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 either curious or not old is both rich and not quiet. Everyone who is strong is not patient and vice versa. Everyone who is either patient or rich is not strong or not happy. Everyone who is either not kind or kind is generous or not curious and vice versa. Everyone who is either not creative or not quiet is not funny. If john is quiet then someone is humble. Everyone who is either strong or curious is not humble. If someone is either calm or quiet then lucy is not patient. Everyone who is either funny or not kind is either not creative or not quiet and vice versa. Everyone who is either not tall or not funny is both old and brave and vice versa. If someone is either not humble or not generous then someone is not humble or tall. Everyone who is both generous and not quiet is both not calm and quiet. Everyone who is both strong and brave is either not calm or not creative. If someone is not wise then someone is not old or kind. If alice is either wise or not funny then someone is both not generous and strong and vice versa. Everyone who is calm or not rich is either not happy or creative and vice versa. Someone is kind or strong. Susan is happy or not wise. Someone is both not humble and not curious. Someone is rich or not kind. Someone is either not curious or not brave. Someone is brave or not brave. Someone is not generous or humble. Someone is not creative. | John is generous. | neutral | (![X]:((curious(X)<~>~old(X))=>(rich(X)&~quiet(X))))&
(![X]:(strong(X)<=>~patient(X)))&
(![X]:((patient(X)<~>rich(X))=>(~strong(X)|~happy(X))))&
(![X]:((~kind(X)<~>kind(X))<=>(generous(X)|~curious(X))))&
(![X]:((~creative(X)<~>~quiet(X))=>~funny(X)))&
((quiet(john))=>(?[X]:(humble(X))))&
(![X]:((strong(X)<~>curious(X))=>~humble(X)))&
((?[X]:((calm(X)<~>quiet(X))))=>(~patient(lucy)))&
(![X]:((funny(X)<~>~kind(X))<=>(~creative(X)<~>~quiet(X))))&
(![X]:((~tall(X)<~>~funny(X))<=>(old(X)&brave(X))))&
((?[X]:((~humble(X)<~>~generous(X))))=>(?[X]:((~humble(X)|tall(X)))))&
(![X]:((generous(X)&~quiet(X))=>(~calm(X)&quiet(X))))&
(![X]:((strong(X)&brave(X))=>(~calm(X)<~>~creative(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~old(X)|kind(X)))))&
(((wise(alice)<~>~funny(alice)))<=>(?[X]:((~generous(X)&strong(X)))))&
(![X]:((calm(X)|~rich(X))<=>(~happy(X)<~>creative(X))))&
(?[X]:((kind(X)|strong(X))))&
((happy(susan)|~wise(susan)))&
(?[X]:((~humble(X)&~curious(X))))&
(?[X]:((rich(X)|~kind(X))))&
(?[X]:((~curious(X)<~>~brave(X))))&
(?[X]:((brave(X)|~brave(X))))&
(?[X]:((~generous(X)|humble(X))))&
(?[X]:(~creative(X))) | generous(john) | [] | null | 0 |
If fred is not funny or not creative then someone is both not calm and not old.
Everyone who is not curious or not generous is not tall and vice versa.
Everyone who is brave or not wise is either happy or patient and vice versa.
Everyone who is not creative or old is both humble and calm.
If susan is both not humble and not wise then john is rich.
Everyone who is strong or humble is old or not humble and vice versa.
If someone is tall then lucy is both brave and not patient and vice versa.
If lucy is both creative and calm then someone is either not old or humble and vice versa.
Everyone who is not happy or generous is both funny and wise.
If someone is both not happy and not quiet then someone is both wise and not brave and vice versa.
Everyone who is not happy is not tall or not quiet.
If susan is either strong or not calm then someone is not humble and vice versa.
Everyone who is not kind or brave is not happy and vice versa.
If someone is curious then fred is not strong or not patient.
If paul is not wise then someone is either quiet or not creative.
Everyone who is both not wise and curious is either rich or not humble.
Fred is not humble.
Someone is either rich or kind.
Someone is both wise and not creative.
Fred is not kind.
John is brave.
Paul is not creative or strong. | Fred is funny. | entailment | (((~funny(fred)|~creative(fred)))=>(?[X]:((~calm(X)&~old(X)))))&
(![X]:((~curious(X)|~generous(X))<=>~tall(X)))&
(![X]:((brave(X)|~wise(X))<=>(happy(X)<~>patient(X))))&
(![X]:((~creative(X)|old(X))=>(humble(X)&calm(X))))&
(((~humble(susan)&~wise(susan)))=>(rich(john)))&
(![X]:((strong(X)|humble(X))<=>(old(X)|~humble(X))))&
((?[X]:(tall(X)))<=>((brave(lucy)&~patient(lucy))))&
(((creative(lucy)&calm(lucy)))<=>(?[X]:((~old(X)<~>humble(X)))))&
(![X]:((~happy(X)|generous(X))=>(funny(X)&wise(X))))&
((?[X]:((~happy(X)&~quiet(X))))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:(~happy(X)=>(~tall(X)|~quiet(X))))&
(((strong(susan)<~>~calm(susan)))<=>(?[X]:(~humble(X))))&
(![X]:((~kind(X)|brave(X))<=>~happy(X)))&
((?[X]:(curious(X)))=>((~strong(fred)|~patient(fred))))&
((~wise(paul))=>(?[X]:((quiet(X)<~>~creative(X)))))&
(![X]:((~wise(X)&curious(X))=>(rich(X)<~>~humble(X))))&
(~humble(fred))&
(?[X]:((rich(X)<~>kind(X))))&
(?[X]:((wise(X)&~creative(X))))&
(~kind(fred))&
(brave(john))&
((~creative(paul)|strong(paul))) | funny(fred) | [
"p8",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7295766330839151681182718
% SZS output start Proof for 7295766330839151681182718
9. ! [X0] : ((generous(X0) | ~happy(X0)) => (wise(X0) & funny(X0))) [input p8]
13. ! [X0] : ((brave(X0) | ~kind(X0)) <=> ~happy(X0)) [input p12]
20. ~kind(fred) [input p19]
23. ~funny(fred) [input hypothesis]
29. ! [X0] : ((wise(X0) & funny(X0)) | (~generous(X0) & happy(X0))) [ennf transformation 9]
64. ! [X0] : (((brave(X0) | ~kind(X0)) | happy(X0)) & (~happy(X0) | (~brave(X0) & kind(X0)))) [nnf transformation 13]
65. ! [X0] : ((brave(X0) | ~kind(X0) | happy(X0)) & (~happy(X0) | (~brave(X0) & kind(X0)))) [flattening 64]
106. happy(X0) | funny(X0) [cnf transformation 29]
119. ~happy(X0) | kind(X0) [cnf transformation 65]
132. ~kind(fred) [cnf transformation 20]
135. ~funny(fred) [cnf transformation 23]
148. 3 <=> funny(fred) [avatar definition]
149. ~funny(fred) <- (~3) [avatar component clause 148]
298. ~3 [avatar split clause 135,148]
323. kind(X1) | funny(X1) [resolution 119,106]
382. funny(fred) [resolution 323,132]
385. $false <- (~3) [subsumption resolution 382,149]
386. 3 [avatar contradiction clause 385]
387. $false [avatar sat refutation 298,386]
% SZS output end Proof for 7295766330839151681182718
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is either not creative or quiet and vice versa.
Everyone who is generous is either humble or rich and vice versa.
Everyone who is brave is either not generous or not tall and vice versa.
Everyone who is both not happy and curious is either not curious or kind and vice versa.
Everyone who is not patient or not happy is either not calm or curious and vice versa.
Everyone who is either not wise or curious is not brave or not tall and vice versa.
If someone is both not brave and patient then someone is either tall or not patient.
Everyone who is both not strong and not curious is either not humble or quiet and vice versa.
Everyone who is happy is not curious or not patient.
Everyone who is either tall or funny is brave and vice versa.
If mary is both rich and not strong then someone is either not kind or not rich.
If someone is old then alice is either funny or old and vice versa.
Everyone who is either happy or not tall is either not humble or not quiet and vice versa.
If paul is either patient or not calm then someone is not creative or old.
Everyone who is either not creative or not humble is both patient and not humble and vice versa.
Everyone who is not rich is either not patient or not kind and vice versa.
Lucy is either not patient or not generous.
Someone is either not humble or humble.
Alice is both curious and not tall.
Someone is calm.
Someone is either not brave or not quiet.
Lucy is either not kind or not rich.
Someone is funny or not generous. | Lucy is not happy. | neutral | (![X]:(rich(X)<=>(~creative(X)<~>quiet(X))))&
(![X]:(generous(X)<=>(humble(X)<~>rich(X))))&
(![X]:(brave(X)<=>(~generous(X)<~>~tall(X))))&
(![X]:((~happy(X)&curious(X))<=>(~curious(X)<~>kind(X))))&
(![X]:((~patient(X)|~happy(X))<=>(~calm(X)<~>curious(X))))&
(![X]:((~wise(X)<~>curious(X))<=>(~brave(X)|~tall(X))))&
((?[X]:((~brave(X)&patient(X))))=>(?[X]:((tall(X)<~>~patient(X)))))&
(![X]:((~strong(X)&~curious(X))<=>(~humble(X)<~>quiet(X))))&
(![X]:(happy(X)=>(~curious(X)|~patient(X))))&
(![X]:((tall(X)<~>funny(X))<=>brave(X)))&
(((rich(mary)&~strong(mary)))=>(?[X]:((~kind(X)<~>~rich(X)))))&
((?[X]:(old(X)))<=>((funny(alice)<~>old(alice))))&
(![X]:((happy(X)<~>~tall(X))<=>(~humble(X)<~>~quiet(X))))&
(((patient(paul)<~>~calm(paul)))=>(?[X]:((~creative(X)|old(X)))))&
(![X]:((~creative(X)<~>~humble(X))<=>(patient(X)&~humble(X))))&
(![X]:(~rich(X)<=>(~patient(X)<~>~kind(X))))&
((~patient(lucy)<~>~generous(lucy)))&
(?[X]:((~humble(X)<~>humble(X))))&
((curious(alice)&~tall(alice)))&
(?[X]:(calm(X)))&
(?[X]:((~brave(X)<~>~quiet(X))))&
((~kind(lucy)<~>~rich(lucy)))&
(?[X]:((funny(X)|~generous(X)))) | ~happy(lucy) | [] | null | 0 |
Everyone who is either not old or not funny is patient and vice versa.
Everyone who is not old is not rich or not brave.
Everyone who is both not tall and rich is both rich and not tall and vice versa.
Everyone who is both strong and curious is both not brave and quiet.
Everyone who is both brave and creative is either brave or patient and vice versa.
Everyone who is kind or not kind is not funny and vice versa.
Everyone who is kind or not quiet is either not funny or not strong.
Everyone who is both not strong and kind is either not happy or not humble and vice versa.
If lucy is happy or tall then someone is both not wise and not humble.
If someone is either not tall or rich then john is generous or not calm.
Everyone who is both not brave and not quiet is wise or not kind.
Everyone who is both not quiet and wise is not kind or not quiet and vice versa.
Everyone who is strong is generous or wise and vice versa.
Everyone who is not kind is either humble or creative and vice versa.
If someone is both happy and not old then someone is humble or not wise.
Everyone who is kind is not old or not happy and vice versa.
Someone is both not patient and creative.
Paul is either not brave or patient.
Someone is curious or generous.
Someone is patient or not brave.
Someone is both patient and calm.
Mary is not kind.
Someone is either not creative or not rich.
Someone is either not brave or kind. | John is not creative. | neutral | (![X]:((~old(X)<~>~funny(X))<=>patient(X)))&
(![X]:(~old(X)=>(~rich(X)|~brave(X))))&
(![X]:((~tall(X)&rich(X))<=>(rich(X)&~tall(X))))&
(![X]:((strong(X)&curious(X))=>(~brave(X)&quiet(X))))&
(![X]:((brave(X)&creative(X))<=>(brave(X)<~>patient(X))))&
(![X]:((kind(X)|~kind(X))<=>~funny(X)))&
(![X]:((kind(X)|~quiet(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((~strong(X)&kind(X))<=>(~happy(X)<~>~humble(X))))&
(((happy(lucy)|tall(lucy)))=>(?[X]:((~wise(X)&~humble(X)))))&
((?[X]:((~tall(X)<~>rich(X))))=>((generous(john)|~calm(john))))&
(![X]:((~brave(X)&~quiet(X))=>(wise(X)|~kind(X))))&
(![X]:((~quiet(X)&wise(X))<=>(~kind(X)|~quiet(X))))&
(![X]:(strong(X)<=>(generous(X)|wise(X))))&
(![X]:(~kind(X)<=>(humble(X)<~>creative(X))))&
((?[X]:((happy(X)&~old(X))))=>(?[X]:((humble(X)|~wise(X)))))&
(![X]:(kind(X)<=>(~old(X)|~happy(X))))&
(?[X]:((~patient(X)&creative(X))))&
((~brave(paul)<~>patient(paul)))&
(?[X]:((curious(X)|generous(X))))&
(?[X]:((patient(X)|~brave(X))))&
(?[X]:((patient(X)&calm(X))))&
(~kind(mary))&
(?[X]:((~creative(X)<~>~rich(X))))&
(?[X]:((~brave(X)<~>kind(X)))) | ~creative(john) | [] | null | 0 |
If lucy is either not humble or not curious then alice is either quiet or strong and vice versa.
If fred is calm then lucy is either not curious or calm and vice versa.
Everyone who is old or tall is both tall and quiet and vice versa.
If lucy is happy then susan is both not strong and curious.
Everyone who is brave is happy and vice versa.
If someone is either quiet or not creative then alice is rich or not old.
Everyone who is both not humble and generous is either not creative or calm.
Everyone who is not humble is either not quiet or wise and vice versa.
Everyone who is generous is both not generous and funny and vice versa.
Everyone who is humble or calm is wise or not humble.
If someone is curious or not strong then someone is both humble and strong.
If susan is not patient or humble then mary is not creative or creative.
Everyone who is both wise and not old is not tall or kind and vice versa.
Everyone who is old or not humble is rich or not creative and vice versa.
Everyone who is either not curious or funny is not patient or curious and vice versa.
Everyone who is either rich or funny is both not strong and tall.
Someone is not quiet or funny.
Someone is not curious.
Someone is creative.
John is either quiet or calm.
Someone is not curious or not old.
Alice is both not tall and not kind. | Lucy is old. | neutral | (((~humble(lucy)<~>~curious(lucy)))<=>((quiet(alice)<~>strong(alice))))&
((calm(fred))<=>((~curious(lucy)<~>calm(lucy))))&
(![X]:((old(X)|tall(X))<=>(tall(X)&quiet(X))))&
((happy(lucy))=>((~strong(susan)&curious(susan))))&
(![X]:(brave(X)<=>happy(X)))&
((?[X]:((quiet(X)<~>~creative(X))))=>((rich(alice)|~old(alice))))&
(![X]:((~humble(X)&generous(X))=>(~creative(X)<~>calm(X))))&
(![X]:(~humble(X)<=>(~quiet(X)<~>wise(X))))&
(![X]:(generous(X)<=>(~generous(X)&funny(X))))&
(![X]:((humble(X)|calm(X))=>(wise(X)|~humble(X))))&
((?[X]:((curious(X)|~strong(X))))=>(?[X]:((humble(X)&strong(X)))))&
(((~patient(susan)|humble(susan)))=>((~creative(mary)|creative(mary))))&
(![X]:((wise(X)&~old(X))<=>(~tall(X)|kind(X))))&
(![X]:((old(X)|~humble(X))<=>(rich(X)|~creative(X))))&
(![X]:((~curious(X)<~>funny(X))<=>(~patient(X)|curious(X))))&
(![X]:((rich(X)<~>funny(X))=>(~strong(X)&tall(X))))&
(?[X]:((~quiet(X)|funny(X))))&
(?[X]:(~curious(X)))&
(?[X]:(creative(X)))&
((quiet(john)<~>calm(john)))&
(?[X]:((~curious(X)|~old(X))))&
((~tall(alice)&~kind(alice))) | old(lucy) | [] | null | 0 |
Everyone who is not brave or patient is rich or not wise and vice versa.
If susan is kind or not curious then someone is not humble.
Everyone who is either strong or rich is either strong or tall.
If lucy is both generous and not tall then someone is calm or not humble.
Everyone who is either not wise or not happy is calm and vice versa.
Everyone who is both brave and generous is both not rich and tall and vice versa.
Everyone who is either strong or tall is both brave and kind and vice versa.
If mary is either not quiet or not calm then someone is both creative and generous and vice versa.
If alice is brave or not calm then fred is both funny and brave.
Everyone who is not happy or not curious is both creative and brave and vice versa.
If someone is calm then john is both tall and kind and vice versa.
Everyone who is both wise and not strong is humble or not kind and vice versa.
If someone is both quiet and humble then someone is either old or not brave.
If someone is curious then john is both not funny and tall.
If john is either old or quiet then mary is both not brave and not funny and vice versa.
If john is brave then susan is both not rich and not patient and vice versa.
Alice is both not patient and quiet.
Mary is not rich.
Someone is tall.
Someone is not humble.
Fred is both humble and kind.
Someone is both patient and happy.
Someone is not calm or not humble.
Susan is either not happy or not generous. | Alice is rich. | neutral | (![X]:((~brave(X)|patient(X))<=>(rich(X)|~wise(X))))&
(((kind(susan)|~curious(susan)))=>(?[X]:(~humble(X))))&
(![X]:((strong(X)<~>rich(X))=>(strong(X)<~>tall(X))))&
(((generous(lucy)&~tall(lucy)))=>(?[X]:((calm(X)|~humble(X)))))&
(![X]:((~wise(X)<~>~happy(X))<=>calm(X)))&
(![X]:((brave(X)&generous(X))<=>(~rich(X)&tall(X))))&
(![X]:((strong(X)<~>tall(X))<=>(brave(X)&kind(X))))&
(((~quiet(mary)<~>~calm(mary)))<=>(?[X]:((creative(X)&generous(X)))))&
(((brave(alice)|~calm(alice)))=>((funny(fred)&brave(fred))))&
(![X]:((~happy(X)|~curious(X))<=>(creative(X)&brave(X))))&
((?[X]:(calm(X)))<=>((tall(john)&kind(john))))&
(![X]:((wise(X)&~strong(X))<=>(humble(X)|~kind(X))))&
((?[X]:((quiet(X)&humble(X))))=>(?[X]:((old(X)<~>~brave(X)))))&
((?[X]:(curious(X)))=>((~funny(john)&tall(john))))&
(((old(john)<~>quiet(john)))<=>((~brave(mary)&~funny(mary))))&
((brave(john))<=>((~rich(susan)&~patient(susan))))&
((~patient(alice)&quiet(alice)))&
(~rich(mary))&
(?[X]:(tall(X)))&
(?[X]:(~humble(X)))&
((humble(fred)&kind(fred)))&
(?[X]:((patient(X)&happy(X))))&
(?[X]:((~calm(X)|~humble(X))))&
((~happy(susan)<~>~generous(susan))) | rich(alice) | [] | null | 0 |
Everyone who is creative or not patient is either rich or not tall and vice versa.
If susan is not kind or calm then someone is either not strong or not calm and vice versa.
Everyone who is not generous is generous.
Everyone who is not humble is rich or patient.
If someone is rich then someone is old or not rich.
If someone is both humble and calm then paul is not kind or not brave.
If someone is either brave or not generous then someone is either creative or not brave and vice versa.
If john is not rich then someone is not old or not creative and vice versa.
Everyone who is both kind and calm is both curious and not wise.
Everyone who is both not humble and not generous is not calm.
Everyone who is not happy or funny is not brave or not kind and vice versa.
If susan is both generous and not wise then fred is either old or strong.
If susan is either not generous or humble then someone is not rich or not wise.
Everyone who is not creative is not kind or not patient and vice versa.
If someone is brave then alice is either creative or not patient and vice versa.
Fred is not rich.
John is either not funny or generous.
Someone is kind or not old.
Someone is either quiet or not funny.
Lucy is either tall or not happy.
John is either calm or not strong.
Someone is either funny or tall.
Paul is either not tall or old. | Paul is not generous. | contradiction | (![X]:((creative(X)|~patient(X))<=>(rich(X)<~>~tall(X))))&
(((~kind(susan)|calm(susan)))<=>(?[X]:((~strong(X)<~>~calm(X)))))&
(![X]:(~generous(X)=>generous(X)))&
(![X]:(~humble(X)=>(rich(X)|patient(X))))&
((?[X]:(rich(X)))=>(?[X]:((old(X)|~rich(X)))))&
((?[X]:((humble(X)&calm(X))))=>((~kind(paul)|~brave(paul))))&
((?[X]:((brave(X)<~>~generous(X))))<=>(?[X]:((creative(X)<~>~brave(X)))))&
((~rich(john))<=>(?[X]:((~old(X)|~creative(X)))))&
(![X]:((kind(X)&calm(X))=>(curious(X)&~wise(X))))&
(![X]:((~humble(X)&~generous(X))=>~calm(X)))&
(![X]:((~happy(X)|funny(X))<=>(~brave(X)|~kind(X))))&
(((generous(susan)&~wise(susan)))=>((old(fred)<~>strong(fred))))&
(((~generous(susan)<~>humble(susan)))=>(?[X]:((~rich(X)|~wise(X)))))&
(![X]:(~creative(X)<=>(~kind(X)|~patient(X))))&
((?[X]:(brave(X)))<=>((creative(alice)<~>~patient(alice))))&
(~rich(fred))&
((~funny(john)<~>generous(john)))&
(?[X]:((kind(X)|~old(X))))&
(?[X]:((quiet(X)<~>~funny(X))))&
((tall(lucy)<~>~happy(lucy)))&
((calm(john)<~>~strong(john)))&
(?[X]:((funny(X)<~>tall(X))))&
((~tall(paul)<~>old(paul))) | ~generous(paul) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 7458055965017818596471467
% SZS output start Proof for 7458055965017818596471467
3. ! [X0] : (~generous(X0) => generous(X0)) [input p2]
24. ~generous(paul) [input hypothesis]
28. ! [X0] : (generous(X0) | generous(X0)) [ennf transformation 3]
96. generous(X0) | generous(X0) [cnf transformation 28]
142. ~generous(paul) [cnf transformation 24]
143. generous(X0) [duplicate literal removal 96]
353. $false [subsumption resolution 142,143]
% SZS output end Proof for 7458055965017818596471467
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and generous is both rich and not creative and vice versa.
Everyone who is creative or not curious is both not humble and not kind.
If someone is curious or not quiet then someone is not kind.
Everyone who is wise is both curious and creative.
If mary is happy or not quiet then someone is both not old and old.
If someone is both not wise and not calm then john is either not wise or curious.
If someone is not quiet or humble then lucy is both tall and not patient and vice versa.
Everyone who is calm or brave is strong.
Everyone who is both not rich and rich is either not creative or not tall and vice versa.
If lucy is quiet or not rich then fred is strong and vice versa.
If lucy is either creative or brave then susan is humble.
If john is not curious or patient then someone is rich and vice versa.
Everyone who is not kind or not old is both not wise and happy.
If paul is funny or not creative then fred is either not brave or generous and vice versa.
Everyone who is brave is rich or not calm and vice versa.
Everyone who is wise is both happy and not rich and vice versa.
Alice is either creative or not creative.
Lucy is not tall or not rich.
Alice is either wise or tall.
John is either brave or curious.
Someone is brave or wise.
Someone is both kind and not patient.
Fred is calm or curious. | Lucy is curious. | entailment | (![X]:((wise(X)&generous(X))<=>(rich(X)&~creative(X))))&
(![X]:((creative(X)|~curious(X))=>(~humble(X)&~kind(X))))&
((?[X]:((curious(X)|~quiet(X))))=>(?[X]:(~kind(X))))&
(![X]:(wise(X)=>(curious(X)&creative(X))))&
(((happy(mary)|~quiet(mary)))=>(?[X]:((~old(X)&old(X)))))&
((?[X]:((~wise(X)&~calm(X))))=>((~wise(john)<~>curious(john))))&
((?[X]:((~quiet(X)|humble(X))))<=>((tall(lucy)&~patient(lucy))))&
(![X]:((calm(X)|brave(X))=>strong(X)))&
(![X]:((~rich(X)&rich(X))<=>(~creative(X)<~>~tall(X))))&
(((quiet(lucy)|~rich(lucy)))<=>(strong(fred)))&
(((creative(lucy)<~>brave(lucy)))=>(humble(susan)))&
(((~curious(john)|patient(john)))<=>(?[X]:(rich(X))))&
(![X]:((~kind(X)|~old(X))=>(~wise(X)&happy(X))))&
(((funny(paul)|~creative(paul)))<=>((~brave(fred)<~>generous(fred))))&
(![X]:(brave(X)<=>(rich(X)|~calm(X))))&
(![X]:(wise(X)<=>(happy(X)&~rich(X))))&
((creative(alice)<~>~creative(alice)))&
((~tall(lucy)|~rich(lucy)))&
((wise(alice)<~>tall(alice)))&
((brave(john)<~>curious(john)))&
(?[X]:((brave(X)|wise(X))))&
(?[X]:((kind(X)&~patient(X))))&
((calm(fred)|curious(fred))) | curious(lucy) | [
"p0",
"p1",
"p3",
"p8",
"p12",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5666936322979445674471126
% SZS output start Proof for 5666936322979445674471126
1. ! [X0] : ((generous(X0) & wise(X0)) <=> (~creative(X0) & rich(X0))) [input p0]
2. ! [X0] : ((~curious(X0) | creative(X0)) => (~kind(X0) & ~humble(X0))) [input p1]
4. ! [X0] : (wise(X0) => (creative(X0) & curious(X0))) [input p3]
9. ! [X0] : ((rich(X0) & ~rich(X0)) <=> (~creative(X0) <~> ~tall(X0))) [input p8]
13. ! [X0] : ((~old(X0) | ~kind(X0)) => (happy(X0) & ~wise(X0))) [input p12]
16. ! [X0] : (wise(X0) <=> (~rich(X0) & happy(X0))) [input p15]
18. ~rich(lucy) | ~tall(lucy) [input p17]
24. ~curious(lucy) [input hypothesis]
26. ! [X0] : ((~kind(X0) & ~humble(X0)) | (curious(X0) & ~creative(X0))) [ennf transformation 2]
28. ! [X0] : ((creative(X0) & curious(X0)) | ~wise(X0)) [ennf transformation 4]
33. ! [X0] : ((happy(X0) & ~wise(X0)) | (old(X0) & kind(X0))) [ennf transformation 13]
34. ! [X0] : (((generous(X0) & wise(X0)) | (creative(X0) | ~rich(X0))) & ((~creative(X0) & rich(X0)) | (~generous(X0) | ~wise(X0)))) [nnf transformation 1]
35. ! [X0] : (((generous(X0) & wise(X0)) | creative(X0) | ~rich(X0)) & ((~creative(X0) & rich(X0)) | ~generous(X0) | ~wise(X0))) [flattening 34]
47. ! [X0] : (((rich(X0) & ~rich(X0)) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0)))) & (((tall(X0) | creative(X0)) & (~tall(X0) | ~creative(X0))) | (~rich(X0) | rich(X0)))) [nnf transformation 9]
48. ! [X0] : (((rich(X0) & ~rich(X0)) | ((~creative(X0) | tall(X0)) & (~tall(X0) | creative(X0)))) & (((tall(X0) | creative(X0)) & (~tall(X0) | ~creative(X0))) | ~rich(X0) | rich(X0))) [flattening 47]
61. ! [X0] : ((wise(X0) | (rich(X0) | ~happy(X0))) & ((~rich(X0) & happy(X0)) | ~wise(X0))) [nnf transformation 16]
62. ! [X0] : ((wise(X0) | rich(X0) | ~happy(X0)) & ((~rich(X0) & happy(X0)) | ~wise(X0))) [flattening 61]
72. ~rich(X0) | creative(X0) | wise(X0) [cnf transformation 35]
77. ~kind(X0) | curious(X0) [cnf transformation 26]
80. ~wise(X0) | curious(X0) [cnf transformation 28]
98. ~rich(X0) | ~creative(X0) | tall(X0) [cnf transformation 48]
100. ~creative(X0) | rich(X0) | tall(X0) [cnf transformation 48]
109. ~wise(X0) | kind(X0) [cnf transformation 33]
111. happy(X0) | kind(X0) [cnf transformation 33]
124. ~happy(X0) | rich(X0) | wise(X0) [cnf transformation 62]
127. ~rich(lucy) | ~tall(lucy) [cnf transformation 18]
136. ~curious(lucy) [cnf transformation 24]
178. 10 <=> tall(lucy) [avatar definition]
201. ~creative(X0) | tall(X0) [subsumption resolution 98,100]
212. 17 <=> rich(lucy) [avatar definition]
213. rich(lucy) <- (17) [avatar component clause 212]
223. 19 <=> creative(lucy) [avatar definition]
224. ~creative(lucy) <- (~19) [avatar component clause 223]
225. creative(lucy) <- (19) [avatar component clause 223]
268. ~10 | ~17 [avatar split clause 127,212,178]
332. tall(lucy) <- (19) [resolution 225,201]
337. 35 <=> wise(lucy) [avatar definition]
338. wise(lucy) <- (35) [avatar component clause 337]
339. ~wise(lucy) <- (~35) [avatar component clause 337]
354. rich(X0) | wise(X0) | kind(X0) [resolution 124,111]
368. kind(X0) | rich(X0) [subsumption resolution 354,109]
424. curious(lucy) <- (35) [resolution 338,80]
425. $false <- (35) [subsumption resolution 424,136]
426. ~35 [avatar contradiction clause 425]
464. curious(X0) | rich(X0) [resolution 368,77]
487. rich(lucy) [resolution 464,136]
491. 10 | ~19 [avatar split clause 332,223,178]
492. 17 [avatar split clause 487,212]
498. creative(lucy) | wise(lucy) <- (17) [resolution 213,72]
504. wise(lucy) <- (17, ~19) [subsumption resolution 498,224]
505. $false <- (17, ~19, ~35) [subsumption resolution 504,339]
506. ~17 | 19 | 35 [avatar contradiction clause 505]
509. $false [avatar sat refutation 268,426,491,492,506]
% SZS output end Proof for 5666936322979445674471126
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong then john is either kind or not calm.
Everyone who is either not patient or not funny is either not funny or strong.
Everyone who is both not curious and not brave is either not strong or curious.
If mary is patient then paul is not generous or wise and vice versa.
Everyone who is both not kind and generous is both tall and not calm and vice versa.
If lucy is both not calm and not curious then alice is not old or humble and vice versa.
If fred is either not humble or calm then someone is either not funny or not generous.
Everyone who is quiet or not strong is both not rich and calm.
If fred is both not creative and generous then someone is either not rich or not generous and vice versa.
If lucy is both old and creative then someone is humble or rich.
Everyone who is not brave is not creative and vice versa.
If paul is not tall or not curious then fred is not creative and vice versa.
Everyone who is strong or calm is either not patient or wise and vice versa.
If someone is wise then someone is both happy and quiet and vice versa.
Everyone who is not creative is both brave and humble and vice versa.
Everyone who is either strong or not patient is not rich and vice versa.
Susan is rich.
Paul is kind.
Susan is calm or not curious.
Susan is not quiet or happy.
Someone is quiet.
Susan is both not happy and not patient.
John is not curious or not wise. | John is quiet. | neutral | ((strong(john))=>((kind(john)<~>~calm(john))))&
(![X]:((~patient(X)<~>~funny(X))=>(~funny(X)<~>strong(X))))&
(![X]:((~curious(X)&~brave(X))=>(~strong(X)<~>curious(X))))&
((patient(mary))<=>((~generous(paul)|wise(paul))))&
(![X]:((~kind(X)&generous(X))<=>(tall(X)&~calm(X))))&
(((~calm(lucy)&~curious(lucy)))<=>((~old(alice)|humble(alice))))&
(((~humble(fred)<~>calm(fred)))=>(?[X]:((~funny(X)<~>~generous(X)))))&
(![X]:((quiet(X)|~strong(X))=>(~rich(X)&calm(X))))&
(((~creative(fred)&generous(fred)))<=>(?[X]:((~rich(X)<~>~generous(X)))))&
(((old(lucy)&creative(lucy)))=>(?[X]:((humble(X)|rich(X)))))&
(![X]:(~brave(X)<=>~creative(X)))&
(((~tall(paul)|~curious(paul)))<=>(~creative(fred)))&
(![X]:((strong(X)|calm(X))<=>(~patient(X)<~>wise(X))))&
((?[X]:(wise(X)))<=>(?[X]:((happy(X)&quiet(X)))))&
(![X]:(~creative(X)<=>(brave(X)&humble(X))))&
(![X]:((strong(X)<~>~patient(X))<=>~rich(X)))&
(rich(susan))&
(kind(paul))&
((calm(susan)|~curious(susan)))&
((~quiet(susan)|happy(susan)))&
(?[X]:(quiet(X)))&
((~happy(susan)&~patient(susan)))&
((~curious(john)|~wise(john))) | quiet(john) | [] | null | 0 |
If lucy is both not patient and not funny then someone is wise and vice versa.
If susan is either not happy or not wise then susan is brave or not rich and vice versa.
Everyone who is brave or old is both not tall and rich.
If alice is not brave or not rich then mary is quiet.
Everyone who is both patient and not tall is not brave or rich and vice versa.
Everyone who is quiet is not old or not happy and vice versa.
If paul is humble or patient then someone is both not generous and humble and vice versa.
If alice is old then someone is curious or not quiet and vice versa.
Everyone who is not patient is old.
If susan is both tall and not creative then someone is either not strong or humble and vice versa.
Everyone who is not patient is both not humble and patient.
If lucy is old or curious then fred is old or not generous and vice versa.
If someone is not creative then mary is both not patient and not quiet and vice versa.
Everyone who is patient or not funny is either not old or not patient and vice versa.
If john is both rich and not old then john is not wise or tall and vice versa.
Everyone who is both not quiet and not calm is both not generous and not quiet.
Someone is happy or not curious.
John is not wise.
Someone is not old or tall.
Susan is either not old or not patient.
Mary is not curious. | John is rich. | entailment | (((~patient(lucy)&~funny(lucy)))<=>(?[X]:(wise(X))))&
(((~happy(susan)<~>~wise(susan)))<=>((brave(susan)|~rich(susan))))&
(![X]:((brave(X)|old(X))=>(~tall(X)&rich(X))))&
(((~brave(alice)|~rich(alice)))=>(quiet(mary)))&
(![X]:((patient(X)&~tall(X))<=>(~brave(X)|rich(X))))&
(![X]:(quiet(X)<=>(~old(X)|~happy(X))))&
(((humble(paul)|patient(paul)))<=>(?[X]:((~generous(X)&humble(X)))))&
((old(alice))<=>(?[X]:((curious(X)|~quiet(X)))))&
(![X]:(~patient(X)=>old(X)))&
(((tall(susan)&~creative(susan)))<=>(?[X]:((~strong(X)<~>humble(X)))))&
(![X]:(~patient(X)=>(~humble(X)&patient(X))))&
(((old(lucy)|curious(lucy)))<=>((old(fred)|~generous(fred))))&
((?[X]:(~creative(X)))<=>((~patient(mary)&~quiet(mary))))&
(![X]:((patient(X)|~funny(X))<=>(~old(X)<~>~patient(X))))&
(((rich(john)&~old(john)))<=>((~wise(john)|tall(john))))&
(![X]:((~quiet(X)&~calm(X))=>(~generous(X)&~quiet(X))))&
(?[X]:((happy(X)|~curious(X))))&
(~wise(john))&
(?[X]:((~old(X)|tall(X))))&
((~old(susan)<~>~patient(susan)))&
(~curious(mary)) | rich(john) | [
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8319360895695787265475566
% SZS output start Proof for 8319360895695787265475566
15. (~old(john) & rich(john)) <=> (tall(john) | ~wise(john)) [input p14]
18. ~wise(john) [input p17]
22. ~rich(john) [input hypothesis]
62. ((~old(john) & rich(john)) | (~tall(john) & wise(john))) & ((tall(john) | ~wise(john)) | (old(john) | ~rich(john))) [nnf transformation 15]
63. ((~old(john) & rich(john)) | (~tall(john) & wise(john))) & (tall(john) | ~wise(john) | old(john) | ~rich(john)) [flattening 62]
123. rich(john) | wise(john) [cnf transformation 63]
128. ~wise(john) [cnf transformation 18]
133. ~rich(john) [cnf transformation 22]
282. 30 <=> wise(john) [avatar definition]
286. 31 <=> rich(john) [avatar definition]
289. 30 | 31 [avatar split clause 123,286,282]
302. ~30 [avatar split clause 128,282]
303. ~31 [avatar split clause 133,286]
304. $false [avatar sat refutation 289,302,303]
% SZS output end Proof for 8319360895695787265475566
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not curious and not brave then susan is both happy and funny and vice versa.
If susan is either calm or not wise then someone is either happy or brave.
Everyone who is both not brave and quiet is both brave and not tall.
If someone is both not funny and quiet then john is either not creative or happy.
If someone is both not calm and calm then susan is strong.
Everyone who is either not creative or patient is kind and vice versa.
Everyone who is not rich is both not rich and not creative and vice versa.
If lucy is either not humble or not quiet then fred is both not funny and not rich and vice versa.
Everyone who is both not humble and not happy is not creative.
If john is both quiet and not rich then someone is not quiet and vice versa.
Everyone who is not tall is either brave or patient.
Everyone who is humble or wise is not patient.
Everyone who is both not patient and not kind is either not rich or funny.
If alice is both strong and not generous then someone is either not quiet or tall.
If fred is both happy and funny then someone is funny or not wise.
If lucy is wise or patient then john is both humble and happy.
Mary is both rich and not patient.
Susan is old.
Fred is not creative or not brave.
Lucy is rich or not tall.
Alice is both wise and not kind.
Paul is either not rich or not creative.
Paul is both happy and not brave.
Alice is old. | John is creative. | contradiction | ((?[X]:((~curious(X)&~brave(X))))<=>((happy(susan)&funny(susan))))&
(((calm(susan)<~>~wise(susan)))=>(?[X]:((happy(X)<~>brave(X)))))&
(![X]:((~brave(X)&quiet(X))=>(brave(X)&~tall(X))))&
((?[X]:((~funny(X)&quiet(X))))=>((~creative(john)<~>happy(john))))&
((?[X]:((~calm(X)&calm(X))))=>(strong(susan)))&
(![X]:((~creative(X)<~>patient(X))<=>kind(X)))&
(![X]:(~rich(X)<=>(~rich(X)&~creative(X))))&
(((~humble(lucy)<~>~quiet(lucy)))<=>((~funny(fred)&~rich(fred))))&
(![X]:((~humble(X)&~happy(X))=>~creative(X)))&
(((quiet(john)&~rich(john)))<=>(?[X]:(~quiet(X))))&
(![X]:(~tall(X)=>(brave(X)<~>patient(X))))&
(![X]:((humble(X)|wise(X))=>~patient(X)))&
(![X]:((~patient(X)&~kind(X))=>(~rich(X)<~>funny(X))))&
(((strong(alice)&~generous(alice)))=>(?[X]:((~quiet(X)<~>tall(X)))))&
(((happy(fred)&funny(fred)))=>(?[X]:((funny(X)|~wise(X)))))&
(((wise(lucy)|patient(lucy)))=>((humble(john)&happy(john))))&
((rich(mary)&~patient(mary)))&
(old(susan))&
((~creative(fred)|~brave(fred)))&
((rich(lucy)|~tall(lucy)))&
((wise(alice)&~kind(alice)))&
((~rich(paul)<~>~creative(paul)))&
((happy(paul)&~brave(paul)))&
(old(alice)) | creative(john) | [
"p2",
"p6",
"p9",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 739195667555682525168295
% SZS output start Proof for 739195667555682525168295
3. ! [X0] : ((quiet(X0) & ~brave(X0)) => (~tall(X0) & brave(X0))) [input p2]
7. ! [X0] : (~rich(X0) <=> (~creative(X0) & ~rich(X0))) [input p6]
10. (~rich(john) & quiet(john)) <=> ? [X0] : ~quiet(X0) [input p9]
23. ~brave(paul) & happy(paul) [input p22]
25. creative(john) [input hypothesis]
31. ! [X0] : ((~tall(X0) & brave(X0)) | (~quiet(X0) | brave(X0))) [ennf transformation 3]
32. ! [X0] : ((~tall(X0) & brave(X0)) | ~quiet(X0) | brave(X0)) [flattening 31]
53. ! [X0] : ((~rich(X0) | (creative(X0) | rich(X0))) & ((~creative(X0) & ~rich(X0)) | rich(X0))) [nnf transformation 7]
54. ! [X0] : ((~rich(X0) | creative(X0) | rich(X0)) & ((~creative(X0) & ~rich(X0)) | rich(X0))) [flattening 53]
57. ((~rich(john) & quiet(john)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | (rich(john) | ~quiet(john))) [nnf transformation 10]
58. ((~rich(john) & quiet(john)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | rich(john) | ~quiet(john)) [flattening 57]
59. ((~rich(john) & quiet(john)) | ! [X0] : quiet(X0)) & (? [X1] : ~quiet(X1) | rich(john) | ~quiet(john)) [rectify 58]
60. ? [X1] : ~quiet(X1) => ~quiet(sK2) [choice axiom]
61. ((~rich(john) & quiet(john)) | ! [X0] : quiet(X0)) & (~quiet(sK2) | rich(john) | ~quiet(john)) [skolemisation 59,60]
75. brave(X0) | ~quiet(X0) | brave(X0) [cnf transformation 32]
84. ~creative(X0) | rich(X0) [cnf transformation 54]
95. ~rich(john) | quiet(X0) [cnf transformation 61]
116. ~brave(paul) [cnf transformation 23]
117. creative(john) [cnf transformation 25]
118. ~quiet(X0) | brave(X0) [duplicate literal removal 75]
166. 11 <=> creative(john) [avatar definition]
168. creative(john) <- (11) [avatar component clause 166]
198. 17 <=> ! [X0] : quiet(X0) [avatar definition]
199. quiet(X0) <- (17) [avatar component clause 198]
201. 18 <=> rich(john) [avatar definition]
204. 17 | ~18 [avatar split clause 95,201,198]
264. 11 [avatar split clause 117,166]
272. rich(john) <- (11) [resolution 84,168]
275. 18 | ~11 [avatar split clause 272,166,201]
276. brave(X0) <- (17) [resolution 118,199]
280. $false <- (17) [resolution 276,116]
281. ~17 [avatar contradiction clause 280]
282. $false [avatar sat refutation 204,264,275,281]
% SZS output end Proof for 739195667555682525168295
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is either quiet or not humble. If someone is not quiet then someone is both rich and not wise and vice versa. Everyone who is both humble and not happy is funny. If fred is curious or calm then fred is both not happy and not funny. Everyone who is both not patient and not wise is not rich. If someone is wise then paul is not generous or strong and vice versa. Everyone who is either not strong or not patient is both not rich and not calm and vice versa. If someone is both creative and rich then someone is either not humble or brave and vice versa. Everyone who is not generous or happy is not happy and vice versa. Everyone who is not creative is either not strong or creative. Everyone who is patient or calm is not humble. If fred is either not quiet or kind then someone is not rich. Everyone who is either not patient or not strong is either kind or not tall. Everyone who is both not curious and not brave is not generous and vice versa. If paul is both not tall and old then susan is either quiet or not calm and vice versa. If someone is both happy and not rich then someone is tall or not patient. Someone is either not calm or curious. Paul is funny or calm. Someone is either creative or humble. Someone is happy or not brave. Someone is not brave. John is both funny and calm. Someone is either not calm or quiet. Someone is not old. | Fred is not funny. | neutral | (![X]:(rich(X)=>(quiet(X)<~>~humble(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((rich(X)&~wise(X)))))&
(![X]:((humble(X)&~happy(X))=>funny(X)))&
(((curious(fred)|calm(fred)))=>((~happy(fred)&~funny(fred))))&
(![X]:((~patient(X)&~wise(X))=>~rich(X)))&
((?[X]:(wise(X)))<=>((~generous(paul)|strong(paul))))&
(![X]:((~strong(X)<~>~patient(X))<=>(~rich(X)&~calm(X))))&
((?[X]:((creative(X)&rich(X))))<=>(?[X]:((~humble(X)<~>brave(X)))))&
(![X]:((~generous(X)|happy(X))<=>~happy(X)))&
(![X]:(~creative(X)=>(~strong(X)<~>creative(X))))&
(![X]:((patient(X)|calm(X))=>~humble(X)))&
(((~quiet(fred)<~>kind(fred)))=>(?[X]:(~rich(X))))&
(![X]:((~patient(X)<~>~strong(X))=>(kind(X)<~>~tall(X))))&
(![X]:((~curious(X)&~brave(X))<=>~generous(X)))&
(((~tall(paul)&old(paul)))<=>((quiet(susan)<~>~calm(susan))))&
((?[X]:((happy(X)&~rich(X))))=>(?[X]:((tall(X)|~patient(X)))))&
(?[X]:((~calm(X)<~>curious(X))))&
((funny(paul)|calm(paul)))&
(?[X]:((creative(X)<~>humble(X))))&
(?[X]:((happy(X)|~brave(X))))&
(?[X]:(~brave(X)))&
((funny(john)&calm(john)))&
(?[X]:((~calm(X)<~>quiet(X))))&
(?[X]:(~old(X))) | ~funny(fred) | [] | null | 0 |
Everyone who is both not creative and not wise is not generous. Everyone who is not patient is both not patient and not brave and vice versa. Everyone who is kind or curious is either not creative or not patient. Everyone who is either not rich or old is either not tall or brave. Everyone who is either rich or not calm is either not calm or not curious and vice versa. Everyone who is both wise and brave is not patient and vice versa. If fred is not kind or not quiet then susan is either strong or quiet and vice versa. If susan is not quiet or not brave then mary is not patient or funny. If susan is not humble then someone is not calm or not wise and vice versa. If someone is not old or not wise then someone is either kind or generous. If susan is humble or not quiet then paul is either humble or not patient and vice versa. Everyone who is both wise and old is both not curious and calm. Everyone who is both not quiet and not patient is rich or not curious and vice versa. Everyone who is humble is either not quiet or kind and vice versa. If paul is either creative or not tall then someone is both not old and brave. Everyone who is either not calm or not creative is not funny or curious. Paul is not quiet or calm. Someone is not calm. Someone is not rich or wise. Fred is calm or not patient. Susan is either old or wise. Mary is not old. | Mary is kind. | neutral | (![X]:((~creative(X)&~wise(X))=>~generous(X)))&
(![X]:(~patient(X)<=>(~patient(X)&~brave(X))))&
(![X]:((kind(X)|curious(X))=>(~creative(X)<~>~patient(X))))&
(![X]:((~rich(X)<~>old(X))=>(~tall(X)<~>brave(X))))&
(![X]:((rich(X)<~>~calm(X))<=>(~calm(X)<~>~curious(X))))&
(![X]:((wise(X)&brave(X))<=>~patient(X)))&
(((~kind(fred)|~quiet(fred)))<=>((strong(susan)<~>quiet(susan))))&
(((~quiet(susan)|~brave(susan)))=>((~patient(mary)|funny(mary))))&
((~humble(susan))<=>(?[X]:((~calm(X)|~wise(X)))))&
((?[X]:((~old(X)|~wise(X))))=>(?[X]:((kind(X)<~>generous(X)))))&
(((humble(susan)|~quiet(susan)))<=>((humble(paul)<~>~patient(paul))))&
(![X]:((wise(X)&old(X))=>(~curious(X)&calm(X))))&
(![X]:((~quiet(X)&~patient(X))<=>(rich(X)|~curious(X))))&
(![X]:(humble(X)<=>(~quiet(X)<~>kind(X))))&
(((creative(paul)<~>~tall(paul)))=>(?[X]:((~old(X)&brave(X)))))&
(![X]:((~calm(X)<~>~creative(X))=>(~funny(X)|curious(X))))&
((~quiet(paul)|calm(paul)))&
(?[X]:(~calm(X)))&
(?[X]:((~rich(X)|wise(X))))&
((calm(fred)|~patient(fred)))&
((old(susan)<~>wise(susan)))&
(~old(mary)) | kind(mary) | [] | null | 0 |
If someone is either patient or tall then fred is either not old or not funny and vice versa.
Everyone who is both brave and not wise is not creative or curious and vice versa.
If mary is either tall or not generous then lucy is both happy and not strong and vice versa.
Everyone who is not quiet or tall is both quiet and not kind.
Everyone who is not tall or generous is not kind or not wise.
If susan is not kind then someone is old or not old and vice versa.
Everyone who is both strong and kind is not quiet and vice versa.
If someone is both curious and not patient then susan is both brave and not brave and vice versa.
Everyone who is strong is old or not calm.
If someone is either not wise or not generous then someone is happy or strong and vice versa.
If someone is brave then someone is either not creative or calm and vice versa.
If lucy is both not wise and not rich then susan is either happy or brave and vice versa.
Everyone who is either wise or strong is both patient and brave.
If paul is not generous or not brave then mary is not brave.
Everyone who is both not curious and not old is calm and vice versa.
Everyone who is rich is either curious or not strong.
Someone is either not rich or happy.
Someone is both not rich and not wise.
Alice is not patient or not humble.
Someone is both kind and funny.
Someone is either not old or curious.
Alice is both old and humble.
Alice is not tall. | Mary is quiet. | entailment | ((?[X]:((patient(X)<~>tall(X))))<=>((~old(fred)<~>~funny(fred))))&
(![X]:((brave(X)&~wise(X))<=>(~creative(X)|curious(X))))&
(((tall(mary)<~>~generous(mary)))<=>((happy(lucy)&~strong(lucy))))&
(![X]:((~quiet(X)|tall(X))=>(quiet(X)&~kind(X))))&
(![X]:((~tall(X)|generous(X))=>(~kind(X)|~wise(X))))&
((~kind(susan))<=>(?[X]:((old(X)|~old(X)))))&
(![X]:((strong(X)&kind(X))<=>~quiet(X)))&
((?[X]:((curious(X)&~patient(X))))<=>((brave(susan)&~brave(susan))))&
(![X]:(strong(X)=>(old(X)|~calm(X))))&
((?[X]:((~wise(X)<~>~generous(X))))<=>(?[X]:((happy(X)|strong(X)))))&
((?[X]:(brave(X)))<=>(?[X]:((~creative(X)<~>calm(X)))))&
(((~wise(lucy)&~rich(lucy)))<=>((happy(susan)<~>brave(susan))))&
(![X]:((wise(X)<~>strong(X))=>(patient(X)&brave(X))))&
(((~generous(paul)|~brave(paul)))=>(~brave(mary)))&
(![X]:((~curious(X)&~old(X))<=>calm(X)))&
(![X]:(rich(X)=>(curious(X)<~>~strong(X))))&
(?[X]:((~rich(X)<~>happy(X))))&
(?[X]:((~rich(X)&~wise(X))))&
((~patient(alice)|~humble(alice)))&
(?[X]:((kind(X)&funny(X))))&
(?[X]:((~old(X)<~>curious(X))))&
((old(alice)&humble(alice)))&
(~tall(alice)) | quiet(mary) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 10808093905695059909939
% SZS output start Proof for 10808093905695059909939
4. ! [X0] : ((tall(X0) | ~quiet(X0)) => (~kind(X0) & quiet(X0))) [input p3]
24. ~quiet(mary) [input hypothesis]
27. ! [X0] : ((~kind(X0) & quiet(X0)) | (~tall(X0) & quiet(X0))) [ennf transformation 4]
99. quiet(X0) | quiet(X0) [cnf transformation 27]
155. ~quiet(mary) [cnf transformation 24]
156. quiet(X0) [duplicate literal removal 99]
353. $false [subsumption resolution 155,156]
% SZS output end Proof for 10808093905695059909939
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is either calm or funny then someone is both not tall and patient and vice versa. If susan is not rich or not quiet then someone is either tall or quiet and vice versa. Everyone who is not rich or funny is rich. If lucy is not calm then mary is quiet. Everyone who is not happy or not tall is either curious or not curious and vice versa. Everyone who is either not kind or not quiet is both not calm and not tall and vice versa. If someone is funny or not brave then someone is both not quiet and not happy. Everyone who is not brave or wise is curious. Everyone who is funny or not funny is both patient and brave. If someone is both funny and quiet then fred is not funny or not brave and vice versa. If mary is both strong and calm then paul is humble. Everyone who is humble is calm or funny. Everyone who is not brave is wise or happy. If someone is either creative or happy then alice is both happy and generous. If fred is both not kind and not humble then someone is not generous. Paul is not happy or tall. Lucy is happy or not patient. Someone is both not curious and old. Someone is both not generous and creative. Alice is both rich and not happy. Someone is curious or not funny. Someone is both not wise and strong. John is rich or calm. | Lucy is not creative. | contradiction | (((calm(john)<~>funny(john)))<=>(?[X]:((~tall(X)&patient(X)))))&
(((~rich(susan)|~quiet(susan)))<=>(?[X]:((tall(X)<~>quiet(X)))))&
(![X]:((~rich(X)|funny(X))=>rich(X)))&
((~calm(lucy))=>(quiet(mary)))&
(![X]:((~happy(X)|~tall(X))<=>(curious(X)<~>~curious(X))))&
(![X]:((~kind(X)<~>~quiet(X))<=>(~calm(X)&~tall(X))))&
((?[X]:((funny(X)|~brave(X))))=>(?[X]:((~quiet(X)&~happy(X)))))&
(![X]:((~brave(X)|wise(X))=>curious(X)))&
(![X]:((funny(X)|~funny(X))=>(patient(X)&brave(X))))&
((?[X]:((funny(X)&quiet(X))))<=>((~funny(fred)|~brave(fred))))&
(((strong(mary)&calm(mary)))=>(humble(paul)))&
(![X]:(humble(X)=>(calm(X)|funny(X))))&
(![X]:(~brave(X)=>(wise(X)|happy(X))))&
((?[X]:((creative(X)<~>happy(X))))=>((happy(alice)&generous(alice))))&
(((~kind(fred)&~humble(fred)))=>(?[X]:(~generous(X))))&
((~happy(paul)|tall(paul)))&
((happy(lucy)|~patient(lucy)))&
(?[X]:((~curious(X)&old(X))))&
(?[X]:((~generous(X)&creative(X))))&
((rich(alice)&~happy(alice)))&
(?[X]:((curious(X)|~funny(X))))&
(?[X]:((~wise(X)&strong(X))))&
((rich(john)|calm(john))) | ~creative(lucy) | [
"p8",
"p13",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4730886940208411717858129
% SZS output start Proof for 4730886940208411717858129
9. ! [X0] : ((~funny(X0) | funny(X0)) => (brave(X0) & patient(X0))) [input p8]
14. ? [X0] : (creative(X0) <~> happy(X0)) => (generous(alice) & happy(alice)) [input p13]
17. ~patient(lucy) | happy(lucy) [input p16]
20. ~happy(alice) & rich(alice) [input p19]
24. ~creative(lucy) [input hypothesis]
31. ! [X0] : ((brave(X0) & patient(X0)) | (funny(X0) & ~funny(X0))) [ennf transformation 9]
38. (generous(alice) & happy(alice)) | ! [X0] : (creative(X0) <=> happy(X0)) [ennf transformation 14]
62. (generous(alice) & happy(alice)) | ! [X0] : ((creative(X0) | ~happy(X0)) & (happy(X0) | ~creative(X0))) [nnf transformation 38]
106. patient(X0) | ~funny(X0) [cnf transformation 31]
107. patient(X0) | funny(X0) [cnf transformation 31]
119. happy(alice) | creative(X0) | ~happy(X0) [cnf transformation 62]
124. ~patient(lucy) | happy(lucy) [cnf transformation 17]
129. ~happy(alice) [cnf transformation 20]
134. ~creative(lucy) [cnf transformation 24]
221. patient(X0) [subsumption resolution 106,107]
260. 26 <=> ! [X0] : (creative(X0) | ~happy(X0)) [avatar definition]
261. ~happy(X0) | creative(X0) <- (26) [avatar component clause 260]
272. 29 <=> happy(alice) [avatar definition]
275. 26 | 29 [avatar split clause 119,272,260]
291. happy(lucy) [subsumption resolution 124,221]
292. ~29 [avatar split clause 129,272]
313. creative(lucy) <- (26) [resolution 261,291]
314. $false <- (26) [subsumption resolution 313,134]
315. ~26 [avatar contradiction clause 314]
316. $false [avatar sat refutation 275,292,315]
% SZS output end Proof for 4730886940208411717858129
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or wise is not funny.
Everyone who is patient or not humble is generous or not curious and vice versa.
Everyone who is either not humble or not curious is old or not wise and vice versa.
If someone is both not calm and not brave then someone is either generous or calm and vice versa.
If alice is rich or generous then mary is both curious and not quiet.
Everyone who is not rich is not generous or kind and vice versa.
Everyone who is patient is both wise and not funny.
Everyone who is either quiet or wise is either patient or tall.
If alice is either funny or not patient then someone is not old and vice versa.
If mary is not creative or kind then mary is both patient and brave.
Everyone who is both not tall and not humble is either happy or not wise.
If someone is either generous or not tall then lucy is both not patient and generous and vice versa.
If someone is both old and not creative then susan is both not curious and not patient.
If lucy is generous or creative then alice is either calm or generous.
Everyone who is either not old or not happy is either not tall or old and vice versa.
Everyone who is either calm or not patient is not rich or tall.
Someone is either strong or not wise.
John is both not curious and happy.
Someone is not calm.
Alice is both creative and not quiet.
Alice is not wise or rich.
Mary is humble or not creative.
