premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is not quiet is both kind and not kind and vice versa.
Everyone who is rich or generous is both not happy and not old and vice versa.
Everyone who is not rich or creative is both not happy and funny.
If someone is patient then someone is brave or not curious and vice versa.
Everyone who is generous or not curious is both calm and not brave and vice versa.
Everyone who is not rich is not curious or not wise and vice versa.
Everyone who is not kind or rich is either not generous or quiet.
Everyone who is both not strong and not creative is calm.
If someone is not brave or patient then someone is both not brave and funny.
Everyone who is not humble or happy is either not tall or not humble and vice versa.
Everyone who is either not rich or not old is both strong and funny and vice versa.
If john is strong or creative then susan is not brave or not old and vice versa.
Everyone who is brave or calm is not kind.
Everyone who is quiet or not quiet is both wise and funny and vice versa.
Everyone who is not old is brave or not brave.
If john is not wise or not quiet then susan is both not old and rich and vice versa.
Lucy is either not kind or happy.
Susan is humble.
Lucy is patient or not old.
Someone is tall.
Paul is either not old or not patient.
Someone is curious or not humble. | Susan is not tall. | contradiction | (![X]:(~quiet(X)<=>(kind(X)&~kind(X))))&
(![X]:((rich(X)|generous(X))<=>(~happy(X)&~old(X))))&
(![X]:((~rich(X)|creative(X))=>(~happy(X)&funny(X))))&
((?[X]:(patient(X)))<=>(?[X]:((brave(X)|~curious(X)))))&
(![X]:((generous(X)|~curious(X))<=>(calm(X)&~brave(X))))&
(![X]:(~rich(X)<=>(~curious(X)|~wise(X))))&
(![X]:((~kind(X)|rich(X))=>(~generous(X)<~>quiet(X))))&
(![X]:((~strong(X)&~creative(X))=>calm(X)))&
((?[X]:((~brave(X)|patient(X))))=>(?[X]:((~brave(X)&funny(X)))))&
(![X]:((~humble(X)|happy(X))<=>(~tall(X)<~>~humble(X))))&
(![X]:((~rich(X)<~>~old(X))<=>(strong(X)&funny(X))))&
(((strong(john)|creative(john)))<=>((~brave(susan)|~old(susan))))&
(![X]:((brave(X)|calm(X))=>~kind(X)))&
(![X]:((quiet(X)|~quiet(X))<=>(wise(X)&funny(X))))&
(![X]:(~old(X)=>(brave(X)|~brave(X))))&
(((~wise(john)|~quiet(john)))<=>((~old(susan)&rich(susan))))&
((~kind(lucy)<~>happy(lucy)))&
(humble(susan))&
((patient(lucy)|~old(lucy)))&
(?[X]:(tall(X)))&
((~old(paul)<~>~patient(paul)))&
(?[X]:((curious(X)|~humble(X)))) | ~tall(susan) | [
"p1",
"p2",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5903726795976040369180411
% SZS output start Proof for 5903726795976040369180411
2. ! [X0] : ((generous(X0) | rich(X0)) <=> (~old(X0) & ~happy(X0))) [input p1]
3. ! [X0] : ((creative(X0) | ~rich(X0)) => (funny(X0) & ~happy(X0))) [input p2]
10. ! [X0] : ((happy(X0) | ~humble(X0)) <=> (~tall(X0) <~> ~humble(X0))) [input p9]
23. ~tall(susan) [input hypothesis]
26. ! [X0] : ((funny(X0) & ~happy(X0)) | (~creative(X0) & rich(X0))) [ennf transformation 3]
36. ! [X0] : (((generous(X0) | rich(X0)) | (old(X0) | happy(X0))) & ((~old(X0) & ~happy(X0)) | (~generous(X0) & ~rich(X0)))) [nnf transformation 2]
37. ! [X0] : ((generous(X0) | rich(X0) | old(X0) | happy(X0)) & ((~old(X0) & ~happy(X0)) | (~generous(X0) & ~rich(X0)))) [flattening 36]
51. ! [X0] : (((happy(X0) | ~humble(X0)) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0)))) & (((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | (~happy(X0) & humble(X0)))) [nnf transformation 10]
52. ! [X0] : ((happy(X0) | ~humble(X0) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0)))) & (((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | (~happy(X0) & humble(X0)))) [flattening 51]
70. ~happy(X0) | ~rich(X0) [cnf transformation 37]
75. ~happy(X0) | rich(X0) [cnf transformation 26]
101. humble(X0) | tall(X0) | humble(X0) [cnf transformation 52]
103. happy(X0) | ~humble(X0) | ~humble(X0) | tall(X0) [cnf transformation 52]
136. ~tall(susan) [cnf transformation 23]
137. humble(X0) | tall(X0) [duplicate literal removal 101]
138. happy(X0) | ~humble(X0) | tall(X0) [duplicate literal removal 103]
140. ~happy(X0) [subsumption resolution 75,70]
182. ~humble(X0) | tall(X0) [subsumption resolution 138,140]
183. tall(X0) [subsumption resolution 137,182]
242. $false [subsumption resolution 136,183]
% SZS output end Proof for 5903726795976040369180411
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is not funny and vice versa. If alice is not brave then someone is not patient or not funny and vice versa. Everyone who is either old or humble is patient or wise. Everyone who is funny or not tall is either rich or wise and vice versa. Everyone who is either not old or tall is either not generous or calm and vice versa. If alice is not calm or not curious then someone is either creative or not generous. Everyone who is not brave or not humble is either kind or creative and vice versa. Everyone who is not happy or not old is not curious or not strong and vice versa. If susan is both rich and funny then susan is quiet. If john is either not funny or curious then someone is strong or not generous. Everyone who is generous or brave is not kind or not tall and vice versa. Everyone who is not curious is generous. Everyone who is both not patient and old is not creative or curious. If someone is either not old or quiet then susan is both quiet and not strong and vice versa. Everyone who is either not quiet or not kind is not quiet or not tall. Everyone who is not calm or creative is not rich and vice versa. Someone is both not tall and humble. Paul is not quiet. Fred is either kind or not humble. Mary is not wise or kind. Alice is creative or not old. Paul is both curious and not generous. Paul is rich. Someone is generous or patient. | Mary is wise. | neutral | (![X]:(~calm(X)<=>~funny(X)))&
((~brave(alice))<=>(?[X]:((~patient(X)|~funny(X)))))&
(![X]:((old(X)<~>humble(X))=>(patient(X)|wise(X))))&
(![X]:((funny(X)|~tall(X))<=>(rich(X)<~>wise(X))))&
(![X]:((~old(X)<~>tall(X))<=>(~generous(X)<~>calm(X))))&
(((~calm(alice)|~curious(alice)))=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:((~brave(X)|~humble(X))<=>(kind(X)<~>creative(X))))&
(![X]:((~happy(X)|~old(X))<=>(~curious(X)|~strong(X))))&
(((rich(susan)&funny(susan)))=>(quiet(susan)))&
(((~funny(john)<~>curious(john)))=>(?[X]:((strong(X)|~generous(X)))))&
(![X]:((generous(X)|brave(X))<=>(~kind(X)|~tall(X))))&
(![X]:(~curious(X)=>generous(X)))&
(![X]:((~patient(X)&old(X))=>(~creative(X)|curious(X))))&
((?[X]:((~old(X)<~>quiet(X))))<=>((quiet(susan)&~strong(susan))))&
(![X]:((~quiet(X)<~>~kind(X))=>(~quiet(X)|~tall(X))))&
(![X]:((~calm(X)|creative(X))<=>~rich(X)))&
(?[X]:((~tall(X)&humble(X))))&
(~quiet(paul))&
((kind(fred)<~>~humble(fred)))&
((~wise(mary)|kind(mary)))&
((creative(alice)|~old(alice)))&
((curious(paul)&~generous(paul)))&
(rich(paul))&
(?[X]:((generous(X)|patient(X)))) | wise(mary) | [] | null | 0 |
Everyone who is old or wise is not tall or happy. Everyone who is generous or not patient is both not brave and old. Everyone who is either not funny or not brave is not brave or wise and vice versa. Everyone who is funny is rich or not tall and vice versa. Everyone who is wise is not strong and vice versa. Everyone who is either strong or rich is both not rich and not curious and vice versa. If mary is both not calm and creative then susan is brave or curious and vice versa. Everyone who is either not tall or generous is not generous or creative. Everyone who is either not humble or funny is strong. Everyone who is either brave or generous is both brave and quiet. Everyone who is funny is either humble or tall. If mary is either not kind or not creative then john is both not creative and not generous and vice versa. Everyone who is both curious and happy is strong or not brave and vice versa. If someone is both not funny and curious then lucy is both not creative and not happy and vice versa. Everyone who is not curious or brave is not patient or not generous. Mary is not generous. Mary is either patient or funny. Someone is old or strong. John is both not generous and quiet. Alice is calm or not creative. Someone is both creative and strong. | Mary is not kind. | neutral | (![X]:((old(X)|wise(X))=>(~tall(X)|happy(X))))&
(![X]:((generous(X)|~patient(X))=>(~brave(X)&old(X))))&
(![X]:((~funny(X)<~>~brave(X))<=>(~brave(X)|wise(X))))&
(![X]:(funny(X)<=>(rich(X)|~tall(X))))&
(![X]:(wise(X)<=>~strong(X)))&
(![X]:((strong(X)<~>rich(X))<=>(~rich(X)&~curious(X))))&
(((~calm(mary)&creative(mary)))<=>((brave(susan)|curious(susan))))&
(![X]:((~tall(X)<~>generous(X))=>(~generous(X)|creative(X))))&
(![X]:((~humble(X)<~>funny(X))=>strong(X)))&
(![X]:((brave(X)<~>generous(X))=>(brave(X)&quiet(X))))&
(![X]:(funny(X)=>(humble(X)<~>tall(X))))&
(((~kind(mary)<~>~creative(mary)))<=>((~creative(john)&~generous(john))))&
(![X]:((curious(X)&happy(X))<=>(strong(X)|~brave(X))))&
((?[X]:((~funny(X)&curious(X))))<=>((~creative(lucy)&~happy(lucy))))&
(![X]:((~curious(X)|brave(X))=>(~patient(X)|~generous(X))))&
(~generous(mary))&
((patient(mary)<~>funny(mary)))&
(?[X]:((old(X)|strong(X))))&
((~generous(john)&quiet(john)))&
((calm(alice)|~creative(alice)))&
(?[X]:((creative(X)&strong(X)))) | ~kind(mary) | [] | null | 0 |
Everyone who is both humble and patient is both wise and not generous. Everyone who is not calm is both not tall and brave. Everyone who is rich or not wise is not funny or not kind and vice versa. Everyone who is curious is not calm or not rich. Everyone who is not patient is both patient and not generous and vice versa. Everyone who is not brave or humble is creative. If someone is both not calm and not humble then someone is humble or not patient. Everyone who is old is both not kind and kind and vice versa. If someone is curious or wise then john is humble or not strong. If someone is not happy or curious then lucy is both creative and old and vice versa. Everyone who is not curious or brave is either not quiet or not wise and vice versa. Everyone who is generous is either not wise or humble and vice versa. If someone is both not humble and not brave then mary is not funny and vice versa. Everyone who is either patient or calm is either creative or wise. If someone is either not creative or funny then lucy is happy or not quiet. Someone is both not curious and not rich. Paul is generous. Alice is either not generous or patient. Someone is not humble. Someone is kind or funny. | Alice is quiet. | entailment | (![X]:((humble(X)&patient(X))=>(wise(X)&~generous(X))))&
(![X]:(~calm(X)=>(~tall(X)&brave(X))))&
(![X]:((rich(X)|~wise(X))<=>(~funny(X)|~kind(X))))&
(![X]:(curious(X)=>(~calm(X)|~rich(X))))&
(![X]:(~patient(X)<=>(patient(X)&~generous(X))))&
(![X]:((~brave(X)|humble(X))=>creative(X)))&
((?[X]:((~calm(X)&~humble(X))))=>(?[X]:((humble(X)|~patient(X)))))&
(![X]:(old(X)<=>(~kind(X)&kind(X))))&
((?[X]:((curious(X)|wise(X))))=>((humble(john)|~strong(john))))&
((?[X]:((~happy(X)|curious(X))))<=>((creative(lucy)&old(lucy))))&
(![X]:((~curious(X)|brave(X))<=>(~quiet(X)<~>~wise(X))))&
(![X]:(generous(X)<=>(~wise(X)<~>humble(X))))&
((?[X]:((~humble(X)&~brave(X))))<=>(~funny(mary)))&
(![X]:((patient(X)<~>calm(X))=>(creative(X)<~>wise(X))))&
((?[X]:((~creative(X)<~>funny(X))))=>((happy(lucy)|~quiet(lucy))))&
(?[X]:((~curious(X)&~rich(X))))&
(generous(paul))&
((~generous(alice)<~>patient(alice)))&
(?[X]:(~humble(X)))&
(?[X]:((kind(X)|funny(X)))) | quiet(alice) | [
"p0",
"p4",
"p7",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5512427216836725140701217
% SZS output start Proof for 5512427216836725140701217
1. ! [X0] : ((patient(X0) & humble(X0)) => (~generous(X0) & wise(X0))) [input p0]
5. ! [X0] : (~patient(X0) <=> (~generous(X0) & patient(X0))) [input p4]
8. ! [X0] : (old(X0) <=> (kind(X0) & ~kind(X0))) [input p7]
10. ? [X0] : (curious(X0) | ~happy(X0)) <=> (old(lucy) & creative(lucy)) [input p9]
11. ! [X0] : ((brave(X0) | ~curious(X0)) <=> (~quiet(X0) <~> ~wise(X0))) [input p10]
12. ! [X0] : (generous(X0) <=> (~wise(X0) <~> humble(X0))) [input p11]
21. ~quiet(alice) [input hypothesis]
25. ! [X0] : ((~generous(X0) & wise(X0)) | (~patient(X0) | ~humble(X0))) [ennf transformation 1]
26. ! [X0] : ((~generous(X0) & wise(X0)) | ~patient(X0) | ~humble(X0)) [flattening 25]
37. ! [X0] : ((~patient(X0) | (generous(X0) | ~patient(X0))) & ((~generous(X0) & patient(X0)) | patient(X0))) [nnf transformation 5]
38. ! [X0] : ((~patient(X0) | generous(X0) | ~patient(X0)) & ((~generous(X0) & patient(X0)) | patient(X0))) [flattening 37]
42. ! [X0] : ((old(X0) | (~kind(X0) | kind(X0))) & ((kind(X0) & ~kind(X0)) | ~old(X0))) [nnf transformation 8]
43. ! [X0] : ((old(X0) | ~kind(X0) | kind(X0)) & ((kind(X0) & ~kind(X0)) | ~old(X0))) [flattening 42]
44. (? [X0] : (curious(X0) | ~happy(X0)) | (~old(lucy) | ~creative(lucy))) & ((old(lucy) & creative(lucy)) | ! [X0] : (~curious(X0) & happy(X0))) [nnf transformation 10]
45. (? [X0] : (curious(X0) | ~happy(X0)) | ~old(lucy) | ~creative(lucy)) & ((old(lucy) & creative(lucy)) | ! [X0] : (~curious(X0) & happy(X0))) [flattening 44]
46. (? [X0] : (curious(X0) | ~happy(X0)) | ~old(lucy) | ~creative(lucy)) & ((old(lucy) & creative(lucy)) | ! [X1] : (~curious(X1) & happy(X1))) [rectify 45]
47. ? [X0] : (curious(X0) | ~happy(X0)) => (curious(sK1) | ~happy(sK1)) [choice axiom]
48. ((curious(sK1) | ~happy(sK1)) | ~old(lucy) | ~creative(lucy)) & ((old(lucy) & creative(lucy)) | ! [X1] : (~curious(X1) & happy(X1))) [skolemisation 46,47]
49. ! [X0] : (((brave(X0) | ~curious(X0)) | ((~quiet(X0) | wise(X0)) & (~wise(X0) | quiet(X0)))) & (((wise(X0) | quiet(X0)) & (~wise(X0) | ~quiet(X0))) | (~brave(X0) & curious(X0)))) [nnf transformation 11]
50. ! [X0] : ((brave(X0) | ~curious(X0) | ((~quiet(X0) | wise(X0)) & (~wise(X0) | quiet(X0)))) & (((wise(X0) | quiet(X0)) & (~wise(X0) | ~quiet(X0))) | (~brave(X0) & curious(X0)))) [flattening 49]
51. ! [X0] : ((generous(X0) | ((~wise(X0) | ~humble(X0)) & (humble(X0) | wise(X0)))) & (((~humble(X0) | wise(X0)) & (humble(X0) | ~wise(X0))) | ~generous(X0))) [nnf transformation 12]
66. ~generous(X0) | ~patient(X0) | ~humble(X0) [cnf transformation 26]
73. patient(X0) | patient(X0) [cnf transformation 38]
75. ~patient(X0) | generous(X0) | ~patient(X0) [cnf transformation 38]
79. ~kind(X0) | ~old(X0) [cnf transformation 43]
80. ~old(X0) | kind(X0) [cnf transformation 43]
85. old(lucy) | ~curious(X1) [cnf transformation 48]
89. wise(X0) | quiet(X0) | curious(X0) [cnf transformation 50]
93. ~generous(X0) | ~wise(X0) | humble(X0) [cnf transformation 51]
113. ~quiet(alice) [cnf transformation 21]
114. patient(X0) [duplicate literal removal 73]
115. ~patient(X0) | generous(X0) [duplicate literal removal 75]
125. ~old(X0) [subsumption resolution 79,80]
126. ~curious(X1) [subsumption resolution 85,125]
128. quiet(X0) | wise(X0) [subsumption resolution 89,126]
162. generous(X0) [resolution 115,114]
163. wise(alice) [resolution 128,113]
169. ~patient(X0) | ~humble(X0) [resolution 66,162]
171. ~humble(X0) [subsumption resolution 169,114]
209. ~wise(X0) | humble(X0) [resolution 93,162]
211. ~wise(X0) [subsumption resolution 209,171]
220. $false [resolution 211,163]
% SZS output end Proof for 5512427216836725140701217
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is either not funny or not generous then paul is both not patient and not tall and vice versa.
If someone is calm then fred is funny.
Everyone who is either funny or not happy is funny or not old and vice versa.
Everyone who is either not creative or not wise is not patient.
If someone is both calm and not humble then someone is either quiet or creative and vice versa.
If someone is both not creative and not tall then someone is not patient or quiet and vice versa.
Everyone who is either not curious or quiet is either funny or happy and vice versa.
Everyone who is both humble and not old is both not curious and not kind and vice versa.
If someone is either quiet or curious then someone is both quiet and not quiet and vice versa.
If alice is either not quiet or old then someone is either not wise or not strong and vice versa.
If someone is both creative and strong then someone is not brave.
If fred is wise or not funny then someone is not old or rich and vice versa.
If someone is either kind or curious then john is wise or not creative.
Everyone who is not brave is both not patient and not calm.
If someone is either not humble or brave then someone is both not funny and generous and vice versa.
Everyone who is not kind is both not happy and calm and vice versa.
Lucy is patient.
Susan is humble or strong.
John is not creative.
Someone is not funny or not old.
Paul is old or funny. | Susan is happy. | entailment | ((?[X]:((~funny(X)<~>~generous(X))))<=>((~patient(paul)&~tall(paul))))&
((?[X]:(calm(X)))=>(funny(fred)))&
(![X]:((funny(X)<~>~happy(X))<=>(funny(X)|~old(X))))&
(![X]:((~creative(X)<~>~wise(X))=>~patient(X)))&
((?[X]:((calm(X)&~humble(X))))<=>(?[X]:((quiet(X)<~>creative(X)))))&
((?[X]:((~creative(X)&~tall(X))))<=>(?[X]:((~patient(X)|quiet(X)))))&
(![X]:((~curious(X)<~>quiet(X))<=>(funny(X)<~>happy(X))))&
(![X]:((humble(X)&~old(X))<=>(~curious(X)&~kind(X))))&
((?[X]:((quiet(X)<~>curious(X))))<=>(?[X]:((quiet(X)&~quiet(X)))))&
(((~quiet(alice)<~>old(alice)))<=>(?[X]:((~wise(X)<~>~strong(X)))))&
((?[X]:((creative(X)&strong(X))))=>(?[X]:(~brave(X))))&
(((wise(fred)|~funny(fred)))<=>(?[X]:((~old(X)|rich(X)))))&
((?[X]:((kind(X)<~>curious(X))))=>((wise(john)|~creative(john))))&
(![X]:(~brave(X)=>(~patient(X)&~calm(X))))&
((?[X]:((~humble(X)<~>brave(X))))<=>(?[X]:((~funny(X)&generous(X)))))&
(![X]:(~kind(X)<=>(~happy(X)&calm(X))))&
(patient(lucy))&
((humble(susan)|strong(susan)))&
(~creative(john))&
(?[X]:((~funny(X)|~old(X))))&
((old(paul)|funny(paul))) | happy(susan) | [
"p2",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1733685461063971920518715
% SZS output start Proof for 1733685461063971920518715
3. ! [X0] : ((funny(X0) <~> ~happy(X0)) <=> (~old(X0) | funny(X0))) [input p2]
7. ! [X0] : ((~curious(X0) <~> quiet(X0)) <=> (funny(X0) <~> happy(X0))) [input p6]
9. ? [X0] : (quiet(X0) <~> curious(X0)) <=> ? [X0] : (~quiet(X0) & quiet(X0)) [input p8]
22. ~happy(susan) [input hypothesis]
25. ? [X0] : (quiet(X0) <~> curious(X0)) <=> ? [X1] : (~quiet(X1) & quiet(X1)) [rectify 9]
39. ! [X0] : ((((happy(X0) | ~funny(X0)) & (~happy(X0) | funny(X0))) | (old(X0) & ~funny(X0))) & ((~old(X0) | funny(X0)) | ((funny(X0) | happy(X0)) & (~happy(X0) | ~funny(X0))))) [nnf transformation 3]
40. ! [X0] : ((((happy(X0) | ~funny(X0)) & (~happy(X0) | funny(X0))) | (old(X0) & ~funny(X0))) & (~old(X0) | funny(X0) | ((funny(X0) | happy(X0)) & (~happy(X0) | ~funny(X0))))) [flattening 39]
52. ! [X0] : ((((~quiet(X0) | curious(X0)) & (quiet(X0) | ~curious(X0))) | ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0)))) & (((~happy(X0) | ~funny(X0)) & (happy(X0) | funny(X0))) | ((~curious(X0) | ~quiet(X0)) & (quiet(X0) | curious(X0))))) [nnf transformation 7]
55. (? [X0] : ((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | ! [X1] : (quiet(X1) | ~quiet(X1))) & (? [X1] : (~quiet(X1) & quiet(X1)) | ! [X0] : ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0)))) [nnf transformation 25]
56. (? [X0] : ((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | ! [X1] : (quiet(X1) | ~quiet(X1))) & (? [X2] : (~quiet(X2) & quiet(X2)) | ! [X3] : ((quiet(X3) | ~curious(X3)) & (curious(X3) | ~quiet(X3)))) [rectify 55]
57. ? [X0] : ((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) => ((~curious(sK5) | ~quiet(sK5)) & (curious(sK5) | quiet(sK5))) [choice axiom]
58. ? [X2] : (~quiet(X2) & quiet(X2)) => (~quiet(sK6) & quiet(sK6)) [choice axiom]
59. (((~curious(sK5) | ~quiet(sK5)) & (curious(sK5) | quiet(sK5))) | ! [X1] : (quiet(X1) | ~quiet(X1))) & ((~quiet(sK6) & quiet(sK6)) | ! [X3] : ((quiet(X3) | ~curious(X3)) & (curious(X3) | ~quiet(X3)))) [skolemisation 56,58,57]
93. happy(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 40]
108. happy(X0) | funny(X0) | quiet(X0) | curious(X0) [cnf transformation 52]
109. happy(X0) | funny(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 52]
110. ~happy(X0) | ~funny(X0) | quiet(X0) | curious(X0) [cnf transformation 52]
111. ~happy(X0) | ~funny(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 52]
120. quiet(sK6) | curious(X3) | ~quiet(X3) [cnf transformation 59]
121. quiet(sK6) | quiet(X3) | ~curious(X3) [cnf transformation 59]
122. ~quiet(sK6) | curious(X3) | ~quiet(X3) [cnf transformation 59]
123. ~quiet(sK6) | quiet(X3) | ~curious(X3) [cnf transformation 59]
157. ~happy(susan) [cnf transformation 22]
159. ~funny(X0) | happy(X0) [duplicate literal removal 93]
258. ~curious(X0) | ~funny(X0) | ~quiet(X0) [subsumption resolution 111,159]
259. ~funny(X0) | quiet(X0) | curious(X0) [subsumption resolution 110,159]
260. ~curious(X0) | happy(X0) | ~quiet(X0) [subsumption resolution 109,258]
261. curious(X0) | quiet(X0) | happy(X0) [subsumption resolution 108,259]
263. 23 <=> ! [X3] : (quiet(X3) | ~curious(X3)) [avatar definition]
264. ~curious(X3) | quiet(X3) <- (23) [avatar component clause 263]
266. 24 <=> quiet(sK6) [avatar definition]
269. 23 | ~24 [avatar split clause 123,266,263]
271. 25 <=> ! [X3] : (curious(X3) | ~quiet(X3)) [avatar definition]
272. ~quiet(X3) | curious(X3) <- (25) [avatar component clause 271]
273. 25 | ~24 [avatar split clause 122,266,271]
274. 23 | 24 [avatar split clause 121,266,263]
275. 25 | 24 [avatar split clause 120,266,271]
493. quiet(X3) | happy(X3) | quiet(X3) <- (23) [resolution 261,264]
494. quiet(X3) | happy(X3) <- (23) [duplicate literal removal 493]
531. curious(X1) | happy(X1) <- (23, 25) [resolution 494,272]
536. happy(X1) | happy(X1) | ~quiet(X1) <- (23, 25) [resolution 531,260]
540. happy(X1) | ~quiet(X1) <- (23, 25) [duplicate literal removal 536]
541. happy(X1) <- (23, 25) [subsumption resolution 540,494]
542. $false <- (23, 25) [resolution 541,157]
545. ~23 | ~25 [avatar contradiction clause 542]
546. $false [avatar sat refutation 269,273,274,275,545]
% SZS output end Proof for 1733685461063971920518715
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or generous is curious. Everyone who is either not patient or wise is both not rich and humble. If someone is not rich then someone is both curious and old. Everyone who is both not old and funny is not strong or patient. If lucy is curious or not creative then john is both not calm and not curious and vice versa. If someone is wise then someone is curious or not humble and vice versa. Everyone who is tall or calm is either not humble or funny. Everyone who is either strong or kind is both not generous and not kind. Everyone who is humble or not calm is either not curious or not strong. Everyone who is both not creative and not kind is either tall or happy and vice versa. If fred is both not wise and wise then mary is either wise or not strong and vice versa. Everyone who is wise or old is either rich or tall. Everyone who is patient or old is not patient and vice versa. If someone is both rich and not old then susan is brave and vice versa. Everyone who is not generous is both not quiet and not wise. If paul is both not creative and funny then someone is both patient and not kind and vice versa. Someone is not tall. Fred is not kind. Fred is both not curious and not kind. Someone is not calm. Someone is wise. Mary is either not happy or curious. Someone is either not generous or wise. | Lucy is not rich. | entailment | (![X]:((~calm(X)|generous(X))=>curious(X)))&
(![X]:((~patient(X)<~>wise(X))=>(~rich(X)&humble(X))))&
((?[X]:(~rich(X)))=>(?[X]:((curious(X)&old(X)))))&
(![X]:((~old(X)&funny(X))=>(~strong(X)|patient(X))))&
(((curious(lucy)|~creative(lucy)))<=>((~calm(john)&~curious(john))))&
((?[X]:(wise(X)))<=>(?[X]:((curious(X)|~humble(X)))))&
(![X]:((tall(X)|calm(X))=>(~humble(X)<~>funny(X))))&
(![X]:((strong(X)<~>kind(X))=>(~generous(X)&~kind(X))))&
(![X]:((humble(X)|~calm(X))=>(~curious(X)<~>~strong(X))))&
(![X]:((~creative(X)&~kind(X))<=>(tall(X)<~>happy(X))))&
(((~wise(fred)&wise(fred)))<=>((wise(mary)<~>~strong(mary))))&
(![X]:((wise(X)|old(X))=>(rich(X)<~>tall(X))))&
(![X]:((patient(X)|old(X))<=>~patient(X)))&
((?[X]:((rich(X)&~old(X))))<=>(brave(susan)))&
(![X]:(~generous(X)=>(~quiet(X)&~wise(X))))&
(((~creative(paul)&funny(paul)))<=>(?[X]:((patient(X)&~kind(X)))))&
(?[X]:(~tall(X)))&
(~kind(fred))&
((~curious(fred)&~kind(fred)))&
(?[X]:(~calm(X)))&
(?[X]:(wise(X)))&
((~happy(mary)<~>curious(mary)))&
(?[X]:((~generous(X)<~>wise(X)))) | ~rich(lucy) | [
"p0",
"p1",
"p4",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8142059918396429647157210
% SZS output start Proof for 8142059918396429647157210
1. ! [X0] : ((generous(X0) | ~calm(X0)) => curious(X0)) [input p0]
2. ! [X0] : ((~patient(X0) <~> wise(X0)) => (humble(X0) & ~rich(X0))) [input p1]
5. (~creative(lucy) | curious(lucy)) <=> (~curious(john) & ~calm(john)) [input p4]
13. ! [X0] : ((old(X0) | patient(X0)) <=> ~patient(X0)) [input p12]
15. ! [X0] : (~generous(X0) => (~wise(X0) & ~quiet(X0))) [input p14]
24. rich(lucy) [input hypothesis]
27. ! [X0] : (~generous(X0) => ~wise(X0)) [pure predicate removal 15]
28. ! [X0] : (curious(X0) | (~generous(X0) & calm(X0))) [ennf transformation 1]
29. ! [X0] : ((humble(X0) & ~rich(X0)) | (~patient(X0) <=> wise(X0))) [ennf transformation 2]
37. ! [X0] : (~wise(X0) | generous(X0)) [ennf transformation 27]
38. ! [X0] : ((humble(X0) & ~rich(X0)) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) [nnf transformation 29]
42. ((~creative(lucy) | curious(lucy)) | (curious(john) | calm(john))) & ((~curious(john) & ~calm(john)) | (creative(lucy) & ~curious(lucy))) [nnf transformation 5]
43. (~creative(lucy) | curious(lucy) | curious(john) | calm(john)) & ((~curious(john) & ~calm(john)) | (creative(lucy) & ~curious(lucy))) [flattening 42]
57. ! [X0] : (((old(X0) | patient(X0)) | patient(X0)) & (~patient(X0) | (~old(X0) & ~patient(X0)))) [nnf transformation 13]
58. ! [X0] : ((old(X0) | patient(X0) | patient(X0)) & (~patient(X0) | (~old(X0) & ~patient(X0)))) [flattening 57]
78. curious(X0) | calm(X0) [cnf transformation 28]
79. ~generous(X0) | curious(X0) [cnf transformation 28]
80. ~rich(X0) | wise(X0) | patient(X0) [cnf transformation 38]
87. ~calm(john) | ~curious(lucy) [cnf transformation 43]
89. ~curious(john) | ~curious(lucy) [cnf transformation 43]
123. ~patient(X0) | ~patient(X0) [cnf transformation 58]
129. ~wise(X0) | generous(X0) [cnf transformation 37]
144. rich(lucy) [cnf transformation 24]
145. ~patient(X0) [duplicate literal removal 123]
166. 5 <=> curious(john) [avatar definition]
168. ~curious(john) <- (~5) [avatar component clause 166]
171. 6 <=> curious(lucy) [avatar definition]
173. ~curious(lucy) <- (~6) [avatar component clause 171]
174. ~6 | ~5 [avatar split clause 89,166,171]
176. 7 <=> calm(john) [avatar definition]
178. ~calm(john) <- (~7) [avatar component clause 176]
180. ~6 | ~7 [avatar split clause 87,176,171]
275. calm(john) <- (~5) [resolution 78,168]
278. $false <- (~5, ~7) [subsumption resolution 275,178]
279. 5 | 7 [avatar contradiction clause 278]
294. wise(lucy) | patient(lucy) [resolution 80,144]
296. wise(lucy) [subsumption resolution 294,145]
298. generous(lucy) [resolution 296,129]
310. curious(lucy) [resolution 298,79]
311. $false <- (~6) [subsumption resolution 310,173]
312. 6 [avatar contradiction clause 311]
313. $false [avatar sat refutation 174,180,279,312]
% SZS output end Proof for 8142059918396429647157210
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is either curious or not curious then alice is old.
Everyone who is either not strong or not brave is not rich or not quiet and vice versa.
Everyone who is curious is calm and vice versa.
Everyone who is either not brave or happy is either not kind or generous.
Everyone who is not funny is either calm or not kind.
If someone is both not calm and rich then john is funny or calm and vice versa.
Everyone who is not brave is both quiet and not funny.
If someone is either not brave or not rich then alice is creative or not generous and vice versa.
Everyone who is not old is calm or quiet.
If someone is not kind or quiet then paul is both not patient and brave.
Everyone who is old or creative is happy.
Everyone who is both not tall and not brave is both old and not old.
Everyone who is both kind and not strong is both humble and not patient.
If susan is both not happy and not generous then someone is creative or not wise.
Everyone who is both generous and not quiet is either old or quiet.
Everyone who is quiet is not wise.
Lucy is old.
Fred is either not generous or not creative.
Alice is wise.
Susan is both not wise and not old.
Fred is brave.
Someone is patient.
Someone is rich.
Someone is either not happy or not generous. | Alice is old. | entailment | (((curious(alice)<~>~curious(alice)))=>(old(alice)))&
(![X]:((~strong(X)<~>~brave(X))<=>(~rich(X)|~quiet(X))))&
(![X]:(curious(X)<=>calm(X)))&
(![X]:((~brave(X)<~>happy(X))=>(~kind(X)<~>generous(X))))&
(![X]:(~funny(X)=>(calm(X)<~>~kind(X))))&
((?[X]:((~calm(X)&rich(X))))<=>((funny(john)|calm(john))))&
(![X]:(~brave(X)=>(quiet(X)&~funny(X))))&
((?[X]:((~brave(X)<~>~rich(X))))<=>((creative(alice)|~generous(alice))))&
(![X]:(~old(X)=>(calm(X)|quiet(X))))&
((?[X]:((~kind(X)|quiet(X))))=>((~patient(paul)&brave(paul))))&
(![X]:((old(X)|creative(X))=>happy(X)))&
(![X]:((~tall(X)&~brave(X))=>(old(X)&~old(X))))&
(![X]:((kind(X)&~strong(X))=>(humble(X)&~patient(X))))&
(((~happy(susan)&~generous(susan)))=>(?[X]:((creative(X)|~wise(X)))))&
(![X]:((generous(X)&~quiet(X))=>(old(X)<~>quiet(X))))&
(![X]:(quiet(X)=>~wise(X)))&
(old(lucy))&
((~generous(fred)<~>~creative(fred)))&
(wise(alice))&
((~wise(susan)&~old(susan)))&
(brave(fred))&
(?[X]:(patient(X)))&
(?[X]:(rich(X)))&
(?[X]:((~happy(X)<~>~generous(X)))) | old(alice) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 8858282244932499934875902
% SZS output start Proof for 8858282244932499934875902
1. (curious(alice) <~> ~curious(alice)) => old(alice) [input p0]
25. ~old(alice) [input hypothesis]
28. old(alice) | (curious(alice) <=> ~curious(alice)) [ennf transformation 1]
43. old(alice) | ((curious(alice) | curious(alice)) & (~curious(alice) | ~curious(alice))) [nnf transformation 28]
70. old(alice) | ~curious(alice) | ~curious(alice) [cnf transformation 43]
71. old(alice) | curious(alice) | curious(alice) [cnf transformation 43]
122. ~old(alice) [cnf transformation 25]
124. old(alice) | ~curious(alice) [duplicate literal removal 70]
125. old(alice) | curious(alice) [duplicate literal removal 71]
127. 1 <=> curious(alice) [avatar definition]
131. 2 <=> old(alice) [avatar definition]
134. 1 | 2 [avatar split clause 125,131,127]
135. ~1 | 2 [avatar split clause 124,131,127]
243. ~2 [avatar split clause 122,131]
244. $false [avatar sat refutation 134,135,243]
% SZS output end Proof for 8858282244932499934875902
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If susan is brave or not old then lucy is both not patient and tall and vice versa.
Everyone who is either funny or happy is not funny or humble and vice versa.
If someone is both not curious and humble then someone is either not old or patient and vice versa.
Everyone who is creative or patient is not kind.
If someone is not funny then someone is either kind or strong.
Everyone who is either kind or calm is patient or curious and vice versa.
If someone is either calm or not humble then someone is either rich or not humble.
If fred is not brave or generous then john is either not strong or not old and vice versa.
If someone is wise or not curious then susan is quiet.
Everyone who is not quiet or quiet is both quiet and not happy and vice versa.
If someone is creative then someone is not tall and vice versa.
If someone is not generous or not strong then someone is either not calm or calm.
If john is tall or not quiet then someone is either creative or not happy and vice versa.
Everyone who is both tall and generous is rich and vice versa.
Everyone who is wise or not old is generous.
Everyone who is either not tall or calm is both happy and not wise and vice versa.
Someone is funny or not generous.
Alice is both not happy and not old.
Paul is either not happy or not strong.
Someone is not happy or not wise.
Someone is generous or brave. | Lucy is not brave. | neutral | (((brave(susan)|~old(susan)))<=>((~patient(lucy)&tall(lucy))))&
(![X]:((funny(X)<~>happy(X))<=>(~funny(X)|humble(X))))&
((?[X]:((~curious(X)&humble(X))))<=>(?[X]:((~old(X)<~>patient(X)))))&
(![X]:((creative(X)|patient(X))=>~kind(X)))&
((?[X]:(~funny(X)))=>(?[X]:((kind(X)<~>strong(X)))))&
(![X]:((kind(X)<~>calm(X))<=>(patient(X)|curious(X))))&
((?[X]:((calm(X)<~>~humble(X))))=>(?[X]:((rich(X)<~>~humble(X)))))&
(((~brave(fred)|generous(fred)))<=>((~strong(john)<~>~old(john))))&
((?[X]:((wise(X)|~curious(X))))=>(quiet(susan)))&
(![X]:((~quiet(X)|quiet(X))<=>(quiet(X)&~happy(X))))&
((?[X]:(creative(X)))<=>(?[X]:(~tall(X))))&
((?[X]:((~generous(X)|~strong(X))))=>(?[X]:((~calm(X)<~>calm(X)))))&
(((tall(john)|~quiet(john)))<=>(?[X]:((creative(X)<~>~happy(X)))))&
(![X]:((tall(X)&generous(X))<=>rich(X)))&
(![X]:((wise(X)|~old(X))=>generous(X)))&
(![X]:((~tall(X)<~>calm(X))<=>(happy(X)&~wise(X))))&
(?[X]:((funny(X)|~generous(X))))&
((~happy(alice)&~old(alice)))&
((~happy(paul)<~>~strong(paul)))&
(?[X]:((~happy(X)|~wise(X))))&
(?[X]:((generous(X)|brave(X)))) | ~brave(lucy) | [] | null | 0 |
Everyone who is both not old and not strong is either humble or happy and vice versa.
Everyone who is both not wise and not generous is not brave and vice versa.
If paul is both tall and not humble then fred is creative.
If someone is both not happy and not humble then lucy is either not wise or strong and vice versa.
If someone is not old or brave then someone is not wise or not strong and vice versa.
If mary is both tall and humble then someone is not creative and vice versa.
If someone is either not strong or calm then mary is happy.
If someone is either humble or curious then susan is not calm or not generous and vice versa.
Everyone who is strong or tall is calm and vice versa.
Everyone who is either funny or not creative is both old and not rich.
Everyone who is not generous or not happy is funny.
If someone is both not tall and not humble then someone is either not creative or creative.
Everyone who is not happy is either not kind or creative and vice versa.
Everyone who is either happy or curious is both not wise and not humble and vice versa.
Everyone who is not strong or generous is either curious or not funny.
If someone is both patient and not quiet then alice is both not patient and humble and vice versa.
Lucy is not happy or not calm.
Paul is calm.
Susan is either not happy or not old.
Someone is old or kind.
John is either curious or creative.
Susan is curious.
Alice is either not generous or kind. | Mary is not calm. | neutral | (![X]:((~old(X)&~strong(X))<=>(humble(X)<~>happy(X))))&
(![X]:((~wise(X)&~generous(X))<=>~brave(X)))&
(((tall(paul)&~humble(paul)))=>(creative(fred)))&
((?[X]:((~happy(X)&~humble(X))))<=>((~wise(lucy)<~>strong(lucy))))&
((?[X]:((~old(X)|brave(X))))<=>(?[X]:((~wise(X)|~strong(X)))))&
(((tall(mary)&humble(mary)))<=>(?[X]:(~creative(X))))&
((?[X]:((~strong(X)<~>calm(X))))=>(happy(mary)))&
((?[X]:((humble(X)<~>curious(X))))<=>((~calm(susan)|~generous(susan))))&
(![X]:((strong(X)|tall(X))<=>calm(X)))&
(![X]:((funny(X)<~>~creative(X))=>(old(X)&~rich(X))))&
(![X]:((~generous(X)|~happy(X))=>funny(X)))&
((?[X]:((~tall(X)&~humble(X))))=>(?[X]:((~creative(X)<~>creative(X)))))&
(![X]:(~happy(X)<=>(~kind(X)<~>creative(X))))&
(![X]:((happy(X)<~>curious(X))<=>(~wise(X)&~humble(X))))&
(![X]:((~strong(X)|generous(X))=>(curious(X)<~>~funny(X))))&
((?[X]:((patient(X)&~quiet(X))))<=>((~patient(alice)&humble(alice))))&
((~happy(lucy)|~calm(lucy)))&
(calm(paul))&
((~happy(susan)<~>~old(susan)))&
(?[X]:((old(X)|kind(X))))&
((curious(john)<~>creative(john)))&
(curious(susan))&
((~generous(alice)<~>kind(alice))) | ~calm(mary) | [] | null | 0 |
If alice is patient then someone is creative or not funny. If someone is either rich or humble then john is either not quiet or not rich. Everyone who is both not old and funny is both not tall and wise and vice versa. If someone is rich or old then alice is wise or not strong and vice versa. Everyone who is both creative and not generous is not humble or strong and vice versa. Everyone who is not curious or humble is not strong or humble and vice versa. If someone is funny then alice is either strong or creative and vice versa. Everyone who is creative is either not patient or not kind. Everyone who is creative or not brave is either strong or not brave and vice versa. If someone is old then alice is calm. Everyone who is either kind or funny is both curious and tall and vice versa. Everyone who is both not old and generous is curious or not wise and vice versa. Everyone who is strong is happy and vice versa. If john is both curious and rich then fred is not patient or calm. If someone is both not patient and tall then john is both not wise and humble. If someone is not tall or wise then lucy is both curious and not curious and vice versa. Someone is not old or not tall. Someone is either not curious or humble. Someone is not creative. Someone is either calm or not rich. Someone is both generous and patient. Someone is either not humble or not wise. Someone is not quiet or calm. John is funny or creative. | Lucy is humble. | entailment | ((patient(alice))=>(?[X]:((creative(X)|~funny(X)))))&
((?[X]:((rich(X)<~>humble(X))))=>((~quiet(john)<~>~rich(john))))&
(![X]:((~old(X)&funny(X))<=>(~tall(X)&wise(X))))&
((?[X]:((rich(X)|old(X))))<=>((wise(alice)|~strong(alice))))&
(![X]:((creative(X)&~generous(X))<=>(~humble(X)|strong(X))))&
(![X]:((~curious(X)|humble(X))<=>(~strong(X)|humble(X))))&
((?[X]:(funny(X)))<=>((strong(alice)<~>creative(alice))))&
(![X]:(creative(X)=>(~patient(X)<~>~kind(X))))&
(![X]:((creative(X)|~brave(X))<=>(strong(X)<~>~brave(X))))&
((?[X]:(old(X)))=>(calm(alice)))&
(![X]:((kind(X)<~>funny(X))<=>(curious(X)&tall(X))))&
(![X]:((~old(X)&generous(X))<=>(curious(X)|~wise(X))))&
(![X]:(strong(X)<=>happy(X)))&
(((curious(john)&rich(john)))=>((~patient(fred)|calm(fred))))&
((?[X]:((~patient(X)&tall(X))))=>((~wise(john)&humble(john))))&
((?[X]:((~tall(X)|wise(X))))<=>((curious(lucy)&~curious(lucy))))&
(?[X]:((~old(X)|~tall(X))))&
(?[X]:((~curious(X)<~>humble(X))))&
(?[X]:(~creative(X)))&
(?[X]:((calm(X)<~>~rich(X))))&
(?[X]:((generous(X)&patient(X))))&
(?[X]:((~humble(X)<~>~wise(X))))&
(?[X]:((~quiet(X)|calm(X))))&
((funny(john)|creative(john))) | humble(lucy) | [
"p4",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8716142174596326662513296
% SZS output start Proof for 8716142174596326662513296
5. ! [X0] : ((~generous(X0) & creative(X0)) <=> (strong(X0) | ~humble(X0))) [input p4]
12. ! [X0] : ((generous(X0) & ~old(X0)) <=> (~wise(X0) | curious(X0))) [input p11]
16. ? [X0] : (wise(X0) | ~tall(X0)) <=> (~curious(lucy) & curious(lucy)) [input p15]
25. ~humble(lucy) [input hypothesis]
43. ! [X0] : (((~generous(X0) & creative(X0)) | (~strong(X0) & humble(X0))) & ((strong(X0) | ~humble(X0)) | (generous(X0) | ~creative(X0)))) [nnf transformation 5]
44. ! [X0] : (((~generous(X0) & creative(X0)) | (~strong(X0) & humble(X0))) & (strong(X0) | ~humble(X0) | generous(X0) | ~creative(X0))) [flattening 43]
56. ! [X0] : (((generous(X0) & ~old(X0)) | (wise(X0) & ~curious(X0))) & ((~wise(X0) | curious(X0)) | (~generous(X0) | old(X0)))) [nnf transformation 12]
57. ! [X0] : (((generous(X0) & ~old(X0)) | (wise(X0) & ~curious(X0))) & (~wise(X0) | curious(X0) | ~generous(X0) | old(X0))) [flattening 56]
59. (? [X0] : (wise(X0) | ~tall(X0)) | (curious(lucy) | ~curious(lucy))) & ((~curious(lucy) & curious(lucy)) | ! [X0] : (~wise(X0) & tall(X0))) [nnf transformation 16]
60. (? [X0] : (wise(X0) | ~tall(X0)) | curious(lucy) | ~curious(lucy)) & ((~curious(lucy) & curious(lucy)) | ! [X0] : (~wise(X0) & tall(X0))) [flattening 59]
61. (? [X0] : (wise(X0) | ~tall(X0)) | curious(lucy) | ~curious(lucy)) & ((~curious(lucy) & curious(lucy)) | ! [X1] : (~wise(X1) & tall(X1))) [rectify 60]
62. ? [X0] : (wise(X0) | ~tall(X0)) => (wise(sK3) | ~tall(sK3)) [choice axiom]
63. ((wise(sK3) | ~tall(sK3)) | curious(lucy) | ~curious(lucy)) & ((~curious(lucy) & curious(lucy)) | ! [X1] : (~wise(X1) & tall(X1))) [skolemisation 61,62]
97. ~generous(X0) | humble(X0) [cnf transformation 44]
126. generous(X0) | wise(X0) [cnf transformation 57]
133. curious(lucy) | ~wise(X1) [cnf transformation 63]
135. ~curious(lucy) | ~wise(X1) [cnf transformation 63]
149. ~humble(lucy) [cnf transformation 25]
257. 24 <=> ! [X1] : ~wise(X1) [avatar definition]
258. ~wise(X1) <- (24) [avatar component clause 257]
260. 25 <=> curious(lucy) [avatar definition]
263. 24 | ~25 [avatar split clause 135,260,257]
268. 24 | 25 [avatar split clause 133,260,257]
335. wise(X1) | humble(X1) [resolution 126,97]
337. humble(X1) <- (24) [subsumption resolution 335,258]
338. $false <- (24) [resolution 337,149]
341. ~24 [avatar contradiction clause 338]
342. $false [avatar sat refutation 263,268,341]
% SZS output end Proof for 8716142174596326662513296
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is both curious and patient then fred is either curious or rich and vice versa.
Everyone who is not brave or not patient is rich or not strong and vice versa.
Everyone who is either not tall or generous is either not funny or not wise.
If john is humble or not kind then someone is tall.
If someone is either quiet or humble then mary is either not patient or creative and vice versa.
Everyone who is either old or brave is not generous.
If lucy is both calm and quiet then paul is not old or not creative and vice versa.
Everyone who is either curious or not rich is patient.
Everyone who is either not funny or not happy is both old and kind and vice versa.
Everyone who is either not kind or not happy is either kind or funny and vice versa.
If john is both curious and not calm then someone is quiet and vice versa.
Everyone who is both curious and calm is either curious or not funny and vice versa.
Everyone who is either not rich or strong is not humble.
If someone is both wise and not brave then john is both not brave and not humble and vice versa.
If paul is not brave or not humble then someone is not creative or wise.
Alice is not rich.
Susan is either not strong or funny.
Mary is both not happy and not calm.
Someone is both kind and not generous.
Someone is creative.
Someone is both not rich and not brave.
Someone is patient.
Susan is either not curious or not quiet. | Alice is not brave. | neutral | (((curious(alice)&patient(alice)))<=>((curious(fred)<~>rich(fred))))&
(![X]:((~brave(X)|~patient(X))<=>(rich(X)|~strong(X))))&
(![X]:((~tall(X)<~>generous(X))=>(~funny(X)<~>~wise(X))))&
(((humble(john)|~kind(john)))=>(?[X]:(tall(X))))&
((?[X]:((quiet(X)<~>humble(X))))<=>((~patient(mary)<~>creative(mary))))&
(![X]:((old(X)<~>brave(X))=>~generous(X)))&
(((calm(lucy)&quiet(lucy)))<=>((~old(paul)|~creative(paul))))&
(![X]:((curious(X)<~>~rich(X))=>patient(X)))&
(![X]:((~funny(X)<~>~happy(X))<=>(old(X)&kind(X))))&
(![X]:((~kind(X)<~>~happy(X))<=>(kind(X)<~>funny(X))))&
(((curious(john)&~calm(john)))<=>(?[X]:(quiet(X))))&
(![X]:((curious(X)&calm(X))<=>(curious(X)<~>~funny(X))))&
(![X]:((~rich(X)<~>strong(X))=>~humble(X)))&
((?[X]:((wise(X)&~brave(X))))<=>((~brave(john)&~humble(john))))&
(((~brave(paul)|~humble(paul)))=>(?[X]:((~creative(X)|wise(X)))))&
(~rich(alice))&
((~strong(susan)<~>funny(susan)))&
((~happy(mary)&~calm(mary)))&
(?[X]:((kind(X)&~generous(X))))&
(?[X]:(creative(X)))&
(?[X]:((~rich(X)&~brave(X))))&
(?[X]:(patient(X)))&
((~curious(susan)<~>~quiet(susan))) | ~brave(alice) | [] | null | 0 |
If paul is either old or calm then someone is not patient or not kind and vice versa.
If someone is both old and not generous then someone is generous or tall.
If lucy is humble then someone is generous or not curious and vice versa.
Everyone who is rich or humble is strong and vice versa.
Everyone who is not happy is both funny and not quiet.
If mary is either not creative or brave then someone is rich or old and vice versa.
Everyone who is both old and brave is not creative or generous.
Everyone who is both not rich and curious is both curious and not humble and vice versa.
If someone is both patient and brave then susan is not funny.
If john is both kind and not kind then someone is old and vice versa.
Everyone who is either not quiet or curious is both patient and not funny and vice versa.
Everyone who is either rich or not strong is wise or patient and vice versa.
Everyone who is curious is not wise or not strong.
Everyone who is not tall or not generous is both tall and not old and vice versa.
Everyone who is tall or generous is both not generous and rich.
Alice is either happy or not strong.
Someone is funny or not kind.
John is old or not happy.
John is not old.
Lucy is both creative and calm. | Alice is strong. | entailment | (((old(paul)<~>calm(paul)))<=>(?[X]:((~patient(X)|~kind(X)))))&
((?[X]:((old(X)&~generous(X))))=>(?[X]:((generous(X)|tall(X)))))&
((humble(lucy))<=>(?[X]:((generous(X)|~curious(X)))))&
(![X]:((rich(X)|humble(X))<=>strong(X)))&
(![X]:(~happy(X)=>(funny(X)&~quiet(X))))&
(((~creative(mary)<~>brave(mary)))<=>(?[X]:((rich(X)|old(X)))))&
(![X]:((old(X)&brave(X))=>(~creative(X)|generous(X))))&
(![X]:((~rich(X)&curious(X))<=>(curious(X)&~humble(X))))&
((?[X]:((patient(X)&brave(X))))=>(~funny(susan)))&
(((kind(john)&~kind(john)))<=>(?[X]:(old(X))))&
(![X]:((~quiet(X)<~>curious(X))<=>(patient(X)&~funny(X))))&
(![X]:((rich(X)<~>~strong(X))<=>(wise(X)|patient(X))))&
(![X]:(curious(X)=>(~wise(X)|~strong(X))))&
(![X]:((~tall(X)|~generous(X))<=>(tall(X)&~old(X))))&
(![X]:((tall(X)|generous(X))=>(~generous(X)&rich(X))))&
((happy(alice)<~>~strong(alice)))&
(?[X]:((funny(X)|~kind(X))))&
((old(john)|~happy(john)))&
(~old(john))&
((creative(lucy)&calm(lucy))) | strong(alice) | [
"p3",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7172432896824141655171102
% SZS output start Proof for 7172432896824141655171102
4. ! [X0] : ((humble(X0) | rich(X0)) <=> strong(X0)) [input p3]
14. ! [X0] : ((~generous(X0) | ~tall(X0)) <=> (~old(X0) & tall(X0))) [input p13]
15. ! [X0] : ((generous(X0) | tall(X0)) => (rich(X0) & ~generous(X0))) [input p14]
21. ~strong(alice) [input hypothesis]
30. ! [X0] : ((rich(X0) & ~generous(X0)) | (~generous(X0) & ~tall(X0))) [ennf transformation 15]
42. ! [X0] : (((humble(X0) | rich(X0)) | ~strong(X0)) & (strong(X0) | (~humble(X0) & ~rich(X0)))) [nnf transformation 4]
43. ! [X0] : ((humble(X0) | rich(X0) | ~strong(X0)) & (strong(X0) | (~humble(X0) & ~rich(X0)))) [flattening 42]
59. ! [X0] : (((~generous(X0) | ~tall(X0)) | (old(X0) | ~tall(X0))) & ((~old(X0) & tall(X0)) | (generous(X0) & tall(X0)))) [nnf transformation 14]
60. ! [X0] : ((~generous(X0) | ~tall(X0) | old(X0) | ~tall(X0)) & ((~old(X0) & tall(X0)) | (generous(X0) & tall(X0)))) [flattening 59]
74. ~rich(X0) | strong(X0) [cnf transformation 43]
107. tall(X0) | tall(X0) [cnf transformation 60]
114. rich(X0) | ~tall(X0) [cnf transformation 30]
123. ~strong(alice) [cnf transformation 21]
125. tall(X0) [duplicate literal removal 107]
233. rich(X0) [subsumption resolution 114,125]
242. 25 <=> strong(alice) [avatar definition]
243. ~strong(alice) <- (~25) [avatar component clause 242]
266. ~25 [avatar split clause 123,242]
277. strong(X0) [resolution 74,233]
279. $false <- (~25) [resolution 277,243]
280. 25 [avatar contradiction clause 279]
281. $false [avatar sat refutation 266,280]
% SZS output end Proof for 7172432896824141655171102
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is either quiet or not strong and vice versa.
Everyone who is either calm or not calm is old.
Everyone who is curious or not creative is not funny and vice versa.
Everyone who is either wise or not curious is both kind and not old.
If john is not brave or patient then lucy is not curious.
Everyone who is either not curious or not old is either not creative or strong and vice versa.
If alice is both not happy and patient then mary is calm.
If someone is calm or strong then mary is both funny and kind.
If someone is not kind or happy then alice is patient.
Everyone who is either not humble or humble is both not calm and not curious and vice versa.
Everyone who is not happy is brave or not strong and vice versa.
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.
Paul is both kind and tall.
Fred is either not happy or patient.
Someone is kind.
Lucy is either not quiet or rich.
Susan is both not rich and not generous.
Susan is not patient or not humble.
Lucy is either patient or strong. | Paul is not wise. | contradiction | (![X]:(~quiet(X)<=>(quiet(X)<~>~strong(X))))&
(![X]:((calm(X)<~>~calm(X))=>old(X)))&
(![X]:((curious(X)|~creative(X))<=>~funny(X)))&
(![X]:((wise(X)<~>~curious(X))=>(kind(X)&~old(X))))&
(((~brave(john)|patient(john)))=>(~curious(lucy)))&
(![X]:((~curious(X)<~>~old(X))<=>(~creative(X)<~>strong(X))))&
(((~happy(alice)&patient(alice)))=>(calm(mary)))&
((?[X]:((calm(X)|strong(X))))=>((funny(mary)&kind(mary))))&
((?[X]:((~kind(X)|happy(X))))=>(patient(alice)))&
(![X]:((~humble(X)<~>humble(X))<=>(~calm(X)&~curious(X))))&
(![X]:(~happy(X)<=>(brave(X)|~strong(X))))&
(![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(paul)&tall(paul)))&
((~happy(fred)<~>patient(fred)))&
(?[X]:(kind(X)))&
((~quiet(lucy)<~>rich(lucy)))&
((~rich(susan)&~generous(susan)))&
((~patient(susan)|~humble(susan)))&
((patient(lucy)<~>strong(lucy))) | ~wise(paul) | [
"p1",
"p3",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 940928680655997449183481
% SZS output start Proof for 940928680655997449183481
2. ! [X0] : ((calm(X0) <~> ~calm(X0)) => old(X0)) [input p1]
4. ! [X0] : ((wise(X0) <~> ~curious(X0)) => (~old(X0) & kind(X0))) [input p3]
10. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> (~curious(X0) & ~calm(X0))) [input p9]
24. ~wise(paul) [input hypothesis]
32. ! [X0] : ((wise(X0) <~> ~curious(X0)) => ~old(X0)) [pure predicate removal 4]
33. ! [X0] : (old(X0) | (calm(X0) <=> ~calm(X0))) [ennf transformation 2]
35. ! [X0] : (~old(X0) | (wise(X0) <=> ~curious(X0))) [ennf transformation 32]
43. ! [X0] : (old(X0) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0)))) [nnf transformation 33]
44. ! [X0] : (~old(X0) | ((wise(X0) | curious(X0)) & (~curious(X0) | ~wise(X0)))) [nnf transformation 35]
46. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (curious(X0) | calm(X0))) & ((~curious(X0) & ~calm(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 10]
47. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | curious(X0) | calm(X0)) & ((~curious(X0) & ~calm(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [flattening 46]
72. old(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 43]
73. old(X0) | calm(X0) | calm(X0) [cnf transformation 43]
77. ~old(X0) | wise(X0) | curious(X0) [cnf transformation 44]
94. ~curious(X0) | humble(X0) | humble(X0) [cnf transformation 47]
95. ~curious(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 47]
134. ~wise(paul) [cnf transformation 24]
143. ~curious(X0) | humble(X0) [duplicate literal removal 94]
144. ~humble(X0) | ~curious(X0) [duplicate literal removal 95]
145. old(X0) | ~calm(X0) [duplicate literal removal 72]
146. old(X0) | calm(X0) [duplicate literal removal 73]
150. old(X0) [subsumption resolution 145,146]
151. wise(X0) | curious(X0) [subsumption resolution 77,150]
196. ~curious(X0) [subsumption resolution 143,144]
263. curious(paul) [resolution 151,134]
264. $false [subsumption resolution 263,196]
% SZS output end Proof for 940928680655997449183481
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or calm then fred is not strong.
If someone is both not humble and not happy then someone is funny or rich and vice versa.
Everyone who is both not wise and not tall is patient and vice versa.
If someone is both quiet and tall then fred is both calm and rich and vice versa.
Everyone who is humble or happy is both not patient and strong.
Everyone who is either rich or not old is not patient or not generous.
If mary is either brave or not generous then john is both not old and happy.
If someone is not creative or calm then john is both not patient and rich and vice versa.
Everyone who is both not happy and not calm is both happy and rich.
Everyone who is both not happy and rich is either not strong or not brave.
Everyone who is both not old and creative is kind.
Everyone who is either not calm or calm is kind or humble and vice versa.
If someone is both not tall and not calm then fred is happy or not quiet.
Everyone who is not old is not patient or creative.
If someone is both tall and funny then fred is both not calm and not generous.
Everyone who is calm or not generous is either not rich or not wise.
Paul is either not funny or brave.
Paul is quiet.
Someone is happy or brave.
Lucy is not old.
John is not funny.
Paul is kind or not funny.
Someone is not tall.
Fred is not quiet or strong. | Mary is humble. | neutral | ((?[X]:((creative(X)|calm(X))))=>(~strong(fred)))&
((?[X]:((~humble(X)&~happy(X))))<=>(?[X]:((funny(X)|rich(X)))))&
(![X]:((~wise(X)&~tall(X))<=>patient(X)))&
((?[X]:((quiet(X)&tall(X))))<=>((calm(fred)&rich(fred))))&
(![X]:((humble(X)|happy(X))=>(~patient(X)&strong(X))))&
(![X]:((rich(X)<~>~old(X))=>(~patient(X)|~generous(X))))&
(((brave(mary)<~>~generous(mary)))=>((~old(john)&happy(john))))&
((?[X]:((~creative(X)|calm(X))))<=>((~patient(john)&rich(john))))&
(![X]:((~happy(X)&~calm(X))=>(happy(X)&rich(X))))&
(![X]:((~happy(X)&rich(X))=>(~strong(X)<~>~brave(X))))&
(![X]:((~old(X)&creative(X))=>kind(X)))&
(![X]:((~calm(X)<~>calm(X))<=>(kind(X)|humble(X))))&
((?[X]:((~tall(X)&~calm(X))))=>((happy(fred)|~quiet(fred))))&
(![X]:(~old(X)=>(~patient(X)|creative(X))))&
((?[X]:((tall(X)&funny(X))))=>((~calm(fred)&~generous(fred))))&
(![X]:((calm(X)|~generous(X))=>(~rich(X)<~>~wise(X))))&
((~funny(paul)<~>brave(paul)))&
(quiet(paul))&
(?[X]:((happy(X)|brave(X))))&
(~old(lucy))&
(~funny(john))&
((kind(paul)|~funny(paul)))&
(?[X]:(~tall(X)))&
((~quiet(fred)|strong(fred))) | humble(mary) | [] | null | 0 |
Everyone who is either not patient or not wise is not tall and vice versa.
If john is both not kind and not strong then lucy is either funny or calm and vice versa.
If mary is quiet or not humble then someone is not creative and vice versa.
If someone is brave or strong then someone is calm or not rich and vice versa.
Everyone who is generous is both not calm and generous and vice versa.
Everyone who is both patient and not creative is tall or old and vice versa.
Everyone who is not brave or creative is brave.
Everyone who is both creative and humble is either calm or not old.
If someone is both not wise and brave then someone is not happy or old.
Everyone who is kind or wise is generous or not generous.
Everyone who is not rich or not brave is strong and vice versa.
Everyone who is both not humble and not brave is humble.
If lucy is either not strong or patient then someone is patient.
Everyone who is both quiet and brave is not tall or not curious.
Everyone who is not patient or creative is both not tall and not humble and vice versa.
Everyone who is both not rich and not kind is either kind or not patient and vice versa.
Mary is both creative and calm.
Fred is either not humble or happy.
Someone is either not humble or not wise.
John is strong.
Someone is funny or tall.
Lucy is either brave or humble. | Mary is not humble. | entailment | (![X]:((~patient(X)<~>~wise(X))<=>~tall(X)))&
(((~kind(john)&~strong(john)))<=>((funny(lucy)<~>calm(lucy))))&
(((quiet(mary)|~humble(mary)))<=>(?[X]:(~creative(X))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((calm(X)|~rich(X)))))&
(![X]:(generous(X)<=>(~calm(X)&generous(X))))&
(![X]:((patient(X)&~creative(X))<=>(tall(X)|old(X))))&
(![X]:((~brave(X)|creative(X))=>brave(X)))&
(![X]:((creative(X)&humble(X))=>(calm(X)<~>~old(X))))&
((?[X]:((~wise(X)&brave(X))))=>(?[X]:((~happy(X)|old(X)))))&
(![X]:((kind(X)|wise(X))=>(generous(X)|~generous(X))))&
(![X]:((~rich(X)|~brave(X))<=>strong(X)))&
(![X]:((~humble(X)&~brave(X))=>humble(X)))&
(((~strong(lucy)<~>patient(lucy)))=>(?[X]:(patient(X))))&
(![X]:((quiet(X)&brave(X))=>(~tall(X)|~curious(X))))&
(![X]:((~patient(X)|creative(X))<=>(~tall(X)&~humble(X))))&
(![X]:((~rich(X)&~kind(X))<=>(kind(X)<~>~patient(X))))&
((creative(mary)&calm(mary)))&
((~humble(fred)<~>happy(fred)))&
(?[X]:((~humble(X)<~>~wise(X))))&
(strong(john))&
(?[X]:((funny(X)|tall(X))))&
((brave(lucy)<~>humble(lucy))) | ~humble(mary) | [
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7877987693850507196493901
% SZS output start Proof for 7877987693850507196493901
15. ! [X0] : ((creative(X0) | ~patient(X0)) <=> (~humble(X0) & ~tall(X0))) [input p14]
17. calm(mary) & creative(mary) [input p16]
23. humble(mary) [input hypothesis]
62. ! [X0] : (((creative(X0) | ~patient(X0)) | (humble(X0) | tall(X0))) & ((~humble(X0) & ~tall(X0)) | (~creative(X0) & patient(X0)))) [nnf transformation 15]
63. ! [X0] : ((creative(X0) | ~patient(X0) | humble(X0) | tall(X0)) & ((~humble(X0) & ~tall(X0)) | (~creative(X0) & patient(X0)))) [flattening 62]
114. ~creative(X0) | ~humble(X0) [cnf transformation 63]
122. creative(mary) [cnf transformation 17]
132. humble(mary) [cnf transformation 23]
167. 7 <=> humble(mary) [avatar definition]
168. humble(mary) <- (7) [avatar component clause 167]
270. 7 [avatar split clause 132,167]
278. ~humble(mary) [resolution 114,122]
280. $false <- (7) [subsumption resolution 278,168]
281. ~7 [avatar contradiction clause 280]
282. $false [avatar sat refutation 270,281]
% SZS output end Proof for 7877987693850507196493901
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both quiet and patient then someone is not humble and vice versa.
If fred is not tall then someone is not kind or not generous.
Everyone who is not kind is either not patient or old.
Everyone who is strong or funny is both strong and kind.
If someone is either not calm or not rich then someone is not generous.
If someone is both not calm and creative then mary is both humble and not patient.
If someone is both not old and tall then someone is both calm and not creative.
Everyone who is not rich or old is not old and vice versa.
If someone is not creative then someone is both not old and not wise and vice versa.
Everyone who is both quiet and not curious is not kind and vice versa.
Everyone who is both old and not generous is both calm and humble.
Everyone who is not patient is both not quiet and quiet.
Everyone who is both happy and calm is humble and vice versa.
Everyone who is either not generous or not rich is both not funny and not creative and vice versa.
Everyone who is both not humble and old is either wise or brave and vice versa.
If someone is both brave and not wise then john is funny and vice versa.
John is not creative or not patient.
Someone is kind.
Someone is not humble.
Lucy is either not old or quiet.
Mary is either old or strong.
Alice is happy or not patient.
