premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is either not happy or not funny is both humble and strong and vice versa.
Everyone who is not old is either patient or not wise and vice versa.
Everyone who is humble or curious is both not old and not wise.
If someone is not rich or not strong then alice is both not curious and not calm.
If someone is funny or not rich then someone is not strong.
Everyone who is not rich is not kind.
If paul is funny then mary is old and vice versa.
If someone is either not happy or strong then john is both not wise and brave.
If someone is both wise and not wise then someone is not patient and vice versa.
If john is either not generous or not happy then lucy is both not rich and generous.
Everyone who is either quiet or brave is either tall or wise and vice versa.
If someone is not tall then someone is strong or not brave.
Everyone who is either old or not curious is both old and calm.
If paul is tall then lucy is both not wise and generous and vice versa.
Everyone who is either tall or not old is either happy or not creative and vice versa.
If someone is either not patient or not generous then someone is not old or not quiet and vice versa.
Alice is either not strong or generous.
John is both not tall and quiet.
Someone is both not tall and not strong.
Susan is kind.
Paul is funny.
Lucy is both tall and strong.
Lucy is not calm.
Someone is rich. | Susan is curious. | contradiction | (![X]:((~happy(X)<~>~funny(X))<=>(humble(X)&strong(X))))&
(![X]:(~old(X)<=>(patient(X)<~>~wise(X))))&
(![X]:((humble(X)|curious(X))=>(~old(X)&~wise(X))))&
((?[X]:((~rich(X)|~strong(X))))=>((~curious(alice)&~calm(alice))))&
((?[X]:((funny(X)|~rich(X))))=>(?[X]:(~strong(X))))&
(![X]:(~rich(X)=>~kind(X)))&
((funny(paul))<=>(old(mary)))&
((?[X]:((~happy(X)<~>strong(X))))=>((~wise(john)&brave(john))))&
((?[X]:((wise(X)&~wise(X))))<=>(?[X]:(~patient(X))))&
(((~generous(john)<~>~happy(john)))=>((~rich(lucy)&generous(lucy))))&
(![X]:((quiet(X)<~>brave(X))<=>(tall(X)<~>wise(X))))&
((?[X]:(~tall(X)))=>(?[X]:((strong(X)|~brave(X)))))&
(![X]:((old(X)<~>~curious(X))=>(old(X)&calm(X))))&
((tall(paul))<=>((~wise(lucy)&generous(lucy))))&
(![X]:((tall(X)<~>~old(X))<=>(happy(X)<~>~creative(X))))&
((?[X]:((~patient(X)<~>~generous(X))))<=>(?[X]:((~old(X)|~quiet(X)))))&
((~strong(alice)<~>generous(alice)))&
((~tall(john)&quiet(john)))&
(?[X]:((~tall(X)&~strong(X))))&
(kind(susan))&
(funny(paul))&
((tall(lucy)&strong(lucy)))&
(~calm(lucy))&
(?[X]:(rich(X))) | curious(susan) | [
"p1",
"p2",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5672709570717484260516099
% SZS output start Proof for 5672709570717484260516099
2. ! [X0] : (~old(X0) <=> (patient(X0) <~> ~wise(X0))) [input p1]
3. ! [X0] : ((curious(X0) | humble(X0)) => (~wise(X0) & ~old(X0))) [input p2]
9. ? [X0] : (~wise(X0) & wise(X0)) <=> ? [X0] : ~patient(X0) [input p8]
13. ! [X0] : ((old(X0) <~> ~curious(X0)) => (calm(X0) & old(X0))) [input p12]
25. curious(susan) [input hypothesis]
27. ? [X0] : (~wise(X0) & wise(X0)) <=> ? [X1] : ~patient(X1) [rectify 9]
30. ! [X0] : ((~wise(X0) & ~old(X0)) | (~curious(X0) & ~humble(X0))) [ennf transformation 3]
37. ! [X0] : ((calm(X0) & old(X0)) | (old(X0) <=> ~curious(X0))) [ennf transformation 13]
40. ! [X0] : ((~old(X0) | ((patient(X0) | wise(X0)) & (~wise(X0) | ~patient(X0)))) & (((wise(X0) | ~patient(X0)) & (~wise(X0) | patient(X0))) | old(X0))) [nnf transformation 2]
46. (? [X0] : (~wise(X0) & wise(X0)) | ! [X1] : patient(X1)) & (? [X1] : ~patient(X1) | ! [X0] : (wise(X0) | ~wise(X0))) [nnf transformation 27]
47. (? [X0] : (~wise(X0) & wise(X0)) | ! [X1] : patient(X1)) & (? [X2] : ~patient(X2) | ! [X3] : (wise(X3) | ~wise(X3))) [rectify 46]
48. ? [X0] : (~wise(X0) & wise(X0)) => (~wise(sK1) & wise(sK1)) [choice axiom]
49. ? [X2] : ~patient(X2) => ~patient(sK2) [choice axiom]
50. ((~wise(sK1) & wise(sK1)) | ! [X1] : patient(X1)) & (~patient(sK2) | ! [X3] : (wise(X3) | ~wise(X3))) [skolemisation 47,49,48]
56. ! [X0] : ((calm(X0) & old(X0)) | ((old(X0) | curious(X0)) & (~curious(X0) | ~old(X0)))) [nnf transformation 37]
77. ~patient(X0) | wise(X0) | old(X0) [cnf transformation 40]
81. ~curious(X0) | ~old(X0) [cnf transformation 30]
83. ~curious(X0) | ~wise(X0) [cnf transformation 30]
98. wise(sK1) | patient(X1) [cnf transformation 50]
99. ~wise(sK1) | patient(X1) [cnf transformation 50]
114. old(X0) | old(X0) | curious(X0) [cnf transformation 56]
146. curious(susan) [cnf transformation 25]
147. curious(X0) | old(X0) [duplicate literal removal 114]
204. 13 <=> ! [X1] : patient(X1) [avatar definition]
205. patient(X1) <- (13) [avatar component clause 204]
207. 14 <=> wise(sK1) [avatar definition]
210. 13 | ~14 [avatar split clause 99,207,204]
211. 13 | 14 [avatar split clause 98,207,204]
268. 27 <=> ! [X1] : old(X1) [avatar definition]
269. old(X1) <- (27) [avatar component clause 268]
301. ~old(susan) [resolution 81,146]
305. ~wise(X0) | old(X0) [resolution 147,83]
321. wise(X0) | old(X0) <- (13) [resolution 77,205]
323. old(X0) <- (13) [subsumption resolution 321,305]
324. 27 | ~13 [avatar split clause 323,204,268]
327. $false <- (27) [resolution 269,301]
328. ~27 [avatar contradiction clause 327]
329. $false [avatar sat refutation 210,211,324,328]
% SZS output end Proof for 5672709570717484260516099
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If alice is funny or humble then fred is both brave and not wise and vice versa.
Everyone who is both not quiet and rich is not creative.
If someone is either wise or calm then lucy is either not calm or generous.
If someone is old or not patient then someone is not creative.
If someone is not happy or not kind then susan is tall or creative.
Everyone who is both funny and curious is either not rich or not kind.
If someone is funny or curious then someone is either happy or not brave and vice versa.
Everyone who is not happy or quiet is both old and not brave and vice versa.
Everyone who is both curious and not strong is not kind or not happy and vice versa.
Everyone who is patient is not generous and vice versa.
Everyone who is strong is either not brave or calm and vice versa.
Everyone who is not quiet or creative is not kind or not generous.
If alice is funny or not curious then someone is humble or tall and vice versa.
Everyone who is wise or quiet is either not kind or not funny and vice versa.
If someone is both kind and not rich then someone is not curious.
Everyone who is rich or not tall is either tall or calm.
Fred is both not humble and not rich.
Someone is both humble and not rich.
Paul is kind or funny.
Someone is either not rich or not wise.
Susan is both not kind and not old.
Fred is funny.
Someone is both brave and not rich.
Someone is either not strong or not wise. | Alice is funny. | neutral | (((funny(alice)|humble(alice)))<=>((brave(fred)&~wise(fred))))&
(![X]:((~quiet(X)&rich(X))=>~creative(X)))&
((?[X]:((wise(X)<~>calm(X))))=>((~calm(lucy)<~>generous(lucy))))&
((?[X]:((old(X)|~patient(X))))=>(?[X]:(~creative(X))))&
((?[X]:((~happy(X)|~kind(X))))=>((tall(susan)|creative(susan))))&
(![X]:((funny(X)&curious(X))=>(~rich(X)<~>~kind(X))))&
((?[X]:((funny(X)|curious(X))))<=>(?[X]:((happy(X)<~>~brave(X)))))&
(![X]:((~happy(X)|quiet(X))<=>(old(X)&~brave(X))))&
(![X]:((curious(X)&~strong(X))<=>(~kind(X)|~happy(X))))&
(![X]:(patient(X)<=>~generous(X)))&
(![X]:(strong(X)<=>(~brave(X)<~>calm(X))))&
(![X]:((~quiet(X)|creative(X))=>(~kind(X)|~generous(X))))&
(((funny(alice)|~curious(alice)))<=>(?[X]:((humble(X)|tall(X)))))&
(![X]:((wise(X)|quiet(X))<=>(~kind(X)<~>~funny(X))))&
((?[X]:((kind(X)&~rich(X))))=>(?[X]:(~curious(X))))&
(![X]:((rich(X)|~tall(X))=>(tall(X)<~>calm(X))))&
((~humble(fred)&~rich(fred)))&
(?[X]:((humble(X)&~rich(X))))&
((kind(paul)|funny(paul)))&
(?[X]:((~rich(X)<~>~wise(X))))&
((~kind(susan)&~old(susan)))&
(funny(fred))&
(?[X]:((brave(X)&~rich(X))))&
(?[X]:((~strong(X)<~>~wise(X)))) | funny(alice) | [] | null | 0 |
Everyone who is creative or not brave is happy. If lucy is not creative then someone is either rich or not wise. If someone is either not patient or not old then someone is both not happy and not humble. If alice is not patient or old then lucy is not curious. If mary is either not humble or creative then someone is either not strong or quiet. If someone is both not curious and not kind then someone is patient or not generous and vice versa. Everyone who is not tall is both not wise and kind and vice versa. Everyone who is both generous and happy is either not creative or patient. Everyone who is either rich or not patient is either not calm or creative and vice versa. Everyone who is old is not calm and vice versa. Everyone who is not old or not funny is either not humble or not brave. If john is either not tall or not rich then john is rich and vice versa. If someone is both happy and curious then someone is either rich or generous. Everyone who is both not patient and wise is either not generous or not humble and vice versa. If someone is old then mary is either generous or creative and vice versa. If paul is brave then paul is not humble and vice versa. Alice is both not quiet and funny. Someone is both not funny and not generous. Mary is wise. Alice is not calm. Paul is both not kind and not humble. Someone is either not quiet or not generous. Lucy is wise. Someone is humble or not patient. | Alice is not old. | contradiction | (![X]:((creative(X)|~brave(X))=>happy(X)))&
((~creative(lucy))=>(?[X]:((rich(X)<~>~wise(X)))))&
((?[X]:((~patient(X)<~>~old(X))))=>(?[X]:((~happy(X)&~humble(X)))))&
(((~patient(alice)|old(alice)))=>(~curious(lucy)))&
(((~humble(mary)<~>creative(mary)))=>(?[X]:((~strong(X)<~>quiet(X)))))&
((?[X]:((~curious(X)&~kind(X))))<=>(?[X]:((patient(X)|~generous(X)))))&
(![X]:(~tall(X)<=>(~wise(X)&kind(X))))&
(![X]:((generous(X)&happy(X))=>(~creative(X)<~>patient(X))))&
(![X]:((rich(X)<~>~patient(X))<=>(~calm(X)<~>creative(X))))&
(![X]:(old(X)<=>~calm(X)))&
(![X]:((~old(X)|~funny(X))=>(~humble(X)<~>~brave(X))))&
(((~tall(john)<~>~rich(john)))<=>(rich(john)))&
((?[X]:((happy(X)&curious(X))))=>(?[X]:((rich(X)<~>generous(X)))))&
(![X]:((~patient(X)&wise(X))<=>(~generous(X)<~>~humble(X))))&
((?[X]:(old(X)))<=>((generous(mary)<~>creative(mary))))&
((brave(paul))<=>(~humble(paul)))&
((~quiet(alice)&funny(alice)))&
(?[X]:((~funny(X)&~generous(X))))&
(wise(mary))&
(~calm(alice))&
((~kind(paul)&~humble(paul)))&
(?[X]:((~quiet(X)<~>~generous(X))))&
(wise(lucy))&
(?[X]:((humble(X)|~patient(X)))) | ~old(alice) | [
"p9",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1038248470384367755899602
% SZS output start Proof for 1038248470384367755899602
10. ! [X0] : (old(X0) <=> ~calm(X0)) [input p9]
20. ~calm(alice) [input p19]
25. ~old(alice) [input hypothesis]
57. ! [X0] : ((old(X0) | calm(X0)) & (~calm(X0) | ~old(X0))) [nnf transformation 10]
111. calm(X0) | old(X0) [cnf transformation 57]
139. ~calm(alice) [cnf transformation 20]
146. ~old(alice) [cnf transformation 25]
182. 8 <=> old(alice) [avatar definition]
184. ~old(alice) <- (~8) [avatar component clause 182]
314. ~8 [avatar split clause 146,182]
320. old(alice) [resolution 111,139]
322. $false <- (~8) [subsumption resolution 320,184]
323. 8 [avatar contradiction clause 322]
324. $false [avatar sat refutation 314,323]
% SZS output end Proof for 1038248470384367755899602
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is happy then someone is both not patient and patient.
Everyone who is not rich or not kind is not tall or tall and vice versa.
Everyone who is not humble or strong is both not happy and not curious and vice versa.
If paul is not old or funny then someone is not wise and vice versa.
Everyone who is not funny or curious is patient and vice versa.
If someone is either humble or not curious then someone is not kind and vice versa.
If someone is both funny and not curious then susan is either not strong or not old and vice versa.
If someone is brave or patient then someone is both funny and wise and vice versa.
Everyone who is creative is rich.
Everyone who is not strong is generous.
If alice is not patient then paul is either not rich or not kind and vice versa.
If someone is not wise then paul is patient or not funny and vice versa.
If john is not rich or quiet then lucy is either not brave or not tall and vice versa.
Everyone who is not patient or happy is calm or not quiet and vice versa.
If paul is either not curious or rich then paul is wise or not wise and vice versa.
Someone is both not humble and not kind.
Lucy is either calm or not funny.
Fred is either tall or not old.
Someone is both kind and not happy.
Alice is not strong.
Someone is not brave or quiet. | Paul is calm. | neutral | ((happy(susan))=>(?[X]:((~patient(X)&patient(X)))))&
(![X]:((~rich(X)|~kind(X))<=>(~tall(X)|tall(X))))&
(![X]:((~humble(X)|strong(X))<=>(~happy(X)&~curious(X))))&
(((~old(paul)|funny(paul)))<=>(?[X]:(~wise(X))))&
(![X]:((~funny(X)|curious(X))<=>patient(X)))&
((?[X]:((humble(X)<~>~curious(X))))<=>(?[X]:(~kind(X))))&
((?[X]:((funny(X)&~curious(X))))<=>((~strong(susan)<~>~old(susan))))&
((?[X]:((brave(X)|patient(X))))<=>(?[X]:((funny(X)&wise(X)))))&
(![X]:(creative(X)=>rich(X)))&
(![X]:(~strong(X)=>generous(X)))&
((~patient(alice))<=>((~rich(paul)<~>~kind(paul))))&
((?[X]:(~wise(X)))<=>((patient(paul)|~funny(paul))))&
(((~rich(john)|quiet(john)))<=>((~brave(lucy)<~>~tall(lucy))))&
(![X]:((~patient(X)|happy(X))<=>(calm(X)|~quiet(X))))&
(((~curious(paul)<~>rich(paul)))<=>((wise(paul)|~wise(paul))))&
(?[X]:((~humble(X)&~kind(X))))&
((calm(lucy)<~>~funny(lucy)))&
((tall(fred)<~>~old(fred)))&
(?[X]:((kind(X)&~happy(X))))&
(~strong(alice))&
(?[X]:((~brave(X)|quiet(X)))) | calm(paul) | [] | null | 0 |
If someone is generous or not tall then someone is rich or funny and vice versa.
If lucy is not funny then someone is either strong or not creative and vice versa.
Everyone who is humble is either calm or patient and vice versa.
Everyone who is either not quiet or creative is tall.
If someone is strong or not happy then someone is curious or not patient.
If someone is both not strong and not quiet then someone is not wise and vice versa.
Everyone who is brave or not brave is not curious.
Everyone who is both tall and generous is old or not funny and vice versa.
Everyone who is both not old and kind is rich or not calm.
If paul is both not kind and not rich then paul is not happy or humble.
If someone is rich then someone is wise and vice versa.
If paul is either brave or creative then someone is creative and vice versa.
If someone is not strong or not tall then john is kind.
Everyone who is either not rich or not calm is not tall.
Everyone who is creative or not quiet is both happy and humble.
Someone is kind or strong.
Susan is both old and strong.
Mary is humble.
Fred is not happy or not quiet.
Mary is either generous or not old.
John is both not tall and not strong.
Alice is brave or not generous. | Alice is not brave. | neutral | ((?[X]:((generous(X)|~tall(X))))<=>(?[X]:((rich(X)|funny(X)))))&
((~funny(lucy))<=>(?[X]:((strong(X)<~>~creative(X)))))&
(![X]:(humble(X)<=>(calm(X)<~>patient(X))))&
(![X]:((~quiet(X)<~>creative(X))=>tall(X)))&
((?[X]:((strong(X)|~happy(X))))=>(?[X]:((curious(X)|~patient(X)))))&
((?[X]:((~strong(X)&~quiet(X))))<=>(?[X]:(~wise(X))))&
(![X]:((brave(X)|~brave(X))=>~curious(X)))&
(![X]:((tall(X)&generous(X))<=>(old(X)|~funny(X))))&
(![X]:((~old(X)&kind(X))=>(rich(X)|~calm(X))))&
(((~kind(paul)&~rich(paul)))=>((~happy(paul)|humble(paul))))&
((?[X]:(rich(X)))<=>(?[X]:(wise(X))))&
(((brave(paul)<~>creative(paul)))<=>(?[X]:(creative(X))))&
((?[X]:((~strong(X)|~tall(X))))=>(kind(john)))&
(![X]:((~rich(X)<~>~calm(X))=>~tall(X)))&
(![X]:((creative(X)|~quiet(X))=>(happy(X)&humble(X))))&
(?[X]:((kind(X)|strong(X))))&
((old(susan)&strong(susan)))&
(humble(mary))&
((~happy(fred)|~quiet(fred)))&
((generous(mary)<~>~old(mary)))&
((~tall(john)&~strong(john)))&
((brave(alice)|~generous(alice))) | ~brave(alice) | [] | null | 0 |
Everyone who is patient or not patient is both not patient and not generous.
If fred is either kind or calm then someone is not kind.
Everyone who is not tall or not patient is not strong.
Everyone who is brave is either not funny or not wise and vice versa.
If alice is not curious or tall then lucy is strong or not generous and vice versa.
If someone is either not happy or funny then susan is not old.
Everyone who is not kind is not humble or not happy.
Everyone who is either not happy or happy is both not wise and funny and vice versa.
If someone is wise then fred is either not quiet or not humble and vice versa.
Everyone who is happy is both not calm and generous.
If lucy is generous or not quiet then someone is both not curious and rich and vice versa.
Everyone who is old is tall and vice versa.
If someone is either wise or not old then someone is either rich or not old.
If someone is not funny then someone is both humble and rich and vice versa.
If john is both not calm and not brave then someone is not funny and vice versa.
If someone is both not tall and patient then someone is calm or quiet.
Someone is not quiet or happy.
Lucy is either not funny or not curious.
Paul is brave or old.
Someone is not rich.
Paul is brave.
Fred is either not creative or not calm.
Susan is either not quiet or not tall.
Lucy is not strong. | Lucy is not wise. | entailment | (![X]:((patient(X)|~patient(X))=>(~patient(X)&~generous(X))))&
(((kind(fred)<~>calm(fred)))=>(?[X]:(~kind(X))))&
(![X]:((~tall(X)|~patient(X))=>~strong(X)))&
(![X]:(brave(X)<=>(~funny(X)<~>~wise(X))))&
(((~curious(alice)|tall(alice)))<=>((strong(lucy)|~generous(lucy))))&
((?[X]:((~happy(X)<~>funny(X))))=>(~old(susan)))&
(![X]:(~kind(X)=>(~humble(X)|~happy(X))))&
(![X]:((~happy(X)<~>happy(X))<=>(~wise(X)&funny(X))))&
((?[X]:(wise(X)))<=>((~quiet(fred)<~>~humble(fred))))&
(![X]:(happy(X)=>(~calm(X)&generous(X))))&
(((generous(lucy)|~quiet(lucy)))<=>(?[X]:((~curious(X)&rich(X)))))&
(![X]:(old(X)<=>tall(X)))&
((?[X]:((wise(X)<~>~old(X))))=>(?[X]:((rich(X)<~>~old(X)))))&
((?[X]:(~funny(X)))<=>(?[X]:((humble(X)&rich(X)))))&
(((~calm(john)&~brave(john)))<=>(?[X]:(~funny(X))))&
((?[X]:((~tall(X)&patient(X))))=>(?[X]:((calm(X)|quiet(X)))))&
(?[X]:((~quiet(X)|happy(X))))&
((~funny(lucy)<~>~curious(lucy)))&
((brave(paul)|old(paul)))&
(?[X]:(~rich(X)))&
(brave(paul))&
((~creative(fred)<~>~calm(fred)))&
((~quiet(susan)<~>~tall(susan)))&
(~strong(lucy)) | ~wise(lucy) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 9064581753881456543237419
% SZS output start Proof for 9064581753881456543237419
8. ! [X0] : ((~happy(X0) <~> happy(X0)) <=> (funny(X0) & ~wise(X0))) [input p7]
25. wise(lucy) [input hypothesis]
45. ! [X0] : ((((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | (~funny(X0) | wise(X0))) & ((funny(X0) & ~wise(X0)) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0))))) [nnf transformation 8]
46. ! [X0] : ((((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | ~funny(X0) | wise(X0)) & ((funny(X0) & ~wise(X0)) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0))))) [flattening 45]
100. ~wise(X0) | happy(X0) | happy(X0) [cnf transformation 46]
101. ~wise(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 46]
141. wise(lucy) [cnf transformation 25]
142. ~wise(X0) | happy(X0) [duplicate literal removal 100]
143. ~wise(X0) | ~happy(X0) [duplicate literal removal 101]
186. ~wise(X0) [subsumption resolution 142,143]
273. $false [subsumption resolution 141,186]
% SZS output end Proof for 9064581753881456543237419
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not rich is either not humble or generous and vice versa.
If john is either kind or creative then someone is either not wise or not brave and vice versa.
If someone is either wise or kind then someone is not patient.
Everyone who is not rich or not curious is both not quiet and not funny and vice versa.
If someone is wise or generous then susan is both not patient and quiet.
If someone is not calm then someone is happy.
Everyone who is tall is strong or kind.
If john is both strong and tall then someone is generous and vice versa.
If someone is funny or not funny then lucy is not patient or not curious.
Everyone who is not wise is not brave or not strong.
Everyone who is not happy or kind is both old and not generous and vice versa.
If mary is either not creative or not rich then someone is either not calm or quiet and vice versa.
Everyone who is creative is not patient or not tall.
Everyone who is both not happy and kind is either not rich or old.
Everyone who is both not generous and not rich is either not kind or funny.
If mary is not tall or calm then alice is either creative or calm.
Mary is kind or funny.
Someone is patient.
Lucy is both not curious and rich.
Alice is both not creative and calm.
Someone is not happy.
Lucy is not quiet.
Lucy is both not quiet and tall.
Alice is either not calm or humble. | Alice is calm. | entailment | (![X]:((~happy(X)<~>~rich(X))<=>(~humble(X)<~>generous(X))))&
(((kind(john)<~>creative(john)))<=>(?[X]:((~wise(X)<~>~brave(X)))))&
((?[X]:((wise(X)<~>kind(X))))=>(?[X]:(~patient(X))))&
(![X]:((~rich(X)|~curious(X))<=>(~quiet(X)&~funny(X))))&
((?[X]:((wise(X)|generous(X))))=>((~patient(susan)&quiet(susan))))&
((?[X]:(~calm(X)))=>(?[X]:(happy(X))))&
(![X]:(tall(X)=>(strong(X)|kind(X))))&
(((strong(john)&tall(john)))<=>(?[X]:(generous(X))))&
((?[X]:((funny(X)|~funny(X))))=>((~patient(lucy)|~curious(lucy))))&
(![X]:(~wise(X)=>(~brave(X)|~strong(X))))&
(![X]:((~happy(X)|kind(X))<=>(old(X)&~generous(X))))&
(((~creative(mary)<~>~rich(mary)))<=>(?[X]:((~calm(X)<~>quiet(X)))))&
(![X]:(creative(X)=>(~patient(X)|~tall(X))))&
(![X]:((~happy(X)&kind(X))=>(~rich(X)<~>old(X))))&
(![X]:((~generous(X)&~rich(X))=>(~kind(X)<~>funny(X))))&
(((~tall(mary)|calm(mary)))=>((creative(alice)<~>calm(alice))))&
((kind(mary)|funny(mary)))&
(?[X]:(patient(X)))&
((~curious(lucy)&rich(lucy)))&
((~creative(alice)&calm(alice)))&
(?[X]:(~happy(X)))&
(~quiet(lucy))&
((~quiet(lucy)&tall(lucy)))&
((~calm(alice)<~>humble(alice))) | calm(alice) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1007306047270462183763356
% SZS output start Proof for 1007306047270462183763356
20. calm(alice) & ~creative(alice) [input p19]
25. ~calm(alice) [input hypothesis]
139. calm(alice) [cnf transformation 20]
146. ~calm(alice) [cnf transformation 25]
288. 31 <=> calm(alice) [avatar definition]
309. 31 [avatar split clause 139,288]
317. ~31 [avatar split clause 146,288]
318. $false [avatar sat refutation 309,317]
% SZS output end Proof for 1007306047270462183763356
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong then fred is strong or not kind.
If someone is either generous or not kind then alice is both not wise and tall and vice versa.
Everyone who is creative or patient is not strong or not generous and vice versa.
Everyone who is either not creative or not strong is both curious and not tall.
If someone is generous then john is both happy and rich.
If lucy is rich then someone is both patient and curious and vice versa.
If fred is both curious and generous then someone is both calm and wise and vice versa.
Everyone who is not curious is not kind or tall.
If mary is either old or not humble then someone is not tall or not wise and vice versa.
Everyone who is curious is rich or curious and vice versa.
If someone is both rich and wise then paul is either old or funny.
Everyone who is both not brave and not kind is funny.
If someone is both not creative and brave then someone is calm or not humble and vice versa.
If someone is either tall or not generous then someone is both not happy and old.
If someone is either not funny or not tall then someone is both not patient and calm and vice versa.
If paul is not calm or not generous then someone is not brave and vice versa.
Someone is happy.
Someone is strong.
Susan is strong.
Mary is creative.
Someone is either not kind or rich.
Someone is old.
Someone is brave.
Someone is both rich and brave. | Mary is not creative. | contradiction | ((?[X]:(~strong(X)))=>((strong(fred)|~kind(fred))))&
((?[X]:((generous(X)<~>~kind(X))))<=>((~wise(alice)&tall(alice))))&
(![X]:((creative(X)|patient(X))<=>(~strong(X)|~generous(X))))&
(![X]:((~creative(X)<~>~strong(X))=>(curious(X)&~tall(X))))&
((?[X]:(generous(X)))=>((happy(john)&rich(john))))&
((rich(lucy))<=>(?[X]:((patient(X)&curious(X)))))&
(((curious(fred)&generous(fred)))<=>(?[X]:((calm(X)&wise(X)))))&
(![X]:(~curious(X)=>(~kind(X)|tall(X))))&
(((old(mary)<~>~humble(mary)))<=>(?[X]:((~tall(X)|~wise(X)))))&
(![X]:(curious(X)<=>(rich(X)|curious(X))))&
((?[X]:((rich(X)&wise(X))))=>((old(paul)<~>funny(paul))))&
(![X]:((~brave(X)&~kind(X))=>funny(X)))&
((?[X]:((~creative(X)&brave(X))))<=>(?[X]:((calm(X)|~humble(X)))))&
((?[X]:((tall(X)<~>~generous(X))))=>(?[X]:((~happy(X)&old(X)))))&
((?[X]:((~funny(X)<~>~tall(X))))<=>(?[X]:((~patient(X)&calm(X)))))&
(((~calm(paul)|~generous(paul)))<=>(?[X]:(~brave(X))))&
(?[X]:(happy(X)))&
(?[X]:(strong(X)))&
(strong(susan))&
(creative(mary))&
(?[X]:((~kind(X)<~>rich(X))))&
(?[X]:(old(X)))&
(?[X]:(brave(X)))&
(?[X]:((rich(X)&brave(X)))) | ~creative(mary) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7138992348929622354903725
% SZS output start Proof for 7138992348929622354903725
20. creative(mary) [input p19]
25. ~creative(mary) [input hypothesis]
153. creative(mary) [cnf transformation 20]
160. ~creative(mary) [cnf transformation 25]
403. $false [subsumption resolution 160,153]
% SZS output end Proof for 7138992348929622354903725
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or happy then someone is calm or wise. Everyone who is curious or tall is funny and vice versa. If fred is not happy or kind then someone is both patient and not old and vice versa. Everyone who is both rich and not curious is either happy or kind and vice versa. Everyone who is both not patient and strong is both not rich and generous. Everyone who is both not brave and funny is patient or not creative and vice versa. If fred is either creative or not happy then lucy is either creative or not tall and vice versa. Everyone who is both not quiet and not creative is not happy. Everyone who is either not quiet or quiet is tall. If fred is curious then mary is either tall or humble and vice versa. Everyone who is both not patient and not tall is either calm or old and vice versa. If someone is not generous then alice is both quiet and happy. Everyone who is both funny and humble is both calm and not quiet and vice versa. Everyone who is either old or kind is happy and vice versa. Susan is either not patient or strong. Paul is both creative and not kind. Someone is not kind or old. Someone is not rich or wise. John is strong. Lucy is old. Someone is either quiet or creative. | Fred is not quiet. | neutral | ((?[X]:((~curious(X)|happy(X))))=>(?[X]:((calm(X)|wise(X)))))&
(![X]:((curious(X)|tall(X))<=>funny(X)))&
(((~happy(fred)|kind(fred)))<=>(?[X]:((patient(X)&~old(X)))))&
(![X]:((rich(X)&~curious(X))<=>(happy(X)<~>kind(X))))&
(![X]:((~patient(X)&strong(X))=>(~rich(X)&generous(X))))&
(![X]:((~brave(X)&funny(X))<=>(patient(X)|~creative(X))))&
(((creative(fred)<~>~happy(fred)))<=>((creative(lucy)<~>~tall(lucy))))&
(![X]:((~quiet(X)&~creative(X))=>~happy(X)))&
(![X]:((~quiet(X)<~>quiet(X))=>tall(X)))&
((curious(fred))<=>((tall(mary)<~>humble(mary))))&
(![X]:((~patient(X)&~tall(X))<=>(calm(X)<~>old(X))))&
((?[X]:(~generous(X)))=>((quiet(alice)&happy(alice))))&
(![X]:((funny(X)&humble(X))<=>(calm(X)&~quiet(X))))&
(![X]:((old(X)<~>kind(X))<=>happy(X)))&
((~patient(susan)<~>strong(susan)))&
((creative(paul)&~kind(paul)))&
(?[X]:((~kind(X)|old(X))))&
(?[X]:((~rich(X)|wise(X))))&
(strong(john))&
(old(lucy))&
(?[X]:((quiet(X)<~>creative(X)))) | ~quiet(fred) | [] | null | 0 |
Everyone who is funny is either not brave or rich. Everyone who is either not calm or generous is both patient and not curious and vice versa. Everyone who is both not rich and brave is not calm or generous. Everyone who is either not patient or wise is either happy or not creative. If fred is not curious then someone is both brave and not old and vice versa. Everyone who is strong or not funny is both not humble and not quiet and vice versa. Everyone who is both not kind and tall is both calm and not wise. Everyone who is not patient or not funny is both patient and not rich and vice versa. Everyone who is brave is creative or patient and vice versa. If fred is tall then someone is not funny or not calm and vice versa. Everyone who is either not strong or happy is not tall or calm. If fred is old or not brave then john is not strong or curious and vice versa. If susan is either not kind or tall then someone is not brave or patient. Everyone who is not quiet or humble is strong. If alice is both not humble and old then someone is not funny and vice versa. Everyone who is both not patient and strong is both generous and not strong. Someone is not rich or old. Fred is either old or generous. Someone is both not happy and not curious. Someone is rich. Susan is kind. Susan is generous or not curious. | Susan is happy. | neutral | (![X]:(funny(X)=>(~brave(X)<~>rich(X))))&
(![X]:((~calm(X)<~>generous(X))<=>(patient(X)&~curious(X))))&
(![X]:((~rich(X)&brave(X))=>(~calm(X)|generous(X))))&
(![X]:((~patient(X)<~>wise(X))=>(happy(X)<~>~creative(X))))&
((~curious(fred))<=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((strong(X)|~funny(X))<=>(~humble(X)&~quiet(X))))&
(![X]:((~kind(X)&tall(X))=>(calm(X)&~wise(X))))&
(![X]:((~patient(X)|~funny(X))<=>(patient(X)&~rich(X))))&
(![X]:(brave(X)<=>(creative(X)|patient(X))))&
((tall(fred))<=>(?[X]:((~funny(X)|~calm(X)))))&
(![X]:((~strong(X)<~>happy(X))=>(~tall(X)|calm(X))))&
(((old(fred)|~brave(fred)))<=>((~strong(john)|curious(john))))&
(((~kind(susan)<~>tall(susan)))=>(?[X]:((~brave(X)|patient(X)))))&
(![X]:((~quiet(X)|humble(X))=>strong(X)))&
(((~humble(alice)&old(alice)))<=>(?[X]:(~funny(X))))&
(![X]:((~patient(X)&strong(X))=>(generous(X)&~strong(X))))&
(?[X]:((~rich(X)|old(X))))&
((old(fred)<~>generous(fred)))&
(?[X]:((~happy(X)&~curious(X))))&
(?[X]:(rich(X)))&
(kind(susan))&
((generous(susan)|~curious(susan))) | happy(susan) | [] | null | 0 |
Everyone who is not creative or strong is either kind or wise. Everyone who is either wise or funny is either not old or old. Everyone who is tall is creative. If someone is both old and not happy then john is not rich or not patient. Everyone who is creative is curious and vice versa. If someone is generous or not patient then paul is either not curious or not creative. Everyone who is brave or not patient is not brave or brave. Everyone who is both brave and humble is not calm and vice versa. If someone is not humble or humble then mary is either not rich or not happy. Everyone who is both not patient and funny is both calm and not kind and vice versa. If alice is both not kind and not wise then mary is either not quiet or humble and vice versa. Everyone who is not humble is not generous. If paul is strong or curious then someone is not kind. If john is both generous and not generous then someone is tall or not funny. If someone is not quiet then fred is funny and vice versa. If someone is not tall then someone is not curious. Someone is not quiet. Fred is both not humble and happy. Paul is rich. Someone is creative. Someone is not rich or not generous. Someone is not quiet or strong. | John is curious. | neutral | (![X]:((~creative(X)|strong(X))=>(kind(X)<~>wise(X))))&
(![X]:((wise(X)<~>funny(X))=>(~old(X)<~>old(X))))&
(![X]:(tall(X)=>creative(X)))&
((?[X]:((old(X)&~happy(X))))=>((~rich(john)|~patient(john))))&
(![X]:(creative(X)<=>curious(X)))&
((?[X]:((generous(X)|~patient(X))))=>((~curious(paul)<~>~creative(paul))))&
(![X]:((brave(X)|~patient(X))=>(~brave(X)|brave(X))))&
(![X]:((brave(X)&humble(X))<=>~calm(X)))&
((?[X]:((~humble(X)|humble(X))))=>((~rich(mary)<~>~happy(mary))))&
(![X]:((~patient(X)&funny(X))<=>(calm(X)&~kind(X))))&
(((~kind(alice)&~wise(alice)))<=>((~quiet(mary)<~>humble(mary))))&
(![X]:(~humble(X)=>~generous(X)))&
(((strong(paul)|curious(paul)))=>(?[X]:(~kind(X))))&
(((generous(john)&~generous(john)))=>(?[X]:((tall(X)|~funny(X)))))&
((?[X]:(~quiet(X)))<=>(funny(fred)))&
((?[X]:(~tall(X)))=>(?[X]:(~curious(X))))&
(?[X]:(~quiet(X)))&
((~humble(fred)&happy(fred)))&
(rich(paul))&
(?[X]:(creative(X)))&
(?[X]:((~rich(X)|~generous(X))))&
(?[X]:((~quiet(X)|strong(X)))) | curious(john) | [] | null | 0 |
Everyone who is both not quiet and not brave is both calm and generous.
Everyone who is wise or patient is either not strong or happy and vice versa.
If someone is creative or not kind then alice is both not tall and not quiet.
Everyone who is humble is quiet or patient.
If susan is both humble and not brave then susan is wise or patient.
If someone is either creative or not brave then fred is not rich and vice versa.
If paul is either not humble or funny then lucy is either patient or strong and vice versa.
Everyone who is not curious or not kind is not strong or curious.
Everyone who is both not tall and creative is both calm and not calm.
Everyone who is either not wise or not quiet is both rich and generous.
If someone is both brave and not calm then fred is not creative or rich and vice versa.
If someone is humble or not tall then someone is generous and vice versa.
Everyone who is generous or kind is not tall.
Everyone who is both patient and not quiet is not patient and vice versa.
If john is both tall and curious then someone is not happy.
Everyone who is not creative or rich is both not old and not humble and vice versa.
Someone is not kind or brave.
Someone is both not tall and not creative.
Someone is calm or not wise.
Lucy is brave.
Someone is kind or not tall.
Someone is both not calm and generous. | Fred is not tall. | entailment | (![X]:((~quiet(X)&~brave(X))=>(calm(X)&generous(X))))&
(![X]:((wise(X)|patient(X))<=>(~strong(X)<~>happy(X))))&
((?[X]:((creative(X)|~kind(X))))=>((~tall(alice)&~quiet(alice))))&
(![X]:(humble(X)=>(quiet(X)|patient(X))))&
(((humble(susan)&~brave(susan)))=>((wise(susan)|patient(susan))))&
((?[X]:((creative(X)<~>~brave(X))))<=>(~rich(fred)))&
(((~humble(paul)<~>funny(paul)))<=>((patient(lucy)<~>strong(lucy))))&
(![X]:((~curious(X)|~kind(X))=>(~strong(X)|curious(X))))&
(![X]:((~tall(X)&creative(X))=>(calm(X)&~calm(X))))&
(![X]:((~wise(X)<~>~quiet(X))=>(rich(X)&generous(X))))&
((?[X]:((brave(X)&~calm(X))))<=>((~creative(fred)|rich(fred))))&
((?[X]:((humble(X)|~tall(X))))<=>(?[X]:(generous(X))))&
(![X]:((generous(X)|kind(X))=>~tall(X)))&
(![X]:((patient(X)&~quiet(X))<=>~patient(X)))&
(((tall(john)&curious(john)))=>(?[X]:(~happy(X))))&
(![X]:((~creative(X)|rich(X))<=>(~old(X)&~humble(X))))&
(?[X]:((~kind(X)|brave(X))))&
(?[X]:((~tall(X)&~creative(X))))&
(?[X]:((calm(X)|~wise(X))))&
(brave(lucy))&
(?[X]:((kind(X)|~tall(X))))&
(?[X]:((~calm(X)&generous(X)))) | ~tall(fred) | [
"p2",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 243379461002387110311323
% SZS output start Proof for 243379461002387110311323
3. ? [X0] : (~kind(X0) | creative(X0)) => (~quiet(alice) & ~tall(alice)) [input p2]
13. ! [X0] : ((kind(X0) | generous(X0)) => ~tall(X0)) [input p12]
14. ! [X0] : ((~quiet(X0) & patient(X0)) <=> ~patient(X0)) [input p13]
23. tall(fred) [input hypothesis]
27. (~quiet(alice) & ~tall(alice)) | ! [X0] : (kind(X0) & ~creative(X0)) [ennf transformation 3]
37. ! [X0] : (~tall(X0) | (~kind(X0) & ~generous(X0))) [ennf transformation 13]
58. ! [X0] : (((~quiet(X0) & patient(X0)) | patient(X0)) & (~patient(X0) | (quiet(X0) | ~patient(X0)))) [nnf transformation 14]
59. ! [X0] : (((~quiet(X0) & patient(X0)) | patient(X0)) & (~patient(X0) | quiet(X0) | ~patient(X0))) [flattening 58]
85. ~quiet(alice) | kind(X0) [cnf transformation 27]
117. ~tall(X0) | ~kind(X0) [cnf transformation 37]
118. ~patient(X0) | quiet(X0) | ~patient(X0) [cnf transformation 59]
119. patient(X0) | patient(X0) [cnf transformation 59]
135. tall(fred) [cnf transformation 23]
136. ~patient(X0) | quiet(X0) [duplicate literal removal 118]
137. patient(X0) [duplicate literal removal 119]
140. 1 <=> ! [X0] : kind(X0) [avatar definition]
141. kind(X0) <- (1) [avatar component clause 140]
143. 2 <=> quiet(alice) [avatar definition]
145. ~quiet(alice) <- (~2) [avatar component clause 143]
146. 1 | ~2 [avatar split clause 85,143,140]
265. quiet(X0) [subsumption resolution 136,137]
300. $false <- (~2) [subsumption resolution 145,265]
301. 2 [avatar contradiction clause 300]
305. ~kind(fred) [resolution 117,135]
306. $false <- (1) [subsumption resolution 305,141]
307. ~1 [avatar contradiction clause 306]
308. $false [avatar sat refutation 146,301,307]
% SZS output end Proof for 243379461002387110311323
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or not creative then susan is both generous and not rich.
Everyone who is rich or strong is both not tall and funny.
Everyone who is not tall or happy is both not calm and curious and vice versa.
If someone is both not brave and old then john is both calm and rich.
Everyone who is curious is either not funny or not tall and vice versa.
Everyone who is both rich and not tall is not funny or kind and vice versa.
Everyone who is both not old and rich is both not rich and not curious.
If mary is both not calm and creative then susan is brave or curious and vice versa.
Everyone who is either not tall or generous is not generous or creative.
Everyone who is either not humble or funny is strong.
Everyone who is either brave or generous is both brave and quiet.
Everyone who is funny is either humble or tall.
If mary is either not kind or not creative then john is both not creative and not generous and vice versa.
Everyone who is not wise is either wise or generous and vice versa.
Everyone who is both curious and happy is strong or not brave and vice versa.
If someone is both not funny and curious then lucy is both not creative and not happy and vice versa.
Fred is happy.
Someone is rich or not old.
Someone is either calm or rich.
Someone is not patient or happy.
Someone is not calm.
Someone is not strong or not funny. | Mary is rich. | entailment | ((?[X]:((kind(X)<~>~creative(X))))=>((generous(susan)&~rich(susan))))&
(![X]:((rich(X)|strong(X))=>(~tall(X)&funny(X))))&
(![X]:((~tall(X)|happy(X))<=>(~calm(X)&curious(X))))&
((?[X]:((~brave(X)&old(X))))=>((calm(john)&rich(john))))&
(![X]:(curious(X)<=>(~funny(X)<~>~tall(X))))&
(![X]:((rich(X)&~tall(X))<=>(~funny(X)|kind(X))))&
(![X]:((~old(X)&rich(X))=>(~rich(X)&~curious(X))))&
(((~calm(mary)&creative(mary)))<=>((brave(susan)|curious(susan))))&
(![X]:((~tall(X)<~>generous(X))=>(~generous(X)|creative(X))))&
(![X]:((~humble(X)<~>funny(X))=>strong(X)))&
(![X]:((brave(X)<~>generous(X))=>(brave(X)&quiet(X))))&
(![X]:(funny(X)=>(humble(X)<~>tall(X))))&
(((~kind(mary)<~>~creative(mary)))<=>((~creative(john)&~generous(john))))&
(![X]:(~wise(X)<=>(wise(X)<~>generous(X))))&
(![X]:((curious(X)&happy(X))<=>(strong(X)|~brave(X))))&
((?[X]:((~funny(X)&curious(X))))<=>((~creative(lucy)&~happy(lucy))))&
(happy(fred))&
(?[X]:((rich(X)|~old(X))))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:((~patient(X)|happy(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~strong(X)|~funny(X)))) | rich(mary) | [
"p5",
"p7",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9007003900453016993138017
% SZS output start Proof for 9007003900453016993138017
6. ! [X0] : ((~tall(X0) & rich(X0)) <=> (kind(X0) | ~funny(X0))) [input p5]
8. (creative(mary) & ~calm(mary)) <=> (curious(susan) | brave(susan)) [input p7]
13. (~kind(mary) <~> ~creative(mary)) <=> (~generous(john) & ~creative(john)) [input p12]
14. ! [X0] : (~wise(X0) <=> (wise(X0) <~> generous(X0))) [input p13]
15. ! [X0] : ((happy(X0) & curious(X0)) <=> (~brave(X0) | strong(X0))) [input p14]
23. ~rich(mary) [input hypothesis]
40. ! [X0] : (((~tall(X0) & rich(X0)) | (~kind(X0) & funny(X0))) & ((kind(X0) | ~funny(X0)) | (tall(X0) | ~rich(X0)))) [nnf transformation 6]
41. ! [X0] : (((~tall(X0) & rich(X0)) | (~kind(X0) & funny(X0))) & (kind(X0) | ~funny(X0) | tall(X0) | ~rich(X0))) [flattening 40]
42. ((creative(mary) & ~calm(mary)) | (~curious(susan) & ~brave(susan))) & ((curious(susan) | brave(susan)) | (~creative(mary) | calm(mary))) [nnf transformation 8]
43. ((creative(mary) & ~calm(mary)) | (~curious(susan) & ~brave(susan))) & (curious(susan) | brave(susan) | ~creative(mary) | calm(mary)) [flattening 42]
48. (((creative(mary) | kind(mary)) & (~creative(mary) | ~kind(mary))) | (generous(john) | creative(john))) & ((~generous(john) & ~creative(john)) | ((~kind(mary) | creative(mary)) & (~creative(mary) | kind(mary)))) [nnf transformation 13]
49. (((creative(mary) | kind(mary)) & (~creative(mary) | ~kind(mary))) | generous(john) | creative(john)) & ((~generous(john) & ~creative(john)) | ((~kind(mary) | creative(mary)) & (~creative(mary) | kind(mary)))) [flattening 48]
50. ! [X0] : ((~wise(X0) | ((wise(X0) | ~generous(X0)) & (generous(X0) | ~wise(X0)))) & (((~generous(X0) | ~wise(X0)) & (generous(X0) | wise(X0))) | wise(X0))) [nnf transformation 14]
51. ! [X0] : (((happy(X0) & curious(X0)) | (brave(X0) & ~strong(X0))) & ((~brave(X0) | strong(X0)) | (~happy(X0) | ~curious(X0)))) [nnf transformation 15]
52. ! [X0] : (((happy(X0) & curious(X0)) | (brave(X0) & ~strong(X0))) & (~brave(X0) | strong(X0) | ~happy(X0) | ~curious(X0))) [flattening 51]
88. ~kind(X0) | rich(X0) [cnf transformation 41]
96. creative(mary) | ~brave(susan) [cnf transformation 43]
97. creative(mary) | ~curious(susan) [cnf transformation 43]
108. ~generous(john) | ~creative(mary) | kind(mary) [cnf transformation 49]
112. generous(X0) | wise(X0) | wise(X0) [cnf transformation 50]
114. ~wise(X0) | generous(X0) | ~wise(X0) [cnf transformation 50]
118. brave(X0) | curious(X0) [cnf transformation 52]
131. ~rich(mary) [cnf transformation 23]
132. generous(X0) | wise(X0) [duplicate literal removal 112]
133. ~wise(X0) | generous(X0) [duplicate literal removal 114]
174. 8 <=> curious(susan) [avatar definition]
176. ~curious(susan) <- (~8) [avatar component clause 174]
178. 9 <=> creative(mary) [avatar definition]
181. ~8 | 9 [avatar split clause 97,178,174]
183. 10 <=> brave(susan) [avatar definition]
185. ~brave(susan) <- (~10) [avatar component clause 183]
186. ~10 | 9 [avatar split clause 96,178,183]
202. 13 <=> generous(john) [avatar definition]
203. ~generous(john) <- (~13) [avatar component clause 202]
206. 14 <=> kind(mary) [avatar definition]
208. kind(mary) <- (14) [avatar component clause 206]
212. 14 | ~9 | ~13 [avatar split clause 108,202,178,206]
215. generous(X0) [subsumption resolution 132,133]
252. $false <- (~13) [subsumption resolution 203,215]
253. 13 [avatar contradiction clause 252]
264. curious(susan) <- (~10) [resolution 118,185]
265. $false <- (~8, ~10) [subsumption resolution 264,176]
266. 8 | 10 [avatar contradiction clause 265]
267. rich(mary) <- (14) [resolution 208,88]
268. $false <- (14) [subsumption resolution 267,131]
269. ~14 [avatar contradiction clause 268]
270. $false [avatar sat refutation 181,186,212,253,266,269]
% SZS output end Proof for 9007003900453016993138017
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old is quiet or not tall.
If fred is either not creative or not old then fred is both generous and tall.
If lucy is either humble or brave then john is either old or not old and vice versa.
Everyone who is either strong or not curious is either not patient or not curious.
Everyone who is both not kind and humble is either old or not happy.
If someone is either rich or patient then someone is either wise or patient and vice versa.
If paul is either not funny or not quiet then susan is both patient and not generous and vice versa.
If someone is not creative then alice is happy or not quiet.
Everyone who is both generous and not patient is either rich or not quiet.
Everyone who is old is either not patient or rich and vice versa.
Everyone who is tall or not curious is both brave and patient and vice versa.
Everyone who is both not happy and creative is old or not curious.
If susan is not wise then someone is both kind and not wise and vice versa.
If mary is both not kind and not funny then someone is both generous and not old.
Everyone who is either not calm or not curious is either happy or not curious and vice versa.
Everyone who is either strong or not calm is either not curious or brave and vice versa.
Someone is not wise or happy.
Fred is kind or generous.
John is not tall or humble.
Someone is not strong.
Mary is not happy.
Mary is both not wise and quiet.
Someone is either not generous or old.
Someone is both funny and generous. | Mary is quiet. | entailment | (![X]:(~old(X)=>(quiet(X)|~tall(X))))&
(((~creative(fred)<~>~old(fred)))=>((generous(fred)&tall(fred))))&
(((humble(lucy)<~>brave(lucy)))<=>((old(john)<~>~old(john))))&
(![X]:((strong(X)<~>~curious(X))=>(~patient(X)<~>~curious(X))))&
(![X]:((~kind(X)&humble(X))=>(old(X)<~>~happy(X))))&
((?[X]:((rich(X)<~>patient(X))))<=>(?[X]:((wise(X)<~>patient(X)))))&
(((~funny(paul)<~>~quiet(paul)))<=>((patient(susan)&~generous(susan))))&
((?[X]:(~creative(X)))=>((happy(alice)|~quiet(alice))))&
(![X]:((generous(X)&~patient(X))=>(rich(X)<~>~quiet(X))))&
(![X]:(old(X)<=>(~patient(X)<~>rich(X))))&
(![X]:((tall(X)|~curious(X))<=>(brave(X)&patient(X))))&
(![X]:((~happy(X)&creative(X))=>(old(X)|~curious(X))))&
((~wise(susan))<=>(?[X]:((kind(X)&~wise(X)))))&
(((~kind(mary)&~funny(mary)))=>(?[X]:((generous(X)&~old(X)))))&
(![X]:((~calm(X)<~>~curious(X))<=>(happy(X)<~>~curious(X))))&
(![X]:((strong(X)<~>~calm(X))<=>(~curious(X)<~>brave(X))))&
(?[X]:((~wise(X)|happy(X))))&
((kind(fred)|generous(fred)))&
((~tall(john)|humble(john)))&
(?[X]:(~strong(X)))&
(~happy(mary))&
((~wise(mary)&quiet(mary)))&
(?[X]:((~generous(X)<~>old(X))))&
(?[X]:((funny(X)&generous(X)))) | quiet(mary) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3841431852635044011310424
% SZS output start Proof for 3841431852635044011310424
22. quiet(mary) & ~wise(mary) [input p21]
25. ~quiet(mary) [input hypothesis]
146. quiet(mary) [cnf transformation 22]
151. ~quiet(mary) [cnf transformation 25]
343. $false [subsumption resolution 151,146]
% SZS output end Proof for 3841431852635044011310424
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is patient then mary is either not strong or old. Everyone who is funny is wise or rich and vice versa. If someone is not old then susan is either not strong or happy. Everyone who is either creative or not strong is not humble or patient and vice versa. Everyone who is both not funny and generous is wise or tall and vice versa. If john is calm or strong then susan is both not calm and not humble. Everyone who is both not calm and not humble is not old and vice versa. If someone is either not funny or generous then someone is both curious and not humble and vice versa. Everyone who is humble or not creative is old and vice versa. Everyone who is not calm or not funny is either not wise or humble. If susan is not generous or not patient then someone is both happy and quiet and vice versa. Everyone who is not funny or generous is either strong or not strong. Everyone who is both not curious and generous is both not rich and not happy. If someone is generous or patient then someone is funny or not strong and vice versa. If lucy is not calm then fred is either wise or not old and vice versa. Someone is not happy. Someone is not strong or not kind. Alice is wise or not patient. Someone is not tall or happy. Lucy is either quiet or not happy. Alice is either not strong or brave. Someone is not calm or creative. | Susan is old. | contradiction | ((patient(paul))=>((~strong(mary)<~>old(mary))))&
(![X]:(funny(X)<=>(wise(X)|rich(X))))&
((?[X]:(~old(X)))=>((~strong(susan)<~>happy(susan))))&
(![X]:((creative(X)<~>~strong(X))<=>(~humble(X)|patient(X))))&
(![X]:((~funny(X)&generous(X))<=>(wise(X)|tall(X))))&
(((calm(john)|strong(john)))=>((~calm(susan)&~humble(susan))))&
(![X]:((~calm(X)&~humble(X))<=>~old(X)))&
((?[X]:((~funny(X)<~>generous(X))))<=>(?[X]:((curious(X)&~humble(X)))))&
(![X]:((humble(X)|~creative(X))<=>old(X)))&
(![X]:((~calm(X)|~funny(X))=>(~wise(X)<~>humble(X))))&
(((~generous(susan)|~patient(susan)))<=>(?[X]:((happy(X)&quiet(X)))))&
(![X]:((~funny(X)|generous(X))=>(strong(X)<~>~strong(X))))&
(![X]:((~curious(X)&generous(X))=>(~rich(X)&~happy(X))))&
((?[X]:((generous(X)|patient(X))))<=>(?[X]:((funny(X)|~strong(X)))))&
((~calm(lucy))<=>((wise(fred)<~>~old(fred))))&
(?[X]:(~happy(X)))&
(?[X]:((~strong(X)|~kind(X))))&
((wise(alice)|~patient(alice)))&
(?[X]:((~tall(X)|happy(X))))&
((quiet(lucy)<~>~happy(lucy)))&
((~strong(alice)<~>brave(alice)))&
(?[X]:((~calm(X)|creative(X)))) | old(susan) | [
"p1",
"p3",
"p4",
"p5",
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7718443056269103965866955
% SZS output start Proof for 7718443056269103965866955
2. ! [X0] : (funny(X0) <=> (rich(X0) | wise(X0))) [input p1]
4. ! [X0] : ((creative(X0) <~> ~strong(X0)) <=> (patient(X0) | ~humble(X0))) [input p3]
5. ! [X0] : ((generous(X0) & ~funny(X0)) <=> (tall(X0) | wise(X0))) [input p4]
6. (strong(john) | calm(john)) => (~humble(susan) & ~calm(susan)) [input p5]
7. ! [X0] : ((~humble(X0) & ~calm(X0)) <=> ~old(X0)) [input p6]
9. ! [X0] : ((~creative(X0) | humble(X0)) <=> old(X0)) [input p8]
10. ! [X0] : ((~funny(X0) | ~calm(X0)) => (~wise(X0) <~> humble(X0))) [input p9]
23. old(susan) [input hypothesis]
29. (~humble(susan) & ~calm(susan)) | (~strong(john) & ~calm(john)) [ennf transformation 6]
30. ! [X0] : ((~wise(X0) <~> humble(X0)) | (funny(X0) & calm(X0))) [ennf transformation 10]
35. ! [X0] : ((funny(X0) | (~rich(X0) & ~wise(X0))) & ((rich(X0) | wise(X0)) | ~funny(X0))) [nnf transformation 2]
36. ! [X0] : ((funny(X0) | (~rich(X0) & ~wise(X0))) & (rich(X0) | wise(X0) | ~funny(X0))) [flattening 35]
38. ! [X0] : ((((strong(X0) | ~creative(X0)) & (~strong(X0) | creative(X0))) | (~patient(X0) & humble(X0))) & ((patient(X0) | ~humble(X0)) | ((creative(X0) | strong(X0)) & (~strong(X0) | ~creative(X0))))) [nnf transformation 4]
39. ! [X0] : ((((strong(X0) | ~creative(X0)) & (~strong(X0) | creative(X0))) | (~patient(X0) & humble(X0))) & (patient(X0) | ~humble(X0) | ((creative(X0) | strong(X0)) & (~strong(X0) | ~creative(X0))))) [flattening 38]
40. ! [X0] : (((generous(X0) & ~funny(X0)) | (~tall(X0) & ~wise(X0))) & ((tall(X0) | wise(X0)) | (~generous(X0) | funny(X0)))) [nnf transformation 5]
41. ! [X0] : (((generous(X0) & ~funny(X0)) | (~tall(X0) & ~wise(X0))) & (tall(X0) | wise(X0) | ~generous(X0) | funny(X0))) [flattening 40]
42. ! [X0] : (((~humble(X0) & ~calm(X0)) | old(X0)) & (~old(X0) | (humble(X0) | calm(X0)))) [nnf transformation 7]
43. ! [X0] : (((~humble(X0) & ~calm(X0)) | old(X0)) & (~old(X0) | humble(X0) | calm(X0))) [flattening 42]
49. ! [X0] : (((~creative(X0) | humble(X0)) | ~old(X0)) & (old(X0) | (creative(X0) & ~humble(X0)))) [nnf transformation 9]
50. ! [X0] : ((~creative(X0) | humble(X0) | ~old(X0)) & (old(X0) | (creative(X0) & ~humble(X0)))) [flattening 49]
51. ! [X0] : (((~humble(X0) | wise(X0)) & (humble(X0) | ~wise(X0))) | (funny(X0) & calm(X0))) [nnf transformation 30]
75. ~wise(X0) | funny(X0) [cnf transformation 36]
83. ~creative(X0) | strong(X0) | humble(X0) [cnf transformation 39]
86. ~funny(X0) | ~wise(X0) [cnf transformation 41]
90. ~calm(susan) | ~calm(john) [cnf transformation 29]
91. ~calm(susan) | ~strong(john) [cnf transformation 29]
94. ~old(X0) | humble(X0) | calm(X0) [cnf transformation 43]
96. ~humble(X0) | old(X0) [cnf transformation 43]
104. creative(X0) | old(X0) [cnf transformation 50]
108. ~humble(X0) | wise(X0) | calm(X0) [cnf transformation 51]
137. old(susan) [cnf transformation 23]
165. ~wise(X0) [subsumption resolution 86,75]
168. 7 <=> strong(john) [avatar definition]
170. ~strong(john) <- (~7) [avatar component clause 168]
177. 9 <=> calm(john) [avatar definition]
179. ~calm(john) <- (~9) [avatar component clause 177]
182. 10 <=> calm(susan) [avatar definition]
185. ~7 | ~10 [avatar split clause 91,182,168]
186. ~9 | ~10 [avatar split clause 90,182,177]
219. ~humble(X0) | calm(X0) [subsumption resolution 108,165]
337. strong(X0) | humble(X0) | old(X0) [resolution 83,104]
338. old(X0) | strong(X0) [subsumption resolution 337,96]
341. humble(susan) | calm(susan) [resolution 94,137]
342. humble(X0) | calm(X0) | strong(X0) [resolution 94,338]
343. calm(susan) [subsumption resolution 341,219]
344. 10 [avatar split clause 343,182]
345. calm(X0) | strong(X0) [subsumption resolution 342,219]
415. strong(john) <- (~9) [resolution 345,179]
417. $false <- (~7, ~9) [subsumption resolution 415,170]
418. 7 | 9 [avatar contradiction clause 417]
419. $false [avatar sat refutation 185,186,344,418]
% SZS output end Proof for 7718443056269103965866955
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either not strong or calm then someone is brave.
If mary is either not wise or not humble then someone is either not rich or not strong and vice versa.
Everyone who is old or not rich is curious.
If mary is both kind and not humble then someone is wise.
Everyone who is happy is either not generous or not curious and vice versa.
If paul is not rich then someone is both not strong and wise.
Everyone who is both not patient and happy is strong or not tall and vice versa.
Everyone who is generous or creative is not creative or old and vice versa.
If paul is either not curious or calm then mary is both tall and not curious.
Everyone who is either creative or curious is both not strong and happy and vice versa.
Everyone who is either happy or not brave is either tall or curious and vice versa.
If paul is both not wise and old then someone is old or patient and vice versa.
Everyone who is humble is either strong or not humble and vice versa.
Everyone who is old is either not calm or not generous.
If someone is either old or not brave then someone is both not funny and funny and vice versa.
If mary is either not kind or curious then someone is tall or not happy and vice versa.
Someone is both creative and tall.
John is not quiet.
Alice is either not generous or not calm.
Someone is either brave or old.
Someone is either funny or quiet.
Fred is both curious and funny.