Alice is not curious. | Alice is tall. | entailment | (![X]:((kind(X)<~>wise(X))=>~funny(X)))&
(![X]:((patient(X)|~humble(X))<=>(generous(X)|~curious(X))))&
(![X]:((~humble(X)<~>~curious(X))<=>(old(X)|~wise(X))))&
((?[X]:((~calm(X)&~brave(X))))<=>(?[X]:((generous(X)<~>calm(X)))))&
(((rich(alice)|generous(alice)))=>((curious(mary)&~quiet(mary))))&
(![X]:(~rich(X)<=>(~generous(X)|kind(X))))&
(![X]:(patient(X)=>(wise(X)&~funny(X))))&
(![X]:((quiet(X)<~>wise(X))=>(patient(X)<~>tall(X))))&
(((funny(alice)<~>~patient(alice)))<=>(?[X]:(~old(X))))&
(((~creative(mary)|kind(mary)))=>((patient(mary)&brave(mary))))&
(![X]:((~tall(X)&~humble(X))=>(happy(X)<~>~wise(X))))&
((?[X]:((generous(X)<~>~tall(X))))<=>((~patient(lucy)&generous(lucy))))&
((?[X]:((old(X)&~creative(X))))=>((~curious(susan)&~patient(susan))))&
(((generous(lucy)|creative(lucy)))=>((calm(alice)<~>generous(alice))))&
(![X]:((~old(X)<~>~happy(X))<=>(~tall(X)<~>old(X))))&
(![X]:((calm(X)<~>~patient(X))=>(~rich(X)|tall(X))))&
(?[X]:((strong(X)<~>~wise(X))))&
((~curious(john)&happy(john)))&
(?[X]:(~calm(X)))&
((creative(alice)&~quiet(alice)))&
((~wise(alice)|rich(alice)))&
((humble(mary)|~creative(mary)))&
(~curious(alice)) | tall(alice) | [
"p1",
"p2",
"p4",
"p6",
"p7",
"p8",
"p12",
"p19",
"p20",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3281120964551875871554624
% SZS output start Proof for 3281120964551875871554624
2. ! [X0] : ((~humble(X0) | patient(X0)) <=> (~curious(X0) | generous(X0))) [input p1]
3. ! [X0] : ((~humble(X0) <~> ~curious(X0)) <=> (~wise(X0) | old(X0))) [input p2]
5. (generous(alice) | rich(alice)) => (~quiet(mary) & curious(mary)) [input p4]
7. ! [X0] : (patient(X0) => (~funny(X0) & wise(X0))) [input p6]
8. ! [X0] : ((quiet(X0) <~> wise(X0)) => (patient(X0) <~> tall(X0))) [input p7]
9. (funny(alice) <~> ~patient(alice)) <=> ? [X0] : ~old(X0) [input p8]
13. ? [X0] : (~creative(X0) & old(X0)) => (~patient(susan) & ~curious(susan)) [input p12]
20. ~quiet(alice) & creative(alice) [input p19]
21. rich(alice) | ~wise(alice) [input p20]
22. ~creative(mary) | humble(mary) [input p21]
23. ~curious(alice) [input p22]
24. ~tall(alice) [input hypothesis]
27. (~quiet(mary) & curious(mary)) | (~generous(alice) & ~rich(alice)) [ennf transformation 5]
28. ! [X0] : ((~funny(X0) & wise(X0)) | ~patient(X0)) [ennf transformation 7]
29. ! [X0] : ((patient(X0) <~> tall(X0)) | (quiet(X0) <=> wise(X0))) [ennf transformation 8]
33. (~patient(susan) & ~curious(susan)) | ! [X0] : (creative(X0) | ~old(X0)) [ennf transformation 13]
38. ! [X0] : (((~humble(X0) | patient(X0)) | (curious(X0) & ~generous(X0))) & ((~curious(X0) | generous(X0)) | (humble(X0) & ~patient(X0)))) [nnf transformation 2]
39. ! [X0] : ((~humble(X0) | patient(X0) | (curious(X0) & ~generous(X0))) & (~curious(X0) | generous(X0) | (humble(X0) & ~patient(X0)))) [flattening 38]
40. ! [X0] : ((((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) | (wise(X0) & ~old(X0))) & ((~wise(X0) | old(X0)) | ((~humble(X0) | curious(X0)) & (~curious(X0) | humble(X0))))) [nnf transformation 3]
41. ! [X0] : ((((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) | (wise(X0) & ~old(X0))) & (~wise(X0) | old(X0) | ((~humble(X0) | curious(X0)) & (~curious(X0) | humble(X0))))) [flattening 40]
49. ! [X0] : (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0)))) [nnf transformation 29]
50. (((patient(alice) | ~funny(alice)) & (~patient(alice) | funny(alice))) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | ((funny(alice) | patient(alice)) & (~patient(alice) | ~funny(alice)))) [nnf transformation 9]
51. (((patient(alice) | ~funny(alice)) & (~patient(alice) | funny(alice))) | ! [X0] : old(X0)) & (? [X1] : ~old(X1) | ((funny(alice) | patient(alice)) & (~patient(alice) | ~funny(alice)))) [rectify 50]
52. ? [X1] : ~old(X1) => ~old(sK2) [choice axiom]
53. (((patient(alice) | ~funny(alice)) & (~patient(alice) | funny(alice))) | ! [X0] : old(X0)) & (~old(sK2) | ((funny(alice) | patient(alice)) & (~patient(alice) | ~funny(alice)))) [skolemisation 51,52]
73. ~humble(X0) | patient(X0) | curious(X0) [cnf transformation 39]
76. ~old(X0) | ~humble(X0) | ~curious(X0) [cnf transformation 41]
78. ~old(X0) | humble(X0) | curious(X0) [cnf transformation 41]
79. curious(X0) | humble(X0) | wise(X0) [cnf transformation 41]
86. curious(mary) | ~rich(alice) [cnf transformation 27]
93. ~patient(X0) | wise(X0) [cnf transformation 28]
94. ~patient(X0) | ~funny(X0) [cnf transformation 28]
96. ~wise(X0) | patient(X0) | quiet(X0) | tall(X0) [cnf transformation 49]
101. ~patient(alice) | funny(alice) | old(X0) [cnf transformation 53]
115. ~curious(susan) | creative(X0) | ~old(X0) [cnf transformation 33]
116. ~patient(susan) | creative(X0) | ~old(X0) [cnf transformation 33]
137. ~quiet(alice) [cnf transformation 20]
138. rich(alice) | ~wise(alice) [cnf transformation 21]
139. ~creative(mary) | humble(mary) [cnf transformation 22]
140. ~curious(alice) [cnf transformation 23]
141. ~tall(alice) [cnf transformation 24]
187. 10 <=> rich(alice) [avatar definition]
192. 11 <=> curious(mary) [avatar definition]
194. curious(mary) <- (11) [avatar component clause 192]
196. ~10 | 11 [avatar split clause 86,192,187]
201. 12 <=> ! [X0] : old(X0) [avatar definition]
202. old(X0) <- (12) [avatar component clause 201]
208. ~patient(alice) | old(X0) [subsumption resolution 101,94]
210. 14 <=> patient(alice) [avatar definition]
211. patient(alice) <- (14) [avatar component clause 210]
212. ~patient(alice) <- (~14) [avatar component clause 210]
213. 12 | ~14 [avatar split clause 208,210,201]
229. 18 <=> creative(mary) [avatar definition]
230. ~creative(mary) <- (~18) [avatar component clause 229]
268. 26 <=> ! [X0] : (creative(X0) | ~old(X0)) [avatar definition]
269. ~old(X0) | creative(X0) <- (26) [avatar component clause 268]
271. 27 <=> patient(susan) [avatar definition]
273. ~patient(susan) <- (~27) [avatar component clause 271]
274. 26 | ~27 [avatar split clause 116,271,268]
276. 28 <=> curious(susan) [avatar definition]
278. ~curious(susan) <- (~28) [avatar component clause 276]
279. 26 | ~28 [avatar split clause 115,276,268]
305. 33 <=> wise(alice) [avatar definition]
306. wise(alice) <- (33) [avatar component clause 305]
307. ~wise(alice) <- (~33) [avatar component clause 305]
308. ~33 | 10 [avatar split clause 138,187,305]
310. 34 <=> humble(mary) [avatar definition]
312. humble(mary) <- (34) [avatar component clause 310]
313. 34 | ~18 [avatar split clause 139,229,310]
343. humble(alice) | wise(alice) [resolution 79,140]
356. 38 <=> humble(susan) [avatar definition]
358. humble(susan) <- (38) [avatar component clause 356]
369. humble(alice) <- (~33) [subsumption resolution 343,307]
395. patient(alice) | curious(alice) <- (~33) [resolution 369,73]
396. curious(alice) <- (~14, ~33) [subsumption resolution 395,212]
397. $false <- (~14, ~33) [subsumption resolution 396,140]
398. 14 | 33 [avatar contradiction clause 397]
480. curious(X1) | humble(X1) <- (12) [resolution 202,78]
481. ~curious(X2) | ~humble(X2) <- (12) [resolution 202,76]
483. wise(alice) <- (14) [resolution 211,93]
486. 33 | ~14 [avatar split clause 483,210,305]
503. patient(alice) | quiet(alice) | tall(alice) <- (33) [resolution 96,306]
558. humble(susan) <- (12, ~28) [resolution 480,278]
562. 38 | ~12 | 28 [avatar split clause 558,276,201,356]
586. ~humble(mary) <- (11, 12) [resolution 481,194]
588. $false <- (11, 12, 34) [subsumption resolution 586,312]
589. ~11 | ~12 | ~34 [avatar contradiction clause 588]
597. patient(alice) | tall(alice) <- (33) [subsumption resolution 503,137]
598. patient(alice) <- (33) [subsumption resolution 597,141]
599. 14 | ~33 [avatar split clause 598,305,210]
613. creative(X0) <- (12, 26) [resolution 202,269]
634. $false <- (12, ~18, 26) [resolution 613,230]
635. ~12 | 18 | ~26 [avatar contradiction clause 634]
638. patient(susan) | curious(susan) <- (38) [resolution 358,73]
639. curious(susan) <- (~27, 38) [subsumption resolution 638,273]
640. $false <- (~27, ~28, 38) [subsumption resolution 639,278]
641. 27 | 28 | ~38 [avatar contradiction clause 640]
642. $false [avatar sat refutation 196,213,274,279,308,313,398,486,562,589,599,635,641]
% SZS output end Proof for 3281120964551875871554624
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or not patient is old or generous and vice versa.
If lucy is either not old or not happy then paul is either calm or tall and vice versa.
If someone is not calm or quiet then someone is either not curious or not quiet and vice versa.
Everyone who is generous or quiet is not humble.
Everyone who is not strong is both humble and calm and vice versa.
If paul is both not calm and brave then lucy is kind and vice versa.
If paul is tall or not funny then mary is tall or brave.
Everyone who is curious or not creative is not rich.
Everyone who is either not happy or wise is happy and vice versa.
Everyone who is both not happy and quiet is not quiet or not humble and vice versa.
If fred is both not tall and generous then someone is patient or wise and vice versa.
If alice is curious or not generous then paul is both not tall and strong.
If alice is not generous then alice is either not creative or tall and vice versa.
Everyone who is either rich or old is quiet.
If mary is not brave then someone is not wise.
Everyone who is either not tall or not kind is not brave or quiet.
Mary is not generous or generous.
Someone is wise.
Someone is either not humble or not wise.
John is quiet.
Lucy is calm or strong.
Someone is not strong or not creative.
Paul is not generous. | Alice is not old. | neutral | (![X]:((~humble(X)|~patient(X))<=>(old(X)|generous(X))))&
(((~old(lucy)<~>~happy(lucy)))<=>((calm(paul)<~>tall(paul))))&
((?[X]:((~calm(X)|quiet(X))))<=>(?[X]:((~curious(X)<~>~quiet(X)))))&
(![X]:((generous(X)|quiet(X))=>~humble(X)))&
(![X]:(~strong(X)<=>(humble(X)&calm(X))))&
(((~calm(paul)&brave(paul)))<=>(kind(lucy)))&
(((tall(paul)|~funny(paul)))=>((tall(mary)|brave(mary))))&
(![X]:((curious(X)|~creative(X))=>~rich(X)))&
(![X]:((~happy(X)<~>wise(X))<=>happy(X)))&
(![X]:((~happy(X)&quiet(X))<=>(~quiet(X)|~humble(X))))&
(((~tall(fred)&generous(fred)))<=>(?[X]:((patient(X)|wise(X)))))&
(((curious(alice)|~generous(alice)))=>((~tall(paul)&strong(paul))))&
((~generous(alice))<=>((~creative(alice)<~>tall(alice))))&
(![X]:((rich(X)<~>old(X))=>quiet(X)))&
((~brave(mary))=>(?[X]:(~wise(X))))&
(![X]:((~tall(X)<~>~kind(X))=>(~brave(X)|quiet(X))))&
((~generous(mary)|generous(mary)))&
(?[X]:(wise(X)))&
(?[X]:((~humble(X)<~>~wise(X))))&
(quiet(john))&
((calm(lucy)|strong(lucy)))&
(?[X]:((~strong(X)|~creative(X))))&
(~generous(paul)) | ~old(alice) | [] | null | 0 |
Everyone who is both humble and not rich is both quiet and not humble. If someone is both not calm and humble then lucy is not calm or generous and vice versa. Everyone who is patient or tall is happy or not old and vice versa. Everyone who is either not quiet or old is either curious or not kind. If john is not humble or not wise then someone is either not brave or not kind. Everyone who is kind or not generous is either curious or not tall and vice versa. If paul is both brave and humble then someone is funny or strong. If someone is both curious and wise then someone is not kind and vice versa. Everyone who is patient is quiet or strong and vice versa. Everyone who is not patient is both not rich and creative. If someone is either generous or strong then someone is both not quiet and not generous and vice versa. If susan is funny then susan is calm. If someone is not tall or generous then someone is not humble or kind and vice versa. If someone is both not patient and not funny then someone is both rich and curious. Everyone who is either kind or not strong is not patient. Everyone who is strong is happy. John is calm or not tall. Someone is both not creative and quiet. John is both not tall and humble. Mary is happy. Paul is both generous and not happy. Lucy is both not quiet and rich. Fred is not old or not brave. Someone is either not generous or not funny. | John is not tall. | entailment | (![X]:((humble(X)&~rich(X))=>(quiet(X)&~humble(X))))&
((?[X]:((~calm(X)&humble(X))))<=>((~calm(lucy)|generous(lucy))))&
(![X]:((patient(X)|tall(X))<=>(happy(X)|~old(X))))&
(![X]:((~quiet(X)<~>old(X))=>(curious(X)<~>~kind(X))))&
(((~humble(john)|~wise(john)))=>(?[X]:((~brave(X)<~>~kind(X)))))&
(![X]:((kind(X)|~generous(X))<=>(curious(X)<~>~tall(X))))&
(((brave(paul)&humble(paul)))=>(?[X]:((funny(X)|strong(X)))))&
((?[X]:((curious(X)&wise(X))))<=>(?[X]:(~kind(X))))&
(![X]:(patient(X)<=>(quiet(X)|strong(X))))&
(![X]:(~patient(X)=>(~rich(X)&creative(X))))&
((?[X]:((generous(X)<~>strong(X))))<=>(?[X]:((~quiet(X)&~generous(X)))))&
((funny(susan))=>(calm(susan)))&
((?[X]:((~tall(X)|generous(X))))<=>(?[X]:((~humble(X)|kind(X)))))&
((?[X]:((~patient(X)&~funny(X))))=>(?[X]:((rich(X)&curious(X)))))&
(![X]:((kind(X)<~>~strong(X))=>~patient(X)))&
(![X]:(strong(X)=>happy(X)))&
((calm(john)|~tall(john)))&
(?[X]:((~creative(X)&quiet(X))))&
((~tall(john)&humble(john)))&
(happy(mary))&
((generous(paul)&~happy(paul)))&
((~quiet(lucy)&rich(lucy)))&
((~old(fred)|~brave(fred)))&
(?[X]:((~generous(X)<~>~funny(X)))) | ~tall(john) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 74924678009486352471398
% SZS output start Proof for 74924678009486352471398
19. humble(john) & ~tall(john) [input p18]
25. tall(john) [input hypothesis]
135. ~tall(john) [cnf transformation 19]
145. tall(john) [cnf transformation 25]
320. 40 <=> tall(john) [avatar definition]
325. ~40 [avatar split clause 135,320]
345. 40 [avatar split clause 145,320]
346. $false [avatar sat refutation 325,345]
% SZS output end Proof for 74924678009486352471398
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is brave or not curious and vice versa. Everyone who is both happy and not creative is not generous or not funny and vice versa. If someone is not creative then lucy is not old or not brave and vice versa. Everyone who is tall or generous is both not quiet and kind. Everyone who is not funny or calm is not quiet. If paul is not quiet then susan is happy or not kind and vice versa. If lucy is either humble or not humble then alice is not generous and vice versa. Everyone who is either tall or not creative is both tall and not rich. If someone is either not rich or not tall then lucy is either not humble or rich. Everyone who is strong or calm is calm and vice versa. Everyone who is either not brave or not patient is both not humble and not strong. Everyone who is either generous or strong is not calm or quiet and vice versa. If someone is either strong or not wise then someone is not kind or curious and vice versa. If someone is both old and not tall then paul is not patient or not brave. If mary is both not strong and happy then lucy is either not old or calm. Everyone who is either not kind or not funny is both funny and not old. Someone is both not generous and not old. Someone is either curious or old. Someone is both creative and generous. Lucy is not patient or not rich. Someone is not humble. Someone is either not strong or kind. John is curious. Alice is not wise or happy. | Susan is not happy. | contradiction | (![X]:(patient(X)<=>(brave(X)|~curious(X))))&
(![X]:((happy(X)&~creative(X))<=>(~generous(X)|~funny(X))))&
((?[X]:(~creative(X)))<=>((~old(lucy)|~brave(lucy))))&
(![X]:((tall(X)|generous(X))=>(~quiet(X)&kind(X))))&
(![X]:((~funny(X)|calm(X))=>~quiet(X)))&
((~quiet(paul))<=>((happy(susan)|~kind(susan))))&
(((humble(lucy)<~>~humble(lucy)))<=>(~generous(alice)))&
(![X]:((tall(X)<~>~creative(X))=>(tall(X)&~rich(X))))&
((?[X]:((~rich(X)<~>~tall(X))))=>((~humble(lucy)<~>rich(lucy))))&
(![X]:((strong(X)|calm(X))<=>calm(X)))&
(![X]:((~brave(X)<~>~patient(X))=>(~humble(X)&~strong(X))))&
(![X]:((generous(X)<~>strong(X))<=>(~calm(X)|quiet(X))))&
((?[X]:((strong(X)<~>~wise(X))))<=>(?[X]:((~kind(X)|curious(X)))))&
((?[X]:((old(X)&~tall(X))))=>((~patient(paul)|~brave(paul))))&
(((~strong(mary)&happy(mary)))=>((~old(lucy)<~>calm(lucy))))&
(![X]:((~kind(X)<~>~funny(X))=>(funny(X)&~old(X))))&
(?[X]:((~generous(X)&~old(X))))&
(?[X]:((curious(X)<~>old(X))))&
(?[X]:((creative(X)&generous(X))))&
((~patient(lucy)|~rich(lucy)))&
(?[X]:(~humble(X)))&
(?[X]:((~strong(X)<~>kind(X))))&
(curious(john))&
((~wise(alice)|happy(alice))) | ~happy(susan) | [
"p1",
"p3",
"p4",
"p5",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2997683280796962348869020
% SZS output start Proof for 2997683280796962348869020
2. ! [X0] : ((~creative(X0) & happy(X0)) <=> (~funny(X0) | ~generous(X0))) [input p1]
4. ! [X0] : ((generous(X0) | tall(X0)) => (kind(X0) & ~quiet(X0))) [input p3]
5. ! [X0] : ((calm(X0) | ~funny(X0)) => ~quiet(X0)) [input p4]
6. ~quiet(paul) <=> (~kind(susan) | happy(susan)) [input p5]
10. ! [X0] : ((calm(X0) | strong(X0)) <=> calm(X0)) [input p9]
12. ! [X0] : ((generous(X0) <~> strong(X0)) <=> (quiet(X0) | ~calm(X0))) [input p11]
25. ~happy(susan) [input hypothesis]
27. ! [X0] : ((kind(X0) & ~quiet(X0)) | (~generous(X0) & ~tall(X0))) [ennf transformation 4]
28. ! [X0] : (~quiet(X0) | (~calm(X0) & funny(X0))) [ennf transformation 5]
39. ! [X0] : (((~creative(X0) & happy(X0)) | (funny(X0) & generous(X0))) & ((~funny(X0) | ~generous(X0)) | (creative(X0) | ~happy(X0)))) [nnf transformation 2]
40. ! [X0] : (((~creative(X0) & happy(X0)) | (funny(X0) & generous(X0))) & (~funny(X0) | ~generous(X0) | creative(X0) | ~happy(X0))) [flattening 39]
46. (~quiet(paul) | (kind(susan) & ~happy(susan))) & ((~kind(susan) | happy(susan)) | quiet(paul)) [nnf transformation 6]
47. (~quiet(paul) | (kind(susan) & ~happy(susan))) & (~kind(susan) | happy(susan) | quiet(paul)) [flattening 46]
51. ! [X0] : (((calm(X0) | strong(X0)) | ~calm(X0)) & (calm(X0) | (~calm(X0) & ~strong(X0)))) [nnf transformation 10]
52. ! [X0] : ((calm(X0) | strong(X0) | ~calm(X0)) & (calm(X0) | (~calm(X0) & ~strong(X0)))) [flattening 51]
54. ! [X0] : ((((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | (~quiet(X0) & calm(X0))) & ((quiet(X0) | ~calm(X0)) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0))))) [nnf transformation 12]
55. ! [X0] : ((((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | (~quiet(X0) & calm(X0))) & (quiet(X0) | ~calm(X0) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0))))) [flattening 54]
79. generous(X0) | happy(X0) [cnf transformation 40]
87. ~quiet(X0) | ~generous(X0) [cnf transformation 27]
89. ~generous(X0) | kind(X0) [cnf transformation 27]
91. ~calm(X0) | ~quiet(X0) [cnf transformation 28]
92. ~kind(susan) | happy(susan) | quiet(paul) [cnf transformation 47]
107. ~strong(X0) | calm(X0) [cnf transformation 52]
116. strong(X0) | generous(X0) | calm(X0) [cnf transformation 55]
145. ~happy(susan) [cnf transformation 25]
169. 5 <=> kind(susan) [avatar definition]
170. ~kind(susan) <- (~5) [avatar component clause 169]
173. 6 <=> quiet(paul) [avatar definition]
174. quiet(paul) <- (6) [avatar component clause 173]
178. 7 <=> happy(susan) [avatar definition]
180. ~happy(susan) <- (~7) [avatar component clause 178]
182. 6 | 7 | ~5 [avatar split clause 92,169,178,173]
208. calm(X0) | generous(X0) [subsumption resolution 116,107]
302. ~7 [avatar split clause 145,178]
309. kind(X0) | happy(X0) [resolution 89,79]
312. generous(X0) | ~quiet(X0) [resolution 208,91]
313. ~quiet(X0) [subsumption resolution 312,87]
355. happy(susan) <- (~5) [resolution 309,170]
358. $false <- (~5, ~7) [subsumption resolution 355,180]
359. 5 | 7 [avatar contradiction clause 358]
360. $false <- (6) [subsumption resolution 174,313]
361. ~6 [avatar contradiction clause 360]
362. $false [avatar sat refutation 182,302,359,361]
% SZS output end Proof for 2997683280796962348869020
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not generous or not patient then someone is either not calm or calm.
If someone is either calm or funny then alice is tall and vice versa.
If fred is both not curious and not quiet then someone is strong or not rich.
Everyone who is both not brave and creative is both kind and not wise.
If alice is not happy then someone is not calm and vice versa.
Everyone who is both not happy and brave is both happy and kind.
Everyone who is both not calm and strong is generous and vice versa.
Everyone who is funny is either not curious or happy and vice versa.
Everyone who is calm is both strong and generous and vice versa.
Everyone who is not patient is both humble and not funny.
If lucy is happy then someone is funny or patient.
Everyone who is old or not kind is both old and not curious.
Everyone who is not calm or strong is either not wise or old and vice versa.
If fred is both not kind and kind then lucy is either creative or humble.
If fred is strong then paul is both not rich and not wise.
Paul is tall.
Someone is not rich or strong. | Paul is not patient. | neutral | ((?[X]:((~generous(X)<~>~patient(X))))=>(?[X]:((~calm(X)<~>calm(X)))))&
((?[X]:((calm(X)<~>funny(X))))<=>(tall(alice)))&
(((~curious(fred)&~quiet(fred)))=>(?[X]:((strong(X)|~rich(X)))))&
(![X]:((~brave(X)&creative(X))=>(kind(X)&~wise(X))))&
((~happy(alice))<=>(?[X]:(~calm(X))))&
(![X]:((~happy(X)&brave(X))=>(happy(X)&kind(X))))&
(![X]:((~calm(X)&strong(X))<=>generous(X)))&
(![X]:(funny(X)<=>(~curious(X)<~>happy(X))))&
(![X]:(calm(X)<=>(strong(X)&generous(X))))&
(![X]:(~patient(X)=>(humble(X)&~funny(X))))&
((happy(lucy))=>(?[X]:((funny(X)|patient(X)))))&
(![X]:((old(X)|~kind(X))=>(old(X)&~curious(X))))&
(![X]:((~calm(X)|strong(X))<=>(~wise(X)<~>old(X))))&
(((~kind(fred)&kind(fred)))=>((creative(lucy)<~>humble(lucy))))&
((strong(fred))=>((~rich(paul)&~wise(paul))))&
(tall(paul))&
(?[X]:((~rich(X)|strong(X)))) | ~patient(paul) | [] | null | 0 |
Everyone who is either generous or not wise is not kind. If john is either not brave or not calm then someone is kind. Everyone who is happy is not strong. If someone is either not creative or not quiet then someone is wise or tall. If someone is not brave then paul is both old and not humble. If mary is kind or not old then someone is either brave or not funny. If someone is generous or wise then someone is not generous and vice versa. If someone is either happy or not quiet then someone is not rich or not happy and vice versa. If fred is either not humble or not old then someone is either not old or not happy and vice versa. If someone is not humble or not patient then someone is not brave. If someone is happy or not happy then lucy is not humble or calm. If susan is either not rich or not old then lucy is both not brave and not kind and vice versa. If alice is creative then paul is either not patient or tall. If someone is wise then someone is both not generous and rich and vice versa. If someone is both not curious and not creative then someone is either not humble or rich. Everyone who is not quiet is old. Susan is kind. Mary is both rich and calm. Paul is either not generous or not calm. Someone is brave. Someone is both not creative and not happy. Someone is either quiet or not funny. Susan is not wise or not curious. Someone is either kind or not brave. | Susan is kind. | entailment | (![X]:((generous(X)<~>~wise(X))=>~kind(X)))&
(((~brave(john)<~>~calm(john)))=>(?[X]:(kind(X))))&
(![X]:(happy(X)=>~strong(X)))&
((?[X]:((~creative(X)<~>~quiet(X))))=>(?[X]:((wise(X)|tall(X)))))&
((?[X]:(~brave(X)))=>((old(paul)&~humble(paul))))&
(((kind(mary)|~old(mary)))=>(?[X]:((brave(X)<~>~funny(X)))))&
((?[X]:((generous(X)|wise(X))))<=>(?[X]:(~generous(X))))&
((?[X]:((happy(X)<~>~quiet(X))))<=>(?[X]:((~rich(X)|~happy(X)))))&
(((~humble(fred)<~>~old(fred)))<=>(?[X]:((~old(X)<~>~happy(X)))))&
((?[X]:((~humble(X)|~patient(X))))=>(?[X]:(~brave(X))))&
((?[X]:((happy(X)|~happy(X))))=>((~humble(lucy)|calm(lucy))))&
(((~rich(susan)<~>~old(susan)))<=>((~brave(lucy)&~kind(lucy))))&
((creative(alice))=>((~patient(paul)<~>tall(paul))))&
((?[X]:(wise(X)))<=>(?[X]:((~generous(X)&rich(X)))))&
((?[X]:((~curious(X)&~creative(X))))=>(?[X]:((~humble(X)<~>rich(X)))))&
(![X]:(~quiet(X)=>old(X)))&
(kind(susan))&
((rich(mary)&calm(mary)))&
((~generous(paul)<~>~calm(paul)))&
(?[X]:(brave(X)))&
(?[X]:((~creative(X)&~happy(X))))&
(?[X]:((quiet(X)<~>~funny(X))))&
((~wise(susan)|~curious(susan)))&
(?[X]:((kind(X)<~>~brave(X)))) | kind(susan) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5255159747466513623181628
% SZS output start Proof for 5255159747466513623181628
17. kind(susan) [input p16]
25. ~kind(susan) [input hypothesis]
142. kind(susan) [cnf transformation 17]
155. ~kind(susan) [cnf transformation 25]
438. $false [subsumption resolution 155,142]
% SZS output end Proof for 5255159747466513623181628
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not funny or not humble then someone is either not patient or patient.
If someone is patient or funny then lucy is not curious.
Everyone who is both not tall and not calm is both strong and curious.
If paul is not kind or brave then fred is not quiet or kind and vice versa.
If alice is either strong or funny then someone is both not rich and tall.
Everyone who is either happy or not calm is either rich or not calm.
Everyone who is not quiet or humble is calm and vice versa.
If someone is both not tall and creative then someone is either funny or calm and vice versa.
Everyone who is both not brave and quiet is either patient or not creative and vice versa.
If someone is not happy then susan is either not curious or not kind and vice versa.
Everyone who is strong is not calm or not strong and vice versa.
Everyone who is brave is not quiet and vice versa.
If someone is either not tall or not creative then susan is both not quiet and strong.
If paul is funny or calm then someone is not kind.
John is not kind.
Paul is rich or not creative.
Someone is tall or not wise.
Someone is either quiet or humble.
Mary is both not funny and not patient.
Someone is both strong and wise.
Susan is either not tall or brave. | Susan is not patient. | entailment | (((~funny(susan)|~humble(susan)))=>(?[X]:((~patient(X)<~>patient(X)))))&
((?[X]:((patient(X)|funny(X))))=>(~curious(lucy)))&
(![X]:((~tall(X)&~calm(X))=>(strong(X)&curious(X))))&
(((~kind(paul)|brave(paul)))<=>((~quiet(fred)|kind(fred))))&
(((strong(alice)<~>funny(alice)))=>(?[X]:((~rich(X)&tall(X)))))&
(![X]:((happy(X)<~>~calm(X))=>(rich(X)<~>~calm(X))))&
(![X]:((~quiet(X)|humble(X))<=>calm(X)))&
((?[X]:((~tall(X)&creative(X))))<=>(?[X]:((funny(X)<~>calm(X)))))&
(![X]:((~brave(X)&quiet(X))<=>(patient(X)<~>~creative(X))))&
((?[X]:(~happy(X)))<=>((~curious(susan)<~>~kind(susan))))&
(![X]:(strong(X)<=>(~calm(X)|~strong(X))))&
(![X]:(brave(X)<=>~quiet(X)))&
((?[X]:((~tall(X)<~>~creative(X))))=>((~quiet(susan)&strong(susan))))&
(((funny(paul)|calm(paul)))=>(?[X]:(~kind(X))))&
(~kind(john))&
((rich(paul)|~creative(paul)))&
(?[X]:((tall(X)|~wise(X))))&
(?[X]:((quiet(X)<~>humble(X))))&
((~funny(mary)&~patient(mary)))&
(?[X]:((strong(X)&wise(X))))&
((~tall(susan)<~>brave(susan))) | ~patient(susan) | [
"p6",
"p8",
"p10",
"p11",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7976692494704335026353799
% SZS output start Proof for 7976692494704335026353799
7. ! [X0] : ((humble(X0) | ~quiet(X0)) <=> calm(X0)) [input p6]
9. ! [X0] : ((quiet(X0) & ~brave(X0)) <=> (patient(X0) <~> ~creative(X0))) [input p8]
11. ! [X0] : (strong(X0) <=> (~strong(X0) | ~calm(X0))) [input p10]
12. ! [X0] : (brave(X0) <=> ~quiet(X0)) [input p11]
13. ? [X0] : (~tall(X0) <~> ~creative(X0)) => (strong(susan) & ~quiet(susan)) [input p12]
21. ~tall(susan) <~> brave(susan) [input p20]
22. patient(susan) [input hypothesis]
30. (strong(susan) & ~quiet(susan)) | ! [X0] : (~tall(X0) <=> ~creative(X0)) [ennf transformation 13]
41. ! [X0] : (((humble(X0) | ~quiet(X0)) | ~calm(X0)) & (calm(X0) | (~humble(X0) & quiet(X0)))) [nnf transformation 7]
42. ! [X0] : ((humble(X0) | ~quiet(X0) | ~calm(X0)) & (calm(X0) | (~humble(X0) & quiet(X0)))) [flattening 41]
48. ! [X0] : (((quiet(X0) & ~brave(X0)) | ((patient(X0) | creative(X0)) & (~creative(X0) | ~patient(X0)))) & (((creative(X0) | ~patient(X0)) & (~creative(X0) | patient(X0))) | (~quiet(X0) | brave(X0)))) [nnf transformation 9]
49. ! [X0] : (((quiet(X0) & ~brave(X0)) | ((patient(X0) | creative(X0)) & (~creative(X0) | ~patient(X0)))) & (((creative(X0) | ~patient(X0)) & (~creative(X0) | patient(X0))) | ~quiet(X0) | brave(X0))) [flattening 48]
54. ! [X0] : ((strong(X0) | (strong(X0) & calm(X0))) & ((~strong(X0) | ~calm(X0)) | ~strong(X0))) [nnf transformation 11]
55. ! [X0] : ((strong(X0) | (strong(X0) & calm(X0))) & (~strong(X0) | ~calm(X0) | ~strong(X0))) [flattening 54]
56. ! [X0] : ((brave(X0) | quiet(X0)) & (~quiet(X0) | ~brave(X0))) [nnf transformation 12]
57. (strong(susan) & ~quiet(susan)) | ! [X0] : ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))) [nnf transformation 30]
67. (~brave(susan) | tall(susan)) & (brave(susan) | ~tall(susan)) [nnf transformation 21]
88. quiet(X0) | calm(X0) [cnf transformation 42]
98. ~quiet(X0) | ~patient(X0) | creative(X0) | brave(X0) [cnf transformation 49]
107. ~strong(X0) | ~calm(X0) | ~strong(X0) [cnf transformation 55]
109. strong(X0) | strong(X0) [cnf transformation 55]
110. ~quiet(X0) | ~brave(X0) [cnf transformation 56]
111. quiet(X0) | brave(X0) [cnf transformation 56]
112. ~quiet(susan) | ~creative(X0) | tall(X0) [cnf transformation 57]
127. brave(susan) | ~tall(susan) [cnf transformation 67]
129. patient(susan) [cnf transformation 22]
130. ~strong(X0) | ~calm(X0) [duplicate literal removal 107]
131. strong(X0) [duplicate literal removal 109]
205. 16 <=> ! [X3] : (~creative(X3) | tall(X3)) [avatar definition]
206. ~creative(X3) | tall(X3) <- (16) [avatar component clause 205]
236. ~calm(X0) [subsumption resolution 130,131]
241. 24 <=> quiet(susan) [avatar definition]
243. ~quiet(susan) <- (~24) [avatar component clause 241]
245. 16 | ~24 [avatar split clause 112,241,205]
284. 33 <=> tall(susan) [avatar definition]
288. 34 <=> brave(susan) [avatar definition]
289. brave(susan) <- (34) [avatar component clause 288]
292. ~33 | 34 [avatar split clause 127,288,284]
296. calm(susan) <- (~24) [resolution 88,243]
299. $false <- (~24) [subsumption resolution 296,236]
300. 24 [avatar contradiction clause 299]
301. ~brave(X0) | calm(X0) [resolution 110,88]
305. ~brave(X0) [subsumption resolution 301,236]
390. ~patient(X0) | creative(X0) | brave(X0) | brave(X0) [resolution 98,111]
395. ~patient(X0) | creative(X0) | brave(X0) [duplicate literal removal 390]
396. ~patient(X0) | creative(X0) [subsumption resolution 395,305]
408. creative(susan) [resolution 396,129]
447. tall(susan) <- (16) [resolution 408,206]
450. 33 | ~16 [avatar split clause 447,205,284]
451. $false <- (34) [subsumption resolution 289,305]
452. ~34 [avatar contradiction clause 451]
453. $false [avatar sat refutation 245,292,300,450,452]
% SZS output end Proof for 7976692494704335026353799
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or not tall is both not creative and quiet.
Everyone who is not creative or curious is not brave and vice versa.
Everyone who is either brave or not patient is either creative or not strong and vice versa.
If someone is both creative and strong then someone is both not wise and calm and vice versa.
Everyone who is both not old and not funny is rich.
Everyone who is wise or not funny is both happy and generous and vice versa.
If someone is either curious or not strong then susan is both not creative and not old and vice versa.
Everyone who is not calm or curious is old.
Everyone who is not humble is both tall and not happy and vice versa.
Everyone who is not patient or wise is either creative or not brave and vice versa.
If someone is not rich then someone is either happy or not strong and vice versa.
Everyone who is not old is either wise or strong.
Everyone who is either creative or funny is not patient or calm.
If someone is either creative or brave then someone is tall and vice versa.
Everyone who is both kind and not happy is patient or not curious.
Everyone who is both calm and not brave is old and vice versa.
Mary is both not tall and not strong.
Someone is not quiet or not tall.
Lucy is not strong or not calm.
Paul is either not tall or strong. | Susan is generous. | entailment | (![X]:((patient(X)|~tall(X))=>(~creative(X)&quiet(X))))&
(![X]:((~creative(X)|curious(X))<=>~brave(X)))&
(![X]:((brave(X)<~>~patient(X))<=>(creative(X)<~>~strong(X))))&
((?[X]:((creative(X)&strong(X))))<=>(?[X]:((~wise(X)&calm(X)))))&
(![X]:((~old(X)&~funny(X))=>rich(X)))&
(![X]:((wise(X)|~funny(X))<=>(happy(X)&generous(X))))&
((?[X]:((curious(X)<~>~strong(X))))<=>((~creative(susan)&~old(susan))))&
(![X]:((~calm(X)|curious(X))=>old(X)))&
(![X]:(~humble(X)<=>(tall(X)&~happy(X))))&
(![X]:((~patient(X)|wise(X))<=>(creative(X)<~>~brave(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((happy(X)<~>~strong(X)))))&
(![X]:(~old(X)=>(wise(X)<~>strong(X))))&
(![X]:((creative(X)<~>funny(X))=>(~patient(X)|calm(X))))&
((?[X]:((creative(X)<~>brave(X))))<=>(?[X]:(tall(X))))&
(![X]:((kind(X)&~happy(X))=>(patient(X)|~curious(X))))&
(![X]:((calm(X)&~brave(X))<=>old(X)))&
((~tall(mary)&~strong(mary)))&
(?[X]:((~quiet(X)|~tall(X))))&
((~strong(lucy)|~calm(lucy)))&
((~tall(paul)<~>strong(paul))) | generous(susan) | [
"p0",
"p1",
"p3",
"p5",
"p7",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 728239575345431891167843
% SZS output start Proof for 728239575345431891167843
1. ! [X0] : ((~tall(X0) | patient(X0)) => (quiet(X0) & ~creative(X0))) [input p0]
2. ! [X0] : ((curious(X0) | ~creative(X0)) <=> ~brave(X0)) [input p1]
4. ? [X0] : (strong(X0) & creative(X0)) <=> ? [X0] : (calm(X0) & ~wise(X0)) [input p3]
6. ! [X0] : ((~funny(X0) | wise(X0)) <=> (generous(X0) & happy(X0))) [input p5]
8. ! [X0] : ((curious(X0) | ~calm(X0)) => old(X0)) [input p7]
10. ! [X0] : ((wise(X0) | ~patient(X0)) <=> (creative(X0) <~> ~brave(X0))) [input p9]
14. ? [X0] : (creative(X0) <~> brave(X0)) <=> ? [X0] : tall(X0) [input p13]
16. ! [X0] : ((~brave(X0) & calm(X0)) <=> old(X0)) [input p15]
21. ~generous(susan) [input hypothesis]
22. ? [X0] : (strong(X0) & creative(X0)) <=> ? [X1] : (calm(X1) & ~wise(X1)) [rectify 4]
24. ? [X0] : (creative(X0) <~> brave(X0)) <=> ? [X1] : tall(X1) [rectify 14]
26. ! [X0] : ((quiet(X0) & ~creative(X0)) | (tall(X0) & ~patient(X0))) [ennf transformation 1]
29. ! [X0] : (old(X0) | (~curious(X0) & calm(X0))) [ennf transformation 8]
33. ! [X0] : (((curious(X0) | ~creative(X0)) | brave(X0)) & (~brave(X0) | (~curious(X0) & creative(X0)))) [nnf transformation 2]
34. ! [X0] : ((curious(X0) | ~creative(X0) | brave(X0)) & (~brave(X0) | (~curious(X0) & creative(X0)))) [flattening 33]
36. (? [X0] : (strong(X0) & creative(X0)) | ! [X1] : (~calm(X1) | wise(X1))) & (? [X1] : (calm(X1) & ~wise(X1)) | ! [X0] : (~strong(X0) | ~creative(X0))) [nnf transformation 22]
37. (? [X0] : (strong(X0) & creative(X0)) | ! [X1] : (~calm(X1) | wise(X1))) & (? [X2] : (calm(X2) & ~wise(X2)) | ! [X3] : (~strong(X3) | ~creative(X3))) [rectify 36]
38. ? [X0] : (strong(X0) & creative(X0)) => (strong(sK0) & creative(sK0)) [choice axiom]
39. ? [X2] : (calm(X2) & ~wise(X2)) => (calm(sK1) & ~wise(sK1)) [choice axiom]
40. ((strong(sK0) & creative(sK0)) | ! [X1] : (~calm(X1) | wise(X1))) & ((calm(sK1) & ~wise(sK1)) | ! [X3] : (~strong(X3) | ~creative(X3))) [skolemisation 37,39,38]
41. ! [X0] : (((~funny(X0) | wise(X0)) | (~generous(X0) | ~happy(X0))) & ((generous(X0) & happy(X0)) | (funny(X0) & ~wise(X0)))) [nnf transformation 6]
42. ! [X0] : ((~funny(X0) | wise(X0) | ~generous(X0) | ~happy(X0)) & ((generous(X0) & happy(X0)) | (funny(X0) & ~wise(X0)))) [flattening 41]
48. ! [X0] : (((wise(X0) | ~patient(X0)) | ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0)))) & (((brave(X0) | ~creative(X0)) & (~brave(X0) | creative(X0))) | (~wise(X0) & patient(X0)))) [nnf transformation 10]
49. ! [X0] : ((wise(X0) | ~patient(X0) | ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0)))) & (((brave(X0) | ~creative(X0)) & (~brave(X0) | creative(X0))) | (~wise(X0) & patient(X0)))) [flattening 48]
57. (? [X0] : ((~brave(X0) | ~creative(X0)) & (brave(X0) | creative(X0))) | ! [X1] : ~tall(X1)) & (? [X1] : tall(X1) | ! [X0] : ((creative(X0) | ~brave(X0)) & (brave(X0) | ~creative(X0)))) [nnf transformation 24]
58. (? [X0] : ((~brave(X0) | ~creative(X0)) & (brave(X0) | creative(X0))) | ! [X1] : ~tall(X1)) & (? [X2] : tall(X2) | ! [X3] : ((creative(X3) | ~brave(X3)) & (brave(X3) | ~creative(X3)))) [rectify 57]
59. ? [X0] : ((~brave(X0) | ~creative(X0)) & (brave(X0) | creative(X0))) => ((~brave(sK5) | ~creative(sK5)) & (brave(sK5) | creative(sK5))) [choice axiom]
60. ? [X2] : tall(X2) => tall(sK6) [choice axiom]
61. (((~brave(sK5) | ~creative(sK5)) & (brave(sK5) | creative(sK5))) | ! [X1] : ~tall(X1)) & (tall(sK6) | ! [X3] : ((creative(X3) | ~brave(X3)) & (brave(X3) | ~creative(X3)))) [skolemisation 58,60,59]
62. ! [X0] : (((~brave(X0) & calm(X0)) | ~old(X0)) & (old(X0) | (brave(X0) | ~calm(X0)))) [nnf transformation 16]
63. ! [X0] : (((~brave(X0) & calm(X0)) | ~old(X0)) & (old(X0) | brave(X0) | ~calm(X0))) [flattening 62]
67. ~creative(X0) | ~patient(X0) [cnf transformation 26]
68. ~creative(X0) | tall(X0) [cnf transformation 26]
71. ~brave(X0) | creative(X0) [cnf transformation 34]
84. creative(sK0) | ~calm(X1) | wise(X1) [cnf transformation 40]
89. ~wise(X0) | generous(X0) [cnf transformation 42]
98. old(X0) | calm(X0) [cnf transformation 29]
102. brave(X0) | ~creative(X0) | patient(X0) [cnf transformation 49]
116. brave(sK5) | creative(sK5) | ~tall(X1) [cnf transformation 61]
117. ~brave(sK5) | ~creative(sK5) | ~tall(X1) [cnf transformation 61]
119. calm(X0) | ~old(X0) [cnf transformation 63]
127. ~generous(susan) [cnf transformation 21]
133. 1 <=> ! [X1] : (~calm(X1) | wise(X1)) [avatar definition]
134. ~calm(X1) | wise(X1) <- (1) [avatar component clause 133]
141. 3 <=> creative(sK0) [avatar definition]
143. creative(sK0) <- (3) [avatar component clause 141]
144. 1 | 3 [avatar split clause 84,141,133]
187. brave(X0) | ~creative(X0) [subsumption resolution 102,67]
214. ~brave(sK5) | ~tall(X1) [subsumption resolution 117,71]
216. 19 <=> ! [X1] : ~tall(X1) [avatar definition]
217. ~tall(X1) <- (19) [avatar component clause 216]
219. 20 <=> brave(sK5) [avatar definition]
222. 19 | ~20 [avatar split clause 214,219,216]
223. brave(sK5) | ~tall(X1) [subsumption resolution 116,187]
224. 19 | 20 [avatar split clause 223,219,216]
225. calm(X0) [subsumption resolution 119,98]
248. tall(sK0) <- (3) [resolution 68,143]
249. $false <- (3, 19) [subsumption resolution 248,217]
250. ~3 | ~19 [avatar contradiction clause 249]
251. wise(X1) <- (1) [subsumption resolution 134,225]
258. generous(X0) <- (1) [resolution 89,251]
259. $false <- (1) [resolution 258,127]
260. ~1 [avatar contradiction clause 259]
261. $false [avatar sat refutation 144,222,224,250,260]
% SZS output end Proof for 728239575345431891167843
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble then john is either not rich or rich and vice versa.
Everyone who is strong or not happy is either not patient or not strong and vice versa.
Everyone who is either strong or not old is both calm and generous.
Everyone who is both strong and old is humble and vice versa.
If someone is calm or not rich then paul is calm and vice versa.
If alice is either not humble or kind then someone is either not brave or calm and vice versa.
If someone is not brave or not funny then someone is not generous or not kind and vice versa.
If someone is calm or generous then someone is not tall or not happy and vice versa.
Everyone who is both tall and creative is both tall and not strong.
If someone is not curious then someone is either strong or generous and vice versa.
If alice is funny or creative then someone is either not creative or tall.
If lucy is not quiet or generous then someone is wise and vice versa.
Everyone who is not creative is not happy or not quiet and vice versa.
If john is both humble and not rich then someone is not humble or not old.
Everyone who is either not rich or humble is either tall or not creative.
If someone is both not funny and calm then susan is either old or not quiet.
Someone is both not strong and not humble.
Susan is not tall.
Paul is happy or not generous.
Mary is old or not brave.
Alice is both humble and strong.
Someone is not patient.
Someone is creative.
Someone is either rich or not strong. | Susan is tall. | contradiction | ((?[X]:(humble(X)))<=>((~rich(john)<~>rich(john))))&
(![X]:((strong(X)|~happy(X))<=>(~patient(X)<~>~strong(X))))&
(![X]:((strong(X)<~>~old(X))=>(calm(X)&generous(X))))&
(![X]:((strong(X)&old(X))<=>humble(X)))&
((?[X]:((calm(X)|~rich(X))))<=>(calm(paul)))&
(((~humble(alice)<~>kind(alice)))<=>(?[X]:((~brave(X)<~>calm(X)))))&
((?[X]:((~brave(X)|~funny(X))))<=>(?[X]:((~generous(X)|~kind(X)))))&
((?[X]:((calm(X)|generous(X))))<=>(?[X]:((~tall(X)|~happy(X)))))&
(![X]:((tall(X)&creative(X))=>(tall(X)&~strong(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((strong(X)<~>generous(X)))))&
(((funny(alice)|creative(alice)))=>(?[X]:((~creative(X)<~>tall(X)))))&
(((~quiet(lucy)|generous(lucy)))<=>(?[X]:(wise(X))))&
(![X]:(~creative(X)<=>(~happy(X)|~quiet(X))))&
(((humble(john)&~rich(john)))=>(?[X]:((~humble(X)|~old(X)))))&
(![X]:((~rich(X)<~>humble(X))=>(tall(X)<~>~creative(X))))&
((?[X]:((~funny(X)&calm(X))))=>((old(susan)<~>~quiet(susan))))&
(?[X]:((~strong(X)&~humble(X))))&
(~tall(susan))&
((happy(paul)|~generous(paul)))&
((old(mary)|~brave(mary)))&
((humble(alice)&strong(alice)))&
(?[X]:(~patient(X)))&
(?[X]:(creative(X)))&
(?[X]:((rich(X)<~>~strong(X)))) | tall(susan) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2270896458029397580632429
% SZS output start Proof for 2270896458029397580632429
18. ~tall(susan) [input p17]
25. tall(susan) [input hypothesis]
153. ~tall(susan) [cnf transformation 18]
162. tall(susan) [cnf transformation 25]
404. $false [subsumption resolution 162,153]
% SZS output end Proof for 2270896458029397580632429
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative then someone is either not happy or not kind and vice versa.
Everyone who is either brave or curious is not strong and vice versa.
Everyone who is both patient and humble is either not tall or not quiet.
Everyone who is both not quiet and happy is both not generous and calm.
If someone is both not calm and not old then someone is both old and not strong and vice versa.
If someone is not patient then susan is old.
Everyone who is happy or not creative is calm and vice versa.
Everyone who is both rich and happy is both patient and not patient.
Everyone who is both happy and quiet is funny or not quiet and vice versa.
Everyone who is not generous is curious or brave and vice versa.
Everyone who is creative or not strong is calm or generous and vice versa.
Everyone who is both funny and not brave is both funny and not kind and vice versa.
Everyone who is either creative or old is either not patient or not strong and vice versa.
If fred is humble then lucy is either not tall or not funny and vice versa.
If mary is strong or tall then someone is rich.
Alice is either not strong or kind.
Someone is not creative.
Someone is both not patient and not happy.
Paul is not happy or not brave.
Someone is both not tall and not curious.
Alice is not creative or wise.
Fred is either curious or not creative.
Alice is curious. | Fred is not calm. | contradiction | ((?[X]:(~creative(X)))<=>(?[X]:((~happy(X)<~>~kind(X)))))&
(![X]:((brave(X)<~>curious(X))<=>~strong(X)))&
(![X]:((patient(X)&humble(X))=>(~tall(X)<~>~quiet(X))))&
(![X]:((~quiet(X)&happy(X))=>(~generous(X)&calm(X))))&
((?[X]:((~calm(X)&~old(X))))<=>(?[X]:((old(X)&~strong(X)))))&
((?[X]:(~patient(X)))=>(old(susan)))&
(![X]:((happy(X)|~creative(X))<=>calm(X)))&
(![X]:((rich(X)&happy(X))=>(patient(X)&~patient(X))))&
(![X]:((happy(X)&quiet(X))<=>(funny(X)|~quiet(X))))&
(![X]:(~generous(X)<=>(curious(X)|brave(X))))&
(![X]:((creative(X)|~strong(X))<=>(calm(X)|generous(X))))&
(![X]:((funny(X)&~brave(X))<=>(funny(X)&~kind(X))))&
(![X]:((creative(X)<~>old(X))<=>(~patient(X)<~>~strong(X))))&
((humble(fred))<=>((~tall(lucy)<~>~funny(lucy))))&
(((strong(mary)|tall(mary)))=>(?[X]:(rich(X))))&
((~strong(alice)<~>kind(alice)))&
(?[X]:(~creative(X)))&
(?[X]:((~patient(X)&~happy(X))))&
((~happy(paul)|~brave(paul)))&
(?[X]:((~tall(X)&~curious(X))))&
((~creative(alice)|wise(alice)))&
((curious(fred)<~>~creative(fred)))&
(curious(alice)) | ~calm(fred) | [
"p6",
"p9",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 424609274155679594694138
% SZS output start Proof for 424609274155679594694138
7. ! [X0] : ((~creative(X0) | happy(X0)) <=> calm(X0)) [input p6]
10. ! [X0] : (~generous(X0) <=> (brave(X0) | curious(X0))) [input p9]
11. ! [X0] : ((~strong(X0) | creative(X0)) <=> (generous(X0) | calm(X0))) [input p10]
22. curious(fred) <~> ~creative(fred) [input p21]
24. ~calm(fred) [input hypothesis]
48. ! [X0] : (((~creative(X0) | happy(X0)) | ~calm(X0)) & (calm(X0) | (creative(X0) & ~happy(X0)))) [nnf transformation 7]
49. ! [X0] : ((~creative(X0) | happy(X0) | ~calm(X0)) & (calm(X0) | (creative(X0) & ~happy(X0)))) [flattening 48]
52. ! [X0] : ((~generous(X0) | (~brave(X0) & ~curious(X0))) & ((brave(X0) | curious(X0)) | generous(X0))) [nnf transformation 10]
53. ! [X0] : ((~generous(X0) | (~brave(X0) & ~curious(X0))) & (brave(X0) | curious(X0) | generous(X0))) [flattening 52]
54. ! [X0] : (((~strong(X0) | creative(X0)) | (~generous(X0) & ~calm(X0))) & ((generous(X0) | calm(X0)) | (strong(X0) & ~creative(X0)))) [nnf transformation 11]
55. ! [X0] : ((~strong(X0) | creative(X0) | (~generous(X0) & ~calm(X0))) & (generous(X0) | calm(X0) | (strong(X0) & ~creative(X0)))) [flattening 54]
69. (creative(fred) | ~curious(fred)) & (~creative(fred) | curious(fred)) [nnf transformation 22]
88. calm(X0) | creative(X0) [cnf transformation 49]
98. ~generous(X0) | ~curious(X0) [cnf transformation 53]
100. generous(X0) | calm(X0) | ~creative(X0) [cnf transformation 55]
130. ~creative(fred) | curious(fred) [cnf transformation 69]
133. ~calm(fred) [cnf transformation 24]
198. calm(X0) | generous(X0) [subsumption resolution 100,88]
253. 25 <=> curious(fred) [avatar definition]
254. curious(fred) <- (25) [avatar component clause 253]
257. 26 <=> creative(fred) [avatar definition]
261. 25 | ~26 [avatar split clause 130,257,253]
267. creative(fred) [resolution 88,133]
271. 26 [avatar split clause 267,257]
282. generous(fred) [resolution 198,133]
285. ~curious(fred) [resolution 282,98]
286. $false <- (25) [subsumption resolution 285,254]
287. ~25 [avatar contradiction clause 286]
288. $false [avatar sat refutation 261,271,287]
% SZS output end Proof for 424609274155679594694138
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or not old is not calm or not quiet.
If someone is both wise and not funny then someone is not rich.
If someone is both not humble and strong then john is either not funny or not curious and vice versa.
If someone is either not wise or wise then paul is strong and vice versa.
Everyone who is not old or creative is either rich or kind and vice versa.
Everyone who is creative or old is either strong or curious and vice versa.
Everyone who is both curious and generous is either old or not humble.
If susan is not humble then paul is funny or not calm and vice versa.
If alice is both wise and not kind then paul is not kind and vice versa.
Everyone who is not kind or not curious is not curious or not rich.
Everyone who is not tall is both not generous and wise.
Everyone who is both tall and not old is both not brave and curious and vice versa.
If someone is either not tall or not creative then susan is tall or generous.
Everyone who is strong or curious is either kind or creative.
Everyone who is not generous is patient.
Everyone who is both not generous and not tall is humble or not generous and vice versa.
Paul is old.
Someone is calm.
Someone is either humble or not happy.
Lucy is not humble or strong.
Lucy is strong.
Someone is either wise or happy.
John is both not tall and not curious. | Paul is strong. | entailment | (![X]:((~generous(X)<~>~old(X))=>(~calm(X)|~quiet(X))))&
((?[X]:((wise(X)&~funny(X))))=>(?[X]:(~rich(X))))&
((?[X]:((~humble(X)&strong(X))))<=>((~funny(john)<~>~curious(john))))&
((?[X]:((~wise(X)<~>wise(X))))<=>(strong(paul)))&
(![X]:((~old(X)|creative(X))<=>(rich(X)<~>kind(X))))&
(![X]:((creative(X)|old(X))<=>(strong(X)<~>curious(X))))&
(![X]:((curious(X)&generous(X))=>(old(X)<~>~humble(X))))&
((~humble(susan))<=>((funny(paul)|~calm(paul))))&
(((wise(alice)&~kind(alice)))<=>(~kind(paul)))&
(![X]:((~kind(X)|~curious(X))=>(~curious(X)|~rich(X))))&
(![X]:(~tall(X)=>(~generous(X)&wise(X))))&
(![X]:((tall(X)&~old(X))<=>(~brave(X)&curious(X))))&
((?[X]:((~tall(X)<~>~creative(X))))=>((tall(susan)|generous(susan))))&
(![X]:((strong(X)|curious(X))=>(kind(X)<~>creative(X))))&
(![X]:(~generous(X)=>patient(X)))&
(![X]:((~generous(X)&~tall(X))<=>(humble(X)|~generous(X))))&
(old(paul))&
(?[X]:(calm(X)))&
(?[X]:((humble(X)<~>~happy(X))))&
((~humble(lucy)|strong(lucy)))&
(strong(lucy))&
(?[X]:((wise(X)<~>happy(X))))&
((~tall(john)&~curious(john))) | strong(paul) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3343856190940698371799523
% SZS output start Proof for 3343856190940698371799523
4. ? [X0] : (~wise(X0) <~> wise(X0)) <=> strong(paul) [input p3]
24. ~strong(paul) [input hypothesis]
44. (? [X0] : ((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ~strong(paul)) & (strong(paul) | ! [X0] : ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) [nnf transformation 4]
45. (? [X0] : ((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ~strong(paul)) & (strong(paul) | ! [X1] : ((~wise(X1) | ~wise(X1)) & (wise(X1) | wise(X1)))) [rectify 44]
46. ? [X0] : ((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) => ((~wise(sK2) | wise(sK2)) & (wise(sK2) | ~wise(sK2))) [choice axiom]
47. (((~wise(sK2) | wise(sK2)) & (wise(sK2) | ~wise(sK2))) | ~strong(paul)) & (strong(paul) | ! [X1] : ((~wise(X1) | ~wise(X1)) & (wise(X1) | wise(X1)))) [skolemisation 45,46]
78. strong(paul) | wise(X1) | wise(X1) [cnf transformation 47]
79. strong(paul) | ~wise(X1) | ~wise(X1) [cnf transformation 47]
131. ~strong(paul) [cnf transformation 24]
132. strong(paul) | wise(X1) [duplicate literal removal 78]
133. strong(paul) | ~wise(X1) [duplicate literal removal 79]
168. 8 <=> ! [X1] : ~wise(X1) [avatar definition]
169. ~wise(X1) <- (8) [avatar component clause 168]
171. 9 <=> strong(paul) [avatar definition]
174. 8 | 9 [avatar split clause 133,171,168]
176. 10 <=> ! [X1] : wise(X1) [avatar definition]
177. wise(X1) <- (10) [avatar component clause 176]
178. 10 | 9 [avatar split clause 132,171,176]
254. ~9 [avatar split clause 131,171]
255. $false <- (8, 10) [subsumption resolution 169,177]
256. ~8 | ~10 [avatar contradiction clause 255]
257. $false [avatar sat refutation 174,178,254,256]
% SZS output end Proof for 3343856190940698371799523
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or not happy is either not curious or not old and vice versa.