Fred is both not calm and quiet. | Lucy is not kind. | contradiction | (((quiet(susan)&patient(susan)))<=>(?[X]:(~humble(X))))&
((~tall(fred))=>(?[X]:((~kind(X)|~generous(X)))))&
(![X]:(~kind(X)=>(~patient(X)<~>old(X))))&
(![X]:((strong(X)|funny(X))=>(strong(X)&kind(X))))&
((?[X]:((~calm(X)<~>~rich(X))))=>(?[X]:(~generous(X))))&
((?[X]:((~calm(X)&creative(X))))=>((humble(mary)&~patient(mary))))&
((?[X]:((~old(X)&tall(X))))=>(?[X]:((calm(X)&~creative(X)))))&
(![X]:((~rich(X)|old(X))<=>~old(X)))&
((?[X]:(~creative(X)))<=>(?[X]:((~old(X)&~wise(X)))))&
(![X]:((quiet(X)&~curious(X))<=>~kind(X)))&
(![X]:((old(X)&~generous(X))=>(calm(X)&humble(X))))&
(![X]:(~patient(X)=>(~quiet(X)&quiet(X))))&
(![X]:((happy(X)&calm(X))<=>humble(X)))&
(![X]:((~generous(X)<~>~rich(X))<=>(~funny(X)&~creative(X))))&
(![X]:((~humble(X)&old(X))<=>(wise(X)<~>brave(X))))&
((?[X]:((brave(X)&~wise(X))))<=>(funny(john)))&
((~creative(john)|~patient(john)))&
(?[X]:(kind(X)))&
(?[X]:(~humble(X)))&
((~old(lucy)<~>quiet(lucy)))&
((old(mary)<~>strong(mary)))&
((happy(alice)|~patient(alice)))&
((~calm(fred)&quiet(fred))) | ~kind(lucy) | [
"p7",
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 618797024191156564774647
% SZS output start Proof for 618797024191156564774647
8. ! [X0] : ((old(X0) | ~rich(X0)) <=> ~old(X0)) [input p7]
10. ! [X0] : ((~curious(X0) & quiet(X0)) <=> ~kind(X0)) [input p9]
20. ~old(lucy) <~> quiet(lucy) [input p19]
24. ~kind(lucy) [input hypothesis]
52. ! [X0] : (((old(X0) | ~rich(X0)) | old(X0)) & (~old(X0) | (~old(X0) & rich(X0)))) [nnf transformation 8]
53. ! [X0] : ((old(X0) | ~rich(X0) | old(X0)) & (~old(X0) | (~old(X0) & rich(X0)))) [flattening 52]
59. ! [X0] : (((~curious(X0) & quiet(X0)) | kind(X0)) & (~kind(X0) | (curious(X0) | ~quiet(X0)))) [nnf transformation 10]
60. ! [X0] : (((~curious(X0) & quiet(X0)) | kind(X0)) & (~kind(X0) | curious(X0) | ~quiet(X0))) [flattening 59]
75. (~quiet(lucy) | old(lucy)) & (quiet(lucy) | ~old(lucy)) [nnf transformation 20]
94. ~old(X0) | ~old(X0) [cnf transformation 53]
100. kind(X0) | quiet(X0) [cnf transformation 60]
128. ~quiet(lucy) | old(lucy) [cnf transformation 75]
134. ~kind(lucy) [cnf transformation 24]
135. ~old(X0) [duplicate literal removal 94]
241. ~quiet(lucy) [subsumption resolution 128,135]
246. quiet(lucy) [resolution 100,134]
248. $false [subsumption resolution 246,241]
% SZS output end Proof for 618797024191156564774647
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not tall is either not generous or quiet. If john is humble then someone is not patient and vice versa. Everyone who is either tall or creative is not funny or not old and vice versa. Everyone who is either creative or wise is either not generous or rich and vice versa. If someone is creative or not quiet then alice is either not tall or patient and vice versa. Everyone who is either quiet or wise is not funny and vice versa. If someone is not kind then mary is both old and kind and vice versa. Everyone who is both rich and not humble is not kind and vice versa. Everyone who is both not brave and not curious is not strong or humble and vice versa. If john is not happy or not curious then mary is not humble. If fred is either rich or not kind then someone is both patient and old and vice versa. Everyone who is not strong is either humble or not old. If mary is both not generous and patient then paul is both calm and not brave. Everyone who is both not curious and not kind is both not quiet and not patient and vice versa. Everyone who is generous or not generous is not humble. If someone is both not calm and funny then john is calm. Fred is either not tall or quiet. Fred is either not rich or not strong. Someone is calm or rich. Someone is both creative and strong. Fred is either humble or not generous. Someone is either not generous or not strong. John is quiet or wise. | Fred is strong. | entailment | (![X]:((tall(X)|~tall(X))=>(~generous(X)<~>quiet(X))))&
((humble(john))<=>(?[X]:(~patient(X))))&
(![X]:((tall(X)<~>creative(X))<=>(~funny(X)|~old(X))))&
(![X]:((creative(X)<~>wise(X))<=>(~generous(X)<~>rich(X))))&
((?[X]:((creative(X)|~quiet(X))))<=>((~tall(alice)<~>patient(alice))))&
(![X]:((quiet(X)<~>wise(X))<=>~funny(X)))&
((?[X]:(~kind(X)))<=>((old(mary)&kind(mary))))&
(![X]:((rich(X)&~humble(X))<=>~kind(X)))&
(![X]:((~brave(X)&~curious(X))<=>(~strong(X)|humble(X))))&
(((~happy(john)|~curious(john)))=>(~humble(mary)))&
(((rich(fred)<~>~kind(fred)))<=>(?[X]:((patient(X)&old(X)))))&
(![X]:(~strong(X)=>(humble(X)<~>~old(X))))&
(((~generous(mary)&patient(mary)))=>((calm(paul)&~brave(paul))))&
(![X]:((~curious(X)&~kind(X))<=>(~quiet(X)&~patient(X))))&
(![X]:((generous(X)|~generous(X))=>~humble(X)))&
((?[X]:((~calm(X)&funny(X))))=>(calm(john)))&
((~tall(fred)<~>quiet(fred)))&
((~rich(fred)<~>~strong(fred)))&
(?[X]:((calm(X)|rich(X))))&
(?[X]:((creative(X)&strong(X))))&
((humble(fred)<~>~generous(fred)))&
(?[X]:((~generous(X)<~>~strong(X))))&
((quiet(john)|wise(john))) | strong(fred) | [
"p1",
"p6",
"p7",
"p10",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2618981202739880388394852
% SZS output start Proof for 2618981202739880388394852
2. humble(john) <=> ? [X0] : ~patient(X0) [input p1]
7. ? [X0] : ~kind(X0) <=> (kind(mary) & old(mary)) [input p6]
8. ! [X0] : ((~humble(X0) & rich(X0)) <=> ~kind(X0)) [input p7]
11. (rich(fred) <~> ~kind(fred)) <=> ? [X0] : (old(X0) & patient(X0)) [input p10]
15. ! [X0] : ((~generous(X0) | generous(X0)) => ~humble(X0)) [input p14]
18. ~rich(fred) <~> ~strong(fred) [input p17]
24. ~strong(fred) [input hypothesis]
34. ! [X0] : (~humble(X0) | (generous(X0) & ~generous(X0))) [ennf transformation 15]
36. (humble(john) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | ~humble(john)) [nnf transformation 2]
37. (humble(john) | ! [X0] : patient(X0)) & (? [X1] : ~patient(X1) | ~humble(john)) [rectify 36]
38. ? [X1] : ~patient(X1) => ~patient(sK0) [choice axiom]
39. (humble(john) | ! [X0] : patient(X0)) & (~patient(sK0) | ~humble(john)) [skolemisation 37,38]
48. (? [X0] : ~kind(X0) | (~kind(mary) | ~old(mary))) & ((kind(mary) & old(mary)) | ! [X0] : kind(X0)) [nnf transformation 7]
49. (? [X0] : ~kind(X0) | ~kind(mary) | ~old(mary)) & ((kind(mary) & old(mary)) | ! [X0] : kind(X0)) [flattening 48]
50. (? [X0] : ~kind(X0) | ~kind(mary) | ~old(mary)) & ((kind(mary) & old(mary)) | ! [X1] : kind(X1)) [rectify 49]
51. ? [X0] : ~kind(X0) => ~kind(sK2) [choice axiom]
52. (~kind(sK2) | ~kind(mary) | ~old(mary)) & ((kind(mary) & old(mary)) | ! [X1] : kind(X1)) [skolemisation 50,51]
53. ! [X0] : (((~humble(X0) & rich(X0)) | kind(X0)) & (~kind(X0) | (humble(X0) | ~rich(X0)))) [nnf transformation 8]
54. ! [X0] : (((~humble(X0) & rich(X0)) | kind(X0)) & (~kind(X0) | humble(X0) | ~rich(X0))) [flattening 53]
57. (((kind(fred) | ~rich(fred)) & (~kind(fred) | rich(fred))) | ! [X0] : (~old(X0) | ~patient(X0))) & (? [X0] : (old(X0) & patient(X0)) | ((rich(fred) | kind(fred)) & (~kind(fred) | ~rich(fred)))) [nnf transformation 11]
58. (((kind(fred) | ~rich(fred)) & (~kind(fred) | rich(fred))) | ! [X0] : (~old(X0) | ~patient(X0))) & (? [X1] : (old(X1) & patient(X1)) | ((rich(fred) | kind(fred)) & (~kind(fred) | ~rich(fred)))) [rectify 57]
59. ? [X1] : (old(X1) & patient(X1)) => (old(sK3) & patient(sK3)) [choice axiom]
60. (((kind(fred) | ~rich(fred)) & (~kind(fred) | rich(fred))) | ! [X0] : (~old(X0) | ~patient(X0))) & ((old(sK3) & patient(sK3)) | ((rich(fred) | kind(fred)) & (~kind(fred) | ~rich(fred)))) [skolemisation 58,59]
65. (strong(fred) | rich(fred)) & (~strong(fred) | ~rich(fred)) [nnf transformation 18]
77. humble(john) | patient(X0) [cnf transformation 39]
102. old(mary) | kind(X1) [cnf transformation 52]
105. ~kind(X0) | humble(X0) | ~rich(X0) [cnf transformation 54]
106. kind(X0) | rich(X0) [cnf transformation 54]
119. kind(fred) | ~rich(fred) | ~old(X0) | ~patient(X0) [cnf transformation 60]
127. ~humble(X0) | ~generous(X0) [cnf transformation 34]
128. ~humble(X0) | generous(X0) [cnf transformation 34]
132. strong(fred) | rich(fred) [cnf transformation 65]
140. ~strong(fred) [cnf transformation 24]
144. 1 <=> ! [X0] : patient(X0) [avatar definition]
145. patient(X0) <- (1) [avatar component clause 144]
147. 2 <=> humble(john) [avatar definition]
149. humble(john) <- (2) [avatar component clause 147]
150. 1 | 2 [avatar split clause 77,147,144]
185. 10 <=> old(mary) [avatar definition]
186. old(mary) <- (10) [avatar component clause 185]
198. 13 <=> ! [X1] : kind(X1) [avatar definition]
199. kind(X1) <- (13) [avatar component clause 198]
201. 13 | 10 [avatar split clause 102,185,198]
211. kind(fred) | ~old(X0) | ~patient(X0) [subsumption resolution 119,106]
213. 16 <=> ! [X0] : (~old(X0) | ~patient(X0)) [avatar definition]
214. ~old(X0) | ~patient(X0) <- (16) [avatar component clause 213]
216. 17 <=> kind(fred) [avatar definition]
217. ~kind(fred) <- (~17) [avatar component clause 216]
218. kind(fred) <- (17) [avatar component clause 216]
219. 16 | 17 [avatar split clause 211,216,213]
222. 18 <=> rich(fred) [avatar definition]
224. rich(fred) <- (18) [avatar component clause 222]
249. ~humble(X0) [subsumption resolution 127,128]
261. 26 <=> strong(fred) [avatar definition]
264. 18 | 26 [avatar split clause 132,261,222]
286. ~26 [avatar split clause 140,261]
287. $false <- (2) [subsumption resolution 149,249]
288. ~2 [avatar contradiction clause 287]
299. ~patient(mary) <- (10, 16) [resolution 214,186]
300. $false <- (1, 10, 16) [subsumption resolution 299,145]
301. ~1 | ~10 | ~16 [avatar contradiction clause 300]
303. $false <- (13, ~17) [resolution 199,217]
304. ~13 | 17 [avatar contradiction clause 303]
328. humble(fred) | ~rich(fred) <- (17) [resolution 105,218]
330. ~rich(fred) <- (17) [subsumption resolution 328,249]
331. $false <- (17, 18) [subsumption resolution 330,224]
332. ~17 | ~18 [avatar contradiction clause 331]
333. $false [avatar sat refutation 150,201,219,264,286,288,301,304,332]
% SZS output end Proof for 2618981202739880388394852
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous or quiet is generous. If alice is not creative then john is generous and vice versa. If someone is both rich and quiet then john is creative. If alice is either humble or not rich then someone is both kind and humble. Everyone who is either rich or not tall is rich and vice versa. If mary is not kind then susan is not humble or calm and vice versa. If someone is either brave or not calm then paul is wise or happy. Everyone who is brave or tall is not strong or not generous. Everyone who is kind or funny is both not creative and humble. Everyone who is quiet is both humble and calm and vice versa. Everyone who is not calm or calm is either not humble or calm and vice versa. If mary is curious then someone is both not calm and creative and vice versa. If john is either happy or not old then john is creative or not old and vice versa. If alice is quiet or not tall then lucy is not quiet or patient. Everyone who is either wise or not humble is not brave or not rich. Everyone who is either creative or curious is both not rich and kind and vice versa. Someone is not quiet or funny. Someone is funny or happy. John is either strong or not creative. Lucy is not kind or not tall. Mary is generous or not tall. Susan is strong. Lucy is both generous and funny. Someone is both quiet and not wise. | Lucy is not calm. | contradiction | (![X]:((generous(X)|quiet(X))=>generous(X)))&
((~creative(alice))<=>(generous(john)))&
((?[X]:((rich(X)&quiet(X))))=>(creative(john)))&
(((humble(alice)<~>~rich(alice)))=>(?[X]:((kind(X)&humble(X)))))&
(![X]:((rich(X)<~>~tall(X))<=>rich(X)))&
((~kind(mary))<=>((~humble(susan)|calm(susan))))&
((?[X]:((brave(X)<~>~calm(X))))=>((wise(paul)|happy(paul))))&
(![X]:((brave(X)|tall(X))=>(~strong(X)|~generous(X))))&
(![X]:((kind(X)|funny(X))=>(~creative(X)&humble(X))))&
(![X]:(quiet(X)<=>(humble(X)&calm(X))))&
(![X]:((~calm(X)|calm(X))<=>(~humble(X)<~>calm(X))))&
((curious(mary))<=>(?[X]:((~calm(X)&creative(X)))))&
(((happy(john)<~>~old(john)))<=>((creative(john)|~old(john))))&
(((quiet(alice)|~tall(alice)))=>((~quiet(lucy)|patient(lucy))))&
(![X]:((wise(X)<~>~humble(X))=>(~brave(X)|~rich(X))))&
(![X]:((creative(X)<~>curious(X))<=>(~rich(X)&kind(X))))&
(?[X]:((~quiet(X)|funny(X))))&
(?[X]:((funny(X)|happy(X))))&
((strong(john)<~>~creative(john)))&
((~kind(lucy)|~tall(lucy)))&
((generous(mary)|~tall(mary)))&
(strong(susan))&
((generous(lucy)&funny(lucy)))&
(?[X]:((quiet(X)&~wise(X)))) | ~calm(lucy) | [
"p8",
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3379891595213902664384038
% SZS output start Proof for 3379891595213902664384038
9. ! [X0] : ((funny(X0) | kind(X0)) => (humble(X0) & ~creative(X0))) [input p8]
11. ! [X0] : ((calm(X0) | ~calm(X0)) <=> (~humble(X0) <~> calm(X0))) [input p10]
23. funny(lucy) & generous(lucy) [input p22]
25. ~calm(lucy) [input hypothesis]
34. ! [X0] : ((humble(X0) & ~creative(X0)) | (~funny(X0) & ~kind(X0))) [ennf transformation 9]
47. ! [X0] : (((calm(X0) | ~calm(X0)) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0)))) & (((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | (~calm(X0) & calm(X0)))) [nnf transformation 11]
48. ! [X0] : ((calm(X0) | ~calm(X0) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0)))) & (((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | (~calm(X0) & calm(X0)))) [flattening 47]
88. ~funny(X0) | humble(X0) [cnf transformation 34]
92. calm(X0) | ~humble(X0) | calm(X0) [cnf transformation 48]
123. funny(lucy) [cnf transformation 23]
126. ~calm(lucy) [cnf transformation 25]
129. ~humble(X0) | calm(X0) [duplicate literal removal 92]
267. humble(lucy) [resolution 88,123]
271. calm(lucy) [resolution 129,267]
274. $false [subsumption resolution 271,126]
% SZS output end Proof for 3379891595213902664384038
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy is either not creative or rich and vice versa.
Everyone who is not generous or not creative is both tall and not calm.
If someone is calm or old then someone is strong and vice versa.
Everyone who is humble is both humble and brave.
If someone is either happy or humble then someone is not patient.
If paul is both not calm and old then someone is both not generous and not kind and vice versa.
Everyone who is curious or wise is rich or calm.
If someone is not calm or tall then paul is curious and vice versa.
Everyone who is rich is either funny or strong.
If fred is both wise and humble then alice is either not strong or tall.
Everyone who is patient is either not wise or not strong.
Everyone who is not calm is both not tall and not quiet and vice versa.
If john is either kind or not curious then someone is either not humble or generous.
If someone is not happy then someone is happy or patient.
If someone is not kind or strong then mary is either humble or not tall.
Everyone who is not rich is not old or not calm.
Someone is not quiet or funny.
Someone is either not calm or curious.
Alice is creative or not quiet.
Mary is both tall and patient.
Susan is happy.
John is both not curious and not happy.
Someone is either curious or strong.
Someone is either generous or not curious. | Paul is creative. | entailment | (![X]:(happy(X)<=>(~creative(X)<~>rich(X))))&
(![X]:((~generous(X)|~creative(X))=>(tall(X)&~calm(X))))&
((?[X]:((calm(X)|old(X))))<=>(?[X]:(strong(X))))&
(![X]:(humble(X)=>(humble(X)&brave(X))))&
((?[X]:((happy(X)<~>humble(X))))=>(?[X]:(~patient(X))))&
(((~calm(paul)&old(paul)))<=>(?[X]:((~generous(X)&~kind(X)))))&
(![X]:((curious(X)|wise(X))=>(rich(X)|calm(X))))&
((?[X]:((~calm(X)|tall(X))))<=>(curious(paul)))&
(![X]:(rich(X)=>(funny(X)<~>strong(X))))&
(((wise(fred)&humble(fred)))=>((~strong(alice)<~>tall(alice))))&
(![X]:(patient(X)=>(~wise(X)<~>~strong(X))))&
(![X]:(~calm(X)<=>(~tall(X)&~quiet(X))))&
(((kind(john)<~>~curious(john)))=>(?[X]:((~humble(X)<~>generous(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((happy(X)|patient(X)))))&
((?[X]:((~kind(X)|strong(X))))=>((humble(mary)<~>~tall(mary))))&
(![X]:(~rich(X)=>(~old(X)|~calm(X))))&
(?[X]:((~quiet(X)|funny(X))))&
(?[X]:((~calm(X)<~>curious(X))))&
((creative(alice)|~quiet(alice)))&
((tall(mary)&patient(mary)))&
(happy(susan))&
((~curious(john)&~happy(john)))&
(?[X]:((curious(X)<~>strong(X))))&
(?[X]:((generous(X)<~>~curious(X)))) | creative(paul) | [
"p1",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 576461343331034747749802
% SZS output start Proof for 576461343331034747749802
2. ! [X0] : ((~creative(X0) | ~generous(X0)) => (~calm(X0) & tall(X0))) [input p1]
12. ! [X0] : (~calm(X0) <=> (~quiet(X0) & ~tall(X0))) [input p11]
25. ~creative(paul) [input hypothesis]
30. ! [X0] : ((~calm(X0) & tall(X0)) | (creative(X0) & generous(X0))) [ennf transformation 2]
66. ! [X0] : ((~calm(X0) | (quiet(X0) | tall(X0))) & ((~quiet(X0) & ~tall(X0)) | calm(X0))) [nnf transformation 12]
67. ! [X0] : ((~calm(X0) | quiet(X0) | tall(X0)) & ((~quiet(X0) & ~tall(X0)) | calm(X0))) [flattening 66]
91. tall(X0) | creative(X0) [cnf transformation 30]
93. ~calm(X0) | creative(X0) [cnf transformation 30]
115. ~tall(X0) | calm(X0) [cnf transformation 67]
141. ~creative(paul) [cnf transformation 25]
342. calm(X0) | creative(X0) [resolution 115,91]
344. creative(X0) [subsumption resolution 342,93]
348. $false [resolution 344,141]
% SZS output end Proof for 576461343331034747749802
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny then someone is happy or not happy and vice versa. Everyone who is rich or creative is either not generous or humble and vice versa. If someone is either creative or happy then fred is either curious or not patient and vice versa. Everyone who is old is either funny or not tall. Everyone who is calm or not funny is both not brave and not rich. If alice is either not quiet or kind then john is not funny or rich and vice versa. Everyone who is not rich is both funny and calm and vice versa. Everyone who is brave is not generous and vice versa. If someone is rich or not patient then someone is generous or not happy and vice versa. If fred is creative or not wise then lucy is tall. If someone is either not humble or not creative then mary is either funny or brave. Everyone who is not brave or calm is wise or not generous and vice versa. If alice is both rich and strong then susan is not curious. Everyone who is not old or not patient is both not patient and not old and vice versa. If paul is not kind or generous then someone is generous or quiet and vice versa. If susan is either calm or strong then someone is both not humble and not quiet and vice versa. Someone is curious or creative. Someone is either not tall or generous. Alice is not creative or creative. Someone is either patient or not creative. John is not curious. Alice is either patient or kind. | Lucy is not creative. | neutral | ((?[X]:(funny(X)))<=>(?[X]:((happy(X)|~happy(X)))))&
(![X]:((rich(X)|creative(X))<=>(~generous(X)<~>humble(X))))&
((?[X]:((creative(X)<~>happy(X))))<=>((curious(fred)<~>~patient(fred))))&
(![X]:(old(X)=>(funny(X)<~>~tall(X))))&
(![X]:((calm(X)|~funny(X))=>(~brave(X)&~rich(X))))&
(((~quiet(alice)<~>kind(alice)))<=>((~funny(john)|rich(john))))&
(![X]:(~rich(X)<=>(funny(X)&calm(X))))&
(![X]:(brave(X)<=>~generous(X)))&
((?[X]:((rich(X)|~patient(X))))<=>(?[X]:((generous(X)|~happy(X)))))&
(((creative(fred)|~wise(fred)))=>(tall(lucy)))&
((?[X]:((~humble(X)<~>~creative(X))))=>((funny(mary)<~>brave(mary))))&
(![X]:((~brave(X)|calm(X))<=>(wise(X)|~generous(X))))&
(((rich(alice)&strong(alice)))=>(~curious(susan)))&
(![X]:((~old(X)|~patient(X))<=>(~patient(X)&~old(X))))&
(((~kind(paul)|generous(paul)))<=>(?[X]:((generous(X)|quiet(X)))))&
(((calm(susan)<~>strong(susan)))<=>(?[X]:((~humble(X)&~quiet(X)))))&
(?[X]:((curious(X)|creative(X))))&
(?[X]:((~tall(X)<~>generous(X))))&
((~creative(alice)|creative(alice)))&
(?[X]:((patient(X)<~>~creative(X))))&
(~curious(john))&
((patient(alice)<~>kind(alice))) | ~creative(lucy) | [] | null | 0 |
Everyone who is both not tall and creative is not brave and vice versa.
Everyone who is either brave or not brave is happy or not wise and vice versa.
If alice is both not quiet and not kind then someone is not brave or curious and vice versa.
If fred is rich or not humble then john is quiet or not kind and vice versa.
If mary is both not kind and not tall then someone is both not humble and not happy and vice versa.
Everyone who is not strong or not old is not old.
If someone is both not generous and creative then lucy is either wise or not happy and vice versa.
Everyone who is not quiet or patient is patient.
If mary is patient then mary is both not happy and not calm.
Everyone who is not quiet or generous is happy and vice versa.
Everyone who is not kind or brave is either wise or happy.
Everyone who is generous is both not rich and strong.
If mary is either not rich or old then someone is curious or not humble and vice versa.
Everyone who is not old is either not old or kind and vice versa.
If someone is not humble then fred is calm or happy and vice versa.
Everyone who is both not funny and happy is not funny and vice versa.
Lucy is wise or humble.
Someone is both not creative and not generous.
Someone is generous.
Alice is either tall or rich.
Someone is not strong.
Alice is either not patient or not brave.
Paul is either brave or patient. | John is happy. | entailment | (![X]:((~tall(X)&creative(X))<=>~brave(X)))&
(![X]:((brave(X)<~>~brave(X))<=>(happy(X)|~wise(X))))&
(((~quiet(alice)&~kind(alice)))<=>(?[X]:((~brave(X)|curious(X)))))&
(((rich(fred)|~humble(fred)))<=>((quiet(john)|~kind(john))))&
(((~kind(mary)&~tall(mary)))<=>(?[X]:((~humble(X)&~happy(X)))))&
(![X]:((~strong(X)|~old(X))=>~old(X)))&
((?[X]:((~generous(X)&creative(X))))<=>((wise(lucy)<~>~happy(lucy))))&
(![X]:((~quiet(X)|patient(X))=>patient(X)))&
((patient(mary))=>((~happy(mary)&~calm(mary))))&
(![X]:((~quiet(X)|generous(X))<=>happy(X)))&
(![X]:((~kind(X)|brave(X))=>(wise(X)<~>happy(X))))&
(![X]:(generous(X)=>(~rich(X)&strong(X))))&
(((~rich(mary)<~>old(mary)))<=>(?[X]:((curious(X)|~humble(X)))))&
(![X]:(~old(X)<=>(~old(X)<~>kind(X))))&
((?[X]:(~humble(X)))<=>((calm(fred)|happy(fred))))&
(![X]:((~funny(X)&happy(X))<=>~funny(X)))&
((wise(lucy)|humble(lucy)))&
(?[X]:((~creative(X)&~generous(X))))&
(?[X]:(generous(X)))&
((tall(alice)<~>rich(alice)))&
(?[X]:(~strong(X)))&
((~patient(alice)<~>~brave(alice)))&
((brave(paul)<~>patient(paul))) | happy(john) | [
"p1",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8893990141541982624301575
% SZS output start Proof for 8893990141541982624301575
2. ! [X0] : ((brave(X0) <~> ~brave(X0)) <=> (~wise(X0) | happy(X0))) [input p1]
11. ! [X0] : ((brave(X0) | ~kind(X0)) => (wise(X0) <~> happy(X0))) [input p10]
14. ! [X0] : (~old(X0) <=> (~old(X0) <~> kind(X0))) [input p13]
24. ~happy(john) [input hypothesis]
28. ! [X0] : ((wise(X0) <~> happy(X0)) | (~brave(X0) & kind(X0))) [ennf transformation 11]
32. ! [X0] : ((((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | (wise(X0) & ~happy(X0))) & ((~wise(X0) | happy(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0))))) [nnf transformation 2]
33. ! [X0] : ((((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | (wise(X0) & ~happy(X0))) & (~wise(X0) | happy(X0) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0))))) [flattening 32]
52. ! [X0] : (((~happy(X0) | ~wise(X0)) & (happy(X0) | wise(X0))) | (~brave(X0) & kind(X0))) [nnf transformation 28]
57. ! [X0] : ((~old(X0) | ((~old(X0) | ~kind(X0)) & (kind(X0) | old(X0)))) & (((~kind(X0) | old(X0)) & (kind(X0) | ~old(X0))) | old(X0))) [nnf transformation 14]
77. ~wise(X0) | happy(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 33]
78. ~wise(X0) | happy(X0) | brave(X0) | brave(X0) [cnf transformation 33]
111. happy(X0) | wise(X0) | kind(X0) [cnf transformation 52]
113. ~happy(X0) | ~wise(X0) | kind(X0) [cnf transformation 52]
124. ~kind(X0) | old(X0) | old(X0) [cnf transformation 57]
126. ~old(X0) | ~old(X0) | ~kind(X0) [cnf transformation 57]
144. ~happy(john) [cnf transformation 24]
145. ~kind(X0) | old(X0) [duplicate literal removal 124]
146. ~old(X0) | ~kind(X0) [duplicate literal removal 126]
147. ~wise(X0) | happy(X0) | ~brave(X0) [duplicate literal removal 77]
148. ~wise(X0) | happy(X0) | brave(X0) [duplicate literal removal 78]
149. ~wise(X0) | happy(X0) [subsumption resolution 147,148]
263. ~wise(X0) | kind(X0) [subsumption resolution 113,149]
265. kind(X0) | happy(X0) [subsumption resolution 111,263]
291. ~kind(X0) [subsumption resolution 145,146]
376. happy(X0) [resolution 265,291]
377. $false [resolution 376,144]
% SZS output end Proof for 8893990141541982624301575
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either quiet or rich then fred is not curious or calm. If someone is not calm or generous then fred is happy or quiet. Everyone who is old is not quiet or calm and vice versa. If someone is not rich or tall then someone is both funny and curious and vice versa. Everyone who is both not curious and not tall is either not strong or funny and vice versa. If someone is happy or patient then someone is both not quiet and not funny. Everyone who is not rich or not creative is curious or happy. If fred is either calm or creative then mary is happy. If someone is both brave and generous then john is not kind or not wise. Everyone who is not strong is both not patient and not kind and vice versa. Everyone who is curious is both tall and not tall. Everyone who is humble is both not generous and calm and vice versa. Everyone who is not generous is calm or not wise. If susan is not wise then someone is not tall and vice versa. If someone is either kind or humble then someone is not strong or humble and vice versa. Someone is not creative or not curious. Someone is rich. Someone is both rich and old. Someone is either not creative or not funny. Someone is both not happy and not strong. | Mary is rich. | entailment | (((quiet(paul)<~>rich(paul)))=>((~curious(fred)|calm(fred))))&
((?[X]:((~calm(X)|generous(X))))=>((happy(fred)|quiet(fred))))&
(![X]:(old(X)<=>(~quiet(X)|calm(X))))&
((?[X]:((~rich(X)|tall(X))))<=>(?[X]:((funny(X)&curious(X)))))&
(![X]:((~curious(X)&~tall(X))<=>(~strong(X)<~>funny(X))))&
((?[X]:((happy(X)|patient(X))))=>(?[X]:((~quiet(X)&~funny(X)))))&
(![X]:((~rich(X)|~creative(X))=>(curious(X)|happy(X))))&
(((calm(fred)<~>creative(fred)))=>(happy(mary)))&
((?[X]:((brave(X)&generous(X))))=>((~kind(john)|~wise(john))))&
(![X]:(~strong(X)<=>(~patient(X)&~kind(X))))&
(![X]:(curious(X)=>(tall(X)&~tall(X))))&
(![X]:(humble(X)<=>(~generous(X)&calm(X))))&
(![X]:(~generous(X)=>(calm(X)|~wise(X))))&
((~wise(susan))<=>(?[X]:(~tall(X))))&
((?[X]:((kind(X)<~>humble(X))))<=>(?[X]:((~strong(X)|humble(X)))))&
(?[X]:((~creative(X)|~curious(X))))&
(?[X]:(rich(X)))&
(?[X]:((rich(X)&old(X))))&
(?[X]:((~creative(X)<~>~funny(X))))&
(?[X]:((~happy(X)&~strong(X)))) | rich(mary) | [
"p3",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1073286613090825595671053
% SZS output start Proof for 1073286613090825595671053
4. ? [X0] : (tall(X0) | ~rich(X0)) <=> ? [X0] : (curious(X0) & funny(X0)) [input p3]
11. ! [X0] : (curious(X0) => (~tall(X0) & tall(X0))) [input p10]
21. ~rich(mary) [input hypothesis]
22. ? [X0] : (tall(X0) | ~rich(X0)) <=> ? [X1] : (curious(X1) & funny(X1)) [rectify 4]
37. ! [X0] : ((~tall(X0) & tall(X0)) | ~curious(X0)) [ennf transformation 11]
41. (? [X0] : (tall(X0) | ~rich(X0)) | ! [X1] : (~curious(X1) | ~funny(X1))) & (? [X1] : (curious(X1) & funny(X1)) | ! [X0] : (~tall(X0) & rich(X0))) [nnf transformation 22]
42. (? [X0] : (tall(X0) | ~rich(X0)) | ! [X1] : (~curious(X1) | ~funny(X1))) & (? [X2] : (curious(X2) & funny(X2)) | ! [X3] : (~tall(X3) & rich(X3))) [rectify 41]
43. ? [X0] : (tall(X0) | ~rich(X0)) => (tall(sK0) | ~rich(sK0)) [choice axiom]
44. ? [X2] : (curious(X2) & funny(X2)) => (curious(sK1) & funny(sK1)) [choice axiom]
45. ((tall(sK0) | ~rich(sK0)) | ! [X1] : (~curious(X1) | ~funny(X1))) & ((curious(sK1) & funny(sK1)) | ! [X3] : (~tall(X3) & rich(X3))) [skolemisation 42,44,43]
83. curious(sK1) | rich(X3) [cnf transformation 45]
103. tall(X0) | ~curious(X0) [cnf transformation 37]
104. ~tall(X0) | ~curious(X0) [cnf transformation 37]
125. ~rich(mary) [cnf transformation 21]
176. 13 <=> curious(sK1) [avatar definition]
178. curious(sK1) <- (13) [avatar component clause 176]
181. 14 <=> ! [X3] : rich(X3) [avatar definition]
182. rich(X3) <- (14) [avatar component clause 181]
183. 14 | 13 [avatar split clause 83,176,181]
218. ~curious(X0) [subsumption resolution 103,104]
278. $false <- (14) [resolution 182,125]
279. ~14 [avatar contradiction clause 278]
280. $false <- (13) [subsumption resolution 178,218]
281. ~13 [avatar contradiction clause 280]
282. $false [avatar sat refutation 183,279,281]
% SZS output end Proof for 1073286613090825595671053
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is not old or strong then someone is not generous or not funny.
If susan is not old then someone is both not generous and creative.
If lucy is happy then someone is not curious and vice versa.
Everyone who is both generous and old is either rich or not calm and vice versa.
If someone is quiet or not calm then paul is not old.
If someone is not calm or not happy then susan is either not rich or creative and vice versa.
Everyone who is either creative or not curious is both not rich and happy and vice versa.
Everyone who is kind is either generous or not quiet.
Everyone who is patient or wise is tall or not rich and vice versa.
Everyone who is not generous is patient and vice versa.
Everyone who is generous is either calm or kind and vice versa.
Everyone who is calm or not kind is both not generous and generous.
Everyone who is not brave is either not calm or brave and vice versa.
If someone is either not rich or generous then someone is either quiet or brave.
Everyone who is old is both not happy and tall.
Someone is not happy.
Someone is not humble.
Someone is either not creative or not curious.
Someone is either humble or not old.
Someone is either not humble or happy.
Someone is not strong. | Paul is wise. | neutral | (((~old(alice)|strong(alice)))=>(?[X]:((~generous(X)|~funny(X)))))&
((~old(susan))=>(?[X]:((~generous(X)&creative(X)))))&
((happy(lucy))<=>(?[X]:(~curious(X))))&
(![X]:((generous(X)&old(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((quiet(X)|~calm(X))))=>(~old(paul)))&
((?[X]:((~calm(X)|~happy(X))))<=>((~rich(susan)<~>creative(susan))))&
(![X]:((creative(X)<~>~curious(X))<=>(~rich(X)&happy(X))))&
(![X]:(kind(X)=>(generous(X)<~>~quiet(X))))&
(![X]:((patient(X)|wise(X))<=>(tall(X)|~rich(X))))&
(![X]:(~generous(X)<=>patient(X)))&
(![X]:(generous(X)<=>(calm(X)<~>kind(X))))&
(![X]:((calm(X)|~kind(X))=>(~generous(X)&generous(X))))&
(![X]:(~brave(X)<=>(~calm(X)<~>brave(X))))&
((?[X]:((~rich(X)<~>generous(X))))=>(?[X]:((quiet(X)<~>brave(X)))))&
(![X]:(old(X)=>(~happy(X)&tall(X))))&
(?[X]:(~happy(X)))&
(?[X]:(~humble(X)))&
(?[X]:((~creative(X)<~>~curious(X))))&
(?[X]:((humble(X)<~>~old(X))))&
(?[X]:((~humble(X)<~>happy(X))))&
(?[X]:(~strong(X))) | wise(paul) | [] | null | 0 |
If someone is rich or brave then mary is both creative and not funny and vice versa. If someone is either not rich or creative then someone is old. Everyone who is not brave or kind is either not tall or not generous. If mary is either generous or humble then fred is creative or quiet. If someone is not happy or not tall then alice is either strong or curious. If john is not strong then someone is wise or kind and vice versa. Everyone who is creative is both calm and not generous. Everyone who is kind is either not kind or brave. Everyone who is either not strong or patient is not calm. If paul is either rich or curious then someone is happy or strong and vice versa. Everyone who is not wise or funny is not happy and vice versa. If mary is both kind and funny then someone is not strong or not brave and vice versa. Everyone who is both old and humble is wise. If someone is not strong then someone is not brave or strong. Everyone who is not generous or not kind is creative. If someone is rich or not rich then someone is both not funny and curious. Someone is not quiet. Someone is both not tall and not funny. Paul is curious or not curious. | Mary is humble. | neutral | ((?[X]:((rich(X)|brave(X))))<=>((creative(mary)&~funny(mary))))&
((?[X]:((~rich(X)<~>creative(X))))=>(?[X]:(old(X))))&
(![X]:((~brave(X)|kind(X))=>(~tall(X)<~>~generous(X))))&
(((generous(mary)<~>humble(mary)))=>((creative(fred)|quiet(fred))))&
((?[X]:((~happy(X)|~tall(X))))=>((strong(alice)<~>curious(alice))))&
((~strong(john))<=>(?[X]:((wise(X)|kind(X)))))&
(![X]:(creative(X)=>(calm(X)&~generous(X))))&
(![X]:(kind(X)=>(~kind(X)<~>brave(X))))&
(![X]:((~strong(X)<~>patient(X))=>~calm(X)))&
(((rich(paul)<~>curious(paul)))<=>(?[X]:((happy(X)|strong(X)))))&
(![X]:((~wise(X)|funny(X))<=>~happy(X)))&
(((kind(mary)&funny(mary)))<=>(?[X]:((~strong(X)|~brave(X)))))&
(![X]:((old(X)&humble(X))=>wise(X)))&
((?[X]:(~strong(X)))=>(?[X]:((~brave(X)|strong(X)))))&
(![X]:((~generous(X)|~kind(X))=>creative(X)))&
((?[X]:((rich(X)|~rich(X))))=>(?[X]:((~funny(X)&curious(X)))))&
(?[X]:(~quiet(X)))&
(?[X]:((~tall(X)&~funny(X))))&
((curious(paul)|~curious(paul))) | humble(mary) | [] | null | 0 |
If someone is kind then lucy is either generous or tall and vice versa. If someone is not tall then someone is old or generous and vice versa. If alice is either old or not kind then lucy is both brave and humble and vice versa. If someone is either kind or not strong then paul is either not humble or tall and vice versa. Everyone who is either not curious or wise is old and vice versa. Everyone who is funny is either not happy or quiet. If john is not creative then someone is either not generous or tall. Everyone who is not rich or calm is either rich or not tall. Everyone who is both not calm and not brave is both not rich and creative. If someone is both tall and humble then someone is both tall and rich and vice versa. If fred is either strong or not wise then someone is either not brave or humble. Everyone who is not funny or calm is quiet or not humble and vice versa. If mary is either not creative or not quiet then someone is both kind and not strong and vice versa. Everyone who is generous is either quiet or not calm and vice versa. Everyone who is calm or not happy is either not old or not tall and vice versa. Everyone who is not patient or not kind is either not strong or not happy and vice versa. Mary is either tall or not old. Someone is both not calm and not strong. Someone is both tall and not humble. Someone is not rich or not old. Mary is not curious. Susan is not tall or generous. Alice is both brave and not creative. | John is not brave. | neutral | ((?[X]:(kind(X)))<=>((generous(lucy)<~>tall(lucy))))&
((?[X]:(~tall(X)))<=>(?[X]:((old(X)|generous(X)))))&
(((old(alice)<~>~kind(alice)))<=>((brave(lucy)&humble(lucy))))&
((?[X]:((kind(X)<~>~strong(X))))<=>((~humble(paul)<~>tall(paul))))&
(![X]:((~curious(X)<~>wise(X))<=>old(X)))&
(![X]:(funny(X)=>(~happy(X)<~>quiet(X))))&
((~creative(john))=>(?[X]:((~generous(X)<~>tall(X)))))&
(![X]:((~rich(X)|calm(X))=>(rich(X)<~>~tall(X))))&
(![X]:((~calm(X)&~brave(X))=>(~rich(X)&creative(X))))&
((?[X]:((tall(X)&humble(X))))<=>(?[X]:((tall(X)&rich(X)))))&
(((strong(fred)<~>~wise(fred)))=>(?[X]:((~brave(X)<~>humble(X)))))&
(![X]:((~funny(X)|calm(X))<=>(quiet(X)|~humble(X))))&
(((~creative(mary)<~>~quiet(mary)))<=>(?[X]:((kind(X)&~strong(X)))))&
(![X]:(generous(X)<=>(quiet(X)<~>~calm(X))))&
(![X]:((calm(X)|~happy(X))<=>(~old(X)<~>~tall(X))))&
(![X]:((~patient(X)|~kind(X))<=>(~strong(X)<~>~happy(X))))&
((tall(mary)<~>~old(mary)))&
(?[X]:((~calm(X)&~strong(X))))&
(?[X]:((tall(X)&~humble(X))))&
(?[X]:((~rich(X)|~old(X))))&
(~curious(mary))&
((~tall(susan)|generous(susan)))&
((brave(alice)&~creative(alice))) | ~brave(john) | [] | null | 0 |
Everyone who is either not generous or not wise is either creative or not generous and vice versa.
Everyone who is tall or wise is not curious or not kind and vice versa.
If alice is not funny then someone is not humble or quiet.
If alice is both patient and not tall then someone is both not calm and not strong.
If lucy is not patient then someone is both patient and not patient.
Everyone who is not humble is both not rich and not generous.
Everyone who is quiet is not wise.
If someone is either curious or old then susan is not rich or not strong and vice versa.
Everyone who is both not patient and not creative is funny and vice versa.
Everyone who is either calm or generous is either not generous or not curious.
If someone is funny or not tall then someone is both funny and not happy and vice versa.
Everyone who is both creative and not quiet is patient or not creative and vice versa.
If someone is either not funny or not old then someone is calm.
If paul is creative or old then alice is either not kind or rich and vice versa.
Someone is not curious.
Paul is either not rich or not wise.
Paul is not curious.
John is either generous or not quiet.
Paul is not wise or not creative. | Lucy is patient. | entailment | (![X]:((~generous(X)<~>~wise(X))<=>(creative(X)<~>~generous(X))))&
(![X]:((tall(X)|wise(X))<=>(~curious(X)|~kind(X))))&
((~funny(alice))=>(?[X]:((~humble(X)|quiet(X)))))&
(((patient(alice)&~tall(alice)))=>(?[X]:((~calm(X)&~strong(X)))))&
((~patient(lucy))=>(?[X]:((patient(X)&~patient(X)))))&
(![X]:(~humble(X)=>(~rich(X)&~generous(X))))&
(![X]:(quiet(X)=>~wise(X)))&
((?[X]:((curious(X)<~>old(X))))<=>((~rich(susan)|~strong(susan))))&
(![X]:((~patient(X)&~creative(X))<=>funny(X)))&
(![X]:((calm(X)<~>generous(X))=>(~generous(X)<~>~curious(X))))&
((?[X]:((funny(X)|~tall(X))))<=>(?[X]:((funny(X)&~happy(X)))))&
(![X]:((creative(X)&~quiet(X))<=>(patient(X)|~creative(X))))&
((?[X]:((~funny(X)<~>~old(X))))=>(?[X]:(calm(X))))&
(((creative(paul)|old(paul)))<=>((~kind(alice)<~>rich(alice))))&
(?[X]:(~curious(X)))&
((~rich(paul)<~>~wise(paul)))&
(~curious(paul))&
((generous(john)<~>~quiet(john)))&
((~wise(paul)|~creative(paul))) | patient(lucy) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 1225523355250632732283600
% SZS output start Proof for 1225523355250632732283600
5. ~patient(lucy) => ? [X0] : (~patient(X0) & patient(X0)) [input p4]
20. ~patient(lucy) [input hypothesis]
26. ? [X0] : (~patient(X0) & patient(X0)) | patient(lucy) [ennf transformation 5]
38. ? [X0] : (~patient(X0) & patient(X0)) => (~patient(sK2) & patient(sK2)) [choice axiom]
39. (~patient(sK2) & patient(sK2)) | patient(lucy) [skolemisation 26,38]
80. patient(sK2) | patient(lucy) [cnf transformation 39]
81. ~patient(sK2) | patient(lucy) [cnf transformation 39]
123. ~patient(lucy) [cnf transformation 20]
166. 8 <=> patient(lucy) [avatar definition]
170. 9 <=> patient(sK2) [avatar definition]
173. 8 | ~9 [avatar split clause 81,170,166]
174. 8 | 9 [avatar split clause 80,170,166]
284. ~8 [avatar split clause 123,166]
285. $false [avatar sat refutation 173,174,284]
% SZS output end Proof for 1225523355250632732283600
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If mary is brave then someone is strong.
If fred is patient then fred is not wise or humble and vice versa.
If someone is not quiet then someone is both quiet and not creative.
Everyone who is either happy or kind is either creative or happy.
Everyone who is calm or not calm is curious or not funny and vice versa.
Everyone who is not old or not brave is calm or old and vice versa.
Everyone who is either creative or not funny is not kind or creative and vice versa.
If susan is kind then john is either not calm or calm and vice versa.
If john is humble then paul is both generous and not happy.
If someone is strong or not quiet then lucy is happy and vice versa.
Everyone who is not calm is both kind and not kind.
Everyone who is not rich is either wise or not wise and vice versa.
Everyone who is not creative or not curious is either not rich or not creative.
Everyone who is kind or not brave is not rich or not strong.
If mary is either not patient or generous then john is both calm and not kind and vice versa.
Everyone who is both not quiet and not wise is strong or not strong.
Someone is patient or not old.
Lucy is not patient.
Someone is both quiet and humble.
Someone is brave or not humble.
Alice is both generous and calm.
Someone is funny.
Fred is either rich or generous. | Alice is not quiet. | contradiction | ((brave(mary))=>(?[X]:(strong(X))))&
((patient(fred))<=>((~wise(fred)|humble(fred))))&
((?[X]:(~quiet(X)))=>(?[X]:((quiet(X)&~creative(X)))))&
(![X]:((happy(X)<~>kind(X))=>(creative(X)<~>happy(X))))&
(![X]:((calm(X)|~calm(X))<=>(curious(X)|~funny(X))))&
(![X]:((~old(X)|~brave(X))<=>(calm(X)|old(X))))&
(![X]:((creative(X)<~>~funny(X))<=>(~kind(X)|creative(X))))&
((kind(susan))<=>((~calm(john)<~>calm(john))))&
((humble(john))=>((generous(paul)&~happy(paul))))&
((?[X]:((strong(X)|~quiet(X))))<=>(happy(lucy)))&
(![X]:(~calm(X)=>(kind(X)&~kind(X))))&
(![X]:(~rich(X)<=>(wise(X)<~>~wise(X))))&
(![X]:((~creative(X)|~curious(X))=>(~rich(X)<~>~creative(X))))&
(![X]:((kind(X)|~brave(X))=>(~rich(X)|~strong(X))))&
(((~patient(mary)<~>generous(mary)))<=>((calm(john)&~kind(john))))&
(![X]:((~quiet(X)&~wise(X))=>(strong(X)|~strong(X))))&
(?[X]:((patient(X)|~old(X))))&
(~patient(lucy))&
(?[X]:((quiet(X)&humble(X))))&
(?[X]:((brave(X)|~humble(X))))&
((generous(alice)&calm(alice)))&
(?[X]:(funny(X)))&
((rich(fred)<~>generous(fred))) | ~quiet(alice) | [
"p2",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 65080133616344160092256
% SZS output start Proof for 65080133616344160092256
3. ? [X0] : ~quiet(X0) => ? [X0] : (~creative(X0) & quiet(X0)) [input p2]
12. ! [X0] : (~rich(X0) <=> (wise(X0) <~> ~wise(X0))) [input p11]
13. ! [X0] : ((~curious(X0) | ~creative(X0)) => (~rich(X0) <~> ~creative(X0))) [input p12]
24. ~quiet(alice) [input hypothesis]
25. ? [X0] : ~quiet(X0) => ? [X1] : (~creative(X1) & quiet(X1)) [rectify 3]
27. ? [X1] : (~creative(X1) & quiet(X1)) | ! [X0] : quiet(X0) [ennf transformation 25]
31. ! [X0] : ((~rich(X0) <~> ~creative(X0)) | (curious(X0) & creative(X0))) [ennf transformation 13]
40. ? [X0] : (~creative(X0) & quiet(X0)) | ! [X1] : quiet(X1) [rectify 27]
41. ? [X0] : (~creative(X0) & quiet(X0)) => (~creative(sK1) & quiet(sK1)) [choice axiom]
42. (~creative(sK1) & quiet(sK1)) | ! [X1] : quiet(X1) [skolemisation 40,41]
55. ! [X0] : ((~rich(X0) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | rich(X0))) [nnf transformation 12]
56. ! [X0] : (((creative(X0) | rich(X0)) & (~creative(X0) | ~rich(X0))) | (curious(X0) & creative(X0))) [nnf transformation 31]
73. ~creative(sK1) | quiet(X1) [cnf transformation 42]
105. ~rich(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 55]
106. ~rich(X0) | wise(X0) | wise(X0) [cnf transformation 55]
109. creative(X0) | rich(X0) | creative(X0) [cnf transformation 56]
130. ~quiet(alice) [cnf transformation 24]
131. creative(X0) | rich(X0) [duplicate literal removal 109]
132. ~rich(X0) | ~wise(X0) [duplicate literal removal 105]
133. ~rich(X0) | wise(X0) [duplicate literal removal 106]
167. 6 <=> ! [X1] : quiet(X1) [avatar definition]
168. quiet(X1) <- (6) [avatar component clause 167]
170. 7 <=> creative(sK1) [avatar definition]
172. ~creative(sK1) <- (~7) [avatar component clause 170]
173. 6 | ~7 [avatar split clause 73,170,167]
224. ~rich(X0) [subsumption resolution 132,133]
226. creative(X0) [subsumption resolution 131,224]
264. $false <- (6) [resolution 168,130]
265. ~6 [avatar contradiction clause 264]
266. $false <- (~7) [subsumption resolution 172,226]
267. 7 [avatar contradiction clause 266]
268. $false [avatar sat refutation 173,265,267]
% SZS output end Proof for 65080133616344160092256
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either happy or not quiet is strong or not quiet and vice versa. Everyone who is either happy or not old is either not calm or creative and vice versa. Everyone who is either quiet or strong is not brave or wise. Everyone who is not happy is both happy and curious and vice versa. Everyone who is both not funny and patient is not generous or not creative. If john is brave or rich then someone is not kind. Everyone who is strong or old is either not patient or not quiet and vice versa. Everyone who is patient is quiet or not calm. Everyone who is both not quiet and not brave is kind or generous and vice versa. If someone is curious then someone is not old. Everyone who is either not brave or patient is not strong. Everyone who is both patient and not patient is humble and vice versa. If fred is calm then fred is strong or not old. Everyone who is either not old or not creative is both brave and not generous. Everyone who is either patient or creative is either brave or generous and vice versa. Someone is old. Someone is wise. Someone is rich. Mary is not funny or tall. | Mary is strong. | entailment | (![X]:((happy(X)<~>~quiet(X))<=>(strong(X)|~quiet(X))))&
(![X]:((happy(X)<~>~old(X))<=>(~calm(X)<~>creative(X))))&
(![X]:((quiet(X)<~>strong(X))=>(~brave(X)|wise(X))))&
(![X]:(~happy(X)<=>(happy(X)&curious(X))))&
(![X]:((~funny(X)&patient(X))=>(~generous(X)|~creative(X))))&
(((brave(john)|rich(john)))=>(?[X]:(~kind(X))))&
(![X]:((strong(X)|old(X))<=>(~patient(X)<~>~quiet(X))))&
(![X]:(patient(X)=>(quiet(X)|~calm(X))))&
(![X]:((~quiet(X)&~brave(X))<=>(kind(X)|generous(X))))&
((?[X]:(curious(X)))=>(?[X]:(~old(X))))&
(![X]:((~brave(X)<~>patient(X))=>~strong(X)))&
(![X]:((patient(X)&~patient(X))<=>humble(X)))&
((calm(fred))=>((strong(fred)|~old(fred))))&
(![X]:((~old(X)<~>~creative(X))=>(brave(X)&~generous(X))))&
(![X]:((patient(X)<~>creative(X))<=>(brave(X)<~>generous(X))))&
(?[X]:(old(X)))&
(?[X]:(wise(X)))&
(?[X]:(rich(X)))&
((~funny(mary)|tall(mary))) | strong(mary) | [
"p0",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3203849521459580208270794
% SZS output start Proof for 3203849521459580208270794
1. ! [X0] : ((happy(X0) <~> ~quiet(X0)) <=> (~quiet(X0) | strong(X0))) [input p0]
4. ! [X0] : (~happy(X0) <=> (curious(X0) & happy(X0))) [input p3]
20. ~strong(mary) [input hypothesis]
34. ! [X0] : ((((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | (quiet(X0) & ~strong(X0))) & ((~quiet(X0) | strong(X0)) | ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0))))) [nnf transformation 1]
35. ! [X0] : ((((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | (quiet(X0) & ~strong(X0))) & (~quiet(X0) | strong(X0) | ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0))))) [flattening 34]
37. ! [X0] : ((~happy(X0) | (~curious(X0) | ~happy(X0))) & ((curious(X0) & happy(X0)) | happy(X0))) [nnf transformation 4]
38. ! [X0] : ((~happy(X0) | ~curious(X0) | ~happy(X0)) & ((curious(X0) & happy(X0)) | happy(X0))) [flattening 37]
55. ~quiet(X0) | strong(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 35]
60. quiet(X0) | ~happy(X0) | quiet(X0) [cnf transformation 35]
69. happy(X0) | happy(X0) [cnf transformation 38]
104. ~strong(mary) [cnf transformation 20]
105. happy(X0) [duplicate literal removal 69]
107. ~quiet(X0) | strong(X0) | ~happy(X0) [duplicate literal removal 55]
108. ~happy(X0) | quiet(X0) [duplicate literal removal 60]
109. ~happy(X0) | strong(X0) [subsumption resolution 107,108]
151. strong(X0) [resolution 109,105]
152. $false [resolution 151,104]
% SZS output end Proof for 3203849521459580208270794
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or not happy then someone is wise or funny and vice versa.
If someone is not calm or strong then someone is brave and vice versa.
Everyone who is not curious or kind is not generous and vice versa.
If fred is not curious then someone is not generous and vice versa.
If someone is either wise or not patient then fred is happy or calm.
If susan is not wise then mary is kind.
Everyone who is either funny or curious is either calm or brave and vice versa.
Everyone who is both generous and creative is brave or humble and vice versa.
If someone is not calm then mary is both not kind and not quiet.
Everyone who is not wise is curious.
If mary is either kind or not patient then someone is wise or funny and vice versa.
If lucy is either not kind or not creative then someone is either old or not tall.
Everyone who is calm or not old is not funny.
Everyone who is either old or not curious is patient or old and vice versa.
If someone is either not happy or quiet then alice is rich.
If someone is humble then john is not happy or strong and vice versa.
Someone is either kind or not strong.
Someone is both funny and not rich.
Someone is either not creative or not tall.
Fred is funny.
Someone is not tall.
Someone is not brave.
Someone is both not kind and not humble.
Someone is brave or kind. | Susan is kind. | contradiction | ((?[X]:((brave(X)<~>~happy(X))))<=>(?[X]:((wise(X)|funny(X)))))&
((?[X]:((~calm(X)|strong(X))))<=>(?[X]:(brave(X))))&
(![X]:((~curious(X)|kind(X))<=>~generous(X)))&
((~curious(fred))<=>(?[X]:(~generous(X))))&
((?[X]:((wise(X)<~>~patient(X))))=>((happy(fred)|calm(fred))))&
((~wise(susan))=>(kind(mary)))&
(![X]:((funny(X)<~>curious(X))<=>(calm(X)<~>brave(X))))&
(![X]:((generous(X)&creative(X))<=>(brave(X)|humble(X))))&
((?[X]:(~calm(X)))=>((~kind(mary)&~quiet(mary))))&
(![X]:(~wise(X)=>curious(X)))&
(((kind(mary)<~>~patient(mary)))<=>(?[X]:((wise(X)|funny(X)))))&
(((~kind(lucy)<~>~creative(lucy)))=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:((calm(X)|~old(X))=>~funny(X)))&
(![X]:((old(X)<~>~curious(X))<=>(patient(X)|old(X))))&
((?[X]:((~happy(X)<~>quiet(X))))=>(rich(alice)))&
((?[X]:(humble(X)))<=>((~happy(john)|strong(john))))&
(?[X]:((kind(X)<~>~strong(X))))&
(?[X]:((funny(X)&~rich(X))))&
(?[X]:((~creative(X)<~>~tall(X))))&
(funny(fred))&
(?[X]:(~tall(X)))&
(?[X]:(~brave(X)))&
(?[X]:((~kind(X)&~humble(X))))&
(?[X]:((brave(X)|kind(X)))) | kind(susan) | [
"p2",
"p3",
"p12",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7508087302677300680431529
% SZS output start Proof for 7508087302677300680431529
3. ! [X0] : ((kind(X0) | ~curious(X0)) <=> ~generous(X0)) [input p2]
4. ~curious(fred) <=> ? [X0] : ~generous(X0) [input p3]
13. ! [X0] : ((~old(X0) | calm(X0)) => ~funny(X0)) [input p12]
14. ! [X0] : ((old(X0) <~> ~curious(X0)) <=> (old(X0) | patient(X0))) [input p13]
20. funny(fred) [input p19]
25. kind(susan) [input hypothesis]
34. ! [X0] : (~funny(X0) | (old(X0) & ~calm(X0))) [ennf transformation 13]
46. ! [X0] : (((kind(X0) | ~curious(X0)) | generous(X0)) & (~generous(X0) | (~kind(X0) & curious(X0)))) [nnf transformation 3]
47. ! [X0] : ((kind(X0) | ~curious(X0) | generous(X0)) & (~generous(X0) | (~kind(X0) & curious(X0)))) [flattening 46]
48. (~curious(fred) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | curious(fred)) [nnf transformation 4]
49. (~curious(fred) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | curious(fred)) [rectify 48]
50. ? [X1] : ~generous(X1) => ~generous(sK4) [choice axiom]
51. (~curious(fred) | ! [X0] : generous(X0)) & (~generous(sK4) | curious(fred)) [skolemisation 49,50]
63. ! [X0] : ((((curious(X0) | ~old(X0)) & (~curious(X0) | old(X0))) | (~old(X0) & ~patient(X0))) & ((old(X0) | patient(X0)) | ((old(X0) | curious(X0)) & (~curious(X0) | ~old(X0))))) [nnf transformation 14]
64. ! [X0] : ((((curious(X0) | ~old(X0)) & (~curious(X0) | old(X0))) | (~old(X0) & ~patient(X0))) & (old(X0) | patient(X0) | ((old(X0) | curious(X0)) & (~curious(X0) | ~old(X0))))) [flattening 63]
97. ~generous(X0) | ~kind(X0) [cnf transformation 47]
100. ~curious(fred) | generous(X0) [cnf transformation 51]
131. ~funny(X0) | old(X0) [cnf transformation 34]
137. curious(X0) | ~old(X0) | ~old(X0) [cnf transformation 64]
149. funny(fred) [cnf transformation 20]
155. kind(susan) [cnf transformation 25]
157. ~old(X0) | curious(X0) [duplicate literal removal 137]
217. 15 <=> ! [X0] : generous(X0) [avatar definition]
218. generous(X0) <- (15) [avatar component clause 217]
220. 16 <=> curious(fred) [avatar definition]
223. 15 | ~16 [avatar split clause 100,220,217]
373. old(fred) [resolution 131,149]
375. curious(fred) [resolution 373,157]
378. 16 [avatar split clause 375,220]
380. ~kind(X0) <- (15) [resolution 218,97]
384. $false <- (15) [resolution 380,155]
385. ~15 [avatar contradiction clause 384]
386. $false [avatar sat refutation 223,378,385]
% SZS output end Proof for 7508087302677300680431529
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is not generous.
Everyone who is wise is not happy and vice versa.
Everyone who is not quiet is not generous or wise.
Everyone who is strong is both creative and calm.
Everyone who is strong is strong or not patient.
If john is brave or not funny then someone is quiet or not quiet.
If john is not calm then alice is not kind or old.
Everyone who is both tall and old is both not tall and generous and vice versa.
Everyone who is generous is calm or not wise and vice versa.
If lucy is both not funny and strong then someone is not old.
If alice is either not kind or not happy then john is generous.
If alice is either happy or calm then lucy is either quiet or strong and vice versa.
If someone is creative then lucy is happy.
Everyone who is both not funny and happy is funny or humble.
Everyone who is either not patient or not funny is curious or not tall and vice versa.
If paul is curious then someone is either not creative or not brave and vice versa.
Paul is not happy.
John is not wise or not creative.
Mary is old.
Lucy is either not tall or not creative.
Someone is either curious or not generous.
Alice is both not humble and not calm.
Susan is wise. | John is not quiet. | neutral | (![X]:(funny(X)=>~generous(X)))&
(![X]:(wise(X)<=>~happy(X)))&
(![X]:(~quiet(X)=>(~generous(X)|wise(X))))&
(![X]:(strong(X)=>(creative(X)&calm(X))))&
(![X]:(strong(X)=>(strong(X)|~patient(X))))&
(((brave(john)|~funny(john)))=>(?[X]:((quiet(X)|~quiet(X)))))&
((~calm(john))=>((~kind(alice)|old(alice))))&
(![X]:((tall(X)&old(X))<=>(~tall(X)&generous(X))))&
(![X]:(generous(X)<=>(calm(X)|~wise(X))))&
(((~funny(lucy)&strong(lucy)))=>(?[X]:(~old(X))))&
(((~kind(alice)<~>~happy(alice)))=>(generous(john)))&
(((happy(alice)<~>calm(alice)))<=>((quiet(lucy)<~>strong(lucy))))&
((?[X]:(creative(X)))=>(happy(lucy)))&
(![X]:((~funny(X)&happy(X))=>(funny(X)|humble(X))))&
(![X]:((~patient(X)<~>~funny(X))<=>(curious(X)|~tall(X))))&
((curious(paul))<=>(?[X]:((~creative(X)<~>~brave(X)))))&
(~happy(paul))&
((~wise(john)|~creative(john)))&
(old(mary))&
((~tall(lucy)<~>~creative(lucy)))&
(?[X]:((curious(X)<~>~generous(X))))&
((~humble(alice)&~calm(alice)))&
(wise(susan)) | ~quiet(john) | [] | null | 0 |
Everyone who is both not strong and curious is patient and vice versa.
Everyone who is either not humble or not calm is brave and vice versa.
Everyone who is both happy and not strong is both strong and funny.
Everyone who is old or funny is not brave or curious and vice versa.
If someone is both not funny and creative then paul is either curious or patient.
Everyone who is both not kind and not strong is either rich or calm and vice versa.
If alice is creative or old then someone is curious or not quiet and vice versa.
If fred is both patient and not humble then susan is both not curious and calm and vice versa.
Everyone who is strong or not patient is not kind or not calm and vice versa.
Everyone who is both happy and not kind is both not creative and not humble.
If paul is creative or not funny then someone is rich and vice versa.
If lucy is either not brave or not patient then someone is humble or calm and vice versa.
Everyone who is calm or not wise is both happy and not funny and vice versa.
Everyone who is either patient or not funny is both strong and funny and vice versa.
If someone is not humble or wise then john is either old or not old and vice versa.
If lucy is both humble and not wise then fred is not kind.
Someone is not rich or wise.
Someone is not generous or patient.
Someone is not brave or not tall.
Someone is not calm. | Alice is brave. | contradiction | (![X]:((~strong(X)&curious(X))<=>patient(X)))&
(![X]:((~humble(X)<~>~calm(X))<=>brave(X)))&
(![X]:((happy(X)&~strong(X))=>(strong(X)&funny(X))))&
(![X]:((old(X)|funny(X))<=>(~brave(X)|curious(X))))&
((?[X]:((~funny(X)&creative(X))))=>((curious(paul)<~>patient(paul))))&
(![X]:((~kind(X)&~strong(X))<=>(rich(X)<~>calm(X))))&
(((creative(alice)|old(alice)))<=>(?[X]:((curious(X)|~quiet(X)))))&
(((patient(fred)&~humble(fred)))<=>((~curious(susan)&calm(susan))))&
(![X]:((strong(X)|~patient(X))<=>(~kind(X)|~calm(X))))&
(![X]:((happy(X)&~kind(X))=>(~creative(X)&~humble(X))))&
(((creative(paul)|~funny(paul)))<=>(?[X]:(rich(X))))&
(((~brave(lucy)<~>~patient(lucy)))<=>(?[X]:((humble(X)|calm(X)))))&
(![X]:((calm(X)|~wise(X))<=>(happy(X)&~funny(X))))&
(![X]:((patient(X)<~>~funny(X))<=>(strong(X)&funny(X))))&
((?[X]:((~humble(X)|wise(X))))<=>((old(john)<~>~old(john))))&
(((humble(lucy)&~wise(lucy)))=>(~kind(fred)))&
(?[X]:((~rich(X)|wise(X))))&
(?[X]:((~generous(X)|patient(X))))&
(?[X]:((~brave(X)|~tall(X))))&
(?[X]:(~calm(X))) | brave(alice) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p8",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3212486121189130631267499
% SZS output start Proof for 3212486121189130631267499
1. ! [X0] : ((curious(X0) & ~strong(X0)) <=> patient(X0)) [input p0]
3. ! [X0] : ((~strong(X0) & happy(X0)) => (funny(X0) & strong(X0))) [input p2]
4. ! [X0] : ((funny(X0) | old(X0)) <=> (curious(X0) | ~brave(X0))) [input p3]
5. ? [X0] : (creative(X0) & ~funny(X0)) => (curious(paul) <~> patient(paul)) [input p4]
7. (old(alice) | creative(alice)) <=> ? [X0] : (~quiet(X0) | curious(X0)) [input p6]
9. ! [X0] : ((~patient(X0) | strong(X0)) <=> (~calm(X0) | ~kind(X0))) [input p8]
13. ! [X0] : ((~wise(X0) | calm(X0)) <=> (~funny(X0) & happy(X0))) [input p12]
14. ! [X0] : ((patient(X0) <~> ~funny(X0)) <=> (funny(X0) & strong(X0))) [input p13]
21. brave(alice) [input hypothesis]
24. ! [X0] : ((funny(X0) & strong(X0)) | (strong(X0) | ~happy(X0))) [ennf transformation 3]
25. ! [X0] : ((funny(X0) & strong(X0)) | strong(X0) | ~happy(X0)) [flattening 24]
26. (curious(paul) <~> patient(paul)) | ! [X0] : (~creative(X0) | funny(X0)) [ennf transformation 5]
31. ! [X0] : (((curious(X0) & ~strong(X0)) | ~patient(X0)) & (patient(X0) | (~curious(X0) | strong(X0)))) [nnf transformation 1]
32. ! [X0] : (((curious(X0) & ~strong(X0)) | ~patient(X0)) & (patient(X0) | ~curious(X0) | strong(X0))) [flattening 31]
34. ! [X0] : (((funny(X0) | old(X0)) | (~curious(X0) & brave(X0))) & ((curious(X0) | ~brave(X0)) | (~funny(X0) & ~old(X0)))) [nnf transformation 4]
35. ! [X0] : ((funny(X0) | old(X0) | (~curious(X0) & brave(X0))) & (curious(X0) | ~brave(X0) | (~funny(X0) & ~old(X0)))) [flattening 34]
36. ((~patient(paul) | ~curious(paul)) & (patient(paul) | curious(paul))) | ! [X0] : (~creative(X0) | funny(X0)) [nnf transformation 26]
39. ((old(alice) | creative(alice)) | ! [X0] : (quiet(X0) & ~curious(X0))) & (? [X0] : (~quiet(X0) | curious(X0)) | (~old(alice) & ~creative(alice))) [nnf transformation 7]
40. (old(alice) | creative(alice) | ! [X0] : (quiet(X0) & ~curious(X0))) & (? [X0] : (~quiet(X0) | curious(X0)) | (~old(alice) & ~creative(alice))) [flattening 39]
41. (old(alice) | creative(alice) | ! [X0] : (quiet(X0) & ~curious(X0))) & (? [X1] : (~quiet(X1) | curious(X1)) | (~old(alice) & ~creative(alice))) [rectify 40]
42. ? [X1] : (~quiet(X1) | curious(X1)) => (~quiet(sK0) | curious(sK0)) [choice axiom]
43. (old(alice) | creative(alice) | ! [X0] : (quiet(X0) & ~curious(X0))) & ((~quiet(sK0) | curious(sK0)) | (~old(alice) & ~creative(alice))) [skolemisation 41,42]
46. ! [X0] : (((~patient(X0) | strong(X0)) | (calm(X0) & kind(X0))) & ((~calm(X0) | ~kind(X0)) | (patient(X0) & ~strong(X0)))) [nnf transformation 9]
47. ! [X0] : ((~patient(X0) | strong(X0) | (calm(X0) & kind(X0))) & (~calm(X0) | ~kind(X0) | (patient(X0) & ~strong(X0)))) [flattening 46]
57. ! [X0] : (((~wise(X0) | calm(X0)) | (funny(X0) | ~happy(X0))) & ((~funny(X0) & happy(X0)) | (wise(X0) & ~calm(X0)))) [nnf transformation 13]
58. ! [X0] : ((~wise(X0) | calm(X0) | funny(X0) | ~happy(X0)) & ((~funny(X0) & happy(X0)) | (wise(X0) & ~calm(X0)))) [flattening 57]
59. ! [X0] : ((((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | (~funny(X0) | ~strong(X0))) & ((funny(X0) & strong(X0)) | ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0))))) [nnf transformation 14]
60. ! [X0] : ((((funny(X0) | ~patient(X0)) & (~funny(X0) | patient(X0))) | ~funny(X0) | ~strong(X0)) & ((funny(X0) & strong(X0)) | ((patient(X0) | funny(X0)) & (~funny(X0) | ~patient(X0))))) [flattening 59]
69. ~curious(X0) | patient(X0) | strong(X0) [cnf transformation 32]
70. ~patient(X0) | ~strong(X0) [cnf transformation 32]
71. ~patient(X0) | curious(X0) [cnf transformation 32]
76. strong(X0) | strong(X0) | ~happy(X0) [cnf transformation 25]
78. ~old(X0) | ~brave(X0) | curious(X0) [cnf transformation 35]
79. ~funny(X0) | ~brave(X0) | curious(X0) [cnf transformation 35]
82. patient(paul) | curious(paul) | ~creative(X0) | funny(X0) [cnf transformation 36]
83. ~patient(paul) | ~curious(paul) | ~creative(X0) | funny(X0) [cnf transformation 36]
92. old(alice) | creative(alice) | ~curious(X0) [cnf transformation 43]
101. ~patient(X0) | strong(X0) | calm(X0) [cnf transformation 47]
113. ~calm(X0) | happy(X0) [cnf transformation 58]
118. strong(X0) | ~funny(X0) | ~patient(X0) [cnf transformation 60]
121. funny(X0) | patient(X0) | funny(X0) [cnf transformation 60]
122. ~funny(X0) | patient(X0) | ~funny(X0) | ~strong(X0) [cnf transformation 60]
133. brave(alice) [cnf transformation 21]
136. funny(X0) | patient(X0) [duplicate literal removal 121]
137. ~funny(X0) | patient(X0) | ~strong(X0) [duplicate literal removal 122]
138. ~happy(X0) | strong(X0) [duplicate literal removal 76]
139. ~patient(paul) | ~creative(X0) | funny(X0) [subsumption resolution 83,71]
141. 1 <=> ! [X0] : (~creative(X0) | funny(X0)) [avatar definition]
142. ~creative(X0) | funny(X0) <- (1) [avatar component clause 141]
144. 2 <=> patient(paul) [avatar definition]
147. 1 | ~2 [avatar split clause 139,144,141]
148. curious(paul) | ~creative(X0) | funny(X0) [subsumption resolution 82,71]
150. 3 <=> curious(paul) [avatar definition]
152. curious(paul) <- (3) [avatar component clause 150]
153. 1 | 3 [avatar split clause 148,150,141]
158. 5 <=> creative(alice) [avatar definition]
160. creative(alice) <- (5) [avatar component clause 158]
162. 6 <=> old(alice) [avatar definition]
164. old(alice) <- (6) [avatar component clause 162]
167. 7 <=> ! [X0] : ~curious(X0) [avatar definition]
168. ~curious(X0) <- (7) [avatar component clause 167]
169. 7 | 5 | 6 [avatar split clause 92,162,158,167]
200. ~patient(X0) | calm(X0) [subsumption resolution 101,70]
248. ~funny(X0) | ~strong(X0) [subsumption resolution 137,70]
249. ~funny(X0) | ~patient(X0) [subsumption resolution 118,70]
291. ~strong(X0) | patient(X0) [resolution 248,136]
292. ~strong(X0) [subsumption resolution 291,70]
295. patient(paul) | strong(paul) <- (3) [resolution 69,152]
310. patient(paul) <- (3) [subsumption resolution 295,292]
311. 2 | ~3 [avatar split clause 310,150,144]
333. ~brave(alice) | curious(alice) <- (6) [resolution 78,164]
334. curious(alice) <- (6) [subsumption resolution 333,133]
337. ~brave(X0) | curious(X0) | patient(X0) [resolution 79,136]
339. ~brave(X0) | curious(X0) [subsumption resolution 337,71]
354. 33 <=> calm(alice) [avatar definition]
356. calm(alice) <- (33) [avatar component clause 354]
365. patient(alice) | strong(alice) <- (6) [resolution 334,69]
366. patient(alice) <- (6) [subsumption resolution 365,292]
372. happy(alice) <- (33) [resolution 356,113]
389. calm(alice) <- (6) [resolution 366,200]
399. strong(alice) <- (33) [resolution 372,138]
401. $false <- (33) [subsumption resolution 399,292]
402. ~33 [avatar contradiction clause 401]
403. 33 | ~6 [avatar split clause 389,162,354]
404. funny(alice) <- (1, 5) [resolution 160,142]
443. ~patient(alice) <- (1, 5) [resolution 404,249]
462. curious(alice) [resolution 339,133]
466. patient(alice) | strong(alice) [resolution 462,69]
467. strong(alice) <- (1, 5) [subsumption resolution 466,443]
468. $false <- (1, 5) [subsumption resolution 467,292]
469. ~1 | ~5 [avatar contradiction clause 468]
474. $false <- (7) [resolution 168,462]
475. ~7 [avatar contradiction clause 474]
476. $false [avatar sat refutation 147,153,169,311,402,403,469,475]
% SZS output end Proof for 3212486121189130631267499
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or not rich is both not generous and not brave.