Someone is either not happy or not generous. | John is calm. | neutral | (((~strong(fred)<~>calm(fred)))=>(?[X]:(brave(X))))&
(((~wise(mary)<~>~humble(mary)))<=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:((old(X)|~rich(X))=>curious(X)))&
(((kind(mary)&~humble(mary)))=>(?[X]:(wise(X))))&
(![X]:(happy(X)<=>(~generous(X)<~>~curious(X))))&
((~rich(paul))=>(?[X]:((~strong(X)&wise(X)))))&
(![X]:((~patient(X)&happy(X))<=>(strong(X)|~tall(X))))&
(![X]:((generous(X)|creative(X))<=>(~creative(X)|old(X))))&
(((~curious(paul)<~>calm(paul)))=>((tall(mary)&~curious(mary))))&
(![X]:((creative(X)<~>curious(X))<=>(~strong(X)&happy(X))))&
(![X]:((happy(X)<~>~brave(X))<=>(tall(X)<~>curious(X))))&
(((~wise(paul)&old(paul)))<=>(?[X]:((old(X)|patient(X)))))&
(![X]:(humble(X)<=>(strong(X)<~>~humble(X))))&
(![X]:(old(X)=>(~calm(X)<~>~generous(X))))&
((?[X]:((old(X)<~>~brave(X))))<=>(?[X]:((~funny(X)&funny(X)))))&
(((~kind(mary)<~>curious(mary)))<=>(?[X]:((tall(X)|~happy(X)))))&
(?[X]:((creative(X)&tall(X))))&
(~quiet(john))&
((~generous(alice)<~>~calm(alice)))&
(?[X]:((brave(X)<~>old(X))))&
(?[X]:((funny(X)<~>quiet(X))))&
((curious(fred)&funny(fred)))&
(?[X]:((~happy(X)<~>~generous(X)))) | calm(john) | [] | null | 0 |
Everyone who is calm or not funny is both rich and not tall. Everyone who is curious is both not funny and not happy. Everyone who is both quiet and not generous is either funny or wise. Everyone who is either brave or not funny is both kind and not happy and vice versa. If paul is both not calm and humble then paul is both humble and not tall. Everyone who is funny or not generous is either not funny or brave and vice versa. If someone is both not calm and funny then someone is not rich or strong. Everyone who is strong is creative or not brave. Everyone who is brave or not old is not kind and vice versa. Everyone who is both rich and funny is both strong and calm and vice versa. Everyone who is not creative is not happy. Everyone who is strong or humble is either quiet or creative. If alice is not funny then lucy is not old. If mary is not wise or not tall then paul is both quiet and not brave and vice versa. Everyone who is brave or not generous is not funny. Lucy is strong or brave. Lucy is not old. Lucy is either not happy or old. Someone is kind or quiet. Someone is either not quiet or wise. Someone is strong or not humble. Lucy is either kind or brave. | Paul is brave. | contradiction | (![X]:((calm(X)|~funny(X))=>(rich(X)&~tall(X))))&
(![X]:(curious(X)=>(~funny(X)&~happy(X))))&
(![X]:((quiet(X)&~generous(X))=>(funny(X)<~>wise(X))))&
(![X]:((brave(X)<~>~funny(X))<=>(kind(X)&~happy(X))))&
(((~calm(paul)&humble(paul)))=>((humble(paul)&~tall(paul))))&
(![X]:((funny(X)|~generous(X))<=>(~funny(X)<~>brave(X))))&
((?[X]:((~calm(X)&funny(X))))=>(?[X]:((~rich(X)|strong(X)))))&
(![X]:(strong(X)=>(creative(X)|~brave(X))))&
(![X]:((brave(X)|~old(X))<=>~kind(X)))&
(![X]:((rich(X)&funny(X))<=>(strong(X)&calm(X))))&
(![X]:(~creative(X)=>~happy(X)))&
(![X]:((strong(X)|humble(X))=>(quiet(X)<~>creative(X))))&
((~funny(alice))=>(~old(lucy)))&
(((~wise(mary)|~tall(mary)))<=>((quiet(paul)&~brave(paul))))&
(![X]:((brave(X)|~generous(X))=>~funny(X)))&
((strong(lucy)|brave(lucy)))&
(~old(lucy))&
((~happy(lucy)<~>old(lucy)))&
(?[X]:((kind(X)|quiet(X))))&
(?[X]:((~quiet(X)<~>wise(X))))&
(?[X]:((strong(X)|~humble(X))))&
((kind(lucy)<~>brave(lucy))) | brave(paul) | [
"p0",
"p5",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5482840102226865751800214
% SZS output start Proof for 5482840102226865751800214
1. ! [X0] : ((~funny(X0) | calm(X0)) => (~tall(X0) & rich(X0))) [input p0]
6. ! [X0] : ((~generous(X0) | funny(X0)) <=> (~funny(X0) <~> brave(X0))) [input p5]
14. (~tall(mary) | ~wise(mary)) <=> (~brave(paul) & quiet(paul)) [input p13]
15. ! [X0] : ((~generous(X0) | brave(X0)) => ~funny(X0)) [input p14]
23. brave(paul) [input hypothesis]
26. ! [X0] : ((~tall(X0) & rich(X0)) | (funny(X0) & ~calm(X0))) [ennf transformation 1]
37. ! [X0] : (~funny(X0) | (generous(X0) & ~brave(X0))) [ennf transformation 15]
41. ! [X0] : (((~generous(X0) | funny(X0)) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0)))) & (((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | (generous(X0) & ~funny(X0)))) [nnf transformation 6]
42. ! [X0] : ((~generous(X0) | funny(X0) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0)))) & (((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | (generous(X0) & ~funny(X0)))) [flattening 41]
51. ((~tall(mary) | ~wise(mary)) | (brave(paul) | ~quiet(paul))) & ((~brave(paul) & quiet(paul)) | (tall(mary) & wise(mary))) [nnf transformation 14]
52. (~tall(mary) | ~wise(mary) | brave(paul) | ~quiet(paul)) & ((~brave(paul) & quiet(paul)) | (tall(mary) & wise(mary))) [flattening 51]
65. ~tall(X0) | funny(X0) [cnf transformation 26]
76. brave(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 42]
100. ~brave(paul) | tall(mary) [cnf transformation 52]
102. ~funny(X0) | ~brave(X0) [cnf transformation 37]
114. brave(paul) [cnf transformation 23]
115. brave(X0) | ~funny(X0) [duplicate literal removal 76]
153. 9 <=> brave(paul) [avatar definition]
161. 11 <=> tall(mary) [avatar definition]
162. tall(mary) <- (11) [avatar component clause 161]
165. 11 | ~9 [avatar split clause 100,153,161]
169. ~funny(X0) [subsumption resolution 102,115]
219. 9 [avatar split clause 114,153]
224. funny(mary) <- (11) [resolution 65,162]
225. $false <- (11) [subsumption resolution 224,169]
226. ~11 [avatar contradiction clause 225]
227. $false [avatar sat refutation 165,219,226]
% SZS output end Proof for 5482840102226865751800214
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not humble or not kind then someone is curious or funny and vice versa.
Everyone who is either not quiet or not creative is both not strong and not kind and vice versa.
Everyone who is calm is not old or not calm and vice versa.
Everyone who is not generous is both not calm and curious and vice versa.
If someone is not humble then alice is old and vice versa.
Everyone who is either not generous or not strong is funny or rich and vice versa.
Everyone who is not wise is either old or not strong and vice versa.
If someone is both not creative and not strong then mary is not happy and vice versa.
If someone is both not old and wise then someone is both not curious and wise and vice versa.
If alice is both humble and tall then someone is not calm.
Everyone who is happy is calm or not generous and vice versa.
Everyone who is not old is either tall or not tall.
If lucy is kind or rich then lucy is either strong or not creative.
Everyone who is not patient or not humble is tall or not funny.
Everyone who is either brave or not strong is brave and vice versa.
Someone is both quiet and not patient.
John is either funny or kind.
Someone is both not old and not kind. | John is wise. | entailment | ((?[X]:((~humble(X)<~>~kind(X))))<=>(?[X]:((curious(X)|funny(X)))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(~strong(X)&~kind(X))))&
(![X]:(calm(X)<=>(~old(X)|~calm(X))))&
(![X]:(~generous(X)<=>(~calm(X)&curious(X))))&
((?[X]:(~humble(X)))<=>(old(alice)))&
(![X]:((~generous(X)<~>~strong(X))<=>(funny(X)|rich(X))))&
(![X]:(~wise(X)<=>(old(X)<~>~strong(X))))&
((?[X]:((~creative(X)&~strong(X))))<=>(~happy(mary)))&
((?[X]:((~old(X)&wise(X))))<=>(?[X]:((~curious(X)&wise(X)))))&
(((humble(alice)&tall(alice)))=>(?[X]:(~calm(X))))&
(![X]:(happy(X)<=>(calm(X)|~generous(X))))&
(![X]:(~old(X)=>(tall(X)<~>~tall(X))))&
(((kind(lucy)|rich(lucy)))=>((strong(lucy)<~>~creative(lucy))))&
(![X]:((~patient(X)|~humble(X))=>(tall(X)|~funny(X))))&
(![X]:((brave(X)<~>~strong(X))<=>brave(X)))&
(?[X]:((quiet(X)&~patient(X))))&
((funny(john)<~>kind(john)))&
(?[X]:((~old(X)&~kind(X)))) | wise(john) | [
"p2",
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 9203311721130506198433150
% SZS output start Proof for 9203311721130506198433150
3. ! [X0] : (calm(X0) <=> (~calm(X0) | ~old(X0))) [input p2]
7. ! [X0] : (~wise(X0) <=> (old(X0) <~> ~strong(X0))) [input p6]
15. ! [X0] : ((brave(X0) <~> ~strong(X0)) <=> brave(X0)) [input p14]
19. ~wise(john) [input hypothesis]
35. ! [X0] : ((calm(X0) | (calm(X0) & old(X0))) & ((~calm(X0) | ~old(X0)) | ~calm(X0))) [nnf transformation 3]
36. ! [X0] : ((calm(X0) | (calm(X0) & old(X0))) & (~calm(X0) | ~old(X0) | ~calm(X0))) [flattening 35]
45. ! [X0] : ((~wise(X0) | ((old(X0) | strong(X0)) & (~strong(X0) | ~old(X0)))) & (((strong(X0) | ~old(X0)) & (~strong(X0) | old(X0))) | wise(X0))) [nnf transformation 7]
61. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | ~brave(X0)) & (brave(X0) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [nnf transformation 15]
79. ~calm(X0) | ~old(X0) | ~calm(X0) [cnf transformation 36]
81. calm(X0) | calm(X0) [cnf transformation 36]
93. ~strong(X0) | old(X0) | wise(X0) [cnf transformation 45]
117. brave(X0) | brave(X0) | strong(X0) [cnf transformation 61]
119. strong(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 61]
126. ~wise(john) [cnf transformation 19]
127. brave(X0) | strong(X0) [duplicate literal removal 117]
128. ~brave(X0) | strong(X0) [duplicate literal removal 119]
129. ~calm(X0) | ~old(X0) [duplicate literal removal 79]
130. calm(X0) [duplicate literal removal 81]
165. ~old(X0) [subsumption resolution 129,130]
172. ~strong(X0) | wise(X0) [subsumption resolution 93,165]
237. strong(X0) [subsumption resolution 127,128]
256. wise(X0) [resolution 172,237]
262. $false [resolution 256,126]
% SZS output end Proof for 9203311721130506198433150
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and not patient then someone is either not happy or old and vice versa.
If fred is either not brave or not creative then mary is either curious or not creative and vice versa.
If paul is both tall and not generous then someone is either strong or not happy and vice versa.
Everyone who is strong is both old and humble and vice versa.
If someone is patient then someone is happy or not quiet and vice versa.
Everyone who is both not quiet and not humble is both tall and patient and vice versa.
If someone is both not quiet and not brave then someone is either not strong or not rich and vice versa.
Everyone who is both not old and happy is both calm and kind.
If someone is not happy or not calm then fred is both generous and not creative and vice versa.
Everyone who is both old and not happy is either not happy or not old and vice versa.
Everyone who is tall is not patient.
If someone is both not patient and not happy then john is not curious or brave and vice versa.
Everyone who is either calm or happy is both old and tall.
Everyone who is not rich or calm is not creative.
If susan is not quiet or wise then mary is not generous or not kind.
If lucy is both humble and not tall then someone is either not calm or quiet and vice versa.
Paul is generous.
Alice is not brave.
Mary is both not humble and patient.
Paul is curious or patient.
Someone is not quiet.
Someone is not creative.
John is funny. | Lucy is not strong. | contradiction | ((?[X]:((~brave(X)&~patient(X))))<=>(?[X]:((~happy(X)<~>old(X)))))&
(((~brave(fred)<~>~creative(fred)))<=>((curious(mary)<~>~creative(mary))))&
(((tall(paul)&~generous(paul)))<=>(?[X]:((strong(X)<~>~happy(X)))))&
(![X]:(strong(X)<=>(old(X)&humble(X))))&
((?[X]:(patient(X)))<=>(?[X]:((happy(X)|~quiet(X)))))&
(![X]:((~quiet(X)&~humble(X))<=>(tall(X)&patient(X))))&
((?[X]:((~quiet(X)&~brave(X))))<=>(?[X]:((~strong(X)<~>~rich(X)))))&
(![X]:((~old(X)&happy(X))=>(calm(X)&kind(X))))&
((?[X]:((~happy(X)|~calm(X))))<=>((generous(fred)&~creative(fred))))&
(![X]:((old(X)&~happy(X))<=>(~happy(X)<~>~old(X))))&
(![X]:(tall(X)=>~patient(X)))&
((?[X]:((~patient(X)&~happy(X))))<=>((~curious(john)|brave(john))))&
(![X]:((calm(X)<~>happy(X))=>(old(X)&tall(X))))&
(![X]:((~rich(X)|calm(X))=>~creative(X)))&
(((~quiet(susan)|wise(susan)))=>((~generous(mary)|~kind(mary))))&
(((humble(lucy)&~tall(lucy)))<=>(?[X]:((~calm(X)<~>quiet(X)))))&
(generous(paul))&
(~brave(alice))&
((~humble(mary)&patient(mary)))&
((curious(paul)|patient(paul)))&
(?[X]:(~quiet(X)))&
(?[X]:(~creative(X)))&
(funny(john)) | ~strong(lucy) | [
"p2",
"p3",
"p5",
"p9",
"p10",
"p12",
"p15",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 363027621286702007586798
% SZS output start Proof for 363027621286702007586798
3. (~generous(paul) & tall(paul)) <=> ? [X0] : (strong(X0) <~> ~happy(X0)) [input p2]
4. ! [X0] : (strong(X0) <=> (humble(X0) & old(X0))) [input p3]
6. ! [X0] : ((~humble(X0) & ~quiet(X0)) <=> (patient(X0) & tall(X0))) [input p5]
10. ! [X0] : ((~happy(X0) & old(X0)) <=> (~happy(X0) <~> ~old(X0))) [input p9]
11. ! [X0] : (tall(X0) => ~patient(X0)) [input p10]
13. ! [X0] : ((calm(X0) <~> happy(X0)) => (tall(X0) & old(X0))) [input p12]
16. (~tall(lucy) & humble(lucy)) <=> ? [X0] : (~calm(X0) <~> quiet(X0)) [input p15]
17. generous(paul) [input p16]
19. patient(mary) & ~humble(mary) [input p18]
24. ~strong(lucy) [input hypothesis]
32. ! [X0] : (~patient(X0) | ~tall(X0)) [ennf transformation 11]
33. ! [X0] : ((tall(X0) & old(X0)) | (calm(X0) <=> happy(X0))) [ennf transformation 13]
43. ((~generous(paul) & tall(paul)) | ! [X0] : ((strong(X0) | happy(X0)) & (~happy(X0) | ~strong(X0)))) & (? [X0] : ((happy(X0) | ~strong(X0)) & (~happy(X0) | strong(X0))) | (generous(paul) | ~tall(paul))) [nnf transformation 3]
44. ((~generous(paul) & tall(paul)) | ! [X0] : ((strong(X0) | happy(X0)) & (~happy(X0) | ~strong(X0)))) & (? [X0] : ((happy(X0) | ~strong(X0)) & (~happy(X0) | strong(X0))) | generous(paul) | ~tall(paul)) [flattening 43]
45. ((~generous(paul) & tall(paul)) | ! [X0] : ((strong(X0) | happy(X0)) & (~happy(X0) | ~strong(X0)))) & (? [X1] : ((happy(X1) | ~strong(X1)) & (~happy(X1) | strong(X1))) | generous(paul) | ~tall(paul)) [rectify 44]
46. ? [X1] : ((happy(X1) | ~strong(X1)) & (~happy(X1) | strong(X1))) => ((happy(sK2) | ~strong(sK2)) & (~happy(sK2) | strong(sK2))) [choice axiom]
47. ((~generous(paul) & tall(paul)) | ! [X0] : ((strong(X0) | happy(X0)) & (~happy(X0) | ~strong(X0)))) & (((happy(sK2) | ~strong(sK2)) & (~happy(sK2) | strong(sK2))) | generous(paul) | ~tall(paul)) [skolemisation 45,46]
48. ! [X0] : ((strong(X0) | (~humble(X0) | ~old(X0))) & ((humble(X0) & old(X0)) | ~strong(X0))) [nnf transformation 4]
49. ! [X0] : ((strong(X0) | ~humble(X0) | ~old(X0)) & ((humble(X0) & old(X0)) | ~strong(X0))) [flattening 48]
55. ! [X0] : (((~humble(X0) & ~quiet(X0)) | (~patient(X0) | ~tall(X0))) & ((patient(X0) & tall(X0)) | (humble(X0) | quiet(X0)))) [nnf transformation 6]
56. ! [X0] : (((~humble(X0) & ~quiet(X0)) | ~patient(X0) | ~tall(X0)) & ((patient(X0) & tall(X0)) | humble(X0) | quiet(X0))) [flattening 55]
67. ! [X0] : (((~happy(X0) & old(X0)) | ((~happy(X0) | old(X0)) & (~old(X0) | happy(X0)))) & (((old(X0) | happy(X0)) & (~old(X0) | ~happy(X0))) | (happy(X0) | ~old(X0)))) [nnf transformation 10]
68. ! [X0] : (((~happy(X0) & old(X0)) | ((~happy(X0) | old(X0)) & (~old(X0) | happy(X0)))) & (((old(X0) | happy(X0)) & (~old(X0) | ~happy(X0))) | happy(X0) | ~old(X0))) [flattening 67]
74. ! [X0] : ((tall(X0) & old(X0)) | ((calm(X0) | ~happy(X0)) & (happy(X0) | ~calm(X0)))) [nnf transformation 33]
75. ((~tall(lucy) & humble(lucy)) | ! [X0] : ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0)))) & (? [X0] : ((~quiet(X0) | calm(X0)) & (quiet(X0) | ~calm(X0))) | (tall(lucy) | ~humble(lucy))) [nnf transformation 16]
76. ((~tall(lucy) & humble(lucy)) | ! [X0] : ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0)))) & (? [X0] : ((~quiet(X0) | calm(X0)) & (quiet(X0) | ~calm(X0))) | tall(lucy) | ~humble(lucy)) [flattening 75]
77. ((~tall(lucy) & humble(lucy)) | ! [X0] : ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0)))) & (? [X1] : ((~quiet(X1) | calm(X1)) & (quiet(X1) | ~calm(X1))) | tall(lucy) | ~humble(lucy)) [rectify 76]
78. ? [X1] : ((~quiet(X1) | calm(X1)) & (quiet(X1) | ~calm(X1))) => ((~quiet(sK9) | calm(sK9)) & (quiet(sK9) | ~calm(sK9))) [choice axiom]
79. ((~tall(lucy) & humble(lucy)) | ! [X0] : ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0)))) & (((~quiet(sK9) | calm(sK9)) & (quiet(sK9) | ~calm(sK9))) | tall(lucy) | ~humble(lucy)) [skolemisation 77,78]
103. ~generous(paul) | strong(X0) | happy(X0) [cnf transformation 47]
104. ~strong(X0) | old(X0) [cnf transformation 49]
105. ~strong(X0) | humble(X0) [cnf transformation 49]
106. ~humble(X0) | strong(X0) | ~old(X0) [cnf transformation 49]
110. quiet(X0) | humble(X0) | tall(X0) [cnf transformation 56]
132. ~happy(X0) | ~happy(X0) | old(X0) [cnf transformation 68]
133. ~tall(X0) | ~patient(X0) [cnf transformation 32]
142. ~happy(X0) | calm(X0) | tall(X0) [cnf transformation 74]
149. humble(lucy) | ~calm(X0) | ~quiet(X0) [cnf transformation 79]
152. generous(paul) [cnf transformation 17]
154. ~humble(mary) [cnf transformation 19]
155. patient(mary) [cnf transformation 19]
159. ~strong(lucy) [cnf transformation 24]
163. ~happy(X0) | old(X0) [duplicate literal removal 132]
220. 12 <=> ! [X0] : (strong(X0) | happy(X0)) [avatar definition]
221. strong(X0) | happy(X0) <- (12) [avatar component clause 220]
223. 13 <=> generous(paul) [avatar definition]
226. 12 | ~13 [avatar split clause 103,223,220]
364. 44 <=> ! [X0] : (~calm(X0) | ~quiet(X0)) [avatar definition]
365. ~calm(X0) | ~quiet(X0) <- (44) [avatar component clause 364]
376. 47 <=> humble(lucy) [avatar definition]
378. humble(lucy) <- (47) [avatar component clause 376]
379. 44 | 47 [avatar split clause 149,376,364]
391. 13 [avatar split clause 152,223]
403. humble(X0) | happy(X0) <- (12) [resolution 221,105]
404. happy(X1) | old(X1) <- (12) [resolution 221,104]
405. old(X1) <- (12) [subsumption resolution 404,163]
436. happy(mary) <- (12) [resolution 403,154]
503. calm(mary) | tall(mary) <- (12) [resolution 142,436]
508. 58 <=> tall(mary) [avatar definition]
509. ~tall(mary) <- (~58) [avatar component clause 508]
510. tall(mary) <- (58) [avatar component clause 508]
512. 59 <=> calm(mary) [avatar definition]
514. calm(mary) <- (59) [avatar component clause 512]
515. 58 | 59 | ~12 [avatar split clause 503,220,512,508]
547. ~patient(mary) <- (58) [resolution 510,133]
548. $false <- (58) [subsumption resolution 547,155]
549. ~58 [avatar contradiction clause 548]
551. ~quiet(mary) <- (44, 59) [resolution 514,365]
556. humble(mary) | tall(mary) <- (44, 59) [resolution 551,110]
558. tall(mary) <- (44, 59) [subsumption resolution 556,154]
559. $false <- (44, ~58, 59) [subsumption resolution 558,509]
560. ~44 | 58 | ~59 [avatar contradiction clause 559]
562. strong(lucy) | ~old(lucy) <- (47) [resolution 378,106]
563. ~old(lucy) <- (47) [subsumption resolution 562,159]
564. $false <- (12, 47) [subsumption resolution 563,405]
565. ~12 | ~47 [avatar contradiction clause 564]
566. $false [avatar sat refutation 226,379,391,515,549,560,565]
% SZS output end Proof for 363027621286702007586798
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is not wise.
Everyone who is both creative and not old is not tall and vice versa.
Everyone who is not rich or brave is not calm or old.
Everyone who is both not strong and curious is not rich or humble and vice versa.
Everyone who is either kind or not curious is either brave or curious.
If fred is both tall and old then someone is either quiet or funny and vice versa.
Everyone who is either not tall or quiet is not strong or creative and vice versa.
Everyone who is both humble and not happy is calm or humble and vice versa.
If someone is curious or not wise then someone is both patient and not humble and vice versa.
If someone is both patient and happy then john is both not rich and calm and vice versa.
Everyone who is not rich is both humble and calm and vice versa.
If someone is not humble then someone is wise or tall.
If someone is not wise then lucy is happy and vice versa.
Everyone who is creative or tall is either not rich or not strong.
Everyone who is not funny or not rich is either not generous or rich and vice versa.
If fred is not patient then john is both strong and not funny.
Someone is not brave or patient.
Someone is funny or tall.
Paul is not strong.
Mary is either not rich or not old.
Someone is brave or calm.
John is not brave or not patient. | Fred is brave. | neutral | (![X]:(~brave(X)=>~wise(X)))&
(![X]:((creative(X)&~old(X))<=>~tall(X)))&
(![X]:((~rich(X)|brave(X))=>(~calm(X)|old(X))))&
(![X]:((~strong(X)&curious(X))<=>(~rich(X)|humble(X))))&
(![X]:((kind(X)<~>~curious(X))=>(brave(X)<~>curious(X))))&
(((tall(fred)&old(fred)))<=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~strong(X)|creative(X))))&
(![X]:((humble(X)&~happy(X))<=>(calm(X)|humble(X))))&
((?[X]:((curious(X)|~wise(X))))<=>(?[X]:((patient(X)&~humble(X)))))&
((?[X]:((patient(X)&happy(X))))<=>((~rich(john)&calm(john))))&
(![X]:(~rich(X)<=>(humble(X)&calm(X))))&
((?[X]:(~humble(X)))=>(?[X]:((wise(X)|tall(X)))))&
((?[X]:(~wise(X)))<=>(happy(lucy)))&
(![X]:((creative(X)|tall(X))=>(~rich(X)<~>~strong(X))))&
(![X]:((~funny(X)|~rich(X))<=>(~generous(X)<~>rich(X))))&
((~patient(fred))=>((strong(john)&~funny(john))))&
(?[X]:((~brave(X)|patient(X))))&
(?[X]:((funny(X)|tall(X))))&
(~strong(paul))&
((~rich(mary)<~>~old(mary)))&
(?[X]:((brave(X)|calm(X))))&
((~brave(john)|~patient(john))) | brave(fred) | [] | null | 0 |
Everyone who is both not generous and not kind is either kind or not tall and vice versa. If someone is either not kind or not curious then someone is either not old or not wise. Everyone who is funny is either not kind or not funny. Everyone who is both not strong and generous is not generous or not quiet. Everyone who is not kind or happy is not tall or not rich. If susan is either not wise or creative then someone is both not happy and tall and vice versa. Everyone who is not quiet is patient or happy. If someone is not tall or funny then someone is not tall or brave. Everyone who is not happy or quiet is not wise or not curious and vice versa. Everyone who is not curious or curious is either wise or funny. Everyone who is strong is not happy or creative and vice versa. If fred is both not calm and generous then someone is either not wise or not humble. If john is either calm or not tall then paul is both not creative and not tall and vice versa. Everyone who is both not old and not happy is either curious or tall. Everyone who is both calm and kind is either old or happy and vice versa. Everyone who is both not tall and not kind is either not tall or humble and vice versa. Someone is not curious or old. Fred is both calm and not old. Alice is not quiet. Fred is not generous or humble. Lucy is both not tall and kind. Lucy is kind. Someone is either not tall or not happy. Fred is both not creative and not curious. | Lucy is not tall. | entailment | (![X]:((~generous(X)&~kind(X))<=>(kind(X)<~>~tall(X))))&
((?[X]:((~kind(X)<~>~curious(X))))=>(?[X]:((~old(X)<~>~wise(X)))))&
(![X]:(funny(X)=>(~kind(X)<~>~funny(X))))&
(![X]:((~strong(X)&generous(X))=>(~generous(X)|~quiet(X))))&
(![X]:((~kind(X)|happy(X))=>(~tall(X)|~rich(X))))&
(((~wise(susan)<~>creative(susan)))<=>(?[X]:((~happy(X)&tall(X)))))&
(![X]:(~quiet(X)=>(patient(X)|happy(X))))&
((?[X]:((~tall(X)|funny(X))))=>(?[X]:((~tall(X)|brave(X)))))&
(![X]:((~happy(X)|quiet(X))<=>(~wise(X)|~curious(X))))&
(![X]:((~curious(X)|curious(X))=>(wise(X)<~>funny(X))))&
(![X]:(strong(X)<=>(~happy(X)|creative(X))))&
(((~calm(fred)&generous(fred)))=>(?[X]:((~wise(X)<~>~humble(X)))))&
(((calm(john)<~>~tall(john)))<=>((~creative(paul)&~tall(paul))))&
(![X]:((~old(X)&~happy(X))=>(curious(X)<~>tall(X))))&
(![X]:((calm(X)&kind(X))<=>(old(X)<~>happy(X))))&
(![X]:((~tall(X)&~kind(X))<=>(~tall(X)<~>humble(X))))&
(?[X]:((~curious(X)|old(X))))&
((calm(fred)&~old(fred)))&
(~quiet(alice))&
((~generous(fred)|humble(fred)))&
((~tall(lucy)&kind(lucy)))&
(kind(lucy))&
(?[X]:((~tall(X)<~>~happy(X))))&
((~creative(fred)&~curious(fred))) | ~tall(lucy) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5404627676018421777349060
% SZS output start Proof for 5404627676018421777349060
21. kind(lucy) & ~tall(lucy) [input p20]
25. tall(lucy) [input hypothesis]
127. ~tall(lucy) [cnf transformation 21]
134. tall(lucy) [cnf transformation 25]
254. $false [subsumption resolution 134,127]
% SZS output end Proof for 5404627676018421777349060
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not kind is not rich or not strong and vice versa. Everyone who is either brave or not tall is either patient or not generous and vice versa. If fred is either brave or not patient then susan is not calm and vice versa. Everyone who is quiet or not curious is both quiet and rich. If mary is not old or not rich then someone is strong. If fred is both not rich and not funny then susan is both not funny and not curious and vice versa. Everyone who is either old or not calm is either old or tall. Everyone who is either creative or not wise is not kind or rich. If someone is either quiet or kind then susan is happy. If someone is either rich or not tall then someone is either kind or not creative and vice versa. If someone is both not strong and not humble then someone is either rich or not curious. Everyone who is both old and not patient is either not quiet or not kind and vice versa. Everyone who is either not calm or quiet is humble and vice versa. Everyone who is both not funny and not quiet is both not funny and not happy and vice versa. If someone is not old then fred is both quiet and not old and vice versa. Everyone who is happy is either not wise or not old. Paul is not quiet or not happy. Someone is generous. Someone is funny. Mary is both strong and not kind. Fred is both humble and not calm. Fred is both not rich and kind. Mary is not tall or not calm. | Fred is generous. | entailment | (![X]:((generous(X)<~>~kind(X))<=>(~rich(X)|~strong(X))))&
(![X]:((brave(X)<~>~tall(X))<=>(patient(X)<~>~generous(X))))&
(((brave(fred)<~>~patient(fred)))<=>(~calm(susan)))&
(![X]:((quiet(X)|~curious(X))=>(quiet(X)&rich(X))))&
(((~old(mary)|~rich(mary)))=>(?[X]:(strong(X))))&
(((~rich(fred)&~funny(fred)))<=>((~funny(susan)&~curious(susan))))&
(![X]:((old(X)<~>~calm(X))=>(old(X)<~>tall(X))))&
(![X]:((creative(X)<~>~wise(X))=>(~kind(X)|rich(X))))&
((?[X]:((quiet(X)<~>kind(X))))=>(happy(susan)))&
((?[X]:((rich(X)<~>~tall(X))))<=>(?[X]:((kind(X)<~>~creative(X)))))&
((?[X]:((~strong(X)&~humble(X))))=>(?[X]:((rich(X)<~>~curious(X)))))&
(![X]:((old(X)&~patient(X))<=>(~quiet(X)<~>~kind(X))))&
(![X]:((~calm(X)<~>quiet(X))<=>humble(X)))&
(![X]:((~funny(X)&~quiet(X))<=>(~funny(X)&~happy(X))))&
((?[X]:(~old(X)))<=>((quiet(fred)&~old(fred))))&
(![X]:(happy(X)=>(~wise(X)<~>~old(X))))&
((~quiet(paul)|~happy(paul)))&
(?[X]:(generous(X)))&
(?[X]:(funny(X)))&
((strong(mary)&~kind(mary)))&
((humble(fred)&~calm(fred)))&
((~rich(fred)&kind(fred)))&
((~tall(mary)|~calm(mary))) | generous(fred) | [
"p0",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 120879009327381932832840
% SZS output start Proof for 120879009327381932832840
1. ! [X0] : ((generous(X0) <~> ~kind(X0)) <=> (~strong(X0) | ~rich(X0))) [input p0]
22. kind(fred) & ~rich(fred) [input p21]
24. ~generous(fred) [input hypothesis]
37. ! [X0] : ((((kind(X0) | ~generous(X0)) & (~kind(X0) | generous(X0))) | (strong(X0) & rich(X0))) & ((~strong(X0) | ~rich(X0)) | ((generous(X0) | kind(X0)) & (~kind(X0) | ~generous(X0))))) [nnf transformation 1]
38. ! [X0] : ((((kind(X0) | ~generous(X0)) & (~kind(X0) | generous(X0))) | (strong(X0) & rich(X0))) & (~strong(X0) | ~rich(X0) | ((generous(X0) | kind(X0)) & (~kind(X0) | ~generous(X0))))) [flattening 37]
74. ~kind(X0) | generous(X0) | rich(X0) [cnf transformation 38]
142. ~rich(fred) [cnf transformation 22]
143. kind(fred) [cnf transformation 22]
145. ~generous(fred) [cnf transformation 24]
192. 10 <=> rich(fred) [avatar definition]
194. ~rich(fred) <- (~10) [avatar component clause 192]
288. ~10 [avatar split clause 142,192]
308. generous(fred) | rich(fred) [resolution 74,143]
309. rich(fred) [subsumption resolution 308,145]
310. $false <- (~10) [subsumption resolution 309,194]
311. 10 [avatar contradiction clause 310]
312. $false [avatar sat refutation 288,311]
% SZS output end Proof for 120879009327381932832840
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not generous then fred is both generous and not curious and vice versa.
If someone is generous or old then fred is strong or tall.
Everyone who is wise or not wise is both not brave and old.
Everyone who is either kind or not tall is either not curious or not strong.
Everyone who is either not wise or not generous is either creative or not funny and vice versa.
If someone is tall then alice is either not calm or not strong and vice versa.
Everyone who is both not happy and not tall is not curious or humble and vice versa.
If someone is either not calm or rich then john is both not kind and patient.
If someone is not generous or not wise then fred is both rich and tall and vice versa.
Everyone who is either not creative or generous is rich.
If lucy is curious or funny then lucy is both calm and tall and vice versa.
If john is not funny then someone is not generous.
Everyone who is not curious is both curious and not wise and vice versa.
If fred is happy then lucy is either not patient or humble.
If someone is not old or humble then paul is both strong and not kind and vice versa.
Susan is either wise or kind.
Someone is not calm or creative.
Someone is happy or not kind.
Mary is old or happy.
Fred is not tall or not wise.
Someone is calm or funny.
Someone is both generous and creative. | Lucy is not generous. | contradiction | ((~generous(alice))<=>((generous(fred)&~curious(fred))))&
((?[X]:((generous(X)|old(X))))=>((strong(fred)|tall(fred))))&
(![X]:((wise(X)|~wise(X))=>(~brave(X)&old(X))))&
(![X]:((kind(X)<~>~tall(X))=>(~curious(X)<~>~strong(X))))&
(![X]:((~wise(X)<~>~generous(X))<=>(creative(X)<~>~funny(X))))&
((?[X]:(tall(X)))<=>((~calm(alice)<~>~strong(alice))))&
(![X]:((~happy(X)&~tall(X))<=>(~curious(X)|humble(X))))&
((?[X]:((~calm(X)<~>rich(X))))=>((~kind(john)&patient(john))))&
((?[X]:((~generous(X)|~wise(X))))<=>((rich(fred)&tall(fred))))&
(![X]:((~creative(X)<~>generous(X))=>rich(X)))&
(((curious(lucy)|funny(lucy)))<=>((calm(lucy)&tall(lucy))))&
((~funny(john))=>(?[X]:(~generous(X))))&
(![X]:(~curious(X)<=>(curious(X)&~wise(X))))&
((happy(fred))=>((~patient(lucy)<~>humble(lucy))))&
((?[X]:((~old(X)|humble(X))))<=>((strong(paul)&~kind(paul))))&
((wise(susan)<~>kind(susan)))&
(?[X]:((~calm(X)|creative(X))))&
(?[X]:((happy(X)|~kind(X))))&
((old(mary)|happy(mary)))&
((~tall(fred)|~wise(fred)))&
(?[X]:((calm(X)|funny(X))))&
(?[X]:((generous(X)&creative(X)))) | ~generous(lucy) | [
"p8",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4500420664962786681212337
% SZS output start Proof for 4500420664962786681212337
9. ? [X0] : (~wise(X0) | ~generous(X0)) <=> (tall(fred) & rich(fred)) [input p8]
13. ! [X0] : (~curious(X0) <=> (~wise(X0) & curious(X0))) [input p12]
20. ~wise(fred) | ~tall(fred) [input p19]
23. ~generous(lucy) [input hypothesis]
44. (? [X0] : (~wise(X0) | ~generous(X0)) | (~tall(fred) | ~rich(fred))) & ((tall(fred) & rich(fred)) | ! [X0] : (wise(X0) & generous(X0))) [nnf transformation 9]
45. (? [X0] : (~wise(X0) | ~generous(X0)) | ~tall(fred) | ~rich(fred)) & ((tall(fred) & rich(fred)) | ! [X0] : (wise(X0) & generous(X0))) [flattening 44]
46. (? [X0] : (~wise(X0) | ~generous(X0)) | ~tall(fred) | ~rich(fred)) & ((tall(fred) & rich(fred)) | ! [X1] : (wise(X1) & generous(X1))) [rectify 45]
47. ? [X0] : (~wise(X0) | ~generous(X0)) => (~wise(sK1) | ~generous(sK1)) [choice axiom]
48. ((~wise(sK1) | ~generous(sK1)) | ~tall(fred) | ~rich(fred)) & ((tall(fred) & rich(fred)) | ! [X1] : (wise(X1) & generous(X1))) [skolemisation 46,47]
54. ! [X0] : ((~curious(X0) | (wise(X0) | ~curious(X0))) & ((~wise(X0) & curious(X0)) | curious(X0))) [nnf transformation 13]
55. ! [X0] : ((~curious(X0) | wise(X0) | ~curious(X0)) & ((~wise(X0) & curious(X0)) | curious(X0))) [flattening 54]
105. tall(fred) | generous(X1) [cnf transformation 48]
116. curious(X0) | curious(X0) [cnf transformation 55]
118. ~curious(X0) | wise(X0) | ~curious(X0) [cnf transformation 55]
131. ~wise(fred) | ~tall(fred) [cnf transformation 20]
135. ~generous(lucy) [cnf transformation 23]
136. curious(X0) [duplicate literal removal 116]
137. ~curious(X0) | wise(X0) [duplicate literal removal 118]
161. 6 <=> tall(fred) [avatar definition]
221. 19 <=> ! [X1] : wise(X1) [avatar definition]
222. wise(X1) <- (19) [avatar component clause 221]
225. 20 <=> ! [X1] : generous(X1) [avatar definition]
226. generous(X1) <- (20) [avatar component clause 225]
227. 20 | 6 [avatar split clause 105,161,225]
321. 40 <=> wise(fred) [avatar definition]
323. ~wise(fred) <- (~40) [avatar component clause 321]
324. ~6 | ~40 [avatar split clause 131,321,161]
345. wise(X0) [resolution 137,136]
346. 19 [avatar split clause 345,221]
348. $false <- (19, ~40) [resolution 222,323]
350. ~19 | 40 [avatar contradiction clause 348]
352. $false <- (20) [resolution 226,135]
357. ~20 [avatar contradiction clause 352]
358. $false [avatar sat refutation 227,324,346,350,357]
% SZS output end Proof for 4500420664962786681212337
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or patient is both humble and not funny and vice versa. Everyone who is either not wise or creative is both not creative and old. If alice is either not rich or kind then someone is either calm or funny and vice versa. If paul is both not tall and not quiet then john is both not brave and not patient and vice versa. If fred is brave or not wise then fred is both not creative and kind. Everyone who is both happy and patient is either not strong or creative and vice versa. Everyone who is creative or happy is not kind or not funny and vice versa. If john is not curious then someone is not kind. Everyone who is calm or not patient is either not patient or not curious. Everyone who is old or not brave is calm. Everyone who is not quiet or kind is both patient and happy. If fred is not calm or curious then paul is either not happy or quiet and vice versa. Everyone who is both not generous and not rich is not tall and vice versa. Everyone who is either rich or not humble is not quiet and vice versa. Everyone who is either not kind or curious is curious or not curious and vice versa. Everyone who is not brave or curious is not creative or generous and vice versa. Paul is calm. Susan is brave. Alice is both not rich and not generous. Lucy is both not curious and patient. Mary is both not curious and not generous. Fred is not brave or not quiet. Mary is not kind. Someone is quiet or not humble. | Lucy is rich. | neutral | (![X]:((~creative(X)<~>patient(X))<=>(humble(X)&~funny(X))))&
(![X]:((~wise(X)<~>creative(X))=>(~creative(X)&old(X))))&
(((~rich(alice)<~>kind(alice)))<=>(?[X]:((calm(X)<~>funny(X)))))&
(((~tall(paul)&~quiet(paul)))<=>((~brave(john)&~patient(john))))&
(((brave(fred)|~wise(fred)))=>((~creative(fred)&kind(fred))))&
(![X]:((happy(X)&patient(X))<=>(~strong(X)<~>creative(X))))&
(![X]:((creative(X)|happy(X))<=>(~kind(X)|~funny(X))))&
((~curious(john))=>(?[X]:(~kind(X))))&
(![X]:((calm(X)|~patient(X))=>(~patient(X)<~>~curious(X))))&
(![X]:((old(X)|~brave(X))=>calm(X)))&
(![X]:((~quiet(X)|kind(X))=>(patient(X)&happy(X))))&
(((~calm(fred)|curious(fred)))<=>((~happy(paul)<~>quiet(paul))))&
(![X]:((~generous(X)&~rich(X))<=>~tall(X)))&
(![X]:((rich(X)<~>~humble(X))<=>~quiet(X)))&
(![X]:((~kind(X)<~>curious(X))<=>(curious(X)|~curious(X))))&
(![X]:((~brave(X)|curious(X))<=>(~creative(X)|generous(X))))&
(calm(paul))&
(brave(susan))&
((~rich(alice)&~generous(alice)))&
((~curious(lucy)&patient(lucy)))&
((~curious(mary)&~generous(mary)))&
((~brave(fred)|~quiet(fred)))&
(~kind(mary))&
(?[X]:((quiet(X)|~humble(X)))) | rich(lucy) | [] | null | 0 |
If someone is not patient or old then mary is not calm or wise. Everyone who is either not brave or happy is either not kind or generous. Everyone who is not funny is either calm or not kind. If someone is both not calm and rich then john is funny or calm and vice versa. Everyone who is not brave is both quiet and not funny. If someone is either not brave or not rich then alice is creative or not generous and vice versa. Everyone who is not old is calm or quiet. If someone is not kind or quiet then paul is both not patient and brave. Everyone who is old or creative is happy. Everyone who is both not tall and not brave is both old and not old. Everyone who is both kind and not strong is both humble and not patient. If susan is both not happy and not generous then someone is creative or not wise. Everyone who is both generous and not quiet is either old or quiet. Everyone who is quiet is not wise. Everyone who is both not humble and kind is both not wise and strong and vice versa. Everyone who is both not tall and calm is not happy or patient and vice versa. Someone is either not happy or not humble. Mary is both not strong and not curious. Fred is not strong or not curious. Someone is either funny or rich. Alice is not old or curious. Susan is not kind or funny. Susan is either strong or patient. | Alice is not old. | neutral | ((?[X]:((~patient(X)|old(X))))=>((~calm(mary)|wise(mary))))&
(![X]:((~brave(X)<~>happy(X))=>(~kind(X)<~>generous(X))))&
(![X]:(~funny(X)=>(calm(X)<~>~kind(X))))&
((?[X]:((~calm(X)&rich(X))))<=>((funny(john)|calm(john))))&
(![X]:(~brave(X)=>(quiet(X)&~funny(X))))&
((?[X]:((~brave(X)<~>~rich(X))))<=>((creative(alice)|~generous(alice))))&
(![X]:(~old(X)=>(calm(X)|quiet(X))))&
((?[X]:((~kind(X)|quiet(X))))=>((~patient(paul)&brave(paul))))&
(![X]:((old(X)|creative(X))=>happy(X)))&
(![X]:((~tall(X)&~brave(X))=>(old(X)&~old(X))))&
(![X]:((kind(X)&~strong(X))=>(humble(X)&~patient(X))))&
(((~happy(susan)&~generous(susan)))=>(?[X]:((creative(X)|~wise(X)))))&
(![X]:((generous(X)&~quiet(X))=>(old(X)<~>quiet(X))))&
(![X]:(quiet(X)=>~wise(X)))&
(![X]:((~humble(X)&kind(X))<=>(~wise(X)&strong(X))))&
(![X]:((~tall(X)&calm(X))<=>(~happy(X)|patient(X))))&
(?[X]:((~happy(X)<~>~humble(X))))&
((~strong(mary)&~curious(mary)))&
((~strong(fred)|~curious(fred)))&
(?[X]:((funny(X)<~>rich(X))))&
((~old(alice)|curious(alice)))&
((~kind(susan)|funny(susan)))&
((strong(susan)<~>patient(susan))) | ~old(alice) | [] | null | 0 |
Everyone who is not quiet or brave is both funny and not funny and vice versa.
If someone is both wise and old then john is both brave and patient.
If paul is happy then someone is either not kind or not patient and vice versa.
Everyone who is either not calm or not happy is either not brave or creative and vice versa.
If someone is either generous or kind then someone is either funny or tall and vice versa.
If someone is humble then someone is either not creative or not rich.
Everyone who is either kind or wise is either not quiet or not curious.
If john is creative or not generous then someone is both patient and creative.
Everyone who is creative or old is both not creative and not brave.
Everyone who is both patient and kind is either strong or wise.
Everyone who is rich is both not rich and not brave.
Everyone who is both kind and curious is tall or not wise.
If mary is not generous then someone is either kind or not rich.
If fred is both kind and not patient then someone is curious and vice versa.
Everyone who is tall or not curious is not strong.
Everyone who is both rich and creative is both wise and kind and vice versa.
Susan is both not curious and happy.
Someone is both tall and not strong.
Someone is either creative or not old.
Someone is either funny or not generous.
Someone is not rich or not brave.
Someone is not strong or not kind. | Mary is humble. | contradiction | (![X]:((~quiet(X)|brave(X))<=>(funny(X)&~funny(X))))&
((?[X]:((wise(X)&old(X))))=>((brave(john)&patient(john))))&
((happy(paul))<=>(?[X]:((~kind(X)<~>~patient(X)))))&
(![X]:((~calm(X)<~>~happy(X))<=>(~brave(X)<~>creative(X))))&
((?[X]:((generous(X)<~>kind(X))))<=>(?[X]:((funny(X)<~>tall(X)))))&
((?[X]:(humble(X)))=>(?[X]:((~creative(X)<~>~rich(X)))))&
(![X]:((kind(X)<~>wise(X))=>(~quiet(X)<~>~curious(X))))&
(((creative(john)|~generous(john)))=>(?[X]:((patient(X)&creative(X)))))&
(![X]:((creative(X)|old(X))=>(~creative(X)&~brave(X))))&
(![X]:((patient(X)&kind(X))=>(strong(X)<~>wise(X))))&
(![X]:(rich(X)=>(~rich(X)&~brave(X))))&
(![X]:((kind(X)&curious(X))=>(tall(X)|~wise(X))))&
((~generous(mary))=>(?[X]:((kind(X)<~>~rich(X)))))&
(((kind(fred)&~patient(fred)))<=>(?[X]:(curious(X))))&
(![X]:((tall(X)|~curious(X))=>~strong(X)))&
(![X]:((rich(X)&creative(X))<=>(wise(X)&kind(X))))&
((~curious(susan)&happy(susan)))&
(?[X]:((tall(X)&~strong(X))))&
(?[X]:((creative(X)<~>~old(X))))&
(?[X]:((funny(X)<~>~generous(X))))&
(?[X]:((~rich(X)|~brave(X))))&
(?[X]:((~strong(X)|~kind(X)))) | humble(mary) | [
"p5",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 305321426517986485592636
% SZS output start Proof for 305321426517986485592636
6. ? [X0] : humble(X0) => ? [X0] : (~creative(X0) <~> ~rich(X0)) [input p5]
9. ! [X0] : ((old(X0) | creative(X0)) => (~brave(X0) & ~creative(X0))) [input p8]
11. ! [X0] : (rich(X0) => (~brave(X0) & ~rich(X0))) [input p10]
23. humble(mary) [input hypothesis]
25. ? [X0] : humble(X0) => ? [X1] : (~creative(X1) <~> ~rich(X1)) [rectify 6]
27. ? [X1] : (~creative(X1) <~> ~rich(X1)) | ! [X0] : ~humble(X0) [ennf transformation 25]
30. ! [X0] : ((~brave(X0) & ~creative(X0)) | (~old(X0) & ~creative(X0))) [ennf transformation 9]
33. ! [X0] : ((~brave(X0) & ~rich(X0)) | ~rich(X0)) [ennf transformation 11]
50. ? [X1] : ((rich(X1) | creative(X1)) & (~rich(X1) | ~creative(X1))) | ! [X0] : ~humble(X0) [nnf transformation 27]
51. ? [X0] : ((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | ! [X1] : ~humble(X1) [rectify 50]
52. ? [X0] : ((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) => ((rich(sK3) | creative(sK3)) & (~rich(sK3) | ~creative(sK3))) [choice axiom]
53. ((rich(sK3) | creative(sK3)) & (~rich(sK3) | ~creative(sK3))) | ! [X1] : ~humble(X1) [skolemisation 51,52]
108. rich(sK3) | creative(sK3) | ~humble(X1) [cnf transformation 53]
117. ~creative(X0) | ~creative(X0) [cnf transformation 30]
123. ~rich(X0) | ~rich(X0) [cnf transformation 33]
147. humble(mary) [cnf transformation 23]
148. ~rich(X0) [duplicate literal removal 123]
149. ~creative(X0) [duplicate literal removal 117]
225. 16 <=> ! [X1] : ~humble(X1) [avatar definition]
226. ~humble(X1) <- (16) [avatar component clause 225]
228. 17 <=> creative(sK3) [avatar definition]
230. creative(sK3) <- (17) [avatar component clause 228]
232. 18 <=> rich(sK3) [avatar definition]
234. rich(sK3) <- (18) [avatar component clause 232]
235. 16 | 17 | 18 [avatar split clause 108,232,228,225]
309. $false <- (16) [resolution 226,147]
310. ~16 [avatar contradiction clause 309]
311. $false <- (17) [subsumption resolution 230,149]
312. ~17 [avatar contradiction clause 311]
313. $false <- (18) [subsumption resolution 234,148]
314. ~18 [avatar contradiction clause 313]
315. $false [avatar sat refutation 235,310,312,314]
% SZS output end Proof for 305321426517986485592636
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or not rich is both generous and not generous.
Everyone who is kind or tall is not quiet and vice versa.
If someone is either not funny or not happy then someone is not patient or quiet and vice versa.
If susan is not curious then someone is either generous or brave and vice versa.
If someone is both generous and creative then someone is not brave or quiet and vice versa.
Everyone who is both funny and not strong is both not tall and not rich.
If john is both not old and curious then alice is not funny.
Everyone who is both not humble and strong is not generous or calm.
Everyone who is either not tall or not old is either not humble or not funny.
If susan is not quiet then susan is either not patient or tall.
Everyone who is both not curious and old is both wise and humble and vice versa.
Everyone who is calm is both tall and not patient and vice versa.
If alice is either curious or not curious then lucy is brave or not happy and vice versa.
Everyone who is generous or not strong is tall or not humble and vice versa.
If someone is brave or not humble then someone is both not quiet and not strong.
Everyone who is rich is both not creative and old and vice versa.
Someone is both happy and not funny.
Someone is not strong.
Someone is not generous or old.
Someone is both not funny and not quiet.
Someone is not happy or not humble.
Someone is funny or not kind. | John is old. | entailment | (![X]:((wise(X)|~rich(X))=>(generous(X)&~generous(X))))&
(![X]:((kind(X)|tall(X))<=>~quiet(X)))&
((?[X]:((~funny(X)<~>~happy(X))))<=>(?[X]:((~patient(X)|quiet(X)))))&
((~curious(susan))<=>(?[X]:((generous(X)<~>brave(X)))))&
((?[X]:((generous(X)&creative(X))))<=>(?[X]:((~brave(X)|quiet(X)))))&
(![X]:((funny(X)&~strong(X))=>(~tall(X)&~rich(X))))&
(((~old(john)&curious(john)))=>(~funny(alice)))&
(![X]:((~humble(X)&strong(X))=>(~generous(X)|calm(X))))&
(![X]:((~tall(X)<~>~old(X))=>(~humble(X)<~>~funny(X))))&
((~quiet(susan))=>((~patient(susan)<~>tall(susan))))&
(![X]:((~curious(X)&old(X))<=>(wise(X)&humble(X))))&
(![X]:(calm(X)<=>(tall(X)&~patient(X))))&
(((curious(alice)<~>~curious(alice)))<=>((brave(lucy)|~happy(lucy))))&
(![X]:((generous(X)|~strong(X))<=>(tall(X)|~humble(X))))&
((?[X]:((brave(X)|~humble(X))))=>(?[X]:((~quiet(X)&~strong(X)))))&
(![X]:(rich(X)<=>(~creative(X)&old(X))))&
(?[X]:((happy(X)&~funny(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~generous(X)|old(X))))&
(?[X]:((~funny(X)&~quiet(X))))&
(?[X]:((~happy(X)|~humble(X))))&
(?[X]:((funny(X)|~kind(X)))) | old(john) | [
"p0",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8527320628230171278867070
% SZS output start Proof for 8527320628230171278867070
1. ! [X0] : ((~rich(X0) | wise(X0)) => (~generous(X0) & generous(X0))) [input p0]
16. ! [X0] : (rich(X0) <=> (old(X0) & ~creative(X0))) [input p15]
23. ~old(john) [input hypothesis]
28. ! [X0] : ((~generous(X0) & generous(X0)) | (rich(X0) & ~wise(X0))) [ennf transformation 1]
66. ! [X0] : ((rich(X0) | (~old(X0) | creative(X0))) & ((old(X0) & ~creative(X0)) | ~rich(X0))) [nnf transformation 16]
67. ! [X0] : ((rich(X0) | ~old(X0) | creative(X0)) & ((old(X0) & ~creative(X0)) | ~rich(X0))) [flattening 66]
81. generous(X0) | rich(X0) [cnf transformation 28]
83. ~generous(X0) | rich(X0) [cnf transformation 28]
133. old(X0) | ~rich(X0) [cnf transformation 67]
143. ~old(john) [cnf transformation 23]
146. rich(X0) [subsumption resolution 81,83]
293. old(X0) [subsumption resolution 133,146]
313. $false [subsumption resolution 143,293]
% SZS output end Proof for 8527320628230171278867070
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is either not wise or not kind and vice versa.
Everyone who is either not wise or not curious is both wise and not curious and vice versa.
If fred is both not generous and calm then someone is not old.
If someone is creative then someone is generous.
Everyone who is both not happy and tall is either not humble or not old.
If mary is not rich then someone is both not happy and old.
Everyone who is generous is both strong and not patient.
Everyone who is quiet or kind is happy or funny and vice versa.
Everyone who is both generous and wise is not humble and vice versa.
If someone is both not tall and not old then someone is brave or not generous and vice versa.
If susan is kind then someone is both funny and patient and vice versa.
Everyone who is not quiet is both creative and funny and vice versa.
Everyone who is not kind or not humble is not generous or not curious.
If john is not curious then someone is wise or not rich.
If someone is kind then someone is both curious and not kind.
Everyone who is kind or quiet is both strong and patient and vice versa.
Alice is either not curious or not wise.
Paul is not creative.
Someone is not tall.
Fred is not kind.
Paul is both not generous and not creative.
Alice is not creative.
Someone is not calm. | Fred is creative. | contradiction | (![X]:(brave(X)<=>(~wise(X)<~>~kind(X))))&
(![X]:((~wise(X)<~>~curious(X))<=>(wise(X)&~curious(X))))&
(((~generous(fred)&calm(fred)))=>(?[X]:(~old(X))))&
((?[X]:(creative(X)))=>(?[X]:(generous(X))))&
(![X]:((~happy(X)&tall(X))=>(~humble(X)<~>~old(X))))&
((~rich(mary))=>(?[X]:((~happy(X)&old(X)))))&
(![X]:(generous(X)=>(strong(X)&~patient(X))))&
(![X]:((quiet(X)|kind(X))<=>(happy(X)|funny(X))))&
(![X]:((generous(X)&wise(X))<=>~humble(X)))&
((?[X]:((~tall(X)&~old(X))))<=>(?[X]:((brave(X)|~generous(X)))))&
((kind(susan))<=>(?[X]:((funny(X)&patient(X)))))&
(![X]:(~quiet(X)<=>(creative(X)&funny(X))))&
(![X]:((~kind(X)|~humble(X))=>(~generous(X)|~curious(X))))&
((~curious(john))=>(?[X]:((wise(X)|~rich(X)))))&
((?[X]:(kind(X)))=>(?[X]:((curious(X)&~kind(X)))))&
(![X]:((kind(X)|quiet(X))<=>(strong(X)&patient(X))))&
((~curious(alice)<~>~wise(alice)))&
(~creative(paul))&
(?[X]:(~tall(X)))&
(~kind(fred))&
((~generous(paul)&~creative(paul)))&
(~creative(alice))&
(?[X]:(~calm(X))) | creative(fred) | [
"p3",
"p6",
"p7",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1067691621650879692976428
% SZS output start Proof for 1067691621650879692976428
4. ? [X0] : creative(X0) => ? [X0] : generous(X0) [input p3]
7. ! [X0] : (generous(X0) => (~patient(X0) & strong(X0))) [input p6]
8. ! [X0] : ((kind(X0) | quiet(X0)) <=> (funny(X0) | happy(X0))) [input p7]
12. ! [X0] : (~quiet(X0) <=> (funny(X0) & creative(X0))) [input p11]
16. ! [X0] : ((quiet(X0) | kind(X0)) <=> (patient(X0) & strong(X0))) [input p15]
24. creative(fred) [input hypothesis]
25. ? [X0] : creative(X0) => ? [X1] : generous(X1) [rectify 4]
30. ? [X1] : generous(X1) | ! [X0] : ~creative(X0) [ennf transformation 25]
34. ! [X0] : ((~patient(X0) & strong(X0)) | ~generous(X0)) [ennf transformation 7]
42. ? [X0] : generous(X0) | ! [X1] : ~creative(X1) [rectify 30]
43. ? [X0] : generous(X0) => generous(sK0) [choice axiom]
44. generous(sK0) | ! [X1] : ~creative(X1) [skolemisation 42,43]
48. ! [X0] : (((kind(X0) | quiet(X0)) | (~funny(X0) & ~happy(X0))) & ((funny(X0) | happy(X0)) | (~kind(X0) & ~quiet(X0)))) [nnf transformation 8]
49. ! [X0] : ((kind(X0) | quiet(X0) | (~funny(X0) & ~happy(X0))) & (funny(X0) | happy(X0) | (~kind(X0) & ~quiet(X0)))) [flattening 48]
61. ! [X0] : ((~quiet(X0) | (~funny(X0) | ~creative(X0))) & ((funny(X0) & creative(X0)) | quiet(X0))) [nnf transformation 12]
62. ! [X0] : ((~quiet(X0) | ~funny(X0) | ~creative(X0)) & ((funny(X0) & creative(X0)) | quiet(X0))) [flattening 61]
68. ! [X0] : (((quiet(X0) | kind(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [nnf transformation 16]
69. ! [X0] : ((quiet(X0) | kind(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~quiet(X0) & ~kind(X0)))) [flattening 68]
83. generous(sK0) | ~creative(X1) [cnf transformation 44]
89. ~patient(X0) | ~generous(X0) [cnf transformation 34]
93. ~funny(X0) | quiet(X0) | kind(X0) [cnf transformation 49]
106. funny(X0) | quiet(X0) [cnf transformation 62]
115. ~kind(X0) | patient(X0) [cnf transformation 69]
116. ~quiet(X0) | patient(X0) [cnf transformation 69]
126. creative(fred) [cnf transformation 24]
132. 1 <=> ! [X1] : ~creative(X1) [avatar definition]
133. ~creative(X1) <- (1) [avatar component clause 132]
135. 2 <=> generous(sK0) [avatar definition]
137. generous(sK0) <- (2) [avatar component clause 135]
138. 1 | 2 [avatar split clause 83,135,132]
241. quiet(X0) | kind(X0) | quiet(X0) [resolution 93,106]
242. quiet(X0) | kind(X0) [duplicate literal removal 241]
316. kind(X1) | patient(X1) [resolution 242,116]
319. patient(X1) [subsumption resolution 316,115]
328. ~generous(X2) [resolution 319,89]
337. $false <- (2) [resolution 328,137]
338. ~2 [avatar contradiction clause 337]
339. $false <- (1) [resolution 133,126]
340. ~1 [avatar contradiction clause 339]
341. $false [avatar sat refutation 138,338,340]
% SZS output end Proof for 1067691621650879692976428
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or old is either quiet or not old.
If paul is either tall or not calm then someone is humble or not quiet.
Everyone who is both generous and strong is both not humble and not happy.
Everyone who is not rich or strong is funny.
Everyone who is both not rich and brave is tall and vice versa.
Everyone who is not strong or kind is either not old or not generous.
Everyone who is either kind or strong is generous or not curious and vice versa.
Everyone who is either quiet or patient is either quiet or creative.
Everyone who is not creative is either old or brave.
If someone is humble then someone is both generous and not kind and vice versa.
Everyone who is old or curious is not tall and vice versa.
If someone is not happy then someone is funny or not humble.
Everyone who is both not creative and creative is both not happy and not calm and vice versa.
Everyone who is either not old or brave is either not creative or not wise.
If someone is not strong then someone is both tall and rich.
If someone is both brave and not happy then someone is humble.
Someone is both not wise and funny.
Alice is not quiet.
Paul is both brave and not rich.
Lucy is not generous or not tall.
