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 curious is both funny and not generous and vice versa. Everyone who is either funny or not creative is either not happy or old and vice versa. If someone is tall or not rich then mary is both rich and old and vice versa. If paul is both happy and old then john is not patient or kind and vice versa. Everyone who is both not rich and not wise is both not rich and calm. Everyone who is happy or not tall is not quiet or not brave. Everyone who is not curious or quiet is both not patient and rich. If john is not strong or tall then someone is brave. If john is both wise and kind then someone is not rich or not funny. Everyone who is both not strong and not wise is both not generous and not funny and vice versa. If paul is not calm then someone is rich and vice versa. Everyone who is not strong is generous. If susan is either not generous or not strong then someone is both wise and not creative. If john is both creative and not wise then john is either not strong or not brave. If john is not funny or calm then someone is both tall and not wise and vice versa. If susan is both not wise and humble then someone is strong or not humble and vice versa. Someone is not tall. Susan is not curious. Alice is curious or calm. Someone is either not calm or not rich. Lucy is not wise or old. Lucy is both not calm and not generous. Someone is rich. | Paul is happy. | neutral | (![X]:(curious(X)<=>(funny(X)&~generous(X))))&
(![X]:((funny(X)<~>~creative(X))<=>(~happy(X)<~>old(X))))&
((?[X]:((tall(X)|~rich(X))))<=>((rich(mary)&old(mary))))&
(((happy(paul)&old(paul)))<=>((~patient(john)|kind(john))))&
(![X]:((~rich(X)&~wise(X))=>(~rich(X)&calm(X))))&
(![X]:((happy(X)|~tall(X))=>(~quiet(X)|~brave(X))))&
(![X]:((~curious(X)|quiet(X))=>(~patient(X)&rich(X))))&
(((~strong(john)|tall(john)))=>(?[X]:(brave(X))))&
(((wise(john)&kind(john)))=>(?[X]:((~rich(X)|~funny(X)))))&
(![X]:((~strong(X)&~wise(X))<=>(~generous(X)&~funny(X))))&
((~calm(paul))<=>(?[X]:(rich(X))))&
(![X]:(~strong(X)=>generous(X)))&
(((~generous(susan)<~>~strong(susan)))=>(?[X]:((wise(X)&~creative(X)))))&
(((creative(john)&~wise(john)))=>((~strong(john)<~>~brave(john))))&
(((~funny(john)|calm(john)))<=>(?[X]:((tall(X)&~wise(X)))))&
(((~wise(susan)&humble(susan)))<=>(?[X]:((strong(X)|~humble(X)))))&
(?[X]:(~tall(X)))&
(~curious(susan))&
((curious(alice)|calm(alice)))&
(?[X]:((~calm(X)<~>~rich(X))))&
((~wise(lucy)|old(lucy)))&
((~calm(lucy)&~generous(lucy)))&
(?[X]:(rich(X))) | happy(paul) | [] | null | 0 |
If mary is both not wise and rich then susan is not tall or kind and vice versa.
Everyone who is creative or not happy is both not rich and not old.
Everyone who is either creative or not tall is both strong and not old.
If susan is both not funny and wise then john is either not happy or brave.
Everyone who is both humble and not strong is either not old or not creative and vice versa.
Everyone who is either brave or not tall is both not brave and not humble.
If john is either old or not kind then someone is either strong or brave.
If mary is both not kind and curious then someone is tall or not brave and vice versa.
Everyone who is either strong or not patient is either tall or wise and vice versa.
Everyone who is not brave is not wise or funny and vice versa.
If paul is both not calm and curious then fred is quiet or not strong.
Everyone who is not wise is not kind.
Everyone who is not funny or not humble is curious or not old.
Everyone who is both not funny and not old is both not funny and not tall and vice versa.
Everyone who is not humble is not old and vice versa.
Everyone who is both not creative and generous is happy or not brave.
Someone is not patient.
Someone is not curious.
Fred is not curious or not generous.
Someone is both not creative and calm.
Someone is both patient and not happy.
Fred is either kind or wise.
Someone is either not tall or not generous.
Fred is either funny or wise. | Fred is not creative. | entailment | (((~wise(mary)&rich(mary)))<=>((~tall(susan)|kind(susan))))&
(![X]:((creative(X)|~happy(X))=>(~rich(X)&~old(X))))&
(![X]:((creative(X)<~>~tall(X))=>(strong(X)&~old(X))))&
(((~funny(susan)&wise(susan)))=>((~happy(john)<~>brave(john))))&
(![X]:((humble(X)&~strong(X))<=>(~old(X)<~>~creative(X))))&
(![X]:((brave(X)<~>~tall(X))=>(~brave(X)&~humble(X))))&
(((old(john)<~>~kind(john)))=>(?[X]:((strong(X)<~>brave(X)))))&
(((~kind(mary)&curious(mary)))<=>(?[X]:((tall(X)|~brave(X)))))&
(![X]:((strong(X)<~>~patient(X))<=>(tall(X)<~>wise(X))))&
(![X]:(~brave(X)<=>(~wise(X)|funny(X))))&
(((~calm(paul)&curious(paul)))=>((quiet(fred)|~strong(fred))))&
(![X]:(~wise(X)=>~kind(X)))&
(![X]:((~funny(X)|~humble(X))=>(curious(X)|~old(X))))&
(![X]:((~funny(X)&~old(X))<=>(~funny(X)&~tall(X))))&
(![X]:(~humble(X)<=>~old(X)))&
(![X]:((~creative(X)&generous(X))=>(happy(X)|~brave(X))))&
(?[X]:(~patient(X)))&
(?[X]:(~curious(X)))&
((~curious(fred)|~generous(fred)))&
(?[X]:((~creative(X)&calm(X))))&
(?[X]:((patient(X)&~happy(X))))&
((kind(fred)<~>wise(fred)))&
(?[X]:((~tall(X)<~>~generous(X))))&
((funny(fred)<~>wise(fred))) | ~creative(fred) | [
"p1",
"p4",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7413193232769500944190512
% SZS output start Proof for 7413193232769500944190512
2. ! [X0] : ((~happy(X0) | creative(X0)) => (~old(X0) & ~rich(X0))) [input p1]
5. ! [X0] : ((~strong(X0) & humble(X0)) <=> (~old(X0) <~> ~creative(X0))) [input p4]
15. ! [X0] : (~humble(X0) <=> ~old(X0)) [input p14]
25. creative(fred) [input hypothesis]
28. ! [X0] : ((~old(X0) & ~rich(X0)) | (happy(X0) & ~creative(X0))) [ennf transformation 2]
43. ! [X0] : (((~strong(X0) & humble(X0)) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0)))) & (((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | (strong(X0) | ~humble(X0)))) [nnf transformation 5]
44. ! [X0] : (((~strong(X0) & humble(X0)) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0)))) & (((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | strong(X0) | ~humble(X0))) [flattening 43]
59. ! [X0] : ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))) [nnf transformation 15]
80. ~old(X0) | ~creative(X0) [cnf transformation 28]
90. humble(X0) | ~creative(X0) | old(X0) [cnf transformation 44]
126. ~humble(X0) | old(X0) [cnf transformation 59]
140. creative(fred) [cnf transformation 25]
185. ~creative(X0) | humble(X0) [subsumption resolution 90,80]
255. humble(fred) [resolution 185,140]
266. old(fred) [resolution 255,126]
273. ~creative(fred) [resolution 266,80]
276. $false [subsumption resolution 273,140]
% SZS output end Proof for 7413193232769500944190512
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is not strong and vice versa. If someone is either generous or not patient then someone is not calm and vice versa. Everyone who is generous is either not generous or not quiet and vice versa. If someone is both humble and quiet then alice is curious or old and vice versa. If susan is either not curious or curious then someone is not curious. If mary is not patient or not kind then paul is either not old or not kind. If lucy is tall or strong then mary is generous or kind. Everyone who is either not funny or tall is tall. Everyone who is tall or not rich is either not strong or happy and vice versa. If susan is generous or not strong then someone is kind or strong and vice versa. Everyone who is both not patient and creative is either not brave or patient and vice versa. Everyone who is calm or kind is not happy or strong and vice versa. If someone is calm then susan is either patient or not generous and vice versa. If fred is curious then fred is strong and vice versa. Everyone who is both not generous and rich is either rich or not calm. If fred is both humble and calm then paul is both not rich and wise and vice versa. Someone is not quiet. Someone is both kind and tall. John is not strong or not creative. Someone is not funny. Mary is both funny and generous. Fred is not quiet. Susan is patient or happy. Someone is not brave or funny. | Fred is not brave. | neutral | (![X]:(kind(X)<=>~strong(X)))&
((?[X]:((generous(X)<~>~patient(X))))<=>(?[X]:(~calm(X))))&
(![X]:(generous(X)<=>(~generous(X)<~>~quiet(X))))&
((?[X]:((humble(X)&quiet(X))))<=>((curious(alice)|old(alice))))&
(((~curious(susan)<~>curious(susan)))=>(?[X]:(~curious(X))))&
(((~patient(mary)|~kind(mary)))=>((~old(paul)<~>~kind(paul))))&
(((tall(lucy)|strong(lucy)))=>((generous(mary)|kind(mary))))&
(![X]:((~funny(X)<~>tall(X))=>tall(X)))&
(![X]:((tall(X)|~rich(X))<=>(~strong(X)<~>happy(X))))&
(((generous(susan)|~strong(susan)))<=>(?[X]:((kind(X)|strong(X)))))&
(![X]:((~patient(X)&creative(X))<=>(~brave(X)<~>patient(X))))&
(![X]:((calm(X)|kind(X))<=>(~happy(X)|strong(X))))&
((?[X]:(calm(X)))<=>((patient(susan)<~>~generous(susan))))&
((curious(fred))<=>(strong(fred)))&
(![X]:((~generous(X)&rich(X))=>(rich(X)<~>~calm(X))))&
(((humble(fred)&calm(fred)))<=>((~rich(paul)&wise(paul))))&
(?[X]:(~quiet(X)))&
(?[X]:((kind(X)&tall(X))))&
((~strong(john)|~creative(john)))&
(?[X]:(~funny(X)))&
((funny(mary)&generous(mary)))&
(~quiet(fred))&
((patient(susan)|happy(susan)))&
(?[X]:((~brave(X)|funny(X)))) | ~brave(fred) | [] | null | 0 |
If someone is creative then susan is both happy and not creative and vice versa.
If susan is both generous and not brave then someone is both happy and not creative.
Everyone who is not brave or not funny is not curious or not patient.
Everyone who is not brave or kind is not brave or brave and vice versa.
Everyone who is funny or not kind is either not strong or curious.
If someone is not rich then lucy is quiet and vice versa.
Everyone who is not happy is both strong and tall.
If mary is both not happy and not kind then fred is both not brave and calm.
Everyone who is both not curious and not tall is tall and vice versa.
Everyone who is not strong is happy.
Everyone who is both not kind and not happy is both not tall and not old and vice versa.
If someone is not kind then lucy is both old and not rich and vice versa.
If someone is not wise or rich then fred is not humble and vice versa.
If someone is either not brave or not funny then fred is both happy and not humble and vice versa.
Everyone who is not rich is rich or not brave and vice versa.
Everyone who is both old and not happy is brave.
Someone is funny or not humble.
Alice is both not humble and generous.
Someone is not patient.
Someone is not humble.
Someone is happy.
Lucy is not strong or funny.
Someone is generous. | Lucy is not curious. | contradiction | ((?[X]:(creative(X)))<=>((happy(susan)&~creative(susan))))&
(((generous(susan)&~brave(susan)))=>(?[X]:((happy(X)&~creative(X)))))&
(![X]:((~brave(X)|~funny(X))=>(~curious(X)|~patient(X))))&
(![X]:((~brave(X)|kind(X))<=>(~brave(X)|brave(X))))&
(![X]:((funny(X)|~kind(X))=>(~strong(X)<~>curious(X))))&
((?[X]:(~rich(X)))<=>(quiet(lucy)))&
(![X]:(~happy(X)=>(strong(X)&tall(X))))&
(((~happy(mary)&~kind(mary)))=>((~brave(fred)&calm(fred))))&
(![X]:((~curious(X)&~tall(X))<=>tall(X)))&
(![X]:(~strong(X)=>happy(X)))&
(![X]:((~kind(X)&~happy(X))<=>(~tall(X)&~old(X))))&
((?[X]:(~kind(X)))<=>((old(lucy)&~rich(lucy))))&
((?[X]:((~wise(X)|rich(X))))<=>(~humble(fred)))&
((?[X]:((~brave(X)<~>~funny(X))))<=>((happy(fred)&~humble(fred))))&
(![X]:(~rich(X)<=>(rich(X)|~brave(X))))&
(![X]:((old(X)&~happy(X))=>brave(X)))&
(?[X]:((funny(X)|~humble(X))))&
((~humble(alice)&generous(alice)))&
(?[X]:(~patient(X)))&
(?[X]:(~humble(X)))&
(?[X]:(happy(X)))&
((~strong(lucy)|funny(lucy)))&
(?[X]:(generous(X))) | ~curious(lucy) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6720684677195029653262838
% SZS output start Proof for 6720684677195029653262838
9. ! [X0] : ((~tall(X0) & ~curious(X0)) <=> tall(X0)) [input p8]
24. ~curious(lucy) [input hypothesis]
51. ! [X0] : (((~tall(X0) & ~curious(X0)) | ~tall(X0)) & (tall(X0) | (tall(X0) | curious(X0)))) [nnf transformation 9]
52. ! [X0] : (((~tall(X0) & ~curious(X0)) | ~tall(X0)) & (tall(X0) | tall(X0) | curious(X0))) [flattening 51]
97. tall(X0) | tall(X0) | curious(X0) [cnf transformation 52]
99. ~tall(X0) | ~tall(X0) [cnf transformation 52]
128. ~curious(lucy) [cnf transformation 24]
131. tall(X0) | curious(X0) [duplicate literal removal 97]
132. ~tall(X0) [duplicate literal removal 99]
197. curious(X0) [subsumption resolution 131,132]
282. $false [subsumption resolution 128,197]
% SZS output end Proof for 6720684677195029653262838
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is brave then someone is kind or not strong and vice versa.
Everyone who is both not happy and funny is either brave or kind and vice versa.
Everyone who is not creative or not brave is either not old or not strong.
Everyone who is both not funny and not patient is wise or rich and vice versa.
Everyone who is not humble is both not tall and generous.
If john is either not tall or not creative then someone is not curious or not old.
Everyone who is both not calm and rich is not funny and vice versa.
Everyone who is either not curious or calm is either patient or not old.
Everyone who is both creative and tall is either not patient or strong.
If someone is not kind or rich then someone is happy.
Everyone who is not funny is both not happy and patient.
Everyone who is both generous and not curious is both not kind and not quiet.
If mary is not kind or not happy then alice is not happy and vice versa.
If someone is both happy and calm then lucy is both calm and not kind.
If someone is either strong or patient then someone is calm or rich.
Someone is either not humble or rich.
Someone is either not humble or not kind.
Someone is strong.
Someone is not generous or not quiet.
Someone is calm or not kind.
Fred is either curious or calm. | Lucy is not funny. | contradiction | ((brave(alice))<=>(?[X]:((kind(X)|~strong(X)))))&
(![X]:((~happy(X)&funny(X))<=>(brave(X)<~>kind(X))))&
(![X]:((~creative(X)|~brave(X))=>(~old(X)<~>~strong(X))))&
(![X]:((~funny(X)&~patient(X))<=>(wise(X)|rich(X))))&
(![X]:(~humble(X)=>(~tall(X)&generous(X))))&
(((~tall(john)<~>~creative(john)))=>(?[X]:((~curious(X)|~old(X)))))&
(![X]:((~calm(X)&rich(X))<=>~funny(X)))&
(![X]:((~curious(X)<~>calm(X))=>(patient(X)<~>~old(X))))&
(![X]:((creative(X)&tall(X))=>(~patient(X)<~>strong(X))))&
((?[X]:((~kind(X)|rich(X))))=>(?[X]:(happy(X))))&
(![X]:(~funny(X)=>(~happy(X)&patient(X))))&
(![X]:((generous(X)&~curious(X))=>(~kind(X)&~quiet(X))))&
(((~kind(mary)|~happy(mary)))<=>(~happy(alice)))&
((?[X]:((happy(X)&calm(X))))=>((calm(lucy)&~kind(lucy))))&
((?[X]:((strong(X)<~>patient(X))))=>(?[X]:((calm(X)|rich(X)))))&
(?[X]:((~humble(X)<~>rich(X))))&
(?[X]:((~humble(X)<~>~kind(X))))&
(?[X]:(strong(X)))&
(?[X]:((~generous(X)|~quiet(X))))&
(?[X]:((calm(X)|~kind(X))))&
((curious(fred)<~>calm(fred))) | ~funny(lucy) | [
"p3",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4913342300140836126198556
% SZS output start Proof for 4913342300140836126198556
4. ! [X0] : ((~patient(X0) & ~funny(X0)) <=> (rich(X0) | wise(X0))) [input p3]
7. ! [X0] : ((rich(X0) & ~calm(X0)) <=> ~funny(X0)) [input p6]
11. ! [X0] : (~funny(X0) => (patient(X0) & ~happy(X0))) [input p10]
22. ~funny(lucy) [input hypothesis]
34. ! [X0] : ((patient(X0) & ~happy(X0)) | funny(X0)) [ennf transformation 11]
46. ! [X0] : (((~patient(X0) & ~funny(X0)) | (~rich(X0) & ~wise(X0))) & ((rich(X0) | wise(X0)) | (patient(X0) | funny(X0)))) [nnf transformation 4]
47. ! [X0] : (((~patient(X0) & ~funny(X0)) | (~rich(X0) & ~wise(X0))) & (rich(X0) | wise(X0) | patient(X0) | funny(X0))) [flattening 46]
51. ! [X0] : (((rich(X0) & ~calm(X0)) | funny(X0)) & (~funny(X0) | (~rich(X0) | calm(X0)))) [nnf transformation 7]
52. ! [X0] : (((rich(X0) & ~calm(X0)) | funny(X0)) & (~funny(X0) | ~rich(X0) | calm(X0))) [flattening 51]
92. ~rich(X0) | ~patient(X0) [cnf transformation 47]
99. rich(X0) | funny(X0) [cnf transformation 52]
109. patient(X0) | funny(X0) [cnf transformation 34]
126. ~funny(lucy) [cnf transformation 22]
263. funny(X0) | ~patient(X0) [resolution 99,92]
265. funny(X0) [subsumption resolution 263,109]
267. $false [resolution 265,126]
% SZS output end Proof for 4913342300140836126198556
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or not kind is either wise or not creative and vice versa. Everyone who is both not quiet and not calm is either strong or rich and vice versa. Everyone who is both funny and creative is both not kind and generous. If someone is either funny or strong then someone is not curious. Everyone who is not old is not quiet or creative. If someone is calm then someone is not curious. If someone is both tall and not patient then someone is funny or not humble. Everyone who is not funny is tall or not strong and vice versa. Everyone who is not funny is both not calm and not humble and vice versa. Everyone who is both happy and patient is calm. If mary is both curious and tall then someone is either happy or not generous and vice versa. Everyone who is both not wise and curious is both not wise and humble and vice versa. If alice is happy then someone is curious or not generous and vice versa. Everyone who is not creative or rich is both funny and not funny. If john is both not generous and humble then lucy is patient or not tall and vice versa. If someone is humble then john is not curious. Someone is both not rich and funny. John is not humble or funny. Someone is either not tall or brave. Someone is both curious and tall. Mary is either creative or tall. | John is not kind. | neutral | (![X]:((~generous(X)<~>~kind(X))<=>(wise(X)<~>~creative(X))))&
(![X]:((~quiet(X)&~calm(X))<=>(strong(X)<~>rich(X))))&
(![X]:((funny(X)&creative(X))=>(~kind(X)&generous(X))))&
((?[X]:((funny(X)<~>strong(X))))=>(?[X]:(~curious(X))))&
(![X]:(~old(X)=>(~quiet(X)|creative(X))))&
((?[X]:(calm(X)))=>(?[X]:(~curious(X))))&
((?[X]:((tall(X)&~patient(X))))=>(?[X]:((funny(X)|~humble(X)))))&
(![X]:(~funny(X)<=>(tall(X)|~strong(X))))&
(![X]:(~funny(X)<=>(~calm(X)&~humble(X))))&
(![X]:((happy(X)&patient(X))=>calm(X)))&
(((curious(mary)&tall(mary)))<=>(?[X]:((happy(X)<~>~generous(X)))))&
(![X]:((~wise(X)&curious(X))<=>(~wise(X)&humble(X))))&
((happy(alice))<=>(?[X]:((curious(X)|~generous(X)))))&
(![X]:((~creative(X)|rich(X))=>(funny(X)&~funny(X))))&
(((~generous(john)&humble(john)))<=>((patient(lucy)|~tall(lucy))))&
((?[X]:(humble(X)))=>(~curious(john)))&
(?[X]:((~rich(X)&funny(X))))&
((~humble(john)|funny(john)))&
(?[X]:((~tall(X)<~>brave(X))))&
(?[X]:((curious(X)&tall(X))))&
((creative(mary)<~>tall(mary))) | ~kind(john) | [] | null | 0 |
Everyone who is either happy or not curious is not tall or curious and vice versa.
Everyone who is not wise is either not kind or humble and vice versa.
If lucy is curious or not kind then lucy is both not funny and generous and vice versa.
Everyone who is both not quiet and generous is both not tall and not happy.
Everyone who is both humble and not generous is not funny or rich and vice versa.
If susan is both quiet and strong then fred is both tall and not funny and vice versa.
If someone is both not rich and patient then someone is both patient and curious.
If mary is not curious then someone is either quiet or not funny.
Everyone who is either humble or not funny is either strong or kind.
If someone is happy then someone is both not funny and not strong and vice versa.
If someone is either not happy or wise then someone is either not brave or strong.
Everyone who is not kind is both not creative and not generous and vice versa.
Everyone who is kind is not brave and vice versa.
If susan is happy or not tall then someone is not kind or not humble and vice versa.
Everyone who is both not generous and not creative is calm or patient and vice versa.
If susan is strong then alice is not calm or not quiet and vice versa.
Susan is happy.
John is funny.
Someone is not old.
Fred is both curious and wise.
Someone is not creative.
Lucy is either not wise or not brave.
Mary is happy or not quiet. | Lucy is calm. | contradiction | (![X]:((happy(X)<~>~curious(X))<=>(~tall(X)|curious(X))))&
(![X]:(~wise(X)<=>(~kind(X)<~>humble(X))))&
(((curious(lucy)|~kind(lucy)))<=>((~funny(lucy)&generous(lucy))))&
(![X]:((~quiet(X)&generous(X))=>(~tall(X)&~happy(X))))&
(![X]:((humble(X)&~generous(X))<=>(~funny(X)|rich(X))))&
(((quiet(susan)&strong(susan)))<=>((tall(fred)&~funny(fred))))&
((?[X]:((~rich(X)&patient(X))))=>(?[X]:((patient(X)&curious(X)))))&
((~curious(mary))=>(?[X]:((quiet(X)<~>~funny(X)))))&
(![X]:((humble(X)<~>~funny(X))=>(strong(X)<~>kind(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~funny(X)&~strong(X)))))&
((?[X]:((~happy(X)<~>wise(X))))=>(?[X]:((~brave(X)<~>strong(X)))))&
(![X]:(~kind(X)<=>(~creative(X)&~generous(X))))&
(![X]:(kind(X)<=>~brave(X)))&
(((happy(susan)|~tall(susan)))<=>(?[X]:((~kind(X)|~humble(X)))))&
(![X]:((~generous(X)&~creative(X))<=>(calm(X)|patient(X))))&
((strong(susan))<=>((~calm(alice)|~quiet(alice))))&
(happy(susan))&
(funny(john))&
(?[X]:(~old(X)))&
((curious(fred)&wise(fred)))&
(?[X]:(~creative(X)))&
((~wise(lucy)<~>~brave(lucy)))&
((happy(mary)|~quiet(mary))) | calm(lucy) | [
"p2",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6034592329808714123478982
% SZS output start Proof for 6034592329808714123478982
3. (~kind(lucy) | curious(lucy)) <=> (generous(lucy) & ~funny(lucy)) [input p2]
12. ! [X0] : (~kind(X0) <=> (~generous(X0) & ~creative(X0))) [input p11]
15. ! [X0] : ((~creative(X0) & ~generous(X0)) <=> (patient(X0) | calm(X0))) [input p14]
24. calm(lucy) [input hypothesis]
38. ((~kind(lucy) | curious(lucy)) | (~generous(lucy) | funny(lucy))) & ((generous(lucy) & ~funny(lucy)) | (kind(lucy) & ~curious(lucy))) [nnf transformation 3]
39. (~kind(lucy) | curious(lucy) | ~generous(lucy) | funny(lucy)) & ((generous(lucy) & ~funny(lucy)) | (kind(lucy) & ~curious(lucy))) [flattening 38]
60. ! [X0] : ((~kind(X0) | (generous(X0) | creative(X0))) & ((~generous(X0) & ~creative(X0)) | kind(X0))) [nnf transformation 12]
61. ! [X0] : ((~kind(X0) | generous(X0) | creative(X0)) & ((~generous(X0) & ~creative(X0)) | kind(X0))) [flattening 60]
68. ! [X0] : (((~creative(X0) & ~generous(X0)) | (~patient(X0) & ~calm(X0))) & ((patient(X0) | calm(X0)) | (creative(X0) | generous(X0)))) [nnf transformation 15]
69. ! [X0] : (((~creative(X0) & ~generous(X0)) | (~patient(X0) & ~calm(X0))) & (patient(X0) | calm(X0) | creative(X0) | generous(X0))) [flattening 68]
88. generous(lucy) | kind(lucy) [cnf transformation 39]
118. ~kind(X0) | generous(X0) | creative(X0) [cnf transformation 61]
126. ~calm(X0) | ~generous(X0) [cnf transformation 69]
128. ~calm(X0) | ~creative(X0) [cnf transformation 69]
141. calm(lucy) [cnf transformation 24]
150. 2 <=> generous(lucy) [avatar definition]
158. 4 <=> kind(lucy) [avatar definition]
159. kind(lucy) <- (4) [avatar component clause 158]
162. 4 | 2 [avatar split clause 88,150,158]
310. ~generous(lucy) [resolution 126,141]
311. ~creative(lucy) [resolution 128,141]
407. generous(lucy) | creative(lucy) <- (4) [resolution 118,159]
421. generous(lucy) <- (4) [subsumption resolution 407,311]
422. 2 | ~4 [avatar split clause 421,158,150]
423. ~2 [avatar split clause 310,150]
424. $false [avatar sat refutation 162,422,423]
% SZS output end Proof for 6034592329808714123478982
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is either not patient or brave and vice versa.
Everyone who is either old or not rich is creative or not wise.
If someone is either not kind or curious then susan is wise and vice versa.
If someone is kind then fred is either not old or rich.
Everyone who is generous or not patient is both funny and happy.
Everyone who is either not funny or not generous is either calm or generous and vice versa.
If someone is both not happy and happy then someone is not wise and vice versa.
Everyone who is either calm or creative is either not tall or strong.
If susan is both tall and old then someone is both generous and wise and vice versa.
Everyone who is either not brave or generous is either not creative or not calm and vice versa.
Everyone who is creative is both generous and strong and vice versa.
Everyone who is not brave or not quiet is generous and vice versa.
If mary is either calm or not kind then someone is not quiet.
Everyone who is either brave or calm is wise or not curious.
Everyone who is both not creative and not strong is tall.
Everyone who is either brave or not calm is not wise.
Paul is either kind or not quiet.
Mary is both not generous and humble.
Someone is curious or not creative.
Alice is both patient and not humble.
Mary is creative or not tall. | Alice is wise. | entailment | (![X]:(~tall(X)<=>(~patient(X)<~>brave(X))))&
(![X]:((old(X)<~>~rich(X))=>(creative(X)|~wise(X))))&
((?[X]:((~kind(X)<~>curious(X))))<=>(wise(susan)))&
((?[X]:(kind(X)))=>((~old(fred)<~>rich(fred))))&
(![X]:((generous(X)|~patient(X))=>(funny(X)&happy(X))))&
(![X]:((~funny(X)<~>~generous(X))<=>(calm(X)<~>generous(X))))&
((?[X]:((~happy(X)&happy(X))))<=>(?[X]:(~wise(X))))&
(![X]:((calm(X)<~>creative(X))=>(~tall(X)<~>strong(X))))&
(((tall(susan)&old(susan)))<=>(?[X]:((generous(X)&wise(X)))))&
(![X]:((~brave(X)<~>generous(X))<=>(~creative(X)<~>~calm(X))))&
(![X]:(creative(X)<=>(generous(X)&strong(X))))&
(![X]:((~brave(X)|~quiet(X))<=>generous(X)))&
(((calm(mary)<~>~kind(mary)))=>(?[X]:(~quiet(X))))&
(![X]:((brave(X)<~>calm(X))=>(wise(X)|~curious(X))))&
(![X]:((~creative(X)&~strong(X))=>tall(X)))&
(![X]:((brave(X)<~>~calm(X))=>~wise(X)))&
((kind(paul)<~>~quiet(paul)))&
((~generous(mary)&humble(mary)))&
(?[X]:((curious(X)|~creative(X))))&
((patient(alice)&~humble(alice)))&
((creative(mary)|~tall(mary))) | wise(alice) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8888505013266780062239693
% SZS output start Proof for 8888505013266780062239693
7. ? [X0] : (happy(X0) & ~happy(X0)) <=> ? [X0] : ~wise(X0) [input p6]
22. ~wise(alice) [input hypothesis]
23. ? [X0] : (happy(X0) & ~happy(X0)) <=> ? [X1] : ~wise(X1) [rectify 7]
43. (? [X0] : (happy(X0) & ~happy(X0)) | ! [X1] : wise(X1)) & (? [X1] : ~wise(X1) | ! [X0] : (~happy(X0) | happy(X0))) [nnf transformation 23]
44. (? [X0] : (happy(X0) & ~happy(X0)) | ! [X1] : wise(X1)) & (? [X2] : ~wise(X2) | ! [X3] : (~happy(X3) | happy(X3))) [rectify 43]
45. ? [X0] : (happy(X0) & ~happy(X0)) => (happy(sK1) & ~happy(sK1)) [choice axiom]
46. ? [X2] : ~wise(X2) => ~wise(sK2) [choice axiom]
47. ((happy(sK1) & ~happy(sK1)) | ! [X1] : wise(X1)) & (~wise(sK2) | ! [X3] : (~happy(X3) | happy(X3))) [skolemisation 44,46,45]
92. ~happy(sK1) | wise(X1) [cnf transformation 47]
93. happy(sK1) | wise(X1) [cnf transformation 47]
131. ~wise(alice) [cnf transformation 22]
175. 9 <=> ! [X1] : wise(X1) [avatar definition]
176. wise(X1) <- (9) [avatar component clause 175]
178. 10 <=> happy(sK1) [avatar definition]
181. 9 | 10 [avatar split clause 93,178,175]
182. 9 | ~10 [avatar split clause 92,178,175]
255. $false <- (9) [resolution 176,131]
256. ~9 [avatar contradiction clause 255]
257. $false [avatar sat refutation 181,182,256]
% SZS output end Proof for 8888505013266780062239693
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or patient is funny or tall and vice versa. If someone is calm then john is both rich and not happy and vice versa. Everyone who is either patient or old is not creative or not tall and vice versa. Everyone who is not funny is kind or patient. If lucy is strong then susan is either wise or rich. Everyone who is either curious or not creative is not old or quiet and vice versa. If lucy is either strong or not happy then someone is either funny or not calm. Everyone who is both generous and old is either not quiet or not patient and vice versa. If paul is brave then someone is kind or not wise. Everyone who is either not funny or humble is both not kind and not wise and vice versa. If someone is not creative or not brave then someone is creative or brave and vice versa. Everyone who is both not humble and patient is both not creative and not calm. Everyone who is rich is both quiet and not old and vice versa. Everyone who is both tall and old is patient. If someone is tall then mary is both not brave and not rich. If someone is either not patient or strong then someone is not humble and vice versa. Someone is not brave or old. Someone is not calm or tall. Someone is both not curious and generous. Someone is either not funny or creative. Someone is both not happy and patient. Someone is both quiet and not creative. Alice is patient. Someone is old. | Alice is patient. | entailment | (![X]:((~happy(X)<~>patient(X))<=>(funny(X)|tall(X))))&
((?[X]:(calm(X)))<=>((rich(john)&~happy(john))))&
(![X]:((patient(X)<~>old(X))<=>(~creative(X)|~tall(X))))&
(![X]:(~funny(X)=>(kind(X)|patient(X))))&
((strong(lucy))=>((wise(susan)<~>rich(susan))))&
(![X]:((curious(X)<~>~creative(X))<=>(~old(X)|quiet(X))))&
(((strong(lucy)<~>~happy(lucy)))=>(?[X]:((funny(X)<~>~calm(X)))))&
(![X]:((generous(X)&old(X))<=>(~quiet(X)<~>~patient(X))))&
((brave(paul))=>(?[X]:((kind(X)|~wise(X)))))&
(![X]:((~funny(X)<~>humble(X))<=>(~kind(X)&~wise(X))))&
((?[X]:((~creative(X)|~brave(X))))<=>(?[X]:((creative(X)|brave(X)))))&
(![X]:((~humble(X)&patient(X))=>(~creative(X)&~calm(X))))&
(![X]:(rich(X)<=>(quiet(X)&~old(X))))&
(![X]:((tall(X)&old(X))=>patient(X)))&
((?[X]:(tall(X)))=>((~brave(mary)&~rich(mary))))&
((?[X]:((~patient(X)<~>strong(X))))<=>(?[X]:(~humble(X))))&
(?[X]:((~brave(X)|old(X))))&
(?[X]:((~calm(X)|tall(X))))&
(?[X]:((~curious(X)&generous(X))))&
(?[X]:((~funny(X)<~>creative(X))))&
(?[X]:((~happy(X)&patient(X))))&
(?[X]:((quiet(X)&~creative(X))))&
(patient(alice))&
(?[X]:(old(X))) | patient(alice) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2739573509854940175464711
% SZS output start Proof for 2739573509854940175464711
23. patient(alice) [input p22]
25. ~patient(alice) [input hypothesis]
153. patient(alice) [cnf transformation 23]
155. ~patient(alice) [cnf transformation 25]
315. $false [subsumption resolution 155,153]
% SZS output end Proof for 2739573509854940175464711
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both generous and not quiet then someone is not patient.
If someone is kind or patient then someone is not generous or not curious.
Everyone who is not curious is strong or not patient and vice versa.
If john is both brave and not rich then alice is both happy and curious.
Everyone who is not rich is both creative and kind and vice versa.
Everyone who is either not creative or creative is both brave and funny and vice versa.
Everyone who is not brave or not strong is wise or not creative.
Everyone who is either not quiet or not brave is wise and vice versa.
Everyone who is not kind is either calm or not calm and vice versa.
Everyone who is curious or strong is not funny or not kind and vice versa.
Everyone who is both not generous and strong is both curious and wise and vice versa.
If someone is both not creative and strong then fred is both old and not happy and vice versa.
Everyone who is both not tall and happy is not kind and vice versa.
Everyone who is not funny or strong is either not tall or brave.
Everyone who is not quiet or not tall is not happy or rich and vice versa.
If mary is not brave then paul is not humble.
Lucy is either not brave or calm.
Susan is either patient or not generous.
Susan is both not tall and rich.
Someone is kind or humble. | John is wise. | contradiction | ((?[X]:((generous(X)&~quiet(X))))=>(?[X]:(~patient(X))))&
((?[X]:((kind(X)|patient(X))))=>(?[X]:((~generous(X)|~curious(X)))))&
(![X]:(~curious(X)<=>(strong(X)|~patient(X))))&
(((brave(john)&~rich(john)))=>((happy(alice)&curious(alice))))&
(![X]:(~rich(X)<=>(creative(X)&kind(X))))&
(![X]:((~creative(X)<~>creative(X))<=>(brave(X)&funny(X))))&
(![X]:((~brave(X)|~strong(X))=>(wise(X)|~creative(X))))&
(![X]:((~quiet(X)<~>~brave(X))<=>wise(X)))&
(![X]:(~kind(X)<=>(calm(X)<~>~calm(X))))&
(![X]:((curious(X)|strong(X))<=>(~funny(X)|~kind(X))))&
(![X]:((~generous(X)&strong(X))<=>(curious(X)&wise(X))))&
((?[X]:((~creative(X)&strong(X))))<=>((old(fred)&~happy(fred))))&
(![X]:((~tall(X)&happy(X))<=>~kind(X)))&
(![X]:((~funny(X)|strong(X))=>(~tall(X)<~>brave(X))))&
(![X]:((~quiet(X)|~tall(X))<=>(~happy(X)|rich(X))))&
((~brave(mary))=>(~humble(paul)))&
((~brave(lucy)<~>calm(lucy)))&
((patient(susan)<~>~generous(susan)))&
((~tall(susan)&rich(susan)))&
(?[X]:((kind(X)|humble(X)))) | wise(john) | [
"p2",
"p5",
"p8",
"p9",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4393782383106817556551592
% SZS output start Proof for 4393782383106817556551592
3. ! [X0] : (~curious(X0) <=> (~patient(X0) | strong(X0))) [input p2]
6. ! [X0] : ((~creative(X0) <~> creative(X0)) <=> (funny(X0) & brave(X0))) [input p5]
9. ! [X0] : (~kind(X0) <=> (calm(X0) <~> ~calm(X0))) [input p8]
10. ! [X0] : ((strong(X0) | curious(X0)) <=> (~kind(X0) | ~funny(X0))) [input p9]
11. ! [X0] : ((strong(X0) & ~generous(X0)) <=> (wise(X0) & curious(X0))) [input p10]
13. ! [X0] : ((happy(X0) & ~tall(X0)) <=> ~kind(X0)) [input p12]
14. ! [X0] : ((strong(X0) | ~funny(X0)) => (~tall(X0) <~> brave(X0))) [input p13]
21. wise(john) [input hypothesis]
30. ! [X0] : ((~tall(X0) <~> brave(X0)) | (~strong(X0) & funny(X0))) [ennf transformation 14]
38. ! [X0] : ((~curious(X0) | (patient(X0) & ~strong(X0))) & ((~patient(X0) | strong(X0)) | curious(X0))) [nnf transformation 3]
39. ! [X0] : ((~curious(X0) | (patient(X0) & ~strong(X0))) & (~patient(X0) | strong(X0) | curious(X0))) [flattening 38]
42. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (~funny(X0) | ~brave(X0))) & ((funny(X0) & brave(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [nnf transformation 6]
43. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | ~funny(X0) | ~brave(X0)) & ((funny(X0) & brave(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [flattening 42]
45. ! [X0] : ((~kind(X0) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0)))) & (((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | kind(X0))) [nnf transformation 9]
46. ! [X0] : (((strong(X0) | curious(X0)) | (kind(X0) & funny(X0))) & ((~kind(X0) | ~funny(X0)) | (~strong(X0) & ~curious(X0)))) [nnf transformation 10]
47. ! [X0] : ((strong(X0) | curious(X0) | (kind(X0) & funny(X0))) & (~kind(X0) | ~funny(X0) | (~strong(X0) & ~curious(X0)))) [flattening 46]
48. ! [X0] : (((strong(X0) & ~generous(X0)) | (~wise(X0) | ~curious(X0))) & ((wise(X0) & curious(X0)) | (~strong(X0) | generous(X0)))) [nnf transformation 11]
49. ! [X0] : (((strong(X0) & ~generous(X0)) | ~wise(X0) | ~curious(X0)) & ((wise(X0) & curious(X0)) | ~strong(X0) | generous(X0))) [flattening 48]
55. ! [X0] : (((happy(X0) & ~tall(X0)) | kind(X0)) & (~kind(X0) | (~happy(X0) | tall(X0)))) [nnf transformation 13]
56. ! [X0] : (((happy(X0) & ~tall(X0)) | kind(X0)) & (~kind(X0) | ~happy(X0) | tall(X0))) [flattening 55]
57. ! [X0] : (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | (~strong(X0) & funny(X0))) [nnf transformation 30]
68. ~strong(X0) | ~curious(X0) [cnf transformation 39]
75. brave(X0) | creative(X0) | creative(X0) [cnf transformation 43]
76. brave(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 43]
89. ~kind(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 45]
90. ~kind(X0) | calm(X0) | calm(X0) [cnf transformation 45]
94. strong(X0) | curious(X0) | kind(X0) [cnf transformation 47]
98. strong(X0) | ~wise(X0) | ~curious(X0) [cnf transformation 49]
104. ~tall(X0) | kind(X0) [cnf transformation 56]
109. ~brave(X0) | tall(X0) | ~strong(X0) [cnf transformation 57]
122. wise(john) [cnf transformation 21]
123. ~kind(X0) | ~calm(X0) [duplicate literal removal 89]
124. ~kind(X0) | calm(X0) [duplicate literal removal 90]
125. brave(X0) | creative(X0) [duplicate literal removal 75]
126. ~creative(X0) | brave(X0) [duplicate literal removal 76]
150. 6 <=> ! [X1] : ~kind(X1) [avatar definition]
151. ~kind(X1) <- (6) [avatar component clause 150]
172. brave(X0) [subsumption resolution 125,126]
175. ~kind(X0) [subsumption resolution 123,124]
176. 6 [avatar split clause 175,150]
179. ~wise(X0) | ~curious(X0) [subsumption resolution 98,68]
204. ~strong(X0) | tall(X0) [subsumption resolution 109,172]
239. ~curious(john) [resolution 179,122]
247. curious(X0) | kind(X0) | tall(X0) [resolution 94,204]
253. tall(X0) | curious(X0) <- (6) [subsumption resolution 247,151]
285. curious(X2) | kind(X2) <- (6) [resolution 253,104]
286. curious(X2) <- (6) [subsumption resolution 285,151]
306. $false <- (6) [resolution 286,239]
307. ~6 [avatar contradiction clause 306]
308. $false [avatar sat refutation 176,307]
% SZS output end Proof for 4393782383106817556551592
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or not patient is either brave or tall and vice versa.
Everyone who is not humble is not tall and vice versa.
Everyone who is not strong or not happy is calm or not brave.
Everyone who is either curious or humble is both kind and not humble.
Everyone who is both rich and wise is either quiet or strong and vice versa.
If alice is both not tall and old then someone is not patient or kind.
Everyone who is not calm is both humble and not strong and vice versa.
Everyone who is wise is old.
Everyone who is not brave is not quiet or creative.
Everyone who is not quiet is either calm or not happy.
If fred is both calm and tall then someone is both rich and creative and vice versa.
Everyone who is quiet or not quiet is not funny and vice versa.
Everyone who is both creative and humble is both not quiet and humble.
Everyone who is either not creative or not quiet is not rich or calm and vice versa.
Everyone who is not creative is both not strong and curious.
Everyone who is not quiet is not rich and vice versa.
Paul is both creative and wise.
Someone is curious or not rich.
Someone is not patient.
Someone is rich or not kind.
Susan is not kind.
Someone is not generous. | Alice is humble. | neutral | (![X]:((~funny(X)<~>~patient(X))<=>(brave(X)<~>tall(X))))&
(![X]:(~humble(X)<=>~tall(X)))&
(![X]:((~strong(X)|~happy(X))=>(calm(X)|~brave(X))))&
(![X]:((curious(X)<~>humble(X))=>(kind(X)&~humble(X))))&
(![X]:((rich(X)&wise(X))<=>(quiet(X)<~>strong(X))))&
(((~tall(alice)&old(alice)))=>(?[X]:((~patient(X)|kind(X)))))&
(![X]:(~calm(X)<=>(humble(X)&~strong(X))))&
(![X]:(wise(X)=>old(X)))&
(![X]:(~brave(X)=>(~quiet(X)|creative(X))))&
(![X]:(~quiet(X)=>(calm(X)<~>~happy(X))))&
(((calm(fred)&tall(fred)))<=>(?[X]:((rich(X)&creative(X)))))&
(![X]:((quiet(X)|~quiet(X))<=>~funny(X)))&
(![X]:((creative(X)&humble(X))=>(~quiet(X)&humble(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>(~rich(X)|calm(X))))&
(![X]:(~creative(X)=>(~strong(X)&curious(X))))&
(![X]:(~quiet(X)<=>~rich(X)))&
((creative(paul)&wise(paul)))&
(?[X]:((curious(X)|~rich(X))))&
(?[X]:(~patient(X)))&
(?[X]:((rich(X)|~kind(X))))&
(~kind(susan))&
(?[X]:(~generous(X))) | humble(alice) | [] | null | 0 |
If mary is both strong and rich then alice is creative and vice versa. If paul is generous then someone is not curious and vice versa. Everyone who is both old and not humble is patient or kind. Everyone who is both not calm and wise is either curious or not funny and vice versa. If alice is not old or not curious then someone is curious. Everyone who is quiet or brave is both not curious and curious and vice versa. If alice is either creative or happy then paul is tall and vice versa. If fred is not strong or wise then mary is rich and vice versa. Everyone who is both not kind and kind is not humble or calm and vice versa. Everyone who is not rich is funny and vice versa. Everyone who is not calm or funny is rich or patient and vice versa. Everyone who is either not brave or rich is not tall. Everyone who is patient or happy is both creative and brave and vice versa. Everyone who is either not brave or calm is not funny or not old and vice versa. If lucy is both strong and not generous then lucy is not generous. Everyone who is either not generous or wise is both curious and strong. Someone is either not wise or strong. Someone is patient or not brave. Someone is not wise or not humble. Someone is not humble or tall. | Alice is not kind. | neutral | (((strong(mary)&rich(mary)))<=>(creative(alice)))&
((generous(paul))<=>(?[X]:(~curious(X))))&
(![X]:((old(X)&~humble(X))=>(patient(X)|kind(X))))&
(![X]:((~calm(X)&wise(X))<=>(curious(X)<~>~funny(X))))&
(((~old(alice)|~curious(alice)))=>(?[X]:(curious(X))))&
(![X]:((quiet(X)|brave(X))<=>(~curious(X)&curious(X))))&
(((creative(alice)<~>happy(alice)))<=>(tall(paul)))&
(((~strong(fred)|wise(fred)))<=>(rich(mary)))&
(![X]:((~kind(X)&kind(X))<=>(~humble(X)|calm(X))))&
(![X]:(~rich(X)<=>funny(X)))&
(![X]:((~calm(X)|funny(X))<=>(rich(X)|patient(X))))&
(![X]:((~brave(X)<~>rich(X))=>~tall(X)))&
(![X]:((patient(X)|happy(X))<=>(creative(X)&brave(X))))&
(![X]:((~brave(X)<~>calm(X))<=>(~funny(X)|~old(X))))&
(((strong(lucy)&~generous(lucy)))=>(~generous(lucy)))&
(![X]:((~generous(X)<~>wise(X))=>(curious(X)&strong(X))))&
(?[X]:((~wise(X)<~>strong(X))))&
(?[X]:((patient(X)|~brave(X))))&
(?[X]:((~wise(X)|~humble(X))))&
(?[X]:((~humble(X)|tall(X)))) | ~kind(alice) | [] | null | 0 |
If mary is either not strong or generous then paul is not calm and vice versa. If susan is either happy or not wise then paul is either not humble or not rich. If fred is either kind or wise then lucy is either not brave or old and vice versa. Everyone who is either funny or not rich is both not wise and not calm. Everyone who is creative or old is both not creative and not brave. Everyone who is both patient and kind is either strong or wise. Everyone who is rich is both not rich and not brave. Everyone who is both kind and curious is tall or not wise. If mary is not generous then someone is either kind or not rich. If fred is both kind and not patient then someone is curious and vice versa. Everyone who is tall or not curious is not strong. Everyone who is both rich and creative is both wise and kind and vice versa. Everyone who is both not humble and not wise is both not curious and happy. Everyone who is either not wise or not generous is either not patient or not old and vice versa. Everyone who is either funny or not generous is both not creative and rich and vice versa. Everyone who is not rich is generous and vice versa. Someone is quiet. Someone is strong. Someone is not calm. Susan is either kind or not kind. Lucy is curious. Susan is old or generous. | Lucy is not happy. | neutral | (((~strong(mary)<~>generous(mary)))<=>(~calm(paul)))&
(((happy(susan)<~>~wise(susan)))=>((~humble(paul)<~>~rich(paul))))&
(((kind(fred)<~>wise(fred)))<=>((~brave(lucy)<~>old(lucy))))&
(![X]:((funny(X)<~>~rich(X))=>(~wise(X)&~calm(X))))&
(![X]:((creative(X)|old(X))=>(~creative(X)&~brave(X))))&
(![X]:((patient(X)&kind(X))=>(strong(X)<~>wise(X))))&
(![X]:(rich(X)=>(~rich(X)&~brave(X))))&
(![X]:((kind(X)&curious(X))=>(tall(X)|~wise(X))))&
((~generous(mary))=>(?[X]:((kind(X)<~>~rich(X)))))&
(((kind(fred)&~patient(fred)))<=>(?[X]:(curious(X))))&
(![X]:((tall(X)|~curious(X))=>~strong(X)))&
(![X]:((rich(X)&creative(X))<=>(wise(X)&kind(X))))&
(![X]:((~humble(X)&~wise(X))=>(~curious(X)&happy(X))))&
(![X]:((~wise(X)<~>~generous(X))<=>(~patient(X)<~>~old(X))))&
(![X]:((funny(X)<~>~generous(X))<=>(~creative(X)&rich(X))))&
(![X]:(~rich(X)<=>generous(X)))&
(?[X]:(quiet(X)))&
(?[X]:(strong(X)))&
(?[X]:(~calm(X)))&
((kind(susan)<~>~kind(susan)))&
(curious(lucy))&
((old(susan)|generous(susan))) | ~happy(lucy) | [] | null | 0 |
Everyone who is either not creative or not strong is either not calm or not rich. If someone is kind then john is not quiet or curious and vice versa. If someone is both generous and not rich then someone is either old or brave and vice versa. Everyone who is not humble is both funny and not patient. If susan is not tall then someone is either not quiet or strong. If someone is not generous or not patient then someone is kind. Everyone who is either curious or not strong is both not creative and kind. Everyone who is both tall and not funny is happy and vice versa. Everyone who is either generous or curious is both tall and not funny. If someone is both not curious and kind then fred is both creative and humble and vice versa. Everyone who is either kind or strong is not strong or not humble and vice versa. Everyone who is calm or wise is both funny and not tall. If someone is not tall or happy then someone is calm or not old and vice versa. Everyone who is kind is not funny or not humble and vice versa. Everyone who is both patient and funny is not humble. If john is both strong and brave then mary is either funny or kind and vice versa. Someone is either generous or happy. John is either wise or not patient. Susan is either rich or patient. Mary is not wise or not happy. John is not happy or humble. Mary is not tall. Mary is either tall or not quiet. Paul is both not curious and not happy. | Mary is happy. | contradiction | (![X]:((~creative(X)<~>~strong(X))=>(~calm(X)<~>~rich(X))))&
((?[X]:(kind(X)))<=>((~quiet(john)|curious(john))))&
((?[X]:((generous(X)&~rich(X))))<=>(?[X]:((old(X)<~>brave(X)))))&
(![X]:(~humble(X)=>(funny(X)&~patient(X))))&
((~tall(susan))=>(?[X]:((~quiet(X)<~>strong(X)))))&
((?[X]:((~generous(X)|~patient(X))))=>(?[X]:(kind(X))))&
(![X]:((curious(X)<~>~strong(X))=>(~creative(X)&kind(X))))&
(![X]:((tall(X)&~funny(X))<=>happy(X)))&
(![X]:((generous(X)<~>curious(X))=>(tall(X)&~funny(X))))&
((?[X]:((~curious(X)&kind(X))))<=>((creative(fred)&humble(fred))))&
(![X]:((kind(X)<~>strong(X))<=>(~strong(X)|~humble(X))))&
(![X]:((calm(X)|wise(X))=>(funny(X)&~tall(X))))&
((?[X]:((~tall(X)|happy(X))))<=>(?[X]:((calm(X)|~old(X)))))&
(![X]:(kind(X)<=>(~funny(X)|~humble(X))))&
(![X]:((patient(X)&funny(X))=>~humble(X)))&
(((strong(john)&brave(john)))<=>((funny(mary)<~>kind(mary))))&
(?[X]:((generous(X)<~>happy(X))))&
((wise(john)<~>~patient(john)))&
((rich(susan)<~>patient(susan)))&
((~wise(mary)|~happy(mary)))&
((~happy(john)|humble(john)))&
(~tall(mary))&
((tall(mary)<~>~quiet(mary)))&
((~curious(paul)&~happy(paul))) | happy(mary) | [
"p7",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 123562915481660987991032
% SZS output start Proof for 123562915481660987991032
8. ! [X0] : ((~funny(X0) & tall(X0)) <=> happy(X0)) [input p7]
22. ~tall(mary) [input p21]
25. happy(mary) [input hypothesis]
56. ! [X0] : (((~funny(X0) & tall(X0)) | ~happy(X0)) & (happy(X0) | (funny(X0) | ~tall(X0)))) [nnf transformation 8]
57. ! [X0] : (((~funny(X0) & tall(X0)) | ~happy(X0)) & (happy(X0) | funny(X0) | ~tall(X0))) [flattening 56]
105. ~happy(X0) | tall(X0) [cnf transformation 57]
147. ~tall(mary) [cnf transformation 22]
152. happy(mary) [cnf transformation 25]
341. 41 <=> happy(mary) [avatar definition]
342. happy(mary) <- (41) [avatar component clause 341]
355. 41 [avatar split clause 152,341]
356. tall(mary) <- (41) [resolution 105,342]
357. $false <- (41) [subsumption resolution 356,147]
358. ~41 [avatar contradiction clause 357]
359. $false [avatar sat refutation 355,358]
% SZS output end Proof for 123562915481660987991032
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If john is strong or not wise then john is either funny or not humble and vice versa.
Everyone who is not strong is both not kind and not brave and vice versa.
If fred is either old or not brave then someone is quiet and vice versa.
Everyone who is kind or calm is both patient and happy and vice versa.
If alice is happy or brave then someone is not kind and vice versa.
Everyone who is both not humble and not tall is not wise or funny and vice versa.
If someone is both creative and not creative then someone is either creative or not wise.
If someone is curious then someone is old.
Everyone who is not calm is strong or not wise and vice versa.
Everyone who is not happy is either patient or not creative.
Everyone who is not generous or not brave is both not happy and not quiet.
Everyone who is not brave or quiet is either not old or not tall and vice versa.
Everyone who is not kind or not generous is either wise or humble.
If someone is both curious and patient then someone is strong and vice versa.
If someone is not generous or not funny then lucy is not happy or not quiet.
Everyone who is both strong and not quiet is either tall or brave.
John is either not brave or patient.
Someone is not generous or not kind.
Susan is not generous or humble.
Someone is both funny and not humble.
Someone is not old.
Someone is not humble.
Someone is humble or calm. | Lucy is not quiet. | neutral | (((strong(john)|~wise(john)))<=>((funny(john)<~>~humble(john))))&
(![X]:(~strong(X)<=>(~kind(X)&~brave(X))))&
(((old(fred)<~>~brave(fred)))<=>(?[X]:(quiet(X))))&
(![X]:((kind(X)|calm(X))<=>(patient(X)&happy(X))))&
(((happy(alice)|brave(alice)))<=>(?[X]:(~kind(X))))&
(![X]:((~humble(X)&~tall(X))<=>(~wise(X)|funny(X))))&
((?[X]:((creative(X)&~creative(X))))=>(?[X]:((creative(X)<~>~wise(X)))))&
((?[X]:(curious(X)))=>(?[X]:(old(X))))&
(![X]:(~calm(X)<=>(strong(X)|~wise(X))))&
(![X]:(~happy(X)=>(patient(X)<~>~creative(X))))&
(![X]:((~generous(X)|~brave(X))=>(~happy(X)&~quiet(X))))&
(![X]:((~brave(X)|quiet(X))<=>(~old(X)<~>~tall(X))))&
(![X]:((~kind(X)|~generous(X))=>(wise(X)<~>humble(X))))&
((?[X]:((curious(X)&patient(X))))<=>(?[X]:(strong(X))))&
((?[X]:((~generous(X)|~funny(X))))=>((~happy(lucy)|~quiet(lucy))))&
(![X]:((strong(X)&~quiet(X))=>(tall(X)<~>brave(X))))&
((~brave(john)<~>patient(john)))&
(?[X]:((~generous(X)|~kind(X))))&
((~generous(susan)|humble(susan)))&
(?[X]:((funny(X)&~humble(X))))&
(?[X]:(~old(X)))&
(?[X]:(~humble(X)))&
(?[X]:((humble(X)|calm(X)))) | ~quiet(lucy) | [] | null | 0 |
Everyone who is creative or not calm is either quiet or not happy.
Everyone who is both funny and not strong is generous or happy and vice versa.
Everyone who is both not curious and calm is both creative and not quiet.
Everyone who is not tall or funny is wise or not rich and vice versa.
If fred is not generous or not patient then someone is wise or calm.
Everyone who is not rich is generous and vice versa.
Everyone who is brave or happy is both curious and creative.
Everyone who is wise or not humble is not creative.
If someone is calm then someone is happy or kind and vice versa.
If john is not wise then paul is funny.
Everyone who is both not quiet and creative is humble.
Everyone who is either not happy or curious is not funny and vice versa.
Everyone who is not calm is both not old and not quiet and vice versa.
If paul is either humble or brave then someone is either not tall or patient.
If lucy is not kind then susan is both humble and strong.
If alice is brave or rich then someone is not old or generous.
Alice is either not generous or not funny.
Mary is not generous or humble.
Someone is either wise or quiet.
Paul is both not brave and not strong.
John is not creative.
Someone is generous or not generous.
Someone is tall. | Paul is old. | neutral | (![X]:((creative(X)|~calm(X))=>(quiet(X)<~>~happy(X))))&
(![X]:((funny(X)&~strong(X))<=>(generous(X)|happy(X))))&
(![X]:((~curious(X)&calm(X))=>(creative(X)&~quiet(X))))&
(![X]:((~tall(X)|funny(X))<=>(wise(X)|~rich(X))))&
(((~generous(fred)|~patient(fred)))=>(?[X]:((wise(X)|calm(X)))))&
(![X]:(~rich(X)<=>generous(X)))&
(![X]:((brave(X)|happy(X))=>(curious(X)&creative(X))))&
(![X]:((wise(X)|~humble(X))=>~creative(X)))&
((?[X]:(calm(X)))<=>(?[X]:((happy(X)|kind(X)))))&
((~wise(john))=>(funny(paul)))&
(![X]:((~quiet(X)&creative(X))=>humble(X)))&
(![X]:((~happy(X)<~>curious(X))<=>~funny(X)))&
(![X]:(~calm(X)<=>(~old(X)&~quiet(X))))&
(((humble(paul)<~>brave(paul)))=>(?[X]:((~tall(X)<~>patient(X)))))&
((~kind(lucy))=>((humble(susan)&strong(susan))))&
(((brave(alice)|rich(alice)))=>(?[X]:((~old(X)|generous(X)))))&
((~generous(alice)<~>~funny(alice)))&
((~generous(mary)|humble(mary)))&
(?[X]:((wise(X)<~>quiet(X))))&
((~brave(paul)&~strong(paul)))&
(~creative(john))&
(?[X]:((generous(X)|~generous(X))))&
(?[X]:(tall(X))) | old(paul) | [] | null | 0 |
Everyone who is both creative and not curious is not kind and vice versa.
Everyone who is both curious and brave is funny or patient and vice versa.
Everyone who is either not creative or not brave is both not funny and not brave and vice versa.
If paul is both creative and not happy then mary is not old or not calm.
Everyone who is either not quiet or not calm is both creative and not wise and vice versa.
If someone is happy or not humble then alice is calm.
Everyone who is either not brave or happy is either not rich or not happy.
If someone is either not humble or not creative then lucy is not wise or not tall and vice versa.
Everyone who is either not patient or wise is either rich or not rich and vice versa.
Everyone who is not brave is both quiet and funny.
Everyone who is both old and not creative is not happy or not strong and vice versa.
If mary is either not brave or calm then someone is not generous or not old.
Everyone who is either not curious or not tall is quiet or calm and vice versa.
If john is both not old and not funny then john is not calm.
If someone is not patient then john is both calm and curious.
If mary is either creative or rich then fred is patient and vice versa.
Alice is either tall or not humble.
Paul is either quiet or not rich.
Paul is both wise and tall.
Lucy is old or creative.
Susan is either calm or not calm.
Someone is wise or not quiet.
Someone is both not quiet and not humble. | Lucy is old. | neutral | (![X]:((creative(X)&~curious(X))<=>~kind(X)))&
(![X]:((curious(X)&brave(X))<=>(funny(X)|patient(X))))&
(![X]:((~creative(X)<~>~brave(X))<=>(~funny(X)&~brave(X))))&
(((creative(paul)&~happy(paul)))=>((~old(mary)|~calm(mary))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(creative(X)&~wise(X))))&
((?[X]:((happy(X)|~humble(X))))=>(calm(alice)))&
(![X]:((~brave(X)<~>happy(X))=>(~rich(X)<~>~happy(X))))&
((?[X]:((~humble(X)<~>~creative(X))))<=>((~wise(lucy)|~tall(lucy))))&
(![X]:((~patient(X)<~>wise(X))<=>(rich(X)<~>~rich(X))))&
(![X]:(~brave(X)=>(quiet(X)&funny(X))))&
(![X]:((old(X)&~creative(X))<=>(~happy(X)|~strong(X))))&
(((~brave(mary)<~>calm(mary)))=>(?[X]:((~generous(X)|~old(X)))))&
(![X]:((~curious(X)<~>~tall(X))<=>(quiet(X)|calm(X))))&
(((~old(john)&~funny(john)))=>(~calm(john)))&
((?[X]:(~patient(X)))=>((calm(john)&curious(john))))&
(((creative(mary)<~>rich(mary)))<=>(patient(fred)))&
((tall(alice)<~>~humble(alice)))&
((quiet(paul)<~>~rich(paul)))&
((wise(paul)&tall(paul)))&
((old(lucy)|creative(lucy)))&
((calm(susan)<~>~calm(susan)))&
(?[X]:((wise(X)|~quiet(X))))&
(?[X]:((~quiet(X)&~humble(X)))) | old(lucy) | [] | null | 0 |
Everyone who is both not generous and not rich is either not generous or not old.
Everyone who is happy is either tall or not quiet.