If someone is calm or not happy then susan is not generous or not happy.
Everyone who is both tall and humble is either not quiet or not humble.
Everyone who is both wise and happy is brave and vice versa.
If someone is both kind and not creative then lucy is both happy and not humble and vice versa.
Everyone who is either tall or not quiet is happy or old and vice versa.
Everyone who is funny or not rich is old or humble and vice versa.
Everyone who is either not kind or patient is both not calm and rich.
If someone is both wise and not wise then john is either quiet or strong.
If mary is either rich or strong then alice is strong or humble and vice versa.
If someone is either not brave or calm then alice is creative and vice versa.
If someone is humble then alice is either strong or humble.
If someone is either old or not strong then alice is either not old or creative and vice versa.
Everyone who is not generous or not funny is both not calm and not curious.
Everyone who is both not creative and not funny is creative or not quiet.
If someone is not patient or not quiet then someone is both brave and not happy and vice versa.
Someone is strong or not rich.
John is not creative.
Paul is not happy or not humble.
Alice is either not wise or not quiet.
Someone is either creative or not tall.
John is not patient or not old. | Susan is not kind. | neutral | (![X]:((funny(X)|~rich(X))=>(~generous(X)&~brave(X))))&
((?[X]:((calm(X)|~happy(X))))=>((~generous(susan)|~happy(susan))))&
(![X]:((tall(X)&humble(X))=>(~quiet(X)<~>~humble(X))))&
(![X]:((wise(X)&happy(X))<=>brave(X)))&
((?[X]:((kind(X)&~creative(X))))<=>((happy(lucy)&~humble(lucy))))&
(![X]:((tall(X)<~>~quiet(X))<=>(happy(X)|old(X))))&
(![X]:((funny(X)|~rich(X))<=>(old(X)|humble(X))))&
(![X]:((~kind(X)<~>patient(X))=>(~calm(X)&rich(X))))&
((?[X]:((wise(X)&~wise(X))))=>((quiet(john)<~>strong(john))))&
(((rich(mary)<~>strong(mary)))<=>((strong(alice)|humble(alice))))&
((?[X]:((~brave(X)<~>calm(X))))<=>(creative(alice)))&
((?[X]:(humble(X)))=>((strong(alice)<~>humble(alice))))&
((?[X]:((old(X)<~>~strong(X))))<=>((~old(alice)<~>creative(alice))))&
(![X]:((~generous(X)|~funny(X))=>(~calm(X)&~curious(X))))&
(![X]:((~creative(X)&~funny(X))=>(creative(X)|~quiet(X))))&
((?[X]:((~patient(X)|~quiet(X))))<=>(?[X]:((brave(X)&~happy(X)))))&
(?[X]:((strong(X)|~rich(X))))&
(~creative(john))&
((~happy(paul)|~humble(paul)))&
((~wise(alice)<~>~quiet(alice)))&
(?[X]:((creative(X)<~>~tall(X))))&
((~patient(john)|~old(john))) | ~kind(susan) | [] | null | 0 |
Everyone who is humble or not curious is both not creative and not generous. Everyone who is rich or not funny is not calm or creative. Everyone who is patient is both curious and happy. Everyone who is not old or not wise is either not happy or tall. Everyone who is patient is both calm and strong. If someone is either not happy or creative then someone is humble or not brave. Everyone who is not calm or not curious is both curious and kind and vice versa. If someone is kind or brave then mary is both calm and not patient. If susan is both tall and patient then lucy is either quiet or strong. If lucy is both not kind and strong then someone is both not brave and wise and vice versa. If someone is both not calm and wise then lucy is curious. If susan is not calm then someone is either not calm or not patient. Everyone who is creative or not calm is both not happy and happy. Everyone who is not brave or not old is wise or strong and vice versa. If someone is not tall or kind then someone is not calm or strong and vice versa. Mary is not generous or calm. Lucy is either calm or quiet. Someone is generous. Mary is not wise or tall. Someone is both not generous and strong. | Lucy is generous. | neutral | (![X]:((humble(X)|~curious(X))=>(~creative(X)&~generous(X))))&
(![X]:((rich(X)|~funny(X))=>(~calm(X)|creative(X))))&
(![X]:(patient(X)=>(curious(X)&happy(X))))&
(![X]:((~old(X)|~wise(X))=>(~happy(X)<~>tall(X))))&
(![X]:(patient(X)=>(calm(X)&strong(X))))&
((?[X]:((~happy(X)<~>creative(X))))=>(?[X]:((humble(X)|~brave(X)))))&
(![X]:((~calm(X)|~curious(X))<=>(curious(X)&kind(X))))&
((?[X]:((kind(X)|brave(X))))=>((calm(mary)&~patient(mary))))&
(((tall(susan)&patient(susan)))=>((quiet(lucy)<~>strong(lucy))))&
(((~kind(lucy)&strong(lucy)))<=>(?[X]:((~brave(X)&wise(X)))))&
((?[X]:((~calm(X)&wise(X))))=>(curious(lucy)))&
((~calm(susan))=>(?[X]:((~calm(X)<~>~patient(X)))))&
(![X]:((creative(X)|~calm(X))=>(~happy(X)&happy(X))))&
(![X]:((~brave(X)|~old(X))<=>(wise(X)|strong(X))))&
((?[X]:((~tall(X)|kind(X))))<=>(?[X]:((~calm(X)|strong(X)))))&
((~generous(mary)|calm(mary)))&
((calm(lucy)<~>quiet(lucy)))&
(?[X]:(generous(X)))&
((~wise(mary)|tall(mary)))&
(?[X]:((~generous(X)&strong(X)))) | generous(lucy) | [] | null | 0 |
If someone is not happy or not funny then someone is both not kind and wise.
Everyone who is not curious is tall or strong and vice versa.
Everyone who is not funny or not generous is not strong and vice versa.
Everyone who is not quiet is either not humble or curious.
Everyone who is both humble and happy is either not tall or funny and vice versa.
If someone is not funny then fred is either not tall or not old.
If john is curious then john is not curious or calm.
If someone is either quiet or kind then lucy is both not generous and not wise.
Everyone who is humble is not happy or old.
Everyone who is tall or old is not tall or strong and vice versa.
If someone is quiet or not old then someone is both not wise and wise.
If someone is both patient and not quiet then fred is calm.
Everyone who is either not tall or not calm is both creative and not wise and vice versa.
If someone is not creative or not generous then someone is both wise and not kind.
If fred is both happy and old then john is funny and vice versa.
Everyone who is both not happy and funny is not funny and vice versa.
Mary is both not curious and patient.
Alice is happy or funny.
Mary is not creative.
Someone is not calm or strong.
Alice is not old or funny.
Alice is both not quiet and creative.
Someone is not calm.
Someone is happy. | Mary is not tall. | entailment | ((?[X]:((~happy(X)|~funny(X))))=>(?[X]:((~kind(X)&wise(X)))))&
(![X]:(~curious(X)<=>(tall(X)|strong(X))))&
(![X]:((~funny(X)|~generous(X))<=>~strong(X)))&
(![X]:(~quiet(X)=>(~humble(X)<~>curious(X))))&
(![X]:((humble(X)&happy(X))<=>(~tall(X)<~>funny(X))))&
((?[X]:(~funny(X)))=>((~tall(fred)<~>~old(fred))))&
((curious(john))=>((~curious(john)|calm(john))))&
((?[X]:((quiet(X)<~>kind(X))))=>((~generous(lucy)&~wise(lucy))))&
(![X]:(humble(X)=>(~happy(X)|old(X))))&
(![X]:((tall(X)|old(X))<=>(~tall(X)|strong(X))))&
((?[X]:((quiet(X)|~old(X))))=>(?[X]:((~wise(X)&wise(X)))))&
((?[X]:((patient(X)&~quiet(X))))=>(calm(fred)))&
(![X]:((~tall(X)<~>~calm(X))<=>(creative(X)&~wise(X))))&
((?[X]:((~creative(X)|~generous(X))))=>(?[X]:((wise(X)&~kind(X)))))&
(((happy(fred)&old(fred)))<=>(funny(john)))&
(![X]:((~happy(X)&funny(X))<=>~funny(X)))&
((~curious(mary)&patient(mary)))&
((happy(alice)|funny(alice)))&
(~creative(mary))&
(?[X]:((~calm(X)|strong(X))))&
((~old(alice)|funny(alice)))&
((~quiet(alice)&creative(alice)))&
(?[X]:(~calm(X)))&
(?[X]:(happy(X))) | ~tall(mary) | [
"p3",
"p4",
"p10",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1173844791813296890376398
% SZS output start Proof for 1173844791813296890376398
4. ! [X0] : (~quiet(X0) => (~humble(X0) <~> curious(X0))) [input p3]
5. ! [X0] : ((happy(X0) & humble(X0)) <=> (~tall(X0) <~> funny(X0))) [input p4]
11. ? [X0] : (~old(X0) | quiet(X0)) => ? [X0] : (wise(X0) & ~wise(X0)) [input p10]
16. ! [X0] : ((funny(X0) & ~happy(X0)) <=> ~funny(X0)) [input p15]
17. patient(mary) & ~curious(mary) [input p16]
25. tall(mary) [input hypothesis]
27. ? [X0] : (~old(X0) | quiet(X0)) => ? [X1] : (wise(X1) & ~wise(X1)) [rectify 11]
30. ! [X0] : ((~humble(X0) <~> curious(X0)) | quiet(X0)) [ennf transformation 4]
37. ? [X1] : (wise(X1) & ~wise(X1)) | ! [X0] : (old(X0) & ~quiet(X0)) [ennf transformation 27]
47. ! [X0] : (((~curious(X0) | humble(X0)) & (curious(X0) | ~humble(X0))) | quiet(X0)) [nnf transformation 30]
48. ! [X0] : (((happy(X0) & humble(X0)) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0)))) & (((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | (~happy(X0) | ~humble(X0)))) [nnf transformation 5]
49. ! [X0] : (((happy(X0) & humble(X0)) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0)))) & (((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | ~happy(X0) | ~humble(X0))) [flattening 48]
54. ? [X0] : (wise(X0) & ~wise(X0)) | ! [X1] : (old(X1) & ~quiet(X1)) [rectify 37]
55. ? [X0] : (wise(X0) & ~wise(X0)) => (wise(sK1) & ~wise(sK1)) [choice axiom]
56. (wise(sK1) & ~wise(sK1)) | ! [X1] : (old(X1) & ~quiet(X1)) [skolemisation 54,55]
64. ! [X0] : (((funny(X0) & ~happy(X0)) | funny(X0)) & (~funny(X0) | (~funny(X0) | happy(X0)))) [nnf transformation 16]
65. ! [X0] : (((funny(X0) & ~happy(X0)) | funny(X0)) & (~funny(X0) | ~funny(X0) | happy(X0))) [flattening 64]
82. ~humble(X0) | curious(X0) | quiet(X0) [cnf transformation 47]
87. ~tall(X0) | humble(X0) | ~funny(X0) [cnf transformation 49]
102. ~wise(sK1) | ~quiet(X1) [cnf transformation 56]
104. wise(sK1) | ~quiet(X1) [cnf transformation 56]
122. funny(X0) | funny(X0) [cnf transformation 65]
123. ~curious(mary) [cnf transformation 17]
133. tall(mary) [cnf transformation 25]
135. funny(X0) [duplicate literal removal 122]
140. 1 <=> ! [X1] : funny(X1) [avatar definition]
141. funny(X1) <- (1) [avatar component clause 140]
198. 14 <=> wise(sK1) [avatar definition]
203. 15 <=> ! [X1] : ~quiet(X1) [avatar definition]
204. ~quiet(X1) <- (15) [avatar component clause 203]
205. 15 | 14 [avatar split clause 104,198,203]
207. 15 | ~14 [avatar split clause 102,198,203]
245. 1 [avatar split clause 135,140]
284. humble(mary) | ~funny(mary) [resolution 87,133]
285. humble(mary) <- (1) [subsumption resolution 284,141]
286. curious(mary) | quiet(mary) <- (1) [resolution 285,82]
287. quiet(mary) <- (1) [subsumption resolution 286,123]
288. $false <- (1, 15) [subsumption resolution 287,204]
289. ~1 | ~15 [avatar contradiction clause 288]
290. $false [avatar sat refutation 205,207,245,289]
% SZS output end Proof for 1173844791813296890376398
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not patient is both not generous and calm.
Everyone who is creative or not quiet is both happy and quiet and vice versa.
Everyone who is not generous is calm or not wise.
If susan is not wise then someone is not tall and vice versa.
If someone is either kind or humble then someone is not strong or humble and vice versa.
Everyone who is not creative is both generous and not creative and vice versa.
If someone is generous or not creative then someone is both not brave and quiet.
Everyone who is both generous and wise is either not generous or tall and vice versa.
Everyone who is both not funny and not creative is both generous and happy and vice versa.
If someone is not happy or not tall then someone is not humble or not calm.
Everyone who is both creative and not quiet is either not calm or not brave and vice versa.
If lucy is either patient or not strong then someone is not kind and vice versa.
Everyone who is both quiet and funny is both not patient and rich and vice versa.
Everyone who is kind or not curious is not brave or calm and vice versa.
If someone is quiet then paul is not generous.
Everyone who is both humble and wise is either not strong or curious.
Someone is either not old or not kind.
Someone is both quiet and patient.
Someone is curious.
John is either rich or wise.
Someone is not quiet or quiet.
Lucy is either brave or curious. | John is not generous. | entailment | (![X]:((creative(X)|~patient(X))=>(~generous(X)&calm(X))))&
(![X]:((creative(X)|~quiet(X))<=>(happy(X)&quiet(X))))&
(![X]:(~generous(X)=>(calm(X)|~wise(X))))&
((~wise(susan))<=>(?[X]:(~tall(X))))&
((?[X]:((kind(X)<~>humble(X))))<=>(?[X]:((~strong(X)|humble(X)))))&
(![X]:(~creative(X)<=>(generous(X)&~creative(X))))&
((?[X]:((generous(X)|~creative(X))))=>(?[X]:((~brave(X)&quiet(X)))))&
(![X]:((generous(X)&wise(X))<=>(~generous(X)<~>tall(X))))&
(![X]:((~funny(X)&~creative(X))<=>(generous(X)&happy(X))))&
((?[X]:((~happy(X)|~tall(X))))=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:((creative(X)&~quiet(X))<=>(~calm(X)<~>~brave(X))))&
(((patient(lucy)<~>~strong(lucy)))<=>(?[X]:(~kind(X))))&
(![X]:((quiet(X)&funny(X))<=>(~patient(X)&rich(X))))&
(![X]:((kind(X)|~curious(X))<=>(~brave(X)|calm(X))))&
((?[X]:(quiet(X)))=>(~generous(paul)))&
(![X]:((humble(X)&wise(X))=>(~strong(X)<~>curious(X))))&
(?[X]:((~old(X)<~>~kind(X))))&
(?[X]:((quiet(X)&patient(X))))&
(?[X]:(curious(X)))&
((rich(john)<~>wise(john)))&
(?[X]:((~quiet(X)|quiet(X))))&
((brave(lucy)<~>curious(lucy))) | ~generous(john) | [
"p0",
"p1",
"p5",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 459592051660347986179357
% SZS output start Proof for 459592051660347986179357
1. ! [X0] : ((~patient(X0) | creative(X0)) => (calm(X0) & ~generous(X0))) [input p0]
2. ! [X0] : ((~quiet(X0) | creative(X0)) <=> (quiet(X0) & happy(X0))) [input p1]
6. ! [X0] : (~creative(X0) <=> (~creative(X0) & generous(X0))) [input p5]
9. ! [X0] : ((~creative(X0) & ~funny(X0)) <=> (happy(X0) & generous(X0))) [input p8]
13. ! [X0] : ((funny(X0) & quiet(X0)) <=> (rich(X0) & ~patient(X0))) [input p12]
23. generous(john) [input hypothesis]
27. ! [X0] : ((calm(X0) & ~generous(X0)) | (patient(X0) & ~creative(X0))) [ennf transformation 1]
35. ! [X0] : (((~quiet(X0) | creative(X0)) | (~quiet(X0) | ~happy(X0))) & ((quiet(X0) & happy(X0)) | (quiet(X0) & ~creative(X0)))) [nnf transformation 2]
36. ! [X0] : ((~quiet(X0) | creative(X0) | ~quiet(X0) | ~happy(X0)) & ((quiet(X0) & happy(X0)) | (quiet(X0) & ~creative(X0)))) [flattening 35]
46. ! [X0] : ((~creative(X0) | (creative(X0) | ~generous(X0))) & ((~creative(X0) & generous(X0)) | creative(X0))) [nnf transformation 6]
47. ! [X0] : ((~creative(X0) | creative(X0) | ~generous(X0)) & ((~creative(X0) & generous(X0)) | creative(X0))) [flattening 46]
53. ! [X0] : (((~creative(X0) & ~funny(X0)) | (~happy(X0) | ~generous(X0))) & ((happy(X0) & generous(X0)) | (creative(X0) | funny(X0)))) [nnf transformation 9]
54. ! [X0] : (((~creative(X0) & ~funny(X0)) | ~happy(X0) | ~generous(X0)) & ((happy(X0) & generous(X0)) | creative(X0) | funny(X0))) [flattening 53]
64. ! [X0] : (((funny(X0) & quiet(X0)) | (~rich(X0) | patient(X0))) & ((rich(X0) & ~patient(X0)) | (~funny(X0) | ~quiet(X0)))) [nnf transformation 13]
65. ! [X0] : (((funny(X0) & quiet(X0)) | ~rich(X0) | patient(X0)) & ((rich(X0) & ~patient(X0)) | ~funny(X0) | ~quiet(X0))) [flattening 64]
80. ~generous(X0) | ~creative(X0) [cnf transformation 27]
81. ~generous(X0) | patient(X0) [cnf transformation 27]
84. ~creative(X0) | happy(X0) [cnf transformation 36]
87. quiet(X0) | quiet(X0) [cnf transformation 36]
88. ~quiet(X0) | creative(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 36]
98. generous(X0) | creative(X0) [cnf transformation 47]
112. happy(X0) | creative(X0) | funny(X0) [cnf transformation 54]
127. ~patient(X0) | ~funny(X0) | ~quiet(X0) [cnf transformation 65]
148. generous(john) [cnf transformation 23]
151. quiet(X0) [duplicate literal removal 87]
152. ~happy(X0) | creative(X0) | ~quiet(X0) [duplicate literal removal 88]
201. 12 <=> ! [X1] : creative(X1) [avatar definition]
202. creative(X1) <- (12) [avatar component clause 201]
213. funny(X0) | happy(X0) [subsumption resolution 112,84]
224. 17 <=> ! [X1] : happy(X1) [avatar definition]
225. happy(X1) <- (17) [avatar component clause 224]
249. ~funny(X0) | ~patient(X0) [subsumption resolution 127,151]
281. ~creative(john) [resolution 80,148]
285. patient(X0) | creative(X0) [resolution 98,81]
297. ~patient(X0) | happy(X0) [resolution 249,213]
342. happy(X0) | creative(X0) [resolution 297,285]
348. happy(X0) [subsumption resolution 342,84]
349. 17 [avatar split clause 348,224]
350. creative(X0) | ~quiet(X0) <- (17) [resolution 225,152]
351. creative(X0) <- (17) [subsumption resolution 350,151]
352. 12 | ~17 [avatar split clause 351,224,201]
353. $false <- (12) [resolution 202,281]
358. ~12 [avatar contradiction clause 353]
359. $false [avatar sat refutation 349,352,358]
% SZS output end Proof for 459592051660347986179357
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is both not happy and quiet and vice versa.
Everyone who is either curious or not patient is either rich or tall.
If john is both not strong and not tall then susan is either curious or not happy and vice versa.
If someone is not rich then someone is either quiet or strong and vice versa.
Everyone who is not wise or not creative is either funny or calm and vice versa.
If someone is either generous or funny then mary is both not generous and not wise.
If someone is both not creative and not funny then someone is both rich and kind.
Everyone who is curious or kind is both strong and patient and vice versa.
Everyone who is either strong or generous is both not strong and curious.
If someone is tall or not humble then someone is funny and vice versa.
Everyone who is not curious is both not wise and kind.
If susan is patient then someone is old or funny.
If someone is patient then someone is generous.
If someone is both not generous and not patient then lucy is either humble or not creative.
If someone is both not old and brave then someone is either quiet or not generous and vice versa.
Everyone who is either not humble or not calm is kind and vice versa.
Fred is not tall or not funny.
Fred is quiet or calm.
Someone is both funny and curious.
Susan is either not calm or not wise.
Susan is both not old and not creative.
John is not creative or patient. | John is patient. | entailment | (![X]:(patient(X)<=>(~happy(X)&quiet(X))))&
(![X]:((curious(X)<~>~patient(X))=>(rich(X)<~>tall(X))))&
(((~strong(john)&~tall(john)))<=>((curious(susan)<~>~happy(susan))))&
((?[X]:(~rich(X)))<=>(?[X]:((quiet(X)<~>strong(X)))))&
(![X]:((~wise(X)|~creative(X))<=>(funny(X)<~>calm(X))))&
((?[X]:((generous(X)<~>funny(X))))=>((~generous(mary)&~wise(mary))))&
((?[X]:((~creative(X)&~funny(X))))=>(?[X]:((rich(X)&kind(X)))))&
(![X]:((curious(X)|kind(X))<=>(strong(X)&patient(X))))&
(![X]:((strong(X)<~>generous(X))=>(~strong(X)&curious(X))))&
((?[X]:((tall(X)|~humble(X))))<=>(?[X]:(funny(X))))&
(![X]:(~curious(X)=>(~wise(X)&kind(X))))&
((patient(susan))=>(?[X]:((old(X)|funny(X)))))&
((?[X]:(patient(X)))=>(?[X]:(generous(X))))&
((?[X]:((~generous(X)&~patient(X))))=>((humble(lucy)<~>~creative(lucy))))&
((?[X]:((~old(X)&brave(X))))<=>(?[X]:((quiet(X)<~>~generous(X)))))&
(![X]:((~humble(X)<~>~calm(X))<=>kind(X)))&
((~tall(fred)|~funny(fred)))&
((quiet(fred)|calm(fred)))&
(?[X]:((funny(X)&curious(X))))&
((~calm(susan)<~>~wise(susan)))&
((~old(susan)&~creative(susan)))&
((~creative(john)|patient(john))) | patient(john) | [
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8836585969461260789127546
% SZS output start Proof for 8836585969461260789127546
8. ! [X0] : ((kind(X0) | curious(X0)) <=> (patient(X0) & strong(X0))) [input p7]
11. ! [X0] : (~curious(X0) => (kind(X0) & ~wise(X0))) [input p10]
23. ~patient(john) [input hypothesis]
33. ! [X0] : ((kind(X0) & ~wise(X0)) | curious(X0)) [ennf transformation 11]
53. ! [X0] : (((kind(X0) | curious(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~kind(X0) & ~curious(X0)))) [nnf transformation 8]
54. ! [X0] : ((kind(X0) | curious(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~kind(X0) & ~curious(X0)))) [flattening 53]
107. ~curious(X0) | patient(X0) [cnf transformation 54]
108. ~kind(X0) | patient(X0) [cnf transformation 54]
118. kind(X0) | curious(X0) [cnf transformation 33]
142. ~patient(john) [cnf transformation 23]
345. 46 <=> patient(john) [avatar definition]
346. ~patient(john) <- (~46) [avatar component clause 345]
349. ~46 [avatar split clause 142,345]
357. curious(X0) | patient(X0) [resolution 118,108]
359. patient(X0) [subsumption resolution 357,107]
363. $false <- (~46) [resolution 359,346]
366. 46 [avatar contradiction clause 363]
367. $false [avatar sat refutation 349,366]
% SZS output end Proof for 8836585969461260789127546
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not strong is not happy or not curious and vice versa. If someone is either not old or creative then someone is not calm or not funny and vice versa. Everyone who is wise or not creative is either not generous or not happy. Everyone who is not rich is either patient or old. Everyone who is not tall or kind is not funny. Everyone who is both generous and not generous is either not quiet or patient and vice versa. Everyone who is both kind and not patient is either not patient or funny and vice versa. Everyone who is not old or curious is both not brave and not creative. Everyone who is creative is not quiet or tall and vice versa. If someone is not kind then someone is not brave or curious. If fred is rich or not humble then john is quiet or not kind and vice versa. If mary is both not kind and not tall then someone is both not humble and not happy and vice versa. Everyone who is not strong or not old is not old. If someone is both not generous and creative then lucy is either wise or not happy and vice versa. Everyone who is not quiet or patient is patient. If mary is patient then mary is both not happy and not calm. Someone is not quiet or generous. Someone is happy. Susan is not wise or brave. Lucy is generous. Someone is brave or not rich. Alice is not rich or not patient. | John is quiet. | entailment | (![X]:((generous(X)&~strong(X))<=>(~happy(X)|~curious(X))))&
((?[X]:((~old(X)<~>creative(X))))<=>(?[X]:((~calm(X)|~funny(X)))))&
(![X]:((wise(X)|~creative(X))=>(~generous(X)<~>~happy(X))))&
(![X]:(~rich(X)=>(patient(X)<~>old(X))))&
(![X]:((~tall(X)|kind(X))=>~funny(X)))&
(![X]:((generous(X)&~generous(X))<=>(~quiet(X)<~>patient(X))))&
(![X]:((kind(X)&~patient(X))<=>(~patient(X)<~>funny(X))))&
(![X]:((~old(X)|curious(X))=>(~brave(X)&~creative(X))))&
(![X]:(creative(X)<=>(~quiet(X)|tall(X))))&
((?[X]:(~kind(X)))=>(?[X]:((~brave(X)|curious(X)))))&
(((rich(fred)|~humble(fred)))<=>((quiet(john)|~kind(john))))&
(((~kind(mary)&~tall(mary)))<=>(?[X]:((~humble(X)&~happy(X)))))&
(![X]:((~strong(X)|~old(X))=>~old(X)))&
((?[X]:((~generous(X)&creative(X))))<=>((wise(lucy)<~>~happy(lucy))))&
(![X]:((~quiet(X)|patient(X))=>patient(X)))&
((patient(mary))=>((~happy(mary)&~calm(mary))))&
(?[X]:((~quiet(X)|generous(X))))&
(?[X]:(happy(X)))&
((~wise(susan)|brave(susan)))&
(generous(lucy))&
(?[X]:((brave(X)|~rich(X))))&
((~rich(alice)|~patient(alice))) | quiet(john) | [
"p0",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2850829173775988396858289
% SZS output start Proof for 2850829173775988396858289
1. ! [X0] : ((~strong(X0) & generous(X0)) <=> (~curious(X0) | ~happy(X0))) [input p0]
8. ! [X0] : ((curious(X0) | ~old(X0)) => (~creative(X0) & ~brave(X0))) [input p7]
9. ! [X0] : (creative(X0) <=> (tall(X0) | ~quiet(X0))) [input p8]
13. ! [X0] : ((~old(X0) | ~strong(X0)) => ~old(X0)) [input p12]
23. ~quiet(john) [input hypothesis]
29. ! [X0] : ((~creative(X0) & ~brave(X0)) | (~curious(X0) & old(X0))) [ennf transformation 8]
31. ! [X0] : (~old(X0) | (old(X0) & strong(X0))) [ennf transformation 13]
34. ! [X0] : (((~strong(X0) & generous(X0)) | (curious(X0) & happy(X0))) & ((~curious(X0) | ~happy(X0)) | (strong(X0) | ~generous(X0)))) [nnf transformation 1]
35. ! [X0] : (((~strong(X0) & generous(X0)) | (curious(X0) & happy(X0))) & (~curious(X0) | ~happy(X0) | strong(X0) | ~generous(X0))) [flattening 34]
47. ! [X0] : ((creative(X0) | (~tall(X0) & quiet(X0))) & ((tall(X0) | ~quiet(X0)) | ~creative(X0))) [nnf transformation 9]
48. ! [X0] : ((creative(X0) | (~tall(X0) & quiet(X0))) & (tall(X0) | ~quiet(X0) | ~creative(X0))) [flattening 47]
73. ~strong(X0) | curious(X0) [cnf transformation 35]
102. ~creative(X0) | old(X0) [cnf transformation 29]
103. ~creative(X0) | ~curious(X0) [cnf transformation 29]
105. quiet(X0) | creative(X0) [cnf transformation 48]
116. ~old(X0) | strong(X0) [cnf transformation 31]
134. ~quiet(john) [cnf transformation 23]
196. 14 <=> quiet(john) [avatar definition]
198. ~quiet(john) <- (~14) [avatar component clause 196]
300. ~14 [avatar split clause 134,196]
309. creative(john) <- (~14) [resolution 105,198]
311. ~curious(john) <- (~14) [resolution 309,103]
312. old(john) <- (~14) [resolution 309,102]
317. strong(john) <- (~14) [resolution 312,116]
440. curious(john) <- (~14) [resolution 317,73]
442. $false <- (~14) [subsumption resolution 440,311]
443. 14 [avatar contradiction clause 442]
444. $false [avatar sat refutation 300,443]
% SZS output end Proof for 2850829173775988396858289
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not quiet is old or wise and vice versa.
Everyone who is calm or quiet is both brave and tall and vice versa.
Everyone who is not strong is not happy.
Everyone who is not wise is both curious and not humble.
Everyone who is wise is either humble or wise.
Everyone who is happy is patient.
Everyone who is both patient and funny is either not strong or calm and vice versa.
Everyone who is creative is not curious or not tall.
Everyone who is not humble or old is both not generous and calm.
If john is both not calm and tall then someone is both not funny and brave and vice versa.
If someone is kind then mary is not patient and vice versa.
If lucy is either curious or funny then someone is not creative.
Everyone who is not strong is either curious or generous.
Everyone who is either generous or not tall is happy or not tall and vice versa.
Someone is either not strong or not humble.
Susan is not strong or calm.
Someone is either not strong or not quiet.
Susan is not wise or brave.
Someone is either not rich or not curious. | Mary is kind. | neutral | (![X]:((humble(X)&~quiet(X))<=>(old(X)|wise(X))))&
(![X]:((calm(X)|quiet(X))<=>(brave(X)&tall(X))))&
(![X]:(~strong(X)=>~happy(X)))&
(![X]:(~wise(X)=>(curious(X)&~humble(X))))&
(![X]:(wise(X)=>(humble(X)<~>wise(X))))&
(![X]:(happy(X)=>patient(X)))&
(![X]:((patient(X)&funny(X))<=>(~strong(X)<~>calm(X))))&
(![X]:(creative(X)=>(~curious(X)|~tall(X))))&
(![X]:((~humble(X)|old(X))=>(~generous(X)&calm(X))))&
(((~calm(john)&tall(john)))<=>(?[X]:((~funny(X)&brave(X)))))&
((?[X]:(kind(X)))<=>(~patient(mary)))&
(((curious(lucy)<~>funny(lucy)))=>(?[X]:(~creative(X))))&
(![X]:(~strong(X)=>(curious(X)<~>generous(X))))&
(![X]:((generous(X)<~>~tall(X))<=>(happy(X)|~tall(X))))&
(?[X]:((~strong(X)<~>~humble(X))))&
((~strong(susan)|calm(susan)))&
(?[X]:((~strong(X)<~>~quiet(X))))&
((~wise(susan)|brave(susan)))&
(?[X]:((~rich(X)<~>~curious(X)))) | kind(mary) | [] | null | 0 |
If susan is both not happy and kind then someone is either not calm or wise and vice versa.
Everyone who is either happy or not humble is humble or tall and vice versa.
Everyone who is kind or calm is both patient and not quiet and vice versa.
Everyone who is not rich or happy is not kind.
Everyone who is either patient or generous is both kind and happy and vice versa.
If john is either not rich or old then paul is either humble or rich and vice versa.
If someone is both creative and quiet then someone is rich and vice versa.
Everyone who is calm is kind.
If someone is either not funny or happy then paul is both rich and not old and vice versa.
If someone is both not old and tall then paul is generous and vice versa.
If someone is not humble or brave then susan is rich or not curious.
Everyone who is happy is calm and vice versa.
Everyone who is both not patient and old is strong and vice versa.
Everyone who is not strong is both funny and not strong.
If paul is either not kind or not creative then fred is both calm and tall.
If someone is old then john is both kind and strong and vice versa.
Someone is not strong or quiet.
Someone is not brave or not tall.
Lucy is either not wise or not happy.
Mary is not happy.
Someone is not wise. | Susan is kind. | entailment | (((~happy(susan)&kind(susan)))<=>(?[X]:((~calm(X)<~>wise(X)))))&
(![X]:((happy(X)<~>~humble(X))<=>(humble(X)|tall(X))))&
(![X]:((kind(X)|calm(X))<=>(patient(X)&~quiet(X))))&
(![X]:((~rich(X)|happy(X))=>~kind(X)))&
(![X]:((patient(X)<~>generous(X))<=>(kind(X)&happy(X))))&
(((~rich(john)<~>old(john)))<=>((humble(paul)<~>rich(paul))))&
((?[X]:((creative(X)&quiet(X))))<=>(?[X]:(rich(X))))&
(![X]:(calm(X)=>kind(X)))&
((?[X]:((~funny(X)<~>happy(X))))<=>((rich(paul)&~old(paul))))&
((?[X]:((~old(X)&tall(X))))<=>(generous(paul)))&
((?[X]:((~humble(X)|brave(X))))=>((rich(susan)|~curious(susan))))&
(![X]:(happy(X)<=>calm(X)))&
(![X]:((~patient(X)&old(X))<=>strong(X)))&
(![X]:(~strong(X)=>(funny(X)&~strong(X))))&
(((~kind(paul)<~>~creative(paul)))=>((calm(fred)&tall(fred))))&
((?[X]:(old(X)))<=>((kind(john)&strong(john))))&
(?[X]:((~strong(X)|quiet(X))))&
(?[X]:((~brave(X)|~tall(X))))&
((~wise(lucy)<~>~happy(lucy)))&
(~happy(mary))&
(?[X]:(~wise(X))) | kind(susan) | [
"p0",
"p3",
"p7",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6998260646325990898983587
% SZS output start Proof for 6998260646325990898983587
1. (kind(susan) & ~happy(susan)) <=> ? [X0] : (~calm(X0) <~> wise(X0)) [input p0]
4. ! [X0] : ((happy(X0) | ~rich(X0)) => ~kind(X0)) [input p3]
8. ! [X0] : (calm(X0) => kind(X0)) [input p7]
12. ! [X0] : (happy(X0) <=> calm(X0)) [input p11]
21. ? [X0] : ~wise(X0) [input p20]
22. ~kind(susan) [input hypothesis]
26. ! [X0] : (~kind(X0) | (~happy(X0) & rich(X0))) [ennf transformation 4]
27. ! [X0] : (kind(X0) | ~calm(X0)) [ennf transformation 8]
30. ((kind(susan) & ~happy(susan)) | ! [X0] : ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0)))) & (? [X0] : ((~wise(X0) | calm(X0)) & (wise(X0) | ~calm(X0))) | (~kind(susan) | happy(susan))) [nnf transformation 1]
31. ((kind(susan) & ~happy(susan)) | ! [X0] : ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0)))) & (? [X0] : ((~wise(X0) | calm(X0)) & (wise(X0) | ~calm(X0))) | ~kind(susan) | happy(susan)) [flattening 30]
32. ((kind(susan) & ~happy(susan)) | ! [X0] : ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0)))) & (? [X1] : ((~wise(X1) | calm(X1)) & (wise(X1) | ~calm(X1))) | ~kind(susan) | happy(susan)) [rectify 31]
33. ? [X1] : ((~wise(X1) | calm(X1)) & (wise(X1) | ~calm(X1))) => ((~wise(sK0) | calm(sK0)) & (wise(sK0) | ~calm(sK0))) [choice axiom]
34. ((kind(susan) & ~happy(susan)) | ! [X0] : ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0)))) & (((~wise(sK0) | calm(sK0)) & (wise(sK0) | ~calm(sK0))) | ~kind(susan) | happy(susan)) [skolemisation 32,33]
56. ! [X0] : ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0))) [nnf transformation 12]
68. ? [X0] : ~wise(X0) => ~wise(sK7) [choice axiom]
69. ~wise(sK7) [skolemisation 21,68]
74. kind(susan) | wise(X0) | calm(X0) [cnf transformation 34]
88. ~kind(X0) | ~happy(X0) [cnf transformation 26]
106. ~calm(X0) | kind(X0) [cnf transformation 27]
117. ~calm(X0) | happy(X0) [cnf transformation 56]
134. ~wise(sK7) [cnf transformation 69]
135. ~kind(susan) [cnf transformation 22]
142. 2 <=> kind(susan) [avatar definition]
147. 3 <=> ! [X0] : (wise(X0) | calm(X0)) [avatar definition]
148. wise(X0) | calm(X0) <- (3) [avatar component clause 147]
149. 3 | 2 [avatar split clause 74,142,147]
312. ~2 [avatar split clause 135,142]
339. calm(sK7) <- (3) [resolution 148,134]
345. happy(sK7) <- (3) [resolution 339,117]
346. kind(sK7) <- (3) [resolution 339,106]
388. ~happy(sK7) <- (3) [resolution 346,88]
391. $false <- (3) [subsumption resolution 388,345]
392. ~3 [avatar contradiction clause 391]
393. $false [avatar sat refutation 149,312,392]
% SZS output end Proof for 6998260646325990898983587
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong or wise then alice is not happy.
Everyone who is not old or not happy is not humble or not rich and vice versa.
Everyone who is not humble is either patient or quiet and vice versa.
Everyone who is strong is both not wise and strong.
Everyone who is not humble is not quiet or not old.
Everyone who is curious or creative is tall.
Everyone who is generous is curious and vice versa.
Everyone who is both not generous and not calm is not happy or not generous and vice versa.
Everyone who is not generous or not old is both quiet and calm.
If alice is both not calm and wise then paul is old.
If someone is either not patient or tall then someone is not tall or not curious and vice versa.
Everyone who is either not tall or generous is not calm or not generous.
Everyone who is both not strong and not tall is funny or not humble and vice versa.
If someone is both generous and not calm then someone is either not funny or not wise and vice versa.
If lucy is not generous then mary is not rich or not funny.
Everyone who is either generous or rich is either creative or old.
John is either brave or not calm.
Mary is strong or not happy.
John is rich or creative.
Someone is either not tall or not patient.
Fred is brave or not humble. | Mary is brave. | neutral | (((~strong(lucy)|wise(lucy)))=>(~happy(alice)))&
(![X]:((~old(X)|~happy(X))<=>(~humble(X)|~rich(X))))&
(![X]:(~humble(X)<=>(patient(X)<~>quiet(X))))&
(![X]:(strong(X)=>(~wise(X)&strong(X))))&
(![X]:(~humble(X)=>(~quiet(X)|~old(X))))&
(![X]:((curious(X)|creative(X))=>tall(X)))&
(![X]:(generous(X)<=>curious(X)))&
(![X]:((~generous(X)&~calm(X))<=>(~happy(X)|~generous(X))))&
(![X]:((~generous(X)|~old(X))=>(quiet(X)&calm(X))))&
(((~calm(alice)&wise(alice)))=>(old(paul)))&
((?[X]:((~patient(X)<~>tall(X))))<=>(?[X]:((~tall(X)|~curious(X)))))&
(![X]:((~tall(X)<~>generous(X))=>(~calm(X)|~generous(X))))&
(![X]:((~strong(X)&~tall(X))<=>(funny(X)|~humble(X))))&
((?[X]:((generous(X)&~calm(X))))<=>(?[X]:((~funny(X)<~>~wise(X)))))&
((~generous(lucy))=>((~rich(mary)|~funny(mary))))&
(![X]:((generous(X)<~>rich(X))=>(creative(X)<~>old(X))))&
((brave(john)<~>~calm(john)))&
((strong(mary)|~happy(mary)))&
((rich(john)|creative(john)))&
(?[X]:((~tall(X)<~>~patient(X))))&
((brave(fred)|~humble(fred))) | brave(mary) | [] | null | 0 |
If mary is old then susan is brave and vice versa.
If alice is not generous or not tall then someone is either happy or generous and vice versa.
If someone is creative then alice is both not generous and not humble.
Everyone who is both not kind and not humble is not strong or not funny and vice versa.
If paul is not curious or not patient then someone is patient and vice versa.
Everyone who is either creative or calm is not calm or humble.
If lucy is either kind or not happy then someone is either not tall or curious.
If someone is both not funny and not brave then susan is both rich and not quiet and vice versa.
If fred is both not happy and happy then lucy is funny.
Everyone who is kind is either quiet or humble and vice versa.
Everyone who is not wise or curious is creative or old.
Everyone who is either not funny or wise is curious.
If fred is both not generous and generous then someone is either quiet or strong and vice versa.
If someone is both wise and not wise then paul is rich.
If someone is funny or not strong then mary is both not patient and not happy and vice versa.
Everyone who is both not humble and old is both not generous and rich and vice versa.
John is rich.
Paul is not wise or quiet.
Lucy is both not humble and kind.
Someone is not calm or brave.
Someone is rich.
Someone is calm or not generous.
Lucy is both rich and not creative.
Someone is both curious and not rich. | John is not calm. | neutral | ((old(mary))<=>(brave(susan)))&
(((~generous(alice)|~tall(alice)))<=>(?[X]:((happy(X)<~>generous(X)))))&
((?[X]:(creative(X)))=>((~generous(alice)&~humble(alice))))&
(![X]:((~kind(X)&~humble(X))<=>(~strong(X)|~funny(X))))&
(((~curious(paul)|~patient(paul)))<=>(?[X]:(patient(X))))&
(![X]:((creative(X)<~>calm(X))=>(~calm(X)|humble(X))))&
(((kind(lucy)<~>~happy(lucy)))=>(?[X]:((~tall(X)<~>curious(X)))))&
((?[X]:((~funny(X)&~brave(X))))<=>((rich(susan)&~quiet(susan))))&
(((~happy(fred)&happy(fred)))=>(funny(lucy)))&
(![X]:(kind(X)<=>(quiet(X)<~>humble(X))))&
(![X]:((~wise(X)|curious(X))=>(creative(X)|old(X))))&
(![X]:((~funny(X)<~>wise(X))=>curious(X)))&
(((~generous(fred)&generous(fred)))<=>(?[X]:((quiet(X)<~>strong(X)))))&
((?[X]:((wise(X)&~wise(X))))=>(rich(paul)))&
((?[X]:((funny(X)|~strong(X))))<=>((~patient(mary)&~happy(mary))))&
(![X]:((~humble(X)&old(X))<=>(~generous(X)&rich(X))))&
(rich(john))&
((~wise(paul)|quiet(paul)))&
((~humble(lucy)&kind(lucy)))&
(?[X]:((~calm(X)|brave(X))))&
(?[X]:(rich(X)))&
(?[X]:((calm(X)|~generous(X))))&
((rich(lucy)&~creative(lucy)))&
(?[X]:((curious(X)&~rich(X)))) | ~calm(john) | [] | null | 0 |
Everyone who is both not brave and not humble is generous.
Everyone who is kind or not quiet is either patient or not curious and vice versa.
If lucy is wise or humble then someone is either not calm or not rich.
Everyone who is not kind is brave and vice versa.
If someone is either patient or strong then alice is not tall or not brave.
If someone is not brave then someone is both not happy and not rich and vice versa.
Everyone who is brave or not old is both tall and not generous.
If john is not quiet or not strong then alice is both not wise and brave.
If someone is kind or generous then someone is both tall and strong and vice versa.
Everyone who is not strong is generous and vice versa.
If someone is both quiet and not funny then someone is tall or not kind and vice versa.
Everyone who is kind or humble is both kind and patient and vice versa.
If someone is creative or kind then someone is either happy or not curious.
If fred is curious then someone is kind or creative.
If someone is not brave then someone is strong.
Everyone who is tall or not funny is either not generous or not wise and vice versa.
Someone is both not generous and old.
John is either brave or strong.
Alice is either funny or not funny.
Someone is not creative.
Someone is either not old or not rich.
Someone is both not funny and not rich.
Fred is both not calm and not creative.
Someone is either not humble or strong. | Alice is not patient. | contradiction | (![X]:((~brave(X)&~humble(X))=>generous(X)))&
(![X]:((kind(X)|~quiet(X))<=>(patient(X)<~>~curious(X))))&
(((wise(lucy)|humble(lucy)))=>(?[X]:((~calm(X)<~>~rich(X)))))&
(![X]:(~kind(X)<=>brave(X)))&
((?[X]:((patient(X)<~>strong(X))))=>((~tall(alice)|~brave(alice))))&
((?[X]:(~brave(X)))<=>(?[X]:((~happy(X)&~rich(X)))))&
(![X]:((brave(X)|~old(X))=>(tall(X)&~generous(X))))&
(((~quiet(john)|~strong(john)))=>((~wise(alice)&brave(alice))))&
((?[X]:((kind(X)|generous(X))))<=>(?[X]:((tall(X)&strong(X)))))&
(![X]:(~strong(X)<=>generous(X)))&
((?[X]:((quiet(X)&~funny(X))))<=>(?[X]:((tall(X)|~kind(X)))))&
(![X]:((kind(X)|humble(X))<=>(kind(X)&patient(X))))&
((?[X]:((creative(X)|kind(X))))=>(?[X]:((happy(X)<~>~curious(X)))))&
((curious(fred))=>(?[X]:((kind(X)|creative(X)))))&
((?[X]:(~brave(X)))=>(?[X]:(strong(X))))&
(![X]:((tall(X)|~funny(X))<=>(~generous(X)<~>~wise(X))))&
(?[X]:((~generous(X)&old(X))))&
((brave(john)<~>strong(john)))&
((funny(alice)<~>~funny(alice)))&
(?[X]:(~creative(X)))&
(?[X]:((~old(X)<~>~rich(X))))&
(?[X]:((~funny(X)&~rich(X))))&
((~calm(fred)&~creative(fred)))&
(?[X]:((~humble(X)<~>strong(X)))) | ~patient(alice) | [
"p3",
"p4",
"p6",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3978802053699191052584451
% SZS output start Proof for 3978802053699191052584451
4. ! [X0] : (~kind(X0) <=> brave(X0)) [input p3]
5. ? [X0] : (patient(X0) <~> strong(X0)) => (~brave(alice) | ~tall(alice)) [input p4]
7. ! [X0] : ((~old(X0) | brave(X0)) => (~generous(X0) & tall(X0))) [input p6]
10. ! [X0] : (~strong(X0) <=> generous(X0)) [input p9]
12. ! [X0] : ((humble(X0) | kind(X0)) <=> (patient(X0) & kind(X0))) [input p11]
16. ! [X0] : ((~funny(X0) | tall(X0)) <=> (~generous(X0) <~> ~wise(X0))) [input p15]
25. ~patient(alice) [input hypothesis]
34. (~brave(alice) | ~tall(alice)) | ! [X0] : (patient(X0) <=> strong(X0)) [ennf transformation 5]
35. ~brave(alice) | ~tall(alice) | ! [X0] : (patient(X0) <=> strong(X0)) [flattening 34]
36. ! [X0] : ((~generous(X0) & tall(X0)) | (old(X0) & ~brave(X0))) [ennf transformation 7]
46. ! [X0] : ((~kind(X0) | ~brave(X0)) & (brave(X0) | kind(X0))) [nnf transformation 4]
47. ~brave(alice) | ~tall(alice) | ! [X0] : ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0))) [nnf transformation 35]
58. ! [X0] : ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0))) [nnf transformation 10]
64. ! [X0] : (((humble(X0) | kind(X0)) | (~patient(X0) | ~kind(X0))) & ((patient(X0) & kind(X0)) | (~humble(X0) & ~kind(X0)))) [nnf transformation 12]
65. ! [X0] : ((humble(X0) | kind(X0) | ~patient(X0) | ~kind(X0)) & ((patient(X0) & kind(X0)) | (~humble(X0) & ~kind(X0)))) [flattening 64]
75. ! [X0] : (((~funny(X0) | tall(X0)) | ((~generous(X0) | wise(X0)) & (~wise(X0) | generous(X0)))) & (((wise(X0) | generous(X0)) & (~wise(X0) | ~generous(X0))) | (funny(X0) & ~tall(X0)))) [nnf transformation 16]
76. ! [X0] : ((~funny(X0) | tall(X0) | ((~generous(X0) | wise(X0)) & (~wise(X0) | generous(X0)))) & (((wise(X0) | generous(X0)) & (~wise(X0) | ~generous(X0))) | (funny(X0) & ~tall(X0)))) [flattening 75]
102. kind(X0) | brave(X0) [cnf transformation 46]
105. ~brave(alice) | ~tall(alice) | patient(X0) | ~strong(X0) [cnf transformation 47]
109. ~brave(X0) | tall(X0) [cnf transformation 36]
111. ~generous(X0) | ~brave(X0) [cnf transformation 36]
122. strong(X0) | generous(X0) [cnf transformation 58]
131. ~kind(X0) | patient(X0) [cnf transformation 65]
140. ~tall(X0) | ~generous(X0) | ~wise(X0) [cnf transformation 76]
142. ~tall(X0) | generous(X0) | wise(X0) [cnf transformation 76]
161. ~patient(alice) [cnf transformation 25]
183. 5 <=> ! [X0] : (patient(X0) | ~strong(X0)) [avatar definition]
184. ~strong(X0) | patient(X0) <- (5) [avatar component clause 183]
186. 6 <=> tall(alice) [avatar definition]
187. tall(alice) <- (6) [avatar component clause 186]
190. 7 <=> brave(alice) [avatar definition]
191. brave(alice) <- (7) [avatar component clause 190]
193. 5 | ~6 | ~7 [avatar split clause 105,190,186,183]
230. 16 <=> wise(alice) [avatar definition]
232. ~wise(alice) <- (~16) [avatar component clause 230]
379. patient(X0) | brave(X0) [resolution 131,102]
445. tall(alice) <- (7) [resolution 191,109]
448. 6 | ~7 [avatar split clause 445,190,186]
452. patient(X0) | generous(X0) <- (5) [resolution 184,122]
469. ~generous(alice) | ~wise(alice) <- (6) [resolution 140,187]
499. generous(alice) | wise(alice) <- (6) [resolution 142,187]
503. generous(alice) <- (6, ~16) [subsumption resolution 499,232]
579. ~brave(alice) <- (6, ~16) [resolution 503,111]
580. $false <- (6, 7, ~16) [subsumption resolution 579,191]
581. ~6 | ~7 | 16 [avatar contradiction clause 580]
583. 65 <=> generous(alice) [avatar definition]
584. ~generous(alice) <- (~65) [avatar component clause 583]
587. ~16 | ~65 | ~6 [avatar split clause 469,186,583,230]
631. brave(alice) [resolution 379,161]
641. generous(alice) <- (5) [resolution 452,161]
646. $false <- (5, ~65) [subsumption resolution 641,584]
647. ~5 | 65 [avatar contradiction clause 646]
656. 7 [avatar split clause 631,190]
662. $false [avatar sat refutation 193,448,581,587,647,656]
% SZS output end Proof for 3978802053699191052584451
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall is not happy or calm and vice versa.
Everyone who is both curious and not curious is both humble and not patient and vice versa.
If someone is old or tall then fred is both not brave and not strong and vice versa.
Everyone who is funny is both generous and patient and vice versa.
Everyone who is either happy or generous is both humble and not wise.
Everyone who is not quiet is not quiet or funny.
Everyone who is not strong is either not quiet or not rich.
If someone is brave then fred is either rich or generous and vice versa.
If someone is both quiet and tall then someone is both not curious and calm and vice versa.
Everyone who is not creative or humble is not old or not happy.
If alice is creative or kind then someone is not old or not happy and vice versa.
Everyone who is not wise or generous is either curious or strong.
If mary is kind or not brave then alice is not strong or not old and vice versa.
Everyone who is not brave is both happy and not wise.
If someone is generous or not quiet then paul is creative or not calm.
If john is either not rich or generous then fred is both not happy and old and vice versa.
Someone is both creative and not funny.
Someone is either kind or quiet.
Lucy is not curious.
John is both not strong and not tall.
Someone is both not quiet and patient.
Someone is not old or happy.
Someone is not patient.
Someone is not tall or creative. | John is curious. | entailment | (![X]:(tall(X)<=>(~happy(X)|calm(X))))&
(![X]:((curious(X)&~curious(X))<=>(humble(X)&~patient(X))))&
((?[X]:((old(X)|tall(X))))<=>((~brave(fred)&~strong(fred))))&
(![X]:(funny(X)<=>(generous(X)&patient(X))))&
(![X]:((happy(X)<~>generous(X))=>(humble(X)&~wise(X))))&
(![X]:(~quiet(X)=>(~quiet(X)|funny(X))))&
(![X]:(~strong(X)=>(~quiet(X)<~>~rich(X))))&
((?[X]:(brave(X)))<=>((rich(fred)<~>generous(fred))))&
((?[X]:((quiet(X)&tall(X))))<=>(?[X]:((~curious(X)&calm(X)))))&
(![X]:((~creative(X)|humble(X))=>(~old(X)|~happy(X))))&
(((creative(alice)|kind(alice)))<=>(?[X]:((~old(X)|~happy(X)))))&
(![X]:((~wise(X)|generous(X))=>(curious(X)<~>strong(X))))&
(((kind(mary)|~brave(mary)))<=>((~strong(alice)|~old(alice))))&
(![X]:(~brave(X)=>(happy(X)&~wise(X))))&
((?[X]:((generous(X)|~quiet(X))))=>((creative(paul)|~calm(paul))))&
(((~rich(john)<~>generous(john)))<=>((~happy(fred)&old(fred))))&
(?[X]:((creative(X)&~funny(X))))&
(?[X]:((kind(X)<~>quiet(X))))&
(~curious(lucy))&
((~strong(john)&~tall(john)))&
(?[X]:((~quiet(X)&patient(X))))&
(?[X]:((~old(X)|happy(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~tall(X)|creative(X)))) | curious(john) | [
"p0",
"p4",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1702797683681892809923488
% SZS output start Proof for 1702797683681892809923488
1. ! [X0] : (tall(X0) <=> (calm(X0) | ~happy(X0))) [input p0]
5. ! [X0] : ((happy(X0) <~> generous(X0)) => (~wise(X0) & humble(X0))) [input p4]
12. ! [X0] : ((generous(X0) | ~wise(X0)) => (curious(X0) <~> strong(X0))) [input p11]
20. ~tall(john) & ~strong(john) [input p19]
25. ~curious(john) [input hypothesis]
27. ! [X0] : ((~wise(X0) & humble(X0)) | (happy(X0) <=> generous(X0))) [ennf transformation 5]
33. ! [X0] : ((curious(X0) <~> strong(X0)) | (~generous(X0) & wise(X0))) [ennf transformation 12]
37. ! [X0] : ((tall(X0) | (~calm(X0) & happy(X0))) & ((calm(X0) | ~happy(X0)) | ~tall(X0))) [nnf transformation 1]
38. ! [X0] : ((tall(X0) | (~calm(X0) & happy(X0))) & (calm(X0) | ~happy(X0) | ~tall(X0))) [flattening 37]
48. ! [X0] : ((~wise(X0) & humble(X0)) | ((happy(X0) | ~generous(X0)) & (generous(X0) | ~happy(X0)))) [nnf transformation 27]
64. ! [X0] : (((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | (~generous(X0) & wise(X0))) [nnf transformation 33]
83. happy(X0) | tall(X0) [cnf transformation 38]
99. ~wise(X0) | generous(X0) | ~happy(X0) [cnf transformation 48]
118. wise(X0) | curious(X0) | strong(X0) [cnf transformation 64]
119. ~generous(X0) | curious(X0) | strong(X0) [cnf transformation 64]
141. ~strong(john) [cnf transformation 20]
142. ~tall(john) [cnf transformation 20]
148. ~curious(john) [cnf transformation 25]
381. curious(X1) | strong(X1) | generous(X1) | ~happy(X1) [resolution 118,99]
383. ~happy(X1) | strong(X1) | curious(X1) [subsumption resolution 381,119]
405. strong(X0) | curious(X0) | tall(X0) [resolution 383,83]
464. curious(john) | tall(john) [resolution 405,141]
465. tall(john) [subsumption resolution 464,148]
466. $false [subsumption resolution 465,142]
% SZS output end Proof for 1702797683681892809923488
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is patient or not patient then someone is not happy or patient.
If alice is not brave then john is both patient and happy.
Everyone who is generous is not funny.
If someone is not rich then someone is either not kind or not calm and vice versa.
Everyone who is both brave and not wise is wise or not wise and vice versa.
Everyone who is curious is either not wise or not creative and vice versa.
If someone is either not wise or not funny then someone is both not strong and generous.
If paul is either not humble or not happy then john is both not tall and not humble and vice versa.
If mary is both not patient and happy then john is kind or not kind.
If paul is old or happy then someone is either strong or brave and vice versa.
If paul is either old or rich then someone is curious or humble and vice versa.
If mary is happy then someone is either tall or not quiet.
If paul is happy then someone is both not calm and funny and vice versa.
Everyone who is kind is not creative or generous.
Everyone who is not patient is wise or quiet and vice versa.
Everyone who is not brave is either not quiet or quiet.
Paul is not curious or humble.
Someone is tall.
Someone is both calm and tall.
Paul is tall.
Susan is either funny or brave.
Someone is not calm or rich. | Paul is patient. | neutral | ((?[X]:((patient(X)|~patient(X))))=>(?[X]:((~happy(X)|patient(X)))))&
((~brave(alice))=>((patient(john)&happy(john))))&
(![X]:(generous(X)=>~funny(X)))&
((?[X]:(~rich(X)))<=>(?[X]:((~kind(X)<~>~calm(X)))))&
(![X]:((brave(X)&~wise(X))<=>(wise(X)|~wise(X))))&
(![X]:(curious(X)<=>(~wise(X)<~>~creative(X))))&
((?[X]:((~wise(X)<~>~funny(X))))=>(?[X]:((~strong(X)&generous(X)))))&
(((~humble(paul)<~>~happy(paul)))<=>((~tall(john)&~humble(john))))&
(((~patient(mary)&happy(mary)))=>((kind(john)|~kind(john))))&
(((old(paul)|happy(paul)))<=>(?[X]:((strong(X)<~>brave(X)))))&
(((old(paul)<~>rich(paul)))<=>(?[X]:((curious(X)|humble(X)))))&
((happy(mary))=>(?[X]:((tall(X)<~>~quiet(X)))))&
((happy(paul))<=>(?[X]:((~calm(X)&funny(X)))))&
(![X]:(kind(X)=>(~creative(X)|generous(X))))&
(![X]:(~patient(X)<=>(wise(X)|quiet(X))))&
(![X]:(~brave(X)=>(~quiet(X)<~>quiet(X))))&
((~curious(paul)|humble(paul)))&
(?[X]:(tall(X)))&
(?[X]:((calm(X)&tall(X))))&
(tall(paul))&
((funny(susan)<~>brave(susan)))&
(?[X]:((~calm(X)|rich(X)))) | patient(paul) | [] | null | 0 |
Everyone who is strong or brave is both not kind and generous and vice versa.
If someone is funny then fred is curious and vice versa.
If paul is both strong and not wise then someone is happy and vice versa.
If mary is both funny and not brave then paul is not happy or quiet and vice versa.
Everyone who is either quiet or brave is either tall or not calm.
Everyone who is tall or not funny is either not calm or not funny.
If someone is either not old or not strong then alice is both old and rich.
If paul is either tall or calm then someone is either calm or happy and vice versa.
Everyone who is creative is brave or strong.
Everyone who is not funny is not strong.
If someone is not humble then someone is both not quiet and happy.
Everyone who is not kind or calm is both not brave and happy and vice versa.
If alice is either not curious or strong then someone is both not funny and not generous and vice versa.
Everyone who is not old is either not tall or curious.
Everyone who is quiet is either not calm or not generous and vice versa.
If someone is calm then someone is not wise or happy.
Someone is patient.
Someone is both not patient and not curious.
Susan is both funny and not quiet.
Someone is quiet or not humble.
Someone is both not creative and calm.
Someone is either not happy or not humble.
