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
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|---|---|---|---|---|---|---|---|
If someone is old then paul is not kind or not rich.
Everyone who is strong is calm.
If fred is either not rich or not patient then fred is both quiet and not brave.
If someone is not happy or funny then mary is either not brave or curious.
Everyone who is both calm and wise is either rich or wise and vice versa.
If paul is not humble then someone is both not curious and brave.
Everyone who is not brave or patient is both patient and not kind and vice versa.
If paul is calm or not old then alice is humble.
If mary is rich then susan is either not calm or brave and vice versa.
If someone is not wise or brave then someone is both kind and not rich and vice versa.
If paul is brave or happy then someone is either tall or not humble and vice versa.
Everyone who is either not old or strong is both not kind and not creative and vice versa.
Everyone who is both tall and not happy is both creative and not wise and vice versa.
Everyone who is either not wise or wise is wise.
Everyone who is not patient is both not happy and humble.
If someone is not wise then susan is not calm or not patient and vice versa.
Mary is either not wise or patient.
Alice is either brave or strong.
Someone is both strong and not funny.
Someone is either wise or not tall.
Someone is not brave or not old.
Someone is not creative or not humble.
Susan is not tall. | Susan is not patient. | contradiction | ((?[X]:(old(X)))=>((~kind(paul)|~rich(paul))))&
(![X]:(strong(X)=>calm(X)))&
(((~rich(fred)<~>~patient(fred)))=>((quiet(fred)&~brave(fred))))&
((?[X]:((~happy(X)|funny(X))))=>((~brave(mary)<~>curious(mary))))&
(![X]:((calm(X)&wise(X))<=>(rich(X)<~>wise(X))))&
((~humble(paul))=>(?[X]:((~curious(X)&brave(X)))))&
(![X]:((~brave(X)|patient(X))<=>(patient(X)&~kind(X))))&
(((calm(paul)|~old(paul)))=>(humble(alice)))&
((rich(mary))<=>((~calm(susan)<~>brave(susan))))&
((?[X]:((~wise(X)|brave(X))))<=>(?[X]:((kind(X)&~rich(X)))))&
(((brave(paul)|happy(paul)))<=>(?[X]:((tall(X)<~>~humble(X)))))&
(![X]:((~old(X)<~>strong(X))<=>(~kind(X)&~creative(X))))&
(![X]:((tall(X)&~happy(X))<=>(creative(X)&~wise(X))))&
(![X]:((~wise(X)<~>wise(X))=>wise(X)))&
(![X]:(~patient(X)=>(~happy(X)&humble(X))))&
((?[X]:(~wise(X)))<=>((~calm(susan)|~patient(susan))))&
((~wise(mary)<~>patient(mary)))&
((brave(alice)<~>strong(alice)))&
(?[X]:((strong(X)&~funny(X))))&
(?[X]:((wise(X)<~>~tall(X))))&
(?[X]:((~brave(X)|~old(X))))&
(?[X]:((~creative(X)|~humble(X))))&
(~tall(susan)) | ~patient(susan) | [
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2685144281539878210117567
% SZS output start Proof for 2685144281539878210117567
14. ! [X0] : ((~wise(X0) <~> wise(X0)) => wise(X0)) [input p13]
16. ? [X0] : ~wise(X0) <=> (~patient(susan) | ~calm(susan)) [input p15]
24. ~patient(susan) [input hypothesis]
36. ! [X0] : (wise(X0) | (~wise(X0) <=> wise(X0))) [ennf transformation 14]
61. ! [X0] : (wise(X0) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) [nnf transformation 36]
62. (? [X0] : ~wise(X0) | (patient(susan) & calm(susan))) & ((~patient(susan) | ~calm(susan)) | ! [X0] : wise(X0)) [nnf transformation 16]
63. (? [X0] : ~wise(X0) | (patient(susan) & calm(susan))) & (~patient(susan) | ~calm(susan) | ! [X0] : wise(X0)) [flattening 62]
64. (? [X0] : ~wise(X0) | (patient(susan) & calm(susan))) & (~patient(susan) | ~calm(susan) | ! [X1] : wise(X1)) [rectify 63]
65. ? [X0] : ~wise(X0) => ~wise(sK4) [choice axiom]
66. (~wise(sK4) | (patient(susan) & calm(susan))) & (~patient(susan) | ~calm(susan) | ! [X1] : wise(X1)) [skolemisation 64,65]
124. wise(X0) | wise(X0) | wise(X0) [cnf transformation 61]
130. ~wise(sK4) | patient(susan) [cnf transformation 66]
141. ~patient(susan) [cnf transformation 24]
142. wise(X0) [duplicate literal removal 124]
251. 24 <=> ! [X3] : wise(X3) [avatar definition]
252. wise(X3) <- (24) [avatar component clause 251]
288. 24 [avatar split clause 142,251]
290. 32 <=> patient(susan) [avatar definition]
294. 33 <=> wise(sK4) [avatar definition]
296. ~wise(sK4) <- (~33) [avatar component clause 294]
297. 32 | ~33 [avatar split clause 130,294,290]
348. ~32 [avatar split clause 141,290]
355. $false <- (24, ~33) [resolution 296,252]
356. ~24 | 33 [avatar contradiction clause 355]
357. $false [avatar sat refutation 288,297,348,356]
% SZS output end Proof for 2685144281539878210117567
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not funny or quiet then fred is happy.
If someone is brave or not wise then susan is both tall and not rich and vice versa.
If someone is humble then lucy is either humble or quiet.
Everyone who is strong is both not wise and strong.
Everyone who is not humble is not quiet or not old.
Everyone who is curious or creative is tall.
Everyone who is generous is curious and vice versa.
Everyone who is both not generous and not calm is not happy or not generous and vice versa.
Everyone who is not generous or not old is both quiet and calm.
If alice is both not calm and wise then paul is old.
If someone is either not patient or tall then someone is not tall or not curious and vice versa.
Everyone who is either not tall or generous is not calm or not generous.
Everyone who is both not strong and not tall is funny or not humble and vice versa.
If someone is both generous and not calm then someone is either not funny or not wise and vice versa.
If lucy is not generous then mary is not rich or not funny.
Everyone who is either generous or rich is either creative or old.
John is either brave or not calm.
Mary is strong or not happy.
John is rich or creative.
Someone is either not tall or not patient.
Fred is brave or not humble. | Susan is quiet. | neutral | (((~funny(john)<~>quiet(john)))=>(happy(fred)))&
((?[X]:((brave(X)|~wise(X))))<=>((tall(susan)&~rich(susan))))&
((?[X]:(humble(X)))=>((humble(lucy)<~>quiet(lucy))))&
(![X]:(strong(X)=>(~wise(X)&strong(X))))&
(![X]:(~humble(X)=>(~quiet(X)|~old(X))))&
(![X]:((curious(X)|creative(X))=>tall(X)))&
(![X]:(generous(X)<=>curious(X)))&
(![X]:((~generous(X)&~calm(X))<=>(~happy(X)|~generous(X))))&
(![X]:((~generous(X)|~old(X))=>(quiet(X)&calm(X))))&
(((~calm(alice)&wise(alice)))=>(old(paul)))&
((?[X]:((~patient(X)<~>tall(X))))<=>(?[X]:((~tall(X)|~curious(X)))))&
(![X]:((~tall(X)<~>generous(X))=>(~calm(X)|~generous(X))))&
(![X]:((~strong(X)&~tall(X))<=>(funny(X)|~humble(X))))&
((?[X]:((generous(X)&~calm(X))))<=>(?[X]:((~funny(X)<~>~wise(X)))))&
((~generous(lucy))=>((~rich(mary)|~funny(mary))))&
(![X]:((generous(X)<~>rich(X))=>(creative(X)<~>old(X))))&
((brave(john)<~>~calm(john)))&
((strong(mary)|~happy(mary)))&
((rich(john)|creative(john)))&
(?[X]:((~tall(X)<~>~patient(X))))&
((brave(fred)|~humble(fred))) | quiet(susan) | [] | null | 0 |
Everyone who is either not creative or creative is not rich or creative.
If someone is calm then someone is funny or humble and vice versa.
If mary is creative or humble then mary is both not strong and not old.
Everyone who is both not brave and not rich is patient.
Everyone who is either tall or curious is not quiet and vice versa.
Everyone who is not quiet is happy or curious and vice versa.
If mary is happy or not quiet then someone is not calm and vice versa.
If alice is both tall and not creative then someone is humble.
Everyone who is tall is both patient and not generous.
Everyone who is both not generous and funny is curious and vice versa.
If mary is quiet then susan is either happy or not brave.
Everyone who is either kind or not generous is both quiet and calm and vice versa.
Everyone who is either not generous or wise is both patient and not quiet and vice versa.
If susan is both humble and not rich then fred is tall and vice versa.
Everyone who is both old and happy is not quiet or old and vice versa.
Everyone who is not wise or not quiet is either creative or rich and vice versa.
Someone is rich or strong.
Alice is not humble or not strong.
Someone is quiet.
Someone is either curious or not rich.
Someone is funny or not rich.
Someone is wise or not calm.
Someone is either not humble or tall.
Someone is not strong or not happy. | Mary is not tall. | entailment | (![X]:((~creative(X)<~>creative(X))=>(~rich(X)|creative(X))))&
((?[X]:(calm(X)))<=>(?[X]:((funny(X)|humble(X)))))&
(((creative(mary)|humble(mary)))=>((~strong(mary)&~old(mary))))&
(![X]:((~brave(X)&~rich(X))=>patient(X)))&
(![X]:((tall(X)<~>curious(X))<=>~quiet(X)))&
(![X]:(~quiet(X)<=>(happy(X)|curious(X))))&
(((happy(mary)|~quiet(mary)))<=>(?[X]:(~calm(X))))&
(((tall(alice)&~creative(alice)))=>(?[X]:(humble(X))))&
(![X]:(tall(X)=>(patient(X)&~generous(X))))&
(![X]:((~generous(X)&funny(X))<=>curious(X)))&
((quiet(mary))=>((happy(susan)<~>~brave(susan))))&
(![X]:((kind(X)<~>~generous(X))<=>(quiet(X)&calm(X))))&
(![X]:((~generous(X)<~>wise(X))<=>(patient(X)&~quiet(X))))&
(((humble(susan)&~rich(susan)))<=>(tall(fred)))&
(![X]:((old(X)&happy(X))<=>(~quiet(X)|old(X))))&
(![X]:((~wise(X)|~quiet(X))<=>(creative(X)<~>rich(X))))&
(?[X]:((rich(X)|strong(X))))&
((~humble(alice)|~strong(alice)))&
(?[X]:(quiet(X)))&
(?[X]:((curious(X)<~>~rich(X))))&
(?[X]:((funny(X)|~rich(X))))&
(?[X]:((wise(X)|~calm(X))))&
(?[X]:((~humble(X)<~>tall(X))))&
(?[X]:((~strong(X)|~happy(X)))) | ~tall(mary) | [
"p0",
"p2",
"p4",
"p5",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6082942083597009735221477
% SZS output start Proof for 6082942083597009735221477
1. ! [X0] : ((~creative(X0) <~> creative(X0)) => (creative(X0) | ~rich(X0))) [input p0]
3. (humble(mary) | creative(mary)) => (~old(mary) & ~strong(mary)) [input p2]
5. ! [X0] : ((tall(X0) <~> curious(X0)) <=> ~quiet(X0)) [input p4]
6. ! [X0] : (~quiet(X0) <=> (curious(X0) | happy(X0))) [input p5]
15. ! [X0] : ((happy(X0) & old(X0)) <=> (old(X0) | ~quiet(X0))) [input p14]
16. ! [X0] : ((~quiet(X0) | ~wise(X0)) <=> (creative(X0) <~> rich(X0))) [input p15]
25. tall(mary) [input hypothesis]
27. ! [X0] : ((creative(X0) | ~rich(X0)) | (~creative(X0) <=> creative(X0))) [ennf transformation 1]
28. ! [X0] : (creative(X0) | ~rich(X0) | (~creative(X0) <=> creative(X0))) [flattening 27]
29. (~old(mary) & ~strong(mary)) | (~humble(mary) & ~creative(mary)) [ennf transformation 3]
36. ! [X0] : (creative(X0) | ~rich(X0) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) [nnf transformation 28]
42. ! [X0] : ((((~curious(X0) | ~tall(X0)) & (curious(X0) | tall(X0))) | quiet(X0)) & (~quiet(X0) | ((tall(X0) | ~curious(X0)) & (curious(X0) | ~tall(X0))))) [nnf transformation 5]
43. ! [X0] : ((~quiet(X0) | (~curious(X0) & ~happy(X0))) & ((curious(X0) | happy(X0)) | quiet(X0))) [nnf transformation 6]
44. ! [X0] : ((~quiet(X0) | (~curious(X0) & ~happy(X0))) & (curious(X0) | happy(X0) | quiet(X0))) [flattening 43]
61. ! [X0] : (((happy(X0) & old(X0)) | (~old(X0) & quiet(X0))) & ((old(X0) | ~quiet(X0)) | (~happy(X0) | ~old(X0)))) [nnf transformation 15]
62. ! [X0] : (((happy(X0) & old(X0)) | (~old(X0) & quiet(X0))) & (old(X0) | ~quiet(X0) | ~happy(X0) | ~old(X0))) [flattening 61]
63. ! [X0] : (((~quiet(X0) | ~wise(X0)) | ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0)))) & (((~rich(X0) | ~creative(X0)) & (rich(X0) | creative(X0))) | (quiet(X0) & wise(X0)))) [nnf transformation 16]
64. ! [X0] : ((~quiet(X0) | ~wise(X0) | ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0)))) & (((~rich(X0) | ~creative(X0)) & (rich(X0) | creative(X0))) | (quiet(X0) & wise(X0)))) [flattening 63]
81. creative(X0) | ~rich(X0) | creative(X0) | creative(X0) [cnf transformation 36]
88. ~old(mary) | ~creative(mary) [cnf transformation 29]
91. ~quiet(X0) | curious(X0) | ~tall(X0) [cnf transformation 42]
97. ~quiet(X0) | ~curious(X0) [cnf transformation 44]
125. quiet(X0) | old(X0) [cnf transformation 62]
130. rich(X0) | creative(X0) | quiet(X0) [cnf transformation 64]
132. ~rich(X0) | ~creative(X0) | quiet(X0) [cnf transformation 64]
145. tall(mary) [cnf transformation 25]
146. ~rich(X0) | creative(X0) [duplicate literal removal 81]
177. 8 <=> old(mary) [avatar definition]
182. 9 <=> creative(mary) [avatar definition]
184. ~creative(mary) <- (~9) [avatar component clause 182]
185. ~9 | ~8 [avatar split clause 88,177,182]
197. 12 <=> quiet(mary) [avatar definition]
198. quiet(mary) <- (12) [avatar component clause 197]
199. ~quiet(mary) <- (~12) [avatar component clause 197]
249. ~rich(X0) | quiet(X0) [subsumption resolution 132,146]
251. quiet(X0) | creative(X0) [subsumption resolution 130,249]
322. old(mary) <- (~12) [resolution 125,199]
326. 8 | 12 [avatar split clause 322,197,177]
345. creative(mary) <- (~12) [resolution 251,199]
346. $false <- (~9, ~12) [subsumption resolution 345,184]
347. 9 | 12 [avatar contradiction clause 346]
348. ~curious(mary) <- (12) [resolution 198,97]
353. curious(mary) | ~tall(mary) <- (12) [resolution 91,198]
360. ~tall(mary) <- (12) [subsumption resolution 353,348]
361. $false <- (12) [subsumption resolution 360,145]
362. ~12 [avatar contradiction clause 361]
367. $false [avatar sat refutation 185,326,347,362]
% SZS output end Proof for 6082942083597009735221477
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or not funny is not strong or happy and vice versa.
If lucy is both not calm and not humble then alice is not quiet or brave.
Everyone who is calm is both not calm and generous and vice versa.
Everyone who is either not creative or not curious is not humble or tall and vice versa.
If someone is not patient then someone is not brave or not wise.
Everyone who is both calm and not humble is curious and vice versa.
Everyone who is either curious or tall is not wise.
Everyone who is either brave or wise is patient or humble and vice versa.
If lucy is creative then lucy is not old or not patient.
If susan is both not creative and not tall then fred is creative and vice versa.
Everyone who is either not quiet or creative is both strong and funny.
Everyone who is not old or not happy is both not rich and not calm.
Everyone who is both brave and not strong is not tall and vice versa.
If someone is both wise and not curious then someone is both generous and tall and vice versa.
If alice is both not generous and kind then fred is curious or not patient and vice versa.
Mary is not kind.
Someone is not wise or not quiet.
Paul is either kind or not generous.
Someone is either rich or not quiet.
Someone is not kind.
Alice is not quiet or not old.
Someone is humble or not calm. | Alice is not calm. | entailment | (![X]:((~old(X)|~funny(X))<=>(~strong(X)|happy(X))))&
(((~calm(lucy)&~humble(lucy)))=>((~quiet(alice)|brave(alice))))&
(![X]:(calm(X)<=>(~calm(X)&generous(X))))&
(![X]:((~creative(X)<~>~curious(X))<=>(~humble(X)|tall(X))))&
((?[X]:(~patient(X)))=>(?[X]:((~brave(X)|~wise(X)))))&
(![X]:((calm(X)&~humble(X))<=>curious(X)))&
(![X]:((curious(X)<~>tall(X))=>~wise(X)))&
(![X]:((brave(X)<~>wise(X))<=>(patient(X)|humble(X))))&
((creative(lucy))=>((~old(lucy)|~patient(lucy))))&
(((~creative(susan)&~tall(susan)))<=>(creative(fred)))&
(![X]:((~quiet(X)<~>creative(X))=>(strong(X)&funny(X))))&
(![X]:((~old(X)|~happy(X))=>(~rich(X)&~calm(X))))&
(![X]:((brave(X)&~strong(X))<=>~tall(X)))&
((?[X]:((wise(X)&~curious(X))))<=>(?[X]:((generous(X)&tall(X)))))&
(((~generous(alice)&kind(alice)))<=>((curious(fred)|~patient(fred))))&
(~kind(mary))&
(?[X]:((~wise(X)|~quiet(X))))&
((kind(paul)<~>~generous(paul)))&
(?[X]:((rich(X)<~>~quiet(X))))&
(?[X]:(~kind(X)))&
((~quiet(alice)|~old(alice)))&
(?[X]:((humble(X)|~calm(X)))) | ~calm(alice) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 4256360908349189516126898
% SZS output start Proof for 4256360908349189516126898
3. ! [X0] : (calm(X0) <=> (generous(X0) & ~calm(X0))) [input p2]
23. calm(alice) [input hypothesis]
36. ! [X0] : ((calm(X0) | (~generous(X0) | calm(X0))) & ((generous(X0) & ~calm(X0)) | ~calm(X0))) [nnf transformation 3]
37. ! [X0] : ((calm(X0) | ~generous(X0) | calm(X0)) & ((generous(X0) & ~calm(X0)) | ~calm(X0))) [flattening 36]
75. ~calm(X0) | ~calm(X0) [cnf transformation 37]
129. calm(alice) [cnf transformation 23]
130. ~calm(X0) [duplicate literal removal 75]
264. $false [subsumption resolution 129,130]
% SZS output end Proof for 4256360908349189516126898
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not generous then someone is either tall or not calm and vice versa. If fred is both kind and strong then mary is tall. If fred is either funny or not creative then someone is brave. Everyone who is kind is either generous or kind. Everyone who is both patient and not curious is both strong and calm. Everyone who is patient or not brave is rich or not tall. If someone is not strong or not curious then john is not rich and vice versa. If someone is either kind or not funny then someone is either wise or kind and vice versa. Everyone who is creative is not happy or not strong and vice versa. Everyone who is not rich is either not brave or tall. Everyone who is either not calm or strong is patient and vice versa. Everyone who is patient or strong is not quiet. If someone is both not calm and tall then paul is both kind and curious. If john is not creative then someone is either strong or not quiet. If someone is both happy and not quiet then someone is not creative or not happy. Everyone who is either not funny or humble is either not creative or not brave. Susan is calm or strong. Mary is creative or not creative. Someone is not humble or not happy. John is both wise and strong. John is funny. Someone is not calm. Susan is either not tall or not wise. | Susan is calm. | neutral | ((~generous(fred))<=>(?[X]:((tall(X)<~>~calm(X)))))&
(((kind(fred)&strong(fred)))=>(tall(mary)))&
(((funny(fred)<~>~creative(fred)))=>(?[X]:(brave(X))))&
(![X]:(kind(X)=>(generous(X)<~>kind(X))))&
(![X]:((patient(X)&~curious(X))=>(strong(X)&calm(X))))&
(![X]:((patient(X)|~brave(X))=>(rich(X)|~tall(X))))&
((?[X]:((~strong(X)|~curious(X))))<=>(~rich(john)))&
((?[X]:((kind(X)<~>~funny(X))))<=>(?[X]:((wise(X)<~>kind(X)))))&
(![X]:(creative(X)<=>(~happy(X)|~strong(X))))&
(![X]:(~rich(X)=>(~brave(X)<~>tall(X))))&
(![X]:((~calm(X)<~>strong(X))<=>patient(X)))&
(![X]:((patient(X)|strong(X))=>~quiet(X)))&
((?[X]:((~calm(X)&tall(X))))=>((kind(paul)&curious(paul))))&
((~creative(john))=>(?[X]:((strong(X)<~>~quiet(X)))))&
((?[X]:((happy(X)&~quiet(X))))=>(?[X]:((~creative(X)|~happy(X)))))&
(![X]:((~funny(X)<~>humble(X))=>(~creative(X)<~>~brave(X))))&
((calm(susan)|strong(susan)))&
((creative(mary)|~creative(mary)))&
(?[X]:((~humble(X)|~happy(X))))&
((wise(john)&strong(john)))&
(funny(john))&
(?[X]:(~calm(X)))&
((~tall(susan)<~>~wise(susan))) | calm(susan) | [] | null | 0 |
If susan is either not happy or not humble then alice is not quiet or patient.
Everyone who is quiet or not kind is not wise.
If someone is both not tall and quiet then alice is not curious.
If someone is both patient and not creative then john is either generous or wise and vice versa.
If someone is humble then susan is strong or old.
Everyone who is kind is not calm or creative and vice versa.
Everyone who is both not generous and not calm is both happy and not humble.
Everyone who is both not rich and not happy is either not creative or tall and vice versa.
If susan is not funny then susan is either not quiet or not strong.
Everyone who is both not rich and not patient is either not generous or not quiet and vice versa.
If someone is not quiet or not tall then john is happy or not kind and vice versa.
Everyone who is either happy or not wise is not curious or not generous and vice versa.
If john is either happy or not curious then someone is not old or not calm and vice versa.
Everyone who is brave or kind is calm and vice versa.
Everyone who is both not wise and patient is either patient or not patient and vice versa.
If fred is both brave and creative then susan is quiet.
Alice is either not calm or quiet.
Someone is either not generous or creative.
Alice is curious.
Fred is strong.
Fred is either tall or humble.
Paul is either not creative or happy.
Lucy is wise or strong. | Paul is kind. | contradiction | (((~happy(susan)<~>~humble(susan)))=>((~quiet(alice)|patient(alice))))&
(![X]:((quiet(X)|~kind(X))=>~wise(X)))&
((?[X]:((~tall(X)&quiet(X))))=>(~curious(alice)))&
((?[X]:((patient(X)&~creative(X))))<=>((generous(john)<~>wise(john))))&
((?[X]:(humble(X)))=>((strong(susan)|old(susan))))&
(![X]:(kind(X)<=>(~calm(X)|creative(X))))&
(![X]:((~generous(X)&~calm(X))=>(happy(X)&~humble(X))))&
(![X]:((~rich(X)&~happy(X))<=>(~creative(X)<~>tall(X))))&
((~funny(susan))=>((~quiet(susan)<~>~strong(susan))))&
(![X]:((~rich(X)&~patient(X))<=>(~generous(X)<~>~quiet(X))))&
((?[X]:((~quiet(X)|~tall(X))))<=>((happy(john)|~kind(john))))&
(![X]:((happy(X)<~>~wise(X))<=>(~curious(X)|~generous(X))))&
(((happy(john)<~>~curious(john)))<=>(?[X]:((~old(X)|~calm(X)))))&
(![X]:((brave(X)|kind(X))<=>calm(X)))&
(![X]:((~wise(X)&patient(X))<=>(patient(X)<~>~patient(X))))&
(((brave(fred)&creative(fred)))=>(quiet(susan)))&
((~calm(alice)<~>quiet(alice)))&
(?[X]:((~generous(X)<~>creative(X))))&
(curious(alice))&
(strong(fred))&
((tall(fred)<~>humble(fred)))&
((~creative(paul)<~>happy(paul)))&
((wise(lucy)|strong(lucy))) | kind(paul) | [
"p2",
"p5",
"p7",
"p9",
"p11",
"p13",
"p14",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 723091872596432125628134
% SZS output start Proof for 723091872596432125628134
3. ? [X0] : (quiet(X0) & ~tall(X0)) => ~curious(alice) [input p2]
6. ! [X0] : (kind(X0) <=> (creative(X0) | ~calm(X0))) [input p5]
8. ! [X0] : ((~happy(X0) & ~rich(X0)) <=> (~creative(X0) <~> tall(X0))) [input p7]
10. ! [X0] : ((~patient(X0) & ~rich(X0)) <=> (~generous(X0) <~> ~quiet(X0))) [input p9]
12. ! [X0] : ((happy(X0) <~> ~wise(X0)) <=> (~generous(X0) | ~curious(X0))) [input p11]
14. ! [X0] : ((kind(X0) | brave(X0)) <=> calm(X0)) [input p13]
15. ! [X0] : ((patient(X0) & ~wise(X0)) <=> (patient(X0) <~> ~patient(X0))) [input p14]
19. curious(alice) [input p18]
22. ~creative(paul) <~> happy(paul) [input p21]
24. kind(paul) [input hypothesis]
32. ~curious(alice) | ! [X0] : (~quiet(X0) | tall(X0)) [ennf transformation 3]
42. ! [X0] : ((kind(X0) | (~creative(X0) & calm(X0))) & ((creative(X0) | ~calm(X0)) | ~kind(X0))) [nnf transformation 6]
43. ! [X0] : ((kind(X0) | (~creative(X0) & calm(X0))) & (creative(X0) | ~calm(X0) | ~kind(X0))) [flattening 42]
44. ! [X0] : (((~happy(X0) & ~rich(X0)) | ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0)))) & (((~tall(X0) | creative(X0)) & (tall(X0) | ~creative(X0))) | (happy(X0) | rich(X0)))) [nnf transformation 8]
45. ! [X0] : (((~happy(X0) & ~rich(X0)) | ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0)))) & (((~tall(X0) | creative(X0)) & (tall(X0) | ~creative(X0))) | happy(X0) | rich(X0))) [flattening 44]
46. ! [X0] : (((~patient(X0) & ~rich(X0)) | ((~generous(X0) | quiet(X0)) & (~quiet(X0) | generous(X0)))) & (((quiet(X0) | generous(X0)) & (~quiet(X0) | ~generous(X0))) | (patient(X0) | rich(X0)))) [nnf transformation 10]
47. ! [X0] : (((~patient(X0) & ~rich(X0)) | ((~generous(X0) | quiet(X0)) & (~quiet(X0) | generous(X0)))) & (((quiet(X0) | generous(X0)) & (~quiet(X0) | ~generous(X0))) | patient(X0) | rich(X0))) [flattening 46]
53. ! [X0] : ((((wise(X0) | ~happy(X0)) & (~wise(X0) | happy(X0))) | (generous(X0) & curious(X0))) & ((~generous(X0) | ~curious(X0)) | ((happy(X0) | wise(X0)) & (~wise(X0) | ~happy(X0))))) [nnf transformation 12]
54. ! [X0] : ((((wise(X0) | ~happy(X0)) & (~wise(X0) | happy(X0))) | (generous(X0) & curious(X0))) & (~generous(X0) | ~curious(X0) | ((happy(X0) | wise(X0)) & (~wise(X0) | ~happy(X0))))) [flattening 53]
59. ! [X0] : (((kind(X0) | brave(X0)) | ~calm(X0)) & (calm(X0) | (~kind(X0) & ~brave(X0)))) [nnf transformation 14]
60. ! [X0] : ((kind(X0) | brave(X0) | ~calm(X0)) & (calm(X0) | (~kind(X0) & ~brave(X0)))) [flattening 59]
61. ! [X0] : (((patient(X0) & ~wise(X0)) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0)))) & (((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | (~patient(X0) | wise(X0)))) [nnf transformation 15]
62. ! [X0] : (((patient(X0) & ~wise(X0)) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0)))) & (((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | ~patient(X0) | wise(X0))) [flattening 61]
68. (~happy(paul) | creative(paul)) & (happy(paul) | ~creative(paul)) [nnf transformation 22]
73. ~curious(alice) | ~quiet(X0) | tall(X0) [cnf transformation 32]
80. ~calm(X0) | creative(X0) | ~kind(X0) [cnf transformation 43]
81. calm(X0) | kind(X0) [cnf transformation 43]
90. ~creative(X0) | ~happy(X0) | ~tall(X0) [cnf transformation 45]
96. ~generous(X0) | ~patient(X0) | quiet(X0) [cnf transformation 47]
106. ~happy(X0) | wise(X0) | generous(X0) [cnf transformation 54]
114. calm(X0) | ~kind(X0) [cnf transformation 60]
118. ~wise(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 62]
121. patient(X0) | patient(X0) | patient(X0) [cnf transformation 62]
127. curious(alice) [cnf transformation 19]
130. happy(paul) | ~creative(paul) [cnf transformation 68]
132. kind(paul) [cnf transformation 24]
135. ~wise(X0) | ~patient(X0) [duplicate literal removal 118]
138. patient(X0) [duplicate literal removal 121]
158. 5 <=> ! [X0] : (~quiet(X0) | tall(X0)) [avatar definition]
159. ~quiet(X0) | tall(X0) <- (5) [avatar component clause 158]
161. 6 <=> curious(alice) [avatar definition]
164. 5 | ~6 [avatar split clause 73,161,158]
217. 18 <=> ! [X0] : calm(X0) [avatar definition]
218. calm(X0) <- (18) [avatar component clause 217]
241. calm(X0) [subsumption resolution 114,81]
242. 18 [avatar split clause 241,217]
243. ~wise(X0) [subsumption resolution 135,138]
273. 6 [avatar split clause 127,161]
285. 31 <=> creative(paul) [avatar definition]
287. creative(paul) <- (31) [avatar component clause 285]
289. 32 <=> happy(paul) [avatar definition]
290. happy(paul) <- (32) [avatar component clause 289]
293. ~31 | 32 [avatar split clause 130,289,285]
316. ~kind(X1) | creative(X1) <- (18) [resolution 80,218]
342. wise(paul) | generous(paul) <- (32) [resolution 106,290]
346. generous(paul) <- (32) [subsumption resolution 342,243]
368. 35 <=> tall(paul) [avatar definition]
369. ~tall(paul) <- (~35) [avatar component clause 368]
377. ~happy(paul) | ~tall(paul) <- (31) [resolution 287,90]
379. ~tall(paul) <- (31, 32) [subsumption resolution 377,290]
380. ~35 | ~31 | ~32 [avatar split clause 379,289,285,368]
408. ~patient(paul) | quiet(paul) <- (32) [resolution 346,96]
409. quiet(paul) <- (32) [subsumption resolution 408,138]
464. creative(paul) <- (18) [resolution 316,132]
480. tall(paul) <- (5, 32) [resolution 409,159]
481. $false <- (5, 32, ~35) [subsumption resolution 480,369]
482. ~5 | ~32 | 35 [avatar contradiction clause 481]
483. 31 | ~18 [avatar split clause 464,217,285]
489. $false [avatar sat refutation 164,242,273,293,380,482,483]
% SZS output end Proof for 723091872596432125628134
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or not generous is happy or not brave and vice versa. If fred is both wise and not kind then lucy is both kind and strong. Everyone who is not curious is either tall or patient and vice versa. If paul is either quiet or not rich then lucy is generous and vice versa. If john is either funny or creative then someone is tall or not tall. If someone is not patient or not calm then someone is both curious and not curious. If john is either generous or not rich then someone is happy or not creative. Everyone who is both tall and quiet is humble or not quiet. If paul is happy then paul is old and vice versa. If someone is not curious then lucy is patient or not old and vice versa. Everyone who is both creative and not calm is humble and vice versa. If lucy is either strong or generous then someone is both patient and not humble. Everyone who is happy or not quiet is both curious and kind and vice versa. Everyone who is not happy or not humble is not creative. Everyone who is either wise or not wise is either generous or not happy and vice versa. If paul is both not curious and not strong then susan is either generous or not brave and vice versa. Someone is both not rich and funny. Someone is funny or not funny. John is either patient or tall. Someone is both not wise and happy. John is not generous or not brave. Someone is not curious. | John is happy. | contradiction | (![X]:((~old(X)|~generous(X))<=>(happy(X)|~brave(X))))&
(((wise(fred)&~kind(fred)))=>((kind(lucy)&strong(lucy))))&
(![X]:(~curious(X)<=>(tall(X)<~>patient(X))))&
(((quiet(paul)<~>~rich(paul)))<=>(generous(lucy)))&
(((funny(john)<~>creative(john)))=>(?[X]:((tall(X)|~tall(X)))))&
((?[X]:((~patient(X)|~calm(X))))=>(?[X]:((curious(X)&~curious(X)))))&
(((generous(john)<~>~rich(john)))=>(?[X]:((happy(X)|~creative(X)))))&
(![X]:((tall(X)&quiet(X))=>(humble(X)|~quiet(X))))&
((happy(paul))<=>(old(paul)))&
((?[X]:(~curious(X)))<=>((patient(lucy)|~old(lucy))))&
(![X]:((creative(X)&~calm(X))<=>humble(X)))&
(((strong(lucy)<~>generous(lucy)))=>(?[X]:((patient(X)&~humble(X)))))&
(![X]:((happy(X)|~quiet(X))<=>(curious(X)&kind(X))))&
(![X]:((~happy(X)|~humble(X))=>~creative(X)))&
(![X]:((wise(X)<~>~wise(X))<=>(generous(X)<~>~happy(X))))&
(((~curious(paul)&~strong(paul)))<=>((generous(susan)<~>~brave(susan))))&
(?[X]:((~rich(X)&funny(X))))&
(?[X]:((funny(X)|~funny(X))))&
((patient(john)<~>tall(john)))&
(?[X]:((~wise(X)&happy(X))))&
((~generous(john)|~brave(john)))&
(?[X]:(~curious(X))) | happy(john) | [
"p2",
"p5",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6088627473732367691440928
% SZS output start Proof for 6088627473732367691440928
3. ! [X0] : (~curious(X0) <=> (tall(X0) <~> patient(X0))) [input p2]
6. ? [X0] : (~calm(X0) | ~patient(X0)) => ? [X0] : (~curious(X0) & curious(X0)) [input p5]
13. ! [X0] : ((~quiet(X0) | happy(X0)) <=> (kind(X0) & curious(X0))) [input p12]
19. patient(john) <~> tall(john) [input p18]
23. happy(john) [input hypothesis]
24. ? [X0] : (~calm(X0) | ~patient(X0)) => ? [X1] : (~curious(X1) & curious(X1)) [rectify 6]
28. ? [X1] : (~curious(X1) & curious(X1)) | ! [X0] : (calm(X0) & patient(X0)) [ennf transformation 24]
36. ! [X0] : ((~curious(X0) | ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0)))) & (((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) | curious(X0))) [nnf transformation 3]
41. ? [X0] : (~curious(X0) & curious(X0)) | ! [X1] : (calm(X1) & patient(X1)) [rectify 28]
42. ? [X0] : (~curious(X0) & curious(X0)) => (~curious(sK1) & curious(sK1)) [choice axiom]
43. (~curious(sK1) & curious(sK1)) | ! [X1] : (calm(X1) & patient(X1)) [skolemisation 41,42]
58. ! [X0] : (((~quiet(X0) | happy(X0)) | (~kind(X0) | ~curious(X0))) & ((kind(X0) & curious(X0)) | (quiet(X0) & ~happy(X0)))) [nnf transformation 13]
59. ! [X0] : ((~quiet(X0) | happy(X0) | ~kind(X0) | ~curious(X0)) & ((kind(X0) & curious(X0)) | (quiet(X0) & ~happy(X0)))) [flattening 58]
67. (~tall(john) | ~patient(john)) & (tall(john) | patient(john)) [nnf transformation 19]
81. ~patient(X0) | tall(X0) | ~curious(X0) [cnf transformation 36]
88. curious(sK1) | patient(X1) [cnf transformation 43]
90. ~curious(sK1) | patient(X1) [cnf transformation 43]
107. ~happy(X0) | curious(X0) [cnf transformation 59]
132. ~tall(john) | ~patient(john) [cnf transformation 67]
137. happy(john) [cnf transformation 23]
181. 9 <=> curious(sK1) [avatar definition]
186. 10 <=> ! [X1] : patient(X1) [avatar definition]
187. patient(X1) <- (10) [avatar component clause 186]
188. 10 | ~9 [avatar split clause 90,181,186]
190. 10 | 9 [avatar split clause 88,181,186]
274. 27 <=> patient(john) [avatar definition]
276. ~patient(john) <- (~27) [avatar component clause 274]
278. 28 <=> tall(john) [avatar definition]
281. ~27 | ~28 [avatar split clause 132,278,274]
289. curious(john) [resolution 107,137]
317. ~curious(X1) | tall(X1) <- (10) [resolution 81,187]
321. tall(john) <- (10) [resolution 317,289]
324. 28 | ~10 [avatar split clause 321,186,278]
325. $false <- (10, ~27) [subsumption resolution 276,187]
326. ~10 | 27 [avatar contradiction clause 325]
327. $false [avatar sat refutation 188,190,281,324,326]
% SZS output end Proof for 6088627473732367691440928
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is funny or brave then someone is rich or brave and vice versa. Everyone who is both kind and wise is both kind and not old. Everyone who is creative is curious and vice versa. If mary is humble or not curious then someone is not calm. Everyone who is strong or not quiet is both not creative and happy. Everyone who is wise is either not strong or not old. Everyone who is happy is both not curious and not calm. Everyone who is not funny is either not strong or not kind and vice versa. Everyone who is funny is either creative or happy and vice versa. Everyone who is both not happy and patient is both old and not brave. If someone is either curious or not creative then someone is both not patient and tall. If someone is either not humble or not patient then someone is both patient and happy and vice versa. Everyone who is not kind is both humble and strong and vice versa. If someone is either not quiet or not happy then fred is both not curious and not creative and vice versa. Everyone who is calm is strong or not rich. If alice is both strong and not curious then paul is either not wise or curious and vice versa. John is humble. Lucy is not wise. Alice is both not happy and not curious. Someone is both quiet and old. Someone is tall or wise. Fred is both not wise and not humble. | Alice is funny. | contradiction | (((funny(lucy)|brave(lucy)))<=>(?[X]:((rich(X)|brave(X)))))&
(![X]:((kind(X)&wise(X))=>(kind(X)&~old(X))))&
(![X]:(creative(X)<=>curious(X)))&
(((humble(mary)|~curious(mary)))=>(?[X]:(~calm(X))))&
(![X]:((strong(X)|~quiet(X))=>(~creative(X)&happy(X))))&
(![X]:(wise(X)=>(~strong(X)<~>~old(X))))&
(![X]:(happy(X)=>(~curious(X)&~calm(X))))&
(![X]:(~funny(X)<=>(~strong(X)<~>~kind(X))))&
(![X]:(funny(X)<=>(creative(X)<~>happy(X))))&
(![X]:((~happy(X)&patient(X))=>(old(X)&~brave(X))))&
((?[X]:((curious(X)<~>~creative(X))))=>(?[X]:((~patient(X)&tall(X)))))&
((?[X]:((~humble(X)<~>~patient(X))))<=>(?[X]:((patient(X)&happy(X)))))&
(![X]:(~kind(X)<=>(humble(X)&strong(X))))&
((?[X]:((~quiet(X)<~>~happy(X))))<=>((~curious(fred)&~creative(fred))))&
(![X]:(calm(X)=>(strong(X)|~rich(X))))&
(((strong(alice)&~curious(alice)))<=>((~wise(paul)<~>curious(paul))))&
(humble(john))&
(~wise(lucy))&
((~happy(alice)&~curious(alice)))&
(?[X]:((quiet(X)&old(X))))&
(?[X]:((tall(X)|wise(X))))&
((~wise(fred)&~humble(fred))) | funny(alice) | [
"p4",
"p7",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2115281867248467164197316
% SZS output start Proof for 2115281867248467164197316
5. ! [X0] : ((~quiet(X0) | strong(X0)) => (happy(X0) & ~creative(X0))) [input p4]
8. ! [X0] : (~funny(X0) <=> (~strong(X0) <~> ~kind(X0))) [input p7]
13. ! [X0] : (~kind(X0) <=> (strong(X0) & humble(X0))) [input p12]
19. ~curious(alice) & ~happy(alice) [input p18]
23. funny(alice) [input hypothesis]
33. ! [X0] : ((happy(X0) & ~creative(X0)) | (quiet(X0) & ~strong(X0))) [ennf transformation 5]
46. ! [X0] : ((~funny(X0) | ((~strong(X0) | kind(X0)) & (~kind(X0) | strong(X0)))) & (((kind(X0) | strong(X0)) & (~kind(X0) | ~strong(X0))) | funny(X0))) [nnf transformation 8]
57. ! [X0] : ((~kind(X0) | (~strong(X0) | ~humble(X0))) & ((strong(X0) & humble(X0)) | kind(X0))) [nnf transformation 13]
58. ! [X0] : ((~kind(X0) | ~strong(X0) | ~humble(X0)) & ((strong(X0) & humble(X0)) | kind(X0))) [flattening 57]
78. ~strong(X0) | happy(X0) [cnf transformation 33]
85. ~kind(X0) | ~funny(X0) | strong(X0) [cnf transformation 46]
102. strong(X0) | kind(X0) [cnf transformation 58]
118. ~happy(alice) [cnf transformation 19]
124. funny(alice) [cnf transformation 23]
243. 26 <=> strong(alice) [avatar definition]
244. ~strong(alice) <- (~26) [avatar component clause 243]
245. strong(alice) <- (26) [avatar component clause 243]
257. kind(alice) <- (~26) [resolution 102,244]
289. ~funny(alice) | strong(alice) <- (~26) [resolution 85,257]
300. strong(alice) <- (~26) [subsumption resolution 289,124]
301. $false <- (~26) [subsumption resolution 300,244]
302. 26 [avatar contradiction clause 301]
314. happy(alice) <- (26) [resolution 245,78]
316. $false <- (26) [subsumption resolution 314,118]
317. ~26 [avatar contradiction clause 316]
318. $false [avatar sat refutation 302,317]
% SZS output end Proof for 2115281867248467164197316
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and calm is both not funny and not happy. Everyone who is not happy is both not curious and not strong and vice versa. Everyone who is funny is patient and vice versa. If someone is not old or not rich then someone is either not strong or not rich. Everyone who is tall or creative is either happy or not rich. If john is calm or not quiet then someone is rich. If someone is either not patient or quiet then someone is both not calm and not kind and vice versa. Everyone who is not curious or curious is not brave. If someone is not generous then lucy is both not funny and generous and vice versa. If paul is funny or not quiet then someone is either not calm or patient and vice versa. Everyone who is not tall or not rich is both not funny and wise and vice versa. If alice is either not calm or happy then paul is not kind and vice versa. Everyone who is not happy or not humble is not tall and vice versa. Everyone who is either patient or not funny is wise. Everyone who is both not patient and tall is patient. Everyone who is not wise or not calm is either not strong or not creative. Someone is either not strong or not rich. Someone is quiet. Someone is either happy or not creative. Alice is old. Someone is not tall or not humble. Someone is strong. Someone is kind or not creative. John is not strong. | Lucy is not generous. | contradiction | (![X]:((~creative(X)&calm(X))=>(~funny(X)&~happy(X))))&
(![X]:(~happy(X)<=>(~curious(X)&~strong(X))))&
(![X]:(funny(X)<=>patient(X)))&
((?[X]:((~old(X)|~rich(X))))=>(?[X]:((~strong(X)<~>~rich(X)))))&
(![X]:((tall(X)|creative(X))=>(happy(X)<~>~rich(X))))&
(((calm(john)|~quiet(john)))=>(?[X]:(rich(X))))&
((?[X]:((~patient(X)<~>quiet(X))))<=>(?[X]:((~calm(X)&~kind(X)))))&
(![X]:((~curious(X)|curious(X))=>~brave(X)))&
((?[X]:(~generous(X)))<=>((~funny(lucy)&generous(lucy))))&
(((funny(paul)|~quiet(paul)))<=>(?[X]:((~calm(X)<~>patient(X)))))&
(![X]:((~tall(X)|~rich(X))<=>(~funny(X)&wise(X))))&
(((~calm(alice)<~>happy(alice)))<=>(~kind(paul)))&
(![X]:((~happy(X)|~humble(X))<=>~tall(X)))&
(![X]:((patient(X)<~>~funny(X))=>wise(X)))&
(![X]:((~patient(X)&tall(X))=>patient(X)))&
(![X]:((~wise(X)|~calm(X))=>(~strong(X)<~>~creative(X))))&
(?[X]:((~strong(X)<~>~rich(X))))&
(?[X]:(quiet(X)))&
(?[X]:((happy(X)<~>~creative(X))))&
(old(alice))&
(?[X]:((~tall(X)|~humble(X))))&
(?[X]:(strong(X)))&
(?[X]:((kind(X)|~creative(X))))&
(~strong(john)) | ~generous(lucy) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3630731384514365480204572
% SZS output start Proof for 3630731384514365480204572
9. ? [X0] : ~generous(X0) <=> (generous(lucy) & ~funny(lucy)) [input p8]
25. ~generous(lucy) [input hypothesis]
55. (? [X0] : ~generous(X0) | (~generous(lucy) | funny(lucy))) & ((generous(lucy) & ~funny(lucy)) | ! [X0] : generous(X0)) [nnf transformation 9]
56. (? [X0] : ~generous(X0) | ~generous(lucy) | funny(lucy)) & ((generous(lucy) & ~funny(lucy)) | ! [X0] : generous(X0)) [flattening 55]
57. (? [X0] : ~generous(X0) | ~generous(lucy) | funny(lucy)) & ((generous(lucy) & ~funny(lucy)) | ! [X1] : generous(X1)) [rectify 56]
58. ? [X0] : ~generous(X0) => ~generous(sK4) [choice axiom]
59. (~generous(sK4) | ~generous(lucy) | funny(lucy)) & ((generous(lucy) & ~funny(lucy)) | ! [X1] : generous(X1)) [skolemisation 57,58]
108. generous(lucy) | generous(X1) [cnf transformation 59]
144. ~generous(lucy) [cnf transformation 25]
209. 15 <=> generous(lucy) [avatar definition]
211. ~generous(lucy) <- (~15) [avatar component clause 209]
218. 17 <=> ! [X1] : generous(X1) [avatar definition]
219. generous(X1) <- (17) [avatar component clause 218]
220. 17 | 15 [avatar split clause 108,209,218]
299. ~15 [avatar split clause 144,209]
300. $false <- (~15, 17) [subsumption resolution 211,219]
301. 15 | ~17 [avatar contradiction clause 300]
302. $false [avatar sat refutation 220,299,301]
% SZS output end Proof for 3630731384514365480204572
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or patient is either brave or not humble and vice versa.
If someone is either rich or not funny then someone is both not strong and not kind.
Everyone who is not creative is funny or strong.
If someone is either not kind or not curious then mary is both funny and not strong.
Everyone who is not kind is not strong or not happy and vice versa.
If someone is humble then someone is patient or old.
If fred is either not generous or not funny then someone is happy.
If mary is either funny or not humble then john is either brave or not wise and vice versa.
If someone is either tall or creative then someone is curious or rich and vice versa.
If someone is not funny or not old then someone is both humble and generous.
If paul is either tall or not quiet then paul is either not rich or not generous and vice versa.
Everyone who is either tall or not funny is both tall and brave and vice versa.
If someone is not strong then someone is either not brave or not happy and vice versa.
If john is happy then paul is not wise and vice versa.
Everyone who is both not strong and generous is not old or humble and vice versa.
If someone is tall or not happy then someone is both not quiet and wise.
John is not brave or not happy.
Someone is not old.
John is either happy or not humble.
Mary is not curious or rich.
Lucy is either old or not curious.
Someone is creative or not creative.
Someone is not strong. | Paul is tall. | neutral | (![X]:((~generous(X)|patient(X))<=>(brave(X)<~>~humble(X))))&
((?[X]:((rich(X)<~>~funny(X))))=>(?[X]:((~strong(X)&~kind(X)))))&
(![X]:(~creative(X)=>(funny(X)|strong(X))))&
((?[X]:((~kind(X)<~>~curious(X))))=>((funny(mary)&~strong(mary))))&
(![X]:(~kind(X)<=>(~strong(X)|~happy(X))))&
((?[X]:(humble(X)))=>(?[X]:((patient(X)|old(X)))))&
(((~generous(fred)<~>~funny(fred)))=>(?[X]:(happy(X))))&
(((funny(mary)<~>~humble(mary)))<=>((brave(john)<~>~wise(john))))&
((?[X]:((tall(X)<~>creative(X))))<=>(?[X]:((curious(X)|rich(X)))))&
((?[X]:((~funny(X)|~old(X))))=>(?[X]:((humble(X)&generous(X)))))&
(((tall(paul)<~>~quiet(paul)))<=>((~rich(paul)<~>~generous(paul))))&
(![X]:((tall(X)<~>~funny(X))<=>(tall(X)&brave(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~brave(X)<~>~happy(X)))))&
((happy(john))<=>(~wise(paul)))&
(![X]:((~strong(X)&generous(X))<=>(~old(X)|humble(X))))&
((?[X]:((tall(X)|~happy(X))))=>(?[X]:((~quiet(X)&wise(X)))))&
((~brave(john)|~happy(john)))&
(?[X]:(~old(X)))&
((happy(john)<~>~humble(john)))&
((~curious(mary)|rich(mary)))&
((old(lucy)<~>~curious(lucy)))&
(?[X]:((creative(X)|~creative(X))))&
(?[X]:(~strong(X))) | tall(paul) | [] | null | 0 |
Everyone who is not calm or not tall is calm or not funny.
Everyone who is funny or brave is not kind or not happy and vice versa.
Everyone who is either not funny or not rich is both not quiet and curious.
If someone is not calm then someone is both not generous and old.
If someone is brave or strong then paul is either not calm or not quiet and vice versa.
Everyone who is either old or humble is both brave and not patient.
Everyone who is humble is not calm or wise.
Everyone who is brave is either not quiet or not creative and vice versa.
If john is either not creative or curious then someone is both not quiet and not rich.
If fred is both not funny and not humble then someone is both not curious and not humble and vice versa.
Everyone who is funny is both not strong and not generous and vice versa.
Everyone who is happy is either not strong or not old and vice versa.
Everyone who is both funny and not creative is curious and vice versa.
Everyone who is calm is funny or not calm and vice versa.
Everyone who is either not old or not humble is either not rich or brave.
Everyone who is either funny or rich is brave.
Fred is both tall and creative.
Fred is not quiet.
Alice is both not patient and not kind.
Someone is both old and not quiet.
Someone is either brave or not rich.
Someone is both rich and not tall.
Paul is not strong or not quiet.
Someone is either creative or happy. | Paul is not rich. | contradiction | (![X]:((~calm(X)|~tall(X))=>(calm(X)|~funny(X))))&
(![X]:((funny(X)|brave(X))<=>(~kind(X)|~happy(X))))&
(![X]:((~funny(X)<~>~rich(X))=>(~quiet(X)&curious(X))))&
((?[X]:(~calm(X)))=>(?[X]:((~generous(X)&old(X)))))&
((?[X]:((brave(X)|strong(X))))<=>((~calm(paul)<~>~quiet(paul))))&
(![X]:((old(X)<~>humble(X))=>(brave(X)&~patient(X))))&
(![X]:(humble(X)=>(~calm(X)|wise(X))))&
(![X]:(brave(X)<=>(~quiet(X)<~>~creative(X))))&
(((~creative(john)<~>curious(john)))=>(?[X]:((~quiet(X)&~rich(X)))))&
(((~funny(fred)&~humble(fred)))<=>(?[X]:((~curious(X)&~humble(X)))))&
(![X]:(funny(X)<=>(~strong(X)&~generous(X))))&
(![X]:(happy(X)<=>(~strong(X)<~>~old(X))))&
(![X]:((funny(X)&~creative(X))<=>curious(X)))&
(![X]:(calm(X)<=>(funny(X)|~calm(X))))&
(![X]:((~old(X)<~>~humble(X))=>(~rich(X)<~>brave(X))))&
(![X]:((funny(X)<~>rich(X))=>brave(X)))&
((tall(fred)&creative(fred)))&
(~quiet(fred))&
((~patient(alice)&~kind(alice)))&
(?[X]:((old(X)&~quiet(X))))&
(?[X]:((brave(X)<~>~rich(X))))&
(?[X]:((rich(X)&~tall(X))))&
((~strong(paul)|~quiet(paul)))&
(?[X]:((creative(X)<~>happy(X)))) | ~rich(paul) | [
"p2",
"p7",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8772831959343889109767609
% SZS output start Proof for 8772831959343889109767609
3. ! [X0] : ((~funny(X0) <~> ~rich(X0)) => (curious(X0) & ~quiet(X0))) [input p2]
8. ! [X0] : (brave(X0) <=> (~quiet(X0) <~> ~creative(X0))) [input p7]
13. ! [X0] : ((~creative(X0) & funny(X0)) <=> curious(X0)) [input p12]
14. ! [X0] : (calm(X0) <=> (~calm(X0) | funny(X0))) [input p13]
16. ! [X0] : ((funny(X0) <~> rich(X0)) => brave(X0)) [input p15]
25. ~rich(paul) [input hypothesis]
32. ! [X0] : ((curious(X0) & ~quiet(X0)) | (~funny(X0) <=> ~rich(X0))) [ennf transformation 3]
37. ! [X0] : (brave(X0) | (funny(X0) <=> rich(X0))) [ennf transformation 16]
40. ! [X0] : ((curious(X0) & ~quiet(X0)) | ((~funny(X0) | rich(X0)) & (~rich(X0) | funny(X0)))) [nnf transformation 32]
49. ! [X0] : ((brave(X0) | ((~quiet(X0) | creative(X0)) & (~creative(X0) | quiet(X0)))) & (((creative(X0) | quiet(X0)) & (~creative(X0) | ~quiet(X0))) | ~brave(X0))) [nnf transformation 8]
61. ! [X0] : (((~creative(X0) & funny(X0)) | ~curious(X0)) & (curious(X0) | (creative(X0) | ~funny(X0)))) [nnf transformation 13]
62. ! [X0] : (((~creative(X0) & funny(X0)) | ~curious(X0)) & (curious(X0) | creative(X0) | ~funny(X0))) [flattening 61]
63. ! [X0] : ((calm(X0) | (calm(X0) & ~funny(X0))) & ((~calm(X0) | funny(X0)) | ~calm(X0))) [nnf transformation 14]
64. ! [X0] : ((calm(X0) | (calm(X0) & ~funny(X0))) & (~calm(X0) | funny(X0) | ~calm(X0))) [flattening 63]
66. ! [X0] : (brave(X0) | ((funny(X0) | ~rich(X0)) & (rich(X0) | ~funny(X0)))) [nnf transformation 37]
84. ~quiet(X0) | ~funny(X0) | rich(X0) [cnf transformation 40]
86. ~funny(X0) | curious(X0) | rich(X0) [cnf transformation 40]
98. ~brave(X0) | quiet(X0) | creative(X0) [cnf transformation 49]
118. ~creative(X0) | ~curious(X0) [cnf transformation 62]
119. ~calm(X0) | funny(X0) | ~calm(X0) [cnf transformation 64]
121. calm(X0) | calm(X0) [cnf transformation 64]
126. ~funny(X0) | rich(X0) | brave(X0) [cnf transformation 66]
141. ~rich(paul) [cnf transformation 25]
142. ~calm(X0) | funny(X0) [duplicate literal removal 119]
143. calm(X0) [duplicate literal removal 121]
146. 1 <=> ! [X1] : calm(X1) [avatar definition]
147. calm(X1) <- (1) [avatar component clause 146]
159. 4 <=> quiet(paul) [avatar definition]
160. ~quiet(paul) <- (~4) [avatar component clause 159]
161. quiet(paul) <- (4) [avatar component clause 159]
229. 1 [avatar split clause 143,146]
263. funny(X0) <- (1) [resolution 142,147]
279. ~funny(paul) | rich(paul) <- (4) [resolution 84,161]
280. rich(paul) <- (1, 4) [subsumption resolution 279,263]
281. $false <- (1, 4) [subsumption resolution 280,141]
282. ~1 | ~4 [avatar contradiction clause 281]
284. curious(X0) | rich(X0) <- (1) [resolution 86,263]
389. rich(X0) | brave(X0) <- (1) [resolution 126,263]
421. brave(paul) <- (1) [resolution 389,141]
494. quiet(paul) | creative(paul) <- (1) [resolution 421,98]
495. creative(paul) <- (1, ~4) [subsumption resolution 494,160]
512. ~curious(paul) <- (1, ~4) [resolution 495,118]
541. rich(paul) <- (1, ~4) [resolution 512,284]
542. $false <- (1, ~4) [subsumption resolution 541,141]
543. ~1 | 4 [avatar contradiction clause 542]
544. $false [avatar sat refutation 229,282,543]
% SZS output end Proof for 8772831959343889109767609
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or wise is not creative and vice versa.
If lucy is either not calm or not happy then susan is both humble and not calm.
If fred is humble then someone is either curious or calm.
If someone is both kind and tall then alice is creative or quiet and vice versa.
If someone is funny then someone is both not quiet and creative.
Everyone who is quiet is both quiet and not rich and vice versa.
If someone is not wise or funny then someone is not tall and vice versa.
Everyone who is both not happy and wise is kind and vice versa.
Everyone who is either not happy or not strong is both kind and not old and vice versa.
If someone is creative or not patient then john is not old and vice versa.
If john is not kind or not calm then someone is wise and vice versa.
If susan is both wise and not calm then someone is either not kind or quiet.
Everyone who is quiet or kind is happy.
If mary is tall then someone is both wise and not quiet.
Everyone who is not curious or not brave is either not rich or curious and vice versa.
Everyone who is either not old or funny is tall.
Lucy is not old or rich.
Susan is both curious and not old.
Lucy is not generous or not brave.
Paul is either not rich or not quiet.
Someone is wise or not patient.