Everyone who is either not brave or not creative is either not humble or kind.
If someone is not curious then someone is both funny and creative.
Everyone who is not creative or not kind is not patient and vice versa.
Everyone who is not rich or rich is not strong.
If fred is happy or quiet then susan is both not quiet and not old.
Everyone who is not happy is not quiet or funny.
Everyone who is funny or humble is not calm or kind and vice versa.
Everyone who is both not generous and generous is both not calm and not strong and vice versa.
Everyone who is patient is either not kind or not patient.
If someone is kind or not funny then someone is not brave.
Everyone who is old is not kind or not humble and vice versa.
If mary is either not strong or not quiet then someone is not strong or funny.
Everyone who is either not rich or patient is funny or strong.
Everyone who is not strong or strong is not old and vice versa.
Someone is wise.
Lucy is either not old or rich.
Someone is humble or patient.
Someone is both humble and calm.
Fred is either not kind or funny. | Mary is not brave. | neutral | (![X]:((~generous(X)&~rich(X))=>(~generous(X)<~>~old(X))))&
(![X]:(happy(X)=>(tall(X)<~>~quiet(X))))&
(![X]:((~brave(X)<~>~creative(X))=>(~humble(X)<~>kind(X))))&
((?[X]:(~curious(X)))=>(?[X]:((funny(X)&creative(X)))))&
(![X]:((~creative(X)|~kind(X))<=>~patient(X)))&
(![X]:((~rich(X)|rich(X))=>~strong(X)))&
(((happy(fred)|quiet(fred)))=>((~quiet(susan)&~old(susan))))&
(![X]:(~happy(X)=>(~quiet(X)|funny(X))))&
(![X]:((funny(X)|humble(X))<=>(~calm(X)|kind(X))))&
(![X]:((~generous(X)&generous(X))<=>(~calm(X)&~strong(X))))&
(![X]:(patient(X)=>(~kind(X)<~>~patient(X))))&
((?[X]:((kind(X)|~funny(X))))=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>(~kind(X)|~humble(X))))&
(((~strong(mary)<~>~quiet(mary)))=>(?[X]:((~strong(X)|funny(X)))))&
(![X]:((~rich(X)<~>patient(X))=>(funny(X)|strong(X))))&
(![X]:((~strong(X)|strong(X))<=>~old(X)))&
(?[X]:(wise(X)))&
((~old(lucy)<~>rich(lucy)))&
(?[X]:((humble(X)|patient(X))))&
(?[X]:((humble(X)&calm(X))))&
((~kind(fred)<~>funny(fred))) | ~brave(mary) | [] | null | 0 |
Everyone who is either not humble or not calm is either not funny or happy and vice versa.
Everyone who is funny is either generous or tall and vice versa.
If someone is not generous or old then someone is not old.
If someone is happy or not kind then someone is either creative or old and vice versa.
If alice is curious then someone is not kind.
If lucy is both wise and not humble then someone is either not old or calm and vice versa.
Everyone who is either not tall or not old is not creative and vice versa.
If mary is tall then fred is either not creative or wise.
If susan is both happy and curious then someone is tall or not curious and vice versa.
Everyone who is both not humble and not tall is brave.
Everyone who is not funny is both brave and kind and vice versa.
Everyone who is not creative is not strong and vice versa.
Everyone who is kind is both strong and not curious and vice versa.
Everyone who is not creative is both not brave and wise and vice versa.
Everyone who is both tall and not tall is either brave or creative and vice versa.
If susan is either not patient or happy then someone is happy.
Someone is both calm and not strong.
John is rich or not wise.
Fred is brave.
Alice is both not creative and not old.
John is not funny.
Susan is either brave or not generous.
Someone is either funny or calm. | Mary is wise. | neutral | (![X]:((~humble(X)<~>~calm(X))<=>(~funny(X)<~>happy(X))))&
(![X]:(funny(X)<=>(generous(X)<~>tall(X))))&
((?[X]:((~generous(X)|old(X))))=>(?[X]:(~old(X))))&
((?[X]:((happy(X)|~kind(X))))<=>(?[X]:((creative(X)<~>old(X)))))&
((curious(alice))=>(?[X]:(~kind(X))))&
(((wise(lucy)&~humble(lucy)))<=>(?[X]:((~old(X)<~>calm(X)))))&
(![X]:((~tall(X)<~>~old(X))<=>~creative(X)))&
((tall(mary))=>((~creative(fred)<~>wise(fred))))&
(((happy(susan)&curious(susan)))<=>(?[X]:((tall(X)|~curious(X)))))&
(![X]:((~humble(X)&~tall(X))=>brave(X)))&
(![X]:(~funny(X)<=>(brave(X)&kind(X))))&
(![X]:(~creative(X)<=>~strong(X)))&
(![X]:(kind(X)<=>(strong(X)&~curious(X))))&
(![X]:(~creative(X)<=>(~brave(X)&wise(X))))&
(![X]:((tall(X)&~tall(X))<=>(brave(X)<~>creative(X))))&
(((~patient(susan)<~>happy(susan)))=>(?[X]:(happy(X))))&
(?[X]:((calm(X)&~strong(X))))&
((rich(john)|~wise(john)))&
(brave(fred))&
((~creative(alice)&~old(alice)))&
(~funny(john))&
((brave(susan)<~>~generous(susan)))&
(?[X]:((funny(X)<~>calm(X)))) | wise(mary) | [] | null | 0 |
If alice is curious or generous then paul is not rich or not wise and vice versa. Everyone who is either not old or generous is both not old and not quiet and vice versa. Everyone who is both rich and not curious is curious and vice versa. If paul is both not happy and rich then someone is either generous or not rich. Everyone who is old is wise and vice versa. Everyone who is not funny or generous is both not happy and not creative. Everyone who is not tall or patient is either not strong or strong and vice versa. Everyone who is either funny or not funny is either not patient or happy and vice versa. Everyone who is not calm or not generous is not happy or creative and vice versa. If mary is generous then someone is not brave or not patient and vice versa. Everyone who is either not wise or not happy is kind or patient and vice versa. Everyone who is either not tall or not calm is not rich. Everyone who is both rich and not patient is tall or curious. If someone is brave or strong then someone is either not tall or happy and vice versa. Someone is either not funny or not generous. John is happy. Susan is not humble. | John is not calm. | neutral | (((curious(alice)|generous(alice)))<=>((~rich(paul)|~wise(paul))))&
(![X]:((~old(X)<~>generous(X))<=>(~old(X)&~quiet(X))))&
(![X]:((rich(X)&~curious(X))<=>curious(X)))&
(((~happy(paul)&rich(paul)))=>(?[X]:((generous(X)<~>~rich(X)))))&
(![X]:(old(X)<=>wise(X)))&
(![X]:((~funny(X)|generous(X))=>(~happy(X)&~creative(X))))&
(![X]:((~tall(X)|patient(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((funny(X)<~>~funny(X))<=>(~patient(X)<~>happy(X))))&
(![X]:((~calm(X)|~generous(X))<=>(~happy(X)|creative(X))))&
((generous(mary))<=>(?[X]:((~brave(X)|~patient(X)))))&
(![X]:((~wise(X)<~>~happy(X))<=>(kind(X)|patient(X))))&
(![X]:((~tall(X)<~>~calm(X))=>~rich(X)))&
(![X]:((rich(X)&~patient(X))=>(tall(X)|curious(X))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(?[X]:((~funny(X)<~>~generous(X))))&
(happy(john))&
(~humble(susan)) | ~calm(john) | [] | null | 0 |
Everyone who is both quiet and kind is both not creative and funny and vice versa. If someone is both not creative and curious then fred is happy or patient. Everyone who is strong is not tall or brave and vice versa. If someone is both not generous and not brave then someone is wise or not quiet. Everyone who is not patient is wise. If fred is both old and kind then someone is either old or not creative and vice versa. Everyone who is not rich or tall is happy. If someone is quiet or wise then paul is both wise and strong and vice versa. If john is kind or not old then susan is calm or creative and vice versa. Everyone who is curious or not calm is either not creative or kind and vice versa. Everyone who is humble is both not old and not generous. If someone is rich then someone is both not calm and humble and vice versa. Everyone who is either kind or patient is not wise and vice versa. If someone is not curious then mary is both calm and not funny. If someone is either rich or funny then john is both not tall and not quiet and vice versa. Everyone who is either not quiet or not generous is quiet. Fred is not rich or calm. Someone is both tall and not calm. Alice is not curious. Mary is either quiet or not curious. Paul is either generous or humble. Someone is either wise or not quiet. Mary is quiet or not calm. Alice is not creative or not patient. | Paul is not strong. | contradiction | (![X]:((quiet(X)&kind(X))<=>(~creative(X)&funny(X))))&
((?[X]:((~creative(X)&curious(X))))=>((happy(fred)|patient(fred))))&
(![X]:(strong(X)<=>(~tall(X)|brave(X))))&
((?[X]:((~generous(X)&~brave(X))))=>(?[X]:((wise(X)|~quiet(X)))))&
(![X]:(~patient(X)=>wise(X)))&
(((old(fred)&kind(fred)))<=>(?[X]:((old(X)<~>~creative(X)))))&
(![X]:((~rich(X)|tall(X))=>happy(X)))&
((?[X]:((quiet(X)|wise(X))))<=>((wise(paul)&strong(paul))))&
(((kind(john)|~old(john)))<=>((calm(susan)|creative(susan))))&
(![X]:((curious(X)|~calm(X))<=>(~creative(X)<~>kind(X))))&
(![X]:(humble(X)=>(~old(X)&~generous(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~calm(X)&humble(X)))))&
(![X]:((kind(X)<~>patient(X))<=>~wise(X)))&
((?[X]:(~curious(X)))=>((calm(mary)&~funny(mary))))&
((?[X]:((rich(X)<~>funny(X))))<=>((~tall(john)&~quiet(john))))&
(![X]:((~quiet(X)<~>~generous(X))=>quiet(X)))&
((~rich(fred)|calm(fred)))&
(?[X]:((tall(X)&~calm(X))))&
(~curious(alice))&
((quiet(mary)<~>~curious(mary)))&
((generous(paul)<~>humble(paul)))&
(?[X]:((wise(X)<~>~quiet(X))))&
((quiet(mary)|~calm(mary)))&
((~creative(alice)|~patient(alice))) | ~strong(paul) | [
"p7",
"p13",
"p18",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5536065988962274201319159
% SZS output start Proof for 5536065988962274201319159
8. ? [X0] : (wise(X0) | quiet(X0)) <=> (strong(paul) & wise(paul)) [input p7]
14. ? [X0] : ~curious(X0) => (~funny(mary) & calm(mary)) [input p13]
19. ~curious(alice) [input p18]
23. ~calm(mary) | quiet(mary) [input p22]
25. ~strong(paul) [input hypothesis]
33. (~funny(mary) & calm(mary)) | ! [X0] : curious(X0) [ennf transformation 14]
47. (? [X0] : (wise(X0) | quiet(X0)) | (~strong(paul) | ~wise(paul))) & ((strong(paul) & wise(paul)) | ! [X0] : (~wise(X0) & ~quiet(X0))) [nnf transformation 8]
48. (? [X0] : (wise(X0) | quiet(X0)) | ~strong(paul) | ~wise(paul)) & ((strong(paul) & wise(paul)) | ! [X0] : (~wise(X0) & ~quiet(X0))) [flattening 47]
49. (? [X0] : (wise(X0) | quiet(X0)) | ~strong(paul) | ~wise(paul)) & ((strong(paul) & wise(paul)) | ! [X1] : (~wise(X1) & ~quiet(X1))) [rectify 48]
50. ? [X0] : (wise(X0) | quiet(X0)) => (wise(sK2) | quiet(sK2)) [choice axiom]
51. ((wise(sK2) | quiet(sK2)) | ~strong(paul) | ~wise(paul)) & ((strong(paul) & wise(paul)) | ! [X1] : (~wise(X1) & ~quiet(X1))) [skolemisation 49,50]
92. strong(paul) | ~quiet(X1) [cnf transformation 51]
114. calm(mary) | curious(X0) [cnf transformation 33]
127. ~curious(alice) [cnf transformation 19]
134. ~calm(mary) | quiet(mary) [cnf transformation 23]
136. ~strong(paul) [cnf transformation 25]
183. 11 <=> strong(paul) [avatar definition]
200. 15 <=> ! [X1] : ~quiet(X1) [avatar definition]
201. ~quiet(X1) <- (15) [avatar component clause 200]
202. 15 | 11 [avatar split clause 92,183,200]
249. 25 <=> ! [X0] : curious(X0) [avatar definition]
250. curious(X0) <- (25) [avatar component clause 249]
257. 27 <=> calm(mary) [avatar definition]
260. 25 | 27 [avatar split clause 114,257,249]
299. 36 <=> quiet(mary) [avatar definition]
300. quiet(mary) <- (36) [avatar component clause 299]
327. 36 | ~27 [avatar split clause 134,257,299]
337. ~11 [avatar split clause 136,183]
338. $false <- (25) [resolution 250,127]
339. ~25 [avatar contradiction clause 338]
340. $false <- (15, 36) [subsumption resolution 300,201]
341. ~15 | ~36 [avatar contradiction clause 340]
342. $false [avatar sat refutation 202,260,327,337,339,341]
% SZS output end Proof for 5536065988962274201319159
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or not curious is patient or not kind and vice versa.
Everyone who is not happy or generous is not patient and vice versa.
Everyone who is strong or not happy is not creative.
If someone is old or kind then someone is either humble or curious.
If lucy is both not wise and creative then mary is not funny and vice versa.
Everyone who is patient or not kind is either not creative or tall and vice versa.
If fred is not rich or not quiet then susan is either not funny or rich and vice versa.
If susan is both tall and generous then paul is patient.
If fred is creative or not funny then someone is humble.
Everyone who is happy or humble is either calm or kind.
Everyone who is not kind is not tall and vice versa.
Everyone who is not humble is either quiet or not funny and vice versa.
Everyone who is wise or not strong is patient or not wise and vice versa.
If john is old or tall then someone is either rich or kind and vice versa.
Everyone who is either not rich or old is either not creative or not wise.
If someone is patient or not kind then lucy is not patient and vice versa.
Paul is either old or quiet.
Susan is not brave or not kind.
Susan is old or not patient.
Mary is patient.
Lucy is either not funny or not humble.
Someone is both not curious and patient.
Alice is both wise and not humble.
John is creative or kind. | Lucy is not tall. | neutral | (![X]:((~humble(X)|~curious(X))<=>(patient(X)|~kind(X))))&
(![X]:((~happy(X)|generous(X))<=>~patient(X)))&
(![X]:((strong(X)|~happy(X))=>~creative(X)))&
((?[X]:((old(X)|kind(X))))=>(?[X]:((humble(X)<~>curious(X)))))&
(((~wise(lucy)&creative(lucy)))<=>(~funny(mary)))&
(![X]:((patient(X)|~kind(X))<=>(~creative(X)<~>tall(X))))&
(((~rich(fred)|~quiet(fred)))<=>((~funny(susan)<~>rich(susan))))&
(((tall(susan)&generous(susan)))=>(patient(paul)))&
(((creative(fred)|~funny(fred)))=>(?[X]:(humble(X))))&
(![X]:((happy(X)|humble(X))=>(calm(X)<~>kind(X))))&
(![X]:(~kind(X)<=>~tall(X)))&
(![X]:(~humble(X)<=>(quiet(X)<~>~funny(X))))&
(![X]:((wise(X)|~strong(X))<=>(patient(X)|~wise(X))))&
(((old(john)|tall(john)))<=>(?[X]:((rich(X)<~>kind(X)))))&
(![X]:((~rich(X)<~>old(X))=>(~creative(X)<~>~wise(X))))&
((?[X]:((patient(X)|~kind(X))))<=>(~patient(lucy)))&
((old(paul)<~>quiet(paul)))&
((~brave(susan)|~kind(susan)))&
((old(susan)|~patient(susan)))&
(patient(mary))&
((~funny(lucy)<~>~humble(lucy)))&
(?[X]:((~curious(X)&patient(X))))&
((wise(alice)&~humble(alice)))&
((creative(john)|kind(john))) | ~tall(lucy) | [] | null | 0 |
Everyone who is either curious or not humble is both patient and old and vice versa.
Everyone who is both not calm and not rich is curious.
If alice is either brave or not humble then someone is not calm.
If someone is either happy or tall then susan is not tall.
If paul is both kind and rich then someone is either curious or not happy.
Everyone who is quiet or not tall is not happy and vice versa.
Everyone who is not brave is both rich and creative and vice versa.
Everyone who is kind or not calm is both not humble and creative.
Everyone who is old is not creative.
Everyone who is both not creative and not happy is either brave or rich.
Everyone who is not creative or not wise is either not wise or calm.
Everyone who is brave is both strong and happy and vice versa.
If fred is humble then mary is rich.
Everyone who is rich is both not curious and not calm.
If someone is either rich or not strong then paul is both not old and humble and vice versa.
If someone is strong then mary is not wise.
Someone is creative.
Mary is generous or not calm.
Someone is old or wise.
Lucy is both tall and generous.
Someone is kind.
Alice is either not wise or wise. | Alice is not quiet. | entailment | (![X]:((curious(X)<~>~humble(X))<=>(patient(X)&old(X))))&
(![X]:((~calm(X)&~rich(X))=>curious(X)))&
(((brave(alice)<~>~humble(alice)))=>(?[X]:(~calm(X))))&
((?[X]:((happy(X)<~>tall(X))))=>(~tall(susan)))&
(((kind(paul)&rich(paul)))=>(?[X]:((curious(X)<~>~happy(X)))))&
(![X]:((quiet(X)|~tall(X))<=>~happy(X)))&
(![X]:(~brave(X)<=>(rich(X)&creative(X))))&
(![X]:((kind(X)|~calm(X))=>(~humble(X)&creative(X))))&
(![X]:(old(X)=>~creative(X)))&
(![X]:((~creative(X)&~happy(X))=>(brave(X)<~>rich(X))))&
(![X]:((~creative(X)|~wise(X))=>(~wise(X)<~>calm(X))))&
(![X]:(brave(X)<=>(strong(X)&happy(X))))&
((humble(fred))=>(rich(mary)))&
(![X]:(rich(X)=>(~curious(X)&~calm(X))))&
((?[X]:((rich(X)<~>~strong(X))))<=>((~old(paul)&humble(paul))))&
((?[X]:(strong(X)))=>(~wise(mary)))&
(?[X]:(creative(X)))&
((generous(mary)|~calm(mary)))&
(?[X]:((old(X)|wise(X))))&
((tall(lucy)&generous(lucy)))&
(?[X]:(kind(X)))&
((~wise(alice)<~>wise(alice))) | ~quiet(alice) | [
"p0",
"p5",
"p6",
"p7",
"p8",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4764172346023716764523458
% SZS output start Proof for 4764172346023716764523458
1. ! [X0] : ((curious(X0) <~> ~humble(X0)) <=> (old(X0) & patient(X0))) [input p0]
6. ! [X0] : ((~tall(X0) | quiet(X0)) <=> ~happy(X0)) [input p5]
7. ! [X0] : (~brave(X0) <=> (creative(X0) & rich(X0))) [input p6]
8. ! [X0] : ((~calm(X0) | kind(X0)) => (creative(X0) & ~humble(X0))) [input p7]
9. ! [X0] : (old(X0) => ~creative(X0)) [input p8]
12. ! [X0] : (brave(X0) <=> (happy(X0) & strong(X0))) [input p11]
14. ! [X0] : (rich(X0) => (~calm(X0) & ~curious(X0))) [input p13]
23. quiet(alice) [input hypothesis]
32. ! [X0] : ((creative(X0) & ~humble(X0)) | (calm(X0) & ~kind(X0))) [ennf transformation 8]
33. ! [X0] : (~creative(X0) | ~old(X0)) [ennf transformation 9]
38. ! [X0] : ((~calm(X0) & ~curious(X0)) | ~rich(X0)) [ennf transformation 14]
40. ! [X0] : ((((humble(X0) | ~curious(X0)) & (~humble(X0) | curious(X0))) | (~old(X0) | ~patient(X0))) & ((old(X0) & patient(X0)) | ((curious(X0) | humble(X0)) & (~humble(X0) | ~curious(X0))))) [nnf transformation 1]
41. ! [X0] : ((((humble(X0) | ~curious(X0)) & (~humble(X0) | curious(X0))) | ~old(X0) | ~patient(X0)) & ((old(X0) & patient(X0)) | ((curious(X0) | humble(X0)) & (~humble(X0) | ~curious(X0))))) [flattening 40]
49. ! [X0] : (((~tall(X0) | quiet(X0)) | happy(X0)) & (~happy(X0) | (tall(X0) & ~quiet(X0)))) [nnf transformation 6]
50. ! [X0] : ((~tall(X0) | quiet(X0) | happy(X0)) & (~happy(X0) | (tall(X0) & ~quiet(X0)))) [flattening 49]
51. ! [X0] : ((~brave(X0) | (~creative(X0) | ~rich(X0))) & ((creative(X0) & rich(X0)) | brave(X0))) [nnf transformation 7]
52. ! [X0] : ((~brave(X0) | ~creative(X0) | ~rich(X0)) & ((creative(X0) & rich(X0)) | brave(X0))) [flattening 51]
55. ! [X0] : ((brave(X0) | (~happy(X0) | ~strong(X0))) & ((happy(X0) & strong(X0)) | ~brave(X0))) [nnf transformation 12]
56. ! [X0] : ((brave(X0) | ~happy(X0) | ~strong(X0)) & ((happy(X0) & strong(X0)) | ~brave(X0))) [flattening 55]
72. old(X0) | curious(X0) | humble(X0) [cnf transformation 41]
82. ~quiet(X0) | ~happy(X0) [cnf transformation 50]
85. brave(X0) | rich(X0) [cnf transformation 52]
89. ~humble(X0) | calm(X0) [cnf transformation 32]
91. creative(X0) | calm(X0) [cnf transformation 32]
92. ~creative(X0) | ~old(X0) [cnf transformation 33]
100. ~brave(X0) | happy(X0) [cnf transformation 56]
103. ~rich(X0) | ~curious(X0) [cnf transformation 38]
104. ~rich(X0) | ~calm(X0) [cnf transformation 38]
118. quiet(alice) [cnf transformation 23]
220. ~happy(alice) [resolution 82,118]
225. ~old(X0) | calm(X0) [resolution 92,91]
230. happy(X0) | rich(X0) [resolution 100,85]
249. curious(X0) | humble(X0) | calm(X0) [resolution 72,225]
253. calm(X0) | curious(X0) [subsumption resolution 249,89]
348. rich(alice) [resolution 230,220]
356. ~calm(alice) [resolution 348,104]
357. ~curious(alice) [resolution 348,103]
388. curious(alice) [resolution 356,253]
389. $false [subsumption resolution 388,357]
% SZS output end Proof for 4764172346023716764523458
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or tall is not old or not calm and vice versa.
Everyone who is not tall or calm is brave or generous.
If john is either curious or humble then lucy is generous and vice versa.
Everyone who is happy or kind is both not rich and not quiet and vice versa.
If someone is generous then someone is not curious or not funny and vice versa.
Everyone who is not patient is kind or patient and vice versa.
Everyone who is either calm or patient is both not old and not patient and vice versa.
If someone is not patient then someone is funny.
If alice is both not tall and tall then someone is both not brave and kind and vice versa.
If someone is either not wise or not quiet then someone is both funny and not happy.
If paul is not kind then someone is both funny and not kind and vice versa.
Everyone who is both not humble and quiet is either kind or curious.
Everyone who is either calm or tall is strong or generous.
Everyone who is not tall is either not rich or not patient and vice versa.
If someone is either not generous or quiet then someone is not generous or not strong.
Everyone who is patient is happy or not humble and vice versa.
John is not calm.
Someone is not old or tall.
Lucy is not patient.
Someone is happy or not curious.
Susan is both wise and generous.
Someone is curious. | Lucy is generous. | neutral | (![X]:((~brave(X)|tall(X))<=>(~old(X)|~calm(X))))&
(![X]:((~tall(X)|calm(X))=>(brave(X)|generous(X))))&
(((curious(john)<~>humble(john)))<=>(generous(lucy)))&
(![X]:((happy(X)|kind(X))<=>(~rich(X)&~quiet(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~curious(X)|~funny(X)))))&
(![X]:(~patient(X)<=>(kind(X)|patient(X))))&
(![X]:((calm(X)<~>patient(X))<=>(~old(X)&~patient(X))))&
((?[X]:(~patient(X)))=>(?[X]:(funny(X))))&
(((~tall(alice)&tall(alice)))<=>(?[X]:((~brave(X)&kind(X)))))&
((?[X]:((~wise(X)<~>~quiet(X))))=>(?[X]:((funny(X)&~happy(X)))))&
((~kind(paul))<=>(?[X]:((funny(X)&~kind(X)))))&
(![X]:((~humble(X)&quiet(X))=>(kind(X)<~>curious(X))))&
(![X]:((calm(X)<~>tall(X))=>(strong(X)|generous(X))))&
(![X]:(~tall(X)<=>(~rich(X)<~>~patient(X))))&
((?[X]:((~generous(X)<~>quiet(X))))=>(?[X]:((~generous(X)|~strong(X)))))&
(![X]:(patient(X)<=>(happy(X)|~humble(X))))&
(~calm(john))&
(?[X]:((~old(X)|tall(X))))&
(~patient(lucy))&
(?[X]:((happy(X)|~curious(X))))&
((wise(susan)&generous(susan)))&
(?[X]:(curious(X))) | generous(lucy) | [] | null | 0 |
If someone is either happy or humble then someone is not patient and vice versa. 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. Everyone who is wise or not wise is not calm and vice versa. Everyone who is both not quiet and not brave is both funny and creative. Everyone who is tall or calm is not strong or not old and vice versa. Everyone who is either not curious or not brave is generous. Fred is not patient. Alice is both kind and not brave. Someone is either not curious or wise. Lucy is not generous. Alice is not curious or not creative. Mary is either creative or rich. Paul is brave or quiet. | Paul is not brave. | contradiction | ((?[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]:((wise(X)|~wise(X))<=>~calm(X)))&
(![X]:((~quiet(X)&~brave(X))=>(funny(X)&creative(X))))&
(![X]:((tall(X)|calm(X))<=>(~strong(X)|~old(X))))&
(![X]:((~curious(X)<~>~brave(X))=>generous(X)))&
(~patient(fred))&
((kind(alice)&~brave(alice)))&
(?[X]:((~curious(X)<~>wise(X))))&
(~generous(lucy))&
((~curious(alice)|~creative(alice)))&
((creative(mary)<~>rich(mary)))&
((brave(paul)|quiet(paul))) | ~brave(paul) | [
"p7",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2298596541682586605545262
% SZS output start Proof for 2298596541682586605545262
8. ! [X0] : (~calm(X0) <=> (~quiet(X0) & ~tall(X0))) [input p7]
13. ! [X0] : ((~wise(X0) | wise(X0)) <=> ~calm(X0)) [input p12]
23. quiet(paul) | brave(paul) [input p22]
24. ~brave(paul) [input hypothesis]
58. ! [X0] : ((~calm(X0) | (quiet(X0) | tall(X0))) & ((~quiet(X0) & ~tall(X0)) | calm(X0))) [nnf transformation 8]
59. ! [X0] : ((~calm(X0) | quiet(X0) | tall(X0)) & ((~quiet(X0) & ~tall(X0)) | calm(X0))) [flattening 58]
67. ! [X0] : (((~wise(X0) | wise(X0)) | calm(X0)) & (~calm(X0) | (wise(X0) & ~wise(X0)))) [nnf transformation 13]
68. ! [X0] : ((~wise(X0) | wise(X0) | calm(X0)) & (~calm(X0) | (wise(X0) & ~wise(X0)))) [flattening 67]
96. ~quiet(X0) | calm(X0) [cnf transformation 59]
108. ~calm(X0) | ~wise(X0) [cnf transformation 68]
109. ~calm(X0) | wise(X0) [cnf transformation 68]
128. quiet(paul) | brave(paul) [cnf transformation 23]
129. ~brave(paul) [cnf transformation 24]
267. ~calm(X0) [subsumption resolution 108,109]
300. 38 <=> brave(paul) [avatar definition]
304. 39 <=> quiet(paul) [avatar definition]
306. quiet(paul) <- (39) [avatar component clause 304]
307. 38 | 39 [avatar split clause 128,304,300]
308. ~38 [avatar split clause 129,300]
309. calm(paul) <- (39) [resolution 96,306]
310. $false <- (39) [subsumption resolution 309,267]
311. ~39 [avatar contradiction clause 310]
312. $false [avatar sat refutation 307,308,311]
% SZS output end Proof for 2298596541682586605545262
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or not curious then someone is funny or not old and vice versa.
If someone is strong then alice is not rich.
Everyone who is either creative or strong is both not humble and not curious and vice versa.
If fred is strong then someone is either tall or not curious.
If john is not patient then alice is happy and vice versa.
If mary is both strong and humble then someone is either not wise or strong and vice versa.
Everyone who is either not kind or humble is not wise.
Everyone who is not generous or not calm is not kind.
Everyone who is either not generous or humble is both old and patient.
Everyone who is kind is either creative or not creative and vice versa.
Everyone who is not tall is not funny.
Everyone who is not tall is both not wise and rich.
If someone is either not humble or brave then someone is both old and not calm and vice versa.
Everyone who is either not patient or not kind is brave.
If someone is brave or happy then someone is either happy or not brave and vice versa.
Lucy is either brave or not old.
Lucy is creative.
Someone is not happy or kind.
Someone is both not strong and funny.
Fred is humble.
Someone is either not kind or creative.
Someone is either strong or not calm.
Someone is both quiet and not creative. | Alice is not tall. | contradiction | ((?[X]:((~humble(X)|~curious(X))))<=>(?[X]:((funny(X)|~old(X)))))&
((?[X]:(strong(X)))=>(~rich(alice)))&
(![X]:((creative(X)<~>strong(X))<=>(~humble(X)&~curious(X))))&
((strong(fred))=>(?[X]:((tall(X)<~>~curious(X)))))&
((~patient(john))<=>(happy(alice)))&
(((strong(mary)&humble(mary)))<=>(?[X]:((~wise(X)<~>strong(X)))))&
(![X]:((~kind(X)<~>humble(X))=>~wise(X)))&
(![X]:((~generous(X)|~calm(X))=>~kind(X)))&
(![X]:((~generous(X)<~>humble(X))=>(old(X)&patient(X))))&
(![X]:(kind(X)<=>(creative(X)<~>~creative(X))))&
(![X]:(~tall(X)=>~funny(X)))&
(![X]:(~tall(X)=>(~wise(X)&rich(X))))&
((?[X]:((~humble(X)<~>brave(X))))<=>(?[X]:((old(X)&~calm(X)))))&
(![X]:((~patient(X)<~>~kind(X))=>brave(X)))&
((?[X]:((brave(X)|happy(X))))<=>(?[X]:((happy(X)<~>~brave(X)))))&
((brave(lucy)<~>~old(lucy)))&
(creative(lucy))&
(?[X]:((~happy(X)|kind(X))))&
(?[X]:((~strong(X)&funny(X))))&
(humble(fred))&
(?[X]:((~kind(X)<~>creative(X))))&
(?[X]:((strong(X)<~>~calm(X))))&
(?[X]:((quiet(X)&~creative(X)))) | ~tall(alice) | [
"p1",
"p7",
"p9",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1138472263250139217682607
% SZS output start Proof for 1138472263250139217682607
2. ? [X0] : strong(X0) => ~rich(alice) [input p1]
8. ! [X0] : ((~calm(X0) | ~generous(X0)) => ~kind(X0)) [input p7]
10. ! [X0] : (kind(X0) <=> (creative(X0) <~> ~creative(X0))) [input p9]
12. ! [X0] : (~tall(X0) => (rich(X0) & ~wise(X0))) [input p11]
22. ? [X0] : (strong(X0) <~> ~calm(X0)) [input p21]
24. ~tall(alice) [input hypothesis]
29. ~rich(alice) | ! [X0] : ~strong(X0) [ennf transformation 2]
32. ! [X0] : (~kind(X0) | (calm(X0) & generous(X0))) [ennf transformation 8]
35. ! [X0] : ((rich(X0) & ~wise(X0)) | tall(X0)) [ennf transformation 12]
55. ! [X0] : ((kind(X0) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | ~kind(X0))) [nnf transformation 10]
75. ? [X0] : ((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) [nnf transformation 22]
76. ? [X0] : ((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) => ((calm(sK11) | ~strong(sK11)) & (~calm(sK11) | strong(sK11))) [choice axiom]
77. (calm(sK11) | ~strong(sK11)) & (~calm(sK11) | strong(sK11)) [skolemisation 75,76]
84. ~rich(alice) | ~strong(X0) [cnf transformation 29]
104. ~kind(X0) | calm(X0) [cnf transformation 32]
111. kind(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 55]
112. kind(X0) | creative(X0) | creative(X0) [cnf transformation 55]
115. tall(X0) | rich(X0) [cnf transformation 35]
139. ~calm(sK11) | strong(sK11) [cnf transformation 77]
142. ~tall(alice) [cnf transformation 24]
143. kind(X0) | ~creative(X0) [duplicate literal removal 111]
144. kind(X0) | creative(X0) [duplicate literal removal 112]
178. 9 <=> ! [X0] : ~strong(X0) [avatar definition]
179. ~strong(X0) <- (9) [avatar component clause 178]
181. 10 <=> rich(alice) [avatar definition]
184. 9 | ~10 [avatar split clause 84,181,178]
237. kind(X0) [subsumption resolution 143,144]
316. 39 <=> strong(sK11) [avatar definition]
317. strong(sK11) <- (39) [avatar component clause 316]
320. 40 <=> calm(sK11) [avatar definition]
321. ~calm(sK11) <- (~40) [avatar component clause 320]
324. 39 | ~40 [avatar split clause 139,320,316]
326. calm(X0) [resolution 104,237]
328. $false <- (~40) [resolution 326,321]
329. 40 [avatar contradiction clause 328]
330. rich(alice) [resolution 115,142]
333. 10 [avatar split clause 330,181]
334. $false <- (9, 39) [resolution 179,317]
335. ~9 | ~39 [avatar contradiction clause 334]
336. $false [avatar sat refutation 184,324,329,333,335]
% SZS output end Proof for 1138472263250139217682607
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not generous then lucy is both not strong and curious.
If lucy is not quiet or wise then someone is both strong and funny.
Everyone who is creative is strong or happy and vice versa.
Everyone who is tall or strong is humble and vice versa.
Everyone who is not patient or not calm is both funny and old.
Everyone who is not rich or wise is either funny or not strong.
Everyone who is not rich or wise is either tall or humble.
If someone is not brave or humble then paul is either not brave or humble and vice versa.
Everyone who is both wise and not funny is both not rich and humble and vice versa.
If lucy is either quiet or humble then alice is tall and vice versa.
If fred is not tall or not wise then lucy is both not generous and not curious and vice versa.
Everyone who is both not calm and not patient is not patient or brave.
If mary is either brave or happy then someone is patient or not curious and vice versa.
If lucy is either not quiet or curious then lucy is curious and vice versa.
Everyone who is both humble and tall is either old or calm.
If alice is both not calm and old then paul is both old and wise and vice versa.
Mary is both not brave and not funny.
Someone is rich or not calm.
Someone is both not kind and humble.
Someone is either rich or humble.
Someone is either generous or not patient.
Mary is both not curious and not wise.
John is not old or brave.
Alice is either not generous or not kind. | Lucy is curious. | contradiction | ((~generous(alice))=>((~strong(lucy)&curious(lucy))))&
(((~quiet(lucy)|wise(lucy)))=>(?[X]:((strong(X)&funny(X)))))&
(![X]:(creative(X)<=>(strong(X)|happy(X))))&
(![X]:((tall(X)|strong(X))<=>humble(X)))&
(![X]:((~patient(X)|~calm(X))=>(funny(X)&old(X))))&
(![X]:((~rich(X)|wise(X))=>(funny(X)<~>~strong(X))))&
(![X]:((~rich(X)|wise(X))=>(tall(X)<~>humble(X))))&
((?[X]:((~brave(X)|humble(X))))<=>((~brave(paul)<~>humble(paul))))&
(![X]:((wise(X)&~funny(X))<=>(~rich(X)&humble(X))))&
(((quiet(lucy)<~>humble(lucy)))<=>(tall(alice)))&
(((~tall(fred)|~wise(fred)))<=>((~generous(lucy)&~curious(lucy))))&
(![X]:((~calm(X)&~patient(X))=>(~patient(X)|brave(X))))&
(((brave(mary)<~>happy(mary)))<=>(?[X]:((patient(X)|~curious(X)))))&
(((~quiet(lucy)<~>curious(lucy)))<=>(curious(lucy)))&
(![X]:((humble(X)&tall(X))=>(old(X)<~>calm(X))))&
(((~calm(alice)&old(alice)))<=>((old(paul)&wise(paul))))&
((~brave(mary)&~funny(mary)))&
(?[X]:((rich(X)|~calm(X))))&
(?[X]:((~kind(X)&humble(X))))&
(?[X]:((rich(X)<~>humble(X))))&
(?[X]:((generous(X)<~>~patient(X))))&
((~curious(mary)&~wise(mary)))&
((~old(john)|brave(john)))&
((~generous(alice)<~>~kind(alice))) | curious(lucy) | [
"p3",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6587878533868175894760045
% SZS output start Proof for 6587878533868175894760045
4. ! [X0] : ((strong(X0) | tall(X0)) <=> humble(X0)) [input p3]
7. ! [X0] : ((wise(X0) | ~rich(X0)) => (tall(X0) <~> humble(X0))) [input p6]
11. (~wise(fred) | ~tall(fred)) <=> (~curious(lucy) & ~generous(lucy)) [input p10]
25. curious(lucy) [input hypothesis]
30. ! [X0] : ((tall(X0) <~> humble(X0)) | (~wise(X0) & rich(X0))) [ennf transformation 7]
37. ! [X0] : (((strong(X0) | tall(X0)) | ~humble(X0)) & (humble(X0) | (~strong(X0) & ~tall(X0)))) [nnf transformation 4]
38. ! [X0] : ((strong(X0) | tall(X0) | ~humble(X0)) & (humble(X0) | (~strong(X0) & ~tall(X0)))) [flattening 37]
40. ! [X0] : (((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | (~wise(X0) & rich(X0))) [nnf transformation 30]
48. ((~wise(fred) | ~tall(fred)) | (curious(lucy) | generous(lucy))) & ((~curious(lucy) & ~generous(lucy)) | (wise(fred) & tall(fred))) [nnf transformation 11]
49. (~wise(fred) | ~tall(fred) | curious(lucy) | generous(lucy)) & ((~curious(lucy) & ~generous(lucy)) | (wise(fred) & tall(fred))) [flattening 48]
75. ~tall(X0) | humble(X0) [cnf transformation 38]
89. ~humble(X0) | ~tall(X0) | ~wise(X0) [cnf transformation 40]
106. ~curious(lucy) | tall(fred) [cnf transformation 49]
107. ~curious(lucy) | wise(fred) [cnf transformation 49]
140. curious(lucy) [cnf transformation 25]
148. 2 <=> curious(lucy) [avatar definition]
177. ~tall(X0) | ~wise(X0) [subsumption resolution 89,75]
224. 16 <=> wise(fred) [avatar definition]
226. wise(fred) <- (16) [avatar component clause 224]
227. 16 | ~2 [avatar split clause 107,148,224]
229. 17 <=> tall(fred) [avatar definition]
231. tall(fred) <- (17) [avatar component clause 229]
232. 17 | ~2 [avatar split clause 106,148,229]
336. 2 [avatar split clause 140,148]
345. ~wise(fred) <- (17) [resolution 177,231]
346. $false <- (16, 17) [subsumption resolution 345,226]
347. ~16 | ~17 [avatar contradiction clause 346]
348. $false [avatar sat refutation 227,232,336,347]
% SZS output end Proof for 6587878533868175894760045
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or not generous is not happy. Everyone who is not tall or not generous is both not old and not patient. Everyone who is rich or creative is old or not patient and vice versa. Everyone who is either not old or kind is not creative or not humble and vice versa. If someone is not strong then someone is not old or not creative and vice versa. If someone is either not rich or funny then someone is not wise or not brave and vice versa. Everyone who is not creative is either not rich or quiet. Everyone who is not curious or quiet is curious or not brave. Everyone who is either not strong or kind is humble or brave and vice versa. Everyone who is calm is brave and vice versa. If lucy is both kind and not funny then someone is either not wise or not strong. Everyone who is both calm and brave is either strong or not humble and vice versa. If paul is curious then someone is either not tall or not creative. If lucy is not tall then mary is both not funny and not curious and vice versa. Everyone who is both creative and curious is either not old or not quiet and vice versa. If someone is either not tall or not brave then someone is not old or funny. Paul is not funny. Mary is not humble. Someone is quiet or not curious. Someone is not old or brave. Someone is both old and not kind. John is not strong. John is calm or kind. Someone is either calm or not creative. | John is not old. | entailment | (![X]:((~creative(X)<~>~generous(X))=>~happy(X)))&
(![X]:((~tall(X)|~generous(X))=>(~old(X)&~patient(X))))&
(![X]:((rich(X)|creative(X))<=>(old(X)|~patient(X))))&
(![X]:((~old(X)<~>kind(X))<=>(~creative(X)|~humble(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~old(X)|~creative(X)))))&
((?[X]:((~rich(X)<~>funny(X))))<=>(?[X]:((~wise(X)|~brave(X)))))&
(![X]:(~creative(X)=>(~rich(X)<~>quiet(X))))&
(![X]:((~curious(X)|quiet(X))=>(curious(X)|~brave(X))))&
(![X]:((~strong(X)<~>kind(X))<=>(humble(X)|brave(X))))&
(![X]:(calm(X)<=>brave(X)))&
(((kind(lucy)&~funny(lucy)))=>(?[X]:((~wise(X)<~>~strong(X)))))&
(![X]:((calm(X)&brave(X))<=>(strong(X)<~>~humble(X))))&
((curious(paul))=>(?[X]:((~tall(X)<~>~creative(X)))))&
((~tall(lucy))<=>((~funny(mary)&~curious(mary))))&
(![X]:((creative(X)&curious(X))<=>(~old(X)<~>~quiet(X))))&
((?[X]:((~tall(X)<~>~brave(X))))=>(?[X]:((~old(X)|funny(X)))))&
(~funny(paul))&
(~humble(mary))&
(?[X]:((quiet(X)|~curious(X))))&
(?[X]:((~old(X)|brave(X))))&
(?[X]:((old(X)&~kind(X))))&
(~strong(john))&
((calm(john)|kind(john)))&
(?[X]:((calm(X)<~>~creative(X)))) | ~old(john) | [
"p3",
"p8",
"p9",
"p11",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1900440083253168431188015
% SZS output start Proof for 1900440083253168431188015
4. ! [X0] : ((~old(X0) <~> kind(X0)) <=> (~humble(X0) | ~creative(X0))) [input p3]
9. ! [X0] : ((~strong(X0) <~> kind(X0)) <=> (brave(X0) | humble(X0))) [input p8]
10. ! [X0] : (calm(X0) <=> brave(X0)) [input p9]
12. ! [X0] : ((brave(X0) & calm(X0)) <=> (strong(X0) <~> ~humble(X0))) [input p11]
22. ~strong(john) [input p21]
23. kind(john) | calm(john) [input p22]
25. old(john) [input hypothesis]
41. ! [X0] : ((((~kind(X0) | old(X0)) & (kind(X0) | ~old(X0))) | (humble(X0) & creative(X0))) & ((~humble(X0) | ~creative(X0)) | ((~old(X0) | ~kind(X0)) & (kind(X0) | old(X0))))) [nnf transformation 4]
42. ! [X0] : ((((~kind(X0) | old(X0)) & (kind(X0) | ~old(X0))) | (humble(X0) & creative(X0))) & (~humble(X0) | ~creative(X0) | ((~old(X0) | ~kind(X0)) & (kind(X0) | old(X0))))) [flattening 41]
54. ! [X0] : ((((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | (~brave(X0) & ~humble(X0))) & ((brave(X0) | humble(X0)) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))))) [nnf transformation 9]
55. ! [X0] : ((((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | (~brave(X0) & ~humble(X0))) & (brave(X0) | humble(X0) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))))) [flattening 54]
56. ! [X0] : ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0))) [nnf transformation 10]
60. ! [X0] : (((brave(X0) & calm(X0)) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0)))) & (((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | (~brave(X0) | ~calm(X0)))) [nnf transformation 12]
61. ! [X0] : (((brave(X0) & calm(X0)) | ((strong(X0) | humble(X0)) & (~humble(X0) | ~strong(X0)))) & (((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | ~brave(X0) | ~calm(X0))) [flattening 60]
91. ~old(X0) | kind(X0) | humble(X0) [cnf transformation 42]
111. ~humble(X0) | strong(X0) | ~kind(X0) [cnf transformation 55]
112. ~brave(X0) | strong(X0) | ~kind(X0) [cnf transformation 55]
113. ~calm(X0) | brave(X0) [cnf transformation 56]
117. ~humble(X0) | strong(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 61]
122. brave(X0) | strong(X0) | humble(X0) [cnf transformation 61]
142. ~strong(john) [cnf transformation 22]
143. kind(john) | calm(john) [cnf transformation 23]
146. old(john) [cnf transformation 25]
225. ~calm(X0) | strong(X0) | ~humble(X0) [subsumption resolution 117,113]
290. 33 <=> calm(john) [avatar definition]
292. calm(john) <- (33) [avatar component clause 290]
294. 34 <=> kind(john) [avatar definition]
296. kind(john) <- (34) [avatar component clause 294]
297. 33 | 34 [avatar split clause 143,294,290]
353. kind(john) | humble(john) [resolution 91,146]
356. 44 <=> humble(john) [avatar definition]
358. humble(john) <- (44) [avatar component clause 356]
359. 44 | 34 [avatar split clause 353,294,356]
397. strong(X0) | humble(X0) | strong(X0) | ~kind(X0) [resolution 122,112]
401. strong(X0) | humble(X0) | ~kind(X0) [duplicate literal removal 397]
402. ~kind(X0) | strong(X0) [subsumption resolution 401,111]
434. strong(john) | ~humble(john) <- (33) [resolution 225,292]
437. ~humble(john) <- (33) [subsumption resolution 434,142]
438. $false <- (33, 44) [subsumption resolution 437,358]
439. ~33 | ~44 [avatar contradiction clause 438]
478. strong(john) <- (34) [resolution 402,296]
479. $false <- (34) [subsumption resolution 478,142]
480. ~34 [avatar contradiction clause 479]
481. $false [avatar sat refutation 297,359,439,480]
% SZS output end Proof for 1900440083253168431188015
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not funny is not brave or wise and vice versa.
Everyone who is both not tall and not strong is either not wise or not strong and vice versa.
Everyone who is both old and creative is either strong or not wise and vice versa.
If paul is not brave then alice is brave and vice versa.
If mary is creative or not calm then lucy is tall or not strong and vice versa.
Everyone who is either creative or not funny is brave and vice versa.
If lucy is both not kind and not humble then fred is both not generous and not curious.
Everyone who is either patient or tall is strong or not tall and vice versa.
Everyone who is not quiet is not wise or not calm.
Everyone who is either not wise or tall is both not rich and not quiet.
If mary is calm or not curious then mary is not old.
Everyone who is either calm or wise is both not patient and not strong.
If fred is both not quiet and not patient then someone is both tall and not happy.
Everyone who is not calm or humble is either not curious or not tall and vice versa.
If mary is not patient or not old then someone is not humble and vice versa.
Everyone who is happy or strong is both brave and not wise and vice versa.
Paul is brave.
Someone is generous or wise.
Someone is either kind or not rich.
Someone is kind or not wise.
Someone is not patient or funny.
Alice is both not rich and not wise.
Lucy is not generous or not patient.
Fred is not funny or patient. | Mary is quiet. | entailment | (![X]:((~patient(X)<~>~funny(X))<=>(~brave(X)|wise(X))))&
(![X]:((~tall(X)&~strong(X))<=>(~wise(X)<~>~strong(X))))&
(![X]:((old(X)&creative(X))<=>(strong(X)<~>~wise(X))))&
((~brave(paul))<=>(brave(alice)))&
(((creative(mary)|~calm(mary)))<=>((tall(lucy)|~strong(lucy))))&
(![X]:((creative(X)<~>~funny(X))<=>brave(X)))&
(((~kind(lucy)&~humble(lucy)))=>((~generous(fred)&~curious(fred))))&
(![X]:((patient(X)<~>tall(X))<=>(strong(X)|~tall(X))))&
(![X]:(~quiet(X)=>(~wise(X)|~calm(X))))&
(![X]:((~wise(X)<~>tall(X))=>(~rich(X)&~quiet(X))))&
(((calm(mary)|~curious(mary)))=>(~old(mary)))&
(![X]:((calm(X)<~>wise(X))=>(~patient(X)&~strong(X))))&
(((~quiet(fred)&~patient(fred)))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((~calm(X)|humble(X))<=>(~curious(X)<~>~tall(X))))&
(((~patient(mary)|~old(mary)))<=>(?[X]:(~humble(X))))&
(![X]:((happy(X)|strong(X))<=>(brave(X)&~wise(X))))&
(brave(paul))&
(?[X]:((generous(X)|wise(X))))&
(?[X]:((kind(X)<~>~rich(X))))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((~patient(X)|funny(X))))&
((~rich(alice)&~wise(alice)))&
((~generous(lucy)|~patient(lucy)))&
((~funny(fred)|patient(fred))) | quiet(mary) | [
"p1",
"p2",
"p7",
"p8",
"p10",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2292122553896868896655157
% SZS output start Proof for 2292122553896868896655157
2. ! [X0] : ((~strong(X0) & ~tall(X0)) <=> (~wise(X0) <~> ~strong(X0))) [input p1]
3. ! [X0] : ((creative(X0) & old(X0)) <=> (strong(X0) <~> ~wise(X0))) [input p2]
8. ! [X0] : ((patient(X0) <~> tall(X0)) <=> (~tall(X0) | strong(X0))) [input p7]
9. ! [X0] : (~quiet(X0) => (~calm(X0) | ~wise(X0))) [input p8]
11. (~curious(mary) | calm(mary)) => ~old(mary) [input p10]
12. ! [X0] : ((calm(X0) <~> wise(X0)) => (~strong(X0) & ~patient(X0))) [input p11]
14. ! [X0] : ((humble(X0) | ~calm(X0)) <=> (~curious(X0) <~> ~tall(X0))) [input p13]
16. ! [X0] : ((strong(X0) | happy(X0)) <=> (~wise(X0) & brave(X0))) [input p15]
25. ~quiet(mary) [input hypothesis]
28. ! [X0] : ((~calm(X0) | ~wise(X0)) | quiet(X0)) [ennf transformation 9]
29. ! [X0] : (~calm(X0) | ~wise(X0) | quiet(X0)) [flattening 28]
31. ~old(mary) | (curious(mary) & ~calm(mary)) [ennf transformation 11]
32. ! [X0] : ((~strong(X0) & ~patient(X0)) | (calm(X0) <=> wise(X0))) [ennf transformation 12]
37. ! [X0] : (((~strong(X0) & ~tall(X0)) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0)))) & (((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | (strong(X0) | tall(X0)))) [nnf transformation 2]
38. ! [X0] : (((~strong(X0) & ~tall(X0)) | ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0)))) & (((strong(X0) | wise(X0)) & (~strong(X0) | ~wise(X0))) | strong(X0) | tall(X0))) [flattening 37]
39. ! [X0] : (((creative(X0) & old(X0)) | ((strong(X0) | wise(X0)) & (~wise(X0) | ~strong(X0)))) & (((wise(X0) | ~strong(X0)) & (~wise(X0) | strong(X0))) | (~creative(X0) | ~old(X0)))) [nnf transformation 3]
40. ! [X0] : (((creative(X0) & old(X0)) | ((strong(X0) | wise(X0)) & (~wise(X0) | ~strong(X0)))) & (((wise(X0) | ~strong(X0)) & (~wise(X0) | strong(X0))) | ~creative(X0) | ~old(X0))) [flattening 39]
45. ! [X0] : ((((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (tall(X0) & ~strong(X0))) & ((~tall(X0) | strong(X0)) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0))))) [nnf transformation 8]
46. ! [X0] : ((((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | (tall(X0) & ~strong(X0))) & (~tall(X0) | strong(X0) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0))))) [flattening 45]
48. ! [X0] : ((~strong(X0) & ~patient(X0)) | ((calm(X0) | ~wise(X0)) & (wise(X0) | ~calm(X0)))) [nnf transformation 32]
51. ! [X0] : (((humble(X0) | ~calm(X0)) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0)))) & (((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | (~humble(X0) & calm(X0)))) [nnf transformation 14]
52. ! [X0] : ((humble(X0) | ~calm(X0) | ((~curious(X0) | tall(X0)) & (~tall(X0) | curious(X0)))) & (((tall(X0) | curious(X0)) & (~tall(X0) | ~curious(X0))) | (~humble(X0) & calm(X0)))) [flattening 51]
58. ! [X0] : (((strong(X0) | happy(X0)) | (wise(X0) | ~brave(X0))) & ((~wise(X0) & brave(X0)) | (~strong(X0) & ~happy(X0)))) [nnf transformation 16]
59. ! [X0] : ((strong(X0) | happy(X0) | wise(X0) | ~brave(X0)) & ((~wise(X0) & brave(X0)) | (~strong(X0) & ~happy(X0)))) [flattening 58]
76. strong(X0) | wise(X0) | strong(X0) | tall(X0) [cnf transformation 38]
79. ~strong(X0) | ~strong(X0) | wise(X0) [cnf transformation 38]
84. old(X0) | strong(X0) | wise(X0) [cnf transformation 40]
100. ~tall(X0) | strong(X0) | patient(X0) | ~tall(X0) [cnf transformation 46]
102. tall(X0) | patient(X0) | tall(X0) [cnf transformation 46]
105. ~calm(X0) | ~wise(X0) | quiet(X0) [cnf transformation 29]
111. ~old(mary) | curious(mary) [cnf transformation 31]
112. ~calm(X0) | wise(X0) | ~patient(X0) [cnf transformation 48]
113. ~wise(X0) | calm(X0) | ~patient(X0) [cnf transformation 48]
118. ~curious(X0) | ~tall(X0) | calm(X0) [cnf transformation 52]
130. ~wise(X0) | ~strong(X0) [cnf transformation 59]
142. ~quiet(mary) [cnf transformation 25]
143. ~tall(X0) | strong(X0) | patient(X0) [duplicate literal removal 100]
144. tall(X0) | patient(X0) [duplicate literal removal 102]
145. strong(X0) | wise(X0) | tall(X0) [duplicate literal removal 76]
146. ~strong(X0) | wise(X0) [duplicate literal removal 79]
147. tall(X0) | wise(X0) [subsumption resolution 145,146]
150. old(X0) | wise(X0) [subsumption resolution 84,146]
171. 5 <=> calm(mary) [avatar definition]
172. calm(mary) <- (5) [avatar component clause 171]
173. ~calm(mary) <- (~5) [avatar component clause 171]
200. strong(X0) | patient(X0) [subsumption resolution 143,144]
202. 11 <=> curious(mary) [avatar definition]
204. curious(mary) <- (11) [avatar component clause 202]
206. 12 <=> old(mary) [avatar definition]
208. ~old(mary) <- (~12) [avatar component clause 206]
209. 11 | ~12 [avatar split clause 111,206,202]
245. ~strong(X0) [subsumption resolution 130,146]
298. wise(mary) <- (~12) [resolution 150,208]
302. patient(X3) [resolution 200,245]
357. calm(mary) | ~patient(mary) <- (~12) [resolution 113,298]
359. ~patient(mary) <- (~5, ~12) [subsumption resolution 357,173]
360. $false <- (~5, ~12) [subsumption resolution 359,302]
361. 5 | 12 [avatar contradiction clause 360]
376. wise(mary) | ~patient(mary) <- (5) [resolution 172,112]
377. ~wise(mary) | quiet(mary) <- (5) [resolution 172,105]
378. wise(mary) <- (5) [subsumption resolution 376,302]
379. quiet(mary) <- (5) [subsumption resolution 377,378]
380. $false <- (5) [subsumption resolution 379,142]
381. ~5 [avatar contradiction clause 380]
385. ~tall(mary) | calm(mary) <- (11) [resolution 118,204]
386. ~tall(mary) <- (~5, 11) [subsumption resolution 385,173]
395. wise(mary) <- (~5, 11) [resolution 386,147]
475. calm(mary) | ~patient(mary) <- (~5, 11) [resolution 395,113]
478. ~patient(mary) <- (~5, 11) [subsumption resolution 475,173]
479. $false <- (~5, 11) [subsumption resolution 478,302]
480. 5 | ~11 [avatar contradiction clause 479]
481. $false [avatar sat refutation 209,361,381,480]
% SZS output end Proof for 2292122553896868896655157
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm or tall then someone is both not curious and old and vice versa. Everyone who is either tall or brave is both not creative and not curious and vice versa. Everyone who is both not curious and patient is patient or not humble. Everyone who is both not generous and old is generous or brave and vice versa. Everyone who is not tall is funny and vice versa. Everyone who is both not patient and tall is not creative and vice versa. If paul is not brave or calm then susan is either wise or not humble. If someone is old then someone is not humble. If someone is not curious or wise then alice is humble or happy and vice versa. Everyone who is not quiet or not humble is either tall or not rich and vice versa. Everyone who is not generous is not patient or not old and vice versa. Everyone who is curious or not tall is wise or not calm. If someone is both wise and calm then lucy is either not patient or not happy and vice versa. If paul is not generous then someone is either not curious or not rich. If alice is happy then someone is either curious or not creative and vice versa. If susan is both patient and not calm then someone is not quiet. Someone is either not brave or quiet. Someone is either not patient or not calm. Paul is strong or happy. Fred is quiet. Lucy is wise. Lucy is either not old or humble. | Alice is brave. | contradiction | ((?[X]:((~calm(X)|tall(X))))<=>(?[X]:((~curious(X)&old(X)))))&
(![X]:((tall(X)<~>brave(X))<=>(~creative(X)&~curious(X))))&
(![X]:((~curious(X)&patient(X))=>(patient(X)|~humble(X))))&
(![X]:((~generous(X)&old(X))<=>(generous(X)|brave(X))))&
(![X]:(~tall(X)<=>funny(X)))&
(![X]:((~patient(X)&tall(X))<=>~creative(X)))&
(((~brave(paul)|calm(paul)))=>((wise(susan)<~>~humble(susan))))&
((?[X]:(old(X)))=>(?[X]:(~humble(X))))&
((?[X]:((~curious(X)|wise(X))))<=>((humble(alice)|happy(alice))))&
(![X]:((~quiet(X)|~humble(X))<=>(tall(X)<~>~rich(X))))&
(![X]:(~generous(X)<=>(~patient(X)|~old(X))))&
(![X]:((curious(X)|~tall(X))=>(wise(X)|~calm(X))))&
((?[X]:((wise(X)&calm(X))))<=>((~patient(lucy)<~>~happy(lucy))))&
((~generous(paul))=>(?[X]:((~curious(X)<~>~rich(X)))))&
((happy(alice))<=>(?[X]:((curious(X)<~>~creative(X)))))&
(((patient(susan)&~calm(susan)))=>(?[X]:(~quiet(X))))&
(?[X]:((~brave(X)<~>quiet(X))))&
(?[X]:((~patient(X)<~>~calm(X))))&
((strong(paul)|happy(paul)))&
(quiet(fred))&
(wise(lucy))&
((~old(lucy)<~>humble(lucy))) | brave(alice) | [
"p0",
"p1",
"p3",
"p5",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 363751796922026374837260
% SZS output start Proof for 363751796922026374837260
1. ? [X0] : (tall(X0) | ~calm(X0)) <=> ? [X0] : (old(X0) & ~curious(X0)) [input p0]
2. ! [X0] : ((tall(X0) <~> brave(X0)) <=> (~curious(X0) & ~creative(X0))) [input p1]
4. ! [X0] : ((old(X0) & ~generous(X0)) <=> (brave(X0) | generous(X0))) [input p3]
6. ! [X0] : ((tall(X0) & ~patient(X0)) <=> ~creative(X0)) [input p5]
11. ! [X0] : (~generous(X0) <=> (~old(X0) | ~patient(X0))) [input p10]
23. brave(alice) [input hypothesis]
24. ? [X0] : (tall(X0) | ~calm(X0)) <=> ? [X1] : (old(X1) & ~curious(X1)) [rectify 1]
36. (? [X0] : (tall(X0) | ~calm(X0)) | ! [X1] : (~old(X1) | curious(X1))) & (? [X1] : (old(X1) & ~curious(X1)) | ! [X0] : (~tall(X0) & calm(X0))) [nnf transformation 24]
37. (? [X0] : (tall(X0) | ~calm(X0)) | ! [X1] : (~old(X1) | curious(X1))) & (? [X2] : (old(X2) & ~curious(X2)) | ! [X3] : (~tall(X3) & calm(X3))) [rectify 36]
38. ? [X0] : (tall(X0) | ~calm(X0)) => (tall(sK0) | ~calm(sK0)) [choice axiom]
39. ? [X2] : (old(X2) & ~curious(X2)) => (old(sK1) & ~curious(sK1)) [choice axiom]
40. ((tall(sK0) | ~calm(sK0)) | ! [X1] : (~old(X1) | curious(X1))) & ((old(sK1) & ~curious(sK1)) | ! [X3] : (~tall(X3) & calm(X3))) [skolemisation 37,39,38]
41. ! [X0] : ((((~brave(X0) | ~tall(X0)) & (brave(X0) | tall(X0))) | (curious(X0) | creative(X0))) & ((~curious(X0) & ~creative(X0)) | ((tall(X0) | ~brave(X0)) & (brave(X0) | ~tall(X0))))) [nnf transformation 2]
42. ! [X0] : ((((~brave(X0) | ~tall(X0)) & (brave(X0) | tall(X0))) | curious(X0) | creative(X0)) & ((~curious(X0) & ~creative(X0)) | ((tall(X0) | ~brave(X0)) & (brave(X0) | ~tall(X0))))) [flattening 41]
43. ! [X0] : (((old(X0) & ~generous(X0)) | (~brave(X0) & ~generous(X0))) & ((brave(X0) | generous(X0)) | (~old(X0) | generous(X0)))) [nnf transformation 4]
44. ! [X0] : (((old(X0) & ~generous(X0)) | (~brave(X0) & ~generous(X0))) & (brave(X0) | generous(X0) | ~old(X0) | generous(X0))) [flattening 43]
46. ! [X0] : (((tall(X0) & ~patient(X0)) | creative(X0)) & (~creative(X0) | (~tall(X0) | patient(X0)))) [nnf transformation 6]
47. ! [X0] : (((tall(X0) & ~patient(X0)) | creative(X0)) & (~creative(X0) | ~tall(X0) | patient(X0))) [flattening 46]
59. ! [X0] : ((~generous(X0) | (old(X0) & patient(X0))) & ((~old(X0) | ~patient(X0)) | generous(X0))) [nnf transformation 11]
60. ! [X0] : ((~generous(X0) | (old(X0) & patient(X0))) & (~old(X0) | ~patient(X0) | generous(X0))) [flattening 59]
82. ~curious(sK1) | ~tall(X3) [cnf transformation 40]
84. old(sK1) | ~tall(X3) [cnf transformation 40]
87. ~creative(X0) | tall(X0) | ~brave(X0) [cnf transformation 42]
91. ~brave(X0) | ~tall(X0) | curious(X0) | creative(X0) [cnf transformation 42]
93. brave(X0) | generous(X0) | ~old(X0) | generous(X0) [cnf transformation 44]
94. ~generous(X0) | ~generous(X0) [cnf transformation 44]
100. ~creative(X0) | ~tall(X0) | patient(X0) [cnf transformation 47]
102. creative(X0) | tall(X0) [cnf transformation 47]
118. ~old(X0) | ~patient(X0) | generous(X0) [cnf transformation 60]
144. brave(alice) [cnf transformation 23]
145. brave(X0) | generous(X0) | ~old(X0) [duplicate literal removal 93]
146. ~generous(X0) [duplicate literal removal 94]
160. 4 <=> ! [X3] : ~tall(X3) [avatar definition]
161. ~tall(X3) <- (4) [avatar component clause 160]
163. 5 <=> old(sK1) [avatar definition]
165. old(sK1) <- (5) [avatar component clause 163]
166. 4 | 5 [avatar split clause 84,163,160]
172. 7 <=> curious(sK1) [avatar definition]
174. ~curious(sK1) <- (~7) [avatar component clause 172]
175. 4 | ~7 [avatar split clause 82,172,160]
177. ~old(X0) | brave(X0) [subsumption resolution 145,146]
232. ~patient(X0) | ~old(X0) [subsumption resolution 118,146]
335. brave(sK1) <- (5) [resolution 177,165]
350. tall(X0) | ~brave(X0) | tall(X0) [resolution 87,102]
352. ~brave(X0) | tall(X0) [duplicate literal removal 350]
370. 45 <=> tall(alice) [avatar definition]
372. tall(alice) <- (45) [avatar component clause 370]
376. tall(alice) [resolution 352,144]
377. tall(sK1) <- (5) [resolution 352,335]
378. 45 [avatar split clause 376,370]
463. ~tall(sK1) | curious(sK1) | creative(sK1) <- (5) [resolution 91,335]
527. curious(sK1) | creative(sK1) <- (5) [subsumption resolution 463,377]
528. creative(sK1) <- (5, ~7) [subsumption resolution 527,174]
541. ~tall(sK1) | patient(sK1) <- (5, ~7) [resolution 528,100]
544. patient(sK1) <- (5, ~7) [subsumption resolution 541,377]
545. ~old(sK1) <- (5, ~7) [resolution 544,232]
547. $false <- (5, ~7) [subsumption resolution 545,165]
548. ~5 | 7 [avatar contradiction clause 547]
555. $false <- (4, 45) [resolution 161,372]
556. ~4 | ~45 [avatar contradiction clause 555]
558. $false [avatar sat refutation 166,175,378,548,556]
% SZS output end Proof for 363751796922026374837260
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both happy and generous then someone is not rich and vice versa.
