premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is not curious or not rich is humble or not calm and vice versa.
Everyone who is both happy and not rich is funny or not creative and vice versa.
Everyone who is either not tall or not curious is both humble and not funny and vice versa.
Everyone who is either not funny or tall is not wise.
If someone is both rich and old then someone is brave or humble.
If lucy is tall or brave then someone is both patient and not patient.
If mary is old then john is either not old or funny and vice versa.
Everyone who is both funny and old is both not curious and not calm and vice versa.
If someone is rich or funny then john is creative or not calm.
Everyone who is humble is both not funny and not old.
Everyone who is not old is not happy and vice versa.
Everyone who is quiet is both not humble and wise and vice versa.
Everyone who is either old or not wise is both not curious and not generous and vice versa.
Everyone who is either not kind or tall is not wise and vice versa.
If paul is both not wise and not happy then someone is kind or tall and vice versa.
If susan is either not rich or kind then mary is tall and vice versa.
Someone is wise or funny.
Someone is happy or old.
Someone is old or quiet.
Fred is either not patient or not kind.
Someone is not curious or not calm. | John is not quiet. | neutral | (![X]:((~curious(X)|~rich(X))<=>(humble(X)|~calm(X))))&
(![X]:((happy(X)&~rich(X))<=>(funny(X)|~creative(X))))&
(![X]:((~tall(X)<~>~curious(X))<=>(humble(X)&~funny(X))))&
(![X]:((~funny(X)<~>tall(X))=>~wise(X)))&
((?[X]:((rich(X)&old(X))))=>(?[X]:((brave(X)|humble(X)))))&
(((tall(lucy)|brave(lucy)))=>(?[X]:((patient(X)&~patient(X)))))&
((old(mary))<=>((~old(john)<~>funny(john))))&
(![X]:((funny(X)&old(X))<=>(~curious(X)&~calm(X))))&
((?[X]:((rich(X)|funny(X))))=>((creative(john)|~calm(john))))&
(![X]:(humble(X)=>(~funny(X)&~old(X))))&
(![X]:(~old(X)<=>~happy(X)))&
(![X]:(quiet(X)<=>(~humble(X)&wise(X))))&
(![X]:((old(X)<~>~wise(X))<=>(~curious(X)&~generous(X))))&
(![X]:((~kind(X)<~>tall(X))<=>~wise(X)))&
(((~wise(paul)&~happy(paul)))<=>(?[X]:((kind(X)|tall(X)))))&
(((~rich(susan)<~>kind(susan)))<=>(tall(mary)))&
(?[X]:((wise(X)|funny(X))))&
(?[X]:((happy(X)|old(X))))&
(?[X]:((old(X)|quiet(X))))&
((~patient(fred)<~>~kind(fred)))&
(?[X]:((~curious(X)|~calm(X)))) | ~quiet(john) | [] | null | 0 |
Everyone who is not humble is not quiet or happy and vice versa.
Everyone who is not tall or not happy is both rich and quiet.
Everyone who is either not curious or kind is humble or patient and vice versa.
Everyone who is not brave is generous or humble and vice versa.
If someone is not happy then someone is not tall and vice versa.
Everyone who is not calm or not generous is either not rich or humble and vice versa.
If lucy is either not strong or humble then lucy is either happy or creative.
If fred is not tall then someone is patient or not calm.
If someone is not generous then someone is both patient and rich and vice versa.
Everyone who is either rich or humble is not happy and vice versa.
If mary is patient then someone is either not patient or funny and vice versa.
If someone is funny or creative then john is either not curious or brave and vice versa.
Everyone who is kind or not humble is not brave or not patient.
Everyone who is not brave is not quiet.
Everyone who is both not calm and not patient is either not wise or not generous.
Everyone who is both not patient and not old is either generous or rich and vice versa.
Someone is either brave or not calm.
Susan is either strong or tall.
John is either not quiet or not happy.
Someone is not strong.
Alice is not wise or old. | Fred is tall. | entailment | (![X]:(~humble(X)<=>(~quiet(X)|happy(X))))&
(![X]:((~tall(X)|~happy(X))=>(rich(X)&quiet(X))))&
(![X]:((~curious(X)<~>kind(X))<=>(humble(X)|patient(X))))&
(![X]:(~brave(X)<=>(generous(X)|humble(X))))&
((?[X]:(~happy(X)))<=>(?[X]:(~tall(X))))&
(![X]:((~calm(X)|~generous(X))<=>(~rich(X)<~>humble(X))))&
(((~strong(lucy)<~>humble(lucy)))=>((happy(lucy)<~>creative(lucy))))&
((~tall(fred))=>(?[X]:((patient(X)|~calm(X)))))&
((?[X]:(~generous(X)))<=>(?[X]:((patient(X)&rich(X)))))&
(![X]:((rich(X)<~>humble(X))<=>~happy(X)))&
((patient(mary))<=>(?[X]:((~patient(X)<~>funny(X)))))&
((?[X]:((funny(X)|creative(X))))<=>((~curious(john)<~>brave(john))))&
(![X]:((kind(X)|~humble(X))=>(~brave(X)|~patient(X))))&
(![X]:(~brave(X)=>~quiet(X)))&
(![X]:((~calm(X)&~patient(X))=>(~wise(X)<~>~generous(X))))&
(![X]:((~patient(X)&~old(X))<=>(generous(X)<~>rich(X))))&
(?[X]:((brave(X)<~>~calm(X))))&
((strong(susan)<~>tall(susan)))&
((~quiet(john)<~>~happy(john)))&
(?[X]:(~strong(X)))&
((~wise(alice)|old(alice))) | tall(fred) | [
"p0",
"p1",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1717014505374905702174869
% SZS output start Proof for 1717014505374905702174869
1. ! [X0] : (~humble(X0) <=> (happy(X0) | ~quiet(X0))) [input p0]
2. ! [X0] : ((~happy(X0) | ~tall(X0)) => (quiet(X0) & rich(X0))) [input p1]
5. ? [X0] : ~happy(X0) <=> ? [X0] : ~tall(X0) [input p4]
10. ! [X0] : ((rich(X0) <~> humble(X0)) <=> ~happy(X0)) [input p9]
22. ~tall(fred) [input hypothesis]
23. ? [X0] : ~happy(X0) <=> ? [X1] : ~tall(X1) [rectify 5]
25. ! [X0] : ((quiet(X0) & rich(X0)) | (happy(X0) & tall(X0))) [ennf transformation 2]
33. ! [X0] : ((~humble(X0) | (~happy(X0) & quiet(X0))) & ((happy(X0) | ~quiet(X0)) | humble(X0))) [nnf transformation 1]
34. ! [X0] : ((~humble(X0) | (~happy(X0) & quiet(X0))) & (happy(X0) | ~quiet(X0) | humble(X0))) [flattening 33]
39. (? [X0] : ~happy(X0) | ! [X1] : tall(X1)) & (? [X1] : ~tall(X1) | ! [X0] : happy(X0)) [nnf transformation 23]
40. (? [X0] : ~happy(X0) | ! [X1] : tall(X1)) & (? [X2] : ~tall(X2) | ! [X3] : happy(X3)) [rectify 39]
41. ? [X0] : ~happy(X0) => ~happy(sK0) [choice axiom]
42. ? [X2] : ~tall(X2) => ~tall(sK1) [choice axiom]
43. (~happy(sK0) | ! [X1] : tall(X1)) & (~tall(sK1) | ! [X3] : happy(X3)) [skolemisation 40,42,41]
54. ! [X0] : ((((~humble(X0) | ~rich(X0)) & (humble(X0) | rich(X0))) | happy(X0)) & (~happy(X0) | ((rich(X0) | ~humble(X0)) & (humble(X0) | ~rich(X0))))) [nnf transformation 10]
73. ~quiet(X0) | happy(X0) | humble(X0) [cnf transformation 34]
75. ~happy(X0) | ~humble(X0) [cnf transformation 34]
77. rich(X0) | happy(X0) [cnf transformation 25]
79. happy(X0) | quiet(X0) [cnf transformation 25]
90. ~happy(sK0) | tall(X1) [cnf transformation 43]
108. ~humble(X0) | ~rich(X0) | happy(X0) [cnf transformation 54]
138. ~tall(fred) [cnf transformation 22]
140. 1 <=> ! [X1] : tall(X1) [avatar definition]
141. tall(X1) <- (1) [avatar component clause 140]
143. 2 <=> happy(sK0) [avatar definition]
145. ~happy(sK0) <- (~2) [avatar component clause 143]
146. 1 | ~2 [avatar split clause 90,143,140]
177. 9 <=> tall(fred) [avatar definition]
178. ~tall(fred) <- (~9) [avatar component clause 177]
210. ~humble(X0) | happy(X0) [subsumption resolution 108,77]
211. ~humble(X0) [subsumption resolution 210,75]
302. ~9 [avatar split clause 138,177]
309. quiet(sK0) <- (~2) [resolution 79,145]
337. happy(sK0) | humble(sK0) <- (~2) [resolution 73,309]
341. humble(sK0) <- (~2) [subsumption resolution 337,145]
342. $false <- (~2) [subsumption resolution 341,211]
343. 2 [avatar contradiction clause 342]
346. $false <- (1, ~9) [resolution 141,178]
349. ~1 | 9 [avatar contradiction clause 346]
351. $false [avatar sat refutation 146,302,343,349]
% SZS output end Proof for 1717014505374905702174869
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or strong is not humble and vice versa. If alice is either not humble or generous then someone is not creative and vice versa. If someone is rich or strong then someone is not kind or wise and vice versa. If someone is both quiet and funny then someone is not generous. Everyone who is either not curious or not tall is generous and vice versa. If someone is not wise or not strong then fred is either generous or not quiet and vice versa. If paul is both brave and not old then alice is generous or not strong. If someone is either funny or not funny then alice is not tall or not calm. Everyone who is either not kind or not old is either happy or brave. If someone is wise then paul is both brave and funny. If someone is old then paul is both curious and not wise. Everyone who is either not calm or not curious is either not calm or not generous and vice versa. If someone is either wise or quiet then someone is both not creative and not rich. If someone is both not strong and not rich then susan is both curious and not funny and vice versa. If mary is either funny or rich then john is either calm or not wise. Everyone who is quiet is either not brave or curious and vice versa. Fred is either calm or not old. Someone is either not funny or humble. Someone is either not funny or quiet. Someone is either not funny or kind. John is either wise or not happy. Someone is either old or not tall. | Paul is rich. | neutral | (![X]:((~funny(X)<~>strong(X))<=>~humble(X)))&
(((~humble(alice)<~>generous(alice)))<=>(?[X]:(~creative(X))))&
((?[X]:((rich(X)|strong(X))))<=>(?[X]:((~kind(X)|wise(X)))))&
((?[X]:((quiet(X)&funny(X))))=>(?[X]:(~generous(X))))&
(![X]:((~curious(X)<~>~tall(X))<=>generous(X)))&
((?[X]:((~wise(X)|~strong(X))))<=>((generous(fred)<~>~quiet(fred))))&
(((brave(paul)&~old(paul)))=>((generous(alice)|~strong(alice))))&
((?[X]:((funny(X)<~>~funny(X))))=>((~tall(alice)|~calm(alice))))&
(![X]:((~kind(X)<~>~old(X))=>(happy(X)<~>brave(X))))&
((?[X]:(wise(X)))=>((brave(paul)&funny(paul))))&
((?[X]:(old(X)))=>((curious(paul)&~wise(paul))))&
(![X]:((~calm(X)<~>~curious(X))<=>(~calm(X)<~>~generous(X))))&
((?[X]:((wise(X)<~>quiet(X))))=>(?[X]:((~creative(X)&~rich(X)))))&
((?[X]:((~strong(X)&~rich(X))))<=>((curious(susan)&~funny(susan))))&
(((funny(mary)<~>rich(mary)))=>((calm(john)<~>~wise(john))))&
(![X]:(quiet(X)<=>(~brave(X)<~>curious(X))))&
((calm(fred)<~>~old(fred)))&
(?[X]:((~funny(X)<~>humble(X))))&
(?[X]:((~funny(X)<~>quiet(X))))&
(?[X]:((~funny(X)<~>kind(X))))&
((wise(john)<~>~happy(john)))&
(?[X]:((old(X)<~>~tall(X)))) | rich(paul) | [] | null | 0 |
If someone is both not rich and creative then paul is both quiet and patient and vice versa.
Everyone who is humble is both not rich and not happy.
Everyone who is either not generous or old is both not brave and not strong.
If susan is not old or not happy then someone is either old or not old.
Everyone who is both not old and not generous is not curious and vice versa.
If someone is both strong and not calm then someone is not quiet or not humble and vice versa.
Everyone who is either not quiet or not curious is either not funny or old and vice versa.
Everyone who is not curious or funny is either curious or strong.
If alice is wise or strong then someone is not creative or curious and vice versa.
If lucy is both not wise and not quiet then someone is both strong and not quiet and vice versa.
Everyone who is either strong or rich is either not strong or tall.
If someone is calm then lucy is curious and vice versa.
If mary is either old or not generous then someone is either not kind or generous and vice versa.
Everyone who is not strong or tall is tall and vice versa.
If paul is either patient or rich then someone is either not funny or not happy and vice versa.
If fred is either not wise or humble then someone is not generous or quiet.
Someone is either not wise or not funny.
Alice is both generous and wise.
Paul is both not old and not quiet.
Someone is old or generous.
Alice is not quiet or wise.
Someone is either not tall or old.
Alice is not creative. | Fred is not happy. | neutral | ((?[X]:((~rich(X)&creative(X))))<=>((quiet(paul)&patient(paul))))&
(![X]:(humble(X)=>(~rich(X)&~happy(X))))&
(![X]:((~generous(X)<~>old(X))=>(~brave(X)&~strong(X))))&
(((~old(susan)|~happy(susan)))=>(?[X]:((old(X)<~>~old(X)))))&
(![X]:((~old(X)&~generous(X))<=>~curious(X)))&
((?[X]:((strong(X)&~calm(X))))<=>(?[X]:((~quiet(X)|~humble(X)))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~funny(X)<~>old(X))))&
(![X]:((~curious(X)|funny(X))=>(curious(X)<~>strong(X))))&
(((wise(alice)|strong(alice)))<=>(?[X]:((~creative(X)|curious(X)))))&
(((~wise(lucy)&~quiet(lucy)))<=>(?[X]:((strong(X)&~quiet(X)))))&
(![X]:((strong(X)<~>rich(X))=>(~strong(X)<~>tall(X))))&
((?[X]:(calm(X)))<=>(curious(lucy)))&
(((old(mary)<~>~generous(mary)))<=>(?[X]:((~kind(X)<~>generous(X)))))&
(![X]:((~strong(X)|tall(X))<=>tall(X)))&
(((patient(paul)<~>rich(paul)))<=>(?[X]:((~funny(X)<~>~happy(X)))))&
(((~wise(fred)<~>humble(fred)))=>(?[X]:((~generous(X)|quiet(X)))))&
(?[X]:((~wise(X)<~>~funny(X))))&
((generous(alice)&wise(alice)))&
((~old(paul)&~quiet(paul)))&
(?[X]:((old(X)|generous(X))))&
((~quiet(alice)|wise(alice)))&
(?[X]:((~tall(X)<~>old(X))))&
(~creative(alice)) | ~happy(fred) | [] | null | 0 |
If alice is either generous or quiet then john is not generous or not wise and vice versa.
Everyone who is either calm or strong is either not patient or curious.
Everyone who is both happy and not funny is both calm and not strong.
Everyone who is either not happy or curious is both funny and humble and vice versa.
Everyone who is both not quiet and generous is not happy or old and vice versa.
If someone is not tall then alice is both curious and not patient.
If someone is either not kind or wise then john is quiet or rich.
If alice is both patient and not humble then someone is both not creative and not calm.
If someone is either not curious or not calm then susan is either not creative or wise.
If someone is curious then someone is wise or not tall and vice versa.
Everyone who is both not brave and not kind is not patient or old.
If mary is happy or not happy then someone is not patient and vice versa.
Everyone who is either patient or curious is strong.
Everyone who is calm or old is either kind or not strong.
If susan is either happy or not strong then someone is patient.
Everyone who is quiet or old is not happy or old and vice versa.
Susan is wise.
Alice is not rich or humble.
Someone is both humble and not patient.
Mary is both not rich and not curious.
Someone is either strong or funny.
Lucy is either generous or wise. | John is not old. | neutral | (((generous(alice)<~>quiet(alice)))<=>((~generous(john)|~wise(john))))&
(![X]:((calm(X)<~>strong(X))=>(~patient(X)<~>curious(X))))&
(![X]:((happy(X)&~funny(X))=>(calm(X)&~strong(X))))&
(![X]:((~happy(X)<~>curious(X))<=>(funny(X)&humble(X))))&
(![X]:((~quiet(X)&generous(X))<=>(~happy(X)|old(X))))&
((?[X]:(~tall(X)))=>((curious(alice)&~patient(alice))))&
((?[X]:((~kind(X)<~>wise(X))))=>((quiet(john)|rich(john))))&
(((patient(alice)&~humble(alice)))=>(?[X]:((~creative(X)&~calm(X)))))&
((?[X]:((~curious(X)<~>~calm(X))))=>((~creative(susan)<~>wise(susan))))&
((?[X]:(curious(X)))<=>(?[X]:((wise(X)|~tall(X)))))&
(![X]:((~brave(X)&~kind(X))=>(~patient(X)|old(X))))&
(((happy(mary)|~happy(mary)))<=>(?[X]:(~patient(X))))&
(![X]:((patient(X)<~>curious(X))=>strong(X)))&
(![X]:((calm(X)|old(X))=>(kind(X)<~>~strong(X))))&
(((happy(susan)<~>~strong(susan)))=>(?[X]:(patient(X))))&
(![X]:((quiet(X)|old(X))<=>(~happy(X)|old(X))))&
(wise(susan))&
((~rich(alice)|humble(alice)))&
(?[X]:((humble(X)&~patient(X))))&
((~rich(mary)&~curious(mary)))&
(?[X]:((strong(X)<~>funny(X))))&
((generous(lucy)<~>wise(lucy))) | ~old(john) | [] | null | 0 |
Everyone who is quiet is not old and vice versa.
If john is both calm and not calm then lucy is not wise.
If someone is both not patient and kind then mary is either not calm or not wise.
Everyone who is not funny or not generous is both happy and brave.
Everyone who is kind or not wise is either not tall or not generous.
Everyone who is not humble is either strong or creative.
Everyone who is kind or not wise is quiet or wise and vice versa.
Everyone who is either curious or strong is happy.
Everyone who is not curious is both not generous and not strong and vice versa.
If fred is quiet then fred is both happy and not creative and vice versa.
Everyone who is both rich and not old is both rich and strong.
Everyone who is old is quiet or happy and vice versa.
Everyone who is either not creative or curious is brave.
Everyone who is not wise or kind is both curious and generous and vice versa.
If someone is both rich and kind then someone is both tall and funny and vice versa.
Everyone who is tall is either not old or rich.
Alice is not funny or not old.
Someone is either generous or tall. | Mary is not curious. | contradiction | (![X]:(quiet(X)<=>~old(X)))&
(((calm(john)&~calm(john)))=>(~wise(lucy)))&
((?[X]:((~patient(X)&kind(X))))=>((~calm(mary)<~>~wise(mary))))&
(![X]:((~funny(X)|~generous(X))=>(happy(X)&brave(X))))&
(![X]:((kind(X)|~wise(X))=>(~tall(X)<~>~generous(X))))&
(![X]:(~humble(X)=>(strong(X)<~>creative(X))))&
(![X]:((kind(X)|~wise(X))<=>(quiet(X)|wise(X))))&
(![X]:((curious(X)<~>strong(X))=>happy(X)))&
(![X]:(~curious(X)<=>(~generous(X)&~strong(X))))&
((quiet(fred))<=>((happy(fred)&~creative(fred))))&
(![X]:((rich(X)&~old(X))=>(rich(X)&strong(X))))&
(![X]:(old(X)<=>(quiet(X)|happy(X))))&
(![X]:((~creative(X)<~>curious(X))=>brave(X)))&
(![X]:((~wise(X)|kind(X))<=>(curious(X)&generous(X))))&
((?[X]:((rich(X)&kind(X))))<=>(?[X]:((tall(X)&funny(X)))))&
(![X]:(tall(X)=>(~old(X)<~>rich(X))))&
((~funny(alice)|~old(alice)))&
(?[X]:((generous(X)<~>tall(X)))) | ~curious(mary) | [
"p0",
"p6",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1776332950689097485735114
% SZS output start Proof for 1776332950689097485735114
1. ! [X0] : (quiet(X0) <=> ~old(X0)) [input p0]
7. ! [X0] : ((~wise(X0) | kind(X0)) <=> (wise(X0) | quiet(X0))) [input p6]
12. ! [X0] : (old(X0) <=> (happy(X0) | quiet(X0))) [input p11]
14. ! [X0] : ((kind(X0) | ~wise(X0)) <=> (generous(X0) & curious(X0))) [input p13]
19. ~curious(mary) [input hypothesis]
33. ! [X0] : ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0))) [nnf transformation 1]
35. ! [X0] : (((~wise(X0) | kind(X0)) | (~wise(X0) & ~quiet(X0))) & ((wise(X0) | quiet(X0)) | (wise(X0) & ~kind(X0)))) [nnf transformation 7]
36. ! [X0] : ((~wise(X0) | kind(X0) | (~wise(X0) & ~quiet(X0))) & (wise(X0) | quiet(X0) | (wise(X0) & ~kind(X0)))) [flattening 35]
42. ! [X0] : ((old(X0) | (~happy(X0) & ~quiet(X0))) & ((happy(X0) | quiet(X0)) | ~old(X0))) [nnf transformation 12]
43. ! [X0] : ((old(X0) | (~happy(X0) & ~quiet(X0))) & (happy(X0) | quiet(X0) | ~old(X0))) [flattening 42]
44. ! [X0] : (((kind(X0) | ~wise(X0)) | (~generous(X0) | ~curious(X0))) & ((generous(X0) & curious(X0)) | (~kind(X0) & wise(X0)))) [nnf transformation 14]
45. ! [X0] : ((kind(X0) | ~wise(X0) | ~generous(X0) | ~curious(X0)) & ((generous(X0) & curious(X0)) | (~kind(X0) & wise(X0)))) [flattening 44]
55. ~old(X0) | ~quiet(X0) [cnf transformation 33]
65. wise(X0) | quiet(X0) | wise(X0) [cnf transformation 36]
67. ~wise(X0) | kind(X0) | ~wise(X0) [cnf transformation 36]
79. old(X0) | ~quiet(X0) [cnf transformation 43]
82. ~kind(X0) | curious(X0) [cnf transformation 45]
95. ~curious(mary) [cnf transformation 19]
96. wise(X0) | quiet(X0) [duplicate literal removal 65]
97. ~wise(X0) | kind(X0) [duplicate literal removal 67]
113. ~quiet(X0) [subsumption resolution 79,55]
174. kind(X0) | quiet(X0) [resolution 97,96]
175. kind(X0) [subsumption resolution 174,113]
177. curious(X1) [resolution 175,82]
189. $false [resolution 177,95]
% SZS output end Proof for 1776332950689097485735114
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not rich or curious then alice is not calm or creative and vice versa.
If susan is both tall and not brave then paul is calm and vice versa.
Everyone who is both not humble and humble is either rich or not brave and vice versa.
Everyone who is both creative and wise is brave.
If someone is not creative or wise then lucy is wise and vice versa.
Everyone who is not funny or not curious is either not funny or not rich.
If someone is both not quiet and not happy then someone is not old or funny.
If fred is not brave or not funny then someone is either rich or not patient.
Everyone who is both kind and strong is both not humble and curious and vice versa.
If paul is not tall then someone is not wise or not creative and vice versa.
If fred is wise then someone is calm and vice versa.
If someone is either not kind or not curious then alice is kind or generous.
If someone is either not brave or not tall then someone is either tall or kind and vice versa.
Everyone who is both strong and not funny is both not rich and brave.
If susan is either kind or not rich then lucy is both not creative and patient and vice versa.
Everyone who is curious is both curious and not curious.
Someone is not brave.
Alice is both not tall and quiet.
Paul is not kind or not generous.
Someone is either not kind or not generous.
Susan is patient or humble.
Paul is either patient or curious.
Someone is quiet.
Fred is either patient or not tall. | Paul is curious. | contradiction | (((~rich(susan)<~>curious(susan)))<=>((~calm(alice)|creative(alice))))&
(((tall(susan)&~brave(susan)))<=>(calm(paul)))&
(![X]:((~humble(X)&humble(X))<=>(rich(X)<~>~brave(X))))&
(![X]:((creative(X)&wise(X))=>brave(X)))&
((?[X]:((~creative(X)|wise(X))))<=>(wise(lucy)))&
(![X]:((~funny(X)|~curious(X))=>(~funny(X)<~>~rich(X))))&
((?[X]:((~quiet(X)&~happy(X))))=>(?[X]:((~old(X)|funny(X)))))&
(((~brave(fred)|~funny(fred)))=>(?[X]:((rich(X)<~>~patient(X)))))&
(![X]:((kind(X)&strong(X))<=>(~humble(X)&curious(X))))&
((~tall(paul))<=>(?[X]:((~wise(X)|~creative(X)))))&
((wise(fred))<=>(?[X]:(calm(X))))&
((?[X]:((~kind(X)<~>~curious(X))))=>((kind(alice)|generous(alice))))&
((?[X]:((~brave(X)<~>~tall(X))))<=>(?[X]:((tall(X)<~>kind(X)))))&
(![X]:((strong(X)&~funny(X))=>(~rich(X)&brave(X))))&
(((kind(susan)<~>~rich(susan)))<=>((~creative(lucy)&patient(lucy))))&
(![X]:(curious(X)=>(curious(X)&~curious(X))))&
(?[X]:(~brave(X)))&
((~tall(alice)&quiet(alice)))&
((~kind(paul)|~generous(paul)))&
(?[X]:((~kind(X)<~>~generous(X))))&
((patient(susan)|humble(susan)))&
((patient(paul)<~>curious(paul)))&
(?[X]:(quiet(X)))&
((patient(fred)<~>~tall(fred))) | curious(paul) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3391170384573732830303356
% SZS output start Proof for 3391170384573732830303356
16. ! [X0] : (curious(X0) => (~curious(X0) & curious(X0))) [input p15]
25. curious(paul) [input hypothesis]
39. ! [X0] : ((~curious(X0) & curious(X0)) | ~curious(X0)) [ennf transformation 16]
134. ~curious(X0) | ~curious(X0) [cnf transformation 39]
145. curious(paul) [cnf transformation 25]
146. ~curious(X0) [duplicate literal removal 134]
369. $false [subsumption resolution 145,146]
% SZS output end Proof for 3391170384573732830303356
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not kind then alice is both curious and not calm. Everyone who is both not generous and not strong is both wise and funny. If mary is not calm then fred is not strong and vice versa. If mary is not strong then mary is both not wise and funny and vice versa. Everyone who is both curious and wise is both not strong and kind. If someone is both wise and not tall then fred is both not kind and humble and vice versa. Everyone who is both not curious and brave is either not generous or humble and vice versa. If someone is both old and not humble then mary is kind or not creative. If someone is either not generous or old then susan is both calm and not happy. Everyone who is not brave is curious or not strong and vice versa. Everyone who is both not brave and humble is rich and vice versa. If someone is not generous or quiet then fred is quiet or not patient. If someone is both happy and kind then someone is either not old or wise. Everyone who is either wise or not patient is either tall or not funny. If someone is either calm or old then lucy is both patient and quiet and vice versa. Everyone who is funny is either not quiet or humble. Someone is either funny or not quiet. Someone is kind or wise. John is brave. Someone is both tall and not old. Someone is either not old or not curious. Mary is either brave or not quiet. Lucy is either curious or old. Someone is either tall or not tall. | Lucy is patient. | neutral | ((~kind(susan))=>((curious(alice)&~calm(alice))))&
(![X]:((~generous(X)&~strong(X))=>(wise(X)&funny(X))))&
((~calm(mary))<=>(~strong(fred)))&
((~strong(mary))<=>((~wise(mary)&funny(mary))))&
(![X]:((curious(X)&wise(X))=>(~strong(X)&kind(X))))&
((?[X]:((wise(X)&~tall(X))))<=>((~kind(fred)&humble(fred))))&
(![X]:((~curious(X)&brave(X))<=>(~generous(X)<~>humble(X))))&
((?[X]:((old(X)&~humble(X))))=>((kind(mary)|~creative(mary))))&
((?[X]:((~generous(X)<~>old(X))))=>((calm(susan)&~happy(susan))))&
(![X]:(~brave(X)<=>(curious(X)|~strong(X))))&
(![X]:((~brave(X)&humble(X))<=>rich(X)))&
((?[X]:((~generous(X)|quiet(X))))=>((quiet(fred)|~patient(fred))))&
((?[X]:((happy(X)&kind(X))))=>(?[X]:((~old(X)<~>wise(X)))))&
(![X]:((wise(X)<~>~patient(X))=>(tall(X)<~>~funny(X))))&
((?[X]:((calm(X)<~>old(X))))<=>((patient(lucy)&quiet(lucy))))&
(![X]:(funny(X)=>(~quiet(X)<~>humble(X))))&
(?[X]:((funny(X)<~>~quiet(X))))&
(?[X]:((kind(X)|wise(X))))&
(brave(john))&
(?[X]:((tall(X)&~old(X))))&
(?[X]:((~old(X)<~>~curious(X))))&
((brave(mary)<~>~quiet(mary)))&
((curious(lucy)<~>old(lucy)))&
(?[X]:((tall(X)<~>~tall(X)))) | patient(lucy) | [] | null | 0 |
Everyone who is rich or not creative is either generous or not calm. If someone is generous or wise then fred is not calm. If someone is creative then someone is either not patient or creative and vice versa. If someone is both generous and humble then mary is kind and vice versa. Everyone who is both curious and not wise is both old and not curious. Everyone who is not tall is both generous and not generous. Everyone who is not generous or happy is wise or not creative and vice versa. If someone is either curious or generous then someone is either not patient or not generous and vice versa. If someone is either not rich or not tall then susan is either not funny or not rich and vice versa. Everyone who is either generous or tall is both brave and not rich and vice versa. If someone is both not happy and creative then someone is both wise and rich. Everyone who is both not brave and creative is either funny or not calm and vice versa. If someone is not quiet or tall then someone is not old. If lucy is either not creative or not strong then john is either not happy or rich. If someone is both rich and not rich then someone is not curious and vice versa. Everyone who is strong or calm is both not brave and not tall and vice versa. Lucy is either funny or not wise. Someone is generous. Someone is not kind. Someone is both not funny and happy. Alice is either tall or not patient. Mary is humble. Someone is either not brave or humble. | Susan is not funny. | contradiction | (![X]:((rich(X)|~creative(X))=>(generous(X)<~>~calm(X))))&
((?[X]:((generous(X)|wise(X))))=>(~calm(fred)))&
((?[X]:(creative(X)))<=>(?[X]:((~patient(X)<~>creative(X)))))&
((?[X]:((generous(X)&humble(X))))<=>(kind(mary)))&
(![X]:((curious(X)&~wise(X))=>(old(X)&~curious(X))))&
(![X]:(~tall(X)=>(generous(X)&~generous(X))))&
(![X]:((~generous(X)|happy(X))<=>(wise(X)|~creative(X))))&
((?[X]:((curious(X)<~>generous(X))))<=>(?[X]:((~patient(X)<~>~generous(X)))))&
((?[X]:((~rich(X)<~>~tall(X))))<=>((~funny(susan)<~>~rich(susan))))&
(![X]:((generous(X)<~>tall(X))<=>(brave(X)&~rich(X))))&
((?[X]:((~happy(X)&creative(X))))=>(?[X]:((wise(X)&rich(X)))))&
(![X]:((~brave(X)&creative(X))<=>(funny(X)<~>~calm(X))))&
((?[X]:((~quiet(X)|tall(X))))=>(?[X]:(~old(X))))&
(((~creative(lucy)<~>~strong(lucy)))=>((~happy(john)<~>rich(john))))&
((?[X]:((rich(X)&~rich(X))))<=>(?[X]:(~curious(X))))&
(![X]:((strong(X)|calm(X))<=>(~brave(X)&~tall(X))))&
((funny(lucy)<~>~wise(lucy)))&
(?[X]:(generous(X)))&
(?[X]:(~kind(X)))&
(?[X]:((~funny(X)&happy(X))))&
((tall(alice)<~>~patient(alice)))&
(humble(mary))&
(?[X]:((~brave(X)<~>humble(X)))) | ~funny(susan) | [
"p0",
"p5",
"p8",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 294520199072970134831018
% SZS output start Proof for 294520199072970134831018
1. ! [X0] : ((~creative(X0) | rich(X0)) => (generous(X0) <~> ~calm(X0))) [input p0]
6. ! [X0] : (~tall(X0) => (~generous(X0) & generous(X0))) [input p5]
9. ? [X0] : (~rich(X0) <~> ~tall(X0)) <=> (~funny(susan) <~> ~rich(susan)) [input p8]
10. ! [X0] : ((generous(X0) <~> tall(X0)) <=> (~rich(X0) & brave(X0))) [input p9]
16. ! [X0] : ((calm(X0) | strong(X0)) <=> (~tall(X0) & ~brave(X0))) [input p15]
24. ~funny(susan) [input hypothesis]
31. ! [X0] : ((generous(X0) <~> ~calm(X0)) | (creative(X0) & ~rich(X0))) [ennf transformation 1]
35. ! [X0] : ((~generous(X0) & generous(X0)) | tall(X0)) [ennf transformation 6]
39. ! [X0] : (((calm(X0) | ~generous(X0)) & (~calm(X0) | generous(X0))) | (creative(X0) & ~rich(X0))) [nnf transformation 31]
56. (? [X0] : ((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | ((~funny(susan) | rich(susan)) & (~rich(susan) | funny(susan)))) & (((rich(susan) | funny(susan)) & (~rich(susan) | ~funny(susan))) | ! [X0] : ((~rich(X0) | tall(X0)) & (~tall(X0) | rich(X0)))) [nnf transformation 9]
57. (? [X0] : ((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) | ((~funny(susan) | rich(susan)) & (~rich(susan) | funny(susan)))) & (((rich(susan) | funny(susan)) & (~rich(susan) | ~funny(susan))) | ! [X1] : ((~rich(X1) | tall(X1)) & (~tall(X1) | rich(X1)))) [rectify 56]
58. ? [X0] : ((tall(X0) | rich(X0)) & (~tall(X0) | ~rich(X0))) => ((tall(sK5) | rich(sK5)) & (~tall(sK5) | ~rich(sK5))) [choice axiom]
59. (((tall(sK5) | rich(sK5)) & (~tall(sK5) | ~rich(sK5))) | ((~funny(susan) | rich(susan)) & (~rich(susan) | funny(susan)))) & (((rich(susan) | funny(susan)) & (~rich(susan) | ~funny(susan))) | ! [X1] : ((~rich(X1) | tall(X1)) & (~tall(X1) | rich(X1)))) [skolemisation 57,58]
60. ! [X0] : ((((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | (rich(X0) | ~brave(X0))) & ((~rich(X0) & brave(X0)) | ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0))))) [nnf transformation 10]
61. ! [X0] : ((((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | rich(X0) | ~brave(X0)) & ((~rich(X0) & brave(X0)) | ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0))))) [flattening 60]
76. ! [X0] : (((calm(X0) | strong(X0)) | (tall(X0) | brave(X0))) & ((~tall(X0) & ~brave(X0)) | (~calm(X0) & ~strong(X0)))) [nnf transformation 16]
77. ! [X0] : ((calm(X0) | strong(X0) | tall(X0) | brave(X0)) & ((~tall(X0) & ~brave(X0)) | (~calm(X0) & ~strong(X0)))) [flattening 76]
91. ~generous(X0) | calm(X0) | ~rich(X0) [cnf transformation 39]
104. generous(X0) | tall(X0) [cnf transformation 35]
105. ~generous(X0) | tall(X0) [cnf transformation 35]
120. rich(susan) | funny(susan) | ~tall(X1) | rich(X1) [cnf transformation 59]
129. ~rich(X0) | generous(X0) | ~tall(X0) [cnf transformation 61]
151. ~tall(X0) | ~calm(X0) [cnf transformation 77]
164. ~funny(susan) [cnf transformation 24]
221. tall(X0) [subsumption resolution 104,105]
260. 22 <=> rich(susan) [avatar definition]
261. ~rich(susan) <- (~22) [avatar component clause 260]
262. rich(susan) <- (22) [avatar component clause 260]
264. 23 <=> funny(susan) [avatar definition]
274. rich(susan) | funny(susan) | rich(X1) [subsumption resolution 120,221]
276. 25 <=> ! [X1] : rich(X1) [avatar definition]
277. rich(X1) <- (25) [avatar component clause 276]
278. 25 | 23 | 22 [avatar split clause 274,260,264,276]
282. ~rich(X0) | generous(X0) [subsumption resolution 129,221]
327. ~calm(X0) [subsumption resolution 151,221]
350. ~23 [avatar split clause 164,264]
356. generous(susan) <- (22) [resolution 282,262]
361. calm(susan) | ~rich(susan) <- (22) [resolution 91,356]
365. ~rich(susan) <- (22) [subsumption resolution 361,327]
366. $false <- (22) [subsumption resolution 365,262]
367. ~22 [avatar contradiction clause 366]
371. $false <- (~22, 25) [subsumption resolution 261,277]
372. 22 | ~25 [avatar contradiction clause 371]
373. $false [avatar sat refutation 278,350,367,372]
% SZS output end Proof for 294520199072970134831018
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is not creative or not curious. If someone is kind then someone is either wise or not quiet and vice versa. If someone is both not calm and old then someone is not creative or not old. Everyone who is both quiet and not calm is either calm or not strong. If lucy is not happy then susan is not wise or strong. Everyone who is not funny or creative is kind and vice versa. Everyone who is both tall and strong is not kind or generous and vice versa. If fred is either wise or not patient then mary is either brave or calm and vice versa. If susan is patient or not funny then paul is either not rich or humble and vice versa. Everyone who is not calm or not funny is patient and vice versa. If susan is both not curious and funny then someone is either not patient or old. If mary is both curious and not kind then someone is not rich or not old. If fred is generous then alice is tall or curious and vice versa. Everyone who is not happy or not calm is strong. If mary is either generous or not curious then someone is not quiet and vice versa. If someone is either not creative or funny then someone is either not calm or creative and vice versa. Someone is either quiet or generous. John is quiet. Mary is creative or not curious. Susan is not tall. Susan is patient or quiet. Someone is both funny and patient. Mary is either strong or not generous. Someone is creative or not rich. | John is not calm. | contradiction | (![X]:(kind(X)=>(~creative(X)|~curious(X))))&
((?[X]:(kind(X)))<=>(?[X]:((wise(X)<~>~quiet(X)))))&
((?[X]:((~calm(X)&old(X))))=>(?[X]:((~creative(X)|~old(X)))))&
(![X]:((quiet(X)&~calm(X))=>(calm(X)<~>~strong(X))))&
((~happy(lucy))=>((~wise(susan)|strong(susan))))&
(![X]:((~funny(X)|creative(X))<=>kind(X)))&
(![X]:((tall(X)&strong(X))<=>(~kind(X)|generous(X))))&
(((wise(fred)<~>~patient(fred)))<=>((brave(mary)<~>calm(mary))))&
(((patient(susan)|~funny(susan)))<=>((~rich(paul)<~>humble(paul))))&
(![X]:((~calm(X)|~funny(X))<=>patient(X)))&
(((~curious(susan)&funny(susan)))=>(?[X]:((~patient(X)<~>old(X)))))&
(((curious(mary)&~kind(mary)))=>(?[X]:((~rich(X)|~old(X)))))&
((generous(fred))<=>((tall(alice)|curious(alice))))&
(![X]:((~happy(X)|~calm(X))=>strong(X)))&
(((generous(mary)<~>~curious(mary)))<=>(?[X]:(~quiet(X))))&
((?[X]:((~creative(X)<~>funny(X))))<=>(?[X]:((~calm(X)<~>creative(X)))))&
(?[X]:((quiet(X)<~>generous(X))))&
(quiet(john))&
((creative(mary)|~curious(mary)))&
(~tall(susan))&
((patient(susan)|quiet(susan)))&
(?[X]:((funny(X)&patient(X))))&
((strong(mary)<~>~generous(mary)))&
(?[X]:((creative(X)|~rich(X)))) | ~calm(john) | [
"p3",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6781077006079514260795315
% SZS output start Proof for 6781077006079514260795315
4. ! [X0] : ((~calm(X0) & quiet(X0)) => (calm(X0) <~> ~strong(X0))) [input p3]
14. ! [X0] : ((~calm(X0) | ~happy(X0)) => strong(X0)) [input p13]
18. quiet(john) [input p17]
25. ~calm(john) [input hypothesis]
29. ! [X0] : (~calm(X0) => strong(X0)) [pure predicate removal 14]
34. ! [X0] : ((calm(X0) <~> ~strong(X0)) | (calm(X0) | ~quiet(X0))) [ennf transformation 4]
35. ! [X0] : ((calm(X0) <~> ~strong(X0)) | calm(X0) | ~quiet(X0)) [flattening 34]
40. ! [X0] : (strong(X0) | calm(X0)) [ennf transformation 29]
49. ! [X0] : (((strong(X0) | ~calm(X0)) & (~strong(X0) | calm(X0))) | calm(X0) | ~quiet(X0)) [nnf transformation 35]
89. ~strong(X0) | calm(X0) | calm(X0) | ~quiet(X0) [cnf transformation 49]
122. strong(X0) | calm(X0) [cnf transformation 40]
137. quiet(john) [cnf transformation 18]
146. ~calm(john) [cnf transformation 25]
147. ~strong(X0) | calm(X0) | ~quiet(X0) [duplicate literal removal 89]
397. calm(X0) | ~quiet(X0) | calm(X0) [resolution 147,122]
399. ~quiet(X0) | calm(X0) [duplicate literal removal 397]
401. calm(john) [resolution 399,137]
403. $false [subsumption resolution 401,146]
% SZS output end Proof for 6781077006079514260795315
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and patient is happy or not brave. Everyone who is old or not strong is either not wise or curious and vice versa. Everyone who is old is both not kind and curious and vice versa. Everyone who is either curious or not rich is both curious and not tall and vice versa. Everyone who is brave is both humble and not creative. If someone is both wise and not generous then someone is both creative and rich and vice versa. Everyone who is not calm or not happy is both kind and patient and vice versa. If paul is either not calm or wise then someone is creative or wise and vice versa. If alice is happy or not patient then someone is humble. If susan is not creative or wise then someone is either brave or tall. Everyone who is not calm or not funny is humble or not tall. Everyone who is both not calm and strong is not patient and vice versa. Everyone who is both not brave and kind is not strong and vice versa. If someone is both patient and not generous then alice is patient. Everyone who is not wise or not quiet is both patient and happy and vice versa. Everyone who is either not creative or not rich is both not creative and not old and vice versa. Someone is not generous. Someone is creative. Someone is not generous or not rich. Someone is old. Someone is either kind or not calm. Susan is not rich or brave. Someone is both not quiet and happy. Someone is both happy and patient. | Alice is not patient. | contradiction | (![X]:((~creative(X)&patient(X))=>(happy(X)|~brave(X))))&
(![X]:((old(X)|~strong(X))<=>(~wise(X)<~>curious(X))))&
(![X]:(old(X)<=>(~kind(X)&curious(X))))&
(![X]:((curious(X)<~>~rich(X))<=>(curious(X)&~tall(X))))&
(![X]:(brave(X)=>(humble(X)&~creative(X))))&
((?[X]:((wise(X)&~generous(X))))<=>(?[X]:((creative(X)&rich(X)))))&
(![X]:((~calm(X)|~happy(X))<=>(kind(X)&patient(X))))&
(((~calm(paul)<~>wise(paul)))<=>(?[X]:((creative(X)|wise(X)))))&
(((happy(alice)|~patient(alice)))=>(?[X]:(humble(X))))&
(((~creative(susan)|wise(susan)))=>(?[X]:((brave(X)<~>tall(X)))))&
(![X]:((~calm(X)|~funny(X))=>(humble(X)|~tall(X))))&
(![X]:((~calm(X)&strong(X))<=>~patient(X)))&
(![X]:((~brave(X)&kind(X))<=>~strong(X)))&
((?[X]:((patient(X)&~generous(X))))=>(patient(alice)))&
(![X]:((~wise(X)|~quiet(X))<=>(patient(X)&happy(X))))&
(![X]:((~creative(X)<~>~rich(X))<=>(~creative(X)&~old(X))))&
(?[X]:(~generous(X)))&
(?[X]:(creative(X)))&
(?[X]:((~generous(X)|~rich(X))))&
(?[X]:(old(X)))&
(?[X]:((kind(X)<~>~calm(X))))&
((~rich(susan)|brave(susan)))&
(?[X]:((~quiet(X)&happy(X))))&
(?[X]:((happy(X)&patient(X)))) | ~patient(alice) | [
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 503835856204499793925403
% SZS output start Proof for 503835856204499793925403
7. ! [X0] : ((~happy(X0) | ~calm(X0)) <=> (patient(X0) & kind(X0))) [input p6]
12. ! [X0] : ((strong(X0) & ~calm(X0)) <=> ~patient(X0)) [input p11]
25. ~patient(alice) [input hypothesis]
47. ! [X0] : (((~happy(X0) | ~calm(X0)) | (~patient(X0) | ~kind(X0))) & ((patient(X0) & kind(X0)) | (happy(X0) & calm(X0)))) [nnf transformation 7]
48. ! [X0] : ((~happy(X0) | ~calm(X0) | ~patient(X0) | ~kind(X0)) & ((patient(X0) & kind(X0)) | (happy(X0) & calm(X0)))) [flattening 47]
56. ! [X0] : (((strong(X0) & ~calm(X0)) | patient(X0)) & (~patient(X0) | (~strong(X0) | calm(X0)))) [nnf transformation 12]
57. ! [X0] : (((strong(X0) & ~calm(X0)) | patient(X0)) & (~patient(X0) | ~strong(X0) | calm(X0))) [flattening 56]
102. patient(X0) | calm(X0) [cnf transformation 48]
116. ~calm(X0) | patient(X0) [cnf transformation 57]
144. ~patient(alice) [cnf transformation 25]
223. patient(X0) [subsumption resolution 116,102]
246. $false [subsumption resolution 144,223]
% SZS output end Proof for 503835856204499793925403
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not brave then fred is creative or curious and vice versa.
Everyone who is generous is both not brave and generous.
If someone is not strong or funny then someone is both kind and humble and vice versa.
Everyone who is kind or not quiet is both curious and old and vice versa.
Everyone who is strong is either not strong or not old.
Everyone who is both humble and not curious is not tall.
If john is not curious then someone is creative or not generous.
Everyone who is kind or not patient is not funny.
If someone is not wise or not generous then fred is not patient and vice versa.
If mary is both patient and not quiet then susan is either calm or not happy and vice versa.
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 not wise and not quiet is brave or kind.
Everyone who is either brave or quiet is not patient and vice versa.
If someone is wise then someone is both brave and not patient.
If someone is not calm then someone is either not strong or happy and vice versa.
Someone is not happy or quiet.
Someone is generous.
Mary is kind.
Someone is not funny or funny.
Mary is humble or brave.
Lucy is both kind and old.
Paul is humble or strong.
Lucy is funny or not quiet. | Susan is curious. | entailment | ((~brave(susan))<=>((creative(fred)|curious(fred))))&
(![X]:(generous(X)=>(~brave(X)&generous(X))))&
((?[X]:((~strong(X)|funny(X))))<=>(?[X]:((kind(X)&humble(X)))))&
(![X]:((kind(X)|~quiet(X))<=>(curious(X)&old(X))))&
(![X]:(strong(X)=>(~strong(X)<~>~old(X))))&
(![X]:((humble(X)&~curious(X))=>~tall(X)))&
((~curious(john))=>(?[X]:((creative(X)|~generous(X)))))&
(![X]:((kind(X)|~patient(X))=>~funny(X)))&
((?[X]:((~wise(X)|~generous(X))))<=>(~patient(fred)))&
(((patient(mary)&~quiet(mary)))<=>((calm(susan)<~>~happy(susan))))&
(![X]:((~happy(X)|~curious(X))<=>(patient(X)&old(X))))&
(![X]:((~generous(X)|~quiet(X))<=>(~brave(X)|happy(X))))&
(![X]:((~wise(X)&~quiet(X))=>(brave(X)|kind(X))))&
(![X]:((brave(X)<~>quiet(X))<=>~patient(X)))&
((?[X]:(wise(X)))=>(?[X]:((brave(X)&~patient(X)))))&
((?[X]:(~calm(X)))<=>(?[X]:((~strong(X)<~>happy(X)))))&
(?[X]:((~happy(X)|quiet(X))))&
(?[X]:(generous(X)))&
(kind(mary))&
(?[X]:((~funny(X)|funny(X))))&
((humble(mary)|brave(mary)))&
((kind(lucy)&old(lucy)))&
((humble(paul)|strong(paul)))&
((funny(lucy)|~quiet(lucy))) | curious(susan) | [
"p0",
"p1",
"p3",
"p8",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 410252681355755569389389
% SZS output start Proof for 410252681355755569389389
1. ~brave(susan) <=> (curious(fred) | creative(fred)) [input p0]
2. ! [X0] : (generous(X0) => (generous(X0) & ~brave(X0))) [input p1]
4. ! [X0] : ((~quiet(X0) | kind(X0)) <=> (old(X0) & curious(X0))) [input p3]
9. ? [X0] : (~generous(X0) | ~wise(X0)) <=> ~patient(fred) [input p8]
11. ! [X0] : ((~curious(X0) | ~happy(X0)) <=> (old(X0) & patient(X0))) [input p10]
12. ! [X0] : ((~quiet(X0) | ~generous(X0)) <=> (happy(X0) | ~brave(X0))) [input p11]
14. ! [X0] : ((brave(X0) <~> quiet(X0)) <=> ~patient(X0)) [input p13]
25. ~curious(susan) [input hypothesis]
30. ! [X0] : ((generous(X0) & ~brave(X0)) | ~generous(X0)) [ennf transformation 2]
37. (~brave(susan) | (~curious(fred) & ~creative(fred))) & ((curious(fred) | creative(fred)) | brave(susan)) [nnf transformation 1]
38. (~brave(susan) | (~curious(fred) & ~creative(fred))) & (curious(fred) | creative(fred) | brave(susan)) [flattening 37]
44. ! [X0] : (((~quiet(X0) | kind(X0)) | (~old(X0) | ~curious(X0))) & ((old(X0) & curious(X0)) | (quiet(X0) & ~kind(X0)))) [nnf transformation 4]
45. ! [X0] : ((~quiet(X0) | kind(X0) | ~old(X0) | ~curious(X0)) & ((old(X0) & curious(X0)) | (quiet(X0) & ~kind(X0)))) [flattening 44]
49. (? [X0] : (~generous(X0) | ~wise(X0)) | patient(fred)) & (~patient(fred) | ! [X0] : (generous(X0) & wise(X0))) [nnf transformation 9]
50. (? [X0] : (~generous(X0) | ~wise(X0)) | patient(fred)) & (~patient(fred) | ! [X1] : (generous(X1) & wise(X1))) [rectify 49]
51. ? [X0] : (~generous(X0) | ~wise(X0)) => (~generous(sK3) | ~wise(sK3)) [choice axiom]
52. ((~generous(sK3) | ~wise(sK3)) | patient(fred)) & (~patient(fred) | ! [X1] : (generous(X1) & wise(X1))) [skolemisation 50,51]
55. ! [X0] : (((~curious(X0) | ~happy(X0)) | (~old(X0) | ~patient(X0))) & ((old(X0) & patient(X0)) | (curious(X0) & happy(X0)))) [nnf transformation 11]
56. ! [X0] : ((~curious(X0) | ~happy(X0) | ~old(X0) | ~patient(X0)) & ((old(X0) & patient(X0)) | (curious(X0) & happy(X0)))) [flattening 55]
57. ! [X0] : (((~quiet(X0) | ~generous(X0)) | (~happy(X0) & brave(X0))) & ((happy(X0) | ~brave(X0)) | (quiet(X0) & generous(X0)))) [nnf transformation 12]
58. ! [X0] : ((~quiet(X0) | ~generous(X0) | (~happy(X0) & brave(X0))) & (happy(X0) | ~brave(X0) | (quiet(X0) & generous(X0)))) [flattening 57]
59. ! [X0] : ((((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | patient(X0)) & (~patient(X0) | ((brave(X0) | ~quiet(X0)) & (quiet(X0) | ~brave(X0))))) [nnf transformation 14]
76. ~brave(susan) | ~curious(fred) [cnf transformation 38]
77. ~generous(X0) | ~brave(X0) [cnf transformation 30]
85. quiet(X0) | curious(X0) [cnf transformation 45]
95. ~patient(fred) | generous(X1) [cnf transformation 52]
104. patient(X0) | curious(X0) [cnf transformation 56]
110. ~quiet(X0) | ~generous(X0) | brave(X0) [cnf transformation 58]
114. ~patient(X0) | brave(X0) | ~quiet(X0) [cnf transformation 59]
132. ~curious(susan) [cnf transformation 25]
135. 1 <=> curious(fred) [avatar definition]
137. ~curious(fred) <- (~1) [avatar component clause 135]
139. 2 <=> brave(susan) [avatar definition]
141. ~brave(susan) <- (~2) [avatar component clause 139]
142. ~1 | ~2 [avatar split clause 76,139,135]
193. 14 <=> patient(fred) [avatar definition]
194. ~patient(fred) <- (~14) [avatar component clause 193]
206. 17 <=> ! [X1] : generous(X1) [avatar definition]
207. generous(X1) <- (17) [avatar component clause 206]
208. 17 | ~14 [avatar split clause 95,193,206]
235. ~quiet(X0) | ~generous(X0) [subsumption resolution 110,77]
328. curious(fred) <- (~14) [resolution 104,194]
330. $false <- (~1, ~14) [subsumption resolution 328,137]
331. 1 | 14 [avatar contradiction clause 330]
360. ~generous(X0) | curious(X0) [resolution 235,85]
361. curious(X0) <- (17) [subsumption resolution 360,207]
363. $false <- (17) [resolution 361,132]
364. ~17 [avatar contradiction clause 363]
387. brave(X0) | ~quiet(X0) | curious(X0) [resolution 114,104]
390. curious(X0) | brave(X0) [subsumption resolution 387,85]
446. brave(susan) [resolution 390,132]
447. $false <- (~2) [subsumption resolution 446,141]
448. 2 [avatar contradiction clause 447]
449. $false [avatar sat refutation 142,208,331,364,448]
% SZS output end Proof for 410252681355755569389389
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not rich is tall and vice versa.
Everyone who is both kind and not patient is either not funny or quiet and vice versa.
Everyone who is quiet is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is not curious or not calm is not calm and vice versa.
Everyone who is either rich or curious is brave or not quiet and vice versa.
If someone is both brave and curious then susan is not humble or curious and vice versa.
Everyone who is generous is generous or not kind and vice versa.
If someone is both kind and quiet then someone is strong or not old.
Everyone who is both old and not calm is not rich or not funny and vice versa.
Everyone who is both rich and not wise is both curious and quiet.
If john is both curious and old then susan is rich and vice versa.
Everyone who is either patient or happy is funny or not curious and vice versa.
If someone is rich or calm then alice is rich or not old and vice versa.
Everyone who is either tall or not funny is both strong and funny and vice versa.
Someone is both brave and not strong.
Lucy is either generous or not brave.
Someone is not strong or not quiet.
Someone is rich.
Someone is either quiet or not curious.