If alice is both happy and not funny then someone is not quiet or not strong.
If someone is both not quiet and brave then paul is both tall and happy.
Everyone who is either old or quiet is kind or patient and vice versa.
Everyone who is kind is calm or not wise and vice versa.
If susan is both humble and funny then someone is quiet.
Everyone who is brave is old and vice versa.
If john is both not wise and not strong then paul is humble and vice versa.
If susan is not generous or not calm then someone is not old or not humble and vice versa.
Everyone who is both not generous and calm is both not calm and generous and vice versa.
If paul is both patient and funny then someone is calm and vice versa.
Everyone who is curious is either not old or curious.
Everyone who is humble or not happy is not quiet or not happy and vice versa.
Everyone who is calm or happy is both not patient and not curious.
If mary is happy then fred is not strong or tall.
If someone is not happy then mary is both rich and not quiet and vice versa.
Someone is either creative or curious.
Mary is not tall.
Paul is quiet or not generous.
Mary is both not strong and not quiet.
Someone is wise or not wise.
John is not quiet.
Fred is not funny. | Mary is not calm. | entailment | (![X]:((funny(X)|~happy(X))<=>(~curious(X)<~>~old(X))))&
(((happy(alice)&~funny(alice)))=>(?[X]:((~quiet(X)|~strong(X)))))&
((?[X]:((~quiet(X)&brave(X))))=>((tall(paul)&happy(paul))))&
(![X]:((old(X)<~>quiet(X))<=>(kind(X)|patient(X))))&
(![X]:(kind(X)<=>(calm(X)|~wise(X))))&
(((humble(susan)&funny(susan)))=>(?[X]:(quiet(X))))&
(![X]:(brave(X)<=>old(X)))&
(((~wise(john)&~strong(john)))<=>(humble(paul)))&
(((~generous(susan)|~calm(susan)))<=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:((~generous(X)&calm(X))<=>(~calm(X)&generous(X))))&
(((patient(paul)&funny(paul)))<=>(?[X]:(calm(X))))&
(![X]:(curious(X)=>(~old(X)<~>curious(X))))&
(![X]:((humble(X)|~happy(X))<=>(~quiet(X)|~happy(X))))&
(![X]:((calm(X)|happy(X))=>(~patient(X)&~curious(X))))&
((happy(mary))=>((~strong(fred)|tall(fred))))&
((?[X]:(~happy(X)))<=>((rich(mary)&~quiet(mary))))&
(?[X]:((creative(X)<~>curious(X))))&
(~tall(mary))&
((quiet(paul)|~generous(paul)))&
((~strong(mary)&~quiet(mary)))&
(?[X]:((wise(X)|~wise(X))))&
(~quiet(john))&
(~funny(fred)) | ~calm(mary) | [
"p0",
"p2",
"p3",
"p6",
"p10",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1706561950023057490196118
% SZS output start Proof for 1706561950023057490196118
1. ! [X0] : ((~happy(X0) | funny(X0)) <=> (~curious(X0) <~> ~old(X0))) [input p0]
3. ? [X0] : (brave(X0) & ~quiet(X0)) => (happy(paul) & tall(paul)) [input p2]
4. ! [X0] : ((old(X0) <~> quiet(X0)) <=> (patient(X0) | kind(X0))) [input p3]
7. ! [X0] : (brave(X0) <=> old(X0)) [input p6]
11. (funny(paul) & patient(paul)) <=> ? [X0] : calm(X0) [input p10]
12. ! [X0] : (curious(X0) => (~old(X0) <~> curious(X0))) [input p11]
14. ! [X0] : ((happy(X0) | calm(X0)) => (~curious(X0) & ~patient(X0))) [input p13]
24. calm(mary) [input hypothesis]
25. ! [X0] : (old(X0) => brave(X0)) [unused predicate definition removal 7]
28. (happy(paul) & tall(paul)) | ! [X0] : (~brave(X0) | quiet(X0)) [ennf transformation 3]
31. ! [X0] : (brave(X0) | ~old(X0)) [ennf transformation 25]
32. ! [X0] : ((~old(X0) <~> curious(X0)) | ~curious(X0)) [ennf transformation 12]
33. ! [X0] : ((~curious(X0) & ~patient(X0)) | (~happy(X0) & ~calm(X0))) [ennf transformation 14]
36. ! [X0] : (((~happy(X0) | funny(X0)) | ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0)))) & (((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | (happy(X0) & ~funny(X0)))) [nnf transformation 1]
37. ! [X0] : ((~happy(X0) | funny(X0) | ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0)))) & (((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | (happy(X0) & ~funny(X0)))) [flattening 36]
40. ! [X0] : ((((~quiet(X0) | ~old(X0)) & (quiet(X0) | old(X0))) | (~patient(X0) & ~kind(X0))) & ((patient(X0) | kind(X0)) | ((old(X0) | ~quiet(X0)) & (quiet(X0) | ~old(X0))))) [nnf transformation 4]
41. ! [X0] : ((((~quiet(X0) | ~old(X0)) & (quiet(X0) | old(X0))) | (~patient(X0) & ~kind(X0))) & (patient(X0) | kind(X0) | ((old(X0) | ~quiet(X0)) & (quiet(X0) | ~old(X0))))) [flattening 40]
55. ((funny(paul) & patient(paul)) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | (~funny(paul) | ~patient(paul))) [nnf transformation 11]
56. ((funny(paul) & patient(paul)) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | ~funny(paul) | ~patient(paul)) [flattening 55]
57. ((funny(paul) & patient(paul)) | ! [X0] : ~calm(X0)) & (? [X1] : calm(X1) | ~funny(paul) | ~patient(paul)) [rectify 56]
58. ? [X1] : calm(X1) => calm(sK3) [choice axiom]
59. ((funny(paul) & patient(paul)) | ! [X0] : ~calm(X0)) & (calm(sK3) | ~funny(paul) | ~patient(paul)) [skolemisation 57,58]
60. ! [X0] : (((~curious(X0) | old(X0)) & (curious(X0) | ~old(X0))) | ~curious(X0)) [nnf transformation 32]
75. ~funny(X0) | curious(X0) | old(X0) [cnf transformation 37]
81. happy(paul) | ~brave(X0) | quiet(X0) [cnf transformation 28]
87. ~patient(X0) | ~old(X0) | ~quiet(X0) [cnf transformation 41]
92. ~old(X0) | brave(X0) [cnf transformation 31]
105. patient(paul) | ~calm(X0) [cnf transformation 59]
106. funny(paul) | ~calm(X0) [cnf transformation 59]
108. ~curious(X0) | old(X0) | ~curious(X0) [cnf transformation 60]
114. ~patient(X0) | ~happy(X0) [cnf transformation 33]
130. calm(mary) [cnf transformation 24]
131. ~curious(X0) | old(X0) [duplicate literal removal 108]
154. 5 <=> ! [X0] : (~brave(X0) | quiet(X0)) [avatar definition]
155. ~brave(X0) | quiet(X0) <- (5) [avatar component clause 154]
157. 6 <=> happy(paul) [avatar definition]
160. 5 | 6 [avatar split clause 81,157,154]
221. 20 <=> ! [X0] : ~calm(X0) [avatar definition]
222. ~calm(X0) <- (20) [avatar component clause 221]
224. 21 <=> funny(paul) [avatar definition]
226. funny(paul) <- (21) [avatar component clause 224]
227. 20 | 21 [avatar split clause 106,224,221]
229. 22 <=> patient(paul) [avatar definition]
231. patient(paul) <- (22) [avatar component clause 229]
232. 20 | 22 [avatar split clause 105,229,221]
280. 33 <=> quiet(paul) [avatar definition]
282. quiet(paul) <- (33) [avatar component clause 280]
289. $false <- (20) [resolution 222,130]
290. ~20 [avatar contradiction clause 289]
296. ~happy(paul) <- (22) [resolution 114,231]
297. ~6 | ~22 [avatar split clause 296,229,157]
304. curious(paul) | old(paul) <- (21) [resolution 75,226]
305. old(paul) <- (21) [subsumption resolution 304,131]
332. brave(paul) <- (21) [resolution 305,92]
355. quiet(paul) <- (5, 21) [resolution 332,155]
356. 33 | ~5 | ~21 [avatar split clause 355,224,154,280]
357. ~old(paul) | ~quiet(paul) <- (22) [resolution 87,231]
358. ~quiet(paul) <- (21, 22) [subsumption resolution 357,305]
359. $false <- (21, 22, 33) [subsumption resolution 358,282]
360. ~21 | ~22 | ~33 [avatar contradiction clause 359]
361. $false [avatar sat refutation 160,227,232,290,297,356,360]
% SZS output end Proof for 1706561950023057490196118
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or old is both not creative and not strong. Everyone who is either not funny or wise is either patient or strong and vice versa. If susan is not wise then someone is both not generous and humble. Everyone who is both not patient and not happy is either rich or generous and vice versa. Everyone who is not calm is both not wise and kind and vice versa. If someone is both not curious and calm then someone is either not generous or brave. Everyone who is either wise or not creative is both creative and humble and vice versa. If paul is both not rich and rich then someone is curious. If someone is not strong or not creative then fred is not brave. If someone is both not curious and not creative then someone is humble. If someone is both kind and tall then someone is both patient and strong. If paul is not kind then someone is not rich and vice versa. Everyone who is either kind or curious is either patient or brave and vice versa. Everyone who is both rich and not kind is both not calm and rich and vice versa. If someone is both not patient and not curious then mary is creative or not rich and vice versa. If fred is either not wise or tall then someone is not calm. Someone is wise. Someone is either wise or not tall. Someone is curious or creative. Mary is either not kind or not rich. Someone is not creative. Alice is tall or curious. Someone is curious or not humble. Susan is both not calm and not brave. | Mary is rich. | contradiction | (![X]:((~quiet(X)<~>old(X))=>(~creative(X)&~strong(X))))&
(![X]:((~funny(X)<~>wise(X))<=>(patient(X)<~>strong(X))))&
((~wise(susan))=>(?[X]:((~generous(X)&humble(X)))))&
(![X]:((~patient(X)&~happy(X))<=>(rich(X)<~>generous(X))))&
(![X]:(~calm(X)<=>(~wise(X)&kind(X))))&
((?[X]:((~curious(X)&calm(X))))=>(?[X]:((~generous(X)<~>brave(X)))))&
(![X]:((wise(X)<~>~creative(X))<=>(creative(X)&humble(X))))&
(((~rich(paul)&rich(paul)))=>(?[X]:(curious(X))))&
((?[X]:((~strong(X)|~creative(X))))=>(~brave(fred)))&
((?[X]:((~curious(X)&~creative(X))))=>(?[X]:(humble(X))))&
((?[X]:((kind(X)&tall(X))))=>(?[X]:((patient(X)&strong(X)))))&
((~kind(paul))<=>(?[X]:(~rich(X))))&
(![X]:((kind(X)<~>curious(X))<=>(patient(X)<~>brave(X))))&
(![X]:((rich(X)&~kind(X))<=>(~calm(X)&rich(X))))&
((?[X]:((~patient(X)&~curious(X))))<=>((creative(mary)|~rich(mary))))&
(((~wise(fred)<~>tall(fred)))=>(?[X]:(~calm(X))))&
(?[X]:(wise(X)))&
(?[X]:((wise(X)<~>~tall(X))))&
(?[X]:((curious(X)|creative(X))))&
((~kind(mary)<~>~rich(mary)))&
(?[X]:(~creative(X)))&
((tall(alice)|curious(alice)))&
(?[X]:((curious(X)|~humble(X))))&
((~calm(susan)&~brave(susan))) | rich(mary) | [
"p4",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2786468840524017031862493
% SZS output start Proof for 2786468840524017031862493
5. ! [X0] : (~calm(X0) <=> (kind(X0) & ~wise(X0))) [input p4]
14. ! [X0] : ((~kind(X0) & rich(X0)) <=> (rich(X0) & ~calm(X0))) [input p13]
20. ~kind(mary) <~> ~rich(mary) [input p19]
25. rich(mary) [input hypothesis]
44. ! [X0] : ((~calm(X0) | (~kind(X0) | wise(X0))) & ((kind(X0) & ~wise(X0)) | calm(X0))) [nnf transformation 5]
45. ! [X0] : ((~calm(X0) | ~kind(X0) | wise(X0)) & ((kind(X0) & ~wise(X0)) | calm(X0))) [flattening 44]
65. ! [X0] : (((~kind(X0) & rich(X0)) | (~rich(X0) | calm(X0))) & ((rich(X0) & ~calm(X0)) | (kind(X0) | ~rich(X0)))) [nnf transformation 14]
66. ! [X0] : (((~kind(X0) & rich(X0)) | ~rich(X0) | calm(X0)) & ((rich(X0) & ~calm(X0)) | kind(X0) | ~rich(X0))) [flattening 65]
82. (rich(mary) | kind(mary)) & (~rich(mary) | ~kind(mary)) [nnf transformation 20]
108. kind(X0) | calm(X0) [cnf transformation 45]
134. ~calm(X0) | kind(X0) | ~rich(X0) [cnf transformation 66]
137. ~kind(X0) | ~rich(X0) | calm(X0) [cnf transformation 66]
149. ~rich(mary) | ~kind(mary) [cnf transformation 82]
150. rich(mary) | kind(mary) [cnf transformation 82]
156. rich(mary) [cnf transformation 25]
232. ~rich(X0) | calm(X0) [subsumption resolution 137,108]
233. kind(X0) | ~rich(X0) [subsumption resolution 134,232]
235. 18 <=> rich(mary) [avatar definition]
291. kind(mary) [subsumption resolution 150,233]
292. ~rich(mary) [subsumption resolution 149,291]
293. ~18 [avatar split clause 292,235]
312. 18 [avatar split clause 156,235]
313. $false [avatar sat refutation 293,312]
% SZS output end Proof for 2786468840524017031862493
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old or rich then lucy is not quiet and vice versa.
Everyone who is not happy is generous.
Everyone who is not wise is both creative and not wise.
If someone is both rich and happy then someone is not generous and vice versa.
If someone is both not brave and not patient then alice is both not quiet and not generous and vice versa.
If susan is both calm and not humble then someone is wise or rich.
Everyone who is either old or humble is not curious.
Everyone who is humble is curious.
If someone is rich then someone is old.
If paul is creative or happy then susan is both not curious and generous and vice versa.
If someone is either not old or not rich then someone is funny or wise.
Everyone who is both wise and not wise is not kind or not strong and vice versa.
If paul is either not humble or not creative then lucy is old and vice versa.
If someone is both not creative and generous then lucy is not tall.
If someone is not curious or patient then someone is not patient.
Everyone who is not old is both not generous and not strong.
Someone is both rich and calm.
Alice is not happy.
Someone is generous.
Someone is not happy.
Someone is not quiet or not wise.
Someone is either not humble or not quiet.
Someone is either brave or not wise. | Paul is old. | entailment | ((?[X]:((old(X)|rich(X))))<=>(~quiet(lucy)))&
(![X]:(~happy(X)=>generous(X)))&
(![X]:(~wise(X)=>(creative(X)&~wise(X))))&
((?[X]:((rich(X)&happy(X))))<=>(?[X]:(~generous(X))))&
((?[X]:((~brave(X)&~patient(X))))<=>((~quiet(alice)&~generous(alice))))&
(((calm(susan)&~humble(susan)))=>(?[X]:((wise(X)|rich(X)))))&
(![X]:((old(X)<~>humble(X))=>~curious(X)))&
(![X]:(humble(X)=>curious(X)))&
((?[X]:(rich(X)))=>(?[X]:(old(X))))&
(((creative(paul)|happy(paul)))<=>((~curious(susan)&generous(susan))))&
((?[X]:((~old(X)<~>~rich(X))))=>(?[X]:((funny(X)|wise(X)))))&
(![X]:((wise(X)&~wise(X))<=>(~kind(X)|~strong(X))))&
(((~humble(paul)<~>~creative(paul)))<=>(old(lucy)))&
((?[X]:((~creative(X)&generous(X))))=>(~tall(lucy)))&
((?[X]:((~curious(X)|patient(X))))=>(?[X]:(~patient(X))))&
(![X]:(~old(X)=>(~generous(X)&~strong(X))))&
(?[X]:((rich(X)&calm(X))))&
(~happy(alice))&
(?[X]:(generous(X)))&
(?[X]:(~happy(X)))&
(?[X]:((~quiet(X)|~wise(X))))&
(?[X]:((~humble(X)<~>~quiet(X))))&
(?[X]:((brave(X)<~>~wise(X)))) | old(paul) | [
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4300166180623074764318239
% SZS output start Proof for 4300166180623074764318239
12. ! [X0] : ((~wise(X0) & wise(X0)) <=> (~strong(X0) | ~kind(X0))) [input p11]
16. ! [X0] : (~old(X0) => (~strong(X0) & ~generous(X0))) [input p15]
24. ~old(paul) [input hypothesis]
39. ! [X0] : ((~strong(X0) & ~generous(X0)) | old(X0)) [ennf transformation 16]
62. ! [X0] : (((~wise(X0) & wise(X0)) | (strong(X0) & kind(X0))) & ((~strong(X0) | ~kind(X0)) | (wise(X0) | ~wise(X0)))) [nnf transformation 12]
63. ! [X0] : (((~wise(X0) & wise(X0)) | (strong(X0) & kind(X0))) & (~strong(X0) | ~kind(X0) | wise(X0) | ~wise(X0))) [flattening 62]
107. wise(X0) | strong(X0) [cnf transformation 63]
109. ~wise(X0) | strong(X0) [cnf transformation 63]
117. ~strong(X0) | old(X0) [cnf transformation 39]
128. ~old(paul) [cnf transformation 24]
237. strong(X0) [subsumption resolution 107,109]
263. old(X0) [subsumption resolution 117,237]
293. $false [subsumption resolution 128,263]
% SZS output end Proof for 4300166180623074764318239
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or tall then someone is either not calm or not tall and vice versa.
Everyone who is funny or curious is either tall or happy.
Everyone who is both calm and not generous is not wise and vice versa.
Everyone who is both not rich and not generous is rich or calm and vice versa.
Everyone who is either tall or not generous is not creative or not kind and vice versa.
If paul is either not funny or not creative then someone is either generous or brave.
If fred is not funny then someone is either funny or not strong and vice versa.
If someone is both kind and rich then someone is both brave and not strong and vice versa.
If susan is not rich or not brave then someone is either humble or not happy and vice versa.
Everyone who is quiet or not curious is both not creative and happy and vice versa.
Everyone who is tall or not strong is both not tall and kind.
If someone is not brave then someone is kind and vice versa.
Everyone who is not calm or strong is both not curious and strong.
Everyone who is both not funny and kind is both not calm and not humble.
Everyone who is either not brave or kind is not strong or wise and vice versa.
If john is not curious then fred is not quiet.
Fred is strong.
Someone is not creative.
Someone is old.
Someone is not humble.
Mary is happy or creative. | Paul is not wise. | entailment | (((~kind(alice)|tall(alice)))<=>(?[X]:((~calm(X)<~>~tall(X)))))&
(![X]:((funny(X)|curious(X))=>(tall(X)<~>happy(X))))&
(![X]:((calm(X)&~generous(X))<=>~wise(X)))&
(![X]:((~rich(X)&~generous(X))<=>(rich(X)|calm(X))))&
(![X]:((tall(X)<~>~generous(X))<=>(~creative(X)|~kind(X))))&
(((~funny(paul)<~>~creative(paul)))=>(?[X]:((generous(X)<~>brave(X)))))&
((~funny(fred))<=>(?[X]:((funny(X)<~>~strong(X)))))&
((?[X]:((kind(X)&rich(X))))<=>(?[X]:((brave(X)&~strong(X)))))&
(((~rich(susan)|~brave(susan)))<=>(?[X]:((humble(X)<~>~happy(X)))))&
(![X]:((quiet(X)|~curious(X))<=>(~creative(X)&happy(X))))&
(![X]:((tall(X)|~strong(X))=>(~tall(X)&kind(X))))&
((?[X]:(~brave(X)))<=>(?[X]:(kind(X))))&
(![X]:((~calm(X)|strong(X))=>(~curious(X)&strong(X))))&
(![X]:((~funny(X)&kind(X))=>(~calm(X)&~humble(X))))&
(![X]:((~brave(X)<~>kind(X))<=>(~strong(X)|wise(X))))&
((~curious(john))=>(~quiet(fred)))&
(strong(fred))&
(?[X]:(~creative(X)))&
(?[X]:(old(X)))&
(?[X]:(~humble(X)))&
((happy(mary)|creative(mary))) | ~wise(paul) | [
"p2",
"p3",
"p4",
"p7",
"p9",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6770410915304710411933260
% SZS output start Proof for 6770410915304710411933260
3. ! [X0] : ((~generous(X0) & calm(X0)) <=> ~wise(X0)) [input p2]
4. ! [X0] : ((~generous(X0) & ~rich(X0)) <=> (calm(X0) | rich(X0))) [input p3]
5. ! [X0] : ((tall(X0) <~> ~generous(X0)) <=> (~kind(X0) | ~creative(X0))) [input p4]
8. ? [X0] : (rich(X0) & kind(X0)) <=> ? [X0] : (~strong(X0) & brave(X0)) [input p7]
10. ! [X0] : ((~curious(X0) | quiet(X0)) <=> (happy(X0) & ~creative(X0))) [input p9]
11. ! [X0] : ((~strong(X0) | tall(X0)) => (kind(X0) & ~tall(X0))) [input p10]
13. ! [X0] : ((strong(X0) | ~calm(X0)) => (strong(X0) & ~curious(X0))) [input p12]
15. ! [X0] : ((~brave(X0) <~> kind(X0)) <=> (wise(X0) | ~strong(X0))) [input p14]
22. wise(paul) [input hypothesis]
23. ? [X0] : (rich(X0) & kind(X0)) <=> ? [X1] : (~strong(X1) & brave(X1)) [rectify 8]
28. ! [X0] : ((kind(X0) & ~tall(X0)) | (strong(X0) & ~tall(X0))) [ennf transformation 11]
29. ! [X0] : ((strong(X0) & ~curious(X0)) | (~strong(X0) & calm(X0))) [ennf transformation 13]
39. ! [X0] : (((~generous(X0) & calm(X0)) | wise(X0)) & (~wise(X0) | (generous(X0) | ~calm(X0)))) [nnf transformation 3]
40. ! [X0] : (((~generous(X0) & calm(X0)) | wise(X0)) & (~wise(X0) | generous(X0) | ~calm(X0))) [flattening 39]
41. ! [X0] : (((~generous(X0) & ~rich(X0)) | (~calm(X0) & ~rich(X0))) & ((calm(X0) | rich(X0)) | (generous(X0) | rich(X0)))) [nnf transformation 4]
42. ! [X0] : (((~generous(X0) & ~rich(X0)) | (~calm(X0) & ~rich(X0))) & (calm(X0) | rich(X0) | generous(X0) | rich(X0))) [flattening 41]
43. ! [X0] : ((((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | (kind(X0) & creative(X0))) & ((~kind(X0) | ~creative(X0)) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0))))) [nnf transformation 5]
44. ! [X0] : ((((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | (kind(X0) & creative(X0))) & (~kind(X0) | ~creative(X0) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0))))) [flattening 43]
52. (? [X0] : (rich(X0) & kind(X0)) | ! [X1] : (strong(X1) | ~brave(X1))) & (? [X1] : (~strong(X1) & brave(X1)) | ! [X0] : (~rich(X0) | ~kind(X0))) [nnf transformation 23]
53. (? [X0] : (rich(X0) & kind(X0)) | ! [X1] : (strong(X1) | ~brave(X1))) & (? [X2] : (~strong(X2) & brave(X2)) | ! [X3] : (~rich(X3) | ~kind(X3))) [rectify 52]
54. ? [X0] : (rich(X0) & kind(X0)) => (rich(sK3) & kind(sK3)) [choice axiom]
55. ? [X2] : (~strong(X2) & brave(X2)) => (~strong(sK4) & brave(sK4)) [choice axiom]
56. ((rich(sK3) & kind(sK3)) | ! [X1] : (strong(X1) | ~brave(X1))) & ((~strong(sK4) & brave(sK4)) | ! [X3] : (~rich(X3) | ~kind(X3))) [skolemisation 53,55,54]
62. ! [X0] : (((~curious(X0) | quiet(X0)) | (~happy(X0) | creative(X0))) & ((happy(X0) & ~creative(X0)) | (curious(X0) & ~quiet(X0)))) [nnf transformation 10]
63. ! [X0] : ((~curious(X0) | quiet(X0) | ~happy(X0) | creative(X0)) & ((happy(X0) & ~creative(X0)) | (curious(X0) & ~quiet(X0)))) [flattening 62]
69. ! [X0] : ((((~kind(X0) | brave(X0)) & (kind(X0) | ~brave(X0))) | (~wise(X0) & strong(X0))) & ((wise(X0) | ~strong(X0)) | ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0))))) [nnf transformation 15]
70. ! [X0] : ((((~kind(X0) | brave(X0)) & (kind(X0) | ~brave(X0))) | (~wise(X0) & strong(X0))) & (wise(X0) | ~strong(X0) | ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0))))) [flattening 69]
85. ~wise(X0) | generous(X0) | ~calm(X0) [cnf transformation 40]
88. calm(X0) | rich(X0) | generous(X0) | rich(X0) [cnf transformation 42]
89. ~rich(X0) | ~rich(X0) [cnf transformation 42]
95. ~generous(X0) | tall(X0) | creative(X0) [cnf transformation 44]
110. rich(sK3) | strong(X1) | ~brave(X1) [cnf transformation 56]
118. ~creative(X0) | curious(X0) [cnf transformation 63]
122. ~tall(X0) | ~tall(X0) [cnf transformation 28]
125. strong(X0) | kind(X0) [cnf transformation 28]
129. ~strong(X0) | ~curious(X0) [cnf transformation 29]
138. ~kind(X0) | brave(X0) | strong(X0) [cnf transformation 70]
145. wise(paul) [cnf transformation 22]
146. ~tall(X0) [duplicate literal removal 122]
147. calm(X0) | rich(X0) | generous(X0) [duplicate literal removal 88]
148. ~rich(X0) [duplicate literal removal 89]
177. generous(X0) | calm(X0) [subsumption resolution 147,148]
179. 7 <=> creative(paul) [avatar definition]
181. creative(paul) <- (7) [avatar component clause 179]
220. ~brave(X1) | strong(X1) [subsumption resolution 110,148]
255. brave(X0) | strong(X0) [subsumption resolution 138,125]
256. strong(X0) [subsumption resolution 255,220]
295. ~curious(X1) [resolution 129,256]
310. generous(paul) | ~calm(paul) [resolution 85,145]
322. generous(paul) [subsumption resolution 310,177]
328. tall(paul) | creative(paul) [resolution 322,95]
332. creative(paul) [subsumption resolution 328,146]
335. 7 [avatar split clause 332,179]
336. curious(paul) <- (7) [resolution 181,118]
337. $false <- (7) [subsumption resolution 336,295]
338. ~7 [avatar contradiction clause 337]
339. $false [avatar sat refutation 335,338]
% SZS output end Proof for 6770410915304710411933260
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and not funny is not kind and vice versa.
Everyone who is both not quiet and creative is both wise and happy.
Everyone who is tall is not quiet and vice versa.
Everyone who is either not curious or not rich is either not wise or not generous.
Everyone who is either not creative or not calm is humble or funny and vice versa.
If someone is not tall then john is not happy.
Everyone who is not happy is not brave.
If someone is either happy or not creative then mary is not patient and vice versa.
If someone is not wise then someone is both kind and not rich and vice versa.
If john is tall then someone is either calm or creative and vice versa.
Everyone who is not humble is generous.
If someone is not funny then someone is kind and vice versa.
Everyone who is not brave is calm or not kind.
Everyone who is kind or not quiet is rich.
If fred is both not patient and creative then someone is both brave and not tall and vice versa.
Everyone who is either not creative or not tall is rich or not brave and vice versa.
Someone is either not happy or not patient.
Fred is either not old or rich.
Someone is not calm.
Fred is strong.
Lucy is either not funny or kind.
Mary is not humble or patient. | Lucy is generous. | neutral | (![X]:((strong(X)&~funny(X))<=>~kind(X)))&
(![X]:((~quiet(X)&creative(X))=>(wise(X)&happy(X))))&
(![X]:(tall(X)<=>~quiet(X)))&
(![X]:((~curious(X)<~>~rich(X))=>(~wise(X)<~>~generous(X))))&
(![X]:((~creative(X)<~>~calm(X))<=>(humble(X)|funny(X))))&
((?[X]:(~tall(X)))=>(~happy(john)))&
(![X]:(~happy(X)=>~brave(X)))&
((?[X]:((happy(X)<~>~creative(X))))<=>(~patient(mary)))&
((?[X]:(~wise(X)))<=>(?[X]:((kind(X)&~rich(X)))))&
((tall(john))<=>(?[X]:((calm(X)<~>creative(X)))))&
(![X]:(~humble(X)=>generous(X)))&
((?[X]:(~funny(X)))<=>(?[X]:(kind(X))))&
(![X]:(~brave(X)=>(calm(X)|~kind(X))))&
(![X]:((kind(X)|~quiet(X))=>rich(X)))&
(((~patient(fred)&creative(fred)))<=>(?[X]:((brave(X)&~tall(X)))))&
(![X]:((~creative(X)<~>~tall(X))<=>(rich(X)|~brave(X))))&
(?[X]:((~happy(X)<~>~patient(X))))&
((~old(fred)<~>rich(fred)))&
(?[X]:(~calm(X)))&
(strong(fred))&
((~funny(lucy)<~>kind(lucy)))&
((~humble(mary)|patient(mary))) | generous(lucy) | [] | null | 0 |
Everyone who is both funny and old is not patient or not strong and vice versa.
If someone is both funny and calm then paul is wise or not curious and vice versa.
If someone is both not rich and strong then john is both wise and curious.
If someone is both funny and not strong then someone is either not humble or funny.
Everyone who is both not old and happy is rich.
If susan is either creative or calm then lucy is both creative and wise and vice versa.
Everyone who is not strong or happy is both creative and not wise and vice versa.
Everyone who is kind is not generous or creative.
If someone is both not strong and kind then someone is kind and vice versa.
If someone is both generous and not generous then someone is kind or not calm.
If someone is strong or old then fred is humble.
Everyone who is generous or not wise is either happy or not wise.
Everyone who is not patient is quiet or not curious.
Everyone who is either not kind or old is both not brave and not old and vice versa.
Everyone who is brave or not curious is both not wise and not brave and vice versa.
Everyone who is both not creative and not humble is not rich and vice versa.
Alice is not creative.
Someone is not generous.
Susan is both old and not tall.
John is calm.
Someone is not creative or generous.
Someone is both quiet and not creative. | Susan is not generous. | neutral | (![X]:((funny(X)&old(X))<=>(~patient(X)|~strong(X))))&
((?[X]:((funny(X)&calm(X))))<=>((wise(paul)|~curious(paul))))&
((?[X]:((~rich(X)&strong(X))))=>((wise(john)&curious(john))))&
((?[X]:((funny(X)&~strong(X))))=>(?[X]:((~humble(X)<~>funny(X)))))&
(![X]:((~old(X)&happy(X))=>rich(X)))&
(((creative(susan)<~>calm(susan)))<=>((creative(lucy)&wise(lucy))))&
(![X]:((~strong(X)|happy(X))<=>(creative(X)&~wise(X))))&
(![X]:(kind(X)=>(~generous(X)|creative(X))))&
((?[X]:((~strong(X)&kind(X))))<=>(?[X]:(kind(X))))&
((?[X]:((generous(X)&~generous(X))))=>(?[X]:((kind(X)|~calm(X)))))&
((?[X]:((strong(X)|old(X))))=>(humble(fred)))&
(![X]:((generous(X)|~wise(X))=>(happy(X)<~>~wise(X))))&
(![X]:(~patient(X)=>(quiet(X)|~curious(X))))&
(![X]:((~kind(X)<~>old(X))<=>(~brave(X)&~old(X))))&
(![X]:((brave(X)|~curious(X))<=>(~wise(X)&~brave(X))))&
(![X]:((~creative(X)&~humble(X))<=>~rich(X)))&
(~creative(alice))&
(?[X]:(~generous(X)))&
((old(susan)&~tall(susan)))&
(calm(john))&
(?[X]:((~creative(X)|generous(X))))&
(?[X]:((quiet(X)&~creative(X)))) | ~generous(susan) | [] | null | 0 |
Everyone who is either not wise or funny is both patient and not calm. Everyone who is both not generous and creative is quiet or brave. Everyone who is old or tall is happy and vice versa. Everyone who is curious or calm is rich or not kind. If someone is both not wise and not strong then fred is curious and vice versa. If someone is either rich or not calm then someone is not patient. If fred is both wise and not brave then paul is tall and vice versa. Everyone who is both not rich and not creative is not calm or happy. Everyone who is both humble and not humble is humble or not strong and vice versa. If mary is curious then someone is both curious and not curious. If lucy is not creative then someone is both quiet and not strong. If someone is both generous and not brave then someone is not happy. Everyone who is either not kind or not generous is both calm and not rich and vice versa. Everyone who is not wise or quiet is old. If someone is patient or generous then someone is both not rich and curious. Everyone who is both not rich and not patient is either not wise or patient. Mary is either not happy or curious. Someone is not happy or not brave. John is happy. Lucy is either humble or not rich. Someone is both quiet and not brave. | Paul is not patient. | neutral | (![X]:((~wise(X)<~>funny(X))=>(patient(X)&~calm(X))))&
(![X]:((~generous(X)&creative(X))=>(quiet(X)|brave(X))))&
(![X]:((old(X)|tall(X))<=>happy(X)))&
(![X]:((curious(X)|calm(X))=>(rich(X)|~kind(X))))&
((?[X]:((~wise(X)&~strong(X))))<=>(curious(fred)))&
((?[X]:((rich(X)<~>~calm(X))))=>(?[X]:(~patient(X))))&
(((wise(fred)&~brave(fred)))<=>(tall(paul)))&
(![X]:((~rich(X)&~creative(X))=>(~calm(X)|happy(X))))&
(![X]:((humble(X)&~humble(X))<=>(humble(X)|~strong(X))))&
((curious(mary))=>(?[X]:((curious(X)&~curious(X)))))&
((~creative(lucy))=>(?[X]:((quiet(X)&~strong(X)))))&
((?[X]:((generous(X)&~brave(X))))=>(?[X]:(~happy(X))))&
(![X]:((~kind(X)<~>~generous(X))<=>(calm(X)&~rich(X))))&
(![X]:((~wise(X)|quiet(X))=>old(X)))&
((?[X]:((patient(X)|generous(X))))=>(?[X]:((~rich(X)&curious(X)))))&
(![X]:((~rich(X)&~patient(X))=>(~wise(X)<~>patient(X))))&
((~happy(mary)<~>curious(mary)))&
(?[X]:((~happy(X)|~brave(X))))&
(happy(john))&
((humble(lucy)<~>~rich(lucy)))&
(?[X]:((quiet(X)&~brave(X)))) | ~patient(paul) | [] | null | 0 |
Everyone who is both old and patient is not kind or old and vice versa.
If someone is not creative then someone is both creative and not brave.
Everyone who is tall or not happy is not strong.
If mary is not kind or old then susan is not generous and vice versa.
Everyone who is not generous is either not generous or wise and vice versa.
If someone is funny or brave then fred is either kind or old and vice versa.
If lucy is both wise and not calm then someone is either not brave or not calm and vice versa.
Everyone who is both not strong and not funny is either old or not creative and vice versa.
If fred is both not curious and wise then paul is either not happy or not brave.
Everyone who is not creative or not kind is both humble and creative.
If someone is either not funny or not brave then lucy is both not creative and not curious and vice versa.
If fred is either kind or creative then alice is both not wise and not calm and vice versa.
If someone is curious or not tall then alice is both wise and patient and vice versa.
Everyone who is curious is brave or rich.
Everyone who is quiet or not curious is not tall or not strong and vice versa.
Everyone who is tall is brave or not creative.
Fred is not generous.
John is quiet.
John is not old or not tall.
Lucy is not wise. | Susan is not generous. | contradiction | (![X]:((old(X)&patient(X))<=>(~kind(X)|old(X))))&
((?[X]:(~creative(X)))=>(?[X]:((creative(X)&~brave(X)))))&
(![X]:((tall(X)|~happy(X))=>~strong(X)))&
(((~kind(mary)|old(mary)))<=>(~generous(susan)))&
(![X]:(~generous(X)<=>(~generous(X)<~>wise(X))))&
((?[X]:((funny(X)|brave(X))))<=>((kind(fred)<~>old(fred))))&
(((wise(lucy)&~calm(lucy)))<=>(?[X]:((~brave(X)<~>~calm(X)))))&
(![X]:((~strong(X)&~funny(X))<=>(old(X)<~>~creative(X))))&
(((~curious(fred)&wise(fred)))=>((~happy(paul)<~>~brave(paul))))&
(![X]:((~creative(X)|~kind(X))=>(humble(X)&creative(X))))&
((?[X]:((~funny(X)<~>~brave(X))))<=>((~creative(lucy)&~curious(lucy))))&
(((kind(fred)<~>creative(fred)))<=>((~wise(alice)&~calm(alice))))&
((?[X]:((curious(X)|~tall(X))))<=>((wise(alice)&patient(alice))))&
(![X]:(curious(X)=>(brave(X)|rich(X))))&
(![X]:((quiet(X)|~curious(X))<=>(~tall(X)|~strong(X))))&
(![X]:(tall(X)=>(brave(X)|~creative(X))))&
(~generous(fred))&
(quiet(john))&
((~old(john)|~tall(john)))&
(~wise(lucy)) | ~generous(susan) | [
"p0",
"p3",
"p4",
"p7",
"p9",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1792741160793407305276229
% SZS output start Proof for 1792741160793407305276229
1. ! [X0] : ((patient(X0) & old(X0)) <=> (old(X0) | ~kind(X0))) [input p0]
4. (old(mary) | ~kind(mary)) <=> ~generous(susan) [input p3]
5. ! [X0] : (~generous(X0) <=> (~generous(X0) <~> wise(X0))) [input p4]
8. ! [X0] : ((~funny(X0) & ~strong(X0)) <=> (old(X0) <~> ~creative(X0))) [input p7]
10. ! [X0] : ((~kind(X0) | ~creative(X0)) => (creative(X0) & humble(X0))) [input p9]
11. ? [X0] : (~funny(X0) <~> ~brave(X0)) <=> (~curious(lucy) & ~creative(lucy)) [input p10]
13. ? [X0] : (~tall(X0) | curious(X0)) <=> (patient(alice) & wise(alice)) [input p12]
16. ! [X0] : (tall(X0) => (~creative(X0) | brave(X0))) [input p15]
21. ~generous(susan) [input hypothesis]
24. ! [X0] : ((~kind(X0) | ~creative(X0)) => creative(X0)) [pure predicate removal 10]
29. ! [X0] : (creative(X0) | (kind(X0) & creative(X0))) [ennf transformation 24]
30. ! [X0] : ((~creative(X0) | brave(X0)) | ~tall(X0)) [ennf transformation 16]
31. ! [X0] : (~creative(X0) | brave(X0) | ~tall(X0)) [flattening 30]
32. ! [X0] : (((patient(X0) & old(X0)) | (~old(X0) & kind(X0))) & ((old(X0) | ~kind(X0)) | (~patient(X0) | ~old(X0)))) [nnf transformation 1]
33. ! [X0] : (((patient(X0) & old(X0)) | (~old(X0) & kind(X0))) & (old(X0) | ~kind(X0) | ~patient(X0) | ~old(X0))) [flattening 32]
37. ((old(mary) | ~kind(mary)) | generous(susan)) & (~generous(susan) | (~old(mary) & kind(mary))) [nnf transformation 4]
38. (old(mary) | ~kind(mary) | generous(susan)) & (~generous(susan) | (~old(mary) & kind(mary))) [flattening 37]
39. ! [X0] : ((~generous(X0) | ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0)))) & (((~wise(X0) | generous(X0)) & (wise(X0) | ~generous(X0))) | generous(X0))) [nnf transformation 5]
49. ! [X0] : (((~funny(X0) & ~strong(X0)) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0)))) & (((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | (funny(X0) | strong(X0)))) [nnf transformation 8]
50. ! [X0] : (((~funny(X0) & ~strong(X0)) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0)))) & (((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | funny(X0) | strong(X0))) [flattening 49]
52. (? [X0] : ((brave(X0) | funny(X0)) & (~brave(X0) | ~funny(X0))) | (curious(lucy) | creative(lucy))) & ((~curious(lucy) & ~creative(lucy)) | ! [X0] : ((~funny(X0) | brave(X0)) & (~brave(X0) | funny(X0)))) [nnf transformation 11]
53. (? [X0] : ((brave(X0) | funny(X0)) & (~brave(X0) | ~funny(X0))) | curious(lucy) | creative(lucy)) & ((~curious(lucy) & ~creative(lucy)) | ! [X0] : ((~funny(X0) | brave(X0)) & (~brave(X0) | funny(X0)))) [flattening 52]
54. (? [X0] : ((brave(X0) | funny(X0)) & (~brave(X0) | ~funny(X0))) | curious(lucy) | creative(lucy)) & ((~curious(lucy) & ~creative(lucy)) | ! [X1] : ((~funny(X1) | brave(X1)) & (~brave(X1) | funny(X1)))) [rectify 53]
55. ? [X0] : ((brave(X0) | funny(X0)) & (~brave(X0) | ~funny(X0))) => ((brave(sK3) | funny(sK3)) & (~brave(sK3) | ~funny(sK3))) [choice axiom]
56. (((brave(sK3) | funny(sK3)) & (~brave(sK3) | ~funny(sK3))) | curious(lucy) | creative(lucy)) & ((~curious(lucy) & ~creative(lucy)) | ! [X1] : ((~funny(X1) | brave(X1)) & (~brave(X1) | funny(X1)))) [skolemisation 54,55]
59. (? [X0] : (~tall(X0) | curious(X0)) | (~patient(alice) | ~wise(alice))) & ((patient(alice) & wise(alice)) | ! [X0] : (tall(X0) & ~curious(X0))) [nnf transformation 13]
60. (? [X0] : (~tall(X0) | curious(X0)) | ~patient(alice) | ~wise(alice)) & ((patient(alice) & wise(alice)) | ! [X0] : (tall(X0) & ~curious(X0))) [flattening 59]
61. (? [X0] : (~tall(X0) | curious(X0)) | ~patient(alice) | ~wise(alice)) & ((patient(alice) & wise(alice)) | ! [X1] : (tall(X1) & ~curious(X1))) [rectify 60]
62. ? [X0] : (~tall(X0) | curious(X0)) => (~tall(sK4) | curious(sK4)) [choice axiom]
63. ((~tall(sK4) | curious(sK4)) | ~patient(alice) | ~wise(alice)) & ((patient(alice) & wise(alice)) | ! [X1] : (tall(X1) & ~curious(X1))) [skolemisation 61,62]
67. kind(X0) | old(X0) [cnf transformation 33]
77. old(mary) | ~kind(mary) | generous(susan) [cnf transformation 38]
79. ~wise(X0) | generous(X0) | generous(X0) [cnf transformation 39]
81. ~generous(X0) | ~generous(X0) | ~wise(X0) [cnf transformation 39]
98. ~funny(X0) | ~creative(X0) | ~old(X0) [cnf transformation 50]
102. creative(X0) | creative(X0) [cnf transformation 29]
104. ~creative(lucy) | ~brave(X1) | funny(X1) [cnf transformation 56]
117. wise(alice) | tall(X1) [cnf transformation 63]
125. ~tall(X0) | brave(X0) | ~creative(X0) [cnf transformation 31]
130. ~generous(susan) [cnf transformation 21]
131. creative(X0) [duplicate literal removal 102]
132. ~wise(X0) | generous(X0) [duplicate literal removal 79]
133. ~wise(X0) | ~generous(X0) [duplicate literal removal 81]
135. 1 <=> ! [X1] : creative(X1) [avatar definition]
136. creative(X1) <- (1) [avatar component clause 135]
147. old(mary) | generous(susan) [subsumption resolution 77,67]
149. 4 <=> generous(susan) [avatar definition]
153. 5 <=> old(mary) [avatar definition]
155. old(mary) <- (5) [avatar component clause 153]
156. 4 | 5 [avatar split clause 147,153,149]
163. ~wise(X0) [subsumption resolution 132,133]
208. 1 [avatar split clause 131,135]
210. 16 <=> creative(lucy) [avatar definition]
211. ~creative(lucy) <- (~16) [avatar component clause 210]
232. 21 <=> ! [X1] : (~brave(X1) | funny(X1)) [avatar definition]
233. ~brave(X1) | funny(X1) <- (21) [avatar component clause 232]
236. 21 | ~16 [avatar split clause 104,210,232]
252. 24 <=> ! [X1] : tall(X1) [avatar definition]
253. tall(X1) <- (24) [avatar component clause 252]
263. tall(X1) [subsumption resolution 117,163]
264. 24 [avatar split clause 263,252]
276. ~4 [avatar split clause 130,149]
277. $false <- (1, ~16) [resolution 211,136]
278. ~1 | 16 [avatar contradiction clause 277]
300. brave(X0) | ~creative(X0) <- (24) [resolution 125,253]
301. brave(X0) <- (1, 24) [subsumption resolution 300,136]
303. funny(X0) <- (1, 21, 24) [resolution 301,233]
309. ~creative(X1) | ~old(X1) <- (1, 21, 24) [resolution 303,98]
313. ~old(X1) <- (1, 21, 24) [subsumption resolution 309,136]
319. $false <- (1, 5, 21, 24) [resolution 313,155]
320. ~1 | ~5 | ~21 | ~24 [avatar contradiction clause 319]
321. $false [avatar sat refutation 156,208,236,264,276,278,320]
% SZS output end Proof for 1792741160793407305276229
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is happy. Everyone who is brave or not kind is not kind or rich and vice versa. Everyone who is either not old or wise is calm or brave and vice versa. Everyone who is not quiet or not strong is either funny or wise and vice versa. Everyone who is either curious or not strong is tall or not patient. Everyone who is calm or not old is not curious or not brave and vice versa. Everyone who is not brave is both not brave and not tall. Everyone who is not humble or humble is not rich or not creative. Everyone who is old is both not tall and generous and vice versa. Everyone who is either calm or curious is generous. Everyone who is not kind or strong is patient or not kind. Everyone who is either not humble or humble is both not curious and not creative. Everyone who is generous is not wise and vice versa. Everyone who is both rich and brave is both happy and not wise and vice versa. If someone is both not creative and happy then mary is both not brave and generous. If lucy is either not happy or rich then paul is either generous or calm. Someone is funny. Someone is either kind or not rich. Someone is brave or kind. | Lucy is not funny. | neutral | (![X]:(~tall(X)=>happy(X)))&
(![X]:((brave(X)|~kind(X))<=>(~kind(X)|rich(X))))&
(![X]:((~old(X)<~>wise(X))<=>(calm(X)|brave(X))))&
(![X]:((~quiet(X)|~strong(X))<=>(funny(X)<~>wise(X))))&
(![X]:((curious(X)<~>~strong(X))=>(tall(X)|~patient(X))))&
(![X]:((calm(X)|~old(X))<=>(~curious(X)|~brave(X))))&
(![X]:(~brave(X)=>(~brave(X)&~tall(X))))&
(![X]:((~humble(X)|humble(X))=>(~rich(X)|~creative(X))))&
(![X]:(old(X)<=>(~tall(X)&generous(X))))&
(![X]:((calm(X)<~>curious(X))=>generous(X)))&
(![X]:((~kind(X)|strong(X))=>(patient(X)|~kind(X))))&
(![X]:((~humble(X)<~>humble(X))=>(~curious(X)&~creative(X))))&
(![X]:(generous(X)<=>~wise(X)))&
(![X]:((rich(X)&brave(X))<=>(happy(X)&~wise(X))))&
((?[X]:((~creative(X)&happy(X))))=>((~brave(mary)&generous(mary))))&
(((~happy(lucy)<~>rich(lucy)))=>((generous(paul)<~>calm(paul))))&
(?[X]:(funny(X)))&
(?[X]:((kind(X)<~>~rich(X))))&
(?[X]:((brave(X)|kind(X)))) | ~funny(lucy) | [] | null | 0 |
Everyone who is either humble or not funny is patient and vice versa. Everyone who is brave or not kind is either wise or not brave and vice versa. Everyone who is either not happy or patient is both tall and funny. If paul is strong or curious then john is both strong and happy. If lucy is tall then someone is not humble or old and vice versa. Everyone who is both not quiet and brave is either not wise or funny. Everyone who is both calm and not creative is not curious. Everyone who is both not patient and not strong is generous and vice versa. Everyone who is not old or wise is both patient and not kind and vice versa. Everyone who is not old is patient or generous and vice versa. Everyone who is both tall and not quiet is curious or not humble. Everyone who is curious or strong is either strong or generous. If someone is quiet or funny then lucy is either humble or not humble. Everyone who is generous is brave and vice versa. Everyone who is either calm or creative is brave or not brave. Everyone who is both not funny and not humble is generous or curious and vice versa. Mary is both funny and not patient. Lucy is happy or not wise. Someone is not calm. John is not quiet or old. Someone is not happy. Someone is either generous or patient. John is either not humble or creative. | John is tall. | neutral | (![X]:((humble(X)<~>~funny(X))<=>patient(X)))&
(![X]:((brave(X)|~kind(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((~happy(X)<~>patient(X))=>(tall(X)&funny(X))))&
(((strong(paul)|curious(paul)))=>((strong(john)&happy(john))))&
((tall(lucy))<=>(?[X]:((~humble(X)|old(X)))))&
(![X]:((~quiet(X)&brave(X))=>(~wise(X)<~>funny(X))))&
(![X]:((calm(X)&~creative(X))=>~curious(X)))&
(![X]:((~patient(X)&~strong(X))<=>generous(X)))&
(![X]:((~old(X)|wise(X))<=>(patient(X)&~kind(X))))&
(![X]:(~old(X)<=>(patient(X)|generous(X))))&
(![X]:((tall(X)&~quiet(X))=>(curious(X)|~humble(X))))&
(![X]:((curious(X)|strong(X))=>(strong(X)<~>generous(X))))&
((?[X]:((quiet(X)|funny(X))))=>((humble(lucy)<~>~humble(lucy))))&
(![X]:(generous(X)<=>brave(X)))&
(![X]:((calm(X)<~>creative(X))=>(brave(X)|~brave(X))))&
(![X]:((~funny(X)&~humble(X))<=>(generous(X)|curious(X))))&
((funny(mary)&~patient(mary)))&
((happy(lucy)|~wise(lucy)))&
(?[X]:(~calm(X)))&
((~quiet(john)|old(john)))&
(?[X]:(~happy(X)))&
(?[X]:((generous(X)<~>patient(X))))&
((~humble(john)<~>creative(john))) | tall(john) | [] | null | 0 |
Everyone who is not tall or not kind is either not rich or kind.
Everyone who is humble or creative is both not quiet and not kind.
If john is either not rich or not strong then someone is both rich and not strong.
Everyone who is either not old or not generous is curious and vice versa.
If lucy is funny or tall then someone is funny.
Everyone who is both not funny and not old is not generous and vice versa.
Everyone who is either not calm or brave is either funny or not kind.
Everyone who is either old or kind is both not kind and curious and vice versa.
If paul is not rich or happy then alice is both quiet and generous.
Everyone who is both not funny and rich is happy or tall and vice versa.
If alice is happy or not calm then someone is rich and vice versa.
If someone is either old or not rich then someone is kind.
Everyone who is either not curious or not tall is not humble or wise.
If lucy is both generous and old then someone is either funny or creative.
John is either not wise or rich.
Paul is old or not brave.
Lucy is not kind or not brave.
Paul is calm or not strong.
Someone is either brave or strong.
Alice is calm or not kind.
Alice is either not patient or rich. | Lucy is happy. | neutral | (![X]:((~tall(X)|~kind(X))=>(~rich(X)<~>kind(X))))&
(![X]:((humble(X)|creative(X))=>(~quiet(X)&~kind(X))))&
(((~rich(john)<~>~strong(john)))=>(?[X]:((rich(X)&~strong(X)))))&
(![X]:((~old(X)<~>~generous(X))<=>curious(X)))&
(((funny(lucy)|tall(lucy)))=>(?[X]:(funny(X))))&
(![X]:((~funny(X)&~old(X))<=>~generous(X)))&
(![X]:((~calm(X)<~>brave(X))=>(funny(X)<~>~kind(X))))&
(![X]:((old(X)<~>kind(X))<=>(~kind(X)&curious(X))))&
(((~rich(paul)|happy(paul)))=>((quiet(alice)&generous(alice))))&
(![X]:((~funny(X)&rich(X))<=>(happy(X)|tall(X))))&
(((happy(alice)|~calm(alice)))<=>(?[X]:(rich(X))))&
((?[X]:((old(X)<~>~rich(X))))=>(?[X]:(kind(X))))&
(![X]:((~curious(X)<~>~tall(X))=>(~humble(X)|wise(X))))&
(((generous(lucy)&old(lucy)))=>(?[X]:((funny(X)<~>creative(X)))))&
((~wise(john)<~>rich(john)))&
((old(paul)|~brave(paul)))&
((~kind(lucy)|~brave(lucy)))&
((calm(paul)|~strong(paul)))&
(?[X]:((brave(X)<~>strong(X))))&
((calm(alice)|~kind(alice)))&
((~patient(alice)<~>rich(alice))) | happy(lucy) | [] | null | 0 |
Everyone who is both not calm and not happy is both funny and humble. If john is happy then someone is both not brave and not old and vice versa. If lucy is either humble or kind then someone is not kind. If someone is both not rich and humble then paul is both not calm and not tall. Everyone who is both funny and wise is both not funny and not curious and vice versa. If fred is not happy or not generous then mary is not funny and vice versa. If fred is not old then someone is curious or not happy. Everyone who is both kind and not curious is both not happy and calm and vice versa. If alice is generous then someone is brave. Everyone who is wise is either humble or not creative. If john is old or wise then john is not curious or not wise and vice versa. Everyone who is both not rich and generous is tall or not creative. If someone is both not funny and not curious then paul is wise or not kind. If susan is either rich or generous then john is strong or not quiet. If paul is both not creative and kind then fred is not calm or calm and vice versa. Everyone who is both wise and not generous is not quiet and vice versa. Alice is not generous. Alice is brave. Mary is both humble and not creative. Someone is quiet. John is not wise or not funny. Someone is not generous or funny. Mary is not rich. Someone is both not wise and strong. | Lucy is not rich. | neutral | (![X]:((~calm(X)&~happy(X))=>(funny(X)&humble(X))))&
((happy(john))<=>(?[X]:((~brave(X)&~old(X)))))&
(((humble(lucy)<~>kind(lucy)))=>(?[X]:(~kind(X))))&
((?[X]:((~rich(X)&humble(X))))=>((~calm(paul)&~tall(paul))))&
(![X]:((funny(X)&wise(X))<=>(~funny(X)&~curious(X))))&
(((~happy(fred)|~generous(fred)))<=>(~funny(mary)))&
((~old(fred))=>(?[X]:((curious(X)|~happy(X)))))&
(![X]:((kind(X)&~curious(X))<=>(~happy(X)&calm(X))))&
((generous(alice))=>(?[X]:(brave(X))))&
(![X]:(wise(X)=>(humble(X)<~>~creative(X))))&
(((old(john)|wise(john)))<=>((~curious(john)|~wise(john))))&
(![X]:((~rich(X)&generous(X))=>(tall(X)|~creative(X))))&
((?[X]:((~funny(X)&~curious(X))))=>((wise(paul)|~kind(paul))))&
(((rich(susan)<~>generous(susan)))=>((strong(john)|~quiet(john))))&
(((~creative(paul)&kind(paul)))<=>((~calm(fred)|calm(fred))))&
(![X]:((wise(X)&~generous(X))<=>~quiet(X)))&
(~generous(alice))&
(brave(alice))&
((humble(mary)&~creative(mary)))&
(?[X]:(quiet(X)))&
((~wise(john)|~funny(john)))&
(?[X]:((~generous(X)|funny(X))))&
(~rich(mary))&
(?[X]:((~wise(X)&strong(X)))) | ~rich(lucy) | [] | null | 0 |
If someone is not old then alice is not creative or not brave. If mary is either not tall or happy then someone is not rich or not wise. Everyone who is not old is either creative or not calm. If someone is either not creative or creative then someone is wise or not tall. Everyone who is not strong is old or not rich. If paul is both not generous and calm then someone is either not quiet or old and vice versa. If lucy is kind or not old then someone is strong or kind. If fred is creative or curious then susan is not quiet or not tall. Everyone who is both not curious and old is not calm and vice versa. Everyone who is creative is quiet and vice versa. Everyone who is calm is both rich and not rich and vice versa. Everyone who is either not brave or not rich is both strong and curious. If someone is both happy and humble then someone is humble or calm. Everyone who is both rich and calm is both kind and not humble. If paul is not wise or generous then someone is kind and vice versa. Someone is either not strong or not tall. Someone is not kind. Alice is both wise and not funny. Susan is curious or old. Someone is strong. Someone is both not tall and not wise. Alice is either quiet or not happy. Someone is both not patient and not calm. | Mary is not creative. | entailment | ((?[X]:(~old(X)))=>((~creative(alice)|~brave(alice))))&
(((~tall(mary)<~>happy(mary)))=>(?[X]:((~rich(X)|~wise(X)))))&
(![X]:(~old(X)=>(creative(X)<~>~calm(X))))&
((?[X]:((~creative(X)<~>creative(X))))=>(?[X]:((wise(X)|~tall(X)))))&
(![X]:(~strong(X)=>(old(X)|~rich(X))))&
(((~generous(paul)&calm(paul)))<=>(?[X]:((~quiet(X)<~>old(X)))))&
(((kind(lucy)|~old(lucy)))=>(?[X]:((strong(X)|kind(X)))))&
(((creative(fred)|curious(fred)))=>((~quiet(susan)|~tall(susan))))&
(![X]:((~curious(X)&old(X))<=>~calm(X)))&
(![X]:(creative(X)<=>quiet(X)))&
(![X]:(calm(X)<=>(rich(X)&~rich(X))))&
(![X]:((~brave(X)<~>~rich(X))=>(strong(X)&curious(X))))&
((?[X]:((happy(X)&humble(X))))=>(?[X]:((humble(X)|calm(X)))))&
(![X]:((rich(X)&calm(X))=>(kind(X)&~humble(X))))&
(((~wise(paul)|generous(paul)))<=>(?[X]:(kind(X))))&
(?[X]:((~strong(X)<~>~tall(X))))&
(?[X]:(~kind(X)))&
((wise(alice)&~funny(alice)))&
((curious(susan)|old(susan)))&
(?[X]:(strong(X)))&
(?[X]:((~tall(X)&~wise(X))))&
((quiet(alice)<~>~happy(alice)))&
(?[X]:((~patient(X)&~calm(X)))) | ~creative(mary) | [
"p5",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5117331360295444292919150
% SZS output start Proof for 5117331360295444292919150
6. (calm(paul) & ~generous(paul)) <=> ? [X0] : (~quiet(X0) <~> old(X0)) [input p5]
9. ! [X0] : ((old(X0) & ~curious(X0)) <=> ~calm(X0)) [input p8]
10. ! [X0] : (creative(X0) <=> quiet(X0)) [input p9]
11. ! [X0] : (calm(X0) <=> (~rich(X0) & rich(X0))) [input p10]
24. creative(mary) [input hypothesis]
51. ((calm(paul) & ~generous(paul)) | ! [X0] : ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (? [X0] : ((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~calm(paul) | generous(paul))) [nnf transformation 6]
52. ((calm(paul) & ~generous(paul)) | ! [X0] : ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (? [X0] : ((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | ~calm(paul) | generous(paul)) [flattening 51]
53. ((calm(paul) & ~generous(paul)) | ! [X0] : ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (? [X1] : ((~old(X1) | quiet(X1)) & (old(X1) | ~quiet(X1))) | ~calm(paul) | generous(paul)) [rectify 52]
54. ? [X1] : ((~old(X1) | quiet(X1)) & (old(X1) | ~quiet(X1))) => ((~old(sK2) | quiet(sK2)) & (old(sK2) | ~quiet(sK2))) [choice axiom]
55. ((calm(paul) & ~generous(paul)) | ! [X0] : ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (((~old(sK2) | quiet(sK2)) & (old(sK2) | ~quiet(sK2))) | ~calm(paul) | generous(paul)) [skolemisation 53,54]
58. ! [X0] : (((old(X0) & ~curious(X0)) | calm(X0)) & (~calm(X0) | (~old(X0) | curious(X0)))) [nnf transformation 9]
59. ! [X0] : (((old(X0) & ~curious(X0)) | calm(X0)) & (~calm(X0) | ~old(X0) | curious(X0))) [flattening 58]
60. ! [X0] : ((creative(X0) | ~quiet(X0)) & (quiet(X0) | ~creative(X0))) [nnf transformation 10]
61. ! [X0] : ((calm(X0) | (rich(X0) | ~rich(X0))) & ((~rich(X0) & rich(X0)) | ~calm(X0))) [nnf transformation 11]
62. ! [X0] : ((calm(X0) | rich(X0) | ~rich(X0)) & ((~rich(X0) & rich(X0)) | ~calm(X0))) [flattening 61]
97. calm(paul) | ~quiet(X0) | ~old(X0) [cnf transformation 55]
104. calm(X0) | old(X0) [cnf transformation 59]
105. ~creative(X0) | quiet(X0) [cnf transformation 60]
107. rich(X0) | ~calm(X0) [cnf transformation 62]
108. ~calm(X0) | ~rich(X0) [cnf transformation 62]
131. creative(mary) [cnf transformation 24]
135. 1 <=> ! [X0] : old(X0) [avatar definition]
136. old(X0) <- (1) [avatar component clause 135]
181. 12 <=> ! [X0] : (~quiet(X0) | ~old(X0)) [avatar definition]
182. ~quiet(X0) | ~old(X0) <- (12) [avatar component clause 181]
184. 13 <=> calm(paul) [avatar definition]
186. calm(paul) <- (13) [avatar component clause 184]
187. 12 | 13 [avatar split clause 97,184,181]
244. ~calm(X0) [subsumption resolution 107,108]
297. $false <- (13) [subsumption resolution 186,244]
298. ~13 [avatar contradiction clause 297]
302. old(X0) [resolution 104,244]
303. 1 [avatar split clause 302,135]
306. quiet(mary) [resolution 105,131]
309. ~old(mary) <- (12) [resolution 182,306]
310. $false <- (1, 12) [subsumption resolution 309,136]
311. ~1 | ~12 [avatar contradiction clause 310]
312. $false [avatar sat refutation 187,298,303,311]
% SZS output end Proof for 5117331360295444292919150
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or not patient is both creative and not old.