If paul is not curious then john is both not patient and calm and vice versa.
Everyone who is quiet is both not brave and not funny.
Everyone who is not happy is both generous and brave and vice versa.
If susan is not strong then john is either not old or not funny and vice versa.
If someone is not old or not wise then someone is old and vice versa.
If someone is both not patient and not brave then someone is either happy or not rich and vice versa.
Everyone who is either not brave or funny is either not happy or not calm and vice versa.
If mary is tall or curious then fred is not quiet or not humble and vice versa.
Everyone who is both not tall and not brave is either not patient or not quiet and vice versa.
Everyone who is wise is patient.
Everyone who is tall or curious is both not brave and calm and vice versa.
If mary is both humble and quiet then paul is not kind and vice versa.
Everyone who is not happy is both strong and not tall and vice versa.
Everyone who is wise is either humble or generous.
Everyone who is both not curious and not calm is either tall or brave.
John is both wise and funny.
Someone is both not calm and not wise.
Fred is old or not kind.
Fred is either not humble or creative.
Someone is either patient or humble.
Someone is both not creative and not happy.
Someone is either tall or not wise. | John is strong. | contradiction | ((?[X]:((happy(X)&generous(X))))<=>(?[X]:(~rich(X))))&
((~curious(paul))<=>((~patient(john)&calm(john))))&
(![X]:(quiet(X)=>(~brave(X)&~funny(X))))&
(![X]:(~happy(X)<=>(generous(X)&brave(X))))&
((~strong(susan))<=>((~old(john)<~>~funny(john))))&
((?[X]:((~old(X)|~wise(X))))<=>(?[X]:(old(X))))&
((?[X]:((~patient(X)&~brave(X))))<=>(?[X]:((happy(X)<~>~rich(X)))))&
(![X]:((~brave(X)<~>funny(X))<=>(~happy(X)<~>~calm(X))))&
(((tall(mary)|curious(mary)))<=>((~quiet(fred)|~humble(fred))))&
(![X]:((~tall(X)&~brave(X))<=>(~patient(X)<~>~quiet(X))))&
(![X]:(wise(X)=>patient(X)))&
(![X]:((tall(X)|curious(X))<=>(~brave(X)&calm(X))))&
(((humble(mary)&quiet(mary)))<=>(~kind(paul)))&
(![X]:(~happy(X)<=>(strong(X)&~tall(X))))&
(![X]:(wise(X)=>(humble(X)<~>generous(X))))&
(![X]:((~curious(X)&~calm(X))=>(tall(X)<~>brave(X))))&
((wise(john)&funny(john)))&
(?[X]:((~calm(X)&~wise(X))))&
((old(fred)|~kind(fred)))&
((~humble(fred)<~>creative(fred)))&
(?[X]:((patient(X)<~>humble(X))))&
(?[X]:((~creative(X)&~happy(X))))&
(?[X]:((tall(X)<~>~wise(X)))) | strong(john) | [
"p2",
"p3",
"p9",
"p10",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 79109576100528055139331
% SZS output start Proof for 79109576100528055139331
3. ! [X0] : (quiet(X0) => (~funny(X0) & ~brave(X0))) [input p2]
4. ! [X0] : (~happy(X0) <=> (brave(X0) & generous(X0))) [input p3]
10. ! [X0] : ((~brave(X0) & ~tall(X0)) <=> (~patient(X0) <~> ~quiet(X0))) [input p9]
11. ! [X0] : (wise(X0) => patient(X0)) [input p10]
14. ! [X0] : (~happy(X0) <=> (~tall(X0) & strong(X0))) [input p13]
17. funny(john) & wise(john) [input p16]
24. strong(john) [input hypothesis]
28. ! [X0] : ((~funny(X0) & ~brave(X0)) | ~quiet(X0)) [ennf transformation 3]
29. ! [X0] : (patient(X0) | ~wise(X0)) [ennf transformation 11]
40. ! [X0] : ((~happy(X0) | (~brave(X0) | ~generous(X0))) & ((brave(X0) & generous(X0)) | happy(X0))) [nnf transformation 4]
41. ! [X0] : ((~happy(X0) | ~brave(X0) | ~generous(X0)) & ((brave(X0) & generous(X0)) | happy(X0))) [flattening 40]
56. ! [X0] : (((~brave(X0) & ~tall(X0)) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0)))) & (((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | (brave(X0) | tall(X0)))) [nnf transformation 10]
57. ! [X0] : (((~brave(X0) & ~tall(X0)) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0)))) & (((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | brave(X0) | tall(X0))) [flattening 56]
62. ! [X0] : ((~happy(X0) | (tall(X0) | ~strong(X0))) & ((~tall(X0) & strong(X0)) | happy(X0))) [nnf transformation 14]
63. ! [X0] : ((~happy(X0) | tall(X0) | ~strong(X0)) & ((~tall(X0) & strong(X0)) | happy(X0))) [flattening 62]
83. ~brave(X0) | ~quiet(X0) [cnf transformation 28]
84. ~funny(X0) | ~quiet(X0) [cnf transformation 28]
86. brave(X0) | happy(X0) [cnf transformation 41]
116. ~tall(X0) | ~patient(X0) | quiet(X0) [cnf transformation 57]
118. ~brave(X0) | ~patient(X0) | quiet(X0) [cnf transformation 57]
119. ~wise(X0) | patient(X0) [cnf transformation 29]
130. ~strong(X0) | tall(X0) | ~happy(X0) [cnf transformation 63]
135. wise(john) [cnf transformation 17]
136. funny(john) [cnf transformation 17]
148. strong(john) [cnf transformation 24]
171. 6 <=> patient(john) [avatar definition]
173. patient(john) <- (6) [avatar component clause 171]
186. 9 <=> funny(john) [avatar definition]
188. funny(john) <- (9) [avatar component clause 186]
280. ~brave(X0) | ~patient(X0) [subsumption resolution 118,83]
298. 9 [avatar split clause 136,186]
334. ~quiet(john) <- (9) [resolution 84,188]
337. patient(john) [resolution 119,135]
340. 6 [avatar split clause 337,171]
348. ~patient(X0) | happy(X0) [resolution 280,86]
354. tall(john) | ~happy(john) [resolution 130,148]
357. 39 <=> happy(john) [avatar definition]
361. 40 <=> tall(john) [avatar definition]
363. tall(john) <- (40) [avatar component clause 361]
364. ~39 | 40 [avatar split clause 354,361,357]
376. happy(john) <- (6) [resolution 348,173]
379. 39 | ~6 [avatar split clause 376,171,357]
384. ~patient(john) | quiet(john) <- (40) [resolution 363,116]
389. quiet(john) <- (6, 40) [subsumption resolution 384,173]
390. $false <- (6, 9, 40) [subsumption resolution 389,334]
391. ~6 | ~9 | ~40 [avatar contradiction clause 390]
392. $false [avatar sat refutation 298,340,364,379,391]
% SZS output end Proof for 79109576100528055139331
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both not generous and humble then someone is both wise and not kind.
If susan is either rich or not old then alice is both not creative and strong and vice versa.
If someone is either wise or humble then mary is either not curious or creative.
If someone is not generous then someone is either not patient or not curious and vice versa.
Everyone who is creative or not curious is not calm and vice versa.
If someone is not brave or not patient then mary is either rich or not strong.
Everyone who is both rich and brave is not curious and vice versa.
Everyone who is not old or not generous is not patient.
If paul is brave or not generous then lucy is both calm and happy and vice versa.
If lucy is not funny then lucy is brave or funny.
Everyone who is not tall or rich is tall and vice versa.
Everyone who is either not calm or not patient is not rich.
If paul is wise or not brave then someone is both curious and kind and vice versa.
If mary is both not wise and not humble then paul is both not creative and humble.
Everyone who is either old or kind is either rich or old.
If john is humble or not strong then someone is calm and vice versa.
Someone is not old.
Someone is not brave.
Someone is not strong or not brave.
Someone is tall or rich.
John is calm.
Someone is not curious.
Susan is funny or strong. | Susan is not tall. | contradiction | (((~generous(lucy)&humble(lucy)))=>(?[X]:((wise(X)&~kind(X)))))&
(((rich(susan)<~>~old(susan)))<=>((~creative(alice)&strong(alice))))&
((?[X]:((wise(X)<~>humble(X))))=>((~curious(mary)<~>creative(mary))))&
((?[X]:(~generous(X)))<=>(?[X]:((~patient(X)<~>~curious(X)))))&
(![X]:((creative(X)|~curious(X))<=>~calm(X)))&
((?[X]:((~brave(X)|~patient(X))))=>((rich(mary)<~>~strong(mary))))&
(![X]:((rich(X)&brave(X))<=>~curious(X)))&
(![X]:((~old(X)|~generous(X))=>~patient(X)))&
(((brave(paul)|~generous(paul)))<=>((calm(lucy)&happy(lucy))))&
((~funny(lucy))=>((brave(lucy)|funny(lucy))))&
(![X]:((~tall(X)|rich(X))<=>tall(X)))&
(![X]:((~calm(X)<~>~patient(X))=>~rich(X)))&
(((wise(paul)|~brave(paul)))<=>(?[X]:((curious(X)&kind(X)))))&
(((~wise(mary)&~humble(mary)))=>((~creative(paul)&humble(paul))))&
(![X]:((old(X)<~>kind(X))=>(rich(X)<~>old(X))))&
(((humble(john)|~strong(john)))<=>(?[X]:(calm(X))))&
(?[X]:(~old(X)))&
(?[X]:(~brave(X)))&
(?[X]:((~strong(X)|~brave(X))))&
(?[X]:((tall(X)|rich(X))))&
(calm(john))&
(?[X]:(~curious(X)))&
((funny(susan)|strong(susan))) | ~tall(susan) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2260588092616451199926090
% SZS output start Proof for 2260588092616451199926090
11. ! [X0] : ((rich(X0) | ~tall(X0)) <=> tall(X0)) [input p10]
24. ~tall(susan) [input hypothesis]
54. ! [X0] : (((rich(X0) | ~tall(X0)) | ~tall(X0)) & (tall(X0) | (~rich(X0) & tall(X0)))) [nnf transformation 11]
55. ! [X0] : ((rich(X0) | ~tall(X0) | ~tall(X0)) & (tall(X0) | (~rich(X0) & tall(X0)))) [flattening 54]
111. tall(X0) | tall(X0) [cnf transformation 55]
136. ~tall(susan) [cnf transformation 24]
139. tall(X0) [duplicate literal removal 111]
328. $false [subsumption resolution 136,139]
% SZS output end Proof for 2260588092616451199926090
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind or strong then paul is quiet.
If someone is either not happy or not calm then alice is both tall and not rich and vice versa.
If someone is not calm or not brave then someone is not calm.
If john is both tall and patient then someone is funny or humble and vice versa.
Everyone who is both humble and calm is not curious or humble.
Everyone who is both not strong and not brave is both happy and not brave and vice versa.
If someone is generous then susan is either not happy or humble.
Everyone who is humble or not creative is either humble or not happy.
Everyone who is not generous or humble is not creative.
Everyone who is both tall and strong is both not humble and not brave and vice versa.
Everyone who is both creative and not curious is both funny and not calm and vice versa.
If fred is not happy then someone is calm or curious and vice versa.
If john is not creative or humble then someone is wise or patient and vice versa.
Everyone who is both not quiet and not creative is happy and vice versa.
Everyone who is both not old and not strong is curious or not patient.
If someone is not happy or not curious then someone is both kind and quiet.
John is either generous or not tall.
John is either kind or not happy.
Someone is both happy and not patient.
John is quiet or strong.
Someone is brave or not old.
John is either brave or not generous.
Alice is humble.
Lucy is rich. | John is humble. | contradiction | ((?[X]:((kind(X)|strong(X))))=>(quiet(paul)))&
((?[X]:((~happy(X)<~>~calm(X))))<=>((tall(alice)&~rich(alice))))&
((?[X]:((~calm(X)|~brave(X))))=>(?[X]:(~calm(X))))&
(((tall(john)&patient(john)))<=>(?[X]:((funny(X)|humble(X)))))&
(![X]:((humble(X)&calm(X))=>(~curious(X)|humble(X))))&
(![X]:((~strong(X)&~brave(X))<=>(happy(X)&~brave(X))))&
((?[X]:(generous(X)))=>((~happy(susan)<~>humble(susan))))&
(![X]:((humble(X)|~creative(X))=>(humble(X)<~>~happy(X))))&
(![X]:((~generous(X)|humble(X))=>~creative(X)))&
(![X]:((tall(X)&strong(X))<=>(~humble(X)&~brave(X))))&
(![X]:((creative(X)&~curious(X))<=>(funny(X)&~calm(X))))&
((~happy(fred))<=>(?[X]:((calm(X)|curious(X)))))&
(((~creative(john)|humble(john)))<=>(?[X]:((wise(X)|patient(X)))))&
(![X]:((~quiet(X)&~creative(X))<=>happy(X)))&
(![X]:((~old(X)&~strong(X))=>(curious(X)|~patient(X))))&
((?[X]:((~happy(X)|~curious(X))))=>(?[X]:((kind(X)&quiet(X)))))&
((generous(john)<~>~tall(john)))&
((kind(john)<~>~happy(john)))&
(?[X]:((happy(X)&~patient(X))))&
((quiet(john)|strong(john)))&
(?[X]:((brave(X)|~old(X))))&
((brave(john)<~>~generous(john)))&
(humble(alice))&
(rich(lucy)) | humble(john) | [
"p3",
"p7",
"p9",
"p13",
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6689389511917963935423200
% SZS output start Proof for 6689389511917963935423200
4. (patient(john) & tall(john)) <=> ? [X0] : (humble(X0) | funny(X0)) [input p3]
8. ! [X0] : ((~creative(X0) | humble(X0)) => (humble(X0) <~> ~happy(X0))) [input p7]
10. ! [X0] : ((strong(X0) & tall(X0)) <=> (~brave(X0) & ~humble(X0))) [input p9]
14. ! [X0] : ((~creative(X0) & ~quiet(X0)) <=> happy(X0)) [input p13]
20. strong(john) | quiet(john) [input p19]
23. humble(alice) [input p22]
25. humble(john) [input hypothesis]
33. ! [X0] : ((humble(X0) <~> ~happy(X0)) | (creative(X0) & ~humble(X0))) [ennf transformation 8]
46. ((patient(john) & tall(john)) | ! [X0] : (~humble(X0) & ~funny(X0))) & (? [X0] : (humble(X0) | funny(X0)) | (~patient(john) | ~tall(john))) [nnf transformation 4]
47. ((patient(john) & tall(john)) | ! [X0] : (~humble(X0) & ~funny(X0))) & (? [X0] : (humble(X0) | funny(X0)) | ~patient(john) | ~tall(john)) [flattening 46]
48. ((patient(john) & tall(john)) | ! [X0] : (~humble(X0) & ~funny(X0))) & (? [X1] : (humble(X1) | funny(X1)) | ~patient(john) | ~tall(john)) [rectify 47]
49. ? [X1] : (humble(X1) | funny(X1)) => (humble(sK2) | funny(sK2)) [choice axiom]
50. ((patient(john) & tall(john)) | ! [X0] : (~humble(X0) & ~funny(X0))) & ((humble(sK2) | funny(sK2)) | ~patient(john) | ~tall(john)) [skolemisation 48,49]
54. ! [X0] : (((happy(X0) | ~humble(X0)) & (~happy(X0) | humble(X0))) | (creative(X0) & ~humble(X0))) [nnf transformation 33]
55. ! [X0] : (((strong(X0) & tall(X0)) | (brave(X0) | humble(X0))) & ((~brave(X0) & ~humble(X0)) | (~strong(X0) | ~tall(X0)))) [nnf transformation 10]
56. ! [X0] : (((strong(X0) & tall(X0)) | brave(X0) | humble(X0)) & ((~brave(X0) & ~humble(X0)) | ~strong(X0) | ~tall(X0))) [flattening 55]
68. ! [X0] : (((~creative(X0) & ~quiet(X0)) | ~happy(X0)) & (happy(X0) | (creative(X0) | quiet(X0)))) [nnf transformation 14]
69. ! [X0] : (((~creative(X0) & ~quiet(X0)) | ~happy(X0)) & (happy(X0) | creative(X0) | quiet(X0))) [flattening 68]
92. tall(john) | ~humble(X0) [cnf transformation 50]
104. happy(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 54]
108. ~humble(X0) | ~strong(X0) | ~tall(X0) [cnf transformation 56]
124. ~happy(X0) | ~quiet(X0) [cnf transformation 69]
137. strong(john) | quiet(john) [cnf transformation 20]
141. humble(alice) [cnf transformation 23]
143. humble(john) [cnf transformation 25]
144. ~humble(X0) | happy(X0) [duplicate literal removal 104]
198. 13 <=> ! [X0] : ~humble(X0) [avatar definition]
199. ~humble(X0) <- (13) [avatar component clause 198]
210. 16 <=> tall(john) [avatar definition]
212. tall(john) <- (16) [avatar component clause 210]
213. 13 | 16 [avatar split clause 92,210,198]
273. 30 <=> humble(john) [avatar definition]
274. humble(john) <- (30) [avatar component clause 273]
315. 39 <=> happy(john) [avatar definition]
317. happy(john) <- (39) [avatar component clause 315]
321. 40 <=> quiet(john) [avatar definition]
325. 41 <=> strong(john) [avatar definition]
327. strong(john) <- (41) [avatar component clause 325]
328. 40 | 41 [avatar split clause 137,325,321]
344. 30 [avatar split clause 143,273]
353. $false <- (13) [resolution 199,141]
354. ~13 [avatar contradiction clause 353]
361. happy(john) <- (30) [resolution 144,274]
364. 39 | ~30 [avatar split clause 361,273,315]
365. ~quiet(john) <- (39) [resolution 317,124]
368. ~40 | ~39 [avatar split clause 365,315,321]
441. ~strong(john) | ~tall(john) <- (30) [resolution 108,274]
444. ~tall(john) <- (30, 41) [subsumption resolution 441,327]
445. $false <- (16, 30, 41) [subsumption resolution 444,212]
446. ~16 | ~30 | ~41 [avatar contradiction clause 445]
447. $false [avatar sat refutation 213,328,344,354,364,368,446]
% SZS output end Proof for 6689389511917963935423200
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or creative is not old or not funny.
Everyone who is wise or patient is both not tall and strong and vice versa.
Everyone who is either not tall or patient is generous or tall.
If paul is rich then someone is either quiet or creative.
Everyone who is both not strong and not patient is not humble or calm.
Everyone who is brave is either not humble or not wise.
If someone is either wise or not quiet then fred is both not brave and calm.
Everyone who is old or not kind is both curious and not happy and vice versa.
Everyone who is brave is not quiet and vice versa.
Everyone who is either old or not patient is either not old or tall and vice versa.
Everyone who is rich or generous is both not creative and wise and vice versa.
Everyone who is not wise is either not tall or wise.
If john is both generous and happy then someone is kind or not old.
Everyone who is not old is not humble or calm.
Everyone who is not quiet or not generous is both tall and happy.
Everyone who is either not funny or humble is not tall or quiet.
Someone is either not quiet or not rich.
Mary is either not patient or old.
Lucy is not patient or happy.
Someone is either not curious or curious.
Someone is either generous or rich.
Paul is strong.
Someone is either not quiet or not calm. | Mary is creative. | contradiction | (![X]:((calm(X)|creative(X))=>(~old(X)|~funny(X))))&
(![X]:((wise(X)|patient(X))<=>(~tall(X)&strong(X))))&
(![X]:((~tall(X)<~>patient(X))=>(generous(X)|tall(X))))&
((rich(paul))=>(?[X]:((quiet(X)<~>creative(X)))))&
(![X]:((~strong(X)&~patient(X))=>(~humble(X)|calm(X))))&
(![X]:(brave(X)=>(~humble(X)<~>~wise(X))))&
((?[X]:((wise(X)<~>~quiet(X))))=>((~brave(fred)&calm(fred))))&
(![X]:((old(X)|~kind(X))<=>(curious(X)&~happy(X))))&
(![X]:(brave(X)<=>~quiet(X)))&
(![X]:((old(X)<~>~patient(X))<=>(~old(X)<~>tall(X))))&
(![X]:((rich(X)|generous(X))<=>(~creative(X)&wise(X))))&
(![X]:(~wise(X)=>(~tall(X)<~>wise(X))))&
(((generous(john)&happy(john)))=>(?[X]:((kind(X)|~old(X)))))&
(![X]:(~old(X)=>(~humble(X)|calm(X))))&
(![X]:((~quiet(X)|~generous(X))=>(tall(X)&happy(X))))&
(![X]:((~funny(X)<~>humble(X))=>(~tall(X)|quiet(X))))&
(?[X]:((~quiet(X)<~>~rich(X))))&
((~patient(mary)<~>old(mary)))&
((~patient(lucy)|happy(lucy)))&
(?[X]:((~curious(X)<~>curious(X))))&
(?[X]:((generous(X)<~>rich(X))))&
(strong(paul))&
(?[X]:((~quiet(X)<~>~calm(X)))) | creative(mary) | [
"p1",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9184799253676587130935752
% SZS output start Proof for 9184799253676587130935752
2. ! [X0] : ((patient(X0) | wise(X0)) <=> (strong(X0) & ~tall(X0))) [input p1]
10. ! [X0] : ((old(X0) <~> ~patient(X0)) <=> (~old(X0) <~> tall(X0))) [input p9]
11. ! [X0] : ((generous(X0) | rich(X0)) <=> (wise(X0) & ~creative(X0))) [input p10]
15. ! [X0] : ((~generous(X0) | ~quiet(X0)) => (happy(X0) & tall(X0))) [input p14]
24. creative(mary) [input hypothesis]
41. ! [X0] : ((happy(X0) & tall(X0)) | (generous(X0) & quiet(X0))) [ennf transformation 15]
44. ! [X0] : (((patient(X0) | wise(X0)) | (~strong(X0) | tall(X0))) & ((strong(X0) & ~tall(X0)) | (~patient(X0) & ~wise(X0)))) [nnf transformation 2]
45. ! [X0] : ((patient(X0) | wise(X0) | ~strong(X0) | tall(X0)) & ((strong(X0) & ~tall(X0)) | (~patient(X0) & ~wise(X0)))) [flattening 44]
54. ! [X0] : ((((patient(X0) | ~old(X0)) & (~patient(X0) | old(X0))) | ((~old(X0) | ~tall(X0)) & (tall(X0) | old(X0)))) & (((~tall(X0) | old(X0)) & (tall(X0) | ~old(X0))) | ((old(X0) | patient(X0)) & (~patient(X0) | ~old(X0))))) [nnf transformation 10]
55. ! [X0] : (((generous(X0) | rich(X0)) | (~wise(X0) | creative(X0))) & ((wise(X0) & ~creative(X0)) | (~generous(X0) & ~rich(X0)))) [nnf transformation 11]
56. ! [X0] : ((generous(X0) | rich(X0) | ~wise(X0) | creative(X0)) & ((wise(X0) & ~creative(X0)) | (~generous(X0) & ~rich(X0)))) [flattening 55]
77. ~tall(X0) | ~patient(X0) [cnf transformation 45]
101. ~tall(X0) | old(X0) | old(X0) | patient(X0) [cnf transformation 54]
105. patient(X0) | ~old(X0) | ~old(X0) | ~tall(X0) [cnf transformation 54]
107. ~generous(X0) | ~creative(X0) [cnf transformation 56]
116. tall(X0) | generous(X0) [cnf transformation 41]
133. creative(mary) [cnf transformation 24]
136. ~tall(X0) | old(X0) | patient(X0) [duplicate literal removal 101]
138. patient(X0) | ~old(X0) | ~tall(X0) [duplicate literal removal 105]
173. ~old(X0) | ~tall(X0) [subsumption resolution 138,77]
175. ~tall(X0) | patient(X0) [subsumption resolution 136,173]
176. ~tall(X0) [subsumption resolution 175,77]
196. generous(X0) [subsumption resolution 116,176]
203. ~creative(X0) [resolution 107,196]
204. $false [resolution 203,133]
% SZS output end Proof for 9184799253676587130935752
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and not funny is either curious or not generous and vice versa. Everyone who is both tall and not generous is creative or wise and vice versa. If someone is not generous or not funny then lucy is either not generous or not wise and vice versa. Everyone who is creative is curious or generous and vice versa. Everyone who is not funny or rich is both not patient and not calm. Everyone who is either creative or not brave is either generous or tall and vice versa. Everyone who is both quiet and not strong is tall and vice versa. Everyone who is strong is happy. Everyone who is both not calm and old is both not patient and generous. Everyone who is both not curious and not generous is both not humble and not quiet and vice versa. Everyone who is not strong is both not strong and humble. If someone is tall or curious then someone is humble and vice versa. Everyone who is not tall is not wise or not patient and vice versa. Everyone who is either not funny or kind is either not old or happy and vice versa. If john is rich or creative then someone is not tall or humble. Everyone who is not happy is either wise or old. Alice is both not happy and funny. Paul is wise or tall. Alice is both not old and not rich. Someone is either not funny or not strong. John is both humble and not generous. | John is generous. | contradiction | (![X]:((quiet(X)&~funny(X))<=>(curious(X)<~>~generous(X))))&
(![X]:((tall(X)&~generous(X))<=>(creative(X)|wise(X))))&
((?[X]:((~generous(X)|~funny(X))))<=>((~generous(lucy)<~>~wise(lucy))))&
(![X]:(creative(X)<=>(curious(X)|generous(X))))&
(![X]:((~funny(X)|rich(X))=>(~patient(X)&~calm(X))))&
(![X]:((creative(X)<~>~brave(X))<=>(generous(X)<~>tall(X))))&
(![X]:((quiet(X)&~strong(X))<=>tall(X)))&
(![X]:(strong(X)=>happy(X)))&
(![X]:((~calm(X)&old(X))=>(~patient(X)&generous(X))))&
(![X]:((~curious(X)&~generous(X))<=>(~humble(X)&~quiet(X))))&
(![X]:(~strong(X)=>(~strong(X)&humble(X))))&
((?[X]:((tall(X)|curious(X))))<=>(?[X]:(humble(X))))&
(![X]:(~tall(X)<=>(~wise(X)|~patient(X))))&
(![X]:((~funny(X)<~>kind(X))<=>(~old(X)<~>happy(X))))&
(((rich(john)|creative(john)))=>(?[X]:((~tall(X)|humble(X)))))&
(![X]:(~happy(X)=>(wise(X)<~>old(X))))&
((~happy(alice)&funny(alice)))&
((wise(paul)|tall(paul)))&
((~old(alice)&~rich(alice)))&
(?[X]:((~funny(X)<~>~strong(X))))&
((humble(john)&~generous(john))) | generous(john) | [
"p1",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 2131133619699420449279708
% SZS output start Proof for 2131133619699420449279708
2. ! [X0] : ((~generous(X0) & tall(X0)) <=> (wise(X0) | creative(X0))) [input p1]
4. ! [X0] : (creative(X0) <=> (generous(X0) | curious(X0))) [input p3]
22. generous(john) [input hypothesis]
36. ! [X0] : (((~generous(X0) & tall(X0)) | (~wise(X0) & ~creative(X0))) & ((wise(X0) | creative(X0)) | (generous(X0) | ~tall(X0)))) [nnf transformation 2]
37. ! [X0] : (((~generous(X0) & tall(X0)) | (~wise(X0) & ~creative(X0))) & (wise(X0) | creative(X0) | generous(X0) | ~tall(X0))) [flattening 36]
42. ! [X0] : ((creative(X0) | (~generous(X0) & ~curious(X0))) & ((generous(X0) | curious(X0)) | ~creative(X0))) [nnf transformation 4]
43. ! [X0] : ((creative(X0) | (~generous(X0) & ~curious(X0))) & (generous(X0) | curious(X0) | ~creative(X0))) [flattening 42]
72. ~generous(X0) | ~creative(X0) [cnf transformation 37]
82. creative(X0) | ~generous(X0) [cnf transformation 43]
130. generous(john) [cnf transformation 22]
159. ~generous(X0) [subsumption resolution 82,72]
217. $false [subsumption resolution 130,159]
% SZS output end Proof for 2131133619699420449279708
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or not funny is both kind and not patient and vice versa.
If mary is rich or not generous then susan is happy and vice versa.
If fred is either happy or not kind then alice is generous.
Everyone who is either not rich or not tall is not creative and vice versa.
Everyone who is both rich and humble is not humble or not calm and vice versa.
Everyone who is happy is not curious or not kind.
If someone is rich or creative then mary is creative.
Everyone who is brave is patient.
If someone is either not calm or not rich then someone is strong or curious and vice versa.
If someone is not generous or old then someone is either kind or not brave.
If someone is both not happy and not generous then someone is brave or not creative and vice versa.
Everyone who is both funny and happy is both not humble and calm and vice versa.
If susan is generous or kind then paul is not creative or not generous.
Everyone who is humble is either rich or not happy and vice versa.
Everyone who is wise or calm is both brave and not wise.
Everyone who is both patient and not strong is not patient and vice versa.
John is not rich.
Someone is curious or generous.
Susan is both curious and humble.
Lucy is both not quiet and patient.
Someone is either not rich or kind.
Someone is rich or not wise.
Fred is both not tall and strong. | John is brave. | entailment | (![X]:((quiet(X)<~>~funny(X))<=>(kind(X)&~patient(X))))&
(((rich(mary)|~generous(mary)))<=>(happy(susan)))&
(((happy(fred)<~>~kind(fred)))=>(generous(alice)))&
(![X]:((~rich(X)<~>~tall(X))<=>~creative(X)))&
(![X]:((rich(X)&humble(X))<=>(~humble(X)|~calm(X))))&
(![X]:(happy(X)=>(~curious(X)|~kind(X))))&
((?[X]:((rich(X)|creative(X))))=>(creative(mary)))&
(![X]:(brave(X)=>patient(X)))&
((?[X]:((~calm(X)<~>~rich(X))))<=>(?[X]:((strong(X)|curious(X)))))&
((?[X]:((~generous(X)|old(X))))=>(?[X]:((kind(X)<~>~brave(X)))))&
((?[X]:((~happy(X)&~generous(X))))<=>(?[X]:((brave(X)|~creative(X)))))&
(![X]:((funny(X)&happy(X))<=>(~humble(X)&calm(X))))&
(((generous(susan)|kind(susan)))=>((~creative(paul)|~generous(paul))))&
(![X]:(humble(X)<=>(rich(X)<~>~happy(X))))&
(![X]:((wise(X)|calm(X))=>(brave(X)&~wise(X))))&
(![X]:((patient(X)&~strong(X))<=>~patient(X)))&
(~rich(john))&
(?[X]:((curious(X)|generous(X))))&
((curious(susan)&humble(susan)))&
((~quiet(lucy)&patient(lucy)))&
(?[X]:((~rich(X)<~>kind(X))))&
(?[X]:((rich(X)|~wise(X))))&
((~tall(fred)&strong(fred))) | brave(john) | [
"p4",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5928546065484678299826569
% SZS output start Proof for 5928546065484678299826569
5. ! [X0] : ((humble(X0) & rich(X0)) <=> (~calm(X0) | ~humble(X0))) [input p4]
15. ! [X0] : ((calm(X0) | wise(X0)) => (~wise(X0) & brave(X0))) [input p14]
17. ~rich(john) [input p16]
24. ~brave(john) [input hypothesis]
28. ! [X0] : (calm(X0) => brave(X0)) [pure predicate removal 15]
39. ! [X0] : (brave(X0) | ~calm(X0)) [ennf transformation 28]
46. ! [X0] : (((humble(X0) & rich(X0)) | (calm(X0) & humble(X0))) & ((~calm(X0) | ~humble(X0)) | (~humble(X0) | ~rich(X0)))) [nnf transformation 5]
47. ! [X0] : (((humble(X0) & rich(X0)) | (calm(X0) & humble(X0))) & (~calm(X0) | ~humble(X0) | ~humble(X0) | ~rich(X0))) [flattening 46]
89. calm(X0) | rich(X0) [cnf transformation 47]
119. ~calm(X0) | brave(X0) [cnf transformation 39]
123. ~rich(john) [cnf transformation 17]
133. ~brave(john) [cnf transformation 24]
283. brave(X1) | rich(X1) [resolution 119,89]
287. rich(john) [resolution 283,133]
290. $false [subsumption resolution 287,123]
% SZS output end Proof for 5928546065484678299826569
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and not humble then someone is wise or not patient and vice versa. Everyone who is both strong and generous is both humble and not creative and vice versa. Everyone who is either not kind or not brave is not creative. If someone is not curious then mary is not calm or not generous and vice versa. Everyone who is either not old or curious is both curious and not tall. Everyone who is both not creative and strong is humble or not tall. Everyone who is both strong and not funny is happy or not calm and vice versa. If someone is rich then someone is both happy and not brave and vice versa. Everyone who is either not old or not generous is not creative and vice versa. Everyone who is both not creative and not humble is tall and vice versa. Everyone who is both rich and not humble is either not humble or curious. If someone is both strong and old then someone is brave or not happy and vice versa. If paul is not tall then john is rich or not funny and vice versa. If someone is old or not happy then john is not curious or kind. Everyone who is not kind is not generous or creative. Everyone who is old or not calm is quiet or not tall. Someone is not old or not curious. John is brave or happy. John is calm or not happy. Alice is not strong or not rich. Someone is not old or not kind. | Paul is not patient. | contradiction | ((?[X]:((tall(X)&~humble(X))))<=>(?[X]:((wise(X)|~patient(X)))))&
(![X]:((strong(X)&generous(X))<=>(humble(X)&~creative(X))))&
(![X]:((~kind(X)<~>~brave(X))=>~creative(X)))&
((?[X]:(~curious(X)))<=>((~calm(mary)|~generous(mary))))&
(![X]:((~old(X)<~>curious(X))=>(curious(X)&~tall(X))))&
(![X]:((~creative(X)&strong(X))=>(humble(X)|~tall(X))))&
(![X]:((strong(X)&~funny(X))<=>(happy(X)|~calm(X))))&
((?[X]:(rich(X)))<=>(?[X]:((happy(X)&~brave(X)))))&
(![X]:((~old(X)<~>~generous(X))<=>~creative(X)))&
(![X]:((~creative(X)&~humble(X))<=>tall(X)))&
(![X]:((rich(X)&~humble(X))=>(~humble(X)<~>curious(X))))&
((?[X]:((strong(X)&old(X))))<=>(?[X]:((brave(X)|~happy(X)))))&
((~tall(paul))<=>((rich(john)|~funny(john))))&
((?[X]:((old(X)|~happy(X))))=>((~curious(john)|kind(john))))&
(![X]:(~kind(X)=>(~generous(X)|creative(X))))&
(![X]:((old(X)|~calm(X))=>(quiet(X)|~tall(X))))&
(?[X]:((~old(X)|~curious(X))))&
((brave(john)|happy(john)))&
((calm(john)|~happy(john)))&
((~strong(alice)|~rich(alice)))&
(?[X]:((~old(X)|~kind(X)))) | ~patient(paul) | [
"p0",
"p1",
"p4",
"p5",
"p6",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3940139520691971781147955
% SZS output start Proof for 3940139520691971781147955
1. ? [X0] : (~humble(X0) & tall(X0)) <=> ? [X0] : (~patient(X0) | wise(X0)) [input p0]
2. ! [X0] : ((generous(X0) & strong(X0)) <=> (~creative(X0) & humble(X0))) [input p1]
5. ! [X0] : ((~old(X0) <~> curious(X0)) => (~tall(X0) & curious(X0))) [input p4]
6. ! [X0] : ((strong(X0) & ~creative(X0)) => (~tall(X0) | humble(X0))) [input p5]
7. ! [X0] : ((~funny(X0) & strong(X0)) <=> (~calm(X0) | happy(X0))) [input p6]
9. ! [X0] : ((~old(X0) <~> ~generous(X0)) <=> ~creative(X0)) [input p8]
10. ! [X0] : ((~humble(X0) & ~creative(X0)) <=> tall(X0)) [input p9]
12. ? [X0] : (old(X0) & strong(X0)) <=> ? [X0] : (~happy(X0) | brave(X0)) [input p11]
22. ~patient(paul) [input hypothesis]
23. ? [X0] : (~humble(X0) & tall(X0)) <=> ? [X1] : (~patient(X1) | wise(X1)) [rectify 1]
25. ? [X0] : (old(X0) & strong(X0)) <=> ? [X1] : (~happy(X1) | brave(X1)) [rectify 12]
28. ! [X0] : ((~tall(X0) & curious(X0)) | (~old(X0) <=> curious(X0))) [ennf transformation 5]
29. ! [X0] : ((~tall(X0) | humble(X0)) | (~strong(X0) | creative(X0))) [ennf transformation 6]
30. ! [X0] : (~tall(X0) | humble(X0) | ~strong(X0) | creative(X0)) [flattening 29]
37. (? [X0] : (~humble(X0) & tall(X0)) | ! [X1] : (patient(X1) & ~wise(X1))) & (? [X1] : (~patient(X1) | wise(X1)) | ! [X0] : (humble(X0) | ~tall(X0))) [nnf transformation 23]
38. (? [X0] : (~humble(X0) & tall(X0)) | ! [X1] : (patient(X1) & ~wise(X1))) & (? [X2] : (~patient(X2) | wise(X2)) | ! [X3] : (humble(X3) | ~tall(X3))) [rectify 37]
39. ? [X0] : (~humble(X0) & tall(X0)) => (~humble(sK0) & tall(sK0)) [choice axiom]
40. ? [X2] : (~patient(X2) | wise(X2)) => (~patient(sK1) | wise(sK1)) [choice axiom]
41. ((~humble(sK0) & tall(sK0)) | ! [X1] : (patient(X1) & ~wise(X1))) & ((~patient(sK1) | wise(sK1)) | ! [X3] : (humble(X3) | ~tall(X3))) [skolemisation 38,40,39]
42. ! [X0] : (((generous(X0) & strong(X0)) | (creative(X0) | ~humble(X0))) & ((~creative(X0) & humble(X0)) | (~generous(X0) | ~strong(X0)))) [nnf transformation 2]
43. ! [X0] : (((generous(X0) & strong(X0)) | creative(X0) | ~humble(X0)) & ((~creative(X0) & humble(X0)) | ~generous(X0) | ~strong(X0))) [flattening 42]
50. ! [X0] : ((~tall(X0) & curious(X0)) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) [nnf transformation 28]
51. ! [X0] : (((~funny(X0) & strong(X0)) | (calm(X0) & ~happy(X0))) & ((~calm(X0) | happy(X0)) | (funny(X0) | ~strong(X0)))) [nnf transformation 7]
52. ! [X0] : (((~funny(X0) & strong(X0)) | (calm(X0) & ~happy(X0))) & (~calm(X0) | happy(X0) | funny(X0) | ~strong(X0))) [flattening 51]
58. ! [X0] : ((((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | creative(X0)) & (~creative(X0) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0))))) [nnf transformation 9]
59. ! [X0] : (((~humble(X0) & ~creative(X0)) | ~tall(X0)) & (tall(X0) | (humble(X0) | creative(X0)))) [nnf transformation 10]
60. ! [X0] : (((~humble(X0) & ~creative(X0)) | ~tall(X0)) & (tall(X0) | humble(X0) | creative(X0))) [flattening 59]
62. (? [X0] : (old(X0) & strong(X0)) | ! [X1] : (happy(X1) & ~brave(X1))) & (? [X1] : (~happy(X1) | brave(X1)) | ! [X0] : (~old(X0) | ~strong(X0))) [nnf transformation 25]
63. (? [X0] : (old(X0) & strong(X0)) | ! [X1] : (happy(X1) & ~brave(X1))) & (? [X2] : (~happy(X2) | brave(X2)) | ! [X3] : (~old(X3) | ~strong(X3))) [rectify 62]
64. ? [X0] : (old(X0) & strong(X0)) => (old(sK5) & strong(sK5)) [choice axiom]
65. ? [X2] : (~happy(X2) | brave(X2)) => (~happy(sK6) | brave(sK6)) [choice axiom]
66. ((old(sK5) & strong(sK5)) | ! [X1] : (happy(X1) & ~brave(X1))) & ((~happy(sK6) | brave(sK6)) | ! [X3] : (~old(X3) | ~strong(X3))) [skolemisation 63,65,64]
75. tall(sK0) | patient(X1) [cnf transformation 41]
77. ~humble(sK0) | patient(X1) [cnf transformation 41]
78. ~generous(X0) | humble(X0) | ~strong(X0) [cnf transformation 43]
79. ~creative(X0) | ~generous(X0) | ~strong(X0) [cnf transformation 43]
81. ~humble(X0) | creative(X0) | generous(X0) [cnf transformation 43]
87. curious(X0) | curious(X0) | old(X0) [cnf transformation 50]
90. ~old(X0) | ~tall(X0) | ~curious(X0) [cnf transformation 50]
91. ~strong(X0) | humble(X0) | ~tall(X0) | creative(X0) [cnf transformation 30]
93. ~happy(X0) | strong(X0) [cnf transformation 52]
101. ~old(X0) | ~creative(X0) | generous(X0) [cnf transformation 58]
102. ~old(X0) | ~generous(X0) | creative(X0) [cnf transformation 58]
103. old(X0) | generous(X0) | creative(X0) [cnf transformation 58]
104. creative(X0) | humble(X0) | tall(X0) [cnf transformation 60]
105. ~creative(X0) | ~tall(X0) [cnf transformation 60]
109. ~happy(sK6) | brave(sK6) | ~old(X3) | ~strong(X3) [cnf transformation 66]
110. strong(sK5) | ~brave(X1) [cnf transformation 66]
111. strong(sK5) | happy(X1) [cnf transformation 66]
112. old(sK5) | ~brave(X1) [cnf transformation 66]
113. old(sK5) | happy(X1) [cnf transformation 66]
125. ~patient(paul) [cnf transformation 22]
127. old(X0) | curious(X0) [duplicate literal removal 87]
129. 1 <=> ! [X1] : patient(X1) [avatar definition]
130. patient(X1) <- (1) [avatar component clause 129]
132. 2 <=> humble(sK0) [avatar definition]
134. ~humble(sK0) <- (~2) [avatar component clause 132]
135. 1 | ~2 [avatar split clause 77,132,129]
141. 4 <=> tall(sK0) [avatar definition]
143. tall(sK0) <- (4) [avatar component clause 141]
144. 1 | 4 [avatar split clause 75,141,129]
173. 11 <=> ! [X1] : curious(X1) [avatar definition]
174. curious(X1) <- (11) [avatar component clause 173]
198. 17 <=> ! [X1] : happy(X1) [avatar definition]
199. happy(X1) <- (17) [avatar component clause 198]
201. 18 <=> old(sK5) [avatar definition]
203. old(sK5) <- (18) [avatar component clause 201]
204. 17 | 18 [avatar split clause 113,201,198]
206. 19 <=> ! [X1] : ~brave(X1) [avatar definition]
207. ~brave(X1) <- (19) [avatar component clause 206]
208. 19 | 18 [avatar split clause 112,201,206]
210. 20 <=> strong(sK5) [avatar definition]
212. strong(sK5) <- (20) [avatar component clause 210]
213. 17 | 20 [avatar split clause 111,210,198]
214. 19 | 20 [avatar split clause 110,210,206]
216. 21 <=> ! [X3] : (~old(X3) | ~strong(X3)) [avatar definition]
217. ~old(X3) | ~strong(X3) <- (21) [avatar component clause 216]
219. 22 <=> brave(sK6) [avatar definition]
221. brave(sK6) <- (22) [avatar component clause 219]
223. 23 <=> happy(sK6) [avatar definition]
225. ~happy(sK6) <- (~23) [avatar component clause 223]
226. 21 | 22 | ~23 [avatar split clause 109,223,219,216]
252. 29 <=> ! [X0] : ~old(X0) [avatar definition]
253. ~old(X0) <- (29) [avatar component clause 252]
301. $false <- (17, ~23) [resolution 225,199]
302. ~17 | 23 [avatar contradiction clause 301]
324. 41 <=> tall(sK5) [avatar definition]
325. tall(sK5) <- (41) [avatar component clause 324]
332. 42 <=> generous(sK5) [avatar definition]
334. generous(sK5) <- (42) [avatar component clause 332]
336. 43 <=> creative(sK5) [avatar definition]
337. creative(sK5) <- (43) [avatar component clause 336]
338. ~creative(sK5) <- (~43) [avatar component clause 336]
358. generous(X2) | creative(X2) | ~tall(X2) | ~curious(X2) [resolution 103,90]
361. ~curious(X2) | ~tall(X2) | generous(X2) [subsumption resolution 358,105]
366. humble(sK5) | tall(sK5) <- (~43) [resolution 104,338]
377. 48 <=> humble(sK5) [avatar definition]
379. humble(sK5) <- (48) [avatar component clause 377]
380. 41 | 48 | 43 [avatar split clause 366,336,377,324]
411. humble(sK5) | ~tall(sK5) | creative(sK5) <- (20) [resolution 91,212]
413. humble(sK5) | creative(sK5) <- (20, 41) [subsumption resolution 411,325]
426. 43 | 48 | ~20 | ~41 [avatar split clause 413,324,210,377,336]
429. humble(sK5) | ~strong(sK5) <- (42) [resolution 334,78]
430. humble(sK5) <- (20, 42) [subsumption resolution 429,212]
431. 48 | ~20 | ~42 [avatar split clause 430,332,210,377]
436. strong(X1) <- (17) [resolution 199,93]
442. $false <- (19, 22) [resolution 221,207]
444. ~19 | ~22 [avatar contradiction clause 442]
454. ~old(X3) <- (17, 21) [subsumption resolution 217,436]
455. 29 | ~17 | ~21 [avatar split clause 454,216,198,252]
460. curious(X1) <- (29) [resolution 253,127]
462. 11 | ~29 [avatar split clause 460,252,173]
504. ~generous(sK5) | creative(sK5) <- (18) [resolution 203,102]
505. ~creative(sK5) | generous(sK5) <- (18) [resolution 203,101]
571. creative(sK5) | generous(sK5) <- (48) [resolution 379,81]
580. 43 | ~42 | ~18 [avatar split clause 504,201,332,336]
581. 42 | 43 | ~48 [avatar split clause 571,377,336,332]
582. 42 | ~43 | ~18 [avatar split clause 505,201,336,332]
588. ~generous(sK5) | ~strong(sK5) <- (43) [resolution 337,79]
620. ~generous(sK5) <- (20, 43) [subsumption resolution 588,212]
621. ~42 | ~20 | ~43 [avatar split clause 620,336,210,332]
627. ~tall(X0) | generous(X0) <- (11) [resolution 174,361]
631. strong(X1) <- (17) [resolution 199,93]
700. generous(sK0) <- (4, 11) [resolution 627,143]
704. humble(sK0) | ~strong(sK0) <- (4, 11) [resolution 700,78]
714. ~strong(sK0) <- (~2, 4, 11) [subsumption resolution 704,134]
715. $false <- (~2, 4, 11, 17) [subsumption resolution 714,631]
716. 2 | ~4 | ~11 | ~17 [avatar contradiction clause 715]
717. $false <- (1) [resolution 130,125]
720. ~1 [avatar contradiction clause 717]
721. $false [avatar sat refutation 135,144,204,208,213,214,226,302,380,426,431,444,455,462,580,581,582,621,716,720]
% SZS output end Proof for 3940139520691971781147955
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and happy is both creative and strong.
Everyone who is both tall and humble is both not patient and strong.
If susan is both not creative and wise then john is both tall and not rich.
Everyone who is both not rich and not strong is either kind or not tall.
Everyone who is both not old and not generous is both strong and tall.
Everyone who is not strong is not rich.
Everyone who is old is both brave and creative and vice versa.
Everyone who is strong or creative is both not wise and old.
Everyone who is either curious or not curious is either calm or not curious and vice versa.
Everyone who is either happy or wise is kind or funny and vice versa.
Everyone who is both calm and happy is either curious or not funny.
If someone is happy then someone is not brave or not curious.
If fred is either not creative or not patient then mary is kind and vice versa.
Everyone who is brave is not old or not kind.
If fred is both strong and generous then alice is both strong and not humble.
Everyone who is happy or wise is not rich or humble.
Susan is both not kind and old.
Someone is either not brave or kind.
Fred is both not old and happy.
Someone is not curious or creative.
Paul is both not quiet and funny.
Alice is brave or not old.
Someone is patient. | John is not creative. | neutral | (![X]:((~brave(X)&happy(X))=>(creative(X)&strong(X))))&
(![X]:((tall(X)&humble(X))=>(~patient(X)&strong(X))))&
(((~creative(susan)&wise(susan)))=>((tall(john)&~rich(john))))&
(![X]:((~rich(X)&~strong(X))=>(kind(X)<~>~tall(X))))&
(![X]:((~old(X)&~generous(X))=>(strong(X)&tall(X))))&
(![X]:(~strong(X)=>~rich(X)))&
(![X]:(old(X)<=>(brave(X)&creative(X))))&
(![X]:((strong(X)|creative(X))=>(~wise(X)&old(X))))&
(![X]:((curious(X)<~>~curious(X))<=>(calm(X)<~>~curious(X))))&
(![X]:((happy(X)<~>wise(X))<=>(kind(X)|funny(X))))&
(![X]:((calm(X)&happy(X))=>(curious(X)<~>~funny(X))))&
((?[X]:(happy(X)))=>(?[X]:((~brave(X)|~curious(X)))))&
(((~creative(fred)<~>~patient(fred)))<=>(kind(mary)))&
(![X]:(brave(X)=>(~old(X)|~kind(X))))&
(((strong(fred)&generous(fred)))=>((strong(alice)&~humble(alice))))&
(![X]:((happy(X)|wise(X))=>(~rich(X)|humble(X))))&
((~kind(susan)&old(susan)))&
(?[X]:((~brave(X)<~>kind(X))))&
((~old(fred)&happy(fred)))&
(?[X]:((~curious(X)|creative(X))))&
((~quiet(paul)&funny(paul)))&
((brave(alice)|~old(alice)))&
(?[X]:(patient(X))) | ~creative(john) | [] | null | 0 |
If someone is not tall or not calm then john is either not brave or not patient and vice versa.
Everyone who is not kind is not funny or not quiet and vice versa.
Everyone who is curious is happy.
If someone is either not curious or not strong then someone is rich.
If mary is not quiet then someone is either humble or not wise.
If someone is either strong or patient then susan is not happy or tall.
Everyone who is either funny or old is both not old and creative and vice versa.
Everyone who is brave is not funny or kind.
If someone is happy then someone is both strong and not strong.
If mary is not generous then someone is quiet or not old and vice versa.
If susan is not patient or not creative then lucy is not patient.
If someone is happy or quiet then john is patient.
Everyone who is humble or calm is calm and vice versa.
Everyone who is both not humble and strong is not funny.
Everyone who is either humble or calm is either not patient or not wise and vice versa.
If john is either not generous or not humble then susan is either kind or not old and vice versa.
Someone is generous or creative.
Someone is quiet or not generous.
Someone is either not funny or not humble.
Someone is both wise and calm.
Someone is both creative and quiet.
Paul is tall or not generous.
