformation 55]
121. wise(alice) [cnf transformation 23]
124. ~old(X0) | ~quiet(X0) [duplicate literal removal 95]
125. generous(X0) | quiet(X0) [duplicate literal removal 85]
126. old(X0) | ~kind(X0) [duplicate literal removal 69]
127. old(X0) | kind(X0) [duplicate literal removal 70]
128. old(X0) [subsumption resolution 126,127]
222. ~quiet(X0) [subsumption resolution 124,128]
268. quiet(X1) | ~wise(X1) [resolution 125,98]
272. ~wise(X1) [subsumption resolution 268,222]
283. $false [resolution 272,121]
% SZS output end Proof for 7649306407119764679249704
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is strong then someone is wise and vice versa.
If alice is either not rich or not funny then someone is wise and vice versa.
Everyone who is both not generous and not funny is both wise and humble.
If someone is not rich then alice is wise and vice versa.
If someone is either rich or quiet then fred is both wise and not patient.
Everyone who is either not old or not wise is either old or strong.
If someone is patient or funny then paul is patient and vice versa.
If someone is both not creative and not tall then someone is funny.
If john is both creative and old then someone is strong and vice versa.
If someone is strong then someone is both not happy and happy and vice versa.
Everyone who is either old or not kind is either not patient or kind.
If someone is either curious or not brave then mary is quiet.
Everyone who is either not generous or not happy is both not brave and creative.
Everyone who is both generous and not kind is either not funny or not quiet.
Everyone who is both kind and generous is either generous or not happy.
If susan is both patient and not rich then fred is creative and vice versa.
John is either not kind or not patient.
Someone is either tall or humble.
Someone is old or not generous.
Lucy is not happy.
Someone is both quiet and not old.
Someone is either curious or funny.
Fred is humble or strong. | Fred is not kind. | neutral | ((strong(paul))<=>(?[X]:(wise(X))))&
(((~rich(alice)<~>~funny(alice)))<=>(?[X]:(wise(X))))&
(![X]:((~generous(X)&~funny(X))=>(wise(X)&humble(X))))&
((?[X]:(~rich(X)))<=>(wise(alice)))&
((?[X]:((rich(X)<~>quiet(X))))=>((wise(fred)&~patient(fred))))&
(![X]:((~old(X)<~>~wise(X))=>(old(X)<~>strong(X))))&
((?[X]:((patient(X)|funny(X))))<=>(patient(paul)))&
((?[X]:((~creative(X)&~tall(X))))=>(?[X]:(funny(X))))&
(((creative(john)&old(john)))<=>(?[X]:(strong(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~happy(X)&happy(X)))))&
(![X]:((old(X)<~>~kind(X))=>(~patient(X)<~>kind(X))))&
((?[X]:((curious(X)<~>~brave(X))))=>(quiet(mary)))&
(![X]:((~generous(X)<~>~happy(X))=>(~brave(X)&creative(X))))&
(![X]:((generous(X)&~kind(X))=>(~funny(X)<~>~quiet(X))))&
(![X]:((kind(X)&generous(X))=>(generous(X)<~>~happy(X))))&
(((patient(susan)&~rich(susan)))<=>(creative(fred)))&
((~kind(john)<~>~patient(john)))&
(?[X]:((tall(X)<~>humble(X))))&
(?[X]:((old(X)|~generous(X))))&
(~happy(lucy))&
(?[X]:((quiet(X)&~old(X))))&
(?[X]:((curious(X)<~>funny(X))))&
((humble(fred)|strong(fred))) | ~kind(fred) | [] | null | 0 |
Everyone who is either not quiet or not creative is wise or generous.
Everyone who is both rich and happy is either happy or not happy.
Everyone who is not old is both not curious and old and vice versa.
Everyone who is patient is either kind or curious.
If someone is both strong and not kind then lucy is either not creative or quiet and vice versa.
Everyone who is both generous and strong is creative or wise and vice versa.
If fred is both not kind and curious then john is brave or not old.
If someone is both not quiet and not happy then john is wise or not brave.
If someone is not patient then someone is patient and vice versa.
If alice is either not calm or creative then someone is both happy and wise.
If lucy is not calm then john is both not quiet and not creative.
If paul is curious or calm then someone is not kind and vice versa.
Everyone who is both happy and brave is either brave or not strong and vice versa.
Everyone who is kind is both old and not old.
If fred is not generous then someone is both generous and not kind.
Everyone who is quiet is not creative and vice versa.
Someone is both not strong and humble.
Someone is either tall or not rich.
Lucy is tall or wise.
Someone is rich or strong.
Someone is patient or not strong.
Alice is either strong or old. | Fred is not creative. | entailment | (![X]:((~quiet(X)<~>~creative(X))=>(wise(X)|generous(X))))&
(![X]:((rich(X)&happy(X))=>(happy(X)<~>~happy(X))))&
(![X]:(~old(X)<=>(~curious(X)&old(X))))&
(![X]:(patient(X)=>(kind(X)<~>curious(X))))&
((?[X]:((strong(X)&~kind(X))))<=>((~creative(lucy)<~>quiet(lucy))))&
(![X]:((generous(X)&strong(X))<=>(creative(X)|wise(X))))&
(((~kind(fred)&curious(fred)))=>((brave(john)|~old(john))))&
((?[X]:((~quiet(X)&~happy(X))))=>((wise(john)|~brave(john))))&
((?[X]:(~patient(X)))<=>(?[X]:(patient(X))))&
(((~calm(alice)<~>creative(alice)))=>(?[X]:((happy(X)&wise(X)))))&
((~calm(lucy))=>((~quiet(john)&~creative(john))))&
(((curious(paul)|calm(paul)))<=>(?[X]:(~kind(X))))&
(![X]:((happy(X)&brave(X))<=>(brave(X)<~>~strong(X))))&
(![X]:(kind(X)=>(old(X)&~old(X))))&
((~generous(fred))=>(?[X]:((generous(X)&~kind(X)))))&
(![X]:(quiet(X)<=>~creative(X)))&
(?[X]:((~strong(X)&humble(X))))&
(?[X]:((tall(X)<~>~rich(X))))&
((tall(lucy)|wise(lucy)))&
(?[X]:((rich(X)|strong(X))))&
(?[X]:((patient(X)|~strong(X))))&
((strong(alice)<~>old(alice))) | ~creative(fred) | [
"p2",
"p4",
"p5",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8729578872949963793898569
% SZS output start Proof for 8729578872949963793898569
3. ! [X0] : (~old(X0) <=> (old(X0) & ~curious(X0))) [input p2]
5. ? [X0] : (~kind(X0) & strong(X0)) <=> (~creative(lucy) <~> quiet(lucy)) [input p4]
6. ! [X0] : ((strong(X0) & generous(X0)) <=> (wise(X0) | creative(X0))) [input p5]
14. ! [X0] : (kind(X0) => (~old(X0) & old(X0))) [input p13]
16. ! [X0] : (quiet(X0) <=> ~creative(X0)) [input p15]
23. creative(fred) [input hypothesis]
37. ! [X0] : ((~old(X0) & old(X0)) | ~kind(X0)) [ennf transformation 14]
41. ! [X0] : ((~old(X0) | (~old(X0) | curious(X0))) & ((old(X0) & ~curious(X0)) | old(X0))) [nnf transformation 3]
42. ! [X0] : ((~old(X0) | ~old(X0) | curious(X0)) & ((old(X0) & ~curious(X0)) | old(X0))) [flattening 41]
44. (? [X0] : (~kind(X0) & strong(X0)) | ((~creative(lucy) | ~quiet(lucy)) & (quiet(lucy) | creative(lucy)))) & (((~quiet(lucy) | creative(lucy)) & (quiet(lucy) | ~creative(lucy))) | ! [X0] : (kind(X0) | ~strong(X0))) [nnf transformation 5]
45. (? [X0] : (~kind(X0) & strong(X0)) | ((~creative(lucy) | ~quiet(lucy)) & (quiet(lucy) | creative(lucy)))) & (((~quiet(lucy) | creative(lucy)) & (quiet(lucy) | ~creative(lucy))) | ! [X1] : (kind(X1) | ~strong(X1))) [rectify 44]
46. ? [X0] : (~kind(X0) & strong(X0)) => (~kind(sK0) & strong(sK0)) [choice axiom]
47. ((~kind(sK0) & strong(sK0)) | ((~creative(lucy) | ~quiet(lucy)) & (quiet(lucy) | creative(lucy)))) & (((~quiet(lucy) | creative(lucy)) & (quiet(lucy) | ~creative(lucy))) | ! [X1] : (kind(X1) | ~strong(X1))) [skolemisation 45,46]
48. ! [X0] : (((strong(X0) & generous(X0)) | (~wise(X0) & ~creative(X0))) & ((wise(X0) | creative(X0)) | (~strong(X0) | ~generous(X0)))) [nnf transformation 6]
49. ! [X0] : (((strong(X0) & generous(X0)) | (~wise(X0) & ~creative(X0))) & (wise(X0) | creative(X0) | ~strong(X0) | ~generous(X0))) [flattening 48]
67. ! [X0] : ((quiet(X0) | creative(X0)) & (~creative(X0) | ~quiet(X0))) [nnf transformation 16]
83. old(X0) | old(X0) [cnf transformation 42]
87. quiet(lucy) | ~creative(lucy) | kind(X1) | ~strong(X1) [cnf transformation 47]
88. ~quiet(lucy) | creative(lucy) | kind(X1) | ~strong(X1) [cnf transformation 47]
96. ~creative(X0) | strong(X0) [cnf transformation 49]
118. ~old(X0) | ~kind(X0) [cnf transformation 37]
121. ~creative(X0) | ~quiet(X0) [cnf transformation 67]
122. creative(X0) | quiet(X0) [cnf transformation 67]
131. creative(fred) [cnf transformation 23]
134. old(X0) [duplicate literal removal 83]
139. 1 <=> quiet(lucy) [avatar definition]
140. quiet(lucy) <- (1) [avatar component clause 139]
141. ~quiet(lucy) <- (~1) [avatar component clause 139]
143. 2 <=> creative(lucy) [avatar definition]
144. creative(lucy) <- (2) [avatar component clause 143]
145. ~creative(lucy) <- (~2) [avatar component clause 143]
159. 5 <=> ! [X1] : (kind(X1) | ~strong(X1)) [avatar definition]
160. kind(X1) | ~strong(X1) <- (5) [avatar component clause 159]
161. 5 | 2 | ~1 [avatar split clause 88,139,143,159]
162. 5 | ~2 | 1 [avatar split clause 87,139,143,159]
254. ~kind(X0) [subsumption resolution 118,134]
310. strong(fred) [resolution 96,131]
318. quiet(lucy) <- (~2) [resolution 122,145]
321. $false <- (~1, ~2) [subsumption resolution 318,141]
322. 1 | 2 [avatar contradiction clause 321]
325. ~quiet(lucy) <- (2) [resolution 144,121]
328. $false <- (1, 2) [subsumption resolution 325,140]
329. ~1 | ~2 [avatar contradiction clause 328]
330. ~strong(X1) <- (5) [subsumption resolution 160,254]
339. $false <- (5) [resolution 330,310]
340. ~5 [avatar contradiction clause 339]
342. $false [avatar sat refutation 161,162,322,329,340]
% SZS output end Proof for 8729578872949963793898569
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not curious is both patient and old and vice versa.
Everyone who is not generous or not quiet is not brave or happy and vice versa.
Everyone who is both funny and not quiet is not funny.
Everyone who is creative is either not brave or not creative and vice versa.
Everyone who is not calm is either curious or not quiet.
Everyone who is both calm and funny is both not strong and creative and vice versa.
If lucy is old then someone is funny and vice versa.
Everyone who is both not old and old is not wise and vice versa.
If susan is funny or not happy then john is both kind and not strong.
Everyone who is not brave or not kind is patient and vice versa.
If john is calm or old then someone is either not brave or not funny and vice versa.
If someone is both not patient and not kind then someone is not rich and vice versa.
Everyone who is both not old and strong is rich or creative.
If lucy is either not curious or not humble then paul is rich.
Everyone who is both not generous and happy is both rich and not kind and vice versa.
Everyone who is either tall or funny is kind or tall and vice versa.
Someone is both tall and happy.
Fred is creative or not tall.
Someone is not humble or not rich.
Someone is either humble or not tall.
Lucy is both curious and patient.
Lucy is not tall.
John is kind or not generous. | John is not wise. | contradiction | (![X]:((~happy(X)|~curious(X))<=>(patient(X)&old(X))))&
(![X]:((~generous(X)|~quiet(X))<=>(~brave(X)|happy(X))))&
(![X]:((funny(X)&~quiet(X))=>~funny(X)))&
(![X]:(creative(X)<=>(~brave(X)<~>~creative(X))))&
(![X]:(~calm(X)=>(curious(X)<~>~quiet(X))))&
(![X]:((calm(X)&funny(X))<=>(~strong(X)&creative(X))))&
((old(lucy))<=>(?[X]:(funny(X))))&
(![X]:((~old(X)&old(X))<=>~wise(X)))&
(((funny(susan)|~happy(susan)))=>((kind(john)&~strong(john))))&
(![X]:((~brave(X)|~kind(X))<=>patient(X)))&
(((calm(john)|old(john)))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
((?[X]:((~patient(X)&~kind(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~old(X)&strong(X))=>(rich(X)|creative(X))))&
(((~curious(lucy)<~>~humble(lucy)))=>(rich(paul)))&
(![X]:((~generous(X)&happy(X))<=>(rich(X)&~kind(X))))&
(![X]:((tall(X)<~>funny(X))<=>(kind(X)|tall(X))))&
(?[X]:((tall(X)&happy(X))))&
((creative(fred)|~tall(fred)))&
(?[X]:((~humble(X)|~rich(X))))&
(?[X]:((humble(X)<~>~tall(X))))&
((curious(lucy)&patient(lucy)))&
(~tall(lucy))&
((kind(john)|~generous(john))) | ~wise(john) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 359063839698609613276929
% SZS output start Proof for 359063839698609613276929
8. ! [X0] : ((old(X0) & ~old(X0)) <=> ~wise(X0)) [input p7]
24. ~wise(john) [input hypothesis]
26. ! [X0] : (~wise(X0) => (old(X0) & ~old(X0))) [unused predicate definition removal 8]
30. ! [X0] : ((old(X0) & ~old(X0)) | wise(X0)) [ennf transformation 26]
93. ~old(X0) | wise(X0) [cnf transformation 30]
94. old(X0) | wise(X0) [cnf transformation 30]
134. ~wise(john) [cnf transformation 24]
154. wise(X0) [subsumption resolution 93,94]
253. $false [subsumption resolution 134,154]
% SZS output end Proof for 359063839698609613276929
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is tall and vice versa.
Everyone who is either curious or not strong is both kind and strong and vice versa.
Everyone who is rich or patient is not curious.
Everyone who is both generous and not rich is both wise and brave and vice versa.
If mary is not rich then paul is happy and vice versa.
Everyone who is not old or not patient is calm or kind and vice versa.
If someone is either not happy or generous then susan is either not rich or not happy.
If someone is not funny or not happy then someone is curious and vice versa.
Everyone who is tall or not strong is not curious.
If fred is not quiet then paul is both not creative and not kind.
Everyone who is either tall or humble is both not rich and not kind.
Everyone who is either quiet or wise is both not brave and not tall and vice versa.
If someone is either tall or not tall then fred is both not old and not brave.
If mary is both not creative and tall then someone is not strong.
Someone is either not curious or rich.
Fred is not tall or not old.
Someone is not kind or not wise.
Susan is strong or not curious.
Someone is not generous.
Fred is not quiet or not rich. | Fred is patient. | neutral | (![X]:(~old(X)<=>tall(X)))&
(![X]:((curious(X)<~>~strong(X))<=>(kind(X)&strong(X))))&
(![X]:((rich(X)|patient(X))=>~curious(X)))&
(![X]:((generous(X)&~rich(X))<=>(wise(X)&brave(X))))&
((~rich(mary))<=>(happy(paul)))&
(![X]:((~old(X)|~patient(X))<=>(calm(X)|kind(X))))&
((?[X]:((~happy(X)<~>generous(X))))=>((~rich(susan)<~>~happy(susan))))&
((?[X]:((~funny(X)|~happy(X))))<=>(?[X]:(curious(X))))&
(![X]:((tall(X)|~strong(X))=>~curious(X)))&
((~quiet(fred))=>((~creative(paul)&~kind(paul))))&
(![X]:((tall(X)<~>humble(X))=>(~rich(X)&~kind(X))))&
(![X]:((quiet(X)<~>wise(X))<=>(~brave(X)&~tall(X))))&
((?[X]:((tall(X)<~>~tall(X))))=>((~old(fred)&~brave(fred))))&
(((~creative(mary)&tall(mary)))=>(?[X]:(~strong(X))))&
(?[X]:((~curious(X)<~>rich(X))))&
((~tall(fred)|~old(fred)))&
(?[X]:((~kind(X)|~wise(X))))&
((strong(susan)|~curious(susan)))&
(?[X]:(~generous(X)))&
((~quiet(fred)|~rich(fred))) | patient(fred) | [] | null | 0 |
Everyone who is either not strong or not curious is not calm and vice versa.
Everyone who is not generous is rich and vice versa.
If susan is either not wise or not kind then lucy is both brave and rich.
If susan is either generous or not strong then fred is not tall or happy and vice versa.
Everyone who is not generous is calm.
If someone is either generous or rich then someone is either not funny or not humble and vice versa.
Everyone who is either rich or not curious is both not patient and generous.
If susan is brave or quiet then someone is either not tall or not humble and vice versa.
Everyone who is either not rich or rich is both not happy and not creative.
If someone is not tall or humble then someone is funny or not calm and vice versa.
Everyone who is both funny and creative is both not humble and brave and vice versa.
Everyone who is not brave is either funny or humble.
If paul is both not happy and not wise then fred is kind and vice versa.
Everyone who is both not curious and old is either not calm or humble and vice versa.
Everyone who is either generous or old is happy or not happy and vice versa.
Everyone who is brave is quiet or kind and vice versa.
Someone is rich or not rich.
Someone is either brave or kind.
Lucy is both not patient and not generous.
Someone is not creative or not funny.
Someone is either not creative or quiet.
Someone is either not wise or not strong.
Fred is not patient or not old.
Someone is strong or not generous. | Lucy is humble. | entailment | (![X]:((~strong(X)<~>~curious(X))<=>~calm(X)))&
(![X]:(~generous(X)<=>rich(X)))&
(((~wise(susan)<~>~kind(susan)))=>((brave(lucy)&rich(lucy))))&
(((generous(susan)<~>~strong(susan)))<=>((~tall(fred)|happy(fred))))&
(![X]:(~generous(X)=>calm(X)))&
((?[X]:((generous(X)<~>rich(X))))<=>(?[X]:((~funny(X)<~>~humble(X)))))&
(![X]:((rich(X)<~>~curious(X))=>(~patient(X)&generous(X))))&
(((brave(susan)|quiet(susan)))<=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:((~rich(X)<~>rich(X))=>(~happy(X)&~creative(X))))&
((?[X]:((~tall(X)|humble(X))))<=>(?[X]:((funny(X)|~calm(X)))))&
(![X]:((funny(X)&creative(X))<=>(~humble(X)&brave(X))))&
(![X]:(~brave(X)=>(funny(X)<~>humble(X))))&
(((~happy(paul)&~wise(paul)))<=>(kind(fred)))&
(![X]:((~curious(X)&old(X))<=>(~calm(X)<~>humble(X))))&
(![X]:((generous(X)<~>old(X))<=>(happy(X)|~happy(X))))&
(![X]:(brave(X)<=>(quiet(X)|kind(X))))&
(?[X]:((rich(X)|~rich(X))))&
(?[X]:((brave(X)<~>kind(X))))&
((~patient(lucy)&~generous(lucy)))&
(?[X]:((~creative(X)|~funny(X))))&
(?[X]:((~creative(X)<~>quiet(X))))&
(?[X]:((~wise(X)<~>~strong(X))))&
((~patient(fred)|~old(fred)))&
(?[X]:((strong(X)|~generous(X)))) | humble(lucy) | [
"p1",
"p4",
"p6",
"p8",
"p13",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7369216845065421957115415
% SZS output start Proof for 7369216845065421957115415
2. ! [X0] : (~generous(X0) <=> rich(X0)) [input p1]
5. ! [X0] : (~generous(X0) => calm(X0)) [input p4]
7. ! [X0] : ((rich(X0) <~> ~curious(X0)) => (generous(X0) & ~patient(X0))) [input p6]
9. ! [X0] : ((~rich(X0) <~> rich(X0)) => (~creative(X0) & ~happy(X0))) [input p8]
14. ! [X0] : ((old(X0) & ~curious(X0)) <=> (~calm(X0) <~> humble(X0))) [input p13]
15. ! [X0] : ((generous(X0) <~> old(X0)) <=> (~happy(X0) | happy(X0))) [input p14]
19. ~generous(lucy) & ~patient(lucy) [input p18]
25. ~humble(lucy) [input hypothesis]
28. ~generous(lucy) [pure predicate removal 19]
29. ! [X0] : ((rich(X0) <~> ~curious(X0)) => generous(X0)) [pure predicate removal 7]
32. ! [X0] : (calm(X0) | generous(X0)) [ennf transformation 5]
33. ! [X0] : (generous(X0) | (rich(X0) <=> ~curious(X0))) [ennf transformation 29]
34. ! [X0] : ((~creative(X0) & ~happy(X0)) | (~rich(X0) <=> rich(X0))) [ennf transformation 9]
37. ! [X0] : ((~generous(X0) | ~rich(X0)) & (rich(X0) | generous(X0))) [nnf transformation 2]
46. ! [X0] : (generous(X0) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0)))) [nnf transformation 33]
52. ! [X0] : ((~creative(X0) & ~happy(X0)) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0)))) [nnf transformation 34]
63. ! [X0] : (((old(X0) & ~curious(X0)) | ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0)))) & (((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | (~old(X0) | curious(X0)))) [nnf transformation 14]
64. ! [X0] : (((old(X0) & ~curious(X0)) | ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0)))) & (((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | ~old(X0) | curious(X0))) [flattening 63]
65. ! [X0] : ((((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | (happy(X0) & ~happy(X0))) & ((~happy(X0) | happy(X0)) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0))))) [nnf transformation 15]
66. ! [X0] : ((((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | (happy(X0) & ~happy(X0))) & (~happy(X0) | happy(X0) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0))))) [flattening 65]
88. rich(X0) | generous(X0) [cnf transformation 37]
89. ~rich(X0) | ~generous(X0) [cnf transformation 37]
100. generous(X0) | calm(X0) [cnf transformation 32]
109. generous(X0) | ~curious(X0) | ~rich(X0) [cnf transformation 46]
117. ~happy(X0) | rich(X0) | rich(X0) [cnf transformation 52]
118. ~happy(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 52]
134. ~old(X0) | ~calm(X0) | humble(X0) | curious(X0) [cnf transformation 64]
143. old(X0) | generous(X0) | happy(X0) [cnf transformation 66]
152. ~generous(lucy) [cnf transformation 28]
159. ~humble(lucy) [cnf transformation 25]
160. ~happy(X0) | rich(X0) [duplicate literal removal 117]
161. ~happy(X0) | ~rich(X0) [duplicate literal removal 118]
228. ~rich(X0) | ~curious(X0) [subsumption resolution 109,89]
258. ~happy(X0) [subsumption resolution 160,161]
305. old(X0) | generous(X0) [subsumption resolution 143,258]
333. ~curious(X0) | generous(X0) [resolution 228,88]
436. ~calm(X1) | humble(X1) | curious(X1) | generous(X1) [resolution 134,305]
438. humble(X1) | curious(X1) | generous(X1) [subsumption resolution 436,100]
439. humble(X1) | generous(X1) [subsumption resolution 438,333]
466. generous(lucy) [resolution 439,159]
472. $false [subsumption resolution 466,152]
% SZS output end Proof for 7369216845065421957115415
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is both creative and curious.
Everyone who is either strong or not funny is not quiet or not humble.
If someone is not quiet then alice is kind or calm and vice versa.
Everyone who is creative is either calm or creative and vice versa.
Everyone who is not calm is both old and wise.
If someone is not brave then someone is not old and vice versa.
If someone is not happy then someone is not wise or humble and vice versa.
Everyone who is both not tall and curious is not humble.
If someone is either not generous or happy then someone is wise or tall and vice versa.
Everyone who is either not quiet or not brave is both rich and humble.
If someone is both tall and kind then alice is not old.
Everyone who is not humble is either not funny or creative and vice versa.
Everyone who is curious or tall is not brave.
Everyone who is old is creative or not humble and vice versa.
Mary is not patient or not humble.
Someone is either not humble or generous.
Someone is both not tall and not patient.
Susan is generous.
Someone is humble or quiet.
Lucy is not strong or not humble.