Everyone who is both strong and wise is either not creative or not kind and vice versa.
If someone is both curious and strong then susan is not curious and vice versa.
Everyone who is both old and generous is either funny or rich.
Everyone who is either not kind or tall is not creative.
If someone is not curious then someone is both kind and not rich and vice versa.
Everyone who is wise or not creative is not patient and vice versa.
Everyone who is either quiet or brave is not calm.
Everyone who is both not funny and not generous is either not creative or tall and vice versa.
Everyone who is creative or not happy is not funny or happy.
If someone is wise or funny then susan is either curious or not generous.
Everyone who is humble is either humble or not strong.
If someone is both not kind and not funny then someone is not old or generous.
If someone is generous or not generous then someone is not old or old.
Everyone who is both old and not old is either tall or happy and vice versa.
John is rich.
Mary is happy.
Mary is either quiet or not funny.
Susan is not creative or brave.
Fred is either not creative or happy.
Alice is calm or not creative.
Paul is both not funny and not patient.
Someone is quiet or humble. | Mary is not creative. | contradiction | (![X]:((~funny(X)|~patient(X))=>(creative(X)&~old(X))))&
(![X]:((strong(X)&wise(X))<=>(~creative(X)<~>~kind(X))))&
((?[X]:((curious(X)&strong(X))))<=>(~curious(susan)))&
(![X]:((old(X)&generous(X))=>(funny(X)<~>rich(X))))&
(![X]:((~kind(X)<~>tall(X))=>~creative(X)))&
((?[X]:(~curious(X)))<=>(?[X]:((kind(X)&~rich(X)))))&
(![X]:((wise(X)|~creative(X))<=>~patient(X)))&
(![X]:((quiet(X)<~>brave(X))=>~calm(X)))&
(![X]:((~funny(X)&~generous(X))<=>(~creative(X)<~>tall(X))))&
(![X]:((creative(X)|~happy(X))=>(~funny(X)|happy(X))))&
((?[X]:((wise(X)|funny(X))))=>((curious(susan)<~>~generous(susan))))&
(![X]:(humble(X)=>(humble(X)<~>~strong(X))))&
((?[X]:((~kind(X)&~funny(X))))=>(?[X]:((~old(X)|generous(X)))))&
((?[X]:((generous(X)|~generous(X))))=>(?[X]:((~old(X)|old(X)))))&
(![X]:((old(X)&~old(X))<=>(tall(X)<~>happy(X))))&
(rich(john))&
(happy(mary))&
((quiet(mary)<~>~funny(mary)))&
((~creative(susan)|brave(susan)))&
((~creative(fred)<~>happy(fred)))&
((calm(alice)|~creative(alice)))&
((~funny(paul)&~patient(paul)))&
(?[X]:((quiet(X)|humble(X)))) | ~creative(mary) | [
"p0",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 4144192651809811082291269
% SZS output start Proof for 4144192651809811082291269
1. ! [X0] : ((~patient(X0) | ~funny(X0)) => (~old(X0) & creative(X0))) [input p0]
7. ! [X0] : ((~creative(X0) | wise(X0)) <=> ~patient(X0)) [input p6]
24. ~creative(mary) [input hypothesis]
28. ! [X0] : ((~old(X0) & creative(X0)) | (patient(X0) & funny(X0))) [ennf transformation 1]
52. ! [X0] : (((~creative(X0) | wise(X0)) | patient(X0)) & (~patient(X0) | (creative(X0) & ~wise(X0)))) [nnf transformation 7]
53. ! [X0] : ((~creative(X0) | wise(X0) | patient(X0)) & (~patient(X0) | (creative(X0) & ~wise(X0)))) [flattening 52]
72. creative(X0) | patient(X0) [cnf transformation 28]
92. ~patient(X0) | creative(X0) [cnf transformation 53]
130. ~creative(mary) [cnf transformation 24]
174. creative(X0) [subsumption resolution 92,72]
228. $false [subsumption resolution 130,174]
% SZS output end Proof for 4144192651809811082291269
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not quiet and generous is old or not creative and vice versa. Everyone who is both not old and not generous is either not happy or not generous. Everyone who is either brave or not tall is either not old or not rich and vice versa. Everyone who is creative is not strong or kind. If alice is not funny or rich then fred is patient. If alice is both old and not creative then someone is happy or not kind and vice versa. Everyone who is either not calm or generous is not old and vice versa. If alice is both not calm and creative then someone is not rich or strong and vice versa. Everyone who is both not kind and not creative is curious or kind and vice versa. If paul is not strong or not brave then alice is not quiet or happy and vice versa. If lucy is both kind and not curious then susan is brave or not curious. If someone is not wise then someone is both brave and quiet and vice versa. If susan is not wise then someone is both kind and not generous and vice versa. If john is either calm or not funny then mary is kind and vice versa. Someone is both not old and wise. Mary is both quiet and creative. Someone is either funny or not wise. Someone is either humble or not creative. | Lucy is not brave. | neutral | (![X]:((~quiet(X)&generous(X))<=>(old(X)|~creative(X))))&
(![X]:((~old(X)&~generous(X))=>(~happy(X)<~>~generous(X))))&
(![X]:((brave(X)<~>~tall(X))<=>(~old(X)<~>~rich(X))))&
(![X]:(creative(X)=>(~strong(X)|kind(X))))&
(((~funny(alice)|rich(alice)))=>(patient(fred)))&
(((old(alice)&~creative(alice)))<=>(?[X]:((happy(X)|~kind(X)))))&
(![X]:((~calm(X)<~>generous(X))<=>~old(X)))&
(((~calm(alice)&creative(alice)))<=>(?[X]:((~rich(X)|strong(X)))))&
(![X]:((~kind(X)&~creative(X))<=>(curious(X)|kind(X))))&
(((~strong(paul)|~brave(paul)))<=>((~quiet(alice)|happy(alice))))&
(((kind(lucy)&~curious(lucy)))=>((brave(susan)|~curious(susan))))&
((?[X]:(~wise(X)))<=>(?[X]:((brave(X)&quiet(X)))))&
((~wise(susan))<=>(?[X]:((kind(X)&~generous(X)))))&
(((calm(john)<~>~funny(john)))<=>(kind(mary)))&
(?[X]:((~old(X)&wise(X))))&
((quiet(mary)&creative(mary)))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:((humble(X)<~>~creative(X)))) | ~brave(lucy) | [] | null | 0 |
If fred is patient then paul is either not brave or happy. Everyone who is quiet or not strong is either not humble or humble. If someone is either generous or quiet then mary is brave. Everyone who is both patient and creative is both not tall and strong. Everyone who is either humble or rich is not humble and vice versa. Everyone who is old or not humble is patient or not brave. If mary is both not humble and happy then susan is not humble or not rich. If paul is either curious or not curious then fred is not quiet and vice versa. If susan is either not curious or not old then someone is both not wise and not rich and vice versa. Everyone who is curious is not brave and vice versa. Everyone who is either not happy or not creative is tall or patient and vice versa. If someone is both creative and tall then mary is strong or old. Everyone who is not patient or humble is either brave or not generous and vice versa. Everyone who is not kind or brave is not rich or happy and vice versa. Everyone who is not rich is both not curious and happy and vice versa. If someone is either happy or curious then someone is both happy and not wise and vice versa. Alice is not kind. Someone is either happy or generous. Someone is not generous. Someone is not brave or not old. Someone is either tall or not funny. Someone is both creative and calm. | Fred is brave. | contradiction | ((patient(fred))=>((~brave(paul)<~>happy(paul))))&
(![X]:((quiet(X)|~strong(X))=>(~humble(X)<~>humble(X))))&
((?[X]:((generous(X)<~>quiet(X))))=>(brave(mary)))&
(![X]:((patient(X)&creative(X))=>(~tall(X)&strong(X))))&
(![X]:((humble(X)<~>rich(X))<=>~humble(X)))&
(![X]:((old(X)|~humble(X))=>(patient(X)|~brave(X))))&
(((~humble(mary)&happy(mary)))=>((~humble(susan)|~rich(susan))))&
(((curious(paul)<~>~curious(paul)))<=>(~quiet(fred)))&
(((~curious(susan)<~>~old(susan)))<=>(?[X]:((~wise(X)&~rich(X)))))&
(![X]:(curious(X)<=>~brave(X)))&
(![X]:((~happy(X)<~>~creative(X))<=>(tall(X)|patient(X))))&
((?[X]:((creative(X)&tall(X))))=>((strong(mary)|old(mary))))&
(![X]:((~patient(X)|humble(X))<=>(brave(X)<~>~generous(X))))&
(![X]:((~kind(X)|brave(X))<=>(~rich(X)|happy(X))))&
(![X]:(~rich(X)<=>(~curious(X)&happy(X))))&
((?[X]:((happy(X)<~>curious(X))))<=>(?[X]:((happy(X)&~wise(X)))))&
(~kind(alice))&
(?[X]:((happy(X)<~>generous(X))))&
(?[X]:(~generous(X)))&
(?[X]:((~brave(X)|~old(X))))&
(?[X]:((tall(X)<~>~funny(X))))&
(?[X]:((creative(X)&calm(X)))) | brave(fred) | [
"p4",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 836526898948318481166072
% SZS output start Proof for 836526898948318481166072
5. ! [X0] : ((humble(X0) <~> rich(X0)) <=> ~humble(X0)) [input p4]
10. ! [X0] : (curious(X0) <=> ~brave(X0)) [input p9]
14. ! [X0] : ((brave(X0) | ~kind(X0)) <=> (happy(X0) | ~rich(X0))) [input p13]
15. ! [X0] : (~rich(X0) <=> (happy(X0) & ~curious(X0))) [input p14]
23. brave(fred) [input hypothesis]
41. ! [X0] : ((((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) | humble(X0)) & (~humble(X0) | ((humble(X0) | ~rich(X0)) & (rich(X0) | ~humble(X0))))) [nnf transformation 5]
47. ! [X0] : ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0))) [nnf transformation 10]
52. ! [X0] : (((brave(X0) | ~kind(X0)) | (~happy(X0) & rich(X0))) & ((happy(X0) | ~rich(X0)) | (~brave(X0) & kind(X0)))) [nnf transformation 14]
53. ! [X0] : ((brave(X0) | ~kind(X0) | (~happy(X0) & rich(X0))) & (happy(X0) | ~rich(X0) | (~brave(X0) & kind(X0)))) [flattening 52]
54. ! [X0] : ((~rich(X0) | (~happy(X0) | curious(X0))) & ((happy(X0) & ~curious(X0)) | rich(X0))) [nnf transformation 15]
55. ! [X0] : ((~rich(X0) | ~happy(X0) | curious(X0)) & ((happy(X0) & ~curious(X0)) | rich(X0))) [flattening 54]
80. ~humble(X0) | rich(X0) | ~humble(X0) [cnf transformation 41]
82. rich(X0) | humble(X0) | humble(X0) [cnf transformation 41]
97. ~curious(X0) | ~brave(X0) [cnf transformation 47]
112. happy(X0) | ~rich(X0) | ~brave(X0) [cnf transformation 53]
117. ~rich(X0) | ~happy(X0) | curious(X0) [cnf transformation 55]
132. brave(fred) [cnf transformation 23]
135. ~humble(X0) | rich(X0) [duplicate literal removal 80]
136. rich(X0) | humble(X0) [duplicate literal removal 82]
163. rich(X0) [subsumption resolution 135,136]
207. ~brave(X0) | happy(X0) [subsumption resolution 112,163]
209. ~happy(X0) | curious(X0) [subsumption resolution 117,163]
269. happy(fred) [resolution 207,132]
276. curious(fred) [resolution 209,269]
296. ~brave(fred) [resolution 276,97]
297. $false [subsumption resolution 296,132]
% SZS output end Proof for 836526898948318481166072
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not curious or not wise then lucy is not humble.
If lucy is both humble and not humble then someone is either not curious or happy and vice versa.
If susan is tall then someone is not old or quiet and vice versa.
Everyone who is not funny is both not curious and not patient and vice versa.
If lucy is either curious or old then susan is happy and vice versa.
Everyone who is both quiet and strong is either not happy or patient.
Everyone who is either not tall or strong is either not patient or strong and vice versa.
If lucy is both not kind and happy then susan is generous and vice versa.
If someone is not funny then someone is funny or tall and vice versa.
Everyone who is both kind and not wise is either calm or happy and vice versa.
If alice is kind then someone is both not calm and not old.
Everyone who is not humble or tall is not rich and vice versa.
If lucy is not rich then susan is both happy and curious and vice versa.
Everyone who is not humble or kind is rich.
Everyone who is both old and tall is patient or old.
If lucy is both not brave and not quiet then someone is both not curious and not wise and vice versa.
Lucy is either generous or not wise.
Someone is curious or not calm.
Mary is either not generous or curious.
Someone is strong or happy.
John is not wise or patient.
Someone is either not old or patient.
Someone is humble or not quiet. | Alice is not patient. | neutral | (((~curious(susan)|~wise(susan)))=>(~humble(lucy)))&
(((humble(lucy)&~humble(lucy)))<=>(?[X]:((~curious(X)<~>happy(X)))))&
((tall(susan))<=>(?[X]:((~old(X)|quiet(X)))))&
(![X]:(~funny(X)<=>(~curious(X)&~patient(X))))&
(((curious(lucy)<~>old(lucy)))<=>(happy(susan)))&
(![X]:((quiet(X)&strong(X))=>(~happy(X)<~>patient(X))))&
(![X]:((~tall(X)<~>strong(X))<=>(~patient(X)<~>strong(X))))&
(((~kind(lucy)&happy(lucy)))<=>(generous(susan)))&
((?[X]:(~funny(X)))<=>(?[X]:((funny(X)|tall(X)))))&
(![X]:((kind(X)&~wise(X))<=>(calm(X)<~>happy(X))))&
((kind(alice))=>(?[X]:((~calm(X)&~old(X)))))&
(![X]:((~humble(X)|tall(X))<=>~rich(X)))&
((~rich(lucy))<=>((happy(susan)&curious(susan))))&
(![X]:((~humble(X)|kind(X))=>rich(X)))&
(![X]:((old(X)&tall(X))=>(patient(X)|old(X))))&
(((~brave(lucy)&~quiet(lucy)))<=>(?[X]:((~curious(X)&~wise(X)))))&
((generous(lucy)<~>~wise(lucy)))&
(?[X]:((curious(X)|~calm(X))))&
((~generous(mary)<~>curious(mary)))&
(?[X]:((strong(X)|happy(X))))&
((~wise(john)|patient(john)))&
(?[X]:((~old(X)<~>patient(X))))&
(?[X]:((humble(X)|~quiet(X)))) | ~patient(alice) | [] | null | 0 |
Everyone who is either not patient or funny is both not kind and rich. If someone is both strong and not curious then someone is either patient or curious. Everyone who is both brave and generous is rich or kind. Everyone who is not humble is not rich or not happy and vice versa. Everyone who is not wise is either not patient or humble. If mary is not creative then someone is either not wise or wise and vice versa. Everyone who is not old or not rich is both tall and happy. If someone is either not tall or wise then someone is either calm or not quiet. Everyone who is either wise or patient is both not old and not humble and vice versa. Everyone who is brave is creative. Everyone who is not humble is rich and vice versa. Everyone who is not generous is both not humble and old and vice versa. If someone is both not tall and humble then someone is either not funny or not strong. If someone is either not patient or quiet then john is either kind or calm. Everyone who is funny is old. If someone is either happy or not brave then someone is either generous or not quiet and vice versa. Susan is either generous or rich. Alice is generous or not wise. Susan is either not generous or calm. Someone is not patient. Susan is not calm or not funny. Someone is both not calm and not funny. Someone is both not funny and rich. | Alice is rich. | entailment | (![X]:((~patient(X)<~>funny(X))=>(~kind(X)&rich(X))))&
((?[X]:((strong(X)&~curious(X))))=>(?[X]:((patient(X)<~>curious(X)))))&
(![X]:((brave(X)&generous(X))=>(rich(X)|kind(X))))&
(![X]:(~humble(X)<=>(~rich(X)|~happy(X))))&
(![X]:(~wise(X)=>(~patient(X)<~>humble(X))))&
((~creative(mary))<=>(?[X]:((~wise(X)<~>wise(X)))))&
(![X]:((~old(X)|~rich(X))=>(tall(X)&happy(X))))&
((?[X]:((~tall(X)<~>wise(X))))=>(?[X]:((calm(X)<~>~quiet(X)))))&
(![X]:((wise(X)<~>patient(X))<=>(~old(X)&~humble(X))))&
(![X]:(brave(X)=>creative(X)))&
(![X]:(~humble(X)<=>rich(X)))&
(![X]:(~generous(X)<=>(~humble(X)&old(X))))&
((?[X]:((~tall(X)&humble(X))))=>(?[X]:((~funny(X)<~>~strong(X)))))&
((?[X]:((~patient(X)<~>quiet(X))))=>((kind(john)<~>calm(john))))&
(![X]:(funny(X)=>old(X)))&
((?[X]:((happy(X)<~>~brave(X))))<=>(?[X]:((generous(X)<~>~quiet(X)))))&
((generous(susan)<~>rich(susan)))&
((generous(alice)|~wise(alice)))&
((~generous(susan)<~>calm(susan)))&
(?[X]:(~patient(X)))&
((~calm(susan)|~funny(susan)))&
(?[X]:((~calm(X)&~funny(X))))&
(?[X]:((~funny(X)&rich(X)))) | rich(alice) | [
"p3",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2466694644286649650717876
% SZS output start Proof for 2466694644286649650717876
4. ! [X0] : (~humble(X0) <=> (~happy(X0) | ~rich(X0))) [input p3]
11. ! [X0] : (~humble(X0) <=> rich(X0)) [input p10]
24. ~rich(alice) [input hypothesis]
45. ! [X0] : ((~humble(X0) | (happy(X0) & rich(X0))) & ((~happy(X0) | ~rich(X0)) | humble(X0))) [nnf transformation 4]
46. ! [X0] : ((~humble(X0) | (happy(X0) & rich(X0))) & (~happy(X0) | ~rich(X0) | humble(X0))) [flattening 45]
58. ! [X0] : ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0))) [nnf transformation 11]
87. ~humble(X0) | rich(X0) [cnf transformation 46]
110. rich(X0) | humble(X0) [cnf transformation 58]
111. ~humble(X0) | ~rich(X0) [cnf transformation 58]
141. ~rich(alice) [cnf transformation 24]
191. ~humble(X0) [subsumption resolution 111,87]
192. rich(X0) [subsumption resolution 110,191]
259. $false [subsumption resolution 141,192]
% SZS output end Proof for 2466694644286649650717876
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is both rich and kind.
If mary is not brave then someone is strong or not happy and vice versa.
If someone is not wise or not rich then someone is curious or kind.
Everyone who is both not rich and patient is not quiet or not old and vice versa.
If john is humble then susan is either not creative or funny.
Everyone who is humble is not calm and vice versa.
Everyone who is either not strong or quiet is both curious and not curious and vice versa.
Everyone who is happy or not old is either not patient or not happy and vice versa.
Everyone who is both not strong and calm is either creative or not generous and vice versa.
If fred is either funny or not patient then someone is both not humble and wise and vice versa.
Everyone who is not generous or not old is not rich or not creative and vice versa.
Everyone who is quiet or not calm is both kind and creative.
If alice is kind then susan is either patient or quiet.
If fred is kind or not brave then someone is generous.
If someone is strong or not calm then susan is either not patient or not curious and vice versa.
Everyone who is kind is tall and vice versa.
Someone is either not humble or not creative.
Someone is either creative or humble.
Alice is both not wise and not happy.
Someone is not curious or not calm.
Lucy is both not brave and happy.
Susan is both not humble and tall. | Susan is rich. | entailment | (![X]:(patient(X)=>(rich(X)&kind(X))))&
((~brave(mary))<=>(?[X]:((strong(X)|~happy(X)))))&
((?[X]:((~wise(X)|~rich(X))))=>(?[X]:((curious(X)|kind(X)))))&
(![X]:((~rich(X)&patient(X))<=>(~quiet(X)|~old(X))))&
((humble(john))=>((~creative(susan)<~>funny(susan))))&
(![X]:(humble(X)<=>~calm(X)))&
(![X]:((~strong(X)<~>quiet(X))<=>(curious(X)&~curious(X))))&
(![X]:((happy(X)|~old(X))<=>(~patient(X)<~>~happy(X))))&
(![X]:((~strong(X)&calm(X))<=>(creative(X)<~>~generous(X))))&
(((funny(fred)<~>~patient(fred)))<=>(?[X]:((~humble(X)&wise(X)))))&
(![X]:((~generous(X)|~old(X))<=>(~rich(X)|~creative(X))))&
(![X]:((quiet(X)|~calm(X))=>(kind(X)&creative(X))))&
((kind(alice))=>((patient(susan)<~>quiet(susan))))&
(((kind(fred)|~brave(fred)))=>(?[X]:(generous(X))))&
((?[X]:((strong(X)|~calm(X))))<=>((~patient(susan)<~>~curious(susan))))&
(![X]:(kind(X)<=>tall(X)))&
(?[X]:((~humble(X)<~>~creative(X))))&
(?[X]:((creative(X)<~>humble(X))))&
((~wise(alice)&~happy(alice)))&
(?[X]:((~curious(X)|~calm(X))))&
((~brave(lucy)&happy(lucy)))&
((~humble(susan)&tall(susan))) | rich(susan) | [
"p0",
"p3",
"p5",
"p6",
"p8",
"p10",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3808560181826991489410702
% SZS output start Proof for 3808560181826991489410702
1. ! [X0] : (patient(X0) => (kind(X0) & rich(X0))) [input p0]
4. ! [X0] : ((patient(X0) & ~rich(X0)) <=> (~old(X0) | ~quiet(X0))) [input p3]
6. ! [X0] : (humble(X0) <=> ~calm(X0)) [input p5]
7. ! [X0] : ((~strong(X0) <~> quiet(X0)) <=> (~curious(X0) & curious(X0))) [input p6]
9. ! [X0] : ((calm(X0) & ~strong(X0)) <=> (creative(X0) <~> ~generous(X0))) [input p8]
11. ! [X0] : ((~old(X0) | ~generous(X0)) <=> (~creative(X0) | ~rich(X0))) [input p10]
12. ! [X0] : ((~calm(X0) | quiet(X0)) => (creative(X0) & kind(X0))) [input p11]
22. tall(susan) & ~humble(susan) [input p21]
23. ~rich(susan) [input hypothesis]
25. ! [X0] : ((kind(X0) & rich(X0)) | ~patient(X0)) [ennf transformation 1]
28. ! [X0] : ((creative(X0) & kind(X0)) | (calm(X0) & ~quiet(X0))) [ennf transformation 12]
38. ! [X0] : (((patient(X0) & ~rich(X0)) | (old(X0) & quiet(X0))) & ((~old(X0) | ~quiet(X0)) | (~patient(X0) | rich(X0)))) [nnf transformation 4]
39. ! [X0] : (((patient(X0) & ~rich(X0)) | (old(X0) & quiet(X0))) & (~old(X0) | ~quiet(X0) | ~patient(X0) | rich(X0))) [flattening 38]
41. ! [X0] : ((humble(X0) | calm(X0)) & (~calm(X0) | ~humble(X0))) [nnf transformation 6]
42. ! [X0] : ((((~quiet(X0) | strong(X0)) & (quiet(X0) | ~strong(X0))) | (curious(X0) | ~curious(X0))) & ((~curious(X0) & curious(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0))))) [nnf transformation 7]
43. ! [X0] : ((((~quiet(X0) | strong(X0)) & (quiet(X0) | ~strong(X0))) | curious(X0) | ~curious(X0)) & ((~curious(X0) & curious(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0))))) [flattening 42]
46. ! [X0] : (((calm(X0) & ~strong(X0)) | ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0)))) & (((generous(X0) | ~creative(X0)) & (~generous(X0) | creative(X0))) | (~calm(X0) | strong(X0)))) [nnf transformation 9]
47. ! [X0] : (((calm(X0) & ~strong(X0)) | ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0)))) & (((generous(X0) | ~creative(X0)) & (~generous(X0) | creative(X0))) | ~calm(X0) | strong(X0))) [flattening 46]
52. ! [X0] : (((~old(X0) | ~generous(X0)) | (creative(X0) & rich(X0))) & ((~creative(X0) | ~rich(X0)) | (old(X0) & generous(X0)))) [nnf transformation 11]
53. ! [X0] : ((~old(X0) | ~generous(X0) | (creative(X0) & rich(X0))) & (~creative(X0) | ~rich(X0) | (old(X0) & generous(X0)))) [flattening 52]
70. ~patient(X0) | rich(X0) [cnf transformation 25]
80. quiet(X0) | patient(X0) [cnf transformation 39]
81. old(X0) | patient(X0) [cnf transformation 39]
85. calm(X0) | humble(X0) [cnf transformation 41]
86. curious(X0) | quiet(X0) | strong(X0) [cnf transformation 43]
87. curious(X0) | ~strong(X0) | ~quiet(X0) [cnf transformation 43]
88. ~curious(X0) | quiet(X0) | strong(X0) [cnf transformation 43]
89. ~quiet(X0) | ~strong(X0) | ~curious(X0) [cnf transformation 43]
99. ~calm(X0) | ~creative(X0) | generous(X0) | strong(X0) [cnf transformation 47]
112. ~generous(X0) | ~old(X0) | rich(X0) [cnf transformation 53]
116. ~quiet(X0) | creative(X0) [cnf transformation 28]
139. ~humble(susan) [cnf transformation 22]
141. ~rich(susan) [cnf transformation 23]
195. ~quiet(X0) | ~strong(X0) [subsumption resolution 87,89]
196. quiet(X0) | strong(X0) [subsumption resolution 86,88]
323. ~strong(X0) | patient(X0) [resolution 195,80]
325. creative(X1) | strong(X1) [resolution 196,116]
417. ~creative(X2) | generous(X2) | strong(X2) | humble(X2) [resolution 99,85]
418. generous(X2) | strong(X2) | humble(X2) [subsumption resolution 417,325]
449. ~old(X2) | humble(X2) | strong(X2) | rich(X2) [resolution 418,112]
459. humble(X0) | strong(X0) | rich(X0) | patient(X0) [resolution 449,81]
462. humble(X0) | rich(X0) | patient(X0) [subsumption resolution 459,323]
463. humble(X0) | rich(X0) [subsumption resolution 462,70]
466. rich(susan) [resolution 463,139]
470. $false [subsumption resolution 466,141]
% SZS output end Proof for 3808560181826991489410702
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or creative is old. Everyone who is either wise or generous is both not wise and wise and vice versa. If fred is either not wise or generous then alice is either not quiet or calm and vice versa. Everyone who is either not kind or calm is both calm and happy and vice versa. Everyone who is either not kind or patient is both not happy and generous. If someone is not old then lucy is not generous or kind and vice versa. Everyone who is either tall or old is either not generous or old. Everyone who is both not calm and not strong is not generous or strong. Everyone who is both generous and happy is both not strong and curious. Everyone who is funny or wise is both strong and not calm and vice versa. If someone is either strong or rich then someone is either not calm or creative and vice versa. Everyone who is both not funny and humble is funny or rich and vice versa. Everyone who is not curious or not tall is funny or not quiet and vice versa. Everyone who is wise is both not old and not kind and vice versa. If someone is either not humble or not wise then alice is not rich. If someone is rich or not old then someone is both not happy and not tall. Alice is patient or not kind. Susan is not generous. Paul is both not funny and not strong. Fred is not kind or strong. Fred is both calm and brave. Mary is generous or tall. Someone is either wise or curious. | Paul is not funny. | entailment | (![X]:((~rich(X)|creative(X))=>old(X)))&
(![X]:((wise(X)<~>generous(X))<=>(~wise(X)&wise(X))))&
(((~wise(fred)<~>generous(fred)))<=>((~quiet(alice)<~>calm(alice))))&
(![X]:((~kind(X)<~>calm(X))<=>(calm(X)&happy(X))))&
(![X]:((~kind(X)<~>patient(X))=>(~happy(X)&generous(X))))&
((?[X]:(~old(X)))<=>((~generous(lucy)|kind(lucy))))&
(![X]:((tall(X)<~>old(X))=>(~generous(X)<~>old(X))))&
(![X]:((~calm(X)&~strong(X))=>(~generous(X)|strong(X))))&
(![X]:((generous(X)&happy(X))=>(~strong(X)&curious(X))))&
(![X]:((funny(X)|wise(X))<=>(strong(X)&~calm(X))))&
((?[X]:((strong(X)<~>rich(X))))<=>(?[X]:((~calm(X)<~>creative(X)))))&
(![X]:((~funny(X)&humble(X))<=>(funny(X)|rich(X))))&
(![X]:((~curious(X)|~tall(X))<=>(funny(X)|~quiet(X))))&
(![X]:(wise(X)<=>(~old(X)&~kind(X))))&
((?[X]:((~humble(X)<~>~wise(X))))=>(~rich(alice)))&
((?[X]:((rich(X)|~old(X))))=>(?[X]:((~happy(X)&~tall(X)))))&
((patient(alice)|~kind(alice)))&
(~generous(susan))&
((~funny(paul)&~strong(paul)))&
((~kind(fred)|strong(fred)))&
((calm(fred)&brave(fred)))&
((generous(mary)|tall(mary)))&
(?[X]:((wise(X)<~>curious(X)))) | ~funny(paul) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2448820211058008615157427
% SZS output start Proof for 2448820211058008615157427
12. ! [X0] : ((humble(X0) & ~funny(X0)) <=> (rich(X0) | funny(X0))) [input p11]
24. funny(paul) [input hypothesis]
56. ! [X0] : (((humble(X0) & ~funny(X0)) | (~rich(X0) & ~funny(X0))) & ((rich(X0) | funny(X0)) | (~humble(X0) | funny(X0)))) [nnf transformation 12]
57. ! [X0] : (((humble(X0) & ~funny(X0)) | (~rich(X0) & ~funny(X0))) & (rich(X0) | funny(X0) | ~humble(X0) | funny(X0))) [flattening 56]
119. ~funny(X0) | ~funny(X0) [cnf transformation 57]
145. funny(paul) [cnf transformation 24]
147. ~funny(X0) [duplicate literal removal 119]
302. $false [subsumption resolution 145,147]
% SZS output end Proof for 2448820211058008615157427
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or not brave is both not strong and not brave.
If susan is tall or not happy then someone is both creative and wise and vice versa.
Everyone who is not curious or patient is both brave and not generous and vice versa.
Everyone who is either funny or quiet is either old or not tall and vice versa.
Everyone who is not generous is wise.
Everyone who is not strong is both not humble and generous.
Everyone who is kind is not brave.
Everyone who is both old and not creative is happy and vice versa.
If someone is both not brave and humble then alice is calm.
If alice is both not wise and old then someone is both humble and not happy.
Everyone who is not patient is either curious or old.
If someone is not quiet or old then someone is both not wise and not kind and vice versa.
Everyone who is not humble or generous is not wise or quiet.
If someone is funny or not tall then someone is either kind or strong and vice versa.
If fred is either not tall or brave then john is happy.
Everyone who is either not funny or not strong is either patient or creative.
Someone is humble or creative.
Susan is either not patient or not strong.
Fred is not creative or not rich.
Someone is patient.
Alice is happy.
Someone is both not generous and strong.
Someone is either creative or not old. | John is not generous. | neutral | (![X]:((kind(X)|~brave(X))=>(~strong(X)&~brave(X))))&
(((tall(susan)|~happy(susan)))<=>(?[X]:((creative(X)&wise(X)))))&
(![X]:((~curious(X)|patient(X))<=>(brave(X)&~generous(X))))&
(![X]:((funny(X)<~>quiet(X))<=>(old(X)<~>~tall(X))))&
(![X]:(~generous(X)=>wise(X)))&
(![X]:(~strong(X)=>(~humble(X)&generous(X))))&
(![X]:(kind(X)=>~brave(X)))&
(![X]:((old(X)&~creative(X))<=>happy(X)))&
((?[X]:((~brave(X)&humble(X))))=>(calm(alice)))&
(((~wise(alice)&old(alice)))=>(?[X]:((humble(X)&~happy(X)))))&
(![X]:(~patient(X)=>(curious(X)<~>old(X))))&
((?[X]:((~quiet(X)|old(X))))<=>(?[X]:((~wise(X)&~kind(X)))))&
(![X]:((~humble(X)|generous(X))=>(~wise(X)|quiet(X))))&
((?[X]:((funny(X)|~tall(X))))<=>(?[X]:((kind(X)<~>strong(X)))))&
(((~tall(fred)<~>brave(fred)))=>(happy(john)))&
(![X]:((~funny(X)<~>~strong(X))=>(patient(X)<~>creative(X))))&
(?[X]:((humble(X)|creative(X))))&
((~patient(susan)<~>~strong(susan)))&
((~creative(fred)|~rich(fred)))&
(?[X]:(patient(X)))&
(happy(alice))&
(?[X]:((~generous(X)&strong(X))))&
(?[X]:((creative(X)<~>~old(X)))) | ~generous(john) | [] | null | 0 |
Everyone who is either old or patient is not strong or not creative and vice versa.
Everyone who is kind or not rich is either not curious or curious.
If susan is both calm and not creative then paul is creative.
Everyone who is both not curious and curious is quiet.
If someone is quiet or funny then someone is rich and vice versa.
Everyone who is either funny or tall is rich or brave and vice versa.
Everyone who is either wise or not calm is not quiet and vice versa.
Everyone who is either not quiet or not creative is generous.
Everyone who is creative is either funny or old and vice versa.
If someone is not old or creative then someone is either tall or not kind and vice versa.
Everyone who is both creative and calm is old.
If someone is both not quiet and not calm then fred is not old or calm and vice versa.
Everyone who is both not creative and kind is not calm or rich and vice versa.
If alice is both old and not calm then someone is quiet or happy and vice versa.
Everyone who is kind is both quiet and generous.
If someone is both not kind and not calm then someone is both not curious and not tall and vice versa.
Paul is both quiet and funny.
Lucy is strong or not patient.
Someone is strong or not humble.
Fred is both brave and not calm.
John is both curious and not kind.
John is not quiet.
Someone is generous.
Paul is not brave or not tall. | Fred is tall. | contradiction | (![X]:((old(X)<~>patient(X))<=>(~strong(X)|~creative(X))))&
(![X]:((kind(X)|~rich(X))=>(~curious(X)<~>curious(X))))&
(((calm(susan)&~creative(susan)))=>(creative(paul)))&
(![X]:((~curious(X)&curious(X))=>quiet(X)))&
((?[X]:((quiet(X)|funny(X))))<=>(?[X]:(rich(X))))&
(![X]:((funny(X)<~>tall(X))<=>(rich(X)|brave(X))))&
(![X]:((wise(X)<~>~calm(X))<=>~quiet(X)))&
(![X]:((~quiet(X)<~>~creative(X))=>generous(X)))&
(![X]:(creative(X)<=>(funny(X)<~>old(X))))&
((?[X]:((~old(X)|creative(X))))<=>(?[X]:((tall(X)<~>~kind(X)))))&
(![X]:((creative(X)&calm(X))=>old(X)))&
((?[X]:((~quiet(X)&~calm(X))))<=>((~old(fred)|calm(fred))))&
(![X]:((~creative(X)&kind(X))<=>(~calm(X)|rich(X))))&
(((old(alice)&~calm(alice)))<=>(?[X]:((quiet(X)|happy(X)))))&
(![X]:(kind(X)=>(quiet(X)&generous(X))))&
((?[X]:((~kind(X)&~calm(X))))<=>(?[X]:((~curious(X)&~tall(X)))))&
((quiet(paul)&funny(paul)))&
((strong(lucy)|~patient(lucy)))&
(?[X]:((strong(X)|~humble(X))))&
((brave(fred)&~calm(fred)))&
((curious(john)&~kind(john)))&
(~quiet(john))&
(?[X]:(generous(X)))&
((~brave(paul)|~tall(paul))) | tall(fred) | [
"p5",
"p8",
"p11",
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5541099257763849566225911
% SZS output start Proof for 5541099257763849566225911
6. ! [X0] : ((funny(X0) <~> tall(X0)) <=> (brave(X0) | rich(X0))) [input p5]
9. ! [X0] : (creative(X0) <=> (funny(X0) <~> old(X0))) [input p8]
12. ? [X0] : (~calm(X0) & ~quiet(X0)) <=> (calm(fred) | ~old(fred)) [input p11]
13. ! [X0] : ((kind(X0) & ~creative(X0)) <=> (rich(X0) | ~calm(X0))) [input p12]
15. ! [X0] : (kind(X0) => (generous(X0) & quiet(X0))) [input p14]
20. ~calm(fred) & brave(fred) [input p19]
25. tall(fred) [input hypothesis]
31. ! [X0] : (kind(X0) => quiet(X0)) [pure predicate removal 15]
40. ! [X0] : (quiet(X0) | ~kind(X0)) [ennf transformation 31]
49. ! [X0] : ((((~tall(X0) | ~funny(X0)) & (tall(X0) | funny(X0))) | (~brave(X0) & ~rich(X0))) & ((brave(X0) | rich(X0)) | ((funny(X0) | ~tall(X0)) & (tall(X0) | ~funny(X0))))) [nnf transformation 6]
50. ! [X0] : ((((~tall(X0) | ~funny(X0)) & (tall(X0) | funny(X0))) | (~brave(X0) & ~rich(X0))) & (brave(X0) | rich(X0) | ((funny(X0) | ~tall(X0)) & (tall(X0) | ~funny(X0))))) [flattening 49]
52. ! [X0] : ((creative(X0) | ((funny(X0) | ~old(X0)) & (old(X0) | ~funny(X0)))) & (((~old(X0) | ~funny(X0)) & (old(X0) | funny(X0))) | ~creative(X0))) [nnf transformation 9]
58. (? [X0] : (~calm(X0) & ~quiet(X0)) | (~calm(fred) & old(fred))) & ((calm(fred) | ~old(fred)) | ! [X0] : (calm(X0) | quiet(X0))) [nnf transformation 12]
59. (? [X0] : (~calm(X0) & ~quiet(X0)) | (~calm(fred) & old(fred))) & (calm(fred) | ~old(fred) | ! [X0] : (calm(X0) | quiet(X0))) [flattening 58]
60. (? [X0] : (~calm(X0) & ~quiet(X0)) | (~calm(fred) & old(fred))) & (calm(fred) | ~old(fred) | ! [X1] : (calm(X1) | quiet(X1))) [rectify 59]
61. ? [X0] : (~calm(X0) & ~quiet(X0)) => (~calm(sK4) & ~quiet(sK4)) [choice axiom]
62. ((~calm(sK4) & ~quiet(sK4)) | (~calm(fred) & old(fred))) & (calm(fred) | ~old(fred) | ! [X1] : (calm(X1) | quiet(X1))) [skolemisation 60,61]
63. ! [X0] : (((kind(X0) & ~creative(X0)) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | (~kind(X0) | creative(X0)))) [nnf transformation 13]
64. ! [X0] : (((kind(X0) & ~creative(X0)) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ~kind(X0) | creative(X0))) [flattening 63]
95. ~brave(X0) | ~funny(X0) | ~tall(X0) [cnf transformation 50]
103. ~old(X0) | funny(X0) | creative(X0) [cnf transformation 52]
112. ~quiet(sK4) | old(fred) [cnf transformation 62]
114. ~calm(sK4) | old(fred) [cnf transformation 62]
117. ~creative(X0) | calm(X0) [cnf transformation 64]
119. calm(X0) | kind(X0) [cnf transformation 64]
126. ~kind(X0) | quiet(X0) [cnf transformation 40]
134. brave(fred) [cnf transformation 20]
135. ~calm(fred) [cnf transformation 20]
140. tall(fred) [cnf transformation 25]
213. 18 <=> calm(fred) [avatar definition]
215. ~calm(fred) <- (~18) [avatar component clause 213]
217. 19 <=> calm(sK4) [avatar definition]
219. ~calm(sK4) <- (~19) [avatar component clause 217]
222. 20 <=> old(fred) [avatar definition]
224. old(fred) <- (20) [avatar component clause 222]
225. 20 | ~19 [avatar split clause 114,217,222]
227. 21 <=> quiet(sK4) [avatar definition]
231. 20 | ~21 [avatar split clause 112,227,222]
282. ~18 [avatar split clause 135,213]
304. kind(sK4) <- (~19) [resolution 119,219]
324. quiet(sK4) <- (~19) [resolution 304,126]
327. 21 | 19 [avatar split clause 324,217,227]
349. 40 <=> funny(fred) [avatar definition]
351. ~funny(fred) <- (~40) [avatar component clause 349]
353. ~funny(fred) | ~tall(fred) [resolution 95,134]
354. ~funny(fred) [subsumption resolution 353,140]
355. ~40 [avatar split clause 354,349]
420. funny(fred) | creative(fred) <- (20) [resolution 103,224]
430. creative(fred) <- (20, ~40) [subsumption resolution 420,351]
510. calm(fred) <- (20, ~40) [resolution 430,117]
521. $false <- (~18, 20, ~40) [subsumption resolution 510,215]
522. 18 | ~20 | 40 [avatar contradiction clause 521]
523. $false [avatar sat refutation 225,231,282,327,355,522]
% SZS output end Proof for 5541099257763849566225911
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not happy and brave is both strong and not wise and vice versa.
Everyone who is either patient or quiet is kind or calm and vice versa.
Everyone who is both not patient and strong is either not creative or not tall and vice versa.
Everyone who is generous is either generous or curious.
If someone is either not curious or curious then paul is humble and vice versa.
Everyone who is not rich or not calm is either not calm or not brave and vice versa.
Everyone who is funny is curious or not patient and vice versa.
If someone is both strong and brave then someone is not rich or tall and vice versa.
Everyone who is strong is not quiet or brave and vice versa.
If someone is both not old and happy then someone is both brave and not old and vice versa.
Everyone who is both not funny and not calm is either calm or not generous and vice versa.
If someone is both kind and happy then mary is both humble and not quiet and vice versa.
Everyone who is either patient or brave is both kind and not old.
If someone is not kind then someone is not curious.
If someone is tall or generous then fred is happy or not patient.
Everyone who is either not rich or happy is not calm or calm.
Someone is either brave or tall.
Mary is both not strong and not curious.
John is either not funny or wise.
John is either not old or humble.
Alice is not happy or not patient.
Fred is funny.
Susan is curious.
Paul is old. | Mary is calm. | entailment | (![X]:((~happy(X)&brave(X))<=>(strong(X)&~wise(X))))&
(![X]:((patient(X)<~>quiet(X))<=>(kind(X)|calm(X))))&
(![X]:((~patient(X)&strong(X))<=>(~creative(X)<~>~tall(X))))&
(![X]:(generous(X)=>(generous(X)<~>curious(X))))&
((?[X]:((~curious(X)<~>curious(X))))<=>(humble(paul)))&
(![X]:((~rich(X)|~calm(X))<=>(~calm(X)<~>~brave(X))))&
(![X]:(funny(X)<=>(curious(X)|~patient(X))))&
((?[X]:((strong(X)&brave(X))))<=>(?[X]:((~rich(X)|tall(X)))))&
(![X]:(strong(X)<=>(~quiet(X)|brave(X))))&
((?[X]:((~old(X)&happy(X))))<=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((~funny(X)&~calm(X))<=>(calm(X)<~>~generous(X))))&
((?[X]:((kind(X)&happy(X))))<=>((humble(mary)&~quiet(mary))))&
(![X]:((patient(X)<~>brave(X))=>(kind(X)&~old(X))))&
((?[X]:(~kind(X)))=>(?[X]:(~curious(X))))&
((?[X]:((tall(X)|generous(X))))=>((happy(fred)|~patient(fred))))&
(![X]:((~rich(X)<~>happy(X))=>(~calm(X)|calm(X))))&
(?[X]:((brave(X)<~>tall(X))))&
((~strong(mary)&~curious(mary)))&
((~funny(john)<~>wise(john)))&
((~old(john)<~>humble(john)))&
((~happy(alice)|~patient(alice)))&
(funny(fred))&
(curious(susan))&
(old(paul)) | calm(mary) | [
"p5",
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5495416659308644797545444
% SZS output start Proof for 5495416659308644797545444
6. ! [X0] : ((~calm(X0) | ~rich(X0)) <=> (~calm(X0) <~> ~brave(X0))) [input p5]
9. ! [X0] : (strong(X0) <=> (brave(X0) | ~quiet(X0))) [input p8]
18. ~curious(mary) & ~strong(mary) [input p17]
25. ~calm(mary) [input hypothesis]
47. ! [X0] : (((~calm(X0) | ~rich(X0)) | ((~calm(X0) | brave(X0)) & (~brave(X0) | calm(X0)))) & (((brave(X0) | calm(X0)) & (~brave(X0) | ~calm(X0))) | (calm(X0) & rich(X0)))) [nnf transformation 6]
48. ! [X0] : ((~calm(X0) | ~rich(X0) | ((~calm(X0) | brave(X0)) & (~brave(X0) | calm(X0)))) & (((brave(X0) | calm(X0)) & (~brave(X0) | ~calm(X0))) | (calm(X0) & rich(X0)))) [flattening 47]
56. ! [X0] : ((strong(X0) | (~brave(X0) & quiet(X0))) & ((brave(X0) | ~quiet(X0)) | ~strong(X0))) [nnf transformation 9]
57. ! [X0] : ((strong(X0) | (~brave(X0) & quiet(X0))) & (brave(X0) | ~quiet(X0) | ~strong(X0))) [flattening 56]
105. brave(X0) | calm(X0) | calm(X0) [cnf transformation 48]
118. ~brave(X0) | strong(X0) [cnf transformation 57]
144. ~strong(mary) [cnf transformation 18]
154. ~calm(mary) [cnf transformation 25]
157. calm(X0) | brave(X0) [duplicate literal removal 105]
323. brave(mary) [resolution 157,154]
325. strong(mary) [resolution 323,118]
326. $false [subsumption resolution 325,144]
% SZS output end Proof for 5495416659308644797545444
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not quiet or humble then susan is patient or happy. If someone is not kind or kind then someone is both not calm and not happy and vice versa. If someone is both tall and quiet then someone is either patient or strong and vice versa. Everyone who is rich is not tall or not wise. Everyone who is either not creative or patient is both patient and not generous. If someone is both not creative and brave then someone is brave and vice versa. If someone is both not rich and not strong then someone is not generous and vice versa. Everyone who is both not rich and not creative is either brave or not generous. If someone is either quiet or not kind then someone is both funny and not funny and vice versa. Everyone who is not tall is not humble and vice versa. If someone is either not tall or not strong then alice is happy or generous and vice versa. Everyone who is not curious is not strong. If someone is wise then mary is happy or not funny. If fred is generous or wise then alice is either not happy or not funny and vice versa. Everyone who is not brave is not creative and vice versa. Everyone who is calm or humble is both calm and humble. Lucy is creative or not strong. Lucy is not curious. Susan is generous or tall. Mary is not tall or quiet. Someone is both curious and humble. Someone is not creative or not funny. Lucy is not rich. | Fred is quiet. | neutral | (((~quiet(fred)|humble(fred)))=>((patient(susan)|happy(susan))))&
((?[X]:((~kind(X)|kind(X))))<=>(?[X]:((~calm(X)&~happy(X)))))&
((?[X]:((tall(X)&quiet(X))))<=>(?[X]:((patient(X)<~>strong(X)))))&
(![X]:(rich(X)=>(~tall(X)|~wise(X))))&
(![X]:((~creative(X)<~>patient(X))=>(patient(X)&~generous(X))))&
((?[X]:((~creative(X)&brave(X))))<=>(?[X]:(brave(X))))&
((?[X]:((~rich(X)&~strong(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~rich(X)&~creative(X))=>(brave(X)<~>~generous(X))))&
((?[X]:((quiet(X)<~>~kind(X))))<=>(?[X]:((funny(X)&~funny(X)))))&
(![X]:(~tall(X)<=>~humble(X)))&
((?[X]:((~tall(X)<~>~strong(X))))<=>((happy(alice)|generous(alice))))&
(![X]:(~curious(X)=>~strong(X)))&
((?[X]:(wise(X)))=>((happy(mary)|~funny(mary))))&
(((generous(fred)|wise(fred)))<=>((~happy(alice)<~>~funny(alice))))&
(![X]:(~brave(X)<=>~creative(X)))&
(![X]:((calm(X)|humble(X))=>(calm(X)&humble(X))))&
((creative(lucy)|~strong(lucy)))&
(~curious(lucy))&
((generous(susan)|tall(susan)))&
((~tall(mary)|quiet(mary)))&
(?[X]:((curious(X)&humble(X))))&
(?[X]:((~creative(X)|~funny(X))))&
(~rich(lucy)) | quiet(fred) | [] | null | 0 |
Everyone who is either not humble or not old is either not wise or not quiet.
Everyone who is either tall or brave is both funny and not rich and vice versa.
Everyone who is either happy or creative is both rich and not calm.
Everyone who is both quiet and curious is happy or tall and vice versa.
If john is wise then john is patient.
If someone is both brave and not curious then someone is either not strong or not humble and vice versa.
Everyone who is funny or not patient is both not brave and creative and vice versa.
Everyone who is both humble and old is either happy or not happy and vice versa.
Everyone who is not kind is either not rich or not wise.
Everyone who is wise is both wise and not rich and vice versa.
If someone is not funny or tall then fred is not creative.
If paul is either rich or calm then someone is both not kind and funny.
If paul is rich or not brave then fred is both rich and kind and vice versa.
If fred is either tall or not brave then someone is either tall or kind.
Everyone who is tall is either not strong or patient and vice versa.
Everyone who is not funny is both curious and not calm.
Fred is either not happy or curious.
Someone is either creative or not funny.
Someone is both kind and not calm.
Someone is tall or not humble.
Someone is either not creative or not quiet.