Susan is either happy or not calm. | Lucy is not rich. | neutral | (![X]:((~quiet(X)<~>wise(X))<=>~creative(X)))&
(((~calm(lucy)<~>~happy(lucy)))=>((humble(susan)&~calm(susan))))&
((humble(fred))=>(?[X]:((curious(X)<~>calm(X)))))&
((?[X]:((kind(X)&tall(X))))<=>((creative(alice)|quiet(alice))))&
((?[X]:(funny(X)))=>(?[X]:((~quiet(X)&creative(X)))))&
(![X]:(quiet(X)<=>(quiet(X)&~rich(X))))&
((?[X]:((~wise(X)|funny(X))))<=>(?[X]:(~tall(X))))&
(![X]:((~happy(X)&wise(X))<=>kind(X)))&
(![X]:((~happy(X)<~>~strong(X))<=>(kind(X)&~old(X))))&
((?[X]:((creative(X)|~patient(X))))<=>(~old(john)))&
(((~kind(john)|~calm(john)))<=>(?[X]:(wise(X))))&
(((wise(susan)&~calm(susan)))=>(?[X]:((~kind(X)<~>quiet(X)))))&
(![X]:((quiet(X)|kind(X))=>happy(X)))&
((tall(mary))=>(?[X]:((wise(X)&~quiet(X)))))&
(![X]:((~curious(X)|~brave(X))<=>(~rich(X)<~>curious(X))))&
(![X]:((~old(X)<~>funny(X))=>tall(X)))&
((~old(lucy)|rich(lucy)))&
((curious(susan)&~old(susan)))&
((~generous(lucy)|~brave(lucy)))&
((~rich(paul)<~>~quiet(paul)))&
(?[X]:((wise(X)|~patient(X))))&
((happy(susan)<~>~calm(susan))) | ~rich(lucy) | [] | null | 0 |
Everyone who is patient is patient or old and vice versa. Everyone who is tall or generous is both humble and generous and vice versa. Everyone who is not patient or not creative is tall or humble. Everyone who is either curious or generous is either creative or humble and vice versa. If mary is brave or not wise then someone is either generous or wise. If susan is both not curious and rich then someone is both not strong and old and vice versa. If john is not brave or rich then fred is not brave and vice versa. If someone is strong or not rich then someone is not brave. Everyone who is not strong is both not patient and not calm. Everyone who is both not brave and not happy is funny or not kind and vice versa. Everyone who is not generous or not old is generous or not humble and vice versa. Everyone who is either not humble or creative is not old or not humble. Everyone who is not brave or tall is both not kind and quiet and vice versa. Everyone who is both not curious and not kind is either rich or patient and vice versa. If someone is either not brave or not humble then lucy is not funny or quiet and vice versa. If alice is either not humble or not quiet then lucy is both not funny and humble and vice versa. Lucy is not old or calm. Paul is kind. Someone is either humble or kind. Alice is not old. Paul is not curious or not humble. John is both curious and old. Mary is generous. Someone is both not patient and curious. | Fred is brave. | contradiction | (![X]:(patient(X)<=>(patient(X)|old(X))))&
(![X]:((tall(X)|generous(X))<=>(humble(X)&generous(X))))&
(![X]:((~patient(X)|~creative(X))=>(tall(X)|humble(X))))&
(![X]:((curious(X)<~>generous(X))<=>(creative(X)<~>humble(X))))&
(((brave(mary)|~wise(mary)))=>(?[X]:((generous(X)<~>wise(X)))))&
(((~curious(susan)&rich(susan)))<=>(?[X]:((~strong(X)&old(X)))))&
(((~brave(john)|rich(john)))<=>(~brave(fred)))&
((?[X]:((strong(X)|~rich(X))))=>(?[X]:(~brave(X))))&
(![X]:(~strong(X)=>(~patient(X)&~calm(X))))&
(![X]:((~brave(X)&~happy(X))<=>(funny(X)|~kind(X))))&
(![X]:((~generous(X)|~old(X))<=>(generous(X)|~humble(X))))&
(![X]:((~humble(X)<~>creative(X))=>(~old(X)|~humble(X))))&
(![X]:((~brave(X)|tall(X))<=>(~kind(X)&quiet(X))))&
(![X]:((~curious(X)&~kind(X))<=>(rich(X)<~>patient(X))))&
((?[X]:((~brave(X)<~>~humble(X))))<=>((~funny(lucy)|quiet(lucy))))&
(((~humble(alice)<~>~quiet(alice)))<=>((~funny(lucy)&humble(lucy))))&
((~old(lucy)|calm(lucy)))&
(kind(paul))&
(?[X]:((humble(X)<~>kind(X))))&
(~old(alice))&
((~curious(paul)|~humble(paul)))&
((curious(john)&old(john)))&
(generous(mary))&
(?[X]:((~patient(X)&curious(X)))) | brave(fred) | [
"p0",
"p6",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5486027688175090428918813
% SZS output start Proof for 5486027688175090428918813
1. ! [X0] : (patient(X0) <=> (old(X0) | patient(X0))) [input p0]
7. (rich(john) | ~brave(john)) <=> ~brave(fred) [input p6]
14. ! [X0] : ((~kind(X0) & ~curious(X0)) <=> (rich(X0) <~> patient(X0))) [input p13]
22. old(john) & curious(john) [input p21]
25. brave(fred) [input hypothesis]
34. ! [X0] : ((patient(X0) | (~old(X0) & ~patient(X0))) & ((old(X0) | patient(X0)) | ~patient(X0))) [nnf transformation 1]
35. ! [X0] : ((patient(X0) | (~old(X0) & ~patient(X0))) & (old(X0) | patient(X0) | ~patient(X0))) [flattening 34]
47. ((rich(john) | ~brave(john)) | brave(fred)) & (~brave(fred) | (~rich(john) & brave(john))) [nnf transformation 7]
48. (rich(john) | ~brave(john) | brave(fred)) & (~brave(fred) | (~rich(john) & brave(john))) [flattening 47]
59. ! [X0] : (((~kind(X0) & ~curious(X0)) | ((rich(X0) | ~patient(X0)) & (patient(X0) | ~rich(X0)))) & (((~patient(X0) | ~rich(X0)) & (patient(X0) | rich(X0))) | (kind(X0) | curious(X0)))) [nnf transformation 14]
60. ! [X0] : (((~kind(X0) & ~curious(X0)) | ((rich(X0) | ~patient(X0)) & (patient(X0) | ~rich(X0)))) & (((~patient(X0) | ~rich(X0)) & (patient(X0) | rich(X0))) | kind(X0) | curious(X0))) [flattening 59]
75. ~old(X0) | patient(X0) [cnf transformation 35]
100. ~brave(fred) | ~rich(john) [cnf transformation 48]
125. ~curious(X0) | rich(X0) | ~patient(X0) [cnf transformation 60]
146. curious(john) [cnf transformation 22]
147. old(john) [cnf transformation 22]
151. brave(fred) [cnf transformation 25]
206. 10 <=> brave(fred) [avatar definition]
214. 12 <=> rich(john) [avatar definition]
215. ~rich(john) <- (~12) [avatar component clause 214]
218. ~12 | ~10 [avatar split clause 100,206,214]
306. 10 [avatar split clause 151,206]
307. patient(john) [resolution 75,147]
348. rich(john) | ~patient(john) [resolution 125,146]
351. ~patient(john) <- (~12) [subsumption resolution 348,215]
352. $false <- (~12) [subsumption resolution 351,307]
353. 12 [avatar contradiction clause 352]
355. $false [avatar sat refutation 218,306,353]
% SZS output end Proof for 5486027688175090428918813
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not curious or not brave then someone is tall and vice versa.
Everyone who is creative is not tall and vice versa.
Everyone who is not wise or humble is not kind.
If alice is both wise and not patient then someone is not rich and vice versa.
If alice is either wise or calm then lucy is both not calm and patient.
Everyone who is both rich and calm is not tall and vice versa.
Everyone who is either creative or curious is either generous or wise.
Everyone who is either generous or not patient is not generous.
If someone is brave or not brave then susan is both not wise and strong.
Everyone who is either humble or rich is both quiet and not quiet and vice versa.
If someone is either wise or humble then susan is creative and vice versa.
If fred is tall then alice is not humble and vice versa.
If john is not strong then someone is either not calm or patient and vice versa.
If someone is both calm and not old then mary is not kind and vice versa.
If susan is both quiet and not happy then mary is either creative or not generous and vice versa.
Everyone who is either not kind or quiet is not generous.
Someone is either not creative or generous.
Fred is not brave.
John is not funny or tall.
John is not strong.
Fred is not funny or not calm.
Paul is either not rich or tall.
Susan is not tall or not curious.
Susan is either humble or funny. | Fred is calm. | neutral | (((~curious(john)<~>~brave(john)))<=>(?[X]:(tall(X))))&
(![X]:(creative(X)<=>~tall(X)))&
(![X]:((~wise(X)|humble(X))=>~kind(X)))&
(((wise(alice)&~patient(alice)))<=>(?[X]:(~rich(X))))&
(((wise(alice)<~>calm(alice)))=>((~calm(lucy)&patient(lucy))))&
(![X]:((rich(X)&calm(X))<=>~tall(X)))&
(![X]:((creative(X)<~>curious(X))=>(generous(X)<~>wise(X))))&
(![X]:((generous(X)<~>~patient(X))=>~generous(X)))&
((?[X]:((brave(X)|~brave(X))))=>((~wise(susan)&strong(susan))))&
(![X]:((humble(X)<~>rich(X))<=>(quiet(X)&~quiet(X))))&
((?[X]:((wise(X)<~>humble(X))))<=>(creative(susan)))&
((tall(fred))<=>(~humble(alice)))&
((~strong(john))<=>(?[X]:((~calm(X)<~>patient(X)))))&
((?[X]:((calm(X)&~old(X))))<=>(~kind(mary)))&
(((quiet(susan)&~happy(susan)))<=>((creative(mary)<~>~generous(mary))))&
(![X]:((~kind(X)<~>quiet(X))=>~generous(X)))&
(?[X]:((~creative(X)<~>generous(X))))&
(~brave(fred))&
((~funny(john)|tall(john)))&
(~strong(john))&
((~funny(fred)|~calm(fred)))&
((~rich(paul)<~>tall(paul)))&
((~tall(susan)|~curious(susan)))&
((humble(susan)<~>funny(susan))) | calm(fred) | [] | null | 0 |
Everyone who is quiet or strong is either humble or happy.
Everyone who is both funny and generous is not patient.
Everyone who is not strong or brave is not strong or quiet.
Everyone who is either not old or not rich is both strong and patient and vice versa.
Everyone who is not creative or not calm is both rich and tall.
If someone is either not curious or kind then someone is wise or strong.
Everyone who is rich is tall or not quiet.
Everyone who is tall or not calm is either calm or generous and vice versa.
Everyone who is both tall and creative is strong.
Everyone who is both not curious and happy is tall or wise.
Everyone who is strong or not generous is either tall or not curious and vice versa.
Everyone who is either not kind or not old is both not happy and not patient.
Everyone who is both brave and not funny is both rich and not happy and vice versa.
Everyone who is not strong or not calm is both curious and creative.
If fred is not quiet then susan is both calm and not funny and vice versa.
If someone is not strong or not brave then fred is both not curious and not wise and vice versa.
Someone is not patient.
Fred is both rich and not wise.
Someone is not wise.
Someone is both not wise and brave.
Someone is humble.
Alice is either not humble or patient.
Lucy is not generous. | Lucy is not kind. | neutral | (![X]:((quiet(X)|strong(X))=>(humble(X)<~>happy(X))))&
(![X]:((funny(X)&generous(X))=>~patient(X)))&
(![X]:((~strong(X)|brave(X))=>(~strong(X)|quiet(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(strong(X)&patient(X))))&
(![X]:((~creative(X)|~calm(X))=>(rich(X)&tall(X))))&
((?[X]:((~curious(X)<~>kind(X))))=>(?[X]:((wise(X)|strong(X)))))&
(![X]:(rich(X)=>(tall(X)|~quiet(X))))&
(![X]:((tall(X)|~calm(X))<=>(calm(X)<~>generous(X))))&
(![X]:((tall(X)&creative(X))=>strong(X)))&
(![X]:((~curious(X)&happy(X))=>(tall(X)|wise(X))))&
(![X]:((strong(X)|~generous(X))<=>(tall(X)<~>~curious(X))))&
(![X]:((~kind(X)<~>~old(X))=>(~happy(X)&~patient(X))))&
(![X]:((brave(X)&~funny(X))<=>(rich(X)&~happy(X))))&
(![X]:((~strong(X)|~calm(X))=>(curious(X)&creative(X))))&
((~quiet(fred))<=>((calm(susan)&~funny(susan))))&
((?[X]:((~strong(X)|~brave(X))))<=>((~curious(fred)&~wise(fred))))&
(?[X]:(~patient(X)))&
((rich(fred)&~wise(fred)))&
(?[X]:(~wise(X)))&
(?[X]:((~wise(X)&brave(X))))&
(?[X]:(humble(X)))&
((~humble(alice)<~>patient(alice)))&
(~generous(lucy)) | ~kind(lucy) | [] | null | 0 |
If someone is not quiet then someone is either not creative or generous and vice versa.
If mary is not patient or creative then someone is both rich and not creative and vice versa.
Everyone who is both calm and not wise is brave.
Everyone who is both kind and quiet is not happy or happy and vice versa.
Everyone who is either curious or kind is quiet or tall and vice versa.
If mary is not quiet or wise then alice is either not creative or patient.
Everyone who is both rich and not humble is both happy and old.
Everyone who is both not curious and not patient is either tall or not kind and vice versa.
Everyone who is either quiet or kind is not kind or not quiet.
Everyone who is both old and not happy is curious or not strong and vice versa.
If lucy is either not patient or wise then someone is both not funny and not tall.
Everyone who is rich is both generous and brave.
If susan is either patient or old then susan is not quiet and vice versa.
If someone is creative then someone is both not generous and not humble and vice versa.
If john is brave or not patient then mary is both not humble and not happy.
Everyone who is either not generous or not kind is both wise and kind.
Mary is funny.
Someone is quiet.
Someone is either creative or not tall.
Someone is either not generous or patient.
John is both not tall and funny.
Someone is not humble.
Mary is both not tall and not creative. | John is patient. | entailment | ((?[X]:(~quiet(X)))<=>(?[X]:((~creative(X)<~>generous(X)))))&
(((~patient(mary)|creative(mary)))<=>(?[X]:((rich(X)&~creative(X)))))&
(![X]:((calm(X)&~wise(X))=>brave(X)))&
(![X]:((kind(X)&quiet(X))<=>(~happy(X)|happy(X))))&
(![X]:((curious(X)<~>kind(X))<=>(quiet(X)|tall(X))))&
(((~quiet(mary)|wise(mary)))=>((~creative(alice)<~>patient(alice))))&
(![X]:((rich(X)&~humble(X))=>(happy(X)&old(X))))&
(![X]:((~curious(X)&~patient(X))<=>(tall(X)<~>~kind(X))))&
(![X]:((quiet(X)<~>kind(X))=>(~kind(X)|~quiet(X))))&
(![X]:((old(X)&~happy(X))<=>(curious(X)|~strong(X))))&
(((~patient(lucy)<~>wise(lucy)))=>(?[X]:((~funny(X)&~tall(X)))))&
(![X]:(rich(X)=>(generous(X)&brave(X))))&
(((patient(susan)<~>old(susan)))<=>(~quiet(susan)))&
((?[X]:(creative(X)))<=>(?[X]:((~generous(X)&~humble(X)))))&
(((brave(john)|~patient(john)))=>((~humble(mary)&~happy(mary))))&
(![X]:((~generous(X)<~>~kind(X))=>(wise(X)&kind(X))))&
(funny(mary))&
(?[X]:(quiet(X)))&
(?[X]:((creative(X)<~>~tall(X))))&
(?[X]:((~generous(X)<~>patient(X))))&
((~tall(john)&funny(john)))&
(?[X]:(~humble(X)))&
((~tall(mary)&~creative(mary))) | patient(john) | [
"p3",
"p4",
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2246701931740669538372076
% SZS output start Proof for 2246701931740669538372076
4. ! [X0] : ((quiet(X0) & kind(X0)) <=> (happy(X0) | ~happy(X0))) [input p3]
5. ! [X0] : ((curious(X0) <~> kind(X0)) <=> (tall(X0) | quiet(X0))) [input p4]
8. ! [X0] : ((~patient(X0) & ~curious(X0)) <=> (tall(X0) <~> ~kind(X0))) [input p7]
21. funny(john) & ~tall(john) [input p20]
24. ~patient(john) [input hypothesis]
47. ! [X0] : (((quiet(X0) & kind(X0)) | (~happy(X0) & happy(X0))) & ((happy(X0) | ~happy(X0)) | (~quiet(X0) | ~kind(X0)))) [nnf transformation 4]
48. ! [X0] : (((quiet(X0) & kind(X0)) | (~happy(X0) & happy(X0))) & (happy(X0) | ~happy(X0) | ~quiet(X0) | ~kind(X0))) [flattening 47]
49. ! [X0] : ((((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | (~tall(X0) & ~quiet(X0))) & ((tall(X0) | quiet(X0)) | ((curious(X0) | ~kind(X0)) & (kind(X0) | ~curious(X0))))) [nnf transformation 5]
50. ! [X0] : ((((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | (~tall(X0) & ~quiet(X0))) & (tall(X0) | quiet(X0) | ((curious(X0) | ~kind(X0)) & (kind(X0) | ~curious(X0))))) [flattening 49]
52. ! [X0] : (((~patient(X0) & ~curious(X0)) | ((tall(X0) | kind(X0)) & (~kind(X0) | ~tall(X0)))) & (((kind(X0) | ~tall(X0)) & (~kind(X0) | tall(X0))) | (patient(X0) | curious(X0)))) [nnf transformation 8]
53. ! [X0] : (((~patient(X0) & ~curious(X0)) | ((tall(X0) | kind(X0)) & (~kind(X0) | ~tall(X0)))) & (((kind(X0) | ~tall(X0)) & (~kind(X0) | tall(X0))) | patient(X0) | curious(X0))) [flattening 52]
87. kind(X0) | happy(X0) [cnf transformation 48]
88. ~happy(X0) | kind(X0) [cnf transformation 48]
89. quiet(X0) | happy(X0) [cnf transformation 48]
90. ~happy(X0) | quiet(X0) [cnf transformation 48]
95. ~kind(X0) | ~curious(X0) | ~quiet(X0) [cnf transformation 50]
103. ~kind(X0) | tall(X0) | patient(X0) | curious(X0) [cnf transformation 53]
143. ~tall(john) [cnf transformation 21]
148. ~patient(john) [cnf transformation 24]
165. 4 <=> ! [X3] : quiet(X3) [avatar definition]
166. quiet(X3) <- (4) [avatar component clause 165]
201. quiet(X0) [subsumption resolution 89,90]
202. 4 [avatar split clause 201,165]
203. kind(X0) [subsumption resolution 87,88]
205. ~curious(X0) | ~quiet(X0) [subsumption resolution 95,203]
228. tall(X0) | patient(X0) | curious(X0) [subsumption resolution 103,203]
287. 28 <=> patient(john) [avatar definition]
288. ~patient(john) <- (~28) [avatar component clause 287]
328. ~28 [avatar split clause 148,287]
352. patient(john) | curious(john) [resolution 228,143]
355. curious(john) <- (~28) [subsumption resolution 352,288]
383. ~quiet(john) <- (~28) [resolution 355,205]
386. $false <- (4, ~28) [subsumption resolution 383,166]
387. ~4 | 28 [avatar contradiction clause 386]
388. $false [avatar sat refutation 202,328,387]
% SZS output end Proof for 2246701931740669538372076
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and kind is wise and vice versa.
If someone is both happy and not kind then paul is not quiet and vice versa.
Everyone who is either not tall or not strong is either tall or kind and vice versa.
If lucy is not happy then someone is both not generous and not wise and vice versa.
If someone is either rich or curious then someone is either calm or generous.
Everyone who is quiet is either not wise or curious.
If paul is old then john is both not curious and funny and vice versa.
Everyone who is both not old and humble is not quiet.
Everyone who is either not old or not strong is both not rich and not brave.
Everyone who is not creative is either happy or humble.
If someone is both happy and not brave then alice is calm or generous.
If someone is both humble and not patient then alice is not curious and vice versa.
If someone is either not patient or kind then alice is either calm or patient and vice versa.
Everyone who is both not generous and not quiet is either generous or not happy and vice versa.
Everyone who is both happy and not funny is either generous or not funny and vice versa.
If someone is either not brave or not kind then someone is not calm or curious.
Someone is creative or generous.
Someone is not strong.
Susan is humble.
Someone is both not wise and kind.
Lucy is both not curious and not strong.
Alice is either not rich or old.
John is not generous. | Paul is not strong. | neutral | (![X]:((brave(X)&kind(X))<=>wise(X)))&
((?[X]:((happy(X)&~kind(X))))<=>(~quiet(paul)))&
(![X]:((~tall(X)<~>~strong(X))<=>(tall(X)<~>kind(X))))&
((~happy(lucy))<=>(?[X]:((~generous(X)&~wise(X)))))&
((?[X]:((rich(X)<~>curious(X))))=>(?[X]:((calm(X)<~>generous(X)))))&
(![X]:(quiet(X)=>(~wise(X)<~>curious(X))))&
((old(paul))<=>((~curious(john)&funny(john))))&
(![X]:((~old(X)&humble(X))=>~quiet(X)))&
(![X]:((~old(X)<~>~strong(X))=>(~rich(X)&~brave(X))))&
(![X]:(~creative(X)=>(happy(X)<~>humble(X))))&
((?[X]:((happy(X)&~brave(X))))=>((calm(alice)|generous(alice))))&
((?[X]:((humble(X)&~patient(X))))<=>(~curious(alice)))&
((?[X]:((~patient(X)<~>kind(X))))<=>((calm(alice)<~>patient(alice))))&
(![X]:((~generous(X)&~quiet(X))<=>(generous(X)<~>~happy(X))))&
(![X]:((happy(X)&~funny(X))<=>(generous(X)<~>~funny(X))))&
((?[X]:((~brave(X)<~>~kind(X))))=>(?[X]:((~calm(X)|curious(X)))))&
(?[X]:((creative(X)|generous(X))))&
(?[X]:(~strong(X)))&
(humble(susan))&
(?[X]:((~wise(X)&kind(X))))&
((~curious(lucy)&~strong(lucy)))&
((~rich(alice)<~>old(alice)))&
(~generous(john)) | ~strong(paul) | [] | null | 0 |
Everyone who is not happy or not funny is both happy and kind and vice versa.
If alice is not quiet then someone is either not tall or not brave.
If fred is both not curious and patient then john is patient.
Everyone who is either funny or not happy is humble or kind.
If susan is either not curious or not brave then alice is either brave or creative and vice versa.
Everyone who is either brave or tall is either not brave or not quiet and vice versa.
If susan is both happy and not strong then susan is either humble or funny and vice versa.
Everyone who is generous is either brave or rich.
Everyone who is patient or not generous is both wise and rich.
If paul is not tall then someone is both humble and not tall.
Everyone who is either calm or funny is both tall and brave and vice versa.
Everyone who is both tall and not creative is kind or not curious.
If someone is either not patient or not old then someone is not old and vice versa.
If someone is either patient or not kind then someone is not calm and vice versa.
If john is not calm or not curious then someone is both rich and not brave and vice versa.
Everyone who is strong is not old.
Mary is calm.
Mary is not old.
Paul is not curious or wise.
Someone is not happy or not generous.
Someone is not old or not strong.
Fred is both not funny and not wise.
Mary is both strong and curious.
Susan is both rich and not funny. | Paul is wise. | neutral | (![X]:((~happy(X)|~funny(X))<=>(happy(X)&kind(X))))&
((~quiet(alice))=>(?[X]:((~tall(X)<~>~brave(X)))))&
(((~curious(fred)&patient(fred)))=>(patient(john)))&
(![X]:((funny(X)<~>~happy(X))=>(humble(X)|kind(X))))&
(((~curious(susan)<~>~brave(susan)))<=>((brave(alice)<~>creative(alice))))&
(![X]:((brave(X)<~>tall(X))<=>(~brave(X)<~>~quiet(X))))&
(((happy(susan)&~strong(susan)))<=>((humble(susan)<~>funny(susan))))&
(![X]:(generous(X)=>(brave(X)<~>rich(X))))&
(![X]:((patient(X)|~generous(X))=>(wise(X)&rich(X))))&
((~tall(paul))=>(?[X]:((humble(X)&~tall(X)))))&
(![X]:((calm(X)<~>funny(X))<=>(tall(X)&brave(X))))&
(![X]:((tall(X)&~creative(X))=>(kind(X)|~curious(X))))&
((?[X]:((~patient(X)<~>~old(X))))<=>(?[X]:(~old(X))))&
((?[X]:((patient(X)<~>~kind(X))))<=>(?[X]:(~calm(X))))&
(((~calm(john)|~curious(john)))<=>(?[X]:((rich(X)&~brave(X)))))&
(![X]:(strong(X)=>~old(X)))&
(calm(mary))&
(~old(mary))&
((~curious(paul)|wise(paul)))&
(?[X]:((~happy(X)|~generous(X))))&
(?[X]:((~old(X)|~strong(X))))&
((~funny(fred)&~wise(fred)))&
((strong(mary)&curious(mary)))&
((rich(susan)&~funny(susan))) | wise(paul) | [] | null | 0 |
Everyone who is not old is not wise and vice versa. Everyone who is both strong and not quiet is both generous and not curious and vice versa. If alice is not quiet or happy then someone is both creative and quiet and vice versa. Everyone who is generous is not rich. Everyone who is either not patient or wise is both wise and rich. If someone is humble or not brave then lucy is patient and vice versa. If someone is generous then fred is curious or quiet and vice versa. If someone is not rich or not brave then lucy is not rich or brave and vice versa. Everyone who is curious or not humble is both kind and quiet and vice versa. Everyone who is not humble or not happy is not curious or not patient and vice versa. Everyone who is not creative is not old. If mary is both funny and kind then someone is not kind or not old and vice versa. If lucy is calm then john is not humble. Everyone who is not curious or strong is not rich or old. Everyone who is curious or rich is either funny or not tall. If someone is both not curious and not rich then lucy is either not strong or not tall. John is humble or not patient. John is both not patient and not happy. Susan is generous. Mary is not patient. Alice is both not kind and not funny. Someone is curious or not brave. Someone is both kind and not happy. Susan is both not humble and not happy. | Susan is not patient. | entailment | (![X]:(~old(X)<=>~wise(X)))&
(![X]:((strong(X)&~quiet(X))<=>(generous(X)&~curious(X))))&
(((~quiet(alice)|happy(alice)))<=>(?[X]:((creative(X)&quiet(X)))))&
(![X]:(generous(X)=>~rich(X)))&
(![X]:((~patient(X)<~>wise(X))=>(wise(X)&rich(X))))&
((?[X]:((humble(X)|~brave(X))))<=>(patient(lucy)))&
((?[X]:(generous(X)))<=>((curious(fred)|quiet(fred))))&
((?[X]:((~rich(X)|~brave(X))))<=>((~rich(lucy)|brave(lucy))))&
(![X]:((curious(X)|~humble(X))<=>(kind(X)&quiet(X))))&
(![X]:((~humble(X)|~happy(X))<=>(~curious(X)|~patient(X))))&
(![X]:(~creative(X)=>~old(X)))&
(((funny(mary)&kind(mary)))<=>(?[X]:((~kind(X)|~old(X)))))&
((calm(lucy))=>(~humble(john)))&
(![X]:((~curious(X)|strong(X))=>(~rich(X)|old(X))))&
(![X]:((curious(X)|rich(X))=>(funny(X)<~>~tall(X))))&
((?[X]:((~curious(X)&~rich(X))))=>((~strong(lucy)<~>~tall(lucy))))&
((humble(john)|~patient(john)))&
((~patient(john)&~happy(john)))&
(generous(susan))&
(~patient(mary))&
((~kind(alice)&~funny(alice)))&
(?[X]:((curious(X)|~brave(X))))&
(?[X]:((kind(X)&~happy(X))))&
((~humble(susan)&~happy(susan))) | ~patient(susan) | [
"p1",
"p8",
"p9",
"p18",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7895819859916499430828048
% SZS output start Proof for 7895819859916499430828048
2. ! [X0] : ((~quiet(X0) & strong(X0)) <=> (~curious(X0) & generous(X0))) [input p1]
9. ! [X0] : ((~humble(X0) | curious(X0)) <=> (quiet(X0) & kind(X0))) [input p8]
10. ! [X0] : ((~happy(X0) | ~humble(X0)) <=> (~patient(X0) | ~curious(X0))) [input p9]
19. generous(susan) [input p18]
24. ~happy(susan) & ~humble(susan) [input p23]
25. patient(susan) [input hypothesis]
35. ! [X0] : (((~quiet(X0) & strong(X0)) | (curious(X0) | ~generous(X0))) & ((~curious(X0) & generous(X0)) | (quiet(X0) | ~strong(X0)))) [nnf transformation 2]
36. ! [X0] : (((~quiet(X0) & strong(X0)) | curious(X0) | ~generous(X0)) & ((~curious(X0) & generous(X0)) | quiet(X0) | ~strong(X0))) [flattening 35]
57. ! [X0] : (((~humble(X0) | curious(X0)) | (~quiet(X0) | ~kind(X0))) & ((quiet(X0) & kind(X0)) | (humble(X0) & ~curious(X0)))) [nnf transformation 9]
58. ! [X0] : ((~humble(X0) | curious(X0) | ~quiet(X0) | ~kind(X0)) & ((quiet(X0) & kind(X0)) | (humble(X0) & ~curious(X0)))) [flattening 57]
59. ! [X0] : (((~happy(X0) | ~humble(X0)) | (patient(X0) & curious(X0))) & ((~patient(X0) | ~curious(X0)) | (happy(X0) & humble(X0)))) [nnf transformation 10]
60. ! [X0] : ((~happy(X0) | ~humble(X0) | (patient(X0) & curious(X0))) & (~patient(X0) | ~curious(X0) | (happy(X0) & humble(X0)))) [flattening 59]
77. ~generous(X0) | curious(X0) | ~quiet(X0) [cnf transformation 36]
101. humble(X0) | quiet(X0) [cnf transformation 58]
103. ~patient(X0) | ~curious(X0) | humble(X0) [cnf transformation 60]
124. generous(susan) [cnf transformation 19]
131. ~humble(susan) [cnf transformation 24]
133. patient(susan) [cnf transformation 25]
287. quiet(susan) [resolution 101,131]
316. 36 <=> curious(susan) [avatar definition]
338. curious(susan) | ~quiet(susan) [resolution 77,124]
366. ~curious(susan) | humble(susan) [resolution 103,133]
375. ~curious(susan) [subsumption resolution 366,131]
376. ~36 [avatar split clause 375,316]
377. curious(susan) [subsumption resolution 338,287]
378. 36 [avatar split clause 377,316]
379. $false [avatar sat refutation 376,378]
% SZS output end Proof for 7895819859916499430828048
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and not quiet is both not happy and not quiet. Everyone who is either not old or not strong is both curious and not old and vice versa. If someone is not quiet or not humble then fred is both not happy and not rich and vice versa. If someone is both strong and not happy then someone is wise or generous and vice versa. If mary is not humble then someone is either wise or strong. If paul is not quiet then someone is kind or not rich. Everyone who is both not tall and not happy is not humble or generous and vice versa. Everyone who is either not happy or funny is either not tall or not patient and vice versa. If someone is either rich or curious then someone is both not kind and kind and vice versa. If susan is not quiet then mary is both not happy and not generous. If someone is not creative or not quiet then lucy is not generous or not happy and vice versa. If mary is either tall or not quiet then someone is either not old or not patient. If susan is tall or generous then lucy is both not old and calm. If someone is strong or not tall then susan is both not rich and not humble and vice versa. If fred is not brave then mary is either not funny or not old and vice versa. Everyone who is not tall is not happy. Fred is quiet or not generous. Someone is either not brave or rich. Fred is brave or tall. Fred is both not curious and not calm. Someone is both curious and not brave. Someone is not brave or creative. Someone is both funny and not calm. Someone is either not curious or not happy. | Susan is happy. | contradiction | (![X]:((~brave(X)&~quiet(X))=>(~happy(X)&~quiet(X))))&
(![X]:((~old(X)<~>~strong(X))<=>(curious(X)&~old(X))))&
((?[X]:((~quiet(X)|~humble(X))))<=>((~happy(fred)&~rich(fred))))&
((?[X]:((strong(X)&~happy(X))))<=>(?[X]:((wise(X)|generous(X)))))&
((~humble(mary))=>(?[X]:((wise(X)<~>strong(X)))))&
((~quiet(paul))=>(?[X]:((kind(X)|~rich(X)))))&
(![X]:((~tall(X)&~happy(X))<=>(~humble(X)|generous(X))))&
(![X]:((~happy(X)<~>funny(X))<=>(~tall(X)<~>~patient(X))))&
((?[X]:((rich(X)<~>curious(X))))<=>(?[X]:((~kind(X)&kind(X)))))&
((~quiet(susan))=>((~happy(mary)&~generous(mary))))&
((?[X]:((~creative(X)|~quiet(X))))<=>((~generous(lucy)|~happy(lucy))))&
(((tall(mary)<~>~quiet(mary)))=>(?[X]:((~old(X)<~>~patient(X)))))&
(((tall(susan)|generous(susan)))=>((~old(lucy)&calm(lucy))))&
((?[X]:((strong(X)|~tall(X))))<=>((~rich(susan)&~humble(susan))))&
((~brave(fred))<=>((~funny(mary)<~>~old(mary))))&
(![X]:(~tall(X)=>~happy(X)))&
((quiet(fred)|~generous(fred)))&
(?[X]:((~brave(X)<~>rich(X))))&
((brave(fred)|tall(fred)))&
((~curious(fred)&~calm(fred)))&
(?[X]:((curious(X)&~brave(X))))&
(?[X]:((~brave(X)|creative(X))))&
(?[X]:((funny(X)&~calm(X))))&
(?[X]:((~curious(X)<~>~happy(X)))) | happy(susan) | [
"p1",
"p6",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6707147358186499295416925
% SZS output start Proof for 6707147358186499295416925
2. ! [X0] : ((~old(X0) <~> ~strong(X0)) <=> (~old(X0) & curious(X0))) [input p1]
7. ! [X0] : ((~happy(X0) & ~tall(X0)) <=> (generous(X0) | ~humble(X0))) [input p6]
14. ? [X0] : (~tall(X0) | strong(X0)) <=> (~humble(susan) & ~rich(susan)) [input p13]
21. ? [X0] : (~brave(X0) & curious(X0)) [input p20]
25. happy(susan) [input hypothesis]
36. ! [X0] : ((((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) | (old(X0) | ~curious(X0))) & ((~old(X0) & curious(X0)) | ((~old(X0) | strong(X0)) & (~strong(X0) | old(X0))))) [nnf transformation 2]
37. ! [X0] : ((((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) | old(X0) | ~curious(X0)) & ((~old(X0) & curious(X0)) | ((~old(X0) | strong(X0)) & (~strong(X0) | old(X0))))) [flattening 36]
53. ! [X0] : (((~happy(X0) & ~tall(X0)) | (~generous(X0) & humble(X0))) & ((generous(X0) | ~humble(X0)) | (happy(X0) | tall(X0)))) [nnf transformation 7]
54. ! [X0] : (((~happy(X0) & ~tall(X0)) | (~generous(X0) & humble(X0))) & (generous(X0) | ~humble(X0) | happy(X0) | tall(X0))) [flattening 53]
69. (? [X0] : (~tall(X0) | strong(X0)) | (humble(susan) | rich(susan))) & ((~humble(susan) & ~rich(susan)) | ! [X0] : (tall(X0) & ~strong(X0))) [nnf transformation 14]
70. (? [X0] : (~tall(X0) | strong(X0)) | humble(susan) | rich(susan)) & ((~humble(susan) & ~rich(susan)) | ! [X0] : (tall(X0) & ~strong(X0))) [flattening 69]
71. (? [X0] : (~tall(X0) | strong(X0)) | humble(susan) | rich(susan)) & ((~humble(susan) & ~rich(susan)) | ! [X1] : (tall(X1) & ~strong(X1))) [rectify 70]
72. ? [X0] : (~tall(X0) | strong(X0)) => (~tall(sK9) | strong(sK9)) [choice axiom]
73. ((~tall(sK9) | strong(sK9)) | humble(susan) | rich(susan)) & ((~humble(susan) & ~rich(susan)) | ! [X1] : (tall(X1) & ~strong(X1))) [skolemisation 71,72]
78. ? [X0] : (~brave(X0) & curious(X0)) => (~brave(sK11) & curious(sK11)) [choice axiom]
79. ~brave(sK11) & curious(sK11) [skolemisation 21,78]
92. ~old(X0) | ~old(X0) | strong(X0) [cnf transformation 37]
94. strong(X0) | old(X0) | old(X0) | ~curious(X0) [cnf transformation 37]
111. ~happy(X0) | humble(X0) [cnf transformation 54]
143. ~humble(susan) | ~strong(X1) [cnf transformation 73]
157. curious(sK11) [cnf transformation 79]
164. happy(susan) [cnf transformation 25]
165. ~old(X0) | strong(X0) [duplicate literal removal 92]
166. ~curious(X0) | old(X0) | strong(X0) [duplicate literal removal 94]
342. 39 <=> humble(susan) [avatar definition]
359. 43 <=> ! [X1] : ~strong(X1) [avatar definition]
360. ~strong(X1) <- (43) [avatar component clause 359]
361. 43 | ~39 [avatar split clause 143,342,359]
423. humble(susan) [resolution 111,164]
426. 39 [avatar split clause 423,342]
449. old(sK11) | strong(sK11) [resolution 166,157]
451. old(sK11) <- (43) [subsumption resolution 449,360]
453. strong(sK11) <- (43) [resolution 451,165]
454. $false <- (43) [subsumption resolution 453,360]
455. ~43 [avatar contradiction clause 454]
456. $false [avatar sat refutation 361,426,455]
% SZS output end Proof for 6707147358186499295416925
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and kind is generous.
If someone is both happy and humble then someone is both rich and not patient and vice versa.
Everyone who is either wise or kind is happy and vice versa.
If lucy is not tall or not happy then lucy is either strong or not quiet and vice versa.
If mary is not creative then someone is either rich or not brave.
Everyone who is wise is either not funny or not strong and vice versa.
Everyone who is both not wise and old is not patient.
If fred is not creative then someone is both happy and not generous.
Everyone who is both brave and humble is not rich or not generous and vice versa.
If someone is quiet or wise then someone is generous or strong.
Everyone who is either wise or happy is both not humble and not patient and vice versa.
Everyone who is either not kind or not happy is not curious.
If lucy is either calm or not patient then someone is strong or not kind and vice versa.
Everyone who is either not brave or strong is both not strong and strong and vice versa.
If mary is not quiet then alice is both patient and creative.
If susan is either generous or calm then someone is both not calm and strong.
Someone is curious.
Someone is both not brave and not funny.
Alice is not curious.
Lucy is either old or not wise.
Someone is both not wise and not brave.
Lucy is not generous.
Someone is either not tall or not patient.
Someone is old. | Lucy is not kind. | entailment | (![X]:((rich(X)&kind(X))=>generous(X)))&
((?[X]:((happy(X)&humble(X))))<=>(?[X]:((rich(X)&~patient(X)))))&
(![X]:((wise(X)<~>kind(X))<=>happy(X)))&
(((~tall(lucy)|~happy(lucy)))<=>((strong(lucy)<~>~quiet(lucy))))&
((~creative(mary))=>(?[X]:((rich(X)<~>~brave(X)))))&
(![X]:(wise(X)<=>(~funny(X)<~>~strong(X))))&
(![X]:((~wise(X)&old(X))=>~patient(X)))&
((~creative(fred))=>(?[X]:((happy(X)&~generous(X)))))&
(![X]:((brave(X)&humble(X))<=>(~rich(X)|~generous(X))))&
((?[X]:((quiet(X)|wise(X))))=>(?[X]:((generous(X)|strong(X)))))&
(![X]:((wise(X)<~>happy(X))<=>(~humble(X)&~patient(X))))&
(![X]:((~kind(X)<~>~happy(X))=>~curious(X)))&
(((calm(lucy)<~>~patient(lucy)))<=>(?[X]:((strong(X)|~kind(X)))))&
(![X]:((~brave(X)<~>strong(X))<=>(~strong(X)&strong(X))))&
((~quiet(mary))=>((patient(alice)&creative(alice))))&
(((generous(susan)<~>calm(susan)))=>(?[X]:((~calm(X)&strong(X)))))&
(?[X]:(curious(X)))&
(?[X]:((~brave(X)&~funny(X))))&
(~curious(alice))&
((old(lucy)<~>~wise(lucy)))&
(?[X]:((~wise(X)&~brave(X))))&
(~generous(lucy))&
(?[X]:((~tall(X)<~>~patient(X))))&
(?[X]:(old(X))) | ~kind(lucy) | [
"p0",
"p2",
"p8",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2391056327596603240228400
% SZS output start Proof for 2391056327596603240228400
1. ! [X0] : ((kind(X0) & rich(X0)) => generous(X0)) [input p0]
3. ! [X0] : ((wise(X0) <~> kind(X0)) <=> happy(X0)) [input p2]
9. ! [X0] : ((humble(X0) & brave(X0)) <=> (~generous(X0) | ~rich(X0))) [input p8]
11. ! [X0] : ((wise(X0) <~> happy(X0)) <=> (~patient(X0) & ~humble(X0))) [input p10]
22. ~generous(lucy) [input p21]
25. kind(lucy) [input hypothesis]
31. ! [X0] : (generous(X0) | (~kind(X0) | ~rich(X0))) [ennf transformation 1]
32. ! [X0] : (generous(X0) | ~kind(X0) | ~rich(X0)) [flattening 31]
44. ! [X0] : ((((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | ~happy(X0)) & (happy(X0) | ((wise(X0) | ~kind(X0)) & (kind(X0) | ~wise(X0))))) [nnf transformation 3]
48. ! [X0] : (((humble(X0) & brave(X0)) | (generous(X0) & rich(X0))) & ((~generous(X0) | ~rich(X0)) | (~humble(X0) | ~brave(X0)))) [nnf transformation 9]
49. ! [X0] : (((humble(X0) & brave(X0)) | (generous(X0) & rich(X0))) & (~generous(X0) | ~rich(X0) | ~humble(X0) | ~brave(X0))) [flattening 48]
53. ! [X0] : ((((~happy(X0) | ~wise(X0)) & (happy(X0) | wise(X0))) | (patient(X0) | humble(X0))) & ((~patient(X0) & ~humble(X0)) | ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0))))) [nnf transformation 11]
54. ! [X0] : ((((~happy(X0) | ~wise(X0)) & (happy(X0) | wise(X0))) | patient(X0) | humble(X0)) & ((~patient(X0) & ~humble(X0)) | ((wise(X0) | ~happy(X0)) & (happy(X0) | ~wise(X0))))) [flattening 53]
77. ~kind(X0) | generous(X0) | ~rich(X0) [cnf transformation 32]
83. ~kind(X0) | wise(X0) | happy(X0) [cnf transformation 44]
85. ~wise(X0) | ~kind(X0) | ~happy(X0) [cnf transformation 44]
100. humble(X0) | rich(X0) [cnf transformation 49]
101. humble(X0) | generous(X0) [cnf transformation 49]
104. ~wise(X0) | happy(X0) | ~humble(X0) [cnf transformation 54]
105. ~humble(X0) | wise(X0) | ~happy(X0) [cnf transformation 54]
137. ~generous(lucy) [cnf transformation 22]
141. kind(lucy) [cnf transformation 25]
185. 10 <=> happy(lucy) [avatar definition]
186. happy(lucy) <- (10) [avatar component clause 185]
187. ~happy(lucy) <- (~10) [avatar component clause 185]
272. 28 <=> wise(lucy) [avatar definition]
273. ~wise(lucy) <- (~28) [avatar component clause 272]
274. wise(lucy) <- (28) [avatar component clause 272]
301. generous(lucy) | ~rich(lucy) [resolution 77,141]
302. ~rich(lucy) [subsumption resolution 301,137]
305. wise(lucy) | happy(lucy) [resolution 83,141]
332. 10 | 28 [avatar split clause 305,272,185]
334. ~kind(lucy) | ~happy(lucy) <- (28) [resolution 274,85]
369. happy(lucy) | ~humble(lucy) <- (28) [resolution 104,274]
371. ~humble(lucy) <- (~10, 28) [subsumption resolution 369,187]
373. rich(lucy) <- (~10, 28) [resolution 371,100]
376. $false <- (~10, 28) [subsumption resolution 373,302]
377. 10 | ~28 [avatar contradiction clause 376]
383. ~happy(lucy) <- (28) [subsumption resolution 334,141]
384. ~10 | ~28 [avatar split clause 383,272,185]
399. ~happy(X0) | wise(X0) | generous(X0) [resolution 105,101]
490. wise(lucy) | generous(lucy) <- (10) [resolution 399,186]
491. generous(lucy) <- (10, ~28) [subsumption resolution 490,273]
492. $false <- (10, ~28) [subsumption resolution 491,137]
493. ~10 | 28 [avatar contradiction clause 492]
494. $false [avatar sat refutation 332,377,384,493]
% SZS output end Proof for 2391056327596603240228400
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and creative then someone is both curious and patient and vice versa.
If someone is either calm or not funny then susan is patient and vice versa.
Everyone who is both creative and quiet is both not brave and not quiet and vice versa.
Everyone who is either happy or quiet is either not patient or generous.
Everyone who is both curious and not curious is kind and vice versa.
If someone is both not rich and calm then someone is either tall or old.
Everyone who is both not kind and not quiet is not strong.
Everyone who is either not rich or not humble is both not strong and quiet.
Everyone who is curious or not creative is tall or generous and vice versa.
If lucy is either not strong or funny then paul is not curious and vice versa.
Everyone who is not wise or funny is not kind or kind and vice versa.
If paul is old or not rich then mary is creative or generous.
If someone is both tall and not brave then lucy is both humble and not tall.
If someone is not strong then someone is not quiet and vice versa.
If susan is both not old and rich then mary is either not wise or not generous.
Everyone who is either not creative or wise is creative and vice versa.
Lucy is brave.
Someone is both not brave and old.
Paul is both old and generous.
Someone is either rich or not strong.
John is creative.
Someone is either creative or not wise.
Alice is not rich or not patient. | Paul is old. | entailment | ((?[X]:((strong(X)&creative(X))))<=>(?[X]:((curious(X)&patient(X)))))&
((?[X]:((calm(X)<~>~funny(X))))<=>(patient(susan)))&
(![X]:((creative(X)&quiet(X))<=>(~brave(X)&~quiet(X))))&
(![X]:((happy(X)<~>quiet(X))=>(~patient(X)<~>generous(X))))&
(![X]:((curious(X)&~curious(X))<=>kind(X)))&
((?[X]:((~rich(X)&calm(X))))=>(?[X]:((tall(X)<~>old(X)))))&
(![X]:((~kind(X)&~quiet(X))=>~strong(X)))&
(![X]:((~rich(X)<~>~humble(X))=>(~strong(X)&quiet(X))))&
(![X]:((curious(X)|~creative(X))<=>(tall(X)|generous(X))))&
(((~strong(lucy)<~>funny(lucy)))<=>(~curious(paul)))&
(![X]:((~wise(X)|funny(X))<=>(~kind(X)|kind(X))))&
(((old(paul)|~rich(paul)))=>((creative(mary)|generous(mary))))&
((?[X]:((tall(X)&~brave(X))))=>((humble(lucy)&~tall(lucy))))&
((?[X]:(~strong(X)))<=>(?[X]:(~quiet(X))))&
(((~old(susan)&rich(susan)))=>((~wise(mary)<~>~generous(mary))))&
(![X]:((~creative(X)<~>wise(X))<=>creative(X)))&
(brave(lucy))&
(?[X]:((~brave(X)&old(X))))&
((old(paul)&generous(paul)))&
(?[X]:((rich(X)<~>~strong(X))))&
(creative(john))&
(?[X]:((creative(X)<~>~wise(X))))&
((~rich(alice)|~patient(alice))) | old(paul) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 310956574394561921928862
% SZS output start Proof for 310956574394561921928862
19. generous(paul) & old(paul) [input p18]
24. ~old(paul) [input hypothesis]
130. old(paul) [cnf transformation 19]
138. ~old(paul) [cnf transformation 24]
237. 21 <=> old(paul) [avatar definition]
285. 21 [avatar split clause 130,237]
306. ~21 [avatar split clause 138,237]
307. $false [avatar sat refutation 285,306]
% SZS output end Proof for 310956574394561921928862
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or not old is not calm or happy.
Everyone who is both curious and not brave is either not funny or not strong and vice versa.
Everyone who is not calm or not generous is either not strong or not patient.
If someone is either not old or not curious then someone is both not kind and not curious.
Everyone who is either not happy or creative is either not kind or not generous.
Everyone who is both tall and not calm is tall or rich.
Everyone who is either wise or creative is either not kind or not generous and vice versa.
Everyone who is generous is both brave and old and vice versa.
If someone is either tall or not curious then someone is either strong or humble.
Everyone who is either not kind or not funny is funny and vice versa.
Everyone who is not quiet or not brave is both not wise and creative.
Everyone who is not quiet is not generous or not brave and vice versa.
Everyone who is both strong and humble is not strong or humble and vice versa.
If someone is funny then alice is either strong or creative and vice versa.
Everyone who is creative is either not patient or not kind.
Alice is old.
Alice is calm.
Someone is not quiet or not kind.
Fred is happy or not old.
Someone is both patient and brave.
Mary is happy or not funny. | Mary is not brave. | contradiction | (![X]:((humble(X)|~old(X))=>(~calm(X)|happy(X))))&
(![X]:((curious(X)&~brave(X))<=>(~funny(X)<~>~strong(X))))&
(![X]:((~calm(X)|~generous(X))=>(~strong(X)<~>~patient(X))))&
((?[X]:((~old(X)<~>~curious(X))))=>(?[X]:((~kind(X)&~curious(X)))))&
(![X]:((~happy(X)<~>creative(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((tall(X)&~calm(X))=>(tall(X)|rich(X))))&
(![X]:((wise(X)<~>creative(X))<=>(~kind(X)<~>~generous(X))))&
(![X]:(generous(X)<=>(brave(X)&old(X))))&
((?[X]:((tall(X)<~>~curious(X))))=>(?[X]:((strong(X)<~>humble(X)))))&
(![X]:((~kind(X)<~>~funny(X))<=>funny(X)))&
(![X]:((~quiet(X)|~brave(X))=>(~wise(X)&creative(X))))&
(![X]:(~quiet(X)<=>(~generous(X)|~brave(X))))&
(![X]:((strong(X)&humble(X))<=>(~strong(X)|humble(X))))&
((?[X]:(funny(X)))<=>((strong(alice)<~>creative(alice))))&
(![X]:(creative(X)=>(~patient(X)<~>~kind(X))))&
(old(alice))&
(calm(alice))&
(?[X]:((~quiet(X)|~kind(X))))&
((happy(fred)|~old(fred)))&
(?[X]:((patient(X)&brave(X))))&
((happy(mary)|~funny(mary))) | ~brave(mary) | [
"p2",
"p7",
"p9",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 672967916246453455650659
% SZS output start Proof for 672967916246453455650659
3. ! [X0] : ((~generous(X0) | ~calm(X0)) => (~strong(X0) <~> ~patient(X0))) [input p2]
8. ! [X0] : (generous(X0) <=> (old(X0) & brave(X0))) [input p7]
10. ! [X0] : ((~kind(X0) <~> ~funny(X0)) <=> funny(X0)) [input p9]
11. ! [X0] : ((~brave(X0) | ~quiet(X0)) => (creative(X0) & ~wise(X0))) [input p10]
13. ! [X0] : ((humble(X0) & strong(X0)) <=> (humble(X0) | ~strong(X0))) [input p12]
15. ! [X0] : (creative(X0) => (~patient(X0) <~> ~kind(X0))) [input p14]
22. ~brave(mary) [input hypothesis]
28. ! [X0] : ((~strong(X0) <~> ~patient(X0)) | (generous(X0) & calm(X0))) [ennf transformation 3]
32. ! [X0] : ((creative(X0) & ~wise(X0)) | (brave(X0) & quiet(X0))) [ennf transformation 11]
33. ! [X0] : ((~patient(X0) <~> ~kind(X0)) | ~creative(X0)) [ennf transformation 15]
36. ! [X0] : (((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | (generous(X0) & calm(X0))) [nnf transformation 28]
43. ! [X0] : ((generous(X0) | (~old(X0) | ~brave(X0))) & ((old(X0) & brave(X0)) | ~generous(X0))) [nnf transformation 8]
44. ! [X0] : ((generous(X0) | ~old(X0) | ~brave(X0)) & ((old(X0) & brave(X0)) | ~generous(X0))) [flattening 43]
49. ! [X0] : ((((funny(X0) | kind(X0)) & (~funny(X0) | ~kind(X0))) | ~funny(X0)) & (funny(X0) | ((~kind(X0) | funny(X0)) & (~funny(X0) | kind(X0))))) [nnf transformation 10]
52. ! [X0] : (((humble(X0) & strong(X0)) | (~humble(X0) & strong(X0))) & ((humble(X0) | ~strong(X0)) | (~humble(X0) | ~strong(X0)))) [nnf transformation 13]
53. ! [X0] : (((humble(X0) & strong(X0)) | (~humble(X0) & strong(X0))) & (humble(X0) | ~strong(X0) | ~humble(X0) | ~strong(X0))) [flattening 52]
58. ! [X0] : (((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | ~creative(X0)) [nnf transformation 33]
72. ~patient(X0) | ~strong(X0) | generous(X0) [cnf transformation 36]
91. ~generous(X0) | brave(X0) [cnf transformation 44]
99. funny(X0) | ~kind(X0) | funny(X0) [cnf transformation 49]
100. ~funny(X0) | ~kind(X0) | ~funny(X0) [cnf transformation 49]
105. creative(X0) | brave(X0) [cnf transformation 32]
111. strong(X0) | ~humble(X0) [cnf transformation 53]
112. strong(X0) | humble(X0) [cnf transformation 53]
119. kind(X0) | patient(X0) | ~creative(X0) [cnf transformation 58]
127. ~brave(mary) [cnf transformation 22]
130. funny(X0) | ~kind(X0) [duplicate literal removal 99]
131. ~kind(X0) | ~funny(X0) [duplicate literal removal 100]
168. ~kind(X0) [subsumption resolution 130,131]
170. strong(X0) [subsumption resolution 111,112]
186. ~creative(X0) | patient(X0) [subsumption resolution 119,168]
208. patient(X0) | brave(X0) [resolution 186,105]
258. ~strong(X0) | generous(X0) | brave(X0) [resolution 72,208]
260. generous(X0) | brave(X0) [subsumption resolution 258,170]
261. brave(X0) [subsumption resolution 260,91]
273. $false [resolution 261,127]
% SZS output end Proof for 672967916246453455650659
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise then someone is not patient or strong and vice versa. Everyone who is both tall and not kind is calm or not kind. Everyone who is calm is not calm or happy and vice versa. Everyone who is either not quiet or not wise is not creative or funny and vice versa. If lucy is not generous or generous then fred is not strong or not creative and vice versa. If susan is old then john is either not patient or not calm and vice versa. If alice is both patient and not patient then john is either strong or not funny and vice versa. Everyone who is not kind is not wise and vice versa. If alice is kind or not rich then someone is either not humble or funny. Everyone who is both not brave and humble is both creative and not strong and vice versa. If someone is both not quiet and not wise then paul is not tall or not wise. Everyone who is not quiet is both wise and not funny and vice versa. Everyone who is either quiet or wise is happy and vice versa. Everyone who is either not wise or creative is both not kind and not creative and vice versa. If susan is both not wise and not patient then someone is either not tall or old and vice versa. Everyone who is either wise or brave is either not calm or not wise and vice versa. Someone is either not wise or wise. Someone is both not funny and quiet. Fred is either patient or not kind. John is either not creative or not strong. Mary is both not humble and curious. John is not patient or generous. Someone is generous or not strong. | Lucy is not creative. | neutral | ((?[X]:(~wise(X)))<=>(?[X]:((~patient(X)|strong(X)))))&
(![X]:((tall(X)&~kind(X))=>(calm(X)|~kind(X))))&
(![X]:(calm(X)<=>(~calm(X)|happy(X))))&
(![X]:((~quiet(X)<~>~wise(X))<=>(~creative(X)|funny(X))))&
(((~generous(lucy)|generous(lucy)))<=>((~strong(fred)|~creative(fred))))&
((old(susan))<=>((~patient(john)<~>~calm(john))))&
(((patient(alice)&~patient(alice)))<=>((strong(john)<~>~funny(john))))&
(![X]:(~kind(X)<=>~wise(X)))&
(((kind(alice)|~rich(alice)))=>(?[X]:((~humble(X)<~>funny(X)))))&
(![X]:((~brave(X)&humble(X))<=>(creative(X)&~strong(X))))&
((?[X]:((~quiet(X)&~wise(X))))=>((~tall(paul)|~wise(paul))))&
(![X]:(~quiet(X)<=>(wise(X)&~funny(X))))&
(![X]:((quiet(X)<~>wise(X))<=>happy(X)))&
(![X]:((~wise(X)<~>creative(X))<=>(~kind(X)&~creative(X))))&
(((~wise(susan)&~patient(susan)))<=>(?[X]:((~tall(X)<~>old(X)))))&
(![X]:((wise(X)<~>brave(X))<=>(~calm(X)<~>~wise(X))))&
(?[X]:((~wise(X)<~>wise(X))))&
(?[X]:((~funny(X)&quiet(X))))&
((patient(fred)<~>~kind(fred)))&
((~creative(john)<~>~strong(john)))&
((~humble(mary)&curious(mary)))&
((~patient(john)|generous(john)))&
(?[X]:((generous(X)|~strong(X)))) | ~creative(lucy) | [] | null | 0 |
Everyone who is old is curious and vice versa.
If lucy is not quiet then someone is curious or quiet and vice versa.
Everyone who is either curious or patient is both not happy and creative and vice versa.
If someone is either calm or funny then someone is quiet or not humble and vice versa.
If lucy is calm then paul is wise.
Everyone who is not humble or not rich is not funny or funny.
If paul is quiet then someone is both tall and not happy.
Everyone who is old is both not wise and not quiet.
Everyone who is both not humble and curious is either creative or not creative and vice versa.
If lucy is either calm or not patient then someone is not old or not strong.
Everyone who is both creative and strong is both tall and not strong and vice versa.
Everyone who is either not generous or humble is both kind and not rich.
If someone is not curious or quiet then susan is either not rich or not calm.
Everyone who is not tall or old is both creative and funny.
Everyone who is both not tall and not curious is humble and vice versa.
Someone is both generous and not calm.
Someone is either not funny or not wise.
Someone is either generous or not curious.
Alice is not rich.
Mary is both old and calm.
Someone is both patient and generous.