Fred is not patient. | Alice is not funny. | entailment | (![X]:(creative(X)=>(creative(X)&curious(X))))&
(![X]:((strong(X)<~>~funny(X))=>(~quiet(X)|~humble(X))))&
((?[X]:(~quiet(X)))<=>((kind(alice)|calm(alice))))&
(![X]:(creative(X)<=>(calm(X)<~>creative(X))))&
(![X]:(~calm(X)=>(old(X)&wise(X))))&
((?[X]:(~brave(X)))<=>(?[X]:(~old(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~wise(X)|humble(X)))))&
(![X]:((~tall(X)&curious(X))=>~humble(X)))&
((?[X]:((~generous(X)<~>happy(X))))<=>(?[X]:((wise(X)|tall(X)))))&
(![X]:((~quiet(X)<~>~brave(X))=>(rich(X)&humble(X))))&
((?[X]:((tall(X)&kind(X))))=>(~old(alice)))&
(![X]:(~humble(X)<=>(~funny(X)<~>creative(X))))&
(![X]:((curious(X)|tall(X))=>~brave(X)))&
(![X]:(old(X)<=>(creative(X)|~humble(X))))&
((~patient(mary)|~humble(mary)))&
(?[X]:((~humble(X)<~>generous(X))))&
(?[X]:((~tall(X)&~patient(X))))&
(generous(susan))&
(?[X]:((humble(X)|quiet(X))))&
((~strong(lucy)|~humble(lucy)))&
(~patient(fred)) | ~funny(alice) | [
"p0",
"p3",
"p4",
"p5",
"p6",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2477286788461203780214208
% SZS output start Proof for 2477286788461203780214208
1. ! [X0] : (creative(X0) => (curious(X0) & creative(X0))) [input p0]
4. ! [X0] : (creative(X0) <=> (calm(X0) <~> creative(X0))) [input p3]
5. ! [X0] : (~calm(X0) => (wise(X0) & old(X0))) [input p4]
6. ? [X0] : ~brave(X0) <=> ? [X0] : ~old(X0) [input p5]
7. ? [X0] : ~happy(X0) <=> ? [X0] : (humble(X0) | ~wise(X0)) [input p6]
12. ! [X0] : (~humble(X0) <=> (~funny(X0) <~> creative(X0))) [input p11]
13. ! [X0] : ((tall(X0) | curious(X0)) => ~brave(X0)) [input p12]
14. ! [X0] : (old(X0) <=> (~humble(X0) | creative(X0))) [input p13]
22. funny(alice) [input hypothesis]
23. ? [X0] : ~brave(X0) <=> ? [X1] : ~old(X1) [rectify 6]
24. ? [X0] : ~happy(X0) <=> ? [X1] : (humble(X1) | ~wise(X1)) [rectify 7]
30. ! [X0] : ((curious(X0) & creative(X0)) | ~creative(X0)) [ennf transformation 1]
33. ! [X0] : ((wise(X0) & old(X0)) | calm(X0)) [ennf transformation 5]
38. ! [X0] : (~brave(X0) | (~tall(X0) & ~curious(X0))) [ennf transformation 13]
45. ! [X0] : ((creative(X0) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0)))) & (((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | ~creative(X0))) [nnf transformation 4]
46. (? [X0] : ~brave(X0) | ! [X1] : old(X1)) & (? [X1] : ~old(X1) | ! [X0] : brave(X0)) [nnf transformation 23]
47. (? [X0] : ~brave(X0) | ! [X1] : old(X1)) & (? [X2] : ~old(X2) | ! [X3] : brave(X3)) [rectify 46]
48. ? [X0] : ~brave(X0) => ~brave(sK1) [choice axiom]
49. ? [X2] : ~old(X2) => ~old(sK2) [choice axiom]
50. (~brave(sK1) | ! [X1] : old(X1)) & (~old(sK2) | ! [X3] : brave(X3)) [skolemisation 47,49,48]
51. (? [X0] : ~happy(X0) | ! [X1] : (~humble(X1) & wise(X1))) & (? [X1] : (humble(X1) | ~wise(X1)) | ! [X0] : happy(X0)) [nnf transformation 24]
52. (? [X0] : ~happy(X0) | ! [X1] : (~humble(X1) & wise(X1))) & (? [X2] : (humble(X2) | ~wise(X2)) | ! [X3] : happy(X3)) [rectify 51]
53. ? [X0] : ~happy(X0) => ~happy(sK3) [choice axiom]
54. ? [X2] : (humble(X2) | ~wise(X2)) => (humble(sK4) | ~wise(sK4)) [choice axiom]
55. (~happy(sK3) | ! [X1] : (~humble(X1) & wise(X1))) & ((humble(sK4) | ~wise(sK4)) | ! [X3] : happy(X3)) [skolemisation 52,54,53]
62. ! [X0] : ((~humble(X0) | ((~funny(X0) | ~creative(X0)) & (creative(X0) | funny(X0)))) & (((~creative(X0) | funny(X0)) & (creative(X0) | ~funny(X0))) | humble(X0))) [nnf transformation 12]
63. ! [X0] : ((old(X0) | (humble(X0) & ~creative(X0))) & ((~humble(X0) | creative(X0)) | ~old(X0))) [nnf transformation 14]
64. ! [X0] : ((old(X0) | (humble(X0) & ~creative(X0))) & (~humble(X0) | creative(X0) | ~old(X0))) [flattening 63]
73. ~creative(X0) | curious(X0) [cnf transformation 30]
80. ~creative(X0) | ~calm(X0) | ~creative(X0) [cnf transformation 45]
81. creative(X0) | creative(X0) | ~calm(X0) [cnf transformation 45]
83. old(X0) | calm(X0) [cnf transformation 33]
84. wise(X0) | calm(X0) [cnf transformation 33]
85. ~old(sK2) | brave(X3) [cnf transformation 50]
87. humble(sK4) | ~wise(sK4) | happy(X3) [cnf transformation 55]
89. ~happy(sK3) | ~humble(X1) [cnf transformation 55]
100. ~funny(X0) | creative(X0) | humble(X0) [cnf transformation 62]
104. ~brave(X0) | ~curious(X0) [cnf transformation 38]
106. ~humble(X0) | creative(X0) | ~old(X0) [cnf transformation 64]
115. funny(alice) [cnf transformation 22]
116. ~creative(X0) | ~calm(X0) [duplicate literal removal 80]
117. ~calm(X0) | creative(X0) [duplicate literal removal 81]
136. ~calm(X0) [subsumption resolution 116,117]
137. wise(X0) [subsumption resolution 84,136]
138. old(X0) [subsumption resolution 83,136]
139. brave(X3) [subsumption resolution 85,138]
141. 5 <=> ! [X1] : ~humble(X1) [avatar definition]
142. ~humble(X1) <- (5) [avatar component clause 141]
144. 6 <=> happy(sK3) [avatar definition]
146. ~happy(sK3) <- (~6) [avatar component clause 144]
147. 5 | ~6 [avatar split clause 89,144,141]
148. humble(sK4) | happy(X3) [subsumption resolution 87,137]
150. 7 <=> ! [X3] : happy(X3) [avatar definition]
151. happy(X3) <- (7) [avatar component clause 150]
153. 8 <=> humble(sK4) [avatar definition]
155. humble(sK4) <- (8) [avatar component clause 153]
156. 7 | 8 [avatar split clause 148,153,150]
178. ~curious(X0) [subsumption resolution 104,139]
179. ~humble(X0) | creative(X0) [subsumption resolution 106,138]
199. $false <- (~6, 7) [subsumption resolution 146,151]
200. 6 | ~7 [avatar contradiction clause 199]
207. creative(sK4) <- (8) [resolution 179,155]
211. curious(sK4) <- (8) [resolution 207,73]
212. $false <- (8) [subsumption resolution 211,178]
213. ~8 [avatar contradiction clause 212]
219. creative(alice) | humble(alice) [resolution 100,115]
220. creative(alice) <- (5) [subsumption resolution 219,142]
221. curious(alice) <- (5) [resolution 220,73]
222. $false <- (5) [subsumption resolution 221,178]
223. ~5 [avatar contradiction clause 222]
224. $false [avatar sat refutation 147,156,200,213,223]
% SZS output end Proof for 2477286788461203780214208
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not calm is brave and vice versa.
If someone is either not brave or kind then someone is not tall.
If someone is not funny or patient then susan is rich or creative and vice versa.
If someone is not creative then john is both old and not funny and vice versa.
If john is brave then john is not quiet.
If someone is not calm then john is either not funny or not brave and vice versa.
If mary is both wise and funny then paul is not rich or creative.
If someone is creative then someone is either patient or strong and vice versa.
Everyone who is both quiet and creative is both humble and not creative.
If lucy is not creative then someone is not happy or not tall and vice versa.
Everyone who is humble or tall is both not generous and not quiet.
Everyone who is humble or not old is both not patient and not brave and vice versa.
Everyone who is both not strong and not creative is brave or not kind.
If alice is not strong then paul is funny and vice versa.
Everyone who is happy or generous is not old or kind.
Everyone who is kind is either not kind or quiet.
Paul is generous.
Mary is both not generous and creative.
Susan is wise.
Lucy is both not funny and not kind.
Mary is both not wise and not funny.
Fred is happy.
Someone is either quiet or not calm. | Paul is not rich. | neutral | (![X]:((~brave(X)<~>~calm(X))<=>brave(X)))&
((?[X]:((~brave(X)<~>kind(X))))=>(?[X]:(~tall(X))))&
((?[X]:((~funny(X)|patient(X))))<=>((rich(susan)|creative(susan))))&
((?[X]:(~creative(X)))<=>((old(john)&~funny(john))))&
((brave(john))=>(~quiet(john)))&
((?[X]:(~calm(X)))<=>((~funny(john)<~>~brave(john))))&
(((wise(mary)&funny(mary)))=>((~rich(paul)|creative(paul))))&
((?[X]:(creative(X)))<=>(?[X]:((patient(X)<~>strong(X)))))&
(![X]:((quiet(X)&creative(X))=>(humble(X)&~creative(X))))&
((~creative(lucy))<=>(?[X]:((~happy(X)|~tall(X)))))&
(![X]:((humble(X)|tall(X))=>(~generous(X)&~quiet(X))))&
(![X]:((humble(X)|~old(X))<=>(~patient(X)&~brave(X))))&
(![X]:((~strong(X)&~creative(X))=>(brave(X)|~kind(X))))&
((~strong(alice))<=>(funny(paul)))&
(![X]:((happy(X)|generous(X))=>(~old(X)|kind(X))))&
(![X]:(kind(X)=>(~kind(X)<~>quiet(X))))&
(generous(paul))&
((~generous(mary)&creative(mary)))&
(wise(susan))&
((~funny(lucy)&~kind(lucy)))&
((~wise(mary)&~funny(mary)))&
(happy(fred))&
(?[X]:((quiet(X)<~>~calm(X)))) | ~rich(paul) | [] | null | 0 |
If paul is both not creative and kind then susan is both happy and not tall.
Everyone who is not quiet or old is not patient or calm and vice versa.
If someone is not creative then paul is old and vice versa.
If susan is either generous or not quiet then lucy is not rich.
Everyone who is wise is creative or happy and vice versa.
Everyone who is funny is both not creative and generous and vice versa.
If paul is either tall or not creative then lucy is calm or not creative and vice versa.
Everyone who is not happy or not humble is rich and vice versa.
If someone is not strong or creative then mary is not rich and vice versa.
If someone is both calm and not humble then fred is either not humble or funny.
Everyone who is brave is either not patient or calm.
Everyone who is kind or not creative is not curious or kind and vice versa.
If lucy is both strong and old then someone is both quiet and strong.
Everyone who is old is both not humble and not funny.
If someone is not patient then fred is not happy.
Everyone who is old is happy or not kind and vice versa.
Someone is either not humble or not strong.
Mary is not kind or wise.
John is not happy.
Alice is curious or not curious.
Someone is either not old or kind.
Someone is generous.
Someone is either not generous or quiet. | Mary is not curious. | neutral | (((~creative(paul)&kind(paul)))=>((happy(susan)&~tall(susan))))&
(![X]:((~quiet(X)|old(X))<=>(~patient(X)|calm(X))))&
((?[X]:(~creative(X)))<=>(old(paul)))&
(((generous(susan)<~>~quiet(susan)))=>(~rich(lucy)))&
(![X]:(wise(X)<=>(creative(X)|happy(X))))&
(![X]:(funny(X)<=>(~creative(X)&generous(X))))&
(((tall(paul)<~>~creative(paul)))<=>((calm(lucy)|~creative(lucy))))&
(![X]:((~happy(X)|~humble(X))<=>rich(X)))&
((?[X]:((~strong(X)|creative(X))))<=>(~rich(mary)))&
((?[X]:((calm(X)&~humble(X))))=>((~humble(fred)<~>funny(fred))))&
(![X]:(brave(X)=>(~patient(X)<~>calm(X))))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)|kind(X))))&
(((strong(lucy)&old(lucy)))=>(?[X]:((quiet(X)&strong(X)))))&
(![X]:(old(X)=>(~humble(X)&~funny(X))))&
((?[X]:(~patient(X)))=>(~happy(fred)))&
(![X]:(old(X)<=>(happy(X)|~kind(X))))&
(?[X]:((~humble(X)<~>~strong(X))))&
((~kind(mary)|wise(mary)))&
(~happy(john))&
((curious(alice)|~curious(alice)))&
(?[X]:((~old(X)<~>kind(X))))&
(?[X]:(generous(X)))&
(?[X]:((~generous(X)<~>quiet(X)))) | ~curious(mary) | [] | null | 0 |
If paul is both not creative and rich then someone is old or happy and vice versa.
If someone is both tall and not strong then someone is either calm or not patient.
If someone is both not creative and not wise then someone is both humble and not wise and vice versa.
Everyone who is tall or not brave is not happy and vice versa.
Everyone who is either generous or creative is either wise or not curious and vice versa.
If someone is strong then susan is not brave and vice versa.
If john is both not kind and not rich then someone is patient and vice versa.
If lucy is funny then fred is either happy or humble.
If alice is both not humble and creative then alice is not funny.
If mary is not strong then fred is both not generous and calm and vice versa.
Everyone who is tall or not brave is not creative or strong.
If someone is either not old or old then someone is not curious and vice versa.
Everyone who is humble or curious is not old or rich and vice versa.
Everyone who is either generous or not generous is either quiet or not brave and vice versa.
Everyone who is not humble or not wise is both not funny and tall.
Everyone who is either not creative or not quiet is both brave and quiet and vice versa.
John is old or not curious.
Alice is either not rich or not generous.
Someone is either generous or not wise.
Someone is not humble.
Someone is either not creative or not patient.
Someone is not tall or humble.
Susan is rich. | John is curious. | contradiction | (((~creative(paul)&rich(paul)))<=>(?[X]:((old(X)|happy(X)))))&
((?[X]:((tall(X)&~strong(X))))=>(?[X]:((calm(X)<~>~patient(X)))))&
((?[X]:((~creative(X)&~wise(X))))<=>(?[X]:((humble(X)&~wise(X)))))&
(![X]:((tall(X)|~brave(X))<=>~happy(X)))&
(![X]:((generous(X)<~>creative(X))<=>(wise(X)<~>~curious(X))))&
((?[X]:(strong(X)))<=>(~brave(susan)))&
(((~kind(john)&~rich(john)))<=>(?[X]:(patient(X))))&
((funny(lucy))=>((happy(fred)<~>humble(fred))))&
(((~humble(alice)&creative(alice)))=>(~funny(alice)))&
((~strong(mary))<=>((~generous(fred)&calm(fred))))&
(![X]:((tall(X)|~brave(X))=>(~creative(X)|strong(X))))&
((?[X]:((~old(X)<~>old(X))))<=>(?[X]:(~curious(X))))&
(![X]:((humble(X)|curious(X))<=>(~old(X)|rich(X))))&
(![X]:((generous(X)<~>~generous(X))<=>(quiet(X)<~>~brave(X))))&
(![X]:((~humble(X)|~wise(X))=>(~funny(X)&tall(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>(brave(X)&quiet(X))))&
((old(john)|~curious(john)))&
((~rich(alice)<~>~generous(alice)))&
(?[X]:((generous(X)<~>~wise(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~creative(X)<~>~patient(X))))&
(?[X]:((~tall(X)|humble(X))))&
(rich(susan)) | curious(john) | [
"p6",
"p12",
"p13",
"p15",
"p16",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 972369412632799705501515
% SZS output start Proof for 972369412632799705501515
7. (~rich(john) & ~kind(john)) <=> ? [X0] : patient(X0) [input p6]
13. ! [X0] : ((curious(X0) | humble(X0)) <=> (rich(X0) | ~old(X0))) [input p12]
14. ! [X0] : ((generous(X0) <~> ~generous(X0)) <=> (quiet(X0) <~> ~brave(X0))) [input p13]
16. ! [X0] : ((~creative(X0) <~> ~quiet(X0)) <=> (quiet(X0) & brave(X0))) [input p15]
17. ~curious(john) | old(john) [input p16]
21. ? [X0] : (~creative(X0) <~> ~patient(X0)) [input p20]
24. curious(john) [input hypothesis]
56. ((~rich(john) & ~kind(john)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | (rich(john) | kind(john))) [nnf transformation 7]
57. ((~rich(john) & ~kind(john)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | rich(john) | kind(john)) [flattening 56]
58. ((~rich(john) & ~kind(john)) | ! [X0] : ~patient(X0)) & (? [X1] : patient(X1) | rich(john) | kind(john)) [rectify 57]
59. ? [X1] : patient(X1) => patient(sK5) [choice axiom]
60. ((~rich(john) & ~kind(john)) | ! [X0] : ~patient(X0)) & (patient(sK5) | rich(john) | kind(john)) [skolemisation 58,59]
68. ! [X0] : (((curious(X0) | humble(X0)) | (~rich(X0) & old(X0))) & ((rich(X0) | ~old(X0)) | (~curious(X0) & ~humble(X0)))) [nnf transformation 13]
69. ! [X0] : ((curious(X0) | humble(X0) | (~rich(X0) & old(X0))) & (rich(X0) | ~old(X0) | (~curious(X0) & ~humble(X0)))) [flattening 68]
70. ! [X0] : ((((generous(X0) | ~generous(X0)) & (~generous(X0) | generous(X0))) | ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0))))) [nnf transformation 14]
71. ! [X0] : ((((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | (~quiet(X0) | ~brave(X0))) & ((quiet(X0) & brave(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0))))) [nnf transformation 16]
72. ! [X0] : ((((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | ~quiet(X0) | ~brave(X0)) & ((quiet(X0) & brave(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0))))) [flattening 71]
79. ? [X0] : ((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) [nnf transformation 21]
80. ? [X0] : ((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) => ((patient(sK10) | creative(sK10)) & (~patient(sK10) | ~creative(sK10))) [choice axiom]
81. (patient(sK10) | creative(sK10)) & (~patient(sK10) | ~creative(sK10)) [skolemisation 79,80]
110. ~rich(john) | ~patient(X0) [cnf transformation 60]
121. ~curious(X0) | ~old(X0) | rich(X0) [cnf transformation 69]
126. brave(X0) | ~quiet(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 70]
127. brave(X0) | ~quiet(X0) | generous(X0) | generous(X0) [cnf transformation 70]
137. quiet(X0) | ~creative(X0) | quiet(X0) [cnf transformation 72]
138. ~quiet(X0) | ~creative(X0) | ~quiet(X0) | ~brave(X0) [cnf transformation 72]
140. ~curious(john) | old(john) [cnf transformation 17]
147. patient(sK10) | creative(sK10) [cnf transformation 81]
150. curious(john) [cnf transformation 24]
151. quiet(X0) | ~creative(X0) [duplicate literal removal 137]
152. ~quiet(X0) | ~creative(X0) | ~brave(X0) [duplicate literal removal 138]
155. brave(X0) | ~quiet(X0) | ~generous(X0) [duplicate literal removal 126]
156. brave(X0) | ~quiet(X0) | generous(X0) [duplicate literal removal 127]
239. 19 <=> ! [X0] : ~patient(X0) [avatar definition]
240. ~patient(X0) <- (19) [avatar component clause 239]
242. 20 <=> rich(john) [avatar definition]
244. ~rich(john) <- (~20) [avatar component clause 242]
245. 19 | ~20 [avatar split clause 110,242,239]
280. ~quiet(X0) | brave(X0) [subsumption resolution 155,156]
282. ~quiet(X0) | ~creative(X0) [subsumption resolution 152,280]
283. ~creative(X0) [subsumption resolution 151,282]
285. 28 <=> old(john) [avatar definition]
287. old(john) <- (28) [avatar component clause 285]
289. 29 <=> curious(john) [avatar definition]
290. curious(john) <- (29) [avatar component clause 289]
292. 28 | ~29 [avatar split clause 140,289,285]
313. patient(sK10) [subsumption resolution 147,283]
315. 29 [avatar split clause 150,289]
319. $false <- (19) [resolution 313,240]
320. ~19 [avatar contradiction clause 319]
361. ~old(john) | rich(john) <- (29) [resolution 121,290]
362. rich(john) <- (28, 29) [subsumption resolution 361,287]
363. $false <- (~20, 28, 29) [subsumption resolution 362,244]
364. 20 | ~28 | ~29 [avatar contradiction clause 363]
365. $false [avatar sat refutation 245,292,315,320,364]
% SZS output end Proof for 972369412632799705501515
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or brave is wise or not old and vice versa. Everyone who is either not curious or curious is not strong and vice versa. If mary is not tall or not creative then paul is wise or not funny and vice versa. Everyone who is either curious or humble is both rich and not rich. Everyone who is both wise and not calm is either not patient or not old and vice versa. If someone is not curious then someone is kind. If someone is either not calm or not tall then mary is quiet. Everyone who is creative is both patient and not strong and vice versa. Everyone who is either not quiet or not humble is both not curious and creative and vice versa. Everyone who is not humble is both happy and not quiet. Everyone who is either not kind or strong is either calm or not creative and vice versa. Everyone who is wise is both not creative and generous. Everyone who is not quiet or not wise is either not curious or curious and vice versa. If someone is both generous and not strong then fred is quiet. Everyone who is not old or not patient is both not old and not calm and vice versa. Everyone who is humble or not brave is both not patient and not generous. Paul is not strong. Paul is both rich and not tall. Someone is not old or quiet. Mary is either funny or creative. Someone is both not happy and not wise. | Mary is calm. | contradiction | (![X]:((~old(X)|brave(X))<=>(wise(X)|~old(X))))&
(![X]:((~curious(X)<~>curious(X))<=>~strong(X)))&
(((~tall(mary)|~creative(mary)))<=>((wise(paul)|~funny(paul))))&
(![X]:((curious(X)<~>humble(X))=>(rich(X)&~rich(X))))&
(![X]:((wise(X)&~calm(X))<=>(~patient(X)<~>~old(X))))&
((?[X]:(~curious(X)))=>(?[X]:(kind(X))))&
((?[X]:((~calm(X)<~>~tall(X))))=>(quiet(mary)))&
(![X]:(creative(X)<=>(patient(X)&~strong(X))))&
(![X]:((~quiet(X)<~>~humble(X))<=>(~curious(X)&creative(X))))&
(![X]:(~humble(X)=>(happy(X)&~quiet(X))))&
(![X]:((~kind(X)<~>strong(X))<=>(calm(X)<~>~creative(X))))&
(![X]:(wise(X)=>(~creative(X)&generous(X))))&
(![X]:((~quiet(X)|~wise(X))<=>(~curious(X)<~>curious(X))))&
((?[X]:((generous(X)&~strong(X))))=>(quiet(fred)))&
(![X]:((~old(X)|~patient(X))<=>(~old(X)&~calm(X))))&
(![X]:((humble(X)|~brave(X))=>(~patient(X)&~generous(X))))&
(~strong(paul))&
((rich(paul)&~tall(paul)))&
(?[X]:((~old(X)|quiet(X))))&
((funny(mary)<~>creative(mary)))&
(?[X]:((~happy(X)&~wise(X)))) | calm(mary) | [
"p0",
"p1",
"p7",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3935416545319253417941463
% SZS output start Proof for 3935416545319253417941463
1. ! [X0] : ((brave(X0) | ~old(X0)) <=> (~old(X0) | wise(X0))) [input p0]
2. ! [X0] : ((~curious(X0) <~> curious(X0)) <=> ~strong(X0)) [input p1]
8. ! [X0] : (creative(X0) <=> (~strong(X0) & patient(X0))) [input p7]
12. ! [X0] : (wise(X0) => (generous(X0) & ~creative(X0))) [input p11]
15. ! [X0] : ((~patient(X0) | ~old(X0)) <=> (~calm(X0) & ~old(X0))) [input p14]
16. ! [X0] : ((~brave(X0) | humble(X0)) => (~generous(X0) & ~patient(X0))) [input p15]
22. calm(mary) [input hypothesis]
28. ! [X0] : ((generous(X0) & ~creative(X0)) | ~wise(X0)) [ennf transformation 12]
30. ! [X0] : ((~generous(X0) & ~patient(X0)) | (brave(X0) & ~humble(X0))) [ennf transformation 16]
31. ! [X0] : (((brave(X0) | ~old(X0)) | (old(X0) & ~wise(X0))) & ((~old(X0) | wise(X0)) | (~brave(X0) & old(X0)))) [nnf transformation 1]
32. ! [X0] : ((brave(X0) | ~old(X0) | (old(X0) & ~wise(X0))) & (~old(X0) | wise(X0) | (~brave(X0) & old(X0)))) [flattening 31]
33. ! [X0] : ((((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | strong(X0)) & (~strong(X0) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0))))) [nnf transformation 2]
43. ! [X0] : ((creative(X0) | (strong(X0) | ~patient(X0))) & ((~strong(X0) & patient(X0)) | ~creative(X0))) [nnf transformation 8]
44. ! [X0] : ((creative(X0) | strong(X0) | ~patient(X0)) & ((~strong(X0) & patient(X0)) | ~creative(X0))) [flattening 43]
50. ! [X0] : (((~patient(X0) | ~old(X0)) | (calm(X0) | old(X0))) & ((~calm(X0) & ~old(X0)) | (patient(X0) & old(X0)))) [nnf transformation 15]
51. ! [X0] : ((~patient(X0) | ~old(X0) | calm(X0) | old(X0)) & ((~calm(X0) & ~old(X0)) | (patient(X0) & old(X0)))) [flattening 50]
58. ~brave(X0) | wise(X0) | ~old(X0) [cnf transformation 32]
61. ~strong(X0) | curious(X0) | curious(X0) [cnf transformation 33]
62. ~strong(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 33]
84. creative(X0) | strong(X0) | ~patient(X0) [cnf transformation 44]
101. ~creative(X0) | ~wise(X0) [cnf transformation 28]
111. ~old(X0) | patient(X0) [cnf transformation 51]
112. ~calm(X0) | old(X0) [cnf transformation 51]
116. ~patient(X0) | brave(X0) [cnf transformation 30]
127. calm(mary) [cnf transformation 22]
130. ~strong(X0) | curious(X0) [duplicate literal removal 61]
131. ~strong(X0) | ~curious(X0) [duplicate literal removal 62]
132. ~strong(X0) [subsumption resolution 130,131]
142. 3 <=> creative(mary) [avatar definition]
143. creative(mary) <- (3) [avatar component clause 142]
175. ~patient(X0) | creative(X0) [subsumption resolution 84,132]
211. old(mary) [resolution 112,127]
213. patient(mary) [resolution 211,111]
225. creative(mary) [resolution 213,175]
226. brave(mary) [resolution 213,116]
232. 3 [avatar split clause 225,142]
234. ~wise(mary) <- (3) [resolution 143,101]
241. wise(mary) | ~old(mary) [resolution 58,226]
242. ~old(mary) <- (3) [subsumption resolution 241,234]
243. $false <- (3) [subsumption resolution 242,211]
244. ~3 [avatar contradiction clause 243]
245. $false [avatar sat refutation 232,244]
% SZS output end Proof for 3935416545319253417941463
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not funny or not wise then john is either not calm or wise and vice versa.