Someone is curious. | John is funny. | neutral | (![X]:((~humble(X)<~>~old(X))=>(~wise(X)<~>~quiet(X))))&
(![X]:((tall(X)<~>brave(X))<=>(funny(X)&~rich(X))))&
(![X]:((happy(X)<~>creative(X))=>(rich(X)&~calm(X))))&
(![X]:((quiet(X)&curious(X))<=>(happy(X)|tall(X))))&
((wise(john))=>(patient(john)))&
((?[X]:((brave(X)&~curious(X))))<=>(?[X]:((~strong(X)<~>~humble(X)))))&
(![X]:((funny(X)|~patient(X))<=>(~brave(X)&creative(X))))&
(![X]:((humble(X)&old(X))<=>(happy(X)<~>~happy(X))))&
(![X]:(~kind(X)=>(~rich(X)<~>~wise(X))))&
(![X]:(wise(X)<=>(wise(X)&~rich(X))))&
((?[X]:((~funny(X)|tall(X))))=>(~creative(fred)))&
(((rich(paul)<~>calm(paul)))=>(?[X]:((~kind(X)&funny(X)))))&
(((rich(paul)|~brave(paul)))<=>((rich(fred)&kind(fred))))&
(((tall(fred)<~>~brave(fred)))=>(?[X]:((tall(X)<~>kind(X)))))&
(![X]:(tall(X)<=>(~strong(X)<~>patient(X))))&
(![X]:(~funny(X)=>(curious(X)&~calm(X))))&
((~happy(fred)<~>curious(fred)))&
(?[X]:((creative(X)<~>~funny(X))))&
(?[X]:((kind(X)&~calm(X))))&
(?[X]:((tall(X)|~humble(X))))&
(?[X]:((~creative(X)<~>~quiet(X))))&
(?[X]:(curious(X))) | funny(john) | [] | null | 0 |
Everyone who is calm is old or not creative and vice versa. If alice is either not wise or old then lucy is not humble or old and vice versa. Everyone who is both generous and not funny is not curious and vice versa. Everyone who is either not brave or not generous is wise or tall and vice versa. If someone is either not strong or not creative then someone is either old or not quiet and vice versa. Everyone who is both not rich and kind is not tall or rich and vice versa. Everyone who is not strong is generous or old and vice versa. Everyone who is curious is both not curious and not patient and vice versa. Everyone who is old is not kind or tall and vice versa. If someone is both rich and patient then fred is both not quiet and not brave. Everyone who is calm or brave is both not wise and brave and vice versa. If someone is either funny or not creative then someone is not curious and vice versa. If someone is both not generous and not tall then someone is not humble or not calm. Everyone who is curious or generous is either not happy or calm and vice versa. If someone is both tall and not wise then fred is both not wise and brave and vice versa. Someone is either not generous or not happy. Mary is old or kind. Someone is kind or not humble. Someone is not brave. Fred is not brave. Mary is patient or funny. | Lucy is not funny. | entailment | (![X]:(calm(X)<=>(old(X)|~creative(X))))&
(((~wise(alice)<~>old(alice)))<=>((~humble(lucy)|old(lucy))))&
(![X]:((generous(X)&~funny(X))<=>~curious(X)))&
(![X]:((~brave(X)<~>~generous(X))<=>(wise(X)|tall(X))))&
((?[X]:((~strong(X)<~>~creative(X))))<=>(?[X]:((old(X)<~>~quiet(X)))))&
(![X]:((~rich(X)&kind(X))<=>(~tall(X)|rich(X))))&
(![X]:(~strong(X)<=>(generous(X)|old(X))))&
(![X]:(curious(X)<=>(~curious(X)&~patient(X))))&
(![X]:(old(X)<=>(~kind(X)|tall(X))))&
((?[X]:((rich(X)&patient(X))))=>((~quiet(fred)&~brave(fred))))&
(![X]:((calm(X)|brave(X))<=>(~wise(X)&brave(X))))&
((?[X]:((funny(X)<~>~creative(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((~generous(X)&~tall(X))))=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:((curious(X)|generous(X))<=>(~happy(X)<~>calm(X))))&
((?[X]:((tall(X)&~wise(X))))<=>((~wise(fred)&brave(fred))))&
(?[X]:((~generous(X)<~>~happy(X))))&
((old(mary)|kind(mary)))&
(?[X]:((kind(X)|~humble(X))))&
(?[X]:(~brave(X)))&
(~brave(fred))&
((patient(mary)|funny(mary))) | ~funny(lucy) | [
"p2",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3916301245660895371486222
% SZS output start Proof for 3916301245660895371486222
3. ! [X0] : ((~funny(X0) & generous(X0)) <=> ~curious(X0)) [input p2]
8. ! [X0] : (curious(X0) <=> (~patient(X0) & ~curious(X0))) [input p7]
22. funny(lucy) [input hypothesis]
32. ! [X0] : (((~funny(X0) & generous(X0)) | curious(X0)) & (~curious(X0) | (funny(X0) | ~generous(X0)))) [nnf transformation 3]
33. ! [X0] : (((~funny(X0) & generous(X0)) | curious(X0)) & (~curious(X0) | funny(X0) | ~generous(X0))) [flattening 32]
45. ! [X0] : ((curious(X0) | (patient(X0) | curious(X0))) & ((~patient(X0) & ~curious(X0)) | ~curious(X0))) [nnf transformation 8]
46. ! [X0] : ((curious(X0) | patient(X0) | curious(X0)) & ((~patient(X0) & ~curious(X0)) | ~curious(X0))) [flattening 45]
84. ~funny(X0) | curious(X0) [cnf transformation 33]
107. ~curious(X0) | ~curious(X0) [cnf transformation 46]
142. funny(lucy) [cnf transformation 22]
143. ~curious(X0) [duplicate literal removal 107]
288. curious(lucy) [resolution 84,142]
289. $false [subsumption resolution 288,143]
% SZS output end Proof for 3916301245660895371486222
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall and funny is either not curious or generous. Everyone who is not generous or not old is creative. Everyone who is funny is either not creative or tall and vice versa. If alice is either not happy or not generous then paul is calm and vice versa. Everyone who is not funny is not generous. Everyone who is not quiet is patient or quiet. If susan is either not kind or not generous then paul is not curious. Everyone who is either not calm or creative is either rich or not rich and vice versa. If someone is patient then someone is not strong or not rich. Everyone who is not rich is not tall. If someone is not kind or not strong then someone is either calm or rich and vice versa. Everyone who is both not rich and not patient is strong and vice versa. Everyone who is creative or patient is not rich and vice versa. If lucy is either not tall or not old then mary is both not wise and strong. Everyone who is not quiet or old is not creative. If someone is both curious and old then john is either not patient or not wise. Fred is funny. Someone is either old or not tall. Someone is tall or not tall. Fred is rich or generous. Susan is both not kind and funny. Someone is brave. Lucy is not kind. Alice is creative or not kind. | Paul is not tall. | entailment | (![X]:((~tall(X)&funny(X))=>(~curious(X)<~>generous(X))))&
(![X]:((~generous(X)|~old(X))=>creative(X)))&
(![X]:(funny(X)<=>(~creative(X)<~>tall(X))))&
(((~happy(alice)<~>~generous(alice)))<=>(calm(paul)))&
(![X]:(~funny(X)=>~generous(X)))&
(![X]:(~quiet(X)=>(patient(X)|quiet(X))))&
(((~kind(susan)<~>~generous(susan)))=>(~curious(paul)))&
(![X]:((~calm(X)<~>creative(X))<=>(rich(X)<~>~rich(X))))&
((?[X]:(patient(X)))=>(?[X]:((~strong(X)|~rich(X)))))&
(![X]:(~rich(X)=>~tall(X)))&
((?[X]:((~kind(X)|~strong(X))))<=>(?[X]:((calm(X)<~>rich(X)))))&
(![X]:((~rich(X)&~patient(X))<=>strong(X)))&
(![X]:((creative(X)|patient(X))<=>~rich(X)))&
(((~tall(lucy)<~>~old(lucy)))=>((~wise(mary)&strong(mary))))&
(![X]:((~quiet(X)|old(X))=>~creative(X)))&
((?[X]:((curious(X)&old(X))))=>((~patient(john)<~>~wise(john))))&
(funny(fred))&
(?[X]:((old(X)<~>~tall(X))))&
(?[X]:((tall(X)|~tall(X))))&
((rich(fred)|generous(fred)))&
((~kind(susan)&funny(susan)))&
(?[X]:(brave(X)))&
(~kind(lucy))&
((creative(alice)|~kind(alice))) | ~tall(paul) | [
"p1",
"p2",
"p4",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 513905103470317875078978
% SZS output start Proof for 513905103470317875078978
2. ! [X0] : ((~old(X0) | ~generous(X0)) => creative(X0)) [input p1]
3. ! [X0] : (funny(X0) <=> (~creative(X0) <~> tall(X0))) [input p2]
5. ! [X0] : (~funny(X0) => ~generous(X0)) [input p4]
10. ! [X0] : (~rich(X0) => ~tall(X0)) [input p9]
13. ! [X0] : ((patient(X0) | creative(X0)) <=> ~rich(X0)) [input p12]
25. tall(paul) [input hypothesis]
33. ! [X0] : (creative(X0) | (old(X0) & generous(X0))) [ennf transformation 2]
34. ! [X0] : (~generous(X0) | funny(X0)) [ennf transformation 5]
37. ! [X0] : (~tall(X0) | rich(X0)) [ennf transformation 10]
42. ! [X0] : ((funny(X0) | ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0)))) & (((~tall(X0) | creative(X0)) & (tall(X0) | ~creative(X0))) | ~funny(X0))) [nnf transformation 3]
56. ! [X0] : (((patient(X0) | creative(X0)) | rich(X0)) & (~rich(X0) | (~patient(X0) & ~creative(X0)))) [nnf transformation 13]
57. ! [X0] : ((patient(X0) | creative(X0) | rich(X0)) & (~rich(X0) | (~patient(X0) & ~creative(X0)))) [flattening 56]
67. creative(X0) | generous(X0) [cnf transformation 33]
70. ~funny(X0) | creative(X0) | ~tall(X0) [cnf transformation 42]
77. ~generous(X0) | funny(X0) [cnf transformation 34]
89. ~tall(X0) | rich(X0) [cnf transformation 37]
99. ~rich(X0) | ~creative(X0) [cnf transformation 57]
118. tall(paul) [cnf transformation 25]
263. rich(paul) [resolution 89,118]
265. ~creative(paul) [resolution 99,263]
275. generous(paul) [resolution 265,67]
369. funny(paul) [resolution 275,77]
373. creative(paul) | ~tall(paul) [resolution 369,70]
374. ~tall(paul) [subsumption resolution 373,265]
375. $false [subsumption resolution 374,118]
% SZS output end Proof for 513905103470317875078978
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is patient or not generous and vice versa.
Everyone who is not humble is either rich or not rich and vice versa.
Everyone who is humble is both humble and not curious and vice versa.
If someone is not tall then paul is tall or not generous and vice versa.
Everyone who is both not calm and funny is not old or rich and vice versa.
Everyone who is not old is either kind or rich and vice versa.
If someone is not humble or not kind then someone is brave and vice versa.
Everyone who is not old is not tall or not wise.
If someone is both not tall and not funny then lucy is both not rich and brave and vice versa.
If lucy is either not brave or patient then paul is either not rich or creative.
If alice is both not humble and not curious then someone is happy or curious.
Everyone who is not old is tall.
Everyone who is either funny or not rich is both kind and not brave.
If someone is old or happy then someone is not curious or not kind and vice versa.
Everyone who is either generous or happy is not old or wise and vice versa.
Everyone who is either not funny or kind is not funny or brave.
Someone is either not strong or happy.
Someone is either curious or not quiet.
Paul is not funny or not calm.
Paul is humble or quiet.
Mary is both not calm and not curious.
Someone is brave or generous. | Lucy is old. | entailment | (![X]:(patient(X)<=>(patient(X)|~generous(X))))&
(![X]:(~humble(X)<=>(rich(X)<~>~rich(X))))&
(![X]:(humble(X)<=>(humble(X)&~curious(X))))&
((?[X]:(~tall(X)))<=>((tall(paul)|~generous(paul))))&
(![X]:((~calm(X)&funny(X))<=>(~old(X)|rich(X))))&
(![X]:(~old(X)<=>(kind(X)<~>rich(X))))&
((?[X]:((~humble(X)|~kind(X))))<=>(?[X]:(brave(X))))&
(![X]:(~old(X)=>(~tall(X)|~wise(X))))&
((?[X]:((~tall(X)&~funny(X))))<=>((~rich(lucy)&brave(lucy))))&
(((~brave(lucy)<~>patient(lucy)))=>((~rich(paul)<~>creative(paul))))&
(((~humble(alice)&~curious(alice)))=>(?[X]:((happy(X)|curious(X)))))&
(![X]:(~old(X)=>tall(X)))&
(![X]:((funny(X)<~>~rich(X))=>(kind(X)&~brave(X))))&
((?[X]:((old(X)|happy(X))))<=>(?[X]:((~curious(X)|~kind(X)))))&
(![X]:((generous(X)<~>happy(X))<=>(~old(X)|wise(X))))&
(![X]:((~funny(X)<~>kind(X))=>(~funny(X)|brave(X))))&
(?[X]:((~strong(X)<~>happy(X))))&
(?[X]:((curious(X)<~>~quiet(X))))&
((~funny(paul)|~calm(paul)))&
((humble(paul)|quiet(paul)))&
((~calm(mary)&~curious(mary)))&
(?[X]:((brave(X)|generous(X)))) | old(lucy) | [
"p4",
"p5",
"p8",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8562532671683784553129500
% SZS output start Proof for 8562532671683784553129500
5. ! [X0] : ((funny(X0) & ~calm(X0)) <=> (rich(X0) | ~old(X0))) [input p4]
6. ! [X0] : (~old(X0) <=> (kind(X0) <~> rich(X0))) [input p5]
9. ? [X0] : (~funny(X0) & ~tall(X0)) <=> (brave(lucy) & ~rich(lucy)) [input p8]
13. ! [X0] : ((funny(X0) <~> ~rich(X0)) => (~brave(X0) & kind(X0))) [input p12]
16. ! [X0] : ((~funny(X0) <~> kind(X0)) => (brave(X0) | ~funny(X0))) [input p15]
23. ~old(lucy) [input hypothesis]
32. ! [X0] : ((~brave(X0) & kind(X0)) | (funny(X0) <=> ~rich(X0))) [ennf transformation 13]
33. ! [X0] : ((brave(X0) | ~funny(X0)) | (~funny(X0) <=> kind(X0))) [ennf transformation 16]
34. ! [X0] : (brave(X0) | ~funny(X0) | (~funny(X0) <=> kind(X0))) [flattening 33]
45. ! [X0] : (((funny(X0) & ~calm(X0)) | (~rich(X0) & old(X0))) & ((rich(X0) | ~old(X0)) | (~funny(X0) | calm(X0)))) [nnf transformation 5]
46. ! [X0] : (((funny(X0) & ~calm(X0)) | (~rich(X0) & old(X0))) & (rich(X0) | ~old(X0) | ~funny(X0) | calm(X0))) [flattening 45]
47. ! [X0] : ((~old(X0) | ((kind(X0) | ~rich(X0)) & (rich(X0) | ~kind(X0)))) & (((~rich(X0) | ~kind(X0)) & (rich(X0) | kind(X0))) | old(X0))) [nnf transformation 6]
53. (? [X0] : (~funny(X0) & ~tall(X0)) | (~brave(lucy) | rich(lucy))) & ((brave(lucy) & ~rich(lucy)) | ! [X0] : (funny(X0) | tall(X0))) [nnf transformation 9]
54. (? [X0] : (~funny(X0) & ~tall(X0)) | ~brave(lucy) | rich(lucy)) & ((brave(lucy) & ~rich(lucy)) | ! [X0] : (funny(X0) | tall(X0))) [flattening 53]
55. (? [X0] : (~funny(X0) & ~tall(X0)) | ~brave(lucy) | rich(lucy)) & ((brave(lucy) & ~rich(lucy)) | ! [X1] : (funny(X1) | tall(X1))) [rectify 54]
56. ? [X0] : (~funny(X0) & ~tall(X0)) => (~funny(sK3) & ~tall(sK3)) [choice axiom]
57. ((~funny(sK3) & ~tall(sK3)) | ~brave(lucy) | rich(lucy)) & ((brave(lucy) & ~rich(lucy)) | ! [X1] : (funny(X1) | tall(X1))) [skolemisation 55,56]
61. ! [X0] : ((~brave(X0) & kind(X0)) | ((funny(X0) | rich(X0)) & (~rich(X0) | ~funny(X0)))) [nnf transformation 32]
69. ! [X0] : (brave(X0) | ~funny(X0) | ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0)))) [nnf transformation 34]
94. old(X0) | funny(X0) [cnf transformation 46]
95. ~rich(X0) | funny(X0) [cnf transformation 46]
96. kind(X0) | rich(X0) | old(X0) [cnf transformation 47]
97. ~kind(X0) | ~rich(X0) | old(X0) [cnf transformation 47]
98. ~kind(X0) | rich(X0) | ~old(X0) [cnf transformation 47]
107. ~funny(sK3) | ~brave(lucy) | rich(lucy) [cnf transformation 57]
114. kind(X0) | ~rich(X0) | ~funny(X0) [cnf transformation 61]
115. kind(X0) | funny(X0) | rich(X0) [cnf transformation 61]
129. brave(X0) | ~funny(X0) | ~funny(X0) | ~kind(X0) [cnf transformation 69]
139. ~old(lucy) [cnf transformation 23]
140. ~kind(X0) | ~funny(X0) | brave(X0) [duplicate literal removal 129]
173. 7 <=> rich(lucy) [avatar definition]
175. rich(lucy) <- (7) [avatar component clause 173]
177. 8 <=> brave(lucy) [avatar definition]
179. ~brave(lucy) <- (~8) [avatar component clause 177]
181. 9 <=> funny(sK3) [avatar definition]
183. ~funny(sK3) <- (~9) [avatar component clause 181]
184. 7 | ~8 | ~9 [avatar split clause 107,181,177,173]
227. kind(X0) | funny(X0) [subsumption resolution 115,95]
228. ~rich(X0) | kind(X0) [subsumption resolution 114,227]
310. rich(X1) | ~old(X1) | funny(X1) [resolution 98,227]
312. ~old(X1) | funny(X1) [subsumption resolution 310,95]
313. funny(X1) [subsumption resolution 312,94]
317. $false <- (~9) [resolution 313,183]
318. 9 [avatar contradiction clause 317]
332. ~funny(X0) | brave(X0) | rich(X0) | old(X0) [resolution 140,96]
334. brave(X0) | rich(X0) | old(X0) [subsumption resolution 332,313]
372. rich(lucy) | old(lucy) <- (~8) [resolution 334,179]
376. rich(lucy) <- (~8) [subsumption resolution 372,139]
377. 7 | 8 [avatar split clause 376,177,173]
378. kind(lucy) <- (7) [resolution 175,228]
382. ~rich(lucy) | old(lucy) <- (7) [resolution 378,97]
386. old(lucy) <- (7) [subsumption resolution 382,175]
387. $false <- (7) [subsumption resolution 386,139]
388. ~7 [avatar contradiction clause 387]
389. $false [avatar sat refutation 184,318,377,388]
% SZS output end Proof for 8562532671683784553129500
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If john is strong or funny then someone is generous and vice versa.
Everyone who is patient is either not wise or tall and vice versa.
Everyone who is either kind or calm is not funny or not calm and vice versa.
Everyone who is either not calm or generous is brave and vice versa.
If someone is both tall and not rich then someone is not humble and vice versa.
Everyone who is not wise is both wise and not old and vice versa.
If someone is either not wise or strong then paul is either not creative or not brave and vice versa.
If mary is both not curious and kind then fred is both not rich and brave and vice versa.
Everyone who is not quiet is not calm.
If someone is not quiet or strong then john is not curious or not wise.
Everyone who is not brave is either tall or not strong and vice versa.
Everyone who is quiet or not patient is creative or tall and vice versa.
Everyone who is happy or not quiet is not quiet or old and vice versa.
If mary is funny then lucy is either generous or not old and vice versa.
If someone is curious or not rich then john is not old or brave.
If mary is both not old and curious then john is both tall and not brave.
Alice is not funny or not patient.
Someone is brave.
Someone is not funny or rich.
Lucy is kind.
Someone is curious or not kind.
Someone is both tall and generous.
Someone is both not rich and curious.
Paul is not happy. | Paul is not creative. | contradiction | (((strong(john)|funny(john)))<=>(?[X]:(generous(X))))&
(![X]:(patient(X)<=>(~wise(X)<~>tall(X))))&
(![X]:((kind(X)<~>calm(X))<=>(~funny(X)|~calm(X))))&
(![X]:((~calm(X)<~>generous(X))<=>brave(X)))&
((?[X]:((tall(X)&~rich(X))))<=>(?[X]:(~humble(X))))&
(![X]:(~wise(X)<=>(wise(X)&~old(X))))&
((?[X]:((~wise(X)<~>strong(X))))<=>((~creative(paul)<~>~brave(paul))))&
(((~curious(mary)&kind(mary)))<=>((~rich(fred)&brave(fred))))&
(![X]:(~quiet(X)=>~calm(X)))&
((?[X]:((~quiet(X)|strong(X))))=>((~curious(john)|~wise(john))))&
(![X]:(~brave(X)<=>(tall(X)<~>~strong(X))))&
(![X]:((quiet(X)|~patient(X))<=>(creative(X)|tall(X))))&
(![X]:((happy(X)|~quiet(X))<=>(~quiet(X)|old(X))))&
((funny(mary))<=>((generous(lucy)<~>~old(lucy))))&
((?[X]:((curious(X)|~rich(X))))=>((~old(john)|brave(john))))&
(((~old(mary)&curious(mary)))=>((tall(john)&~brave(john))))&
((~funny(alice)|~patient(alice)))&
(?[X]:(brave(X)))&
(?[X]:((~funny(X)|rich(X))))&
(kind(lucy))&
(?[X]:((curious(X)|~kind(X))))&
(?[X]:((tall(X)&generous(X))))&
(?[X]:((~rich(X)&curious(X))))&
(~happy(paul)) | ~creative(paul) | [
"p1",
"p5",
"p11",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7356142813392832550703303
% SZS output start Proof for 7356142813392832550703303
2. ! [X0] : (patient(X0) <=> (~wise(X0) <~> tall(X0))) [input p1]
6. ! [X0] : (~wise(X0) <=> (~old(X0) & wise(X0))) [input p5]
12. ! [X0] : ((~patient(X0) | quiet(X0)) <=> (tall(X0) | creative(X0))) [input p11]
13. ! [X0] : ((~quiet(X0) | happy(X0)) <=> (old(X0) | ~quiet(X0))) [input p12]
24. ~happy(paul) [input p23]
25. ~creative(paul) [input hypothesis]
39. ! [X0] : ((patient(X0) | ((~wise(X0) | ~tall(X0)) & (tall(X0) | wise(X0)))) & (((~tall(X0) | wise(X0)) & (tall(X0) | ~wise(X0))) | ~patient(X0))) [nnf transformation 2]
48. ! [X0] : ((~wise(X0) | (old(X0) | ~wise(X0))) & ((~old(X0) & wise(X0)) | wise(X0))) [nnf transformation 6]
49. ! [X0] : ((~wise(X0) | old(X0) | ~wise(X0)) & ((~old(X0) & wise(X0)) | wise(X0))) [flattening 48]
57. ! [X0] : (((~patient(X0) | quiet(X0)) | (~tall(X0) & ~creative(X0))) & ((tall(X0) | creative(X0)) | (patient(X0) & ~quiet(X0)))) [nnf transformation 12]
58. ! [X0] : ((~patient(X0) | quiet(X0) | (~tall(X0) & ~creative(X0))) & (tall(X0) | creative(X0) | (patient(X0) & ~quiet(X0)))) [flattening 57]
59. ! [X0] : (((~quiet(X0) | happy(X0)) | (~old(X0) & quiet(X0))) & ((old(X0) | ~quiet(X0)) | (quiet(X0) & ~happy(X0)))) [nnf transformation 13]
60. ! [X0] : ((~quiet(X0) | happy(X0) | (~old(X0) & quiet(X0))) & (old(X0) | ~quiet(X0) | (quiet(X0) & ~happy(X0)))) [flattening 59]
75. ~wise(X0) | tall(X0) | ~patient(X0) [cnf transformation 39]
78. ~tall(X0) | ~wise(X0) | patient(X0) [cnf transformation 39]
92. wise(X0) | wise(X0) [cnf transformation 49]
94. ~wise(X0) | old(X0) | ~wise(X0) [cnf transformation 49]
115. creative(X0) | tall(X0) | patient(X0) [cnf transformation 58]
117. ~tall(X0) | quiet(X0) | ~patient(X0) [cnf transformation 58]
121. ~quiet(X0) | happy(X0) | ~old(X0) [cnf transformation 60]
139. ~happy(paul) [cnf transformation 24]
140. ~creative(paul) [cnf transformation 25]
141. wise(X0) [duplicate literal removal 92]
142. ~wise(X0) | old(X0) [duplicate literal removal 94]
191. 11 <=> creative(paul) [avatar definition]
193. ~creative(paul) <- (~11) [avatar component clause 191]
308. ~11 [avatar split clause 140,191]
312. old(X0) [resolution 142,141]
319. ~patient(X0) | tall(X0) [resolution 75,141]
413. 47 <=> tall(paul) [avatar definition]
414. tall(paul) <- (47) [avatar component clause 413]
456. tall(paul) | patient(paul) <- (~11) [resolution 115,193]
503. tall(paul) <- (~11) [subsumption resolution 456,319]
504. 47 | 11 [avatar split clause 503,191,413]
519. quiet(paul) | ~patient(paul) <- (47) [resolution 414,117]
521. ~wise(paul) | patient(paul) <- (47) [resolution 414,78]
525. 53 <=> patient(paul) [avatar definition]
529. 54 <=> quiet(paul) [avatar definition]
531. quiet(paul) <- (54) [avatar component clause 529]
532. ~53 | 54 | ~47 [avatar split clause 519,413,529,525]
533. patient(paul) <- (47) [subsumption resolution 521,141]
534. 53 | ~47 [avatar split clause 533,413,525]
597. happy(paul) | ~old(paul) <- (54) [resolution 531,121]
599. ~old(paul) <- (54) [subsumption resolution 597,139]
600. $false <- (54) [subsumption resolution 599,312]
601. ~54 [avatar contradiction clause 600]
602. $false [avatar sat refutation 308,504,532,534,601]
% SZS output end Proof for 7356142813392832550703303
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either wise or kind is tall or not old and vice versa.
Everyone who is not humble is either not strong or not tall.
Everyone who is both rich and funny is both creative and funny and vice versa.
Everyone who is not generous or not calm is either brave or creative.
Everyone who is generous is either not strong or not curious.
Everyone who is not brave or not old is both patient and not humble.
Everyone who is happy is not brave and vice versa.
Everyone who is not brave is curious and vice versa.
Everyone who is either calm or brave is both not quiet and funny.
If mary is not brave then someone is not happy or strong.
Everyone who is not strong or not brave is funny or rich.
Everyone who is not happy or calm is either creative or kind and vice versa.
If someone is either old or not wise then susan is either brave or old and vice versa.
Everyone who is quiet is both calm and old.
Everyone who is both creative and strong is not curious or wise.
If susan is kind then someone is either quiet or not funny.
Alice is either happy or not calm.
Susan is not patient.
Alice is either not quiet or not strong.
Someone is both not quiet and brave.
Someone is strong or not quiet.
Alice is not creative.
Someone is kind.
Someone is brave or not funny. | Alice is quiet. | contradiction | (![X]:((wise(X)<~>kind(X))<=>(tall(X)|~old(X))))&
(![X]:(~humble(X)=>(~strong(X)<~>~tall(X))))&
(![X]:((rich(X)&funny(X))<=>(creative(X)&funny(X))))&
(![X]:((~generous(X)|~calm(X))=>(brave(X)<~>creative(X))))&
(![X]:(generous(X)=>(~strong(X)<~>~curious(X))))&
(![X]:((~brave(X)|~old(X))=>(patient(X)&~humble(X))))&
(![X]:(happy(X)<=>~brave(X)))&
(![X]:(~brave(X)<=>curious(X)))&
(![X]:((calm(X)<~>brave(X))=>(~quiet(X)&funny(X))))&
((~brave(mary))=>(?[X]:((~happy(X)|strong(X)))))&
(![X]:((~strong(X)|~brave(X))=>(funny(X)|rich(X))))&
(![X]:((~happy(X)|calm(X))<=>(creative(X)<~>kind(X))))&
((?[X]:((old(X)<~>~wise(X))))<=>((brave(susan)<~>old(susan))))&
(![X]:(quiet(X)=>(calm(X)&old(X))))&
(![X]:((creative(X)&strong(X))=>(~curious(X)|wise(X))))&
((kind(susan))=>(?[X]:((quiet(X)<~>~funny(X)))))&
((happy(alice)<~>~calm(alice)))&
(~patient(susan))&
((~quiet(alice)<~>~strong(alice)))&
(?[X]:((~quiet(X)&brave(X))))&
(?[X]:((strong(X)|~quiet(X))))&
(~creative(alice))&
(?[X]:(kind(X)))&
(?[X]:((brave(X)|~funny(X)))) | quiet(alice) | [
"p6",
"p8",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5759132836693961760900230
% SZS output start Proof for 5759132836693961760900230
7. ! [X0] : (happy(X0) <=> ~brave(X0)) [input p6]
9. ! [X0] : ((calm(X0) <~> brave(X0)) => (funny(X0) & ~quiet(X0))) [input p8]
14. ! [X0] : (quiet(X0) => (old(X0) & calm(X0))) [input p13]
17. happy(alice) <~> ~calm(alice) [input p16]
25. quiet(alice) [input hypothesis]
30. ! [X0] : ((funny(X0) & ~quiet(X0)) | (calm(X0) <=> brave(X0))) [ennf transformation 9]
34. ! [X0] : ((old(X0) & calm(X0)) | ~quiet(X0)) [ennf transformation 14]
45. ! [X0] : ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0))) [nnf transformation 7]
47. ! [X0] : ((funny(X0) & ~quiet(X0)) | ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0)))) [nnf transformation 30]
59. (calm(alice) | ~happy(alice)) & (~calm(alice) | happy(alice)) [nnf transformation 17]
91. ~happy(X0) | ~brave(X0) [cnf transformation 45]
95. ~quiet(X0) | brave(X0) | ~calm(X0) [cnf transformation 47]
116. ~quiet(X0) | calm(X0) [cnf transformation 34]
121. ~calm(alice) | happy(alice) [cnf transformation 59]
132. quiet(alice) [cnf transformation 25]
191. 13 <=> happy(alice) [avatar definition]
192. happy(alice) <- (13) [avatar component clause 191]
195. 14 <=> calm(alice) [avatar definition]
197. calm(alice) <- (14) [avatar component clause 195]
199. 13 | ~14 [avatar split clause 121,195,191]
201. 15 <=> quiet(alice) [avatar definition]
203. quiet(alice) <- (15) [avatar component clause 201]
228. 15 [avatar split clause 132,201]
241. calm(alice) <- (15) [resolution 116,203]
244. 14 | ~15 [avatar split clause 241,201,195]
245. ~brave(alice) <- (13) [resolution 192,91]
323. brave(alice) | ~calm(alice) <- (15) [resolution 95,203]
324. ~calm(alice) <- (13, 15) [subsumption resolution 323,245]
325. $false <- (13, 14, 15) [subsumption resolution 324,197]
326. ~13 | ~14 | ~15 [avatar contradiction clause 325]
327. $false [avatar sat refutation 199,228,244,326]
% SZS output end Proof for 5759132836693961760900230
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or tall is rich or old and vice versa. If someone is either patient or not wise then lucy is either patient or funny. If lucy is either not generous or not patient then lucy is both tall and not brave and vice versa. If someone is not humble then john is creative and vice versa. If mary is either not brave or not wise then john is funny or not kind and vice versa. If someone is kind then someone is both generous and not brave and vice versa. If someone is not patient or not generous then lucy is brave or not wise and vice versa. If lucy is not quiet or not creative then john is strong or not creative and vice versa. If someone is patient or funny then fred is not old and vice versa. If lucy is both funny and not funny then someone is funny or not patient and vice versa. Everyone who is both calm and not generous is either not quiet or old. If susan is either not rich or not humble then paul is not kind. Everyone who is either creative or not curious is humble. If someone is funny then fred is not curious or brave. If someone is either not quiet or creative then someone is both not quiet and not tall and vice versa. If alice is both patient and curious then someone is both humble and not creative. John is either creative or tall. Alice is both not rich and humble. Someone is either rich or creative. Fred is strong or humble. Alice is either curious or kind. Someone is either not quiet or wise. Mary is tall or kind. | Susan is not funny. | entailment | (![X]:((~curious(X)|tall(X))<=>(rich(X)|old(X))))&
((?[X]:((patient(X)<~>~wise(X))))=>((patient(lucy)<~>funny(lucy))))&
(((~generous(lucy)<~>~patient(lucy)))<=>((tall(lucy)&~brave(lucy))))&
((?[X]:(~humble(X)))<=>(creative(john)))&
(((~brave(mary)<~>~wise(mary)))<=>((funny(john)|~kind(john))))&
((?[X]:(kind(X)))<=>(?[X]:((generous(X)&~brave(X)))))&
((?[X]:((~patient(X)|~generous(X))))<=>((brave(lucy)|~wise(lucy))))&
(((~quiet(lucy)|~creative(lucy)))<=>((strong(john)|~creative(john))))&
((?[X]:((patient(X)|funny(X))))<=>(~old(fred)))&
(((funny(lucy)&~funny(lucy)))<=>(?[X]:((funny(X)|~patient(X)))))&
(![X]:((calm(X)&~generous(X))=>(~quiet(X)<~>old(X))))&
(((~rich(susan)<~>~humble(susan)))=>(~kind(paul)))&
(![X]:((creative(X)<~>~curious(X))=>humble(X)))&
((?[X]:(funny(X)))=>((~curious(fred)|brave(fred))))&
((?[X]:((~quiet(X)<~>creative(X))))<=>(?[X]:((~quiet(X)&~tall(X)))))&
(((patient(alice)&curious(alice)))=>(?[X]:((humble(X)&~creative(X)))))&
((creative(john)<~>tall(john)))&
((~rich(alice)&humble(alice)))&
(?[X]:((rich(X)<~>creative(X))))&
((strong(fred)|humble(fred)))&
((curious(alice)<~>kind(alice)))&
(?[X]:((~quiet(X)<~>wise(X))))&
((tall(mary)|kind(mary))) | ~funny(susan) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3365920285517051462731951
% SZS output start Proof for 3365920285517051462731951
10. (~funny(lucy) & funny(lucy)) <=> ? [X0] : (~patient(X0) | funny(X0)) [input p9]
24. funny(susan) [input hypothesis]
62. ((~funny(lucy) & funny(lucy)) | ! [X0] : (patient(X0) & ~funny(X0))) & (? [X0] : (~patient(X0) | funny(X0)) | (funny(lucy) | ~funny(lucy))) [nnf transformation 10]
63. ((~funny(lucy) & funny(lucy)) | ! [X0] : (patient(X0) & ~funny(X0))) & (? [X0] : (~patient(X0) | funny(X0)) | funny(lucy) | ~funny(lucy)) [flattening 62]
64. ((~funny(lucy) & funny(lucy)) | ! [X0] : (patient(X0) & ~funny(X0))) & (? [X1] : (~patient(X1) | funny(X1)) | funny(lucy) | ~funny(lucy)) [rectify 63]
65. ? [X1] : (~patient(X1) | funny(X1)) => (~patient(sK5) | funny(sK5)) [choice axiom]
66. ((~funny(lucy) & funny(lucy)) | ! [X0] : (patient(X0) & ~funny(X0))) & ((~patient(sK5) | funny(sK5)) | funny(lucy) | ~funny(lucy)) [skolemisation 64,65]
121. funny(lucy) | ~funny(X0) [cnf transformation 66]
123. ~funny(lucy) | ~funny(X0) [cnf transformation 66]
150. funny(susan) [cnf transformation 24]
159. 3 <=> funny(lucy) [avatar definition]
295. 31 <=> ! [X1] : ~funny(X1) [avatar definition]
296. ~funny(X1) <- (31) [avatar component clause 295]
303. 31 | ~3 [avatar split clause 123,159,295]
305. 31 | 3 [avatar split clause 121,159,295]
439. $false <- (31) [resolution 296,150]
440. ~31 [avatar contradiction clause 439]
441. $false [avatar sat refutation 303,305,440]
% SZS output end Proof for 3365920285517051462731951
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.016 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not tall then paul is not old or not strong and vice versa.
Everyone who is both funny and not funny is both not kind and happy and vice versa.
If alice is not quiet then someone is either not funny or curious and vice versa.
Everyone who is either happy or not funny is happy or not creative and vice versa.
Everyone who is both not creative and not patient is not old.
If alice is happy then someone is both not funny and not old.
If someone is either funny or not creative then john is both strong and patient.
Everyone who is kind or not happy is not happy or generous and vice versa.
If someone is both happy and brave then mary is either not kind or not creative.
If paul is either not tall or curious then someone is both strong and happy and vice versa.
If someone is both generous and not quiet then someone is both creative and curious.
Everyone who is both happy and creative is either rich or quiet.
Everyone who is either brave or calm is generous and vice versa.
Everyone who is both curious and not kind is curious and vice versa.
If someone is not generous then fred is either not rich or not strong.
Everyone who is either not creative or not wise is not wise.
Someone is both not humble and curious.
Someone is either calm or not old.
Someone is both curious and not happy.
Someone is both brave and rich.
Lucy is either creative or calm.
Paul is funny.
Mary is both funny and patient.
Fred is not wise. | Mary is not kind. | neutral | ((?[X]:(~tall(X)))<=>((~old(paul)|~strong(paul))))&
(![X]:((funny(X)&~funny(X))<=>(~kind(X)&happy(X))))&
((~quiet(alice))<=>(?[X]:((~funny(X)<~>curious(X)))))&
(![X]:((happy(X)<~>~funny(X))<=>(happy(X)|~creative(X))))&
(![X]:((~creative(X)&~patient(X))=>~old(X)))&
((happy(alice))=>(?[X]:((~funny(X)&~old(X)))))&
((?[X]:((funny(X)<~>~creative(X))))=>((strong(john)&patient(john))))&
(![X]:((kind(X)|~happy(X))<=>(~happy(X)|generous(X))))&
((?[X]:((happy(X)&brave(X))))=>((~kind(mary)<~>~creative(mary))))&
(((~tall(paul)<~>curious(paul)))<=>(?[X]:((strong(X)&happy(X)))))&
((?[X]:((generous(X)&~quiet(X))))=>(?[X]:((creative(X)&curious(X)))))&
(![X]:((happy(X)&creative(X))=>(rich(X)<~>quiet(X))))&
(![X]:((brave(X)<~>calm(X))<=>generous(X)))&
(![X]:((curious(X)&~kind(X))<=>curious(X)))&
((?[X]:(~generous(X)))=>((~rich(fred)<~>~strong(fred))))&
(![X]:((~creative(X)<~>~wise(X))=>~wise(X)))&
(?[X]:((~humble(X)&curious(X))))&
(?[X]:((calm(X)<~>~old(X))))&
(?[X]:((curious(X)&~happy(X))))&
(?[X]:((brave(X)&rich(X))))&
((creative(lucy)<~>calm(lucy)))&
(funny(paul))&
((funny(mary)&patient(mary)))&
(~wise(fred)) | ~kind(mary) | [] | null | 0 |
Everyone who is brave or generous is either tall or strong and vice versa. Everyone who is not curious or not calm is either strong or not humble. If someone is not happy then john is either not happy or tall and vice versa. If someone is either not kind or tall then someone is not humble. Everyone who is both humble and not funny is either not strong or not happy and vice versa. Everyone who is both not kind and creative is calm. If someone is both patient and calm then lucy is brave or quiet. If someone is both not creative and wise then mary is both wise and not old and vice versa. Everyone who is not strong or not calm is curious or not strong and vice versa. If susan is not generous then someone is not funny. Everyone who is generous or not generous is both not brave and not wise and vice versa. Everyone who is funny is both not strong and not kind and vice versa. If someone is either happy or not old then paul is both not quiet and not kind. Everyone who is kind or not strong is both not funny and not humble. If mary is not generous or brave then alice is rich or calm. Mary is happy or not creative. Someone is calm. Fred is strong or not generous. Someone is either humble or not curious. Someone is not kind or humble. | Alice is not happy. | entailment | (![X]:((brave(X)|generous(X))<=>(tall(X)<~>strong(X))))&
(![X]:((~curious(X)|~calm(X))=>(strong(X)<~>~humble(X))))&
((?[X]:(~happy(X)))<=>((~happy(john)<~>tall(john))))&
((?[X]:((~kind(X)<~>tall(X))))=>(?[X]:(~humble(X))))&
(![X]:((humble(X)&~funny(X))<=>(~strong(X)<~>~happy(X))))&
(![X]:((~kind(X)&creative(X))=>calm(X)))&
((?[X]:((patient(X)&calm(X))))=>((brave(lucy)|quiet(lucy))))&
((?[X]:((~creative(X)&wise(X))))<=>((wise(mary)&~old(mary))))&
(![X]:((~strong(X)|~calm(X))<=>(curious(X)|~strong(X))))&
((~generous(susan))=>(?[X]:(~funny(X))))&
(![X]:((generous(X)|~generous(X))<=>(~brave(X)&~wise(X))))&
(![X]:(funny(X)<=>(~strong(X)&~kind(X))))&
((?[X]:((happy(X)<~>~old(X))))=>((~quiet(paul)&~kind(paul))))&
(![X]:((kind(X)|~strong(X))=>(~funny(X)&~humble(X))))&
(((~generous(mary)|brave(mary)))=>((rich(alice)|calm(alice))))&
((happy(mary)|~creative(mary)))&
(?[X]:(calm(X)))&
((strong(fred)|~generous(fred)))&
(?[X]:((humble(X)<~>~curious(X))))&
(?[X]:((~kind(X)|humble(X)))) | ~happy(alice) | [
"p1",
"p4",
"p8",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6411746976661872494415416
% SZS output start Proof for 6411746976661872494415416
2. ! [X0] : ((~calm(X0) | ~curious(X0)) => (strong(X0) <~> ~humble(X0))) [input p1]
5. ! [X0] : ((~funny(X0) & humble(X0)) <=> (~strong(X0) <~> ~happy(X0))) [input p4]
9. ! [X0] : ((~calm(X0) | ~strong(X0)) <=> (~strong(X0) | curious(X0))) [input p8]
12. ! [X0] : (funny(X0) <=> (~kind(X0) & ~strong(X0))) [input p11]
14. ! [X0] : ((~strong(X0) | kind(X0)) => (~humble(X0) & ~funny(X0))) [input p13]
21. happy(alice) [input hypothesis]
26. ! [X0] : ((strong(X0) <~> ~humble(X0)) | (calm(X0) & curious(X0))) [ennf transformation 2]
32. ! [X0] : ((~humble(X0) & ~funny(X0)) | (strong(X0) & ~kind(X0))) [ennf transformation 14]
35. ! [X0] : (((humble(X0) | ~strong(X0)) & (~humble(X0) | strong(X0))) | (calm(X0) & curious(X0))) [nnf transformation 26]
44. ! [X0] : (((~funny(X0) & humble(X0)) | ((~strong(X0) | happy(X0)) & (~happy(X0) | strong(X0)))) & (((happy(X0) | strong(X0)) & (~happy(X0) | ~strong(X0))) | (funny(X0) | ~humble(X0)))) [nnf transformation 5]
45. ! [X0] : (((~funny(X0) & humble(X0)) | ((~strong(X0) | happy(X0)) & (~happy(X0) | strong(X0)))) & (((happy(X0) | strong(X0)) & (~happy(X0) | ~strong(X0))) | funny(X0) | ~humble(X0))) [flattening 44]
51. ! [X0] : (((~calm(X0) | ~strong(X0)) | (strong(X0) & ~curious(X0))) & ((~strong(X0) | curious(X0)) | (calm(X0) & strong(X0)))) [nnf transformation 9]
52. ! [X0] : ((~calm(X0) | ~strong(X0) | (strong(X0) & ~curious(X0))) & (~strong(X0) | curious(X0) | (calm(X0) & strong(X0)))) [flattening 51]
57. ! [X0] : ((funny(X0) | (kind(X0) | strong(X0))) & ((~kind(X0) & ~strong(X0)) | ~funny(X0))) [nnf transformation 12]
58. ! [X0] : ((funny(X0) | kind(X0) | strong(X0)) & ((~kind(X0) & ~strong(X0)) | ~funny(X0))) [flattening 57]
75. ~strong(X0) | humble(X0) | curious(X0) [cnf transformation 35]
76. ~strong(X0) | humble(X0) | calm(X0) [cnf transformation 35]
83. ~happy(X0) | ~strong(X0) | funny(X0) | ~humble(X0) [cnf transformation 45]
85. ~happy(X0) | humble(X0) | strong(X0) [cnf transformation 45]
96. ~calm(X0) | ~strong(X0) | ~curious(X0) [cnf transformation 52]
104. ~funny(X0) | ~strong(X0) [cnf transformation 58]
110. ~funny(X0) | strong(X0) [cnf transformation 32]
112. ~humble(X0) | strong(X0) [cnf transformation 32]
119. happy(alice) [cnf transformation 21]
197. ~funny(X0) [subsumption resolution 110,104]
231. humble(alice) | strong(alice) [resolution 85,119]
232. strong(alice) [subsumption resolution 231,112]
233. humble(alice) | calm(alice) [resolution 232,76]
234. humble(alice) | curious(alice) [resolution 232,75]
238. 24 <=> calm(alice) [avatar definition]
240. calm(alice) <- (24) [avatar component clause 238]
242. 25 <=> humble(alice) [avatar definition]
244. humble(alice) <- (25) [avatar component clause 242]
245. 24 | 25 [avatar split clause 233,242,238]
247. 26 <=> curious(alice) [avatar definition]
250. 26 | 25 [avatar split clause 234,242,247]
267. ~strong(alice) | ~curious(alice) <- (24) [resolution 96,240]
277. ~curious(alice) <- (24) [subsumption resolution 267,232]
278. ~26 | ~24 [avatar split clause 277,238,247]
293. ~strong(alice) | funny(alice) | ~humble(alice) [resolution 83,119]
294. funny(alice) | ~humble(alice) [subsumption resolution 293,232]
295. ~humble(alice) [subsumption resolution 294,197]
296. $false <- (25) [subsumption resolution 295,244]
297. ~25 [avatar contradiction clause 296]
298. $false [avatar sat refutation 245,250,278,297]
% SZS output end Proof for 6411746976661872494415416
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not kind and not old then lucy is either not funny or not kind and vice versa.
Everyone who is rich or not tall is both not calm and not wise.
Everyone who is brave or creative is strong or not generous and vice versa.
If susan is not creative then susan is tall or wise.
Everyone who is either rich or not old is both patient and tall and vice versa.
If susan is rich then paul is not curious.
Everyone who is not quiet is either not quiet or wise.
Everyone who is not wise or not quiet is not humble.
If alice is curious then alice is both not quiet and not brave and vice versa.
Everyone who is either not generous or not curious is either strong or not quiet.
Everyone who is not brave is curious or not strong and vice versa.
Everyone who is both kind and quiet is both rich and not quiet.
Everyone who is not tall is either calm or patient and vice versa.
If someone is both not rich and not happy then someone is creative and vice versa.
If mary is kind or creative then fred is not brave and vice versa.
Everyone who is not kind is both not generous and not old.
Someone is both not calm and not wise.
John is both tall and wise.
John is happy or kind.
Someone is both happy and rich.
Someone is patient.
Paul is both rich and not calm.
Alice is both not calm and not tall. | John is patient. | entailment | ((?[X]:((~kind(X)&~old(X))))<=>((~funny(lucy)<~>~kind(lucy))))&
(![X]:((rich(X)|~tall(X))=>(~calm(X)&~wise(X))))&
(![X]:((brave(X)|creative(X))<=>(strong(X)|~generous(X))))&
((~creative(susan))=>((tall(susan)|wise(susan))))&
(![X]:((rich(X)<~>~old(X))<=>(patient(X)&tall(X))))&
((rich(susan))=>(~curious(paul)))&
(![X]:(~quiet(X)=>(~quiet(X)<~>wise(X))))&
(![X]:((~wise(X)|~quiet(X))=>~humble(X)))&
((curious(alice))<=>((~quiet(alice)&~brave(alice))))&
(![X]:((~generous(X)<~>~curious(X))=>(strong(X)<~>~quiet(X))))&
(![X]:(~brave(X)<=>(curious(X)|~strong(X))))&
(![X]:((kind(X)&quiet(X))=>(rich(X)&~quiet(X))))&
(![X]:(~tall(X)<=>(calm(X)<~>patient(X))))&
((?[X]:((~rich(X)&~happy(X))))<=>(?[X]:(creative(X))))&
(((kind(mary)|creative(mary)))<=>(~brave(fred)))&
(![X]:(~kind(X)=>(~generous(X)&~old(X))))&
(?[X]:((~calm(X)&~wise(X))))&
((tall(john)&wise(john)))&
((happy(john)|kind(john)))&
(?[X]:((happy(X)&rich(X))))&
(?[X]:(patient(X)))&
((rich(paul)&~calm(paul)))&
((~calm(alice)&~tall(alice))) | patient(john) | [
"p1",
"p4",
"p6",
"p11",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2937597344767503221544820
% SZS output start Proof for 2937597344767503221544820
2. ! [X0] : ((~tall(X0) | rich(X0)) => (~wise(X0) & ~calm(X0))) [input p1]
5. ! [X0] : ((rich(X0) <~> ~old(X0)) <=> (tall(X0) & patient(X0))) [input p4]
7. ! [X0] : (~quiet(X0) => (~quiet(X0) <~> wise(X0))) [input p6]
12. ! [X0] : ((quiet(X0) & kind(X0)) => (~quiet(X0) & rich(X0))) [input p11]
16. ! [X0] : (~kind(X0) => (~old(X0) & ~generous(X0))) [input p15]
18. wise(john) & tall(john) [input p17]
24. ~patient(john) [input hypothesis]
27. ! [X0] : ((~wise(X0) & ~calm(X0)) | (tall(X0) & ~rich(X0))) [ennf transformation 2]
31. ! [X0] : ((~quiet(X0) <~> wise(X0)) | quiet(X0)) [ennf transformation 7]
33. ! [X0] : ((~quiet(X0) & rich(X0)) | (~quiet(X0) | ~kind(X0))) [ennf transformation 12]
34. ! [X0] : ((~quiet(X0) & rich(X0)) | ~quiet(X0) | ~kind(X0)) [flattening 33]
35. ! [X0] : ((~old(X0) & ~generous(X0)) | kind(X0)) [ennf transformation 16]
42. ! [X0] : ((((old(X0) | ~rich(X0)) & (~old(X0) | rich(X0))) | (~tall(X0) | ~patient(X0))) & ((tall(X0) & patient(X0)) | ((rich(X0) | old(X0)) & (~old(X0) | ~rich(X0))))) [nnf transformation 5]
43. ! [X0] : ((((old(X0) | ~rich(X0)) & (~old(X0) | rich(X0))) | ~tall(X0) | ~patient(X0)) & ((tall(X0) & patient(X0)) | ((rich(X0) | old(X0)) & (~old(X0) | ~rich(X0))))) [flattening 42]
44. ! [X0] : (((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | quiet(X0)) [nnf transformation 31]
72. ~wise(X0) | ~rich(X0) [cnf transformation 27]
80. patient(X0) | rich(X0) | old(X0) [cnf transformation 43]
87. ~wise(X0) | quiet(X0) | quiet(X0) [cnf transformation 44]
99. ~quiet(X0) | ~quiet(X0) | ~kind(X0) [cnf transformation 34]
111. ~old(X0) | kind(X0) [cnf transformation 35]
115. wise(john) [cnf transformation 18]
124. ~patient(john) [cnf transformation 24]
125. ~quiet(X0) | ~kind(X0) [duplicate literal removal 99]
126. ~wise(X0) | quiet(X0) [duplicate literal removal 87]
229. 22 <=> kind(john) [avatar definition]
230. ~kind(john) <- (~22) [avatar component clause 229]
233. ~rich(john) [resolution 72,115]
237. quiet(john) [resolution 126,115]
238. ~kind(john) [resolution 237,125]
239. ~22 [avatar split clause 238,229]
271. rich(john) | old(john) [resolution 80,124]
272. old(john) [subsumption resolution 271,233]
275. kind(john) [resolution 272,111]
276. $false <- (~22) [subsumption resolution 275,230]
277. 22 [avatar contradiction clause 276]
278. $false [avatar sat refutation 239,277]
% SZS output end Proof for 2937597344767503221544820
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall then alice is not creative and vice versa.
If lucy is not rich or tall then someone is strong.
If fred is both not funny and not curious then paul is either not quiet or not tall and vice versa.
Everyone who is old or generous is old or patient.
If someone is both not generous and rich then someone is either not quiet or tall and vice versa.
Everyone who is not tall is not happy or not quiet.
If susan is humble or not generous then susan is either not kind or patient and vice versa.
Everyone who is both not quiet and not funny is not funny or not tall and vice versa.
If someone is funny or not brave then someone is generous.
Everyone who is strong or not creative is both quiet and not curious and vice versa.
Everyone who is either not happy or creative is not rich and vice versa.
If fred is both creative and humble then someone is both not wise and generous and vice versa.
If someone is either rich or creative then someone is either patient or not strong.
Everyone who is both not creative and calm is not brave.
If someone is not curious or not creative then lucy is creative or brave and vice versa.
Everyone who is both old and not humble is patient.
Susan is either tall or funny.
Someone is either rich or not wise.
Someone is humble or curious.
Mary is both quiet and not curious.
Lucy is both not old and curious.
Paul is not old or strong.
Susan is both creative and humble.
Paul is both not quiet and brave. | Mary is not funny. | contradiction | ((~tall(alice))<=>(~creative(alice)))&
(((~rich(lucy)|tall(lucy)))=>(?[X]:(strong(X))))&
(((~funny(fred)&~curious(fred)))<=>((~quiet(paul)<~>~tall(paul))))&
(![X]:((old(X)|generous(X))=>(old(X)|patient(X))))&
((?[X]:((~generous(X)&rich(X))))<=>(?[X]:((~quiet(X)<~>tall(X)))))&
(![X]:(~tall(X)=>(~happy(X)|~quiet(X))))&
(((humble(susan)|~generous(susan)))<=>((~kind(susan)<~>patient(susan))))&
(![X]:((~quiet(X)&~funny(X))<=>(~funny(X)|~tall(X))))&
((?[X]:((funny(X)|~brave(X))))=>(?[X]:(generous(X))))&
(![X]:((strong(X)|~creative(X))<=>(quiet(X)&~curious(X))))&
(![X]:((~happy(X)<~>creative(X))<=>~rich(X)))&
(((creative(fred)&humble(fred)))<=>(?[X]:((~wise(X)&generous(X)))))&
((?[X]:((rich(X)<~>creative(X))))=>(?[X]:((patient(X)<~>~strong(X)))))&
(![X]:((~creative(X)&calm(X))=>~brave(X)))&
((?[X]:((~curious(X)|~creative(X))))<=>((creative(lucy)|brave(lucy))))&
(![X]:((old(X)&~humble(X))=>patient(X)))&
((tall(susan)<~>funny(susan)))&
(?[X]:((rich(X)<~>~wise(X))))&
(?[X]:((humble(X)|curious(X))))&
((quiet(mary)&~curious(mary)))&
((~old(lucy)&curious(lucy)))&
((~old(paul)|strong(paul)))&
((creative(susan)&humble(susan)))&
((~quiet(paul)&brave(paul))) | ~funny(mary) | [
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7622285200478674329395487
% SZS output start Proof for 7622285200478674329395487
8. ! [X0] : ((~funny(X0) & ~quiet(X0)) <=> (~tall(X0) | ~funny(X0))) [input p7]
20. ~curious(mary) & quiet(mary) [input p19]
25. ~funny(mary) [input hypothesis]
51. ! [X0] : (((~funny(X0) & ~quiet(X0)) | (tall(X0) & funny(X0))) & ((~tall(X0) | ~funny(X0)) | (funny(X0) | quiet(X0)))) [nnf transformation 8]
52. ! [X0] : (((~funny(X0) & ~quiet(X0)) | (tall(X0) & funny(X0))) & (~tall(X0) | ~funny(X0) | funny(X0) | quiet(X0))) [flattening 51]
105. ~quiet(X0) | funny(X0) [cnf transformation 52]
138. quiet(mary) [cnf transformation 20]
147. ~funny(mary) [cnf transformation 25]
356. funny(mary) [resolution 105,138]
357. $false [subsumption resolution 356,147]
% SZS output end Proof for 7622285200478674329395487
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either not generous or humble then someone is not humble and vice versa.
If mary is both funny and generous then someone is wise or not strong.
If susan is not strong or not quiet then someone is not rich or curious.
Everyone who is wise is both not wise and not old and vice versa.
Everyone who is either not curious or not happy is both wise and not funny.
If someone is both creative and brave then alice is not old or brave and vice versa.
If paul is both old and not funny then lucy is either brave or tall.
Everyone who is old or patient is either not creative or humble.
Everyone who is either not rich or not strong is either generous or not tall.
Everyone who is both brave and not curious is curious and vice versa.
If someone is both patient and not wise then john is either not brave or not curious and vice versa.
If john is not old or not quiet then paul is either not curious or not calm.
Everyone who is either rich or not curious is both brave and wise and vice versa.
Everyone who is both patient and happy is not humble or not kind.
Everyone who is either not generous or not quiet is either tall or not strong and vice versa.
Everyone who is either rich or not happy is generous or creative and vice versa.
Someone is not humble.
Lucy is either creative or old.
John is not quiet or not old.
Lucy is either tall or happy.
Paul is either not old or old.