Fred is not kind. | Paul is not funny. | contradiction | (![X]:(old(X)<=>curious(X)))&
((~quiet(lucy))<=>(?[X]:((curious(X)|quiet(X)))))&
(![X]:((curious(X)<~>patient(X))<=>(~happy(X)&creative(X))))&
((?[X]:((calm(X)<~>funny(X))))<=>(?[X]:((quiet(X)|~humble(X)))))&
((calm(lucy))=>(wise(paul)))&
(![X]:((~humble(X)|~rich(X))=>(~funny(X)|funny(X))))&
((quiet(paul))=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:(old(X)=>(~wise(X)&~quiet(X))))&
(![X]:((~humble(X)&curious(X))<=>(creative(X)<~>~creative(X))))&
(((calm(lucy)<~>~patient(lucy)))=>(?[X]:((~old(X)|~strong(X)))))&
(![X]:((creative(X)&strong(X))<=>(tall(X)&~strong(X))))&
(![X]:((~generous(X)<~>humble(X))=>(kind(X)&~rich(X))))&
((?[X]:((~curious(X)|quiet(X))))=>((~rich(susan)<~>~calm(susan))))&
(![X]:((~tall(X)|old(X))=>(creative(X)&funny(X))))&
(![X]:((~tall(X)&~curious(X))<=>humble(X)))&
(?[X]:((generous(X)&~calm(X))))&
(?[X]:((~funny(X)<~>~wise(X))))&
(?[X]:((generous(X)<~>~curious(X))))&
(~rich(alice))&
((old(mary)&calm(mary)))&
(?[X]:((patient(X)&generous(X))))&
(~kind(fred)) | ~funny(paul) | [
"p0",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5598681691541987992709566
% SZS output start Proof for 5598681691541987992709566
1. ! [X0] : (old(X0) <=> curious(X0)) [input p0]
9. ! [X0] : ((curious(X0) & ~humble(X0)) <=> (creative(X0) <~> ~creative(X0))) [input p8]
14. ! [X0] : ((old(X0) | ~tall(X0)) => (funny(X0) & creative(X0))) [input p13]
23. ~funny(paul) [input hypothesis]
33. ! [X0] : ((funny(X0) & creative(X0)) | (~old(X0) & tall(X0))) [ennf transformation 14]
34. ! [X0] : ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0))) [nnf transformation 1]
48. ! [X0] : (((curious(X0) & ~humble(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | (~curious(X0) | humble(X0)))) [nnf transformation 9]
49. ! [X0] : (((curious(X0) & ~humble(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | ~curious(X0) | humble(X0))) [flattening 48]
70. ~curious(X0) | old(X0) [cnf transformation 34]
97. curious(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 49]
98. curious(X0) | creative(X0) | creative(X0) [cnf transformation 49]
116. ~old(X0) | funny(X0) [cnf transformation 33]
132. ~funny(paul) [cnf transformation 23]
137. curious(X0) | ~creative(X0) [duplicate literal removal 97]
138. curious(X0) | creative(X0) [duplicate literal removal 98]
214. curious(X0) [subsumption resolution 137,138]
254. old(X0) [resolution 70,214]
261. funny(X0) [resolution 116,254]
262. $false [resolution 261,132]
% SZS output end Proof for 5598681691541987992709566
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and rich is strong or not strong and vice versa. Everyone who is humble is creative or not patient and vice versa. If paul is either humble or generous then someone is either brave or not quiet and vice versa. If someone is both old and tall then someone is either humble or not quiet. Everyone who is not tall or wise is not creative. If mary is either quiet or not humble then someone is both not humble and strong and vice versa. If susan is not tall then someone is strong or not patient and vice versa. If someone is curious or old then lucy is both not old and rich and vice versa. Everyone who is not rich or not brave is funny and vice versa. If someone is not generous then mary is both curious and not happy and vice versa. Everyone who is either not strong or strong is creative or calm. Everyone who is both not quiet and funny is not brave or generous. Everyone who is not tall or not generous is strong or not rich and vice versa. If someone is not calm then someone is rich or kind. If alice is either not humble or patient then someone is calm or not happy. Everyone who is not humble or not tall is both old and not humble and vice versa. Someone is brave or not curious. Someone is either funny or tall. Lucy is funny. Someone is happy or not tall. Susan is not strong or not old. Someone is both not happy and kind. | Alice is not strong. | entailment | (![X]:((patient(X)&rich(X))<=>(strong(X)|~strong(X))))&
(![X]:(humble(X)<=>(creative(X)|~patient(X))))&
(((humble(paul)<~>generous(paul)))<=>(?[X]:((brave(X)<~>~quiet(X)))))&
((?[X]:((old(X)&tall(X))))=>(?[X]:((humble(X)<~>~quiet(X)))))&
(![X]:((~tall(X)|wise(X))=>~creative(X)))&
(((quiet(mary)<~>~humble(mary)))<=>(?[X]:((~humble(X)&strong(X)))))&
((~tall(susan))<=>(?[X]:((strong(X)|~patient(X)))))&
((?[X]:((curious(X)|old(X))))<=>((~old(lucy)&rich(lucy))))&
(![X]:((~rich(X)|~brave(X))<=>funny(X)))&
((?[X]:(~generous(X)))<=>((curious(mary)&~happy(mary))))&
(![X]:((~strong(X)<~>strong(X))=>(creative(X)|calm(X))))&
(![X]:((~quiet(X)&funny(X))=>(~brave(X)|generous(X))))&
(![X]:((~tall(X)|~generous(X))<=>(strong(X)|~rich(X))))&
((?[X]:(~calm(X)))=>(?[X]:((rich(X)|kind(X)))))&
(((~humble(alice)<~>patient(alice)))=>(?[X]:((calm(X)|~happy(X)))))&
(![X]:((~humble(X)|~tall(X))<=>(old(X)&~humble(X))))&
(?[X]:((brave(X)|~curious(X))))&
(?[X]:((funny(X)<~>tall(X))))&
(funny(lucy))&
(?[X]:((happy(X)|~tall(X))))&
((~strong(susan)|~old(susan)))&
(?[X]:((~happy(X)&kind(X)))) | ~strong(alice) | [
"p0",
"p6",
"p12",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1352943039669695067488184
% SZS output start Proof for 1352943039669695067488184
1. ! [X0] : ((rich(X0) & patient(X0)) <=> (~strong(X0) | strong(X0))) [input p0]
7. ~tall(susan) <=> ? [X0] : (~patient(X0) | strong(X0)) [input p6]
13. ! [X0] : ((~generous(X0) | ~tall(X0)) <=> (~rich(X0) | strong(X0))) [input p12]
16. ! [X0] : ((~tall(X0) | ~humble(X0)) <=> (~humble(X0) & old(X0))) [input p15]
21. ~old(susan) | ~strong(susan) [input p20]
23. strong(alice) [input hypothesis]
35. ! [X0] : (((rich(X0) & patient(X0)) | (strong(X0) & ~strong(X0))) & ((~strong(X0) | strong(X0)) | (~rich(X0) | ~patient(X0)))) [nnf transformation 1]
36. ! [X0] : (((rich(X0) & patient(X0)) | (strong(X0) & ~strong(X0))) & (~strong(X0) | strong(X0) | ~rich(X0) | ~patient(X0))) [flattening 35]
51. (~tall(susan) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X0] : (~patient(X0) | strong(X0)) | tall(susan)) [nnf transformation 7]
52. (~tall(susan) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X1] : (~patient(X1) | strong(X1)) | tall(susan)) [rectify 51]
53. ? [X1] : (~patient(X1) | strong(X1)) => (~patient(sK3) | strong(sK3)) [choice axiom]
54. (~tall(susan) | ! [X0] : (patient(X0) & ~strong(X0))) & ((~patient(sK3) | strong(sK3)) | tall(susan)) [skolemisation 52,53]
67. ! [X0] : (((~generous(X0) | ~tall(X0)) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | (generous(X0) & tall(X0)))) [nnf transformation 13]
68. ! [X0] : ((~generous(X0) | ~tall(X0) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | (generous(X0) & tall(X0)))) [flattening 67]
69. ! [X0] : (((~tall(X0) | ~humble(X0)) | (humble(X0) | ~old(X0))) & ((~humble(X0) & old(X0)) | (tall(X0) & humble(X0)))) [nnf transformation 16]
70. ! [X0] : ((~tall(X0) | ~humble(X0) | humble(X0) | ~old(X0)) & ((~humble(X0) & old(X0)) | (tall(X0) & humble(X0)))) [flattening 69]
83. rich(X0) | ~strong(X0) [cnf transformation 36]
84. strong(X0) | rich(X0) [cnf transformation 36]
106. ~tall(susan) | ~strong(X0) [cnf transformation 54]
120. ~rich(X0) | strong(X0) | tall(X0) [cnf transformation 68]
125. tall(X0) | old(X0) [cnf transformation 70]
134. ~old(susan) | ~strong(susan) [cnf transformation 21]
136. strong(alice) [cnf transformation 23]
137. rich(X0) [subsumption resolution 83,84]
209. 15 <=> ! [X0] : ~strong(X0) [avatar definition]
210. ~strong(X0) <- (15) [avatar component clause 209]
212. 16 <=> tall(susan) [avatar definition]
214. ~tall(susan) <- (~16) [avatar component clause 212]
215. 15 | ~16 [avatar split clause 106,212,209]
264. tall(X0) | strong(X0) [subsumption resolution 120,137]
294. 33 <=> strong(susan) [avatar definition]
296. ~strong(susan) <- (~33) [avatar component clause 294]
298. 34 <=> old(susan) [avatar definition]
301. ~33 | ~34 [avatar split clause 134,298,294]
302. $false <- (15) [resolution 210,136]
303. ~15 [avatar contradiction clause 302]
306. old(susan) <- (~16) [resolution 125,214]
311. 34 | 16 [avatar split clause 306,212,298]
333. strong(susan) <- (~16) [resolution 264,214]
336. $false <- (~16, ~33) [subsumption resolution 333,296]
337. 16 | 33 [avatar contradiction clause 336]
338. $false [avatar sat refutation 215,301,303,311,337]
% SZS output end Proof for 1352943039669695067488184
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious then someone is not patient or old. Everyone who is wise or not old is not humble or patient and vice versa. Everyone who is either not old or brave is not old and vice versa. Everyone who is not patient or not calm is both not brave and humble. If fred is both generous and not calm then alice is tall and vice versa. Everyone who is both not kind and humble is funny or curious. Everyone who is old is either not rich or strong. Everyone who is both not generous and rich is either strong or not creative and vice versa. If someone is patient or funny then susan is either not creative or happy and vice versa. If paul is both happy and not wise then someone is not kind or brave. If paul is not quiet or not curious then fred is both humble and old. If someone is both quiet and tall then paul is both tall and old and vice versa. Everyone who is either tall or generous is either creative or tall. If john is both not brave and patient then lucy is both curious and patient and vice versa. If susan is both not curious and not strong then alice is both wise and not patient. Everyone who is not funny or calm is either calm or not happy and vice versa. Paul is not funny or kind. Someone is either brave or not humble. Lucy is both not patient and happy. Someone is either strong or not curious. Mary is either happy or strong. | John is not rich. | neutral | ((curious(lucy))=>(?[X]:((~patient(X)|old(X)))))&
(![X]:((wise(X)|~old(X))<=>(~humble(X)|patient(X))))&
(![X]:((~old(X)<~>brave(X))<=>~old(X)))&
(![X]:((~patient(X)|~calm(X))=>(~brave(X)&humble(X))))&
(((generous(fred)&~calm(fred)))<=>(tall(alice)))&
(![X]:((~kind(X)&humble(X))=>(funny(X)|curious(X))))&
(![X]:(old(X)=>(~rich(X)<~>strong(X))))&
(![X]:((~generous(X)&rich(X))<=>(strong(X)<~>~creative(X))))&
((?[X]:((patient(X)|funny(X))))<=>((~creative(susan)<~>happy(susan))))&
(((happy(paul)&~wise(paul)))=>(?[X]:((~kind(X)|brave(X)))))&
(((~quiet(paul)|~curious(paul)))=>((humble(fred)&old(fred))))&
((?[X]:((quiet(X)&tall(X))))<=>((tall(paul)&old(paul))))&
(![X]:((tall(X)<~>generous(X))=>(creative(X)<~>tall(X))))&
(((~brave(john)&patient(john)))<=>((curious(lucy)&patient(lucy))))&
(((~curious(susan)&~strong(susan)))=>((wise(alice)&~patient(alice))))&
(![X]:((~funny(X)|calm(X))<=>(calm(X)<~>~happy(X))))&
((~funny(paul)|kind(paul)))&
(?[X]:((brave(X)<~>~humble(X))))&
((~patient(lucy)&happy(lucy)))&
(?[X]:((strong(X)<~>~curious(X))))&
((happy(mary)<~>strong(mary))) | ~rich(john) | [] | null | 0 |
If someone is calm then someone is either strong or not quiet and vice versa.
Everyone who is either curious or patient is not quiet or not strong.
Everyone who is both brave and old is either generous or not creative and vice versa.
Everyone who is creative or strong is not generous or not calm and vice versa.
If john is strong or not calm then fred is not rich or not brave.
Everyone who is not old is not tall or calm and vice versa.
If fred is either not generous or tall then someone is not creative.
Everyone who is either not kind or funny is not funny.
Everyone who is not patient or old is not brave or quiet and vice versa.
If someone is creative or generous then someone is either not strong or not creative and vice versa.
Everyone who is not happy or not curious is either generous or not old and vice versa.
Everyone who is old is not tall or not generous.
Everyone who is creative or not strong is either not curious or brave and vice versa.
If paul is not curious then john is both old and creative.
Everyone who is not strong is both not wise and tall and vice versa.
Everyone who is not kind is both not tall and not wise and vice versa.
Susan is both curious and patient.
Someone is either strong or not calm.
Alice is not tall or creative.
Lucy is not funny or humble.
Someone is either calm or patient.
Someone is either not funny or curious.
Lucy is not funny. | Alice is not old. | entailment | ((?[X]:(calm(X)))<=>(?[X]:((strong(X)<~>~quiet(X)))))&
(![X]:((curious(X)<~>patient(X))=>(~quiet(X)|~strong(X))))&
(![X]:((brave(X)&old(X))<=>(generous(X)<~>~creative(X))))&
(![X]:((creative(X)|strong(X))<=>(~generous(X)|~calm(X))))&
(((strong(john)|~calm(john)))=>((~rich(fred)|~brave(fred))))&
(![X]:(~old(X)<=>(~tall(X)|calm(X))))&
(((~generous(fred)<~>tall(fred)))=>(?[X]:(~creative(X))))&
(![X]:((~kind(X)<~>funny(X))=>~funny(X)))&
(![X]:((~patient(X)|old(X))<=>(~brave(X)|quiet(X))))&
((?[X]:((creative(X)|generous(X))))<=>(?[X]:((~strong(X)<~>~creative(X)))))&
(![X]:((~happy(X)|~curious(X))<=>(generous(X)<~>~old(X))))&
(![X]:(old(X)=>(~tall(X)|~generous(X))))&
(![X]:((creative(X)|~strong(X))<=>(~curious(X)<~>brave(X))))&
((~curious(paul))=>((old(john)&creative(john))))&
(![X]:(~strong(X)<=>(~wise(X)&tall(X))))&
(![X]:(~kind(X)<=>(~tall(X)&~wise(X))))&
((curious(susan)&patient(susan)))&
(?[X]:((strong(X)<~>~calm(X))))&
((~tall(alice)|creative(alice)))&
((~funny(lucy)|humble(lucy)))&
(?[X]:((calm(X)<~>patient(X))))&
(?[X]:((~funny(X)<~>curious(X))))&
(~funny(lucy)) | ~old(alice) | [
"p2",
"p5",
"p10",
"p11",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 741383685359322601889776
% SZS output start Proof for 741383685359322601889776
3. ! [X0] : ((old(X0) & brave(X0)) <=> (generous(X0) <~> ~creative(X0))) [input p2]
6. ! [X0] : (~old(X0) <=> (calm(X0) | ~tall(X0))) [input p5]
11. ! [X0] : ((~curious(X0) | ~happy(X0)) <=> (generous(X0) <~> ~old(X0))) [input p10]
12. ! [X0] : (old(X0) => (~generous(X0) | ~tall(X0))) [input p11]
13. ! [X0] : ((~strong(X0) | creative(X0)) <=> (~curious(X0) <~> brave(X0))) [input p12]
19. creative(alice) | ~tall(alice) [input p18]
24. old(alice) [input hypothesis]
33. ! [X0] : ((~generous(X0) | ~tall(X0)) | ~old(X0)) [ennf transformation 12]
34. ! [X0] : (~generous(X0) | ~tall(X0) | ~old(X0)) [flattening 33]
42. ! [X0] : (((old(X0) & brave(X0)) | ((generous(X0) | creative(X0)) & (~creative(X0) | ~generous(X0)))) & (((creative(X0) | ~generous(X0)) & (~creative(X0) | generous(X0))) | (~old(X0) | ~brave(X0)))) [nnf transformation 3]
43. ! [X0] : (((old(X0) & brave(X0)) | ((generous(X0) | creative(X0)) & (~creative(X0) | ~generous(X0)))) & (((creative(X0) | ~generous(X0)) & (~creative(X0) | generous(X0))) | ~old(X0) | ~brave(X0))) [flattening 42]
46. ! [X0] : ((~old(X0) | (~calm(X0) & tall(X0))) & ((calm(X0) | ~tall(X0)) | old(X0))) [nnf transformation 6]
47. ! [X0] : ((~old(X0) | (~calm(X0) & tall(X0))) & (calm(X0) | ~tall(X0) | old(X0))) [flattening 46]
59. ! [X0] : (((~curious(X0) | ~happy(X0)) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0)))) & (((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | (curious(X0) & happy(X0)))) [nnf transformation 11]
60. ! [X0] : ((~curious(X0) | ~happy(X0) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0)))) & (((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | (curious(X0) & happy(X0)))) [flattening 59]
61. ! [X0] : (((~strong(X0) | creative(X0)) | ((~curious(X0) | ~brave(X0)) & (brave(X0) | curious(X0)))) & (((~brave(X0) | curious(X0)) & (brave(X0) | ~curious(X0))) | (strong(X0) & ~creative(X0)))) [nnf transformation 13]
62. ! [X0] : ((~strong(X0) | creative(X0) | ((~curious(X0) | ~brave(X0)) & (brave(X0) | curious(X0)))) & (((~brave(X0) | curious(X0)) & (brave(X0) | ~curious(X0))) | (strong(X0) & ~creative(X0)))) [flattening 61]
82. ~creative(X0) | generous(X0) | ~old(X0) | ~brave(X0) [cnf transformation 43]
93. ~old(X0) | tall(X0) [cnf transformation 47]
110. ~old(X0) | generous(X0) | curious(X0) [cnf transformation 60]
115. ~generous(X0) | ~tall(X0) | ~old(X0) [cnf transformation 34]
116. ~creative(X0) | ~curious(X0) | brave(X0) [cnf transformation 62]
134. creative(alice) | ~tall(alice) [cnf transformation 19]
140. old(alice) [cnf transformation 24]
215. ~generous(X0) | ~old(X0) [subsumption resolution 115,93]
241. 23 <=> tall(alice) [avatar definition]
245. 24 <=> creative(alice) [avatar definition]
247. creative(alice) <- (24) [avatar component clause 245]
248. ~23 | 24 [avatar split clause 134,245,241]
269. tall(alice) [resolution 93,140]
272. 23 [avatar split clause 269,241]
284. 30 <=> generous(alice) [avatar definition]
285. generous(alice) <- (30) [avatar component clause 284]
286. ~generous(alice) <- (~30) [avatar component clause 284]
288. 31 <=> brave(alice) [avatar definition]
290. brave(alice) <- (31) [avatar component clause 288]
383. generous(alice) | curious(alice) [resolution 110,140]
384. curious(alice) <- (~30) [subsumption resolution 383,286]
393. ~curious(alice) | brave(alice) <- (24) [resolution 116,247]
398. brave(alice) <- (24, ~30) [subsumption resolution 393,384]
416. 31 | ~24 | 30 [avatar split clause 398,284,245,288]
533. generous(alice) | ~old(alice) | ~brave(alice) <- (24) [resolution 82,247]
546. generous(alice) | ~brave(alice) <- (24) [subsumption resolution 533,140]
547. generous(alice) <- (24, 31) [subsumption resolution 546,290]
548. 30 | ~24 | ~31 [avatar split clause 547,288,245,284]
558. ~old(alice) <- (30) [resolution 285,215]
559. $false <- (30) [subsumption resolution 558,140]
560. ~30 [avatar contradiction clause 559]
561. $false [avatar sat refutation 248,272,416,548,560]
% SZS output end Proof for 741383685359322601889776
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either wise or creative then someone is brave. If lucy is both funny and calm then someone is both not tall and wise. Everyone who is rich or not brave is brave or not patient. If someone is not old then paul is both patient and not rich and vice versa. If fred is not old then paul is either happy or creative. If susan is happy then someone is both not calm and not generous and vice versa. Everyone who is funny or not happy is both quiet and not brave. Everyone who is both calm and curious is either creative or calm and vice versa. Everyone who is both old and creative is not funny or not tall. Everyone who is not funny is old. Everyone who is either rich or curious is either calm or not funny and vice versa. Everyone who is both patient and brave is either not curious or not patient. Everyone who is funny is not wise or rich. Everyone who is not generous or kind is generous and vice versa. If someone is patient or old then someone is either patient or tall and vice versa. If someone is humble or curious then someone is both rich and humble and vice versa. Alice is both not old and not strong. Fred is tall. Fred is not creative. Mary is not kind or not happy. Someone is either brave or not kind. Someone is quiet or not brave. Lucy is tall. | Paul is curious. | contradiction | (((wise(fred)<~>creative(fred)))=>(?[X]:(brave(X))))&
(((funny(lucy)&calm(lucy)))=>(?[X]:((~tall(X)&wise(X)))))&
(![X]:((rich(X)|~brave(X))=>(brave(X)|~patient(X))))&
((?[X]:(~old(X)))<=>((patient(paul)&~rich(paul))))&
((~old(fred))=>((happy(paul)<~>creative(paul))))&
((happy(susan))<=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:((funny(X)|~happy(X))=>(quiet(X)&~brave(X))))&
(![X]:((calm(X)&curious(X))<=>(creative(X)<~>calm(X))))&
(![X]:((old(X)&creative(X))=>(~funny(X)|~tall(X))))&
(![X]:(~funny(X)=>old(X)))&
(![X]:((rich(X)<~>curious(X))<=>(calm(X)<~>~funny(X))))&
(![X]:((patient(X)&brave(X))=>(~curious(X)<~>~patient(X))))&
(![X]:(funny(X)=>(~wise(X)|rich(X))))&
(![X]:((~generous(X)|kind(X))<=>generous(X)))&
((?[X]:((patient(X)|old(X))))<=>(?[X]:((patient(X)<~>tall(X)))))&
((?[X]:((humble(X)|curious(X))))<=>(?[X]:((rich(X)&humble(X)))))&
((~old(alice)&~strong(alice)))&
(tall(fred))&
(~creative(fred))&
((~kind(mary)|~happy(mary)))&
(?[X]:((brave(X)<~>~kind(X))))&
(?[X]:((quiet(X)|~brave(X))))&
(tall(lucy)) | curious(paul) | [
"p2",
"p3",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2346270534941838688279395
% SZS output start Proof for 2346270534941838688279395
3. ! [X0] : ((~brave(X0) | rich(X0)) => (~patient(X0) | brave(X0))) [input p2]
4. ? [X0] : ~old(X0) <=> (~rich(paul) & patient(paul)) [input p3]
12. ! [X0] : ((brave(X0) & patient(X0)) => (~curious(X0) <~> ~patient(X0))) [input p11]
17. ~strong(alice) & ~old(alice) [input p16]
24. curious(paul) [input hypothesis]
27. ~old(alice) [pure predicate removal 17]
33. ! [X0] : ((~patient(X0) | brave(X0)) | (brave(X0) & ~rich(X0))) [ennf transformation 3]
34. ! [X0] : (~patient(X0) | brave(X0) | (brave(X0) & ~rich(X0))) [flattening 33]
40. ! [X0] : ((~curious(X0) <~> ~patient(X0)) | (~brave(X0) | ~patient(X0))) [ennf transformation 12]
41. ! [X0] : ((~curious(X0) <~> ~patient(X0)) | ~brave(X0) | ~patient(X0)) [flattening 40]
49. (? [X0] : ~old(X0) | (rich(paul) | ~patient(paul))) & ((~rich(paul) & patient(paul)) | ! [X0] : old(X0)) [nnf transformation 4]
50. (? [X0] : ~old(X0) | rich(paul) | ~patient(paul)) & ((~rich(paul) & patient(paul)) | ! [X0] : old(X0)) [flattening 49]
51. (? [X0] : ~old(X0) | rich(paul) | ~patient(paul)) & ((~rich(paul) & patient(paul)) | ! [X1] : old(X1)) [rectify 50]
52. ? [X0] : ~old(X0) => ~old(sK2) [choice axiom]
53. (~old(sK2) | rich(paul) | ~patient(paul)) & ((~rich(paul) & patient(paul)) | ! [X1] : old(X1)) [skolemisation 51,52]
62. ! [X0] : (((patient(X0) | curious(X0)) & (~patient(X0) | ~curious(X0))) | ~brave(X0) | ~patient(X0)) [nnf transformation 41]
83. ~patient(X0) | brave(X0) | brave(X0) [cnf transformation 34]
84. patient(paul) | old(X1) [cnf transformation 53]
110. ~patient(X0) | ~curious(X0) | ~brave(X0) | ~patient(X0) [cnf transformation 62]
127. ~old(alice) [cnf transformation 27]
134. curious(paul) [cnf transformation 24]
137. ~patient(X0) | ~curious(X0) | ~brave(X0) [duplicate literal removal 110]
140. ~patient(X0) | brave(X0) [duplicate literal removal 83]
174. 8 <=> patient(paul) [avatar definition]
175. patient(paul) <- (8) [avatar component clause 174]
187. 11 <=> ! [X1] : old(X1) [avatar definition]
188. old(X1) <- (11) [avatar component clause 187]
190. 11 | 8 [avatar split clause 84,174,187]
224. ~curious(X0) | ~patient(X0) [subsumption resolution 137,140]
327. $false <- (11) [resolution 188,127]
330. ~11 [avatar contradiction clause 327]
334. ~patient(paul) [resolution 224,134]
335. $false <- (8) [subsumption resolution 334,175]
336. ~8 [avatar contradiction clause 335]
337. $false [avatar sat refutation 190,330,336]
% SZS output end Proof for 2346270534941838688279395
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either not generous or rich then someone is either happy or generous.
If alice is not generous then someone is humble or not wise and vice versa.
Everyone who is rich is humble and vice versa.
If fred is either happy or strong then lucy is either funny or not wise.
If someone is brave or not old then mary is quiet or not happy.
Everyone who is not humble is not tall or rich and vice versa.
Everyone who is either not old or not brave is not generous or not humble and vice versa.
If someone is not rich then someone is tall or not creative and vice versa.
Everyone who is both old and not rich is either not wise or not brave.
Everyone who is not old or not wise is happy or not patient and vice versa.
If someone is either rich or not brave then lucy is either not strong or kind and vice versa.
Everyone who is not patient is either not kind or funny and vice versa.
If lucy is not quiet or curious then susan is creative.
If john is both tall and old then someone is not curious and vice versa.
Everyone who is either not kind or not calm is both not patient and rich.
Everyone who is not wise or calm is both old and patient.
Mary is both strong and curious.
Lucy is old.
Paul is either patient or funny.
Susan is not curious or not rich.
Someone is both creative and brave.
John is either curious or not strong.
Susan is not humble or not rich. | Susan is wise. | entailment | (((~generous(paul)<~>rich(paul)))=>(?[X]:((happy(X)<~>generous(X)))))&
((~generous(alice))<=>(?[X]:((humble(X)|~wise(X)))))&
(![X]:(rich(X)<=>humble(X)))&
(((happy(fred)<~>strong(fred)))=>((funny(lucy)<~>~wise(lucy))))&
((?[X]:((brave(X)|~old(X))))=>((quiet(mary)|~happy(mary))))&
(![X]:(~humble(X)<=>(~tall(X)|rich(X))))&
(![X]:((~old(X)<~>~brave(X))<=>(~generous(X)|~humble(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((tall(X)|~creative(X)))))&
(![X]:((old(X)&~rich(X))=>(~wise(X)<~>~brave(X))))&
(![X]:((~old(X)|~wise(X))<=>(happy(X)|~patient(X))))&
((?[X]:((rich(X)<~>~brave(X))))<=>((~strong(lucy)<~>kind(lucy))))&
(![X]:(~patient(X)<=>(~kind(X)<~>funny(X))))&
(((~quiet(lucy)|curious(lucy)))=>(creative(susan)))&
(((tall(john)&old(john)))<=>(?[X]:(~curious(X))))&
(![X]:((~kind(X)<~>~calm(X))=>(~patient(X)&rich(X))))&
(![X]:((~wise(X)|calm(X))=>(old(X)&patient(X))))&
((strong(mary)&curious(mary)))&
(old(lucy))&
((patient(paul)<~>funny(paul)))&
((~curious(susan)|~rich(susan)))&
(?[X]:((creative(X)&brave(X))))&
((curious(john)<~>~strong(john)))&
((~humble(susan)|~rich(susan))) | wise(susan) | [
"p1",
"p2",
"p5",
"p6",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 266823044649509096456616
% SZS output start Proof for 266823044649509096456616
2. ~generous(alice) <=> ? [X0] : (~wise(X0) | humble(X0)) [input p1]
3. ! [X0] : (rich(X0) <=> humble(X0)) [input p2]
6. ! [X0] : (~humble(X0) <=> (rich(X0) | ~tall(X0))) [input p5]
7. ! [X0] : ((~old(X0) <~> ~brave(X0)) <=> (~humble(X0) | ~generous(X0))) [input p6]
9. ! [X0] : ((~rich(X0) & old(X0)) => (~wise(X0) <~> ~brave(X0))) [input p8]
16. ! [X0] : ((calm(X0) | ~wise(X0)) => (patient(X0) & old(X0))) [input p15]
24. ~wise(susan) [input hypothesis]
30. ! [X0] : ((~wise(X0) <~> ~brave(X0)) | (rich(X0) | ~old(X0))) [ennf transformation 9]
31. ! [X0] : ((~wise(X0) <~> ~brave(X0)) | rich(X0) | ~old(X0)) [flattening 30]
34. ! [X0] : ((patient(X0) & old(X0)) | (~calm(X0) & wise(X0))) [ennf transformation 16]
38. (~generous(alice) | ! [X0] : (wise(X0) & ~humble(X0))) & (? [X0] : (~wise(X0) | humble(X0)) | generous(alice)) [nnf transformation 2]
39. (~generous(alice) | ! [X0] : (wise(X0) & ~humble(X0))) & (? [X1] : (~wise(X1) | humble(X1)) | generous(alice)) [rectify 38]
40. ? [X1] : (~wise(X1) | humble(X1)) => (~wise(sK1) | humble(sK1)) [choice axiom]
41. (~generous(alice) | ! [X0] : (wise(X0) & ~humble(X0))) & ((~wise(sK1) | humble(sK1)) | generous(alice)) [skolemisation 39,40]
42. ! [X0] : ((rich(X0) | ~humble(X0)) & (humble(X0) | ~rich(X0))) [nnf transformation 3]
44. ! [X0] : ((~humble(X0) | (~rich(X0) & tall(X0))) & ((rich(X0) | ~tall(X0)) | humble(X0))) [nnf transformation 6]
45. ! [X0] : ((~humble(X0) | (~rich(X0) & tall(X0))) & (rich(X0) | ~tall(X0) | humble(X0))) [flattening 44]
46. ! [X0] : ((((brave(X0) | old(X0)) & (~brave(X0) | ~old(X0))) | (humble(X0) & generous(X0))) & ((~humble(X0) | ~generous(X0)) | ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0))))) [nnf transformation 7]
47. ! [X0] : ((((brave(X0) | old(X0)) & (~brave(X0) | ~old(X0))) | (humble(X0) & generous(X0))) & (~humble(X0) | ~generous(X0) | ((~old(X0) | brave(X0)) & (~brave(X0) | old(X0))))) [flattening 46]
53. ! [X0] : (((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | rich(X0) | ~old(X0)) [nnf transformation 31]
75. ~wise(sK1) | humble(sK1) | generous(alice) [cnf transformation 41]
77. ~generous(alice) | wise(X0) [cnf transformation 41]
78. ~rich(X0) | humble(X0) [cnf transformation 42]
79. ~humble(X0) | rich(X0) [cnf transformation 42]
86. ~humble(X0) | ~rich(X0) [cnf transformation 45]
90. ~old(X0) | ~brave(X0) | humble(X0) [cnf transformation 47]
92. old(X0) | brave(X0) | humble(X0) [cnf transformation 47]
97. brave(X0) | wise(X0) | rich(X0) | ~old(X0) [cnf transformation 53]
122. old(X0) | wise(X0) [cnf transformation 34]
137. ~wise(susan) [cnf transformation 24]
159. 5 <=> ! [X0] : wise(X0) [avatar definition]
160. wise(X0) <- (5) [avatar component clause 159]
162. 6 <=> generous(alice) [avatar definition]
165. 5 | ~6 [avatar split clause 77,162,159]
171. 8 <=> humble(sK1) [avatar definition]
173. humble(sK1) <- (8) [avatar component clause 171]
175. 9 <=> wise(sK1) [avatar definition]
177. ~wise(sK1) <- (~9) [avatar component clause 175]
178. 6 | 8 | ~9 [avatar split clause 75,175,171,162]
199. ~rich(X0) [subsumption resolution 86,78]
211. ~old(X0) | wise(X0) | brave(X0) [subsumption resolution 97,199]
319. ~brave(X0) | humble(X0) | wise(X0) [resolution 90,122]
387. wise(X0) | brave(X0) | brave(X0) | humble(X0) [resolution 211,92]
392. wise(X0) | brave(X0) | humble(X0) [duplicate literal removal 387]
396. wise(X0) | humble(X0) [subsumption resolution 392,319]
479. humble(sK1) <- (~9) [resolution 396,177]
480. 8 | 9 [avatar split clause 479,175,171]
482. rich(sK1) <- (8) [resolution 173,79]
483. $false <- (8) [subsumption resolution 482,199]
484. ~8 [avatar contradiction clause 483]
485. $false <- (5) [resolution 160,137]
486. ~5 [avatar contradiction clause 485]
487. $false [avatar sat refutation 165,178,480,484,486]
% SZS output end Proof for 266823044649509096456616
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and humble is calm or tall. Everyone who is brave or not patient is kind or humble and vice versa. Everyone who is happy is not brave or not calm and vice versa. If someone is both not curious and not happy then alice is either kind or tall and vice versa. If paul is not old or tall then fred is either patient or not kind and vice versa. If fred is quiet then someone is either brave or humble. Everyone who is either not creative or not patient is not humble and vice versa. Everyone who is both humble and not curious is creative and vice versa. If someone is funny then someone is calm or not patient and vice versa. If paul is both curious and not curious then someone is both not creative and strong and vice versa. If someone is both brave and not rich then lucy is either not humble or rich and vice versa. Everyone who is either rich or creative is either not happy or wise. Everyone who is not strong or patient is either not curious or not patient and vice versa. Everyone who is both not quiet and generous is not calm and vice versa. Everyone who is not brave or not rich is strong and vice versa. If someone is brave or not kind then someone is not creative or happy. Someone is not humble. Someone is brave or not quiet. Lucy is both not wise and brave. Someone is both calm and not curious. Fred is both not old and not quiet. John is generous. | Lucy is strong. | contradiction | (![X]:((patient(X)&humble(X))=>(calm(X)|tall(X))))&
(![X]:((brave(X)|~patient(X))<=>(kind(X)|humble(X))))&
(![X]:(happy(X)<=>(~brave(X)|~calm(X))))&
((?[X]:((~curious(X)&~happy(X))))<=>((kind(alice)<~>tall(alice))))&
(((~old(paul)|tall(paul)))<=>((patient(fred)<~>~kind(fred))))&
((quiet(fred))=>(?[X]:((brave(X)<~>humble(X)))))&
(![X]:((~creative(X)<~>~patient(X))<=>~humble(X)))&
(![X]:((humble(X)&~curious(X))<=>creative(X)))&
((?[X]:(funny(X)))<=>(?[X]:((calm(X)|~patient(X)))))&
(((curious(paul)&~curious(paul)))<=>(?[X]:((~creative(X)&strong(X)))))&
((?[X]:((brave(X)&~rich(X))))<=>((~humble(lucy)<~>rich(lucy))))&
(![X]:((rich(X)<~>creative(X))=>(~happy(X)<~>wise(X))))&
(![X]:((~strong(X)|patient(X))<=>(~curious(X)<~>~patient(X))))&
(![X]:((~quiet(X)&generous(X))<=>~calm(X)))&
(![X]:((~brave(X)|~rich(X))<=>strong(X)))&
((?[X]:((brave(X)|~kind(X))))=>(?[X]:((~creative(X)|happy(X)))))&
(?[X]:(~humble(X)))&
(?[X]:((brave(X)|~quiet(X))))&
((~wise(lucy)&brave(lucy)))&
(?[X]:((calm(X)&~curious(X))))&
((~old(fred)&~quiet(fred)))&
(generous(john)) | strong(lucy) | [
"p7",
"p9",
"p10",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 945261421212136634100695
% SZS output start Proof for 945261421212136634100695
8. ! [X0] : ((~curious(X0) & humble(X0)) <=> creative(X0)) [input p7]
10. (~curious(paul) & curious(paul)) <=> ? [X0] : (strong(X0) & ~creative(X0)) [input p9]
11. ? [X0] : (~rich(X0) & brave(X0)) <=> (~humble(lucy) <~> rich(lucy)) [input p10]
15. ! [X0] : ((~rich(X0) | ~brave(X0)) <=> strong(X0)) [input p14]
19. brave(lucy) & ~wise(lucy) [input p18]
23. strong(lucy) [input hypothesis]
45. ! [X0] : (((~curious(X0) & humble(X0)) | ~creative(X0)) & (creative(X0) | (curious(X0) | ~humble(X0)))) [nnf transformation 8]
46. ! [X0] : (((~curious(X0) & humble(X0)) | ~creative(X0)) & (creative(X0) | curious(X0) | ~humble(X0))) [flattening 45]
52. ((~curious(paul) & curious(paul)) | ! [X0] : (~strong(X0) | creative(X0))) & (? [X0] : (strong(X0) & ~creative(X0)) | (curious(paul) | ~curious(paul))) [nnf transformation 10]
53. ((~curious(paul) & curious(paul)) | ! [X0] : (~strong(X0) | creative(X0))) & (? [X0] : (strong(X0) & ~creative(X0)) | curious(paul) | ~curious(paul)) [flattening 52]
54. ((~curious(paul) & curious(paul)) | ! [X0] : (~strong(X0) | creative(X0))) & (? [X1] : (strong(X1) & ~creative(X1)) | curious(paul) | ~curious(paul)) [rectify 53]
55. ? [X1] : (strong(X1) & ~creative(X1)) => (strong(sK4) & ~creative(sK4)) [choice axiom]
56. ((~curious(paul) & curious(paul)) | ! [X0] : (~strong(X0) | creative(X0))) & ((strong(sK4) & ~creative(sK4)) | curious(paul) | ~curious(paul)) [skolemisation 54,55]
57. (? [X0] : (~rich(X0) & brave(X0)) | ((~humble(lucy) | ~rich(lucy)) & (rich(lucy) | humble(lucy)))) & (((~rich(lucy) | humble(lucy)) & (rich(lucy) | ~humble(lucy))) | ! [X0] : (rich(X0) | ~brave(X0))) [nnf transformation 11]
58. (? [X0] : (~rich(X0) & brave(X0)) | ((~humble(lucy) | ~rich(lucy)) & (rich(lucy) | humble(lucy)))) & (((~rich(lucy) | humble(lucy)) & (rich(lucy) | ~humble(lucy))) | ! [X1] : (rich(X1) | ~brave(X1))) [rectify 57]
59. ? [X0] : (~rich(X0) & brave(X0)) => (~rich(sK5) & brave(sK5)) [choice axiom]
60. ((~rich(sK5) & brave(sK5)) | ((~humble(lucy) | ~rich(lucy)) & (rich(lucy) | humble(lucy)))) & (((~rich(lucy) | humble(lucy)) & (rich(lucy) | ~humble(lucy))) | ! [X1] : (rich(X1) | ~brave(X1))) [skolemisation 58,59]
66. ! [X0] : (((~rich(X0) | ~brave(X0)) | ~strong(X0)) & (strong(X0) | (rich(X0) & brave(X0)))) [nnf transformation 15]
67. ! [X0] : ((~rich(X0) | ~brave(X0) | ~strong(X0)) & (strong(X0) | (rich(X0) & brave(X0)))) [flattening 66]
104. ~creative(X0) | humble(X0) [cnf transformation 46]
111. curious(paul) | ~strong(X0) | creative(X0) [cnf transformation 56]
112. ~curious(paul) | ~strong(X0) | creative(X0) [cnf transformation 56]
113. rich(lucy) | ~humble(lucy) | rich(X1) | ~brave(X1) [cnf transformation 60]
134. ~rich(X0) | ~brave(X0) | ~strong(X0) [cnf transformation 67]
140. brave(lucy) [cnf transformation 19]
146. strong(lucy) [cnf transformation 23]
235. 19 <=> ! [X0] : (~strong(X0) | creative(X0)) [avatar definition]
236. ~strong(X0) | creative(X0) <- (19) [avatar component clause 235]
238. 20 <=> curious(paul) [avatar definition]
241. 19 | ~20 [avatar split clause 112,238,235]
242. 19 | 20 [avatar split clause 111,238,235]
244. 21 <=> rich(lucy) [avatar definition]
245. rich(lucy) <- (21) [avatar component clause 244]
246. ~rich(lucy) <- (~21) [avatar component clause 244]
248. 22 <=> humble(lucy) [avatar definition]
264. 25 <=> ! [X1] : (rich(X1) | ~brave(X1)) [avatar definition]
265. ~brave(X1) | rich(X1) <- (25) [avatar component clause 264]
267. 25 | ~22 | 21 [avatar split clause 113,244,248,264]
298. creative(lucy) <- (19) [resolution 236,146]
314. humble(lucy) <- (19) [resolution 298,104]
317. 22 | ~19 [avatar split clause 314,235,248]
422. ~brave(lucy) | ~strong(lucy) <- (21) [resolution 134,245]
423. ~strong(lucy) <- (21) [subsumption resolution 422,140]
424. $false <- (21) [subsumption resolution 423,146]
425. ~21 [avatar contradiction clause 424]
427. rich(lucy) <- (25) [resolution 265,140]
430. $false <- (~21, 25) [subsumption resolution 427,246]
431. 21 | ~25 [avatar contradiction clause 430]
434. $false [avatar sat refutation 241,242,267,317,425,431]
% SZS output end Proof for 945261421212136634100695
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is funny.
Everyone who is happy or wise is not rich.
Everyone who is brave or not happy is both brave and not rich.
If someone is either not old or not brave then alice is both generous and not old and vice versa.
If someone is either curious or old then fred is either generous or quiet.
If alice is curious then susan is not creative or not curious.
Everyone who is not quiet is humble and vice versa.
Everyone who is either curious or wise is both patient and not wise and vice versa.
If mary is not strong or not tall then someone is not rich or not humble and vice versa.
Everyone who is quiet is both quiet and not brave.
If someone is both tall and funny then someone is both brave and not rich.
If someone is both wise and generous then someone is funny.
If someone is not generous or generous then fred is both brave and not kind and vice versa.
Everyone who is either not old or generous is tall or not happy and vice versa.
Everyone who is both not old and not tall is either not wise or old and vice versa.
If alice is both not funny and not curious then alice is both humble and kind and vice versa.
Someone is not funny.
Alice is happy or old.
Susan is not patient or not curious.
Mary is not kind.
Someone is both strong and old.
Alice is not tall.
Someone is either kind or creative. | Fred is not wise. | entailment | (![X]:(~generous(X)=>funny(X)))&
(![X]:((happy(X)|wise(X))=>~rich(X)))&
(![X]:((brave(X)|~happy(X))=>(brave(X)&~rich(X))))&
((?[X]:((~old(X)<~>~brave(X))))<=>((generous(alice)&~old(alice))))&
((?[X]:((curious(X)<~>old(X))))=>((generous(fred)<~>quiet(fred))))&
((curious(alice))=>((~creative(susan)|~curious(susan))))&
(![X]:(~quiet(X)<=>humble(X)))&
(![X]:((curious(X)<~>wise(X))<=>(patient(X)&~wise(X))))&
(((~strong(mary)|~tall(mary)))<=>(?[X]:((~rich(X)|~humble(X)))))&
(![X]:(quiet(X)=>(quiet(X)&~brave(X))))&
((?[X]:((tall(X)&funny(X))))=>(?[X]:((brave(X)&~rich(X)))))&
((?[X]:((wise(X)&generous(X))))=>(?[X]:(funny(X))))&
((?[X]:((~generous(X)|generous(X))))<=>((brave(fred)&~kind(fred))))&
(![X]:((~old(X)<~>generous(X))<=>(tall(X)|~happy(X))))&
(![X]:((~old(X)&~tall(X))<=>(~wise(X)<~>old(X))))&
(((~funny(alice)&~curious(alice)))<=>((humble(alice)&kind(alice))))&
(?[X]:(~funny(X)))&
((happy(alice)|old(alice)))&
((~patient(susan)|~curious(susan)))&
(~kind(mary))&
(?[X]:((strong(X)&old(X))))&
(~tall(alice))&
(?[X]:((kind(X)<~>creative(X)))) | ~wise(fred) | [
"p4",
"p7",
"p9",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5274145472791305979727994
% SZS output start Proof for 5274145472791305979727994
5. ? [X0] : (curious(X0) <~> old(X0)) => (generous(fred) <~> quiet(fred)) [input p4]
8. ! [X0] : ((curious(X0) <~> wise(X0)) <=> (~wise(X0) & patient(X0))) [input p7]
10. ! [X0] : (quiet(X0) => (~brave(X0) & quiet(X0))) [input p9]
13. ? [X0] : (generous(X0) | ~generous(X0)) <=> (~kind(fred) & brave(fred)) [input p12]
14. ! [X0] : ((~old(X0) <~> generous(X0)) <=> (~happy(X0) | tall(X0))) [input p13]
15. ! [X0] : ((~tall(X0) & ~old(X0)) <=> (~wise(X0) <~> old(X0))) [input p14]
24. wise(fred) [input hypothesis]
30. (generous(fred) <~> quiet(fred)) | ! [X0] : (curious(X0) <=> old(X0)) [ennf transformation 5]
33. ! [X0] : ((~brave(X0) & quiet(X0)) | ~quiet(X0)) [ennf transformation 10]
41. ((~quiet(fred) | ~generous(fred)) & (quiet(fred) | generous(fred))) | ! [X0] : ((curious(X0) | ~old(X0)) & (old(X0) | ~curious(X0))) [nnf transformation 30]
43. ! [X0] : ((((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | (wise(X0) | ~patient(X0))) & ((~wise(X0) & patient(X0)) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0))))) [nnf transformation 8]
44. ! [X0] : ((((~wise(X0) | ~curious(X0)) & (wise(X0) | curious(X0))) | wise(X0) | ~patient(X0)) & ((~wise(X0) & patient(X0)) | ((curious(X0) | ~wise(X0)) & (wise(X0) | ~curious(X0))))) [flattening 43]
56. (? [X0] : (generous(X0) | ~generous(X0)) | (kind(fred) | ~brave(fred))) & ((~kind(fred) & brave(fred)) | ! [X0] : (~generous(X0) & generous(X0))) [nnf transformation 13]
57. (? [X0] : (generous(X0) | ~generous(X0)) | kind(fred) | ~brave(fred)) & ((~kind(fred) & brave(fred)) | ! [X0] : (~generous(X0) & generous(X0))) [flattening 56]
58. (? [X0] : (generous(X0) | ~generous(X0)) | kind(fred) | ~brave(fred)) & ((~kind(fred) & brave(fred)) | ! [X1] : (~generous(X1) & generous(X1))) [rectify 57]
59. ? [X0] : (generous(X0) | ~generous(X0)) => (generous(sK4) | ~generous(sK4)) [choice axiom]
60. ((generous(sK4) | ~generous(sK4)) | kind(fred) | ~brave(fred)) & ((~kind(fred) & brave(fred)) | ! [X1] : (~generous(X1) & generous(X1))) [skolemisation 58,59]
61. ! [X0] : ((((~generous(X0) | old(X0)) & (generous(X0) | ~old(X0))) | (happy(X0) & ~tall(X0))) & ((~happy(X0) | tall(X0)) | ((~old(X0) | ~generous(X0)) & (generous(X0) | old(X0))))) [nnf transformation 14]
62. ! [X0] : ((((~generous(X0) | old(X0)) & (generous(X0) | ~old(X0))) | (happy(X0) & ~tall(X0))) & (~happy(X0) | tall(X0) | ((~old(X0) | ~generous(X0)) & (generous(X0) | old(X0))))) [flattening 61]
63. ! [X0] : (((~tall(X0) & ~old(X0)) | ((~wise(X0) | ~old(X0)) & (old(X0) | wise(X0)))) & (((~old(X0) | wise(X0)) & (old(X0) | ~wise(X0))) | (tall(X0) | old(X0)))) [nnf transformation 15]
64. ! [X0] : (((~tall(X0) & ~old(X0)) | ((~wise(X0) | ~old(X0)) & (old(X0) | wise(X0)))) & (((~old(X0) | wise(X0)) & (old(X0) | ~wise(X0))) | tall(X0) | old(X0))) [flattening 63]
87. quiet(fred) | generous(fred) | old(X0) | ~curious(X0) [cnf transformation 41]
97. ~wise(X0) | curious(X0) | ~wise(X0) [cnf transformation 44]
105. ~quiet(X0) | ~brave(X0) [cnf transformation 33]
109. brave(fred) | generous(X1) [cnf transformation 60]
118. ~tall(X0) | old(X0) | ~generous(X0) [cnf transformation 62]
120. old(X0) | ~wise(X0) | tall(X0) | old(X0) [cnf transformation 64]
123. ~old(X0) | ~wise(X0) | ~old(X0) [cnf transformation 64]
139. wise(fred) [cnf transformation 24]
140. old(X0) | ~wise(X0) | tall(X0) [duplicate literal removal 120]
141. ~old(X0) | ~wise(X0) [duplicate literal removal 123]
142. ~wise(X0) | curious(X0) [duplicate literal removal 97]
177. 8 <=> generous(fred) [avatar definition]
181. 9 <=> quiet(fred) [avatar definition]
182. quiet(fred) <- (9) [avatar component clause 181]
186. 10 <=> ! [X0] : (old(X0) | ~curious(X0)) [avatar definition]
187. ~curious(X0) | old(X0) <- (10) [avatar component clause 186]
190. 10 | 8 | 9 [avatar split clause 87,181,177,186]
243. 23 <=> ! [X1] : generous(X1) [avatar definition]
244. generous(X1) <- (23) [avatar component clause 243]
247. 24 <=> brave(fred) [avatar definition]
249. brave(fred) <- (24) [avatar component clause 247]
251. 23 | 24 [avatar split clause 109,247,243]
252. ~wise(X0) | tall(X0) [subsumption resolution 140,141]
303. curious(fred) [resolution 142,139]
309. tall(fred) [resolution 252,139]
340. old(fred) | ~generous(fred) [resolution 118,309]
341. old(fred) <- (23) [subsumption resolution 340,244]
344. ~wise(fred) <- (23) [resolution 341,141]
345. $false <- (23) [subsumption resolution 344,139]
346. ~23 [avatar contradiction clause 345]
348. 34 <=> old(fred) [avatar definition]
349. ~old(fred) <- (~34) [avatar component clause 348]
350. old(fred) <- (34) [avatar component clause 348]
351. ~8 | 34 [avatar split clause 340,348,177]
380. ~wise(fred) <- (34) [resolution 350,141]
381. $false <- (34) [subsumption resolution 380,139]
382. ~34 [avatar contradiction clause 381]
383. ~brave(fred) <- (9) [resolution 182,105]
384. $false <- (9, 24) [subsumption resolution 383,249]
385. ~9 | ~24 [avatar contradiction clause 384]
389. old(fred) <- (10) [resolution 187,303]
391. $false <- (10, ~34) [subsumption resolution 389,349]
392. ~10 | 34 [avatar contradiction clause 391]
393. $false [avatar sat refutation 190,251,346,351,382,385,392]
% SZS output end Proof for 5274145472791305979727994
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is wise.
Everyone who is both not wise and not calm is not funny or calm.
Everyone who is not funny is not curious or old and vice versa.
Everyone who is both not brave and not happy is happy or not happy.
If alice is both not wise and not funny then paul is not old and vice versa.
If someone is either wise or calm then john is both creative and not old.
Everyone who is not brave or not humble is not generous and vice versa.
Everyone who is both curious and rich is not happy and vice versa.
If alice is both generous and brave then alice is either not calm or tall.
If someone is either not happy or funny then someone is either rich or not tall and vice versa.
Everyone who is not humble or not creative is both not rich and not generous and vice versa.
Everyone who is both not old and tall is not strong or not happy and vice versa.
Everyone who is either patient or not quiet is both wise and strong and vice versa.
If paul is both humble and not generous then someone is old and vice versa.
If susan is both not quiet and kind then someone is not happy or not funny and vice versa.
If someone is not generous or wise then lucy is happy or rich and vice versa.
Someone is not generous or generous.
Mary is either not funny or happy.
Someone is wise or not strong.
Fred is brave or patient.
Someone is not wise or not quiet.
Paul is calm or curious.
Someone is not tall or not strong. | Alice is humble. | neutral | (![X]:(generous(X)=>wise(X)))&
(![X]:((~wise(X)&~calm(X))=>(~funny(X)|calm(X))))&
(![X]:(~funny(X)<=>(~curious(X)|old(X))))&
(![X]:((~brave(X)&~happy(X))=>(happy(X)|~happy(X))))&
(((~wise(alice)&~funny(alice)))<=>(~old(paul)))&
((?[X]:((wise(X)<~>calm(X))))=>((creative(john)&~old(john))))&
(![X]:((~brave(X)|~humble(X))<=>~generous(X)))&
(![X]:((curious(X)&rich(X))<=>~happy(X)))&
(((generous(alice)&brave(alice)))=>((~calm(alice)<~>tall(alice))))&
((?[X]:((~happy(X)<~>funny(X))))<=>(?[X]:((rich(X)<~>~tall(X)))))&
(![X]:((~humble(X)|~creative(X))<=>(~rich(X)&~generous(X))))&
(![X]:((~old(X)&tall(X))<=>(~strong(X)|~happy(X))))&
(![X]:((patient(X)<~>~quiet(X))<=>(wise(X)&strong(X))))&
(((humble(paul)&~generous(paul)))<=>(?[X]:(old(X))))&
(((~quiet(susan)&kind(susan)))<=>(?[X]:((~happy(X)|~funny(X)))))&
((?[X]:((~generous(X)|wise(X))))<=>((happy(lucy)|rich(lucy))))&
(?[X]:((~generous(X)|generous(X))))&
((~funny(mary)<~>happy(mary)))&
(?[X]:((wise(X)|~strong(X))))&
((brave(fred)|patient(fred)))&
(?[X]:((~wise(X)|~quiet(X))))&
((calm(paul)|curious(paul)))&
(?[X]:((~tall(X)|~strong(X)))) | humble(alice) | [] | null | 0 |
If john is not kind or not humble then someone is both not strong and not generous.
Everyone who is either not rich or not happy is old and vice versa.
If someone is both not brave and not funny then someone is either not funny or generous and vice versa.
If someone is funny or not tall then john is both not tall and wise and vice versa.
If paul is either wise or humble then lucy is either funny or rich and vice versa.
Everyone who is either not happy or tall is tall.
If someone is not quiet then john is both not calm and curious.
Everyone who is either not rich or not old is either quiet or rich and vice versa.
If someone is generous or not funny then john is not strong.
Everyone who is not kind is not quiet and vice versa.
Everyone who is not wise or not calm is either not generous or not patient.
If fred is either patient or old then paul is not funny and vice versa.
If someone is both not quiet and not humble then john is both not generous and not funny.
Everyone who is not patient is both patient and not patient and vice versa.
Everyone who is not strong or not curious is both humble and not humble and vice versa.
Everyone who is not funny is either happy or curious and vice versa.
Someone is kind or not curious.
Someone is both calm and not wise.
John is either creative or kind.
John is either happy or not wise.
Susan is tall.
Alice is both not old and strong.