Alice is not creative. | Paul is not tall. | entailment | (![X]:((strong(X)|brave(X))<=>(~kind(X)&generous(X))))&
((?[X]:(funny(X)))<=>(curious(fred)))&
(((strong(paul)&~wise(paul)))<=>(?[X]:(happy(X))))&
(((funny(mary)&~brave(mary)))<=>((~happy(paul)|quiet(paul))))&
(![X]:((quiet(X)<~>brave(X))=>(tall(X)<~>~calm(X))))&
(![X]:((tall(X)|~funny(X))=>(~calm(X)<~>~funny(X))))&
((?[X]:((~old(X)<~>~strong(X))))=>((old(alice)&rich(alice))))&
(((tall(paul)<~>calm(paul)))<=>(?[X]:((calm(X)<~>happy(X)))))&
(![X]:(creative(X)=>(brave(X)|strong(X))))&
(![X]:(~funny(X)=>~strong(X)))&
((?[X]:(~humble(X)))=>(?[X]:((~quiet(X)&happy(X)))))&
(![X]:((~kind(X)|calm(X))<=>(~brave(X)&happy(X))))&
(((~curious(alice)<~>strong(alice)))<=>(?[X]:((~funny(X)&~generous(X)))))&
(![X]:(~old(X)=>(~tall(X)<~>curious(X))))&
(![X]:(quiet(X)<=>(~calm(X)<~>~generous(X))))&
((?[X]:(calm(X)))=>(?[X]:((~wise(X)|happy(X)))))&
(?[X]:(patient(X)))&
(?[X]:((~patient(X)&~curious(X))))&
((funny(susan)&~quiet(susan)))&
(?[X]:((quiet(X)|~humble(X))))&
(?[X]:((~creative(X)&calm(X))))&
(?[X]:((~happy(X)<~>~humble(X))))&
(~creative(alice)) | ~tall(paul) | [
"p0",
"p2",
"p4",
"p5",
"p9",
"p11",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5195250649480870817700307
% SZS output start Proof for 5195250649480870817700307
1. ! [X0] : ((brave(X0) | strong(X0)) <=> (generous(X0) & ~kind(X0))) [input p0]
3. (~wise(paul) & strong(paul)) <=> ? [X0] : happy(X0) [input p2]
5. ! [X0] : ((quiet(X0) <~> brave(X0)) => (tall(X0) <~> ~calm(X0))) [input p4]
6. ! [X0] : ((~funny(X0) | tall(X0)) => (~calm(X0) <~> ~funny(X0))) [input p5]
10. ! [X0] : (~funny(X0) => ~strong(X0)) [input p9]
12. ! [X0] : ((calm(X0) | ~kind(X0)) <=> (happy(X0) & ~brave(X0))) [input p11]
15. ! [X0] : (quiet(X0) <=> (~calm(X0) <~> ~generous(X0))) [input p14]
21. ? [X0] : (calm(X0) & ~creative(X0)) [input p20]
24. tall(paul) [input hypothesis]
27. ? [X0] : calm(X0) [pure predicate removal 21]
31. ! [X0] : ((tall(X0) <~> ~calm(X0)) | (quiet(X0) <=> brave(X0))) [ennf transformation 5]
32. ! [X0] : ((~calm(X0) <~> ~funny(X0)) | (funny(X0) & ~tall(X0))) [ennf transformation 6]
34. ! [X0] : (~strong(X0) | funny(X0)) [ennf transformation 10]
38. ! [X0] : (((brave(X0) | strong(X0)) | (~generous(X0) | kind(X0))) & ((generous(X0) & ~kind(X0)) | (~brave(X0) & ~strong(X0)))) [nnf transformation 1]
39. ! [X0] : ((brave(X0) | strong(X0) | ~generous(X0) | kind(X0)) & ((generous(X0) & ~kind(X0)) | (~brave(X0) & ~strong(X0)))) [flattening 38]
44. ((~wise(paul) & strong(paul)) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | (wise(paul) | ~strong(paul))) [nnf transformation 3]
45. ((~wise(paul) & strong(paul)) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | wise(paul) | ~strong(paul)) [flattening 44]
46. ((~wise(paul) & strong(paul)) | ! [X0] : ~happy(X0)) & (? [X1] : happy(X1) | wise(paul) | ~strong(paul)) [rectify 45]
47. ? [X1] : happy(X1) => happy(sK1) [choice axiom]
48. ((~wise(paul) & strong(paul)) | ! [X0] : ~happy(X0)) & (happy(sK1) | wise(paul) | ~strong(paul)) [skolemisation 46,47]
51. ! [X0] : (((calm(X0) | ~tall(X0)) & (~calm(X0) | tall(X0))) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0)))) [nnf transformation 31]
52. ! [X0] : (((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) | (funny(X0) & ~tall(X0))) [nnf transformation 32]
61. ! [X0] : (((calm(X0) | ~kind(X0)) | (~happy(X0) | brave(X0))) & ((happy(X0) & ~brave(X0)) | (~calm(X0) & kind(X0)))) [nnf transformation 12]
62. ! [X0] : ((calm(X0) | ~kind(X0) | ~happy(X0) | brave(X0)) & ((happy(X0) & ~brave(X0)) | (~calm(X0) & kind(X0)))) [flattening 61]
68. ! [X0] : ((quiet(X0) | ((~calm(X0) | generous(X0)) & (~generous(X0) | calm(X0)))) & (((generous(X0) | calm(X0)) & (~generous(X0) | ~calm(X0))) | ~quiet(X0))) [nnf transformation 15]
78. ? [X0] : calm(X0) => calm(sK9) [choice axiom]
79. calm(sK9) [skolemisation 27,78]
84. ~kind(X0) | ~brave(X0) [cnf transformation 39]
85. ~strong(X0) | generous(X0) [cnf transformation 39]
91. strong(paul) | ~happy(X0) [cnf transformation 48]
100. ~tall(X0) | calm(X0) | brave(X0) | ~quiet(X0) [cnf transformation 51]
102. ~calm(X0) | ~funny(X0) | ~tall(X0) [cnf transformation 52]
116. ~strong(X0) | funny(X0) [cnf transformation 34]
119. ~brave(X0) | kind(X0) [cnf transformation 62]
122. happy(X0) | ~calm(X0) [cnf transformation 62]
134. ~generous(X0) | quiet(X0) | calm(X0) [cnf transformation 68]
143. calm(sK9) [cnf transformation 79]
146. tall(paul) [cnf transformation 24]
162. 4 <=> ! [X0] : ~happy(X0) [avatar definition]
163. ~happy(X0) <- (4) [avatar component clause 162]
170. 6 <=> strong(paul) [avatar definition]
172. strong(paul) <- (6) [avatar component clause 170]
173. 4 | 6 [avatar split clause 91,170,162]
180. 8 <=> quiet(paul) [avatar definition]
181. quiet(paul) <- (8) [avatar component clause 180]
182. ~quiet(paul) <- (~8) [avatar component clause 180]
216. 16 <=> tall(paul) [avatar definition]
217. tall(paul) <- (16) [avatar component clause 216]
220. 17 <=> calm(paul) [avatar definition]
221. calm(paul) <- (17) [avatar component clause 220]
222. ~calm(paul) <- (~17) [avatar component clause 220]
225. 18 <=> ! [X0] : (happy(X0) | ~calm(X0)) [avatar definition]
226. ~calm(X0) | happy(X0) <- (18) [avatar component clause 225]
256. 18 [avatar split clause 122,225]
257. ~brave(X0) [subsumption resolution 119,84]
314. 16 [avatar split clause 146,216]
321. generous(paul) <- (6) [resolution 85,172]
322. funny(paul) <- (6) [resolution 116,172]
335. happy(sK9) <- (18) [resolution 226,143]
339. ~funny(paul) | ~tall(paul) <- (17) [resolution 102,221]
343. ~tall(paul) <- (6, 17) [subsumption resolution 339,322]
344. $false <- (6, 16, 17) [subsumption resolution 343,217]
345. ~6 | ~16 | ~17 [avatar contradiction clause 344]
422. quiet(paul) | calm(paul) <- (6) [resolution 134,321]
423. calm(paul) <- (6, ~8) [subsumption resolution 422,182]
424. $false <- (6, ~8, ~17) [subsumption resolution 423,222]
425. ~6 | 8 | 17 [avatar contradiction clause 424]
430. $false <- (4, 18) [resolution 163,335]
433. ~4 | ~18 [avatar contradiction clause 430]
500. calm(paul) | brave(paul) | ~quiet(paul) <- (16) [resolution 100,217]
501. brave(paul) | ~quiet(paul) <- (16, ~17) [subsumption resolution 500,222]
502. ~quiet(paul) <- (16, ~17) [subsumption resolution 501,257]
503. $false <- (8, 16, ~17) [subsumption resolution 502,181]
504. ~8 | ~16 | 17 [avatar contradiction clause 503]
505. $false [avatar sat refutation 173,256,314,345,425,433,504]
% SZS output end Proof for 5195250649480870817700307
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not kind then someone is either wise or not kind and vice versa. Everyone who is both patient and not wise is strong. Everyone who is both rich and not quiet is not old or creative and vice versa. Everyone who is both happy and not kind is not humble or not tall and vice versa. Everyone who is both calm and tall is humble or old and vice versa. Everyone who is not funny is rich and vice versa. Everyone who is both not kind and not quiet is both strong and not rich and vice versa. Everyone who is curious is both rich and not curious. If someone is both not quiet and wise then fred is not strong or kind and vice versa. Everyone who is both kind and not humble is not curious or not tall. Everyone who is either not brave or curious is not happy or strong. Everyone who is either calm or not funny is either not strong or funny. Everyone who is both not old and humble is both humble and patient. If someone is both not brave and not generous then someone is creative or not strong. If someone is generous or creative then fred is both humble and creative and vice versa. Everyone who is either not generous or wise is either not kind or not curious. Lucy is patient. Someone is not wise. Someone is kind or wise. Paul is either not creative or not curious. John is either calm or brave. Someone is quiet or calm. Someone is both old and rich. | Paul is not tall. | contradiction | (((quiet(paul)|~kind(paul)))<=>(?[X]:((wise(X)<~>~kind(X)))))&
(![X]:((patient(X)&~wise(X))=>strong(X)))&
(![X]:((rich(X)&~quiet(X))<=>(~old(X)|creative(X))))&
(![X]:((happy(X)&~kind(X))<=>(~humble(X)|~tall(X))))&
(![X]:((calm(X)&tall(X))<=>(humble(X)|old(X))))&
(![X]:(~funny(X)<=>rich(X)))&
(![X]:((~kind(X)&~quiet(X))<=>(strong(X)&~rich(X))))&
(![X]:(curious(X)=>(rich(X)&~curious(X))))&
((?[X]:((~quiet(X)&wise(X))))<=>((~strong(fred)|kind(fred))))&
(![X]:((kind(X)&~humble(X))=>(~curious(X)|~tall(X))))&
(![X]:((~brave(X)<~>curious(X))=>(~happy(X)|strong(X))))&
(![X]:((calm(X)<~>~funny(X))=>(~strong(X)<~>funny(X))))&
(![X]:((~old(X)&humble(X))=>(humble(X)&patient(X))))&
((?[X]:((~brave(X)&~generous(X))))=>(?[X]:((creative(X)|~strong(X)))))&
((?[X]:((generous(X)|creative(X))))<=>((humble(fred)&creative(fred))))&
(![X]:((~generous(X)<~>wise(X))=>(~kind(X)<~>~curious(X))))&
(patient(lucy))&
(?[X]:(~wise(X)))&
(?[X]:((kind(X)|wise(X))))&
((~creative(paul)<~>~curious(paul)))&
((calm(john)<~>brave(john)))&
(?[X]:((quiet(X)|calm(X))))&
(?[X]:((old(X)&rich(X)))) | ~tall(paul) | [
"p2",
"p3",
"p6",
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 206747813116452825823342
% SZS output start Proof for 206747813116452825823342
3. ! [X0] : ((~quiet(X0) & rich(X0)) <=> (creative(X0) | ~old(X0))) [input p2]
4. ! [X0] : ((~kind(X0) & happy(X0)) <=> (~tall(X0) | ~humble(X0))) [input p3]
7. ! [X0] : ((~quiet(X0) & ~kind(X0)) <=> (~rich(X0) & strong(X0))) [input p6]
8. ! [X0] : (curious(X0) => (~curious(X0) & rich(X0))) [input p7]
20. ~creative(paul) <~> ~curious(paul) [input p19]
24. ~tall(paul) [input hypothesis]
28. ! [X0] : ((~curious(X0) & rich(X0)) | ~curious(X0)) [ennf transformation 8]
43. ! [X0] : (((~quiet(X0) & rich(X0)) | (~creative(X0) & old(X0))) & ((creative(X0) | ~old(X0)) | (quiet(X0) | ~rich(X0)))) [nnf transformation 3]
44. ! [X0] : (((~quiet(X0) & rich(X0)) | (~creative(X0) & old(X0))) & (creative(X0) | ~old(X0) | quiet(X0) | ~rich(X0))) [flattening 43]
45. ! [X0] : (((~kind(X0) & happy(X0)) | (tall(X0) & humble(X0))) & ((~tall(X0) | ~humble(X0)) | (kind(X0) | ~happy(X0)))) [nnf transformation 4]
46. ! [X0] : (((~kind(X0) & happy(X0)) | (tall(X0) & humble(X0))) & (~tall(X0) | ~humble(X0) | kind(X0) | ~happy(X0))) [flattening 45]
50. ! [X0] : (((~quiet(X0) & ~kind(X0)) | (rich(X0) | ~strong(X0))) & ((~rich(X0) & strong(X0)) | (quiet(X0) | kind(X0)))) [nnf transformation 7]
51. ! [X0] : (((~quiet(X0) & ~kind(X0)) | rich(X0) | ~strong(X0)) & ((~rich(X0) & strong(X0)) | quiet(X0) | kind(X0))) [flattening 50]
72. (curious(paul) | creative(paul)) & (~curious(paul) | ~creative(paul)) [nnf transformation 20]
87. ~creative(X0) | rich(X0) [cnf transformation 44]
89. ~creative(X0) | ~quiet(X0) [cnf transformation 44]
94. ~kind(X0) | tall(X0) [cnf transformation 46]
103. ~rich(X0) | quiet(X0) | kind(X0) [cnf transformation 51]
107. ~curious(X0) | ~curious(X0) [cnf transformation 28]
136. curious(paul) | creative(paul) [cnf transformation 72]
142. ~tall(paul) [cnf transformation 24]
145. ~curious(X0) [duplicate literal removal 107]
150. 2 <=> quiet(paul) [avatar definition]
154. 3 <=> kind(paul) [avatar definition]
155. kind(paul) <- (3) [avatar component clause 154]
249. creative(paul) [subsumption resolution 136,145]
270. rich(paul) [resolution 87,249]
273. ~quiet(paul) [resolution 89,249]
322. quiet(paul) | kind(paul) [resolution 103,270]
340. ~2 [avatar split clause 273,150]
342. 3 | 2 [avatar split clause 322,150,154]
343. tall(paul) <- (3) [resolution 155,94]
345. $false <- (3) [subsumption resolution 343,142]
346. ~3 [avatar contradiction clause 345]
347. $false [avatar sat refutation 340,342,346]
% SZS output end Proof for 206747813116452825823342
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy or not old then paul is not wise and vice versa. Everyone who is funny or tall is both not kind and old and vice versa. Everyone who is both brave and rich is not rich or not patient and vice versa. If john is either not generous or quiet then someone is not patient or rich and vice versa. If susan is kind or not tall then susan is either not happy or rich. If someone is either not rich or patient then john is not wise or not old and vice versa. Everyone who is either happy or not humble is quiet or brave. Everyone who is both curious and quiet is both not old and not tall and vice versa. If someone is happy or strong then mary is not generous. Everyone who is not generous is not patient or not humble and vice versa. Everyone who is both not patient and not happy is old or not rich. Everyone who is not creative is not old or not brave. If susan is not creative or curious then paul is both curious and rich and vice versa. Everyone who is wise is either quiet or old. Everyone who is not brave is not brave or brave and vice versa. If alice is both not generous and quiet then susan is either curious or patient and vice versa. Fred is not wise. Someone is either not rich or funny. Alice is both not brave and strong. John is funny. Alice is both not humble and not old. Susan is patient. Someone is both not kind and rich. | Alice is not quiet. | contradiction | ((?[X]:((~happy(X)|~old(X))))<=>(~wise(paul)))&
(![X]:((funny(X)|tall(X))<=>(~kind(X)&old(X))))&
(![X]:((brave(X)&rich(X))<=>(~rich(X)|~patient(X))))&
(((~generous(john)<~>quiet(john)))<=>(?[X]:((~patient(X)|rich(X)))))&
(((kind(susan)|~tall(susan)))=>((~happy(susan)<~>rich(susan))))&
((?[X]:((~rich(X)<~>patient(X))))<=>((~wise(john)|~old(john))))&
(![X]:((happy(X)<~>~humble(X))=>(quiet(X)|brave(X))))&
(![X]:((curious(X)&quiet(X))<=>(~old(X)&~tall(X))))&
((?[X]:((happy(X)|strong(X))))=>(~generous(mary)))&
(![X]:(~generous(X)<=>(~patient(X)|~humble(X))))&
(![X]:((~patient(X)&~happy(X))=>(old(X)|~rich(X))))&
(![X]:(~creative(X)=>(~old(X)|~brave(X))))&
(((~creative(susan)|curious(susan)))<=>((curious(paul)&rich(paul))))&
(![X]:(wise(X)=>(quiet(X)<~>old(X))))&
(![X]:(~brave(X)<=>(~brave(X)|brave(X))))&
(((~generous(alice)&quiet(alice)))<=>((curious(susan)<~>patient(susan))))&
(~wise(fred))&
(?[X]:((~rich(X)<~>funny(X))))&
((~brave(alice)&strong(alice)))&
(funny(john))&
((~humble(alice)&~old(alice)))&
(patient(susan))&
(?[X]:((~kind(X)&rich(X)))) | ~quiet(alice) | [
"p1",
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3650272397338568046571033
% SZS output start Proof for 3650272397338568046571033
2. ! [X0] : ((tall(X0) | funny(X0)) <=> (old(X0) & ~kind(X0))) [input p1]
8. ! [X0] : ((quiet(X0) & curious(X0)) <=> (~tall(X0) & ~old(X0))) [input p7]
21. ~old(alice) & ~humble(alice) [input p20]
24. ~quiet(alice) [input hypothesis]
38. ! [X0] : (((tall(X0) | funny(X0)) | (~old(X0) | kind(X0))) & ((old(X0) & ~kind(X0)) | (~tall(X0) & ~funny(X0)))) [nnf transformation 2]
39. ! [X0] : ((tall(X0) | funny(X0) | ~old(X0) | kind(X0)) & ((old(X0) & ~kind(X0)) | (~tall(X0) & ~funny(X0)))) [flattening 38]
53. ! [X0] : (((quiet(X0) & curious(X0)) | (tall(X0) | old(X0))) & ((~tall(X0) & ~old(X0)) | (~quiet(X0) | ~curious(X0)))) [nnf transformation 8]
54. ! [X0] : (((quiet(X0) & curious(X0)) | tall(X0) | old(X0)) & ((~tall(X0) & ~old(X0)) | ~quiet(X0) | ~curious(X0))) [flattening 53]
75. ~tall(X0) | old(X0) [cnf transformation 39]
103. quiet(X0) | tall(X0) | old(X0) [cnf transformation 54]
134. ~old(alice) [cnf transformation 21]
138. ~quiet(alice) [cnf transformation 24]
219. quiet(X0) | old(X0) [subsumption resolution 103,75]
255. 23 <=> quiet(alice) [avatar definition]
256. ~quiet(alice) <- (~23) [avatar component clause 255]
270. ~23 [avatar split clause 138,255]
280. old(alice) <- (~23) [resolution 219,256]
281. $false <- (~23) [subsumption resolution 280,134]
282. 23 [avatar contradiction clause 281]
283. $false [avatar sat refutation 270,282]
% SZS output end Proof for 3650272397338568046571033
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not funny or rich then lucy is not brave or not kind.
Everyone who is old is strong or not old and vice versa.
Everyone who is either kind or not happy is not strong or patient and vice versa.
If fred is either happy or not kind then someone is both not quiet and not creative and vice versa.
If someone is both humble and funny then fred is not kind or not rich.
Everyone who is not calm or happy is not curious and vice versa.
Everyone who is either not tall or not generous is both not quiet and brave.
Everyone who is not funny is kind or strong and vice versa.
Everyone who is either creative or not curious is both wise and not calm.
Everyone who is both not happy and tall is old or not rich.
Everyone who is tall or not generous is generous and vice versa.
If someone is both not rich and not curious then someone is not tall.
Everyone who is rich or not curious is not strong or not tall and vice versa.
Everyone who is either not funny or kind is calm and vice versa.
Everyone who is either not happy or humble is happy.
If someone is both wise and not curious then someone is tall.
Lucy is either not brave or not tall.
Mary is wise or not quiet.
Someone is not kind or not funny.
Paul is wise or not creative. | Paul is not patient. | contradiction | ((?[X]:((~funny(X)<~>rich(X))))=>((~brave(lucy)|~kind(lucy))))&
(![X]:(old(X)<=>(strong(X)|~old(X))))&
(![X]:((kind(X)<~>~happy(X))<=>(~strong(X)|patient(X))))&
(((happy(fred)<~>~kind(fred)))<=>(?[X]:((~quiet(X)&~creative(X)))))&
((?[X]:((humble(X)&funny(X))))=>((~kind(fred)|~rich(fred))))&
(![X]:((~calm(X)|happy(X))<=>~curious(X)))&
(![X]:((~tall(X)<~>~generous(X))=>(~quiet(X)&brave(X))))&
(![X]:(~funny(X)<=>(kind(X)|strong(X))))&
(![X]:((creative(X)<~>~curious(X))=>(wise(X)&~calm(X))))&
(![X]:((~happy(X)&tall(X))=>(old(X)|~rich(X))))&
(![X]:((tall(X)|~generous(X))<=>generous(X)))&
((?[X]:((~rich(X)&~curious(X))))=>(?[X]:(~tall(X))))&
(![X]:((rich(X)|~curious(X))<=>(~strong(X)|~tall(X))))&
(![X]:((~funny(X)<~>kind(X))<=>calm(X)))&
(![X]:((~happy(X)<~>humble(X))=>happy(X)))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:(tall(X))))&
((~brave(lucy)<~>~tall(lucy)))&
((wise(mary)|~quiet(mary)))&
(?[X]:((~kind(X)|~funny(X))))&
((wise(paul)|~creative(paul))) | ~patient(paul) | [
"p1",
"p2",
"p5",
"p7",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4148560313169667975152363
% SZS output start Proof for 4148560313169667975152363
2. ! [X0] : (old(X0) <=> (~old(X0) | strong(X0))) [input p1]
3. ! [X0] : ((kind(X0) <~> ~happy(X0)) <=> (patient(X0) | ~strong(X0))) [input p2]
6. ! [X0] : ((happy(X0) | ~calm(X0)) <=> ~curious(X0)) [input p5]
8. ! [X0] : (~funny(X0) <=> (strong(X0) | kind(X0))) [input p7]
11. ! [X0] : ((~generous(X0) | tall(X0)) <=> generous(X0)) [input p10]
13. ! [X0] : ((~curious(X0) | rich(X0)) <=> (~tall(X0) | ~strong(X0))) [input p12]
14. ! [X0] : ((~funny(X0) <~> kind(X0)) <=> calm(X0)) [input p13]
21. ~patient(paul) [input hypothesis]
36. ! [X0] : ((old(X0) | (old(X0) & ~strong(X0))) & ((~old(X0) | strong(X0)) | ~old(X0))) [nnf transformation 2]
37. ! [X0] : ((old(X0) | (old(X0) & ~strong(X0))) & (~old(X0) | strong(X0) | ~old(X0))) [flattening 36]
38. ! [X0] : ((((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | (~patient(X0) & strong(X0))) & ((patient(X0) | ~strong(X0)) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))))) [nnf transformation 3]
39. ! [X0] : ((((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | (~patient(X0) & strong(X0))) & (patient(X0) | ~strong(X0) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))))) [flattening 38]
44. ! [X0] : (((happy(X0) | ~calm(X0)) | curious(X0)) & (~curious(X0) | (~happy(X0) & calm(X0)))) [nnf transformation 6]
45. ! [X0] : ((happy(X0) | ~calm(X0) | curious(X0)) & (~curious(X0) | (~happy(X0) & calm(X0)))) [flattening 44]
47. ! [X0] : ((~funny(X0) | (~strong(X0) & ~kind(X0))) & ((strong(X0) | kind(X0)) | funny(X0))) [nnf transformation 8]
48. ! [X0] : ((~funny(X0) | (~strong(X0) & ~kind(X0))) & (strong(X0) | kind(X0) | funny(X0))) [flattening 47]
50. ! [X0] : (((~generous(X0) | tall(X0)) | ~generous(X0)) & (generous(X0) | (generous(X0) & ~tall(X0)))) [nnf transformation 11]
51. ! [X0] : ((~generous(X0) | tall(X0) | ~generous(X0)) & (generous(X0) | (generous(X0) & ~tall(X0)))) [flattening 50]
55. ! [X0] : (((~curious(X0) | rich(X0)) | (tall(X0) & strong(X0))) & ((~tall(X0) | ~strong(X0)) | (curious(X0) & ~rich(X0)))) [nnf transformation 13]
56. ! [X0] : ((~curious(X0) | rich(X0) | (tall(X0) & strong(X0))) & (~tall(X0) | ~strong(X0) | (curious(X0) & ~rich(X0)))) [flattening 55]
57. ! [X0] : ((((~kind(X0) | funny(X0)) & (kind(X0) | ~funny(X0))) | ~calm(X0)) & (calm(X0) | ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0))))) [nnf transformation 14]
67. ~old(X0) | strong(X0) | ~old(X0) [cnf transformation 37]
69. old(X0) | old(X0) [cnf transformation 37]
71. patient(X0) | ~strong(X0) | kind(X0) | happy(X0) [cnf transformation 39]
83. ~curious(X0) | calm(X0) [cnf transformation 45]
84. ~curious(X0) | ~happy(X0) [cnf transformation 45]
92. ~funny(X0) | ~strong(X0) [cnf transformation 48]
99. generous(X0) | generous(X0) [cnf transformation 51]
100. ~generous(X0) | tall(X0) | ~generous(X0) [cnf transformation 51]
103. ~tall(X0) | ~strong(X0) | curious(X0) [cnf transformation 56]
109. ~kind(X0) | funny(X0) | ~calm(X0) [cnf transformation 57]
118. ~patient(paul) [cnf transformation 21]
120. generous(X0) [duplicate literal removal 99]
121. ~generous(X0) | tall(X0) [duplicate literal removal 100]
122. ~old(X0) | strong(X0) [duplicate literal removal 67]
123. old(X0) [duplicate literal removal 69]
140. strong(X0) [subsumption resolution 122,123]
141. patient(X0) | kind(X0) | happy(X0) [subsumption resolution 71,140]
176. ~funny(X0) [subsumption resolution 92,140]
186. ~tall(X0) | curious(X0) [subsumption resolution 103,140]
188. ~calm(X0) | ~kind(X0) [subsumption resolution 109,176]
222. tall(X0) [resolution 121,120]
230. curious(X0) [resolution 186,222]
232. ~happy(X1) [resolution 230,84]
233. calm(X2) [resolution 230,83]
236. ~kind(X0) [resolution 233,188]
253. kind(paul) | happy(paul) [resolution 141,118]
258. happy(paul) [subsumption resolution 253,236]
259. $false [subsumption resolution 258,232]
% SZS output end Proof for 4148560313169667975152363
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both creative and not humble then fred is funny. Everyone who is curious or not happy is either humble or not creative and vice versa. Everyone who is not funny or not humble is both not calm and rich. Everyone who is not rich is not curious. If someone is not strong then alice is not calm or not happy and vice versa. If someone is both patient and not generous then someone is not tall and vice versa. Everyone who is either quiet or not happy is brave. If someone is strong or tall then someone is either kind or funny and vice versa. If alice is either quiet or not old then someone is both not strong and not kind and vice versa. Everyone who is tall or brave is either not brave or not funny. If john is not tall or quiet then john is both rich and not strong and vice versa. Everyone who is either generous or wise is not rich and vice versa. If someone is not patient then someone is both old and not calm. Everyone who is both not quiet and not brave is both rich and not funny and vice versa. Everyone who is either tall or creative is not patient. Everyone who is brave is calm or strong. Someone is brave or not brave. Susan is both tall and not old. Alice is not kind or not strong. Fred is either generous or humble. Someone is both not tall and patient. Alice is both not kind and old. Fred is kind or rich. | Susan is quiet. | entailment | (((creative(lucy)&~humble(lucy)))=>(funny(fred)))&
(![X]:((curious(X)|~happy(X))<=>(humble(X)<~>~creative(X))))&
(![X]:((~funny(X)|~humble(X))=>(~calm(X)&rich(X))))&
(![X]:(~rich(X)=>~curious(X)))&
((?[X]:(~strong(X)))<=>((~calm(alice)|~happy(alice))))&
((?[X]:((patient(X)&~generous(X))))<=>(?[X]:(~tall(X))))&
(![X]:((quiet(X)<~>~happy(X))=>brave(X)))&
((?[X]:((strong(X)|tall(X))))<=>(?[X]:((kind(X)<~>funny(X)))))&
(((quiet(alice)<~>~old(alice)))<=>(?[X]:((~strong(X)&~kind(X)))))&
(![X]:((tall(X)|brave(X))=>(~brave(X)<~>~funny(X))))&
(((~tall(john)|quiet(john)))<=>((rich(john)&~strong(john))))&
(![X]:((generous(X)<~>wise(X))<=>~rich(X)))&
((?[X]:(~patient(X)))=>(?[X]:((old(X)&~calm(X)))))&
(![X]:((~quiet(X)&~brave(X))<=>(rich(X)&~funny(X))))&
(![X]:((tall(X)<~>creative(X))=>~patient(X)))&
(![X]:(brave(X)=>(calm(X)|strong(X))))&
(?[X]:((brave(X)|~brave(X))))&
((tall(susan)&~old(susan)))&
((~kind(alice)|~strong(alice)))&
((generous(fred)<~>humble(fred)))&
(?[X]:((~tall(X)&patient(X))))&
((~kind(alice)&old(alice)))&
((kind(fred)|rich(fred))) | quiet(susan) | [
"p2",
"p9",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 9091280211305089382687729
% SZS output start Proof for 9091280211305089382687729
3. ! [X0] : ((~humble(X0) | ~funny(X0)) => (rich(X0) & ~calm(X0))) [input p2]
10. ! [X0] : ((brave(X0) | tall(X0)) => (~brave(X0) <~> ~funny(X0))) [input p9]
14. ! [X0] : ((~brave(X0) & ~quiet(X0)) <=> (~funny(X0) & rich(X0))) [input p13]
18. ~old(susan) & tall(susan) [input p17]
24. ~quiet(susan) [input hypothesis]
30. ! [X0] : ((rich(X0) & ~calm(X0)) | (humble(X0) & funny(X0))) [ennf transformation 3]
33. ! [X0] : ((~brave(X0) <~> ~funny(X0)) | (~brave(X0) & ~tall(X0))) [ennf transformation 10]
60. ! [X0] : (((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | (~brave(X0) & ~tall(X0))) [nnf transformation 33]
67. ! [X0] : (((~brave(X0) & ~quiet(X0)) | (funny(X0) | ~rich(X0))) & ((~funny(X0) & rich(X0)) | (brave(X0) | quiet(X0)))) [nnf transformation 14]
68. ! [X0] : (((~brave(X0) & ~quiet(X0)) | funny(X0) | ~rich(X0)) & ((~funny(X0) & rich(X0)) | brave(X0) | quiet(X0))) [flattening 67]
84. rich(X0) | funny(X0) [cnf transformation 30]
108. ~funny(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 60]
109. ~tall(X0) | brave(X0) | funny(X0) [cnf transformation 60]
123. ~funny(X0) | brave(X0) | quiet(X0) [cnf transformation 68]
125. ~brave(X0) | funny(X0) | ~rich(X0) [cnf transformation 68]
130. tall(susan) [cnf transformation 18]
140. ~quiet(susan) [cnf transformation 24]
141. ~brave(X0) | ~funny(X0) [duplicate literal removal 108]
287. ~brave(X0) | ~rich(X0) [subsumption resolution 125,141]
289. ~funny(X0) | quiet(X0) [subsumption resolution 123,141]
329. brave(susan) | funny(susan) [resolution 109,130]
331. 39 <=> funny(susan) [avatar definition]
332. ~funny(susan) <- (~39) [avatar component clause 331]
333. funny(susan) <- (39) [avatar component clause 331]
335. 40 <=> brave(susan) [avatar definition]
337. brave(susan) <- (40) [avatar component clause 335]
338. 39 | 40 [avatar split clause 329,335,331]
361. quiet(susan) <- (39) [resolution 333,289]
362. $false <- (39) [subsumption resolution 361,140]
363. ~39 [avatar contradiction clause 362]
366. ~rich(susan) <- (40) [resolution 337,287]
375. funny(susan) <- (40) [resolution 366,84]
376. $false <- (~39, 40) [subsumption resolution 375,332]
377. 39 | ~40 [avatar contradiction clause 376]
378. $false [avatar sat refutation 338,363,377]
% SZS output end Proof for 9091280211305089382687729
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or happy is either not old or kind and vice versa. If someone is either curious or quiet then someone is quiet or generous and vice versa. Everyone who is either not kind or not calm is patient and vice versa. If alice is not happy or brave then someone is creative. If someone is both generous and quiet then someone is either not kind or calm and vice versa. Everyone who is not brave or old is both not funny and quiet. Everyone who is both patient and kind is generous and vice versa. Everyone who is either curious or patient is curious or not quiet and vice versa. Everyone who is wise is either calm or funny and vice versa. If someone is either brave or not old then lucy is strong. If john is both not strong and not curious then someone is both not generous and not tall. Everyone who is both quiet and curious is wise or happy and vice versa. If alice is either brave or not humble then someone is brave or not strong and vice versa. Lucy is either tall or not creative. Susan is patient or not tall. Someone is brave. Someone is not happy or not curious. Alice is either funny or wise. Someone is either not quiet or not funny. | John is happy. | contradiction | (![X]:((humble(X)|happy(X))<=>(~old(X)<~>kind(X))))&
((?[X]:((curious(X)<~>quiet(X))))<=>(?[X]:((quiet(X)|generous(X)))))&
(![X]:((~kind(X)<~>~calm(X))<=>patient(X)))&
(((~happy(alice)|brave(alice)))=>(?[X]:(creative(X))))&
((?[X]:((generous(X)&quiet(X))))<=>(?[X]:((~kind(X)<~>calm(X)))))&
(![X]:((~brave(X)|old(X))=>(~funny(X)&quiet(X))))&
(![X]:((patient(X)&kind(X))<=>generous(X)))&
(![X]:((curious(X)<~>patient(X))<=>(curious(X)|~quiet(X))))&
(![X]:(wise(X)<=>(calm(X)<~>funny(X))))&
((?[X]:((brave(X)<~>~old(X))))=>(strong(lucy)))&
(((~strong(john)&~curious(john)))=>(?[X]:((~generous(X)&~tall(X)))))&
(![X]:((quiet(X)&curious(X))<=>(wise(X)|happy(X))))&
(((brave(alice)<~>~humble(alice)))<=>(?[X]:((brave(X)|~strong(X)))))&
((tall(lucy)<~>~creative(lucy)))&
((patient(susan)|~tall(susan)))&
(?[X]:(brave(X)))&
(?[X]:((~happy(X)|~curious(X))))&
((funny(alice)<~>wise(alice)))&
(?[X]:((~quiet(X)<~>~funny(X)))) | happy(john) | [
"p2",
"p4",
"p6",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 9135554012578861938301411
% SZS output start Proof for 9135554012578861938301411
3. ! [X0] : ((~kind(X0) <~> ~calm(X0)) <=> patient(X0)) [input p2]
5. ? [X0] : (quiet(X0) & generous(X0)) <=> ? [X0] : (~kind(X0) <~> calm(X0)) [input p4]
7. ! [X0] : ((kind(X0) & patient(X0)) <=> generous(X0)) [input p6]
8. ! [X0] : ((curious(X0) <~> patient(X0)) <=> (~quiet(X0) | curious(X0))) [input p7]
12. ! [X0] : ((curious(X0) & quiet(X0)) <=> (happy(X0) | wise(X0))) [input p11]
20. happy(john) [input hypothesis]
22. ? [X0] : (quiet(X0) & generous(X0)) <=> ? [X1] : (~kind(X1) <~> calm(X1)) [rectify 5]
35. ! [X0] : ((((calm(X0) | kind(X0)) & (~calm(X0) | ~kind(X0))) | ~patient(X0)) & (patient(X0) | ((~kind(X0) | calm(X0)) & (~calm(X0) | kind(X0))))) [nnf transformation 3]
38. (? [X0] : (quiet(X0) & generous(X0)) | ! [X1] : ((~kind(X1) | ~calm(X1)) & (calm(X1) | kind(X1)))) & (? [X1] : ((~calm(X1) | kind(X1)) & (calm(X1) | ~kind(X1))) | ! [X0] : (~quiet(X0) | ~generous(X0))) [nnf transformation 22]
39. (? [X0] : (quiet(X0) & generous(X0)) | ! [X1] : ((~kind(X1) | ~calm(X1)) & (calm(X1) | kind(X1)))) & (? [X2] : ((~calm(X2) | kind(X2)) & (calm(X2) | ~kind(X2))) | ! [X3] : (~quiet(X3) | ~generous(X3))) [rectify 38]
40. ? [X0] : (quiet(X0) & generous(X0)) => (quiet(sK3) & generous(sK3)) [choice axiom]
41. ? [X2] : ((~calm(X2) | kind(X2)) & (calm(X2) | ~kind(X2))) => ((~calm(sK4) | kind(sK4)) & (calm(sK4) | ~kind(sK4))) [choice axiom]
42. ((quiet(sK3) & generous(sK3)) | ! [X1] : ((~kind(X1) | ~calm(X1)) & (calm(X1) | kind(X1)))) & (((~calm(sK4) | kind(sK4)) & (calm(sK4) | ~kind(sK4))) | ! [X3] : (~quiet(X3) | ~generous(X3))) [skolemisation 39,41,40]
43. ! [X0] : (((kind(X0) & patient(X0)) | ~generous(X0)) & (generous(X0) | (~kind(X0) | ~patient(X0)))) [nnf transformation 7]
44. ! [X0] : (((kind(X0) & patient(X0)) | ~generous(X0)) & (generous(X0) | ~kind(X0) | ~patient(X0))) [flattening 43]
45. ! [X0] : ((((~patient(X0) | ~curious(X0)) & (patient(X0) | curious(X0))) | (quiet(X0) & ~curious(X0))) & ((~quiet(X0) | curious(X0)) | ((curious(X0) | ~patient(X0)) & (patient(X0) | ~curious(X0))))) [nnf transformation 8]
46. ! [X0] : ((((~patient(X0) | ~curious(X0)) & (patient(X0) | curious(X0))) | (quiet(X0) & ~curious(X0))) & (~quiet(X0) | curious(X0) | ((curious(X0) | ~patient(X0)) & (patient(X0) | ~curious(X0))))) [flattening 45]
51. ! [X0] : (((curious(X0) & quiet(X0)) | (~happy(X0) & ~wise(X0))) & ((happy(X0) | wise(X0)) | (~curious(X0) | ~quiet(X0)))) [nnf transformation 12]
52. ! [X0] : (((curious(X0) & quiet(X0)) | (~happy(X0) & ~wise(X0))) & (happy(X0) | wise(X0) | ~curious(X0) | ~quiet(X0))) [flattening 51]
78. ~calm(X0) | patient(X0) | kind(X0) [cnf transformation 35]
79. ~kind(X0) | patient(X0) | calm(X0) [cnf transformation 35]
86. generous(sK3) | calm(X1) | kind(X1) [cnf transformation 42]
87. generous(sK3) | ~kind(X1) | ~calm(X1) [cnf transformation 42]
88. quiet(sK3) | calm(X1) | kind(X1) [cnf transformation 42]
89. quiet(sK3) | ~kind(X1) | ~calm(X1) [cnf transformation 42]
95. ~generous(X0) | patient(X0) [cnf transformation 44]
98. ~quiet(X0) | curious(X0) | curious(X0) | ~patient(X0) [cnf transformation 46]
101. ~patient(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 46]
113. ~happy(X0) | quiet(X0) [cnf transformation 52]
131. happy(john) [cnf transformation 20]
132. ~quiet(X0) | curious(X0) | ~patient(X0) [duplicate literal removal 98]
133. ~patient(X0) | ~curious(X0) [duplicate literal removal 101]
183. 12 <=> ! [X1] : (~kind(X1) | ~calm(X1)) [avatar definition]
184. ~calm(X1) | ~kind(X1) <- (12) [avatar component clause 183]
186. 13 <=> quiet(sK3) [avatar definition]
188. quiet(sK3) <- (13) [avatar component clause 186]
189. 12 | 13 [avatar split clause 89,186,183]
191. 14 <=> ! [X1] : (calm(X1) | kind(X1)) [avatar definition]
192. calm(X1) | kind(X1) <- (14) [avatar component clause 191]
193. 14 | 13 [avatar split clause 88,186,191]
195. 15 <=> generous(sK3) [avatar definition]
197. generous(sK3) <- (15) [avatar component clause 195]
198. 12 | 15 [avatar split clause 87,195,183]
199. 14 | 15 [avatar split clause 86,195,191]
213. ~patient(X0) | ~quiet(X0) [subsumption resolution 132,133]
313. quiet(john) [resolution 113,131]
321. patient(sK3) <- (15) [resolution 197,95]
322. ~quiet(sK3) <- (15) [resolution 321,213]
324. $false <- (13, 15) [subsumption resolution 322,188]
325. ~13 | ~15 [avatar contradiction clause 324]
344. patient(X0) | kind(X0) | kind(X0) <- (14) [resolution 78,192]
345. patient(X0) | kind(X0) <- (14) [duplicate literal removal 344]
346. ~quiet(X0) | kind(X0) <- (14) [resolution 345,213]
368. kind(john) <- (14) [resolution 346,313]
376. patient(john) | calm(john) <- (14) [resolution 368,79]
380. 42 <=> calm(john) [avatar definition]
382. calm(john) <- (42) [avatar component clause 380]
384. 43 <=> patient(john) [avatar definition]
386. patient(john) <- (43) [avatar component clause 384]
387. 42 | 43 | ~14 [avatar split clause 376,191,384,380]
595. ~quiet(john) <- (43) [resolution 386,213]
598. $false <- (43) [subsumption resolution 595,313]
599. ~43 [avatar contradiction clause 598]
614. ~kind(john) <- (12, 42) [resolution 382,184]
624. $false <- (12, 14, 42) [subsumption resolution 614,368]
625. ~12 | ~14 | ~42 [avatar contradiction clause 624]
626. $false [avatar sat refutation 189,193,198,199,325,387,599,625]
% SZS output end Proof for 9135554012578861938301411
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not funny or not kind then someone is either creative or not kind and vice versa. Everyone who is both not happy and creative is both not creative and not happy and vice versa. If someone is either not creative or rich then alice is not wise or not kind and vice versa. If john is not humble or generous then mary is humble. Everyone who is either not patient or calm is either kind or calm and vice versa. If john is not patient then lucy is either not quiet or humble and vice versa. Everyone who is both wise and not quiet is creative and vice versa. Everyone who is not patient or wise is both not patient and quiet. If someone is both not old and humble then mary is either humble or rich. Everyone who is funny is either not creative or not kind and vice versa. If someone is either not calm or not curious then someone is not strong or not rich. Everyone who is not wise is not funny. If someone is not happy then susan is not patient. If alice is both not patient and not quiet then someone is either not brave or not wise and vice versa. If someone is both not generous and rich then paul is either curious or rich and vice versa. Fred is not brave or wise. Fred is either creative or calm. Lucy is not funny or not tall. Alice is strong. Someone is either humble or not quiet. Someone is not old. Someone is not old or calm. | Paul is patient. | contradiction | ((?[X]:((~funny(X)<~>~kind(X))))<=>(?[X]:((creative(X)<~>~kind(X)))))&
(![X]:((~happy(X)&creative(X))<=>(~creative(X)&~happy(X))))&
((?[X]:((~creative(X)<~>rich(X))))<=>((~wise(alice)|~kind(alice))))&
(((~humble(john)|generous(john)))=>(humble(mary)))&
(![X]:((~patient(X)<~>calm(X))<=>(kind(X)<~>calm(X))))&
((~patient(john))<=>((~quiet(lucy)<~>humble(lucy))))&
(![X]:((wise(X)&~quiet(X))<=>creative(X)))&
(![X]:((~patient(X)|wise(X))=>(~patient(X)&quiet(X))))&
((?[X]:((~old(X)&humble(X))))=>((humble(mary)<~>rich(mary))))&
(![X]:(funny(X)<=>(~creative(X)<~>~kind(X))))&
((?[X]:((~calm(X)<~>~curious(X))))=>(?[X]:((~strong(X)|~rich(X)))))&
(![X]:(~wise(X)=>~funny(X)))&
((?[X]:(~happy(X)))=>(~patient(susan)))&
(((~patient(alice)&~quiet(alice)))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
((?[X]:((~generous(X)&rich(X))))<=>((curious(paul)<~>rich(paul))))&
((~brave(fred)|wise(fred)))&
((creative(fred)<~>calm(fred)))&
((~funny(lucy)|~tall(lucy)))&
(strong(alice))&
(?[X]:((humble(X)<~>~quiet(X))))&
(?[X]:(~old(X)))&
(?[X]:((~old(X)|calm(X)))) | patient(paul) | [
"p0",
"p4",
"p6",
"p7",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7693291403458910151710989
% SZS output start Proof for 7693291403458910151710989
1. ? [X0] : (~funny(X0) <~> ~kind(X0)) <=> ? [X0] : (creative(X0) <~> ~kind(X0)) [input p0]
5. ! [X0] : ((~patient(X0) <~> calm(X0)) <=> (kind(X0) <~> calm(X0))) [input p4]
7. ! [X0] : ((~quiet(X0) & wise(X0)) <=> creative(X0)) [input p6]
8. ! [X0] : ((wise(X0) | ~patient(X0)) => (quiet(X0) & ~patient(X0))) [input p7]
10. ! [X0] : (funny(X0) <=> (~creative(X0) <~> ~kind(X0))) [input p9]
12. ! [X0] : (~wise(X0) => ~funny(X0)) [input p11]
23. patient(paul) [input hypothesis]
24. ? [X0] : (~funny(X0) <~> ~kind(X0)) <=> ? [X1] : (creative(X1) <~> ~kind(X1)) [rectify 1]
28. ! [X0] : ((quiet(X0) & ~patient(X0)) | (~wise(X0) & patient(X0))) [ennf transformation 8]
31. ! [X0] : (~funny(X0) | wise(X0)) [ennf transformation 12]
33. (? [X0] : ((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | ! [X1] : ((creative(X1) | kind(X1)) & (~kind(X1) | ~creative(X1)))) & (? [X1] : ((kind(X1) | ~creative(X1)) & (~kind(X1) | creative(X1))) | ! [X0] : ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0)))) [nnf transformation 24]
34. (? [X0] : ((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) | ! [X1] : ((creative(X1) | kind(X1)) & (~kind(X1) | ~creative(X1)))) & (? [X2] : ((kind(X2) | ~creative(X2)) & (~kind(X2) | creative(X2))) | ! [X3] : ((~funny(X3) | kind(X3)) & (~kind(X3) | funny(X3)))) [rectify 33]
35. ? [X0] : ((kind(X0) | funny(X0)) & (~kind(X0) | ~funny(X0))) => ((kind(sK0) | funny(sK0)) & (~kind(sK0) | ~funny(sK0))) [choice axiom]
36. ? [X2] : ((kind(X2) | ~creative(X2)) & (~kind(X2) | creative(X2))) => ((kind(sK1) | ~creative(sK1)) & (~kind(sK1) | creative(sK1))) [choice axiom]
37. (((kind(sK0) | funny(sK0)) & (~kind(sK0) | ~funny(sK0))) | ! [X1] : ((creative(X1) | kind(X1)) & (~kind(X1) | ~creative(X1)))) & (((kind(sK1) | ~creative(sK1)) & (~kind(sK1) | creative(sK1))) | ! [X3] : ((~funny(X3) | kind(X3)) & (~kind(X3) | funny(X3)))) [skolemisation 34,36,35]
45. ! [X0] : ((((~calm(X0) | patient(X0)) & (calm(X0) | ~patient(X0))) | ((kind(X0) | ~calm(X0)) & (calm(X0) | ~kind(X0)))) & (((~calm(X0) | ~kind(X0)) & (calm(X0) | kind(X0))) | ((~patient(X0) | ~calm(X0)) & (calm(X0) | patient(X0))))) [nnf transformation 5]
47. ! [X0] : (((~quiet(X0) & wise(X0)) | ~creative(X0)) & (creative(X0) | (quiet(X0) | ~wise(X0)))) [nnf transformation 7]
48. ! [X0] : (((~quiet(X0) & wise(X0)) | ~creative(X0)) & (creative(X0) | quiet(X0) | ~wise(X0))) [flattening 47]
50. ! [X0] : ((funny(X0) | ((~creative(X0) | kind(X0)) & (~kind(X0) | creative(X0)))) & (((kind(X0) | creative(X0)) & (~kind(X0) | ~creative(X0))) | ~funny(X0))) [nnf transformation 10]
77. ~kind(sK0) | ~funny(sK0) | creative(X1) | kind(X1) [cnf transformation 37]
79. kind(sK0) | funny(sK0) | creative(X1) | kind(X1) [cnf transformation 37]
92. calm(X0) | kind(X0) | calm(X0) | patient(X0) [cnf transformation 45]
95. ~calm(X0) | ~kind(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 45]
96. calm(X0) | ~patient(X0) | calm(X0) | ~kind(X0) [cnf transformation 45]
99. ~calm(X0) | patient(X0) | kind(X0) | ~calm(X0) [cnf transformation 45]
105. ~creative(X0) | wise(X0) [cnf transformation 48]
106. ~quiet(X0) | ~creative(X0) [cnf transformation 48]
108. ~patient(X0) | ~wise(X0) [cnf transformation 28]
109. quiet(X0) | patient(X0) [cnf transformation 28]
115. ~kind(X0) | funny(X0) | creative(X0) [cnf transformation 50]
119. ~funny(X0) | wise(X0) [cnf transformation 31]
141. patient(paul) [cnf transformation 23]
142. calm(X0) | kind(X0) | patient(X0) [duplicate literal removal 92]
143. ~calm(X0) | ~kind(X0) | ~patient(X0) [duplicate literal removal 95]
144. ~patient(X0) | calm(X0) | ~kind(X0) [duplicate literal removal 96]
145. ~calm(X0) | patient(X0) | kind(X0) [duplicate literal removal 99]
149. 1 <=> ! [X1] : (creative(X1) | kind(X1)) [avatar definition]
150. creative(X1) | kind(X1) <- (1) [avatar component clause 149]
152. 2 <=> funny(sK0) [avatar definition]
153. ~funny(sK0) <- (~2) [avatar component clause 152]
154. funny(sK0) <- (2) [avatar component clause 152]
156. 3 <=> kind(sK0) [avatar definition]
157. ~kind(sK0) <- (~3) [avatar component clause 156]
158. kind(sK0) <- (3) [avatar component clause 156]
159. 1 | 2 | 3 [avatar split clause 79,156,152,149]
164. 1 | ~2 | ~3 [avatar split clause 77,156,152,149]
227. ~patient(X0) | ~kind(X0) [subsumption resolution 143,144]
228. patient(X0) | kind(X0) [subsumption resolution 142,145]
354. ~creative(X0) | patient(X0) [resolution 109,106]
362. wise(sK0) <- (2) [resolution 119,154]
365. ~kind(paul) [resolution 227,141]
371. ~wise(X1) | kind(X1) [resolution 228,108]
387. 44 <=> creative(sK0) [avatar definition]
389. creative(sK0) <- (44) [avatar component clause 387]
463. kind(sK0) <- (2) [resolution 371,362]
465. $false <- (2, ~3) [subsumption resolution 463,157]
466. ~2 | 3 [avatar contradiction clause 465]
470. kind(X3) | wise(X3) <- (1) [resolution 150,105]
479. kind(X3) <- (1) [subsumption resolution 470,371]
481. $false <- (1) [resolution 479,365]
486. ~1 [avatar contradiction clause 481]
487. funny(sK0) | creative(sK0) <- (3) [resolution 158,115]
500. creative(sK0) <- (~2, 3) [subsumption resolution 487,153]
501. 44 | 2 | ~3 [avatar split clause 500,156,152,387]
502. patient(sK0) <- (44) [resolution 389,354]
505. wise(sK0) <- (44) [resolution 389,105]
542. ~wise(sK0) <- (44) [resolution 502,108]
546. $false <- (44) [subsumption resolution 542,505]
547. ~44 [avatar contradiction clause 546]
548. $false [avatar sat refutation 159,164,466,486,501,547]
% SZS output end Proof for 7693291403458910151710989
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not old is either brave or not happy and vice versa.
Everyone who is either quiet or tall is not happy or not humble and vice versa.
Everyone who is not generous or not kind is both generous and creative and vice versa.
Everyone who is both old and not strong is both humble and old and vice versa.
Everyone who is not kind is either not rich or humble.
Everyone who is not patient is funny.
Everyone who is funny is either old or not happy and vice versa.
If john is funny then fred is either wise or creative.
Everyone who is either quiet or happy is both not old and not tall and vice versa.
If lucy is either patient or not calm then alice is both wise and not tall and vice versa.
If paul is both not calm and tall then someone is both curious and kind.
If someone is both not curious and kind then susan is both not wise and not curious.
Everyone who is both rich and not calm is either not brave or not rich and vice versa.
Everyone who is both not happy and not rich is both generous and not old.
If someone is not calm then someone is both not wise and not quiet and vice versa.
Everyone who is not happy or not brave is not quiet.
Lucy is either quiet or not generous.
Someone is both curious and not old.
Paul is calm.
Someone is not kind or tall.
Mary is not curious or not old.
Susan is not kind or not old.
Someone is either rich or not brave.
Someone is happy or not creative. | Lucy is not humble. | contradiction | (![X]:((~happy(X)<~>~old(X))<=>(brave(X)<~>~happy(X))))&
(![X]:((quiet(X)<~>tall(X))<=>(~happy(X)|~humble(X))))&
(![X]:((~generous(X)|~kind(X))<=>(generous(X)&creative(X))))&
(![X]:((old(X)&~strong(X))<=>(humble(X)&old(X))))&
(![X]:(~kind(X)=>(~rich(X)<~>humble(X))))&
(![X]:(~patient(X)=>funny(X)))&
(![X]:(funny(X)<=>(old(X)<~>~happy(X))))&
((funny(john))=>((wise(fred)<~>creative(fred))))&
(![X]:((quiet(X)<~>happy(X))<=>(~old(X)&~tall(X))))&
(((patient(lucy)<~>~calm(lucy)))<=>((wise(alice)&~tall(alice))))&
(((~calm(paul)&tall(paul)))=>(?[X]:((curious(X)&kind(X)))))&
((?[X]:((~curious(X)&kind(X))))=>((~wise(susan)&~curious(susan))))&
(![X]:((rich(X)&~calm(X))<=>(~brave(X)<~>~rich(X))))&
(![X]:((~happy(X)&~rich(X))=>(generous(X)&~old(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~wise(X)&~quiet(X)))))&
(![X]:((~happy(X)|~brave(X))=>~quiet(X)))&
((quiet(lucy)<~>~generous(lucy)))&
(?[X]:((curious(X)&~old(X))))&
(calm(paul))&
(?[X]:((~kind(X)|tall(X))))&
((~curious(mary)|~old(mary)))&
((~kind(susan)|~old(susan)))&
(?[X]:((rich(X)<~>~brave(X))))&
(?[X]:((happy(X)|~creative(X)))) | ~humble(lucy) | [
"p0",
"p1",
"p2",
"p8",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 30838765954586896069015
% SZS output start Proof for 30838765954586896069015
1. ! [X0] : ((~happy(X0) <~> ~old(X0)) <=> (brave(X0) <~> ~happy(X0))) [input p0]
2. ! [X0] : ((quiet(X0) <~> tall(X0)) <=> (~humble(X0) | ~happy(X0))) [input p1]
3. ! [X0] : ((~kind(X0) | ~generous(X0)) <=> (creative(X0) & generous(X0))) [input p2]
9. ! [X0] : ((quiet(X0) <~> happy(X0)) <=> (~tall(X0) & ~old(X0))) [input p8]
16. ! [X0] : ((~brave(X0) | ~happy(X0)) => ~quiet(X0)) [input p15]
17. quiet(lucy) <~> ~generous(lucy) [input p16]
25. ~humble(lucy) [input hypothesis]
35. ! [X0] : (~quiet(X0) | (brave(X0) & happy(X0))) [ennf transformation 16]
36. ! [X0] : ((((old(X0) | happy(X0)) & (~old(X0) | ~happy(X0))) | ((brave(X0) | happy(X0)) & (~happy(X0) | ~brave(X0)))) & (((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | ((~happy(X0) | old(X0)) & (~old(X0) | happy(X0))))) [nnf transformation 1]
37. ! [X0] : ((((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (humble(X0) & happy(X0))) & ((~humble(X0) | ~happy(X0)) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0))))) [nnf transformation 2]
38. ! [X0] : ((((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (humble(X0) & happy(X0))) & (~humble(X0) | ~happy(X0) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0))))) [flattening 37]
39. ! [X0] : (((~kind(X0) | ~generous(X0)) | (~creative(X0) | ~generous(X0))) & ((creative(X0) & generous(X0)) | (kind(X0) & generous(X0)))) [nnf transformation 3]
40. ! [X0] : ((~kind(X0) | ~generous(X0) | ~creative(X0) | ~generous(X0)) & ((creative(X0) & generous(X0)) | (kind(X0) & generous(X0)))) [flattening 39]
46. ! [X0] : ((((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | (tall(X0) | old(X0))) & ((~tall(X0) & ~old(X0)) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0))))) [nnf transformation 9]
47. ! [X0] : ((((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | tall(X0) | old(X0)) & ((~tall(X0) & ~old(X0)) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0))))) [flattening 46]
59. (generous(lucy) | ~quiet(lucy)) & (~generous(lucy) | quiet(lucy)) [nnf transformation 17]
71. happy(X0) | ~brave(X0) | ~old(X0) | happy(X0) [cnf transformation 36]
73. ~old(X0) | ~happy(X0) | ~happy(X0) | ~brave(X0) [cnf transformation 36]
82. ~tall(X0) | ~quiet(X0) | humble(X0) [cnf transformation 38]
83. generous(X0) | generous(X0) [cnf transformation 40]
106. ~quiet(X0) | ~happy(X0) | tall(X0) | old(X0) [cnf transformation 47]
128. ~quiet(X0) | happy(X0) [cnf transformation 35]
129. ~quiet(X0) | brave(X0) [cnf transformation 35]
130. ~generous(lucy) | quiet(lucy) [cnf transformation 59]
141. ~humble(lucy) [cnf transformation 25]
144. generous(X0) [duplicate literal removal 83]
147. happy(X0) | ~brave(X0) | ~old(X0) [duplicate literal removal 71]
148. ~brave(X0) | ~happy(X0) | ~old(X0) [duplicate literal removal 73]
150. ~brave(X0) | ~old(X0) [subsumption resolution 147,148]
241. quiet(lucy) [subsumption resolution 130,144]
292. happy(lucy) [resolution 128,241]
293. brave(lucy) [resolution 129,241]
295. ~old(lucy) [resolution 150,293]
482. ~happy(lucy) | tall(lucy) | old(lucy) [resolution 106,241]
483. tall(lucy) | old(lucy) [subsumption resolution 482,292]
484. tall(lucy) [subsumption resolution 483,295]
486. ~quiet(lucy) | humble(lucy) [resolution 484,82]
488. humble(lucy) [subsumption resolution 486,241]
489. $false [subsumption resolution 488,141]
% SZS output end Proof for 30838765954586896069015
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is not quiet then someone is brave or not curious.
Everyone who is either creative or not old is either not calm or not old and vice versa.
If someone is calm then someone is either not brave or not generous and vice versa.
If alice is old then someone is either not calm or not happy and vice versa.
Everyone who is either tall or old is not tall or kind and vice versa.
If someone is either humble or not kind then someone is not patient or not tall and vice versa.
Everyone who is not calm or not curious is both patient and wise.
If susan is either not strong or not happy then someone is either not wise or not old.
Everyone who is both not generous and creative is either not patient or humble and vice versa.
Everyone who is wise or tall is both patient and not kind and vice versa.
Everyone who is not creative or not kind is not funny or not patient.
If paul is generous then someone is both not happy and not funny and vice versa.
Everyone who is not kind is either creative or wise and vice versa.
If paul is either not funny or not wise then fred is not generous or humble and vice versa.
Everyone who is both not humble and not wise is both not humble and kind and vice versa.
Everyone who is either not strong or funny is not kind.
John is curious or not calm.
Someone is both not kind and patient.
Someone is not patient or not wise.
Fred is brave or not kind.
Someone is either quiet or happy.
Fred is not brave. | Fred is calm. | entailment | ((~quiet(john))=>(?[X]:((brave(X)|~curious(X)))))&
(![X]:((creative(X)<~>~old(X))<=>(~calm(X)<~>~old(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~brave(X)<~>~generous(X)))))&
((old(alice))<=>(?[X]:((~calm(X)<~>~happy(X)))))&
(![X]:((tall(X)<~>old(X))<=>(~tall(X)|kind(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>(?[X]:((~patient(X)|~tall(X)))))&
(![X]:((~calm(X)|~curious(X))=>(patient(X)&wise(X))))&
(((~strong(susan)<~>~happy(susan)))=>(?[X]:((~wise(X)<~>~old(X)))))&
(![X]:((~generous(X)&creative(X))<=>(~patient(X)<~>humble(X))))&
(![X]:((wise(X)|tall(X))<=>(patient(X)&~kind(X))))&
(![X]:((~creative(X)|~kind(X))=>(~funny(X)|~patient(X))))&
((generous(paul))<=>(?[X]:((~happy(X)&~funny(X)))))&
(![X]:(~kind(X)<=>(creative(X)<~>wise(X))))&
(((~funny(paul)<~>~wise(paul)))<=>((~generous(fred)|humble(fred))))&
(![X]:((~humble(X)&~wise(X))<=>(~humble(X)&kind(X))))&
(![X]:((~strong(X)<~>funny(X))=>~kind(X)))&
((curious(john)|~calm(john)))&
(?[X]:((~kind(X)&patient(X))))&
(?[X]:((~patient(X)|~wise(X))))&
((brave(fred)|~kind(fred)))&
(?[X]:((quiet(X)<~>happy(X))))&
(~brave(fred)) | calm(fred) | [
"p1",
"p6",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6764997915448416782329898
% SZS output start Proof for 6764997915448416782329898
2. ! [X0] : ((creative(X0) <~> ~old(X0)) <=> (~calm(X0) <~> ~old(X0))) [input p1]
7. ! [X0] : ((~curious(X0) | ~calm(X0)) => (wise(X0) & patient(X0))) [input p6]
10. ! [X0] : ((tall(X0) | wise(X0)) <=> (~kind(X0) & patient(X0))) [input p9]
13. ! [X0] : (~kind(X0) <=> (creative(X0) <~> wise(X0))) [input p12]
23. ~calm(fred) [input hypothesis]
27. ! [X0] : ((wise(X0) & patient(X0)) | (curious(X0) & calm(X0))) [ennf transformation 7]
34. ! [X0] : ((((old(X0) | ~creative(X0)) & (~old(X0) | creative(X0))) | ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0)))) & (((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | ((creative(X0) | old(X0)) & (~old(X0) | ~creative(X0))))) [nnf transformation 2]
56. ! [X0] : (((tall(X0) | wise(X0)) | (kind(X0) | ~patient(X0))) & ((~kind(X0) & patient(X0)) | (~tall(X0) & ~wise(X0)))) [nnf transformation 10]
57. ! [X0] : ((tall(X0) | wise(X0) | kind(X0) | ~patient(X0)) & ((~kind(X0) & patient(X0)) | (~tall(X0) & ~wise(X0)))) [flattening 56]
62. ! [X0] : ((~kind(X0) | ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0)))) & (((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | kind(X0))) [nnf transformation 13]
79. old(X0) | calm(X0) | creative(X0) | old(X0) [cnf transformation 34]
80. ~old(X0) | creative(X0) | ~old(X0) | calm(X0) [cnf transformation 34]
106. wise(X0) | calm(X0) [cnf transformation 27]
120. ~wise(X0) | ~kind(X0) [cnf transformation 57]
129. ~wise(X0) | ~creative(X0) | kind(X0) [cnf transformation 62]
130. ~kind(X0) | wise(X0) | ~creative(X0) [cnf transformation 62]
152. ~calm(fred) [cnf transformation 23]
156. old(X0) | calm(X0) | creative(X0) [duplicate literal removal 79]
157. ~old(X0) | creative(X0) | calm(X0) [duplicate literal removal 80]
172. calm(X0) | creative(X0) [subsumption resolution 156,157]
294. ~kind(X0) | ~creative(X0) [subsumption resolution 130,120]
295. ~wise(X0) | ~creative(X0) [subsumption resolution 129,294]
396. ~creative(X1) | calm(X1) [resolution 295,106]
397. calm(X1) [subsumption resolution 396,172]
400. $false [resolution 397,152]
% SZS output end Proof for 6764997915448416782329898
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is either kind or not patient then someone is not calm or not patient.
Everyone who is either not old or rich is strong.
If someone is both not strong and wise then someone is not quiet.
If someone is either not quiet or not generous then alice is either happy or not happy.
If someone is happy or not funny then someone is brave or tall and vice versa.
Everyone who is either kind or happy is both calm and humble.
If someone is quiet then someone is both not calm and not creative and vice versa.
Everyone who is both wise and not kind is old and vice versa.
Everyone who is both not funny and rich is generous and vice versa.
Everyone who is not creative or tall is creative and vice versa.
Everyone who is either funny or not brave is brave and vice versa.
Everyone who is humble or calm is either not rich or wise.
Everyone who is not old or not tall is creative and vice versa.
If john is both tall and not curious then someone is not happy.
If john is both not patient and quiet then someone is not wise or brave.
Everyone who is not generous is happy and vice versa.
Someone is both humble and not calm.
John is not calm or wise.
Someone is either not brave or not creative.
John is happy or not humble.
Someone is not generous.
Fred is kind or not happy.
Paul is both rich and not brave. | Fred is quiet. | contradiction | (((kind(alice)<~>~patient(alice)))=>(?[X]:((~calm(X)|~patient(X)))))&
(![X]:((~old(X)<~>rich(X))=>strong(X)))&
((?[X]:((~strong(X)&wise(X))))=>(?[X]:(~quiet(X))))&
((?[X]:((~quiet(X)<~>~generous(X))))=>((happy(alice)<~>~happy(alice))))&
((?[X]:((happy(X)|~funny(X))))<=>(?[X]:((brave(X)|tall(X)))))&
(![X]:((kind(X)<~>happy(X))=>(calm(X)&humble(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((~calm(X)&~creative(X)))))&
(![X]:((wise(X)&~kind(X))<=>old(X)))&
(![X]:((~funny(X)&rich(X))<=>generous(X)))&
(![X]:((~creative(X)|tall(X))<=>creative(X)))&
(![X]:((funny(X)<~>~brave(X))<=>brave(X)))&
(![X]:((humble(X)|calm(X))=>(~rich(X)<~>wise(X))))&
(![X]:((~old(X)|~tall(X))<=>creative(X)))&
(((tall(john)&~curious(john)))=>(?[X]:(~happy(X))))&
(((~patient(john)&quiet(john)))=>(?[X]:((~wise(X)|brave(X)))))&
(![X]:(~generous(X)<=>happy(X)))&
(?[X]:((humble(X)&~calm(X))))&
((~calm(john)|wise(john)))&
(?[X]:((~brave(X)<~>~creative(X))))&
((happy(john)|~humble(john)))&
(?[X]:(~generous(X)))&
((kind(fred)|~happy(fred)))&
((rich(paul)&~brave(paul))) | quiet(fred) | [
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5305650971854693511772471
% SZS output start Proof for 5305650971854693511772471
7. ? [X0] : quiet(X0) <=> ? [X0] : (~creative(X0) & ~calm(X0)) [input p6]
10. ! [X0] : ((tall(X0) | ~creative(X0)) <=> creative(X0)) [input p9]
24. quiet(fred) [input hypothesis]
27. ? [X0] : quiet(X0) <=> ? [X1] : (~creative(X1) & ~calm(X1)) [rectify 7]
47. (? [X0] : quiet(X0) | ! [X1] : (creative(X1) | calm(X1))) & (? [X1] : (~creative(X1) & ~calm(X1)) | ! [X0] : ~quiet(X0)) [nnf transformation 27]
48. (? [X0] : quiet(X0) | ! [X1] : (creative(X1) | calm(X1))) & (? [X2] : (~creative(X2) & ~calm(X2)) | ! [X3] : ~quiet(X3)) [rectify 47]
49. ? [X0] : quiet(X0) => quiet(sK3) [choice axiom]
50. ? [X2] : (~creative(X2) & ~calm(X2)) => (~creative(sK4) & ~calm(sK4)) [choice axiom]
51. (quiet(sK3) | ! [X1] : (creative(X1) | calm(X1))) & ((~creative(sK4) & ~calm(sK4)) | ! [X3] : ~quiet(X3)) [skolemisation 48,50,49]
56. ! [X0] : (((tall(X0) | ~creative(X0)) | ~creative(X0)) & (creative(X0) | (~tall(X0) & creative(X0)))) [nnf transformation 10]
57. ! [X0] : ((tall(X0) | ~creative(X0) | ~creative(X0)) & (creative(X0) | (~tall(X0) & creative(X0)))) [flattening 56]
87. ~creative(sK4) | ~quiet(X3) [cnf transformation 51]
95. creative(X0) | creative(X0) [cnf transformation 57]
122. quiet(fred) [cnf transformation 24]
125. creative(X0) [duplicate literal removal 95]
186. 15 <=> ! [X3] : ~quiet(X3) [avatar definition]
187. ~quiet(X3) <- (15) [avatar component clause 186]
189. 16 <=> creative(sK4) [avatar definition]
191. ~creative(sK4) <- (~16) [avatar component clause 189]
192. 15 | ~16 [avatar split clause 87,189,186]
246. $false <- (~16) [subsumption resolution 191,125]
247. 16 [avatar contradiction clause 246]
250. $false <- (15) [resolution 187,122]
251. ~15 [avatar contradiction clause 250]
252. $false [avatar sat refutation 192,247,251]
% SZS output end Proof for 5305650971854693511772471
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or curious is strong.
Everyone who is not brave or humble is not generous or curious and vice versa.
Everyone who is both not strong and rich is both not curious and not strong and vice versa.
Everyone who is happy or funny is either not strong or patient.
Everyone who is strong or patient is not wise and vice versa.
Everyone who is not patient or not kind is both funny and not happy and vice versa.
Everyone who is either not old or not rich is both not creative and old and vice versa.
Everyone who is both not happy and quiet is not wise.
If paul is quiet then susan is both rich and humble.
Everyone who is either not curious or not quiet is happy.
Everyone who is generous is creative or not happy and vice versa.
If mary is both creative and not quiet then someone is either not generous or not humble.
If lucy is quiet or brave then someone is both not humble and quiet and vice versa.
If lucy is both not kind and not brave then alice is either happy or old and vice versa.
Everyone who is either generous or not old is either rich or quiet and vice versa.
Someone is not humble.
Someone is both brave and not quiet.
Susan is not kind.
Lucy is not tall or humble.
Alice is not patient or brave.
Someone is curious or not quiet.
Lucy is wise.