Someone is rich or not brave. | Susan is not creative. | entailment | (((~generous(mary)<~>humble(mary)))<=>(?[X]:(~humble(X))))&
(((funny(mary)&generous(mary)))=>(?[X]:((wise(X)|~strong(X)))))&
(((~strong(susan)|~quiet(susan)))=>(?[X]:((~rich(X)|curious(X)))))&
(![X]:(wise(X)<=>(~wise(X)&~old(X))))&
(![X]:((~curious(X)<~>~happy(X))=>(wise(X)&~funny(X))))&
((?[X]:((creative(X)&brave(X))))<=>((~old(alice)|brave(alice))))&
(((old(paul)&~funny(paul)))=>((brave(lucy)<~>tall(lucy))))&
(![X]:((old(X)|patient(X))=>(~creative(X)<~>humble(X))))&
(![X]:((~rich(X)<~>~strong(X))=>(generous(X)<~>~tall(X))))&
(![X]:((brave(X)&~curious(X))<=>curious(X)))&
((?[X]:((patient(X)&~wise(X))))<=>((~brave(john)<~>~curious(john))))&
(((~old(john)|~quiet(john)))=>((~curious(paul)<~>~calm(paul))))&
(![X]:((rich(X)<~>~curious(X))<=>(brave(X)&wise(X))))&
(![X]:((patient(X)&happy(X))=>(~humble(X)|~kind(X))))&
(![X]:((~generous(X)<~>~quiet(X))<=>(tall(X)<~>~strong(X))))&
(![X]:((rich(X)<~>~happy(X))<=>(generous(X)|creative(X))))&
(?[X]:(~humble(X)))&
((creative(lucy)<~>old(lucy)))&
((~quiet(john)|~old(john)))&
((tall(lucy)<~>happy(lucy)))&
((~old(paul)<~>old(paul)))&
(?[X]:((rich(X)|~brave(X)))) | ~creative(susan) | [
"p3",
"p4",
"p9",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3279685284019070006977932
% SZS output start Proof for 3279685284019070006977932
4. ! [X0] : (wise(X0) <=> (~old(X0) & ~wise(X0))) [input p3]
5. ! [X0] : ((~curious(X0) <~> ~happy(X0)) => (~funny(X0) & wise(X0))) [input p4]
10. ! [X0] : ((~curious(X0) & brave(X0)) <=> curious(X0)) [input p9]
13. ! [X0] : ((rich(X0) <~> ~curious(X0)) <=> (wise(X0) & brave(X0))) [input p12]
16. ! [X0] : ((rich(X0) <~> ~happy(X0)) <=> (creative(X0) | generous(X0))) [input p15]
23. creative(susan) [input hypothesis]
28. ! [X0] : ((~funny(X0) & wise(X0)) | (~curious(X0) <=> ~happy(X0))) [ennf transformation 5]
42. ! [X0] : ((wise(X0) | (old(X0) | wise(X0))) & ((~old(X0) & ~wise(X0)) | ~wise(X0))) [nnf transformation 4]
43. ! [X0] : ((wise(X0) | old(X0) | wise(X0)) & ((~old(X0) & ~wise(X0)) | ~wise(X0))) [flattening 42]
44. ! [X0] : ((~funny(X0) & wise(X0)) | ((~curious(X0) | happy(X0)) & (~happy(X0) | curious(X0)))) [nnf transformation 28]
53. ! [X0] : (((~curious(X0) & brave(X0)) | ~curious(X0)) & (curious(X0) | (curious(X0) | ~brave(X0)))) [nnf transformation 10]
54. ! [X0] : (((~curious(X0) & brave(X0)) | ~curious(X0)) & (curious(X0) | curious(X0) | ~brave(X0))) [flattening 53]
60. ! [X0] : ((((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | (~wise(X0) | ~brave(X0))) & ((wise(X0) & brave(X0)) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0))))) [nnf transformation 13]
61. ! [X0] : ((((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | ~wise(X0) | ~brave(X0)) & ((wise(X0) & brave(X0)) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0))))) [flattening 60]
63. ! [X0] : ((((happy(X0) | ~rich(X0)) & (~happy(X0) | rich(X0))) | (~creative(X0) & ~generous(X0))) & ((creative(X0) | generous(X0)) | ((rich(X0) | happy(X0)) & (~happy(X0) | ~rich(X0))))) [nnf transformation 16]
64. ! [X0] : ((((happy(X0) | ~rich(X0)) & (~happy(X0) | rich(X0))) | (~creative(X0) & ~generous(X0))) & (creative(X0) | generous(X0) | ((rich(X0) | happy(X0)) & (~happy(X0) | ~rich(X0))))) [flattening 63]
79. ~wise(X0) | ~wise(X0) [cnf transformation 43]
82. wise(X0) | ~happy(X0) | curious(X0) [cnf transformation 44]
103. ~curious(X0) | ~curious(X0) [cnf transformation 54]
117. wise(X0) | rich(X0) | curious(X0) [cnf transformation 61]
133. happy(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 64]
143. creative(susan) [cnf transformation 23]
145. ~curious(X0) [duplicate literal removal 103]
146. ~wise(X0) [duplicate literal removal 79]
199. ~happy(X0) | curious(X0) [subsumption resolution 82,146]
262. rich(X0) | curious(X0) [subsumption resolution 117,146]
263. rich(X0) [subsumption resolution 262,145]
264. ~creative(X0) | happy(X0) [subsumption resolution 133,263]
302. happy(susan) [resolution 264,143]
304. curious(susan) [resolution 302,199]
305. $false [subsumption resolution 304,145]
% SZS output end Proof for 3279685284019070006977932
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or wise is both tall and curious and vice versa. Everyone who is tall or quiet is both not happy and not humble. Everyone who is both not creative and not old is not creative or happy and vice versa. If someone is both not quiet and funny then someone is both curious and old and vice versa. Everyone who is both not generous and not quiet is happy or wise and vice versa. Everyone who is either kind or humble is not patient. Everyone who is not happy is not old. If someone is either rich or patient then someone is wise or curious and vice versa. Everyone who is either not quiet or not humble is either funny or not humble. If someone is either happy or not old then lucy is not curious and vice versa. If someone is not patient then lucy is not quiet and vice versa. Everyone who is calm is not happy or not wise and vice versa. If paul is generous then someone is curious and vice versa. Everyone who is both not rich and humble is either not brave or wise. If john is either brave or tall then susan is kind. Everyone who is not rich is happy and vice versa. Fred is kind. Alice is either not calm or kind. Lucy is both not patient and not creative. Alice is either not patient or not creative. Someone is both strong and not funny. Susan is either patient or calm. Alice is both rich and not funny. | Fred is not curious. | contradiction | (![X]:((kind(X)|wise(X))<=>(tall(X)&curious(X))))&
(![X]:((tall(X)|quiet(X))=>(~happy(X)&~humble(X))))&
(![X]:((~creative(X)&~old(X))<=>(~creative(X)|happy(X))))&
((?[X]:((~quiet(X)&funny(X))))<=>(?[X]:((curious(X)&old(X)))))&
(![X]:((~generous(X)&~quiet(X))<=>(happy(X)|wise(X))))&
(![X]:((kind(X)<~>humble(X))=>~patient(X)))&
(![X]:(~happy(X)=>~old(X)))&
((?[X]:((rich(X)<~>patient(X))))<=>(?[X]:((wise(X)|curious(X)))))&
(![X]:((~quiet(X)<~>~humble(X))=>(funny(X)<~>~humble(X))))&
((?[X]:((happy(X)<~>~old(X))))<=>(~curious(lucy)))&
((?[X]:(~patient(X)))<=>(~quiet(lucy)))&
(![X]:(calm(X)<=>(~happy(X)|~wise(X))))&
((generous(paul))<=>(?[X]:(curious(X))))&
(![X]:((~rich(X)&humble(X))=>(~brave(X)<~>wise(X))))&
(((brave(john)<~>tall(john)))=>(kind(susan)))&
(![X]:(~rich(X)<=>happy(X)))&
(kind(fred))&
((~calm(alice)<~>kind(alice)))&
((~patient(lucy)&~creative(lucy)))&
((~patient(alice)<~>~creative(alice)))&
(?[X]:((strong(X)&~funny(X))))&
((patient(susan)<~>calm(susan)))&
((rich(alice)&~funny(alice))) | ~curious(fred) | [
"p0",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4064276230966858675965675
% SZS output start Proof for 4064276230966858675965675
1. ! [X0] : ((wise(X0) | kind(X0)) <=> (curious(X0) & tall(X0))) [input p0]
17. kind(fred) [input p16]
24. ~curious(fred) [input hypothesis]
35. ! [X0] : (((wise(X0) | kind(X0)) | (~curious(X0) | ~tall(X0))) & ((curious(X0) & tall(X0)) | (~wise(X0) & ~kind(X0)))) [nnf transformation 1]
36. ! [X0] : ((wise(X0) | kind(X0) | ~curious(X0) | ~tall(X0)) & ((curious(X0) & tall(X0)) | (~wise(X0) & ~kind(X0)))) [flattening 35]
77. ~kind(X0) | curious(X0) [cnf transformation 36]
128. kind(fred) [cnf transformation 17]
140. ~curious(fred) [cnf transformation 24]
292. curious(fred) [resolution 77,128]
293. $false [subsumption resolution 292,140]
% SZS output end Proof for 4064276230966858675965675
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or brave is happy and vice versa. If someone is either tall or wise then paul is either not funny or humble. If lucy is not quiet then someone is both tall and humble and vice versa. If lucy is not wise then someone is either not generous or happy. Everyone who is tall is old or not quiet. If mary is calm or brave then someone is either not wise or tall. If someone is kind or tall then someone is generous. If susan is either not wise or patient then someone is wise or brave. If paul is funny or not tall then fred is funny or patient and vice versa. Everyone who is not generous or not strong is both not creative and generous and vice versa. Everyone who is old or tall is both not wise and creative and vice versa. If alice is not rich then john is not tall or not creative and vice versa. Everyone who is both happy and quiet is rich or funny. If someone is both curious and funny then someone is not generous or not calm and vice versa. If someone is not creative then john is not kind and vice versa. Everyone who is either rich or curious is both humble and not brave. Someone is either not quiet or not curious. Someone is either not quiet or wise. Someone is not calm. John is not calm or rich. Someone is either rich or brave. Someone is both not happy and creative. Susan is either not humble or not quiet. Someone is not rich or creative. | Susan is not generous. | contradiction | (![X]:((~quiet(X)|brave(X))<=>happy(X)))&
((?[X]:((tall(X)<~>wise(X))))=>((~funny(paul)<~>humble(paul))))&
((~quiet(lucy))<=>(?[X]:((tall(X)&humble(X)))))&
((~wise(lucy))=>(?[X]:((~generous(X)<~>happy(X)))))&
(![X]:(tall(X)=>(old(X)|~quiet(X))))&
(((calm(mary)|brave(mary)))=>(?[X]:((~wise(X)<~>tall(X)))))&
((?[X]:((kind(X)|tall(X))))=>(?[X]:(generous(X))))&
(((~wise(susan)<~>patient(susan)))=>(?[X]:((wise(X)|brave(X)))))&
(((funny(paul)|~tall(paul)))<=>((funny(fred)|patient(fred))))&
(![X]:((~generous(X)|~strong(X))<=>(~creative(X)&generous(X))))&
(![X]:((old(X)|tall(X))<=>(~wise(X)&creative(X))))&
((~rich(alice))<=>((~tall(john)|~creative(john))))&
(![X]:((happy(X)&quiet(X))=>(rich(X)|funny(X))))&
((?[X]:((curious(X)&funny(X))))<=>(?[X]:((~generous(X)|~calm(X)))))&
((?[X]:(~creative(X)))<=>(~kind(john)))&
(![X]:((rich(X)<~>curious(X))=>(humble(X)&~brave(X))))&
(?[X]:((~quiet(X)<~>~curious(X))))&
(?[X]:((~quiet(X)<~>wise(X))))&
(?[X]:(~calm(X)))&
((~calm(john)|rich(john)))&
(?[X]:((rich(X)<~>brave(X))))&
(?[X]:((~happy(X)&creative(X))))&
((~humble(susan)<~>~quiet(susan)))&
(?[X]:((~rich(X)|creative(X)))) | ~generous(susan) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4376210272248684917508407
% SZS output start Proof for 4376210272248684917508407
10. ! [X0] : ((~strong(X0) | ~generous(X0)) <=> (generous(X0) & ~creative(X0))) [input p9]
25. ~generous(susan) [input hypothesis]
59. ! [X0] : (((~strong(X0) | ~generous(X0)) | (~generous(X0) | creative(X0))) & ((generous(X0) & ~creative(X0)) | (strong(X0) & generous(X0)))) [nnf transformation 10]
60. ! [X0] : ((~strong(X0) | ~generous(X0) | ~generous(X0) | creative(X0)) & ((generous(X0) & ~creative(X0)) | (strong(X0) & generous(X0)))) [flattening 59]
118. generous(X0) | generous(X0) [cnf transformation 60]
154. ~generous(susan) [cnf transformation 25]
155. generous(X0) [duplicate literal removal 118]
382. $false [subsumption resolution 154,155]
% SZS output end Proof for 4376210272248684917508407
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not tall or patient then john is both not calm and not brave and vice versa.
If someone is not old or not curious then someone is both not brave and strong and vice versa.
If fred is quiet then john is both not strong and not curious.
Everyone who is not strong is both quiet and patient and vice versa.
Everyone who is either wise or not strong is not patient.
Everyone who is not old or tall is either not kind or generous.
If john is either not curious or rich then someone is not curious.
Everyone who is either not generous or not funny is generous and vice versa.
If susan is not curious then someone is not patient.
Everyone who is either not happy or patient is not generous or not funny and vice versa.
Everyone who is not wise or not funny is happy or not quiet.
If susan is not curious or not wise then susan is wise and vice versa.
Everyone who is kind or wise is either not funny or patient.
If someone is not generous then alice is either curious or humble.
Everyone who is not happy or not wise is both not patient and not rich.
Mary is both curious and not creative.
Fred is not wise.
Fred is brave or not patient.
Someone is either not generous or not wise.
John is not rich or not humble. | Alice is strong. | entailment | ((?[X]:((~tall(X)|patient(X))))<=>((~calm(john)&~brave(john))))&
((?[X]:((~old(X)|~curious(X))))<=>(?[X]:((~brave(X)&strong(X)))))&
((quiet(fred))=>((~strong(john)&~curious(john))))&
(![X]:(~strong(X)<=>(quiet(X)&patient(X))))&
(![X]:((wise(X)<~>~strong(X))=>~patient(X)))&
(![X]:((~old(X)|tall(X))=>(~kind(X)<~>generous(X))))&
(((~curious(john)<~>rich(john)))=>(?[X]:(~curious(X))))&
(![X]:((~generous(X)<~>~funny(X))<=>generous(X)))&
((~curious(susan))=>(?[X]:(~patient(X))))&
(![X]:((~happy(X)<~>patient(X))<=>(~generous(X)|~funny(X))))&
(![X]:((~wise(X)|~funny(X))=>(happy(X)|~quiet(X))))&
(((~curious(susan)|~wise(susan)))<=>(wise(susan)))&
(![X]:((kind(X)|wise(X))=>(~funny(X)<~>patient(X))))&
((?[X]:(~generous(X)))=>((curious(alice)<~>humble(alice))))&
(![X]:((~happy(X)|~wise(X))=>(~patient(X)&~rich(X))))&
((curious(mary)&~creative(mary)))&
(~wise(fred))&
((brave(fred)|~patient(fred)))&
(?[X]:((~generous(X)<~>~wise(X))))&
((~rich(john)|~humble(john))) | strong(alice) | [
"p3",
"p7",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5610492431118526758321224
% SZS output start Proof for 5610492431118526758321224
4. ! [X0] : (~strong(X0) <=> (patient(X0) & quiet(X0))) [input p3]
8. ! [X0] : ((~generous(X0) <~> ~funny(X0)) <=> generous(X0)) [input p7]
13. ! [X0] : ((wise(X0) | kind(X0)) => (~funny(X0) <~> patient(X0))) [input p12]
15. ! [X0] : ((~wise(X0) | ~happy(X0)) => (~rich(X0) & ~patient(X0))) [input p14]
21. ~strong(alice) [input hypothesis]
31. ! [X0] : ((~funny(X0) <~> patient(X0)) | (~wise(X0) & ~kind(X0))) [ennf transformation 13]
33. ! [X0] : ((~rich(X0) & ~patient(X0)) | (wise(X0) & happy(X0))) [ennf transformation 15]
44. ! [X0] : ((~strong(X0) | (~patient(X0) | ~quiet(X0))) & ((patient(X0) & quiet(X0)) | strong(X0))) [nnf transformation 4]
45. ! [X0] : ((~strong(X0) | ~patient(X0) | ~quiet(X0)) & ((patient(X0) & quiet(X0)) | strong(X0))) [flattening 44]
51. ! [X0] : ((((funny(X0) | generous(X0)) & (~funny(X0) | ~generous(X0))) | ~generous(X0)) & (generous(X0) | ((~generous(X0) | funny(X0)) & (~funny(X0) | generous(X0))))) [nnf transformation 8]
58. ! [X0] : (((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | (~wise(X0) & ~kind(X0))) [nnf transformation 31]
76. strong(X0) | patient(X0) [cnf transformation 45]
86. generous(X0) | ~funny(X0) | generous(X0) [cnf transformation 51]
88. ~funny(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 51]
105. ~patient(X0) | funny(X0) | ~wise(X0) [cnf transformation 58]
109. ~patient(X0) | wise(X0) [cnf transformation 33]
118. ~strong(alice) [cnf transformation 21]
121. generous(X0) | ~funny(X0) [duplicate literal removal 86]
122. ~funny(X0) | ~generous(X0) [duplicate literal removal 88]
141. 5 <=> ! [X1] : ~patient(X1) [avatar definition]
142. ~patient(X1) <- (5) [avatar component clause 141]
205. ~funny(X0) [subsumption resolution 121,122]
225. ~patient(X0) | ~wise(X0) [subsumption resolution 105,205]
240. ~patient(X0) [subsumption resolution 109,225]
241. 5 [avatar split clause 240,141]
267. patient(alice) [resolution 76,118]
268. $false <- (5) [subsumption resolution 267,142]
269. ~5 [avatar contradiction clause 268]
270. $false [avatar sat refutation 241,269]
% SZS output end Proof for 5610492431118526758321224
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not curious and not kind is not calm or not brave. Everyone who is either rich or calm is both creative and not happy. If someone is both rich and not quiet then john is both not old and not kind. If someone is not quiet then someone is either creative or brave. Everyone who is either humble or not rich is rich or not funny and vice versa. Everyone who is strong is strong or funny and vice versa. Everyone who is either creative or wise is strong and vice versa. Everyone who is not kind or kind is happy or rich. If mary is either happy or not happy then someone is not brave or humble. Everyone who is not kind is not old. If susan is either curious or not happy then someone is both not curious and not strong. Everyone who is both quiet and not patient is strong and vice versa. If someone is not brave then someone is not wise or humble and vice versa. If someone is creative or not rich then mary is either old or calm and vice versa. If susan is both not old and not quiet then someone is both kind and not strong and vice versa. If someone is either not brave or not kind then john is either humble or curious and vice versa. Someone is funny. Someone is not happy. Someone is not curious or kind. Paul is both curious and old. Someone is either tall or not happy. Someone is not old. Someone is not quiet. Someone is not calm. | Paul is not curious. | contradiction | (![X]:((~curious(X)&~kind(X))=>(~calm(X)|~brave(X))))&
(![X]:((rich(X)<~>calm(X))=>(creative(X)&~happy(X))))&
((?[X]:((rich(X)&~quiet(X))))=>((~old(john)&~kind(john))))&
((?[X]:(~quiet(X)))=>(?[X]:((creative(X)<~>brave(X)))))&
(![X]:((humble(X)<~>~rich(X))<=>(rich(X)|~funny(X))))&
(![X]:(strong(X)<=>(strong(X)|funny(X))))&
(![X]:((creative(X)<~>wise(X))<=>strong(X)))&
(![X]:((~kind(X)|kind(X))=>(happy(X)|rich(X))))&
(((happy(mary)<~>~happy(mary)))=>(?[X]:((~brave(X)|humble(X)))))&
(![X]:(~kind(X)=>~old(X)))&
(((curious(susan)<~>~happy(susan)))=>(?[X]:((~curious(X)&~strong(X)))))&
(![X]:((quiet(X)&~patient(X))<=>strong(X)))&
((?[X]:(~brave(X)))<=>(?[X]:((~wise(X)|humble(X)))))&
((?[X]:((creative(X)|~rich(X))))<=>((old(mary)<~>calm(mary))))&
(((~old(susan)&~quiet(susan)))<=>(?[X]:((kind(X)&~strong(X)))))&
((?[X]:((~brave(X)<~>~kind(X))))<=>((humble(john)<~>curious(john))))&
(?[X]:(funny(X)))&
(?[X]:(~happy(X)))&
(?[X]:((~curious(X)|kind(X))))&
((curious(paul)&old(paul)))&
(?[X]:((tall(X)<~>~happy(X))))&
(?[X]:(~old(X)))&
(?[X]:(~quiet(X)))&
(?[X]:(~calm(X))) | ~curious(paul) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3397917576008024368792054
% SZS output start Proof for 3397917576008024368792054
20. old(paul) & curious(paul) [input p19]
25. ~curious(paul) [input hypothesis]
147. curious(paul) [cnf transformation 20]
154. ~curious(paul) [cnf transformation 25]
345. $false [subsumption resolution 154,147]
% SZS output end Proof for 3397917576008024368792054
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either not humble or generous then someone is both patient and tall. If lucy is creative then someone is either not patient or creative and vice versa. Everyone who is not brave is not calm. If susan is not quiet then alice is not tall or quiet and vice versa. If susan is generous or patient then mary is both wise and old. If someone is not curious then alice is creative or calm. Everyone who is not patient or not brave is not curious and vice versa. Everyone who is either not tall or happy is both not creative and not funny. If fred is not kind or not old then someone is happy and vice versa. Everyone who is either not patient or not creative is not wise and vice versa. If someone is not patient or wise then alice is both brave and not patient. Everyone who is either humble or not quiet is both quiet and not brave and vice versa. If paul is both old and not happy then john is generous or strong and vice versa. If someone is both not curious and not rich then someone is not curious. If someone is not rich or not curious then paul is both quiet and brave and vice versa. John is both generous and not calm. Alice is humble or old. Someone is both humble and rich. John is both quiet and wise. Someone is either brave or not happy. Someone is both curious and patient. | Paul is humble. | contradiction | (((~humble(paul)<~>generous(paul)))=>(?[X]:((patient(X)&tall(X)))))&
((creative(lucy))<=>(?[X]:((~patient(X)<~>creative(X)))))&
(![X]:(~brave(X)=>~calm(X)))&
((~quiet(susan))<=>((~tall(alice)|quiet(alice))))&
(((generous(susan)|patient(susan)))=>((wise(mary)&old(mary))))&
((?[X]:(~curious(X)))=>((creative(alice)|calm(alice))))&
(![X]:((~patient(X)|~brave(X))<=>~curious(X)))&
(![X]:((~tall(X)<~>happy(X))=>(~creative(X)&~funny(X))))&
(((~kind(fred)|~old(fred)))<=>(?[X]:(happy(X))))&
(![X]:((~patient(X)<~>~creative(X))<=>~wise(X)))&
((?[X]:((~patient(X)|wise(X))))=>((brave(alice)&~patient(alice))))&
(![X]:((humble(X)<~>~quiet(X))<=>(quiet(X)&~brave(X))))&
(((old(paul)&~happy(paul)))<=>((generous(john)|strong(john))))&
((?[X]:((~curious(X)&~rich(X))))=>(?[X]:(~curious(X))))&
((?[X]:((~rich(X)|~curious(X))))<=>((quiet(paul)&brave(paul))))&
((generous(john)&~calm(john)))&
((humble(alice)|old(alice)))&
(?[X]:((humble(X)&rich(X))))&
((quiet(john)&wise(john)))&
(?[X]:((brave(X)<~>~happy(X))))&
(?[X]:((curious(X)&patient(X)))) | humble(paul) | [
"p6",
"p10",
"p11",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5221052658941554766440678
% SZS output start Proof for 5221052658941554766440678
7. ! [X0] : ((~brave(X0) | ~patient(X0)) <=> ~curious(X0)) [input p6]
11. ? [X0] : (wise(X0) | ~patient(X0)) => (~patient(alice) & brave(alice)) [input p10]
12. ! [X0] : ((humble(X0) <~> ~quiet(X0)) <=> (~brave(X0) & quiet(X0))) [input p11]
15. ? [X0] : (~curious(X0) | ~rich(X0)) <=> (brave(paul) & quiet(paul)) [input p14]
19. wise(john) & quiet(john) [input p18]
22. humble(paul) [input hypothesis]
31. (~patient(alice) & brave(alice)) | ! [X0] : (~wise(X0) & patient(X0)) [ennf transformation 11]
42. ! [X0] : (((~brave(X0) | ~patient(X0)) | curious(X0)) & (~curious(X0) | (brave(X0) & patient(X0)))) [nnf transformation 7]
43. ! [X0] : ((~brave(X0) | ~patient(X0) | curious(X0)) & (~curious(X0) | (brave(X0) & patient(X0)))) [flattening 42]
51. ! [X0] : ((((quiet(X0) | ~humble(X0)) & (~quiet(X0) | humble(X0))) | (brave(X0) | ~quiet(X0))) & ((~brave(X0) & quiet(X0)) | ((humble(X0) | quiet(X0)) & (~quiet(X0) | ~humble(X0))))) [nnf transformation 12]
52. ! [X0] : ((((quiet(X0) | ~humble(X0)) & (~quiet(X0) | humble(X0))) | brave(X0) | ~quiet(X0)) & ((~brave(X0) & quiet(X0)) | ((humble(X0) | quiet(X0)) & (~quiet(X0) | ~humble(X0))))) [flattening 51]
58. (? [X0] : (~curious(X0) | ~rich(X0)) | (~brave(paul) | ~quiet(paul))) & ((brave(paul) & quiet(paul)) | ! [X0] : (curious(X0) & rich(X0))) [nnf transformation 15]
59. (? [X0] : (~curious(X0) | ~rich(X0)) | ~brave(paul) | ~quiet(paul)) & ((brave(paul) & quiet(paul)) | ! [X0] : (curious(X0) & rich(X0))) [flattening 58]
60. (? [X0] : (~curious(X0) | ~rich(X0)) | ~brave(paul) | ~quiet(paul)) & ((brave(paul) & quiet(paul)) | ! [X1] : (curious(X1) & rich(X1))) [rectify 59]
61. ? [X0] : (~curious(X0) | ~rich(X0)) => (~curious(sK4) | ~rich(sK4)) [choice axiom]
62. ((~curious(sK4) | ~rich(sK4)) | ~brave(paul) | ~quiet(paul)) & ((brave(paul) & quiet(paul)) | ! [X1] : (curious(X1) & rich(X1))) [skolemisation 60,61]
87. ~curious(X0) | patient(X0) [cnf transformation 43]
102. ~patient(alice) | ~wise(X0) [cnf transformation 31]
105. ~quiet(X0) | ~brave(X0) | ~humble(X0) [cnf transformation 52]
116. quiet(paul) | curious(X1) [cnf transformation 62]
118. brave(paul) | curious(X1) [cnf transformation 62]
126. wise(john) [cnf transformation 19]
131. humble(paul) [cnf transformation 22]
139. 2 <=> humble(paul) [avatar definition]
140. humble(paul) <- (2) [avatar component clause 139]
212. 17 <=> ! [X0] : curious(X0) [avatar definition]
213. curious(X0) <- (17) [avatar component clause 212]
242. 24 <=> ! [X0] : ~wise(X0) [avatar definition]
243. ~wise(X0) <- (24) [avatar component clause 242]
245. 25 <=> patient(alice) [avatar definition]
247. ~patient(alice) <- (~25) [avatar component clause 245]
248. 24 | ~25 [avatar split clause 102,245,242]
250. 26 <=> ! [X0] : patient(X0) [avatar definition]
251. patient(X0) <- (26) [avatar component clause 250]
289. 34 <=> quiet(paul) [avatar definition]
290. quiet(paul) <- (34) [avatar component clause 289]
293. 35 <=> brave(paul) [avatar definition]
305. 17 | 35 [avatar split clause 118,293,212]
310. 17 | 34 [avatar split clause 116,289,212]
332. 2 [avatar split clause 131,139]
340. $false <- (24) [resolution 243,126]
341. ~24 [avatar contradiction clause 340]
396. ~brave(paul) | ~humble(paul) <- (34) [resolution 105,290]
410. ~brave(paul) <- (2, 34) [subsumption resolution 396,140]
411. ~35 | ~2 | ~34 [avatar split clause 410,289,139,293]
413. patient(X1) <- (17) [resolution 213,87]
414. 26 | ~17 [avatar split clause 413,212,250]
427. $false <- (~25, 26) [resolution 251,247]
428. 25 | ~26 [avatar contradiction clause 427]
430. $false [avatar sat refutation 248,305,310,332,341,411,414,428]
% SZS output end Proof for 5221052658941554766440678
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not curious or funny is not humble.
If fred is funny or brave then susan is not wise.
If susan is not old then alice is both not calm and patient and vice versa.
If someone is not calm then paul is both not happy and strong and vice versa.
Everyone who is both curious and not wise is strong and vice versa.
Everyone who is both old and not creative is calm or not calm.
Everyone who is old is either happy or not happy.
Everyone who is either not wise or not generous is both not patient and brave and vice versa.
Everyone who is happy or tall is either calm or quiet.
If lucy is not humble then someone is not calm or not happy and vice versa.
Everyone who is quiet or kind is both not calm and not quiet and vice versa.
Everyone who is either kind or calm is both calm and brave and vice versa.
If fred is either not strong or not tall then someone is patient or not curious.
If someone is either strong or brave then someone is both calm and not rich.
If paul is not rich or funny then someone is either not generous or not tall.
Everyone who is either curious or not humble is both not old and not kind and vice versa.
Alice is tall.
Someone is not funny.
Lucy is creative or kind.
Someone is either not curious or strong.
Someone is not tall.
John is generous or not generous.
Paul is not curious or funny.
Someone is generous. | Susan is not quiet. | entailment | (![X]:((~curious(X)|funny(X))=>~humble(X)))&
(((funny(fred)|brave(fred)))=>(~wise(susan)))&
((~old(susan))<=>((~calm(alice)&patient(alice))))&
((?[X]:(~calm(X)))<=>((~happy(paul)&strong(paul))))&
(![X]:((curious(X)&~wise(X))<=>strong(X)))&
(![X]:((old(X)&~creative(X))=>(calm(X)|~calm(X))))&
(![X]:(old(X)=>(happy(X)<~>~happy(X))))&
(![X]:((~wise(X)<~>~generous(X))<=>(~patient(X)&brave(X))))&
(![X]:((happy(X)|tall(X))=>(calm(X)<~>quiet(X))))&
((~humble(lucy))<=>(?[X]:((~calm(X)|~happy(X)))))&
(![X]:((quiet(X)|kind(X))<=>(~calm(X)&~quiet(X))))&
(![X]:((kind(X)<~>calm(X))<=>(calm(X)&brave(X))))&
(((~strong(fred)<~>~tall(fred)))=>(?[X]:((patient(X)|~curious(X)))))&
((?[X]:((strong(X)<~>brave(X))))=>(?[X]:((calm(X)&~rich(X)))))&
(((~rich(paul)|funny(paul)))=>(?[X]:((~generous(X)<~>~tall(X)))))&
(![X]:((curious(X)<~>~humble(X))<=>(~old(X)&~kind(X))))&
(tall(alice))&
(?[X]:(~funny(X)))&
((creative(lucy)|kind(lucy)))&
(?[X]:((~curious(X)<~>strong(X))))&
(?[X]:(~tall(X)))&
((generous(john)|~generous(john)))&
((~curious(paul)|funny(paul)))&
(?[X]:(generous(X))) | ~quiet(susan) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8671740163335435001834038
% SZS output start Proof for 8671740163335435001834038
11. ! [X0] : ((kind(X0) | quiet(X0)) <=> (~quiet(X0) & ~calm(X0))) [input p10]
25. quiet(susan) [input hypothesis]
53. ! [X0] : (((kind(X0) | quiet(X0)) | (quiet(X0) | calm(X0))) & ((~quiet(X0) & ~calm(X0)) | (~kind(X0) & ~quiet(X0)))) [nnf transformation 11]
54. ! [X0] : ((kind(X0) | quiet(X0) | quiet(X0) | calm(X0)) & ((~quiet(X0) & ~calm(X0)) | (~kind(X0) & ~quiet(X0)))) [flattening 53]
108. ~quiet(X0) | ~quiet(X0) [cnf transformation 54]
141. quiet(susan) [cnf transformation 25]
144. ~quiet(X0) [duplicate literal removal 108]
287. $false [subsumption resolution 141,144]
% SZS output end Proof for 8671740163335435001834038
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not wise and kind then mary is either tall or funny. Everyone who is both not patient and quiet is generous and vice versa. Everyone who is both rich and patient is either happy or rich and vice versa. If mary is patient or not tall then mary is not kind or not funny and vice versa. If someone is either humble or calm then someone is not kind. Everyone who is either funny or not funny is not kind and vice versa. If paul is either wise or strong then someone is either not kind or not strong and vice versa. Everyone who is not wise is not brave or funny and vice versa. If lucy is both generous and kind then susan is not patient. If someone is not funny then alice is either rich or not rich. Everyone who is either kind or humble is kind or brave and vice versa. Everyone who is patient is both not kind and not happy and vice versa. If someone is not patient then mary is both not happy and not old. If mary is either not quiet or not strong then john is not old or not funny and vice versa. Everyone who is quiet is wise. Everyone who is both patient and old is not generous. Someone is happy. Lucy is either not old or not happy. Someone is either not funny or strong. Someone is humble or not creative. Paul is either humble or not old. Alice is not wise or not funny. Someone is curious or funny. Someone is either generous or not strong. | John is not old. | neutral | ((?[X]:((~wise(X)&kind(X))))=>((tall(mary)<~>funny(mary))))&
(![X]:((~patient(X)&quiet(X))<=>generous(X)))&
(![X]:((rich(X)&patient(X))<=>(happy(X)<~>rich(X))))&
(((patient(mary)|~tall(mary)))<=>((~kind(mary)|~funny(mary))))&
((?[X]:((humble(X)<~>calm(X))))=>(?[X]:(~kind(X))))&
(![X]:((funny(X)<~>~funny(X))<=>~kind(X)))&
(((wise(paul)<~>strong(paul)))<=>(?[X]:((~kind(X)<~>~strong(X)))))&
(![X]:(~wise(X)<=>(~brave(X)|funny(X))))&
(((generous(lucy)&kind(lucy)))=>(~patient(susan)))&
((?[X]:(~funny(X)))=>((rich(alice)<~>~rich(alice))))&
(![X]:((kind(X)<~>humble(X))<=>(kind(X)|brave(X))))&
(![X]:(patient(X)<=>(~kind(X)&~happy(X))))&
((?[X]:(~patient(X)))=>((~happy(mary)&~old(mary))))&
(((~quiet(mary)<~>~strong(mary)))<=>((~old(john)|~funny(john))))&
(![X]:(quiet(X)=>wise(X)))&
(![X]:((patient(X)&old(X))=>~generous(X)))&
(?[X]:(happy(X)))&
((~old(lucy)<~>~happy(lucy)))&
(?[X]:((~funny(X)<~>strong(X))))&
(?[X]:((humble(X)|~creative(X))))&
((humble(paul)<~>~old(paul)))&
((~wise(alice)|~funny(alice)))&
(?[X]:((curious(X)|funny(X))))&
(?[X]:((generous(X)<~>~strong(X)))) | ~old(john) | [] | null | 0 |
Everyone who is either not happy or not creative is strong or brave.
If someone is not brave or funny then someone is both not happy and not humble and vice versa.
Everyone who is not old or kind is both not calm and not generous and vice versa.
Everyone who is either not old or not creative is both quiet and funny and vice versa.
If mary is calm then john is not quiet or creative.
If mary is not wise then someone is not curious.
Everyone who is either kind or not tall is not wise or not calm and vice versa.
Everyone who is both generous and not brave is not tall or not creative and vice versa.
Everyone who is not happy is either patient or generous.
Everyone who is both not rich and not tall is either old or happy and vice versa.
Everyone who is not humble or not calm is quiet.
Everyone who is creative is quiet.
If john is not old then someone is both not funny and kind and vice versa.
If someone is not curious then susan is either patient or not humble.
Everyone who is both not patient and not happy is both not tall and not generous.
If john is not strong or rich then someone is either not strong or old.
Someone is not generous.
John is both patient and not brave.
Someone is either quiet or funny.
Lucy is either not funny or quiet.
Lucy is creative.
Someone is both humble and not tall.
Someone is either curious or brave.
Susan is both tall and funny. | John is quiet. | entailment | (![X]:((~happy(X)<~>~creative(X))=>(strong(X)|brave(X))))&
((?[X]:((~brave(X)|funny(X))))<=>(?[X]:((~happy(X)&~humble(X)))))&
(![X]:((~old(X)|kind(X))<=>(~calm(X)&~generous(X))))&
(![X]:((~old(X)<~>~creative(X))<=>(quiet(X)&funny(X))))&
((calm(mary))=>((~quiet(john)|creative(john))))&
((~wise(mary))=>(?[X]:(~curious(X))))&
(![X]:((kind(X)<~>~tall(X))<=>(~wise(X)|~calm(X))))&
(![X]:((generous(X)&~brave(X))<=>(~tall(X)|~creative(X))))&
(![X]:(~happy(X)=>(patient(X)<~>generous(X))))&
(![X]:((~rich(X)&~tall(X))<=>(old(X)<~>happy(X))))&
(![X]:((~humble(X)|~calm(X))=>quiet(X)))&
(![X]:(creative(X)=>quiet(X)))&
((~old(john))<=>(?[X]:((~funny(X)&kind(X)))))&
((?[X]:(~curious(X)))=>((patient(susan)<~>~humble(susan))))&
(![X]:((~patient(X)&~happy(X))=>(~tall(X)&~generous(X))))&
(((~strong(john)|rich(john)))=>(?[X]:((~strong(X)<~>old(X)))))&
(?[X]:(~generous(X)))&
((patient(john)&~brave(john)))&
(?[X]:((quiet(X)<~>funny(X))))&
((~funny(lucy)<~>quiet(lucy)))&
(creative(lucy))&
(?[X]:((humble(X)&~tall(X))))&
(?[X]:((curious(X)<~>brave(X))))&
((tall(susan)&funny(susan))) | quiet(john) | [
"p2",
"p3",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 772524121057171947930231
% SZS output start Proof for 772524121057171947930231
3. ! [X0] : ((kind(X0) | ~old(X0)) <=> (~generous(X0) & ~calm(X0))) [input p2]
4. ! [X0] : ((~old(X0) <~> ~creative(X0)) <=> (funny(X0) & quiet(X0))) [input p3]
11. ! [X0] : ((~calm(X0) | ~humble(X0)) => quiet(X0)) [input p10]
12. ! [X0] : (creative(X0) => quiet(X0)) [input p11]
25. ~quiet(john) [input hypothesis]
33. ! [X0] : (quiet(X0) | (calm(X0) & humble(X0))) [ennf transformation 11]
34. ! [X0] : (quiet(X0) | ~creative(X0)) [ennf transformation 12]
45. ! [X0] : (((kind(X0) | ~old(X0)) | (generous(X0) | calm(X0))) & ((~generous(X0) & ~calm(X0)) | (~kind(X0) & old(X0)))) [nnf transformation 3]
46. ! [X0] : ((kind(X0) | ~old(X0) | generous(X0) | calm(X0)) & ((~generous(X0) & ~calm(X0)) | (~kind(X0) & old(X0)))) [flattening 45]
47. ! [X0] : ((((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | (~funny(X0) | ~quiet(X0))) & ((funny(X0) & quiet(X0)) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0))))) [nnf transformation 4]
48. ! [X0] : ((((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | ~funny(X0) | ~quiet(X0)) & ((funny(X0) & quiet(X0)) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0))))) [flattening 47]
84. ~calm(X0) | old(X0) [cnf transformation 46]
90. ~old(X0) | quiet(X0) | creative(X0) [cnf transformation 48]
117. quiet(X0) | calm(X0) [cnf transformation 33]
118. ~creative(X0) | quiet(X0) [cnf transformation 34]
144. ~quiet(john) [cnf transformation 25]
180. 9 <=> quiet(john) [avatar definition]
182. ~quiet(john) <- (~9) [avatar component clause 180]
184. 10 <=> creative(john) [avatar definition]
186. creative(john) <- (10) [avatar component clause 184]
203. 14 <=> old(john) [avatar definition]
204. old(john) <- (14) [avatar component clause 203]
281. ~9 [avatar split clause 144,180]
290. calm(john) <- (~9) [resolution 117,182]
298. old(john) <- (~9) [resolution 290,84]
302. quiet(john) | creative(john) <- (14) [resolution 90,204]
304. creative(john) <- (~9, 14) [subsumption resolution 302,182]
305. 10 | 9 | ~14 [avatar split clause 304,203,180,184]
308. quiet(john) <- (10) [resolution 186,118]
309. $false <- (~9, 10) [subsumption resolution 308,182]
310. 9 | ~10 [avatar contradiction clause 309]
311. 14 | 9 [avatar split clause 298,180,203]
312. $false [avatar sat refutation 281,305,310,311]
% SZS output end Proof for 772524121057171947930231
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind is either not strong or brave.
Everyone who is calm is both not brave and curious.
Everyone who is strong is not curious or quiet.
If someone is quiet then susan is both rich and creative and vice versa.
If lucy is either funny or happy then someone is not strong and vice versa.
Everyone who is not rich is both happy and kind.
If fred is either not patient or not calm then lucy is not tall or tall.
If someone is either not kind or not generous then someone is either calm or not humble and vice versa.
Everyone who is not strong is either tall or happy.
Everyone who is brave or old is either not calm or not generous and vice versa.
If someone is either not tall or not patient then john is funny and vice versa.
Everyone who is both not funny and quiet is both quiet and not brave.
Everyone who is tall or strong is not strong.
Everyone who is calm or not tall is not patient or not generous and vice versa.
Everyone who is tall is not kind or humble.
If someone is both patient and kind then paul is either not happy or not rich.
Mary is generous or not brave.
Fred is not funny or wise.
Someone is both not rich and not old.
John is both old and not tall.
Someone is not rich or generous.
Someone is curious.
Paul is strong or not quiet.
Someone is either not tall or not wise. | John is tall. | contradiction | (![X]:(~kind(X)=>(~strong(X)<~>brave(X))))&
(![X]:(calm(X)=>(~brave(X)&curious(X))))&
(![X]:(strong(X)=>(~curious(X)|quiet(X))))&
((?[X]:(quiet(X)))<=>((rich(susan)&creative(susan))))&
(((funny(lucy)<~>happy(lucy)))<=>(?[X]:(~strong(X))))&
(![X]:(~rich(X)=>(happy(X)&kind(X))))&
(((~patient(fred)<~>~calm(fred)))=>((~tall(lucy)|tall(lucy))))&
((?[X]:((~kind(X)<~>~generous(X))))<=>(?[X]:((calm(X)<~>~humble(X)))))&
(![X]:(~strong(X)=>(tall(X)<~>happy(X))))&
(![X]:((brave(X)|old(X))<=>(~calm(X)<~>~generous(X))))&
((?[X]:((~tall(X)<~>~patient(X))))<=>(funny(john)))&
(![X]:((~funny(X)&quiet(X))=>(quiet(X)&~brave(X))))&
(![X]:((tall(X)|strong(X))=>~strong(X)))&
(![X]:((calm(X)|~tall(X))<=>(~patient(X)|~generous(X))))&
(![X]:(tall(X)=>(~kind(X)|humble(X))))&
((?[X]:((patient(X)&kind(X))))=>((~happy(paul)<~>~rich(paul))))&
((generous(mary)|~brave(mary)))&
((~funny(fred)|wise(fred)))&
(?[X]:((~rich(X)&~old(X))))&
((old(john)&~tall(john)))&
(?[X]:((~rich(X)|generous(X))))&
(?[X]:(curious(X)))&
((strong(paul)|~quiet(paul)))&
(?[X]:((~tall(X)<~>~wise(X)))) | tall(john) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1654869194552023025231226
% SZS output start Proof for 1654869194552023025231226
20. ~tall(john) & old(john) [input p19]
25. tall(john) [input hypothesis]
128. ~tall(john) [cnf transformation 20]
134. tall(john) [cnf transformation 25]
274. $false [subsumption resolution 134,128]
% SZS output end Proof for 1654869194552023025231226
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is tall and vice versa.
Everyone who is either quiet or generous is both not rich and not funny.
Everyone who is either not strong or patient is humble or wise and vice versa.
If lucy is both quiet and not quiet then susan is curious and vice versa.
Everyone who is either not quiet or not tall is either not brave or not creative and vice versa.
If someone is either kind or not brave then someone is patient or kind and vice versa.
If someone is both quiet and not tall then alice is both tall and happy and vice versa.
If susan is either not patient or brave then john is old or strong and vice versa.
Everyone who is not old or not strong is both funny and kind and vice versa.
Everyone who is either not curious or happy is not calm.
Everyone who is not generous is brave or kind and vice versa.
Everyone who is strong or calm is quiet and vice versa.
Everyone who is not generous is humble.
Everyone who is both not rich and generous is not kind and vice versa.
Everyone who is not calm is not rich and vice versa.
Everyone who is either patient or not quiet is not curious or wise and vice versa.
Someone is either tall or not brave.
Paul is not brave or not happy.
Susan is not quiet or not funny.
Someone is either not calm or curious.
Someone is either not kind or strong.
Alice is both not generous and not tall.
Someone is not quiet or not tall. | Lucy is not calm. | entailment | (![X]:(old(X)<=>tall(X)))&
(![X]:((quiet(X)<~>generous(X))=>(~rich(X)&~funny(X))))&
(![X]:((~strong(X)<~>patient(X))<=>(humble(X)|wise(X))))&
(((quiet(lucy)&~quiet(lucy)))<=>(curious(susan)))&
(![X]:((~quiet(X)<~>~tall(X))<=>(~brave(X)<~>~creative(X))))&
((?[X]:((kind(X)<~>~brave(X))))<=>(?[X]:((patient(X)|kind(X)))))&
((?[X]:((quiet(X)&~tall(X))))<=>((tall(alice)&happy(alice))))&
(((~patient(susan)<~>brave(susan)))<=>((old(john)|strong(john))))&
(![X]:((~old(X)|~strong(X))<=>(funny(X)&kind(X))))&
(![X]:((~curious(X)<~>happy(X))=>~calm(X)))&
(![X]:(~generous(X)<=>(brave(X)|kind(X))))&
(![X]:((strong(X)|calm(X))<=>quiet(X)))&
(![X]:(~generous(X)=>humble(X)))&
(![X]:((~rich(X)&generous(X))<=>~kind(X)))&
(![X]:(~calm(X)<=>~rich(X)))&
(![X]:((patient(X)<~>~quiet(X))<=>(~curious(X)|wise(X))))&
(?[X]:((tall(X)<~>~brave(X))))&
((~brave(paul)|~happy(paul)))&
((~quiet(susan)|~funny(susan)))&
(?[X]:((~calm(X)<~>curious(X))))&
(?[X]:((~kind(X)<~>strong(X))))&
((~generous(alice)&~tall(alice)))&
(?[X]:((~quiet(X)|~tall(X)))) | ~calm(lucy) | [
"p1",
"p10",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8784771370070855082120874
% SZS output start Proof for 8784771370070855082120874
2. ! [X0] : ((quiet(X0) <~> generous(X0)) => (~funny(X0) & ~rich(X0))) [input p1]
11. ! [X0] : (~generous(X0) <=> (kind(X0) | brave(X0))) [input p10]
12. ! [X0] : ((calm(X0) | strong(X0)) <=> quiet(X0)) [input p11]
14. ! [X0] : ((generous(X0) & ~rich(X0)) <=> ~kind(X0)) [input p13]
15. ! [X0] : (~calm(X0) <=> ~rich(X0)) [input p14]
24. calm(lucy) [input hypothesis]
26. ! [X0] : ((~funny(X0) & ~rich(X0)) | (quiet(X0) <=> generous(X0))) [ennf transformation 2]
30. ! [X0] : ((~funny(X0) & ~rich(X0)) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0)))) [nnf transformation 26]
51. ! [X0] : ((~generous(X0) | (~kind(X0) & ~brave(X0))) & ((kind(X0) | brave(X0)) | generous(X0))) [nnf transformation 11]
52. ! [X0] : ((~generous(X0) | (~kind(X0) & ~brave(X0))) & (kind(X0) | brave(X0) | generous(X0))) [flattening 51]
53. ! [X0] : (((calm(X0) | strong(X0)) | ~quiet(X0)) & (quiet(X0) | (~calm(X0) & ~strong(X0)))) [nnf transformation 12]
54. ! [X0] : ((calm(X0) | strong(X0) | ~quiet(X0)) & (quiet(X0) | (~calm(X0) & ~strong(X0)))) [flattening 53]
55. ! [X0] : (((generous(X0) & ~rich(X0)) | kind(X0)) & (~kind(X0) | (~generous(X0) | rich(X0)))) [nnf transformation 14]
56. ! [X0] : (((generous(X0) & ~rich(X0)) | kind(X0)) & (~kind(X0) | ~generous(X0) | rich(X0))) [flattening 55]
57. ! [X0] : ((~calm(X0) | rich(X0)) & (~rich(X0) | calm(X0))) [nnf transformation 15]
73. ~rich(X0) | generous(X0) | ~quiet(X0) [cnf transformation 30]
119. ~kind(X0) | ~generous(X0) [cnf transformation 52]
121. ~calm(X0) | quiet(X0) [cnf transformation 54]
125. ~rich(X0) | kind(X0) [cnf transformation 56]
128. ~calm(X0) | rich(X0) [cnf transformation 57]
146. calm(lucy) [cnf transformation 24]
152. 2 <=> quiet(lucy) [avatar definition]
153. quiet(lucy) <- (2) [avatar component clause 152]
297. quiet(lucy) [resolution 121,146]
298. 2 [avatar split clause 297,152]
301. rich(lucy) [resolution 128,146]
307. kind(lucy) [resolution 301,125]
308. generous(lucy) | ~quiet(lucy) [resolution 73,301]
309. generous(lucy) <- (2) [subsumption resolution 308,153]
332. ~generous(lucy) [resolution 307,119]
333. $false <- (2) [subsumption resolution 332,309]
334. ~2 [avatar contradiction clause 333]
335. $false [avatar sat refutation 298,334]
% SZS output end Proof for 8784771370070855082120874
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is not happy or not curious.
Everyone who is both brave and not old is either not kind or not generous.
If someone is either generous or not quiet then lucy is not calm and vice versa.
If john is calm then someone is not tall and vice versa.
If alice is both not happy and not patient then someone is not brave.
Everyone who is either wise or creative is either not calm or patient.
If someone is funny then someone is strong or kind and vice versa.
Everyone who is either quiet or calm is either rich or not generous.
If someone is not tall then john is brave.
If someone is wise then someone is funny.
Everyone who is both curious and not tall is rich and vice versa.
If someone is not old or generous then someone is either patient or old and vice versa.
If fred is both not brave and happy then someone is brave and vice versa.
Everyone who is both not wise and strong is wise or rich and vice versa.
Everyone who is either curious or not rich is not happy.
Everyone who is not kind is both rich and not brave.
John is generous or not brave.
Someone is either curious or not strong.
Someone is kind.
Susan is both not funny and curious.
Someone is not strong.
John is both calm and not humble.
Someone is either not calm or not tall.
Someone is not brave or wise. | Fred is happy. | entailment | (![X]:(rich(X)=>(~happy(X)|~curious(X))))&
(![X]:((brave(X)&~old(X))=>(~kind(X)<~>~generous(X))))&
((?[X]:((generous(X)<~>~quiet(X))))<=>(~calm(lucy)))&
((calm(john))<=>(?[X]:(~tall(X))))&
(((~happy(alice)&~patient(alice)))=>(?[X]:(~brave(X))))&
(![X]:((wise(X)<~>creative(X))=>(~calm(X)<~>patient(X))))&
((?[X]:(funny(X)))<=>(?[X]:((strong(X)|kind(X)))))&
(![X]:((quiet(X)<~>calm(X))=>(rich(X)<~>~generous(X))))&
((?[X]:(~tall(X)))=>(brave(john)))&
((?[X]:(wise(X)))=>(?[X]:(funny(X))))&
(![X]:((curious(X)&~tall(X))<=>rich(X)))&
((?[X]:((~old(X)|generous(X))))<=>(?[X]:((patient(X)<~>old(X)))))&
(((~brave(fred)&happy(fred)))<=>(?[X]:(brave(X))))&
(![X]:((~wise(X)&strong(X))<=>(wise(X)|rich(X))))&
(![X]:((curious(X)<~>~rich(X))=>~happy(X)))&
(![X]:(~kind(X)=>(rich(X)&~brave(X))))&
((generous(john)|~brave(john)))&
(?[X]:((curious(X)<~>~strong(X))))&
(?[X]:(kind(X)))&
((~funny(susan)&curious(susan)))&
(?[X]:(~strong(X)))&
((calm(john)&~humble(john)))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:((~brave(X)|wise(X)))) | happy(fred) | [
"p3",
"p8",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 9076593422682610233673203
% SZS output start Proof for 9076593422682610233673203
4. calm(john) <=> ? [X0] : ~tall(X0) [input p3]
9. ? [X0] : ~tall(X0) => brave(john) [input p8]
13. (happy(fred) & ~brave(fred)) <=> ? [X0] : brave(X0) [input p12]
22. ~humble(john) & calm(john) [input p21]
25. ~happy(fred) [input hypothesis]
29. calm(john) [pure predicate removal 22]
38. brave(john) | ! [X0] : tall(X0) [ennf transformation 9]
47. (calm(john) | ! [X0] : tall(X0)) & (? [X0] : ~tall(X0) | ~calm(john)) [nnf transformation 4]
48. (calm(john) | ! [X0] : tall(X0)) & (? [X1] : ~tall(X1) | ~calm(john)) [rectify 47]
49. ? [X1] : ~tall(X1) => ~tall(sK1) [choice axiom]
50. (calm(john) | ! [X0] : tall(X0)) & (~tall(sK1) | ~calm(john)) [skolemisation 48,49]
70. ((happy(fred) & ~brave(fred)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | (~happy(fred) | brave(fred))) [nnf transformation 13]
71. ((happy(fred) & ~brave(fred)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | ~happy(fred) | brave(fred)) [flattening 70]
72. ((happy(fred) & ~brave(fred)) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | ~happy(fred) | brave(fred)) [rectify 71]
73. ? [X1] : brave(X1) => brave(sK8) [choice axiom]
74. ((happy(fred) & ~brave(fred)) | ! [X0] : ~brave(X0)) & (brave(sK8) | ~happy(fred) | brave(fred)) [skolemisation 72,73]
97. ~tall(sK1) | ~calm(john) [cnf transformation 50]
111. brave(john) | tall(X0) [cnf transformation 38]
124. happy(fred) | ~brave(X0) [cnf transformation 74]
141. calm(john) [cnf transformation 29]
145. ~happy(fred) [cnf transformation 25]
171. 6 <=> ! [X0] : tall(X0) [avatar definition]
172. tall(X0) <- (6) [avatar component clause 171]
174. 7 <=> calm(john) [avatar definition]
179. 8 <=> tall(sK1) [avatar definition]
181. ~tall(sK1) <- (~8) [avatar component clause 179]
182. ~7 | ~8 [avatar split clause 97,179,174]
221. 18 <=> brave(john) [avatar definition]
223. brave(john) <- (18) [avatar component clause 221]
224. 6 | 18 [avatar split clause 111,221,171]
268. 29 <=> ! [X0] : ~brave(X0) [avatar definition]
269. ~brave(X0) <- (29) [avatar component clause 268]
271. 30 <=> happy(fred) [avatar definition]
274. 29 | 30 [avatar split clause 124,271,268]
302. 7 [avatar split clause 141,174]
322. ~30 [avatar split clause 145,271]
325. $false <- (6, ~8) [resolution 181,172]
326. ~6 | 8 [avatar contradiction clause 325]
327. $false <- (18, 29) [subsumption resolution 223,269]
328. ~18 | ~29 [avatar contradiction clause 327]
329. $false [avatar sat refutation 182,224,274,302,322,326,328]
% SZS output end Proof for 9076593422682610233673203
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or not brave is not patient and vice versa. Everyone who is either not generous or not brave is both not happy and not funny and vice versa. Everyone who is curious is either not kind or kind and vice versa. Everyone who is kind or not rich is not wise or not strong. Everyone who is not old is kind or not funny and vice versa. If someone is either brave or patient then lucy is either not strong or generous and vice versa. Everyone who is brave or calm is kind or not humble and vice versa. If mary is not kind then someone is not patient or strong and vice versa. If someone is both humble and curious then alice is happy or not creative. Everyone who is strong or old is not rich or calm and vice versa. Everyone who is either old or not tall is either quiet or rich and vice versa. If mary is both old and not curious then lucy is not curious or wise. If someone is not old then someone is either patient or not calm. Everyone who is funny is either not curious or humble and vice versa. Everyone who is not old is rich. Everyone who is either not tall or tall is not strong. John is both humble and happy. Someone is either not funny or happy. Someone is either not rich or not strong. Someone is both not kind and not humble. Fred is generous. Fred is not quiet. Someone is not wise. | Fred is not rich. | contradiction | (![X]:((~calm(X)<~>~brave(X))<=>~patient(X)))&
(![X]:((~generous(X)<~>~brave(X))<=>(~happy(X)&~funny(X))))&
(![X]:(curious(X)<=>(~kind(X)<~>kind(X))))&
(![X]:((kind(X)|~rich(X))=>(~wise(X)|~strong(X))))&
(![X]:(~old(X)<=>(kind(X)|~funny(X))))&
((?[X]:((brave(X)<~>patient(X))))<=>((~strong(lucy)<~>generous(lucy))))&
(![X]:((brave(X)|calm(X))<=>(kind(X)|~humble(X))))&
((~kind(mary))<=>(?[X]:((~patient(X)|strong(X)))))&
((?[X]:((humble(X)&curious(X))))=>((happy(alice)|~creative(alice))))&
(![X]:((strong(X)|old(X))<=>(~rich(X)|calm(X))))&
(![X]:((old(X)<~>~tall(X))<=>(quiet(X)<~>rich(X))))&
(((old(mary)&~curious(mary)))=>((~curious(lucy)|wise(lucy))))&
((?[X]:(~old(X)))=>(?[X]:((patient(X)<~>~calm(X)))))&
(![X]:(funny(X)<=>(~curious(X)<~>humble(X))))&
(![X]:(~old(X)=>rich(X)))&
(![X]:((~tall(X)<~>tall(X))=>~strong(X)))&
((humble(john)&happy(john)))&
(?[X]:((~funny(X)<~>happy(X))))&
(?[X]:((~rich(X)<~>~strong(X))))&
(?[X]:((~kind(X)&~humble(X))))&
(generous(fred))&
(~quiet(fred))&
(?[X]:(~wise(X))) | ~rich(fred) | [
"p1",
"p2",
"p4",
"p6",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3485951223153087584748771
% SZS output start Proof for 3485951223153087584748771
2. ! [X0] : ((~generous(X0) <~> ~brave(X0)) <=> (~funny(X0) & ~happy(X0))) [input p1]
3. ! [X0] : (curious(X0) <=> (~kind(X0) <~> kind(X0))) [input p2]
5. ! [X0] : (~old(X0) <=> (~funny(X0) | kind(X0))) [input p4]
7. ! [X0] : ((calm(X0) | brave(X0)) <=> (~humble(X0) | kind(X0))) [input p6]
14. ! [X0] : (funny(X0) <=> (~curious(X0) <~> humble(X0))) [input p13]
15. ! [X0] : (~old(X0) => rich(X0)) [input p14]
21. generous(fred) [input p20]
24. ~rich(fred) [input hypothesis]
32. ! [X0] : (rich(X0) | old(X0)) [ennf transformation 15]
35. ! [X0] : ((((brave(X0) | generous(X0)) & (~brave(X0) | ~generous(X0))) | (funny(X0) | happy(X0))) & ((~funny(X0) & ~happy(X0)) | ((~generous(X0) | brave(X0)) & (~brave(X0) | generous(X0))))) [nnf transformation 2]
36. ! [X0] : ((((brave(X0) | generous(X0)) & (~brave(X0) | ~generous(X0))) | funny(X0) | happy(X0)) & ((~funny(X0) & ~happy(X0)) | ((~generous(X0) | brave(X0)) & (~brave(X0) | generous(X0))))) [flattening 35]
37. ! [X0] : ((curious(X0) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ~curious(X0))) [nnf transformation 3]
38. ! [X0] : ((~old(X0) | (funny(X0) & ~kind(X0))) & ((~funny(X0) | kind(X0)) | old(X0))) [nnf transformation 5]
39. ! [X0] : ((~old(X0) | (funny(X0) & ~kind(X0))) & (~funny(X0) | kind(X0) | old(X0))) [flattening 38]
44. ! [X0] : (((calm(X0) | brave(X0)) | (humble(X0) & ~kind(X0))) & ((~humble(X0) | kind(X0)) | (~calm(X0) & ~brave(X0)))) [nnf transformation 7]
45. ! [X0] : ((calm(X0) | brave(X0) | (humble(X0) & ~kind(X0))) & (~humble(X0) | kind(X0) | (~calm(X0) & ~brave(X0)))) [flattening 44]
57. ! [X0] : ((funny(X0) | ((~curious(X0) | ~humble(X0)) & (humble(X0) | curious(X0)))) & (((~humble(X0) | curious(X0)) & (humble(X0) | ~curious(X0))) | ~funny(X0))) [nnf transformation 14]
76. ~funny(X0) | ~generous(X0) | brave(X0) [cnf transformation 36]
81. curious(X0) | kind(X0) | kind(X0) [cnf transformation 37]
82. curious(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 37]
86. ~old(X0) | ~kind(X0) [cnf transformation 39]
87. ~old(X0) | funny(X0) [cnf transformation 39]
96. ~humble(X0) | kind(X0) | ~brave(X0) [cnf transformation 45]
118. humble(X0) | ~curious(X0) | ~funny(X0) [cnf transformation 57]
122. old(X0) | rich(X0) [cnf transformation 32]
133. generous(fred) [cnf transformation 21]
136. ~rich(fred) [cnf transformation 24]
139. curious(X0) | kind(X0) [duplicate literal removal 81]
140. ~kind(X0) | curious(X0) [duplicate literal removal 82]
141. curious(X0) [subsumption resolution 139,140]
207. ~funny(X0) | humble(X0) [subsumption resolution 118,141]
230. rich(X0) | funny(X0) [resolution 122,87]
234. funny(fred) [resolution 230,136]
235. humble(fred) [resolution 234,207]
294. ~generous(fred) | brave(fred) [resolution 76,234]
295. brave(fred) [subsumption resolution 294,133]
310. 25 <=> old(fred) [avatar definition]
311. ~old(fred) <- (~25) [avatar component clause 310]
312. old(fred) <- (25) [avatar component clause 310]
314. 26 <=> kind(fred) [avatar definition]
316. kind(fred) <- (26) [avatar component clause 314]
320. kind(fred) | ~brave(fred) [resolution 96,235]
321. kind(fred) [subsumption resolution 320,295]
322. 26 [avatar split clause 321,314]
542. ~kind(fred) <- (25) [resolution 312,86]
543. $false <- (25, 26) [subsumption resolution 542,316]
544. ~25 | ~26 [avatar contradiction clause 543]
549. rich(fred) <- (~25) [resolution 311,122]
553. $false <- (~25) [subsumption resolution 549,136]
554. 25 [avatar contradiction clause 553]
555. $false [avatar sat refutation 322,544,554]
% SZS output end Proof for 3485951223153087584748771
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both calm and not tall then fred is quiet.
If someone is either not kind or not curious then john is both old and not tall and vice versa.
Everyone who is both not funny and not creative is not kind.
Everyone who is either not old or not brave is either happy or not kind.
If someone is either not creative or happy then someone is both not wise and not quiet and vice versa.
Everyone who is calm or not brave is not calm and vice versa.
Everyone who is both not tall and generous is not wise and vice versa.
If someone is either rich or not patient then john is both kind and not generous.
Everyone who is both not brave and kind is either calm or happy and vice versa.
Everyone who is not calm is either calm or wise.
Everyone who is both not patient and not curious is humble and vice versa.
Everyone who is either generous or not creative is not happy or brave and vice versa.
If lucy is not quiet or not happy then mary is both quiet and calm.