John is calm or wise. | Alice is humble. | entailment | (((~kind(john)|~humble(john)))=>(?[X]:((~strong(X)&~generous(X)))))&
(![X]:((~rich(X)<~>~happy(X))<=>old(X)))&
((?[X]:((~brave(X)&~funny(X))))<=>(?[X]:((~funny(X)<~>generous(X)))))&
((?[X]:((funny(X)|~tall(X))))<=>((~tall(john)&wise(john))))&
(((wise(paul)<~>humble(paul)))<=>((funny(lucy)<~>rich(lucy))))&
(![X]:((~happy(X)<~>tall(X))=>tall(X)))&
((?[X]:(~quiet(X)))=>((~calm(john)&curious(john))))&
(![X]:((~rich(X)<~>~old(X))<=>(quiet(X)<~>rich(X))))&
((?[X]:((generous(X)|~funny(X))))=>(~strong(john)))&
(![X]:(~kind(X)<=>~quiet(X)))&
(![X]:((~wise(X)|~calm(X))=>(~generous(X)<~>~patient(X))))&
(((patient(fred)<~>old(fred)))<=>(~funny(paul)))&
((?[X]:((~quiet(X)&~humble(X))))=>((~generous(john)&~funny(john))))&
(![X]:(~patient(X)<=>(patient(X)&~patient(X))))&
(![X]:((~strong(X)|~curious(X))<=>(humble(X)&~humble(X))))&
(![X]:(~funny(X)<=>(happy(X)<~>curious(X))))&
(?[X]:((kind(X)|~curious(X))))&
(?[X]:((calm(X)&~wise(X))))&
((creative(john)<~>kind(john)))&
((happy(john)<~>~wise(john)))&
(tall(susan))&
((~old(alice)&strong(alice)))&
((calm(john)|wise(john))) | humble(alice) | [
"p7",
"p8",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7937084679955169804999546
% SZS output start Proof for 7937084679955169804999546
8. ! [X0] : ((~rich(X0) <~> ~old(X0)) <=> (quiet(X0) <~> rich(X0))) [input p7]
9. ? [X0] : (~funny(X0) | generous(X0)) => ~strong(john) [input p8]
13. ? [X0] : (~humble(X0) & ~quiet(X0)) => (~funny(john) & ~generous(john)) [input p12]
15. ! [X0] : ((~curious(X0) | ~strong(X0)) <=> (~humble(X0) & humble(X0))) [input p14]
22. strong(alice) & ~old(alice) [input p21]
24. ~humble(alice) [input hypothesis]
29. ~strong(john) | ! [X0] : (funny(X0) & ~generous(X0)) [ennf transformation 9]
31. (~funny(john) & ~generous(john)) | ! [X0] : (humble(X0) | quiet(X0)) [ennf transformation 13]
47. ! [X0] : ((((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | ((quiet(X0) | ~rich(X0)) & (rich(X0) | ~quiet(X0)))) & (((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0))))) [nnf transformation 8]
53. ! [X0] : (((~curious(X0) | ~strong(X0)) | (humble(X0) | ~humble(X0))) & ((~humble(X0) & humble(X0)) | (curious(X0) & strong(X0)))) [nnf transformation 15]
54. ! [X0] : ((~curious(X0) | ~strong(X0) | humble(X0) | ~humble(X0)) & ((~humble(X0) & humble(X0)) | (curious(X0) & strong(X0)))) [flattening 53]
96. ~rich(X0) | ~quiet(X0) | ~rich(X0) | old(X0) [cnf transformation 47]
99. old(X0) | rich(X0) | rich(X0) | ~quiet(X0) [cnf transformation 47]
102. ~strong(john) | funny(X0) [cnf transformation 29]
114. ~funny(john) | humble(X0) | quiet(X0) [cnf transformation 31]
118. humble(X0) | strong(X0) [cnf transformation 54]
120. ~humble(X0) | strong(X0) [cnf transformation 54]
135. ~old(alice) [cnf transformation 22]
138. ~humble(alice) [cnf transformation 24]
142. ~rich(X0) | ~quiet(X0) | old(X0) [duplicate literal removal 96]
144. old(X0) | rich(X0) | ~quiet(X0) [duplicate literal removal 99]
261. ~quiet(X0) | old(X0) [subsumption resolution 142,144]
264. 25 <=> ! [X0] : funny(X0) [avatar definition]
265. funny(X0) <- (25) [avatar component clause 264]
267. 26 <=> strong(john) [avatar definition]
269. ~strong(john) <- (~26) [avatar component clause 267]
270. 25 | ~26 [avatar split clause 102,267,264]
292. 31 <=> ! [X0] : (humble(X0) | quiet(X0)) [avatar definition]
293. quiet(X0) | humble(X0) <- (31) [avatar component clause 292]
295. 32 <=> funny(john) [avatar definition]
297. ~funny(john) <- (~32) [avatar component clause 295]
298. 31 | ~32 [avatar split clause 114,295,292]
305. strong(X0) [subsumption resolution 118,120]
324. $false <- (~26) [subsumption resolution 269,305]
325. 26 [avatar contradiction clause 324]
340. $false <- (25, ~32) [resolution 297,265]
341. ~25 | 32 [avatar contradiction clause 340]
357. old(X0) | humble(X0) <- (31) [resolution 293,261]
400. humble(alice) <- (31) [resolution 357,135]
404. $false <- (31) [subsumption resolution 400,138]
405. ~31 [avatar contradiction clause 404]
407. $false [avatar sat refutation 270,298,325,341,405]
% SZS output end Proof for 7937084679955169804999546
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not creative and quiet then alice is both not kind and kind. If mary is not wise then susan is happy or not happy and vice versa. If john is funny then paul is not creative and vice versa. Everyone who is not happy is not patient or happy and vice versa. Everyone who is either not strong or not tall is humble and vice versa. If fred is not strong then someone is either tall or creative and vice versa. If lucy is both not tall and not kind then john is not strong or curious and vice versa. Everyone who is either old or not quiet is humble and vice versa. Everyone who is both not wise and not quiet is not rich or not curious and vice versa. Everyone who is not funny or not tall is both not kind and rich. Everyone who is tall is both not creative and not patient and vice versa. Everyone who is either not happy or strong is brave and vice versa. Everyone who is both not kind and tall is both tall and not strong and vice versa. If lucy is not happy or generous then someone is old. If mary is both not curious and generous then alice is not humble and vice versa. Everyone who is not humble is happy. Fred is quiet or brave. John is either not generous or creative. Susan is either not rich or happy. Lucy is not happy or humble. Lucy is either curious or not strong. Lucy is strong. Someone is strong or not strong. Someone is not rich. | Fred is quiet. | contradiction | ((?[X]:((~creative(X)&quiet(X))))=>((~kind(alice)&kind(alice))))&
((~wise(mary))<=>((happy(susan)|~happy(susan))))&
((funny(john))<=>(~creative(paul)))&
(![X]:(~happy(X)<=>(~patient(X)|happy(X))))&
(![X]:((~strong(X)<~>~tall(X))<=>humble(X)))&
((~strong(fred))<=>(?[X]:((tall(X)<~>creative(X)))))&
(((~tall(lucy)&~kind(lucy)))<=>((~strong(john)|curious(john))))&
(![X]:((old(X)<~>~quiet(X))<=>humble(X)))&
(![X]:((~wise(X)&~quiet(X))<=>(~rich(X)|~curious(X))))&
(![X]:((~funny(X)|~tall(X))=>(~kind(X)&rich(X))))&
(![X]:(tall(X)<=>(~creative(X)&~patient(X))))&
(![X]:((~happy(X)<~>strong(X))<=>brave(X)))&
(![X]:((~kind(X)&tall(X))<=>(tall(X)&~strong(X))))&
(((~happy(lucy)|generous(lucy)))=>(?[X]:(old(X))))&
(((~curious(mary)&generous(mary)))<=>(~humble(alice)))&
(![X]:(~humble(X)=>happy(X)))&
((quiet(fred)|brave(fred)))&
((~generous(john)<~>creative(john)))&
((~rich(susan)<~>happy(susan)))&
((~happy(lucy)|humble(lucy)))&
((curious(lucy)<~>~strong(lucy)))&
(strong(lucy))&
(?[X]:((strong(X)|~strong(X))))&
(?[X]:(~rich(X))) | quiet(fred) | [
"p0",
"p3",
"p4",
"p5",
"p9",
"p10",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8002225549088488739388814
% SZS output start Proof for 8002225549088488739388814
1. ? [X0] : (quiet(X0) & ~creative(X0)) => (kind(alice) & ~kind(alice)) [input p0]
4. ! [X0] : (~happy(X0) <=> (happy(X0) | ~patient(X0))) [input p3]
5. ! [X0] : ((~strong(X0) <~> ~tall(X0)) <=> humble(X0)) [input p4]
6. ~strong(fred) <=> ? [X0] : (tall(X0) <~> creative(X0)) [input p5]
10. ! [X0] : ((~tall(X0) | ~funny(X0)) => (rich(X0) & ~kind(X0))) [input p9]
11. ! [X0] : (tall(X0) <=> (~patient(X0) & ~creative(X0))) [input p10]
16. ! [X0] : (~humble(X0) => happy(X0)) [input p15]
19. ~rich(susan) <~> happy(susan) [input p18]
25. quiet(fred) [input hypothesis]
27. (kind(alice) & ~kind(alice)) | ! [X0] : (~quiet(X0) | creative(X0)) [ennf transformation 1]
28. ! [X0] : ((rich(X0) & ~kind(X0)) | (tall(X0) & funny(X0))) [ennf transformation 10]
31. ! [X0] : (happy(X0) | humble(X0)) [ennf transformation 16]
35. ! [X0] : ((~happy(X0) | (~happy(X0) & patient(X0))) & ((happy(X0) | ~patient(X0)) | happy(X0))) [nnf transformation 4]
36. ! [X0] : ((~happy(X0) | (~happy(X0) & patient(X0))) & (happy(X0) | ~patient(X0) | happy(X0))) [flattening 35]
37. ! [X0] : ((((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | ~humble(X0)) & (humble(X0) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))))) [nnf transformation 5]
38. (~strong(fred) | ! [X0] : ((tall(X0) | ~creative(X0)) & (creative(X0) | ~tall(X0)))) & (? [X0] : ((~creative(X0) | ~tall(X0)) & (creative(X0) | tall(X0))) | strong(fred)) [nnf transformation 6]
39. (~strong(fred) | ! [X0] : ((tall(X0) | ~creative(X0)) & (creative(X0) | ~tall(X0)))) & (? [X1] : ((~creative(X1) | ~tall(X1)) & (creative(X1) | tall(X1))) | strong(fred)) [rectify 38]
40. ? [X1] : ((~creative(X1) | ~tall(X1)) & (creative(X1) | tall(X1))) => ((~creative(sK0) | ~tall(sK0)) & (creative(sK0) | tall(sK0))) [choice axiom]
41. (~strong(fred) | ! [X0] : ((tall(X0) | ~creative(X0)) & (creative(X0) | ~tall(X0)))) & (((~creative(sK0) | ~tall(sK0)) & (creative(sK0) | tall(sK0))) | strong(fred)) [skolemisation 39,40]
47. ! [X0] : ((tall(X0) | (patient(X0) | creative(X0))) & ((~patient(X0) & ~creative(X0)) | ~tall(X0))) [nnf transformation 11]
48. ! [X0] : ((tall(X0) | patient(X0) | creative(X0)) & ((~patient(X0) & ~creative(X0)) | ~tall(X0))) [flattening 47]
57. (~happy(susan) | rich(susan)) & (happy(susan) | ~rich(susan)) [nnf transformation 19]
63. ~kind(alice) | ~quiet(X0) | creative(X0) [cnf transformation 27]
64. kind(alice) | ~quiet(X0) | creative(X0) [cnf transformation 27]
72. ~happy(X0) | ~happy(X0) [cnf transformation 36]
76. ~humble(X0) | strong(X0) | tall(X0) [cnf transformation 37]
79. ~strong(fred) | creative(X0) | ~tall(X0) [cnf transformation 41]
98. rich(X0) | tall(X0) [cnf transformation 28]
99. ~tall(X0) | ~creative(X0) [cnf transformation 48]
113. happy(X0) | humble(X0) [cnf transformation 31]
117. happy(susan) | ~rich(susan) [cnf transformation 57]
125. quiet(fred) [cnf transformation 25]
127. ~happy(X0) [duplicate literal removal 72]
129. 1 <=> ! [X0] : (~quiet(X0) | creative(X0)) [avatar definition]
130. ~quiet(X0) | creative(X0) <- (1) [avatar component clause 129]
132. 2 <=> kind(alice) [avatar definition]
135. 1 | 2 [avatar split clause 64,132,129]
136. 1 | ~2 [avatar split clause 63,132,129]
162. 8 <=> strong(fred) [avatar definition]
167. 9 <=> ! [X0] : (creative(X0) | ~tall(X0)) [avatar definition]
168. creative(X0) | ~tall(X0) <- (9) [avatar component clause 167]
169. 9 | ~8 [avatar split clause 79,162,167]
230. humble(X0) [subsumption resolution 113,127]
232. 21 <=> quiet(fred) [avatar definition]
234. quiet(fred) <- (21) [avatar component clause 232]
250. ~rich(susan) [subsumption resolution 117,127]
262. 21 [avatar split clause 125,232]
268. tall(susan) [resolution 98,250]
269. creative(fred) <- (1, 21) [resolution 130,234]
283. tall(X0) | strong(X0) [resolution 76,230]
291. ~creative(X2) | strong(X2) [resolution 283,99]
367. strong(fred) <- (1, 21) [resolution 291,269]
373. 8 | ~1 | ~21 [avatar split clause 367,232,129,162]
374. ~tall(X0) <- (9) [subsumption resolution 168,99]
380. $false <- (9) [resolution 374,268]
383. ~9 [avatar contradiction clause 380]
386. $false [avatar sat refutation 135,136,169,262,373,383]
% SZS output end Proof for 8002225549088488739388814
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If alice is strong then someone is both wise and quiet. If john is creative then someone is both wise and quiet and vice versa. If someone is both happy and old then someone is wise and vice versa. Everyone who is generous is either old or not calm and vice versa. Everyone who is not old is both quiet and strong. If someone is either rich or kind then john is either kind or wise. Everyone who is patient or not happy is calm and vice versa. If alice is calm then someone is wise. Everyone who is rich or creative is happy. If someone is either creative or not generous then mary is either not curious or not creative and vice versa. Everyone who is brave or rich is not quiet. Everyone who is rich or not wise is either not strong or tall and vice versa. Everyone who is strong is not generous or brave and vice versa. Everyone who is both not old and curious is not quiet or rich and vice versa. If someone is not old or not calm then alice is not quiet or creative and vice versa. If someone is either not generous or kind then alice is curious or not kind and vice versa. Someone is not brave. Paul is both not patient and not strong. Someone is either kind or not calm. Susan is brave or not old. Someone is not generous or old. Someone is both not rich and not patient. John is both creative and not tall. | Alice is creative. | entailment | ((strong(alice))=>(?[X]:((wise(X)&quiet(X)))))&
((creative(john))<=>(?[X]:((wise(X)&quiet(X)))))&
((?[X]:((happy(X)&old(X))))<=>(?[X]:(wise(X))))&
(![X]:(generous(X)<=>(old(X)<~>~calm(X))))&
(![X]:(~old(X)=>(quiet(X)&strong(X))))&
((?[X]:((rich(X)<~>kind(X))))=>((kind(john)<~>wise(john))))&
(![X]:((patient(X)|~happy(X))<=>calm(X)))&
((calm(alice))=>(?[X]:(wise(X))))&
(![X]:((rich(X)|creative(X))=>happy(X)))&
((?[X]:((creative(X)<~>~generous(X))))<=>((~curious(mary)<~>~creative(mary))))&
(![X]:((brave(X)|rich(X))=>~quiet(X)))&
(![X]:((rich(X)|~wise(X))<=>(~strong(X)<~>tall(X))))&
(![X]:(strong(X)<=>(~generous(X)|brave(X))))&
(![X]:((~old(X)&curious(X))<=>(~quiet(X)|rich(X))))&
((?[X]:((~old(X)|~calm(X))))<=>((~quiet(alice)|creative(alice))))&
((?[X]:((~generous(X)<~>kind(X))))<=>((curious(alice)|~kind(alice))))&
(?[X]:(~brave(X)))&
((~patient(paul)&~strong(paul)))&
(?[X]:((kind(X)<~>~calm(X))))&
((brave(susan)|~old(susan)))&
(?[X]:((~generous(X)|old(X))))&
(?[X]:((~rich(X)&~patient(X))))&
((creative(john)&~tall(john))) | creative(alice) | [
"p4",
"p10",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8588781892205596286555696
% SZS output start Proof for 8588781892205596286555696
5. ! [X0] : (~old(X0) => (strong(X0) & quiet(X0))) [input p4]
11. ! [X0] : ((rich(X0) | brave(X0)) => ~quiet(X0)) [input p10]
14. ! [X0] : ((curious(X0) & ~old(X0)) <=> (rich(X0) | ~quiet(X0))) [input p13]
15. ? [X0] : (~calm(X0) | ~old(X0)) <=> (creative(alice) | ~quiet(alice)) [input p14]
20. ~old(susan) | brave(susan) [input p19]
24. ~creative(alice) [input hypothesis]
27. ! [X0] : ((strong(X0) & quiet(X0)) | old(X0)) [ennf transformation 5]
31. ! [X0] : (~quiet(X0) | (~rich(X0) & ~brave(X0))) [ennf transformation 11]
57. ! [X0] : (((curious(X0) & ~old(X0)) | (~rich(X0) & quiet(X0))) & ((rich(X0) | ~quiet(X0)) | (~curious(X0) | old(X0)))) [nnf transformation 14]
58. ! [X0] : (((curious(X0) & ~old(X0)) | (~rich(X0) & quiet(X0))) & (rich(X0) | ~quiet(X0) | ~curious(X0) | old(X0))) [flattening 57]
59. (? [X0] : (~calm(X0) | ~old(X0)) | (~creative(alice) & quiet(alice))) & ((creative(alice) | ~quiet(alice)) | ! [X0] : (calm(X0) & old(X0))) [nnf transformation 15]
60. (? [X0] : (~calm(X0) | ~old(X0)) | (~creative(alice) & quiet(alice))) & (creative(alice) | ~quiet(alice) | ! [X0] : (calm(X0) & old(X0))) [flattening 59]
61. (? [X0] : (~calm(X0) | ~old(X0)) | (~creative(alice) & quiet(alice))) & (creative(alice) | ~quiet(alice) | ! [X1] : (calm(X1) & old(X1))) [rectify 60]
62. ? [X0] : (~calm(X0) | ~old(X0)) => (~calm(sK6) | ~old(sK6)) [choice axiom]
63. ((~calm(sK6) | ~old(sK6)) | (~creative(alice) & quiet(alice))) & (creative(alice) | ~quiet(alice) | ! [X1] : (calm(X1) & old(X1))) [skolemisation 61,62]
90. old(X0) | quiet(X0) [cnf transformation 27]
110. ~brave(X0) | ~quiet(X0) [cnf transformation 31]
122. ~old(X0) | quiet(X0) [cnf transformation 58]
126. creative(alice) | ~quiet(alice) | old(X1) [cnf transformation 63]
141. ~old(susan) | brave(susan) [cnf transformation 20]
147. ~creative(alice) [cnf transformation 24]
258. quiet(X0) [subsumption resolution 122,90]
261. 25 <=> creative(alice) [avatar definition]
278. creative(alice) | old(X1) [subsumption resolution 126,258]
280. 29 <=> ! [X1] : old(X1) [avatar definition]
281. old(X1) <- (29) [avatar component clause 280]
282. 29 | 25 [avatar split clause 278,261,280]
322. 38 <=> brave(susan) [avatar definition]
324. brave(susan) <- (38) [avatar component clause 322]
326. 39 <=> old(susan) [avatar definition]
328. ~old(susan) <- (~39) [avatar component clause 326]
329. 38 | ~39 [avatar split clause 141,326,322]
340. ~25 [avatar split clause 147,261]
350. $false <- (29, ~39) [resolution 328,281]
351. ~29 | 39 [avatar contradiction clause 350]
354. ~quiet(susan) <- (38) [resolution 110,324]
355. $false <- (38) [subsumption resolution 354,258]
356. ~38 [avatar contradiction clause 355]
357. $false [avatar sat refutation 282,329,340,351,356]
% SZS output end Proof for 8588781892205596286555696
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble then paul is not calm or not wise.
Everyone who is not rich is both not happy and creative.
If someone is not kind then alice is both not creative and happy and vice versa.
Everyone who is generous is not rich or not old and vice versa.
Everyone who is happy or curious is generous or calm and vice versa.
If someone is not strong or rich then paul is not tall and vice versa.
Everyone who is happy is funny or rich.
If paul is both strong and not generous then susan is either happy or not wise.
Everyone who is not old or happy is wise or kind and vice versa.
If lucy is not creative or not rich then someone is generous and vice versa.
Everyone who is either calm or not rich is either generous or patient.
Everyone who is either not creative or strong is not creative and vice versa.
Everyone who is not patient is not funny or not quiet.
Everyone who is either not funny or not curious is either wise or funny.
If someone is wise or not happy then john is both happy and curious and vice versa.
Susan is not patient.
Fred is kind.
Someone is either not brave or rich.
John is quiet.
Alice is not strong. | Fred is generous. | neutral | ((?[X]:(humble(X)))=>((~calm(paul)|~wise(paul))))&
(![X]:(~rich(X)=>(~happy(X)&creative(X))))&
((?[X]:(~kind(X)))<=>((~creative(alice)&happy(alice))))&
(![X]:(generous(X)<=>(~rich(X)|~old(X))))&
(![X]:((happy(X)|curious(X))<=>(generous(X)|calm(X))))&
((?[X]:((~strong(X)|rich(X))))<=>(~tall(paul)))&
(![X]:(happy(X)=>(funny(X)|rich(X))))&
(((strong(paul)&~generous(paul)))=>((happy(susan)<~>~wise(susan))))&
(![X]:((~old(X)|happy(X))<=>(wise(X)|kind(X))))&
(((~creative(lucy)|~rich(lucy)))<=>(?[X]:(generous(X))))&
(![X]:((calm(X)<~>~rich(X))=>(generous(X)<~>patient(X))))&
(![X]:((~creative(X)<~>strong(X))<=>~creative(X)))&
(![X]:(~patient(X)=>(~funny(X)|~quiet(X))))&
(![X]:((~funny(X)<~>~curious(X))=>(wise(X)<~>funny(X))))&
((?[X]:((wise(X)|~happy(X))))<=>((happy(john)&curious(john))))&
(~patient(susan))&
(kind(fred))&
(?[X]:((~brave(X)<~>rich(X))))&
(quiet(john))&
(~strong(alice)) | generous(fred) | [] | null | 0 |
Everyone who is not brave is both strong and not quiet and vice versa. Everyone who is not creative is both not patient and rich and vice versa. Everyone who is patient or not generous is both kind and old and vice versa. If someone is not rich then someone is both not tall and wise and vice versa. If susan is both not creative and not wise then someone is humble and vice versa. Everyone who is kind is brave or not curious and vice versa. If fred is either wise or not strong then someone is creative and vice versa. Everyone who is not brave is both happy and funny and vice versa. Everyone who is either brave or generous is either not rich or rich and vice versa. Everyone who is both strong and not strong is not happy and vice versa. Everyone who is either curious or not generous is calm or curious and vice versa. If paul is either not old or not funny then someone is both happy and old. Everyone who is not rich or not generous is not old and vice versa. Everyone who is not funny is either not brave or not funny. Everyone who is not old is either not curious or not humble and vice versa. Everyone who is strong or not tall is not strong or generous and vice versa. John is not curious or strong. Lucy is curious or not kind. Someone is not kind. Someone is either not generous or not old. Someone is not patient. | Paul is patient. | neutral | (![X]:(~brave(X)<=>(strong(X)&~quiet(X))))&
(![X]:(~creative(X)<=>(~patient(X)&rich(X))))&
(![X]:((patient(X)|~generous(X))<=>(kind(X)&old(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~tall(X)&wise(X)))))&
(((~creative(susan)&~wise(susan)))<=>(?[X]:(humble(X))))&
(![X]:(kind(X)<=>(brave(X)|~curious(X))))&
(((wise(fred)<~>~strong(fred)))<=>(?[X]:(creative(X))))&
(![X]:(~brave(X)<=>(happy(X)&funny(X))))&
(![X]:((brave(X)<~>generous(X))<=>(~rich(X)<~>rich(X))))&
(![X]:((strong(X)&~strong(X))<=>~happy(X)))&
(![X]:((curious(X)<~>~generous(X))<=>(calm(X)|curious(X))))&
(((~old(paul)<~>~funny(paul)))=>(?[X]:((happy(X)&old(X)))))&
(![X]:((~rich(X)|~generous(X))<=>~old(X)))&
(![X]:(~funny(X)=>(~brave(X)<~>~funny(X))))&
(![X]:(~old(X)<=>(~curious(X)<~>~humble(X))))&
(![X]:((strong(X)|~tall(X))<=>(~strong(X)|generous(X))))&
((~curious(john)|strong(john)))&
((curious(lucy)|~kind(lucy)))&
(?[X]:(~kind(X)))&
(?[X]:((~generous(X)<~>~old(X))))&
(?[X]:(~patient(X))) | patient(paul) | [] | null | 0 |
If alice is either not happy or strong then paul is funny and vice versa.
If susan is either not wise or kind then alice is both not strong and not rich.
If john is both not funny and not happy then paul is both strong and not wise.
If mary is both not curious and rich then someone is not creative.
Everyone who is either not patient or not wise is creative and vice versa.
Everyone who is humble is not humble.
If fred is not humble or old then someone is brave or creative and vice versa.
If susan is both not patient and curious then susan is either calm or not happy.
If someone is either quiet or not creative then someone is both brave and not happy.
If fred is quiet or brave then someone is old.
Everyone who is either quiet or not happy is both not quiet and rich.
If someone is either happy or not generous then someone is creative and vice versa.
If fred is either calm or happy then john is not happy and vice versa.
If someone is not curious or tall then someone is both wise and not brave.
If paul is patient or not funny then lucy is both not brave and not tall.
Everyone who is happy is both quiet and curious and vice versa.
Mary is both funny and not curious.
Someone is either not rich or not brave.
John is either not humble or creative.
Susan is both not quiet and tall.
Someone is both funny and not brave.
Someone is wise.
Someone is not kind.
Someone is wise or not kind. | Alice is happy. | contradiction | (((~happy(alice)<~>strong(alice)))<=>(funny(paul)))&
(((~wise(susan)<~>kind(susan)))=>((~strong(alice)&~rich(alice))))&
(((~funny(john)&~happy(john)))=>((strong(paul)&~wise(paul))))&
(((~curious(mary)&rich(mary)))=>(?[X]:(~creative(X))))&
(![X]:((~patient(X)<~>~wise(X))<=>creative(X)))&
(![X]:(humble(X)=>~humble(X)))&
(((~humble(fred)|old(fred)))<=>(?[X]:((brave(X)|creative(X)))))&
(((~patient(susan)&curious(susan)))=>((calm(susan)<~>~happy(susan))))&
((?[X]:((quiet(X)<~>~creative(X))))=>(?[X]:((brave(X)&~happy(X)))))&
(((quiet(fred)|brave(fred)))=>(?[X]:(old(X))))&
(![X]:((quiet(X)<~>~happy(X))=>(~quiet(X)&rich(X))))&
((?[X]:((happy(X)<~>~generous(X))))<=>(?[X]:(creative(X))))&
(((calm(fred)<~>happy(fred)))<=>(~happy(john)))&
((?[X]:((~curious(X)|tall(X))))=>(?[X]:((wise(X)&~brave(X)))))&
(((patient(paul)|~funny(paul)))=>((~brave(lucy)&~tall(lucy))))&
(![X]:(happy(X)<=>(quiet(X)&curious(X))))&
((funny(mary)&~curious(mary)))&
(?[X]:((~rich(X)<~>~brave(X))))&
((~humble(john)<~>creative(john)))&
((~quiet(susan)&tall(susan)))&
(?[X]:((funny(X)&~brave(X))))&
(?[X]:(wise(X)))&
(?[X]:(~kind(X)))&
(?[X]:((wise(X)|~kind(X)))) | happy(alice) | [
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 160026088952432213614270
% SZS output start Proof for 160026088952432213614270
11. ! [X0] : ((quiet(X0) <~> ~happy(X0)) => (rich(X0) & ~quiet(X0))) [input p10]
16. ! [X0] : (happy(X0) <=> (curious(X0) & quiet(X0))) [input p15]
25. happy(alice) [input hypothesis]
39. ! [X0] : ((rich(X0) & ~quiet(X0)) | (quiet(X0) <=> ~happy(X0))) [ennf transformation 11]
59. ! [X0] : ((rich(X0) & ~quiet(X0)) | ((quiet(X0) | happy(X0)) & (~happy(X0) | ~quiet(X0)))) [nnf transformation 39]
69. ! [X0] : ((happy(X0) | (~curious(X0) | ~quiet(X0))) & ((curious(X0) & quiet(X0)) | ~happy(X0))) [nnf transformation 16]
70. ! [X0] : ((happy(X0) | ~curious(X0) | ~quiet(X0)) & ((curious(X0) & quiet(X0)) | ~happy(X0))) [flattening 69]
111. ~quiet(X0) | ~happy(X0) | ~quiet(X0) [cnf transformation 59]
131. quiet(X0) | ~happy(X0) [cnf transformation 70]
147. happy(alice) [cnf transformation 25]
148. ~quiet(X0) | ~happy(X0) [duplicate literal removal 111]
350. ~happy(X0) [subsumption resolution 131,148]
372. $false [subsumption resolution 147,350]
% SZS output end Proof for 160026088952432213614270
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or strong is either generous or not tall. Everyone who is not humble or generous is not rich and vice versa. Everyone who is calm or not rich is not brave. Everyone who is both generous and not creative is either patient or funny and vice versa. Everyone who is calm or quiet is not patient or kind. Everyone who is either not funny or rich is both not happy and rich. Everyone who is either wise or not humble is not curious and vice versa. If someone is either brave or not brave then lucy is both tall and not rich and vice versa. If alice is both old and creative then susan is not kind or not rich and vice versa. If someone is tall or not kind then someone is either calm or old and vice versa. Everyone who is both not kind and happy is not rich or generous. Everyone who is either not happy or wise is either not rich or quiet. If someone is humble or not strong then someone is not funny and vice versa. Everyone who is either not tall or strong is both humble and patient and vice versa. Everyone who is not quiet is not kind or not generous and vice versa. Everyone who is curious is both not humble and not calm and vice versa. Susan is funny. Someone is both wise and old. Paul is both kind and not generous. Someone is both kind and humble. Alice is both not old and not curious. Someone is not kind. Someone is not wise or old. Someone is both strong and not patient. | Lucy is not humble. | neutral | (![X]:((~kind(X)|strong(X))=>(generous(X)<~>~tall(X))))&
(![X]:((~humble(X)|generous(X))<=>~rich(X)))&
(![X]:((calm(X)|~rich(X))=>~brave(X)))&
(![X]:((generous(X)&~creative(X))<=>(patient(X)<~>funny(X))))&
(![X]:((calm(X)|quiet(X))=>(~patient(X)|kind(X))))&
(![X]:((~funny(X)<~>rich(X))=>(~happy(X)&rich(X))))&
(![X]:((wise(X)<~>~humble(X))<=>~curious(X)))&
((?[X]:((brave(X)<~>~brave(X))))<=>((tall(lucy)&~rich(lucy))))&
(((old(alice)&creative(alice)))<=>((~kind(susan)|~rich(susan))))&
((?[X]:((tall(X)|~kind(X))))<=>(?[X]:((calm(X)<~>old(X)))))&
(![X]:((~kind(X)&happy(X))=>(~rich(X)|generous(X))))&
(![X]:((~happy(X)<~>wise(X))=>(~rich(X)<~>quiet(X))))&
((?[X]:((humble(X)|~strong(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~tall(X)<~>strong(X))<=>(humble(X)&patient(X))))&
(![X]:(~quiet(X)<=>(~kind(X)|~generous(X))))&
(![X]:(curious(X)<=>(~humble(X)&~calm(X))))&
(funny(susan))&
(?[X]:((wise(X)&old(X))))&
((kind(paul)&~generous(paul)))&
(?[X]:((kind(X)&humble(X))))&
((~old(alice)&~curious(alice)))&
(?[X]:(~kind(X)))&
(?[X]:((~wise(X)|old(X))))&
(?[X]:((strong(X)&~patient(X)))) | ~humble(lucy) | [] | null | 0 |
Everyone who is either not calm or curious is not rich.
If someone is both not humble and old then someone is old or humble.
Everyone who is both not humble and not kind is either strong or funny and vice versa.
If someone is either not curious or creative then someone is happy.
Everyone who is either not wise or humble is not kind or kind.
If susan is either not strong or curious then mary is either not creative or quiet.
Everyone who is not strong or curious is strong and vice versa.
If john is not calm then someone is tall or not patient.
If someone is both not curious and not wise then someone is either not tall or not strong and vice versa.
Everyone who is not funny or not curious is not strong or old and vice versa.
If someone is happy then someone is either not patient or kind and vice versa.
Everyone who is generous or brave is both happy and not strong.
Everyone who is wise is patient and vice versa.
Everyone who is rich or not old is both creative and curious and vice versa.
Everyone who is tall or not quiet is quiet and vice versa.
Everyone who is old is both calm and not curious and vice versa.
Someone is either not funny or not happy.
Someone is generous or not generous.
Someone is not rich or brave.
John is not wise or generous. | Mary is not wise. | neutral | (![X]:((~calm(X)<~>curious(X))=>~rich(X)))&
((?[X]:((~humble(X)&old(X))))=>(?[X]:((old(X)|humble(X)))))&
(![X]:((~humble(X)&~kind(X))<=>(strong(X)<~>funny(X))))&
((?[X]:((~curious(X)<~>creative(X))))=>(?[X]:(happy(X))))&
(![X]:((~wise(X)<~>humble(X))=>(~kind(X)|kind(X))))&
(((~strong(susan)<~>curious(susan)))=>((~creative(mary)<~>quiet(mary))))&
(![X]:((~strong(X)|curious(X))<=>strong(X)))&
((~calm(john))=>(?[X]:((tall(X)|~patient(X)))))&
((?[X]:((~curious(X)&~wise(X))))<=>(?[X]:((~tall(X)<~>~strong(X)))))&
(![X]:((~funny(X)|~curious(X))<=>(~strong(X)|old(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~patient(X)<~>kind(X)))))&
(![X]:((generous(X)|brave(X))=>(happy(X)&~strong(X))))&
(![X]:(wise(X)<=>patient(X)))&
(![X]:((rich(X)|~old(X))<=>(creative(X)&curious(X))))&
(![X]:((tall(X)|~quiet(X))<=>quiet(X)))&
(![X]:(old(X)<=>(calm(X)&~curious(X))))&
(?[X]:((~funny(X)<~>~happy(X))))&
(?[X]:((generous(X)|~generous(X))))&
(?[X]:((~rich(X)|brave(X))))&
((~wise(john)|generous(john))) | ~wise(mary) | [] | null | 0 |
Everyone who is both not old and kind is both not rich and not wise and vice versa.
Everyone who is tall is kind and vice versa.
If mary is not curious or calm then mary is either not calm or not patient.
Everyone who is both old and quiet is not strong.
Everyone who is not tall or not kind is quiet and vice versa.
Everyone who is not old or not rich is curious.
If someone is either kind or not calm then paul is either tall or not funny.
If someone is both wise and not creative then someone is not quiet.
Everyone who is not quiet is humble or happy.
If someone is generous then someone is not humble or wise and vice versa.
Everyone who is either calm or tall is either not patient or not happy and vice versa.
If someone is generous or curious then mary is not creative and vice versa.
Everyone who is not rich or calm is both not wise and generous.
If someone is not patient then someone is tall or not happy.
If someone is generous or rich then susan is patient.
Everyone who is not old is kind and vice versa.
Someone is not tall.
Fred is curious or generous.
Mary is either not wise or not humble.
Paul is both not funny and kind.
Someone is funny. | Susan is not kind. | neutral | (![X]:((~old(X)&kind(X))<=>(~rich(X)&~wise(X))))&
(![X]:(tall(X)<=>kind(X)))&
(((~curious(mary)|calm(mary)))=>((~calm(mary)<~>~patient(mary))))&
(![X]:((old(X)&quiet(X))=>~strong(X)))&
(![X]:((~tall(X)|~kind(X))<=>quiet(X)))&
(![X]:((~old(X)|~rich(X))=>curious(X)))&
((?[X]:((kind(X)<~>~calm(X))))=>((tall(paul)<~>~funny(paul))))&
((?[X]:((wise(X)&~creative(X))))=>(?[X]:(~quiet(X))))&
(![X]:(~quiet(X)=>(humble(X)|happy(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~humble(X)|wise(X)))))&
(![X]:((calm(X)<~>tall(X))<=>(~patient(X)<~>~happy(X))))&
((?[X]:((generous(X)|curious(X))))<=>(~creative(mary)))&
(![X]:((~rich(X)|calm(X))=>(~wise(X)&generous(X))))&
((?[X]:(~patient(X)))=>(?[X]:((tall(X)|~happy(X)))))&
((?[X]:((generous(X)|rich(X))))=>(patient(susan)))&
(![X]:(~old(X)<=>kind(X)))&
(?[X]:(~tall(X)))&
((curious(fred)|generous(fred)))&
((~wise(mary)<~>~humble(mary)))&
((~funny(paul)&kind(paul)))&
(?[X]:(funny(X))) | ~kind(susan) | [] | null | 0 |
Everyone who is either not rich or not happy is both not humble and wise. If lucy is not quiet then susan is either funny or not creative and vice versa. If someone is both not quiet and patient then susan is not calm or tall. If fred is not creative or strong then someone is old and vice versa. If lucy is either funny or not rich then john is not creative and vice versa. Everyone who is not brave is not humble or happy. Everyone who is not strong or creative is creative. If fred is either not patient or not calm then paul is not funny. Everyone who is strong is both humble and patient. If paul is happy then susan is happy or old and vice versa. Everyone who is both kind and not happy is both not curious and not strong. Everyone who is both old and rich is creative and vice versa. If someone is rich then alice is wise. Everyone who is both not kind and creative is both not funny and brave. If mary is not rich then someone is either not generous or old and vice versa. If someone is funny or not creative then someone is both not calm and not funny. Someone is not strong. Fred is both curious and not funny. Someone is wise or calm. Susan is not creative or not happy. Fred is curious. Someone is both not wise and not quiet. Someone is not humble. Susan is either funny or not patient. | Fred is not patient. | contradiction | (![X]:((~rich(X)<~>~happy(X))=>(~humble(X)&wise(X))))&
((~quiet(lucy))<=>((funny(susan)<~>~creative(susan))))&
((?[X]:((~quiet(X)&patient(X))))=>((~calm(susan)|tall(susan))))&
(((~creative(fred)|strong(fred)))<=>(?[X]:(old(X))))&
(((funny(lucy)<~>~rich(lucy)))<=>(~creative(john)))&
(![X]:(~brave(X)=>(~humble(X)|happy(X))))&
(![X]:((~strong(X)|creative(X))=>creative(X)))&
(((~patient(fred)<~>~calm(fred)))=>(~funny(paul)))&
(![X]:(strong(X)=>(humble(X)&patient(X))))&
((happy(paul))<=>((happy(susan)|old(susan))))&
(![X]:((kind(X)&~happy(X))=>(~curious(X)&~strong(X))))&
(![X]:((old(X)&rich(X))<=>creative(X)))&
((?[X]:(rich(X)))=>(wise(alice)))&
(![X]:((~kind(X)&creative(X))=>(~funny(X)&brave(X))))&
((~rich(mary))<=>(?[X]:((~generous(X)<~>old(X)))))&
((?[X]:((funny(X)|~creative(X))))=>(?[X]:((~calm(X)&~funny(X)))))&
(?[X]:(~strong(X)))&
((curious(fred)&~funny(fred)))&
(?[X]:((wise(X)|calm(X))))&
((~creative(susan)|~happy(susan)))&
(curious(fred))&
(?[X]:((~wise(X)&~quiet(X))))&
(?[X]:(~humble(X)))&
((funny(susan)<~>~patient(susan))) | ~patient(fred) | [
"p3",
"p6",
"p8",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2859002431577477762596523
% SZS output start Proof for 2859002431577477762596523
4. (strong(fred) | ~creative(fred)) <=> ? [X0] : old(X0) [input p3]
7. ! [X0] : ((creative(X0) | ~strong(X0)) => creative(X0)) [input p6]
9. ! [X0] : (strong(X0) => (patient(X0) & humble(X0))) [input p8]
12. ! [X0] : ((rich(X0) & old(X0)) <=> creative(X0)) [input p11]
17. ? [X0] : ~strong(X0) [input p16]
25. ~patient(fred) [input hypothesis]
31. ! [X0] : (creative(X0) | (~creative(X0) & strong(X0))) [ennf transformation 7]
33. ! [X0] : ((patient(X0) & humble(X0)) | ~strong(X0)) [ennf transformation 9]
42. ((strong(fred) | ~creative(fred)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | (~strong(fred) & creative(fred))) [nnf transformation 4]
43. (strong(fred) | ~creative(fred) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | (~strong(fred) & creative(fred))) [flattening 42]
44. (strong(fred) | ~creative(fred) | ! [X0] : ~old(X0)) & (? [X1] : old(X1) | (~strong(fred) & creative(fred))) [rectify 43]
45. ? [X1] : old(X1) => old(sK0) [choice axiom]
46. (strong(fred) | ~creative(fred) | ! [X0] : ~old(X0)) & (old(sK0) | (~strong(fred) & creative(fred))) [skolemisation 44,45]
51. ! [X0] : (((rich(X0) & old(X0)) | ~creative(X0)) & (creative(X0) | (~rich(X0) | ~old(X0)))) [nnf transformation 12]
52. ! [X0] : (((rich(X0) & old(X0)) | ~creative(X0)) & (creative(X0) | ~rich(X0) | ~old(X0))) [flattening 51]
60. ? [X0] : ~strong(X0) => ~strong(sK3) [choice axiom]
61. ~strong(sK3) [skolemisation 17,60]
79. strong(fred) | ~creative(fred) | ~old(X0) [cnf transformation 46]
84. strong(X0) | creative(X0) [cnf transformation 31]
89. ~strong(X0) | patient(X0) [cnf transformation 33]
96. ~creative(X0) | old(X0) [cnf transformation 52]
108. ~strong(sK3) [cnf transformation 61]
119. ~patient(fred) [cnf transformation 25]
137. 4 <=> ! [X0] : ~old(X0) [avatar definition]
138. ~old(X0) <- (4) [avatar component clause 137]
140. 5 <=> creative(fred) [avatar definition]
142. ~creative(fred) <- (~5) [avatar component clause 140]
144. 6 <=> strong(fred) [avatar definition]
145. ~strong(fred) <- (~6) [avatar component clause 144]
146. strong(fred) <- (6) [avatar component clause 144]
147. 4 | ~5 | 6 [avatar split clause 79,144,140,137]
175. 12 <=> patient(fred) [avatar definition]
177. ~patient(fred) <- (~12) [avatar component clause 175]
263. ~12 [avatar split clause 119,175]
264. creative(sK3) [resolution 84,108]
269. old(sK3) [resolution 96,264]
272. $false <- (4) [subsumption resolution 269,138]
273. ~4 [avatar contradiction clause 272]
274. patient(fred) <- (6) [resolution 146,89]
276. $false <- (6, ~12) [subsumption resolution 274,177]
277. ~6 | 12 [avatar contradiction clause 276]
278. creative(fred) <- (~6) [resolution 145,84]
279. $false <- (~5, ~6) [subsumption resolution 278,142]
280. 5 | 6 [avatar contradiction clause 279]
281. $false [avatar sat refutation 147,263,273,277,280]
% SZS output end Proof for 2859002431577477762596523
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or curious is both curious and calm and vice versa.
Everyone who is humble is both generous and not old.
Everyone who is kind is calm and vice versa.
If someone is both creative and old then john is either calm or generous and vice versa.
If mary is kind then mary is generous and vice versa.
If someone is both tall and not patient then someone is patient or rich and vice versa.
Everyone who is funny is either not creative or old.
Everyone who is not patient is funny.
Everyone who is not funny is both brave and not brave and vice versa.
Everyone who is not tall is humble.
If alice is both curious and not wise then someone is both generous and strong.
Everyone who is strong is not creative and vice versa.
Everyone who is not brave is either not strong or not creative and vice versa.
If paul is quiet or funny then someone is strong and vice versa.
Everyone who is strong or not tall is both not kind and not generous.
Someone is either not old or happy.
Susan is not wise.
Susan is quiet.
Lucy is not wise or wise.
Someone is not creative. | Mary is not humble. | entailment | (![X]:((happy(X)|curious(X))<=>(curious(X)&calm(X))))&
(![X]:(humble(X)=>(generous(X)&~old(X))))&
(![X]:(kind(X)<=>calm(X)))&
((?[X]:((creative(X)&old(X))))<=>((calm(john)<~>generous(john))))&
((kind(mary))<=>(generous(mary)))&
((?[X]:((tall(X)&~patient(X))))<=>(?[X]:((patient(X)|rich(X)))))&
(![X]:(funny(X)=>(~creative(X)<~>old(X))))&
(![X]:(~patient(X)=>funny(X)))&
(![X]:(~funny(X)<=>(brave(X)&~brave(X))))&
(![X]:(~tall(X)=>humble(X)))&
(((curious(alice)&~wise(alice)))=>(?[X]:((generous(X)&strong(X)))))&
(![X]:(strong(X)<=>~creative(X)))&
(![X]:(~brave(X)<=>(~strong(X)<~>~creative(X))))&
(((quiet(paul)|funny(paul)))<=>(?[X]:(strong(X))))&
(![X]:((strong(X)|~tall(X))=>(~kind(X)&~generous(X))))&
(?[X]:((~old(X)<~>happy(X))))&
(~wise(susan))&
(quiet(susan))&
((~wise(lucy)|wise(lucy)))&
(?[X]:(~creative(X))) | ~humble(mary) | [
"p1",
"p4",
"p6",
"p8",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3781050680575045573262896
% SZS output start Proof for 3781050680575045573262896
2. ! [X0] : (humble(X0) => (~old(X0) & generous(X0))) [input p1]
5. kind(mary) <=> generous(mary) [input p4]
7. ! [X0] : (funny(X0) => (~creative(X0) <~> old(X0))) [input p6]
9. ! [X0] : (~funny(X0) <=> (~brave(X0) & brave(X0))) [input p8]
12. ! [X0] : (strong(X0) <=> ~creative(X0)) [input p11]
15. ! [X0] : ((~tall(X0) | strong(X0)) => (~generous(X0) & ~kind(X0))) [input p14]
21. humble(mary) [input hypothesis]
23. ! [X0] : ((~old(X0) & generous(X0)) | ~humble(X0)) [ennf transformation 2]
24. ! [X0] : ((~creative(X0) <~> old(X0)) | ~funny(X0)) [ennf transformation 7]
29. ! [X0] : ((~generous(X0) & ~kind(X0)) | (tall(X0) & ~strong(X0))) [ennf transformation 15]
37. (kind(mary) | ~generous(mary)) & (generous(mary) | ~kind(mary)) [nnf transformation 5]
43. ! [X0] : (((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | ~funny(X0)) [nnf transformation 24]
44. ! [X0] : ((~funny(X0) | (brave(X0) | ~brave(X0))) & ((~brave(X0) & brave(X0)) | funny(X0))) [nnf transformation 9]
45. ! [X0] : ((~funny(X0) | brave(X0) | ~brave(X0)) & ((~brave(X0) & brave(X0)) | funny(X0))) [flattening 44]
48. ! [X0] : ((strong(X0) | creative(X0)) & (~creative(X0) | ~strong(X0))) [nnf transformation 12]
65. ~humble(X0) | generous(X0) [cnf transformation 23]
66. ~old(X0) | ~humble(X0) [cnf transformation 23]
76. kind(mary) | ~generous(mary) [cnf transformation 37]
82. ~funny(X0) | ~creative(X0) | old(X0) [cnf transformation 43]
85. brave(X0) | funny(X0) [cnf transformation 45]
86. ~brave(X0) | funny(X0) [cnf transformation 45]
92. strong(X0) | creative(X0) [cnf transformation 48]
100. ~strong(X0) | ~kind(X0) [cnf transformation 29]
110. humble(mary) [cnf transformation 21]
137. 6 <=> generous(mary) [avatar definition]
141. 7 <=> kind(mary) [avatar definition]
143. kind(mary) <- (7) [avatar component clause 141]
144. ~6 | 7 [avatar split clause 76,141,137]
176. funny(X0) [subsumption resolution 85,86]
209. generous(mary) [resolution 65,110]
212. 6 [avatar split clause 209,137]
221. ~kind(X0) | creative(X0) [resolution 100,92]
238. ~creative(X1) | old(X1) [resolution 82,176]
239. creative(mary) <- (7) [resolution 221,143]
245. old(mary) <- (7) [resolution 238,239]
247. ~humble(mary) <- (7) [resolution 245,66]
248. $false <- (7) [subsumption resolution 247,110]
249. ~7 [avatar contradiction clause 248]
250. $false [avatar sat refutation 144,212,249]
% SZS output end Proof for 3781050680575045573262896
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not quiet and curious is both calm and funny and vice versa.
If susan is both brave and not happy then john is not creative or old.
If lucy is not brave or tall then someone is calm and vice versa.
If someone is either creative or old then mary is not wise and vice versa.
If john is calm or humble then susan is either not patient or kind and vice versa.
Everyone who is either humble or curious is not funny or not happy.
If someone is both not tall and not rich then someone is either patient or curious and vice versa.
Everyone who is both not brave and creative is either wise or not curious and vice versa.
Everyone who is both not old and not strong is both not quiet and old.
Everyone who is not strong is either tall or not happy and vice versa.
Everyone who is funny is either rich or calm.
If someone is not happy then susan is both not old and old and vice versa.
Everyone who is either not funny or kind is strong.
If mary is patient then susan is not generous and vice versa.
Everyone who is old is quiet or humble.
If paul is not strong then someone is not happy or not strong.
Someone is either not funny or not curious.
Paul is funny.
Susan is not patient.
Someone is either patient or not calm.
Paul is both not generous and tall.
John is humble or not tall. | Susan is not creative. | neutral | (![X]:((~quiet(X)&curious(X))<=>(calm(X)&funny(X))))&
(((brave(susan)&~happy(susan)))=>((~creative(john)|old(john))))&
(((~brave(lucy)|tall(lucy)))<=>(?[X]:(calm(X))))&
((?[X]:((creative(X)<~>old(X))))<=>(~wise(mary)))&
(((calm(john)|humble(john)))<=>((~patient(susan)<~>kind(susan))))&
(![X]:((humble(X)<~>curious(X))=>(~funny(X)|~happy(X))))&
((?[X]:((~tall(X)&~rich(X))))<=>(?[X]:((patient(X)<~>curious(X)))))&
(![X]:((~brave(X)&creative(X))<=>(wise(X)<~>~curious(X))))&
(![X]:((~old(X)&~strong(X))=>(~quiet(X)&old(X))))&
(![X]:(~strong(X)<=>(tall(X)<~>~happy(X))))&
(![X]:(funny(X)=>(rich(X)<~>calm(X))))&
((?[X]:(~happy(X)))<=>((~old(susan)&old(susan))))&
(![X]:((~funny(X)<~>kind(X))=>strong(X)))&
((patient(mary))<=>(~generous(susan)))&
(![X]:(old(X)=>(quiet(X)|humble(X))))&
((~strong(paul))=>(?[X]:((~happy(X)|~strong(X)))))&
(?[X]:((~funny(X)<~>~curious(X))))&
(funny(paul))&
(~patient(susan))&
(?[X]:((patient(X)<~>~calm(X))))&
((~generous(paul)&tall(paul)))&
((humble(john)|~tall(john))) | ~creative(susan) | [] | null | 0 |
Everyone who is strong is both not old and not brave and vice versa.
Everyone who is not tall is tall or wise and vice versa.
Everyone who is not brave is wise or not tall and vice versa.
Everyone who is brave or not wise is kind or not strong.
If someone is both not wise and not generous then lucy is not creative or old and vice versa.
If someone is happy then someone is not curious or not wise.
If someone is not old then someone is either not happy or not humble and vice versa.
Everyone who is both brave and not old is not curious.
Everyone who is both not curious and not happy is strong or not calm and vice versa.
Everyone who is not old or generous is not old or happy and vice versa.
Everyone who is either rich or not strong is not kind or not strong and vice versa.
If someone is both tall and not generous then someone is either not old or not calm.
If paul is patient then someone is either not kind or wise.
Everyone who is both not patient and patient is funny.
Everyone who is either not rich or not old is rich or wise and vice versa.
Someone is not old or not tall.
Someone is either not curious or brave.
Someone is both funny and calm.
Mary is rich or not tall.
Paul is not strong or calm.
Someone is not rich or patient.
Someone is both strong and patient.
Mary is not quiet or not kind. | Mary is tall. | contradiction | (![X]:(strong(X)<=>(~old(X)&~brave(X))))&
(![X]:(~tall(X)<=>(tall(X)|wise(X))))&
(![X]:(~brave(X)<=>(wise(X)|~tall(X))))&
(![X]:((brave(X)|~wise(X))=>(kind(X)|~strong(X))))&
((?[X]:((~wise(X)&~generous(X))))<=>((~creative(lucy)|old(lucy))))&
((?[X]:(happy(X)))=>(?[X]:((~curious(X)|~wise(X)))))&
((?[X]:(~old(X)))<=>(?[X]:((~happy(X)<~>~humble(X)))))&
(![X]:((brave(X)&~old(X))=>~curious(X)))&
(![X]:((~curious(X)&~happy(X))<=>(strong(X)|~calm(X))))&
(![X]:((~old(X)|generous(X))<=>(~old(X)|happy(X))))&
(![X]:((rich(X)<~>~strong(X))<=>(~kind(X)|~strong(X))))&
((?[X]:((tall(X)&~generous(X))))=>(?[X]:((~old(X)<~>~calm(X)))))&
((patient(paul))=>(?[X]:((~kind(X)<~>wise(X)))))&
(![X]:((~patient(X)&patient(X))=>funny(X)))&
(![X]:((~rich(X)<~>~old(X))<=>(rich(X)|wise(X))))&
(?[X]:((~old(X)|~tall(X))))&
(?[X]:((~curious(X)<~>brave(X))))&
(?[X]:((funny(X)&calm(X))))&
((rich(mary)|~tall(mary)))&
((~strong(paul)|calm(paul)))&
(?[X]:((~rich(X)|patient(X))))&
(?[X]:((strong(X)&patient(X))))&
((~quiet(mary)|~kind(mary))) | tall(mary) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 2473735557762325677527173
% SZS output start Proof for 2473735557762325677527173
2. ! [X0] : (~tall(X0) <=> (wise(X0) | tall(X0))) [input p1]
24. tall(mary) [input hypothesis]
40. ! [X0] : ((~tall(X0) | (~wise(X0) & ~tall(X0))) & ((wise(X0) | tall(X0)) | tall(X0))) [nnf transformation 2]
41. ! [X0] : ((~tall(X0) | (~wise(X0) & ~tall(X0))) & (wise(X0) | tall(X0) | tall(X0))) [flattening 40]
87. ~tall(X0) | ~tall(X0) [cnf transformation 41]
139. tall(mary) [cnf transformation 24]
145. ~tall(X0) [duplicate literal removal 87]
232. $false [subsumption resolution 139,145]
% SZS output end Proof for 2473735557762325677527173
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind or calm then lucy is tall or wise and vice versa. Everyone who is either humble or not generous is either not humble or not happy and vice versa. If john is generous or not strong then lucy is not brave or creative. Everyone who is both tall and not old is either not rich or tall and vice versa. If paul is both not funny and kind then lucy is not creative or patient and vice versa. If someone is both not brave and kind then fred is either rich or not wise. Everyone who is both not rich and not tall is both brave and funny. Everyone who is kind or wise is not curious or quiet and vice versa. If someone is either not strong or not creative then lucy is either humble or not patient. If alice is either not creative or not humble then someone is not old and vice versa. Everyone who is either not old or not tall is both not generous and not happy and vice versa. Everyone who is strong is either curious or strong. If john is not creative then someone is either not patient or tall. Everyone who is not calm or rich is both humble and not funny. Everyone who is funny or not wise is tall. Everyone who is tall is both happy and not creative. Someone is both patient and not quiet. John is either wise or not happy. Someone is either strong or curious. Someone is both calm and humble. Fred is either happy or not rich. Lucy is both not wise and not creative. John is either curious or not tall. Someone is either strong or tall. | John is not happy. | contradiction | ((?[X]:((kind(X)|calm(X))))<=>((tall(lucy)|wise(lucy))))&
(![X]:((humble(X)<~>~generous(X))<=>(~humble(X)<~>~happy(X))))&
(((generous(john)|~strong(john)))=>((~brave(lucy)|creative(lucy))))&
(![X]:((tall(X)&~old(X))<=>(~rich(X)<~>tall(X))))&
(((~funny(paul)&kind(paul)))<=>((~creative(lucy)|patient(lucy))))&
((?[X]:((~brave(X)&kind(X))))=>((rich(fred)<~>~wise(fred))))&
(![X]:((~rich(X)&~tall(X))=>(brave(X)&funny(X))))&
(![X]:((kind(X)|wise(X))<=>(~curious(X)|quiet(X))))&
((?[X]:((~strong(X)<~>~creative(X))))=>((humble(lucy)<~>~patient(lucy))))&
(((~creative(alice)<~>~humble(alice)))<=>(?[X]:(~old(X))))&
(![X]:((~old(X)<~>~tall(X))<=>(~generous(X)&~happy(X))))&
(![X]:(strong(X)=>(curious(X)<~>strong(X))))&
((~creative(john))=>(?[X]:((~patient(X)<~>tall(X)))))&
(![X]:((~calm(X)|rich(X))=>(humble(X)&~funny(X))))&
(![X]:((funny(X)|~wise(X))=>tall(X)))&
(![X]:(tall(X)=>(happy(X)&~creative(X))))&
(?[X]:((patient(X)&~quiet(X))))&
((wise(john)<~>~happy(john)))&
(?[X]:((strong(X)<~>curious(X))))&
(?[X]:((calm(X)&humble(X))))&
((happy(fred)<~>~rich(fred)))&
((~wise(lucy)&~creative(lucy)))&
((curious(john)<~>~tall(john)))&
(?[X]:((strong(X)<~>tall(X)))) | ~happy(john) | [
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7746923225122767093573517
% SZS output start Proof for 7746923225122767093573517
15. ! [X0] : ((~wise(X0) | funny(X0)) => tall(X0)) [input p14]
16. ! [X0] : (tall(X0) => (~creative(X0) & happy(X0))) [input p15]
18. wise(john) <~> ~happy(john) [input p17]
25. ~happy(john) [input hypothesis]
35. ! [X0] : (tall(X0) | (wise(X0) & ~funny(X0))) [ennf transformation 15]
36. ! [X0] : ((~creative(X0) & happy(X0)) | ~tall(X0)) [ennf transformation 16]
63. (happy(john) | ~wise(john)) & (~happy(john) | wise(john)) [nnf transformation 18]
130. wise(X0) | tall(X0) [cnf transformation 35]
131. ~tall(X0) | happy(X0) [cnf transformation 36]
136. happy(john) | ~wise(john) [cnf transformation 63]
149. ~happy(john) [cnf transformation 25]
282. 27 <=> wise(john) [avatar definition]
284. ~wise(john) <- (~27) [avatar component clause 282]
286. 28 <=> happy(john) [avatar definition]
287. ~happy(john) <- (~28) [avatar component clause 286]
289. ~27 | 28 [avatar split clause 136,286,282]
313. 33 <=> tall(john) [avatar definition]
315. tall(john) <- (33) [avatar component clause 313]
328. ~28 [avatar split clause 149,286]
335. tall(john) <- (~27) [resolution 130,284]
338. 33 | 27 [avatar split clause 335,282,313]
340. happy(john) <- (33) [resolution 131,315]
341. $false <- (~28, 33) [subsumption resolution 340,287]
342. 28 | ~33 [avatar contradiction clause 341]
343. $false [avatar sat refutation 289,328,338,342]
% SZS output end Proof for 7746923225122767093573517
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is either not rich or not happy.
Everyone who is both wise and quiet is not creative and vice versa.
If someone is not tall or calm then someone is not quiet and vice versa.
Everyone who is both not happy and calm is either patient or generous and vice versa.
Everyone who is curious or not creative is not kind or kind and vice versa.
Everyone who is either not funny or not wise is either funny or not wise.
If alice is not happy or kind then someone is both quiet and not funny.
If fred is either not tall or not funny then someone is calm and vice versa.
Everyone who is not patient is brave.
Everyone who is wise or quiet is not rich or strong.
If paul is brave then someone is happy and vice versa.
Everyone who is calm is both kind and patient.
Everyone who is old or kind is either wise or funny and vice versa.
If john is either rich or not generous then someone is funny and vice versa.
If fred is either brave or not old then someone is either curious or creative and vice versa.
If paul is patient then susan is not wise or calm and vice versa.
Susan is either funny or quiet.
Susan is not tall.
Someone is both strong and not quiet.
Lucy is strong or generous.
Someone is patient.
Someone is calm or brave.