Someone is brave or not rich. | Alice is wise. | contradiction | (![X]:((humble(X)|curious(X))=>strong(X)))&
(![X]:((~brave(X)|humble(X))<=>(~generous(X)|curious(X))))&
(![X]:((~strong(X)&rich(X))<=>(~curious(X)&~strong(X))))&
(![X]:((happy(X)|funny(X))=>(~strong(X)<~>patient(X))))&
(![X]:((strong(X)|patient(X))<=>~wise(X)))&
(![X]:((~patient(X)|~kind(X))<=>(funny(X)&~happy(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(~creative(X)&old(X))))&
(![X]:((~happy(X)&quiet(X))=>~wise(X)))&
((quiet(paul))=>((rich(susan)&humble(susan))))&
(![X]:((~curious(X)<~>~quiet(X))=>happy(X)))&
(![X]:(generous(X)<=>(creative(X)|~happy(X))))&
(((creative(mary)&~quiet(mary)))=>(?[X]:((~generous(X)<~>~humble(X)))))&
(((quiet(lucy)|brave(lucy)))<=>(?[X]:((~humble(X)&quiet(X)))))&
(((~kind(lucy)&~brave(lucy)))<=>((happy(alice)<~>old(alice))))&
(![X]:((generous(X)<~>~old(X))<=>(rich(X)<~>quiet(X))))&
(?[X]:(~humble(X)))&
(?[X]:((brave(X)&~quiet(X))))&
(~kind(susan))&
((~tall(lucy)|humble(lucy)))&
((~patient(alice)|brave(alice)))&
(?[X]:((curious(X)|~quiet(X))))&
(wise(lucy))&
(?[X]:((brave(X)|~rich(X)))) | wise(alice) | [
"p0",
"p1",
"p2",
"p4",
"p5",
"p6",
"p10",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 76439148943368045199441
% SZS output start Proof for 76439148943368045199441
1. ! [X0] : ((curious(X0) | humble(X0)) => strong(X0)) [input p0]
2. ! [X0] : ((humble(X0) | ~brave(X0)) <=> (curious(X0) | ~generous(X0))) [input p1]
3. ! [X0] : ((rich(X0) & ~strong(X0)) <=> (~strong(X0) & ~curious(X0))) [input p2]
5. ! [X0] : ((patient(X0) | strong(X0)) <=> ~wise(X0)) [input p4]
6. ! [X0] : ((~kind(X0) | ~patient(X0)) <=> (~happy(X0) & funny(X0))) [input p5]
7. ! [X0] : ((~old(X0) <~> ~rich(X0)) <=> (old(X0) & ~creative(X0))) [input p6]
11. ! [X0] : (generous(X0) <=> (~happy(X0) | creative(X0))) [input p10]
14. (~brave(lucy) & ~kind(lucy)) <=> (happy(alice) <~> old(alice)) [input p13]
22. wise(lucy) [input p21]
24. wise(alice) [input hypothesis]
26. ! [X0] : (strong(X0) | (~curious(X0) & ~humble(X0))) [ennf transformation 1]
34. ! [X0] : (((humble(X0) | ~brave(X0)) | (~curious(X0) & generous(X0))) & ((curious(X0) | ~generous(X0)) | (~humble(X0) & brave(X0)))) [nnf transformation 2]
35. ! [X0] : ((humble(X0) | ~brave(X0) | (~curious(X0) & generous(X0))) & (curious(X0) | ~generous(X0) | (~humble(X0) & brave(X0)))) [flattening 34]
36. ! [X0] : (((rich(X0) & ~strong(X0)) | (strong(X0) | curious(X0))) & ((~strong(X0) & ~curious(X0)) | (~rich(X0) | strong(X0)))) [nnf transformation 3]
37. ! [X0] : (((rich(X0) & ~strong(X0)) | strong(X0) | curious(X0)) & ((~strong(X0) & ~curious(X0)) | ~rich(X0) | strong(X0))) [flattening 36]
39. ! [X0] : (((patient(X0) | strong(X0)) | wise(X0)) & (~wise(X0) | (~patient(X0) & ~strong(X0)))) [nnf transformation 5]
40. ! [X0] : ((patient(X0) | strong(X0) | wise(X0)) & (~wise(X0) | (~patient(X0) & ~strong(X0)))) [flattening 39]
41. ! [X0] : (((~kind(X0) | ~patient(X0)) | (happy(X0) | ~funny(X0))) & ((~happy(X0) & funny(X0)) | (kind(X0) & patient(X0)))) [nnf transformation 6]
42. ! [X0] : ((~kind(X0) | ~patient(X0) | happy(X0) | ~funny(X0)) & ((~happy(X0) & funny(X0)) | (kind(X0) & patient(X0)))) [flattening 41]
43. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (~old(X0) | creative(X0))) & ((old(X0) & ~creative(X0)) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [nnf transformation 7]
44. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | ~old(X0) | creative(X0)) & ((old(X0) & ~creative(X0)) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [flattening 43]
46. ! [X0] : ((generous(X0) | (happy(X0) & ~creative(X0))) & ((~happy(X0) | creative(X0)) | ~generous(X0))) [nnf transformation 11]
47. ! [X0] : ((generous(X0) | (happy(X0) & ~creative(X0))) & (~happy(X0) | creative(X0) | ~generous(X0))) [flattening 46]
56. ((~brave(lucy) & ~kind(lucy)) | ((happy(alice) | ~old(alice)) & (old(alice) | ~happy(alice)))) & (((~old(alice) | ~happy(alice)) & (old(alice) | happy(alice))) | (brave(lucy) | kind(lucy))) [nnf transformation 14]
57. ((~brave(lucy) & ~kind(lucy)) | ((happy(alice) | ~old(alice)) & (old(alice) | ~happy(alice)))) & (((~old(alice) | ~happy(alice)) & (old(alice) | happy(alice))) | brave(lucy) | kind(lucy)) [flattening 56]
68. ~curious(X0) | strong(X0) [cnf transformation 26]
69. ~generous(X0) | curious(X0) | brave(X0) [cnf transformation 35]
76. rich(X0) | strong(X0) | curious(X0) [cnf transformation 37]
81. ~wise(X0) | ~strong(X0) [cnf transformation 40]
82. ~wise(X0) | ~patient(X0) [cnf transformation 40]
86. ~happy(X0) | patient(X0) [cnf transformation 42]
87. ~happy(X0) | kind(X0) [cnf transformation 42]
91. old(X0) | ~rich(X0) | old(X0) [cnf transformation 44]
102. happy(X0) | generous(X0) [cnf transformation 47]
113. ~kind(lucy) | happy(alice) | ~old(alice) [cnf transformation 57]
115. ~brave(lucy) | happy(alice) | ~old(alice) [cnf transformation 57]
130. wise(lucy) [cnf transformation 22]
132. wise(alice) [cnf transformation 24]
133. ~rich(X0) | old(X0) [duplicate literal removal 91]
135. rich(X0) | strong(X0) [subsumption resolution 76,68]
176. 10 <=> brave(lucy) [avatar definition]
177. ~brave(lucy) <- (~10) [avatar component clause 176]
193. 13 <=> old(alice) [avatar definition]
197. 14 <=> happy(alice) [avatar definition]
199. happy(alice) <- (14) [avatar component clause 197]
200. ~13 | 14 | ~10 [avatar split clause 115,176,197,193]
203. 15 <=> kind(lucy) [avatar definition]
205. ~kind(lucy) <- (~15) [avatar component clause 203]
206. ~13 | 14 | ~15 [avatar split clause 113,203,197,193]
215. 16 <=> patient(alice) [avatar definition]
241. ~strong(lucy) [resolution 81,130]
242. ~strong(alice) [resolution 81,132]
244. ~patient(alice) [resolution 82,132]
249. kind(X0) | generous(X0) [resolution 102,87]
260. patient(alice) <- (14) [resolution 199,86]
263. 16 | ~14 [avatar split clause 260,197,215]
264. ~16 [avatar split clause 244,215]
291. 26 <=> generous(lucy) [avatar definition]
293. generous(lucy) <- (26) [avatar component clause 291]
380. 37 <=> rich(alice) [avatar definition]
381. rich(alice) <- (37) [avatar component clause 380]
382. ~rich(alice) <- (~37) [avatar component clause 380]
384. strong(alice) <- (~37) [resolution 382,135]
385. $false <- (~37) [subsumption resolution 384,242]
386. 37 [avatar contradiction clause 385]
391. old(alice) <- (37) [resolution 381,133]
393. generous(lucy) <- (~15) [resolution 249,205]
394. 26 | 15 [avatar split clause 393,203,291]
395. 13 | ~37 [avatar split clause 391,380,193]
482. curious(lucy) | brave(lucy) <- (26) [resolution 293,69]
483. curious(lucy) <- (~10, 26) [subsumption resolution 482,177]
554. strong(lucy) <- (~10, 26) [resolution 483,68]
556. $false <- (~10, 26) [subsumption resolution 554,241]
557. 10 | ~26 [avatar contradiction clause 556]
558. $false [avatar sat refutation 200,206,263,264,386,394,395,557]
% SZS output end Proof for 76439148943368045199441
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is happy or not kind and vice versa.
Everyone who is not quiet or not rich is not quiet or not brave and vice versa.
If someone is not happy then mary is creative or brave.
If john is quiet then someone is both not generous and creative and vice versa.
If john is kind or not rich then john is both not creative and old and vice versa.
If susan is quiet or not brave then john is both not rich and not generous.
Everyone who is either creative or generous is patient.
If someone is both funny and not kind then mary is either generous or old and vice versa.
Everyone who is both not old and funny is both not strong and tall.
If mary is strong or not happy then lucy is not strong and vice versa.
If someone is not curious or not kind then lucy is curious or not funny and vice versa.
If fred is brave or calm then someone is both funny and not curious.
Everyone who is either not brave or not quiet is not brave or not tall and vice versa.
If someone is strong then fred is either creative or not patient and vice versa.
Everyone who is not funny is kind or not quiet and vice versa.
Everyone who is not humble or not tall is not tall.
Someone is either strong or not kind.
Someone is curious or tall.
Someone is either happy or creative.
Fred is not kind.
John is funny.
Someone is not creative.
Someone is not happy or not rich.
John is quiet or happy. | John is not old. | contradiction | (![X]:(~brave(X)<=>(happy(X)|~kind(X))))&
(![X]:((~quiet(X)|~rich(X))<=>(~quiet(X)|~brave(X))))&
((?[X]:(~happy(X)))=>((creative(mary)|brave(mary))))&
((quiet(john))<=>(?[X]:((~generous(X)&creative(X)))))&
(((kind(john)|~rich(john)))<=>((~creative(john)&old(john))))&
(((quiet(susan)|~brave(susan)))=>((~rich(john)&~generous(john))))&
(![X]:((creative(X)<~>generous(X))=>patient(X)))&
((?[X]:((funny(X)&~kind(X))))<=>((generous(mary)<~>old(mary))))&
(![X]:((~old(X)&funny(X))=>(~strong(X)&tall(X))))&
(((strong(mary)|~happy(mary)))<=>(~strong(lucy)))&
((?[X]:((~curious(X)|~kind(X))))<=>((curious(lucy)|~funny(lucy))))&
(((brave(fred)|calm(fred)))=>(?[X]:((funny(X)&~curious(X)))))&
(![X]:((~brave(X)<~>~quiet(X))<=>(~brave(X)|~tall(X))))&
((?[X]:(strong(X)))<=>((creative(fred)<~>~patient(fred))))&
(![X]:(~funny(X)<=>(kind(X)|~quiet(X))))&
(![X]:((~humble(X)|~tall(X))=>~tall(X)))&
(?[X]:((strong(X)<~>~kind(X))))&
(?[X]:((curious(X)|tall(X))))&
(?[X]:((happy(X)<~>creative(X))))&
(~kind(fred))&
(funny(john))&
(?[X]:(~creative(X)))&
(?[X]:((~happy(X)|~rich(X))))&
((quiet(john)|happy(john))) | ~old(john) | [
"p0",
"p1",
"p4",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7434197526789945362357545
% SZS output start Proof for 7434197526789945362357545
1. ! [X0] : (~brave(X0) <=> (~kind(X0) | happy(X0))) [input p0]
2. ! [X0] : ((~rich(X0) | ~quiet(X0)) <=> (~brave(X0) | ~quiet(X0))) [input p1]
5. (~rich(john) | kind(john)) <=> (old(john) & ~creative(john)) [input p4]
15. ! [X0] : (~funny(X0) <=> (~quiet(X0) | kind(X0))) [input p14]
21. funny(john) [input p20]
25. ~old(john) [input hypothesis]
36. ! [X0] : ((~brave(X0) | (kind(X0) & ~happy(X0))) & ((~kind(X0) | happy(X0)) | brave(X0))) [nnf transformation 1]
37. ! [X0] : ((~brave(X0) | (kind(X0) & ~happy(X0))) & (~kind(X0) | happy(X0) | brave(X0))) [flattening 36]
38. ! [X0] : (((~rich(X0) | ~quiet(X0)) | (brave(X0) & quiet(X0))) & ((~brave(X0) | ~quiet(X0)) | (rich(X0) & quiet(X0)))) [nnf transformation 2]
39. ! [X0] : ((~rich(X0) | ~quiet(X0) | (brave(X0) & quiet(X0))) & (~brave(X0) | ~quiet(X0) | (rich(X0) & quiet(X0)))) [flattening 38]
44. ((~rich(john) | kind(john)) | (~old(john) | creative(john))) & ((old(john) & ~creative(john)) | (rich(john) & ~kind(john))) [nnf transformation 5]
45. (~rich(john) | kind(john) | ~old(john) | creative(john)) & ((old(john) & ~creative(john)) | (rich(john) & ~kind(john))) [flattening 44]
66. ! [X0] : ((~funny(X0) | (quiet(X0) & ~kind(X0))) & ((~quiet(X0) | kind(X0)) | funny(X0))) [nnf transformation 15]
67. ! [X0] : ((~funny(X0) | (quiet(X0) & ~kind(X0))) & (~quiet(X0) | kind(X0) | funny(X0))) [flattening 66]
82. ~brave(X0) | kind(X0) [cnf transformation 37]
86. ~rich(X0) | ~quiet(X0) | brave(X0) [cnf transformation 39]
93. old(john) | ~kind(john) [cnf transformation 45]
94. old(john) | rich(john) [cnf transformation 45]
131. ~funny(X0) | quiet(X0) [cnf transformation 67]
139. funny(john) [cnf transformation 21]
143. ~old(john) [cnf transformation 25]
162. 5 <=> quiet(john) [avatar definition]
164. quiet(john) <- (5) [avatar component clause 162]
181. 9 <=> old(john) [avatar definition]
185. 10 <=> kind(john) [avatar definition]
186. ~kind(john) <- (~10) [avatar component clause 185]
189. 11 <=> rich(john) [avatar definition]
190. rich(john) <- (11) [avatar component clause 189]
193. 11 | 9 [avatar split clause 94,181,189]
194. ~10 | 9 [avatar split clause 93,181,185]
356. ~9 [avatar split clause 143,181]
364. quiet(john) [resolution 131,139]
380. ~quiet(john) | brave(john) <- (11) [resolution 86,190]
381. brave(john) <- (5, 11) [subsumption resolution 380,164]
382. kind(john) <- (5, 11) [resolution 381,82]
383. $false <- (5, ~10, 11) [subsumption resolution 382,186]
384. ~5 | 10 | ~11 [avatar contradiction clause 383]
386. 5 [avatar split clause 364,162]
387. $false [avatar sat refutation 193,194,356,384,386]
% SZS output end Proof for 7434197526789945362357545
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either curious or not humble then someone is not wise and vice versa.
If someone is not tall or not calm then susan is not happy.
If alice is both wise and not quiet then someone is wise and vice versa.
If someone is funny then lucy is either not happy or not tall and vice versa.
If someone is old then fred is both rich and not strong.
Everyone who is not kind or not generous is both old and not generous.
If alice is both not wise and not happy then john is either not quiet or not tall and vice versa.
If fred is either creative or patient then paul is both not happy and not brave.
Everyone who is patient or not creative is either generous or not old.
Everyone who is rich is not old or old and vice versa.
Everyone who is rich is both strong and kind and vice versa.
Everyone who is both generous and strong is either funny or old and vice versa.
Everyone who is either not old or wise is either rich or not old.
If lucy is both curious and wise then susan is old and vice versa.
Susan is curious or not quiet.
Someone is happy.
Someone is both rich and not calm.
John is both tall and not brave.
Paul is patient or not humble.
Someone is brave or not humble. | Fred is not creative. | contradiction | ((?[X]:((curious(X)<~>~humble(X))))<=>(?[X]:(~wise(X))))&
((?[X]:((~tall(X)|~calm(X))))=>(~happy(susan)))&
(((wise(alice)&~quiet(alice)))<=>(?[X]:(wise(X))))&
((?[X]:(funny(X)))<=>((~happy(lucy)<~>~tall(lucy))))&
((?[X]:(old(X)))=>((rich(fred)&~strong(fred))))&
(![X]:((~kind(X)|~generous(X))=>(old(X)&~generous(X))))&
(((~wise(alice)&~happy(alice)))<=>((~quiet(john)<~>~tall(john))))&
(((creative(fred)<~>patient(fred)))=>((~happy(paul)&~brave(paul))))&
(![X]:((patient(X)|~creative(X))=>(generous(X)<~>~old(X))))&
(![X]:(rich(X)<=>(~old(X)|old(X))))&
(![X]:(rich(X)<=>(strong(X)&kind(X))))&
(![X]:((generous(X)&strong(X))<=>(funny(X)<~>old(X))))&
(![X]:((~old(X)<~>wise(X))=>(rich(X)<~>~old(X))))&
(((curious(lucy)&wise(lucy)))<=>(old(susan)))&
((curious(susan)|~quiet(susan)))&
(?[X]:(happy(X)))&
(?[X]:((rich(X)&~calm(X))))&
((tall(john)&~brave(john)))&
((patient(paul)|~humble(paul)))&
(?[X]:((brave(X)|~humble(X)))) | ~creative(fred) | [
"p4",
"p5",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1688215651346650280368146
% SZS output start Proof for 1688215651346650280368146
5. ? [X0] : old(X0) => (~strong(fred) & rich(fred)) [input p4]
6. ! [X0] : ((~generous(X0) | ~kind(X0)) => (~generous(X0) & old(X0))) [input p5]
9. ! [X0] : ((~creative(X0) | patient(X0)) => (generous(X0) <~> ~old(X0))) [input p8]
10. ! [X0] : (rich(X0) <=> (old(X0) | ~old(X0))) [input p9]
11. ! [X0] : (rich(X0) <=> (kind(X0) & strong(X0))) [input p10]
21. ~creative(fred) [input hypothesis]
24. (~strong(fred) & rich(fred)) | ! [X0] : ~old(X0) [ennf transformation 5]
25. ! [X0] : ((~generous(X0) & old(X0)) | (generous(X0) & kind(X0))) [ennf transformation 6]
27. ! [X0] : ((generous(X0) <~> ~old(X0)) | (creative(X0) & ~patient(X0))) [ennf transformation 9]
46. ! [X0] : (((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | (creative(X0) & ~patient(X0))) [nnf transformation 27]
47. ! [X0] : ((rich(X0) | (~old(X0) & old(X0))) & ((old(X0) | ~old(X0)) | ~rich(X0))) [nnf transformation 10]
48. ! [X0] : ((rich(X0) | (~old(X0) & old(X0))) & (old(X0) | ~old(X0) | ~rich(X0))) [flattening 47]
49. ! [X0] : ((rich(X0) | (~kind(X0) | ~strong(X0))) & ((kind(X0) & strong(X0)) | ~rich(X0))) [nnf transformation 11]
50. ! [X0] : ((rich(X0) | ~kind(X0) | ~strong(X0)) & ((kind(X0) & strong(X0)) | ~rich(X0))) [flattening 49]
76. ~strong(fred) | ~old(X0) [cnf transformation 24]
78. generous(X0) | old(X0) [cnf transformation 25]
94. old(X0) | ~generous(X0) | creative(X0) [cnf transformation 46]
96. rich(X0) | old(X0) [cnf transformation 48]
97. ~old(X0) | rich(X0) [cnf transformation 48]
98. strong(X0) | ~rich(X0) [cnf transformation 50]
122. ~creative(fred) [cnf transformation 21]
200. 18 <=> ! [X0] : ~old(X0) [avatar definition]
201. ~old(X0) <- (18) [avatar component clause 200]
203. 19 <=> strong(fred) [avatar definition]
205. ~strong(fred) <- (~19) [avatar component clause 203]
206. 18 | ~19 [avatar split clause 76,203,200]
235. 25 <=> creative(fred) [avatar definition]
236. ~creative(fred) <- (~25) [avatar component clause 235]
250. creative(X0) | old(X0) [subsumption resolution 94,78]
254. rich(X0) [subsumption resolution 96,97]
256. strong(X0) [subsumption resolution 98,254]
305. ~25 [avatar split clause 122,235]
307. old(fred) <- (~25) [resolution 250,236]
308. $false <- (18, ~25) [subsumption resolution 307,201]
309. ~18 | 25 [avatar contradiction clause 308]
310. $false <- (~19) [subsumption resolution 205,256]
311. 19 [avatar contradiction clause 310]
312. $false [avatar sat refutation 206,305,309,311]
% SZS output end Proof for 1688215651346650280368146
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old or not calm then mary is humble.
Everyone who is both creative and quiet is tall or happy and vice versa.
Everyone who is either rich or kind is not kind or not happy.
If mary is not strong then someone is either not calm or creative and vice versa.
If susan is both not old and not happy then someone is not rich or not tall and vice versa.
If someone is both calm and rich then john is not patient or happy.
If john is quiet or kind then someone is either funny or old.
If someone is both not funny and not patient then someone is not strong.
If alice is either strong or not generous then someone is not generous or humble.
Everyone who is both not generous and creative is not strong or not curious.
If paul is not old or creative then lucy is not creative.
Everyone who is either not rich or not funny is either not generous or wise.
If someone is old then lucy is curious or not generous.
If john is either tall or not brave then fred is both brave and not calm.
Everyone who is happy or funny is patient or not rich and vice versa.
Lucy is happy.
Someone is not funny or not generous.
Fred is not patient or rich.
Someone is brave.
Someone is wise or tall.
Lucy is not quiet or strong.
John is either not wise or not rich.
Paul is either rich or kind. | Lucy is not creative. | contradiction | ((?[X]:((old(X)|~calm(X))))=>(humble(mary)))&
(![X]:((creative(X)&quiet(X))<=>(tall(X)|happy(X))))&
(![X]:((rich(X)<~>kind(X))=>(~kind(X)|~happy(X))))&
((~strong(mary))<=>(?[X]:((~calm(X)<~>creative(X)))))&
(((~old(susan)&~happy(susan)))<=>(?[X]:((~rich(X)|~tall(X)))))&
((?[X]:((calm(X)&rich(X))))=>((~patient(john)|happy(john))))&
(((quiet(john)|kind(john)))=>(?[X]:((funny(X)<~>old(X)))))&
((?[X]:((~funny(X)&~patient(X))))=>(?[X]:(~strong(X))))&
(((strong(alice)<~>~generous(alice)))=>(?[X]:((~generous(X)|humble(X)))))&
(![X]:((~generous(X)&creative(X))=>(~strong(X)|~curious(X))))&
(((~old(paul)|creative(paul)))=>(~creative(lucy)))&
(![X]:((~rich(X)<~>~funny(X))=>(~generous(X)<~>wise(X))))&
((?[X]:(old(X)))=>((curious(lucy)|~generous(lucy))))&
(((tall(john)<~>~brave(john)))=>((brave(fred)&~calm(fred))))&
(![X]:((happy(X)|funny(X))<=>(patient(X)|~rich(X))))&
(happy(lucy))&
(?[X]:((~funny(X)|~generous(X))))&
((~patient(fred)|rich(fred)))&
(?[X]:(brave(X)))&
(?[X]:((wise(X)|tall(X))))&
((~quiet(lucy)|strong(lucy)))&
((~wise(john)<~>~rich(john)))&
((rich(paul)<~>kind(paul))) | ~creative(lucy) | [
"p1",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6407654323527955479460047
% SZS output start Proof for 6407654323527955479460047
2. ! [X0] : ((quiet(X0) & creative(X0)) <=> (happy(X0) | tall(X0))) [input p1]
16. happy(lucy) [input p15]
24. ~creative(lucy) [input hypothesis]
41. ! [X0] : (((quiet(X0) & creative(X0)) | (~happy(X0) & ~tall(X0))) & ((happy(X0) | tall(X0)) | (~quiet(X0) | ~creative(X0)))) [nnf transformation 2]
42. ! [X0] : (((quiet(X0) & creative(X0)) | (~happy(X0) & ~tall(X0))) & (happy(X0) | tall(X0) | ~quiet(X0) | ~creative(X0))) [flattening 41]
73. ~happy(X0) | creative(X0) [cnf transformation 42]
109. happy(lucy) [cnf transformation 16]
119. ~creative(lucy) [cnf transformation 24]
215. 22 <=> creative(lucy) [avatar definition]
217. ~creative(lucy) <- (~22) [avatar component clause 215]
312. ~22 [avatar split clause 119,215]
313. creative(lucy) [resolution 73,109]
314. $false <- (~22) [subsumption resolution 313,217]
315. 22 [avatar contradiction clause 314]
316. $false [avatar sat refutation 312,315]
% SZS output end Proof for 6407654323527955479460047
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or patient is both not old and not strong and vice versa.
If someone is either old or not rich then mary is humble.
Everyone who is both patient and not calm is rich.
Everyone who is patient or not rich is happy or generous and vice versa.
If paul is either not strong or creative then someone is tall.
Everyone who is either strong or not kind is not patient.
If mary is both not creative and not generous then someone is not old.
If mary is not kind then someone is both happy and kind.
Everyone who is either kind or strong is creative.
If alice is not tall then someone is both not kind and not rich and vice versa.
Everyone who is not funny or not humble is not quiet or not brave and vice versa.
Everyone who is both not creative and humble is not generous and vice versa.
Everyone who is both not calm and generous is either not quiet or generous and vice versa.
If susan is both tall and patient then alice is both not creative and not patient and vice versa.
If someone is both patient and not creative then someone is curious and vice versa.
John is either not calm or humble.
Susan is strong or not rich.
Someone is brave.
Fred is happy or patient.
Someone is not brave. | John is curious. | contradiction | (![X]:((~kind(X)|patient(X))<=>(~old(X)&~strong(X))))&
((?[X]:((old(X)<~>~rich(X))))=>(humble(mary)))&
(![X]:((patient(X)&~calm(X))=>rich(X)))&
(![X]:((patient(X)|~rich(X))<=>(happy(X)|generous(X))))&
(((~strong(paul)<~>creative(paul)))=>(?[X]:(tall(X))))&
(![X]:((strong(X)<~>~kind(X))=>~patient(X)))&
(((~creative(mary)&~generous(mary)))=>(?[X]:(~old(X))))&
((~kind(mary))=>(?[X]:((happy(X)&kind(X)))))&
(![X]:((kind(X)<~>strong(X))=>creative(X)))&
((~tall(alice))<=>(?[X]:((~kind(X)&~rich(X)))))&
(![X]:((~funny(X)|~humble(X))<=>(~quiet(X)|~brave(X))))&
(![X]:((~creative(X)&humble(X))<=>~generous(X)))&
(![X]:((~calm(X)&generous(X))<=>(~quiet(X)<~>generous(X))))&
(((tall(susan)&patient(susan)))<=>((~creative(alice)&~patient(alice))))&
((?[X]:((patient(X)&~creative(X))))<=>(?[X]:(curious(X))))&
((~calm(john)<~>humble(john)))&
((strong(susan)|~rich(susan)))&
(?[X]:(brave(X)))&
((happy(fred)|patient(fred)))&
(?[X]:(~brave(X))) | curious(john) | [
"p0",
"p5",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5675260419123314930501879
% SZS output start Proof for 5675260419123314930501879
1. ! [X0] : ((patient(X0) | ~kind(X0)) <=> (~strong(X0) & ~old(X0))) [input p0]
6. ! [X0] : ((strong(X0) <~> ~kind(X0)) => ~patient(X0)) [input p5]
9. ! [X0] : ((kind(X0) <~> strong(X0)) => creative(X0)) [input p8]
15. ? [X0] : (~creative(X0) & patient(X0)) <=> ? [X0] : curious(X0) [input p14]
21. curious(john) [input hypothesis]
22. ? [X0] : (~creative(X0) & patient(X0)) <=> ? [X1] : curious(X1) [rectify 15]
27. ! [X0] : (~patient(X0) | (strong(X0) <=> ~kind(X0))) [ennf transformation 6]
31. ! [X0] : (creative(X0) | (kind(X0) <=> strong(X0))) [ennf transformation 9]
32. ! [X0] : (((patient(X0) | ~kind(X0)) | (strong(X0) | old(X0))) & ((~strong(X0) & ~old(X0)) | (~patient(X0) & kind(X0)))) [nnf transformation 1]
33. ! [X0] : ((patient(X0) | ~kind(X0) | strong(X0) | old(X0)) & ((~strong(X0) & ~old(X0)) | (~patient(X0) & kind(X0)))) [flattening 32]
40. ! [X0] : (~patient(X0) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0)))) [nnf transformation 27]
45. ! [X0] : (creative(X0) | ((kind(X0) | ~strong(X0)) & (strong(X0) | ~kind(X0)))) [nnf transformation 31]
58. (? [X0] : (~creative(X0) & patient(X0)) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : (creative(X0) | ~patient(X0))) [nnf transformation 22]
59. (? [X0] : (~creative(X0) & patient(X0)) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : (creative(X3) | ~patient(X3))) [rectify 58]
60. ? [X0] : (~creative(X0) & patient(X0)) => (~creative(sK4) & patient(sK4)) [choice axiom]
61. ? [X2] : curious(X2) => curious(sK5) [choice axiom]
62. ((~creative(sK4) & patient(sK4)) | ! [X1] : ~curious(X1)) & (curious(sK5) | ! [X3] : (creative(X3) | ~patient(X3))) [skolemisation 59,61,60]
71. ~strong(X0) | ~patient(X0) [cnf transformation 33]
83. ~patient(X0) | strong(X0) | kind(X0) [cnf transformation 40]
87. ~kind(X0) | strong(X0) | creative(X0) [cnf transformation 45]
110. patient(sK4) | ~curious(X1) [cnf transformation 62]
111. ~creative(sK4) | ~curious(X1) [cnf transformation 62]
118. curious(john) [cnf transformation 21]
147. ~patient(X0) | kind(X0) [subsumption resolution 83,71]
215. 21 <=> ! [X1] : ~curious(X1) [avatar definition]
216. ~curious(X1) <- (21) [avatar component clause 215]
218. 22 <=> creative(sK4) [avatar definition]
220. ~creative(sK4) <- (~22) [avatar component clause 218]
221. 21 | ~22 [avatar split clause 111,218,215]
223. 23 <=> patient(sK4) [avatar definition]
225. patient(sK4) <- (23) [avatar component clause 223]
226. 21 | 23 [avatar split clause 110,223,215]
263. $false <- (21) [resolution 216,118]
264. ~21 [avatar contradiction clause 263]
267. kind(sK4) <- (23) [resolution 147,225]
317. strong(sK4) | creative(sK4) <- (23) [resolution 87,267]
323. strong(sK4) <- (~22, 23) [subsumption resolution 317,220]
366. ~patient(sK4) <- (~22, 23) [resolution 323,71]
368. $false <- (~22, 23) [subsumption resolution 366,225]
369. 22 | ~23 [avatar contradiction clause 368]
370. $false [avatar sat refutation 221,226,264,369]
% SZS output end Proof for 5675260419123314930501879
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is both rich and calm and vice versa.
Everyone who is either not wise or not tall is both not kind and not strong.
Everyone who is not calm is both kind and not humble and vice versa.
Everyone who is both not curious and not patient is either not strong or wise.
Everyone who is not generous is curious or not quiet and vice versa.
Everyone who is not old or wise is both creative and not patient.
If fred is either not funny or quiet then fred is both kind and not calm.
If john is creative or funny then someone is not humble or not strong.
If paul is calm or creative then someone is both kind and not tall and vice versa.
If alice is patient then lucy is brave or patient and vice versa.
Everyone who is either not funny or brave is either happy or not strong.
Everyone who is not funny or not creative is curious or not happy and vice versa.
Everyone who is calm is both brave and quiet and vice versa.
If paul is not curious or humble then alice is generous.
Everyone who is not curious or tall is not tall or strong and vice versa.
If someone is not patient then someone is quiet.
Alice is both old and quiet.
Paul is either not strong or not calm.
Lucy is not humble or kind.
Someone is both not tall and quiet.
Someone is not humble.
Fred is both funny and not brave.
Alice is both brave and wise.
Mary is not quiet. | Mary is kind. | entailment | (![X]:(~wise(X)<=>(rich(X)&calm(X))))&
(![X]:((~wise(X)<~>~tall(X))=>(~kind(X)&~strong(X))))&
(![X]:(~calm(X)<=>(kind(X)&~humble(X))))&
(![X]:((~curious(X)&~patient(X))=>(~strong(X)<~>wise(X))))&
(![X]:(~generous(X)<=>(curious(X)|~quiet(X))))&
(![X]:((~old(X)|wise(X))=>(creative(X)&~patient(X))))&
(((~funny(fred)<~>quiet(fred)))=>((kind(fred)&~calm(fred))))&
(((creative(john)|funny(john)))=>(?[X]:((~humble(X)|~strong(X)))))&
(((calm(paul)|creative(paul)))<=>(?[X]:((kind(X)&~tall(X)))))&
((patient(alice))<=>((brave(lucy)|patient(lucy))))&
(![X]:((~funny(X)<~>brave(X))=>(happy(X)<~>~strong(X))))&
(![X]:((~funny(X)|~creative(X))<=>(curious(X)|~happy(X))))&
(![X]:(calm(X)<=>(brave(X)&quiet(X))))&
(((~curious(paul)|humble(paul)))=>(generous(alice)))&
(![X]:((~curious(X)|tall(X))<=>(~tall(X)|strong(X))))&
((?[X]:(~patient(X)))=>(?[X]:(quiet(X))))&
((old(alice)&quiet(alice)))&
((~strong(paul)<~>~calm(paul)))&
((~humble(lucy)|kind(lucy)))&
(?[X]:((~tall(X)&quiet(X))))&
(?[X]:(~humble(X)))&
((funny(fred)&~brave(fred)))&
((brave(alice)&wise(alice)))&
(~quiet(mary)) | kind(mary) | [
"p2",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8114075959621058718852340
% SZS output start Proof for 8114075959621058718852340
3. ! [X0] : (~calm(X0) <=> (~humble(X0) & kind(X0))) [input p2]
13. ! [X0] : (calm(X0) <=> (quiet(X0) & brave(X0))) [input p12]
24. ~quiet(mary) [input p23]
25. ~kind(mary) [input hypothesis]
43. ! [X0] : ((~calm(X0) | (humble(X0) | ~kind(X0))) & ((~humble(X0) & kind(X0)) | calm(X0))) [nnf transformation 3]
44. ! [X0] : ((~calm(X0) | humble(X0) | ~kind(X0)) & ((~humble(X0) & kind(X0)) | calm(X0))) [flattening 43]
59. ! [X0] : ((calm(X0) | (~quiet(X0) | ~brave(X0))) & ((quiet(X0) & brave(X0)) | ~calm(X0))) [nnf transformation 13]
60. ! [X0] : ((calm(X0) | ~quiet(X0) | ~brave(X0)) & ((quiet(X0) & brave(X0)) | ~calm(X0))) [flattening 59]
78. kind(X0) | calm(X0) [cnf transformation 44]
110. ~calm(X0) | quiet(X0) [cnf transformation 60]
130. ~quiet(mary) [cnf transformation 24]
131. ~kind(mary) [cnf transformation 25]
253. calm(mary) [resolution 78,131]
269. quiet(mary) [resolution 110,253]
270. $false [subsumption resolution 269,130]
% SZS output end Proof for 8114075959621058718852340
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or quiet is either generous or not strong. If susan is either not tall or tall then lucy is both brave and funny and vice versa. If fred is wise or not happy then someone is both not patient and not humble. Everyone who is either not creative or not generous is both brave and not brave and vice versa. If someone is not happy then alice is either quiet or not strong and vice versa. Everyone who is not rich is both not strong and not happy. If someone is not humble or calm then fred is both calm and rich. If john is not happy or old then someone is both not wise and not generous. If alice is both funny and not calm then susan is not humble. If someone is not humble or creative then alice is either calm or not funny and vice versa. If john is not humble then someone is both kind and not humble and vice versa. If alice is either happy or not curious then someone is not rich or not funny and vice versa. If someone is not old or generous then paul is wise. If someone is either old or not calm then someone is both not generous and funny. Everyone who is either not rich or not patient is kind or patient. Everyone who is not happy is either kind or not happy. Someone is rich. Someone is brave. Lucy is either not old or patient. Someone is either wise or not brave. Paul is both creative and not calm. Someone is either not strong or funny. Alice is not old. | Alice is old. | contradiction | (![X]:((strong(X)|quiet(X))=>(generous(X)<~>~strong(X))))&
(((~tall(susan)<~>tall(susan)))<=>((brave(lucy)&funny(lucy))))&
(((wise(fred)|~happy(fred)))=>(?[X]:((~patient(X)&~humble(X)))))&
(![X]:((~creative(X)<~>~generous(X))<=>(brave(X)&~brave(X))))&
((?[X]:(~happy(X)))<=>((quiet(alice)<~>~strong(alice))))&
(![X]:(~rich(X)=>(~strong(X)&~happy(X))))&
((?[X]:((~humble(X)|calm(X))))=>((calm(fred)&rich(fred))))&
(((~happy(john)|old(john)))=>(?[X]:((~wise(X)&~generous(X)))))&
(((funny(alice)&~calm(alice)))=>(~humble(susan)))&
((?[X]:((~humble(X)|creative(X))))<=>((calm(alice)<~>~funny(alice))))&
((~humble(john))<=>(?[X]:((kind(X)&~humble(X)))))&
(((happy(alice)<~>~curious(alice)))<=>(?[X]:((~rich(X)|~funny(X)))))&
((?[X]:((~old(X)|generous(X))))=>(wise(paul)))&
((?[X]:((old(X)<~>~calm(X))))=>(?[X]:((~generous(X)&funny(X)))))&
(![X]:((~rich(X)<~>~patient(X))=>(kind(X)|patient(X))))&
(![X]:(~happy(X)=>(kind(X)<~>~happy(X))))&
(?[X]:(rich(X)))&
(?[X]:(brave(X)))&
((~old(lucy)<~>patient(lucy)))&
(?[X]:((wise(X)<~>~brave(X))))&
((creative(paul)&~calm(paul)))&
(?[X]:((~strong(X)<~>funny(X))))&
(~old(alice)) | old(alice) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2511351671174212477324433
% SZS output start Proof for 2511351671174212477324433
23. ~old(alice) [input p22]
24. old(alice) [input hypothesis]
150. ~old(alice) [cnf transformation 23]
151. old(alice) [cnf transformation 24]
390. $false [subsumption resolution 151,150]
% SZS output end Proof for 2511351671174212477324433
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall or not patient is both funny and generous and vice versa.
Everyone who is rich or not wise is either not calm or not old and vice versa.
If alice is not old or happy then someone is both brave and strong.
Everyone who is wise or calm is not wise.
Everyone who is either not kind or not curious is humble.
Everyone who is not patient is strong and vice versa.
Everyone who is humble is creative or not creative and vice versa.
Everyone who is both not rich and funny is either strong or not brave and vice versa.
Everyone who is kind or curious is either generous or not creative.
Everyone who is brave or strong is either brave or not wise.
Everyone who is either funny or not generous is not kind or calm.
If john is curious then paul is wise.
If someone is not generous or not rich then mary is brave or not calm and vice versa.
Everyone who is not wise or not rich is not curious.
Everyone who is not generous is not brave.
Susan is not kind.
Someone is both not tall and not calm.
Mary is not rich.
John is not creative.
Someone is not humble or not calm.
Someone is either rich or generous.
Lucy is both kind and old. | Lucy is not strong. | entailment | (![X]:((tall(X)|~patient(X))<=>(funny(X)&generous(X))))&
(![X]:((rich(X)|~wise(X))<=>(~calm(X)<~>~old(X))))&
(((~old(alice)|happy(alice)))=>(?[X]:((brave(X)&strong(X)))))&
(![X]:((wise(X)|calm(X))=>~wise(X)))&
(![X]:((~kind(X)<~>~curious(X))=>humble(X)))&
(![X]:(~patient(X)<=>strong(X)))&
(![X]:(humble(X)<=>(creative(X)|~creative(X))))&
(![X]:((~rich(X)&funny(X))<=>(strong(X)<~>~brave(X))))&
(![X]:((kind(X)|curious(X))=>(generous(X)<~>~creative(X))))&
(![X]:((brave(X)|strong(X))=>(brave(X)<~>~wise(X))))&
(![X]:((funny(X)<~>~generous(X))=>(~kind(X)|calm(X))))&
((curious(john))=>(wise(paul)))&
((?[X]:((~generous(X)|~rich(X))))<=>((brave(mary)|~calm(mary))))&
(![X]:((~wise(X)|~rich(X))=>~curious(X)))&
(![X]:(~generous(X)=>~brave(X)))&
(~kind(susan))&
(?[X]:((~tall(X)&~calm(X))))&
(~rich(mary))&
(~creative(john))&
(?[X]:((~humble(X)|~calm(X))))&
(?[X]:((rich(X)<~>generous(X))))&
((kind(lucy)&old(lucy))) | ~strong(lucy) | [
"p0",
"p1",
"p3",
"p5",
"p7",
"p9",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2382179173892334681551
% SZS output start Proof for 2382179173892334681551
1. ! [X0] : ((~patient(X0) | tall(X0)) <=> (generous(X0) & funny(X0))) [input p0]
2. ! [X0] : ((~wise(X0) | rich(X0)) <=> (~calm(X0) <~> ~old(X0))) [input p1]
4. ! [X0] : ((calm(X0) | wise(X0)) => ~wise(X0)) [input p3]
6. ! [X0] : (~patient(X0) <=> strong(X0)) [input p5]
8. ! [X0] : ((funny(X0) & ~rich(X0)) <=> (strong(X0) <~> ~brave(X0))) [input p7]
10. ! [X0] : ((strong(X0) | brave(X0)) => (brave(X0) <~> ~wise(X0))) [input p9]
11. ! [X0] : ((funny(X0) <~> ~generous(X0)) => (calm(X0) | ~kind(X0))) [input p10]
22. old(lucy) & kind(lucy) [input p21]
23. strong(lucy) [input hypothesis]
26. ! [X0] : (~wise(X0) | (~calm(X0) & ~wise(X0))) [ennf transformation 4]
29. ! [X0] : ((brave(X0) <~> ~wise(X0)) | (~strong(X0) & ~brave(X0))) [ennf transformation 10]
30. ! [X0] : ((calm(X0) | ~kind(X0)) | (funny(X0) <=> ~generous(X0))) [ennf transformation 11]
31. ! [X0] : (calm(X0) | ~kind(X0) | (funny(X0) <=> ~generous(X0))) [flattening 30]
35. ! [X0] : (((~patient(X0) | tall(X0)) | (~generous(X0) | ~funny(X0))) & ((generous(X0) & funny(X0)) | (patient(X0) & ~tall(X0)))) [nnf transformation 1]
36. ! [X0] : ((~patient(X0) | tall(X0) | ~generous(X0) | ~funny(X0)) & ((generous(X0) & funny(X0)) | (patient(X0) & ~tall(X0)))) [flattening 35]
37. ! [X0] : (((~wise(X0) | rich(X0)) | ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0)))) & (((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | (wise(X0) & ~rich(X0)))) [nnf transformation 2]
38. ! [X0] : ((~wise(X0) | rich(X0) | ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0)))) & (((old(X0) | calm(X0)) & (~old(X0) | ~calm(X0))) | (wise(X0) & ~rich(X0)))) [flattening 37]
42. ! [X0] : ((~patient(X0) | ~strong(X0)) & (strong(X0) | patient(X0))) [nnf transformation 6]
45. ! [X0] : (((funny(X0) & ~rich(X0)) | ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0)))) & (((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | (~funny(X0) | rich(X0)))) [nnf transformation 8]
46. ! [X0] : (((funny(X0) & ~rich(X0)) | ((strong(X0) | brave(X0)) & (~brave(X0) | ~strong(X0)))) & (((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | ~funny(X0) | rich(X0))) [flattening 45]
48. ! [X0] : (((wise(X0) | ~brave(X0)) & (~wise(X0) | brave(X0))) | (~strong(X0) & ~brave(X0))) [nnf transformation 29]
49. ! [X0] : (calm(X0) | ~kind(X0) | ((funny(X0) | generous(X0)) & (~generous(X0) | ~funny(X0)))) [nnf transformation 31]
63. funny(X0) | patient(X0) [cnf transformation 36]
65. generous(X0) | patient(X0) [cnf transformation 36]
68. ~old(X0) | ~calm(X0) | wise(X0) [cnf transformation 38]
75. ~wise(X0) | ~wise(X0) [cnf transformation 26]
80. ~strong(X0) | ~patient(X0) [cnf transformation 42]
89. strong(X0) | funny(X0) | brave(X0) [cnf transformation 46]
96. wise(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 48]
98. ~kind(X0) | calm(X0) | ~generous(X0) | ~funny(X0) [cnf transformation 49]
116. kind(lucy) [cnf transformation 22]
117. old(lucy) [cnf transformation 22]
118. strong(lucy) [cnf transformation 23]
119. wise(X0) | ~brave(X0) [duplicate literal removal 96]
120. ~wise(X0) [duplicate literal removal 75]
137. ~brave(X0) [subsumption resolution 119,120]
177. ~patient(lucy) [resolution 80,118]
191. 12 <=> calm(lucy) [avatar definition]
193. ~calm(lucy) <- (~12) [avatar component clause 191]
204. ~calm(lucy) | wise(lucy) [resolution 68,117]
206. ~calm(lucy) [subsumption resolution 204,120]
207. ~12 [avatar split clause 206,191]
231. funny(X3) | brave(X3) | ~patient(X3) [resolution 89,80]
233. funny(X3) | ~patient(X3) [subsumption resolution 231,137]
234. funny(X3) [subsumption resolution 233,63]
243. 18 <=> generous(lucy) [avatar definition]
244. generous(lucy) <- (18) [avatar component clause 243]
245. ~generous(lucy) <- (~18) [avatar component clause 243]
247. patient(lucy) <- (~18) [resolution 245,65]
248. $false <- (~18) [subsumption resolution 247,177]
249. 18 [avatar contradiction clause 248]
285. calm(lucy) | ~generous(lucy) | ~funny(lucy) [resolution 98,116]
286. ~generous(lucy) | ~funny(lucy) <- (~12) [subsumption resolution 285,193]
287. ~funny(lucy) <- (~12, 18) [subsumption resolution 286,244]
288. $false <- (~12, 18) [subsumption resolution 287,234]
289. 12 | ~18 [avatar contradiction clause 288]
290. $false [avatar sat refutation 207,249,289]
% SZS output end Proof for 2382179173892334681551
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is brave then lucy is rich. If someone is either not funny or wise then someone is not brave and vice versa. Everyone who is not old is not wise or strong. Everyone who is generous is not creative or strong and vice versa. If susan is both not patient and not creative then someone is either not strong or creative and vice versa. Everyone who is both funny and rich is either not creative or curious and vice versa. Everyone who is either not curious or curious is both not happy and not generous. Everyone who is either kind or not wise is old and vice versa. If someone is patient then someone is calm and vice versa. Everyone who is not wise or not curious is quiet. If mary is not funny then someone is either creative or not patient and vice versa. If lucy is both generous and tall then someone is curious or not kind. If someone is funny then susan is either not happy or strong and vice versa. Everyone who is kind or calm is either not happy or brave and vice versa. If someone is both not brave and quiet then someone is kind or brave and vice versa. Everyone who is both kind and not happy is kind or patient and vice versa. Mary is not calm. Someone is either not funny or not quiet. Mary is both not generous and not wise. John is both wise and not calm. Someone is either creative or not patient. Someone is not quiet. Mary is either not brave or quiet. | Mary is old. | entailment | ((brave(mary))=>(rich(lucy)))&
((?[X]:((~funny(X)<~>wise(X))))<=>(?[X]:(~brave(X))))&
(![X]:(~old(X)=>(~wise(X)|strong(X))))&
(![X]:(generous(X)<=>(~creative(X)|strong(X))))&
(((~patient(susan)&~creative(susan)))<=>(?[X]:((~strong(X)<~>creative(X)))))&
(![X]:((funny(X)&rich(X))<=>(~creative(X)<~>curious(X))))&
(![X]:((~curious(X)<~>curious(X))=>(~happy(X)&~generous(X))))&
(![X]:((kind(X)<~>~wise(X))<=>old(X)))&
((?[X]:(patient(X)))<=>(?[X]:(calm(X))))&
(![X]:((~wise(X)|~curious(X))=>quiet(X)))&
((~funny(mary))<=>(?[X]:((creative(X)<~>~patient(X)))))&
(((generous(lucy)&tall(lucy)))=>(?[X]:((curious(X)|~kind(X)))))&
((?[X]:(funny(X)))<=>((~happy(susan)<~>strong(susan))))&
(![X]:((kind(X)|calm(X))<=>(~happy(X)<~>brave(X))))&
((?[X]:((~brave(X)&quiet(X))))<=>(?[X]:((kind(X)|brave(X)))))&
(![X]:((kind(X)&~happy(X))<=>(kind(X)|patient(X))))&
(~calm(mary))&
(?[X]:((~funny(X)<~>~quiet(X))))&
((~generous(mary)&~wise(mary)))&
((wise(john)&~calm(john)))&
(?[X]:((creative(X)<~>~patient(X))))&
(?[X]:(~quiet(X)))&
((~brave(mary)<~>quiet(mary))) | old(mary) | [
"p6",
"p7",
"p9",
"p13",
"p18",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 437431547904698134585842
% SZS output start Proof for 437431547904698134585842
7. ! [X0] : ((~curious(X0) <~> curious(X0)) => (~generous(X0) & ~happy(X0))) [input p6]
8. ! [X0] : ((kind(X0) <~> ~wise(X0)) <=> old(X0)) [input p7]
10. ! [X0] : ((~curious(X0) | ~wise(X0)) => quiet(X0)) [input p9]
14. ! [X0] : ((calm(X0) | kind(X0)) <=> (~happy(X0) <~> brave(X0))) [input p13]
19. ~wise(mary) & ~generous(mary) [input p18]
23. ~brave(mary) <~> quiet(mary) [input p22]
24. ~old(mary) [input hypothesis]
34. ! [X0] : ((~generous(X0) & ~happy(X0)) | (~curious(X0) <=> curious(X0))) [ennf transformation 7]
35. ! [X0] : (quiet(X0) | (curious(X0) & wise(X0))) [ennf transformation 10]
48. ! [X0] : ((~generous(X0) & ~happy(X0)) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0)))) [nnf transformation 34]
49. ! [X0] : ((((wise(X0) | ~kind(X0)) & (~wise(X0) | kind(X0))) | ~old(X0)) & (old(X0) | ((kind(X0) | wise(X0)) & (~wise(X0) | ~kind(X0))))) [nnf transformation 8]
63. ! [X0] : (((calm(X0) | kind(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) & (((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~calm(X0) & ~kind(X0)))) [nnf transformation 14]
64. ! [X0] : ((calm(X0) | kind(X0) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) & (((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~calm(X0) & ~kind(X0)))) [flattening 63]
80. (~quiet(mary) | brave(mary)) & (quiet(mary) | ~brave(mary)) [nnf transformation 23]
101. ~happy(X0) | curious(X0) | curious(X0) [cnf transformation 48]
102. ~happy(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 48]
106. kind(X0) | old(X0) | wise(X0) [cnf transformation 49]
111. quiet(X0) | wise(X0) [cnf transformation 35]
123. ~brave(X0) | happy(X0) | ~kind(X0) [cnf transformation 64]
141. ~wise(mary) [cnf transformation 19]
148. ~quiet(mary) | brave(mary) [cnf transformation 80]
149. ~old(mary) [cnf transformation 24]
150. ~happy(X0) | curious(X0) [duplicate literal removal 101]
151. ~happy(X0) | ~curious(X0) [duplicate literal removal 102]
155. 1 <=> brave(mary) [avatar definition]
156. brave(mary) <- (1) [avatar component clause 155]
217. ~happy(X0) [subsumption resolution 150,151]
273. ~kind(X0) | ~brave(X0) [subsumption resolution 123,217]
325. 38 <=> quiet(mary) [avatar definition]
327. ~quiet(mary) <- (~38) [avatar component clause 325]
328. 1 | ~38 [avatar split clause 148,325,155]
350. wise(mary) <- (~38) [resolution 111,327]
351. $false <- (~38) [subsumption resolution 350,141]
352. 38 [avatar contradiction clause 351]
486. ~brave(X1) | wise(X1) | old(X1) [resolution 106,273]
527. wise(mary) | old(mary) <- (1) [resolution 486,156]
528. old(mary) <- (1) [subsumption resolution 527,141]
529. $false <- (1) [subsumption resolution 528,149]
530. ~1 [avatar contradiction clause 529]
531. $false [avatar sat refutation 328,352,530]
% SZS output end Proof for 437431547904698134585842
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not funny is humble or not kind and vice versa.
Everyone who is funny or calm is both not rich and strong and vice versa.
Everyone who is either generous or not strong is not wise or old and vice versa.
If someone is humble or not rich then susan is both generous and not tall and vice versa.
If paul is not old then someone is not old or tall and vice versa.
Everyone who is either rich or curious is strong or generous.
Everyone who is quiet is either not wise or not creative.
Everyone who is both generous and old is humble or wise.
If someone is both not wise and not brave then someone is either not humble or not quiet.
Everyone who is happy or not happy is both not humble and kind.
Everyone who is both not funny and quiet is curious or strong and vice versa.
If someone is either generous or not quiet then paul is both not generous and not quiet and vice versa.
If someone is both humble and not creative then someone is not old or not humble.
Everyone who is either not humble or not kind is both not wise and not patient and vice versa.
Everyone who is not kind or curious is either humble or not brave and vice versa.
Lucy is curious or humble.
Susan is either not wise or not rich.
Someone is brave or quiet.
Someone is not tall or generous.
Mary is humble or not patient.
Mary is not humble or not old. | Mary is not curious. | contradiction | (![X]:((generous(X)&~funny(X))<=>(humble(X)|~kind(X))))&
(![X]:((funny(X)|calm(X))<=>(~rich(X)&strong(X))))&
(![X]:((generous(X)<~>~strong(X))<=>(~wise(X)|old(X))))&
((?[X]:((humble(X)|~rich(X))))<=>((generous(susan)&~tall(susan))))&
((~old(paul))<=>(?[X]:((~old(X)|tall(X)))))&
(![X]:((rich(X)<~>curious(X))=>(strong(X)|generous(X))))&
(![X]:(quiet(X)=>(~wise(X)<~>~creative(X))))&
(![X]:((generous(X)&old(X))=>(humble(X)|wise(X))))&
((?[X]:((~wise(X)&~brave(X))))=>(?[X]:((~humble(X)<~>~quiet(X)))))&
(![X]:((happy(X)|~happy(X))=>(~humble(X)&kind(X))))&
(![X]:((~funny(X)&quiet(X))<=>(curious(X)|strong(X))))&
((?[X]:((generous(X)<~>~quiet(X))))<=>((~generous(paul)&~quiet(paul))))&
((?[X]:((humble(X)&~creative(X))))=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:((~humble(X)<~>~kind(X))<=>(~wise(X)&~patient(X))))&
(![X]:((~kind(X)|curious(X))<=>(humble(X)<~>~brave(X))))&
((curious(lucy)|humble(lucy)))&
((~wise(susan)<~>~rich(susan)))&
(?[X]:((brave(X)|quiet(X))))&
(?[X]:((~tall(X)|generous(X))))&
((humble(mary)|~patient(mary)))&
((~humble(mary)|~old(mary))) | ~curious(mary) | [
"p0",
"p1",
"p2",
"p3",
"p5",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5964697668606572359496248
% SZS output start Proof for 5964697668606572359496248
1. ! [X0] : ((~funny(X0) & generous(X0)) <=> (~kind(X0) | humble(X0))) [input p0]
2. ! [X0] : ((calm(X0) | funny(X0)) <=> (strong(X0) & ~rich(X0))) [input p1]
3. ! [X0] : ((generous(X0) <~> ~strong(X0)) <=> (old(X0) | ~wise(X0))) [input p2]
4. ? [X0] : (~rich(X0) | humble(X0)) <=> (~tall(susan) & generous(susan)) [input p3]
6. ! [X0] : ((rich(X0) <~> curious(X0)) => (generous(X0) | strong(X0))) [input p5]
10. ! [X0] : ((~happy(X0) | happy(X0)) => (kind(X0) & ~humble(X0))) [input p9]
11. ! [X0] : ((quiet(X0) & ~funny(X0)) <=> (strong(X0) | curious(X0))) [input p10]
14. ! [X0] : ((~humble(X0) <~> ~kind(X0)) <=> (~patient(X0) & ~wise(X0))) [input p13]
22. ~curious(mary) [input hypothesis]
25. ! [X0] : ((generous(X0) | strong(X0)) | (rich(X0) <=> curious(X0))) [ennf transformation 6]
26. ! [X0] : (generous(X0) | strong(X0) | (rich(X0) <=> curious(X0))) [flattening 25]
31. ! [X0] : ((kind(X0) & ~humble(X0)) | (happy(X0) & ~happy(X0))) [ennf transformation 10]
33. ! [X0] : (((~funny(X0) & generous(X0)) | (kind(X0) & ~humble(X0))) & ((~kind(X0) | humble(X0)) | (funny(X0) | ~generous(X0)))) [nnf transformation 1]
34. ! [X0] : (((~funny(X0) & generous(X0)) | (kind(X0) & ~humble(X0))) & (~kind(X0) | humble(X0) | funny(X0) | ~generous(X0))) [flattening 33]
35. ! [X0] : (((calm(X0) | funny(X0)) | (~strong(X0) | rich(X0))) & ((strong(X0) & ~rich(X0)) | (~calm(X0) & ~funny(X0)))) [nnf transformation 2]
36. ! [X0] : ((calm(X0) | funny(X0) | ~strong(X0) | rich(X0)) & ((strong(X0) & ~rich(X0)) | (~calm(X0) & ~funny(X0)))) [flattening 35]
37. ! [X0] : ((((strong(X0) | ~generous(X0)) & (~strong(X0) | generous(X0))) | (~old(X0) & wise(X0))) & ((old(X0) | ~wise(X0)) | ((generous(X0) | strong(X0)) & (~strong(X0) | ~generous(X0))))) [nnf transformation 3]
38. ! [X0] : ((((strong(X0) | ~generous(X0)) & (~strong(X0) | generous(X0))) | (~old(X0) & wise(X0))) & (old(X0) | ~wise(X0) | ((generous(X0) | strong(X0)) & (~strong(X0) | ~generous(X0))))) [flattening 37]
39. (? [X0] : (~rich(X0) | humble(X0)) | (tall(susan) | ~generous(susan))) & ((~tall(susan) & generous(susan)) | ! [X0] : (rich(X0) & ~humble(X0))) [nnf transformation 4]
40. (? [X0] : (~rich(X0) | humble(X0)) | tall(susan) | ~generous(susan)) & ((~tall(susan) & generous(susan)) | ! [X0] : (rich(X0) & ~humble(X0))) [flattening 39]
41. (? [X0] : (~rich(X0) | humble(X0)) | tall(susan) | ~generous(susan)) & ((~tall(susan) & generous(susan)) | ! [X1] : (rich(X1) & ~humble(X1))) [rectify 40]
42. ? [X0] : (~rich(X0) | humble(X0)) => (~rich(sK0) | humble(sK0)) [choice axiom]
43. ((~rich(sK0) | humble(sK0)) | tall(susan) | ~generous(susan)) & ((~tall(susan) & generous(susan)) | ! [X1] : (rich(X1) & ~humble(X1))) [skolemisation 41,42]
48. ! [X0] : (generous(X0) | strong(X0) | ((rich(X0) | ~curious(X0)) & (curious(X0) | ~rich(X0)))) [nnf transformation 26]
54. ! [X0] : (((quiet(X0) & ~funny(X0)) | (~strong(X0) & ~curious(X0))) & ((strong(X0) | curious(X0)) | (~quiet(X0) | funny(X0)))) [nnf transformation 11]
55. ! [X0] : (((quiet(X0) & ~funny(X0)) | (~strong(X0) & ~curious(X0))) & (strong(X0) | curious(X0) | ~quiet(X0) | funny(X0))) [flattening 54]
64. ! [X0] : ((((kind(X0) | humble(X0)) & (~kind(X0) | ~humble(X0))) | (patient(X0) | wise(X0))) & ((~patient(X0) & ~wise(X0)) | ((~humble(X0) | kind(X0)) & (~kind(X0) | humble(X0))))) [nnf transformation 14]
65. ! [X0] : ((((kind(X0) | humble(X0)) & (~kind(X0) | ~humble(X0))) | patient(X0) | wise(X0)) & ((~patient(X0) & ~wise(X0)) | ((~humble(X0) | kind(X0)) & (~kind(X0) | humble(X0))))) [flattening 64]
73. ~kind(X0) | humble(X0) | funny(X0) | ~generous(X0) [cnf transformation 34]
80. ~funny(X0) | strong(X0) [cnf transformation 36]
85. ~strong(X0) | generous(X0) | wise(X0) [cnf transformation 38]
90. generous(susan) | rich(X1) [cnf transformation 43]
97. ~rich(X0) | strong(X0) | curious(X0) | generous(X0) [cnf transformation 48]
104. ~humble(X0) | ~happy(X0) [cnf transformation 31]
105. ~humble(X0) | happy(X0) [cnf transformation 31]
106. kind(X0) | ~happy(X0) [cnf transformation 31]
107. happy(X0) | kind(X0) [cnf transformation 31]
110. ~funny(X0) | ~strong(X0) [cnf transformation 55]
120. ~wise(X0) | ~kind(X0) | humble(X0) [cnf transformation 65]
139. ~curious(mary) [cnf transformation 22]
141. 1 <=> generous(susan) [avatar definition]
142. generous(susan) <- (1) [avatar component clause 141]
158. 5 <=> ! [X1] : rich(X1) [avatar definition]
159. rich(X1) <- (5) [avatar component clause 158]
162. 6 <=> ! [X1] : ~humble(X1) [avatar definition]
163. ~humble(X1) <- (6) [avatar component clause 162]
165. 5 | 1 [avatar split clause 90,141,158]
201. kind(X0) [subsumption resolution 106,107]
202. ~humble(X0) [subsumption resolution 104,105]
203. 6 [avatar split clause 202,162]
204. ~funny(X0) [subsumption resolution 110,80]
248. ~wise(X0) | humble(X0) [subsumption resolution 120,201]
372. humble(X1) | funny(X1) | ~generous(X1) [resolution 73,201]
373. funny(X1) | ~generous(X1) <- (6) [subsumption resolution 372,163]
374. ~generous(X1) <- (6) [subsumption resolution 373,204]
380. strong(X0) | curious(X0) | generous(X0) <- (5) [resolution 97,159]
381. curious(X0) | strong(X0) <- (5, 6) [subsumption resolution 380,374]
385. strong(mary) <- (5, 6) [resolution 381,139]
393. generous(mary) | wise(mary) <- (5, 6) [resolution 385,85]
395. wise(mary) <- (5, 6) [subsumption resolution 393,374]
408. humble(mary) <- (5, 6) [resolution 395,248]
409. $false <- (5, 6) [subsumption resolution 408,163]
410. ~5 | ~6 [avatar contradiction clause 409]
424. $false <- (1, 6) [subsumption resolution 142,374]
425. ~1 | ~6 [avatar contradiction clause 424]
426. $false [avatar sat refutation 165,203,410,425]
% SZS output end Proof for 5964697668606572359496248
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is both strong and tall and vice versa.
If someone is rich then alice is either not quiet or not curious and vice versa.
If mary is both not brave and not curious then alice is calm or brave.
If someone is not generous then someone is not happy or calm and vice versa.
If john is happy then susan is generous and vice versa.
If someone is either patient or kind then someone is kind or not kind and vice versa.
Everyone who is both not rich and rich is old or tall.
Everyone who is not funny is both curious and not patient and vice versa.
Everyone who is not humble or patient is wise and vice versa.
Everyone who is not kind is both wise and patient and vice versa.
Everyone who is not funny is either not brave or brave and vice versa.
If someone is both kind and wise then fred is both not humble and not wise.
If someone is both not rich and generous then someone is happy or old and vice versa.
If someone is not old then alice is not kind or quiet and vice versa.
Everyone who is funny is both humble and creative.
Everyone who is kind is not quiet and vice versa.
Lucy is not tall or not strong.
Susan is both humble and creative.
Susan is creative or not calm.
Alice is both not rich and not happy.
Someone is creative or not old.
Someone is not rich or wise. | John is not old. | contradiction | (![X]:(~kind(X)<=>(strong(X)&tall(X))))&
((?[X]:(rich(X)))<=>((~quiet(alice)<~>~curious(alice))))&
(((~brave(mary)&~curious(mary)))=>((calm(alice)|brave(alice))))&
((?[X]:(~generous(X)))<=>(?[X]:((~happy(X)|calm(X)))))&
((happy(john))<=>(generous(susan)))&
((?[X]:((patient(X)<~>kind(X))))<=>(?[X]:((kind(X)|~kind(X)))))&
(![X]:((~rich(X)&rich(X))=>(old(X)|tall(X))))&
(![X]:(~funny(X)<=>(curious(X)&~patient(X))))&
(![X]:((~humble(X)|patient(X))<=>wise(X)))&
(![X]:(~kind(X)<=>(wise(X)&patient(X))))&
(![X]:(~funny(X)<=>(~brave(X)<~>brave(X))))&
((?[X]:((kind(X)&wise(X))))=>((~humble(fred)&~wise(fred))))&
((?[X]:((~rich(X)&generous(X))))<=>(?[X]:((happy(X)|old(X)))))&
((?[X]:(~old(X)))<=>((~kind(alice)|quiet(alice))))&
(![X]:(funny(X)=>(humble(X)&creative(X))))&
(![X]:(kind(X)<=>~quiet(X)))&
((~tall(lucy)|~strong(lucy)))&
((humble(susan)&creative(susan)))&
((creative(susan)|~calm(susan)))&
((~rich(alice)&~happy(alice)))&
(?[X]:((creative(X)|~old(X))))&
(?[X]:((~rich(X)|wise(X)))) | ~old(john) | [
"p7",
"p9",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 14851699260792032872045
% SZS output start Proof for 14851699260792032872045
8. ! [X0] : (~funny(X0) <=> (~patient(X0) & curious(X0))) [input p7]
10. ! [X0] : (~kind(X0) <=> (patient(X0) & wise(X0))) [input p9]
11. ! [X0] : (~funny(X0) <=> (~brave(X0) <~> brave(X0))) [input p10]
14. ? [X0] : ~old(X0) <=> (quiet(alice) | ~kind(alice)) [input p13]
16. ! [X0] : (kind(X0) <=> ~quiet(X0)) [input p15]
23. ~old(john) [input hypothesis]
54. ! [X0] : ((~funny(X0) | (patient(X0) | ~curious(X0))) & ((~patient(X0) & curious(X0)) | funny(X0))) [nnf transformation 8]
55. ! [X0] : ((~funny(X0) | patient(X0) | ~curious(X0)) & ((~patient(X0) & curious(X0)) | funny(X0))) [flattening 54]
58. ! [X0] : ((~kind(X0) | (~patient(X0) | ~wise(X0))) & ((patient(X0) & wise(X0)) | kind(X0))) [nnf transformation 10]
59. ! [X0] : ((~kind(X0) | ~patient(X0) | ~wise(X0)) & ((patient(X0) & wise(X0)) | kind(X0))) [flattening 58]
60. ! [X0] : ((~funny(X0) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) & (((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | funny(X0))) [nnf transformation 11]
66. (? [X0] : ~old(X0) | (~quiet(alice) & kind(alice))) & ((quiet(alice) | ~kind(alice)) | ! [X0] : old(X0)) [nnf transformation 14]
67. (? [X0] : ~old(X0) | (~quiet(alice) & kind(alice))) & (quiet(alice) | ~kind(alice) | ! [X0] : old(X0)) [flattening 66]
68. (? [X0] : ~old(X0) | (~quiet(alice) & kind(alice))) & (quiet(alice) | ~kind(alice) | ! [X1] : old(X1)) [rectify 67]
69. ? [X0] : ~old(X0) => ~old(sK7) [choice axiom]
70. (~old(sK7) | (~quiet(alice) & kind(alice))) & (quiet(alice) | ~kind(alice) | ! [X1] : old(X1)) [skolemisation 68,69]
71. ! [X0] : ((kind(X0) | quiet(X0)) & (~quiet(X0) | ~kind(X0))) [nnf transformation 16]
95. ~patient(X0) | funny(X0) [cnf transformation 55]
101. patient(X0) | kind(X0) [cnf transformation 59]
105. ~funny(X0) | brave(X0) | brave(X0) [cnf transformation 60]
106. ~funny(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 60]
114. quiet(alice) | ~kind(alice) | old(X1) [cnf transformation 70]
118. ~quiet(X0) | ~kind(X0) [cnf transformation 71]
125. ~old(john) [cnf transformation 23]
126. ~funny(X0) | brave(X0) [duplicate literal removal 105]
127. ~funny(X0) | ~brave(X0) [duplicate literal removal 106]
133. 2 <=> quiet(alice) [avatar definition]
134. quiet(alice) <- (2) [avatar component clause 133]
199. 17 <=> ! [X1] : kind(X1) [avatar definition]
200. kind(X1) <- (17) [avatar component clause 199]
217. ~funny(X0) [subsumption resolution 126,127]
267. 32 <=> kind(alice) [avatar definition]
268. ~kind(alice) <- (~32) [avatar component clause 267]
272. 33 <=> ! [X1] : old(X1) [avatar definition]
273. old(X1) <- (33) [avatar component clause 272]
274. 33 | ~32 | 2 [avatar split clause 114,133,267,272]
304. kind(X1) | funny(X1) [resolution 101,95]
306. kind(X1) [subsumption resolution 304,217]
307. 17 [avatar split clause 306,199]
308. $false <- (17, ~32) [resolution 200,268]
309. ~17 | 32 [avatar contradiction clause 308]
310. $false <- (33) [resolution 273,125]
313. ~33 [avatar contradiction clause 310]
316. ~kind(alice) <- (2) [resolution 118,134]
317. $false <- (2, 17) [subsumption resolution 316,200]
318. ~2 | ~17 [avatar contradiction clause 317]
319. $false [avatar sat refutation 274,307,309,313,318]
% SZS output end Proof for 14851699260792032872045
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or brave then someone is strong and vice versa. Everyone who is funny or wise is quiet and vice versa. If alice is not curious or kind then susan is both not wise and quiet and vice versa. If mary is not strong then someone is not old and vice versa. Everyone who is not old is quiet and vice versa. If alice is either generous or not strong then lucy is both not calm and patient and vice versa. Everyone who is not patient is generous. If someone is not wise then mary is either wise or not kind. If fred is creative then someone is not quiet or not creative. If john is both quiet and not creative then susan is generous or not humble and vice versa. Everyone who is both strong and tall is not kind or not humble and vice versa. Everyone who is either not kind or not tall is both not wise and not quiet. If someone is both not funny and patient then someone is both calm and humble. Everyone who is both funny and generous is both strong and curious. If john is kind then mary is both not patient and not kind. Everyone who is not generous or curious is not strong or calm and vice versa. John is not calm. Fred is happy. John is not generous. Someone is not wise. Someone is either generous or kind. John is not quiet or humble. | Susan is quiet. | contradiction | ((?[X]:((tall(X)|brave(X))))<=>(?[X]:(strong(X))))&
(![X]:((funny(X)|wise(X))<=>quiet(X)))&
(((~curious(alice)|kind(alice)))<=>((~wise(susan)&quiet(susan))))&
((~strong(mary))<=>(?[X]:(~old(X))))&
(![X]:(~old(X)<=>quiet(X)))&
(((generous(alice)<~>~strong(alice)))<=>((~calm(lucy)&patient(lucy))))&
(![X]:(~patient(X)=>generous(X)))&
((?[X]:(~wise(X)))=>((wise(mary)<~>~kind(mary))))&
((creative(fred))=>(?[X]:((~quiet(X)|~creative(X)))))&
(((quiet(john)&~creative(john)))<=>((generous(susan)|~humble(susan))))&
(![X]:((strong(X)&tall(X))<=>(~kind(X)|~humble(X))))&
(![X]:((~kind(X)<~>~tall(X))=>(~wise(X)&~quiet(X))))&
((?[X]:((~funny(X)&patient(X))))=>(?[X]:((calm(X)&humble(X)))))&
(![X]:((funny(X)&generous(X))=>(strong(X)&curious(X))))&
((kind(john))=>((~patient(mary)&~kind(mary))))&
(![X]:((~generous(X)|curious(X))<=>(~strong(X)|calm(X))))&
(~calm(john))&
(happy(fred))&
(~generous(john))&
(?[X]:(~wise(X)))&
(?[X]:((generous(X)<~>kind(X))))&
((~quiet(john)|humble(john))) | quiet(susan) | [
"p3",
"p4",
"p10",
"p14",
"p15",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 698634452256691277622396
% SZS output start Proof for 698634452256691277622396
4. ~strong(mary) <=> ? [X0] : ~old(X0) [input p3]
5. ! [X0] : (~old(X0) <=> quiet(X0)) [input p4]
11. ! [X0] : ((tall(X0) & strong(X0)) <=> (~humble(X0) | ~kind(X0))) [input p10]
15. kind(john) => (~kind(mary) & ~patient(mary)) [input p14]
16. ! [X0] : ((curious(X0) | ~generous(X0)) <=> (calm(X0) | ~strong(X0))) [input p15]
17. ~calm(john) [input p16]
19. ~generous(john) [input p18]
23. quiet(susan) [input hypothesis]
34. (~kind(mary) & ~patient(mary)) | ~kind(john) [ennf transformation 15]
44. (~strong(mary) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | strong(mary)) [nnf transformation 4]
45. (~strong(mary) | ! [X0] : old(X0)) & (? [X1] : ~old(X1) | strong(mary)) [rectify 44]
46. ? [X1] : ~old(X1) => ~old(sK2) [choice axiom]
47. (~strong(mary) | ! [X0] : old(X0)) & (~old(sK2) | strong(mary)) [skolemisation 45,46]
48. ! [X0] : ((~old(X0) | ~quiet(X0)) & (quiet(X0) | old(X0))) [nnf transformation 5]
56. ! [X0] : (((tall(X0) & strong(X0)) | (humble(X0) & kind(X0))) & ((~humble(X0) | ~kind(X0)) | (~tall(X0) | ~strong(X0)))) [nnf transformation 11]
57. ! [X0] : (((tall(X0) & strong(X0)) | (humble(X0) & kind(X0))) & (~humble(X0) | ~kind(X0) | ~tall(X0) | ~strong(X0))) [flattening 56]
62. ! [X0] : (((curious(X0) | ~generous(X0)) | (~calm(X0) & strong(X0))) & ((calm(X0) | ~strong(X0)) | (~curious(X0) & generous(X0)))) [nnf transformation 16]
63. ! [X0] : ((curious(X0) | ~generous(X0) | (~calm(X0) & strong(X0))) & (calm(X0) | ~strong(X0) | (~curious(X0) & generous(X0)))) [flattening 62]
81. ~strong(mary) | old(X0) [cnf transformation 47]
83. ~old(X0) | ~quiet(X0) [cnf transformation 48]
100. kind(X0) | strong(X0) [cnf transformation 57]
113. ~kind(mary) | ~kind(john) [cnf transformation 34]
114. ~strong(X0) | calm(X0) | generous(X0) [cnf transformation 63]
118. ~calm(john) [cnf transformation 17]
119. ~generous(john) [cnf transformation 19]
124. quiet(susan) [cnf transformation 23]
154. 8 <=> quiet(susan) [avatar definition]
155. quiet(susan) <- (8) [avatar component clause 154]
171. 11 <=> ! [X0] : old(X0) [avatar definition]
172. old(X0) <- (11) [avatar component clause 171]
174. 12 <=> strong(mary) [avatar definition]
177. 11 | ~12 [avatar split clause 81,174,171]
213. 20 <=> kind(mary) [avatar definition]
214. ~kind(mary) <- (~20) [avatar component clause 213]
270. 31 <=> kind(john) [avatar definition]
272. ~kind(john) <- (~31) [avatar component clause 270]
273. ~31 | ~20 [avatar split clause 113,213,270]
294. 8 [avatar split clause 124,154]
297. strong(mary) <- (~20) [resolution 100,214]
298. strong(john) <- (~31) [resolution 100,272]
302. 12 | 20 [avatar split clause 297,213,174]
304. ~quiet(X0) <- (11) [resolution 172,83]
309. $false <- (8, 11) [resolution 304,155]
310. ~8 | ~11 [avatar contradiction clause 309]
356. calm(john) | generous(john) <- (~31) [resolution 114,298]
359. generous(john) <- (~31) [subsumption resolution 356,118]
360. $false <- (~31) [subsumption resolution 359,119]
361. 31 [avatar contradiction clause 360]
371. $false [avatar sat refutation 177,273,294,302,310,361]
% SZS output end Proof for 698634452256691277622396
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or not creative is both not old and not tall.