Someone is either humble or not wise. | Alice is not funny. | contradiction | (![X]:((~strong(X)&~rich(X))<=>tall(X)))&
(![X]:((kind(X)&~patient(X))<=>(~funny(X)<~>quiet(X))))&
(![X]:(quiet(X)<=>(happy(X)|generous(X))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
((?[X]:((brave(X)&curious(X))))<=>((~humble(susan)|curious(susan))))&
(![X]:(generous(X)<=>(generous(X)|~kind(X))))&
((?[X]:((kind(X)&quiet(X))))=>(?[X]:((strong(X)|~old(X)))))&
(![X]:((old(X)&~calm(X))<=>(~rich(X)|~funny(X))))&
(![X]:((rich(X)&~wise(X))=>(curious(X)&quiet(X))))&
(((curious(john)&old(john)))<=>(rich(susan)))&
(![X]:((patient(X)<~>happy(X))<=>(funny(X)|~curious(X))))&
((?[X]:((rich(X)|calm(X))))<=>((rich(alice)|~old(alice))))&
(![X]:((tall(X)<~>~funny(X))<=>(strong(X)&funny(X))))&
(?[X]:((brave(X)&~strong(X))))&
((generous(lucy)<~>~brave(lucy)))&
(?[X]:((~strong(X)|~quiet(X))))&
(?[X]:(rich(X)))&
(?[X]:((quiet(X)<~>~curious(X))))&
(?[X]:((humble(X)<~>~wise(X)))) | ~funny(alice) | [
"p0",
"p3",
"p10",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 567496579482639164703528
% SZS output start Proof for 567496579482639164703528
1. ! [X0] : ((~rich(X0) & ~strong(X0)) <=> tall(X0)) [input p0]
4. ! [X0] : ((~rich(X0) | ~wise(X0)) => (~brave(X0) & ~happy(X0))) [input p3]
11. ! [X0] : ((~calm(X0) & old(X0)) <=> (~funny(X0) | ~rich(X0))) [input p10]
15. ? [X0] : (calm(X0) | rich(X0)) <=> (~old(alice) | rich(alice)) [input p14]
16. ! [X0] : ((tall(X0) <~> ~funny(X0)) <=> (funny(X0) & strong(X0))) [input p15]
17. ? [X0] : (~strong(X0) & brave(X0)) [input p16]
23. ~funny(alice) [input hypothesis]
25. ! [X0] : ((~brave(X0) & ~happy(X0)) | (rich(X0) & wise(X0))) [ennf transformation 4]
29. ! [X0] : (((~rich(X0) & ~strong(X0)) | ~tall(X0)) & (tall(X0) | (rich(X0) | strong(X0)))) [nnf transformation 1]
30. ! [X0] : (((~rich(X0) & ~strong(X0)) | ~tall(X0)) & (tall(X0) | rich(X0) | strong(X0))) [flattening 29]
51. ! [X0] : (((~calm(X0) & old(X0)) | (funny(X0) & rich(X0))) & ((~funny(X0) | ~rich(X0)) | (calm(X0) | ~old(X0)))) [nnf transformation 11]
52. ! [X0] : (((~calm(X0) & old(X0)) | (funny(X0) & rich(X0))) & (~funny(X0) | ~rich(X0) | calm(X0) | ~old(X0))) [flattening 51]
57. (? [X0] : (calm(X0) | rich(X0)) | (old(alice) & ~rich(alice))) & ((~old(alice) | rich(alice)) | ! [X0] : (~calm(X0) & ~rich(X0))) [nnf transformation 15]
58. (? [X0] : (calm(X0) | rich(X0)) | (old(alice) & ~rich(alice))) & (~old(alice) | rich(alice) | ! [X0] : (~calm(X0) & ~rich(X0))) [flattening 57]
59. (? [X0] : (calm(X0) | rich(X0)) | (old(alice) & ~rich(alice))) & (~old(alice) | rich(alice) | ! [X1] : (~calm(X1) & ~rich(X1))) [rectify 58]
60. ? [X0] : (calm(X0) | rich(X0)) => (calm(sK2) | rich(sK2)) [choice axiom]
61. ((calm(sK2) | rich(sK2)) | (old(alice) & ~rich(alice))) & (~old(alice) | rich(alice) | ! [X1] : (~calm(X1) & ~rich(X1))) [skolemisation 59,60]
62. ! [X0] : ((((funny(X0) | ~tall(X0)) & (~funny(X0) | tall(X0))) | (~funny(X0) | ~strong(X0))) & ((funny(X0) & strong(X0)) | ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0))))) [nnf transformation 16]
63. ! [X0] : ((((funny(X0) | ~tall(X0)) & (~funny(X0) | tall(X0))) | ~funny(X0) | ~strong(X0)) & ((funny(X0) & strong(X0)) | ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0))))) [flattening 62]
64. ? [X0] : (~strong(X0) & brave(X0)) => (~strong(sK3) & brave(sK3)) [choice axiom]
65. ~strong(sK3) & brave(sK3) [skolemisation 17,64]
79. ~tall(X0) | ~rich(X0) [cnf transformation 30]
92. ~brave(X0) | rich(X0) [cnf transformation 25]
118. old(X0) | rich(X0) [cnf transformation 52]
133. ~old(alice) | rich(alice) | ~rich(X1) [cnf transformation 61]
140. funny(X0) | tall(X0) | funny(X0) [cnf transformation 63]
143. brave(sK3) [cnf transformation 65]
153. ~funny(alice) [cnf transformation 23]
154. funny(X0) | tall(X0) [duplicate literal removal 140]
219. 13 <=> rich(alice) [avatar definition]
228. rich(alice) | ~rich(X1) [subsumption resolution 133,118]
230. 15 <=> ! [X1] : ~rich(X1) [avatar definition]
231. ~rich(X1) <- (15) [avatar component clause 230]
232. 15 | 13 [avatar split clause 228,219,230]
275. rich(sK3) [resolution 92,143]
280. tall(alice) [resolution 154,153]
281. ~rich(alice) [resolution 280,79]
285. ~13 [avatar split clause 281,219]
288. $false <- (15) [resolution 231,275]
291. ~15 [avatar contradiction clause 288]
294. $false [avatar sat refutation 232,285,291]
% SZS output end Proof for 567496579482639164703528
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not calm or strong then someone is both calm and patient.
Everyone who is either not funny or not patient is not generous.
Everyone who is either not tall or not wise is kind.
Everyone who is generous is old or not old and vice versa.
If someone is brave or humble then lucy is both creative and not strong and vice versa.
If someone is either not quiet or wise then fred is funny.
Everyone who is not quiet or not generous is either creative or not humble and vice versa.
Everyone who is both quiet and rich is humble and vice versa.
If alice is either not curious or humble then paul is not happy and vice versa.
If paul is quiet then mary is not creative and vice versa.
If lucy is not happy then someone is not strong and vice versa.
Everyone who is curious or not generous is not quiet.
If someone is generous then someone is not strong and vice versa.
If john is either not strong or not creative then someone is not funny.
Everyone who is either not rich or not calm is not brave or not rich and vice versa.
Everyone who is not old or wise is either wise or not patient and vice versa.
Alice is both brave and not patient.
Someone is both not happy and not curious.
Someone is not humble.
Fred is strong or brave.
Someone is both generous and not quiet.
Fred is not funny or not tall.
Someone is old or not curious. | Alice is not funny. | entailment | ((?[X]:((~calm(X)<~>strong(X))))=>(?[X]:((calm(X)&patient(X)))))&
(![X]:((~funny(X)<~>~patient(X))=>~generous(X)))&
(![X]:((~tall(X)<~>~wise(X))=>kind(X)))&
(![X]:(generous(X)<=>(old(X)|~old(X))))&
((?[X]:((brave(X)|humble(X))))<=>((creative(lucy)&~strong(lucy))))&
((?[X]:((~quiet(X)<~>wise(X))))=>(funny(fred)))&
(![X]:((~quiet(X)|~generous(X))<=>(creative(X)<~>~humble(X))))&
(![X]:((quiet(X)&rich(X))<=>humble(X)))&
(((~curious(alice)<~>humble(alice)))<=>(~happy(paul)))&
((quiet(paul))<=>(~creative(mary)))&
((~happy(lucy))<=>(?[X]:(~strong(X))))&
(![X]:((curious(X)|~generous(X))=>~quiet(X)))&
((?[X]:(generous(X)))<=>(?[X]:(~strong(X))))&
(((~strong(john)<~>~creative(john)))=>(?[X]:(~funny(X))))&
(![X]:((~rich(X)<~>~calm(X))<=>(~brave(X)|~rich(X))))&
(![X]:((~old(X)|wise(X))<=>(wise(X)<~>~patient(X))))&
((brave(alice)&~patient(alice)))&
(?[X]:((~happy(X)&~curious(X))))&
(?[X]:(~humble(X)))&
((strong(fred)|brave(fred)))&
(?[X]:((generous(X)&~quiet(X))))&
((~funny(fred)|~tall(fred)))&
(?[X]:((old(X)|~curious(X)))) | ~funny(alice) | [
"p1",
"p3",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1837748007895965510877317
% SZS output start Proof for 1837748007895965510877317
2. ! [X0] : ((~funny(X0) <~> ~patient(X0)) => ~generous(X0)) [input p1]
4. ! [X0] : (generous(X0) <=> (~old(X0) | old(X0))) [input p3]
17. ~patient(alice) & brave(alice) [input p16]
24. funny(alice) [input hypothesis]
30. ! [X0] : (~generous(X0) | (~funny(X0) <=> ~patient(X0))) [ennf transformation 2]
38. ! [X0] : (~generous(X0) | ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) [nnf transformation 30]
39. ! [X0] : ((generous(X0) | (old(X0) & ~old(X0))) & ((~old(X0) | old(X0)) | ~generous(X0))) [nnf transformation 4]
40. ! [X0] : ((generous(X0) | (old(X0) & ~old(X0))) & (~old(X0) | old(X0) | ~generous(X0))) [flattening 39]
82. ~generous(X0) | ~funny(X0) | patient(X0) [cnf transformation 38]
84. generous(X0) | ~old(X0) [cnf transformation 40]
85. old(X0) | generous(X0) [cnf transformation 40]
129. ~patient(alice) [cnf transformation 17]
137. funny(alice) [cnf transformation 24]
160. generous(X0) [subsumption resolution 84,85]
278. ~funny(X0) | patient(X0) [resolution 82,160]
286. patient(alice) [resolution 278,137]
289. $false [subsumption resolution 286,129]
% SZS output end Proof for 1837748007895965510877317
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not quiet and strong then alice is both not calm and wise.
If fred is either not patient or brave then mary is both happy and not rich.
If john is not creative then paul is creative or old and vice versa.
If susan is not patient then john is not creative.
Everyone who is both not rich and strong is not strong and vice versa.
If someone is not funny then someone is either not curious or tall.
If someone is not generous then mary is both not happy and not generous and vice versa.
Everyone who is either not generous or happy is not rich.
If fred is quiet then alice is both not tall and not generous.
Everyone who is not rich or calm is either quiet or funny and vice versa.
If alice is either rich or strong then alice is both not tall and not funny and vice versa.
Everyone who is curious or kind is wise.
Everyone who is not wise or kind is not old or not quiet and vice versa.
Someone is rich.
Someone is either not patient or creative.
Paul is not wise.
Someone is generous or not tall.
Someone is humble or not funny. | Alice is not calm. | entailment | ((?[X]:((~quiet(X)&strong(X))))=>((~calm(alice)&wise(alice))))&
(((~patient(fred)<~>brave(fred)))=>((happy(mary)&~rich(mary))))&
((~creative(john))<=>((creative(paul)|old(paul))))&
((~patient(susan))=>(~creative(john)))&
(![X]:((~rich(X)&strong(X))<=>~strong(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~curious(X)<~>tall(X)))))&
((?[X]:(~generous(X)))<=>((~happy(mary)&~generous(mary))))&
(![X]:((~generous(X)<~>happy(X))=>~rich(X)))&
((quiet(fred))=>((~tall(alice)&~generous(alice))))&
(![X]:((~rich(X)|calm(X))<=>(quiet(X)<~>funny(X))))&
(((rich(alice)<~>strong(alice)))<=>((~tall(alice)&~funny(alice))))&
(![X]:((curious(X)|kind(X))=>wise(X)))&
(![X]:((~wise(X)|kind(X))<=>(~old(X)|~quiet(X))))&
(?[X]:(rich(X)))&
(?[X]:((~patient(X)<~>creative(X))))&
(~wise(paul))&
(?[X]:((generous(X)|~tall(X))))&
(?[X]:((humble(X)|~funny(X)))) | ~calm(alice) | [
"p0",
"p4",
"p6",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1745042077237877484440559
% SZS output start Proof for 1745042077237877484440559
1. ? [X0] : (strong(X0) & ~quiet(X0)) => (wise(alice) & ~calm(alice)) [input p0]
5. ! [X0] : ((strong(X0) & ~rich(X0)) <=> ~strong(X0)) [input p4]
7. ? [X0] : ~generous(X0) <=> (~generous(mary) & ~happy(mary)) [input p6]
8. ! [X0] : ((~generous(X0) <~> happy(X0)) => ~rich(X0)) [input p7]
9. quiet(fred) => (~generous(alice) & ~tall(alice)) [input p8]
19. calm(alice) [input hypothesis]
22. (wise(alice) & ~calm(alice)) | ! [X0] : (~strong(X0) | quiet(X0)) [ennf transformation 1]
26. ! [X0] : (~rich(X0) | (~generous(X0) <=> happy(X0))) [ennf transformation 8]
27. (~generous(alice) & ~tall(alice)) | ~quiet(fred) [ennf transformation 9]
32. ! [X0] : (((strong(X0) & ~rich(X0)) | strong(X0)) & (~strong(X0) | (~strong(X0) | rich(X0)))) [nnf transformation 5]
33. ! [X0] : (((strong(X0) & ~rich(X0)) | strong(X0)) & (~strong(X0) | ~strong(X0) | rich(X0))) [flattening 32]
38. (? [X0] : ~generous(X0) | (generous(mary) | happy(mary))) & ((~generous(mary) & ~happy(mary)) | ! [X0] : generous(X0)) [nnf transformation 7]
39. (? [X0] : ~generous(X0) | generous(mary) | happy(mary)) & ((~generous(mary) & ~happy(mary)) | ! [X0] : generous(X0)) [flattening 38]
40. (? [X0] : ~generous(X0) | generous(mary) | happy(mary)) & ((~generous(mary) & ~happy(mary)) | ! [X1] : generous(X1)) [rectify 39]
41. ? [X0] : ~generous(X0) => ~generous(sK1) [choice axiom]
42. (~generous(sK1) | generous(mary) | happy(mary)) & ((~generous(mary) & ~happy(mary)) | ! [X1] : generous(X1)) [skolemisation 40,41]
43. ! [X0] : (~rich(X0) | ((~generous(X0) | ~happy(X0)) & (happy(X0) | generous(X0)))) [nnf transformation 26]
57. ~calm(alice) | ~strong(X0) | quiet(X0) [cnf transformation 22]
67. ~strong(X0) | ~strong(X0) | rich(X0) [cnf transformation 33]
69. strong(X0) | strong(X0) [cnf transformation 33]
72. ~happy(mary) | generous(X1) [cnf transformation 42]
73. ~generous(mary) | generous(X1) [cnf transformation 42]
75. ~rich(X0) | happy(X0) | generous(X0) [cnf transformation 43]
78. ~generous(alice) | ~quiet(fred) [cnf transformation 27]
102. calm(alice) [cnf transformation 19]
103. ~strong(X0) | rich(X0) [duplicate literal removal 67]
104. strong(X0) [duplicate literal removal 69]
106. 1 <=> ! [X0] : (~strong(X0) | quiet(X0)) [avatar definition]
107. ~strong(X0) | quiet(X0) <- (1) [avatar component clause 106]
114. 3 <=> calm(alice) [avatar definition]
117. 1 | ~3 [avatar split clause 57,114,106]
133. 7 <=> happy(mary) [avatar definition]
134. ~happy(mary) <- (~7) [avatar component clause 133]
158. rich(X0) [subsumption resolution 103,104]
173. 15 <=> generous(mary) [avatar definition]
174. ~generous(mary) <- (~15) [avatar component clause 173]
182. 17 <=> ! [X1] : generous(X1) [avatar definition]
183. generous(X1) <- (17) [avatar component clause 182]
184. 17 | ~15 [avatar split clause 73,173,182]
185. 17 | ~7 [avatar split clause 72,133,182]
187. generous(X0) | happy(X0) [subsumption resolution 75,158]
189. 18 <=> quiet(fred) [avatar definition]
191. ~quiet(fred) <- (~18) [avatar component clause 189]
193. 19 <=> generous(alice) [avatar definition]
195. ~generous(alice) <- (~19) [avatar component clause 193]
196. ~18 | ~19 [avatar split clause 78,193,189]
230. 3 [avatar split clause 102,114]
231. quiet(X0) <- (1) [subsumption resolution 107,104]
232. $false <- (1, ~18) [resolution 231,191]
233. ~1 | 18 [avatar contradiction clause 232]
236. happy(mary) <- (~15) [resolution 187,174]
238. $false <- (~7, ~15) [subsumption resolution 236,134]
239. 7 | 15 [avatar contradiction clause 238]
241. $false <- (17, ~19) [resolution 183,195]
244. ~17 | 19 [avatar contradiction clause 241]
245. $false [avatar sat refutation 117,184,185,196,230,233,239,244]
% SZS output end Proof for 1745042077237877484440559
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not kind then someone is both quiet and humble and vice versa.
Everyone who is either quiet or not strong is rich or tall.
Everyone who is calm or not generous is either calm or not happy.
Everyone who is both not wise and old is either wise or not happy.
Everyone who is kind or not funny is both not creative and not funny and vice versa.
If susan is funny or kind then susan is kind or not funny.
If someone is either not patient or old then susan is either tall or kind.
If someone is both calm and not curious then susan is both not generous and not quiet and vice versa.
If fred is either not rich or not humble then someone is both not funny and not humble and vice versa.
Everyone who is not wise or wise is either not curious or not brave and vice versa.
Everyone who is either humble or not happy is not curious and vice versa.
If someone is either not happy or rich then someone is not rich and vice versa.
If someone is either generous or not humble then someone is either not strong or quiet.
If someone is both patient and curious then paul is not brave and vice versa.
Everyone who is calm is both strong and calm and vice versa.
Everyone who is not old or not generous is not patient.
Someone is both patient and wise.
Someone is either tall or not quiet.
Someone is both not tall and patient.
Someone is either patient or not happy.
Someone is either kind or not wise.
Someone is both generous and creative.
Someone is both humble and creative.
Someone is both strong and not quiet. | Susan is not funny. | entailment | ((?[X]:(~kind(X)))<=>(?[X]:((quiet(X)&humble(X)))))&
(![X]:((quiet(X)<~>~strong(X))=>(rich(X)|tall(X))))&
(![X]:((calm(X)|~generous(X))=>(calm(X)<~>~happy(X))))&
(![X]:((~wise(X)&old(X))=>(wise(X)<~>~happy(X))))&
(![X]:((kind(X)|~funny(X))<=>(~creative(X)&~funny(X))))&
(((funny(susan)|kind(susan)))=>((kind(susan)|~funny(susan))))&
((?[X]:((~patient(X)<~>old(X))))=>((tall(susan)<~>kind(susan))))&
((?[X]:((calm(X)&~curious(X))))<=>((~generous(susan)&~quiet(susan))))&
(((~rich(fred)<~>~humble(fred)))<=>(?[X]:((~funny(X)&~humble(X)))))&
(![X]:((~wise(X)|wise(X))<=>(~curious(X)<~>~brave(X))))&
(![X]:((humble(X)<~>~happy(X))<=>~curious(X)))&
((?[X]:((~happy(X)<~>rich(X))))<=>(?[X]:(~rich(X))))&
((?[X]:((generous(X)<~>~humble(X))))=>(?[X]:((~strong(X)<~>quiet(X)))))&
((?[X]:((patient(X)&curious(X))))<=>(~brave(paul)))&
(![X]:(calm(X)<=>(strong(X)&calm(X))))&
(![X]:((~old(X)|~generous(X))=>~patient(X)))&
(?[X]:((patient(X)&wise(X))))&
(?[X]:((tall(X)<~>~quiet(X))))&
(?[X]:((~tall(X)&patient(X))))&
(?[X]:((patient(X)<~>~happy(X))))&
(?[X]:((kind(X)<~>~wise(X))))&
(?[X]:((generous(X)&creative(X))))&
(?[X]:((humble(X)&creative(X))))&
(?[X]:((strong(X)&~quiet(X)))) | ~funny(susan) | [
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 8099613157451640571315827
% SZS output start Proof for 8099613157451640571315827
5. ! [X0] : ((~funny(X0) | kind(X0)) <=> (~funny(X0) & ~creative(X0))) [input p4]
6. (kind(susan) | funny(susan)) => (~funny(susan) | kind(susan)) [input p5]
25. funny(susan) [input hypothesis]
34. (~funny(susan) | kind(susan)) | (~kind(susan) & ~funny(susan)) [ennf transformation 6]
35. ~funny(susan) | kind(susan) | (~kind(susan) & ~funny(susan)) [flattening 34]
47. ! [X0] : (((~funny(X0) | kind(X0)) | (funny(X0) | creative(X0))) & ((~funny(X0) & ~creative(X0)) | (funny(X0) & ~kind(X0)))) [nnf transformation 5]
48. ! [X0] : ((~funny(X0) | kind(X0) | funny(X0) | creative(X0)) & ((~funny(X0) & ~creative(X0)) | (funny(X0) & ~kind(X0)))) [flattening 47]
109. ~funny(X0) | ~kind(X0) [cnf transformation 48]
112. ~funny(susan) | kind(susan) | ~funny(susan) [cnf transformation 35]
170. funny(susan) [cnf transformation 25]
171. ~funny(susan) | kind(susan) [duplicate literal removal 112]
195. ~funny(susan) [subsumption resolution 171,109]
355. $false [subsumption resolution 170,195]
% SZS output end Proof for 8099613157451640571315827
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not happy is kind and vice versa.
If someone is not old or humble then someone is kind.
Everyone who is both not tall and not kind is either not kind or rich.
Everyone who is both not old and not generous is both quiet and rich.
If paul is not generous then lucy is kind.
If paul is both humble and not strong then someone is tall and vice versa.
Everyone who is both not kind and not curious is kind and vice versa.
If mary is funny or rich then john is either not strong or not quiet and vice versa.
If someone is both not brave and tall then paul is not strong and vice versa.
Everyone who is not rich is both not kind and not quiet and vice versa.
If alice is both not rich and not creative then fred is not strong and vice versa.
If lucy is not wise then lucy is both generous and funny.
Everyone who is not rich or not creative is funny and vice versa.
Everyone who is not rich is either not tall or not patient.
If mary is either strong or calm then paul is not humble.
If john is both not quiet and not rich then someone is either not wise or brave.
Someone is not wise or tall.
Someone is not brave.
Susan is not generous.
Alice is not kind or calm.
Someone is either kind or not tall. | Mary is strong. | neutral | (![X]:((creative(X)|~happy(X))<=>kind(X)))&
((?[X]:((~old(X)|humble(X))))=>(?[X]:(kind(X))))&
(![X]:((~tall(X)&~kind(X))=>(~kind(X)<~>rich(X))))&
(![X]:((~old(X)&~generous(X))=>(quiet(X)&rich(X))))&
((~generous(paul))=>(kind(lucy)))&
(((humble(paul)&~strong(paul)))<=>(?[X]:(tall(X))))&
(![X]:((~kind(X)&~curious(X))<=>kind(X)))&
(((funny(mary)|rich(mary)))<=>((~strong(john)<~>~quiet(john))))&
((?[X]:((~brave(X)&tall(X))))<=>(~strong(paul)))&
(![X]:(~rich(X)<=>(~kind(X)&~quiet(X))))&
(((~rich(alice)&~creative(alice)))<=>(~strong(fred)))&
((~wise(lucy))=>((generous(lucy)&funny(lucy))))&
(![X]:((~rich(X)|~creative(X))<=>funny(X)))&
(![X]:(~rich(X)=>(~tall(X)<~>~patient(X))))&
(((strong(mary)<~>calm(mary)))=>(~humble(paul)))&
(((~quiet(john)&~rich(john)))=>(?[X]:((~wise(X)<~>brave(X)))))&
(?[X]:((~wise(X)|tall(X))))&
(?[X]:(~brave(X)))&
(~generous(susan))&
((~kind(alice)|calm(alice)))&
(?[X]:((kind(X)<~>~tall(X)))) | strong(mary) | [] | null | 0 |
If someone is brave then mary is both not generous and old and vice versa. Everyone who is either tall or curious is either happy or not calm. Everyone who is both not kind and not creative is both not generous and not old. Everyone who is not brave is either not happy or not brave. If paul is rich then paul is not wise or not generous and vice versa. Everyone who is not kind is happy and vice versa. If john is both wise and not calm then someone is patient or not brave. Everyone who is generous is both not humble and not happy. Everyone who is tall or not brave is both tall and not curious. If someone is either creative or not humble then someone is not happy or old and vice versa. Everyone who is both not generous and humble is both happy and brave. Everyone who is either not generous or not old is both not kind and not curious and vice versa. If someone is both not happy and not calm then someone is either calm or rich and vice versa. Everyone who is not brave is strong. Everyone who is tall is both not wise and not funny. Everyone who is either not humble or old is both not rich and not old. Someone is creative. Fred is not calm or not humble. Lucy is either kind or not quiet. Someone is not happy or tall. Someone is curious or not rich. Someone is brave. Fred is both not rich and not quiet. | Mary is not humble. | entailment | ((?[X]:(brave(X)))<=>((~generous(mary)&old(mary))))&
(![X]:((tall(X)<~>curious(X))=>(happy(X)<~>~calm(X))))&
(![X]:((~kind(X)&~creative(X))=>(~generous(X)&~old(X))))&
(![X]:(~brave(X)=>(~happy(X)<~>~brave(X))))&
((rich(paul))<=>((~wise(paul)|~generous(paul))))&
(![X]:(~kind(X)<=>happy(X)))&
(((wise(john)&~calm(john)))=>(?[X]:((patient(X)|~brave(X)))))&
(![X]:(generous(X)=>(~humble(X)&~happy(X))))&
(![X]:((tall(X)|~brave(X))=>(tall(X)&~curious(X))))&
((?[X]:((creative(X)<~>~humble(X))))<=>(?[X]:((~happy(X)|old(X)))))&
(![X]:((~generous(X)&humble(X))=>(happy(X)&brave(X))))&
(![X]:((~generous(X)<~>~old(X))<=>(~kind(X)&~curious(X))))&
((?[X]:((~happy(X)&~calm(X))))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:(~brave(X)=>strong(X)))&
(![X]:(tall(X)=>(~wise(X)&~funny(X))))&
(![X]:((~humble(X)<~>old(X))=>(~rich(X)&~old(X))))&
(?[X]:(creative(X)))&
((~calm(fred)|~humble(fred)))&
((kind(lucy)<~>~quiet(lucy)))&
(?[X]:((~happy(X)|tall(X))))&
(?[X]:((curious(X)|~rich(X))))&
(?[X]:(brave(X)))&
((~rich(fred)&~quiet(fred))) | ~humble(mary) | [
"p0",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 9128516300951365277235374
% SZS output start Proof for 9128516300951365277235374
1. ? [X0] : brave(X0) <=> (old(mary) & ~generous(mary)) [input p0]
16. ! [X0] : ((~humble(X0) <~> old(X0)) => (~old(X0) & ~rich(X0))) [input p15]
22. ? [X0] : brave(X0) [input p21]
24. humble(mary) [input hypothesis]
39. ! [X0] : ((~old(X0) & ~rich(X0)) | (~humble(X0) <=> old(X0))) [ennf transformation 16]
40. (? [X0] : brave(X0) | (~old(mary) | generous(mary))) & ((old(mary) & ~generous(mary)) | ! [X0] : ~brave(X0)) [nnf transformation 1]
41. (? [X0] : brave(X0) | ~old(mary) | generous(mary)) & ((old(mary) & ~generous(mary)) | ! [X0] : ~brave(X0)) [flattening 40]
42. (? [X0] : brave(X0) | ~old(mary) | generous(mary)) & ((old(mary) & ~generous(mary)) | ! [X1] : ~brave(X1)) [rectify 41]
43. ? [X0] : brave(X0) => brave(sK0) [choice axiom]
44. (brave(sK0) | ~old(mary) | generous(mary)) & ((old(mary) & ~generous(mary)) | ! [X1] : ~brave(X1)) [skolemisation 42,43]
62. ! [X0] : ((~old(X0) & ~rich(X0)) | ((~humble(X0) | ~old(X0)) & (old(X0) | humble(X0)))) [nnf transformation 39]
70. ? [X0] : brave(X0) => brave(sK8) [choice axiom]
71. brave(sK8) [skolemisation 22,70]
73. old(mary) | ~brave(X1) [cnf transformation 44]
118. ~old(X0) | ~humble(X0) | ~old(X0) [cnf transformation 62]
125. brave(sK8) [cnf transformation 71]
128. humble(mary) [cnf transformation 24]
129. ~humble(X0) | ~old(X0) [duplicate literal removal 118]
136. 2 <=> old(mary) [avatar definition]
145. 4 <=> ! [X1] : ~brave(X1) [avatar definition]
146. ~brave(X1) <- (4) [avatar component clause 145]
147. 4 | 2 [avatar split clause 73,136,145]
272. ~old(mary) [resolution 129,128]
275. ~2 [avatar split clause 272,136]
276. $false <- (4) [resolution 146,125]
279. ~4 [avatar contradiction clause 276]
280. $false [avatar sat refutation 147,275,279]
% SZS output end Proof for 9128516300951365277235374
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If john is both not kind and not creative then mary is kind or generous. Everyone who is either humble or quiet is brave or not brave and vice versa. Everyone who is not tall or not generous is both not tall and funny and vice versa. If fred is either not rich or not humble then john is both not calm and not curious and vice versa. If mary is both not creative and patient then someone is both not funny and not humble. Everyone who is patient is both not humble and tall. If someone is both old and not kind then fred is happy. If john is rich or not wise then someone is either not curious or generous and vice versa. Everyone who is not wise or not old is not kind or not tall. Everyone who is rich is both funny and curious. If mary is both kind and rich then john is both kind and not curious. If someone is either creative or not kind then lucy is either not humble or tall. Everyone who is funny or not tall is both quiet and patient and vice versa. Everyone who is either not humble or not creative is not strong or kind. Everyone who is both not generous and wise is curious and vice versa. If someone is tall or creative then someone is either not brave or not quiet. Paul is not rich or brave. Mary is tall. Someone is calm or humble. Someone is not brave. John is strong. Someone is either happy or funny. Someone is not kind or not old. Paul is either brave or funny. | Paul is not tall. | contradiction | (((~kind(john)&~creative(john)))=>((kind(mary)|generous(mary))))&
(![X]:((humble(X)<~>quiet(X))<=>(brave(X)|~brave(X))))&
(![X]:((~tall(X)|~generous(X))<=>(~tall(X)&funny(X))))&
(((~rich(fred)<~>~humble(fred)))<=>((~calm(john)&~curious(john))))&
(((~creative(mary)&patient(mary)))=>(?[X]:((~funny(X)&~humble(X)))))&
(![X]:(patient(X)=>(~humble(X)&tall(X))))&
((?[X]:((old(X)&~kind(X))))=>(happy(fred)))&
(((rich(john)|~wise(john)))<=>(?[X]:((~curious(X)<~>generous(X)))))&
(![X]:((~wise(X)|~old(X))=>(~kind(X)|~tall(X))))&
(![X]:(rich(X)=>(funny(X)&curious(X))))&
(((kind(mary)&rich(mary)))=>((kind(john)&~curious(john))))&
((?[X]:((creative(X)<~>~kind(X))))=>((~humble(lucy)<~>tall(lucy))))&
(![X]:((funny(X)|~tall(X))<=>(quiet(X)&patient(X))))&
(![X]:((~humble(X)<~>~creative(X))=>(~strong(X)|kind(X))))&
(![X]:((~generous(X)&wise(X))<=>curious(X)))&
((?[X]:((tall(X)|creative(X))))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
((~rich(paul)|brave(paul)))&
(tall(mary))&
(?[X]:((calm(X)|humble(X))))&
(?[X]:(~brave(X)))&
(strong(john))&
(?[X]:((happy(X)<~>funny(X))))&
(?[X]:((~kind(X)|~old(X))))&
((brave(paul)<~>funny(paul))) | ~tall(paul) | [
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 389695413579808803959505
% SZS output start Proof for 389695413579808803959505
6. ! [X0] : (patient(X0) => (tall(X0) & ~humble(X0))) [input p5]
13. ! [X0] : ((~tall(X0) | funny(X0)) <=> (patient(X0) & quiet(X0))) [input p12]
25. ~tall(paul) [input hypothesis]
31. ! [X0] : ((tall(X0) & ~humble(X0)) | ~patient(X0)) [ennf transformation 6]
56. ! [X0] : (((~tall(X0) | funny(X0)) | (~patient(X0) | ~quiet(X0))) & ((patient(X0) & quiet(X0)) | (tall(X0) & ~funny(X0)))) [nnf transformation 13]
57. ! [X0] : ((~tall(X0) | funny(X0) | ~patient(X0) | ~quiet(X0)) & ((patient(X0) & quiet(X0)) | (tall(X0) & ~funny(X0)))) [flattening 56]
96. tall(X0) | ~patient(X0) [cnf transformation 31]
117. patient(X0) | tall(X0) [cnf transformation 57]
138. ~tall(paul) [cnf transformation 25]
259. tall(X0) [subsumption resolution 117,96]
321. $false [subsumption resolution 138,259]
% SZS output end Proof for 389695413579808803959505
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is either curious or kind and vice versa.
Everyone who is both not funny and rich is both not calm and humble.
Everyone who is rich is funny or not curious.
If someone is both brave and patient then susan is happy and vice versa.
Everyone who is both quiet and not humble is brave or curious.
Everyone who is both not curious and not tall is either not tall or not happy and vice versa.
If someone is patient or kind then fred is either not quiet or not kind and vice versa.
Everyone who is not generous or not wise is humble or brave.
If paul is brave or wise then paul is not generous or not curious and vice versa.
If someone is creative then susan is tall.
Everyone who is both not strong and funny is either not humble or not calm and vice versa.
Everyone who is not rich or not happy is not old.
Everyone who is both not strong and not humble is not generous and vice versa.
Everyone who is not strong or patient is kind or not quiet.
If john is funny or not tall then someone is either brave or not wise and vice versa.
Everyone who is either not humble or rich is both not kind and not wise and vice versa.
Susan is both not strong and kind.
Susan is rich.
Someone is either rich or not strong.
Someone is both quiet and not kind.
John is humble or not tall.
Paul is both not rich and humble.
Someone is either rich or not curious. | Susan is not humble. | entailment | (![X]:(~creative(X)<=>(curious(X)<~>kind(X))))&
(![X]:((~funny(X)&rich(X))=>(~calm(X)&humble(X))))&
(![X]:(rich(X)=>(funny(X)|~curious(X))))&
((?[X]:((brave(X)&patient(X))))<=>(happy(susan)))&
(![X]:((quiet(X)&~humble(X))=>(brave(X)|curious(X))))&
(![X]:((~curious(X)&~tall(X))<=>(~tall(X)<~>~happy(X))))&
((?[X]:((patient(X)|kind(X))))<=>((~quiet(fred)<~>~kind(fred))))&
(![X]:((~generous(X)|~wise(X))=>(humble(X)|brave(X))))&
(((brave(paul)|wise(paul)))<=>((~generous(paul)|~curious(paul))))&
((?[X]:(creative(X)))=>(tall(susan)))&
(![X]:((~strong(X)&funny(X))<=>(~humble(X)<~>~calm(X))))&
(![X]:((~rich(X)|~happy(X))=>~old(X)))&
(![X]:((~strong(X)&~humble(X))<=>~generous(X)))&
(![X]:((~strong(X)|patient(X))=>(kind(X)|~quiet(X))))&
(((funny(john)|~tall(john)))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(![X]:((~humble(X)<~>rich(X))<=>(~kind(X)&~wise(X))))&
((~strong(susan)&kind(susan)))&
(rich(susan))&
(?[X]:((rich(X)<~>~strong(X))))&
(?[X]:((quiet(X)&~kind(X))))&
((humble(john)|~tall(john)))&
((~rich(paul)&humble(paul)))&
(?[X]:((rich(X)<~>~curious(X)))) | ~humble(susan) | [
"p15",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2775921823843887092928728
% SZS output start Proof for 2775921823843887092928728
16. ! [X0] : ((~humble(X0) <~> rich(X0)) <=> (~wise(X0) & ~kind(X0))) [input p15]
17. kind(susan) & ~strong(susan) [input p16]
18. rich(susan) [input p17]
24. humble(susan) [input hypothesis]
61. ! [X0] : ((((~rich(X0) | humble(X0)) & (rich(X0) | ~humble(X0))) | (wise(X0) | kind(X0))) & ((~wise(X0) & ~kind(X0)) | ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0))))) [nnf transformation 16]
62. ! [X0] : ((((~rich(X0) | humble(X0)) & (rich(X0) | ~humble(X0))) | wise(X0) | kind(X0)) & ((~wise(X0) & ~kind(X0)) | ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0))))) [flattening 61]
117. ~humble(X0) | ~kind(X0) | ~rich(X0) [cnf transformation 62]
123. kind(susan) [cnf transformation 17]
124. rich(susan) [cnf transformation 18]
134. humble(susan) [cnf transformation 24]
365. ~kind(susan) | ~rich(susan) [resolution 117,134]
367. ~rich(susan) [subsumption resolution 365,123]
368. $false [subsumption resolution 367,124]
% SZS output end Proof for 2775921823843887092928728
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich then alice is generous or not tall. If someone is either quiet or not strong then paul is either not patient or not quiet and vice versa. If fred is not old or not tall then someone is either old or not calm and vice versa. Everyone who is not humble or quiet is not quiet and vice versa. If someone is either not curious or old then someone is not funny and vice versa. Everyone who is either not kind or old is not funny. If someone is patient then susan is quiet and vice versa. Everyone who is either not creative or not old is curious or patient and vice versa. Everyone who is either not happy or curious is patient or not strong. If paul is either wise or funny then someone is funny and vice versa. Everyone who is not calm or not happy is not funny and vice versa. If someone is generous or not strong then paul is both not quiet and creative and vice versa. If someone is not tall or not rich then paul is both not tall and not patient and vice versa. If susan is not patient or patient then someone is happy. If mary is both humble and rich then someone is funny or not strong. If john is quiet or not patient then someone is both generous and old. Mary is tall. Susan is either curious or rich. Someone is either not wise or not funny. Fred is both brave and old. Mary is either patient or not patient. Someone is not old or not funny. Susan is old. Mary is old or not rich. | Fred is humble. | contradiction | ((?[X]:(~rich(X)))=>((generous(alice)|~tall(alice))))&
((?[X]:((quiet(X)<~>~strong(X))))<=>((~patient(paul)<~>~quiet(paul))))&
(((~old(fred)|~tall(fred)))<=>(?[X]:((old(X)<~>~calm(X)))))&
(![X]:((~humble(X)|quiet(X))<=>~quiet(X)))&
((?[X]:((~curious(X)<~>old(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~kind(X)<~>old(X))=>~funny(X)))&
((?[X]:(patient(X)))<=>(quiet(susan)))&
(![X]:((~creative(X)<~>~old(X))<=>(curious(X)|patient(X))))&
(![X]:((~happy(X)<~>curious(X))=>(patient(X)|~strong(X))))&
(((wise(paul)<~>funny(paul)))<=>(?[X]:(funny(X))))&
(![X]:((~calm(X)|~happy(X))<=>~funny(X)))&
((?[X]:((generous(X)|~strong(X))))<=>((~quiet(paul)&creative(paul))))&
((?[X]:((~tall(X)|~rich(X))))<=>((~tall(paul)&~patient(paul))))&
(((~patient(susan)|patient(susan)))=>(?[X]:(happy(X))))&
(((humble(mary)&rich(mary)))=>(?[X]:((funny(X)|~strong(X)))))&
(((quiet(john)|~patient(john)))=>(?[X]:((generous(X)&old(X)))))&
(tall(mary))&
((curious(susan)<~>rich(susan)))&
(?[X]:((~wise(X)<~>~funny(X))))&
((brave(fred)&old(fred)))&
((patient(mary)<~>~patient(mary)))&
(?[X]:((~old(X)|~funny(X))))&
(old(susan))&
((old(mary)|~rich(mary))) | humble(fred) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 2912963889966332925898579
% SZS output start Proof for 2912963889966332925898579
4. ! [X0] : ((quiet(X0) | ~humble(X0)) <=> ~quiet(X0)) [input p3]
25. humble(fred) [input hypothesis]
46. ! [X0] : (((quiet(X0) | ~humble(X0)) | quiet(X0)) & (~quiet(X0) | (~quiet(X0) & humble(X0)))) [nnf transformation 4]
47. ! [X0] : ((quiet(X0) | ~humble(X0) | quiet(X0)) & (~quiet(X0) | (~quiet(X0) & humble(X0)))) [flattening 46]
106. ~quiet(X0) | ~quiet(X0) [cnf transformation 47]
107. quiet(X0) | ~humble(X0) | quiet(X0) [cnf transformation 47]
159. humble(fred) [cnf transformation 25]
160. ~quiet(X0) [duplicate literal removal 106]
161. ~humble(X0) | quiet(X0) [duplicate literal removal 107]
387. quiet(fred) [resolution 161,159]
388. $false [subsumption resolution 387,160]
% SZS output end Proof for 2912963889966332925898579
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either wise or brave then john is not calm.
Everyone who is patient is generous or rich and vice versa.
Everyone who is both not rich and rich is not tall and vice versa.
Everyone who is kind is either humble or not rich and vice versa.
If someone is tall then paul is both not curious and not strong.
Everyone who is brave is either not brave or patient.
Everyone who is both not brave and kind is patient and vice versa.
Everyone who is both funny and humble is both not patient and not humble.
Everyone who is both old and not generous is both not creative and curious.
Everyone who is humble or strong is both not creative and not funny.
Everyone who is wise or not generous is both not rich and not patient.
If john is brave or not funny then someone is either rich or not quiet and vice versa.
Everyone who is either wise or not wise is either not rich or funny and vice versa.
Everyone who is both not old and old is not kind and vice versa.
Everyone who is either not calm or quiet is both not calm and not old.
Someone is happy.
Alice is not humble or not creative.
Fred is tall or generous.
Someone is not tall or not happy.
Lucy is either curious or rich.
Someone is either not humble or funny.
Someone is either not rich or curious. | Lucy is not humble. | entailment | (((wise(john)<~>brave(john)))=>(~calm(john)))&
(![X]:(patient(X)<=>(generous(X)|rich(X))))&
(![X]:((~rich(X)&rich(X))<=>~tall(X)))&
(![X]:(kind(X)<=>(humble(X)<~>~rich(X))))&
((?[X]:(tall(X)))=>((~curious(paul)&~strong(paul))))&
(![X]:(brave(X)=>(~brave(X)<~>patient(X))))&
(![X]:((~brave(X)&kind(X))<=>patient(X)))&
(![X]:((funny(X)&humble(X))=>(~patient(X)&~humble(X))))&
(![X]:((old(X)&~generous(X))=>(~creative(X)&curious(X))))&
(![X]:((humble(X)|strong(X))=>(~creative(X)&~funny(X))))&
(![X]:((wise(X)|~generous(X))=>(~rich(X)&~patient(X))))&
(((brave(john)|~funny(john)))<=>(?[X]:((rich(X)<~>~quiet(X)))))&
(![X]:((wise(X)<~>~wise(X))<=>(~rich(X)<~>funny(X))))&
(![X]:((~old(X)&old(X))<=>~kind(X)))&
(![X]:((~calm(X)<~>quiet(X))=>(~calm(X)&~old(X))))&
(?[X]:(happy(X)))&
((~humble(alice)|~creative(alice)))&
((tall(fred)|generous(fred)))&
(?[X]:((~tall(X)|~happy(X))))&
((curious(lucy)<~>rich(lucy)))&
(?[X]:((~humble(X)<~>funny(X))))&
(?[X]:((~rich(X)<~>curious(X)))) | ~humble(lucy) | [
"p3",
"p7",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4209177177390676189625605
% SZS output start Proof for 4209177177390676189625605
4. ! [X0] : (kind(X0) <=> (humble(X0) <~> ~rich(X0))) [input p3]
8. ! [X0] : ((humble(X0) & funny(X0)) => (~humble(X0) & ~patient(X0))) [input p7]
11. ! [X0] : ((~generous(X0) | wise(X0)) => (~patient(X0) & ~rich(X0))) [input p10]
13. ! [X0] : ((wise(X0) <~> ~wise(X0)) <=> (~rich(X0) <~> funny(X0))) [input p12]
14. ! [X0] : ((old(X0) & ~old(X0)) <=> ~kind(X0)) [input p13]
23. humble(lucy) [input hypothesis]
32. ! [X0] : ((~humble(X0) & ~patient(X0)) | (~humble(X0) | ~funny(X0))) [ennf transformation 8]
33. ! [X0] : ((~humble(X0) & ~patient(X0)) | ~humble(X0) | ~funny(X0)) [flattening 32]
37. ! [X0] : ((~patient(X0) & ~rich(X0)) | (generous(X0) & ~wise(X0))) [ennf transformation 11]
44. ! [X0] : ((kind(X0) | ((humble(X0) | rich(X0)) & (~rich(X0) | ~humble(X0)))) & (((rich(X0) | ~humble(X0)) & (~rich(X0) | humble(X0))) | ~kind(X0))) [nnf transformation 4]
53. ! [X0] : ((((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0)))) & (((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0))))) [nnf transformation 13]
54. ! [X0] : (((old(X0) & ~old(X0)) | kind(X0)) & (~kind(X0) | (~old(X0) | old(X0)))) [nnf transformation 14]
55. ! [X0] : (((old(X0) & ~old(X0)) | kind(X0)) & (~kind(X0) | ~old(X0) | old(X0))) [flattening 54]
77. ~humble(X0) | rich(X0) | ~kind(X0) [cnf transformation 44]
87. ~humble(X0) | ~humble(X0) | ~funny(X0) [cnf transformation 33]
90. ~rich(X0) | ~wise(X0) [cnf transformation 37]
101. funny(X0) | ~rich(X0) | wise(X0) | wise(X0) [cnf transformation 53]
109. ~old(X0) | kind(X0) [cnf transformation 55]
110. old(X0) | kind(X0) [cnf transformation 55]
124. humble(lucy) [cnf transformation 23]
127. funny(X0) | ~rich(X0) | wise(X0) [duplicate literal removal 101]
130. ~funny(X0) | ~humble(X0) [duplicate literal removal 87]
175. ~rich(X0) | funny(X0) [subsumption resolution 127,90]
176. kind(X0) [subsumption resolution 109,110]
183. 10 <=> rich(lucy) [avatar definition]
184. rich(lucy) <- (10) [avatar component clause 183]
207. rich(lucy) | ~kind(lucy) [resolution 77,124]
211. rich(lucy) [subsumption resolution 207,176]
212. 10 [avatar split clause 211,183]
213. funny(lucy) <- (10) [resolution 184,175]
218. ~humble(lucy) <- (10) [resolution 213,130]
219. $false <- (10) [subsumption resolution 218,124]
220. ~10 [avatar contradiction clause 219]
221. $false [avatar sat refutation 212,220]
% SZS output end Proof for 4209177177390676189625605
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both funny and not happy then paul is quiet.
Everyone who is not wise or not creative is both old and not creative and vice versa.
If someone is both not patient and calm then john is both rich and not generous.
If someone is either not patient or creative then someone is not funny.
Everyone who is both not brave and kind is funny.
If susan is both curious and happy then alice is either quiet or not old.
Everyone who is humble or kind is generous or not patient.
Everyone who is not humble is both kind and not rich and vice versa.
Everyone who is not patient or not creative is either brave or not funny.
If someone is either not tall or not strong then someone is both not wise and not old.
Everyone who is not funny or curious is calm.
Everyone who is not brave is not strong.
Everyone who is either tall or kind is generous or humble and vice versa.
If someone is both patient and not funny then someone is happy and vice versa.
Everyone who is not old or humble is both not humble and creative and vice versa.
Everyone who is old or calm is not kind.
Fred is generous or curious.
Someone is either curious or tall.
Alice is either not curious or old.
Fred is funny.
John is wise.
Fred is kind or not quiet.
Someone is strong. | John is brave. | entailment | ((?[X]:((funny(X)&~happy(X))))=>(quiet(paul)))&
(![X]:((~wise(X)|~creative(X))<=>(old(X)&~creative(X))))&
((?[X]:((~patient(X)&calm(X))))=>((rich(john)&~generous(john))))&
((?[X]:((~patient(X)<~>creative(X))))=>(?[X]:(~funny(X))))&
(![X]:((~brave(X)&kind(X))=>funny(X)))&
(((curious(susan)&happy(susan)))=>((quiet(alice)<~>~old(alice))))&
(![X]:((humble(X)|kind(X))=>(generous(X)|~patient(X))))&
(![X]:(~humble(X)<=>(kind(X)&~rich(X))))&
(![X]:((~patient(X)|~creative(X))=>(brave(X)<~>~funny(X))))&
((?[X]:((~tall(X)<~>~strong(X))))=>(?[X]:((~wise(X)&~old(X)))))&
(![X]:((~funny(X)|curious(X))=>calm(X)))&
(![X]:(~brave(X)=>~strong(X)))&
(![X]:((tall(X)<~>kind(X))<=>(generous(X)|humble(X))))&
((?[X]:((patient(X)&~funny(X))))<=>(?[X]:(happy(X))))&
(![X]:((~old(X)|humble(X))<=>(~humble(X)&creative(X))))&
(![X]:((old(X)|calm(X))=>~kind(X)))&
((generous(fred)|curious(fred)))&
(?[X]:((curious(X)<~>tall(X))))&
((~curious(alice)<~>old(alice)))&
(funny(fred))&
(wise(john))&
((kind(fred)|~quiet(fred)))&
(?[X]:(strong(X))) | brave(john) | [
"p1",
"p3",
"p7",
"p8",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7049792593390184867447789
% SZS output start Proof for 7049792593390184867447789
2. ! [X0] : ((~creative(X0) | ~wise(X0)) <=> (~creative(X0) & old(X0))) [input p1]
4. ? [X0] : (~patient(X0) <~> creative(X0)) => ? [X0] : ~funny(X0) [input p3]
8. ! [X0] : (~humble(X0) <=> (~rich(X0) & kind(X0))) [input p7]
9. ! [X0] : ((~creative(X0) | ~patient(X0)) => (brave(X0) <~> ~funny(X0))) [input p8]
11. ! [X0] : ((curious(X0) | ~funny(X0)) => calm(X0)) [input p10]
15. ! [X0] : ((humble(X0) | ~old(X0)) <=> (creative(X0) & ~humble(X0))) [input p14]
16. ! [X0] : ((calm(X0) | old(X0)) => ~kind(X0)) [input p15]
24. ~brave(john) [input hypothesis]
25. ? [X0] : (~patient(X0) <~> creative(X0)) => ? [X1] : ~funny(X1) [rectify 4]
30. ? [X1] : ~funny(X1) | ! [X0] : (~patient(X0) <=> creative(X0)) [ennf transformation 25]
37. ! [X0] : ((brave(X0) <~> ~funny(X0)) | (creative(X0) & patient(X0))) [ennf transformation 9]
39. ! [X0] : (calm(X0) | (~curious(X0) & funny(X0))) [ennf transformation 11]
41. ! [X0] : (~kind(X0) | (~calm(X0) & ~old(X0))) [ennf transformation 16]
42. ! [X0] : (((~creative(X0) | ~wise(X0)) | (creative(X0) | ~old(X0))) & ((~creative(X0) & old(X0)) | (creative(X0) & wise(X0)))) [nnf transformation 2]
43. ! [X0] : ((~creative(X0) | ~wise(X0) | creative(X0) | ~old(X0)) & ((~creative(X0) & old(X0)) | (creative(X0) & wise(X0)))) [flattening 42]
44. ? [X1] : ~funny(X1) | ! [X0] : ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0))) [nnf transformation 30]
45. ? [X0] : ~funny(X0) | ! [X1] : ((~patient(X1) | ~creative(X1)) & (creative(X1) | patient(X1))) [rectify 44]
46. ? [X0] : ~funny(X0) => ~funny(sK0) [choice axiom]
47. ~funny(sK0) | ! [X1] : ((~patient(X1) | ~creative(X1)) & (creative(X1) | patient(X1))) [skolemisation 45,46]
49. ! [X0] : ((~humble(X0) | (rich(X0) | ~kind(X0))) & ((~rich(X0) & kind(X0)) | humble(X0))) [nnf transformation 8]
50. ! [X0] : ((~humble(X0) | rich(X0) | ~kind(X0)) & ((~rich(X0) & kind(X0)) | humble(X0))) [flattening 49]
51. ! [X0] : (((funny(X0) | ~brave(X0)) & (~funny(X0) | brave(X0))) | (creative(X0) & patient(X0))) [nnf transformation 37]
63. ! [X0] : (((humble(X0) | ~old(X0)) | (~creative(X0) | humble(X0))) & ((creative(X0) & ~humble(X0)) | (~humble(X0) & old(X0)))) [nnf transformation 15]
64. ! [X0] : ((humble(X0) | ~old(X0) | ~creative(X0) | humble(X0)) & ((creative(X0) & ~humble(X0)) | (~humble(X0) & old(X0)))) [flattening 63]
73. old(X0) | creative(X0) [cnf transformation 43]
80. ~funny(sK0) | ~patient(X1) | ~creative(X1) [cnf transformation 47]
86. humble(X0) | kind(X0) [cnf transformation 50]
89. ~funny(X0) | brave(X0) | patient(X0) [cnf transformation 51]
97. calm(X0) | funny(X0) [cnf transformation 39]
110. ~humble(X0) | ~humble(X0) [cnf transformation 64]
114. ~kind(X0) | ~old(X0) [cnf transformation 41]
115. ~kind(X0) | ~calm(X0) [cnf transformation 41]
125. ~brave(john) [cnf transformation 24]
126. ~humble(X0) [duplicate literal removal 110]
150. 6 <=> ! [X1] : (~patient(X1) | ~creative(X1)) [avatar definition]
151. ~patient(X1) | ~creative(X1) <- (6) [avatar component clause 150]
153. 7 <=> funny(sK0) [avatar definition]
155. ~funny(sK0) <- (~7) [avatar component clause 153]
156. 6 | ~7 [avatar split clause 80,153,150]
260. kind(X0) [resolution 86,126]
264. ~old(X0) [resolution 114,260]
265. ~calm(X0) [resolution 115,260]
266. creative(X0) [resolution 264,73]
278. ~patient(X1) <- (6) [subsumption resolution 151,266]
279. funny(X0) [resolution 265,97]
295. brave(X0) | patient(X0) [resolution 89,279]
298. brave(X0) <- (6) [subsumption resolution 295,278]
306. $false <- (6) [resolution 298,125]
308. ~6 [avatar contradiction clause 306]
311. $false <- (~7) [subsumption resolution 155,279]
312. 7 [avatar contradiction clause 311]
313. $false [avatar sat refutation 156,308,312]
% SZS output end Proof for 7049792593390184867447789
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and not humble is funny or humble and vice versa. If someone is not quiet or generous then fred is both not strong and quiet and vice versa. If fred is both kind and not rich then alice is either humble or strong and vice versa. If alice is both strong and tall then someone is not calm or quiet. Everyone who is either funny or not humble is quiet or not curious and vice versa. Everyone who is either not rich or not kind is rich or not patient. If someone is both rich and not strong then alice is either not patient or strong. If alice is not brave or not calm then fred is both not wise and brave. Everyone who is not generous is not rich and vice versa. Everyone who is humble or not strong is calm or not kind. Everyone who is not rich is strong or not kind. If john is either tall or strong then someone is tall or strong. Everyone who is not tall or patient is humble or not creative and vice versa. If someone is either strong or humble then lucy is both not creative and not brave. If fred is calm then someone is both not humble and not calm. Fred is both not old and not creative. Someone is both not brave and old. Someone is both not tall and not patient. Alice is both not brave and rich. Paul is either calm or generous. Someone is not tall. Someone is both patient and not creative. Someone is either not creative or creative. | Alice is strong. | contradiction | (![X]:((~quiet(X)&~humble(X))<=>(funny(X)|humble(X))))&
((?[X]:((~quiet(X)|generous(X))))<=>((~strong(fred)&quiet(fred))))&
(((kind(fred)&~rich(fred)))<=>((humble(alice)<~>strong(alice))))&
(((strong(alice)&tall(alice)))=>(?[X]:((~calm(X)|quiet(X)))))&
(![X]:((funny(X)<~>~humble(X))<=>(quiet(X)|~curious(X))))&
(![X]:((~rich(X)<~>~kind(X))=>(rich(X)|~patient(X))))&
((?[X]:((rich(X)&~strong(X))))=>((~patient(alice)<~>strong(alice))))&
(((~brave(alice)|~calm(alice)))=>((~wise(fred)&brave(fred))))&
(![X]:(~generous(X)<=>~rich(X)))&
(![X]:((humble(X)|~strong(X))=>(calm(X)|~kind(X))))&
(![X]:(~rich(X)=>(strong(X)|~kind(X))))&
(((tall(john)<~>strong(john)))=>(?[X]:((tall(X)|strong(X)))))&
(![X]:((~tall(X)|patient(X))<=>(humble(X)|~creative(X))))&
((?[X]:((strong(X)<~>humble(X))))=>((~creative(lucy)&~brave(lucy))))&
((calm(fred))=>(?[X]:((~humble(X)&~calm(X)))))&
((~old(fred)&~creative(fred)))&
(?[X]:((~brave(X)&old(X))))&
(?[X]:((~tall(X)&~patient(X))))&
((~brave(alice)&rich(alice)))&
((calm(paul)<~>generous(paul)))&
(?[X]:(~tall(X)))&
(?[X]:((patient(X)&~creative(X))))&
(?[X]:((~creative(X)<~>creative(X)))) | strong(alice) | [
"p0",
"p1",
"p2",
"p8",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7417076372349330988853143
% SZS output start Proof for 7417076372349330988853143
1. ! [X0] : ((~humble(X0) & ~quiet(X0)) <=> (humble(X0) | funny(X0))) [input p0]
2. ? [X0] : (generous(X0) | ~quiet(X0)) <=> (quiet(fred) & ~strong(fred)) [input p1]
3. (~rich(fred) & kind(fred)) <=> (humble(alice) <~> strong(alice)) [input p2]
9. ! [X0] : (~generous(X0) <=> ~rich(X0)) [input p8]
11. ! [X0] : (~rich(X0) => (~kind(X0) | strong(X0))) [input p10]
19. rich(alice) & ~brave(alice) [input p18]
24. strong(alice) [input hypothesis]
34. ! [X0] : ((~kind(X0) | strong(X0)) | rich(X0)) [ennf transformation 11]
35. ! [X0] : (~kind(X0) | strong(X0) | rich(X0)) [flattening 34]
39. ! [X0] : (((~humble(X0) & ~quiet(X0)) | (~humble(X0) & ~funny(X0))) & ((humble(X0) | funny(X0)) | (humble(X0) | quiet(X0)))) [nnf transformation 1]
40. ! [X0] : (((~humble(X0) & ~quiet(X0)) | (~humble(X0) & ~funny(X0))) & (humble(X0) | funny(X0) | humble(X0) | quiet(X0))) [flattening 39]
41. (? [X0] : (generous(X0) | ~quiet(X0)) | (~quiet(fred) | strong(fred))) & ((quiet(fred) & ~strong(fred)) | ! [X0] : (~generous(X0) & quiet(X0))) [nnf transformation 2]
42. (? [X0] : (generous(X0) | ~quiet(X0)) | ~quiet(fred) | strong(fred)) & ((quiet(fred) & ~strong(fred)) | ! [X0] : (~generous(X0) & quiet(X0))) [flattening 41]
43. (? [X0] : (generous(X0) | ~quiet(X0)) | ~quiet(fred) | strong(fred)) & ((quiet(fred) & ~strong(fred)) | ! [X1] : (~generous(X1) & quiet(X1))) [rectify 42]
44. ? [X0] : (generous(X0) | ~quiet(X0)) => (generous(sK0) | ~quiet(sK0)) [choice axiom]
45. ((generous(sK0) | ~quiet(sK0)) | ~quiet(fred) | strong(fred)) & ((quiet(fred) & ~strong(fred)) | ! [X1] : (~generous(X1) & quiet(X1))) [skolemisation 43,44]
46. ((~rich(fred) & kind(fred)) | ((humble(alice) | ~strong(alice)) & (strong(alice) | ~humble(alice)))) & (((~strong(alice) | ~humble(alice)) & (strong(alice) | humble(alice))) | (rich(fred) | ~kind(fred))) [nnf transformation 3]
47. ((~rich(fred) & kind(fred)) | ((humble(alice) | ~strong(alice)) & (strong(alice) | ~humble(alice)))) & (((~strong(alice) | ~humble(alice)) & (strong(alice) | humble(alice))) | rich(fred) | ~kind(fred)) [flattening 46]
54. ! [X0] : ((~generous(X0) | rich(X0)) & (~rich(X0) | generous(X0))) [nnf transformation 9]
79. ~humble(X0) | ~humble(X0) [cnf transformation 40]
81. ~strong(fred) | ~generous(X1) [cnf transformation 45]
88. kind(fred) | humble(alice) | ~strong(alice) [cnf transformation 47]
90. ~rich(fred) | humble(alice) | ~strong(alice) [cnf transformation 47]
104. ~rich(X0) | generous(X0) [cnf transformation 54]
108. ~kind(X0) | strong(X0) | rich(X0) [cnf transformation 35]
128. rich(alice) [cnf transformation 19]
136. strong(alice) [cnf transformation 24]
139. ~humble(X0) [duplicate literal removal 79]
142. 1 <=> strong(fred) [avatar definition]
159. 5 <=> ! [X1] : ~generous(X1) [avatar definition]
160. ~generous(X1) <- (5) [avatar component clause 159]
166. 5 | ~1 [avatar split clause 81,142,159]
168. ~rich(fred) | ~strong(alice) [subsumption resolution 90,139]
170. 7 <=> strong(alice) [avatar definition]
174. 8 <=> rich(fred) [avatar definition]
176. ~rich(fred) <- (~8) [avatar component clause 174]
177. ~7 | ~8 [avatar split clause 168,174,170]
178. kind(fred) | ~strong(alice) [subsumption resolution 88,139]
180. 9 <=> kind(fred) [avatar definition]
182. kind(fred) <- (9) [avatar component clause 180]
183. ~7 | 9 [avatar split clause 178,180,170]
278. 7 [avatar split clause 136,170]
279. generous(alice) [resolution 104,128]
287. strong(fred) | rich(fred) <- (9) [resolution 108,182]
291. strong(fred) <- (~8, 9) [subsumption resolution 287,176]
292. 1 | 8 | ~9 [avatar split clause 291,180,174,142]
293. $false <- (5) [resolution 160,279]
294. ~5 [avatar contradiction clause 293]
295. $false [avatar sat refutation 166,177,183,278,292,294]
% SZS output end Proof for 7417076372349330988853143
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or not strong is creative or not creative and vice versa.