John is not wise. | John is calm. | entailment | ((?[X]:((~tall(X)|~calm(X))))<=>((~brave(john)<~>~patient(john))))&
(![X]:(~kind(X)<=>(~funny(X)|~quiet(X))))&
(![X]:(curious(X)=>happy(X)))&
((?[X]:((~curious(X)<~>~strong(X))))=>(?[X]:(rich(X))))&
((~quiet(mary))=>(?[X]:((humble(X)<~>~wise(X)))))&
((?[X]:((strong(X)<~>patient(X))))=>((~happy(susan)|tall(susan))))&
(![X]:((funny(X)<~>old(X))<=>(~old(X)&creative(X))))&
(![X]:(brave(X)=>(~funny(X)|kind(X))))&
((?[X]:(happy(X)))=>(?[X]:((strong(X)&~strong(X)))))&
((~generous(mary))<=>(?[X]:((quiet(X)|~old(X)))))&
(((~patient(susan)|~creative(susan)))=>(~patient(lucy)))&
((?[X]:((happy(X)|quiet(X))))=>(patient(john)))&
(![X]:((humble(X)|calm(X))<=>calm(X)))&
(![X]:((~humble(X)&strong(X))=>~funny(X)))&
(![X]:((humble(X)<~>calm(X))<=>(~patient(X)<~>~wise(X))))&
(((~generous(john)<~>~humble(john)))<=>((kind(susan)<~>~old(susan))))&
(?[X]:((generous(X)|creative(X))))&
(?[X]:((quiet(X)|~generous(X))))&
(?[X]:((~funny(X)<~>~humble(X))))&
(?[X]:((wise(X)&calm(X))))&
(?[X]:((creative(X)&quiet(X))))&
((tall(paul)|~generous(paul)))&
(~wise(john)) | calm(john) | [
"p11",
"p12",
"p14",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3923952287388173482641221
% SZS output start Proof for 3923952287388173482641221
12. ? [X0] : (quiet(X0) | happy(X0)) => patient(john) [input p11]
13. ! [X0] : ((calm(X0) | humble(X0)) <=> calm(X0)) [input p12]
15. ! [X0] : ((humble(X0) <~> calm(X0)) <=> (~patient(X0) <~> ~wise(X0))) [input p14]
21. ? [X0] : (quiet(X0) & creative(X0)) [input p20]
23. ~wise(john) [input p22]
24. ~calm(john) [input hypothesis]
31. ? [X0] : quiet(X0) => patient(john) [pure predicate removal 12]
37. patient(john) | ! [X0] : ~quiet(X0) [ennf transformation 31]
53. ! [X0] : (((calm(X0) | humble(X0)) | ~calm(X0)) & (calm(X0) | (~calm(X0) & ~humble(X0)))) [nnf transformation 13]
54. ! [X0] : ((calm(X0) | humble(X0) | ~calm(X0)) & (calm(X0) | (~calm(X0) & ~humble(X0)))) [flattening 53]
55. ! [X0] : ((((~calm(X0) | ~humble(X0)) & (calm(X0) | humble(X0))) | ((~patient(X0) | wise(X0)) & (~wise(X0) | patient(X0)))) & (((wise(X0) | patient(X0)) & (~wise(X0) | ~patient(X0))) | ((humble(X0) | ~calm(X0)) & (calm(X0) | ~humble(X0))))) [nnf transformation 15]
66. ? [X0] : (quiet(X0) & creative(X0)) => (quiet(sK7) & creative(sK7)) [choice axiom]
67. quiet(sK7) & creative(sK7) [skolemisation 21,66]
91. patient(john) | ~quiet(X0) [cnf transformation 37]
92. ~humble(X0) | calm(X0) [cnf transformation 54]
100. calm(X0) | humble(X0) | ~patient(X0) | wise(X0) [cnf transformation 55]
102. ~calm(X0) | ~humble(X0) | ~patient(X0) | wise(X0) [cnf transformation 55]
118. quiet(sK7) [cnf transformation 67]
120. ~wise(john) [cnf transformation 23]
121. ~calm(john) [cnf transformation 24]
125. 1 <=> patient(john) [avatar definition]
127. patient(john) <- (1) [avatar component clause 125]
175. 12 <=> ! [X0] : ~quiet(X0) [avatar definition]
176. ~quiet(X0) <- (12) [avatar component clause 175]
201. 12 | 1 [avatar split clause 91,125,175]
202. ~humble(X0) | ~patient(X0) | wise(X0) [subsumption resolution 102,92]
204. ~patient(X0) | calm(X0) | wise(X0) [subsumption resolution 100,202]
267. $false <- (12) [resolution 176,118]
268. ~12 [avatar contradiction clause 267]
327. calm(john) | wise(john) <- (1) [resolution 204,127]
328. wise(john) <- (1) [subsumption resolution 327,121]
329. $false <- (1) [subsumption resolution 328,120]
330. ~1 [avatar contradiction clause 329]
331. $false [avatar sat refutation 201,268,330]
% SZS output end Proof for 3923952287388173482641221
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both not quiet and not humble then someone is both rich and happy and vice versa. Everyone who is happy or not patient is patient or not patient. Everyone who is curious or not funny is both creative and not funny and vice versa. Everyone who is tall is not generous. Everyone who is either creative or not kind is not old and vice versa. Everyone who is quiet or not strong is happy or kind. Everyone who is either wise or tall is either not creative or not strong. If susan is both not generous and not patient then paul is both not kind and not patient. Everyone who is not generous or generous is either not tall or humble and vice versa. Everyone who is humble or generous is happy or wise. If fred is either calm or creative then fred is either strong or creative and vice versa. Everyone who is either not calm or not happy is either funny or wise and vice versa. If someone is both kind and brave then someone is creative and vice versa. If alice is both generous and brave then someone is not rich. Everyone who is either quiet or strong is not quiet and vice versa. Everyone who is both rich and calm is happy or creative and vice versa. Fred is not rich or not patient. Mary is brave or not wise. Susan is both generous and rich. Alice is both not funny and humble. Someone is not calm or funny. Mary is funny. Paul is not old. | Fred is generous. | contradiction | (((~quiet(alice)&~humble(alice)))<=>(?[X]:((rich(X)&happy(X)))))&
(![X]:((happy(X)|~patient(X))=>(patient(X)|~patient(X))))&
(![X]:((curious(X)|~funny(X))<=>(creative(X)&~funny(X))))&
(![X]:(tall(X)=>~generous(X)))&
(![X]:((creative(X)<~>~kind(X))<=>~old(X)))&
(![X]:((quiet(X)|~strong(X))=>(happy(X)|kind(X))))&
(![X]:((wise(X)<~>tall(X))=>(~creative(X)<~>~strong(X))))&
(((~generous(susan)&~patient(susan)))=>((~kind(paul)&~patient(paul))))&
(![X]:((~generous(X)|generous(X))<=>(~tall(X)<~>humble(X))))&
(![X]:((humble(X)|generous(X))=>(happy(X)|wise(X))))&
(((calm(fred)<~>creative(fred)))<=>((strong(fred)<~>creative(fred))))&
(![X]:((~calm(X)<~>~happy(X))<=>(funny(X)<~>wise(X))))&
((?[X]:((kind(X)&brave(X))))<=>(?[X]:(creative(X))))&
(((generous(alice)&brave(alice)))=>(?[X]:(~rich(X))))&
(![X]:((quiet(X)<~>strong(X))<=>~quiet(X)))&
(![X]:((rich(X)&calm(X))<=>(happy(X)|creative(X))))&
((~rich(fred)|~patient(fred)))&
((brave(mary)|~wise(mary)))&
((generous(susan)&rich(susan)))&
((~funny(alice)&humble(alice)))&
(?[X]:((~calm(X)|funny(X))))&
(funny(mary))&
(~old(paul)) | generous(fred) | [
"p0",
"p2",
"p3",
"p6",
"p9",
"p10",
"p11",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4194016056279698031877510
% SZS output start Proof for 4194016056279698031877510
1. (~humble(alice) & ~quiet(alice)) <=> ? [X0] : (happy(X0) & rich(X0)) [input p0]
3. ! [X0] : ((~funny(X0) | curious(X0)) <=> (~funny(X0) & creative(X0))) [input p2]
4. ! [X0] : (tall(X0) => ~generous(X0)) [input p3]
7. ! [X0] : ((wise(X0) <~> tall(X0)) => (~creative(X0) <~> ~strong(X0))) [input p6]
10. ! [X0] : ((generous(X0) | humble(X0)) => (wise(X0) | happy(X0))) [input p9]
11. (calm(fred) <~> creative(fred)) <=> (strong(fred) <~> creative(fred)) [input p10]
12. ! [X0] : ((~calm(X0) <~> ~happy(X0)) <=> (funny(X0) <~> wise(X0))) [input p11]
15. ! [X0] : ((quiet(X0) <~> strong(X0)) <=> ~quiet(X0)) [input p14]
16. ! [X0] : ((calm(X0) & rich(X0)) <=> (creative(X0) | happy(X0))) [input p15]
20. humble(alice) & ~funny(alice) [input p19]
24. generous(fred) [input hypothesis]
29. ! [X0] : (~generous(X0) | ~tall(X0)) [ennf transformation 4]
33. ! [X0] : ((~creative(X0) <~> ~strong(X0)) | (wise(X0) <=> tall(X0))) [ennf transformation 7]
36. ! [X0] : ((wise(X0) | happy(X0)) | (~generous(X0) & ~humble(X0))) [ennf transformation 10]
37. ! [X0] : (wise(X0) | happy(X0) | (~generous(X0) & ~humble(X0))) [flattening 36]
40. ((~humble(alice) & ~quiet(alice)) | ! [X0] : (~happy(X0) | ~rich(X0))) & (? [X0] : (happy(X0) & rich(X0)) | (humble(alice) | quiet(alice))) [nnf transformation 1]
41. ((~humble(alice) & ~quiet(alice)) | ! [X0] : (~happy(X0) | ~rich(X0))) & (? [X0] : (happy(X0) & rich(X0)) | humble(alice) | quiet(alice)) [flattening 40]
42. ((~humble(alice) & ~quiet(alice)) | ! [X0] : (~happy(X0) | ~rich(X0))) & (? [X1] : (happy(X1) & rich(X1)) | humble(alice) | quiet(alice)) [rectify 41]
43. ? [X1] : (happy(X1) & rich(X1)) => (happy(sK0) & rich(sK0)) [choice axiom]
44. ((~humble(alice) & ~quiet(alice)) | ! [X0] : (~happy(X0) | ~rich(X0))) & ((happy(sK0) & rich(sK0)) | humble(alice) | quiet(alice)) [skolemisation 42,43]
45. ! [X0] : (((~funny(X0) | curious(X0)) | (funny(X0) | ~creative(X0))) & ((~funny(X0) & creative(X0)) | (funny(X0) & ~curious(X0)))) [nnf transformation 3]
46. ! [X0] : ((~funny(X0) | curious(X0) | funny(X0) | ~creative(X0)) & ((~funny(X0) & creative(X0)) | (funny(X0) & ~curious(X0)))) [flattening 45]
48. ! [X0] : (((strong(X0) | creative(X0)) & (~strong(X0) | ~creative(X0))) | ((wise(X0) | ~tall(X0)) & (tall(X0) | ~wise(X0)))) [nnf transformation 33]
51. (((~creative(fred) | ~calm(fred)) & (creative(fred) | calm(fred))) | ((strong(fred) | ~creative(fred)) & (creative(fred) | ~strong(fred)))) & (((~creative(fred) | ~strong(fred)) & (creative(fred) | strong(fred))) | ((calm(fred) | ~creative(fred)) & (creative(fred) | ~calm(fred)))) [nnf transformation 11]
52. ! [X0] : ((((happy(X0) | calm(X0)) & (~happy(X0) | ~calm(X0))) | ((funny(X0) | ~wise(X0)) & (wise(X0) | ~funny(X0)))) & (((~wise(X0) | ~funny(X0)) & (wise(X0) | funny(X0))) | ((~calm(X0) | happy(X0)) & (~happy(X0) | calm(X0))))) [nnf transformation 12]
60. ! [X0] : ((((~strong(X0) | ~quiet(X0)) & (strong(X0) | quiet(X0))) | quiet(X0)) & (~quiet(X0) | ((quiet(X0) | ~strong(X0)) & (strong(X0) | ~quiet(X0))))) [nnf transformation 15]
61. ! [X0] : (((calm(X0) & rich(X0)) | (~creative(X0) & ~happy(X0))) & ((creative(X0) | happy(X0)) | (~calm(X0) | ~rich(X0)))) [nnf transformation 16]
62. ! [X0] : (((calm(X0) & rich(X0)) | (~creative(X0) & ~happy(X0))) & (creative(X0) | happy(X0) | ~calm(X0) | ~rich(X0))) [flattening 61]
68. ~humble(alice) | ~happy(X0) | ~rich(X0) [cnf transformation 44]
72. creative(X0) | funny(X0) [cnf transformation 46]
76. ~generous(X0) | ~tall(X0) [cnf transformation 29]
81. ~wise(X0) | ~creative(X0) | tall(X0) | ~strong(X0) [cnf transformation 48]
94. ~generous(X0) | happy(X0) | wise(X0) [cnf transformation 37]
99. creative(fred) | calm(fred) | creative(fred) | ~strong(fred) [cnf transformation 51]
106. ~calm(X0) | ~funny(X0) | ~wise(X0) | happy(X0) [cnf transformation 52]
115. ~quiet(X0) | strong(X0) | ~quiet(X0) [cnf transformation 60]
117. strong(X0) | quiet(X0) | quiet(X0) [cnf transformation 60]
120. ~happy(X0) | rich(X0) [cnf transformation 62]
129. humble(alice) [cnf transformation 20]
133. generous(fred) [cnf transformation 24]
134. ~quiet(X0) | strong(X0) [duplicate literal removal 115]
135. strong(X0) | quiet(X0) [duplicate literal removal 117]
138. creative(fred) | calm(fred) | ~strong(fred) [duplicate literal removal 99]
142. 1 <=> ! [X0] : (~happy(X0) | ~rich(X0)) [avatar definition]
143. ~happy(X0) | ~rich(X0) <- (1) [avatar component clause 142]
145. 2 <=> humble(alice) [avatar definition]
148. 1 | ~2 [avatar split clause 68,145,142]
186. 10 <=> strong(fred) [avatar definition]
187. ~strong(fred) <- (~10) [avatar component clause 186]
190. 11 <=> calm(fred) [avatar definition]
191. calm(fred) <- (11) [avatar component clause 190]
194. 12 <=> creative(fred) [avatar definition]
196. ~creative(fred) <- (~12) [avatar component clause 194]
198. ~10 | 11 | 12 [avatar split clause 138,194,190,186]
235. strong(X0) [subsumption resolution 134,135]
255. 2 [avatar split clause 129,145]
265. $false <- (~10) [subsumption resolution 187,235]
266. 10 [avatar contradiction clause 265]
267. ~happy(X0) <- (1) [subsumption resolution 143,120]
273. ~tall(fred) [resolution 76,133]
309. happy(fred) | wise(fred) [resolution 94,133]
311. wise(fred) <- (1) [subsumption resolution 309,267]
314. ~creative(fred) | tall(fred) | ~strong(fred) <- (1) [resolution 311,81]
315. ~creative(fred) | ~strong(fred) <- (1) [subsumption resolution 314,273]
316. ~creative(fred) <- (1) [subsumption resolution 315,235]
317. ~12 | ~1 [avatar split clause 316,142,194]
318. funny(fred) <- (~12) [resolution 196,72]
355. ~funny(fred) | ~wise(fred) | happy(fred) <- (11) [resolution 106,191]
357. ~wise(fred) | happy(fred) <- (11, ~12) [subsumption resolution 355,318]
358. happy(fred) <- (1, 11, ~12) [subsumption resolution 357,311]
359. $false <- (1, 11, ~12) [subsumption resolution 358,267]
360. ~1 | ~11 | 12 [avatar contradiction clause 359]
364. $false [avatar sat refutation 148,198,255,266,317,360]
% SZS output end Proof for 4194016056279698031877510
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is wise or not calm then someone is both strong and curious.
If someone is either kind or not wise then paul is either patient or happy and vice versa.
Everyone who is curious or not tall is curious or not calm and vice versa.
If someone is not patient or not quiet then someone is calm or not brave.
If someone is brave or not creative then someone is brave or quiet and vice versa.
Everyone who is not funny is not patient or not curious.
If lucy is both not humble and humble then susan is calm and vice versa.
Everyone who is both curious and not creative is brave or rich and vice versa.
Everyone who is both wise and curious is either not brave or brave and vice versa.
Everyone who is not funny or creative is not wise or patient and vice versa.
If paul is creative or patient then someone is both generous and not happy and vice versa.
Everyone who is both not creative and tall is not rich or happy.
If someone is patient then someone is happy or not curious.
Everyone who is old is kind or happy.
If someone is either quiet or not creative then someone is either tall or funny.
If someone is either rich or funny then lucy is not generous and vice versa.
Paul is not tall.
Paul is either quiet or not humble.
Susan is not old.
John is calm or strong.
Mary is not curious or generous.
Someone is generous or not quiet. | Susan is wise. | entailment | (((wise(john)|~calm(john)))=>(?[X]:((strong(X)&curious(X)))))&
((?[X]:((kind(X)<~>~wise(X))))<=>((patient(paul)<~>happy(paul))))&
(![X]:((curious(X)|~tall(X))<=>(curious(X)|~calm(X))))&
((?[X]:((~patient(X)|~quiet(X))))=>(?[X]:((calm(X)|~brave(X)))))&
((?[X]:((brave(X)|~creative(X))))<=>(?[X]:((brave(X)|quiet(X)))))&
(![X]:(~funny(X)=>(~patient(X)|~curious(X))))&
(((~humble(lucy)&humble(lucy)))<=>(calm(susan)))&
(![X]:((curious(X)&~creative(X))<=>(brave(X)|rich(X))))&
(![X]:((wise(X)&curious(X))<=>(~brave(X)<~>brave(X))))&
(![X]:((~funny(X)|creative(X))<=>(~wise(X)|patient(X))))&
(((creative(paul)|patient(paul)))<=>(?[X]:((generous(X)&~happy(X)))))&
(![X]:((~creative(X)&tall(X))=>(~rich(X)|happy(X))))&
((?[X]:(patient(X)))=>(?[X]:((happy(X)|~curious(X)))))&
(![X]:(old(X)=>(kind(X)|happy(X))))&
((?[X]:((quiet(X)<~>~creative(X))))=>(?[X]:((tall(X)<~>funny(X)))))&
((?[X]:((rich(X)<~>funny(X))))<=>(~generous(lucy)))&
(~tall(paul))&
((quiet(paul)<~>~humble(paul)))&
(~old(susan))&
((calm(john)|strong(john)))&
((~curious(mary)|generous(mary)))&
(?[X]:((generous(X)|~quiet(X)))) | wise(susan) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7681353877061722760266250
% SZS output start Proof for 7681353877061722760266250
9. ! [X0] : ((curious(X0) & wise(X0)) <=> (~brave(X0) <~> brave(X0))) [input p8]
23. ~wise(susan) [input hypothesis]
60. ! [X0] : (((curious(X0) & wise(X0)) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) & (((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | (~curious(X0) | ~wise(X0)))) [nnf transformation 9]
61. ! [X0] : (((curious(X0) & wise(X0)) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) & (((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | ~curious(X0) | ~wise(X0))) [flattening 60]
114. wise(X0) | brave(X0) | brave(X0) [cnf transformation 61]
115. wise(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 61]
142. ~wise(susan) [cnf transformation 23]
143. wise(X0) | brave(X0) [duplicate literal removal 114]
144. wise(X0) | ~brave(X0) [duplicate literal removal 115]
247. wise(X0) [subsumption resolution 143,144]
341. $false [subsumption resolution 142,247]
% SZS output end Proof for 7681353877061722760266250
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not brave or not kind then lucy is not creative. If someone is not kind or kind then lucy is happy or calm. Everyone who is not wise is both kind and not humble. Everyone who is either not curious or not kind is either creative or wise and vice versa. Everyone who is either calm or strong is either not kind or not wise. If fred is both wise and quiet then someone is both patient and not rich. If someone is both not patient and strong then someone is not wise and vice versa. Everyone who is happy or not brave is both kind and not quiet and vice versa. Everyone who is both not tall and quiet is tall or humble. Everyone who is old is not strong or not tall and vice versa. If susan is calm then someone is either wise or not old and vice versa. If lucy is either generous or funny then susan is both funny and not quiet and vice versa. Everyone who is not brave or not curious is both wise and funny. Everyone who is not tall or not humble is old and vice versa. Everyone who is either brave or not curious is not generous and vice versa. If someone is brave then fred is tall and vice versa. Someone is both not humble and not kind. Someone is either not generous or quiet. Alice is creative. Someone is patient or not humble. Mary is either strong or not creative. Susan is not generous or not curious. Mary is not old. Susan is either humble or not tall. | Lucy is happy. | neutral | (((~brave(mary)|~kind(mary)))=>(~creative(lucy)))&
((?[X]:((~kind(X)|kind(X))))=>((happy(lucy)|calm(lucy))))&
(![X]:(~wise(X)=>(kind(X)&~humble(X))))&
(![X]:((~curious(X)<~>~kind(X))<=>(creative(X)<~>wise(X))))&
(![X]:((calm(X)<~>strong(X))=>(~kind(X)<~>~wise(X))))&
(((wise(fred)&quiet(fred)))=>(?[X]:((patient(X)&~rich(X)))))&
((?[X]:((~patient(X)&strong(X))))<=>(?[X]:(~wise(X))))&
(![X]:((happy(X)|~brave(X))<=>(kind(X)&~quiet(X))))&
(![X]:((~tall(X)&quiet(X))=>(tall(X)|humble(X))))&
(![X]:(old(X)<=>(~strong(X)|~tall(X))))&
((calm(susan))<=>(?[X]:((wise(X)<~>~old(X)))))&
(((generous(lucy)<~>funny(lucy)))<=>((funny(susan)&~quiet(susan))))&
(![X]:((~brave(X)|~curious(X))=>(wise(X)&funny(X))))&
(![X]:((~tall(X)|~humble(X))<=>old(X)))&
(![X]:((brave(X)<~>~curious(X))<=>~generous(X)))&
((?[X]:(brave(X)))<=>(tall(fred)))&
(?[X]:((~humble(X)&~kind(X))))&
(?[X]:((~generous(X)<~>quiet(X))))&
(creative(alice))&
(?[X]:((patient(X)|~humble(X))))&
((strong(mary)<~>~creative(mary)))&
((~generous(susan)|~curious(susan)))&
(~old(mary))&
((humble(susan)<~>~tall(susan))) | happy(lucy) | [] | null | 0 |
Everyone who is not creative or not kind is not brave and vice versa.
Everyone who is both not patient and tall is wise or not rich.
Everyone who is not curious or not funny is not happy or calm.
Everyone who is not generous is either not funny or not calm.
If fred is brave then mary is not rich.
Everyone who is both not humble and not strong is both wise and not happy and vice versa.
If someone is not quiet then someone is either not wise or not generous.
Everyone who is either not tall or not happy is happy and vice versa.
If susan is kind or not happy then john is generous.
Everyone who is happy is either not rich or quiet and vice versa.
If someone is old or strong then someone is either not humble or not creative and vice versa.
Everyone who is either quiet or not calm is not calm or happy and vice versa.
If someone is both generous and not generous then someone is either not funny or rich and vice versa.
Everyone who is either tall or funny is both creative and old.
Everyone who is not brave or not curious is either not wise or not curious and vice versa.
If someone is either humble or not happy then someone is not quiet or kind and vice versa.
John is either quiet or not funny.
Someone is both not rich and strong.
Someone is brave or not patient.
Paul is not calm or kind.
Someone is not tall.
Someone is both old and happy.
John is both not happy and kind. | John is not funny. | entailment | (![X]:((~creative(X)|~kind(X))<=>~brave(X)))&
(![X]:((~patient(X)&tall(X))=>(wise(X)|~rich(X))))&
(![X]:((~curious(X)|~funny(X))=>(~happy(X)|calm(X))))&
(![X]:(~generous(X)=>(~funny(X)<~>~calm(X))))&
((brave(fred))=>(~rich(mary)))&
(![X]:((~humble(X)&~strong(X))<=>(wise(X)&~happy(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~wise(X)<~>~generous(X)))))&
(![X]:((~tall(X)<~>~happy(X))<=>happy(X)))&
(((kind(susan)|~happy(susan)))=>(generous(john)))&
(![X]:(happy(X)<=>(~rich(X)<~>quiet(X))))&
((?[X]:((old(X)|strong(X))))<=>(?[X]:((~humble(X)<~>~creative(X)))))&
(![X]:((quiet(X)<~>~calm(X))<=>(~calm(X)|happy(X))))&
((?[X]:((generous(X)&~generous(X))))<=>(?[X]:((~funny(X)<~>rich(X)))))&
(![X]:((tall(X)<~>funny(X))=>(creative(X)&old(X))))&
(![X]:((~brave(X)|~curious(X))<=>(~wise(X)<~>~curious(X))))&
((?[X]:((humble(X)<~>~happy(X))))<=>(?[X]:((~quiet(X)|kind(X)))))&
((quiet(john)<~>~funny(john)))&
(?[X]:((~rich(X)&strong(X))))&
(?[X]:((brave(X)|~patient(X))))&
((~calm(paul)|kind(paul)))&
(?[X]:(~tall(X)))&
(?[X]:((old(X)&happy(X))))&
((~happy(john)&kind(john))) | ~funny(john) | [
"p11",
"p16",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1024956752429187661648616
% SZS output start Proof for 1024956752429187661648616
12. ! [X0] : ((quiet(X0) <~> ~calm(X0)) <=> (happy(X0) | ~calm(X0))) [input p11]
17. quiet(john) <~> ~funny(john) [input p16]
23. kind(john) & ~happy(john) [input p22]
24. funny(john) [input hypothesis]
54. ! [X0] : ((((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) | (~happy(X0) & calm(X0))) & ((happy(X0) | ~calm(X0)) | ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0))))) [nnf transformation 12]
55. ! [X0] : ((((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) | (~happy(X0) & calm(X0))) & (happy(X0) | ~calm(X0) | ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0))))) [flattening 54]
69. (funny(john) | ~quiet(john)) & (~funny(john) | quiet(john)) [nnf transformation 17]
109. happy(X0) | ~calm(X0) | ~calm(X0) | ~quiet(X0) [cnf transformation 55]
113. calm(X0) | ~quiet(X0) | calm(X0) [cnf transformation 55]
137. ~funny(john) | quiet(john) [cnf transformation 69]
146. ~happy(john) [cnf transformation 23]
148. funny(john) [cnf transformation 24]
151. happy(X0) | ~calm(X0) | ~quiet(X0) [duplicate literal removal 109]
152. ~quiet(X0) | calm(X0) [duplicate literal removal 113]
226. ~quiet(X0) | happy(X0) [subsumption resolution 151,152]
275. 27 <=> quiet(john) [avatar definition]
276. quiet(john) <- (27) [avatar component clause 275]
279. 28 <=> funny(john) [avatar definition]
283. 27 | ~28 [avatar split clause 137,279,275]
302. 28 [avatar split clause 148,279]
308. happy(john) <- (27) [resolution 226,276]
309. $false <- (27) [subsumption resolution 308,146]
310. ~27 [avatar contradiction clause 309]
311. $false [avatar sat refutation 283,302,310]
% SZS output end Proof for 1024956752429187661648616
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not rich or kind then paul is humble.
Everyone who is either not tall or old is generous.
If fred is curious or humble then susan is either not wise or brave.
If alice is both wise and not brave then alice is either generous or quiet and vice versa.
If alice is either not quiet or not brave then someone is either not tall or curious.
Everyone who is either not humble or old is strong or not old.
Everyone who is both not brave and not quiet is not generous.
Everyone who is not kind is both wise and strong.
If someone is either quiet or not brave then someone is either not generous or not strong and vice versa.
Everyone who is not quiet or wise is both brave and not old and vice versa.
If susan is not funny or humble then alice is wise.
Everyone who is either humble or not quiet is brave.
Everyone who is tall or happy is both not curious and curious and vice versa.
If someone is both curious and rich then someone is calm.
Everyone who is not quiet is both happy and humble.
If someone is patient then paul is both strong and patient.
Someone is strong or not old.
Susan is strong.
Someone is both not wise and rich.
Someone is both curious and not kind.
Fred is both not generous and humble.
Susan is not funny.
Someone is either quiet or humble. | Paul is not brave. | contradiction | ((?[X]:((~rich(X)<~>kind(X))))=>(humble(paul)))&
(![X]:((~tall(X)<~>old(X))=>generous(X)))&
(((curious(fred)|humble(fred)))=>((~wise(susan)<~>brave(susan))))&
(((wise(alice)&~brave(alice)))<=>((generous(alice)<~>quiet(alice))))&
(((~quiet(alice)<~>~brave(alice)))=>(?[X]:((~tall(X)<~>curious(X)))))&
(![X]:((~humble(X)<~>old(X))=>(strong(X)|~old(X))))&
(![X]:((~brave(X)&~quiet(X))=>~generous(X)))&
(![X]:(~kind(X)=>(wise(X)&strong(X))))&
((?[X]:((quiet(X)<~>~brave(X))))<=>(?[X]:((~generous(X)<~>~strong(X)))))&
(![X]:((~quiet(X)|wise(X))<=>(brave(X)&~old(X))))&
(((~funny(susan)|humble(susan)))=>(wise(alice)))&
(![X]:((humble(X)<~>~quiet(X))=>brave(X)))&
(![X]:((tall(X)|happy(X))<=>(~curious(X)&curious(X))))&
((?[X]:((curious(X)&rich(X))))=>(?[X]:(calm(X))))&
(![X]:(~quiet(X)=>(happy(X)&humble(X))))&
((?[X]:(patient(X)))=>((strong(paul)&patient(paul))))&
(?[X]:((strong(X)|~old(X))))&
(strong(susan))&
(?[X]:((~wise(X)&rich(X))))&
(?[X]:((curious(X)&~kind(X))))&
((~generous(fred)&humble(fred)))&
(~funny(susan))&
(?[X]:((quiet(X)<~>humble(X)))) | ~brave(paul) | [
"p0",
"p7",
"p11",
"p12",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5195699142097423923488797
% SZS output start Proof for 5195699142097423923488797
1. ? [X0] : (~rich(X0) <~> kind(X0)) => humble(paul) [input p0]
8. ! [X0] : (~kind(X0) => (strong(X0) & wise(X0))) [input p7]
12. ! [X0] : ((humble(X0) <~> ~quiet(X0)) => brave(X0)) [input p11]
13. ! [X0] : ((happy(X0) | tall(X0)) <=> (curious(X0) & ~curious(X0))) [input p12]
15. ! [X0] : (~quiet(X0) => (humble(X0) & happy(X0))) [input p14]
19. ? [X0] : (rich(X0) & ~wise(X0)) [input p18]
24. ~brave(paul) [input hypothesis]
28. humble(paul) | ! [X0] : (~rich(X0) <=> kind(X0)) [ennf transformation 1]
36. ! [X0] : ((strong(X0) & wise(X0)) | kind(X0)) [ennf transformation 8]
38. ! [X0] : (brave(X0) | (humble(X0) <=> ~quiet(X0))) [ennf transformation 12]
39. ! [X0] : ((humble(X0) & happy(X0)) | quiet(X0)) [ennf transformation 15]
41. humble(paul) | ! [X0] : ((~rich(X0) | ~kind(X0)) & (kind(X0) | rich(X0))) [nnf transformation 28]
57. ! [X0] : (brave(X0) | ((humble(X0) | quiet(X0)) & (~quiet(X0) | ~humble(X0)))) [nnf transformation 38]
58. ! [X0] : (((happy(X0) | tall(X0)) | (~curious(X0) | curious(X0))) & ((curious(X0) & ~curious(X0)) | (~happy(X0) & ~tall(X0)))) [nnf transformation 13]
59. ! [X0] : ((happy(X0) | tall(X0) | ~curious(X0) | curious(X0)) & ((curious(X0) & ~curious(X0)) | (~happy(X0) & ~tall(X0)))) [flattening 58]
62. ? [X0] : (rich(X0) & ~wise(X0)) => (rich(sK4) & ~wise(sK4)) [choice axiom]
63. rich(sK4) & ~wise(sK4) [skolemisation 19,62]
70. humble(paul) | ~rich(X0) | ~kind(X0) [cnf transformation 41]
90. wise(X0) | kind(X0) [cnf transformation 36]
107. ~quiet(X0) | brave(X0) | ~humble(X0) [cnf transformation 57]
110. ~curious(X0) | ~happy(X0) [cnf transformation 59]
112. ~happy(X0) | curious(X0) [cnf transformation 59]
114. happy(X0) | quiet(X0) [cnf transformation 39]
120. ~wise(sK4) [cnf transformation 63]
121. rich(sK4) [cnf transformation 63]
129. ~brave(paul) [cnf transformation 24]
132. 1 <=> ! [X0] : (~rich(X0) | ~kind(X0)) [avatar definition]
133. ~kind(X0) | ~rich(X0) <- (1) [avatar component clause 132]
135. 2 <=> humble(paul) [avatar definition]
137. humble(paul) <- (2) [avatar component clause 135]
138. 1 | 2 [avatar split clause 70,135,132]
244. ~happy(X0) [subsumption resolution 110,112]
246. quiet(X0) [subsumption resolution 114,244]
274. kind(sK4) [resolution 90,120]
297. ~humble(X1) | brave(X1) [resolution 107,246]
300. brave(paul) <- (2) [resolution 297,137]
302. $false <- (2) [subsumption resolution 300,129]
303. ~2 [avatar contradiction clause 302]
308. ~rich(sK4) <- (1) [resolution 133,274]
309. $false <- (1) [subsumption resolution 308,121]
310. ~1 [avatar contradiction clause 309]
311. $false [avatar sat refutation 138,303,310]
% SZS output end Proof for 5195699142097423923488797
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either not strong or not kind then someone is both not patient and humble and vice versa.
Everyone who is both creative and not generous is not quiet or curious.
Everyone who is funny or not happy is funny or not kind.
Everyone who is either not old or not strong is creative or not kind.
Everyone who is either kind or brave is calm or not old.
If someone is either not curious or tall then fred is both not tall and generous.
If john is either not generous or not quiet then someone is both tall and not patient and vice versa.
Everyone who is either patient or strong is funny.
If lucy is humble then paul is generous and vice versa.
Everyone who is creative or not patient is either old or brave.
If susan is both funny and not generous then someone is patient or not generous.
Everyone who is both happy and not quiet is both happy and not patient and vice versa.
If john is not kind or old then susan is not humble and vice versa.
Everyone who is either not happy or not quiet is brave.
Everyone who is either not curious or not creative is either not wise or not kind.
Everyone who is not old or not quiet is both old and not tall.
Someone is both not calm and kind.
Someone is not tall or rich.
Fred is old or kind.
Mary is creative or not curious.
Alice is either not brave or funny.
Someone is not kind.
Paul is not tall.
Someone is both not wise and not happy. | Susan is not old. | contradiction | (((~strong(mary)<~>~kind(mary)))<=>(?[X]:((~patient(X)&humble(X)))))&
(![X]:((creative(X)&~generous(X))=>(~quiet(X)|curious(X))))&
(![X]:((funny(X)|~happy(X))=>(funny(X)|~kind(X))))&
(![X]:((~old(X)<~>~strong(X))=>(creative(X)|~kind(X))))&
(![X]:((kind(X)<~>brave(X))=>(calm(X)|~old(X))))&
((?[X]:((~curious(X)<~>tall(X))))=>((~tall(fred)&generous(fred))))&
(((~generous(john)<~>~quiet(john)))<=>(?[X]:((tall(X)&~patient(X)))))&
(![X]:((patient(X)<~>strong(X))=>funny(X)))&
((humble(lucy))<=>(generous(paul)))&
(![X]:((creative(X)|~patient(X))=>(old(X)<~>brave(X))))&
(((funny(susan)&~generous(susan)))=>(?[X]:((patient(X)|~generous(X)))))&
(![X]:((happy(X)&~quiet(X))<=>(happy(X)&~patient(X))))&
(((~kind(john)|old(john)))<=>(~humble(susan)))&
(![X]:((~happy(X)<~>~quiet(X))=>brave(X)))&
(![X]:((~curious(X)<~>~creative(X))=>(~wise(X)<~>~kind(X))))&
(![X]:((~old(X)|~quiet(X))=>(old(X)&~tall(X))))&
(?[X]:((~calm(X)&kind(X))))&
(?[X]:((~tall(X)|rich(X))))&
((old(fred)|kind(fred)))&
((creative(mary)|~curious(mary)))&
((~brave(alice)<~>funny(alice)))&
(?[X]:(~kind(X)))&
(~tall(paul))&
(?[X]:((~wise(X)&~happy(X)))) | ~old(susan) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8920174356494316096874031
% SZS output start Proof for 8920174356494316096874031
16. ! [X0] : ((~quiet(X0) | ~old(X0)) => (~tall(X0) & old(X0))) [input p15]
25. ~old(susan) [input hypothesis]
42. ! [X0] : ((~tall(X0) & old(X0)) | (quiet(X0) & old(X0))) [ennf transformation 16]
117. old(X0) | old(X0) [cnf transformation 42]
131. ~old(susan) [cnf transformation 25]
132. old(X0) [duplicate literal removal 117]
262. $false [subsumption resolution 131,132]
% SZS output end Proof for 8920174356494316096874031
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or not wise is both calm and humble and vice versa.
Everyone who is not happy is both patient and not curious.
Everyone who is not old is both generous and not brave and vice versa.
Everyone who is old or not funny is either old or calm.
Everyone who is either rich or not tall is either patient or not brave and vice versa.
Everyone who is both funny and rich is both not calm and not generous and vice versa.
Everyone who is both not calm and curious is either not calm or calm and vice versa.
If fred is both not old and brave then someone is both wise and not quiet.
Everyone who is creative is either not humble or wise.
If someone is old or patient then someone is creative.
If susan is not quiet then someone is either generous or calm and vice versa.
Everyone who is not brave or humble is wise and vice versa.
Everyone who is both not strong and old is either not strong or curious.
If paul is either not kind or quiet then someone is both quiet and patient.
If john is funny then susan is both not curious and creative and vice versa.
If someone is funny or rich then alice is tall or rich.
Someone is not patient.
Mary is not brave.
Someone is not wise or patient.
John is generous.
Someone is kind.
Someone is either creative or curious.
Paul is either not curious or not tall. | John is strong. | entailment | (![X]:((~humble(X)|~wise(X))<=>(calm(X)&humble(X))))&
(![X]:(~happy(X)=>(patient(X)&~curious(X))))&
(![X]:(~old(X)<=>(generous(X)&~brave(X))))&
(![X]:((old(X)|~funny(X))=>(old(X)<~>calm(X))))&
(![X]:((rich(X)<~>~tall(X))<=>(patient(X)<~>~brave(X))))&
(![X]:((funny(X)&rich(X))<=>(~calm(X)&~generous(X))))&
(![X]:((~calm(X)&curious(X))<=>(~calm(X)<~>calm(X))))&
(((~old(fred)&brave(fred)))=>(?[X]:((wise(X)&~quiet(X)))))&
(![X]:(creative(X)=>(~humble(X)<~>wise(X))))&
((?[X]:((old(X)|patient(X))))=>(?[X]:(creative(X))))&
((~quiet(susan))<=>(?[X]:((generous(X)<~>calm(X)))))&
(![X]:((~brave(X)|humble(X))<=>wise(X)))&
(![X]:((~strong(X)&old(X))=>(~strong(X)<~>curious(X))))&
(((~kind(paul)<~>quiet(paul)))=>(?[X]:((quiet(X)&patient(X)))))&
((funny(john))<=>((~curious(susan)&creative(susan))))&
((?[X]:((funny(X)|rich(X))))=>((tall(alice)|rich(alice))))&
(?[X]:(~patient(X)))&
(~brave(mary))&
(?[X]:((~wise(X)|patient(X))))&
(generous(john))&
(?[X]:(kind(X)))&
(?[X]:((creative(X)<~>curious(X))))&
((~curious(paul)<~>~tall(paul))) | strong(john) | [
"p3",
"p6",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8904665944732906083814498
% SZS output start Proof for 8904665944732906083814498
4. ! [X0] : ((~funny(X0) | old(X0)) => (old(X0) <~> calm(X0))) [input p3]
7. ! [X0] : ((curious(X0) & ~calm(X0)) <=> (~calm(X0) <~> calm(X0))) [input p6]
13. ! [X0] : ((old(X0) & ~strong(X0)) => (~strong(X0) <~> curious(X0))) [input p12]
15. funny(john) <=> (creative(susan) & ~curious(susan)) [input p14]
24. ~strong(john) [input hypothesis]
27. ! [X0] : ((old(X0) <~> calm(X0)) | (funny(X0) & ~old(X0))) [ennf transformation 4]
32. ! [X0] : ((~strong(X0) <~> curious(X0)) | (~old(X0) | strong(X0))) [ennf transformation 13]
33. ! [X0] : ((~strong(X0) <~> curious(X0)) | ~old(X0) | strong(X0)) [flattening 32]
41. ! [X0] : (((~calm(X0) | ~old(X0)) & (calm(X0) | old(X0))) | (funny(X0) & ~old(X0))) [nnf transformation 27]
45. ! [X0] : (((curious(X0) & ~calm(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0)))) & (((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | (~curious(X0) | calm(X0)))) [nnf transformation 7]
46. ! [X0] : (((curious(X0) & ~calm(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0)))) & (((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | ~curious(X0) | calm(X0))) [flattening 45]
59. ! [X0] : (((~curious(X0) | strong(X0)) & (curious(X0) | ~strong(X0))) | ~old(X0) | strong(X0)) [nnf transformation 33]
63. (funny(john) | (~creative(susan) | curious(susan))) & ((creative(susan) & ~curious(susan)) | ~funny(john)) [nnf transformation 15]
64. (funny(john) | ~creative(susan) | curious(susan)) & ((creative(susan) & ~curious(susan)) | ~funny(john)) [flattening 63]
84. funny(X0) | old(X0) | calm(X0) [cnf transformation 41]
102. ~calm(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 46]
103. curious(X0) | calm(X0) | calm(X0) [cnf transformation 46]
104. curious(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 46]
119. ~curious(X0) | strong(X0) | ~old(X0) | strong(X0) [cnf transformation 59]
124. ~curious(susan) | ~funny(john) [cnf transformation 64]
138. ~strong(john) [cnf transformation 24]
139. ~curious(X0) | strong(X0) | ~old(X0) [duplicate literal removal 119]
143. ~calm(X0) [duplicate literal removal 102]
144. curious(X0) | calm(X0) [duplicate literal removal 103]
145. ~calm(X0) | curious(X0) [duplicate literal removal 104]
149. curious(X0) [subsumption resolution 144,145]
179. ~old(X0) | strong(X0) [subsumption resolution 139,149]
201. 11 <=> funny(john) [avatar definition]
203. ~funny(john) <- (~11) [avatar component clause 201]
209. ~funny(john) [subsumption resolution 124,149]
210. ~11 [avatar split clause 209,201]
239. 17 <=> old(john) [avatar definition]
240. old(john) <- (17) [avatar component clause 239]
256. old(john) | calm(john) <- (~11) [resolution 84,203]
260. old(john) <- (~11) [subsumption resolution 256,143]
261. 17 | 11 [avatar split clause 260,201,239]
262. strong(john) <- (17) [resolution 240,179]
264. $false <- (17) [subsumption resolution 262,138]
265. ~17 [avatar contradiction clause 264]
266. $false [avatar sat refutation 210,261,265]
% SZS output end Proof for 8904665944732906083814498
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not rich or not humble then paul is quiet or not tall.
Everyone who is both curious and wise is both not rich and not funny and vice versa.
Everyone who is creative or not happy is strong.
Everyone who is both not rich and wise is happy and vice versa.
If someone is both not humble and not wise then someone is not calm.
If someone is not kind or not patient then someone is brave or not curious and vice versa.
Everyone who is not funny or not kind is tall or not wise.
If someone is both funny and not rich then fred is either not funny or calm.
Everyone who is not patient is both not curious and patient and vice versa.
If someone is either tall or not creative then someone is either wise or happy.
If someone is rich or calm then alice is not curious and vice versa.
Everyone who is both patient and humble is both not funny and patient.
If paul is both generous and not happy then fred is both not humble and wise.
If someone is not creative or wise then fred is not creative and vice versa.
Everyone who is either kind or not quiet is not patient or rich.
Everyone who is not creative is not kind.
Someone is either wise or patient.
Someone is both patient and not funny.
Alice is either calm or not happy.
Someone is either quiet or not curious.
Someone is kind. | Alice is funny. | entailment | (((~rich(lucy)|~humble(lucy)))=>((quiet(paul)|~tall(paul))))&
(![X]:((curious(X)&wise(X))<=>(~rich(X)&~funny(X))))&
(![X]:((creative(X)|~happy(X))=>strong(X)))&
(![X]:((~rich(X)&wise(X))<=>happy(X)))&
((?[X]:((~humble(X)&~wise(X))))=>(?[X]:(~calm(X))))&
((?[X]:((~kind(X)|~patient(X))))<=>(?[X]:((brave(X)|~curious(X)))))&
(![X]:((~funny(X)|~kind(X))=>(tall(X)|~wise(X))))&
((?[X]:((funny(X)&~rich(X))))=>((~funny(fred)<~>calm(fred))))&
(![X]:(~patient(X)<=>(~curious(X)&patient(X))))&
((?[X]:((tall(X)<~>~creative(X))))=>(?[X]:((wise(X)<~>happy(X)))))&
((?[X]:((rich(X)|calm(X))))<=>(~curious(alice)))&
(![X]:((patient(X)&humble(X))=>(~funny(X)&patient(X))))&
(((generous(paul)&~happy(paul)))=>((~humble(fred)&wise(fred))))&
((?[X]:((~creative(X)|wise(X))))<=>(~creative(fred)))&
(![X]:((kind(X)<~>~quiet(X))=>(~patient(X)|rich(X))))&
(![X]:(~creative(X)=>~kind(X)))&
(?[X]:((wise(X)<~>patient(X))))&
(?[X]:((patient(X)&~funny(X))))&
((calm(alice)<~>~happy(alice)))&
(?[X]:((quiet(X)<~>~curious(X))))&
(?[X]:(kind(X))) | funny(alice) | [
"p1",
"p3",
"p8",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 25110589211372935885295
% SZS output start Proof for 25110589211372935885295
2. ! [X0] : ((wise(X0) & curious(X0)) <=> (~funny(X0) & ~rich(X0))) [input p1]
4. ! [X0] : ((wise(X0) & ~rich(X0)) <=> happy(X0)) [input p3]
9. ! [X0] : (~patient(X0) <=> (patient(X0) & ~curious(X0))) [input p8]
11. ? [X0] : (calm(X0) | rich(X0)) <=> ~curious(alice) [input p10]
19. calm(alice) <~> ~happy(alice) [input p18]
22. ~funny(alice) [input hypothesis]
40. ! [X0] : (((wise(X0) & curious(X0)) | (funny(X0) | rich(X0))) & ((~funny(X0) & ~rich(X0)) | (~wise(X0) | ~curious(X0)))) [nnf transformation 2]
41. ! [X0] : (((wise(X0) & curious(X0)) | funny(X0) | rich(X0)) & ((~funny(X0) & ~rich(X0)) | ~wise(X0) | ~curious(X0))) [flattening 40]
42. ! [X0] : (((wise(X0) & ~rich(X0)) | ~happy(X0)) & (happy(X0) | (~wise(X0) | rich(X0)))) [nnf transformation 4]
43. ! [X0] : (((wise(X0) & ~rich(X0)) | ~happy(X0)) & (happy(X0) | ~wise(X0) | rich(X0))) [flattening 42]
53. ! [X0] : ((~patient(X0) | (~patient(X0) | curious(X0))) & ((patient(X0) & ~curious(X0)) | patient(X0))) [nnf transformation 9]
54. ! [X0] : ((~patient(X0) | ~patient(X0) | curious(X0)) & ((patient(X0) & ~curious(X0)) | patient(X0))) [flattening 53]
59. (? [X0] : (calm(X0) | rich(X0)) | curious(alice)) & (~curious(alice) | ! [X0] : (~calm(X0) & ~rich(X0))) [nnf transformation 11]
60. (? [X0] : (calm(X0) | rich(X0)) | curious(alice)) & (~curious(alice) | ! [X1] : (~calm(X1) & ~rich(X1))) [rectify 59]
61. ? [X0] : (calm(X0) | rich(X0)) => (calm(sK4) | rich(sK4)) [choice axiom]
62. ((calm(sK4) | rich(sK4)) | curious(alice)) & (~curious(alice) | ! [X1] : (~calm(X1) & ~rich(X1))) [skolemisation 60,61]
73. (happy(alice) | ~calm(alice)) & (~happy(alice) | calm(alice)) [nnf transformation 19]
84. funny(X0) | wise(X0) | rich(X0) [cnf transformation 41]
85. ~wise(X0) | happy(X0) | rich(X0) [cnf transformation 43]
98. patient(X0) | patient(X0) [cnf transformation 54]
99. ~patient(X0) | ~patient(X0) | curious(X0) [cnf transformation 54]
104. ~curious(alice) | ~rich(X1) [cnf transformation 62]
105. ~curious(alice) | ~calm(X1) [cnf transformation 62]
119. ~happy(alice) | calm(alice) [cnf transformation 73]
124. ~funny(alice) [cnf transformation 22]
125. patient(X0) [duplicate literal removal 98]
126. ~patient(X0) | curious(X0) [duplicate literal removal 99]
154. 7 <=> ! [X1] : curious(X1) [avatar definition]
155. curious(X1) <- (7) [avatar component clause 154]
170. 11 <=> ! [X3] : patient(X3) [avatar definition]
171. patient(X3) <- (11) [avatar component clause 170]
198. 11 [avatar split clause 125,170]
222. 22 <=> curious(alice) [avatar definition]
223. ~curious(alice) <- (~22) [avatar component clause 222]
235. 25 <=> ! [X1] : ~calm(X1) [avatar definition]
236. ~calm(X1) <- (25) [avatar component clause 235]
237. 25 | ~22 [avatar split clause 105,222,235]
239. 26 <=> ! [X1] : ~rich(X1) [avatar definition]
240. ~rich(X1) <- (26) [avatar component clause 239]
241. 26 | ~22 [avatar split clause 104,222,239]
274. 34 <=> calm(alice) [avatar definition]
275. calm(alice) <- (34) [avatar component clause 274]
278. 35 <=> happy(alice) [avatar definition]
282. 34 | ~35 [avatar split clause 119,278,274]
299. curious(X0) <- (11) [resolution 126,171]
300. 7 | ~11 [avatar split clause 299,170,154]
302. $false <- (7, ~22) [resolution 155,223]
307. ~7 | 22 [avatar contradiction clause 302]
321. wise(alice) | rich(alice) [resolution 84,124]
324. wise(alice) <- (26) [subsumption resolution 321,240]
331. happy(alice) | rich(alice) <- (26) [resolution 324,85]
337. happy(alice) <- (26) [subsumption resolution 331,240]
338. 35 | ~26 [avatar split clause 337,239,278]
339. $false <- (25, 34) [subsumption resolution 275,236]
340. ~25 | ~34 [avatar contradiction clause 339]
341. $false [avatar sat refutation 198,237,241,282,300,307,338,340]
% SZS output end Proof for 25110589211372935885295
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise is both not quiet and not wise and vice versa. If someone is brave or kind then john is either not patient or not quiet and vice versa. Everyone who is not creative is both not funny and not old and vice versa. If mary is not old then someone is both not strong and patient. Everyone who is not creative or happy is either tall or not quiet and vice versa. If someone is both not funny and old then someone is not brave or not kind. Everyone who is either creative or not humble is both strong and not creative. Everyone who is both not kind and strong is calm or not kind. Everyone who is not humble is either not quiet or not wise. Everyone who is not old or calm is not humble or patient and vice versa. Everyone who is either not happy or patient is either curious or not brave. Someone is quiet or wise. Susan is not happy or tall. Mary is not quiet or not rich. Someone is either not strong or not old. Alice is not generous. Mary is tall. Susan is not happy or not rich. | Mary is humble. | neutral | (![X]:(wise(X)<=>(~quiet(X)&~wise(X))))&
((?[X]:((brave(X)|kind(X))))<=>((~patient(john)<~>~quiet(john))))&
(![X]:(~creative(X)<=>(~funny(X)&~old(X))))&
((~old(mary))=>(?[X]:((~strong(X)&patient(X)))))&
(![X]:((~creative(X)|happy(X))<=>(tall(X)<~>~quiet(X))))&
((?[X]:((~funny(X)&old(X))))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((creative(X)<~>~humble(X))=>(strong(X)&~creative(X))))&
(![X]:((~kind(X)&strong(X))=>(calm(X)|~kind(X))))&
(![X]:(~humble(X)=>(~quiet(X)<~>~wise(X))))&
(![X]:((~old(X)|calm(X))<=>(~humble(X)|patient(X))))&
(![X]:((~happy(X)<~>patient(X))=>(curious(X)<~>~brave(X))))&
(?[X]:((quiet(X)|wise(X))))&
((~happy(susan)|tall(susan)))&
((~quiet(mary)|~rich(mary)))&
(?[X]:((~strong(X)<~>~old(X))))&
(~generous(alice))&
(tall(mary))&
((~happy(susan)|~rich(susan))) | humble(mary) | [] | null | 0 |
If someone is strong then susan is not patient and vice versa. If someone is either happy or not kind then someone is both not happy and not brave and vice versa. Everyone who is not generous is not calm or not happy and vice versa. Everyone who is either quiet or not funny is both happy and quiet and vice versa. If someone is either generous or not creative then paul is humble and vice versa. Everyone who is both not rich and not brave is both not brave and not curious. Everyone who is not wise or old is old or rich and vice versa. If someone is either patient or not humble then someone is tall or not tall and vice versa. Everyone who is either not patient or not creative is rich. Everyone who is not wise or not tall is both not kind and generous and vice versa. If someone is both funny and not quiet then paul is not creative or not curious and vice versa. Everyone who is patient is not patient or not funny and vice versa. If someone is both kind and not happy then someone is either not creative or tall and vice versa. If susan is either not tall or kind then fred is both brave and not wise. If john is both not happy and funny then someone is either not old or not rich and vice versa. If john is either not calm or quiet then someone is both not curious and not generous. Mary is either not humble or happy. Mary is both not old and not curious. Alice is both not happy and not rich. Paul is not kind or not humble. | Alice is strong. | contradiction | ((?[X]:(strong(X)))<=>(~patient(susan)))&
((?[X]:((happy(X)<~>~kind(X))))<=>(?[X]:((~happy(X)&~brave(X)))))&
(![X]:(~generous(X)<=>(~calm(X)|~happy(X))))&
(![X]:((quiet(X)<~>~funny(X))<=>(happy(X)&quiet(X))))&
((?[X]:((generous(X)<~>~creative(X))))<=>(humble(paul)))&
(![X]:((~rich(X)&~brave(X))=>(~brave(X)&~curious(X))))&
(![X]:((~wise(X)|old(X))<=>(old(X)|rich(X))))&
((?[X]:((patient(X)<~>~humble(X))))<=>(?[X]:((tall(X)|~tall(X)))))&
(![X]:((~patient(X)<~>~creative(X))=>rich(X)))&
(![X]:((~wise(X)|~tall(X))<=>(~kind(X)&generous(X))))&
((?[X]:((funny(X)&~quiet(X))))<=>((~creative(paul)|~curious(paul))))&
(![X]:(patient(X)<=>(~patient(X)|~funny(X))))&
((?[X]:((kind(X)&~happy(X))))<=>(?[X]:((~creative(X)<~>tall(X)))))&
(((~tall(susan)<~>kind(susan)))=>((brave(fred)&~wise(fred))))&
(((~happy(john)&funny(john)))<=>(?[X]:((~old(X)<~>~rich(X)))))&
(((~calm(john)<~>quiet(john)))=>(?[X]:((~curious(X)&~generous(X)))))&
((~humble(mary)<~>happy(mary)))&
((~old(mary)&~curious(mary)))&
((~happy(alice)&~rich(alice)))&
((~kind(paul)|~humble(paul))) | strong(alice) | [
"p0",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4987619829813202770949727
% SZS output start Proof for 4987619829813202770949727
1. ? [X0] : strong(X0) <=> ~patient(susan) [input p0]
12. ! [X0] : (patient(X0) <=> (~funny(X0) | ~patient(X0))) [input p11]
21. strong(alice) [input hypothesis]
30. (? [X0] : strong(X0) | patient(susan)) & (~patient(susan) | ! [X0] : ~strong(X0)) [nnf transformation 1]
31. (? [X0] : strong(X0) | patient(susan)) & (~patient(susan) | ! [X1] : ~strong(X1)) [rectify 30]
32. ? [X0] : strong(X0) => strong(sK0) [choice axiom]
33. (strong(sK0) | patient(susan)) & (~patient(susan) | ! [X1] : ~strong(X1)) [skolemisation 31,32]
62. ! [X0] : ((patient(X0) | (funny(X0) & patient(X0))) & ((~funny(X0) | ~patient(X0)) | ~patient(X0))) [nnf transformation 12]
63. ! [X0] : ((patient(X0) | (funny(X0) & patient(X0))) & (~funny(X0) | ~patient(X0) | ~patient(X0))) [flattening 62]
79. ~patient(susan) | ~strong(X1) [cnf transformation 33]
125. patient(X0) | patient(X0) [cnf transformation 63]
154. strong(alice) [cnf transformation 21]
156. patient(X0) [duplicate literal removal 125]
160. 1 <=> patient(susan) [avatar definition]
161. ~patient(susan) <- (~1) [avatar component clause 160]
169. 3 <=> ! [X1] : ~strong(X1) [avatar definition]
170. ~strong(X1) <- (3) [avatar component clause 169]
171. 3 | ~1 [avatar split clause 79,160,169]
365. $false <- (~1) [subsumption resolution 161,156]
366. 1 [avatar contradiction clause 365]
367. $false <- (3) [resolution 170,154]
370. ~3 [avatar contradiction clause 367]
371. $false [avatar sat refutation 171,366,370]
% SZS output end Proof for 4987619829813202770949727
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and strong is not creative or creative.
If someone is both not brave and curious then someone is either not happy or creative and vice versa.
Everyone who is both funny and kind is not strong.
Everyone who is tall or calm is both not calm and creative and vice versa.
If john is not kind or not patient then lucy is both humble and creative and vice versa.
Everyone who is happy or not funny is both not strong and not happy and vice versa.
Everyone who is both brave and not generous is both curious and quiet and vice versa.
If someone is both not curious and not wise then paul is wise or patient.
If alice is rich then someone is either funny or brave and vice versa.
If someone is patient or not funny then someone is not humble or not happy.
If mary is brave or generous then mary is not humble.
Everyone who is either kind or quiet is strong and vice versa.
Everyone who is tall or wise is not quiet or happy and vice versa.
Everyone who is not strong or not creative is either curious or not funny and vice versa.
Everyone who is both not happy and not brave is not tall.
If mary is strong then mary is not creative or not brave and vice versa.
Mary is either not happy or wise.
Someone is either humble or tall.
Someone is both old and not funny.
Lucy is either patient or not happy.
Paul is either not happy or old. | Lucy is curious. | contradiction | (![X]:((old(X)&strong(X))=>(~creative(X)|creative(X))))&
((?[X]:((~brave(X)&curious(X))))<=>(?[X]:((~happy(X)<~>creative(X)))))&
(![X]:((funny(X)&kind(X))=>~strong(X)))&
(![X]:((tall(X)|calm(X))<=>(~calm(X)&creative(X))))&
(((~kind(john)|~patient(john)))<=>((humble(lucy)&creative(lucy))))&
(![X]:((happy(X)|~funny(X))<=>(~strong(X)&~happy(X))))&
(![X]:((brave(X)&~generous(X))<=>(curious(X)&quiet(X))))&
((?[X]:((~curious(X)&~wise(X))))=>((wise(paul)|patient(paul))))&
((rich(alice))<=>(?[X]:((funny(X)<~>brave(X)))))&
((?[X]:((patient(X)|~funny(X))))=>(?[X]:((~humble(X)|~happy(X)))))&
(((brave(mary)|generous(mary)))=>(~humble(mary)))&
(![X]:((kind(X)<~>quiet(X))<=>strong(X)))&
(![X]:((tall(X)|wise(X))<=>(~quiet(X)|happy(X))))&
(![X]:((~strong(X)|~creative(X))<=>(curious(X)<~>~funny(X))))&
(![X]:((~happy(X)&~brave(X))=>~tall(X)))&
((strong(mary))<=>((~creative(mary)|~brave(mary))))&
((~happy(mary)<~>wise(mary)))&
(?[X]:((humble(X)<~>tall(X))))&
(?[X]:((old(X)&~funny(X))))&
((patient(lucy)<~>~happy(lucy)))&
((~happy(paul)<~>old(paul))) | curious(lucy) | [
"p1",
"p2",
"p5",
"p6",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1612966990753846077854458
% SZS output start Proof for 1612966990753846077854458
2. ? [X0] : (curious(X0) & ~brave(X0)) <=> ? [X0] : (~happy(X0) <~> creative(X0)) [input p1]
3. ! [X0] : ((kind(X0) & funny(X0)) => ~strong(X0)) [input p2]
6. ! [X0] : ((~funny(X0) | happy(X0)) <=> (~happy(X0) & ~strong(X0))) [input p5]
7. ! [X0] : ((~generous(X0) & brave(X0)) <=> (quiet(X0) & curious(X0))) [input p6]
12. ! [X0] : ((kind(X0) <~> quiet(X0)) <=> strong(X0)) [input p11]
14. ! [X0] : ((~creative(X0) | ~strong(X0)) <=> (curious(X0) <~> ~funny(X0))) [input p13]
22. curious(lucy) [input hypothesis]
23. ? [X0] : (curious(X0) & ~brave(X0)) <=> ? [X1] : (~happy(X1) <~> creative(X1)) [rectify 2]
27. ! [X0] : (~strong(X0) | (~kind(X0) | ~funny(X0))) [ennf transformation 3]
28. ! [X0] : (~strong(X0) | ~kind(X0) | ~funny(X0)) [flattening 27]
35. (? [X0] : (curious(X0) & ~brave(X0)) | ! [X1] : ((~happy(X1) | ~creative(X1)) & (creative(X1) | happy(X1)))) & (? [X1] : ((~creative(X1) | happy(X1)) & (creative(X1) | ~happy(X1))) | ! [X0] : (~curious(X0) | brave(X0))) [nnf transformation 23]
36. (? [X0] : (curious(X0) & ~brave(X0)) | ! [X1] : ((~happy(X1) | ~creative(X1)) & (creative(X1) | happy(X1)))) & (? [X2] : ((~creative(X2) | happy(X2)) & (creative(X2) | ~happy(X2))) | ! [X3] : (~curious(X3) | brave(X3))) [rectify 35]
37. ? [X0] : (curious(X0) & ~brave(X0)) => (curious(sK0) & ~brave(sK0)) [choice axiom]
38. ? [X2] : ((~creative(X2) | happy(X2)) & (creative(X2) | ~happy(X2))) => ((~creative(sK1) | happy(sK1)) & (creative(sK1) | ~happy(sK1))) [choice axiom]
39. ((curious(sK0) & ~brave(sK0)) | ! [X1] : ((~happy(X1) | ~creative(X1)) & (creative(X1) | happy(X1)))) & (((~creative(sK1) | happy(sK1)) & (creative(sK1) | ~happy(sK1))) | ! [X3] : (~curious(X3) | brave(X3))) [skolemisation 36,38,37]
44. ! [X0] : (((~funny(X0) | happy(X0)) | (happy(X0) | strong(X0))) & ((~happy(X0) & ~strong(X0)) | (funny(X0) & ~happy(X0)))) [nnf transformation 6]
45. ! [X0] : ((~funny(X0) | happy(X0) | happy(X0) | strong(X0)) & ((~happy(X0) & ~strong(X0)) | (funny(X0) & ~happy(X0)))) [flattening 44]
46. ! [X0] : (((~generous(X0) & brave(X0)) | (~quiet(X0) | ~curious(X0))) & ((quiet(X0) & curious(X0)) | (generous(X0) | ~brave(X0)))) [nnf transformation 7]
47. ! [X0] : (((~generous(X0) & brave(X0)) | ~quiet(X0) | ~curious(X0)) & ((quiet(X0) & curious(X0)) | generous(X0) | ~brave(X0))) [flattening 46]
55. ! [X0] : ((((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | ~strong(X0)) & (strong(X0) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0))))) [nnf transformation 12]
58. ! [X0] : (((~creative(X0) | ~strong(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) & (((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (creative(X0) & strong(X0)))) [nnf transformation 14]
59. ! [X0] : ((~creative(X0) | ~strong(X0) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0)))) & (((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (creative(X0) & strong(X0)))) [flattening 58]
73. ~brave(sK0) | creative(X1) | happy(X1) [cnf transformation 39]
75. curious(sK0) | creative(X1) | happy(X1) [cnf transformation 39]
77. ~kind(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 28]
89. ~strong(X0) | funny(X0) [cnf transformation 45]
90. ~happy(X0) | ~happy(X0) [cnf transformation 45]
92. ~funny(X0) | happy(X0) | happy(X0) | strong(X0) [cnf transformation 45]
95. ~quiet(X0) | brave(X0) | ~curious(X0) [cnf transformation 47]
108. ~strong(X0) | kind(X0) | quiet(X0) [cnf transformation 55]
116. funny(X0) | ~curious(X0) | strong(X0) [cnf transformation 59]
118. ~creative(X0) | ~strong(X0) | ~funny(X0) | ~curious(X0) [cnf transformation 59]
134. curious(lucy) [cnf transformation 22]
135. ~happy(X0) [duplicate literal removal 90]
136. ~funny(X0) | happy(X0) | strong(X0) [duplicate literal removal 92]
143. 2 <=> curious(sK0) [avatar definition]
145. curious(sK0) <- (2) [avatar component clause 143]
148. 3 <=> ! [X1] : (creative(X1) | happy(X1)) [avatar definition]
149. creative(X1) | happy(X1) <- (3) [avatar component clause 148]
150. 3 | 2 [avatar split clause 75,143,148]
152. 4 <=> brave(sK0) [avatar definition]
154. ~brave(sK0) <- (~4) [avatar component clause 152]
156. 3 | ~4 [avatar split clause 73,152,148]
241. ~curious(X0) | ~strong(X0) | ~creative(X0) [subsumption resolution 118,89]
242. ~curious(X0) | funny(X0) [subsumption resolution 116,89]
273. funny(lucy) [resolution 242,134]
347. creative(X1) <- (3) [subsumption resolution 149,135]
365. happy(lucy) | strong(lucy) [resolution 136,273]
367. strong(lucy) [subsumption resolution 365,135]
390. ~strong(lucy) | ~creative(lucy) [resolution 241,134]
391. ~creative(lucy) [subsumption resolution 390,367]
394. $false <- (3) [subsumption resolution 391,347]
395. ~3 [avatar contradiction clause 394]
402. funny(sK0) <- (2) [resolution 145,242]
408. 36 <=> strong(sK0) [avatar definition]
409. strong(sK0) <- (36) [avatar component clause 408]
413. 37 <=> funny(sK0) [avatar definition]
415. funny(sK0) <- (37) [avatar component clause 413]
419. 37 | ~2 [avatar split clause 402,143,413]
434. happy(sK0) | strong(sK0) <- (37) [resolution 415,136]
437. strong(sK0) <- (37) [subsumption resolution 434,135]
438. 36 | ~37 [avatar split clause 437,413,408]
439. kind(sK0) | quiet(sK0) <- (36) [resolution 409,108]
442. 40 <=> quiet(sK0) [avatar definition]
444. quiet(sK0) <- (40) [avatar component clause 442]
446. 41 <=> kind(sK0) [avatar definition]
448. kind(sK0) <- (41) [avatar component clause 446]
449. 40 | 41 | ~36 [avatar split clause 439,408,446,442]
484. ~strong(sK0) | ~funny(sK0) <- (41) [resolution 448,77]
485. ~funny(sK0) <- (36, 41) [subsumption resolution 484,409]
486. $false <- (36, 37, 41) [subsumption resolution 485,415]
487. ~36 | ~37 | ~41 [avatar contradiction clause 486]
491. brave(sK0) | ~curious(sK0) <- (40) [resolution 444,95]
494. ~curious(sK0) <- (~4, 40) [subsumption resolution 491,154]
495. $false <- (2, ~4, 40) [subsumption resolution 494,145]
496. ~2 | 4 | ~40 [avatar contradiction clause 495]
497. $false [avatar sat refutation 150,156,395,419,438,449,487,496]
% SZS output end Proof for 1612966990753846077854458
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave or quiet is either not brave or not strong and vice versa.
If someone is both not kind and curious then someone is both not happy and quiet and vice versa.
If susan is either old or strong then mary is not happy or quiet.
Everyone who is both not curious and not calm is either not tall or not quiet.
Everyone who is wise is generous and vice versa.
If someone is both humble and not strong then fred is not old and vice versa.
If fred is both not wise and not generous then someone is either old or calm and vice versa.
If someone is curious or not creative then paul is both old and quiet.
Everyone who is both not happy and generous is not calm and vice versa.
Everyone who is not strong is kind or old and vice versa.
Everyone who is kind or old is quiet and vice versa.
Everyone who is both not humble and funny is either not generous or creative and vice versa.
Everyone who is funny or generous is not quiet.
If someone is either tall or kind then fred is calm.
Everyone who is wise or not patient is not generous.
If fred is both quiet and not quiet then mary is happy and vice versa.
Someone is patient or not humble.
Alice is either not calm or not old.
John is not curious or old.
Someone is either not quiet or tall.
Paul is creative or humble.
Alice is both not funny and not strong.