Someone is both not brave and happy. | Susan is calm. | contradiction | (![X]:(~patient(X)=>(~rich(X)<~>~happy(X))))&
(![X]:((wise(X)&quiet(X))<=>~creative(X)))&
((?[X]:((~tall(X)|calm(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((~happy(X)&calm(X))<=>(patient(X)<~>generous(X))))&
(![X]:((curious(X)|~creative(X))<=>(~kind(X)|kind(X))))&
(![X]:((~funny(X)<~>~wise(X))=>(funny(X)<~>~wise(X))))&
(((~happy(alice)|kind(alice)))=>(?[X]:((quiet(X)&~funny(X)))))&
(((~tall(fred)<~>~funny(fred)))<=>(?[X]:(calm(X))))&
(![X]:(~patient(X)=>brave(X)))&
(![X]:((wise(X)|quiet(X))=>(~rich(X)|strong(X))))&
((brave(paul))<=>(?[X]:(happy(X))))&
(![X]:(calm(X)=>(kind(X)&patient(X))))&
(![X]:((old(X)|kind(X))<=>(wise(X)<~>funny(X))))&
(((rich(john)<~>~generous(john)))<=>(?[X]:(funny(X))))&
(((brave(fred)<~>~old(fred)))<=>(?[X]:((curious(X)<~>creative(X)))))&
((patient(paul))<=>((~wise(susan)|calm(susan))))&
((funny(susan)<~>quiet(susan)))&
(~tall(susan))&
(?[X]:((strong(X)&~quiet(X))))&
((strong(lucy)|generous(lucy)))&
(?[X]:(patient(X)))&
(?[X]:((calm(X)|brave(X))))&
(?[X]:((~brave(X)&happy(X)))) | calm(susan) | [
"p5",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1306401449360516861937801
% SZS output start Proof for 1306401449360516861937801
6. ! [X0] : ((~funny(X0) <~> ~wise(X0)) => (funny(X0) <~> ~wise(X0))) [input p5]
12. ! [X0] : (calm(X0) => (patient(X0) & kind(X0))) [input p11]
13. ! [X0] : ((kind(X0) | old(X0)) <=> (wise(X0) <~> funny(X0))) [input p12]
24. calm(susan) [input hypothesis]
30. ! [X0] : ((funny(X0) <~> ~wise(X0)) | (~funny(X0) <=> ~wise(X0))) [ennf transformation 6]
33. ! [X0] : ((patient(X0) & kind(X0)) | ~calm(X0)) [ennf transformation 12]
46. ! [X0] : (((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | ((~funny(X0) | wise(X0)) & (~wise(X0) | funny(X0)))) [nnf transformation 30]
57. ! [X0] : (((kind(X0) | old(X0)) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0)))) & (((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | (~kind(X0) & ~old(X0)))) [nnf transformation 13]
58. ! [X0] : ((kind(X0) | old(X0) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0)))) & (((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | (~kind(X0) & ~old(X0)))) [flattening 57]
96. ~wise(X0) | funny(X0) | ~wise(X0) | funny(X0) [cnf transformation 46]
99. wise(X0) | ~funny(X0) | ~funny(X0) | wise(X0) [cnf transformation 46]
111. ~calm(X0) | kind(X0) [cnf transformation 33]
114. funny(X0) | wise(X0) | ~kind(X0) [cnf transformation 58]
116. ~funny(X0) | ~wise(X0) | ~kind(X0) [cnf transformation 58]
142. calm(susan) [cnf transformation 24]
143. ~wise(X0) | funny(X0) [duplicate literal removal 96]
144. wise(X0) | ~funny(X0) [duplicate literal removal 99]
219. ~wise(X0) | ~kind(X0) [subsumption resolution 116,143]
221. wise(X0) | ~kind(X0) [subsumption resolution 114,144]
222. ~kind(X0) [subsumption resolution 221,219]
273. 26 <=> calm(susan) [avatar definition]
274. calm(susan) <- (26) [avatar component clause 273]
306. 26 [avatar split clause 142,273]
316. kind(susan) <- (26) [resolution 111,274]
319. $false <- (26) [subsumption resolution 316,222]
320. ~26 [avatar contradiction clause 319]
325. $false [avatar sat refutation 306,320]
% SZS output end Proof for 1306401449360516861937801
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not patient then paul is both curious and tall and vice versa. Everyone who is not calm is both brave and not kind and vice versa. Everyone who is both humble and tall is not creative or kind and vice versa. If alice is not wise or patient then someone is both not kind and not happy. Everyone who is happy or humble is old and vice versa. Everyone who is either tall or rich is not quiet or not brave and vice versa. Everyone who is either creative or not creative is curious or old and vice versa. Everyone who is quiet or humble is rich or not happy and vice versa. Everyone who is both strong and calm is either humble or happy and vice versa. Everyone who is curious is not patient or quiet and vice versa. If someone is not kind or old then alice is creative or not old and vice versa. Everyone who is funny is creative. Everyone who is either not strong or kind is either strong or not happy and vice versa. If someone is either not creative or patient then paul is both not kind and funny. If someone is both not funny and happy then fred is both not generous and happy. If alice is not strong or happy then someone is either not patient or brave. Someone is patient or not funny. Mary is not tall or not old. Paul is either quiet or not curious. Someone is both wise and not creative. Lucy is rich or generous. Someone is both patient and not humble. Susan is either not strong or humble. Fred is both old and creative. | Paul is funny. | entailment | ((?[X]:((funny(X)<~>~patient(X))))<=>((curious(paul)&tall(paul))))&
(![X]:(~calm(X)<=>(brave(X)&~kind(X))))&
(![X]:((humble(X)&tall(X))<=>(~creative(X)|kind(X))))&
(((~wise(alice)|patient(alice)))=>(?[X]:((~kind(X)&~happy(X)))))&
(![X]:((happy(X)|humble(X))<=>old(X)))&
(![X]:((tall(X)<~>rich(X))<=>(~quiet(X)|~brave(X))))&
(![X]:((creative(X)<~>~creative(X))<=>(curious(X)|old(X))))&
(![X]:((quiet(X)|humble(X))<=>(rich(X)|~happy(X))))&
(![X]:((strong(X)&calm(X))<=>(humble(X)<~>happy(X))))&
(![X]:(curious(X)<=>(~patient(X)|quiet(X))))&
((?[X]:((~kind(X)|old(X))))<=>((creative(alice)|~old(alice))))&
(![X]:(funny(X)=>creative(X)))&
(![X]:((~strong(X)<~>kind(X))<=>(strong(X)<~>~happy(X))))&
((?[X]:((~creative(X)<~>patient(X))))=>((~kind(paul)&funny(paul))))&
((?[X]:((~funny(X)&happy(X))))=>((~generous(fred)&happy(fred))))&
(((~strong(alice)|happy(alice)))=>(?[X]:((~patient(X)<~>brave(X)))))&
(?[X]:((patient(X)|~funny(X))))&
((~tall(mary)|~old(mary)))&
((quiet(paul)<~>~curious(paul)))&
(?[X]:((wise(X)&~creative(X))))&
((rich(lucy)|generous(lucy)))&
(?[X]:((patient(X)&~humble(X))))&
((~strong(susan)<~>humble(susan)))&
((old(fred)&creative(fred))) | funny(paul) | [
"p2",
"p13",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7373728250455837735589622
% SZS output start Proof for 7373728250455837735589622
3. ! [X0] : ((tall(X0) & humble(X0)) <=> (kind(X0) | ~creative(X0))) [input p2]
14. ? [X0] : (~creative(X0) <~> patient(X0)) => (funny(paul) & ~kind(paul)) [input p13]
22. ? [X0] : (~humble(X0) & patient(X0)) [input p21]
25. ~funny(paul) [input hypothesis]
30. (funny(paul) & ~kind(paul)) | ! [X0] : (~creative(X0) <=> patient(X0)) [ennf transformation 14]
40. ! [X0] : (((tall(X0) & humble(X0)) | (~kind(X0) & creative(X0))) & ((kind(X0) | ~creative(X0)) | (~tall(X0) | ~humble(X0)))) [nnf transformation 3]
41. ! [X0] : (((tall(X0) & humble(X0)) | (~kind(X0) & creative(X0))) & (kind(X0) | ~creative(X0) | ~tall(X0) | ~humble(X0))) [flattening 40]
62. (funny(paul) & ~kind(paul)) | ! [X0] : ((~creative(X0) | ~patient(X0)) & (patient(X0) | creative(X0))) [nnf transformation 30]
71. ? [X0] : (~humble(X0) & patient(X0)) => (~humble(sK6) & patient(sK6)) [choice axiom]
72. ~humble(sK6) & patient(sK6) [skolemisation 22,71]
84. creative(X0) | humble(X0) [cnf transformation 41]
134. funny(paul) | ~creative(X0) | ~patient(X0) [cnf transformation 62]
147. patient(sK6) [cnf transformation 72]
148. ~humble(sK6) [cnf transformation 72]
153. ~funny(paul) [cnf transformation 25]
232. 16 <=> ! [X0] : (~creative(X0) | ~patient(X0)) [avatar definition]
233. ~creative(X0) | ~patient(X0) <- (16) [avatar component clause 232]
235. 17 <=> funny(paul) [avatar definition]
238. 16 | 17 [avatar split clause 134,235,232]
324. ~17 [avatar split clause 153,235]
342. ~patient(X1) | humble(X1) <- (16) [resolution 233,84]
549. humble(sK6) <- (16) [resolution 342,147]
550. $false <- (16) [subsumption resolution 549,148]
551. ~16 [avatar contradiction clause 550]
552. $false [avatar sat refutation 238,324,551]
% SZS output end Proof for 7373728250455837735589622
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is both quiet and not funny. Everyone who is either not humble or funny is old and vice versa. Everyone who is strong or not generous is happy or creative. Everyone who is either not creative or not generous is not brave. If someone is not generous or tall then mary is both not curious and patient. Everyone who is either happy or not tall is both not patient and not quiet. Everyone who is both not kind and humble is either old or humble and vice versa. Everyone who is patient is both not funny and brave and vice versa. Everyone who is not quiet is funny and vice versa. Everyone who is either not calm or not rich is humble or not quiet. Everyone who is strong or not old is patient or not old and vice versa. Everyone who is both not brave and old is both not old and kind and vice versa. If fred is both not old and not kind then someone is either not rich or not tall. If someone is not tall then john is not happy or brave and vice versa. Everyone who is either creative or not funny is either not brave or not old and vice versa. Everyone who is either not generous or curious is either not curious or happy. Someone is tall or not strong. Lucy is either kind or not funny. Paul is not brave. Someone is not wise or not patient. Someone is both not creative and not old. Someone is happy. | Lucy is quiet. | entailment | (![X]:(~funny(X)=>(quiet(X)&~funny(X))))&
(![X]:((~humble(X)<~>funny(X))<=>old(X)))&
(![X]:((strong(X)|~generous(X))=>(happy(X)|creative(X))))&
(![X]:((~creative(X)<~>~generous(X))=>~brave(X)))&
((?[X]:((~generous(X)|tall(X))))=>((~curious(mary)&patient(mary))))&
(![X]:((happy(X)<~>~tall(X))=>(~patient(X)&~quiet(X))))&
(![X]:((~kind(X)&humble(X))<=>(old(X)<~>humble(X))))&
(![X]:(patient(X)<=>(~funny(X)&brave(X))))&
(![X]:(~quiet(X)<=>funny(X)))&
(![X]:((~calm(X)<~>~rich(X))=>(humble(X)|~quiet(X))))&
(![X]:((strong(X)|~old(X))<=>(patient(X)|~old(X))))&
(![X]:((~brave(X)&old(X))<=>(~old(X)&kind(X))))&
(((~old(fred)&~kind(fred)))=>(?[X]:((~rich(X)<~>~tall(X)))))&
((?[X]:(~tall(X)))<=>((~happy(john)|brave(john))))&
(![X]:((creative(X)<~>~funny(X))<=>(~brave(X)<~>~old(X))))&
(![X]:((~generous(X)<~>curious(X))=>(~curious(X)<~>happy(X))))&
(?[X]:((tall(X)|~strong(X))))&
((kind(lucy)<~>~funny(lucy)))&
(~brave(paul))&
(?[X]:((~wise(X)|~patient(X))))&
(?[X]:((~creative(X)&~old(X))))&
(?[X]:(happy(X))) | quiet(lucy) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p6",
"p7",
"p11",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 651273373133122018645665
% SZS output start Proof for 651273373133122018645665
1. ! [X0] : (~funny(X0) => (~funny(X0) & quiet(X0))) [input p0]
2. ! [X0] : ((~humble(X0) <~> funny(X0)) <=> old(X0)) [input p1]
3. ! [X0] : ((~generous(X0) | strong(X0)) => (creative(X0) | happy(X0))) [input p2]
4. ! [X0] : ((~creative(X0) <~> ~generous(X0)) => ~brave(X0)) [input p3]
5. ? [X0] : (tall(X0) | ~generous(X0)) => (patient(mary) & ~curious(mary)) [input p4]
7. ! [X0] : ((humble(X0) & ~kind(X0)) <=> (old(X0) <~> humble(X0))) [input p6]
8. ! [X0] : (patient(X0) <=> (brave(X0) & ~funny(X0))) [input p7]
12. ! [X0] : ((old(X0) & ~brave(X0)) <=> (kind(X0) & ~old(X0))) [input p11]
15. ! [X0] : ((creative(X0) <~> ~funny(X0)) <=> (~brave(X0) <~> ~old(X0))) [input p14]
16. ! [X0] : ((~generous(X0) <~> curious(X0)) => (~curious(X0) <~> happy(X0))) [input p15]
18. kind(lucy) <~> ~funny(lucy) [input p17]
23. ~quiet(lucy) [input hypothesis]
25. ! [X0] : ((~funny(X0) & quiet(X0)) | funny(X0)) [ennf transformation 1]
26. ! [X0] : ((creative(X0) | happy(X0)) | (generous(X0) & ~strong(X0))) [ennf transformation 3]
27. ! [X0] : (creative(X0) | happy(X0) | (generous(X0) & ~strong(X0))) [flattening 26]
28. ! [X0] : (~brave(X0) | (~creative(X0) <=> ~generous(X0))) [ennf transformation 4]
29. (patient(mary) & ~curious(mary)) | ! [X0] : (~tall(X0) & generous(X0)) [ennf transformation 5]
35. ! [X0] : ((~curious(X0) <~> happy(X0)) | (~generous(X0) <=> curious(X0))) [ennf transformation 16]
36. ! [X0] : ((((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | ~old(X0)) & (old(X0) | ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0))))) [nnf transformation 2]
37. ! [X0] : (~brave(X0) | ((~creative(X0) | generous(X0)) & (~generous(X0) | creative(X0)))) [nnf transformation 28]
39. ! [X0] : (((humble(X0) & ~kind(X0)) | ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0)))) & (((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | (~humble(X0) | kind(X0)))) [nnf transformation 7]
40. ! [X0] : (((humble(X0) & ~kind(X0)) | ((old(X0) | ~humble(X0)) & (humble(X0) | ~old(X0)))) & (((~humble(X0) | ~old(X0)) & (humble(X0) | old(X0))) | ~humble(X0) | kind(X0))) [flattening 39]
41. ! [X0] : ((patient(X0) | (~brave(X0) | funny(X0))) & ((brave(X0) & ~funny(X0)) | ~patient(X0))) [nnf transformation 8]
42. ! [X0] : ((patient(X0) | ~brave(X0) | funny(X0)) & ((brave(X0) & ~funny(X0)) | ~patient(X0))) [flattening 41]
47. ! [X0] : (((old(X0) & ~brave(X0)) | (~kind(X0) | old(X0))) & ((kind(X0) & ~old(X0)) | (~old(X0) | brave(X0)))) [nnf transformation 12]
48. ! [X0] : (((old(X0) & ~brave(X0)) | ~kind(X0) | old(X0)) & ((kind(X0) & ~old(X0)) | ~old(X0) | brave(X0))) [flattening 47]
57. ! [X0] : ((((funny(X0) | ~creative(X0)) & (~funny(X0) | creative(X0))) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0)))) & (((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0))))) [nnf transformation 15]
58. ! [X0] : (((~happy(X0) | curious(X0)) & (happy(X0) | ~curious(X0))) | ((~generous(X0) | ~curious(X0)) & (curious(X0) | generous(X0)))) [nnf transformation 35]
61. (funny(lucy) | ~kind(lucy)) & (~funny(lucy) | kind(lucy)) [nnf transformation 18]
66. quiet(X0) | funny(X0) [cnf transformation 25]
70. ~old(X0) | ~humble(X0) | funny(X0) [cnf transformation 36]
73. creative(X0) | happy(X0) | generous(X0) [cnf transformation 27]
74. ~brave(X0) | ~generous(X0) | creative(X0) [cnf transformation 37]
76. ~curious(mary) | generous(X0) [cnf transformation 29]
78. patient(mary) | generous(X0) [cnf transformation 29]
88. humble(X0) | humble(X0) | ~old(X0) [cnf transformation 40]
90. ~patient(X0) | ~funny(X0) [cnf transformation 42]
91. ~patient(X0) | brave(X0) [cnf transformation 42]
101. ~old(X0) | ~old(X0) | brave(X0) [cnf transformation 48]
104. old(X0) | ~kind(X0) | old(X0) [cnf transformation 48]
110. ~old(X0) | ~brave(X0) | ~funny(X0) | ~creative(X0) [cnf transformation 57]
117. ~brave(X0) | ~creative(X0) | funny(X0) | old(X0) [cnf transformation 57]
120. ~happy(X0) | curious(X0) | curious(X0) | generous(X0) [cnf transformation 58]
123. ~funny(lucy) | kind(lucy) [cnf transformation 61]
129. ~quiet(lucy) [cnf transformation 23]
131. ~happy(X0) | curious(X0) | generous(X0) [duplicate literal removal 120]
132. ~old(X0) | brave(X0) [duplicate literal removal 101]
133. ~kind(X0) | old(X0) [duplicate literal removal 104]
135. ~old(X0) | humble(X0) [duplicate literal removal 88]
140. 2 <=> patient(mary) [avatar definition]
142. patient(mary) <- (2) [avatar component clause 140]
145. 3 <=> ! [X0] : generous(X0) [avatar definition]
146. generous(X0) <- (3) [avatar component clause 145]
147. 3 | 2 [avatar split clause 78,140,145]
149. 4 <=> curious(mary) [avatar definition]
153. 3 | ~4 [avatar split clause 76,149,145]
192. ~creative(X0) | ~funny(X0) | ~old(X0) [subsumption resolution 110,132]
203. 14 <=> kind(lucy) [avatar definition]
204. kind(lucy) <- (14) [avatar component clause 203]
207. 15 <=> funny(lucy) [avatar definition]
209. funny(lucy) <- (15) [avatar component clause 207]
211. 14 | ~15 [avatar split clause 123,207,203]
212. funny(lucy) [resolution 66,129]
215. 15 [avatar split clause 212,207]
216. ~funny(mary) <- (2) [resolution 90,142]
217. brave(mary) <- (2) [resolution 91,142]
220. old(lucy) <- (14) [resolution 133,204]
221. brave(lucy) <- (14) [resolution 220,132]
265. ~generous(mary) | creative(mary) <- (2) [resolution 74,217]
267. ~generous(lucy) | creative(lucy) <- (14) [resolution 74,221]
269. 20 <=> creative(mary) [avatar definition]
270. ~creative(mary) <- (~20) [avatar component clause 269]
271. creative(mary) <- (20) [avatar component clause 269]
273. 21 <=> generous(mary) [avatar definition]
275. ~generous(mary) <- (~21) [avatar component clause 273]
276. 20 | ~21 | ~2 [avatar split clause 265,140,273,269]
287. 24 <=> creative(lucy) [avatar definition]
289. creative(lucy) <- (24) [avatar component clause 287]
291. 25 <=> generous(lucy) [avatar definition]
293. ~generous(lucy) <- (~25) [avatar component clause 291]
294. 24 | ~25 | ~14 [avatar split clause 267,203,291,287]
304. happy(mary) | generous(mary) <- (~20) [resolution 270,73]
305. happy(mary) <- (~20, ~21) [subsumption resolution 304,275]
321. 26 <=> old(mary) [avatar definition]
322. old(mary) <- (26) [avatar component clause 321]
330. curious(mary) | generous(mary) <- (~20, ~21) [resolution 131,305]
348. curious(mary) <- (~20, ~21) [subsumption resolution 330,275]
349. 4 | 20 | 21 [avatar split clause 348,273,269,149]
352. $false <- (3, ~25) [resolution 146,293]
353. ~3 | 25 [avatar contradiction clause 352]
390. ~creative(mary) | funny(mary) | old(mary) <- (2) [resolution 117,217]
394. funny(mary) | old(mary) <- (2, 20) [subsumption resolution 390,271]
395. old(mary) <- (2, 20) [subsumption resolution 394,216]
398. 26 | ~2 | ~20 [avatar split clause 395,269,140,321]
401. ~humble(mary) | funny(mary) <- (26) [resolution 322,70]
403. humble(mary) <- (26) [resolution 322,135]
405. ~humble(mary) <- (2, 26) [subsumption resolution 401,216]
406. $false <- (2, 26) [subsumption resolution 403,405]
407. ~2 | ~26 [avatar contradiction clause 406]
476. ~funny(lucy) | ~old(lucy) <- (24) [resolution 289,192]
478. ~old(lucy) <- (15, 24) [subsumption resolution 476,209]
479. $false <- (14, 15, 24) [subsumption resolution 478,220]
480. ~14 | ~15 | ~24 [avatar contradiction clause 479]
481. $false [avatar sat refutation 147,153,211,215,276,294,349,353,398,407,480]
% SZS output end Proof for 651273373133122018645665
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or not funny is both not quiet and patient and vice versa.
Everyone who is both not quiet and not patient is either not generous or patient and vice versa.
If paul is either calm or not brave then someone is both humble and not brave and vice versa.
If someone is not kind then susan is either not brave or not old and vice versa.
Everyone who is both rich and not humble is both not calm and tall.
If someone is both not funny and strong then paul is brave or kind.
If someone is generous then lucy is both happy and strong.
If lucy is happy then someone is both brave and not creative and vice versa.
Everyone who is not patient is not strong and vice versa.
If paul is not brave or not happy then paul is either calm or not old and vice versa.
If john is humble then alice is both creative and not curious.
Everyone who is not patient is both tall and not tall.
Everyone who is not old or wise is not humble and vice versa.
Everyone who is not brave or not strong is not happy and vice versa.
If someone is both strong and not old then someone is not tall or tall and vice versa.
If lucy is either not curious or generous then lucy is patient or not wise and vice versa.
Alice is not rich or not tall.
Someone is both calm and not humble.
John is humble or brave.
Susan is either not curious or not old.
Someone is either strong or curious. | Lucy is funny. | neutral | (![X]:((~tall(X)|~funny(X))<=>(~quiet(X)&patient(X))))&
(![X]:((~quiet(X)&~patient(X))<=>(~generous(X)<~>patient(X))))&
(((calm(paul)<~>~brave(paul)))<=>(?[X]:((humble(X)&~brave(X)))))&
((?[X]:(~kind(X)))<=>((~brave(susan)<~>~old(susan))))&
(![X]:((rich(X)&~humble(X))=>(~calm(X)&tall(X))))&
((?[X]:((~funny(X)&strong(X))))=>((brave(paul)|kind(paul))))&
((?[X]:(generous(X)))=>((happy(lucy)&strong(lucy))))&
((happy(lucy))<=>(?[X]:((brave(X)&~creative(X)))))&
(![X]:(~patient(X)<=>~strong(X)))&
(((~brave(paul)|~happy(paul)))<=>((calm(paul)<~>~old(paul))))&
((humble(john))=>((creative(alice)&~curious(alice))))&
(![X]:(~patient(X)=>(tall(X)&~tall(X))))&
(![X]:((~old(X)|wise(X))<=>~humble(X)))&
(![X]:((~brave(X)|~strong(X))<=>~happy(X)))&
((?[X]:((strong(X)&~old(X))))<=>(?[X]:((~tall(X)|tall(X)))))&
(((~curious(lucy)<~>generous(lucy)))<=>((patient(lucy)|~wise(lucy))))&
((~rich(alice)|~tall(alice)))&
(?[X]:((calm(X)&~humble(X))))&
((humble(john)|brave(john)))&
((~curious(susan)<~>~old(susan)))&
(?[X]:((strong(X)<~>curious(X)))) | funny(lucy) | [] | null | 0 |
Everyone who is curious is not funny and vice versa.
If alice is both not generous and strong then john is both not tall and not quiet.
If someone is brave or quiet then alice is either not strong or wise.
If someone is both not happy and not quiet then someone is patient or not kind.
If someone is both not strong and not wise then paul is either not calm or not happy and vice versa.
If mary is both not strong and rich then lucy is both kind and brave and vice versa.
Everyone who is both not creative and generous is not quiet or not generous and vice versa.
Everyone who is either not happy or rich is either not tall or patient and vice versa.
If someone is calm then susan is either not funny or not creative.
Everyone who is either not quiet or kind is not calm or not kind.
Everyone who is either not strong or not happy is not quiet or kind and vice versa.
Everyone who is not wise is old.
If someone is both wise and brave then someone is not happy or quiet and vice versa.
If someone is either strong or old then fred is strong or not curious and vice versa.
Everyone who is humble or not tall is either not quiet or not tall and vice versa.
Everyone who is funny or not funny is either strong or not strong.
Someone is both not patient and not tall.
Someone is generous.
Someone is not creative or humble.
Alice is both not patient and not old.
John is not curious or not brave.
Someone is both not quiet and not kind. | John is kind. | neutral | (![X]:(curious(X)<=>~funny(X)))&
(((~generous(alice)&strong(alice)))=>((~tall(john)&~quiet(john))))&
((?[X]:((brave(X)|quiet(X))))=>((~strong(alice)<~>wise(alice))))&
((?[X]:((~happy(X)&~quiet(X))))=>(?[X]:((patient(X)|~kind(X)))))&
((?[X]:((~strong(X)&~wise(X))))<=>((~calm(paul)<~>~happy(paul))))&
(((~strong(mary)&rich(mary)))<=>((kind(lucy)&brave(lucy))))&
(![X]:((~creative(X)&generous(X))<=>(~quiet(X)|~generous(X))))&
(![X]:((~happy(X)<~>rich(X))<=>(~tall(X)<~>patient(X))))&
((?[X]:(calm(X)))=>((~funny(susan)<~>~creative(susan))))&
(![X]:((~quiet(X)<~>kind(X))=>(~calm(X)|~kind(X))))&
(![X]:((~strong(X)<~>~happy(X))<=>(~quiet(X)|kind(X))))&
(![X]:(~wise(X)=>old(X)))&
((?[X]:((wise(X)&brave(X))))<=>(?[X]:((~happy(X)|quiet(X)))))&
((?[X]:((strong(X)<~>old(X))))<=>((strong(fred)|~curious(fred))))&
(![X]:((humble(X)|~tall(X))<=>(~quiet(X)<~>~tall(X))))&
(![X]:((funny(X)|~funny(X))=>(strong(X)<~>~strong(X))))&
(?[X]:((~patient(X)&~tall(X))))&
(?[X]:(generous(X)))&
(?[X]:((~creative(X)|humble(X))))&
((~patient(alice)&~old(alice)))&
((~curious(john)|~brave(john)))&
(?[X]:((~quiet(X)&~kind(X)))) | kind(john) | [] | null | 0 |
If mary is not rich or brave then someone is not generous or not creative and vice versa. Everyone who is not generous or not kind is humble and vice versa. Everyone who is both creative and not humble is both not curious and brave and vice versa. Everyone who is brave is either patient or not creative and vice versa. Everyone who is not wise is quiet or not creative. If someone is generous or not curious then someone is both brave and not humble and vice versa. If mary is either not kind or happy then fred is not creative and vice versa. Everyone who is both not rich and not quiet is both not generous and tall. If someone is both not creative and not curious then someone is creative or kind and vice versa. If lucy is either not calm or not patient then someone is either not strong or not tall and vice versa. Everyone who is patient is not funny. Everyone who is either not wise or generous is both funny and not rich. If susan is either not brave or generous then someone is generous or not brave and vice versa. If someone is not strong or not calm then someone is tall or calm. If someone is either brave or not generous then fred is both not happy and happy. If fred is tall or funny then someone is calm or generous. Someone is happy. Someone is not tall. Fred is brave. Susan is both not quiet and strong. John is wise. Fred is both tall and curious. Mary is both not generous and not patient. | Mary is not creative. | entailment | (((~rich(mary)|brave(mary)))<=>(?[X]:((~generous(X)|~creative(X)))))&
(![X]:((~generous(X)|~kind(X))<=>humble(X)))&
(![X]:((creative(X)&~humble(X))<=>(~curious(X)&brave(X))))&
(![X]:(brave(X)<=>(patient(X)<~>~creative(X))))&
(![X]:(~wise(X)=>(quiet(X)|~creative(X))))&
((?[X]:((generous(X)|~curious(X))))<=>(?[X]:((brave(X)&~humble(X)))))&
(((~kind(mary)<~>happy(mary)))<=>(~creative(fred)))&
(![X]:((~rich(X)&~quiet(X))=>(~generous(X)&tall(X))))&
((?[X]:((~creative(X)&~curious(X))))<=>(?[X]:((creative(X)|kind(X)))))&
(((~calm(lucy)<~>~patient(lucy)))<=>(?[X]:((~strong(X)<~>~tall(X)))))&
(![X]:(patient(X)=>~funny(X)))&
(![X]:((~wise(X)<~>generous(X))=>(funny(X)&~rich(X))))&
(((~brave(susan)<~>generous(susan)))<=>(?[X]:((generous(X)|~brave(X)))))&
((?[X]:((~strong(X)|~calm(X))))=>(?[X]:((tall(X)|calm(X)))))&
((?[X]:((brave(X)<~>~generous(X))))=>((~happy(fred)&happy(fred))))&
(((tall(fred)|funny(fred)))=>(?[X]:((calm(X)|generous(X)))))&
(?[X]:(happy(X)))&
(?[X]:(~tall(X)))&
(brave(fred))&
((~quiet(susan)&strong(susan)))&
(wise(john))&
((tall(fred)&curious(fred)))&
((~generous(mary)&~patient(mary))) | ~creative(mary) | [
"p1",
"p5",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5347563949617456704431873
% SZS output start Proof for 5347563949617456704431873
2. ! [X0] : ((~kind(X0) | ~generous(X0)) <=> humble(X0)) [input p1]
6. ? [X0] : (~curious(X0) | generous(X0)) <=> ? [X0] : (~humble(X0) & brave(X0)) [input p5]
9. ? [X0] : (~curious(X0) & ~creative(X0)) <=> ? [X0] : (kind(X0) | creative(X0)) [input p8]
15. ? [X0] : (brave(X0) <~> ~generous(X0)) => (happy(fred) & ~happy(fred)) [input p14]
24. creative(mary) [input hypothesis]
25. ? [X0] : (~curious(X0) | generous(X0)) <=> ? [X1] : (~humble(X1) & brave(X1)) [rectify 6]
26. ? [X0] : (~curious(X0) & ~creative(X0)) <=> ? [X1] : (kind(X1) | creative(X1)) [rectify 9]
35. (happy(fred) & ~happy(fred)) | ! [X0] : (brave(X0) <=> ~generous(X0)) [ennf transformation 15]
42. ! [X0] : (((~kind(X0) | ~generous(X0)) | ~humble(X0)) & (humble(X0) | (kind(X0) & generous(X0)))) [nnf transformation 2]
43. ! [X0] : ((~kind(X0) | ~generous(X0) | ~humble(X0)) & (humble(X0) | (kind(X0) & generous(X0)))) [flattening 42]
47. (? [X0] : (~curious(X0) | generous(X0)) | ! [X1] : (humble(X1) | ~brave(X1))) & (? [X1] : (~humble(X1) & brave(X1)) | ! [X0] : (curious(X0) & ~generous(X0))) [nnf transformation 25]
48. (? [X0] : (~curious(X0) | generous(X0)) | ! [X1] : (humble(X1) | ~brave(X1))) & (? [X2] : (~humble(X2) & brave(X2)) | ! [X3] : (curious(X3) & ~generous(X3))) [rectify 47]
49. ? [X0] : (~curious(X0) | generous(X0)) => (~curious(sK1) | generous(sK1)) [choice axiom]
50. ? [X2] : (~humble(X2) & brave(X2)) => (~humble(sK2) & brave(sK2)) [choice axiom]
51. ((~curious(sK1) | generous(sK1)) | ! [X1] : (humble(X1) | ~brave(X1))) & ((~humble(sK2) & brave(sK2)) | ! [X3] : (curious(X3) & ~generous(X3))) [skolemisation 48,50,49]
53. (? [X0] : (~curious(X0) & ~creative(X0)) | ! [X1] : (~kind(X1) & ~creative(X1))) & (? [X1] : (kind(X1) | creative(X1)) | ! [X0] : (curious(X0) | creative(X0))) [nnf transformation 26]
54. (? [X0] : (~curious(X0) & ~creative(X0)) | ! [X1] : (~kind(X1) & ~creative(X1))) & (? [X2] : (kind(X2) | creative(X2)) | ! [X3] : (curious(X3) | creative(X3))) [rectify 53]
55. ? [X0] : (~curious(X0) & ~creative(X0)) => (~curious(sK3) & ~creative(sK3)) [choice axiom]
56. ? [X2] : (kind(X2) | creative(X2)) => (kind(sK4) | creative(sK4)) [choice axiom]
57. ((~curious(sK3) & ~creative(sK3)) | ! [X1] : (~kind(X1) & ~creative(X1))) & ((kind(sK4) | creative(sK4)) | ! [X3] : (curious(X3) | creative(X3))) [skolemisation 54,56,55]
70. (happy(fred) & ~happy(fred)) | ! [X0] : ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0))) [nnf transformation 35]
81. humble(X0) | generous(X0) [cnf transformation 43]
94. brave(sK2) | curious(X3) [cnf transformation 51]
96. ~humble(sK2) | curious(X3) [cnf transformation 51]
107. ~curious(sK3) | ~creative(X1) [cnf transformation 57]
130. ~happy(fred) | ~generous(X0) | ~brave(X0) [cnf transformation 70]
132. happy(fred) | ~generous(X0) | ~brave(X0) [cnf transformation 70]
146. creative(mary) [cnf transformation 24]
186. 10 <=> ! [X3] : curious(X3) [avatar definition]
187. curious(X3) <- (10) [avatar component clause 186]
189. 11 <=> humble(sK2) [avatar definition]
191. ~humble(sK2) <- (~11) [avatar component clause 189]
192. 10 | ~11 [avatar split clause 96,189,186]
198. 13 <=> brave(sK2) [avatar definition]
200. brave(sK2) <- (13) [avatar component clause 198]
201. 10 | 13 [avatar split clause 94,198,186]
223. 18 <=> curious(sK3) [avatar definition]
225. ~curious(sK3) <- (~18) [avatar component clause 223]
228. 19 <=> ! [X1] : ~creative(X1) [avatar definition]
229. ~creative(X1) <- (19) [avatar component clause 228]
230. 19 | ~18 [avatar split clause 107,223,228]
324. 40 <=> happy(fred) [avatar definition]
329. 41 <=> ! [X0] : (~generous(X0) | ~brave(X0)) [avatar definition]
330. ~generous(X0) | ~brave(X0) <- (41) [avatar component clause 329]
331. 41 | 40 [avatar split clause 132,324,329]
333. 41 | ~40 [avatar split clause 130,324,329]
353. generous(sK2) <- (~11) [resolution 81,191]
375. ~brave(sK2) <- (~11, 41) [resolution 330,353]
378. $false <- (~11, 13, 41) [subsumption resolution 375,200]
379. 11 | ~13 | ~41 [avatar contradiction clause 378]
383. $false <- (10, ~18) [resolution 187,225]
384. ~10 | 18 [avatar contradiction clause 383]
388. $false <- (19) [resolution 229,146]
391. ~19 [avatar contradiction clause 388]
392. $false [avatar sat refutation 192,201,230,331,333,379,384,391]
% SZS output end Proof for 5347563949617456704431873
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not brave or patient is not quiet or not kind. Everyone who is not kind or not humble is either not happy or strong. Everyone who is both not quiet and not creative is both not kind and quiet and vice versa. If someone is generous or not brave then alice is not curious or not creative. If mary is either not old or not happy then someone is not rich or not curious. Everyone who is brave or rich is calm or not tall. If someone is either not quiet or curious then someone is patient and vice versa. Everyone who is calm or wise is humble or not kind. If someone is either not tall or not funny then fred is either old or funny and vice versa. Everyone who is not brave is either wise or patient and vice versa. If fred is either not brave or not strong then someone is either happy or rich. If someone is not quiet then alice is not creative and vice versa. If lucy is not strong then someone is not calm or not happy and vice versa. Everyone who is not calm is not brave or not patient. If lucy is not quiet or strong then lucy is both wise and not humble and vice versa. If susan is patient then fred is either generous or calm. Someone is strong. Lucy is both not wise and not funny. Someone is quiet or not wise. Someone is not tall. Someone is not patient. Someone is either not funny or not generous. Someone is not wise. | Alice is creative. | neutral | (![X]:((~brave(X)|patient(X))=>(~quiet(X)|~kind(X))))&
(![X]:((~kind(X)|~humble(X))=>(~happy(X)<~>strong(X))))&
(![X]:((~quiet(X)&~creative(X))<=>(~kind(X)&quiet(X))))&
((?[X]:((generous(X)|~brave(X))))=>((~curious(alice)|~creative(alice))))&
(((~old(mary)<~>~happy(mary)))=>(?[X]:((~rich(X)|~curious(X)))))&
(![X]:((brave(X)|rich(X))=>(calm(X)|~tall(X))))&
((?[X]:((~quiet(X)<~>curious(X))))<=>(?[X]:(patient(X))))&
(![X]:((calm(X)|wise(X))=>(humble(X)|~kind(X))))&
((?[X]:((~tall(X)<~>~funny(X))))<=>((old(fred)<~>funny(fred))))&
(![X]:(~brave(X)<=>(wise(X)<~>patient(X))))&
(((~brave(fred)<~>~strong(fred)))=>(?[X]:((happy(X)<~>rich(X)))))&
((?[X]:(~quiet(X)))<=>(~creative(alice)))&
((~strong(lucy))<=>(?[X]:((~calm(X)|~happy(X)))))&
(![X]:(~calm(X)=>(~brave(X)|~patient(X))))&
(((~quiet(lucy)|strong(lucy)))<=>((wise(lucy)&~humble(lucy))))&
((patient(susan))=>((generous(fred)<~>calm(fred))))&
(?[X]:(strong(X)))&
((~wise(lucy)&~funny(lucy)))&
(?[X]:((quiet(X)|~wise(X))))&
(?[X]:(~tall(X)))&
(?[X]:(~patient(X)))&
(?[X]:((~funny(X)<~>~generous(X))))&
(?[X]:(~wise(X))) | creative(alice) | [] | null | 0 |
If john is both tall and brave then john is patient and vice versa. Everyone who is either curious or not funny is not kind and vice versa. Everyone who is rich or not wise is not kind or generous. Everyone who is kind is not creative or old and vice versa. Everyone who is not funny or not brave is both not happy and curious. Everyone who is not wise is generous and vice versa. Everyone who is tall or patient is both funny and kind and vice versa. If someone is tall or not calm then susan is either rich or not strong. Everyone who is either generous or not strong is not kind. If someone is not curious then alice is both patient and not wise and vice versa. Everyone who is patient is not old or creative. If paul is either tall or not kind then someone is not kind. Everyone who is wise or not strong is rich or not kind. Everyone who is happy or not humble is both humble and not patient and vice versa. If mary is humble then someone is either not humble or not patient. If mary is kind or not curious then john is either not funny or wise. Someone is not kind. Lucy is kind or not patient. Alice is both not happy and not tall. Someone is either not old or not patient. Fred is either quiet or not old. Someone is happy or curious. | Paul is not funny. | contradiction | (((tall(john)&brave(john)))<=>(patient(john)))&
(![X]:((curious(X)<~>~funny(X))<=>~kind(X)))&
(![X]:((rich(X)|~wise(X))=>(~kind(X)|generous(X))))&
(![X]:(kind(X)<=>(~creative(X)|old(X))))&
(![X]:((~funny(X)|~brave(X))=>(~happy(X)&curious(X))))&
(![X]:(~wise(X)<=>generous(X)))&
(![X]:((tall(X)|patient(X))<=>(funny(X)&kind(X))))&
((?[X]:((tall(X)|~calm(X))))=>((rich(susan)<~>~strong(susan))))&
(![X]:((generous(X)<~>~strong(X))=>~kind(X)))&
((?[X]:(~curious(X)))<=>((patient(alice)&~wise(alice))))&
(![X]:(patient(X)=>(~old(X)|creative(X))))&
(((tall(paul)<~>~kind(paul)))=>(?[X]:(~kind(X))))&
(![X]:((wise(X)|~strong(X))=>(rich(X)|~kind(X))))&
(![X]:((happy(X)|~humble(X))<=>(humble(X)&~patient(X))))&
((humble(mary))=>(?[X]:((~humble(X)<~>~patient(X)))))&
(((kind(mary)|~curious(mary)))=>((~funny(john)<~>wise(john))))&
(?[X]:(~kind(X)))&
((kind(lucy)|~patient(lucy)))&
((~happy(alice)&~tall(alice)))&
(?[X]:((~old(X)<~>~patient(X))))&
((quiet(fred)<~>~old(fred)))&
(?[X]:((happy(X)|curious(X)))) | ~funny(paul) | [
"p4",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3421695344632707817367598
% SZS output start Proof for 3421695344632707817367598
5. ! [X0] : ((~brave(X0) | ~funny(X0)) => (curious(X0) & ~happy(X0))) [input p4]
7. ! [X0] : ((patient(X0) | tall(X0)) <=> (kind(X0) & funny(X0))) [input p6]
14. ! [X0] : ((~humble(X0) | happy(X0)) <=> (~patient(X0) & humble(X0))) [input p13]
23. ~funny(paul) [input hypothesis]
27. ! [X0] : ((curious(X0) & ~happy(X0)) | (brave(X0) & funny(X0))) [ennf transformation 5]
43. ! [X0] : (((patient(X0) | tall(X0)) | (~kind(X0) | ~funny(X0))) & ((kind(X0) & funny(X0)) | (~patient(X0) & ~tall(X0)))) [nnf transformation 7]
44. ! [X0] : ((patient(X0) | tall(X0) | ~kind(X0) | ~funny(X0)) & ((kind(X0) & funny(X0)) | (~patient(X0) & ~tall(X0)))) [flattening 43]
55. ! [X0] : (((~humble(X0) | happy(X0)) | (patient(X0) | ~humble(X0))) & ((~patient(X0) & humble(X0)) | (humble(X0) & ~happy(X0)))) [nnf transformation 14]
56. ! [X0] : ((~humble(X0) | happy(X0) | patient(X0) | ~humble(X0)) & ((~patient(X0) & humble(X0)) | (humble(X0) & ~happy(X0)))) [flattening 55]
81. ~happy(X0) | funny(X0) [cnf transformation 27]
88. ~patient(X0) | funny(X0) [cnf transformation 44]
105. humble(X0) | humble(X0) [cnf transformation 56]
108. ~humble(X0) | happy(X0) | patient(X0) | ~humble(X0) [cnf transformation 56]
124. ~funny(paul) [cnf transformation 23]
125. humble(X0) [duplicate literal removal 105]
126. ~humble(X0) | happy(X0) | patient(X0) [duplicate literal removal 108]
347. happy(X0) | patient(X0) [resolution 126,125]
380. patient(X2) | funny(X2) [resolution 347,81]
383. funny(X2) [subsumption resolution 380,88]
428. $false [resolution 383,124]
% SZS output end Proof for 3421695344632707817367598
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is not rich or not funny and vice versa.
Everyone who is both not rich and quiet is both happy and old and vice versa.
Everyone who is not creative or creative is not old or quiet and vice versa.
Everyone who is quiet is curious or not brave and vice versa.
Everyone who is creative or not kind is not wise or not curious.
If lucy is wise or not brave then someone is not happy or not funny and vice versa.
Everyone who is not creative or strong is both not tall and patient.
If someone is old or not funny then mary is old.
If alice is both generous and old then susan is humble and vice versa.
Everyone who is wise or not old is either rich or not humble.
Everyone who is both not strong and brave is strong or old.
If someone is either patient or not rich then john is both not quiet and not patient.
If alice is either rich or creative then mary is either not generous or humble.
Everyone who is not kind or generous is not kind.
Everyone who is calm is not rich or not happy.
Everyone who is kind or not patient is humble.
Fred is not humble or kind.
Alice is patient or rich.
Someone is brave or not funny.
Someone is tall.
Someone is either not wise or strong.
Someone is either not rich or not happy. | Lucy is not brave. | entailment | (![X]:(rich(X)<=>(~rich(X)|~funny(X))))&
(![X]:((~rich(X)&quiet(X))<=>(happy(X)&old(X))))&
(![X]:((~creative(X)|creative(X))<=>(~old(X)|quiet(X))))&
(![X]:(quiet(X)<=>(curious(X)|~brave(X))))&
(![X]:((creative(X)|~kind(X))=>(~wise(X)|~curious(X))))&
(((wise(lucy)|~brave(lucy)))<=>(?[X]:((~happy(X)|~funny(X)))))&
(![X]:((~creative(X)|strong(X))=>(~tall(X)&patient(X))))&
((?[X]:((old(X)|~funny(X))))=>(old(mary)))&
(((generous(alice)&old(alice)))<=>(humble(susan)))&
(![X]:((wise(X)|~old(X))=>(rich(X)<~>~humble(X))))&
(![X]:((~strong(X)&brave(X))=>(strong(X)|old(X))))&
((?[X]:((patient(X)<~>~rich(X))))=>((~quiet(john)&~patient(john))))&
(((rich(alice)<~>creative(alice)))=>((~generous(mary)<~>humble(mary))))&
(![X]:((~kind(X)|generous(X))=>~kind(X)))&
(![X]:(calm(X)=>(~rich(X)|~happy(X))))&
(![X]:((kind(X)|~patient(X))=>humble(X)))&
((~humble(fred)|kind(fred)))&
((patient(alice)|rich(alice)))&
(?[X]:((brave(X)|~funny(X))))&
(?[X]:(tall(X)))&
(?[X]:((~wise(X)<~>strong(X))))&
(?[X]:((~rich(X)<~>~happy(X)))) | ~brave(lucy) | [
"p0",
"p2",
"p3",
"p4",
"p5",
"p6",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8129601204394482868471577
% SZS output start Proof for 8129601204394482868471577
1. ! [X0] : (rich(X0) <=> (~funny(X0) | ~rich(X0))) [input p0]
3. ! [X0] : ((creative(X0) | ~creative(X0)) <=> (quiet(X0) | ~old(X0))) [input p2]
4. ! [X0] : (quiet(X0) <=> (~brave(X0) | curious(X0))) [input p3]
5. ! [X0] : ((~kind(X0) | creative(X0)) => (~curious(X0) | ~wise(X0))) [input p4]
6. (~brave(lucy) | wise(lucy)) <=> ? [X0] : (~funny(X0) | ~happy(X0)) [input p5]
7. ! [X0] : ((strong(X0) | ~creative(X0)) => (patient(X0) & ~tall(X0))) [input p6]
11. ! [X0] : ((brave(X0) & ~strong(X0)) => (old(X0) | strong(X0))) [input p10]
12. ? [X0] : (patient(X0) <~> ~rich(X0)) => (~patient(john) & ~quiet(john)) [input p11]
23. brave(lucy) [input hypothesis]
25. ! [X0] : ((~curious(X0) | ~wise(X0)) | (kind(X0) & ~creative(X0))) [ennf transformation 5]
26. ! [X0] : (~curious(X0) | ~wise(X0) | (kind(X0) & ~creative(X0))) [flattening 25]
27. ! [X0] : ((patient(X0) & ~tall(X0)) | (~strong(X0) & creative(X0))) [ennf transformation 7]
30. ! [X0] : ((old(X0) | strong(X0)) | (~brave(X0) | strong(X0))) [ennf transformation 11]
31. ! [X0] : (old(X0) | strong(X0) | ~brave(X0) | strong(X0)) [flattening 30]
32. (~patient(john) & ~quiet(john)) | ! [X0] : (patient(X0) <=> ~rich(X0)) [ennf transformation 12]
36. ! [X0] : ((rich(X0) | (funny(X0) & rich(X0))) & ((~funny(X0) | ~rich(X0)) | ~rich(X0))) [nnf transformation 1]
37. ! [X0] : ((rich(X0) | (funny(X0) & rich(X0))) & (~funny(X0) | ~rich(X0) | ~rich(X0))) [flattening 36]
40. ! [X0] : (((creative(X0) | ~creative(X0)) | (~quiet(X0) & old(X0))) & ((quiet(X0) | ~old(X0)) | (~creative(X0) & creative(X0)))) [nnf transformation 3]
41. ! [X0] : ((creative(X0) | ~creative(X0) | (~quiet(X0) & old(X0))) & (quiet(X0) | ~old(X0) | (~creative(X0) & creative(X0)))) [flattening 40]
42. ! [X0] : ((quiet(X0) | (brave(X0) & ~curious(X0))) & ((~brave(X0) | curious(X0)) | ~quiet(X0))) [nnf transformation 4]
43. ! [X0] : ((quiet(X0) | (brave(X0) & ~curious(X0))) & (~brave(X0) | curious(X0) | ~quiet(X0))) [flattening 42]
44. ((~brave(lucy) | wise(lucy)) | ! [X0] : (funny(X0) & happy(X0))) & (? [X0] : (~funny(X0) | ~happy(X0)) | (brave(lucy) & ~wise(lucy))) [nnf transformation 6]
45. (~brave(lucy) | wise(lucy) | ! [X0] : (funny(X0) & happy(X0))) & (? [X0] : (~funny(X0) | ~happy(X0)) | (brave(lucy) & ~wise(lucy))) [flattening 44]
46. (~brave(lucy) | wise(lucy) | ! [X0] : (funny(X0) & happy(X0))) & (? [X1] : (~funny(X1) | ~happy(X1)) | (brave(lucy) & ~wise(lucy))) [rectify 45]
47. ? [X1] : (~funny(X1) | ~happy(X1)) => (~funny(sK0) | ~happy(sK0)) [choice axiom]
48. (~brave(lucy) | wise(lucy) | ! [X0] : (funny(X0) & happy(X0))) & ((~funny(sK0) | ~happy(sK0)) | (brave(lucy) & ~wise(lucy))) [skolemisation 46,47]
52. (~patient(john) & ~quiet(john)) | ! [X0] : ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0))) [nnf transformation 32]
64. ~funny(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 37]
65. rich(X0) | rich(X0) [cnf transformation 37]
71. quiet(X0) | ~old(X0) | creative(X0) [cnf transformation 41]
72. ~creative(X0) | ~old(X0) | quiet(X0) [cnf transformation 41]
75. ~brave(X0) | curious(X0) | ~quiet(X0) [cnf transformation 43]
77. brave(X0) | quiet(X0) [cnf transformation 43]
78. ~wise(X0) | ~curious(X0) | ~creative(X0) [cnf transformation 26]
83. ~brave(lucy) | wise(lucy) | funny(X0) [cnf transformation 48]
86. patient(X0) | creative(X0) [cnf transformation 27]
87. ~strong(X0) | patient(X0) [cnf transformation 27]
97. old(X0) | strong(X0) | ~brave(X0) | strong(X0) [cnf transformation 31]
98. ~quiet(john) | ~rich(X0) | ~patient(X0) [cnf transformation 52]
100. ~patient(john) | ~rich(X0) | ~patient(X0) [cnf transformation 52]
118. brave(lucy) [cnf transformation 23]
119. ~brave(X0) | strong(X0) | old(X0) [duplicate literal removal 97]
120. ~funny(X0) | ~rich(X0) [duplicate literal removal 64]
121. rich(X0) [duplicate literal removal 65]
122. ~funny(X0) [subsumption resolution 120,121]
124. ~old(X0) | quiet(X0) [subsumption resolution 71,72]
125. ~brave(lucy) | wise(lucy) [subsumption resolution 83,122]
127. 1 <=> wise(lucy) [avatar definition]
129. wise(lucy) <- (1) [avatar component clause 127]
131. 2 <=> brave(lucy) [avatar definition]
132. brave(lucy) <- (2) [avatar component clause 131]
134. 1 | ~2 [avatar split clause 125,131,127]
157. ~patient(john) | ~patient(X0) [subsumption resolution 100,121]
159. 7 <=> ! [X0] : ~patient(X0) [avatar definition]
160. ~patient(X0) <- (7) [avatar component clause 159]
162. 8 <=> patient(john) [avatar definition]
164. ~patient(john) <- (~8) [avatar component clause 162]
165. 7 | ~8 [avatar split clause 157,162,159]
166. ~quiet(john) | ~patient(X0) [subsumption resolution 98,121]
168. 9 <=> quiet(john) [avatar definition]
171. 7 | ~9 [avatar split clause 166,168,159]
208. 2 [avatar split clause 118,131]
239. curious(lucy) | ~quiet(lucy) <- (2) [resolution 75,132]
242. 19 <=> quiet(lucy) [avatar definition]
246. 20 <=> curious(lucy) [avatar definition]
249. ~19 | 20 | ~2 [avatar split clause 239,131,246,242]
265. ~curious(lucy) | ~creative(lucy) <- (1) [resolution 78,129]
267. 23 <=> creative(lucy) [avatar definition]
269. ~creative(lucy) <- (~23) [avatar component clause 267]
270. ~23 | ~20 | ~1 [avatar split clause 265,127,246,267]
272. strong(lucy) | old(lucy) <- (2) [resolution 119,132]
273. strong(X0) | old(X0) | quiet(X0) [resolution 119,77]
275. 24 <=> old(lucy) [avatar definition]
277. old(lucy) <- (24) [avatar component clause 275]
279. 25 <=> strong(lucy) [avatar definition]
281. strong(lucy) <- (25) [avatar component clause 279]
282. 24 | 25 | ~2 [avatar split clause 272,131,279,275]
283. strong(X0) | quiet(X0) [subsumption resolution 273,124]
285. quiet(lucy) <- (24) [resolution 277,124]
290. 19 | ~24 [avatar split clause 285,275,242]
296. patient(lucy) <- (25) [resolution 281,87]
299. patient(X0) | quiet(X0) [resolution 283,87]
300. quiet(john) <- (~8) [resolution 299,164]
303. 9 | 8 [avatar split clause 300,162,168]
305. creative(X1) <- (7) [resolution 160,86]
306. $false <- (7, 25) [resolution 160,296]
311. ~7 | ~25 [avatar contradiction clause 306]
323. $false <- (7, ~23) [resolution 305,269]
324. ~7 | 23 [avatar contradiction clause 323]
325. $false [avatar sat refutation 134,165,171,208,249,270,282,290,303,311,324]
% SZS output end Proof for 8129601204394482868471577
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is not funny.
Everyone who is both curious and generous is both tall and not old and vice versa.
Everyone who is either not patient or creative is patient or strong.
Everyone who is not strong or old is both not kind and quiet.
If mary is both quiet and not generous then someone is old or not strong.
Everyone who is old or not calm is happy.
Everyone who is patient or not calm is not wise and vice versa.
Everyone who is either kind or humble is not wise or brave.
If john is curious then someone is not creative or funny and vice versa.
Everyone who is rich is funny or strong and vice versa.
If someone is funny then john is not rich or not old.
Everyone who is calm or patient is both strong and not old and vice versa.
Everyone who is both wise and not happy is not humble or funny.
Everyone who is creative or not brave is patient and vice versa.
If someone is not quiet or not kind then someone is not wise or not calm.
If fred is both not kind and rich then someone is happy or wise and vice versa.
Someone is old or creative.
Someone is either quiet or not generous.
Someone is either wise or curious.
Someone is both not quiet and not generous.
Susan is not creative or not rich.
Someone is both creative and not kind.
Someone is not calm or wise. | Mary is creative. | neutral | (![X]:(~kind(X)=>~funny(X)))&
(![X]:((curious(X)&generous(X))<=>(tall(X)&~old(X))))&
(![X]:((~patient(X)<~>creative(X))=>(patient(X)|strong(X))))&
(![X]:((~strong(X)|old(X))=>(~kind(X)&quiet(X))))&
(((quiet(mary)&~generous(mary)))=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((old(X)|~calm(X))=>happy(X)))&
(![X]:((patient(X)|~calm(X))<=>~wise(X)))&
(![X]:((kind(X)<~>humble(X))=>(~wise(X)|brave(X))))&
((curious(john))<=>(?[X]:((~creative(X)|funny(X)))))&
(![X]:(rich(X)<=>(funny(X)|strong(X))))&
((?[X]:(funny(X)))=>((~rich(john)|~old(john))))&
(![X]:((calm(X)|patient(X))<=>(strong(X)&~old(X))))&
(![X]:((wise(X)&~happy(X))=>(~humble(X)|funny(X))))&
(![X]:((creative(X)|~brave(X))<=>patient(X)))&
((?[X]:((~quiet(X)|~kind(X))))=>(?[X]:((~wise(X)|~calm(X)))))&
(((~kind(fred)&rich(fred)))<=>(?[X]:((happy(X)|wise(X)))))&
(?[X]:((old(X)|creative(X))))&
(?[X]:((quiet(X)<~>~generous(X))))&
(?[X]:((wise(X)<~>curious(X))))&
(?[X]:((~quiet(X)&~generous(X))))&
((~creative(susan)|~rich(susan)))&
(?[X]:((creative(X)&~kind(X))))&
(?[X]:((~calm(X)|wise(X)))) | creative(mary) | [] | null | 0 |
Everyone who is not strong is not wise or not brave and vice versa.
If someone is either rich or happy then someone is either brave or not patient and vice versa.
If someone is not happy then someone is both generous and not brave and vice versa.
If someone is either brave or curious then someone is not tall.
If mary is not brave or wise then paul is both kind and not wise.
If lucy is funny or humble then someone is either strong or not brave and vice versa.
Everyone who is both generous and not calm is both quiet and old.
Everyone who is calm is both not calm and not funny.
Everyone who is either brave or not funny is either not creative or not wise.
Everyone who is curious or patient is both calm and not wise and vice versa.
Everyone who is either not calm or not generous is not happy or not old.
If lucy is funny or not tall then mary is old and vice versa.
Everyone who is either rich or not patient is patient.
If someone is both humble and rich then paul is both kind and not brave and vice versa.
Everyone who is humble is not creative.
Everyone who is tall is either strong or patient.
Someone is both humble and funny.
Fred is both not generous and old.
Susan is not strong.
Lucy is not creative.
Fred is both kind and not funny.
Lucy is either old or not funny. | Susan is not rich. | contradiction | (![X]:(~strong(X)<=>(~wise(X)|~brave(X))))&
((?[X]:((rich(X)<~>happy(X))))<=>(?[X]:((brave(X)<~>~patient(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:((generous(X)&~brave(X)))))&
((?[X]:((brave(X)<~>curious(X))))=>(?[X]:(~tall(X))))&
(((~brave(mary)|wise(mary)))=>((kind(paul)&~wise(paul))))&
(((funny(lucy)|humble(lucy)))<=>(?[X]:((strong(X)<~>~brave(X)))))&
(![X]:((generous(X)&~calm(X))=>(quiet(X)&old(X))))&
(![X]:(calm(X)=>(~calm(X)&~funny(X))))&
(![X]:((brave(X)<~>~funny(X))=>(~creative(X)<~>~wise(X))))&
(![X]:((curious(X)|patient(X))<=>(calm(X)&~wise(X))))&
(![X]:((~calm(X)<~>~generous(X))=>(~happy(X)|~old(X))))&
(((funny(lucy)|~tall(lucy)))<=>(old(mary)))&
(![X]:((rich(X)<~>~patient(X))=>patient(X)))&
((?[X]:((humble(X)&rich(X))))<=>((kind(paul)&~brave(paul))))&
(![X]:(humble(X)=>~creative(X)))&
(![X]:(tall(X)=>(strong(X)<~>patient(X))))&
(?[X]:((humble(X)&funny(X))))&
((~generous(fred)&old(fred)))&
(~strong(susan))&
(~creative(lucy))&
((kind(fred)&~funny(fred)))&
((old(lucy)<~>~funny(lucy))) | ~rich(susan) | [
"p7",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7701085837149709731333863
% SZS output start Proof for 7701085837149709731333863
8. ! [X0] : (calm(X0) => (~funny(X0) & ~calm(X0))) [input p7]
10. ! [X0] : ((patient(X0) | curious(X0)) <=> (~wise(X0) & calm(X0))) [input p9]
13. ! [X0] : ((rich(X0) <~> ~patient(X0)) => patient(X0)) [input p12]
23. ~rich(susan) [input hypothesis]
32. ! [X0] : ((~funny(X0) & ~calm(X0)) | ~calm(X0)) [ennf transformation 8]
36. ! [X0] : (patient(X0) | (rich(X0) <=> ~patient(X0))) [ennf transformation 13]
61. ! [X0] : (((patient(X0) | curious(X0)) | (wise(X0) | ~calm(X0))) & ((~wise(X0) & calm(X0)) | (~patient(X0) & ~curious(X0)))) [nnf transformation 10]
62. ! [X0] : ((patient(X0) | curious(X0) | wise(X0) | ~calm(X0)) & ((~wise(X0) & calm(X0)) | (~patient(X0) & ~curious(X0)))) [flattening 61]
66. ! [X0] : (patient(X0) | ((rich(X0) | patient(X0)) & (~patient(X0) | ~rich(X0)))) [nnf transformation 36]
103. ~calm(X0) | ~calm(X0) [cnf transformation 32]
110. calm(X0) | ~patient(X0) [cnf transformation 62]
120. patient(X0) | rich(X0) | patient(X0) [cnf transformation 66]
138. ~rich(susan) [cnf transformation 23]
139. patient(X0) | rich(X0) [duplicate literal removal 120]
140. ~calm(X0) [duplicate literal removal 103]
258. ~patient(X0) [subsumption resolution 110,140]
272. rich(X0) [subsumption resolution 139,258]
296. $false [subsumption resolution 138,272]
% SZS output end Proof for 7701085837149709731333863
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or not calm is both not tall and not curious. Everyone who is either strong or wise is not wise or not kind and vice versa. If someone is calm then susan is both rich and wise. If someone is not calm then john is kind or quiet. Everyone who is either not humble or not strong is both tall and funny and vice versa. If lucy is old or generous then mary is both not humble and strong and vice versa. Everyone who is not calm or tall is not calm or curious and vice versa. Everyone who is both not tall and strong is quiet or strong and vice versa. If alice is tall or not patient then fred is not rich and vice versa. If fred is both wise and not creative then someone is not creative or not strong and vice versa. If someone is either old or not generous then fred is not wise. If someone is rich then paul is humble. If lucy is both not strong and curious then mary is either not strong or not wise. Everyone who is kind is both tall and brave and vice versa. If lucy is wise then someone is quiet. Everyone who is either not quiet or kind is not old. Someone is both creative and not brave. Susan is either generous or tall. Paul is either not kind or not brave. Lucy is either generous or humble. Someone is both not kind and not old. Susan is either patient or rich. | Alice is strong. | entailment | (![X]:((patient(X)|~calm(X))=>(~tall(X)&~curious(X))))&
(![X]:((strong(X)<~>wise(X))<=>(~wise(X)|~kind(X))))&
((?[X]:(calm(X)))=>((rich(susan)&wise(susan))))&
((?[X]:(~calm(X)))=>((kind(john)|quiet(john))))&
(![X]:((~humble(X)<~>~strong(X))<=>(tall(X)&funny(X))))&
(((old(lucy)|generous(lucy)))<=>((~humble(mary)&strong(mary))))&
(![X]:((~calm(X)|tall(X))<=>(~calm(X)|curious(X))))&
(![X]:((~tall(X)&strong(X))<=>(quiet(X)|strong(X))))&
(((tall(alice)|~patient(alice)))<=>(~rich(fred)))&
(((wise(fred)&~creative(fred)))<=>(?[X]:((~creative(X)|~strong(X)))))&
((?[X]:((old(X)<~>~generous(X))))=>(~wise(fred)))&
((?[X]:(rich(X)))=>(humble(paul)))&
(((~strong(lucy)&curious(lucy)))=>((~strong(mary)<~>~wise(mary))))&
(![X]:(kind(X)<=>(tall(X)&brave(X))))&
((wise(lucy))=>(?[X]:(quiet(X))))&
(![X]:((~quiet(X)<~>kind(X))=>~old(X)))&
(?[X]:((creative(X)&~brave(X))))&
((generous(susan)<~>tall(susan)))&
((~kind(paul)<~>~brave(paul)))&
((generous(lucy)<~>humble(lucy)))&
(?[X]:((~kind(X)&~old(X))))&
((patient(susan)<~>rich(susan))) | strong(alice) | [
"p4",
"p5",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2463172657462771248283021
% SZS output start Proof for 2463172657462771248283021
5. ! [X0] : ((~humble(X0) <~> ~strong(X0)) <=> (funny(X0) & tall(X0))) [input p4]
6. (generous(lucy) | old(lucy)) <=> (strong(mary) & ~humble(mary)) [input p5]
8. ! [X0] : ((strong(X0) & ~tall(X0)) <=> (strong(X0) | quiet(X0))) [input p7]
10. (~creative(fred) & wise(fred)) <=> ? [X0] : (~strong(X0) | ~creative(X0)) [input p9]
11. ? [X0] : (old(X0) <~> ~generous(X0)) => ~wise(fred) [input p10]
23. ~strong(alice) [input hypothesis]
28. ~wise(fred) | ! [X0] : (old(X0) <=> ~generous(X0)) [ennf transformation 11]
36. ! [X0] : ((((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | (~funny(X0) | ~tall(X0))) & ((funny(X0) & tall(X0)) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0))))) [nnf transformation 5]
37. ! [X0] : ((((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | ~funny(X0) | ~tall(X0)) & ((funny(X0) & tall(X0)) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0))))) [flattening 36]
38. ((generous(lucy) | old(lucy)) | (~strong(mary) | humble(mary))) & ((strong(mary) & ~humble(mary)) | (~generous(lucy) & ~old(lucy))) [nnf transformation 6]
39. (generous(lucy) | old(lucy) | ~strong(mary) | humble(mary)) & ((strong(mary) & ~humble(mary)) | (~generous(lucy) & ~old(lucy))) [flattening 38]
42. ! [X0] : (((strong(X0) & ~tall(X0)) | (~strong(X0) & ~quiet(X0))) & ((strong(X0) | quiet(X0)) | (~strong(X0) | tall(X0)))) [nnf transformation 8]
43. ! [X0] : (((strong(X0) & ~tall(X0)) | (~strong(X0) & ~quiet(X0))) & (strong(X0) | quiet(X0) | ~strong(X0) | tall(X0))) [flattening 42]
46. ((~creative(fred) & wise(fred)) | ! [X0] : (strong(X0) & creative(X0))) & (? [X0] : (~strong(X0) | ~creative(X0)) | (creative(fred) | ~wise(fred))) [nnf transformation 10]
47. ((~creative(fred) & wise(fred)) | ! [X0] : (strong(X0) & creative(X0))) & (? [X0] : (~strong(X0) | ~creative(X0)) | creative(fred) | ~wise(fred)) [flattening 46]
48. ((~creative(fred) & wise(fred)) | ! [X0] : (strong(X0) & creative(X0))) & (? [X1] : (~strong(X1) | ~creative(X1)) | creative(fred) | ~wise(fred)) [rectify 47]
49. ? [X1] : (~strong(X1) | ~creative(X1)) => (~strong(sK0) | ~creative(sK0)) [choice axiom]
50. ((~creative(fred) & wise(fred)) | ! [X0] : (strong(X0) & creative(X0))) & ((~strong(sK0) | ~creative(sK0)) | creative(fred) | ~wise(fred)) [skolemisation 48,49]
51. ~wise(fred) | ! [X0] : ((old(X0) | generous(X0)) & (~generous(X0) | ~old(X0))) [nnf transformation 28]
79. ~strong(X0) | tall(X0) | humble(X0) [cnf transformation 37]
85. ~humble(mary) | ~old(lucy) [cnf transformation 39]
86. ~humble(mary) | ~generous(lucy) [cnf transformation 39]
87. strong(mary) | ~old(lucy) [cnf transformation 39]
88. strong(mary) | ~generous(lucy) [cnf transformation 39]
96. ~strong(X0) | ~tall(X0) [cnf transformation 43]
104. wise(fred) | strong(X0) [cnf transformation 50]
108. ~wise(fred) | old(X0) | generous(X0) [cnf transformation 51]
130. ~strong(alice) [cnf transformation 23]
160. 7 <=> humble(mary) [avatar definition]
164. 8 <=> strong(mary) [avatar definition]
165. strong(mary) <- (8) [avatar component clause 164]
168. 9 <=> old(lucy) [avatar definition]
169. ~old(lucy) <- (~9) [avatar component clause 168]
172. 10 <=> generous(lucy) [avatar definition]
173. ~generous(lucy) <- (~10) [avatar component clause 172]
176. ~10 | 8 [avatar split clause 88,164,172]
177. ~9 | 8 [avatar split clause 87,164,168]
178. ~10 | ~7 [avatar split clause 86,160,172]
179. ~9 | ~7 [avatar split clause 85,160,168]
199. 14 <=> ! [X0] : strong(X0) [avatar definition]
200. strong(X0) <- (14) [avatar component clause 199]
211. 17 <=> wise(fred) [avatar definition]
214. 14 | 17 [avatar split clause 104,211,199]
226. 20 <=> ! [X0] : (old(X0) | generous(X0)) [avatar definition]
227. generous(X0) | old(X0) <- (20) [avatar component clause 226]
228. 20 | ~17 [avatar split clause 108,211,226]
289. $false <- (14) [resolution 200,130]
290. ~14 [avatar contradiction clause 289]
295. ~tall(mary) <- (8) [resolution 96,165]
330. tall(mary) | humble(mary) <- (8) [resolution 79,165]
332. humble(mary) <- (8) [subsumption resolution 330,295]
338. 7 | ~8 [avatar split clause 332,164,160]
340. old(lucy) <- (~10, 20) [resolution 173,227]
341. $false <- (~9, ~10, 20) [subsumption resolution 340,169]
342. 9 | 10 | ~20 [avatar contradiction clause 341]
343. $false [avatar sat refutation 176,177,178,179,214,228,290,338,342]
% SZS output end Proof for 2463172657462771248283021
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not patient or funny then fred is not curious. If someone is either wise or brave then john is not brave. If someone is both creative and patient then someone is either patient or not quiet. Everyone who is both not quiet and wise is tall or old and vice versa. If someone is not quiet then someone is both rich and not patient. If someone is not funny then paul is rich. If someone is rich or generous then alice is both old and not brave and vice versa. Everyone who is not quiet or not strong is both quiet and not generous. Everyone who is either not generous or not wise is not curious and vice versa. Everyone who is kind or not creative is both happy and generous. If john is rich or not humble then someone is both not happy and humble and vice versa. If susan is not funny or not patient then john is either not tall or funny. If fred is not humble or not patient then fred is tall or not tall. Everyone who is not generous or not funny is both not brave and patient and vice versa. Everyone who is either creative or rich is strong. Everyone who is either old or not funny is calm and vice versa. John is either not brave or not strong. Lucy is funny or not curious. Someone is not brave or humble. Someone is strong or not wise. Mary is not generous or calm. Someone is either not quiet or quiet. | John is creative. | entailment | ((?[X]:((~patient(X)<~>funny(X))))=>(~curious(fred)))&
((?[X]:((wise(X)<~>brave(X))))=>(~brave(john)))&
((?[X]:((creative(X)&patient(X))))=>(?[X]:((patient(X)<~>~quiet(X)))))&
(![X]:((~quiet(X)&wise(X))<=>(tall(X)|old(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((rich(X)&~patient(X)))))&
((?[X]:(~funny(X)))=>(rich(paul)))&
((?[X]:((rich(X)|generous(X))))<=>((old(alice)&~brave(alice))))&
(![X]:((~quiet(X)|~strong(X))=>(quiet(X)&~generous(X))))&
(![X]:((~generous(X)<~>~wise(X))<=>~curious(X)))&
(![X]:((kind(X)|~creative(X))=>(happy(X)&generous(X))))&
(((rich(john)|~humble(john)))<=>(?[X]:((~happy(X)&humble(X)))))&
(((~funny(susan)|~patient(susan)))=>((~tall(john)<~>funny(john))))&
(((~humble(fred)|~patient(fred)))=>((tall(fred)|~tall(fred))))&
(![X]:((~generous(X)|~funny(X))<=>(~brave(X)&patient(X))))&
(![X]:((creative(X)<~>rich(X))=>strong(X)))&
(![X]:((old(X)<~>~funny(X))<=>calm(X)))&
((~brave(john)<~>~strong(john)))&
((funny(lucy)|~curious(lucy)))&
(?[X]:((~brave(X)|humble(X))))&
(?[X]:((strong(X)|~wise(X))))&
((~generous(mary)|calm(mary)))&
(?[X]:((~quiet(X)<~>quiet(X)))) | creative(john) | [
"p3",
"p6",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3266136802875424437122603
% SZS output start Proof for 3266136802875424437122603
4. ! [X0] : ((wise(X0) & ~quiet(X0)) <=> (old(X0) | tall(X0))) [input p3]
7. ? [X0] : (generous(X0) | rich(X0)) <=> (~brave(alice) & old(alice)) [input p6]
8. ! [X0] : ((~strong(X0) | ~quiet(X0)) => (~generous(X0) & quiet(X0))) [input p7]
10. ! [X0] : ((~creative(X0) | kind(X0)) => (generous(X0) & happy(X0))) [input p9]
23. ~creative(john) [input hypothesis]
28. ! [X0] : (~creative(X0) => (generous(X0) & happy(X0))) [pure predicate removal 10]
34. ! [X0] : ((~generous(X0) & quiet(X0)) | (strong(X0) & quiet(X0))) [ennf transformation 8]
36. ! [X0] : ((generous(X0) & happy(X0)) | creative(X0)) [ennf transformation 28]
48. ! [X0] : (((wise(X0) & ~quiet(X0)) | (~old(X0) & ~tall(X0))) & ((old(X0) | tall(X0)) | (~wise(X0) | quiet(X0)))) [nnf transformation 4]
49. ! [X0] : (((wise(X0) & ~quiet(X0)) | (~old(X0) & ~tall(X0))) & (old(X0) | tall(X0) | ~wise(X0) | quiet(X0))) [flattening 48]
53. (? [X0] : (generous(X0) | rich(X0)) | (brave(alice) | ~old(alice))) & ((~brave(alice) & old(alice)) | ! [X0] : (~generous(X0) & ~rich(X0))) [nnf transformation 7]
54. (? [X0] : (generous(X0) | rich(X0)) | brave(alice) | ~old(alice)) & ((~brave(alice) & old(alice)) | ! [X0] : (~generous(X0) & ~rich(X0))) [flattening 53]
55. (? [X0] : (generous(X0) | rich(X0)) | brave(alice) | ~old(alice)) & ((~brave(alice) & old(alice)) | ! [X1] : (~generous(X1) & ~rich(X1))) [rectify 54]
56. ? [X0] : (generous(X0) | rich(X0)) => (generous(sK2) | rich(sK2)) [choice axiom]
57. ((generous(sK2) | rich(sK2)) | brave(alice) | ~old(alice)) & ((~brave(alice) & old(alice)) | ! [X1] : (~generous(X1) & ~rich(X1))) [skolemisation 55,56]
85. ~old(X0) | ~quiet(X0) [cnf transformation 49]
92. old(alice) | ~generous(X1) [cnf transformation 57]
96. quiet(X0) | quiet(X0) [cnf transformation 34]
103. generous(X0) | creative(X0) [cnf transformation 36]
132. ~creative(john) [cnf transformation 23]
133. quiet(X0) [duplicate literal removal 96]
172. 10 <=> ! [X1] : quiet(X1) [avatar definition]
173. quiet(X1) <- (10) [avatar component clause 172]
193. 15 <=> old(alice) [avatar definition]
194. old(alice) <- (15) [avatar component clause 193]
210. 19 <=> ! [X1] : ~generous(X1) [avatar definition]
211. ~generous(X1) <- (19) [avatar component clause 210]
217. 19 | 15 [avatar split clause 92,193,210]
219. 10 [avatar split clause 133,172]
311. ~quiet(alice) <- (15) [resolution 85,194]
312. $false <- (10, 15) [subsumption resolution 311,173]
313. ~10 | ~15 [avatar contradiction clause 312]
325. creative(X2) <- (19) [resolution 103,211]
329. $false <- (19) [resolution 325,132]
330. ~19 [avatar contradiction clause 329]
331. $false [avatar sat refutation 217,219,313,330]
% SZS output end Proof for 3266136802875424437122603
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or not brave is not strong or creative.