Everyone who is both not quiet and not wise is both rich and not funny and vice versa.
If alice is both curious and not happy then alice is not old or tall and vice versa.
If lucy is both calm and not creative then someone is both funny and old.
If mary is both not rich and creative then susan is not happy or not creative and vice versa.
If fred is curious or wise then someone is both happy and old.
If someone is strong then someone is both not patient and patient.
Everyone who is both not kind and creative is calm.
If someone is both patient and calm then lucy is brave or quiet.
If someone is both not creative and wise then mary is both wise and not old and vice versa.
Everyone who is not strong or not calm is curious or not strong and vice versa.
If susan is not generous then someone is not funny.
Everyone who is generous or not generous is both not brave and not wise and vice versa.
Everyone who is funny is both not strong and not kind and vice versa.
If someone is either happy or not old then paul is both not quiet and not kind.
Everyone who is kind or not strong is both not funny and not humble.
Someone is both not creative and not generous.
Fred is either patient or curious.
Someone is either rich or generous.
Someone is not creative or not funny.
Someone is both not humble and not curious. | Alice is not funny. | entailment | (![X]:((brave(X)|~strong(X))<=>(creative(X)|~creative(X))))&
(![X]:((~quiet(X)&~wise(X))<=>(rich(X)&~funny(X))))&
(((curious(alice)&~happy(alice)))<=>((~old(alice)|tall(alice))))&
(((calm(lucy)&~creative(lucy)))=>(?[X]:((funny(X)&old(X)))))&
(((~rich(mary)&creative(mary)))<=>((~happy(susan)|~creative(susan))))&
(((curious(fred)|wise(fred)))=>(?[X]:((happy(X)&old(X)))))&
((?[X]:(strong(X)))=>(?[X]:((~patient(X)&patient(X)))))&
(![X]:((~kind(X)&creative(X))=>calm(X)))&
((?[X]:((patient(X)&calm(X))))=>((brave(lucy)|quiet(lucy))))&
((?[X]:((~creative(X)&wise(X))))<=>((wise(mary)&~old(mary))))&
(![X]:((~strong(X)|~calm(X))<=>(curious(X)|~strong(X))))&
((~generous(susan))=>(?[X]:(~funny(X))))&
(![X]:((generous(X)|~generous(X))<=>(~brave(X)&~wise(X))))&
(![X]:(funny(X)<=>(~strong(X)&~kind(X))))&
((?[X]:((happy(X)<~>~old(X))))=>((~quiet(paul)&~kind(paul))))&
(![X]:((kind(X)|~strong(X))=>(~funny(X)&~humble(X))))&
(?[X]:((~creative(X)&~generous(X))))&
((patient(fred)<~>curious(fred)))&
(?[X]:((rich(X)<~>generous(X))))&
(?[X]:((~creative(X)|~funny(X))))&
(?[X]:((~humble(X)&~curious(X)))) | ~funny(alice) | [
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 650898738438330351234358
% SZS output start Proof for 650898738438330351234358
14. ! [X0] : (funny(X0) <=> (~kind(X0) & ~strong(X0))) [input p13]
16. ! [X0] : ((~strong(X0) | kind(X0)) => (~humble(X0) & ~funny(X0))) [input p15]
22. funny(alice) [input hypothesis]
25. ! [X0] : ((~strong(X0) | kind(X0)) => ~funny(X0)) [pure predicate removal 16]
36. ! [X0] : (~funny(X0) | (strong(X0) & ~kind(X0))) [ennf transformation 25]
63. ! [X0] : ((funny(X0) | (kind(X0) | strong(X0))) & ((~kind(X0) & ~strong(X0)) | ~funny(X0))) [nnf transformation 14]
64. ! [X0] : ((funny(X0) | kind(X0) | strong(X0)) & ((~kind(X0) & ~strong(X0)) | ~funny(X0))) [flattening 63]
118. ~strong(X0) | ~funny(X0) [cnf transformation 64]
126. ~funny(X0) | strong(X0) [cnf transformation 36]
135. funny(alice) [cnf transformation 22]
290. ~funny(X0) [subsumption resolution 126,118]
307. $false [subsumption resolution 135,290]
% SZS output end Proof for 650898738438330351234358
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or rich is kind.
If someone is both not funny and old then someone is wise.
If someone is not old or not wise then someone is either not old or not brave.
If someone is patient or creative then mary is not curious or quiet.
Everyone who is not generous is not happy and vice versa.
If someone is both not brave and not strong then lucy is either not tall or rich and vice versa.
Everyone who is old or not calm is tall or quiet.
Everyone who is both not wise and old is either not rich or funny and vice versa.
Everyone who is either calm or not generous is not old or calm and vice versa.
Everyone who is brave is both kind and wise.
Everyone who is tall or patient is both old and not quiet.
If someone is either not tall or not generous then someone is happy or funny and vice versa.
If alice is tall then someone is both old and creative.
If someone is not kind then john is both not creative and not curious and vice versa.
Everyone who is either not creative or generous is both not calm and not tall.
If mary is generous then someone is either not quiet or quiet and vice versa.
Someone is calm or not patient.
Someone is not brave or not kind.
Someone is both not old and not happy.
Someone is calm or kind.
Someone is not rich.
Susan is either not creative or not generous.
Susan is not old or humble.
Fred is either calm or not happy. | Susan is not funny. | neutral | (![X]:((humble(X)|rich(X))=>kind(X)))&
((?[X]:((~funny(X)&old(X))))=>(?[X]:(wise(X))))&
((?[X]:((~old(X)|~wise(X))))=>(?[X]:((~old(X)<~>~brave(X)))))&
((?[X]:((patient(X)|creative(X))))=>((~curious(mary)|quiet(mary))))&
(![X]:(~generous(X)<=>~happy(X)))&
((?[X]:((~brave(X)&~strong(X))))<=>((~tall(lucy)<~>rich(lucy))))&
(![X]:((old(X)|~calm(X))=>(tall(X)|quiet(X))))&
(![X]:((~wise(X)&old(X))<=>(~rich(X)<~>funny(X))))&
(![X]:((calm(X)<~>~generous(X))<=>(~old(X)|calm(X))))&
(![X]:(brave(X)=>(kind(X)&wise(X))))&
(![X]:((tall(X)|patient(X))=>(old(X)&~quiet(X))))&
((?[X]:((~tall(X)<~>~generous(X))))<=>(?[X]:((happy(X)|funny(X)))))&
((tall(alice))=>(?[X]:((old(X)&creative(X)))))&
((?[X]:(~kind(X)))<=>((~creative(john)&~curious(john))))&
(![X]:((~creative(X)<~>generous(X))=>(~calm(X)&~tall(X))))&
((generous(mary))<=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(?[X]:((calm(X)|~patient(X))))&
(?[X]:((~brave(X)|~kind(X))))&
(?[X]:((~old(X)&~happy(X))))&
(?[X]:((calm(X)|kind(X))))&
(?[X]:(~rich(X)))&
((~creative(susan)<~>~generous(susan)))&
((~old(susan)|humble(susan)))&
((calm(fred)<~>~happy(fred))) | ~funny(susan) | [] | null | 0 |
If susan is humble then john is either not wise or not patient and vice versa.
If john is either calm or curious then someone is either generous or curious.
Everyone who is either not happy or funny is brave or not strong.
Everyone who is either not wise or humble is both humble and quiet.
Everyone who is funny is either kind or funny.
If someone is both generous and calm then lucy is either not wise or not creative.
If fred is wise then mary is not calm and vice versa.
If mary is either not kind or calm then alice is both not patient and funny and vice versa.
If paul is both tall and kind then paul is quiet or not rich and vice versa.
Everyone who is either humble or old is either not rich or not patient.
Everyone who is either not calm or rich is not calm and vice versa.
If lucy is either not brave or strong then fred is not quiet and vice versa.
Everyone who is funny or not kind is both not tall and not quiet and vice versa.
Everyone who is quiet or creative is calm or not quiet.
Everyone who is patient is not kind or generous and vice versa.
Everyone who is not creative or not rich is both wise and not creative.
Someone is curious or not old.
Someone is both not old and generous.
Lucy is either calm or not creative.
Alice is both old and not funny.
Mary is either patient or tall.
Someone is either happy or funny.
Mary is brave.
Mary is either old or brave. | Lucy is calm. | contradiction | ((humble(susan))<=>((~wise(john)<~>~patient(john))))&
(((calm(john)<~>curious(john)))=>(?[X]:((generous(X)<~>curious(X)))))&
(![X]:((~happy(X)<~>funny(X))=>(brave(X)|~strong(X))))&
(![X]:((~wise(X)<~>humble(X))=>(humble(X)&quiet(X))))&
(![X]:(funny(X)=>(kind(X)<~>funny(X))))&
((?[X]:((generous(X)&calm(X))))=>((~wise(lucy)<~>~creative(lucy))))&
((wise(fred))<=>(~calm(mary)))&
(((~kind(mary)<~>calm(mary)))<=>((~patient(alice)&funny(alice))))&
(((tall(paul)&kind(paul)))<=>((quiet(paul)|~rich(paul))))&
(![X]:((humble(X)<~>old(X))=>(~rich(X)<~>~patient(X))))&
(![X]:((~calm(X)<~>rich(X))<=>~calm(X)))&
(((~brave(lucy)<~>strong(lucy)))<=>(~quiet(fred)))&
(![X]:((funny(X)|~kind(X))<=>(~tall(X)&~quiet(X))))&
(![X]:((quiet(X)|creative(X))=>(calm(X)|~quiet(X))))&
(![X]:(patient(X)<=>(~kind(X)|generous(X))))&
(![X]:((~creative(X)|~rich(X))=>(wise(X)&~creative(X))))&
(?[X]:((curious(X)|~old(X))))&
(?[X]:((~old(X)&generous(X))))&
((calm(lucy)<~>~creative(lucy)))&
((old(alice)&~funny(alice)))&
((patient(mary)<~>tall(mary)))&
(?[X]:((happy(X)<~>funny(X))))&
(brave(mary))&
((old(mary)<~>brave(mary))) | calm(lucy) | [
"p10",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 797902906708209581494193
% SZS output start Proof for 797902906708209581494193
11. ! [X0] : ((~calm(X0) <~> rich(X0)) <=> ~calm(X0)) [input p10]
16. ! [X0] : ((~rich(X0) | ~creative(X0)) => (~creative(X0) & wise(X0))) [input p15]
19. calm(lucy) <~> ~creative(lucy) [input p18]
25. calm(lucy) [input hypothesis]
35. ! [X0] : ((~creative(X0) & wise(X0)) | (rich(X0) & creative(X0))) [ennf transformation 16]
50. ! [X0] : ((((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | calm(X0)) & (~calm(X0) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0))))) [nnf transformation 11]
60. (creative(lucy) | ~calm(lucy)) & (~creative(lucy) | calm(lucy)) [nnf transformation 19]
102. ~calm(X0) | ~calm(X0) | ~rich(X0) [cnf transformation 50]
104. ~rich(X0) | calm(X0) | calm(X0) [cnf transformation 50]
122. ~creative(X0) | rich(X0) [cnf transformation 35]
127. creative(lucy) | ~calm(lucy) [cnf transformation 60]
137. calm(lucy) [cnf transformation 25]
139. ~calm(X0) | ~rich(X0) [duplicate literal removal 102]
140. ~rich(X0) | calm(X0) [duplicate literal removal 104]
241. ~rich(X0) [subsumption resolution 139,140]
259. ~creative(X0) [subsumption resolution 122,241]
270. ~calm(lucy) [subsumption resolution 127,259]
293. $false [subsumption resolution 137,270]
% SZS output end Proof for 797902906708209581494193
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not wise is brave and vice versa.
Everyone who is rich is quiet or kind.
If someone is either not funny or not strong then fred is not old and vice versa.
Everyone who is both generous and quiet is either humble or not humble.
If someone is both not tall and happy then lucy is not patient or quiet.
Everyone who is both not patient and not rich is strong.
Everyone who is both rich and strong is both not funny and wise and vice versa.
Everyone who is both not creative and humble is either not calm or funny.
Everyone who is not kind or not old is both not old and not happy.
Everyone who is old or generous is both calm and not quiet and vice versa.
Everyone who is not quiet is not kind.
Everyone who is not quiet or patient is either not calm or brave and vice versa.
If someone is rich then someone is either creative or generous and vice versa.
If lucy is not curious then someone is both wise and not strong and vice versa.
If someone is curious or not creative then someone is not wise or not funny and vice versa.
If someone is quiet or funny then someone is not quiet or tall and vice versa.
Lucy is either not quiet or not tall.
Fred is rich.
Alice is either not funny or wise.
Someone is both creative and rich.
Someone is either not brave or wise.
Someone is patient.
Alice is not wise.
Someone is both not brave and not old. | Alice is old. | contradiction | (![X]:((strong(X)|~wise(X))<=>brave(X)))&
(![X]:(rich(X)=>(quiet(X)|kind(X))))&
((?[X]:((~funny(X)<~>~strong(X))))<=>(~old(fred)))&
(![X]:((generous(X)&quiet(X))=>(humble(X)<~>~humble(X))))&
((?[X]:((~tall(X)&happy(X))))=>((~patient(lucy)|quiet(lucy))))&
(![X]:((~patient(X)&~rich(X))=>strong(X)))&
(![X]:((rich(X)&strong(X))<=>(~funny(X)&wise(X))))&
(![X]:((~creative(X)&humble(X))=>(~calm(X)<~>funny(X))))&
(![X]:((~kind(X)|~old(X))=>(~old(X)&~happy(X))))&
(![X]:((old(X)|generous(X))<=>(calm(X)&~quiet(X))))&
(![X]:(~quiet(X)=>~kind(X)))&
(![X]:((~quiet(X)|patient(X))<=>(~calm(X)<~>brave(X))))&
((?[X]:(rich(X)))<=>(?[X]:((creative(X)<~>generous(X)))))&
((~curious(lucy))<=>(?[X]:((wise(X)&~strong(X)))))&
((?[X]:((curious(X)|~creative(X))))<=>(?[X]:((~wise(X)|~funny(X)))))&
((?[X]:((quiet(X)|funny(X))))<=>(?[X]:((~quiet(X)|tall(X)))))&
((~quiet(lucy)<~>~tall(lucy)))&
(rich(fred))&
((~funny(alice)<~>wise(alice)))&
(?[X]:((creative(X)&rich(X))))&
(?[X]:((~brave(X)<~>wise(X))))&
(?[X]:(patient(X)))&
(~wise(alice))&
(?[X]:((~brave(X)&~old(X)))) | old(alice) | [
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1302621603779673334964542
% SZS output start Proof for 1302621603779673334964542
9. ! [X0] : ((~old(X0) | ~kind(X0)) => (~happy(X0) & ~old(X0))) [input p8]
10. ! [X0] : ((generous(X0) | old(X0)) <=> (~quiet(X0) & calm(X0))) [input p9]
11. ! [X0] : (~quiet(X0) => ~kind(X0)) [input p10]
25. old(alice) [input hypothesis]
29. ! [X0] : ((~old(X0) | ~kind(X0)) => ~old(X0)) [pure predicate removal 9]
39. ! [X0] : (~old(X0) | (old(X0) & kind(X0))) [ennf transformation 29]
40. ! [X0] : (~kind(X0) | quiet(X0)) [ennf transformation 11]
51. ! [X0] : (((generous(X0) | old(X0)) | (quiet(X0) | ~calm(X0))) & ((~quiet(X0) & calm(X0)) | (~generous(X0) & ~old(X0)))) [nnf transformation 10]
52. ! [X0] : ((generous(X0) | old(X0) | quiet(X0) | ~calm(X0)) & ((~quiet(X0) & calm(X0)) | (~generous(X0) & ~old(X0)))) [flattening 51]
102. ~old(X0) | kind(X0) [cnf transformation 39]
106. ~old(X0) | ~quiet(X0) [cnf transformation 52]
109. ~kind(X0) | quiet(X0) [cnf transformation 40]
144. old(alice) [cnf transformation 25]
304. kind(alice) [resolution 102,144]
306. ~quiet(alice) [resolution 106,144]
307. quiet(alice) [resolution 109,304]
308. $false [subsumption resolution 307,306]
% SZS output end Proof for 1302621603779673334964542
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and brave is humble and vice versa.
Everyone who is both calm and not tall is both not strong and generous and vice versa.
Everyone who is either not kind or wise is not generous or generous.
If paul is not wise or not rich then someone is not generous or not kind.
Everyone who is both not quiet and kind is either generous or not old and vice versa.
Everyone who is old is both not wise and strong and vice versa.
Everyone who is both humble and strong is not strong or not creative.
If john is calm then susan is either rich or not humble.
Everyone who is both brave and not strong is not rich and vice versa.
Everyone who is either happy or not humble is both not strong and brave.
If mary is not strong or not old then susan is rich or not wise and vice versa.
Everyone who is not old is not wise or rich.
If susan is not creative or patient then someone is not happy.
If someone is generous then someone is strong or not creative and vice versa.
Everyone who is either not tall or not calm is both not humble and humble.
If someone is not calm then someone is not creative and vice versa.
Someone is not kind or kind.
Someone is not quiet or not tall.
Susan is both brave and curious.
Someone is generous.
Alice is not rich.
John is humble or not rich.
Someone is either not humble or strong.
Susan is either not wise or wise. | Alice is not patient. | neutral | (![X]:((tall(X)&brave(X))<=>humble(X)))&
(![X]:((calm(X)&~tall(X))<=>(~strong(X)&generous(X))))&
(![X]:((~kind(X)<~>wise(X))=>(~generous(X)|generous(X))))&
(((~wise(paul)|~rich(paul)))=>(?[X]:((~generous(X)|~kind(X)))))&
(![X]:((~quiet(X)&kind(X))<=>(generous(X)<~>~old(X))))&
(![X]:(old(X)<=>(~wise(X)&strong(X))))&
(![X]:((humble(X)&strong(X))=>(~strong(X)|~creative(X))))&
((calm(john))=>((rich(susan)<~>~humble(susan))))&
(![X]:((brave(X)&~strong(X))<=>~rich(X)))&
(![X]:((happy(X)<~>~humble(X))=>(~strong(X)&brave(X))))&
(((~strong(mary)|~old(mary)))<=>((rich(susan)|~wise(susan))))&
(![X]:(~old(X)=>(~wise(X)|rich(X))))&
(((~creative(susan)|patient(susan)))=>(?[X]:(~happy(X))))&
((?[X]:(generous(X)))<=>(?[X]:((strong(X)|~creative(X)))))&
(![X]:((~tall(X)<~>~calm(X))=>(~humble(X)&humble(X))))&
((?[X]:(~calm(X)))<=>(?[X]:(~creative(X))))&
(?[X]:((~kind(X)|kind(X))))&
(?[X]:((~quiet(X)|~tall(X))))&
((brave(susan)&curious(susan)))&
(?[X]:(generous(X)))&
(~rich(alice))&
((humble(john)|~rich(john)))&
(?[X]:((~humble(X)<~>strong(X))))&
((~wise(susan)<~>wise(susan))) | ~patient(alice) | [] | null | 0 |
Everyone who is both not calm and wise is either not happy or not generous and vice versa. Everyone who is not calm or strong is both curious and not curious and vice versa. Everyone who is both rich and kind is both humble and not humble and vice versa. If someone is either strong or not creative then john is humble and vice versa. Everyone who is either calm or rich is not humble or funny. Everyone who is not generous is not patient. Everyone who is either not tall or quiet is either happy or brave. Everyone who is either not rich or funny is not calm or quiet. If someone is both not funny and not strong then someone is either not creative or not curious. Everyone who is both humble and not kind is not old or calm and vice versa. Everyone who is either calm or patient is either not patient or wise. Everyone who is either quiet or rich is not curious. If someone is old or curious then fred is either funny or creative and vice versa. Everyone who is both quiet and not curious is both calm and not calm and vice versa. If someone is either not tall or brave then john is both old and tall and vice versa. Everyone who is not tall is funny. Someone is both not creative and patient. Mary is either not generous or not humble. Paul is both generous and not rich. Fred is not patient. Someone is calm. Someone is not brave. Someone is either not curious or not humble. Susan is not happy or brave. | Mary is strong. | contradiction | (![X]:((~calm(X)&wise(X))<=>(~happy(X)<~>~generous(X))))&
(![X]:((~calm(X)|strong(X))<=>(curious(X)&~curious(X))))&
(![X]:((rich(X)&kind(X))<=>(humble(X)&~humble(X))))&
((?[X]:((strong(X)<~>~creative(X))))<=>(humble(john)))&
(![X]:((calm(X)<~>rich(X))=>(~humble(X)|funny(X))))&
(![X]:(~generous(X)=>~patient(X)))&
(![X]:((~tall(X)<~>quiet(X))=>(happy(X)<~>brave(X))))&
(![X]:((~rich(X)<~>funny(X))=>(~calm(X)|quiet(X))))&
((?[X]:((~funny(X)&~strong(X))))=>(?[X]:((~creative(X)<~>~curious(X)))))&
(![X]:((humble(X)&~kind(X))<=>(~old(X)|calm(X))))&
(![X]:((calm(X)<~>patient(X))=>(~patient(X)<~>wise(X))))&
(![X]:((quiet(X)<~>rich(X))=>~curious(X)))&
((?[X]:((old(X)|curious(X))))<=>((funny(fred)<~>creative(fred))))&
(![X]:((quiet(X)&~curious(X))<=>(calm(X)&~calm(X))))&
((?[X]:((~tall(X)<~>brave(X))))<=>((old(john)&tall(john))))&
(![X]:(~tall(X)=>funny(X)))&
(?[X]:((~creative(X)&patient(X))))&
((~generous(mary)<~>~humble(mary)))&
((generous(paul)&~rich(paul)))&
(~patient(fred))&
(?[X]:(calm(X)))&
(?[X]:(~brave(X)))&
(?[X]:((~curious(X)<~>~humble(X))))&
((~happy(susan)|brave(susan))) | strong(mary) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 417099121323328449310802
% SZS output start Proof for 417099121323328449310802
2. ! [X0] : ((strong(X0) | ~calm(X0)) <=> (~curious(X0) & curious(X0))) [input p1]
25. strong(mary) [input hypothesis]
39. ! [X0] : (((strong(X0) | ~calm(X0)) | (curious(X0) | ~curious(X0))) & ((~curious(X0) & curious(X0)) | (~strong(X0) & calm(X0)))) [nnf transformation 2]
40. ! [X0] : ((strong(X0) | ~calm(X0) | curious(X0) | ~curious(X0)) & ((~curious(X0) & curious(X0)) | (~strong(X0) & calm(X0)))) [flattening 39]
86. curious(X0) | ~strong(X0) [cnf transformation 40]
88. ~curious(X0) | ~strong(X0) [cnf transformation 40]
149. strong(mary) [cnf transformation 25]
152. ~strong(X0) [subsumption resolution 86,88]
259. $false [subsumption resolution 149,152]
% SZS output end Proof for 417099121323328449310802
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is kind or quiet then fred is either generous or calm and vice versa.
Everyone who is both not old and not creative is both creative and not wise and vice versa.
Everyone who is old or not calm is brave or generous and vice versa.
Everyone who is not brave is brave or tall and vice versa.
If someone is old or wise then someone is funny and vice versa.
Everyone who is either not funny or kind is rich and vice versa.
Everyone who is kind or curious is not patient and vice versa.
Everyone who is not generous or calm is patient or not old.
If alice is both wise and funny then someone is creative or rich.
Everyone who is not wise is not calm or wise.
If fred is not calm or not brave then paul is brave or quiet and vice versa.
Everyone who is either curious or generous is humble and vice versa.
Everyone who is either tall or not humble is either creative or strong and vice versa.
Everyone who is humble is creative or not patient and vice versa.
If paul is either humble or generous then someone is either brave or not quiet and vice versa.
Someone is old or tall.
Someone is either humble or not quiet.
Lucy is not generous.
Someone is strong.
Someone is either not calm or not tall. | Paul is not strong. | neutral | (((kind(susan)|quiet(susan)))<=>((generous(fred)<~>calm(fred))))&
(![X]:((~old(X)&~creative(X))<=>(creative(X)&~wise(X))))&
(![X]:((old(X)|~calm(X))<=>(brave(X)|generous(X))))&
(![X]:(~brave(X)<=>(brave(X)|tall(X))))&
((?[X]:((old(X)|wise(X))))<=>(?[X]:(funny(X))))&
(![X]:((~funny(X)<~>kind(X))<=>rich(X)))&
(![X]:((kind(X)|curious(X))<=>~patient(X)))&
(![X]:((~generous(X)|calm(X))=>(patient(X)|~old(X))))&
(((wise(alice)&funny(alice)))=>(?[X]:((creative(X)|rich(X)))))&
(![X]:(~wise(X)=>(~calm(X)|wise(X))))&
(((~calm(fred)|~brave(fred)))<=>((brave(paul)|quiet(paul))))&
(![X]:((curious(X)<~>generous(X))<=>humble(X)))&
(![X]:((tall(X)<~>~humble(X))<=>(creative(X)<~>strong(X))))&
(![X]:(humble(X)<=>(creative(X)|~patient(X))))&
(((humble(paul)<~>generous(paul)))<=>(?[X]:((brave(X)<~>~quiet(X)))))&
(?[X]:((old(X)|tall(X))))&
(?[X]:((humble(X)<~>~quiet(X))))&
(~generous(lucy))&
(?[X]:(strong(X)))&
(?[X]:((~calm(X)<~>~tall(X)))) | ~strong(paul) | [] | null | 0 |
Everyone who is not generous is not humble or not calm and vice versa.
Everyone who is either not calm or not strong is not funny.
If fred is not brave or not curious then someone is both curious and not generous and vice versa.
Everyone who is both not happy and not curious is old or not wise.
Everyone who is curious or tall is not rich and vice versa.
If someone is quiet or not generous then fred is both not generous and strong.
Everyone who is either happy or not rich is not rich and vice versa.
If someone is creative then john is strong and vice versa.
If someone is creative then someone is curious.
Everyone who is not humble is both creative and rich and vice versa.
Everyone who is either not tall or tall is not strong.
Everyone who is funny is both happy and patient.
Everyone who is patient is tall or wise and vice versa.
If someone is both not humble and not calm then lucy is wise and vice versa.
If susan is both not brave and not creative then john is not creative.
Everyone who is quiet is not kind or creative.
Lucy is not creative.
Someone is either not tall or not patient.
Lucy is not quiet or patient.
Someone is either not funny or quiet.
Susan is not wise. | Fred is happy. | contradiction | (![X]:(~generous(X)<=>(~humble(X)|~calm(X))))&
(![X]:((~calm(X)<~>~strong(X))=>~funny(X)))&
(((~brave(fred)|~curious(fred)))<=>(?[X]:((curious(X)&~generous(X)))))&
(![X]:((~happy(X)&~curious(X))=>(old(X)|~wise(X))))&
(![X]:((curious(X)|tall(X))<=>~rich(X)))&
((?[X]:((quiet(X)|~generous(X))))=>((~generous(fred)&strong(fred))))&
(![X]:((happy(X)<~>~rich(X))<=>~rich(X)))&
((?[X]:(creative(X)))<=>(strong(john)))&
((?[X]:(creative(X)))=>(?[X]:(curious(X))))&
(![X]:(~humble(X)<=>(creative(X)&rich(X))))&
(![X]:((~tall(X)<~>tall(X))=>~strong(X)))&
(![X]:(funny(X)=>(happy(X)&patient(X))))&
(![X]:(patient(X)<=>(tall(X)|wise(X))))&
((?[X]:((~humble(X)&~calm(X))))<=>(wise(lucy)))&
(((~brave(susan)&~creative(susan)))=>(~creative(john)))&
(![X]:(quiet(X)=>(~kind(X)|creative(X))))&
(~creative(lucy))&
(?[X]:((~tall(X)<~>~patient(X))))&
((~quiet(lucy)|patient(lucy)))&
(?[X]:((~funny(X)<~>quiet(X))))&
(~wise(susan)) | happy(fred) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 7588980835800275359568823
% SZS output start Proof for 7588980835800275359568823
7. ! [X0] : ((happy(X0) <~> ~rich(X0)) <=> ~rich(X0)) [input p6]
22. happy(fred) [input hypothesis]
43. ! [X0] : ((((rich(X0) | ~happy(X0)) & (~rich(X0) | happy(X0))) | rich(X0)) & (~rich(X0) | ((happy(X0) | rich(X0)) & (~rich(X0) | ~happy(X0))))) [nnf transformation 7]
83. ~rich(X0) | ~rich(X0) | ~happy(X0) [cnf transformation 43]
86. rich(X0) | ~happy(X0) | rich(X0) [cnf transformation 43]
111. happy(fred) [cnf transformation 22]
114. ~rich(X0) | ~happy(X0) [duplicate literal removal 83]
115. rich(X0) | ~happy(X0) [duplicate literal removal 86]
158. ~happy(X0) [subsumption resolution 114,115]
222. $false [subsumption resolution 111,158]
% SZS output end Proof for 7588980835800275359568823
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is strong and vice versa.
If susan is either not kind or not patient then someone is rich or not happy.
Everyone who is either strong or kind is both generous and brave and vice versa.
Everyone who is not brave or happy is either not rich or patient.
If someone is not quiet or not wise then someone is either not curious or happy and vice versa.
If someone is both funny and rich then mary is not creative or not humble.
Everyone who is either calm or rich is not quiet or not tall and vice versa.
Everyone who is either old or humble is both happy and not strong and vice versa.
If someone is kind then someone is brave or generous.
If alice is both not calm and tall then someone is both old and funny.
Everyone who is kind or tall is both wise and not happy.
If john is either not patient or generous then lucy is either calm or generous.
If someone is kind then someone is both creative and not brave and vice versa.
Everyone who is not calm or old is curious and vice versa.
Everyone who is not old is both funny and not patient.
Everyone who is both not old and quiet is both wise and old and vice versa.
Someone is either not patient or not old.
Fred is both brave and not creative.
Someone is both not brave and happy.
Someone is wise.
Someone is both not strong and brave.
Someone is both rich and not patient.
John is tall.
Lucy is funny or curious. | Susan is creative. | neutral | (![X]:(rich(X)<=>strong(X)))&
(((~kind(susan)<~>~patient(susan)))=>(?[X]:((rich(X)|~happy(X)))))&
(![X]:((strong(X)<~>kind(X))<=>(generous(X)&brave(X))))&
(![X]:((~brave(X)|happy(X))=>(~rich(X)<~>patient(X))))&
((?[X]:((~quiet(X)|~wise(X))))<=>(?[X]:((~curious(X)<~>happy(X)))))&
((?[X]:((funny(X)&rich(X))))=>((~creative(mary)|~humble(mary))))&
(![X]:((calm(X)<~>rich(X))<=>(~quiet(X)|~tall(X))))&
(![X]:((old(X)<~>humble(X))<=>(happy(X)&~strong(X))))&
((?[X]:(kind(X)))=>(?[X]:((brave(X)|generous(X)))))&
(((~calm(alice)&tall(alice)))=>(?[X]:((old(X)&funny(X)))))&
(![X]:((kind(X)|tall(X))=>(wise(X)&~happy(X))))&
(((~patient(john)<~>generous(john)))=>((calm(lucy)<~>generous(lucy))))&
((?[X]:(kind(X)))<=>(?[X]:((creative(X)&~brave(X)))))&
(![X]:((~calm(X)|old(X))<=>curious(X)))&
(![X]:(~old(X)=>(funny(X)&~patient(X))))&
(![X]:((~old(X)&quiet(X))<=>(wise(X)&old(X))))&
(?[X]:((~patient(X)<~>~old(X))))&
((brave(fred)&~creative(fred)))&
(?[X]:((~brave(X)&happy(X))))&
(?[X]:(wise(X)))&
(?[X]:((~strong(X)&brave(X))))&
(?[X]:((rich(X)&~patient(X))))&
(tall(john))&
((funny(lucy)|curious(lucy))) | creative(susan) | [] | null | 0 |
Everyone who is not funny is either strong or old.
If paul is both not calm and not old then john is both not strong and not rich.
If susan is both not calm and not old then someone is not strong.
If susan is not happy then lucy is either humble or quiet and vice versa.
Everyone who is either not calm or quiet is either brave or quiet.
Everyone who is both happy and strong is not patient.
Everyone who is either not kind or not generous is calm or strong and vice versa.
If susan is either not creative or not old then alice is both funny and not generous.
Everyone who is not humble is both generous and not generous and vice versa.
If susan is strong or not kind then someone is both not old and curious.
If susan is both not tall and not creative then lucy is either brave or not rich and vice versa.
Everyone who is either old or not kind is both wise and not calm.
If someone is not creative or old then lucy is old or generous and vice versa.
Everyone who is funny is tall and vice versa.
Everyone who is not happy or humble is either not tall or not patient.
If someone is not patient or brave then someone is both kind and happy and vice versa.
Someone is both not generous and not rich.
Someone is creative.
Someone is old.
Someone is either creative or not patient.
John is humble.
Someone is generous.
Someone is not funny or rich. | John is not rich. | neutral | (![X]:(~funny(X)=>(strong(X)<~>old(X))))&
(((~calm(paul)&~old(paul)))=>((~strong(john)&~rich(john))))&
(((~calm(susan)&~old(susan)))=>(?[X]:(~strong(X))))&
((~happy(susan))<=>((humble(lucy)<~>quiet(lucy))))&
(![X]:((~calm(X)<~>quiet(X))=>(brave(X)<~>quiet(X))))&
(![X]:((happy(X)&strong(X))=>~patient(X)))&
(![X]:((~kind(X)<~>~generous(X))<=>(calm(X)|strong(X))))&
(((~creative(susan)<~>~old(susan)))=>((funny(alice)&~generous(alice))))&
(![X]:(~humble(X)<=>(generous(X)&~generous(X))))&
(((strong(susan)|~kind(susan)))=>(?[X]:((~old(X)&curious(X)))))&
(((~tall(susan)&~creative(susan)))<=>((brave(lucy)<~>~rich(lucy))))&
(![X]:((old(X)<~>~kind(X))=>(wise(X)&~calm(X))))&
((?[X]:((~creative(X)|old(X))))<=>((old(lucy)|generous(lucy))))&
(![X]:(funny(X)<=>tall(X)))&
(![X]:((~happy(X)|humble(X))=>(~tall(X)<~>~patient(X))))&
((?[X]:((~patient(X)|brave(X))))<=>(?[X]:((kind(X)&happy(X)))))&
(?[X]:((~generous(X)&~rich(X))))&
(?[X]:(creative(X)))&
(?[X]:(old(X)))&
(?[X]:((creative(X)<~>~patient(X))))&
(humble(john))&
(?[X]:(generous(X)))&
(?[X]:((~funny(X)|rich(X)))) | ~rich(john) | [] | null | 0 |
Everyone who is both strong and not calm is not quiet and vice versa.
Everyone who is happy is both not curious and curious.
If paul is both not quiet and happy then someone is either rich or not creative and vice versa.
Everyone who is either not rich or not strong is strong and vice versa.
If susan is both not brave and not quiet then someone is either brave or not strong.
If someone is not humble then someone is both funny and not brave.
Everyone who is both not tall and generous is either strong or kind.
Everyone who is either patient or old is kind or not creative and vice versa.
Everyone who is not tall is both not funny and not calm.
If lucy is not funny then paul is not curious.
Everyone who is both curious and strong is brave and vice versa.
Everyone who is either rich or tall is happy and vice versa.
Everyone who is humble or not generous is old and vice versa.
Everyone who is either not curious or generous is either old or not quiet and vice versa.
Everyone who is either humble or not wise is either happy or not rich.
If lucy is both wise and not wise then fred is both not strong and not generous.
Someone is creative or not wise.
Someone is both curious and not kind.
Someone is either not curious or quiet.
Lucy is both brave and not funny.
Lucy is either not happy or calm.
Someone is not generous. | Lucy is funny. | contradiction | (![X]:((strong(X)&~calm(X))<=>~quiet(X)))&
(![X]:(happy(X)=>(~curious(X)&curious(X))))&
(((~quiet(paul)&happy(paul)))<=>(?[X]:((rich(X)<~>~creative(X)))))&
(![X]:((~rich(X)<~>~strong(X))<=>strong(X)))&
(((~brave(susan)&~quiet(susan)))=>(?[X]:((brave(X)<~>~strong(X)))))&
((?[X]:(~humble(X)))=>(?[X]:((funny(X)&~brave(X)))))&
(![X]:((~tall(X)&generous(X))=>(strong(X)<~>kind(X))))&
(![X]:((patient(X)<~>old(X))<=>(kind(X)|~creative(X))))&
(![X]:(~tall(X)=>(~funny(X)&~calm(X))))&
((~funny(lucy))=>(~curious(paul)))&
(![X]:((curious(X)&strong(X))<=>brave(X)))&
(![X]:((rich(X)<~>tall(X))<=>happy(X)))&
(![X]:((humble(X)|~generous(X))<=>old(X)))&
(![X]:((~curious(X)<~>generous(X))<=>(old(X)<~>~quiet(X))))&
(![X]:((humble(X)<~>~wise(X))=>(happy(X)<~>~rich(X))))&
(((wise(lucy)&~wise(lucy)))=>((~strong(fred)&~generous(fred))))&
(?[X]:((creative(X)|~wise(X))))&
(?[X]:((curious(X)&~kind(X))))&
(?[X]:((~curious(X)<~>quiet(X))))&
((brave(lucy)&~funny(lucy)))&
((~happy(lucy)<~>calm(lucy)))&
(?[X]:(~generous(X))) | funny(lucy) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6471135459709070944330370
% SZS output start Proof for 6471135459709070944330370
20. ~funny(lucy) & brave(lucy) [input p19]
23. funny(lucy) [input hypothesis]
130. ~funny(lucy) [cnf transformation 20]
134. funny(lucy) [cnf transformation 23]
173. 8 <=> funny(lucy) [avatar definition]
206. ~8 [avatar split clause 130,173]
208. 8 [avatar split clause 134,173]
209. $false [avatar sat refutation 206,208]
% SZS output end Proof for 6471135459709070944330370
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind or not humble then fred is both not wise and creative and vice versa. Everyone who is not tall is both not funny and not wise. Everyone who is not curious or not calm is funny and vice versa. Everyone who is both not tall and not strong is either not wise or not humble. Everyone who is humble is funny and vice versa. Everyone who is either not happy or funny is not calm. If someone is tall or not patient then someone is rich or wise and vice versa. Everyone who is both not quiet and not humble is rich or funny. Everyone who is happy or not calm is not creative or calm. Everyone who is wise is either not patient or patient and vice versa. Everyone who is calm is both not humble and patient. Everyone who is kind or brave is humble and vice versa. If someone is humble then john is both funny and not old. If someone is either not brave or not creative then someone is both not generous and curious. If someone is either not curious or wise then john is either patient or not curious. Everyone who is both not curious and not kind is both not wise and not old. Someone is not happy or not kind. Someone is rich. Someone is either not old or strong. Someone is not calm or wise. Someone is either not kind or rich. | Fred is quiet. | neutral | ((?[X]:((kind(X)|~humble(X))))<=>((~wise(fred)&creative(fred))))&
(![X]:(~tall(X)=>(~funny(X)&~wise(X))))&
(![X]:((~curious(X)|~calm(X))<=>funny(X)))&
(![X]:((~tall(X)&~strong(X))=>(~wise(X)<~>~humble(X))))&
(![X]:(humble(X)<=>funny(X)))&
(![X]:((~happy(X)<~>funny(X))=>~calm(X)))&
((?[X]:((tall(X)|~patient(X))))<=>(?[X]:((rich(X)|wise(X)))))&
(![X]:((~quiet(X)&~humble(X))=>(rich(X)|funny(X))))&
(![X]:((happy(X)|~calm(X))=>(~creative(X)|calm(X))))&
(![X]:(wise(X)<=>(~patient(X)<~>patient(X))))&
(![X]:(calm(X)=>(~humble(X)&patient(X))))&
(![X]:((kind(X)|brave(X))<=>humble(X)))&
((?[X]:(humble(X)))=>((funny(john)&~old(john))))&
((?[X]:((~brave(X)<~>~creative(X))))=>(?[X]:((~generous(X)&curious(X)))))&
((?[X]:((~curious(X)<~>wise(X))))=>((patient(john)<~>~curious(john))))&
(![X]:((~curious(X)&~kind(X))=>(~wise(X)&~old(X))))&
(?[X]:((~happy(X)|~kind(X))))&
(?[X]:(rich(X)))&
(?[X]:((~old(X)<~>strong(X))))&
(?[X]:((~calm(X)|wise(X))))&
(?[X]:((~kind(X)<~>rich(X)))) | quiet(fred) | [] | null | 0 |
Everyone who is either quiet or not kind is both not creative and generous.
If someone is not patient or not creative then someone is both not rich and generous and vice versa.
Everyone who is not tall is kind and vice versa.
Everyone who is both wise and brave is both not generous and not brave.
If susan is both not rich and brave then someone is curious and vice versa.
Everyone who is both patient and happy is both not humble and rich and vice versa.
Everyone who is either not happy or not curious is both generous and tall.
Everyone who is not kind or not old is both not calm and funny.
Everyone who is not quiet or tall is not humble or tall and vice versa.
Everyone who is not calm or not tall is tall or generous.
If someone is either quiet or not rich then john is both not curious and strong and vice versa.
If someone is not strong then someone is both not curious and not strong and vice versa.
If someone is rich then someone is either not creative or happy and vice versa.
Everyone who is not humble is not rich.
Everyone who is not quiet or old is both not creative and creative and vice versa.
If alice is both not calm and not old then fred is not kind or creative.
Susan is either not quiet or tall.
Someone is strong.
Mary is rich or curious.
Someone is either rich or not wise.
Someone is both rich and not brave.
Someone is either calm or not curious.
Fred is both not rich and not brave.
Someone is either patient or not calm. | Susan is not quiet. | contradiction | (![X]:((quiet(X)<~>~kind(X))=>(~creative(X)&generous(X))))&
((?[X]:((~patient(X)|~creative(X))))<=>(?[X]:((~rich(X)&generous(X)))))&
(![X]:(~tall(X)<=>kind(X)))&
(![X]:((wise(X)&brave(X))=>(~generous(X)&~brave(X))))&
(((~rich(susan)&brave(susan)))<=>(?[X]:(curious(X))))&
(![X]:((patient(X)&happy(X))<=>(~humble(X)&rich(X))))&
(![X]:((~happy(X)<~>~curious(X))=>(generous(X)&tall(X))))&
(![X]:((~kind(X)|~old(X))=>(~calm(X)&funny(X))))&
(![X]:((~quiet(X)|tall(X))<=>(~humble(X)|tall(X))))&
(![X]:((~calm(X)|~tall(X))=>(tall(X)|generous(X))))&
((?[X]:((quiet(X)<~>~rich(X))))<=>((~curious(john)&strong(john))))&
((?[X]:(~strong(X)))<=>(?[X]:((~curious(X)&~strong(X)))))&
((?[X]:(rich(X)))<=>(?[X]:((~creative(X)<~>happy(X)))))&
(![X]:(~humble(X)=>~rich(X)))&
(![X]:((~quiet(X)|old(X))<=>(~creative(X)&creative(X))))&
(((~calm(alice)&~old(alice)))=>((~kind(fred)|creative(fred))))&
((~quiet(susan)<~>tall(susan)))&
(?[X]:(strong(X)))&
((rich(mary)|curious(mary)))&
(?[X]:((rich(X)<~>~wise(X))))&
(?[X]:((rich(X)&~brave(X))))&
(?[X]:((calm(X)<~>~curious(X))))&
((~rich(fred)&~brave(fred)))&
(?[X]:((patient(X)<~>~calm(X)))) | ~quiet(susan) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1179676785541918500810444
% SZS output start Proof for 1179676785541918500810444
15. ! [X0] : ((old(X0) | ~quiet(X0)) <=> (creative(X0) & ~creative(X0))) [input p14]
25. ~quiet(susan) [input hypothesis]
72. ! [X0] : (((old(X0) | ~quiet(X0)) | (~creative(X0) | creative(X0))) & ((creative(X0) & ~creative(X0)) | (~old(X0) & quiet(X0)))) [nnf transformation 15]
73. ! [X0] : ((old(X0) | ~quiet(X0) | ~creative(X0) | creative(X0)) & ((creative(X0) & ~creative(X0)) | (~old(X0) & quiet(X0)))) [flattening 72]
134. ~creative(X0) | quiet(X0) [cnf transformation 73]
136. creative(X0) | quiet(X0) [cnf transformation 73]
154. ~quiet(susan) [cnf transformation 25]
280. quiet(X0) [subsumption resolution 134,136]
335. $false [subsumption resolution 154,280]
% SZS output end Proof for 1179676785541918500810444
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is not patient and vice versa. Everyone who is not old or not creative is both generous and not strong. Everyone who is both wise and strong is not funny and vice versa. Everyone who is not happy or creative is both curious and quiet and vice versa. Everyone who is either not happy or not calm is brave. If lucy is either not funny or not curious then susan is both funny and strong. Everyone who is either not strong or not tall is both patient and not strong. Everyone who is both funny and calm is happy. Everyone who is not funny is not tall and vice versa. Everyone who is either quiet or not old is either funny or not calm. If someone is both not tall and not curious then someone is kind and vice versa. Everyone who is either generous or not happy is not curious and vice versa. If mary is either strong or not calm then someone is either brave or not kind and vice versa. If someone is not calm or not humble then someone is both creative and not humble and vice versa. John is not creative or old. Someone is not kind. Someone is not funny or humble. | Mary is old. | entailment | (![X]:(~strong(X)<=>~patient(X)))&
(![X]:((~old(X)|~creative(X))=>(generous(X)&~strong(X))))&
(![X]:((wise(X)&strong(X))<=>~funny(X)))&
(![X]:((~happy(X)|creative(X))<=>(curious(X)&quiet(X))))&
(![X]:((~happy(X)<~>~calm(X))=>brave(X)))&
(((~funny(lucy)<~>~curious(lucy)))=>((funny(susan)&strong(susan))))&
(![X]:((~strong(X)<~>~tall(X))=>(patient(X)&~strong(X))))&
(![X]:((funny(X)&calm(X))=>happy(X)))&
(![X]:(~funny(X)<=>~tall(X)))&
(![X]:((quiet(X)<~>~old(X))=>(funny(X)<~>~calm(X))))&
((?[X]:((~tall(X)&~curious(X))))<=>(?[X]:(kind(X))))&
(![X]:((generous(X)<~>~happy(X))<=>~curious(X)))&
(((strong(mary)<~>~calm(mary)))<=>(?[X]:((brave(X)<~>~kind(X)))))&
((?[X]:((~calm(X)|~humble(X))))<=>(?[X]:((creative(X)&~humble(X)))))&
((~creative(john)|old(john)))&
(?[X]:(~kind(X)))&
(?[X]:((~funny(X)|humble(X)))) | old(mary) | [
"p0",
"p1",
"p2",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2641733029866653988475159
% SZS output start Proof for 2641733029866653988475159
1. ! [X0] : (~strong(X0) <=> ~patient(X0)) [input p0]
2. ! [X0] : ((~creative(X0) | ~old(X0)) => (~strong(X0) & generous(X0))) [input p1]
3. ! [X0] : ((strong(X0) & wise(X0)) <=> ~funny(X0)) [input p2]
7. ! [X0] : ((~strong(X0) <~> ~tall(X0)) => (~strong(X0) & patient(X0))) [input p6]
9. ! [X0] : (~funny(X0) <=> ~tall(X0)) [input p8]
18. ~old(mary) [input hypothesis]
21. ! [X0] : ((~strong(X0) & generous(X0)) | (creative(X0) & old(X0))) [ennf transformation 2]
24. ! [X0] : ((~strong(X0) & patient(X0)) | (~strong(X0) <=> ~tall(X0))) [ennf transformation 7]
28. ! [X0] : ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0))) [nnf transformation 1]
29. ! [X0] : (((strong(X0) & wise(X0)) | funny(X0)) & (~funny(X0) | (~strong(X0) | ~wise(X0)))) [nnf transformation 3]
30. ! [X0] : (((strong(X0) & wise(X0)) | funny(X0)) & (~funny(X0) | ~strong(X0) | ~wise(X0))) [flattening 29]
35. ! [X0] : ((~strong(X0) & patient(X0)) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0)))) [nnf transformation 24]
36. ! [X0] : ((~funny(X0) | tall(X0)) & (~tall(X0) | funny(X0))) [nnf transformation 9]
57. ~patient(X0) | strong(X0) [cnf transformation 28]
58. ~strong(X0) | patient(X0) [cnf transformation 28]
61. ~strong(X0) | old(X0) [cnf transformation 21]
65. funny(X0) | strong(X0) [cnf transformation 30]
77. patient(X0) | ~tall(X0) | strong(X0) [cnf transformation 35]
80. ~strong(X0) | ~strong(X0) | tall(X0) [cnf transformation 35]
83. ~funny(X0) | tall(X0) [cnf transformation 36]
111. ~old(mary) [cnf transformation 18]
112. ~strong(X0) | tall(X0) [duplicate literal removal 80]
133. ~tall(X0) | patient(X0) [subsumption resolution 77,58]
161. 11 <=> strong(mary) [avatar definition]
162. strong(mary) <- (11) [avatar component clause 161]
163. ~strong(mary) <- (~11) [avatar component clause 161]
243. old(mary) <- (11) [resolution 61,162]
244. $false <- (11) [subsumption resolution 243,111]
245. ~11 [avatar contradiction clause 244]
262. tall(X0) | strong(X0) [resolution 83,65]
265. tall(X0) [subsumption resolution 262,112]
272. patient(X0) [resolution 133,265]
280. strong(X0) [resolution 272,57]
298. $false <- (~11) [resolution 280,163]
299. 11 [avatar contradiction clause 298]
300. $false [avatar sat refutation 245,299]
% SZS output end Proof for 2641733029866653988475159
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both quiet and happy then someone is not funny or not happy. Everyone who is not wise is funny or not creative. Everyone who is either not old or not calm is both not wise and not quiet. Everyone who is either tall or kind is humble or not strong and vice versa. Everyone who is curious or rich is either not old or not tall. If someone is not patient or brave then someone is either not patient or not funny. Everyone who is happy is both curious and not strong and vice versa. If someone is either funny or kind then paul is both not happy and strong. Everyone who is either generous or calm is not old or not rich and vice versa. Everyone who is either funny or not strong is both not patient and not kind. Everyone who is not humble is both not old and not quiet. If susan is both old and not strong then mary is creative and vice versa. Everyone who is both creative and not wise is not humble and vice versa. If someone is quiet or not wise then susan is not patient or funny and vice versa. Everyone who is either not quiet or happy is curious or not quiet and vice versa. Everyone who is both not strong and generous is old. Someone is wise or rich. Someone is not humble or not calm. Alice is old or not calm. Someone is either not funny or rich. Alice is both not generous and patient. Someone is both humble and not tall. Alice is both creative and tall. Paul is both not curious and not calm. | Alice is not rich. | entailment | ((?[X]:((quiet(X)&happy(X))))=>(?[X]:((~funny(X)|~happy(X)))))&
(![X]:(~wise(X)=>(funny(X)|~creative(X))))&
(![X]:((~old(X)<~>~calm(X))=>(~wise(X)&~quiet(X))))&
(![X]:((tall(X)<~>kind(X))<=>(humble(X)|~strong(X))))&
(![X]:((curious(X)|rich(X))=>(~old(X)<~>~tall(X))))&
((?[X]:((~patient(X)|brave(X))))=>(?[X]:((~patient(X)<~>~funny(X)))))&
(![X]:(happy(X)<=>(curious(X)&~strong(X))))&
((?[X]:((funny(X)<~>kind(X))))=>((~happy(paul)&strong(paul))))&
(![X]:((generous(X)<~>calm(X))<=>(~old(X)|~rich(X))))&
(![X]:((funny(X)<~>~strong(X))=>(~patient(X)&~kind(X))))&
(![X]:(~humble(X)=>(~old(X)&~quiet(X))))&
(((old(susan)&~strong(susan)))<=>(creative(mary)))&
(![X]:((creative(X)&~wise(X))<=>~humble(X)))&
((?[X]:((quiet(X)|~wise(X))))<=>((~patient(susan)|funny(susan))))&
(![X]:((~quiet(X)<~>happy(X))<=>(curious(X)|~quiet(X))))&
(![X]:((~strong(X)&generous(X))=>old(X)))&
(?[X]:((wise(X)|rich(X))))&
(?[X]:((~humble(X)|~calm(X))))&
((old(alice)|~calm(alice)))&
(?[X]:((~funny(X)<~>rich(X))))&
((~generous(alice)&patient(alice)))&
(?[X]:((humble(X)&~tall(X))))&
((creative(alice)&tall(alice)))&
((~curious(paul)&~calm(paul))) | ~rich(alice) | [
"p4",
"p8",
"p18",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5385771719966636787131774
% SZS output start Proof for 5385771719966636787131774
5. ! [X0] : ((rich(X0) | curious(X0)) => (~old(X0) <~> ~tall(X0))) [input p4]
9. ! [X0] : ((generous(X0) <~> calm(X0)) <=> (~rich(X0) | ~old(X0))) [input p8]
19. ~calm(alice) | old(alice) [input p18]
21. patient(alice) & ~generous(alice) [input p20]
23. tall(alice) & creative(alice) [input p22]
25. rich(alice) [input hypothesis]
33. ! [X0] : ((~old(X0) <~> ~tall(X0)) | (~rich(X0) & ~curious(X0))) [ennf transformation 5]
46. ! [X0] : (((tall(X0) | old(X0)) & (~tall(X0) | ~old(X0))) | (~rich(X0) & ~curious(X0))) [nnf transformation 33]
54. ! [X0] : ((((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) | (rich(X0) & old(X0))) & ((~rich(X0) | ~old(X0)) | ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0))))) [nnf transformation 9]
55. ! [X0] : ((((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) | (rich(X0) & old(X0))) & (~rich(X0) | ~old(X0) | ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0))))) [flattening 54]
90. ~rich(X0) | ~old(X0) | ~tall(X0) [cnf transformation 46]
104. generous(X0) | calm(X0) | old(X0) [cnf transformation 55]
133. ~calm(alice) | old(alice) [cnf transformation 19]
136. ~generous(alice) [cnf transformation 21]
141. tall(alice) [cnf transformation 23]
144. rich(alice) [cnf transformation 25]
250. 24 <=> old(alice) [avatar definition]
251. ~old(alice) <- (~24) [avatar component clause 250]
254. 25 <=> calm(alice) [avatar definition]
256. ~calm(alice) <- (~25) [avatar component clause 254]
257. 24 | ~25 [avatar split clause 133,254,250]
303. ~old(alice) | ~tall(alice) [resolution 90,144]
305. ~old(alice) [subsumption resolution 303,141]
306. ~24 [avatar split clause 305,250]
319. calm(alice) | old(alice) [resolution 104,136]
320. old(alice) <- (~25) [subsumption resolution 319,256]
321. $false <- (~24, ~25) [subsumption resolution 320,251]
322. 24 | 25 [avatar contradiction clause 321]
323. $false [avatar sat refutation 257,306,322]
% SZS output end Proof for 5385771719966636787131774
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is either generous or not wise and vice versa.