Someone is curious or not tall. | Alice is not funny. | contradiction | (![X]:((~curious(X)<~>old(X))=>(quiet(X)<~>~old(X))))&
(((tall(paul)<~>~calm(paul)))=>(?[X]:((humble(X)|~quiet(X)))))&
(![X]:((generous(X)&strong(X))=>(~humble(X)&~happy(X))))&
(![X]:((~rich(X)|strong(X))=>funny(X)))&
(![X]:((~rich(X)&brave(X))<=>tall(X)))&
(![X]:((~strong(X)|kind(X))=>(~old(X)<~>~generous(X))))&
(![X]:((kind(X)<~>strong(X))<=>(generous(X)|~curious(X))))&
(![X]:((quiet(X)<~>patient(X))=>(quiet(X)<~>creative(X))))&
(![X]:(~creative(X)=>(old(X)<~>brave(X))))&
((?[X]:(humble(X)))<=>(?[X]:((generous(X)&~kind(X)))))&
(![X]:((old(X)|curious(X))<=>~tall(X)))&
((?[X]:(~happy(X)))=>(?[X]:((funny(X)|~humble(X)))))&
(![X]:((~creative(X)&creative(X))<=>(~happy(X)&~calm(X))))&
(![X]:((~old(X)<~>brave(X))=>(~creative(X)<~>~wise(X))))&
((?[X]:(~strong(X)))=>(?[X]:((tall(X)&rich(X)))))&
((?[X]:((brave(X)&~happy(X))))=>(?[X]:(humble(X))))&
(?[X]:((~wise(X)&funny(X))))&
(~quiet(alice))&
((brave(paul)&~rich(paul)))&
((~generous(lucy)|~tall(lucy)))&
(?[X]:((curious(X)|~tall(X)))) | ~funny(alice) | [
"p3",
"p4",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7152549145082879775537970
% SZS output start Proof for 7152549145082879775537970
4. ! [X0] : ((strong(X0) | ~rich(X0)) => funny(X0)) [input p3]
5. ! [X0] : ((brave(X0) & ~rich(X0)) <=> tall(X0)) [input p4]
15. ? [X0] : ~strong(X0) => ? [X0] : (rich(X0) & tall(X0)) [input p14]
22. ~funny(alice) [input hypothesis]
25. ? [X0] : ~strong(X0) => ? [X1] : (rich(X1) & tall(X1)) [rectify 15]
31. ! [X0] : (funny(X0) | (~strong(X0) & rich(X0))) [ennf transformation 4]
37. ? [X1] : (rich(X1) & tall(X1)) | ! [X0] : strong(X0) [ennf transformation 25]
43. ! [X0] : (((brave(X0) & ~rich(X0)) | ~tall(X0)) & (tall(X0) | (~brave(X0) | rich(X0)))) [nnf transformation 5]
44. ! [X0] : (((brave(X0) & ~rich(X0)) | ~tall(X0)) & (tall(X0) | ~brave(X0) | rich(X0))) [flattening 43]
63. ? [X0] : (rich(X0) & tall(X0)) | ! [X1] : strong(X1) [rectify 37]
64. ? [X0] : (rich(X0) & tall(X0)) => (rich(sK4) & tall(sK4)) [choice axiom]
65. (rich(sK4) & tall(sK4)) | ! [X1] : strong(X1) [skolemisation 63,64]
82. ~strong(X0) | funny(X0) [cnf transformation 31]
84. ~rich(X0) | ~tall(X0) [cnf transformation 44]
117. tall(sK4) | strong(X1) [cnf transformation 65]
118. rich(sK4) | strong(X1) [cnf transformation 65]
127. ~funny(alice) [cnf transformation 22]
187. 13 <=> ! [X1] : strong(X1) [avatar definition]
188. strong(X1) <- (13) [avatar component clause 187]
190. 14 <=> rich(sK4) [avatar definition]
192. rich(sK4) <- (14) [avatar component clause 190]
193. 13 | 14 [avatar split clause 118,190,187]
195. 15 <=> tall(sK4) [avatar definition]
197. tall(sK4) <- (15) [avatar component clause 195]
198. 13 | 15 [avatar split clause 117,195,187]
218. funny(X0) <- (13) [resolution 82,188]
220. $false <- (13) [resolution 218,127]
221. ~13 [avatar contradiction clause 220]
222. ~tall(sK4) <- (14) [resolution 192,84]
223. $false <- (14, 15) [subsumption resolution 222,197]
224. ~14 | ~15 [avatar contradiction clause 223]
225. $false [avatar sat refutation 193,198,221,224]
% SZS output end Proof for 7152549145082879775537970
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong or not rich then susan is not rich or curious and vice versa.
If someone is not calm then paul is curious or creative.
Everyone who is not wise or curious is both not generous and kind and vice versa.
If john is both not old and happy then john is not generous or wise and vice versa.
Everyone who is not kind or not patient is both not funny and funny and vice versa.
Everyone who is either rich or not tall is both not quiet and tall.
Everyone who is not calm is both not happy and tall.
Everyone who is either not generous or calm is funny and vice versa.
Everyone who is happy is either tall or not creative.
If someone is either creative or brave then fred is not creative or not quiet and vice versa.
Everyone who is not wise or not rich is both not old and tall and vice versa.
If someone is both not tall and quiet then someone is both not wise and not rich.
Everyone who is both patient and happy is either not strong or not happy and vice versa.
Everyone who is both brave and curious is either quiet or not brave and vice versa.
Everyone who is wise is either kind or rich and vice versa.
Someone is either not generous or not tall.
Someone is both wise and not funny.
Paul is either calm or wise.
Someone is either not curious or funny.
Someone is not rich or creative.
Mary is either not quiet or not patient. | Mary is curious. | contradiction | ((?[X]:((strong(X)|~rich(X))))<=>((~rich(susan)|curious(susan))))&
((?[X]:(~calm(X)))=>((curious(paul)|creative(paul))))&
(![X]:((~wise(X)|curious(X))<=>(~generous(X)&kind(X))))&
(((~old(john)&happy(john)))<=>((~generous(john)|wise(john))))&
(![X]:((~kind(X)|~patient(X))<=>(~funny(X)&funny(X))))&
(![X]:((rich(X)<~>~tall(X))=>(~quiet(X)&tall(X))))&
(![X]:(~calm(X)=>(~happy(X)&tall(X))))&
(![X]:((~generous(X)<~>calm(X))<=>funny(X)))&
(![X]:(happy(X)=>(tall(X)<~>~creative(X))))&
((?[X]:((creative(X)<~>brave(X))))<=>((~creative(fred)|~quiet(fred))))&
(![X]:((~wise(X)|~rich(X))<=>(~old(X)&tall(X))))&
((?[X]:((~tall(X)&quiet(X))))=>(?[X]:((~wise(X)&~rich(X)))))&
(![X]:((patient(X)&happy(X))<=>(~strong(X)<~>~happy(X))))&
(![X]:((brave(X)&curious(X))<=>(quiet(X)<~>~brave(X))))&
(![X]:(wise(X)<=>(kind(X)<~>rich(X))))&
(?[X]:((~generous(X)<~>~tall(X))))&
(?[X]:((wise(X)&~funny(X))))&
((calm(paul)<~>wise(paul)))&
(?[X]:((~curious(X)<~>funny(X))))&
(?[X]:((~rich(X)|creative(X))))&
((~quiet(mary)<~>~patient(mary))) | curious(mary) | [
"p4",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 557310739651981207619976
% SZS output start Proof for 557310739651981207619976
5. ! [X0] : ((~patient(X0) | ~kind(X0)) <=> (funny(X0) & ~funny(X0))) [input p4]
14. ! [X0] : ((curious(X0) & brave(X0)) <=> (quiet(X0) <~> ~brave(X0))) [input p13]
21. ~quiet(mary) <~> ~patient(mary) [input p20]
22. curious(mary) [input hypothesis]
39. ! [X0] : (((~patient(X0) | ~kind(X0)) | (~funny(X0) | funny(X0))) & ((funny(X0) & ~funny(X0)) | (patient(X0) & kind(X0)))) [nnf transformation 5]
40. ! [X0] : ((~patient(X0) | ~kind(X0) | ~funny(X0) | funny(X0)) & ((funny(X0) & ~funny(X0)) | (patient(X0) & kind(X0)))) [flattening 39]
56. ! [X0] : (((curious(X0) & brave(X0)) | ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | (~curious(X0) | ~brave(X0)))) [nnf transformation 14]
57. ! [X0] : (((curious(X0) & brave(X0)) | ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | ~curious(X0) | ~brave(X0))) [flattening 56]
70. (patient(mary) | quiet(mary)) & (~patient(mary) | ~quiet(mary)) [nnf transformation 21]
87. ~funny(X0) | patient(X0) [cnf transformation 40]
89. funny(X0) | patient(X0) [cnf transformation 40]
122. ~brave(X0) | quiet(X0) | ~curious(X0) | ~brave(X0) [cnf transformation 57]
125. brave(X0) | quiet(X0) | brave(X0) [cnf transformation 57]
141. ~patient(mary) | ~quiet(mary) [cnf transformation 70]
143. curious(mary) [cnf transformation 22]
144. ~brave(X0) | quiet(X0) | ~curious(X0) [duplicate literal removal 122]
145. brave(X0) | quiet(X0) [duplicate literal removal 125]
207. patient(X0) [subsumption resolution 87,89]
253. ~curious(X0) | quiet(X0) [subsumption resolution 144,145]
295. ~quiet(mary) [subsumption resolution 141,207]
308. quiet(mary) [resolution 253,143]
309. $false [subsumption resolution 308,295]
% SZS output end Proof for 557310739651981207619976
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not strong is either not curious or wise and vice versa. If someone is either happy or not kind then someone is patient or strong and vice versa. Everyone who is either humble or old is both not funny and humble and vice versa. Everyone who is not quiet is funny and vice versa. Everyone who is not kind is brave and vice versa. Everyone who is either not generous or calm is quiet or rich. Everyone who is not rich or not kind is calm or not rich and vice versa. If someone is either creative or calm then mary is either not funny or generous. If john is not happy or kind then someone is both patient and quiet and vice versa. If someone is either creative or wise then mary is either not humble or not tall. Everyone who is both funny and not strong is both not generous and creative and vice versa. Everyone who is not humble or not old is humble. If someone is not old or brave then someone is not old or patient and vice versa. Everyone who is both rich and not old is generous or creative and vice versa. If lucy is either quiet or not old then someone is either curious or quiet. If someone is both creative and old then someone is calm or brave. Mary is not calm. Someone is old or funny. John is both brave and tall. Someone is both rich and not kind. Paul is either generous or not old. Someone is not happy. Susan is not patient or not humble. | Mary is not creative. | entailment | (![X]:((humble(X)|~strong(X))<=>(~curious(X)<~>wise(X))))&
((?[X]:((happy(X)<~>~kind(X))))<=>(?[X]:((patient(X)|strong(X)))))&
(![X]:((humble(X)<~>old(X))<=>(~funny(X)&humble(X))))&
(![X]:(~quiet(X)<=>funny(X)))&
(![X]:(~kind(X)<=>brave(X)))&
(![X]:((~generous(X)<~>calm(X))=>(quiet(X)|rich(X))))&
(![X]:((~rich(X)|~kind(X))<=>(calm(X)|~rich(X))))&
((?[X]:((creative(X)<~>calm(X))))=>((~funny(mary)<~>generous(mary))))&
(((~happy(john)|kind(john)))<=>(?[X]:((patient(X)&quiet(X)))))&
((?[X]:((creative(X)<~>wise(X))))=>((~humble(mary)<~>~tall(mary))))&
(![X]:((funny(X)&~strong(X))<=>(~generous(X)&creative(X))))&
(![X]:((~humble(X)|~old(X))=>humble(X)))&
((?[X]:((~old(X)|brave(X))))<=>(?[X]:((~old(X)|patient(X)))))&
(![X]:((rich(X)&~old(X))<=>(generous(X)|creative(X))))&
(((quiet(lucy)<~>~old(lucy)))=>(?[X]:((curious(X)<~>quiet(X)))))&
((?[X]:((creative(X)&old(X))))=>(?[X]:((calm(X)|brave(X)))))&
(~calm(mary))&
(?[X]:((old(X)|funny(X))))&
((brave(john)&tall(john)))&
(?[X]:((rich(X)&~kind(X))))&
((generous(paul)<~>~old(paul)))&
(?[X]:(~happy(X)))&
((~patient(susan)|~humble(susan))) | ~creative(mary) | [
"p2",
"p7",
"p10",
"p11",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2359456585885242904994883
% SZS output start Proof for 2359456585885242904994883
3. ! [X0] : ((humble(X0) <~> old(X0)) <=> (humble(X0) & ~funny(X0))) [input p2]
8. ? [X0] : (creative(X0) <~> calm(X0)) => (~funny(mary) <~> generous(mary)) [input p7]
11. ! [X0] : ((~strong(X0) & funny(X0)) <=> (creative(X0) & ~generous(X0))) [input p10]
12. ! [X0] : ((~old(X0) | ~humble(X0)) => humble(X0)) [input p11]
14. ! [X0] : ((~old(X0) & rich(X0)) <=> (creative(X0) | generous(X0))) [input p13]
17. ~calm(mary) [input p16]
24. creative(mary) [input hypothesis]
30. (~funny(mary) <~> generous(mary)) | ! [X0] : (creative(X0) <=> calm(X0)) [ennf transformation 8]
32. ! [X0] : (humble(X0) | (old(X0) & humble(X0))) [ennf transformation 12]
42. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | (~humble(X0) | funny(X0))) & ((humble(X0) & ~funny(X0)) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [nnf transformation 3]
43. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | ~humble(X0) | funny(X0)) & ((humble(X0) & ~funny(X0)) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [flattening 42]
49. ((~generous(mary) | funny(mary)) & (generous(mary) | ~funny(mary))) | ! [X0] : ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0))) [nnf transformation 30]
56. ! [X0] : (((~strong(X0) & funny(X0)) | (~creative(X0) | generous(X0))) & ((creative(X0) & ~generous(X0)) | (strong(X0) | ~funny(X0)))) [nnf transformation 11]
57. ! [X0] : (((~strong(X0) & funny(X0)) | ~creative(X0) | generous(X0)) & ((creative(X0) & ~generous(X0)) | strong(X0) | ~funny(X0))) [flattening 56]
63. ! [X0] : (((~old(X0) & rich(X0)) | (~creative(X0) & ~generous(X0))) & ((creative(X0) | generous(X0)) | (old(X0) | ~rich(X0)))) [nnf transformation 14]
64. ! [X0] : (((~old(X0) & rich(X0)) | (~creative(X0) & ~generous(X0))) & (creative(X0) | generous(X0) | old(X0) | ~rich(X0))) [flattening 63]
90. ~funny(X0) | old(X0) | ~humble(X0) [cnf transformation 43]
93. humble(X0) | humble(X0) | ~old(X0) [cnf transformation 43]
108. ~generous(mary) | funny(mary) | calm(X0) | ~creative(X0) [cnf transformation 49]
121. ~creative(X0) | funny(X0) | generous(X0) [cnf transformation 57]
124. humble(X0) | old(X0) [cnf transformation 32]
133. ~creative(X0) | ~old(X0) [cnf transformation 64]
139. ~calm(mary) [cnf transformation 17]
149. creative(mary) [cnf transformation 24]
151. ~old(X0) | humble(X0) [duplicate literal removal 93]
191. 10 <=> funny(mary) [avatar definition]
193. funny(mary) <- (10) [avatar component clause 191]
195. 11 <=> generous(mary) [avatar definition]
200. 12 <=> ! [X0] : (calm(X0) | ~creative(X0)) [avatar definition]
201. ~creative(X0) | calm(X0) <- (12) [avatar component clause 200]
202. 12 | 10 | ~11 [avatar split clause 108,195,191,200]
247. humble(X0) [subsumption resolution 124,151]
311. ~old(mary) [resolution 133,149]
344. funny(mary) | generous(mary) [resolution 121,149]
351. old(mary) | ~humble(mary) <- (10) [resolution 193,90]
352. ~humble(mary) <- (10) [subsumption resolution 351,311]
353. $false <- (10) [subsumption resolution 352,247]
354. ~10 [avatar contradiction clause 353]
355. 11 | 10 [avatar split clause 344,191,195]
360. calm(mary) <- (12) [resolution 201,149]
361. $false <- (12) [subsumption resolution 360,139]
362. ~12 [avatar contradiction clause 361]
363. $false [avatar sat refutation 202,354,355,362]
% SZS output end Proof for 2359456585885242904994883
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is both calm and wise then someone is not strong and vice versa.
Everyone who is not brave or not happy is either humble or not generous and vice versa.
Everyone who is tall or rich is either brave or curious and vice versa.
If lucy is not happy or generous then someone is both brave and not rich.
If someone is either not wise or strong then fred is happy.
Everyone who is either not happy or not wise is humble and vice versa.
If someone is both not old and calm then john is both brave and not humble and vice versa.
If someone is strong then susan is either tall or not rich.
If john is not humble or not strong then lucy is both not curious and brave.
Everyone who is funny is both not strong and curious and vice versa.
Everyone who is not humble or humble is not humble or not generous.
Everyone who is both not kind and not happy is both not curious and not patient and vice versa.
Everyone who is not creative or rich is not old and vice versa.
Everyone who is not kind or tall is both calm and not curious and vice versa.
Everyone who is not rich is not happy or rich and vice versa.
Everyone who is both not tall and humble is both not old and quiet and vice versa.
Someone is either calm or creative.
Someone is both not funny and not kind.
Alice is both not funny and not happy.
Someone is curious.
Mary is not curious.
Someone is not happy or creative.
Someone is both not curious and old. | Lucy is not generous. | entailment | (((calm(john)&wise(john)))<=>(?[X]:(~strong(X))))&
(![X]:((~brave(X)|~happy(X))<=>(humble(X)<~>~generous(X))))&
(![X]:((tall(X)|rich(X))<=>(brave(X)<~>curious(X))))&
(((~happy(lucy)|generous(lucy)))=>(?[X]:((brave(X)&~rich(X)))))&
((?[X]:((~wise(X)<~>strong(X))))=>(happy(fred)))&
(![X]:((~happy(X)<~>~wise(X))<=>humble(X)))&
((?[X]:((~old(X)&calm(X))))<=>((brave(john)&~humble(john))))&
((?[X]:(strong(X)))=>((tall(susan)<~>~rich(susan))))&
(((~humble(john)|~strong(john)))=>((~curious(lucy)&brave(lucy))))&
(![X]:(funny(X)<=>(~strong(X)&curious(X))))&
(![X]:((~humble(X)|humble(X))=>(~humble(X)|~generous(X))))&
(![X]:((~kind(X)&~happy(X))<=>(~curious(X)&~patient(X))))&
(![X]:((~creative(X)|rich(X))<=>~old(X)))&
(![X]:((~kind(X)|tall(X))<=>(calm(X)&~curious(X))))&
(![X]:(~rich(X)<=>(~happy(X)|rich(X))))&
(![X]:((~tall(X)&humble(X))<=>(~old(X)&quiet(X))))&
(?[X]:((calm(X)<~>creative(X))))&
(?[X]:((~funny(X)&~kind(X))))&
((~funny(alice)&~happy(alice)))&
(?[X]:(curious(X)))&
(~curious(mary))&
(?[X]:((~happy(X)|creative(X))))&
(?[X]:((~curious(X)&old(X)))) | ~generous(lucy) | [
"p1",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7953815803616028770851572
% SZS output start Proof for 7953815803616028770851572
2. ! [X0] : ((~happy(X0) | ~brave(X0)) <=> (humble(X0) <~> ~generous(X0))) [input p1]
11. ! [X0] : ((humble(X0) | ~humble(X0)) => (~generous(X0) | ~humble(X0))) [input p10]
15. ! [X0] : (~rich(X0) <=> (rich(X0) | ~happy(X0))) [input p14]
24. generous(lucy) [input hypothesis]
32. ! [X0] : ((~generous(X0) | ~humble(X0)) | (~humble(X0) & humble(X0))) [ennf transformation 11]
33. ! [X0] : (~generous(X0) | ~humble(X0) | (~humble(X0) & humble(X0))) [flattening 32]
39. ! [X0] : (((~happy(X0) | ~brave(X0)) | ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0)))) & (((generous(X0) | ~humble(X0)) & (~generous(X0) | humble(X0))) | (happy(X0) & brave(X0)))) [nnf transformation 2]
40. ! [X0] : ((~happy(X0) | ~brave(X0) | ((humble(X0) | generous(X0)) & (~generous(X0) | ~humble(X0)))) & (((generous(X0) | ~humble(X0)) & (~generous(X0) | humble(X0))) | (happy(X0) & brave(X0)))) [flattening 39]
59. ! [X0] : ((~rich(X0) | (~rich(X0) & happy(X0))) & ((rich(X0) | ~happy(X0)) | rich(X0))) [nnf transformation 15]
60. ! [X0] : ((~rich(X0) | (~rich(X0) & happy(X0))) & (rich(X0) | ~happy(X0) | rich(X0))) [flattening 59]
78. ~generous(X0) | humble(X0) | happy(X0) [cnf transformation 40]
111. ~generous(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 33]
124. rich(X0) | ~happy(X0) | rich(X0) [cnf transformation 60]
126. ~rich(X0) | ~rich(X0) [cnf transformation 60]
142. generous(lucy) [cnf transformation 24]
143. rich(X0) | ~happy(X0) [duplicate literal removal 124]
144. ~rich(X0) [duplicate literal removal 126]
145. ~generous(X0) | ~humble(X0) [duplicate literal removal 111]
165. 5 <=> generous(lucy) [avatar definition]
166. generous(lucy) <- (5) [avatar component clause 165]
248. ~happy(X0) [subsumption resolution 143,144]
259. 5 [avatar split clause 142,165]
267. ~humble(lucy) <- (5) [resolution 145,166]
284. humble(lucy) | happy(lucy) <- (5) [resolution 78,166]
285. happy(lucy) <- (5) [subsumption resolution 284,267]
286. $false <- (5) [subsumption resolution 285,248]
287. ~5 [avatar contradiction clause 286]
288. $false [avatar sat refutation 259,287]
% SZS output end Proof for 7953815803616028770851572
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either kind or not calm then lucy is either not brave or not calm and vice versa.
If mary is not calm or wise then alice is strong or tall and vice versa.
Everyone who is quiet is not strong.
Everyone who is both not creative and curious is humble or curious and vice versa.
If john is not patient or not quiet then someone is not patient or funny and vice versa.
If susan is both calm and kind then alice is kind or tall.
If someone is either not brave or not humble then someone is either tall or generous and vice versa.
If someone is old or rich then someone is not calm or happy.
If susan is curious then lucy is either patient or old.
If someone is both not quiet and kind then someone is tall or not strong.
Everyone who is not brave is not calm or not kind.
Everyone who is not generous is either old or tall and vice versa.
If someone is creative then alice is either happy or not old and vice versa.
Everyone who is not curious or generous is either happy or tall and vice versa.
Everyone who is generous is both strong and not strong.
Everyone who is not rich is both not old and not calm and vice versa.
Someone is either curious or strong.
Susan is both not wise and curious.
Lucy is not wise.
Someone is not humble or not patient.
Mary is either not creative or tall.
Susan is curious or strong.
Someone is not kind or generous.
Fred is not generous or not patient. | Fred is calm. | neutral | (((kind(mary)<~>~calm(mary)))<=>((~brave(lucy)<~>~calm(lucy))))&
(((~calm(mary)|wise(mary)))<=>((strong(alice)|tall(alice))))&
(![X]:(quiet(X)=>~strong(X)))&
(![X]:((~creative(X)&curious(X))<=>(humble(X)|curious(X))))&
(((~patient(john)|~quiet(john)))<=>(?[X]:((~patient(X)|funny(X)))))&
(((calm(susan)&kind(susan)))=>((kind(alice)|tall(alice))))&
((?[X]:((~brave(X)<~>~humble(X))))<=>(?[X]:((tall(X)<~>generous(X)))))&
((?[X]:((old(X)|rich(X))))=>(?[X]:((~calm(X)|happy(X)))))&
((curious(susan))=>((patient(lucy)<~>old(lucy))))&
((?[X]:((~quiet(X)&kind(X))))=>(?[X]:((tall(X)|~strong(X)))))&
(![X]:(~brave(X)=>(~calm(X)|~kind(X))))&
(![X]:(~generous(X)<=>(old(X)<~>tall(X))))&
((?[X]:(creative(X)))<=>((happy(alice)<~>~old(alice))))&
(![X]:((~curious(X)|generous(X))<=>(happy(X)<~>tall(X))))&
(![X]:(generous(X)=>(strong(X)&~strong(X))))&
(![X]:(~rich(X)<=>(~old(X)&~calm(X))))&
(?[X]:((curious(X)<~>strong(X))))&
((~wise(susan)&curious(susan)))&
(~wise(lucy))&
(?[X]:((~humble(X)|~patient(X))))&
((~creative(mary)<~>tall(mary)))&
((curious(susan)|strong(susan)))&
(?[X]:((~kind(X)|generous(X))))&
((~generous(fred)|~patient(fred))) | calm(fred) | [] | null | 0 |
If fred is patient then fred is either not brave or quiet and vice versa.
If susan is not generous then someone is rich and vice versa.
Everyone who is either not tall or rich is both happy and tall.
Everyone who is either wise or tall is not brave.
If susan is either kind or not humble then someone is happy or patient and vice versa.
Everyone who is not creative or rich is either quiet or not curious and vice versa.
Everyone who is both brave and old is tall and vice versa.
Everyone who is either not humble or tall is not wise and vice versa.
Everyone who is generous or brave is either not happy or kind.
Everyone who is either old or patient is either not happy or wise.
If susan is not old then someone is patient.
Everyone who is both not rich and patient is not strong.
Everyone who is not curious or not calm is not quiet.
Everyone who is not wise is strong or not old and vice versa.
If someone is both not old and generous then someone is both happy and funny and vice versa.
Everyone who is either not rich or not wise is either not creative or curious.
Someone is not funny.
Mary is happy or strong.
Lucy is both not creative and not wise.
Someone is calm or not humble.
Mary is funny or not brave.
Someone is both not happy and tall.
John is either strong or generous. | Lucy is not quiet. | entailment | ((patient(fred))<=>((~brave(fred)<~>quiet(fred))))&
((~generous(susan))<=>(?[X]:(rich(X))))&
(![X]:((~tall(X)<~>rich(X))=>(happy(X)&tall(X))))&
(![X]:((wise(X)<~>tall(X))=>~brave(X)))&
(((kind(susan)<~>~humble(susan)))<=>(?[X]:((happy(X)|patient(X)))))&
(![X]:((~creative(X)|rich(X))<=>(quiet(X)<~>~curious(X))))&
(![X]:((brave(X)&old(X))<=>tall(X)))&
(![X]:((~humble(X)<~>tall(X))<=>~wise(X)))&
(![X]:((generous(X)|brave(X))=>(~happy(X)<~>kind(X))))&
(![X]:((old(X)<~>patient(X))=>(~happy(X)<~>wise(X))))&
((~old(susan))=>(?[X]:(patient(X))))&
(![X]:((~rich(X)&patient(X))=>~strong(X)))&
(![X]:((~curious(X)|~calm(X))=>~quiet(X)))&
(![X]:(~wise(X)<=>(strong(X)|~old(X))))&
((?[X]:((~old(X)&generous(X))))<=>(?[X]:((happy(X)&funny(X)))))&
(![X]:((~rich(X)<~>~wise(X))=>(~creative(X)<~>curious(X))))&
(?[X]:(~funny(X)))&
((happy(mary)|strong(mary)))&
((~creative(lucy)&~wise(lucy)))&
(?[X]:((calm(X)|~humble(X))))&
((funny(mary)|~brave(mary)))&
(?[X]:((~happy(X)&tall(X))))&
((strong(john)<~>generous(john))) | ~quiet(lucy) | [
"p2",
"p3",
"p6",
"p12",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7508054031945427092359969
% SZS output start Proof for 7508054031945427092359969
3. ! [X0] : ((~tall(X0) <~> rich(X0)) => (tall(X0) & happy(X0))) [input p2]
4. ! [X0] : ((wise(X0) <~> tall(X0)) => ~brave(X0)) [input p3]
7. ! [X0] : ((old(X0) & brave(X0)) <=> tall(X0)) [input p6]
13. ! [X0] : ((~calm(X0) | ~curious(X0)) => ~quiet(X0)) [input p12]
16. ! [X0] : ((~rich(X0) <~> ~wise(X0)) => (~creative(X0) <~> curious(X0))) [input p15]
19. ~wise(lucy) & ~creative(lucy) [input p18]
24. quiet(lucy) [input hypothesis]
26. ! [X0] : (~curious(X0) => ~quiet(X0)) [pure predicate removal 13]
28. ! [X0] : ((tall(X0) & happy(X0)) | (~tall(X0) <=> rich(X0))) [ennf transformation 3]
29. ! [X0] : (~brave(X0) | (wise(X0) <=> tall(X0))) [ennf transformation 4]
35. ! [X0] : (~quiet(X0) | curious(X0)) [ennf transformation 26]
36. ! [X0] : ((~creative(X0) <~> curious(X0)) | (~rich(X0) <=> ~wise(X0))) [ennf transformation 16]
42. ! [X0] : ((tall(X0) & happy(X0)) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0)))) [nnf transformation 28]
43. ! [X0] : (~brave(X0) | ((wise(X0) | ~tall(X0)) & (tall(X0) | ~wise(X0)))) [nnf transformation 29]
50. ! [X0] : (((old(X0) & brave(X0)) | ~tall(X0)) & (tall(X0) | (~old(X0) | ~brave(X0)))) [nnf transformation 7]
51. ! [X0] : (((old(X0) & brave(X0)) | ~tall(X0)) & (tall(X0) | ~old(X0) | ~brave(X0))) [flattening 50]
64. ! [X0] : (((~curious(X0) | creative(X0)) & (curious(X0) | ~creative(X0))) | ((~rich(X0) | wise(X0)) & (~wise(X0) | rich(X0)))) [nnf transformation 36]
78. tall(X0) | rich(X0) | tall(X0) [cnf transformation 42]
81. ~tall(X0) | wise(X0) | ~brave(X0) [cnf transformation 43]
95. ~tall(X0) | brave(X0) [cnf transformation 51]
111. ~quiet(X0) | curious(X0) [cnf transformation 35]
122. ~curious(X0) | creative(X0) | ~rich(X0) | wise(X0) [cnf transformation 64]
125. ~creative(lucy) [cnf transformation 19]
126. ~wise(lucy) [cnf transformation 19]
132. quiet(lucy) [cnf transformation 24]
133. tall(X0) | rich(X0) [duplicate literal removal 78]
260. curious(lucy) [resolution 111,132]
265. rich(X1) | brave(X1) [resolution 133,95]
277. wise(X0) | ~brave(X0) | rich(X0) [resolution 81,133]
279. wise(X0) | rich(X0) [subsumption resolution 277,265]
292. rich(lucy) [resolution 279,126]
372. creative(lucy) | ~rich(lucy) | wise(lucy) [resolution 122,260]
373. ~rich(lucy) | wise(lucy) [subsumption resolution 372,125]
374. wise(lucy) [subsumption resolution 373,292]
375. $false [subsumption resolution 374,126]
% SZS output end Proof for 7508054031945427092359969
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not calm or wise then mary is strong or wise.
Everyone who is both funny and not creative is not happy or wise and vice versa.
If mary is both tall and not quiet then someone is either curious or not happy.
If john is not tall or tall then someone is kind and vice versa.
If lucy is generous or quiet then someone is both humble and not calm and vice versa.
If alice is both calm and not quiet then someone is kind.
Everyone who is generous or quiet is both not calm and humble and vice versa.
Everyone who is either funny or not tall is not calm or not rich and vice versa.
Everyone who is not rich or tall is both humble and creative and vice versa.
If mary is both not curious and not brave then paul is not strong or rich and vice versa.
Everyone who is not wise or kind is not humble or generous and vice versa.
Everyone who is both humble and wise is both calm and not old.
If mary is not quiet then someone is curious and vice versa.
If john is not funny then someone is both not funny and creative.
If alice is curious or not quiet then lucy is not humble or old and vice versa.
Everyone who is humble is both tall and not patient.
Someone is both not quiet and not brave.
Someone is rich or not calm.
Alice is humble or quiet.
Someone is not rich.
Alice is either quiet or not wise.
Someone is both not happy and not old.
Fred is either not happy or calm. | Alice is not creative. | contradiction | (((~calm(lucy)<~>wise(lucy)))=>((strong(mary)|wise(mary))))&
(![X]:((funny(X)&~creative(X))<=>(~happy(X)|wise(X))))&
(((tall(mary)&~quiet(mary)))=>(?[X]:((curious(X)<~>~happy(X)))))&
(((~tall(john)|tall(john)))<=>(?[X]:(kind(X))))&
(((generous(lucy)|quiet(lucy)))<=>(?[X]:((humble(X)&~calm(X)))))&
(((calm(alice)&~quiet(alice)))=>(?[X]:(kind(X))))&
(![X]:((generous(X)|quiet(X))<=>(~calm(X)&humble(X))))&
(![X]:((funny(X)<~>~tall(X))<=>(~calm(X)|~rich(X))))&
(![X]:((~rich(X)|tall(X))<=>(humble(X)&creative(X))))&
(((~curious(mary)&~brave(mary)))<=>((~strong(paul)|rich(paul))))&
(![X]:((~wise(X)|kind(X))<=>(~humble(X)|generous(X))))&
(![X]:((humble(X)&wise(X))=>(calm(X)&~old(X))))&
((~quiet(mary))<=>(?[X]:(curious(X))))&
((~funny(john))=>(?[X]:((~funny(X)&creative(X)))))&
(((curious(alice)|~quiet(alice)))<=>((~humble(lucy)|old(lucy))))&
(![X]:(humble(X)=>(tall(X)&~patient(X))))&
(?[X]:((~quiet(X)&~brave(X))))&
(?[X]:((rich(X)|~calm(X))))&
((humble(alice)|quiet(alice)))&
(?[X]:(~rich(X)))&
((quiet(alice)<~>~wise(alice)))&
(?[X]:((~happy(X)&~old(X))))&
((~happy(fred)<~>calm(fred))) | ~creative(alice) | [
"p6",
"p8",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8991144187342335490962478
% SZS output start Proof for 8991144187342335490962478
7. ! [X0] : ((quiet(X0) | generous(X0)) <=> (humble(X0) & ~calm(X0))) [input p6]
9. ! [X0] : ((tall(X0) | ~rich(X0)) <=> (creative(X0) & humble(X0))) [input p8]
16. ! [X0] : (humble(X0) => (~patient(X0) & tall(X0))) [input p15]
19. quiet(alice) | humble(alice) [input p18]
24. ~creative(alice) [input hypothesis]
25. ! [X0] : (humble(X0) => tall(X0)) [pure predicate removal 16]
35. ! [X0] : (tall(X0) | ~humble(X0)) [ennf transformation 25]
54. ! [X0] : (((quiet(X0) | generous(X0)) | (~humble(X0) | calm(X0))) & ((humble(X0) & ~calm(X0)) | (~quiet(X0) & ~generous(X0)))) [nnf transformation 7]
55. ! [X0] : ((quiet(X0) | generous(X0) | ~humble(X0) | calm(X0)) & ((humble(X0) & ~calm(X0)) | (~quiet(X0) & ~generous(X0)))) [flattening 54]
58. ! [X0] : (((tall(X0) | ~rich(X0)) | (~creative(X0) | ~humble(X0))) & ((creative(X0) & humble(X0)) | (~tall(X0) & rich(X0)))) [nnf transformation 9]
59. ! [X0] : ((tall(X0) | ~rich(X0) | ~creative(X0) | ~humble(X0)) & ((creative(X0) & humble(X0)) | (~tall(X0) & rich(X0)))) [flattening 58]
103. ~quiet(X0) | humble(X0) [cnf transformation 55]
114. ~tall(X0) | creative(X0) [cnf transformation 59]
135. ~humble(X0) | tall(X0) [cnf transformation 35]
139. quiet(alice) | humble(alice) [cnf transformation 19]
147. ~creative(alice) [cnf transformation 24]
300. humble(alice) [subsumption resolution 139,103]
326. tall(alice) [resolution 135,300]
349. creative(alice) [resolution 326,114]
352. $false [subsumption resolution 349,147]
% SZS output end Proof for 8991144187342335490962478
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is both not curious and creative.
Everyone who is not calm is not tall or humble and vice versa.
Everyone who is not creative or funny is either wise or generous and vice versa.
If someone is both not rich and humble then someone is curious and vice versa.
If john is not curious or not funny then alice is both not patient and brave and vice versa.
Everyone who is either not patient or not generous is both funny and not old and vice versa.
If someone is kind then someone is funny and vice versa.
If fred is both patient and calm then someone is both not funny and not old.
If someone is kind or patient then lucy is not quiet or not old and vice versa.
Everyone who is either creative or funny is not happy.
If someone is both quiet and not kind then mary is both curious and creative.
Everyone who is either not generous or wise is not creative or humble and vice versa.
Everyone who is both kind and patient is both kind and not tall.
Everyone who is both humble and not patient is not brave or calm.
If alice is both not kind and not happy then someone is generous or not funny.
Everyone who is not patient is both happy and not old and vice versa.
Someone is not old or tall.
Lucy is not patient.
Someone is happy or not curious.
Susan is both wise and generous.
Someone is curious.
John is both wise and not happy. | Lucy is kind. | neutral | (![X]:(~calm(X)=>(~curious(X)&creative(X))))&
(![X]:(~calm(X)<=>(~tall(X)|humble(X))))&
(![X]:((~creative(X)|funny(X))<=>(wise(X)<~>generous(X))))&
((?[X]:((~rich(X)&humble(X))))<=>(?[X]:(curious(X))))&
(((~curious(john)|~funny(john)))<=>((~patient(alice)&brave(alice))))&
(![X]:((~patient(X)<~>~generous(X))<=>(funny(X)&~old(X))))&
((?[X]:(kind(X)))<=>(?[X]:(funny(X))))&
(((patient(fred)&calm(fred)))=>(?[X]:((~funny(X)&~old(X)))))&
((?[X]:((kind(X)|patient(X))))<=>((~quiet(lucy)|~old(lucy))))&
(![X]:((creative(X)<~>funny(X))=>~happy(X)))&
((?[X]:((quiet(X)&~kind(X))))=>((curious(mary)&creative(mary))))&
(![X]:((~generous(X)<~>wise(X))<=>(~creative(X)|humble(X))))&
(![X]:((kind(X)&patient(X))=>(kind(X)&~tall(X))))&
(![X]:((humble(X)&~patient(X))=>(~brave(X)|calm(X))))&
(((~kind(alice)&~happy(alice)))=>(?[X]:((generous(X)|~funny(X)))))&
(![X]:(~patient(X)<=>(happy(X)&~old(X))))&
(?[X]:((~old(X)|tall(X))))&
(~patient(lucy))&
(?[X]:((happy(X)|~curious(X))))&
((wise(susan)&generous(susan)))&
(?[X]:(curious(X)))&
((wise(john)&~happy(john))) | kind(lucy) | [] | null | 0 |
Everyone who is both not wise and old is either brave or curious. Everyone who is both kind and not humble is not patient or patient. Everyone who is either not humble or humble is both curious and calm and vice versa. If fred is not happy or not curious then alice is generous or calm and vice versa. If someone is either generous or rich then someone is not humble or old and vice versa. Everyone who is old is generous. Everyone who is both not calm and kind is both humble and not old. If someone is funny then lucy is curious or not strong and vice versa. If someone is either not patient or quiet then someone is both curious and creative and vice versa. Everyone who is not funny is creative or not generous and vice versa. If mary is both brave and not generous then someone is both not humble and not happy and vice versa. Everyone who is both not wise and not patient is not creative and vice versa. If someone is not calm or not curious then someone is not quiet and vice versa. If someone is not funny or not rich then lucy is kind. If someone is not creative or not old then someone is both not happy and not tall. If someone is not old then someone is both not humble and not calm. Fred is either not humble or old. Alice is creative or not funny. Fred is calm. Susan is either kind or not tall. Someone is not creative or generous. Someone is humble. Someone is either creative or not happy. | Alice is not calm. | contradiction | (![X]:((~wise(X)&old(X))=>(brave(X)<~>curious(X))))&
(![X]:((kind(X)&~humble(X))=>(~patient(X)|patient(X))))&
(![X]:((~humble(X)<~>humble(X))<=>(curious(X)&calm(X))))&
(((~happy(fred)|~curious(fred)))<=>((generous(alice)|calm(alice))))&
((?[X]:((generous(X)<~>rich(X))))<=>(?[X]:((~humble(X)|old(X)))))&
(![X]:(old(X)=>generous(X)))&
(![X]:((~calm(X)&kind(X))=>(humble(X)&~old(X))))&
((?[X]:(funny(X)))<=>((curious(lucy)|~strong(lucy))))&
((?[X]:((~patient(X)<~>quiet(X))))<=>(?[X]:((curious(X)&creative(X)))))&
(![X]:(~funny(X)<=>(creative(X)|~generous(X))))&
(((brave(mary)&~generous(mary)))<=>(?[X]:((~humble(X)&~happy(X)))))&
(![X]:((~wise(X)&~patient(X))<=>~creative(X)))&
((?[X]:((~calm(X)|~curious(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:((~funny(X)|~rich(X))))=>(kind(lucy)))&
((?[X]:((~creative(X)|~old(X))))=>(?[X]:((~happy(X)&~tall(X)))))&
((?[X]:(~old(X)))=>(?[X]:((~humble(X)&~calm(X)))))&
((~humble(fred)<~>old(fred)))&
((creative(alice)|~funny(alice)))&
(calm(fred))&
((kind(susan)<~>~tall(susan)))&
(?[X]:((~creative(X)|generous(X))))&
(?[X]:(humble(X)))&
(?[X]:((creative(X)<~>~happy(X)))) | ~calm(alice) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 170676024781273823149793
% SZS output start Proof for 170676024781273823149793
3. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> (calm(X0) & curious(X0))) [input p2]
24. ~calm(alice) [input hypothesis]
41. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (~calm(X0) | ~curious(X0))) & ((calm(X0) & curious(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 3]
42. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | ~calm(X0) | ~curious(X0)) & ((calm(X0) & curious(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [flattening 41]
94. calm(X0) | humble(X0) | humble(X0) [cnf transformation 42]
95. calm(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 42]
151. ~calm(alice) [cnf transformation 24]
154. calm(X0) | humble(X0) [duplicate literal removal 94]
155. calm(X0) | ~humble(X0) [duplicate literal removal 95]
156. calm(X0) [subsumption resolution 154,155]
334. $false [subsumption resolution 151,156]
% SZS output end Proof for 170676024781273823149793
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and not old then susan is either wise or funny. If someone is generous or not old then alice is not rich or funny. Everyone who is not brave is either not tall or strong and vice versa. If susan is not funny or not happy then paul is both not strong and humble and vice versa. If someone is either not patient or strong then john is not creative and vice versa. Everyone who is generous is both not tall and not quiet. Everyone who is strong or tall is both old and quiet and vice versa. If someone is either not kind or not humble then someone is patient and vice versa. If someone is not curious or not creative then someone is curious. If someone is either not generous or not patient then someone is not old and vice versa. If someone is strong then paul is either patient or not kind. If alice is both curious and not quiet then lucy is happy or not patient and vice versa. If alice is both not brave and not tall then someone is either rich or curious and vice versa. Everyone who is both not old and strong is either not quiet or brave and vice versa. Everyone who is humble is not wise or not funny. If paul is not calm then alice is both happy and generous. Mary is quiet or happy. Someone is not happy. Someone is brave or curious. Someone is both not rich and not kind. Someone is both calm and strong. Paul is either kind or happy. Alice is not funny or not wise. | Paul is not calm. | contradiction | ((?[X]:((old(X)&~old(X))))=>((wise(susan)<~>funny(susan))))&
((?[X]:((generous(X)|~old(X))))=>((~rich(alice)|funny(alice))))&
(![X]:(~brave(X)<=>(~tall(X)<~>strong(X))))&
(((~funny(susan)|~happy(susan)))<=>((~strong(paul)&humble(paul))))&
((?[X]:((~patient(X)<~>strong(X))))<=>(~creative(john)))&
(![X]:(generous(X)=>(~tall(X)&~quiet(X))))&
(![X]:((strong(X)|tall(X))<=>(old(X)&quiet(X))))&
((?[X]:((~kind(X)<~>~humble(X))))<=>(?[X]:(patient(X))))&
((?[X]:((~curious(X)|~creative(X))))=>(?[X]:(curious(X))))&
((?[X]:((~generous(X)<~>~patient(X))))<=>(?[X]:(~old(X))))&
((?[X]:(strong(X)))=>((patient(paul)<~>~kind(paul))))&
(((curious(alice)&~quiet(alice)))<=>((happy(lucy)|~patient(lucy))))&
(((~brave(alice)&~tall(alice)))<=>(?[X]:((rich(X)<~>curious(X)))))&
(![X]:((~old(X)&strong(X))<=>(~quiet(X)<~>brave(X))))&
(![X]:(humble(X)=>(~wise(X)|~funny(X))))&
((~calm(paul))=>((happy(alice)&generous(alice))))&
((quiet(mary)|happy(mary)))&
(?[X]:(~happy(X)))&
(?[X]:((brave(X)|curious(X))))&
(?[X]:((~rich(X)&~kind(X))))&
(?[X]:((calm(X)&strong(X))))&
((kind(paul)<~>happy(paul)))&
((~funny(alice)|~wise(alice))) | ~calm(paul) | [
"p2",
"p5",
"p6",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1917737725874468248722123
% SZS output start Proof for 1917737725874468248722123
3. ! [X0] : (~brave(X0) <=> (~tall(X0) <~> strong(X0))) [input p2]
6. ! [X0] : (generous(X0) => (~quiet(X0) & ~tall(X0))) [input p5]
7. ! [X0] : ((tall(X0) | strong(X0)) <=> (quiet(X0) & old(X0))) [input p6]
14. ! [X0] : ((strong(X0) & ~old(X0)) <=> (~quiet(X0) <~> brave(X0))) [input p13]
16. ~calm(paul) => (generous(alice) & happy(alice)) [input p15]
24. ~calm(paul) [input hypothesis]
31. ! [X0] : ((~quiet(X0) & ~tall(X0)) | ~generous(X0)) [ennf transformation 6]
36. (generous(alice) & happy(alice)) | calm(paul) [ennf transformation 16]
38. ! [X0] : ((~brave(X0) | ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0)))) & (((~strong(X0) | tall(X0)) & (strong(X0) | ~tall(X0))) | brave(X0))) [nnf transformation 3]
45. ! [X0] : (((tall(X0) | strong(X0)) | (~quiet(X0) | ~old(X0))) & ((quiet(X0) & old(X0)) | (~tall(X0) & ~strong(X0)))) [nnf transformation 7]
46. ! [X0] : ((tall(X0) | strong(X0) | ~quiet(X0) | ~old(X0)) & ((quiet(X0) & old(X0)) | (~tall(X0) & ~strong(X0)))) [flattening 45]
68. ! [X0] : (((strong(X0) & ~old(X0)) | ((~quiet(X0) | ~brave(X0)) & (brave(X0) | quiet(X0)))) & (((~brave(X0) | quiet(X0)) & (brave(X0) | ~quiet(X0))) | (~strong(X0) | old(X0)))) [nnf transformation 14]
69. ! [X0] : (((strong(X0) & ~old(X0)) | ((~quiet(X0) | ~brave(X0)) & (brave(X0) | quiet(X0)))) & (((~brave(X0) | quiet(X0)) & (brave(X0) | ~quiet(X0))) | ~strong(X0) | old(X0))) [flattening 68]
85. ~brave(X0) | strong(X0) | tall(X0) [cnf transformation 38]
96. ~tall(X0) | ~generous(X0) [cnf transformation 31]
97. ~quiet(X0) | ~generous(X0) [cnf transformation 31]
100. ~strong(X0) | quiet(X0) [cnf transformation 46]
130. strong(X0) | brave(X0) | quiet(X0) [cnf transformation 69]
134. generous(alice) | calm(paul) [cnf transformation 36]
145. ~calm(paul) [cnf transformation 24]
282. 32 <=> quiet(alice) [avatar definition]
283. quiet(alice) <- (32) [avatar component clause 282]
302. 36 <=> tall(alice) [avatar definition]
303. tall(alice) <- (36) [avatar component clause 302]
304. ~tall(alice) <- (~36) [avatar component clause 302]
311. 38 <=> brave(alice) [avatar definition]
312. brave(alice) <- (38) [avatar component clause 311]
326. quiet(X0) | brave(X0) [subsumption resolution 130,100]
328. 41 <=> calm(paul) [avatar definition]
332. 42 <=> generous(alice) [avatar definition]
334. generous(alice) <- (42) [avatar component clause 332]
335. 41 | 42 [avatar split clause 134,332,328]
370. ~41 [avatar split clause 145,328]
375. ~generous(alice) <- (36) [resolution 96,303]
376. $false <- (36, 42) [subsumption resolution 375,334]
377. ~36 | ~42 [avatar contradiction clause 376]
384. ~generous(X0) | brave(X0) [resolution 326,97]
386. brave(alice) <- (42) [resolution 384,334]
398. strong(alice) | tall(alice) <- (38) [resolution 85,312]
409. strong(alice) <- (~36, 38) [subsumption resolution 398,304]
412. quiet(alice) <- (~36, 38) [resolution 409,100]
414. 32 | 36 | ~38 [avatar split clause 412,311,302,282]
415. ~generous(alice) <- (32) [resolution 283,97]
416. $false <- (32, 42) [subsumption resolution 415,334]
417. ~32 | ~42 [avatar contradiction clause 416]
418. 38 | ~42 [avatar split clause 386,332,311]
419. $false [avatar sat refutation 335,370,377,414,417,418]
% SZS output end Proof for 1917737725874468248722123
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is funny or curious then someone is humble.
Everyone who is either kind or not tall is not calm and vice versa.
Everyone who is not curious is both not happy and generous and vice versa.
Everyone who is not wise or not strong is either old or not curious and vice versa.
Everyone who is either happy or not generous is either not happy or not funny and vice versa.
If alice is creative or curious then paul is not old or funny.
Everyone who is either not rich or generous is happy or not old.
Everyone who is both tall and not brave is generous and vice versa.
If mary is both curious and old then someone is not brave or kind.
If someone is not calm then someone is creative and vice versa.
Everyone who is not funny or not humble is both creative and strong and vice versa.
Everyone who is calm or patient is not strong or funny and vice versa.
Everyone who is not patient is kind.
Everyone who is either strong or not strong is either not funny or patient and vice versa.
If someone is either not creative or not funny then someone is not brave or not happy and vice versa.
If someone is both not tall and not patient then someone is not calm and vice versa.
Someone is both rich and not strong.
Someone is both not kind and rich.
Someone is patient.
Susan is not generous or not quiet.
Someone is not creative or creative.
Someone is strong or not old.
Someone is either not wise or old. | Paul is funny. | entailment | (((funny(susan)|curious(susan)))=>(?[X]:(humble(X))))&
(![X]:((kind(X)<~>~tall(X))<=>~calm(X)))&
(![X]:(~curious(X)<=>(~happy(X)&generous(X))))&
(![X]:((~wise(X)|~strong(X))<=>(old(X)<~>~curious(X))))&
(![X]:((happy(X)<~>~generous(X))<=>(~happy(X)<~>~funny(X))))&
(((creative(alice)|curious(alice)))=>((~old(paul)|funny(paul))))&
(![X]:((~rich(X)<~>generous(X))=>(happy(X)|~old(X))))&
(![X]:((tall(X)&~brave(X))<=>generous(X)))&
(((curious(mary)&old(mary)))=>(?[X]:((~brave(X)|kind(X)))))&
((?[X]:(~calm(X)))<=>(?[X]:(creative(X))))&
(![X]:((~funny(X)|~humble(X))<=>(creative(X)&strong(X))))&
(![X]:((calm(X)|patient(X))<=>(~strong(X)|funny(X))))&
(![X]:(~patient(X)=>kind(X)))&
(![X]:((strong(X)<~>~strong(X))<=>(~funny(X)<~>patient(X))))&
((?[X]:((~creative(X)<~>~funny(X))))<=>(?[X]:((~brave(X)|~happy(X)))))&
((?[X]:((~tall(X)&~patient(X))))<=>(?[X]:(~calm(X))))&
(?[X]:((rich(X)&~strong(X))))&
(?[X]:((~kind(X)&rich(X))))&
(?[X]:(patient(X)))&
((~generous(susan)|~quiet(susan)))&
(?[X]:((~creative(X)|creative(X))))&
(?[X]:((strong(X)|~old(X))))&
(?[X]:((~wise(X)<~>old(X)))) | funny(paul) | [
"p4",
"p7",
"p9",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3082507397963371923459228
% SZS output start Proof for 3082507397963371923459228
5. ! [X0] : ((happy(X0) <~> ~generous(X0)) <=> (~happy(X0) <~> ~funny(X0))) [input p4]
8. ! [X0] : ((~brave(X0) & tall(X0)) <=> generous(X0)) [input p7]
10. ? [X0] : ~calm(X0) <=> ? [X0] : creative(X0) [input p9]
11. ! [X0] : ((~humble(X0) | ~funny(X0)) <=> (strong(X0) & creative(X0))) [input p10]
14. ! [X0] : ((strong(X0) <~> ~strong(X0)) <=> (~funny(X0) <~> patient(X0))) [input p13]
16. ? [X0] : (~patient(X0) & ~tall(X0)) <=> ? [X0] : ~calm(X0) [input p15]
24. ~funny(paul) [input hypothesis]
25. ? [X0] : ~calm(X0) <=> ? [X1] : creative(X1) [rectify 10]
27. ? [X0] : (~patient(X0) & ~tall(X0)) <=> ? [X1] : ~calm(X1) [rectify 16]
44. ! [X0] : ((((generous(X0) | ~happy(X0)) & (~generous(X0) | happy(X0))) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0)))) & (((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0))))) [nnf transformation 5]
46. ! [X0] : (((~brave(X0) & tall(X0)) | ~generous(X0)) & (generous(X0) | (brave(X0) | ~tall(X0)))) [nnf transformation 8]
47. ! [X0] : (((~brave(X0) & tall(X0)) | ~generous(X0)) & (generous(X0) | brave(X0) | ~tall(X0))) [flattening 46]
50. (? [X0] : ~calm(X0) | ! [X1] : ~creative(X1)) & (? [X1] : creative(X1) | ! [X0] : calm(X0)) [nnf transformation 25]
51. (? [X0] : ~calm(X0) | ! [X1] : ~creative(X1)) & (? [X2] : creative(X2) | ! [X3] : calm(X3)) [rectify 50]
52. ? [X0] : ~calm(X0) => ~calm(sK2) [choice axiom]
53. ? [X2] : creative(X2) => creative(sK3) [choice axiom]
54. (~calm(sK2) | ! [X1] : ~creative(X1)) & (creative(sK3) | ! [X3] : calm(X3)) [skolemisation 51,53,52]
55. ! [X0] : (((~humble(X0) | ~funny(X0)) | (~strong(X0) | ~creative(X0))) & ((strong(X0) & creative(X0)) | (humble(X0) & funny(X0)))) [nnf transformation 11]
56. ! [X0] : ((~humble(X0) | ~funny(X0) | ~strong(X0) | ~creative(X0)) & ((strong(X0) & creative(X0)) | (humble(X0) & funny(X0)))) [flattening 55]
59. ! [X0] : ((((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ((~funny(X0) | ~patient(X0)) & (patient(X0) | funny(X0)))) & (((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0))))) [nnf transformation 14]
65. (? [X0] : (~patient(X0) & ~tall(X0)) | ! [X1] : calm(X1)) & (? [X1] : ~calm(X1) | ! [X0] : (patient(X0) | tall(X0))) [nnf transformation 27]
66. (? [X0] : (~patient(X0) & ~tall(X0)) | ! [X1] : calm(X1)) & (? [X2] : ~calm(X2) | ! [X3] : (patient(X3) | tall(X3))) [rectify 65]
67. ? [X0] : (~patient(X0) & ~tall(X0)) => (~patient(sK6) & ~tall(sK6)) [choice axiom]
68. ? [X2] : ~calm(X2) => ~calm(sK7) [choice axiom]
69. ((~patient(sK6) & ~tall(sK6)) | ! [X1] : calm(X1)) & (~calm(sK7) | ! [X3] : (patient(X3) | tall(X3))) [skolemisation 66,68,67]
101. funny(X0) | happy(X0) | happy(X0) | generous(X0) [cnf transformation 44]
105. generous(X0) | ~happy(X0) | ~happy(X0) | funny(X0) [cnf transformation 44]
111. ~generous(X0) | tall(X0) [cnf transformation 47]
115. ~calm(sK2) | ~creative(X1) [cnf transformation 54]
116. creative(X0) | funny(X0) [cnf transformation 56]
118. strong(X0) | funny(X0) [cnf transformation 56]
126. patient(X0) | ~funny(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 59]
127. patient(X0) | ~funny(X0) | strong(X0) | strong(X0) [cnf transformation 59]
141. ~tall(sK6) | calm(X1) [cnf transformation 69]
142. ~patient(sK6) | calm(X1) [cnf transformation 69]
152. ~funny(paul) [cnf transformation 24]
153. patient(X0) | ~funny(X0) | ~strong(X0) [duplicate literal removal 126]
154. patient(X0) | ~funny(X0) | strong(X0) [duplicate literal removal 127]
158. funny(X0) | happy(X0) | generous(X0) [duplicate literal removal 101]
160. generous(X0) | ~happy(X0) | funny(X0) [duplicate literal removal 105]
175. generous(X0) | funny(X0) [subsumption resolution 158,160]
186. 6 <=> funny(paul) [avatar definition]
187. ~funny(paul) <- (~6) [avatar component clause 186]
213. 12 <=> ! [X1] : ~creative(X1) [avatar definition]
214. ~creative(X1) <- (12) [avatar component clause 213]
216. 13 <=> calm(sK2) [avatar definition]
218. ~calm(sK2) <- (~13) [avatar component clause 216]
219. 12 | ~13 [avatar split clause 115,216,213]
221. 14 <=> ! [X3] : calm(X3) [avatar definition]
222. calm(X3) <- (14) [avatar component clause 221]
230. patient(X0) | strong(X0) [subsumption resolution 154,118]
231. ~funny(X0) | patient(X0) [subsumption resolution 153,230]
250. 20 <=> ! [X3] : funny(X3) [avatar definition]
251. funny(X3) <- (20) [avatar component clause 250]
267. 24 <=> patient(sK6) [avatar definition]
269. ~patient(sK6) <- (~24) [avatar component clause 267]
270. 14 | ~24 [avatar split clause 142,267,221]
272. 25 <=> tall(sK6) [avatar definition]
274. ~tall(sK6) <- (~25) [avatar component clause 272]
275. 14 | ~25 [avatar split clause 141,272,221]
303. ~6 [avatar split clause 152,186]
304. $false <- (~13, 14) [subsumption resolution 218,222]
305. 13 | ~14 [avatar contradiction clause 304]
316. tall(X0) | funny(X0) [resolution 175,111]
328. funny(sK6) <- (~25) [resolution 316,274]
332. patient(sK6) <- (~25) [resolution 328,231]
333. $false <- (~24, ~25) [subsumption resolution 332,269]
334. 24 | 25 [avatar contradiction clause 333]
342. funny(X1) <- (12) [resolution 214,116]
344. 20 | ~12 [avatar split clause 342,213,250]
352. $false <- (~6, 20) [resolution 251,187]
353. 6 | ~20 [avatar contradiction clause 352]
355. $false [avatar sat refutation 219,270,275,303,305,334,344,353]
% SZS output end Proof for 3082507397963371923459228
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or generous is humble and vice versa.
Everyone who is old is either happy or not creative.
Everyone who is either not tall or not wise is either patient or tall and vice versa.
Everyone who is rich or curious is happy.
Everyone who is patient is either happy or creative and vice versa.
Everyone who is both not kind and not generous is either not curious or not wise.
Everyone who is wise is happy or brave and vice versa.
Everyone who is both not generous and not quiet is not tall or not old.
If someone is not wise then fred is both creative and not funny and vice versa.
If alice is rich or not creative then fred is both not patient and brave and vice versa.
If mary is both tall and not patient then someone is either not strong or not funny.
If john is not patient or not rich then someone is both not kind and kind and vice versa.
If someone is not wise then someone is either not calm or not quiet and vice versa.
If paul is either patient or not kind then someone is both tall and not creative.
Everyone who is either not happy or rich is not calm or rich and vice versa.
Fred is both not tall and not humble.
Someone is wise.
Someone is not brave or patient.
Susan is not generous.
Fred is both not rich and not generous.