Everyone who is either strong or not old is both patient and not brave and vice versa.
If paul is either not brave or not generous then someone is either quiet or not humble and vice versa.
Everyone who is both quiet and not kind is not creative or funny and vice versa.
Everyone who is either humble or not happy is either calm or brave.
Everyone who is both wise and happy is not kind or not humble.
Everyone who is both rich and happy is not humble or not rich and vice versa.
Everyone who is generous is not funny and vice versa.
Everyone who is not quiet or funny is happy.
If someone is either humble or not funny then someone is not funny.
If someone is either generous or happy then someone is either not funny or happy and vice versa.
Everyone who is either not happy or not humble is not patient or not strong and vice versa.
If someone is creative then someone is funny.
If alice is both not generous and not tall then someone is both not patient and strong.
Everyone who is wise or not wise is both not generous and not humble and vice versa.
If john is both not calm and strong then someone is both tall and humble.
Susan is either calm or not patient.
Someone is not tall or not kind.
Someone is not old.
Susan is either not tall or not brave.
Someone is either wise or not old.
Susan is either patient or not generous.
Someone is quiet. | John is not old. | neutral | (((~funny(lucy)|~wise(lucy)))<=>((~calm(john)<~>wise(john))))&
(![X]:((strong(X)<~>~old(X))<=>(patient(X)&~brave(X))))&
(((~brave(paul)<~>~generous(paul)))<=>(?[X]:((quiet(X)<~>~humble(X)))))&
(![X]:((quiet(X)&~kind(X))<=>(~creative(X)|funny(X))))&
(![X]:((humble(X)<~>~happy(X))=>(calm(X)<~>brave(X))))&
(![X]:((wise(X)&happy(X))=>(~kind(X)|~humble(X))))&
(![X]:((rich(X)&happy(X))<=>(~humble(X)|~rich(X))))&
(![X]:(generous(X)<=>~funny(X)))&
(![X]:((~quiet(X)|funny(X))=>happy(X)))&
((?[X]:((humble(X)<~>~funny(X))))=>(?[X]:(~funny(X))))&
((?[X]:((generous(X)<~>happy(X))))<=>(?[X]:((~funny(X)<~>happy(X)))))&
(![X]:((~happy(X)<~>~humble(X))<=>(~patient(X)|~strong(X))))&
((?[X]:(creative(X)))=>(?[X]:(funny(X))))&
(((~generous(alice)&~tall(alice)))=>(?[X]:((~patient(X)&strong(X)))))&
(![X]:((wise(X)|~wise(X))<=>(~generous(X)&~humble(X))))&
(((~calm(john)&strong(john)))=>(?[X]:((tall(X)&humble(X)))))&
((calm(susan)<~>~patient(susan)))&
(?[X]:((~tall(X)|~kind(X))))&
(?[X]:(~old(X)))&
((~tall(susan)<~>~brave(susan)))&
(?[X]:((wise(X)<~>~old(X))))&
((patient(susan)<~>~generous(susan)))&
(?[X]:(quiet(X))) | ~old(john) | [] | null | 0 |
Everyone who is both brave and not calm is both not old and curious and vice versa.
Everyone who is both not quiet and patient is both rich and brave and vice versa.
Everyone who is not old or humble is not kind and vice versa.
Everyone who is not calm or humble is not creative or strong and vice versa.
If fred is both happy and patient then someone is humble or not wise and vice versa.
If john is either humble or happy then susan is both not brave and not rich.
Everyone who is either funny or rich is either not creative or not funny.
Everyone who is both patient and rich is both strong and humble.
Everyone who is not funny is not creative or tall and vice versa.
Everyone who is humble is both brave and not old.
Everyone who is both not brave and not wise is both rich and not quiet.
Everyone who is happy or patient is both not humble and humble and vice versa.
Everyone who is either tall or curious is calm or creative and vice versa.
If paul is not tall then someone is happy or brave.
If someone is not humble then lucy is brave or not humble and vice versa.
Everyone who is not strong is kind.
Someone is not strong.
John is both old and kind.
John is either not curious or not wise.
Someone is both wise and kind.
Mary is quiet.
Paul is not tall or funny.
Alice is old or not tall.
Mary is not brave or not happy. | Susan is creative. | neutral | (![X]:((brave(X)&~calm(X))<=>(~old(X)&curious(X))))&
(![X]:((~quiet(X)&patient(X))<=>(rich(X)&brave(X))))&
(![X]:((~old(X)|humble(X))<=>~kind(X)))&
(![X]:((~calm(X)|humble(X))<=>(~creative(X)|strong(X))))&
(((happy(fred)&patient(fred)))<=>(?[X]:((humble(X)|~wise(X)))))&
(((humble(john)<~>happy(john)))=>((~brave(susan)&~rich(susan))))&
(![X]:((funny(X)<~>rich(X))=>(~creative(X)<~>~funny(X))))&
(![X]:((patient(X)&rich(X))=>(strong(X)&humble(X))))&
(![X]:(~funny(X)<=>(~creative(X)|tall(X))))&
(![X]:(humble(X)=>(brave(X)&~old(X))))&
(![X]:((~brave(X)&~wise(X))=>(rich(X)&~quiet(X))))&
(![X]:((happy(X)|patient(X))<=>(~humble(X)&humble(X))))&
(![X]:((tall(X)<~>curious(X))<=>(calm(X)|creative(X))))&
((~tall(paul))=>(?[X]:((happy(X)|brave(X)))))&
((?[X]:(~humble(X)))<=>((brave(lucy)|~humble(lucy))))&
(![X]:(~strong(X)=>kind(X)))&
(?[X]:(~strong(X)))&
((old(john)&kind(john)))&
((~curious(john)<~>~wise(john)))&
(?[X]:((wise(X)&kind(X))))&
(quiet(mary))&
((~tall(paul)|funny(paul)))&
((old(alice)|~tall(alice)))&
((~brave(mary)|~happy(mary))) | creative(susan) | [] | null | 0 |
If someone is both not brave and strong then someone is either kind or curious.
Everyone who is both not kind and not wise is either tall or not rich.
Everyone who is both brave and creative is either not curious or creative and vice versa.
Everyone who is both not calm and not rich is not funny.
Everyone who is either brave or patient is humble.
If mary is not rich or quiet then someone is either rich or not brave.
Everyone who is either brave or not curious is quiet.
If someone is either humble or not creative then john is not rich or happy and vice versa.
If john is kind or not kind then someone is both not old and not brave and vice versa.
If alice is either not strong or not quiet then someone is quiet or not old.
Everyone who is both not humble and not patient is not old.
Everyone who is either not generous or not happy is happy and vice versa.
If lucy is happy or not happy then john is happy and vice versa.
Everyone who is either not wise or patient is not wise or not humble and vice versa.
If someone is not kind then paul is both not rich and not old and vice versa.
If paul is not generous or strong then paul is not curious or wise and vice versa.
Lucy is both not funny and not kind.
Someone is both not tall and not wise.
Susan is either not calm or rich.
Susan is either patient or not curious.
Alice is not wise.
Fred is not patient or not kind.
Someone is either not generous or happy. | Susan is not funny. | neutral | ((?[X]:((~brave(X)&strong(X))))=>(?[X]:((kind(X)<~>curious(X)))))&
(![X]:((~kind(X)&~wise(X))=>(tall(X)<~>~rich(X))))&
(![X]:((brave(X)&creative(X))<=>(~curious(X)<~>creative(X))))&
(![X]:((~calm(X)&~rich(X))=>~funny(X)))&
(![X]:((brave(X)<~>patient(X))=>humble(X)))&
(((~rich(mary)|quiet(mary)))=>(?[X]:((rich(X)<~>~brave(X)))))&
(![X]:((brave(X)<~>~curious(X))=>quiet(X)))&
((?[X]:((humble(X)<~>~creative(X))))<=>((~rich(john)|happy(john))))&
(((kind(john)|~kind(john)))<=>(?[X]:((~old(X)&~brave(X)))))&
(((~strong(alice)<~>~quiet(alice)))=>(?[X]:((quiet(X)|~old(X)))))&
(![X]:((~humble(X)&~patient(X))=>~old(X)))&
(![X]:((~generous(X)<~>~happy(X))<=>happy(X)))&
(((happy(lucy)|~happy(lucy)))<=>(happy(john)))&
(![X]:((~wise(X)<~>patient(X))<=>(~wise(X)|~humble(X))))&
((?[X]:(~kind(X)))<=>((~rich(paul)&~old(paul))))&
(((~generous(paul)|strong(paul)))<=>((~curious(paul)|wise(paul))))&
((~funny(lucy)&~kind(lucy)))&
(?[X]:((~tall(X)&~wise(X))))&
((~calm(susan)<~>rich(susan)))&
((patient(susan)<~>~curious(susan)))&
(~wise(alice))&
((~patient(fred)|~kind(fred)))&
(?[X]:((~generous(X)<~>happy(X)))) | ~funny(susan) | [] | null | 0 |
If someone is not generous or not funny then someone is quiet or happy and vice versa.
Everyone who is not happy or funny is calm or old.
Everyone who is not humble is old or not strong and vice versa.
If john is creative then someone is both not funny and calm and vice versa.
If someone is funny then someone is both creative and not quiet and vice versa.
Everyone who is not rich is rich or not rich.
Everyone who is not brave or not strong is either not rich or funny.
Everyone who is tall or old is both humble and quiet and vice versa.
Everyone who is either not quiet or not calm is humble.
If someone is not kind or not generous then someone is both rich and patient and vice versa.
Everyone who is both old and creative is old or wise.
Everyone who is brave is both wise and creative and vice versa.
If someone is either not tall or not rich then someone is not old.
Everyone who is both humble and not strong is humble and vice versa.
Everyone who is not curious is either not kind or not strong.
If john is humble then susan is not funny or not calm and vice versa.
Paul is either not humble or not funny.
Lucy is patient.
Mary is not old.
Lucy is either tall or brave.
Someone is not wise.
Paul is either funny or not happy. | Susan is not strong. | entailment | ((?[X]:((~generous(X)|~funny(X))))<=>(?[X]:((quiet(X)|happy(X)))))&
(![X]:((~happy(X)|funny(X))=>(calm(X)|old(X))))&
(![X]:(~humble(X)<=>(old(X)|~strong(X))))&
((creative(john))<=>(?[X]:((~funny(X)&calm(X)))))&
((?[X]:(funny(X)))<=>(?[X]:((creative(X)&~quiet(X)))))&
(![X]:(~rich(X)=>(rich(X)|~rich(X))))&
(![X]:((~brave(X)|~strong(X))=>(~rich(X)<~>funny(X))))&
(![X]:((tall(X)|old(X))<=>(humble(X)&quiet(X))))&
(![X]:((~quiet(X)<~>~calm(X))=>humble(X)))&
((?[X]:((~kind(X)|~generous(X))))<=>(?[X]:((rich(X)&patient(X)))))&
(![X]:((old(X)&creative(X))=>(old(X)|wise(X))))&
(![X]:(brave(X)<=>(wise(X)&creative(X))))&
((?[X]:((~tall(X)<~>~rich(X))))=>(?[X]:(~old(X))))&
(![X]:((humble(X)&~strong(X))<=>humble(X)))&
(![X]:(~curious(X)=>(~kind(X)<~>~strong(X))))&
((humble(john))<=>((~funny(susan)|~calm(susan))))&
((~humble(paul)<~>~funny(paul)))&
(patient(lucy))&
(~old(mary))&
((tall(lucy)<~>brave(lucy)))&
(?[X]:(~wise(X)))&
((funny(paul)<~>~happy(paul))) | ~strong(susan) | [
"p2",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2921549795804815776862053
% SZS output start Proof for 2921549795804815776862053
3. ! [X0] : (~humble(X0) <=> (~strong(X0) | old(X0))) [input p2]
8. ! [X0] : ((old(X0) | tall(X0)) <=> (quiet(X0) & humble(X0))) [input p7]
14. ! [X0] : ((~strong(X0) & humble(X0)) <=> humble(X0)) [input p13]
23. strong(susan) [input hypothesis]
43. ! [X0] : ((~humble(X0) | (strong(X0) & ~old(X0))) & ((~strong(X0) | old(X0)) | humble(X0))) [nnf transformation 3]
44. ! [X0] : ((~humble(X0) | (strong(X0) & ~old(X0))) & (~strong(X0) | old(X0) | humble(X0))) [flattening 43]
55. ! [X0] : (((old(X0) | tall(X0)) | (~quiet(X0) | ~humble(X0))) & ((quiet(X0) & humble(X0)) | (~old(X0) & ~tall(X0)))) [nnf transformation 8]
56. ! [X0] : ((old(X0) | tall(X0) | ~quiet(X0) | ~humble(X0)) & ((quiet(X0) & humble(X0)) | (~old(X0) & ~tall(X0)))) [flattening 55]
69. ! [X0] : (((~strong(X0) & humble(X0)) | ~humble(X0)) & (humble(X0) | (strong(X0) | ~humble(X0)))) [nnf transformation 14]
70. ! [X0] : (((~strong(X0) & humble(X0)) | ~humble(X0)) & (humble(X0) | strong(X0) | ~humble(X0))) [flattening 69]
84. ~strong(X0) | old(X0) | humble(X0) [cnf transformation 44]
85. ~humble(X0) | ~old(X0) [cnf transformation 44]
86. ~humble(X0) | strong(X0) [cnf transformation 44]
99. humble(X0) | ~old(X0) [cnf transformation 56]
118. ~strong(X0) | ~humble(X0) [cnf transformation 70]
131. strong(susan) [cnf transformation 23]
205. ~old(X0) [subsumption resolution 99,85]
233. ~humble(X0) [subsumption resolution 118,86]
276. old(susan) | humble(susan) [resolution 84,131]
277. humble(susan) [subsumption resolution 276,205]
278. $false [subsumption resolution 277,233]
% SZS output end Proof for 2921549795804815776862053
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not old is either not funny or quiet.
Everyone who is both not old and humble is not kind and vice versa.
If someone is both patient and not brave then paul is funny or kind.
Everyone who is tall is not generous.
Everyone who is not curious is humble.
Everyone who is funny is either wise or generous and vice versa.
If someone is funny or not patient then someone is either not creative or creative and vice versa.
Everyone who is not rich is not tall or humble.
If susan is brave or not quiet then john is either not kind or not strong and vice versa.
Everyone who is kind or not curious is either calm or not calm and vice versa.
If someone is not funny or humble then someone is not generous.
Everyone who is strong or not humble is not quiet or not generous and vice versa.
Everyone who is not tall is both patient and curious.
Everyone who is not strong or not kind is rich.
Everyone who is both not patient and generous is either not creative or humble.
If someone is either not quiet or old then someone is not happy or tall and vice versa.
Lucy is either not humble or old.
Paul is either not humble or not kind.
Paul is either strong or not strong.
Someone is generous or not generous.
Alice is both not curious and happy.
Someone is patient or not quiet.
Someone is both brave and old.
Paul is both not old and happy. | Paul is happy. | entailment | (![X]:((humble(X)|~old(X))=>(~funny(X)<~>quiet(X))))&
(![X]:((~old(X)&humble(X))<=>~kind(X)))&
((?[X]:((patient(X)&~brave(X))))=>((funny(paul)|kind(paul))))&
(![X]:(tall(X)=>~generous(X)))&
(![X]:(~curious(X)=>humble(X)))&
(![X]:(funny(X)<=>(wise(X)<~>generous(X))))&
((?[X]:((funny(X)|~patient(X))))<=>(?[X]:((~creative(X)<~>creative(X)))))&
(![X]:(~rich(X)=>(~tall(X)|humble(X))))&
(((brave(susan)|~quiet(susan)))<=>((~kind(john)<~>~strong(john))))&
(![X]:((kind(X)|~curious(X))<=>(calm(X)<~>~calm(X))))&
((?[X]:((~funny(X)|humble(X))))=>(?[X]:(~generous(X))))&
(![X]:((strong(X)|~humble(X))<=>(~quiet(X)|~generous(X))))&
(![X]:(~tall(X)=>(patient(X)&curious(X))))&
(![X]:((~strong(X)|~kind(X))=>rich(X)))&
(![X]:((~patient(X)&generous(X))=>(~creative(X)<~>humble(X))))&
((?[X]:((~quiet(X)<~>old(X))))<=>(?[X]:((~happy(X)|tall(X)))))&
((~humble(lucy)<~>old(lucy)))&
((~humble(paul)<~>~kind(paul)))&
((strong(paul)<~>~strong(paul)))&
(?[X]:((generous(X)|~generous(X))))&
((~curious(alice)&happy(alice)))&
(?[X]:((patient(X)|~quiet(X))))&
(?[X]:((brave(X)&old(X))))&
((~old(paul)&happy(paul))) | happy(paul) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1320233925321600590651675
% SZS output start Proof for 1320233925321600590651675
24. happy(paul) & ~old(paul) [input p23]
25. ~happy(paul) [input hypothesis]
134. happy(paul) [cnf transformation 24]
135. ~happy(paul) [cnf transformation 25]
261. $false [subsumption resolution 135,134]
% SZS output end Proof for 1320233925321600590651675
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or not creative then susan is both generous and not rich.
Everyone who is both not tall and funny is not tall or happy.
Everyone who is generous or not patient is both not brave and old.
Everyone who is either not funny or not brave is not brave or wise and vice versa.
Everyone who is funny is rich or not tall and vice versa.
Everyone who is wise is not strong and vice versa.
Everyone who is either strong or rich is both not rich and not curious and vice versa.
If mary is both not calm and creative then susan is brave or curious and vice versa.
Everyone who is either not tall or generous is not generous or creative.
Everyone who is either not humble or funny is strong.
Everyone who is either brave or generous is both brave and quiet.
Everyone who is funny is either humble or tall.
If mary is either not kind or not creative then john is both not creative and not generous and vice versa.
Everyone who is both curious and happy is strong or not brave and vice versa.
If someone is both not funny and curious then lucy is both not creative and not happy and vice versa.
Fred is happy.
Someone is rich or not old.
Someone is either calm or rich.
Someone is not patient or happy.
Lucy is both brave and not generous.
Someone is not calm.
Someone is not strong or not funny.
Someone is both kind and not old. | Lucy is not kind. | contradiction | ((?[X]:((kind(X)<~>~creative(X))))=>((generous(susan)&~rich(susan))))&
(![X]:((~tall(X)&funny(X))=>(~tall(X)|happy(X))))&
(![X]:((generous(X)|~patient(X))=>(~brave(X)&old(X))))&
(![X]:((~funny(X)<~>~brave(X))<=>(~brave(X)|wise(X))))&
(![X]:(funny(X)<=>(rich(X)|~tall(X))))&
(![X]:(wise(X)<=>~strong(X)))&
(![X]:((strong(X)<~>rich(X))<=>(~rich(X)&~curious(X))))&
(((~calm(mary)&creative(mary)))<=>((brave(susan)|curious(susan))))&
(![X]:((~tall(X)<~>generous(X))=>(~generous(X)|creative(X))))&
(![X]:((~humble(X)<~>funny(X))=>strong(X)))&
(![X]:((brave(X)<~>generous(X))=>(brave(X)&quiet(X))))&
(![X]:(funny(X)=>(humble(X)<~>tall(X))))&
(((~kind(mary)<~>~creative(mary)))<=>((~creative(john)&~generous(john))))&
(![X]:((curious(X)&happy(X))<=>(strong(X)|~brave(X))))&
((?[X]:((~funny(X)&curious(X))))<=>((~creative(lucy)&~happy(lucy))))&
(happy(fred))&
(?[X]:((rich(X)|~old(X))))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:((~patient(X)|happy(X))))&
((brave(lucy)&~generous(lucy)))&
(?[X]:(~calm(X)))&
(?[X]:((~strong(X)|~funny(X))))&
(?[X]:((kind(X)&~old(X)))) | ~kind(lucy) | [
"p0",
"p2",
"p4",
"p5",
"p6",
"p9",
"p10",
"p11",
"p13",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3663084227950111737822990
% SZS output start Proof for 3663084227950111737822990
1. ? [X0] : (kind(X0) <~> ~creative(X0)) => (~rich(susan) & generous(susan)) [input p0]
3. ! [X0] : ((~patient(X0) | generous(X0)) => (old(X0) & ~brave(X0))) [input p2]
5. ! [X0] : (funny(X0) <=> (~tall(X0) | rich(X0))) [input p4]
6. ! [X0] : (wise(X0) <=> ~strong(X0)) [input p5]
7. ! [X0] : ((strong(X0) <~> rich(X0)) <=> (~curious(X0) & ~rich(X0))) [input p6]
10. ! [X0] : ((~humble(X0) <~> funny(X0)) => strong(X0)) [input p9]
11. ! [X0] : ((brave(X0) <~> generous(X0)) => (quiet(X0) & brave(X0))) [input p10]
12. ! [X0] : (funny(X0) => (humble(X0) <~> tall(X0))) [input p11]
14. ! [X0] : ((happy(X0) & curious(X0)) <=> (~brave(X0) | strong(X0))) [input p13]
15. ? [X0] : (curious(X0) & ~funny(X0)) <=> (~happy(lucy) & ~creative(lucy)) [input p14]
22. ? [X0] : (~funny(X0) | ~strong(X0)) [input p21]
24. ~kind(lucy) [input hypothesis]
25. ! [X0] : ((brave(X0) <~> generous(X0)) => brave(X0)) [pure predicate removal 11]
26. (~rich(susan) & generous(susan)) | ! [X0] : (kind(X0) <=> ~creative(X0)) [ennf transformation 1]
29. ! [X0] : ((old(X0) & ~brave(X0)) | (patient(X0) & ~generous(X0))) [ennf transformation 3]
32. ! [X0] : (strong(X0) | (~humble(X0) <=> funny(X0))) [ennf transformation 10]
33. ! [X0] : (brave(X0) | (brave(X0) <=> generous(X0))) [ennf transformation 25]
34. ! [X0] : ((humble(X0) <~> tall(X0)) | ~funny(X0)) [ennf transformation 12]
35. (~rich(susan) & generous(susan)) | ! [X0] : ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0))) [nnf transformation 26]
38. ! [X0] : ((funny(X0) | (tall(X0) & ~rich(X0))) & ((~tall(X0) | rich(X0)) | ~funny(X0))) [nnf transformation 5]
39. ! [X0] : ((funny(X0) | (tall(X0) & ~rich(X0))) & (~tall(X0) | rich(X0) | ~funny(X0))) [flattening 38]
40. ! [X0] : ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0))) [nnf transformation 6]
41. ! [X0] : ((((~rich(X0) | ~strong(X0)) & (rich(X0) | strong(X0))) | (curious(X0) | rich(X0))) & ((~curious(X0) & ~rich(X0)) | ((strong(X0) | ~rich(X0)) & (rich(X0) | ~strong(X0))))) [nnf transformation 7]
42. ! [X0] : ((((~rich(X0) | ~strong(X0)) & (rich(X0) | strong(X0))) | curious(X0) | rich(X0)) & ((~curious(X0) & ~rich(X0)) | ((strong(X0) | ~rich(X0)) & (rich(X0) | ~strong(X0))))) [flattening 41]
46. ! [X0] : (strong(X0) | ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0)))) [nnf transformation 32]
47. ! [X0] : (brave(X0) | ((brave(X0) | ~generous(X0)) & (generous(X0) | ~brave(X0)))) [nnf transformation 33]
48. ! [X0] : (((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | ~funny(X0)) [nnf transformation 34]
51. ! [X0] : (((happy(X0) & curious(X0)) | (brave(X0) & ~strong(X0))) & ((~brave(X0) | strong(X0)) | (~happy(X0) | ~curious(X0)))) [nnf transformation 14]
52. ! [X0] : (((happy(X0) & curious(X0)) | (brave(X0) & ~strong(X0))) & (~brave(X0) | strong(X0) | ~happy(X0) | ~curious(X0))) [flattening 51]
53. (? [X0] : (curious(X0) & ~funny(X0)) | (happy(lucy) | creative(lucy))) & ((~happy(lucy) & ~creative(lucy)) | ! [X0] : (~curious(X0) | funny(X0))) [nnf transformation 15]
54. (? [X0] : (curious(X0) & ~funny(X0)) | happy(lucy) | creative(lucy)) & ((~happy(lucy) & ~creative(lucy)) | ! [X0] : (~curious(X0) | funny(X0))) [flattening 53]
55. (? [X0] : (curious(X0) & ~funny(X0)) | happy(lucy) | creative(lucy)) & ((~happy(lucy) & ~creative(lucy)) | ! [X1] : (~curious(X1) | funny(X1))) [rectify 54]
56. ? [X0] : (curious(X0) & ~funny(X0)) => (curious(sK0) & ~funny(sK0)) [choice axiom]
57. ((curious(sK0) & ~funny(sK0)) | happy(lucy) | creative(lucy)) & ((~happy(lucy) & ~creative(lucy)) | ! [X1] : (~curious(X1) | funny(X1))) [skolemisation 55,56]
67. ? [X0] : (~funny(X0) | ~strong(X0)) => (~funny(sK5) | ~strong(sK5)) [choice axiom]
68. ~funny(sK5) | ~strong(sK5) [skolemisation 22,67]
72. generous(susan) | kind(X0) | creative(X0) [cnf transformation 35]
76. ~brave(X0) | ~generous(X0) [cnf transformation 29]
86. ~funny(X0) | rich(X0) | ~tall(X0) [cnf transformation 39]
87. ~rich(X0) | funny(X0) [cnf transformation 39]
88. funny(X0) | tall(X0) [cnf transformation 39]
89. ~strong(X0) | ~wise(X0) [cnf transformation 40]
90. strong(X0) | wise(X0) [cnf transformation 40]
92. ~rich(X0) | strong(X0) | ~rich(X0) [cnf transformation 42]
93. ~curious(X0) | rich(X0) | ~strong(X0) [cnf transformation 42]
95. rich(X0) | strong(X0) | curious(X0) | rich(X0) [cnf transformation 42]
105. ~humble(X0) | strong(X0) | ~funny(X0) [cnf transformation 46]
107. brave(X0) | brave(X0) | ~generous(X0) [cnf transformation 47]
108. tall(X0) | humble(X0) | ~funny(X0) [cnf transformation 48]
117. ~strong(X0) | curious(X0) [cnf transformation 52]
121. ~creative(lucy) | ~curious(X1) | funny(X1) [cnf transformation 57]
133. ~funny(sK5) | ~strong(sK5) [cnf transformation 68]
136. ~kind(lucy) [cnf transformation 24]
137. brave(X0) | ~generous(X0) [duplicate literal removal 107]
139. ~rich(X0) | strong(X0) [duplicate literal removal 92]
140. curious(X0) | strong(X0) | rich(X0) [duplicate literal removal 95]
144. 1 <=> ! [X0] : (kind(X0) | creative(X0)) [avatar definition]
145. creative(X0) | kind(X0) <- (1) [avatar component clause 144]
156. 4 <=> generous(susan) [avatar definition]
158. generous(susan) <- (4) [avatar component clause 156]
159. 1 | 4 [avatar split clause 72,156,144]
183. ~generous(X0) [subsumption resolution 137,76]
184. humble(X0) | tall(X0) [subsumption resolution 108,88]
200. 11 <=> creative(lucy) [avatar definition]
201. ~creative(lucy) <- (~11) [avatar component clause 200]
218. 15 <=> ! [X1] : (~curious(X1) | funny(X1)) [avatar definition]
219. ~curious(X1) | funny(X1) <- (15) [avatar component clause 218]
221. 15 | ~11 [avatar split clause 121,200,218]
251. 22 <=> strong(sK5) [avatar definition]
253. ~strong(sK5) <- (~22) [avatar component clause 251]
255. 23 <=> funny(sK5) [avatar definition]
257. ~funny(sK5) <- (~23) [avatar component clause 255]
258. ~22 | ~23 [avatar split clause 133,255,251]
259. $false <- (4) [subsumption resolution 158,183]
260. ~4 [avatar contradiction clause 259]
268. curious(X0) | wise(X0) [resolution 117,90]
275. kind(lucy) <- (1, ~11) [resolution 145,201]
276. $false <- (1, ~11) [subsumption resolution 275,136]
277. ~1 | 11 [avatar contradiction clause 276]
310. strong(X1) | ~funny(X1) | tall(X1) [resolution 105,184]
312. strong(X1) | tall(X1) [subsumption resolution 310,88]
324. wise(X1) | rich(X1) | ~strong(X1) [resolution 268,93]
327. ~strong(X1) | rich(X1) [subsumption resolution 324,89]
330. strong(X2) | rich(X2) | funny(X2) <- (15) [resolution 140,219]
334. rich(X2) | funny(X2) <- (15) [subsumption resolution 330,327]
335. funny(X2) <- (15) [subsumption resolution 334,87]
338. $false <- (15, ~23) [resolution 335,257]
339. ~tall(X0) | rich(X0) <- (15) [resolution 335,86]
340. ~15 | 23 [avatar contradiction clause 338]
406. rich(X0) | tall(X0) [resolution 327,312]
409. rich(X0) <- (15) [subsumption resolution 406,339]
416. strong(X0) <- (15) [resolution 409,139]
433. $false <- (15, ~22) [resolution 416,253]
439. ~15 | 22 [avatar contradiction clause 433]
440. $false [avatar sat refutation 159,221,258,260,277,340,439]
% SZS output end Proof for 3663084227950111737822990
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not kind then someone is either not humble or tall.