Mary is either humble or wise. | Paul is humble. | neutral | (![X]:((brave(X)|quiet(X))<=>(~brave(X)<~>~strong(X))))&
((?[X]:((~kind(X)&curious(X))))<=>(?[X]:((~happy(X)&quiet(X)))))&
(((old(susan)<~>strong(susan)))=>((~happy(mary)|quiet(mary))))&
(![X]:((~curious(X)&~calm(X))=>(~tall(X)<~>~quiet(X))))&
(![X]:(wise(X)<=>generous(X)))&
((?[X]:((humble(X)&~strong(X))))<=>(~old(fred)))&
(((~wise(fred)&~generous(fred)))<=>(?[X]:((old(X)<~>calm(X)))))&
((?[X]:((curious(X)|~creative(X))))=>((old(paul)&quiet(paul))))&
(![X]:((~happy(X)&generous(X))<=>~calm(X)))&
(![X]:(~strong(X)<=>(kind(X)|old(X))))&
(![X]:((kind(X)|old(X))<=>quiet(X)))&
(![X]:((~humble(X)&funny(X))<=>(~generous(X)<~>creative(X))))&
(![X]:((funny(X)|generous(X))=>~quiet(X)))&
((?[X]:((tall(X)<~>kind(X))))=>(calm(fred)))&
(![X]:((wise(X)|~patient(X))=>~generous(X)))&
(((quiet(fred)&~quiet(fred)))<=>(happy(mary)))&
(?[X]:((patient(X)|~humble(X))))&
((~calm(alice)<~>~old(alice)))&
((~curious(john)|old(john)))&
(?[X]:((~quiet(X)<~>tall(X))))&
((creative(paul)|humble(paul)))&
((~funny(alice)&~strong(alice)))&
((humble(mary)<~>wise(mary))) | humble(paul) | [] | null | 0 |
If fred is both not quiet and rich then someone is not patient or not strong and vice versa.
If lucy is curious then susan is both humble and not calm.
Everyone who is both quiet and not rich is calm and vice versa.
If susan is either not strong or wise then someone is either not happy or old and vice versa.
Everyone who is both calm and curious is kind or curious.
If someone is old then fred is either humble or quiet and vice versa.
Everyone who is both brave and kind is not calm or strong and vice versa.
Everyone who is brave is either wise or humble.
Everyone who is not old or humble is strong or not rich.
Everyone who is humble is old or not curious.
Everyone who is either patient or not humble is not patient.
Everyone who is not patient is humble.
Everyone who is kind is either not quiet or creative and vice versa.
Everyone who is not wise or not quiet is both happy and not curious and vice versa.
If mary is calm or not patient then someone is either calm or not tall.
Everyone who is not curious or not strong is either patient or strong and vice versa.
Someone is either creative or humble.
Paul is not humble or creative.
Susan is either patient or curious.
Paul is either humble or happy.
Someone is happy. | Paul is not happy. | contradiction | (((~quiet(fred)&rich(fred)))<=>(?[X]:((~patient(X)|~strong(X)))))&
((curious(lucy))=>((humble(susan)&~calm(susan))))&
(![X]:((quiet(X)&~rich(X))<=>calm(X)))&
(((~strong(susan)<~>wise(susan)))<=>(?[X]:((~happy(X)<~>old(X)))))&
(![X]:((calm(X)&curious(X))=>(kind(X)|curious(X))))&
((?[X]:(old(X)))<=>((humble(fred)<~>quiet(fred))))&
(![X]:((brave(X)&kind(X))<=>(~calm(X)|strong(X))))&
(![X]:(brave(X)=>(wise(X)<~>humble(X))))&
(![X]:((~old(X)|humble(X))=>(strong(X)|~rich(X))))&
(![X]:(humble(X)=>(old(X)|~curious(X))))&
(![X]:((patient(X)<~>~humble(X))=>~patient(X)))&
(![X]:(~patient(X)=>humble(X)))&
(![X]:(kind(X)<=>(~quiet(X)<~>creative(X))))&
(![X]:((~wise(X)|~quiet(X))<=>(happy(X)&~curious(X))))&
(((calm(mary)|~patient(mary)))=>(?[X]:((calm(X)<~>~tall(X)))))&
(![X]:((~curious(X)|~strong(X))<=>(patient(X)<~>strong(X))))&
(?[X]:((creative(X)<~>humble(X))))&
((~humble(paul)|creative(paul)))&
((patient(susan)<~>curious(susan)))&
((humble(paul)<~>happy(paul)))&
(?[X]:(happy(X))) | ~happy(paul) | [
"p6",
"p7",
"p10",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 461521570745752603353039
% SZS output start Proof for 461521570745752603353039
7. ! [X0] : ((kind(X0) & brave(X0)) <=> (strong(X0) | ~calm(X0))) [input p6]
8. ! [X0] : (brave(X0) => (wise(X0) <~> humble(X0))) [input p7]
11. ! [X0] : ((patient(X0) <~> ~humble(X0)) => ~patient(X0)) [input p10]
14. ! [X0] : ((~quiet(X0) | ~wise(X0)) <=> (~curious(X0) & happy(X0))) [input p13]
16. ! [X0] : ((~strong(X0) | ~curious(X0)) <=> (patient(X0) <~> strong(X0))) [input p15]
20. humble(paul) <~> happy(paul) [input p19]
22. ~happy(paul) [input hypothesis]
26. ! [X0] : ((wise(X0) <~> humble(X0)) | ~brave(X0)) [ennf transformation 8]
31. ! [X0] : (~patient(X0) | (patient(X0) <=> ~humble(X0))) [ennf transformation 11]
49. ! [X0] : (((kind(X0) & brave(X0)) | (~strong(X0) & calm(X0))) & ((strong(X0) | ~calm(X0)) | (~kind(X0) | ~brave(X0)))) [nnf transformation 7]
50. ! [X0] : (((kind(X0) & brave(X0)) | (~strong(X0) & calm(X0))) & (strong(X0) | ~calm(X0) | ~kind(X0) | ~brave(X0))) [flattening 49]
51. ! [X0] : (((~humble(X0) | ~wise(X0)) & (humble(X0) | wise(X0))) | ~brave(X0)) [nnf transformation 26]
52. ! [X0] : (~patient(X0) | ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0)))) [nnf transformation 31]
54. ! [X0] : (((~quiet(X0) | ~wise(X0)) | (curious(X0) | ~happy(X0))) & ((~curious(X0) & happy(X0)) | (quiet(X0) & wise(X0)))) [nnf transformation 14]
55. ! [X0] : ((~quiet(X0) | ~wise(X0) | curious(X0) | ~happy(X0)) & ((~curious(X0) & happy(X0)) | (quiet(X0) & wise(X0)))) [flattening 54]
59. ! [X0] : (((~strong(X0) | ~curious(X0)) | ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0)))) & (((~strong(X0) | ~patient(X0)) & (strong(X0) | patient(X0))) | (strong(X0) & curious(X0)))) [nnf transformation 16]
60. ! [X0] : ((~strong(X0) | ~curious(X0) | ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0)))) & (((~strong(X0) | ~patient(X0)) & (strong(X0) | patient(X0))) | (strong(X0) & curious(X0)))) [flattening 59]
65. (~happy(paul) | ~humble(paul)) & (happy(paul) | humble(paul)) [nnf transformation 20]
93. ~strong(X0) | brave(X0) [cnf transformation 50]
97. ~brave(X0) | ~wise(X0) | ~humble(X0) [cnf transformation 51]
101. ~patient(X0) | ~humble(X0) | ~patient(X0) [cnf transformation 52]
108. happy(X0) | wise(X0) [cnf transformation 55]
118. strong(X0) | patient(X0) | strong(X0) [cnf transformation 60]
128. happy(paul) | humble(paul) [cnf transformation 65]
131. ~happy(paul) [cnf transformation 22]
132. strong(X0) | patient(X0) [duplicate literal removal 118]
134. ~humble(X0) | ~patient(X0) [duplicate literal removal 101]
252. 25 <=> humble(paul) [avatar definition]
253. humble(paul) <- (25) [avatar component clause 252]
271. 29 <=> happy(paul) [avatar definition]
273. ~happy(paul) <- (~29) [avatar component clause 271]
275. 25 | 29 [avatar split clause 128,271,252]
276. ~29 [avatar split clause 131,271]
279. wise(paul) <- (~29) [resolution 108,273]
284. brave(X1) | patient(X1) [resolution 132,93]
447. patient(X1) | ~wise(X1) | ~humble(X1) [resolution 284,97]
449. ~wise(X1) | ~humble(X1) [subsumption resolution 447,134]
498. ~humble(paul) <- (~29) [resolution 449,279]
500. $false <- (25, ~29) [subsumption resolution 498,253]
501. ~25 | 29 [avatar contradiction clause 500]
502. $false [avatar sat refutation 275,276,501]
% SZS output end Proof for 461521570745752603353039
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either humble or not calm then someone is not generous or not patient. Everyone who is either calm or patient is both not strong and curious. If susan is either not generous or rich then someone is both curious and not strong and vice versa. Everyone who is either kind or funny is not calm or old and vice versa. Everyone who is both humble and not curious is both curious and quiet and vice versa. If someone is calm or not humble then lucy is either creative or not funny and vice versa. If alice is both quiet and not calm then susan is old and vice versa. If john is quiet then fred is either patient or tall and vice versa. If someone is not happy then someone is tall or brave. If someone is not strong then someone is either calm or patient and vice versa. If someone is old or quiet then mary is brave or not generous and vice versa. If someone is happy then alice is both quiet and humble. Everyone who is not kind or not humble is both not generous and not strong and vice versa. Everyone who is not brave is both not kind and not patient. If john is both not funny and not curious then someone is either rich or not kind and vice versa. If someone is patient or not strong then someone is both generous and not kind. Alice is either not brave or creative. Fred is either generous or strong. John is both brave and not creative. Someone is not creative or happy. Mary is either not quiet or not brave. Lucy is not wise or not kind. Paul is not funny. | Mary is not kind. | contradiction | (((humble(john)<~>~calm(john)))=>(?[X]:((~generous(X)|~patient(X)))))&
(![X]:((calm(X)<~>patient(X))=>(~strong(X)&curious(X))))&
(((~generous(susan)<~>rich(susan)))<=>(?[X]:((curious(X)&~strong(X)))))&
(![X]:((kind(X)<~>funny(X))<=>(~calm(X)|old(X))))&
(![X]:((humble(X)&~curious(X))<=>(curious(X)&quiet(X))))&
((?[X]:((calm(X)|~humble(X))))<=>((creative(lucy)<~>~funny(lucy))))&
(((quiet(alice)&~calm(alice)))<=>(old(susan)))&
((quiet(john))<=>((patient(fred)<~>tall(fred))))&
((?[X]:(~happy(X)))=>(?[X]:((tall(X)|brave(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((calm(X)<~>patient(X)))))&
((?[X]:((old(X)|quiet(X))))<=>((brave(mary)|~generous(mary))))&
((?[X]:(happy(X)))=>((quiet(alice)&humble(alice))))&
(![X]:((~kind(X)|~humble(X))<=>(~generous(X)&~strong(X))))&
(![X]:(~brave(X)=>(~kind(X)&~patient(X))))&
(((~funny(john)&~curious(john)))<=>(?[X]:((rich(X)<~>~kind(X)))))&
((?[X]:((patient(X)|~strong(X))))=>(?[X]:((generous(X)&~kind(X)))))&
((~brave(alice)<~>creative(alice)))&
((generous(fred)<~>strong(fred)))&
((brave(john)&~creative(john)))&
(?[X]:((~creative(X)|happy(X))))&
((~quiet(mary)<~>~brave(mary)))&
((~wise(lucy)|~kind(lucy)))&
(~funny(paul)) | ~kind(mary) | [
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 877721487443455099041517
% SZS output start Proof for 877721487443455099041517
13. ! [X0] : ((~humble(X0) | ~kind(X0)) <=> (~strong(X0) & ~generous(X0))) [input p12]
16. ? [X0] : (~strong(X0) | patient(X0)) => ? [X0] : (~kind(X0) & generous(X0)) [input p15]
24. ~kind(mary) [input hypothesis]
27. ? [X0] : (~strong(X0) | patient(X0)) => ? [X1] : (~kind(X1) & generous(X1)) [rectify 16]
34. ? [X1] : (~kind(X1) & generous(X1)) | ! [X0] : (strong(X0) & ~patient(X0)) [ennf transformation 27]
67. ! [X0] : (((~humble(X0) | ~kind(X0)) | (strong(X0) | generous(X0))) & ((~strong(X0) & ~generous(X0)) | (humble(X0) & kind(X0)))) [nnf transformation 13]
68. ! [X0] : ((~humble(X0) | ~kind(X0) | strong(X0) | generous(X0)) & ((~strong(X0) & ~generous(X0)) | (humble(X0) & kind(X0)))) [flattening 67]
74. ? [X0] : (~kind(X0) & generous(X0)) | ! [X1] : (strong(X1) & ~patient(X1)) [rectify 34]
75. ? [X0] : (~kind(X0) & generous(X0)) => (~kind(sK8) & generous(sK8)) [choice axiom]
76. (~kind(sK8) & generous(sK8)) | ! [X1] : (strong(X1) & ~patient(X1)) [skolemisation 74,75]
128. ~generous(X0) | kind(X0) [cnf transformation 68]
130. ~strong(X0) | kind(X0) [cnf transformation 68]
142. generous(sK8) | strong(X1) [cnf transformation 76]
144. ~kind(sK8) | strong(X1) [cnf transformation 76]
155. ~kind(mary) [cnf transformation 24]
285. 28 <=> ! [X3] : strong(X3) [avatar definition]
286. strong(X3) <- (28) [avatar component clause 285]
361. 45 <=> kind(sK8) [avatar definition]
363. ~kind(sK8) <- (~45) [avatar component clause 361]
364. 28 | ~45 [avatar split clause 144,361,285]
370. 47 <=> generous(sK8) [avatar definition]
372. generous(sK8) <- (47) [avatar component clause 370]
373. 28 | 47 [avatar split clause 142,370,285]
424. kind(sK8) <- (47) [resolution 128,372]
425. $false <- (~45, 47) [subsumption resolution 424,363]
426. 45 | ~47 [avatar contradiction clause 425]
430. kind(X0) <- (28) [resolution 130,286]
437. $false <- (28) [resolution 430,155]
442. ~28 [avatar contradiction clause 437]
443. $false [avatar sat refutation 364,373,426,442]
% SZS output end Proof for 877721487443455099041517
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave then john is not calm or not patient. If someone is not generous or not kind then alice is generous. Everyone who is funny or brave is not rich and vice versa. Everyone who is not humble is either not brave or tall and vice versa. If lucy is not happy then fred is not humble or tall. Everyone who is both humble and not creative is both strong and brave. If lucy is both not happy and not creative then lucy is both old and not calm. Everyone who is not calm or creative is quiet or brave and vice versa. Everyone who is not calm or strong is not creative. If someone is rich or not kind then mary is either wise or not old. Everyone who is both not strong and not tall is not calm or not happy and vice versa. Everyone who is not humble or humble is humble. If someone is either not curious or not calm then someone is old. If alice is quiet or old then someone is not generous and vice versa. Everyone who is both not rich and not humble is not strong. Someone is both creative and humble. Susan is either wise or not calm. Someone is patient. John is both old and generous. Mary is either not patient or patient. Fred is not happy or curious. | Fred is not rich. | neutral | ((?[X]:(~brave(X)))=>((~calm(john)|~patient(john))))&
((?[X]:((~generous(X)|~kind(X))))=>(generous(alice)))&
(![X]:((funny(X)|brave(X))<=>~rich(X)))&
(![X]:(~humble(X)<=>(~brave(X)<~>tall(X))))&
((~happy(lucy))=>((~humble(fred)|tall(fred))))&
(![X]:((humble(X)&~creative(X))=>(strong(X)&brave(X))))&
(((~happy(lucy)&~creative(lucy)))=>((old(lucy)&~calm(lucy))))&
(![X]:((~calm(X)|creative(X))<=>(quiet(X)|brave(X))))&
(![X]:((~calm(X)|strong(X))=>~creative(X)))&
((?[X]:((rich(X)|~kind(X))))=>((wise(mary)<~>~old(mary))))&
(![X]:((~strong(X)&~tall(X))<=>(~calm(X)|~happy(X))))&
(![X]:((~humble(X)|humble(X))=>humble(X)))&
((?[X]:((~curious(X)<~>~calm(X))))=>(?[X]:(old(X))))&
(((quiet(alice)|old(alice)))<=>(?[X]:(~generous(X))))&
(![X]:((~rich(X)&~humble(X))=>~strong(X)))&
(?[X]:((creative(X)&humble(X))))&
((wise(susan)<~>~calm(susan)))&
(?[X]:(patient(X)))&
((old(john)&generous(john)))&
((~patient(mary)<~>patient(mary)))&
((~happy(fred)|curious(fred))) | ~rich(fred) | [] | null | 0 |
If someone is happy then mary is patient.
If alice is both not quiet and brave then someone is not kind or not wise and vice versa.
Everyone who is either not strong or not funny is patient or not generous.
Everyone who is both not calm and not funny is not quiet or funny.
Everyone who is either kind or tall is wise or not calm and vice versa.
Everyone who is both quiet and not tall is either not curious or quiet and vice versa.
If susan is not rich or creative then fred is kind or old.
If someone is creative or not kind then someone is not old or humble and vice versa.
Everyone who is creative is strong or not tall and vice versa.
If lucy is humble then someone is not wise.
If someone is not rich then john is both brave and not curious and vice versa.
Everyone who is both not old and not curious is not wise.
Everyone who is either not brave or brave is both not happy and calm.
Everyone who is quiet is patient and vice versa.
If someone is not rich or not curious then someone is not calm.
Everyone who is not strong is either kind or not generous.
Someone is both not generous and old.
Someone is rich or not creative.
Lucy is curious or not funny.
Someone is curious or wise.
Someone is not calm or curious. | John is not quiet. | neutral | ((?[X]:(happy(X)))=>(patient(mary)))&
(((~quiet(alice)&brave(alice)))<=>(?[X]:((~kind(X)|~wise(X)))))&
(![X]:((~strong(X)<~>~funny(X))=>(patient(X)|~generous(X))))&
(![X]:((~calm(X)&~funny(X))=>(~quiet(X)|funny(X))))&
(![X]:((kind(X)<~>tall(X))<=>(wise(X)|~calm(X))))&
(![X]:((quiet(X)&~tall(X))<=>(~curious(X)<~>quiet(X))))&
(((~rich(susan)|creative(susan)))=>((kind(fred)|old(fred))))&
((?[X]:((creative(X)|~kind(X))))<=>(?[X]:((~old(X)|humble(X)))))&
(![X]:(creative(X)<=>(strong(X)|~tall(X))))&
((humble(lucy))=>(?[X]:(~wise(X))))&
((?[X]:(~rich(X)))<=>((brave(john)&~curious(john))))&
(![X]:((~old(X)&~curious(X))=>~wise(X)))&
(![X]:((~brave(X)<~>brave(X))=>(~happy(X)&calm(X))))&
(![X]:(quiet(X)<=>patient(X)))&
((?[X]:((~rich(X)|~curious(X))))=>(?[X]:(~calm(X))))&
(![X]:(~strong(X)=>(kind(X)<~>~generous(X))))&
(?[X]:((~generous(X)&old(X))))&
(?[X]:((rich(X)|~creative(X))))&
((curious(lucy)|~funny(lucy)))&
(?[X]:((curious(X)|wise(X))))&
(?[X]:((~calm(X)|curious(X)))) | ~quiet(john) | [] | null | 0 |
Everyone who is not tall or not curious is not wise and vice versa. If mary is either not patient or not calm then lucy is not kind. Everyone who is not humble is either wise or tall and vice versa. If susan is either creative or not curious then someone is patient or not kind. Everyone who is both patient and not happy is quiet and vice versa. If someone is either strong or quiet then someone is wise. Everyone who is both old and strong is not calm and vice versa. Everyone who is not generous is humble or generous and vice versa. Everyone who is both wise and not generous is either not curious or rich. If susan is curious or not strong then someone is not strong or not brave. Everyone who is both kind and not old is both rich and not happy. Everyone who is happy is not creative and vice versa. If someone is humble then paul is not tall and vice versa. Everyone who is rich or patient is creative. Everyone who is both humble and old is curious. Everyone who is either old or not kind is both curious and not creative and vice versa. Someone is both wise and creative. Someone is not patient or not wise. Lucy is patient or brave. Someone is patient or not strong. Someone is kind. Alice is curious. Someone is either not tall or calm. Someone is either not rich or calm. | Susan is not generous. | entailment | (![X]:((~tall(X)|~curious(X))<=>~wise(X)))&
(((~patient(mary)<~>~calm(mary)))=>(~kind(lucy)))&
(![X]:(~humble(X)<=>(wise(X)<~>tall(X))))&
(((creative(susan)<~>~curious(susan)))=>(?[X]:((patient(X)|~kind(X)))))&
(![X]:((patient(X)&~happy(X))<=>quiet(X)))&
((?[X]:((strong(X)<~>quiet(X))))=>(?[X]:(wise(X))))&
(![X]:((old(X)&strong(X))<=>~calm(X)))&
(![X]:(~generous(X)<=>(humble(X)|generous(X))))&
(![X]:((wise(X)&~generous(X))=>(~curious(X)<~>rich(X))))&
(((curious(susan)|~strong(susan)))=>(?[X]:((~strong(X)|~brave(X)))))&
(![X]:((kind(X)&~old(X))=>(rich(X)&~happy(X))))&
(![X]:(happy(X)<=>~creative(X)))&
((?[X]:(humble(X)))<=>(~tall(paul)))&
(![X]:((rich(X)|patient(X))=>creative(X)))&
(![X]:((humble(X)&old(X))=>curious(X)))&
(![X]:((old(X)<~>~kind(X))<=>(curious(X)&~creative(X))))&
(?[X]:((wise(X)&creative(X))))&
(?[X]:((~patient(X)|~wise(X))))&
((patient(lucy)|brave(lucy)))&
(?[X]:((patient(X)|~strong(X))))&
(?[X]:(kind(X)))&
(curious(alice))&
(?[X]:((~tall(X)<~>calm(X))))&
(?[X]:((~rich(X)<~>calm(X)))) | ~generous(susan) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8001927573485037778248587
% SZS output start Proof for 8001927573485037778248587
8. ! [X0] : (~generous(X0) <=> (generous(X0) | humble(X0))) [input p7]
25. generous(susan) [input hypothesis]
53. ! [X0] : ((~generous(X0) | (~generous(X0) & ~humble(X0))) & ((generous(X0) | humble(X0)) | generous(X0))) [nnf transformation 8]
54. ! [X0] : ((~generous(X0) | (~generous(X0) & ~humble(X0))) & (generous(X0) | humble(X0) | generous(X0))) [flattening 53]
100. ~generous(X0) | ~generous(X0) [cnf transformation 54]
131. generous(susan) [cnf transformation 25]
133. ~generous(X0) [duplicate literal removal 100]
248. $false [subsumption resolution 131,133]
% SZS output end Proof for 8001927573485037778248587
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is calm or wise then someone is both not rich and not generous.
If alice is not quiet then mary is not funny or not quiet.
Everyone who is either not kind or curious is either tall or not humble and vice versa.
If someone is tall then someone is not brave or not wise.
If john is humble or not rich then lucy is both not old and wise and vice versa.
Everyone who is tall or creative is both not curious and not rich and vice versa.
Everyone who is humble or curious is happy or not funny and vice versa.
If someone is both kind and not kind then susan is funny.
Everyone who is both old and not strong is either brave or wise and vice versa.
Everyone who is both not wise and not kind is either not patient or quiet.
Everyone who is old is both patient and kind.
Everyone who is either not funny or generous is either quiet or not patient and vice versa.
Everyone who is calm or not wise is not rich or humble.
Everyone who is either quiet or funny is not wise or generous and vice versa.
If someone is brave then someone is not happy and vice versa.
Everyone who is either not tall or not rich is happy or wise.
Lucy is not brave.
Lucy is either not wise or quiet.
Fred is both humble and not happy.
Susan is either humble or not funny.
Someone is both strong and tall.
Fred is either happy or old. | Alice is curious. | neutral | (((calm(susan)|wise(susan)))=>(?[X]:((~rich(X)&~generous(X)))))&
((~quiet(alice))=>((~funny(mary)|~quiet(mary))))&
(![X]:((~kind(X)<~>curious(X))<=>(tall(X)<~>~humble(X))))&
((?[X]:(tall(X)))=>(?[X]:((~brave(X)|~wise(X)))))&
(((humble(john)|~rich(john)))<=>((~old(lucy)&wise(lucy))))&
(![X]:((tall(X)|creative(X))<=>(~curious(X)&~rich(X))))&
(![X]:((humble(X)|curious(X))<=>(happy(X)|~funny(X))))&
((?[X]:((kind(X)&~kind(X))))=>(funny(susan)))&
(![X]:((old(X)&~strong(X))<=>(brave(X)<~>wise(X))))&
(![X]:((~wise(X)&~kind(X))=>(~patient(X)<~>quiet(X))))&
(![X]:(old(X)=>(patient(X)&kind(X))))&
(![X]:((~funny(X)<~>generous(X))<=>(quiet(X)<~>~patient(X))))&
(![X]:((calm(X)|~wise(X))=>(~rich(X)|humble(X))))&
(![X]:((quiet(X)<~>funny(X))<=>(~wise(X)|generous(X))))&
((?[X]:(brave(X)))<=>(?[X]:(~happy(X))))&
(![X]:((~tall(X)<~>~rich(X))=>(happy(X)|wise(X))))&
(~brave(lucy))&
((~wise(lucy)<~>quiet(lucy)))&
((humble(fred)&~happy(fred)))&
((humble(susan)<~>~funny(susan)))&
(?[X]:((strong(X)&tall(X))))&
((happy(fred)<~>old(fred))) | curious(alice) | [] | null | 0 |
Everyone who is both strong and patient is not humble or kind and vice versa.
If john is not tall then john is either not quiet or wise.
If susan is tall or not happy then someone is both not curious and not old.
If someone is tall or not calm then someone is not quiet and vice versa.
Everyone who is either strong or not strong is both wise and happy and vice versa.
Everyone who is humble or generous is strong.
Everyone who is either happy or not creative is tall or brave.
If someone is either not wise or quiet then john is old and vice versa.
Everyone who is strong is curious and vice versa.
Everyone who is either not humble or not funny is not kind and vice versa.
If someone is both not creative and calm then fred is either tall or curious and vice versa.
If someone is not tall then fred is either rich or not calm and vice versa.
If someone is rich or not strong then someone is both not funny and not wise.
Everyone who is both not strong and not tall is calm or old and vice versa.
Everyone who is either funny or creative is not old or curious.
John is rich or wise.
John is either not old or patient.
Someone is not funny or not humble.
Someone is curious or not kind.
Someone is either not funny or happy.
John is both not kind and creative.
Someone is either kind or not kind. | Fred is curious. | entailment | (![X]:((strong(X)&patient(X))<=>(~humble(X)|kind(X))))&
((~tall(john))=>((~quiet(john)<~>wise(john))))&
(((tall(susan)|~happy(susan)))=>(?[X]:((~curious(X)&~old(X)))))&
((?[X]:((tall(X)|~calm(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((strong(X)<~>~strong(X))<=>(wise(X)&happy(X))))&
(![X]:((humble(X)|generous(X))=>strong(X)))&
(![X]:((happy(X)<~>~creative(X))=>(tall(X)|brave(X))))&
((?[X]:((~wise(X)<~>quiet(X))))<=>(old(john)))&
(![X]:(strong(X)<=>curious(X)))&
(![X]:((~humble(X)<~>~funny(X))<=>~kind(X)))&
((?[X]:((~creative(X)&calm(X))))<=>((tall(fred)<~>curious(fred))))&
((?[X]:(~tall(X)))<=>((rich(fred)<~>~calm(fred))))&
((?[X]:((rich(X)|~strong(X))))=>(?[X]:((~funny(X)&~wise(X)))))&
(![X]:((~strong(X)&~tall(X))<=>(calm(X)|old(X))))&
(![X]:((funny(X)<~>creative(X))=>(~old(X)|curious(X))))&
((rich(john)|wise(john)))&
((~old(john)<~>patient(john)))&
(?[X]:((~funny(X)|~humble(X))))&
(?[X]:((curious(X)|~kind(X))))&
(?[X]:((~funny(X)<~>happy(X))))&
((~kind(john)&creative(john)))&
(?[X]:((kind(X)<~>~kind(X)))) | curious(fred) | [
"p0",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4674205676536521790559610
% SZS output start Proof for 4674205676536521790559610
1. ! [X0] : ((patient(X0) & strong(X0)) <=> (kind(X0) | ~humble(X0))) [input p0]
6. ! [X0] : ((generous(X0) | humble(X0)) => strong(X0)) [input p5]
9. ! [X0] : (strong(X0) <=> curious(X0)) [input p8]
23. ~curious(fred) [input hypothesis]
27. ! [X0] : (humble(X0) => strong(X0)) [pure predicate removal 6]
30. ! [X0] : (strong(X0) | ~humble(X0)) [ennf transformation 27]
34. ! [X0] : (((patient(X0) & strong(X0)) | (~kind(X0) & humble(X0))) & ((kind(X0) | ~humble(X0)) | (~patient(X0) | ~strong(X0)))) [nnf transformation 1]
35. ! [X0] : (((patient(X0) & strong(X0)) | (~kind(X0) & humble(X0))) & (kind(X0) | ~humble(X0) | ~patient(X0) | ~strong(X0))) [flattening 34]
50. ! [X0] : ((strong(X0) | ~curious(X0)) & (curious(X0) | ~strong(X0))) [nnf transformation 9]
78. strong(X0) | humble(X0) [cnf transformation 35]
97. strong(X0) | ~humble(X0) [cnf transformation 30]
102. curious(X0) | ~strong(X0) [cnf transformation 50]
140. ~curious(fred) [cnf transformation 23]
205. strong(X0) [subsumption resolution 97,78]
221. curious(X0) [subsumption resolution 102,205]
276. $false [subsumption resolution 140,221]
% SZS output end Proof for 4674205676536521790559610
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either curious or not creative then john is not creative or tall.
If lucy is both not wise and wise then someone is not rich.
Everyone who is not curious is quiet and vice versa.
Everyone who is both not quiet and happy is funny and vice versa.
If mary is brave or rich then someone is both old and curious.
Everyone who is both not kind and not rich is quiet or curious and vice versa.
Everyone who is brave is funny or not generous and vice versa.
Everyone who is either old or not creative is not rich and vice versa.
Everyone who is not creative is not brave and vice versa.
Everyone who is both not humble and not quiet is either not brave or creative.
Everyone who is both calm and not humble is not brave and vice versa.
If susan is curious then lucy is either not kind or quiet.
Everyone who is brave or patient is tall or quiet and vice versa.
If john is tall then someone is either happy or wise and vice versa.
If someone is not rich or not wise then fred is both calm and curious and vice versa.
If someone is either not rich or not wise then someone is both creative and curious and vice versa.
Someone is either curious or patient.
Mary is happy or humble.
Paul is calm or not generous.
Someone is either not generous or not funny.
Lucy is both not funny and calm.
Someone is not brave.
Someone is wise or creative. | Lucy is calm. | entailment | (((curious(fred)<~>~creative(fred)))=>((~creative(john)|tall(john))))&
(((~wise(lucy)&wise(lucy)))=>(?[X]:(~rich(X))))&
(![X]:(~curious(X)<=>quiet(X)))&
(![X]:((~quiet(X)&happy(X))<=>funny(X)))&
(((brave(mary)|rich(mary)))=>(?[X]:((old(X)&curious(X)))))&
(![X]:((~kind(X)&~rich(X))<=>(quiet(X)|curious(X))))&
(![X]:(brave(X)<=>(funny(X)|~generous(X))))&
(![X]:((old(X)<~>~creative(X))<=>~rich(X)))&
(![X]:(~creative(X)<=>~brave(X)))&
(![X]:((~humble(X)&~quiet(X))=>(~brave(X)<~>creative(X))))&
(![X]:((calm(X)&~humble(X))<=>~brave(X)))&
((curious(susan))=>((~kind(lucy)<~>quiet(lucy))))&
(![X]:((brave(X)|patient(X))<=>(tall(X)|quiet(X))))&
((tall(john))<=>(?[X]:((happy(X)<~>wise(X)))))&
((?[X]:((~rich(X)|~wise(X))))<=>((calm(fred)&curious(fred))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>(?[X]:((creative(X)&curious(X)))))&
(?[X]:((curious(X)<~>patient(X))))&
((happy(mary)|humble(mary)))&
((calm(paul)|~generous(paul)))&
(?[X]:((~generous(X)<~>~funny(X))))&
((~funny(lucy)&calm(lucy)))&
(?[X]:(~brave(X)))&
(?[X]:((wise(X)|creative(X)))) | calm(lucy) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6179914764081153500286291
% SZS output start Proof for 6179914764081153500286291
21. calm(lucy) & ~funny(lucy) [input p20]
24. ~calm(lucy) [input hypothesis]
137. calm(lucy) [cnf transformation 21]
140. ~calm(lucy) [cnf transformation 24]
314. $false [subsumption resolution 140,137]
% SZS output end Proof for 6179914764081153500286291
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or brave is either not curious or generous. If someone is not old or not wise then fred is not humble and vice versa. Everyone who is not humble or creative is not wise or calm and vice versa. Everyone who is not rich or rich is creative or wise. If someone is wise then someone is happy. Everyone who is not strong is both patient and not creative and vice versa. Everyone who is either wise or calm is either not patient or not creative and vice versa. Everyone who is either calm or not patient is rich or not creative. Everyone who is not creative or patient is either not wise or not brave. If someone is not calm then someone is kind. If john is either kind or not humble then susan is both not happy and brave and vice versa. Everyone who is wise is happy or not wise and vice versa. Everyone who is either happy or not humble is not curious and vice versa. If john is not tall then someone is not calm or happy. Everyone who is either not brave or wise is both not funny and not brave and vice versa. Everyone who is not creative or not happy is both curious and not creative. Someone is curious or not wise. Mary is both not kind and wise. Paul is either rich or humble. Someone is both curious and tall. Someone is kind. Someone is not curious or funny. Fred is not curious. | Susan is brave. | contradiction | (![X]:((~quiet(X)<~>brave(X))=>(~curious(X)<~>generous(X))))&
((?[X]:((~old(X)|~wise(X))))<=>(~humble(fred)))&
(![X]:((~humble(X)|creative(X))<=>(~wise(X)|calm(X))))&
(![X]:((~rich(X)|rich(X))=>(creative(X)|wise(X))))&
((?[X]:(wise(X)))=>(?[X]:(happy(X))))&
(![X]:(~strong(X)<=>(patient(X)&~creative(X))))&
(![X]:((wise(X)<~>calm(X))<=>(~patient(X)<~>~creative(X))))&
(![X]:((calm(X)<~>~patient(X))=>(rich(X)|~creative(X))))&
(![X]:((~creative(X)|patient(X))=>(~wise(X)<~>~brave(X))))&
((?[X]:(~calm(X)))=>(?[X]:(kind(X))))&
(((kind(john)<~>~humble(john)))<=>((~happy(susan)&brave(susan))))&
(![X]:(wise(X)<=>(happy(X)|~wise(X))))&
(![X]:((happy(X)<~>~humble(X))<=>~curious(X)))&
((~tall(john))=>(?[X]:((~calm(X)|happy(X)))))&
(![X]:((~brave(X)<~>wise(X))<=>(~funny(X)&~brave(X))))&
(![X]:((~creative(X)|~happy(X))=>(curious(X)&~creative(X))))&
(?[X]:((curious(X)|~wise(X))))&
((~kind(mary)&wise(mary)))&
((rich(paul)<~>humble(paul)))&
(?[X]:((curious(X)&tall(X))))&
(?[X]:(kind(X)))&
(?[X]:((~curious(X)|funny(X))))&
(~curious(fred)) | brave(susan) | [
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 606847964273488108898813
% SZS output start Proof for 606847964273488108898813
12. ! [X0] : (wise(X0) <=> (~wise(X0) | happy(X0))) [input p11]
15. ! [X0] : ((~brave(X0) <~> wise(X0)) <=> (~brave(X0) & ~funny(X0))) [input p14]
24. brave(susan) [input hypothesis]
56. ! [X0] : ((wise(X0) | (wise(X0) & ~happy(X0))) & ((~wise(X0) | happy(X0)) | ~wise(X0))) [nnf transformation 12]
57. ! [X0] : ((wise(X0) | (wise(X0) & ~happy(X0))) & (~wise(X0) | happy(X0) | ~wise(X0))) [flattening 56]
59. ! [X0] : ((((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | (brave(X0) | funny(X0))) & ((~brave(X0) & ~funny(X0)) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0))))) [nnf transformation 15]
60. ! [X0] : ((((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | brave(X0) | funny(X0)) & ((~brave(X0) & ~funny(X0)) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0))))) [flattening 59]
107. wise(X0) | wise(X0) [cnf transformation 57]
115. ~brave(X0) | ~brave(X0) | ~wise(X0) [cnf transformation 60]
131. brave(susan) [cnf transformation 24]
132. ~wise(X0) | ~brave(X0) [duplicate literal removal 115]
135. wise(X0) [duplicate literal removal 107]
150. 4 <=> ! [X1] : wise(X1) [avatar definition]
151. wise(X1) <- (4) [avatar component clause 150]
187. 11 <=> brave(susan) [avatar definition]
188. brave(susan) <- (11) [avatar component clause 187]
204. 4 [avatar split clause 135,150]
233. 11 [avatar split clause 131,187]
245. ~brave(X0) <- (4) [resolution 132,151]
248. $false <- (4, 11) [resolution 245,188]
249. ~4 | ~11 [avatar contradiction clause 248]
250. $false [avatar sat refutation 204,233,249]
% SZS output end Proof for 606847964273488108898813
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or brave then someone is both curious and wise and vice versa.
Everyone who is not creative or humble is both strong and not tall and vice versa.
Everyone who is either not strong or brave is curious or generous and vice versa.
If susan is patient or quiet then john is either not humble or not happy.
Everyone who is not creative or quiet is both curious and not creative.
Everyone who is either patient or strong is both not kind and creative and vice versa.
If someone is either not strong or patient then someone is strong or wise and vice versa.
Everyone who is either happy or not creative is either tall or brave.
If mary is generous or not curious then john is either not generous or curious.
Everyone who is strong or not generous is either not humble or not generous and vice versa.
Everyone who is both not humble and not wise is both not wise and not rich and vice versa.
Everyone who is not brave is quiet or kind.
Everyone who is brave is not strong and vice versa.
If someone is brave then someone is both not wise and funny and vice versa.
Everyone who is both patient and kind is both rich and wise and vice versa.
Fred is not brave.
Someone is either creative or not funny.
Someone is happy or creative.
Lucy is curious or not brave.
Paul is both creative and not tall.
Alice is rich or strong.
Someone is either generous or patient. | John is not quiet. | entailment | ((?[X]:((quiet(X)<~>brave(X))))<=>(?[X]:((curious(X)&wise(X)))))&
(![X]:((~creative(X)|humble(X))<=>(strong(X)&~tall(X))))&
(![X]:((~strong(X)<~>brave(X))<=>(curious(X)|generous(X))))&
(((patient(susan)|quiet(susan)))=>((~humble(john)<~>~happy(john))))&
(![X]:((~creative(X)|quiet(X))=>(curious(X)&~creative(X))))&
(![X]:((patient(X)<~>strong(X))<=>(~kind(X)&creative(X))))&
((?[X]:((~strong(X)<~>patient(X))))<=>(?[X]:((strong(X)|wise(X)))))&
(![X]:((happy(X)<~>~creative(X))=>(tall(X)<~>brave(X))))&
(((generous(mary)|~curious(mary)))=>((~generous(john)<~>curious(john))))&
(![X]:((strong(X)|~generous(X))<=>(~humble(X)<~>~generous(X))))&
(![X]:((~humble(X)&~wise(X))<=>(~wise(X)&~rich(X))))&
(![X]:(~brave(X)=>(quiet(X)|kind(X))))&
(![X]:(brave(X)<=>~strong(X)))&
((?[X]:(brave(X)))<=>(?[X]:((~wise(X)&funny(X)))))&
(![X]:((patient(X)&kind(X))<=>(rich(X)&wise(X))))&
(~brave(fred))&
(?[X]:((creative(X)<~>~funny(X))))&
(?[X]:((happy(X)|creative(X))))&
((curious(lucy)|~brave(lucy)))&
((creative(paul)&~tall(paul)))&
((rich(alice)|strong(alice)))&
(?[X]:((generous(X)<~>patient(X)))) | ~quiet(john) | [
"p1",
"p2",
"p3",
"p4",
"p5",
"p7",
"p9",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 385280363410342261478631
% SZS output start Proof for 385280363410342261478631
2. ! [X0] : ((humble(X0) | ~creative(X0)) <=> (~tall(X0) & strong(X0))) [input p1]
3. ! [X0] : ((~strong(X0) <~> brave(X0)) <=> (generous(X0) | curious(X0))) [input p2]
4. (quiet(susan) | patient(susan)) => (~humble(john) <~> ~happy(john)) [input p3]
5. ! [X0] : ((quiet(X0) | ~creative(X0)) => (~creative(X0) & curious(X0))) [input p4]
6. ! [X0] : ((patient(X0) <~> strong(X0)) <=> (creative(X0) & ~kind(X0))) [input p5]
8. ! [X0] : ((happy(X0) <~> ~creative(X0)) => (tall(X0) <~> brave(X0))) [input p7]
10. ! [X0] : ((~generous(X0) | strong(X0)) <=> (~humble(X0) <~> ~generous(X0))) [input p9]
12. ! [X0] : (~brave(X0) => (kind(X0) | quiet(X0))) [input p11]
13. ! [X0] : (brave(X0) <=> ~strong(X0)) [input p12]
23. quiet(john) [input hypothesis]
27. (~humble(john) <~> ~happy(john)) | (~quiet(susan) & ~patient(susan)) [ennf transformation 4]
28. ! [X0] : ((~creative(X0) & curious(X0)) | (~quiet(X0) & creative(X0))) [ennf transformation 5]
29. ! [X0] : ((tall(X0) <~> brave(X0)) | (happy(X0) <=> ~creative(X0))) [ennf transformation 8]
31. ! [X0] : ((kind(X0) | quiet(X0)) | brave(X0)) [ennf transformation 12]
32. ! [X0] : (kind(X0) | quiet(X0) | brave(X0)) [flattening 31]
38. ! [X0] : (((humble(X0) | ~creative(X0)) | (tall(X0) | ~strong(X0))) & ((~tall(X0) & strong(X0)) | (~humble(X0) & creative(X0)))) [nnf transformation 2]
39. ! [X0] : ((humble(X0) | ~creative(X0) | tall(X0) | ~strong(X0)) & ((~tall(X0) & strong(X0)) | (~humble(X0) & creative(X0)))) [flattening 38]
40. ! [X0] : ((((~brave(X0) | strong(X0)) & (brave(X0) | ~strong(X0))) | (~generous(X0) & ~curious(X0))) & ((generous(X0) | curious(X0)) | ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0))))) [nnf transformation 3]
41. ! [X0] : ((((~brave(X0) | strong(X0)) & (brave(X0) | ~strong(X0))) | (~generous(X0) & ~curious(X0))) & (generous(X0) | curious(X0) | ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0))))) [flattening 40]
42. ((happy(john) | humble(john)) & (~happy(john) | ~humble(john))) | (~quiet(susan) & ~patient(susan)) [nnf transformation 27]
43. ! [X0] : ((((~strong(X0) | ~patient(X0)) & (strong(X0) | patient(X0))) | (~creative(X0) | kind(X0))) & ((creative(X0) & ~kind(X0)) | ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0))))) [nnf transformation 6]
44. ! [X0] : ((((~strong(X0) | ~patient(X0)) & (strong(X0) | patient(X0))) | ~creative(X0) | kind(X0)) & ((creative(X0) & ~kind(X0)) | ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0))))) [flattening 43]
50. ! [X0] : (((~brave(X0) | ~tall(X0)) & (brave(X0) | tall(X0))) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0)))) [nnf transformation 29]
52. ! [X0] : (((~generous(X0) | strong(X0)) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0)))) & (((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | (generous(X0) & ~strong(X0)))) [nnf transformation 10]
53. ! [X0] : ((~generous(X0) | strong(X0) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0)))) & (((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | (generous(X0) & ~strong(X0)))) [flattening 52]
56. ! [X0] : ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))) [nnf transformation 13]
78. strong(X0) | creative(X0) [cnf transformation 39]
79. ~humble(X0) | strong(X0) [cnf transformation 39]
80. ~tall(X0) | creative(X0) [cnf transformation 39]
86. ~generous(X0) | ~strong(X0) | brave(X0) [cnf transformation 41]
89. ~happy(john) | ~humble(john) | ~patient(susan) [cnf transformation 42]
96. ~creative(X0) | ~quiet(X0) [cnf transformation 28]
98. ~kind(X0) | patient(X0) | ~strong(X0) [cnf transformation 44]
100. creative(X0) | patient(X0) | ~strong(X0) [cnf transformation 44]
110. brave(X0) | tall(X0) | happy(X0) | creative(X0) [cnf transformation 50]
120. generous(X0) | humble(X0) | generous(X0) [cnf transformation 53]
121. ~generous(X0) | strong(X0) | ~generous(X0) | humble(X0) [cnf transformation 53]
127. kind(X0) | quiet(X0) | brave(X0) [cnf transformation 32]
128. ~strong(X0) | ~brave(X0) [cnf transformation 56]
147. quiet(john) [cnf transformation 23]
148. generous(X0) | humble(X0) [duplicate literal removal 120]
149. ~generous(X0) | strong(X0) | humble(X0) [duplicate literal removal 121]
182. 8 <=> quiet(susan) [avatar definition]
186. 9 <=> humble(john) [avatar definition]
190. 10 <=> happy(john) [avatar definition]
191. ~happy(john) <- (~10) [avatar component clause 190]
195. 11 <=> patient(susan) [avatar definition]
197. ~patient(susan) <- (~11) [avatar component clause 195]
200. ~11 | ~9 | ~10 [avatar split clause 89,190,186,195]
202. patient(X0) | creative(X0) [subsumption resolution 100,78]
238. happy(X0) | brave(X0) | creative(X0) [subsumption resolution 110,80]
244. 21 <=> generous(john) [avatar definition]
245. ~generous(john) <- (~21) [avatar component clause 244]
246. generous(john) <- (21) [avatar component clause 244]
259. ~generous(X0) | strong(X0) [subsumption resolution 149,79]
270. 26 <=> ! [X3] : ~brave(X3) [avatar definition]
271. ~brave(X3) <- (26) [avatar component clause 270]
349. humble(john) <- (~21) [resolution 148,245]
351. 9 | 21 [avatar split clause 349,244,186]
354. creative(susan) <- (~11) [resolution 202,197]
358. strong(X0) | humble(X0) [resolution 259,148]
359. strong(X0) [subsumption resolution 358,79]
360. ~quiet(susan) <- (~11) [resolution 354,96]
374. ~brave(X1) [resolution 359,128]
382. 26 [avatar split clause 374,270]
441. ~strong(john) | brave(john) <- (21) [resolution 246,86]
444. brave(john) <- (21) [subsumption resolution 441,359]
445. $false <- (21, 26) [subsumption resolution 444,271]
446. ~21 | ~26 [avatar contradiction clause 445]
451. quiet(X0) | brave(X0) | patient(X0) | ~strong(X0) [resolution 127,98]
453. quiet(X0) | patient(X0) | ~strong(X0) <- (26) [subsumption resolution 451,271]
454. patient(X0) | quiet(X0) <- (26) [subsumption resolution 453,359]
472. quiet(susan) <- (~11, 26) [resolution 454,197]
475. 8 | 11 | ~26 [avatar split clause 472,270,195,182]
476. ~8 | 11 [avatar split clause 360,195,182]
485. brave(john) | creative(john) <- (~10) [resolution 238,191]
487. creative(john) <- (~10, 26) [subsumption resolution 485,271]
488. ~quiet(john) <- (~10, 26) [resolution 487,96]
489. $false <- (~10, 26) [subsumption resolution 488,147]
490. 10 | ~26 [avatar contradiction clause 489]
491. $false [avatar sat refutation 200,351,382,446,475,476,490]
% SZS output end Proof for 385280363410342261478631
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and not quiet is not creative or not calm. Everyone who is not rich is both funny and wise. Everyone who is either funny or tall is strong or not generous and vice versa. Everyone who is both generous and not calm is kind. If paul is brave then alice is kind. Everyone who is either happy or kind is both not curious and wise and vice versa. Everyone who is generous or funny is rich or happy. Everyone who is patient is curious or happy and vice versa. If alice is tall or not humble then someone is wise or old. If alice is not calm then paul is either not happy or tall. Everyone who is both not old and not tall is not patient and vice versa. If someone is not wise then someone is humble or creative and vice versa. If lucy is either not strong or wise then someone is either not curious or generous and vice versa. Everyone who is both curious and quiet is patient and vice versa. If john is not rich then someone is old. Someone is not curious or funny. Alice is either funny or not curious. John is quiet or not generous. Mary is not humble or not generous. Mary is both not creative and not kind. Someone is not generous. John is both patient and happy. | Alice is humble. | neutral | (![X]:((curious(X)&~quiet(X))=>(~creative(X)|~calm(X))))&
(![X]:(~rich(X)=>(funny(X)&wise(X))))&
(![X]:((funny(X)<~>tall(X))<=>(strong(X)|~generous(X))))&
(![X]:((generous(X)&~calm(X))=>kind(X)))&
((brave(paul))=>(kind(alice)))&
(![X]:((happy(X)<~>kind(X))<=>(~curious(X)&wise(X))))&
(![X]:((generous(X)|funny(X))=>(rich(X)|happy(X))))&
(![X]:(patient(X)<=>(curious(X)|happy(X))))&
(((tall(alice)|~humble(alice)))=>(?[X]:((wise(X)|old(X)))))&
((~calm(alice))=>((~happy(paul)<~>tall(paul))))&
(![X]:((~old(X)&~tall(X))<=>~patient(X)))&
((?[X]:(~wise(X)))<=>(?[X]:((humble(X)|creative(X)))))&
(((~strong(lucy)<~>wise(lucy)))<=>(?[X]:((~curious(X)<~>generous(X)))))&
(![X]:((curious(X)&quiet(X))<=>patient(X)))&
((~rich(john))=>(?[X]:(old(X))))&
(?[X]:((~curious(X)|funny(X))))&
((funny(alice)<~>~curious(alice)))&
((quiet(john)|~generous(john)))&
((~humble(mary)|~generous(mary)))&
((~creative(mary)&~kind(mary)))&
(?[X]:(~generous(X)))&
((patient(john)&happy(john))) | humble(alice) | [] | null | 0 |
If fred is either happy or not old then alice is either not curious or wise and vice versa.
If paul is humble then someone is either old or not kind.
If someone is kind or generous then someone is either not humble or curious and vice versa.
If lucy is either wise or old then someone is not kind and vice versa.
If someone is not strong then paul is old and vice versa.
Everyone who is generous or patient is either not kind or happy and vice versa.
Everyone who is both not humble and tall is rich and vice versa.
Everyone who is not calm or funny is either not humble or rich and vice versa.
If lucy is both calm and not rich then paul is not curious or not humble.
If john is both creative and not funny then someone is both not patient and not generous.
Everyone who is both not brave and rich is humble or quiet and vice versa.
If someone is both not creative and not brave then someone is both not humble and old and vice versa.
If someone is either funny or not curious then lucy is patient.
Everyone who is both rich and not creative is both not tall and wise and vice versa.
Everyone who is not curious or not old is humble or not tall.
If paul is both not old and not strong then someone is kind or calm and vice versa.
Someone is both not wise and patient.
Someone is not calm.
John is either not humble or curious. | Lucy is creative. | neutral | (((happy(fred)<~>~old(fred)))<=>((~curious(alice)<~>wise(alice))))&
((humble(paul))=>(?[X]:((old(X)<~>~kind(X)))))&
((?[X]:((kind(X)|generous(X))))<=>(?[X]:((~humble(X)<~>curious(X)))))&
(((wise(lucy)<~>old(lucy)))<=>(?[X]:(~kind(X))))&
((?[X]:(~strong(X)))<=>(old(paul)))&
(![X]:((generous(X)|patient(X))<=>(~kind(X)<~>happy(X))))&
(![X]:((~humble(X)&tall(X))<=>rich(X)))&
(![X]:((~calm(X)|funny(X))<=>(~humble(X)<~>rich(X))))&
(((calm(lucy)&~rich(lucy)))=>((~curious(paul)|~humble(paul))))&
(((creative(john)&~funny(john)))=>(?[X]:((~patient(X)&~generous(X)))))&
(![X]:((~brave(X)&rich(X))<=>(humble(X)|quiet(X))))&
((?[X]:((~creative(X)&~brave(X))))<=>(?[X]:((~humble(X)&old(X)))))&
((?[X]:((funny(X)<~>~curious(X))))=>(patient(lucy)))&
(![X]:((rich(X)&~creative(X))<=>(~tall(X)&wise(X))))&
(![X]:((~curious(X)|~old(X))=>(humble(X)|~tall(X))))&
(((~old(paul)&~strong(paul)))<=>(?[X]:((kind(X)|calm(X)))))&
(?[X]:((~wise(X)&patient(X))))&
(?[X]:(~calm(X)))&
((~humble(john)<~>curious(john))) | creative(lucy) | [] | null | 0 |
Everyone who is either calm or not calm is tall and vice versa.
Everyone who is not quiet or not tall is either happy or brave.
If john is both tall and not curious then mary is not strong.
Everyone who is not strong or creative is not happy or not funny and vice versa.
Everyone who is either funny or brave is both not creative and not strong and vice versa.
If fred is either not humble or not rich then someone is either not old or happy and vice versa.
Everyone who is both not old and old is kind and vice versa.
Everyone who is both happy and not funny is strong or old.
Everyone who is not generous is both not happy and not wise and vice versa.
If mary is both rich and not humble then susan is old and vice versa.
If someone is both generous and rich then mary is either not humble or not old.
If lucy is either creative or not generous then someone is kind and vice versa.
Everyone who is both not happy and not curious is both not strong and not quiet and vice versa.
If fred is not tall then paul is either not creative or calm.
If john is both not generous and old then someone is not tall or rich and vice versa.
Everyone who is either not brave or strong is strong or not tall and vice versa.
Someone is either brave or not strong.
Alice is curious.
Someone is rich.
Someone is both not patient and rich.
Someone is both happy and funny.
Someone is patient or not kind.
Someone is strong or generous. | Susan is not happy. | neutral | (![X]:((calm(X)<~>~calm(X))<=>tall(X)))&
(![X]:((~quiet(X)|~tall(X))=>(happy(X)<~>brave(X))))&
(((tall(john)&~curious(john)))=>(~strong(mary)))&
(![X]:((~strong(X)|creative(X))<=>(~happy(X)|~funny(X))))&
(![X]:((funny(X)<~>brave(X))<=>(~creative(X)&~strong(X))))&
(((~humble(fred)<~>~rich(fred)))<=>(?[X]:((~old(X)<~>happy(X)))))&
(![X]:((~old(X)&old(X))<=>kind(X)))&
(![X]:((happy(X)&~funny(X))=>(strong(X)|old(X))))&
(![X]:(~generous(X)<=>(~happy(X)&~wise(X))))&
(((rich(mary)&~humble(mary)))<=>(old(susan)))&
((?[X]:((generous(X)&rich(X))))=>((~humble(mary)<~>~old(mary))))&
(((creative(lucy)<~>~generous(lucy)))<=>(?[X]:(kind(X))))&
(![X]:((~happy(X)&~curious(X))<=>(~strong(X)&~quiet(X))))&
((~tall(fred))=>((~creative(paul)<~>calm(paul))))&
(((~generous(john)&old(john)))<=>(?[X]:((~tall(X)|rich(X)))))&
(![X]:((~brave(X)<~>strong(X))<=>(strong(X)|~tall(X))))&
(?[X]:((brave(X)<~>~strong(X))))&
(curious(alice))&
(?[X]:(rich(X)))&
(?[X]:((~patient(X)&rich(X))))&
(?[X]:((happy(X)&funny(X))))&
(?[X]:((patient(X)|~kind(X))))&
(?[X]:((strong(X)|generous(X)))) | ~happy(susan) | [] | null | 0 |
If someone is both funny and not quiet then someone is not funny or quiet.
Everyone who is either not humble or not rich is calm and vice versa.
Everyone who is either humble or calm is either strong or rich.
Everyone who is not happy is either not happy or not humble and vice versa.
Everyone who is both not humble and kind is both not humble and quiet and vice versa.
If fred is either humble or curious then someone is both not humble and not calm.
Everyone who is rich or not generous is old or not rich and vice versa.
Everyone who is not wise is curious.
Everyone who is both old and creative is both not rich and not old and vice versa.
If lucy is either not generous or generous then mary is both humble and not patient and vice versa.
Everyone who is wise is not curious and vice versa.
Everyone who is old is either not tall or strong.
Everyone who is not rich or not old is creative or not old.
If mary is funny or not kind then john is not funny or humble and vice versa.
If someone is rich then someone is old and vice versa.
Everyone who is both not quiet and rich is strong and vice versa.
John is both rich and curious.
John is either brave or creative.
Someone is not funny.
Someone is not creative.
Someone is wise.
Paul is happy or not calm.
Paul is generous. | Paul is brave. | neutral | ((?[X]:((funny(X)&~quiet(X))))=>(?[X]:((~funny(X)|quiet(X)))))&
(![X]:((~humble(X)<~>~rich(X))<=>calm(X)))&
(![X]:((humble(X)<~>calm(X))=>(strong(X)<~>rich(X))))&
(![X]:(~happy(X)<=>(~happy(X)<~>~humble(X))))&
(![X]:((~humble(X)&kind(X))<=>(~humble(X)&quiet(X))))&
(((humble(fred)<~>curious(fred)))=>(?[X]:((~humble(X)&~calm(X)))))&
(![X]:((rich(X)|~generous(X))<=>(old(X)|~rich(X))))&
(![X]:(~wise(X)=>curious(X)))&
(![X]:((old(X)&creative(X))<=>(~rich(X)&~old(X))))&
(((~generous(lucy)<~>generous(lucy)))<=>((humble(mary)&~patient(mary))))&
(![X]:(wise(X)<=>~curious(X)))&
(![X]:(old(X)=>(~tall(X)<~>strong(X))))&
(![X]:((~rich(X)|~old(X))=>(creative(X)|~old(X))))&
(((funny(mary)|~kind(mary)))<=>((~funny(john)|humble(john))))&
((?[X]:(rich(X)))<=>(?[X]:(old(X))))&
(![X]:((~quiet(X)&rich(X))<=>strong(X)))&
((rich(john)&curious(john)))&
((brave(john)<~>creative(john)))&
(?[X]:(~funny(X)))&
(?[X]:(~creative(X)))&
(?[X]:(wise(X)))&
((happy(paul)|~calm(paul)))&
(generous(paul)) | brave(paul) | [] | null | 0 |
If mary is generous then someone is humble or tall and vice versa.
Everyone who is both not generous and brave is both calm and old.
If alice is either not calm or strong then lucy is not curious.
Everyone who is quiet or not funny is patient or not humble and vice versa.
Everyone who is both happy and calm is wise or not brave and vice versa.
If lucy is both happy and not old then someone is both not wise and not strong.
If someone is both funny and not rich then lucy is not tall.
Everyone who is either rich or not funny is patient and vice versa.
Everyone who is both not funny and rich is not wise or strong and vice versa.
If susan is either curious or tall then someone is both not strong and calm.
If someone is both not curious and funny then susan is both happy and not kind and vice versa.
Everyone who is rich or not strong is generous and vice versa.
Everyone who is not quiet or humble is brave or not calm.
Everyone who is not tall is either not calm or humble and vice versa.
Everyone who is either calm or humble is both creative and generous and vice versa.
Everyone who is both not funny and not brave is not funny or strong and vice versa.
Someone is not wise or curious.
Mary is calm.
Lucy is both not humble and patient.
Someone is both not humble and not funny.
Mary is not rich or rich.
Someone is both not funny and not kind.
Someone is quiet or tall.
Fred is quiet. | Alice is not brave. | neutral | ((generous(mary))<=>(?[X]:((humble(X)|tall(X)))))&
(![X]:((~generous(X)&brave(X))=>(calm(X)&old(X))))&
(((~calm(alice)<~>strong(alice)))=>(~curious(lucy)))&
(![X]:((quiet(X)|~funny(X))<=>(patient(X)|~humble(X))))&
(![X]:((happy(X)&calm(X))<=>(wise(X)|~brave(X))))&
(((happy(lucy)&~old(lucy)))=>(?[X]:((~wise(X)&~strong(X)))))&
((?[X]:((funny(X)&~rich(X))))=>(~tall(lucy)))&
(![X]:((rich(X)<~>~funny(X))<=>patient(X)))&
(![X]:((~funny(X)&rich(X))<=>(~wise(X)|strong(X))))&
(((curious(susan)<~>tall(susan)))=>(?[X]:((~strong(X)&calm(X)))))&
((?[X]:((~curious(X)&funny(X))))<=>((happy(susan)&~kind(susan))))&
(![X]:((rich(X)|~strong(X))<=>generous(X)))&
(![X]:((~quiet(X)|humble(X))=>(brave(X)|~calm(X))))&
(![X]:(~tall(X)<=>(~calm(X)<~>humble(X))))&
(![X]:((calm(X)<~>humble(X))<=>(creative(X)&generous(X))))&
(![X]:((~funny(X)&~brave(X))<=>(~funny(X)|strong(X))))&
(?[X]:((~wise(X)|curious(X))))&
(calm(mary))&
((~humble(lucy)&patient(lucy)))&
(?[X]:((~humble(X)&~funny(X))))&
((~rich(mary)|rich(mary)))&
(?[X]:((~funny(X)&~kind(X))))&
(?[X]:((quiet(X)|tall(X))))&
(quiet(fred)) | ~brave(alice) | [] | null | 0 |
If someone is funny or patient then someone is not calm.
Everyone who is not tall is not kind or not brave and vice versa.
Everyone who is not generous or tall is either not generous or brave and vice versa.
Everyone who is either old or rich is both wise and not brave and vice versa.
Everyone who is not calm or not happy is both not patient and not kind.
Everyone who is rich or not curious is rich.
Everyone who is either quiet or not tall is either not creative or not calm.
If someone is humble or not humble then someone is either humble or not calm.
Everyone who is both not quiet and brave is either creative or curious and vice versa.
Everyone who is either not rich or not happy is either not strong or not quiet and vice versa.