Everyone who is creative or rich is tall or not funny and vice versa.
If someone is not calm or not tall then lucy is both not strong and not old.
If someone is both patient and not curious then someone is creative or not quiet and vice versa.
Everyone who is calm is either not calm or not patient and vice versa.
Everyone who is either not tall or tall is not creative or creative and vice versa.
Everyone who is either not humble or not quiet is both calm and not quiet and vice versa.
If john is either happy or not rich then susan is tall.
If someone is either old or generous then someone is either kind or not calm.
Everyone who is not funny or wise is rich or not humble and vice versa.
Everyone who is not happy is both not wise and not kind.
If fred is both patient and old then fred is both not curious and wise and vice versa.
Everyone who is either rich or strong is not wise.
If john is not calm then someone is both not strong and funny.
Everyone who is both not tall and not calm is both curious and old and vice versa.
Fred is either tall or not patient.
Someone is either generous or humble.
Fred is either strong or kind.
Mary is not patient or humble.
Someone is not curious or funny.
Lucy is both not tall and not old. | Susan is not funny. | neutral | (![X]:(~generous(X)<=>(generous(X)<~>~wise(X))))&
(![X]:((creative(X)|rich(X))<=>(tall(X)|~funny(X))))&
((?[X]:((~calm(X)|~tall(X))))=>((~strong(lucy)&~old(lucy))))&
((?[X]:((patient(X)&~curious(X))))<=>(?[X]:((creative(X)|~quiet(X)))))&
(![X]:(calm(X)<=>(~calm(X)<~>~patient(X))))&
(![X]:((~tall(X)<~>tall(X))<=>(~creative(X)|creative(X))))&
(![X]:((~humble(X)<~>~quiet(X))<=>(calm(X)&~quiet(X))))&
(((happy(john)<~>~rich(john)))=>(tall(susan)))&
((?[X]:((old(X)<~>generous(X))))=>(?[X]:((kind(X)<~>~calm(X)))))&
(![X]:((~funny(X)|wise(X))<=>(rich(X)|~humble(X))))&
(![X]:(~happy(X)=>(~wise(X)&~kind(X))))&
(((patient(fred)&old(fred)))<=>((~curious(fred)&wise(fred))))&
(![X]:((rich(X)<~>strong(X))=>~wise(X)))&
((~calm(john))=>(?[X]:((~strong(X)&funny(X)))))&
(![X]:((~tall(X)&~calm(X))<=>(curious(X)&old(X))))&
((tall(fred)<~>~patient(fred)))&
(?[X]:((generous(X)<~>humble(X))))&
((strong(fred)<~>kind(fred)))&
((~patient(mary)|humble(mary)))&
(?[X]:((~curious(X)|funny(X))))&
((~tall(lucy)&~old(lucy))) | ~funny(susan) | [] | null | 0 |
Everyone who is either funny or not old is both rich and not patient and vice versa.
Everyone who is old or not curious is not curious and vice versa.
If someone is either not calm or not wise then fred is funny or old and vice versa.
Everyone who is rich is not brave or not strong.
Everyone who is not creative or tall is humble and vice versa.
If someone is not humble or generous then someone is both creative and quiet and vice versa.
If paul is either tall or old then john is either happy or kind.
Everyone who is not funny or not strong is not brave.
Everyone who is generous or not old is not curious.
If mary is either brave or quiet then alice is both not creative and not quiet and vice versa.
Everyone who is either not curious or not calm is not humble.
If mary is both happy and humble then alice is strong or not humble.
Everyone who is not tall or brave is either calm or strong and vice versa.
If john is calm then susan is both not kind and old and vice versa.
Everyone who is both not funny and creative is either humble or not calm and vice versa.
If fred is not tall or happy then alice is either curious or not funny and vice versa.
Paul is both quiet and kind.
Susan is either calm or funny.
Someone is happy or not funny.
Paul is not generous.
Paul is both old and strong.
Alice is both not patient and old.
Someone is both strong and humble. | Susan is old. | neutral | (![X]:((funny(X)<~>~old(X))<=>(rich(X)&~patient(X))))&
(![X]:((old(X)|~curious(X))<=>~curious(X)))&
((?[X]:((~calm(X)<~>~wise(X))))<=>((funny(fred)|old(fred))))&
(![X]:(rich(X)=>(~brave(X)|~strong(X))))&
(![X]:((~creative(X)|tall(X))<=>humble(X)))&
((?[X]:((~humble(X)|generous(X))))<=>(?[X]:((creative(X)&quiet(X)))))&
(((tall(paul)<~>old(paul)))=>((happy(john)<~>kind(john))))&
(![X]:((~funny(X)|~strong(X))=>~brave(X)))&
(![X]:((generous(X)|~old(X))=>~curious(X)))&
(((brave(mary)<~>quiet(mary)))<=>((~creative(alice)&~quiet(alice))))&
(![X]:((~curious(X)<~>~calm(X))=>~humble(X)))&
(((happy(mary)&humble(mary)))=>((strong(alice)|~humble(alice))))&
(![X]:((~tall(X)|brave(X))<=>(calm(X)<~>strong(X))))&
((calm(john))<=>((~kind(susan)&old(susan))))&
(![X]:((~funny(X)&creative(X))<=>(humble(X)<~>~calm(X))))&
(((~tall(fred)|happy(fred)))<=>((curious(alice)<~>~funny(alice))))&
((quiet(paul)&kind(paul)))&
((calm(susan)<~>funny(susan)))&
(?[X]:((happy(X)|~funny(X))))&
(~generous(paul))&
((old(paul)&strong(paul)))&
((~patient(alice)&old(alice)))&
(?[X]:((strong(X)&humble(X)))) | old(susan) | [] | null | 0 |
Everyone who is either creative or funny is either not creative or not old and vice versa.
Everyone who is wise or not humble is happy or curious.
If alice is rich then someone is rich or not wise.
Everyone who is creative is not humble.
If fred is not generous or not brave then someone is not patient or not old.
If alice is not rich or not patient then someone is both not happy and wise.
Everyone who is not wise is both happy and wise.
Everyone who is generous or not wise is happy and vice versa.
Everyone who is not funny is both not patient and not calm.
Everyone who is old or not wise is either not calm or curious and vice versa.
If paul is both strong and brave then alice is brave or not brave.
Everyone who is curious is either creative or funny and vice versa.
Everyone who is either kind or not creative is both tall and not creative and vice versa.
If someone is either not humble or not strong then susan is not curious.
Everyone who is not curious is either kind or creative and vice versa.
If fred is not patient then someone is either not rich or patient.
Someone is brave.
Someone is not patient or strong.
Someone is both tall and not brave.
John is creative.
Lucy is tall.
Someone is not strong. | Lucy is humble. | neutral | (![X]:((creative(X)<~>funny(X))<=>(~creative(X)<~>~old(X))))&
(![X]:((wise(X)|~humble(X))=>(happy(X)|curious(X))))&
((rich(alice))=>(?[X]:((rich(X)|~wise(X)))))&
(![X]:(creative(X)=>~humble(X)))&
(((~generous(fred)|~brave(fred)))=>(?[X]:((~patient(X)|~old(X)))))&
(((~rich(alice)|~patient(alice)))=>(?[X]:((~happy(X)&wise(X)))))&
(![X]:(~wise(X)=>(happy(X)&wise(X))))&
(![X]:((generous(X)|~wise(X))<=>happy(X)))&
(![X]:(~funny(X)=>(~patient(X)&~calm(X))))&
(![X]:((old(X)|~wise(X))<=>(~calm(X)<~>curious(X))))&
(((strong(paul)&brave(paul)))=>((brave(alice)|~brave(alice))))&
(![X]:(curious(X)<=>(creative(X)<~>funny(X))))&
(![X]:((kind(X)<~>~creative(X))<=>(tall(X)&~creative(X))))&
((?[X]:((~humble(X)<~>~strong(X))))=>(~curious(susan)))&
(![X]:(~curious(X)<=>(kind(X)<~>creative(X))))&
((~patient(fred))=>(?[X]:((~rich(X)<~>patient(X)))))&
(?[X]:(brave(X)))&
(?[X]:((~patient(X)|strong(X))))&
(?[X]:((tall(X)&~brave(X))))&
(creative(john))&
(tall(lucy))&
(?[X]:(~strong(X))) | humble(lucy) | [] | null | 0 |
Everyone who is either curious or not curious is not rich or not calm.
Everyone who is either not generous or tall is tall or not funny.
Everyone who is not kind is both calm and generous and vice versa.
If someone is both not curious and not generous then someone is quiet or brave and vice versa.
If someone is either not calm or strong then paul is not quiet and vice versa.
Everyone who is not curious is both calm and old and vice versa.
Everyone who is not generous or not humble is both not patient and not kind and vice versa.
If someone is either not old or funny then someone is either not kind or not happy.
Everyone who is not old is either kind or funny and vice versa.
Everyone who is either not creative or brave is both quiet and creative.
If susan is strong then alice is both generous and not funny.
Everyone who is not old is both patient and not generous and vice versa.
If someone is both patient and not old then someone is both calm and patient.
If paul is funny then lucy is either not kind or calm and vice versa.
Everyone who is generous is either not happy or rich and vice versa.
Everyone who is humble is not brave and vice versa.
Someone is either tall or happy.
John is both happy and tall.
Someone is both not curious and not rich.
Fred is not tall.
Lucy is either not calm or tall. | Alice is not strong. | neutral | (![X]:((curious(X)<~>~curious(X))=>(~rich(X)|~calm(X))))&
(![X]:((~generous(X)<~>tall(X))=>(tall(X)|~funny(X))))&
(![X]:(~kind(X)<=>(calm(X)&generous(X))))&
((?[X]:((~curious(X)&~generous(X))))<=>(?[X]:((quiet(X)|brave(X)))))&
((?[X]:((~calm(X)<~>strong(X))))<=>(~quiet(paul)))&
(![X]:(~curious(X)<=>(calm(X)&old(X))))&
(![X]:((~generous(X)|~humble(X))<=>(~patient(X)&~kind(X))))&
((?[X]:((~old(X)<~>funny(X))))=>(?[X]:((~kind(X)<~>~happy(X)))))&
(![X]:(~old(X)<=>(kind(X)<~>funny(X))))&
(![X]:((~creative(X)<~>brave(X))=>(quiet(X)&creative(X))))&
((strong(susan))=>((generous(alice)&~funny(alice))))&
(![X]:(~old(X)<=>(patient(X)&~generous(X))))&
((?[X]:((patient(X)&~old(X))))=>(?[X]:((calm(X)&patient(X)))))&
((funny(paul))<=>((~kind(lucy)<~>calm(lucy))))&
(![X]:(generous(X)<=>(~happy(X)<~>rich(X))))&
(![X]:(humble(X)<=>~brave(X)))&
(?[X]:((tall(X)<~>happy(X))))&
((happy(john)&tall(john)))&
(?[X]:((~curious(X)&~rich(X))))&
(~tall(fred))&
((~calm(lucy)<~>tall(lucy))) | ~strong(alice) | [] | null | 0 |
If someone is funny or generous then lucy is not calm. Everyone who is not tall is not calm or not kind and vice versa. Everyone who is either not strong or not happy is not quiet or kind and vice versa. Everyone who is not wise is old. If someone is both wise and brave then someone is not happy or quiet and vice versa. If someone is either strong or old then fred is strong or not curious and vice versa. Everyone who is humble or not tall is either not quiet or not tall and vice versa. Everyone who is funny or not funny is either strong or not strong. Everyone who is either rich or old is kind. Everyone who is funny or generous is not creative or humble and vice versa. Everyone who is funny is tall or funny and vice versa. Everyone who is either not happy or creative is not kind or curious and vice versa. Everyone who is both not rich and old is kind or not kind. If mary is not curious or kind then mary is both not creative and not rich and vice versa. Everyone who is not curious or tall is either not generous or rich and vice versa. Alice is both happy and rich. Someone is not strong. Someone is not patient. Someone is kind. Someone is both not creative and strong. Someone is either not happy or kind. Paul is both patient and tall. | Alice is wise. | neutral | ((?[X]:((funny(X)|generous(X))))=>(~calm(lucy)))&
(![X]:(~tall(X)<=>(~calm(X)|~kind(X))))&
(![X]:((~strong(X)<~>~happy(X))<=>(~quiet(X)|kind(X))))&
(![X]:(~wise(X)=>old(X)))&
((?[X]:((wise(X)&brave(X))))<=>(?[X]:((~happy(X)|quiet(X)))))&
((?[X]:((strong(X)<~>old(X))))<=>((strong(fred)|~curious(fred))))&
(![X]:((humble(X)|~tall(X))<=>(~quiet(X)<~>~tall(X))))&
(![X]:((funny(X)|~funny(X))=>(strong(X)<~>~strong(X))))&
(![X]:((rich(X)<~>old(X))=>kind(X)))&
(![X]:((funny(X)|generous(X))<=>(~creative(X)|humble(X))))&
(![X]:(funny(X)<=>(tall(X)|funny(X))))&
(![X]:((~happy(X)<~>creative(X))<=>(~kind(X)|curious(X))))&
(![X]:((~rich(X)&old(X))=>(kind(X)|~kind(X))))&
(((~curious(mary)|kind(mary)))<=>((~creative(mary)&~rich(mary))))&
(![X]:((~curious(X)|tall(X))<=>(~generous(X)<~>rich(X))))&
((happy(alice)&rich(alice)))&
(?[X]:(~strong(X)))&
(?[X]:(~patient(X)))&
(?[X]:(kind(X)))&
(?[X]:((~creative(X)&strong(X))))&
(?[X]:((~happy(X)<~>kind(X))))&
((patient(paul)&tall(paul))) | wise(alice) | [] | null | 0 |
If someone is not kind then fred is not generous or not brave and vice versa.
Everyone who is not strong is both not rich and not old and vice versa.
If someone is not generous or not quiet then someone is both not creative and not funny and vice versa.
Everyone who is not generous is both generous and not quiet and vice versa.
Everyone who is both kind and humble is not creative and vice versa.
If lucy is either not curious or not old then fred is patient or not strong.
Everyone who is happy is either patient or curious and vice versa.
Everyone who is both creative and not humble is either wise or kind and vice versa.
Everyone who is calm or not curious is not patient.
Everyone who is both wise and happy is funny or not happy.
Everyone who is both humble and not happy is curious or not calm and vice versa.
If someone is not creative or patient then someone is either not funny or rich and vice versa.
Everyone who is wise or not strong is both not strong and kind.
If someone is both not brave and tall then someone is not happy and vice versa.
If someone is not happy or not tall then fred is either tall or not rich and vice versa.
If john is both not wise and curious then someone is rich or not calm and vice versa.
Paul is either wise or patient.
Someone is either tall or not funny.
Someone is either creative or kind.
Mary is either humble or tall.
Someone is both not curious and not strong.
Someone is creative.
Someone is both rich and not wise. | Lucy is creative. | neutral | ((?[X]:(~kind(X)))<=>((~generous(fred)|~brave(fred))))&
(![X]:(~strong(X)<=>(~rich(X)&~old(X))))&
((?[X]:((~generous(X)|~quiet(X))))<=>(?[X]:((~creative(X)&~funny(X)))))&
(![X]:(~generous(X)<=>(generous(X)&~quiet(X))))&
(![X]:((kind(X)&humble(X))<=>~creative(X)))&
(((~curious(lucy)<~>~old(lucy)))=>((patient(fred)|~strong(fred))))&
(![X]:(happy(X)<=>(patient(X)<~>curious(X))))&
(![X]:((creative(X)&~humble(X))<=>(wise(X)<~>kind(X))))&
(![X]:((calm(X)|~curious(X))=>~patient(X)))&
(![X]:((wise(X)&happy(X))=>(funny(X)|~happy(X))))&
(![X]:((humble(X)&~happy(X))<=>(curious(X)|~calm(X))))&
((?[X]:((~creative(X)|patient(X))))<=>(?[X]:((~funny(X)<~>rich(X)))))&
(![X]:((wise(X)|~strong(X))=>(~strong(X)&kind(X))))&
((?[X]:((~brave(X)&tall(X))))<=>(?[X]:(~happy(X))))&
((?[X]:((~happy(X)|~tall(X))))<=>((tall(fred)<~>~rich(fred))))&
(((~wise(john)&curious(john)))<=>(?[X]:((rich(X)|~calm(X)))))&
((wise(paul)<~>patient(paul)))&
(?[X]:((tall(X)<~>~funny(X))))&
(?[X]:((creative(X)<~>kind(X))))&
((humble(mary)<~>tall(mary)))&
(?[X]:((~curious(X)&~strong(X))))&
(?[X]:(creative(X)))&
(?[X]:((rich(X)&~wise(X)))) | creative(lucy) | [] | null | 0 |
If fred is either kind or not tall then someone is not strong or not curious.
Everyone who is either not calm or not brave is kind or curious and vice versa.
Everyone who is humble or kind is both not kind and not generous and vice versa.
Everyone who is not wise is both not generous and humble and vice versa.
Everyone who is generous or humble is both wise and happy.
If someone is both wise and creative then someone is funny or not brave.
If susan is either happy or calm then someone is both not brave and not humble.
Everyone who is generous or not happy is generous or rich.
Everyone who is both not patient and humble is not happy or not generous.
Everyone who is happy or brave is not patient or wise and vice versa.
If alice is both not funny and kind then someone is both kind and not happy.
Everyone who is not strong is brave and vice versa.
If susan is not rich or humble then someone is tall or not rich.
Everyone who is both not creative and quiet is not tall or patient and vice versa.
Everyone who is creative or not creative is quiet or not kind.
John is either calm or funny.
Someone is not humble or not tall.
Someone is both funny and not tall.
Someone is brave.
Lucy is either creative or brave.
Someone is brave or not funny.
Alice is both rich and wise. | Lucy is generous. | entailment | (((kind(fred)<~>~tall(fred)))=>(?[X]:((~strong(X)|~curious(X)))))&
(![X]:((~calm(X)<~>~brave(X))<=>(kind(X)|curious(X))))&
(![X]:((humble(X)|kind(X))<=>(~kind(X)&~generous(X))))&
(![X]:(~wise(X)<=>(~generous(X)&humble(X))))&
(![X]:((generous(X)|humble(X))=>(wise(X)&happy(X))))&
((?[X]:((wise(X)&creative(X))))=>(?[X]:((funny(X)|~brave(X)))))&
(((happy(susan)<~>calm(susan)))=>(?[X]:((~brave(X)&~humble(X)))))&
(![X]:((generous(X)|~happy(X))=>(generous(X)|rich(X))))&
(![X]:((~patient(X)&humble(X))=>(~happy(X)|~generous(X))))&
(![X]:((happy(X)|brave(X))<=>(~patient(X)|wise(X))))&
(((~funny(alice)&kind(alice)))=>(?[X]:((kind(X)&~happy(X)))))&
(![X]:(~strong(X)<=>brave(X)))&
(((~rich(susan)|humble(susan)))=>(?[X]:((tall(X)|~rich(X)))))&
(![X]:((~creative(X)&quiet(X))<=>(~tall(X)|patient(X))))&
(![X]:((creative(X)|~creative(X))=>(quiet(X)|~kind(X))))&
((calm(john)<~>funny(john)))&
(?[X]:((~humble(X)|~tall(X))))&
(?[X]:((funny(X)&~tall(X))))&
(?[X]:(brave(X)))&
((creative(lucy)<~>brave(lucy)))&
(?[X]:((brave(X)|~funny(X))))&
((rich(alice)&wise(alice))) | generous(lucy) | [
"p2",
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 6543648953869877838138640
% SZS output start Proof for 6543648953869877838138640
3. ! [X0] : ((kind(X0) | humble(X0)) <=> (~generous(X0) & ~kind(X0))) [input p2]
4. ! [X0] : (~wise(X0) <=> (humble(X0) & ~generous(X0))) [input p3]
5. ! [X0] : ((humble(X0) | generous(X0)) => (happy(X0) & wise(X0))) [input p4]
23. ~generous(lucy) [input hypothesis]
27. ! [X0] : ((happy(X0) & wise(X0)) | (~humble(X0) & ~generous(X0))) [ennf transformation 5]
45. ! [X0] : (((kind(X0) | humble(X0)) | (generous(X0) | kind(X0))) & ((~generous(X0) & ~kind(X0)) | (~kind(X0) & ~humble(X0)))) [nnf transformation 3]
46. ! [X0] : ((kind(X0) | humble(X0) | generous(X0) | kind(X0)) & ((~generous(X0) & ~kind(X0)) | (~kind(X0) & ~humble(X0)))) [flattening 45]
47. ! [X0] : ((~wise(X0) | (~humble(X0) | generous(X0))) & ((humble(X0) & ~generous(X0)) | wise(X0))) [nnf transformation 4]
48. ! [X0] : ((~wise(X0) | ~humble(X0) | generous(X0)) & ((humble(X0) & ~generous(X0)) | wise(X0))) [flattening 47]
82. ~kind(X0) | ~kind(X0) [cnf transformation 46]
83. ~generous(X0) | ~humble(X0) [cnf transformation 46]
85. kind(X0) | humble(X0) | generous(X0) | kind(X0) [cnf transformation 46]
88. ~wise(X0) | ~humble(X0) | generous(X0) [cnf transformation 48]
90. wise(X0) | ~humble(X0) [cnf transformation 27]
128. ~generous(lucy) [cnf transformation 23]
129. ~kind(X0) [duplicate literal removal 82]
130. generous(X0) | humble(X0) | kind(X0) [duplicate literal removal 85]
149. ~wise(X0) | ~humble(X0) [subsumption resolution 88,83]
150. ~humble(X0) [subsumption resolution 90,149]
267. humble(lucy) | kind(lucy) [resolution 130,128]
272. kind(lucy) [subsumption resolution 267,150]
273. $false [subsumption resolution 272,129]
% SZS output end Proof for 6543648953869877838138640
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and not calm is both patient and not tall.
If someone is tall or rich then someone is either strong or not humble.
Everyone who is either old or funny is both not wise and not patient.
Everyone who is either wise or funny is both wise and not creative.
If someone is both not funny and creative then john is not brave and vice versa.
If alice is both tall and kind then someone is not funny.
Everyone who is not tall is not kind and vice versa.
Everyone who is humble is either old or not happy and vice versa.
Everyone who is both not creative and not rich is funny or not tall.
If someone is rich or kind then someone is generous or not curious.
Everyone who is both wise and generous is either not kind or not brave and vice versa.
Everyone who is not curious or generous is rich or humble and vice versa.
If someone is both wise and brave then mary is kind.
Everyone who is either not calm or curious is both wise and not old.
If someone is not brave or wise then lucy is not funny or kind.
Everyone who is quiet or brave is both not kind and not creative.
John is both patient and not rich.
John is curious.
Someone is either humble or happy.
Mary is patient.
Someone is tall.
Someone is not kind.
John is both not funny and not happy.
Someone is wise or old. | Alice is kind. | neutral | (![X]:((strong(X)&~calm(X))=>(patient(X)&~tall(X))))&
((?[X]:((tall(X)|rich(X))))=>(?[X]:((strong(X)<~>~humble(X)))))&
(![X]:((old(X)<~>funny(X))=>(~wise(X)&~patient(X))))&
(![X]:((wise(X)<~>funny(X))=>(wise(X)&~creative(X))))&
((?[X]:((~funny(X)&creative(X))))<=>(~brave(john)))&
(((tall(alice)&kind(alice)))=>(?[X]:(~funny(X))))&
(![X]:(~tall(X)<=>~kind(X)))&
(![X]:(humble(X)<=>(old(X)<~>~happy(X))))&
(![X]:((~creative(X)&~rich(X))=>(funny(X)|~tall(X))))&
((?[X]:((rich(X)|kind(X))))=>(?[X]:((generous(X)|~curious(X)))))&
(![X]:((wise(X)&generous(X))<=>(~kind(X)<~>~brave(X))))&
(![X]:((~curious(X)|generous(X))<=>(rich(X)|humble(X))))&
((?[X]:((wise(X)&brave(X))))=>(kind(mary)))&
(![X]:((~calm(X)<~>curious(X))=>(wise(X)&~old(X))))&
((?[X]:((~brave(X)|wise(X))))=>((~funny(lucy)|kind(lucy))))&
(![X]:((quiet(X)|brave(X))=>(~kind(X)&~creative(X))))&
((patient(john)&~rich(john)))&
(curious(john))&
(?[X]:((humble(X)<~>happy(X))))&
(patient(mary))&
(?[X]:(tall(X)))&
(?[X]:(~kind(X)))&
((~funny(john)&~happy(john)))&
(?[X]:((wise(X)|old(X)))) | kind(alice) | [] | null | 0 |
If mary is not humble or not strong then fred is not creative and vice versa.
If someone is either strong or kind then someone is either wise or happy.
Everyone who is either kind or not strong is tall and vice versa.
Everyone who is kind or rich is not strong or calm.
If fred is creative then someone is not funny and vice versa.
Everyone who is both not brave and patient is brave and vice versa.
If someone is both patient and brave then fred is not quiet.
Everyone who is funny or not calm is patient and vice versa.
Everyone who is either not humble or not funny is not tall.
Everyone who is generous or old is both not curious and tall.
If someone is both not creative and not humble then susan is either not kind or generous and vice versa.
Everyone who is either creative or not wise is not calm or not brave and vice versa.
If mary is not rich or curious then susan is calm or not brave.
If lucy is both strong and not tall then fred is old and vice versa.
Everyone who is not strong is both not brave and funny and vice versa.
Everyone who is calm or quiet is both not funny and wise and vice versa.
Fred is old or not generous.
Someone is not kind.
Someone is both rich and curious.
John is not humble.
John is not generous or kind.
John is either patient or not rich.
Mary is either not old or curious. | Fred is not kind. | neutral | (((~humble(mary)|~strong(mary)))<=>(~creative(fred)))&
((?[X]:((strong(X)<~>kind(X))))=>(?[X]:((wise(X)<~>happy(X)))))&
(![X]:((kind(X)<~>~strong(X))<=>tall(X)))&
(![X]:((kind(X)|rich(X))=>(~strong(X)|calm(X))))&
((creative(fred))<=>(?[X]:(~funny(X))))&
(![X]:((~brave(X)&patient(X))<=>brave(X)))&
((?[X]:((patient(X)&brave(X))))=>(~quiet(fred)))&
(![X]:((funny(X)|~calm(X))<=>patient(X)))&
(![X]:((~humble(X)<~>~funny(X))=>~tall(X)))&
(![X]:((generous(X)|old(X))=>(~curious(X)&tall(X))))&
((?[X]:((~creative(X)&~humble(X))))<=>((~kind(susan)<~>generous(susan))))&
(![X]:((creative(X)<~>~wise(X))<=>(~calm(X)|~brave(X))))&
(((~rich(mary)|curious(mary)))=>((calm(susan)|~brave(susan))))&
(((strong(lucy)&~tall(lucy)))<=>(old(fred)))&
(![X]:(~strong(X)<=>(~brave(X)&funny(X))))&
(![X]:((calm(X)|quiet(X))<=>(~funny(X)&wise(X))))&
((old(fred)|~generous(fred)))&
(?[X]:(~kind(X)))&
(?[X]:((rich(X)&curious(X))))&
(~humble(john))&
((~generous(john)|kind(john)))&
((patient(john)<~>~rich(john)))&
((~old(mary)<~>curious(mary))) | ~kind(fred) | [] | null | 0 |
Everyone who is either happy or quiet is both tall and not strong and vice versa.
Everyone who is not quiet or not funny is both quiet and old and vice versa.
Everyone who is old is either not curious or calm and vice versa.
If fred is both not old and patient then alice is both humble and not wise.
If alice is generous or not tall then someone is not calm or rich and vice versa.
If lucy is both not kind and wise then someone is brave.
If someone is either quiet or not calm then someone is both not curious and not humble and vice versa.
Everyone who is generous or not generous is not calm.
If paul is wise or rich then susan is both not kind and patient and vice versa.
If fred is either brave or not quiet then alice is either not old or patient.
If someone is either not strong or generous then mary is both old and not curious and vice versa.
Everyone who is not kind or not brave is either old or curious and vice versa.
If fred is both calm and creative then susan is both not old and not curious and vice versa.
Everyone who is not happy is humble or not creative and vice versa.
If susan is not patient or quiet then lucy is generous.
Mary is both wise and not curious.
Someone is not kind.
Someone is both generous and not wise.
Someone is patient.
Someone is kind.
Someone is brave or not happy.
Someone is both not wise and not creative. | Mary is not happy. | entailment | (![X]:((happy(X)<~>quiet(X))<=>(tall(X)&~strong(X))))&
(![X]:((~quiet(X)|~funny(X))<=>(quiet(X)&old(X))))&
(![X]:(old(X)<=>(~curious(X)<~>calm(X))))&
(((~old(fred)&patient(fred)))=>((humble(alice)&~wise(alice))))&
(((generous(alice)|~tall(alice)))<=>(?[X]:((~calm(X)|rich(X)))))&
(((~kind(lucy)&wise(lucy)))=>(?[X]:(brave(X))))&
((?[X]:((quiet(X)<~>~calm(X))))<=>(?[X]:((~curious(X)&~humble(X)))))&
(![X]:((generous(X)|~generous(X))=>~calm(X)))&
(((wise(paul)|rich(paul)))<=>((~kind(susan)&patient(susan))))&
(((brave(fred)<~>~quiet(fred)))=>((~old(alice)<~>patient(alice))))&
((?[X]:((~strong(X)<~>generous(X))))<=>((old(mary)&~curious(mary))))&
(![X]:((~kind(X)|~brave(X))<=>(old(X)<~>curious(X))))&
(((calm(fred)&creative(fred)))<=>((~old(susan)&~curious(susan))))&
(![X]:(~happy(X)<=>(humble(X)|~creative(X))))&
(((~patient(susan)|quiet(susan)))=>(generous(lucy)))&
((wise(mary)&~curious(mary)))&
(?[X]:(~kind(X)))&
(?[X]:((generous(X)&~wise(X))))&
(?[X]:(patient(X)))&
(?[X]:(kind(X)))&
(?[X]:((brave(X)|~happy(X))))&
(?[X]:((~wise(X)&~creative(X)))) | ~happy(mary) | [
"p1",
"p6",
"p7",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6396725558737949674585155
% SZS output start Proof for 6396725558737949674585155
2. ! [X0] : ((~funny(X0) | ~quiet(X0)) <=> (old(X0) & quiet(X0))) [input p1]
7. ? [X0] : (quiet(X0) <~> ~calm(X0)) <=> ? [X0] : (~humble(X0) & ~curious(X0)) [input p6]
8. ! [X0] : ((~generous(X0) | generous(X0)) => ~calm(X0)) [input p7]
14. ! [X0] : (~happy(X0) <=> (~creative(X0) | humble(X0))) [input p13]
16. ~curious(mary) & wise(mary) [input p15]
23. happy(mary) [input hypothesis]
24. ? [X0] : (quiet(X0) <~> ~calm(X0)) <=> ? [X1] : (~humble(X1) & ~curious(X1)) [rectify 7]
29. ! [X0] : (~calm(X0) | (generous(X0) & ~generous(X0))) [ennf transformation 8]
34. ! [X0] : (((~funny(X0) | ~quiet(X0)) | (~old(X0) | ~quiet(X0))) & ((old(X0) & quiet(X0)) | (funny(X0) & quiet(X0)))) [nnf transformation 2]
35. ! [X0] : ((~funny(X0) | ~quiet(X0) | ~old(X0) | ~quiet(X0)) & ((old(X0) & quiet(X0)) | (funny(X0) & quiet(X0)))) [flattening 34]
44. (? [X0] : ((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) | ! [X1] : (humble(X1) | curious(X1))) & (? [X1] : (~humble(X1) & ~curious(X1)) | ! [X0] : ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0)))) [nnf transformation 24]
45. (? [X0] : ((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) | ! [X1] : (humble(X1) | curious(X1))) & (? [X2] : (~humble(X2) & ~curious(X2)) | ! [X3] : ((quiet(X3) | calm(X3)) & (~calm(X3) | ~quiet(X3)))) [rectify 44]
46. ? [X0] : ((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) => ((calm(sK2) | ~quiet(sK2)) & (~calm(sK2) | quiet(sK2))) [choice axiom]
47. ? [X2] : (~humble(X2) & ~curious(X2)) => (~humble(sK3) & ~curious(sK3)) [choice axiom]
48. (((calm(sK2) | ~quiet(sK2)) & (~calm(sK2) | quiet(sK2))) | ! [X1] : (humble(X1) | curious(X1))) & ((~humble(sK3) & ~curious(sK3)) | ! [X3] : ((quiet(X3) | calm(X3)) & (~calm(X3) | ~quiet(X3)))) [skolemisation 45,47,46]
61. ! [X0] : ((~happy(X0) | (creative(X0) & ~humble(X0))) & ((~creative(X0) | humble(X0)) | happy(X0))) [nnf transformation 14]
62. ! [X0] : ((~happy(X0) | (creative(X0) & ~humble(X0))) & (~creative(X0) | humble(X0) | happy(X0))) [flattening 61]
81. quiet(X0) | quiet(X0) [cnf transformation 35]
102. calm(sK2) | ~quiet(sK2) | humble(X1) | curious(X1) [cnf transformation 48]
103. ~calm(X0) | ~generous(X0) [cnf transformation 29]
104. ~calm(X0) | generous(X0) [cnf transformation 29]
131. ~humble(X0) | ~happy(X0) [cnf transformation 62]
136. ~curious(mary) [cnf transformation 16]
145. happy(mary) [cnf transformation 23]
146. quiet(X0) [duplicate literal removal 81]
205. calm(sK2) | humble(X1) | curious(X1) [subsumption resolution 102,146]
207. 14 <=> ! [X1] : (humble(X1) | curious(X1)) [avatar definition]
208. humble(X1) | curious(X1) <- (14) [avatar component clause 207]
210. 15 <=> calm(sK2) [avatar definition]
212. calm(sK2) <- (15) [avatar component clause 210]
213. 14 | 15 [avatar split clause 205,210,207]
216. 16 <=> ! [X3] : ~calm(X3) [avatar definition]
217. ~calm(X3) <- (16) [avatar component clause 216]
229. ~calm(X0) [subsumption resolution 103,104]
230. 16 [avatar split clause 229,216]
273. 27 <=> curious(mary) [avatar definition]
274. ~curious(mary) <- (~27) [avatar component clause 273]
317. ~27 [avatar split clause 136,273]
328. ~happy(X0) | curious(X0) <- (14) [resolution 208,131]
330. curious(mary) <- (14) [resolution 328,145]
331. $false <- (14, ~27) [subsumption resolution 330,274]
332. ~14 | 27 [avatar contradiction clause 331]
333. $false <- (15, 16) [subsumption resolution 212,217]
334. ~15 | ~16 [avatar contradiction clause 333]
335. $false [avatar sat refutation 213,230,317,332,334]
% SZS output end Proof for 6396725558737949674585155
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not wise is both kind and generous and vice versa. If alice is either curious or old then someone is both happy and kind. Everyone who is either not brave or curious is happy. Everyone who is not tall or not generous is either tall or not rich and vice versa. If alice is wise or not brave then fred is both quiet and not kind and vice versa. If alice is not humble then someone is both not old and humble. If alice is either not wise or quiet then john is both old and not strong and vice versa. Everyone who is wise is either not humble or happy and vice versa. If someone is not old then lucy is not quiet or wise. Everyone who is curious is either creative or not generous. Everyone who is not happy is kind or rich and vice versa. If john is either not funny or happy then someone is not curious or strong and vice versa. Everyone who is not patient or not quiet is kind. Everyone who is both not wise and not quiet is either patient or generous and vice versa. If someone is not brave or creative then fred is either not funny or not tall. If lucy is not rich or creative then fred is both not patient and humble. Someone is brave. Someone is either kind or not humble. Paul is either tall or creative. Susan is either not creative or kind. Paul is both strong and not curious. Lucy is both humble and calm. Someone is either rich or humble. Someone is creative or not generous. | Fred is not quiet. | entailment | (![X]:((curious(X)|~wise(X))<=>(kind(X)&generous(X))))&
(((curious(alice)<~>old(alice)))=>(?[X]:((happy(X)&kind(X)))))&
(![X]:((~brave(X)<~>curious(X))=>happy(X)))&
(![X]:((~tall(X)|~generous(X))<=>(tall(X)<~>~rich(X))))&
(((wise(alice)|~brave(alice)))<=>((quiet(fred)&~kind(fred))))&
((~humble(alice))=>(?[X]:((~old(X)&humble(X)))))&
(((~wise(alice)<~>quiet(alice)))<=>((old(john)&~strong(john))))&
(![X]:(wise(X)<=>(~humble(X)<~>happy(X))))&
((?[X]:(~old(X)))=>((~quiet(lucy)|wise(lucy))))&
(![X]:(curious(X)=>(creative(X)<~>~generous(X))))&
(![X]:(~happy(X)<=>(kind(X)|rich(X))))&
(((~funny(john)<~>happy(john)))<=>(?[X]:((~curious(X)|strong(X)))))&
(![X]:((~patient(X)|~quiet(X))=>kind(X)))&
(![X]:((~wise(X)&~quiet(X))<=>(patient(X)<~>generous(X))))&
((?[X]:((~brave(X)|creative(X))))=>((~funny(fred)<~>~tall(fred))))&
(((~rich(lucy)|creative(lucy)))=>((~patient(fred)&humble(fred))))&
(?[X]:(brave(X)))&
(?[X]:((kind(X)<~>~humble(X))))&
((tall(paul)<~>creative(paul)))&
((~creative(susan)<~>kind(susan)))&
((strong(paul)&~curious(paul)))&
((humble(lucy)&calm(lucy)))&
(?[X]:((rich(X)<~>humble(X))))&
(?[X]:((creative(X)|~generous(X)))) | ~quiet(fred) | [
"p0",
"p3",
"p7",
"p10",
"p12",
"p13",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2523512379499972957954077
% SZS output start Proof for 2523512379499972957954077
1. ! [X0] : ((~wise(X0) | curious(X0)) <=> (generous(X0) & kind(X0))) [input p0]
4. ! [X0] : ((~generous(X0) | ~tall(X0)) <=> (tall(X0) <~> ~rich(X0))) [input p3]
8. ! [X0] : (wise(X0) <=> (~humble(X0) <~> happy(X0))) [input p7]
11. ! [X0] : (~happy(X0) <=> (rich(X0) | kind(X0))) [input p10]
13. ! [X0] : ((~quiet(X0) | ~patient(X0)) => kind(X0)) [input p12]
14. ! [X0] : ((~quiet(X0) & ~wise(X0)) <=> (patient(X0) <~> generous(X0))) [input p13]
16. (creative(lucy) | ~rich(lucy)) => (humble(fred) & ~patient(fred)) [input p15]
22. calm(lucy) & humble(lucy) [input p21]
25. quiet(fred) [input hypothesis]
26. humble(lucy) [pure predicate removal 22]
33. ! [X0] : (kind(X0) | (quiet(X0) & patient(X0))) [ennf transformation 13]
35. (humble(fred) & ~patient(fred)) | (~creative(lucy) & rich(lucy)) [ennf transformation 16]
36. ! [X0] : (((~wise(X0) | curious(X0)) | (~generous(X0) | ~kind(X0))) & ((generous(X0) & kind(X0)) | (wise(X0) & ~curious(X0)))) [nnf transformation 1]
37. ! [X0] : ((~wise(X0) | curious(X0) | ~generous(X0) | ~kind(X0)) & ((generous(X0) & kind(X0)) | (wise(X0) & ~curious(X0)))) [flattening 36]
42. ! [X0] : (((~generous(X0) | ~tall(X0)) | ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0)))) & (((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) | (generous(X0) & tall(X0)))) [nnf transformation 4]
43. ! [X0] : ((~generous(X0) | ~tall(X0) | ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0)))) & (((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) | (generous(X0) & tall(X0)))) [flattening 42]
50. ! [X0] : ((wise(X0) | ((~humble(X0) | ~happy(X0)) & (happy(X0) | humble(X0)))) & (((~happy(X0) | humble(X0)) & (happy(X0) | ~humble(X0))) | ~wise(X0))) [nnf transformation 8]
52. ! [X0] : ((~happy(X0) | (~rich(X0) & ~kind(X0))) & ((rich(X0) | kind(X0)) | happy(X0))) [nnf transformation 11]
53. ! [X0] : ((~happy(X0) | (~rich(X0) & ~kind(X0))) & (rich(X0) | kind(X0) | happy(X0))) [flattening 52]
58. ! [X0] : (((~quiet(X0) & ~wise(X0)) | ((patient(X0) | ~generous(X0)) & (generous(X0) | ~patient(X0)))) & (((~generous(X0) | ~patient(X0)) & (generous(X0) | patient(X0))) | (quiet(X0) | wise(X0)))) [nnf transformation 14]
59. ! [X0] : (((~quiet(X0) & ~wise(X0)) | ((patient(X0) | ~generous(X0)) & (generous(X0) | ~patient(X0)))) & (((~generous(X0) | ~patient(X0)) & (generous(X0) | patient(X0))) | quiet(X0) | wise(X0))) [flattening 58]
76. generous(X0) | wise(X0) [cnf transformation 37]
84. ~rich(X0) | tall(X0) | tall(X0) [cnf transformation 43]
88. ~generous(X0) | ~tall(X0) | ~rich(X0) | ~tall(X0) [cnf transformation 43]
103. ~humble(X0) | happy(X0) | ~wise(X0) [cnf transformation 50]
111. ~happy(X0) | ~kind(X0) [cnf transformation 53]
112. ~rich(X0) | ~happy(X0) [cnf transformation 53]
119. patient(X0) | kind(X0) [cnf transformation 33]
126. ~quiet(X0) | patient(X0) | ~generous(X0) [cnf transformation 59]
131. ~patient(fred) | rich(lucy) [cnf transformation 35]
133. humble(fred) | rich(lucy) [cnf transformation 35]
144. humble(lucy) [cnf transformation 26]
148. quiet(fred) [cnf transformation 25]
149. ~rich(X0) | tall(X0) [duplicate literal removal 84]
150. ~rich(X0) | ~tall(X0) | ~generous(X0) [duplicate literal removal 88]
172. 5 <=> quiet(fred) [avatar definition]
173. quiet(fred) <- (5) [avatar component clause 172]
176. 6 <=> kind(fred) [avatar definition]
178. kind(fred) <- (6) [avatar component clause 176]
232. 17 <=> wise(lucy) [avatar definition]
290. 29 <=> humble(fred) [avatar definition]
292. humble(fred) <- (29) [avatar component clause 290]
295. 30 <=> rich(lucy) [avatar definition]
297. rich(lucy) <- (30) [avatar component clause 295]
298. 30 | 29 [avatar split clause 133,290,295]
300. 31 <=> patient(fred) [avatar definition]
302. ~patient(fred) <- (~31) [avatar component clause 300]
304. 30 | ~31 [avatar split clause 131,300,295]
354. 5 [avatar split clause 148,172]
360. kind(fred) <- (~31) [resolution 119,302]
363. 6 | 31 [avatar split clause 360,300,176]
394. happy(lucy) | ~wise(lucy) [resolution 103,144]
396. happy(fred) | ~wise(fred) <- (29) [resolution 103,292]
398. 46 <=> happy(lucy) [avatar definition]
401. ~17 | 46 [avatar split clause 394,398,232]
403. 47 <=> wise(fred) [avatar definition]
405. ~wise(fred) <- (~47) [avatar component clause 403]
407. 48 <=> happy(fred) [avatar definition]
409. happy(fred) <- (48) [avatar component clause 407]
410. ~47 | 48 | ~29 [avatar split clause 396,290,407,403]
432. patient(fred) | ~generous(fred) <- (5) [resolution 126,173]
434. ~generous(fred) <- (5, ~31) [subsumption resolution 432,302]
441. wise(fred) <- (5, ~31) [resolution 434,76]
442. $false <- (5, ~31, ~47) [subsumption resolution 441,405]
443. ~5 | 31 | 47 [avatar contradiction clause 442]
449. ~tall(lucy) | ~generous(lucy) <- (30) [resolution 297,150]
451. tall(lucy) <- (30) [resolution 297,149]
454. 50 <=> generous(lucy) [avatar definition]
456. ~generous(lucy) <- (~50) [avatar component clause 454]
458. 51 <=> tall(lucy) [avatar definition]
461. ~50 | ~51 | ~30 [avatar split clause 449,295,458,454]
463. 51 | ~30 [avatar split clause 451,295,458]
469. ~kind(fred) <- (48) [resolution 409,111]
470. $false <- (6, 48) [subsumption resolution 469,178]
471. ~6 | ~48 [avatar contradiction clause 470]
476. ~happy(lucy) <- (30) [resolution 297,112]
484. wise(lucy) <- (~50) [resolution 456,76]
487. 17 | 50 [avatar split clause 484,454,232]
489. ~46 | ~30 [avatar split clause 476,295,398]
490. $false [avatar sat refutation 298,304,354,363,401,410,443,461,463,471,487,489]
% SZS output end Proof for 2523512379499972957954077
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either kind or not calm then mary is creative.
If someone is funny or humble then fred is either not brave or rich and vice versa.
Everyone who is either curious or not calm is both not wise and not humble.
Everyone who is either not curious or rich is either quiet or not tall.
Everyone who is either not old or strong is either strong or not wise and vice versa.
Everyone who is curious is either not generous or not calm and vice versa.
If john is either not generous or wise then someone is both creative and happy and vice versa.
If mary is both generous and not old then someone is either not wise or not calm and vice versa.
Everyone who is both patient and wise is brave or generous and vice versa.
Everyone who is brave or kind is old or brave.
If alice is either not curious or not patient then someone is generous.
Everyone who is either not creative or rich is either not happy or not wise and vice versa.
Everyone who is patient is not wise or not tall.
Everyone who is either not old or not tall is not rich.
Everyone who is either not tall or happy is humble or kind.
Everyone who is not rich or creative is rich or creative.
Fred is both not strong and kind.
Someone is both not kind and not humble.
John is both not kind and humble.
Alice is either calm or not strong.
Someone is both not tall and funny. | John is curious. | contradiction | (((kind(paul)<~>~calm(paul)))=>(creative(mary)))&
((?[X]:((funny(X)|humble(X))))<=>((~brave(fred)<~>rich(fred))))&
(![X]:((curious(X)<~>~calm(X))=>(~wise(X)&~humble(X))))&
(![X]:((~curious(X)<~>rich(X))=>(quiet(X)<~>~tall(X))))&
(![X]:((~old(X)<~>strong(X))<=>(strong(X)<~>~wise(X))))&
(![X]:(curious(X)<=>(~generous(X)<~>~calm(X))))&
(((~generous(john)<~>wise(john)))<=>(?[X]:((creative(X)&happy(X)))))&
(((generous(mary)&~old(mary)))<=>(?[X]:((~wise(X)<~>~calm(X)))))&
(![X]:((patient(X)&wise(X))<=>(brave(X)|generous(X))))&
(![X]:((brave(X)|kind(X))=>(old(X)|brave(X))))&
(((~curious(alice)<~>~patient(alice)))=>(?[X]:(generous(X))))&
(![X]:((~creative(X)<~>rich(X))<=>(~happy(X)<~>~wise(X))))&
(![X]:(patient(X)=>(~wise(X)|~tall(X))))&
(![X]:((~old(X)<~>~tall(X))=>~rich(X)))&
(![X]:((~tall(X)<~>happy(X))=>(humble(X)|kind(X))))&
(![X]:((~rich(X)|creative(X))=>(rich(X)|creative(X))))&
((~strong(fred)&kind(fred)))&
(?[X]:((~kind(X)&~humble(X))))&
((~kind(john)&humble(john)))&
((calm(alice)<~>~strong(alice)))&
(?[X]:((~tall(X)&funny(X)))) | curious(john) | [
"p2",
"p4",
"p5",
"p7",
"p8",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5065827475516861306813011
% SZS output start Proof for 5065827475516861306813011
3. ! [X0] : ((curious(X0) <~> ~calm(X0)) => (~humble(X0) & ~wise(X0))) [input p2]
5. ! [X0] : ((~old(X0) <~> strong(X0)) <=> (strong(X0) <~> ~wise(X0))) [input p4]
6. ! [X0] : (curious(X0) <=> (~generous(X0) <~> ~calm(X0))) [input p5]
8. (~old(mary) & generous(mary)) <=> ? [X0] : (~wise(X0) <~> ~calm(X0)) [input p7]
9. ! [X0] : ((wise(X0) & patient(X0)) <=> (generous(X0) | brave(X0))) [input p8]
19. humble(john) & ~kind(john) [input p18]
22. curious(john) [input hypothesis]
24. ! [X0] : ((~humble(X0) & ~wise(X0)) | (curious(X0) <=> ~calm(X0))) [ennf transformation 3]
41. ! [X0] : ((~humble(X0) & ~wise(X0)) | ((curious(X0) | calm(X0)) & (~calm(X0) | ~curious(X0)))) [nnf transformation 24]
43. ! [X0] : ((((~strong(X0) | old(X0)) & (strong(X0) | ~old(X0))) | ((strong(X0) | wise(X0)) & (~wise(X0) | ~strong(X0)))) & (((wise(X0) | ~strong(X0)) & (~wise(X0) | strong(X0))) | ((~old(X0) | ~strong(X0)) & (strong(X0) | old(X0))))) [nnf transformation 5]
44. ! [X0] : ((curious(X0) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0)))) & (((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | ~curious(X0))) [nnf transformation 6]
49. ((~old(mary) & generous(mary)) | ! [X0] : ((~wise(X0) | calm(X0)) & (~calm(X0) | wise(X0)))) & (? [X0] : ((calm(X0) | wise(X0)) & (~calm(X0) | ~wise(X0))) | (old(mary) | ~generous(mary))) [nnf transformation 8]
50. ((~old(mary) & generous(mary)) | ! [X0] : ((~wise(X0) | calm(X0)) & (~calm(X0) | wise(X0)))) & (? [X0] : ((calm(X0) | wise(X0)) & (~calm(X0) | ~wise(X0))) | old(mary) | ~generous(mary)) [flattening 49]
51. ((~old(mary) & generous(mary)) | ! [X0] : ((~wise(X0) | calm(X0)) & (~calm(X0) | wise(X0)))) & (? [X1] : ((calm(X1) | wise(X1)) & (~calm(X1) | ~wise(X1))) | old(mary) | ~generous(mary)) [rectify 50]
52. ? [X1] : ((calm(X1) | wise(X1)) & (~calm(X1) | ~wise(X1))) => ((calm(sK2) | wise(sK2)) & (~calm(sK2) | ~wise(sK2))) [choice axiom]
53. ((~old(mary) & generous(mary)) | ! [X0] : ((~wise(X0) | calm(X0)) & (~calm(X0) | wise(X0)))) & (((calm(sK2) | wise(sK2)) & (~calm(sK2) | ~wise(sK2))) | old(mary) | ~generous(mary)) [skolemisation 51,52]
54. ! [X0] : (((wise(X0) & patient(X0)) | (~generous(X0) & ~brave(X0))) & ((generous(X0) | brave(X0)) | (~wise(X0) | ~patient(X0)))) [nnf transformation 9]
55. ! [X0] : (((wise(X0) & patient(X0)) | (~generous(X0) & ~brave(X0))) & (generous(X0) | brave(X0) | ~wise(X0) | ~patient(X0))) [flattening 54]
75. ~wise(X0) | ~calm(X0) | ~curious(X0) [cnf transformation 41]
77. ~curious(X0) | ~calm(X0) | ~humble(X0) [cnf transformation 41]
83. ~wise(X0) | strong(X0) | strong(X0) | old(X0) [cnf transformation 43]
89. ~strong(X0) | old(X0) | ~wise(X0) | ~strong(X0) [cnf transformation 43]
92. ~curious(X0) | generous(X0) | calm(X0) [cnf transformation 44]
104. generous(mary) | ~wise(X0) | calm(X0) [cnf transformation 53]
106. ~old(mary) | ~wise(X0) | calm(X0) [cnf transformation 53]
111. ~generous(X0) | wise(X0) [cnf transformation 55]
136. humble(john) [cnf transformation 19]
141. curious(john) [cnf transformation 22]
143. ~wise(X0) | strong(X0) | old(X0) [duplicate literal removal 83]
146. ~strong(X0) | old(X0) | ~wise(X0) [duplicate literal removal 89]
190. ~wise(X0) | old(X0) [subsumption resolution 143,146]
195. 11 <=> generous(john) [avatar definition]
196. ~generous(john) <- (~11) [avatar component clause 195]
197. generous(john) <- (11) [avatar component clause 195]
199. 12 <=> wise(john) [avatar definition]
200. wise(john) <- (12) [avatar component clause 199]
201. ~wise(john) <- (~12) [avatar component clause 199]
217. 15 <=> ! [X0] : (~wise(X0) | calm(X0)) [avatar definition]
218. ~wise(X0) | calm(X0) <- (15) [avatar component clause 217]
220. 16 <=> old(mary) [avatar definition]
222. ~old(mary) <- (~16) [avatar component clause 220]
223. 15 | ~16 [avatar split clause 106,220,217]
229. 18 <=> generous(mary) [avatar definition]
231. generous(mary) <- (18) [avatar component clause 229]
232. 15 | 18 [avatar split clause 104,229,217]
269. wise(john) <- (11) [resolution 111,197]
270. $false <- (11, ~12) [subsumption resolution 269,201]
271. ~11 | 12 [avatar contradiction clause 270]
275. calm(john) <- (12, 15) [resolution 218,200]
277. ~calm(john) | ~curious(john) <- (12) [resolution 75,200]
278. ~curious(john) <- (12, 15) [subsumption resolution 277,275]
279. $false <- (12, 15) [subsumption resolution 278,141]
280. ~12 | ~15 [avatar contradiction clause 279]
282. wise(mary) <- (18) [resolution 231,111]
291. old(mary) <- (18) [resolution 282,190]
302. $false <- (~16, 18) [subsumption resolution 291,222]
303. 16 | ~18 [avatar contradiction clause 302]
310. ~calm(john) | ~humble(john) [resolution 77,141]
311. ~calm(john) [subsumption resolution 310,136]
313. generous(john) | calm(john) [resolution 92,141]
314. calm(john) <- (~11) [subsumption resolution 313,196]
315. $false <- (~11) [subsumption resolution 314,311]
316. 11 [avatar contradiction clause 315]
317. $false [avatar sat refutation 223,232,271,280,303,316]
% SZS output end Proof for 5065827475516861306813011
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not patient is both not creative and not funny and vice versa.
Everyone who is calm or funny is either not quiet or not funny.
Everyone who is strong or generous is creative and vice versa.
Everyone who is either not creative or not funny is either quiet or not humble and vice versa.
If susan is both not rich and quiet then alice is either not kind or kind and vice versa.
If someone is happy or not calm then lucy is both generous and not generous and vice versa.
Everyone who is brave or not generous is not funny or not calm.
If mary is not kind then mary is either wise or strong and vice versa.
If someone is not wise then someone is both wise and not strong and vice versa.
Everyone who is either old or happy is not quiet or not old.
Everyone who is not quiet is rich or creative.
If someone is either not creative or not generous then someone is tall or quiet.
If someone is not kind then someone is both not wise and old.
Everyone who is either patient or not humble is wise.
Everyone who is not humble or humble is generous and vice versa.
Alice is not happy.
Someone is patient or wise.
Paul is both generous and not tall.
Someone is either brave or happy.
Fred is both humble and not brave.
Fred is either not humble or not quiet.