If someone is not old then lucy is either rich or not quiet and vice versa.
If someone is not humble then paul is wise.
Someone is not humble.
Fred is either not kind or not funny.
Someone is not quiet or tall.
Paul is rich or happy.
Susan is wise or not old.
Susan is not calm or not wise.
Someone is either wise or not kind. | Alice is generous. | entailment | (((calm(alice)&~tall(alice)))=>(quiet(fred)))&
((?[X]:((~kind(X)<~>~curious(X))))<=>((old(john)&~tall(john))))&
(![X]:((~funny(X)&~creative(X))=>~kind(X)))&
(![X]:((~old(X)<~>~brave(X))=>(happy(X)<~>~kind(X))))&
((?[X]:((~creative(X)<~>happy(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
(![X]:((calm(X)|~brave(X))<=>~calm(X)))&
(![X]:((~tall(X)&generous(X))<=>~wise(X)))&
((?[X]:((rich(X)<~>~patient(X))))=>((kind(john)&~generous(john))))&
(![X]:((~brave(X)&kind(X))<=>(calm(X)<~>happy(X))))&
(![X]:(~calm(X)=>(calm(X)<~>wise(X))))&
(![X]:((~patient(X)&~curious(X))<=>humble(X)))&
(![X]:((generous(X)<~>~creative(X))<=>(~happy(X)|brave(X))))&
(((~quiet(lucy)|~happy(lucy)))=>((quiet(mary)&calm(mary))))&
((?[X]:(~old(X)))<=>((rich(lucy)<~>~quiet(lucy))))&
((?[X]:(~humble(X)))=>(wise(paul)))&
(?[X]:(~humble(X)))&
((~kind(fred)<~>~funny(fred)))&
(?[X]:((~quiet(X)|tall(X))))&
((rich(paul)|happy(paul)))&
((wise(susan)|~old(susan)))&
((~calm(susan)|~wise(susan)))&
(?[X]:((wise(X)<~>~kind(X)))) | generous(alice) | [
"p4",
"p5",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4580538519542123662782154
% SZS output start Proof for 4580538519542123662782154
5. ? [X0] : (~creative(X0) <~> happy(X0)) <=> ? [X0] : (~quiet(X0) & ~wise(X0)) [input p4]
6. ! [X0] : ((~brave(X0) | calm(X0)) <=> ~calm(X0)) [input p5]
10. ! [X0] : (~calm(X0) => (calm(X0) <~> wise(X0))) [input p9]
12. ! [X0] : ((generous(X0) <~> ~creative(X0)) <=> (brave(X0) | ~happy(X0))) [input p11]
23. ~generous(alice) [input hypothesis]
24. ? [X0] : (~creative(X0) <~> happy(X0)) <=> ? [X1] : (~quiet(X1) & ~wise(X1)) [rectify 5]
31. ! [X0] : ((calm(X0) <~> wise(X0)) | calm(X0)) [ennf transformation 10]
40. (? [X0] : ((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | ! [X1] : (quiet(X1) | wise(X1))) & (? [X1] : (~quiet(X1) & ~wise(X1)) | ! [X0] : ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0)))) [nnf transformation 24]
41. (? [X0] : ((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | ! [X1] : (quiet(X1) | wise(X1))) & (? [X2] : (~quiet(X2) & ~wise(X2)) | ! [X3] : ((~creative(X3) | ~happy(X3)) & (happy(X3) | creative(X3)))) [rectify 40]
42. ? [X0] : ((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) => ((~happy(sK1) | creative(sK1)) & (happy(sK1) | ~creative(sK1))) [choice axiom]
43. ? [X2] : (~quiet(X2) & ~wise(X2)) => (~quiet(sK2) & ~wise(sK2)) [choice axiom]
44. (((~happy(sK1) | creative(sK1)) & (happy(sK1) | ~creative(sK1))) | ! [X1] : (quiet(X1) | wise(X1))) & ((~quiet(sK2) & ~wise(sK2)) | ! [X3] : ((~creative(X3) | ~happy(X3)) & (happy(X3) | creative(X3)))) [skolemisation 41,43,42]
45. ! [X0] : (((~brave(X0) | calm(X0)) | calm(X0)) & (~calm(X0) | (brave(X0) & ~calm(X0)))) [nnf transformation 6]
46. ! [X0] : ((~brave(X0) | calm(X0) | calm(X0)) & (~calm(X0) | (brave(X0) & ~calm(X0)))) [flattening 45]
52. ! [X0] : (((~wise(X0) | ~calm(X0)) & (wise(X0) | calm(X0))) | calm(X0)) [nnf transformation 31]
55. ! [X0] : ((((creative(X0) | ~generous(X0)) & (~creative(X0) | generous(X0))) | (~brave(X0) & happy(X0))) & ((brave(X0) | ~happy(X0)) | ((generous(X0) | creative(X0)) & (~creative(X0) | ~generous(X0))))) [nnf transformation 12]
56. ! [X0] : ((((creative(X0) | ~generous(X0)) & (~creative(X0) | generous(X0))) | (~brave(X0) & happy(X0))) & (brave(X0) | ~happy(X0) | ((generous(X0) | creative(X0)) & (~creative(X0) | ~generous(X0))))) [flattening 55]
81. ~wise(sK2) | happy(X3) | creative(X3) [cnf transformation 44]
82. ~wise(sK2) | ~creative(X3) | ~happy(X3) [cnf transformation 44]
87. ~calm(X0) | ~calm(X0) [cnf transformation 46]
89. ~brave(X0) | calm(X0) | calm(X0) [cnf transformation 46]
103. wise(X0) | calm(X0) | calm(X0) [cnf transformation 52]
109. ~happy(X0) | brave(X0) | generous(X0) | creative(X0) [cnf transformation 56]
110. ~creative(X0) | generous(X0) | happy(X0) [cnf transformation 56]
132. ~generous(alice) [cnf transformation 23]
133. wise(X0) | calm(X0) [duplicate literal removal 103]
134. ~calm(X0) [duplicate literal removal 87]
135. ~brave(X0) | calm(X0) [duplicate literal removal 89]
191. 13 <=> ! [X3] : (~creative(X3) | ~happy(X3)) [avatar definition]
192. ~happy(X3) | ~creative(X3) <- (13) [avatar component clause 191]
199. 15 <=> ! [X3] : (happy(X3) | creative(X3)) [avatar definition]
200. happy(X3) | creative(X3) <- (15) [avatar component clause 199]
203. 16 <=> wise(sK2) [avatar definition]
205. ~wise(sK2) <- (~16) [avatar component clause 203]
206. 13 | ~16 [avatar split clause 82,203,191]
207. 15 | ~16 [avatar split clause 81,203,199]
228. wise(X0) [subsumption resolution 133,134]
275. $false <- (~16) [subsumption resolution 205,228]
276. 16 [avatar contradiction clause 275]
381. brave(X0) | generous(X0) | creative(X0) | creative(X0) <- (15) [resolution 109,200]
383. generous(X0) | brave(X0) | creative(X0) <- (15) [duplicate literal removal 381]
402. brave(alice) | creative(alice) <- (15) [resolution 383,132]
411. 43 <=> creative(alice) [avatar definition]
413. creative(alice) <- (43) [avatar component clause 411]
415. 44 <=> brave(alice) [avatar definition]
417. brave(alice) <- (44) [avatar component clause 415]
418. 43 | 44 | ~15 [avatar split clause 402,199,415,411]
420. generous(alice) | happy(alice) <- (43) [resolution 413,110]
421. happy(alice) <- (43) [subsumption resolution 420,132]
432. ~creative(alice) <- (13, 43) [resolution 421,192]
433. $false <- (13, 43) [subsumption resolution 432,413]
434. ~13 | ~43 [avatar contradiction clause 433]
438. calm(alice) <- (44) [resolution 417,135]
449. $false <- (44) [subsumption resolution 438,134]
450. ~44 [avatar contradiction clause 449]
451. $false [avatar sat refutation 206,207,276,418,434,450]
% SZS output end Proof for 4580538519542123662782154
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and not brave is curious and vice versa. If lucy is either not patient or creative then someone is not old or not creative and vice versa. Everyone who is both tall and not calm is both strong and creative. Everyone who is either not happy or not patient is both not calm and not old and vice versa. If someone is not humble then someone is both funny and not funny. Everyone who is not funny is both not kind and not patient and vice versa. If mary is either tall or brave then someone is either wise or funny and vice versa. Everyone who is both not funny and not creative is either not humble or brave and vice versa. If someone is not quiet then john is tall or funny. Everyone who is either not wise or calm is not kind. If alice is both curious and tall then paul is either not generous or not rich. Everyone who is not calm is either not tall or tall. If lucy is both quiet and not calm then someone is both tall and not patient and vice versa. Everyone who is both not patient and not humble is not generous and vice versa. If someone is not old then susan is both generous and not quiet. If someone is both happy and rich then fred is both not strong and tall and vice versa. Fred is not wise. Someone is not quiet. Someone is not happy or creative. Susan is old or not quiet. Someone is humble. Someone is brave. Mary is either not rich or brave. Someone is either not humble or happy. | Susan is patient. | neutral | (![X]:((~rich(X)&~brave(X))<=>curious(X)))&
(((~patient(lucy)<~>creative(lucy)))<=>(?[X]:((~old(X)|~creative(X)))))&
(![X]:((tall(X)&~calm(X))=>(strong(X)&creative(X))))&
(![X]:((~happy(X)<~>~patient(X))<=>(~calm(X)&~old(X))))&
((?[X]:(~humble(X)))=>(?[X]:((funny(X)&~funny(X)))))&
(![X]:(~funny(X)<=>(~kind(X)&~patient(X))))&
(((tall(mary)<~>brave(mary)))<=>(?[X]:((wise(X)<~>funny(X)))))&
(![X]:((~funny(X)&~creative(X))<=>(~humble(X)<~>brave(X))))&
((?[X]:(~quiet(X)))=>((tall(john)|funny(john))))&
(![X]:((~wise(X)<~>calm(X))=>~kind(X)))&
(((curious(alice)&tall(alice)))=>((~generous(paul)<~>~rich(paul))))&
(![X]:(~calm(X)=>(~tall(X)<~>tall(X))))&
(((quiet(lucy)&~calm(lucy)))<=>(?[X]:((tall(X)&~patient(X)))))&
(![X]:((~patient(X)&~humble(X))<=>~generous(X)))&
((?[X]:(~old(X)))=>((generous(susan)&~quiet(susan))))&
((?[X]:((happy(X)&rich(X))))<=>((~strong(fred)&tall(fred))))&
(~wise(fred))&
(?[X]:(~quiet(X)))&
(?[X]:((~happy(X)|creative(X))))&
((old(susan)|~quiet(susan)))&
(?[X]:(humble(X)))&
(?[X]:(brave(X)))&
((~rich(mary)<~>brave(mary)))&
(?[X]:((~humble(X)<~>happy(X)))) | patient(susan) | [] | null | 0 |
Everyone who is not kind is both creative and generous and vice versa.
If someone is not funny or not generous then alice is creative or happy and vice versa.
Everyone who is either humble or wise is not curious.
If someone is not humble then someone is wise or strong and vice versa.
Everyone who is funny is old or funny.
If someone is both old and generous then someone is not wise or creative and vice versa.
If mary is strong or creative then someone is generous and vice versa.
If fred is both kind and not creative then someone is not curious and vice versa.
If lucy is both not rich and not humble then someone is creative or not funny.
Everyone who is humble or not patient is either not tall or patient.
Everyone who is rich is strong and vice versa.
Everyone who is generous is both not funny and old.
Everyone who is not funny or funny is both not tall and not rich.
If lucy is either not strong or not quiet then alice is old and vice versa.
Everyone who is either not brave or calm is not strong.
Everyone who is both not generous and wise is both wise and rich and vice versa.
Someone is not funny.
Someone is curious.
Lucy is brave or not old.
Mary is both brave and humble.
Paul is not creative or curious.
Alice is either kind or not tall. | Mary is not happy. | neutral | (![X]:(~kind(X)<=>(creative(X)&generous(X))))&
((?[X]:((~funny(X)|~generous(X))))<=>((creative(alice)|happy(alice))))&
(![X]:((humble(X)<~>wise(X))=>~curious(X)))&
((?[X]:(~humble(X)))<=>(?[X]:((wise(X)|strong(X)))))&
(![X]:(funny(X)=>(old(X)|funny(X))))&
((?[X]:((old(X)&generous(X))))<=>(?[X]:((~wise(X)|creative(X)))))&
(((strong(mary)|creative(mary)))<=>(?[X]:(generous(X))))&
(((kind(fred)&~creative(fred)))<=>(?[X]:(~curious(X))))&
(((~rich(lucy)&~humble(lucy)))=>(?[X]:((creative(X)|~funny(X)))))&
(![X]:((humble(X)|~patient(X))=>(~tall(X)<~>patient(X))))&
(![X]:(rich(X)<=>strong(X)))&
(![X]:(generous(X)=>(~funny(X)&old(X))))&
(![X]:((~funny(X)|funny(X))=>(~tall(X)&~rich(X))))&
(((~strong(lucy)<~>~quiet(lucy)))<=>(old(alice)))&
(![X]:((~brave(X)<~>calm(X))=>~strong(X)))&
(![X]:((~generous(X)&wise(X))<=>(wise(X)&rich(X))))&
(?[X]:(~funny(X)))&
(?[X]:(curious(X)))&
((brave(lucy)|~old(lucy)))&
((brave(mary)&humble(mary)))&
((~creative(paul)|curious(paul)))&
((kind(alice)<~>~tall(alice))) | ~happy(mary) | [] | null | 0 |
Everyone who is both not creative and not old is either wise or happy.
Everyone who is not strong is either not happy or kind.
Everyone who is not happy is both not rich and not happy and vice versa.
If fred is either funny or happy then alice is not rich.
Everyone who is not curious or not tall is not happy or not old.
If fred is either quiet or funny then someone is both not patient and not calm and vice versa.
Everyone who is creative or quiet is either wise or calm and vice versa.
If alice is both not calm and tall then someone is both quiet and not wise and vice versa.
Everyone who is kind is both not quiet and kind and vice versa.
Everyone who is calm or humble is not brave and vice versa.
Everyone who is both calm and not quiet is not brave.
If someone is not old or curious then mary is both calm and humble.
Everyone who is either patient or not old is both happy and curious and vice versa.
Everyone who is both not curious and not happy is not happy and vice versa.
Everyone who is either quiet or not kind is not kind and vice versa.
Everyone who is not quiet or not brave is either humble or happy and vice versa.
Fred is either creative or wise.
Susan is both patient and not humble.
Someone is humble or not tall.
Someone is not quiet or not patient.
Someone is both not strong and not happy.
Lucy is kind or not wise.
Someone is not wise or quiet.
Mary is not old. | Lucy is not tall. | neutral | (![X]:((~creative(X)&~old(X))=>(wise(X)<~>happy(X))))&
(![X]:(~strong(X)=>(~happy(X)<~>kind(X))))&
(![X]:(~happy(X)<=>(~rich(X)&~happy(X))))&
(((funny(fred)<~>happy(fred)))=>(~rich(alice)))&
(![X]:((~curious(X)|~tall(X))=>(~happy(X)|~old(X))))&
(((quiet(fred)<~>funny(fred)))<=>(?[X]:((~patient(X)&~calm(X)))))&
(![X]:((creative(X)|quiet(X))<=>(wise(X)<~>calm(X))))&
(((~calm(alice)&tall(alice)))<=>(?[X]:((quiet(X)&~wise(X)))))&
(![X]:(kind(X)<=>(~quiet(X)&kind(X))))&
(![X]:((calm(X)|humble(X))<=>~brave(X)))&
(![X]:((calm(X)&~quiet(X))=>~brave(X)))&
((?[X]:((~old(X)|curious(X))))=>((calm(mary)&humble(mary))))&
(![X]:((patient(X)<~>~old(X))<=>(happy(X)&curious(X))))&
(![X]:((~curious(X)&~happy(X))<=>~happy(X)))&
(![X]:((quiet(X)<~>~kind(X))<=>~kind(X)))&
(![X]:((~quiet(X)|~brave(X))<=>(humble(X)<~>happy(X))))&
((creative(fred)<~>wise(fred)))&
((patient(susan)&~humble(susan)))&
(?[X]:((humble(X)|~tall(X))))&
(?[X]:((~quiet(X)|~patient(X))))&
(?[X]:((~strong(X)&~happy(X))))&
((kind(lucy)|~wise(lucy)))&
(?[X]:((~wise(X)|quiet(X))))&
(~old(mary)) | ~tall(lucy) | [] | null | 0 |
Everyone who is creative is both rich and not patient and vice versa. Everyone who is either not funny or old is patient or not calm. If someone is either wise or patient then someone is either not strong or rich. If paul is either not funny or quiet then fred is not generous or not brave and vice versa. If someone is not generous then someone is either wise or old. If someone is not kind or patient then lucy is both old and not calm and vice versa. Everyone who is not generous is both not quiet and kind. Everyone who is wise or not patient is not brave. Everyone who is not wise or humble is not humble. Everyone who is not happy or funny is not curious. If john is creative then someone is not wise. Everyone who is either not rich or not strong is both not happy and quiet and vice versa. If someone is either not tall or not kind then susan is tall or strong. Everyone who is creative is not funny or not strong and vice versa. If someone is calm then someone is either calm or not humble. If alice is either not generous or old then alice is not quiet or creative. Someone is both patient and quiet. Susan is rich or not rich. Someone is not creative or calm. Someone is kind. Someone is either not curious or happy. Mary is both generous and kind. Someone is either patient or not creative. Alice is strong. | Fred is not humble. | entailment | (![X]:(creative(X)<=>(rich(X)&~patient(X))))&
(![X]:((~funny(X)<~>old(X))=>(patient(X)|~calm(X))))&
((?[X]:((wise(X)<~>patient(X))))=>(?[X]:((~strong(X)<~>rich(X)))))&
(((~funny(paul)<~>quiet(paul)))<=>((~generous(fred)|~brave(fred))))&
((?[X]:(~generous(X)))=>(?[X]:((wise(X)<~>old(X)))))&
((?[X]:((~kind(X)|patient(X))))<=>((old(lucy)&~calm(lucy))))&
(![X]:(~generous(X)=>(~quiet(X)&kind(X))))&
(![X]:((wise(X)|~patient(X))=>~brave(X)))&
(![X]:((~wise(X)|humble(X))=>~humble(X)))&
(![X]:((~happy(X)|funny(X))=>~curious(X)))&
((creative(john))=>(?[X]:(~wise(X))))&
(![X]:((~rich(X)<~>~strong(X))<=>(~happy(X)&quiet(X))))&
((?[X]:((~tall(X)<~>~kind(X))))=>((tall(susan)|strong(susan))))&
(![X]:(creative(X)<=>(~funny(X)|~strong(X))))&
((?[X]:(calm(X)))=>(?[X]:((calm(X)<~>~humble(X)))))&
(((~generous(alice)<~>old(alice)))=>((~quiet(alice)|creative(alice))))&
(?[X]:((patient(X)&quiet(X))))&
((rich(susan)|~rich(susan)))&
(?[X]:((~creative(X)|calm(X))))&
(?[X]:(kind(X)))&
(?[X]:((~curious(X)<~>happy(X))))&
((generous(mary)&kind(mary)))&
(?[X]:((patient(X)<~>~creative(X))))&
(strong(alice)) | ~humble(fred) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5129319166426332635380238
% SZS output start Proof for 5129319166426332635380238
9. ! [X0] : ((humble(X0) | ~wise(X0)) => ~humble(X0)) [input p8]
25. humble(fred) [input hypothesis]
35. ! [X0] : (~humble(X0) | (~humble(X0) & wise(X0))) [ennf transformation 9]
112. ~humble(X0) | ~humble(X0) [cnf transformation 35]
143. humble(fred) [cnf transformation 25]
144. ~humble(X0) [duplicate literal removal 112]
293. $false [subsumption resolution 143,144]
% SZS output end Proof for 5129319166426332635380238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old then someone is both happy and not creative and vice versa.
If alice is both not wise and happy then lucy is not generous or kind.
Everyone who is not happy is happy or not strong and vice versa.
If paul is either funny or not kind then fred is not kind.
If fred is funny then fred is humble and vice versa.
If someone is strong then someone is funny and vice versa.
If john is not rich then lucy is both not old and not funny and vice versa.
Everyone who is either not humble or quiet is both not old and not patient.
If someone is either funny or rich then john is both kind and brave and vice versa.
Everyone who is both creative and not calm is either calm or funny and vice versa.
If someone is both not happy and curious then someone is creative or happy.
Everyone who is humble or quiet is either funny or not generous.
Everyone who is either not wise or patient is curious.
If someone is either tall or strong then someone is either not curious or not quiet.
Everyone who is kind or not tall is either kind or not happy and vice versa.
If someone is both wise and rich then someone is not generous or strong and vice versa.
Someone is either not rich or curious.
Mary is not happy.
Someone is not brave or funny.
Someone is both not creative and not funny. | Lucy is calm. | contradiction | ((?[X]:(old(X)))<=>(?[X]:((happy(X)&~creative(X)))))&
(((~wise(alice)&happy(alice)))=>((~generous(lucy)|kind(lucy))))&
(![X]:(~happy(X)<=>(happy(X)|~strong(X))))&
(((funny(paul)<~>~kind(paul)))=>(~kind(fred)))&
((funny(fred))<=>(humble(fred)))&
((?[X]:(strong(X)))<=>(?[X]:(funny(X))))&
((~rich(john))<=>((~old(lucy)&~funny(lucy))))&
(![X]:((~humble(X)<~>quiet(X))=>(~old(X)&~patient(X))))&
((?[X]:((funny(X)<~>rich(X))))<=>((kind(john)&brave(john))))&
(![X]:((creative(X)&~calm(X))<=>(calm(X)<~>funny(X))))&
((?[X]:((~happy(X)&curious(X))))=>(?[X]:((creative(X)|happy(X)))))&
(![X]:((humble(X)|quiet(X))=>(funny(X)<~>~generous(X))))&
(![X]:((~wise(X)<~>patient(X))=>curious(X)))&
((?[X]:((tall(X)<~>strong(X))))=>(?[X]:((~curious(X)<~>~quiet(X)))))&
(![X]:((kind(X)|~tall(X))<=>(kind(X)<~>~happy(X))))&
((?[X]:((wise(X)&rich(X))))<=>(?[X]:((~generous(X)|strong(X)))))&
(?[X]:((~rich(X)<~>curious(X))))&
(~happy(mary))&
(?[X]:((~brave(X)|funny(X))))&
(?[X]:((~creative(X)&~funny(X)))) | calm(lucy) | [
"p2",
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6113751750366413687413935
% SZS output start Proof for 6113751750366413687413935
3. ! [X0] : (~happy(X0) <=> (~strong(X0) | happy(X0))) [input p2]
6. ? [X0] : strong(X0) <=> ? [X0] : funny(X0) [input p5]
10. ! [X0] : ((~calm(X0) & creative(X0)) <=> (calm(X0) <~> funny(X0))) [input p9]
21. calm(lucy) [input hypothesis]
23. ? [X0] : strong(X0) <=> ? [X1] : funny(X1) [rectify 6]
40. ! [X0] : ((~happy(X0) | (strong(X0) & ~happy(X0))) & ((~strong(X0) | happy(X0)) | happy(X0))) [nnf transformation 3]
41. ! [X0] : ((~happy(X0) | (strong(X0) & ~happy(X0))) & (~strong(X0) | happy(X0) | happy(X0))) [flattening 40]
44. (? [X0] : strong(X0) | ! [X1] : ~funny(X1)) & (? [X1] : funny(X1) | ! [X0] : ~strong(X0)) [nnf transformation 23]
45. (? [X0] : strong(X0) | ! [X1] : ~funny(X1)) & (? [X2] : funny(X2) | ! [X3] : ~strong(X3)) [rectify 44]
46. ? [X0] : strong(X0) => strong(sK2) [choice axiom]
47. ? [X2] : funny(X2) => funny(sK3) [choice axiom]
48. (strong(sK2) | ! [X1] : ~funny(X1)) & (funny(sK3) | ! [X3] : ~strong(X3)) [skolemisation 45,47,46]
57. ! [X0] : (((~calm(X0) & creative(X0)) | ((calm(X0) | ~funny(X0)) & (funny(X0) | ~calm(X0)))) & (((~funny(X0) | ~calm(X0)) & (funny(X0) | calm(X0))) | (calm(X0) | ~creative(X0)))) [nnf transformation 10]
58. ! [X0] : (((~calm(X0) & creative(X0)) | ((calm(X0) | ~funny(X0)) & (funny(X0) | ~calm(X0)))) & (((~funny(X0) | ~calm(X0)) & (funny(X0) | calm(X0))) | calm(X0) | ~creative(X0))) [flattening 57]
86. ~strong(X0) | happy(X0) | happy(X0) [cnf transformation 41]
87. ~happy(X0) | ~happy(X0) [cnf transformation 41]
94. strong(sK2) | ~funny(X1) [cnf transformation 48]
112. ~calm(X0) | funny(X0) | ~calm(X0) [cnf transformation 58]
142. calm(lucy) [cnf transformation 21]
146. ~calm(X0) | funny(X0) [duplicate literal removal 112]
147. ~strong(X0) | happy(X0) [duplicate literal removal 86]
148. ~happy(X0) [duplicate literal removal 87]
187. ~strong(X0) [subsumption resolution 147,148]
212. ~funny(X1) [subsumption resolution 94,187]
245. ~calm(X0) [subsumption resolution 146,212]
292. $false [subsumption resolution 142,245]
% SZS output end Proof for 6113751750366413687413935
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or funny then fred is not curious. If someone is either wise or brave then john is not brave. If someone is both creative and patient then someone is either patient or not quiet. Everyone who is both not quiet and wise is tall or old and vice versa. If someone is not quiet then someone is both rich and not patient. If someone is not funny then paul is rich. If someone is rich or generous then alice is both old and not brave and vice versa. Everyone who is not quiet or not strong is both quiet and not generous. Everyone who is either not generous or not wise is not curious and vice versa. Everyone who is kind or not creative is both happy and generous. If john is rich or not humble then someone is both not happy and humble and vice versa. If susan is not funny or not patient then john is either not tall or funny. If fred is not humble or not patient then fred is tall or not tall. Everyone who is not generous or not funny is both not brave and patient and vice versa. Everyone who is either creative or rich is strong. Everyone who is either old or not funny is calm and vice versa. John is either not brave or not strong. Lucy is funny or not curious. Someone is not brave or humble. Someone is strong or not wise. Mary is not generous or calm. Someone is either not quiet or quiet. | Susan is not calm. | entailment | ((?[X]:((~patient(X)<~>funny(X))))=>(~curious(fred)))&
((?[X]:((wise(X)<~>brave(X))))=>(~brave(john)))&
((?[X]:((creative(X)&patient(X))))=>(?[X]:((patient(X)<~>~quiet(X)))))&
(![X]:((~quiet(X)&wise(X))<=>(tall(X)|old(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((rich(X)&~patient(X)))))&
((?[X]:(~funny(X)))=>(rich(paul)))&
((?[X]:((rich(X)|generous(X))))<=>((old(alice)&~brave(alice))))&
(![X]:((~quiet(X)|~strong(X))=>(quiet(X)&~generous(X))))&
(![X]:((~generous(X)<~>~wise(X))<=>~curious(X)))&
(![X]:((kind(X)|~creative(X))=>(happy(X)&generous(X))))&
(((rich(john)|~humble(john)))<=>(?[X]:((~happy(X)&humble(X)))))&
(((~funny(susan)|~patient(susan)))=>((~tall(john)<~>funny(john))))&
(((~humble(fred)|~patient(fred)))=>((tall(fred)|~tall(fred))))&
(![X]:((~generous(X)|~funny(X))<=>(~brave(X)&patient(X))))&
(![X]:((creative(X)<~>rich(X))=>strong(X)))&
(![X]:((old(X)<~>~funny(X))<=>calm(X)))&
((~brave(john)<~>~strong(john)))&
((funny(lucy)|~curious(lucy)))&
(?[X]:((~brave(X)|humble(X))))&
(?[X]:((strong(X)|~wise(X))))&
((~generous(mary)|calm(mary)))&
(?[X]:((~quiet(X)<~>quiet(X)))) | ~calm(susan) | [
"p3",
"p5",
"p6",
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 727953465414215875014974
% SZS output start Proof for 727953465414215875014974
4. ! [X0] : ((wise(X0) & ~quiet(X0)) <=> (old(X0) | tall(X0))) [input p3]
6. ? [X0] : ~funny(X0) => rich(paul) [input p5]
7. ? [X0] : (generous(X0) | rich(X0)) <=> (~brave(alice) & old(alice)) [input p6]
8. ! [X0] : ((~strong(X0) | ~quiet(X0)) => (~generous(X0) & quiet(X0))) [input p7]
16. ! [X0] : ((old(X0) <~> ~funny(X0)) <=> calm(X0)) [input p15]
23. calm(susan) [input hypothesis]
26. ! [X0] : (calm(X0) => (old(X0) <~> ~funny(X0))) [unused predicate definition removal 16]
33. rich(paul) | ! [X0] : funny(X0) [ennf transformation 6]
34. ! [X0] : ((~generous(X0) & quiet(X0)) | (strong(X0) & quiet(X0))) [ennf transformation 8]
41. ! [X0] : ((old(X0) <~> ~funny(X0)) | ~calm(X0)) [ennf transformation 26]
48. ! [X0] : (((wise(X0) & ~quiet(X0)) | (~old(X0) & ~tall(X0))) & ((old(X0) | tall(X0)) | (~wise(X0) | quiet(X0)))) [nnf transformation 4]
49. ! [X0] : (((wise(X0) & ~quiet(X0)) | (~old(X0) & ~tall(X0))) & (old(X0) | tall(X0) | ~wise(X0) | quiet(X0))) [flattening 48]
53. (? [X0] : (generous(X0) | rich(X0)) | (brave(alice) | ~old(alice))) & ((~brave(alice) & old(alice)) | ! [X0] : (~generous(X0) & ~rich(X0))) [nnf transformation 7]
54. (? [X0] : (generous(X0) | rich(X0)) | brave(alice) | ~old(alice)) & ((~brave(alice) & old(alice)) | ! [X0] : (~generous(X0) & ~rich(X0))) [flattening 53]
55. (? [X0] : (generous(X0) | rich(X0)) | brave(alice) | ~old(alice)) & ((~brave(alice) & old(alice)) | ! [X1] : (~generous(X1) & ~rich(X1))) [rectify 54]
56. ? [X0] : (generous(X0) | rich(X0)) => (generous(sK2) | rich(sK2)) [choice axiom]
57. ((generous(sK2) | rich(sK2)) | brave(alice) | ~old(alice)) & ((~brave(alice) & old(alice)) | ! [X1] : (~generous(X1) & ~rich(X1))) [skolemisation 55,56]
68. ! [X0] : (((funny(X0) | ~old(X0)) & (~funny(X0) | old(X0))) | ~calm(X0)) [nnf transformation 41]
85. ~old(X0) | ~quiet(X0) [cnf transformation 49]
90. rich(paul) | funny(X0) [cnf transformation 33]
91. old(alice) | ~rich(X1) [cnf transformation 57]
96. quiet(X0) | quiet(X0) [cnf transformation 34]
122. ~calm(X0) | old(X0) | ~funny(X0) [cnf transformation 68]
132. calm(susan) [cnf transformation 23]
133. quiet(X0) [duplicate literal removal 96]
172. 10 <=> ! [X1] : quiet(X1) [avatar definition]
173. quiet(X1) <- (10) [avatar component clause 172]
185. 13 <=> ! [X0] : funny(X0) [avatar definition]
186. funny(X0) <- (13) [avatar component clause 185]
188. 14 <=> rich(paul) [avatar definition]
190. rich(paul) <- (14) [avatar component clause 188]
191. 13 | 14 [avatar split clause 90,188,185]
193. 15 <=> old(alice) [avatar definition]
194. old(alice) <- (15) [avatar component clause 193]
214. 20 <=> ! [X1] : ~rich(X1) [avatar definition]
215. ~rich(X1) <- (20) [avatar component clause 214]
218. 20 | 15 [avatar split clause 91,193,214]
219. 10 [avatar split clause 133,172]
311. ~quiet(alice) <- (15) [resolution 85,194]
312. $false <- (10, 15) [subsumption resolution 311,173]
313. ~10 | ~15 [avatar contradiction clause 312]
315. $false <- (14, 20) [resolution 215,190]
316. ~14 | ~20 [avatar contradiction clause 315]
355. old(susan) | ~funny(susan) [resolution 122,132]
357. old(susan) <- (13) [subsumption resolution 355,186]
360. ~quiet(susan) <- (13) [resolution 357,85]
361. $false <- (10, 13) [subsumption resolution 360,173]
362. ~10 | ~13 [avatar contradiction clause 361]
363. $false [avatar sat refutation 191,218,219,313,316,362]
% SZS output end Proof for 727953465414215875014974
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not strong is not quiet and vice versa.
If someone is either not funny or creative then fred is not curious and vice versa.
If someone is either not rich or not old then someone is either humble or not strong and vice versa.
Everyone who is not calm or not quiet is not quiet and vice versa.
Everyone who is both generous and not funny is either not calm or not brave and vice versa.
Everyone who is rich or not tall is either tall or rich and vice versa.
If fred is either not creative or kind then someone is not curious or wise and vice versa.
If fred is either not kind or happy then mary is either generous or old and vice versa.
If paul is happy or generous then paul is not happy or not wise.
Everyone who is not rich is both old and not wise and vice versa.
If someone is patient then fred is both kind and creative.
Everyone who is not brave is old or patient.
Everyone who is not tall is not kind.
Everyone who is either not rich or not calm is old or not kind.
If someone is either not calm or happy then lucy is either not generous or curious and vice versa.
Everyone who is both not rich and strong is not funny or tall.
Susan is not patient or calm.
Someone is both brave and curious.
Someone is not strong or not humble.
Paul is not quiet.
Susan is patient or old.
Mary is not generous or wise.
Mary is not calm or not brave. | Mary is not old. | neutral | (![X]:((~brave(X)<~>~strong(X))<=>~quiet(X)))&
((?[X]:((~funny(X)<~>creative(X))))<=>(~curious(fred)))&
((?[X]:((~rich(X)<~>~old(X))))<=>(?[X]:((humble(X)<~>~strong(X)))))&
(![X]:((~calm(X)|~quiet(X))<=>~quiet(X)))&
(![X]:((generous(X)&~funny(X))<=>(~calm(X)<~>~brave(X))))&
(![X]:((rich(X)|~tall(X))<=>(tall(X)<~>rich(X))))&
(((~creative(fred)<~>kind(fred)))<=>(?[X]:((~curious(X)|wise(X)))))&
(((~kind(fred)<~>happy(fred)))<=>((generous(mary)<~>old(mary))))&
(((happy(paul)|generous(paul)))=>((~happy(paul)|~wise(paul))))&
(![X]:(~rich(X)<=>(old(X)&~wise(X))))&
((?[X]:(patient(X)))=>((kind(fred)&creative(fred))))&
(![X]:(~brave(X)=>(old(X)|patient(X))))&
(![X]:(~tall(X)=>~kind(X)))&
(![X]:((~rich(X)<~>~calm(X))=>(old(X)|~kind(X))))&
((?[X]:((~calm(X)<~>happy(X))))<=>((~generous(lucy)<~>curious(lucy))))&
(![X]:((~rich(X)&strong(X))=>(~funny(X)|tall(X))))&
((~patient(susan)|calm(susan)))&
(?[X]:((brave(X)&curious(X))))&
(?[X]:((~strong(X)|~humble(X))))&
(~quiet(paul))&
((patient(susan)|old(susan)))&
((~generous(mary)|wise(mary)))&
((~calm(mary)|~brave(mary))) | ~old(mary) | [] | null | 0 |
If mary is not happy then paul is not happy.
If susan is either not wise or not calm then alice is both not strong and strong.
Everyone who is quiet or generous is kind or brave and vice versa.
If someone is creative then someone is either quiet or strong and vice versa.
Everyone who is both funny and not kind is either not rich or not generous and vice versa.
If someone is either funny or rich then someone is not tall or not old.
Everyone who is not strong is both humble and calm.
Everyone who is either not happy or not generous is not creative and vice versa.
Everyone who is generous is both not calm and not humble and vice versa.
If alice is both funny and humble then someone is calm or strong.
If someone is not tall or tall then fred is both not tall and not calm.
Everyone who is not calm is both not humble and quiet and vice versa.
Everyone who is wise is old or not funny.
If someone is not quiet or wise then fred is generous or not generous and vice versa.
Everyone who is both not creative and not old is either not quiet or strong and vice versa.
Someone is not brave.
Someone is not funny or not kind.
Someone is happy or not calm.
Someone is not funny or calm.
Mary is not strong.
Lucy is either patient or not rich.
Someone is both patient and not kind. | Fred is creative. | contradiction | ((~happy(mary))=>(~happy(paul)))&
(((~wise(susan)<~>~calm(susan)))=>((~strong(alice)&strong(alice))))&
(![X]:((quiet(X)|generous(X))<=>(kind(X)|brave(X))))&
((?[X]:(creative(X)))<=>(?[X]:((quiet(X)<~>strong(X)))))&
(![X]:((funny(X)&~kind(X))<=>(~rich(X)<~>~generous(X))))&
((?[X]:((funny(X)<~>rich(X))))=>(?[X]:((~tall(X)|~old(X)))))&
(![X]:(~strong(X)=>(humble(X)&calm(X))))&
(![X]:((~happy(X)<~>~generous(X))<=>~creative(X)))&
(![X]:(generous(X)<=>(~calm(X)&~humble(X))))&
(((funny(alice)&humble(alice)))=>(?[X]:((calm(X)|strong(X)))))&
((?[X]:((~tall(X)|tall(X))))=>((~tall(fred)&~calm(fred))))&
(![X]:(~calm(X)<=>(~humble(X)&quiet(X))))&
(![X]:(wise(X)=>(old(X)|~funny(X))))&
((?[X]:((~quiet(X)|wise(X))))<=>((generous(fred)|~generous(fred))))&
(![X]:((~creative(X)&~old(X))<=>(~quiet(X)<~>strong(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~funny(X)|~kind(X))))&
(?[X]:((happy(X)|~calm(X))))&
(?[X]:((~funny(X)|calm(X))))&
(~strong(mary))&
((patient(lucy)<~>~rich(lucy)))&
(?[X]:((patient(X)&~kind(X)))) | creative(fred) | [
"p6",
"p8",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8779232452133990528917449
% SZS output start Proof for 8779232452133990528917449
7. ! [X0] : (~strong(X0) => (calm(X0) & humble(X0))) [input p6]
9. ! [X0] : (generous(X0) <=> (~humble(X0) & ~calm(X0))) [input p8]
11. ? [X0] : (tall(X0) | ~tall(X0)) => (~calm(fred) & ~tall(fred)) [input p10]
12. ! [X0] : (~calm(X0) <=> (quiet(X0) & ~humble(X0))) [input p11]
15. ! [X0] : ((~old(X0) & ~creative(X0)) <=> (~quiet(X0) <~> strong(X0))) [input p14]
23. creative(fred) [input hypothesis]
29. ! [X0] : ((calm(X0) & humble(X0)) | strong(X0)) [ennf transformation 7]
32. (~calm(fred) & ~tall(fred)) | ! [X0] : (~tall(X0) & tall(X0)) [ennf transformation 11]
50. ! [X0] : ((generous(X0) | (humble(X0) | calm(X0))) & ((~humble(X0) & ~calm(X0)) | ~generous(X0))) [nnf transformation 9]
51. ! [X0] : ((generous(X0) | humble(X0) | calm(X0)) & ((~humble(X0) & ~calm(X0)) | ~generous(X0))) [flattening 50]
54. ! [X0] : ((~calm(X0) | (~quiet(X0) | humble(X0))) & ((quiet(X0) & ~humble(X0)) | calm(X0))) [nnf transformation 12]
55. ! [X0] : ((~calm(X0) | ~quiet(X0) | humble(X0)) & ((quiet(X0) & ~humble(X0)) | calm(X0))) [flattening 54]
61. ! [X0] : (((~old(X0) & ~creative(X0)) | ((~quiet(X0) | ~strong(X0)) & (strong(X0) | quiet(X0)))) & (((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | (old(X0) | creative(X0)))) [nnf transformation 15]
62. ! [X0] : (((~old(X0) & ~creative(X0)) | ((~quiet(X0) | ~strong(X0)) & (strong(X0) | quiet(X0)))) & (((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | old(X0) | creative(X0))) [flattening 61]
95. humble(X0) | strong(X0) [cnf transformation 29]
102. ~humble(X0) | ~generous(X0) [cnf transformation 51]
103. humble(X0) | generous(X0) | calm(X0) [cnf transformation 51]
106. ~tall(fred) | ~tall(X0) [cnf transformation 32]
107. ~calm(fred) | tall(X0) [cnf transformation 32]
109. ~humble(X0) | calm(X0) [cnf transformation 55]
110. quiet(X0) | calm(X0) [cnf transformation 55]
120. ~creative(X0) | ~quiet(X0) | ~strong(X0) [cnf transformation 62]
132. creative(fred) [cnf transformation 23]
200. 16 <=> ! [X0] : ~tall(X0) [avatar definition]
201. ~tall(X0) <- (16) [avatar component clause 200]
203. 17 <=> calm(fred) [avatar definition]
205. ~calm(fred) <- (~17) [avatar component clause 203]
208. 18 <=> ! [X0] : tall(X0) [avatar definition]
209. tall(X0) <- (18) [avatar component clause 208]
210. 18 | ~17 [avatar split clause 107,203,208]
212. 19 <=> tall(fred) [avatar definition]
214. ~tall(fred) <- (~19) [avatar component clause 212]
215. 16 | ~19 [avatar split clause 106,212,200]
218. 20 <=> generous(fred) [avatar definition]
219. ~generous(fred) <- (~20) [avatar component clause 218]
220. generous(fred) <- (20) [avatar component clause 218]
274. ~generous(X0) | strong(X0) [resolution 102,95]
323. generous(X0) | calm(X0) | calm(X0) [resolution 103,109]
325. generous(X0) | calm(X0) [duplicate literal removal 323]
331. calm(fred) <- (~20) [resolution 325,219]
335. 17 | 20 [avatar split clause 331,218,203]
336. $false <- (16, 18) [subsumption resolution 201,209]
337. ~16 | ~18 [avatar contradiction clause 336]
340. $false <- (18, ~19) [resolution 209,214]
341. ~18 | 19 [avatar contradiction clause 340]
345. strong(fred) <- (20) [resolution 220,274]
398. ~quiet(fred) | ~strong(fred) [resolution 120,132]
401. ~quiet(fred) <- (20) [subsumption resolution 398,345]
425. calm(fred) <- (20) [resolution 401,110]
426. $false <- (~17, 20) [subsumption resolution 425,205]
427. 17 | ~20 [avatar contradiction clause 426]
428. $false [avatar sat refutation 210,215,335,337,341,427]
% SZS output end Proof for 8779232452133990528917449
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both not quiet and not calm then someone is both not patient and rich and vice versa. Everyone who is either not quiet or not generous is either brave or humble and vice versa. Everyone who is either not quiet or wise is either curious or patient. Everyone who is not funny or not curious is both rich and brave. Everyone who is either curious or not brave is not patient or rich. Everyone who is both patient and happy is funny and vice versa. If mary is quiet or happy then someone is both patient and humble. If someone is either old or not humble then someone is either old or not happy. Everyone who is both not humble and not calm is either brave or not generous. Everyone who is generous or wise is either not creative or not wise. Everyone who is humble is not generous and vice versa. If someone is not wise or happy then someone is either funny or not kind and vice versa. Everyone who is curious is not tall and vice versa. Everyone who is not happy is not creative. If lucy is either not calm or not wise then someone is creative. Everyone who is both wise and old is funny or not strong. Lucy is rich or funny. Someone is both humble and not generous. Someone is both not happy and patient. Lucy is not strong or patient. Paul is both old and not strong. Lucy is wise. Someone is not kind. Mary is not patient or humble. | Mary is happy. | neutral | (((~quiet(lucy)&~calm(lucy)))<=>(?[X]:((~patient(X)&rich(X)))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(brave(X)<~>humble(X))))&
(![X]:((~quiet(X)<~>wise(X))=>(curious(X)<~>patient(X))))&
(![X]:((~funny(X)|~curious(X))=>(rich(X)&brave(X))))&
(![X]:((curious(X)<~>~brave(X))=>(~patient(X)|rich(X))))&
(![X]:((patient(X)&happy(X))<=>funny(X)))&
(((quiet(mary)|happy(mary)))=>(?[X]:((patient(X)&humble(X)))))&
((?[X]:((old(X)<~>~humble(X))))=>(?[X]:((old(X)<~>~happy(X)))))&
(![X]:((~humble(X)&~calm(X))=>(brave(X)<~>~generous(X))))&
(![X]:((generous(X)|wise(X))=>(~creative(X)<~>~wise(X))))&
(![X]:(humble(X)<=>~generous(X)))&
((?[X]:((~wise(X)|happy(X))))<=>(?[X]:((funny(X)<~>~kind(X)))))&
(![X]:(curious(X)<=>~tall(X)))&
(![X]:(~happy(X)=>~creative(X)))&
(((~calm(lucy)<~>~wise(lucy)))=>(?[X]:(creative(X))))&
(![X]:((wise(X)&old(X))=>(funny(X)|~strong(X))))&
((rich(lucy)|funny(lucy)))&
(?[X]:((humble(X)&~generous(X))))&
(?[X]:((~happy(X)&patient(X))))&
((~strong(lucy)|patient(lucy)))&
((old(paul)&~strong(paul)))&
(wise(lucy))&
(?[X]:(~kind(X)))&
((~patient(mary)|humble(mary))) | happy(mary) | [] | null | 0 |
Everyone who is both not old and brave is both tall and not humble.
If alice is not happy or not kind then someone is either not wise or not curious.
If someone is both not rich and curious then mary is not curious.
If someone is either not creative or happy then someone is either not happy or generous.
Everyone who is not curious or brave is either not creative or not kind.
If lucy is not calm or calm then someone is either wise or not happy.
If john is either not patient or not happy then lucy is either patient or strong.
Everyone who is either not old or not rich is not quiet and vice versa.
Everyone who is old is either not calm or not generous and vice versa.
Everyone who is both humble and brave is either kind or not curious and vice versa.
If someone is not kind or not generous then someone is both not tall and strong and vice versa.
Everyone who is both not happy and tall is not patient.
If someone is either not patient or wise then someone is either quiet or calm and vice versa.
Everyone who is both not tall and not calm is tall and vice versa.
If alice is not calm or generous then alice is not calm.
Everyone who is either happy or creative is not kind and vice versa.
Mary is either not brave or tall.
Mary is strong.
Mary is old.
Someone is either not rich or not kind.
Someone is not humble or not generous.
Someone is either not kind or not funny.
Someone is old or not tall.
Lucy is both not funny and not quiet. | Alice is not tall. | entailment | (![X]:((~old(X)&brave(X))=>(tall(X)&~humble(X))))&
(((~happy(alice)|~kind(alice)))=>(?[X]:((~wise(X)<~>~curious(X)))))&
((?[X]:((~rich(X)&curious(X))))=>(~curious(mary)))&
((?[X]:((~creative(X)<~>happy(X))))=>(?[X]:((~happy(X)<~>generous(X)))))&
(![X]:((~curious(X)|brave(X))=>(~creative(X)<~>~kind(X))))&
(((~calm(lucy)|calm(lucy)))=>(?[X]:((wise(X)<~>~happy(X)))))&
(((~patient(john)<~>~happy(john)))=>((patient(lucy)<~>strong(lucy))))&
(![X]:((~old(X)<~>~rich(X))<=>~quiet(X)))&
(![X]:(old(X)<=>(~calm(X)<~>~generous(X))))&
(![X]:((humble(X)&brave(X))<=>(kind(X)<~>~curious(X))))&
((?[X]:((~kind(X)|~generous(X))))<=>(?[X]:((~tall(X)&strong(X)))))&
(![X]:((~happy(X)&tall(X))=>~patient(X)))&
((?[X]:((~patient(X)<~>wise(X))))<=>(?[X]:((quiet(X)<~>calm(X)))))&
(![X]:((~tall(X)&~calm(X))<=>tall(X)))&
(((~calm(alice)|generous(alice)))=>(~calm(alice)))&
(![X]:((happy(X)<~>creative(X))<=>~kind(X)))&
((~brave(mary)<~>tall(mary)))&
(strong(mary))&
(old(mary))&
(?[X]:((~rich(X)<~>~kind(X))))&
(?[X]:((~humble(X)|~generous(X))))&
(?[X]:((~kind(X)<~>~funny(X))))&
(?[X]:((old(X)|~tall(X))))&
((~funny(lucy)&~quiet(lucy))) | ~tall(alice) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3597794784822708695605303
% SZS output start Proof for 3597794784822708695605303
14. ! [X0] : ((~calm(X0) & ~tall(X0)) <=> tall(X0)) [input p13]
25. tall(alice) [input hypothesis]
66. ! [X0] : (((~calm(X0) & ~tall(X0)) | ~tall(X0)) & (tall(X0) | (calm(X0) | tall(X0)))) [nnf transformation 14]
67. ! [X0] : (((~calm(X0) & ~tall(X0)) | ~tall(X0)) & (tall(X0) | calm(X0) | tall(X0))) [flattening 66]
132. ~tall(X0) | ~tall(X0) [cnf transformation 67]
152. tall(alice) [cnf transformation 25]
154. ~tall(X0) [duplicate literal removal 132]
335. $false [subsumption resolution 152,154]
% SZS output end Proof for 3597794784822708695605303
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and generous is both not patient and not strong and vice versa.
If someone is either not brave or not patient then paul is not funny or not quiet.
Everyone who is both not happy and curious is patient and vice versa.
If mary is tall then someone is either not kind or not generous and vice versa.
If mary is not generous or not patient then someone is patient or not humble and vice versa.
Everyone who is both brave and not rich is either kind or not calm.
Everyone who is either not happy or not curious is old.
Everyone who is old is old or not strong and vice versa.
Everyone who is not kind is not patient and vice versa.
Everyone who is not patient is both not humble and brave.
Everyone who is both not happy and curious is happy and vice versa.
Everyone who is funny or patient is not happy.
If paul is wise then someone is not kind and vice versa.
If someone is curious or not wise then john is calm or patient and vice versa.
Everyone who is quiet is either curious or rich.
Someone is not tall or humble.
Someone is either funny or strong.
Someone is not tall or quiet.
Someone is either curious or generous.
Paul is either generous or not quiet. | Mary is tall. | entailment | (![X]:((wise(X)&generous(X))<=>(~patient(X)&~strong(X))))&
((?[X]:((~brave(X)<~>~patient(X))))=>((~funny(paul)|~quiet(paul))))&
(![X]:((~happy(X)&curious(X))<=>patient(X)))&
((tall(mary))<=>(?[X]:((~kind(X)<~>~generous(X)))))&
(((~generous(mary)|~patient(mary)))<=>(?[X]:((patient(X)|~humble(X)))))&
(![X]:((brave(X)&~rich(X))=>(kind(X)<~>~calm(X))))&
(![X]:((~happy(X)<~>~curious(X))=>old(X)))&
(![X]:(old(X)<=>(old(X)|~strong(X))))&
(![X]:(~kind(X)<=>~patient(X)))&
(![X]:(~patient(X)=>(~humble(X)&brave(X))))&
(![X]:((~happy(X)&curious(X))<=>happy(X)))&
(![X]:((funny(X)|patient(X))=>~happy(X)))&
((wise(paul))<=>(?[X]:(~kind(X))))&
((?[X]:((curious(X)|~wise(X))))<=>((calm(john)|patient(john))))&
(![X]:(quiet(X)=>(curious(X)<~>rich(X))))&
(?[X]:((~tall(X)|humble(X))))&
(?[X]:((funny(X)<~>strong(X))))&
(?[X]:((~tall(X)|quiet(X))))&
(?[X]:((curious(X)<~>generous(X))))&
((generous(paul)<~>~quiet(paul))) | tall(mary) | [
"p2",
"p3",
"p8",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 975717729076622967415259
% SZS output start Proof for 975717729076622967415259
3. ! [X0] : ((curious(X0) & ~happy(X0)) <=> patient(X0)) [input p2]
4. tall(mary) <=> ? [X0] : (~kind(X0) <~> ~generous(X0)) [input p3]
9. ! [X0] : (~kind(X0) <=> ~patient(X0)) [input p8]
11. ! [X0] : ((curious(X0) & ~happy(X0)) <=> happy(X0)) [input p10]
19. ? [X0] : (curious(X0) <~> generous(X0)) [input p18]
21. ~tall(mary) [input hypothesis]
33. ! [X0] : (((curious(X0) & ~happy(X0)) | ~patient(X0)) & (patient(X0) | (~curious(X0) | happy(X0)))) [nnf transformation 3]
34. ! [X0] : (((curious(X0) & ~happy(X0)) | ~patient(X0)) & (patient(X0) | ~curious(X0) | happy(X0))) [flattening 33]
35. (tall(mary) | ! [X0] : ((~kind(X0) | generous(X0)) & (~generous(X0) | kind(X0)))) & (? [X0] : ((generous(X0) | kind(X0)) & (~generous(X0) | ~kind(X0))) | ~tall(mary)) [nnf transformation 4]
36. (tall(mary) | ! [X0] : ((~kind(X0) | generous(X0)) & (~generous(X0) | kind(X0)))) & (? [X1] : ((generous(X1) | kind(X1)) & (~generous(X1) | ~kind(X1))) | ~tall(mary)) [rectify 35]
37. ? [X1] : ((generous(X1) | kind(X1)) & (~generous(X1) | ~kind(X1))) => ((generous(sK0) | kind(sK0)) & (~generous(sK0) | ~kind(sK0))) [choice axiom]
38. (tall(mary) | ! [X0] : ((~kind(X0) | generous(X0)) & (~generous(X0) | kind(X0)))) & (((generous(sK0) | kind(sK0)) & (~generous(sK0) | ~kind(sK0))) | ~tall(mary)) [skolemisation 36,37]
48. ! [X0] : ((~kind(X0) | patient(X0)) & (~patient(X0) | kind(X0))) [nnf transformation 9]
49. ! [X0] : (((curious(X0) & ~happy(X0)) | ~happy(X0)) & (happy(X0) | (~curious(X0) | happy(X0)))) [nnf transformation 11]
50. ! [X0] : (((curious(X0) & ~happy(X0)) | ~happy(X0)) & (happy(X0) | ~curious(X0) | happy(X0))) [flattening 49]
68. ? [X0] : ((~generous(X0) | ~curious(X0)) & (generous(X0) | curious(X0))) [nnf transformation 19]
69. ? [X0] : ((~generous(X0) | ~curious(X0)) & (generous(X0) | curious(X0))) => ((~generous(sK7) | ~curious(sK7)) & (generous(sK7) | curious(sK7))) [choice axiom]
70. (~generous(sK7) | ~curious(sK7)) & (generous(sK7) | curious(sK7)) [skolemisation 68,69]
80. ~patient(X0) | curious(X0) [cnf transformation 34]
83. tall(mary) | ~generous(X0) | kind(X0) [cnf transformation 38]
97. ~kind(X0) | patient(X0) [cnf transformation 48]
100. happy(X0) | ~curious(X0) | happy(X0) [cnf transformation 50]
101. ~happy(X0) | ~happy(X0) [cnf transformation 50]
117. generous(sK7) | curious(sK7) [cnf transformation 70]
121. ~tall(mary) [cnf transformation 21]
122. happy(X0) | ~curious(X0) [duplicate literal removal 100]
123. ~happy(X0) [duplicate literal removal 101]
144. 6 <=> tall(mary) [avatar definition]
149. 7 <=> ! [X0] : (~generous(X0) | kind(X0)) [avatar definition]
150. ~generous(X0) | kind(X0) <- (7) [avatar component clause 149]
151. 7 | 6 [avatar split clause 83,144,149]
188. ~curious(X0) [subsumption resolution 122,123]
251. generous(sK7) [subsumption resolution 117,188]
258. ~6 [avatar split clause 121,144]
265. kind(sK7) <- (7) [resolution 150,251]
267. patient(sK7) <- (7) [resolution 265,97]
270. curious(sK7) <- (7) [resolution 267,80]
272. $false <- (7) [subsumption resolution 270,188]
273. ~7 [avatar contradiction clause 272]
274. $false [avatar sat refutation 151,258,273]
% SZS output end Proof for 975717729076622967415259
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient or not creative then susan is both creative and not quiet and vice versa. Everyone who is not brave is not rich or patient. If someone is either not wise or patient then fred is kind or quiet and vice versa. If someone is either happy or not funny then someone is not old and vice versa. If someone is patient or old then someone is both wise and not kind. If john is both not kind and calm then paul is not funny and vice versa. Everyone who is either old or humble is both happy and not funny and vice versa. Everyone who is happy or strong is tall or not creative and vice versa. If lucy is either not funny or curious then someone is both happy and funny. If someone is both not strong and curious then john is not funny. If someone is both not brave and not old then susan is either brave or not generous and vice versa. Everyone who is either old or curious is both quiet and not brave. Everyone who is both not kind and not quiet is both old and not calm and vice versa. Everyone who is wise is funny and vice versa. Everyone who is both not creative and not old is either strong or funny and vice versa. Everyone who is funny is both not creative and old. Fred is both not wise and strong. Someone is both not tall and not happy. Paul is either kind or funny. Fred is rich or wise. Someone is both creative and not humble. Someone is not generous. Lucy is kind. | Susan is strong. | contradiction | ((?[X]:((~patient(X)|~creative(X))))<=>((creative(susan)&~quiet(susan))))&
(![X]:(~brave(X)=>(~rich(X)|patient(X))))&
((?[X]:((~wise(X)<~>patient(X))))<=>((kind(fred)|quiet(fred))))&
((?[X]:((happy(X)<~>~funny(X))))<=>(?[X]:(~old(X))))&
((?[X]:((patient(X)|old(X))))=>(?[X]:((wise(X)&~kind(X)))))&
(((~kind(john)&calm(john)))<=>(~funny(paul)))&
(![X]:((old(X)<~>humble(X))<=>(happy(X)&~funny(X))))&
(![X]:((happy(X)|strong(X))<=>(tall(X)|~creative(X))))&
(((~funny(lucy)<~>curious(lucy)))=>(?[X]:((happy(X)&funny(X)))))&
((?[X]:((~strong(X)&curious(X))))=>(~funny(john)))&
((?[X]:((~brave(X)&~old(X))))<=>((brave(susan)<~>~generous(susan))))&
(![X]:((old(X)<~>curious(X))=>(quiet(X)&~brave(X))))&
(![X]:((~kind(X)&~quiet(X))<=>(old(X)&~calm(X))))&
(![X]:(wise(X)<=>funny(X)))&
(![X]:((~creative(X)&~old(X))<=>(strong(X)<~>funny(X))))&
(![X]:(funny(X)=>(~creative(X)&old(X))))&
((~wise(fred)&strong(fred)))&
(?[X]:((~tall(X)&~happy(X))))&
((kind(paul)<~>funny(paul)))&
((rich(fred)|wise(fred)))&
(?[X]:((creative(X)&~humble(X))))&
(?[X]:(~generous(X)))&
(kind(lucy)) | strong(susan) | [
"p0",
"p13",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7562653219375896986362267
% SZS output start Proof for 7562653219375896986362267
1. ? [X0] : (~creative(X0) | ~patient(X0)) <=> (~quiet(susan) & creative(susan)) [input p0]
14. ! [X0] : (wise(X0) <=> funny(X0)) [input p13]
15. ! [X0] : ((~old(X0) & ~creative(X0)) <=> (strong(X0) <~> funny(X0))) [input p14]
16. ! [X0] : (funny(X0) => (old(X0) & ~creative(X0))) [input p15]
17. strong(fred) & ~wise(fred) [input p16]
24. strong(susan) [input hypothesis]
33. ! [X0] : ((old(X0) & ~creative(X0)) | ~funny(X0)) [ennf transformation 16]
34. (? [X0] : (~creative(X0) | ~patient(X0)) | (quiet(susan) | ~creative(susan))) & ((~quiet(susan) & creative(susan)) | ! [X0] : (creative(X0) & patient(X0))) [nnf transformation 1]
35. (? [X0] : (~creative(X0) | ~patient(X0)) | quiet(susan) | ~creative(susan)) & ((~quiet(susan) & creative(susan)) | ! [X0] : (creative(X0) & patient(X0))) [flattening 34]
36. (? [X0] : (~creative(X0) | ~patient(X0)) | quiet(susan) | ~creative(susan)) & ((~quiet(susan) & creative(susan)) | ! [X1] : (creative(X1) & patient(X1))) [rectify 35]
37. ? [X0] : (~creative(X0) | ~patient(X0)) => (~creative(sK0) | ~patient(sK0)) [choice axiom]
38. ((~creative(sK0) | ~patient(sK0)) | quiet(susan) | ~creative(susan)) & ((~quiet(susan) & creative(susan)) | ! [X1] : (creative(X1) & patient(X1))) [skolemisation 36,37]
68. ! [X0] : ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0))) [nnf transformation 14]
69. ! [X0] : (((~old(X0) & ~creative(X0)) | ((strong(X0) | ~funny(X0)) & (funny(X0) | ~strong(X0)))) & (((~funny(X0) | ~strong(X0)) & (funny(X0) | strong(X0))) | (old(X0) | creative(X0)))) [nnf transformation 15]
70. ! [X0] : (((~old(X0) & ~creative(X0)) | ((strong(X0) | ~funny(X0)) & (funny(X0) | ~strong(X0)))) & (((~funny(X0) | ~strong(X0)) & (funny(X0) | strong(X0))) | old(X0) | creative(X0))) [flattening 69]
79. creative(susan) | creative(X1) [cnf transformation 38]
131. ~funny(X0) | wise(X0) [cnf transformation 68]
134. ~strong(X0) | funny(X0) | ~creative(X0) [cnf transformation 70]
138. ~funny(X0) | ~creative(X0) [cnf transformation 33]
140. ~wise(fred) [cnf transformation 17]
141. strong(fred) [cnf transformation 17]
151. strong(susan) [cnf transformation 24]
153. 1 <=> creative(susan) [avatar definition]
170. 5 <=> ! [X1] : creative(X1) [avatar definition]
171. creative(X1) <- (5) [avatar component clause 170]
177. 5 | 1 [avatar split clause 79,153,170]
374. funny(fred) | ~creative(fred) [resolution 134,141]
375. funny(susan) | ~creative(susan) [resolution 134,151]
377. funny(fred) <- (5) [subsumption resolution 374,171]
381. wise(fred) <- (5) [resolution 377,131]
386. $false <- (5) [subsumption resolution 381,140]
387. ~5 [avatar contradiction clause 386]
388. ~creative(susan) [subsumption resolution 375,138]
389. ~1 [avatar split clause 388,153]
396. $false [avatar sat refutation 177,387,389]
% SZS output end Proof for 7562653219375896986362267
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both funny and not generous then susan is either wise or creative. Everyone who is kind is both not calm and tall and vice versa. Everyone who is not brave or creative is not happy. Everyone who is both brave and rich is quiet or not old and vice versa. Everyone who is both not quiet and funny is quiet or humble. Everyone who is not quiet or calm is creative or not patient and vice versa. If mary is not generous then someone is not old and vice versa. Everyone who is old is quiet. Everyone who is not strong or generous is not happy. If fred is either old or wise then alice is both not calm and not happy. If john is either happy or not brave then someone is not curious or not rich and vice versa. If alice is either creative or not wise then someone is curious and vice versa. Everyone who is rich is not strong or not humble. Everyone who is both strong and rich is not generous or not kind. If susan is funny then someone is not wise or happy and vice versa. Everyone who is both not curious and humble is old or not strong and vice versa. Lucy is either humble or not wise. Alice is both brave and not creative. Someone is either old or not calm. | John is wise. | neutral | (((funny(paul)&~generous(paul)))=>((wise(susan)<~>creative(susan))))&
(![X]:(kind(X)<=>(~calm(X)&tall(X))))&
(![X]:((~brave(X)|creative(X))=>~happy(X)))&
(![X]:((brave(X)&rich(X))<=>(quiet(X)|~old(X))))&
(![X]:((~quiet(X)&funny(X))=>(quiet(X)|humble(X))))&
(![X]:((~quiet(X)|calm(X))<=>(creative(X)|~patient(X))))&
((~generous(mary))<=>(?[X]:(~old(X))))&
(![X]:(old(X)=>quiet(X)))&
(![X]:((~strong(X)|generous(X))=>~happy(X)))&
(((old(fred)<~>wise(fred)))=>((~calm(alice)&~happy(alice))))&
(((happy(john)<~>~brave(john)))<=>(?[X]:((~curious(X)|~rich(X)))))&
(((creative(alice)<~>~wise(alice)))<=>(?[X]:(curious(X))))&
(![X]:(rich(X)=>(~strong(X)|~humble(X))))&
(![X]:((strong(X)&rich(X))=>(~generous(X)|~kind(X))))&
((funny(susan))<=>(?[X]:((~wise(X)|happy(X)))))&
(![X]:((~curious(X)&humble(X))<=>(old(X)|~strong(X))))&
((humble(lucy)<~>~wise(lucy)))&
((brave(alice)&~creative(alice)))&
(?[X]:((old(X)<~>~calm(X)))) | wise(john) | [] | null | 0 |
Everyone who is both not happy and old is strong.