If mary is either not humble or humble then susan is both generous and curious and vice versa.
Everyone who is not calm is both not rich and kind.
Everyone who is strong is both generous and funny and vice versa.
If someone is either old or not generous then someone is quiet or not creative and vice versa.
If someone is both not wise and not funny then mary is not old or rich and vice versa.
Everyone who is rich or not happy is both not rich and generous and vice versa.
If someone is both not kind and happy then susan is calm or not brave.
Everyone who is not brave is either not calm or not old and vice versa.
Everyone who is either calm or not curious is both rich and humble and vice versa.
If someone is creative or kind then fred is both not tall and not quiet.
If someone is either not curious or not creative then someone is either not generous or not brave and vice versa.
If alice is not brave or brave then someone is generous and vice versa.
If john is patient or humble then someone is both creative and not happy.
Everyone who is both not brave and not generous is strong or not patient and vice versa.
Everyone who is not curious or not rich is either happy or creative.
Someone is either not old or strong.
Lucy is not tall or funny.
Alice is funny.
Paul is not calm or not kind.
John is either curious or kind.
Someone is creative or wise. | Susan is brave. | neutral | (![X]:((~old(X)<~>~brave(X))=>(~strong(X)|creative(X))))&
(((~humble(mary)<~>humble(mary)))<=>((generous(susan)&curious(susan))))&
(![X]:(~calm(X)=>(~rich(X)&kind(X))))&
(![X]:(strong(X)<=>(generous(X)&funny(X))))&
((?[X]:((old(X)<~>~generous(X))))<=>(?[X]:((quiet(X)|~creative(X)))))&
((?[X]:((~wise(X)&~funny(X))))<=>((~old(mary)|rich(mary))))&
(![X]:((rich(X)|~happy(X))<=>(~rich(X)&generous(X))))&
((?[X]:((~kind(X)&happy(X))))=>((calm(susan)|~brave(susan))))&
(![X]:(~brave(X)<=>(~calm(X)<~>~old(X))))&
(![X]:((calm(X)<~>~curious(X))<=>(rich(X)&humble(X))))&
((?[X]:((creative(X)|kind(X))))=>((~tall(fred)&~quiet(fred))))&
((?[X]:((~curious(X)<~>~creative(X))))<=>(?[X]:((~generous(X)<~>~brave(X)))))&
(((~brave(alice)|brave(alice)))<=>(?[X]:(generous(X))))&
(((patient(john)|humble(john)))=>(?[X]:((creative(X)&~happy(X)))))&
(![X]:((~brave(X)&~generous(X))<=>(strong(X)|~patient(X))))&
(![X]:((~curious(X)|~rich(X))=>(happy(X)<~>creative(X))))&
(?[X]:((~old(X)<~>strong(X))))&
((~tall(lucy)|funny(lucy)))&
(funny(alice))&
((~calm(paul)|~kind(paul)))&
((curious(john)<~>kind(john)))&
(?[X]:((creative(X)|wise(X)))) | brave(susan) | [] | null | 0 |
If someone is old or quiet then fred is both generous and funny and vice versa.
Everyone who is not generous or not happy is quiet.
If someone is both curious and brave then john is not wise and vice versa.
If someone is either old or curious then mary is either quiet or not rich and vice versa.
If someone is both funny and not wise then someone is both tall and not happy and vice versa.
Everyone who is either patient or creative is not creative.
If someone is funny or rich then fred is either not calm or humble and vice versa.
Everyone who is humble is not funny and vice versa.
Everyone who is both not brave and rich is both tall and not humble and vice versa.
If someone is not funny or rich then mary is tall.
If someone is both old and creative then fred is both not brave and strong.
If someone is both strong and funny then someone is happy and vice versa.
Everyone who is happy is both not curious and not kind and vice versa.
Everyone who is tall or not calm is either not happy or not strong and vice versa.
If someone is not humble then someone is both not brave and not generous and vice versa.
Everyone who is both not generous and quiet is not old or not brave and vice versa.
Someone is tall or strong.
Paul is both kind and generous.
John is quiet or not curious.
Alice is both funny and tall.
Someone is either not patient or strong.
Fred is both wise and patient.
Alice is both tall and not creative. | Paul is not wise. | neutral | ((?[X]:((old(X)|quiet(X))))<=>((generous(fred)&funny(fred))))&
(![X]:((~generous(X)|~happy(X))=>quiet(X)))&
((?[X]:((curious(X)&brave(X))))<=>(~wise(john)))&
((?[X]:((old(X)<~>curious(X))))<=>((quiet(mary)<~>~rich(mary))))&
((?[X]:((funny(X)&~wise(X))))<=>(?[X]:((tall(X)&~happy(X)))))&
(![X]:((patient(X)<~>creative(X))=>~creative(X)))&
((?[X]:((funny(X)|rich(X))))<=>((~calm(fred)<~>humble(fred))))&
(![X]:(humble(X)<=>~funny(X)))&
(![X]:((~brave(X)&rich(X))<=>(tall(X)&~humble(X))))&
((?[X]:((~funny(X)|rich(X))))=>(tall(mary)))&
((?[X]:((old(X)&creative(X))))=>((~brave(fred)&strong(fred))))&
((?[X]:((strong(X)&funny(X))))<=>(?[X]:(happy(X))))&
(![X]:(happy(X)<=>(~curious(X)&~kind(X))))&
(![X]:((tall(X)|~calm(X))<=>(~happy(X)<~>~strong(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((~brave(X)&~generous(X)))))&
(![X]:((~generous(X)&quiet(X))<=>(~old(X)|~brave(X))))&
(?[X]:((tall(X)|strong(X))))&
((kind(paul)&generous(paul)))&
((quiet(john)|~curious(john)))&
((funny(alice)&tall(alice)))&
(?[X]:((~patient(X)<~>strong(X))))&
((wise(fred)&patient(fred)))&
((tall(alice)&~creative(alice))) | ~wise(paul) | [] | null | 0 |
If someone is humble then alice is not curious or humble and vice versa.
If someone is either not tall or calm then paul is both funny and rich and vice versa.
If alice is kind then lucy is happy and vice versa.
If paul is not creative then fred is either quiet or not happy and vice versa.
Everyone who is both happy and funny is both happy and strong and vice versa.
If mary is old then someone is curious or patient.
Everyone who is strong is both tall and humble and vice versa.
If john is creative then susan is not creative.
Everyone who is both wise and happy is not old.
Everyone who is either happy or quiet is not brave.
If someone is brave or rich then john is both not funny and not happy.
Everyone who is tall is not brave and vice versa.
Everyone who is generous is not happy and vice versa.
Everyone who is either not strong or funny is both generous and humble and vice versa.
If paul is both not kind and not brave then mary is either not wise or not curious and vice versa.
Everyone who is not curious is both old and not kind and vice versa.
John is both tall and not strong.
Someone is either not patient or not happy.
Fred is both not wise and strong.
Fred is humble.
Mary is both not patient and not kind.
Someone is either creative or old.
Susan is curious.
Someone is either calm or tall. | Alice is not funny. | contradiction | ((?[X]:(humble(X)))<=>((~curious(alice)|humble(alice))))&
((?[X]:((~tall(X)<~>calm(X))))<=>((funny(paul)&rich(paul))))&
((kind(alice))<=>(happy(lucy)))&
((~creative(paul))<=>((quiet(fred)<~>~happy(fred))))&
(![X]:((happy(X)&funny(X))<=>(happy(X)&strong(X))))&
((old(mary))=>(?[X]:((curious(X)|patient(X)))))&
(![X]:(strong(X)<=>(tall(X)&humble(X))))&
((creative(john))=>(~creative(susan)))&
(![X]:((wise(X)&happy(X))=>~old(X)))&
(![X]:((happy(X)<~>quiet(X))=>~brave(X)))&
((?[X]:((brave(X)|rich(X))))=>((~funny(john)&~happy(john))))&
(![X]:(tall(X)<=>~brave(X)))&
(![X]:(generous(X)<=>~happy(X)))&
(![X]:((~strong(X)<~>funny(X))<=>(generous(X)&humble(X))))&
(((~kind(paul)&~brave(paul)))<=>((~wise(mary)<~>~curious(mary))))&
(![X]:(~curious(X)<=>(old(X)&~kind(X))))&
((tall(john)&~strong(john)))&
(?[X]:((~patient(X)<~>~happy(X))))&
((~wise(fred)&strong(fred)))&
(humble(fred))&
((~patient(mary)&~kind(mary)))&
(?[X]:((creative(X)<~>old(X))))&
(curious(susan))&
(?[X]:((calm(X)<~>tall(X)))) | ~funny(alice) | [
"p4",
"p6",
"p10",
"p11",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7359760406876942181855385
% SZS output start Proof for 7359760406876942181855385
5. ! [X0] : ((funny(X0) & happy(X0)) <=> (strong(X0) & happy(X0))) [input p4]
7. ! [X0] : (strong(X0) <=> (humble(X0) & tall(X0))) [input p6]
11. ? [X0] : (rich(X0) | brave(X0)) => (~happy(john) & ~funny(john)) [input p10]
12. ! [X0] : (tall(X0) <=> ~brave(X0)) [input p11]
13. ! [X0] : (generous(X0) <=> ~happy(X0)) [input p12]
14. ! [X0] : ((~strong(X0) <~> funny(X0)) <=> (humble(X0) & generous(X0))) [input p13]
17. ~strong(john) & tall(john) [input p16]
25. ~funny(alice) [input hypothesis]
31. (~happy(john) & ~funny(john)) | ! [X0] : (~rich(X0) & ~brave(X0)) [ennf transformation 11]
44. ! [X0] : (((funny(X0) & happy(X0)) | (~strong(X0) | ~happy(X0))) & ((strong(X0) & happy(X0)) | (~funny(X0) | ~happy(X0)))) [nnf transformation 5]
45. ! [X0] : (((funny(X0) & happy(X0)) | ~strong(X0) | ~happy(X0)) & ((strong(X0) & happy(X0)) | ~funny(X0) | ~happy(X0))) [flattening 44]
48. ! [X0] : ((strong(X0) | (~humble(X0) | ~tall(X0))) & ((humble(X0) & tall(X0)) | ~strong(X0))) [nnf transformation 7]
49. ! [X0] : ((strong(X0) | ~humble(X0) | ~tall(X0)) & ((humble(X0) & tall(X0)) | ~strong(X0))) [flattening 48]
51. ! [X0] : ((tall(X0) | brave(X0)) & (~brave(X0) | ~tall(X0))) [nnf transformation 12]
52. ! [X0] : ((generous(X0) | happy(X0)) & (~happy(X0) | ~generous(X0))) [nnf transformation 13]
53. ! [X0] : ((((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | (~humble(X0) | ~generous(X0))) & ((humble(X0) & generous(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0))))) [nnf transformation 14]
54. ! [X0] : ((((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | ~humble(X0) | ~generous(X0)) & ((humble(X0) & generous(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0))))) [flattening 53]
86. ~strong(X0) | funny(X0) | ~happy(X0) [cnf transformation 45]
89. ~strong(X0) | humble(X0) [cnf transformation 49]
90. ~tall(X0) | ~humble(X0) | strong(X0) [cnf transformation 49]
95. ~funny(john) | ~brave(X0) [cnf transformation 31]
100. brave(X0) | tall(X0) [cnf transformation 51]
102. generous(X0) | happy(X0) [cnf transformation 52]
105. humble(X0) | funny(X0) | strong(X0) [cnf transformation 54]
107. funny(X0) | ~strong(X0) | ~humble(X0) | ~generous(X0) [cnf transformation 54]
118. tall(john) [cnf transformation 17]
119. ~strong(john) [cnf transformation 17]
132. ~funny(alice) [cnf transformation 25]
134. 1 <=> humble(alice) [avatar definition]
135. humble(alice) <- (1) [avatar component clause 134]
236. 23 <=> ! [X0] : ~brave(X0) [avatar definition]
237. ~brave(X0) <- (23) [avatar component clause 236]
240. 24 <=> funny(john) [avatar definition]
242. ~funny(john) <- (~24) [avatar component clause 240]
244. 23 | ~24 [avatar split clause 95,240,236]
245. ~generous(X0) | ~strong(X0) | funny(X0) [subsumption resolution 107,89]
246. funny(X0) | humble(X0) [subsumption resolution 105,89]
306. humble(alice) [resolution 246,132]
307. humble(john) <- (~24) [resolution 246,242]
308. 1 [avatar split clause 306,134]
310. ~humble(john) | strong(john) [resolution 90,118]
313. strong(john) <- (~24) [subsumption resolution 310,307]
314. $false <- (~24) [subsumption resolution 313,119]
315. 24 [avatar contradiction clause 314]
328. tall(X0) <- (23) [resolution 237,100]
332. ~humble(X0) | strong(X0) <- (23) [resolution 328,90]
338. strong(alice) <- (1, 23) [resolution 332,135]
382. ~strong(X1) | funny(X1) | happy(X1) [resolution 245,102]
384. ~strong(X1) | funny(X1) [subsumption resolution 382,86]
389. funny(alice) <- (1, 23) [resolution 384,338]
393. $false <- (1, 23) [subsumption resolution 389,132]
394. ~1 | ~23 [avatar contradiction clause 393]
397. $false [avatar sat refutation 244,308,315,394]
% SZS output end Proof for 7359760406876942181855385
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is not humble or not creative.
If susan is funny or not kind then someone is either not patient or wise.
If fred is both not strong and quiet then paul is not brave or funny and vice versa.
If fred is quiet or generous then someone is both not patient and kind and vice versa.
Everyone who is both not calm and brave is both not patient and not curious.
Everyone who is either not rich or not patient is either not tall or calm and vice versa.
If lucy is not kind or happy then someone is either not generous or humble and vice versa.
Everyone who is not generous or not funny is not funny or funny and vice versa.
If lucy is not curious or not patient then paul is calm.
If someone is not generous then paul is either strong or wise and vice versa.
Everyone who is either not calm or not creative is brave or funny and vice versa.
If someone is either happy or not curious then someone is both not brave and strong.
Everyone who is both not creative and quiet is not tall and vice versa.
If lucy is not patient then susan is both quiet and creative.
Everyone who is not humble or calm is not tall and vice versa.
Everyone who is not curious is quiet or generous and vice versa.
Someone is either calm or not strong.
Lucy is either not curious or not quiet.
Lucy is not quiet or strong.
Someone is both curious and not brave.
Someone is old.
Someone is kind or not happy.
Fred is not calm.
Lucy is either creative or not curious. | Lucy is tall. | contradiction | (![X]:((generous(X)|humble(X))=>(~humble(X)|~creative(X))))&
(((funny(susan)|~kind(susan)))=>(?[X]:((~patient(X)<~>wise(X)))))&
(((~strong(fred)&quiet(fred)))<=>((~brave(paul)|funny(paul))))&
(((quiet(fred)|generous(fred)))<=>(?[X]:((~patient(X)&kind(X)))))&
(![X]:((~calm(X)&brave(X))=>(~patient(X)&~curious(X))))&
(![X]:((~rich(X)<~>~patient(X))<=>(~tall(X)<~>calm(X))))&
(((~kind(lucy)|happy(lucy)))<=>(?[X]:((~generous(X)<~>humble(X)))))&
(![X]:((~generous(X)|~funny(X))<=>(~funny(X)|funny(X))))&
(((~curious(lucy)|~patient(lucy)))=>(calm(paul)))&
((?[X]:(~generous(X)))<=>((strong(paul)<~>wise(paul))))&
(![X]:((~calm(X)<~>~creative(X))<=>(brave(X)|funny(X))))&
((?[X]:((happy(X)<~>~curious(X))))=>(?[X]:((~brave(X)&strong(X)))))&
(![X]:((~creative(X)&quiet(X))<=>~tall(X)))&
((~patient(lucy))=>((quiet(susan)&creative(susan))))&
(![X]:((~humble(X)|calm(X))<=>~tall(X)))&
(![X]:(~curious(X)<=>(quiet(X)|generous(X))))&
(?[X]:((calm(X)<~>~strong(X))))&
((~curious(lucy)<~>~quiet(lucy)))&
((~quiet(lucy)|strong(lucy)))&
(?[X]:((curious(X)&~brave(X))))&
(?[X]:(old(X)))&
(?[X]:((kind(X)|~happy(X))))&
(~calm(fred))&
((creative(lucy)<~>~curious(lucy))) | tall(lucy) | [
"p0",
"p12",
"p14",
"p17",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7451471305963278798527192
% SZS output start Proof for 7451471305963278798527192
1. ! [X0] : ((humble(X0) | generous(X0)) => (~creative(X0) | ~humble(X0))) [input p0]
13. ! [X0] : ((quiet(X0) & ~creative(X0)) <=> ~tall(X0)) [input p12]
15. ! [X0] : ((calm(X0) | ~humble(X0)) <=> ~tall(X0)) [input p14]
18. ~curious(lucy) <~> ~quiet(lucy) [input p17]
24. creative(lucy) <~> ~curious(lucy) [input p23]
25. tall(lucy) [input hypothesis]
28. ! [X0] : ((~creative(X0) | ~humble(X0)) | (~humble(X0) & ~generous(X0))) [ennf transformation 1]
29. ! [X0] : (~creative(X0) | ~humble(X0) | (~humble(X0) & ~generous(X0))) [flattening 28]
64. ! [X0] : (((quiet(X0) & ~creative(X0)) | tall(X0)) & (~tall(X0) | (~quiet(X0) | creative(X0)))) [nnf transformation 13]
65. ! [X0] : (((quiet(X0) & ~creative(X0)) | tall(X0)) & (~tall(X0) | ~quiet(X0) | creative(X0))) [flattening 64]
66. ! [X0] : (((calm(X0) | ~humble(X0)) | tall(X0)) & (~tall(X0) | (~calm(X0) & humble(X0)))) [nnf transformation 15]
67. ! [X0] : ((calm(X0) | ~humble(X0) | tall(X0)) & (~tall(X0) | (~calm(X0) & humble(X0)))) [flattening 66]
73. (quiet(lucy) | curious(lucy)) & (~quiet(lucy) | ~curious(lucy)) [nnf transformation 18]
78. (curious(lucy) | ~creative(lucy)) & (~curious(lucy) | creative(lucy)) [nnf transformation 24]
80. ~creative(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 29]
131. ~tall(X0) | ~quiet(X0) | creative(X0) [cnf transformation 65]
136. ~tall(X0) | humble(X0) [cnf transformation 67]
145. quiet(lucy) | curious(lucy) [cnf transformation 73]
151. ~curious(lucy) | creative(lucy) [cnf transformation 78]
153. tall(lucy) [cnf transformation 25]
156. ~creative(X0) | ~humble(X0) [duplicate literal removal 80]
256. 21 <=> curious(lucy) [avatar definition]
318. 34 <=> quiet(lucy) [avatar definition]
321. 21 | 34 [avatar split clause 145,318,256]
337. 38 <=> creative(lucy) [avatar definition]
338. creative(lucy) <- (38) [avatar component clause 337]
341. 38 | ~21 [avatar split clause 151,256,337]
342. humble(lucy) [resolution 136,153]
357. ~quiet(lucy) | creative(lucy) [resolution 131,153]
362. 38 | ~34 [avatar split clause 357,318,337]
369. ~humble(lucy) <- (38) [resolution 338,156]
371. $false <- (38) [subsumption resolution 369,342]
372. ~38 [avatar contradiction clause 371]
373. $false [avatar sat refutation 321,341,362,372]
% SZS output end Proof for 7451471305963278798527192
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not kind or strong then mary is both brave and not calm and vice versa.
Everyone who is both not happy and not tall is rich or tall and vice versa.
If someone is strong or patient then someone is either not rich or creative and vice versa.
Everyone who is not humble is not funny.
Everyone who is both not curious and not happy is generous.
Everyone who is rich or generous is strong.
Everyone who is not kind is either not funny or not happy.
If fred is both not patient and humble then john is either curious or not humble.
Everyone who is strong or not generous is wise and vice versa.
If someone is not rich or not creative then john is either brave or rich and vice versa.
If someone is both not old and old then paul is both not patient and not quiet.
Everyone who is either not happy or not humble is both not kind and not brave and vice versa.
If paul is either patient or not kind then someone is both not curious and wise and vice versa.
Everyone who is kind or not humble is brave or tall.
If someone is either brave or not rich then paul is both humble and not humble and vice versa.
If someone is both not patient and not creative then someone is not creative.
Someone is rich.
Someone is not brave.
Fred is quiet.
Someone is either funny or humble.
Someone is not brave or not kind.
Lucy is funny.
Someone is not quiet. | Paul is not patient. | neutral | ((?[X]:((~kind(X)<~>strong(X))))<=>((brave(mary)&~calm(mary))))&
(![X]:((~happy(X)&~tall(X))<=>(rich(X)|tall(X))))&
((?[X]:((strong(X)|patient(X))))<=>(?[X]:((~rich(X)<~>creative(X)))))&
(![X]:(~humble(X)=>~funny(X)))&
(![X]:((~curious(X)&~happy(X))=>generous(X)))&
(![X]:((rich(X)|generous(X))=>strong(X)))&
(![X]:(~kind(X)=>(~funny(X)<~>~happy(X))))&
(((~patient(fred)&humble(fred)))=>((curious(john)<~>~humble(john))))&
(![X]:((strong(X)|~generous(X))<=>wise(X)))&
((?[X]:((~rich(X)|~creative(X))))<=>((brave(john)<~>rich(john))))&
((?[X]:((~old(X)&old(X))))=>((~patient(paul)&~quiet(paul))))&
(![X]:((~happy(X)<~>~humble(X))<=>(~kind(X)&~brave(X))))&
(((patient(paul)<~>~kind(paul)))<=>(?[X]:((~curious(X)&wise(X)))))&
(![X]:((kind(X)|~humble(X))=>(brave(X)|tall(X))))&
((?[X]:((brave(X)<~>~rich(X))))<=>((humble(paul)&~humble(paul))))&
((?[X]:((~patient(X)&~creative(X))))=>(?[X]:(~creative(X))))&
(?[X]:(rich(X)))&
(?[X]:(~brave(X)))&
(quiet(fred))&
(?[X]:((funny(X)<~>humble(X))))&
(?[X]:((~brave(X)|~kind(X))))&
(funny(lucy))&
(?[X]:(~quiet(X))) | ~patient(paul) | [] | null | 0 |
Everyone who is either not strong or not old is either wise or tall.
Everyone who is either not humble or strong is both kind and wise.
Everyone who is both curious and not strong is both rich and generous.
Everyone who is both not kind and not tall is both not kind and wise.
If someone is not creative or not quiet then mary is both not generous and patient.
If someone is not patient or not old then someone is both not wise and not kind and vice versa.
Everyone who is humble is both humble and not strong.
Everyone who is tall is not funny.
Everyone who is either generous or wise is quiet or not kind and vice versa.
Everyone who is strong is humble and vice versa.
Everyone who is both quiet and not patient is either brave or old and vice versa.
Everyone who is not generous is quiet or creative and vice versa.
If someone is both happy and not tall then someone is either old or creative and vice versa.
If someone is not funny then someone is both not kind and strong and vice versa.
Lucy is both rich and wise.
Someone is not tall.
Alice is either not patient or not rich.
Mary is both brave and not rich.
Mary is happy. | Lucy is brave. | entailment | (![X]:((~strong(X)<~>~old(X))=>(wise(X)<~>tall(X))))&
(![X]:((~humble(X)<~>strong(X))=>(kind(X)&wise(X))))&
(![X]:((curious(X)&~strong(X))=>(rich(X)&generous(X))))&
(![X]:((~kind(X)&~tall(X))=>(~kind(X)&wise(X))))&
((?[X]:((~creative(X)|~quiet(X))))=>((~generous(mary)&patient(mary))))&
((?[X]:((~patient(X)|~old(X))))<=>(?[X]:((~wise(X)&~kind(X)))))&
(![X]:(humble(X)=>(humble(X)&~strong(X))))&
(![X]:(tall(X)=>~funny(X)))&
(![X]:((generous(X)<~>wise(X))<=>(quiet(X)|~kind(X))))&
(![X]:(strong(X)<=>humble(X)))&
(![X]:((quiet(X)&~patient(X))<=>(brave(X)<~>old(X))))&
(![X]:(~generous(X)<=>(quiet(X)|creative(X))))&
((?[X]:((happy(X)&~tall(X))))<=>(?[X]:((old(X)<~>creative(X)))))&
((?[X]:(~funny(X)))<=>(?[X]:((~kind(X)&strong(X)))))&
((rich(lucy)&wise(lucy)))&
(?[X]:(~tall(X)))&
((~patient(alice)<~>~rich(alice)))&
((brave(mary)&~rich(mary)))&
(happy(mary)) | brave(lucy) | [
"p1",
"p5",
"p6",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 753398776888803173460545
% SZS output start Proof for 753398776888803173460545
2. ! [X0] : ((~humble(X0) <~> strong(X0)) => (wise(X0) & kind(X0))) [input p1]
6. ? [X0] : (~old(X0) | ~patient(X0)) <=> ? [X0] : (~kind(X0) & ~wise(X0)) [input p5]
7. ! [X0] : (humble(X0) => (~strong(X0) & humble(X0))) [input p6]
10. ! [X0] : (strong(X0) <=> humble(X0)) [input p9]
11. ! [X0] : ((~patient(X0) & quiet(X0)) <=> (brave(X0) <~> old(X0))) [input p10]
20. ~brave(lucy) [input hypothesis]
21. ? [X0] : (~old(X0) | ~patient(X0)) <=> ? [X1] : (~kind(X1) & ~wise(X1)) [rectify 6]
26. ! [X0] : ((wise(X0) & kind(X0)) | (~humble(X0) <=> strong(X0))) [ennf transformation 2]
30. ! [X0] : ((~strong(X0) & humble(X0)) | ~humble(X0)) [ennf transformation 7]
33. ! [X0] : ((wise(X0) & kind(X0)) | ((~humble(X0) | ~strong(X0)) & (strong(X0) | humble(X0)))) [nnf transformation 26]
34. (? [X0] : (~old(X0) | ~patient(X0)) | ! [X1] : (kind(X1) | wise(X1))) & (? [X1] : (~kind(X1) & ~wise(X1)) | ! [X0] : (old(X0) & patient(X0))) [nnf transformation 21]
35. (? [X0] : (~old(X0) | ~patient(X0)) | ! [X1] : (kind(X1) | wise(X1))) & (? [X2] : (~kind(X2) & ~wise(X2)) | ! [X3] : (old(X3) & patient(X3))) [rectify 34]
36. ? [X0] : (~old(X0) | ~patient(X0)) => (~old(sK0) | ~patient(sK0)) [choice axiom]
37. ? [X2] : (~kind(X2) & ~wise(X2)) => (~kind(sK1) & ~wise(sK1)) [choice axiom]
38. ((~old(sK0) | ~patient(sK0)) | ! [X1] : (kind(X1) | wise(X1))) & ((~kind(sK1) & ~wise(sK1)) | ! [X3] : (old(X3) & patient(X3))) [skolemisation 35,37,36]
41. ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0))) [nnf transformation 10]
42. ! [X0] : (((~patient(X0) & quiet(X0)) | ((brave(X0) | ~old(X0)) & (old(X0) | ~brave(X0)))) & (((~old(X0) | ~brave(X0)) & (old(X0) | brave(X0))) | (patient(X0) | ~quiet(X0)))) [nnf transformation 11]
43. ! [X0] : (((~patient(X0) & quiet(X0)) | ((brave(X0) | ~old(X0)) & (old(X0) | ~brave(X0)))) & (((~old(X0) | ~brave(X0)) & (old(X0) | brave(X0))) | patient(X0) | ~quiet(X0))) [flattening 42]
65. humble(X0) | strong(X0) | wise(X0) [cnf transformation 33]
73. ~wise(sK1) | patient(X3) [cnf transformation 38]
74. ~wise(sK1) | old(X3) [cnf transformation 38]
79. ~humble(X0) | ~strong(X0) [cnf transformation 30]
87. humble(X0) | ~strong(X0) [cnf transformation 41]
88. strong(X0) | ~humble(X0) [cnf transformation 41]
94. ~patient(X0) | brave(X0) | ~old(X0) [cnf transformation 43]
115. ~brave(lucy) [cnf transformation 20]
147. 8 <=> ! [X3] : old(X3) [avatar definition]
148. old(X3) <- (8) [avatar component clause 147]
155. 10 <=> ! [X3] : patient(X3) [avatar definition]
156. patient(X3) <- (10) [avatar component clause 155]
159. 11 <=> wise(sK1) [avatar definition]
161. ~wise(sK1) <- (~11) [avatar component clause 159]
162. 8 | ~11 [avatar split clause 74,159,147]
163. 10 | ~11 [avatar split clause 73,159,155]
164. ~humble(X0) [subsumption resolution 88,79]
165. ~strong(X0) [subsumption resolution 87,164]
225. strong(X2) | wise(X2) [resolution 65,164]
226. wise(X2) [subsumption resolution 225,165]
227. $false <- (~11) [resolution 226,161]
228. 11 [avatar contradiction clause 227]
256. brave(X0) | ~old(X0) <- (10) [resolution 94,156]
258. brave(X0) <- (8, 10) [subsumption resolution 256,148]
265. $false <- (8, 10) [resolution 258,115]
268. ~8 | ~10 [avatar contradiction clause 265]
269. $false [avatar sat refutation 162,163,228,268]
% SZS output end Proof for 753398776888803173460545
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or not patient is either not curious or strong and vice versa. Everyone who is not calm is either not tall or not old. Everyone who is not kind is both quiet and brave and vice versa. If someone is not happy or generous then someone is funny or humble and vice versa. If someone is both curious and not humble then someone is not patient or brave. Everyone who is both funny and happy is humble. Everyone who is strong is either generous or not strong and vice versa. Everyone who is funny is both humble and kind. Everyone who is not funny or humble is not funny or calm and vice versa. If someone is not wise then lucy is rich or not old. If john is both creative and not patient then someone is not brave and vice versa. If john is brave then john is curious or not brave and vice versa. Everyone who is not patient or not curious is either strong or not humble. If someone is either not humble or brave then alice is calm. Everyone who is wise or old is not curious and vice versa. Someone is both not tall and curious. Someone is either not old or not rich. Someone is old. Someone is either not tall or not quiet. Paul is not kind. Susan is both rich and wise. Lucy is either not quiet or not brave. | John is tall. | neutral | (![X]:((tall(X)<~>~patient(X))<=>(~curious(X)<~>strong(X))))&
(![X]:(~calm(X)=>(~tall(X)<~>~old(X))))&
(![X]:(~kind(X)<=>(quiet(X)&brave(X))))&
((?[X]:((~happy(X)|generous(X))))<=>(?[X]:((funny(X)|humble(X)))))&
((?[X]:((curious(X)&~humble(X))))=>(?[X]:((~patient(X)|brave(X)))))&
(![X]:((funny(X)&happy(X))=>humble(X)))&
(![X]:(strong(X)<=>(generous(X)<~>~strong(X))))&
(![X]:(funny(X)=>(humble(X)&kind(X))))&
(![X]:((~funny(X)|humble(X))<=>(~funny(X)|calm(X))))&
((?[X]:(~wise(X)))=>((rich(lucy)|~old(lucy))))&
(((creative(john)&~patient(john)))<=>(?[X]:(~brave(X))))&
((brave(john))<=>((curious(john)|~brave(john))))&
(![X]:((~patient(X)|~curious(X))=>(strong(X)<~>~humble(X))))&
((?[X]:((~humble(X)<~>brave(X))))=>(calm(alice)))&
(![X]:((wise(X)|old(X))<=>~curious(X)))&
(?[X]:((~tall(X)&curious(X))))&
(?[X]:((~old(X)<~>~rich(X))))&
(?[X]:(old(X)))&
(?[X]:((~tall(X)<~>~quiet(X))))&
(~kind(paul))&
((rich(susan)&wise(susan)))&
((~quiet(lucy)<~>~brave(lucy))) | tall(john) | [] | null | 0 |
Everyone who is both not old and funny is tall and vice versa. Everyone who is wise is not calm or not funny and vice versa. If susan is kind then someone is not quiet or calm. If alice is either not strong or happy then someone is strong or not tall. If paul is calm then susan is not curious and vice versa. Everyone who is both humble and calm is not old or not kind. If lucy is both not wise and not curious then fred is both not humble and not old and vice versa. Everyone who is not humble is either calm or kind and vice versa. Everyone who is either not strong or curious is either not creative or not quiet and vice versa. Everyone who is curious is not calm or happy and vice versa. If paul is tall or old then alice is not generous. Everyone who is either not humble or quiet is both not calm and calm. If someone is calm then someone is both tall and wise. Everyone who is both rich and kind is not generous or not humble. If susan is brave or not happy then fred is both not generous and not tall and vice versa. Everyone who is not generous or generous is not patient and vice versa. Paul is not old. Someone is either not strong or kind. Paul is generous or not curious. Mary is patient or tall. Lucy is either humble or old. Fred is not funny or funny. Someone is either not curious or kind. John is not quiet. | Alice is tall. | neutral | (![X]:((~old(X)&funny(X))<=>tall(X)))&
(![X]:(wise(X)<=>(~calm(X)|~funny(X))))&
((kind(susan))=>(?[X]:((~quiet(X)|calm(X)))))&
(((~strong(alice)<~>happy(alice)))=>(?[X]:((strong(X)|~tall(X)))))&
((calm(paul))<=>(~curious(susan)))&
(![X]:((humble(X)&calm(X))=>(~old(X)|~kind(X))))&
(((~wise(lucy)&~curious(lucy)))<=>((~humble(fred)&~old(fred))))&
(![X]:(~humble(X)<=>(calm(X)<~>kind(X))))&
(![X]:((~strong(X)<~>curious(X))<=>(~creative(X)<~>~quiet(X))))&
(![X]:(curious(X)<=>(~calm(X)|happy(X))))&
(((tall(paul)|old(paul)))=>(~generous(alice)))&
(![X]:((~humble(X)<~>quiet(X))=>(~calm(X)&calm(X))))&
((?[X]:(calm(X)))=>(?[X]:((tall(X)&wise(X)))))&
(![X]:((rich(X)&kind(X))=>(~generous(X)|~humble(X))))&
(((brave(susan)|~happy(susan)))<=>((~generous(fred)&~tall(fred))))&
(![X]:((~generous(X)|generous(X))<=>~patient(X)))&
(~old(paul))&
(?[X]:((~strong(X)<~>kind(X))))&
((generous(paul)|~curious(paul)))&
((patient(mary)|tall(mary)))&
((humble(lucy)<~>old(lucy)))&
((~funny(fred)|funny(fred)))&
(?[X]:((~curious(X)<~>kind(X))))&
(~quiet(john)) | tall(alice) | [] | null | 0 |
If susan is either not creative or funny then someone is either not brave or tall.
If someone is wise or patient then someone is both funny and rich.
Everyone who is both strong and creative is brave or not happy and vice versa.
Everyone who is both not funny and funny is not tall and vice versa.
Everyone who is not tall is quiet or not humble.
If mary is not tall then someone is not rich or not brave and vice versa.
If john is either calm or not strong then someone is not wise or quiet.
If someone is not curious or not wise then someone is curious or not creative.
Everyone who is quiet is either creative or quiet.
Everyone who is either rich or not humble is not patient and vice versa.
Everyone who is either strong or not brave is creative and vice versa.
Everyone who is either strong or humble is either generous or calm and vice versa.
Everyone who is either not happy or not curious is either brave or strong.
If someone is curious then paul is not happy or generous.
Everyone who is either creative or not kind is humble and vice versa.
Everyone who is not curious or not kind is both not tall and rich.
Someone is both humble and not patient.
Alice is either humble or quiet.
Someone is either not happy or generous.
Lucy is not quiet or creative.
Someone is creative.
Someone is either not curious or generous. | Paul is not quiet. | entailment | (((~creative(susan)<~>funny(susan)))=>(?[X]:((~brave(X)<~>tall(X)))))&
((?[X]:((wise(X)|patient(X))))=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((strong(X)&creative(X))<=>(brave(X)|~happy(X))))&
(![X]:((~funny(X)&funny(X))<=>~tall(X)))&
(![X]:(~tall(X)=>(quiet(X)|~humble(X))))&
((~tall(mary))<=>(?[X]:((~rich(X)|~brave(X)))))&
(((calm(john)<~>~strong(john)))=>(?[X]:((~wise(X)|quiet(X)))))&
((?[X]:((~curious(X)|~wise(X))))=>(?[X]:((curious(X)|~creative(X)))))&
(![X]:(quiet(X)=>(creative(X)<~>quiet(X))))&
(![X]:((rich(X)<~>~humble(X))<=>~patient(X)))&
(![X]:((strong(X)<~>~brave(X))<=>creative(X)))&
(![X]:((strong(X)<~>humble(X))<=>(generous(X)<~>calm(X))))&
(![X]:((~happy(X)<~>~curious(X))=>(brave(X)<~>strong(X))))&
((?[X]:(curious(X)))=>((~happy(paul)|generous(paul))))&
(![X]:((creative(X)<~>~kind(X))<=>humble(X)))&
(![X]:((~curious(X)|~kind(X))=>(~tall(X)&rich(X))))&
(?[X]:((humble(X)&~patient(X))))&
((humble(alice)<~>quiet(alice)))&
(?[X]:((~happy(X)<~>generous(X))))&
((~quiet(lucy)|creative(lucy)))&
(?[X]:(creative(X)))&
(?[X]:((~curious(X)<~>generous(X)))) | ~quiet(paul) | [
"p2",
"p3",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2681076353824493271461722
% SZS output start Proof for 2681076353824493271461722
3. ! [X0] : ((creative(X0) & strong(X0)) <=> (~happy(X0) | brave(X0))) [input p2]
4. ! [X0] : ((funny(X0) & ~funny(X0)) <=> ~tall(X0)) [input p3]
6. ~tall(mary) <=> ? [X0] : (~brave(X0) | ~rich(X0)) [input p5]
9. ! [X0] : (quiet(X0) => (creative(X0) <~> quiet(X0))) [input p8]
23. quiet(paul) [input hypothesis]
33. ! [X0] : ((creative(X0) <~> quiet(X0)) | ~quiet(X0)) [ennf transformation 9]
45. ! [X0] : (((creative(X0) & strong(X0)) | (happy(X0) & ~brave(X0))) & ((~happy(X0) | brave(X0)) | (~creative(X0) | ~strong(X0)))) [nnf transformation 3]
46. ! [X0] : (((creative(X0) & strong(X0)) | (happy(X0) & ~brave(X0))) & (~happy(X0) | brave(X0) | ~creative(X0) | ~strong(X0))) [flattening 45]
47. ! [X0] : (((funny(X0) & ~funny(X0)) | tall(X0)) & (~tall(X0) | (~funny(X0) | funny(X0)))) [nnf transformation 4]
48. ! [X0] : (((funny(X0) & ~funny(X0)) | tall(X0)) & (~tall(X0) | ~funny(X0) | funny(X0))) [flattening 47]
49. (~tall(mary) | ! [X0] : (brave(X0) & rich(X0))) & (? [X0] : (~brave(X0) | ~rich(X0)) | tall(mary)) [nnf transformation 6]
50. (~tall(mary) | ! [X0] : (brave(X0) & rich(X0))) & (? [X1] : (~brave(X1) | ~rich(X1)) | tall(mary)) [rectify 49]
51. ? [X1] : (~brave(X1) | ~rich(X1)) => (~brave(sK2) | ~rich(sK2)) [choice axiom]
52. (~tall(mary) | ! [X0] : (brave(X0) & rich(X0))) & ((~brave(sK2) | ~rich(sK2)) | tall(mary)) [skolemisation 50,51]
59. ! [X0] : (((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) | ~quiet(X0)) [nnf transformation 33]
87. ~brave(X0) | creative(X0) [cnf transformation 46]
90. ~funny(X0) | tall(X0) [cnf transformation 48]
91. tall(X0) | funny(X0) [cnf transformation 48]
95. ~tall(mary) | brave(X0) [cnf transformation 52]
101. ~quiet(X0) | ~creative(X0) | ~quiet(X0) [cnf transformation 59]
139. quiet(paul) [cnf transformation 23]
140. ~quiet(X0) | ~creative(X0) [duplicate literal removal 101]
179. tall(X0) [subsumption resolution 90,91]
180. brave(X0) [subsumption resolution 95,179]
275. creative(X0) [resolution 87,180]
284. ~creative(paul) [resolution 140,139]
285. $false [subsumption resolution 284,275]
% SZS output end Proof for 2681076353824493271461722
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or kind is not tall or not rich and vice versa.
Everyone who is both not brave and not calm is humble or not rich.
Everyone who is not generous or not quiet is creative or brave and vice versa.
If someone is curious or wise then someone is either creative or not curious.
Everyone who is generous is either not kind or not funny.
Everyone who is either happy or not old is both calm and brave.
If someone is strong or not kind then mary is both not tall and not humble.
Everyone who is either not quiet or rich is not generous and vice versa.
Everyone who is quiet is not quiet.
If fred is either not patient or not old then someone is not calm or calm and vice versa.
Everyone who is both not calm and tall is both not rich and old.
If alice is either not brave or wise then mary is kind and vice versa.
If fred is both not wise and not kind then someone is both curious and not old and vice versa.
Everyone who is both rich and not old is both not curious and not generous.
Everyone who is either funny or patient is not generous or wise and vice versa.
Everyone who is wise is not old or happy and vice versa.
Someone is not creative.
Mary is not rich or not old.
Someone is both calm and wise.
Mary is not brave.
Someone is either not tall or quiet.
Someone is either not patient or curious.
Someone is both not quiet and old.
Someone is not calm. | Mary is kind. | entailment | (![X]:((rich(X)|kind(X))<=>(~tall(X)|~rich(X))))&
(![X]:((~brave(X)&~calm(X))=>(humble(X)|~rich(X))))&
(![X]:((~generous(X)|~quiet(X))<=>(creative(X)|brave(X))))&
((?[X]:((curious(X)|wise(X))))=>(?[X]:((creative(X)<~>~curious(X)))))&
(![X]:(generous(X)=>(~kind(X)<~>~funny(X))))&
(![X]:((happy(X)<~>~old(X))=>(calm(X)&brave(X))))&
((?[X]:((strong(X)|~kind(X))))=>((~tall(mary)&~humble(mary))))&
(![X]:((~quiet(X)<~>rich(X))<=>~generous(X)))&
(![X]:(quiet(X)=>~quiet(X)))&
(((~patient(fred)<~>~old(fred)))<=>(?[X]:((~calm(X)|calm(X)))))&
(![X]:((~calm(X)&tall(X))=>(~rich(X)&old(X))))&
(((~brave(alice)<~>wise(alice)))<=>(kind(mary)))&
(((~wise(fred)&~kind(fred)))<=>(?[X]:((curious(X)&~old(X)))))&
(![X]:((rich(X)&~old(X))=>(~curious(X)&~generous(X))))&
(![X]:((funny(X)<~>patient(X))<=>(~generous(X)|wise(X))))&
(![X]:(wise(X)<=>(~old(X)|happy(X))))&
(?[X]:(~creative(X)))&
((~rich(mary)|~old(mary)))&
(?[X]:((calm(X)&wise(X))))&
(~brave(mary))&
(?[X]:((~tall(X)<~>quiet(X))))&
(?[X]:((~patient(X)<~>curious(X))))&
(?[X]:((~quiet(X)&old(X))))&
(?[X]:(~calm(X))) | kind(mary) | [
"p0",
"p7",
"p8",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8027180475610555911467372
% SZS output start Proof for 8027180475610555911467372
1. ! [X0] : ((kind(X0) | rich(X0)) <=> (~rich(X0) | ~tall(X0))) [input p0]
8. ! [X0] : ((~quiet(X0) <~> rich(X0)) <=> ~generous(X0)) [input p7]
9. ! [X0] : (quiet(X0) => ~quiet(X0)) [input p8]
14. ! [X0] : ((~old(X0) & rich(X0)) => (~generous(X0) & ~curious(X0))) [input p13]
18. ~old(mary) | ~rich(mary) [input p17]
25. ~kind(mary) [input hypothesis]
34. ! [X0] : (~quiet(X0) | ~quiet(X0)) [ennf transformation 9]
37. ! [X0] : ((~generous(X0) & ~curious(X0)) | (old(X0) | ~rich(X0))) [ennf transformation 14]
38. ! [X0] : ((~generous(X0) & ~curious(X0)) | old(X0) | ~rich(X0)) [flattening 37]
39. ! [X0] : (((kind(X0) | rich(X0)) | (rich(X0) & tall(X0))) & ((~rich(X0) | ~tall(X0)) | (~kind(X0) & ~rich(X0)))) [nnf transformation 1]
40. ! [X0] : ((kind(X0) | rich(X0) | (rich(X0) & tall(X0))) & (~rich(X0) | ~tall(X0) | (~kind(X0) & ~rich(X0)))) [flattening 39]
49. ! [X0] : ((((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | generous(X0)) & (~generous(X0) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0))))) [nnf transformation 8]
81. kind(X0) | rich(X0) | rich(X0) [cnf transformation 40]
102. ~rich(X0) | quiet(X0) | generous(X0) [cnf transformation 49]
103. ~quiet(X0) | ~quiet(X0) [cnf transformation 34]
121. ~generous(X0) | old(X0) | ~rich(X0) [cnf transformation 38]
132. ~old(mary) | ~rich(mary) [cnf transformation 18]
143. ~kind(mary) [cnf transformation 25]
144. ~quiet(X0) [duplicate literal removal 103]
146. kind(X0) | rich(X0) [duplicate literal removal 81]
197. 12 <=> kind(mary) [avatar definition]
199. ~kind(mary) <- (~12) [avatar component clause 197]
236. 20 <=> rich(mary) [avatar definition]
237. rich(mary) <- (20) [avatar component clause 236]
240. 21 <=> old(mary) [avatar definition]
242. ~old(mary) <- (~21) [avatar component clause 240]
243. ~20 | ~21 [avatar split clause 132,240,236]
255. ~12 [avatar split clause 143,197]
258. rich(mary) <- (~12) [resolution 146,199]
261. 20 | 12 [avatar split clause 258,197,236]
355. quiet(mary) | generous(mary) <- (20) [resolution 102,237]
356. generous(mary) <- (20) [subsumption resolution 355,144]
361. old(mary) | ~rich(mary) <- (20) [resolution 121,356]
362. ~rich(mary) <- (20, ~21) [subsumption resolution 361,242]
363. $false <- (20, ~21) [subsumption resolution 362,237]
364. ~20 | 21 [avatar contradiction clause 363]
365. $false [avatar sat refutation 243,255,261,364]
% SZS output end Proof for 8027180475610555911467372
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is kind then someone is not quiet or happy. If paul is not calm or not creative then john is both not kind and not quiet and vice versa. If someone is not patient or not funny then someone is curious and vice versa. Everyone who is either not generous or rich is both humble and rich. Everyone who is not curious is quiet or not brave and vice versa. If someone is not kind then someone is not tall or humble and vice versa. If someone is not curious or not funny then fred is both calm and not strong and vice versa. Everyone who is not happy is either rich or not wise. Everyone who is both not old and not creative is not humble. Everyone who is either wise or quiet is not curious or not calm. If someone is not strong or not rich then john is tall or quiet and vice versa. If someone is not brave or patient then someone is kind or humble and vice versa. Everyone who is not old is either quiet or calm and vice versa. If someone is either curious or rich then someone is either not strong or not patient. If someone is either wise or quiet then someone is not happy or not creative and vice versa. Everyone who is not humble or not kind is rich or not tall and vice versa. Alice is either not strong or patient. Someone is funny or humble. Paul is generous or not rich. Alice is strong or humble. Paul is both not humble and creative. Paul is either curious or not calm. John is calm. John is not curious. | John is not old. | neutral | ((kind(alice))=>(?[X]:((~quiet(X)|happy(X)))))&
(((~calm(paul)|~creative(paul)))<=>((~kind(john)&~quiet(john))))&
((?[X]:((~patient(X)|~funny(X))))<=>(?[X]:(curious(X))))&
(![X]:((~generous(X)<~>rich(X))=>(humble(X)&rich(X))))&
(![X]:(~curious(X)<=>(quiet(X)|~brave(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((~tall(X)|humble(X)))))&
((?[X]:((~curious(X)|~funny(X))))<=>((calm(fred)&~strong(fred))))&
(![X]:(~happy(X)=>(rich(X)<~>~wise(X))))&
(![X]:((~old(X)&~creative(X))=>~humble(X)))&
(![X]:((wise(X)<~>quiet(X))=>(~curious(X)|~calm(X))))&
((?[X]:((~strong(X)|~rich(X))))<=>((tall(john)|quiet(john))))&
((?[X]:((~brave(X)|patient(X))))<=>(?[X]:((kind(X)|humble(X)))))&
(![X]:(~old(X)<=>(quiet(X)<~>calm(X))))&
((?[X]:((curious(X)<~>rich(X))))=>(?[X]:((~strong(X)<~>~patient(X)))))&
((?[X]:((wise(X)<~>quiet(X))))<=>(?[X]:((~happy(X)|~creative(X)))))&
(![X]:((~humble(X)|~kind(X))<=>(rich(X)|~tall(X))))&
((~strong(alice)<~>patient(alice)))&
(?[X]:((funny(X)|humble(X))))&
((generous(paul)|~rich(paul)))&
((strong(alice)|humble(alice)))&
((~humble(paul)&creative(paul)))&
((curious(paul)<~>~calm(paul)))&
(calm(john))&
(~curious(john)) | ~old(john) | [] | null | 0 |
If someone is both strong and not quiet then mary is both not brave and not tall and vice versa.
If someone is not brave or humble then alice is not patient or not rich and vice versa.
Everyone who is not humble is kind.
If susan is not humble then someone is not tall.
Everyone who is both curious and not tall is either not generous or strong and vice versa.
Everyone who is not creative or not strong is not kind or not humble.
If alice is both strong and 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.
Mary is not kind or not creative.
Someone is both curious and not quiet.
Lucy is not wise or not patient.
Paul is both not curious and rich.
Someone is both not funny and not strong.
Someone is old.
John is curious or not humble.