Mary is either generous or not brave. | Susan is patient. | contradiction | (![X]:((~old(X)<~>~patient(X))<=>(~creative(X)&~funny(X))))&
(![X]:((calm(X)|funny(X))=>(~quiet(X)<~>~funny(X))))&
(![X]:((strong(X)|generous(X))<=>creative(X)))&
(![X]:((~creative(X)<~>~funny(X))<=>(quiet(X)<~>~humble(X))))&
(((~rich(susan)&quiet(susan)))<=>((~kind(alice)<~>kind(alice))))&
((?[X]:((happy(X)|~calm(X))))<=>((generous(lucy)&~generous(lucy))))&
(![X]:((brave(X)|~generous(X))=>(~funny(X)|~calm(X))))&
((~kind(mary))<=>((wise(mary)<~>strong(mary))))&
((?[X]:(~wise(X)))<=>(?[X]:((wise(X)&~strong(X)))))&
(![X]:((old(X)<~>happy(X))=>(~quiet(X)|~old(X))))&
(![X]:(~quiet(X)=>(rich(X)|creative(X))))&
((?[X]:((~creative(X)<~>~generous(X))))=>(?[X]:((tall(X)|quiet(X)))))&
((?[X]:(~kind(X)))=>(?[X]:((~wise(X)&old(X)))))&
(![X]:((patient(X)<~>~humble(X))=>wise(X)))&
(![X]:((~humble(X)|humble(X))<=>generous(X)))&
(~happy(alice))&
(?[X]:((patient(X)|wise(X))))&
((generous(paul)&~tall(paul)))&
(?[X]:((brave(X)<~>happy(X))))&
((humble(fred)&~brave(fred)))&
((~humble(fred)<~>~quiet(fred)))&
((generous(mary)<~>~brave(mary))) | patient(susan) | [
"p0",
"p2",
"p4",
"p5",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 436161373106787383954535
% SZS output start Proof for 436161373106787383954535
1. ! [X0] : ((~old(X0) <~> ~patient(X0)) <=> (~funny(X0) & ~creative(X0))) [input p0]
3. ! [X0] : ((generous(X0) | strong(X0)) <=> creative(X0)) [input p2]
5. (quiet(susan) & ~rich(susan)) <=> (~kind(alice) <~> kind(alice)) [input p4]
6. ? [X0] : (~calm(X0) | happy(X0)) <=> (~generous(lucy) & generous(lucy)) [input p5]
10. ! [X0] : ((old(X0) <~> happy(X0)) => (~old(X0) | ~quiet(X0))) [input p9]
15. ! [X0] : ((humble(X0) | ~humble(X0)) <=> generous(X0)) [input p14]
23. patient(susan) [input hypothesis]
30. ! [X0] : ((~old(X0) | ~quiet(X0)) | (old(X0) <=> happy(X0))) [ennf transformation 10]
31. ! [X0] : (~old(X0) | ~quiet(X0) | (old(X0) <=> happy(X0))) [flattening 30]
37. ! [X0] : ((((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | (funny(X0) | creative(X0))) & ((~funny(X0) & ~creative(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0))))) [nnf transformation 1]
38. ! [X0] : ((((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | funny(X0) | creative(X0)) & ((~funny(X0) & ~creative(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0))))) [flattening 37]
40. ! [X0] : (((generous(X0) | strong(X0)) | ~creative(X0)) & (creative(X0) | (~generous(X0) & ~strong(X0)))) [nnf transformation 3]
41. ! [X0] : ((generous(X0) | strong(X0) | ~creative(X0)) & (creative(X0) | (~generous(X0) & ~strong(X0)))) [flattening 40]
43. ((quiet(susan) & ~rich(susan)) | ((~kind(alice) | ~kind(alice)) & (kind(alice) | kind(alice)))) & (((~kind(alice) | kind(alice)) & (kind(alice) | ~kind(alice))) | (~quiet(susan) | rich(susan))) [nnf transformation 5]
44. ((quiet(susan) & ~rich(susan)) | ((~kind(alice) | ~kind(alice)) & (kind(alice) | kind(alice)))) & (((~kind(alice) | kind(alice)) & (kind(alice) | ~kind(alice))) | ~quiet(susan) | rich(susan)) [flattening 43]
45. (? [X0] : (~calm(X0) | happy(X0)) | (generous(lucy) | ~generous(lucy))) & ((~generous(lucy) & generous(lucy)) | ! [X0] : (calm(X0) & ~happy(X0))) [nnf transformation 6]
46. (? [X0] : (~calm(X0) | happy(X0)) | generous(lucy) | ~generous(lucy)) & ((~generous(lucy) & generous(lucy)) | ! [X0] : (calm(X0) & ~happy(X0))) [flattening 45]
47. (? [X0] : (~calm(X0) | happy(X0)) | generous(lucy) | ~generous(lucy)) & ((~generous(lucy) & generous(lucy)) | ! [X1] : (calm(X1) & ~happy(X1))) [rectify 46]
48. ? [X0] : (~calm(X0) | happy(X0)) => (~calm(sK0) | happy(sK0)) [choice axiom]
49. ((~calm(sK0) | happy(sK0)) | generous(lucy) | ~generous(lucy)) & ((~generous(lucy) & generous(lucy)) | ! [X1] : (calm(X1) & ~happy(X1))) [skolemisation 47,48]
56. ! [X0] : (~old(X0) | ~quiet(X0) | ((old(X0) | ~happy(X0)) & (happy(X0) | ~old(X0)))) [nnf transformation 31]
65. ! [X0] : (((humble(X0) | ~humble(X0)) | ~generous(X0)) & (generous(X0) | (~humble(X0) & humble(X0)))) [nnf transformation 15]
66. ! [X0] : ((humble(X0) | ~humble(X0) | ~generous(X0)) & (generous(X0) | (~humble(X0) & humble(X0)))) [flattening 65]
74. ~creative(X0) | ~patient(X0) | old(X0) [cnf transformation 38]
85. ~generous(X0) | creative(X0) [cnf transformation 41]
99. quiet(susan) | kind(alice) | kind(alice) [cnf transformation 44]
100. quiet(susan) | ~kind(alice) | ~kind(alice) [cnf transformation 44]
101. generous(lucy) | ~happy(X1) [cnf transformation 49]
103. ~generous(lucy) | ~happy(X1) [cnf transformation 49]
115. ~old(X0) | ~quiet(X0) | happy(X0) | ~old(X0) [cnf transformation 56]
124. generous(X0) | humble(X0) [cnf transformation 66]
125. ~humble(X0) | generous(X0) [cnf transformation 66]
139. patient(susan) [cnf transformation 23]
140. ~quiet(X0) | ~old(X0) | happy(X0) [duplicate literal removal 115]
143. quiet(susan) | kind(alice) [duplicate literal removal 99]
144. quiet(susan) | ~kind(alice) [duplicate literal removal 100]
151. 1 <=> kind(alice) [avatar definition]
155. 2 <=> quiet(susan) [avatar definition]
157. quiet(susan) <- (2) [avatar component clause 155]
158. ~1 | 2 [avatar split clause 144,155,151]
159. 1 | 2 [avatar split clause 143,155,151]
170. 5 <=> generous(lucy) [avatar definition]
175. 6 <=> ! [X1] : ~happy(X1) [avatar definition]
176. ~happy(X1) <- (6) [avatar component clause 175]
177. 6 | ~5 [avatar split clause 103,170,175]
179. 6 | 5 [avatar split clause 101,170,175]
242. generous(X0) [subsumption resolution 124,125]
275. creative(X0) [resolution 85,242]
311. ~old(susan) | happy(susan) <- (2) [resolution 140,157]
317. ~old(susan) <- (2, 6) [subsumption resolution 311,176]
345. ~patient(X2) | old(X2) [resolution 275,74]
379. old(susan) [resolution 345,139]
382. $false <- (2, 6) [subsumption resolution 379,317]
383. ~2 | ~6 [avatar contradiction clause 382]
384. $false [avatar sat refutation 158,159,177,179,383]
% SZS output end Proof for 436161373106787383954535
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is creative then lucy is brave or not patient.
Everyone who is both old and not quiet is either brave or not old.
Everyone who is not kind is not curious.
Everyone who is either not curious or brave is creative.
If someone is both not rich and not generous then someone is not calm.
If john is both creative and curious then lucy is both kind and wise and vice versa.
Everyone who is both old and not strong is brave or funny and vice versa.
Everyone who is happy or creative is not generous and vice versa.
Everyone who is generous is not humble and vice versa.
Everyone who is brave or not calm is strong and vice versa.
Everyone who is both happy and patient is either strong or patient and vice versa.
If someone is both rich and not curious then fred is not brave.
Everyone who is both funny and wise is not tall or not happy and vice versa.
Everyone who is either humble or not rich is both not strong and not funny and vice versa.
Everyone who is both not creative and not strong is not patient.
If someone is not happy or not old then john is either strong or not tall.
Alice is both creative and not generous.
Someone is wise.
Someone is both curious and creative.
John is both not strong and not tall.
Mary is either wise or not generous.
Fred is not wise.
Someone is not creative. | Alice is not tall. | contradiction | ((creative(alice))=>((brave(lucy)|~patient(lucy))))&
(![X]:((old(X)&~quiet(X))=>(brave(X)<~>~old(X))))&
(![X]:(~kind(X)=>~curious(X)))&
(![X]:((~curious(X)<~>brave(X))=>creative(X)))&
((?[X]:((~rich(X)&~generous(X))))=>(?[X]:(~calm(X))))&
(((creative(john)&curious(john)))<=>((kind(lucy)&wise(lucy))))&
(![X]:((old(X)&~strong(X))<=>(brave(X)|funny(X))))&
(![X]:((happy(X)|creative(X))<=>~generous(X)))&
(![X]:(generous(X)<=>~humble(X)))&
(![X]:((brave(X)|~calm(X))<=>strong(X)))&
(![X]:((happy(X)&patient(X))<=>(strong(X)<~>patient(X))))&
((?[X]:((rich(X)&~curious(X))))=>(~brave(fred)))&
(![X]:((funny(X)&wise(X))<=>(~tall(X)|~happy(X))))&
(![X]:((humble(X)<~>~rich(X))<=>(~strong(X)&~funny(X))))&
(![X]:((~creative(X)&~strong(X))=>~patient(X)))&
((?[X]:((~happy(X)|~old(X))))=>((strong(john)<~>~tall(john))))&
((creative(alice)&~generous(alice)))&
(?[X]:(wise(X)))&
(?[X]:((curious(X)&creative(X))))&
((~strong(john)&~tall(john)))&
((wise(mary)<~>~generous(mary)))&
(~wise(fred))&
(?[X]:(~creative(X))) | ~tall(alice) | [
"p4",
"p6",
"p8",
"p9",
"p10",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4104024830322229213420111
% SZS output start Proof for 4104024830322229213420111
5. ? [X0] : (~generous(X0) & ~rich(X0)) => ? [X0] : ~calm(X0) [input p4]
7. ! [X0] : ((~strong(X0) & old(X0)) <=> (funny(X0) | brave(X0))) [input p6]
9. ! [X0] : (generous(X0) <=> ~humble(X0)) [input p8]
10. ! [X0] : ((~calm(X0) | brave(X0)) <=> strong(X0)) [input p9]
11. ! [X0] : ((patient(X0) & happy(X0)) <=> (strong(X0) <~> patient(X0))) [input p10]
13. ! [X0] : ((wise(X0) & funny(X0)) <=> (~happy(X0) | ~tall(X0))) [input p12]
14. ! [X0] : ((humble(X0) <~> ~rich(X0)) <=> (~funny(X0) & ~strong(X0))) [input p13]
17. ~generous(alice) & creative(alice) [input p16]
24. ~tall(alice) [input hypothesis]
25. ? [X0] : (~generous(X0) & ~rich(X0)) => ? [X1] : ~calm(X1) [rectify 5]
31. ? [X1] : ~calm(X1) | ! [X0] : (generous(X0) | rich(X0)) [ennf transformation 25]
37. ? [X0] : ~calm(X0) | ! [X1] : (generous(X1) | rich(X1)) [rectify 31]
38. ? [X0] : ~calm(X0) => ~calm(sK0) [choice axiom]
39. ~calm(sK0) | ! [X1] : (generous(X1) | rich(X1)) [skolemisation 37,38]
42. ! [X0] : (((~strong(X0) & old(X0)) | (~funny(X0) & ~brave(X0))) & ((funny(X0) | brave(X0)) | (strong(X0) | ~old(X0)))) [nnf transformation 7]
43. ! [X0] : (((~strong(X0) & old(X0)) | (~funny(X0) & ~brave(X0))) & (funny(X0) | brave(X0) | strong(X0) | ~old(X0))) [flattening 42]
46. ! [X0] : ((generous(X0) | humble(X0)) & (~humble(X0) | ~generous(X0))) [nnf transformation 9]
47. ! [X0] : (((~calm(X0) | brave(X0)) | ~strong(X0)) & (strong(X0) | (calm(X0) & ~brave(X0)))) [nnf transformation 10]
48. ! [X0] : ((~calm(X0) | brave(X0) | ~strong(X0)) & (strong(X0) | (calm(X0) & ~brave(X0)))) [flattening 47]
49. ! [X0] : (((patient(X0) & happy(X0)) | ((strong(X0) | ~patient(X0)) & (patient(X0) | ~strong(X0)))) & (((~patient(X0) | ~strong(X0)) & (patient(X0) | strong(X0))) | (~patient(X0) | ~happy(X0)))) [nnf transformation 11]
50. ! [X0] : (((patient(X0) & happy(X0)) | ((strong(X0) | ~patient(X0)) & (patient(X0) | ~strong(X0)))) & (((~patient(X0) | ~strong(X0)) & (patient(X0) | strong(X0))) | ~patient(X0) | ~happy(X0))) [flattening 49]
51. ! [X0] : (((wise(X0) & funny(X0)) | (happy(X0) & tall(X0))) & ((~happy(X0) | ~tall(X0)) | (~wise(X0) | ~funny(X0)))) [nnf transformation 13]
52. ! [X0] : (((wise(X0) & funny(X0)) | (happy(X0) & tall(X0))) & (~happy(X0) | ~tall(X0) | ~wise(X0) | ~funny(X0))) [flattening 51]
53. ! [X0] : ((((rich(X0) | ~humble(X0)) & (~rich(X0) | humble(X0))) | (funny(X0) | strong(X0))) & ((~funny(X0) & ~strong(X0)) | ((humble(X0) | rich(X0)) & (~rich(X0) | ~humble(X0))))) [nnf transformation 14]
54. ! [X0] : ((((rich(X0) | ~humble(X0)) & (~rich(X0) | humble(X0))) | funny(X0) | strong(X0)) & ((~funny(X0) & ~strong(X0)) | ((humble(X0) | rich(X0)) & (~rich(X0) | ~humble(X0))))) [flattening 53]
67. ~calm(sK0) | generous(X1) | rich(X1) [cnf transformation 39]
76. ~funny(X0) | ~strong(X0) [cnf transformation 43]
81. humble(X0) | generous(X0) [cnf transformation 46]
83. strong(X0) | calm(X0) [cnf transformation 48]
86. ~patient(X0) | ~strong(X0) | ~patient(X0) | ~happy(X0) [cnf transformation 50]
89. patient(X0) | patient(X0) | ~strong(X0) [cnf transformation 50]
93. tall(X0) | funny(X0) [cnf transformation 52]
94. happy(X0) | funny(X0) [cnf transformation 52]
99. ~humble(X0) | ~rich(X0) | ~funny(X0) [cnf transformation 54]
109. ~generous(alice) [cnf transformation 17]
119. ~tall(alice) [cnf transformation 24]
120. ~patient(X0) | ~strong(X0) | ~happy(X0) [duplicate literal removal 86]
121. ~strong(X0) | patient(X0) [duplicate literal removal 89]
136. 4 <=> ! [X1] : (generous(X1) | rich(X1)) [avatar definition]
137. generous(X1) | rich(X1) <- (4) [avatar component clause 136]
139. 5 <=> calm(sK0) [avatar definition]
141. ~calm(sK0) <- (~5) [avatar component clause 139]
142. 4 | ~5 [avatar split clause 67,139,136]
165. ~happy(X0) | ~strong(X0) [subsumption resolution 120,121]
201. funny(alice) [resolution 93,119]
215. ~strong(X1) | funny(X1) [resolution 165,94]
216. ~strong(X1) [subsumption resolution 215,76]
217. calm(X0) [resolution 216,83]
230. $false <- (~5) [resolution 217,141]
231. 5 [avatar contradiction clause 230]
238. ~rich(X0) | ~funny(X0) | generous(X0) [resolution 99,81]
239. ~funny(X0) | generous(X0) <- (4) [subsumption resolution 238,137]
296. generous(alice) <- (4) [resolution 239,201]
299. $false <- (4) [subsumption resolution 296,109]
300. ~4 [avatar contradiction clause 299]
301. $false [avatar sat refutation 142,231,300]
% SZS output end Proof for 4104024830322229213420111
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not humble or quiet then susan is both rich and not rich and vice versa.
If someone is both not patient and not humble then someone is calm.
Everyone who is either not rich or strong is either not generous or generous.
Everyone who is not creative is not wise and vice versa.
Everyone who is either kind or old is both brave and quiet and vice versa.
Everyone who is both kind and calm is not humble.
If someone is both calm and brave then mary is happy.
Everyone who is old is both not tall and not quiet and vice versa.
Everyone who is either happy or tall is not happy and vice versa.
If someone is either not happy or rich then fred is not humble or not calm and vice versa.
Everyone who is either not tall or quiet is either not tall or creative and vice versa.
If john is generous then someone is kind and vice versa.
If someone is wise then fred is strong or humble and vice versa.
Everyone who is either rich or calm is either not generous or not calm.
If alice is not happy then susan is both not tall and not humble.
Everyone who is either funny or calm is either not creative or not patient and vice versa.
Someone is not quiet or funny.
Someone is not patient.
Someone is humble or not quiet.
Susan is kind.
John is either not quiet or rich.
Someone is either not creative or not rich.
Someone is either not quiet or not patient. | Fred is not tall. | contradiction | (((~humble(lucy)<~>quiet(lucy)))<=>((rich(susan)&~rich(susan))))&
((?[X]:((~patient(X)&~humble(X))))=>(?[X]:(calm(X))))&
(![X]:((~rich(X)<~>strong(X))=>(~generous(X)<~>generous(X))))&
(![X]:(~creative(X)<=>~wise(X)))&
(![X]:((kind(X)<~>old(X))<=>(brave(X)&quiet(X))))&
(![X]:((kind(X)&calm(X))=>~humble(X)))&
((?[X]:((calm(X)&brave(X))))=>(happy(mary)))&
(![X]:(old(X)<=>(~tall(X)&~quiet(X))))&
(![X]:((happy(X)<~>tall(X))<=>~happy(X)))&
((?[X]:((~happy(X)<~>rich(X))))<=>((~humble(fred)|~calm(fred))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~tall(X)<~>creative(X))))&
((generous(john))<=>(?[X]:(kind(X))))&
((?[X]:(wise(X)))<=>((strong(fred)|humble(fred))))&
(![X]:((rich(X)<~>calm(X))=>(~generous(X)<~>~calm(X))))&
((~happy(alice))=>((~tall(susan)&~humble(susan))))&
(![X]:((funny(X)<~>calm(X))<=>(~creative(X)<~>~patient(X))))&
(?[X]:((~quiet(X)|funny(X))))&
(?[X]:(~patient(X)))&
(?[X]:((humble(X)|~quiet(X))))&
(kind(susan))&
((~quiet(john)<~>rich(john)))&
(?[X]:((~creative(X)<~>~rich(X))))&
(?[X]:((~quiet(X)<~>~patient(X)))) | ~tall(fred) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8318440847773043425985897
% SZS output start Proof for 8318440847773043425985897
9. ! [X0] : ((happy(X0) <~> tall(X0)) <=> ~happy(X0)) [input p8]
24. ~tall(fred) [input hypothesis]
44. ! [X0] : ((((~tall(X0) | ~happy(X0)) & (tall(X0) | happy(X0))) | happy(X0)) & (~happy(X0) | ((happy(X0) | ~tall(X0)) & (tall(X0) | ~happy(X0))))) [nnf transformation 9]
99. ~happy(X0) | tall(X0) | ~happy(X0) [cnf transformation 44]
101. tall(X0) | happy(X0) | happy(X0) [cnf transformation 44]
146. ~tall(fred) [cnf transformation 24]
153. ~happy(X0) | tall(X0) [duplicate literal removal 99]
154. tall(X0) | happy(X0) [duplicate literal removal 101]
187. tall(X0) [subsumption resolution 153,154]
304. $false [subsumption resolution 146,187]
% SZS output end Proof for 8318440847773043425985897
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not generous or rich then someone is both calm and not calm and vice versa.
If paul is both humble and not old then lucy is kind or not tall.
Everyone who is both rich and not brave is not generous and vice versa.
Everyone who is rich is not quiet or not generous and vice versa.
Everyone who is strong is curious or happy.
Everyone who is not happy is not funny and vice versa.
Everyone who is both not calm and rich is strong.
If fred is brave or not generous then someone is brave and vice versa.
If someone is not old or old then fred is both curious and creative.
If someone is curious or calm then someone is rich and vice versa.
If someone is either not generous or not tall then susan is strong or kind and vice versa.
If john is not rich or funny then alice is patient or humble and vice versa.
If lucy is tall or not funny then someone is both not strong and not funny.
If lucy is not old or quiet then alice is either not patient or not quiet and vice versa.
If someone is not brave then someone is both not curious and creative and vice versa.
If someone is generous then fred is old or not generous and vice versa.
Mary is not tall.
Someone is not creative or strong.
Someone is brave.
Lucy is both generous and not old.
Someone is kind.
Paul is not tall or strong.
Alice is both rich and not kind.
Someone is creative. | Lucy is not generous. | contradiction | (((~generous(john)<~>rich(john)))<=>(?[X]:((calm(X)&~calm(X)))))&
(((humble(paul)&~old(paul)))=>((kind(lucy)|~tall(lucy))))&
(![X]:((rich(X)&~brave(X))<=>~generous(X)))&
(![X]:(rich(X)<=>(~quiet(X)|~generous(X))))&
(![X]:(strong(X)=>(curious(X)|happy(X))))&
(![X]:(~happy(X)<=>~funny(X)))&
(![X]:((~calm(X)&rich(X))=>strong(X)))&
(((brave(fred)|~generous(fred)))<=>(?[X]:(brave(X))))&
((?[X]:((~old(X)|old(X))))=>((curious(fred)&creative(fred))))&
((?[X]:((curious(X)|calm(X))))<=>(?[X]:(rich(X))))&
((?[X]:((~generous(X)<~>~tall(X))))<=>((strong(susan)|kind(susan))))&
(((~rich(john)|funny(john)))<=>((patient(alice)|humble(alice))))&
(((tall(lucy)|~funny(lucy)))=>(?[X]:((~strong(X)&~funny(X)))))&
(((~old(lucy)|quiet(lucy)))<=>((~patient(alice)<~>~quiet(alice))))&
((?[X]:(~brave(X)))<=>(?[X]:((~curious(X)&creative(X)))))&
((?[X]:(generous(X)))<=>((old(fred)|~generous(fred))))&
(~tall(mary))&
(?[X]:((~creative(X)|strong(X))))&
(?[X]:(brave(X)))&
((generous(lucy)&~old(lucy)))&
(?[X]:(kind(X)))&
((~tall(paul)|strong(paul)))&
((rich(alice)&~kind(alice)))&
(?[X]:(creative(X))) | ~generous(lucy) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1180504033028840966696348
% SZS output start Proof for 1180504033028840966696348
20. ~old(lucy) & generous(lucy) [input p19]
25. ~generous(lucy) [input hypothesis]
140. generous(lucy) [cnf transformation 20]
147. ~generous(lucy) [cnf transformation 25]
373. $false [subsumption resolution 147,140]
% SZS output end Proof for 1180504033028840966696348
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not humble is both not brave and not humble.
Everyone who is either not funny or wise is both patient and not quiet and vice versa.
If lucy is humble then someone is wise.
If someone is either brave or patient then fred is both creative and quiet.
Everyone who is both not curious and humble is happy.
If john is not humble then fred is not strong or curious.
Everyone who is either not humble or calm is curious.
Everyone who is quiet is either not patient or not brave.
If alice is not funny or humble then someone is not brave.
Everyone who is both not brave and old is not curious or kind.
If someone is not quiet or not creative then mary is funny and vice versa.
Everyone who is not quiet is calm.
If someone is happy or strong then alice is both not happy and wise and vice versa.
If john is either happy or not funny then susan is not creative.
If someone is curious then lucy is generous and vice versa.
Everyone who is either not generous or not calm is not quiet or not strong.
Someone is not wise or patient.
Paul is creative or generous.
Lucy is both not patient and not kind.
Lucy is either patient or strong.
Someone is not curious or quiet.
Someone is not happy or quiet.
Paul is not happy or generous.
Someone is either not happy or rich. | Lucy is not patient. | entailment | (![X]:((generous(X)&~humble(X))=>(~brave(X)&~humble(X))))&
(![X]:((~funny(X)<~>wise(X))<=>(patient(X)&~quiet(X))))&
((humble(lucy))=>(?[X]:(wise(X))))&
((?[X]:((brave(X)<~>patient(X))))=>((creative(fred)&quiet(fred))))&
(![X]:((~curious(X)&humble(X))=>happy(X)))&
((~humble(john))=>((~strong(fred)|curious(fred))))&
(![X]:((~humble(X)<~>calm(X))=>curious(X)))&
(![X]:(quiet(X)=>(~patient(X)<~>~brave(X))))&
(((~funny(alice)|humble(alice)))=>(?[X]:(~brave(X))))&
(![X]:((~brave(X)&old(X))=>(~curious(X)|kind(X))))&
((?[X]:((~quiet(X)|~creative(X))))<=>(funny(mary)))&
(![X]:(~quiet(X)=>calm(X)))&
((?[X]:((happy(X)|strong(X))))<=>((~happy(alice)&wise(alice))))&
(((happy(john)<~>~funny(john)))=>(~creative(susan)))&
((?[X]:(curious(X)))<=>(generous(lucy)))&
(![X]:((~generous(X)<~>~calm(X))=>(~quiet(X)|~strong(X))))&
(?[X]:((~wise(X)|patient(X))))&
((creative(paul)|generous(paul)))&
((~patient(lucy)&~kind(lucy)))&
((patient(lucy)<~>strong(lucy)))&
(?[X]:((~curious(X)|quiet(X))))&
(?[X]:((~happy(X)|quiet(X))))&
((~happy(paul)|generous(paul)))&
(?[X]:((~happy(X)<~>rich(X)))) | ~patient(lucy) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 632059378988334529551813
% SZS output start Proof for 632059378988334529551813
19. ~kind(lucy) & ~patient(lucy) [input p18]
25. patient(lucy) [input hypothesis]
27. ~patient(lucy) [pure predicate removal 19]
115. ~patient(lucy) [cnf transformation 27]
123. patient(lucy) [cnf transformation 25]
306. $false [subsumption resolution 123,115]
% SZS output end Proof for 632059378988334529551813
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either humble or not patient then someone is old or not kind.
Everyone who is both curious and not rich is either not curious or old and vice versa.
Everyone who is both not humble and old is both not patient and not brave and vice versa.
If someone is old or not quiet then someone is not generous and vice versa.
Everyone who is either generous or not curious is not humble or funny and vice versa.
If someone is either brave or wise then lucy is both calm and not calm.
Everyone who is either funny or quiet is not brave and vice versa.
If someone is not brave or not kind then lucy is both not curious and not humble and vice versa.
Everyone who is wise or not curious is either rich or brave.
If lucy is generous or not happy then john is not patient or old and vice versa.
If someone is both wise and not funny then john is rich and vice versa.
If someone is both not humble and wise then paul is either not humble or patient.
If someone is funny or not tall then lucy is not wise.
Everyone who is not old or not curious is either not kind or brave and vice versa.
Everyone who is not kind or rich is quiet or wise.
Everyone who is either old or not old is happy and vice versa.
Someone is both creative and not patient.
Someone is kind or not humble.
Someone is quiet.
Someone is either not strong or old.
Lucy is tall.
Someone is not happy or not tall.
Someone is either not curious or strong.
Fred is not generous. | John is funny. | contradiction | ((?[X]:((humble(X)<~>~patient(X))))=>(?[X]:((old(X)|~kind(X)))))&
(![X]:((curious(X)&~rich(X))<=>(~curious(X)<~>old(X))))&
(![X]:((~humble(X)&old(X))<=>(~patient(X)&~brave(X))))&
((?[X]:((old(X)|~quiet(X))))<=>(?[X]:(~generous(X))))&
(![X]:((generous(X)<~>~curious(X))<=>(~humble(X)|funny(X))))&
((?[X]:((brave(X)<~>wise(X))))=>((calm(lucy)&~calm(lucy))))&
(![X]:((funny(X)<~>quiet(X))<=>~brave(X)))&
((?[X]:((~brave(X)|~kind(X))))<=>((~curious(lucy)&~humble(lucy))))&
(![X]:((wise(X)|~curious(X))=>(rich(X)<~>brave(X))))&
(((generous(lucy)|~happy(lucy)))<=>((~patient(john)|old(john))))&
((?[X]:((wise(X)&~funny(X))))<=>(rich(john)))&
((?[X]:((~humble(X)&wise(X))))=>((~humble(paul)<~>patient(paul))))&
((?[X]:((funny(X)|~tall(X))))=>(~wise(lucy)))&
(![X]:((~old(X)|~curious(X))<=>(~kind(X)<~>brave(X))))&
(![X]:((~kind(X)|rich(X))=>(quiet(X)|wise(X))))&
(![X]:((old(X)<~>~old(X))<=>happy(X)))&
(?[X]:((creative(X)&~patient(X))))&
(?[X]:((kind(X)|~humble(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~strong(X)<~>old(X))))&
(tall(lucy))&
(?[X]:((~happy(X)|~tall(X))))&
(?[X]:((~curious(X)<~>strong(X))))&
(~generous(fred)) | funny(john) | [
"p1",
"p4",
"p5",
"p6",
"p7",
"p8",
"p9",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3623197763072713904360437
% SZS output start Proof for 3623197763072713904360437
2. ! [X0] : ((~rich(X0) & curious(X0)) <=> (~curious(X0) <~> old(X0))) [input p1]
5. ! [X0] : ((generous(X0) <~> ~curious(X0)) <=> (funny(X0) | ~humble(X0))) [input p4]
6. ? [X0] : (brave(X0) <~> wise(X0)) => (~calm(lucy) & calm(lucy)) [input p5]
7. ! [X0] : ((funny(X0) <~> quiet(X0)) <=> ~brave(X0)) [input p6]
8. ? [X0] : (~kind(X0) | ~brave(X0)) <=> (~humble(lucy) & ~curious(lucy)) [input p7]
9. ! [X0] : ((~curious(X0) | wise(X0)) => (rich(X0) <~> brave(X0))) [input p8]
10. (~happy(lucy) | generous(lucy)) <=> (old(john) | ~patient(john)) [input p9]
13. ? [X0] : (~tall(X0) | funny(X0)) => ~wise(lucy) [input p12]
15. ! [X0] : ((rich(X0) | ~kind(X0)) => (wise(X0) | quiet(X0))) [input p14]
16. ! [X0] : ((old(X0) <~> ~old(X0)) <=> happy(X0)) [input p15]
25. funny(john) [input hypothesis]
30. (~calm(lucy) & calm(lucy)) | ! [X0] : (brave(X0) <=> wise(X0)) [ennf transformation 6]
31. ! [X0] : ((rich(X0) <~> brave(X0)) | (curious(X0) & ~wise(X0))) [ennf transformation 9]
33. ~wise(lucy) | ! [X0] : (tall(X0) & ~funny(X0)) [ennf transformation 13]
34. ! [X0] : ((wise(X0) | quiet(X0)) | (~rich(X0) & kind(X0))) [ennf transformation 15]
35. ! [X0] : (wise(X0) | quiet(X0) | (~rich(X0) & kind(X0))) [flattening 34]
40. ! [X0] : (((~rich(X0) & curious(X0)) | ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0)))) & (((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | (rich(X0) | ~curious(X0)))) [nnf transformation 2]
41. ! [X0] : (((~rich(X0) & curious(X0)) | ((~curious(X0) | ~old(X0)) & (old(X0) | curious(X0)))) & (((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | rich(X0) | ~curious(X0))) [flattening 40]
49. ! [X0] : ((((curious(X0) | ~generous(X0)) & (~curious(X0) | generous(X0))) | (~funny(X0) & humble(X0))) & ((funny(X0) | ~humble(X0)) | ((generous(X0) | curious(X0)) & (~curious(X0) | ~generous(X0))))) [nnf transformation 5]
50. ! [X0] : ((((curious(X0) | ~generous(X0)) & (~curious(X0) | generous(X0))) | (~funny(X0) & humble(X0))) & (funny(X0) | ~humble(X0) | ((generous(X0) | curious(X0)) & (~curious(X0) | ~generous(X0))))) [flattening 49]
51. (~calm(lucy) & calm(lucy)) | ! [X0] : ((brave(X0) | ~wise(X0)) & (wise(X0) | ~brave(X0))) [nnf transformation 30]
52. ! [X0] : ((((~quiet(X0) | ~funny(X0)) & (quiet(X0) | funny(X0))) | brave(X0)) & (~brave(X0) | ((funny(X0) | ~quiet(X0)) & (quiet(X0) | ~funny(X0))))) [nnf transformation 7]
53. (? [X0] : (~kind(X0) | ~brave(X0)) | (humble(lucy) | curious(lucy))) & ((~humble(lucy) & ~curious(lucy)) | ! [X0] : (kind(X0) & brave(X0))) [nnf transformation 8]
54. (? [X0] : (~kind(X0) | ~brave(X0)) | humble(lucy) | curious(lucy)) & ((~humble(lucy) & ~curious(lucy)) | ! [X0] : (kind(X0) & brave(X0))) [flattening 53]
55. (? [X0] : (~kind(X0) | ~brave(X0)) | humble(lucy) | curious(lucy)) & ((~humble(lucy) & ~curious(lucy)) | ! [X1] : (kind(X1) & brave(X1))) [rectify 54]
56. ? [X0] : (~kind(X0) | ~brave(X0)) => (~kind(sK3) | ~brave(sK3)) [choice axiom]
57. ((~kind(sK3) | ~brave(sK3)) | humble(lucy) | curious(lucy)) & ((~humble(lucy) & ~curious(lucy)) | ! [X1] : (kind(X1) & brave(X1))) [skolemisation 55,56]
58. ! [X0] : (((~brave(X0) | ~rich(X0)) & (brave(X0) | rich(X0))) | (curious(X0) & ~wise(X0))) [nnf transformation 31]
59. ((~happy(lucy) | generous(lucy)) | (~old(john) & patient(john))) & ((old(john) | ~patient(john)) | (happy(lucy) & ~generous(lucy))) [nnf transformation 10]
60. (~happy(lucy) | generous(lucy) | (~old(john) & patient(john))) & (old(john) | ~patient(john) | (happy(lucy) & ~generous(lucy))) [flattening 59]
68. ! [X0] : ((((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) | ~happy(X0)) & (happy(X0) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0))))) [nnf transformation 16]
85. old(X0) | ~curious(X0) | rich(X0) | ~curious(X0) [cnf transformation 41]
87. curious(X0) | old(X0) | curious(X0) [cnf transformation 41]
102. ~generous(X0) | curious(X0) | humble(X0) [cnf transformation 50]
104. calm(lucy) | wise(X0) | ~brave(X0) [cnf transformation 51]
105. calm(lucy) | brave(X0) | ~wise(X0) [cnf transformation 51]
106. ~calm(lucy) | wise(X0) | ~brave(X0) [cnf transformation 51]
107. ~calm(lucy) | brave(X0) | ~wise(X0) [cnf transformation 51]
111. ~funny(X0) | ~quiet(X0) | brave(X0) [cnf transformation 52]
112. ~curious(lucy) | brave(X1) [cnf transformation 57]
114. ~humble(lucy) | brave(X1) [cnf transformation 57]
119. ~wise(X0) | ~rich(X0) | ~brave(X0) [cnf transformation 58]
124. ~happy(lucy) | generous(lucy) | ~old(john) [cnf transformation 60]
130. ~wise(lucy) | ~funny(X0) [cnf transformation 33]
139. ~rich(X0) | quiet(X0) | wise(X0) [cnf transformation 35]
140. happy(X0) | ~old(X0) | ~old(X0) [cnf transformation 68]
141. happy(X0) | old(X0) | old(X0) [cnf transformation 68]
154. funny(john) [cnf transformation 25]
155. happy(X0) | ~old(X0) [duplicate literal removal 140]
156. happy(X0) | old(X0) [duplicate literal removal 141]
157. old(X0) | ~curious(X0) | rich(X0) [duplicate literal removal 85]
158. curious(X0) | old(X0) [duplicate literal removal 87]
175. rich(X0) | old(X0) [subsumption resolution 157,158]
201. 11 <=> ! [X0] : (brave(X0) | ~wise(X0)) [avatar definition]
202. ~wise(X0) | brave(X0) <- (11) [avatar component clause 201]
204. 12 <=> calm(lucy) [avatar definition]
207. 11 | ~12 [avatar split clause 107,204,201]
209. 13 <=> ! [X0] : (wise(X0) | ~brave(X0)) [avatar definition]
210. ~brave(X0) | wise(X0) <- (13) [avatar component clause 209]
211. 13 | ~12 [avatar split clause 106,204,209]
212. 11 | 12 [avatar split clause 105,204,201]
213. 13 | 12 [avatar split clause 104,204,209]
215. 14 <=> curious(lucy) [avatar definition]
216. ~curious(lucy) <- (~14) [avatar component clause 215]
219. 15 <=> humble(lucy) [avatar definition]
236. 19 <=> ! [X1] : brave(X1) [avatar definition]
237. brave(X1) <- (19) [avatar component clause 236]
238. 19 | ~15 [avatar split clause 114,219,236]
240. 19 | ~14 [avatar split clause 112,215,236]
242. 20 <=> old(john) [avatar definition]
244. ~old(john) <- (~20) [avatar component clause 242]
246. 21 <=> generous(lucy) [avatar definition]
248. generous(lucy) <- (21) [avatar component clause 246]
250. 22 <=> happy(lucy) [avatar definition]
252. ~happy(lucy) <- (~22) [avatar component clause 250]
253. ~20 | 21 | ~22 [avatar split clause 124,250,246,242]
262. 24 <=> rich(john) [avatar definition]
263. rich(john) <- (24) [avatar component clause 262]
264. ~rich(john) <- (~24) [avatar component clause 262]
296. 32 <=> wise(lucy) [avatar definition]
298. ~wise(lucy) <- (~32) [avatar component clause 296]
301. 33 <=> ! [X0] : ~funny(X0) [avatar definition]
302. ~funny(X0) <- (33) [avatar component clause 301]
303. 33 | ~32 [avatar split clause 130,296,301]
304. happy(X0) [subsumption resolution 155,156]
335. $false <- (~22) [subsumption resolution 252,304]
336. 22 [avatar contradiction clause 335]
405. curious(lucy) | humble(lucy) <- (21) [resolution 102,248]
406. humble(lucy) <- (~14, 21) [subsumption resolution 405,216]
409. 15 | 14 | ~21 [avatar split clause 406,246,215,219]
431. wise(X1) <- (13, 19) [resolution 237,210]
439. $false <- (13, 19, ~32) [resolution 431,298]
441. ~13 | ~19 | 32 [avatar contradiction clause 439]
446. 52 <=> brave(john) [avatar definition]
447. brave(john) <- (52) [avatar component clause 446]
448. ~brave(john) <- (~52) [avatar component clause 446]
450. 53 <=> quiet(john) [avatar definition]
451. ~quiet(john) <- (~53) [avatar component clause 450]
456. $false <- (33) [resolution 302,154]
457. ~33 [avatar contradiction clause 456]
473. ~quiet(john) | brave(john) [resolution 111,154]
566. old(john) <- (~24) [resolution 264,175]
567. $false <- (~20, ~24) [subsumption resolution 566,244]
568. 20 | 24 [avatar contradiction clause 567]
599. quiet(john) | wise(john) <- (24) [resolution 139,263]
609. wise(john) <- (24, ~53) [subsumption resolution 599,451]
614. brave(john) <- (11, 24, ~53) [resolution 609,202]
615. $false <- (11, 24, ~52, ~53) [subsumption resolution 614,448]
616. ~11 | ~24 | 52 | 53 [avatar contradiction clause 615]
617. 52 | ~53 [avatar split clause 473,450,446]
619. 69 <=> wise(john) [avatar definition]
621. wise(john) <- (69) [avatar component clause 619]
627. wise(john) <- (13, 52) [resolution 447,210]
628. 69 | ~13 | ~52 [avatar split clause 627,446,209,619]
639. ~rich(john) | ~brave(john) <- (69) [resolution 621,119]
642. ~brave(john) <- (24, 69) [subsumption resolution 639,263]
643. $false <- (24, 52, 69) [subsumption resolution 642,447]
644. ~24 | ~52 | ~69 [avatar contradiction clause 643]
645. $false [avatar sat refutation 207,211,212,213,238,240,253,303,336,409,441,457,568,616,617,628,644]
% SZS output end Proof for 3623197763072713904360437
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not quiet or not tall then someone is both not creative and not tall.
Everyone who is either not strong or creative is strong and vice versa.
If john is both not humble and tall then lucy is not quiet.
If someone is not rich then paul is either not brave or not humble.
Everyone who is happy is not curious.
If susan is either wise or tall then alice is both not humble and not funny and vice versa.
Everyone who is either not funny or not quiet is curious or not tall and vice versa.
Everyone who is both not calm and strong is both not strong and quiet and vice versa.
If paul is funny then someone is not happy or not creative.
If fred is either kind or brave then someone is not strong or not tall.
Everyone who is either not old or not wise is both not curious and old and vice versa.
If someone is both brave and kind then susan is either tall or not funny.
Everyone who is creative or generous is brave.
If paul is either old or wise then someone is either creative or calm and vice versa.
If someone is both generous and not strong then john is both strong and quiet and vice versa.
Everyone who is strong is not humble and vice versa.
John is not generous or quiet.
Someone is either brave or patient.
Alice is generous or patient.
Someone is quiet or not strong.
Someone is not rich.
John is both not calm and kind.
Mary is calm. | Susan is not calm. | contradiction | ((?[X]:((~quiet(X)<~>~tall(X))))=>(?[X]:((~creative(X)&~tall(X)))))&
(![X]:((~strong(X)<~>creative(X))<=>strong(X)))&
(((~humble(john)&tall(john)))=>(~quiet(lucy)))&
((?[X]:(~rich(X)))=>((~brave(paul)<~>~humble(paul))))&
(![X]:(happy(X)=>~curious(X)))&
(((wise(susan)<~>tall(susan)))<=>((~humble(alice)&~funny(alice))))&
(![X]:((~funny(X)<~>~quiet(X))<=>(curious(X)|~tall(X))))&
(![X]:((~calm(X)&strong(X))<=>(~strong(X)&quiet(X))))&
((funny(paul))=>(?[X]:((~happy(X)|~creative(X)))))&
(((kind(fred)<~>brave(fred)))=>(?[X]:((~strong(X)|~tall(X)))))&
(![X]:((~old(X)<~>~wise(X))<=>(~curious(X)&old(X))))&
((?[X]:((brave(X)&kind(X))))=>((tall(susan)<~>~funny(susan))))&
(![X]:((creative(X)|generous(X))=>brave(X)))&
(((old(paul)<~>wise(paul)))<=>(?[X]:((creative(X)<~>calm(X)))))&
((?[X]:((generous(X)&~strong(X))))<=>((strong(john)&quiet(john))))&
(![X]:(strong(X)<=>~humble(X)))&
((~generous(john)|quiet(john)))&
(?[X]:((brave(X)<~>patient(X))))&
((generous(alice)|patient(alice)))&
(?[X]:((quiet(X)|~strong(X))))&
(?[X]:(~rich(X)))&
((~calm(john)&kind(john)))&
(calm(mary)) | ~calm(susan) | [
"p0",
"p1",
"p6",
"p7",
"p11",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2579611508403706499188460
% SZS output start Proof for 2579611508403706499188460
1. ? [X0] : (~quiet(X0) <~> ~tall(X0)) => ? [X0] : (~tall(X0) & ~creative(X0)) [input p0]
2. ! [X0] : ((~strong(X0) <~> creative(X0)) <=> strong(X0)) [input p1]
7. ! [X0] : ((~funny(X0) <~> ~quiet(X0)) <=> (~tall(X0) | curious(X0))) [input p6]
8. ! [X0] : ((strong(X0) & ~calm(X0)) <=> (quiet(X0) & ~strong(X0))) [input p7]
12. ? [X0] : (kind(X0) & brave(X0)) => (tall(susan) <~> ~funny(susan)) [input p11]
13. ! [X0] : ((generous(X0) | creative(X0)) => brave(X0)) [input p12]
22. kind(john) & ~calm(john) [input p21]
24. ~calm(susan) [input hypothesis]
25. ? [X0] : (~quiet(X0) <~> ~tall(X0)) => ? [X1] : (~tall(X1) & ~creative(X1)) [rectify 1]
28. ? [X1] : (~tall(X1) & ~creative(X1)) | ! [X0] : (~quiet(X0) <=> ~tall(X0)) [ennf transformation 25]
33. (tall(susan) <~> ~funny(susan)) | ! [X0] : (~kind(X0) | ~brave(X0)) [ennf transformation 12]
34. ! [X0] : (brave(X0) | (~generous(X0) & ~creative(X0))) [ennf transformation 13]
35. ? [X1] : (~tall(X1) & ~creative(X1)) | ! [X0] : ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0))) [nnf transformation 28]
36. ? [X0] : (~tall(X0) & ~creative(X0)) | ! [X1] : ((~quiet(X1) | tall(X1)) & (~tall(X1) | quiet(X1))) [rectify 35]
37. ? [X0] : (~tall(X0) & ~creative(X0)) => (~tall(sK0) & ~creative(sK0)) [choice axiom]
38. (~tall(sK0) & ~creative(sK0)) | ! [X1] : ((~quiet(X1) | tall(X1)) & (~tall(X1) | quiet(X1))) [skolemisation 36,37]
39. ! [X0] : ((((~creative(X0) | strong(X0)) & (creative(X0) | ~strong(X0))) | ~strong(X0)) & (strong(X0) | ((~strong(X0) | ~creative(X0)) & (creative(X0) | strong(X0))))) [nnf transformation 2]
43. ! [X0] : ((((quiet(X0) | funny(X0)) & (~quiet(X0) | ~funny(X0))) | (tall(X0) & ~curious(X0))) & ((~tall(X0) | curious(X0)) | ((~funny(X0) | quiet(X0)) & (~quiet(X0) | funny(X0))))) [nnf transformation 7]
44. ! [X0] : ((((quiet(X0) | funny(X0)) & (~quiet(X0) | ~funny(X0))) | (tall(X0) & ~curious(X0))) & (~tall(X0) | curious(X0) | ((~funny(X0) | quiet(X0)) & (~quiet(X0) | funny(X0))))) [flattening 43]
45. ! [X0] : (((strong(X0) & ~calm(X0)) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | (~strong(X0) | calm(X0)))) [nnf transformation 8]
46. ! [X0] : (((strong(X0) & ~calm(X0)) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | ~strong(X0) | calm(X0))) [flattening 45]
52. ((funny(susan) | ~tall(susan)) & (~funny(susan) | tall(susan))) | ! [X0] : (~kind(X0) | ~brave(X0)) [nnf transformation 33]
70. ~creative(sK0) | ~tall(X1) | quiet(X1) [cnf transformation 38]
71. ~creative(sK0) | ~quiet(X1) | tall(X1) [cnf transformation 38]
74. strong(X0) | creative(X0) | strong(X0) [cnf transformation 39]
76. creative(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 39]
92. funny(X0) | quiet(X0) | tall(X0) [cnf transformation 44]
93. ~strong(X0) | ~strong(X0) | calm(X0) [cnf transformation 46]
96. strong(X0) | ~quiet(X0) | strong(X0) [cnf transformation 46]
105. ~funny(susan) | tall(susan) | ~kind(X0) | ~brave(X0) [cnf transformation 52]
107. brave(X0) | ~creative(X0) [cnf transformation 34]
130. kind(john) [cnf transformation 22]
132. ~calm(susan) [cnf transformation 24]
135. ~strong(X0) | calm(X0) [duplicate literal removal 93]
136. ~quiet(X0) | strong(X0) [duplicate literal removal 96]
137. strong(X0) | creative(X0) [duplicate literal removal 74]
138. ~strong(X0) | creative(X0) [duplicate literal removal 76]
140. 1 <=> ! [X1] : (~quiet(X1) | tall(X1)) [avatar definition]
141. ~quiet(X1) | tall(X1) <- (1) [avatar component clause 140]
148. 3 <=> ! [X1] : (~tall(X1) | quiet(X1)) [avatar definition]
149. ~tall(X1) | quiet(X1) <- (3) [avatar component clause 148]
152. 4 <=> creative(sK0) [avatar definition]
154. ~creative(sK0) <- (~4) [avatar component clause 152]
155. 1 | ~4 [avatar split clause 71,152,140]
156. 3 | ~4 [avatar split clause 70,152,148]
157. creative(X0) [subsumption resolution 137,138]
197. 14 <=> tall(susan) [avatar definition]
198. tall(susan) <- (14) [avatar component clause 197]
225. 19 <=> ! [X0] : (~kind(X0) | ~brave(X0)) [avatar definition]
226. ~kind(X0) | ~brave(X0) <- (19) [avatar component clause 225]
228. 20 <=> funny(susan) [avatar definition]
229. ~funny(susan) <- (~20) [avatar component clause 228]
232. 19 | 14 | ~20 [avatar split clause 105,228,197,225]
233. brave(X0) [subsumption resolution 107,157]
306. $false <- (~4) [subsumption resolution 154,157]
307. 4 [avatar contradiction clause 306]
337. quiet(susan) | tall(susan) <- (~20) [resolution 92,229]
348. tall(susan) <- (1, ~20) [subsumption resolution 337,141]
349. 14 | ~1 | 20 [avatar split clause 348,228,140,197]
350. ~kind(X0) <- (19) [subsumption resolution 226,233]
353. quiet(susan) <- (3, 14) [resolution 198,149]
354. $false <- (19) [resolution 350,130]
355. ~19 [avatar contradiction clause 354]
368. strong(susan) <- (3, 14) [resolution 353,136]
384. calm(susan) <- (3, 14) [resolution 368,135]
385. $false <- (3, 14) [subsumption resolution 384,132]
386. ~3 | ~14 [avatar contradiction clause 385]
387. $false [avatar sat refutation 155,156,232,307,349,355,386]
% SZS output end Proof for 2579611508403706499188460
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not calm or not happy is both quiet and not creative. If someone is both brave and generous then john is both not calm and wise and vice versa. Everyone who is rich is not quiet. Everyone who is either calm or not old is either tall or not tall and vice versa. If lucy is patient then someone is both not curious and not happy and vice versa. Everyone who is either not tall or not strong is not calm or generous. If paul is either not brave or not curious then fred is rich or not humble. Everyone who is both happy and not strong is happy. If lucy is not rich then someone is quiet or not generous and vice versa. If paul is wise or not funny then fred is either not kind or humble. Everyone who is either not patient or not funny is brave and vice versa. Everyone who is either not old or not creative is not creative and vice versa. Everyone who is not wise or humble is both rich and calm. Everyone who is either not old or funny is old. If fred is both curious and not creative then fred is not quiet or creative. If fred is both not brave and calm then mary is not patient or rich and vice versa. Someone is not generous or not old. Fred is kind or quiet. John is not wise or not happy. Someone is both happy and not generous. Mary is either calm or strong. Lucy is both not strong and quiet. Fred is not patient. | Paul is old. | entailment | (![X]:((~calm(X)<~>~happy(X))=>(quiet(X)&~creative(X))))&
((?[X]:((brave(X)&generous(X))))<=>((~calm(john)&wise(john))))&
(![X]:(rich(X)=>~quiet(X)))&
(![X]:((calm(X)<~>~old(X))<=>(tall(X)<~>~tall(X))))&
((patient(lucy))<=>(?[X]:((~curious(X)&~happy(X)))))&
(![X]:((~tall(X)<~>~strong(X))=>(~calm(X)|generous(X))))&
(((~brave(paul)<~>~curious(paul)))=>((rich(fred)|~humble(fred))))&
(![X]:((happy(X)&~strong(X))=>happy(X)))&
((~rich(lucy))<=>(?[X]:((quiet(X)|~generous(X)))))&
(((wise(paul)|~funny(paul)))=>((~kind(fred)<~>humble(fred))))&
(![X]:((~patient(X)<~>~funny(X))<=>brave(X)))&
(![X]:((~old(X)<~>~creative(X))<=>~creative(X)))&
(![X]:((~wise(X)|humble(X))=>(rich(X)&calm(X))))&
(![X]:((~old(X)<~>funny(X))=>old(X)))&
(((curious(fred)&~creative(fred)))=>((~quiet(fred)|creative(fred))))&
(((~brave(fred)&calm(fred)))<=>((~patient(mary)|rich(mary))))&
(?[X]:((~generous(X)|~old(X))))&
((kind(fred)|quiet(fred)))&
((~wise(john)|~happy(john)))&
(?[X]:((happy(X)&~generous(X))))&
((calm(mary)<~>strong(mary)))&
((~strong(lucy)&quiet(lucy)))&
(~patient(fred)) | old(paul) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7781953445142689591889149
% SZS output start Proof for 7781953445142689591889149
12. ! [X0] : ((~old(X0) <~> ~creative(X0)) <=> ~creative(X0)) [input p11]
24. ~old(paul) [input hypothesis]
57. ! [X0] : ((((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | creative(X0)) & (~creative(X0) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0))))) [nnf transformation 12]
102. ~creative(X0) | ~creative(X0) | old(X0) [cnf transformation 57]
105. creative(X0) | old(X0) | creative(X0) [cnf transformation 57]
128. ~old(paul) [cnf transformation 24]
131. ~creative(X0) | old(X0) [duplicate literal removal 102]
132. creative(X0) | old(X0) [duplicate literal removal 105]
235. old(X0) [subsumption resolution 131,132]
287. $false [subsumption resolution 128,235]
% SZS output end Proof for 7781953445142689591889149
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious or kind is both curious and not brave. Everyone who is funny or quiet is not quiet and vice versa. If alice is curious then someone is calm and vice versa. Everyone who is both not humble and curious is either not funny or not calm and vice versa. If mary is either not wise or not creative then someone is rich. Everyone who is either happy or funny is not tall and vice versa. If someone is not creative or humble then john is not generous and vice versa. If susan is not happy then lucy is both not happy and happy. Everyone who is wise or generous is either not humble or not brave and vice versa. If alice is quiet then john is either quiet or brave and vice versa. If someone is not curious then lucy is quiet. If someone is old then someone is both patient and calm and vice versa. If paul is either not happy or not funny then someone is strong. Everyone who is not brave or not rich is tall or not old and vice versa. If susan is patient or strong then someone is not strong and vice versa. Everyone who is either not old or not funny is either not humble or funny. Someone is generous. Paul is either not funny or not generous. Someone is both tall and wise. Someone is either humble or not creative. Someone is creative. Someone is not happy or not quiet. Someone is either wise or creative. Someone is creative or not calm. | Susan is funny. | entailment | (![X]:((curious(X)|kind(X))=>(curious(X)&~brave(X))))&
(![X]:((funny(X)|quiet(X))<=>~quiet(X)))&
((curious(alice))<=>(?[X]:(calm(X))))&
(![X]:((~humble(X)&curious(X))<=>(~funny(X)<~>~calm(X))))&
(((~wise(mary)<~>~creative(mary)))=>(?[X]:(rich(X))))&
(![X]:((happy(X)<~>funny(X))<=>~tall(X)))&
((?[X]:((~creative(X)|humble(X))))<=>(~generous(john)))&
((~happy(susan))=>((~happy(lucy)&happy(lucy))))&
(![X]:((wise(X)|generous(X))<=>(~humble(X)<~>~brave(X))))&
((quiet(alice))<=>((quiet(john)<~>brave(john))))&
((?[X]:(~curious(X)))=>(quiet(lucy)))&
((?[X]:(old(X)))<=>(?[X]:((patient(X)&calm(X)))))&
(((~happy(paul)<~>~funny(paul)))=>(?[X]:(strong(X))))&
(![X]:((~brave(X)|~rich(X))<=>(tall(X)|~old(X))))&
(((patient(susan)|strong(susan)))<=>(?[X]:(~strong(X))))&
(![X]:((~old(X)<~>~funny(X))=>(~humble(X)<~>funny(X))))&
(?[X]:(generous(X)))&
((~funny(paul)<~>~generous(paul)))&
(?[X]:((tall(X)&wise(X))))&
(?[X]:((humble(X)<~>~creative(X))))&
(?[X]:(creative(X)))&
(?[X]:((~happy(X)|~quiet(X))))&
(?[X]:((wise(X)<~>creative(X))))&
(?[X]:((creative(X)|~calm(X)))) | funny(susan) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 8056567399207597953131800
% SZS output start Proof for 8056567399207597953131800
2. ! [X0] : ((quiet(X0) | funny(X0)) <=> ~quiet(X0)) [input p1]
25. ~funny(susan) [input hypothesis]
34. ! [X0] : (((quiet(X0) | funny(X0)) | quiet(X0)) & (~quiet(X0) | (~quiet(X0) & ~funny(X0)))) [nnf transformation 2]
35. ! [X0] : ((quiet(X0) | funny(X0) | quiet(X0)) & (~quiet(X0) | (~quiet(X0) & ~funny(X0)))) [flattening 34]
89. ~quiet(X0) | ~quiet(X0) [cnf transformation 35]
90. quiet(X0) | funny(X0) | quiet(X0) [cnf transformation 35]
149. ~funny(susan) [cnf transformation 25]
152. ~quiet(X0) [duplicate literal removal 89]
153. quiet(X0) | funny(X0) [duplicate literal removal 90]
305. funny(X0) [resolution 153,152]
306. $false [resolution 305,149]
% SZS output end Proof for 8056567399207597953131800
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old or humble then mary is either kind or curious and vice versa.
If mary is quiet then lucy is generous.
Everyone who is either not strong or brave is either patient or quiet and vice versa.
If someone is not creative then someone is not curious.
Everyone who is both humble and not rich is not patient.
If someone is rich or funny then alice is not strong or generous and vice versa.
If someone is both patient and brave then alice is calm and vice versa.
Everyone who is kind is not creative and vice versa.
Everyone who is either strong or humble is not calm and vice versa.
Everyone who is both not patient and kind is both not funny and old.
If lucy is funny then someone is either not old or not calm and vice versa.
Everyone who is not quiet or not creative is both strong and humble.
If paul is humble then susan is not generous and vice versa.
Everyone who is not wise is either not wise or not kind and vice versa.
Everyone who is either wise or tall is both creative and not funny.
Everyone who is humble is either not patient or rich.
Lucy is not quiet or not humble.
Paul is not humble or rich.
Someone is both not curious and happy.
Susan is either not rich or kind.
Fred is both not creative and humble.