If john is kind then someone is either happy or calm and vice versa.
Everyone who is not creative or brave is calm.
If john is old or quiet then mary is not wise or creative.
Everyone who is tall or generous is either not humble or not funny and vice versa.
Everyone who is not brave or generous is not brave.
Everyone who is both not creative and not tall is both not happy and strong and vice versa.
Everyone who is patient is not patient or not funny and vice versa.
Everyone who is not calm is either not kind or not patient.
If someone is not tall then fred is not patient.
Everyone who is either not calm or rich is both kind and rich and vice versa.
If fred is not strong then mary is creative.
Everyone who is either not happy or not humble is either not happy or not patient and vice versa.
If someone is patient or not creative then someone is both not rich and not creative.
Everyone who is patient or happy is both calm and not happy.
If someone is both not tall and not calm then john is both not creative and calm and vice versa.
Someone is not creative or kind.
Susan is either humble or rich.
Mary is either wise or humble.
Someone is rich.
Someone is not curious or funny.
Someone is not creative. | Fred is not funny. | entailment | ((?[X]:(~kind(X)))=>(?[X]:((~humble(X)<~>tall(X)))))&
((kind(john))<=>(?[X]:((happy(X)<~>calm(X)))))&
(![X]:((~creative(X)|brave(X))=>calm(X)))&
(((old(john)|quiet(john)))=>((~wise(mary)|creative(mary))))&
(![X]:((tall(X)|generous(X))<=>(~humble(X)<~>~funny(X))))&
(![X]:((~brave(X)|generous(X))=>~brave(X)))&
(![X]:((~creative(X)&~tall(X))<=>(~happy(X)&strong(X))))&
(![X]:(patient(X)<=>(~patient(X)|~funny(X))))&
(![X]:(~calm(X)=>(~kind(X)<~>~patient(X))))&
((?[X]:(~tall(X)))=>(~patient(fred)))&
(![X]:((~calm(X)<~>rich(X))<=>(kind(X)&rich(X))))&
((~strong(fred))=>(creative(mary)))&
(![X]:((~happy(X)<~>~humble(X))<=>(~happy(X)<~>~patient(X))))&
((?[X]:((patient(X)|~creative(X))))=>(?[X]:((~rich(X)&~creative(X)))))&
(![X]:((patient(X)|happy(X))=>(calm(X)&~happy(X))))&
((?[X]:((~tall(X)&~calm(X))))<=>((~creative(john)&calm(john))))&
(?[X]:((~creative(X)|kind(X))))&
((humble(susan)<~>rich(susan)))&
((wise(mary)<~>humble(mary)))&
(?[X]:(rich(X)))&
(?[X]:((~curious(X)|funny(X))))&
(?[X]:(~creative(X))) | ~funny(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3845054336967522673429219
% SZS output start Proof for 3845054336967522673429219
8. ! [X0] : (patient(X0) <=> (~funny(X0) | ~patient(X0))) [input p7]
23. funny(fred) [input hypothesis]
49. ! [X0] : ((patient(X0) | (funny(X0) & patient(X0))) & ((~funny(X0) | ~patient(X0)) | ~patient(X0))) [nnf transformation 8]
50. ! [X0] : ((patient(X0) | (funny(X0) & patient(X0))) & (~funny(X0) | ~patient(X0) | ~patient(X0))) [flattening 49]
91. ~funny(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 50]
92. patient(X0) | patient(X0) [cnf transformation 50]
131. funny(fred) [cnf transformation 23]
139. ~funny(X0) | ~patient(X0) [duplicate literal removal 91]
140. patient(X0) [duplicate literal removal 92]
176. ~funny(X0) [subsumption resolution 139,140]
222. $false [subsumption resolution 131,176]
% SZS output end Proof for 3845054336967522673429219
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is generous.
Everyone who is not curious is not funny or not creative and vice versa.
Everyone who is curious is either happy or not patient and vice versa.
If someone is kind or creative then lucy is both humble and not happy.
Everyone who is both creative and not creative is not generous or not quiet and vice versa.
Everyone who is both not curious and kind is both not happy and not strong.
If mary is both not old and brave then someone is happy and vice versa.
Everyone who is both old and not funny is either not curious or not old and vice versa.
If someone is either funny or not tall then someone is both not creative and kind.
Everyone who is not humble or not brave is not humble or humble.
If someone is both patient and not rich then someone is both wise and not old.
If lucy is humble or not calm then someone is either generous or strong.
If someone is not creative or not quiet then john is not generous.
Everyone who is not happy or creative is both calm and quiet.
Everyone who is curious is either creative or generous and vice versa.
Someone is wise.
John is not patient.
Lucy is either kind or not humble.
Someone is either calm or wise.
Lucy is rich.
Mary is either tall or not happy.
Susan is either strong or brave. | Lucy is creative. | entailment | (![X]:(~curious(X)=>generous(X)))&
(![X]:(~curious(X)<=>(~funny(X)|~creative(X))))&
(![X]:(curious(X)<=>(happy(X)<~>~patient(X))))&
((?[X]:((kind(X)|creative(X))))=>((humble(lucy)&~happy(lucy))))&
(![X]:((creative(X)&~creative(X))<=>(~generous(X)|~quiet(X))))&
(![X]:((~curious(X)&kind(X))=>(~happy(X)&~strong(X))))&
(((~old(mary)&brave(mary)))<=>(?[X]:(happy(X))))&
(![X]:((old(X)&~funny(X))<=>(~curious(X)<~>~old(X))))&
((?[X]:((funny(X)<~>~tall(X))))=>(?[X]:((~creative(X)&kind(X)))))&
(![X]:((~humble(X)|~brave(X))=>(~humble(X)|humble(X))))&
((?[X]:((patient(X)&~rich(X))))=>(?[X]:((wise(X)&~old(X)))))&
(((humble(lucy)|~calm(lucy)))=>(?[X]:((generous(X)<~>strong(X)))))&
((?[X]:((~creative(X)|~quiet(X))))=>(~generous(john)))&
(![X]:((~happy(X)|creative(X))=>(calm(X)&quiet(X))))&
(![X]:(curious(X)<=>(creative(X)<~>generous(X))))&
(?[X]:(wise(X)))&
(~patient(john))&
((kind(lucy)<~>~humble(lucy)))&
(?[X]:((calm(X)<~>wise(X))))&
(rich(lucy))&
((tall(mary)<~>~happy(mary)))&
((strong(susan)<~>brave(susan))) | creative(lucy) | [
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3677058156704202211884353
% SZS output start Proof for 3677058156704202211884353
5. ! [X0] : ((~creative(X0) & creative(X0)) <=> (~quiet(X0) | ~generous(X0))) [input p4]
13. ? [X0] : (~quiet(X0) | ~creative(X0)) => ~generous(john) [input p12]
23. ~creative(lucy) [input hypothesis]
36. ~generous(john) | ! [X0] : (quiet(X0) & creative(X0)) [ennf transformation 13]
41. ! [X0] : (((~creative(X0) & creative(X0)) | (quiet(X0) & generous(X0))) & ((~quiet(X0) | ~generous(X0)) | (creative(X0) | ~creative(X0)))) [nnf transformation 5]
42. ! [X0] : (((~creative(X0) & creative(X0)) | (quiet(X0) & generous(X0))) & (~quiet(X0) | ~generous(X0) | creative(X0) | ~creative(X0))) [flattening 41]
79. creative(X0) | generous(X0) [cnf transformation 42]
81. ~creative(X0) | generous(X0) [cnf transformation 42]
104. ~generous(john) | creative(X0) [cnf transformation 36]
124. ~creative(lucy) [cnf transformation 23]
147. generous(X0) [subsumption resolution 79,81]
197. creative(X0) [subsumption resolution 104,147]
228. $false [subsumption resolution 124,197]
% SZS output end Proof for 3677058156704202211884353
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is both rich and calm and vice versa.
Everyone who is either not wise or not tall is both not kind and not strong.
Everyone who is not calm is both kind and not humble and vice versa.
Everyone who is both not curious and not patient is either not strong or wise.
Everyone who is not generous is curious or not quiet and vice versa.
Everyone who is not old or wise is both creative and not patient.
If fred is either not funny or quiet then fred is both kind and not calm.
If john is creative or funny then someone is not humble or not strong.
If paul is calm or creative then someone is both kind and not tall and vice versa.
If alice is patient then lucy is brave or patient and vice versa.
Everyone who is either not funny or brave is either happy or not strong.
Everyone who is not funny or not creative is curious or not happy and vice versa.
Everyone who is calm is both brave and quiet and vice versa.
If paul is not curious or humble then alice is generous.
Everyone who is not curious or tall is not tall or strong and vice versa.
If someone is not patient then someone is quiet.
Alice is both old and quiet.
Paul is either not strong or not calm.
Lucy is not humble or kind.
Someone is both not tall and quiet.
Someone is not humble.
Fred is both funny and not brave.
Alice is both brave and wise.
Mary is not quiet. | Alice is strong. | entailment | (![X]:(~wise(X)<=>(rich(X)&calm(X))))&
(![X]:((~wise(X)<~>~tall(X))=>(~kind(X)&~strong(X))))&
(![X]:(~calm(X)<=>(kind(X)&~humble(X))))&
(![X]:((~curious(X)&~patient(X))=>(~strong(X)<~>wise(X))))&
(![X]:(~generous(X)<=>(curious(X)|~quiet(X))))&
(![X]:((~old(X)|wise(X))=>(creative(X)&~patient(X))))&
(((~funny(fred)<~>quiet(fred)))=>((kind(fred)&~calm(fred))))&
(((creative(john)|funny(john)))=>(?[X]:((~humble(X)|~strong(X)))))&
(((calm(paul)|creative(paul)))<=>(?[X]:((kind(X)&~tall(X)))))&
((patient(alice))<=>((brave(lucy)|patient(lucy))))&
(![X]:((~funny(X)<~>brave(X))=>(happy(X)<~>~strong(X))))&
(![X]:((~funny(X)|~creative(X))<=>(curious(X)|~happy(X))))&
(![X]:(calm(X)<=>(brave(X)&quiet(X))))&
(((~curious(paul)|humble(paul)))=>(generous(alice)))&
(![X]:((~curious(X)|tall(X))<=>(~tall(X)|strong(X))))&
((?[X]:(~patient(X)))=>(?[X]:(quiet(X))))&
((old(alice)&quiet(alice)))&
((~strong(paul)<~>~calm(paul)))&
((~humble(lucy)|kind(lucy)))&
(?[X]:((~tall(X)&quiet(X))))&
(?[X]:(~humble(X)))&
((funny(fred)&~brave(fred)))&
((brave(alice)&wise(alice)))&
(~quiet(mary)) | strong(alice) | [
"p3",
"p5",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 839760683719434654664500
% SZS output start Proof for 839760683719434654664500
4. ! [X0] : ((~patient(X0) & ~curious(X0)) => (~strong(X0) <~> wise(X0))) [input p3]
6. ! [X0] : ((wise(X0) | ~old(X0)) => (~patient(X0) & creative(X0))) [input p5]
15. ! [X0] : ((tall(X0) | ~curious(X0)) <=> (strong(X0) | ~tall(X0))) [input p14]
23. wise(alice) & brave(alice) [input p22]
25. ~strong(alice) [input hypothesis]
28. ! [X0] : (wise(X0) => (~patient(X0) & creative(X0))) [pure predicate removal 6]
31. ! [X0] : ((~strong(X0) <~> wise(X0)) | (patient(X0) | curious(X0))) [ennf transformation 4]
32. ! [X0] : ((~strong(X0) <~> wise(X0)) | patient(X0) | curious(X0)) [flattening 31]
34. ! [X0] : ((~patient(X0) & creative(X0)) | ~wise(X0)) [ennf transformation 28]
45. ! [X0] : (((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | patient(X0) | curious(X0)) [nnf transformation 32]
61. ! [X0] : (((tall(X0) | ~curious(X0)) | (~strong(X0) & tall(X0))) & ((strong(X0) | ~tall(X0)) | (~tall(X0) & curious(X0)))) [nnf transformation 15]
62. ! [X0] : ((tall(X0) | ~curious(X0) | (~strong(X0) & tall(X0))) & (strong(X0) | ~tall(X0) | (~tall(X0) & curious(X0)))) [flattening 61]
82. ~wise(X0) | strong(X0) | patient(X0) | curious(X0) [cnf transformation 45]
86. ~patient(X0) | ~wise(X0) [cnf transformation 34]
115. strong(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 62]
116. tall(X0) | ~curious(X0) | tall(X0) [cnf transformation 62]
129. wise(alice) [cnf transformation 23]
131. ~strong(alice) [cnf transformation 25]
132. ~tall(X0) | strong(X0) [duplicate literal removal 115]
133. ~curious(X0) | tall(X0) [duplicate literal removal 116]
201. 15 <=> patient(alice) [avatar definition]
202. ~patient(alice) <- (~15) [avatar component clause 201]
203. patient(alice) <- (15) [avatar component clause 201]
263. ~wise(alice) <- (15) [resolution 203,86]
264. $false <- (15) [subsumption resolution 263,129]
265. ~15 [avatar contradiction clause 264]
360. strong(alice) | patient(alice) | curious(alice) [resolution 82,129]
363. patient(alice) | curious(alice) [subsumption resolution 360,131]
364. curious(alice) <- (~15) [subsumption resolution 363,202]
399. tall(alice) <- (~15) [resolution 364,133]
439. strong(alice) <- (~15) [resolution 399,132]
440. $false <- (~15) [subsumption resolution 439,131]
441. 15 [avatar contradiction clause 440]
442. $false [avatar sat refutation 265,441]
% SZS output end Proof for 839760683719434654664500
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall is both rich and calm and vice versa. If someone is not humble or rich then paul is both wise and not quiet and vice versa. Everyone who is rich or not brave 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 tall is both creative and not kind and vice versa. Paul is either strong or quiet. Mary is either not funny or not calm. Lucy is either patient or funny. Someone is tall or old. Paul is either generous or humble. Paul is not quiet. Someone is not patient or not humble. | Lucy is not curious. | entailment | (![X]:(tall(X)<=>(rich(X)&calm(X))))&
((?[X]:((~humble(X)|rich(X))))<=>((wise(paul)&~quiet(paul))))&
(![X]:((rich(X)|~brave(X))<=>(calm(X)&happy(X))))&
((?[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)|tall(X))<=>(creative(X)&~kind(X))))&
((strong(paul)<~>quiet(paul)))&
((~funny(mary)<~>~calm(mary)))&
((patient(lucy)<~>funny(lucy)))&
(?[X]:((tall(X)|old(X))))&
((generous(paul)<~>humble(paul)))&
(~quiet(paul))&
(?[X]:((~patient(X)|~humble(X)))) | ~curious(lucy) | [
"p2",
"p8",
"p10",
"p11",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5092339999888972697732565
% SZS output start Proof for 5092339999888972697732565
3. ! [X0] : ((~brave(X0) | rich(X0)) <=> (happy(X0) & calm(X0))) [input p2]
9. ! [X0] : ((brave(X0) & ~happy(X0)) => (kind(X0) & happy(X0))) [input p8]
11. ! [X0] : (funny(X0) <=> (~curious(X0) <~> happy(X0))) [input p10]
12. ! [X0] : (~patient(X0) => (~funny(X0) & humble(X0))) [input p11]
18. patient(lucy) <~> funny(lucy) [input p17]
23. curious(lucy) [input hypothesis]
31. ! [X0] : ((kind(X0) & happy(X0)) | (~brave(X0) | happy(X0))) [ennf transformation 9]
32. ! [X0] : ((kind(X0) & happy(X0)) | ~brave(X0) | happy(X0)) [flattening 31]
33. ! [X0] : ((~funny(X0) & humble(X0)) | patient(X0)) [ennf transformation 12]
43. ! [X0] : (((~brave(X0) | rich(X0)) | (~happy(X0) | ~calm(X0))) & ((happy(X0) & calm(X0)) | (brave(X0) & ~rich(X0)))) [nnf transformation 3]
44. ! [X0] : ((~brave(X0) | rich(X0) | ~happy(X0) | ~calm(X0)) & ((happy(X0) & calm(X0)) | (brave(X0) & ~rich(X0)))) [flattening 43]
61. ! [X0] : ((funny(X0) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0)))) & (((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | ~funny(X0))) [nnf transformation 11]
68. (~funny(lucy) | ~patient(lucy)) & (funny(lucy) | patient(lucy)) [nnf transformation 18]
85. happy(X0) | brave(X0) [cnf transformation 44]
100. happy(X0) | ~brave(X0) | happy(X0) [cnf transformation 32]
108. funny(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 61]
110. ~funny(X0) | patient(X0) [cnf transformation 33]
126. ~funny(lucy) | ~patient(lucy) [cnf transformation 68]
132. curious(lucy) [cnf transformation 23]
133. happy(X0) | ~brave(X0) [duplicate literal removal 100]
244. happy(X0) [subsumption resolution 133,85]
245. ~curious(X0) | funny(X0) [subsumption resolution 108,244]
265. ~funny(lucy) [subsumption resolution 126,110]
320. funny(lucy) [resolution 245,132]
321. $false [subsumption resolution 320,265]
% SZS output end Proof for 5092339999888972697732565
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old is tall and vice versa.
If susan is tall or funny then someone is both not brave and calm and vice versa.
Everyone who is not tall or kind is either not old or not rich and vice versa.
If someone is either not calm or generous then paul is either not kind or not calm and vice versa.
Everyone who is rich or not happy is not rich.
If someone is both not quiet and not humble then fred is not patient or tall.
If john is not rich or not old then lucy is brave or generous and vice versa.
Everyone who is humble or not creative is either not rich or strong and vice versa.
If someone is either not creative or not strong then someone is both not old and happy.
If alice is quiet then someone is both not wise and not generous.
If lucy is not old or creative then mary is not calm and vice versa.
Everyone who is both not kind and tall is brave or generous.
If john is wise or old then fred is both brave and strong and vice versa.
If someone is rich or tall then susan is both funny and not brave.
If someone is old then lucy is both not tall and generous.
Everyone who is either not tall or strong is patient and vice versa.
Someone is either kind or not old.
Alice is either strong or not humble.
Mary is not brave.
Someone is either not wise or old.
Someone is both calm and quiet.
Lucy is either old or not happy.
Someone is brave.
John is both not wise and generous. | Alice is not strong. | entailment | (![X]:(~old(X)<=>tall(X)))&
(((tall(susan)|funny(susan)))<=>(?[X]:((~brave(X)&calm(X)))))&
(![X]:((~tall(X)|kind(X))<=>(~old(X)<~>~rich(X))))&
((?[X]:((~calm(X)<~>generous(X))))<=>((~kind(paul)<~>~calm(paul))))&
(![X]:((rich(X)|~happy(X))=>~rich(X)))&
((?[X]:((~quiet(X)&~humble(X))))=>((~patient(fred)|tall(fred))))&
(((~rich(john)|~old(john)))<=>((brave(lucy)|generous(lucy))))&
(![X]:((humble(X)|~creative(X))<=>(~rich(X)<~>strong(X))))&
((?[X]:((~creative(X)<~>~strong(X))))=>(?[X]:((~old(X)&happy(X)))))&
((quiet(alice))=>(?[X]:((~wise(X)&~generous(X)))))&
(((~old(lucy)|creative(lucy)))<=>(~calm(mary)))&
(![X]:((~kind(X)&tall(X))=>(brave(X)|generous(X))))&
(((wise(john)|old(john)))<=>((brave(fred)&strong(fred))))&
((?[X]:((rich(X)|tall(X))))=>((funny(susan)&~brave(susan))))&
((?[X]:(old(X)))=>((~tall(lucy)&generous(lucy))))&
(![X]:((~tall(X)<~>strong(X))<=>patient(X)))&
(?[X]:((kind(X)<~>~old(X))))&
((strong(alice)<~>~humble(alice)))&
(~brave(mary))&
(?[X]:((~wise(X)<~>old(X))))&
(?[X]:((calm(X)&quiet(X))))&
((old(lucy)<~>~happy(lucy)))&
(?[X]:(brave(X)))&
((~wise(john)&generous(john))) | ~strong(alice) | [
"p4",
"p7",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4570528404346929466951882
% SZS output start Proof for 4570528404346929466951882
5. ! [X0] : ((~happy(X0) | rich(X0)) => ~rich(X0)) [input p4]
8. ! [X0] : ((~creative(X0) | humble(X0)) <=> (~rich(X0) <~> strong(X0))) [input p7]
18. strong(alice) <~> ~humble(alice) [input p17]
25. strong(alice) [input hypothesis]
28. ! [X0] : (~rich(X0) | (happy(X0) & ~rich(X0))) [ennf transformation 5]
52. ! [X0] : (((~creative(X0) | humble(X0)) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | (creative(X0) & ~humble(X0)))) [nnf transformation 8]
53. ! [X0] : ((~creative(X0) | humble(X0) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | (creative(X0) & ~humble(X0)))) [flattening 52]
68. (humble(alice) | ~strong(alice)) & (~humble(alice) | strong(alice)) [nnf transformation 18]
98. ~rich(X0) | ~rich(X0) [cnf transformation 28]
107. ~strong(X0) | rich(X0) | ~humble(X0) [cnf transformation 53]
137. humble(alice) | ~strong(alice) [cnf transformation 68]
148. strong(alice) [cnf transformation 25]
149. ~rich(X0) [duplicate literal removal 98]
235. ~strong(X0) | ~humble(X0) [subsumption resolution 107,149]
323. ~strong(alice) [subsumption resolution 137,235]
342. $false [subsumption resolution 148,323]
% SZS output end Proof for 4570528404346929466951882
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both patient and humble then someone is both not wise and rich.
Everyone who is not curious is either humble or creative.
If susan is rich then someone is not kind.
Everyone who is kind or not old is tall or not curious and vice versa.
Everyone who is generous or not brave is either generous or not creative and vice versa.
Everyone who is not creative or not curious is either not patient or happy and vice versa.
Everyone who is both strong and not happy is either not rich or not funny and vice versa.
If someone is creative or not kind then someone is both not old and kind.
If someone is not calm then john is either strong or not old.
If someone is happy then someone is not tall.
If someone is both strong and old then someone is brave and vice versa.
Everyone who is not patient is brave or quiet and vice versa.
Everyone who is patient is both not calm and rich and vice versa.
Everyone who is generous is strong or not rich.
If john is not humble or not happy then someone is not kind.
Everyone who is either wise or tall is not kind and vice versa.
Someone is not generous.
Mary is not rich.
Someone is either brave or old.
Alice is both curious and not wise.
Someone is kind or not generous.
Someone is either not kind or not quiet.