Susan is either calm or rich. | Mary is patient. | contradiction | ((?[X]:((strong(X)&~quiet(X))))<=>((~brave(mary)&~tall(mary))))&
((?[X]:((~brave(X)|humble(X))))<=>((~patient(alice)|~rich(alice))))&
(![X]:(~humble(X)=>kind(X)))&
((~humble(susan))=>(?[X]:(~tall(X))))&
(![X]:((curious(X)&~tall(X))<=>(~generous(X)<~>strong(X))))&
(![X]:((~creative(X)|~strong(X))=>(~kind(X)|~humble(X))))&
(((strong(alice)&rich(alice)))<=>(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))))&
((~kind(mary)|~creative(mary)))&
(?[X]:((curious(X)&~quiet(X))))&
((~wise(lucy)|~patient(lucy)))&
((~curious(paul)&rich(paul)))&
(?[X]:((~funny(X)&~strong(X))))&
(?[X]:(old(X)))&
((curious(john)|~humble(john)))&
((calm(susan)<~>rich(susan))) | patient(mary) | [
"p5",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 954356180648130060240400
% SZS output start Proof for 954356180648130060240400
6. ! [X0] : ((~strong(X0) | ~creative(X0)) => (~humble(X0) | ~kind(X0))) [input p5]
9. ! [X0] : ((~strong(X0) | tall(X0)) => humble(X0)) [input p8]
10. (patient(mary) | ~calm(mary)) <=> ? [X0] : (kind(X0) & ~strong(X0)) [input p9]
25. patient(mary) [input hypothesis]
28. ! [X0] : ((~humble(X0) | ~kind(X0)) | (strong(X0) & creative(X0))) [ennf transformation 6]
29. ! [X0] : (~humble(X0) | ~kind(X0) | (strong(X0) & creative(X0))) [flattening 28]
30. ! [X0] : (humble(X0) | (strong(X0) & ~tall(X0))) [ennf transformation 9]
51. ((patient(mary) | ~calm(mary)) | ! [X0] : (~kind(X0) | strong(X0))) & (? [X0] : (kind(X0) & ~strong(X0)) | (~patient(mary) & calm(mary))) [nnf transformation 10]
52. (patient(mary) | ~calm(mary) | ! [X0] : (~kind(X0) | strong(X0))) & (? [X0] : (kind(X0) & ~strong(X0)) | (~patient(mary) & calm(mary))) [flattening 51]
53. (patient(mary) | ~calm(mary) | ! [X0] : (~kind(X0) | strong(X0))) & (? [X1] : (kind(X1) & ~strong(X1)) | (~patient(mary) & calm(mary))) [rectify 52]
54. ? [X1] : (kind(X1) & ~strong(X1)) => (kind(sK3) & ~strong(sK3)) [choice axiom]
55. (patient(mary) | ~calm(mary) | ! [X0] : (~kind(X0) | strong(X0))) & ((kind(sK3) & ~strong(sK3)) | (~patient(mary) & calm(mary))) [skolemisation 53,54]
91. ~kind(X0) | ~humble(X0) | strong(X0) [cnf transformation 29]
100. humble(X0) | strong(X0) [cnf transformation 30]
102. ~strong(sK3) | ~patient(mary) [cnf transformation 55]
104. kind(sK3) | ~patient(mary) [cnf transformation 55]
144. patient(mary) [cnf transformation 25]
225. 18 <=> patient(mary) [avatar definition]
230. 19 <=> kind(sK3) [avatar definition]
232. kind(sK3) <- (19) [avatar component clause 230]
233. ~18 | 19 [avatar split clause 104,230,225]
236. 20 <=> strong(sK3) [avatar definition]
238. ~strong(sK3) <- (~20) [avatar component clause 236]
239. ~18 | ~20 [avatar split clause 102,236,225]
318. 18 [avatar split clause 144,225]
330. 38 <=> humble(sK3) [avatar definition]
332. ~humble(sK3) <- (~38) [avatar component clause 330]
334. ~humble(sK3) | strong(sK3) <- (19) [resolution 91,232]
336. strong(sK3) <- (~38) [resolution 332,100]
337. $false <- (~20, ~38) [subsumption resolution 336,238]
338. 20 | 38 [avatar contradiction clause 337]
339. ~humble(sK3) <- (19, ~20) [subsumption resolution 334,238]
340. ~38 | ~19 | 20 [avatar split clause 339,236,230,330]
341. $false [avatar sat refutation 233,239,318,338,340]
% SZS output end Proof for 954356180648130060240400
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or not wise is both kind and not curious. Everyone who is not creative is either brave or not rich and vice versa. Everyone who is old is not rich and vice versa. If fred is patient then lucy is not curious or happy. Everyone who is both not patient and rich is both creative and not humble and vice versa. Everyone who is not old or rich is generous or not kind and vice versa. Everyone who is either not brave or creative is not quiet or quiet and vice versa. Everyone who is not happy is either generous or not generous. If john is quiet then someone is either old or kind. If alice is not kind then alice is either not happy or not generous. Everyone who is funny is either not calm or not old and vice versa. If mary is not calm or not brave then someone is both kind and creative and vice versa. If someone is not generous or creative then john is happy or kind. Everyone who is either not kind or not tall is either not kind or not generous. Everyone who is either not rich or wise is calm. If paul is either generous or kind then alice is either not calm or not tall. Fred is either kind or wise. Lucy is either not humble or curious. Someone is happy or not brave. Someone is either happy or not happy. Someone is both funny and not humble. Someone is either old or strong. Paul is both not wise and strong. Someone is not tall. | Lucy is generous. | contradiction | (![X]:((rich(X)|~wise(X))=>(kind(X)&~curious(X))))&
(![X]:(~creative(X)<=>(brave(X)<~>~rich(X))))&
(![X]:(old(X)<=>~rich(X)))&
((patient(fred))=>((~curious(lucy)|happy(lucy))))&
(![X]:((~patient(X)&rich(X))<=>(creative(X)&~humble(X))))&
(![X]:((~old(X)|rich(X))<=>(generous(X)|~kind(X))))&
(![X]:((~brave(X)<~>creative(X))<=>(~quiet(X)|quiet(X))))&
(![X]:(~happy(X)=>(generous(X)<~>~generous(X))))&
((quiet(john))=>(?[X]:((old(X)<~>kind(X)))))&
((~kind(alice))=>((~happy(alice)<~>~generous(alice))))&
(![X]:(funny(X)<=>(~calm(X)<~>~old(X))))&
(((~calm(mary)|~brave(mary)))<=>(?[X]:((kind(X)&creative(X)))))&
((?[X]:((~generous(X)|creative(X))))=>((happy(john)|kind(john))))&
(![X]:((~kind(X)<~>~tall(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((~rich(X)<~>wise(X))=>calm(X)))&
(((generous(paul)<~>kind(paul)))=>((~calm(alice)<~>~tall(alice))))&
((kind(fred)<~>wise(fred)))&
((~humble(lucy)<~>curious(lucy)))&
(?[X]:((happy(X)|~brave(X))))&
(?[X]:((happy(X)<~>~happy(X))))&
(?[X]:((funny(X)&~humble(X))))&
(?[X]:((old(X)<~>strong(X))))&
((~wise(paul)&strong(paul)))&
(?[X]:(~tall(X))) | generous(lucy) | [
"p1",
"p2",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8087215015705502210244912
% SZS output start Proof for 8087215015705502210244912
2. ! [X0] : (~creative(X0) <=> (brave(X0) <~> ~rich(X0))) [input p1]
3. ! [X0] : (old(X0) <=> ~rich(X0)) [input p2]
6. ! [X0] : ((rich(X0) | ~old(X0)) <=> (~kind(X0) | generous(X0))) [input p5]
7. ! [X0] : ((~brave(X0) <~> creative(X0)) <=> (quiet(X0) | ~quiet(X0))) [input p6]
25. generous(lucy) [input hypothesis]
39. ! [X0] : ((~creative(X0) | ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0)))) & (((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | creative(X0))) [nnf transformation 2]
40. ! [X0] : ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))) [nnf transformation 3]
43. ! [X0] : (((rich(X0) | ~old(X0)) | (kind(X0) & ~generous(X0))) & ((~kind(X0) | generous(X0)) | (~rich(X0) & old(X0)))) [nnf transformation 6]
44. ! [X0] : ((rich(X0) | ~old(X0) | (kind(X0) & ~generous(X0))) & (~kind(X0) | generous(X0) | (~rich(X0) & old(X0)))) [flattening 43]
45. ! [X0] : ((((~creative(X0) | brave(X0)) & (creative(X0) | ~brave(X0))) | (~quiet(X0) & quiet(X0))) & ((quiet(X0) | ~quiet(X0)) | ((~brave(X0) | ~creative(X0)) & (creative(X0) | brave(X0))))) [nnf transformation 7]
46. ! [X0] : ((((~creative(X0) | brave(X0)) & (creative(X0) | ~brave(X0))) | (~quiet(X0) & quiet(X0))) & (quiet(X0) | ~quiet(X0) | ((~brave(X0) | ~creative(X0)) & (creative(X0) | brave(X0))))) [flattening 45]
79. ~rich(X0) | brave(X0) | creative(X0) [cnf transformation 39]
81. ~brave(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 39]
83. ~old(X0) | ~rich(X0) [cnf transformation 40]
84. old(X0) | rich(X0) [cnf transformation 40]
92. rich(X0) | ~old(X0) | ~generous(X0) [cnf transformation 44]
96. creative(X0) | ~brave(X0) | quiet(X0) [cnf transformation 46]
97. creative(X0) | ~brave(X0) | ~quiet(X0) [cnf transformation 46]
98. ~creative(X0) | brave(X0) | quiet(X0) [cnf transformation 46]
99. ~creative(X0) | brave(X0) | ~quiet(X0) [cnf transformation 46]
139. generous(lucy) [cnf transformation 25]
156. ~generous(X0) | ~old(X0) [subsumption resolution 92,83]
158. ~creative(X0) | brave(X0) [subsumption resolution 98,99]
159. ~brave(X0) | creative(X0) [subsumption resolution 96,97]
294. ~old(lucy) [resolution 156,139]
296. rich(lucy) [resolution 294,84]
306. brave(lucy) | creative(lucy) [resolution 296,79]
309. brave(lucy) [subsumption resolution 306,158]
324. 31 <=> creative(lucy) [avatar definition]
337. ~rich(lucy) | ~creative(lucy) [resolution 309,81]
339. creative(lucy) [resolution 309,159]
340. ~creative(lucy) [subsumption resolution 337,296]
341. ~31 [avatar split clause 340,324]
342. 31 [avatar split clause 339,324]
343. $false [avatar sat refutation 341,342]
% SZS output end Proof for 8087215015705502210244912
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is either calm or old and vice versa. Everyone who is either not brave or generous is tall or not rich. Everyone who is both not curious and patient is both patient and curious and vice versa. If paul is not happy or not curious then someone is either not funny or strong. Everyone who is either not creative or not generous is not strong or generous. Everyone who is either brave or not wise is not kind or funny. Everyone who is strong or funny is either not curious or not happy and vice versa. If someone is wise then susan is funny or generous and vice versa. Everyone who is either not creative or humble is not strong or curious. If paul is both not calm and not patient then someone is not rich and vice versa. If someone is either brave or not happy then fred is not funny or not happy and vice versa. Everyone who is not generous or not strong is either not calm or curious. If alice is not generous or quiet then susan is either not rich or not brave and vice versa. If alice is both not patient and kind then someone is both not happy and not quiet and vice versa. Everyone who is both not generous and funny is either not quiet or not humble. If john is both not wise and curious then someone is both not quiet and not happy and vice versa. John is not creative or generous. Someone is both not quiet and tall. Someone is not rich or not patient. Someone is strong or quiet. Someone is not tall. Someone is humble. | Fred is creative. | neutral | (![X]:((~happy(X)<~>~curious(X))<=>(calm(X)<~>old(X))))&
(![X]:((~brave(X)<~>generous(X))=>(tall(X)|~rich(X))))&
(![X]:((~curious(X)&patient(X))<=>(patient(X)&curious(X))))&
(((~happy(paul)|~curious(paul)))=>(?[X]:((~funny(X)<~>strong(X)))))&
(![X]:((~creative(X)<~>~generous(X))=>(~strong(X)|generous(X))))&
(![X]:((brave(X)<~>~wise(X))=>(~kind(X)|funny(X))))&
(![X]:((strong(X)|funny(X))<=>(~curious(X)<~>~happy(X))))&
((?[X]:(wise(X)))<=>((funny(susan)|generous(susan))))&
(![X]:((~creative(X)<~>humble(X))=>(~strong(X)|curious(X))))&
(((~calm(paul)&~patient(paul)))<=>(?[X]:(~rich(X))))&
((?[X]:((brave(X)<~>~happy(X))))<=>((~funny(fred)|~happy(fred))))&
(![X]:((~generous(X)|~strong(X))=>(~calm(X)<~>curious(X))))&
(((~generous(alice)|quiet(alice)))<=>((~rich(susan)<~>~brave(susan))))&
(((~patient(alice)&kind(alice)))<=>(?[X]:((~happy(X)&~quiet(X)))))&
(![X]:((~generous(X)&funny(X))=>(~quiet(X)<~>~humble(X))))&
(((~wise(john)&curious(john)))<=>(?[X]:((~quiet(X)&~happy(X)))))&
((~creative(john)|generous(john)))&
(?[X]:((~quiet(X)&tall(X))))&
(?[X]:((~rich(X)|~patient(X))))&
(?[X]:((strong(X)|quiet(X))))&
(?[X]:(~tall(X)))&
(?[X]:(humble(X))) | creative(fred) | [] | null | 0 |
Everyone who is either tall or not wise is curious or happy and vice versa. Everyone who is not tall is wise or quiet. Everyone who is both not creative and not quiet is not strong or old and vice versa. If someone is both not old and kind then someone is both not funny and funny. If someone is either calm or kind then someone is curious and vice versa. Everyone who is either brave or not strong is tall. Everyone who is brave or wise is both strong and not strong and vice versa. If mary is both not creative and not funny then someone is kind or funny. Everyone who is either curious or strong is both strong and creative and vice versa. If someone is either not generous or not happy then someone is either curious or quiet and vice versa. If someone is humble then alice is both not generous and not calm and vice versa. If someone is not calm then fred is either brave or humble and vice versa. Everyone who is not patient or creative is both creative and not generous and vice versa. Everyone who is quiet is either not strong or brave and vice versa. Everyone who is not wise or not tall is not curious and vice versa. Everyone who is funny is quiet or creative and vice versa. Susan is both creative and not rich. Lucy is tall. Alice is not kind. Someone is either calm or not patient. | Mary is brave. | contradiction | (![X]:((tall(X)<~>~wise(X))<=>(curious(X)|happy(X))))&
(![X]:(~tall(X)=>(wise(X)|quiet(X))))&
(![X]:((~creative(X)&~quiet(X))<=>(~strong(X)|old(X))))&
((?[X]:((~old(X)&kind(X))))=>(?[X]:((~funny(X)&funny(X)))))&
((?[X]:((calm(X)<~>kind(X))))<=>(?[X]:(curious(X))))&
(![X]:((brave(X)<~>~strong(X))=>tall(X)))&
(![X]:((brave(X)|wise(X))<=>(strong(X)&~strong(X))))&
(((~creative(mary)&~funny(mary)))=>(?[X]:((kind(X)|funny(X)))))&
(![X]:((curious(X)<~>strong(X))<=>(strong(X)&creative(X))))&
((?[X]:((~generous(X)<~>~happy(X))))<=>(?[X]:((curious(X)<~>quiet(X)))))&
((?[X]:(humble(X)))<=>((~generous(alice)&~calm(alice))))&
((?[X]:(~calm(X)))<=>((brave(fred)<~>humble(fred))))&
(![X]:((~patient(X)|creative(X))<=>(creative(X)&~generous(X))))&
(![X]:(quiet(X)<=>(~strong(X)<~>brave(X))))&
(![X]:((~wise(X)|~tall(X))<=>~curious(X)))&
(![X]:(funny(X)<=>(quiet(X)|creative(X))))&
((creative(susan)&~rich(susan)))&
(tall(lucy))&
(~kind(alice))&
(?[X]:((calm(X)<~>~patient(X)))) | brave(mary) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 4862034851928514862941072
% SZS output start Proof for 4862034851928514862941072
7. ! [X0] : ((wise(X0) | brave(X0)) <=> (~strong(X0) & strong(X0))) [input p6]
21. brave(mary) [input hypothesis]
45. ! [X0] : (((wise(X0) | brave(X0)) | (strong(X0) | ~strong(X0))) & ((~strong(X0) & strong(X0)) | (~wise(X0) & ~brave(X0)))) [nnf transformation 7]
46. ! [X0] : ((wise(X0) | brave(X0) | strong(X0) | ~strong(X0)) & ((~strong(X0) & strong(X0)) | (~wise(X0) & ~brave(X0)))) [flattening 45]
95. strong(X0) | ~brave(X0) [cnf transformation 46]
97. ~strong(X0) | ~brave(X0) [cnf transformation 46]
142. brave(mary) [cnf transformation 21]
180. ~brave(X0) [subsumption resolution 95,97]
286. $false [subsumption resolution 142,180]
% SZS output end Proof for 4862034851928514862941072
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is both generous and not rich.
If susan is either not strong or not humble then someone is either not funny or not brave.
Everyone who is not happy is either not patient or brave.
Everyone who is both strong and not kind is not patient and vice versa.
If john is curious then someone is either strong or not generous.
Everyone who is not strong is not tall and vice versa.
Everyone who is both humble and quiet is rich and vice versa.
Everyone who is humble or not rich is not calm and vice versa.
Everyone who is either not funny or not happy is either not quiet or not generous and vice versa.
If someone is happy then fred is both not strong and brave and vice versa.
If john is not old or rich then someone is generous or kind and vice versa.
If someone is not brave then someone is both not wise and not calm and vice versa.
If lucy is not brave then susan is either brave or not strong and vice versa.
If lucy is both not patient and not old then lucy is creative and vice versa.
If someone is not rich or not wise then someone is both not brave and not tall and vice versa.
If someone is both not generous and generous then someone is patient or curious.
Someone is either kind or not curious.
Someone is not kind.
John is both not curious and kind.
Someone is both not calm and creative.
Someone is not tall or curious.
Someone is both generous and old.
Mary is both patient and kind.
Someone is wise or funny. | Mary is not calm. | entailment | (![X]:(~patient(X)=>(generous(X)&~rich(X))))&
(((~strong(susan)<~>~humble(susan)))=>(?[X]:((~funny(X)<~>~brave(X)))))&
(![X]:(~happy(X)=>(~patient(X)<~>brave(X))))&
(![X]:((strong(X)&~kind(X))<=>~patient(X)))&
((curious(john))=>(?[X]:((strong(X)<~>~generous(X)))))&
(![X]:(~strong(X)<=>~tall(X)))&
(![X]:((humble(X)&quiet(X))<=>rich(X)))&
(![X]:((humble(X)|~rich(X))<=>~calm(X)))&
(![X]:((~funny(X)<~>~happy(X))<=>(~quiet(X)<~>~generous(X))))&
((?[X]:(happy(X)))<=>((~strong(fred)&brave(fred))))&
(((~old(john)|rich(john)))<=>(?[X]:((generous(X)|kind(X)))))&
((?[X]:(~brave(X)))<=>(?[X]:((~wise(X)&~calm(X)))))&
((~brave(lucy))<=>((brave(susan)<~>~strong(susan))))&
(((~patient(lucy)&~old(lucy)))<=>(creative(lucy)))&
((?[X]:((~rich(X)|~wise(X))))<=>(?[X]:((~brave(X)&~tall(X)))))&
((?[X]:((~generous(X)&generous(X))))=>(?[X]:((patient(X)|curious(X)))))&
(?[X]:((kind(X)<~>~curious(X))))&
(?[X]:(~kind(X)))&
((~curious(john)&kind(john)))&
(?[X]:((~calm(X)&creative(X))))&
(?[X]:((~tall(X)|curious(X))))&
(?[X]:((generous(X)&old(X))))&
((patient(mary)&kind(mary)))&
(?[X]:((wise(X)|funny(X)))) | ~calm(mary) | [
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2391341579130343841902145
% SZS output start Proof for 2391341579130343841902145
7. ! [X0] : ((quiet(X0) & humble(X0)) <=> rich(X0)) [input p6]
8. ! [X0] : ((~rich(X0) | humble(X0)) <=> ~calm(X0)) [input p7]
25. calm(mary) [input hypothesis]
44. ! [X0] : (((quiet(X0) & humble(X0)) | ~rich(X0)) & (rich(X0) | (~quiet(X0) | ~humble(X0)))) [nnf transformation 7]
45. ! [X0] : (((quiet(X0) & humble(X0)) | ~rich(X0)) & (rich(X0) | ~quiet(X0) | ~humble(X0))) [flattening 44]
46. ! [X0] : (((~rich(X0) | humble(X0)) | calm(X0)) & (~calm(X0) | (rich(X0) & ~humble(X0)))) [nnf transformation 8]
47. ! [X0] : ((~rich(X0) | humble(X0) | calm(X0)) & (~calm(X0) | (rich(X0) & ~humble(X0)))) [flattening 46]
104. ~rich(X0) | humble(X0) [cnf transformation 45]
106. ~calm(X0) | ~humble(X0) [cnf transformation 47]
107. ~calm(X0) | rich(X0) [cnf transformation 47]
153. calm(mary) [cnf transformation 25]
353. ~humble(mary) [resolution 106,153]
354. rich(mary) [resolution 107,153]
356. humble(mary) [resolution 354,104]
358. $false [subsumption resolution 356,353]
% SZS output end Proof for 2391341579130343841902145
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not wise or creative then someone is both brave and not wise and vice versa.
Everyone who is both curious and brave is not curious or not patient and vice versa.
Everyone who is either not happy or not brave is either not generous or calm.
If someone is both generous and not curious then lucy is either not humble or calm.
Everyone who is not strong is not rich or not wise and vice versa.
If someone is not creative or not calm then alice is either kind or quiet and vice versa.
If paul is both not generous and wise then alice is either rich or not old.
Everyone who is not quiet or not tall is either kind or brave and vice versa.
Everyone who is either not brave or not calm is not tall and vice versa.
If someone is both not tall and kind then lucy is not happy or not strong and vice versa.
If someone is both kind and not kind then fred is either calm or not creative and vice versa.
Everyone who is both not tall and not calm is brave and vice versa.
If someone is both strong and not old then someone is old or not kind and vice versa.
If someone is both not patient and not old then someone is creative.
Everyone who is either brave or not brave is both not brave and not tall and vice versa.
If someone is not wise then fred is not tall and vice versa.
Alice is not calm or not funny.
Someone is kind or not brave.
Lucy is both happy and not humble.
John is not kind or not happy.
Someone is not generous.
Susan is curious. | Fred is curious. | entailment | ((?[X]:((~wise(X)<~>creative(X))))<=>(?[X]:((brave(X)&~wise(X)))))&
(![X]:((curious(X)&brave(X))<=>(~curious(X)|~patient(X))))&
(![X]:((~happy(X)<~>~brave(X))=>(~generous(X)<~>calm(X))))&
((?[X]:((generous(X)&~curious(X))))=>((~humble(lucy)<~>calm(lucy))))&
(![X]:(~strong(X)<=>(~rich(X)|~wise(X))))&
((?[X]:((~creative(X)|~calm(X))))<=>((kind(alice)<~>quiet(alice))))&
(((~generous(paul)&wise(paul)))=>((rich(alice)<~>~old(alice))))&
(![X]:((~quiet(X)|~tall(X))<=>(kind(X)<~>brave(X))))&
(![X]:((~brave(X)<~>~calm(X))<=>~tall(X)))&
((?[X]:((~tall(X)&kind(X))))<=>((~happy(lucy)|~strong(lucy))))&
((?[X]:((kind(X)&~kind(X))))<=>((calm(fred)<~>~creative(fred))))&
(![X]:((~tall(X)&~calm(X))<=>brave(X)))&
((?[X]:((strong(X)&~old(X))))<=>(?[X]:((old(X)|~kind(X)))))&
((?[X]:((~patient(X)&~old(X))))=>(?[X]:(creative(X))))&
(![X]:((brave(X)<~>~brave(X))<=>(~brave(X)&~tall(X))))&
((?[X]:(~wise(X)))<=>(~tall(fred)))&
((~calm(alice)|~funny(alice)))&
(?[X]:((kind(X)|~brave(X))))&
((happy(lucy)&~humble(lucy)))&
((~kind(john)|~happy(john)))&
(?[X]:(~generous(X)))&
(curious(susan)) | curious(fred) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 3957507266415510545102294
% SZS output start Proof for 3957507266415510545102294
2. ! [X0] : ((brave(X0) & curious(X0)) <=> (~patient(X0) | ~curious(X0))) [input p1]
23. ~curious(fred) [input hypothesis]
38. ! [X0] : (((brave(X0) & curious(X0)) | (patient(X0) & curious(X0))) & ((~patient(X0) | ~curious(X0)) | (~brave(X0) | ~curious(X0)))) [nnf transformation 2]
39. ! [X0] : (((brave(X0) & curious(X0)) | (patient(X0) & curious(X0))) & (~patient(X0) | ~curious(X0) | ~brave(X0) | ~curious(X0))) [flattening 38]
88. curious(X0) | curious(X0) [cnf transformation 39]
153. ~curious(fred) [cnf transformation 23]
161. curious(X0) [duplicate literal removal 88]
330. $false [subsumption resolution 153,161]
% SZS output end Proof for 3957507266415510545102294
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is old or not generous and vice versa. If alice is curious then someone is wise. Everyone who is not brave or not funny is both not generous and not strong. If someone is not wise or rich then someone is old or not brave and vice versa. Everyone who is either not happy or not tall is both curious and strong and vice versa. Everyone who is either not patient or strong is both kind and not funny and vice versa. If susan is both not tall and not old then someone is both wise and not rich. Everyone who is generous is not kind or not wise and vice versa. Everyone who is both wise and not creative is curious and vice versa. If someone is either not kind or creative then someone is either not patient or old. Everyone who is brave is not tall or generous and vice versa. Everyone who is generous or calm is either happy or tall. If someone is either not curious or rich then paul is creative or not curious and vice versa. Everyone who is either creative or old is not patient or quiet. If susan is curious or not generous then fred is both not patient and tall and vice versa. Someone is both not tall and not happy. Someone is both not brave and kind. John is not wise or not creative. Lucy is kind or not patient. Someone is not kind. Someone is either not quiet or not kind. Paul is either not calm or tall. | Fred is not kind. | entailment | (![X]:(patient(X)<=>(old(X)|~generous(X))))&
((curious(alice))=>(?[X]:(wise(X))))&
(![X]:((~brave(X)|~funny(X))=>(~generous(X)&~strong(X))))&
((?[X]:((~wise(X)|rich(X))))<=>(?[X]:((old(X)|~brave(X)))))&
(![X]:((~happy(X)<~>~tall(X))<=>(curious(X)&strong(X))))&
(![X]:((~patient(X)<~>strong(X))<=>(kind(X)&~funny(X))))&
(((~tall(susan)&~old(susan)))=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:(generous(X)<=>(~kind(X)|~wise(X))))&
(![X]:((wise(X)&~creative(X))<=>curious(X)))&
((?[X]:((~kind(X)<~>creative(X))))=>(?[X]:((~patient(X)<~>old(X)))))&
(![X]:(brave(X)<=>(~tall(X)|generous(X))))&
(![X]:((generous(X)|calm(X))=>(happy(X)<~>tall(X))))&
((?[X]:((~curious(X)<~>rich(X))))<=>((creative(paul)|~curious(paul))))&
(![X]:((creative(X)<~>old(X))=>(~patient(X)|quiet(X))))&
(((curious(susan)|~generous(susan)))<=>((~patient(fred)&tall(fred))))&
(?[X]:((~tall(X)&~happy(X))))&
(?[X]:((~brave(X)&kind(X))))&
((~wise(john)|~creative(john)))&
((kind(lucy)|~patient(lucy)))&
(?[X]:(~kind(X)))&
(?[X]:((~quiet(X)<~>~kind(X))))&
((~calm(paul)<~>tall(paul))) | ~kind(fred) | [
"p0",
"p4",
"p7",
"p8",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2656938619168904077639701
% SZS output start Proof for 2656938619168904077639701
1. ! [X0] : (patient(X0) <=> (~generous(X0) | old(X0))) [input p0]
5. ! [X0] : ((~happy(X0) <~> ~tall(X0)) <=> (strong(X0) & curious(X0))) [input p4]
8. ! [X0] : (generous(X0) <=> (~wise(X0) | ~kind(X0))) [input p7]
9. ! [X0] : ((~creative(X0) & wise(X0)) <=> curious(X0)) [input p8]
12. ! [X0] : ((calm(X0) | generous(X0)) => (happy(X0) <~> tall(X0))) [input p11]
15. (~generous(susan) | curious(susan)) <=> (tall(fred) & ~patient(fred)) [input p14]
23. kind(fred) [input hypothesis]
31. ! [X0] : ((happy(X0) <~> tall(X0)) | (~calm(X0) & ~generous(X0))) [ennf transformation 12]
34. ! [X0] : ((patient(X0) | (generous(X0) & ~old(X0))) & ((~generous(X0) | old(X0)) | ~patient(X0))) [nnf transformation 1]
35. ! [X0] : ((patient(X0) | (generous(X0) & ~old(X0))) & (~generous(X0) | old(X0) | ~patient(X0))) [flattening 34]
43. ! [X0] : ((((tall(X0) | happy(X0)) & (~tall(X0) | ~happy(X0))) | (~strong(X0) | ~curious(X0))) & ((strong(X0) & curious(X0)) | ((~happy(X0) | tall(X0)) & (~tall(X0) | happy(X0))))) [nnf transformation 5]
44. ! [X0] : ((((tall(X0) | happy(X0)) & (~tall(X0) | ~happy(X0))) | ~strong(X0) | ~curious(X0)) & ((strong(X0) & curious(X0)) | ((~happy(X0) | tall(X0)) & (~tall(X0) | happy(X0))))) [flattening 43]
49. ! [X0] : ((generous(X0) | (wise(X0) & kind(X0))) & ((~wise(X0) | ~kind(X0)) | ~generous(X0))) [nnf transformation 8]
50. ! [X0] : ((generous(X0) | (wise(X0) & kind(X0))) & (~wise(X0) | ~kind(X0) | ~generous(X0))) [flattening 49]
51. ! [X0] : (((~creative(X0) & wise(X0)) | ~curious(X0)) & (curious(X0) | (creative(X0) | ~wise(X0)))) [nnf transformation 9]
52. ! [X0] : (((~creative(X0) & wise(X0)) | ~curious(X0)) & (curious(X0) | creative(X0) | ~wise(X0))) [flattening 51]
59. ! [X0] : (((~tall(X0) | ~happy(X0)) & (tall(X0) | happy(X0))) | (~calm(X0) & ~generous(X0))) [nnf transformation 31]
66. ((~generous(susan) | curious(susan)) | (~tall(fred) | patient(fred))) & ((tall(fred) & ~patient(fred)) | (generous(susan) & ~curious(susan))) [nnf transformation 15]
67. (~generous(susan) | curious(susan) | ~tall(fred) | patient(fred)) & ((tall(fred) & ~patient(fred)) | (generous(susan) & ~curious(susan))) [flattening 66]
80. generous(X0) | patient(X0) [cnf transformation 35]
90. ~tall(X0) | curious(X0) | happy(X0) [cnf transformation 44]
91. ~happy(X0) | curious(X0) | tall(X0) [cnf transformation 44]
104. ~kind(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 50]
108. ~curious(X0) | wise(X0) [cnf transformation 52]
117. ~generous(X0) | happy(X0) | tall(X0) [cnf transformation 59]
119. ~tall(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 59]
129. ~patient(fred) | ~curious(susan) [cnf transformation 67]
130. ~patient(fred) | generous(susan) [cnf transformation 67]
131. tall(fred) | ~curious(susan) [cnf transformation 67]
132. tall(fred) | generous(susan) [cnf transformation 67]
145. kind(fred) [cnf transformation 23]
190. 11 <=> tall(susan) [avatar definition]
191. ~tall(susan) <- (~11) [avatar component clause 190]
192. tall(susan) <- (11) [avatar component clause 190]
255. 25 <=> patient(fred) [avatar definition]
256. ~patient(fred) <- (~25) [avatar component clause 255]
259. 26 <=> tall(fred) [avatar definition]
260. tall(fred) <- (26) [avatar component clause 259]
263. 27 <=> curious(susan) [avatar definition]
267. 28 <=> generous(susan) [avatar definition]
268. generous(susan) <- (28) [avatar component clause 267]
271. 28 | 26 [avatar split clause 132,259,267]
272. ~27 | 26 [avatar split clause 131,259,263]
273. 28 | ~25 [avatar split clause 130,255,267]
274. ~27 | ~25 [avatar split clause 129,255,263]
371. curious(susan) | happy(susan) <- (11) [resolution 90,192]
375. 45 <=> happy(susan) [avatar definition]
377. happy(susan) <- (45) [avatar component clause 375]
378. 45 | 27 | ~11 [avatar split clause 371,190,263,375]
380. 46 <=> happy(fred) [avatar definition]
384. 47 <=> curious(fred) [avatar definition]
386. curious(fred) <- (47) [avatar component clause 384]
405. ~wise(fred) | ~generous(fred) [resolution 104,145]
418. 50 <=> generous(fred) [avatar definition]
419. generous(fred) <- (50) [avatar component clause 418]
420. ~generous(fred) <- (~50) [avatar component clause 418]
422. 51 <=> wise(fred) [avatar definition]
425. ~50 | ~51 [avatar split clause 405,422,418]
436. happy(susan) | tall(susan) <- (28) [resolution 117,268]
441. happy(susan) <- (~11, 28) [subsumption resolution 436,191]
442. 45 | 11 | ~28 [avatar split clause 441,267,190,375]
502. curious(susan) | tall(susan) <- (45) [resolution 377,91]
511. curious(fred) | happy(fred) <- (26) [resolution 260,90]
516. ~happy(fred) | ~generous(fred) <- (26) [resolution 119,260]
520. ~happy(fred) <- (26, 50) [subsumption resolution 516,419]
521. ~46 | ~26 | ~50 [avatar split clause 520,418,259,380]
522. 46 | 47 | ~26 [avatar split clause 511,259,384,380]
528. wise(fred) <- (47) [resolution 386,108]
536. 51 | ~47 [avatar split clause 528,384,422]
544. patient(fred) <- (~50) [resolution 420,80]
545. $false <- (~25, ~50) [subsumption resolution 544,256]
546. 25 | 50 [avatar contradiction clause 545]
547. 11 | 27 | ~45 [avatar split clause 502,375,263,190]
553. ~happy(susan) | ~generous(susan) <- (11) [resolution 192,119]
557. ~generous(susan) <- (11, 45) [subsumption resolution 553,377]
558. $false <- (11, 28, 45) [subsumption resolution 557,268]
559. ~11 | ~28 | ~45 [avatar contradiction clause 558]
560. $false [avatar sat refutation 271,272,273,274,378,425,442,521,522,536,546,547,559]
% SZS output end Proof for 2656938619168904077639701
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy is wise or not strong and vice versa.
Everyone who is not patient is either calm or strong.
Everyone who is either not rich or not funny is both funny and not generous.
If someone is old then john is both not funny and not quiet.
If someone is rich or not curious then someone is both quiet and not curious.
If someone is patient or not creative then fred is both not wise and not brave.
Everyone who is both patient and humble is not funny or not calm.
If susan is either not humble or funny then someone is both creative and not brave.
If someone is not tall then paul is funny.
Everyone who is both not rich and not humble is either humble or old.
Everyone who is both not curious and kind is either not brave or not funny and vice versa.
If someone is both strong and not funny then mary is both not curious and tall and vice versa.
Everyone who is both not kind and calm is both not funny and humble and vice versa.
Everyone who is creative or not curious is both not happy and not creative and vice versa.
If fred is both not old and calm then susan is either not happy or not humble and vice versa.
If someone is either strong or funny then someone is either patient or rich and vice versa.
Someone is not rich or not creative.
Someone is either wise or funny.
Lucy is both not kind and not rich.
Alice is both not patient and tall.
Mary is not calm or not humble.
John is not patient or not generous.
Mary is not quiet or happy. | Paul is not old. | neutral | (![X]:(happy(X)<=>(wise(X)|~strong(X))))&
(![X]:(~patient(X)=>(calm(X)<~>strong(X))))&
(![X]:((~rich(X)<~>~funny(X))=>(funny(X)&~generous(X))))&
((?[X]:(old(X)))=>((~funny(john)&~quiet(john))))&
((?[X]:((rich(X)|~curious(X))))=>(?[X]:((quiet(X)&~curious(X)))))&
((?[X]:((patient(X)|~creative(X))))=>((~wise(fred)&~brave(fred))))&
(![X]:((patient(X)&humble(X))=>(~funny(X)|~calm(X))))&
(((~humble(susan)<~>funny(susan)))=>(?[X]:((creative(X)&~brave(X)))))&
((?[X]:(~tall(X)))=>(funny(paul)))&
(![X]:((~rich(X)&~humble(X))=>(humble(X)<~>old(X))))&
(![X]:((~curious(X)&kind(X))<=>(~brave(X)<~>~funny(X))))&
((?[X]:((strong(X)&~funny(X))))<=>((~curious(mary)&tall(mary))))&
(![X]:((~kind(X)&calm(X))<=>(~funny(X)&humble(X))))&
(![X]:((creative(X)|~curious(X))<=>(~happy(X)&~creative(X))))&
(((~old(fred)&calm(fred)))<=>((~happy(susan)<~>~humble(susan))))&
((?[X]:((strong(X)<~>funny(X))))<=>(?[X]:((patient(X)<~>rich(X)))))&
(?[X]:((~rich(X)|~creative(X))))&
(?[X]:((wise(X)<~>funny(X))))&
((~kind(lucy)&~rich(lucy)))&
((~patient(alice)&tall(alice)))&
((~calm(mary)|~humble(mary)))&
((~patient(john)|~generous(john)))&
((~quiet(mary)|happy(mary))) | ~old(paul) | [] | null | 0 |
If someone is either rich or not curious then someone is creative and vice versa.
Everyone who is not creative or creative is both calm and strong.
Everyone who is both not strong and humble is not humble.
Everyone who is creative or strong is both not wise and creative and vice versa.
If mary is both kind and not humble then paul is not patient.
Everyone who is both curious and not creative is not patient or brave.
Everyone who is happy is both humble and not old and vice versa.
Everyone who is brave or not brave is not humble or not rich and vice versa.
If someone is generous then someone is either not brave or happy.
Everyone who is either not creative or rich is either not old or funny.
Everyone who is rich is old or calm.
Everyone who is not curious or curious is both generous and tall and vice versa.
Everyone who is either not happy or quiet is happy or kind.
Everyone who is not curious is both not tall and not curious.
If someone is either happy or patient then someone is both not humble and not quiet and vice versa.
If someone is not kind then someone is either brave or curious and vice versa.
Someone is both generous and not quiet.
Fred is both not wise and quiet.
Lucy is not strong or generous.
Someone is both funny and generous.
Someone is either not old or not happy.
Someone is both not rich and patient.
Someone is not funny or wise.
Lucy is both calm and not quiet. | Mary is not calm. | contradiction | ((?[X]:((rich(X)<~>~curious(X))))<=>(?[X]:(creative(X))))&
(![X]:((~creative(X)|creative(X))=>(calm(X)&strong(X))))&
(![X]:((~strong(X)&humble(X))=>~humble(X)))&
(![X]:((creative(X)|strong(X))<=>(~wise(X)&creative(X))))&
(((kind(mary)&~humble(mary)))=>(~patient(paul)))&
(![X]:((curious(X)&~creative(X))=>(~patient(X)|brave(X))))&
(![X]:(happy(X)<=>(humble(X)&~old(X))))&
(![X]:((brave(X)|~brave(X))<=>(~humble(X)|~rich(X))))&
((?[X]:(generous(X)))=>(?[X]:((~brave(X)<~>happy(X)))))&
(![X]:((~creative(X)<~>rich(X))=>(~old(X)<~>funny(X))))&
(![X]:(rich(X)=>(old(X)|calm(X))))&
(![X]:((~curious(X)|curious(X))<=>(generous(X)&tall(X))))&
(![X]:((~happy(X)<~>quiet(X))=>(happy(X)|kind(X))))&
(![X]:(~curious(X)=>(~tall(X)&~curious(X))))&
((?[X]:((happy(X)<~>patient(X))))<=>(?[X]:((~humble(X)&~quiet(X)))))&
((?[X]:(~kind(X)))<=>(?[X]:((brave(X)<~>curious(X)))))&
(?[X]:((generous(X)&~quiet(X))))&
((~wise(fred)&quiet(fred)))&
((~strong(lucy)|generous(lucy)))&
(?[X]:((funny(X)&generous(X))))&
(?[X]:((~old(X)<~>~happy(X))))&
(?[X]:((~rich(X)&patient(X))))&
(?[X]:((~funny(X)|wise(X))))&
((calm(lucy)&~quiet(lucy))) | ~calm(mary) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 9051713454814976360968609
% SZS output start Proof for 9051713454814976360968609
2. ! [X0] : ((creative(X0) | ~creative(X0)) => (strong(X0) & calm(X0))) [input p1]
25. ~calm(mary) [input hypothesis]
30. ! [X0] : ((strong(X0) & calm(X0)) | (~creative(X0) & creative(X0))) [ennf transformation 2]
88. calm(X0) | creative(X0) [cnf transformation 30]
89. calm(X0) | ~creative(X0) [cnf transformation 30]
147. ~calm(mary) [cnf transformation 25]
176. calm(X0) [subsumption resolution 88,89]
270. $false [subsumption resolution 147,176]
% SZS output end Proof for 9051713454814976360968609
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or patient is not brave and vice versa.
If someone is either rich or happy then someone is either brave or not patient and vice versa.
If someone is not happy then someone is both generous and not brave and vice versa.
If someone is either brave or curious then someone is not tall.
If mary is not brave or wise then paul is both kind and not wise.
If lucy is funny or humble then someone is either strong or not brave and vice versa.
Everyone who is both generous and not calm is both quiet and old.
Everyone who is calm is both not calm and not funny.
Everyone who is either brave or not funny is either not creative or not wise.
Everyone who is curious or patient is both calm and not wise and vice versa.
Everyone who is either not calm or not generous is not happy or not old.
If lucy is funny or not tall then mary is old and vice versa.
Everyone who is either rich or not patient is patient.
If someone is both humble and rich then paul is both kind and not brave and vice versa.
Everyone who is humble is not creative.
Everyone who is tall is either strong or patient.
Someone is both humble and funny.
Fred is both not generous and old.
Susan is not strong.
Lucy is not creative.
Fred is both kind and not funny.
Lucy is either old or not funny. | Mary is not curious. | entailment | (![X]:((kind(X)|patient(X))<=>~brave(X)))&
((?[X]:((rich(X)<~>happy(X))))<=>(?[X]:((brave(X)<~>~patient(X)))))&
((?[X]:(~happy(X)))<=>(?[X]:((generous(X)&~brave(X)))))&
((?[X]:((brave(X)<~>curious(X))))=>(?[X]:(~tall(X))))&
(((~brave(mary)|wise(mary)))=>((kind(paul)&~wise(paul))))&
(((funny(lucy)|humble(lucy)))<=>(?[X]:((strong(X)<~>~brave(X)))))&
(![X]:((generous(X)&~calm(X))=>(quiet(X)&old(X))))&
(![X]:(calm(X)=>(~calm(X)&~funny(X))))&
(![X]:((brave(X)<~>~funny(X))=>(~creative(X)<~>~wise(X))))&
(![X]:((curious(X)|patient(X))<=>(calm(X)&~wise(X))))&
(![X]:((~calm(X)<~>~generous(X))=>(~happy(X)|~old(X))))&
(((funny(lucy)|~tall(lucy)))<=>(old(mary)))&
(![X]:((rich(X)<~>~patient(X))=>patient(X)))&
((?[X]:((humble(X)&rich(X))))<=>((kind(paul)&~brave(paul))))&
(![X]:(humble(X)=>~creative(X)))&
(![X]:(tall(X)=>(strong(X)<~>patient(X))))&
(?[X]:((humble(X)&funny(X))))&
((~generous(fred)&old(fred)))&
(~strong(susan))&
(~creative(lucy))&
((kind(fred)&~funny(fred)))&
((old(lucy)<~>~funny(lucy))) | ~curious(mary) | [
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3810012639162676434236694
% SZS output start Proof for 3810012639162676434236694
8. ! [X0] : (calm(X0) => (~funny(X0) & ~calm(X0))) [input p7]
10. ! [X0] : ((patient(X0) | curious(X0)) <=> (~wise(X0) & calm(X0))) [input p9]
23. curious(mary) [input hypothesis]
32. ! [X0] : ((~funny(X0) & ~calm(X0)) | ~calm(X0)) [ennf transformation 8]
61. ! [X0] : (((patient(X0) | curious(X0)) | (wise(X0) | ~calm(X0))) & ((~wise(X0) & calm(X0)) | (~patient(X0) & ~curious(X0)))) [nnf transformation 10]
62. ! [X0] : ((patient(X0) | curious(X0) | wise(X0) | ~calm(X0)) & ((~wise(X0) & calm(X0)) | (~patient(X0) & ~curious(X0)))) [flattening 61]
103. ~calm(X0) | ~calm(X0) [cnf transformation 32]
109. calm(X0) | ~curious(X0) [cnf transformation 62]
138. curious(mary) [cnf transformation 23]
140. ~calm(X0) [duplicate literal removal 103]
258. ~curious(X0) [subsumption resolution 109,140]
296. $false [subsumption resolution 138,258]
% SZS output end Proof for 3810012639162676434236694
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm then someone is either funny or not curious and vice versa. Everyone who is either not kind or rich is either quiet or creative and vice versa. Everyone who is not curious or tall is both not funny and not patient and vice versa. Everyone who is humble is either old or kind. If someone is either not rich or old then someone is either not curious or patient. If someone is either wise or rich then someone is not brave and vice versa. Everyone who is not funny or quiet is both not happy and generous and vice versa. If john is either not quiet or happy then someone is either rich or not rich. If paul is either not kind or curious then paul is both not rich and not calm. Everyone who is brave or not curious is not curious and vice versa. Everyone who is not quiet or happy is tall or old. Everyone who is both not creative and generous is both wise and patient. Everyone who is either happy or kind is wise and vice versa. If john is not quiet or not brave then paul is patient or not strong and vice versa. If paul is not patient then someone is either generous or not happy and vice versa. If someone is tall or not humble then someone is quiet or humble and vice versa. Someone is brave or strong. Someone is not quiet or not humble. Someone is either not calm or not kind. Someone is not funny. Someone is curious or rich. John is not calm or funny. Alice is tall. Someone is funny. | Paul is rich. | neutral | ((?[X]:(calm(X)))<=>(?[X]:((funny(X)<~>~curious(X)))))&
(![X]:((~kind(X)<~>rich(X))<=>(quiet(X)<~>creative(X))))&
(![X]:((~curious(X)|tall(X))<=>(~funny(X)&~patient(X))))&
(![X]:(humble(X)=>(old(X)<~>kind(X))))&
((?[X]:((~rich(X)<~>old(X))))=>(?[X]:((~curious(X)<~>patient(X)))))&
((?[X]:((wise(X)<~>rich(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~funny(X)|quiet(X))<=>(~happy(X)&generous(X))))&
(((~quiet(john)<~>happy(john)))=>(?[X]:((rich(X)<~>~rich(X)))))&
(((~kind(paul)<~>curious(paul)))=>((~rich(paul)&~calm(paul))))&
(![X]:((brave(X)|~curious(X))<=>~curious(X)))&
(![X]:((~quiet(X)|happy(X))=>(tall(X)|old(X))))&
(![X]:((~creative(X)&generous(X))=>(wise(X)&patient(X))))&
(![X]:((happy(X)<~>kind(X))<=>wise(X)))&
(((~quiet(john)|~brave(john)))<=>((patient(paul)|~strong(paul))))&
((~patient(paul))<=>(?[X]:((generous(X)<~>~happy(X)))))&
((?[X]:((tall(X)|~humble(X))))<=>(?[X]:((quiet(X)|humble(X)))))&
(?[X]:((brave(X)|strong(X))))&
(?[X]:((~quiet(X)|~humble(X))))&
(?[X]:((~calm(X)<~>~kind(X))))&
(?[X]:(~funny(X)))&
(?[X]:((curious(X)|rich(X))))&
((~calm(john)|funny(john)))&
(tall(alice))&
(?[X]:(funny(X))) | rich(paul) | [] | null | 0 |
Everyone who is funny or not rich is generous or not wise. If someone is not patient then lucy is not rich and vice versa. Everyone who is not creative is generous and vice versa. Everyone who is not brave is both tall and not happy. If fred is not creative or tall then john is both humble and not wise and vice versa. Everyone who is kind or calm is both not rich and patient and vice versa. Everyone who is either not generous or not brave is either happy or not creative. Everyone who is not rich or not old is not calm or curious and vice versa. If someone is both not patient and not quiet then someone is creative. If someone is both generous and creative then someone is both kind and not rich. Everyone who is creative or generous is either creative or not humble and vice versa. Everyone who is either strong or not calm is not humble or funny and vice versa. If john is either not rich or wise then someone is both strong and calm and vice versa. Everyone who is not happy or brave is either not happy or quiet and vice versa. Someone is either strong or generous. Someone is quiet. Mary is both funny and generous. John is not creative. Susan is curious or quiet. Someone is not rich. Paul is curious or funny. | Lucy is rich. | neutral | (![X]:((funny(X)|~rich(X))=>(generous(X)|~wise(X))))&
((?[X]:(~patient(X)))<=>(~rich(lucy)))&
(![X]:(~creative(X)<=>generous(X)))&
(![X]:(~brave(X)=>(tall(X)&~happy(X))))&
(((~creative(fred)|tall(fred)))<=>((humble(john)&~wise(john))))&
(![X]:((kind(X)|calm(X))<=>(~rich(X)&patient(X))))&
(![X]:((~generous(X)<~>~brave(X))=>(happy(X)<~>~creative(X))))&
(![X]:((~rich(X)|~old(X))<=>(~calm(X)|curious(X))))&
((?[X]:((~patient(X)&~quiet(X))))=>(?[X]:(creative(X))))&
((?[X]:((generous(X)&creative(X))))=>(?[X]:((kind(X)&~rich(X)))))&
(![X]:((creative(X)|generous(X))<=>(creative(X)<~>~humble(X))))&
(![X]:((strong(X)<~>~calm(X))<=>(~humble(X)|funny(X))))&
(((~rich(john)<~>wise(john)))<=>(?[X]:((strong(X)&calm(X)))))&
(![X]:((~happy(X)|brave(X))<=>(~happy(X)<~>quiet(X))))&
(?[X]:((strong(X)<~>generous(X))))&
(?[X]:(quiet(X)))&
((funny(mary)&generous(mary)))&
(~creative(john))&
((curious(susan)|quiet(susan)))&
(?[X]:(~rich(X)))&
((curious(paul)|funny(paul))) | rich(lucy) | [] | null | 0 |
Everyone who is both not happy and patient is humble or not brave.
Everyone who is not strong or generous is both patient and strong and vice versa.
If someone is either brave or quiet then alice is either not wise or not old.
If someone is not calm or creative then susan is quiet and vice versa.
If fred is both not funny and not generous then alice is tall or not curious and vice versa.
Everyone who is both calm and not patient is either creative or wise.
If someone is happy or not generous then someone is kind and vice versa.
If someone is not quiet then someone is old.
If someone is either not generous or not calm then someone is not rich or calm.
Everyone who is strong or not old is kind.
Everyone who is creative or kind is not old or not creative.
Everyone who is generous or not tall is not generous and vice versa.
If someone is both generous and not creative then someone is not quiet and vice versa.
If john is generous or wise then someone is rich and vice versa.
If alice is brave or not creative then someone is both generous and calm and vice versa.
If mary is not patient then someone is either old or generous and vice versa.
Someone is either not generous or brave.
Paul is kind.
Someone is not funny or curious.
Someone is brave.
Someone is not humble.
Someone is humble or rich. | Mary is not generous. | entailment | (![X]:((~happy(X)&patient(X))=>(humble(X)|~brave(X))))&
(![X]:((~strong(X)|generous(X))<=>(patient(X)&strong(X))))&
((?[X]:((brave(X)<~>quiet(X))))=>((~wise(alice)<~>~old(alice))))&
((?[X]:((~calm(X)|creative(X))))<=>(quiet(susan)))&
(((~funny(fred)&~generous(fred)))<=>((tall(alice)|~curious(alice))))&
(![X]:((calm(X)&~patient(X))=>(creative(X)<~>wise(X))))&
((?[X]:((happy(X)|~generous(X))))<=>(?[X]:(kind(X))))&
((?[X]:(~quiet(X)))=>(?[X]:(old(X))))&
((?[X]:((~generous(X)<~>~calm(X))))=>(?[X]:((~rich(X)|calm(X)))))&
(![X]:((strong(X)|~old(X))=>kind(X)))&
(![X]:((creative(X)|kind(X))=>(~old(X)|~creative(X))))&
(![X]:((generous(X)|~tall(X))<=>~generous(X)))&
((?[X]:((generous(X)&~creative(X))))<=>(?[X]:(~quiet(X))))&
(((generous(john)|wise(john)))<=>(?[X]:(rich(X))))&
(((brave(alice)|~creative(alice)))<=>(?[X]:((generous(X)&calm(X)))))&
((~patient(mary))<=>(?[X]:((old(X)<~>generous(X)))))&
(?[X]:((~generous(X)<~>brave(X))))&
(kind(paul))&
(?[X]:((~funny(X)|curious(X))))&
(?[X]:(brave(X)))&
(?[X]:(~humble(X)))&
(?[X]:((humble(X)|rich(X)))) | ~generous(mary) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1393125749321850453452021
% SZS output start Proof for 1393125749321850453452021
12. ! [X0] : ((~tall(X0) | generous(X0)) <=> ~generous(X0)) [input p11]
23. generous(mary) [input hypothesis]
60. ! [X0] : (((~tall(X0) | generous(X0)) | generous(X0)) & (~generous(X0) | (tall(X0) & ~generous(X0)))) [nnf transformation 12]
61. ! [X0] : ((~tall(X0) | generous(X0) | generous(X0)) & (~generous(X0) | (tall(X0) & ~generous(X0)))) [flattening 60]
122. ~generous(X0) | ~generous(X0) [cnf transformation 61]
147. generous(mary) [cnf transformation 23]
148. ~generous(X0) [duplicate literal removal 122]
336. $false [subsumption resolution 147,148]
% SZS output end Proof for 1393125749321850453452021
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy then someone is kind or rich and vice versa. Everyone who is both brave and curious is both brave and not old and vice versa. Everyone who is not brave or brave is both not old and strong. Everyone who is strong is both not creative and not brave and vice versa. If lucy is either rich or calm then paul is not brave. Everyone who is not old is either wise or creative. Everyone who is both patient and humble is both humble and old. Everyone who is either tall or not patient is either not kind or wise and vice versa. Everyone who is creative is not curious or calm and vice versa. If fred is generous or not curious then susan is not humble and vice versa. If someone is either patient or not old then someone is both not humble and creative. If someone is both wise and not curious then someone is both not rich and not old. Everyone who is both tall and funny is not tall and vice versa. Everyone who is both not generous and not kind is either not generous or not curious and vice versa. Lucy is either not generous or kind. Someone is not creative or not tall. Someone is wise or not wise. Someone is brave or not rich. | Fred is not wise. | contradiction | ((?[X]:(happy(X)))<=>(?[X]:((kind(X)|rich(X)))))&
(![X]:((brave(X)&curious(X))<=>(brave(X)&~old(X))))&
(![X]:((~brave(X)|brave(X))=>(~old(X)&strong(X))))&
(![X]:(strong(X)<=>(~creative(X)&~brave(X))))&
(((rich(lucy)<~>calm(lucy)))=>(~brave(paul)))&
(![X]:(~old(X)=>(wise(X)<~>creative(X))))&
(![X]:((patient(X)&humble(X))=>(humble(X)&old(X))))&
(![X]:((tall(X)<~>~patient(X))<=>(~kind(X)<~>wise(X))))&
(![X]:(creative(X)<=>(~curious(X)|calm(X))))&
(((generous(fred)|~curious(fred)))<=>(~humble(susan)))&
((?[X]:((patient(X)<~>~old(X))))=>(?[X]:((~humble(X)&creative(X)))))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:((~rich(X)&~old(X)))))&
(![X]:((tall(X)&funny(X))<=>~tall(X)))&
(![X]:((~generous(X)&~kind(X))<=>(~generous(X)<~>~curious(X))))&
((~generous(lucy)<~>kind(lucy)))&
(?[X]:((~creative(X)|~tall(X))))&
(?[X]:((wise(X)|~wise(X))))&
(?[X]:((brave(X)|~rich(X)))) | ~wise(fred) | [
"p2",
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 7662104922174576395201442
% SZS output start Proof for 7662104922174576395201442
3. ! [X0] : ((brave(X0) | ~brave(X0)) => (strong(X0) & ~old(X0))) [input p2]
4. ! [X0] : (strong(X0) <=> (~brave(X0) & ~creative(X0))) [input p3]
6. ! [X0] : (~old(X0) => (wise(X0) <~> creative(X0))) [input p5]
19. ~wise(fred) [input hypothesis]
23. ! [X0] : (strong(X0) => (~brave(X0) & ~creative(X0))) [unused predicate definition removal 4]
24. ! [X0] : ((strong(X0) & ~old(X0)) | (~brave(X0) & brave(X0))) [ennf transformation 3]
25. ! [X0] : ((~brave(X0) & ~creative(X0)) | ~strong(X0)) [ennf transformation 23]
27. ! [X0] : ((wise(X0) <~> creative(X0)) | old(X0)) [ennf transformation 6]
40. ! [X0] : (((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | old(X0)) [nnf transformation 27]
71. ~old(X0) | brave(X0) [cnf transformation 24]
72. ~old(X0) | ~brave(X0) [cnf transformation 24]
73. strong(X0) | brave(X0) [cnf transformation 24]
74. strong(X0) | ~brave(X0) [cnf transformation 24]
75. ~creative(X0) | ~strong(X0) [cnf transformation 25]
79. creative(X0) | wise(X0) | old(X0) [cnf transformation 40]
117. ~wise(fred) [cnf transformation 19]
146. strong(X0) [subsumption resolution 73,74]
147. ~old(X0) [subsumption resolution 71,72]
149. ~creative(X0) [subsumption resolution 75,146]
150. wise(X0) | old(X0) [subsumption resolution 79,149]
151. wise(X0) [subsumption resolution 150,147]
184. $false [subsumption resolution 117,151]
% SZS output end Proof for 7662104922174576395201442
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or strong then someone is not humble and vice versa.
Everyone who is both not patient and not calm is either not happy or not funny.
Everyone who is either generous or happy is both not old and creative and vice versa.
If mary is both not brave and not rich then someone is not tall or curious.
If lucy is either not old or not funny then someone is funny and vice versa.
Everyone who is wise is either not humble or creative and vice versa.
If john is either strong or funny then someone is either not creative or not tall.
If lucy is either calm or funny then someone is not old and vice versa.
If someone is both curious and tall then someone is old and vice versa.
Everyone who is tall or creative is both calm and generous and vice versa.
Everyone who is both wise and not funny is not humble or happy and vice versa.
Everyone who is not calm or old is kind or not calm and vice versa.
If fred is not tall or not humble then someone is either not kind or old.
Everyone who is both not patient and not rich is not brave and vice versa.
Everyone who is either not old or creative is either not kind or calm.
If susan is not old then john is curious or not calm.
Someone is not kind.
Mary is both generous and calm.
Lucy is not brave.
Lucy is both not quiet and calm.
Someone is not calm or generous.
Mary is either quiet or brave.
John is both wise and kind.