If someone is generous or not creative then someone is brave or not calm and vice versa.
If john is either not quiet or humble then someone is either rich or creative and vice versa.
Everyone who is both generous and not tall is quiet or not kind.
If lucy is both kind and humble then lucy is not happy or happy and vice versa.
Everyone who is kind is not patient or not rich.
Everyone who is either not creative or not kind is either not strong or not creative.
Lucy is either not patient or not funny.
Someone is not kind or not quiet.
Lucy is rich.
John is either patient or kind.
Someone is not funny.
Someone is either tall or not humble.
Someone is not humble.
Alice is either not rich or not curious. | Lucy is not generous. | neutral | ((?[X]:((funny(X)|patient(X))))=>(?[X]:(~calm(X))))&
(![X]:(~tall(X)<=>(~kind(X)|~brave(X))))&
(![X]:((~generous(X)|tall(X))<=>(~generous(X)<~>brave(X))))&
(![X]:((old(X)<~>rich(X))<=>(wise(X)&~brave(X))))&
(![X]:((~calm(X)|~happy(X))=>(~patient(X)&~kind(X))))&
(![X]:((rich(X)|~curious(X))=>rich(X)))&
(![X]:((quiet(X)<~>~tall(X))=>(~creative(X)<~>~calm(X))))&
((?[X]:((humble(X)|~humble(X))))=>(?[X]:((humble(X)<~>~calm(X)))))&
(![X]:((~quiet(X)&brave(X))<=>(creative(X)<~>curious(X))))&
(![X]:((~rich(X)<~>~happy(X))<=>(~strong(X)<~>~quiet(X))))&
((?[X]:((generous(X)|~creative(X))))<=>(?[X]:((brave(X)|~calm(X)))))&
(((~quiet(john)<~>humble(john)))<=>(?[X]:((rich(X)<~>creative(X)))))&
(![X]:((generous(X)&~tall(X))=>(quiet(X)|~kind(X))))&
(((kind(lucy)&humble(lucy)))<=>((~happy(lucy)|happy(lucy))))&
(![X]:(kind(X)=>(~patient(X)|~rich(X))))&
(![X]:((~creative(X)<~>~kind(X))=>(~strong(X)<~>~creative(X))))&
((~patient(lucy)<~>~funny(lucy)))&
(?[X]:((~kind(X)|~quiet(X))))&
(rich(lucy))&
((patient(john)<~>kind(john)))&
(?[X]:(~funny(X)))&
(?[X]:((tall(X)<~>~humble(X))))&
(?[X]:(~humble(X)))&
((~rich(alice)<~>~curious(alice))) | ~generous(lucy) | [] | null | 0 |
If alice is either wise or brave then paul is both rich and not old.
Everyone who is not creative is not calm or not brave and vice versa.
Everyone who is happy is both curious and not strong.
Everyone who is not quiet or not humble is not patient or tall.
Everyone who is humble is either not creative or not tall and vice versa.
Everyone who is both not wise and old is both brave and old and vice versa.
If someone is both happy and curious then someone is both not calm and kind.
Everyone who is patient or not brave is brave or not wise.
Everyone who is happy or not happy is not humble or brave.
Everyone who is not funny is either not old or not curious and vice versa.
Everyone who is happy or not generous is both tall and old and vice versa.
If paul is either kind or not calm then susan is either not brave or kind.
If mary is happy or funny then someone is either old or not funny and vice versa.
Everyone who is both kind and quiet is not humble and vice versa.
Everyone who is both strong and not creative is both not brave and strong and vice versa.
Everyone who is not kind or not patient is either funny or not kind and vice versa.
Someone is not patient or funny.
Someone is not rich or patient.
Someone is both calm and not wise.
Mary is either calm or rich.
Susan is either not calm or strong.
Someone is not strong.
Someone is either not generous or brave.
Someone is not calm or happy. | Paul is not wise. | neutral | (((wise(alice)<~>brave(alice)))=>((rich(paul)&~old(paul))))&
(![X]:(~creative(X)<=>(~calm(X)|~brave(X))))&
(![X]:(happy(X)=>(curious(X)&~strong(X))))&
(![X]:((~quiet(X)|~humble(X))=>(~patient(X)|tall(X))))&
(![X]:(humble(X)<=>(~creative(X)<~>~tall(X))))&
(![X]:((~wise(X)&old(X))<=>(brave(X)&old(X))))&
((?[X]:((happy(X)&curious(X))))=>(?[X]:((~calm(X)&kind(X)))))&
(![X]:((patient(X)|~brave(X))=>(brave(X)|~wise(X))))&
(![X]:((happy(X)|~happy(X))=>(~humble(X)|brave(X))))&
(![X]:(~funny(X)<=>(~old(X)<~>~curious(X))))&
(![X]:((happy(X)|~generous(X))<=>(tall(X)&old(X))))&
(((kind(paul)<~>~calm(paul)))=>((~brave(susan)<~>kind(susan))))&
(((happy(mary)|funny(mary)))<=>(?[X]:((old(X)<~>~funny(X)))))&
(![X]:((kind(X)&quiet(X))<=>~humble(X)))&
(![X]:((strong(X)&~creative(X))<=>(~brave(X)&strong(X))))&
(![X]:((~kind(X)|~patient(X))<=>(funny(X)<~>~kind(X))))&
(?[X]:((~patient(X)|funny(X))))&
(?[X]:((~rich(X)|patient(X))))&
(?[X]:((calm(X)&~wise(X))))&
((calm(mary)<~>rich(mary)))&
((~calm(susan)<~>strong(susan)))&
(?[X]:(~strong(X)))&
(?[X]:((~generous(X)<~>brave(X))))&
(?[X]:((~calm(X)|happy(X)))) | ~wise(paul) | [] | null | 0 |
If paul is humble or not calm then susan is either not old or curious.
Everyone who is not humble is either calm or not rich and vice versa.
Everyone who is humble or wise is either not brave or rich and vice versa.
If lucy is both old and patient then someone is either quiet or rich and vice versa.
If john is both curious and not wise then paul is either creative or not tall and vice versa.
Everyone who is not rich or not generous is both brave and quiet.
Everyone who is not quiet is curious or not kind.
Everyone who is quiet or humble is patient or generous and vice versa.
Everyone who is either wise or not quiet is not wise or not old and vice versa.
If someone is calm or not old then alice is strong or curious and vice versa.
Everyone who is both wise and not happy is not happy and vice versa.
If someone is not tall or not calm then someone is not generous or not funny and vice versa.
If mary is curious or not wise then someone is quiet and vice versa.
If mary is not quiet then lucy is both not kind and humble.
Someone is not tall.
Lucy is curious.
Someone is not patient or not kind.
Someone is both not creative and not calm.
Someone is not wise or old. | Susan is strong. | neutral | (((humble(paul)|~calm(paul)))=>((~old(susan)<~>curious(susan))))&
(![X]:(~humble(X)<=>(calm(X)<~>~rich(X))))&
(![X]:((humble(X)|wise(X))<=>(~brave(X)<~>rich(X))))&
(((old(lucy)&patient(lucy)))<=>(?[X]:((quiet(X)<~>rich(X)))))&
(((curious(john)&~wise(john)))<=>((creative(paul)<~>~tall(paul))))&
(![X]:((~rich(X)|~generous(X))=>(brave(X)&quiet(X))))&
(![X]:(~quiet(X)=>(curious(X)|~kind(X))))&
(![X]:((quiet(X)|humble(X))<=>(patient(X)|generous(X))))&
(![X]:((wise(X)<~>~quiet(X))<=>(~wise(X)|~old(X))))&
((?[X]:((calm(X)|~old(X))))<=>((strong(alice)|curious(alice))))&
(![X]:((wise(X)&~happy(X))<=>~happy(X)))&
((?[X]:((~tall(X)|~calm(X))))<=>(?[X]:((~generous(X)|~funny(X)))))&
(((curious(mary)|~wise(mary)))<=>(?[X]:(quiet(X))))&
((~quiet(mary))=>((~kind(lucy)&humble(lucy))))&
(?[X]:(~tall(X)))&
(curious(lucy))&
(?[X]:((~patient(X)|~kind(X))))&
(?[X]:((~creative(X)&~calm(X))))&
(?[X]:((~wise(X)|old(X)))) | strong(susan) | [] | null | 0 |
Everyone who is not happy or not creative is not curious or not strong and vice versa. If lucy is either happy or not brave then lucy is either not kind or generous and vice versa. Everyone who is old is both strong and kind and vice versa. Everyone who is both not strong and tall is patient or not strong and vice versa. If someone is strong then mary is both not quiet and curious. If paul is both funny and not brave then alice is not creative or not happy. Everyone who is quiet is either old or not strong and vice versa. Everyone who is both old and not funny is old and vice versa. Everyone who is both not funny and not kind is not calm or funny. Everyone who is both brave and not funny is either not rich or funny and vice versa. Everyone who is both wise and rich is not curious or not quiet and vice versa. If mary is not humble then susan is both not calm and not brave. If someone is kind or not funny then fred is not happy. If someone is either not brave or wise then someone is not curious or not humble. Everyone who is either quiet or tall is not funny or not brave and vice versa. Everyone who is both wise and quiet is both creative and not funny and vice versa. Someone is either not quiet or happy. Someone is either happy or not happy. Someone is not curious or calm. Someone is either not funny or creative. Someone is quiet. | Lucy is not wise. | entailment | (![X]:((~happy(X)|~creative(X))<=>(~curious(X)|~strong(X))))&
(((happy(lucy)<~>~brave(lucy)))<=>((~kind(lucy)<~>generous(lucy))))&
(![X]:(old(X)<=>(strong(X)&kind(X))))&
(![X]:((~strong(X)&tall(X))<=>(patient(X)|~strong(X))))&
((?[X]:(strong(X)))=>((~quiet(mary)&curious(mary))))&
(((funny(paul)&~brave(paul)))=>((~creative(alice)|~happy(alice))))&
(![X]:(quiet(X)<=>(old(X)<~>~strong(X))))&
(![X]:((old(X)&~funny(X))<=>old(X)))&
(![X]:((~funny(X)&~kind(X))=>(~calm(X)|funny(X))))&
(![X]:((brave(X)&~funny(X))<=>(~rich(X)<~>funny(X))))&
(![X]:((wise(X)&rich(X))<=>(~curious(X)|~quiet(X))))&
((~humble(mary))=>((~calm(susan)&~brave(susan))))&
((?[X]:((kind(X)|~funny(X))))=>(~happy(fred)))&
((?[X]:((~brave(X)<~>wise(X))))=>(?[X]:((~curious(X)|~humble(X)))))&
(![X]:((quiet(X)<~>tall(X))<=>(~funny(X)|~brave(X))))&
(![X]:((wise(X)&quiet(X))<=>(creative(X)&~funny(X))))&
(?[X]:((~quiet(X)<~>happy(X))))&
(?[X]:((happy(X)<~>~happy(X))))&
(?[X]:((~curious(X)|calm(X))))&
(?[X]:((~funny(X)<~>creative(X))))&
(?[X]:(quiet(X))) | ~wise(lucy) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p9",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5352247694277409035981446
% SZS output start Proof for 5352247694277409035981446
1. ! [X0] : ((~creative(X0) | ~happy(X0)) <=> (~strong(X0) | ~curious(X0))) [input p0]
3. ! [X0] : (old(X0) <=> (kind(X0) & strong(X0))) [input p2]
4. ! [X0] : ((tall(X0) & ~strong(X0)) <=> (~strong(X0) | patient(X0))) [input p3]
5. ? [X0] : strong(X0) => (curious(mary) & ~quiet(mary)) [input p4]
7. ! [X0] : (quiet(X0) <=> (old(X0) <~> ~strong(X0))) [input p6]
10. ! [X0] : ((~funny(X0) & brave(X0)) <=> (~rich(X0) <~> funny(X0))) [input p9]
11. ! [X0] : ((rich(X0) & wise(X0)) <=> (~quiet(X0) | ~curious(X0))) [input p10]
15. ! [X0] : ((quiet(X0) <~> tall(X0)) <=> (~brave(X0) | ~funny(X0))) [input p14]
16. ! [X0] : ((quiet(X0) & wise(X0)) <=> (~funny(X0) & creative(X0))) [input p15]
22. wise(lucy) [input hypothesis]
24. (curious(mary) & ~quiet(mary)) | ! [X0] : ~strong(X0) [ennf transformation 5]
32. ! [X0] : (((~creative(X0) | ~happy(X0)) | (strong(X0) & curious(X0))) & ((~strong(X0) | ~curious(X0)) | (creative(X0) & happy(X0)))) [nnf transformation 1]
33. ! [X0] : ((~creative(X0) | ~happy(X0) | (strong(X0) & curious(X0))) & (~strong(X0) | ~curious(X0) | (creative(X0) & happy(X0)))) [flattening 32]
35. ! [X0] : ((old(X0) | (~kind(X0) | ~strong(X0))) & ((kind(X0) & strong(X0)) | ~old(X0))) [nnf transformation 3]
36. ! [X0] : ((old(X0) | ~kind(X0) | ~strong(X0)) & ((kind(X0) & strong(X0)) | ~old(X0))) [flattening 35]
37. ! [X0] : (((tall(X0) & ~strong(X0)) | (strong(X0) & ~patient(X0))) & ((~strong(X0) | patient(X0)) | (~tall(X0) | strong(X0)))) [nnf transformation 4]
38. ! [X0] : (((tall(X0) & ~strong(X0)) | (strong(X0) & ~patient(X0))) & (~strong(X0) | patient(X0) | ~tall(X0) | strong(X0))) [flattening 37]
39. ! [X0] : ((quiet(X0) | ((old(X0) | strong(X0)) & (~strong(X0) | ~old(X0)))) & (((strong(X0) | ~old(X0)) & (~strong(X0) | old(X0))) | ~quiet(X0))) [nnf transformation 7]
42. ! [X0] : (((~funny(X0) & brave(X0)) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0)))) & (((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | (funny(X0) | ~brave(X0)))) [nnf transformation 10]
43. ! [X0] : (((~funny(X0) & brave(X0)) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0)))) & (((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | funny(X0) | ~brave(X0))) [flattening 42]
44. ! [X0] : (((rich(X0) & wise(X0)) | (quiet(X0) & curious(X0))) & ((~quiet(X0) | ~curious(X0)) | (~rich(X0) | ~wise(X0)))) [nnf transformation 11]
45. ! [X0] : (((rich(X0) & wise(X0)) | (quiet(X0) & curious(X0))) & (~quiet(X0) | ~curious(X0) | ~rich(X0) | ~wise(X0))) [flattening 44]
50. ! [X0] : ((((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (brave(X0) & funny(X0))) & ((~brave(X0) | ~funny(X0)) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0))))) [nnf transformation 15]
51. ! [X0] : ((((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (brave(X0) & funny(X0))) & (~brave(X0) | ~funny(X0) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0))))) [flattening 50]
52. ! [X0] : (((quiet(X0) & wise(X0)) | (funny(X0) | ~creative(X0))) & ((~funny(X0) & creative(X0)) | (~quiet(X0) | ~wise(X0)))) [nnf transformation 16]
53. ! [X0] : (((quiet(X0) & wise(X0)) | funny(X0) | ~creative(X0)) & ((~funny(X0) & creative(X0)) | ~quiet(X0) | ~wise(X0))) [flattening 52]
68. ~strong(X0) | ~curious(X0) | creative(X0) [cnf transformation 33]
79. ~old(X0) | strong(X0) [cnf transformation 36]
86. tall(X0) | strong(X0) [cnf transformation 38]
87. ~quiet(mary) | ~strong(X0) [cnf transformation 24]
88. curious(mary) | ~strong(X0) [cnf transformation 24]
93. quiet(X0) | old(X0) | strong(X0) [cnf transformation 39]
103. ~funny(X0) | ~rich(X0) | ~funny(X0) [cnf transformation 43]
108. rich(X0) | quiet(X0) [cnf transformation 45]
119. ~quiet(X0) | ~tall(X0) | funny(X0) [cnf transformation 51]
122. ~wise(X0) | ~quiet(X0) | ~funny(X0) [cnf transformation 53]
124. ~creative(X0) | funny(X0) | quiet(X0) [cnf transformation 53]
133. wise(lucy) [cnf transformation 22]
135. ~rich(X0) | ~funny(X0) [duplicate literal removal 103]
162. 5 <=> ! [X0] : ~strong(X0) [avatar definition]
163. ~strong(X0) <- (5) [avatar component clause 162]
165. 6 <=> curious(mary) [avatar definition]
167. curious(mary) <- (6) [avatar component clause 165]
168. 5 | 6 [avatar split clause 88,165,162]
170. 7 <=> quiet(mary) [avatar definition]
172. ~quiet(mary) <- (~7) [avatar component clause 170]
173. 5 | ~7 [avatar split clause 87,170,162]
191. quiet(X0) | strong(X0) [subsumption resolution 93,79]
265. ~funny(X0) | quiet(X0) [resolution 135,108]
349. ~tall(X1) | funny(X1) | strong(X1) [resolution 119,191]
399. funny(X1) | strong(X1) [subsumption resolution 349,86]
410. strong(mary) <- (~7) [resolution 172,191]
423. ~quiet(lucy) | ~funny(lucy) [resolution 122,133]
467. ~curious(mary) | creative(mary) <- (~7) [resolution 410,68]
469. creative(mary) <- (6, ~7) [subsumption resolution 467,167]
530. funny(mary) | quiet(mary) <- (6, ~7) [resolution 469,124]
534. funny(mary) <- (6, ~7) [subsumption resolution 530,172]
584. quiet(mary) <- (6, ~7) [resolution 534,265]
586. $false <- (6, ~7) [subsumption resolution 584,172]
587. ~6 | 7 [avatar contradiction clause 586]
588. ~funny(lucy) [subsumption resolution 423,265]
653. strong(lucy) [resolution 588,399]
664. $false <- (5) [subsumption resolution 653,163]
665. ~5 [avatar contradiction clause 664]
667. $false [avatar sat refutation 168,173,587,665]
% SZS output end Proof for 5352247694277409035981446
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and strong is either not curious or curious and vice versa.
If someone is not wise or not calm then someone is both not funny and not kind.
Everyone who is not rich or not generous is both humble and patient.
Everyone who is either humble or not quiet is old or not curious and vice versa.
If mary is creative then someone is either old or not tall and vice versa.
Everyone who is either wise or not kind is either not generous or tall and vice versa.
Everyone who is not kind or funny is rich or not wise and vice versa.
Everyone who is tall is both humble and not humble and vice versa.
Everyone who is either not creative or not quiet is tall and vice versa.
If someone is not generous then someone is kind or not old.
Everyone who is both not funny and rich is not patient or not brave and vice versa.
Everyone who is either brave or tall is not kind or happy.
Everyone who is either kind or patient is tall or not quiet and vice versa.
Everyone who is both happy and not tall is generous or calm.
Everyone who is either not creative or not happy is not wise.
If someone is either old or not humble then lucy is kind or creative.
Someone is both strong and not curious.
Someone is not happy.
Alice is not tall or not strong.
Alice is either calm or humble.
Someone is either curious or not curious.
Someone is not funny.
Paul is not patient or not quiet. | Mary is not kind. | entailment | (![X]:((~quiet(X)&strong(X))<=>(~curious(X)<~>curious(X))))&
((?[X]:((~wise(X)|~calm(X))))=>(?[X]:((~funny(X)&~kind(X)))))&
(![X]:((~rich(X)|~generous(X))=>(humble(X)&patient(X))))&
(![X]:((humble(X)<~>~quiet(X))<=>(old(X)|~curious(X))))&
((creative(mary))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:((wise(X)<~>~kind(X))<=>(~generous(X)<~>tall(X))))&
(![X]:((~kind(X)|funny(X))<=>(rich(X)|~wise(X))))&
(![X]:(tall(X)<=>(humble(X)&~humble(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>tall(X)))&
((?[X]:(~generous(X)))=>(?[X]:((kind(X)|~old(X)))))&
(![X]:((~funny(X)&rich(X))<=>(~patient(X)|~brave(X))))&
(![X]:((brave(X)<~>tall(X))=>(~kind(X)|happy(X))))&
(![X]:((kind(X)<~>patient(X))<=>(tall(X)|~quiet(X))))&
(![X]:((happy(X)&~tall(X))=>(generous(X)|calm(X))))&
(![X]:((~creative(X)<~>~happy(X))=>~wise(X)))&
((?[X]:((old(X)<~>~humble(X))))=>((kind(lucy)|creative(lucy))))&
(?[X]:((strong(X)&~curious(X))))&
(?[X]:(~happy(X)))&
((~tall(alice)|~strong(alice)))&
((calm(alice)<~>humble(alice)))&
(?[X]:((curious(X)<~>~curious(X))))&
(?[X]:(~funny(X)))&
((~patient(paul)|~quiet(paul))) | ~kind(mary) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p7",
"p8",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6957468503347556778268951
% SZS output start Proof for 6957468503347556778268951
1. ! [X0] : ((strong(X0) & ~quiet(X0)) <=> (~curious(X0) <~> curious(X0))) [input p0]
3. ! [X0] : ((~generous(X0) | ~rich(X0)) => (patient(X0) & humble(X0))) [input p2]
4. ! [X0] : ((humble(X0) <~> ~quiet(X0)) <=> (~curious(X0) | old(X0))) [input p3]
5. creative(mary) <=> ? [X0] : (old(X0) <~> ~tall(X0)) [input p4]
7. ! [X0] : ((funny(X0) | ~kind(X0)) <=> (~wise(X0) | rich(X0))) [input p6]
8. ! [X0] : (tall(X0) <=> (~humble(X0) & humble(X0))) [input p7]
9. ! [X0] : ((~creative(X0) <~> ~quiet(X0)) <=> tall(X0)) [input p8]
11. ! [X0] : ((rich(X0) & ~funny(X0)) <=> (~brave(X0) | ~patient(X0))) [input p10]
13. ! [X0] : ((kind(X0) <~> patient(X0)) <=> (~quiet(X0) | tall(X0))) [input p12]
24. kind(mary) [input hypothesis]
28. ! [X0] : ((patient(X0) & humble(X0)) | (generous(X0) & rich(X0))) [ennf transformation 3]
37. ! [X0] : (((strong(X0) & ~quiet(X0)) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0)))) & (((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | (~strong(X0) | quiet(X0)))) [nnf transformation 1]
38. ! [X0] : (((strong(X0) & ~quiet(X0)) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0)))) & (((~curious(X0) | curious(X0)) & (curious(X0) | ~curious(X0))) | ~strong(X0) | quiet(X0))) [flattening 37]
42. ! [X0] : ((((quiet(X0) | ~humble(X0)) & (~quiet(X0) | humble(X0))) | (curious(X0) & ~old(X0))) & ((~curious(X0) | old(X0)) | ((humble(X0) | quiet(X0)) & (~quiet(X0) | ~humble(X0))))) [nnf transformation 4]
43. ! [X0] : ((((quiet(X0) | ~humble(X0)) & (~quiet(X0) | humble(X0))) | (curious(X0) & ~old(X0))) & (~curious(X0) | old(X0) | ((humble(X0) | quiet(X0)) & (~quiet(X0) | ~humble(X0))))) [flattening 42]
44. (creative(mary) | ! [X0] : ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (? [X0] : ((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | ~creative(mary)) [nnf transformation 5]
45. (creative(mary) | ! [X0] : ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (? [X1] : ((tall(X1) | ~old(X1)) & (~tall(X1) | old(X1))) | ~creative(mary)) [rectify 44]
46. ? [X1] : ((tall(X1) | ~old(X1)) & (~tall(X1) | old(X1))) => ((tall(sK1) | ~old(sK1)) & (~tall(sK1) | old(sK1))) [choice axiom]
47. (creative(mary) | ! [X0] : ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0)))) & (((tall(sK1) | ~old(sK1)) & (~tall(sK1) | old(sK1))) | ~creative(mary)) [skolemisation 45,46]
49. ! [X0] : (((funny(X0) | ~kind(X0)) | (wise(X0) & ~rich(X0))) & ((~wise(X0) | rich(X0)) | (~funny(X0) & kind(X0)))) [nnf transformation 7]
50. ! [X0] : ((funny(X0) | ~kind(X0) | (wise(X0) & ~rich(X0))) & (~wise(X0) | rich(X0) | (~funny(X0) & kind(X0)))) [flattening 49]
51. ! [X0] : ((tall(X0) | (humble(X0) | ~humble(X0))) & ((~humble(X0) & humble(X0)) | ~tall(X0))) [nnf transformation 8]
52. ! [X0] : ((tall(X0) | humble(X0) | ~humble(X0)) & ((~humble(X0) & humble(X0)) | ~tall(X0))) [flattening 51]
53. ! [X0] : ((((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | ~tall(X0)) & (tall(X0) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0))))) [nnf transformation 9]
57. ! [X0] : (((rich(X0) & ~funny(X0)) | (brave(X0) & patient(X0))) & ((~brave(X0) | ~patient(X0)) | (~rich(X0) | funny(X0)))) [nnf transformation 11]
58. ! [X0] : (((rich(X0) & ~funny(X0)) | (brave(X0) & patient(X0))) & (~brave(X0) | ~patient(X0) | ~rich(X0) | funny(X0))) [flattening 57]
60. ! [X0] : ((((~patient(X0) | ~kind(X0)) & (patient(X0) | kind(X0))) | (quiet(X0) & ~tall(X0))) & ((~quiet(X0) | tall(X0)) | ((kind(X0) | ~patient(X0)) & (patient(X0) | ~kind(X0))))) [nnf transformation 13]
61. ! [X0] : ((((~patient(X0) | ~kind(X0)) & (patient(X0) | kind(X0))) | (quiet(X0) & ~tall(X0))) & (~quiet(X0) | tall(X0) | ((kind(X0) | ~patient(X0)) & (patient(X0) | ~kind(X0))))) [flattening 60]
76. ~quiet(X0) | curious(X0) | curious(X0) [cnf transformation 38]
77. ~quiet(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 38]
84. humble(X0) | rich(X0) [cnf transformation 28]
92. quiet(X0) | ~humble(X0) | ~old(X0) [cnf transformation 43]
97. creative(mary) | old(X0) | tall(X0) [cnf transformation 47]
108. ~rich(X0) | ~kind(X0) | funny(X0) [cnf transformation 50]
110. humble(X0) | ~tall(X0) [cnf transformation 52]
111. ~tall(X0) | ~humble(X0) [cnf transformation 52]
114. tall(X0) | ~creative(X0) | quiet(X0) [cnf transformation 53]
119. ~funny(X0) | patient(X0) [cnf transformation 58]
130. ~patient(X0) | ~kind(X0) | quiet(X0) [cnf transformation 61]
146. kind(mary) [cnf transformation 24]
147. ~quiet(X0) | curious(X0) [duplicate literal removal 76]
148. ~curious(X0) | ~quiet(X0) [duplicate literal removal 77]
152. ~quiet(X0) [subsumption resolution 147,148]
172. ~old(X0) | ~humble(X0) [subsumption resolution 92,152]
175. 5 <=> ! [X0] : (old(X0) | tall(X0)) [avatar definition]
176. old(X0) | tall(X0) <- (5) [avatar component clause 175]
178. 6 <=> creative(mary) [avatar definition]
180. creative(mary) <- (6) [avatar component clause 178]
181. 5 | 6 [avatar split clause 97,178,175]
196. ~tall(X0) [subsumption resolution 110,111]
197. ~creative(X0) | quiet(X0) [subsumption resolution 114,196]
198. ~creative(X0) [subsumption resolution 197,152]
212. ~patient(X0) | ~kind(X0) [subsumption resolution 130,152]
235. $false <- (6) [subsumption resolution 180,198]
236. ~6 [avatar contradiction clause 235]
237. old(X0) <- (5) [subsumption resolution 176,196]
246. ~humble(X0) <- (5) [resolution 172,237]
250. rich(X1) <- (5) [resolution 246,84]
256. ~kind(X1) | funny(X1) <- (5) [resolution 108,250]
272. 20 <=> funny(mary) [avatar definition]
274. funny(mary) <- (20) [avatar component clause 272]
277. funny(mary) <- (5) [resolution 256,146]
278. 20 | ~5 [avatar split clause 277,175,272]
282. patient(mary) <- (20) [resolution 274,119]
287. ~kind(mary) <- (20) [resolution 282,212]
288. $false <- (20) [subsumption resolution 287,146]
289. ~20 [avatar contradiction clause 288]
290. $false [avatar sat refutation 181,236,278,289]
% SZS output end Proof for 6957468503347556778268951
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble then someone is both not quiet and humble and vice versa. Everyone who is brave or strong is both rich and kind. If someone is not tall or not patient then someone is both not creative and not kind. If lucy is both not funny and old then susan is either curious or not humble and vice versa. Everyone who is both humble and tall is tall or creative. Everyone who is both funny and curious is either not rich or not kind. If someone is funny or curious then someone is either happy or not brave and vice versa. Everyone who is not happy or quiet is both old and not brave and vice versa. Everyone who is both curious and not strong is not kind or not happy and vice versa. Everyone who is patient is not generous and vice versa. Everyone who is strong is either not brave or calm and vice versa. Everyone who is not quiet or creative is not kind or not generous. If alice is funny or not curious then someone is humble or tall and vice versa. Everyone who is wise or quiet is either not kind or not funny and vice versa. If someone is both kind and not rich then someone is not curious. Everyone who is rich or not tall is either tall or calm. Fred is both not humble and not rich. Someone is both humble and not rich. Paul is kind or funny. Someone is either not rich or not wise. Susan is both not kind and not old. Fred is funny. Someone is either not strong or not wise. | Fred is not wise. | entailment | ((?[X]:(humble(X)))<=>(?[X]:((~quiet(X)&humble(X)))))&
(![X]:((brave(X)|strong(X))=>(rich(X)&kind(X))))&
((?[X]:((~tall(X)|~patient(X))))=>(?[X]:((~creative(X)&~kind(X)))))&
(((~funny(lucy)&old(lucy)))<=>((curious(susan)<~>~humble(susan))))&
(![X]:((humble(X)&tall(X))=>(tall(X)|creative(X))))&
(![X]:((funny(X)&curious(X))=>(~rich(X)<~>~kind(X))))&
((?[X]:((funny(X)|curious(X))))<=>(?[X]:((happy(X)<~>~brave(X)))))&
(![X]:((~happy(X)|quiet(X))<=>(old(X)&~brave(X))))&
(![X]:((curious(X)&~strong(X))<=>(~kind(X)|~happy(X))))&
(![X]:(patient(X)<=>~generous(X)))&
(![X]:(strong(X)<=>(~brave(X)<~>calm(X))))&
(![X]:((~quiet(X)|creative(X))=>(~kind(X)|~generous(X))))&
(((funny(alice)|~curious(alice)))<=>(?[X]:((humble(X)|tall(X)))))&
(![X]:((wise(X)|quiet(X))<=>(~kind(X)<~>~funny(X))))&
((?[X]:((kind(X)&~rich(X))))=>(?[X]:(~curious(X))))&
(![X]:((rich(X)|~tall(X))=>(tall(X)<~>calm(X))))&
((~humble(fred)&~rich(fred)))&
(?[X]:((humble(X)&~rich(X))))&
((kind(paul)|funny(paul)))&
(?[X]:((~rich(X)<~>~wise(X))))&
((~kind(susan)&~old(susan)))&
(funny(fred))&
(?[X]:((~strong(X)<~>~wise(X)))) | ~wise(fred) | [
"p5",
"p8",
"p13",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2426045370090775265371535
% SZS output start Proof for 2426045370090775265371535
6. ! [X0] : ((curious(X0) & funny(X0)) => (~rich(X0) <~> ~kind(X0))) [input p5]
9. ! [X0] : ((~strong(X0) & curious(X0)) <=> (~happy(X0) | ~kind(X0))) [input p8]
14. ! [X0] : ((quiet(X0) | wise(X0)) <=> (~kind(X0) <~> ~funny(X0))) [input p13]
17. ~rich(fred) & ~humble(fred) [input p16]
22. funny(fred) [input p21]
24. wise(fred) [input hypothesis]
37. ! [X0] : ((~rich(X0) <~> ~kind(X0)) | (~curious(X0) | ~funny(X0))) [ennf transformation 6]
38. ! [X0] : ((~rich(X0) <~> ~kind(X0)) | ~curious(X0) | ~funny(X0)) [flattening 37]
51. ! [X0] : (((kind(X0) | rich(X0)) & (~kind(X0) | ~rich(X0))) | ~curious(X0) | ~funny(X0)) [nnf transformation 38]
59. ! [X0] : (((~strong(X0) & curious(X0)) | (happy(X0) & kind(X0))) & ((~happy(X0) | ~kind(X0)) | (strong(X0) | ~curious(X0)))) [nnf transformation 9]
60. ! [X0] : (((~strong(X0) & curious(X0)) | (happy(X0) & kind(X0))) & (~happy(X0) | ~kind(X0) | strong(X0) | ~curious(X0))) [flattening 59]
67. ! [X0] : (((quiet(X0) | wise(X0)) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0)))) & (((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | (~quiet(X0) & ~wise(X0)))) [nnf transformation 14]
68. ! [X0] : ((quiet(X0) | wise(X0) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0)))) & (((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | (~quiet(X0) & ~wise(X0)))) [flattening 67]
98. ~curious(X0) | rich(X0) | kind(X0) | ~funny(X0) [cnf transformation 51]
111. curious(X0) | kind(X0) [cnf transformation 60]
123. ~wise(X0) | ~kind(X0) | ~funny(X0) [cnf transformation 68]
135. ~rich(fred) [cnf transformation 17]
143. funny(fred) [cnf transformation 22]
146. wise(fred) [cnf transformation 24]
345. ~kind(fred) | ~funny(fred) [resolution 123,146]
346. ~kind(fred) [subsumption resolution 345,143]
379. rich(X0) | kind(X0) | ~funny(X0) | kind(X0) [resolution 98,111]
382. ~funny(X0) | kind(X0) | rich(X0) [duplicate literal removal 379]
386. kind(fred) | rich(fred) [resolution 382,143]
388. rich(fred) [subsumption resolution 386,346]
389. $false [subsumption resolution 388,135]
% SZS output end Proof for 2426045370090775265371535
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or not rich is either not creative or not humble. Everyone who is patient or not humble is both kind and funny. Everyone who is either quiet or not happy is tall. If someone is kind or not creative then mary is both funny and happy and vice versa. If someone is tall or creative then lucy is creative and vice versa. If someone is either humble or not strong then someone is patient and vice versa. Everyone who is wise or humble is creative and vice versa. Everyone who is not creative or kind is both not curious and happy. If alice is either not brave or not calm then john is strong and vice versa. If susan is both not calm and not creative then alice is both happy and wise and vice versa. Everyone who is not strong or not kind is both not happy and tall. If someone is not patient or not calm then someone is not quiet and vice versa. Everyone who is either not tall or not brave is both rich and not creative and vice versa. Everyone who is calm is both wise and not tall and vice versa. If mary is not calm or humble then someone is not patient. If someone is not funny then alice is either not humble or quiet. Someone is both not curious and not brave. Someone is not brave or strong. Susan is curious. Someone is both not creative and not curious. Someone is curious or not generous. Someone is both not old and not humble. | Mary is not curious. | entailment | (![X]:((curious(X)<~>~rich(X))=>(~creative(X)<~>~humble(X))))&
(![X]:((patient(X)|~humble(X))=>(kind(X)&funny(X))))&
(![X]:((quiet(X)<~>~happy(X))=>tall(X)))&
((?[X]:((kind(X)|~creative(X))))<=>((funny(mary)&happy(mary))))&
((?[X]:((tall(X)|creative(X))))<=>(creative(lucy)))&
((?[X]:((humble(X)<~>~strong(X))))<=>(?[X]:(patient(X))))&
(![X]:((wise(X)|humble(X))<=>creative(X)))&
(![X]:((~creative(X)|kind(X))=>(~curious(X)&happy(X))))&
(((~brave(alice)<~>~calm(alice)))<=>(strong(john)))&
(((~calm(susan)&~creative(susan)))<=>((happy(alice)&wise(alice))))&
(![X]:((~strong(X)|~kind(X))=>(~happy(X)&tall(X))))&
((?[X]:((~patient(X)|~calm(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((~tall(X)<~>~brave(X))<=>(rich(X)&~creative(X))))&
(![X]:(calm(X)<=>(wise(X)&~tall(X))))&
(((~calm(mary)|humble(mary)))=>(?[X]:(~patient(X))))&
((?[X]:(~funny(X)))=>((~humble(alice)<~>quiet(alice))))&
(?[X]:((~curious(X)&~brave(X))))&
(?[X]:((~brave(X)|strong(X))))&
(curious(susan))&
(?[X]:((~creative(X)&~curious(X))))&
(?[X]:((curious(X)|~generous(X))))&
(?[X]:((~old(X)&~humble(X)))) | ~curious(mary) | [
"p3",
"p7",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 841500713415074942819329
% SZS output start Proof for 841500713415074942819329
4. ? [X0] : (~creative(X0) | kind(X0)) <=> (happy(mary) & funny(mary)) [input p3]
8. ! [X0] : ((kind(X0) | ~creative(X0)) => (happy(X0) & ~curious(X0))) [input p7]
11. ! [X0] : ((~kind(X0) | ~strong(X0)) => (tall(X0) & ~happy(X0))) [input p10]
20. ? [X0] : (~curious(X0) & ~creative(X0)) [input p19]
23. curious(mary) [input hypothesis]
31. ! [X0] : ((happy(X0) & ~curious(X0)) | (~kind(X0) & creative(X0))) [ennf transformation 8]
32. ! [X0] : ((tall(X0) & ~happy(X0)) | (kind(X0) & strong(X0))) [ennf transformation 11]
37. (? [X0] : (~creative(X0) | kind(X0)) | (~happy(mary) | ~funny(mary))) & ((happy(mary) & funny(mary)) | ! [X0] : (creative(X0) & ~kind(X0))) [nnf transformation 4]
38. (? [X0] : (~creative(X0) | kind(X0)) | ~happy(mary) | ~funny(mary)) & ((happy(mary) & funny(mary)) | ! [X0] : (creative(X0) & ~kind(X0))) [flattening 37]
39. (? [X0] : (~creative(X0) | kind(X0)) | ~happy(mary) | ~funny(mary)) & ((happy(mary) & funny(mary)) | ! [X1] : (creative(X1) & ~kind(X1))) [rectify 38]
40. ? [X0] : (~creative(X0) | kind(X0)) => (~creative(sK0) | kind(sK0)) [choice axiom]
41. ((~creative(sK0) | kind(sK0)) | ~happy(mary) | ~funny(mary)) & ((happy(mary) & funny(mary)) | ! [X1] : (creative(X1) & ~kind(X1))) [skolemisation 39,40]
72. ? [X0] : (~curious(X0) & ~creative(X0)) => (~curious(sK9) & ~creative(sK9)) [choice axiom]
73. ~curious(sK9) & ~creative(sK9) [skolemisation 20,72]
89. happy(mary) | creative(X1) [cnf transformation 41]
102. ~kind(X0) | ~curious(X0) [cnf transformation 31]
114. ~happy(X0) | kind(X0) [cnf transformation 32]
137. ~creative(sK9) [cnf transformation 73]
140. curious(mary) [cnf transformation 23]
146. 2 <=> happy(mary) [avatar definition]
147. happy(mary) <- (2) [avatar component clause 146]
159. 5 <=> ! [X1] : creative(X1) [avatar definition]
160. creative(X1) <- (5) [avatar component clause 159]
161. 5 | 2 [avatar split clause 89,146,159]
310. $false <- (5) [resolution 160,137]
311. ~5 [avatar contradiction clause 310]
330. kind(mary) <- (2) [resolution 114,147]
334. ~curious(mary) <- (2) [resolution 330,102]
335. $false <- (2) [subsumption resolution 334,140]
336. ~2 [avatar contradiction clause 335]
337. $false [avatar sat refutation 161,311,336]
% SZS output end Proof for 841500713415074942819329
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and not wise is both brave and old. If someone is old then alice is quiet. If fred is creative or wise then fred is either curious or tall and vice versa. Everyone who is both not tall and not calm is either not generous or not strong. Everyone who is not calm or not creative is both not calm and humble and vice versa. Everyone who is curious or not tall is wise and vice versa. If someone is not patient or not quiet then fred is either kind or happy and vice versa. Everyone who is either not brave or not tall is both strong and not kind and vice versa. If someone is not tall then alice is strong. If alice is not humble then paul is either not humble or not rich. Everyone who is either not strong or brave is not brave and vice versa. Everyone who is not rich or brave is not strong or brave. If alice is patient or wise then someone is both funny and not patient and vice versa. If paul is creative then mary is both not happy and not old. Everyone who is not happy or strong is both happy and creative. Everyone who is either creative or not kind is both not generous and brave. Susan is brave. Susan is not tall or calm. Someone is not quiet or brave. Someone is not tall or wise. Someone is not curious or not patient. Someone is both quiet and calm. Lucy is not funny. Someone is either not generous or not rich. | Lucy is not strong. | entailment | (![X]:((funny(X)&~wise(X))=>(brave(X)&old(X))))&
((?[X]:(old(X)))=>(quiet(alice)))&
(((creative(fred)|wise(fred)))<=>((curious(fred)<~>tall(fred))))&
(![X]:((~tall(X)&~calm(X))=>(~generous(X)<~>~strong(X))))&
(![X]:((~calm(X)|~creative(X))<=>(~calm(X)&humble(X))))&
(![X]:((curious(X)|~tall(X))<=>wise(X)))&
((?[X]:((~patient(X)|~quiet(X))))<=>((kind(fred)<~>happy(fred))))&
(![X]:((~brave(X)<~>~tall(X))<=>(strong(X)&~kind(X))))&
((?[X]:(~tall(X)))=>(strong(alice)))&
((~humble(alice))=>((~humble(paul)<~>~rich(paul))))&
(![X]:((~strong(X)<~>brave(X))<=>~brave(X)))&
(![X]:((~rich(X)|brave(X))=>(~strong(X)|brave(X))))&
(((patient(alice)|wise(alice)))<=>(?[X]:((funny(X)&~patient(X)))))&
((creative(paul))=>((~happy(mary)&~old(mary))))&
(![X]:((~happy(X)|strong(X))=>(happy(X)&creative(X))))&
(![X]:((creative(X)<~>~kind(X))=>(~generous(X)&brave(X))))&
(brave(susan))&
((~tall(susan)|calm(susan)))&
(?[X]:((~quiet(X)|brave(X))))&
(?[X]:((~tall(X)|wise(X))))&
(?[X]:((~curious(X)|~patient(X))))&
(?[X]:((quiet(X)&calm(X))))&
(~funny(lucy))&
(?[X]:((~generous(X)<~>~rich(X)))) | ~strong(lucy) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8620724903009368870118157
% SZS output start Proof for 8620724903009368870118157
11. ! [X0] : ((~strong(X0) <~> brave(X0)) <=> ~brave(X0)) [input p10]
25. strong(lucy) [input hypothesis]
52. ! [X0] : ((((~brave(X0) | strong(X0)) & (brave(X0) | ~strong(X0))) | brave(X0)) & (~brave(X0) | ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0))))) [nnf transformation 11]
105. ~brave(X0) | ~strong(X0) | ~brave(X0) [cnf transformation 52]
106. brave(X0) | ~strong(X0) | brave(X0) [cnf transformation 52]
135. strong(lucy) [cnf transformation 25]
137. ~brave(X0) | ~strong(X0) [duplicate literal removal 105]
138. brave(X0) | ~strong(X0) [duplicate literal removal 106]
219. ~strong(X0) [subsumption resolution 137,138]
296. $false [subsumption resolution 135,219]
% SZS output end Proof for 8620724903009368870118157
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is creative or old then mary is not kind. Everyone who is not curious is both quiet and not happy and vice versa. Everyone who is either not calm or brave is either creative or wise. Everyone who is either creative or not calm is patient and vice versa. If fred is happy or wise then paul is patient or generous and vice versa. If mary is not happy then someone is either brave or not quiet. If someone is not kind or not wise then mary is humble. Everyone who is not kind or creative is humble or not kind. Everyone who is not brave is not quiet and vice versa. If someone is brave then someone is rich or wise and vice versa. Everyone who is both not generous and patient is either curious or not patient. If fred is funny or not curious then someone is brave and vice versa. Everyone who is both rich and not generous is either rich or not quiet. If fred is humble then mary is both not patient and strong and vice versa. Everyone who is both not curious and tall is not curious or not brave. If someone is both not patient and not curious then fred is not curious and vice versa. Lucy is not wise. Someone is not humble. Someone is patient or rich. Someone is either rich or not strong. Someone is either not happy or kind. Mary is either not creative or strong. Someone is not creative. Susan is both not tall and not generous. | Susan is not generous. | entailment | (((creative(fred)|old(fred)))=>(~kind(mary)))&
(![X]:(~curious(X)<=>(quiet(X)&~happy(X))))&
(![X]:((~calm(X)<~>brave(X))=>(creative(X)<~>wise(X))))&
(![X]:((creative(X)<~>~calm(X))<=>patient(X)))&
(((happy(fred)|wise(fred)))<=>((patient(paul)|generous(paul))))&
((~happy(mary))=>(?[X]:((brave(X)<~>~quiet(X)))))&
((?[X]:((~kind(X)|~wise(X))))=>(humble(mary)))&
(![X]:((~kind(X)|creative(X))=>(humble(X)|~kind(X))))&
(![X]:(~brave(X)<=>~quiet(X)))&
((?[X]:(brave(X)))<=>(?[X]:((rich(X)|wise(X)))))&
(![X]:((~generous(X)&patient(X))=>(curious(X)<~>~patient(X))))&
(((funny(fred)|~curious(fred)))<=>(?[X]:(brave(X))))&
(![X]:((rich(X)&~generous(X))=>(rich(X)<~>~quiet(X))))&
((humble(fred))<=>((~patient(mary)&strong(mary))))&
(![X]:((~curious(X)&tall(X))=>(~curious(X)|~brave(X))))&
((?[X]:((~patient(X)&~curious(X))))<=>(~curious(fred)))&
(~wise(lucy))&
(?[X]:(~humble(X)))&
(?[X]:((patient(X)|rich(X))))&
(?[X]:((rich(X)<~>~strong(X))))&
(?[X]:((~happy(X)<~>kind(X))))&
((~creative(mary)<~>strong(mary)))&
(?[X]:(~creative(X)))&
((~tall(susan)&~generous(susan))) | ~generous(susan) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 78788778521702761596855
% SZS output start Proof for 78788778521702761596855
24. ~generous(susan) & ~tall(susan) [input p23]
25. generous(susan) [input hypothesis]
28. ~generous(susan) [pure predicate removal 24]
131. ~generous(susan) [cnf transformation 28]
132. generous(susan) [cnf transformation 25]
293. $false [subsumption resolution 132,131]
% SZS output end Proof for 78788778521702761596855
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not quiet and not kind is not tall. Everyone who is patient is old or quiet and vice versa. If alice is either kind or not brave then someone is either funny or not generous and vice versa. If susan is not strong then mary is old. If susan is not wise then someone is calm and vice versa. Everyone who is not wise is strong. Everyone who is not tall or happy is curious and vice versa. If someone is both not calm and not patient then someone is calm or tall. Everyone who is both curious and not old is either curious or strong and vice versa. If someone is curious or not happy then someone is either not strong or funny. If someone is either tall or happy then someone is not quiet. If someone is both calm and quiet then john is not old and vice versa. Everyone who is not creative is either not creative or quiet and vice versa. Everyone who is either not tall or not curious is not generous and vice versa. If someone is not rich then mary is either not funny or not calm and vice versa. Everyone who is strong or quiet is both strong and not kind and vice versa. Someone is either not creative or not kind. Someone is not wise or not patient. Alice is not creative or humble. Susan is kind or not humble. Someone is quiet or humble. Lucy is either not kind or strong. Fred is not wise. Someone is both not kind and creative. | Fred is not tall. | entailment | (![X]:((~quiet(X)&~kind(X))=>~tall(X)))&
(![X]:(patient(X)<=>(old(X)|quiet(X))))&
(((kind(alice)<~>~brave(alice)))<=>(?[X]:((funny(X)<~>~generous(X)))))&
((~strong(susan))=>(old(mary)))&
((~wise(susan))<=>(?[X]:(calm(X))))&
(![X]:(~wise(X)=>strong(X)))&
(![X]:((~tall(X)|happy(X))<=>curious(X)))&
((?[X]:((~calm(X)&~patient(X))))=>(?[X]:((calm(X)|tall(X)))))&
(![X]:((curious(X)&~old(X))<=>(curious(X)<~>strong(X))))&
((?[X]:((curious(X)|~happy(X))))=>(?[X]:((~strong(X)<~>funny(X)))))&
((?[X]:((tall(X)<~>happy(X))))=>(?[X]:(~quiet(X))))&
((?[X]:((calm(X)&quiet(X))))<=>(~old(john)))&
(![X]:(~creative(X)<=>(~creative(X)<~>quiet(X))))&
(![X]:((~tall(X)<~>~curious(X))<=>~generous(X)))&
((?[X]:(~rich(X)))<=>((~funny(mary)<~>~calm(mary))))&
(![X]:((strong(X)|quiet(X))<=>(strong(X)&~kind(X))))&
(?[X]:((~creative(X)<~>~kind(X))))&
(?[X]:((~wise(X)|~patient(X))))&
((~creative(alice)|humble(alice)))&
((kind(susan)|~humble(susan)))&
(?[X]:((quiet(X)|humble(X))))&
((~kind(lucy)<~>strong(lucy)))&
(~wise(fred))&
(?[X]:((~kind(X)&creative(X)))) | ~tall(fred) | [
"p0",
"p5",
"p12",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 885459578488981052135187
% SZS output start Proof for 885459578488981052135187
1. ! [X0] : ((~kind(X0) & ~quiet(X0)) => ~tall(X0)) [input p0]
6. ! [X0] : (~wise(X0) => strong(X0)) [input p5]
13. ! [X0] : (~creative(X0) <=> (~creative(X0) <~> quiet(X0))) [input p12]
16. ! [X0] : ((quiet(X0) | strong(X0)) <=> (~kind(X0) & strong(X0))) [input p15]
23. ~wise(fred) [input p22]
25. tall(fred) [input hypothesis]
29. ! [X0] : (~tall(X0) | (kind(X0) | quiet(X0))) [ennf transformation 1]
30. ! [X0] : (~tall(X0) | kind(X0) | quiet(X0)) [flattening 29]
32. ! [X0] : (strong(X0) | wise(X0)) [ennf transformation 6]
65. ! [X0] : ((~creative(X0) | ((~creative(X0) | ~quiet(X0)) & (quiet(X0) | creative(X0)))) & (((~quiet(X0) | creative(X0)) & (quiet(X0) | ~creative(X0))) | creative(X0))) [nnf transformation 13]
71. ! [X0] : (((quiet(X0) | strong(X0)) | (kind(X0) | ~strong(X0))) & ((~kind(X0) & strong(X0)) | (~quiet(X0) & ~strong(X0)))) [nnf transformation 16]
72. ! [X0] : ((quiet(X0) | strong(X0) | kind(X0) | ~strong(X0)) & ((~kind(X0) & strong(X0)) | (~quiet(X0) & ~strong(X0)))) [flattening 71]
83. ~tall(X0) | kind(X0) | quiet(X0) [cnf transformation 30]
98. wise(X0) | strong(X0) [cnf transformation 32]
119. ~quiet(X0) | creative(X0) | creative(X0) [cnf transformation 65]
121. ~creative(X0) | ~creative(X0) | ~quiet(X0) [cnf transformation 65]
132. ~strong(X0) | ~kind(X0) [cnf transformation 72]
143. ~wise(fred) [cnf transformation 23]
146. tall(fred) [cnf transformation 25]
147. ~quiet(X0) | creative(X0) [duplicate literal removal 119]
148. ~creative(X0) | ~quiet(X0) [duplicate literal removal 121]
264. ~quiet(X0) [subsumption resolution 147,148]
331. strong(fred) [resolution 98,143]
335. ~kind(fred) [resolution 132,331]
347. kind(fred) | quiet(fred) [resolution 83,146]
348. quiet(fred) [subsumption resolution 347,335]
349. $false [subsumption resolution 348,264]
% SZS output end Proof for 885459578488981052135187
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or wise is patient or not quiet.
Everyone who is either not old or not generous is kind.
If someone is funny then john is either creative or not strong.
If john is either wise or not curious then alice is both old and kind and vice versa.
If someone is creative then john is not patient.
Everyone who is rich is either not old or not rich.
If someone is not curious then someone is not calm.
Everyone who is either strong or curious is either not generous or not brave and vice versa.
If someone is humble then mary is not strong or brave and vice versa.
Everyone who is either not creative or not brave is both old and not funny and vice versa.
Everyone who is either rich or not brave is both creative and not old and vice versa.
If someone is both creative and not calm then someone is both not patient and creative.
Everyone who is both not curious and kind is not funny or kind and vice versa.
If alice is both quiet and not happy then fred is either strong or rich.
Everyone who is not strong or not calm is either calm or humble.
Everyone who is not brave is strong.
Someone is not rich or not strong.
Paul is not generous or not old.
Lucy is either humble or quiet.
Someone is creative.
Lucy is not calm.
Paul is happy.
Someone is not happy or not calm.
Mary is not curious. | Mary is not brave. | contradiction | (![X]:((curious(X)<~>wise(X))=>(patient(X)|~quiet(X))))&
(![X]:((~old(X)<~>~generous(X))=>kind(X)))&
((?[X]:(funny(X)))=>((creative(john)<~>~strong(john))))&
(((wise(john)<~>~curious(john)))<=>((old(alice)&kind(alice))))&
((?[X]:(creative(X)))=>(~patient(john)))&
(![X]:(rich(X)=>(~old(X)<~>~rich(X))))&
((?[X]:(~curious(X)))=>(?[X]:(~calm(X))))&
(![X]:((strong(X)<~>curious(X))<=>(~generous(X)<~>~brave(X))))&
((?[X]:(humble(X)))<=>((~strong(mary)|brave(mary))))&
(![X]:((~creative(X)<~>~brave(X))<=>(old(X)&~funny(X))))&
(![X]:((rich(X)<~>~brave(X))<=>(creative(X)&~old(X))))&
((?[X]:((creative(X)&~calm(X))))=>(?[X]:((~patient(X)&creative(X)))))&
(![X]:((~curious(X)&kind(X))<=>(~funny(X)|kind(X))))&
(((quiet(alice)&~happy(alice)))=>((strong(fred)<~>rich(fred))))&
(![X]:((~strong(X)|~calm(X))=>(calm(X)<~>humble(X))))&
(![X]:(~brave(X)=>strong(X)))&
(?[X]:((~rich(X)|~strong(X))))&
((~generous(paul)|~old(paul)))&
((humble(lucy)<~>quiet(lucy)))&
(?[X]:(creative(X)))&
(~calm(lucy))&
(happy(paul))&
(?[X]:((~happy(X)|~calm(X))))&
(~curious(mary)) | ~brave(mary) | [
"p8",
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2915337314905026761942950
% SZS output start Proof for 2915337314905026761942950
9. ? [X0] : humble(X0) <=> (brave(mary) | ~strong(mary)) [input p8]
15. ! [X0] : ((~calm(X0) | ~strong(X0)) => (calm(X0) <~> humble(X0))) [input p14]
16. ! [X0] : (~brave(X0) => strong(X0)) [input p15]
21. ~calm(lucy) [input p20]
25. ~brave(mary) [input hypothesis]
38. ! [X0] : ((calm(X0) <~> humble(X0)) | (calm(X0) & strong(X0))) [ennf transformation 15]
39. ! [X0] : (strong(X0) | brave(X0)) [ennf transformation 16]
50. (? [X0] : humble(X0) | (~brave(mary) & strong(mary))) & ((brave(mary) | ~strong(mary)) | ! [X0] : ~humble(X0)) [nnf transformation 9]
51. (? [X0] : humble(X0) | (~brave(mary) & strong(mary))) & (brave(mary) | ~strong(mary) | ! [X0] : ~humble(X0)) [flattening 50]
52. (? [X0] : humble(X0) | (~brave(mary) & strong(mary))) & (brave(mary) | ~strong(mary) | ! [X1] : ~humble(X1)) [rectify 51]
53. ? [X0] : humble(X0) => humble(sK1) [choice axiom]
54. (humble(sK1) | (~brave(mary) & strong(mary))) & (brave(mary) | ~strong(mary) | ! [X1] : ~humble(X1)) [skolemisation 52,53]
65. ! [X0] : (((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | (calm(X0) & strong(X0))) [nnf transformation 38]
97. brave(mary) | ~strong(mary) | ~humble(X1) [cnf transformation 54]
122. humble(X0) | calm(X0) | calm(X0) [cnf transformation 65]
125. brave(X0) | strong(X0) [cnf transformation 39]
131. ~calm(lucy) [cnf transformation 21]
135. ~brave(mary) [cnf transformation 25]
136. humble(X0) | calm(X0) [duplicate literal removal 122]
190. 12 <=> brave(mary) [avatar definition]
192. ~brave(mary) <- (~12) [avatar component clause 190]
199. 14 <=> strong(mary) [avatar definition]
204. 15 <=> ! [X1] : ~humble(X1) [avatar definition]
205. ~humble(X1) <- (15) [avatar component clause 204]
206. 15 | ~14 | 12 [avatar split clause 97,190,199,204]
277. ~12 [avatar split clause 135,190]
279. strong(mary) <- (~12) [resolution 125,192]
282. 14 | 12 [avatar split clause 279,190,199]
287. calm(X0) <- (15) [resolution 136,205]
288. $false <- (15) [resolution 287,131]
293. ~15 [avatar contradiction clause 288]
294. $false [avatar sat refutation 206,277,282,293]
% SZS output end Proof for 2915337314905026761942950
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not rich then someone is calm or not quiet.
Everyone who is not strong is both not creative and not tall and vice versa.
Everyone who is old is not curious or happy.
Everyone who is both calm and not happy is patient and vice versa.
Everyone who is not wise or wise is not humble or strong and vice versa.
Everyone who is either brave or tall is not curious.
If alice is both not wise and creative then john is not happy.
Everyone who is both humble and not old is rich.
Everyone who is creative or not tall is not old and vice versa.
If someone is either not creative or not quiet then someone is not generous.
Everyone who is either funny or not funny is strong and vice versa.
If someone is happy or not calm then someone is funny or not humble and vice versa.
If fred is both kind and not kind then someone is calm or generous and vice versa.
If someone is humble or not kind then someone is patient and vice versa.
Everyone who is both brave and quiet is not strong and vice versa.
Everyone who is either not calm or not brave is wise or happy.
Lucy is either kind or not funny.
Fred is not brave.
Someone is not humble or tall.
Fred is either not quiet or not creative.
Someone is rich or not generous.
Someone is both funny and old.
John is either not wise or quiet.
Fred is either generous or not funny. | Fred is humble. | contradiction | ((?[X]:((happy(X)|~rich(X))))=>(?[X]:((calm(X)|~quiet(X)))))&
(![X]:(~strong(X)<=>(~creative(X)&~tall(X))))&
(![X]:(old(X)=>(~curious(X)|happy(X))))&
(![X]:((calm(X)&~happy(X))<=>patient(X)))&
(![X]:((~wise(X)|wise(X))<=>(~humble(X)|strong(X))))&
(![X]:((brave(X)<~>tall(X))=>~curious(X)))&
(((~wise(alice)&creative(alice)))=>(~happy(john)))&
(![X]:((humble(X)&~old(X))=>rich(X)))&
(![X]:((creative(X)|~tall(X))<=>~old(X)))&
((?[X]:((~creative(X)<~>~quiet(X))))=>(?[X]:(~generous(X))))&
(![X]:((funny(X)<~>~funny(X))<=>strong(X)))&
((?[X]:((happy(X)|~calm(X))))<=>(?[X]:((funny(X)|~humble(X)))))&
(((kind(fred)&~kind(fred)))<=>(?[X]:((calm(X)|generous(X)))))&
((?[X]:((humble(X)|~kind(X))))<=>(?[X]:(patient(X))))&
(![X]:((brave(X)&quiet(X))<=>~strong(X)))&
(![X]:((~calm(X)<~>~brave(X))=>(wise(X)|happy(X))))&
((kind(lucy)<~>~funny(lucy)))&
(~brave(fred))&
(?[X]:((~humble(X)|tall(X))))&
((~quiet(fred)<~>~creative(fred)))&
(?[X]:((rich(X)|~generous(X))))&
(?[X]:((funny(X)&old(X))))&
((~wise(john)<~>quiet(john)))&
((generous(fred)<~>~funny(fred))) | humble(fred) | [
"p3",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4013003453664353658999858
% SZS output start Proof for 4013003453664353658999858
4. ! [X0] : ((~happy(X0) & calm(X0)) <=> patient(X0)) [input p3]
13. (~kind(fred) & kind(fred)) <=> ? [X0] : (generous(X0) | calm(X0)) [input p12]
14. ? [X0] : (~kind(X0) | humble(X0)) <=> ? [X0] : patient(X0) [input p13]
25. humble(fred) [input hypothesis]
29. ? [X0] : (~kind(X0) | humble(X0)) <=> ? [X1] : patient(X1) [rectify 14]
48. ! [X0] : (((~happy(X0) & calm(X0)) | ~patient(X0)) & (patient(X0) | (happy(X0) | ~calm(X0)))) [nnf transformation 4]
49. ! [X0] : (((~happy(X0) & calm(X0)) | ~patient(X0)) & (patient(X0) | happy(X0) | ~calm(X0))) [flattening 48]
62. ((~kind(fred) & kind(fred)) | ! [X0] : (~generous(X0) & ~calm(X0))) & (? [X0] : (generous(X0) | calm(X0)) | (kind(fred) | ~kind(fred))) [nnf transformation 13]
63. ((~kind(fred) & kind(fred)) | ! [X0] : (~generous(X0) & ~calm(X0))) & (? [X0] : (generous(X0) | calm(X0)) | kind(fred) | ~kind(fred)) [flattening 62]
64. ((~kind(fred) & kind(fred)) | ! [X0] : (~generous(X0) & ~calm(X0))) & (? [X1] : (generous(X1) | calm(X1)) | kind(fred) | ~kind(fred)) [rectify 63]
65. ? [X1] : (generous(X1) | calm(X1)) => (generous(sK4) | calm(sK4)) [choice axiom]
66. ((~kind(fred) & kind(fred)) | ! [X0] : (~generous(X0) & ~calm(X0))) & ((generous(sK4) | calm(sK4)) | kind(fred) | ~kind(fred)) [skolemisation 64,65]
67. (? [X0] : (~kind(X0) | humble(X0)) | ! [X1] : ~patient(X1)) & (? [X1] : patient(X1) | ! [X0] : (kind(X0) & ~humble(X0))) [nnf transformation 29]
68. (? [X0] : (~kind(X0) | humble(X0)) | ! [X1] : ~patient(X1)) & (? [X2] : patient(X2) | ! [X3] : (kind(X3) & ~humble(X3))) [rectify 67]
69. ? [X0] : (~kind(X0) | humble(X0)) => (~kind(sK5) | humble(sK5)) [choice axiom]
70. ? [X2] : patient(X2) => patient(sK6) [choice axiom]
71. ((~kind(sK5) | humble(sK5)) | ! [X1] : ~patient(X1)) & (patient(sK6) | ! [X3] : (kind(X3) & ~humble(X3))) [skolemisation 68,70,69]
88. ~patient(X0) | calm(X0) [cnf transformation 49]
108. kind(fred) | ~calm(X0) [cnf transformation 66]
110. ~kind(fred) | ~calm(X0) [cnf transformation 66]
112. patient(sK6) | ~humble(X3) [cnf transformation 71]
132. humble(fred) [cnf transformation 25]
207. 18 <=> kind(fred) [avatar definition]
212. 19 <=> ! [X0] : ~calm(X0) [avatar definition]
213. ~calm(X0) <- (19) [avatar component clause 212]
214. 19 | ~18 [avatar split clause 110,207,212]
216. 19 | 18 [avatar split clause 108,207,212]
233. 24 <=> patient(sK6) [avatar definition]
235. patient(sK6) <- (24) [avatar component clause 233]
238. 25 <=> ! [X3] : ~humble(X3) [avatar definition]
239. ~humble(X3) <- (25) [avatar component clause 238]
240. 25 | 24 [avatar split clause 112,233,238]
291. calm(sK6) <- (24) [resolution 88,235]
292. $false <- (19, 24) [subsumption resolution 291,213]
293. ~19 | ~24 [avatar contradiction clause 292]
298. $false <- (25) [resolution 239,132]
299. ~25 [avatar contradiction clause 298]
300. $false [avatar sat refutation 214,216,240,293,299]
% SZS output end Proof for 4013003453664353658999858
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and curious is both wise and tall.