Someone is calm. | Fred is not quiet. | contradiction | (![X]:((~curious(X)<~>generous(X))<=>humble(X)))&
(![X]:(old(X)=>(happy(X)<~>~creative(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(patient(X)<~>tall(X))))&
(![X]:((rich(X)|curious(X))=>happy(X)))&
(![X]:(patient(X)<=>(happy(X)<~>creative(X))))&
(![X]:((~kind(X)&~generous(X))=>(~curious(X)<~>~wise(X))))&
(![X]:(wise(X)<=>(happy(X)|brave(X))))&
(![X]:((~generous(X)&~quiet(X))=>(~tall(X)|~old(X))))&
((?[X]:(~wise(X)))<=>((creative(fred)&~funny(fred))))&
(((rich(alice)|~creative(alice)))<=>((~patient(fred)&brave(fred))))&
(((tall(mary)&~patient(mary)))=>(?[X]:((~strong(X)<~>~funny(X)))))&
(((~patient(john)|~rich(john)))<=>(?[X]:((~kind(X)&kind(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)<~>~quiet(X)))))&
(((patient(paul)<~>~kind(paul)))=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:((~happy(X)<~>rich(X))<=>(~calm(X)|rich(X))))&
((~tall(fred)&~humble(fred)))&
(?[X]:(wise(X)))&
(?[X]:((~brave(X)|patient(X))))&
(~generous(susan))&
((~rich(fred)&~generous(fred)))&
(?[X]:(calm(X))) | ~quiet(fred) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p8",
"p12",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 1198080193644619550881611
% SZS output start Proof for 1198080193644619550881611
1. ! [X0] : ((~curious(X0) <~> generous(X0)) <=> humble(X0)) [input p0]
3. ! [X0] : ((~tall(X0) <~> ~wise(X0)) <=> (patient(X0) <~> tall(X0))) [input p2]
4. ! [X0] : ((curious(X0) | rich(X0)) => happy(X0)) [input p3]
5. ! [X0] : (patient(X0) <=> (happy(X0) <~> creative(X0))) [input p4]
7. ! [X0] : (wise(X0) <=> (brave(X0) | happy(X0))) [input p6]
9. ? [X0] : ~wise(X0) <=> (~funny(fred) & creative(fred)) [input p8]
13. ? [X0] : ~wise(X0) <=> ? [X0] : (~calm(X0) <~> ~quiet(X0)) [input p12]
15. ! [X0] : ((~happy(X0) <~> rich(X0)) <=> (rich(X0) | ~calm(X0))) [input p14]
16. ~humble(fred) & ~tall(fred) [input p15]
20. ~generous(fred) & ~rich(fred) [input p19]
22. ~quiet(fred) [input hypothesis]
23. ? [X0] : ~wise(X0) <=> ? [X1] : (~calm(X1) <~> ~quiet(X1)) [rectify 13]
24. ! [X0] : ((~curious(X0) <~> generous(X0)) => humble(X0)) [unused predicate definition removal 1]
27. ! [X0] : (humble(X0) | (~curious(X0) <=> generous(X0))) [ennf transformation 24]
28. ! [X0] : (happy(X0) | (~curious(X0) & ~rich(X0))) [ennf transformation 4]
34. ! [X0] : (humble(X0) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0)))) [nnf transformation 27]
35. ! [X0] : ((((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))))) [nnf transformation 3]
36. ! [X0] : ((patient(X0) | ((happy(X0) | ~creative(X0)) & (creative(X0) | ~happy(X0)))) & (((~creative(X0) | ~happy(X0)) & (creative(X0) | happy(X0))) | ~patient(X0))) [nnf transformation 5]
38. ! [X0] : ((wise(X0) | (~brave(X0) & ~happy(X0))) & ((brave(X0) | happy(X0)) | ~wise(X0))) [nnf transformation 7]
39. ! [X0] : ((wise(X0) | (~brave(X0) & ~happy(X0))) & (brave(X0) | happy(X0) | ~wise(X0))) [flattening 38]
40. (? [X0] : ~wise(X0) | (funny(fred) | ~creative(fred))) & ((~funny(fred) & creative(fred)) | ! [X0] : wise(X0)) [nnf transformation 9]
41. (? [X0] : ~wise(X0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X0] : wise(X0)) [flattening 40]
42. (? [X0] : ~wise(X0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X1] : wise(X1)) [rectify 41]
43. ? [X0] : ~wise(X0) => ~wise(sK0) [choice axiom]
44. (~wise(sK0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X1] : wise(X1)) [skolemisation 42,43]
55. (? [X0] : ~wise(X0) | ! [X1] : ((~calm(X1) | quiet(X1)) & (~quiet(X1) | calm(X1)))) & (? [X1] : ((quiet(X1) | calm(X1)) & (~quiet(X1) | ~calm(X1))) | ! [X0] : wise(X0)) [nnf transformation 23]
56. (? [X0] : ~wise(X0) | ! [X1] : ((~calm(X1) | quiet(X1)) & (~quiet(X1) | calm(X1)))) & (? [X2] : ((quiet(X2) | calm(X2)) & (~quiet(X2) | ~calm(X2))) | ! [X3] : wise(X3)) [rectify 55]
57. ? [X0] : ~wise(X0) => ~wise(sK3) [choice axiom]
58. ? [X2] : ((quiet(X2) | calm(X2)) & (~quiet(X2) | ~calm(X2))) => ((quiet(sK4) | calm(sK4)) & (~quiet(sK4) | ~calm(sK4))) [choice axiom]
59. (~wise(sK3) | ! [X1] : ((~calm(X1) | quiet(X1)) & (~quiet(X1) | calm(X1)))) & (((quiet(sK4) | calm(sK4)) & (~quiet(sK4) | ~calm(sK4))) | ! [X3] : wise(X3)) [skolemisation 56,58,57]
63. ! [X0] : ((((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))))) [nnf transformation 15]
64. ! [X0] : ((((~rich(X0) | happy(X0)) & (rich(X0) | ~happy(X0))) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ((~happy(X0) | ~rich(X0)) & (rich(X0) | happy(X0))))) [flattening 63]
71. humble(X0) | generous(X0) | curious(X0) [cnf transformation 34]
73. tall(X0) | patient(X0) | ~wise(X0) | tall(X0) [cnf transformation 35]
78. ~wise(X0) | ~tall(X0) | patient(X0) | ~tall(X0) [cnf transformation 35]
82. ~curious(X0) | happy(X0) [cnf transformation 28]
84. ~patient(X0) | ~happy(X0) | ~creative(X0) [cnf transformation 36]
90. ~happy(X0) | wise(X0) [cnf transformation 39]
92. creative(fred) | wise(X1) [cnf transformation 44]
110. ~wise(sK3) | ~calm(X1) | quiet(X1) [cnf transformation 59]
117. ~happy(X0) | rich(X0) | calm(X0) [cnf transformation 64]
122. ~humble(fred) [cnf transformation 16]
126. ~rich(fred) [cnf transformation 20]
127. ~generous(fred) [cnf transformation 20]
129. ~quiet(fred) [cnf transformation 22]
132. tall(X0) | patient(X0) | ~wise(X0) [duplicate literal removal 73]
134. ~wise(X0) | ~tall(X0) | patient(X0) [duplicate literal removal 78]
137. ~wise(X0) | patient(X0) [subsumption resolution 132,134]
139. 1 <=> creative(fred) [avatar definition]
152. 4 <=> ! [X1] : wise(X1) [avatar definition]
153. wise(X1) <- (4) [avatar component clause 152]
155. 4 | 1 [avatar split clause 92,139,152]
157. 5 <=> patient(fred) [avatar definition]
159. patient(fred) <- (5) [avatar component clause 157]
212. 16 <=> ! [X1] : (~calm(X1) | quiet(X1)) [avatar definition]
213. ~calm(X1) | quiet(X1) <- (16) [avatar component clause 212]
215. 17 <=> wise(sK3) [avatar definition]
217. ~wise(sK3) <- (~17) [avatar component clause 215]
218. 16 | ~17 [avatar split clause 110,215,212]
263. $false <- (4, ~17) [resolution 217,153]
264. ~4 | 17 [avatar contradiction clause 263]
277. generous(fred) | curious(fred) [resolution 71,122]
278. curious(fred) [subsumption resolution 277,127]
292. happy(fred) [resolution 278,82]
410. rich(fred) | calm(fred) [resolution 292,117]
412. wise(fred) [resolution 292,90]
413. calm(fred) [subsumption resolution 410,126]
447. patient(fred) [resolution 412,137]
452. 5 [avatar split clause 447,157]
454. ~happy(fred) | ~creative(fred) <- (5) [resolution 159,84]
457. ~creative(fred) <- (5) [subsumption resolution 454,292]
460. ~1 | ~5 [avatar split clause 457,157,139]
484. quiet(fred) <- (16) [resolution 413,213]
486. $false <- (16) [subsumption resolution 484,129]
487. ~16 [avatar contradiction clause 486]
488. $false [avatar sat refutation 155,218,264,452,460,487]
% SZS output end Proof for 1198080193644619550881611
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and strong then someone is curious.
Everyone who is not tall or not creative is both quiet and not brave and vice versa.
If someone is both old and happy then john is not wise or generous and vice versa.
If lucy is either old or not kind then paul is either not generous or creative.
If someone is creative or not tall then fred is not generous.
Everyone who is either not curious or kind is either not creative or not happy.
If someone is brave or not strong then susan is wise or tall and vice versa.
Everyone who is kind is both not quiet and creative and vice versa.
If someone is both kind and not wise then mary is not brave or not strong and vice versa.
Everyone who is both not wise and not patient is either generous or funny.
If someone is either not curious or not brave then alice is either not creative or not wise and vice versa.
Everyone who is not old is either rich or calm.
Everyone who is either not creative or not old is both brave and not happy.
Everyone who is not funny or brave is either not calm or humble.
Everyone who is both creative and not humble is both not rich and not creative.
If mary is both creative and quiet then someone is generous or humble and vice versa.
Paul is both creative and not old.
Someone is not quiet or not funny.
Someone is not kind or not rich.
Paul is not old or not quiet.
Alice is either not tall or wise.
Someone is not curious.
Alice is both not rich and not calm.
Paul is not generous. | Lucy is not creative. | contradiction | ((?[X]:((~tall(X)&strong(X))))=>(?[X]:(curious(X))))&
(![X]:((~tall(X)|~creative(X))<=>(quiet(X)&~brave(X))))&
((?[X]:((old(X)&happy(X))))<=>((~wise(john)|generous(john))))&
(((old(lucy)<~>~kind(lucy)))=>((~generous(paul)<~>creative(paul))))&
((?[X]:((creative(X)|~tall(X))))=>(~generous(fred)))&
(![X]:((~curious(X)<~>kind(X))=>(~creative(X)<~>~happy(X))))&
((?[X]:((brave(X)|~strong(X))))<=>((wise(susan)|tall(susan))))&
(![X]:(kind(X)<=>(~quiet(X)&creative(X))))&
((?[X]:((kind(X)&~wise(X))))<=>((~brave(mary)|~strong(mary))))&
(![X]:((~wise(X)&~patient(X))=>(generous(X)<~>funny(X))))&
((?[X]:((~curious(X)<~>~brave(X))))<=>((~creative(alice)<~>~wise(alice))))&
(![X]:(~old(X)=>(rich(X)<~>calm(X))))&
(![X]:((~creative(X)<~>~old(X))=>(brave(X)&~happy(X))))&
(![X]:((~funny(X)|brave(X))=>(~calm(X)<~>humble(X))))&
(![X]:((creative(X)&~humble(X))=>(~rich(X)&~creative(X))))&
(((creative(mary)&quiet(mary)))<=>(?[X]:((generous(X)|humble(X)))))&
((creative(paul)&~old(paul)))&
(?[X]:((~quiet(X)|~funny(X))))&
(?[X]:((~kind(X)|~rich(X))))&
((~old(paul)|~quiet(paul)))&
((~tall(alice)<~>wise(alice)))&
(?[X]:(~curious(X)))&
((~rich(alice)&~calm(alice)))&
(~generous(paul)) | ~creative(lucy) | [
"p1",
"p3",
"p7",
"p12",
"p16",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3914344970206190088740556
% SZS output start Proof for 3914344970206190088740556
2. ! [X0] : ((~creative(X0) | ~tall(X0)) <=> (~brave(X0) & quiet(X0))) [input p1]
4. (old(lucy) <~> ~kind(lucy)) => (~generous(paul) <~> creative(paul)) [input p3]
8. ! [X0] : (kind(X0) <=> (creative(X0) & ~quiet(X0))) [input p7]
13. ! [X0] : ((~creative(X0) <~> ~old(X0)) => (~happy(X0) & brave(X0))) [input p12]
17. ~old(paul) & creative(paul) [input p16]
24. ~generous(paul) [input p23]
25. ~creative(lucy) [input hypothesis]
29. (~generous(paul) <~> creative(paul)) | (old(lucy) <=> ~kind(lucy)) [ennf transformation 4]
33. ! [X0] : ((~happy(X0) & brave(X0)) | (~creative(X0) <=> ~old(X0))) [ennf transformation 13]
40. ! [X0] : (((~creative(X0) | ~tall(X0)) | (brave(X0) | ~quiet(X0))) & ((~brave(X0) & quiet(X0)) | (creative(X0) & tall(X0)))) [nnf transformation 2]
41. ! [X0] : ((~creative(X0) | ~tall(X0) | brave(X0) | ~quiet(X0)) & ((~brave(X0) & quiet(X0)) | (creative(X0) & tall(X0)))) [flattening 40]
47. ((~creative(paul) | generous(paul)) & (creative(paul) | ~generous(paul))) | ((old(lucy) | kind(lucy)) & (~kind(lucy) | ~old(lucy))) [nnf transformation 29]
54. ! [X0] : ((kind(X0) | (~creative(X0) | quiet(X0))) & ((creative(X0) & ~quiet(X0)) | ~kind(X0))) [nnf transformation 8]
55. ! [X0] : ((kind(X0) | ~creative(X0) | quiet(X0)) & ((creative(X0) & ~quiet(X0)) | ~kind(X0))) [flattening 54]
66. ! [X0] : ((~happy(X0) & brave(X0)) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0)))) [nnf transformation 33]
84. ~brave(X0) | creative(X0) [cnf transformation 41]
94. ~creative(paul) | generous(paul) | old(lucy) | kind(lucy) [cnf transformation 47]
106. ~kind(X0) | creative(X0) [cnf transformation 55]
123. brave(X0) | ~old(X0) | creative(X0) [cnf transformation 66]
138. creative(paul) [cnf transformation 17]
148. ~generous(paul) [cnf transformation 24]
149. ~creative(lucy) [cnf transformation 25]
184. 8 <=> kind(lucy) [avatar definition]
186. kind(lucy) <- (8) [avatar component clause 184]
188. 9 <=> old(lucy) [avatar definition]
190. old(lucy) <- (9) [avatar component clause 188]
192. 10 <=> generous(paul) [avatar definition]
196. 11 <=> creative(paul) [avatar definition]
199. 8 | 9 | 10 | ~11 [avatar split clause 94,196,192,188,184]
296. ~old(X0) | creative(X0) [subsumption resolution 123,84]
324. 11 [avatar split clause 138,196]
349. ~10 [avatar split clause 148,192]
357. creative(lucy) <- (8) [resolution 106,186]
359. $false <- (8) [subsumption resolution 357,149]
360. ~8 [avatar contradiction clause 359]
381. creative(lucy) <- (9) [resolution 296,190]
382. $false <- (9) [subsumption resolution 381,149]
383. ~9 [avatar contradiction clause 382]
384. $false [avatar sat refutation 199,324,349,360,383]
% SZS output end Proof for 3914344970206190088740556
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or kind is not old. If someone is happy then someone is both not strong and not brave. If someone is creative or not calm then lucy is rich or calm and vice versa. If someone is strong then alice is either generous or not calm. If someone is not tall then someone is either not brave or quiet. If fred is either tall or humble then lucy is either not funny or kind. Everyone who is either old or not generous is patient. Everyone who is tall or rich is both not tall and rich and vice versa. Everyone who is not curious or rich is either funny or happy. If someone is funny or kind then someone is either not wise or humble and vice versa. Everyone who is happy is not old and vice versa. Everyone who is not happy is both generous and calm. Everyone who is old or rich is kind. Everyone who is funny is not creative or not kind. Everyone who is not humble or old is rich or not curious. If lucy is curious then fred is either strong or creative. Alice is either not curious or old. Someone is not generous. Someone is not tall. Fred is both not strong and not creative. John is either not old or curious. Fred is generous. | Lucy is not strong. | neutral | (![X]:((generous(X)|kind(X))=>~old(X)))&
((?[X]:(happy(X)))=>(?[X]:((~strong(X)&~brave(X)))))&
((?[X]:((creative(X)|~calm(X))))<=>((rich(lucy)|calm(lucy))))&
((?[X]:(strong(X)))=>((generous(alice)<~>~calm(alice))))&
((?[X]:(~tall(X)))=>(?[X]:((~brave(X)<~>quiet(X)))))&
(((tall(fred)<~>humble(fred)))=>((~funny(lucy)<~>kind(lucy))))&
(![X]:((old(X)<~>~generous(X))=>patient(X)))&
(![X]:((tall(X)|rich(X))<=>(~tall(X)&rich(X))))&
(![X]:((~curious(X)|rich(X))=>(funny(X)<~>happy(X))))&
((?[X]:((funny(X)|kind(X))))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:(happy(X)<=>~old(X)))&
(![X]:(~happy(X)=>(generous(X)&calm(X))))&
(![X]:((old(X)|rich(X))=>kind(X)))&
(![X]:(funny(X)=>(~creative(X)|~kind(X))))&
(![X]:((~humble(X)|old(X))=>(rich(X)|~curious(X))))&
((curious(lucy))=>((strong(fred)<~>creative(fred))))&
((~curious(alice)<~>old(alice)))&
(?[X]:(~generous(X)))&
(?[X]:(~tall(X)))&
((~strong(fred)&~creative(fred)))&
((~old(john)<~>curious(john)))&
(generous(fred)) | ~strong(lucy) | [] | null | 0 |
Everyone who is not kind is not patient or not strong and vice versa.
Everyone who is not old is either not curious or old.
If someone is both not rich and not generous then alice is not strong.
Everyone who is happy or not curious is either brave or not humble and vice versa.
If lucy is quiet or not wise then someone is not brave or kind.
Everyone who is not creative or quiet is both not creative and quiet and vice versa.
Everyone who is brave or not wise is both not rich and creative and vice versa.
Everyone who is curious is either curious or humble and vice versa.
If alice is either not creative or curious then mary is quiet.
If someone is either not humble or not kind then lucy is both generous and not quiet and vice versa.
Everyone who is both calm and strong is both quiet and wise.
If lucy is both rich and not generous then paul is either creative or not tall and vice versa.
If someone is rich then paul is both not old and strong.
If someone is not creative or wise then fred is humble.
Everyone who is not kind or funny is either patient or tall and vice versa.
If alice is not patient then someone is brave.
Paul is either creative or not brave.
Lucy is both not funny and patient.
Paul is both generous and not kind.
Lucy is not happy or creative.
Mary is both not humble and creative.
Lucy is strong.
Susan is happy or generous. | Mary is patient. | neutral | (![X]:(~kind(X)<=>(~patient(X)|~strong(X))))&
(![X]:(~old(X)=>(~curious(X)<~>old(X))))&
((?[X]:((~rich(X)&~generous(X))))=>(~strong(alice)))&
(![X]:((happy(X)|~curious(X))<=>(brave(X)<~>~humble(X))))&
(((quiet(lucy)|~wise(lucy)))=>(?[X]:((~brave(X)|kind(X)))))&
(![X]:((~creative(X)|quiet(X))<=>(~creative(X)&quiet(X))))&
(![X]:((brave(X)|~wise(X))<=>(~rich(X)&creative(X))))&
(![X]:(curious(X)<=>(curious(X)<~>humble(X))))&
(((~creative(alice)<~>curious(alice)))=>(quiet(mary)))&
((?[X]:((~humble(X)<~>~kind(X))))<=>((generous(lucy)&~quiet(lucy))))&
(![X]:((calm(X)&strong(X))=>(quiet(X)&wise(X))))&
(((rich(lucy)&~generous(lucy)))<=>((creative(paul)<~>~tall(paul))))&
((?[X]:(rich(X)))=>((~old(paul)&strong(paul))))&
((?[X]:((~creative(X)|wise(X))))=>(humble(fred)))&
(![X]:((~kind(X)|funny(X))<=>(patient(X)<~>tall(X))))&
((~patient(alice))=>(?[X]:(brave(X))))&
((creative(paul)<~>~brave(paul)))&
((~funny(lucy)&patient(lucy)))&
((generous(paul)&~kind(paul)))&
((~happy(lucy)|creative(lucy)))&
((~humble(mary)&creative(mary)))&
(strong(lucy))&
((happy(susan)|generous(susan))) | patient(mary) | [] | null | 0 |
If mary is both generous and calm then susan is both wise and not calm.
Everyone who is calm or not generous is wise or creative and vice versa.
Everyone who is rich is not brave and vice versa.
Everyone who is funny or brave is tall or not generous.
If lucy is either generous or rich then fred is either not wise or not rich and vice versa.
Everyone who is rich is not kind.
Everyone who is not funny is both kind and calm and vice versa.
If someone is not creative then lucy is not humble or not kind.
If someone is both patient and curious then lucy is calm or humble.
If alice is both not old and not wise then paul is either curious or humble.
If alice is not quiet then someone is not calm.
Everyone who is either brave or not kind is calm or tall.
Everyone who is not quiet or quiet is not happy or not calm and vice versa.
Everyone who is creative or calm is wise or not kind and vice versa.
Everyone who is old is both generous and calm.
If someone is both funny and not old then someone is both rich and not rich and vice versa.
Susan is not creative or old.
Someone is both not humble and not funny.
Someone is either not rich or not creative.
Susan is both not old and not creative.
Someone is either not patient or not brave.
Someone is not wise or not rich.
Someone is either quiet or not humble.
Someone is both old and not quiet. | Susan is not rich. | entailment | (((generous(mary)&calm(mary)))=>((wise(susan)&~calm(susan))))&
(![X]:((calm(X)|~generous(X))<=>(wise(X)|creative(X))))&
(![X]:(rich(X)<=>~brave(X)))&
(![X]:((funny(X)|brave(X))=>(tall(X)|~generous(X))))&
(((generous(lucy)<~>rich(lucy)))<=>((~wise(fred)<~>~rich(fred))))&
(![X]:(rich(X)=>~kind(X)))&
(![X]:(~funny(X)<=>(kind(X)&calm(X))))&
((?[X]:(~creative(X)))=>((~humble(lucy)|~kind(lucy))))&
((?[X]:((patient(X)&curious(X))))=>((calm(lucy)|humble(lucy))))&
(((~old(alice)&~wise(alice)))=>((curious(paul)<~>humble(paul))))&
((~quiet(alice))=>(?[X]:(~calm(X))))&
(![X]:((brave(X)<~>~kind(X))=>(calm(X)|tall(X))))&
(![X]:((~quiet(X)|quiet(X))<=>(~happy(X)|~calm(X))))&
(![X]:((creative(X)|calm(X))<=>(wise(X)|~kind(X))))&
(![X]:(old(X)=>(generous(X)&calm(X))))&
((?[X]:((funny(X)&~old(X))))<=>(?[X]:((rich(X)&~rich(X)))))&
((~creative(susan)|old(susan)))&
(?[X]:((~humble(X)&~funny(X))))&
(?[X]:((~rich(X)<~>~creative(X))))&
((~old(susan)&~creative(susan)))&
(?[X]:((~patient(X)<~>~brave(X))))&
(?[X]:((~wise(X)|~rich(X))))&
(?[X]:((quiet(X)<~>~humble(X))))&
(?[X]:((old(X)&~quiet(X)))) | ~rich(susan) | [
"p5",
"p6",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2272689417154741715661162
% SZS output start Proof for 2272689417154741715661162
6. ! [X0] : (rich(X0) => ~kind(X0)) [input p5]
7. ! [X0] : (~funny(X0) <=> (calm(X0) & kind(X0))) [input p6]
16. ? [X0] : (~old(X0) & funny(X0)) <=> ? [X0] : (~rich(X0) & rich(X0)) [input p15]
20. ~creative(susan) & ~old(susan) [input p19]
25. rich(susan) [input hypothesis]
26. ? [X0] : (~old(X0) & funny(X0)) <=> ? [X1] : (~rich(X1) & rich(X1)) [rectify 16]
31. ! [X0] : (~kind(X0) | ~rich(X0)) [ennf transformation 6]
44. ! [X0] : ((~funny(X0) | (~calm(X0) | ~kind(X0))) & ((calm(X0) & kind(X0)) | funny(X0))) [nnf transformation 7]
45. ! [X0] : ((~funny(X0) | ~calm(X0) | ~kind(X0)) & ((calm(X0) & kind(X0)) | funny(X0))) [flattening 44]
53. (? [X0] : (~old(X0) & funny(X0)) | ! [X1] : (rich(X1) | ~rich(X1))) & (? [X1] : (~rich(X1) & rich(X1)) | ! [X0] : (old(X0) | ~funny(X0))) [nnf transformation 26]
54. (? [X0] : (~old(X0) & funny(X0)) | ! [X1] : (rich(X1) | ~rich(X1))) & (? [X2] : (~rich(X2) & rich(X2)) | ! [X3] : (old(X3) | ~funny(X3))) [rectify 53]
55. ? [X0] : (~old(X0) & funny(X0)) => (~old(sK1) & funny(sK1)) [choice axiom]
56. ? [X2] : (~rich(X2) & rich(X2)) => (~rich(sK2) & rich(sK2)) [choice axiom]
57. ((~old(sK1) & funny(sK1)) | ! [X1] : (rich(X1) | ~rich(X1))) & ((~rich(sK2) & rich(sK2)) | ! [X3] : (old(X3) | ~funny(X3))) [skolemisation 54,56,55]
89. ~kind(X0) | ~rich(X0) [cnf transformation 31]
90. kind(X0) | funny(X0) [cnf transformation 45]
108. rich(sK2) | old(X3) | ~funny(X3) [cnf transformation 57]
109. ~rich(sK2) | old(X3) | ~funny(X3) [cnf transformation 57]
117. ~old(susan) [cnf transformation 20]
126. rich(susan) [cnf transformation 25]
218. 20 <=> ! [X3] : (old(X3) | ~funny(X3)) [avatar definition]
219. ~funny(X3) | old(X3) <- (20) [avatar component clause 218]
221. 21 <=> rich(sK2) [avatar definition]
224. 20 | ~21 [avatar split clause 109,221,218]
225. 20 | 21 [avatar split clause 108,221,218]
231. 23 <=> old(susan) [avatar definition]
232. ~old(susan) <- (~23) [avatar component clause 231]
246. ~23 [avatar split clause 117,231]
279. ~rich(X0) | funny(X0) [resolution 90,89]
351. funny(susan) [resolution 279,126]
358. old(susan) <- (20) [resolution 351,219]
359. $false <- (20, ~23) [subsumption resolution 358,232]
360. ~20 | 23 [avatar contradiction clause 359]
361. $false [avatar sat refutation 224,225,246,360]
% SZS output end Proof for 2272689417154741715661162
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is either kind or happy. If someone is both wise and creative then someone is patient or not calm. Everyone who is either wise or not rich is old or not funny and vice versa. If someone is not strong or not kind then mary is not wise and vice versa. Everyone who is funny or not strong is both not generous and brave and vice versa. Everyone who is both not kind and not happy is either not quiet or patient and vice versa. Everyone who is either old or not creative is both not calm and tall and vice versa. Everyone who is tall is not kind or happy and vice versa. Everyone who is not patient or patient is both not humble and not funny and vice versa. Everyone who is not old is both not funny and not calm and vice versa. Everyone who is either not kind or happy is either not brave or not generous. Everyone who is either not humble or not rich is either not tall or funny and vice versa. Everyone who is not old or patient is not creative. If someone is both not generous and funny then fred is both funny and not generous and vice versa. If someone is rich then someone is not quiet and vice versa. Everyone who is not old is both wise and strong and vice versa. Someone is either not happy or creative. Susan is not rich. Susan is not patient. John is either not strong or not calm. Someone is either not kind or not happy. Someone is brave or creative. | John is not brave. | contradiction | (![X]:(calm(X)=>(kind(X)<~>happy(X))))&
((?[X]:((wise(X)&creative(X))))=>(?[X]:((patient(X)|~calm(X)))))&
(![X]:((wise(X)<~>~rich(X))<=>(old(X)|~funny(X))))&
((?[X]:((~strong(X)|~kind(X))))<=>(~wise(mary)))&
(![X]:((funny(X)|~strong(X))<=>(~generous(X)&brave(X))))&
(![X]:((~kind(X)&~happy(X))<=>(~quiet(X)<~>patient(X))))&
(![X]:((old(X)<~>~creative(X))<=>(~calm(X)&tall(X))))&
(![X]:(tall(X)<=>(~kind(X)|happy(X))))&
(![X]:((~patient(X)|patient(X))<=>(~humble(X)&~funny(X))))&
(![X]:(~old(X)<=>(~funny(X)&~calm(X))))&
(![X]:((~kind(X)<~>happy(X))=>(~brave(X)<~>~generous(X))))&
(![X]:((~humble(X)<~>~rich(X))<=>(~tall(X)<~>funny(X))))&
(![X]:((~old(X)|patient(X))=>~creative(X)))&
((?[X]:((~generous(X)&funny(X))))<=>((funny(fred)&~generous(fred))))&
((?[X]:(rich(X)))<=>(?[X]:(~quiet(X))))&
(![X]:(~old(X)<=>(wise(X)&strong(X))))&
(?[X]:((~happy(X)<~>creative(X))))&
(~rich(susan))&
(~patient(susan))&
((~strong(john)<~>~calm(john)))&
(?[X]:((~kind(X)<~>~happy(X))))&
(?[X]:((brave(X)|creative(X)))) | ~brave(john) | [
"p2",
"p4",
"p6",
"p8",
"p9",
"p11",
"p12",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8432146453577808048620472
% SZS output start Proof for 8432146453577808048620472
3. ! [X0] : ((wise(X0) <~> ~rich(X0)) <=> (~funny(X0) | old(X0))) [input p2]
5. ! [X0] : ((~strong(X0) | funny(X0)) <=> (brave(X0) & ~generous(X0))) [input p4]
7. ! [X0] : ((old(X0) <~> ~creative(X0)) <=> (tall(X0) & ~calm(X0))) [input p6]
9. ! [X0] : ((patient(X0) | ~patient(X0)) <=> (~funny(X0) & ~humble(X0))) [input p8]
10. ! [X0] : (~old(X0) <=> (~calm(X0) & ~funny(X0))) [input p9]
12. ! [X0] : ((~humble(X0) <~> ~rich(X0)) <=> (~tall(X0) <~> funny(X0))) [input p11]
13. ! [X0] : ((patient(X0) | ~old(X0)) => ~creative(X0)) [input p12]
16. ! [X0] : (~old(X0) <=> (strong(X0) & wise(X0))) [input p15]
20. ~strong(john) <~> ~calm(john) [input p19]
23. ~brave(john) [input hypothesis]
29. ! [X0] : (~creative(X0) | (~patient(X0) & old(X0))) [ennf transformation 13]
34. ! [X0] : ((((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | (funny(X0) & ~old(X0))) & ((~funny(X0) | old(X0)) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0))))) [nnf transformation 3]
35. ! [X0] : ((((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | (funny(X0) & ~old(X0))) & (~funny(X0) | old(X0) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0))))) [flattening 34]
40. ! [X0] : (((~strong(X0) | funny(X0)) | (~brave(X0) | generous(X0))) & ((brave(X0) & ~generous(X0)) | (strong(X0) & ~funny(X0)))) [nnf transformation 5]
41. ! [X0] : ((~strong(X0) | funny(X0) | ~brave(X0) | generous(X0)) & ((brave(X0) & ~generous(X0)) | (strong(X0) & ~funny(X0)))) [flattening 40]
44. ! [X0] : ((((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | (~tall(X0) | calm(X0))) & ((tall(X0) & ~calm(X0)) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0))))) [nnf transformation 7]
45. ! [X0] : ((((creative(X0) | ~old(X0)) & (~creative(X0) | old(X0))) | ~tall(X0) | calm(X0)) & ((tall(X0) & ~calm(X0)) | ((old(X0) | creative(X0)) & (~creative(X0) | ~old(X0))))) [flattening 44]
48. ! [X0] : (((patient(X0) | ~patient(X0)) | (funny(X0) | humble(X0))) & ((~funny(X0) & ~humble(X0)) | (~patient(X0) & patient(X0)))) [nnf transformation 9]
49. ! [X0] : ((patient(X0) | ~patient(X0) | funny(X0) | humble(X0)) & ((~funny(X0) & ~humble(X0)) | (~patient(X0) & patient(X0)))) [flattening 48]
50. ! [X0] : ((~old(X0) | (calm(X0) | funny(X0))) & ((~calm(X0) & ~funny(X0)) | old(X0))) [nnf transformation 10]
51. ! [X0] : ((~old(X0) | calm(X0) | funny(X0)) & ((~calm(X0) & ~funny(X0)) | old(X0))) [flattening 50]
53. ! [X0] : ((((rich(X0) | humble(X0)) & (~rich(X0) | ~humble(X0))) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0)))) & (((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | ((~humble(X0) | rich(X0)) & (~rich(X0) | humble(X0))))) [nnf transformation 12]
64. ! [X0] : ((~old(X0) | (~strong(X0) | ~wise(X0))) & ((strong(X0) & wise(X0)) | old(X0))) [nnf transformation 16]
65. ! [X0] : ((~old(X0) | ~strong(X0) | ~wise(X0)) & ((strong(X0) & wise(X0)) | old(X0))) [flattening 64]
69. (calm(john) | strong(john)) & (~calm(john) | ~strong(john)) [nnf transformation 20]
83. ~wise(X0) | rich(X0) | funny(X0) [cnf transformation 35]
90. brave(X0) | strong(X0) [cnf transformation 41]
101. tall(X0) | old(X0) | creative(X0) [cnf transformation 45]
107. ~humble(X0) | patient(X0) [cnf transformation 49]
108. ~humble(X0) | ~patient(X0) [cnf transformation 49]
109. ~funny(X0) | patient(X0) [cnf transformation 49]
110. ~funny(X0) | ~patient(X0) [cnf transformation 49]
114. ~old(X0) | calm(X0) | funny(X0) [cnf transformation 51]
119. funny(X0) | ~tall(X0) | ~rich(X0) | humble(X0) [cnf transformation 53]
127. ~creative(X0) | old(X0) [cnf transformation 29]
135. old(X0) | wise(X0) [cnf transformation 65]
137. ~strong(X0) | ~old(X0) | ~wise(X0) [cnf transformation 65]
142. ~calm(john) | ~strong(john) [cnf transformation 69]
147. ~brave(john) [cnf transformation 23]
181. ~funny(X0) [subsumption resolution 109,110]
182. ~humble(X0) [subsumption resolution 107,108]
183. ~old(X0) | calm(X0) [subsumption resolution 114,181]
186. ~tall(X0) | ~rich(X0) | humble(X0) [subsumption resolution 119,181]
187. ~tall(X0) | ~rich(X0) [subsumption resolution 186,182]
215. 15 <=> strong(john) [avatar definition]
216. ~strong(john) <- (~15) [avatar component clause 215]
217. strong(john) <- (15) [avatar component clause 215]
219. 16 <=> calm(john) [avatar definition]
220. ~calm(john) <- (~16) [avatar component clause 219]
223. ~15 | ~16 [avatar split clause 142,219,215]
245. strong(john) [resolution 90,147]
246. wise(X0) | calm(X0) [resolution 183,135]
322. old(X0) | creative(X0) | ~rich(X0) [resolution 101,187]
323. ~rich(X0) | old(X0) [subsumption resolution 322,127]
329. ~old(john) | ~wise(john) <- (15) [resolution 137,217]
333. 27 <=> wise(john) [avatar definition]
334. wise(john) <- (27) [avatar component clause 333]
335. ~wise(john) <- (~27) [avatar component clause 333]
337. 28 <=> old(john) [avatar definition]
340. ~27 | ~28 | ~15 [avatar split clause 329,215,337,333]
341. calm(john) <- (~27) [resolution 335,246]
342. $false <- (~16, ~27) [subsumption resolution 341,220]
343. 16 | 27 [avatar contradiction clause 342]
344. rich(john) | funny(john) <- (27) [resolution 334,83]
345. rich(john) <- (27) [subsumption resolution 344,181]
439. old(john) <- (27) [resolution 323,345]
442. 28 | ~27 [avatar split clause 439,333,337]
445. $false <- (~15) [subsumption resolution 245,216]
446. 15 [avatar contradiction clause 445]
456. $false [avatar sat refutation 223,340,343,442,446]
% SZS output end Proof for 8432146453577808048620472
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either patient or funny then lucy is both quiet and brave. Everyone who is either kind or calm is either wise or creative. Everyone who is either not strong or not patient is both not funny and strong. Everyone who is not brave or old is either kind or not old and vice versa. If mary is humble then someone is either quiet or not quiet. Everyone who is not funny or kind is not creative and vice versa. If mary is either not calm or strong then someone is both strong and wise and vice versa. Everyone who is humble or not humble is not curious or not happy. If alice is both not curious and not happy then paul is both curious and wise. Everyone who is not brave is both wise and funny. Everyone who is humble is either tall or not wise and vice versa. If fred is not funny or strong then someone is both not strong and generous and vice versa. Everyone who is not old is either strong or not old. If someone is either not wise or not kind then mary is either old or creative. Everyone who is either humble or curious is either strong or kind. Everyone who is both not rich and not tall is not rich. Someone is not happy. Someone is generous or brave. Alice is either not tall or quiet. Lucy is both patient and calm. Someone is either not strong or brave. Someone is not quiet. Someone is rich. Someone is not patient or strong. | Lucy is not kind. | contradiction | ((?[X]:((patient(X)<~>funny(X))))=>((quiet(lucy)&brave(lucy))))&
(![X]:((kind(X)<~>calm(X))=>(wise(X)<~>creative(X))))&
(![X]:((~strong(X)<~>~patient(X))=>(~funny(X)&strong(X))))&
(![X]:((~brave(X)|old(X))<=>(kind(X)<~>~old(X))))&
((humble(mary))=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:((~funny(X)|kind(X))<=>~creative(X)))&
(((~calm(mary)<~>strong(mary)))<=>(?[X]:((strong(X)&wise(X)))))&
(![X]:((humble(X)|~humble(X))=>(~curious(X)|~happy(X))))&
(((~curious(alice)&~happy(alice)))=>((curious(paul)&wise(paul))))&
(![X]:(~brave(X)=>(wise(X)&funny(X))))&
(![X]:(humble(X)<=>(tall(X)<~>~wise(X))))&
(((~funny(fred)|strong(fred)))<=>(?[X]:((~strong(X)&generous(X)))))&
(![X]:(~old(X)=>(strong(X)<~>~old(X))))&
((?[X]:((~wise(X)<~>~kind(X))))=>((old(mary)<~>creative(mary))))&
(![X]:((humble(X)<~>curious(X))=>(strong(X)<~>kind(X))))&
(![X]:((~rich(X)&~tall(X))=>~rich(X)))&
(?[X]:(~happy(X)))&
(?[X]:((generous(X)|brave(X))))&
((~tall(alice)<~>quiet(alice)))&
((patient(lucy)&calm(lucy)))&
(?[X]:((~strong(X)<~>brave(X))))&
(?[X]:(~quiet(X)))&
(?[X]:(rich(X)))&
(?[X]:((~patient(X)|strong(X)))) | ~kind(lucy) | [
"p2",
"p3",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5086322976811202053581651
% SZS output start Proof for 5086322976811202053581651
3. ! [X0] : ((~strong(X0) <~> ~patient(X0)) => (strong(X0) & ~funny(X0))) [input p2]
4. ! [X0] : ((old(X0) | ~brave(X0)) <=> (kind(X0) <~> ~old(X0))) [input p3]
13. ! [X0] : (~old(X0) => (strong(X0) <~> ~old(X0))) [input p12]
20. calm(lucy) & patient(lucy) [input p19]
25. ~kind(lucy) [input hypothesis]
28. ! [X0] : ((strong(X0) & ~funny(X0)) | (~strong(X0) <=> ~patient(X0))) [ennf transformation 3]
35. ! [X0] : ((strong(X0) <~> ~old(X0)) | old(X0)) [ennf transformation 13]
42. ! [X0] : ((strong(X0) & ~funny(X0)) | ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0)))) [nnf transformation 28]
43. ! [X0] : (((old(X0) | ~brave(X0)) | ((kind(X0) | old(X0)) & (~old(X0) | ~kind(X0)))) & (((old(X0) | ~kind(X0)) & (~old(X0) | kind(X0))) | (~old(X0) & brave(X0)))) [nnf transformation 4]
44. ! [X0] : ((old(X0) | ~brave(X0) | ((kind(X0) | old(X0)) & (~old(X0) | ~kind(X0)))) & (((old(X0) | ~kind(X0)) & (~old(X0) | kind(X0))) | (~old(X0) & brave(X0)))) [flattening 43]
60. ! [X0] : (((old(X0) | ~strong(X0)) & (~old(X0) | strong(X0))) | old(X0)) [nnf transformation 35]
87. strong(X0) | ~patient(X0) | strong(X0) [cnf transformation 42]
90. ~old(X0) | kind(X0) | ~old(X0) [cnf transformation 44]
122. old(X0) | ~strong(X0) | old(X0) [cnf transformation 60]
136. patient(lucy) [cnf transformation 20]
143. ~kind(lucy) [cnf transformation 25]
144. ~strong(X0) | old(X0) [duplicate literal removal 122]
145. ~old(X0) | kind(X0) [duplicate literal removal 90]
147. ~patient(X0) | strong(X0) [duplicate literal removal 87]
283. strong(lucy) [resolution 147,136]
285. old(lucy) [resolution 283,144]
301. kind(lucy) [resolution 285,145]
302. $false [subsumption resolution 301,143]
% SZS output end Proof for 5086322976811202053581651
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or patient then mary is either wise or happy and vice versa. If someone is quiet or not quiet then someone is not brave or not funny. Everyone who is old or not strong is both generous and not happy. Everyone who is either rich or quiet is quiet or not old. Everyone who is happy or not tall is either not brave or not kind and vice versa. If paul is either not rich or generous then alice is not strong or kind and vice versa. If someone is both not strong and not rich then alice is both quiet and curious and vice versa. If someone is old or not old then someone is wise. Everyone who is either not patient or kind is not wise or not patient and vice versa. Everyone who is not patient is not creative. Everyone who is generous is not quiet. If susan is either funny or wise then someone is either not curious or not old. If mary is not humble then john is strong. Everyone who is either not creative or not happy is both tall and not brave and vice versa. If susan is not strong or not creative then lucy is patient or curious and vice versa. Everyone who is both generous and not rich is rich and vice versa. Someone is not quiet. Someone is either not funny or quiet. Someone is not tall or not happy. Someone is either happy or curious. Someone is strong. Someone is either not wise or calm. Fred is either old or not rich. | Paul is generous. | contradiction | ((?[X]:((~wise(X)<~>patient(X))))<=>((wise(mary)<~>happy(mary))))&
((?[X]:((quiet(X)|~quiet(X))))=>(?[X]:((~brave(X)|~funny(X)))))&
(![X]:((old(X)|~strong(X))=>(generous(X)&~happy(X))))&
(![X]:((rich(X)<~>quiet(X))=>(quiet(X)|~old(X))))&
(![X]:((happy(X)|~tall(X))<=>(~brave(X)<~>~kind(X))))&
(((~rich(paul)<~>generous(paul)))<=>((~strong(alice)|kind(alice))))&
((?[X]:((~strong(X)&~rich(X))))<=>((quiet(alice)&curious(alice))))&
((?[X]:((old(X)|~old(X))))=>(?[X]:(wise(X))))&
(![X]:((~patient(X)<~>kind(X))<=>(~wise(X)|~patient(X))))&
(![X]:(~patient(X)=>~creative(X)))&
(![X]:(generous(X)=>~quiet(X)))&
(((funny(susan)<~>wise(susan)))=>(?[X]:((~curious(X)<~>~old(X)))))&
((~humble(mary))=>(strong(john)))&
(![X]:((~creative(X)<~>~happy(X))<=>(tall(X)&~brave(X))))&
(((~strong(susan)|~creative(susan)))<=>((patient(lucy)|curious(lucy))))&
(![X]:((generous(X)&~rich(X))<=>rich(X)))&
(?[X]:(~quiet(X)))&
(?[X]:((~funny(X)<~>quiet(X))))&
(?[X]:((~tall(X)|~happy(X))))&
(?[X]:((happy(X)<~>curious(X))))&
(?[X]:(strong(X)))&
(?[X]:((~wise(X)<~>calm(X))))&
((old(fred)<~>~rich(fred))) | generous(paul) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6179772528246855750410989
% SZS output start Proof for 6179772528246855750410989
16. ! [X0] : ((~rich(X0) & generous(X0)) <=> rich(X0)) [input p15]
24. generous(paul) [input hypothesis]
65. ! [X0] : (((~rich(X0) & generous(X0)) | ~rich(X0)) & (rich(X0) | (rich(X0) | ~generous(X0)))) [nnf transformation 16]
66. ! [X0] : (((~rich(X0) & generous(X0)) | ~rich(X0)) & (rich(X0) | rich(X0) | ~generous(X0))) [flattening 65]
139. rich(X0) | rich(X0) | ~generous(X0) [cnf transformation 66]
141. ~rich(X0) | ~rich(X0) [cnf transformation 66]
153. generous(paul) [cnf transformation 24]
154. rich(X0) | ~generous(X0) [duplicate literal removal 139]
155. ~rich(X0) [duplicate literal removal 141]
303. ~generous(X0) [subsumption resolution 154,155]
344. $false [subsumption resolution 153,303]
% SZS output end Proof for 6179772528246855750410989
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not old is both not funny and wise.
If someone is brave then susan is quiet.
Everyone who is either curious or strong is not quiet and vice versa.
If someone is either old or not strong then alice is either humble or calm and vice versa.
If lucy is tall or not tall then someone is not strong or happy.
Everyone who is either wise or patient is either humble or calm and vice versa.
Everyone who is generous is either not strong or not tall.
Everyone who is either kind or not old is not patient or wise and vice versa.
If john is either not curious or not tall then someone is both funny and not strong.
Everyone who is funny or calm is not brave and vice versa.
If someone is either happy or not happy then susan is brave and vice versa.
Everyone who is both patient and happy is both rich and curious and vice versa.
Everyone who is not happy is not happy or humble.
Everyone who is old or tall is either not kind or not patient and vice versa.
Everyone who is both not brave and quiet is both not quiet and curious and vice versa.
Everyone who is not old is both kind and not wise.
Alice is both kind and tall.
Someone is both not calm and rich.
Someone is generous.
Someone is both not calm and patient.
John is tall or not happy.
Mary is generous.
Lucy is either humble or rich. | John is curious. | neutral | (![X]:((brave(X)|~old(X))=>(~funny(X)&wise(X))))&
((?[X]:(brave(X)))=>(quiet(susan)))&
(![X]:((curious(X)<~>strong(X))<=>~quiet(X)))&
((?[X]:((old(X)<~>~strong(X))))<=>((humble(alice)<~>calm(alice))))&
(((tall(lucy)|~tall(lucy)))=>(?[X]:((~strong(X)|happy(X)))))&
(![X]:((wise(X)<~>patient(X))<=>(humble(X)<~>calm(X))))&
(![X]:(generous(X)=>(~strong(X)<~>~tall(X))))&
(![X]:((kind(X)<~>~old(X))<=>(~patient(X)|wise(X))))&
(((~curious(john)<~>~tall(john)))=>(?[X]:((funny(X)&~strong(X)))))&
(![X]:((funny(X)|calm(X))<=>~brave(X)))&
((?[X]:((happy(X)<~>~happy(X))))<=>(brave(susan)))&
(![X]:((patient(X)&happy(X))<=>(rich(X)&curious(X))))&
(![X]:(~happy(X)=>(~happy(X)|humble(X))))&
(![X]:((old(X)|tall(X))<=>(~kind(X)<~>~patient(X))))&
(![X]:((~brave(X)&quiet(X))<=>(~quiet(X)&curious(X))))&
(![X]:(~old(X)=>(kind(X)&~wise(X))))&
((kind(alice)&tall(alice)))&
(?[X]:((~calm(X)&rich(X))))&
(?[X]:(generous(X)))&
(?[X]:((~calm(X)&patient(X))))&
((tall(john)|~happy(john)))&
(generous(mary))&
((humble(lucy)<~>rich(lucy))) | curious(john) | [] | null | 0 |
If alice is not quiet or not wise then someone is happy.
Everyone who is not strong is tall or not funny and vice versa.
Everyone who is wise or brave is either funny or not happy and vice versa.
If susan is both not kind and calm then someone is not curious and vice versa.
Everyone who is tall is quiet and vice versa.
If someone is either tall or not wise then someone is both not generous and brave and vice versa.
If susan is not strong then someone is quiet.
If someone is both creative and not patient then someone is either not humble or not patient.
If someone is not patient or not tall then someone is either not old or not creative and vice versa.
Everyone who is either humble or wise is not wise or not quiet and vice versa.
Everyone who is not tall is both not generous and not curious and vice versa.
Everyone who is either wise or not generous is both brave and not humble.
Everyone who is quiet is old or not calm and vice versa.
If someone is either rich or humble then someone is either humble or old.
If someone is either funny or tall then john is not tall or not kind.
Everyone who is not creative is either calm or not generous and vice versa.
Someone is kind.
Alice is creative.
Lucy is brave or not generous.
Susan is not wise or humble.
Someone is happy or wise. | Alice is not strong. | neutral | (((~quiet(alice)|~wise(alice)))=>(?[X]:(happy(X))))&
(![X]:(~strong(X)<=>(tall(X)|~funny(X))))&
(![X]:((wise(X)|brave(X))<=>(funny(X)<~>~happy(X))))&
(((~kind(susan)&calm(susan)))<=>(?[X]:(~curious(X))))&
(![X]:(tall(X)<=>quiet(X)))&
((?[X]:((tall(X)<~>~wise(X))))<=>(?[X]:((~generous(X)&brave(X)))))&
((~strong(susan))=>(?[X]:(quiet(X))))&
((?[X]:((creative(X)&~patient(X))))=>(?[X]:((~humble(X)<~>~patient(X)))))&
((?[X]:((~patient(X)|~tall(X))))<=>(?[X]:((~old(X)<~>~creative(X)))))&
(![X]:((humble(X)<~>wise(X))<=>(~wise(X)|~quiet(X))))&
(![X]:(~tall(X)<=>(~generous(X)&~curious(X))))&
(![X]:((wise(X)<~>~generous(X))=>(brave(X)&~humble(X))))&
(![X]:(quiet(X)<=>(old(X)|~calm(X))))&
((?[X]:((rich(X)<~>humble(X))))=>(?[X]:((humble(X)<~>old(X)))))&
((?[X]:((funny(X)<~>tall(X))))=>((~tall(john)|~kind(john))))&
(![X]:(~creative(X)<=>(calm(X)<~>~generous(X))))&
(?[X]:(kind(X)))&
(creative(alice))&
((brave(lucy)|~generous(lucy)))&
((~wise(susan)|humble(susan)))&
(?[X]:((happy(X)|wise(X)))) | ~strong(alice) | [] | null | 0 |
Everyone who is quiet or funny is either kind or funny and vice versa.
Everyone who is either happy or not patient is calm.
Everyone who is either generous or old is not curious and vice versa.
If alice is either not kind or not brave then paul is not happy or rich and vice versa.
Everyone who is kind is either not quiet or not curious.
Everyone who is not wise or not brave is calm or not old and vice versa.
Everyone who is strong or not old is both patient and funny and vice versa.
If john is either humble or generous then alice is wise and vice versa.
Everyone who is humble or not generous is both patient and not generous.
Everyone who is curious is wise and vice versa.
If mary is both not brave and not creative then someone is either patient or not tall.
Everyone who is both not funny and not humble is either generous or not quiet and vice versa.
Everyone who is not rich or not kind is either not brave or not quiet.
Everyone who is rich or not strong is not calm or old.
Everyone who is either happy or kind is not calm and vice versa.
Everyone who is either brave or not creative is either not happy or not funny and vice versa.
Fred is not kind or curious.
Mary is either creative or not curious.
John is either not old or not curious.
Someone is either not calm or rich.
Someone is generous.
Mary is either kind or not kind.
Someone is either not creative or not calm. | Mary is not creative. | entailment | (![X]:((quiet(X)|funny(X))<=>(kind(X)<~>funny(X))))&
(![X]:((happy(X)<~>~patient(X))=>calm(X)))&
(![X]:((generous(X)<~>old(X))<=>~curious(X)))&
(((~kind(alice)<~>~brave(alice)))<=>((~happy(paul)|rich(paul))))&
(![X]:(kind(X)=>(~quiet(X)<~>~curious(X))))&
(![X]:((~wise(X)|~brave(X))<=>(calm(X)|~old(X))))&
(![X]:((strong(X)|~old(X))<=>(patient(X)&funny(X))))&
(((humble(john)<~>generous(john)))<=>(wise(alice)))&
(![X]:((humble(X)|~generous(X))=>(patient(X)&~generous(X))))&
(![X]:(curious(X)<=>wise(X)))&
(((~brave(mary)&~creative(mary)))=>(?[X]:((patient(X)<~>~tall(X)))))&
(![X]:((~funny(X)&~humble(X))<=>(generous(X)<~>~quiet(X))))&
(![X]:((~rich(X)|~kind(X))=>(~brave(X)<~>~quiet(X))))&
(![X]:((rich(X)|~strong(X))=>(~calm(X)|old(X))))&
(![X]:((happy(X)<~>kind(X))<=>~calm(X)))&
(![X]:((brave(X)<~>~creative(X))<=>(~happy(X)<~>~funny(X))))&
((~kind(fred)|curious(fred)))&
((creative(mary)<~>~curious(mary)))&
((~old(john)<~>~curious(john)))&
(?[X]:((~calm(X)<~>rich(X))))&
(?[X]:(generous(X)))&
((kind(mary)<~>~kind(mary)))&
(?[X]:((~creative(X)<~>~calm(X)))) | ~creative(mary) | [
"p0",
"p1",
"p2",
"p4",
"p5",
"p6",
"p8",
"p9",
"p11",
"p12",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6854167946323415645972148
% SZS output start Proof for 6854167946323415645972148
1. ! [X0] : ((funny(X0) | quiet(X0)) <=> (kind(X0) <~> funny(X0))) [input p0]
2. ! [X0] : ((happy(X0) <~> ~patient(X0)) => calm(X0)) [input p1]
3. ! [X0] : ((generous(X0) <~> old(X0)) <=> ~curious(X0)) [input p2]
5. ! [X0] : (kind(X0) => (~quiet(X0) <~> ~curious(X0))) [input p4]
6. ! [X0] : ((~brave(X0) | ~wise(X0)) <=> (~old(X0) | calm(X0))) [input p5]
7. ! [X0] : ((~old(X0) | strong(X0)) <=> (funny(X0) & patient(X0))) [input p6]
9. ! [X0] : ((~generous(X0) | humble(X0)) => (~generous(X0) & patient(X0))) [input p8]
10. ! [X0] : (curious(X0) <=> wise(X0)) [input p9]
12. ! [X0] : ((~humble(X0) & ~funny(X0)) <=> (generous(X0) <~> ~quiet(X0))) [input p11]
13. ! [X0] : ((~kind(X0) | ~rich(X0)) => (~brave(X0) <~> ~quiet(X0))) [input p12]
15. ! [X0] : ((happy(X0) <~> kind(X0)) <=> ~calm(X0)) [input p14]
16. ! [X0] : ((brave(X0) <~> ~creative(X0)) <=> (~happy(X0) <~> ~funny(X0))) [input p15]
18. creative(mary) <~> ~curious(mary) [input p17]
24. creative(mary) [input hypothesis]
25. ! [X0] : (calm(X0) | (happy(X0) <=> ~patient(X0))) [ennf transformation 2]
26. ! [X0] : ((~quiet(X0) <~> ~curious(X0)) | ~kind(X0)) [ennf transformation 5]
27. ! [X0] : ((~generous(X0) & patient(X0)) | (generous(X0) & ~humble(X0))) [ennf transformation 9]
30. ! [X0] : ((~brave(X0) <~> ~quiet(X0)) | (kind(X0) & rich(X0))) [ennf transformation 13]
33. ! [X0] : (((funny(X0) | quiet(X0)) | ((kind(X0) | ~funny(X0)) & (funny(X0) | ~kind(X0)))) & (((~funny(X0) | ~kind(X0)) & (funny(X0) | kind(X0))) | (~funny(X0) & ~quiet(X0)))) [nnf transformation 1]
34. ! [X0] : ((funny(X0) | quiet(X0) | ((kind(X0) | ~funny(X0)) & (funny(X0) | ~kind(X0)))) & (((~funny(X0) | ~kind(X0)) & (funny(X0) | kind(X0))) | (~funny(X0) & ~quiet(X0)))) [flattening 33]
35. ! [X0] : (calm(X0) | ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0)))) [nnf transformation 25]
36. ! [X0] : ((((~old(X0) | ~generous(X0)) & (old(X0) | generous(X0))) | curious(X0)) & (~curious(X0) | ((generous(X0) | ~old(X0)) & (old(X0) | ~generous(X0))))) [nnf transformation 3]
39. ! [X0] : (((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | ~kind(X0)) [nnf transformation 26]
40. ! [X0] : (((~brave(X0) | ~wise(X0)) | (old(X0) & ~calm(X0))) & ((~old(X0) | calm(X0)) | (brave(X0) & wise(X0)))) [nnf transformation 6]
41. ! [X0] : ((~brave(X0) | ~wise(X0) | (old(X0) & ~calm(X0))) & (~old(X0) | calm(X0) | (brave(X0) & wise(X0)))) [flattening 40]
42. ! [X0] : (((~old(X0) | strong(X0)) | (~funny(X0) | ~patient(X0))) & ((funny(X0) & patient(X0)) | (old(X0) & ~strong(X0)))) [nnf transformation 7]
43. ! [X0] : ((~old(X0) | strong(X0) | ~funny(X0) | ~patient(X0)) & ((funny(X0) & patient(X0)) | (old(X0) & ~strong(X0)))) [flattening 42]
45. ! [X0] : ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0))) [nnf transformation 10]
49. ! [X0] : (((~humble(X0) & ~funny(X0)) | ((generous(X0) | quiet(X0)) & (~quiet(X0) | ~generous(X0)))) & (((quiet(X0) | ~generous(X0)) & (~quiet(X0) | generous(X0))) | (humble(X0) | funny(X0)))) [nnf transformation 12]
50. ! [X0] : (((~humble(X0) & ~funny(X0)) | ((generous(X0) | quiet(X0)) & (~quiet(X0) | ~generous(X0)))) & (((quiet(X0) | ~generous(X0)) & (~quiet(X0) | generous(X0))) | humble(X0) | funny(X0))) [flattening 49]
51. ! [X0] : (((quiet(X0) | brave(X0)) & (~quiet(X0) | ~brave(X0))) | (kind(X0) & rich(X0))) [nnf transformation 30]
52. ! [X0] : ((((~kind(X0) | ~happy(X0)) & (kind(X0) | happy(X0))) | calm(X0)) & (~calm(X0) | ((happy(X0) | ~kind(X0)) & (kind(X0) | ~happy(X0))))) [nnf transformation 15]
53. ! [X0] : ((((creative(X0) | ~brave(X0)) & (~creative(X0) | brave(X0))) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0)))) & (((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | ((brave(X0) | creative(X0)) & (~creative(X0) | ~brave(X0))))) [nnf transformation 16]
54. (curious(mary) | ~creative(mary)) & (~curious(mary) | creative(mary)) [nnf transformation 18]
65. ~quiet(X0) | kind(X0) | funny(X0) [cnf transformation 34]
68. ~funny(X0) | ~kind(X0) | ~funny(X0) [cnf transformation 34]
71. ~patient(X0) | calm(X0) | ~happy(X0) [cnf transformation 35]
74. ~curious(X0) | generous(X0) | ~old(X0) [cnf transformation 36]
83. ~curious(X0) | ~quiet(X0) | ~kind(X0) [cnf transformation 39]
87. ~wise(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 41]
92. old(X0) | funny(X0) [cnf transformation 43]
99. generous(X0) | patient(X0) [cnf transformation 27]
100. ~humble(X0) | ~generous(X0) [cnf transformation 27]
102. ~curious(X0) | wise(X0) [cnf transformation 45]
107. quiet(X0) | ~generous(X0) | humble(X0) | funny(X0) [cnf transformation 50]
108. ~generous(X0) | ~quiet(X0) | ~funny(X0) [cnf transformation 50]
111. ~humble(X0) | generous(X0) | quiet(X0) [cnf transformation 50]
115. brave(X0) | quiet(X0) | kind(X0) [cnf transformation 51]
118. ~calm(X0) | kind(X0) | ~happy(X0) [cnf transformation 52]
120. calm(X0) | happy(X0) | kind(X0) [cnf transformation 52]
122. ~creative(X0) | ~happy(X0) | ~funny(X0) | ~brave(X0) [cnf transformation 53]
126. ~creative(X0) | brave(X0) | ~funny(X0) | happy(X0) [cnf transformation 53]
132. curious(mary) | ~creative(mary) [cnf transformation 54]
142. creative(mary) [cnf transformation 24]
143. ~kind(X0) | ~funny(X0) [duplicate literal removal 68]
184. 8 <=> brave(mary) [avatar definition]
185. ~brave(mary) <- (~8) [avatar component clause 184]
188. 9 <=> creative(mary) [avatar definition]
190. creative(mary) <- (9) [avatar component clause 188]
201. ~humble(X0) | quiet(X0) [subsumption resolution 111,100]
202. ~generous(X0) | quiet(X0) | funny(X0) [subsumption resolution 107,201]
213. 14 <=> curious(mary) [avatar definition]
215. curious(mary) <- (14) [avatar component clause 213]
216. ~9 | 14 [avatar split clause 132,213,188]
248. 9 [avatar split clause 142,188]
250. wise(mary) <- (14) [resolution 102,215]
285. 27 <=> generous(mary) [avatar definition]
286. generous(mary) <- (27) [avatar component clause 285]
287. ~generous(mary) <- (~27) [avatar component clause 285]
289. 28 <=> old(mary) [avatar definition]
290. ~old(mary) <- (~28) [avatar component clause 289]
293. generous(mary) | ~old(mary) <- (14) [resolution 74,215]
296. patient(mary) <- (~27) [resolution 287,99]
309. calm(mary) | ~happy(mary) <- (~27) [resolution 296,71]
311. 29 <=> happy(mary) [avatar definition]
312. happy(mary) <- (29) [avatar component clause 311]
315. 30 <=> calm(mary) [avatar definition]
316. ~calm(mary) <- (~30) [avatar component clause 315]
317. calm(mary) <- (30) [avatar component clause 315]
318. ~29 | 30 | 27 [avatar split clause 309,285,315,311]
319. ~quiet(mary) | ~kind(mary) <- (14) [resolution 83,215]
322. 31 <=> kind(mary) [avatar definition]
323. kind(mary) <- (31) [avatar component clause 322]
324. ~kind(mary) <- (~31) [avatar component clause 322]
326. 32 <=> quiet(mary) [avatar definition]
327. quiet(mary) <- (32) [avatar component clause 326]
328. ~quiet(mary) <- (~32) [avatar component clause 326]
329. ~31 | ~32 | ~14 [avatar split clause 319,213,326,322]
370. ~brave(mary) | ~calm(mary) <- (14) [resolution 87,250]
371. ~30 | ~8 | ~14 [avatar split clause 370,213,184,315]
387. ~28 | 27 | ~14 [avatar split clause 293,213,285,289]
388. ~quiet(mary) | ~funny(mary) <- (27) [resolution 286,108]
390. 40 <=> funny(mary) [avatar definition]
391. funny(mary) <- (40) [avatar component clause 390]
393. ~40 | ~32 | ~27 [avatar split clause 388,285,326,390]
506. happy(mary) | kind(mary) <- (~30) [resolution 120,316]
517. ~funny(mary) <- (31) [resolution 323,143]
518. ~40 | ~31 [avatar split clause 517,322,390]
527. 31 | 29 | 30 [avatar split clause 506,315,311,322]
543. quiet(mary) | funny(mary) <- (27) [resolution 202,286]
546. funny(mary) <- (27, ~32) [subsumption resolution 543,328]
550. 40 | ~27 | 32 [avatar split clause 546,326,285,390]
573. ~happy(mary) | ~funny(mary) | ~brave(mary) <- (9) [resolution 122,190]
578. ~happy(mary) | ~brave(mary) <- (9, 40) [subsumption resolution 573,391]
579. ~8 | ~29 | ~9 | ~40 [avatar split clause 578,390,188,311,184]
580. quiet(mary) | kind(mary) <- (~8) [resolution 185,115]
584. quiet(mary) <- (~8, ~31) [subsumption resolution 580,324]
585. 32 | 8 | 31 [avatar split clause 584,322,184,326]
591. funny(mary) <- (~28) [resolution 290,92]
608. kind(mary) | funny(mary) <- (32) [resolution 327,65]
609. brave(mary) | ~funny(mary) | happy(mary) <- (9) [resolution 126,190]
612. ~funny(mary) | happy(mary) <- (~8, 9) [subsumption resolution 609,185]
615. 29 | ~40 | 8 | ~9 [avatar split clause 612,188,184,390,311]
616. funny(mary) <- (~31, 32) [subsumption resolution 608,324]
617. 40 | 31 | ~32 [avatar split clause 616,326,322,390]
624. 40 | 28 [avatar split clause 591,289,390]
1144. kind(mary) | ~happy(mary) <- (30) [resolution 317,118]
1146. ~happy(mary) <- (30, ~31) [subsumption resolution 1144,324]
1147. $false <- (29, 30, ~31) [subsumption resolution 1146,312]
1148. ~29 | ~30 | 31 [avatar contradiction clause 1147]
1151. $false [avatar sat refutation 216,248,318,329,371,387,393,518,527,550,579,585,615,617,624,1148]
% SZS output end Proof for 6854167946323415645972148
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not generous and not strong then mary is not curious or rich.