If susan is not quiet then someone is brave or not humble.
If someone is both funny and not curious then mary is either patient or tall.
Everyone who is old is not patient or tall and vice versa.
Everyone who is happy is not generous and vice versa.
Everyone who is either not old or not rich is either not wise or wise.
Everyone who is rich is either not creative or not patient.
If someone is both tall and not patient then susan is either not tall or patient.
If someone is not kind or not happy then someone is humble.
If someone is not strong then susan is both not tall and not humble and vice versa.
Everyone who is both not quiet and quiet is both not quiet and not generous and vice versa.
If alice is either not generous or not wise then lucy is both not rich and funny.
Everyone who is not quiet or not old is not strong and vice versa.
Everyone who is not brave or not curious is brave or not humble.
If fred is either strong or not rich then someone is not strong or not creative.
Mary is either old or quiet.
Susan is both not creative and calm.
Fred is strong or not kind.
Alice is tall.
John is either calm or generous.
Someone is both wise and not old.
Lucy is either not wise or rich.
Fred is strong or not funny. | Susan is curious. | neutral | (![X]:((~happy(X)|~creative(X))=>(~old(X)&~tall(X))))&
((~quiet(susan))=>(?[X]:((brave(X)|~humble(X)))))&
((?[X]:((funny(X)&~curious(X))))=>((patient(mary)<~>tall(mary))))&
(![X]:(old(X)<=>(~patient(X)|tall(X))))&
(![X]:(happy(X)<=>~generous(X)))&
(![X]:((~old(X)<~>~rich(X))=>(~wise(X)<~>wise(X))))&
(![X]:(rich(X)=>(~creative(X)<~>~patient(X))))&
((?[X]:((tall(X)&~patient(X))))=>((~tall(susan)<~>patient(susan))))&
((?[X]:((~kind(X)|~happy(X))))=>(?[X]:(humble(X))))&
((?[X]:(~strong(X)))<=>((~tall(susan)&~humble(susan))))&
(![X]:((~quiet(X)&quiet(X))<=>(~quiet(X)&~generous(X))))&
(((~generous(alice)<~>~wise(alice)))=>((~rich(lucy)&funny(lucy))))&
(![X]:((~quiet(X)|~old(X))<=>~strong(X)))&
(![X]:((~brave(X)|~curious(X))=>(brave(X)|~humble(X))))&
(((strong(fred)<~>~rich(fred)))=>(?[X]:((~strong(X)|~creative(X)))))&
((old(mary)<~>quiet(mary)))&
((~creative(susan)&calm(susan)))&
((strong(fred)|~kind(fred)))&
(tall(alice))&
((calm(john)<~>generous(john)))&
(?[X]:((wise(X)&~old(X))))&
((~wise(lucy)<~>rich(lucy)))&
((strong(fred)|~funny(fred))) | curious(susan) | [] | null | 0 |
Everyone who is not strong or not brave is either tall or not quiet.
Everyone who is not wise or not funny is generous or not quiet and vice versa.
Everyone who is generous is not wise.
Everyone who is either funny or not tall is kind or curious.
Everyone who is funny or strong is brave.
Everyone who is not patient is calm or not calm.
Everyone who is not strong or not tall is rich or creative and vice versa.
Everyone who is not kind is both wise and generous and vice versa.
If mary is not kind or calm then someone is either not humble or tall.
Everyone who is either old or generous is either not calm or not creative and vice versa.
Everyone who is not patient or patient is both tall and not humble and vice versa.
Everyone who is not tall or kind is not happy and vice versa.
Everyone who is not curious or happy is both strong and not tall.
If someone is brave then someone is both humble and not old.
Everyone who is not rich is not calm.
Everyone who is both not wise and not quiet is either not brave or not kind.
Susan is not brave.
Susan is either not generous or quiet.
John is calm or not wise.
Lucy is not quiet or kind.
Someone is calm.
Someone is both not old and not happy. | Lucy is calm. | neutral | (![X]:((~strong(X)|~brave(X))=>(tall(X)<~>~quiet(X))))&
(![X]:((~wise(X)|~funny(X))<=>(generous(X)|~quiet(X))))&
(![X]:(generous(X)=>~wise(X)))&
(![X]:((funny(X)<~>~tall(X))=>(kind(X)|curious(X))))&
(![X]:((funny(X)|strong(X))=>brave(X)))&
(![X]:(~patient(X)=>(calm(X)|~calm(X))))&
(![X]:((~strong(X)|~tall(X))<=>(rich(X)|creative(X))))&
(![X]:(~kind(X)<=>(wise(X)&generous(X))))&
(((~kind(mary)|calm(mary)))=>(?[X]:((~humble(X)<~>tall(X)))))&
(![X]:((old(X)<~>generous(X))<=>(~calm(X)<~>~creative(X))))&
(![X]:((~patient(X)|patient(X))<=>(tall(X)&~humble(X))))&
(![X]:((~tall(X)|kind(X))<=>~happy(X)))&
(![X]:((~curious(X)|happy(X))=>(strong(X)&~tall(X))))&
((?[X]:(brave(X)))=>(?[X]:((humble(X)&~old(X)))))&
(![X]:(~rich(X)=>~calm(X)))&
(![X]:((~wise(X)&~quiet(X))=>(~brave(X)<~>~kind(X))))&
(~brave(susan))&
((~generous(susan)<~>quiet(susan)))&
((calm(john)|~wise(john)))&
((~quiet(lucy)|kind(lucy)))&
(?[X]:(calm(X)))&
(?[X]:((~old(X)&~happy(X)))) | calm(lucy) | [] | null | 0 |
Everyone who is not humble is not old.
If someone is curious or not strong then john is either creative or old and vice versa.
Everyone who is either old or not generous is either not tall or not quiet and vice versa.
Everyone who is both brave and rich is either not creative or not old.
Everyone who is not patient or not rich is not strong or not brave.
Everyone who is not tall or wise is not funny or quiet and vice versa.
Everyone who is humble or not wise is wise.
Everyone who is either not old or not calm is not curious.
If john is either patient or not tall then alice is generous or not quiet and vice versa.
If paul is both tall and humble then john is either brave or not rich and vice versa.
If someone is not happy or not old then someone is not strong or old and vice versa.
If someone is either not old or funny then paul is not creative or not tall.
If someone is either creative or funny then fred is either wise or not curious.
Everyone who is not tall or wise is either not humble or not old and vice versa.
If someone is not curious then someone is either strong or not creative and vice versa.
Everyone who is either humble or generous is both not humble and wise and vice versa.
Alice is either not patient or not tall.
John is both not curious and brave.
Susan is both tall and not funny.
Alice is either not curious or brave.
John is both strong and not funny.
Lucy is funny.
Someone is not strong. | Paul is creative. | contradiction | (![X]:(~humble(X)=>~old(X)))&
((?[X]:((curious(X)|~strong(X))))<=>((creative(john)<~>old(john))))&
(![X]:((old(X)<~>~generous(X))<=>(~tall(X)<~>~quiet(X))))&
(![X]:((brave(X)&rich(X))=>(~creative(X)<~>~old(X))))&
(![X]:((~patient(X)|~rich(X))=>(~strong(X)|~brave(X))))&
(![X]:((~tall(X)|wise(X))<=>(~funny(X)|quiet(X))))&
(![X]:((humble(X)|~wise(X))=>wise(X)))&
(![X]:((~old(X)<~>~calm(X))=>~curious(X)))&
(((patient(john)<~>~tall(john)))<=>((generous(alice)|~quiet(alice))))&
(((tall(paul)&humble(paul)))<=>((brave(john)<~>~rich(john))))&
((?[X]:((~happy(X)|~old(X))))<=>(?[X]:((~strong(X)|old(X)))))&
((?[X]:((~old(X)<~>funny(X))))=>((~creative(paul)|~tall(paul))))&
((?[X]:((creative(X)<~>funny(X))))=>((wise(fred)<~>~curious(fred))))&
(![X]:((~tall(X)|wise(X))<=>(~humble(X)<~>~old(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((strong(X)<~>~creative(X)))))&
(![X]:((humble(X)<~>generous(X))<=>(~humble(X)&wise(X))))&
((~patient(alice)<~>~tall(alice)))&
((~curious(john)&brave(john)))&
((tall(susan)&~funny(susan)))&
((~curious(alice)<~>brave(alice)))&
((strong(john)&~funny(john)))&
(funny(lucy))&
(?[X]:(~strong(X))) | creative(paul) | [
"p0",
"p4",
"p6",
"p9",
"p11",
"p13",
"p17",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1557741722267571689914572
% SZS output start Proof for 1557741722267571689914572
1. ! [X0] : (~humble(X0) => ~old(X0)) [input p0]
5. ! [X0] : ((~rich(X0) | ~patient(X0)) => (~brave(X0) | ~strong(X0))) [input p4]
7. ! [X0] : ((~wise(X0) | humble(X0)) => wise(X0)) [input p6]
10. (humble(paul) & tall(paul)) <=> (brave(john) <~> ~rich(john)) [input p9]
12. ? [X0] : (~old(X0) <~> funny(X0)) => (~tall(paul) | ~creative(paul)) [input p11]
14. ! [X0] : ((wise(X0) | ~tall(X0)) <=> (~humble(X0) <~> ~old(X0))) [input p13]
18. brave(john) & ~curious(john) [input p17]
19. ~funny(susan) & tall(susan) [input p18]
21. ~funny(john) & strong(john) [input p20]
24. creative(paul) [input hypothesis]
27. ! [X0] : (~old(X0) | humble(X0)) [ennf transformation 1]
30. ! [X0] : ((~brave(X0) | ~strong(X0)) | (rich(X0) & patient(X0))) [ennf transformation 5]
31. ! [X0] : (~brave(X0) | ~strong(X0) | (rich(X0) & patient(X0))) [flattening 30]
32. ! [X0] : (wise(X0) | (wise(X0) & ~humble(X0))) [ennf transformation 7]
34. (~tall(paul) | ~creative(paul)) | ! [X0] : (~old(X0) <=> funny(X0)) [ennf transformation 12]
35. ~tall(paul) | ~creative(paul) | ! [X0] : (~old(X0) <=> funny(X0)) [flattening 34]
48. ((humble(paul) & tall(paul)) | ((brave(john) | rich(john)) & (~rich(john) | ~brave(john)))) & (((rich(john) | ~brave(john)) & (~rich(john) | brave(john))) | (~humble(paul) | ~tall(paul))) [nnf transformation 10]
49. ((humble(paul) & tall(paul)) | ((brave(john) | rich(john)) & (~rich(john) | ~brave(john)))) & (((rich(john) | ~brave(john)) & (~rich(john) | brave(john))) | ~humble(paul) | ~tall(paul)) [flattening 48]
55. ~tall(paul) | ~creative(paul) | ! [X0] : ((~old(X0) | ~funny(X0)) & (funny(X0) | old(X0))) [nnf transformation 35]
57. ! [X0] : (((wise(X0) | ~tall(X0)) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0)))) & (((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | (~wise(X0) & tall(X0)))) [nnf transformation 14]
58. ! [X0] : ((wise(X0) | ~tall(X0) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0)))) & (((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | (~wise(X0) & tall(X0)))) [flattening 57]
70. ~old(X0) | humble(X0) [cnf transformation 27]
88. ~brave(X0) | ~strong(X0) | rich(X0) [cnf transformation 31]
94. wise(X0) | wise(X0) [cnf transformation 32]
105. tall(paul) | ~rich(john) | ~brave(john) [cnf transformation 49]
113. ~tall(paul) | ~creative(paul) | funny(X0) | old(X0) [cnf transformation 55]
120. ~old(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 58]
122. old(X0) | humble(X0) | ~wise(X0) [cnf transformation 58]
138. brave(john) [cnf transformation 18]
140. ~funny(susan) [cnf transformation 19]
143. strong(john) [cnf transformation 21]
147. creative(paul) [cnf transformation 24]
150. wise(X0) [duplicate literal removal 94]
202. 11 <=> rich(john) [avatar definition]
206. 12 <=> brave(john) [avatar definition]
208. brave(john) <- (12) [avatar component clause 206]
216. 14 <=> tall(paul) [avatar definition]
220. ~12 | ~11 | 14 [avatar split clause 105,216,202,206]
224. 15 <=> ! [X1] : ~old(X1) [avatar definition]
225. ~old(X1) <- (15) [avatar component clause 224]
256. 23 <=> creative(paul) [avatar definition]
261. 24 <=> ! [X0] : (funny(X0) | old(X0)) [avatar definition]
262. funny(X0) | old(X0) <- (24) [avatar component clause 261]
263. 24 | ~23 | ~14 [avatar split clause 113,216,256,261]
278. old(X0) | humble(X0) [subsumption resolution 122,150]
279. humble(X0) [subsumption resolution 278,70]
280. ~old(X0) | ~wise(X0) [subsumption resolution 120,279]
281. ~old(X0) [subsumption resolution 280,150]
282. 15 [avatar split clause 281,224]
320. 12 [avatar split clause 138,206]
331. 23 [avatar split clause 147,256]
339. ~strong(john) | rich(john) <- (12) [resolution 88,208]
340. rich(john) <- (12) [subsumption resolution 339,143]
343. 11 | ~12 [avatar split clause 340,206,202]
344. funny(X0) <- (15, 24) [subsumption resolution 262,225]
345. $false <- (15, 24) [resolution 344,140]
348. ~15 | ~24 [avatar contradiction clause 345]
349. $false [avatar sat refutation 220,263,282,320,331,343,348]
% SZS output end Proof for 1557741722267571689914572
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or happy is either not old or kind and vice versa. If someone is either curious or quiet then someone is quiet or generous and vice versa. Everyone who is either not kind or not calm is patient and vice versa. If alice is not happy or brave then someone is creative. If someone is both generous and quiet then someone is either not kind or calm and vice versa. Everyone who is not brave or old is both not funny and quiet. Everyone who is both patient and kind is generous and vice versa. Everyone who is either curious or patient is curious or not quiet and vice versa. Everyone who is wise is either calm or funny and vice versa. If someone is either brave or not old then lucy is strong. If john is both not strong and not curious then someone is both not generous and not tall. Everyone who is both quiet and curious is wise or happy and vice versa. If alice is either brave or not humble then someone is brave or not strong and vice versa. Lucy is either tall or not creative. Susan is patient or not tall. Someone is brave. Someone is not happy or not curious. Alice is either funny or wise. Someone is either not quiet or not funny. | Lucy is not generous. | entailment | (![X]:((humble(X)|happy(X))<=>(~old(X)<~>kind(X))))&
((?[X]:((curious(X)<~>quiet(X))))<=>(?[X]:((quiet(X)|generous(X)))))&
(![X]:((~kind(X)<~>~calm(X))<=>patient(X)))&
(((~happy(alice)|brave(alice)))=>(?[X]:(creative(X))))&
((?[X]:((generous(X)&quiet(X))))<=>(?[X]:((~kind(X)<~>calm(X)))))&
(![X]:((~brave(X)|old(X))=>(~funny(X)&quiet(X))))&
(![X]:((patient(X)&kind(X))<=>generous(X)))&
(![X]:((curious(X)<~>patient(X))<=>(curious(X)|~quiet(X))))&
(![X]:(wise(X)<=>(calm(X)<~>funny(X))))&
((?[X]:((brave(X)<~>~old(X))))=>(strong(lucy)))&
(((~strong(john)&~curious(john)))=>(?[X]:((~generous(X)&~tall(X)))))&
(![X]:((quiet(X)&curious(X))<=>(wise(X)|happy(X))))&
(((brave(alice)<~>~humble(alice)))<=>(?[X]:((brave(X)|~strong(X)))))&
((tall(lucy)<~>~creative(lucy)))&
((patient(susan)|~tall(susan)))&
(?[X]:(brave(X)))&
(?[X]:((~happy(X)|~curious(X))))&
((funny(alice)<~>wise(alice)))&
(?[X]:((~quiet(X)<~>~funny(X)))) | ~generous(lucy) | [
"p0",
"p1",
"p2",
"p4",
"p5",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 722691985672302901295369
% SZS output start Proof for 722691985672302901295369
1. ! [X0] : ((happy(X0) | humble(X0)) <=> (~old(X0) <~> kind(X0))) [input p0]
2. ? [X0] : (curious(X0) <~> quiet(X0)) <=> ? [X0] : (generous(X0) | quiet(X0)) [input p1]
3. ! [X0] : ((~kind(X0) <~> ~calm(X0)) <=> patient(X0)) [input p2]
5. ? [X0] : (quiet(X0) & generous(X0)) <=> ? [X0] : (~kind(X0) <~> calm(X0)) [input p4]
6. ! [X0] : ((old(X0) | ~brave(X0)) => (quiet(X0) & ~funny(X0))) [input p5]
7. ! [X0] : ((kind(X0) & patient(X0)) <=> generous(X0)) [input p6]
8. ! [X0] : ((curious(X0) <~> patient(X0)) <=> (~quiet(X0) | curious(X0))) [input p7]
20. generous(lucy) [input hypothesis]
21. ? [X0] : (curious(X0) <~> quiet(X0)) <=> ? [X1] : (generous(X1) | quiet(X1)) [rectify 2]
22. ? [X0] : (quiet(X0) & generous(X0)) <=> ? [X1] : (~kind(X1) <~> calm(X1)) [rectify 5]
24. ! [X0] : ((quiet(X0) & ~funny(X0)) | (~old(X0) & brave(X0))) [ennf transformation 6]
28. ! [X0] : (((happy(X0) | humble(X0)) | ((~old(X0) | ~kind(X0)) & (kind(X0) | old(X0)))) & (((~kind(X0) | old(X0)) & (kind(X0) | ~old(X0))) | (~happy(X0) & ~humble(X0)))) [nnf transformation 1]
29. ! [X0] : ((happy(X0) | humble(X0) | ((~old(X0) | ~kind(X0)) & (kind(X0) | old(X0)))) & (((~kind(X0) | old(X0)) & (kind(X0) | ~old(X0))) | (~happy(X0) & ~humble(X0)))) [flattening 28]
30. (? [X0] : ((~quiet(X0) | ~curious(X0)) & (quiet(X0) | curious(X0))) | ! [X1] : (~generous(X1) & ~quiet(X1))) & (? [X1] : (generous(X1) | quiet(X1)) | ! [X0] : ((curious(X0) | ~quiet(X0)) & (quiet(X0) | ~curious(X0)))) [nnf transformation 21]
31. (? [X0] : ((~quiet(X0) | ~curious(X0)) & (quiet(X0) | curious(X0))) | ! [X1] : (~generous(X1) & ~quiet(X1))) & (? [X2] : (generous(X2) | quiet(X2)) | ! [X3] : ((curious(X3) | ~quiet(X3)) & (quiet(X3) | ~curious(X3)))) [rectify 30]
32. ? [X0] : ((~quiet(X0) | ~curious(X0)) & (quiet(X0) | curious(X0))) => ((~quiet(sK0) | ~curious(sK0)) & (quiet(sK0) | curious(sK0))) [choice axiom]
33. ? [X2] : (generous(X2) | quiet(X2)) => (generous(sK1) | quiet(sK1)) [choice axiom]
34. (((~quiet(sK0) | ~curious(sK0)) & (quiet(sK0) | curious(sK0))) | ! [X1] : (~generous(X1) & ~quiet(X1))) & ((generous(sK1) | quiet(sK1)) | ! [X3] : ((curious(X3) | ~quiet(X3)) & (quiet(X3) | ~curious(X3)))) [skolemisation 31,33,32]
35. ! [X0] : ((((calm(X0) | kind(X0)) & (~calm(X0) | ~kind(X0))) | ~patient(X0)) & (patient(X0) | ((~kind(X0) | calm(X0)) & (~calm(X0) | kind(X0))))) [nnf transformation 3]
38. (? [X0] : (quiet(X0) & generous(X0)) | ! [X1] : ((~kind(X1) | ~calm(X1)) & (calm(X1) | kind(X1)))) & (? [X1] : ((~calm(X1) | kind(X1)) & (calm(X1) | ~kind(X1))) | ! [X0] : (~quiet(X0) | ~generous(X0))) [nnf transformation 22]
39. (? [X0] : (quiet(X0) & generous(X0)) | ! [X1] : ((~kind(X1) | ~calm(X1)) & (calm(X1) | kind(X1)))) & (? [X2] : ((~calm(X2) | kind(X2)) & (calm(X2) | ~kind(X2))) | ! [X3] : (~quiet(X3) | ~generous(X3))) [rectify 38]
40. ? [X0] : (quiet(X0) & generous(X0)) => (quiet(sK3) & generous(sK3)) [choice axiom]
41. ? [X2] : ((~calm(X2) | kind(X2)) & (calm(X2) | ~kind(X2))) => ((~calm(sK4) | kind(sK4)) & (calm(sK4) | ~kind(sK4))) [choice axiom]
42. ((quiet(sK3) & generous(sK3)) | ! [X1] : ((~kind(X1) | ~calm(X1)) & (calm(X1) | kind(X1)))) & (((~calm(sK4) | kind(sK4)) & (calm(sK4) | ~kind(sK4))) | ! [X3] : (~quiet(X3) | ~generous(X3))) [skolemisation 39,41,40]
43. ! [X0] : (((kind(X0) & patient(X0)) | ~generous(X0)) & (generous(X0) | (~kind(X0) | ~patient(X0)))) [nnf transformation 7]
44. ! [X0] : (((kind(X0) & patient(X0)) | ~generous(X0)) & (generous(X0) | ~kind(X0) | ~patient(X0))) [flattening 43]
45. ! [X0] : ((((~patient(X0) | ~curious(X0)) & (patient(X0) | curious(X0))) | (quiet(X0) & ~curious(X0))) & ((~quiet(X0) | curious(X0)) | ((curious(X0) | ~patient(X0)) & (patient(X0) | ~curious(X0))))) [nnf transformation 8]
46. ! [X0] : ((((~patient(X0) | ~curious(X0)) & (patient(X0) | curious(X0))) | (quiet(X0) & ~curious(X0))) & (~quiet(X0) | curious(X0) | ((curious(X0) | ~patient(X0)) & (patient(X0) | ~curious(X0))))) [flattening 45]
68. ~kind(X0) | old(X0) | ~humble(X0) [cnf transformation 29]
69. ~kind(X0) | old(X0) | ~happy(X0) [cnf transformation 29]
70. kind(X0) | humble(X0) | happy(X0) | old(X0) [cnf transformation 29]
75. quiet(sK0) | curious(sK0) | ~generous(X1) [cnf transformation 34]
78. ~calm(X0) | patient(X0) | kind(X0) [cnf transformation 35]
79. ~kind(X0) | patient(X0) | calm(X0) [cnf transformation 35]
86. generous(sK3) | calm(X1) | kind(X1) [cnf transformation 42]
87. generous(sK3) | ~kind(X1) | ~calm(X1) [cnf transformation 42]
88. quiet(sK3) | calm(X1) | kind(X1) [cnf transformation 42]
89. quiet(sK3) | ~kind(X1) | ~calm(X1) [cnf transformation 42]
93. ~old(X0) | quiet(X0) [cnf transformation 24]
95. ~generous(X0) | patient(X0) [cnf transformation 44]
98. ~quiet(X0) | curious(X0) | curious(X0) | ~patient(X0) [cnf transformation 46]
101. ~patient(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 46]
102. ~patient(X0) | ~curious(X0) | quiet(X0) [cnf transformation 46]
131. generous(lucy) [cnf transformation 20]
132. ~quiet(X0) | curious(X0) | ~patient(X0) [duplicate literal removal 98]
133. ~patient(X0) | ~curious(X0) [duplicate literal removal 101]
135. 1 <=> ! [X1] : ~generous(X1) [avatar definition]
136. ~generous(X1) <- (1) [avatar component clause 135]
138. 2 <=> curious(sK0) [avatar definition]
139. curious(sK0) <- (2) [avatar component clause 138]
142. 3 <=> quiet(sK0) [avatar definition]
143. quiet(sK0) <- (3) [avatar component clause 142]
144. ~quiet(sK0) <- (~3) [avatar component clause 142]
150. 1 | 2 | 3 [avatar split clause 75,142,138,135]
183. 12 <=> ! [X1] : (~kind(X1) | ~calm(X1)) [avatar definition]
184. ~calm(X1) | ~kind(X1) <- (12) [avatar component clause 183]
186. 13 <=> quiet(sK3) [avatar definition]
188. quiet(sK3) <- (13) [avatar component clause 186]
189. 12 | 13 [avatar split clause 89,186,183]
191. 14 <=> ! [X1] : (calm(X1) | kind(X1)) [avatar definition]
192. calm(X1) | kind(X1) <- (14) [avatar component clause 191]
193. 14 | 13 [avatar split clause 88,186,191]
195. 15 <=> generous(sK3) [avatar definition]
197. generous(sK3) <- (15) [avatar component clause 195]
198. 12 | 15 [avatar split clause 87,195,183]
199. 14 | 15 [avatar split clause 86,195,191]
213. ~patient(X0) | ~quiet(X0) [subsumption resolution 132,133]
321. patient(sK3) <- (15) [resolution 197,95]
323. ~quiet(sK3) <- (15) [resolution 321,213]
325. $false <- (13, 15) [subsumption resolution 323,188]
326. ~13 | ~15 [avatar contradiction clause 325]
362. patient(X0) | kind(X0) | kind(X0) <- (14) [resolution 78,192]
363. patient(X0) | kind(X0) <- (14) [duplicate literal removal 362]
388. ~curious(X0) | kind(X0) | quiet(X0) <- (14) [resolution 363,102]
392. ~quiet(X4) | kind(X4) <- (14) [resolution 363,213]
397. kind(sK3) <- (13, 14) [resolution 392,188]
458. kind(sK0) <- (3, 14) [resolution 143,392]
467. patient(sK3) | calm(sK3) <- (13, 14) [resolution 397,79]
471. 55 <=> calm(sK3) [avatar definition]
473. calm(sK3) <- (55) [avatar component clause 471]
475. 56 <=> patient(sK3) [avatar definition]
477. patient(sK3) <- (56) [avatar component clause 475]
478. 55 | 56 | ~13 | ~14 [avatar split clause 467,191,186,475,471]
504. patient(X0) | happy(X0) | old(X0) | humble(X0) | calm(X0) [resolution 70,79]
575. ~curious(X5) | old(X5) | humble(X5) | calm(X5) | happy(X5) [resolution 504,133]
581. patient(sK0) | calm(sK0) <- (3, 14) [resolution 458,79]
585. 65 <=> happy(sK0) [avatar definition]
589. 66 <=> old(sK0) [avatar definition]
590. old(sK0) <- (66) [avatar component clause 589]
591. ~old(sK0) <- (~66) [avatar component clause 589]
593. 67 <=> humble(sK0) [avatar definition]
594. ~humble(sK0) <- (~67) [avatar component clause 593]
598. 68 <=> calm(sK0) [avatar definition]
600. calm(sK0) <- (68) [avatar component clause 598]
602. 69 <=> patient(sK0) [avatar definition]
604. patient(sK0) <- (69) [avatar component clause 602]
605. 68 | 69 | ~3 | ~14 [avatar split clause 581,191,142,602,598]
776. ~kind(sK3) <- (12, 55) [resolution 473,184]
782. $false <- (12, 13, 14, 55) [subsumption resolution 776,397]
783. ~12 | ~13 | ~14 | ~55 [avatar contradiction clause 782]
789. ~quiet(sK3) <- (56) [resolution 477,213]
794. $false <- (13, 56) [subsumption resolution 789,188]
795. ~13 | ~56 [avatar contradiction clause 794]
809. $false <- (1) [resolution 136,131]
814. ~1 [avatar contradiction clause 809]
829. quiet(sK0) <- (66) [resolution 590,93]
834. ~quiet(sK0) <- (69) [resolution 604,213]
838. $false <- (3, 69) [subsumption resolution 834,143]
839. ~3 | ~69 [avatar contradiction clause 838]
842. ~kind(sK0) <- (12, 68) [resolution 600,184]
848. $false <- (3, 12, 14, 68) [subsumption resolution 842,458]
849. ~3 | ~12 | ~14 | ~68 [avatar contradiction clause 848]
850. 3 | ~66 [avatar split clause 829,589,142]
853. old(sK0) | humble(sK0) | calm(sK0) | happy(sK0) <- (2) [resolution 139,575]
854. kind(sK0) | quiet(sK0) <- (2, 14) [resolution 139,388]
856. kind(sK0) <- (2, ~3, 14) [subsumption resolution 854,144]
861. old(sK0) | ~happy(sK0) <- (2, ~3, 14) [resolution 856,69]
862. old(sK0) | ~humble(sK0) <- (2, ~3, 14) [resolution 856,68]
866. ~humble(sK0) <- (2, ~3, 14, ~66) [subsumption resolution 862,591]
869. ~67 | ~2 | 3 | ~14 | 66 [avatar split clause 866,589,191,142,138,593]
872. humble(sK0) | calm(sK0) | happy(sK0) <- (2, ~66) [subsumption resolution 853,591]
882. ~happy(sK0) <- (2, ~3, 14, ~66) [subsumption resolution 861,591]
883. ~65 | ~2 | 3 | ~14 | 66 [avatar split clause 882,589,191,142,138,585]
884. calm(sK0) | happy(sK0) <- (2, ~66, ~67) [subsumption resolution 872,594]
885. 65 | 68 | ~2 | 66 | 67 [avatar split clause 884,593,589,138,598,585]
913. ~kind(sK0) <- (12, 68) [resolution 600,184]
914. $false <- (2, ~3, 12, 14, 68) [subsumption resolution 913,856]
915. ~2 | 3 | ~12 | ~14 | ~68 [avatar contradiction clause 914]
916. $false [avatar sat refutation 150,189,193,198,199,326,478,605,783,795,814,839,849,850,869,883,885,915]
% SZS output end Proof for 722691985672302901295369
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is calm and vice versa.
Everyone who is both patient and not happy is not happy or not old.
If alice is either not old or not happy then someone is either generous or not funny and vice versa.
If susan is both funny and generous then lucy is generous and vice versa.
If someone is not strong or funny then someone is both curious and not strong.
Everyone who is either wise or not calm is quiet and vice versa.
Everyone who is not humble is either not creative or not happy.
Everyone who is either not humble or not tall is both happy and wise.
Everyone who is not brave is curious or not rich.
Everyone who is generous or not rich is not kind.
Everyone who is both not happy and calm is either brave or not brave and vice versa.
Everyone who is not old or rich is both curious and wise and vice versa.
Everyone who is either not rich or not generous is not old or calm and vice versa.
If someone is happy then someone is both not old and not happy and vice versa.
If lucy is not patient then lucy is wise and vice versa.
Everyone who is not funny or curious is either not brave or calm.
Fred is both not curious and generous.
Someone is either quiet or not funny.
Someone is either quiet or not curious.
Someone is quiet or not strong.
Someone is strong.
Mary is not generous or rich.
Someone is not patient or creative. | Mary is not curious. | contradiction | (![X]:(old(X)<=>calm(X)))&
(![X]:((patient(X)&~happy(X))=>(~happy(X)|~old(X))))&
(((~old(alice)<~>~happy(alice)))<=>(?[X]:((generous(X)<~>~funny(X)))))&
(((funny(susan)&generous(susan)))<=>(generous(lucy)))&
((?[X]:((~strong(X)|funny(X))))=>(?[X]:((curious(X)&~strong(X)))))&
(![X]:((wise(X)<~>~calm(X))<=>quiet(X)))&
(![X]:(~humble(X)=>(~creative(X)<~>~happy(X))))&
(![X]:((~humble(X)<~>~tall(X))=>(happy(X)&wise(X))))&
(![X]:(~brave(X)=>(curious(X)|~rich(X))))&
(![X]:((generous(X)|~rich(X))=>~kind(X)))&
(![X]:((~happy(X)&calm(X))<=>(brave(X)<~>~brave(X))))&
(![X]:((~old(X)|rich(X))<=>(curious(X)&wise(X))))&
(![X]:((~rich(X)<~>~generous(X))<=>(~old(X)|calm(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~old(X)&~happy(X)))))&
((~patient(lucy))<=>(wise(lucy)))&
(![X]:((~funny(X)|curious(X))=>(~brave(X)<~>calm(X))))&
((~curious(fred)&generous(fred)))&
(?[X]:((quiet(X)<~>~funny(X))))&
(?[X]:((quiet(X)<~>~curious(X))))&
(?[X]:((quiet(X)|~strong(X))))&
(?[X]:(strong(X)))&
((~generous(mary)|rich(mary)))&
(?[X]:((~patient(X)|creative(X)))) | ~curious(mary) | [
"p10",
"p11",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 687251480173180113445828
% SZS output start Proof for 687251480173180113445828
11. ! [X0] : ((calm(X0) & ~happy(X0)) <=> (brave(X0) <~> ~brave(X0))) [input p10]
12. ! [X0] : ((rich(X0) | ~old(X0)) <=> (wise(X0) & curious(X0))) [input p11]
13. ! [X0] : ((~rich(X0) <~> ~generous(X0)) <=> (calm(X0) | ~old(X0))) [input p12]
22. rich(mary) | ~generous(mary) [input p21]
24. ~curious(mary) [input hypothesis]
49. ! [X0] : (((calm(X0) & ~happy(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | (~calm(X0) | happy(X0)))) [nnf transformation 11]
50. ! [X0] : (((calm(X0) & ~happy(X0)) | ((brave(X0) | brave(X0)) & (~brave(X0) | ~brave(X0)))) & (((brave(X0) | ~brave(X0)) & (~brave(X0) | brave(X0))) | ~calm(X0) | happy(X0))) [flattening 49]
51. ! [X0] : (((rich(X0) | ~old(X0)) | (~wise(X0) | ~curious(X0))) & ((wise(X0) & curious(X0)) | (~rich(X0) & old(X0)))) [nnf transformation 12]
52. ! [X0] : ((rich(X0) | ~old(X0) | ~wise(X0) | ~curious(X0)) & ((wise(X0) & curious(X0)) | (~rich(X0) & old(X0)))) [flattening 51]
53. ! [X0] : ((((generous(X0) | rich(X0)) & (~generous(X0) | ~rich(X0))) | (~calm(X0) & old(X0))) & ((calm(X0) | ~old(X0)) | ((~rich(X0) | generous(X0)) & (~generous(X0) | rich(X0))))) [nnf transformation 13]
54. ! [X0] : ((((generous(X0) | rich(X0)) & (~generous(X0) | ~rich(X0))) | (~calm(X0) & old(X0))) & (calm(X0) | ~old(X0) | ((~rich(X0) | generous(X0)) & (~generous(X0) | rich(X0))))) [flattening 53]
107. calm(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 50]
108. calm(X0) | brave(X0) | brave(X0) [cnf transformation 50]
110. ~rich(X0) | curious(X0) [cnf transformation 52]
117. ~generous(X0) | ~rich(X0) | ~calm(X0) [cnf transformation 54]
119. generous(X0) | rich(X0) | ~calm(X0) [cnf transformation 54]
137. rich(mary) | ~generous(mary) [cnf transformation 22]
139. ~curious(mary) [cnf transformation 24]
142. calm(X0) | ~brave(X0) [duplicate literal removal 107]
143. brave(X0) | calm(X0) [duplicate literal removal 108]
207. calm(X0) [subsumption resolution 142,143]
209. rich(X0) | generous(X0) [subsumption resolution 119,207]
210. ~rich(X0) | ~generous(X0) [subsumption resolution 117,207]
254. ~generous(mary) [subsumption resolution 137,210]
272. curious(X1) | generous(X1) [resolution 209,110]
288. generous(mary) [resolution 272,139]
290. $false [subsumption resolution 288,254]
% SZS output end Proof for 687251480173180113445828
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and old is both quiet and not creative and vice versa.
If lucy is both not patient and patient then alice is not quiet or not wise and vice versa.
Everyone who is both humble and happy is brave or not humble and vice versa.
Everyone who is creative or not patient is not happy.
Everyone who is quiet or not kind is not tall or not creative.
If someone is either not brave or generous then someone is either tall or not curious and vice versa.
If someone is both not humble and not quiet then someone is both not quiet and patient.
If someone is generous or old then paul is either not rich or creative and vice versa.
Everyone who is kind or rich is either calm or not humble.
Everyone who is either tall or happy is both not wise and not happy and vice versa.
Everyone who is either rich or not kind is not strong.
If lucy is not wise or funny then someone is curious.
If fred is either patient or not curious then someone is tall and vice versa.
If someone is not funny then someone is patient.
If someone is both rich and not wise then someone is not kind and vice versa.
Everyone who is not strong or brave is not patient and vice versa.
Someone is either funny or quiet.
Fred is brave or not rich.
Someone is creative or not brave.
Alice is both not curious and calm.
Susan is not patient or not quiet.
Susan is strong.
Alice is either not tall or not old.
John is either creative or not tall. | Susan is not calm. | contradiction | (![X]:((~kind(X)&old(X))<=>(quiet(X)&~creative(X))))&
(((~patient(lucy)&patient(lucy)))<=>((~quiet(alice)|~wise(alice))))&
(![X]:((humble(X)&happy(X))<=>(brave(X)|~humble(X))))&
(![X]:((creative(X)|~patient(X))=>~happy(X)))&
(![X]:((quiet(X)|~kind(X))=>(~tall(X)|~creative(X))))&
((?[X]:((~brave(X)<~>generous(X))))<=>(?[X]:((tall(X)<~>~curious(X)))))&
((?[X]:((~humble(X)&~quiet(X))))=>(?[X]:((~quiet(X)&patient(X)))))&
((?[X]:((generous(X)|old(X))))<=>((~rich(paul)<~>creative(paul))))&
(![X]:((kind(X)|rich(X))=>(calm(X)<~>~humble(X))))&
(![X]:((tall(X)<~>happy(X))<=>(~wise(X)&~happy(X))))&
(![X]:((rich(X)<~>~kind(X))=>~strong(X)))&
(((~wise(lucy)|funny(lucy)))=>(?[X]:(curious(X))))&
(((patient(fred)<~>~curious(fred)))<=>(?[X]:(tall(X))))&
((?[X]:(~funny(X)))=>(?[X]:(patient(X))))&
((?[X]:((rich(X)&~wise(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~strong(X)|brave(X))<=>~patient(X)))&
(?[X]:((funny(X)<~>quiet(X))))&
((brave(fred)|~rich(fred)))&
(?[X]:((creative(X)|~brave(X))))&
((~curious(alice)&calm(alice)))&
((~patient(susan)|~quiet(susan)))&
(strong(susan))&
((~tall(alice)<~>~old(alice)))&
((creative(john)<~>~tall(john))) | ~calm(susan) | [
"p2",
"p8",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7552639398125935625175817
% SZS output start Proof for 7552639398125935625175817
3. ! [X0] : ((happy(X0) & humble(X0)) <=> (~humble(X0) | brave(X0))) [input p2]
9. ! [X0] : ((rich(X0) | kind(X0)) => (calm(X0) <~> ~humble(X0))) [input p8]
11. ! [X0] : ((rich(X0) <~> ~kind(X0)) => ~strong(X0)) [input p10]
22. strong(susan) [input p21]
25. ~calm(susan) [input hypothesis]
34. ! [X0] : ((calm(X0) <~> ~humble(X0)) | (~rich(X0) & ~kind(X0))) [ennf transformation 9]
35. ! [X0] : (~strong(X0) | (rich(X0) <=> ~kind(X0))) [ennf transformation 11]
42. ! [X0] : (((happy(X0) & humble(X0)) | (humble(X0) & ~brave(X0))) & ((~humble(X0) | brave(X0)) | (~happy(X0) | ~humble(X0)))) [nnf transformation 3]
43. ! [X0] : (((happy(X0) & humble(X0)) | (humble(X0) & ~brave(X0))) & (~humble(X0) | brave(X0) | ~happy(X0) | ~humble(X0))) [flattening 42]
56. ! [X0] : (((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | (~rich(X0) & ~kind(X0))) [nnf transformation 34]
59. ! [X0] : (~strong(X0) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0)))) [nnf transformation 35]
94. humble(X0) | humble(X0) [cnf transformation 43]
117. ~humble(X0) | calm(X0) | ~kind(X0) [cnf transformation 56]
118. ~humble(X0) | calm(X0) | ~rich(X0) [cnf transformation 56]
128. ~strong(X0) | rich(X0) | kind(X0) [cnf transformation 59]
149. strong(susan) [cnf transformation 22]
154. ~calm(susan) [cnf transformation 25]
158. humble(X0) [duplicate literal removal 94]
240. ~rich(X0) | calm(X0) [subsumption resolution 118,158]
241. ~kind(X0) | calm(X0) [subsumption resolution 117,158]
418. 51 <=> rich(susan) [avatar definition]
419. rich(susan) <- (51) [avatar component clause 418]
422. 52 <=> kind(susan) [avatar definition]
423. kind(susan) <- (52) [avatar component clause 422]
426. rich(susan) | kind(susan) [resolution 128,149]
429. calm(susan) <- (52) [resolution 423,241]
430. $false <- (52) [subsumption resolution 429,154]
431. ~52 [avatar contradiction clause 430]
432. 52 | 51 [avatar split clause 426,418,422]
435. calm(susan) <- (51) [resolution 419,240]
436. $false <- (51) [subsumption resolution 435,154]
437. ~51 [avatar contradiction clause 436]
438. $false [avatar sat refutation 431,432,437]
% SZS output end Proof for 7552639398125935625175817
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or not calm then someone is either not patient or rich. If mary is quiet or strong then someone is both not rich and quiet and vice versa. If alice is strong then mary is either tall or humble. If someone is either funny or not old then alice is quiet or strong. Everyone who is not brave is both happy and not calm. Everyone who is either not brave or calm is both not old and not generous. If mary is kind or not wise then fred is not wise or kind and vice versa. If lucy is not humble then alice is both tall and funny and vice versa. Everyone who is humble is both not tall and quiet and vice versa. Everyone who is old or not happy is not quiet or not generous and vice versa. Everyone who is either not humble or quiet is both tall and not old and vice versa. Everyone who is not curious is not brave or not happy and vice versa. If paul is both strong and not rich then paul is happy or humble. If paul is not funny then someone is old. Everyone who is curious or humble is not old and vice versa. Everyone who is either generous or not curious is not creative. Fred is either not kind or not curious. Fred is patient or creative. John is not generous or not rich. Mary is either humble or kind. Fred is not funny. Someone is strong or not brave. | John is not calm. | entailment | ((?[X]:((brave(X)<~>~calm(X))))=>(?[X]:((~patient(X)<~>rich(X)))))&
(((quiet(mary)|strong(mary)))<=>(?[X]:((~rich(X)&quiet(X)))))&
((strong(alice))=>((tall(mary)<~>humble(mary))))&
((?[X]:((funny(X)<~>~old(X))))=>((quiet(alice)|strong(alice))))&
(![X]:(~brave(X)=>(happy(X)&~calm(X))))&
(![X]:((~brave(X)<~>calm(X))=>(~old(X)&~generous(X))))&
(((kind(mary)|~wise(mary)))<=>((~wise(fred)|kind(fred))))&
((~humble(lucy))<=>((tall(alice)&funny(alice))))&
(![X]:(humble(X)<=>(~tall(X)&quiet(X))))&
(![X]:((old(X)|~happy(X))<=>(~quiet(X)|~generous(X))))&
(![X]:((~humble(X)<~>quiet(X))<=>(tall(X)&~old(X))))&
(![X]:(~curious(X)<=>(~brave(X)|~happy(X))))&
(((strong(paul)&~rich(paul)))=>((happy(paul)|humble(paul))))&
((~funny(paul))=>(?[X]:(old(X))))&
(![X]:((curious(X)|humble(X))<=>~old(X)))&
(![X]:((generous(X)<~>~curious(X))=>~creative(X)))&
((~kind(fred)<~>~curious(fred)))&
((patient(fred)|creative(fred)))&
((~generous(john)|~rich(john)))&
((humble(mary)<~>kind(mary)))&
(~funny(fred))&
(?[X]:((strong(X)|~brave(X)))) | ~calm(john) | [
"p4",
"p5",
"p8",
"p9",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1812543776007540356329969
% SZS output start Proof for 1812543776007540356329969
5. ! [X0] : (~brave(X0) => (~calm(X0) & happy(X0))) [input p4]
6. ! [X0] : ((~brave(X0) <~> calm(X0)) => (~generous(X0) & ~old(X0))) [input p5]
9. ! [X0] : (humble(X0) <=> (quiet(X0) & ~tall(X0))) [input p8]
10. ! [X0] : ((~happy(X0) | old(X0)) <=> (~generous(X0) | ~quiet(X0))) [input p9]
11. ! [X0] : ((~humble(X0) <~> quiet(X0)) <=> (~old(X0) & tall(X0))) [input p10]
12. ! [X0] : (~curious(X0) <=> (~happy(X0) | ~brave(X0))) [input p11]
15. ! [X0] : ((humble(X0) | curious(X0)) <=> ~old(X0)) [input p14]
23. calm(john) [input hypothesis]
29. ! [X0] : ((~calm(X0) & happy(X0)) | brave(X0)) [ennf transformation 5]
30. ! [X0] : ((~generous(X0) & ~old(X0)) | (~brave(X0) <=> calm(X0))) [ennf transformation 6]
46. ! [X0] : ((~generous(X0) & ~old(X0)) | ((~brave(X0) | ~calm(X0)) & (calm(X0) | brave(X0)))) [nnf transformation 30]
51. ! [X0] : ((humble(X0) | (~quiet(X0) | tall(X0))) & ((quiet(X0) & ~tall(X0)) | ~humble(X0))) [nnf transformation 9]
52. ! [X0] : ((humble(X0) | ~quiet(X0) | tall(X0)) & ((quiet(X0) & ~tall(X0)) | ~humble(X0))) [flattening 51]
53. ! [X0] : (((~happy(X0) | old(X0)) | (generous(X0) & quiet(X0))) & ((~generous(X0) | ~quiet(X0)) | (happy(X0) & ~old(X0)))) [nnf transformation 10]
54. ! [X0] : ((~happy(X0) | old(X0) | (generous(X0) & quiet(X0))) & (~generous(X0) | ~quiet(X0) | (happy(X0) & ~old(X0)))) [flattening 53]
55. ! [X0] : ((((~quiet(X0) | humble(X0)) & (quiet(X0) | ~humble(X0))) | (old(X0) | ~tall(X0))) & ((~old(X0) & tall(X0)) | ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0))))) [nnf transformation 11]
56. ! [X0] : ((((~quiet(X0) | humble(X0)) & (quiet(X0) | ~humble(X0))) | old(X0) | ~tall(X0)) & ((~old(X0) & tall(X0)) | ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0))))) [flattening 55]
57. ! [X0] : ((~curious(X0) | (happy(X0) & brave(X0))) & ((~happy(X0) | ~brave(X0)) | curious(X0))) [nnf transformation 12]
58. ! [X0] : ((~curious(X0) | (happy(X0) & brave(X0))) & (~happy(X0) | ~brave(X0) | curious(X0))) [flattening 57]
61. ! [X0] : (((humble(X0) | curious(X0)) | old(X0)) & (~old(X0) | (~humble(X0) & ~curious(X0)))) [nnf transformation 15]
62. ! [X0] : ((humble(X0) | curious(X0) | old(X0)) & (~old(X0) | (~humble(X0) & ~curious(X0)))) [flattening 61]
82. ~calm(X0) | brave(X0) [cnf transformation 29]
84. ~old(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 46]
94. ~humble(X0) | ~tall(X0) [cnf transformation 52]
95. ~humble(X0) | quiet(X0) [cnf transformation 52]
96. ~quiet(X0) | humble(X0) | tall(X0) [cnf transformation 52]
99. ~happy(X0) | old(X0) | quiet(X0) [cnf transformation 54]
101. tall(X0) | quiet(X0) | humble(X0) [cnf transformation 56]
102. tall(X0) | ~humble(X0) | ~quiet(X0) [cnf transformation 56]
103. ~old(X0) | quiet(X0) | humble(X0) [cnf transformation 56]
104. ~old(X0) | ~humble(X0) | ~quiet(X0) [cnf transformation 56]
106. ~quiet(X0) | humble(X0) | old(X0) | ~tall(X0) [cnf transformation 56]
109. ~curious(X0) | happy(X0) [cnf transformation 58]
114. curious(X0) | humble(X0) | old(X0) [cnf transformation 62]
125. calm(john) [cnf transformation 23]
196. ~old(X0) | ~calm(X0) [subsumption resolution 84,82]
233. ~quiet(X0) | humble(X0) | old(X0) [subsumption resolution 106,96]
234. ~old(X0) | ~humble(X0) [subsumption resolution 104,95]
235. ~old(X0) | quiet(X0) [subsumption resolution 103,234]
236. ~quiet(X0) | tall(X0) [subsumption resolution 102,96]
237. humble(X0) | tall(X0) [subsumption resolution 101,236]
310. tall(X0) | quiet(X0) [resolution 237,95]
313. tall(X0) [subsumption resolution 310,236]
329. happy(X1) | old(X1) | humble(X1) [resolution 114,109]
356. old(X2) | humble(X2) | old(X2) | quiet(X2) [resolution 329,99]
357. old(X2) | humble(X2) | quiet(X2) [duplicate literal removal 356]
359. humble(X2) | quiet(X2) [subsumption resolution 357,235]
360. quiet(X2) [subsumption resolution 359,95]
361. old(X0) | humble(X0) [resolution 360,233]
372. ~calm(X3) | humble(X3) [resolution 361,196]
377. humble(john) [resolution 372,125]
379. ~tall(john) [resolution 377,94]
380. $false [subsumption resolution 379,313]
% SZS output end Proof for 1812543776007540356329969
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either wise or creative then someone is both tall and not curious and vice versa.
If someone is not patient or patient then paul is both old and curious.
Everyone who is rich or not calm is not humble and vice versa.
If alice is not funny or not curious then someone is old or strong and vice versa.
If someone is creative or happy then john is funny and vice versa.
If someone is either not strong or kind then someone is either not creative or rich and vice versa.
Everyone who is rich or not generous is either not generous or patient.
Everyone who is either old or not funny is kind and vice versa.
Everyone who is either not patient or not kind is not brave and vice versa.
If someone is not brave or strong then someone is either quiet or not patient.
Everyone who is not curious or not old is not kind or not creative and vice versa.
If someone is not calm then someone is both rich and not wise and vice versa.
If someone is both not creative and strong then someone is either strong or brave and vice versa.
Everyone who is either not wise or not kind is both brave and funny.
If paul is not wise or quiet then someone is either humble or funny.
Everyone who is both not wise and not curious is not happy.
Someone is rich.
Someone is both funny and humble.
Alice is curious or not wise.
Someone is not calm or not rich.
Susan is not generous.
Alice is either not tall or humble.
Alice is calm or funny.
John is patient. | Paul is not funny. | contradiction | ((?[X]:((wise(X)<~>creative(X))))<=>(?[X]:((tall(X)&~curious(X)))))&
((?[X]:((~patient(X)|patient(X))))=>((old(paul)&curious(paul))))&
(![X]:((rich(X)|~calm(X))<=>~humble(X)))&
(((~funny(alice)|~curious(alice)))<=>(?[X]:((old(X)|strong(X)))))&
((?[X]:((creative(X)|happy(X))))<=>(funny(john)))&
((?[X]:((~strong(X)<~>kind(X))))<=>(?[X]:((~creative(X)<~>rich(X)))))&
(![X]:((rich(X)|~generous(X))=>(~generous(X)<~>patient(X))))&
(![X]:((old(X)<~>~funny(X))<=>kind(X)))&
(![X]:((~patient(X)<~>~kind(X))<=>~brave(X)))&
((?[X]:((~brave(X)|strong(X))))=>(?[X]:((quiet(X)<~>~patient(X)))))&
(![X]:((~curious(X)|~old(X))<=>(~kind(X)|~creative(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((rich(X)&~wise(X)))))&
((?[X]:((~creative(X)&strong(X))))<=>(?[X]:((strong(X)<~>brave(X)))))&
(![X]:((~wise(X)<~>~kind(X))=>(brave(X)&funny(X))))&
(((~wise(paul)|quiet(paul)))=>(?[X]:((humble(X)<~>funny(X)))))&
(![X]:((~wise(X)&~curious(X))=>~happy(X)))&
(?[X]:(rich(X)))&
(?[X]:((funny(X)&humble(X))))&
((curious(alice)|~wise(alice)))&
(?[X]:((~calm(X)|~rich(X))))&
(~generous(susan))&
((~tall(alice)<~>humble(alice)))&
((calm(alice)|funny(alice)))&
(patient(john)) | ~funny(paul) | [
"p1",
"p6",
"p7",
"p10",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5795865153177398867380171
% SZS output start Proof for 5795865153177398867380171
2. ? [X0] : (patient(X0) | ~patient(X0)) => (curious(paul) & old(paul)) [input p1]
7. ! [X0] : ((~generous(X0) | rich(X0)) => (~generous(X0) <~> patient(X0))) [input p6]
8. ! [X0] : ((old(X0) <~> ~funny(X0)) <=> kind(X0)) [input p7]
11. ! [X0] : ((~old(X0) | ~curious(X0)) <=> (~creative(X0) | ~kind(X0))) [input p10]
21. ~generous(susan) [input p20]
25. ~funny(paul) [input hypothesis]
31. (curious(paul) & old(paul)) | ! [X0] : (~patient(X0) & patient(X0)) [ennf transformation 2]
32. ! [X0] : ((~generous(X0) <~> patient(X0)) | (generous(X0) & ~rich(X0))) [ennf transformation 7]
59. ! [X0] : (((~patient(X0) | generous(X0)) & (patient(X0) | ~generous(X0))) | (generous(X0) & ~rich(X0))) [nnf transformation 32]
60. ! [X0] : ((((funny(X0) | ~old(X0)) & (~funny(X0) | old(X0))) | ~kind(X0)) & (kind(X0) | ((old(X0) | funny(X0)) & (~funny(X0) | ~old(X0))))) [nnf transformation 8]
66. ! [X0] : (((~old(X0) | ~curious(X0)) | (creative(X0) & kind(X0))) & ((~creative(X0) | ~kind(X0)) | (old(X0) & curious(X0)))) [nnf transformation 11]
67. ! [X0] : ((~old(X0) | ~curious(X0) | (creative(X0) & kind(X0))) & (~creative(X0) | ~kind(X0) | (old(X0) & curious(X0)))) [flattening 66]
95. old(paul) | patient(X0) [cnf transformation 31]
97. curious(paul) | patient(X0) [cnf transformation 31]
120. ~patient(X0) | generous(X0) | generous(X0) [cnf transformation 59]
124. ~kind(X0) | ~old(X0) | funny(X0) [cnf transformation 60]
135. ~old(X0) | ~curious(X0) | kind(X0) [cnf transformation 67]
160. ~generous(susan) [cnf transformation 21]
165. ~funny(paul) [cnf transformation 25]
166. ~patient(X0) | generous(X0) [duplicate literal removal 120]
202. 9 <=> curious(paul) [avatar definition]
204. curious(paul) <- (9) [avatar component clause 202]
207. 10 <=> ! [X0] : patient(X0) [avatar definition]
208. patient(X0) <- (10) [avatar component clause 207]
209. 10 | 9 [avatar split clause 97,202,207]
211. 11 <=> old(paul) [avatar definition]
213. old(paul) <- (11) [avatar component clause 211]
215. 10 | 11 [avatar split clause 95,211,207]
430. generous(X0) <- (10) [resolution 166,208]
439. $false <- (10) [resolution 430,160]
440. ~10 [avatar contradiction clause 439]
510. ~curious(paul) | kind(paul) <- (11) [resolution 135,213]
513. kind(paul) <- (9, 11) [subsumption resolution 510,204]
531. ~old(paul) | funny(paul) <- (9, 11) [resolution 513,124]
542. funny(paul) <- (9, 11) [subsumption resolution 531,213]
543. $false <- (9, 11) [subsumption resolution 542,165]
544. ~9 | ~11 [avatar contradiction clause 543]
545. $false [avatar sat refutation 209,215,440,544]
% SZS output end Proof for 5795865153177398867380171
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If someone is funny then someone is both not strong and not old.
Everyone who is both curious and kind is not creative.
If susan is either not patient or brave then someone is brave.
Everyone who is quiet is funny or not creative.
If someone is either not brave or not humble then lucy is not humble or not funny and vice versa.
Everyone who is old is both quiet and not creative.
If alice is happy then someone is not strong.
Everyone who is humble or not brave is not generous and vice versa.
Everyone who is either quiet or patient is both rich and not humble and vice versa.
Everyone who is both old and creative is patient or happy.
If lucy is both not generous and funny then fred is either funny or happy.
If someone is either funny or humble then john is either not strong or not funny and vice versa.
Everyone who is not strong or not funny is both calm and strong and vice versa.
If paul is not funny or not humble then someone is either generous or not calm.
If someone is not quiet or patient then someone is both not rich and not creative and vice versa.
If fred is both not quiet and brave then someone is either not calm or not brave and vice versa.
John is either kind or generous.
Lucy is either not old or funny.
Someone is kind.
Mary is not old or not funny.
Alice is not wise or not quiet.
Someone is kind or rich.
Mary is either not funny or patient.
Someone is both rich and not curious. | Susan is not funny. | entailment | ((?[X]:(funny(X)))=>(?[X]:((~strong(X)&~old(X)))))&
(![X]:((curious(X)&kind(X))=>~creative(X)))&
(((~patient(susan)<~>brave(susan)))=>(?[X]:(brave(X))))&
(![X]:(quiet(X)=>(funny(X)|~creative(X))))&
((?[X]:((~brave(X)<~>~humble(X))))<=>((~humble(lucy)|~funny(lucy))))&
(![X]:(old(X)=>(quiet(X)&~creative(X))))&
((happy(alice))=>(?[X]:(~strong(X))))&
(![X]:((humble(X)|~brave(X))<=>~generous(X)))&
(![X]:((quiet(X)<~>patient(X))<=>(rich(X)&~humble(X))))&
(![X]:((old(X)&creative(X))=>(patient(X)|happy(X))))&
(((~generous(lucy)&funny(lucy)))=>((funny(fred)<~>happy(fred))))&
((?[X]:((funny(X)<~>humble(X))))<=>((~strong(john)<~>~funny(john))))&
(![X]:((~strong(X)|~funny(X))<=>(calm(X)&strong(X))))&
(((~funny(paul)|~humble(paul)))=>(?[X]:((generous(X)<~>~calm(X)))))&
((?[X]:((~quiet(X)|patient(X))))<=>(?[X]:((~rich(X)&~creative(X)))))&
(((~quiet(fred)&brave(fred)))<=>(?[X]:((~calm(X)<~>~brave(X)))))&
((kind(john)<~>generous(john)))&
((~old(lucy)<~>funny(lucy)))&
(?[X]:(kind(X)))&
((~old(mary)|~funny(mary)))&
((~wise(alice)|~quiet(alice)))&
(?[X]:((kind(X)|rich(X))))&
((~funny(mary)<~>patient(mary)))&
(?[X]:((rich(X)&~curious(X)))) | ~funny(susan) | [
"p0",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4653870311465833597724109
% SZS output start Proof for 4653870311465833597724109
1. ? [X0] : funny(X0) => ? [X0] : (~old(X0) & ~strong(X0)) [input p0]
13. ! [X0] : ((~funny(X0) | ~strong(X0)) <=> (strong(X0) & calm(X0))) [input p12]
25. funny(susan) [input hypothesis]
26. ? [X0] : funny(X0) => ? [X1] : (~old(X1) & ~strong(X1)) [rectify 1]
31. ? [X1] : (~old(X1) & ~strong(X1)) | ! [X0] : ~funny(X0) [ennf transformation 26]
42. ? [X0] : (~old(X0) & ~strong(X0)) | ! [X1] : ~funny(X1) [rectify 31]
43. ? [X0] : (~old(X0) & ~strong(X0)) => (~old(sK0) & ~strong(sK0)) [choice axiom]
44. (~old(sK0) & ~strong(sK0)) | ! [X1] : ~funny(X1) [skolemisation 42,43]
64. ! [X0] : (((~funny(X0) | ~strong(X0)) | (~strong(X0) | ~calm(X0))) & ((strong(X0) & calm(X0)) | (funny(X0) & strong(X0)))) [nnf transformation 13]
65. ! [X0] : ((~funny(X0) | ~strong(X0) | ~strong(X0) | ~calm(X0)) & ((strong(X0) & calm(X0)) | (funny(X0) & strong(X0)))) [flattening 64]
88. ~strong(sK0) | ~funny(X1) [cnf transformation 44]
124. strong(X0) | strong(X0) [cnf transformation 65]
152. funny(susan) [cnf transformation 25]
153. strong(X0) [duplicate literal removal 124]
156. 1 <=> ! [X1] : ~funny(X1) [avatar definition]
157. ~funny(X1) <- (1) [avatar component clause 156]
164. 3 <=> strong(sK0) [avatar definition]
166. ~strong(sK0) <- (~3) [avatar component clause 164]
167. 1 | ~3 [avatar split clause 88,164,156]
383. $false <- (~3) [subsumption resolution 166,153]
384. 3 [avatar contradiction clause 383]
385. $false <- (1) [resolution 157,152]
386. ~1 [avatar contradiction clause 385]
387. $false [avatar sat refutation 167,384,386]
% SZS output end Proof for 4653870311465833597724109
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or not old is both kind and happy and vice versa.
Everyone who is not quiet is either old or not curious and vice versa.
If lucy is both patient and creative then fred is not wise.
Everyone who is not curious or not generous is rich.
Everyone who is both brave and not funny is not creative or happy and vice versa.
If someone is strong or generous then alice is either curious or tall.
If someone is both brave and generous then john is wise.
If someone is either not old or not strong then alice is either not wise or curious and vice versa.
If someone is either not calm or tall then mary is either not kind or not quiet and vice versa.
If paul is both not generous and not wise then susan is not curious and vice versa.
Everyone who is not generous or happy is happy or tall.
Everyone who is not brave or not old is rich and vice versa.
Everyone who is both generous and patient is patient or quiet and vice versa.
If mary is not calm then someone is generous.
If someone is creative then alice is both not curious and not creative and vice versa.
If someone is both tall and not rich then alice is not brave and vice versa.
Someone is either old or not strong.
Someone is not funny.
John is either not kind or not curious.
Someone is humble.
John is either not generous or not old.
Someone is both not brave and not strong.
Susan is not quiet or not tall.