If someone is both generous and not happy then someone is not strong.
If john is both not happy and happy then someone is kind or tall.
If fred is both not patient and brave then someone is both not quiet and wise.
Everyone who is not wise or not curious is not humble or quiet.
If fred is either not strong or not tall then fred is both funny and not brave and vice versa.
If someone is both generous and funny then someone is both not brave and curious.
If someone is either not funny or funny then someone is not patient and vice versa.
Everyone who is calm or not patient is not calm.
Everyone who is either curious or calm is both not funny and not tall.
If someone is calm or not humble then someone is both creative and curious and vice versa.
Everyone who is not humble is strong or rich and vice versa.
If someone is wise or not happy then john is tall or not calm.
If lucy is brave or not strong then fred is old and vice versa.
Everyone who is not patient or happy is not kind and vice versa.
If john is humble or not kind then alice is not old or not strong.
Someone is brave or not happy.
John is not happy.
Someone is either not old or creative.
Paul is both funny and brave.
Someone is either calm or not curious.
Someone is not creative.
Alice is both old and kind.
Paul is not curious. | John is not strong. | entailment | (![X]:((~calm(X)&curious(X))=>(wise(X)&tall(X))))&
((?[X]:((generous(X)&~happy(X))))=>(?[X]:(~strong(X))))&
(((~happy(john)&happy(john)))=>(?[X]:((kind(X)|tall(X)))))&
(((~patient(fred)&brave(fred)))=>(?[X]:((~quiet(X)&wise(X)))))&
(![X]:((~wise(X)|~curious(X))=>(~humble(X)|quiet(X))))&
(((~strong(fred)<~>~tall(fred)))<=>((funny(fred)&~brave(fred))))&
((?[X]:((generous(X)&funny(X))))=>(?[X]:((~brave(X)&curious(X)))))&
((?[X]:((~funny(X)<~>funny(X))))<=>(?[X]:(~patient(X))))&
(![X]:((calm(X)|~patient(X))=>~calm(X)))&
(![X]:((curious(X)<~>calm(X))=>(~funny(X)&~tall(X))))&
((?[X]:((calm(X)|~humble(X))))<=>(?[X]:((creative(X)&curious(X)))))&
(![X]:(~humble(X)<=>(strong(X)|rich(X))))&
((?[X]:((wise(X)|~happy(X))))=>((tall(john)|~calm(john))))&
(((brave(lucy)|~strong(lucy)))<=>(old(fred)))&
(![X]:((~patient(X)|happy(X))<=>~kind(X)))&
(((humble(john)|~kind(john)))=>((~old(alice)|~strong(alice))))&
(?[X]:((brave(X)|~happy(X))))&
(~happy(john))&
(?[X]:((~old(X)<~>creative(X))))&
((funny(paul)&brave(paul)))&
(?[X]:((calm(X)<~>~curious(X))))&
(?[X]:(~creative(X)))&
((old(alice)&kind(alice)))&
(~curious(paul)) | ~strong(john) | [
"p0",
"p8",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1743754334168487629764047
% SZS output start Proof for 1743754334168487629764047
1. ! [X0] : ((curious(X0) & ~calm(X0)) => (tall(X0) & wise(X0))) [input p0]
9. ! [X0] : ((~patient(X0) | calm(X0)) => ~calm(X0)) [input p8]
10. ! [X0] : ((curious(X0) <~> calm(X0)) => (~tall(X0) & ~funny(X0))) [input p9]
11. ? [X0] : (~humble(X0) | calm(X0)) <=> ? [X0] : (curious(X0) & creative(X0)) [input p10]
12. ! [X0] : (~humble(X0) <=> (rich(X0) | strong(X0))) [input p11]
25. strong(john) [input hypothesis]
29. ? [X0] : (~humble(X0) | calm(X0)) <=> ? [X1] : (curious(X1) & creative(X1)) [rectify 11]
33. ! [X0] : ((tall(X0) & wise(X0)) | (~curious(X0) | calm(X0))) [ennf transformation 1]
34. ! [X0] : ((tall(X0) & wise(X0)) | ~curious(X0) | calm(X0)) [flattening 33]
41. ! [X0] : (~calm(X0) | (patient(X0) & ~calm(X0))) [ennf transformation 9]
42. ! [X0] : ((~tall(X0) & ~funny(X0)) | (curious(X0) <=> calm(X0))) [ennf transformation 10]
59. ! [X0] : ((~tall(X0) & ~funny(X0)) | ((curious(X0) | ~calm(X0)) & (calm(X0) | ~curious(X0)))) [nnf transformation 42]
60. (? [X0] : (~humble(X0) | calm(X0)) | ! [X1] : (~curious(X1) | ~creative(X1))) & (? [X1] : (curious(X1) & creative(X1)) | ! [X0] : (humble(X0) & ~calm(X0))) [nnf transformation 29]
61. (? [X0] : (~humble(X0) | calm(X0)) | ! [X1] : (~curious(X1) | ~creative(X1))) & (? [X2] : (curious(X2) & creative(X2)) | ! [X3] : (humble(X3) & ~calm(X3))) [rectify 60]
62. ? [X0] : (~humble(X0) | calm(X0)) => (~humble(sK4) | calm(sK4)) [choice axiom]
63. ? [X2] : (curious(X2) & creative(X2)) => (curious(sK5) & creative(sK5)) [choice axiom]
64. ((~humble(sK4) | calm(sK4)) | ! [X1] : (~curious(X1) | ~creative(X1))) & ((curious(sK5) & creative(sK5)) | ! [X3] : (humble(X3) & ~calm(X3))) [skolemisation 61,63,62]
65. ! [X0] : ((~humble(X0) | (~rich(X0) & ~strong(X0))) & ((rich(X0) | strong(X0)) | humble(X0))) [nnf transformation 12]
66. ! [X0] : ((~humble(X0) | (~rich(X0) & ~strong(X0))) & (rich(X0) | strong(X0) | humble(X0))) [flattening 65]
80. ~curious(X0) | tall(X0) | calm(X0) [cnf transformation 34]
96. ~calm(X0) | ~calm(X0) [cnf transformation 41]
100. ~tall(X0) | calm(X0) | ~curious(X0) [cnf transformation 59]
105. curious(sK5) | humble(X3) [cnf transformation 64]
108. ~humble(X0) | ~strong(X0) [cnf transformation 66]
131. strong(john) [cnf transformation 25]
132. ~calm(X0) [duplicate literal removal 96]
183. ~tall(X0) | ~curious(X0) [subsumption resolution 100,132]
195. 13 <=> ! [X3] : humble(X3) [avatar definition]
196. humble(X3) <- (13) [avatar component clause 195]
198. 14 <=> curious(sK5) [avatar definition]
200. curious(sK5) <- (14) [avatar component clause 198]
201. 13 | 14 [avatar split clause 105,198,195]
263. ~strong(X0) <- (13) [resolution 108,196]
264. $false <- (13) [resolution 263,131]
265. ~13 [avatar contradiction clause 264]
275. tall(sK5) | calm(sK5) <- (14) [resolution 80,200]
276. tall(sK5) <- (14) [subsumption resolution 275,132]
277. ~curious(sK5) <- (14) [resolution 276,183]
278. $false <- (14) [subsumption resolution 277,200]
279. ~14 [avatar contradiction clause 278]
280. $false [avatar sat refutation 201,265,279]
% SZS output end Proof for 1743754334168487629764047
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or not funny is not old.
If someone is tall then someone is old.
Everyone who is funny is either not brave or not funny.
If paul is either not creative or not brave then someone is generous or patient and vice versa.
Everyone who is either not quiet or brave is calm or tall and vice versa.
Everyone who is both strong and not humble is either not creative or not tall and vice versa.
Everyone who is not wise or not kind is either generous or not patient.
Everyone who is kind is curious and vice versa.
If paul is either wise or creative then fred is not tall or not brave.
If someone is both brave and not happy then someone is old.
Everyone who is not wise is both humble and creative.
If mary is both not creative and calm then someone is not funny or not creative.
If someone is quiet or calm then alice is either kind or old and vice versa.
If lucy is brave then mary is both patient and tall.
Everyone who is generous is patient and vice versa.
Everyone who is both not generous and not creative is not rich or not funny.
Mary is either humble or not happy.
Someone is either funny or not curious.
Alice is strong or not tall.
Someone is both not calm and not quiet.
Someone is not curious.
Someone is kind.
Lucy is not funny or not old.
Someone is tall. | Mary is happy. | neutral | (![X]:((~kind(X)|~funny(X))=>~old(X)))&
((?[X]:(tall(X)))=>(?[X]:(old(X))))&
(![X]:(funny(X)=>(~brave(X)<~>~funny(X))))&
(((~creative(paul)<~>~brave(paul)))<=>(?[X]:((generous(X)|patient(X)))))&
(![X]:((~quiet(X)<~>brave(X))<=>(calm(X)|tall(X))))&
(![X]:((strong(X)&~humble(X))<=>(~creative(X)<~>~tall(X))))&
(![X]:((~wise(X)|~kind(X))=>(generous(X)<~>~patient(X))))&
(![X]:(kind(X)<=>curious(X)))&
(((wise(paul)<~>creative(paul)))=>((~tall(fred)|~brave(fred))))&
((?[X]:((brave(X)&~happy(X))))=>(?[X]:(old(X))))&
(![X]:(~wise(X)=>(humble(X)&creative(X))))&
(((~creative(mary)&calm(mary)))=>(?[X]:((~funny(X)|~creative(X)))))&
((?[X]:((quiet(X)|calm(X))))<=>((kind(alice)<~>old(alice))))&
((brave(lucy))=>((patient(mary)&tall(mary))))&
(![X]:(generous(X)<=>patient(X)))&
(![X]:((~generous(X)&~creative(X))=>(~rich(X)|~funny(X))))&
((humble(mary)<~>~happy(mary)))&
(?[X]:((funny(X)<~>~curious(X))))&
((strong(alice)|~tall(alice)))&
(?[X]:((~calm(X)&~quiet(X))))&
(?[X]:(~curious(X)))&
(?[X]:(kind(X)))&
((~funny(lucy)|~old(lucy)))&
(?[X]:(tall(X))) | happy(mary) | [] | null | 0 |
Everyone who is either happy or not patient is not patient or not rich and vice versa.
If alice is not kind then mary is happy and vice versa.
If someone is both not funny and funny then fred is not curious or brave.
Everyone who is not happy or not strong is either wise or not tall and vice versa.
Everyone who is rich or happy is either funny or not generous.
If someone is not wise then someone is brave or tall.
Everyone who is not kind or not wise is both generous and not rich and vice versa.
If someone is both curious and old then john is tall and vice versa.
If someone is either happy or not kind then susan is both not wise and not curious.
Everyone who is not patient is both not humble and not strong and vice versa.
Everyone who is creative is not curious or not strong and vice versa.
If fred is either not creative or calm then someone is both humble and rich and vice versa.
If mary is not curious or not strong then someone is not tall or not happy and vice versa.
Everyone who is both calm and old is both not strong and curious and vice versa.
Everyone who is both not tall and humble is either calm or not calm.
Everyone who is either not happy or not patient is funny or calm.
Lucy is both calm and not tall.
Someone is either not quiet or old.
Someone is either not patient or not humble.
Susan is either not kind or humble.
John is not rich or funny.
Someone is both not happy and not old.
Someone is either not calm or kind. | Fred is not generous. | neutral | (![X]:((happy(X)<~>~patient(X))<=>(~patient(X)|~rich(X))))&
((~kind(alice))<=>(happy(mary)))&
((?[X]:((~funny(X)&funny(X))))=>((~curious(fred)|brave(fred))))&
(![X]:((~happy(X)|~strong(X))<=>(wise(X)<~>~tall(X))))&
(![X]:((rich(X)|happy(X))=>(funny(X)<~>~generous(X))))&
((?[X]:(~wise(X)))=>(?[X]:((brave(X)|tall(X)))))&
(![X]:((~kind(X)|~wise(X))<=>(generous(X)&~rich(X))))&
((?[X]:((curious(X)&old(X))))<=>(tall(john)))&
((?[X]:((happy(X)<~>~kind(X))))=>((~wise(susan)&~curious(susan))))&
(![X]:(~patient(X)<=>(~humble(X)&~strong(X))))&
(![X]:(creative(X)<=>(~curious(X)|~strong(X))))&
(((~creative(fred)<~>calm(fred)))<=>(?[X]:((humble(X)&rich(X)))))&
(((~curious(mary)|~strong(mary)))<=>(?[X]:((~tall(X)|~happy(X)))))&
(![X]:((calm(X)&old(X))<=>(~strong(X)&curious(X))))&
(![X]:((~tall(X)&humble(X))=>(calm(X)<~>~calm(X))))&
(![X]:((~happy(X)<~>~patient(X))=>(funny(X)|calm(X))))&
((calm(lucy)&~tall(lucy)))&
(?[X]:((~quiet(X)<~>old(X))))&
(?[X]:((~patient(X)<~>~humble(X))))&
((~kind(susan)<~>humble(susan)))&
((~rich(john)|funny(john)))&
(?[X]:((~happy(X)&~old(X))))&
(?[X]:((~calm(X)<~>kind(X)))) | ~generous(fred) | [] | null | 0 |
Everyone who is patient is not old and vice versa.
If lucy is generous or not humble then paul is both tall and not creative.
If someone is both humble and not humble then someone is both strong and not quiet.
Everyone who is not patient or not humble is either funny or not funny and vice versa.
Everyone who is both not tall and not old is both tall and rich and vice versa.
Everyone who is either generous or calm is calm or old and vice versa.
If mary is either not funny or humble then someone is either not humble or happy and vice versa.
Everyone who is either funny or not brave is not rich or tall and vice versa.
Everyone who is not quiet is both quiet and not curious and vice versa.
Everyone who is not kind or funny is not quiet or generous.
Everyone who is strong is generous or calm.
If someone is both not tall and not humble then john is both strong and tall.
If someone is not old then someone is either curious or not tall and vice versa.
If mary is not wise or not calm then someone is strong.
Everyone who is either not happy or not tall is old.
Everyone who is patient is both not humble and not tall and vice versa.
Someone is not tall.
Mary is old or not curious.
Someone is humble or not curious.
Someone is both not strong and quiet.
Paul is not tall or rich.
Someone is either wise or happy.
Someone is both generous and not brave.
Mary is not kind. | Mary is not calm. | entailment | (![X]:(patient(X)<=>~old(X)))&
(((generous(lucy)|~humble(lucy)))=>((tall(paul)&~creative(paul))))&
((?[X]:((humble(X)&~humble(X))))=>(?[X]:((strong(X)&~quiet(X)))))&
(![X]:((~patient(X)|~humble(X))<=>(funny(X)<~>~funny(X))))&
(![X]:((~tall(X)&~old(X))<=>(tall(X)&rich(X))))&
(![X]:((generous(X)<~>calm(X))<=>(calm(X)|old(X))))&
(((~funny(mary)<~>humble(mary)))<=>(?[X]:((~humble(X)<~>happy(X)))))&
(![X]:((funny(X)<~>~brave(X))<=>(~rich(X)|tall(X))))&
(![X]:(~quiet(X)<=>(quiet(X)&~curious(X))))&
(![X]:((~kind(X)|funny(X))=>(~quiet(X)|generous(X))))&
(![X]:(strong(X)=>(generous(X)|calm(X))))&
((?[X]:((~tall(X)&~humble(X))))=>((strong(john)&tall(john))))&
((?[X]:(~old(X)))<=>(?[X]:((curious(X)<~>~tall(X)))))&
(((~wise(mary)|~calm(mary)))=>(?[X]:(strong(X))))&
(![X]:((~happy(X)<~>~tall(X))=>old(X)))&
(![X]:(patient(X)<=>(~humble(X)&~tall(X))))&
(?[X]:(~tall(X)))&
((old(mary)|~curious(mary)))&
(?[X]:((humble(X)|~curious(X))))&
(?[X]:((~strong(X)&quiet(X))))&
((~tall(paul)|rich(paul)))&
(?[X]:((wise(X)<~>happy(X))))&
(?[X]:((generous(X)&~brave(X))))&
(~kind(mary)) | ~calm(mary) | [
"p5",
"p8",
"p9",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3906621886821976789187542
% SZS output start Proof for 3906621886821976789187542
6. ! [X0] : ((generous(X0) <~> calm(X0)) <=> (old(X0) | calm(X0))) [input p5]
9. ! [X0] : (~quiet(X0) <=> (~curious(X0) & quiet(X0))) [input p8]
10. ! [X0] : ((funny(X0) | ~kind(X0)) => (generous(X0) | ~quiet(X0))) [input p9]
24. ~kind(mary) [input p23]
25. calm(mary) [input hypothesis]
31. ! [X0] : ((generous(X0) | ~quiet(X0)) | (~funny(X0) & kind(X0))) [ennf transformation 10]
32. ! [X0] : (generous(X0) | ~quiet(X0) | (~funny(X0) & kind(X0))) [flattening 31]
46. ! [X0] : ((((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) | (~old(X0) & ~calm(X0))) & ((old(X0) | calm(X0)) | ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0))))) [nnf transformation 6]
47. ! [X0] : ((((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) | (~old(X0) & ~calm(X0))) & (old(X0) | calm(X0) | ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0))))) [flattening 46]
54. ! [X0] : ((~quiet(X0) | (curious(X0) | ~quiet(X0))) & ((~curious(X0) & quiet(X0)) | quiet(X0))) [nnf transformation 9]
55. ! [X0] : ((~quiet(X0) | curious(X0) | ~quiet(X0)) & ((~curious(X0) & quiet(X0)) | quiet(X0))) [flattening 54]
97. ~calm(X0) | ~generous(X0) | ~calm(X0) [cnf transformation 47]
113. quiet(X0) | quiet(X0) [cnf transformation 55]
116. generous(X0) | ~quiet(X0) | kind(X0) [cnf transformation 32]
142. ~kind(mary) [cnf transformation 24]
143. calm(mary) [cnf transformation 25]
144. quiet(X0) [duplicate literal removal 113]
147. ~calm(X0) | ~generous(X0) [duplicate literal removal 97]
201. kind(X0) | generous(X0) [subsumption resolution 116,144]
241. 19 <=> calm(mary) [avatar definition]
243. calm(mary) <- (19) [avatar component clause 241]
285. 19 [avatar split clause 143,241]
301. ~generous(mary) <- (19) [resolution 147,243]
310. generous(mary) [resolution 201,142]
311. $false <- (19) [subsumption resolution 310,301]
312. ~19 [avatar contradiction clause 311]
313. $false [avatar sat refutation 285,312]
% SZS output end Proof for 3906621886821976789187542
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is brave then fred is not kind.
If someone is not curious or not tall then lucy is both calm and not calm.
Everyone who is patient or not generous is not tall or not quiet.
If someone is both not funny and funny then someone is either funny or curious and vice versa.
If someone is creative or not generous then someone is humble.
Everyone who is not rich or not tall is old or not strong and vice versa.
Everyone who is either not funny or not calm is not old.
Everyone who is happy or humble is either not creative or brave.
Everyone who is either not wise or not rich is wise or not kind.
Everyone who is both not creative and generous is either not creative or not humble and vice versa.
If fred is not kind then someone is both quiet and curious.
Everyone who is both happy and creative is funny or patient.
Everyone who is both wise and strong is either strong or not tall and vice versa.
Everyone who is patient or not funny is both generous and not funny and vice versa.
Everyone who is either strong or not tall is rich.
Everyone who is not creative is not funny or not generous.
Someone is humble.
John is either not funny or not kind.
Someone is rich.
Paul is either generous or not generous.
Fred is not creative or not wise.
Someone is either not calm or not creative.
Someone is not creative or not tall.
John is both not happy and strong. | Lucy is not tall. | contradiction | ((?[X]:(brave(X)))=>(~kind(fred)))&
((?[X]:((~curious(X)|~tall(X))))=>((calm(lucy)&~calm(lucy))))&
(![X]:((patient(X)|~generous(X))=>(~tall(X)|~quiet(X))))&
((?[X]:((~funny(X)&funny(X))))<=>(?[X]:((funny(X)<~>curious(X)))))&
((?[X]:((creative(X)|~generous(X))))=>(?[X]:(humble(X))))&
(![X]:((~rich(X)|~tall(X))<=>(old(X)|~strong(X))))&
(![X]:((~funny(X)<~>~calm(X))=>~old(X)))&
(![X]:((happy(X)|humble(X))=>(~creative(X)<~>brave(X))))&
(![X]:((~wise(X)<~>~rich(X))=>(wise(X)|~kind(X))))&
(![X]:((~creative(X)&generous(X))<=>(~creative(X)<~>~humble(X))))&
((~kind(fred))=>(?[X]:((quiet(X)&curious(X)))))&
(![X]:((happy(X)&creative(X))=>(funny(X)|patient(X))))&
(![X]:((wise(X)&strong(X))<=>(strong(X)<~>~tall(X))))&
(![X]:((patient(X)|~funny(X))<=>(generous(X)&~funny(X))))&
(![X]:((strong(X)<~>~tall(X))=>rich(X)))&
(![X]:(~creative(X)=>(~funny(X)|~generous(X))))&
(?[X]:(humble(X)))&
((~funny(john)<~>~kind(john)))&
(?[X]:(rich(X)))&
((generous(paul)<~>~generous(paul)))&
((~creative(fred)|~wise(fred)))&
(?[X]:((~calm(X)<~>~creative(X))))&
(?[X]:((~creative(X)|~tall(X))))&
((~happy(john)&strong(john))) | ~tall(lucy) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 5665828401894452784126073
% SZS output start Proof for 5665828401894452784126073
2. ? [X0] : (~tall(X0) | ~curious(X0)) => (~calm(lucy) & calm(lucy)) [input p1]
25. ~tall(lucy) [input hypothesis]
32. (~calm(lucy) & calm(lucy)) | ! [X0] : (tall(X0) & curious(X0)) [ennf transformation 2]
79. calm(lucy) | tall(X0) [cnf transformation 32]
81. ~calm(lucy) | tall(X0) [cnf transformation 32]
135. ~tall(lucy) [cnf transformation 25]
150. 3 <=> ! [X0] : tall(X0) [avatar definition]
151. tall(X0) <- (3) [avatar component clause 150]
153. 4 <=> calm(lucy) [avatar definition]
156. 3 | ~4 [avatar split clause 81,153,150]
161. 3 | 4 [avatar split clause 79,153,150]
239. $false <- (3) [resolution 151,135]
240. ~3 [avatar contradiction clause 239]
241. $false [avatar sat refutation 156,161,240]
% SZS output end Proof for 5665828401894452784126073
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both not funny and wise then paul is not calm. Everyone who is quiet or not curious is both not brave and kind and vice versa. If john is both not quiet and wise then someone is humble and vice versa. If susan is not rich then mary is either not funny or not tall. If someone is either rich or not tall then someone is either not kind or creative and vice versa. If paul is both generous and not kind then someone is funny or not old and vice versa. Everyone who is not curious or not humble is both funny and humble. If someone is both not quiet and not curious then someone is not humble and vice versa. If john is tall or not humble then someone is not funny or not quiet and vice versa. If someone is either not creative or not calm then someone is either tall or old. Everyone who is not kind or curious is either not strong or not humble. Everyone who is not creative or happy is either not patient or calm and vice versa. If someone is not humble or creative then someone is both not funny and not brave. Everyone who is not funny or not creative is old or quiet. Everyone who is both not calm and old is either calm or not patient and vice versa. Someone is strong. Mary is not creative. Someone is both funny and quiet. Paul is old or not humble. Paul is either not old or creative. Susan is both calm and funny. Someone is not rich or creative. Someone is both quiet and rich. | Paul is curious. | entailment | (((~funny(paul)&wise(paul)))=>(~calm(paul)))&
(![X]:((quiet(X)|~curious(X))<=>(~brave(X)&kind(X))))&
(((~quiet(john)&wise(john)))<=>(?[X]:(humble(X))))&
((~rich(susan))=>((~funny(mary)<~>~tall(mary))))&
((?[X]:((rich(X)<~>~tall(X))))<=>(?[X]:((~kind(X)<~>creative(X)))))&
(((generous(paul)&~kind(paul)))<=>(?[X]:((funny(X)|~old(X)))))&
(![X]:((~curious(X)|~humble(X))=>(funny(X)&humble(X))))&
((?[X]:((~quiet(X)&~curious(X))))<=>(?[X]:(~humble(X))))&
(((tall(john)|~humble(john)))<=>(?[X]:((~funny(X)|~quiet(X)))))&
((?[X]:((~creative(X)<~>~calm(X))))=>(?[X]:((tall(X)<~>old(X)))))&
(![X]:((~kind(X)|curious(X))=>(~strong(X)<~>~humble(X))))&
(![X]:((~creative(X)|happy(X))<=>(~patient(X)<~>calm(X))))&
((?[X]:((~humble(X)|creative(X))))=>(?[X]:((~funny(X)&~brave(X)))))&
(![X]:((~funny(X)|~creative(X))=>(old(X)|quiet(X))))&
(![X]:((~calm(X)&old(X))<=>(calm(X)<~>~patient(X))))&
(?[X]:(strong(X)))&
(~creative(mary))&
(?[X]:((funny(X)&quiet(X))))&
((old(paul)|~humble(paul)))&
((~old(paul)<~>creative(paul)))&
((calm(susan)&funny(susan)))&
(?[X]:((~rich(X)|creative(X))))&
(?[X]:((quiet(X)&rich(X)))) | curious(paul) | [
"p1",
"p5",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5971818652785454069529506
% SZS output start Proof for 5971818652785454069529506
2. ! [X0] : ((~curious(X0) | quiet(X0)) <=> (kind(X0) & ~brave(X0))) [input p1]
6. (~kind(paul) & generous(paul)) <=> ? [X0] : (~old(X0) | funny(X0)) [input p5]
18. ? [X0] : (quiet(X0) & funny(X0)) [input p17]
24. ~curious(paul) [input hypothesis]
38. ! [X0] : (((~curious(X0) | quiet(X0)) | (~kind(X0) | brave(X0))) & ((kind(X0) & ~brave(X0)) | (curious(X0) & ~quiet(X0)))) [nnf transformation 2]
39. ! [X0] : ((~curious(X0) | quiet(X0) | ~kind(X0) | brave(X0)) & ((kind(X0) & ~brave(X0)) | (curious(X0) & ~quiet(X0)))) [flattening 38]
51. ((~kind(paul) & generous(paul)) | ! [X0] : (old(X0) & ~funny(X0))) & (? [X0] : (~old(X0) | funny(X0)) | (kind(paul) | ~generous(paul))) [nnf transformation 6]
52. ((~kind(paul) & generous(paul)) | ! [X0] : (old(X0) & ~funny(X0))) & (? [X0] : (~old(X0) | funny(X0)) | kind(paul) | ~generous(paul)) [flattening 51]
53. ((~kind(paul) & generous(paul)) | ! [X0] : (old(X0) & ~funny(X0))) & (? [X1] : (~old(X1) | funny(X1)) | kind(paul) | ~generous(paul)) [rectify 52]
54. ? [X1] : (~old(X1) | funny(X1)) => (~old(sK3) | funny(sK3)) [choice axiom]
55. ((~kind(paul) & generous(paul)) | ! [X0] : (old(X0) & ~funny(X0))) & ((~old(sK3) | funny(sK3)) | kind(paul) | ~generous(paul)) [skolemisation 53,54]
80. ? [X0] : (quiet(X0) & funny(X0)) => (quiet(sK10) & funny(sK10)) [choice axiom]
81. quiet(sK10) & funny(sK10) [skolemisation 18,80]
91. kind(X0) | curious(X0) [cnf transformation 39]
109. ~kind(paul) | ~funny(X0) [cnf transformation 55]
150. funny(sK10) [cnf transformation 81]
160. ~curious(paul) [cnf transformation 24]
249. 20 <=> kind(paul) [avatar definition]
251. ~kind(paul) <- (~20) [avatar component clause 249]
254. 21 <=> ! [X0] : ~funny(X0) [avatar definition]
255. ~funny(X0) <- (21) [avatar component clause 254]
256. 21 | ~20 [avatar split clause 109,249,254]
343. $false <- (21) [resolution 255,150]
346. ~21 [avatar contradiction clause 343]
352. curious(paul) <- (~20) [resolution 91,251]
353. $false <- (~20) [subsumption resolution 352,160]
354. 20 [avatar contradiction clause 353]
355. $false [avatar sat refutation 256,346,354]
% SZS output end Proof for 5971818652785454069529506
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not generous and not creative is both not curious and wise.
If fred is kind then someone is strong.
Everyone who is not quiet is not humble or not funny and vice versa.
If someone is either funny or not happy then someone is kind.
If someone is not quiet or not strong then lucy is both quiet and not brave and vice versa.
If someone is either old or not happy then alice is wise and vice versa.
If someone is not creative or quiet then mary is not patient and vice versa.
Everyone who is either not humble or not strong is humble or old and vice versa.
Everyone who is not humble or not brave is either not strong or happy.
Everyone who is not strong is either brave or not wise.
Everyone who is not creative is either not quiet or not patient and vice versa.
Everyone who is both funny and not tall is curious and vice versa.
Everyone who is not generous or strong is creative and vice versa.
Everyone who is both not creative and not brave is calm or not creative.
Everyone who is both generous and not humble is both patient and not brave.
If someone is both not wise and not calm then fred is creative or not rich and vice versa.
Someone is tall.
Someone is either not old or generous.
Someone is either curious or calm.
Mary is calm.
John is both not rich and wise.
Susan is both wise and not tall.
Someone is curious or wise.
John is both patient and not rich. | Lucy is strong. | contradiction | (![X]:((~generous(X)&~creative(X))=>(~curious(X)&wise(X))))&
((kind(fred))=>(?[X]:(strong(X))))&
(![X]:(~quiet(X)<=>(~humble(X)|~funny(X))))&
((?[X]:((funny(X)<~>~happy(X))))=>(?[X]:(kind(X))))&
((?[X]:((~quiet(X)|~strong(X))))<=>((quiet(lucy)&~brave(lucy))))&
((?[X]:((old(X)<~>~happy(X))))<=>(wise(alice)))&
((?[X]:((~creative(X)|quiet(X))))<=>(~patient(mary)))&
(![X]:((~humble(X)<~>~strong(X))<=>(humble(X)|old(X))))&
(![X]:((~humble(X)|~brave(X))=>(~strong(X)<~>happy(X))))&
(![X]:(~strong(X)=>(brave(X)<~>~wise(X))))&
(![X]:(~creative(X)<=>(~quiet(X)<~>~patient(X))))&
(![X]:((funny(X)&~tall(X))<=>curious(X)))&
(![X]:((~generous(X)|strong(X))<=>creative(X)))&
(![X]:((~creative(X)&~brave(X))=>(calm(X)|~creative(X))))&
(![X]:((generous(X)&~humble(X))=>(patient(X)&~brave(X))))&
((?[X]:((~wise(X)&~calm(X))))<=>((creative(fred)|~rich(fred))))&
(?[X]:(tall(X)))&
(?[X]:((~old(X)<~>generous(X))))&
(?[X]:((curious(X)<~>calm(X))))&
(calm(mary))&
((~rich(john)&wise(john)))&
((wise(susan)&~tall(susan)))&
(?[X]:((curious(X)|wise(X))))&
((patient(john)&~rich(john))) | strong(lucy) | [
"p2",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6307124450614551651553364
% SZS output start Proof for 6307124450614551651553364
3. ! [X0] : (~quiet(X0) <=> (~funny(X0) | ~humble(X0))) [input p2]
5. ? [X0] : (~strong(X0) | ~quiet(X0)) <=> (~brave(lucy) & quiet(lucy)) [input p4]
8. ! [X0] : ((~humble(X0) <~> ~strong(X0)) <=> (old(X0) | humble(X0))) [input p7]
25. strong(lucy) [input hypothesis]
39. ! [X0] : ((~quiet(X0) | (funny(X0) & humble(X0))) & ((~funny(X0) | ~humble(X0)) | quiet(X0))) [nnf transformation 3]
40. ! [X0] : ((~quiet(X0) | (funny(X0) & humble(X0))) & (~funny(X0) | ~humble(X0) | quiet(X0))) [flattening 39]
45. (? [X0] : (~strong(X0) | ~quiet(X0)) | (brave(lucy) | ~quiet(lucy))) & ((~brave(lucy) & quiet(lucy)) | ! [X0] : (strong(X0) & quiet(X0))) [nnf transformation 5]
46. (? [X0] : (~strong(X0) | ~quiet(X0)) | brave(lucy) | ~quiet(lucy)) & ((~brave(lucy) & quiet(lucy)) | ! [X0] : (strong(X0) & quiet(X0))) [flattening 45]
47. (? [X0] : (~strong(X0) | ~quiet(X0)) | brave(lucy) | ~quiet(lucy)) & ((~brave(lucy) & quiet(lucy)) | ! [X1] : (strong(X1) & quiet(X1))) [rectify 46]
48. ? [X0] : (~strong(X0) | ~quiet(X0)) => (~strong(sK2) | ~quiet(sK2)) [choice axiom]
49. ((~strong(sK2) | ~quiet(sK2)) | brave(lucy) | ~quiet(lucy)) & ((~brave(lucy) & quiet(lucy)) | ! [X1] : (strong(X1) & quiet(X1))) [skolemisation 47,48]
58. ! [X0] : ((((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | (~old(X0) & ~humble(X0))) & ((old(X0) | humble(X0)) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0))))) [nnf transformation 8]
59. ! [X0] : ((((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | (~old(X0) & ~humble(X0))) & (old(X0) | humble(X0) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0))))) [flattening 58]
86. ~quiet(X0) | humble(X0) [cnf transformation 40]
90. quiet(lucy) | quiet(X1) [cnf transformation 49]
104. ~strong(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 59]
145. strong(lucy) [cnf transformation 25]
147. ~humble(X0) | ~strong(X0) [duplicate literal removal 104]
170. 6 <=> quiet(lucy) [avatar definition]
171. quiet(lucy) <- (6) [avatar component clause 170]
172. ~quiet(lucy) <- (~6) [avatar component clause 170]
191. 11 <=> ! [X1] : quiet(X1) [avatar definition]
192. quiet(X1) <- (11) [avatar component clause 191]
195. 11 | 6 [avatar split clause 90,170,191]
294. humble(lucy) <- (6) [resolution 86,171]
301. ~strong(lucy) <- (6) [resolution 147,294]
302. $false <- (6) [subsumption resolution 301,145]
303. ~6 [avatar contradiction clause 302]
304. $false <- (~6, 11) [subsumption resolution 172,192]
305. 6 | ~11 [avatar contradiction clause 304]
306. $false [avatar sat refutation 195,303,305]
% SZS output end Proof for 6307124450614551651553364
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is not old or generous then someone is patient or not strong and vice versa.
Everyone who is generous or funny is both not humble and patient and vice versa.
Everyone who is either curious or not generous is not curious and vice versa.
Everyone who is both not rich and not patient is either patient or not curious.
If someone is calm or not creative then alice is not brave.
Everyone who is not strong or not curious is either funny or not curious and vice versa.
If mary is both not kind and not humble then someone is not rich and vice versa.
Everyone who is both not humble and not rich is not strong and vice versa.
If lucy is either quiet or not humble then mary is either old or generous and vice versa.
If someone is either not calm or kind then john is tall or not rich.
If john is happy or strong then someone is both not calm and wise and vice versa.
If someone is either wise or patient then fred is not kind.
If someone is not old then someone is either not patient or not wise.
Everyone who is both brave and not wise is not brave or not kind and vice versa.
Everyone who is not wise or not brave is quiet or calm.
Someone is not funny.
Someone is not tall or not curious.
Mary is not tall or funny.
Someone is either patient or not humble.
Lucy is either not funny or wise.
Someone is tall or not tall. | John is calm. | contradiction | (((~old(john)|generous(john)))<=>(?[X]:((patient(X)|~strong(X)))))&
(![X]:((generous(X)|funny(X))<=>(~humble(X)&patient(X))))&
(![X]:((curious(X)<~>~generous(X))<=>~curious(X)))&
(![X]:((~rich(X)&~patient(X))=>(patient(X)<~>~curious(X))))&
((?[X]:((calm(X)|~creative(X))))=>(~brave(alice)))&
(![X]:((~strong(X)|~curious(X))<=>(funny(X)<~>~curious(X))))&
(((~kind(mary)&~humble(mary)))<=>(?[X]:(~rich(X))))&
(![X]:((~humble(X)&~rich(X))<=>~strong(X)))&
(((quiet(lucy)<~>~humble(lucy)))<=>((old(mary)<~>generous(mary))))&
((?[X]:((~calm(X)<~>kind(X))))=>((tall(john)|~rich(john))))&
(((happy(john)|strong(john)))<=>(?[X]:((~calm(X)&wise(X)))))&
((?[X]:((wise(X)<~>patient(X))))=>(~kind(fred)))&
((?[X]:(~old(X)))=>(?[X]:((~patient(X)<~>~wise(X)))))&
(![X]:((brave(X)&~wise(X))<=>(~brave(X)|~kind(X))))&
(![X]:((~wise(X)|~brave(X))=>(quiet(X)|calm(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~tall(X)|~curious(X))))&
((~tall(mary)|funny(mary)))&
(?[X]:((patient(X)<~>~humble(X))))&
((~funny(lucy)<~>wise(lucy)))&
(?[X]:((tall(X)|~tall(X)))) | calm(john) | [
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 9052944134445257409931320
% SZS output start Proof for 9052944134445257409931320
5. ? [X0] : (~creative(X0) | calm(X0)) => ~brave(alice) [input p4]
14. ! [X0] : ((~wise(X0) & brave(X0)) <=> (~kind(X0) | ~brave(X0))) [input p13]
22. calm(john) [input hypothesis]
24. ? [X0] : calm(X0) => ~brave(alice) [pure predicate removal 5]
27. ~brave(alice) | ! [X0] : ~calm(X0) [ennf transformation 24]
64. ! [X0] : (((~wise(X0) & brave(X0)) | (kind(X0) & brave(X0))) & ((~kind(X0) | ~brave(X0)) | (wise(X0) | ~brave(X0)))) [nnf transformation 14]
65. ! [X0] : (((~wise(X0) & brave(X0)) | (kind(X0) & brave(X0))) & (~kind(X0) | ~brave(X0) | wise(X0) | ~brave(X0))) [flattening 64]
91. ~brave(alice) | ~calm(X0) [cnf transformation 27]
124. brave(X0) | brave(X0) [cnf transformation 65]
138. calm(john) [cnf transformation 22]
140. brave(X0) [duplicate literal removal 124]
174. 7 <=> ! [X0] : ~calm(X0) [avatar definition]
175. ~calm(X0) <- (7) [avatar component clause 174]
177. 8 <=> brave(alice) [avatar definition]
179. ~brave(alice) <- (~8) [avatar component clause 177]
180. 7 | ~8 [avatar split clause 91,177,174]
323. $false <- (~8) [subsumption resolution 179,140]
324. 8 [avatar contradiction clause 323]
327. $false <- (7) [resolution 175,138]
328. ~7 [avatar contradiction clause 327]
329. $false [avatar sat refutation 180,324,328]
% SZS output end Proof for 9052944134445257409931320
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or brave is calm and vice versa.
If someone is both not curious and humble then lucy is not wise or rich.
Everyone who is quiet or not calm is not rich.
If fred is rich then someone is old or not kind and vice versa.
Everyone who is both creative and not kind is funny and vice versa.
If fred is both kind and not humble then someone is not creative or not funny.
Everyone who is not kind or generous is both not strong and not kind and vice versa.
If lucy is not strong or not tall then someone is happy and vice versa.
Everyone who is not wise or not brave is not strong or rich and vice versa.
If someone is patient or rich then someone is not creative or rich and vice versa.
If someone is patient or not strong then john is old and vice versa.
Everyone who is kind or not funny is not strong or not happy.
If someone is tall then someone is not kind or happy and vice versa.
If someone is both not curious and wise then lucy is both not calm and wise.
Everyone who is either curious or not brave is either not rich or not funny.
If mary is both quiet and old then alice is not curious or brave and vice versa.
Someone is old.
Fred is quiet or not funny.
Someone is both creative and not quiet.
Fred is either not kind or not creative.
Someone is happy or not rich.
Someone is humble. | John is not old. | contradiction | (![X]:((~calm(X)|brave(X))<=>calm(X)))&
((?[X]:((~curious(X)&humble(X))))=>((~wise(lucy)|rich(lucy))))&
(![X]:((quiet(X)|~calm(X))=>~rich(X)))&
((rich(fred))<=>(?[X]:((old(X)|~kind(X)))))&
(![X]:((creative(X)&~kind(X))<=>funny(X)))&
(((kind(fred)&~humble(fred)))=>(?[X]:((~creative(X)|~funny(X)))))&
(![X]:((~kind(X)|generous(X))<=>(~strong(X)&~kind(X))))&
(((~strong(lucy)|~tall(lucy)))<=>(?[X]:(happy(X))))&
(![X]:((~wise(X)|~brave(X))<=>(~strong(X)|rich(X))))&
((?[X]:((patient(X)|rich(X))))<=>(?[X]:((~creative(X)|rich(X)))))&
((?[X]:((patient(X)|~strong(X))))<=>(old(john)))&
(![X]:((kind(X)|~funny(X))=>(~strong(X)|~happy(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~kind(X)|happy(X)))))&
((?[X]:((~curious(X)&wise(X))))=>((~calm(lucy)&wise(lucy))))&
(![X]:((curious(X)<~>~brave(X))=>(~rich(X)<~>~funny(X))))&
(((quiet(mary)&old(mary)))<=>((~curious(alice)|brave(alice))))&
(?[X]:(old(X)))&
((quiet(fred)|~funny(fred)))&
(?[X]:((creative(X)&~quiet(X))))&
((~kind(fred)<~>~creative(fred)))&
(?[X]:((happy(X)|~rich(X))))&
(?[X]:(humble(X))) | ~old(john) | [
"p6",
"p7",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7750166261543370863133027
% SZS output start Proof for 7750166261543370863133027
7. ! [X0] : ((generous(X0) | ~kind(X0)) <=> (~kind(X0) & ~strong(X0))) [input p6]
8. (~tall(lucy) | ~strong(lucy)) <=> ? [X0] : happy(X0) [input p7]
11. ? [X0] : (~strong(X0) | patient(X0)) <=> old(john) [input p10]
12. ! [X0] : ((~funny(X0) | kind(X0)) => (~happy(X0) | ~strong(X0))) [input p11]
13. ? [X0] : tall(X0) <=> ? [X0] : (happy(X0) | ~kind(X0)) [input p12]
23. ~old(john) [input hypothesis]
25. ? [X0] : tall(X0) <=> ? [X1] : (happy(X1) | ~kind(X1)) [rectify 13]
31. ! [X0] : ((~happy(X0) | ~strong(X0)) | (funny(X0) & ~kind(X0))) [ennf transformation 12]
32. ! [X0] : (~happy(X0) | ~strong(X0) | (funny(X0) & ~kind(X0))) [flattening 31]
45. ! [X0] : (((generous(X0) | ~kind(X0)) | (kind(X0) | strong(X0))) & ((~kind(X0) & ~strong(X0)) | (~generous(X0) & kind(X0)))) [nnf transformation 7]
46. ! [X0] : ((generous(X0) | ~kind(X0) | kind(X0) | strong(X0)) & ((~kind(X0) & ~strong(X0)) | (~generous(X0) & kind(X0)))) [flattening 45]
47. ((~tall(lucy) | ~strong(lucy)) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | (tall(lucy) & strong(lucy))) [nnf transformation 8]
48. (~tall(lucy) | ~strong(lucy) | ! [X0] : ~happy(X0)) & (? [X0] : happy(X0) | (tall(lucy) & strong(lucy))) [flattening 47]
49. (~tall(lucy) | ~strong(lucy) | ! [X0] : ~happy(X0)) & (? [X1] : happy(X1) | (tall(lucy) & strong(lucy))) [rectify 48]
50. ? [X1] : happy(X1) => happy(sK2) [choice axiom]
51. (~tall(lucy) | ~strong(lucy) | ! [X0] : ~happy(X0)) & (happy(sK2) | (tall(lucy) & strong(lucy))) [skolemisation 49,50]
59. (? [X0] : (~strong(X0) | patient(X0)) | ~old(john)) & (old(john) | ! [X0] : (strong(X0) & ~patient(X0))) [nnf transformation 11]
60. (? [X0] : (~strong(X0) | patient(X0)) | ~old(john)) & (old(john) | ! [X1] : (strong(X1) & ~patient(X1))) [rectify 59]
61. ? [X0] : (~strong(X0) | patient(X0)) => (~strong(sK5) | patient(sK5)) [choice axiom]
62. ((~strong(sK5) | patient(sK5)) | ~old(john)) & (old(john) | ! [X1] : (strong(X1) & ~patient(X1))) [skolemisation 60,61]
63. (? [X0] : tall(X0) | ! [X1] : (~happy(X1) & kind(X1))) & (? [X1] : (happy(X1) | ~kind(X1)) | ! [X0] : ~tall(X0)) [nnf transformation 25]
64. (? [X0] : tall(X0) | ! [X1] : (~happy(X1) & kind(X1))) & (? [X2] : (happy(X2) | ~kind(X2)) | ! [X3] : ~tall(X3)) [rectify 63]
65. ? [X0] : tall(X0) => tall(sK6) [choice axiom]
66. ? [X2] : (happy(X2) | ~kind(X2)) => (happy(sK7) | ~kind(sK7)) [choice axiom]
67. (tall(sK6) | ! [X1] : (~happy(X1) & kind(X1))) & ((happy(sK7) | ~kind(sK7)) | ! [X3] : ~tall(X3)) [skolemisation 64,66,65]
93. ~strong(X0) | kind(X0) [cnf transformation 46]
99. happy(sK2) | tall(lucy) [cnf transformation 51]
110. old(john) | strong(X1) [cnf transformation 62]
112. ~happy(X0) | ~strong(X0) | ~kind(X0) [cnf transformation 32]
114. happy(sK7) | ~kind(sK7) | ~tall(X3) [cnf transformation 67]
136. ~old(john) [cnf transformation 23]
152. 4 <=> ! [X0] : kind(X0) [avatar definition]
153. kind(X0) <- (4) [avatar component clause 152]
194. 14 <=> tall(lucy) [avatar definition]
195. tall(lucy) <- (14) [avatar component clause 194]
199. 15 <=> happy(sK2) [avatar definition]
201. happy(sK2) <- (15) [avatar component clause 199]
202. 14 | 15 [avatar split clause 99,199,194]
234. 23 <=> old(john) [avatar definition]
247. 26 <=> ! [X1] : strong(X1) [avatar definition]
248. strong(X1) <- (26) [avatar component clause 247]
249. 26 | 23 [avatar split clause 110,234,247]
251. ~happy(X0) | ~strong(X0) [subsumption resolution 112,93]
259. 28 <=> ! [X3] : ~tall(X3) [avatar definition]
260. ~tall(X3) <- (28) [avatar component clause 259]
262. 29 <=> kind(sK7) [avatar definition]
264. ~kind(sK7) <- (~29) [avatar component clause 262]
266. 30 <=> happy(sK7) [avatar definition]
268. happy(sK7) <- (30) [avatar component clause 266]
269. 28 | ~29 | 30 [avatar split clause 114,266,262,259]
321. ~23 [avatar split clause 136,234]
328. $false <- (4, ~29) [resolution 264,153]
329. ~4 | 29 [avatar contradiction clause 328]
330. kind(X0) <- (26) [resolution 93,248]
331. 4 | ~26 [avatar split clause 330,247,152]
332. $false <- (14, 28) [resolution 260,195]
335. ~14 | ~28 [avatar contradiction clause 332]
340. ~strong(sK2) <- (15) [resolution 251,201]
341. ~strong(sK7) <- (30) [resolution 251,268]
342. $false <- (15, 26) [subsumption resolution 340,248]
343. ~15 | ~26 [avatar contradiction clause 342]
344. $false <- (26, 30) [subsumption resolution 341,248]
345. ~26 | ~30 [avatar contradiction clause 344]
346. $false [avatar sat refutation 202,249,269,321,329,331,335,343,345]
% SZS output end Proof for 7750166261543370863133027
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and curious is not patient and vice versa.
If someone is either strong or kind then alice is not curious and vice versa.
Everyone who is either not wise or not patient is both strong and not brave.
Everyone who is either not rich or generous is generous.
Everyone who is not brave is not quiet.
If alice is both patient and not rich then someone is rich.
Everyone who is old or kind is not happy or quiet.
If lucy is not tall or not patient then someone is not humble or not patient.
If someone is either not quiet or not funny then fred is humble.
Everyone who is either old or humble is either old or not generous and vice versa.
Everyone who is both not brave and not funny is happy or curious and vice versa.
Everyone who is both quiet and not happy is either not strong or calm.
Everyone who is not creative is either quiet or strong and vice versa.
If lucy is either not happy or generous then someone is not calm or not curious and vice versa.
If paul is not patient then paul is both not wise and not strong.
If someone is both strong and kind then paul is strong or rich.
Alice is not humble or not strong.
Paul is either quiet or old.
Paul is strong or not wise.
John is creative.
Susan is either funny or quiet.
Someone is wise.
Someone is generous.
Someone is either funny or not generous. | Fred is not generous. | entailment | (![X]:((happy(X)&curious(X))<=>~patient(X)))&
((?[X]:((strong(X)<~>kind(X))))<=>(~curious(alice)))&
(![X]:((~wise(X)<~>~patient(X))=>(strong(X)&~brave(X))))&
(![X]:((~rich(X)<~>generous(X))=>generous(X)))&
(![X]:(~brave(X)=>~quiet(X)))&
(((patient(alice)&~rich(alice)))=>(?[X]:(rich(X))))&
(![X]:((old(X)|kind(X))=>(~happy(X)|quiet(X))))&
(((~tall(lucy)|~patient(lucy)))=>(?[X]:((~humble(X)|~patient(X)))))&
((?[X]:((~quiet(X)<~>~funny(X))))=>(humble(fred)))&
(![X]:((old(X)<~>humble(X))<=>(old(X)<~>~generous(X))))&
(![X]:((~brave(X)&~funny(X))<=>(happy(X)|curious(X))))&
(![X]:((quiet(X)&~happy(X))=>(~strong(X)<~>calm(X))))&
(![X]:(~creative(X)<=>(quiet(X)<~>strong(X))))&
(((~happy(lucy)<~>generous(lucy)))<=>(?[X]:((~calm(X)|~curious(X)))))&
((~patient(paul))=>((~wise(paul)&~strong(paul))))&
((?[X]:((strong(X)&kind(X))))=>((strong(paul)|rich(paul))))&
((~humble(alice)|~strong(alice)))&
((quiet(paul)<~>old(paul)))&
((strong(paul)|~wise(paul)))&
(creative(john))&
((funny(susan)<~>quiet(susan)))&
(?[X]:(wise(X)))&
(?[X]:(generous(X)))&
(?[X]:((funny(X)<~>~generous(X)))) | ~generous(fred) | [
"p8",
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 386183473626307644673154
% SZS output start Proof for 386183473626307644673154
9. ? [X0] : (~quiet(X0) <~> ~funny(X0)) => humble(fred) [input p8]
10. ! [X0] : ((old(X0) <~> humble(X0)) <=> (old(X0) <~> ~generous(X0))) [input p9]
21. funny(susan) <~> quiet(susan) [input p20]
25. generous(fred) [input hypothesis]
36. humble(fred) | ! [X0] : (~quiet(X0) <=> ~funny(X0)) [ennf transformation 9]
55. humble(fred) | ! [X0] : ((~quiet(X0) | funny(X0)) & (~funny(X0) | quiet(X0))) [nnf transformation 36]
56. ! [X0] : ((((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | ((old(X0) | generous(X0)) & (~generous(X0) | ~old(X0)))) & (((generous(X0) | ~old(X0)) & (~generous(X0) | old(X0))) | ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0))))) [nnf transformation 10]
66. (~quiet(susan) | ~funny(susan)) & (quiet(susan) | funny(susan)) [nnf transformation 21]
92. humble(fred) | ~funny(X0) | quiet(X0) [cnf transformation 55]
93. humble(fred) | ~quiet(X0) | funny(X0) [cnf transformation 55]
95. ~generous(X0) | old(X0) | old(X0) | ~humble(X0) [cnf transformation 56]
100. ~humble(X0) | ~old(X0) | ~generous(X0) | ~old(X0) [cnf transformation 56]
125. quiet(susan) | funny(susan) [cnf transformation 66]
126. ~quiet(susan) | ~funny(susan) [cnf transformation 66]
131. generous(fred) [cnf transformation 25]
132. ~generous(X0) | old(X0) | ~humble(X0) [duplicate literal removal 95]
135. ~humble(X0) | ~old(X0) | ~generous(X0) [duplicate literal removal 100]
186. 12 <=> ! [X0] : (~quiet(X0) | funny(X0)) [avatar definition]
187. ~quiet(X0) | funny(X0) <- (12) [avatar component clause 186]
189. 13 <=> humble(fred) [avatar definition]
191. humble(fred) <- (13) [avatar component clause 189]
192. 12 | 13 [avatar split clause 93,189,186]
194. 14 <=> ! [X0] : (~funny(X0) | quiet(X0)) [avatar definition]
195. ~funny(X0) | quiet(X0) <- (14) [avatar component clause 194]
196. 14 | 13 [avatar split clause 92,189,194]
198. ~humble(X0) | ~generous(X0) [subsumption resolution 132,135]
270. 30 <=> funny(susan) [avatar definition]
271. funny(susan) <- (30) [avatar component clause 270]
272. ~funny(susan) <- (~30) [avatar component clause 270]
274. 31 <=> quiet(susan) [avatar definition]
275. quiet(susan) <- (31) [avatar component clause 274]
276. ~quiet(susan) <- (~31) [avatar component clause 274]
277. ~30 | ~31 [avatar split clause 126,274,270]
278. 30 | 31 [avatar split clause 125,274,270]
302. ~generous(fred) <- (13) [resolution 198,191]
304. $false <- (13) [subsumption resolution 302,131]
305. ~13 [avatar contradiction clause 304]
310. quiet(susan) <- (14, 30) [resolution 195,271]
312. $false <- (14, 30, ~31) [subsumption resolution 310,276]
313. ~14 | ~30 | 31 [avatar contradiction clause 312]
314. funny(susan) <- (12, 31) [resolution 275,187]
316. $false <- (12, ~30, 31) [subsumption resolution 314,272]
317. ~12 | 30 | ~31 [avatar contradiction clause 316]
318. $false [avatar sat refutation 192,196,277,278,305,313,317]
% SZS output end Proof for 386183473626307644673154
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is curious is not generous and vice versa.
Everyone who is kind or not curious is both brave and generous and vice versa.
Everyone who is not creative or wise is either tall or brave and vice versa.
Everyone who is not rich or happy is either happy or calm.
If fred is both not patient and happy then fred is generous and vice versa.
Everyone who is not happy or calm is both funny and not brave and vice versa.
If lucy is humble then john is kind.
Everyone who is either not brave or not happy is patient and vice versa.
If someone is both calm and strong then someone is either not generous or not curious and vice versa.
Everyone who is not wise or not rich is quiet or calm.
If susan is not happy or tall then someone is either calm or not calm.
Everyone who is not creative or not patient is not generous and vice versa.
Everyone who is both not quiet and not rich is not brave.
Everyone who is either creative or not curious is not rich and vice versa.
Everyone who is both humble and old is either not kind or tall.
If lucy is either not funny or not old then someone is either not strong or strong.
Someone is both not quiet and creative.
Someone is either not kind or humble.
Susan is both not wise and happy.
Someone is either not happy or not patient.
Mary is either not humble or patient.
Alice is quiet.
Someone is not brave or rich. | Lucy is curious. | entailment | (![X]:(curious(X)<=>~generous(X)))&
(![X]:((kind(X)|~curious(X))<=>(brave(X)&generous(X))))&
(![X]:((~creative(X)|wise(X))<=>(tall(X)<~>brave(X))))&
(![X]:((~rich(X)|happy(X))=>(happy(X)<~>calm(X))))&
(((~patient(fred)&happy(fred)))<=>(generous(fred)))&
(![X]:((~happy(X)|calm(X))<=>(funny(X)&~brave(X))))&
((humble(lucy))=>(kind(john)))&
(![X]:((~brave(X)<~>~happy(X))<=>patient(X)))&
((?[X]:((calm(X)&strong(X))))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
(![X]:((~wise(X)|~rich(X))=>(quiet(X)|calm(X))))&
(((~happy(susan)|tall(susan)))=>(?[X]:((calm(X)<~>~calm(X)))))&
(![X]:((~creative(X)|~patient(X))<=>~generous(X)))&
(![X]:((~quiet(X)&~rich(X))=>~brave(X)))&
(![X]:((creative(X)<~>~curious(X))<=>~rich(X)))&
(![X]:((humble(X)&old(X))=>(~kind(X)<~>tall(X))))&
(((~funny(lucy)<~>~old(lucy)))=>(?[X]:((~strong(X)<~>strong(X)))))&
(?[X]:((~quiet(X)&creative(X))))&
(?[X]:((~kind(X)<~>humble(X))))&
((~wise(susan)&happy(susan)))&
(?[X]:((~happy(X)<~>~patient(X))))&
((~humble(mary)<~>patient(mary)))&
(quiet(alice))&
(?[X]:((~brave(X)|rich(X)))) | curious(lucy) | [
"p0",
"p1",
"p5",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3278093975400646062905612
% SZS output start Proof for 3278093975400646062905612
1. ! [X0] : (curious(X0) <=> ~generous(X0)) [input p0]
2. ! [X0] : ((~curious(X0) | kind(X0)) <=> (generous(X0) & brave(X0))) [input p1]
6. ! [X0] : ((calm(X0) | ~happy(X0)) <=> (~brave(X0) & funny(X0))) [input p5]
8. ! [X0] : ((~brave(X0) <~> ~happy(X0)) <=> patient(X0)) [input p7]
12. ! [X0] : ((~patient(X0) | ~creative(X0)) <=> ~generous(X0)) [input p11]
24. ~curious(lucy) [input hypothesis]
38. ! [X0] : ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0))) [nnf transformation 1]
39. ! [X0] : (((~curious(X0) | kind(X0)) | (~generous(X0) | ~brave(X0))) & ((generous(X0) & brave(X0)) | (curious(X0) & ~kind(X0)))) [nnf transformation 2]
40. ! [X0] : ((~curious(X0) | kind(X0) | ~generous(X0) | ~brave(X0)) & ((generous(X0) & brave(X0)) | (curious(X0) & ~kind(X0)))) [flattening 39]
46. ! [X0] : (((calm(X0) | ~happy(X0)) | (brave(X0) | ~funny(X0))) & ((~brave(X0) & funny(X0)) | (~calm(X0) & happy(X0)))) [nnf transformation 6]
47. ! [X0] : ((calm(X0) | ~happy(X0) | brave(X0) | ~funny(X0)) & ((~brave(X0) & funny(X0)) | (~calm(X0) & happy(X0)))) [flattening 46]
48. ! [X0] : ((((happy(X0) | brave(X0)) & (~happy(X0) | ~brave(X0))) | ~patient(X0)) & (patient(X0) | ((~brave(X0) | happy(X0)) & (~happy(X0) | brave(X0))))) [nnf transformation 8]
57. ! [X0] : (((~patient(X0) | ~creative(X0)) | generous(X0)) & (~generous(X0) | (patient(X0) & creative(X0)))) [nnf transformation 12]
58. ! [X0] : ((~patient(X0) | ~creative(X0) | generous(X0)) & (~generous(X0) | (patient(X0) & creative(X0)))) [flattening 57]
76. generous(X0) | curious(X0) [cnf transformation 38]
78. brave(X0) | curious(X0) [cnf transformation 40]
97. ~brave(X0) | happy(X0) [cnf transformation 47]
103. ~happy(X0) | ~brave(X0) | ~patient(X0) [cnf transformation 48]
104. happy(X0) | brave(X0) | ~patient(X0) [cnf transformation 48]
118. ~generous(X0) | patient(X0) [cnf transformation 58]
141. ~curious(lucy) [cnf transformation 24]
168. ~patient(X0) | happy(X0) [subsumption resolution 104,97]
169. ~patient(X0) | ~brave(X0) [subsumption resolution 103,168]
172. 6 <=> ! [X1] : curious(X1) [avatar definition]
173. curious(X1) <- (6) [avatar component clause 172]
225. $false <- (6) [resolution 173,141]
226. ~6 [avatar contradiction clause 225]
235. patient(X0) | curious(X0) [resolution 118,76]
243. curious(X0) | ~brave(X0) [resolution 235,169]
245. curious(X0) [subsumption resolution 243,78]
246. 6 [avatar split clause 245,172]
247. $false [avatar sat refutation 226,246]
% SZS output end Proof for 3278093975400646062905612
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is patient or not strong then someone is both not happy and kind and vice versa.