Everyone who is not patient or kind is happy and vice versa.
Everyone who is both not strong and strong is both funny and not happy and vice versa.
If someone is both not brave and not rich then someone is both not kind and not happy and vice versa.
Everyone who is not calm or not creative is curious or funny.
Everyone who is funny is both not strong and quiet.
If fred is strong or old then someone is rich.
Everyone who is not funny or rich is not patient and vice versa.
If someone is creative or patient then fred is both kind and not strong.
Everyone who is both tall and not old is either quiet or not generous.
If someone is rich or not rich then someone is not quiet.
Everyone who is either creative or brave is either not kind or not rich and vice versa.
If someone is brave then susan is either not kind or tall and vice versa.
Everyone who is either kind or funny is not rich and vice versa.
Everyone who is strong or curious is not old.
If someone is either wise or not wise then fred is generous or not kind and vice versa.
Someone is both not curious and calm.
Someone is rich.
Fred is either humble or kind.
Someone is not tall or calm.
Fred is both tall and rich.
Lucy is not curious or not kind.
Someone is both humble and not quiet. | Mary is wise. | neutral | (((~generous(fred)&~strong(fred)))=>((~curious(mary)|rich(mary))))&
(![X]:((~patient(X)|kind(X))<=>happy(X)))&
(![X]:((~strong(X)&strong(X))<=>(funny(X)&~happy(X))))&
((?[X]:((~brave(X)&~rich(X))))<=>(?[X]:((~kind(X)&~happy(X)))))&
(![X]:((~calm(X)|~creative(X))=>(curious(X)|funny(X))))&
(![X]:(funny(X)=>(~strong(X)&quiet(X))))&
(((strong(fred)|old(fred)))=>(?[X]:(rich(X))))&
(![X]:((~funny(X)|rich(X))<=>~patient(X)))&
((?[X]:((creative(X)|patient(X))))=>((kind(fred)&~strong(fred))))&
(![X]:((tall(X)&~old(X))=>(quiet(X)<~>~generous(X))))&
((?[X]:((rich(X)|~rich(X))))=>(?[X]:(~quiet(X))))&
(![X]:((creative(X)<~>brave(X))<=>(~kind(X)<~>~rich(X))))&
((?[X]:(brave(X)))<=>((~kind(susan)<~>tall(susan))))&
(![X]:((kind(X)<~>funny(X))<=>~rich(X)))&
(![X]:((strong(X)|curious(X))=>~old(X)))&
((?[X]:((wise(X)<~>~wise(X))))<=>((generous(fred)|~kind(fred))))&
(?[X]:((~curious(X)&calm(X))))&
(?[X]:(rich(X)))&
((humble(fred)<~>kind(fred)))&
(?[X]:((~tall(X)|calm(X))))&
((tall(fred)&rich(fred)))&
((~curious(lucy)|~kind(lucy)))&
(?[X]:((humble(X)&~quiet(X)))) | wise(mary) | [] | null | 0 |
If someone is not humble or not happy then alice is both not generous and not rich. If fred is both happy and strong then susan is not curious. If paul is either tall or not old then mary is not tall. If someone is either not funny or funny then someone is either not kind or old. Everyone who is either happy or brave is either not patient or not kind and vice versa. If someone is either wise or tall then someone is both happy and tall and vice versa. Everyone who is both not rich and wise is either creative or not creative and vice versa. Everyone who is either rich or not curious is not brave and vice versa. Everyone who is kind or brave is both not quiet and patient. Everyone who is both not tall and not curious is strong. Everyone who is not happy or brave is not tall or not humble and vice versa. Everyone who is not curious or not funny is both not brave and not humble and vice versa. Everyone who is both not patient and not funny is not old or not curious and vice versa. Everyone who is patient is both tall and quiet and vice versa. If susan is both not calm and not generous then susan is old or brave. If someone is either patient or quiet then someone is not rich or brave. Someone is either not creative or not kind. Someone is strong. Mary is either not generous or not old. Someone is both not quiet and not funny. Someone is happy or wise. | Mary is not wise. | contradiction | ((?[X]:((~humble(X)|~happy(X))))=>((~generous(alice)&~rich(alice))))&
(((happy(fred)&strong(fred)))=>(~curious(susan)))&
(((tall(paul)<~>~old(paul)))=>(~tall(mary)))&
((?[X]:((~funny(X)<~>funny(X))))=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((happy(X)<~>brave(X))<=>(~patient(X)<~>~kind(X))))&
((?[X]:((wise(X)<~>tall(X))))<=>(?[X]:((happy(X)&tall(X)))))&
(![X]:((~rich(X)&wise(X))<=>(creative(X)<~>~creative(X))))&
(![X]:((rich(X)<~>~curious(X))<=>~brave(X)))&
(![X]:((kind(X)|brave(X))=>(~quiet(X)&patient(X))))&
(![X]:((~tall(X)&~curious(X))=>strong(X)))&
(![X]:((~happy(X)|brave(X))<=>(~tall(X)|~humble(X))))&
(![X]:((~curious(X)|~funny(X))<=>(~brave(X)&~humble(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~old(X)|~curious(X))))&
(![X]:(patient(X)<=>(tall(X)&quiet(X))))&
(((~calm(susan)&~generous(susan)))=>((old(susan)|brave(susan))))&
((?[X]:((patient(X)<~>quiet(X))))=>(?[X]:((~rich(X)|brave(X)))))&
(?[X]:((~creative(X)<~>~kind(X))))&
(?[X]:(strong(X)))&
((~generous(mary)<~>~old(mary)))&
(?[X]:((~quiet(X)&~funny(X))))&
(?[X]:((happy(X)|wise(X)))) | ~wise(mary) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 1333918516631467698882188
% SZS output start Proof for 1333918516631467698882188
7. ! [X0] : ((wise(X0) & ~rich(X0)) <=> (creative(X0) <~> ~creative(X0))) [input p6]
22. ~wise(mary) [input hypothesis]
47. ! [X0] : (((wise(X0) & ~rich(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | (~wise(X0) | rich(X0)))) [nnf transformation 7]
48. ! [X0] : (((wise(X0) & ~rich(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | ~wise(X0) | rich(X0))) [flattening 47]
101. wise(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 48]
102. wise(X0) | creative(X0) | creative(X0) [cnf transformation 48]
139. ~wise(mary) [cnf transformation 22]
142. wise(X0) | ~creative(X0) [duplicate literal removal 101]
143. wise(X0) | creative(X0) [duplicate literal removal 102]
242. wise(X0) [subsumption resolution 142,143]
266. $false [subsumption resolution 139,242]
% SZS output end Proof for 1333918516631467698882188
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is both not brave and creative.
Everyone who is not rich is old.
Everyone who is both quiet and not calm is either not rich or humble and vice versa.
If lucy is humble then lucy is either creative or quiet and vice versa.
If john is both not patient and tall then susan is not curious or not funny.
If lucy is both not kind and not tall then someone is either generous or not creative.
If someone is either not wise or not humble then susan is generous.
If someone is creative then fred is both not brave and not humble.
Everyone who is patient or not tall is happy or generous.
Everyone who is both not brave and patient is not patient or not rich.
Everyone who is funny is not kind or not generous and vice versa.
If susan is either not patient or not humble then alice is not tall.
Everyone who is both not happy and happy is both tall and not patient.
If someone is both happy and not generous then alice is both rich and kind and vice versa.
Everyone who is either tall or not brave is quiet or not wise and vice versa.
If lucy is either curious or not wise then someone is both kind and not rich and vice versa.
Alice is both not tall and not wise.
John is not generous.
Someone is kind or not calm.
Lucy is either funny or not strong.
Someone is both old and not rich.
Fred is either wise or not generous.
Someone is not generous or funny.
Someone is calm. | Fred is not generous. | neutral | (![X]:(~quiet(X)=>(~brave(X)&creative(X))))&
(![X]:(~rich(X)=>old(X)))&
(![X]:((quiet(X)&~calm(X))<=>(~rich(X)<~>humble(X))))&
((humble(lucy))<=>((creative(lucy)<~>quiet(lucy))))&
(((~patient(john)&tall(john)))=>((~curious(susan)|~funny(susan))))&
(((~kind(lucy)&~tall(lucy)))=>(?[X]:((generous(X)<~>~creative(X)))))&
((?[X]:((~wise(X)<~>~humble(X))))=>(generous(susan)))&
((?[X]:(creative(X)))=>((~brave(fred)&~humble(fred))))&
(![X]:((patient(X)|~tall(X))=>(happy(X)|generous(X))))&
(![X]:((~brave(X)&patient(X))=>(~patient(X)|~rich(X))))&
(![X]:(funny(X)<=>(~kind(X)|~generous(X))))&
(((~patient(susan)<~>~humble(susan)))=>(~tall(alice)))&
(![X]:((~happy(X)&happy(X))=>(tall(X)&~patient(X))))&
((?[X]:((happy(X)&~generous(X))))<=>((rich(alice)&kind(alice))))&
(![X]:((tall(X)<~>~brave(X))<=>(quiet(X)|~wise(X))))&
(((curious(lucy)<~>~wise(lucy)))<=>(?[X]:((kind(X)&~rich(X)))))&
((~tall(alice)&~wise(alice)))&
(~generous(john))&
(?[X]:((kind(X)|~calm(X))))&
((funny(lucy)<~>~strong(lucy)))&
(?[X]:((old(X)&~rich(X))))&
((wise(fred)<~>~generous(fred)))&
(?[X]:((~generous(X)|funny(X))))&
(?[X]:(calm(X))) | ~generous(fred) | [] | null | 0 |
Everyone who is not curious or not funny is not calm or happy.
Everyone who is not quiet or not humble is not brave or old and vice versa.
If someone is both humble and old then john is tall and vice versa.
Everyone who is not humble is not happy.
Everyone who is either not wise or not brave is both tall and not tall and vice versa.
Everyone who is funny is not humble or not old and vice versa.
If someone is humble or not old then john is either brave or calm.
Everyone who is both quiet and calm is either funny or not old.
Everyone who is either brave or not tall is both not tall and brave and vice versa.
Everyone who is both patient and creative is brave or not brave.
Everyone who is tall or strong is calm or patient and vice versa.
Everyone who is not creative is generous or humble and vice versa.
Everyone who is not curious or happy is either quiet or kind and vice versa.
If fred is either generous or not tall then john is either wise or funny.
Everyone who is either humble or creative is not quiet.
Everyone who is quiet is not creative or not generous.
Alice is both creative and not patient.
Someone is old.
Paul is either wise or calm.
Alice is not quiet.
Someone is both tall and humble.
Lucy is both strong and not calm.
Someone is patient or not humble. | John is humble. | neutral | (![X]:((~curious(X)|~funny(X))=>(~calm(X)|happy(X))))&
(![X]:((~quiet(X)|~humble(X))<=>(~brave(X)|old(X))))&
((?[X]:((humble(X)&old(X))))<=>(tall(john)))&
(![X]:(~humble(X)=>~happy(X)))&
(![X]:((~wise(X)<~>~brave(X))<=>(tall(X)&~tall(X))))&
(![X]:(funny(X)<=>(~humble(X)|~old(X))))&
((?[X]:((humble(X)|~old(X))))=>((brave(john)<~>calm(john))))&
(![X]:((quiet(X)&calm(X))=>(funny(X)<~>~old(X))))&
(![X]:((brave(X)<~>~tall(X))<=>(~tall(X)&brave(X))))&
(![X]:((patient(X)&creative(X))=>(brave(X)|~brave(X))))&
(![X]:((tall(X)|strong(X))<=>(calm(X)|patient(X))))&
(![X]:(~creative(X)<=>(generous(X)|humble(X))))&
(![X]:((~curious(X)|happy(X))<=>(quiet(X)<~>kind(X))))&
(((generous(fred)<~>~tall(fred)))=>((wise(john)<~>funny(john))))&
(![X]:((humble(X)<~>creative(X))=>~quiet(X)))&
(![X]:(quiet(X)=>(~creative(X)|~generous(X))))&
((creative(alice)&~patient(alice)))&
(?[X]:(old(X)))&
((wise(paul)<~>calm(paul)))&
(~quiet(alice))&
(?[X]:((tall(X)&humble(X))))&
((strong(lucy)&~calm(lucy)))&
(?[X]:((patient(X)|~humble(X)))) | humble(john) | [] | null | 0 |
If someone is either not humble or happy then fred is not wise or not tall and vice versa.
If fred is not brave or generous then fred is both not creative and not patient.
Everyone who is not funny or not humble is not calm.
If paul is creative or not funny then fred is creative and vice versa.
Everyone who is either not wise or rich is humble or tall.
Everyone who is either not brave or not wise is either kind or old and vice versa.
If someone is not creative then someone is either not calm or not rich.
If someone is not tall then someone is wise and vice versa.
Everyone who is either not quiet or strong is curious and vice versa.
Everyone who is either kind or not kind is both generous and curious and vice versa.
Everyone who is not strong is not creative and vice versa.
If someone is curious or calm then john is not rich.
Everyone who is either not generous or rich is not happy or brave.
Everyone who is either not curious or not kind is quiet and vice versa.
Someone is either rich or kind.
Lucy is either not wise or curious.
Susan is happy or not generous.
Mary is both not wise and not patient.
Lucy is humble or not brave.
Someone is both humble and not brave.
Someone is quiet or not calm.
Someone is both not happy and old. | Susan is old. | neutral | ((?[X]:((~humble(X)<~>happy(X))))<=>((~wise(fred)|~tall(fred))))&
(((~brave(fred)|generous(fred)))=>((~creative(fred)&~patient(fred))))&
(![X]:((~funny(X)|~humble(X))=>~calm(X)))&
(((creative(paul)|~funny(paul)))<=>(creative(fred)))&
(![X]:((~wise(X)<~>rich(X))=>(humble(X)|tall(X))))&
(![X]:((~brave(X)<~>~wise(X))<=>(kind(X)<~>old(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~calm(X)<~>~rich(X)))))&
((?[X]:(~tall(X)))<=>(?[X]:(wise(X))))&
(![X]:((~quiet(X)<~>strong(X))<=>curious(X)))&
(![X]:((kind(X)<~>~kind(X))<=>(generous(X)&curious(X))))&
(![X]:(~strong(X)<=>~creative(X)))&
((?[X]:((curious(X)|calm(X))))=>(~rich(john)))&
(![X]:((~generous(X)<~>rich(X))=>(~happy(X)|brave(X))))&
(![X]:((~curious(X)<~>~kind(X))<=>quiet(X)))&
(?[X]:((rich(X)<~>kind(X))))&
((~wise(lucy)<~>curious(lucy)))&
((happy(susan)|~generous(susan)))&
((~wise(mary)&~patient(mary)))&
((humble(lucy)|~brave(lucy)))&
(?[X]:((humble(X)&~brave(X))))&
(?[X]:((quiet(X)|~calm(X))))&
(?[X]:((~happy(X)&old(X)))) | old(susan) | [] | null | 0 |
Everyone who is both not happy and strong is quiet. If someone is either not funny or not quiet then susan is both old and not strong and vice versa. If john is not patient or funny then someone is generous or patient. Everyone who is both brave and not curious is not patient or not brave and vice versa. If paul is either humble or not happy then someone is both happy and kind. Everyone who is curious or not kind is not kind and vice versa. If someone is both old and humble then paul is either generous or not kind and vice versa. If susan is not generous or old then someone is not brave or not curious. Everyone who is calm is both not creative and funny and vice versa. Everyone who is kind is not humble and vice versa. If someone is wise or not wise then someone is rich. Everyone who is rich or old is both patient and not old. Everyone who is not quiet is curious and vice versa. If someone is both funny and not calm then someone is both not rich and not creative and vice versa. Susan is both not humble and not happy. Someone is both tall and not rich. Paul is generous or brave. Someone is either wise or kind. Someone is not tall. | Susan is rich. | contradiction | (![X]:((~happy(X)&strong(X))=>quiet(X)))&
((?[X]:((~funny(X)<~>~quiet(X))))<=>((old(susan)&~strong(susan))))&
(((~patient(john)|funny(john)))=>(?[X]:((generous(X)|patient(X)))))&
(![X]:((brave(X)&~curious(X))<=>(~patient(X)|~brave(X))))&
(((humble(paul)<~>~happy(paul)))=>(?[X]:((happy(X)&kind(X)))))&
(![X]:((curious(X)|~kind(X))<=>~kind(X)))&
((?[X]:((old(X)&humble(X))))<=>((generous(paul)<~>~kind(paul))))&
(((~generous(susan)|old(susan)))=>(?[X]:((~brave(X)|~curious(X)))))&
(![X]:(calm(X)<=>(~creative(X)&funny(X))))&
(![X]:(kind(X)<=>~humble(X)))&
((?[X]:((wise(X)|~wise(X))))=>(?[X]:(rich(X))))&
(![X]:((rich(X)|old(X))=>(patient(X)&~old(X))))&
(![X]:(~quiet(X)<=>curious(X)))&
((?[X]:((funny(X)&~calm(X))))<=>(?[X]:((~rich(X)&~creative(X)))))&
((~humble(susan)&~happy(susan)))&
(?[X]:((tall(X)&~rich(X))))&
((generous(paul)|brave(paul)))&
(?[X]:((wise(X)<~>kind(X))))&
(?[X]:(~tall(X))) | rich(susan) | [
"p3",
"p5",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7576208261131399711854277
% SZS output start Proof for 7576208261131399711854277
4. ! [X0] : ((~curious(X0) & brave(X0)) <=> (~brave(X0) | ~patient(X0))) [input p3]
6. ! [X0] : ((~kind(X0) | curious(X0)) <=> ~kind(X0)) [input p5]
10. ! [X0] : (kind(X0) <=> ~humble(X0)) [input p9]
12. ! [X0] : ((old(X0) | rich(X0)) => (~old(X0) & patient(X0))) [input p11]
15. ~happy(susan) & ~humble(susan) [input p14]
20. rich(susan) [input hypothesis]
29. ! [X0] : ((~old(X0) & patient(X0)) | (~old(X0) & ~rich(X0))) [ennf transformation 12]
37. ! [X0] : (((~curious(X0) & brave(X0)) | (brave(X0) & patient(X0))) & ((~brave(X0) | ~patient(X0)) | (curious(X0) | ~brave(X0)))) [nnf transformation 4]
38. ! [X0] : (((~curious(X0) & brave(X0)) | (brave(X0) & patient(X0))) & (~brave(X0) | ~patient(X0) | curious(X0) | ~brave(X0))) [flattening 37]
42. ! [X0] : (((~kind(X0) | curious(X0)) | kind(X0)) & (~kind(X0) | (kind(X0) & ~curious(X0)))) [nnf transformation 6]
43. ! [X0] : ((~kind(X0) | curious(X0) | kind(X0)) & (~kind(X0) | (kind(X0) & ~curious(X0)))) [flattening 42]
52. ! [X0] : ((kind(X0) | humble(X0)) & (~humble(X0) | ~kind(X0))) [nnf transformation 10]
78. ~brave(X0) | ~patient(X0) | curious(X0) | ~brave(X0) [cnf transformation 38]
80. brave(X0) | brave(X0) [cnf transformation 38]
87. ~kind(X0) | ~curious(X0) [cnf transformation 43]
102. kind(X0) | humble(X0) [cnf transformation 52]
105. ~rich(X0) | patient(X0) [cnf transformation 29]
115. ~humble(susan) [cnf transformation 15]
123. rich(susan) [cnf transformation 20]
125. ~brave(X0) | ~patient(X0) | curious(X0) [duplicate literal removal 78]
126. brave(X0) [duplicate literal removal 80]
173. ~patient(X0) | curious(X0) [subsumption resolution 125,126]
285. ~curious(X1) | humble(X1) [resolution 102,87]
286. patient(susan) [resolution 105,123]
295. curious(susan) [resolution 173,286]
322. humble(susan) [resolution 285,295]
323. $false [subsumption resolution 322,115]
% SZS output end Proof for 7576208261131399711854277
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not quiet then someone is funny or not curious.
If alice is not wise then lucy is both not strong and patient.
If someone is either not calm or not humble then fred is either not strong or humble and vice versa.
Everyone who is not rich is not old.
Everyone who is either rich or wise is either creative or curious.
Everyone who is not happy or curious is not happy.
If someone is not rich or happy then lucy is rich or not curious and vice versa.
Everyone who is not wise or not old is not creative and vice versa.
If someone is patient then someone is both calm and curious and vice versa.
If paul is strong then someone is both not humble and not curious and vice versa.
If someone is either patient or strong then someone is not strong and vice versa.
If fred is both old and not humble then alice is generous.
If lucy is both rich and not patient then someone is happy or kind and vice versa.
If someone is not humble or patient then lucy is not kind or humble and vice versa.
If susan is both not kind and wise then someone is both quiet and kind.
Everyone who is happy or not curious is strong or not curious.
Lucy is not rich.
Someone is curious.
Someone is generous.
Fred is old.
Someone is either not rich or patient.
Someone is not calm or not old.
Someone is both strong and not rich. | Lucy is not creative. | entailment | ((?[X]:(~quiet(X)))=>(?[X]:((funny(X)|~curious(X)))))&
((~wise(alice))=>((~strong(lucy)&patient(lucy))))&
((?[X]:((~calm(X)<~>~humble(X))))<=>((~strong(fred)<~>humble(fred))))&
(![X]:(~rich(X)=>~old(X)))&
(![X]:((rich(X)<~>wise(X))=>(creative(X)<~>curious(X))))&
(![X]:((~happy(X)|curious(X))=>~happy(X)))&
((?[X]:((~rich(X)|happy(X))))<=>((rich(lucy)|~curious(lucy))))&
(![X]:((~wise(X)|~old(X))<=>~creative(X)))&
((?[X]:(patient(X)))<=>(?[X]:((calm(X)&curious(X)))))&
((strong(paul))<=>(?[X]:((~humble(X)&~curious(X)))))&
((?[X]:((patient(X)<~>strong(X))))<=>(?[X]:(~strong(X))))&
(((old(fred)&~humble(fred)))=>(generous(alice)))&
(((rich(lucy)&~patient(lucy)))<=>(?[X]:((happy(X)|kind(X)))))&
((?[X]:((~humble(X)|patient(X))))<=>((~kind(lucy)|humble(lucy))))&
(((~kind(susan)&wise(susan)))=>(?[X]:((quiet(X)&kind(X)))))&
(![X]:((happy(X)|~curious(X))=>(strong(X)|~curious(X))))&
(~rich(lucy))&
(?[X]:(curious(X)))&
(?[X]:(generous(X)))&
(old(fred))&
(?[X]:((~rich(X)<~>patient(X))))&
(?[X]:((~calm(X)|~old(X))))&
(?[X]:((strong(X)&~rich(X)))) | ~creative(lucy) | [
"p3",
"p7",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6958384266288656209769099
% SZS output start Proof for 6958384266288656209769099
4. ! [X0] : (~rich(X0) => ~old(X0)) [input p3]
8. ! [X0] : ((~old(X0) | ~wise(X0)) <=> ~creative(X0)) [input p7]
17. ~rich(lucy) [input p16]
24. creative(lucy) [input hypothesis]
33. ! [X0] : (~old(X0) | rich(X0)) [ennf transformation 4]
50. ! [X0] : (((~old(X0) | ~wise(X0)) | creative(X0)) & (~creative(X0) | (old(X0) & wise(X0)))) [nnf transformation 8]
51. ! [X0] : ((~old(X0) | ~wise(X0) | creative(X0)) & (~creative(X0) | (old(X0) & wise(X0)))) [flattening 50]
97. ~old(X0) | rich(X0) [cnf transformation 33]
109. ~creative(X0) | old(X0) [cnf transformation 51]
133. ~rich(lucy) [cnf transformation 17]
141. creative(lucy) [cnf transformation 24]
200. 13 <=> rich(lucy) [avatar definition]
202. ~rich(lucy) <- (~13) [avatar component clause 200]
328. ~13 [avatar split clause 133,200]
360. old(lucy) [resolution 109,141]
368. rich(lucy) [resolution 360,97]
369. $false <- (~13) [subsumption resolution 368,202]
370. 13 [avatar contradiction clause 369]
371. $false [avatar sat refutation 328,370]
% SZS output end Proof for 6958384266288656209769099
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious and not curious is not calm and vice versa.
Everyone who is both not humble and not funny is both not calm and humble and vice versa.
If lucy is either funny or kind then mary is not kind or not tall and vice versa.
Everyone who is not strong or not tall is either patient or strong and vice versa.
Everyone who is both generous and not generous is both not brave and not patient and vice versa.
Everyone who is not curious is not old or not humble.
If someone is not tall or not kind then john is not calm or not kind and vice versa.
If someone is either creative or not tall then someone is both funny and not generous.
If someone is either not curious or happy then fred is not humble or calm and vice versa.
If susan is either not creative or not patient then paul is either not patient or not wise and vice versa.
If someone is both not generous and creative then mary is both not generous and not calm.
Everyone who is wise is both happy and not wise and vice versa.
Everyone who is both kind and not creative is not calm and vice versa.
Everyone who is not patient or quiet is both rich and generous.
If john is either brave or not calm then alice is either old or not brave.
Everyone who is humble or tall is quiet or not humble and vice versa.
Alice is not rich or not tall.
Lucy is not old or not strong.
Susan is either rich or not patient.
Someone is both tall and not curious.
Someone is not patient or happy. | John is wise. | contradiction | (![X]:((curious(X)&~curious(X))<=>~calm(X)))&
(![X]:((~humble(X)&~funny(X))<=>(~calm(X)&humble(X))))&
(((funny(lucy)<~>kind(lucy)))<=>((~kind(mary)|~tall(mary))))&
(![X]:((~strong(X)|~tall(X))<=>(patient(X)<~>strong(X))))&
(![X]:((generous(X)&~generous(X))<=>(~brave(X)&~patient(X))))&
(![X]:(~curious(X)=>(~old(X)|~humble(X))))&
((?[X]:((~tall(X)|~kind(X))))<=>((~calm(john)|~kind(john))))&
((?[X]:((creative(X)<~>~tall(X))))=>(?[X]:((funny(X)&~generous(X)))))&
((?[X]:((~curious(X)<~>happy(X))))<=>((~humble(fred)|calm(fred))))&
(((~creative(susan)<~>~patient(susan)))<=>((~patient(paul)<~>~wise(paul))))&
((?[X]:((~generous(X)&creative(X))))=>((~generous(mary)&~calm(mary))))&
(![X]:(wise(X)<=>(happy(X)&~wise(X))))&
(![X]:((kind(X)&~creative(X))<=>~calm(X)))&
(![X]:((~patient(X)|quiet(X))=>(rich(X)&generous(X))))&
(((brave(john)<~>~calm(john)))=>((old(alice)<~>~brave(alice))))&
(![X]:((humble(X)|tall(X))<=>(quiet(X)|~humble(X))))&
((~rich(alice)|~tall(alice)))&
((~old(lucy)|~strong(lucy)))&
((rich(susan)<~>~patient(susan)))&
(?[X]:((tall(X)&~curious(X))))&
(?[X]:((~patient(X)|happy(X)))) | wise(john) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3357028218640538104751339
% SZS output start Proof for 3357028218640538104751339
12. ! [X0] : (wise(X0) <=> (~wise(X0) & happy(X0))) [input p11]
22. wise(john) [input hypothesis]
55. ! [X0] : ((wise(X0) | (wise(X0) | ~happy(X0))) & ((~wise(X0) & happy(X0)) | ~wise(X0))) [nnf transformation 12]
56. ! [X0] : ((wise(X0) | wise(X0) | ~happy(X0)) & ((~wise(X0) & happy(X0)) | ~wise(X0))) [flattening 55]
116. ~wise(X0) | ~wise(X0) [cnf transformation 56]
140. wise(john) [cnf transformation 22]
143. ~wise(X0) [duplicate literal removal 116]
304. $false [subsumption resolution 140,143]
% SZS output end Proof for 3357028218640538104751339
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is either curious or not humble and vice versa.
Everyone who is both not brave and creative is not kind.
If someone is patient then someone is not brave.
If someone is both strong and wise then fred is kind or not wise and vice versa.
If lucy is both not wise and tall then someone is both not tall and not old.
If someone is either humble or not curious then someone is both not rich and happy and vice versa.
Everyone who is not wise is either strong or wise.
Everyone who is either not happy or humble is not humble and vice versa.
If mary is either not old or not humble then paul is curious or old.
Everyone who is either not creative or happy is not patient.
If alice is either not funny or wise then susan is both not generous and not patient and vice versa.
Everyone who is brave or creative is calm and vice versa.
Everyone who is not kind or wise is not tall.
Everyone who is generous or not creative is not quiet or calm.
Everyone who is both wise and not rich is either not tall or not patient.
Everyone who is not tall is not calm.
John is either not brave or not tall.
Someone is either not generous or quiet.
Someone is kind or not brave.
Someone is not calm.
Mary is not happy.
Lucy is not old.
Paul is strong or not strong. | John is brave. | contradiction | (![X]:(brave(X)<=>(curious(X)<~>~humble(X))))&
(![X]:((~brave(X)&creative(X))=>~kind(X)))&
((?[X]:(patient(X)))=>(?[X]:(~brave(X))))&
((?[X]:((strong(X)&wise(X))))<=>((kind(fred)|~wise(fred))))&
(((~wise(lucy)&tall(lucy)))=>(?[X]:((~tall(X)&~old(X)))))&
((?[X]:((humble(X)<~>~curious(X))))<=>(?[X]:((~rich(X)&happy(X)))))&
(![X]:(~wise(X)=>(strong(X)<~>wise(X))))&
(![X]:((~happy(X)<~>humble(X))<=>~humble(X)))&
(((~old(mary)<~>~humble(mary)))=>((curious(paul)|old(paul))))&
(![X]:((~creative(X)<~>happy(X))=>~patient(X)))&
(((~funny(alice)<~>wise(alice)))<=>((~generous(susan)&~patient(susan))))&
(![X]:((brave(X)|creative(X))<=>calm(X)))&
(![X]:((~kind(X)|wise(X))=>~tall(X)))&
(![X]:((generous(X)|~creative(X))=>(~quiet(X)|calm(X))))&
(![X]:((wise(X)&~rich(X))=>(~tall(X)<~>~patient(X))))&
(![X]:(~tall(X)=>~calm(X)))&
((~brave(john)<~>~tall(john)))&
(?[X]:((~generous(X)<~>quiet(X))))&
(?[X]:((kind(X)|~brave(X))))&
(?[X]:(~calm(X)))&
(~happy(mary))&
(~old(lucy))&
((strong(paul)|~strong(paul))) | brave(john) | [
"p11",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4599528695481381472619566
% SZS output start Proof for 4599528695481381472619566
12. ! [X0] : ((creative(X0) | brave(X0)) <=> calm(X0)) [input p11]
16. ! [X0] : (~tall(X0) => ~calm(X0)) [input p15]
17. ~brave(john) <~> ~tall(john) [input p16]
24. brave(john) [input hypothesis]
41. ! [X0] : (~calm(X0) | tall(X0)) [ennf transformation 16]
64. ! [X0] : (((creative(X0) | brave(X0)) | ~calm(X0)) & (calm(X0) | (~creative(X0) & ~brave(X0)))) [nnf transformation 12]
65. ! [X0] : ((creative(X0) | brave(X0) | ~calm(X0)) & (calm(X0) | (~creative(X0) & ~brave(X0)))) [flattening 64]
67. (tall(john) | brave(john)) & (~tall(john) | ~brave(john)) [nnf transformation 17]
110. ~brave(X0) | calm(X0) [cnf transformation 65]
119. ~calm(X0) | tall(X0) [cnf transformation 41]
120. ~tall(john) | ~brave(john) [cnf transformation 67]
129. brave(john) [cnf transformation 24]
259. 27 <=> brave(john) [avatar definition]
261. brave(john) <- (27) [avatar component clause 259]
263. 28 <=> tall(john) [avatar definition]
264. ~tall(john) <- (~28) [avatar component clause 263]
267. ~27 | ~28 [avatar split clause 120,263,259]
287. 27 [avatar split clause 129,259]
290. calm(john) <- (27) [resolution 110,261]
291. tall(john) <- (27) [resolution 119,290]
292. $false <- (27, ~28) [subsumption resolution 291,264]
293. ~27 | 28 [avatar contradiction clause 292]
294. $false [avatar sat refutation 267,287,293]
% SZS output end Proof for 4599528695481381472619566
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If mary is either calm or not generous then mary is both not old and not quiet. If someone is either kind or not creative then mary is either not kind or not humble. If someone is both not strong and not kind then someone is both not patient and not rich and vice versa. Everyone who is both old and creative is strong and vice versa. If someone is either not patient or happy then susan is either happy or patient. Everyone who is kind is not curious. If mary is either not rich or funny then paul is not happy and vice versa. If someone is not generous then someone is both happy and wise and vice versa. Everyone who is patient is strong. Everyone who is patient is not rich. If someone is both not creative and not tall then fred is both not brave and not patient. Everyone who is wise is both not quiet and kind. Everyone who is wise or not funny is creative and vice versa. Everyone who is quiet is calm and vice versa. Everyone who is both generous and not curious is not strong. If someone is happy then someone is brave and vice versa. Someone is curious. Paul is either not quiet or generous. Alice is both patient and not rich. Someone is either not funny or happy. Someone is not quiet or happy. Someone is not kind. Fred is funny. Mary is either calm or not patient. | Alice is old. | entailment | (((calm(mary)<~>~generous(mary)))=>((~old(mary)&~quiet(mary))))&
((?[X]:((kind(X)<~>~creative(X))))=>((~kind(mary)<~>~humble(mary))))&
((?[X]:((~strong(X)&~kind(X))))<=>(?[X]:((~patient(X)&~rich(X)))))&
(![X]:((old(X)&creative(X))<=>strong(X)))&
((?[X]:((~patient(X)<~>happy(X))))=>((happy(susan)<~>patient(susan))))&
(![X]:(kind(X)=>~curious(X)))&
(((~rich(mary)<~>funny(mary)))<=>(~happy(paul)))&
((?[X]:(~generous(X)))<=>(?[X]:((happy(X)&wise(X)))))&
(![X]:(patient(X)=>strong(X)))&
(![X]:(patient(X)=>~rich(X)))&
((?[X]:((~creative(X)&~tall(X))))=>((~brave(fred)&~patient(fred))))&
(![X]:(wise(X)=>(~quiet(X)&kind(X))))&
(![X]:((wise(X)|~funny(X))<=>creative(X)))&
(![X]:(quiet(X)<=>calm(X)))&
(![X]:((generous(X)&~curious(X))=>~strong(X)))&
((?[X]:(happy(X)))<=>(?[X]:(brave(X))))&
(?[X]:(curious(X)))&
((~quiet(paul)<~>generous(paul)))&
((patient(alice)&~rich(alice)))&
(?[X]:((~funny(X)<~>happy(X))))&
(?[X]:((~quiet(X)|happy(X))))&
(?[X]:(~kind(X)))&
(funny(fred))&
((calm(mary)<~>~patient(mary))) | old(alice) | [
"p3",
"p8",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2840090491927467305435091
% SZS output start Proof for 2840090491927467305435091
4. ! [X0] : ((creative(X0) & old(X0)) <=> strong(X0)) [input p3]
9. ! [X0] : (patient(X0) => strong(X0)) [input p8]
19. ~rich(alice) & patient(alice) [input p18]
25. ~old(alice) [input hypothesis]
34. ! [X0] : (strong(X0) | ~patient(X0)) [ennf transformation 9]
46. ! [X0] : (((creative(X0) & old(X0)) | ~strong(X0)) & (strong(X0) | (~creative(X0) | ~old(X0)))) [nnf transformation 4]
47. ! [X0] : (((creative(X0) & old(X0)) | ~strong(X0)) & (strong(X0) | ~creative(X0) | ~old(X0))) [flattening 46]
87. ~strong(X0) | old(X0) [cnf transformation 47]
101. ~patient(X0) | strong(X0) [cnf transformation 34]
116. patient(alice) [cnf transformation 19]
125. ~old(alice) [cnf transformation 25]
307. strong(alice) [resolution 101,116]
310. old(alice) [resolution 307,87]
311. $false [subsumption resolution 310,125]
% SZS output end Proof for 2840090491927467305435091
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is brave and vice versa.
If someone is not kind or old then someone is creative.
Everyone who is both not patient and happy is not patient.
Everyone who is not curious is not calm or not humble and vice versa.
Everyone who is either quiet or happy is creative and vice versa.
Everyone who is either strong or kind is quiet or not strong.
Everyone who is either creative or brave is either not quiet or not wise.
Everyone who is either not old or patient is both generous and not brave.
If fred is both not kind and not old then paul is not calm.
If paul is both funny and not strong then mary is kind or not curious.
Everyone who is either quiet or not patient is wise and vice versa.
Everyone who is both humble and curious is not humble or not patient and vice versa.
If someone is both not curious and not old then john is not patient and vice versa.
If someone is both not wise and tall then someone is tall and vice versa.
If lucy is creative or not creative then someone is either calm or not kind and vice versa.
If susan is either not brave or quiet then alice is quiet or not old and vice versa.
John is both funny and not generous.
Alice is not curious.
Mary is either old or rich.
John is not kind or patient.
Someone is both not generous and curious.
Someone is either old or not rich. | Fred is calm. | neutral | (![X]:(~funny(X)<=>brave(X)))&
((?[X]:((~kind(X)|old(X))))=>(?[X]:(creative(X))))&
(![X]:((~patient(X)&happy(X))=>~patient(X)))&
(![X]:(~curious(X)<=>(~calm(X)|~humble(X))))&
(![X]:((quiet(X)<~>happy(X))<=>creative(X)))&
(![X]:((strong(X)<~>kind(X))=>(quiet(X)|~strong(X))))&
(![X]:((creative(X)<~>brave(X))=>(~quiet(X)<~>~wise(X))))&
(![X]:((~old(X)<~>patient(X))=>(generous(X)&~brave(X))))&
(((~kind(fred)&~old(fred)))=>(~calm(paul)))&
(((funny(paul)&~strong(paul)))=>((kind(mary)|~curious(mary))))&
(![X]:((quiet(X)<~>~patient(X))<=>wise(X)))&
(![X]:((humble(X)&curious(X))<=>(~humble(X)|~patient(X))))&
((?[X]:((~curious(X)&~old(X))))<=>(~patient(john)))&
((?[X]:((~wise(X)&tall(X))))<=>(?[X]:(tall(X))))&
(((creative(lucy)|~creative(lucy)))<=>(?[X]:((calm(X)<~>~kind(X)))))&
(((~brave(susan)<~>quiet(susan)))<=>((quiet(alice)|~old(alice))))&
((funny(john)&~generous(john)))&
(~curious(alice))&
((old(mary)<~>rich(mary)))&
((~kind(john)|patient(john)))&
(?[X]:((~generous(X)&curious(X))))&
(?[X]:((old(X)<~>~rich(X)))) | calm(fred) | [] | null | 0 |
Everyone who is funny is both not tall and not rich and vice versa. If someone is both tall and quiet then someone is both not old and not quiet. Everyone who is either curious or not curious is not old or kind and vice versa. Everyone who is not brave or curious is not curious and vice versa. If someone is curious or humble then john is creative. If someone is either not kind or not happy then alice is both funny and not humble and vice versa. Everyone who is both generous and not generous is generous. Everyone who is both brave and not patient is either wise or not quiet. Everyone who is either tall or patient is both not quiet and not creative. Everyone who is either not funny or not kind is curious or not patient and vice versa. If someone is either creative or brave then someone is wise or kind. Everyone who is both creative and strong is patient or old and vice versa. If someone is quiet or not strong then fred is both quiet and not strong and vice versa. Everyone who is funny or creative is not tall or not rich and vice versa. Everyone who is curious or not funny is calm or generous. If alice is both not calm and kind then someone is either tall or not strong and vice versa. Someone is either not creative or kind. Paul is not strong. Someone is funny or not patient. Someone is both calm and rich. Someone is either not generous or not creative. Someone is both tall and rich. | Alice is not creative. | neutral | (![X]:(funny(X)<=>(~tall(X)&~rich(X))))&
((?[X]:((tall(X)&quiet(X))))=>(?[X]:((~old(X)&~quiet(X)))))&
(![X]:((curious(X)<~>~curious(X))<=>(~old(X)|kind(X))))&
(![X]:((~brave(X)|curious(X))<=>~curious(X)))&
((?[X]:((curious(X)|humble(X))))=>(creative(john)))&
((?[X]:((~kind(X)<~>~happy(X))))<=>((funny(alice)&~humble(alice))))&
(![X]:((generous(X)&~generous(X))=>generous(X)))&
(![X]:((brave(X)&~patient(X))=>(wise(X)<~>~quiet(X))))&
(![X]:((tall(X)<~>patient(X))=>(~quiet(X)&~creative(X))))&
(![X]:((~funny(X)<~>~kind(X))<=>(curious(X)|~patient(X))))&
((?[X]:((creative(X)<~>brave(X))))=>(?[X]:((wise(X)|kind(X)))))&
(![X]:((creative(X)&strong(X))<=>(patient(X)|old(X))))&
((?[X]:((quiet(X)|~strong(X))))<=>((quiet(fred)&~strong(fred))))&
(![X]:((funny(X)|creative(X))<=>(~tall(X)|~rich(X))))&
(![X]:((curious(X)|~funny(X))=>(calm(X)|generous(X))))&
(((~calm(alice)&kind(alice)))<=>(?[X]:((tall(X)<~>~strong(X)))))&
(?[X]:((~creative(X)<~>kind(X))))&
(~strong(paul))&
(?[X]:((funny(X)|~patient(X))))&
(?[X]:((calm(X)&rich(X))))&
(?[X]:((~generous(X)<~>~creative(X))))&
(?[X]:((tall(X)&rich(X)))) | ~creative(alice) | [] | null | 0 |
Everyone who is either patient or old is both not curious and not humble.
If susan is either strong or not happy then someone is either happy or generous and vice versa.
Everyone who is both not rich and generous is both not tall and patient.
Everyone who is not tall is both funny and not calm.
Everyone who is both not funny and not humble is not brave or creative and vice versa.
If susan is both not humble and not happy then fred is either brave or not brave.
If susan is not funny then alice is not kind or happy.
If someone is not calm then susan is either generous or tall.
Everyone who is calm or not generous is both not creative and patient and vice versa.
Everyone who is both not old and kind is tall or not old and vice versa.
Everyone who is both rich and not old is old or not quiet.
Everyone who is happy or funny is both creative and kind.
If lucy is both not funny and not tall then someone is either not curious or not wise.
Everyone who is both not curious and creative is both not quiet and not generous.
Everyone who is either not tall or old is humble.
If alice is quiet or strong then someone is either calm or not tall.
Someone is happy or rich.
Susan is either humble or rich.
Someone is not rich or patient.
Someone is wise or not strong. | Lucy is funny. | contradiction | (![X]:((patient(X)<~>old(X))=>(~curious(X)&~humble(X))))&
(((strong(susan)<~>~happy(susan)))<=>(?[X]:((happy(X)<~>generous(X)))))&
(![X]:((~rich(X)&generous(X))=>(~tall(X)&patient(X))))&
(![X]:(~tall(X)=>(funny(X)&~calm(X))))&
(![X]:((~funny(X)&~humble(X))<=>(~brave(X)|creative(X))))&
(((~humble(susan)&~happy(susan)))=>((brave(fred)<~>~brave(fred))))&
((~funny(susan))=>((~kind(alice)|happy(alice))))&
((?[X]:(~calm(X)))=>((generous(susan)<~>tall(susan))))&
(![X]:((calm(X)|~generous(X))<=>(~creative(X)&patient(X))))&
(![X]:((~old(X)&kind(X))<=>(tall(X)|~old(X))))&
(![X]:((rich(X)&~old(X))=>(old(X)|~quiet(X))))&
(![X]:((happy(X)|funny(X))=>(creative(X)&kind(X))))&
(((~funny(lucy)&~tall(lucy)))=>(?[X]:((~curious(X)<~>~wise(X)))))&
(![X]:((~curious(X)&creative(X))=>(~quiet(X)&~generous(X))))&
(![X]:((~tall(X)<~>old(X))=>humble(X)))&
(((quiet(alice)|strong(alice)))=>(?[X]:((calm(X)<~>~tall(X)))))&
(?[X]:((happy(X)|rich(X))))&
((humble(susan)<~>rich(susan)))&
(?[X]:((~rich(X)|patient(X))))&
(?[X]:((wise(X)|~strong(X)))) | funny(lucy) | [
"p4",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3394133861924848606907808
% SZS output start Proof for 3394133861924848606907808
5. ! [X0] : ((~humble(X0) & ~funny(X0)) <=> (creative(X0) | ~brave(X0))) [input p4]
12. ! [X0] : ((funny(X0) | happy(X0)) => (kind(X0) & creative(X0))) [input p11]
21. funny(lucy) [input hypothesis]
34. ! [X0] : ((kind(X0) & creative(X0)) | (~funny(X0) & ~happy(X0))) [ennf transformation 12]
46. ! [X0] : (((~humble(X0) & ~funny(X0)) | (~creative(X0) & brave(X0))) & ((creative(X0) | ~brave(X0)) | (humble(X0) | funny(X0)))) [nnf transformation 5]
47. ! [X0] : (((~humble(X0) & ~funny(X0)) | (~creative(X0) & brave(X0))) & (creative(X0) | ~brave(X0) | humble(X0) | funny(X0))) [flattening 46]
86. ~funny(X0) | ~creative(X0) [cnf transformation 47]
105. creative(X0) | ~funny(X0) [cnf transformation 34]
120. funny(lucy) [cnf transformation 21]
177. ~funny(X0) [subsumption resolution 105,86]
229. $false [subsumption resolution 120,177]
% SZS output end Proof for 3394133861924848606907808
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or creative is calm. Everyone who is either not patient or generous is both funny and not curious. Everyone who is both not old and old is not rich or old and vice versa. Everyone who is rich is kind. If fred is kind or not strong then someone is either calm or not strong. Everyone who is strong or not calm is generous. Everyone who is either happy or not rich is not tall and vice versa. If paul is both not rich and creative then someone is not generous or not funny and vice versa. If someone is either not tall or kind then susan is not calm or kind. If mary is both brave and old then lucy is either strong or curious. Everyone who is either not old or brave is either not patient or not brave. If lucy is funny or not kind then someone is tall or not rich and vice versa. Everyone who is both not rich and not brave is not kind and vice versa. If someone is tall then mary is quiet. Everyone who is both not humble and old is both not strong and not rich. If someone is not rich or funny then alice is tall or funny and vice versa. Someone is not humble or humble. Lucy is not curious. John is both not quiet and strong. Mary is patient. Someone is humble. Someone is brave or rich. | Paul is funny. | entailment | (![X]:((~generous(X)<~>creative(X))=>calm(X)))&
(![X]:((~patient(X)<~>generous(X))=>(funny(X)&~curious(X))))&
(![X]:((~old(X)&old(X))<=>(~rich(X)|old(X))))&
(![X]:(rich(X)=>kind(X)))&
(((kind(fred)|~strong(fred)))=>(?[X]:((calm(X)<~>~strong(X)))))&
(![X]:((strong(X)|~calm(X))=>generous(X)))&
(![X]:((happy(X)<~>~rich(X))<=>~tall(X)))&
(((~rich(paul)&creative(paul)))<=>(?[X]:((~generous(X)|~funny(X)))))&
((?[X]:((~tall(X)<~>kind(X))))=>((~calm(susan)|kind(susan))))&
(((brave(mary)&old(mary)))=>((strong(lucy)<~>curious(lucy))))&
(![X]:((~old(X)<~>brave(X))=>(~patient(X)<~>~brave(X))))&
(((funny(lucy)|~kind(lucy)))<=>(?[X]:((tall(X)|~rich(X)))))&
(![X]:((~rich(X)&~brave(X))<=>~kind(X)))&
((?[X]:(tall(X)))=>(quiet(mary)))&
(![X]:((~humble(X)&old(X))=>(~strong(X)&~rich(X))))&
((?[X]:((~rich(X)|funny(X))))<=>((tall(alice)|funny(alice))))&
(?[X]:((~humble(X)|humble(X))))&
(~curious(lucy))&
((~quiet(john)&strong(john)))&
(patient(mary))&
(?[X]:(humble(X)))&
(?[X]:((brave(X)|rich(X)))) | funny(paul) | [
"p2",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8932415324520378113318046
% SZS output start Proof for 8932415324520378113318046
3. ! [X0] : ((old(X0) & ~old(X0)) <=> (old(X0) | ~rich(X0))) [input p2]
8. (creative(paul) & ~rich(paul)) <=> ? [X0] : (~funny(X0) | ~generous(X0)) [input p7]
23. ~funny(paul) [input hypothesis]
39. ! [X0] : (((old(X0) & ~old(X0)) | (~old(X0) & rich(X0))) & ((old(X0) | ~rich(X0)) | (~old(X0) | old(X0)))) [nnf transformation 3]
40. ! [X0] : (((old(X0) & ~old(X0)) | (~old(X0) & rich(X0))) & (old(X0) | ~rich(X0) | ~old(X0) | old(X0))) [flattening 39]
45. ((creative(paul) & ~rich(paul)) | ! [X0] : (funny(X0) & generous(X0))) & (? [X0] : (~funny(X0) | ~generous(X0)) | (~creative(paul) | rich(paul))) [nnf transformation 8]
46. ((creative(paul) & ~rich(paul)) | ! [X0] : (funny(X0) & generous(X0))) & (? [X0] : (~funny(X0) | ~generous(X0)) | ~creative(paul) | rich(paul)) [flattening 45]
47. ((creative(paul) & ~rich(paul)) | ! [X0] : (funny(X0) & generous(X0))) & (? [X1] : (~funny(X1) | ~generous(X1)) | ~creative(paul) | rich(paul)) [rectify 46]
48. ? [X1] : (~funny(X1) | ~generous(X1)) => (~funny(sK1) | ~generous(sK1)) [choice axiom]
49. ((creative(paul) & ~rich(paul)) | ! [X0] : (funny(X0) & generous(X0))) & ((~funny(sK1) | ~generous(sK1)) | ~creative(paul) | rich(paul)) [skolemisation 47,48]
79. ~old(X0) | ~old(X0) [cnf transformation 40]
80. rich(X0) | old(X0) [cnf transformation 40]
95. ~rich(paul) | funny(X0) [cnf transformation 49]
127. ~funny(paul) [cnf transformation 23]
131. ~old(X0) [duplicate literal removal 79]
153. 5 <=> ! [X0] : funny(X0) [avatar definition]
154. funny(X0) <- (5) [avatar component clause 153]
165. 8 <=> rich(paul) [avatar definition]
167. ~rich(paul) <- (~8) [avatar component clause 165]
168. 5 | ~8 [avatar split clause 95,165,153]
259. old(paul) <- (~8) [resolution 80,167]
262. $false <- (~8) [subsumption resolution 259,131]
263. 8 [avatar contradiction clause 262]
268. $false <- (5) [resolution 154,127]
271. ~5 [avatar contradiction clause 268]
272. $false [avatar sat refutation 168,263,271]
% SZS output end Proof for 8932415324520378113318046
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or not strong is not kind. Everyone who is rich is curious and vice versa. Everyone who is not wise or not funny is both not curious and not tall and vice versa. Everyone who is both not strong and not brave is both patient and brave. If fred is humble then someone is either not old or not creative and vice versa. Everyone who is calm is wise or strong. Everyone who is either quiet or rich is both quiet and brave. If someone is quiet then someone is generous or curious. If lucy is both not rich and brave then fred is tall. If lucy is both not generous and patient then someone is both old and not tall. If fred is humble or not calm then someone is kind or not curious. If someone is both wise and not funny then someone is wise. 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. Someone is quiet or not old. Someone is either quiet or funny. Someone is both wise and not funny. Fred is happy or old. Someone is both not creative and old. Someone is both patient and not kind. Alice is quiet. Someone is not creative. | Lucy is not rich. | neutral | (![X]:((rich(X)|~strong(X))=>~kind(X)))&
(![X]:(rich(X)<=>curious(X)))&
(![X]:((~wise(X)|~funny(X))<=>(~curious(X)&~tall(X))))&
(![X]:((~strong(X)&~brave(X))=>(patient(X)&brave(X))))&
((humble(fred))<=>(?[X]:((~old(X)<~>~creative(X)))))&
(![X]:(calm(X)=>(wise(X)|strong(X))))&
(![X]:((quiet(X)<~>rich(X))=>(quiet(X)&brave(X))))&
((?[X]:(quiet(X)))=>(?[X]:((generous(X)|curious(X)))))&
(((~rich(lucy)&brave(lucy)))=>(tall(fred)))&
(((~generous(lucy)&patient(lucy)))=>(?[X]:((old(X)&~tall(X)))))&
(((humble(fred)|~calm(fred)))=>(?[X]:((kind(X)|~curious(X)))))&
((?[X]:((wise(X)&~funny(X))))=>(?[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))))&
(?[X]:((quiet(X)<~>funny(X))))&
(?[X]:((wise(X)&~funny(X))))&
((happy(fred)|old(fred)))&
(?[X]:((~creative(X)&old(X))))&
(?[X]:((patient(X)&~kind(X))))&
(quiet(alice))&
(?[X]:(~creative(X))) | ~rich(lucy) | [] | null | 0 |
Everyone who is either not curious or patient is humble or not generous and vice versa.
Everyone who is not kind or not funny is not wise and vice versa.
If someone is either not patient or quiet then someone is both brave and not wise and vice versa.
If someone is both not curious and not kind then fred is wise.
Everyone who is both not happy and calm is either not happy or quiet and vice versa.
Everyone who is both humble and not patient is rich.
Everyone who is either not funny or old is patient or brave.
If fred is either not funny or not quiet then mary is either generous or not humble and vice versa.
If john is either not humble or kind then fred is either not funny or rich.
Everyone who is calm or happy is strong.
Everyone who is either not rich or not curious is generous.
If lucy is old or not quiet then alice is not rich.
If lucy is both brave and kind then someone is both not old and creative and vice versa.
If someone is creative or patient then susan is not patient or generous.
Everyone who is calm is wise and vice versa.
Everyone who is tall or not funny is either funny or tall.
Lucy is generous.
Someone is old or not generous.
Mary is wise.
Someone is both not humble and happy.
Someone is not humble.
Someone is both brave and kind.
Someone is happy or funny.
Someone is funny or not funny. | Mary is generous. | neutral | (![X]:((~curious(X)<~>patient(X))<=>(humble(X)|~generous(X))))&
(![X]:((~kind(X)|~funny(X))<=>~wise(X)))&
((?[X]:((~patient(X)<~>quiet(X))))<=>(?[X]:((brave(X)&~wise(X)))))&
((?[X]:((~curious(X)&~kind(X))))=>(wise(fred)))&
(![X]:((~happy(X)&calm(X))<=>(~happy(X)<~>quiet(X))))&
(![X]:((humble(X)&~patient(X))=>rich(X)))&
(![X]:((~funny(X)<~>old(X))=>(patient(X)|brave(X))))&
(((~funny(fred)<~>~quiet(fred)))<=>((generous(mary)<~>~humble(mary))))&
(((~humble(john)<~>kind(john)))=>((~funny(fred)<~>rich(fred))))&
(![X]:((calm(X)|happy(X))=>strong(X)))&
(![X]:((~rich(X)<~>~curious(X))=>generous(X)))&
(((old(lucy)|~quiet(lucy)))=>(~rich(alice)))&
(((brave(lucy)&kind(lucy)))<=>(?[X]:((~old(X)&creative(X)))))&
((?[X]:((creative(X)|patient(X))))=>((~patient(susan)|generous(susan))))&
(![X]:(calm(X)<=>wise(X)))&
(![X]:((tall(X)|~funny(X))=>(funny(X)<~>tall(X))))&
(generous(lucy))&
(?[X]:((old(X)|~generous(X))))&
(wise(mary))&
(?[X]:((~humble(X)&happy(X))))&
(?[X]:(~humble(X)))&
(?[X]:((brave(X)&kind(X))))&
(?[X]:((happy(X)|funny(X))))&
(?[X]:((funny(X)|~funny(X)))) | generous(mary) | [] | null | 0 |
Everyone who is either not happy or tall is tall and vice versa.
Everyone who is either not quiet or not patient is both not tall and rich.
If someone is both not brave and kind then susan is brave.
If someone is either not calm or quiet then someone is wise or not tall and vice versa.
If mary is either tall or kind then mary is patient and vice versa.
Everyone who is not patient is not kind or not tall.
If someone is both quiet and humble then someone is not humble or creative.
Everyone who is not calm is not funny or rich and vice versa.
If mary is not curious or not rich then mary is not creative.
If someone is both funny and not patient then someone is old.
Everyone who is not old is not creative or not kind.
Everyone who is brave is either not rich or not quiet.
Everyone who is happy or tall is both not funny and not quiet and vice versa.
Everyone who is not brave or not happy is strong.
Everyone who is both tall and not tall is either not funny or not creative.
Susan is both not quiet and old.
John is both brave and not wise.
Mary is either not rich or calm.
Someone is humble or not strong.
Susan is not funny.
Someone is not humble or tall.
Someone is not humble. | Susan is not calm. | entailment | (![X]:((~happy(X)<~>tall(X))<=>tall(X)))&
(![X]:((~quiet(X)<~>~patient(X))=>(~tall(X)&rich(X))))&
((?[X]:((~brave(X)&kind(X))))=>(brave(susan)))&
((?[X]:((~calm(X)<~>quiet(X))))<=>(?[X]:((wise(X)|~tall(X)))))&
(((tall(mary)<~>kind(mary)))<=>(patient(mary)))&
(![X]:(~patient(X)=>(~kind(X)|~tall(X))))&
((?[X]:((quiet(X)&humble(X))))=>(?[X]:((~humble(X)|creative(X)))))&
(![X]:(~calm(X)<=>(~funny(X)|rich(X))))&
(((~curious(mary)|~rich(mary)))=>(~creative(mary)))&
((?[X]:((funny(X)&~patient(X))))=>(?[X]:(old(X))))&
(![X]:(~old(X)=>(~creative(X)|~kind(X))))&
(![X]:(brave(X)=>(~rich(X)<~>~quiet(X))))&
(![X]:((happy(X)|tall(X))<=>(~funny(X)&~quiet(X))))&
(![X]:((~brave(X)|~happy(X))=>strong(X)))&
(![X]:((tall(X)&~tall(X))=>(~funny(X)<~>~creative(X))))&
((~quiet(susan)&old(susan)))&
((brave(john)&~wise(john)))&
((~rich(mary)<~>calm(mary)))&
(?[X]:((humble(X)|~strong(X))))&
(~funny(susan))&
(?[X]:((~humble(X)|tall(X))))&
(?[X]:(~humble(X))) | ~calm(susan) | [
"p0",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7203591709617194056518150
% SZS output start Proof for 7203591709617194056518150
1. ! [X0] : ((~happy(X0) <~> tall(X0)) <=> tall(X0)) [input p0]
8. ! [X0] : (~calm(X0) <=> (rich(X0) | ~funny(X0))) [input p7]
13. ! [X0] : ((tall(X0) | happy(X0)) <=> (~quiet(X0) & ~funny(X0))) [input p12]
23. calm(susan) [input hypothesis]
41. ! [X0] : ((((~tall(X0) | happy(X0)) & (tall(X0) | ~happy(X0))) | ~tall(X0)) & (tall(X0) | ((~happy(X0) | ~tall(X0)) & (tall(X0) | happy(X0))))) [nnf transformation 1]
52. ! [X0] : ((~calm(X0) | (~rich(X0) & funny(X0))) & ((rich(X0) | ~funny(X0)) | calm(X0))) [nnf transformation 8]
53. ! [X0] : ((~calm(X0) | (~rich(X0) & funny(X0))) & (rich(X0) | ~funny(X0) | calm(X0))) [flattening 52]
55. ! [X0] : (((tall(X0) | happy(X0)) | (quiet(X0) | funny(X0))) & ((~quiet(X0) & ~funny(X0)) | (~tall(X0) & ~happy(X0)))) [nnf transformation 13]
56. ! [X0] : ((tall(X0) | happy(X0) | quiet(X0) | funny(X0)) & ((~quiet(X0) & ~funny(X0)) | (~tall(X0) & ~happy(X0)))) [flattening 55]
65. tall(X0) | tall(X0) | happy(X0) [cnf transformation 41]
68. ~tall(X0) | happy(X0) | ~tall(X0) [cnf transformation 41]
87. ~calm(X0) | funny(X0) [cnf transformation 53]
92. ~funny(X0) | ~happy(X0) [cnf transformation 56]
110. calm(susan) [cnf transformation 23]
111. tall(X0) | happy(X0) [duplicate literal removal 65]
112. ~tall(X0) | happy(X0) [duplicate literal removal 68]
113. happy(X0) [subsumption resolution 111,112]
194. ~funny(X0) [subsumption resolution 92,113]
216. funny(susan) [resolution 87,110]
217. $false [subsumption resolution 216,194]
% SZS output end Proof for 7203591709617194056518150
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not kind is either rich or not creative and vice versa.
Everyone who is not brave is happy or not rich and vice versa.
If susan is both humble and not strong then paul is both not rich and not curious and vice versa.
Everyone who is rich or quiet is not old or brave and vice versa.
Everyone who is either not quiet or kind is either creative or not calm and vice versa.
Everyone who is tall is not quiet.
If john is either not quiet or not rich then alice is either tall or calm.