Someone is calm. | John is not quiet. | entailment | (![X]:((brave(X)|~old(X))<=>(kind(X)&happy(X))))&
(![X]:(~quiet(X)<=>(old(X)<~>~curious(X))))&
(((patient(lucy)&creative(lucy)))=>(~wise(fred)))&
(![X]:((~curious(X)|~generous(X))=>rich(X)))&
(![X]:((brave(X)&~funny(X))<=>(~creative(X)|happy(X))))&
((?[X]:((strong(X)|generous(X))))=>((curious(alice)<~>tall(alice))))&
((?[X]:((brave(X)&generous(X))))=>(wise(john)))&
((?[X]:((~old(X)<~>~strong(X))))<=>((~wise(alice)<~>curious(alice))))&
((?[X]:((~calm(X)<~>tall(X))))<=>((~kind(mary)<~>~quiet(mary))))&
(((~generous(paul)&~wise(paul)))<=>(~curious(susan)))&
(![X]:((~generous(X)|happy(X))=>(happy(X)|tall(X))))&
(![X]:((~brave(X)|~old(X))<=>rich(X)))&
(![X]:((generous(X)&patient(X))<=>(patient(X)|quiet(X))))&
((~calm(mary))=>(?[X]:(generous(X))))&
((?[X]:(creative(X)))<=>((~curious(alice)&~creative(alice))))&
((?[X]:((tall(X)&~rich(X))))<=>(~brave(alice)))&
(?[X]:((old(X)<~>~strong(X))))&
(?[X]:(~funny(X)))&
((~kind(john)<~>~curious(john)))&
(?[X]:(humble(X)))&
((~generous(john)<~>~old(john)))&
(?[X]:((~brave(X)&~strong(X))))&
((~quiet(susan)|~tall(susan)))&
(?[X]:(calm(X))) | ~quiet(john) | [
"p0",
"p1",
"p12",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5568608758545682767479355
% SZS output start Proof for 5568608758545682767479355
1. ! [X0] : ((~old(X0) | brave(X0)) <=> (happy(X0) & kind(X0))) [input p0]
2. ! [X0] : (~quiet(X0) <=> (old(X0) <~> ~curious(X0))) [input p1]
13. ! [X0] : ((patient(X0) & generous(X0)) <=> (quiet(X0) | patient(X0))) [input p12]
19. ~kind(john) <~> ~curious(john) [input p18]
21. ~generous(john) <~> ~old(john) [input p20]
25. quiet(john) [input hypothesis]
35. ! [X0] : (((~old(X0) | brave(X0)) | (~happy(X0) | ~kind(X0))) & ((happy(X0) & kind(X0)) | (old(X0) & ~brave(X0)))) [nnf transformation 1]
36. ! [X0] : ((~old(X0) | brave(X0) | ~happy(X0) | ~kind(X0)) & ((happy(X0) & kind(X0)) | (old(X0) & ~brave(X0)))) [flattening 35]
37. ! [X0] : ((~quiet(X0) | ((old(X0) | curious(X0)) & (~curious(X0) | ~old(X0)))) & (((curious(X0) | ~old(X0)) & (~curious(X0) | old(X0))) | quiet(X0))) [nnf transformation 2]
53. ! [X0] : (((patient(X0) & generous(X0)) | (~quiet(X0) & ~patient(X0))) & ((quiet(X0) | patient(X0)) | (~patient(X0) | ~generous(X0)))) [nnf transformation 13]
54. ! [X0] : (((patient(X0) & generous(X0)) | (~quiet(X0) & ~patient(X0))) & (quiet(X0) | patient(X0) | ~patient(X0) | ~generous(X0))) [flattening 53]
71. (curious(john) | kind(john)) & (~curious(john) | ~kind(john)) [nnf transformation 19]
72. (old(john) | generous(john)) & (~old(john) | ~generous(john)) [nnf transformation 21]
78. kind(X0) | old(X0) [cnf transformation 36]
85. ~quiet(X0) | old(X0) | curious(X0) [cnf transformation 37]
125. ~quiet(X0) | generous(X0) [cnf transformation 54]
138. ~curious(john) | ~kind(john) [cnf transformation 71]
140. ~old(john) | ~generous(john) [cnf transformation 72]
146. quiet(john) [cnf transformation 25]
309. 35 <=> kind(john) [avatar definition]
310. ~kind(john) <- (~35) [avatar component clause 309]
313. 36 <=> curious(john) [avatar definition]
317. ~35 | ~36 [avatar split clause 138,313,309]
319. 37 <=> generous(john) [avatar definition]
323. 38 <=> old(john) [avatar definition]
324. ~old(john) <- (~38) [avatar component clause 323]
327. ~37 | ~38 [avatar split clause 140,323,319]
369. generous(john) [resolution 125,146]
397. old(john) | curious(john) [resolution 85,146]
403. old(john) <- (~35) [resolution 310,78]
404. $false <- (~35, ~38) [subsumption resolution 403,324]
405. 35 | 38 [avatar contradiction clause 404]
407. 37 [avatar split clause 369,319]
408. 36 | 38 [avatar split clause 397,323,313]
409. $false [avatar sat refutation 317,327,405,407,408]
% SZS output end Proof for 5568608758545682767479355
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not quiet or not patient then alice is not old or brave and vice versa. If someone is calm or not brave then someone is humble. Everyone who is curious or not funny is funny or wise. Everyone who is both calm and not rich is either not calm or not patient. Everyone who is either humble or not strong is brave or not patient. If someone is not old or funny then someone is both wise and creative and vice versa. If someone is not happy or not tall then fred is both kind and old and vice versa. If someone is not calm then someone is either not tall or not kind and vice versa. If someone is quiet then someone is patient. If someone is either not creative or not rich then someone is brave or humble and vice versa. Everyone who is not old or kind is both humble and not old and vice versa. Everyone who is both not calm and not happy is both not old and not strong and vice versa. If someone is curious then someone is both not curious and happy and vice versa. Everyone who is old is creative or brave and vice versa. Everyone who is not rich is both creative and brave and vice versa. If fred is both not rich and kind then john is not curious or humble. John is calm or generous. Someone is not strong. Fred is both patient and happy. Someone is humble or old. Paul is either not strong or not curious. Someone is humble or not strong. Someone is strong. Fred is either curious or not tall. | Fred is not tall. | contradiction | ((?[X]:((~quiet(X)|~patient(X))))<=>((~old(alice)|brave(alice))))&
((?[X]:((calm(X)|~brave(X))))=>(?[X]:(humble(X))))&
(![X]:((curious(X)|~funny(X))=>(funny(X)|wise(X))))&
(![X]:((calm(X)&~rich(X))=>(~calm(X)<~>~patient(X))))&
(![X]:((humble(X)<~>~strong(X))=>(brave(X)|~patient(X))))&
((?[X]:((~old(X)|funny(X))))<=>(?[X]:((wise(X)&creative(X)))))&
((?[X]:((~happy(X)|~tall(X))))<=>((kind(fred)&old(fred))))&
((?[X]:(~calm(X)))<=>(?[X]:((~tall(X)<~>~kind(X)))))&
((?[X]:(quiet(X)))=>(?[X]:(patient(X))))&
((?[X]:((~creative(X)<~>~rich(X))))<=>(?[X]:((brave(X)|humble(X)))))&
(![X]:((~old(X)|kind(X))<=>(humble(X)&~old(X))))&
(![X]:((~calm(X)&~happy(X))<=>(~old(X)&~strong(X))))&
((?[X]:(curious(X)))<=>(?[X]:((~curious(X)&happy(X)))))&
(![X]:(old(X)<=>(creative(X)|brave(X))))&
(![X]:(~rich(X)<=>(creative(X)&brave(X))))&
(((~rich(fred)&kind(fred)))=>((~curious(john)|humble(john))))&
((calm(john)|generous(john)))&
(?[X]:(~strong(X)))&
((patient(fred)&happy(fred)))&
(?[X]:((humble(X)|old(X))))&
((~strong(paul)<~>~curious(paul)))&
(?[X]:((humble(X)|~strong(X))))&
(?[X]:(strong(X)))&
((curious(fred)<~>~tall(fred))) | ~tall(fred) | [
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6797343212973424880736986
% SZS output start Proof for 6797343212973424880736986
7. ? [X0] : (~tall(X0) | ~happy(X0)) <=> (old(fred) & kind(fred)) [input p6]
11. ! [X0] : ((kind(X0) | ~old(X0)) <=> (~old(X0) & humble(X0))) [input p10]
25. ~tall(fred) [input hypothesis]
58. (? [X0] : (~tall(X0) | ~happy(X0)) | (~old(fred) | ~kind(fred))) & ((old(fred) & kind(fred)) | ! [X0] : (tall(X0) & happy(X0))) [nnf transformation 7]
59. (? [X0] : (~tall(X0) | ~happy(X0)) | ~old(fred) | ~kind(fred)) & ((old(fred) & kind(fred)) | ! [X0] : (tall(X0) & happy(X0))) [flattening 58]
60. (? [X0] : (~tall(X0) | ~happy(X0)) | ~old(fred) | ~kind(fred)) & ((old(fred) & kind(fred)) | ! [X1] : (tall(X1) & happy(X1))) [rectify 59]
61. ? [X0] : (~tall(X0) | ~happy(X0)) => (~tall(sK4) | ~happy(sK4)) [choice axiom]
62. ((~tall(sK4) | ~happy(sK4)) | ~old(fred) | ~kind(fred)) & ((old(fred) & kind(fred)) | ! [X1] : (tall(X1) & happy(X1))) [skolemisation 60,61]
76. ! [X0] : (((kind(X0) | ~old(X0)) | (old(X0) | ~humble(X0))) & ((~old(X0) & humble(X0)) | (~kind(X0) & old(X0)))) [nnf transformation 11]
77. ! [X0] : ((kind(X0) | ~old(X0) | old(X0) | ~humble(X0)) & ((~old(X0) & humble(X0)) | (~kind(X0) & old(X0)))) [flattening 76]
117. kind(fred) | tall(X1) [cnf transformation 62]
119. old(fred) | tall(X1) [cnf transformation 62]
135. ~kind(X0) | ~old(X0) [cnf transformation 77]
161. ~tall(fred) [cnf transformation 25]
233. 17 <=> kind(fred) [avatar definition]
234. kind(fred) <- (17) [avatar component clause 233]
237. 18 <=> old(fred) [avatar definition]
250. 21 <=> ! [X1] : tall(X1) [avatar definition]
251. tall(X1) <- (21) [avatar component clause 250]
252. 21 | 18 [avatar split clause 119,237,250]
257. 21 | 17 [avatar split clause 117,233,250]
384. 52 <=> tall(fred) [avatar definition]
385. ~tall(fred) <- (~52) [avatar component clause 384]
389. ~52 [avatar split clause 161,384]
404. ~old(fred) <- (17) [resolution 135,234]
407. ~18 | ~17 [avatar split clause 404,233,237]
408. $false <- (21, ~52) [resolution 251,385]
409. ~21 | 52 [avatar contradiction clause 408]
410. $false [avatar sat refutation 252,257,389,407,409]
% SZS output end Proof for 6797343212973424880736986
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not kind or not funny then someone is not wise or not calm.
Everyone who is both not strong and strong is both rich and not rich.
Everyone who is both not funny and humble is wise.
Everyone who is both not rich and tall is both happy and generous.
If john is tall then someone is not curious.
Everyone who is rich is either generous or calm and vice versa.
If someone is generous then someone is either not wise or not patient and vice versa.
Everyone who is quiet is both not strong and tall and vice versa.
If someone is both not kind and not strong then someone is not brave or not kind and vice versa.
If paul is not funny or not creative then someone is not happy or not tall.
If someone is either generous or patient then fred is humble and vice versa.
Everyone who is either not humble or not patient is either happy or funny.
Everyone who is either not patient or not humble is both happy and not calm.
If fred is not calm then alice is not quiet or not tall.
Everyone who is strong is not wise and vice versa.
If someone is not generous or not happy then someone is not happy and vice versa.
Susan is both not patient and kind.
Someone is both not calm and patient.
Paul is not calm or kind.
Someone is not brave.
Lucy is not tall or creative.
Alice is both not brave and calm.
Someone is both not patient and generous.
Someone is both not kind and creative. | Alice is not creative. | neutral | (((~kind(paul)|~funny(paul)))=>(?[X]:((~wise(X)|~calm(X)))))&
(![X]:((~strong(X)&strong(X))=>(rich(X)&~rich(X))))&
(![X]:((~funny(X)&humble(X))=>wise(X)))&
(![X]:((~rich(X)&tall(X))=>(happy(X)&generous(X))))&
((tall(john))=>(?[X]:(~curious(X))))&
(![X]:(rich(X)<=>(generous(X)<~>calm(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~wise(X)<~>~patient(X)))))&
(![X]:(quiet(X)<=>(~strong(X)&tall(X))))&
((?[X]:((~kind(X)&~strong(X))))<=>(?[X]:((~brave(X)|~kind(X)))))&
(((~funny(paul)|~creative(paul)))=>(?[X]:((~happy(X)|~tall(X)))))&
((?[X]:((generous(X)<~>patient(X))))<=>(humble(fred)))&
(![X]:((~humble(X)<~>~patient(X))=>(happy(X)<~>funny(X))))&
(![X]:((~patient(X)<~>~humble(X))=>(happy(X)&~calm(X))))&
((~calm(fred))=>((~quiet(alice)|~tall(alice))))&
(![X]:(strong(X)<=>~wise(X)))&
((?[X]:((~generous(X)|~happy(X))))<=>(?[X]:(~happy(X))))&
((~patient(susan)&kind(susan)))&
(?[X]:((~calm(X)&patient(X))))&
((~calm(paul)|kind(paul)))&
(?[X]:(~brave(X)))&
((~tall(lucy)|creative(lucy)))&
((~brave(alice)&calm(alice)))&
(?[X]:((~patient(X)&generous(X))))&
(?[X]:((~kind(X)&creative(X)))) | ~creative(alice) | [] | null | 0 |
If someone is not funny then someone is either not funny or patient and vice versa.
Everyone who is not patient or not generous is either calm or not happy.
Everyone who is not tall or not happy is both not calm and old.
If someone is both tall and not strong then john is both wise and not humble and vice versa.
If someone is brave then paul is both quiet and rich.
Everyone who is either happy or rich is not calm or not creative and vice versa.
If someone is kind then fred is rich and vice versa.
If someone is creative or brave then someone is both wise and kind and vice versa.
If alice is not generous or not tall then paul is not quiet and vice versa.
Everyone who is both calm and not curious is kind or patient and vice versa.
Everyone who is either not funny or not generous is either not curious or tall.
Everyone who is humble is not tall.
If paul is humble or not brave then alice is generous.
Everyone who is calm is both not creative and not strong.
If someone is not quiet or generous then alice is old.
Someone is either not tall or creative.
Mary is not old or not rich.
Someone is both not calm and tall.
Lucy is kind or humble.
Someone is not brave or not old.
Someone is humble or brave.
Someone is both curious and generous. | Fred is not kind. | entailment | ((?[X]:(~funny(X)))<=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:((~patient(X)|~generous(X))=>(calm(X)<~>~happy(X))))&
(![X]:((~tall(X)|~happy(X))=>(~calm(X)&old(X))))&
((?[X]:((tall(X)&~strong(X))))<=>((wise(john)&~humble(john))))&
((?[X]:(brave(X)))=>((quiet(paul)&rich(paul))))&
(![X]:((happy(X)<~>rich(X))<=>(~calm(X)|~creative(X))))&
((?[X]:(kind(X)))<=>(rich(fred)))&
((?[X]:((creative(X)|brave(X))))<=>(?[X]:((wise(X)&kind(X)))))&
(((~generous(alice)|~tall(alice)))<=>(~quiet(paul)))&
(![X]:((calm(X)&~curious(X))<=>(kind(X)|patient(X))))&
(![X]:((~funny(X)<~>~generous(X))=>(~curious(X)<~>tall(X))))&
(![X]:(humble(X)=>~tall(X)))&
(((humble(paul)|~brave(paul)))=>(generous(alice)))&
(![X]:(calm(X)=>(~creative(X)&~strong(X))))&
((?[X]:((~quiet(X)|generous(X))))=>(old(alice)))&
(?[X]:((~tall(X)<~>creative(X))))&
((~old(mary)|~rich(mary)))&
(?[X]:((~calm(X)&tall(X))))&
((kind(lucy)|humble(lucy)))&
(?[X]:((~brave(X)|~old(X))))&
(?[X]:((humble(X)|brave(X))))&
(?[X]:((curious(X)&generous(X)))) | ~kind(fred) | [
"p2",
"p5",
"p6",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8383243067193113945366320
% SZS output start Proof for 8383243067193113945366320
3. ! [X0] : ((~happy(X0) | ~tall(X0)) => (old(X0) & ~calm(X0))) [input p2]
6. ! [X0] : ((happy(X0) <~> rich(X0)) <=> (~creative(X0) | ~calm(X0))) [input p5]
7. ? [X0] : kind(X0) <=> rich(fred) [input p6]
10. ! [X0] : ((~curious(X0) & calm(X0)) <=> (patient(X0) | kind(X0))) [input p9]
14. ! [X0] : (calm(X0) => (~strong(X0) & ~creative(X0))) [input p13]
23. kind(fred) [input hypothesis]
27. ! [X0] : ((old(X0) & ~calm(X0)) | (happy(X0) & tall(X0))) [ennf transformation 3]
32. ! [X0] : ((~strong(X0) & ~creative(X0)) | ~calm(X0)) [ennf transformation 14]
45. ! [X0] : ((((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | (creative(X0) & calm(X0))) & ((~creative(X0) | ~calm(X0)) | ((happy(X0) | ~rich(X0)) & (rich(X0) | ~happy(X0))))) [nnf transformation 6]
46. ! [X0] : ((((~rich(X0) | ~happy(X0)) & (rich(X0) | happy(X0))) | (creative(X0) & calm(X0))) & (~creative(X0) | ~calm(X0) | ((happy(X0) | ~rich(X0)) & (rich(X0) | ~happy(X0))))) [flattening 45]
47. (? [X0] : kind(X0) | ~rich(fred)) & (rich(fred) | ! [X0] : ~kind(X0)) [nnf transformation 7]
48. (? [X0] : kind(X0) | ~rich(fred)) & (rich(fred) | ! [X1] : ~kind(X1)) [rectify 47]
49. ? [X0] : kind(X0) => kind(sK3) [choice axiom]
50. (kind(sK3) | ~rich(fred)) & (rich(fred) | ! [X1] : ~kind(X1)) [skolemisation 48,49]
58. ! [X0] : (((~curious(X0) & calm(X0)) | (~patient(X0) & ~kind(X0))) & ((patient(X0) | kind(X0)) | (curious(X0) | ~calm(X0)))) [nnf transformation 10]
59. ! [X0] : (((~curious(X0) & calm(X0)) | (~patient(X0) & ~kind(X0))) & (patient(X0) | kind(X0) | curious(X0) | ~calm(X0))) [flattening 58]
81. ~calm(X0) | happy(X0) [cnf transformation 27]
95. ~rich(X0) | ~happy(X0) | creative(X0) [cnf transformation 46]
96. rich(fred) | ~kind(X1) [cnf transformation 50]
107. ~kind(X0) | calm(X0) [cnf transformation 59]
118. ~creative(X0) | ~calm(X0) [cnf transformation 32]
132. kind(fred) [cnf transformation 23]
197. 15 <=> rich(fred) [avatar definition]
198. rich(fred) <- (15) [avatar component clause 197]
206. 17 <=> ! [X1] : ~kind(X1) [avatar definition]
207. ~kind(X1) <- (17) [avatar component clause 206]
208. 17 | 15 [avatar split clause 96,197,206]
315. calm(fred) [resolution 107,132]
318. happy(fred) [resolution 315,81]
355. $false <- (17) [resolution 207,132]
360. ~17 [avatar contradiction clause 355]
361. ~happy(fred) | creative(fred) <- (15) [resolution 198,95]
363. creative(fred) <- (15) [subsumption resolution 361,318]
369. ~calm(fred) <- (15) [resolution 363,118]
370. $false <- (15) [subsumption resolution 369,315]
371. ~15 [avatar contradiction clause 370]
372. $false [avatar sat refutation 208,360,371]
% SZS output end Proof for 8383243067193113945366320
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not calm then alice is not rich or strong and vice versa. Everyone who is both not creative and not funny is either wise or funny and vice versa. If paul is not old or brave then someone is not calm and vice versa. If lucy is brave or not rich then mary is either not quiet or generous and vice versa. Everyone who is not wise or not funny is either generous or rich. Everyone who is either not curious or patient is not quiet or tall and vice versa. Everyone who is both not rich and generous is either calm or not happy and vice versa. If someone is not calm then john is quiet and vice versa. Everyone who is not kind or not funny is either not funny or quiet. Everyone who is both not funny and not strong is tall. Everyone who is humble is both not wise and not patient and vice versa. Everyone who is quiet or creative is both not strong and humble and vice versa. Everyone who is either not kind or humble is either generous or strong. Everyone who is either old or not tall is old. Paul is either not tall or calm. Someone is either happy or not humble. Mary is not generous or not funny. Someone is strong. Someone is both not old and not quiet. | John is not patient. | neutral | ((?[X]:((funny(X)|~calm(X))))<=>((~rich(alice)|strong(alice))))&
(![X]:((~creative(X)&~funny(X))<=>(wise(X)<~>funny(X))))&
(((~old(paul)|brave(paul)))<=>(?[X]:(~calm(X))))&
(((brave(lucy)|~rich(lucy)))<=>((~quiet(mary)<~>generous(mary))))&
(![X]:((~wise(X)|~funny(X))=>(generous(X)<~>rich(X))))&
(![X]:((~curious(X)<~>patient(X))<=>(~quiet(X)|tall(X))))&
(![X]:((~rich(X)&generous(X))<=>(calm(X)<~>~happy(X))))&
((?[X]:(~calm(X)))<=>(quiet(john)))&
(![X]:((~kind(X)|~funny(X))=>(~funny(X)<~>quiet(X))))&
(![X]:((~funny(X)&~strong(X))=>tall(X)))&
(![X]:(humble(X)<=>(~wise(X)&~patient(X))))&
(![X]:((quiet(X)|creative(X))<=>(~strong(X)&humble(X))))&
(![X]:((~kind(X)<~>humble(X))=>(generous(X)<~>strong(X))))&
(![X]:((old(X)<~>~tall(X))=>old(X)))&
((~tall(paul)<~>calm(paul)))&
(?[X]:((happy(X)<~>~humble(X))))&
((~generous(mary)|~funny(mary)))&
(?[X]:(strong(X)))&
(?[X]:((~old(X)&~quiet(X)))) | ~patient(john) | [] | null | 0 |
If alice is both curious and strong then alice is not tall or not patient.
Everyone who is old is both creative and quiet and vice versa.
Everyone who is humble is both not quiet and rich and vice versa.
If mary is either funny or not happy then susan is strong and vice versa.
Everyone who is both not old and kind is either curious or not brave and vice versa.
Everyone who is not strong is not quiet or not patient and vice versa.
If susan is either rich or not curious then paul is not strong.
Everyone who is both wise and not calm is both funny and not creative.
If fred is either creative or not old then someone is either not funny or not creative and vice versa.
If john is both calm and funny then lucy is either generous or not quiet.
Everyone who is brave is strong and vice versa.
Everyone who is either kind or not generous is kind and vice versa.
If alice is both curious and creative then john is quiet and vice versa.
Everyone who is both not curious and wise is not patient.
Everyone who is either not humble or not calm is old.
Someone is rich.
John is not tall or not happy.
Someone is humble or curious.
Someone is curious or generous.
Susan is both tall and not calm.
Fred is either not old or humble.
Someone is either curious or not rich.
Someone is both curious and rich. | Susan is old. | neutral | (((curious(alice)&strong(alice)))=>((~tall(alice)|~patient(alice))))&
(![X]:(old(X)<=>(creative(X)&quiet(X))))&
(![X]:(humble(X)<=>(~quiet(X)&rich(X))))&
(((funny(mary)<~>~happy(mary)))<=>(strong(susan)))&
(![X]:((~old(X)&kind(X))<=>(curious(X)<~>~brave(X))))&
(![X]:(~strong(X)<=>(~quiet(X)|~patient(X))))&
(((rich(susan)<~>~curious(susan)))=>(~strong(paul)))&
(![X]:((wise(X)&~calm(X))=>(funny(X)&~creative(X))))&
(((creative(fred)<~>~old(fred)))<=>(?[X]:((~funny(X)<~>~creative(X)))))&
(((calm(john)&funny(john)))=>((generous(lucy)<~>~quiet(lucy))))&
(![X]:(brave(X)<=>strong(X)))&
(![X]:((kind(X)<~>~generous(X))<=>kind(X)))&
(((curious(alice)&creative(alice)))<=>(quiet(john)))&
(![X]:((~curious(X)&wise(X))=>~patient(X)))&
(![X]:((~humble(X)<~>~calm(X))=>old(X)))&
(?[X]:(rich(X)))&
((~tall(john)|~happy(john)))&
(?[X]:((humble(X)|curious(X))))&
(?[X]:((curious(X)|generous(X))))&
((tall(susan)&~calm(susan)))&
((~old(fred)<~>humble(fred)))&
(?[X]:((curious(X)<~>~rich(X))))&
(?[X]:((curious(X)&rich(X)))) | old(susan) | [] | null | 0 |
If john is both patient and tall then someone is not old and vice versa.
Everyone who is both strong and tall is either not quiet or old and vice versa.
Everyone who is calm is either humble or not quiet.
Everyone who is either not quiet or not kind is not quiet or not humble.
Everyone who is brave or rich is both not calm and not generous and vice versa.
Everyone who is humble or not generous is either strong or not creative and vice versa.
If lucy is old or generous then someone is generous.
Everyone who is not wise is humble or patient.
Everyone who is strong is not strong or not quiet.
If susan is not funny then someone is either funny or not calm.
If alice is either not kind or rich then someone is either not funny or not generous and vice versa.
If lucy is not strong then someone is calm and vice versa.
Everyone who is not strong or not humble is both not generous and generous.
Everyone who is not calm is not happy or wise.
Everyone who is both brave and not wise is either humble or not creative and vice versa.
Everyone who is either wise or not rich is either not tall or not humble and vice versa.
Someone is creative or old.
Someone is either creative or happy.
Lucy is either generous or not wise.
Someone is either kind or not strong.
Someone is either brave or not creative.
Susan is either not strong or not curious.
Someone is not brave or curious. | John is not old. | entailment | (((patient(john)&tall(john)))<=>(?[X]:(~old(X))))&
(![X]:((strong(X)&tall(X))<=>(~quiet(X)<~>old(X))))&
(![X]:(calm(X)=>(humble(X)<~>~quiet(X))))&
(![X]:((~quiet(X)<~>~kind(X))=>(~quiet(X)|~humble(X))))&
(![X]:((brave(X)|rich(X))<=>(~calm(X)&~generous(X))))&
(![X]:((humble(X)|~generous(X))<=>(strong(X)<~>~creative(X))))&
(((old(lucy)|generous(lucy)))=>(?[X]:(generous(X))))&
(![X]:(~wise(X)=>(humble(X)|patient(X))))&
(![X]:(strong(X)=>(~strong(X)|~quiet(X))))&
((~funny(susan))=>(?[X]:((funny(X)<~>~calm(X)))))&
(((~kind(alice)<~>rich(alice)))<=>(?[X]:((~funny(X)<~>~generous(X)))))&
((~strong(lucy))<=>(?[X]:(calm(X))))&
(![X]:((~strong(X)|~humble(X))=>(~generous(X)&generous(X))))&
(![X]:(~calm(X)=>(~happy(X)|wise(X))))&
(![X]:((brave(X)&~wise(X))<=>(humble(X)<~>~creative(X))))&
(![X]:((wise(X)<~>~rich(X))<=>(~tall(X)<~>~humble(X))))&
(?[X]:((creative(X)|old(X))))&
(?[X]:((creative(X)<~>happy(X))))&
((generous(lucy)<~>~wise(lucy)))&
(?[X]:((kind(X)<~>~strong(X))))&
(?[X]:((brave(X)<~>~creative(X))))&
((~strong(susan)<~>~curious(susan)))&
(?[X]:((~brave(X)|curious(X)))) | ~old(john) | [
"p0",
"p1",
"p4",
"p5",
"p6",
"p8",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6213943507097672064578307
% SZS output start Proof for 6213943507097672064578307
1. (tall(john) & patient(john)) <=> ? [X0] : ~old(X0) [input p0]
2. ! [X0] : ((tall(X0) & strong(X0)) <=> (~quiet(X0) <~> old(X0))) [input p1]
5. ! [X0] : ((rich(X0) | brave(X0)) <=> (~generous(X0) & ~calm(X0))) [input p4]
6. ! [X0] : ((~generous(X0) | humble(X0)) <=> (strong(X0) <~> ~creative(X0))) [input p5]
7. (generous(lucy) | old(lucy)) => ? [X0] : generous(X0) [input p6]
9. ! [X0] : (strong(X0) => (~quiet(X0) | ~strong(X0))) [input p8]
13. ! [X0] : ((~humble(X0) | ~strong(X0)) => (generous(X0) & ~generous(X0))) [input p12]
15. ! [X0] : ((~wise(X0) & brave(X0)) <=> (humble(X0) <~> ~creative(X0))) [input p14]
24. old(john) [input hypothesis]
28. ? [X0] : generous(X0) | (~generous(lucy) & ~old(lucy)) [ennf transformation 7]
31. ! [X0] : ((~quiet(X0) | ~strong(X0)) | ~strong(X0)) [ennf transformation 9]
32. ! [X0] : (~quiet(X0) | ~strong(X0) | ~strong(X0)) [flattening 31]
34. ! [X0] : ((generous(X0) & ~generous(X0)) | (humble(X0) & strong(X0))) [ennf transformation 13]
37. ((tall(john) & patient(john)) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | (~tall(john) | ~patient(john))) [nnf transformation 1]
38. ((tall(john) & patient(john)) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | ~tall(john) | ~patient(john)) [flattening 37]
39. ((tall(john) & patient(john)) | ! [X0] : old(X0)) & (? [X1] : ~old(X1) | ~tall(john) | ~patient(john)) [rectify 38]
40. ? [X1] : ~old(X1) => ~old(sK0) [choice axiom]
41. ((tall(john) & patient(john)) | ! [X0] : old(X0)) & (~old(sK0) | ~tall(john) | ~patient(john)) [skolemisation 39,40]
42. ! [X0] : (((tall(X0) & strong(X0)) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~tall(X0) | ~strong(X0)))) [nnf transformation 2]
43. ! [X0] : (((tall(X0) & strong(X0)) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | ~tall(X0) | ~strong(X0))) [flattening 42]
46. ! [X0] : (((rich(X0) | brave(X0)) | (generous(X0) | calm(X0))) & ((~generous(X0) & ~calm(X0)) | (~rich(X0) & ~brave(X0)))) [nnf transformation 5]
47. ! [X0] : ((rich(X0) | brave(X0) | generous(X0) | calm(X0)) & ((~generous(X0) & ~calm(X0)) | (~rich(X0) & ~brave(X0)))) [flattening 46]
48. ! [X0] : (((~generous(X0) | humble(X0)) | ((strong(X0) | creative(X0)) & (~creative(X0) | ~strong(X0)))) & (((creative(X0) | ~strong(X0)) & (~creative(X0) | strong(X0))) | (generous(X0) & ~humble(X0)))) [nnf transformation 6]
49. ! [X0] : ((~generous(X0) | humble(X0) | ((strong(X0) | creative(X0)) & (~creative(X0) | ~strong(X0)))) & (((creative(X0) | ~strong(X0)) & (~creative(X0) | strong(X0))) | (generous(X0) & ~humble(X0)))) [flattening 48]
50. ? [X0] : generous(X0) => generous(sK1) [choice axiom]
51. generous(sK1) | (~generous(lucy) & ~old(lucy)) [skolemisation 28,50]
63. ! [X0] : (((~wise(X0) & brave(X0)) | ((humble(X0) | creative(X0)) & (~creative(X0) | ~humble(X0)))) & (((creative(X0) | ~humble(X0)) & (~creative(X0) | humble(X0))) | (wise(X0) | ~brave(X0)))) [nnf transformation 15]
64. ! [X0] : (((~wise(X0) & brave(X0)) | ((humble(X0) | creative(X0)) & (~creative(X0) | ~humble(X0)))) & (((creative(X0) | ~humble(X0)) & (~creative(X0) | humble(X0))) | wise(X0) | ~brave(X0))) [flattening 63]
83. tall(john) | old(X0) [cnf transformation 41]
85. ~strong(X0) | quiet(X0) | ~tall(X0) | ~old(X0) [cnf transformation 43]
96. ~generous(X0) | ~brave(X0) [cnf transformation 47]
101. ~humble(X0) | ~strong(X0) | creative(X0) [cnf transformation 49]
105. generous(sK1) | ~old(lucy) [cnf transformation 51]
108. ~quiet(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 32]
121. ~generous(X0) | strong(X0) [cnf transformation 34]
122. ~generous(X0) | humble(X0) [cnf transformation 34]
123. generous(X0) | strong(X0) [cnf transformation 34]
124. generous(X0) | humble(X0) [cnf transformation 34]
128. brave(X0) | ~creative(X0) | ~humble(X0) [cnf transformation 64]
152. old(john) [cnf transformation 24]
153. ~quiet(X0) | ~strong(X0) [duplicate literal removal 108]
156. 1 <=> ! [X0] : old(X0) [avatar definition]
157. old(X0) <- (1) [avatar component clause 156]
159. 2 <=> tall(john) [avatar definition]
161. tall(john) <- (2) [avatar component clause 159]
162. 1 | 2 [avatar split clause 83,159,156]
178. 6 <=> generous(sK1) [avatar definition]
180. generous(sK1) <- (6) [avatar component clause 178]
183. 7 <=> old(lucy) [avatar definition]
185. ~old(lucy) <- (~7) [avatar component clause 183]
186. ~7 | 6 [avatar split clause 105,178,183]
244. humble(X0) [subsumption resolution 122,124]
245. strong(X0) [subsumption resolution 121,123]
247. ~creative(X0) | brave(X0) [subsumption resolution 128,244]
326. ~strong(X0) | creative(X0) [resolution 101,244]
327. creative(X0) [subsumption resolution 326,245]
331. brave(X2) [resolution 327,247]
377. $false <- (1, ~7) [resolution 157,185]
378. ~1 | 7 [avatar contradiction clause 377]
382. ~brave(sK1) <- (6) [resolution 180,96]
383. $false <- (6) [subsumption resolution 382,331]
384. ~6 [avatar contradiction clause 383]
397. ~old(X0) | ~tall(X0) | quiet(X0) [resolution 85,245]
418. ~tall(john) | quiet(john) [resolution 397,152]
420. quiet(john) <- (2) [subsumption resolution 418,161]
425. ~strong(john) <- (2) [resolution 420,153]
426. $false <- (2) [subsumption resolution 425,245]
427. ~2 [avatar contradiction clause 426]
428. $false [avatar sat refutation 162,186,378,384,427]
% SZS output end Proof for 6213943507097672064578307
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or kind is both creative and calm and vice versa.
If someone is both wise and calm then someone is not calm.
If alice is both kind and not brave then alice is both old and not strong and vice versa.
If someone is patient then john is rich.
If mary is funny then someone is not wise or not strong.
Everyone who is curious or not old is brave or not wise.
Everyone who is tall is not generous and vice versa.
Everyone who is brave is patient and vice versa.
Everyone who is either patient or not strong is both not calm and brave and vice versa.
Everyone who is not strong is kind or not calm and vice versa.
If susan is old or not tall then someone is quiet.
If someone is both quiet and happy then fred is happy or generous and vice versa.
Everyone who is not wise or not rich is both not happy and not brave.
Everyone who is either not curious or not brave is curious or funny and vice versa.
Everyone who is 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.
Paul is both not humble and not generous.
Someone is either not funny or not wise.
Someone is either not brave or not funny.
Alice is both calm and not tall.
Susan is not funny or funny.
Someone is both not tall and not wise. | Paul is curious. | entailment | (![X]:((~wise(X)<~>kind(X))<=>(creative(X)&calm(X))))&
((?[X]:((wise(X)&calm(X))))=>(?[X]:(~calm(X))))&
(((kind(alice)&~brave(alice)))<=>((old(alice)&~strong(alice))))&
((?[X]:(patient(X)))=>(rich(john)))&
((funny(mary))=>(?[X]:((~wise(X)|~strong(X)))))&
(![X]:((curious(X)|~old(X))=>(brave(X)|~wise(X))))&
(![X]:(tall(X)<=>~generous(X)))&
(![X]:(brave(X)<=>patient(X)))&
(![X]:((patient(X)<~>~strong(X))<=>(~calm(X)&brave(X))))&
(![X]:(~strong(X)<=>(kind(X)|~calm(X))))&
(((old(susan)|~tall(susan)))=>(?[X]:(quiet(X))))&
((?[X]:((quiet(X)&happy(X))))<=>((happy(fred)|generous(fred))))&
(![X]:((~wise(X)|~rich(X))=>(~happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>~brave(X))<=>(curious(X)|funny(X))))&
(![X]:((~curious(X)|~calm(X))<=>~calm(X)))&
(![X]:((rich(X)<~>curious(X))<=>(brave(X)|~quiet(X))))&
((~humble(paul)&~generous(paul)))&
(?[X]:((~funny(X)<~>~wise(X))))&
(?[X]:((~brave(X)<~>~funny(X))))&
((calm(alice)&~tall(alice)))&
((~funny(susan)|funny(susan)))&
(?[X]:((~tall(X)&~wise(X)))) | curious(paul) | [
"p7",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3342937417163126743147449
% SZS output start Proof for 3342937417163126743147449
8. ! [X0] : (brave(X0) <=> patient(X0)) [input p7]
9. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (brave(X0) & ~calm(X0))) [input p8]
10. ! [X0] : (~strong(X0) <=> (~calm(X0) | kind(X0))) [input p9]
15. ! [X0] : ((~calm(X0) | ~curious(X0)) <=> ~calm(X0)) [input p14]
23. ~curious(paul) [input hypothesis]
43. ! [X0] : ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0))) [nnf transformation 8]
44. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (~brave(X0) | calm(X0))) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 9]
45. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | ~brave(X0) | calm(X0)) & ((brave(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [flattening 44]
46. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & ((~calm(X0) | kind(X0)) | strong(X0))) [nnf transformation 10]
47. ! [X0] : ((~strong(X0) | (calm(X0) & ~kind(X0))) & (~calm(X0) | kind(X0) | strong(X0))) [flattening 46]
57. ! [X0] : (((~calm(X0) | ~curious(X0)) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [nnf transformation 15]
58. ! [X0] : ((~calm(X0) | ~curious(X0) | calm(X0)) & (~calm(X0) | (calm(X0) & curious(X0)))) [flattening 57]
86. ~brave(X0) | patient(X0) [cnf transformation 43]
87. ~patient(X0) | brave(X0) [cnf transformation 43]
91. brave(X0) | patient(X0) | strong(X0) [cnf transformation 45]
93. strong(X0) | ~patient(X0) | ~brave(X0) | calm(X0) [cnf transformation 45]
96. ~strong(X0) | calm(X0) [cnf transformation 47]
114. ~calm(X0) | curious(X0) [cnf transformation 58]
133. ~curious(paul) [cnf transformation 23]
185. ~brave(X0) | strong(X0) | calm(X0) [subsumption resolution 93,86]
186. patient(X0) | strong(X0) [subsumption resolution 91,86]
247. strong(X0) | brave(X0) [resolution 186,87]
248. brave(X0) | calm(X0) [resolution 247,96]
368. strong(X0) | calm(X0) | calm(X0) [resolution 185,248]
370. strong(X0) | calm(X0) [duplicate literal removal 368]
371. calm(X0) [subsumption resolution 370,96]
374. curious(X1) [resolution 371,114]
411. $false [resolution 374,133]
% SZS output end Proof for 3342937417163126743147449
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or patient is not happy and vice versa.
Everyone who is both not strong and not old is both curious and strong.
Everyone who is both generous and rich is both not strong and rich.
Everyone who is both not kind and not generous is not patient and vice versa.
Everyone who is wise or not quiet is patient or wise and vice versa.
Everyone who is brave or happy is both not generous and happy and vice versa.
If fred is humble or not curious then someone is both not generous and tall and vice versa.
If susan is curious or happy then john is either not generous or funny.
If fred is either not quiet or kind then someone is not patient or not generous.
Everyone who is not humble is both not humble and not old and vice versa.
If fred is not funny or not creative then alice is both not curious and not tall.
Everyone who is either not strong or generous is either not happy or not brave and vice versa.
If someone is both not rich and not old then someone is wise or patient.
If someone is patient or not kind then someone is generous or rich.
If john is curious or not kind then fred is both not creative and humble and vice versa.
Everyone who is rich is wise or not funny.
Fred is both not calm and not humble.
Fred is not humble.
Someone is both quiet and not brave.
Mary is either not creative or not rich.
Someone is either not happy or calm.
John is not generous or curious. | John is not wise. | neutral | (![X]:((~curious(X)<~>patient(X))<=>~happy(X)))&
(![X]:((~strong(X)&~old(X))=>(curious(X)&strong(X))))&
(![X]:((generous(X)&rich(X))=>(~strong(X)&rich(X))))&
(![X]:((~kind(X)&~generous(X))<=>~patient(X)))&
(![X]:((wise(X)|~quiet(X))<=>(patient(X)|wise(X))))&
(![X]:((brave(X)|happy(X))<=>(~generous(X)&happy(X))))&
(((humble(fred)|~curious(fred)))<=>(?[X]:((~generous(X)&tall(X)))))&
(((curious(susan)|happy(susan)))=>((~generous(john)<~>funny(john))))&
(((~quiet(fred)<~>kind(fred)))=>(?[X]:((~patient(X)|~generous(X)))))&
(![X]:(~humble(X)<=>(~humble(X)&~old(X))))&
(((~funny(fred)|~creative(fred)))=>((~curious(alice)&~tall(alice))))&
(![X]:((~strong(X)<~>generous(X))<=>(~happy(X)<~>~brave(X))))&
((?[X]:((~rich(X)&~old(X))))=>(?[X]:((wise(X)|patient(X)))))&
((?[X]:((patient(X)|~kind(X))))=>(?[X]:((generous(X)|rich(X)))))&
(((curious(john)|~kind(john)))<=>((~creative(fred)&humble(fred))))&
(![X]:(rich(X)=>(wise(X)|~funny(X))))&
((~calm(fred)&~humble(fred)))&
(~humble(fred))&
(?[X]:((quiet(X)&~brave(X))))&
((~creative(mary)<~>~rich(mary)))&
(?[X]:((~happy(X)<~>calm(X))))&
((~generous(john)|curious(john))) | ~wise(john) | [] | null | 0 |
Everyone who is happy or brave is both funny and creative and vice versa.
Everyone who is both kind and humble is both kind and brave.
Everyone who is either not patient or old is either not rich or tall and vice versa.
Everyone who is not happy or calm is strong or not curious.
Everyone who is both not humble and old is not brave and vice versa.
Everyone who is either curious or not curious is not happy.
If john is curious then someone is strong or not calm.
Everyone who is both quiet and strong is not strong or humble.
If someone is not wise then someone is both wise and not creative.
If paul is both happy and not rich then someone is not happy.
If someone is either creative or not brave then someone is both old and happy.
Everyone who is not rich or not calm is either tall or generous and vice versa.
Everyone who is either not tall or not humble is humble.
Everyone who is both curious and not generous is both not tall and happy.
Everyone who is either patient or funny is not humble or not patient.
Someone is either not happy or not strong.
Mary is either not patient or tall.
Someone is not quiet.
Alice is not calm or not brave.
Paul is kind.
Someone is either not curious or not patient.
Mary is either not brave or generous.
Susan is either not kind or rich. | Susan is old. | entailment | (![X]:((happy(X)|brave(X))<=>(funny(X)&creative(X))))&
(![X]:((kind(X)&humble(X))=>(kind(X)&brave(X))))&
(![X]:((~patient(X)<~>old(X))<=>(~rich(X)<~>tall(X))))&
(![X]:((~happy(X)|calm(X))=>(strong(X)|~curious(X))))&
(![X]:((~humble(X)&old(X))<=>~brave(X)))&
(![X]:((curious(X)<~>~curious(X))=>~happy(X)))&
((curious(john))=>(?[X]:((strong(X)|~calm(X)))))&
(![X]:((quiet(X)&strong(X))=>(~strong(X)|humble(X))))&
((?[X]:(~wise(X)))=>(?[X]:((wise(X)&~creative(X)))))&
(((happy(paul)&~rich(paul)))=>(?[X]:(~happy(X))))&
((?[X]:((creative(X)<~>~brave(X))))=>(?[X]:((old(X)&happy(X)))))&
(![X]:((~rich(X)|~calm(X))<=>(tall(X)<~>generous(X))))&
(![X]:((~tall(X)<~>~humble(X))=>humble(X)))&
(![X]:((curious(X)&~generous(X))=>(~tall(X)&happy(X))))&
(![X]:((patient(X)<~>funny(X))=>(~humble(X)|~patient(X))))&
(?[X]:((~happy(X)<~>~strong(X))))&
((~patient(mary)<~>tall(mary)))&
(?[X]:(~quiet(X)))&
((~calm(alice)|~brave(alice)))&
(kind(paul))&
(?[X]:((~curious(X)<~>~patient(X))))&
((~brave(mary)<~>generous(mary)))&
((~kind(susan)<~>rich(susan))) | old(susan) | [
"p0",
"p4",
"p5",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8089031475148489289279815
% SZS output start Proof for 8089031475148489289279815
1. ! [X0] : ((brave(X0) | happy(X0)) <=> (creative(X0) & funny(X0))) [input p0]
5. ! [X0] : ((old(X0) & ~humble(X0)) <=> ~brave(X0)) [input p4]
6. ! [X0] : ((curious(X0) <~> ~curious(X0)) => ~happy(X0)) [input p5]
11. ? [X0] : (creative(X0) <~> ~brave(X0)) => ? [X0] : (happy(X0) & old(X0)) [input p10]
24. ~old(susan) [input hypothesis]
26. ? [X0] : (creative(X0) <~> ~brave(X0)) => ? [X1] : (happy(X1) & old(X1)) [rectify 11]
34. ! [X0] : (~happy(X0) | (curious(X0) <=> ~curious(X0))) [ennf transformation 6]
38. ? [X1] : (happy(X1) & old(X1)) | ! [X0] : (creative(X0) <=> ~brave(X0)) [ennf transformation 26]
44. ! [X0] : (((brave(X0) | happy(X0)) | (~creative(X0) | ~funny(X0))) & ((creative(X0) & funny(X0)) | (~brave(X0) & ~happy(X0)))) [nnf transformation 1]
45. ! [X0] : ((brave(X0) | happy(X0) | ~creative(X0) | ~funny(X0)) & ((creative(X0) & funny(X0)) | (~brave(X0) & ~happy(X0)))) [flattening 44]
47. ! [X0] : (((old(X0) & ~humble(X0)) | brave(X0)) & (~brave(X0) | (~old(X0) | humble(X0)))) [nnf transformation 5]
48. ! [X0] : (((old(X0) & ~humble(X0)) | brave(X0)) & (~brave(X0) | ~old(X0) | humble(X0))) [flattening 47]
49. ! [X0] : (~happy(X0) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) [nnf transformation 34]
54. ? [X1] : (happy(X1) & old(X1)) | ! [X0] : ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0))) [nnf transformation 38]
55. ? [X0] : (happy(X0) & old(X0)) | ! [X1] : ((creative(X1) | brave(X1)) & (~brave(X1) | ~creative(X1))) [rectify 54]
56. ? [X0] : (happy(X0) & old(X0)) => (happy(sK2) & old(sK2)) [choice axiom]
57. (happy(sK2) & old(sK2)) | ! [X1] : ((creative(X1) | brave(X1)) & (~brave(X1) | ~creative(X1))) [skolemisation 55,56]
74. ~brave(X0) | creative(X0) [cnf transformation 45]
90. old(X0) | brave(X0) [cnf transformation 48]
91. ~happy(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 49]
92. ~happy(X0) | curious(X0) | curious(X0) [cnf transformation 49]
97. happy(sK2) | ~brave(X1) | ~creative(X1) [cnf transformation 57]
98. happy(sK2) | creative(X1) | brave(X1) [cnf transformation 57]
123. ~old(susan) [cnf transformation 24]
126. ~happy(X0) | ~curious(X0) [duplicate literal removal 91]
127. ~happy(X0) | curious(X0) [duplicate literal removal 92]
128. ~happy(X0) [subsumption resolution 126,127]
142. creative(X1) | brave(X1) [subsumption resolution 98,128]
143. creative(X1) [subsumption resolution 142,74]
144. ~brave(X1) | ~creative(X1) [subsumption resolution 97,128]
145. ~brave(X1) [subsumption resolution 144,143]
179. brave(susan) [resolution 90,123]
180. $false [subsumption resolution 179,145]
% SZS output end Proof for 8089031475148489289279815
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong is strong or not patient.
If someone is happy then someone is not happy and vice versa.
Everyone who is not patient is both humble and funny and vice versa.
Everyone who is wise is either not tall or happy and vice versa.
If someone is not strong or not calm then fred is either not quiet or funny and vice versa.
Everyone who is both not quiet and patient is either not rich or humble and vice versa.
Everyone who is both kind and funny is either not calm or kind.
If someone is calm or kind then susan is either funny or generous and vice versa.
Everyone who is either not funny or quiet is not quiet and vice versa.
Everyone who is not tall is either not patient or not rich.
Everyone who is not humble or funny is both not tall and not happy and vice versa.
Everyone who is happy or wise is both generous and not tall and vice versa.
If someone is either not curious or calm then someone is both not strong and funny and vice versa.
If someone is both not generous and not happy then lucy is not tall.
Everyone who is either quiet or strong is old.
Everyone who is either not rich or not calm is both not old and kind and vice versa.
Someone is wise.
Someone is not humble or brave.
Someone is both creative and not quiet.
Fred is either not curious or not strong.
Someone is either happy or not creative.
Fred is either strong or rich.
Alice is not happy. | Susan is generous. | entailment | (![X]:(strong(X)=>(strong(X)|~patient(X))))&
((?[X]:(happy(X)))<=>(?[X]:(~happy(X))))&
(![X]:(~patient(X)<=>(humble(X)&funny(X))))&
(![X]:(wise(X)<=>(~tall(X)<~>happy(X))))&
((?[X]:((~strong(X)|~calm(X))))<=>((~quiet(fred)<~>funny(fred))))&
(![X]:((~quiet(X)&patient(X))<=>(~rich(X)<~>humble(X))))&
(![X]:((kind(X)&funny(X))=>(~calm(X)<~>kind(X))))&
((?[X]:((calm(X)|kind(X))))<=>((funny(susan)<~>generous(susan))))&
(![X]:((~funny(X)<~>quiet(X))<=>~quiet(X)))&
(![X]:(~tall(X)=>(~patient(X)<~>~rich(X))))&
(![X]:((~humble(X)|funny(X))<=>(~tall(X)&~happy(X))))&
(![X]:((happy(X)|wise(X))<=>(generous(X)&~tall(X))))&
((?[X]:((~curious(X)<~>calm(X))))<=>(?[X]:((~strong(X)&funny(X)))))&
((?[X]:((~generous(X)&~happy(X))))=>(~tall(lucy)))&
(![X]:((quiet(X)<~>strong(X))=>old(X)))&
(![X]:((~rich(X)<~>~calm(X))<=>(~old(X)&kind(X))))&
(?[X]:(wise(X)))&
(?[X]:((~humble(X)|brave(X))))&
(?[X]:((creative(X)&~quiet(X))))&
((~curious(fred)<~>~strong(fred)))&
(?[X]:((happy(X)<~>~creative(X))))&
((strong(fred)<~>rich(fred)))&
(~happy(alice)) | generous(susan) | [
"p7",
"p8",
"p12",
"p15",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7968674473861177266424500
% SZS output start Proof for 7968674473861177266424500
8. ? [X0] : (kind(X0) | calm(X0)) <=> (funny(susan) <~> generous(susan)) [input p7]
9. ! [X0] : ((~funny(X0) <~> quiet(X0)) <=> ~quiet(X0)) [input p8]
13. ? [X0] : (~curious(X0) <~> calm(X0)) <=> ? [X0] : (funny(X0) & ~strong(X0)) [input p12]
16. ! [X0] : ((~rich(X0) <~> ~calm(X0)) <=> (kind(X0) & ~old(X0))) [input p15]
20. ~curious(fred) <~> ~strong(fred) [input p19]
22. strong(fred) <~> rich(fred) [input p21]
24. ~generous(susan) [input hypothesis]
26. ? [X0] : (~curious(X0) <~> calm(X0)) <=> ? [X1] : (funny(X1) & ~strong(X1)) [rectify 13]
50. (? [X0] : (kind(X0) | calm(X0)) | ((funny(susan) | ~generous(susan)) & (generous(susan) | ~funny(susan)))) & (((~generous(susan) | ~funny(susan)) & (generous(susan) | funny(susan))) | ! [X0] : (~kind(X0) & ~calm(X0))) [nnf transformation 8]
51. (? [X0] : (kind(X0) | calm(X0)) | ((funny(susan) | ~generous(susan)) & (generous(susan) | ~funny(susan)))) & (((~generous(susan) | ~funny(susan)) & (generous(susan) | funny(susan))) | ! [X1] : (~kind(X1) & ~calm(X1))) [rectify 50]
52. ? [X0] : (kind(X0) | calm(X0)) => (kind(sK3) | calm(sK3)) [choice axiom]
53. ((kind(sK3) | calm(sK3)) | ((funny(susan) | ~generous(susan)) & (generous(susan) | ~funny(susan)))) & (((~generous(susan) | ~funny(susan)) & (generous(susan) | funny(susan))) | ! [X1] : (~kind(X1) & ~calm(X1))) [skolemisation 51,52]
54. ! [X0] : ((((~quiet(X0) | funny(X0)) & (quiet(X0) | ~funny(X0))) | quiet(X0)) & (~quiet(X0) | ((~funny(X0) | ~quiet(X0)) & (quiet(X0) | funny(X0))))) [nnf transformation 9]
60. (? [X0] : ((~calm(X0) | curious(X0)) & (calm(X0) | ~curious(X0))) | ! [X1] : (~funny(X1) | strong(X1))) & (? [X1] : (funny(X1) & ~strong(X1)) | ! [X0] : ((~curious(X0) | ~calm(X0)) & (calm(X0) | curious(X0)))) [nnf transformation 26]
61. (? [X0] : ((~calm(X0) | curious(X0)) & (calm(X0) | ~curious(X0))) | ! [X1] : (~funny(X1) | strong(X1))) & (? [X2] : (funny(X2) & ~strong(X2)) | ! [X3] : ((~curious(X3) | ~calm(X3)) & (calm(X3) | curious(X3)))) [rectify 60]
62. ? [X0] : ((~calm(X0) | curious(X0)) & (calm(X0) | ~curious(X0))) => ((~calm(sK4) | curious(sK4)) & (calm(sK4) | ~curious(sK4))) [choice axiom]
63. ? [X2] : (funny(X2) & ~strong(X2)) => (funny(sK5) & ~strong(sK5)) [choice axiom]
64. (((~calm(sK4) | curious(sK4)) & (calm(sK4) | ~curious(sK4))) | ! [X1] : (~funny(X1) | strong(X1))) & ((funny(sK5) & ~strong(sK5)) | ! [X3] : ((~curious(X3) | ~calm(X3)) & (calm(X3) | curious(X3)))) [skolemisation 61,63,62]
66. ! [X0] : ((((calm(X0) | rich(X0)) & (~calm(X0) | ~rich(X0))) | (~kind(X0) | old(X0))) & ((kind(X0) & ~old(X0)) | ((~rich(X0) | calm(X0)) & (~calm(X0) | rich(X0))))) [nnf transformation 16]
67. ! [X0] : ((((calm(X0) | rich(X0)) & (~calm(X0) | ~rich(X0))) | ~kind(X0) | old(X0)) & ((kind(X0) & ~old(X0)) | ((~rich(X0) | calm(X0)) & (~calm(X0) | rich(X0))))) [flattening 66]
72. (strong(fred) | curious(fred)) & (~strong(fred) | ~curious(fred)) [nnf transformation 20]
76. (~rich(fred) | ~strong(fred)) & (rich(fred) | strong(fred)) [nnf transformation 22]
101. generous(susan) | funny(susan) | ~calm(X1) [cnf transformation 53]
102. generous(susan) | funny(susan) | ~kind(X1) [cnf transformation 53]
108. ~quiet(X0) | ~funny(X0) | ~quiet(X0) [cnf transformation 54]
109. quiet(X0) | ~funny(X0) | quiet(X0) [cnf transformation 54]
125. funny(sK5) | calm(X3) | curious(X3) [cnf transformation 64]
135. ~rich(X0) | kind(X0) | calm(X0) [cnf transformation 67]
141. ~strong(fred) | ~curious(fred) [cnf transformation 72]
145. rich(fred) | strong(fred) [cnf transformation 76]
148. ~generous(susan) [cnf transformation 24]
149. ~quiet(X0) | ~funny(X0) [duplicate literal removal 108]
150. ~funny(X0) | quiet(X0) [duplicate literal removal 109]
199. 11 <=> generous(susan) [avatar definition]
203. 12 <=> funny(susan) [avatar definition]
205. funny(susan) <- (12) [avatar component clause 203]
217. 15 <=> ! [X1] : ~kind(X1) [avatar definition]
218. ~kind(X1) <- (15) [avatar component clause 217]
221. 16 <=> ! [X1] : ~calm(X1) [avatar definition]
222. ~calm(X1) <- (16) [avatar component clause 221]
224. 15 | 12 | 11 [avatar split clause 102,199,203,217]
225. 16 | 12 | 11 [avatar split clause 101,199,203,221]
226. ~funny(X0) [subsumption resolution 149,150]
231. curious(X3) | calm(X3) [subsumption resolution 125,226]
242. 19 <=> curious(fred) [avatar definition]
243. ~curious(fred) <- (~19) [avatar component clause 242]
246. 20 <=> strong(fred) [avatar definition]
250. ~19 | ~20 [avatar split clause 141,246,242]
262. 23 <=> rich(fred) [avatar definition]
263. rich(fred) <- (23) [avatar component clause 262]
266. 20 | 23 [avatar split clause 145,262,246]
267. ~11 [avatar split clause 148,199]
268. $false <- (12) [subsumption resolution 205,226]
269. ~12 [avatar contradiction clause 268]
281. calm(fred) <- (~19) [resolution 231,243]
283. $false <- (16, ~19) [subsumption resolution 281,222]
284. ~16 | 19 [avatar contradiction clause 283]
329. kind(fred) | calm(fred) <- (23) [resolution 135,263]
330. calm(fred) <- (15, 23) [subsumption resolution 329,218]
331. $false <- (15, 16, 23) [subsumption resolution 330,222]
332. ~15 | ~16 | ~23 [avatar contradiction clause 331]
333. $false [avatar sat refutation 224,225,250,266,267,269,284,332]
% SZS output end Proof for 7968674473861177266424500
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either not kind or humble then john is wise.
Everyone who is not curious is both quiet and curious and vice versa.
Everyone who is both not strong and not happy is calm or creative.
If susan is either not funny or kind then someone is both not strong and kind and vice versa.
Everyone who is either old or funny is calm and vice versa.
Everyone who is generous is not happy and vice versa.
Everyone who is not patient is quiet.
If john is both happy and quiet then someone is either not old or happy.
If someone is either not strong or not generous then someone is quiet and vice versa.
Everyone who is not funny is creative and vice versa.
Everyone who is not funny or not happy is not old or happy and vice versa.
Everyone who is not generous or not funny is both not strong and humble.
Everyone who is both not strong and not creative is quiet or not calm and vice versa.
Everyone who is both not tall and not rich is not creative or not kind and vice versa.
Everyone who is patient or generous is funny or not old and vice versa.
Fred is either quiet or not wise.
Lucy is either kind or not curious.
Someone is either brave or patient.
Someone is humble. | Fred is creative. | contradiction | (((~kind(mary)<~>humble(mary)))=>(wise(john)))&
(![X]:(~curious(X)<=>(quiet(X)&curious(X))))&
(![X]:((~strong(X)&~happy(X))=>(calm(X)|creative(X))))&
(((~funny(susan)<~>kind(susan)))<=>(?[X]:((~strong(X)&kind(X)))))&
(![X]:((old(X)<~>funny(X))<=>calm(X)))&
(![X]:(generous(X)<=>~happy(X)))&
(![X]:(~patient(X)=>quiet(X)))&
(((happy(john)&quiet(john)))=>(?[X]:((~old(X)<~>happy(X)))))&
((?[X]:((~strong(X)<~>~generous(X))))<=>(?[X]:(quiet(X))))&
(![X]:(~funny(X)<=>creative(X)))&
(![X]:((~funny(X)|~happy(X))<=>(~old(X)|happy(X))))&
(![X]:((~generous(X)|~funny(X))=>(~strong(X)&humble(X))))&
(![X]:((~strong(X)&~creative(X))<=>(quiet(X)|~calm(X))))&
(![X]:((~tall(X)&~rich(X))<=>(~creative(X)|~kind(X))))&
(![X]:((patient(X)|generous(X))<=>(funny(X)|~old(X))))&
((quiet(fred)<~>~wise(fred)))&
((kind(lucy)<~>~curious(lucy)))&
(?[X]:((brave(X)<~>patient(X))))&
(?[X]:(humble(X))) | creative(fred) | [
"p1",
"p4",
"p5",
"p6",
"p8",
"p9",
"p10",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7672969658341589606456363
% SZS output start Proof for 7672969658341589606456363
2. ! [X0] : (~curious(X0) <=> (curious(X0) & quiet(X0))) [input p1]
5. ! [X0] : ((old(X0) <~> funny(X0)) <=> calm(X0)) [input p4]
6. ! [X0] : (generous(X0) <=> ~happy(X0)) [input p5]
7. ! [X0] : (~patient(X0) => quiet(X0)) [input p6]
9. ? [X0] : (~strong(X0) <~> ~generous(X0)) <=> ? [X0] : quiet(X0) [input p8]
10. ! [X0] : (~funny(X0) <=> creative(X0)) [input p9]
11. ! [X0] : ((~happy(X0) | ~funny(X0)) <=> (happy(X0) | ~old(X0))) [input p10]
12. ! [X0] : ((~funny(X0) | ~generous(X0)) => (humble(X0) & ~strong(X0))) [input p11]
13. ! [X0] : ((~creative(X0) & ~strong(X0)) <=> (~calm(X0) | quiet(X0))) [input p12]
15. ! [X0] : ((generous(X0) | patient(X0)) <=> (~old(X0) | funny(X0))) [input p14]
20. creative(fred) [input hypothesis]
21. ? [X0] : (~strong(X0) <~> ~generous(X0)) <=> ? [X1] : quiet(X1) [rectify 9]
25. ! [X0] : (quiet(X0) | patient(X0)) [ennf transformation 7]
28. ! [X0] : ((humble(X0) & ~strong(X0)) | (funny(X0) & generous(X0))) [ennf transformation 12]
30. ! [X0] : ((~curious(X0) | (~curious(X0) | ~quiet(X0))) & ((curious(X0) & quiet(X0)) | curious(X0))) [nnf transformation 2]
31. ! [X0] : ((~curious(X0) | ~curious(X0) | ~quiet(X0)) & ((curious(X0) & quiet(X0)) | curious(X0))) [flattening 30]
36. ! [X0] : ((((~funny(X0) | ~old(X0)) & (funny(X0) | old(X0))) | ~calm(X0)) & (calm(X0) | ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0))))) [nnf transformation 5]
37. ! [X0] : ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0))) [nnf transformation 6]
41. (? [X0] : ((generous(X0) | strong(X0)) & (~generous(X0) | ~strong(X0))) | ! [X1] : ~quiet(X1)) & (? [X1] : quiet(X1) | ! [X0] : ((~strong(X0) | generous(X0)) & (~generous(X0) | strong(X0)))) [nnf transformation 21]
42. (? [X0] : ((generous(X0) | strong(X0)) & (~generous(X0) | ~strong(X0))) | ! [X1] : ~quiet(X1)) & (? [X2] : quiet(X2) | ! [X3] : ((~strong(X3) | generous(X3)) & (~generous(X3) | strong(X3)))) [rectify 41]
43. ? [X0] : ((generous(X0) | strong(X0)) & (~generous(X0) | ~strong(X0))) => ((generous(sK2) | strong(sK2)) & (~generous(sK2) | ~strong(sK2))) [choice axiom]
44. ? [X2] : quiet(X2) => quiet(sK3) [choice axiom]
45. (((generous(sK2) | strong(sK2)) & (~generous(sK2) | ~strong(sK2))) | ! [X1] : ~quiet(X1)) & (quiet(sK3) | ! [X3] : ((~strong(X3) | generous(X3)) & (~generous(X3) | strong(X3)))) [skolemisation 42,44,43]
46. ! [X0] : ((~funny(X0) | ~creative(X0)) & (creative(X0) | funny(X0))) [nnf transformation 10]
47. ! [X0] : (((~happy(X0) | ~funny(X0)) | (~happy(X0) & old(X0))) & ((happy(X0) | ~old(X0)) | (happy(X0) & funny(X0)))) [nnf transformation 11]
48. ! [X0] : ((~happy(X0) | ~funny(X0) | (~happy(X0) & old(X0))) & (happy(X0) | ~old(X0) | (happy(X0) & funny(X0)))) [flattening 47]
49. ! [X0] : (((~creative(X0) & ~strong(X0)) | (calm(X0) & ~quiet(X0))) & ((~calm(X0) | quiet(X0)) | (creative(X0) | strong(X0)))) [nnf transformation 13]
50. ! [X0] : (((~creative(X0) & ~strong(X0)) | (calm(X0) & ~quiet(X0))) & (~calm(X0) | quiet(X0) | creative(X0) | strong(X0))) [flattening 49]
53. ! [X0] : (((generous(X0) | patient(X0)) | (old(X0) & ~funny(X0))) & ((~old(X0) | funny(X0)) | (~generous(X0) & ~patient(X0)))) [nnf transformation 15]
54. ! [X0] : ((generous(X0) | patient(X0) | (old(X0) & ~funny(X0))) & (~old(X0) | funny(X0) | (~generous(X0) & ~patient(X0)))) [flattening 53]
65. curious(X0) | curious(X0) [cnf transformation 31]
66. ~curious(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 31]
76. ~calm(X0) | old(X0) | funny(X0) [cnf transformation 36]
79. generous(X0) | happy(X0) [cnf transformation 37]
80. patient(X0) | quiet(X0) [cnf transformation 25]
83. quiet(sK3) | ~generous(X3) | strong(X3) [cnf transformation 45]
85. ~generous(sK2) | ~strong(sK2) | ~quiet(X1) [cnf transformation 45]
86. generous(sK2) | strong(sK2) | ~quiet(X1) [cnf transformation 45]
88. ~funny(X0) | ~creative(X0) [cnf transformation 46]
92. ~happy(X0) | ~funny(X0) | ~happy(X0) [cnf transformation 48]
94. ~strong(X0) | funny(X0) [cnf transformation 28]
101. ~creative(X0) | calm(X0) [cnf transformation 50]
107. ~patient(X0) | funny(X0) | ~old(X0) [cnf transformation 54]
118. creative(fred) [cnf transformation 20]
120. ~funny(X0) | ~happy(X0) [duplicate literal removal 92]
121. curious(X0) [duplicate literal removal 65]
122. ~quiet(X0) | ~curious(X0) [duplicate literal removal 66]
181. 13 <=> ! [X1] : ~quiet(X1) [avatar definition]
182. ~quiet(X1) <- (13) [avatar component clause 181]
184. 14 <=> strong(sK2) [avatar definition]
185. ~strong(sK2) <- (~14) [avatar component clause 184]
186. strong(sK2) <- (14) [avatar component clause 184]
188. 15 <=> generous(sK2) [avatar definition]
189. ~generous(sK2) <- (~15) [avatar component clause 188]
190. generous(sK2) <- (15) [avatar component clause 188]
191. 13 | 14 | 15 [avatar split clause 86,188,184,181]
192. 13 | ~14 | ~15 [avatar split clause 85,188,184,181]
197. 17 <=> quiet(sK3) [avatar definition]
199. quiet(sK3) <- (17) [avatar component clause 197]
202. 18 <=> ! [X3] : (~generous(X3) | strong(X3)) [avatar definition]
203. ~generous(X3) | strong(X3) <- (18) [avatar component clause 202]
204. 18 | 17 [avatar split clause 83,197,202]
229. happy(sK2) <- (~15) [resolution 79,189]
234. funny(sK2) <- (14) [resolution 94,186]
242. calm(fred) [resolution 101,118]
246. ~happy(sK2) <- (14) [resolution 120,234]
247. $false <- (14, ~15) [subsumption resolution 246,229]
248. ~14 | 15 [avatar contradiction clause 247]
250. ~curious(sK3) <- (17) [resolution 122,199]
252. $false <- (17) [subsumption resolution 250,121]
253. ~17 [avatar contradiction clause 252]
264. strong(sK2) <- (15, 18) [resolution 203,190]
265. $false <- (~14, 15, 18) [subsumption resolution 264,185]
266. 14 | ~15 | ~18 [avatar contradiction clause 265]
286. old(fred) | funny(fred) [resolution 76,242]
288. 25 <=> funny(fred) [avatar definition]
289. ~funny(fred) <- (~25) [avatar component clause 288]
290. funny(fred) <- (25) [avatar component clause 288]
292. 26 <=> old(fred) [avatar definition]
294. old(fred) <- (26) [avatar component clause 292]
295. 25 | 26 [avatar split clause 286,292,288]
299. funny(X0) | ~old(X0) | quiet(X0) [resolution 107,80]
301. ~old(X0) | funny(X0) <- (13) [subsumption resolution 299,182]
363. ~creative(fred) <- (25) [resolution 290,88]
373. $false <- (25) [subsumption resolution 363,118]
374. ~25 [avatar contradiction clause 373]
397. funny(fred) <- (13, 26) [resolution 301,294]
399. $false <- (13, ~25, 26) [subsumption resolution 397,289]
400. ~13 | 25 | ~26 [avatar contradiction clause 399]
401. $false [avatar sat refutation 191,192,204,248,253,266,295,374,400]
% SZS output end Proof for 7672969658341589606456363
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not rich or not generous then john is not happy and vice versa. Everyone who is both generous and brave is both funny and not creative and vice versa. If paul is wise then john is not kind or not creative and vice versa. If someone is both patient and not humble then mary is both wise and not brave and vice versa. Everyone who is either not patient or old is not humble. Everyone who is either patient or tall is patient or strong and vice versa. If someone is both not curious and calm then paul is both not rich and not patient. Everyone who is quiet is not happy. If someone is either not curious or not calm then lucy is not funny or strong. If someone is not funny then susan is both creative and not kind and vice versa. If someone is humble then someone is not generous or quiet and vice versa. If someone is either not funny or tall then lucy is both rich and brave and vice versa. If someone is both humble and kind then someone is happy or not wise and vice versa. Everyone who is happy is both generous and not curious and vice versa. If someone is both humble and happy then john is happy or funny and vice versa. If john is both not humble and not curious then paul is not quiet and vice versa. Paul is not patient. Mary is both rich and creative. John is quiet or not curious. Fred is either not quiet or generous. Alice is not tall or quiet. Paul is not kind. Someone is either strong or not patient. Mary is both curious and calm. | Fred is not humble. | neutral | ((?[X]:((~rich(X)<~>~generous(X))))<=>(~happy(john)))&
(![X]:((generous(X)&brave(X))<=>(funny(X)&~creative(X))))&
((wise(paul))<=>((~kind(john)|~creative(john))))&
((?[X]:((patient(X)&~humble(X))))<=>((wise(mary)&~brave(mary))))&
(![X]:((~patient(X)<~>old(X))=>~humble(X)))&
(![X]:((patient(X)<~>tall(X))<=>(patient(X)|strong(X))))&
((?[X]:((~curious(X)&calm(X))))=>((~rich(paul)&~patient(paul))))&
(![X]:(quiet(X)=>~happy(X)))&
((?[X]:((~curious(X)<~>~calm(X))))=>((~funny(lucy)|strong(lucy))))&
((?[X]:(~funny(X)))<=>((creative(susan)&~kind(susan))))&
((?[X]:(humble(X)))<=>(?[X]:((~generous(X)|quiet(X)))))&
((?[X]:((~funny(X)<~>tall(X))))<=>((rich(lucy)&brave(lucy))))&
((?[X]:((humble(X)&kind(X))))<=>(?[X]:((happy(X)|~wise(X)))))&
(![X]:(happy(X)<=>(generous(X)&~curious(X))))&
((?[X]:((humble(X)&happy(X))))<=>((happy(john)|funny(john))))&
(((~humble(john)&~curious(john)))<=>(~quiet(paul)))&
(~patient(paul))&
((rich(mary)&creative(mary)))&
((quiet(john)|~curious(john)))&
((~quiet(fred)<~>generous(fred)))&
((~tall(alice)|quiet(alice)))&
(~kind(paul))&
(?[X]:((strong(X)<~>~patient(X))))&
((curious(mary)&calm(mary))) | ~humble(fred) | [] | null | 0 |
If someone is either curious or kind then fred is wise or old.