John is either brave or calm. | John is brave. | contradiction | ((?[X]:((~old(X)|humble(X))))<=>((kind(mary)<~>curious(mary))))&
((quiet(mary))=>(generous(lucy)))&
(![X]:((~strong(X)<~>brave(X))<=>(patient(X)<~>quiet(X))))&
((?[X]:(~creative(X)))=>(?[X]:(~curious(X))))&
(![X]:((humble(X)&~rich(X))=>~patient(X)))&
((?[X]:((rich(X)|funny(X))))<=>((~strong(alice)|generous(alice))))&
((?[X]:((patient(X)&brave(X))))<=>(calm(alice)))&
(![X]:(kind(X)<=>~creative(X)))&
(![X]:((strong(X)<~>humble(X))<=>~calm(X)))&
(![X]:((~patient(X)&kind(X))=>(~funny(X)&old(X))))&
((funny(lucy))<=>(?[X]:((~old(X)<~>~calm(X)))))&
(![X]:((~quiet(X)|~creative(X))=>(strong(X)&humble(X))))&
((humble(paul))<=>(~generous(susan)))&
(![X]:(~wise(X)<=>(~wise(X)<~>~kind(X))))&
(![X]:((wise(X)<~>tall(X))=>(creative(X)&~funny(X))))&
(![X]:(humble(X)=>(~patient(X)<~>rich(X))))&
((~quiet(lucy)|~humble(lucy)))&
((~humble(paul)|rich(paul)))&
(?[X]:((~curious(X)&happy(X))))&
((~rich(susan)<~>kind(susan)))&
((~creative(fred)&humble(fred)))&
((brave(john)<~>calm(john))) | brave(john) | [
"p7",
"p8",
"p11",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4551004786967086025138129
% SZS output start Proof for 4551004786967086025138129
8. ! [X0] : (kind(X0) <=> ~creative(X0)) [input p7]
9. ! [X0] : ((strong(X0) <~> humble(X0)) <=> ~calm(X0)) [input p8]
12. ! [X0] : ((~creative(X0) | ~quiet(X0)) => (humble(X0) & strong(X0))) [input p11]
14. ! [X0] : (~wise(X0) <=> (~wise(X0) <~> ~kind(X0))) [input p13]
22. brave(john) <~> calm(john) [input p21]
23. brave(john) [input hypothesis]
32. ! [X0] : ((humble(X0) & strong(X0)) | (creative(X0) & quiet(X0))) [ennf transformation 12]
52. ! [X0] : ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0))) [nnf transformation 8]
53. ! [X0] : ((((~humble(X0) | ~strong(X0)) & (humble(X0) | strong(X0))) | calm(X0)) & (~calm(X0) | ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0))))) [nnf transformation 9]
59. ! [X0] : ((~wise(X0) | ((~wise(X0) | kind(X0)) & (~kind(X0) | wise(X0)))) & (((kind(X0) | wise(X0)) & (~kind(X0) | ~wise(X0))) | wise(X0))) [nnf transformation 14]
65. (~calm(john) | ~brave(john)) & (calm(john) | brave(john)) [nnf transformation 22]
90. ~creative(X0) | ~kind(X0) [cnf transformation 52]
95. ~strong(X0) | ~humble(X0) | calm(X0) [cnf transformation 53]
103. creative(X0) | strong(X0) [cnf transformation 32]
105. creative(X0) | humble(X0) [cnf transformation 32]
109. kind(X0) | wise(X0) | wise(X0) [cnf transformation 59]
111. ~wise(X0) | ~wise(X0) | kind(X0) [cnf transformation 59]
126. ~calm(john) | ~brave(john) [cnf transformation 65]
127. brave(john) [cnf transformation 23]
128. kind(X0) | wise(X0) [duplicate literal removal 109]
129. ~wise(X0) | kind(X0) [duplicate literal removal 111]
251. kind(X0) [subsumption resolution 128,129]
268. 31 <=> brave(john) [avatar definition]
272. 32 <=> calm(john) [avatar definition]
274. ~calm(john) <- (~32) [avatar component clause 272]
275. ~31 | ~32 [avatar split clause 126,272,268]
277. 31 [avatar split clause 127,268]
282. strong(X0) | ~kind(X0) [resolution 103,90]
283. strong(X0) [subsumption resolution 282,251]
288. humble(X0) | ~kind(X0) [resolution 105,90]
289. humble(X0) [subsumption resolution 288,251]
309. ~humble(X0) | calm(X0) [resolution 95,283]
312. calm(X0) [subsumption resolution 309,289]
313. $false <- (~32) [resolution 312,274]
317. 32 [avatar contradiction clause 313]
319. $false [avatar sat refutation 275,277,317]
% SZS output end Proof for 4551004786967086025138129
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If fred is strong then alice is either not brave or strong.
If someone is either not humble or curious then lucy is funny.
If someone is not humble or not funny then someone is not wise or not brave.
If someone is either not curious or not rich then someone is not old and vice versa.
If someone is old then someone is generous or not patient and vice versa.
Everyone who is kind or not rich is not humble and vice versa.
If paul is not generous then someone is either curious or kind.
Everyone who is both not creative and not funny is old and vice versa.
If someone is rich then paul is both tall and not funny.
Everyone who is either not humble or not curious is not calm.
If someone is either not strong or brave then someone is not creative or not rich and vice versa.
If mary is both humble and not generous then alice is not wise and vice versa.
If someone is patient or not wise then paul is both not kind and curious and vice versa.
Everyone who is calm or not calm is creative or not curious.
Everyone who is both not kind and creative is not rich.
Everyone who is both not patient and quiet is not happy or old and vice versa.
Someone is not brave.
Paul is humble or not strong.
Mary is either generous or not rich.
Someone is both quiet and not strong.
John is not curious.
Someone is rich or curious.
Paul is humble. | Paul is not patient. | entailment | ((strong(fred))=>((~brave(alice)<~>strong(alice))))&
((?[X]:((~humble(X)<~>curious(X))))=>(funny(lucy)))&
((?[X]:((~humble(X)|~funny(X))))=>(?[X]:((~wise(X)|~brave(X)))))&
((?[X]:((~curious(X)<~>~rich(X))))<=>(?[X]:(~old(X))))&
((?[X]:(old(X)))<=>(?[X]:((generous(X)|~patient(X)))))&
(![X]:((kind(X)|~rich(X))<=>~humble(X)))&
((~generous(paul))=>(?[X]:((curious(X)<~>kind(X)))))&
(![X]:((~creative(X)&~funny(X))<=>old(X)))&
((?[X]:(rich(X)))=>((tall(paul)&~funny(paul))))&
(![X]:((~humble(X)<~>~curious(X))=>~calm(X)))&
((?[X]:((~strong(X)<~>brave(X))))<=>(?[X]:((~creative(X)|~rich(X)))))&
(((humble(mary)&~generous(mary)))<=>(~wise(alice)))&
((?[X]:((patient(X)|~wise(X))))<=>((~kind(paul)&curious(paul))))&
(![X]:((calm(X)|~calm(X))=>(creative(X)|~curious(X))))&
(![X]:((~kind(X)&creative(X))=>~rich(X)))&
(![X]:((~patient(X)&quiet(X))<=>(~happy(X)|old(X))))&
(?[X]:(~brave(X)))&
((humble(paul)|~strong(paul)))&
((generous(mary)<~>~rich(mary)))&
(?[X]:((quiet(X)&~strong(X))))&
(~curious(john))&
(?[X]:((rich(X)|curious(X))))&
(humble(paul)) | ~patient(paul) | [
"p5",
"p12",
"p13",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2674848392939473601753254
% SZS output start Proof for 2674848392939473601753254
6. ! [X0] : ((~rich(X0) | kind(X0)) <=> ~humble(X0)) [input p5]
13. ? [X0] : (~wise(X0) | patient(X0)) <=> (curious(paul) & ~kind(paul)) [input p12]
14. ! [X0] : ((~calm(X0) | calm(X0)) => (~curious(X0) | creative(X0))) [input p13]
15. ! [X0] : ((creative(X0) & ~kind(X0)) => ~rich(X0)) [input p14]
23. humble(paul) [input p22]
24. patient(paul) [input hypothesis]
36. ! [X0] : ((~curious(X0) | creative(X0)) | (calm(X0) & ~calm(X0))) [ennf transformation 14]
37. ! [X0] : (~curious(X0) | creative(X0) | (calm(X0) & ~calm(X0))) [flattening 36]
38. ! [X0] : (~rich(X0) | (~creative(X0) | kind(X0))) [ennf transformation 15]
39. ! [X0] : (~rich(X0) | ~creative(X0) | kind(X0)) [flattening 38]
55. ! [X0] : (((~rich(X0) | kind(X0)) | humble(X0)) & (~humble(X0) | (rich(X0) & ~kind(X0)))) [nnf transformation 6]
56. ! [X0] : ((~rich(X0) | kind(X0) | humble(X0)) & (~humble(X0) | (rich(X0) & ~kind(X0)))) [flattening 55]
70. (? [X0] : (~wise(X0) | patient(X0)) | (~curious(paul) | kind(paul))) & ((curious(paul) & ~kind(paul)) | ! [X0] : (wise(X0) & ~patient(X0))) [nnf transformation 13]
71. (? [X0] : (~wise(X0) | patient(X0)) | ~curious(paul) | kind(paul)) & ((curious(paul) & ~kind(paul)) | ! [X0] : (wise(X0) & ~patient(X0))) [flattening 70]
72. (? [X0] : (~wise(X0) | patient(X0)) | ~curious(paul) | kind(paul)) & ((curious(paul) & ~kind(paul)) | ! [X1] : (wise(X1) & ~patient(X1))) [rectify 71]
73. ? [X0] : (~wise(X0) | patient(X0)) => (~wise(sK8) | patient(sK8)) [choice axiom]
74. ((~wise(sK8) | patient(sK8)) | ~curious(paul) | kind(paul)) & ((curious(paul) & ~kind(paul)) | ! [X1] : (wise(X1) & ~patient(X1))) [skolemisation 72,73]
98. ~humble(X0) | rich(X0) [cnf transformation 56]
117. ~kind(paul) | ~patient(X1) [cnf transformation 74]
119. curious(paul) | ~patient(X1) [cnf transformation 74]
122. ~curious(X0) | creative(X0) | ~calm(X0) [cnf transformation 37]
123. ~curious(X0) | creative(X0) | calm(X0) [cnf transformation 37]
124. ~creative(X0) | ~rich(X0) | kind(X0) [cnf transformation 39]
138. humble(paul) [cnf transformation 23]
139. patient(paul) [cnf transformation 24]
303. 39 <=> kind(paul) [avatar definition]
304. ~kind(paul) <- (~39) [avatar component clause 303]
307. 40 <=> curious(paul) [avatar definition]
308. curious(paul) <- (40) [avatar component clause 307]
324. 44 <=> ! [X1] : ~patient(X1) [avatar definition]
325. ~patient(X1) <- (44) [avatar component clause 324]
326. 44 | 40 [avatar split clause 119,307,324]
328. 44 | ~39 [avatar split clause 117,303,324]
329. ~curious(X0) | creative(X0) [subsumption resolution 122,123]
331. 45 <=> humble(paul) [avatar definition]
333. humble(paul) <- (45) [avatar component clause 331]
354. 45 [avatar split clause 138,331]
357. rich(paul) <- (45) [resolution 98,333]
363. creative(paul) <- (40) [resolution 329,308]
396. ~rich(paul) | kind(paul) <- (40) [resolution 124,363]
400. kind(paul) <- (40, 45) [subsumption resolution 396,357]
401. $false <- (~39, 40, 45) [subsumption resolution 400,304]
402. 39 | ~40 | ~45 [avatar contradiction clause 401]
407. $false <- (44) [resolution 325,139]
408. ~44 [avatar contradiction clause 407]
409. $false [avatar sat refutation 326,328,354,402,408]
% SZS output end Proof for 2674848392939473601753254
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich is both tall and not brave and vice versa.
Everyone who is either not curious or strong is either funny or patient.
If mary is both not funny and happy then alice is old or curious and vice versa.
Everyone who is either calm or not patient is either strong or happy and vice versa.
If fred is not strong then alice is both not patient and wise and vice versa.
Everyone who is both strong and not happy is both generous and not tall.
Everyone who is not calm or humble is both not humble and calm.
Everyone who is either not calm or patient is both not happy and not patient.
If fred is either humble or tall then someone is not generous or not quiet and vice versa.
If alice is either not wise or not happy then susan is either generous or not old.
Everyone who is tall is generous.
If someone is not calm or not wise then lucy is either humble or funny.
If someone is either not brave or not tall then someone is either not curious or quiet and vice versa.
If john is creative or not brave then someone is either brave or not rich and vice versa.
Everyone who is either funny or not creative is either calm or wise and vice versa.
Everyone who is either quiet or not old is both not strong and not quiet.
Mary is either wise or curious.
Lucy is not old.
John is not kind.
John is calm.
Someone is generous or not funny.
Alice is tall. | John is funny. | neutral | (![X]:(rich(X)<=>(tall(X)&~brave(X))))&
(![X]:((~curious(X)<~>strong(X))=>(funny(X)<~>patient(X))))&
(((~funny(mary)&happy(mary)))<=>((old(alice)|curious(alice))))&
(![X]:((calm(X)<~>~patient(X))<=>(strong(X)<~>happy(X))))&
((~strong(fred))<=>((~patient(alice)&wise(alice))))&
(![X]:((strong(X)&~happy(X))=>(generous(X)&~tall(X))))&
(![X]:((~calm(X)|humble(X))=>(~humble(X)&calm(X))))&
(![X]:((~calm(X)<~>patient(X))=>(~happy(X)&~patient(X))))&
(((humble(fred)<~>tall(fred)))<=>(?[X]:((~generous(X)|~quiet(X)))))&
(((~wise(alice)<~>~happy(alice)))=>((generous(susan)<~>~old(susan))))&
(![X]:(tall(X)=>generous(X)))&
((?[X]:((~calm(X)|~wise(X))))=>((humble(lucy)<~>funny(lucy))))&
((?[X]:((~brave(X)<~>~tall(X))))<=>(?[X]:((~curious(X)<~>quiet(X)))))&
(((creative(john)|~brave(john)))<=>(?[X]:((brave(X)<~>~rich(X)))))&
(![X]:((funny(X)<~>~creative(X))<=>(calm(X)<~>wise(X))))&
(![X]:((quiet(X)<~>~old(X))=>(~strong(X)&~quiet(X))))&
((wise(mary)<~>curious(mary)))&
(~old(lucy))&
(~kind(john))&
(calm(john))&
(?[X]:((generous(X)|~funny(X))))&
(tall(alice)) | funny(john) | [] | null | 0 |
Everyone who is not strong or not generous is both old and not tall and vice versa.
Everyone who is both tall and not creative is both not funny and quiet and vice versa.
Everyone who is rich or not strong is both not funny and not patient and vice versa.
Everyone who is curious is either not quiet or not rich.
If someone is both not wise and brave then alice is either tall or not wise and vice versa.
Everyone who is creative or not funny is not old or funny.
Everyone who is creative or not creative is not generous or not old and vice versa.
Everyone who is not generous is patient or not rich and vice versa.
If lucy is both not patient and creative then someone is calm.
Everyone who is not humble is either not creative or not tall.
If paul is either calm or not strong then someone is not quiet and vice versa.
If fred is not rich or not curious then alice is happy.
If someone is rich then paul is not humble and vice versa.
If mary is either curious or not strong then lucy is either not happy or not calm and vice versa.
Everyone who is creative is both quiet and humble and vice versa.
If mary is both not kind and creative then someone is not kind or happy and vice versa.
Mary is not brave.
John is not creative.
Paul is both not kind and not brave.
Alice is either funny or curious.
Someone is wise.
Alice is either wise or not calm.
Someone is both not generous and not tall. | Alice is happy. | neutral | (![X]:((~strong(X)|~generous(X))<=>(old(X)&~tall(X))))&
(![X]:((tall(X)&~creative(X))<=>(~funny(X)&quiet(X))))&
(![X]:((rich(X)|~strong(X))<=>(~funny(X)&~patient(X))))&
(![X]:(curious(X)=>(~quiet(X)<~>~rich(X))))&
((?[X]:((~wise(X)&brave(X))))<=>((tall(alice)<~>~wise(alice))))&
(![X]:((creative(X)|~funny(X))=>(~old(X)|funny(X))))&
(![X]:((creative(X)|~creative(X))<=>(~generous(X)|~old(X))))&
(![X]:(~generous(X)<=>(patient(X)|~rich(X))))&
(((~patient(lucy)&creative(lucy)))=>(?[X]:(calm(X))))&
(![X]:(~humble(X)=>(~creative(X)<~>~tall(X))))&
(((calm(paul)<~>~strong(paul)))<=>(?[X]:(~quiet(X))))&
(((~rich(fred)|~curious(fred)))=>(happy(alice)))&
((?[X]:(rich(X)))<=>(~humble(paul)))&
(((curious(mary)<~>~strong(mary)))<=>((~happy(lucy)<~>~calm(lucy))))&
(![X]:(creative(X)<=>(quiet(X)&humble(X))))&
(((~kind(mary)&creative(mary)))<=>(?[X]:((~kind(X)|happy(X)))))&
(~brave(mary))&
(~creative(john))&
((~kind(paul)&~brave(paul)))&
((funny(alice)<~>curious(alice)))&
(?[X]:(wise(X)))&
((wise(alice)<~>~calm(alice)))&
(?[X]:((~generous(X)&~tall(X)))) | happy(alice) | [] | null | 0 |
Everyone who is generous or strong is not humble.
Everyone who is not curious or old is calm.
If someone is not brave or not humble then susan is brave or creative and vice versa.
Everyone who is both rich and not funny is both rich and not rich and vice versa.
If alice is either tall or not rich then someone is not creative or not funny.
Everyone who is humble or not generous is both rich and not kind and vice versa.
If paul is kind or not quiet then paul is quiet and vice versa.
If someone is brave or quiet then alice is not kind or curious and vice versa.
If someone is either not kind or strong then someone is not kind.
If mary is generous then alice is either not brave or tall.
If paul is generous or not generous then fred is both not patient and not old.
Everyone who is both humble and wise is curious or funny and vice versa.
If someone is tall or strong then someone is not creative and vice versa.
Everyone who is not strong is either not creative or not curious.
Everyone who is both strong and tall is either not rich or not wise.
Everyone who is not strong or kind is kind or strong.
Someone is not happy.
Paul is brave or patient.
Someone is either strong or old.
Someone is either curious or not old.
Someone is either quiet or old. | Susan is not kind. | neutral | (![X]:((generous(X)|strong(X))=>~humble(X)))&
(![X]:((~curious(X)|old(X))=>calm(X)))&
((?[X]:((~brave(X)|~humble(X))))<=>((brave(susan)|creative(susan))))&
(![X]:((rich(X)&~funny(X))<=>(rich(X)&~rich(X))))&
(((tall(alice)<~>~rich(alice)))=>(?[X]:((~creative(X)|~funny(X)))))&
(![X]:((humble(X)|~generous(X))<=>(rich(X)&~kind(X))))&
(((kind(paul)|~quiet(paul)))<=>(quiet(paul)))&
((?[X]:((brave(X)|quiet(X))))<=>((~kind(alice)|curious(alice))))&
((?[X]:((~kind(X)<~>strong(X))))=>(?[X]:(~kind(X))))&
((generous(mary))=>((~brave(alice)<~>tall(alice))))&
(((generous(paul)|~generous(paul)))=>((~patient(fred)&~old(fred))))&
(![X]:((humble(X)&wise(X))<=>(curious(X)|funny(X))))&
((?[X]:((tall(X)|strong(X))))<=>(?[X]:(~creative(X))))&
(![X]:(~strong(X)=>(~creative(X)<~>~curious(X))))&
(![X]:((strong(X)&tall(X))=>(~rich(X)<~>~wise(X))))&
(![X]:((~strong(X)|kind(X))=>(kind(X)|strong(X))))&
(?[X]:(~happy(X)))&
((brave(paul)|patient(paul)))&
(?[X]:((strong(X)<~>old(X))))&
(?[X]:((curious(X)<~>~old(X))))&
(?[X]:((quiet(X)<~>old(X)))) | ~kind(susan) | [] | null | 0 |
If someone is brave or not brave then someone is either creative or not curious. Everyone who is rich is not creative or not tall. If john is either not generous or not wise then someone is not strong and vice versa. If someone is either not tall or quiet then someone is both not patient and old and vice versa. Everyone who is old or not calm is not patient or not wise. If mary is either not patient or wise then someone is either not brave or not rich. If someone is both old and not tall then lucy is tall or not tall and vice versa. If someone is both tall and not calm then someone is either funny or wise and vice versa. Everyone who is not tall or not quiet is strong. If someone is happy or generous then someone is both not strong and not happy. If someone is strong or creative then paul is not old or quiet and vice versa. If someone is brave or humble then lucy is both old and not kind and vice versa. If mary is not happy or not quiet then someone is both rich and brave and vice versa. If someone is both strong and not curious then someone is both wise and not happy. If someone is not strong then someone is both calm and patient and vice versa. Everyone who is rich is both not rich and tall. Someone is quiet or not kind. Someone is happy or not kind. Someone is quiet or not generous. Mary is not funny. Susan is both not strong and old. Fred is both brave and creative. Someone is humble or not rich. Someone is patient. | John is wise. | neutral | ((?[X]:((brave(X)|~brave(X))))=>(?[X]:((creative(X)<~>~curious(X)))))&
(![X]:(rich(X)=>(~creative(X)|~tall(X))))&
(((~generous(john)<~>~wise(john)))<=>(?[X]:(~strong(X))))&
((?[X]:((~tall(X)<~>quiet(X))))<=>(?[X]:((~patient(X)&old(X)))))&
(![X]:((old(X)|~calm(X))=>(~patient(X)|~wise(X))))&
(((~patient(mary)<~>wise(mary)))=>(?[X]:((~brave(X)<~>~rich(X)))))&
((?[X]:((old(X)&~tall(X))))<=>((tall(lucy)|~tall(lucy))))&
((?[X]:((tall(X)&~calm(X))))<=>(?[X]:((funny(X)<~>wise(X)))))&
(![X]:((~tall(X)|~quiet(X))=>strong(X)))&
((?[X]:((happy(X)|generous(X))))=>(?[X]:((~strong(X)&~happy(X)))))&
((?[X]:((strong(X)|creative(X))))<=>((~old(paul)|quiet(paul))))&
((?[X]:((brave(X)|humble(X))))<=>((old(lucy)&~kind(lucy))))&
(((~happy(mary)|~quiet(mary)))<=>(?[X]:((rich(X)&brave(X)))))&
((?[X]:((strong(X)&~curious(X))))=>(?[X]:((wise(X)&~happy(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((calm(X)&patient(X)))))&
(![X]:(rich(X)=>(~rich(X)&tall(X))))&
(?[X]:((quiet(X)|~kind(X))))&
(?[X]:((happy(X)|~kind(X))))&
(?[X]:((quiet(X)|~generous(X))))&
(~funny(mary))&
((~strong(susan)&old(susan)))&
((brave(fred)&creative(fred)))&
(?[X]:((humble(X)|~rich(X))))&
(?[X]:(patient(X))) | wise(john) | [] | null | 0 |
Everyone who is not wise or not creative is creative and vice versa.
If someone is not happy then john is strong and vice versa.
Everyone who is either happy or brave is not old and vice versa.
If someone is not humble then susan is not happy.
Everyone who is happy is both not humble and brave and vice versa.
If someone is either not happy or not humble then someone is either strong or brave and vice versa.
If someone is creative or not tall then someone is both creative and curious and vice versa.
Everyone who is funny is both brave and generous.
If fred is funny or not patient then someone is old or humble.
If someone is both not strong and curious then mary is either not generous or not wise and vice versa.
If alice is either not strong or not generous then someone is either tall or funny.
Everyone who is either kind or not tall is both not quiet and not funny.
Everyone who is calm or creative is not wise or not brave and vice versa.
Everyone who is not wise is rich.
Everyone who is not humble is either strong or tall and vice versa.
If someone is not creative then lucy is tall and vice versa.
Lucy is both not calm and not strong.
Fred is either patient or not quiet.
John is not tall or not quiet.
Someone is not calm or happy.
John is both creative and happy.
Someone is both strong and not calm.
Lucy is not brave.
Someone is both not patient and brave. | Susan is happy. | contradiction | (![X]:((~wise(X)|~creative(X))<=>creative(X)))&
((?[X]:(~happy(X)))<=>(strong(john)))&
(![X]:((happy(X)<~>brave(X))<=>~old(X)))&
((?[X]:(~humble(X)))=>(~happy(susan)))&
(![X]:(happy(X)<=>(~humble(X)&brave(X))))&
((?[X]:((~happy(X)<~>~humble(X))))<=>(?[X]:((strong(X)<~>brave(X)))))&
((?[X]:((creative(X)|~tall(X))))<=>(?[X]:((creative(X)&curious(X)))))&
(![X]:(funny(X)=>(brave(X)&generous(X))))&
(((funny(fred)|~patient(fred)))=>(?[X]:((old(X)|humble(X)))))&
((?[X]:((~strong(X)&curious(X))))<=>((~generous(mary)<~>~wise(mary))))&
(((~strong(alice)<~>~generous(alice)))=>(?[X]:((tall(X)<~>funny(X)))))&
(![X]:((kind(X)<~>~tall(X))=>(~quiet(X)&~funny(X))))&
(![X]:((calm(X)|creative(X))<=>(~wise(X)|~brave(X))))&
(![X]:(~wise(X)=>rich(X)))&
(![X]:(~humble(X)<=>(strong(X)<~>tall(X))))&
((?[X]:(~creative(X)))<=>(tall(lucy)))&
((~calm(lucy)&~strong(lucy)))&
((patient(fred)<~>~quiet(fred)))&
((~tall(john)|~quiet(john)))&
(?[X]:((~calm(X)|happy(X))))&
((creative(john)&happy(john)))&
(?[X]:((strong(X)&~calm(X))))&
(~brave(lucy))&
(?[X]:((~patient(X)&brave(X)))) | happy(susan) | [
"p3",
"p4",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3890628873443470910757015
% SZS output start Proof for 3890628873443470910757015
4. ? [X0] : ~humble(X0) => ~happy(susan) [input p3]
5. ! [X0] : (happy(X0) <=> (brave(X0) & ~humble(X0))) [input p4]
21. happy(john) & creative(john) [input p20]
25. happy(susan) [input hypothesis]
31. ~happy(susan) | ! [X0] : humble(X0) [ennf transformation 4]
43. ! [X0] : ((happy(X0) | (~brave(X0) | humble(X0))) & ((brave(X0) & ~humble(X0)) | ~happy(X0))) [nnf transformation 5]
44. ! [X0] : ((happy(X0) | ~brave(X0) | humble(X0)) & ((brave(X0) & ~humble(X0)) | ~happy(X0))) [flattening 43]
86. ~happy(susan) | humble(X0) [cnf transformation 31]
87. ~humble(X0) | ~happy(X0) [cnf transformation 44]
138. happy(john) [cnf transformation 21]
144. happy(susan) [cnf transformation 25]
161. 4 <=> ! [X0] : humble(X0) [avatar definition]
162. humble(X0) <- (4) [avatar component clause 161]
164. 5 <=> happy(susan) [avatar definition]
167. 4 | ~5 [avatar split clause 86,164,161]
186. 10 <=> ! [X3] : ~happy(X3) [avatar definition]
187. ~happy(X3) <- (10) [avatar component clause 186]
304. 5 [avatar split clause 144,164]
307. ~happy(X0) <- (4) [resolution 87,162]
310. 10 | ~4 [avatar split clause 307,161,186]
311. $false <- (10) [resolution 187,138]
316. ~10 [avatar contradiction clause 311]
317. $false [avatar sat refutation 167,304,310,316]
% SZS output end Proof for 3890628873443470910757015
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not brave or not strong is both quiet and not strong and vice versa.
Everyone who is strong is either not rich or not happy.
Everyone who is strong or not humble is not patient.
Everyone who is strong is not creative or humble and vice versa.
Everyone who is not strong or happy is both funny and not patient.
If someone is not quiet then mary is curious.
If mary is either not generous or patient then someone is not strong and vice versa.
If someone is not strong then someone is not quiet.
If someone is either not tall or not creative then john is both not curious and not kind.
Everyone who is both strong and not rich is both not generous and funny and vice versa.
If john is not generous then susan is both old and quiet.
If someone is quiet or not quiet then someone is either wise or not wise and vice versa.
Everyone who is either happy or not kind is both not humble and not brave and vice versa.
Everyone who is both not happy and not brave is either happy or not generous and vice versa.
Everyone who is wise or generous is either patient or old.
Everyone who is not wise or curious is both quiet and not brave.
Mary is both rich and quiet.
Someone is happy.
Someone is not creative.
Lucy is not kind or funny.
Someone is both not rich and wise.
Someone is not funny. | John is not happy. | neutral | (![X]:((~brave(X)<~>~strong(X))<=>(quiet(X)&~strong(X))))&
(![X]:(strong(X)=>(~rich(X)<~>~happy(X))))&
(![X]:((strong(X)|~humble(X))=>~patient(X)))&
(![X]:(strong(X)<=>(~creative(X)|humble(X))))&
(![X]:((~strong(X)|happy(X))=>(funny(X)&~patient(X))))&
((?[X]:(~quiet(X)))=>(curious(mary)))&
(((~generous(mary)<~>patient(mary)))<=>(?[X]:(~strong(X))))&
((?[X]:(~strong(X)))=>(?[X]:(~quiet(X))))&
((?[X]:((~tall(X)<~>~creative(X))))=>((~curious(john)&~kind(john))))&
(![X]:((strong(X)&~rich(X))<=>(~generous(X)&funny(X))))&
((~generous(john))=>((old(susan)&quiet(susan))))&
((?[X]:((quiet(X)|~quiet(X))))<=>(?[X]:((wise(X)<~>~wise(X)))))&
(![X]:((happy(X)<~>~kind(X))<=>(~humble(X)&~brave(X))))&
(![X]:((~happy(X)&~brave(X))<=>(happy(X)<~>~generous(X))))&
(![X]:((wise(X)|generous(X))=>(patient(X)<~>old(X))))&
(![X]:((~wise(X)|curious(X))=>(quiet(X)&~brave(X))))&
((rich(mary)&quiet(mary)))&
(?[X]:(happy(X)))&
(?[X]:(~creative(X)))&
((~kind(lucy)|funny(lucy)))&
(?[X]:((~rich(X)&wise(X))))&
(?[X]:(~funny(X))) | ~happy(john) | [] | null | 0 |
Everyone who is both not old and humble is not strong and vice versa.
If someone is both rich and not creative then lucy is both not calm and funny and vice versa.
Everyone who is either not strong or not humble is either not old or patient and vice versa.
If fred is either not creative or not funny then someone is both not tall and not funny.
Everyone who is both not creative and rich is either not patient or humble.
If someone is strong then someone is both happy and quiet.
Everyone who is funny is both not curious and not humble.
If susan is patient then someone is creative.
Everyone who is both wise and not funny is not rich or quiet and vice versa.
Everyone who is both calm and funny is both curious and kind and vice versa.
Everyone who is not strong is either wise or quiet.
If mary is both quiet and patient then someone is either not quiet or curious.
Everyone who is either curious or humble is tall or humble and vice versa.
If someone is kind or not old then someone is not old.
If susan is not funny then mary is happy or quiet.
Everyone who is creative or quiet is both not happy and not quiet.
Someone is not wise or not happy.
Someone is calm or funny.
Someone is both not happy and humble.
Someone is either curious or brave. | Lucy is not kind. | neutral | (![X]:((~old(X)&humble(X))<=>~strong(X)))&
((?[X]:((rich(X)&~creative(X))))<=>((~calm(lucy)&funny(lucy))))&
(![X]:((~strong(X)<~>~humble(X))<=>(~old(X)<~>patient(X))))&
(((~creative(fred)<~>~funny(fred)))=>(?[X]:((~tall(X)&~funny(X)))))&
(![X]:((~creative(X)&rich(X))=>(~patient(X)<~>humble(X))))&
((?[X]:(strong(X)))=>(?[X]:((happy(X)&quiet(X)))))&
(![X]:(funny(X)=>(~curious(X)&~humble(X))))&
((patient(susan))=>(?[X]:(creative(X))))&
(![X]:((wise(X)&~funny(X))<=>(~rich(X)|quiet(X))))&
(![X]:((calm(X)&funny(X))<=>(curious(X)&kind(X))))&
(![X]:(~strong(X)=>(wise(X)<~>quiet(X))))&
(((quiet(mary)&patient(mary)))=>(?[X]:((~quiet(X)<~>curious(X)))))&
(![X]:((curious(X)<~>humble(X))<=>(tall(X)|humble(X))))&
((?[X]:((kind(X)|~old(X))))=>(?[X]:(~old(X))))&
((~funny(susan))=>((happy(mary)|quiet(mary))))&
(![X]:((creative(X)|quiet(X))=>(~happy(X)&~quiet(X))))&
(?[X]:((~wise(X)|~happy(X))))&
(?[X]:((calm(X)|funny(X))))&
(?[X]:((~happy(X)&humble(X))))&
(?[X]:((curious(X)<~>brave(X)))) | ~kind(lucy) | [] | null | 0 |
Everyone who is either not creative or not brave is not tall and vice versa.
Everyone who is either not calm or not generous is not old or old and vice versa.
If someone is either funny or brave then john is either old or funny.
Everyone who is not wise or strong is either not strong or funny and vice versa.
Everyone who is not generous or not rich is tall.
Everyone who is both old and brave is both old and not wise and vice versa.
Everyone who is rich is wise or not humble and vice versa.
If lucy is either creative or not generous then someone is both tall and rich and vice versa.
If someone is not generous or old then someone is both calm and humble and vice versa.
Everyone who is either not generous or not funny is not tall or humble and vice versa.
If someone is curious or not funny then mary is not generous and vice versa.
If someone is strong then someone is both curious and not funny and vice versa.
Everyone who is not happy is both creative and tall.
If susan is both not curious and not generous then john is patient or not strong and vice versa.
If mary is either not creative or old then someone is not creative and vice versa.
Everyone who is either quiet or not kind is either calm or not generous.
Someone is either old or strong.
Someone is both not funny and patient.
Lucy is not curious or happy.
Someone is not curious or kind.
Someone is creative.
John is either not wise or happy.
Lucy is both rich and tall.
Someone is not humble. | Mary is strong. | neutral | (![X]:((~creative(X)<~>~brave(X))<=>~tall(X)))&
(![X]:((~calm(X)<~>~generous(X))<=>(~old(X)|old(X))))&
((?[X]:((funny(X)<~>brave(X))))=>((old(john)<~>funny(john))))&
(![X]:((~wise(X)|strong(X))<=>(~strong(X)<~>funny(X))))&
(![X]:((~generous(X)|~rich(X))=>tall(X)))&
(![X]:((old(X)&brave(X))<=>(old(X)&~wise(X))))&
(![X]:(rich(X)<=>(wise(X)|~humble(X))))&
(((creative(lucy)<~>~generous(lucy)))<=>(?[X]:((tall(X)&rich(X)))))&
((?[X]:((~generous(X)|old(X))))<=>(?[X]:((calm(X)&humble(X)))))&
(![X]:((~generous(X)<~>~funny(X))<=>(~tall(X)|humble(X))))&
((?[X]:((curious(X)|~funny(X))))<=>(~generous(mary)))&
((?[X]:(strong(X)))<=>(?[X]:((curious(X)&~funny(X)))))&
(![X]:(~happy(X)=>(creative(X)&tall(X))))&
(((~curious(susan)&~generous(susan)))<=>((patient(john)|~strong(john))))&
(((~creative(mary)<~>old(mary)))<=>(?[X]:(~creative(X))))&
(![X]:((quiet(X)<~>~kind(X))=>(calm(X)<~>~generous(X))))&
(?[X]:((old(X)<~>strong(X))))&
(?[X]:((~funny(X)&patient(X))))&
((~curious(lucy)|happy(lucy)))&
(?[X]:((~curious(X)|kind(X))))&
(?[X]:(creative(X)))&
((~wise(john)<~>happy(john)))&
((rich(lucy)&tall(lucy)))&
(?[X]:(~humble(X))) | strong(mary) | [] | null | 0 |
Everyone who is humble or calm is both old and not curious and vice versa. Everyone who is generous or wise is both not happy and funny. Everyone who is generous or patient is not rich. Everyone who is calm or not funny is both wise and humble and vice versa. Everyone who is either creative or not brave is tall or not quiet. If lucy is not strong then someone is brave or funny. If lucy is both not funny and not curious then someone is not strong and vice versa. Everyone who is not wise is both not strong and old and vice versa. Everyone who is not rich is either generous or not humble. Everyone who is creative is old and vice versa. Everyone who is creative or happy is either not funny or curious and vice versa. Everyone who is either patient or kind is tall. If john is not rich or funny then lucy is not brave or not humble and vice versa. Lucy is brave. Someone is wise. Paul is either not funny or not rich. Someone is not humble or old. | Paul is curious. | neutral | (![X]:((humble(X)|calm(X))<=>(old(X)&~curious(X))))&
(![X]:((generous(X)|wise(X))=>(~happy(X)&funny(X))))&
(![X]:((generous(X)|patient(X))=>~rich(X)))&
(![X]:((calm(X)|~funny(X))<=>(wise(X)&humble(X))))&
(![X]:((creative(X)<~>~brave(X))=>(tall(X)|~quiet(X))))&
((~strong(lucy))=>(?[X]:((brave(X)|funny(X)))))&
(((~funny(lucy)&~curious(lucy)))<=>(?[X]:(~strong(X))))&
(![X]:(~wise(X)<=>(~strong(X)&old(X))))&
(![X]:(~rich(X)=>(generous(X)<~>~humble(X))))&
(![X]:(creative(X)<=>old(X)))&
(![X]:((creative(X)|happy(X))<=>(~funny(X)<~>curious(X))))&
(![X]:((patient(X)<~>kind(X))=>tall(X)))&
(((~rich(john)|funny(john)))<=>((~brave(lucy)|~humble(lucy))))&
(brave(lucy))&
(?[X]:(wise(X)))&
((~funny(paul)<~>~rich(paul)))&
(?[X]:((~humble(X)|old(X)))) | curious(paul) | [] | null | 0 |
Everyone who is both not rich and strong is both not funny and not creative.
If someone is not funny then fred is either not old or not rich.
Everyone who is brave or not brave is happy or not quiet.
If john is both not brave and strong then alice is calm or brave.
Everyone who is either not rich or calm is humble.
If susan is patient then fred is either not calm or not wise and vice versa.
Everyone who is both strong and calm is both brave and not funny.
Everyone who is both not creative and not rich is both not quiet and quiet.
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.
Someone is either not creative or brave.
Someone is both creative and happy.
Someone is not strong or humble.
Mary is not funny.
Someone is tall.
Fred is both not happy and not generous. | Mary is not brave. | entailment | (![X]:((~rich(X)&strong(X))=>(~funny(X)&~creative(X))))&
((?[X]:(~funny(X)))=>((~old(fred)<~>~rich(fred))))&
(![X]:((brave(X)|~brave(X))=>(happy(X)|~quiet(X))))&
(((~brave(john)&strong(john)))=>((calm(alice)|brave(alice))))&
(![X]:((~rich(X)<~>calm(X))=>humble(X)))&
((patient(susan))<=>((~calm(fred)<~>~wise(fred))))&
(![X]:((strong(X)&calm(X))=>(brave(X)&~funny(X))))&
(![X]:((~creative(X)&~rich(X))=>(~quiet(X)&quiet(X))))&
((?[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]:((~creative(X)<~>brave(X))))&
(?[X]:((creative(X)&happy(X))))&
(?[X]:((~strong(X)|humble(X))))&
(~funny(mary))&
(?[X]:(tall(X)))&
((~happy(fred)&~generous(fred))) | ~brave(mary) | [
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8031674116478176686707897
% SZS output start Proof for 8031674116478176686707897
12. ! [X0] : (brave(X0) <=> (~happy(X0) & ~rich(X0))) [input p11]
13. (~strong(john) & generous(john)) <=> ? [X0] : (~rich(X0) | ~patient(X0)) [input p12]
15. ? [X0] : (generous(X0) | ~kind(X0)) <=> ? [X0] : (~funny(X0) & funny(X0)) [input p14]
23. brave(mary) [input hypothesis]
24. ? [X0] : (generous(X0) | ~kind(X0)) <=> ? [X1] : (~funny(X1) & funny(X1)) [rectify 15]
48. ! [X0] : ((brave(X0) | (happy(X0) | rich(X0))) & ((~happy(X0) & ~rich(X0)) | ~brave(X0))) [nnf transformation 12]
49. ! [X0] : ((brave(X0) | happy(X0) | rich(X0)) & ((~happy(X0) & ~rich(X0)) | ~brave(X0))) [flattening 48]
50. ((~strong(john) & generous(john)) | ! [X0] : (rich(X0) & patient(X0))) & (? [X0] : (~rich(X0) | ~patient(X0)) | (strong(john) | ~generous(john))) [nnf transformation 13]
51. ((~strong(john) & generous(john)) | ! [X0] : (rich(X0) & patient(X0))) & (? [X0] : (~rich(X0) | ~patient(X0)) | strong(john) | ~generous(john)) [flattening 50]
52. ((~strong(john) & generous(john)) | ! [X0] : (rich(X0) & patient(X0))) & (? [X1] : (~rich(X1) | ~patient(X1)) | strong(john) | ~generous(john)) [rectify 51]
53. ? [X1] : (~rich(X1) | ~patient(X1)) => (~rich(sK1) | ~patient(sK1)) [choice axiom]
54. ((~strong(john) & generous(john)) | ! [X0] : (rich(X0) & patient(X0))) & ((~rich(sK1) | ~patient(sK1)) | strong(john) | ~generous(john)) [skolemisation 52,53]
60. (? [X0] : (generous(X0) | ~kind(X0)) | ! [X1] : (funny(X1) | ~funny(X1))) & (? [X1] : (~funny(X1) & funny(X1)) | ! [X0] : (~generous(X0) & kind(X0))) [nnf transformation 24]
61. (? [X0] : (generous(X0) | ~kind(X0)) | ! [X1] : (funny(X1) | ~funny(X1))) & (? [X2] : (~funny(X2) & funny(X2)) | ! [X3] : (~generous(X3) & kind(X3))) [rectify 60]
62. ? [X0] : (generous(X0) | ~kind(X0)) => (generous(sK3) | ~kind(sK3)) [choice axiom]
63. ? [X2] : (~funny(X2) & funny(X2)) => (~funny(sK4) & funny(sK4)) [choice axiom]
64. ((generous(sK3) | ~kind(sK3)) | ! [X1] : (funny(X1) | ~funny(X1))) & ((~funny(sK4) & funny(sK4)) | ! [X3] : (~generous(X3) & kind(X3))) [skolemisation 61,63,62]
103. ~brave(X0) | ~rich(X0) [cnf transformation 49]
108. generous(john) | rich(X0) [cnf transformation 54]
117. funny(sK4) | ~generous(X3) [cnf transformation 64]
119. ~funny(sK4) | ~generous(X3) [cnf transformation 64]
136. brave(mary) [cnf transformation 23]
226. 20 <=> ! [X0] : rich(X0) [avatar definition]
227. rich(X0) <- (20) [avatar component clause 226]
234. 22 <=> generous(john) [avatar definition]
236. generous(john) <- (22) [avatar component clause 234]
237. 20 | 22 [avatar split clause 108,234,226]
269. 29 <=> ! [X3] : ~generous(X3) [avatar definition]
270. ~generous(X3) <- (29) [avatar component clause 269]
272. 30 <=> funny(sK4) [avatar definition]
275. 29 | ~30 [avatar split clause 119,272,269]
280. 29 | 30 [avatar split clause 117,272,269]
311. $false <- (22, 29) [subsumption resolution 236,270]
312. ~22 | ~29 [avatar contradiction clause 311]
313. ~rich(mary) [resolution 103,136]
314. $false <- (20) [subsumption resolution 313,227]
315. ~20 [avatar contradiction clause 314]
316. $false [avatar sat refutation 237,275,280,312,315]
% SZS output end Proof for 8031674116478176686707897
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not patient is not happy or calm. Everyone who is both not curious and patient is both generous and not patient and vice versa. If someone is both not patient and tall then mary is either not patient or not brave and vice versa. Everyone who is either rich or tall is old or not old. If fred is rich then lucy is tall and vice versa. If paul is both not wise and tall then susan is calm and vice versa. Everyone who is creative is wise. If someone is both old and wise then susan is either rich or not kind. If mary is both funny and not happy then susan is happy or quiet. Everyone who is either strong or calm is not brave or not wise. If paul is both not wise and quiet then paul is both not wise and generous and vice versa. If susan is not creative then someone is both curious and not kind and vice versa. If john is not tall or not quiet then someone is both not patient and not wise and vice versa. Everyone who is both not brave and curious is not old and vice versa. Everyone who is quiet is rich or not strong. If lucy is rich or old then john is both not funny and not patient and vice versa. Someone is either not calm or quiet. Someone is not old or happy. John is rich or not patient. Lucy is either not tall or not quiet. Fred is not creative. Someone is funny. Alice is rich. Someone is not wise or not brave. | Fred is rich. | neutral | (![X]:((~rich(X)&~patient(X))=>(~happy(X)|calm(X))))&
(![X]:((~curious(X)&patient(X))<=>(generous(X)&~patient(X))))&
((?[X]:((~patient(X)&tall(X))))<=>((~patient(mary)<~>~brave(mary))))&
(![X]:((rich(X)<~>tall(X))=>(old(X)|~old(X))))&
((rich(fred))<=>(tall(lucy)))&
(((~wise(paul)&tall(paul)))<=>(calm(susan)))&
(![X]:(creative(X)=>wise(X)))&
((?[X]:((old(X)&wise(X))))=>((rich(susan)<~>~kind(susan))))&
(((funny(mary)&~happy(mary)))=>((happy(susan)|quiet(susan))))&
(![X]:((strong(X)<~>calm(X))=>(~brave(X)|~wise(X))))&
(((~wise(paul)&quiet(paul)))<=>((~wise(paul)&generous(paul))))&
((~creative(susan))<=>(?[X]:((curious(X)&~kind(X)))))&
(((~tall(john)|~quiet(john)))<=>(?[X]:((~patient(X)&~wise(X)))))&
(![X]:((~brave(X)&curious(X))<=>~old(X)))&
(![X]:(quiet(X)=>(rich(X)|~strong(X))))&
(((rich(lucy)|old(lucy)))<=>((~funny(john)&~patient(john))))&
(?[X]:((~calm(X)<~>quiet(X))))&
(?[X]:((~old(X)|happy(X))))&
((rich(john)|~patient(john)))&
((~tall(lucy)<~>~quiet(lucy)))&
(~creative(fred))&
(?[X]:(funny(X)))&
(rich(alice))&
(?[X]:((~wise(X)|~brave(X)))) | rich(fred) | [] | null | 0 |
Everyone who is either quiet or calm is both not generous and not funny.
Everyone who is either creative or rich is tall.
If someone is both funny and old then someone is both kind and not tall.
Everyone who is both humble and not creative is not quiet or funny.
If paul is quiet or not brave then john is not happy or not wise.
If susan is both not happy and not patient then paul is either not humble or creative.
Everyone who is both quiet and wise is rich and vice versa.
Everyone who is not calm is calm.
Everyone who is generous or not kind is calm and vice versa.
If someone is not old or rich then someone is kind or not happy and vice versa.
If someone is either old or humble then someone is either not funny or patient and vice versa.
Everyone who is curious or not humble is both creative and kind and vice versa.
Everyone who is both not patient and not calm is kind.
If john is not kind then john is generous and vice versa.
If someone is curious or brave then mary is not creative.
Everyone who is both not generous and not kind is both curious and old.
Lucy is both not happy and not wise.
Someone is both brave and generous.
Someone is both old and not funny.
Someone is both calm and not rich.
Someone is tall.
Lucy is not strong or not curious.
Lucy is both generous and calm.
Someone is either strong or not generous. | Mary is quiet. | entailment | (![X]:((quiet(X)<~>calm(X))=>(~generous(X)&~funny(X))))&
(![X]:((creative(X)<~>rich(X))=>tall(X)))&
((?[X]:((funny(X)&old(X))))=>(?[X]:((kind(X)&~tall(X)))))&
(![X]:((humble(X)&~creative(X))=>(~quiet(X)|funny(X))))&
(((quiet(paul)|~brave(paul)))=>((~happy(john)|~wise(john))))&
(((~happy(susan)&~patient(susan)))=>((~humble(paul)<~>creative(paul))))&
(![X]:((quiet(X)&wise(X))<=>rich(X)))&
(![X]:(~calm(X)=>calm(X)))&
(![X]:((generous(X)|~kind(X))<=>calm(X)))&
((?[X]:((~old(X)|rich(X))))<=>(?[X]:((kind(X)|~happy(X)))))&
((?[X]:((old(X)<~>humble(X))))<=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:((curious(X)|~humble(X))<=>(creative(X)&kind(X))))&
(![X]:((~patient(X)&~calm(X))=>kind(X)))&
((~kind(john))<=>(generous(john)))&
((?[X]:((curious(X)|brave(X))))=>(~creative(mary)))&
(![X]:((~generous(X)&~kind(X))=>(curious(X)&old(X))))&
((~happy(lucy)&~wise(lucy)))&
(?[X]:((brave(X)&generous(X))))&
(?[X]:((old(X)&~funny(X))))&
(?[X]:((calm(X)&~rich(X))))&
(?[X]:(tall(X)))&
((~strong(lucy)|~curious(lucy)))&
((generous(lucy)&calm(lucy)))&
(?[X]:((strong(X)<~>~generous(X)))) | quiet(mary) | [
"p0",
"p7",
"p8",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7133677606222222814218973
% SZS output start Proof for 7133677606222222814218973
1. ! [X0] : ((quiet(X0) <~> calm(X0)) => (~funny(X0) & ~generous(X0))) [input p0]
8. ! [X0] : (~calm(X0) => calm(X0)) [input p7]
9. ! [X0] : ((~kind(X0) | generous(X0)) <=> calm(X0)) [input p8]
12. ! [X0] : ((~humble(X0) | curious(X0)) <=> (kind(X0) & creative(X0))) [input p11]
16. ! [X0] : ((~kind(X0) & ~generous(X0)) => (old(X0) & curious(X0))) [input p15]
25. ~quiet(mary) [input hypothesis]
29. ! [X0] : ((~funny(X0) & ~generous(X0)) | (quiet(X0) <=> calm(X0))) [ennf transformation 1]
38. ! [X0] : (calm(X0) | calm(X0)) [ennf transformation 8]
42. ! [X0] : ((old(X0) & curious(X0)) | (kind(X0) | generous(X0))) [ennf transformation 16]
43. ! [X0] : ((old(X0) & curious(X0)) | kind(X0) | generous(X0)) [flattening 42]
44. ! [X0] : ((~funny(X0) & ~generous(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0)))) [nnf transformation 29]
52. ! [X0] : (((~kind(X0) | generous(X0)) | ~calm(X0)) & (calm(X0) | (kind(X0) & ~generous(X0)))) [nnf transformation 9]
53. ! [X0] : ((~kind(X0) | generous(X0) | ~calm(X0)) & (calm(X0) | (kind(X0) & ~generous(X0)))) [flattening 52]
64. ! [X0] : (((~humble(X0) | curious(X0)) | (~kind(X0) | ~creative(X0))) & ((kind(X0) & creative(X0)) | (humble(X0) & ~curious(X0)))) [nnf transformation 12]
65. ! [X0] : ((~humble(X0) | curious(X0) | ~kind(X0) | ~creative(X0)) & ((kind(X0) & creative(X0)) | (humble(X0) & ~curious(X0)))) [flattening 64]
79. ~generous(X0) | quiet(X0) | ~calm(X0) [cnf transformation 44]
94. calm(X0) | calm(X0) [cnf transformation 38]
97. ~kind(X0) | generous(X0) | ~calm(X0) [cnf transformation 53]
112. ~curious(X0) | kind(X0) [cnf transformation 65]
120. curious(X0) | kind(X0) | generous(X0) [cnf transformation 43]
136. ~quiet(mary) [cnf transformation 25]
137. calm(X0) [duplicate literal removal 94]
187. ~kind(X0) | generous(X0) [subsumption resolution 97,137]
271. kind(X0) | generous(X0) [subsumption resolution 120,112]
272. generous(X0) [subsumption resolution 271,187]
294. quiet(X0) | ~calm(X0) [resolution 79,272]
296. quiet(X0) [subsumption resolution 294,137]
297. $false [resolution 296,136]
% SZS output end Proof for 7133677606222222814218973
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is both not funny and wise. Everyone who is both not tall and not strong is either happy or not wise and vice versa. If someone is kind then susan is both not tall and not strong. Everyone who is both not brave and not happy is both kind and not creative and vice versa. If someone is not generous or not quiet then someone is not brave and vice versa. Everyone who is not old or old is not happy. Everyone who is both tall and calm is generous and vice versa. Everyone who is not strong is not brave or not tall and vice versa. If someone is either not old or patient then someone is humble and vice versa. If someone is strong then alice is curious. Everyone who is both not funny and old is kind or rich. Everyone who is either not rich or patient is either not brave or not patient and vice versa. Everyone who is both not funny and funny is both not brave and not strong and vice versa. If lucy is not wise then someone is either not patient or not funny. If someone is either humble or wise then someone is either not brave or kind. Paul is not tall or curious. Fred is both not funny and tall. Someone is either not old or not creative. Someone is not old or kind. Susan is either not kind or curious. | Susan is not quiet. | contradiction | (![X]:(~humble(X)=>(~funny(X)&wise(X))))&
(![X]:((~tall(X)&~strong(X))<=>(happy(X)<~>~wise(X))))&
((?[X]:(kind(X)))=>((~tall(susan)&~strong(susan))))&
(![X]:((~brave(X)&~happy(X))<=>(kind(X)&~creative(X))))&
((?[X]:((~generous(X)|~quiet(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~old(X)|old(X))=>~happy(X)))&
(![X]:((tall(X)&calm(X))<=>generous(X)))&
(![X]:(~strong(X)<=>(~brave(X)|~tall(X))))&
((?[X]:((~old(X)<~>patient(X))))<=>(?[X]:(humble(X))))&
((?[X]:(strong(X)))=>(curious(alice)))&
(![X]:((~funny(X)&old(X))=>(kind(X)|rich(X))))&
(![X]:((~rich(X)<~>patient(X))<=>(~brave(X)<~>~patient(X))))&
(![X]:((~funny(X)&funny(X))<=>(~brave(X)&~strong(X))))&
((~wise(lucy))=>(?[X]:((~patient(X)<~>~funny(X)))))&
((?[X]:((humble(X)<~>wise(X))))=>(?[X]:((~brave(X)<~>kind(X)))))&
((~tall(paul)|curious(paul)))&
((~funny(fred)&tall(fred)))&
(?[X]:((~old(X)<~>~creative(X))))&
(?[X]:((~old(X)|kind(X))))&
((~kind(susan)<~>curious(susan))) | ~quiet(susan) | [
"p4",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6369633637434107481474453
% SZS output start Proof for 6369633637434107481474453
5. ? [X0] : (~quiet(X0) | ~generous(X0)) <=> ? [X0] : ~brave(X0) [input p4]
8. ! [X0] : (~strong(X0) <=> (~tall(X0) | ~brave(X0))) [input p7]
13. ! [X0] : ((funny(X0) & ~funny(X0)) <=> (~strong(X0) & ~brave(X0))) [input p12]
21. ~quiet(susan) [input hypothesis]
22. ? [X0] : (~quiet(X0) | ~generous(X0)) <=> ? [X1] : ~brave(X1) [rectify 5]
37. (? [X0] : (~quiet(X0) | ~generous(X0)) | ! [X1] : brave(X1)) & (? [X1] : ~brave(X1) | ! [X0] : (quiet(X0) & generous(X0))) [nnf transformation 22]
38. (? [X0] : (~quiet(X0) | ~generous(X0)) | ! [X1] : brave(X1)) & (? [X2] : ~brave(X2) | ! [X3] : (quiet(X3) & generous(X3))) [rectify 37]
39. ? [X0] : (~quiet(X0) | ~generous(X0)) => (~quiet(sK0) | ~generous(sK0)) [choice axiom]
40. ? [X2] : ~brave(X2) => ~brave(sK1) [choice axiom]
41. ((~quiet(sK0) | ~generous(sK0)) | ! [X1] : brave(X1)) & (~brave(sK1) | ! [X3] : (quiet(X3) & generous(X3))) [skolemisation 38,40,39]
44. ! [X0] : ((~strong(X0) | (tall(X0) & brave(X0))) & ((~tall(X0) | ~brave(X0)) | strong(X0))) [nnf transformation 8]
45. ! [X0] : ((~strong(X0) | (tall(X0) & brave(X0))) & (~tall(X0) | ~brave(X0) | strong(X0))) [flattening 44]
52. ! [X0] : (((funny(X0) & ~funny(X0)) | (strong(X0) | brave(X0))) & ((~strong(X0) & ~brave(X0)) | (~funny(X0) | funny(X0)))) [nnf transformation 13]
53. ! [X0] : (((funny(X0) & ~funny(X0)) | strong(X0) | brave(X0)) & ((~strong(X0) & ~brave(X0)) | ~funny(X0) | funny(X0))) [flattening 52]
82. ~brave(sK1) | quiet(X3) [cnf transformation 41]
90. ~strong(X0) | brave(X0) [cnf transformation 45]
108. ~funny(X0) | strong(X0) | brave(X0) [cnf transformation 53]
109. funny(X0) | strong(X0) | brave(X0) [cnf transformation 53]
124. ~quiet(susan) [cnf transformation 21]
143. 4 <=> ! [X1] : brave(X1) [avatar definition]
144. brave(X1) <- (4) [avatar component clause 143]
155. 7 <=> ! [X3] : quiet(X3) [avatar definition]
156. quiet(X3) <- (7) [avatar component clause 155]
158. 8 <=> brave(sK1) [avatar definition]
160. ~brave(sK1) <- (~8) [avatar component clause 158]
161. 7 | ~8 [avatar split clause 82,158,155]
202. funny(X0) | brave(X0) [subsumption resolution 109,90]
203. ~funny(X0) | brave(X0) [subsumption resolution 108,90]
204. brave(X0) [subsumption resolution 203,202]
205. 4 [avatar split clause 204,143]
280. $false <- (4, ~8) [resolution 160,144]
281. ~4 | 8 [avatar contradiction clause 280]
282. $false <- (7) [resolution 156,124]
283. ~7 [avatar contradiction clause 282]
284. $false [avatar sat refutation 161,205,281,283]
% SZS output end Proof for 6369633637434107481474453
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If alice is humble then john is either not calm or patient.