If mary is either tall or calm then someone is either strong or happy.
Everyone who is humble is either wise or rich and vice versa.
If someone is calm or creative then alice is not generous or strong and vice versa.
If lucy is funny then alice is both humble and happy and vice versa.
Everyone who is not tall is calm and vice versa.
If alice is both creative and not generous then someone is both funny and kind and vice versa.
Everyone who is not strong or patient is curious or not happy and vice versa.
Everyone who is both not brave and humble is not quiet.
If lucy is either not rich or old then someone is generous.
Everyone who is not brave or not calm is both not humble and curious and vice versa.
If someone is both tall and curious then fred is both strong and not happy and vice versa.
Everyone who is both calm and not patient is happy or rich and vice versa.
If mary is not humble or humble then lucy is either rich or kind.
If lucy is both patient and old then mary is tall or not rich and vice versa.
Everyone who is both old and generous is kind.
Someone is not funny or strong.
Alice is old or not kind.
Susan is wise.
Paul is not tall or humble.
Susan is not brave.
Mary is both not generous and not brave.
Lucy is patient.
Someone is kind. | Paul is not calm. | contradiction | (![X]:((~happy(X)&old(X))=>strong(X)))&
(((tall(mary)<~>calm(mary)))=>(?[X]:((strong(X)<~>happy(X)))))&
(![X]:(humble(X)<=>(wise(X)<~>rich(X))))&
((?[X]:((calm(X)|creative(X))))<=>((~generous(alice)|strong(alice))))&
((funny(lucy))<=>((humble(alice)&happy(alice))))&
(![X]:(~tall(X)<=>calm(X)))&
(((creative(alice)&~generous(alice)))<=>(?[X]:((funny(X)&kind(X)))))&
(![X]:((~strong(X)|patient(X))<=>(curious(X)|~happy(X))))&
(![X]:((~brave(X)&humble(X))=>~quiet(X)))&
(((~rich(lucy)<~>old(lucy)))=>(?[X]:(generous(X))))&
(![X]:((~brave(X)|~calm(X))<=>(~humble(X)&curious(X))))&
((?[X]:((tall(X)&curious(X))))<=>((strong(fred)&~happy(fred))))&
(![X]:((calm(X)&~patient(X))<=>(happy(X)|rich(X))))&
(((~humble(mary)|humble(mary)))=>((rich(lucy)<~>kind(lucy))))&
(((patient(lucy)&old(lucy)))<=>((tall(mary)|~rich(mary))))&
(![X]:((old(X)&generous(X))=>kind(X)))&
(?[X]:((~funny(X)|strong(X))))&
((old(alice)|~kind(alice)))&
(wise(susan))&
((~tall(paul)|humble(paul)))&
(~brave(susan))&
((~generous(mary)&~brave(mary)))&
(patient(lucy))&
(?[X]:(kind(X))) | ~calm(paul) | [
"p5",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1378256219292190624395448
% SZS output start Proof for 1378256219292190624395448
6. ! [X0] : (~tall(X0) <=> calm(X0)) [input p5]
11. ! [X0] : ((~calm(X0) | ~brave(X0)) <=> (curious(X0) & ~humble(X0))) [input p10]
20. humble(paul) | ~tall(paul) [input p19]
25. ~calm(paul) [input hypothesis]
45. ! [X0] : ((~tall(X0) | ~calm(X0)) & (calm(X0) | tall(X0))) [nnf transformation 6]
56. ! [X0] : (((~calm(X0) | ~brave(X0)) | (~curious(X0) | humble(X0))) & ((curious(X0) & ~humble(X0)) | (calm(X0) & brave(X0)))) [nnf transformation 11]
57. ! [X0] : ((~calm(X0) | ~brave(X0) | ~curious(X0) | humble(X0)) & ((curious(X0) & ~humble(X0)) | (calm(X0) & brave(X0)))) [flattening 56]
88. calm(X0) | tall(X0) [cnf transformation 45]
101. ~humble(X0) | calm(X0) [cnf transformation 57]
127. humble(paul) | ~tall(paul) [cnf transformation 20]
133. ~calm(paul) [cnf transformation 25]
295. 34 <=> tall(paul) [avatar definition]
299. 35 <=> humble(paul) [avatar definition]
301. humble(paul) <- (35) [avatar component clause 299]
302. ~34 | 35 [avatar split clause 127,299,295]
304. tall(paul) [resolution 88,133]
310. 34 [avatar split clause 304,295]
315. calm(paul) <- (35) [resolution 101,301]
316. $false <- (35) [subsumption resolution 315,133]
317. ~35 [avatar contradiction clause 316]
318. $false [avatar sat refutation 302,310,317]
% SZS output end Proof for 1378256219292190624395448
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and strong is not funny and vice versa.
Everyone who is both not creative and calm is not brave or not kind.
If alice is generous or not calm then someone is both not funny and quiet and vice versa.
Everyone who is not strong or curious is either kind or happy and vice versa.
Everyone who is both happy and not humble is not brave or not humble and vice versa.
Everyone who is both curious and rich is generous.
Everyone who is either patient or not curious is both humble and happy and vice versa.
Everyone who is not strong is either creative or calm.
If alice is both humble and curious then someone is both not happy and not old and vice versa.
Everyone who is either not old or not quiet is not kind and vice versa.
Everyone who is both not strong and not humble is either funny or not wise.
Everyone who is not old or not kind is either quiet or not calm and vice versa.
If fred is both rich and not calm then someone is patient and vice versa.
Everyone who is either humble or creative is patient.
If alice is funny or patient then alice is happy.
If john is strong or not generous then alice is not funny and vice versa.
Fred is either funny or not brave.
John is not wise or generous.
Someone is both not creative and curious.
Susan is not old.
Someone is both curious and not rich.
Someone is generous or calm.
Mary is patient or funny.
Someone is either wise or not rich. | Alice is patient. | neutral | (![X]:((~curious(X)&strong(X))<=>~funny(X)))&
(![X]:((~creative(X)&calm(X))=>(~brave(X)|~kind(X))))&
(((generous(alice)|~calm(alice)))<=>(?[X]:((~funny(X)&quiet(X)))))&
(![X]:((~strong(X)|curious(X))<=>(kind(X)<~>happy(X))))&
(![X]:((happy(X)&~humble(X))<=>(~brave(X)|~humble(X))))&
(![X]:((curious(X)&rich(X))=>generous(X)))&
(![X]:((patient(X)<~>~curious(X))<=>(humble(X)&happy(X))))&
(![X]:(~strong(X)=>(creative(X)<~>calm(X))))&
(((humble(alice)&curious(alice)))<=>(?[X]:((~happy(X)&~old(X)))))&
(![X]:((~old(X)<~>~quiet(X))<=>~kind(X)))&
(![X]:((~strong(X)&~humble(X))=>(funny(X)<~>~wise(X))))&
(![X]:((~old(X)|~kind(X))<=>(quiet(X)<~>~calm(X))))&
(((rich(fred)&~calm(fred)))<=>(?[X]:(patient(X))))&
(![X]:((humble(X)<~>creative(X))=>patient(X)))&
(((funny(alice)|patient(alice)))=>(happy(alice)))&
(((strong(john)|~generous(john)))<=>(~funny(alice)))&
((funny(fred)<~>~brave(fred)))&
((~wise(john)|generous(john)))&
(?[X]:((~creative(X)&curious(X))))&
(~old(susan))&
(?[X]:((curious(X)&~rich(X))))&
(?[X]:((generous(X)|calm(X))))&
((patient(mary)|funny(mary)))&
(?[X]:((wise(X)<~>~rich(X)))) | patient(alice) | [] | null | 0 |
Everyone who is both not strong and rich is not creative and vice versa.
Everyone who is not tall is either quiet or curious.
If alice is not tall then alice is not kind and vice versa.
Everyone who is both humble and not strong is generous or calm and vice versa.
Everyone who is both not old and not generous is happy or not strong and vice versa.
If someone is old or not brave then paul is happy or not kind.
Everyone who is either not patient or not curious is funny or not generous and vice versa.
If someone is both not generous and not wise then alice is either not brave or not strong and vice versa.
If john is not happy or old then someone is not old.
If someone is not creative then someone is both not patient and rich and vice versa.
Everyone who is both not patient and calm is both not happy and strong.
If someone is not brave or not patient then paul is not curious.
If someone is brave then john is both not wise and generous.
If john is not wise then someone is not calm or kind and vice versa.
If someone is both not rich and old then fred is calm and vice versa.
Everyone who is either not brave or not quiet is both wise and old.
Lucy is either kind or not creative.
Someone is both curious and funny.
Lucy is either not tall or wise.
Paul is either happy or not humble.
Someone is either kind or not creative.
Susan is either not quiet or not wise.
Fred is not patient or funny. | Alice is not generous. | entailment | (![X]:((~strong(X)&rich(X))<=>~creative(X)))&
(![X]:(~tall(X)=>(quiet(X)<~>curious(X))))&
((~tall(alice))<=>(~kind(alice)))&
(![X]:((humble(X)&~strong(X))<=>(generous(X)|calm(X))))&
(![X]:((~old(X)&~generous(X))<=>(happy(X)|~strong(X))))&
((?[X]:((old(X)|~brave(X))))=>((happy(paul)|~kind(paul))))&
(![X]:((~patient(X)<~>~curious(X))<=>(funny(X)|~generous(X))))&
((?[X]:((~generous(X)&~wise(X))))<=>((~brave(alice)<~>~strong(alice))))&
(((~happy(john)|old(john)))=>(?[X]:(~old(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~patient(X)&rich(X)))))&
(![X]:((~patient(X)&calm(X))=>(~happy(X)&strong(X))))&
((?[X]:((~brave(X)|~patient(X))))=>(~curious(paul)))&
((?[X]:(brave(X)))=>((~wise(john)&generous(john))))&
((~wise(john))<=>(?[X]:((~calm(X)|kind(X)))))&
((?[X]:((~rich(X)&old(X))))<=>(calm(fred)))&
(![X]:((~brave(X)<~>~quiet(X))=>(wise(X)&old(X))))&
((kind(lucy)<~>~creative(lucy)))&
(?[X]:((curious(X)&funny(X))))&
((~tall(lucy)<~>wise(lucy)))&
((happy(paul)<~>~humble(paul)))&
(?[X]:((kind(X)<~>~creative(X))))&
((~quiet(susan)<~>~wise(susan)))&
((~patient(fred)|funny(fred))) | ~generous(alice) | [
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 9121678224748763729113459
% SZS output start Proof for 9121678224748763729113459
4. ! [X0] : ((~strong(X0) & humble(X0)) <=> (calm(X0) | generous(X0))) [input p3]
5. ! [X0] : ((~generous(X0) & ~old(X0)) <=> (~strong(X0) | happy(X0))) [input p4]
24. generous(alice) [input hypothesis]
39. ! [X0] : (((~strong(X0) & humble(X0)) | (~calm(X0) & ~generous(X0))) & ((calm(X0) | generous(X0)) | (strong(X0) | ~humble(X0)))) [nnf transformation 4]
40. ! [X0] : (((~strong(X0) & humble(X0)) | (~calm(X0) & ~generous(X0))) & (calm(X0) | generous(X0) | strong(X0) | ~humble(X0))) [flattening 39]
41. ! [X0] : (((~generous(X0) & ~old(X0)) | (strong(X0) & ~happy(X0))) & ((~strong(X0) | happy(X0)) | (generous(X0) | old(X0)))) [nnf transformation 5]
42. ! [X0] : (((~generous(X0) & ~old(X0)) | (strong(X0) & ~happy(X0))) & (~strong(X0) | happy(X0) | generous(X0) | old(X0))) [flattening 41]
84. ~strong(X0) | ~generous(X0) [cnf transformation 40]
90. ~generous(X0) | strong(X0) [cnf transformation 42]
139. generous(alice) [cnf transformation 24]
150. ~generous(X0) [subsumption resolution 90,84]
325. $false [subsumption resolution 139,150]
% SZS output end Proof for 9121678224748763729113459
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not humble and not creative then susan is tall or funny.
If fred is either not kind or not generous then someone is not calm.
If someone is patient or not generous then susan is either not rich or not strong and vice versa.
Everyone who is quiet is both not old and rich.
If lucy is both not calm and generous then someone is both happy and not humble.
Everyone who is not quiet is both tall and not humble.
Everyone who is both not humble and happy is both patient and humble.
If fred is both not old and not patient then someone is not funny and vice versa.
If someone is not calm or not happy then fred is not patient or funny and vice versa.
If alice is both strong and not strong then someone is both calm and not generous.
Everyone who is both humble and creative is rich and vice versa.
If alice is both quiet and not tall then someone is not old.
Everyone who is either creative or calm is happy or not wise.
If susan is curious or creative then susan is not happy or wise.
If someone is not quiet or rich then someone is both old and calm and vice versa.
Everyone who is not happy or not tall is not wise or old and vice versa.
Someone is both not kind and brave.
Fred is not quiet or not brave.
Mary is curious.
Someone is not curious or rich.
Fred is both wise and not curious.
Fred is either not humble or brave.
Someone is quiet.
Lucy is not strong or not old. | Fred is rich. | contradiction | ((?[X]:((~humble(X)&~creative(X))))=>((tall(susan)|funny(susan))))&
(((~kind(fred)<~>~generous(fred)))=>(?[X]:(~calm(X))))&
((?[X]:((patient(X)|~generous(X))))<=>((~rich(susan)<~>~strong(susan))))&
(![X]:(quiet(X)=>(~old(X)&rich(X))))&
(((~calm(lucy)&generous(lucy)))=>(?[X]:((happy(X)&~humble(X)))))&
(![X]:(~quiet(X)=>(tall(X)&~humble(X))))&
(![X]:((~humble(X)&happy(X))=>(patient(X)&humble(X))))&
(((~old(fred)&~patient(fred)))<=>(?[X]:(~funny(X))))&
((?[X]:((~calm(X)|~happy(X))))<=>((~patient(fred)|funny(fred))))&
(((strong(alice)&~strong(alice)))=>(?[X]:((calm(X)&~generous(X)))))&
(![X]:((humble(X)&creative(X))<=>rich(X)))&
(((quiet(alice)&~tall(alice)))=>(?[X]:(~old(X))))&
(![X]:((creative(X)<~>calm(X))=>(happy(X)|~wise(X))))&
(((curious(susan)|creative(susan)))=>((~happy(susan)|wise(susan))))&
((?[X]:((~quiet(X)|rich(X))))<=>(?[X]:((old(X)&calm(X)))))&
(![X]:((~happy(X)|~tall(X))<=>(~wise(X)|old(X))))&
(?[X]:((~kind(X)&brave(X))))&
((~quiet(fred)|~brave(fred)))&
(curious(mary))&
(?[X]:((~curious(X)|rich(X))))&
((wise(fred)&~curious(fred)))&
((~humble(fred)<~>brave(fred)))&
(?[X]:(quiet(X)))&
((~strong(lucy)|~old(lucy))) | rich(fred) | [
"p5",
"p10",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7574208089681607893517361
% SZS output start Proof for 7574208089681607893517361
6. ! [X0] : (~quiet(X0) => (~humble(X0) & tall(X0))) [input p5]
11. ! [X0] : ((creative(X0) & humble(X0)) <=> rich(X0)) [input p10]
18. ~brave(fred) | ~quiet(fred) [input p17]
22. ~humble(fred) <~> brave(fred) [input p21]
25. rich(fred) [input hypothesis]
33. ! [X0] : ((~humble(X0) & tall(X0)) | quiet(X0)) [ennf transformation 6]
65. ! [X0] : (((creative(X0) & humble(X0)) | ~rich(X0)) & (rich(X0) | (~creative(X0) | ~humble(X0)))) [nnf transformation 11]
66. ! [X0] : (((creative(X0) & humble(X0)) | ~rich(X0)) & (rich(X0) | ~creative(X0) | ~humble(X0))) [flattening 65]
81. (~brave(fred) | humble(fred)) & (brave(fred) | ~humble(fred)) [nnf transformation 22]
98. ~humble(X0) | quiet(X0) [cnf transformation 33]
111. ~rich(X0) | humble(X0) [cnf transformation 66]
129. ~brave(fred) | ~quiet(fred) [cnf transformation 18]
134. brave(fred) | ~humble(fred) [cnf transformation 81]
138. rich(fred) [cnf transformation 25]
299. 36 <=> quiet(fred) [avatar definition]
301. ~quiet(fred) <- (~36) [avatar component clause 299]
303. 37 <=> brave(fred) [avatar definition]
306. ~36 | ~37 [avatar split clause 129,303,299]
317. 40 <=> humble(fred) [avatar definition]
319. humble(fred) <- (40) [avatar component clause 317]
321. ~40 | 37 [avatar split clause 134,303,317]
339. humble(fred) [resolution 111,138]
343. 40 [avatar split clause 339,317]
345. quiet(fred) <- (40) [resolution 319,98]
346. $false <- (~36, 40) [subsumption resolution 345,301]
347. 36 | ~40 [avatar contradiction clause 346]
348. $false [avatar sat refutation 306,321,343,347]
% SZS output end Proof for 7574208089681607893517361
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is both brave and tall.
If john is tall then lucy is both not wise and not kind.
Everyone who is both patient and happy is not calm or humble and vice versa.
If someone is both generous and not old then lucy is rich.
If mary is either not brave or not wise then someone is both not patient and not tall.
If someone is strong then someone is happy or not brave.
Everyone who is not curious or strong is either not humble or not brave.
Everyone who is not strong or tall is both quiet and tall.
Everyone who is kind or not curious is both patient and generous and vice versa.
Everyone who is not generous or curious is funny.
Everyone who is either not quiet or not patient is strong or wise and vice versa.
If fred is both patient and wise then fred is both not quiet and not funny.
Everyone who is not strong or tall is both happy and tall.
Everyone who is both brave and rich is not creative.
Everyone who is creative or not creative is not curious or not tall and vice versa.
If paul is either humble or funny then someone is either not wise or humble and vice versa.
Someone is both creative and tall.
Mary is happy.
Paul is both not generous and strong.
Fred is not quiet or brave.
Someone is both creative and generous.
Someone is tall.
John is both not quiet and generous. | Paul is not brave. | entailment | (![X]:(~humble(X)=>(brave(X)&tall(X))))&
((tall(john))=>((~wise(lucy)&~kind(lucy))))&
(![X]:((patient(X)&happy(X))<=>(~calm(X)|humble(X))))&
((?[X]:((generous(X)&~old(X))))=>(rich(lucy)))&
(((~brave(mary)<~>~wise(mary)))=>(?[X]:((~patient(X)&~tall(X)))))&
((?[X]:(strong(X)))=>(?[X]:((happy(X)|~brave(X)))))&
(![X]:((~curious(X)|strong(X))=>(~humble(X)<~>~brave(X))))&
(![X]:((~strong(X)|tall(X))=>(quiet(X)&tall(X))))&
(![X]:((kind(X)|~curious(X))<=>(patient(X)&generous(X))))&
(![X]:((~generous(X)|curious(X))=>funny(X)))&
(![X]:((~quiet(X)<~>~patient(X))<=>(strong(X)|wise(X))))&
(((patient(fred)&wise(fred)))=>((~quiet(fred)&~funny(fred))))&
(![X]:((~strong(X)|tall(X))=>(happy(X)&tall(X))))&
(![X]:((brave(X)&rich(X))=>~creative(X)))&
(![X]:((creative(X)|~creative(X))<=>(~curious(X)|~tall(X))))&
(((humble(paul)<~>funny(paul)))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(?[X]:((creative(X)&tall(X))))&
(happy(mary))&
((~generous(paul)&strong(paul)))&
((~quiet(fred)|brave(fred)))&
(?[X]:((creative(X)&generous(X))))&
(?[X]:(tall(X)))&
((~quiet(john)&generous(john))) | ~brave(paul) | [
"p0",
"p6",
"p7",
"p8",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 727238903944823320465765
% SZS output start Proof for 727238903944823320465765
1. ! [X0] : (~humble(X0) => (tall(X0) & brave(X0))) [input p0]
7. ! [X0] : ((strong(X0) | ~curious(X0)) => (~humble(X0) <~> ~brave(X0))) [input p6]
8. ! [X0] : ((tall(X0) | ~strong(X0)) => (tall(X0) & quiet(X0))) [input p7]
9. ! [X0] : ((~curious(X0) | kind(X0)) <=> (generous(X0) & patient(X0))) [input p8]
15. ! [X0] : ((~creative(X0) | creative(X0)) <=> (~tall(X0) | ~curious(X0))) [input p14]
19. strong(paul) & ~generous(paul) [input p18]
24. brave(paul) [input hypothesis]
28. ! [X0] : ((tall(X0) & brave(X0)) | humble(X0)) [ennf transformation 1]
32. ! [X0] : ((~humble(X0) <~> ~brave(X0)) | (~strong(X0) & curious(X0))) [ennf transformation 7]
33. ! [X0] : ((tall(X0) & quiet(X0)) | (~tall(X0) & strong(X0))) [ennf transformation 8]
46. ! [X0] : (((brave(X0) | humble(X0)) & (~brave(X0) | ~humble(X0))) | (~strong(X0) & curious(X0))) [nnf transformation 32]
47. ! [X0] : (((~curious(X0) | kind(X0)) | (~generous(X0) | ~patient(X0))) & ((generous(X0) & patient(X0)) | (curious(X0) & ~kind(X0)))) [nnf transformation 9]
48. ! [X0] : ((~curious(X0) | kind(X0) | ~generous(X0) | ~patient(X0)) & ((generous(X0) & patient(X0)) | (curious(X0) & ~kind(X0)))) [flattening 47]
51. ! [X0] : (((~creative(X0) | creative(X0)) | (tall(X0) & curious(X0))) & ((~tall(X0) | ~curious(X0)) | (creative(X0) & ~creative(X0)))) [nnf transformation 15]
52. ! [X0] : ((~creative(X0) | creative(X0) | (tall(X0) & curious(X0))) & (~tall(X0) | ~curious(X0) | (creative(X0) & ~creative(X0)))) [flattening 51]
64. tall(X0) | humble(X0) [cnf transformation 28]
78. ~strong(X0) | ~humble(X0) | ~brave(X0) [cnf transformation 46]
83. strong(X0) | tall(X0) [cnf transformation 33]
88. curious(X0) | generous(X0) [cnf transformation 48]
104. ~tall(X0) | ~curious(X0) | ~creative(X0) [cnf transformation 52]
105. ~curious(X0) | ~tall(X0) | creative(X0) [cnf transformation 52]
119. ~generous(paul) [cnf transformation 19]
127. brave(paul) [cnf transformation 24]
189. ~curious(X0) | ~tall(X0) [subsumption resolution 104,105]
259. ~tall(X0) | generous(X0) [resolution 189,88]
264. ~humble(X1) | ~brave(X1) | tall(X1) [resolution 78,83]
268. ~brave(X1) | tall(X1) [subsumption resolution 264,64]
360. tall(paul) [resolution 268,127]
380. generous(paul) [resolution 360,259]
383. $false [subsumption resolution 380,119]
% SZS output end Proof for 727238903944823320465765
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and funny is wise or patient. Everyone who is both creative and kind is not happy. If someone is strong then someone is creative and vice versa. If someone is either quiet or calm then someone is either not wise or not curious and vice versa. Everyone who is either tall or funny is both not curious and not funny. Everyone who is not calm or not rich is either rich or tall and vice versa. If someone is not wise then fred is not old and vice versa. Everyone who is both curious and not rich is not creative or not calm and vice versa. If paul is either not tall or not brave then john is either not creative or not tall. Everyone who is either generous or not happy is old or generous and vice versa. Everyone who is both humble and brave is either happy or tall and vice versa. If someone is calm then someone is strong or patient and vice versa. If alice is either creative or brave then mary is either not generous or kind. Everyone who is both old and not curious is brave. Everyone who is not humble or quiet is both not funny and not kind. Everyone who is both rich and not patient is humble or rich and vice versa. Someone is not strong. Alice is brave. Paul is both not kind and old. Paul is quiet. Someone is creative. Someone is not funny. Someone is both not strong and not rich. Susan is both not humble and tall. | John is calm. | entailment | (![X]:((wise(X)&funny(X))=>(wise(X)|patient(X))))&
(![X]:((creative(X)&kind(X))=>~happy(X)))&
((?[X]:(strong(X)))<=>(?[X]:(creative(X))))&
((?[X]:((quiet(X)<~>calm(X))))<=>(?[X]:((~wise(X)<~>~curious(X)))))&
(![X]:((tall(X)<~>funny(X))=>(~curious(X)&~funny(X))))&
(![X]:((~calm(X)|~rich(X))<=>(rich(X)<~>tall(X))))&
((?[X]:(~wise(X)))<=>(~old(fred)))&
(![X]:((curious(X)&~rich(X))<=>(~creative(X)|~calm(X))))&
(((~tall(paul)<~>~brave(paul)))=>((~creative(john)<~>~tall(john))))&
(![X]:((generous(X)<~>~happy(X))<=>(old(X)|generous(X))))&
(![X]:((humble(X)&brave(X))<=>(happy(X)<~>tall(X))))&
((?[X]:(calm(X)))<=>(?[X]:((strong(X)|patient(X)))))&
(((creative(alice)<~>brave(alice)))=>((~generous(mary)<~>kind(mary))))&
(![X]:((old(X)&~curious(X))=>brave(X)))&
(![X]:((~humble(X)|quiet(X))=>(~funny(X)&~kind(X))))&
(![X]:((rich(X)&~patient(X))<=>(humble(X)|rich(X))))&
(?[X]:(~strong(X)))&
(brave(alice))&
((~kind(paul)&old(paul)))&
(quiet(paul))&
(?[X]:(creative(X)))&
(?[X]:(~funny(X)))&
(?[X]:((~strong(X)&~rich(X))))&
((~humble(susan)&tall(susan))) | calm(john) | [
"p4",
"p5",
"p7",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8663232765823548166996246
% SZS output start Proof for 8663232765823548166996246
5. ! [X0] : ((tall(X0) <~> funny(X0)) => (~funny(X0) & ~curious(X0))) [input p4]
6. ! [X0] : ((~rich(X0) | ~calm(X0)) <=> (rich(X0) <~> tall(X0))) [input p5]
8. ! [X0] : ((~rich(X0) & curious(X0)) <=> (~calm(X0) | ~creative(X0))) [input p7]
15. ! [X0] : ((quiet(X0) | ~humble(X0)) => (~kind(X0) & ~funny(X0))) [input p14]
16. ! [X0] : ((~patient(X0) & rich(X0)) <=> (rich(X0) | humble(X0))) [input p15]
25. ~calm(john) [input hypothesis]
33. ! [X0] : ((~funny(X0) & ~curious(X0)) | (tall(X0) <=> funny(X0))) [ennf transformation 5]
38. ! [X0] : ((~kind(X0) & ~funny(X0)) | (~quiet(X0) & humble(X0))) [ennf transformation 15]
49. ! [X0] : ((~funny(X0) & ~curious(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) [nnf transformation 33]
50. ! [X0] : (((~rich(X0) | ~calm(X0)) | ((rich(X0) | ~tall(X0)) & (tall(X0) | ~rich(X0)))) & (((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | (rich(X0) & calm(X0)))) [nnf transformation 6]
51. ! [X0] : ((~rich(X0) | ~calm(X0) | ((rich(X0) | ~tall(X0)) & (tall(X0) | ~rich(X0)))) & (((~tall(X0) | ~rich(X0)) & (tall(X0) | rich(X0))) | (rich(X0) & calm(X0)))) [flattening 50]
56. ! [X0] : (((~rich(X0) & curious(X0)) | (calm(X0) & creative(X0))) & ((~calm(X0) | ~creative(X0)) | (rich(X0) | ~curious(X0)))) [nnf transformation 8]
57. ! [X0] : (((~rich(X0) & curious(X0)) | (calm(X0) & creative(X0))) & (~calm(X0) | ~creative(X0) | rich(X0) | ~curious(X0))) [flattening 56]
69. ! [X0] : (((~patient(X0) & rich(X0)) | (~rich(X0) & ~humble(X0))) & ((rich(X0) | humble(X0)) | (patient(X0) | ~rich(X0)))) [nnf transformation 16]
70. ! [X0] : (((~patient(X0) & rich(X0)) | (~rich(X0) & ~humble(X0))) & (rich(X0) | humble(X0) | patient(X0) | ~rich(X0))) [flattening 69]
91. ~tall(X0) | funny(X0) | ~curious(X0) [cnf transformation 49]
96. tall(X0) | rich(X0) | rich(X0) [cnf transformation 51]
97. ~rich(X0) | ~tall(X0) | calm(X0) [cnf transformation 51]
99. ~rich(X0) | ~calm(X0) | tall(X0) | ~rich(X0) [cnf transformation 51]
105. curious(X0) | calm(X0) [cnf transformation 57]
107. ~rich(X0) | calm(X0) [cnf transformation 57]
132. ~funny(X0) | humble(X0) [cnf transformation 38]
137. ~humble(X0) | rich(X0) [cnf transformation 70]
152. ~calm(john) [cnf transformation 25]
155. rich(X0) | tall(X0) [duplicate literal removal 96]
156. ~rich(X0) | ~calm(X0) | tall(X0) [duplicate literal removal 99]
300. tall(X1) | calm(X1) [resolution 155,107]
409. ~calm(X0) | tall(X0) | tall(X0) [resolution 156,155]
410. ~calm(X0) | tall(X0) [duplicate literal removal 409]
411. tall(X0) [subsumption resolution 410,300]
415. ~curious(X2) | funny(X2) [resolution 411,91]
462. calm(X0) | funny(X0) [resolution 415,105]
481. funny(john) [resolution 462,152]
486. humble(john) [resolution 481,132]
494. rich(john) [resolution 486,137]
508. ~tall(john) | calm(john) [resolution 494,97]
512. calm(john) [subsumption resolution 508,411]
513. $false [subsumption resolution 512,152]
% SZS output end Proof for 8663232765823548166996246
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not brave is happy and vice versa. If lucy is not old then someone is brave or patient and vice versa. If fred is both not creative and not strong then john is humble or not tall. Everyone who is not old or rich is not tall. Everyone who is not rich is both old and creative and vice versa. Everyone who is either brave or not wise is either not quiet or strong and vice versa. If paul is both old and humble then fred is not curious or quiet and vice versa. If someone is not brave or old then someone is either calm or creative. Everyone who is old is either not wise or rich. Everyone who is either patient or not brave is not happy or brave and vice versa. Everyone who is brave is funny or not old. Everyone who is brave is both happy and old and vice versa. If susan is either wise or not strong then lucy is both not humble and not funny. If someone is either brave or calm then someone is strong or not creative. If john is tall then fred is either not kind or tall. Someone is both kind and not wise. Susan is not tall. Lucy is either creative or not creative. Someone is both not creative and not humble. Someone is not strong or not creative. Lucy is funny or happy. | Paul is quiet. | neutral | (![X]:((~patient(X)|~brave(X))<=>happy(X)))&
((~old(lucy))<=>(?[X]:((brave(X)|patient(X)))))&
(((~creative(fred)&~strong(fred)))=>((humble(john)|~tall(john))))&
(![X]:((~old(X)|rich(X))=>~tall(X)))&
(![X]:(~rich(X)<=>(old(X)&creative(X))))&
(![X]:((brave(X)<~>~wise(X))<=>(~quiet(X)<~>strong(X))))&
(((old(paul)&humble(paul)))<=>((~curious(fred)|quiet(fred))))&
((?[X]:((~brave(X)|old(X))))=>(?[X]:((calm(X)<~>creative(X)))))&
(![X]:(old(X)=>(~wise(X)<~>rich(X))))&
(![X]:((patient(X)<~>~brave(X))<=>(~happy(X)|brave(X))))&
(![X]:(brave(X)=>(funny(X)|~old(X))))&
(![X]:(brave(X)<=>(happy(X)&old(X))))&
(((wise(susan)<~>~strong(susan)))=>((~humble(lucy)&~funny(lucy))))&
((?[X]:((brave(X)<~>calm(X))))=>(?[X]:((strong(X)|~creative(X)))))&
((tall(john))=>((~kind(fred)<~>tall(fred))))&
(?[X]:((kind(X)&~wise(X))))&
(~tall(susan))&
((creative(lucy)<~>~creative(lucy)))&
(?[X]:((~creative(X)&~humble(X))))&
(?[X]:((~strong(X)|~creative(X))))&
((funny(lucy)|happy(lucy))) | quiet(paul) | [] | null | 0 |
If mary is brave then someone is not happy or not calm and vice versa.
Everyone who is not creative or not wise is both not old and happy and vice versa.
Everyone who is either not strong or generous is not patient.
If someone is patient or calm then someone is old.
Everyone who is calm or strong is kind and vice versa.
If someone is either not strong or tall then someone is either not funny or brave and vice versa.
If susan is kind or tall then susan is not strong and vice versa.
If someone is both calm and kind then someone is both not generous and not curious and vice versa.
Everyone who is not humble or strong is both quiet and not calm.
Everyone who is not strong is brave or not old.
Everyone who is not strong or happy is not quiet and vice versa.
If someone is not happy or strong then someone is both creative and not tall and vice versa.
If someone is both not funny and creative then someone is both wise and tall and vice versa.
Everyone who is not patient is both humble and funny and vice versa.
Everyone who is both rich and patient is wise or curious and vice versa.
Everyone who is either not quiet or not humble is either funny or not humble.
Fred is not calm.
Someone is either not wise or curious.
Someone is either calm or not rich.
Alice is both quiet and not brave.
Someone is both not funny and not brave.
Someone is calm.
Someone is either wise or humble.
Susan is both not rich and tall. | Fred is not strong. | neutral | ((brave(mary))<=>(?[X]:((~happy(X)|~calm(X)))))&
(![X]:((~creative(X)|~wise(X))<=>(~old(X)&happy(X))))&
(![X]:((~strong(X)<~>generous(X))=>~patient(X)))&
((?[X]:((patient(X)|calm(X))))=>(?[X]:(old(X))))&
(![X]:((calm(X)|strong(X))<=>kind(X)))&
((?[X]:((~strong(X)<~>tall(X))))<=>(?[X]:((~funny(X)<~>brave(X)))))&
(((kind(susan)|tall(susan)))<=>(~strong(susan)))&
((?[X]:((calm(X)&kind(X))))<=>(?[X]:((~generous(X)&~curious(X)))))&
(![X]:((~humble(X)|strong(X))=>(quiet(X)&~calm(X))))&
(![X]:(~strong(X)=>(brave(X)|~old(X))))&
(![X]:((~strong(X)|happy(X))<=>~quiet(X)))&
((?[X]:((~happy(X)|strong(X))))<=>(?[X]:((creative(X)&~tall(X)))))&
((?[X]:((~funny(X)&creative(X))))<=>(?[X]:((wise(X)&tall(X)))))&
(![X]:(~patient(X)<=>(humble(X)&funny(X))))&
(![X]:((rich(X)&patient(X))<=>(wise(X)|curious(X))))&
(![X]:((~quiet(X)<~>~humble(X))=>(funny(X)<~>~humble(X))))&
(~calm(fred))&
(?[X]:((~wise(X)<~>curious(X))))&
(?[X]:((calm(X)<~>~rich(X))))&
((quiet(alice)&~brave(alice)))&
(?[X]:((~funny(X)&~brave(X))))&
(?[X]:(calm(X)))&
(?[X]:((wise(X)<~>humble(X))))&
((~rich(susan)&tall(susan))) | ~strong(fred) | [] | null | 0 |
If lucy is either not patient or creative then someone is not wise and vice versa. Everyone who is not kind is not brave or not strong and vice versa. If lucy is not curious then someone is both happy and wise. If fred is not rich or funny then fred is both strong and not old. Everyone who is either tall or curious is both happy and not wise and vice versa. Everyone who is either tall or curious is both not quiet and not happy and vice versa. Everyone who is either not happy or kind is not rich or kind. Everyone who is both funny and old is both not happy and wise and vice versa. If fred is not generous then someone is tall or not tall. Everyone who is not humble is not patient. If someone is not patient then lucy is either not tall or strong and vice versa. Everyone who is not tall or not calm is brave or kind and vice versa. Everyone who is wise or not funny is both not kind and not generous. If someone is either strong or wise then someone is both quiet and not happy. If paul is both not strong and not generous then fred is both not old and not generous. Everyone who is patient is happy or not creative and vice versa. Paul is not funny or not tall. Someone is funny. Alice is not wise. Someone is either happy or patient. Someone is patient. Paul is curious. Someone is not wise or funny. Someone is both not calm and patient. | Lucy is not happy. | contradiction | (((~patient(lucy)<~>creative(lucy)))<=>(?[X]:(~wise(X))))&
(![X]:(~kind(X)<=>(~brave(X)|~strong(X))))&
((~curious(lucy))=>(?[X]:((happy(X)&wise(X)))))&
(((~rich(fred)|funny(fred)))=>((strong(fred)&~old(fred))))&
(![X]:((tall(X)<~>curious(X))<=>(happy(X)&~wise(X))))&
(![X]:((tall(X)<~>curious(X))<=>(~quiet(X)&~happy(X))))&
(![X]:((~happy(X)<~>kind(X))=>(~rich(X)|kind(X))))&
(![X]:((funny(X)&old(X))<=>(~happy(X)&wise(X))))&
((~generous(fred))=>(?[X]:((tall(X)|~tall(X)))))&
(![X]:(~humble(X)=>~patient(X)))&
((?[X]:(~patient(X)))<=>((~tall(lucy)<~>strong(lucy))))&
(![X]:((~tall(X)|~calm(X))<=>(brave(X)|kind(X))))&
(![X]:((wise(X)|~funny(X))=>(~kind(X)&~generous(X))))&
((?[X]:((strong(X)<~>wise(X))))=>(?[X]:((quiet(X)&~happy(X)))))&
(((~strong(paul)&~generous(paul)))=>((~old(fred)&~generous(fred))))&
(![X]:(patient(X)<=>(happy(X)|~creative(X))))&
((~funny(paul)|~tall(paul)))&
(?[X]:(funny(X)))&
(~wise(alice))&
(?[X]:((happy(X)<~>patient(X))))&
(?[X]:(patient(X)))&
(curious(paul))&
(?[X]:((~wise(X)|funny(X))))&
(?[X]:((~calm(X)&patient(X)))) | ~happy(lucy) | [
"p0",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1724167750900254559281814
% SZS output start Proof for 1724167750900254559281814
1. (~patient(lucy) <~> creative(lucy)) <=> ? [X0] : ~wise(X0) [input p0]
16. ! [X0] : (patient(X0) <=> (~creative(X0) | happy(X0))) [input p15]
19. ~wise(alice) [input p18]
25. ~happy(lucy) [input hypothesis]
37. (((~creative(lucy) | patient(lucy)) & (creative(lucy) | ~patient(lucy))) | ! [X0] : wise(X0)) & (? [X0] : ~wise(X0) | ((~patient(lucy) | ~creative(lucy)) & (creative(lucy) | patient(lucy)))) [nnf transformation 1]
38. (((~creative(lucy) | patient(lucy)) & (creative(lucy) | ~patient(lucy))) | ! [X0] : wise(X0)) & (? [X1] : ~wise(X1) | ((~patient(lucy) | ~creative(lucy)) & (creative(lucy) | patient(lucy)))) [rectify 37]
39. ? [X1] : ~wise(X1) => ~wise(sK0) [choice axiom]
40. (((~creative(lucy) | patient(lucy)) & (creative(lucy) | ~patient(lucy))) | ! [X0] : wise(X0)) & (~wise(sK0) | ((~patient(lucy) | ~creative(lucy)) & (creative(lucy) | patient(lucy)))) [skolemisation 38,39]
64. ! [X0] : ((patient(X0) | (creative(X0) & ~happy(X0))) & ((~creative(X0) | happy(X0)) | ~patient(X0))) [nnf transformation 16]
65. ! [X0] : ((patient(X0) | (creative(X0) & ~happy(X0))) & (~creative(X0) | happy(X0) | ~patient(X0))) [flattening 64]
79. creative(lucy) | ~patient(lucy) | wise(X0) [cnf transformation 40]
80. ~creative(lucy) | patient(lucy) | wise(X0) [cnf transformation 40]
127. ~creative(X0) | happy(X0) | ~patient(X0) [cnf transformation 65]
129. creative(X0) | patient(X0) [cnf transformation 65]
132. ~wise(alice) [cnf transformation 19]
140. ~happy(lucy) [cnf transformation 25]
143. 1 <=> ! [X0] : wise(X0) [avatar definition]
144. wise(X0) <- (1) [avatar component clause 143]
146. 2 <=> patient(lucy) [avatar definition]
147. ~patient(lucy) <- (~2) [avatar component clause 146]
148. patient(lucy) <- (2) [avatar component clause 146]
150. 3 <=> creative(lucy) [avatar definition]
151. creative(lucy) <- (3) [avatar component clause 150]
152. ~creative(lucy) <- (~3) [avatar component clause 150]
153. 1 | 2 | ~3 [avatar split clause 80,150,146,143]
154. 1 | ~2 | 3 [avatar split clause 79,150,146,143]
273. patient(lucy) <- (~3) [resolution 129,152]
274. $false <- (~2, ~3) [subsumption resolution 273,147]
275. 2 | 3 [avatar contradiction clause 274]
276. $false <- (1) [resolution 144,132]
281. ~1 [avatar contradiction clause 276]
328. happy(lucy) | ~patient(lucy) <- (3) [resolution 127,151]
329. ~patient(lucy) <- (3) [subsumption resolution 328,140]
330. $false <- (2, 3) [subsumption resolution 329,148]
331. ~2 | ~3 [avatar contradiction clause 330]
332. $false [avatar sat refutation 153,154,275,281,331]
% SZS output end Proof for 1724167750900254559281814
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either brave or humble then susan is not happy or calm and vice versa.
Everyone who is both not funny and not calm is generous or not strong.
If someone is humble or happy then john is kind or patient and vice versa.
Everyone who is either not humble or not happy is kind or not generous and vice versa.
Everyone who is both not calm and not funny is either not humble or wise.
If lucy is both not kind and generous then alice is strong or funny and vice versa.
If fred is creative or old then someone is either not calm or not patient and vice versa.
Everyone who is both funny and not funny is humble or not curious and vice versa.
If mary is strong or not creative then someone is either not patient or not generous and vice versa.
Everyone who is both not old and not calm is creative and vice versa.
Everyone who is both calm and wise is happy.
Everyone who is not tall is both funny and curious and vice versa.
Everyone who is either not humble or not patient is tall.
If susan is both not happy and brave then someone is old or not rich.
Everyone who is not tall or funny is either generous or not rich and vice versa.
Everyone who is calm is both generous and not old and vice versa.
Someone is not curious or not calm.
Paul is either not strong or wise.
Someone is not brave.
John is both old and brave.
Paul is old.
Someone is not old.
Someone is strong or happy.
Paul is not tall or funny. | Paul is old. | entailment | (((brave(paul)<~>humble(paul)))<=>((~happy(susan)|calm(susan))))&
(![X]:((~funny(X)&~calm(X))=>(generous(X)|~strong(X))))&
((?[X]:((humble(X)|happy(X))))<=>((kind(john)|patient(john))))&
(![X]:((~humble(X)<~>~happy(X))<=>(kind(X)|~generous(X))))&
(![X]:((~calm(X)&~funny(X))=>(~humble(X)<~>wise(X))))&
(((~kind(lucy)&generous(lucy)))<=>((strong(alice)|funny(alice))))&
(((creative(fred)|old(fred)))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
(![X]:((funny(X)&~funny(X))<=>(humble(X)|~curious(X))))&
(((strong(mary)|~creative(mary)))<=>(?[X]:((~patient(X)<~>~generous(X)))))&
(![X]:((~old(X)&~calm(X))<=>creative(X)))&
(![X]:((calm(X)&wise(X))=>happy(X)))&
(![X]:(~tall(X)<=>(funny(X)&curious(X))))&
(![X]:((~humble(X)<~>~patient(X))=>tall(X)))&
(((~happy(susan)&brave(susan)))=>(?[X]:((old(X)|~rich(X)))))&
(![X]:((~tall(X)|funny(X))<=>(generous(X)<~>~rich(X))))&
(![X]:(calm(X)<=>(generous(X)&~old(X))))&
(?[X]:((~curious(X)|~calm(X))))&
((~strong(paul)<~>wise(paul)))&
(?[X]:(~brave(X)))&
((old(john)&brave(john)))&
(old(paul))&
(?[X]:(~old(X)))&
(?[X]:((strong(X)|happy(X))))&
((~tall(paul)|funny(paul))) | old(paul) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8904785439607568451025
% SZS output start Proof for 8904785439607568451025
21. old(paul) [input p20]
25. ~old(paul) [input hypothesis]
145. old(paul) [cnf transformation 21]
149. ~old(paul) [cnf transformation 25]
315. $false [subsumption resolution 149,145]
% SZS output end Proof for 8904785439607568451025
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is both wise and brave.
If someone is not wise or not funny then john is either not quiet or funny and vice versa.
Everyone who is not happy is not strong.
Everyone who is creative or not generous is not funny or not curious.
Everyone who is creative is creative or not generous and vice versa.
Everyone who is funny is not tall and vice versa.
Everyone who is not calm or curious is not brave and vice versa.
If someone is generous then fred is either not happy or not creative and vice versa.
If someone is patient then alice is both strong and not generous and vice versa.
Everyone who is either humble or not patient is funny or curious and vice versa.
Everyone who is not quiet is both not old and tall.
Everyone who is kind is generous and vice versa.
Everyone who is both generous and not creative is both strong and generous.
If fred is both funny and quiet then john is both not kind and not curious.
Everyone who is strong is not humble or tall and vice versa.
If mary is not humble or not generous then someone is not calm or not strong.
Paul is both not curious and not strong.
Someone is either not strong or not humble.
Someone is either not brave or funny.
Someone is not brave.
Fred is both strong and not creative.
John is calm or generous. | Fred is generous. | entailment | (![X]:(calm(X)=>(wise(X)&brave(X))))&
((?[X]:((~wise(X)|~funny(X))))<=>((~quiet(john)<~>funny(john))))&
(![X]:(~happy(X)=>~strong(X)))&
(![X]:((creative(X)|~generous(X))=>(~funny(X)|~curious(X))))&
(![X]:(creative(X)<=>(creative(X)|~generous(X))))&
(![X]:(funny(X)<=>~tall(X)))&
(![X]:((~calm(X)|curious(X))<=>~brave(X)))&
((?[X]:(generous(X)))<=>((~happy(fred)<~>~creative(fred))))&
((?[X]:(patient(X)))<=>((strong(alice)&~generous(alice))))&
(![X]:((humble(X)<~>~patient(X))<=>(funny(X)|curious(X))))&
(![X]:(~quiet(X)=>(~old(X)&tall(X))))&
(![X]:(kind(X)<=>generous(X)))&
(![X]:((generous(X)&~creative(X))=>(strong(X)&generous(X))))&
(((funny(fred)&quiet(fred)))=>((~kind(john)&~curious(john))))&
(![X]:(strong(X)<=>(~humble(X)|tall(X))))&
(((~humble(mary)|~generous(mary)))=>(?[X]:((~calm(X)|~strong(X)))))&
((~curious(paul)&~strong(paul)))&
(?[X]:((~strong(X)<~>~humble(X))))&
(?[X]:((~brave(X)<~>funny(X))))&
(?[X]:(~brave(X)))&
((strong(fred)&~creative(fred)))&
((calm(john)|generous(john))) | generous(fred) | [
"p4",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 539521400243049326802699
% SZS output start Proof for 539521400243049326802699
5. ! [X0] : (creative(X0) <=> (~generous(X0) | creative(X0))) [input p4]
21. ~creative(fred) & strong(fred) [input p20]
23. ~generous(fred) [input hypothesis]
41. ! [X0] : ((creative(X0) | (generous(X0) & ~creative(X0))) & ((~generous(X0) | creative(X0)) | ~creative(X0))) [nnf transformation 5]
42. ! [X0] : ((creative(X0) | (generous(X0) & ~creative(X0))) & (~generous(X0) | creative(X0) | ~creative(X0))) [flattening 41]
82. generous(X0) | creative(X0) [cnf transformation 42]
120. ~creative(fred) [cnf transformation 21]
122. ~generous(fred) [cnf transformation 23]
152. 7 <=> creative(fred) [avatar definition]
153. ~creative(fred) <- (~7) [avatar component clause 152]
244. ~7 [avatar split clause 120,152]
258. creative(fred) [resolution 82,122]
260. $false <- (~7) [subsumption resolution 258,153]
261. 7 [avatar contradiction clause 260]
262. $false [avatar sat refutation 244,261]
% SZS output end Proof for 539521400243049326802699
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet or not curious is not curious or rich and vice versa.
If mary is both not old and not kind then someone is both curious and creative.
Everyone who is wise is either tall or not curious and vice versa.
Everyone who is both not humble and not happy is quiet or curious.
Everyone who is either not wise or not curious is both not curious and not generous and vice versa.
Everyone who is both not wise and kind is patient or not calm and vice versa.
If someone is not creative then someone is not generous.
If susan is not rich or not strong then someone is either not calm or generous.
Everyone who is not curious or creative is curious and vice versa.
If alice is not creative or creative then alice is either wise or not rich.
Everyone who is either funny or not rich is not strong and vice versa.
If john is both patient and not old then someone is creative or not happy.
Everyone who is either not generous or generous is either not creative or old and vice versa.
If fred is both not rich and not wise then someone is not kind or not creative.
Alice is tall or old.
Someone is either not wise or funny.
Lucy is both not strong and curious.
Someone is either generous or not calm.
Someone is both generous and strong.
Susan is rich. | Susan is creative. | entailment | (![X]:((quiet(X)|~curious(X))<=>(~curious(X)|rich(X))))&
(((~old(mary)&~kind(mary)))=>(?[X]:((curious(X)&creative(X)))))&
(![X]:(wise(X)<=>(tall(X)<~>~curious(X))))&
(![X]:((~humble(X)&~happy(X))=>(quiet(X)|curious(X))))&
(![X]:((~wise(X)<~>~curious(X))<=>(~curious(X)&~generous(X))))&
(![X]:((~wise(X)&kind(X))<=>(patient(X)|~calm(X))))&
((?[X]:(~creative(X)))=>(?[X]:(~generous(X))))&
(((~rich(susan)|~strong(susan)))=>(?[X]:((~calm(X)<~>generous(X)))))&
(![X]:((~curious(X)|creative(X))<=>curious(X)))&
(((~creative(alice)|creative(alice)))=>((wise(alice)<~>~rich(alice))))&
(![X]:((funny(X)<~>~rich(X))<=>~strong(X)))&
(((patient(john)&~old(john)))=>(?[X]:((creative(X)|~happy(X)))))&
(![X]:((~generous(X)<~>generous(X))<=>(~creative(X)<~>old(X))))&
(((~rich(fred)&~wise(fred)))=>(?[X]:((~kind(X)|~creative(X)))))&
((tall(alice)|old(alice)))&
(?[X]:((~wise(X)<~>funny(X))))&
((~strong(lucy)&curious(lucy)))&
(?[X]:((generous(X)<~>~calm(X))))&
(?[X]:((generous(X)&strong(X))))&
(rich(susan)) | creative(susan) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3384995353399224478639065
% SZS output start Proof for 3384995353399224478639065
9. ! [X0] : ((creative(X0) | ~curious(X0)) <=> curious(X0)) [input p8]
21. ~creative(susan) [input hypothesis]
47. ! [X0] : (((creative(X0) | ~curious(X0)) | ~curious(X0)) & (curious(X0) | (~creative(X0) & curious(X0)))) [nnf transformation 9]
48. ! [X0] : ((creative(X0) | ~curious(X0) | ~curious(X0)) & (curious(X0) | (~creative(X0) & curious(X0)))) [flattening 47]
88. curious(X0) | curious(X0) [cnf transformation 48]
90. creative(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 48]
118. ~creative(susan) [cnf transformation 21]
123. curious(X0) [duplicate literal removal 88]
124. ~curious(X0) | creative(X0) [duplicate literal removal 90]
146. 5 <=> ! [X1] : creative(X1) [avatar definition]
147. creative(X1) <- (5) [avatar component clause 146]
240. creative(X0) [resolution 124,123]
241. 5 [avatar split clause 240,146]
243. $false <- (5) [resolution 147,118]
248. ~5 [avatar contradiction clause 243]
249. $false [avatar sat refutation 241,248]
% SZS output end Proof for 3384995353399224478639065
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
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