If someone is funny or creative then paul is not generous and vice versa.
If someone is both brave and not calm then lucy is both quiet and not strong.
If john is either rich or wise then mary is not generous.
If someone is calm or not generous then someone is kind or wise.
Everyone who is either patient or not old is not wise or not calm and vice versa.
If lucy is not rich then mary is curious or not funny and vice versa.
If susan is both not calm and brave then someone is either not creative or not humble and vice versa.
Everyone who is not generous or not strong is both rich and not curious.
Everyone who is both not tall and not brave is not tall.
Lucy is not funny.
Someone is not patient or quiet.
Someone is both strong and happy.
Susan is both not tall and patient.
Someone is either brave or curious.
Fred is brave or not funny.
Someone is rich or not humble. | Lucy is quiet. | neutral | (![X]:((generous(X)<~>~kind(X))<=>(rich(X)<~>~creative(X))))&
(![X]:(~brave(X)<=>(happy(X)|~rich(X))))&
(((humble(susan)&~strong(susan)))<=>((~rich(paul)&~curious(paul))))&
(![X]:((rich(X)|quiet(X))<=>(~old(X)|brave(X))))&
(![X]:((~quiet(X)<~>kind(X))<=>(creative(X)<~>~calm(X))))&
(![X]:(tall(X)=>~quiet(X)))&
(((~quiet(john)<~>~rich(john)))=>((tall(alice)<~>calm(alice))))&
((?[X]:((funny(X)|creative(X))))<=>(~generous(paul)))&
((?[X]:((brave(X)&~calm(X))))=>((quiet(lucy)&~strong(lucy))))&
(((rich(john)<~>wise(john)))=>(~generous(mary)))&
((?[X]:((calm(X)|~generous(X))))=>(?[X]:((kind(X)|wise(X)))))&
(![X]:((patient(X)<~>~old(X))<=>(~wise(X)|~calm(X))))&
((~rich(lucy))<=>((curious(mary)|~funny(mary))))&
(((~calm(susan)&brave(susan)))<=>(?[X]:((~creative(X)<~>~humble(X)))))&
(![X]:((~generous(X)|~strong(X))=>(rich(X)&~curious(X))))&
(![X]:((~tall(X)&~brave(X))=>~tall(X)))&
(~funny(lucy))&
(?[X]:((~patient(X)|quiet(X))))&
(?[X]:((strong(X)&happy(X))))&
((~tall(susan)&patient(susan)))&
(?[X]:((brave(X)<~>curious(X))))&
((brave(fred)|~funny(fred)))&
(?[X]:((rich(X)|~humble(X)))) | quiet(lucy) | [] | null | 0 |
If someone is both old and not generous then paul is both not creative and not wise. If someone is both strong and not calm then someone is rich and vice versa. If someone is either humble or not patient then alice is either wise or brave and vice versa. Everyone who is not funny is not funny or not tall. If fred is either strong or funny then someone is creative or not creative. Everyone who is creative or quiet is either old or tall and vice versa. Everyone who is both not tall and not calm is generous and vice versa. Everyone who is not calm is tall or wise and vice versa. Everyone who is both not kind and quiet is not generous or kind and vice versa. Everyone who is not funny or humble is either not tall or not quiet. If someone is both not strong and not rich then john is both not funny and not curious and vice versa. Everyone who is either tall or humble is not tall and vice versa. If john is quiet or happy then fred is strong and vice versa. If mary is not patient or curious then someone is either tall or calm. Everyone who is both old and not strong is either not kind or creative. Someone is either not quiet or not generous. Paul is not creative or wise. Someone is both curious and not patient. | Alice is old. | entailment | ((?[X]:((old(X)&~generous(X))))=>((~creative(paul)&~wise(paul))))&
((?[X]:((strong(X)&~calm(X))))<=>(?[X]:(rich(X))))&
((?[X]:((humble(X)<~>~patient(X))))<=>((wise(alice)<~>brave(alice))))&
(![X]:(~funny(X)=>(~funny(X)|~tall(X))))&
(((strong(fred)<~>funny(fred)))=>(?[X]:((creative(X)|~creative(X)))))&
(![X]:((creative(X)|quiet(X))<=>(old(X)<~>tall(X))))&
(![X]:((~tall(X)&~calm(X))<=>generous(X)))&
(![X]:(~calm(X)<=>(tall(X)|wise(X))))&
(![X]:((~kind(X)&quiet(X))<=>(~generous(X)|kind(X))))&
(![X]:((~funny(X)|humble(X))=>(~tall(X)<~>~quiet(X))))&
((?[X]:((~strong(X)&~rich(X))))<=>((~funny(john)&~curious(john))))&
(![X]:((tall(X)<~>humble(X))<=>~tall(X)))&
(((quiet(john)|happy(john)))<=>(strong(fred)))&
(((~patient(mary)|curious(mary)))=>(?[X]:((tall(X)<~>calm(X)))))&
(![X]:((old(X)&~strong(X))=>(~kind(X)<~>creative(X))))&
(?[X]:((~quiet(X)<~>~generous(X))))&
((~creative(paul)|wise(paul)))&
(?[X]:((curious(X)&~patient(X)))) | old(alice) | [
"p5",
"p6",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2939675665322141206960178
% SZS output start Proof for 2939675665322141206960178
6. ! [X0] : ((quiet(X0) | creative(X0)) <=> (old(X0) <~> tall(X0))) [input p5]
7. ! [X0] : ((~calm(X0) & ~tall(X0)) <=> generous(X0)) [input p6]
9. ! [X0] : ((quiet(X0) & ~kind(X0)) <=> (kind(X0) | ~generous(X0))) [input p8]
10. ! [X0] : ((humble(X0) | ~funny(X0)) => (~tall(X0) <~> ~quiet(X0))) [input p9]
12. ! [X0] : ((tall(X0) <~> humble(X0)) <=> ~tall(X0)) [input p11]
19. ~old(alice) [input hypothesis]
25. ! [X0] : ((~tall(X0) <~> ~quiet(X0)) | (~humble(X0) & funny(X0))) [ennf transformation 10]
41. ! [X0] : (((quiet(X0) | creative(X0)) | ((old(X0) | ~tall(X0)) & (tall(X0) | ~old(X0)))) & (((~tall(X0) | ~old(X0)) & (tall(X0) | old(X0))) | (~quiet(X0) & ~creative(X0)))) [nnf transformation 6]
42. ! [X0] : ((quiet(X0) | creative(X0) | ((old(X0) | ~tall(X0)) & (tall(X0) | ~old(X0)))) & (((~tall(X0) | ~old(X0)) & (tall(X0) | old(X0))) | (~quiet(X0) & ~creative(X0)))) [flattening 41]
43. ! [X0] : (((~calm(X0) & ~tall(X0)) | ~generous(X0)) & (generous(X0) | (calm(X0) | tall(X0)))) [nnf transformation 7]
44. ! [X0] : (((~calm(X0) & ~tall(X0)) | ~generous(X0)) & (generous(X0) | calm(X0) | tall(X0))) [flattening 43]
47. ! [X0] : (((quiet(X0) & ~kind(X0)) | (~kind(X0) & generous(X0))) & ((kind(X0) | ~generous(X0)) | (~quiet(X0) | kind(X0)))) [nnf transformation 9]
48. ! [X0] : (((quiet(X0) & ~kind(X0)) | (~kind(X0) & generous(X0))) & (kind(X0) | ~generous(X0) | ~quiet(X0) | kind(X0))) [flattening 47]
49. ! [X0] : (((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | (~humble(X0) & funny(X0))) [nnf transformation 25]
55. ! [X0] : ((((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | tall(X0)) & (~tall(X0) | ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0))))) [nnf transformation 12]
84. ~quiet(X0) | old(X0) | tall(X0) [cnf transformation 42]
90. ~tall(X0) | ~generous(X0) [cnf transformation 44]
98. quiet(X0) | generous(X0) [cnf transformation 48]
101. ~quiet(X0) | ~tall(X0) | ~humble(X0) [cnf transformation 49]
103. ~humble(X0) | tall(X0) | quiet(X0) [cnf transformation 49]
108. ~tall(X0) | humble(X0) | ~tall(X0) [cnf transformation 55]
110. humble(X0) | tall(X0) | tall(X0) [cnf transformation 55]
126. ~old(alice) [cnf transformation 19]
127. ~tall(X0) | humble(X0) [duplicate literal removal 108]
128. tall(X0) | humble(X0) [duplicate literal removal 110]
219. humble(X0) [subsumption resolution 127,128]
293. ~tall(X0) | ~humble(X0) | generous(X0) [resolution 101,98]
294. ~tall(X0) | generous(X0) [subsumption resolution 293,219]
295. ~tall(X0) [subsumption resolution 294,90]
331. tall(X0) | quiet(X0) [resolution 103,219]
332. quiet(X0) [subsumption resolution 331,295]
342. old(X3) | tall(X3) [resolution 332,84]
344. old(X3) [subsumption resolution 342,295]
357. $false [resolution 344,126]
% SZS output end Proof for 2939675665322141206960178
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is both rich and humble and vice versa.
Everyone who is not tall is both generous and not old and vice versa.
Everyone who is not patient is not creative and vice versa.
Everyone who is curious is not kind and vice versa.
Everyone who is both not brave and brave is both not rich and creative and vice versa.
If someone is not happy then someone is either generous or not patient and vice versa.
Everyone who is kind is either not generous or old.
If lucy is not rich or not funny then susan is not creative or not happy and vice versa.
Everyone who is not patient is either creative or calm and vice versa.
If lucy is not quiet or wise then lucy is either not funny or strong and vice versa.
If someone is both calm and creative then fred is not rich and vice versa.
Everyone who is both happy and not patient is both generous and not tall.
Everyone who is either patient or creative is not strong or happy.
If someone is not old then alice is both brave and not generous.
Everyone who is either curious or not calm is curious or not rich.
If someone is either brave or not happy then fred is not humble.
Someone is either not happy or not patient.
Someone is both not rich and not brave.
Lucy is both not creative and not funny.
Someone is both rich and not old.
Someone is either creative or funny.
Fred is both not generous and not curious.
Paul is not humble. | Paul is tall. | contradiction | (![X]:(~happy(X)<=>(rich(X)&humble(X))))&
(![X]:(~tall(X)<=>(generous(X)&~old(X))))&
(![X]:(~patient(X)<=>~creative(X)))&
(![X]:(curious(X)<=>~kind(X)))&
(![X]:((~brave(X)&brave(X))<=>(~rich(X)&creative(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((generous(X)<~>~patient(X)))))&
(![X]:(kind(X)=>(~generous(X)<~>old(X))))&
(((~rich(lucy)|~funny(lucy)))<=>((~creative(susan)|~happy(susan))))&
(![X]:(~patient(X)<=>(creative(X)<~>calm(X))))&
(((~quiet(lucy)|wise(lucy)))<=>((~funny(lucy)<~>strong(lucy))))&
((?[X]:((calm(X)&creative(X))))<=>(~rich(fred)))&
(![X]:((happy(X)&~patient(X))=>(generous(X)&~tall(X))))&
(![X]:((patient(X)<~>creative(X))=>(~strong(X)|happy(X))))&
((?[X]:(~old(X)))=>((brave(alice)&~generous(alice))))&
(![X]:((curious(X)<~>~calm(X))=>(curious(X)|~rich(X))))&
((?[X]:((brave(X)<~>~happy(X))))=>(~humble(fred)))&
(?[X]:((~happy(X)<~>~patient(X))))&
(?[X]:((~rich(X)&~brave(X))))&
((~creative(lucy)&~funny(lucy)))&
(?[X]:((rich(X)&~old(X))))&
(?[X]:((creative(X)<~>funny(X))))&
((~generous(fred)&~curious(fred)))&
(~humble(paul)) | tall(paul) | [
"p0",
"p2",
"p4",
"p8",
"p10",
"p11",
"p21",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7756024723665855971511101
% SZS output start Proof for 7756024723665855971511101
1. ! [X0] : (~happy(X0) <=> (humble(X0) & rich(X0))) [input p0]
3. ! [X0] : (~patient(X0) <=> ~creative(X0)) [input p2]
5. ! [X0] : ((brave(X0) & ~brave(X0)) <=> (creative(X0) & ~rich(X0))) [input p4]
9. ! [X0] : (~patient(X0) <=> (creative(X0) <~> calm(X0))) [input p8]
11. ? [X0] : (creative(X0) & calm(X0)) <=> ~rich(fred) [input p10]
12. ! [X0] : ((~patient(X0) & happy(X0)) => (~tall(X0) & generous(X0))) [input p11]
22. ~curious(fred) & ~generous(fred) [input p21]
23. ~humble(paul) [input p22]
24. tall(paul) [input hypothesis]
27. ! [X0] : ((~tall(X0) & generous(X0)) | (patient(X0) | ~happy(X0))) [ennf transformation 12]
28. ! [X0] : ((~tall(X0) & generous(X0)) | patient(X0) | ~happy(X0)) [flattening 27]
35. ! [X0] : ((~happy(X0) | (~humble(X0) | ~rich(X0))) & ((humble(X0) & rich(X0)) | happy(X0))) [nnf transformation 1]
36. ! [X0] : ((~happy(X0) | ~humble(X0) | ~rich(X0)) & ((humble(X0) & rich(X0)) | happy(X0))) [flattening 35]
39. ! [X0] : ((~patient(X0) | creative(X0)) & (~creative(X0) | patient(X0))) [nnf transformation 3]
41. ! [X0] : (((brave(X0) & ~brave(X0)) | (~creative(X0) | rich(X0))) & ((creative(X0) & ~rich(X0)) | (~brave(X0) | brave(X0)))) [nnf transformation 5]
42. ! [X0] : (((brave(X0) & ~brave(X0)) | ~creative(X0) | rich(X0)) & ((creative(X0) & ~rich(X0)) | ~brave(X0) | brave(X0))) [flattening 41]
51. ! [X0] : ((~patient(X0) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) & (((~calm(X0) | ~creative(X0)) & (calm(X0) | creative(X0))) | patient(X0))) [nnf transformation 9]
54. (? [X0] : (creative(X0) & calm(X0)) | rich(fred)) & (~rich(fred) | ! [X0] : (~creative(X0) | ~calm(X0))) [nnf transformation 11]
55. (? [X0] : (creative(X0) & calm(X0)) | rich(fred)) & (~rich(fred) | ! [X1] : (~creative(X1) | ~calm(X1))) [rectify 54]
56. ? [X0] : (creative(X0) & calm(X0)) => (creative(sK2) & calm(sK2)) [choice axiom]
57. ((creative(sK2) & calm(sK2)) | rich(fred)) & (~rich(fred) | ! [X1] : (~creative(X1) | ~calm(X1))) [skolemisation 55,56]
71. rich(X0) | happy(X0) [cnf transformation 36]
72. humble(X0) | happy(X0) [cnf transformation 36]
77. ~creative(X0) | patient(X0) [cnf transformation 39]
78. ~patient(X0) | creative(X0) [cnf transformation 39]
83. ~brave(X0) | ~creative(X0) | rich(X0) [cnf transformation 42]
84. ~creative(X0) | brave(X0) | rich(X0) [cnf transformation 42]
95. calm(X0) | creative(X0) | patient(X0) [cnf transformation 51]
97. ~patient(X0) | calm(X0) | ~creative(X0) [cnf transformation 51]
105. ~rich(fred) | ~creative(X1) | ~calm(X1) [cnf transformation 57]
108. ~happy(X0) | patient(X0) | generous(X0) [cnf transformation 28]
109. ~tall(X0) | patient(X0) | ~happy(X0) [cnf transformation 28]
128. ~generous(fred) [cnf transformation 22]
130. ~humble(paul) [cnf transformation 23]
131. tall(paul) [cnf transformation 24]
133. ~creative(X0) | rich(X0) [subsumption resolution 83,84]
179. ~creative(X0) | calm(X0) [subsumption resolution 97,77]
180. calm(X0) | creative(X0) [subsumption resolution 95,78]
181. calm(X0) [subsumption resolution 180,179]
201. 14 <=> rich(fred) [avatar definition]
202. ~rich(fred) <- (~14) [avatar component clause 201]
209. ~rich(fred) | ~creative(X1) [subsumption resolution 105,181]
211. 16 <=> ! [X1] : ~creative(X1) [avatar definition]
212. ~creative(X1) <- (16) [avatar component clause 211]
213. 16 | ~14 [avatar split clause 209,201,211]
263. happy(fred) <- (~14) [resolution 71,202]
264. happy(paul) [resolution 72,130]
284. patient(fred) | generous(fred) <- (~14) [resolution 108,263]
288. patient(fred) <- (~14) [subsumption resolution 284,128]
294. 28 <=> patient(paul) [avatar definition]
296. patient(paul) <- (28) [avatar component clause 294]
310. patient(paul) | ~happy(paul) [resolution 109,131]
321. patient(paul) [subsumption resolution 310,264]
322. 28 [avatar split clause 321,294]
357. creative(fred) <- (~14) [resolution 288,78]
371. creative(paul) <- (28) [resolution 296,78]
390. rich(fred) <- (~14) [resolution 357,133]
393. $false <- (~14) [subsumption resolution 390,202]
394. 14 [avatar contradiction clause 393]
426. $false <- (16, 28) [resolution 371,212]
431. ~16 | ~28 [avatar contradiction clause 426]
442. $false [avatar sat refutation 213,322,394,431]
% SZS output end Proof for 7756024723665855971511101
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not strong is either not wise or not curious and vice versa.
Everyone who is both not strong and happy is funny or not strong and vice versa.
Everyone who is both not patient and happy is both tall and not wise.
Everyone who is strong or not rich is not funny or patient.
If someone is either happy or not tall then someone is not rich and vice versa.
Everyone who is not happy or quiet is both not brave and funny.
Everyone who is both not creative and not humble is not calm or not rich.
Everyone who is either curious or not funny is not rich or rich and vice versa.
Everyone who is not creative or wise is not creative.
Everyone who is not strong is either not quiet or rich.
Everyone who is curious or happy is not rich and vice versa.
Everyone who is not creative is either strong or not patient.
If fred is creative or funny then someone is not brave or not funny.
Everyone who is not kind or not brave is both not quiet and creative.
Everyone who is patient is both not rich and not patient.
Everyone who is not brave or not old is either not wise or tall.
Someone is either not calm or kind.
Susan is not old or not generous.
Lucy is not patient.
Paul is either happy or quiet.
Paul is creative or not happy.
Lucy is either calm or funny. | Lucy is curious. | contradiction | (![X]:((quiet(X)|~strong(X))<=>(~wise(X)<~>~curious(X))))&
(![X]:((~strong(X)&happy(X))<=>(funny(X)|~strong(X))))&
(![X]:((~patient(X)&happy(X))=>(tall(X)&~wise(X))))&
(![X]:((strong(X)|~rich(X))=>(~funny(X)|patient(X))))&
((?[X]:((happy(X)<~>~tall(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~happy(X)|quiet(X))=>(~brave(X)&funny(X))))&
(![X]:((~creative(X)&~humble(X))=>(~calm(X)|~rich(X))))&
(![X]:((curious(X)<~>~funny(X))<=>(~rich(X)|rich(X))))&
(![X]:((~creative(X)|wise(X))=>~creative(X)))&
(![X]:(~strong(X)=>(~quiet(X)<~>rich(X))))&
(![X]:((curious(X)|happy(X))<=>~rich(X)))&
(![X]:(~creative(X)=>(strong(X)<~>~patient(X))))&
(((creative(fred)|funny(fred)))=>(?[X]:((~brave(X)|~funny(X)))))&
(![X]:((~kind(X)|~brave(X))=>(~quiet(X)&creative(X))))&
(![X]:(patient(X)=>(~rich(X)&~patient(X))))&
(![X]:((~brave(X)|~old(X))=>(~wise(X)<~>tall(X))))&
(?[X]:((~calm(X)<~>kind(X))))&
((~old(susan)|~generous(susan)))&
(~patient(lucy))&
((happy(paul)<~>quiet(paul)))&
((creative(paul)|~happy(paul)))&
((calm(lucy)<~>funny(lucy))) | curious(lucy) | [
"p1",
"p3",
"p5",
"p7",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7669428075147848697811649
% SZS output start Proof for 7669428075147848697811649
2. ! [X0] : ((happy(X0) & ~strong(X0)) <=> (~strong(X0) | funny(X0))) [input p1]
4. ! [X0] : ((~rich(X0) | strong(X0)) => (patient(X0) | ~funny(X0))) [input p3]
6. ! [X0] : ((quiet(X0) | ~happy(X0)) => (funny(X0) & ~brave(X0))) [input p5]
8. ! [X0] : ((curious(X0) <~> ~funny(X0)) <=> (rich(X0) | ~rich(X0))) [input p7]
11. ! [X0] : ((happy(X0) | curious(X0)) <=> ~rich(X0)) [input p10]
15. ! [X0] : (patient(X0) => (~patient(X0) & ~rich(X0))) [input p14]
23. curious(lucy) [input hypothesis]
30. ! [X0] : ((patient(X0) | ~funny(X0)) | (rich(X0) & ~strong(X0))) [ennf transformation 4]
31. ! [X0] : (patient(X0) | ~funny(X0) | (rich(X0) & ~strong(X0))) [flattening 30]
32. ! [X0] : ((funny(X0) & ~brave(X0)) | (~quiet(X0) & happy(X0))) [ennf transformation 6]
38. ! [X0] : ((~patient(X0) & ~rich(X0)) | ~patient(X0)) [ennf transformation 15]
42. ! [X0] : (((happy(X0) & ~strong(X0)) | (strong(X0) & ~funny(X0))) & ((~strong(X0) | funny(X0)) | (~happy(X0) | strong(X0)))) [nnf transformation 2]
43. ! [X0] : (((happy(X0) & ~strong(X0)) | (strong(X0) & ~funny(X0))) & (~strong(X0) | funny(X0) | ~happy(X0) | strong(X0))) [flattening 42]
49. ! [X0] : ((((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (~rich(X0) & rich(X0))) & ((rich(X0) | ~rich(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0))))) [nnf transformation 8]
50. ! [X0] : ((((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (~rich(X0) & rich(X0))) & (rich(X0) | ~rich(X0) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0))))) [flattening 49]
52. ! [X0] : (((happy(X0) | curious(X0)) | rich(X0)) & (~rich(X0) | (~happy(X0) & ~curious(X0)))) [nnf transformation 11]
53. ! [X0] : ((happy(X0) | curious(X0) | rich(X0)) & (~rich(X0) | (~happy(X0) & ~curious(X0)))) [flattening 52]
72. ~funny(X0) | happy(X0) [cnf transformation 43]
77. ~funny(X0) | patient(X0) | rich(X0) [cnf transformation 31]
84. funny(X0) | happy(X0) [cnf transformation 32]
90. funny(X0) | ~curious(X0) | rich(X0) [cnf transformation 50]
91. funny(X0) | ~curious(X0) | ~rich(X0) [cnf transformation 50]
97. ~rich(X0) | ~happy(X0) [cnf transformation 53]
108. ~patient(X0) | ~patient(X0) [cnf transformation 38]
119. curious(lucy) [cnf transformation 23]
120. ~patient(X0) [duplicate literal removal 108]
146. happy(X0) [subsumption resolution 84,72]
147. ~curious(X0) | funny(X0) [subsumption resolution 90,91]
149. ~rich(X0) [subsumption resolution 97,146]
185. 14 <=> funny(lucy) [avatar definition]
186. funny(lucy) <- (14) [avatar component clause 185]
196. funny(lucy) [resolution 147,119]
199. 14 [avatar split clause 196,185]
218. patient(lucy) | rich(lucy) <- (14) [resolution 77,186]
219. rich(lucy) <- (14) [subsumption resolution 218,120]
220. $false <- (14) [subsumption resolution 219,149]
221. ~14 [avatar contradiction clause 220]
222. $false [avatar sat refutation 199,221]
% SZS output end Proof for 7669428075147848697811649
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not tall is either not quiet or not creative.
Everyone who is both not kind and not rich is both kind and creative.
If someone is both curious and not humble then someone is either kind or not funny and vice versa.
If lucy is rich or not creative then someone is not old and vice versa.
Everyone who is strong is not wise or not rich and vice versa.
If someone is strong or not curious then lucy is either rich or not brave.
If someone is both not calm and wise then someone is both not funny and happy and vice versa.
Everyone who is not strong is not humble and vice versa.
If someone is curious or humble then paul is not old or not wise and vice versa.
Everyone who is both not funny and funny is either humble or not patient and vice versa.
If someone is either wise or not patient then someone is kind or not creative.
If someone is rich or creative then susan is either not creative or not generous.
Everyone who is not wise is either generous or humble and vice versa.
If someone is either not humble or not strong then mary is either not rich or wise.
If lucy is not curious then paul is wise and vice versa.
Everyone who is either happy or brave is not creative.
Someone is happy or not brave.
Someone is not brave or not wise.
Lucy is not strong.
Susan is either not calm or not funny.
Alice is not strong or happy.
Someone is not tall.
Someone is not calm. | Lucy is patient. | entailment | (![X]:((~old(X)|~tall(X))=>(~quiet(X)<~>~creative(X))))&
(![X]:((~kind(X)&~rich(X))=>(kind(X)&creative(X))))&
((?[X]:((curious(X)&~humble(X))))<=>(?[X]:((kind(X)<~>~funny(X)))))&
(((rich(lucy)|~creative(lucy)))<=>(?[X]:(~old(X))))&
(![X]:(strong(X)<=>(~wise(X)|~rich(X))))&
((?[X]:((strong(X)|~curious(X))))=>((rich(lucy)<~>~brave(lucy))))&
((?[X]:((~calm(X)&wise(X))))<=>(?[X]:((~funny(X)&happy(X)))))&
(![X]:(~strong(X)<=>~humble(X)))&
((?[X]:((curious(X)|humble(X))))<=>((~old(paul)|~wise(paul))))&
(![X]:((~funny(X)&funny(X))<=>(humble(X)<~>~patient(X))))&
((?[X]:((wise(X)<~>~patient(X))))=>(?[X]:((kind(X)|~creative(X)))))&
((?[X]:((rich(X)|creative(X))))=>((~creative(susan)<~>~generous(susan))))&
(![X]:(~wise(X)<=>(generous(X)<~>humble(X))))&
((?[X]:((~humble(X)<~>~strong(X))))=>((~rich(mary)<~>wise(mary))))&
((~curious(lucy))<=>(wise(paul)))&
(![X]:((happy(X)<~>brave(X))=>~creative(X)))&
(?[X]:((happy(X)|~brave(X))))&
(?[X]:((~brave(X)|~wise(X))))&
(~strong(lucy))&
((~calm(susan)<~>~funny(susan)))&
((~strong(alice)|happy(alice)))&
(?[X]:(~tall(X)))&
(?[X]:(~calm(X))) | patient(lucy) | [
"p7",
"p9",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6794640231431859374740665
% SZS output start Proof for 6794640231431859374740665
8. ! [X0] : (~strong(X0) <=> ~humble(X0)) [input p7]
10. ! [X0] : ((funny(X0) & ~funny(X0)) <=> (humble(X0) <~> ~patient(X0))) [input p9]
19. ~strong(lucy) [input p18]
24. ~patient(lucy) [input hypothesis]
55. ! [X0] : ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))) [nnf transformation 8]
61. ! [X0] : (((funny(X0) & ~funny(X0)) | ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0)))) & (((patient(X0) | ~humble(X0)) & (~patient(X0) | humble(X0))) | (~funny(X0) | funny(X0)))) [nnf transformation 10]
62. ! [X0] : (((funny(X0) & ~funny(X0)) | ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0)))) & (((patient(X0) | ~humble(X0)) & (~patient(X0) | humble(X0))) | ~funny(X0) | funny(X0))) [flattening 61]
107. ~humble(X0) | strong(X0) [cnf transformation 55]
116. ~funny(X0) | humble(X0) | patient(X0) [cnf transformation 62]
118. funny(X0) | humble(X0) | patient(X0) [cnf transformation 62]
139. ~strong(lucy) [cnf transformation 19]
145. ~patient(lucy) [cnf transformation 24]
262. patient(X0) | humble(X0) [subsumption resolution 116,118]
349. humble(lucy) [resolution 262,145]
350. strong(lucy) [resolution 349,107]
351. $false [subsumption resolution 350,139]
% SZS output end Proof for 6794640231431859374740665
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or creative is happy or not generous. Everyone who is rich or wise is not creative or happy and vice versa. Everyone who is either not patient or not brave is creative or not tall. Everyone who is funny is not quiet or rich and vice versa. If lucy is wise then someone is both wise and not patient. Everyone who is happy or not calm is both not strong and humble and vice versa. Everyone who is tall or not brave is either rich or not curious and vice versa. Everyone who is rich or tall is either not curious or happy and vice versa. Everyone who is either calm or not humble is rich or brave and vice versa. Everyone who is not curious is either not tall or humble. Everyone who is both not brave and not old is either not calm or not wise and vice versa. If someone is both not generous and not strong then alice is either strong or patient and vice versa. If lucy is either old or humble then someone is both old and not kind and vice versa. Everyone who is not wise or creative is curious or not kind and vice versa. Everyone who is not happy is not brave and vice versa. Someone is not funny or calm. Alice is not humble or brave. John is not old or not brave. Someone is either not generous or not curious. Mary is old or not patient. Someone is either not patient or tall. Someone is not rich or not humble. | Alice is not funny. | contradiction | (![X]:((quiet(X)<~>creative(X))=>(happy(X)|~generous(X))))&
(![X]:((rich(X)|wise(X))<=>(~creative(X)|happy(X))))&
(![X]:((~patient(X)<~>~brave(X))=>(creative(X)|~tall(X))))&
(![X]:(funny(X)<=>(~quiet(X)|rich(X))))&
((wise(lucy))=>(?[X]:((wise(X)&~patient(X)))))&
(![X]:((happy(X)|~calm(X))<=>(~strong(X)&humble(X))))&
(![X]:((tall(X)|~brave(X))<=>(rich(X)<~>~curious(X))))&
(![X]:((rich(X)|tall(X))<=>(~curious(X)<~>happy(X))))&
(![X]:((calm(X)<~>~humble(X))<=>(rich(X)|brave(X))))&
(![X]:(~curious(X)=>(~tall(X)<~>humble(X))))&
(![X]:((~brave(X)&~old(X))<=>(~calm(X)<~>~wise(X))))&
((?[X]:((~generous(X)&~strong(X))))<=>((strong(alice)<~>patient(alice))))&
(((old(lucy)<~>humble(lucy)))<=>(?[X]:((old(X)&~kind(X)))))&
(![X]:((~wise(X)|creative(X))<=>(curious(X)|~kind(X))))&
(![X]:(~happy(X)<=>~brave(X)))&
(?[X]:((~funny(X)|calm(X))))&
((~humble(alice)|brave(alice)))&
((~old(john)|~brave(john)))&
(?[X]:((~generous(X)<~>~curious(X))))&
((old(mary)|~patient(mary)))&
(?[X]:((~patient(X)<~>tall(X))))&
(?[X]:((~rich(X)|~humble(X)))) | ~funny(alice) | [
"p3",
"p5",
"p6",
"p7",
"p8",
"p9",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1242113503079972648966514
% SZS output start Proof for 1242113503079972648966514
4. ! [X0] : (funny(X0) <=> (rich(X0) | ~quiet(X0))) [input p3]
6. ! [X0] : ((~calm(X0) | happy(X0)) <=> (humble(X0) & ~strong(X0))) [input p5]
7. ! [X0] : ((~brave(X0) | tall(X0)) <=> (rich(X0) <~> ~curious(X0))) [input p6]
8. ! [X0] : ((tall(X0) | rich(X0)) <=> (~curious(X0) <~> happy(X0))) [input p7]
9. ! [X0] : ((calm(X0) <~> ~humble(X0)) <=> (brave(X0) | rich(X0))) [input p8]
10. ! [X0] : (~curious(X0) => (~tall(X0) <~> humble(X0))) [input p9]
15. ! [X0] : (~happy(X0) <=> ~brave(X0)) [input p14]
17. brave(alice) | ~humble(alice) [input p16]
23. ~funny(alice) [input hypothesis]
24. ! [X0] : ((rich(X0) | ~quiet(X0)) => funny(X0)) [unused predicate definition removal 4]
29. ! [X0] : (funny(X0) | (~rich(X0) & quiet(X0))) [ennf transformation 24]
31. ! [X0] : ((~tall(X0) <~> humble(X0)) | curious(X0)) [ennf transformation 10]
38. ! [X0] : (((~calm(X0) | happy(X0)) | (~humble(X0) | strong(X0))) & ((humble(X0) & ~strong(X0)) | (calm(X0) & ~happy(X0)))) [nnf transformation 6]
39. ! [X0] : ((~calm(X0) | happy(X0) | ~humble(X0) | strong(X0)) & ((humble(X0) & ~strong(X0)) | (calm(X0) & ~happy(X0)))) [flattening 38]
40. ! [X0] : (((~brave(X0) | tall(X0)) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0)))) & (((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | (brave(X0) & ~tall(X0)))) [nnf transformation 7]
41. ! [X0] : ((~brave(X0) | tall(X0) | ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0)))) & (((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | (brave(X0) & ~tall(X0)))) [flattening 40]
42. ! [X0] : (((tall(X0) | rich(X0)) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0)))) & (((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (~tall(X0) & ~rich(X0)))) [nnf transformation 8]
43. ! [X0] : ((tall(X0) | rich(X0) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0)))) & (((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | (~tall(X0) & ~rich(X0)))) [flattening 42]
44. ! [X0] : ((((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | (~brave(X0) & ~rich(X0))) & ((brave(X0) | rich(X0)) | ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0))))) [nnf transformation 9]
45. ! [X0] : ((((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | (~brave(X0) & ~rich(X0))) & (brave(X0) | rich(X0) | ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0))))) [flattening 44]
46. ! [X0] : (((~humble(X0) | tall(X0)) & (humble(X0) | ~tall(X0))) | curious(X0)) [nnf transformation 31]
59. ! [X0] : ((~happy(X0) | brave(X0)) & (~brave(X0) | happy(X0))) [nnf transformation 15]
79. ~rich(X0) | funny(X0) [cnf transformation 29]
85. humble(X0) | calm(X0) [cnf transformation 39]
87. ~curious(X0) | rich(X0) | ~tall(X0) [cnf transformation 41]
88. ~curious(X0) | rich(X0) | brave(X0) [cnf transformation 41]
96. ~tall(X0) | curious(X0) | ~happy(X0) [cnf transformation 43]
97. curious(X0) | rich(X0) | happy(X0) | tall(X0) [cnf transformation 43]
98. tall(X0) | rich(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 43]
103. humble(X0) | ~calm(X0) | ~rich(X0) [cnf transformation 45]
104. humble(X0) | ~calm(X0) | ~brave(X0) [cnf transformation 45]
105. ~tall(X0) | humble(X0) | curious(X0) [cnf transformation 46]
106. ~humble(X0) | tall(X0) | curious(X0) [cnf transformation 46]
129. ~brave(X0) | happy(X0) [cnf transformation 59]
130. ~happy(X0) | brave(X0) [cnf transformation 59]
132. brave(alice) | ~humble(alice) [cnf transformation 17]
140. ~funny(alice) [cnf transformation 23]
155. ~curious(X0) | rich(X0) | ~happy(X0) [subsumption resolution 98,87]
156. ~brave(X0) | humble(X0) [subsumption resolution 104,85]
157. ~rich(X0) | humble(X0) [subsumption resolution 103,85]
222. 16 <=> humble(alice) [avatar definition]
224. ~humble(alice) <- (~16) [avatar component clause 222]
226. 17 <=> brave(alice) [avatar definition]
228. brave(alice) <- (17) [avatar component clause 226]
229. ~16 | 17 [avatar split clause 132,226,222]
387. rich(X1) | happy(X1) | tall(X1) | rich(X1) | brave(X1) [resolution 97,88]
398. rich(X1) | happy(X1) | tall(X1) | brave(X1) [duplicate literal removal 387]
400. tall(X1) | rich(X1) | brave(X1) [subsumption resolution 398,130]
485. rich(X2) | brave(X2) | humble(X2) | curious(X2) [resolution 400,105]
498. rich(X2) | humble(X2) | curious(X2) [subsumption resolution 485,156]
499. curious(X2) | humble(X2) [subsumption resolution 498,157]
592. 54 <=> rich(alice) [avatar definition]
593. ~rich(alice) <- (~54) [avatar component clause 592]
594. rich(alice) <- (54) [avatar component clause 592]
653. humble(X1) | rich(X1) | brave(X1) [resolution 499,88]
661. humble(X1) | rich(X1) [subsumption resolution 653,156]
662. humble(X1) [subsumption resolution 661,157]
678. funny(alice) <- (54) [resolution 594,79]
680. 57 <=> happy(alice) [avatar definition]
681. happy(alice) <- (57) [avatar component clause 680]
684. 58 <=> curious(alice) [avatar definition]
686. curious(alice) <- (58) [avatar component clause 684]
690. $false <- (54) [subsumption resolution 678,140]
691. ~54 [avatar contradiction clause 690]
726. curious(X2) | tall(X2) [resolution 662,106]
727. $false <- (~16) [resolution 662,224]
730. 16 [avatar contradiction clause 727]
763. happy(alice) <- (17) [resolution 228,129]
766. 57 | ~17 [avatar split clause 763,226,680]
826. ~happy(X6) | rich(X6) | tall(X6) [resolution 726,155]
997. rich(alice) | tall(alice) <- (57) [resolution 826,681]
999. tall(alice) <- (~54, 57) [subsumption resolution 997,593]
1030. curious(alice) | ~happy(alice) <- (~54, 57) [resolution 999,96]
1032. curious(alice) <- (~54, 57) [subsumption resolution 1030,681]
1033. 58 | 54 | ~57 [avatar split clause 1032,680,592,684]
1040. rich(alice) | ~happy(alice) <- (58) [resolution 686,155]
1044. ~happy(alice) <- (~54, 58) [subsumption resolution 1040,593]
1045. $false <- (~54, 57, 58) [subsumption resolution 1044,681]
1046. 54 | ~57 | ~58 [avatar contradiction clause 1045]
1047. $false [avatar sat refutation 229,691,730,766,1033,1046]
% SZS output end Proof for 1242113503079972648966514
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is both not brave and not happy and vice versa. If john is either strong or humble then fred is both not calm and happy and vice versa. If someone is either not curious or rich then someone is not patient or wise and vice versa. Everyone who is either not strong or not creative is either old or not strong. Everyone who is both wise and not old is both not old and happy and vice versa. Everyone who is creative is not tall or generous and vice versa. Everyone who is not old is both not patient and quiet. If alice is calm then paul is not quiet. Everyone who is both not quiet and patient is not rich or quiet and vice versa. If susan is happy then susan is both not rich and calm. If someone is either not brave or strong then someone is both not kind and rich and vice versa. Everyone who is humble is old and vice versa. Everyone who is quiet or not creative is generous. Everyone who is both not brave and not calm is either strong or patient. If lucy is tall then someone is either not old or not tall. If alice is either not patient or wise then john is either curious or not funny. Someone is both not brave and not wise. Someone is either not creative or not kind. Someone is either tall or wise. John is not tall. Someone is not kind. Someone is either happy or not brave. Fred is either kind or quiet. | Alice is not strong. | contradiction | (![X]:(~generous(X)<=>(~brave(X)&~happy(X))))&
(((strong(john)<~>humble(john)))<=>((~calm(fred)&happy(fred))))&
((?[X]:((~curious(X)<~>rich(X))))<=>(?[X]:((~patient(X)|wise(X)))))&
(![X]:((~strong(X)<~>~creative(X))=>(old(X)<~>~strong(X))))&
(![X]:((wise(X)&~old(X))<=>(~old(X)&happy(X))))&
(![X]:(creative(X)<=>(~tall(X)|generous(X))))&
(![X]:(~old(X)=>(~patient(X)&quiet(X))))&
((calm(alice))=>(~quiet(paul)))&
(![X]:((~quiet(X)&patient(X))<=>(~rich(X)|quiet(X))))&
((happy(susan))=>((~rich(susan)&calm(susan))))&
((?[X]:((~brave(X)<~>strong(X))))<=>(?[X]:((~kind(X)&rich(X)))))&
(![X]:(humble(X)<=>old(X)))&
(![X]:((quiet(X)|~creative(X))=>generous(X)))&
(![X]:((~brave(X)&~calm(X))=>(strong(X)<~>patient(X))))&
((tall(lucy))=>(?[X]:((~old(X)<~>~tall(X)))))&
(((~patient(alice)<~>wise(alice)))=>((curious(john)<~>~funny(john))))&
(?[X]:((~brave(X)&~wise(X))))&
(?[X]:((~creative(X)<~>~kind(X))))&
(?[X]:((tall(X)<~>wise(X))))&
(~tall(john))&
(?[X]:(~kind(X)))&
(?[X]:((happy(X)<~>~brave(X))))&
((kind(fred)<~>quiet(fred))) | ~strong(alice) | [
"p3",
"p5",
"p6",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2040930219164765191887659
% SZS output start Proof for 2040930219164765191887659
4. ! [X0] : ((~strong(X0) <~> ~creative(X0)) => (old(X0) <~> ~strong(X0))) [input p3]
6. ! [X0] : (creative(X0) <=> (generous(X0) | ~tall(X0))) [input p5]
7. ! [X0] : (~old(X0) => (quiet(X0) & ~patient(X0))) [input p6]
9. ! [X0] : ((patient(X0) & ~quiet(X0)) <=> (quiet(X0) | ~rich(X0))) [input p8]
13. ! [X0] : ((~creative(X0) | quiet(X0)) => generous(X0)) [input p12]
24. ~strong(alice) [input hypothesis]
27. ! [X0] : ((old(X0) <~> ~strong(X0)) | (~strong(X0) <=> ~creative(X0))) [ennf transformation 4]
28. ! [X0] : ((quiet(X0) & ~patient(X0)) | old(X0)) [ennf transformation 7]
31. ! [X0] : (generous(X0) | (creative(X0) & ~quiet(X0))) [ennf transformation 13]
45. ! [X0] : (((strong(X0) | ~old(X0)) & (~strong(X0) | old(X0))) | ((~strong(X0) | creative(X0)) & (~creative(X0) | strong(X0)))) [nnf transformation 27]
48. ! [X0] : ((creative(X0) | (~generous(X0) & tall(X0))) & ((generous(X0) | ~tall(X0)) | ~creative(X0))) [nnf transformation 6]
49. ! [X0] : ((creative(X0) | (~generous(X0) & tall(X0))) & (generous(X0) | ~tall(X0) | ~creative(X0))) [flattening 48]
50. ! [X0] : (((patient(X0) & ~quiet(X0)) | (~quiet(X0) & rich(X0))) & ((quiet(X0) | ~rich(X0)) | (~patient(X0) | quiet(X0)))) [nnf transformation 9]
51. ! [X0] : (((patient(X0) & ~quiet(X0)) | (~quiet(X0) & rich(X0))) & (quiet(X0) | ~rich(X0) | ~patient(X0) | quiet(X0))) [flattening 50]
94. strong(X0) | ~old(X0) | ~creative(X0) | strong(X0) [cnf transformation 45]
102. ~generous(X0) | creative(X0) [cnf transformation 49]
104. quiet(X0) | old(X0) [cnf transformation 28]
108. ~quiet(X0) | ~quiet(X0) [cnf transformation 51]
122. generous(X0) | creative(X0) [cnf transformation 31]
143. ~strong(alice) [cnf transformation 24]
145. ~quiet(X0) [duplicate literal removal 108]
147. ~old(X0) | strong(X0) | ~creative(X0) [duplicate literal removal 94]
259. creative(X0) [subsumption resolution 122,102]
318. old(X0) [resolution 104,145]
344. strong(X0) | ~creative(X0) [resolution 147,318]
345. strong(X0) [subsumption resolution 344,259]
349. $false [resolution 345,143]
% SZS output end Proof for 2040930219164765191887659
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and quiet is not tall or rich and vice versa. If someone is both not kind and tall then susan is either not kind or not funny and vice versa. If someone is curious then lucy is not patient or not happy and vice versa. Everyone who is both not quiet and rich is both calm and wise and vice versa. Everyone who is not curious or strong is not quiet and vice versa. Everyone who is rich is tall and vice versa. Everyone who is funny or not curious is both creative and not kind. If someone is either happy or not kind then someone is not old or quiet. Everyone who is funny or not calm is not old or happy and vice versa. If paul is either patient or generous then someone is not strong or creative and vice versa. Everyone who is old is not patient and vice versa. Everyone who is happy or generous is not funny. Everyone who is not humble or kind is both quiet and calm. Everyone who is either not wise or humble is either generous or curious. Everyone who is not tall is not calm and vice versa. If alice is tall then someone is either old or rich. Someone is not old. John is both humble and not happy. Someone is not kind or old. Lucy is not funny or not quiet. Lucy is either brave or not wise. Fred is not kind. Mary is not funny or calm. | John is not tall. | neutral | (![X]:((creative(X)&quiet(X))<=>(~tall(X)|rich(X))))&
((?[X]:((~kind(X)&tall(X))))<=>((~kind(susan)<~>~funny(susan))))&
((?[X]:(curious(X)))<=>((~patient(lucy)|~happy(lucy))))&
(![X]:((~quiet(X)&rich(X))<=>(calm(X)&wise(X))))&
(![X]:((~curious(X)|strong(X))<=>~quiet(X)))&
(![X]:(rich(X)<=>tall(X)))&
(![X]:((funny(X)|~curious(X))=>(creative(X)&~kind(X))))&
((?[X]:((happy(X)<~>~kind(X))))=>(?[X]:((~old(X)|quiet(X)))))&
(![X]:((funny(X)|~calm(X))<=>(~old(X)|happy(X))))&
(((patient(paul)<~>generous(paul)))<=>(?[X]:((~strong(X)|creative(X)))))&
(![X]:(old(X)<=>~patient(X)))&
(![X]:((happy(X)|generous(X))=>~funny(X)))&
(![X]:((~humble(X)|kind(X))=>(quiet(X)&calm(X))))&
(![X]:((~wise(X)<~>humble(X))=>(generous(X)<~>curious(X))))&
(![X]:(~tall(X)<=>~calm(X)))&
((tall(alice))=>(?[X]:((old(X)<~>rich(X)))))&
(?[X]:(~old(X)))&
((humble(john)&~happy(john)))&
(?[X]:((~kind(X)|old(X))))&
((~funny(lucy)|~quiet(lucy)))&
((brave(lucy)<~>~wise(lucy)))&
(~kind(fred))&
((~funny(mary)|calm(mary))) | ~tall(john) | [] | null | 0 |
If someone is not rich then fred is both not patient and patient and vice versa. Everyone who is not calm or not happy is both strong and creative and vice versa. Everyone who is not strong is both kind and not wise. If fred is funny then someone is both tall and strong and vice versa. Everyone who is either humble or rich is not old. Everyone who is not curious is either not old or not patient. Everyone who is calm is both wise and not generous. If someone is not kind or not tall then susan is both not creative and curious and vice versa. Everyone who is not quiet is not patient. Everyone who is either not brave or not tall is both not old and brave. Everyone who is both not generous and not creative is not creative or rich. Everyone who is both tall and quiet is both calm and not wise. Everyone who is not patient or not old is both not old and not kind and vice versa. Everyone who is not tall is either kind or patient. If someone is either humble or generous then lucy is either wise or not tall and vice versa. Everyone who is not curious is either not calm or calm. Mary is curious or tall. Fred is curious or not old. Someone is curious. Paul is old or not kind. Someone is patient. Alice is either calm or tall. Susan is wise. Mary is either curious or wise. | Susan is not generous. | entailment | ((?[X]:(~rich(X)))<=>((~patient(fred)&patient(fred))))&
(![X]:((~calm(X)|~happy(X))<=>(strong(X)&creative(X))))&
(![X]:(~strong(X)=>(kind(X)&~wise(X))))&
((funny(fred))<=>(?[X]:((tall(X)&strong(X)))))&
(![X]:((humble(X)<~>rich(X))=>~old(X)))&
(![X]:(~curious(X)=>(~old(X)<~>~patient(X))))&
(![X]:(calm(X)=>(wise(X)&~generous(X))))&
((?[X]:((~kind(X)|~tall(X))))<=>((~creative(susan)&curious(susan))))&
(![X]:(~quiet(X)=>~patient(X)))&
(![X]:((~brave(X)<~>~tall(X))=>(~old(X)&brave(X))))&
(![X]:((~generous(X)&~creative(X))=>(~creative(X)|rich(X))))&
(![X]:((tall(X)&quiet(X))=>(calm(X)&~wise(X))))&
(![X]:((~patient(X)|~old(X))<=>(~old(X)&~kind(X))))&
(![X]:(~tall(X)=>(kind(X)<~>patient(X))))&
((?[X]:((humble(X)<~>generous(X))))<=>((wise(lucy)<~>~tall(lucy))))&
(![X]:(~curious(X)=>(~calm(X)<~>calm(X))))&
((curious(mary)|tall(mary)))&
((curious(fred)|~old(fred)))&
(?[X]:(curious(X)))&
((old(paul)|~kind(paul)))&
(?[X]:(patient(X)))&
((calm(alice)<~>tall(alice)))&
(wise(susan))&
((curious(mary)<~>wise(mary))) | ~generous(susan) | [
"p1",
"p6",
"p7",
"p8",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 233105327295078953935001
% SZS output start Proof for 233105327295078953935001
2. ! [X0] : ((~happy(X0) | ~calm(X0)) <=> (creative(X0) & strong(X0))) [input p1]
7. ! [X0] : (calm(X0) => (~generous(X0) & wise(X0))) [input p6]
8. ? [X0] : (~tall(X0) | ~kind(X0)) <=> (curious(susan) & ~creative(susan)) [input p7]
9. ! [X0] : (~quiet(X0) => ~patient(X0)) [input p8]
12. ! [X0] : ((quiet(X0) & tall(X0)) => (~wise(X0) & calm(X0))) [input p11]
21. ? [X0] : patient(X0) [input p20]
25. generous(susan) [input hypothesis]
29. ! [X0] : ((~generous(X0) & wise(X0)) | ~calm(X0)) [ennf transformation 7]
30. ! [X0] : (~patient(X0) | quiet(X0)) [ennf transformation 9]
34. ! [X0] : ((~wise(X0) & calm(X0)) | (~quiet(X0) | ~tall(X0))) [ennf transformation 12]
35. ! [X0] : ((~wise(X0) & calm(X0)) | ~quiet(X0) | ~tall(X0)) [flattening 34]
43. ! [X0] : (((~happy(X0) | ~calm(X0)) | (~creative(X0) | ~strong(X0))) & ((creative(X0) & strong(X0)) | (happy(X0) & calm(X0)))) [nnf transformation 2]
44. ! [X0] : ((~happy(X0) | ~calm(X0) | ~creative(X0) | ~strong(X0)) & ((creative(X0) & strong(X0)) | (happy(X0) & calm(X0)))) [flattening 43]
51. (? [X0] : (~tall(X0) | ~kind(X0)) | (~curious(susan) | creative(susan))) & ((curious(susan) & ~creative(susan)) | ! [X0] : (tall(X0) & kind(X0))) [nnf transformation 8]
52. (? [X0] : (~tall(X0) | ~kind(X0)) | ~curious(susan) | creative(susan)) & ((curious(susan) & ~creative(susan)) | ! [X0] : (tall(X0) & kind(X0))) [flattening 51]
53. (? [X0] : (~tall(X0) | ~kind(X0)) | ~curious(susan) | creative(susan)) & ((curious(susan) & ~creative(susan)) | ! [X1] : (tall(X1) & kind(X1))) [rectify 52]
54. ? [X0] : (~tall(X0) | ~kind(X0)) => (~tall(sK2) | ~kind(sK2)) [choice axiom]
55. ((~tall(sK2) | ~kind(sK2)) | ~curious(susan) | creative(susan)) & ((curious(susan) & ~creative(susan)) | ! [X1] : (tall(X1) & kind(X1))) [skolemisation 53,54]
67. ? [X0] : patient(X0) => patient(sK5) [choice axiom]
68. patient(sK5) [skolemisation 21,67]
76. creative(X0) | calm(X0) [cnf transformation 44]
88. ~calm(X0) | wise(X0) [cnf transformation 29]
89. ~generous(X0) | ~calm(X0) [cnf transformation 29]
91. ~creative(susan) | tall(X1) [cnf transformation 55]
95. ~patient(X0) | quiet(X0) [cnf transformation 30]
101. ~quiet(X0) | calm(X0) | ~tall(X0) [cnf transformation 35]
102. ~quiet(X0) | ~wise(X0) | ~tall(X0) [cnf transformation 35]
124. patient(sK5) [cnf transformation 68]
130. generous(susan) [cnf transformation 25]
160. 7 <=> creative(susan) [avatar definition]
161. ~creative(susan) <- (~7) [avatar component clause 160]
177. 11 <=> ! [X1] : tall(X1) [avatar definition]
178. tall(X1) <- (11) [avatar component clause 177]
184. 11 | ~7 [avatar split clause 91,160,177]
252. calm(susan) <- (~7) [resolution 76,161]
258. ~calm(susan) [resolution 89,130]
259. $false <- (~7) [subsumption resolution 258,252]
260. 7 [avatar contradiction clause 259]
268. quiet(sK5) [resolution 95,124]
294. calm(sK5) | ~tall(sK5) [resolution 101,268]
296. calm(sK5) <- (11) [subsumption resolution 294,178]
298. wise(sK5) <- (11) [resolution 296,88]
299. ~wise(sK5) | ~tall(sK5) [resolution 102,268]
301. ~tall(sK5) <- (11) [subsumption resolution 299,298]
302. $false <- (11) [subsumption resolution 301,178]
303. ~11 [avatar contradiction clause 302]
305. $false [avatar sat refutation 184,260,303]
% SZS output end Proof for 233105327295078953935001
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both old and funny then alice is both strong and not curious.
If lucy is both not calm and not patient then someone is both creative and not old and vice versa.
Everyone who is kind or tall is both not tall and old and vice versa.
Everyone who is quiet is both calm and not funny.
If john is either calm or not happy then someone is both humble and creative.
Everyone who is not happy is either not old or funny and vice versa.
Everyone who is curious is either tall or happy.
Everyone who is calm is either not kind or creative and vice versa.
Everyone who is not funny is not curious and vice versa.
Everyone who is both not wise and not humble is both brave and not tall.
If someone is tall or brave then someone is kind or not rich.
Everyone who is both strong and not patient is calm.
If paul is calm then someone is not happy or wise.
If someone is either patient or not funny then someone is generous or not creative.
Everyone who is both generous and not generous is either not curious or tall and vice versa.
If mary is both not patient and not creative then someone is either quiet or happy and vice versa.
John is both not patient and wise.
Someone is either funny or not wise.
Someone is tall or not patient.
Fred is not patient or not wise.
Someone is both curious and not brave.
Someone is both creative and funny. | Lucy is not patient. | entailment | ((?[X]:((old(X)&funny(X))))=>((strong(alice)&~curious(alice))))&
(((~calm(lucy)&~patient(lucy)))<=>(?[X]:((creative(X)&~old(X)))))&
(![X]:((kind(X)|tall(X))<=>(~tall(X)&old(X))))&
(![X]:(quiet(X)=>(calm(X)&~funny(X))))&
(((calm(john)<~>~happy(john)))=>(?[X]:((humble(X)&creative(X)))))&
(![X]:(~happy(X)<=>(~old(X)<~>funny(X))))&
(![X]:(curious(X)=>(tall(X)<~>happy(X))))&
(![X]:(calm(X)<=>(~kind(X)<~>creative(X))))&
(![X]:(~funny(X)<=>~curious(X)))&
(![X]:((~wise(X)&~humble(X))=>(brave(X)&~tall(X))))&
((?[X]:((tall(X)|brave(X))))=>(?[X]:((kind(X)|~rich(X)))))&
(![X]:((strong(X)&~patient(X))=>calm(X)))&
((calm(paul))=>(?[X]:((~happy(X)|wise(X)))))&
((?[X]:((patient(X)<~>~funny(X))))=>(?[X]:((generous(X)|~creative(X)))))&
(![X]:((generous(X)&~generous(X))<=>(~curious(X)<~>tall(X))))&
(((~patient(mary)&~creative(mary)))<=>(?[X]:((quiet(X)<~>happy(X)))))&
((~patient(john)&wise(john)))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:((tall(X)|~patient(X))))&
((~patient(fred)|~wise(fred)))&
(?[X]:((curious(X)&~brave(X))))&
(?[X]:((creative(X)&funny(X)))) | ~patient(lucy) | [
"p0",
"p1",
"p2",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 554881186700308426829086
% SZS output start Proof for 554881186700308426829086
1. ? [X0] : (funny(X0) & old(X0)) => (~curious(alice) & strong(alice)) [input p0]
2. (~patient(lucy) & ~calm(lucy)) <=> ? [X0] : (~old(X0) & creative(X0)) [input p1]
3. ! [X0] : ((tall(X0) | kind(X0)) <=> (old(X0) & ~tall(X0))) [input p2]
15. ! [X0] : ((~generous(X0) & generous(X0)) <=> (~curious(X0) <~> tall(X0))) [input p14]
22. ? [X0] : (funny(X0) & creative(X0)) [input p21]
23. patient(lucy) [input hypothesis]
30. (~curious(alice) & strong(alice)) | ! [X0] : (~funny(X0) | ~old(X0)) [ennf transformation 1]
38. ((~patient(lucy) & ~calm(lucy)) | ! [X0] : (old(X0) | ~creative(X0))) & (? [X0] : (~old(X0) & creative(X0)) | (patient(lucy) | calm(lucy))) [nnf transformation 2]
39. ((~patient(lucy) & ~calm(lucy)) | ! [X0] : (old(X0) | ~creative(X0))) & (? [X0] : (~old(X0) & creative(X0)) | patient(lucy) | calm(lucy)) [flattening 38]
40. ((~patient(lucy) & ~calm(lucy)) | ! [X0] : (old(X0) | ~creative(X0))) & (? [X1] : (~old(X1) & creative(X1)) | patient(lucy) | calm(lucy)) [rectify 39]
41. ? [X1] : (~old(X1) & creative(X1)) => (~old(sK0) & creative(sK0)) [choice axiom]
42. ((~patient(lucy) & ~calm(lucy)) | ! [X0] : (old(X0) | ~creative(X0))) & ((~old(sK0) & creative(sK0)) | patient(lucy) | calm(lucy)) [skolemisation 40,41]
43. ! [X0] : (((tall(X0) | kind(X0)) | (~old(X0) | tall(X0))) & ((old(X0) & ~tall(X0)) | (~tall(X0) & ~kind(X0)))) [nnf transformation 3]
44. ! [X0] : ((tall(X0) | kind(X0) | ~old(X0) | tall(X0)) & ((old(X0) & ~tall(X0)) | (~tall(X0) & ~kind(X0)))) [flattening 43]
58. ! [X0] : (((~generous(X0) & generous(X0)) | ((~curious(X0) | ~tall(X0)) & (tall(X0) | curious(X0)))) & (((~tall(X0) | curious(X0)) & (tall(X0) | ~curious(X0))) | (generous(X0) | ~generous(X0)))) [nnf transformation 15]
59. ! [X0] : (((~generous(X0) & generous(X0)) | ((~curious(X0) | ~tall(X0)) & (tall(X0) | curious(X0)))) & (((~tall(X0) | curious(X0)) & (tall(X0) | ~curious(X0))) | generous(X0) | ~generous(X0))) [flattening 58]
72. ? [X0] : (funny(X0) & creative(X0)) => (funny(sK8) & creative(sK8)) [choice axiom]
73. funny(sK8) & creative(sK8) [skolemisation 22,72]
75. ~curious(alice) | ~funny(X0) | ~old(X0) [cnf transformation 30]
79. ~patient(lucy) | old(X0) | ~creative(X0) [cnf transformation 42]
81. ~tall(X0) | ~tall(X0) [cnf transformation 44]
107. generous(X0) | tall(X0) | curious(X0) [cnf transformation 59]
109. ~generous(X0) | tall(X0) | curious(X0) [cnf transformation 59]
124. creative(sK8) [cnf transformation 73]
125. funny(sK8) [cnf transformation 73]
126. patient(lucy) [cnf transformation 23]
127. ~tall(X0) [duplicate literal removal 81]
130. 1 <=> ! [X0] : (~funny(X0) | ~old(X0)) [avatar definition]
131. ~funny(X0) | ~old(X0) <- (1) [avatar component clause 130]
133. 2 <=> curious(alice) [avatar definition]
135. ~curious(alice) <- (~2) [avatar component clause 133]
136. 1 | ~2 [avatar split clause 75,133,130]
143. 4 <=> ! [X0] : (old(X0) | ~creative(X0)) [avatar definition]
144. ~creative(X0) | old(X0) <- (4) [avatar component clause 143]
146. 5 <=> patient(lucy) [avatar definition]
149. 4 | ~5 [avatar split clause 79,146,143]
209. ~generous(X0) | curious(X0) [subsumption resolution 109,127]
210. generous(X0) | curious(X0) [subsumption resolution 107,127]
211. curious(X0) [subsumption resolution 210,209]
260. 5 [avatar split clause 126,146]
261. $false <- (~2) [subsumption resolution 135,211]
262. 2 [avatar contradiction clause 261]
268. ~old(sK8) <- (1) [resolution 131,125]
270. old(sK8) <- (4) [resolution 144,124]
272. $false <- (1, 4) [subsumption resolution 270,268]
273. ~1 | ~4 [avatar contradiction clause 272]
276. $false [avatar sat refutation 136,149,260,262,273]
% SZS output end Proof for 554881186700308426829086
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or funny is both not quiet and quiet. Everyone who is both not humble and tall is quiet or wise. If mary is creative or not kind then someone is kind or not happy and vice versa. If someone is kind then mary is both not brave and not generous. Everyone who is generous or tall is either wise or not quiet and vice versa. Everyone who is both quiet and patient is either calm or not generous. If someone is tall or not rich then someone is both not old and generous. Everyone who is funny or kind is either not rich or generous. If someone is either not old or not wise then someone is not old and vice versa. Everyone who is old is not wise or not kind and vice versa. If lucy is not patient or generous then lucy is either strong or old and vice versa. Everyone who is either funny or not funny is either rich or not generous and vice versa. If someone is either creative or brave then fred is either curious or patient and vice versa. Everyone who is both not calm and not funny is generous and vice versa. Everyone who is either not tall or not creative is either not old or not happy and vice versa. John is brave. Alice is either not patient or not happy. Fred is not kind. Someone is either quiet or not humble. | John is not kind. | entailment | (![X]:((kind(X)<~>funny(X))=>(~quiet(X)&quiet(X))))&
(![X]:((~humble(X)&tall(X))=>(quiet(X)|wise(X))))&
(((creative(mary)|~kind(mary)))<=>(?[X]:((kind(X)|~happy(X)))))&
((?[X]:(kind(X)))=>((~brave(mary)&~generous(mary))))&
(![X]:((generous(X)|tall(X))<=>(wise(X)<~>~quiet(X))))&
(![X]:((quiet(X)&patient(X))=>(calm(X)<~>~generous(X))))&
((?[X]:((tall(X)|~rich(X))))=>(?[X]:((~old(X)&generous(X)))))&
(![X]:((funny(X)|kind(X))=>(~rich(X)<~>generous(X))))&
((?[X]:((~old(X)<~>~wise(X))))<=>(?[X]:(~old(X))))&
(![X]:(old(X)<=>(~wise(X)|~kind(X))))&
(((~patient(lucy)|generous(lucy)))<=>((strong(lucy)<~>old(lucy))))&
(![X]:((funny(X)<~>~funny(X))<=>(rich(X)<~>~generous(X))))&
((?[X]:((creative(X)<~>brave(X))))<=>((curious(fred)<~>patient(fred))))&
(![X]:((~calm(X)&~funny(X))<=>generous(X)))&
(![X]:((~tall(X)<~>~creative(X))<=>(~old(X)<~>~happy(X))))&
(brave(john))&
((~patient(alice)<~>~happy(alice)))&
(~kind(fred))&
(?[X]:((quiet(X)<~>~humble(X)))) | ~kind(john) | [
"p0",
"p3",
"p6",
"p7",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5134348389876536789576780
% SZS output start Proof for 5134348389876536789576780
1. ! [X0] : ((kind(X0) <~> funny(X0)) => (quiet(X0) & ~quiet(X0))) [input p0]
4. ? [X0] : kind(X0) => (~generous(mary) & ~brave(mary)) [input p3]
7. ? [X0] : (~rich(X0) | tall(X0)) => ? [X0] : (generous(X0) & ~old(X0)) [input p6]
8. ! [X0] : ((kind(X0) | funny(X0)) => (~rich(X0) <~> generous(X0))) [input p7]
10. ! [X0] : (old(X0) <=> (~kind(X0) | ~wise(X0))) [input p9]
12. ! [X0] : ((funny(X0) <~> ~funny(X0)) <=> (rich(X0) <~> ~generous(X0))) [input p11]
14. ! [X0] : ((~funny(X0) & ~calm(X0)) <=> generous(X0)) [input p13]
20. kind(john) [input hypothesis]
21. ? [X0] : (~rich(X0) | tall(X0)) => ? [X1] : (generous(X1) & ~old(X1)) [rectify 7]
23. ! [X0] : ((quiet(X0) & ~quiet(X0)) | (kind(X0) <=> funny(X0))) [ennf transformation 1]
26. (~generous(mary) & ~brave(mary)) | ! [X0] : ~kind(X0) [ennf transformation 4]
29. ? [X1] : (generous(X1) & ~old(X1)) | ! [X0] : (rich(X0) & ~tall(X0)) [ennf transformation 21]
30. ! [X0] : ((~rich(X0) <~> generous(X0)) | (~kind(X0) & ~funny(X0))) [ennf transformation 8]
31. ! [X0] : ((quiet(X0) & ~quiet(X0)) | ((kind(X0) | ~funny(X0)) & (funny(X0) | ~kind(X0)))) [nnf transformation 23]
40. ? [X0] : (generous(X0) & ~old(X0)) | ! [X1] : (rich(X1) & ~tall(X1)) [rectify 29]
41. ? [X0] : (generous(X0) & ~old(X0)) => (generous(sK1) & ~old(sK1)) [choice axiom]
42. (generous(sK1) & ~old(sK1)) | ! [X1] : (rich(X1) & ~tall(X1)) [skolemisation 40,41]
43. ! [X0] : (((~generous(X0) | rich(X0)) & (generous(X0) | ~rich(X0))) | (~kind(X0) & ~funny(X0))) [nnf transformation 30]
49. ! [X0] : ((old(X0) | (kind(X0) & wise(X0))) & ((~kind(X0) | ~wise(X0)) | ~old(X0))) [nnf transformation 10]
50. ! [X0] : ((old(X0) | (kind(X0) & wise(X0))) & (~kind(X0) | ~wise(X0) | ~old(X0))) [flattening 49]
53. ! [X0] : ((((funny(X0) | ~funny(X0)) & (~funny(X0) | funny(X0))) | ((rich(X0) | generous(X0)) & (~generous(X0) | ~rich(X0)))) & (((generous(X0) | ~rich(X0)) & (~generous(X0) | rich(X0))) | ((funny(X0) | funny(X0)) & (~funny(X0) | ~funny(X0))))) [nnf transformation 12]
58. ! [X0] : (((~funny(X0) & ~calm(X0)) | ~generous(X0)) & (generous(X0) | (funny(X0) | calm(X0)))) [nnf transformation 14]
59. ! [X0] : (((~funny(X0) & ~calm(X0)) | ~generous(X0)) & (generous(X0) | funny(X0) | calm(X0))) [flattening 58]
65. ~quiet(X0) | funny(X0) | ~kind(X0) [cnf transformation 31]
67. ~kind(X0) | funny(X0) | quiet(X0) [cnf transformation 31]
75. ~generous(mary) | ~kind(X0) [cnf transformation 26]
85. ~old(sK1) | rich(X1) [cnf transformation 42]
87. generous(sK1) | rich(X1) [cnf transformation 42]
88. generous(X0) | ~rich(X0) | ~funny(X0) [cnf transformation 43]
98. old(X0) | kind(X0) [cnf transformation 50]
108. generous(X0) | ~rich(X0) | funny(X0) | funny(X0) [cnf transformation 53]
123. ~generous(X0) | ~funny(X0) [cnf transformation 59]
138. kind(john) [cnf transformation 20]
142. generous(X0) | ~rich(X0) | funny(X0) [duplicate literal removal 108]
144. ~kind(X0) | funny(X0) [subsumption resolution 65,67]
158. 4 <=> ! [X0] : ~kind(X0) [avatar definition]
159. ~kind(X0) <- (4) [avatar component clause 158]
172. 7 <=> generous(mary) [avatar definition]
174. ~generous(mary) <- (~7) [avatar component clause 172]
175. 4 | ~7 [avatar split clause 75,172,158]
182. 9 <=> ! [X1] : rich(X1) [avatar definition]
183. rich(X1) <- (9) [avatar component clause 182]
185. 10 <=> generous(sK1) [avatar definition]
187. generous(sK1) <- (10) [avatar component clause 185]
188. 9 | 10 [avatar split clause 87,185,182]
194. 12 <=> old(sK1) [avatar definition]
196. ~old(sK1) <- (~12) [avatar component clause 194]
197. 9 | ~12 [avatar split clause 85,194,182]
246. ~rich(X0) | generous(X0) [subsumption resolution 142,88]
304. generous(X0) <- (9) [resolution 246,183]
306. $false <- (~7, 9) [resolution 304,174]
309. 7 | ~9 [avatar contradiction clause 306]
314. ~funny(sK1) <- (10) [resolution 187,123]
315. kind(sK1) <- (~12) [resolution 196,98]
325. funny(sK1) <- (~12) [resolution 315,144]
327. $false <- (10, ~12) [subsumption resolution 325,314]
328. ~10 | 12 [avatar contradiction clause 327]
329. $false <- (4) [resolution 159,138]
332. ~4 [avatar contradiction clause 329]
333. $false [avatar sat refutation 175,188,197,309,328,332]
% SZS output end Proof for 5134348389876536789576780
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or humble is funny and vice versa.