Alice is not curious or brave. | John is not happy. | neutral | (((patient(paul)&humble(paul)))=>(?[X]:((~wise(X)&rich(X)))))&
(![X]:(~curious(X)=>(humble(X)<~>creative(X))))&
((rich(susan))=>(?[X]:(~kind(X))))&
(![X]:((kind(X)|~old(X))<=>(tall(X)|~curious(X))))&
(![X]:((generous(X)|~brave(X))<=>(generous(X)<~>~creative(X))))&
(![X]:((~creative(X)|~curious(X))<=>(~patient(X)<~>happy(X))))&
(![X]:((strong(X)&~happy(X))<=>(~rich(X)<~>~funny(X))))&
((?[X]:((creative(X)|~kind(X))))=>(?[X]:((~old(X)&kind(X)))))&
((?[X]:(~calm(X)))=>((strong(john)<~>~old(john))))&
((?[X]:(happy(X)))=>(?[X]:(~tall(X))))&
((?[X]:((strong(X)&old(X))))<=>(?[X]:(brave(X))))&
(![X]:(~patient(X)<=>(brave(X)|quiet(X))))&
(![X]:(patient(X)<=>(~calm(X)&rich(X))))&
(![X]:(generous(X)=>(strong(X)|~rich(X))))&
(((~humble(john)|~happy(john)))=>(?[X]:(~kind(X))))&
(![X]:((wise(X)<~>tall(X))<=>~kind(X)))&
(?[X]:(~generous(X)))&
(~rich(mary))&
(?[X]:((brave(X)<~>old(X))))&
((curious(alice)&~wise(alice)))&
(?[X]:((kind(X)|~generous(X))))&
(?[X]:((~kind(X)<~>~quiet(X))))&
((~curious(alice)|brave(alice))) | ~happy(john) | [] | null | 0 |
Everyone who is not old is not rich or rich and vice versa.
Everyone who is both wise and brave is strong or not curious.
Everyone who is wise or not calm is not patient and vice versa.
Everyone who is tall is either rich or not funny and vice versa.
If someone is both old and not curious then someone is tall or funny and vice versa.
If someone is brave or wise then someone is either kind or humble and vice versa.
If someone is not rich then mary is wise or not calm and vice versa.
If paul is not strong then mary is not tall or patient.
Everyone who is not old or funny is funny or not quiet and vice versa.
Everyone who is either calm or wise is either wise or strong.
If mary is either not old or humble then someone is not quiet.
If someone is rich or not quiet then john is both kind and happy.
If someone is either not patient or wise then someone is either brave or not patient and vice versa.
If someone is wise or old then someone is old or curious.
Everyone who is strong is both happy and not curious.
If someone is either not tall or patient then susan is either not curious or brave.
Fred is curious.
John is not generous.
Someone is not tall.
Lucy is not tall or quiet.
Someone is either tall or not tall.
Alice is creative or old. | Mary is not calm. | contradiction | (![X]:(~old(X)<=>(~rich(X)|rich(X))))&
(![X]:((wise(X)&brave(X))=>(strong(X)|~curious(X))))&
(![X]:((wise(X)|~calm(X))<=>~patient(X)))&
(![X]:(tall(X)<=>(rich(X)<~>~funny(X))))&
((?[X]:((old(X)&~curious(X))))<=>(?[X]:((tall(X)|funny(X)))))&
((?[X]:((brave(X)|wise(X))))<=>(?[X]:((kind(X)<~>humble(X)))))&
((?[X]:(~rich(X)))<=>((wise(mary)|~calm(mary))))&
((~strong(paul))=>((~tall(mary)|patient(mary))))&
(![X]:((~old(X)|funny(X))<=>(funny(X)|~quiet(X))))&
(![X]:((calm(X)<~>wise(X))=>(wise(X)<~>strong(X))))&
(((~old(mary)<~>humble(mary)))=>(?[X]:(~quiet(X))))&
((?[X]:((rich(X)|~quiet(X))))=>((kind(john)&happy(john))))&
((?[X]:((~patient(X)<~>wise(X))))<=>(?[X]:((brave(X)<~>~patient(X)))))&
((?[X]:((wise(X)|old(X))))=>(?[X]:((old(X)|curious(X)))))&
(![X]:(strong(X)=>(happy(X)&~curious(X))))&
((?[X]:((~tall(X)<~>patient(X))))=>((~curious(susan)<~>brave(susan))))&
(curious(fred))&
(~generous(john))&
(?[X]:(~tall(X)))&
((~tall(lucy)|quiet(lucy)))&
(?[X]:((tall(X)<~>~tall(X))))&
((creative(alice)|old(alice))) | ~calm(mary) | [
"p0",
"p3",
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 2659754376430795011216207
% SZS output start Proof for 2659754376430795011216207
1. ! [X0] : (~old(X0) <=> (rich(X0) | ~rich(X0))) [input p0]
4. ! [X0] : (tall(X0) <=> (rich(X0) <~> ~funny(X0))) [input p3]
5. ? [X0] : (~curious(X0) & old(X0)) <=> ? [X0] : (funny(X0) | tall(X0)) [input p4]
7. ? [X0] : ~rich(X0) <=> (~calm(mary) | wise(mary)) [input p6]
23. ~calm(mary) [input hypothesis]
24. ? [X0] : (~curious(X0) & old(X0)) <=> ? [X1] : (funny(X1) | tall(X1)) [rectify 5]
42. ! [X0] : ((~old(X0) | (~rich(X0) & rich(X0))) & ((rich(X0) | ~rich(X0)) | old(X0))) [nnf transformation 1]
43. ! [X0] : ((~old(X0) | (~rich(X0) & rich(X0))) & (rich(X0) | ~rich(X0) | old(X0))) [flattening 42]
46. ! [X0] : ((tall(X0) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0)))) & (((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | ~tall(X0))) [nnf transformation 4]
47. (? [X0] : (~curious(X0) & old(X0)) | ! [X1] : (~funny(X1) & ~tall(X1))) & (? [X1] : (funny(X1) | tall(X1)) | ! [X0] : (curious(X0) | ~old(X0))) [nnf transformation 24]
48. (? [X0] : (~curious(X0) & old(X0)) | ! [X1] : (~funny(X1) & ~tall(X1))) & (? [X2] : (funny(X2) | tall(X2)) | ! [X3] : (curious(X3) | ~old(X3))) [rectify 47]
49. ? [X0] : (~curious(X0) & old(X0)) => (~curious(sK0) & old(sK0)) [choice axiom]
50. ? [X2] : (funny(X2) | tall(X2)) => (funny(sK1) | tall(sK1)) [choice axiom]
51. ((~curious(sK0) & old(sK0)) | ! [X1] : (~funny(X1) & ~tall(X1))) & ((funny(sK1) | tall(sK1)) | ! [X3] : (curious(X3) | ~old(X3))) [skolemisation 48,50,49]
57. (? [X0] : ~rich(X0) | (calm(mary) & ~wise(mary))) & ((~calm(mary) | wise(mary)) | ! [X0] : rich(X0)) [nnf transformation 7]
58. (? [X0] : ~rich(X0) | (calm(mary) & ~wise(mary))) & (~calm(mary) | wise(mary) | ! [X0] : rich(X0)) [flattening 57]
59. (? [X0] : ~rich(X0) | (calm(mary) & ~wise(mary))) & (~calm(mary) | wise(mary) | ! [X1] : rich(X1)) [rectify 58]
60. ? [X0] : ~rich(X0) => ~rich(sK4) [choice axiom]
61. (~rich(sK4) | (calm(mary) & ~wise(mary))) & (~calm(mary) | wise(mary) | ! [X1] : rich(X1)) [skolemisation 59,60]
83. ~old(X0) | rich(X0) [cnf transformation 43]
84. ~rich(X0) | ~old(X0) [cnf transformation 43]
92. funny(X0) | rich(X0) | tall(X0) [cnf transformation 46]
94. old(sK0) | ~tall(X1) [cnf transformation 51]
95. old(sK0) | ~funny(X1) [cnf transformation 51]
106. ~rich(sK4) | calm(mary) [cnf transformation 61]
140. ~calm(mary) [cnf transformation 23]
143. ~old(X0) [subsumption resolution 83,84]
145. 1 <=> ! [X1] : ~funny(X1) [avatar definition]
146. ~funny(X1) <- (1) [avatar component clause 145]
153. 3 <=> ! [X1] : ~tall(X1) [avatar definition]
154. ~tall(X1) <- (3) [avatar component clause 153]
156. ~funny(X1) [subsumption resolution 95,143]
157. 1 [avatar split clause 156,145]
158. ~tall(X1) [subsumption resolution 94,143]
159. 3 [avatar split clause 158,153]
195. 12 <=> calm(mary) [avatar definition]
199. 13 <=> rich(sK4) [avatar definition]
201. ~rich(sK4) <- (~13) [avatar component clause 199]
202. 12 | ~13 [avatar split clause 106,199,195]
209. 15 <=> ! [X1] : rich(X1) [avatar definition]
210. rich(X1) <- (15) [avatar component clause 209]
316. ~12 [avatar split clause 140,195]
320. rich(X2) | tall(X2) <- (1) [resolution 92,146]
323. rich(X2) <- (1, 3) [subsumption resolution 320,154]
324. 15 | ~1 | ~3 [avatar split clause 323,153,145,209]
325. $false <- (~13, 15) [resolution 210,201]
327. 13 | ~15 [avatar contradiction clause 325]
328. $false [avatar sat refutation 157,159,202,316,324,327]
% SZS output end Proof for 2659754376430795011216207
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or rich is not humble and vice versa. Everyone who is happy or funny is not wise and vice versa. Everyone who is funny is both quiet and generous. Everyone who is not happy is both quiet and not tall. If someone is either not rich or patient then paul is both not wise and creative. Everyone who is generous or not brave is both not curious and calm and vice versa. If someone is both not kind and not humble then someone is not brave and vice versa. If someone is not patient then mary is both not patient and not generous. Everyone who is both not creative and not curious is either not humble or not patient and vice versa. If someone is humble or not creative then john is both creative and tall and vice versa. If mary is not brave then someone is not quiet and vice versa. Everyone who is either not creative or wise is not tall or wise and vice versa. Everyone who is both quiet and not wise is both wise and not quiet. Everyone who is not creative is either not creative or not tall and vice versa. Everyone who is brave is either not kind or calm. John is either wise or not calm. Lucy is both not strong and curious. Susan is both not rich and not strong. John is tall or not strong. Alice is either wise or brave. Someone is patient or strong. | Mary is not patient. | entailment | (![X]:((~funny(X)<~>rich(X))<=>~humble(X)))&
(![X]:((happy(X)|funny(X))<=>~wise(X)))&
(![X]:(funny(X)=>(quiet(X)&generous(X))))&
(![X]:(~happy(X)=>(quiet(X)&~tall(X))))&
((?[X]:((~rich(X)<~>patient(X))))=>((~wise(paul)&creative(paul))))&
(![X]:((generous(X)|~brave(X))<=>(~curious(X)&calm(X))))&
((?[X]:((~kind(X)&~humble(X))))<=>(?[X]:(~brave(X))))&
((?[X]:(~patient(X)))=>((~patient(mary)&~generous(mary))))&
(![X]:((~creative(X)&~curious(X))<=>(~humble(X)<~>~patient(X))))&
((?[X]:((humble(X)|~creative(X))))<=>((creative(john)&tall(john))))&
((~brave(mary))<=>(?[X]:(~quiet(X))))&
(![X]:((~creative(X)<~>wise(X))<=>(~tall(X)|wise(X))))&
(![X]:((quiet(X)&~wise(X))=>(wise(X)&~quiet(X))))&
(![X]:(~creative(X)<=>(~creative(X)<~>~tall(X))))&
(![X]:(brave(X)=>(~kind(X)<~>calm(X))))&
((wise(john)<~>~calm(john)))&
((~strong(lucy)&curious(lucy)))&
((~rich(susan)&~strong(susan)))&
((tall(john)|~strong(john)))&
((wise(alice)<~>brave(alice)))&
(?[X]:((patient(X)|strong(X)))) | ~patient(mary) | [
"p1",
"p3",
"p6",
"p7",
"p8",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3676119904584173062471673
% SZS output start Proof for 3676119904584173062471673
2. ! [X0] : ((funny(X0) | happy(X0)) <=> ~wise(X0)) [input p1]
4. ! [X0] : (~happy(X0) => (~tall(X0) & quiet(X0))) [input p3]
7. ? [X0] : (~humble(X0) & ~kind(X0)) <=> ? [X0] : ~brave(X0) [input p6]
8. ? [X0] : ~patient(X0) => (~generous(mary) & ~patient(mary)) [input p7]
9. ! [X0] : ((~curious(X0) & ~creative(X0)) <=> (~humble(X0) <~> ~patient(X0))) [input p8]
11. ~brave(mary) <=> ? [X0] : ~quiet(X0) [input p10]
12. ! [X0] : ((~creative(X0) <~> wise(X0)) <=> (wise(X0) | ~tall(X0))) [input p11]
13. ! [X0] : ((~wise(X0) & quiet(X0)) => (~quiet(X0) & wise(X0))) [input p12]
14. ! [X0] : (~creative(X0) <=> (~creative(X0) <~> ~tall(X0))) [input p13]
22. patient(mary) [input hypothesis]
23. ? [X0] : (~humble(X0) & ~kind(X0)) <=> ? [X1] : ~brave(X1) [rectify 7]
25. ! [X0] : ((~tall(X0) & quiet(X0)) | happy(X0)) [ennf transformation 4]
27. (~generous(mary) & ~patient(mary)) | ! [X0] : patient(X0) [ennf transformation 8]
28. ! [X0] : ((~quiet(X0) & wise(X0)) | (wise(X0) | ~quiet(X0))) [ennf transformation 13]
29. ! [X0] : ((~quiet(X0) & wise(X0)) | wise(X0) | ~quiet(X0)) [flattening 28]
32. ! [X0] : (((funny(X0) | happy(X0)) | wise(X0)) & (~wise(X0) | (~funny(X0) & ~happy(X0)))) [nnf transformation 2]
33. ! [X0] : ((funny(X0) | happy(X0) | wise(X0)) & (~wise(X0) | (~funny(X0) & ~happy(X0)))) [flattening 32]
37. (? [X0] : (~humble(X0) & ~kind(X0)) | ! [X1] : brave(X1)) & (? [X1] : ~brave(X1) | ! [X0] : (humble(X0) | kind(X0))) [nnf transformation 23]
38. (? [X0] : (~humble(X0) & ~kind(X0)) | ! [X1] : brave(X1)) & (? [X2] : ~brave(X2) | ! [X3] : (humble(X3) | kind(X3))) [rectify 37]
39. ? [X0] : (~humble(X0) & ~kind(X0)) => (~humble(sK0) & ~kind(sK0)) [choice axiom]
40. ? [X2] : ~brave(X2) => ~brave(sK1) [choice axiom]
41. ((~humble(sK0) & ~kind(sK0)) | ! [X1] : brave(X1)) & (~brave(sK1) | ! [X3] : (humble(X3) | kind(X3))) [skolemisation 38,40,39]
42. ! [X0] : (((~curious(X0) & ~creative(X0)) | ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0)))) & (((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) | (curious(X0) | creative(X0)))) [nnf transformation 9]
43. ! [X0] : (((~curious(X0) & ~creative(X0)) | ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0)))) & (((patient(X0) | humble(X0)) & (~patient(X0) | ~humble(X0))) | curious(X0) | creative(X0))) [flattening 42]
49. (~brave(mary) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | brave(mary)) [nnf transformation 11]
50. (~brave(mary) | ! [X0] : quiet(X0)) & (? [X1] : ~quiet(X1) | brave(mary)) [rectify 49]
51. ? [X1] : ~quiet(X1) => ~quiet(sK3) [choice axiom]
52. (~brave(mary) | ! [X0] : quiet(X0)) & (~quiet(sK3) | brave(mary)) [skolemisation 50,51]
53. ! [X0] : ((((~wise(X0) | creative(X0)) & (wise(X0) | ~creative(X0))) | (~wise(X0) & tall(X0))) & ((wise(X0) | ~tall(X0)) | ((~creative(X0) | ~wise(X0)) & (wise(X0) | creative(X0))))) [nnf transformation 12]
54. ! [X0] : ((((~wise(X0) | creative(X0)) & (wise(X0) | ~creative(X0))) | (~wise(X0) & tall(X0))) & (wise(X0) | ~tall(X0) | ((~creative(X0) | ~wise(X0)) & (wise(X0) | creative(X0))))) [flattening 53]
55. ! [X0] : ((~creative(X0) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0)))) & (((tall(X0) | creative(X0)) & (~tall(X0) | ~creative(X0))) | creative(X0))) [nnf transformation 14]
65. ~wise(X0) | ~happy(X0) [cnf transformation 33]
71. ~tall(X0) | happy(X0) [cnf transformation 25]
83. ~humble(sK0) | brave(X1) [cnf transformation 41]
84. ~patient(mary) | patient(X0) [cnf transformation 27]
88. ~creative(X0) | ~patient(X0) | humble(X0) [cnf transformation 43]
98. ~brave(mary) | quiet(X0) [cnf transformation 52]
99. wise(X0) | ~tall(X0) | wise(X0) | creative(X0) [cnf transformation 54]
104. ~wise(X0) | creative(X0) | ~wise(X0) [cnf transformation 54]
106. ~quiet(X0) | wise(X0) | ~quiet(X0) [cnf transformation 29]
108. tall(X0) | creative(X0) | creative(X0) [cnf transformation 55]
110. ~creative(X0) | ~creative(X0) | tall(X0) [cnf transformation 55]
123. patient(mary) [cnf transformation 22]
124. tall(X0) | creative(X0) [duplicate literal removal 108]
125. ~creative(X0) | tall(X0) [duplicate literal removal 110]
127. ~quiet(X0) | wise(X0) [duplicate literal removal 106]
128. wise(X0) | ~tall(X0) | creative(X0) [duplicate literal removal 99]
129. ~wise(X0) | creative(X0) [duplicate literal removal 104]
149. 5 <=> ! [X1] : brave(X1) [avatar definition]
150. brave(X1) <- (5) [avatar component clause 149]
152. 6 <=> humble(sK0) [avatar definition]
154. ~humble(sK0) <- (~6) [avatar component clause 152]
155. 5 | ~6 [avatar split clause 83,152,149]
170. 10 <=> ! [X0] : patient(X0) [avatar definition]
171. patient(X0) <- (10) [avatar component clause 170]
178. 12 <=> patient(mary) [avatar definition]
181. 10 | ~12 [avatar split clause 84,178,170]
200. 17 <=> ! [X1] : creative(X1) [avatar definition]
201. creative(X1) <- (17) [avatar component clause 200]
210. 19 <=> ! [X0] : quiet(X0) [avatar definition]
211. quiet(X0) <- (19) [avatar component clause 210]
213. 20 <=> brave(mary) [avatar definition]
215. ~brave(mary) <- (~20) [avatar component clause 213]
216. 19 | ~20 [avatar split clause 98,213,210]
222. ~tall(X0) | creative(X0) [subsumption resolution 128,129]
223. creative(X0) [subsumption resolution 124,222]
224. 17 [avatar split clause 223,200]
260. 12 [avatar split clause 123,178]
270. tall(X0) <- (17) [resolution 125,201]
271. happy(X0) <- (17) [resolution 270,71]
308. ~patient(X0) | humble(X0) <- (17) [resolution 88,201]
309. humble(X0) <- (10, 17) [subsumption resolution 308,171]
310. $false <- (~6, 10, 17) [resolution 309,154]
313. 6 | ~10 | ~17 [avatar contradiction clause 310]
315. $false <- (5, ~20) [resolution 150,215]
316. ~5 | 20 [avatar contradiction clause 315]
319. wise(X0) <- (19) [resolution 211,127]
324. ~happy(X2) <- (19) [resolution 319,65]
331. $false <- (17, 19) [subsumption resolution 324,271]
332. ~17 | ~19 [avatar contradiction clause 331]
333. $false [avatar sat refutation 155,181,216,224,260,313,316,332]
% SZS output end Proof for 3676119904584173062471673
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative or patient is both not rich and tall and vice versa. Everyone who is funny or strong is either patient or quiet and vice versa. If lucy is not curious then someone is either happy or creative. If someone is old or not kind then alice is not happy and vice versa. Everyone who is both not old and wise is generous or funny. Everyone who is both happy and rich is either not kind or not curious. If someone is both happy and kind then someone is either wise or brave and vice versa. Everyone who is either not calm or old is funny and vice versa. Everyone who is wise or tall is happy or not happy. Everyone who is not old is not patient and vice versa. Everyone who is funny or wise is both kind and not kind and vice versa. Everyone who is quiet or generous is not generous and vice versa. If someone is either not strong or strong then someone is either not kind or kind and vice versa. If someone is both not creative and not kind then lucy is not curious or not wise and vice versa. If someone is tall or brave then susan is both not calm and brave. Everyone who is either not curious or not creative is either not brave or not curious and vice versa. Susan is quiet or not calm. Susan is either not calm or not humble. Fred is generous or not kind. Susan is happy. Alice is both not kind and not tall. Someone is not quiet or not happy. Someone is not happy or not creative. | Susan is curious. | neutral | (![X]:((creative(X)|patient(X))<=>(~rich(X)&tall(X))))&
(![X]:((funny(X)|strong(X))<=>(patient(X)<~>quiet(X))))&
((~curious(lucy))=>(?[X]:((happy(X)<~>creative(X)))))&
((?[X]:((old(X)|~kind(X))))<=>(~happy(alice)))&
(![X]:((~old(X)&wise(X))=>(generous(X)|funny(X))))&
(![X]:((happy(X)&rich(X))=>(~kind(X)<~>~curious(X))))&
((?[X]:((happy(X)&kind(X))))<=>(?[X]:((wise(X)<~>brave(X)))))&
(![X]:((~calm(X)<~>old(X))<=>funny(X)))&
(![X]:((wise(X)|tall(X))=>(happy(X)|~happy(X))))&
(![X]:(~old(X)<=>~patient(X)))&
(![X]:((funny(X)|wise(X))<=>(kind(X)&~kind(X))))&
(![X]:((quiet(X)|generous(X))<=>~generous(X)))&
((?[X]:((~strong(X)<~>strong(X))))<=>(?[X]:((~kind(X)<~>kind(X)))))&
((?[X]:((~creative(X)&~kind(X))))<=>((~curious(lucy)|~wise(lucy))))&
((?[X]:((tall(X)|brave(X))))=>((~calm(susan)&brave(susan))))&
(![X]:((~curious(X)<~>~creative(X))<=>(~brave(X)<~>~curious(X))))&
((quiet(susan)|~calm(susan)))&
((~calm(susan)<~>~humble(susan)))&
((generous(fred)|~kind(fred)))&
(happy(susan))&
((~kind(alice)&~tall(alice)))&
(?[X]:((~quiet(X)|~happy(X))))&
(?[X]:((~happy(X)|~creative(X)))) | curious(susan) | [] | null | 0 |
Everyone who is either not strong or rich is both not strong and kind.
If someone is not wise then john is calm and vice versa.
Everyone who is both brave and not curious is generous.
Everyone who is not curious or strong is old or not quiet and vice versa.
Everyone who is creative or not tall is old or funny.
If john is not quiet or not strong then paul is not creative.
If someone is either not humble or curious then susan is wise or not strong.
If someone is not calm or not generous then someone is not brave or not quiet and vice versa.
If someone is rich then someone is either not creative or not humble and vice versa.
Everyone who is both not wise and generous is not calm or creative.
Everyone who is not brave is happy.
Everyone who is funny or creative is either not quiet or creative and vice versa.
If someone is either not tall or not creative then someone is not tall or not funny.
Everyone who is funny is either humble or not brave and vice versa.
If someone is old or not strong then someone is not wise.
Everyone who is tall is not tall.
Someone is both curious and not strong.
Mary is creative.
Fred is generous or strong.
Fred is both not quiet and strong.
Susan is brave or not creative.
Fred is either not old or old.
Someone is creative or not curious. | Fred is not generous. | neutral | (![X]:((~strong(X)<~>rich(X))=>(~strong(X)&kind(X))))&
((?[X]:(~wise(X)))<=>(calm(john)))&
(![X]:((brave(X)&~curious(X))=>generous(X)))&
(![X]:((~curious(X)|strong(X))<=>(old(X)|~quiet(X))))&
(![X]:((creative(X)|~tall(X))=>(old(X)|funny(X))))&
(((~quiet(john)|~strong(john)))=>(~creative(paul)))&
((?[X]:((~humble(X)<~>curious(X))))=>((wise(susan)|~strong(susan))))&
((?[X]:((~calm(X)|~generous(X))))<=>(?[X]:((~brave(X)|~quiet(X)))))&
((?[X]:(rich(X)))<=>(?[X]:((~creative(X)<~>~humble(X)))))&
(![X]:((~wise(X)&generous(X))=>(~calm(X)|creative(X))))&
(![X]:(~brave(X)=>happy(X)))&
(![X]:((funny(X)|creative(X))<=>(~quiet(X)<~>creative(X))))&
((?[X]:((~tall(X)<~>~creative(X))))=>(?[X]:((~tall(X)|~funny(X)))))&
(![X]:(funny(X)<=>(humble(X)<~>~brave(X))))&
((?[X]:((old(X)|~strong(X))))=>(?[X]:(~wise(X))))&
(![X]:(tall(X)=>~tall(X)))&
(?[X]:((curious(X)&~strong(X))))&
(creative(mary))&
((generous(fred)|strong(fred)))&
((~quiet(fred)&strong(fred)))&
((brave(susan)|~creative(susan)))&
((~old(fred)<~>old(fred)))&
(?[X]:((creative(X)|~curious(X)))) | ~generous(fred) | [] | null | 0 |
Everyone who is both not tall and not funny is quiet or not old and vice versa.
If someone is not old then someone is either kind or not wise.
If someone is funny or tall then someone is humble and vice versa.
Everyone who is calm or not calm is both brave and not quiet and vice versa.
Everyone who is not curious or kind is either happy or humble.
Everyone who is both not curious and strong is either not funny or wise and vice versa.
Everyone who is not old or not brave is either generous or funny and vice versa.
Everyone who is both not happy and not quiet is both generous and not humble and vice versa.
If someone is both not tall and not kind then mary is both not tall and not funny and vice versa.
If someone is both not strong and humble then fred is creative.
If someone is both rich and happy then someone is curious or not happy and vice versa.
Everyone who is either tall or curious is either not wise or not rich.
Everyone who is kind or not humble is funny or wise.
Everyone who is both not curious and not patient is not quiet.
Everyone who is both not old and not humble is not quiet.
If fred is not funny or not old then someone is either not humble or calm.
Susan is not curious.
Mary is humble.
John is either not generous or not strong.
Paul is both not strong and not curious.
Someone is funny.
Someone is kind or not calm.
Mary is either not creative or rich.