Everyone who is not rich is not wise.
Everyone who is either wise or not curious is strong.
If fred is both not kind and happy then someone is either not old or not kind and vice versa.
Everyone who is not rich is both not tall and not creative and vice versa.
Everyone who is not happy is both not funny and not curious and vice versa.
If someone is not wise or not quiet then someone is not old.
If someone is not funny then someone is wise.
If lucy is both rich and not generous then mary is calm.
If someone is either not creative or calm then someone is creative or calm and vice versa.
If someone is either not rich or not strong then someone is humble or not strong.
If someone is either not patient or brave then alice is not rich or not generous and vice versa.
Everyone who is not curious or generous is either not old or tall and vice versa.
Everyone who is patient is both not humble and humble.
Everyone who is both calm and funny is both quiet and strong and vice versa.
If someone is not patient or rich then alice is funny or not quiet.
Someone is both not creative and strong.
Mary is both not happy and old.
Susan is either calm or strong.
Someone is not humble or not kind.
Mary is happy or generous.
Someone is either not rich or not wise.
Someone is generous.
John is not old. | Susan is patient. | contradiction | ((humble(alice))=>((~calm(john)<~>patient(john))))&
(![X]:(~rich(X)=>~wise(X)))&
(![X]:((wise(X)<~>~curious(X))=>strong(X)))&
(((~kind(fred)&happy(fred)))<=>(?[X]:((~old(X)<~>~kind(X)))))&
(![X]:(~rich(X)<=>(~tall(X)&~creative(X))))&
(![X]:(~happy(X)<=>(~funny(X)&~curious(X))))&
((?[X]:((~wise(X)|~quiet(X))))=>(?[X]:(~old(X))))&
((?[X]:(~funny(X)))=>(?[X]:(wise(X))))&
(((rich(lucy)&~generous(lucy)))=>(calm(mary)))&
((?[X]:((~creative(X)<~>calm(X))))<=>(?[X]:((creative(X)|calm(X)))))&
((?[X]:((~rich(X)<~>~strong(X))))=>(?[X]:((humble(X)|~strong(X)))))&
((?[X]:((~patient(X)<~>brave(X))))<=>((~rich(alice)|~generous(alice))))&
(![X]:((~curious(X)|generous(X))<=>(~old(X)<~>tall(X))))&
(![X]:(patient(X)=>(~humble(X)&humble(X))))&
(![X]:((calm(X)&funny(X))<=>(quiet(X)&strong(X))))&
((?[X]:((~patient(X)|rich(X))))=>((funny(alice)|~quiet(alice))))&
(?[X]:((~creative(X)&strong(X))))&
((~happy(mary)&old(mary)))&
((calm(susan)<~>strong(susan)))&
(?[X]:((~humble(X)|~kind(X))))&
((happy(mary)|generous(mary)))&
(?[X]:((~rich(X)<~>~wise(X))))&
(?[X]:(generous(X)))&
(~old(john)) | patient(susan) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1273665256014965356511901
% SZS output start Proof for 1273665256014965356511901
14. ! [X0] : (patient(X0) => (humble(X0) & ~humble(X0))) [input p13]
25. patient(susan) [input hypothesis]
38. ! [X0] : ((humble(X0) & ~humble(X0)) | ~patient(X0)) [ennf transformation 14]
127. ~humble(X0) | ~patient(X0) [cnf transformation 38]
128. humble(X0) | ~patient(X0) [cnf transformation 38]
147. patient(susan) [cnf transformation 25]
301. ~patient(X0) [subsumption resolution 127,128]
338. $false [subsumption resolution 147,301]
% SZS output end Proof for 1273665256014965356511901
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or strong then paul is not strong.
Everyone who is either happy or not strong is generous.
If mary is either not generous or not kind then susan is both strong and not curious and vice versa.
If john is brave or creative then fred is quiet.
Everyone who is both not quiet and not creative is both happy and not generous.
Everyone who is old is either funny or not curious.
If someone is strong then lucy is either not quiet or patient.
If alice is funny then someone is both creative and not humble and vice versa.
Everyone who is both not generous and curious is both quiet and wise and vice versa.
If someone is both strong and not old then someone is both humble and not tall.
If lucy is both strong and kind then someone is both not generous and not strong.
Everyone who is either not funny or not strong is rich.
Everyone who is both not humble and not quiet is either not kind or tall.
If someone is both not tall and tall then someone is either not rich or patient.
Everyone who is not wise or patient is both not quiet and not curious.
Everyone who is generous or not humble is either not funny or not calm.
Someone is not old.
Someone is not patient.
Alice is not wise.
Mary is either happy or generous.
Someone is both funny and not tall.
Paul is both creative and brave.
Someone is not brave or not old.
Someone is funny. | Fred is not patient. | neutral | ((?[X]:((wise(X)|strong(X))))=>(~strong(paul)))&
(![X]:((happy(X)<~>~strong(X))=>generous(X)))&
(((~generous(mary)<~>~kind(mary)))<=>((strong(susan)&~curious(susan))))&
(((brave(john)|creative(john)))=>(quiet(fred)))&
(![X]:((~quiet(X)&~creative(X))=>(happy(X)&~generous(X))))&
(![X]:(old(X)=>(funny(X)<~>~curious(X))))&
((?[X]:(strong(X)))=>((~quiet(lucy)<~>patient(lucy))))&
((funny(alice))<=>(?[X]:((creative(X)&~humble(X)))))&
(![X]:((~generous(X)&curious(X))<=>(quiet(X)&wise(X))))&
((?[X]:((strong(X)&~old(X))))=>(?[X]:((humble(X)&~tall(X)))))&
(((strong(lucy)&kind(lucy)))=>(?[X]:((~generous(X)&~strong(X)))))&
(![X]:((~funny(X)<~>~strong(X))=>rich(X)))&
(![X]:((~humble(X)&~quiet(X))=>(~kind(X)<~>tall(X))))&
((?[X]:((~tall(X)&tall(X))))=>(?[X]:((~rich(X)<~>patient(X)))))&
(![X]:((~wise(X)|patient(X))=>(~quiet(X)&~curious(X))))&
(![X]:((generous(X)|~humble(X))=>(~funny(X)<~>~calm(X))))&
(?[X]:(~old(X)))&
(?[X]:(~patient(X)))&
(~wise(alice))&
((happy(mary)<~>generous(mary)))&
(?[X]:((funny(X)&~tall(X))))&
((creative(paul)&brave(paul)))&
(?[X]:((~brave(X)|~old(X))))&
(?[X]:(funny(X))) | ~patient(fred) | [] | null | 0 |
Everyone who is both not curious and creative is generous or not calm and vice versa. If susan is both not calm and happy then someone is both rich and not old and vice versa. If someone is not brave or not patient then fred is old and vice versa. If lucy is not creative then fred is not wise and vice versa. Everyone who is brave or not tall is calm or not rich and vice versa. Everyone who is both rich and not patient is tall or curious. Everyone who is not creative is both not quiet and happy. If someone is brave or strong then someone is either not tall or happy and vice versa. Everyone who is not wise or not kind is happy. If fred is either not calm or tall then lucy is not brave or kind. If someone is either creative or wise then john is not tall or tall and vice versa. Everyone who is either not happy or not calm is not tall and vice versa. Everyone who is either tall or not quiet is either wise or not funny and vice versa. Everyone who is both rich and strong is tall or not tall and vice versa. Everyone who is not humble is rich. Someone is not calm or funny. Mary is not patient or not tall. Someone is either curious or not tall. John is not curious. Paul is either not curious or strong. Someone is both strong and humble. Susan is either not patient or not happy. | John is not old. | contradiction | (![X]:((~curious(X)&creative(X))<=>(generous(X)|~calm(X))))&
(((~calm(susan)&happy(susan)))<=>(?[X]:((rich(X)&~old(X)))))&
((?[X]:((~brave(X)|~patient(X))))<=>(old(fred)))&
((~creative(lucy))<=>(~wise(fred)))&
(![X]:((brave(X)|~tall(X))<=>(calm(X)|~rich(X))))&
(![X]:((rich(X)&~patient(X))=>(tall(X)|curious(X))))&
(![X]:(~creative(X)=>(~quiet(X)&happy(X))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((~wise(X)|~kind(X))=>happy(X)))&
(((~calm(fred)<~>tall(fred)))=>((~brave(lucy)|kind(lucy))))&
((?[X]:((creative(X)<~>wise(X))))<=>((~tall(john)|tall(john))))&
(![X]:((~happy(X)<~>~calm(X))<=>~tall(X)))&
(![X]:((tall(X)<~>~quiet(X))<=>(wise(X)<~>~funny(X))))&
(![X]:((rich(X)&strong(X))<=>(tall(X)|~tall(X))))&
(![X]:(~humble(X)=>rich(X)))&
(?[X]:((~calm(X)|funny(X))))&
((~patient(mary)|~tall(mary)))&
(?[X]:((curious(X)<~>~tall(X))))&
(~curious(john))&
((~curious(paul)<~>strong(paul)))&
(?[X]:((strong(X)&humble(X))))&
((~patient(susan)<~>~happy(susan))) | ~old(john) | [
"p1",
"p4",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5571370237660475420981583
% SZS output start Proof for 5571370237660475420981583
2. (happy(susan) & ~calm(susan)) <=> ? [X0] : (~old(X0) & rich(X0)) [input p1]
5. ! [X0] : ((~tall(X0) | brave(X0)) <=> (~rich(X0) | calm(X0))) [input p4]
12. ! [X0] : ((~happy(X0) <~> ~calm(X0)) <=> ~tall(X0)) [input p11]
14. ! [X0] : ((strong(X0) & rich(X0)) <=> (~tall(X0) | tall(X0))) [input p13]
23. ~old(john) [input hypothesis]
35. ((happy(susan) & ~calm(susan)) | ! [X0] : (old(X0) | ~rich(X0))) & (? [X0] : (~old(X0) & rich(X0)) | (~happy(susan) | calm(susan))) [nnf transformation 2]
36. ((happy(susan) & ~calm(susan)) | ! [X0] : (old(X0) | ~rich(X0))) & (? [X0] : (~old(X0) & rich(X0)) | ~happy(susan) | calm(susan)) [flattening 35]
37. ((happy(susan) & ~calm(susan)) | ! [X0] : (old(X0) | ~rich(X0))) & (? [X1] : (~old(X1) & rich(X1)) | ~happy(susan) | calm(susan)) [rectify 36]
38. ? [X1] : (~old(X1) & rich(X1)) => (~old(sK0) & rich(sK0)) [choice axiom]
39. ((happy(susan) & ~calm(susan)) | ! [X0] : (old(X0) | ~rich(X0))) & ((~old(sK0) & rich(sK0)) | ~happy(susan) | calm(susan)) [skolemisation 37,38]
45. ! [X0] : (((~tall(X0) | brave(X0)) | (rich(X0) & ~calm(X0))) & ((~rich(X0) | calm(X0)) | (tall(X0) & ~brave(X0)))) [nnf transformation 5]
46. ! [X0] : ((~tall(X0) | brave(X0) | (rich(X0) & ~calm(X0))) & (~rich(X0) | calm(X0) | (tall(X0) & ~brave(X0)))) [flattening 45]
57. ! [X0] : ((((calm(X0) | happy(X0)) & (~calm(X0) | ~happy(X0))) | tall(X0)) & (~tall(X0) | ((~happy(X0) | calm(X0)) & (~calm(X0) | happy(X0))))) [nnf transformation 12]
59. ! [X0] : (((strong(X0) & rich(X0)) | (tall(X0) & ~tall(X0))) & ((~tall(X0) | tall(X0)) | (~strong(X0) | ~rich(X0)))) [nnf transformation 14]
60. ! [X0] : (((strong(X0) & rich(X0)) | (tall(X0) & ~tall(X0))) & (~tall(X0) | tall(X0) | ~strong(X0) | ~rich(X0))) [flattening 59]
77. ~calm(susan) | old(X0) | ~rich(X0) [cnf transformation 39]
78. happy(susan) | old(X0) | ~rich(X0) [cnf transformation 39]
85. ~rich(X0) | calm(X0) | tall(X0) [cnf transformation 46]
105. ~tall(X0) | ~happy(X0) | calm(X0) [cnf transformation 57]
117. rich(X0) | ~tall(X0) [cnf transformation 60]
118. tall(X0) | rich(X0) [cnf transformation 60]
131. ~old(john) [cnf transformation 23]
133. 1 <=> ! [X0] : (old(X0) | ~rich(X0)) [avatar definition]
134. old(X0) | ~rich(X0) <- (1) [avatar component clause 133]
136. 2 <=> happy(susan) [avatar definition]
138. happy(susan) <- (2) [avatar component clause 136]
139. 1 | 2 [avatar split clause 78,136,133]
141. 3 <=> calm(susan) [avatar definition]
144. 1 | ~3 [avatar split clause 77,141,133]
237. rich(X0) [subsumption resolution 117,118]
284. tall(X0) | calm(X0) [resolution 85,237]
295. ~happy(X0) | calm(X0) | calm(X0) [resolution 105,284]
297. ~happy(X0) | calm(X0) [duplicate literal removal 295]
488. calm(susan) <- (2) [resolution 297,138]
500. 3 | ~2 [avatar split clause 488,136,141]
505. old(X0) <- (1) [subsumption resolution 134,237]
520. $false <- (1) [resolution 505,131]
523. ~1 [avatar contradiction clause 520]
524. $false [avatar sat refutation 139,144,500,523]
% SZS output end Proof for 5571370237660475420981583
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is old or not tall then paul is wise or curious.
Everyone who is not humble is either not tall or creative and vice versa.
Everyone who is either not humble or wise is either not kind or not funny.
Everyone who is strong or generous is both not tall and not strong.
Everyone who is both not patient and humble is generous and vice versa.
If someone is either brave or not old then lucy is either rich or not tall and vice versa.
If mary is brave then paul is either humble or funny.
Everyone who is curious is not funny and vice versa.
If someone is tall or funny then someone is not funny or quiet and vice versa.
Everyone who is not old or not creative is either tall or not calm and vice versa.
Everyone who is not generous is not happy.
Everyone who is not old is not curious.
Everyone who is either not happy or strong is not tall.
If someone is both not old and happy then someone is funny.
If someone is not happy then someone is generous.
Everyone who is either old or not wise is not humble.
Someone is brave.
Lucy is not old or not rich.
Paul is not funny.
John is not old.
Someone is either rich or not patient.
Lucy is not happy.
John is rich or kind.
Paul is either not quiet or not tall. | Paul is humble. | neutral | (((old(lucy)|~tall(lucy)))=>((wise(paul)|curious(paul))))&
(![X]:(~humble(X)<=>(~tall(X)<~>creative(X))))&
(![X]:((~humble(X)<~>wise(X))=>(~kind(X)<~>~funny(X))))&
(![X]:((strong(X)|generous(X))=>(~tall(X)&~strong(X))))&
(![X]:((~patient(X)&humble(X))<=>generous(X)))&
((?[X]:((brave(X)<~>~old(X))))<=>((rich(lucy)<~>~tall(lucy))))&
((brave(mary))=>((humble(paul)<~>funny(paul))))&
(![X]:(curious(X)<=>~funny(X)))&
((?[X]:((tall(X)|funny(X))))<=>(?[X]:((~funny(X)|quiet(X)))))&
(![X]:((~old(X)|~creative(X))<=>(tall(X)<~>~calm(X))))&
(![X]:(~generous(X)=>~happy(X)))&
(![X]:(~old(X)=>~curious(X)))&
(![X]:((~happy(X)<~>strong(X))=>~tall(X)))&
((?[X]:((~old(X)&happy(X))))=>(?[X]:(funny(X))))&
((?[X]:(~happy(X)))=>(?[X]:(generous(X))))&
(![X]:((old(X)<~>~wise(X))=>~humble(X)))&
(?[X]:(brave(X)))&
((~old(lucy)|~rich(lucy)))&
(~funny(paul))&
(~old(john))&
(?[X]:((rich(X)<~>~patient(X))))&
(~happy(lucy))&
((rich(john)|kind(john)))&
((~quiet(paul)<~>~tall(paul))) | humble(paul) | [] | null | 0 |
Everyone who is either calm or tall is not humble.
If paul is not curious or humble then someone is both not strong and calm and vice versa.
Everyone who is either creative or strong is either not patient or not tall.
If paul is either calm or patient then paul is not brave or not kind and vice versa.
Everyone who is either kind or not patient is either not wise or not brave.
If mary is not brave then lucy is either not calm or not old and vice versa.
If fred is both old and not humble then someone is strong and vice versa.
Everyone who is not patient or creative is tall and vice versa.
If someone is either kind or not funny then someone is calm and vice versa.
Everyone who is both wise and not quiet is not strong and vice versa.
If susan is not happy then mary is both not kind and not funny and vice versa.
Everyone who is not tall is either not humble or not quiet.
Everyone who is not calm is curious or strong and vice versa.
If someone is patient or not wise then alice is either generous or humble.
If susan is not old or generous then paul is either wise or not tall and vice versa.
Everyone who is either strong or kind is not tall and vice versa.
Susan is tall.
Mary is old or not generous.
Someone is patient or rich.
Paul is brave or not brave.
Someone is brave or not rich.
John is not tall or not creative.
Someone is not funny.
Lucy is not rich. | Paul is funny. | neutral | (![X]:((calm(X)<~>tall(X))=>~humble(X)))&
(((~curious(paul)|humble(paul)))<=>(?[X]:((~strong(X)&calm(X)))))&
(![X]:((creative(X)<~>strong(X))=>(~patient(X)<~>~tall(X))))&
(((calm(paul)<~>patient(paul)))<=>((~brave(paul)|~kind(paul))))&
(![X]:((kind(X)<~>~patient(X))=>(~wise(X)<~>~brave(X))))&
((~brave(mary))<=>((~calm(lucy)<~>~old(lucy))))&
(((old(fred)&~humble(fred)))<=>(?[X]:(strong(X))))&
(![X]:((~patient(X)|creative(X))<=>tall(X)))&
((?[X]:((kind(X)<~>~funny(X))))<=>(?[X]:(calm(X))))&
(![X]:((wise(X)&~quiet(X))<=>~strong(X)))&
((~happy(susan))<=>((~kind(mary)&~funny(mary))))&
(![X]:(~tall(X)=>(~humble(X)<~>~quiet(X))))&
(![X]:(~calm(X)<=>(curious(X)|strong(X))))&
((?[X]:((patient(X)|~wise(X))))=>((generous(alice)<~>humble(alice))))&
(((~old(susan)|generous(susan)))<=>((wise(paul)<~>~tall(paul))))&
(![X]:((strong(X)<~>kind(X))<=>~tall(X)))&
(tall(susan))&
((old(mary)|~generous(mary)))&
(?[X]:((patient(X)|rich(X))))&
((brave(paul)|~brave(paul)))&
(?[X]:((brave(X)|~rich(X))))&
((~tall(john)|~creative(john)))&
(?[X]:(~funny(X)))&
(~rich(lucy)) | funny(paul) | [] | null | 0 |
Everyone who is not quiet is either curious or not brave.
If paul is either not generous or not old then someone is funny and vice versa.
If someone is not creative then someone is not wise and vice versa.
If lucy is either not kind or not happy then john is not happy or not old.
Everyone who is both not curious and old is kind and vice versa.
Everyone who is quiet or calm is not curious and vice versa.
Everyone who is not humble is calm.
Everyone who is both patient and funny is curious or rich.
Everyone who is not rich or patient is both happy and not quiet and vice versa.
If lucy is either not tall or patient then susan is brave and vice versa.
Everyone who is patient is old or calm and vice versa.
If someone is either quiet or brave then john is either tall or quiet.
If someone is not wise then john is not funny or not wise and vice versa.
If mary is not humble then someone is not creative or quiet and vice versa.
If fred is either not creative or not brave then someone is curious or rich and vice versa.
Everyone who is either happy or brave is not rich.
Fred is not tall or humble.
Mary is funny or not quiet.
Paul is quiet or strong.
Someone is not strong or not funny.
Susan is both strong and calm.
Alice is not strong or not generous. | Fred is quiet. | neutral | (![X]:(~quiet(X)=>(curious(X)<~>~brave(X))))&
(((~generous(paul)<~>~old(paul)))<=>(?[X]:(funny(X))))&
((?[X]:(~creative(X)))<=>(?[X]:(~wise(X))))&
(((~kind(lucy)<~>~happy(lucy)))=>((~happy(john)|~old(john))))&
(![X]:((~curious(X)&old(X))<=>kind(X)))&
(![X]:((quiet(X)|calm(X))<=>~curious(X)))&
(![X]:(~humble(X)=>calm(X)))&
(![X]:((patient(X)&funny(X))=>(curious(X)|rich(X))))&
(![X]:((~rich(X)|patient(X))<=>(happy(X)&~quiet(X))))&
(((~tall(lucy)<~>patient(lucy)))<=>(brave(susan)))&
(![X]:(patient(X)<=>(old(X)|calm(X))))&
((?[X]:((quiet(X)<~>brave(X))))=>((tall(john)<~>quiet(john))))&
((?[X]:(~wise(X)))<=>((~funny(john)|~wise(john))))&
((~humble(mary))<=>(?[X]:((~creative(X)|quiet(X)))))&
(((~creative(fred)<~>~brave(fred)))<=>(?[X]:((curious(X)|rich(X)))))&
(![X]:((happy(X)<~>brave(X))=>~rich(X)))&
((~tall(fred)|humble(fred)))&
((funny(mary)|~quiet(mary)))&
((quiet(paul)|strong(paul)))&
(?[X]:((~strong(X)|~funny(X))))&
((strong(susan)&calm(susan)))&
((~strong(alice)|~generous(alice))) | quiet(fred) | [] | null | 0 |
If john is not brave or not strong then someone is funny.
Everyone who is either strong or curious is not strong or brave and vice versa.
Everyone who is creative or kind is not happy.
If someone is both not generous and not curious then lucy is not generous or not wise.
Everyone who is either calm or not brave is not creative or not calm.
If someone is both not brave and quiet then lucy is either not old or not creative and vice versa.
Everyone who is humble is either rich or kind and vice versa.
If someone is not old or strong then someone is not wise or not strong.
If someone is humble then someone is not quiet.
If someone is rich or not funny then susan is not rich or not calm.
Everyone who is both not humble and strong is either kind or strong.
If someone is humble or strong then john is both not wise and rich.
Everyone who is happy or brave is both not rich and happy.
If someone is not quiet or not kind then alice is not humble or quiet.
If someone is either calm or happy then alice is not quiet or not rich and vice versa.
Everyone who is both happy and curious is wise or rich and vice versa.
Someone is either not old or not generous.
John is either brave or not curious.
Someone is not wise or not curious.
Someone is both not creative and not funny.
Someone is either strong or not rich.
Someone is both curious and not rich.
Someone is brave or not kind. | Lucy is not humble. | entailment | (((~brave(john)|~strong(john)))=>(?[X]:(funny(X))))&
(![X]:((strong(X)<~>curious(X))<=>(~strong(X)|brave(X))))&
(![X]:((creative(X)|kind(X))=>~happy(X)))&
((?[X]:((~generous(X)&~curious(X))))=>((~generous(lucy)|~wise(lucy))))&
(![X]:((calm(X)<~>~brave(X))=>(~creative(X)|~calm(X))))&
((?[X]:((~brave(X)&quiet(X))))<=>((~old(lucy)<~>~creative(lucy))))&
(![X]:(humble(X)<=>(rich(X)<~>kind(X))))&
((?[X]:((~old(X)|strong(X))))=>(?[X]:((~wise(X)|~strong(X)))))&
((?[X]:(humble(X)))=>(?[X]:(~quiet(X))))&
((?[X]:((rich(X)|~funny(X))))=>((~rich(susan)|~calm(susan))))&
(![X]:((~humble(X)&strong(X))=>(kind(X)<~>strong(X))))&
((?[X]:((humble(X)|strong(X))))=>((~wise(john)&rich(john))))&
(![X]:((happy(X)|brave(X))=>(~rich(X)&happy(X))))&
((?[X]:((~quiet(X)|~kind(X))))=>((~humble(alice)|quiet(alice))))&
((?[X]:((calm(X)<~>happy(X))))<=>((~quiet(alice)|~rich(alice))))&
(![X]:((happy(X)&curious(X))<=>(wise(X)|rich(X))))&
(?[X]:((~old(X)<~>~generous(X))))&
((brave(john)<~>~curious(john)))&
(?[X]:((~wise(X)|~curious(X))))&
(?[X]:((~creative(X)&~funny(X))))&
(?[X]:((strong(X)<~>~rich(X))))&
(?[X]:((curious(X)&~rich(X))))&
(?[X]:((brave(X)|~kind(X)))) | ~humble(lucy) | [
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 76746055551865213304636
% SZS output start Proof for 76746055551865213304636
12. ? [X0] : (strong(X0) | humble(X0)) => (rich(john) & ~wise(john)) [input p11]
13. ! [X0] : ((brave(X0) | happy(X0)) => (happy(X0) & ~rich(X0))) [input p12]
16. ! [X0] : ((curious(X0) & happy(X0)) <=> (rich(X0) | wise(X0))) [input p15]
24. humble(lucy) [input hypothesis]
39. (rich(john) & ~wise(john)) | ! [X0] : (~strong(X0) & ~humble(X0)) [ennf transformation 12]
40. ! [X0] : ((happy(X0) & ~rich(X0)) | (~brave(X0) & ~happy(X0))) [ennf transformation 13]
65. ! [X0] : (((curious(X0) & happy(X0)) | (~rich(X0) & ~wise(X0))) & ((rich(X0) | wise(X0)) | (~curious(X0) | ~happy(X0)))) [nnf transformation 16]
66. ! [X0] : (((curious(X0) & happy(X0)) | (~rich(X0) & ~wise(X0))) & (rich(X0) | wise(X0) | ~curious(X0) | ~happy(X0))) [flattening 65]
114. rich(john) | ~humble(X0) [cnf transformation 39]
116. ~rich(X0) | ~happy(X0) [cnf transformation 40]
130. happy(X0) | ~rich(X0) [cnf transformation 66]
145. humble(lucy) [cnf transformation 24]
219. 16 <=> ! [X1] : ~humble(X1) [avatar definition]
220. ~humble(X1) <- (16) [avatar component clause 219]
239. 21 <=> ! [X0] : ~rich(X0) [avatar definition]
240. ~rich(X0) <- (21) [avatar component clause 239]
243. 22 <=> rich(john) [avatar definition]
245. rich(john) <- (22) [avatar component clause 243]
247. 16 | 22 [avatar split clause 114,243,219]
294. ~rich(X0) [subsumption resolution 130,116]
295. 21 [avatar split clause 294,239]
330. $false <- (16) [resolution 220,145]
331. ~16 [avatar contradiction clause 330]
332. $false <- (21, 22) [subsumption resolution 245,240]
333. ~21 | ~22 [avatar contradiction clause 332]
334. $false [avatar sat refutation 247,295,331,333]
% SZS output end Proof for 76746055551865213304636
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not humble is curious or not creative and vice versa.
Everyone who is not patient or happy is both not creative and not wise.
Everyone who is funny or brave is either strong or not calm and vice versa.
Everyone who is not funny or not kind is old or curious.
If fred is either creative or happy then john is not calm.
Everyone who is not strong or generous is both not funny and not kind.
If john is both not rich and old then fred is both wise and rich and vice versa.
Everyone who is either humble or not curious is both not strong and curious and vice versa.
Everyone who is both not calm and not happy is either not calm or not curious.
If someone is not strong or happy then alice is both old and not creative and vice versa.
If someone is not generous or not rich then someone is creative.
Everyone who is either not generous or happy is both not calm and patient and vice versa.
Everyone who is not rich or funny is not kind or not quiet and vice versa.
Everyone who is not creative or humble is not funny and vice versa.
Everyone who is old or not old is either not funny or not wise and vice versa.
Everyone who is not quiet or not brave is not kind or funny.
Someone is strong.
Mary is both not strong and not rich.
Someone is brave or funny.
Someone is curious or not tall.
Someone is either generous or quiet.
Lucy is funny or brave.
Paul is not happy or quiet. | Paul is kind. | contradiction | (![X]:((funny(X)<~>~humble(X))<=>(curious(X)|~creative(X))))&
(![X]:((~patient(X)|happy(X))=>(~creative(X)&~wise(X))))&
(![X]:((funny(X)|brave(X))<=>(strong(X)<~>~calm(X))))&
(![X]:((~funny(X)|~kind(X))=>(old(X)|curious(X))))&
(((creative(fred)<~>happy(fred)))=>(~calm(john)))&
(![X]:((~strong(X)|generous(X))=>(~funny(X)&~kind(X))))&
(((~rich(john)&old(john)))<=>((wise(fred)&rich(fred))))&
(![X]:((humble(X)<~>~curious(X))<=>(~strong(X)&curious(X))))&
(![X]:((~calm(X)&~happy(X))=>(~calm(X)<~>~curious(X))))&
((?[X]:((~strong(X)|happy(X))))<=>((old(alice)&~creative(alice))))&
((?[X]:((~generous(X)|~rich(X))))=>(?[X]:(creative(X))))&
(![X]:((~generous(X)<~>happy(X))<=>(~calm(X)&patient(X))))&
(![X]:((~rich(X)|funny(X))<=>(~kind(X)|~quiet(X))))&
(![X]:((~creative(X)|humble(X))<=>~funny(X)))&
(![X]:((old(X)|~old(X))<=>(~funny(X)<~>~wise(X))))&
(![X]:((~quiet(X)|~brave(X))=>(~kind(X)|funny(X))))&
(?[X]:(strong(X)))&
((~strong(mary)&~rich(mary)))&
(?[X]:((brave(X)|funny(X))))&
(?[X]:((curious(X)|~tall(X))))&
(?[X]:((generous(X)<~>quiet(X))))&
((funny(lucy)|brave(lucy)))&
((~happy(paul)|quiet(paul))) | kind(paul) | [
"p0",
"p1",
"p2",
"p5",
"p7",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7587922091987201773276493
% SZS output start Proof for 7587922091987201773276493
1. ! [X0] : ((funny(X0) <~> ~humble(X0)) <=> (~creative(X0) | curious(X0))) [input p0]
2. ! [X0] : ((happy(X0) | ~patient(X0)) => (~wise(X0) & ~creative(X0))) [input p1]
3. ! [X0] : ((brave(X0) | funny(X0)) <=> (strong(X0) <~> ~calm(X0))) [input p2]
6. ! [X0] : ((generous(X0) | ~strong(X0)) => (~kind(X0) & ~funny(X0))) [input p5]
8. ! [X0] : ((humble(X0) <~> ~curious(X0)) <=> (curious(X0) & ~strong(X0))) [input p7]
12. ! [X0] : ((~generous(X0) <~> happy(X0)) <=> (patient(X0) & ~calm(X0))) [input p11]
14. ! [X0] : ((humble(X0) | ~creative(X0)) <=> ~funny(X0)) [input p13]
15. ! [X0] : ((~old(X0) | old(X0)) <=> (~funny(X0) <~> ~wise(X0))) [input p14]
16. ! [X0] : ((~brave(X0) | ~quiet(X0)) => (funny(X0) | ~kind(X0))) [input p15]
24. kind(paul) [input hypothesis]
27. ! [X0] : ((~wise(X0) & ~creative(X0)) | (~happy(X0) & patient(X0))) [ennf transformation 2]
31. ! [X0] : ((~kind(X0) & ~funny(X0)) | (~generous(X0) & strong(X0))) [ennf transformation 6]
35. ! [X0] : ((funny(X0) | ~kind(X0)) | (brave(X0) & quiet(X0))) [ennf transformation 16]
36. ! [X0] : (funny(X0) | ~kind(X0) | (brave(X0) & quiet(X0))) [flattening 35]
37. ! [X0] : ((((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | (creative(X0) & ~curious(X0))) & ((~creative(X0) | curious(X0)) | ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0))))) [nnf transformation 1]
38. ! [X0] : ((((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | (creative(X0) & ~curious(X0))) & (~creative(X0) | curious(X0) | ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0))))) [flattening 37]
39. ! [X0] : (((brave(X0) | funny(X0)) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0)))) & (((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | (~brave(X0) & ~funny(X0)))) [nnf transformation 3]
40. ! [X0] : ((brave(X0) | funny(X0) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0)))) & (((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | (~brave(X0) & ~funny(X0)))) [flattening 39]
44. ! [X0] : ((((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | (~curious(X0) | strong(X0))) & ((curious(X0) & ~strong(X0)) | ((humble(X0) | curious(X0)) & (~curious(X0) | ~humble(X0))))) [nnf transformation 8]
45. ! [X0] : ((((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | ~curious(X0) | strong(X0)) & ((curious(X0) & ~strong(X0)) | ((humble(X0) | curious(X0)) & (~curious(X0) | ~humble(X0))))) [flattening 44]
55. ! [X0] : ((((~happy(X0) | generous(X0)) & (happy(X0) | ~generous(X0))) | (~patient(X0) | calm(X0))) & ((patient(X0) & ~calm(X0)) | ((~generous(X0) | ~happy(X0)) & (happy(X0) | generous(X0))))) [nnf transformation 12]
56. ! [X0] : ((((~happy(X0) | generous(X0)) & (happy(X0) | ~generous(X0))) | ~patient(X0) | calm(X0)) & ((patient(X0) & ~calm(X0)) | ((~generous(X0) | ~happy(X0)) & (happy(X0) | generous(X0))))) [flattening 55]
59. ! [X0] : (((humble(X0) | ~creative(X0)) | funny(X0)) & (~funny(X0) | (~humble(X0) & creative(X0)))) [nnf transformation 14]
60. ! [X0] : ((humble(X0) | ~creative(X0) | funny(X0)) & (~funny(X0) | (~humble(X0) & creative(X0)))) [flattening 59]
61. ! [X0] : (((~old(X0) | old(X0)) | ((~funny(X0) | wise(X0)) & (~wise(X0) | funny(X0)))) & (((wise(X0) | funny(X0)) & (~wise(X0) | ~funny(X0))) | (old(X0) & ~old(X0)))) [nnf transformation 15]
62. ! [X0] : ((~old(X0) | old(X0) | ((~funny(X0) | wise(X0)) & (~wise(X0) | funny(X0)))) & (((wise(X0) | funny(X0)) & (~wise(X0) | ~funny(X0))) | (old(X0) & ~old(X0)))) [flattening 61]
74. ~curious(X0) | ~funny(X0) | humble(X0) [cnf transformation 38]
79. ~wise(X0) | ~happy(X0) [cnf transformation 27]
83. ~strong(X0) | calm(X0) | ~brave(X0) [cnf transformation 40]
92. ~kind(X0) | strong(X0) [cnf transformation 31]
93. ~generous(X0) | ~kind(X0) [cnf transformation 31]
101. curious(X0) | humble(X0) | curious(X0) [cnf transformation 45]
113. ~calm(X0) | happy(X0) | generous(X0) [cnf transformation 56]
124. ~humble(X0) | ~funny(X0) [cnf transformation 60]
128. wise(X0) | funny(X0) | ~old(X0) [cnf transformation 62]
129. old(X0) | funny(X0) | wise(X0) [cnf transformation 62]
133. ~kind(X0) | funny(X0) | brave(X0) [cnf transformation 36]
142. kind(paul) [cnf transformation 24]
144. curious(X0) | humble(X0) [duplicate literal removal 101]
221. wise(X0) | funny(X0) [subsumption resolution 128,129]
252. 23 <=> happy(paul) [avatar definition]
253. happy(paul) <- (23) [avatar component clause 252]
254. ~happy(paul) <- (~23) [avatar component clause 252]
263. strong(paul) [resolution 92,142]
268. ~happy(X0) | funny(X0) [resolution 221,79]
276. ~funny(X0) | humble(X0) | humble(X0) [resolution 74,144]
277. ~funny(X0) | humble(X0) [duplicate literal removal 276]
278. ~funny(X0) [subsumption resolution 277,124]
289. calm(paul) | ~brave(paul) [resolution 83,263]
292. 25 <=> brave(paul) [avatar definition]
296. 26 <=> calm(paul) [avatar definition]
298. calm(paul) <- (26) [avatar component clause 296]
299. ~25 | 26 [avatar split clause 289,296,292]
375. funny(paul) | brave(paul) [resolution 133,142]
376. brave(paul) [subsumption resolution 375,278]
379. 25 [avatar split clause 376,292]
390. happy(paul) | generous(paul) <- (26) [resolution 298,113]
393. generous(paul) <- (~23, 26) [subsumption resolution 390,254]
399. ~kind(paul) <- (~23, 26) [resolution 393,93]
401. $false <- (~23, 26) [subsumption resolution 399,142]
402. 23 | ~26 [avatar contradiction clause 401]
408. funny(paul) <- (23) [resolution 253,268]
410. $false <- (23) [subsumption resolution 408,278]
411. ~23 [avatar contradiction clause 410]
412. $false [avatar sat refutation 299,379,402,411]
% SZS output end Proof for 7587922091987201773276493
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old then mary is either not kind or not strong and vice versa.
Everyone who is quiet or tall is not quiet.
Everyone who is funny is not quiet.
Everyone who is creative or not happy is creative or not humble and vice versa.
Everyone who is not humble is both not kind and not curious.
Everyone who is not old or funny is not funny or wise and vice versa.
If someone is not wise then lucy is both not calm and curious.
If alice is curious or not patient then fred is either not old or not strong and vice versa.
If alice is either not kind or rich then mary is either not strong or not tall.
Everyone who is not strong or happy is calm or strong.
If someone is calm then someone is rich or generous and vice versa.
If someone is both funny and not quiet then someone is either tall or curious and vice versa.
Everyone who is both creative and quiet is either not happy or not brave.
If lucy is either quiet or not funny then someone is strong.
If paul is either humble or not happy then someone is both not rich and not humble.
Everyone who is rich is either rich or not curious and vice versa.
Fred is not creative.
John is both strong and not patient.
Someone is both wise and not happy.
Paul is either not patient or not rich.
Someone is both not tall and not wise.
Someone is both strong and wise.
Alice is patient. | Fred is not curious. | contradiction | ((?[X]:(old(X)))<=>((~kind(mary)<~>~strong(mary))))&
(![X]:((quiet(X)|tall(X))=>~quiet(X)))&
(![X]:(funny(X)=>~quiet(X)))&
(![X]:((creative(X)|~happy(X))<=>(creative(X)|~humble(X))))&
(![X]:(~humble(X)=>(~kind(X)&~curious(X))))&
(![X]:((~old(X)|funny(X))<=>(~funny(X)|wise(X))))&
((?[X]:(~wise(X)))=>((~calm(lucy)&curious(lucy))))&
(((curious(alice)|~patient(alice)))<=>((~old(fred)<~>~strong(fred))))&
(((~kind(alice)<~>rich(alice)))=>((~strong(mary)<~>~tall(mary))))&
(![X]:((~strong(X)|happy(X))=>(calm(X)|strong(X))))&
((?[X]:(calm(X)))<=>(?[X]:((rich(X)|generous(X)))))&
((?[X]:((funny(X)&~quiet(X))))<=>(?[X]:((tall(X)<~>curious(X)))))&
(![X]:((creative(X)&quiet(X))=>(~happy(X)<~>~brave(X))))&
(((quiet(lucy)<~>~funny(lucy)))=>(?[X]:(strong(X))))&
(((humble(paul)<~>~happy(paul)))=>(?[X]:((~rich(X)&~humble(X)))))&
(![X]:(rich(X)<=>(rich(X)<~>~curious(X))))&
(~creative(fred))&
((strong(john)&~patient(john)))&
(?[X]:((wise(X)&~happy(X))))&
((~patient(paul)<~>~rich(paul)))&
(?[X]:((~tall(X)&~wise(X))))&
(?[X]:((strong(X)&wise(X))))&
(patient(alice)) | ~curious(fred) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6008292606494421501511415
% SZS output start Proof for 6008292606494421501511415
16. ! [X0] : (rich(X0) <=> (rich(X0) <~> ~curious(X0))) [input p15]
24. ~curious(fred) [input hypothesis]
66. ! [X0] : ((rich(X0) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0)))) & (((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | ~rich(X0))) [nnf transformation 16]
123. curious(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 66]
125. rich(X0) | rich(X0) | curious(X0) [cnf transformation 66]
138. ~curious(fred) [cnf transformation 24]
139. curious(X0) | ~rich(X0) [duplicate literal removal 123]
140. rich(X0) | curious(X0) [duplicate literal removal 125]
296. curious(X0) [subsumption resolution 139,140]
308. $false [subsumption resolution 138,296]
% SZS output end Proof for 6008292606494421501511415
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not strong and not creative then lucy is either not calm or not tall. If someone is both not patient and not humble then lucy is either not kind or brave and vice versa. Everyone who is either curious or not curious is both not wise and not calm. If someone is both not tall and quiet then someone is brave or funny. If mary is both not happy and not curious then someone is brave and vice versa. Everyone who is not generous is both curious and rich. Everyone who is either not strong or not creative is both generous and calm and vice versa. Everyone who is either curious or patient is both not kind and rich. Everyone who is both not brave and humble is either old or tall and vice versa. If mary is strong then susan is both not creative and tall. If alice is both not happy and not old then alice is not creative and vice versa. Everyone who is curious or not curious is either not tall or not humble. Everyone who is not humble or quiet is happy. If someone is either not calm or not old then john is either old or not humble and vice versa. Everyone who is not brave or happy is rich or curious and vice versa. Everyone who is either not creative or not wise is either rich or not quiet and vice versa. Lucy is not generous or not wise. Someone is patient. Someone is either not brave or tall. Someone is both not strong and not quiet. John is not generous. Someone is not brave. Someone is not strong or patient. Someone is both not patient and rich. | Lucy is tall. | entailment | ((?[X]:((~strong(X)&~creative(X))))=>((~calm(lucy)<~>~tall(lucy))))&
((?[X]:((~patient(X)&~humble(X))))<=>((~kind(lucy)<~>brave(lucy))))&
(![X]:((curious(X)<~>~curious(X))=>(~wise(X)&~calm(X))))&
((?[X]:((~tall(X)&quiet(X))))=>(?[X]:((brave(X)|funny(X)))))&
(((~happy(mary)&~curious(mary)))<=>(?[X]:(brave(X))))&
(![X]:(~generous(X)=>(curious(X)&rich(X))))&
(![X]:((~strong(X)<~>~creative(X))<=>(generous(X)&calm(X))))&
(![X]:((curious(X)<~>patient(X))=>(~kind(X)&rich(X))))&
(![X]:((~brave(X)&humble(X))<=>(old(X)<~>tall(X))))&
((strong(mary))=>((~creative(susan)&tall(susan))))&
(((~happy(alice)&~old(alice)))<=>(~creative(alice)))&
(![X]:((curious(X)|~curious(X))=>(~tall(X)<~>~humble(X))))&
(![X]:((~humble(X)|quiet(X))=>happy(X)))&
((?[X]:((~calm(X)<~>~old(X))))<=>((old(john)<~>~humble(john))))&
(![X]:((~brave(X)|happy(X))<=>(rich(X)|curious(X))))&
(![X]:((~creative(X)<~>~wise(X))<=>(rich(X)<~>~quiet(X))))&
((~generous(lucy)|~wise(lucy)))&
(?[X]:(patient(X)))&
(?[X]:((~brave(X)<~>tall(X))))&
(?[X]:((~strong(X)&~quiet(X))))&
(~generous(john))&
(?[X]:(~brave(X)))&
(?[X]:((~strong(X)|patient(X))))&
(?[X]:((~patient(X)&rich(X)))) | tall(lucy) | [
"p0",
"p2",
"p6",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6420865412911450824717022
% SZS output start Proof for 6420865412911450824717022
1. ? [X0] : (~creative(X0) & ~strong(X0)) => (~calm(lucy) <~> ~tall(lucy)) [input p0]
3. ! [X0] : ((curious(X0) <~> ~curious(X0)) => (~calm(X0) & ~wise(X0))) [input p2]
7. ! [X0] : ((~strong(X0) <~> ~creative(X0)) <=> (calm(X0) & generous(X0))) [input p6]
20. ? [X0] : (~quiet(X0) & ~strong(X0)) [input p19]
25. ~tall(lucy) [input hypothesis]
28. (~calm(lucy) <~> ~tall(lucy)) | ! [X0] : (creative(X0) | strong(X0)) [ennf transformation 1]
29. ! [X0] : ((~calm(X0) & ~wise(X0)) | (curious(X0) <=> ~curious(X0))) [ennf transformation 3]
35. ((tall(lucy) | calm(lucy)) & (~tall(lucy) | ~calm(lucy))) | ! [X0] : (creative(X0) | strong(X0)) [nnf transformation 28]
40. ! [X0] : ((~calm(X0) & ~wise(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) [nnf transformation 29]
46. ! [X0] : ((((creative(X0) | strong(X0)) & (~creative(X0) | ~strong(X0))) | (~calm(X0) | ~generous(X0))) & ((calm(X0) & generous(X0)) | ((~strong(X0) | creative(X0)) & (~creative(X0) | strong(X0))))) [nnf transformation 7]
47. ! [X0] : ((((creative(X0) | strong(X0)) & (~creative(X0) | ~strong(X0))) | ~calm(X0) | ~generous(X0)) & ((calm(X0) & generous(X0)) | ((~strong(X0) | creative(X0)) & (~creative(X0) | strong(X0))))) [flattening 46]
66. ? [X0] : (~quiet(X0) & ~strong(X0)) => (~quiet(sK5) & ~strong(sK5)) [choice axiom]
67. ~quiet(sK5) & ~strong(sK5) [skolemisation 20,66]
75. tall(lucy) | calm(lucy) | creative(X0) | strong(X0) [cnf transformation 35]
84. ~calm(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 40]
85. ~calm(X0) | curious(X0) | curious(X0) [cnf transformation 40]
93. calm(X0) | ~creative(X0) | strong(X0) [cnf transformation 47]
94. calm(X0) | ~strong(X0) | creative(X0) [cnf transformation 47]
142. ~strong(sK5) [cnf transformation 67]
149. ~tall(lucy) [cnf transformation 25]
152. ~calm(X0) | ~curious(X0) [duplicate literal removal 84]
153. ~calm(X0) | curious(X0) [duplicate literal removal 85]
155. 1 <=> ! [X0] : (creative(X0) | strong(X0)) [avatar definition]
156. creative(X0) | strong(X0) <- (1) [avatar component clause 155]
158. 2 <=> calm(lucy) [avatar definition]
160. calm(lucy) <- (2) [avatar component clause 158]
162. 3 <=> tall(lucy) [avatar definition]
165. 1 | 2 | 3 [avatar split clause 75,162,158,155]
192. ~calm(X0) [subsumption resolution 152,153]
212. ~strong(X0) | creative(X0) [subsumption resolution 94,192]
213. ~creative(X0) | strong(X0) [subsumption resolution 93,192]
291. ~3 [avatar split clause 149,162]
292. $false <- (2) [subsumption resolution 160,192]
293. ~2 [avatar contradiction clause 292]
294. creative(X0) <- (1) [subsumption resolution 156,212]
299. strong(X0) <- (1) [resolution 213,294]
304. $false <- (1) [resolution 299,142]
307. ~1 [avatar contradiction clause 304]
309. $false [avatar sat refutation 165,291,293,307]
% SZS output end Proof for 6420865412911450824717022
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either strong or curious then susan is both strong and not strong and vice versa.
Everyone who is not generous is not wise.
Everyone who is both not rich and tall is not generous.
Everyone who is either not funny or rich is patient.
Everyone who is both kind and not generous is either not calm or rich and vice versa.
Everyone who is not generous is patient and vice versa.
Everyone who is creative is either rich or not quiet and vice versa.
If someone is kind or not happy then someone is both not generous and not humble and vice versa.
Everyone who is either generous or strong is both not wise and not brave and vice versa.
Everyone who is both curious and not wise is not generous and vice versa.
Everyone who is both generous and not brave is both not wise and not humble and vice versa.
Everyone who is patient or curious is either kind or not kind and vice versa.
Everyone who is calm is not happy and vice versa.
Someone is either calm or happy.
Someone is tall or kind.
Alice is brave.
Someone is either not creative or not wise.
Someone is patient or not humble.
Alice is calm or not old. | Alice is generous. | entailment | ((?[X]:((strong(X)<~>curious(X))))<=>((strong(susan)&~strong(susan))))&
(![X]:(~generous(X)=>~wise(X)))&
(![X]:((~rich(X)&tall(X))=>~generous(X)))&
(![X]:((~funny(X)<~>rich(X))=>patient(X)))&
(![X]:((kind(X)&~generous(X))<=>(~calm(X)<~>rich(X))))&
(![X]:(~generous(X)<=>patient(X)))&
(![X]:(creative(X)<=>(rich(X)<~>~quiet(X))))&
((?[X]:((kind(X)|~happy(X))))<=>(?[X]:((~generous(X)&~humble(X)))))&
(![X]:((generous(X)<~>strong(X))<=>(~wise(X)&~brave(X))))&
(![X]:((curious(X)&~wise(X))<=>~generous(X)))&
(![X]:((generous(X)&~brave(X))<=>(~wise(X)&~humble(X))))&
(![X]:((patient(X)|curious(X))<=>(kind(X)<~>~kind(X))))&
(![X]:(calm(X)<=>~happy(X)))&
(?[X]:((calm(X)<~>happy(X))))&
(?[X]:((tall(X)|kind(X))))&
(brave(alice))&
(?[X]:((~creative(X)<~>~wise(X))))&
(?[X]:((patient(X)|~humble(X))))&
((calm(alice)|~old(alice))) | generous(alice) | [
"p0",
"p8",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 714437839749897367429725
% SZS output start Proof for 714437839749897367429725
1. ? [X0] : (strong(X0) <~> curious(X0)) <=> (~strong(susan) & strong(susan)) [input p0]
9. ! [X0] : ((generous(X0) <~> strong(X0)) <=> (~brave(X0) & ~wise(X0))) [input p8]
10. ! [X0] : ((~wise(X0) & curious(X0)) <=> ~generous(X0)) [input p9]
16. brave(alice) [input p15]
20. ~generous(alice) [input hypothesis]
27. (? [X0] : ((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | (strong(susan) | ~strong(susan))) & ((~strong(susan) & strong(susan)) | ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) [nnf transformation 1]
28. (? [X0] : ((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | strong(susan) | ~strong(susan)) & ((~strong(susan) & strong(susan)) | ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0)))) [flattening 27]
29. (? [X0] : ((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) | strong(susan) | ~strong(susan)) & ((~strong(susan) & strong(susan)) | ! [X1] : ((strong(X1) | ~curious(X1)) & (curious(X1) | ~strong(X1)))) [rectify 28]
30. ? [X0] : ((~curious(X0) | ~strong(X0)) & (curious(X0) | strong(X0))) => ((~curious(sK0) | ~strong(sK0)) & (curious(sK0) | strong(sK0))) [choice axiom]
31. (((~curious(sK0) | ~strong(sK0)) & (curious(sK0) | strong(sK0))) | strong(susan) | ~strong(susan)) & ((~strong(susan) & strong(susan)) | ! [X1] : ((strong(X1) | ~curious(X1)) & (curious(X1) | ~strong(X1)))) [skolemisation 29,30]
42. ! [X0] : ((((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | (brave(X0) | wise(X0))) & ((~brave(X0) & ~wise(X0)) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0))))) [nnf transformation 9]
43. ! [X0] : ((((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | brave(X0) | wise(X0)) & ((~brave(X0) & ~wise(X0)) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0))))) [flattening 42]
44. ! [X0] : (((~wise(X0) & curious(X0)) | generous(X0)) & (~generous(X0) | (wise(X0) | ~curious(X0)))) [nnf transformation 10]
45. ! [X0] : (((~wise(X0) & curious(X0)) | generous(X0)) & (~generous(X0) | wise(X0) | ~curious(X0))) [flattening 44]
62. strong(susan) | strong(X1) | ~curious(X1) [cnf transformation 31]
64. ~strong(susan) | strong(X1) | ~curious(X1) [cnf transformation 31]
91. ~brave(X0) | generous(X0) | ~strong(X0) [cnf transformation 43]
95. generous(X0) | curious(X0) [cnf transformation 45]
112. brave(alice) [cnf transformation 16]
116. ~generous(alice) [cnf transformation 20]
120. 1 <=> ! [X1] : (strong(X1) | ~curious(X1)) [avatar definition]
121. ~curious(X1) | strong(X1) <- (1) [avatar component clause 120]
123. 2 <=> strong(susan) [avatar definition]
126. 1 | ~2 [avatar split clause 64,123,120]
131. 1 | 2 [avatar split clause 62,123,120]
198. curious(alice) [resolution 95,116]
201. strong(alice) <- (1) [resolution 121,198]
243. generous(alice) | ~strong(alice) [resolution 91,112]
244. ~strong(alice) [subsumption resolution 243,116]
245. $false <- (1) [subsumption resolution 244,201]
246. ~1 [avatar contradiction clause 245]
247. $false [avatar sat refutation 126,131,246]
% SZS output end Proof for 714437839749897367429725
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and happy is kind and vice versa.
If lucy is quiet or calm then john is creative or not generous.
If alice is both strong and kind then mary is not calm or generous.
If mary is either creative or not patient then someone is either strong or quiet.
Everyone who is strong or wise is either quiet or happy and vice versa.
If someone is not old or not brave then someone is either not kind or not happy.
Everyone who is old or not kind is not generous.
If john is both not old and creative then someone is either kind or generous and vice versa.
Everyone who is not creative or wise is either old or not kind and vice versa.
Everyone who is both not brave and not creative is either quiet or wise.
Everyone who is either not humble or not happy is either not kind or creative and vice versa.
If someone is not generous or humble then someone is not generous and vice versa.
If someone is strong then someone is not wise or humble and vice versa.
If someone is both not calm and not humble then someone is calm or wise and vice versa.
If alice is either patient or funny then susan is patient and vice versa.
Everyone who is both not old and happy is both not wise and quiet.
Someone is calm or brave.
Someone is curious.
Someone is not rich or not brave.
Paul is brave.
Mary is curious.