Everyone who is either not happy or rich is not calm.
If susan is either wise or humble then paul is either old or creative.
If susan is not happy then someone is both rich and kind.
Everyone who is generous or calm is both wise and not kind and vice versa.
If alice is not tall or not funny then lucy is either tall or humble.
Everyone who is both quiet and calm is both not generous and curious and vice versa.
Everyone who is not patient is both not tall and generous and vice versa.
Everyone who is either not curious or wise is generous or kind and vice versa.
Everyone who is not funny is both creative and calm.
If someone is either old or not tall then fred is either rich or not rich and vice versa.
If someone is either strong or kind then someone is either strong or patient and vice versa.
If paul is generous then someone is either not brave or strong and vice versa.
If someone is happy or not strong then fred is not humble.
Everyone who is either rich or not funny is either not creative or not brave.
If someone is generous then someone is both calm and not kind.
Someone is either not wise or funny.
Alice is both happy and generous.
Mary is not patient.
John is both not creative and generous.
Someone is both happy and not brave.
Susan is happy or patient.
Someone is either funny or happy.
Someone is not kind. | Fred is humble. | contradiction | (![X]:((patient(X)<~>humble(X))<=>funny(X)))&
(![X]:((~happy(X)<~>rich(X))=>~calm(X)))&
(((wise(susan)<~>humble(susan)))=>((old(paul)<~>creative(paul))))&
((~happy(susan))=>(?[X]:((rich(X)&kind(X)))))&
(![X]:((generous(X)|calm(X))<=>(wise(X)&~kind(X))))&
(((~tall(alice)|~funny(alice)))=>((tall(lucy)<~>humble(lucy))))&
(![X]:((quiet(X)&calm(X))<=>(~generous(X)&curious(X))))&
(![X]:(~patient(X)<=>(~tall(X)&generous(X))))&
(![X]:((~curious(X)<~>wise(X))<=>(generous(X)|kind(X))))&
(![X]:(~funny(X)=>(creative(X)&calm(X))))&
((?[X]:((old(X)<~>~tall(X))))<=>((rich(fred)<~>~rich(fred))))&
((?[X]:((strong(X)<~>kind(X))))<=>(?[X]:((strong(X)<~>patient(X)))))&
((generous(paul))<=>(?[X]:((~brave(X)<~>strong(X)))))&
((?[X]:((happy(X)|~strong(X))))=>(~humble(fred)))&
(![X]:((rich(X)<~>~funny(X))=>(~creative(X)<~>~brave(X))))&
((?[X]:(generous(X)))=>(?[X]:((calm(X)&~kind(X)))))&
(?[X]:((~wise(X)<~>funny(X))))&
((happy(alice)&generous(alice)))&
(~patient(mary))&
((~creative(john)&generous(john)))&
(?[X]:((happy(X)&~brave(X))))&
((happy(susan)|patient(susan)))&
(?[X]:((funny(X)<~>happy(X))))&
(?[X]:(~kind(X))) | humble(fred) | [
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 119168489050416045340760
% SZS output start Proof for 119168489050416045340760
14. ? [X0] : (~strong(X0) | happy(X0)) => ~humble(fred) [input p13]
18. generous(alice) & happy(alice) [input p17]
25. humble(fred) [input hypothesis]
33. ~humble(fred) | ! [X0] : (strong(X0) & ~happy(X0)) [ennf transformation 14]
133. ~humble(fred) | ~happy(X0) [cnf transformation 33]
143. happy(alice) [cnf transformation 18]
154. humble(fred) [cnf transformation 25]
293. 29 <=> humble(fred) [avatar definition]
298. 30 <=> ! [X0] : ~happy(X0) [avatar definition]
299. ~happy(X0) <- (30) [avatar component clause 298]
300. 30 | ~29 [avatar split clause 133,293,298]
341. 29 [avatar split clause 154,293]
349. $false <- (30) [resolution 299,143]
352. ~30 [avatar contradiction clause 349]
353. $false [avatar sat refutation 300,341,352]
% SZS output end Proof for 119168489050416045340760
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and funny is both not rich and quiet and vice versa. Everyone who is both not generous and curious is humble. Everyone who is either quiet or old is either not creative or curious. Everyone who is rich is either kind or not creative. Everyone who is either calm or not calm is generous or tall and vice versa. Everyone who is both not strong and calm is funny. Everyone who is not quiet is both not calm and not happy and vice versa. Everyone who is either rich or funny is humble or not quiet. If susan is not old or brave then someone is either strong or not calm and vice versa. Everyone who is either not funny or not calm is either not rich or not quiet and vice versa. If alice is not strong then mary is both not calm and not patient. If susan is calm or not rich then lucy is both old and not curious. If someone is not patient then paul is both calm and strong and vice versa. Everyone who is not brave or not tall is both not strong and patient. If paul is either not humble or funny then paul is either humble or generous. Everyone who is either not calm or kind is both happy and not calm and vice versa. Paul is not kind or funny. Alice is brave or not strong. Someone is not humble. Someone is both not creative and not humble. Someone is not tall. Someone is not brave or rich. Someone is funny. | Alice is tall. | entailment | (![X]:((quiet(X)&funny(X))<=>(~rich(X)&quiet(X))))&
(![X]:((~generous(X)&curious(X))=>humble(X)))&
(![X]:((quiet(X)<~>old(X))=>(~creative(X)<~>curious(X))))&
(![X]:(rich(X)=>(kind(X)<~>~creative(X))))&
(![X]:((calm(X)<~>~calm(X))<=>(generous(X)|tall(X))))&
(![X]:((~strong(X)&calm(X))=>funny(X)))&
(![X]:(~quiet(X)<=>(~calm(X)&~happy(X))))&
(![X]:((rich(X)<~>funny(X))=>(humble(X)|~quiet(X))))&
(((~old(susan)|brave(susan)))<=>(?[X]:((strong(X)<~>~calm(X)))))&
(![X]:((~funny(X)<~>~calm(X))<=>(~rich(X)<~>~quiet(X))))&
((~strong(alice))=>((~calm(mary)&~patient(mary))))&
(((calm(susan)|~rich(susan)))=>((old(lucy)&~curious(lucy))))&
((?[X]:(~patient(X)))<=>((calm(paul)&strong(paul))))&
(![X]:((~brave(X)|~tall(X))=>(~strong(X)&patient(X))))&
(((~humble(paul)<~>funny(paul)))=>((humble(paul)<~>generous(paul))))&
(![X]:((~calm(X)<~>kind(X))<=>(happy(X)&~calm(X))))&
((~kind(paul)|funny(paul)))&
((brave(alice)|~strong(alice)))&
(?[X]:(~humble(X)))&
(?[X]:((~creative(X)&~humble(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~brave(X)|rich(X))))&
(?[X]:(funny(X))) | tall(alice) | [
"p0",
"p6",
"p9",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6653913170803127323530572
% SZS output start Proof for 6653913170803127323530572
1. ! [X0] : ((funny(X0) & quiet(X0)) <=> (quiet(X0) & ~rich(X0))) [input p0]
7. ! [X0] : (~quiet(X0) <=> (~happy(X0) & ~calm(X0))) [input p6]
10. ! [X0] : ((~funny(X0) <~> ~calm(X0)) <=> (~rich(X0) <~> ~quiet(X0))) [input p9]
11. ~strong(alice) => (~patient(mary) & ~calm(mary)) [input p10]
13. ? [X0] : ~patient(X0) <=> (strong(paul) & calm(paul)) [input p12]
14. ! [X0] : ((~tall(X0) | ~brave(X0)) => (patient(X0) & ~strong(X0))) [input p13]
24. ~tall(alice) [input hypothesis]
33. (~patient(mary) & ~calm(mary)) | strong(alice) [ennf transformation 11]
35. ! [X0] : ((patient(X0) & ~strong(X0)) | (tall(X0) & brave(X0))) [ennf transformation 14]
37. ! [X0] : (((funny(X0) & quiet(X0)) | (~quiet(X0) | rich(X0))) & ((quiet(X0) & ~rich(X0)) | (~funny(X0) | ~quiet(X0)))) [nnf transformation 1]
38. ! [X0] : (((funny(X0) & quiet(X0)) | ~quiet(X0) | rich(X0)) & ((quiet(X0) & ~rich(X0)) | ~funny(X0) | ~quiet(X0))) [flattening 37]
43. ! [X0] : ((~quiet(X0) | (happy(X0) | calm(X0))) & ((~happy(X0) & ~calm(X0)) | quiet(X0))) [nnf transformation 7]
44. ! [X0] : ((~quiet(X0) | happy(X0) | calm(X0)) & ((~happy(X0) & ~calm(X0)) | quiet(X0))) [flattening 43]
51. ! [X0] : ((((calm(X0) | funny(X0)) & (~calm(X0) | ~funny(X0))) | ((~rich(X0) | quiet(X0)) & (~quiet(X0) | rich(X0)))) & (((quiet(X0) | rich(X0)) & (~quiet(X0) | ~rich(X0))) | ((~funny(X0) | calm(X0)) & (~calm(X0) | funny(X0))))) [nnf transformation 10]
52. (? [X0] : ~patient(X0) | (~strong(paul) | ~calm(paul))) & ((strong(paul) & calm(paul)) | ! [X0] : patient(X0)) [nnf transformation 13]
53. (? [X0] : ~patient(X0) | ~strong(paul) | ~calm(paul)) & ((strong(paul) & calm(paul)) | ! [X0] : patient(X0)) [flattening 52]
54. (? [X0] : ~patient(X0) | ~strong(paul) | ~calm(paul)) & ((strong(paul) & calm(paul)) | ! [X1] : patient(X1)) [rectify 53]
55. ? [X0] : ~patient(X0) => ~patient(sK1) [choice axiom]
56. (~patient(sK1) | ~strong(paul) | ~calm(paul)) & ((strong(paul) & calm(paul)) | ! [X1] : patient(X1)) [skolemisation 54,55]
70. ~rich(X0) | ~funny(X0) | ~quiet(X0) [cnf transformation 38]
73. ~quiet(X0) | funny(X0) | rich(X0) [cnf transformation 38]
88. ~calm(X0) | quiet(X0) [cnf transformation 44]
99. ~quiet(X0) | ~rich(X0) | ~calm(X0) | funny(X0) [cnf transformation 51]
103. ~calm(X0) | ~funny(X0) | ~quiet(X0) | rich(X0) [cnf transformation 51]
108. ~patient(mary) | strong(alice) [cnf transformation 33]
113. calm(paul) | patient(X1) [cnf transformation 56]
117. ~strong(X0) | tall(X0) [cnf transformation 35]
138. ~tall(alice) [cnf transformation 24]
178. ~calm(X0) | ~quiet(X0) | rich(X0) [subsumption resolution 103,73]
179. ~calm(X0) | rich(X0) [subsumption resolution 178,88]
181. ~rich(X0) | ~calm(X0) | funny(X0) [subsumption resolution 99,88]
182. ~calm(X0) | funny(X0) [subsumption resolution 181,179]
184. 7 <=> strong(alice) [avatar definition]
186. strong(alice) <- (7) [avatar component clause 184]
188. 8 <=> patient(mary) [avatar definition]
190. ~patient(mary) <- (~8) [avatar component clause 188]
191. 7 | ~8 [avatar split clause 108,188,184]
218. 14 <=> calm(paul) [avatar definition]
219. calm(paul) <- (14) [avatar component clause 218]
231. 17 <=> ! [X1] : patient(X1) [avatar definition]
232. patient(X1) <- (17) [avatar component clause 231]
234. 17 | 14 [avatar split clause 113,218,231]
236. 18 <=> funny(paul) [avatar definition]
277. $false <- (~8, 17) [resolution 232,190]
280. 8 | ~17 [avatar contradiction clause 277]
281. tall(alice) <- (7) [resolution 186,117]
283. $false <- (7) [subsumption resolution 281,138]
284. ~7 [avatar contradiction clause 283]
288. quiet(paul) <- (14) [resolution 219,88]
291. rich(paul) <- (14) [resolution 179,219]
292. funny(paul) <- (14) [resolution 182,219]
306. ~funny(paul) | ~quiet(paul) <- (14) [resolution 291,70]
310. ~funny(paul) <- (14) [subsumption resolution 306,288]
311. ~18 | ~14 [avatar split clause 310,218,236]
312. 18 | ~14 [avatar split clause 292,218,236]
313. $false [avatar sat refutation 191,234,280,284,311,312]
% SZS output end Proof for 6653913170803127323530572
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or creative is both not wise and not happy and vice versa.
Everyone who is kind or quiet is not funny or not calm and vice versa.
Everyone who is not strong or wise is tall.
Everyone who is not humble or strong is not kind or not generous.
Everyone who is not calm or rich is not quiet or generous and vice versa.
Everyone who is brave is both not quiet and generous.
Everyone who is not strong or rich is creative.
If someone is not calm then someone is not humble.
Everyone who is creative is both not tall and old.
Everyone who is either not kind or not humble is both rich and not funny and vice versa.
Everyone who is either not curious or quiet is either funny or strong.
Everyone who is not patient or not happy is either not calm or not happy.
Everyone who is strong is not old.
If someone is either creative or not happy then lucy is not humble and vice versa.
If fred is either calm or patient then someone is not rich or not strong.
Fred is either calm or kind.
Someone is generous or not old.
Susan is not creative or not humble. | Fred is not brave. | entailment | (![X]:((~calm(X)<~>creative(X))<=>(~wise(X)&~happy(X))))&
(![X]:((kind(X)|quiet(X))<=>(~funny(X)|~calm(X))))&
(![X]:((~strong(X)|wise(X))=>tall(X)))&
(![X]:((~humble(X)|strong(X))=>(~kind(X)|~generous(X))))&
(![X]:((~calm(X)|rich(X))<=>(~quiet(X)|generous(X))))&
(![X]:(brave(X)=>(~quiet(X)&generous(X))))&
(![X]:((~strong(X)|rich(X))=>creative(X)))&
((?[X]:(~calm(X)))=>(?[X]:(~humble(X))))&
(![X]:(creative(X)=>(~tall(X)&old(X))))&
(![X]:((~kind(X)<~>~humble(X))<=>(rich(X)&~funny(X))))&
(![X]:((~curious(X)<~>quiet(X))=>(funny(X)<~>strong(X))))&
(![X]:((~patient(X)|~happy(X))=>(~calm(X)<~>~happy(X))))&
(![X]:(strong(X)=>~old(X)))&
((?[X]:((creative(X)<~>~happy(X))))<=>(~humble(lucy)))&
(((calm(fred)<~>patient(fred)))=>(?[X]:((~rich(X)|~strong(X)))))&
((calm(fred)<~>kind(fred)))&
(?[X]:((generous(X)|~old(X))))&
((~creative(susan)|~humble(susan))) | ~brave(fred) | [
"p0",
"p2",
"p4",
"p5",
"p6",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5643600589002638651186779
% SZS output start Proof for 5643600589002638651186779
1. ! [X0] : ((~calm(X0) <~> creative(X0)) <=> (~happy(X0) & ~wise(X0))) [input p0]
3. ! [X0] : ((wise(X0) | ~strong(X0)) => tall(X0)) [input p2]
5. ! [X0] : ((rich(X0) | ~calm(X0)) <=> (generous(X0) | ~quiet(X0))) [input p4]
6. ! [X0] : (brave(X0) => (generous(X0) & ~quiet(X0))) [input p5]
7. ! [X0] : ((rich(X0) | ~strong(X0)) => creative(X0)) [input p6]
9. ! [X0] : (creative(X0) => (old(X0) & ~tall(X0))) [input p8]
12. ! [X0] : ((~happy(X0) | ~patient(X0)) => (~calm(X0) <~> ~happy(X0))) [input p11]
13. ! [X0] : (strong(X0) => ~old(X0)) [input p12]
19. brave(fred) [input hypothesis]
21. ! [X0] : (tall(X0) | (~wise(X0) & strong(X0))) [ennf transformation 3]
24. ! [X0] : ((generous(X0) & ~quiet(X0)) | ~brave(X0)) [ennf transformation 6]
25. ! [X0] : (creative(X0) | (~rich(X0) & strong(X0))) [ennf transformation 7]
27. ! [X0] : ((old(X0) & ~tall(X0)) | ~creative(X0)) [ennf transformation 9]
29. ! [X0] : ((~calm(X0) <~> ~happy(X0)) | (happy(X0) & patient(X0))) [ennf transformation 12]
30. ! [X0] : (~old(X0) | ~strong(X0)) [ennf transformation 13]
32. ! [X0] : ((((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | (happy(X0) | wise(X0))) & ((~happy(X0) & ~wise(X0)) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0))))) [nnf transformation 1]
33. ! [X0] : ((((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | happy(X0) | wise(X0)) & ((~happy(X0) & ~wise(X0)) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0))))) [flattening 32]
36. ! [X0] : (((rich(X0) | ~calm(X0)) | (~generous(X0) & quiet(X0))) & ((generous(X0) | ~quiet(X0)) | (~rich(X0) & calm(X0)))) [nnf transformation 5]
37. ! [X0] : ((rich(X0) | ~calm(X0) | (~generous(X0) & quiet(X0))) & (generous(X0) | ~quiet(X0) | (~rich(X0) & calm(X0)))) [flattening 36]
44. ! [X0] : (((happy(X0) | calm(X0)) & (~happy(X0) | ~calm(X0))) | (happy(X0) & patient(X0))) [nnf transformation 29]
57. ~happy(X0) | creative(X0) | calm(X0) [cnf transformation 33]
65. tall(X0) | strong(X0) [cnf transformation 21]
72. ~generous(X0) | ~calm(X0) | rich(X0) [cnf transformation 37]
74. ~brave(X0) | generous(X0) [cnf transformation 24]
75. strong(X0) | creative(X0) [cnf transformation 25]
76. ~rich(X0) | creative(X0) [cnf transformation 25]
78. ~tall(X0) | ~creative(X0) [cnf transformation 27]
79. ~creative(X0) | old(X0) [cnf transformation 27]
93. happy(X0) | calm(X0) | happy(X0) [cnf transformation 44]
94. ~old(X0) | ~strong(X0) [cnf transformation 30]
105. brave(fred) [cnf transformation 19]
106. happy(X0) | calm(X0) [duplicate literal removal 93]
108. 1 <=> ! [X1] : calm(X1) [avatar definition]
109. calm(X1) <- (1) [avatar component clause 108]
142. 9 <=> calm(fred) [avatar definition]
143. ~calm(fred) <- (~9) [avatar component clause 142]
144. calm(fred) <- (9) [avatar component clause 142]
180. generous(fred) [resolution 74,105]
182. ~creative(X0) | strong(X0) [resolution 78,65]
183. strong(X0) [subsumption resolution 182,75]
187. creative(X0) | calm(X0) | calm(X0) [resolution 57,106]
188. creative(X0) | calm(X0) [duplicate literal removal 187]
191. old(X0) | calm(X0) [resolution 188,79]
193. calm(X0) | ~strong(X0) [resolution 191,94]
194. calm(X0) [subsumption resolution 193,183]
195. 1 [avatar split clause 194,108]
207. ~calm(fred) | rich(fred) [resolution 72,180]
208. rich(fred) <- (9) [subsumption resolution 207,144]
210. creative(fred) <- (9) [resolution 208,76]
211. old(fred) <- (9) [resolution 210,79]
212. ~strong(fred) <- (9) [resolution 211,94]
213. $false <- (9) [subsumption resolution 212,183]
214. ~9 [avatar contradiction clause 213]
223. $false <- (1, ~9) [subsumption resolution 143,109]
224. ~1 | 9 [avatar contradiction clause 223]
225. $false [avatar sat refutation 195,214,224]
% SZS output end Proof for 5643600589002638651186779
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet is both old and generous. Everyone who is not old or kind is either not rich or not strong. If someone is both brave and not generous then someone is brave. If fred is either wise or tall then someone is either not old or creative and vice versa. Everyone who is not generous is rich and vice versa. Everyone who is either not strong or generous is both not old and wise. Everyone who is tall or not wise is either not tall or not strong. Everyone who is either brave or not wise is not humble and vice versa. If alice is humble then someone is both not happy and not strong and vice versa. Everyone who is either not calm or not creative is either rich or not humble. If mary is either not brave or not funny then someone is wise and vice versa. If lucy is generous then someone is generous. If alice is not quiet then susan is both not old and creative and vice versa. If someone is either old or not wise then someone is both not generous and not calm and vice versa. Everyone who is funny is rich or generous. Everyone who is both old and not patient is not old and vice versa. John is either calm or rich. Someone is both tall and not brave. Fred is either not creative or funny. Fred is either old or not tall. Someone is either humble or wise. John is humble. | Lucy is humble. | neutral | (![X]:(~quiet(X)=>(old(X)&generous(X))))&
(![X]:((~old(X)|kind(X))=>(~rich(X)<~>~strong(X))))&
((?[X]:((brave(X)&~generous(X))))=>(?[X]:(brave(X))))&
(((wise(fred)<~>tall(fred)))<=>(?[X]:((~old(X)<~>creative(X)))))&
(![X]:(~generous(X)<=>rich(X)))&
(![X]:((~strong(X)<~>generous(X))=>(~old(X)&wise(X))))&
(![X]:((tall(X)|~wise(X))=>(~tall(X)<~>~strong(X))))&
(![X]:((brave(X)<~>~wise(X))<=>~humble(X)))&
((humble(alice))<=>(?[X]:((~happy(X)&~strong(X)))))&
(![X]:((~calm(X)<~>~creative(X))=>(rich(X)<~>~humble(X))))&
(((~brave(mary)<~>~funny(mary)))<=>(?[X]:(wise(X))))&
((generous(lucy))=>(?[X]:(generous(X))))&
((~quiet(alice))<=>((~old(susan)&creative(susan))))&
((?[X]:((old(X)<~>~wise(X))))<=>(?[X]:((~generous(X)&~calm(X)))))&
(![X]:(funny(X)=>(rich(X)|generous(X))))&
(![X]:((old(X)&~patient(X))<=>~old(X)))&
((calm(john)<~>rich(john)))&
(?[X]:((tall(X)&~brave(X))))&
((~creative(fred)<~>funny(fred)))&
((old(fred)<~>~tall(fred)))&
(?[X]:((humble(X)<~>wise(X))))&
(humble(john)) | humble(lucy) | [] | null | 0 |
If someone is either not curious or not quiet then someone is not generous or not patient.
If fred is either not tall or not kind then someone is both strong and brave.
Everyone who is wise is not happy and vice versa.
Everyone who is both not creative and old is not calm or old and vice versa.
If someone is both calm and happy then john is both not happy and not kind and vice versa.
If mary is either curious or not patient then someone is not rich or strong and vice versa.
Everyone who is not brave is either wise or creative and vice versa.
If someone is not generous or strong then paul is patient and vice versa.
If someone is either not strong or not rich then someone is both brave and curious and vice versa.
If someone is both not generous and happy then someone is both quiet and old.
Everyone who is both not old and not calm is old or not kind.
If someone is either not old or not curious then john is both humble and not wise and vice versa.
Everyone who is calm or curious is either happy or not brave.
If someone is tall or not wise then someone is both tall and creative.
If someone is not tall then someone is either not wise or not quiet.
Everyone who is brave is either not rich or not funny and vice versa.
Someone is both not patient and not kind.
Mary is either strong or humble.
Someone is both not brave and kind.
Fred is not curious.
Paul is not funny or not generous.
Someone is both quiet and funny.
Fred is not quiet or not generous.
Someone is not humble or not calm. | Fred is not creative. | entailment | ((?[X]:((~curious(X)<~>~quiet(X))))=>(?[X]:((~generous(X)|~patient(X)))))&
(((~tall(fred)<~>~kind(fred)))=>(?[X]:((strong(X)&brave(X)))))&
(![X]:(wise(X)<=>~happy(X)))&
(![X]:((~creative(X)&old(X))<=>(~calm(X)|old(X))))&
((?[X]:((calm(X)&happy(X))))<=>((~happy(john)&~kind(john))))&
(((curious(mary)<~>~patient(mary)))<=>(?[X]:((~rich(X)|strong(X)))))&
(![X]:(~brave(X)<=>(wise(X)<~>creative(X))))&
((?[X]:((~generous(X)|strong(X))))<=>(patient(paul)))&
((?[X]:((~strong(X)<~>~rich(X))))<=>(?[X]:((brave(X)&curious(X)))))&
((?[X]:((~generous(X)&happy(X))))=>(?[X]:((quiet(X)&old(X)))))&
(![X]:((~old(X)&~calm(X))=>(old(X)|~kind(X))))&
((?[X]:((~old(X)<~>~curious(X))))<=>((humble(john)&~wise(john))))&
(![X]:((calm(X)|curious(X))=>(happy(X)<~>~brave(X))))&
((?[X]:((tall(X)|~wise(X))))=>(?[X]:((tall(X)&creative(X)))))&
((?[X]:(~tall(X)))=>(?[X]:((~wise(X)<~>~quiet(X)))))&
(![X]:(brave(X)<=>(~rich(X)<~>~funny(X))))&
(?[X]:((~patient(X)&~kind(X))))&
((strong(mary)<~>humble(mary)))&
(?[X]:((~brave(X)&kind(X))))&
(~curious(fred))&
((~funny(paul)|~generous(paul)))&
(?[X]:((quiet(X)&funny(X))))&
((~quiet(fred)|~generous(fred)))&
(?[X]:((~humble(X)|~calm(X)))) | ~creative(fred) | [
"p2",
"p3",
"p4",
"p6",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 988769485285451963569269
% SZS output start Proof for 988769485285451963569269
3. ! [X0] : (wise(X0) <=> ~happy(X0)) [input p2]
4. ! [X0] : ((old(X0) & ~creative(X0)) <=> (old(X0) | ~calm(X0))) [input p3]
5. ? [X0] : (happy(X0) & calm(X0)) <=> (~kind(john) & ~happy(john)) [input p4]
7. ! [X0] : (~brave(X0) <=> (wise(X0) <~> creative(X0))) [input p6]
13. ! [X0] : ((curious(X0) | calm(X0)) => (happy(X0) <~> ~brave(X0))) [input p12]
14. ? [X0] : (~wise(X0) | tall(X0)) => ? [X0] : (creative(X0) & tall(X0)) [input p13]
25. creative(fred) [input hypothesis]
29. ? [X0] : (~wise(X0) | tall(X0)) => ? [X1] : (creative(X1) & tall(X1)) [rectify 14]
36. ! [X0] : ((happy(X0) <~> ~brave(X0)) | (~curious(X0) & ~calm(X0))) [ennf transformation 13]
37. ? [X1] : (creative(X1) & tall(X1)) | ! [X0] : (wise(X0) & ~tall(X0)) [ennf transformation 29]
46. ! [X0] : ((wise(X0) | happy(X0)) & (~happy(X0) | ~wise(X0))) [nnf transformation 3]
47. ! [X0] : (((old(X0) & ~creative(X0)) | (~old(X0) & calm(X0))) & ((old(X0) | ~calm(X0)) | (~old(X0) | creative(X0)))) [nnf transformation 4]
48. ! [X0] : (((old(X0) & ~creative(X0)) | (~old(X0) & calm(X0))) & (old(X0) | ~calm(X0) | ~old(X0) | creative(X0))) [flattening 47]
49. (? [X0] : (happy(X0) & calm(X0)) | (kind(john) | happy(john))) & ((~kind(john) & ~happy(john)) | ! [X0] : (~happy(X0) | ~calm(X0))) [nnf transformation 5]
50. (? [X0] : (happy(X0) & calm(X0)) | kind(john) | happy(john)) & ((~kind(john) & ~happy(john)) | ! [X0] : (~happy(X0) | ~calm(X0))) [flattening 49]
51. (? [X0] : (happy(X0) & calm(X0)) | kind(john) | happy(john)) & ((~kind(john) & ~happy(john)) | ! [X1] : (~happy(X1) | ~calm(X1))) [rectify 50]
52. ? [X0] : (happy(X0) & calm(X0)) => (happy(sK2) & calm(sK2)) [choice axiom]
53. ((happy(sK2) & calm(sK2)) | kind(john) | happy(john)) & ((~kind(john) & ~happy(john)) | ! [X1] : (~happy(X1) | ~calm(X1))) [skolemisation 51,52]
58. ! [X0] : ((~brave(X0) | ((wise(X0) | ~creative(X0)) & (creative(X0) | ~wise(X0)))) & (((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | brave(X0))) [nnf transformation 7]
76. ! [X0] : (((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | (~curious(X0) & ~calm(X0))) [nnf transformation 36]
77. ? [X0] : (creative(X0) & tall(X0)) | ! [X1] : (wise(X1) & ~tall(X1)) [rectify 37]
78. ? [X0] : (creative(X0) & tall(X0)) => (creative(sK9) & tall(sK9)) [choice axiom]
79. (creative(sK9) & tall(sK9)) | ! [X1] : (wise(X1) & ~tall(X1)) [skolemisation 77,78]
100. ~happy(X0) | ~wise(X0) [cnf transformation 46]
101. happy(X0) | wise(X0) [cnf transformation 46]
103. ~creative(X0) | calm(X0) [cnf transformation 48]
107. ~happy(john) | ~happy(X1) | ~calm(X1) [cnf transformation 53]
108. ~kind(john) | ~happy(X1) | ~calm(X1) [cnf transformation 53]
110. happy(sK2) | kind(john) | happy(john) [cnf transformation 53]
118. ~creative(X0) | ~wise(X0) | brave(X0) [cnf transformation 58]
120. ~creative(X0) | wise(X0) | ~brave(X0) [cnf transformation 58]
139. ~calm(X0) | happy(X0) | ~brave(X0) [cnf transformation 76]
141. ~calm(X0) | ~happy(X0) | brave(X0) [cnf transformation 76]
146. creative(sK9) | wise(X1) [cnf transformation 79]
165. creative(fred) [cnf transformation 25]
204. 9 <=> happy(john) [avatar definition]
208. 10 <=> kind(john) [avatar definition]
212. 11 <=> happy(sK2) [avatar definition]
214. happy(sK2) <- (11) [avatar component clause 212]
215. 9 | 10 | 11 [avatar split clause 110,212,208,204]
222. 13 <=> ! [X1] : (~happy(X1) | ~calm(X1)) [avatar definition]
223. ~calm(X1) | ~happy(X1) <- (13) [avatar component clause 222]
224. 13 | ~10 [avatar split clause 108,208,222]
225. 13 | ~9 [avatar split clause 107,204,222]
345. 40 <=> ! [X1] : wise(X1) [avatar definition]
346. wise(X1) <- (40) [avatar component clause 345]
348. 41 <=> creative(sK9) [avatar definition]
350. creative(sK9) <- (41) [avatar component clause 348]
351. 40 | 41 [avatar split clause 146,348,345]
418. ~wise(sK2) <- (11) [resolution 100,214]
419. $false <- (11, 40) [subsumption resolution 418,346]
420. ~11 | ~40 [avatar contradiction clause 419]
424. calm(fred) [resolution 103,165]
425. calm(sK9) <- (41) [resolution 103,350]
428. ~happy(fred) <- (13) [resolution 223,424]
431. wise(fred) <- (13) [resolution 428,101]
441. ~wise(fred) | brave(fred) [resolution 118,165]
442. ~wise(sK9) | brave(sK9) <- (41) [resolution 118,350]
451. wise(sK9) | ~brave(sK9) <- (41) [resolution 120,350]
455. happy(fred) | ~brave(fred) [resolution 139,424]
457. happy(sK9) | ~brave(sK9) <- (41) [resolution 139,425]
459. ~brave(fred) <- (13) [subsumption resolution 455,428]
467. ~wise(fred) <- (13) [subsumption resolution 441,459]
470. $false <- (13) [subsumption resolution 431,467]
471. ~13 [avatar contradiction clause 470]
488. 58 <=> brave(sK9) [avatar definition]
492. 59 <=> wise(sK9) [avatar definition]
493. wise(sK9) <- (59) [avatar component clause 492]
494. ~wise(sK9) <- (~59) [avatar component clause 492]
495. 58 | ~59 | ~41 [avatar split clause 442,348,492,488]
497. ~58 | 59 | ~41 [avatar split clause 451,348,492,488]
499. 60 <=> happy(sK9) [avatar definition]
500. ~happy(sK9) <- (~60) [avatar component clause 499]
501. happy(sK9) <- (60) [avatar component clause 499]
502. ~58 | 60 | ~41 [avatar split clause 457,348,499,488]
523. ~happy(sK9) | brave(sK9) <- (41) [resolution 141,425]
622. wise(sK9) <- (~60) [resolution 500,101]
623. $false <- (~59, ~60) [subsumption resolution 622,494]
624. 59 | 60 [avatar contradiction clause 623]
625. 58 | ~60 | ~41 [avatar split clause 523,348,499,488]
644. ~wise(sK9) <- (60) [resolution 501,100]
645. $false <- (59, 60) [subsumption resolution 644,493]
646. ~59 | ~60 [avatar contradiction clause 645]
647. $false [avatar sat refutation 215,224,225,351,420,471,495,497,502,624,625,646]
% SZS output end Proof for 988769485285451963569269
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong then susan is not patient and vice versa. If someone is either happy or not kind then someone is both not happy and not brave and vice versa. Everyone who is not generous is not calm or not happy and vice versa. Everyone who is either quiet or not funny is both happy and quiet and vice versa. If someone is either generous or not creative then paul is humble and vice versa. Everyone who is both not rich and not brave is both not brave and not curious. Everyone who is not wise or old is old or rich and vice versa. If someone is either patient or not humble then someone is tall or not tall and vice versa. Everyone who is either not patient or not creative is rich. Everyone who is not wise or not tall is both not kind and generous and vice versa. If someone is both funny and not quiet then paul is not creative or not curious and vice versa. Everyone who is patient is not patient or not funny and vice versa. If someone is both kind and not happy then someone is either not creative or tall and vice versa. If susan is either not tall or kind then fred is both brave and not wise. If john is both not happy and funny then someone is either not old or not rich and vice versa. If john is either not calm or quiet then someone is both not curious and not generous. Mary is either not humble or happy. Mary is both not old and not curious. Alice is both not happy and not rich. Paul is not kind or not humble. | Paul is generous. | contradiction | ((?[X]:(strong(X)))<=>(~patient(susan)))&
((?[X]:((happy(X)<~>~kind(X))))<=>(?[X]:((~happy(X)&~brave(X)))))&
(![X]:(~generous(X)<=>(~calm(X)|~happy(X))))&
(![X]:((quiet(X)<~>~funny(X))<=>(happy(X)&quiet(X))))&
((?[X]:((generous(X)<~>~creative(X))))<=>(humble(paul)))&
(![X]:((~rich(X)&~brave(X))=>(~brave(X)&~curious(X))))&
(![X]:((~wise(X)|old(X))<=>(old(X)|rich(X))))&
((?[X]:((patient(X)<~>~humble(X))))<=>(?[X]:((tall(X)|~tall(X)))))&
(![X]:((~patient(X)<~>~creative(X))=>rich(X)))&
(![X]:((~wise(X)|~tall(X))<=>(~kind(X)&generous(X))))&
((?[X]:((funny(X)&~quiet(X))))<=>((~creative(paul)|~curious(paul))))&
(![X]:(patient(X)<=>(~patient(X)|~funny(X))))&
((?[X]:((kind(X)&~happy(X))))<=>(?[X]:((~creative(X)<~>tall(X)))))&
(((~tall(susan)<~>kind(susan)))=>((brave(fred)&~wise(fred))))&
(((~happy(john)&funny(john)))<=>(?[X]:((~old(X)<~>~rich(X)))))&
(((~calm(john)<~>quiet(john)))=>(?[X]:((~curious(X)&~generous(X)))))&
((~humble(mary)<~>happy(mary)))&
((~old(mary)&~curious(mary)))&
((~happy(alice)&~rich(alice)))&
((~kind(paul)|~humble(paul))) | generous(paul) | [
"p2",
"p3",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 290256744145483388824779
% SZS output start Proof for 290256744145483388824779
3. ! [X0] : (~generous(X0) <=> (~happy(X0) | ~calm(X0))) [input p2]
4. ! [X0] : ((quiet(X0) <~> ~funny(X0)) <=> (quiet(X0) & happy(X0))) [input p3]
11. ? [X0] : (~quiet(X0) & funny(X0)) <=> (~curious(paul) | ~creative(paul)) [input p10]
12. ! [X0] : (patient(X0) <=> (~funny(X0) | ~patient(X0))) [input p11]
21. generous(paul) [input hypothesis]
39. ! [X0] : ((~generous(X0) | (happy(X0) & calm(X0))) & ((~happy(X0) | ~calm(X0)) | generous(X0))) [nnf transformation 3]
40. ! [X0] : ((~generous(X0) | (happy(X0) & calm(X0))) & (~happy(X0) | ~calm(X0) | generous(X0))) [flattening 39]
41. ! [X0] : ((((funny(X0) | ~quiet(X0)) & (~funny(X0) | quiet(X0))) | (~quiet(X0) | ~happy(X0))) & ((quiet(X0) & happy(X0)) | ((quiet(X0) | funny(X0)) & (~funny(X0) | ~quiet(X0))))) [nnf transformation 4]
42. ! [X0] : ((((funny(X0) | ~quiet(X0)) & (~funny(X0) | quiet(X0))) | ~quiet(X0) | ~happy(X0)) & ((quiet(X0) & happy(X0)) | ((quiet(X0) | funny(X0)) & (~funny(X0) | ~quiet(X0))))) [flattening 41]
57. (? [X0] : (~quiet(X0) & funny(X0)) | (curious(paul) & creative(paul))) & ((~curious(paul) | ~creative(paul)) | ! [X0] : (quiet(X0) | ~funny(X0))) [nnf transformation 11]
58. (? [X0] : (~quiet(X0) & funny(X0)) | (curious(paul) & creative(paul))) & (~curious(paul) | ~creative(paul) | ! [X0] : (quiet(X0) | ~funny(X0))) [flattening 57]
59. (? [X0] : (~quiet(X0) & funny(X0)) | (curious(paul) & creative(paul))) & (~curious(paul) | ~creative(paul) | ! [X1] : (quiet(X1) | ~funny(X1))) [rectify 58]
60. ? [X0] : (~quiet(X0) & funny(X0)) => (~quiet(sK6) & funny(sK6)) [choice axiom]
61. ((~quiet(sK6) & funny(sK6)) | (curious(paul) & creative(paul))) & (~curious(paul) | ~creative(paul) | ! [X1] : (quiet(X1) | ~funny(X1))) [skolemisation 59,60]
62. ! [X0] : ((patient(X0) | (funny(X0) & patient(X0))) & ((~funny(X0) | ~patient(X0)) | ~patient(X0))) [nnf transformation 12]
63. ! [X0] : ((patient(X0) | (funny(X0) & patient(X0))) & (~funny(X0) | ~patient(X0) | ~patient(X0))) [flattening 62]
89. ~generous(X0) | happy(X0) [cnf transformation 40]
93. quiet(X0) | quiet(X0) | funny(X0) [cnf transformation 42]
95. funny(X0) | ~quiet(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 42]
119. ~curious(paul) | ~creative(paul) | quiet(X1) | ~funny(X1) [cnf transformation 61]
120. funny(sK6) | creative(paul) [cnf transformation 61]
121. funny(sK6) | curious(paul) [cnf transformation 61]
124. ~funny(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 63]
125. patient(X0) | patient(X0) [cnf transformation 63]
154. generous(paul) [cnf transformation 21]
155. ~funny(X0) | ~patient(X0) [duplicate literal removal 124]
156. patient(X0) [duplicate literal removal 125]
157. funny(X0) | quiet(X0) [duplicate literal removal 93]
158. ~quiet(X0) | funny(X0) | ~happy(X0) [duplicate literal removal 95]
244. 20 <=> curious(paul) [avatar definition]
253. 22 <=> creative(paul) [avatar definition]
258. 23 <=> funny(sK6) [avatar definition]
260. funny(sK6) <- (23) [avatar component clause 258]
261. 20 | 23 [avatar split clause 121,258,244]
262. 22 | 23 [avatar split clause 120,258,253]
263. ~curious(paul) | ~creative(paul) | quiet(X1) [subsumption resolution 119,157]
265. 24 <=> ! [X1] : quiet(X1) [avatar definition]
266. quiet(X1) <- (24) [avatar component clause 265]
267. 24 | ~22 | ~20 [avatar split clause 263,244,253,265]
268. ~funny(X0) [subsumption resolution 155,156]
361. $false <- (23) [subsumption resolution 260,268]
362. ~23 [avatar contradiction clause 361]
372. happy(paul) [resolution 89,154]
422. funny(X0) | ~happy(X0) <- (24) [resolution 158,266]
423. ~happy(X0) <- (24) [subsumption resolution 422,268]
424. $false <- (24) [resolution 423,372]
427. ~24 [avatar contradiction clause 424]
428. $false [avatar sat refutation 261,262,267,362,427]
% SZS output end Proof for 290256744145483388824779
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or not humble is both old and not tall.
Everyone who is strong or old is both not wise and rich and vice versa.
Everyone who is calm or old is both not patient and old and vice versa.
If someone is either not creative or quiet then fred is kind or not happy and vice versa.
If lucy is either not tall or generous then john is either generous or happy.
Everyone who is brave is not kind.
Everyone who is either not patient or patient is either not old or old and vice versa.
Everyone who is both old and funny is both not calm and old.
Everyone who is not wise is not tall.
Everyone who is not brave or strong is generous or not curious and vice versa.
Everyone who is either wise or not funny is both not humble and not patient and vice versa.
Everyone who is both not creative and creative is both not funny and wise and vice versa.
If someone is tall or not curious then fred is wise and vice versa.
If john is not patient then someone is both wise and happy.
If someone is either not humble or not old then someone is both not tall and not creative.
Someone is strong.
Someone is both not happy and calm.
Someone is creative or kind.
Paul is either not humble or not quiet.
Someone is either not creative or not happy.
Alice is either patient or rich.
Someone is creative. | Paul is curious. | entailment | (![X]:((kind(X)|~humble(X))=>(old(X)&~tall(X))))&
(![X]:((strong(X)|old(X))<=>(~wise(X)&rich(X))))&
(![X]:((calm(X)|old(X))<=>(~patient(X)&old(X))))&
((?[X]:((~creative(X)<~>quiet(X))))<=>((kind(fred)|~happy(fred))))&
(((~tall(lucy)<~>generous(lucy)))=>((generous(john)<~>happy(john))))&
(![X]:(brave(X)=>~kind(X)))&
(![X]:((~patient(X)<~>patient(X))<=>(~old(X)<~>old(X))))&
(![X]:((old(X)&funny(X))=>(~calm(X)&old(X))))&
(![X]:(~wise(X)=>~tall(X)))&
(![X]:((~brave(X)|strong(X))<=>(generous(X)|~curious(X))))&
(![X]:((wise(X)<~>~funny(X))<=>(~humble(X)&~patient(X))))&
(![X]:((~creative(X)&creative(X))<=>(~funny(X)&wise(X))))&
((?[X]:((tall(X)|~curious(X))))<=>(wise(fred)))&
((~patient(john))=>(?[X]:((wise(X)&happy(X)))))&
((?[X]:((~humble(X)<~>~old(X))))=>(?[X]:((~tall(X)&~creative(X)))))&
(?[X]:(strong(X)))&
(?[X]:((~happy(X)&calm(X))))&
(?[X]:((creative(X)|kind(X))))&
((~humble(paul)<~>~quiet(paul)))&
(?[X]:((~creative(X)<~>~happy(X))))&
((patient(alice)<~>rich(alice)))&
(?[X]:(creative(X))) | curious(paul) | [
"p0",
"p1",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 50537178342649873481261
% SZS output start Proof for 50537178342649873481261
1. ! [X0] : ((~humble(X0) | kind(X0)) => (~tall(X0) & old(X0))) [input p0]
2. ! [X0] : ((old(X0) | strong(X0)) <=> (rich(X0) & ~wise(X0))) [input p1]
11. ! [X0] : ((wise(X0) <~> ~funny(X0)) <=> (~patient(X0) & ~humble(X0))) [input p10]
12. ! [X0] : ((creative(X0) & ~creative(X0)) <=> (wise(X0) & ~funny(X0))) [input p11]
13. ? [X0] : (~curious(X0) | tall(X0)) <=> wise(fred) [input p12]
23. ~curious(paul) [input hypothesis]
25. ! [X0] : ((~tall(X0) & old(X0)) | (humble(X0) & ~kind(X0))) [ennf transformation 1]
33. ! [X0] : (((old(X0) | strong(X0)) | (~rich(X0) | wise(X0))) & ((rich(X0) & ~wise(X0)) | (~old(X0) & ~strong(X0)))) [nnf transformation 2]
34. ! [X0] : ((old(X0) | strong(X0) | ~rich(X0) | wise(X0)) & ((rich(X0) & ~wise(X0)) | (~old(X0) & ~strong(X0)))) [flattening 33]
46. ! [X0] : ((((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | (patient(X0) | humble(X0))) & ((~patient(X0) & ~humble(X0)) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0))))) [nnf transformation 11]
47. ! [X0] : ((((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | patient(X0) | humble(X0)) & ((~patient(X0) & ~humble(X0)) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0))))) [flattening 46]
48. ! [X0] : (((creative(X0) & ~creative(X0)) | (~wise(X0) | funny(X0))) & ((wise(X0) & ~funny(X0)) | (~creative(X0) | creative(X0)))) [nnf transformation 12]
49. ! [X0] : (((creative(X0) & ~creative(X0)) | ~wise(X0) | funny(X0)) & ((wise(X0) & ~funny(X0)) | ~creative(X0) | creative(X0))) [flattening 48]
50. (? [X0] : (~curious(X0) | tall(X0)) | ~wise(fred)) & (wise(fred) | ! [X0] : (curious(X0) & ~tall(X0))) [nnf transformation 13]
51. (? [X0] : (~curious(X0) | tall(X0)) | ~wise(fred)) & (wise(fred) | ! [X1] : (curious(X1) & ~tall(X1))) [rectify 50]
52. ? [X0] : (~curious(X0) | tall(X0)) => (~curious(sK1) | tall(sK1)) [choice axiom]
53. ((~curious(sK1) | tall(sK1)) | ~wise(fred)) & (wise(fred) | ! [X1] : (curious(X1) & ~tall(X1))) [skolemisation 51,52]
74. old(X0) | humble(X0) [cnf transformation 25]
78. ~wise(X0) | ~old(X0) [cnf transformation 34]
113. ~funny(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 47]
121. ~creative(X0) | ~wise(X0) | funny(X0) [cnf transformation 49]
122. creative(X0) | ~wise(X0) | funny(X0) [cnf transformation 49]
124. wise(fred) | curious(X1) [cnf transformation 53]
143. ~curious(paul) [cnf transformation 23]
201. ~wise(X0) | funny(X0) [subsumption resolution 121,122]
203. 11 <=> wise(fred) [avatar definition]
204. wise(fred) <- (11) [avatar component clause 203]
216. 14 <=> ! [X1] : curious(X1) [avatar definition]
217. curious(X1) <- (14) [avatar component clause 216]
218. 14 | 11 [avatar split clause 124,203,216]
299. ~old(fred) <- (11) [resolution 78,204]
300. humble(fred) <- (11) [resolution 299,74]
311. funny(fred) <- (11) [resolution 201,204]
314. ~humble(fred) | ~wise(fred) <- (11) [resolution 113,311]
315. ~wise(fred) <- (11) [subsumption resolution 314,300]
316. $false <- (11) [subsumption resolution 315,204]
317. ~11 [avatar contradiction clause 316]
318. $false <- (14) [resolution 217,143]
323. ~14 [avatar contradiction clause 318]
324. $false [avatar sat refutation 218,317,323]
% SZS output end Proof for 50537178342649873481261
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or quiet is either not generous or generous and vice versa. If someone is not calm then someone is old or not funny and vice versa. Everyone who is not brave is kind and vice versa. Everyone who is either not happy or strong is both not rich and not calm. Everyone who is tall or strong is both not curious and wise and vice versa. If someone is both old and not kind then someone is humble. If susan is both funny and patient then someone is either not strong or rich and vice versa. Everyone who is both kind and brave is either not strong or kind. Everyone who is both tall and not brave is happy. If someone is either not generous or not rich then someone is not rich or kind. Everyone who is not humble or not generous is either patient or strong and vice versa. Everyone who is either humble or not wise is either not calm or humble. If mary is either not generous or not happy then someone is both not funny and tall and vice versa. Everyone who is not funny is not rich or quiet. If mary is not calm then john is not rich and vice versa. Everyone who is either funny or calm is both creative and brave and vice versa. John is either not creative or not old. Someone is brave or tall. Mary is rich. Someone is not old or not generous. Lucy is either not strong or humble. Someone is not quiet or quiet. Someone is calm. Mary is both calm and quiet. | Mary is quiet. | entailment | (![X]:((wise(X)<~>quiet(X))<=>(~generous(X)<~>generous(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((old(X)|~funny(X)))))&
(![X]:(~brave(X)<=>kind(X)))&
(![X]:((~happy(X)<~>strong(X))=>(~rich(X)&~calm(X))))&
(![X]:((tall(X)|strong(X))<=>(~curious(X)&wise(X))))&
((?[X]:((old(X)&~kind(X))))=>(?[X]:(humble(X))))&
(((funny(susan)&patient(susan)))<=>(?[X]:((~strong(X)<~>rich(X)))))&
(![X]:((kind(X)&brave(X))=>(~strong(X)<~>kind(X))))&
(![X]:((tall(X)&~brave(X))=>happy(X)))&
((?[X]:((~generous(X)<~>~rich(X))))=>(?[X]:((~rich(X)|kind(X)))))&
(![X]:((~humble(X)|~generous(X))<=>(patient(X)<~>strong(X))))&
(![X]:((humble(X)<~>~wise(X))=>(~calm(X)<~>humble(X))))&
(((~generous(mary)<~>~happy(mary)))<=>(?[X]:((~funny(X)&tall(X)))))&
(![X]:(~funny(X)=>(~rich(X)|quiet(X))))&
((~calm(mary))<=>(~rich(john)))&
(![X]:((funny(X)<~>calm(X))<=>(creative(X)&brave(X))))&
((~creative(john)<~>~old(john)))&
(?[X]:((brave(X)|tall(X))))&
(rich(mary))&
(?[X]:((~old(X)|~generous(X))))&
((~strong(lucy)<~>humble(lucy)))&
(?[X]:((~quiet(X)|quiet(X))))&
(?[X]:(calm(X)))&
((calm(mary)&quiet(mary))) | quiet(mary) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7135698082849213325769871
% SZS output start Proof for 7135698082849213325769871
24. quiet(mary) & calm(mary) [input p23]
25. ~quiet(mary) [input hypothesis]
151. quiet(mary) [cnf transformation 24]
152. ~quiet(mary) [cnf transformation 25]
312. $false [subsumption resolution 152,151]
% SZS output end Proof for 7135698082849213325769871
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is not happy or curious then susan is either generous or not wise.
If fred is either humble or tall then someone is generous.
Everyone who is humble or not tall is not rich or not brave and vice versa.
If someone is not tall then someone is both happy and curious and vice versa.
Everyone who is both not strong and patient is either wise or calm.
Everyone who is quiet or not creative is calm and vice versa.
Everyone who is either old or humble is brave.
Everyone who is not brave is wise.
Everyone who is curious is humble or quiet.
Everyone who is not calm is quiet or humble and vice versa.
If someone is not old or quiet then susan is either not creative or quiet and vice versa.
If john is either creative or not funny then someone is curious or tall.
If someone is not strong or not humble then fred is both not kind and not happy.
Everyone who is not calm or not old is either generous or patient and vice versa.
If mary is not curious or not quiet then someone is both funny and generous.
If john is either happy or funny then someone is either brave or not patient and vice versa.
Alice is humble or tall.
Susan is tall.
Someone is happy or creative.
Someone is kind or generous.
Someone is not brave.
Someone is not creative or rich.
Lucy is not curious or wise. | Alice is not patient. | neutral | (((~happy(john)|curious(john)))=>((generous(susan)<~>~wise(susan))))&
(((humble(fred)<~>tall(fred)))=>(?[X]:(generous(X))))&
(![X]:((humble(X)|~tall(X))<=>(~rich(X)|~brave(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((happy(X)&curious(X)))))&
(![X]:((~strong(X)&patient(X))=>(wise(X)<~>calm(X))))&
(![X]:((quiet(X)|~creative(X))<=>calm(X)))&
(![X]:((old(X)<~>humble(X))=>brave(X)))&
(![X]:(~brave(X)=>wise(X)))&
(![X]:(curious(X)=>(humble(X)|quiet(X))))&
(![X]:(~calm(X)<=>(quiet(X)|humble(X))))&
((?[X]:((~old(X)|quiet(X))))<=>((~creative(susan)<~>quiet(susan))))&
(((creative(john)<~>~funny(john)))=>(?[X]:((curious(X)|tall(X)))))&
((?[X]:((~strong(X)|~humble(X))))=>((~kind(fred)&~happy(fred))))&
(![X]:((~calm(X)|~old(X))<=>(generous(X)<~>patient(X))))&
(((~curious(mary)|~quiet(mary)))=>(?[X]:((funny(X)&generous(X)))))&
(((happy(john)<~>funny(john)))<=>(?[X]:((brave(X)<~>~patient(X)))))&
((humble(alice)|tall(alice)))&
(tall(susan))&
(?[X]:((happy(X)|creative(X))))&
(?[X]:((kind(X)|generous(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~creative(X)|rich(X))))&
((~curious(lucy)|wise(lucy))) | ~patient(alice) | [] | null | 0 |
If someone is calm or happy then someone is both strong and not curious and vice versa.
Everyone who is not funny is not generous or not old and vice versa.
Everyone who is not tall is both generous and not old and vice versa.
Everyone who is curious is both quiet and generous.
If fred is not kind then someone is either not patient or not happy and vice versa.
Everyone who is either not old or strong is not old and vice versa.
Everyone who is not old is either wise or not patient.
If lucy is both not humble and not calm then susan is either not wise or quiet.
Everyone who is old is generous.
Everyone who is not patient is either generous or happy and vice versa.
If susan is kind then someone is both quiet and not kind.
Everyone who is both not humble and rich is both funny and generous and vice versa.
If paul is either brave or not patient then john is generous and vice versa.
Everyone who is not tall is not wise and vice versa.
If john is happy then someone is tall and vice versa.
If alice is either not tall or not brave then mary is curious and vice versa.
Someone is both quiet and not calm.
Someone is either humble or old.
Paul is either creative or quiet.
Someone is either not tall or old.