John is creative or old. | Mary is kind. | contradiction | (![X]:((~tall(X)&~funny(X))<=>(quiet(X)|~old(X))))&
((?[X]:(~old(X)))=>(?[X]:((kind(X)<~>~wise(X)))))&
((?[X]:((funny(X)|tall(X))))<=>(?[X]:(humble(X))))&
(![X]:((calm(X)|~calm(X))<=>(brave(X)&~quiet(X))))&
(![X]:((~curious(X)|kind(X))=>(happy(X)<~>humble(X))))&
(![X]:((~curious(X)&strong(X))<=>(~funny(X)<~>wise(X))))&
(![X]:((~old(X)|~brave(X))<=>(generous(X)<~>funny(X))))&
(![X]:((~happy(X)&~quiet(X))<=>(generous(X)&~humble(X))))&
((?[X]:((~tall(X)&~kind(X))))<=>((~tall(mary)&~funny(mary))))&
((?[X]:((~strong(X)&humble(X))))=>(creative(fred)))&
((?[X]:((rich(X)&happy(X))))<=>(?[X]:((curious(X)|~happy(X)))))&
(![X]:((tall(X)<~>curious(X))=>(~wise(X)<~>~rich(X))))&
(![X]:((kind(X)|~humble(X))=>(funny(X)|wise(X))))&
(![X]:((~curious(X)&~patient(X))=>~quiet(X)))&
(![X]:((~old(X)&~humble(X))=>~quiet(X)))&
(((~funny(fred)|~old(fred)))=>(?[X]:((~humble(X)<~>calm(X)))))&
(~curious(susan))&
(humble(mary))&
((~generous(john)<~>~strong(john)))&
((~strong(paul)&~curious(paul)))&
(?[X]:(funny(X)))&
(?[X]:((kind(X)|~calm(X))))&
((~creative(mary)<~>rich(mary)))&
((creative(john)|old(john))) | kind(mary) | [
"p3",
"p4",
"p7",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 202109421187832433256934
% SZS output start Proof for 202109421187832433256934
4. ! [X0] : ((~calm(X0) | calm(X0)) <=> (~quiet(X0) & brave(X0))) [input p3]
5. ! [X0] : ((kind(X0) | ~curious(X0)) => (happy(X0) <~> humble(X0))) [input p4]
8. ! [X0] : ((~quiet(X0) & ~happy(X0)) <=> (~humble(X0) & generous(X0))) [input p7]
18. humble(mary) [input p17]
25. kind(mary) [input hypothesis]
31. ! [X0] : ((happy(X0) <~> humble(X0)) | (~kind(X0) & curious(X0))) [ennf transformation 5]
50. ! [X0] : (((~calm(X0) | calm(X0)) | (quiet(X0) | ~brave(X0))) & ((~quiet(X0) & brave(X0)) | (calm(X0) & ~calm(X0)))) [nnf transformation 4]
51. ! [X0] : ((~calm(X0) | calm(X0) | quiet(X0) | ~brave(X0)) & ((~quiet(X0) & brave(X0)) | (calm(X0) & ~calm(X0)))) [flattening 50]
52. ! [X0] : (((~humble(X0) | ~happy(X0)) & (humble(X0) | happy(X0))) | (~kind(X0) & curious(X0))) [nnf transformation 31]
57. ! [X0] : (((~quiet(X0) & ~happy(X0)) | (humble(X0) | ~generous(X0))) & ((~humble(X0) & generous(X0)) | (quiet(X0) | happy(X0)))) [nnf transformation 8]
58. ! [X0] : (((~quiet(X0) & ~happy(X0)) | humble(X0) | ~generous(X0)) & ((~humble(X0) & generous(X0)) | quiet(X0) | happy(X0))) [flattening 57]
91. ~quiet(X0) | ~calm(X0) [cnf transformation 51]
92. ~quiet(X0) | calm(X0) [cnf transformation 51]
97. ~happy(X0) | ~humble(X0) | ~kind(X0) [cnf transformation 52]
111. ~humble(X0) | quiet(X0) | happy(X0) [cnf transformation 58]
136. humble(mary) [cnf transformation 18]
146. kind(mary) [cnf transformation 25]
184. ~quiet(X0) [subsumption resolution 91,92]
190. ~humble(X0) | happy(X0) [subsumption resolution 111,184]
319. happy(mary) [resolution 190,136]
353. ~humble(mary) | ~kind(mary) [resolution 97,319]
356. ~kind(mary) [subsumption resolution 353,136]
357. $false [subsumption resolution 356,146]
% SZS output end Proof for 202109421187832433256934
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or kind is both happy and humble.
Everyone who is strong or not quiet is not happy or not rich.
If someone is generous then mary is either not happy or rich and vice versa.
If john is not brave or not happy then someone is patient or not tall and vice versa.
Everyone who is kind or generous is both rich and not calm.
Everyone who is funny is either calm or not rich.
Everyone who is either not strong or not generous is tall or not strong.
If paul is either funny or creative then someone is funny or not curious.
If paul is both creative and not humble then someone is strong or not quiet.
Everyone who is either quiet or creative is not generous.
If mary is not creative then someone is not brave.
Everyone who is old or not old is kind.
Everyone who is generous is both not patient and not curious and vice versa.
If susan is kind or not strong then susan is not wise or generous and vice versa.
If someone is not strong then paul is rich or not kind.
Someone is either wise or strong.
Lucy is not patient or not happy.
Alice is humble or not happy.
Alice is rich.
Paul is both not strong and not tall. | Susan is not quiet. | contradiction | (![X]:((~happy(X)|kind(X))=>(happy(X)&humble(X))))&
(![X]:((strong(X)|~quiet(X))=>(~happy(X)|~rich(X))))&
((?[X]:(generous(X)))<=>((~happy(mary)<~>rich(mary))))&
(((~brave(john)|~happy(john)))<=>(?[X]:((patient(X)|~tall(X)))))&
(![X]:((kind(X)|generous(X))=>(rich(X)&~calm(X))))&
(![X]:(funny(X)=>(calm(X)<~>~rich(X))))&
(![X]:((~strong(X)<~>~generous(X))=>(tall(X)|~strong(X))))&
(((funny(paul)<~>creative(paul)))=>(?[X]:((funny(X)|~curious(X)))))&
(((creative(paul)&~humble(paul)))=>(?[X]:((strong(X)|~quiet(X)))))&
(![X]:((quiet(X)<~>creative(X))=>~generous(X)))&
((~creative(mary))=>(?[X]:(~brave(X))))&
(![X]:((old(X)|~old(X))=>kind(X)))&
(![X]:(generous(X)<=>(~patient(X)&~curious(X))))&
(((kind(susan)|~strong(susan)))<=>((~wise(susan)|generous(susan))))&
((?[X]:(~strong(X)))=>((rich(paul)|~kind(paul))))&
(?[X]:((wise(X)<~>strong(X))))&
((~patient(lucy)|~happy(lucy)))&
((humble(alice)|~happy(alice)))&
(rich(alice))&
((~strong(paul)&~tall(paul))) | ~quiet(susan) | [
"p0",
"p1",
"p4",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1614951456826435103819953
% SZS output start Proof for 1614951456826435103819953
1. ! [X0] : ((kind(X0) | ~happy(X0)) => (humble(X0) & happy(X0))) [input p0]
2. ! [X0] : ((~quiet(X0) | strong(X0)) => (~rich(X0) | ~happy(X0))) [input p1]
5. ! [X0] : ((generous(X0) | kind(X0)) => (~calm(X0) & rich(X0))) [input p4]
12. ! [X0] : ((~old(X0) | old(X0)) => kind(X0)) [input p11]
21. ~quiet(susan) [input hypothesis]
22. ! [X0] : ((kind(X0) | ~happy(X0)) => happy(X0)) [pure predicate removal 1]
25. ! [X0] : (happy(X0) | (~kind(X0) & happy(X0))) [ennf transformation 22]
26. ! [X0] : ((~rich(X0) | ~happy(X0)) | (quiet(X0) & ~strong(X0))) [ennf transformation 2]
27. ! [X0] : (~rich(X0) | ~happy(X0) | (quiet(X0) & ~strong(X0))) [flattening 26]
28. ! [X0] : ((~calm(X0) & rich(X0)) | (~generous(X0) & ~kind(X0))) [ennf transformation 5]
35. ! [X0] : (kind(X0) | (old(X0) & ~old(X0))) [ennf transformation 12]
62. happy(X0) | happy(X0) [cnf transformation 25]
65. ~rich(X0) | ~happy(X0) | quiet(X0) [cnf transformation 27]
74. ~kind(X0) | rich(X0) [cnf transformation 28]
87. kind(X0) | ~old(X0) [cnf transformation 35]
88. old(X0) | kind(X0) [cnf transformation 35]
103. ~quiet(susan) [cnf transformation 21]
105. happy(X0) [duplicate literal removal 62]
106. ~rich(X0) | quiet(X0) [subsumption resolution 65,105]
173. kind(X0) [subsumption resolution 87,88]
201. rich(X0) [resolution 74,173]
208. quiet(X0) [resolution 106,201]
211. $false [resolution 208,103]
% SZS output end Proof for 1614951456826435103819953
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is brave then someone is either calm or rich and vice versa.
If john is not old then alice is both not strong and quiet and vice versa.
Everyone who is not old or old is kind or not curious.
If someone is either not wise or tall then fred is either not happy or brave and vice versa.
Everyone who is either funny or patient is not tall or curious and vice versa.
If someone is wise or strong then someone is both funny and not strong.
If lucy is both curious and not calm then john is either not generous or quiet and vice versa.
Everyone who is generous or not rich is not quiet or rich and vice versa.
Everyone who is either strong or kind is either not strong or wise.
If mary is humble or not creative then mary is generous or curious and vice versa.
If someone is either not curious or not quiet then john is not happy or wise and vice versa.
If someone is both not calm and not strong then someone is both kind and curious.
Everyone who is quiet is not curious or funny and vice versa.
Everyone who is patient or tall is both not generous and tall.
If someone is humble or not quiet then john is either not old or not creative and vice versa.
Everyone who is funny or not funny is generous.
Fred is both calm and humble.
Someone is creative.
Paul is not wise.
Alice is not creative or old.
John is both not creative and wise.
Fred is not quiet or not brave. | Mary is rich. | entailment | ((?[X]:(brave(X)))<=>(?[X]:((calm(X)<~>rich(X)))))&
((~old(john))<=>((~strong(alice)&quiet(alice))))&
(![X]:((~old(X)|old(X))=>(kind(X)|~curious(X))))&
((?[X]:((~wise(X)<~>tall(X))))<=>((~happy(fred)<~>brave(fred))))&
(![X]:((funny(X)<~>patient(X))<=>(~tall(X)|curious(X))))&
((?[X]:((wise(X)|strong(X))))=>(?[X]:((funny(X)&~strong(X)))))&
(((curious(lucy)&~calm(lucy)))<=>((~generous(john)<~>quiet(john))))&
(![X]:((generous(X)|~rich(X))<=>(~quiet(X)|rich(X))))&
(![X]:((strong(X)<~>kind(X))=>(~strong(X)<~>wise(X))))&
(((humble(mary)|~creative(mary)))<=>((generous(mary)|curious(mary))))&
((?[X]:((~curious(X)<~>~quiet(X))))<=>((~happy(john)|wise(john))))&
((?[X]:((~calm(X)&~strong(X))))=>(?[X]:((kind(X)&curious(X)))))&
(![X]:(quiet(X)<=>(~curious(X)|funny(X))))&
(![X]:((patient(X)|tall(X))=>(~generous(X)&tall(X))))&
((?[X]:((humble(X)|~quiet(X))))<=>((~old(john)<~>~creative(john))))&
(![X]:((funny(X)|~funny(X))=>generous(X)))&
((calm(fred)&humble(fred)))&
(?[X]:(creative(X)))&
(~wise(paul))&
((~creative(alice)|old(alice)))&
((~creative(john)&wise(john)))&
((~quiet(fred)|~brave(fred))) | rich(mary) | [
"p4",
"p7",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 923410455217358969313597
% SZS output start Proof for 923410455217358969313597
5. ! [X0] : ((funny(X0) <~> patient(X0)) <=> (curious(X0) | ~tall(X0))) [input p4]
8. ! [X0] : ((~rich(X0) | generous(X0)) <=> (rich(X0) | ~quiet(X0))) [input p7]
13. ! [X0] : (quiet(X0) <=> (funny(X0) | ~curious(X0))) [input p12]
14. ! [X0] : ((tall(X0) | patient(X0)) => (tall(X0) & ~generous(X0))) [input p13]
16. ! [X0] : ((~funny(X0) | funny(X0)) => generous(X0)) [input p15]
23. ~rich(mary) [input hypothesis]
32. ! [X0] : ((tall(X0) & ~generous(X0)) | (~tall(X0) & ~patient(X0))) [ennf transformation 14]
33. ! [X0] : (generous(X0) | (funny(X0) & ~funny(X0))) [ennf transformation 16]
45. ! [X0] : ((((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | (~curious(X0) & tall(X0))) & ((curious(X0) | ~tall(X0)) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0))))) [nnf transformation 5]
46. ! [X0] : ((((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | (~curious(X0) & tall(X0))) & (curious(X0) | ~tall(X0) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0))))) [flattening 45]
52. ! [X0] : (((~rich(X0) | generous(X0)) | (~rich(X0) & quiet(X0))) & ((rich(X0) | ~quiet(X0)) | (rich(X0) & ~generous(X0)))) [nnf transformation 8]
53. ! [X0] : ((~rich(X0) | generous(X0) | (~rich(X0) & quiet(X0))) & (rich(X0) | ~quiet(X0) | (rich(X0) & ~generous(X0)))) [flattening 52]
65. ! [X0] : ((quiet(X0) | (~funny(X0) & curious(X0))) & ((funny(X0) | ~curious(X0)) | ~quiet(X0))) [nnf transformation 13]
66. ! [X0] : ((quiet(X0) | (~funny(X0) & curious(X0))) & (funny(X0) | ~curious(X0) | ~quiet(X0))) [flattening 65]
92. patient(X0) | funny(X0) | tall(X0) [cnf transformation 46]
107. rich(X0) | ~quiet(X0) | rich(X0) [cnf transformation 53]
128. ~funny(X0) | quiet(X0) [cnf transformation 66]
130. ~generous(X0) | ~tall(X0) [cnf transformation 32]
131. ~patient(X0) | tall(X0) [cnf transformation 32]
139. generous(X0) | ~funny(X0) [cnf transformation 33]
140. generous(X0) | funny(X0) [cnf transformation 33]
149. ~rich(mary) [cnf transformation 23]
152. ~quiet(X0) | rich(X0) [duplicate literal removal 107]
341. 40 <=> ! [X1] : quiet(X1) [avatar definition]
342. quiet(X1) <- (40) [avatar component clause 341]
350. generous(X0) [subsumption resolution 139,140]
376. ~tall(X0) [resolution 130,350]
389. funny(X0) | tall(X0) | tall(X0) [resolution 92,131]
391. funny(X0) | tall(X0) [duplicate literal removal 389]
392. funny(X0) [subsumption resolution 391,376]
393. quiet(X0) [resolution 392,128]
394. 40 [avatar split clause 393,341]
395. rich(X0) <- (40) [resolution 342,152]
422. $false <- (40) [resolution 395,149]
426. ~40 [avatar contradiction clause 422]
427. $false [avatar sat refutation 394,426]
% SZS output end Proof for 923410455217358969313597
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either old or quiet then someone is both not happy and tall.
If someone is not rich then someone is not creative and vice versa.
Everyone who is happy or not patient is both curious and strong.
Everyone who is strong is not creative and vice versa.
Everyone who is both quiet and not generous is either not brave or not tall and vice versa.
Everyone who is either creative or tall is both not rich and creative and vice versa.
Everyone who is both quiet and creative is not curious and vice versa.
Everyone who is both funny and humble is not patient or happy.
If alice is not quiet or wise then susan is not humble or not old and vice versa.
Everyone who is creative or humble is kind or not patient.
Everyone who is not generous is wise or not rich and vice versa.
Everyone who is both old and not wise is not creative or not patient and vice versa.
If someone is patient or not old then alice is both wise and happy.
Everyone who is humble is either humble or not calm and vice versa.
Everyone who is either brave or not quiet is either creative or not kind and vice versa.
Someone is both calm and old.
John is quiet or rich.
Mary is generous or wise.
Someone is both old and not creative.
Mary is kind or rich.
Someone is both kind and humble.
Paul is either curious or not calm. | Alice is not quiet. | contradiction | (((old(alice)<~>quiet(alice)))=>(?[X]:((~happy(X)&tall(X)))))&
((?[X]:(~rich(X)))<=>(?[X]:(~creative(X))))&
(![X]:((happy(X)|~patient(X))=>(curious(X)&strong(X))))&
(![X]:(strong(X)<=>~creative(X)))&
(![X]:((quiet(X)&~generous(X))<=>(~brave(X)<~>~tall(X))))&
(![X]:((creative(X)<~>tall(X))<=>(~rich(X)&creative(X))))&
(![X]:((quiet(X)&creative(X))<=>~curious(X)))&
(![X]:((funny(X)&humble(X))=>(~patient(X)|happy(X))))&
(((~quiet(alice)|wise(alice)))<=>((~humble(susan)|~old(susan))))&
(![X]:((creative(X)|humble(X))=>(kind(X)|~patient(X))))&
(![X]:(~generous(X)<=>(wise(X)|~rich(X))))&
(![X]:((old(X)&~wise(X))<=>(~creative(X)|~patient(X))))&
((?[X]:((patient(X)|~old(X))))=>((wise(alice)&happy(alice))))&
(![X]:(humble(X)<=>(humble(X)<~>~calm(X))))&
(![X]:((brave(X)<~>~quiet(X))<=>(creative(X)<~>~kind(X))))&
(?[X]:((calm(X)&old(X))))&
((quiet(john)|rich(john)))&
((generous(mary)|wise(mary)))&
(?[X]:((old(X)&~creative(X))))&
((kind(mary)|rich(mary)))&
(?[X]:((kind(X)&humble(X))))&
((curious(paul)<~>~calm(paul))) | ~quiet(alice) | [
"p0",
"p2",
"p3",
"p5",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6026624506172400711347260
% SZS output start Proof for 6026624506172400711347260
1. (old(alice) <~> quiet(alice)) => ? [X0] : (tall(X0) & ~happy(X0)) [input p0]
3. ! [X0] : ((~patient(X0) | happy(X0)) => (strong(X0) & curious(X0))) [input p2]
4. ! [X0] : (strong(X0) <=> ~creative(X0)) [input p3]
6. ! [X0] : ((creative(X0) <~> tall(X0)) <=> (creative(X0) & ~rich(X0))) [input p5]
12. ! [X0] : ((~wise(X0) & old(X0)) <=> (~patient(X0) | ~creative(X0))) [input p11]
13. ? [X0] : (~old(X0) | patient(X0)) => (happy(alice) & wise(alice)) [input p12]
23. ~quiet(alice) [input hypothesis]
25. ! [X0] : (strong(X0) => ~creative(X0)) [unused predicate definition removal 4]
27. ? [X0] : (tall(X0) & ~happy(X0)) | (old(alice) <=> quiet(alice)) [ennf transformation 1]
28. ! [X0] : ((strong(X0) & curious(X0)) | (patient(X0) & ~happy(X0))) [ennf transformation 3]
29. ! [X0] : (~creative(X0) | ~strong(X0)) [ennf transformation 25]
32. (happy(alice) & wise(alice)) | ! [X0] : (old(X0) & ~patient(X0)) [ennf transformation 13]
33. ? [X0] : (tall(X0) & ~happy(X0)) | ((old(alice) | ~quiet(alice)) & (quiet(alice) | ~old(alice))) [nnf transformation 27]
34. ? [X0] : (tall(X0) & ~happy(X0)) => (tall(sK0) & ~happy(sK0)) [choice axiom]
35. (tall(sK0) & ~happy(sK0)) | ((old(alice) | ~quiet(alice)) & (quiet(alice) | ~old(alice))) [skolemisation 33,34]
43. ! [X0] : ((((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (~creative(X0) | rich(X0))) & ((creative(X0) & ~rich(X0)) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0))))) [nnf transformation 6]
44. ! [X0] : ((((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | ~creative(X0) | rich(X0)) & ((creative(X0) & ~rich(X0)) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0))))) [flattening 43]
51. ! [X0] : (((~wise(X0) & old(X0)) | (patient(X0) & creative(X0))) & ((~patient(X0) | ~creative(X0)) | (wise(X0) | ~old(X0)))) [nnf transformation 12]
52. ! [X0] : (((~wise(X0) & old(X0)) | (patient(X0) & creative(X0))) & (~patient(X0) | ~creative(X0) | wise(X0) | ~old(X0))) [flattening 51]
64. tall(sK0) | quiet(alice) | ~old(alice) [cnf transformation 35]
70. ~happy(X0) | strong(X0) [cnf transformation 28]
71. strong(X0) | patient(X0) [cnf transformation 28]
72. ~strong(X0) | ~creative(X0) [cnf transformation 29]
82. creative(X0) | creative(X0) | ~tall(X0) [cnf transformation 44]
99. patient(X0) | old(X0) [cnf transformation 52]
100. ~wise(X0) | creative(X0) [cnf transformation 52]
102. wise(alice) | ~patient(X0) [cnf transformation 32]
104. happy(alice) | ~patient(X0) [cnf transformation 32]
129. ~quiet(alice) [cnf transformation 23]
132. ~tall(X0) | creative(X0) [duplicate literal removal 82]
135. 1 <=> quiet(alice) [avatar definition]
139. 2 <=> old(alice) [avatar definition]
140. ~old(alice) <- (~2) [avatar component clause 139]
143. 3 <=> tall(sK0) [avatar definition]
145. tall(sK0) <- (3) [avatar component clause 143]
147. ~2 | 1 | 3 [avatar split clause 64,143,135,139]
175. 10 <=> wise(alice) [avatar definition]
177. wise(alice) <- (10) [avatar component clause 175]
187. 12 <=> ! [X0] : old(X0) [avatar definition]
188. old(X0) <- (12) [avatar component clause 187]
190. 13 <=> happy(alice) [avatar definition]
192. happy(alice) <- (13) [avatar component clause 190]
195. 14 <=> ! [X0] : ~patient(X0) [avatar definition]
196. ~patient(X0) <- (14) [avatar component clause 195]
197. 14 | 13 [avatar split clause 104,190,195]
199. 14 | 10 [avatar split clause 102,175,195]
229. ~1 [avatar split clause 129,135]
232. ~creative(X0) | patient(X0) [resolution 72,71]
243. $false <- (~2, 12) [resolution 188,140]
246. 2 | ~12 [avatar contradiction clause 243]
247. strong(alice) <- (13) [resolution 192,70]
249. old(X0) <- (14) [resolution 99,196]
250. 12 | ~14 [avatar split clause 249,195,187]
251. creative(alice) <- (10) [resolution 100,177]
253. ~creative(alice) <- (13) [resolution 247,72]
254. $false <- (10, 13) [subsumption resolution 253,251]
255. ~10 | ~13 [avatar contradiction clause 254]
261. creative(sK0) <- (3) [resolution 132,145]
284. patient(sK0) <- (3) [resolution 232,261]
285. $false <- (3, 14) [subsumption resolution 284,196]
286. ~3 | ~14 [avatar contradiction clause 285]
287. $false [avatar sat refutation 147,197,199,229,246,250,255,286]
% SZS output end Proof for 6026624506172400711347260
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or tall is strong and vice versa.
Everyone who is either funny or not old is generous.
If lucy is both rich and funny then john is not tall and vice versa.
If someone is both not strong and kind then someone is happy and vice versa.
If john is both happy and not old then someone is either brave or not tall.
Everyone who is not humble is generous or kind.
If mary is creative then someone is humble or patient and vice versa.
Everyone who is not patient is both strong and patient and vice versa.
If someone is either strong or not happy then someone is either not curious or not rich.
Everyone who is not quiet or not funny is both not humble and not happy and vice versa.
Everyone who is not creative is either old or kind.
If someone is both strong and kind then someone is both not rich and kind.
If someone is either not happy or patient then susan is either not strong or not old.
Everyone who is both not generous and not happy is generous or curious and vice versa.
Everyone who is both humble and happy is not quiet or brave and vice versa.
Alice is not kind or not generous.
Susan is wise.
Someone is not tall or strong.
John is either not rich or not brave.
Someone is either calm or not kind.