Everyone who is both calm and strong is either not wise or old.
If someone is tall or not humble then someone is either creative or generous.
Everyone who is not tall or not rich is both old and not curious.
If john is either not funny or creative then paul is humble or curious and vice versa.
Everyone who is wise is old or strong.
Everyone who is not funny or brave is curious and vice versa.
Everyone who is humble is both not curious and not kind and vice versa.
Everyone who is either not tall or old is both not creative and patient.
If someone is kind then someone is curious and vice versa.
Everyone who is not kind is humble or not generous.
Everyone who is either not generous or calm is not quiet or not tall and vice versa.
Everyone who is both brave and not happy is old or not creative and vice versa.
Everyone who is not old is curious.
Everyone who is happy or old is not old and vice versa.
Someone is both generous and curious.
Mary is rich or curious.
John is creative or not curious.
Someone is rich or strong.
Mary is both generous and not brave.
Someone is either kind or not funny. | Mary is not creative. | contradiction | (((patient(lucy)|~strong(lucy)))<=>(?[X]:((~happy(X)&kind(X)))))&
(![X]:((calm(X)&strong(X))=>(~wise(X)<~>old(X))))&
((?[X]:((tall(X)|~humble(X))))=>(?[X]:((creative(X)<~>generous(X)))))&
(![X]:((~tall(X)|~rich(X))=>(old(X)&~curious(X))))&
(((~funny(john)<~>creative(john)))<=>((humble(paul)|curious(paul))))&
(![X]:(wise(X)=>(old(X)|strong(X))))&
(![X]:((~funny(X)|brave(X))<=>curious(X)))&
(![X]:(humble(X)<=>(~curious(X)&~kind(X))))&
(![X]:((~tall(X)<~>old(X))=>(~creative(X)&patient(X))))&
((?[X]:(kind(X)))<=>(?[X]:(curious(X))))&
(![X]:(~kind(X)=>(humble(X)|~generous(X))))&
(![X]:((~generous(X)<~>calm(X))<=>(~quiet(X)|~tall(X))))&
(![X]:((brave(X)&~happy(X))<=>(old(X)|~creative(X))))&
(![X]:(~old(X)=>curious(X)))&
(![X]:((happy(X)|old(X))<=>~old(X)))&
(?[X]:((generous(X)&curious(X))))&
((rich(mary)|curious(mary)))&
((creative(john)|~curious(john)))&
(?[X]:((rich(X)|strong(X))))&
((generous(mary)&~brave(mary)))&
(?[X]:((kind(X)<~>~funny(X)))) | ~creative(mary) | [
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 686998929835374763171165
% SZS output start Proof for 686998929835374763171165
13. ! [X0] : ((~happy(X0) & brave(X0)) <=> (~creative(X0) | old(X0))) [input p12]
20. ~brave(mary) & generous(mary) [input p19]
22. ~creative(mary) [input hypothesis]
62. ! [X0] : (((~happy(X0) & brave(X0)) | (creative(X0) & ~old(X0))) & ((~creative(X0) | old(X0)) | (happy(X0) | ~brave(X0)))) [nnf transformation 13]
63. ! [X0] : (((~happy(X0) & brave(X0)) | (creative(X0) & ~old(X0))) & (~creative(X0) | old(X0) | happy(X0) | ~brave(X0))) [flattening 62]
112. brave(X0) | creative(X0) [cnf transformation 63]
123. ~brave(mary) [cnf transformation 20]
126. ~creative(mary) [cnf transformation 22]
240. creative(mary) [resolution 112,123]
242. $false [subsumption resolution 240,126]
% SZS output end Proof for 686998929835374763171165
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is wise then mary is either brave or not happy.
If john is calm then someone is both not quiet and not old and vice versa.
If someone is funny then someone is quiet or calm and vice versa.
Everyone who is not creative is not humble or not tall and vice versa.
Everyone who is not quiet or not generous is either not humble or not curious and vice versa.
Everyone who is either not generous or not happy is either patient or not generous and vice versa.
If alice is both kind and not happy then john is tall or kind.
If alice is curious or brave then lucy is not funny and vice versa.
If susan is either not humble or old then someone is either wise or not old and vice versa.
Everyone who is not humble or not curious is not funny or old.
Everyone who is brave is patient or strong and vice versa.
Everyone who is quiet is kind and vice versa.
Everyone who is old or quiet is not generous and vice versa.
If someone is not patient or creative then lucy is both funny and creative.
Everyone who is either brave or not funny is both not patient and wise.
Everyone who is rich is both creative and not creative and vice versa.
Someone is not funny or not strong.
Someone is quiet or not brave.
Someone is both tall and humble.
Lucy is both calm and not kind.
John is not humble.
Paul is not calm.
Someone is either strong or not brave. | Lucy is curious. | contradiction | ((wise(lucy))=>((brave(mary)<~>~happy(mary))))&
((calm(john))<=>(?[X]:((~quiet(X)&~old(X)))))&
((?[X]:(funny(X)))<=>(?[X]:((quiet(X)|calm(X)))))&
(![X]:(~creative(X)<=>(~humble(X)|~tall(X))))&
(![X]:((~quiet(X)|~generous(X))<=>(~humble(X)<~>~curious(X))))&
(![X]:((~generous(X)<~>~happy(X))<=>(patient(X)<~>~generous(X))))&
(((kind(alice)&~happy(alice)))=>((tall(john)|kind(john))))&
(((curious(alice)|brave(alice)))<=>(~funny(lucy)))&
(((~humble(susan)<~>old(susan)))<=>(?[X]:((wise(X)<~>~old(X)))))&
(![X]:((~humble(X)|~curious(X))=>(~funny(X)|old(X))))&
(![X]:(brave(X)<=>(patient(X)|strong(X))))&
(![X]:(quiet(X)<=>kind(X)))&
(![X]:((old(X)|quiet(X))<=>~generous(X)))&
((?[X]:((~patient(X)|creative(X))))=>((funny(lucy)&creative(lucy))))&
(![X]:((brave(X)<~>~funny(X))=>(~patient(X)&wise(X))))&
(![X]:(rich(X)<=>(creative(X)&~creative(X))))&
(?[X]:((~funny(X)|~strong(X))))&
(?[X]:((quiet(X)|~brave(X))))&
(?[X]:((tall(X)&humble(X))))&
((calm(lucy)&~kind(lucy)))&
(~humble(john))&
(~calm(paul))&
(?[X]:((strong(X)<~>~brave(X)))) | curious(lucy) | [
"p3",
"p4",
"p11",
"p13",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7797676442100289979968671
% SZS output start Proof for 7797676442100289979968671
4. ! [X0] : (~creative(X0) <=> (~tall(X0) | ~humble(X0))) [input p3]
5. ! [X0] : ((~generous(X0) | ~quiet(X0)) <=> (~humble(X0) <~> ~curious(X0))) [input p4]
12. ! [X0] : (quiet(X0) <=> kind(X0)) [input p11]
14. ? [X0] : (creative(X0) | ~patient(X0)) => (creative(lucy) & funny(lucy)) [input p13]
19. ? [X0] : (humble(X0) & tall(X0)) [input p18]
20. ~kind(lucy) & calm(lucy) [input p19]
24. curious(lucy) [input hypothesis]
31. (creative(lucy) & funny(lucy)) | ! [X0] : (~creative(X0) & patient(X0)) [ennf transformation 14]
43. ! [X0] : ((~creative(X0) | (tall(X0) & humble(X0))) & ((~tall(X0) | ~humble(X0)) | creative(X0))) [nnf transformation 4]
44. ! [X0] : ((~creative(X0) | (tall(X0) & humble(X0))) & (~tall(X0) | ~humble(X0) | creative(X0))) [flattening 43]
45. ! [X0] : (((~generous(X0) | ~quiet(X0)) | ((~humble(X0) | curious(X0)) & (~curious(X0) | humble(X0)))) & (((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) | (generous(X0) & quiet(X0)))) [nnf transformation 5]
46. ! [X0] : ((~generous(X0) | ~quiet(X0) | ((~humble(X0) | curious(X0)) & (~curious(X0) | humble(X0)))) & (((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) | (generous(X0) & quiet(X0)))) [flattening 45]
56. ! [X0] : ((quiet(X0) | ~kind(X0)) & (kind(X0) | ~quiet(X0))) [nnf transformation 12]
64. ? [X0] : (humble(X0) & tall(X0)) => (humble(sK6) & tall(sK6)) [choice axiom]
65. humble(sK6) & tall(sK6) [skolemisation 19,64]
77. ~tall(X0) | ~humble(X0) | creative(X0) [cnf transformation 44]
78. ~creative(X0) | humble(X0) [cnf transformation 44]
80. ~curious(X0) | ~humble(X0) | quiet(X0) [cnf transformation 46]
111. ~quiet(X0) | kind(X0) [cnf transformation 56]
119. creative(lucy) | ~creative(X0) [cnf transformation 31]
126. tall(sK6) [cnf transformation 65]
127. humble(sK6) [cnf transformation 65]
129. ~kind(lucy) [cnf transformation 20]
134. curious(lucy) [cnf transformation 24]
260. 27 <=> ! [X0] : ~creative(X0) [avatar definition]
261. ~creative(X0) <- (27) [avatar component clause 260]
263. 28 <=> creative(lucy) [avatar definition]
265. creative(lucy) <- (28) [avatar component clause 263]
266. 27 | 28 [avatar split clause 119,263,260]
307. humble(lucy) <- (28) [resolution 78,265]
320. ~humble(sK6) | creative(sK6) [resolution 77,126]
322. creative(sK6) [subsumption resolution 320,127]
325. ~humble(lucy) | quiet(lucy) [resolution 80,134]
326. quiet(lucy) <- (28) [subsumption resolution 325,307]
327. kind(lucy) <- (28) [resolution 326,111]
328. $false <- (28) [subsumption resolution 327,129]
329. ~28 [avatar contradiction clause 328]
339. $false <- (27) [resolution 261,322]
340. ~27 [avatar contradiction clause 339]
341. $false [avatar sat refutation 266,329,340]
% SZS output end Proof for 7797676442100289979968671
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not humble and not old is both not creative and not old and vice versa.
Everyone who is either creative or tall is both calm and not old and vice versa.
Everyone who is either wise or strong is either not quiet or not curious and vice versa.
Everyone who is either not brave or not happy is not quiet or calm and vice versa.
Everyone who is brave is not tall and vice versa.
Everyone who is either not patient or not strong is wise.
Everyone who is either not wise or not old is not brave.
Everyone who is both kind and not happy is both not funny and not calm.
Everyone who is humble is quiet.
If someone is tall then paul is both patient and not patient and vice versa.
Everyone who is quiet is old and vice versa.
Everyone who is tall is not happy or kind and vice versa.
If alice is not funny or curious then someone is both strong and not rich.
If someone is not brave or humble then someone is calm.
Everyone who is both kind and wise is both funny and generous.
Everyone who is both strong and not funny is either not funny or not old and vice versa.
Someone is patient.
Alice is not creative.
Lucy is old or not patient.
Someone is either not kind or not wise.
Mary is either patient or not curious. | Alice is old. | entailment | (![X]:((~humble(X)&~old(X))<=>(~creative(X)&~old(X))))&
(![X]:((creative(X)<~>tall(X))<=>(calm(X)&~old(X))))&
(![X]:((wise(X)<~>strong(X))<=>(~quiet(X)<~>~curious(X))))&
(![X]:((~brave(X)<~>~happy(X))<=>(~quiet(X)|calm(X))))&
(![X]:(brave(X)<=>~tall(X)))&
(![X]:((~patient(X)<~>~strong(X))=>wise(X)))&
(![X]:((~wise(X)<~>~old(X))=>~brave(X)))&
(![X]:((kind(X)&~happy(X))=>(~funny(X)&~calm(X))))&
(![X]:(humble(X)=>quiet(X)))&
((?[X]:(tall(X)))<=>((patient(paul)&~patient(paul))))&
(![X]:(quiet(X)<=>old(X)))&
(![X]:(tall(X)<=>(~happy(X)|kind(X))))&
(((~funny(alice)|curious(alice)))=>(?[X]:((strong(X)&~rich(X)))))&
((?[X]:((~brave(X)|humble(X))))=>(?[X]:(calm(X))))&
(![X]:((kind(X)&wise(X))=>(funny(X)&generous(X))))&
(![X]:((strong(X)&~funny(X))<=>(~funny(X)<~>~old(X))))&
(?[X]:(patient(X)))&
(~creative(alice))&
((old(lucy)|~patient(lucy)))&
(?[X]:((~kind(X)<~>~wise(X))))&
((patient(mary)<~>~curious(mary))) | old(alice) | [
"p3",
"p4",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5930203518751712467819444
% SZS output start Proof for 5930203518751712467819444
4. ! [X0] : ((~brave(X0) <~> ~happy(X0)) <=> (calm(X0) | ~quiet(X0))) [input p3]
5. ! [X0] : (brave(X0) <=> ~tall(X0)) [input p4]
10. ? [X0] : tall(X0) <=> (~patient(paul) & patient(paul)) [input p9]
11. ! [X0] : (quiet(X0) <=> old(X0)) [input p10]
12. ! [X0] : (tall(X0) <=> (kind(X0) | ~happy(X0))) [input p11]
22. ~old(alice) [input hypothesis]
40. ! [X0] : ((((happy(X0) | brave(X0)) & (~happy(X0) | ~brave(X0))) | (~calm(X0) & quiet(X0))) & ((calm(X0) | ~quiet(X0)) | ((~brave(X0) | happy(X0)) & (~happy(X0) | brave(X0))))) [nnf transformation 4]
41. ! [X0] : ((((happy(X0) | brave(X0)) & (~happy(X0) | ~brave(X0))) | (~calm(X0) & quiet(X0))) & (calm(X0) | ~quiet(X0) | ((~brave(X0) | happy(X0)) & (~happy(X0) | brave(X0))))) [flattening 40]
42. ! [X0] : ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0))) [nnf transformation 5]
45. (? [X0] : tall(X0) | (patient(paul) | ~patient(paul))) & ((~patient(paul) & patient(paul)) | ! [X0] : ~tall(X0)) [nnf transformation 10]
46. (? [X0] : tall(X0) | patient(paul) | ~patient(paul)) & ((~patient(paul) & patient(paul)) | ! [X0] : ~tall(X0)) [flattening 45]
47. (? [X0] : tall(X0) | patient(paul) | ~patient(paul)) & ((~patient(paul) & patient(paul)) | ! [X1] : ~tall(X1)) [rectify 46]
48. ? [X0] : tall(X0) => tall(sK0) [choice axiom]
49. (tall(sK0) | patient(paul) | ~patient(paul)) & ((~patient(paul) & patient(paul)) | ! [X1] : ~tall(X1)) [skolemisation 47,48]
50. ! [X0] : ((quiet(X0) | ~old(X0)) & (old(X0) | ~quiet(X0))) [nnf transformation 11]
51. ! [X0] : ((tall(X0) | (~kind(X0) & happy(X0))) & ((kind(X0) | ~happy(X0)) | ~tall(X0))) [nnf transformation 12]
52. ! [X0] : ((tall(X0) | (~kind(X0) & happy(X0))) & (kind(X0) | ~happy(X0) | ~tall(X0))) [flattening 51]
86. ~happy(X0) | ~brave(X0) | quiet(X0) [cnf transformation 41]
91. brave(X0) | tall(X0) [cnf transformation 42]
99. patient(paul) | ~tall(X1) [cnf transformation 49]
100. ~patient(paul) | ~tall(X1) [cnf transformation 49]
102. ~quiet(X0) | old(X0) [cnf transformation 50]
105. happy(X0) | tall(X0) [cnf transformation 52]
125. ~old(alice) [cnf transformation 22]
129. 1 <=> ! [X1] : ~tall(X1) [avatar definition]
130. ~tall(X1) <- (1) [avatar component clause 129]
132. 2 <=> patient(paul) [avatar definition]
135. 1 | ~2 [avatar split clause 100,132,129]
136. 1 | 2 [avatar split clause 99,132,129]
200. ~brave(X0) | quiet(X0) | tall(X0) [resolution 86,105]
201. ~brave(X0) | quiet(X0) <- (1) [subsumption resolution 200,130]
204. quiet(X0) | tall(X0) <- (1) [resolution 201,91]
205. quiet(X0) <- (1) [subsumption resolution 204,130]
209. old(X0) <- (1) [resolution 205,102]
250. $false <- (1) [resolution 209,125]
252. ~1 [avatar contradiction clause 250]
253. $false [avatar sat refutation 135,136,252]
% SZS output end Proof for 5930203518751712467819444
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is not calm or not patient. Everyone who is not tall or not old is either not generous or humble and vice versa. Everyone who is both not quiet and tall is calm or not happy and vice versa. If paul is not curious then mary is both generous and not strong. Everyone who is tall is either wise or old. If someone is kind then susan is not patient and vice versa. Everyone who is generous is either not calm or tall and vice versa. Everyone who is both rich and not old is both old and strong and vice versa. Everyone who is wise or brave is not creative. If someone is either not curious or calm then someone is either not creative or tall and vice versa. If paul is either not generous or not patient then someone is old or not strong and vice versa. If someone is either not calm or not happy then mary is both not generous and not rich. If someone is both not tall and not humble then someone is both calm and not happy and vice versa. Everyone who is either brave or not creative is either brave or happy. Everyone who is not humble is both strong and not funny and vice versa. If someone is either old or not kind then someone is creative. Someone is wise or not creative. Someone is curious or humble. Someone is either funny or rich. Mary is both humble and strong. Alice is not quiet. Someone is humble. Someone is either not calm or not humble. | Susan is not quiet. | entailment | (![X]:(funny(X)=>(~calm(X)|~patient(X))))&
(![X]:((~tall(X)|~old(X))<=>(~generous(X)<~>humble(X))))&
(![X]:((~quiet(X)&tall(X))<=>(calm(X)|~happy(X))))&
((~curious(paul))=>((generous(mary)&~strong(mary))))&
(![X]:(tall(X)=>(wise(X)<~>old(X))))&
((?[X]:(kind(X)))<=>(~patient(susan)))&
(![X]:(generous(X)<=>(~calm(X)<~>tall(X))))&
(![X]:((rich(X)&~old(X))<=>(old(X)&strong(X))))&
(![X]:((wise(X)|brave(X))=>~creative(X)))&
((?[X]:((~curious(X)<~>calm(X))))<=>(?[X]:((~creative(X)<~>tall(X)))))&
(((~generous(paul)<~>~patient(paul)))<=>(?[X]:((old(X)|~strong(X)))))&
((?[X]:((~calm(X)<~>~happy(X))))=>((~generous(mary)&~rich(mary))))&
((?[X]:((~tall(X)&~humble(X))))<=>(?[X]:((calm(X)&~happy(X)))))&
(![X]:((brave(X)<~>~creative(X))=>(brave(X)<~>happy(X))))&
(![X]:(~humble(X)<=>(strong(X)&~funny(X))))&
((?[X]:((old(X)<~>~kind(X))))=>(?[X]:(creative(X))))&
(?[X]:((wise(X)|~creative(X))))&
(?[X]:((curious(X)|humble(X))))&
(?[X]:((funny(X)<~>rich(X))))&
((humble(mary)&strong(mary)))&
(~quiet(alice))&
(?[X]:(humble(X)))&
(?[X]:((~calm(X)<~>~humble(X)))) | ~quiet(susan) | [
"p1",
"p2",
"p7",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2885282307478796714592311
% SZS output start Proof for 2885282307478796714592311
2. ! [X0] : ((~old(X0) | ~tall(X0)) <=> (~generous(X0) <~> humble(X0))) [input p1]
3. ! [X0] : ((tall(X0) & ~quiet(X0)) <=> (~happy(X0) | calm(X0))) [input p2]
8. ! [X0] : ((~old(X0) & rich(X0)) <=> (strong(X0) & old(X0))) [input p7]
12. ? [X0] : (~calm(X0) <~> ~happy(X0)) => (~rich(mary) & ~generous(mary)) [input p11]
20. strong(mary) & humble(mary) [input p19]
24. quiet(susan) [input hypothesis]
33. (~rich(mary) & ~generous(mary)) | ! [X0] : (~calm(X0) <=> ~happy(X0)) [ennf transformation 12]
36. ! [X0] : (((~old(X0) | ~tall(X0)) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0)))) & (((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | (old(X0) & tall(X0)))) [nnf transformation 2]
37. ! [X0] : ((~old(X0) | ~tall(X0) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0)))) & (((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | (old(X0) & tall(X0)))) [flattening 36]
38. ! [X0] : (((tall(X0) & ~quiet(X0)) | (happy(X0) & ~calm(X0))) & ((~happy(X0) | calm(X0)) | (~tall(X0) | quiet(X0)))) [nnf transformation 3]
39. ! [X0] : (((tall(X0) & ~quiet(X0)) | (happy(X0) & ~calm(X0))) & (~happy(X0) | calm(X0) | ~tall(X0) | quiet(X0))) [flattening 38]
46. ! [X0] : (((~old(X0) & rich(X0)) | (~strong(X0) | ~old(X0))) & ((strong(X0) & old(X0)) | (old(X0) | ~rich(X0)))) [nnf transformation 8]
47. ! [X0] : (((~old(X0) & rich(X0)) | ~strong(X0) | ~old(X0)) & ((strong(X0) & old(X0)) | old(X0) | ~rich(X0))) [flattening 46]
57. (~rich(mary) & ~generous(mary)) | ! [X0] : ((~calm(X0) | happy(X0)) & (~happy(X0) | calm(X0))) [nnf transformation 33]
86. ~humble(X0) | generous(X0) | old(X0) [cnf transformation 37]
90. ~quiet(X0) | ~calm(X0) [cnf transformation 39]
91. ~quiet(X0) | happy(X0) [cnf transformation 39]
107. ~old(X0) | ~strong(X0) | ~old(X0) [cnf transformation 47]
124. ~generous(mary) | ~happy(X0) | calm(X0) [cnf transformation 57]
145. humble(mary) [cnf transformation 20]
146. strong(mary) [cnf transformation 20]
151. quiet(susan) [cnf transformation 24]
155. ~strong(X0) | ~old(X0) [duplicate literal removal 107]
161. 2 <=> strong(mary) [avatar definition]
162. strong(mary) <- (2) [avatar component clause 161]
166. 3 <=> generous(mary) [avatar definition]
256. 22 <=> ! [X0] : (~happy(X0) | calm(X0)) [avatar definition]
257. ~happy(X0) | calm(X0) <- (22) [avatar component clause 256]
260. 22 | ~3 [avatar split clause 124,166,256]
316. 2 [avatar split clause 146,161]
327. ~calm(susan) [resolution 90,151]
328. happy(susan) [resolution 91,151]
334. ~old(mary) <- (2) [resolution 155,162]
366. generous(mary) | old(mary) [resolution 86,145]
420. generous(mary) <- (2) [subsumption resolution 366,334]
421. 3 | ~2 [avatar split clause 420,161,166]
434. calm(susan) <- (22) [resolution 257,328]
436. $false <- (22) [subsumption resolution 434,327]
437. ~22 [avatar contradiction clause 436]
439. $false [avatar sat refutation 260,316,421,437]
% SZS output end Proof for 2885282307478796714592311
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and quiet is old or not patient.
Everyone who is humble is either not creative or not rich and vice versa.
Everyone who is both rich and not patient is both not happy and wise and vice versa.
Everyone who is either not old or not humble is not wise and vice versa.
If fred is either not patient or quiet then mary is either old or not funny and vice versa.
If someone is not calm or not rich then someone is not rich or not brave.
If alice is either not curious or not patient then john is not kind and vice versa.
Everyone who is humble is funny.
Everyone who is both patient and not happy is either quiet or not creative and vice versa.
Everyone who is either not creative or not wise is funny.
If someone is quiet or tall then paul is not calm or calm.
If mary is both humble and old then paul is both not wise and not calm.
Everyone who is both not generous and wise is not generous or not tall and vice versa.
Everyone who is both not rich and not calm is either not quiet or old and vice versa.
Everyone who is either old or funny is not calm and vice versa.
Everyone who is either not humble or happy is both not funny and not wise and vice versa.
Lucy is either not quiet or not calm.
John is both patient and kind.
Someone is both brave and not happy.
Alice is both not quiet and generous.
Someone is old.
Someone is not creative. | Alice is not creative. | contradiction | (![X]:((~wise(X)&quiet(X))=>(old(X)|~patient(X))))&
(![X]:(humble(X)<=>(~creative(X)<~>~rich(X))))&
(![X]:((rich(X)&~patient(X))<=>(~happy(X)&wise(X))))&
(![X]:((~old(X)<~>~humble(X))<=>~wise(X)))&
(((~patient(fred)<~>quiet(fred)))<=>((old(mary)<~>~funny(mary))))&
((?[X]:((~calm(X)|~rich(X))))=>(?[X]:((~rich(X)|~brave(X)))))&
(((~curious(alice)<~>~patient(alice)))<=>(~kind(john)))&
(![X]:(humble(X)=>funny(X)))&
(![X]:((patient(X)&~happy(X))<=>(quiet(X)<~>~creative(X))))&
(![X]:((~creative(X)<~>~wise(X))=>funny(X)))&
((?[X]:((quiet(X)|tall(X))))=>((~calm(paul)|calm(paul))))&
(((humble(mary)&old(mary)))=>((~wise(paul)&~calm(paul))))&
(![X]:((~generous(X)&wise(X))<=>(~generous(X)|~tall(X))))&
(![X]:((~rich(X)&~calm(X))<=>(~quiet(X)<~>old(X))))&
(![X]:((old(X)<~>funny(X))<=>~calm(X)))&
(![X]:((~humble(X)<~>happy(X))<=>(~funny(X)&~wise(X))))&
((~quiet(lucy)<~>~calm(lucy)))&
((patient(john)&kind(john)))&
(?[X]:((brave(X)&~happy(X))))&
((~quiet(alice)&generous(alice)))&
(?[X]:(old(X)))&
(?[X]:(~creative(X))) | ~creative(alice) | [
"p1",
"p2",
"p3",
"p8",
"p13",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4930791600443088515490719
% SZS output start Proof for 4930791600443088515490719
2. ! [X0] : (humble(X0) <=> (~creative(X0) <~> ~rich(X0))) [input p1]
3. ! [X0] : ((~patient(X0) & rich(X0)) <=> (wise(X0) & ~happy(X0))) [input p2]
4. ! [X0] : ((~old(X0) <~> ~humble(X0)) <=> ~wise(X0)) [input p3]
9. ! [X0] : ((~happy(X0) & patient(X0)) <=> (quiet(X0) <~> ~creative(X0))) [input p8]
14. ! [X0] : ((~calm(X0) & ~rich(X0)) <=> (~quiet(X0) <~> old(X0))) [input p13]
15. ! [X0] : ((old(X0) <~> funny(X0)) <=> ~calm(X0)) [input p14]
16. ! [X0] : ((~humble(X0) <~> happy(X0)) <=> (~wise(X0) & ~funny(X0))) [input p15]
20. generous(alice) & ~quiet(alice) [input p19]
23. ~creative(alice) [input hypothesis]
34. ! [X0] : ((humble(X0) | ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0)))) & (((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | ~humble(X0))) [nnf transformation 2]
35. ! [X0] : (((~patient(X0) & rich(X0)) | (~wise(X0) | happy(X0))) & ((wise(X0) & ~happy(X0)) | (patient(X0) | ~rich(X0)))) [nnf transformation 3]
36. ! [X0] : (((~patient(X0) & rich(X0)) | ~wise(X0) | happy(X0)) & ((wise(X0) & ~happy(X0)) | patient(X0) | ~rich(X0))) [flattening 35]
37. ! [X0] : ((((humble(X0) | old(X0)) & (~humble(X0) | ~old(X0))) | wise(X0)) & (~wise(X0) | ((~old(X0) | humble(X0)) & (~humble(X0) | old(X0))))) [nnf transformation 4]
43. ! [X0] : (((~happy(X0) & patient(X0)) | ((quiet(X0) | creative(X0)) & (~creative(X0) | ~quiet(X0)))) & (((creative(X0) | ~quiet(X0)) & (~creative(X0) | quiet(X0))) | (happy(X0) | ~patient(X0)))) [nnf transformation 9]
44. ! [X0] : (((~happy(X0) & patient(X0)) | ((quiet(X0) | creative(X0)) & (~creative(X0) | ~quiet(X0)))) & (((creative(X0) | ~quiet(X0)) & (~creative(X0) | quiet(X0))) | happy(X0) | ~patient(X0))) [flattening 43]
48. ! [X0] : (((~calm(X0) & ~rich(X0)) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (calm(X0) | rich(X0)))) [nnf transformation 14]
49. ! [X0] : (((~calm(X0) & ~rich(X0)) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | calm(X0) | rich(X0))) [flattening 48]
50. ! [X0] : ((((~funny(X0) | ~old(X0)) & (funny(X0) | old(X0))) | calm(X0)) & (~calm(X0) | ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0))))) [nnf transformation 15]
51. ! [X0] : ((((~happy(X0) | humble(X0)) & (happy(X0) | ~humble(X0))) | (wise(X0) | funny(X0))) & ((~wise(X0) & ~funny(X0)) | ((~humble(X0) | ~happy(X0)) & (happy(X0) | humble(X0))))) [nnf transformation 16]
52. ! [X0] : ((((~happy(X0) | humble(X0)) & (happy(X0) | ~humble(X0))) | wise(X0) | funny(X0)) & ((~wise(X0) & ~funny(X0)) | ((~humble(X0) | ~happy(X0)) & (happy(X0) | humble(X0))))) [flattening 51]
62. ~humble(X0) | creative(X0) | rich(X0) [cnf transformation 34]
63. ~rich(X0) | humble(X0) | creative(X0) [cnf transformation 34]
68. ~patient(X0) | ~wise(X0) | happy(X0) [cnf transformation 36]
71. ~humble(X0) | ~old(X0) | wise(X0) [cnf transformation 37]
72. humble(X0) | old(X0) | wise(X0) [cnf transformation 37]
91. creative(X0) | quiet(X0) | patient(X0) [cnf transformation 44]
93. ~happy(X0) | quiet(X0) | creative(X0) [cnf transformation 44]
106. ~old(X0) | quiet(X0) | calm(X0) | rich(X0) [cnf transformation 49]
107. ~rich(X0) | old(X0) | quiet(X0) [cnf transformation 49]
111. ~calm(X0) | funny(X0) | ~old(X0) [cnf transformation 50]
115. ~funny(X0) | happy(X0) | humble(X0) [cnf transformation 52]
127. ~quiet(alice) [cnf transformation 20]
131. ~creative(alice) [cnf transformation 23]
181. 11 <=> patient(alice) [avatar definition]
183. patient(alice) <- (11) [avatar component clause 181]
239. rich(X2) | wise(X2) | creative(X2) | old(X2) [resolution 72,62]
244. quiet(alice) | patient(alice) [resolution 91,131]
257. patient(alice) [subsumption resolution 244,127]
260. 11 [avatar split clause 257,181]
261. ~wise(alice) | happy(alice) <- (11) [resolution 183,68]
263. 23 <=> happy(alice) [avatar definition]
265. happy(alice) <- (23) [avatar component clause 263]
267. 24 <=> wise(alice) [avatar definition]
269. ~wise(alice) <- (~24) [avatar component clause 267]
270. 23 | ~24 | ~11 [avatar split clause 261,181,267,263]
449. wise(X1) | creative(X1) | old(X1) | old(X1) | quiet(X1) [resolution 239,107]
455. creative(X1) | wise(X1) | old(X1) | quiet(X1) [duplicate literal removal 449]
611. wise(alice) | old(alice) | quiet(alice) [resolution 455,131]
617. old(alice) | quiet(alice) <- (~24) [subsumption resolution 611,269]
618. old(alice) <- (~24) [subsumption resolution 617,127]
863. quiet(alice) | calm(alice) | rich(alice) <- (~24) [resolution 618,106]
865. calm(alice) | rich(alice) <- (~24) [subsumption resolution 863,127]
867. 70 <=> rich(alice) [avatar definition]
869. rich(alice) <- (70) [avatar component clause 867]
871. 71 <=> calm(alice) [avatar definition]
873. calm(alice) <- (71) [avatar component clause 871]
874. 70 | 71 | 24 [avatar split clause 865,267,871,867]
1223. humble(alice) | creative(alice) <- (70) [resolution 869,63]
1225. humble(alice) <- (70) [subsumption resolution 1223,131]
1267. ~old(alice) | wise(alice) <- (70) [resolution 1225,71]
1271. wise(alice) <- (~24, 70) [subsumption resolution 1267,618]
1272. $false <- (~24, 70) [subsumption resolution 1271,269]
1273. 24 | ~70 [avatar contradiction clause 1272]
1277. funny(alice) | ~old(alice) <- (71) [resolution 873,111]
1280. funny(alice) <- (~24, 71) [subsumption resolution 1277,618]
1292. happy(alice) | humble(alice) <- (~24, 71) [resolution 1280,115]
1295. 84 <=> humble(alice) [avatar definition]
1297. humble(alice) <- (84) [avatar component clause 1295]
1298. 84 | 23 | 24 | ~71 [avatar split clause 1292,871,267,263,1295]
1301. quiet(alice) | creative(alice) <- (23) [resolution 265,93]
1305. creative(alice) <- (23) [subsumption resolution 1301,127]
1306. $false <- (23) [subsumption resolution 1305,131]
1307. ~23 [avatar contradiction clause 1306]
1310. ~old(alice) | wise(alice) <- (84) [resolution 1297,71]
1314. wise(alice) <- (~24, 84) [subsumption resolution 1310,618]
1315. $false <- (~24, 84) [subsumption resolution 1314,269]
1316. 24 | ~84 [avatar contradiction clause 1315]
1320. $false [avatar sat refutation 260,270,874,1273,1298,1307,1316]
% SZS output end Proof for 4930791600443088515490719
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is generous. If someone is either tall or not funny then alice is wise or not patient. Everyone who is both not curious and humble is both not generous and brave and vice versa. If someone is either not brave or not tall then lucy is either not kind or not patient. If someone is curious then fred is both funny and not curious and vice versa. If fred is creative or not strong then mary is not wise and vice versa. If fred is either not tall or not old then someone is both not kind and not generous. Everyone who is both strong and not strong is calm or tall and vice versa. Everyone who is old or humble is either not curious or wise and vice versa. If susan is either not humble or not quiet then someone is tall and vice versa. Everyone who is either not strong or tall is not tall or not patient and vice versa. If someone is both not strong and happy then lucy is not brave and vice versa. If someone is not calm or not humble then someone is either not kind or not funny. If someone is both patient and quiet then fred is either brave or generous. Everyone who is not generous or not calm is not wise or rich and vice versa. If mary is wise then mary is tall or creative. Someone is either not kind or quiet. Someone is not brave. Mary is patient. Paul is either not creative or not curious. Susan is either not patient or happy. Someone is not generous. | Susan is not tall. | entailment | (![X]:(~humble(X)=>generous(X)))&
((?[X]:((tall(X)<~>~funny(X))))=>((wise(alice)|~patient(alice))))&
(![X]:((~curious(X)&humble(X))<=>(~generous(X)&brave(X))))&
((?[X]:((~brave(X)<~>~tall(X))))=>((~kind(lucy)<~>~patient(lucy))))&
((?[X]:(curious(X)))<=>((funny(fred)&~curious(fred))))&
(((creative(fred)|~strong(fred)))<=>(~wise(mary)))&
(((~tall(fred)<~>~old(fred)))=>(?[X]:((~kind(X)&~generous(X)))))&
(![X]:((strong(X)&~strong(X))<=>(calm(X)|tall(X))))&
(![X]:((old(X)|humble(X))<=>(~curious(X)<~>wise(X))))&
(((~humble(susan)<~>~quiet(susan)))<=>(?[X]:(tall(X))))&
(![X]:((~strong(X)<~>tall(X))<=>(~tall(X)|~patient(X))))&
((?[X]:((~strong(X)&happy(X))))<=>(~brave(lucy)))&
((?[X]:((~calm(X)|~humble(X))))=>(?[X]:((~kind(X)<~>~funny(X)))))&
((?[X]:((patient(X)&quiet(X))))=>((brave(fred)<~>generous(fred))))&
(![X]:((~generous(X)|~calm(X))<=>(~wise(X)|rich(X))))&
((wise(mary))=>((tall(mary)|creative(mary))))&
(?[X]:((~kind(X)<~>quiet(X))))&
(?[X]:(~brave(X)))&
(patient(mary))&
((~creative(paul)<~>~curious(paul)))&
((~patient(susan)<~>happy(susan)))&
(?[X]:(~generous(X))) | ~tall(susan) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3531227307850625771885801
% SZS output start Proof for 3531227307850625771885801
8. ! [X0] : ((~strong(X0) & strong(X0)) <=> (tall(X0) | calm(X0))) [input p7]
23. tall(susan) [input hypothesis]
48. ! [X0] : (((~strong(X0) & strong(X0)) | (~tall(X0) & ~calm(X0))) & ((tall(X0) | calm(X0)) | (strong(X0) | ~strong(X0)))) [nnf transformation 8]
49. ! [X0] : (((~strong(X0) & strong(X0)) | (~tall(X0) & ~calm(X0))) & (tall(X0) | calm(X0) | strong(X0) | ~strong(X0))) [flattening 48]
101. strong(X0) | ~tall(X0) [cnf transformation 49]
103. ~strong(X0) | ~tall(X0) [cnf transformation 49]
143. tall(susan) [cnf transformation 23]
233. ~tall(X0) [subsumption resolution 101,103]
330. $false [subsumption resolution 143,233]
% SZS output end Proof for 3531227307850625771885801
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or funny then paul is not patient or not strong and vice versa.
Everyone who is both humble and tall is not funny and vice versa.
If paul is funny then someone is either wise or not happy and vice versa.
Everyone who is not wise is not generous or curious.
If mary is both not humble and not curious then susan is brave or not creative.
If lucy is patient or strong then john is either rich or not creative and vice versa.
If susan is not curious then someone is both not strong and calm.
If someone is strong or old then susan is brave.
Everyone who is humble is both not kind and kind and vice versa.
Everyone who is not happy or curious is both not creative and creative.
If lucy is both not brave and not old then lucy is not brave and vice versa.
Everyone who is either not old or wise is not quiet.
Everyone who is not kind or not old is both not old and wise and vice versa.
If mary is patient then someone is either patient or not brave.
If someone is either rich or not strong then john is curious and vice versa.
If susan is either rich or not brave then someone is not old.
Someone is both not humble and not brave.
Fred is rich.
Someone is not rich.
Someone is not kind or not old.
Mary is not old or not patient.
Someone is not humble or kind.
Someone is old. | Mary is not patient. | neutral | ((?[X]:((curious(X)|funny(X))))<=>((~patient(paul)|~strong(paul))))&
(![X]:((humble(X)&tall(X))<=>~funny(X)))&
((funny(paul))<=>(?[X]:((wise(X)<~>~happy(X)))))&
(![X]:(~wise(X)=>(~generous(X)|curious(X))))&
(((~humble(mary)&~curious(mary)))=>((brave(susan)|~creative(susan))))&
(((patient(lucy)|strong(lucy)))<=>((rich(john)<~>~creative(john))))&
((~curious(susan))=>(?[X]:((~strong(X)&calm(X)))))&
((?[X]:((strong(X)|old(X))))=>(brave(susan)))&
(![X]:(humble(X)<=>(~kind(X)&kind(X))))&
(![X]:((~happy(X)|curious(X))=>(~creative(X)&creative(X))))&
(((~brave(lucy)&~old(lucy)))<=>(~brave(lucy)))&
(![X]:((~old(X)<~>wise(X))=>~quiet(X)))&
(![X]:((~kind(X)|~old(X))<=>(~old(X)&wise(X))))&
((patient(mary))=>(?[X]:((patient(X)<~>~brave(X)))))&
((?[X]:((rich(X)<~>~strong(X))))<=>(curious(john)))&
(((rich(susan)<~>~brave(susan)))=>(?[X]:(~old(X))))&
(?[X]:((~humble(X)&~brave(X))))&
(rich(fred))&
(?[X]:(~rich(X)))&
(?[X]:((~kind(X)|~old(X))))&
((~old(mary)|~patient(mary)))&
(?[X]:((~humble(X)|kind(X))))&
(?[X]:(old(X))) | ~patient(mary) | [] | null | 0 |
If fred is both strong and not happy then someone is not wise or not funny.
Everyone who is not tall is not happy or not funny and vice versa.
If someone is not quiet or curious then someone is tall or not strong and vice versa.
Everyone who is creative or not strong is both brave and not happy.
If mary is either not strong or not tall then someone is not quiet.
If fred is either not strong or strong then lucy is not quiet or not patient.
Everyone who is not tall or old is either brave or not funny and vice versa.
If fred is both humble and not calm then someone is not brave or not humble and vice versa.
Everyone who is not calm or not quiet is not strong or brave and vice versa.
Everyone who is not tall or not old is kind.
Everyone who is not humble is strong or not patient.
If alice is tall then someone is creative.
Everyone who is not kind or not funny is either not strong or strong and vice versa.
Everyone who is either creative or not kind is both not quiet and wise and vice versa.
If someone is either not old or not funny then paul is either not calm or brave.
Someone is tall.
Someone is either wise or creative.
Someone is humble.
Someone is old or funny.
Lucy is either strong or not old.
Someone is either wise or not brave. | Alice is strong. | entailment | (((strong(fred)&~happy(fred)))=>(?[X]:((~wise(X)|~funny(X)))))&
(![X]:(~tall(X)<=>(~happy(X)|~funny(X))))&
((?[X]:((~quiet(X)|curious(X))))<=>(?[X]:((tall(X)|~strong(X)))))&
(![X]:((creative(X)|~strong(X))=>(brave(X)&~happy(X))))&
(((~strong(mary)<~>~tall(mary)))=>(?[X]:(~quiet(X))))&
(((~strong(fred)<~>strong(fred)))=>((~quiet(lucy)|~patient(lucy))))&
(![X]:((~tall(X)|old(X))<=>(brave(X)<~>~funny(X))))&
(((humble(fred)&~calm(fred)))<=>(?[X]:((~brave(X)|~humble(X)))))&
(![X]:((~calm(X)|~quiet(X))<=>(~strong(X)|brave(X))))&
(![X]:((~tall(X)|~old(X))=>kind(X)))&
(![X]:(~humble(X)=>(strong(X)|~patient(X))))&
((tall(alice))=>(?[X]:(creative(X))))&
(![X]:((~kind(X)|~funny(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((creative(X)<~>~kind(X))<=>(~quiet(X)&wise(X))))&
((?[X]:((~old(X)<~>~funny(X))))=>((~calm(paul)<~>brave(paul))))&
(?[X]:(tall(X)))&
(?[X]:((wise(X)<~>creative(X))))&
(?[X]:(humble(X)))&
(?[X]:((old(X)|funny(X))))&
((strong(lucy)<~>~old(lucy)))&
(?[X]:((wise(X)<~>~brave(X)))) | strong(alice) | [
"p1",
"p3",
"p6",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5983865690052948364686105
% SZS output start Proof for 5983865690052948364686105
2. ! [X0] : (~tall(X0) <=> (~funny(X0) | ~happy(X0))) [input p1]
4. ! [X0] : ((~strong(X0) | creative(X0)) => (~happy(X0) & brave(X0))) [input p3]
7. ! [X0] : ((old(X0) | ~tall(X0)) <=> (brave(X0) <~> ~funny(X0))) [input p6]
10. ! [X0] : ((~old(X0) | ~tall(X0)) => kind(X0)) [input p9]
13. ! [X0] : ((~funny(X0) | ~kind(X0)) <=> (~strong(X0) <~> strong(X0))) [input p12]
22. ~strong(alice) [input hypothesis]
28. ! [X0] : ((~happy(X0) & brave(X0)) | (strong(X0) & ~creative(X0))) [ennf transformation 4]
30. ! [X0] : (kind(X0) | (old(X0) & tall(X0))) [ennf transformation 10]
35. ! [X0] : ((~tall(X0) | (funny(X0) & happy(X0))) & ((~funny(X0) | ~happy(X0)) | tall(X0))) [nnf transformation 2]
36. ! [X0] : ((~tall(X0) | (funny(X0) & happy(X0))) & (~funny(X0) | ~happy(X0) | tall(X0))) [flattening 35]
45. ! [X0] : (((old(X0) | ~tall(X0)) | ((brave(X0) | funny(X0)) & (~funny(X0) | ~brave(X0)))) & (((funny(X0) | ~brave(X0)) & (~funny(X0) | brave(X0))) | (~old(X0) & tall(X0)))) [nnf transformation 7]
46. ! [X0] : ((old(X0) | ~tall(X0) | ((brave(X0) | funny(X0)) & (~funny(X0) | ~brave(X0)))) & (((funny(X0) | ~brave(X0)) & (~funny(X0) | brave(X0))) | (~old(X0) & tall(X0)))) [flattening 45]
56. ! [X0] : (((~funny(X0) | ~kind(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) & (((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | (funny(X0) & kind(X0)))) [nnf transformation 13]
57. ! [X0] : ((~funny(X0) | ~kind(X0) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) & (((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | (funny(X0) & kind(X0)))) [flattening 56]
76. ~tall(X0) | happy(X0) [cnf transformation 36]
77. ~tall(X0) | funny(X0) [cnf transformation 36]
83. brave(X0) | strong(X0) [cnf transformation 28]
85. ~happy(X0) | strong(X0) [cnf transformation 28]
90. funny(X0) | ~brave(X0) | tall(X0) [cnf transformation 46]
103. kind(X0) | tall(X0) [cnf transformation 30]
110. ~funny(X0) | ~kind(X0) | strong(X0) | strong(X0) [cnf transformation 57]
111. ~funny(X0) | ~kind(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 57]
131. ~strong(alice) [cnf transformation 22]
132. ~funny(X0) | ~kind(X0) | strong(X0) [duplicate literal removal 110]
133. ~kind(X0) | ~funny(X0) | ~strong(X0) [duplicate literal removal 111]
198. ~brave(X0) | funny(X0) [subsumption resolution 90,77]
229. 22 <=> tall(alice) [avatar definition]
230. tall(alice) <- (22) [avatar component clause 229]
231. ~tall(alice) <- (~22) [avatar component clause 229]
237. ~kind(X0) | ~funny(X0) [subsumption resolution 132,133]
308. funny(X0) | strong(X0) [resolution 198,83]
314. ~funny(X1) | tall(X1) [resolution 237,103]
439. tall(X0) | strong(X0) [resolution 314,308]
472. happy(alice) <- (22) [resolution 230,76]
544. strong(alice) <- (22) [resolution 472,85]
545. $false <- (22) [subsumption resolution 544,131]
546. ~22 [avatar contradiction clause 545]
947. strong(alice) <- (~22) [resolution 439,231]
953. $false <- (~22) [subsumption resolution 947,131]
954. 22 [avatar contradiction clause 953]
955. $false [avatar sat refutation 546,954]
% SZS output end Proof for 5983865690052948364686105
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both funny and not happy then someone is calm or brave and vice versa.
Everyone who is either strong or not happy is both not old and not curious.
Everyone who is both tall and not calm is not quiet and vice versa.
Everyone who is either not rich or rich is old.
Everyone who is either not brave or strong is both brave and not wise.
If someone is both not calm and not generous then someone is creative or not happy and vice versa.
If someone is not happy then mary is both not funny and happy and vice versa.
Everyone who is tall is not patient or kind.
Everyone who is funny is either not strong or not brave.
Everyone who is wise or not humble is either not kind or not brave.
Everyone who is not curious or happy is patient or not calm.
Everyone who is not creative or not rich is patient or rich and vice versa.
If someone is both not rich and not brave then lucy is not rich or not strong.
Everyone who is either patient or brave is not curious.
Everyone who is humble is kind.
If lucy is not brave or funny then paul is generous and vice versa.
Paul is either creative or calm.
Someone is not wise or not brave.
Someone is creative.
Lucy is not tall or not old.
Susan is either kind or wise.
Alice is wise.
John is either not calm or patient. | Mary is funny. | contradiction | ((?[X]:((funny(X)&~happy(X))))<=>(?[X]:((calm(X)|brave(X)))))&
(![X]:((strong(X)<~>~happy(X))=>(~old(X)&~curious(X))))&
(![X]:((tall(X)&~calm(X))<=>~quiet(X)))&
(![X]:((~rich(X)<~>rich(X))=>old(X)))&
(![X]:((~brave(X)<~>strong(X))=>(brave(X)&~wise(X))))&
((?[X]:((~calm(X)&~generous(X))))<=>(?[X]:((creative(X)|~happy(X)))))&
((?[X]:(~happy(X)))<=>((~funny(mary)&happy(mary))))&
(![X]:(tall(X)=>(~patient(X)|kind(X))))&
(![X]:(funny(X)=>(~strong(X)<~>~brave(X))))&
(![X]:((wise(X)|~humble(X))=>(~kind(X)<~>~brave(X))))&
(![X]:((~curious(X)|happy(X))=>(patient(X)|~calm(X))))&
(![X]:((~creative(X)|~rich(X))<=>(patient(X)|rich(X))))&
((?[X]:((~rich(X)&~brave(X))))=>((~rich(lucy)|~strong(lucy))))&
(![X]:((patient(X)<~>brave(X))=>~curious(X)))&
(![X]:(humble(X)=>kind(X)))&
(((~brave(lucy)|funny(lucy)))<=>(generous(paul)))&
((creative(paul)<~>calm(paul)))&
(?[X]:((~wise(X)|~brave(X))))&
(?[X]:(creative(X)))&
((~tall(lucy)|~old(lucy)))&
((kind(susan)<~>wise(susan)))&
(wise(alice))&
((~calm(john)<~>patient(john))) | funny(mary) | [
"p0",
"p1",
"p3",
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 6313621938120116220457455
% SZS output start Proof for 6313621938120116220457455
1. ? [X0] : (~happy(X0) & funny(X0)) <=> ? [X0] : (brave(X0) | calm(X0)) [input p0]
2. ! [X0] : ((strong(X0) <~> ~happy(X0)) => (~curious(X0) & ~old(X0))) [input p1]
4. ! [X0] : ((~rich(X0) <~> rich(X0)) => old(X0)) [input p3]
5. ! [X0] : ((~brave(X0) <~> strong(X0)) => (~wise(X0) & brave(X0))) [input p4]
7. ? [X0] : ~happy(X0) <=> (happy(mary) & ~funny(mary)) [input p6]
24. funny(mary) [input hypothesis]
25. ? [X0] : (~happy(X0) & funny(X0)) <=> ? [X1] : (brave(X1) | calm(X1)) [rectify 1]
29. ! [X0] : ((~curious(X0) & ~old(X0)) | (strong(X0) <=> ~happy(X0))) [ennf transformation 2]
30. ! [X0] : (old(X0) | (~rich(X0) <=> rich(X0))) [ennf transformation 4]
31. ! [X0] : ((~wise(X0) & brave(X0)) | (~brave(X0) <=> strong(X0))) [ennf transformation 5]
40. (? [X0] : (~happy(X0) & funny(X0)) | ! [X1] : (~brave(X1) & ~calm(X1))) & (? [X1] : (brave(X1) | calm(X1)) | ! [X0] : (happy(X0) | ~funny(X0))) [nnf transformation 25]
41. (? [X0] : (~happy(X0) & funny(X0)) | ! [X1] : (~brave(X1) & ~calm(X1))) & (? [X2] : (brave(X2) | calm(X2)) | ! [X3] : (happy(X3) | ~funny(X3))) [rectify 40]
42. ? [X0] : (~happy(X0) & funny(X0)) => (~happy(sK0) & funny(sK0)) [choice axiom]
43. ? [X2] : (brave(X2) | calm(X2)) => (brave(sK1) | calm(sK1)) [choice axiom]
44. ((~happy(sK0) & funny(sK0)) | ! [X1] : (~brave(X1) & ~calm(X1))) & ((brave(sK1) | calm(sK1)) | ! [X3] : (happy(X3) | ~funny(X3))) [skolemisation 41,43,42]
45. ! [X0] : ((~curious(X0) & ~old(X0)) | ((strong(X0) | happy(X0)) & (~happy(X0) | ~strong(X0)))) [nnf transformation 29]
46. ! [X0] : (old(X0) | ((~rich(X0) | ~rich(X0)) & (rich(X0) | rich(X0)))) [nnf transformation 30]
47. ! [X0] : ((~wise(X0) & brave(X0)) | ((~brave(X0) | ~strong(X0)) & (strong(X0) | brave(X0)))) [nnf transformation 31]
53. (? [X0] : ~happy(X0) | (~happy(mary) | funny(mary))) & ((happy(mary) & ~funny(mary)) | ! [X0] : happy(X0)) [nnf transformation 7]
54. (? [X0] : ~happy(X0) | ~happy(mary) | funny(mary)) & ((happy(mary) & ~funny(mary)) | ! [X0] : happy(X0)) [flattening 53]
55. (? [X0] : ~happy(X0) | ~happy(mary) | funny(mary)) & ((happy(mary) & ~funny(mary)) | ! [X1] : happy(X1)) [rectify 54]
56. ? [X0] : ~happy(X0) => ~happy(sK4) [choice axiom]
57. (~happy(sK4) | ~happy(mary) | funny(mary)) & ((happy(mary) & ~funny(mary)) | ! [X1] : happy(X1)) [skolemisation 55,56]
76. ~happy(sK0) | ~brave(X1) [cnf transformation 44]
77. ~old(X0) | ~happy(X0) | ~strong(X0) [cnf transformation 45]
81. old(X0) | rich(X0) | rich(X0) [cnf transformation 46]
82. old(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 46]
83. brave(X0) | strong(X0) | brave(X0) [cnf transformation 47]
92. ~funny(mary) | happy(X1) [cnf transformation 57]
123. funny(mary) [cnf transformation 24]
126. strong(X0) | brave(X0) [duplicate literal removal 83]
127. old(X0) | rich(X0) [duplicate literal removal 81]
128. ~rich(X0) | old(X0) [duplicate literal removal 82]
130. 1 <=> ! [X1] : ~brave(X1) [avatar definition]
131. ~brave(X1) <- (1) [avatar component clause 130]
133. 2 <=> happy(sK0) [avatar definition]
135. ~happy(sK0) <- (~2) [avatar component clause 133]
136. 1 | ~2 [avatar split clause 76,133,130]
159. old(X0) [subsumption resolution 127,128]
161. 8 <=> ! [X1] : happy(X1) [avatar definition]
162. happy(X1) <- (8) [avatar component clause 161]
191. 15 <=> funny(mary) [avatar definition]
204. 8 | ~15 [avatar split clause 92,191,161]
271. 15 [avatar split clause 123,191]
272. $false <- (~2, 8) [subsumption resolution 135,162]
273. 2 | ~8 [avatar contradiction clause 272]
291. ~happy(X0) | ~strong(X0) [resolution 77,159]
292. ~strong(X0) <- (8) [subsumption resolution 291,162]
294. brave(X0) <- (8) [resolution 292,126]
297. $false <- (1, 8) [subsumption resolution 294,131]
298. ~1 | ~8 [avatar contradiction clause 297]
299. $false [avatar sat refutation 136,204,271,273,298]
% SZS output end Proof for 6313621938120116220457455
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is both creative and not brave.
Everyone who is both not humble and creative is not patient or kind and vice versa.
Everyone who is not rich is either not wise or happy and vice versa.
Everyone who is either quiet or strong is brave.
Everyone who is either not curious or calm is creative or not rich and vice versa.
Everyone who is either not humble or not creative is either kind or rich.
Everyone who is either not happy or not humble is not quiet or not creative.
If someone is patient then someone is generous or old.
If someone is either not humble or not curious then someone is not tall.
Everyone who is rich is both kind and not rich.
Everyone who is calm is both not curious and wise.
If someone is either tall or patient then someone is either tall or not wise and vice versa.
If someone is funny or not creative then fred is either patient or not funny and vice versa.
If paul is not old or humble then someone is both happy and not creative and vice versa.
If mary is not wise then someone is either rich or not brave.
If someone is not creative then someone is not strong or rich.
John is either calm or not wise.
Someone is old.
Someone is both not rich and tall.
Someone is not quiet or not tall.
Alice is not rich.
Someone is either not kind or happy.
Someone is not wise or kind.
Someone is either not patient or calm. | Paul is rich. | contradiction | (![X]:(~rich(X)=>(creative(X)&~brave(X))))&
(![X]:((~humble(X)&creative(X))<=>(~patient(X)|kind(X))))&
(![X]:(~rich(X)<=>(~wise(X)<~>happy(X))))&
(![X]:((quiet(X)<~>strong(X))=>brave(X)))&
(![X]:((~curious(X)<~>calm(X))<=>(creative(X)|~rich(X))))&
(![X]:((~humble(X)<~>~creative(X))=>(kind(X)<~>rich(X))))&
(![X]:((~happy(X)<~>~humble(X))=>(~quiet(X)|~creative(X))))&
((?[X]:(patient(X)))=>(?[X]:((generous(X)|old(X)))))&
((?[X]:((~humble(X)<~>~curious(X))))=>(?[X]:(~tall(X))))&
(![X]:(rich(X)=>(kind(X)&~rich(X))))&
(![X]:(calm(X)=>(~curious(X)&wise(X))))&
((?[X]:((tall(X)<~>patient(X))))<=>(?[X]:((tall(X)<~>~wise(X)))))&
((?[X]:((funny(X)|~creative(X))))<=>((patient(fred)<~>~funny(fred))))&
(((~old(paul)|humble(paul)))<=>(?[X]:((happy(X)&~creative(X)))))&
((~wise(mary))=>(?[X]:((rich(X)<~>~brave(X)))))&
((?[X]:(~creative(X)))=>(?[X]:((~strong(X)|rich(X)))))&
((calm(john)<~>~wise(john)))&
(?[X]:(old(X)))&
(?[X]:((~rich(X)&tall(X))))&
(?[X]:((~quiet(X)|~tall(X))))&
(~rich(alice))&
(?[X]:((~kind(X)<~>happy(X))))&
(?[X]:((~wise(X)|kind(X))))&
(?[X]:((~patient(X)<~>calm(X)))) | rich(paul) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4983218138407433011785175
% SZS output start Proof for 4983218138407433011785175
10. ! [X0] : (rich(X0) => (~rich(X0) & kind(X0))) [input p9]
25. rich(paul) [input hypothesis]
37. ! [X0] : ((~rich(X0) & kind(X0)) | ~rich(X0)) [ennf transformation 10]
116. ~rich(X0) | ~rich(X0) [cnf transformation 37]
153. rich(paul) [cnf transformation 25]
154. ~rich(X0) [duplicate literal removal 116]
313. $false [subsumption resolution 153,154]
% SZS output end Proof for 4983218138407433011785175
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or not brave is both wise and not brave. If susan is both not humble and brave then alice is either creative or quiet. If lucy is creative then john is not brave or not funny. If john is not patient or not rich then susan is both not funny and not kind and vice versa. If someone is either not old or not funny then alice is not kind or quiet. If someone is both old and creative then fred is old or happy. Everyone who is either strong or not happy is either not rich or not quiet and vice versa. Everyone who is not happy or not humble is either not strong or brave and vice versa. If someone is tall or not tall then someone is calm and vice versa. If someone is quiet then mary is either strong or calm and vice versa. Everyone who is not curious or strong is either strong or patient and vice versa. If alice is either wise or not rich then someone is wise and vice versa. If someone is happy or tall then someone is brave and vice versa. If someone is both wise and not funny then fred is either quiet or not strong. If john is either not calm or creative then someone is not happy and vice versa. Everyone who is not calm or not generous is either not creative or curious and vice versa. Paul is both funny and not curious. Someone is creative. Someone is either not calm or old. Mary is either not calm or strong. Lucy is both old and kind. Someone is either not calm or not wise. Someone is happy. | Paul is not funny. | contradiction | (![X]:((~generous(X)|~brave(X))=>(wise(X)&~brave(X))))&
(((~humble(susan)&brave(susan)))=>((creative(alice)<~>quiet(alice))))&
((creative(lucy))=>((~brave(john)|~funny(john))))&
(((~patient(john)|~rich(john)))<=>((~funny(susan)&~kind(susan))))&
((?[X]:((~old(X)<~>~funny(X))))=>((~kind(alice)|quiet(alice))))&
((?[X]:((old(X)&creative(X))))=>((old(fred)|happy(fred))))&
(![X]:((strong(X)<~>~happy(X))<=>(~rich(X)<~>~quiet(X))))&
(![X]:((~happy(X)|~humble(X))<=>(~strong(X)<~>brave(X))))&
((?[X]:((tall(X)|~tall(X))))<=>(?[X]:(calm(X))))&
((?[X]:(quiet(X)))<=>((strong(mary)<~>calm(mary))))&
(![X]:((~curious(X)|strong(X))<=>(strong(X)<~>patient(X))))&
(((wise(alice)<~>~rich(alice)))<=>(?[X]:(wise(X))))&
((?[X]:((happy(X)|tall(X))))<=>(?[X]:(brave(X))))&
((?[X]:((wise(X)&~funny(X))))=>((quiet(fred)<~>~strong(fred))))&
(((~calm(john)<~>creative(john)))<=>(?[X]:(~happy(X))))&
(![X]:((~calm(X)|~generous(X))<=>(~creative(X)<~>curious(X))))&
((funny(paul)&~curious(paul)))&
(?[X]:(creative(X)))&
(?[X]:((~calm(X)<~>old(X))))&
((~calm(mary)<~>strong(mary)))&
((old(lucy)&kind(lucy)))&
(?[X]:((~calm(X)<~>~wise(X))))&
(?[X]:(happy(X))) | ~funny(paul) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5704435538533718483204866
% SZS output start Proof for 5704435538533718483204866
17. ~curious(paul) & funny(paul) [input p16]
24. ~funny(paul) [input hypothesis]
143. funny(paul) [cnf transformation 17]
155. ~funny(paul) [cnf transformation 24]
359. $false [subsumption resolution 155,143]
% SZS output end Proof for 5704435538533718483204866
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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