Everyone who is brave or not quiet is quiet and vice versa.
Everyone who is both brave and not old is kind and vice versa.
Everyone who is creative or not wise is not calm.
Everyone who is brave or creative is either brave or curious.
Everyone who is rich or not curious is both not tall and generous and vice versa.
Everyone who is either strong or happy is both tall and not creative.
Everyone who is not kind is both creative and not old.
Everyone who is either not rich or not strong is not tall and vice versa.
If john is not happy or creative then mary is both old and not generous.
Everyone who is not calm or not patient is either creative or kind.
Everyone who is both not calm and not happy is rich or not happy.
If someone is not tall or not brave then susan is either funny or not funny and vice versa.
If someone is either brave or not brave then alice is not curious or not creative.
Everyone who is calm is creative.
Everyone who is calm is either not tall or not happy.
Someone is not strong or not funny.
Someone is both not humble and not creative.
Alice is patient or happy.
Susan is either not tall or not brave.
Someone is both funny and not happy.
Someone is either rich or not wise. | Mary is not old. | entailment | ((?[X]:((curious(X)<~>kind(X))))=>((wise(fred)|old(fred))))&
(![X]:((brave(X)|~quiet(X))<=>quiet(X)))&
(![X]:((brave(X)&~old(X))<=>kind(X)))&
(![X]:((creative(X)|~wise(X))=>~calm(X)))&
(![X]:((brave(X)|creative(X))=>(brave(X)<~>curious(X))))&
(![X]:((rich(X)|~curious(X))<=>(~tall(X)&generous(X))))&
(![X]:((strong(X)<~>happy(X))=>(tall(X)&~creative(X))))&
(![X]:(~kind(X)=>(creative(X)&~old(X))))&
(![X]:((~rich(X)<~>~strong(X))<=>~tall(X)))&
(((~happy(john)|creative(john)))=>((old(mary)&~generous(mary))))&
(![X]:((~calm(X)|~patient(X))=>(creative(X)<~>kind(X))))&
(![X]:((~calm(X)&~happy(X))=>(rich(X)|~happy(X))))&
((?[X]:((~tall(X)|~brave(X))))<=>((funny(susan)<~>~funny(susan))))&
((?[X]:((brave(X)<~>~brave(X))))=>((~curious(alice)|~creative(alice))))&
(![X]:(calm(X)=>creative(X)))&
(![X]:(calm(X)=>(~tall(X)<~>~happy(X))))&
(?[X]:((~strong(X)|~funny(X))))&
(?[X]:((~humble(X)&~creative(X))))&
((patient(alice)|happy(alice)))&
((~tall(susan)<~>~brave(susan)))&
(?[X]:((funny(X)&~happy(X))))&
(?[X]:((rich(X)<~>~wise(X)))) | ~old(mary) | [
"p2",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1329647568700288148839263
% SZS output start Proof for 1329647568700288148839263
3. ! [X0] : ((~old(X0) & brave(X0)) <=> kind(X0)) [input p2]
8. ! [X0] : (~kind(X0) => (~old(X0) & creative(X0))) [input p7]
23. old(mary) [input hypothesis]
32. ! [X0] : ((~old(X0) & creative(X0)) | kind(X0)) [ennf transformation 8]
44. ! [X0] : (((~old(X0) & brave(X0)) | ~kind(X0)) & (kind(X0) | (old(X0) | ~brave(X0)))) [nnf transformation 3]
45. ! [X0] : (((~old(X0) & brave(X0)) | ~kind(X0)) & (kind(X0) | old(X0) | ~brave(X0))) [flattening 44]
75. ~old(X0) | ~kind(X0) [cnf transformation 45]
92. ~old(X0) | kind(X0) [cnf transformation 32]
123. old(mary) [cnf transformation 23]
147. ~old(X0) [subsumption resolution 92,75]
229. $false [subsumption resolution 123,147]
% SZS output end Proof for 1329647568700288148839263
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is either not funny or not creative and vice versa.
Everyone who is not quiet or not rich is not wise or quiet.
Everyone who is not tall or not kind is humble.
If someone is curious then someone is both not calm and not brave.
Everyone who is either curious or not rich is calm or tall and vice versa.
Everyone who is kind is both not kind and strong.
Everyone who is not humble is either happy or old and vice versa.
If someone is either not calm or tall then john is either not rich or not funny.
If paul is either quiet or not old then someone is strong or not quiet and vice versa.
If someone is either humble or not patient then someone is both calm and patient and vice versa.
If john is both not old and rich then someone is both patient and not old.
Everyone who is tall or not strong is both not generous and not tall.
Everyone who is both calm and generous is not old or wise and vice versa.
Everyone who is quiet is both creative and rich and vice versa.
If paul is old then susan is not patient and vice versa.
Everyone who is both not wise and generous is wise.
Someone is not funny.
Someone is not generous or not happy.
Someone is tall or creative.
Paul is both curious and not kind.
Fred is funny. | Paul is happy. | entailment | (![X]:(happy(X)<=>(~funny(X)<~>~creative(X))))&
(![X]:((~quiet(X)|~rich(X))=>(~wise(X)|quiet(X))))&
(![X]:((~tall(X)|~kind(X))=>humble(X)))&
((?[X]:(curious(X)))=>(?[X]:((~calm(X)&~brave(X)))))&
(![X]:((curious(X)<~>~rich(X))<=>(calm(X)|tall(X))))&
(![X]:(kind(X)=>(~kind(X)&strong(X))))&
(![X]:(~humble(X)<=>(happy(X)<~>old(X))))&
((?[X]:((~calm(X)<~>tall(X))))=>((~rich(john)<~>~funny(john))))&
(((quiet(paul)<~>~old(paul)))<=>(?[X]:((strong(X)|~quiet(X)))))&
((?[X]:((humble(X)<~>~patient(X))))<=>(?[X]:((calm(X)&patient(X)))))&
(((~old(john)&rich(john)))=>(?[X]:((patient(X)&~old(X)))))&
(![X]:((tall(X)|~strong(X))=>(~generous(X)&~tall(X))))&
(![X]:((calm(X)&generous(X))<=>(~old(X)|wise(X))))&
(![X]:(quiet(X)<=>(creative(X)&rich(X))))&
((old(paul))<=>(~patient(susan)))&
(![X]:((~wise(X)&generous(X))=>wise(X)))&
(?[X]:(~funny(X)))&
(?[X]:((~generous(X)|~happy(X))))&
(?[X]:((tall(X)|creative(X))))&
((curious(paul)&~kind(paul)))&
(funny(fred)) | happy(paul) | [
"p1",
"p2",
"p6",
"p8",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 253542042698670856370814
% SZS output start Proof for 253542042698670856370814
2. ! [X0] : ((~rich(X0) | ~quiet(X0)) => (quiet(X0) | ~wise(X0))) [input p1]
3. ! [X0] : ((~kind(X0) | ~tall(X0)) => humble(X0)) [input p2]
7. ! [X0] : (~humble(X0) <=> (happy(X0) <~> old(X0))) [input p6]
9. (quiet(paul) <~> ~old(paul)) <=> ? [X0] : (~quiet(X0) | strong(X0)) [input p8]
12. ! [X0] : ((~strong(X0) | tall(X0)) => (~tall(X0) & ~generous(X0))) [input p11]
13. ! [X0] : ((generous(X0) & calm(X0)) <=> (wise(X0) | ~old(X0))) [input p12]
16. ! [X0] : ((generous(X0) & ~wise(X0)) => wise(X0)) [input p15]
22. ~happy(paul) [input hypothesis]
26. ! [X0] : ((quiet(X0) | ~wise(X0)) | (rich(X0) & quiet(X0))) [ennf transformation 2]
27. ! [X0] : (quiet(X0) | ~wise(X0) | (rich(X0) & quiet(X0))) [flattening 26]
28. ! [X0] : (humble(X0) | (kind(X0) & tall(X0))) [ennf transformation 3]
34. ! [X0] : ((~tall(X0) & ~generous(X0)) | (strong(X0) & ~tall(X0))) [ennf transformation 12]
35. ! [X0] : (wise(X0) | (~generous(X0) | wise(X0))) [ennf transformation 16]
36. ! [X0] : (wise(X0) | ~generous(X0) | wise(X0)) [flattening 35]
43. ! [X0] : ((~humble(X0) | ((happy(X0) | ~old(X0)) & (old(X0) | ~happy(X0)))) & (((~old(X0) | ~happy(X0)) & (old(X0) | happy(X0))) | humble(X0))) [nnf transformation 7]
45. (((old(paul) | ~quiet(paul)) & (~old(paul) | quiet(paul))) | ! [X0] : (quiet(X0) & ~strong(X0))) & (? [X0] : (~quiet(X0) | strong(X0)) | ((quiet(paul) | old(paul)) & (~old(paul) | ~quiet(paul)))) [nnf transformation 9]
46. (((old(paul) | ~quiet(paul)) & (~old(paul) | quiet(paul))) | ! [X0] : (quiet(X0) & ~strong(X0))) & (? [X1] : (~quiet(X1) | strong(X1)) | ((quiet(paul) | old(paul)) & (~old(paul) | ~quiet(paul)))) [rectify 45]
47. ? [X1] : (~quiet(X1) | strong(X1)) => (~quiet(sK1) | strong(sK1)) [choice axiom]
48. (((old(paul) | ~quiet(paul)) & (~old(paul) | quiet(paul))) | ! [X0] : (quiet(X0) & ~strong(X0))) & ((~quiet(sK1) | strong(sK1)) | ((quiet(paul) | old(paul)) & (~old(paul) | ~quiet(paul)))) [skolemisation 46,47]
56. ! [X0] : (((generous(X0) & calm(X0)) | (~wise(X0) & old(X0))) & ((wise(X0) | ~old(X0)) | (~generous(X0) | ~calm(X0)))) [nnf transformation 13]
57. ! [X0] : (((generous(X0) & calm(X0)) | (~wise(X0) & old(X0))) & (wise(X0) | ~old(X0) | ~generous(X0) | ~calm(X0))) [flattening 56]
71. quiet(X0) | ~wise(X0) | quiet(X0) [cnf transformation 27]
73. humble(X0) | tall(X0) [cnf transformation 28]
87. ~old(X0) | happy(X0) | ~humble(X0) [cnf transformation 43]
96. old(paul) | ~quiet(paul) | ~strong(X0) [cnf transformation 48]
107. ~generous(X0) | strong(X0) [cnf transformation 34]
108. ~tall(X0) | ~tall(X0) [cnf transformation 34]
113. generous(X0) | old(X0) [cnf transformation 57]
120. wise(X0) | ~generous(X0) | wise(X0) [cnf transformation 36]
127. ~happy(paul) [cnf transformation 22]
128. ~generous(X0) | wise(X0) [duplicate literal removal 120]
129. ~tall(X0) [duplicate literal removal 108]
131. ~wise(X0) | quiet(X0) [duplicate literal removal 71]
162. 8 <=> quiet(paul) [avatar definition]
166. 9 <=> old(paul) [avatar definition]
167. ~old(paul) <- (~9) [avatar component clause 166]
168. old(paul) <- (9) [avatar component clause 166]
171. 10 <=> ! [X0] : ~strong(X0) [avatar definition]
172. ~strong(X0) <- (10) [avatar component clause 171]
173. 10 | ~8 | 9 [avatar split clause 96,166,162,171]
250. old(X0) | strong(X0) [resolution 113,107]
253. old(X0) | wise(X0) [resolution 128,113]
317. happy(paul) | ~humble(paul) <- (9) [resolution 87,168]
324. ~humble(paul) <- (9) [subsumption resolution 317,127]
331. tall(paul) <- (9) [resolution 324,73]
334. $false <- (9) [subsumption resolution 331,129]
335. ~9 [avatar contradiction clause 334]
337. wise(paul) <- (~9) [resolution 167,253]
338. strong(paul) <- (~9) [resolution 167,250]
460. quiet(paul) <- (~9) [resolution 337,131]
465. 8 | 9 [avatar split clause 460,166,162]
507. $false <- (~9, 10) [resolution 338,172]
508. 9 | ~10 [avatar contradiction clause 507]
509. $false [avatar sat refutation 173,335,465,508]
% SZS output end Proof for 253542042698670856370814
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not curious and calm is both humble and patient and vice versa. If someone is not rich or brave then lucy is both old and wise. Everyone who is not humble is generous or tall. Everyone who is curious is both humble and rich and vice versa. If someone is both not patient and strong then john is strong and vice versa. If susan is calm or not kind then fred is both creative and not happy and vice versa. If fred is both not quiet and kind then someone is both wise and funny and vice versa. If someone is either not brave or not curious then someone is both rich and calm and vice versa. Everyone who is wise is both not humble and old and vice versa. If someone is generous then paul is not quiet or strong. If someone is kind or patient then lucy is either brave or not old. If someone is both not quiet and quiet then mary is creative and vice versa. If fred is not humble then fred is either creative or not strong. Everyone who is happy is either funny or kind. If someone is quiet then john is not brave and vice versa. Everyone who is not kind or strong is either kind or calm and vice versa. Someone is calm or not rich. Alice is calm or quiet. Lucy is happy. Fred is both patient and brave. Paul is not strong. Paul is brave or generous. Susan is not old or quiet. Mary is both not wise and not happy. | Lucy is not funny. | entailment | (![X]:((~curious(X)&calm(X))<=>(humble(X)&patient(X))))&
((?[X]:((~rich(X)|brave(X))))=>((old(lucy)&wise(lucy))))&
(![X]:(~humble(X)=>(generous(X)|tall(X))))&
(![X]:(curious(X)<=>(humble(X)&rich(X))))&
((?[X]:((~patient(X)&strong(X))))<=>(strong(john)))&
(((calm(susan)|~kind(susan)))<=>((creative(fred)&~happy(fred))))&
(((~quiet(fred)&kind(fred)))<=>(?[X]:((wise(X)&funny(X)))))&
((?[X]:((~brave(X)<~>~curious(X))))<=>(?[X]:((rich(X)&calm(X)))))&
(![X]:(wise(X)<=>(~humble(X)&old(X))))&
((?[X]:(generous(X)))=>((~quiet(paul)|strong(paul))))&
((?[X]:((kind(X)|patient(X))))=>((brave(lucy)<~>~old(lucy))))&
((?[X]:((~quiet(X)&quiet(X))))<=>(creative(mary)))&
((~humble(fred))=>((creative(fred)<~>~strong(fred))))&
(![X]:(happy(X)=>(funny(X)<~>kind(X))))&
((?[X]:(quiet(X)))<=>(~brave(john)))&
(![X]:((~kind(X)|strong(X))<=>(kind(X)<~>calm(X))))&
(?[X]:((calm(X)|~rich(X))))&
((calm(alice)|quiet(alice)))&
(happy(lucy))&
((patient(fred)&brave(fred)))&
(~strong(paul))&
((brave(paul)|generous(paul)))&
((~old(susan)|quiet(susan)))&
((~wise(mary)&~happy(mary))) | ~funny(lucy) | [
"p0",
"p1",
"p3",
"p8",
"p13",
"p15",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 412781783277560215296827
% SZS output start Proof for 412781783277560215296827
1. ! [X0] : ((calm(X0) & ~curious(X0)) <=> (patient(X0) & humble(X0))) [input p0]
2. ? [X0] : (brave(X0) | ~rich(X0)) => (wise(lucy) & old(lucy)) [input p1]
4. ! [X0] : (curious(X0) <=> (rich(X0) & humble(X0))) [input p3]
9. ! [X0] : (wise(X0) <=> (old(X0) & ~humble(X0))) [input p8]
14. ! [X0] : (happy(X0) => (funny(X0) <~> kind(X0))) [input p13]
16. ! [X0] : ((strong(X0) | ~kind(X0)) <=> (kind(X0) <~> calm(X0))) [input p15]
19. happy(lucy) [input p18]
20. brave(fred) & patient(fred) [input p19]
25. funny(lucy) [input hypothesis]
28. (wise(lucy) & old(lucy)) | ! [X0] : (~brave(X0) & rich(X0)) [ennf transformation 2]
33. ! [X0] : ((funny(X0) <~> kind(X0)) | ~happy(X0)) [ennf transformation 14]
34. ! [X0] : (((calm(X0) & ~curious(X0)) | (~patient(X0) | ~humble(X0))) & ((patient(X0) & humble(X0)) | (~calm(X0) | curious(X0)))) [nnf transformation 1]
35. ! [X0] : (((calm(X0) & ~curious(X0)) | ~patient(X0) | ~humble(X0)) & ((patient(X0) & humble(X0)) | ~calm(X0) | curious(X0))) [flattening 34]
36. ! [X0] : ((curious(X0) | (~rich(X0) | ~humble(X0))) & ((rich(X0) & humble(X0)) | ~curious(X0))) [nnf transformation 4]
37. ! [X0] : ((curious(X0) | ~rich(X0) | ~humble(X0)) & ((rich(X0) & humble(X0)) | ~curious(X0))) [flattening 36]
54. ! [X0] : ((wise(X0) | (~old(X0) | humble(X0))) & ((old(X0) & ~humble(X0)) | ~wise(X0))) [nnf transformation 9]
55. ! [X0] : ((wise(X0) | ~old(X0) | humble(X0)) & ((old(X0) & ~humble(X0)) | ~wise(X0))) [flattening 54]
62. ! [X0] : (((~kind(X0) | ~funny(X0)) & (kind(X0) | funny(X0))) | ~happy(X0)) [nnf transformation 33]
67. ! [X0] : (((strong(X0) | ~kind(X0)) | ((kind(X0) | ~calm(X0)) & (calm(X0) | ~kind(X0)))) & (((~calm(X0) | ~kind(X0)) & (calm(X0) | kind(X0))) | (~strong(X0) & kind(X0)))) [nnf transformation 16]
68. ! [X0] : ((strong(X0) | ~kind(X0) | ((kind(X0) | ~calm(X0)) & (calm(X0) | ~kind(X0)))) & (((~calm(X0) | ~kind(X0)) & (calm(X0) | kind(X0))) | (~strong(X0) & kind(X0)))) [flattening 67]
71. ~calm(X0) | humble(X0) | curious(X0) [cnf transformation 35]
78. wise(lucy) | ~brave(X0) [cnf transformation 28]
79. ~curious(X0) | humble(X0) [cnf transformation 37]
100. ~wise(X0) | ~humble(X0) [cnf transformation 55]
114. ~funny(X0) | ~kind(X0) | ~happy(X0) [cnf transformation 62]
117. calm(X0) | kind(X0) | kind(X0) [cnf transformation 68]
125. happy(lucy) [cnf transformation 19]
127. brave(fred) [cnf transformation 20]
133. funny(lucy) [cnf transformation 25]
134. kind(X0) | calm(X0) [duplicate literal removal 117]
137. 1 <=> ! [X0] : ~brave(X0) [avatar definition]
138. ~brave(X0) <- (1) [avatar component clause 137]
140. 2 <=> wise(lucy) [avatar definition]
142. wise(lucy) <- (2) [avatar component clause 140]
143. 1 | 2 [avatar split clause 78,140,137]
343. ~humble(lucy) <- (2) [resolution 100,142]
413. ~kind(lucy) | ~happy(lucy) [resolution 114,133]
415. ~kind(lucy) [subsumption resolution 413,125]
425. calm(lucy) [resolution 415,134]
432. humble(lucy) | curious(lucy) [resolution 425,71]
434. 52 <=> curious(lucy) [avatar definition]
436. curious(lucy) <- (52) [avatar component clause 434]
442. curious(lucy) <- (2) [subsumption resolution 432,343]
443. 52 | ~2 [avatar split clause 442,140,434]
467. humble(lucy) <- (52) [resolution 436,79]
468. $false <- (2, 52) [subsumption resolution 467,343]
469. ~2 | ~52 [avatar contradiction clause 468]
471. $false <- (1) [resolution 138,127]
474. ~1 [avatar contradiction clause 471]
476. $false [avatar sat refutation 143,443,469,474]
% SZS output end Proof for 412781783277560215296827
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or not generous is either not brave or not curious and vice versa. Everyone who is both not funny and quiet is not strong or funny and vice versa. Everyone who is not brave or humble is happy or brave. If someone is either not humble or quiet then someone is humble or happy and vice versa. Everyone who is both quiet and not curious is both not rich and not kind and vice versa. Everyone who is not wise or funny is either not brave or wise and vice versa. If someone is either not funny or brave then alice is not tall or not patient. Everyone who is either calm or not rich is either old or calm and vice versa. Everyone who is both strong and not old is either funny or calm and vice versa. If alice is either generous or not funny then paul is not funny or not rich and vice versa. Everyone who is either not tall or old is either creative or calm and vice versa. Everyone who is tall or strong is not old or not brave and vice versa. Everyone who is brave is not strong or not tall and vice versa. Everyone who is not calm is both humble and not rich. If susan is either not patient or not old then lucy is either tall or not old. Everyone who is both not humble and calm is both patient and not curious and vice versa. Mary is tall or not curious. Someone is happy or not funny. Someone is both not quiet and not wise. Someone is either humble or not calm. Susan is either curious or rich. Someone is either strong or old. | Paul is happy. | entailment | (![X]:((~creative(X)|~generous(X))<=>(~brave(X)<~>~curious(X))))&
(![X]:((~funny(X)&quiet(X))<=>(~strong(X)|funny(X))))&
(![X]:((~brave(X)|humble(X))=>(happy(X)|brave(X))))&
((?[X]:((~humble(X)<~>quiet(X))))<=>(?[X]:((humble(X)|happy(X)))))&
(![X]:((quiet(X)&~curious(X))<=>(~rich(X)&~kind(X))))&
(![X]:((~wise(X)|funny(X))<=>(~brave(X)<~>wise(X))))&
((?[X]:((~funny(X)<~>brave(X))))=>((~tall(alice)|~patient(alice))))&
(![X]:((calm(X)<~>~rich(X))<=>(old(X)<~>calm(X))))&
(![X]:((strong(X)&~old(X))<=>(funny(X)<~>calm(X))))&
(((generous(alice)<~>~funny(alice)))<=>((~funny(paul)|~rich(paul))))&
(![X]:((~tall(X)<~>old(X))<=>(creative(X)<~>calm(X))))&
(![X]:((tall(X)|strong(X))<=>(~old(X)|~brave(X))))&
(![X]:(brave(X)<=>(~strong(X)|~tall(X))))&
(![X]:(~calm(X)=>(humble(X)&~rich(X))))&
(((~patient(susan)<~>~old(susan)))=>((tall(lucy)<~>~old(lucy))))&
(![X]:((~humble(X)&calm(X))<=>(patient(X)&~curious(X))))&
((tall(mary)|~curious(mary)))&
(?[X]:((happy(X)|~funny(X))))&
(?[X]:((~quiet(X)&~wise(X))))&
(?[X]:((humble(X)<~>~calm(X))))&
((curious(susan)<~>rich(susan)))&
(?[X]:((strong(X)<~>old(X)))) | happy(paul) | [
"p1",
"p2",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 3045668127893862702507346
% SZS output start Proof for 3045668127893862702507346
2. ! [X0] : ((quiet(X0) & ~funny(X0)) <=> (funny(X0) | ~strong(X0))) [input p1]
3. ! [X0] : ((humble(X0) | ~brave(X0)) => (brave(X0) | happy(X0))) [input p2]
6. ! [X0] : ((funny(X0) | ~wise(X0)) <=> (~brave(X0) <~> wise(X0))) [input p5]
23. ~happy(paul) [input hypothesis]
25. ! [X0] : ((brave(X0) | happy(X0)) | (~humble(X0) & brave(X0))) [ennf transformation 3]
26. ! [X0] : (brave(X0) | happy(X0) | (~humble(X0) & brave(X0))) [flattening 25]
33. ! [X0] : (((quiet(X0) & ~funny(X0)) | (~funny(X0) & strong(X0))) & ((funny(X0) | ~strong(X0)) | (~quiet(X0) | funny(X0)))) [nnf transformation 2]
34. ! [X0] : (((quiet(X0) & ~funny(X0)) | (~funny(X0) & strong(X0))) & (funny(X0) | ~strong(X0) | ~quiet(X0) | funny(X0))) [flattening 33]
42. ! [X0] : (((funny(X0) | ~wise(X0)) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0)))) & (((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | (~funny(X0) & wise(X0)))) [nnf transformation 6]
43. ! [X0] : ((funny(X0) | ~wise(X0) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0)))) & (((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | (~funny(X0) & wise(X0)))) [flattening 42]
77. ~funny(X0) | ~funny(X0) [cnf transformation 34]
80. brave(X0) | happy(X0) | brave(X0) [cnf transformation 26]
92. wise(X0) | ~brave(X0) | wise(X0) [cnf transformation 43]
97. funny(X0) | ~wise(X0) | ~brave(X0) | ~wise(X0) [cnf transformation 43]
155. ~happy(paul) [cnf transformation 23]
160. wise(X0) | ~brave(X0) [duplicate literal removal 92]
161. funny(X0) | ~wise(X0) | ~brave(X0) [duplicate literal removal 97]
162. happy(X0) | brave(X0) [duplicate literal removal 80]
164. ~funny(X0) [duplicate literal removal 77]
200. ~wise(X0) | ~brave(X0) [subsumption resolution 161,164]
201. ~brave(X0) [subsumption resolution 160,200]
269. brave(paul) [resolution 162,155]
270. $false [subsumption resolution 269,201]
% SZS output end Proof for 3045668127893862702507346
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is either not old or not quiet.
Everyone who is either not creative or not wise is both rich and not kind.
If paul is both rich and not wise then someone is rich.
If alice is funny then someone is either curious or not funny.
If alice is not tall then someone is not old and vice versa.
If lucy is both patient and not rich then someone is either not wise or not generous and vice versa.
If someone is not old then someone is not quiet and vice versa.
If someone is either not kind or creative then alice is not curious.
If someone is kind or creative then mary is both happy and not happy and vice versa.
Everyone who is old or not patient is both not tall and not brave.
Everyone who is either brave or not rich is either not patient or wise and vice versa.
Everyone who is patient is either not wise or old and vice versa.
Everyone who is rich is not rich or not funny and vice versa.
Everyone who is both strong and not generous is not kind and vice versa.
Everyone who is either quiet or tall is both not humble and old and vice versa.
Everyone who is either tall or patient is not happy or kind.
Mary is not generous.
Someone is not calm or not old.
Alice is either happy or not old.
Mary is quiet or curious.
Susan is not creative or not curious. | Lucy is happy. | neutral | (![X]:(creative(X)=>(~old(X)<~>~quiet(X))))&
(![X]:((~creative(X)<~>~wise(X))=>(rich(X)&~kind(X))))&
(((rich(paul)&~wise(paul)))=>(?[X]:(rich(X))))&
((funny(alice))=>(?[X]:((curious(X)<~>~funny(X)))))&
((~tall(alice))<=>(?[X]:(~old(X))))&
(((patient(lucy)&~rich(lucy)))<=>(?[X]:((~wise(X)<~>~generous(X)))))&
((?[X]:(~old(X)))<=>(?[X]:(~quiet(X))))&
((?[X]:((~kind(X)<~>creative(X))))=>(~curious(alice)))&
((?[X]:((kind(X)|creative(X))))<=>((happy(mary)&~happy(mary))))&
(![X]:((old(X)|~patient(X))=>(~tall(X)&~brave(X))))&
(![X]:((brave(X)<~>~rich(X))<=>(~patient(X)<~>wise(X))))&
(![X]:(patient(X)<=>(~wise(X)<~>old(X))))&
(![X]:(rich(X)<=>(~rich(X)|~funny(X))))&
(![X]:((strong(X)&~generous(X))<=>~kind(X)))&
(![X]:((quiet(X)<~>tall(X))<=>(~humble(X)&old(X))))&
(![X]:((tall(X)<~>patient(X))=>(~happy(X)|kind(X))))&
(~generous(mary))&
(?[X]:((~calm(X)|~old(X))))&
((happy(alice)<~>~old(alice)))&
((quiet(mary)|curious(mary)))&
((~creative(susan)|~curious(susan))) | happy(lucy) | [] | null | 0 |
If someone is either humble or not old then alice is either brave or not rich. If susan is either not humble or not funny then paul is not humble or wise and vice versa. If someone is both not creative and wise then someone is not rich or strong. Everyone who is not patient or quiet is old or not patient and vice versa. If someone is either not wise or not rich then paul is either happy or patient. Everyone who is not brave or not tall is either tall or not happy. If someone is not humble or brave then someone is both generous and creative. Everyone who is either creative or happy is both not funny and not kind. Everyone who is either creative or curious is either curious or happy and vice versa. Everyone who is either not curious or creative is both not curious and not rich. Everyone who is tall or not calm is either curious or not tall. Everyone who is not wise or not old is either not generous or quiet and vice versa. If someone is not calm then mary is either old or tall. If john is either curious or not quiet then paul is either not funny or calm. Everyone who is either kind or not happy is not funny or not strong. If someone is tall or brave then someone is not tall. Susan is not patient or not funny. Alice is both calm and not happy. Paul is curious. Lucy is generous. Someone is old. Someone is curious or calm. Someone is either not generous or tall. | Lucy is not tall. | entailment | ((?[X]:((humble(X)<~>~old(X))))=>((brave(alice)<~>~rich(alice))))&
(((~humble(susan)<~>~funny(susan)))<=>((~humble(paul)|wise(paul))))&
((?[X]:((~creative(X)&wise(X))))=>(?[X]:((~rich(X)|strong(X)))))&
(![X]:((~patient(X)|quiet(X))<=>(old(X)|~patient(X))))&
((?[X]:((~wise(X)<~>~rich(X))))=>((happy(paul)<~>patient(paul))))&
(![X]:((~brave(X)|~tall(X))=>(tall(X)<~>~happy(X))))&
((?[X]:((~humble(X)|brave(X))))=>(?[X]:((generous(X)&creative(X)))))&
(![X]:((creative(X)<~>happy(X))=>(~funny(X)&~kind(X))))&
(![X]:((creative(X)<~>curious(X))<=>(curious(X)<~>happy(X))))&
(![X]:((~curious(X)<~>creative(X))=>(~curious(X)&~rich(X))))&
(![X]:((tall(X)|~calm(X))=>(curious(X)<~>~tall(X))))&
(![X]:((~wise(X)|~old(X))<=>(~generous(X)<~>quiet(X))))&
((?[X]:(~calm(X)))=>((old(mary)<~>tall(mary))))&
(((curious(john)<~>~quiet(john)))=>((~funny(paul)<~>calm(paul))))&
(![X]:((kind(X)<~>~happy(X))=>(~funny(X)|~strong(X))))&
((?[X]:((tall(X)|brave(X))))=>(?[X]:(~tall(X))))&
((~patient(susan)|~funny(susan)))&
((calm(alice)&~happy(alice)))&
(curious(paul))&
(generous(lucy))&
(?[X]:(old(X)))&
(?[X]:((curious(X)|calm(X))))&
(?[X]:((~generous(X)<~>tall(X)))) | ~tall(lucy) | [
"p5",
"p6",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7699110389295260933890413
% SZS output start Proof for 7699110389295260933890413
6. ! [X0] : ((~tall(X0) | ~brave(X0)) => (tall(X0) <~> ~happy(X0))) [input p5]
7. ? [X0] : (brave(X0) | ~humble(X0)) => ? [X0] : (creative(X0) & generous(X0)) [input p6]
9. ! [X0] : ((creative(X0) <~> curious(X0)) <=> (curious(X0) <~> happy(X0))) [input p8]
10. ! [X0] : ((~curious(X0) <~> creative(X0)) => (~rich(X0) & ~curious(X0))) [input p9]
11. ! [X0] : ((~calm(X0) | tall(X0)) => (curious(X0) <~> ~tall(X0))) [input p10]
24. tall(lucy) [input hypothesis]
26. ? [X0] : (brave(X0) | ~humble(X0)) => ? [X1] : (creative(X1) & generous(X1)) [rectify 7]
31. ! [X0] : ((tall(X0) <~> ~happy(X0)) | (tall(X0) & brave(X0))) [ennf transformation 6]
32. ? [X1] : (creative(X1) & generous(X1)) | ! [X0] : (~brave(X0) & humble(X0)) [ennf transformation 26]
34. ! [X0] : ((~rich(X0) & ~curious(X0)) | (~curious(X0) <=> creative(X0))) [ennf transformation 10]
35. ! [X0] : ((curious(X0) <~> ~tall(X0)) | (calm(X0) & ~tall(X0))) [ennf transformation 11]
50. ! [X0] : (((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | (tall(X0) & brave(X0))) [nnf transformation 31]
51. ? [X0] : (creative(X0) & generous(X0)) | ! [X1] : (~brave(X1) & humble(X1)) [rectify 32]
52. ? [X0] : (creative(X0) & generous(X0)) => (creative(sK1) & generous(sK1)) [choice axiom]
53. (creative(sK1) & generous(sK1)) | ! [X1] : (~brave(X1) & humble(X1)) [skolemisation 51,52]
55. ! [X0] : ((((~curious(X0) | ~creative(X0)) & (curious(X0) | creative(X0))) | ((curious(X0) | ~happy(X0)) & (happy(X0) | ~curious(X0)))) & (((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | ((creative(X0) | ~curious(X0)) & (curious(X0) | ~creative(X0))))) [nnf transformation 9]
56. ! [X0] : ((~rich(X0) & ~curious(X0)) | ((~curious(X0) | ~creative(X0)) & (creative(X0) | curious(X0)))) [nnf transformation 34]
57. ! [X0] : (((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) | (calm(X0) & ~tall(X0))) [nnf transformation 35]
93. ~happy(X0) | tall(X0) | tall(X0) [cnf transformation 50]
94. ~tall(X0) | happy(X0) | brave(X0) [cnf transformation 50]
99. creative(sK1) | ~brave(X1) [cnf transformation 53]
104. happy(X0) | curious(X0) | curious(X0) | ~creative(X0) [cnf transformation 55]
107. ~happy(X0) | ~curious(X0) | creative(X0) | ~curious(X0) [cnf transformation 55]
109. curious(X0) | creative(X0) | curious(X0) | ~happy(X0) [cnf transformation 55]
110. ~curious(X0) | ~creative(X0) | happy(X0) | ~curious(X0) [cnf transformation 55]
113. ~curious(X0) | ~curious(X0) | ~creative(X0) [cnf transformation 56]
116. ~tall(X0) | curious(X0) | ~tall(X0) [cnf transformation 57]
145. tall(lucy) [cnf transformation 24]
146. ~tall(X0) | curious(X0) [duplicate literal removal 116]
147. ~curious(X0) | ~creative(X0) [duplicate literal removal 113]
148. happy(X0) | curious(X0) | ~creative(X0) [duplicate literal removal 104]
149. ~happy(X0) | ~curious(X0) | creative(X0) [duplicate literal removal 107]
150. curious(X0) | creative(X0) | ~happy(X0) [duplicate literal removal 109]
151. ~curious(X0) | ~creative(X0) | happy(X0) [duplicate literal removal 110]
152. ~happy(X0) | tall(X0) [duplicate literal removal 93]
224. 16 <=> ! [X1] : ~brave(X1) [avatar definition]
225. ~brave(X1) <- (16) [avatar component clause 224]
227. 17 <=> creative(sK1) [avatar definition]
229. creative(sK1) <- (17) [avatar component clause 227]
230. 16 | 17 [avatar split clause 99,227,224]
241. ~happy(X0) | creative(X0) [subsumption resolution 149,150]
242. ~creative(X0) | happy(X0) [subsumption resolution 148,151]
313. curious(lucy) [resolution 146,145]
316. ~creative(lucy) [resolution 313,147]
331. happy(lucy) | brave(lucy) [resolution 94,145]
332. happy(lucy) <- (16) [subsumption resolution 331,225]
333. creative(lucy) <- (16) [resolution 332,241]
335. $false <- (16) [subsumption resolution 333,316]
336. ~16 [avatar contradiction clause 335]
347. happy(sK1) <- (17) [resolution 229,242]
353. 39 <=> happy(sK1) [avatar definition]
355. happy(sK1) <- (39) [avatar component clause 353]
357. 39 | ~17 [avatar split clause 347,227,353]
360. tall(sK1) <- (39) [resolution 355,152]
362. curious(sK1) <- (39) [resolution 360,146]
363. ~creative(sK1) <- (39) [resolution 362,147]
364. $false <- (17, 39) [subsumption resolution 363,229]
365. ~17 | ~39 [avatar contradiction clause 364]
366. $false [avatar sat refutation 230,336,357,365]
% SZS output end Proof for 7699110389295260933890413
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not brave or not strong then someone is funny and vice versa.
Everyone who is not tall is either not old or old and vice versa.
Everyone who is either kind or not funny is humble or creative.
If someone is both funny and curious then fred is not wise.
If someone is either humble or not wise then someone is rich.
If someone is both tall and not rich then fred is strong or quiet.
Everyone who is curious or tall is both not curious and humble.
Everyone who is not rich is humble or not generous and vice versa.
Everyone who is either brave or old is both old and not quiet.
Everyone who is creative or old is strong or old and vice versa.
If someone is not quiet then someone is either happy or not generous and vice versa.
If someone is both not wise and funny then lucy is both not wise and not happy.
If someone is both not wise and not brave then john is either rich or wise.
Everyone who is tall is both not curious and not happy and vice versa.
Everyone who is wise or not generous is rich and vice versa.
Alice is either curious or not funny.
Lucy is both not patient and brave.
Mary is either rich or not happy.
Alice is both rich and strong.
John is both patient and not strong.
Someone is funny.
Mary is patient or not wise. | Lucy is not old. | contradiction | (((~brave(mary)<~>~strong(mary)))<=>(?[X]:(funny(X))))&
(![X]:(~tall(X)<=>(~old(X)<~>old(X))))&
(![X]:((kind(X)<~>~funny(X))=>(humble(X)|creative(X))))&
((?[X]:((funny(X)&curious(X))))=>(~wise(fred)))&
((?[X]:((humble(X)<~>~wise(X))))=>(?[X]:(rich(X))))&
((?[X]:((tall(X)&~rich(X))))=>((strong(fred)|quiet(fred))))&
(![X]:((curious(X)|tall(X))=>(~curious(X)&humble(X))))&
(![X]:(~rich(X)<=>(humble(X)|~generous(X))))&
(![X]:((brave(X)<~>old(X))=>(old(X)&~quiet(X))))&
(![X]:((creative(X)|old(X))<=>(strong(X)|old(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((happy(X)<~>~generous(X)))))&
((?[X]:((~wise(X)&funny(X))))=>((~wise(lucy)&~happy(lucy))))&
((?[X]:((~wise(X)&~brave(X))))=>((rich(john)<~>wise(john))))&
(![X]:(tall(X)<=>(~curious(X)&~happy(X))))&
(![X]:((wise(X)|~generous(X))<=>rich(X)))&
((curious(alice)<~>~funny(alice)))&
((~patient(lucy)&brave(lucy)))&
((rich(mary)<~>~happy(mary)))&
((rich(alice)&strong(alice)))&
((patient(john)&~strong(john)))&
(?[X]:(funny(X)))&
((patient(mary)|~wise(mary))) | ~old(lucy) | [
"p8",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4715794545312223259807912
% SZS output start Proof for 4715794545312223259807912
9. ! [X0] : ((brave(X0) <~> old(X0)) => (~quiet(X0) & old(X0))) [input p8]
17. brave(lucy) & ~patient(lucy) [input p16]
23. ~old(lucy) [input hypothesis]
33. ! [X0] : ((~quiet(X0) & old(X0)) | (brave(X0) <=> old(X0))) [ennf transformation 9]
48. ! [X0] : ((~quiet(X0) & old(X0)) | ((brave(X0) | ~old(X0)) & (old(X0) | ~brave(X0)))) [nnf transformation 33]
86. old(X0) | old(X0) | ~brave(X0) [cnf transformation 48]
111. brave(lucy) [cnf transformation 17]
120. ~old(lucy) [cnf transformation 23]
121. ~brave(X0) | old(X0) [duplicate literal removal 86]
243. old(lucy) [resolution 121,111]
245. $false [subsumption resolution 243,120]
% SZS output end Proof for 4715794545312223259807912
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not wise is both not funny and not tall. If someone is either not happy or not funny then someone is both not curious and not old. Everyone who is not quiet or creative is funny and vice versa. Everyone who is not old is both generous and not kind and vice versa. If susan is either strong or not calm then someone is not humble or patient and vice versa. If someone is both not old and not kind then john is either not curious or not strong. If someone is not patient then someone is either rich or not patient. If someone is either not old or wise then someone is calm or creative. Everyone who is happy or not calm is either strong or not brave and vice versa. Everyone who is either wise or quiet is either not creative or wise. Everyone who is either not creative or not wise is both not kind and quiet and vice versa. If someone is wise or not rich then susan is either not curious or not happy and vice versa. Everyone who is both not strong and not rich is patient and vice versa. Everyone who is not humble is not kind or funny and vice versa. If someone is either creative or not quiet then someone is strong and vice versa. Everyone who is brave or not curious is humble or happy and vice versa. Fred is creative or not calm. Mary is both not patient and not kind. Someone is both not brave and humble. Mary is not strong. Someone is generous or not generous. Someone is both humble and not wise. John is not patient. Someone is not funny. | John is not tall. | neutral | (![X]:(~wise(X)=>(~funny(X)&~tall(X))))&
((?[X]:((~happy(X)<~>~funny(X))))=>(?[X]:((~curious(X)&~old(X)))))&
(![X]:((~quiet(X)|creative(X))<=>funny(X)))&
(![X]:(~old(X)<=>(generous(X)&~kind(X))))&
(((strong(susan)<~>~calm(susan)))<=>(?[X]:((~humble(X)|patient(X)))))&
((?[X]:((~old(X)&~kind(X))))=>((~curious(john)<~>~strong(john))))&
((?[X]:(~patient(X)))=>(?[X]:((rich(X)<~>~patient(X)))))&
((?[X]:((~old(X)<~>wise(X))))=>(?[X]:((calm(X)|creative(X)))))&
(![X]:((happy(X)|~calm(X))<=>(strong(X)<~>~brave(X))))&
(![X]:((wise(X)<~>quiet(X))=>(~creative(X)<~>wise(X))))&
(![X]:((~creative(X)<~>~wise(X))<=>(~kind(X)&quiet(X))))&
((?[X]:((wise(X)|~rich(X))))<=>((~curious(susan)<~>~happy(susan))))&
(![X]:((~strong(X)&~rich(X))<=>patient(X)))&
(![X]:(~humble(X)<=>(~kind(X)|funny(X))))&
((?[X]:((creative(X)<~>~quiet(X))))<=>(?[X]:(strong(X))))&
(![X]:((brave(X)|~curious(X))<=>(humble(X)|happy(X))))&
((creative(fred)|~calm(fred)))&
((~patient(mary)&~kind(mary)))&
(?[X]:((~brave(X)&humble(X))))&
(~strong(mary))&
(?[X]:((generous(X)|~generous(X))))&
(?[X]:((humble(X)&~wise(X))))&
(~patient(john))&
(?[X]:(~funny(X))) | ~tall(john) | [] | null | 0 |
Everyone who is not patient is old or not rich and vice versa.
Everyone who is both not tall and not brave is quiet or not rich and vice versa.
Everyone who is both old and happy is either not quiet or not old.
Everyone who is either kind or patient is both not rich and not quiet.
If susan is funny or brave then someone is both kind and brave and vice versa.
Everyone who is strong is both not brave and not patient and vice versa.
Everyone who is not happy or not calm is either not old or not rich and vice versa.
If someone is not calm then someone is happy or not rich and vice versa.
Everyone who is either not old or tall is not generous or not calm.
Everyone who is both strong and not tall is both generous and not funny and vice versa.
Everyone who is old or happy is either not calm or not curious and vice versa.
Everyone who is either patient or brave is quiet.
Everyone who is both not curious and not old is not tall.
Everyone who is both not wise and curious is either not strong or not kind.
Everyone who is not funny is patient or calm and vice versa.
Everyone who is calm or not happy is not old and vice versa.
Paul is both not funny and calm.
Fred is not patient or not quiet.
Alice is either not humble or not rich.
Susan is not tall. | Alice is not calm. | contradiction | (![X]:(~patient(X)<=>(old(X)|~rich(X))))&
(![X]:((~tall(X)&~brave(X))<=>(quiet(X)|~rich(X))))&
(![X]:((old(X)&happy(X))=>(~quiet(X)<~>~old(X))))&
(![X]:((kind(X)<~>patient(X))=>(~rich(X)&~quiet(X))))&
(((funny(susan)|brave(susan)))<=>(?[X]:((kind(X)&brave(X)))))&
(![X]:(strong(X)<=>(~brave(X)&~patient(X))))&
(![X]:((~happy(X)|~calm(X))<=>(~old(X)<~>~rich(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((happy(X)|~rich(X)))))&
(![X]:((~old(X)<~>tall(X))=>(~generous(X)|~calm(X))))&
(![X]:((strong(X)&~tall(X))<=>(generous(X)&~funny(X))))&
(![X]:((old(X)|happy(X))<=>(~calm(X)<~>~curious(X))))&
(![X]:((patient(X)<~>brave(X))=>quiet(X)))&
(![X]:((~curious(X)&~old(X))=>~tall(X)))&
(![X]:((~wise(X)&curious(X))=>(~strong(X)<~>~kind(X))))&
(![X]:(~funny(X)<=>(patient(X)|calm(X))))&
(![X]:((calm(X)|~happy(X))<=>~old(X)))&
((~funny(paul)&calm(paul)))&
((~patient(fred)|~quiet(fred)))&
((~humble(alice)<~>~rich(alice)))&
(~tall(susan)) | ~calm(alice) | [
"p0",
"p1",
"p5",
"p6",
"p7",
"p8",
"p9",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6954644982110483203965948
% SZS output start Proof for 6954644982110483203965948
1. ! [X0] : (~patient(X0) <=> (~rich(X0) | old(X0))) [input p0]
2. ! [X0] : ((~brave(X0) & ~tall(X0)) <=> (~rich(X0) | quiet(X0))) [input p1]
6. ! [X0] : (strong(X0) <=> (~patient(X0) & ~brave(X0))) [input p5]
7. ! [X0] : ((~calm(X0) | ~happy(X0)) <=> (~old(X0) <~> ~rich(X0))) [input p6]
8. ? [X0] : ~calm(X0) <=> ? [X0] : (~rich(X0) | happy(X0)) [input p7]
9. ! [X0] : ((~old(X0) <~> tall(X0)) => (~calm(X0) | ~generous(X0))) [input p8]
10. ! [X0] : ((~tall(X0) & strong(X0)) <=> (~funny(X0) & generous(X0))) [input p9]
12. ! [X0] : ((patient(X0) <~> brave(X0)) => quiet(X0)) [input p11]
15. ! [X0] : (~funny(X0) <=> (calm(X0) | patient(X0))) [input p14]
16. ! [X0] : ((~happy(X0) | calm(X0)) <=> ~old(X0)) [input p15]
21. ~calm(alice) [input hypothesis]
22. ? [X0] : ~calm(X0) <=> ? [X1] : (~rich(X1) | happy(X1)) [rectify 8]
27. ! [X0] : ((~calm(X0) | ~generous(X0)) | (~old(X0) <=> tall(X0))) [ennf transformation 9]
28. ! [X0] : (~calm(X0) | ~generous(X0) | (~old(X0) <=> tall(X0))) [flattening 27]
29. ! [X0] : (quiet(X0) | (patient(X0) <=> brave(X0))) [ennf transformation 12]
32. ! [X0] : ((~patient(X0) | (rich(X0) & ~old(X0))) & ((~rich(X0) | old(X0)) | patient(X0))) [nnf transformation 1]
33. ! [X0] : ((~patient(X0) | (rich(X0) & ~old(X0))) & (~rich(X0) | old(X0) | patient(X0))) [flattening 32]
34. ! [X0] : (((~brave(X0) & ~tall(X0)) | (rich(X0) & ~quiet(X0))) & ((~rich(X0) | quiet(X0)) | (brave(X0) | tall(X0)))) [nnf transformation 2]
35. ! [X0] : (((~brave(X0) & ~tall(X0)) | (rich(X0) & ~quiet(X0))) & (~rich(X0) | quiet(X0) | brave(X0) | tall(X0))) [flattening 34]
43. ! [X0] : ((strong(X0) | (patient(X0) | brave(X0))) & ((~patient(X0) & ~brave(X0)) | ~strong(X0))) [nnf transformation 6]
44. ! [X0] : ((strong(X0) | patient(X0) | brave(X0)) & ((~patient(X0) & ~brave(X0)) | ~strong(X0))) [flattening 43]
45. ! [X0] : (((~calm(X0) | ~happy(X0)) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0)))) & (((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (calm(X0) & happy(X0)))) [nnf transformation 7]
46. ! [X0] : ((~calm(X0) | ~happy(X0) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0)))) & (((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (calm(X0) & happy(X0)))) [flattening 45]
47. (? [X0] : ~calm(X0) | ! [X1] : (rich(X1) & ~happy(X1))) & (? [X1] : (~rich(X1) | happy(X1)) | ! [X0] : calm(X0)) [nnf transformation 22]
48. (? [X0] : ~calm(X0) | ! [X1] : (rich(X1) & ~happy(X1))) & (? [X2] : (~rich(X2) | happy(X2)) | ! [X3] : calm(X3)) [rectify 47]
49. ? [X0] : ~calm(X0) => ~calm(sK1) [choice axiom]
50. ? [X2] : (~rich(X2) | happy(X2)) => (~rich(sK2) | happy(sK2)) [choice axiom]
51. (~calm(sK1) | ! [X1] : (rich(X1) & ~happy(X1))) & ((~rich(sK2) | happy(sK2)) | ! [X3] : calm(X3)) [skolemisation 48,50,49]
52. ! [X0] : (~calm(X0) | ~generous(X0) | ((~old(X0) | ~tall(X0)) & (tall(X0) | old(X0)))) [nnf transformation 28]
53. ! [X0] : (((~tall(X0) & strong(X0)) | (funny(X0) | ~generous(X0))) & ((~funny(X0) & generous(X0)) | (tall(X0) | ~strong(X0)))) [nnf transformation 10]
54. ! [X0] : (((~tall(X0) & strong(X0)) | funny(X0) | ~generous(X0)) & ((~funny(X0) & generous(X0)) | tall(X0) | ~strong(X0))) [flattening 53]
57. ! [X0] : (quiet(X0) | ((patient(X0) | ~brave(X0)) & (brave(X0) | ~patient(X0)))) [nnf transformation 29]
58. ! [X0] : ((~funny(X0) | (~calm(X0) & ~patient(X0))) & ((calm(X0) | patient(X0)) | funny(X0))) [nnf transformation 15]
59. ! [X0] : ((~funny(X0) | (~calm(X0) & ~patient(X0))) & (calm(X0) | patient(X0) | funny(X0))) [flattening 58]
60. ! [X0] : (((~happy(X0) | calm(X0)) | old(X0)) & (~old(X0) | (happy(X0) & ~calm(X0)))) [nnf transformation 16]
61. ! [X0] : ((~happy(X0) | calm(X0) | old(X0)) & (~old(X0) | (happy(X0) & ~calm(X0)))) [flattening 60]
65. ~patient(X0) | rich(X0) [cnf transformation 33]
68. ~tall(X0) | rich(X0) [cnf transformation 35]
69. ~quiet(X0) | ~brave(X0) [cnf transformation 35]
84. strong(X0) | patient(X0) | brave(X0) [cnf transformation 44]
86. ~rich(X0) | ~old(X0) | calm(X0) [cnf transformation 46]
89. ~calm(X0) | ~happy(X0) | ~rich(X0) | old(X0) [cnf transformation 46]
91. ~rich(sK2) | happy(sK2) | calm(X3) [cnf transformation 51]
94. ~generous(X0) | ~calm(X0) | tall(X0) | old(X0) [cnf transformation 52]
96. ~strong(X0) | tall(X0) | generous(X0) [cnf transformation 54]
97. ~strong(X0) | tall(X0) | ~funny(X0) [cnf transformation 54]
107. quiet(X0) | patient(X0) | ~brave(X0) [cnf transformation 57]
109. calm(X0) | patient(X0) | funny(X0) [cnf transformation 59]
110. ~funny(X0) | ~patient(X0) [cnf transformation 59]
112. ~calm(X0) | ~old(X0) [cnf transformation 61]
114. ~happy(X0) | calm(X0) | old(X0) [cnf transformation 61]
121. ~calm(alice) [cnf transformation 21]
149. 6 <=> ! [X1] : rich(X1) [avatar definition]
150. rich(X1) <- (6) [avatar component clause 149]
161. 9 <=> ! [X3] : calm(X3) [avatar definition]
162. calm(X3) <- (9) [avatar component clause 161]
164. 10 <=> happy(sK2) [avatar definition]
166. happy(sK2) <- (10) [avatar component clause 164]
168. 11 <=> rich(sK2) [avatar definition]
170. ~rich(sK2) <- (~11) [avatar component clause 168]
171. 9 | 10 | ~11 [avatar split clause 91,168,164,161]
172. ~brave(X0) | patient(X0) [subsumption resolution 107,69]
232. tall(X0) | generous(X0) | patient(X0) | brave(X0) [resolution 96,84]
233. generous(X0) | tall(X0) | patient(X0) [subsumption resolution 232,172]
236. tall(X0) | ~funny(X0) | patient(X0) | brave(X0) [resolution 97,84]
237. ~funny(X0) | tall(X0) | brave(X0) [subsumption resolution 236,110]
296. tall(X1) | patient(X1) | ~calm(X1) | tall(X1) | old(X1) [resolution 233,94]
299. tall(X1) | patient(X1) | ~calm(X1) | old(X1) [duplicate literal removal 296]
300. ~calm(X1) | patient(X1) | tall(X1) [subsumption resolution 299,112]
449. patient(X0) | tall(X0) | patient(X0) | funny(X0) [resolution 300,109]
451. funny(X0) | tall(X0) | patient(X0) [duplicate literal removal 449]
517. tall(X0) | patient(X0) | tall(X0) | brave(X0) [resolution 451,237]
524. tall(X0) | patient(X0) | brave(X0) [duplicate literal removal 517]
525. tall(X0) | patient(X0) [subsumption resolution 524,172]
535. 38 <=> calm(sK2) [avatar definition]
537. calm(sK2) <- (38) [avatar component clause 535]
541. calm(sK2) | old(sK2) <- (10) [resolution 166,114]
566. 41 <=> old(sK2) [avatar definition]
568. old(sK2) <- (41) [avatar component clause 566]
569. 41 | 38 | ~10 [avatar split clause 541,164,535,566]
582. patient(X1) | rich(X1) [resolution 525,68]
586. rich(X1) [subsumption resolution 582,65]
587. 6 [avatar split clause 586,149]
589. ~old(X1) | calm(X1) <- (6) [resolution 150,86]
592. ~old(X1) <- (6) [subsumption resolution 589,112]
601. $false <- (9) [resolution 162,121]
610. ~9 [avatar contradiction clause 601]
618. $false <- (6, 41) [subsumption resolution 568,592]
619. ~6 | ~41 [avatar contradiction clause 618]
702. ~happy(sK2) | ~rich(sK2) | old(sK2) <- (38) [resolution 537,89]
705. ~rich(sK2) | old(sK2) <- (10, 38) [subsumption resolution 702,166]
709. old(sK2) <- (6, 10, 38) [subsumption resolution 705,150]
710. $false <- (6, 10, 38) [subsumption resolution 709,592]
711. ~6 | ~10 | ~38 [avatar contradiction clause 710]
712. $false <- (6, ~11) [subsumption resolution 170,150]
713. ~6 | 11 [avatar contradiction clause 712]
714. $false [avatar sat refutation 171,569,587,610,619,711,713]
% SZS output end Proof for 6954644982110483203965948
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both not humble and not creative then someone is either quiet or not old.
Everyone who is not patient or not old is not old or not tall.
If someone is not generous or generous then someone is not strong and vice versa.
Everyone who is kind is not happy.
Everyone who is not wise is both kind and not tall and vice versa.
Everyone who is not kind is either calm or patient.
If lucy is not happy or quiet then lucy is both kind and generous and vice versa.
If someone is not kind or patient then fred is both funny and not generous.
If someone is funny or not kind then someone is both not humble and not rich and vice versa.
Everyone who is either patient or humble is both not strong and curious.
Everyone who is either not funny or quiet is not humble.
Everyone who is either not old or happy is old and vice versa.
Everyone who is both wise and humble is not strong or wise.
If john is both not creative and not rich then lucy is both not brave and happy.
If lucy is not brave or humble then fred is wise.
If paul is not calm then someone is not kind or not strong and vice versa.
Someone is both not funny and wise.
Someone is tall or not tall.
Paul is either wise or not old.
Susan is both quiet and not creative.
Someone is both strong and happy.
Someone is tall or not curious.
Someone is not creative. | John is not wise. | contradiction | (((~humble(alice)&~creative(alice)))=>(?[X]:((quiet(X)<~>~old(X)))))&
(![X]:((~patient(X)|~old(X))=>(~old(X)|~tall(X))))&
((?[X]:((~generous(X)|generous(X))))<=>(?[X]:(~strong(X))))&
(![X]:(kind(X)=>~happy(X)))&
(![X]:(~wise(X)<=>(kind(X)&~tall(X))))&
(![X]:(~kind(X)=>(calm(X)<~>patient(X))))&
(((~happy(lucy)|quiet(lucy)))<=>((kind(lucy)&generous(lucy))))&
((?[X]:((~kind(X)|patient(X))))=>((funny(fred)&~generous(fred))))&
((?[X]:((funny(X)|~kind(X))))<=>(?[X]:((~humble(X)&~rich(X)))))&
(![X]:((patient(X)<~>humble(X))=>(~strong(X)&curious(X))))&
(![X]:((~funny(X)<~>quiet(X))=>~humble(X)))&
(![X]:((~old(X)<~>happy(X))<=>old(X)))&
(![X]:((wise(X)&humble(X))=>(~strong(X)|wise(X))))&
(((~creative(john)&~rich(john)))=>((~brave(lucy)&happy(lucy))))&
(((~brave(lucy)|humble(lucy)))=>(wise(fred)))&
((~calm(paul))<=>(?[X]:((~kind(X)|~strong(X)))))&
(?[X]:((~funny(X)&wise(X))))&
(?[X]:((tall(X)|~tall(X))))&
((wise(paul)<~>~old(paul)))&
((quiet(susan)&~creative(susan)))&
(?[X]:((strong(X)&happy(X))))&
(?[X]:((tall(X)|~curious(X))))&
(?[X]:(~creative(X))) | ~wise(john) | [
"p3",
"p4",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5136349812091160440107851
% SZS output start Proof for 5136349812091160440107851
4. ! [X0] : (kind(X0) => ~happy(X0)) [input p3]
5. ! [X0] : (~wise(X0) <=> (~tall(X0) & kind(X0))) [input p4]
12. ! [X0] : ((~old(X0) <~> happy(X0)) <=> old(X0)) [input p11]
24. ~wise(john) [input hypothesis]
31. ! [X0] : (~happy(X0) | ~kind(X0)) [ennf transformation 4]
49. ! [X0] : ((~wise(X0) | (tall(X0) | ~kind(X0))) & ((~tall(X0) & kind(X0)) | wise(X0))) [nnf transformation 5]
50. ! [X0] : ((~wise(X0) | tall(X0) | ~kind(X0)) & ((~tall(X0) & kind(X0)) | wise(X0))) [flattening 49]
61. ! [X0] : ((((~happy(X0) | old(X0)) & (happy(X0) | ~old(X0))) | ~old(X0)) & (old(X0) | ((~old(X0) | ~happy(X0)) & (happy(X0) | old(X0))))) [nnf transformation 12]
84. ~happy(X0) | ~kind(X0) [cnf transformation 31]
85. wise(X0) | kind(X0) [cnf transformation 50]
110. old(X0) | happy(X0) | old(X0) [cnf transformation 61]
112. happy(X0) | ~old(X0) | ~old(X0) [cnf transformation 61]
133. ~wise(john) [cnf transformation 24]
134. old(X0) | happy(X0) [duplicate literal removal 110]
135. happy(X0) | ~old(X0) [duplicate literal removal 112]
231. happy(X0) [subsumption resolution 134,135]
294. ~kind(X0) [resolution 84,231]
295. kind(john) [resolution 85,133]
297. $false [subsumption resolution 295,294]
% SZS output end Proof for 5136349812091160440107851
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not funny or tall then lucy is not creative or not happy and vice versa.
Everyone who is generous or not curious is both not wise and funny and vice versa.
Everyone who is old or not humble is not wise.
Everyone who is either not quiet or tall is not generous and vice versa.
If someone is either calm or not creative then susan is humble or old and vice versa.
Everyone who is not tall or not quiet is tall or rich and vice versa.
If someone is both old and strong then lucy is quiet.
If lucy is either funny or not quiet then fred is quiet and vice versa.
If mary is generous then someone is either not calm or old and vice versa.
Everyone who is not tall is both strong and old.
Everyone who is curious is either not calm or generous and vice versa.
If susan is not strong or funny then john is either quiet or not patient.
Everyone who is not funny or curious is kind and vice versa.
If someone is not brave then someone is not brave or curious and vice versa.
Everyone who is not strong is both not wise and tall.
If someone is either kind or quiet then mary is not calm.
Someone is patient.
Paul is curious.
John is either tall or brave.
Someone is not quiet.
Paul is not rich.
Susan is not kind.
Susan is creative.
Alice is not kind. | Lucy is not generous. | contradiction | ((?[X]:((~funny(X)<~>tall(X))))<=>((~creative(lucy)|~happy(lucy))))&
(![X]:((generous(X)|~curious(X))<=>(~wise(X)&funny(X))))&
(![X]:((old(X)|~humble(X))=>~wise(X)))&
(![X]:((~quiet(X)<~>tall(X))<=>~generous(X)))&
((?[X]:((calm(X)<~>~creative(X))))<=>((humble(susan)|old(susan))))&
(![X]:((~tall(X)|~quiet(X))<=>(tall(X)|rich(X))))&
((?[X]:((old(X)&strong(X))))=>(quiet(lucy)))&
(((funny(lucy)<~>~quiet(lucy)))<=>(quiet(fred)))&
((generous(mary))<=>(?[X]:((~calm(X)<~>old(X)))))&
(![X]:(~tall(X)=>(strong(X)&old(X))))&
(![X]:(curious(X)<=>(~calm(X)<~>generous(X))))&
(((~strong(susan)|funny(susan)))=>((quiet(john)<~>~patient(john))))&
(![X]:((~funny(X)|curious(X))<=>kind(X)))&
((?[X]:(~brave(X)))<=>(?[X]:((~brave(X)|curious(X)))))&
(![X]:(~strong(X)=>(~wise(X)&tall(X))))&
((?[X]:((kind(X)<~>quiet(X))))=>(~calm(mary)))&
(?[X]:(patient(X)))&
(curious(paul))&
((tall(john)<~>brave(john)))&
(?[X]:(~quiet(X)))&
(~rich(paul))&
(~kind(susan))&
(creative(susan))&
(~kind(alice)) | ~generous(lucy) | [
"p3",
"p5",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5607911703488754010743238
% SZS output start Proof for 5607911703488754010743238
4. ! [X0] : ((~quiet(X0) <~> tall(X0)) <=> ~generous(X0)) [input p3]
6. ! [X0] : ((~quiet(X0) | ~tall(X0)) <=> (rich(X0) | tall(X0))) [input p5]
7. ? [X0] : (strong(X0) & old(X0)) => quiet(lucy) [input p6]
10. ! [X0] : (~tall(X0) => (old(X0) & strong(X0))) [input p9]
25. ~generous(lucy) [input hypothesis]
28. quiet(lucy) | ! [X0] : (~strong(X0) | ~old(X0)) [ennf transformation 7]
29. ! [X0] : ((old(X0) & strong(X0)) | tall(X0)) [ennf transformation 10]
40. ! [X0] : ((((~tall(X0) | quiet(X0)) & (tall(X0) | ~quiet(X0))) | generous(X0)) & (~generous(X0) | ((~quiet(X0) | ~tall(X0)) & (tall(X0) | quiet(X0))))) [nnf transformation 4]
46. ! [X0] : (((~quiet(X0) | ~tall(X0)) | (~rich(X0) & ~tall(X0))) & ((rich(X0) | tall(X0)) | (quiet(X0) & tall(X0)))) [nnf transformation 6]
47. ! [X0] : ((~quiet(X0) | ~tall(X0) | (~rich(X0) & ~tall(X0))) & (rich(X0) | tall(X0) | (quiet(X0) & tall(X0)))) [flattening 46]
83. ~quiet(X0) | tall(X0) | generous(X0) [cnf transformation 40]
84. ~tall(X0) | quiet(X0) | generous(X0) [cnf transformation 40]
93. ~quiet(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 47]
95. quiet(lucy) | ~strong(X0) | ~old(X0) [cnf transformation 28]
104. strong(X0) | tall(X0) [cnf transformation 29]
105. old(X0) | tall(X0) [cnf transformation 29]
133. ~generous(lucy) [cnf transformation 25]
135. ~quiet(X0) | ~tall(X0) [duplicate literal removal 93]
193. 13 <=> ! [X0] : (~strong(X0) | ~old(X0)) [avatar definition]
194. ~strong(X0) | ~old(X0) <- (13) [avatar component clause 193]
196. 14 <=> quiet(lucy) [avatar definition]
198. quiet(lucy) <- (14) [avatar component clause 196]
199. 13 | 14 [avatar split clause 95,196,193]
308. ~tall(lucy) <- (14) [resolution 135,198]
331. tall(lucy) | generous(lucy) <- (14) [resolution 83,198]
332. generous(lucy) <- (14) [subsumption resolution 331,308]
333. $false <- (14) [subsumption resolution 332,133]
334. ~14 [avatar contradiction clause 333]
349. ~old(X0) | tall(X0) <- (13) [resolution 194,104]
350. tall(X0) <- (13) [subsumption resolution 349,105]
353. quiet(X0) | generous(X0) <- (13) [resolution 84,350]
359. generous(X2) | ~tall(X2) <- (13) [resolution 353,135]
365. generous(X2) <- (13) [subsumption resolution 359,350]
367. $false <- (13) [resolution 365,133]
372. ~13 [avatar contradiction clause 367]
373. $false [avatar sat refutation 199,334,372]
% SZS output end Proof for 5607911703488754010743238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not humble or not rich is brave or not kind and vice versa.
If someone is not generous then someone is patient.
Everyone who is either not funny or patient is old or not generous.
If someone is quiet or patient then someone is either wise or funny.
If someone is both not generous and old then paul is patient.
If someone is both not brave and old then someone is either kind or not patient and vice versa.
Everyone who is not patient or not old is not funny or wise and vice versa.
Everyone who is not creative is both not wise and tall and vice versa.
Everyone who is both not patient and not calm is both not creative and not brave.
Everyone who is rich is either calm or rich.
If mary is not brave then susan is funny or not calm and vice versa.
Everyone who is either not humble or funny is both generous and not generous.
Everyone who is both creative and not kind is not humble.
If susan is not kind then susan is not funny or patient.
If someone is either brave or not rich then someone is not curious and vice versa.
John is either not tall or not kind.
Someone is either tall or rich.
Someone is both funny and not brave.
Someone is not generous or not patient.
Someone is either not curious or not tall.
Someone is both not old and not curious.
Someone is generous or not quiet.
Fred is either not creative or not calm. | Susan is generous. | neutral | (![X]:((~humble(X)<~>~rich(X))<=>(brave(X)|~kind(X))))&
((?[X]:(~generous(X)))=>(?[X]:(patient(X))))&
(![X]:((~funny(X)<~>patient(X))=>(old(X)|~generous(X))))&
((?[X]:((quiet(X)|patient(X))))=>(?[X]:((wise(X)<~>funny(X)))))&
((?[X]:((~generous(X)&old(X))))=>(patient(paul)))&
((?[X]:((~brave(X)&old(X))))<=>(?[X]:((kind(X)<~>~patient(X)))))&
(![X]:((~patient(X)|~old(X))<=>(~funny(X)|wise(X))))&
(![X]:(~creative(X)<=>(~wise(X)&tall(X))))&
(![X]:((~patient(X)&~calm(X))=>(~creative(X)&~brave(X))))&
(![X]:(rich(X)=>(calm(X)<~>rich(X))))&
((~brave(mary))<=>((funny(susan)|~calm(susan))))&
(![X]:((~humble(X)<~>funny(X))=>(generous(X)&~generous(X))))&
(![X]:((creative(X)&~kind(X))=>~humble(X)))&
((~kind(susan))=>((~funny(susan)|patient(susan))))&
((?[X]:((brave(X)<~>~rich(X))))<=>(?[X]:(~curious(X))))&
((~tall(john)<~>~kind(john)))&
(?[X]:((tall(X)<~>rich(X))))&
(?[X]:((funny(X)&~brave(X))))&
(?[X]:((~generous(X)|~patient(X))))&
(?[X]:((~curious(X)<~>~tall(X))))&
(?[X]:((~old(X)&~curious(X))))&
(?[X]:((generous(X)|~quiet(X))))&
((~creative(fred)<~>~calm(fred))) | generous(susan) | [] | null | 0 |
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