Someone is rich. | Alice is kind. | contradiction | (![X]:((~funny(X)|tall(X))<=>strong(X)))&
(![X]:((funny(X)<~>~old(X))=>generous(X)))&
(((rich(lucy)&funny(lucy)))<=>(~tall(john)))&
((?[X]:((~strong(X)&kind(X))))<=>(?[X]:(happy(X))))&
(((happy(john)&~old(john)))=>(?[X]:((brave(X)<~>~tall(X)))))&
(![X]:(~humble(X)=>(generous(X)|kind(X))))&
((creative(mary))<=>(?[X]:((humble(X)|patient(X)))))&
(![X]:(~patient(X)<=>(strong(X)&patient(X))))&
((?[X]:((strong(X)<~>~happy(X))))=>(?[X]:((~curious(X)<~>~rich(X)))))&
(![X]:((~quiet(X)|~funny(X))<=>(~humble(X)&~happy(X))))&
(![X]:(~creative(X)=>(old(X)<~>kind(X))))&
((?[X]:((strong(X)&kind(X))))=>(?[X]:((~rich(X)&kind(X)))))&
((?[X]:((~happy(X)<~>patient(X))))=>((~strong(susan)<~>~old(susan))))&
(![X]:((~generous(X)&~happy(X))<=>(generous(X)|curious(X))))&
(![X]:((humble(X)&happy(X))<=>(~quiet(X)|brave(X))))&
((~kind(alice)|~generous(alice)))&
(wise(susan))&
(?[X]:((~tall(X)|strong(X))))&
((~rich(john)<~>~brave(john)))&
(?[X]:((calm(X)<~>~kind(X))))&
(?[X]:(rich(X))) | kind(alice) | [
"p0",
"p1",
"p3",
"p7",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2811505018750194628208954
% SZS output start Proof for 2811505018750194628208954
1. ! [X0] : ((tall(X0) | ~funny(X0)) <=> strong(X0)) [input p0]
2. ! [X0] : ((funny(X0) <~> ~old(X0)) => generous(X0)) [input p1]
4. ? [X0] : (kind(X0) & ~strong(X0)) <=> ? [X0] : happy(X0) [input p3]
8. ! [X0] : (~patient(X0) <=> (patient(X0) & strong(X0))) [input p7]
13. ? [X0] : (~happy(X0) <~> patient(X0)) => (~strong(susan) <~> ~old(susan)) [input p12]
14. ! [X0] : ((~happy(X0) & ~generous(X0)) <=> (curious(X0) | generous(X0))) [input p13]
22. kind(alice) [input hypothesis]
23. ? [X0] : (kind(X0) & ~strong(X0)) <=> ? [X1] : happy(X1) [rectify 4]
27. ! [X0] : (generous(X0) | (funny(X0) <=> ~old(X0))) [ennf transformation 2]
35. (~strong(susan) <~> ~old(susan)) | ! [X0] : (~happy(X0) <=> patient(X0)) [ennf transformation 13]
36. ! [X0] : (((tall(X0) | ~funny(X0)) | ~strong(X0)) & (strong(X0) | (~tall(X0) & funny(X0)))) [nnf transformation 1]
37. ! [X0] : ((tall(X0) | ~funny(X0) | ~strong(X0)) & (strong(X0) | (~tall(X0) & funny(X0)))) [flattening 36]
38. ! [X0] : (generous(X0) | ((funny(X0) | old(X0)) & (~old(X0) | ~funny(X0)))) [nnf transformation 27]
41. (? [X0] : (kind(X0) & ~strong(X0)) | ! [X1] : ~happy(X1)) & (? [X1] : happy(X1) | ! [X0] : (~kind(X0) | strong(X0))) [nnf transformation 23]
42. (? [X0] : (kind(X0) & ~strong(X0)) | ! [X1] : ~happy(X1)) & (? [X2] : happy(X2) | ! [X3] : (~kind(X3) | strong(X3))) [rectify 41]
43. ? [X0] : (kind(X0) & ~strong(X0)) => (kind(sK0) & ~strong(sK0)) [choice axiom]
44. ? [X2] : happy(X2) => happy(sK1) [choice axiom]
45. ((kind(sK0) & ~strong(sK0)) | ! [X1] : ~happy(X1)) & (happy(sK1) | ! [X3] : (~kind(X3) | strong(X3))) [skolemisation 42,44,43]
53. ! [X0] : ((~patient(X0) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | patient(X0))) [nnf transformation 8]
54. ! [X0] : ((~patient(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | patient(X0))) [flattening 53]
65. ((old(susan) | strong(susan)) & (~old(susan) | ~strong(susan))) | ! [X0] : ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0))) [nnf transformation 35]
66. ! [X0] : (((~happy(X0) & ~generous(X0)) | (~curious(X0) & ~generous(X0))) & ((curious(X0) | generous(X0)) | (happy(X0) | generous(X0)))) [nnf transformation 14]
67. ! [X0] : (((~happy(X0) & ~generous(X0)) | (~curious(X0) & ~generous(X0))) & (curious(X0) | generous(X0) | happy(X0) | generous(X0))) [flattening 66]
78. strong(X0) | funny(X0) [cnf transformation 37]
81. ~old(X0) | generous(X0) | ~funny(X0) [cnf transformation 38]
86. happy(sK1) | ~kind(X3) | strong(X3) [cnf transformation 45]
96. patient(X0) | patient(X0) [cnf transformation 54]
97. ~patient(X0) | ~patient(X0) | ~strong(X0) [cnf transformation 54]
114. old(susan) | strong(susan) | ~happy(X0) | ~patient(X0) [cnf transformation 65]
116. ~generous(X0) | ~generous(X0) [cnf transformation 67]
132. kind(alice) [cnf transformation 22]
134. ~generous(X0) [duplicate literal removal 116]
135. patient(X0) [duplicate literal removal 96]
136. ~patient(X0) | ~strong(X0) [duplicate literal removal 97]
153. 4 <=> ! [X1] : ~happy(X1) [avatar definition]
154. ~happy(X1) <- (4) [avatar component clause 153]
166. 7 <=> ! [X3] : (~kind(X3) | strong(X3)) [avatar definition]
167. ~kind(X3) | strong(X3) <- (7) [avatar component clause 166]
169. 8 <=> happy(sK1) [avatar definition]
171. happy(sK1) <- (8) [avatar component clause 169]
172. 7 | 8 [avatar split clause 86,169,166]
243. old(susan) | strong(susan) | ~happy(X0) [subsumption resolution 114,135]
245. 25 <=> strong(susan) [avatar definition]
247. strong(susan) <- (25) [avatar component clause 245]
249. 26 <=> old(susan) [avatar definition]
251. old(susan) <- (26) [avatar component clause 249]
252. 4 | 25 | 26 [avatar split clause 243,249,245,153]
285. $false <- (4, 8) [subsumption resolution 171,154]
286. ~4 | ~8 [avatar contradiction clause 285]
291. ~strong(X0) [resolution 136,135]
292. funny(X0) [resolution 291,78]
293. strong(alice) <- (7) [resolution 167,132]
295. $false <- (7) [subsumption resolution 293,291]
296. ~7 [avatar contradiction clause 295]
299. $false <- (25) [subsumption resolution 247,291]
300. ~25 [avatar contradiction clause 299]
307. generous(susan) | ~funny(susan) <- (26) [resolution 81,251]
308. ~funny(susan) <- (26) [subsumption resolution 307,134]
309. $false <- (26) [subsumption resolution 308,292]
310. ~26 [avatar contradiction clause 309]
311. $false [avatar sat refutation 172,252,286,296,300,310]
% SZS output end Proof for 2811505018750194628208954
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is happy and vice versa.
If someone is not wise or not tall then someone is not creative or happy.
Everyone who is not tall is quiet and vice versa.
If lucy is not funny then paul is both happy and brave and vice versa.
Everyone who is both not patient and not humble is not wise and vice versa.
If someone is either not funny or not old then someone is both patient and not strong.
Everyone who is either not wise or not calm is tall.
If lucy is not patient or generous then someone is quiet or not old and vice versa.
If someone is not kind then paul is not rich.
If someone is not generous then someone is not curious or not funny.
Everyone who is tall is kind.
Everyone who is not wise or creative is both generous and not humble.
If alice is not kind or happy then lucy is either humble or not funny.
Everyone who is both not patient and not kind is both not tall and happy and vice versa.
Everyone who is either not generous or creative is both not calm and not quiet and vice versa.
Everyone who is kind is not funny or not happy.
Paul is curious.
Mary is either strong or funny.
Paul is either not quiet or not humble.
Someone is happy.
Paul is both not rich and quiet.
Someone is both not creative and not wise.
Someone is either calm or not tall. | Paul is not kind. | entailment | (![X]:(~tall(X)<=>happy(X)))&
((?[X]:((~wise(X)|~tall(X))))=>(?[X]:((~creative(X)|happy(X)))))&
(![X]:(~tall(X)<=>quiet(X)))&
((~funny(lucy))<=>((happy(paul)&brave(paul))))&
(![X]:((~patient(X)&~humble(X))<=>~wise(X)))&
((?[X]:((~funny(X)<~>~old(X))))=>(?[X]:((patient(X)&~strong(X)))))&
(![X]:((~wise(X)<~>~calm(X))=>tall(X)))&
(((~patient(lucy)|generous(lucy)))<=>(?[X]:((quiet(X)|~old(X)))))&
((?[X]:(~kind(X)))=>(~rich(paul)))&
((?[X]:(~generous(X)))=>(?[X]:((~curious(X)|~funny(X)))))&
(![X]:(tall(X)=>kind(X)))&
(![X]:((~wise(X)|creative(X))=>(generous(X)&~humble(X))))&
(((~kind(alice)|happy(alice)))=>((humble(lucy)<~>~funny(lucy))))&
(![X]:((~patient(X)&~kind(X))<=>(~tall(X)&happy(X))))&
(![X]:((~generous(X)<~>creative(X))<=>(~calm(X)&~quiet(X))))&
(![X]:(kind(X)=>(~funny(X)|~happy(X))))&
(curious(paul))&
((strong(mary)<~>funny(mary)))&
((~quiet(paul)<~>~humble(paul)))&
(?[X]:(happy(X)))&
((~rich(paul)&quiet(paul)))&
(?[X]:((~creative(X)&~wise(X))))&
(?[X]:((calm(X)<~>~tall(X)))) | ~kind(paul) | [
"p0",
"p2",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8571536396094654161680242
% SZS output start Proof for 8571536396094654161680242
1. ! [X0] : (~tall(X0) <=> happy(X0)) [input p0]
3. ! [X0] : (~tall(X0) <=> quiet(X0)) [input p2]
14. ! [X0] : ((~kind(X0) & ~patient(X0)) <=> (happy(X0) & ~tall(X0))) [input p13]
21. quiet(paul) & ~rich(paul) [input p20]
24. kind(paul) [input hypothesis]
28. quiet(paul) [pure predicate removal 21]
39. ! [X0] : ((~tall(X0) | ~happy(X0)) & (happy(X0) | tall(X0))) [nnf transformation 1]
43. ! [X0] : ((~tall(X0) | ~quiet(X0)) & (quiet(X0) | tall(X0))) [nnf transformation 3]
62. ! [X0] : (((~kind(X0) & ~patient(X0)) | (~happy(X0) | tall(X0))) & ((happy(X0) & ~tall(X0)) | (kind(X0) | patient(X0)))) [nnf transformation 14]
63. ! [X0] : (((~kind(X0) & ~patient(X0)) | ~happy(X0) | tall(X0)) & ((happy(X0) & ~tall(X0)) | kind(X0) | patient(X0))) [flattening 62]
75. happy(X0) | tall(X0) [cnf transformation 39]
76. ~happy(X0) | ~tall(X0) [cnf transformation 39]
80. ~quiet(X0) | ~tall(X0) [cnf transformation 43]
110. ~kind(X0) | ~happy(X0) | tall(X0) [cnf transformation 63]
124. quiet(paul) [cnf transformation 28]
129. kind(paul) [cnf transformation 24]
147. 5 <=> happy(paul) [avatar definition]
149. ~happy(paul) <- (~5) [avatar component clause 147]
233. ~kind(X0) | ~happy(X0) [subsumption resolution 110,76]
250. 26 <=> quiet(paul) [avatar definition]
252. quiet(paul) <- (26) [avatar component clause 250]
259. 26 [avatar split clause 124,250]
273. ~tall(paul) <- (26) [resolution 80,252]
275. ~happy(paul) [resolution 233,129]
278. ~5 [avatar split clause 275,147]
279. tall(paul) <- (~5) [resolution 149,75]
280. $false <- (~5, 26) [subsumption resolution 279,273]
281. 5 | ~26 [avatar contradiction clause 280]
282. $false [avatar sat refutation 259,278,281]
% SZS output end Proof for 8571536396094654161680242
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is generous.
Everyone who is both not tall and brave is rich.
If mary is both not kind and patient then someone is either not generous or not wise.
If someone is both not wise and not brave then mary is calm or creative.
Everyone who is either tall or not funny is either not rich or quiet.
If someone is happy then susan is both not generous and brave and vice versa.
Everyone who is either not old or patient is both wise and not brave.
Everyone who is not generous or kind is either calm or not quiet and vice versa.
Everyone who is both tall and curious is generous or not wise.
If someone is old or not humble then someone is both not wise and not humble and vice versa.
Everyone who is not kind or strong is either not quiet or rich.
If someone is kind or not rich then someone is patient.
Everyone who is not happy is both not kind and tall.
Everyone who is not creative is either wise or not kind.
Everyone who is curious or old is not old and vice versa.
If someone is wise or not happy then someone is rich and vice versa.
Fred is either not calm or not rich.
Someone is strong or not calm.
John is either happy or brave.
Fred is not calm or tall.
Paul is not patient or not brave.
Someone is not creative. | Susan is not tall. | contradiction | (![X]:(patient(X)=>generous(X)))&
(![X]:((~tall(X)&brave(X))=>rich(X)))&
(((~kind(mary)&patient(mary)))=>(?[X]:((~generous(X)<~>~wise(X)))))&
((?[X]:((~wise(X)&~brave(X))))=>((calm(mary)|creative(mary))))&
(![X]:((tall(X)<~>~funny(X))=>(~rich(X)<~>quiet(X))))&
((?[X]:(happy(X)))<=>((~generous(susan)&brave(susan))))&
(![X]:((~old(X)<~>patient(X))=>(wise(X)&~brave(X))))&
(![X]:((~generous(X)|kind(X))<=>(calm(X)<~>~quiet(X))))&
(![X]:((tall(X)&curious(X))=>(generous(X)|~wise(X))))&
((?[X]:((old(X)|~humble(X))))<=>(?[X]:((~wise(X)&~humble(X)))))&
(![X]:((~kind(X)|strong(X))=>(~quiet(X)<~>rich(X))))&
((?[X]:((kind(X)|~rich(X))))=>(?[X]:(patient(X))))&
(![X]:(~happy(X)=>(~kind(X)&tall(X))))&
(![X]:(~creative(X)=>(wise(X)<~>~kind(X))))&
(![X]:((curious(X)|old(X))<=>~old(X)))&
((?[X]:((wise(X)|~happy(X))))<=>(?[X]:(rich(X))))&
((~calm(fred)<~>~rich(fred)))&
(?[X]:((strong(X)|~calm(X))))&
((happy(john)<~>brave(john)))&
((~calm(fred)|tall(fred)))&
((~patient(paul)|~brave(paul)))&
(?[X]:(~creative(X))) | ~tall(susan) | [
"p0",
"p5",
"p6",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5098320862127271963448315
% SZS output start Proof for 5098320862127271963448315
1. ! [X0] : (patient(X0) => generous(X0)) [input p0]
6. ? [X0] : happy(X0) <=> (brave(susan) & ~generous(susan)) [input p5]
7. ! [X0] : ((~old(X0) <~> patient(X0)) => (~brave(X0) & wise(X0))) [input p6]
13. ! [X0] : (~happy(X0) => (tall(X0) & ~kind(X0))) [input p12]
15. ! [X0] : ((old(X0) | curious(X0)) <=> ~old(X0)) [input p14]
23. ~tall(susan) [input hypothesis]
27. ! [X0] : (generous(X0) | ~patient(X0)) [ennf transformation 1]
35. ! [X0] : ((~brave(X0) & wise(X0)) | (~old(X0) <=> patient(X0))) [ennf transformation 7]
40. ! [X0] : ((tall(X0) & ~kind(X0)) | happy(X0)) [ennf transformation 13]
46. (? [X0] : happy(X0) | (~brave(susan) | generous(susan))) & ((brave(susan) & ~generous(susan)) | ! [X0] : ~happy(X0)) [nnf transformation 6]
47. (? [X0] : happy(X0) | ~brave(susan) | generous(susan)) & ((brave(susan) & ~generous(susan)) | ! [X0] : ~happy(X0)) [flattening 46]
48. (? [X0] : happy(X0) | ~brave(susan) | generous(susan)) & ((brave(susan) & ~generous(susan)) | ! [X1] : ~happy(X1)) [rectify 47]
49. ? [X0] : happy(X0) => happy(sK1) [choice axiom]
50. (happy(sK1) | ~brave(susan) | generous(susan)) & ((brave(susan) & ~generous(susan)) | ! [X1] : ~happy(X1)) [skolemisation 48,49]
51. ! [X0] : ((~brave(X0) & wise(X0)) | ((~old(X0) | ~patient(X0)) & (patient(X0) | old(X0)))) [nnf transformation 35]
64. ! [X0] : (((old(X0) | curious(X0)) | old(X0)) & (~old(X0) | (~old(X0) & ~curious(X0)))) [nnf transformation 15]
65. ! [X0] : ((old(X0) | curious(X0) | old(X0)) & (~old(X0) | (~old(X0) & ~curious(X0)))) [flattening 64]
77. ~patient(X0) | generous(X0) [cnf transformation 27]
86. ~generous(susan) | ~happy(X1) [cnf transformation 50]
87. brave(susan) | ~happy(X1) [cnf transformation 50]
91. ~brave(X0) | patient(X0) | old(X0) [cnf transformation 51]
112. happy(X0) | tall(X0) [cnf transformation 40]
116. ~old(X0) | ~old(X0) [cnf transformation 65]
129. ~tall(susan) [cnf transformation 23]
130. ~old(X0) [duplicate literal removal 116]
163. 8 <=> generous(susan) [avatar definition]
164. ~generous(susan) <- (~8) [avatar component clause 163]
167. 9 <=> brave(susan) [avatar definition]
168. brave(susan) <- (9) [avatar component clause 167]
176. 11 <=> ! [X1] : ~happy(X1) [avatar definition]
177. ~happy(X1) <- (11) [avatar component clause 176]
178. 11 | 9 [avatar split clause 87,167,176]
179. 11 | ~8 [avatar split clause 86,163,176]
201. 17 <=> ! [X3] : ~old(X3) [avatar definition]
202. ~old(X3) <- (17) [avatar component clause 201]
222. 17 [avatar split clause 130,201]
311. patient(susan) | old(susan) <- (9) [resolution 91,168]
312. patient(susan) <- (9, 17) [subsumption resolution 311,202]
313. generous(susan) <- (9, 17) [resolution 312,77]
314. $false <- (~8, 9, 17) [subsumption resolution 313,164]
315. 8 | ~9 | ~17 [avatar contradiction clause 314]
318. tall(X0) <- (11) [resolution 177,112]
324. $false <- (11) [resolution 318,129]
325. ~11 [avatar contradiction clause 324]
326. $false [avatar sat refutation 178,179,222,315,325]
% SZS output end Proof for 5098320862127271963448315
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet or not patient then alice is not old or brave and vice versa. If someone is calm or not brave then someone is humble. Everyone who is curious or not funny is funny or wise. Everyone who is both calm and not rich is either not calm or not patient. Everyone who is either humble or not strong is brave or not patient. If someone is not old or funny then someone is both wise and creative and vice versa. If someone is not happy or not tall then fred is both kind and old and vice versa. If someone is not calm then someone is either not tall or not kind and vice versa. If someone is quiet then someone is patient. If someone is either not creative or not rich then someone is brave or humble and vice versa. Everyone who is not old or kind is both humble and not old and vice versa. Everyone who is both not calm and not happy is both not old and not strong and vice versa. If someone is curious then someone is both not curious and happy and vice versa. Everyone who is old is creative or brave and vice versa. Everyone who is not rich is both creative and brave and vice versa. If fred is both not rich and kind then john is not curious or humble. John is calm or generous. Someone is not strong. Fred is both patient and happy. Someone is humble or old. Paul is either not strong or not curious. Someone is humble or not strong. Someone is strong. Fred is either curious or not tall. | Fred is kind. | contradiction | ((?[X]:((~quiet(X)|~patient(X))))<=>((~old(alice)|brave(alice))))&
((?[X]:((calm(X)|~brave(X))))=>(?[X]:(humble(X))))&
(![X]:((curious(X)|~funny(X))=>(funny(X)|wise(X))))&
(![X]:((calm(X)&~rich(X))=>(~calm(X)<~>~patient(X))))&
(![X]:((humble(X)<~>~strong(X))=>(brave(X)|~patient(X))))&
((?[X]:((~old(X)|funny(X))))<=>(?[X]:((wise(X)&creative(X)))))&
((?[X]:((~happy(X)|~tall(X))))<=>((kind(fred)&old(fred))))&
((?[X]:(~calm(X)))<=>(?[X]:((~tall(X)<~>~kind(X)))))&
((?[X]:(quiet(X)))=>(?[X]:(patient(X))))&
((?[X]:((~creative(X)<~>~rich(X))))<=>(?[X]:((brave(X)|humble(X)))))&
(![X]:((~old(X)|kind(X))<=>(humble(X)&~old(X))))&
(![X]:((~calm(X)&~happy(X))<=>(~old(X)&~strong(X))))&
((?[X]:(curious(X)))<=>(?[X]:((~curious(X)&happy(X)))))&
(![X]:(old(X)<=>(creative(X)|brave(X))))&
(![X]:(~rich(X)<=>(creative(X)&brave(X))))&
(((~rich(fred)&kind(fred)))=>((~curious(john)|humble(john))))&
((calm(john)|generous(john)))&
(?[X]:(~strong(X)))&
((patient(fred)&happy(fred)))&
(?[X]:((humble(X)|old(X))))&
((~strong(paul)<~>~curious(paul)))&
(?[X]:((humble(X)|~strong(X))))&
(?[X]:(strong(X)))&
((curious(fred)<~>~tall(fred))) | kind(fred) | [
"p4",
"p10",
"p11",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4652655810709489502416065
% SZS output start Proof for 4652655810709489502416065
5. ! [X0] : ((humble(X0) <~> ~strong(X0)) => (~patient(X0) | brave(X0))) [input p4]
11. ! [X0] : ((kind(X0) | ~old(X0)) <=> (~old(X0) & humble(X0))) [input p10]
12. ! [X0] : ((~happy(X0) & ~calm(X0)) <=> (~strong(X0) & ~old(X0))) [input p11]
14. ! [X0] : (old(X0) <=> (brave(X0) | creative(X0))) [input p13]
19. happy(fred) & patient(fred) [input p18]
25. kind(fred) [input hypothesis]
38. ! [X0] : ((~patient(X0) | brave(X0)) | (humble(X0) <=> ~strong(X0))) [ennf transformation 5]
39. ! [X0] : (~patient(X0) | brave(X0) | (humble(X0) <=> ~strong(X0))) [flattening 38]
52. ! [X0] : (~patient(X0) | brave(X0) | ((humble(X0) | strong(X0)) & (~strong(X0) | ~humble(X0)))) [nnf transformation 39]
76. ! [X0] : (((kind(X0) | ~old(X0)) | (old(X0) | ~humble(X0))) & ((~old(X0) & humble(X0)) | (~kind(X0) & old(X0)))) [nnf transformation 11]
77. ! [X0] : ((kind(X0) | ~old(X0) | old(X0) | ~humble(X0)) & ((~old(X0) & humble(X0)) | (~kind(X0) & old(X0)))) [flattening 76]
78. ! [X0] : (((~happy(X0) & ~calm(X0)) | (strong(X0) | old(X0))) & ((~strong(X0) & ~old(X0)) | (happy(X0) | calm(X0)))) [nnf transformation 12]
79. ! [X0] : (((~happy(X0) & ~calm(X0)) | strong(X0) | old(X0)) & ((~strong(X0) & ~old(X0)) | happy(X0) | calm(X0))) [flattening 78]
85. ! [X0] : ((old(X0) | (~brave(X0) & ~creative(X0))) & ((brave(X0) | creative(X0)) | ~old(X0))) [nnf transformation 14]
86. ! [X0] : ((old(X0) | (~brave(X0) & ~creative(X0))) & (brave(X0) | creative(X0) | ~old(X0))) [flattening 85]
109. ~strong(X0) | brave(X0) | ~patient(X0) | ~humble(X0) [cnf transformation 52]
133. ~kind(X0) | humble(X0) [cnf transformation 77]
135. ~kind(X0) | ~old(X0) [cnf transformation 77]
140. ~happy(X0) | strong(X0) | old(X0) [cnf transformation 79]
146. ~brave(X0) | old(X0) [cnf transformation 86]
152. patient(fred) [cnf transformation 19]
153. happy(fred) [cnf transformation 19]
161. kind(fred) [cnf transformation 25]
233. 17 <=> kind(fred) [avatar definition]
234. kind(fred) <- (17) [avatar component clause 233]
237. 18 <=> old(fred) [avatar definition]
239. ~old(fred) <- (~18) [avatar component clause 237]
389. 17 [avatar split clause 161,233]
403. humble(fred) <- (17) [resolution 133,234]
404. ~old(fred) <- (17) [resolution 135,234]
407. ~18 | ~17 [avatar split clause 404,233,237]
440. strong(fred) | old(fred) [resolution 140,153]
443. strong(fred) <- (~18) [subsumption resolution 440,239]
474. brave(fred) | ~patient(fred) | ~humble(fred) <- (~18) [resolution 109,443]
478. brave(fred) | ~humble(fred) <- (~18) [subsumption resolution 474,152]
479. brave(fred) <- (17, ~18) [subsumption resolution 478,403]
524. old(fred) <- (17, ~18) [resolution 479,146]
525. $false <- (17, ~18) [subsumption resolution 524,239]
526. ~17 | 18 [avatar contradiction clause 525]
527. $false [avatar sat refutation 389,407,526]
% SZS output end Proof for 4652655810709489502416065
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not tall or not generous then lucy is kind or not rich and vice versa.
If someone is tall or curious then someone is curious.
Everyone who is either not rich or not creative is either calm or not quiet and vice versa.
Everyone who is not humble is both patient and rich.
If susan is wise then paul is both curious and funny.
Everyone who is either patient or not generous is both not rich and patient and vice versa.
Everyone who is not patient or rich is both calm and creative.
Everyone who is either not generous or not brave is either happy or not creative.
Everyone who is not rich or not old is not calm or curious and vice versa.
If someone is both not patient and not quiet then someone is creative.
If someone is both generous and creative then someone is both kind and not rich.
Everyone who is creative or generous is either creative or not humble and vice versa.
Everyone who is either strong or not calm is not humble or funny and vice versa.
Everyone who is both not patient and not kind is both rich and brave and vice versa.
If john is either not rich or wise then someone is both strong and calm and vice versa.
Everyone who is not happy or brave is either not happy or quiet and vice versa.
Someone is either strong or generous.
Someone is quiet.
Mary is both funny and generous.
Susan is curious or quiet.
Someone is not rich.