Someone is kind or not tall. | Fred is old. | contradiction | ((?[X]:((calm(X)|happy(X))))<=>(?[X]:((strong(X)&~curious(X)))))&
(![X]:(~funny(X)<=>(~generous(X)|~old(X))))&
(![X]:(~tall(X)<=>(generous(X)&~old(X))))&
(![X]:(curious(X)=>(quiet(X)&generous(X))))&
((~kind(fred))<=>(?[X]:((~patient(X)<~>~happy(X)))))&
(![X]:((~old(X)<~>strong(X))<=>~old(X)))&
(![X]:(~old(X)=>(wise(X)<~>~patient(X))))&
(((~humble(lucy)&~calm(lucy)))=>((~wise(susan)<~>quiet(susan))))&
(![X]:(old(X)=>generous(X)))&
(![X]:(~patient(X)<=>(generous(X)<~>happy(X))))&
((kind(susan))=>(?[X]:((quiet(X)&~kind(X)))))&
(![X]:((~humble(X)&rich(X))<=>(funny(X)&generous(X))))&
(((brave(paul)<~>~patient(paul)))<=>(generous(john)))&
(![X]:(~tall(X)<=>~wise(X)))&
((happy(john))<=>(?[X]:(tall(X))))&
(((~tall(alice)<~>~brave(alice)))<=>(curious(mary)))&
(?[X]:((quiet(X)&~calm(X))))&
(?[X]:((humble(X)<~>old(X))))&
((creative(paul)<~>quiet(paul)))&
(?[X]:((~tall(X)<~>old(X))))&
(?[X]:((kind(X)|~tall(X)))) | old(fred) | [
"p0",
"p2",
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1291991697120525029567796
% SZS output start Proof for 1291991697120525029567796
1. ? [X0] : (happy(X0) | calm(X0)) <=> ? [X0] : (~curious(X0) & strong(X0)) [input p0]
3. ! [X0] : (~tall(X0) <=> (~old(X0) & generous(X0))) [input p2]
6. ! [X0] : ((~old(X0) <~> strong(X0)) <=> ~old(X0)) [input p5]
15. happy(john) <=> ? [X0] : tall(X0) [input p14]
22. old(fred) [input hypothesis]
23. ? [X0] : (happy(X0) | calm(X0)) <=> ? [X1] : (~curious(X1) & strong(X1)) [rectify 1]
30. (? [X0] : (happy(X0) | calm(X0)) | ! [X1] : (curious(X1) | ~strong(X1))) & (? [X1] : (~curious(X1) & strong(X1)) | ! [X0] : (~happy(X0) & ~calm(X0))) [nnf transformation 23]
31. (? [X0] : (happy(X0) | calm(X0)) | ! [X1] : (curious(X1) | ~strong(X1))) & (? [X2] : (~curious(X2) & strong(X2)) | ! [X3] : (~happy(X3) & ~calm(X3))) [rectify 30]
32. ? [X0] : (happy(X0) | calm(X0)) => (happy(sK0) | calm(sK0)) [choice axiom]
33. ? [X2] : (~curious(X2) & strong(X2)) => (~curious(sK1) & strong(sK1)) [choice axiom]
34. ((happy(sK0) | calm(sK0)) | ! [X1] : (curious(X1) | ~strong(X1))) & ((~curious(sK1) & strong(sK1)) | ! [X3] : (~happy(X3) & ~calm(X3))) [skolemisation 31,33,32]
37. ! [X0] : ((~tall(X0) | (old(X0) | ~generous(X0))) & ((~old(X0) & generous(X0)) | tall(X0))) [nnf transformation 3]
38. ! [X0] : ((~tall(X0) | old(X0) | ~generous(X0)) & ((~old(X0) & generous(X0)) | tall(X0))) [flattening 37]
43. ! [X0] : ((((~strong(X0) | old(X0)) & (strong(X0) | ~old(X0))) | old(X0)) & (~old(X0) | ((~old(X0) | ~strong(X0)) & (strong(X0) | old(X0))))) [nnf transformation 6]
53. (happy(john) | ! [X0] : ~tall(X0)) & (? [X0] : tall(X0) | ~happy(john)) [nnf transformation 15]
54. (happy(john) | ! [X0] : ~tall(X0)) & (? [X1] : tall(X1) | ~happy(john)) [rectify 53]
55. ? [X1] : tall(X1) => tall(sK4) [choice axiom]
56. (happy(john) | ! [X0] : ~tall(X0)) & (tall(sK4) | ~happy(john)) [skolemisation 54,55]
70. strong(sK1) | ~happy(X3) [cnf transformation 34]
78. ~old(X0) | tall(X0) [cnf transformation 38]
87. ~old(X0) | ~old(X0) | ~strong(X0) [cnf transformation 43]
89. ~strong(X0) | old(X0) | old(X0) [cnf transformation 43]
112. happy(john) | ~tall(X0) [cnf transformation 56]
126. old(fred) [cnf transformation 22]
127. ~old(X0) | ~strong(X0) [duplicate literal removal 87]
128. ~strong(X0) | old(X0) [duplicate literal removal 89]
142. 4 <=> ! [X3] : ~happy(X3) [avatar definition]
143. ~happy(X3) <- (4) [avatar component clause 142]
154. 7 <=> strong(sK1) [avatar definition]
156. strong(sK1) <- (7) [avatar component clause 154]
157. 4 | 7 [avatar split clause 70,154,142]
181. ~strong(X0) [subsumption resolution 127,128]
233. 23 <=> ! [X0] : ~tall(X0) [avatar definition]
234. ~tall(X0) <- (23) [avatar component clause 233]
236. 24 <=> happy(john) [avatar definition]
238. happy(john) <- (24) [avatar component clause 236]
239. 23 | 24 [avatar split clause 112,236,233]
301. $false <- (7) [subsumption resolution 156,181]
302. ~7 [avatar contradiction clause 301]
309. tall(fred) [resolution 78,126]
310. $false <- (23) [subsumption resolution 309,234]
311. ~23 [avatar contradiction clause 310]
312. $false <- (4, 24) [subsumption resolution 238,143]
313. ~4 | ~24 [avatar contradiction clause 312]
314. $false [avatar sat refutation 157,239,302,311,313]
% SZS output end Proof for 1291991697120525029567796
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or not curious is either not creative or strong and vice versa. Everyone who is both brave and not creative is either not kind or not happy and vice versa. Everyone who is not strong is both strong and calm and vice versa. If someone is strong then paul is happy and vice versa. If susan is patient or not quiet then lucy is not strong and vice versa. If mary is brave then john is both not calm and not patient. If someone is not patient then someone is not tall or strong and vice versa. Everyone who is both not happy and not humble is wise or not funny and vice versa. Everyone who is calm or not humble is brave. Everyone who is generous is not wise and vice versa. Everyone who is humble is either rich or not old and vice versa. If someone is either not funny or not strong then john is not strong or not humble. Everyone who is not generous is both not creative and not patient and vice versa. If alice is either wise or not patient then someone is both not generous and brave. Lucy is both not rich and patient. Fred is humble. Lucy is generous or curious. Someone is both happy and kind. Mary is not old. | Alice is not patient. | contradiction | (![X]:((curious(X)<~>~curious(X))<=>(~creative(X)<~>strong(X))))&
(![X]:((brave(X)&~creative(X))<=>(~kind(X)<~>~happy(X))))&
(![X]:(~strong(X)<=>(strong(X)&calm(X))))&
((?[X]:(strong(X)))<=>(happy(paul)))&
(((patient(susan)|~quiet(susan)))<=>(~strong(lucy)))&
((brave(mary))=>((~calm(john)&~patient(john))))&
((?[X]:(~patient(X)))<=>(?[X]:((~tall(X)|strong(X)))))&
(![X]:((~happy(X)&~humble(X))<=>(wise(X)|~funny(X))))&
(![X]:((calm(X)|~humble(X))=>brave(X)))&
(![X]:(generous(X)<=>~wise(X)))&
(![X]:(humble(X)<=>(rich(X)<~>~old(X))))&
((?[X]:((~funny(X)<~>~strong(X))))=>((~strong(john)|~humble(john))))&
(![X]:(~generous(X)<=>(~creative(X)&~patient(X))))&
(((wise(alice)<~>~patient(alice)))=>(?[X]:((~generous(X)&brave(X)))))&
((~rich(lucy)&patient(lucy)))&
(humble(fred))&
((generous(lucy)|curious(lucy)))&
(?[X]:((happy(X)&kind(X))))&
(~old(mary)) | ~patient(alice) | [
"p0",
"p2",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7287524003365966642437833
% SZS output start Proof for 7287524003365966642437833
1. ! [X0] : ((curious(X0) <~> ~curious(X0)) <=> (~creative(X0) <~> strong(X0))) [input p0]
3. ! [X0] : (~strong(X0) <=> (calm(X0) & strong(X0))) [input p2]
10. ! [X0] : (generous(X0) <=> ~wise(X0)) [input p9]
13. ! [X0] : (~generous(X0) <=> (~patient(X0) & ~creative(X0))) [input p12]
14. (wise(alice) <~> ~patient(alice)) => ? [X0] : (brave(X0) & ~generous(X0)) [input p13]
20. ~patient(alice) [input hypothesis]
26. ? [X0] : (brave(X0) & ~generous(X0)) | (wise(alice) <=> ~patient(alice)) [ennf transformation 14]
27. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | ((~creative(X0) | ~strong(X0)) & (strong(X0) | creative(X0)))) & (((~strong(X0) | creative(X0)) & (strong(X0) | ~creative(X0))) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [nnf transformation 1]
30. ! [X0] : ((~strong(X0) | (~calm(X0) | ~strong(X0))) & ((calm(X0) & strong(X0)) | strong(X0))) [nnf transformation 3]
31. ! [X0] : ((~strong(X0) | ~calm(X0) | ~strong(X0)) & ((calm(X0) & strong(X0)) | strong(X0))) [flattening 30]
45. ! [X0] : ((generous(X0) | wise(X0)) & (~wise(X0) | ~generous(X0))) [nnf transformation 10]
48. ! [X0] : ((~generous(X0) | (patient(X0) | creative(X0))) & ((~patient(X0) & ~creative(X0)) | generous(X0))) [nnf transformation 13]
49. ! [X0] : ((~generous(X0) | patient(X0) | creative(X0)) & ((~patient(X0) & ~creative(X0)) | generous(X0))) [flattening 48]
50. ? [X0] : (brave(X0) & ~generous(X0)) | ((wise(alice) | patient(alice)) & (~patient(alice) | ~wise(alice))) [nnf transformation 26]
51. ? [X0] : (brave(X0) & ~generous(X0)) => (brave(sK3) & ~generous(sK3)) [choice axiom]
52. (brave(sK3) & ~generous(sK3)) | ((wise(alice) | patient(alice)) & (~patient(alice) | ~wise(alice))) [skolemisation 50,51]
57. ~strong(X0) | creative(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 27]
58. ~strong(X0) | creative(X0) | curious(X0) | curious(X0) [cnf transformation 27]
69. strong(X0) | strong(X0) [cnf transformation 31]
89. ~generous(X0) | ~wise(X0) [cnf transformation 45]
97. ~creative(X0) | generous(X0) [cnf transformation 49]
101. ~generous(sK3) | wise(alice) | patient(alice) [cnf transformation 52]
111. ~patient(alice) [cnf transformation 20]
112. strong(X0) [duplicate literal removal 69]
116. ~strong(X0) | creative(X0) | ~curious(X0) [duplicate literal removal 57]
117. ~strong(X0) | creative(X0) | curious(X0) [duplicate literal removal 58]
118. ~strong(X0) | creative(X0) [subsumption resolution 116,117]
149. 6 <=> patient(alice) [avatar definition]
153. 7 <=> wise(alice) [avatar definition]
155. wise(alice) <- (7) [avatar component clause 153]
163. 9 <=> generous(sK3) [avatar definition]
165. ~generous(sK3) <- (~9) [avatar component clause 163]
166. 6 | 7 | ~9 [avatar split clause 101,163,153,149]
177. ~6 [avatar split clause 111,149]
191. creative(X0) [resolution 118,112]
193. generous(X1) [resolution 191,97]
207. ~wise(X0) [resolution 193,89]
210. $false <- (7) [resolution 207,155]
211. ~7 [avatar contradiction clause 210]
212. $false <- (~9) [subsumption resolution 165,193]
213. 9 [avatar contradiction clause 212]
214. $false [avatar sat refutation 166,177,211,213]
% SZS output end Proof for 7287524003365966642437833
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not quiet or calm is both not creative and rich and vice versa.
If someone is not generous then paul is humble or patient and vice versa.
Everyone who is not happy is not strong and vice versa.
Everyone who is calm is both calm and not strong.
Everyone who is either kind or tall is not quiet or not old.
If mary is curious or not kind then john is not quiet or wise and vice versa.
Everyone who is not kind or not tall is both not generous and happy and vice versa.
If someone is either not curious or not brave then someone is not quiet or not happy and vice versa.
Everyone who is rich is not humble or not calm and vice versa.
Everyone who is strong is not curious or kind and vice versa.
Everyone who is happy or curious is both old and not calm and vice versa.
Everyone who is humble is not strong.
Everyone who is both not happy and not humble is not tall and vice versa.
If john is not brave or generous then someone is either tall or creative.
Everyone who is not calm or wise is either not generous or kind.
Everyone who is both brave and strong is not funny or tall and vice versa.
Someone is either calm or funny.
Someone is not curious or not humble.
Fred is both not kind and patient.
Paul is wise.
Fred is either creative or not generous.
Susan is not quiet.
Mary is either quiet or not rich. | John is calm. | contradiction | (![X]:((~quiet(X)<~>calm(X))<=>(~creative(X)&rich(X))))&
((?[X]:(~generous(X)))<=>((humble(paul)|patient(paul))))&
(![X]:(~happy(X)<=>~strong(X)))&
(![X]:(calm(X)=>(calm(X)&~strong(X))))&
(![X]:((kind(X)<~>tall(X))=>(~quiet(X)|~old(X))))&
(((curious(mary)|~kind(mary)))<=>((~quiet(john)|wise(john))))&
(![X]:((~kind(X)|~tall(X))<=>(~generous(X)&happy(X))))&
((?[X]:((~curious(X)<~>~brave(X))))<=>(?[X]:((~quiet(X)|~happy(X)))))&
(![X]:(rich(X)<=>(~humble(X)|~calm(X))))&
(![X]:(strong(X)<=>(~curious(X)|kind(X))))&
(![X]:((happy(X)|curious(X))<=>(old(X)&~calm(X))))&
(![X]:(humble(X)=>~strong(X)))&
(![X]:((~happy(X)&~humble(X))<=>~tall(X)))&
(((~brave(john)|generous(john)))=>(?[X]:((tall(X)<~>creative(X)))))&
(![X]:((~calm(X)|wise(X))=>(~generous(X)<~>kind(X))))&
(![X]:((brave(X)&strong(X))<=>(~funny(X)|tall(X))))&
(?[X]:((calm(X)<~>funny(X))))&
(?[X]:((~curious(X)|~humble(X))))&
((~kind(fred)&patient(fred)))&
(wise(paul))&
((creative(fred)<~>~generous(fred)))&
(~quiet(susan))&
((quiet(mary)<~>~rich(mary))) | calm(john) | [
"p3",
"p6",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4031633471797301747177122
% SZS output start Proof for 4031633471797301747177122
4. ! [X0] : (calm(X0) => (~strong(X0) & calm(X0))) [input p3]
7. ! [X0] : ((~tall(X0) | ~kind(X0)) <=> (happy(X0) & ~generous(X0))) [input p6]
13. ! [X0] : ((~humble(X0) & ~happy(X0)) <=> ~tall(X0)) [input p12]
16. ! [X0] : ((strong(X0) & brave(X0)) <=> (tall(X0) | ~funny(X0))) [input p15]
24. calm(john) [input hypothesis]
26. ! [X0] : ((~strong(X0) & calm(X0)) | ~calm(X0)) [ennf transformation 4]
43. ! [X0] : (((~tall(X0) | ~kind(X0)) | (~happy(X0) | generous(X0))) & ((happy(X0) & ~generous(X0)) | (tall(X0) & kind(X0)))) [nnf transformation 7]
44. ! [X0] : ((~tall(X0) | ~kind(X0) | ~happy(X0) | generous(X0)) & ((happy(X0) & ~generous(X0)) | (tall(X0) & kind(X0)))) [flattening 43]
56. ! [X0] : (((~humble(X0) & ~happy(X0)) | tall(X0)) & (~tall(X0) | (humble(X0) | happy(X0)))) [nnf transformation 13]
57. ! [X0] : (((~humble(X0) & ~happy(X0)) | tall(X0)) & (~tall(X0) | humble(X0) | happy(X0))) [flattening 56]
62. ! [X0] : (((strong(X0) & brave(X0)) | (~tall(X0) & funny(X0))) & ((tall(X0) | ~funny(X0)) | (~strong(X0) | ~brave(X0)))) [nnf transformation 16]
63. ! [X0] : (((strong(X0) & brave(X0)) | (~tall(X0) & funny(X0))) & (tall(X0) | ~funny(X0) | ~strong(X0) | ~brave(X0))) [flattening 62]
83. ~strong(X0) | ~calm(X0) [cnf transformation 26]
93. happy(X0) | tall(X0) [cnf transformation 44]
114. ~happy(X0) | tall(X0) [cnf transformation 57]
128. strong(X0) | ~tall(X0) [cnf transformation 63]
140. calm(john) [cnf transformation 24]
213. tall(X0) [subsumption resolution 114,93]
231. strong(X0) [subsumption resolution 128,213]
277. ~calm(X0) [resolution 83,231]
278. $false [resolution 277,140]
% SZS output end Proof for 4031633471797301747177122
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong is not generous and vice versa.
If john is not rich or not calm then someone is not strong or not wise.
Everyone who is not calm or not strong is both not wise and not happy and vice versa.
If lucy is both not creative and not generous then paul is not kind or not tall and vice versa.
If someone is generous then mary is both not brave and brave and vice versa.
Everyone who is both not kind and not happy is either not kind or patient.
Everyone who is both kind and not quiet is wise.
If someone is generous or funny then john is not kind or curious and vice versa.
If someone is not calm then someone is both tall and not generous and vice versa.
If fred is either not generous or not tall then someone is calm and vice versa.
If someone is either not creative or not curious then alice is happy and vice versa.
If someone is either not generous or patient then susan is tall or not curious and vice versa.
Everyone who is both not tall and not wise is either strong or not strong.
If fred is either not strong or tall then alice is both not quiet and old and vice versa.
Someone is not strong or not funny.
Someone is not tall or not creative.
Susan is both not patient and not brave.
John is creative.
Paul is not quiet.
Someone is either humble or happy.
Someone is both happy and not brave.
Mary is either calm or not brave. | Lucy is brave. | neutral | (![X]:(strong(X)<=>~generous(X)))&
(((~rich(john)|~calm(john)))=>(?[X]:((~strong(X)|~wise(X)))))&
(![X]:((~calm(X)|~strong(X))<=>(~wise(X)&~happy(X))))&
(((~creative(lucy)&~generous(lucy)))<=>((~kind(paul)|~tall(paul))))&
((?[X]:(generous(X)))<=>((~brave(mary)&brave(mary))))&
(![X]:((~kind(X)&~happy(X))=>(~kind(X)<~>patient(X))))&
(![X]:((kind(X)&~quiet(X))=>wise(X)))&
((?[X]:((generous(X)|funny(X))))<=>((~kind(john)|curious(john))))&
((?[X]:(~calm(X)))<=>(?[X]:((tall(X)&~generous(X)))))&
(((~generous(fred)<~>~tall(fred)))<=>(?[X]:(calm(X))))&
((?[X]:((~creative(X)<~>~curious(X))))<=>(happy(alice)))&
((?[X]:((~generous(X)<~>patient(X))))<=>((tall(susan)|~curious(susan))))&
(![X]:((~tall(X)&~wise(X))=>(strong(X)<~>~strong(X))))&
(((~strong(fred)<~>tall(fred)))<=>((~quiet(alice)&old(alice))))&
(?[X]:((~strong(X)|~funny(X))))&
(?[X]:((~tall(X)|~creative(X))))&
((~patient(susan)&~brave(susan)))&
(creative(john))&
(~quiet(paul))&
(?[X]:((humble(X)<~>happy(X))))&
(?[X]:((happy(X)&~brave(X))))&
((calm(mary)<~>~brave(mary))) | brave(lucy) | [] | null | 0 |
If someone is generous then paul is both wise and quiet and vice versa.
If john is not wise then fred is either curious or wise and vice versa.
If someone is not brave or not patient then someone is both old and patient and vice versa.
If someone is both quiet and not old then john is either old or curious and vice versa.
If someone is old or kind then lucy is both not humble and not funny.
If someone is wise or not patient then paul is not brave.
Everyone who is both generous and calm is not brave and vice versa.
If someone is not wise or not strong then someone is not humble or not creative and vice versa.
If susan is curious or not humble then someone is not brave.
If someone is not wise then someone is either happy or not humble.
If susan is either not funny or happy then alice is not happy and vice versa.
If susan is happy or not brave then someone is not calm or not tall and vice versa.
Everyone who is wise or patient is not creative and vice versa.
Everyone who is wise is both not humble and patient.
Everyone who is both not funny and creative is not funny and vice versa.
If susan is not humble then someone is rich or happy and vice versa.
Someone is brave or rich.
Alice is both kind and not wise.
Susan is quiet or humble.
Mary is patient.
Someone is not humble or not curious.
Alice is both not generous and not old.
Someone is not wise or calm. | Mary is not funny. | contradiction | ((?[X]:(generous(X)))<=>((wise(paul)&quiet(paul))))&
((~wise(john))<=>((curious(fred)<~>wise(fred))))&
((?[X]:((~brave(X)|~patient(X))))<=>(?[X]:((old(X)&patient(X)))))&
((?[X]:((quiet(X)&~old(X))))<=>((old(john)<~>curious(john))))&
((?[X]:((old(X)|kind(X))))=>((~humble(lucy)&~funny(lucy))))&
((?[X]:((wise(X)|~patient(X))))=>(~brave(paul)))&
(![X]:((generous(X)&calm(X))<=>~brave(X)))&
((?[X]:((~wise(X)|~strong(X))))<=>(?[X]:((~humble(X)|~creative(X)))))&
(((curious(susan)|~humble(susan)))=>(?[X]:(~brave(X))))&
((?[X]:(~wise(X)))=>(?[X]:((happy(X)<~>~humble(X)))))&
(((~funny(susan)<~>happy(susan)))<=>(~happy(alice)))&
(((happy(susan)|~brave(susan)))<=>(?[X]:((~calm(X)|~tall(X)))))&
(![X]:((wise(X)|patient(X))<=>~creative(X)))&
(![X]:(wise(X)=>(~humble(X)&patient(X))))&
(![X]:((~funny(X)&creative(X))<=>~funny(X)))&
((~humble(susan))<=>(?[X]:((rich(X)|happy(X)))))&
(?[X]:((brave(X)|rich(X))))&
((kind(alice)&~wise(alice)))&
((quiet(susan)|humble(susan)))&
(patient(mary))&
(?[X]:((~humble(X)|~curious(X))))&
((~generous(alice)&~old(alice)))&
(?[X]:((~wise(X)|calm(X)))) | ~funny(mary) | [
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7223785961058797968206746
% SZS output start Proof for 7223785961058797968206746
13. ! [X0] : ((patient(X0) | wise(X0)) <=> ~creative(X0)) [input p12]
15. ! [X0] : ((creative(X0) & ~funny(X0)) <=> ~funny(X0)) [input p14]
20. patient(mary) [input p19]
24. ~funny(mary) [input hypothesis]
67. ! [X0] : (((patient(X0) | wise(X0)) | creative(X0)) & (~creative(X0) | (~patient(X0) & ~wise(X0)))) [nnf transformation 13]
68. ! [X0] : ((patient(X0) | wise(X0) | creative(X0)) & (~creative(X0) | (~patient(X0) & ~wise(X0)))) [flattening 67]
69. ! [X0] : (((creative(X0) & ~funny(X0)) | funny(X0)) & (~funny(X0) | (~creative(X0) | funny(X0)))) [nnf transformation 15]
70. ! [X0] : (((creative(X0) & ~funny(X0)) | funny(X0)) & (~funny(X0) | ~creative(X0) | funny(X0))) [flattening 69]
125. ~creative(X0) | ~patient(X0) [cnf transformation 68]
131. creative(X0) | funny(X0) [cnf transformation 70]
139. patient(mary) [cnf transformation 20]
144. ~funny(mary) [cnf transformation 24]
438. ~patient(X0) | funny(X0) [resolution 131,125]
440. funny(mary) [resolution 438,139]
443. $false [subsumption resolution 440,144]
% SZS output end Proof for 7223785961058797968206746
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not creative or not happy then fred is both strong and wise. Everyone who is old or not tall is not brave or curious. If paul is not humble then paul is not quiet or strong and vice versa. Everyone who is not quiet is either strong or not brave and vice versa. If paul is not generous or not patient then alice is both not curious and not creative and vice versa. If someone is old then john is either not funny or tall. If fred is either wise or kind then someone is not happy or not kind. Everyone who is not humble is brave. If alice is not generous then someone is tall and vice versa. Everyone who is either not quiet or not wise is both not brave and patient. If someone is both not rich and not curious then someone is not humble or quiet and vice versa. Everyone who is both not patient and not tall is old or funny and vice versa. Everyone who is patient or not wise is funny and vice versa. Everyone who is not patient or brave is not generous and vice versa. Everyone who is wise is either not wise or not funny and vice versa. Someone is not curious. Paul is not generous. Fred is both wise and kind. Someone is both not kind and quiet. Someone is both quiet and rich. John is not old. Paul is not happy or brave. Someone is not brave. | John is not creative. | neutral | ((?[X]:((~creative(X)<~>~happy(X))))=>((strong(fred)&wise(fred))))&
(![X]:((old(X)|~tall(X))=>(~brave(X)|curious(X))))&
((~humble(paul))<=>((~quiet(paul)|strong(paul))))&
(![X]:(~quiet(X)<=>(strong(X)<~>~brave(X))))&
(((~generous(paul)|~patient(paul)))<=>((~curious(alice)&~creative(alice))))&
((?[X]:(old(X)))=>((~funny(john)<~>tall(john))))&
(((wise(fred)<~>kind(fred)))=>(?[X]:((~happy(X)|~kind(X)))))&
(![X]:(~humble(X)=>brave(X)))&
((~generous(alice))<=>(?[X]:(tall(X))))&
(![X]:((~quiet(X)<~>~wise(X))=>(~brave(X)&patient(X))))&
((?[X]:((~rich(X)&~curious(X))))<=>(?[X]:((~humble(X)|quiet(X)))))&
(![X]:((~patient(X)&~tall(X))<=>(old(X)|funny(X))))&
(![X]:((patient(X)|~wise(X))<=>funny(X)))&
(![X]:((~patient(X)|brave(X))<=>~generous(X)))&
(![X]:(wise(X)<=>(~wise(X)<~>~funny(X))))&
(?[X]:(~curious(X)))&
(~generous(paul))&
((wise(fred)&kind(fred)))&
(?[X]:((~kind(X)&quiet(X))))&
(?[X]:((quiet(X)&rich(X))))&
(~old(john))&
((~happy(paul)|brave(paul)))&
(?[X]:(~brave(X))) | ~creative(john) | [] | null | 0 |
If someone is both not rich and calm then paul is not humble or happy.
If john is both not curious and kind then mary is not brave and vice versa.
Everyone who is either not kind or generous is calm or kind.
If susan is both tall and quiet then someone is both not patient and wise.
If someone is not old then someone is both creative and not quiet and vice versa.
If lucy is both not funny and brave then someone is strong or not rich.
Everyone who is not rich is both rich and not old and vice versa.
If alice is either not funny or happy then alice is both not happy and curious.
Everyone who is both not calm and not quiet is not rich or tall.
Everyone who is either quiet or funny is either humble or wise and vice versa.
If susan is kind or not patient then someone is both not brave and kind.
If someone is either funny or not humble then mary is kind and vice versa.
Everyone who is not creative or happy is both not strong and not curious and vice versa.
If fred is not generous then mary is not brave or not old.
Everyone who is both not calm and quiet is both rich and not curious.
Everyone who is not rich or not curious is either rich or not curious.
Alice is not generous or patient.
Someone is funny or rich.
Lucy is not generous.
Someone is kind or brave.
Someone is either not kind or calm.
Lucy is not brave. | Lucy is calm. | entailment | ((?[X]:((~rich(X)&calm(X))))=>((~humble(paul)|happy(paul))))&
(((~curious(john)&kind(john)))<=>(~brave(mary)))&
(![X]:((~kind(X)<~>generous(X))=>(calm(X)|kind(X))))&
(((tall(susan)&quiet(susan)))=>(?[X]:((~patient(X)&wise(X)))))&
((?[X]:(~old(X)))<=>(?[X]:((creative(X)&~quiet(X)))))&
(((~funny(lucy)&brave(lucy)))=>(?[X]:((strong(X)|~rich(X)))))&
(![X]:(~rich(X)<=>(rich(X)&~old(X))))&
(((~funny(alice)<~>happy(alice)))=>((~happy(alice)&curious(alice))))&
(![X]:((~calm(X)&~quiet(X))=>(~rich(X)|tall(X))))&
(![X]:((quiet(X)<~>funny(X))<=>(humble(X)<~>wise(X))))&
(((kind(susan)|~patient(susan)))=>(?[X]:((~brave(X)&kind(X)))))&
((?[X]:((funny(X)<~>~humble(X))))<=>(kind(mary)))&
(![X]:((~creative(X)|happy(X))<=>(~strong(X)&~curious(X))))&
((~generous(fred))=>((~brave(mary)|~old(mary))))&
(![X]:((~calm(X)&quiet(X))=>(rich(X)&~curious(X))))&
(![X]:((~rich(X)|~curious(X))=>(rich(X)<~>~curious(X))))&
((~generous(alice)|patient(alice)))&
(?[X]:((funny(X)|rich(X))))&
(~generous(lucy))&
(?[X]:((kind(X)|brave(X))))&
(?[X]:((~kind(X)<~>calm(X))))&
(~brave(lucy)) | calm(lucy) | [
"p4",
"p6",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4193808099633541667826023
% SZS output start Proof for 4193808099633541667826023
5. ? [X0] : ~old(X0) <=> ? [X0] : (~quiet(X0) & creative(X0)) [input p4]
7. ! [X0] : (~rich(X0) <=> (~old(X0) & rich(X0))) [input p6]
13. ! [X0] : ((happy(X0) | ~creative(X0)) <=> (~curious(X0) & ~strong(X0))) [input p12]
15. ! [X0] : ((quiet(X0) & ~calm(X0)) => (~curious(X0) & rich(X0))) [input p14]
16. ! [X0] : ((~curious(X0) | ~rich(X0)) => (rich(X0) <~> ~curious(X0))) [input p15]
23. ~calm(lucy) [input hypothesis]
24. ? [X0] : ~old(X0) <=> ? [X1] : (~quiet(X1) & creative(X1)) [rectify 5]
39. ! [X0] : ((~curious(X0) & rich(X0)) | (~quiet(X0) | calm(X0))) [ennf transformation 15]
40. ! [X0] : ((~curious(X0) & rich(X0)) | ~quiet(X0) | calm(X0)) [flattening 39]
41. ! [X0] : ((rich(X0) <~> ~curious(X0)) | (curious(X0) & rich(X0))) [ennf transformation 16]
47. (? [X0] : ~old(X0) | ! [X1] : (quiet(X1) | ~creative(X1))) & (? [X1] : (~quiet(X1) & creative(X1)) | ! [X0] : old(X0)) [nnf transformation 24]
48. (? [X0] : ~old(X0) | ! [X1] : (quiet(X1) | ~creative(X1))) & (? [X2] : (~quiet(X2) & creative(X2)) | ! [X3] : old(X3)) [rectify 47]
49. ? [X0] : ~old(X0) => ~old(sK1) [choice axiom]
50. ? [X2] : (~quiet(X2) & creative(X2)) => (~quiet(sK2) & creative(sK2)) [choice axiom]
51. (~old(sK1) | ! [X1] : (quiet(X1) | ~creative(X1))) & ((~quiet(sK2) & creative(sK2)) | ! [X3] : old(X3)) [skolemisation 48,50,49]
54. ! [X0] : ((~rich(X0) | (old(X0) | ~rich(X0))) & ((~old(X0) & rich(X0)) | rich(X0))) [nnf transformation 7]
55. ! [X0] : ((~rich(X0) | old(X0) | ~rich(X0)) & ((~old(X0) & rich(X0)) | rich(X0))) [flattening 54]
64. ! [X0] : (((happy(X0) | ~creative(X0)) | (curious(X0) | strong(X0))) & ((~curious(X0) & ~strong(X0)) | (~happy(X0) & creative(X0)))) [nnf transformation 13]
65. ! [X0] : ((happy(X0) | ~creative(X0) | curious(X0) | strong(X0)) & ((~curious(X0) & ~strong(X0)) | (~happy(X0) & creative(X0)))) [flattening 64]
66. ! [X0] : (((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | (curious(X0) & rich(X0))) [nnf transformation 41]
84. ~old(sK1) | quiet(X1) | ~creative(X1) [cnf transformation 51]
86. rich(X0) | rich(X0) [cnf transformation 55]
88. ~rich(X0) | old(X0) | ~rich(X0) [cnf transformation 55]
112. ~curious(X0) | creative(X0) [cnf transformation 65]
117. ~quiet(X0) | ~curious(X0) | calm(X0) [cnf transformation 40]
121. curious(X0) | ~rich(X0) | curious(X0) [cnf transformation 66]
129. ~calm(lucy) [cnf transformation 23]
131. curious(X0) | ~rich(X0) [duplicate literal removal 121]
133. rich(X0) [duplicate literal removal 86]
134. ~rich(X0) | old(X0) [duplicate literal removal 88]
182. 11 <=> ! [X1] : (quiet(X1) | ~creative(X1)) [avatar definition]
183. ~creative(X1) | quiet(X1) <- (11) [avatar component clause 182]
185. 12 <=> old(sK1) [avatar definition]
187. ~old(sK1) <- (~12) [avatar component clause 185]
188. 11 | ~12 [avatar split clause 84,185,182]
190. 13 <=> ! [X3] : old(X3) [avatar definition]
191. old(X3) <- (13) [avatar component clause 190]
286. curious(X0) [subsumption resolution 131,133]
316. $false <- (~12, 13) [subsumption resolution 187,191]
317. 12 | ~13 [avatar contradiction clause 316]
321. creative(X0) [resolution 112,286]
323. old(X0) [resolution 134,133]
324. 13 [avatar split clause 323,190]
330. quiet(X0) <- (11) [resolution 183,321]
335. ~curious(X0) | calm(X0) <- (11) [resolution 117,330]
336. calm(X0) <- (11) [subsumption resolution 335,286]
337. $false <- (11) [resolution 336,129]
340. ~11 [avatar contradiction clause 337]
341. $false [avatar sat refutation 188,317,324,340]
% SZS output end Proof for 4193808099633541667826023
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is not creative or patient and vice versa. Everyone who is wise or kind is both old and not brave. Everyone who is not calm is either kind or happy and vice versa. Everyone who is both strong and not tall is strong or not strong and vice versa. Everyone who is not kind or not humble is not happy and vice versa. If someone is rich then paul is old and vice versa. Everyone who is both creative and wise is both old and not old and vice versa. Everyone who is tall or not strong is humble. If mary is not calm or patient then someone is both not strong and kind and vice versa. If alice is patient then susan is either not quiet or not strong and vice versa. If someone is old or not rich then john is either not old or not quiet and vice versa. Everyone who is both not calm and not patient is both creative and rich and vice versa. Everyone who is either patient or quiet is either funny or patient. Everyone who is either tall or not old is either not quiet or quiet. Everyone who is not generous or not wise is patient or funny and vice versa. Everyone who is not humble is either calm or not tall. Someone is either not quiet or not creative. Someone is not humble. Mary is either not kind or not calm. Someone is both funny and old. Someone is both quiet and kind. Paul is kind. Susan is both not calm and not generous. | Susan is not old. | contradiction | (![X]:(happy(X)<=>(~creative(X)|patient(X))))&
(![X]:((wise(X)|kind(X))=>(old(X)&~brave(X))))&
(![X]:(~calm(X)<=>(kind(X)<~>happy(X))))&
(![X]:((strong(X)&~tall(X))<=>(strong(X)|~strong(X))))&
(![X]:((~kind(X)|~humble(X))<=>~happy(X)))&
((?[X]:(rich(X)))<=>(old(paul)))&
(![X]:((creative(X)&wise(X))<=>(old(X)&~old(X))))&
(![X]:((tall(X)|~strong(X))=>humble(X)))&
(((~calm(mary)|patient(mary)))<=>(?[X]:((~strong(X)&kind(X)))))&
((patient(alice))<=>((~quiet(susan)<~>~strong(susan))))&
((?[X]:((old(X)|~rich(X))))<=>((~old(john)<~>~quiet(john))))&
(![X]:((~calm(X)&~patient(X))<=>(creative(X)&rich(X))))&
(![X]:((patient(X)<~>quiet(X))=>(funny(X)<~>patient(X))))&
(![X]:((tall(X)<~>~old(X))=>(~quiet(X)<~>quiet(X))))&
(![X]:((~generous(X)|~wise(X))<=>(patient(X)|funny(X))))&
(![X]:(~humble(X)=>(calm(X)<~>~tall(X))))&
(?[X]:((~quiet(X)<~>~creative(X))))&
(?[X]:(~humble(X)))&
((~kind(mary)<~>~calm(mary)))&
(?[X]:((funny(X)&old(X))))&
(?[X]:((quiet(X)&kind(X))))&
(kind(paul))&
((~calm(susan)&~generous(susan))) | ~old(susan) | [
"p1",
"p2",
"p4",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 777980506138975589124125
% SZS output start Proof for 777980506138975589124125
2. ! [X0] : ((kind(X0) | wise(X0)) => (~brave(X0) & old(X0))) [input p1]
3. ! [X0] : (~calm(X0) <=> (kind(X0) <~> happy(X0))) [input p2]
5. ! [X0] : ((~humble(X0) | ~kind(X0)) <=> ~happy(X0)) [input p4]
23. ~generous(susan) & ~calm(susan) [input p22]
24. ~old(susan) [input hypothesis]
25. ! [X0] : ((kind(X0) | wise(X0)) => old(X0)) [pure predicate removal 2]
26. ! [X0] : (old(X0) | (~kind(X0) & ~wise(X0))) [ennf transformation 25]
33. ! [X0] : ((~calm(X0) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) & (((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | calm(X0))) [nnf transformation 3]
36. ! [X0] : (((~humble(X0) | ~kind(X0)) | happy(X0)) & (~happy(X0) | (humble(X0) & kind(X0)))) [nnf transformation 5]
37. ! [X0] : ((~humble(X0) | ~kind(X0) | happy(X0)) & (~happy(X0) | (humble(X0) & kind(X0)))) [flattening 36]
75. ~kind(X0) | old(X0) [cnf transformation 26]
76. calm(X0) | kind(X0) | happy(X0) [cnf transformation 33]
85. ~happy(X0) | kind(X0) [cnf transformation 37]
139. ~calm(susan) [cnf transformation 23]
141. ~old(susan) [cnf transformation 24]
249. kind(susan) | happy(susan) [resolution 76,139]
251. kind(susan) [subsumption resolution 249,85]
253. old(susan) [resolution 251,75]
254. $false [subsumption resolution 253,141]
% SZS output end Proof for 777980506138975589124125
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind then john is not kind or generous and vice versa. If someone is either quiet or creative then susan is patient and vice versa. If someone is either not strong or not calm then someone is humble or not patient and vice versa. Everyone who is both not funny and not wise is either funny or not patient. If someone is either generous or funny then someone is both tall and not wise. If someone is both not brave and not wise then alice is either not quiet or calm. Everyone who is quiet or humble is either not old or kind and vice versa. If alice is happy or not quiet then someone is either quiet or not quiet and vice versa. Everyone who is both strong and not calm is not quiet and vice versa. Everyone who is not brave or calm is not patient or humble. Everyone who is not kind or tall is both kind and not quiet. If someone is both not tall and patient then alice is rich and vice versa. Everyone who is both not generous and not brave is not calm and vice versa. Everyone who is not calm or not kind is both humble and strong. Everyone who is not curious or strong is wise and vice versa. Everyone who is both not brave and not patient is brave or humble and vice versa. Alice is both not creative and strong. Someone is both not funny and curious. Someone is generous or not old. Someone is both not brave and quiet. John is not strong or not quiet. Paul is generous or not generous. Someone is not patient. | Alice is not strong. | contradiction | ((?[X]:(kind(X)))<=>((~kind(john)|generous(john))))&
((?[X]:((quiet(X)<~>creative(X))))<=>(patient(susan)))&
((?[X]:((~strong(X)<~>~calm(X))))<=>(?[X]:((humble(X)|~patient(X)))))&
(![X]:((~funny(X)&~wise(X))=>(funny(X)<~>~patient(X))))&
((?[X]:((generous(X)<~>funny(X))))=>(?[X]:((tall(X)&~wise(X)))))&
((?[X]:((~brave(X)&~wise(X))))=>((~quiet(alice)<~>calm(alice))))&
(![X]:((quiet(X)|humble(X))<=>(~old(X)<~>kind(X))))&
(((happy(alice)|~quiet(alice)))<=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:((strong(X)&~calm(X))<=>~quiet(X)))&
(![X]:((~brave(X)|calm(X))=>(~patient(X)|humble(X))))&
(![X]:((~kind(X)|tall(X))=>(kind(X)&~quiet(X))))&
((?[X]:((~tall(X)&patient(X))))<=>(rich(alice)))&
(![X]:((~generous(X)&~brave(X))<=>~calm(X)))&
(![X]:((~calm(X)|~kind(X))=>(humble(X)&strong(X))))&
(![X]:((~curious(X)|strong(X))<=>wise(X)))&
(![X]:((~brave(X)&~patient(X))<=>(brave(X)|humble(X))))&
((~creative(alice)&strong(alice)))&
(?[X]:((~funny(X)&curious(X))))&
(?[X]:((generous(X)|~old(X))))&
(?[X]:((~brave(X)&quiet(X))))&
((~strong(john)|~quiet(john)))&
((generous(paul)|~generous(paul)))&
(?[X]:(~patient(X))) | ~strong(alice) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8725753208611126248191850
% SZS output start Proof for 8725753208611126248191850
17. strong(alice) & ~creative(alice) [input p16]
24. ~strong(alice) [input hypothesis]
143. strong(alice) [cnf transformation 17]
152. ~strong(alice) [cnf transformation 24]
313. $false [subsumption resolution 152,143]
% SZS output end Proof for 8725753208611126248191850
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not generous and not happy then susan is either not strong or generous and vice versa. If lucy is both not generous and generous then john is not patient and vice versa. If someone is either not quiet or not old then alice is not creative. Everyone who is either not kind or not rich is either creative or not happy. Everyone who is quiet or not rich is funny or not kind and vice versa. If alice is either not kind or happy then susan is not happy and vice versa. Everyone who is both not generous and generous is both not humble and happy. Everyone who is not rich or strong is wise or funny and vice versa. Everyone who is either creative or not rich is tall. Everyone who is both wise and rich is not curious or quiet and vice versa. If susan is not quiet then fred is either not wise or creative and vice versa. If someone is both funny and quiet then someone is brave or not curious and vice versa. If lucy is either patient or funny then someone is both happy and not patient and vice versa. If someone is not creative then susan is both wise and brave and vice versa. If someone is quiet or not generous then someone is not brave and vice versa. If someone is both rich and funny then mary is either not wise or old. Fred is both humble and not quiet. Someone is both old and not tall. Alice is not generous or not quiet. Someone is either wise or not calm. Paul is both not funny and calm. Someone is rich. Alice is brave or patient. Mary is both patient and curious. | Susan is wise. | entailment | ((?[X]:((~generous(X)&~happy(X))))<=>((~strong(susan)<~>generous(susan))))&
(((~generous(lucy)&generous(lucy)))<=>(~patient(john)))&
((?[X]:((~quiet(X)<~>~old(X))))=>(~creative(alice)))&
(![X]:((~kind(X)<~>~rich(X))=>(creative(X)<~>~happy(X))))&
(![X]:((quiet(X)|~rich(X))<=>(funny(X)|~kind(X))))&
(((~kind(alice)<~>happy(alice)))<=>(~happy(susan)))&
(![X]:((~generous(X)&generous(X))=>(~humble(X)&happy(X))))&
(![X]:((~rich(X)|strong(X))<=>(wise(X)|funny(X))))&
(![X]:((creative(X)<~>~rich(X))=>tall(X)))&
(![X]:((wise(X)&rich(X))<=>(~curious(X)|quiet(X))))&
((~quiet(susan))<=>((~wise(fred)<~>creative(fred))))&
((?[X]:((funny(X)&quiet(X))))<=>(?[X]:((brave(X)|~curious(X)))))&
(((patient(lucy)<~>funny(lucy)))<=>(?[X]:((happy(X)&~patient(X)))))&
((?[X]:(~creative(X)))<=>((wise(susan)&brave(susan))))&
((?[X]:((quiet(X)|~generous(X))))<=>(?[X]:(~brave(X))))&
((?[X]:((rich(X)&funny(X))))=>((~wise(mary)<~>old(mary))))&
((humble(fred)&~quiet(fred)))&
(?[X]:((old(X)&~tall(X))))&
((~generous(alice)|~quiet(alice)))&
(?[X]:((wise(X)<~>~calm(X))))&
((~funny(paul)&calm(paul)))&
(?[X]:(rich(X)))&
((brave(alice)|patient(alice)))&
((patient(mary)&curious(mary))) | wise(susan) | [
"p2",
"p8",
"p9",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4656752560166750944422577
% SZS output start Proof for 4656752560166750944422577
3. ? [X0] : (~quiet(X0) <~> ~old(X0)) => ~creative(alice) [input p2]
9. ! [X0] : ((creative(X0) <~> ~rich(X0)) => tall(X0)) [input p8]
10. ! [X0] : ((rich(X0) & wise(X0)) <=> (quiet(X0) | ~curious(X0))) [input p9]
14. ? [X0] : ~creative(X0) <=> (brave(susan) & wise(susan)) [input p13]
18. ? [X0] : (~tall(X0) & old(X0)) [input p17]
25. ~wise(susan) [input hypothesis]
28. ~creative(alice) | ! [X0] : (~quiet(X0) <=> ~old(X0)) [ennf transformation 3]
32. ! [X0] : (tall(X0) | (creative(X0) <=> ~rich(X0))) [ennf transformation 9]
40. ~creative(alice) | ! [X0] : ((~quiet(X0) | old(X0)) & (~old(X0) | quiet(X0))) [nnf transformation 28]
47. ! [X0] : (tall(X0) | ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) [nnf transformation 32]
48. ! [X0] : (((rich(X0) & wise(X0)) | (~quiet(X0) & curious(X0))) & ((quiet(X0) | ~curious(X0)) | (~rich(X0) | ~wise(X0)))) [nnf transformation 10]
49. ! [X0] : (((rich(X0) & wise(X0)) | (~quiet(X0) & curious(X0))) & (quiet(X0) | ~curious(X0) | ~rich(X0) | ~wise(X0))) [flattening 48]
60. (? [X0] : ~creative(X0) | (~brave(susan) | ~wise(susan))) & ((brave(susan) & wise(susan)) | ! [X0] : creative(X0)) [nnf transformation 14]
61. (? [X0] : ~creative(X0) | ~brave(susan) | ~wise(susan)) & ((brave(susan) & wise(susan)) | ! [X0] : creative(X0)) [flattening 60]
62. (? [X0] : ~creative(X0) | ~brave(susan) | ~wise(susan)) & ((brave(susan) & wise(susan)) | ! [X1] : creative(X1)) [rectify 61]
63. ? [X0] : ~creative(X0) => ~creative(sK4) [choice axiom]
64. (~creative(sK4) | ~brave(susan) | ~wise(susan)) & ((brave(susan) & wise(susan)) | ! [X1] : creative(X1)) [skolemisation 62,63]
71. ? [X0] : (~tall(X0) & old(X0)) => (~tall(sK7) & old(sK7)) [choice axiom]
72. ~tall(sK7) & old(sK7) [skolemisation 18,71]
87. ~creative(alice) | ~old(X0) | quiet(X0) [cnf transformation 40]
107. ~rich(X0) | tall(X0) | ~creative(X0) [cnf transformation 47]
113. ~quiet(X0) | rich(X0) [cnf transformation 49]
129. wise(susan) | creative(X1) [cnf transformation 64]
139. old(sK7) [cnf transformation 72]
140. ~tall(sK7) [cnf transformation 72]
150. ~wise(susan) [cnf transformation 25]
190. 9 <=> creative(alice) [avatar definition]
192. ~creative(alice) <- (~9) [avatar component clause 190]
195. 10 <=> ! [X0] : (~old(X0) | quiet(X0)) [avatar definition]
196. ~old(X0) | quiet(X0) <- (10) [avatar component clause 195]
197. 10 | ~9 [avatar split clause 87,190,195]
286. 29 <=> wise(susan) [avatar definition]
299. 32 <=> ! [X1] : creative(X1) [avatar definition]
300. creative(X1) <- (32) [avatar component clause 299]
302. 32 | 29 [avatar split clause 129,286,299]
368. ~29 [avatar split clause 150,286]
371. $false <- (~9, 32) [subsumption resolution 192,300]
372. 9 | ~32 [avatar contradiction clause 371]
382. quiet(sK7) <- (10) [resolution 196,139]
385. rich(sK7) <- (10) [resolution 382,113]
483. tall(sK7) | ~creative(sK7) <- (10) [resolution 107,385]
487. ~creative(sK7) <- (10) [subsumption resolution 483,140]
488. $false <- (10, 32) [subsumption resolution 487,300]
489. ~10 | ~32 [avatar contradiction clause 488]
491. $false [avatar sat refutation 197,302,368,372,489]
% SZS output end Proof for 4656752560166750944422577
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is not funny and vice versa.
Everyone who is not wise is both not creative and not tall.
Everyone who is not tall is either patient or not humble.
Everyone who is not quiet is not strong or wise.
If someone is either kind or not creative then someone is both kind and tall and vice versa.
If someone is both not strong and not patient then john is both not calm and not humble.
If fred is brave or not strong then susan is both not old and wise.
If someone is not wise or brave then mary is either not funny or tall and vice versa.
Everyone who is not rich is either calm or brave.
Everyone who is both curious and calm is not funny and vice versa.
If someone is humble or wise then mary is either not creative or not calm and vice versa.
Everyone who is both strong and not patient is not curious or not brave and vice versa.
If mary is not kind then someone is patient or not quiet.
Everyone who is wise or funny is not tall or not strong and vice versa.
Everyone who is both funny and wise is brave or not generous and vice versa.
Susan is rich or not happy.
Susan is calm.
Someone is both rich and happy.
Mary is generous.
Someone is both not old and not kind. | Fred is kind. | neutral | (![X]:(wise(X)<=>~funny(X)))&
(![X]:(~wise(X)=>(~creative(X)&~tall(X))))&
(![X]:(~tall(X)=>(patient(X)<~>~humble(X))))&
(![X]:(~quiet(X)=>(~strong(X)|wise(X))))&
((?[X]:((kind(X)<~>~creative(X))))<=>(?[X]:((kind(X)&tall(X)))))&
((?[X]:((~strong(X)&~patient(X))))=>((~calm(john)&~humble(john))))&
(((brave(fred)|~strong(fred)))=>((~old(susan)&wise(susan))))&
((?[X]:((~wise(X)|brave(X))))<=>((~funny(mary)<~>tall(mary))))&
(![X]:(~rich(X)=>(calm(X)<~>brave(X))))&
(![X]:((curious(X)&calm(X))<=>~funny(X)))&
((?[X]:((humble(X)|wise(X))))<=>((~creative(mary)<~>~calm(mary))))&
(![X]:((strong(X)&~patient(X))<=>(~curious(X)|~brave(X))))&
((~kind(mary))=>(?[X]:((patient(X)|~quiet(X)))))&
(![X]:((wise(X)|funny(X))<=>(~tall(X)|~strong(X))))&
(![X]:((funny(X)&wise(X))<=>(brave(X)|~generous(X))))&
((rich(susan)|~happy(susan)))&
(calm(susan))&
(?[X]:((rich(X)&happy(X))))&
(generous(mary))&
(?[X]:((~old(X)&~kind(X)))) | kind(fred) | [] | null | 0 |
If someone is both not humble and not happy then paul is either humble or quiet and vice versa.
Everyone who is not rich is not happy or not generous.
Everyone who is either not strong or not calm is not patient.
If paul is not calm or curious then someone is either not quiet or humble and vice versa.
Everyone who is either not calm or calm is either not happy or brave and vice versa.
Everyone who is not old or not brave is not strong and vice versa.
Everyone who is both brave and not patient is either rich or old and vice versa.
Everyone who is not funny is both happy and not kind and vice versa.
Everyone who is not strong or not creative is not patient and vice versa.
Everyone who is both not old and quiet is not wise or not quiet and vice versa.
If john is either not quiet or brave then someone is generous.
Everyone who is not wise is happy.
If someone is both quiet and not generous then someone is both creative and not brave.
If someone is either generous or humble then someone is strong and vice versa.
If alice is not creative then susan is not creative.
If someone is humble or brave then someone is not quiet.
Someone is not happy or not old.
Paul is old.
Someone is both rich and tall.
Someone is not kind or wise.
Alice is either old or tall.
Someone is curious or kind. | John is not rich. | contradiction | ((?[X]:((~humble(X)&~happy(X))))<=>((humble(paul)<~>quiet(paul))))&
(![X]:(~rich(X)=>(~happy(X)|~generous(X))))&
(![X]:((~strong(X)<~>~calm(X))=>~patient(X)))&
(((~calm(paul)|curious(paul)))<=>(?[X]:((~quiet(X)<~>humble(X)))))&
(![X]:((~calm(X)<~>calm(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((~old(X)|~brave(X))<=>~strong(X)))&
(![X]:((brave(X)&~patient(X))<=>(rich(X)<~>old(X))))&
(![X]:(~funny(X)<=>(happy(X)&~kind(X))))&
(![X]:((~strong(X)|~creative(X))<=>~patient(X)))&
(![X]:((~old(X)&quiet(X))<=>(~wise(X)|~quiet(X))))&
(((~quiet(john)<~>brave(john)))=>(?[X]:(generous(X))))&
(![X]:(~wise(X)=>happy(X)))&
((?[X]:((quiet(X)&~generous(X))))=>(?[X]:((creative(X)&~brave(X)))))&
((?[X]:((generous(X)<~>humble(X))))<=>(?[X]:(strong(X))))&
((~creative(alice))=>(~creative(susan)))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(~quiet(X))))&
(?[X]:((~happy(X)|~old(X))))&
(old(paul))&
(?[X]:((rich(X)&tall(X))))&
(?[X]:((~kind(X)|wise(X))))&
((old(alice)<~>tall(alice)))&
(?[X]:((curious(X)|kind(X)))) | ~rich(john) | [
"p4",
"p6",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 392502687314912833700756
% SZS output start Proof for 392502687314912833700756
5. ! [X0] : ((~calm(X0) <~> calm(X0)) <=> (~happy(X0) <~> brave(X0))) [input p4]
7. ! [X0] : ((~patient(X0) & brave(X0)) <=> (rich(X0) <~> old(X0))) [input p6]
10. ! [X0] : ((quiet(X0) & ~old(X0)) <=> (~quiet(X0) | ~wise(X0))) [input p9]
12. ! [X0] : (~wise(X0) => happy(X0)) [input p11]
16. ? [X0] : (brave(X0) | humble(X0)) => ? [X0] : ~quiet(X0) [input p15]
23. ~rich(john) [input hypothesis]
26. ? [X0] : (brave(X0) | humble(X0)) => ? [X1] : ~quiet(X1) [rectify 16]
31. ! [X0] : (happy(X0) | wise(X0)) [ennf transformation 12]
34. ? [X1] : ~quiet(X1) | ! [X0] : (~brave(X0) & ~humble(X0)) [ennf transformation 26]
45. ! [X0] : ((((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) & (((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0))))) [nnf transformation 5]
48. ! [X0] : (((~patient(X0) & brave(X0)) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0)))) & (((~old(X0) | ~rich(X0)) & (old(X0) | rich(X0))) | (patient(X0) | ~brave(X0)))) [nnf transformation 7]
49. ! [X0] : (((~patient(X0) & brave(X0)) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0)))) & (((~old(X0) | ~rich(X0)) & (old(X0) | rich(X0))) | patient(X0) | ~brave(X0))) [flattening 48]
52. ! [X0] : (((quiet(X0) & ~old(X0)) | (quiet(X0) & wise(X0))) & ((~quiet(X0) | ~wise(X0)) | (~quiet(X0) | old(X0)))) [nnf transformation 10]
53. ! [X0] : (((quiet(X0) & ~old(X0)) | (quiet(X0) & wise(X0))) & (~quiet(X0) | ~wise(X0) | ~quiet(X0) | old(X0))) [flattening 52]
65. ? [X0] : ~quiet(X0) | ! [X1] : (~brave(X1) & ~humble(X1)) [rectify 34]
66. ? [X0] : ~quiet(X0) => ~quiet(sK6) [choice axiom]
67. ~quiet(sK6) | ! [X1] : (~brave(X1) & ~humble(X1)) [skolemisation 65,66]
92. brave(X0) | ~happy(X0) | calm(X0) | calm(X0) [cnf transformation 45]
93. brave(X0) | ~happy(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 45]
106. ~old(X0) | rich(X0) | brave(X0) [cnf transformation 49]
112. ~quiet(X0) | ~wise(X0) | ~quiet(X0) | old(X0) [cnf transformation 53]
116. quiet(X0) | quiet(X0) [cnf transformation 53]
119. wise(X0) | happy(X0) [cnf transformation 31]
128. ~quiet(sK6) | ~brave(X1) [cnf transformation 67]
137. ~rich(john) [cnf transformation 23]
138. ~quiet(X0) | ~wise(X0) | old(X0) [duplicate literal removal 112]
139. quiet(X0) [duplicate literal removal 116]
140. brave(X0) | ~happy(X0) | calm(X0) [duplicate literal removal 92]
141. ~calm(X0) | ~happy(X0) | brave(X0) [duplicate literal removal 93]
198. ~happy(X0) | brave(X0) [subsumption resolution 140,141]
199. ~wise(X0) | old(X0) [subsumption resolution 138,139]
259. ~brave(X1) [subsumption resolution 128,139]
317. old(X0) | happy(X0) [resolution 199,119]
328. rich(X0) | brave(X0) | happy(X0) [resolution 106,317]
331. rich(X0) | happy(X0) [subsumption resolution 328,259]
344. happy(john) [resolution 331,137]
346. brave(john) [resolution 344,198]
347. $false [subsumption resolution 346,259]
% SZS output end Proof for 392502687314912833700756
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not old or not humble then someone is calm.
Everyone who is not old is either funny or not old.
If someone is either not happy or not generous then john is both tall and not quiet.
If john is either patient or not wise then paul is curious.
If someone is not calm or not kind then someone is both not old and generous.
Everyone who is not old or not creative is both wise and not funny and vice versa.
Everyone who is both not quiet and generous is humble or not funny and vice versa.
If someone is not generous then someone is both not generous and quiet.
If alice is not tall then someone is not creative or not quiet and vice versa.
If susan is either rich or patient then lucy is either curious or not humble.
Everyone who is either not quiet or not creative is both strong and brave and vice versa.
Everyone who is both happy and strong is brave or quiet and vice versa.
Everyone who is both old and brave is not brave and vice versa.
If fred is rich then alice is wise or not curious and vice versa.
If fred is both not brave and not old then someone is either creative or not quiet.
If someone is old then susan is not rich or old and vice versa.
Someone is tall or not funny.
Alice is strong or not creative.
Fred is wise or curious.
Paul is rich or not old.
Paul is both kind and strong.
Someone is either not happy or not old. | Lucy is not strong. | contradiction | (((~old(mary)<~>~humble(mary)))=>(?[X]:(calm(X))))&
(![X]:(~old(X)=>(funny(X)<~>~old(X))))&
((?[X]:((~happy(X)<~>~generous(X))))=>((tall(john)&~quiet(john))))&
(((patient(john)<~>~wise(john)))=>(curious(paul)))&
((?[X]:((~calm(X)|~kind(X))))=>(?[X]:((~old(X)&generous(X)))))&
(![X]:((~old(X)|~creative(X))<=>(wise(X)&~funny(X))))&
(![X]:((~quiet(X)&generous(X))<=>(humble(X)|~funny(X))))&
((?[X]:(~generous(X)))=>(?[X]:((~generous(X)&quiet(X)))))&
((~tall(alice))<=>(?[X]:((~creative(X)|~quiet(X)))))&
(((rich(susan)<~>patient(susan)))=>((curious(lucy)<~>~humble(lucy))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(strong(X)&brave(X))))&
(![X]:((happy(X)&strong(X))<=>(brave(X)|quiet(X))))&
(![X]:((old(X)&brave(X))<=>~brave(X)))&
((rich(fred))<=>((wise(alice)|~curious(alice))))&
(((~brave(fred)&~old(fred)))=>(?[X]:((creative(X)<~>~quiet(X)))))&
((?[X]:(old(X)))<=>((~rich(susan)|old(susan))))&
(?[X]:((tall(X)|~funny(X))))&
((strong(alice)|~creative(alice)))&
((wise(fred)|curious(fred)))&
((rich(paul)|~old(paul)))&
((kind(paul)&strong(paul)))&
(?[X]:((~happy(X)<~>~old(X)))) | ~strong(lucy) | [
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 39132029914793055348411
% SZS output start Proof for 39132029914793055348411
12. ! [X0] : ((strong(X0) & happy(X0)) <=> (quiet(X0) | brave(X0))) [input p11]
13. ! [X0] : ((brave(X0) & old(X0)) <=> ~brave(X0)) [input p12]
23. ~strong(lucy) [input hypothesis]
54. ! [X0] : (((strong(X0) & happy(X0)) | (~quiet(X0) & ~brave(X0))) & ((quiet(X0) | brave(X0)) | (~strong(X0) | ~happy(X0)))) [nnf transformation 12]
55. ! [X0] : (((strong(X0) & happy(X0)) | (~quiet(X0) & ~brave(X0))) & (quiet(X0) | brave(X0) | ~strong(X0) | ~happy(X0))) [flattening 54]
56. ! [X0] : (((brave(X0) & old(X0)) | brave(X0)) & (~brave(X0) | (~brave(X0) | ~old(X0)))) [nnf transformation 13]
57. ! [X0] : (((brave(X0) & old(X0)) | brave(X0)) & (~brave(X0) | ~brave(X0) | ~old(X0))) [flattening 56]
109. ~brave(X0) | strong(X0) [cnf transformation 55]
113. brave(X0) | brave(X0) [cnf transformation 57]
129. ~strong(lucy) [cnf transformation 23]
131. brave(X0) [duplicate literal removal 113]
270. strong(X0) [resolution 109,131]
271. $false [resolution 270,129]
% SZS output end Proof for 39132029914793055348411
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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