Someone is both calm and funny. | John is humble. | contradiction | (![X]:((~kind(X)&happy(X))<=>kind(X)))&
(((quiet(lucy)|calm(lucy)))=>((creative(john)|~generous(john))))&
(((strong(alice)&kind(alice)))=>((~calm(mary)|generous(mary))))&
(((creative(mary)<~>~patient(mary)))=>(?[X]:((strong(X)<~>quiet(X)))))&
(![X]:((strong(X)|wise(X))<=>(quiet(X)<~>happy(X))))&
((?[X]:((~old(X)|~brave(X))))=>(?[X]:((~kind(X)<~>~happy(X)))))&
(![X]:((old(X)|~kind(X))=>~generous(X)))&
(((~old(john)&creative(john)))<=>(?[X]:((kind(X)<~>generous(X)))))&
(![X]:((~creative(X)|wise(X))<=>(old(X)<~>~kind(X))))&
(![X]:((~brave(X)&~creative(X))=>(quiet(X)<~>wise(X))))&
(![X]:((~humble(X)<~>~happy(X))<=>(~kind(X)<~>creative(X))))&
((?[X]:((~generous(X)|humble(X))))<=>(?[X]:(~generous(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~wise(X)|humble(X)))))&
((?[X]:((~calm(X)&~humble(X))))<=>(?[X]:((calm(X)|wise(X)))))&
(((patient(alice)<~>funny(alice)))<=>(patient(susan)))&
(![X]:((~old(X)&happy(X))=>(~wise(X)&quiet(X))))&
(?[X]:((calm(X)|brave(X))))&
(?[X]:(curious(X)))&
(?[X]:((~rich(X)|~brave(X))))&
(brave(paul))&
(curious(mary))&
(?[X]:((calm(X)&funny(X)))) | humble(john) | [
"p0",
"p5",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5023109508158643382940616
% SZS output start Proof for 5023109508158643382940616
1. ! [X0] : ((happy(X0) & ~kind(X0)) <=> kind(X0)) [input p0]
6. ? [X0] : (~brave(X0) | ~old(X0)) => ? [X0] : (~kind(X0) <~> ~happy(X0)) [input p5]
9. ! [X0] : ((wise(X0) | ~creative(X0)) <=> (old(X0) <~> ~kind(X0))) [input p8]
11. ! [X0] : ((~humble(X0) <~> ~happy(X0)) <=> (~kind(X0) <~> creative(X0))) [input p10]
23. humble(john) [input hypothesis]
24. ? [X0] : (~brave(X0) | ~old(X0)) => ? [X1] : (~kind(X1) <~> ~happy(X1)) [rectify 6]
31. ? [X0] : ~old(X0) => ? [X1] : (~kind(X1) <~> ~happy(X1)) [pure predicate removal 24]
40. ? [X1] : (~kind(X1) <~> ~happy(X1)) | ! [X0] : old(X0) [ennf transformation 31]
44. ! [X0] : (((happy(X0) & ~kind(X0)) | ~kind(X0)) & (kind(X0) | (~happy(X0) | kind(X0)))) [nnf transformation 1]
45. ! [X0] : (((happy(X0) & ~kind(X0)) | ~kind(X0)) & (kind(X0) | ~happy(X0) | kind(X0))) [flattening 44]
51. ? [X1] : ((happy(X1) | kind(X1)) & (~happy(X1) | ~kind(X1))) | ! [X0] : old(X0) [nnf transformation 40]
52. ? [X0] : ((happy(X0) | kind(X0)) & (~happy(X0) | ~kind(X0))) | ! [X1] : old(X1) [rectify 51]
53. ? [X0] : ((happy(X0) | kind(X0)) & (~happy(X0) | ~kind(X0))) => ((happy(sK1) | kind(sK1)) & (~happy(sK1) | ~kind(sK1))) [choice axiom]
54. ((happy(sK1) | kind(sK1)) & (~happy(sK1) | ~kind(sK1))) | ! [X1] : old(X1) [skolemisation 52,53]
60. ! [X0] : (((wise(X0) | ~creative(X0)) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0)))) & (((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | (~wise(X0) & creative(X0)))) [nnf transformation 9]
61. ! [X0] : ((wise(X0) | ~creative(X0) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0)))) & (((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | (~wise(X0) & creative(X0)))) [flattening 60]
62. ! [X0] : ((((happy(X0) | humble(X0)) & (~happy(X0) | ~humble(X0))) | ((~kind(X0) | ~creative(X0)) & (creative(X0) | kind(X0)))) & (((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | ((~humble(X0) | happy(X0)) & (~happy(X0) | humble(X0))))) [nnf transformation 11]
81. kind(X0) | ~happy(X0) | kind(X0) [cnf transformation 45]
82. ~kind(X0) | ~kind(X0) [cnf transformation 45]
98. happy(sK1) | kind(sK1) | old(X1) [cnf transformation 54]
109. kind(X0) | ~old(X0) | creative(X0) [cnf transformation 61]
116. ~creative(X0) | kind(X0) | ~humble(X0) | happy(X0) [cnf transformation 62]
140. humble(john) [cnf transformation 23]
141. kind(X0) | ~happy(X0) [duplicate literal removal 81]
142. ~kind(X0) [duplicate literal removal 82]
143. ~happy(X0) [subsumption resolution 141,142]
185. kind(sK1) | old(X1) [subsumption resolution 98,143]
186. old(X1) [subsumption resolution 185,142]
190. ~old(X0) | creative(X0) [subsumption resolution 109,142]
191. creative(X0) [subsumption resolution 190,186]
192. kind(X0) | ~humble(X0) | happy(X0) [subsumption resolution 116,191]
193. ~humble(X0) | happy(X0) [subsumption resolution 192,142]
194. ~humble(X0) [subsumption resolution 193,143]
230. $false [subsumption resolution 140,194]
% SZS output end Proof for 5023109508158643382940616
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or tall is tall and vice versa. If paul is both not happy and strong then someone is not old. Everyone who is brave is either not funny or brave. Everyone who is either wise or rich is both not humble and calm and vice versa. Everyone who is both not humble and not tall is 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. Everyone who is both humble and calm is either not humble or calm and vice versa. If john is either creative or curious then someone is rich or not wise and vice versa. Everyone who is creative or not brave is not wise or not patient and vice versa. If fred is strong then someone is both not humble and wise. If someone is generous or humble then someone is either quiet or not quiet and vice versa. If susan is kind or tall then john is not humble. If mary is funny or not wise then susan is not strong and vice versa. If paul is kind then someone is calm and vice versa. Someone is either not old or not kind. Paul is not quiet or not funny. Someone is not happy. Someone is rich or calm. Alice is either funny or humble. Fred is generous. | Mary is rich. | neutral | (![X]:((happy(X)|tall(X))<=>tall(X)))&
(((~happy(paul)&strong(paul)))=>(?[X]:(~old(X))))&
(![X]:(brave(X)=>(~funny(X)<~>brave(X))))&
(![X]:((wise(X)<~>rich(X))<=>(~humble(X)&calm(X))))&
(![X]:((~humble(X)&~tall(X))=>kind(X)))&
((?[X]:((~kind(X)|happy(X))))=>(patient(alice)))&
(![X]:((~humble(X)<~>humble(X))<=>(~calm(X)&~curious(X))))&
(![X]:(~happy(X)<=>(brave(X)|~strong(X))))&
(![X]:((humble(X)&calm(X))<=>(~humble(X)<~>calm(X))))&
(((creative(john)<~>curious(john)))<=>(?[X]:((rich(X)|~wise(X)))))&
(![X]:((creative(X)|~brave(X))<=>(~wise(X)|~patient(X))))&
((strong(fred))=>(?[X]:((~humble(X)&wise(X)))))&
((?[X]:((generous(X)|humble(X))))<=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(((kind(susan)|tall(susan)))=>(~humble(john)))&
(((funny(mary)|~wise(mary)))<=>(~strong(susan)))&
((kind(paul))<=>(?[X]:(calm(X))))&
(?[X]:((~old(X)<~>~kind(X))))&
((~quiet(paul)|~funny(paul)))&
(?[X]:(~happy(X)))&
(?[X]:((rich(X)|calm(X))))&
((funny(alice)<~>humble(alice)))&
(generous(fred)) | rich(mary) | [] | null | 0 |
Everyone who is both not brave and creative is generous or not old.
If someone is not humble or calm then someone is humble or creative.
If paul is both happy and not quiet then susan is not wise or old and vice versa.
Everyone who is both not happy and patient is either not humble or calm and vice versa.
Everyone who is both happy and brave is not generous or not tall and vice versa.
If lucy is both not patient and not curious then someone is not strong or not humble.
Everyone who is not calm or not kind is either not calm or generous.
Everyone who is patient is both not wise and not humble.
Everyone who is both creative and funny is not patient.
Everyone who is humble is not patient or not brave and vice versa.
If john is old or curious then someone is both kind and not tall and vice versa.
If someone is either not old or quiet then someone is not funny.
If someone is both patient and not brave then someone is both tall and strong.
If lucy is either funny or not calm then someone is tall or strong.
Everyone who is not funny or not curious is both kind and not generous.
Everyone who is both tall and not kind is either calm or not tall and vice versa.
Susan is not tall.
Someone is not patient or brave.
Paul is curious.
Someone is both calm and patient.
Alice is curious or not humble.
Someone is both curious and not old.
Someone is both patient and old. | Paul is not old. | neutral | (![X]:((~brave(X)&creative(X))=>(generous(X)|~old(X))))&
((?[X]:((~humble(X)|calm(X))))=>(?[X]:((humble(X)|creative(X)))))&
(((happy(paul)&~quiet(paul)))<=>((~wise(susan)|old(susan))))&
(![X]:((~happy(X)&patient(X))<=>(~humble(X)<~>calm(X))))&
(![X]:((happy(X)&brave(X))<=>(~generous(X)|~tall(X))))&
(((~patient(lucy)&~curious(lucy)))=>(?[X]:((~strong(X)|~humble(X)))))&
(![X]:((~calm(X)|~kind(X))=>(~calm(X)<~>generous(X))))&
(![X]:(patient(X)=>(~wise(X)&~humble(X))))&
(![X]:((creative(X)&funny(X))=>~patient(X)))&
(![X]:(humble(X)<=>(~patient(X)|~brave(X))))&
(((old(john)|curious(john)))<=>(?[X]:((kind(X)&~tall(X)))))&
((?[X]:((~old(X)<~>quiet(X))))=>(?[X]:(~funny(X))))&
((?[X]:((patient(X)&~brave(X))))=>(?[X]:((tall(X)&strong(X)))))&
(((funny(lucy)<~>~calm(lucy)))=>(?[X]:((tall(X)|strong(X)))))&
(![X]:((~funny(X)|~curious(X))=>(kind(X)&~generous(X))))&
(![X]:((tall(X)&~kind(X))<=>(calm(X)<~>~tall(X))))&
(~tall(susan))&
(?[X]:((~patient(X)|brave(X))))&
(curious(paul))&
(?[X]:((calm(X)&patient(X))))&
((curious(alice)|~humble(alice)))&
(?[X]:((curious(X)&~old(X))))&
(?[X]:((patient(X)&old(X)))) | ~old(paul) | [] | null | 0 |
If someone is not happy or not calm then someone is either not calm or brave.
Everyone who is rich is both quiet and not strong and vice versa.
Everyone who is both rich and not old is both curious and not brave and vice versa.
Everyone who is not funny is either calm or quiet and vice versa.
If someone is both quiet and not curious then someone is old or not happy.
Everyone who is either patient or creative is strong or not generous.
Everyone who is creative or not rich is brave or not happy and vice versa.
If someone is not generous then fred is not wise and vice versa.
If alice is humble then someone is not rich.
If someone is both not tall and not rich then someone is either not kind or not creative.
If someone is both patient and funny then someone is either not strong or not patient.
Everyone who is curious is both rich and wise.
If someone is not curious then someone is not creative and vice versa.
Everyone who is not tall is humble.
If someone is not curious or not calm then someone is either tall or not rich.
Everyone who is tall or not strong is not old and vice versa.
Someone is happy or not strong.
Someone is both creative and curious.
Someone is both quiet and wise.
Paul is not brave.
Someone is either tall or quiet.
Someone is both not happy and not calm.
Paul is not curious or curious.
Someone is tall. | Paul is not curious. | neutral | ((?[X]:((~happy(X)|~calm(X))))=>(?[X]:((~calm(X)<~>brave(X)))))&
(![X]:(rich(X)<=>(quiet(X)&~strong(X))))&
(![X]:((rich(X)&~old(X))<=>(curious(X)&~brave(X))))&
(![X]:(~funny(X)<=>(calm(X)<~>quiet(X))))&
((?[X]:((quiet(X)&~curious(X))))=>(?[X]:((old(X)|~happy(X)))))&
(![X]:((patient(X)<~>creative(X))=>(strong(X)|~generous(X))))&
(![X]:((creative(X)|~rich(X))<=>(brave(X)|~happy(X))))&
((?[X]:(~generous(X)))<=>(~wise(fred)))&
((humble(alice))=>(?[X]:(~rich(X))))&
((?[X]:((~tall(X)&~rich(X))))=>(?[X]:((~kind(X)<~>~creative(X)))))&
((?[X]:((patient(X)&funny(X))))=>(?[X]:((~strong(X)<~>~patient(X)))))&
(![X]:(curious(X)=>(rich(X)&wise(X))))&
((?[X]:(~curious(X)))<=>(?[X]:(~creative(X))))&
(![X]:(~tall(X)=>humble(X)))&
((?[X]:((~curious(X)|~calm(X))))=>(?[X]:((tall(X)<~>~rich(X)))))&
(![X]:((tall(X)|~strong(X))<=>~old(X)))&
(?[X]:((happy(X)|~strong(X))))&
(?[X]:((creative(X)&curious(X))))&
(?[X]:((quiet(X)&wise(X))))&
(~brave(paul))&
(?[X]:((tall(X)<~>quiet(X))))&
(?[X]:((~happy(X)&~calm(X))))&
((~curious(paul)|curious(paul)))&
(?[X]:(tall(X))) | ~curious(paul) | [] | null | 0 |
If someone is both wise and not wise then someone is not calm.
If someone is either not old or rich then someone is both creative and not tall and vice versa.
If someone is both rich and tall then john is either not strong or kind and vice versa.
If lucy is calm or wise then someone is both not funny and not old.
If someone is both brave and not tall then someone is not kind or patient and vice versa.
If someone is both not calm and not creative then someone is either creative or tall and vice versa.
If susan is not generous then someone is both not creative and not happy and vice versa.
Everyone who is both humble and rich is either not humble or not calm and vice versa.
Everyone who is not happy is both brave and happy.
Everyone who is strong or quiet is not kind.
If someone is both not wise and kind then someone is either not generous or generous.
Everyone who is not brave or generous is funny or tall.
If mary is not humble then mary is wise and vice versa.
Everyone who is not quiet is both calm and old.
Everyone who is either not brave or not generous is both old and not quiet and vice versa.
If someone is not quiet then someone is either not strong or strong.
Someone is wise or not quiet.
Mary is brave.
John is happy.
Alice is both wise and not old.
Susan is happy.
Someone is not creative or strong.
John is both rich and not strong.
Fred is either tall or quiet. | John is kind. | contradiction | ((?[X]:((wise(X)&~wise(X))))=>(?[X]:(~calm(X))))&
((?[X]:((~old(X)<~>rich(X))))<=>(?[X]:((creative(X)&~tall(X)))))&
((?[X]:((rich(X)&tall(X))))<=>((~strong(john)<~>kind(john))))&
(((calm(lucy)|wise(lucy)))=>(?[X]:((~funny(X)&~old(X)))))&
((?[X]:((brave(X)&~tall(X))))<=>(?[X]:((~kind(X)|patient(X)))))&
((?[X]:((~calm(X)&~creative(X))))<=>(?[X]:((creative(X)<~>tall(X)))))&
((~generous(susan))<=>(?[X]:((~creative(X)&~happy(X)))))&
(![X]:((humble(X)&rich(X))<=>(~humble(X)<~>~calm(X))))&
(![X]:(~happy(X)=>(brave(X)&happy(X))))&
(![X]:((strong(X)|quiet(X))=>~kind(X)))&
((?[X]:((~wise(X)&kind(X))))=>(?[X]:((~generous(X)<~>generous(X)))))&
(![X]:((~brave(X)|generous(X))=>(funny(X)|tall(X))))&
((~humble(mary))<=>(wise(mary)))&
(![X]:(~quiet(X)=>(calm(X)&old(X))))&
(![X]:((~brave(X)<~>~generous(X))<=>(old(X)&~quiet(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~strong(X)<~>strong(X)))))&
(?[X]:((wise(X)|~quiet(X))))&
(brave(mary))&
(happy(john))&
((wise(alice)&~old(alice)))&
(happy(susan))&
(?[X]:((~creative(X)|strong(X))))&
((rich(john)&~strong(john)))&
((tall(fred)<~>quiet(fred))) | kind(john) | [
"p7",
"p9",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2846951829542113156746567
% SZS output start Proof for 2846951829542113156746567
8. ! [X0] : ((rich(X0) & humble(X0)) <=> (~humble(X0) <~> ~calm(X0))) [input p7]
10. ! [X0] : ((quiet(X0) | strong(X0)) => ~kind(X0)) [input p9]
14. ! [X0] : (~quiet(X0) => (old(X0) & calm(X0))) [input p13]
23. ~strong(john) & rich(john) [input p22]
25. kind(john) [input hypothesis]
35. ! [X0] : (~kind(X0) | (~quiet(X0) & ~strong(X0))) [ennf transformation 10]
39. ! [X0] : ((old(X0) & calm(X0)) | quiet(X0)) [ennf transformation 14]
69. ! [X0] : (((rich(X0) & humble(X0)) | ((~humble(X0) | calm(X0)) & (~calm(X0) | humble(X0)))) & (((calm(X0) | humble(X0)) & (~calm(X0) | ~humble(X0))) | (~rich(X0) | ~humble(X0)))) [nnf transformation 8]
70. ! [X0] : (((rich(X0) & humble(X0)) | ((~humble(X0) | calm(X0)) & (~calm(X0) | humble(X0)))) & (((calm(X0) | humble(X0)) & (~calm(X0) | ~humble(X0))) | ~rich(X0) | ~humble(X0))) [flattening 69]
118. ~calm(X0) | ~humble(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 70]
120. humble(X0) | ~calm(X0) | humble(X0) [cnf transformation 70]
127. ~quiet(X0) | ~kind(X0) [cnf transformation 35]
134. quiet(X0) | calm(X0) [cnf transformation 39]
151. rich(john) [cnf transformation 23]
155. kind(john) [cnf transformation 25]
157. ~calm(X0) | ~humble(X0) | ~rich(X0) [duplicate literal removal 118]
158. ~calm(X0) | humble(X0) [duplicate literal removal 120]
191. 8 <=> kind(john) [avatar definition]
192. kind(john) <- (8) [avatar component clause 191]
311. ~rich(X0) | ~calm(X0) [subsumption resolution 157,158]
353. 8 [avatar split clause 155,191]
361. ~kind(X0) | calm(X0) [resolution 134,127]
378. ~calm(john) [resolution 311,151]
383. calm(john) <- (8) [resolution 361,192]
384. $false <- (8) [subsumption resolution 383,378]
385. ~8 [avatar contradiction clause 384]
386. $false [avatar sat refutation 353,385]
% SZS output end Proof for 2846951829542113156746567
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is old.
If someone is either not funny or not curious then fred is either not kind or happy and vice versa.
If susan is both patient and creative then someone is tall or not generous and vice versa.
If fred is not creative or not happy then someone is either not quiet or not rich.
If mary is patient or not kind then susan is either not rich or not quiet.
Everyone who is not tall or rich is patient.
If someone is strong then fred is both old and humble.
Everyone who is both not funny and not brave is not strong and vice versa.
If fred is either kind or brave then someone is not strong or not tall.
Everyone who is either not old or not wise is both not curious and old and vice versa.
If someone is both brave and kind then susan is either tall or not funny.
Everyone who is creative or generous is brave.
If paul is either old or wise then someone is either creative or calm and vice versa.
If someone is both generous and not strong then john is both strong and quiet and vice versa.
Everyone who is strong is not humble and vice versa.
Everyone who is not patient is either not old or kind and vice versa.
Someone is generous.
Someone is both rich and funny.
Someone is not happy.
Alice is old or not curious.
Someone is either not tall or creative.
Someone is old.
Someone is either creative or not kind.
John is either not creative or kind. | Susan is not creative. | contradiction | (![X]:(~brave(X)=>old(X)))&
((?[X]:((~funny(X)<~>~curious(X))))<=>((~kind(fred)<~>happy(fred))))&
(((patient(susan)&creative(susan)))<=>(?[X]:((tall(X)|~generous(X)))))&
(((~creative(fred)|~happy(fred)))=>(?[X]:((~quiet(X)<~>~rich(X)))))&
(((patient(mary)|~kind(mary)))=>((~rich(susan)<~>~quiet(susan))))&
(![X]:((~tall(X)|rich(X))=>patient(X)))&
((?[X]:(strong(X)))=>((old(fred)&humble(fred))))&
(![X]:((~funny(X)&~brave(X))<=>~strong(X)))&
(((kind(fred)<~>brave(fred)))=>(?[X]:((~strong(X)|~tall(X)))))&
(![X]:((~old(X)<~>~wise(X))<=>(~curious(X)&old(X))))&
((?[X]:((brave(X)&kind(X))))=>((tall(susan)<~>~funny(susan))))&
(![X]:((creative(X)|generous(X))=>brave(X)))&
(((old(paul)<~>wise(paul)))<=>(?[X]:((creative(X)<~>calm(X)))))&
((?[X]:((generous(X)&~strong(X))))<=>((strong(john)&quiet(john))))&
(![X]:(strong(X)<=>~humble(X)))&
(![X]:(~patient(X)<=>(~old(X)<~>kind(X))))&
(?[X]:(generous(X)))&
(?[X]:((rich(X)&funny(X))))&
(?[X]:(~happy(X)))&
((old(alice)|~curious(alice)))&
(?[X]:((~tall(X)<~>creative(X))))&
(?[X]:(old(X)))&
(?[X]:((creative(X)<~>~kind(X))))&
((~creative(john)<~>kind(john))) | ~creative(susan) | [
"p2",
"p6",
"p7",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2154519399408111278417017
% SZS output start Proof for 2154519399408111278417017
3. (creative(susan) & patient(susan)) <=> ? [X0] : (~generous(X0) | tall(X0)) [input p2]
7. ? [X0] : strong(X0) => (humble(fred) & old(fred)) [input p6]
8. ! [X0] : ((~brave(X0) & ~funny(X0)) <=> ~strong(X0)) [input p7]
12. ! [X0] : ((generous(X0) | creative(X0)) => brave(X0)) [input p11]
15. ! [X0] : (strong(X0) <=> ~humble(X0)) [input p14]
25. ~creative(susan) [input hypothesis]
30. (humble(fred) & old(fred)) | ! [X0] : ~strong(X0) [ennf transformation 7]
33. ! [X0] : (brave(X0) | (~generous(X0) & ~creative(X0))) [ennf transformation 12]
38. ((creative(susan) & patient(susan)) | ! [X0] : (generous(X0) & ~tall(X0))) & (? [X0] : (~generous(X0) | tall(X0)) | (~creative(susan) | ~patient(susan))) [nnf transformation 3]
39. ((creative(susan) & patient(susan)) | ! [X0] : (generous(X0) & ~tall(X0))) & (? [X0] : (~generous(X0) | tall(X0)) | ~creative(susan) | ~patient(susan)) [flattening 38]
40. ((creative(susan) & patient(susan)) | ! [X0] : (generous(X0) & ~tall(X0))) & (? [X1] : (~generous(X1) | tall(X1)) | ~creative(susan) | ~patient(susan)) [rectify 39]
41. ? [X1] : (~generous(X1) | tall(X1)) => (~generous(sK1) | tall(sK1)) [choice axiom]
42. ((creative(susan) & patient(susan)) | ! [X0] : (generous(X0) & ~tall(X0))) & ((~generous(sK1) | tall(sK1)) | ~creative(susan) | ~patient(susan)) [skolemisation 40,41]
47. ! [X0] : (((~brave(X0) & ~funny(X0)) | strong(X0)) & (~strong(X0) | (brave(X0) | funny(X0)))) [nnf transformation 8]
48. ! [X0] : (((~brave(X0) & ~funny(X0)) | strong(X0)) & (~strong(X0) | brave(X0) | funny(X0))) [flattening 47]
64. ! [X0] : ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0))) [nnf transformation 15]
94. creative(susan) | generous(X0) [cnf transformation 42]
106. humble(fred) | ~strong(X0) [cnf transformation 30]
109. ~brave(X0) | strong(X0) [cnf transformation 48]
121. ~generous(X0) | brave(X0) [cnf transformation 33]
134. ~humble(X0) | ~strong(X0) [cnf transformation 64]
152. ~creative(susan) [cnf transformation 25]
186. 7 <=> ! [X0] : generous(X0) [avatar definition]
187. generous(X0) <- (7) [avatar component clause 186]
189. 8 <=> creative(susan) [avatar definition]
192. 7 | 8 [avatar split clause 94,189,186]
249. 20 <=> ! [X0] : ~strong(X0) [avatar definition]
250. ~strong(X0) <- (20) [avatar component clause 249]
252. 21 <=> humble(fred) [avatar definition]
254. humble(fred) <- (21) [avatar component clause 252]
255. 20 | 21 [avatar split clause 106,252,249]
382. ~8 [avatar split clause 152,189]
398. brave(X0) <- (7) [resolution 121,187]
401. ~strong(fred) <- (21) [resolution 134,254]
402. strong(X0) <- (7) [resolution 398,109]
405. $false <- (7, 21) [resolution 402,401]
406. ~7 | ~21 [avatar contradiction clause 405]
410. $false <- (7, 20) [subsumption resolution 250,402]
411. ~7 | ~20 [avatar contradiction clause 410]
412. $false [avatar sat refutation 192,255,382,406,411]
% SZS output end Proof for 2154519399408111278417017
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If john is either creative or brave then john is either strong or funny and vice versa.
Everyone who is either not strong or not tall is quiet.
Everyone who is both funny and creative is either not patient or rich and vice versa.
Everyone who is both curious and not rich is humble.
If lucy is either quiet or funny then someone is either wise or not happy.
Everyone who is not funny is not curious or strong.
If someone is both generous and not funny then someone is either calm or generous.
If someone is either wise or not old then someone is tall or not generous and vice versa.
Everyone who is both not wise and old is both brave and not quiet and vice versa.
Everyone who is not old or not brave is not curious or not creative and vice versa.
Everyone who is not quiet is both not tall and not generous.
Everyone who is not creative or not rich is both wise and not wise.
If mary is curious then susan is either not tall or quiet.
If someone is either kind or wise then susan is either not calm or generous.
Everyone who is either curious or not wise is not rich and vice versa.
Everyone who is both rich and curious is both generous and not funny.
Someone is not quiet.
John is not happy or not tall.
Mary is either not wise or funny.
Someone is funny or not creative.
Someone is curious or funny. | Lucy is not rich. | contradiction | (((creative(john)<~>brave(john)))<=>((strong(john)<~>funny(john))))&
(![X]:((~strong(X)<~>~tall(X))=>quiet(X)))&
(![X]:((funny(X)&creative(X))<=>(~patient(X)<~>rich(X))))&
(![X]:((curious(X)&~rich(X))=>humble(X)))&
(((quiet(lucy)<~>funny(lucy)))=>(?[X]:((wise(X)<~>~happy(X)))))&
(![X]:(~funny(X)=>(~curious(X)|strong(X))))&
((?[X]:((generous(X)&~funny(X))))=>(?[X]:((calm(X)<~>generous(X)))))&
((?[X]:((wise(X)<~>~old(X))))<=>(?[X]:((tall(X)|~generous(X)))))&
(![X]:((~wise(X)&old(X))<=>(brave(X)&~quiet(X))))&
(![X]:((~old(X)|~brave(X))<=>(~curious(X)|~creative(X))))&
(![X]:(~quiet(X)=>(~tall(X)&~generous(X))))&
(![X]:((~creative(X)|~rich(X))=>(wise(X)&~wise(X))))&
((curious(mary))=>((~tall(susan)<~>quiet(susan))))&
((?[X]:((kind(X)<~>wise(X))))=>((~calm(susan)<~>generous(susan))))&
(![X]:((curious(X)<~>~wise(X))<=>~rich(X)))&
(![X]:((rich(X)&curious(X))=>(generous(X)&~funny(X))))&
(?[X]:(~quiet(X)))&
((~happy(john)|~tall(john)))&
((~wise(mary)<~>funny(mary)))&
(?[X]:((funny(X)|~creative(X))))&
(?[X]:((curious(X)|funny(X)))) | ~rich(lucy) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2712176918466861688930275
% SZS output start Proof for 2712176918466861688930275
12. ! [X0] : ((~rich(X0) | ~creative(X0)) => (~wise(X0) & wise(X0))) [input p11]
22. ~rich(lucy) [input hypothesis]
32. ! [X0] : ((~wise(X0) & wise(X0)) | (rich(X0) & creative(X0))) [ennf transformation 12]
107. wise(X0) | rich(X0) [cnf transformation 32]
109. ~wise(X0) | rich(X0) [cnf transformation 32]
128. ~rich(lucy) [cnf transformation 22]
220. rich(X0) [subsumption resolution 107,109]
286. $false [subsumption resolution 128,220]
% SZS output end Proof for 2712176918466861688930275
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet or not patient is creative.
If john is not patient then someone is both wise and not kind and vice versa.
If fred is not humble then someone is curious.
If alice is not patient then fred is either not strong or not quiet and vice versa.
Everyone who is strong or not rich is both creative and not patient.
Everyone who is both not happy and quiet is either not old or not happy and vice versa.
Everyone who is both funny and not creative is not quiet or not wise and vice versa.
If someone is quiet or not wise then someone is both not old and not rich and vice versa.
Everyone who is either strong or old is not kind or humble.
Everyone who is quiet is old or not funny and vice versa.
If someone is either not curious or kind then paul is both not calm and not creative and vice versa.
Everyone who is both not funny and not humble is both not old and brave.
Everyone who is old or not tall is patient.
If john is old then someone is not happy.
Fred is patient.
Mary is either patient or not rich.
Paul is not curious.
John is both kind and not curious.
Lucy is rich or not rich.
Someone is not strong.
Someone is not tall or not patient. | Alice is not funny. | contradiction | (![X]:((quiet(X)|~patient(X))=>creative(X)))&
((~patient(john))<=>(?[X]:((wise(X)&~kind(X)))))&
((~humble(fred))=>(?[X]:(curious(X))))&
((~patient(alice))<=>((~strong(fred)<~>~quiet(fred))))&
(![X]:((strong(X)|~rich(X))=>(creative(X)&~patient(X))))&
(![X]:((~happy(X)&quiet(X))<=>(~old(X)<~>~happy(X))))&
(![X]:((funny(X)&~creative(X))<=>(~quiet(X)|~wise(X))))&
((?[X]:((quiet(X)|~wise(X))))<=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:((strong(X)<~>old(X))=>(~kind(X)|humble(X))))&
(![X]:(quiet(X)<=>(old(X)|~funny(X))))&
((?[X]:((~curious(X)<~>kind(X))))<=>((~calm(paul)&~creative(paul))))&
(![X]:((~funny(X)&~humble(X))=>(~old(X)&brave(X))))&
(![X]:((old(X)|~tall(X))=>patient(X)))&
((old(john))=>(?[X]:(~happy(X))))&
(patient(fred))&
((patient(mary)<~>~rich(mary)))&
(~curious(paul))&
((kind(john)&~curious(john)))&
((rich(lucy)|~rich(lucy)))&
(?[X]:(~strong(X)))&
(?[X]:((~tall(X)|~patient(X)))) | ~funny(alice) | [
"p4",
"p5",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1826734962743766659807698
% SZS output start Proof for 1826734962743766659807698
5. ! [X0] : ((~rich(X0) | strong(X0)) => (~patient(X0) & creative(X0))) [input p4]
6. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> (~old(X0) <~> ~happy(X0))) [input p5]
7. ! [X0] : ((~creative(X0) & funny(X0)) <=> (~wise(X0) | ~quiet(X0))) [input p6]
8. ? [X0] : (~wise(X0) | quiet(X0)) <=> ? [X0] : (~rich(X0) & ~old(X0)) [input p7]
22. ~funny(alice) [input hypothesis]
23. ? [X0] : (~wise(X0) | quiet(X0)) <=> ? [X1] : (~rich(X1) & ~old(X1)) [rectify 8]
29. ! [X0] : ((~patient(X0) & creative(X0)) | (rich(X0) & ~strong(X0))) [ennf transformation 5]
37. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0)))) & (((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | (~quiet(X0) | happy(X0)))) [nnf transformation 6]
38. ! [X0] : (((quiet(X0) & ~happy(X0)) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0)))) & (((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | ~quiet(X0) | happy(X0))) [flattening 37]
39. ! [X0] : (((~creative(X0) & funny(X0)) | (wise(X0) & quiet(X0))) & ((~wise(X0) | ~quiet(X0)) | (creative(X0) | ~funny(X0)))) [nnf transformation 7]
40. ! [X0] : (((~creative(X0) & funny(X0)) | (wise(X0) & quiet(X0))) & (~wise(X0) | ~quiet(X0) | creative(X0) | ~funny(X0))) [flattening 39]
41. (? [X0] : (~wise(X0) | quiet(X0)) | ! [X1] : (rich(X1) | old(X1))) & (? [X1] : (~rich(X1) & ~old(X1)) | ! [X0] : (wise(X0) & ~quiet(X0))) [nnf transformation 23]
42. (? [X0] : (~wise(X0) | quiet(X0)) | ! [X1] : (rich(X1) | old(X1))) & (? [X2] : (~rich(X2) & ~old(X2)) | ! [X3] : (wise(X3) & ~quiet(X3))) [rectify 41]
43. ? [X0] : (~wise(X0) | quiet(X0)) => (~wise(sK1) | quiet(sK1)) [choice axiom]
44. ? [X2] : (~rich(X2) & ~old(X2)) => (~rich(sK2) & ~old(sK2)) [choice axiom]
45. ((~wise(sK1) | quiet(sK1)) | ! [X1] : (rich(X1) | old(X1))) & ((~rich(sK2) & ~old(sK2)) | ! [X3] : (wise(X3) & ~quiet(X3))) [skolemisation 42,44,43]
70. rich(X0) | creative(X0) [cnf transformation 29]
74. happy(X0) | old(X0) | ~quiet(X0) | happy(X0) [cnf transformation 38]
75. ~happy(X0) | ~happy(X0) | old(X0) [cnf transformation 38]
80. funny(X0) | quiet(X0) [cnf transformation 40]
82. ~creative(X0) | quiet(X0) [cnf transformation 40]
84. ~old(sK2) | ~quiet(X3) [cnf transformation 45]
86. ~rich(sK2) | ~quiet(X3) [cnf transformation 45]
110. ~funny(alice) [cnf transformation 22]
111. happy(X0) | old(X0) | ~quiet(X0) [duplicate literal removal 74]
112. ~happy(X0) | old(X0) [duplicate literal removal 75]
147. ~quiet(X0) | old(X0) [subsumption resolution 111,112]
164. 12 <=> rich(sK2) [avatar definition]
166. ~rich(sK2) <- (~12) [avatar component clause 164]
169. 13 <=> ! [X3] : ~quiet(X3) [avatar definition]
170. ~quiet(X3) <- (13) [avatar component clause 169]
171. 13 | ~12 [avatar split clause 86,164,169]
173. 14 <=> old(sK2) [avatar definition]
175. ~old(sK2) <- (~14) [avatar component clause 173]
177. 13 | ~14 [avatar split clause 84,173,169]
235. creative(sK2) <- (~12) [resolution 70,166]
239. quiet(alice) [resolution 80,110]
245. quiet(sK2) <- (~12) [resolution 82,235]
259. old(sK2) <- (~12) [resolution 147,245]
260. $false <- (~12, ~14) [subsumption resolution 259,175]
261. 12 | 14 [avatar contradiction clause 260]
267. $false <- (13) [resolution 170,239]
270. ~13 [avatar contradiction clause 267]
272. $false [avatar sat refutation 171,177,261,270]
% SZS output end Proof for 1826734962743766659807698
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and curious is calm or not calm and vice versa.
Everyone who is happy or tall is both not tall and rich.
If fred is both not old and not quiet then alice is either wise or kind.
Everyone who is both not patient and not humble is not creative.
Everyone who is both not humble and brave is either old or brave and vice versa.
Everyone who is patient is brave.
If fred is either not wise or not strong then someone is both strong and happy and vice versa.
If susan is creative or not brave then mary is tall or quiet.
If mary is not old then someone is not funny and vice versa.
Everyone who is not wise or quiet is not creative or not wise.
Everyone who is curious is both calm and not kind and vice versa.
If someone is both not funny and not old then someone is strong or not tall.
If someone is both not wise and funny then lucy is either humble or wise.
If fred is not calm or strong then john is not quiet and vice versa.
Everyone who is either not calm or not brave is either not tall or wise.
Everyone who is both not tall and curious is not kind and vice versa.
Someone is old or wise.
John is generous.
Susan is either calm or not funny.
Mary is either not funny or not wise.
Someone is humble.
Alice is not quiet or happy. | Lucy is not curious. | contradiction | (![X]:((old(X)&curious(X))<=>(calm(X)|~calm(X))))&
(![X]:((happy(X)|tall(X))=>(~tall(X)&rich(X))))&
(((~old(fred)&~quiet(fred)))=>((wise(alice)<~>kind(alice))))&
(![X]:((~patient(X)&~humble(X))=>~creative(X)))&
(![X]:((~humble(X)&brave(X))<=>(old(X)<~>brave(X))))&
(![X]:(patient(X)=>brave(X)))&
(((~wise(fred)<~>~strong(fred)))<=>(?[X]:((strong(X)&happy(X)))))&
(((creative(susan)|~brave(susan)))=>((tall(mary)|quiet(mary))))&
((~old(mary))<=>(?[X]:(~funny(X))))&
(![X]:((~wise(X)|quiet(X))=>(~creative(X)|~wise(X))))&
(![X]:(curious(X)<=>(calm(X)&~kind(X))))&
((?[X]:((~funny(X)&~old(X))))=>(?[X]:((strong(X)|~tall(X)))))&
((?[X]:((~wise(X)&funny(X))))=>((humble(lucy)<~>wise(lucy))))&
(((~calm(fred)|strong(fred)))<=>(~quiet(john)))&
(![X]:((~calm(X)<~>~brave(X))=>(~tall(X)<~>wise(X))))&
(![X]:((~tall(X)&curious(X))<=>~kind(X)))&
(?[X]:((old(X)|wise(X))))&
(generous(john))&
((calm(susan)<~>~funny(susan)))&
((~funny(mary)<~>~wise(mary)))&
(?[X]:(humble(X)))&
((~quiet(alice)|happy(alice))) | ~curious(lucy) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 5645421448826591261302839
% SZS output start Proof for 5645421448826591261302839
1. ! [X0] : ((curious(X0) & old(X0)) <=> (~calm(X0) | calm(X0))) [input p0]
23. ~curious(lucy) [input hypothesis]
39. ! [X0] : (((curious(X0) & old(X0)) | (calm(X0) & ~calm(X0))) & ((~calm(X0) | calm(X0)) | (~curious(X0) | ~old(X0)))) [nnf transformation 1]
40. ! [X0] : (((curious(X0) & old(X0)) | (calm(X0) & ~calm(X0))) & (~calm(X0) | calm(X0) | ~curious(X0) | ~old(X0))) [flattening 39]
72. curious(X0) | ~calm(X0) [cnf transformation 40]
73. curious(X0) | calm(X0) [cnf transformation 40]
116. ~curious(lucy) [cnf transformation 23]
120. curious(X0) [subsumption resolution 72,73]
180. $false [subsumption resolution 116,120]
% SZS output end Proof for 5645421448826591261302839
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either funny or not old then someone is not wise and vice versa.
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.
Someone is both wise and rich.
Someone is quiet or not strong.
Someone is either not rich or old.
Paul is wise.
Paul is either rich or not happy. | Susan is not patient. | contradiction | (((funny(lucy)<~>~old(lucy)))<=>(?[X]:(~wise(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))))&
(?[X]:((wise(X)&rich(X))))&
(?[X]:((quiet(X)|~strong(X))))&
(?[X]:((~rich(X)<~>old(X))))&
(wise(paul))&
((rich(paul)<~>~happy(paul))) | ~patient(susan) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 1922617522682036786473791
% SZS output start Proof for 1922617522682036786473791
7. ! [X0] : (~patient(X0) <=> (patient(X0) & strong(X0))) [input p6]
20. ~patient(susan) [input hypothesis]
50. ! [X0] : ((~patient(X0) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | patient(X0))) [nnf transformation 7]
51. ! [X0] : ((~patient(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | patient(X0))) [flattening 50]
92. patient(X0) | patient(X0) [cnf transformation 51]
129. ~patient(susan) [cnf transformation 20]
132. patient(X0) [duplicate literal removal 92]
290. $false [subsumption resolution 129,132]
% SZS output end Proof for 1922617522682036786473791
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both not creative and not quiet then someone is kind. If mary is both happy and not wise then paul is both not quiet and not funny and vice versa. Everyone who is both not rich and not curious is either quiet or not calm and vice versa. Everyone who is both creative and strong is not curious or calm and vice versa. If someone is both old and not tall then susan is not wise. If lucy is calm or not curious then paul is either patient or curious. If someone is not humble then someone is either not wise or not old. If someone is not kind then john is either tall or not curious and vice versa. Everyone who is either not brave or not wise is both tall and not brave and vice versa. Everyone who is either not generous or not creative is either not funny or old. If mary is both not quiet and not rich then john is both generous and quiet. Everyone who is both not old and curious is not old. If someone is not brave then paul is either wise or funny. Everyone who is not old is humble and vice versa. If someone is not wise or creative then susan is generous or wise. Everyone who is not old is both funny and not old. Alice is either not old or not brave. Paul is not kind or humble. Someone is either calm or wise. Someone is curious. Lucy is both strong and tall. Alice is both not creative and wise. Someone is not calm. Susan is tall. | Alice is calm. | contradiction | (((~creative(paul)&~quiet(paul)))=>(?[X]:(kind(X))))&
(((happy(mary)&~wise(mary)))<=>((~quiet(paul)&~funny(paul))))&
(![X]:((~rich(X)&~curious(X))<=>(quiet(X)<~>~calm(X))))&
(![X]:((creative(X)&strong(X))<=>(~curious(X)|calm(X))))&
((?[X]:((old(X)&~tall(X))))=>(~wise(susan)))&
(((calm(lucy)|~curious(lucy)))=>((patient(paul)<~>curious(paul))))&
((?[X]:(~humble(X)))=>(?[X]:((~wise(X)<~>~old(X)))))&
((?[X]:(~kind(X)))<=>((tall(john)<~>~curious(john))))&
(![X]:((~brave(X)<~>~wise(X))<=>(tall(X)&~brave(X))))&
(![X]:((~generous(X)<~>~creative(X))=>(~funny(X)<~>old(X))))&
(((~quiet(mary)&~rich(mary)))=>((generous(john)&quiet(john))))&
(![X]:((~old(X)&curious(X))=>~old(X)))&
((?[X]:(~brave(X)))=>((wise(paul)<~>funny(paul))))&
(![X]:(~old(X)<=>humble(X)))&
((?[X]:((~wise(X)|creative(X))))=>((generous(susan)|wise(susan))))&
(![X]:(~old(X)=>(funny(X)&~old(X))))&
((~old(alice)<~>~brave(alice)))&
((~kind(paul)|humble(paul)))&
(?[X]:((calm(X)<~>wise(X))))&
(?[X]:(curious(X)))&
((strong(lucy)&tall(lucy)))&
((~creative(alice)&wise(alice)))&
(?[X]:(~calm(X)))&
(tall(susan)) | calm(alice) | [
"p3",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5079755286420847989215897
% SZS output start Proof for 5079755286420847989215897
4. ! [X0] : ((strong(X0) & creative(X0)) <=> (calm(X0) | ~curious(X0))) [input p3]
22. wise(alice) & ~creative(alice) [input p21]
25. calm(alice) [input hypothesis]
47. ! [X0] : (((strong(X0) & creative(X0)) | (~calm(X0) & curious(X0))) & ((calm(X0) | ~curious(X0)) | (~strong(X0) | ~creative(X0)))) [nnf transformation 4]
48. ! [X0] : (((strong(X0) & creative(X0)) | (~calm(X0) & curious(X0))) & (calm(X0) | ~curious(X0) | ~strong(X0) | ~creative(X0))) [flattening 47]
84. ~calm(X0) | creative(X0) [cnf transformation 48]
127. ~creative(alice) [cnf transformation 22]
131. calm(alice) [cnf transformation 25]
292. creative(alice) [resolution 84,131]
294. $false [subsumption resolution 292,127]
% SZS output end Proof for 5079755286420847989215897
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then fred is not tall or happy and vice versa. If someone is not brave or not generous then susan is old and vice versa. Everyone who is either not generous or funny is humble or not generous and vice versa. Everyone who is wise or not strong is both not wise and not old. If susan is either not curious or strong then mary is not funny or not generous. Everyone who is either creative or humble is both not calm and not curious and vice versa. If susan is both creative and curious then john is not patient or quiet and vice versa. Everyone who is generous is not tall. Everyone who is not generous is rich. Everyone who is calm is not brave. Everyone who is both not kind and humble is either creative or not rich and vice versa. If someone is brave or not creative then someone is not rich and vice versa. Everyone who is either not patient or tall is both wise and calm. If paul is both not old and not humble then someone is both rich and not curious and vice versa. If john is happy then someone is not happy or humble. If alice is either not calm or not rich then someone is either quiet or wise. Someone is both not quiet and happy. Mary is both not patient and not wise. Susan is both not brave and not kind. Someone is not tall or generous. Paul is not strong or not tall. Fred is either tall or not happy. Someone is either humble or not funny. Someone is not creative. | Mary is rich. | entailment | ((?[X]:(~generous(X)))<=>((~tall(fred)|happy(fred))))&
((?[X]:((~brave(X)|~generous(X))))<=>(old(susan)))&
(![X]:((~generous(X)<~>funny(X))<=>(humble(X)|~generous(X))))&
(![X]:((wise(X)|~strong(X))=>(~wise(X)&~old(X))))&
(((~curious(susan)<~>strong(susan)))=>((~funny(mary)|~generous(mary))))&
(![X]:((creative(X)<~>humble(X))<=>(~calm(X)&~curious(X))))&
(((creative(susan)&curious(susan)))<=>((~patient(john)|quiet(john))))&
(![X]:(generous(X)=>~tall(X)))&
(![X]:(~generous(X)=>rich(X)))&
(![X]:(calm(X)=>~brave(X)))&
(![X]:((~kind(X)&humble(X))<=>(creative(X)<~>~rich(X))))&
((?[X]:((brave(X)|~creative(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~patient(X)<~>tall(X))=>(wise(X)&calm(X))))&
(((~old(paul)&~humble(paul)))<=>(?[X]:((rich(X)&~curious(X)))))&
((happy(john))=>(?[X]:((~happy(X)|humble(X)))))&
(((~calm(alice)<~>~rich(alice)))=>(?[X]:((quiet(X)<~>wise(X)))))&
(?[X]:((~quiet(X)&happy(X))))&
((~patient(mary)&~wise(mary)))&
((~brave(susan)&~kind(susan)))&
(?[X]:((~tall(X)|generous(X))))&
((~strong(paul)|~tall(paul)))&
((tall(fred)<~>~happy(fred)))&
(?[X]:((humble(X)<~>~funny(X))))&
(?[X]:(~creative(X))) | rich(mary) | [
"p3",
"p7",
"p8",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2553587599859548418934563
% SZS output start Proof for 2553587599859548418934563
4. ! [X0] : ((~strong(X0) | wise(X0)) => (~old(X0) & ~wise(X0))) [input p3]
8. ! [X0] : (generous(X0) => ~tall(X0)) [input p7]
9. ! [X0] : (~generous(X0) => rich(X0)) [input p8]
13. ! [X0] : ((~patient(X0) <~> tall(X0)) => (calm(X0) & wise(X0))) [input p12]
18. ~wise(mary) & ~patient(mary) [input p17]
25. ~rich(mary) [input hypothesis]
27. ! [X0] : ((~old(X0) & ~wise(X0)) | (strong(X0) & ~wise(X0))) [ennf transformation 4]
30. ! [X0] : (~tall(X0) | ~generous(X0)) [ennf transformation 8]
31. ! [X0] : (rich(X0) | generous(X0)) [ennf transformation 9]
33. ! [X0] : ((calm(X0) & wise(X0)) | (~patient(X0) <=> tall(X0))) [ennf transformation 13]
59. ! [X0] : ((calm(X0) & wise(X0)) | ((~patient(X0) | ~tall(X0)) & (tall(X0) | patient(X0)))) [nnf transformation 33]
92. ~wise(X0) | ~wise(X0) [cnf transformation 27]
109. ~tall(X0) | ~generous(X0) [cnf transformation 30]
110. rich(X0) | generous(X0) [cnf transformation 31]
121. wise(X0) | tall(X0) | patient(X0) [cnf transformation 59]
136. ~patient(mary) [cnf transformation 18]
147. ~rich(mary) [cnf transformation 25]
148. ~wise(X0) [duplicate literal removal 92]
246. patient(X0) | tall(X0) [subsumption resolution 121,148]
322. generous(mary) [resolution 110,147]
326. tall(mary) [resolution 246,136]
329. ~generous(mary) [resolution 326,109]
330. $false [subsumption resolution 329,322]
% SZS output end Proof for 2553587599859548418934563
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not rich or not curious is not wise or not happy.
If someone is patient then alice is generous.
If someone is either tall or not strong then someone is not brave or tall and vice versa.
Everyone who is creative or not quiet is either not kind or rich and vice versa.
Everyone who is either not strong or kind is either not strong or rich and vice versa.
If john is not rich then paul is either funny or patient.
If someone is both not curious and not wise then susan is not quiet and vice versa.
Everyone who is both not rich and not kind is not wise and vice versa.
Everyone who is both not wise and not kind is happy and vice versa.
Everyone who is not tall or not wise is generous and vice versa.
Everyone who is either not happy or kind is humble or not quiet and vice versa.
Everyone who is brave is humble or not curious.
Everyone who is not rich or not curious is wise or not tall.
If mary is either not happy or not creative then lucy is not calm and vice versa.
If john is brave or not old then someone is not creative or tall.
Everyone who is not generous is either rich or creative.
Alice is either curious or kind.
Someone is patient or creative.
Lucy is not brave or not calm.
John is either not rich or not calm.
Lucy is happy.
Someone is kind or patient.
Fred is both not calm and quiet. | Mary is creative. | entailment | (![X]:((~rich(X)<~>~curious(X))=>(~wise(X)|~happy(X))))&
((?[X]:(patient(X)))=>(generous(alice)))&
((?[X]:((tall(X)<~>~strong(X))))<=>(?[X]:((~brave(X)|tall(X)))))&
(![X]:((creative(X)|~quiet(X))<=>(~kind(X)<~>rich(X))))&
(![X]:((~strong(X)<~>kind(X))<=>(~strong(X)<~>rich(X))))&
((~rich(john))=>((funny(paul)<~>patient(paul))))&
((?[X]:((~curious(X)&~wise(X))))<=>(~quiet(susan)))&
(![X]:((~rich(X)&~kind(X))<=>~wise(X)))&
(![X]:((~wise(X)&~kind(X))<=>happy(X)))&
(![X]:((~tall(X)|~wise(X))<=>generous(X)))&
(![X]:((~happy(X)<~>kind(X))<=>(humble(X)|~quiet(X))))&
(![X]:(brave(X)=>(humble(X)|~curious(X))))&
(![X]:((~rich(X)|~curious(X))=>(wise(X)|~tall(X))))&
(((~happy(mary)<~>~creative(mary)))<=>(~calm(lucy)))&
(((brave(john)|~old(john)))=>(?[X]:((~creative(X)|tall(X)))))&
(![X]:(~generous(X)=>(rich(X)<~>creative(X))))&
((curious(alice)<~>kind(alice)))&
(?[X]:((patient(X)|creative(X))))&
((~brave(lucy)|~calm(lucy)))&
((~rich(john)<~>~calm(john)))&
(happy(lucy))&
(?[X]:((kind(X)|patient(X))))&
((~calm(fred)&quiet(fred))) | creative(mary) | [
"p3",
"p4",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6710600557114544515641064
% SZS output start Proof for 6710600557114544515641064
4. ! [X0] : ((~quiet(X0) | creative(X0)) <=> (~kind(X0) <~> rich(X0))) [input p3]
5. ! [X0] : ((~strong(X0) <~> kind(X0)) <=> (~strong(X0) <~> rich(X0))) [input p4]
8. ! [X0] : ((~kind(X0) & ~rich(X0)) <=> ~wise(X0)) [input p7]
9. ! [X0] : ((~kind(X0) & ~wise(X0)) <=> happy(X0)) [input p8]
11. ! [X0] : ((~happy(X0) <~> kind(X0)) <=> (~quiet(X0) | humble(X0))) [input p10]
24. ~creative(mary) [input hypothesis]
46. ! [X0] : (((~quiet(X0) | creative(X0)) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0)))) & (((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | (quiet(X0) & ~creative(X0)))) [nnf transformation 4]
47. ! [X0] : ((~quiet(X0) | creative(X0) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0)))) & (((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | (quiet(X0) & ~creative(X0)))) [flattening 46]
48. ! [X0] : ((((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | ((~strong(X0) | ~rich(X0)) & (rich(X0) | strong(X0)))) & (((~rich(X0) | strong(X0)) & (rich(X0) | ~strong(X0))) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))))) [nnf transformation 5]
54. ! [X0] : (((~kind(X0) & ~rich(X0)) | wise(X0)) & (~wise(X0) | (kind(X0) | rich(X0)))) [nnf transformation 8]
55. ! [X0] : (((~kind(X0) & ~rich(X0)) | wise(X0)) & (~wise(X0) | kind(X0) | rich(X0))) [flattening 54]
56. ! [X0] : (((~kind(X0) & ~wise(X0)) | ~happy(X0)) & (happy(X0) | (kind(X0) | wise(X0)))) [nnf transformation 9]
57. ! [X0] : (((~kind(X0) & ~wise(X0)) | ~happy(X0)) & (happy(X0) | kind(X0) | wise(X0))) [flattening 56]
58. ! [X0] : ((((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) | (quiet(X0) & ~humble(X0))) & ((~quiet(X0) | humble(X0)) | ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0))))) [nnf transformation 11]
59. ! [X0] : ((((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) | (quiet(X0) & ~humble(X0))) & (~quiet(X0) | humble(X0) | ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0))))) [flattening 58]
83. ~quiet(X0) | creative(X0) | rich(X0) | kind(X0) [cnf transformation 47]
84. ~kind(X0) | creative(X0) | ~quiet(X0) | ~rich(X0) [cnf transformation 47]
86. rich(X0) | ~strong(X0) | ~strong(X0) | ~kind(X0) [cnf transformation 48]
87. ~rich(X0) | strong(X0) | kind(X0) | strong(X0) [cnf transformation 48]
90. kind(X0) | ~strong(X0) | ~strong(X0) | ~rich(X0) [cnf transformation 48]
91. ~kind(X0) | strong(X0) | rich(X0) | strong(X0) [cnf transformation 48]
98. ~wise(X0) | kind(X0) | rich(X0) [cnf transformation 55]
101. happy(X0) | kind(X0) | wise(X0) [cnf transformation 57]
103. ~kind(X0) | ~happy(X0) [cnf transformation 57]
108. kind(X0) | ~happy(X0) | quiet(X0) [cnf transformation 59]
110. ~kind(X0) | happy(X0) | quiet(X0) [cnf transformation 59]
131. ~creative(mary) [cnf transformation 24]
132. rich(X0) | ~strong(X0) | ~kind(X0) [duplicate literal removal 86]
133. ~rich(X0) | strong(X0) | kind(X0) [duplicate literal removal 87]
134. ~strong(X0) | kind(X0) | ~rich(X0) [duplicate literal removal 90]
135. ~kind(X0) | strong(X0) | rich(X0) [duplicate literal removal 91]
178. ~rich(X0) | kind(X0) [subsumption resolution 133,134]
179. ~kind(X0) | rich(X0) [subsumption resolution 132,135]
212. ~wise(X0) | kind(X0) [subsumption resolution 98,178]
213. kind(X0) | happy(X0) [subsumption resolution 101,212]
214. ~kind(X0) | quiet(X0) [subsumption resolution 110,103]
216. kind(X0) | quiet(X0) [subsumption resolution 108,213]
217. quiet(X0) [subsumption resolution 216,214]
229. 20 <=> creative(mary) [avatar definition]
230. ~creative(mary) <- (~20) [avatar component clause 229]
288. ~20 [avatar split clause 131,229]
311. happy(X0) | rich(X0) [resolution 213,179]
394. creative(X0) | rich(X0) | kind(X0) [resolution 83,217]
395. kind(X0) | creative(X0) [subsumption resolution 394,178]
397. creative(X1) | ~quiet(X1) | ~rich(X1) | happy(X1) [resolution 84,213]
404. creative(X1) | ~rich(X1) | happy(X1) [subsumption resolution 397,217]
405. creative(X1) | happy(X1) [subsumption resolution 404,311]
445. creative(X4) | ~happy(X4) [resolution 395,103]
451. creative(X4) [subsumption resolution 445,405]
464. $false <- (~20) [resolution 451,230]
468. 20 [avatar contradiction clause 464]
469. $false [avatar sat refutation 288,468]
% SZS output end Proof for 6710600557114544515641064
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is not tall.
Everyone who is not tall is not tall or strong and vice versa.
Everyone who is not wise or tall is calm or not brave and vice versa.
Everyone who is not strong or curious is both creative and brave and vice versa.
Everyone who is patient is not strong or not brave.
Everyone who is humble is both wise and not humble and vice versa.
If someone is either not happy or not calm then john is either generous or not humble.
If alice is both kind and quiet then someone is creative or not patient.
Everyone who is funny is kind or not kind and vice versa.
If paul is either curious or not brave then someone is both not kind and not funny and vice versa.
Everyone who is either patient or brave is funny or calm and vice versa.
If lucy is either generous or not patient then someone is both humble and tall and vice versa.
Everyone who is patient or wise is quiet and vice versa.
Everyone who is wise is either creative or not funny.
If someone is not happy then someone is kind.
Everyone who is either rich or tall is either not funny or not kind and vice versa.
John is rich or not curious.
John is both not patient and not quiet.
Someone is both not curious and brave.
John is either not happy or not creative.
John is either patient or strong.
Susan is both not creative and brave.
Someone is not brave or not wise.
Alice is not calm or kind. | Alice is not brave. | neutral | (![X]:(~calm(X)=>~tall(X)))&
(![X]:(~tall(X)<=>(~tall(X)|strong(X))))&
(![X]:((~wise(X)|tall(X))<=>(calm(X)|~brave(X))))&
(![X]:((~strong(X)|curious(X))<=>(creative(X)&brave(X))))&
(![X]:(patient(X)=>(~strong(X)|~brave(X))))&
(![X]:(humble(X)<=>(wise(X)&~humble(X))))&
((?[X]:((~happy(X)<~>~calm(X))))=>((generous(john)<~>~humble(john))))&
(((kind(alice)&quiet(alice)))=>(?[X]:((creative(X)|~patient(X)))))&
(![X]:(funny(X)<=>(kind(X)|~kind(X))))&
(((curious(paul)<~>~brave(paul)))<=>(?[X]:((~kind(X)&~funny(X)))))&
(![X]:((patient(X)<~>brave(X))<=>(funny(X)|calm(X))))&
(((generous(lucy)<~>~patient(lucy)))<=>(?[X]:((humble(X)&tall(X)))))&
(![X]:((patient(X)|wise(X))<=>quiet(X)))&
(![X]:(wise(X)=>(creative(X)<~>~funny(X))))&
((?[X]:(~happy(X)))=>(?[X]:(kind(X))))&
(![X]:((rich(X)<~>tall(X))<=>(~funny(X)<~>~kind(X))))&
((rich(john)|~curious(john)))&
((~patient(john)&~quiet(john)))&
(?[X]:((~curious(X)&brave(X))))&
((~happy(john)<~>~creative(john)))&
((patient(john)<~>strong(john)))&
((~creative(susan)&brave(susan)))&
(?[X]:((~brave(X)|~wise(X))))&
((~calm(alice)|kind(alice))) | ~brave(alice) | [] | null | 0 |
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