Paul is curious or funny. | Lucy is not generous. | neutral | (((~tall(john)|~generous(john)))<=>((kind(lucy)|~rich(lucy))))&
((?[X]:((tall(X)|curious(X))))=>(?[X]:(curious(X))))&
(![X]:((~rich(X)<~>~creative(X))<=>(calm(X)<~>~quiet(X))))&
(![X]:(~humble(X)=>(patient(X)&rich(X))))&
((wise(susan))=>((curious(paul)&funny(paul))))&
(![X]:((patient(X)<~>~generous(X))<=>(~rich(X)&patient(X))))&
(![X]:((~patient(X)|rich(X))=>(calm(X)&creative(X))))&
(![X]:((~generous(X)<~>~brave(X))=>(happy(X)<~>~creative(X))))&
(![X]:((~rich(X)|~old(X))<=>(~calm(X)|curious(X))))&
((?[X]:((~patient(X)&~quiet(X))))=>(?[X]:(creative(X))))&
((?[X]:((generous(X)&creative(X))))=>(?[X]:((kind(X)&~rich(X)))))&
(![X]:((creative(X)|generous(X))<=>(creative(X)<~>~humble(X))))&
(![X]:((strong(X)<~>~calm(X))<=>(~humble(X)|funny(X))))&
(![X]:((~patient(X)&~kind(X))<=>(rich(X)&brave(X))))&
(((~rich(john)<~>wise(john)))<=>(?[X]:((strong(X)&calm(X)))))&
(![X]:((~happy(X)|brave(X))<=>(~happy(X)<~>quiet(X))))&
(?[X]:((strong(X)<~>generous(X))))&
(?[X]:(quiet(X)))&
((funny(mary)&generous(mary)))&
((curious(susan)|quiet(susan)))&
(?[X]:(~rich(X)))&
((curious(paul)|funny(paul))) | ~generous(lucy) | [] | null | 0 |
Everyone who is not calm is not creative or rich and vice versa. If mary is both humble and kind then susan is either calm or not old and vice versa. Everyone who is happy is either not happy or brave. If someone is both brave and happy then alice is either quiet or not old and vice versa. Everyone who is both not curious and creative is not humble. Everyone who is funny or not creative is both not old and kind. Everyone who is both old and happy is kind or old and vice versa. If someone is either funny or not calm then someone is patient and vice versa. If lucy is either strong or not old then someone is not happy. If someone is either not brave or happy then someone is not old and vice versa. Everyone who is either not generous or not quiet is either old or not curious and vice versa. Everyone who is either not calm or not strong is both creative and rich. If lucy is old then alice is not quiet or tall. If mary is not tall then alice is not generous or calm and vice versa. Everyone who is either happy or not brave is brave and vice versa. Paul is either not strong or kind. Someone is curious or not patient. Lucy is both not wise and humble. Someone is either not old or not patient. | Susan is tall. | neutral | (![X]:(~calm(X)<=>(~creative(X)|rich(X))))&
(((humble(mary)&kind(mary)))<=>((calm(susan)<~>~old(susan))))&
(![X]:(happy(X)=>(~happy(X)<~>brave(X))))&
((?[X]:((brave(X)&happy(X))))<=>((quiet(alice)<~>~old(alice))))&
(![X]:((~curious(X)&creative(X))=>~humble(X)))&
(![X]:((funny(X)|~creative(X))=>(~old(X)&kind(X))))&
(![X]:((old(X)&happy(X))<=>(kind(X)|old(X))))&
((?[X]:((funny(X)<~>~calm(X))))<=>(?[X]:(patient(X))))&
(((strong(lucy)<~>~old(lucy)))=>(?[X]:(~happy(X))))&
((?[X]:((~brave(X)<~>happy(X))))<=>(?[X]:(~old(X))))&
(![X]:((~generous(X)<~>~quiet(X))<=>(old(X)<~>~curious(X))))&
(![X]:((~calm(X)<~>~strong(X))=>(creative(X)&rich(X))))&
((old(lucy))=>((~quiet(alice)|tall(alice))))&
((~tall(mary))<=>((~generous(alice)|calm(alice))))&
(![X]:((happy(X)<~>~brave(X))<=>brave(X)))&
((~strong(paul)<~>kind(paul)))&
(?[X]:((curious(X)|~patient(X))))&
((~wise(lucy)&humble(lucy)))&
(?[X]:((~old(X)<~>~patient(X)))) | tall(susan) | [] | null | 0 |
Everyone who is not strong is not old or not happy and vice versa.
Everyone who is not humble is either not patient or not happy.
Everyone who is not curious is both not quiet and wise and vice versa.
Everyone who is not kind or patient is both not rich and not creative and vice versa.
Everyone who is not funny or happy is either tall or wise.
If someone is not funny then john is both not calm and funny and vice versa.
If someone is either not creative or kind then someone is not funny and vice versa.
If someone is not funny or patient then someone is both not creative and not happy and vice versa.
If susan is rich then paul is creative.
If someone is curious or not quiet then john is not creative or not wise and vice versa.
If lucy is calm then someone is humble.
Everyone who is rich or curious is wise.
If lucy is both not patient and not quiet then someone is not strong or funny and vice versa.
If someone is not wise or kind then lucy is patient.
Everyone who is happy is both not patient and not old.
Everyone who is generous or not strong is funny or not kind and vice versa.
Alice is old.
Fred is both quiet and curious.
Lucy is either not generous or rich.
Someone is brave.
Someone is both not rich and not creative.
Someone is funny.
Someone is either not tall or not curious. | Lucy is not patient. | entailment | (![X]:(~strong(X)<=>(~old(X)|~happy(X))))&
(![X]:(~humble(X)=>(~patient(X)<~>~happy(X))))&
(![X]:(~curious(X)<=>(~quiet(X)&wise(X))))&
(![X]:((~kind(X)|patient(X))<=>(~rich(X)&~creative(X))))&
(![X]:((~funny(X)|happy(X))=>(tall(X)<~>wise(X))))&
((?[X]:(~funny(X)))<=>((~calm(john)&funny(john))))&
((?[X]:((~creative(X)<~>kind(X))))<=>(?[X]:(~funny(X))))&
((?[X]:((~funny(X)|patient(X))))<=>(?[X]:((~creative(X)&~happy(X)))))&
((rich(susan))=>(creative(paul)))&
((?[X]:((curious(X)|~quiet(X))))<=>((~creative(john)|~wise(john))))&
((calm(lucy))=>(?[X]:(humble(X))))&
(![X]:((rich(X)|curious(X))=>wise(X)))&
(((~patient(lucy)&~quiet(lucy)))<=>(?[X]:((~strong(X)|funny(X)))))&
((?[X]:((~wise(X)|kind(X))))=>(patient(lucy)))&
(![X]:(happy(X)=>(~patient(X)&~old(X))))&
(![X]:((generous(X)|~strong(X))<=>(funny(X)|~kind(X))))&
(old(alice))&
((quiet(fred)&curious(fred)))&
((~generous(lucy)<~>rich(lucy)))&
(?[X]:(brave(X)))&
(?[X]:((~rich(X)&~creative(X))))&
(?[X]:(funny(X)))&
(?[X]:((~tall(X)<~>~curious(X)))) | ~patient(lucy) | [
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8515500455466827839189443
% SZS output start Proof for 8515500455466827839189443
6. ? [X0] : ~funny(X0) <=> (funny(john) & ~calm(john)) [input p5]
13. (~quiet(lucy) & ~patient(lucy)) <=> ? [X0] : (funny(X0) | ~strong(X0)) [input p12]
24. patient(lucy) [input hypothesis]
42. (? [X0] : ~funny(X0) | (~funny(john) | calm(john))) & ((funny(john) & ~calm(john)) | ! [X0] : funny(X0)) [nnf transformation 6]
43. (? [X0] : ~funny(X0) | ~funny(john) | calm(john)) & ((funny(john) & ~calm(john)) | ! [X0] : funny(X0)) [flattening 42]
44. (? [X0] : ~funny(X0) | ~funny(john) | calm(john)) & ((funny(john) & ~calm(john)) | ! [X1] : funny(X1)) [rectify 43]
45. ? [X0] : ~funny(X0) => ~funny(sK0) [choice axiom]
46. (~funny(sK0) | ~funny(john) | calm(john)) & ((funny(john) & ~calm(john)) | ! [X1] : funny(X1)) [skolemisation 44,45]
62. ((~quiet(lucy) & ~patient(lucy)) | ! [X0] : (~funny(X0) & strong(X0))) & (? [X0] : (funny(X0) | ~strong(X0)) | (quiet(lucy) | patient(lucy))) [nnf transformation 13]
63. ((~quiet(lucy) & ~patient(lucy)) | ! [X0] : (~funny(X0) & strong(X0))) & (? [X0] : (funny(X0) | ~strong(X0)) | quiet(lucy) | patient(lucy)) [flattening 62]
64. ((~quiet(lucy) & ~patient(lucy)) | ! [X0] : (~funny(X0) & strong(X0))) & (? [X1] : (funny(X1) | ~strong(X1)) | quiet(lucy) | patient(lucy)) [rectify 63]
65. ? [X1] : (funny(X1) | ~strong(X1)) => (funny(sK6) | ~strong(sK6)) [choice axiom]
66. ((~quiet(lucy) & ~patient(lucy)) | ! [X0] : (~funny(X0) & strong(X0))) & ((funny(sK6) | ~strong(sK6)) | quiet(lucy) | patient(lucy)) [skolemisation 64,65]
93. funny(john) | funny(X1) [cnf transformation 46]
113. ~patient(lucy) | ~funny(X0) [cnf transformation 66]
134. patient(lucy) [cnf transformation 24]
140. 2 <=> funny(john) [avatar definition]
141. funny(john) <- (2) [avatar component clause 140]
149. 4 <=> ! [X1] : funny(X1) [avatar definition]
150. funny(X1) <- (4) [avatar component clause 149]
151. 4 | 2 [avatar split clause 93,140,149]
230. 22 <=> ! [X0] : ~funny(X0) [avatar definition]
231. ~funny(X0) <- (22) [avatar component clause 230]
242. 25 <=> patient(lucy) [avatar definition]
245. 22 | ~25 [avatar split clause 113,242,230]
280. 25 [avatar split clause 134,242]
281. $false <- (2, 22) [subsumption resolution 141,231]
282. ~2 | ~22 [avatar contradiction clause 281]
283. $false <- (4, 22) [subsumption resolution 150,231]
284. ~4 | ~22 [avatar contradiction clause 283]
285. $false [avatar sat refutation 151,245,280,282,284]
% SZS output end Proof for 8515500455466827839189443
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm or brave then lucy is not funny.
Everyone who is either not strong or tall is either not happy or not quiet.
Everyone who is rich or generous is not patient and vice versa.
Everyone who is either not patient or not tall is not kind and vice versa.
Everyone who is rich is both not patient and not kind and vice versa.
If someone is rich or not patient then someone is either not wise or not rich and vice versa.
If someone is either happy or not patient then paul is not rich and vice versa.
Everyone who is not kind is either not old or tall and vice versa.
Everyone who is either wise or creative is not funny.
Everyone who is not generous or generous is not kind and vice versa.
If lucy is funny then someone is both not generous and not happy and vice versa.
Everyone who is either patient or not old is both not funny and generous.
Everyone who is not humble or not calm is either strong or happy.
Everyone who is not generous is not brave or quiet and vice versa.
Everyone who is either not happy or kind is either calm or humble and vice versa.
Someone is either not patient or patient.
Someone is not creative.
Someone is both calm and not humble.
Susan is either not curious or funny.
Alice is strong or not funny.
Lucy is either not creative or curious. | Susan is not happy. | neutral | ((?[X]:((~calm(X)|brave(X))))=>(~funny(lucy)))&
(![X]:((~strong(X)<~>tall(X))=>(~happy(X)<~>~quiet(X))))&
(![X]:((rich(X)|generous(X))<=>~patient(X)))&
(![X]:((~patient(X)<~>~tall(X))<=>~kind(X)))&
(![X]:(rich(X)<=>(~patient(X)&~kind(X))))&
((?[X]:((rich(X)|~patient(X))))<=>(?[X]:((~wise(X)<~>~rich(X)))))&
((?[X]:((happy(X)<~>~patient(X))))<=>(~rich(paul)))&
(![X]:(~kind(X)<=>(~old(X)<~>tall(X))))&
(![X]:((wise(X)<~>creative(X))=>~funny(X)))&
(![X]:((~generous(X)|generous(X))<=>~kind(X)))&
((funny(lucy))<=>(?[X]:((~generous(X)&~happy(X)))))&
(![X]:((patient(X)<~>~old(X))=>(~funny(X)&generous(X))))&
(![X]:((~humble(X)|~calm(X))=>(strong(X)<~>happy(X))))&
(![X]:(~generous(X)<=>(~brave(X)|quiet(X))))&
(![X]:((~happy(X)<~>kind(X))<=>(calm(X)<~>humble(X))))&
(?[X]:((~patient(X)<~>patient(X))))&
(?[X]:(~creative(X)))&
(?[X]:((calm(X)&~humble(X))))&
((~curious(susan)<~>funny(susan)))&
((strong(alice)|~funny(alice)))&
((~creative(lucy)<~>curious(lucy))) | ~happy(susan) | [] | null | 0 |
If john is either wise or not old then susan is curious and vice versa. Everyone who is both curious and not wise is both not rich and funny. If paul is either curious or not funny then someone is not happy and vice versa. Everyone who is both not kind and not rich is creative and vice versa. If fred is both strong and wise then john is either generous or patient and vice versa. Everyone who is both old and tall is both curious and kind and vice versa. Everyone who is rich or kind is both not rich and strong and vice versa. Everyone who is either not humble or tall is both funny and calm and vice versa. If alice is both funny and kind then mary is patient and vice versa. If alice is both not rich and brave then someone is either not brave or funny and vice versa. If someone is either not quiet or not humble then alice is both not brave and curious. If john is strong or calm then someone is both not generous and not curious and vice versa. Everyone who is happy or not creative is brave. If someone is either humble or brave then alice is not creative or generous. Everyone who is either tall or humble is not funny or not tall and vice versa. If someone is either patient or not wise then someone is both wise and not wise. Someone is either kind or not funny. Someone is not funny or not generous. Susan is kind. Someone is curious. Someone is both not strong and curious. Alice is strong. Someone is not tall or not quiet. | John is kind. | neutral | (((wise(john)<~>~old(john)))<=>(curious(susan)))&
(![X]:((curious(X)&~wise(X))=>(~rich(X)&funny(X))))&
(((curious(paul)<~>~funny(paul)))<=>(?[X]:(~happy(X))))&
(![X]:((~kind(X)&~rich(X))<=>creative(X)))&
(((strong(fred)&wise(fred)))<=>((generous(john)<~>patient(john))))&
(![X]:((old(X)&tall(X))<=>(curious(X)&kind(X))))&
(![X]:((rich(X)|kind(X))<=>(~rich(X)&strong(X))))&
(![X]:((~humble(X)<~>tall(X))<=>(funny(X)&calm(X))))&
(((funny(alice)&kind(alice)))<=>(patient(mary)))&
(((~rich(alice)&brave(alice)))<=>(?[X]:((~brave(X)<~>funny(X)))))&
((?[X]:((~quiet(X)<~>~humble(X))))=>((~brave(alice)&curious(alice))))&
(((strong(john)|calm(john)))<=>(?[X]:((~generous(X)&~curious(X)))))&
(![X]:((happy(X)|~creative(X))=>brave(X)))&
((?[X]:((humble(X)<~>brave(X))))=>((~creative(alice)|generous(alice))))&
(![X]:((tall(X)<~>humble(X))<=>(~funny(X)|~tall(X))))&
((?[X]:((patient(X)<~>~wise(X))))=>(?[X]:((wise(X)&~wise(X)))))&
(?[X]:((kind(X)<~>~funny(X))))&
(?[X]:((~funny(X)|~generous(X))))&
(kind(susan))&
(?[X]:(curious(X)))&
(?[X]:((~strong(X)&curious(X))))&
(strong(alice))&
(?[X]:((~tall(X)|~quiet(X)))) | kind(john) | [] | null | 0 |
If someone is strong then someone is not rich. If someone is both wise and not curious then someone is generous or not patient and vice versa. Everyone who is both not wise and curious is not curious or not rich and vice versa. If someone is not creative or wise then fred is creative and vice versa. If paul is either humble or wise then john is patient or not rich and vice versa. If someone is either rich or quiet then someone is both not creative and quiet. Everyone who is both not patient and brave is either not humble or not generous and vice versa. Everyone who is not patient is rich or not kind. If someone is not kind or old then paul is either creative or generous and vice versa. Everyone who is tall is quiet or patient and vice versa. Everyone who is either old or rich is either quiet or not quiet. Everyone who is not kind or humble is either calm or funny and vice versa. If someone is not generous or tall then john is either kind or not creative and vice versa. If susan is both tall and rich then someone is old or not funny. If susan is not patient then someone is both tall and not strong. If fred is either not rich or funny then someone is quiet or not funny. Someone is patient or curious. Fred is either not old or brave. John is both not creative and not rich. Mary is both not old and strong. Someone is both tall and not quiet. Paul is either humble or not old. Fred is calm. | Paul is not rich. | contradiction | ((?[X]:(strong(X)))=>(?[X]:(~rich(X))))&
((?[X]:((wise(X)&~curious(X))))<=>(?[X]:((generous(X)|~patient(X)))))&
(![X]:((~wise(X)&curious(X))<=>(~curious(X)|~rich(X))))&
((?[X]:((~creative(X)|wise(X))))<=>(creative(fred)))&
(((humble(paul)<~>wise(paul)))<=>((patient(john)|~rich(john))))&
((?[X]:((rich(X)<~>quiet(X))))=>(?[X]:((~creative(X)&quiet(X)))))&
(![X]:((~patient(X)&brave(X))<=>(~humble(X)<~>~generous(X))))&
(![X]:(~patient(X)=>(rich(X)|~kind(X))))&
((?[X]:((~kind(X)|old(X))))<=>((creative(paul)<~>generous(paul))))&
(![X]:(tall(X)<=>(quiet(X)|patient(X))))&
(![X]:((old(X)<~>rich(X))=>(quiet(X)<~>~quiet(X))))&
(![X]:((~kind(X)|humble(X))<=>(calm(X)<~>funny(X))))&
((?[X]:((~generous(X)|tall(X))))<=>((kind(john)<~>~creative(john))))&
(((tall(susan)&rich(susan)))=>(?[X]:((old(X)|~funny(X)))))&
((~patient(susan))=>(?[X]:((tall(X)&~strong(X)))))&
(((~rich(fred)<~>funny(fred)))=>(?[X]:((quiet(X)|~funny(X)))))&
(?[X]:((patient(X)|curious(X))))&
((~old(fred)<~>brave(fred)))&
((~creative(john)&~rich(john)))&
((~old(mary)&strong(mary)))&
(?[X]:((tall(X)&~quiet(X))))&
((humble(paul)<~>~old(paul)))&
(calm(fred)) | ~rich(paul) | [
"p1",
"p2",
"p4",
"p6",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3234926946773600833367473
% SZS output start Proof for 3234926946773600833367473
2. ? [X0] : (~curious(X0) & wise(X0)) <=> ? [X0] : (~patient(X0) | generous(X0)) [input p1]
3. ! [X0] : ((curious(X0) & ~wise(X0)) <=> (~rich(X0) | ~curious(X0))) [input p2]
5. (humble(paul) <~> wise(paul)) <=> (~rich(john) | patient(john)) [input p4]
7. ! [X0] : ((brave(X0) & ~patient(X0)) <=> (~humble(X0) <~> ~generous(X0))) [input p6]
19. ~rich(john) & ~creative(john) [input p18]
24. ~rich(paul) [input hypothesis]
26. ? [X0] : (~curious(X0) & wise(X0)) <=> ? [X1] : (~patient(X1) | generous(X1)) [rectify 2]
40. (? [X0] : (~curious(X0) & wise(X0)) | ! [X1] : (patient(X1) & ~generous(X1))) & (? [X1] : (~patient(X1) | generous(X1)) | ! [X0] : (curious(X0) | ~wise(X0))) [nnf transformation 26]
41. (? [X0] : (~curious(X0) & wise(X0)) | ! [X1] : (patient(X1) & ~generous(X1))) & (? [X2] : (~patient(X2) | generous(X2)) | ! [X3] : (curious(X3) | ~wise(X3))) [rectify 40]
42. ? [X0] : (~curious(X0) & wise(X0)) => (~curious(sK1) & wise(sK1)) [choice axiom]
43. ? [X2] : (~patient(X2) | generous(X2)) => (~patient(sK2) | generous(sK2)) [choice axiom]
44. ((~curious(sK1) & wise(sK1)) | ! [X1] : (patient(X1) & ~generous(X1))) & ((~patient(sK2) | generous(sK2)) | ! [X3] : (curious(X3) | ~wise(X3))) [skolemisation 41,43,42]
45. ! [X0] : (((curious(X0) & ~wise(X0)) | (rich(X0) & curious(X0))) & ((~rich(X0) | ~curious(X0)) | (~curious(X0) | wise(X0)))) [nnf transformation 3]
46. ! [X0] : (((curious(X0) & ~wise(X0)) | (rich(X0) & curious(X0))) & (~rich(X0) | ~curious(X0) | ~curious(X0) | wise(X0))) [flattening 45]
51. (((~wise(paul) | ~humble(paul)) & (wise(paul) | humble(paul))) | (rich(john) & ~patient(john))) & ((~rich(john) | patient(john)) | ((humble(paul) | ~wise(paul)) & (wise(paul) | ~humble(paul)))) [nnf transformation 5]
52. (((~wise(paul) | ~humble(paul)) & (wise(paul) | humble(paul))) | (rich(john) & ~patient(john))) & (~rich(john) | patient(john) | ((humble(paul) | ~wise(paul)) & (wise(paul) | ~humble(paul)))) [flattening 51]
57. ! [X0] : (((brave(X0) & ~patient(X0)) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0)))) & (((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | (~brave(X0) | patient(X0)))) [nnf transformation 7]
58. ! [X0] : (((brave(X0) & ~patient(X0)) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0)))) & (((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | ~brave(X0) | patient(X0))) [flattening 57]
89. ~curious(sK1) | ~generous(X1) [cnf transformation 44]
90. ~curious(sK1) | patient(X1) [cnf transformation 44]
93. ~wise(X0) | rich(X0) [cnf transformation 46]
94. curious(X0) | curious(X0) [cnf transformation 46]
102. wise(paul) | humble(paul) | rich(john) [cnf transformation 52]
112. ~humble(X0) | ~patient(X0) | generous(X0) [cnf transformation 58]
150. ~rich(john) [cnf transformation 19]
158. ~rich(paul) [cnf transformation 24]
160. curious(X0) [duplicate literal removal 94]
170. 3 <=> ! [X1] : patient(X1) [avatar definition]
171. patient(X1) <- (3) [avatar component clause 170]
173. 4 <=> curious(sK1) [avatar definition]
175. ~curious(sK1) <- (~4) [avatar component clause 173]
176. 3 | ~4 [avatar split clause 90,173,170]
178. 5 <=> ! [X1] : ~generous(X1) [avatar definition]
179. ~generous(X1) <- (5) [avatar component clause 178]
180. 5 | ~4 [avatar split clause 89,173,178]
222. 15 <=> rich(john) [avatar definition]
226. 16 <=> humble(paul) [avatar definition]
227. humble(paul) <- (16) [avatar component clause 226]
230. 17 <=> wise(paul) [avatar definition]
231. wise(paul) <- (17) [avatar component clause 230]
239. 15 | 16 | 17 [avatar split clause 102,230,226,222]
376. ~15 [avatar split clause 150,222]
386. $false <- (~4) [subsumption resolution 175,160]
387. 4 [avatar contradiction clause 386]
391. rich(paul) <- (17) [resolution 93,231]
392. $false <- (17) [subsumption resolution 391,158]
393. ~17 [avatar contradiction clause 392]
402. ~patient(paul) | generous(paul) <- (16) [resolution 112,227]
403. generous(paul) <- (3, 16) [subsumption resolution 402,171]
404. $false <- (3, 5, 16) [subsumption resolution 403,179]
405. ~3 | ~5 | ~16 [avatar contradiction clause 404]
406. $false [avatar sat refutation 176,180,239,376,387,393,405]
% SZS output end Proof for 3234926946773600833367473
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is curious or not curious then paul is both not quiet and generous. If mary is creative or not patient then mary is either happy or not patient and vice versa. Everyone who is tall or happy is either quiet or generous. Everyone who is rich is not kind. If someone is brave then susan is not funny or not generous and vice versa. Everyone who is rich or not old is not tall and vice versa. If someone is either brave or generous then someone is both not kind and not rich. Everyone who is not strong is either not patient or wise. Everyone who is both calm and wise is either not funny or not old and vice versa. Everyone who is not strong is either funny or happy. Everyone who is both rich and not funny is both not curious and generous and vice versa. If someone is not curious then lucy is either creative or kind and vice versa. Everyone who is wise or funny is not strong and vice versa. If fred is either not quiet or not happy then someone is either kind or happy. If susan is either curious or tall then someone is both funny and not creative and vice versa. Everyone who is both humble and not generous is both not tall and kind and vice versa. Paul is wise. Susan is brave. Someone is tall or not humble. Fred is not calm. Lucy is either not tall or creative. Mary is not tall or humble. Someone is either not curious or not brave. Someone is funny or not creative. | Fred is not quiet. | neutral | (((curious(john)|~curious(john)))=>((~quiet(paul)&generous(paul))))&
(((creative(mary)|~patient(mary)))<=>((happy(mary)<~>~patient(mary))))&
(![X]:((tall(X)|happy(X))=>(quiet(X)<~>generous(X))))&
(![X]:(rich(X)=>~kind(X)))&
((?[X]:(brave(X)))<=>((~funny(susan)|~generous(susan))))&
(![X]:((rich(X)|~old(X))<=>~tall(X)))&
((?[X]:((brave(X)<~>generous(X))))=>(?[X]:((~kind(X)&~rich(X)))))&
(![X]:(~strong(X)=>(~patient(X)<~>wise(X))))&
(![X]:((calm(X)&wise(X))<=>(~funny(X)<~>~old(X))))&
(![X]:(~strong(X)=>(funny(X)<~>happy(X))))&
(![X]:((rich(X)&~funny(X))<=>(~curious(X)&generous(X))))&
((?[X]:(~curious(X)))<=>((creative(lucy)<~>kind(lucy))))&
(![X]:((wise(X)|funny(X))<=>~strong(X)))&
(((~quiet(fred)<~>~happy(fred)))=>(?[X]:((kind(X)<~>happy(X)))))&
(((curious(susan)<~>tall(susan)))<=>(?[X]:((funny(X)&~creative(X)))))&
(![X]:((humble(X)&~generous(X))<=>(~tall(X)&kind(X))))&
(wise(paul))&
(brave(susan))&
(?[X]:((tall(X)|~humble(X))))&
(~calm(fred))&
((~tall(lucy)<~>creative(lucy)))&
((~tall(mary)|humble(mary)))&
(?[X]:((~curious(X)<~>~brave(X))))&
(?[X]:((funny(X)|~creative(X)))) | ~quiet(fred) | [] | null | 0 |
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