Mary is both kind and generous. | Mary is brave. | neutral | ((?[X]:((~humble(X)|strong(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~patient(X)&~calm(X))=>(~happy(X)<~>~funny(X))))&
(![X]:((generous(X)<~>happy(X))<=>(~old(X)&creative(X))))&
(((~brave(mary)&~rich(mary)))=>(?[X]:((~tall(X)|curious(X)))))&
(((~old(lucy)<~>~funny(lucy)))<=>(?[X]:(funny(X))))&
(![X]:(wise(X)<=>(~humble(X)<~>creative(X))))&
(((strong(john)<~>funny(john)))=>(?[X]:((~creative(X)<~>~tall(X)))))&
(((calm(lucy)<~>funny(lucy)))<=>(?[X]:(~old(X))))&
((?[X]:((curious(X)&tall(X))))<=>(?[X]:(old(X))))&
(![X]:((tall(X)|creative(X))<=>(calm(X)&generous(X))))&
(![X]:((wise(X)&~funny(X))<=>(~humble(X)|happy(X))))&
(![X]:((~calm(X)|old(X))<=>(kind(X)|~calm(X))))&
(((~tall(fred)|~humble(fred)))=>(?[X]:((~kind(X)<~>old(X)))))&
(![X]:((~patient(X)&~rich(X))<=>~brave(X)))&
(![X]:((~old(X)<~>creative(X))=>(~kind(X)<~>calm(X))))&
((~old(susan))=>((curious(john)|~calm(john))))&
(?[X]:(~kind(X)))&
((generous(mary)&calm(mary)))&
(~brave(lucy))&
((~quiet(lucy)&calm(lucy)))&
(?[X]:((~calm(X)|generous(X))))&
((quiet(mary)<~>brave(mary)))&
((wise(john)&kind(john)))&
((kind(mary)&generous(mary))) | brave(mary) | [] | null | 0 |
If susan is either strong or funny then someone is not wise or not tall. Everyone who is brave is either wise or not happy and vice versa. Everyone who is both not tall and happy is kind or not curious and vice versa. Everyone who is not tall is both not tall and funny and vice versa. If lucy is not calm or not creative then someone is calm and vice versa. Everyone who is either tall or kind is humble and vice versa. If lucy is not brave or calm then someone is not kind or wise. Everyone who is either not quiet or curious is either old or not patient. Everyone who is both rich and not happy is either not quiet or not calm. Everyone who is kind or happy is either not rich or not funny and vice versa. If john is not patient then lucy is happy. Everyone who is funny is not humble and vice versa. Everyone who is brave is not curious. Everyone who is not rich is both rich and patient and vice versa. Everyone who is both not kind and funny is not creative and vice versa. If someone is not rich then lucy is either calm or not humble. Alice is both not strong and not wise. Mary is old or not humble. Someone is not curious or not old. Fred is generous. Fred is not brave or strong. Alice is generous. | Alice is funny. | contradiction | (((strong(susan)<~>funny(susan)))=>(?[X]:((~wise(X)|~tall(X)))))&
(![X]:(brave(X)<=>(wise(X)<~>~happy(X))))&
(![X]:((~tall(X)&happy(X))<=>(kind(X)|~curious(X))))&
(![X]:(~tall(X)<=>(~tall(X)&funny(X))))&
(((~calm(lucy)|~creative(lucy)))<=>(?[X]:(calm(X))))&
(![X]:((tall(X)<~>kind(X))<=>humble(X)))&
(((~brave(lucy)|calm(lucy)))=>(?[X]:((~kind(X)|wise(X)))))&
(![X]:((~quiet(X)<~>curious(X))=>(old(X)<~>~patient(X))))&
(![X]:((rich(X)&~happy(X))=>(~quiet(X)<~>~calm(X))))&
(![X]:((kind(X)|happy(X))<=>(~rich(X)<~>~funny(X))))&
((~patient(john))=>(happy(lucy)))&
(![X]:(funny(X)<=>~humble(X)))&
(![X]:(brave(X)=>~curious(X)))&
(![X]:(~rich(X)<=>(rich(X)&patient(X))))&
(![X]:((~kind(X)&funny(X))<=>~creative(X)))&
((?[X]:(~rich(X)))=>((calm(lucy)<~>~humble(lucy))))&
((~strong(alice)&~wise(alice)))&
((old(mary)|~humble(mary)))&
(?[X]:((~curious(X)|~old(X))))&
(generous(fred))&
((~brave(fred)|strong(fred)))&
(generous(alice)) | funny(alice) | [
"p1",
"p2",
"p9",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 451927521972853581927223
% SZS output start Proof for 451927521972853581927223
2. ! [X0] : (brave(X0) <=> (wise(X0) <~> ~happy(X0))) [input p1]
3. ! [X0] : ((happy(X0) & ~tall(X0)) <=> (~curious(X0) | kind(X0))) [input p2]
10. ! [X0] : ((happy(X0) | kind(X0)) <=> (~rich(X0) <~> ~funny(X0))) [input p9]
13. ! [X0] : (brave(X0) => ~curious(X0)) [input p12]
14. ! [X0] : (~rich(X0) <=> (patient(X0) & rich(X0))) [input p13]
17. ~wise(alice) & ~strong(alice) [input p16]
23. funny(alice) [input hypothesis]
32. ! [X0] : (~curious(X0) | ~brave(X0)) [ennf transformation 13]
37. ! [X0] : ((brave(X0) | ((wise(X0) | happy(X0)) & (~happy(X0) | ~wise(X0)))) & (((happy(X0) | ~wise(X0)) & (~happy(X0) | wise(X0))) | ~brave(X0))) [nnf transformation 2]
38. ! [X0] : (((happy(X0) & ~tall(X0)) | (curious(X0) & ~kind(X0))) & ((~curious(X0) | kind(X0)) | (~happy(X0) | tall(X0)))) [nnf transformation 3]
39. ! [X0] : (((happy(X0) & ~tall(X0)) | (curious(X0) & ~kind(X0))) & (~curious(X0) | kind(X0) | ~happy(X0) | tall(X0))) [flattening 38]
52. ! [X0] : (((happy(X0) | kind(X0)) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) & (((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | (~happy(X0) & ~kind(X0)))) [nnf transformation 10]
53. ! [X0] : ((happy(X0) | kind(X0) | ((~rich(X0) | funny(X0)) & (~funny(X0) | rich(X0)))) & (((funny(X0) | rich(X0)) & (~funny(X0) | ~rich(X0))) | (~happy(X0) & ~kind(X0)))) [flattening 52]
55. ! [X0] : ((~rich(X0) | (~patient(X0) | ~rich(X0))) & ((patient(X0) & rich(X0)) | rich(X0))) [nnf transformation 14]
56. ! [X0] : ((~rich(X0) | ~patient(X0) | ~rich(X0)) & ((patient(X0) & rich(X0)) | rich(X0))) [flattening 55]
67. happy(X0) | wise(X0) | brave(X0) [cnf transformation 37]
72. curious(X0) | happy(X0) [cnf transformation 39]
92. ~rich(X0) | ~funny(X0) | ~happy(X0) [cnf transformation 53]
100. ~curious(X0) | ~brave(X0) [cnf transformation 32]
101. rich(X0) | rich(X0) [cnf transformation 56]
102. rich(X0) | patient(X0) [cnf transformation 56]
103. ~rich(X0) | ~patient(X0) | ~rich(X0) [cnf transformation 56]
110. ~wise(alice) [cnf transformation 17]
114. funny(alice) [cnf transformation 23]
115. rich(X0) [duplicate literal removal 101]
116. ~rich(X0) | ~patient(X0) [duplicate literal removal 103]
216. ~brave(X0) | happy(X0) [resolution 100,72]
218. ~patient(X1) [resolution 116,115]
254. ~funny(X0) | ~happy(X0) | patient(X0) [resolution 92,102]
256. ~happy(X0) | ~funny(X0) [subsumption resolution 254,218]
259. ~funny(X0) | wise(X0) | brave(X0) [resolution 256,67]
305. wise(alice) | brave(alice) [resolution 259,114]
309. brave(alice) [subsumption resolution 305,110]
376. happy(alice) [resolution 309,216]
400. ~funny(alice) [resolution 376,256]
403. $false [subsumption resolution 400,114]
% SZS output end Proof for 451927521972853581927223
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or quiet then lucy is both calm and not generous and vice versa.
Everyone who is either strong or not generous is not rich.
If someone is both not funny and curious then susan is tall or old.
If alice is not creative or happy then lucy is not quiet or calm.
Everyone who is both funny and not humble is both strong and brave.
Everyone who is not quiet or not rich is both curious and not humble and vice versa.
Everyone who is not strong or not creative is both strong and humble and vice versa.
Everyone who is either old or not humble is both not old and patient.
Everyone who is tall or patient is both not generous and happy and vice versa.
Everyone who is brave is both not strong and humble.
Everyone who is not humble is not tall or not rich and vice versa.
Everyone who is both creative and quiet is creative or not brave and vice versa.
Everyone who is funny is brave or not quiet.
Everyone who is humble or wise is both not humble and kind.
If paul is strong then someone is both old and calm and vice versa.
Someone is not wise or not tall.
Alice is not funny or not old.
Someone is not brave or tall.
Someone is not tall. | Lucy is generous. | contradiction | ((?[X]:((~humble(X)|quiet(X))))<=>((calm(lucy)&~generous(lucy))))&
(![X]:((strong(X)<~>~generous(X))=>~rich(X)))&
((?[X]:((~funny(X)&curious(X))))=>((tall(susan)|old(susan))))&
(((~creative(alice)|happy(alice)))=>((~quiet(lucy)|calm(lucy))))&
(![X]:((funny(X)&~humble(X))=>(strong(X)&brave(X))))&
(![X]:((~quiet(X)|~rich(X))<=>(curious(X)&~humble(X))))&
(![X]:((~strong(X)|~creative(X))<=>(strong(X)&humble(X))))&
(![X]:((old(X)<~>~humble(X))=>(~old(X)&patient(X))))&
(![X]:((tall(X)|patient(X))<=>(~generous(X)&happy(X))))&
(![X]:(brave(X)=>(~strong(X)&humble(X))))&
(![X]:(~humble(X)<=>(~tall(X)|~rich(X))))&
(![X]:((creative(X)&quiet(X))<=>(creative(X)|~brave(X))))&
(![X]:(funny(X)=>(brave(X)|~quiet(X))))&
(![X]:((humble(X)|wise(X))=>(~humble(X)&kind(X))))&
((strong(paul))<=>(?[X]:((old(X)&calm(X)))))&
(?[X]:((~wise(X)|~tall(X))))&
((~funny(alice)|~old(alice)))&
(?[X]:((~brave(X)|tall(X))))&
(?[X]:(~tall(X))) | generous(lucy) | [
"p0",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 277209963954853953466718
% SZS output start Proof for 277209963954853953466718
1. ? [X0] : (quiet(X0) | ~humble(X0)) <=> (~generous(lucy) & calm(lucy)) [input p0]
14. ! [X0] : ((wise(X0) | humble(X0)) => (kind(X0) & ~humble(X0))) [input p13]
20. generous(lucy) [input hypothesis]
21. ! [X0] : ((wise(X0) | humble(X0)) => ~humble(X0)) [pure predicate removal 14]
22. ! [X0] : (humble(X0) => ~humble(X0)) [pure predicate removal 21]
35. ! [X0] : (~humble(X0) | ~humble(X0)) [ennf transformation 22]
36. (? [X0] : (quiet(X0) | ~humble(X0)) | (generous(lucy) | ~calm(lucy))) & ((~generous(lucy) & calm(lucy)) | ! [X0] : (~quiet(X0) & humble(X0))) [nnf transformation 1]
37. (? [X0] : (quiet(X0) | ~humble(X0)) | generous(lucy) | ~calm(lucy)) & ((~generous(lucy) & calm(lucy)) | ! [X0] : (~quiet(X0) & humble(X0))) [flattening 36]
38. (? [X0] : (quiet(X0) | ~humble(X0)) | generous(lucy) | ~calm(lucy)) & ((~generous(lucy) & calm(lucy)) | ! [X1] : (~quiet(X1) & humble(X1))) [rectify 37]
39. ? [X0] : (quiet(X0) | ~humble(X0)) => (quiet(sK0) | ~humble(sK0)) [choice axiom]
40. ((quiet(sK0) | ~humble(sK0)) | generous(lucy) | ~calm(lucy)) & ((~generous(lucy) & calm(lucy)) | ! [X1] : (~quiet(X1) & humble(X1))) [skolemisation 38,39]
63. ~generous(lucy) | humble(X1) [cnf transformation 40]
103. ~humble(X0) | ~humble(X0) [cnf transformation 35]
110. generous(lucy) [cnf transformation 20]
111. ~humble(X0) [duplicate literal removal 103]
120. 2 <=> generous(lucy) [avatar definition]
137. 6 <=> ! [X1] : humble(X1) [avatar definition]
138. humble(X1) <- (6) [avatar component clause 137]
139. 6 | ~2 [avatar split clause 63,120,137]
175. 2 [avatar split clause 110,120]
179. $false <- (6) [subsumption resolution 138,111]
180. ~6 [avatar contradiction clause 179]
183. $false [avatar sat refutation 139,175,180]
% SZS output end Proof for 277209963954853953466718
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not humble and humble then paul is calm and vice versa.
Everyone who is both quiet and not wise is not curious or quiet and vice versa.
Everyone who is quiet or humble is not quiet and vice versa.
Everyone who is not generous or not tall is both not rich and kind and vice versa.
If alice is either not brave or not patient then someone is both wise and not generous.
Everyone who is not humble is not funny and vice versa.
If someone is both kind and not happy then susan is both kind and quiet.
Everyone who is brave or not patient is either not curious or not generous and vice versa.
Everyone who is either funny or creative is either curious or not strong and vice versa.
If someone is not kind or quiet then susan is curious or generous.
Everyone who is both creative and curious is brave and vice versa.
Everyone who is not tall is either not kind or rich.
If someone is humble then paul is curious or not happy and vice versa.
If alice is both not tall and not funny then someone is funny.
Everyone who is both not brave and tall is either not patient or not curious.
Someone is wise.
Someone is both not wise and not generous.
Someone is not rich.
Lucy is not creative or brave.
Susan is strong. | Paul is calm. | contradiction | ((?[X]:((~humble(X)&humble(X))))<=>(calm(paul)))&
(![X]:((quiet(X)&~wise(X))<=>(~curious(X)|quiet(X))))&
(![X]:((quiet(X)|humble(X))<=>~quiet(X)))&
(![X]:((~generous(X)|~tall(X))<=>(~rich(X)&kind(X))))&
(((~brave(alice)<~>~patient(alice)))=>(?[X]:((wise(X)&~generous(X)))))&
(![X]:(~humble(X)<=>~funny(X)))&
((?[X]:((kind(X)&~happy(X))))=>((kind(susan)&quiet(susan))))&
(![X]:((brave(X)|~patient(X))<=>(~curious(X)<~>~generous(X))))&
(![X]:((funny(X)<~>creative(X))<=>(curious(X)<~>~strong(X))))&
((?[X]:((~kind(X)|quiet(X))))=>((curious(susan)|generous(susan))))&
(![X]:((creative(X)&curious(X))<=>brave(X)))&
(![X]:(~tall(X)=>(~kind(X)<~>rich(X))))&
((?[X]:(humble(X)))<=>((curious(paul)|~happy(paul))))&
(((~tall(alice)&~funny(alice)))=>(?[X]:(funny(X))))&
(![X]:((~brave(X)&tall(X))=>(~patient(X)<~>~curious(X))))&
(?[X]:(wise(X)))&
(?[X]:((~wise(X)&~generous(X))))&
(?[X]:(~rich(X)))&
((~creative(lucy)|brave(lucy)))&
(strong(susan)) | calm(paul) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 1522036066531843847443820
% SZS output start Proof for 1522036066531843847443820
1. ? [X0] : (humble(X0) & ~humble(X0)) <=> calm(paul) [input p0]
21. calm(paul) [input hypothesis]
31. (? [X0] : (humble(X0) & ~humble(X0)) | ~calm(paul)) & (calm(paul) | ! [X0] : (~humble(X0) | humble(X0))) [nnf transformation 1]
32. (? [X0] : (humble(X0) & ~humble(X0)) | ~calm(paul)) & (calm(paul) | ! [X1] : (~humble(X1) | humble(X1))) [rectify 31]
33. ? [X0] : (humble(X0) & ~humble(X0)) => (humble(sK0) & ~humble(sK0)) [choice axiom]
34. ((humble(sK0) & ~humble(sK0)) | ~calm(paul)) & (calm(paul) | ! [X1] : (~humble(X1) | humble(X1))) [skolemisation 32,33]
66. ~humble(sK0) | ~calm(paul) [cnf transformation 34]
67. humble(sK0) | ~calm(paul) [cnf transformation 34]
122. calm(paul) [cnf transformation 21]
126. 1 <=> calm(paul) [avatar definition]
130. 2 <=> humble(sK0) [avatar definition]
133. ~1 | 2 [avatar split clause 67,130,126]
134. ~1 | ~2 [avatar split clause 66,130,126]
200. 1 [avatar split clause 122,126]
201. $false [avatar sat refutation 133,134,200]
% SZS output end Proof for 1522036066531843847443820
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either creative or not rich then someone is not happy or wise and vice versa.
If someone is kind then alice is either not brave or not patient and vice versa.
Everyone who is wise or not wise is rich.
Everyone who is both rich and not kind is both funny and strong and vice versa.
If someone is either tall or generous then someone is both not old and not wise.
Everyone who is not old or not calm is not tall or creative.
Everyone who is either not kind or not rich is either not creative or curious and vice versa.
Everyone who is both patient and not kind is both not curious and not happy.
Everyone who is not patient is not funny or kind and vice versa.
If someone is both not quiet and rich then mary is either not happy or not brave.
Everyone who is both not humble and strong is both kind and not quiet and vice versa.
If lucy is not curious or not old then john is both tall and not generous and vice versa.
Everyone who is both quiet and funny is not brave and vice versa.
Everyone who is both not wise and not kind is not old or not funny.
If someone is not humble or happy then paul is both not tall and not generous and vice versa.
Everyone who is calm or generous is either rich or patient and vice versa.
Mary is both not humble and not brave.
Someone is both tall and brave.
Someone is both not funny and not wise.
Someone is either tall or happy.
Someone is generous or not curious.
John is patient.
Someone is not rich or not wise.
Paul is either generous or kind. | Mary is quiet. | entailment | (((creative(fred)<~>~rich(fred)))<=>(?[X]:((~happy(X)|wise(X)))))&
((?[X]:(kind(X)))<=>((~brave(alice)<~>~patient(alice))))&
(![X]:((wise(X)|~wise(X))=>rich(X)))&
(![X]:((rich(X)&~kind(X))<=>(funny(X)&strong(X))))&
((?[X]:((tall(X)<~>generous(X))))=>(?[X]:((~old(X)&~wise(X)))))&
(![X]:((~old(X)|~calm(X))=>(~tall(X)|creative(X))))&
(![X]:((~kind(X)<~>~rich(X))<=>(~creative(X)<~>curious(X))))&
(![X]:((patient(X)&~kind(X))=>(~curious(X)&~happy(X))))&
(![X]:(~patient(X)<=>(~funny(X)|kind(X))))&
((?[X]:((~quiet(X)&rich(X))))=>((~happy(mary)<~>~brave(mary))))&
(![X]:((~humble(X)&strong(X))<=>(kind(X)&~quiet(X))))&
(((~curious(lucy)|~old(lucy)))<=>((tall(john)&~generous(john))))&
(![X]:((quiet(X)&funny(X))<=>~brave(X)))&
(![X]:((~wise(X)&~kind(X))=>(~old(X)|~funny(X))))&
((?[X]:((~humble(X)|happy(X))))<=>((~tall(paul)&~generous(paul))))&
(![X]:((calm(X)|generous(X))<=>(rich(X)<~>patient(X))))&
((~humble(mary)&~brave(mary)))&
(?[X]:((tall(X)&brave(X))))&
(?[X]:((~funny(X)&~wise(X))))&
(?[X]:((tall(X)<~>happy(X))))&
(?[X]:((generous(X)|~curious(X))))&
(patient(john))&
(?[X]:((~rich(X)|~wise(X))))&
((generous(paul)<~>kind(paul))) | quiet(mary) | [
"p12",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4664602101216726539727645
% SZS output start Proof for 4664602101216726539727645
13. ! [X0] : ((funny(X0) & quiet(X0)) <=> ~brave(X0)) [input p12]
17. ~brave(mary) & ~humble(mary) [input p16]
25. ~quiet(mary) [input hypothesis]
58. ! [X0] : (((funny(X0) & quiet(X0)) | brave(X0)) & (~brave(X0) | (~funny(X0) | ~quiet(X0)))) [nnf transformation 13]
59. ! [X0] : (((funny(X0) & quiet(X0)) | brave(X0)) & (~brave(X0) | ~funny(X0) | ~quiet(X0))) [flattening 58]
126. quiet(X0) | brave(X0) [cnf transformation 59]
141. ~brave(mary) [cnf transformation 17]
153. ~quiet(mary) [cnf transformation 25]
236. 17 <=> brave(mary) [avatar definition]
237. ~brave(mary) <- (~17) [avatar component clause 236]
296. ~17 [avatar split clause 141,236]
340. brave(mary) [resolution 126,153]
341. $false <- (~17) [subsumption resolution 340,237]
342. 17 [avatar contradiction clause 341]
343. $false [avatar sat refutation 296,342]
% SZS output end Proof for 4664602101216726539727645
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not wise is not creative and vice versa. Everyone who is both not generous and calm is either not wise or not funny. Everyone who is both not quiet and patient is both wise and not funny. Everyone who is not strong is not curious or patient and vice versa. If paul is both not quiet and not patient then someone is both not wise and wise and vice versa. Everyone who is both not brave and brave is both kind and quiet and vice versa. Everyone who is generous is both not calm and not patient and vice versa. Everyone who is either not brave or strong is patient or not wise and vice versa. Everyone who is strong is both strong and not creative. If lucy is not happy then john is old and vice versa. Everyone who is both old and curious is not patient. Everyone who is both not happy and generous is both happy and not generous. Everyone who is both not quiet and brave is either not curious or happy. If someone is both creative and not patient then someone is both tall and strong. Everyone who is both not wise and curious is either not wise or not quiet. If lucy is both not creative and not rich then alice is both creative and not old and vice versa. Fred is humble. Alice is both rich and humble. Someone is not humble. Someone is not brave or funny. Someone is kind or old. Someone is creative or brave. Alice is calm. John is not patient. | Lucy is not happy. | neutral | (![X]:((calm(X)<~>~wise(X))<=>~creative(X)))&
(![X]:((~generous(X)&calm(X))=>(~wise(X)<~>~funny(X))))&
(![X]:((~quiet(X)&patient(X))=>(wise(X)&~funny(X))))&
(![X]:(~strong(X)<=>(~curious(X)|patient(X))))&
(((~quiet(paul)&~patient(paul)))<=>(?[X]:((~wise(X)&wise(X)))))&
(![X]:((~brave(X)&brave(X))<=>(kind(X)&quiet(X))))&
(![X]:(generous(X)<=>(~calm(X)&~patient(X))))&
(![X]:((~brave(X)<~>strong(X))<=>(patient(X)|~wise(X))))&
(![X]:(strong(X)=>(strong(X)&~creative(X))))&
((~happy(lucy))<=>(old(john)))&
(![X]:((old(X)&curious(X))=>~patient(X)))&
(![X]:((~happy(X)&generous(X))=>(happy(X)&~generous(X))))&
(![X]:((~quiet(X)&brave(X))=>(~curious(X)<~>happy(X))))&
((?[X]:((creative(X)&~patient(X))))=>(?[X]:((tall(X)&strong(X)))))&
(![X]:((~wise(X)&curious(X))=>(~wise(X)<~>~quiet(X))))&
(((~creative(lucy)&~rich(lucy)))<=>((creative(alice)&~old(alice))))&
(humble(fred))&
((rich(alice)&humble(alice)))&
(?[X]:(~humble(X)))&
(?[X]:((~brave(X)|funny(X))))&
(?[X]:((kind(X)|old(X))))&
(?[X]:((creative(X)|brave(X))))&
(calm(alice))&
(~patient(john)) | ~happy(lucy) | [] | null | 0 |
Everyone who is not calm or calm is either not quiet or not tall.
Everyone who is brave is both wise and calm and vice versa.
Everyone who is either not happy or not funny is either not curious or not wise.
Everyone who is not calm or not happy is not tall or tall.
If mary is either kind or not strong then mary is both happy and not quiet and vice versa.
Everyone who is funny or not old is not strong or humble.
Everyone who is either not humble or not curious is tall and vice versa.
Everyone who is both happy and kind is not wise.
If someone is either not tall or happy then someone is both not funny and not quiet.
If susan is not old or wise then someone is not patient.
If susan is either not kind or generous then john is not funny or not wise and vice versa.
If mary is both not rich and calm then someone is not funny and vice versa.
Everyone who is calm or creative is not humble or kind and vice versa.
If someone is not funny then alice is both not quiet and quiet and vice versa.
Everyone who is not wise is not strong or wise and vice versa.
Everyone who is both old and not strong is happy.
Someone is not quiet or not old.
Lucy is either happy or not kind.
Someone is creative or generous.
Someone is kind. | Mary is tall. | neutral | (![X]:((~calm(X)|calm(X))=>(~quiet(X)<~>~tall(X))))&
(![X]:(brave(X)<=>(wise(X)&calm(X))))&
(![X]:((~happy(X)<~>~funny(X))=>(~curious(X)<~>~wise(X))))&
(![X]:((~calm(X)|~happy(X))=>(~tall(X)|tall(X))))&
(((kind(mary)<~>~strong(mary)))<=>((happy(mary)&~quiet(mary))))&
(![X]:((funny(X)|~old(X))=>(~strong(X)|humble(X))))&
(![X]:((~humble(X)<~>~curious(X))<=>tall(X)))&
(![X]:((happy(X)&kind(X))=>~wise(X)))&
((?[X]:((~tall(X)<~>happy(X))))=>(?[X]:((~funny(X)&~quiet(X)))))&
(((~old(susan)|wise(susan)))=>(?[X]:(~patient(X))))&
(((~kind(susan)<~>generous(susan)))<=>((~funny(john)|~wise(john))))&
(((~rich(mary)&calm(mary)))<=>(?[X]:(~funny(X))))&
(![X]:((calm(X)|creative(X))<=>(~humble(X)|kind(X))))&
((?[X]:(~funny(X)))<=>((~quiet(alice)&quiet(alice))))&
(![X]:(~wise(X)<=>(~strong(X)|wise(X))))&
(![X]:((old(X)&~strong(X))=>happy(X)))&
(?[X]:((~quiet(X)|~old(X))))&
((happy(lucy)<~>~kind(lucy)))&
(?[X]:((creative(X)|generous(X))))&
(?[X]:(kind(X))) | tall(mary) | [] | null | 0 |
Everyone who is brave is not old and vice versa.
If paul is not creative then someone is either old or wise and vice versa.
Everyone who is both not happy and not patient is either old or not happy and vice versa.
If mary is either not brave or brave then lucy is not funny.
If someone is either generous or old then someone is either creative or wise and vice versa.
Everyone who is not kind or not curious is either not generous or not happy.
Everyone who is not old or funny is not calm and vice versa.
If someone is both rich and not curious then someone is either not kind or brave and vice versa.
If someone is humble then someone is funny.
If alice is kind then alice is either creative or kind and vice versa.
If someone is patient or funny then fred is not strong and vice versa.
Everyone who is both old and not happy is either rich or calm.
If someone is not old then fred is brave and vice versa.
Everyone who is creative or generous is either happy or not old and vice versa.
Everyone who is both not rich and generous is either not calm or funny and vice versa.
Everyone who is generous or curious is patient.
Alice is not kind or not strong.
Mary is wise or not curious.
Someone is both curious and humble.
Lucy is not creative.
Lucy is either not generous or humble.
Fred is either creative or not wise.
Someone is either not quiet or patient. | Mary is not generous. | entailment | (![X]:(brave(X)<=>~old(X)))&
((~creative(paul))<=>(?[X]:((old(X)<~>wise(X)))))&
(![X]:((~happy(X)&~patient(X))<=>(old(X)<~>~happy(X))))&
(((~brave(mary)<~>brave(mary)))=>(~funny(lucy)))&
((?[X]:((generous(X)<~>old(X))))<=>(?[X]:((creative(X)<~>wise(X)))))&
(![X]:((~kind(X)|~curious(X))=>(~generous(X)<~>~happy(X))))&
(![X]:((~old(X)|funny(X))<=>~calm(X)))&
((?[X]:((rich(X)&~curious(X))))<=>(?[X]:((~kind(X)<~>brave(X)))))&
((?[X]:(humble(X)))=>(?[X]:(funny(X))))&
((kind(alice))<=>((creative(alice)<~>kind(alice))))&
((?[X]:((patient(X)|funny(X))))<=>(~strong(fred)))&
(![X]:((old(X)&~happy(X))=>(rich(X)<~>calm(X))))&
((?[X]:(~old(X)))<=>(brave(fred)))&
(![X]:((creative(X)|generous(X))<=>(happy(X)<~>~old(X))))&
(![X]:((~rich(X)&generous(X))<=>(~calm(X)<~>funny(X))))&
(![X]:((generous(X)|curious(X))=>patient(X)))&
((~kind(alice)|~strong(alice)))&
((wise(mary)|~curious(mary)))&
(?[X]:((curious(X)&humble(X))))&
(~creative(lucy))&
((~generous(lucy)<~>humble(lucy)))&
((creative(fred)<~>~wise(fred)))&
(?[X]:((~quiet(X)<~>patient(X)))) | ~generous(mary) | [
"p2",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3210431307767984002677692
% SZS output start Proof for 3210431307767984002677692
3. ! [X0] : ((~patient(X0) & ~happy(X0)) <=> (old(X0) <~> ~happy(X0))) [input p2]
14. ! [X0] : ((generous(X0) | creative(X0)) <=> (happy(X0) <~> ~old(X0))) [input p13]
16. ! [X0] : ((curious(X0) | generous(X0)) => patient(X0)) [input p15]
24. generous(mary) [input hypothesis]
33. ! [X0] : (patient(X0) | (~curious(X0) & ~generous(X0))) [ennf transformation 16]
39. ! [X0] : (((~patient(X0) & ~happy(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | (patient(X0) | happy(X0)))) [nnf transformation 3]
40. ! [X0] : (((~patient(X0) & ~happy(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | patient(X0) | happy(X0))) [flattening 39]
68. ! [X0] : (((generous(X0) | creative(X0)) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0)))) & (((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | (~generous(X0) & ~creative(X0)))) [nnf transformation 14]
69. ! [X0] : ((generous(X0) | creative(X0) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0)))) & (((old(X0) | ~happy(X0)) & (~old(X0) | happy(X0))) | (~generous(X0) & ~creative(X0)))) [flattening 68]
87. ~happy(X0) | ~happy(X0) | ~old(X0) [cnf transformation 40]
90. ~patient(X0) | old(X0) | happy(X0) [cnf transformation 40]
127. ~old(X0) | happy(X0) | ~generous(X0) [cnf transformation 69]
129. old(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 69]
138. ~generous(X0) | patient(X0) [cnf transformation 33]
151. generous(mary) [cnf transformation 24]
157. ~happy(X0) | ~old(X0) [duplicate literal removal 87]
312. ~generous(X0) | ~happy(X0) [subsumption resolution 129,157]
314. ~generous(X0) | ~old(X0) [subsumption resolution 127,312]
368. patient(mary) [resolution 138,151]
378. ~happy(mary) [resolution 312,151]
380. ~old(mary) [resolution 314,151]
391. old(mary) | happy(mary) [resolution 90,368]
396. happy(mary) [subsumption resolution 391,380]
397. $false [subsumption resolution 396,378]
% SZS output end Proof for 3210431307767984002677692
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is both not humble and not generous and vice versa. Everyone who is not quiet or not strong is not brave and vice versa. Everyone who is either curious or strong is either not quiet or not brave. If mary is both not calm and not quiet then someone is either happy or not happy and vice versa. If alice is not creative or not strong then someone is either not calm or not humble and vice versa. If susan is not kind or not tall then susan is rich or not quiet and vice versa. If lucy is not generous then someone is either not strong or not calm and vice versa. Everyone who is not humble or rich is not patient and vice versa. If alice is both not strong and funny then someone is creative or not happy and vice versa. If someone is either not curious or not strong then paul is not brave or not patient. If susan is both not quiet and not calm then mary is strong. If mary is either not generous or quiet then someone is either wise or not strong and vice versa. If someone is both not calm and not humble then someone is either patient or rich and vice versa. Everyone who is patient or not patient is not curious. If fred is happy or not rich then paul is not humble or not brave and vice versa. Someone is either creative or humble. Someone is both not rich and not curious. Someone is either not brave or not wise. Mary is both happy and not calm. | Lucy is not humble. | entailment | (![X]:(~strong(X)<=>(~humble(X)&~generous(X))))&
(![X]:((~quiet(X)|~strong(X))<=>~brave(X)))&
(![X]:((curious(X)<~>strong(X))=>(~quiet(X)<~>~brave(X))))&
(((~calm(mary)&~quiet(mary)))<=>(?[X]:((happy(X)<~>~happy(X)))))&
(((~creative(alice)|~strong(alice)))<=>(?[X]:((~calm(X)<~>~humble(X)))))&
(((~kind(susan)|~tall(susan)))<=>((rich(susan)|~quiet(susan))))&
((~generous(lucy))<=>(?[X]:((~strong(X)<~>~calm(X)))))&
(![X]:((~humble(X)|rich(X))<=>~patient(X)))&
(((~strong(alice)&funny(alice)))<=>(?[X]:((creative(X)|~happy(X)))))&
((?[X]:((~curious(X)<~>~strong(X))))=>((~brave(paul)|~patient(paul))))&
(((~quiet(susan)&~calm(susan)))=>(strong(mary)))&
(((~generous(mary)<~>quiet(mary)))<=>(?[X]:((wise(X)<~>~strong(X)))))&
((?[X]:((~calm(X)&~humble(X))))<=>(?[X]:((patient(X)<~>rich(X)))))&
(![X]:((patient(X)|~patient(X))=>~curious(X)))&
(((happy(fred)|~rich(fred)))<=>((~humble(paul)|~brave(paul))))&
(?[X]:((creative(X)<~>humble(X))))&
(?[X]:((~rich(X)&~curious(X))))&
(?[X]:((~brave(X)<~>~wise(X))))&
((happy(mary)&~calm(mary))) | ~humble(lucy) | [
"p0",
"p1",
"p2",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8734105748892902064856493
% SZS output start Proof for 8734105748892902064856493
1. ! [X0] : (~strong(X0) <=> (~generous(X0) & ~humble(X0))) [input p0]
2. ! [X0] : ((~strong(X0) | ~quiet(X0)) <=> ~brave(X0)) [input p1]
3. ! [X0] : ((curious(X0) <~> strong(X0)) => (~quiet(X0) <~> ~brave(X0))) [input p2]
14. ! [X0] : ((~patient(X0) | patient(X0)) => ~curious(X0)) [input p13]
20. humble(lucy) [input hypothesis]
22. ! [X0] : ((~quiet(X0) <~> ~brave(X0)) | (curious(X0) <=> strong(X0))) [ennf transformation 3]
27. ! [X0] : (~curious(X0) | (patient(X0) & ~patient(X0))) [ennf transformation 14]
28. ! [X0] : ((~strong(X0) | (generous(X0) | humble(X0))) & ((~generous(X0) & ~humble(X0)) | strong(X0))) [nnf transformation 1]
29. ! [X0] : ((~strong(X0) | generous(X0) | humble(X0)) & ((~generous(X0) & ~humble(X0)) | strong(X0))) [flattening 28]
30. ! [X0] : (((~strong(X0) | ~quiet(X0)) | brave(X0)) & (~brave(X0) | (strong(X0) & quiet(X0)))) [nnf transformation 2]
31. ! [X0] : ((~strong(X0) | ~quiet(X0) | brave(X0)) & (~brave(X0) | (strong(X0) & quiet(X0)))) [flattening 30]
32. ! [X0] : (((brave(X0) | quiet(X0)) & (~brave(X0) | ~quiet(X0))) | ((curious(X0) | ~strong(X0)) & (strong(X0) | ~curious(X0)))) [nnf transformation 22]
76. ~humble(X0) | strong(X0) [cnf transformation 29]
79. ~brave(X0) | quiet(X0) [cnf transformation 31]
81. ~quiet(X0) | ~strong(X0) | brave(X0) [cnf transformation 31]
83. ~brave(X0) | ~quiet(X0) | curious(X0) | ~strong(X0) [cnf transformation 32]
85. brave(X0) | quiet(X0) | curious(X0) | ~strong(X0) [cnf transformation 32]
131. ~curious(X0) | ~patient(X0) [cnf transformation 27]
132. ~curious(X0) | patient(X0) [cnf transformation 27]
145. humble(lucy) [cnf transformation 20]
150. ~strong(X0) | curious(X0) | brave(X0) [subsumption resolution 85,81]
152. ~quiet(X0) | curious(X0) | ~strong(X0) [subsumption resolution 83,150]
346. ~curious(X0) [subsumption resolution 131,132]
384. strong(lucy) [resolution 76,145]
466. curious(lucy) | brave(lucy) [resolution 150,384]
468. brave(lucy) [subsumption resolution 466,346]
483. quiet(lucy) [resolution 468,79]
487. curious(lucy) | ~strong(lucy) [resolution 483,152]
489. ~strong(lucy) [subsumption resolution 487,346]
490. $false [subsumption resolution 489,384]
% SZS output end Proof for 8734105748892902064856493
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and humble then john is both not tall and funny. If someone is both curious and strong then fred is both not creative and funny. Everyone who is not patient or strong is both not curious and not humble and vice versa. Everyone who is old is not happy. Everyone who is not wise is either not brave or not happy and vice versa. If john is not creative then someone is either not brave or not creative and vice versa. Everyone who is either strong or not calm is either curious or not brave and vice versa. Everyone who is both not kind and not patient is both not tall and not humble and vice versa. Everyone who is either not humble or patient is both calm and creative. Everyone who is either curious or brave is either old or not wise and vice versa. If someone is not happy or not patient then someone is either not calm or not kind and vice versa. Everyone who is not strong is both happy and brave. Everyone who is not humble is curious. Everyone who is both tall and not funny is not strong and vice versa. If someone is kind or funny then someone is both generous and not quiet and vice versa. If someone is funny or not calm then someone is either not creative or not kind. Someone is either kind or not creative. Someone is either humble or brave. | Fred is not humble. | entailment | ((?[X]:((~tall(X)&humble(X))))=>((~tall(john)&funny(john))))&
((?[X]:((curious(X)&strong(X))))=>((~creative(fred)&funny(fred))))&
(![X]:((~patient(X)|strong(X))<=>(~curious(X)&~humble(X))))&
(![X]:(old(X)=>~happy(X)))&
(![X]:(~wise(X)<=>(~brave(X)<~>~happy(X))))&
((~creative(john))<=>(?[X]:((~brave(X)<~>~creative(X)))))&
(![X]:((strong(X)<~>~calm(X))<=>(curious(X)<~>~brave(X))))&
(![X]:((~kind(X)&~patient(X))<=>(~tall(X)&~humble(X))))&
(![X]:((~humble(X)<~>patient(X))=>(calm(X)&creative(X))))&
(![X]:((curious(X)<~>brave(X))<=>(old(X)<~>~wise(X))))&
((?[X]:((~happy(X)|~patient(X))))<=>(?[X]:((~calm(X)<~>~kind(X)))))&
(![X]:(~strong(X)=>(happy(X)&brave(X))))&
(![X]:(~humble(X)=>curious(X)))&
(![X]:((tall(X)&~funny(X))<=>~strong(X)))&
((?[X]:((kind(X)|funny(X))))<=>(?[X]:((generous(X)&~quiet(X)))))&
((?[X]:((funny(X)|~calm(X))))=>(?[X]:((~creative(X)<~>~kind(X)))))&
(?[X]:((kind(X)<~>~creative(X))))&
(?[X]:((humble(X)<~>brave(X)))) | ~humble(fred) | [
"p2",
"p3",
"p4",
"p6",
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3106644072074603950712644
% SZS output start Proof for 3106644072074603950712644
3. ! [X0] : ((strong(X0) | ~patient(X0)) <=> (~humble(X0) & ~curious(X0))) [input p2]
4. ! [X0] : (old(X0) => ~happy(X0)) [input p3]
5. ! [X0] : (~wise(X0) <=> (~brave(X0) <~> ~happy(X0))) [input p4]
7. ! [X0] : ((strong(X0) <~> ~calm(X0)) <=> (curious(X0) <~> ~brave(X0))) [input p6]
8. ! [X0] : ((~patient(X0) & ~kind(X0)) <=> (~humble(X0) & ~tall(X0))) [input p7]
9. ! [X0] : ((~humble(X0) <~> patient(X0)) => (creative(X0) & calm(X0))) [input p8]
10. ! [X0] : ((curious(X0) <~> brave(X0)) <=> (old(X0) <~> ~wise(X0))) [input p9]
11. ? [X0] : (~patient(X0) | ~happy(X0)) <=> ? [X0] : (~calm(X0) <~> ~kind(X0)) [input p10]
12. ! [X0] : (~strong(X0) => (brave(X0) & happy(X0))) [input p11]
13. ! [X0] : (~humble(X0) => curious(X0)) [input p12]
14. ! [X0] : ((~funny(X0) & tall(X0)) <=> ~strong(X0)) [input p13]
15. ? [X0] : (funny(X0) | kind(X0)) <=> ? [X0] : (~quiet(X0) & generous(X0)) [input p14]
19. humble(fred) [input hypothesis]
20. ? [X0] : (~patient(X0) | ~happy(X0)) <=> ? [X1] : (~calm(X1) <~> ~kind(X1)) [rectify 11]
21. ? [X0] : (funny(X0) | kind(X0)) <=> ? [X1] : (~quiet(X1) & generous(X1)) [rectify 15]
25. ! [X0] : (~happy(X0) | ~old(X0)) [ennf transformation 4]
26. ! [X0] : ((creative(X0) & calm(X0)) | (~humble(X0) <=> patient(X0))) [ennf transformation 9]
27. ! [X0] : ((brave(X0) & happy(X0)) | strong(X0)) [ennf transformation 12]
28. ! [X0] : (curious(X0) | humble(X0)) [ennf transformation 13]
30. ! [X0] : (((strong(X0) | ~patient(X0)) | (humble(X0) | curious(X0))) & ((~humble(X0) & ~curious(X0)) | (~strong(X0) & patient(X0)))) [nnf transformation 3]
31. ! [X0] : ((strong(X0) | ~patient(X0) | humble(X0) | curious(X0)) & ((~humble(X0) & ~curious(X0)) | (~strong(X0) & patient(X0)))) [flattening 30]
32. ! [X0] : ((~wise(X0) | ((~brave(X0) | happy(X0)) & (~happy(X0) | brave(X0)))) & (((happy(X0) | brave(X0)) & (~happy(X0) | ~brave(X0))) | wise(X0))) [nnf transformation 5]
37. ! [X0] : ((((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0))))) [nnf transformation 7]
38. ! [X0] : (((~patient(X0) & ~kind(X0)) | (humble(X0) | tall(X0))) & ((~humble(X0) & ~tall(X0)) | (patient(X0) | kind(X0)))) [nnf transformation 8]
39. ! [X0] : (((~patient(X0) & ~kind(X0)) | humble(X0) | tall(X0)) & ((~humble(X0) & ~tall(X0)) | patient(X0) | kind(X0))) [flattening 38]
40. ! [X0] : ((creative(X0) & calm(X0)) | ((~humble(X0) | ~patient(X0)) & (patient(X0) | humble(X0)))) [nnf transformation 26]
41. ! [X0] : ((((~brave(X0) | ~curious(X0)) & (brave(X0) | curious(X0))) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0)))) & (((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | ((curious(X0) | ~brave(X0)) & (brave(X0) | ~curious(X0))))) [nnf transformation 10]
42. (? [X0] : (~patient(X0) | ~happy(X0)) | ! [X1] : ((~calm(X1) | kind(X1)) & (~kind(X1) | calm(X1)))) & (? [X1] : ((kind(X1) | calm(X1)) & (~kind(X1) | ~calm(X1))) | ! [X0] : (patient(X0) & happy(X0))) [nnf transformation 20]
43. (? [X0] : (~patient(X0) | ~happy(X0)) | ! [X1] : ((~calm(X1) | kind(X1)) & (~kind(X1) | calm(X1)))) & (? [X2] : ((kind(X2) | calm(X2)) & (~kind(X2) | ~calm(X2))) | ! [X3] : (patient(X3) & happy(X3))) [rectify 42]
44. ? [X0] : (~patient(X0) | ~happy(X0)) => (~patient(sK1) | ~happy(sK1)) [choice axiom]
45. ? [X2] : ((kind(X2) | calm(X2)) & (~kind(X2) | ~calm(X2))) => ((kind(sK2) | calm(sK2)) & (~kind(sK2) | ~calm(sK2))) [choice axiom]
46. ((~patient(sK1) | ~happy(sK1)) | ! [X1] : ((~calm(X1) | kind(X1)) & (~kind(X1) | calm(X1)))) & (((kind(sK2) | calm(sK2)) & (~kind(sK2) | ~calm(sK2))) | ! [X3] : (patient(X3) & happy(X3))) [skolemisation 43,45,44]
47. ! [X0] : (((~funny(X0) & tall(X0)) | strong(X0)) & (~strong(X0) | (funny(X0) | ~tall(X0)))) [nnf transformation 14]
48. ! [X0] : (((~funny(X0) & tall(X0)) | strong(X0)) & (~strong(X0) | funny(X0) | ~tall(X0))) [flattening 47]
49. (? [X0] : (funny(X0) | kind(X0)) | ! [X1] : (quiet(X1) | ~generous(X1))) & (? [X1] : (~quiet(X1) & generous(X1)) | ! [X0] : (~funny(X0) & ~kind(X0))) [nnf transformation 21]
50. (? [X0] : (funny(X0) | kind(X0)) | ! [X1] : (quiet(X1) | ~generous(X1))) & (? [X2] : (~quiet(X2) & generous(X2)) | ! [X3] : (~funny(X3) & ~kind(X3))) [rectify 49]
51. ? [X0] : (funny(X0) | kind(X0)) => (funny(sK3) | kind(sK3)) [choice axiom]
52. ? [X2] : (~quiet(X2) & generous(X2)) => (~quiet(sK4) & generous(sK4)) [choice axiom]
53. ((funny(sK3) | kind(sK3)) | ! [X1] : (quiet(X1) | ~generous(X1))) & ((~quiet(sK4) & generous(sK4)) | ! [X3] : (~funny(X3) & ~kind(X3))) [skolemisation 50,52,51]
68. ~curious(X0) | patient(X0) [cnf transformation 31]
69. ~curious(X0) | ~strong(X0) [cnf transformation 31]
70. ~humble(X0) | patient(X0) [cnf transformation 31]
71. ~strong(X0) | ~humble(X0) [cnf transformation 31]
73. ~happy(X0) | ~old(X0) [cnf transformation 25]
74. ~brave(X0) | ~happy(X0) | wise(X0) [cnf transformation 32]
86. ~calm(X0) | strong(X0) | ~brave(X0) | ~curious(X0) [cnf transformation 37]
93. ~patient(X0) | humble(X0) | tall(X0) [cnf transformation 39]
95. calm(X0) | ~humble(X0) | ~patient(X0) [cnf transformation 40]
99. ~brave(X0) | old(X0) | curious(X0) | ~wise(X0) [cnf transformation 41]
106. ~kind(sK2) | ~calm(sK2) | happy(X3) [cnf transformation 46]
108. kind(sK2) | calm(sK2) | happy(X3) [cnf transformation 46]
110. ~patient(sK1) | ~happy(sK1) | ~kind(X1) | calm(X1) [cnf transformation 46]
111. ~patient(sK1) | ~happy(sK1) | ~calm(X1) | kind(X1) [cnf transformation 46]
112. happy(X0) | strong(X0) [cnf transformation 27]
113. brave(X0) | strong(X0) [cnf transformation 27]
114. curious(X0) | humble(X0) [cnf transformation 28]
115. ~strong(X0) | funny(X0) | ~tall(X0) [cnf transformation 48]
116. strong(X0) | tall(X0) [cnf transformation 48]
117. ~funny(X0) | strong(X0) [cnf transformation 48]
118. generous(sK4) | ~kind(X3) [cnf transformation 53]
120. ~quiet(sK4) | ~kind(X3) [cnf transformation 53]
122. funny(sK3) | kind(sK3) | quiet(X1) | ~generous(X1) [cnf transformation 53]
131. humble(fred) [cnf transformation 19]
133. 1 <=> ! [X0] : (~humble(X0) | tall(X0)) [avatar definition]
134. ~humble(X0) | tall(X0) <- (1) [avatar component clause 133]
146. 4 <=> ! [X0] : (~strong(X0) | ~curious(X0)) [avatar definition]
147. ~strong(X0) | ~curious(X0) <- (4) [avatar component clause 146]
158. 4 [avatar split clause 69,146]
183. ~humble(X0) | calm(X0) [subsumption resolution 95,70]
186. 12 <=> ! [X1] : (~calm(X1) | kind(X1)) [avatar definition]
187. ~calm(X1) | kind(X1) <- (12) [avatar component clause 186]
189. 13 <=> happy(sK1) [avatar definition]
191. ~happy(sK1) <- (~13) [avatar component clause 189]
193. 14 <=> patient(sK1) [avatar definition]
195. ~patient(sK1) <- (~14) [avatar component clause 193]
196. 12 | ~13 | ~14 [avatar split clause 111,193,189,186]
198. 15 <=> ! [X1] : (~kind(X1) | calm(X1)) [avatar definition]
199. ~kind(X1) | calm(X1) <- (15) [avatar component clause 198]
200. 15 | ~13 | ~14 [avatar split clause 110,193,189,198]
202. 16 <=> ! [X3] : patient(X3) [avatar definition]
203. patient(X3) <- (16) [avatar component clause 202]
205. 17 <=> calm(sK2) [avatar definition]
206. ~calm(sK2) <- (~17) [avatar component clause 205]
207. calm(sK2) <- (17) [avatar component clause 205]
209. 18 <=> kind(sK2) [avatar definition]
210. ~kind(sK2) <- (~18) [avatar component clause 209]
211. kind(sK2) <- (18) [avatar component clause 209]
214. 19 <=> ! [X3] : happy(X3) [avatar definition]
215. happy(X3) <- (19) [avatar component clause 214]
216. 19 | 17 | 18 [avatar split clause 108,209,205,214]
218. 19 | ~17 | ~18 [avatar split clause 106,209,205,214]
220. 20 <=> ! [X1] : (quiet(X1) | ~generous(X1)) [avatar definition]
221. ~generous(X1) | quiet(X1) <- (20) [avatar component clause 220]
223. 21 <=> kind(sK3) [avatar definition]
225. kind(sK3) <- (21) [avatar component clause 223]
227. 22 <=> funny(sK3) [avatar definition]
228. ~funny(sK3) <- (~22) [avatar component clause 227]
229. funny(sK3) <- (22) [avatar component clause 227]
230. 20 | 21 | 22 [avatar split clause 122,227,223,220]
235. 24 <=> quiet(sK4) [avatar definition]
237. ~quiet(sK4) <- (~24) [avatar component clause 235]
240. 25 <=> ! [X3] : ~kind(X3) [avatar definition]
241. ~kind(X3) <- (25) [avatar component clause 240]
242. 25 | ~24 [avatar split clause 120,235,240]
244. 26 <=> generous(sK4) [avatar definition]
246. generous(sK4) <- (26) [avatar component clause 244]
248. 25 | 26 [avatar split clause 118,244,240]
288. strong(sK1) <- (~13) [resolution 112,191]
291. ~humble(sK1) <- (~13) [resolution 288,71]
292. humble(X0) | patient(X0) [resolution 114,68]
293. patient(X0) [subsumption resolution 292,70]
294. 16 [avatar split clause 293,202]
295. tall(X0) | ~humble(X0) [resolution 116,71]
296. 1 [avatar split clause 295,133]
303. ~curious(sK1) <- (4, ~13) [resolution 147,288]
316. calm(fred) [resolution 183,131]
318. quiet(sK4) <- (20, 26) [resolution 221,246]
319. $false <- (20, ~24, 26) [subsumption resolution 318,237]
320. ~20 | 24 | ~26 [avatar contradiction clause 319]
323. strong(sK3) <- (22) [resolution 229,117]
366. ~curious(sK3) <- (4, 22) [resolution 323,147]
367. ~humble(sK3) <- (22) [resolution 323,71]
372. humble(sK1) <- (4, ~13) [resolution 303,114]
373. $false <- (4, ~13) [subsumption resolution 372,291]
374. ~4 | 13 [avatar contradiction clause 373]
375. $false <- (~14, 16) [subsumption resolution 195,203]
376. 14 | ~16 [avatar contradiction clause 375]
388. kind(sK2) <- (12, 17) [resolution 187,207]
389. kind(fred) <- (12) [resolution 187,316]
390. $false <- (12, 17, ~18) [subsumption resolution 388,210]
391. ~12 | ~17 | 18 [avatar contradiction clause 390]
393. calm(sK2) <- (15, 18) [resolution 199,211]
394. $false <- (15, ~17, 18) [subsumption resolution 393,206]
395. ~15 | 17 | ~18 [avatar contradiction clause 394]
397. ~old(X0) <- (19) [resolution 215,73]
426. humble(X1) | tall(X1) <- (16) [resolution 93,203]
428. tall(X1) <- (1, 16) [subsumption resolution 426,134]
453. humble(sK3) <- (4, 22) [resolution 366,114]
454. $false <- (4, 22) [subsumption resolution 453,367]
455. ~4 | ~22 [avatar contradiction clause 454]
457. calm(sK3) <- (15, 21) [resolution 225,199]
465. 42 <=> strong(sK3) [avatar definition]
466. strong(sK3) <- (42) [avatar component clause 465]
467. ~strong(sK3) <- (~42) [avatar component clause 465]
469. 43 <=> brave(sK3) [avatar definition]
470. brave(sK3) <- (43) [avatar component clause 469]
471. ~brave(sK3) <- (~43) [avatar component clause 469]
478. strong(sK3) | ~brave(sK3) | ~curious(sK3) <- (15, 21) [resolution 86,457]
481. ~brave(sK3) | ~curious(sK3) <- (15, 21, ~42) [subsumption resolution 478,467]
483. 44 <=> curious(sK3) [avatar definition]
486. ~44 | ~43 | ~15 | ~21 | 42 [avatar split clause 481,465,223,198,469,483]
499. strong(sK3) <- (~43) [resolution 471,113]
502. 42 | 43 [avatar split clause 499,469,465]
505. funny(sK3) | ~tall(sK3) <- (42) [resolution 466,115]
508. ~tall(sK3) <- (~22, 42) [subsumption resolution 505,228]
509. $false <- (1, 16, ~22, 42) [subsumption resolution 508,428]
510. ~1 | ~16 | 22 | ~42 [avatar contradiction clause 509]
577. old(sK3) | curious(sK3) | ~wise(sK3) <- (43) [resolution 470,99]
581. ~happy(sK3) | wise(sK3) <- (43) [resolution 470,74]
582. curious(sK3) | ~wise(sK3) <- (19, 43) [subsumption resolution 577,397]
584. wise(sK3) <- (19, 43) [subsumption resolution 581,215]
587. curious(sK3) <- (19, 43) [subsumption resolution 582,584]
588. 44 | ~19 | ~43 [avatar split clause 587,469,214,483]
589. $false <- (12, 25) [resolution 241,389]
590. ~12 | ~25 [avatar contradiction clause 589]
591. $false [avatar sat refutation 158,196,200,216,218,230,242,248,294,296,320,374,376,391,395,455,486,502,510,588,590]
% SZS output end Proof for 3106644072074603950712644
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is both not strong and generous and vice versa.
If mary is both not creative and calm then someone is generous and vice versa.
If someone is either tall or not tall then someone is both tall and not generous.
If fred is not strong then susan is both curious and kind.
Everyone who is both not funny and tall is both not tall and not generous.
If someone is either not kind or not rich then john is either happy or not happy.
Everyone who is either strong or not happy is either old or not kind and vice versa.
Everyone who is strong is both not generous and not brave and vice versa.
If paul is both not kind and funny then someone is both not calm and not generous.
Everyone who is both not quiet and not tall is both not creative and funny.
Everyone who is either curious or humble is strong and vice versa.
Everyone who is both quiet and not curious is either not tall or not creative and vice versa.
If fred is not old then someone is either not wise or not tall.
If someone is both not humble and not patient then alice is not curious or old and vice versa.
Everyone who is both old and tall is generous or not tall and vice versa.
Everyone who is not strong is not tall.
Someone is both not quiet and strong.
Someone is not rich.
Someone is rich.
Someone is either old or quiet.
Someone is either not patient or not old.
John is both not quiet and kind.
Mary is strong or not tall. | John is old. | contradiction | (![X]:(~kind(X)<=>(~strong(X)&generous(X))))&
(((~creative(mary)&calm(mary)))<=>(?[X]:(generous(X))))&
((?[X]:((tall(X)<~>~tall(X))))=>(?[X]:((tall(X)&~generous(X)))))&
((~strong(fred))=>((curious(susan)&kind(susan))))&
(![X]:((~funny(X)&tall(X))=>(~tall(X)&~generous(X))))&
((?[X]:((~kind(X)<~>~rich(X))))=>((happy(john)<~>~happy(john))))&
(![X]:((strong(X)<~>~happy(X))<=>(old(X)<~>~kind(X))))&
(![X]:(strong(X)<=>(~generous(X)&~brave(X))))&
(((~kind(paul)&funny(paul)))=>(?[X]:((~calm(X)&~generous(X)))))&
(![X]:((~quiet(X)&~tall(X))=>(~creative(X)&funny(X))))&
(![X]:((curious(X)<~>humble(X))<=>strong(X)))&
(![X]:((quiet(X)&~curious(X))<=>(~tall(X)<~>~creative(X))))&
((~old(fred))=>(?[X]:((~wise(X)<~>~tall(X)))))&
((?[X]:((~humble(X)&~patient(X))))<=>((~curious(alice)|old(alice))))&
(![X]:((old(X)&tall(X))<=>(generous(X)|~tall(X))))&
(![X]:(~strong(X)=>~tall(X)))&
(?[X]:((~quiet(X)&strong(X))))&
(?[X]:(~rich(X)))&
(?[X]:(rich(X)))&
(?[X]:((old(X)<~>quiet(X))))&
(?[X]:((~patient(X)<~>~old(X))))&
((~quiet(john)&kind(john)))&
((strong(mary)|~tall(mary))) | old(john) | [
"p1",
"p7",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1743457954622179254764526
% SZS output start Proof for 1743457954622179254764526
2. (calm(mary) & ~creative(mary)) <=> ? [X0] : generous(X0) [input p1]
8. ! [X0] : (strong(X0) <=> (~brave(X0) & ~generous(X0))) [input p7]
15. ! [X0] : ((tall(X0) & old(X0)) <=> (~tall(X0) | generous(X0))) [input p14]
16. ! [X0] : (~strong(X0) => ~tall(X0)) [input p15]
24. old(john) [input hypothesis]
36. ! [X0] : (~tall(X0) | strong(X0)) [ennf transformation 16]
39. ((calm(mary) & ~creative(mary)) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | (~calm(mary) | creative(mary))) [nnf transformation 2]
40. ((calm(mary) & ~creative(mary)) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | ~calm(mary) | creative(mary)) [flattening 39]
41. ((calm(mary) & ~creative(mary)) | ! [X0] : ~generous(X0)) & (? [X1] : generous(X1) | ~calm(mary) | creative(mary)) [rectify 40]
42. ? [X1] : generous(X1) => generous(sK0) [choice axiom]
43. ((calm(mary) & ~creative(mary)) | ! [X0] : ~generous(X0)) & (generous(sK0) | ~calm(mary) | creative(mary)) [skolemisation 41,42]
50. ! [X0] : ((strong(X0) | (brave(X0) | generous(X0))) & ((~brave(X0) & ~generous(X0)) | ~strong(X0))) [nnf transformation 8]
51. ! [X0] : ((strong(X0) | brave(X0) | generous(X0)) & ((~brave(X0) & ~generous(X0)) | ~strong(X0))) [flattening 50]
65. ! [X0] : (((tall(X0) & old(X0)) | (tall(X0) & ~generous(X0))) & ((~tall(X0) | generous(X0)) | (~tall(X0) | ~old(X0)))) [nnf transformation 15]
66. ! [X0] : (((tall(X0) & old(X0)) | (tall(X0) & ~generous(X0))) & (~tall(X0) | generous(X0) | ~tall(X0) | ~old(X0))) [flattening 65]
82. generous(sK0) | ~calm(mary) | creative(mary) [cnf transformation 43]
83. ~creative(mary) | ~generous(X0) [cnf transformation 43]
84. calm(mary) | ~generous(X0) [cnf transformation 43]
105. ~generous(X0) | ~strong(X0) [cnf transformation 51]
129. ~tall(X0) | generous(X0) | ~tall(X0) | ~old(X0) [cnf transformation 66]
133. tall(X0) | tall(X0) [cnf transformation 66]
134. ~tall(X0) | strong(X0) [cnf transformation 36]
146. old(john) [cnf transformation 24]
147. ~old(X0) | generous(X0) | ~tall(X0) [duplicate literal removal 129]
148. tall(X0) [duplicate literal removal 133]
155. 1 <=> ! [X0] : ~generous(X0) [avatar definition]
156. ~generous(X0) <- (1) [avatar component clause 155]
158. 2 <=> calm(mary) [avatar definition]
161. 1 | 2 [avatar split clause 84,158,155]
163. 3 <=> creative(mary) [avatar definition]
166. 1 | ~3 [avatar split clause 83,163,155]
168. 4 <=> generous(sK0) [avatar definition]
170. generous(sK0) <- (4) [avatar component clause 168]
171. 3 | ~2 | 4 [avatar split clause 82,168,158,163]
173. 5 <=> ! [X1] : tall(X1) [avatar definition]
174. tall(X1) <- (5) [avatar component clause 173]
265. 5 [avatar split clause 148,173]
291. ~strong(sK0) <- (4) [resolution 105,170]
298. strong(X0) <- (5) [resolution 134,174]
301. $false <- (4, 5) [resolution 298,291]
302. ~4 | ~5 [avatar contradiction clause 301]
351. generous(john) | ~tall(john) [resolution 147,146]
356. ~tall(john) <- (1) [subsumption resolution 351,156]
357. $false <- (1, 5) [subsumption resolution 356,174]
358. ~1 | ~5 [avatar contradiction clause 357]
362. $false [avatar sat refutation 161,166,171,265,302,358]
% SZS output end Proof for 1743457954622179254764526
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not tall then john is either happy or not kind and vice versa. If someone is not patient then someone is not happy and vice versa. Everyone who is calm or curious is either not happy or quiet. If lucy is both not generous and happy then susan is both not quiet and not calm. If someone is brave or not calm then paul is both curious and not happy and vice versa. If someone is either not wise or not curious then mary is generous or old and vice versa. Everyone who is either old or rich is not creative and vice versa. Everyone who is humble is tall or not tall. 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 either not calm or quiet then someone is both not curious and not generous. Mary is either not humble or happy. Mary is happy. Mary is both not old and not curious. Someone is not wise. Paul is not kind or not humble. | Fred is patient. | entailment | ((?[X]:((strong(X)<~>~tall(X))))<=>((happy(john)<~>~kind(john))))&
((?[X]:(~patient(X)))<=>(?[X]:(~happy(X))))&
(![X]:((calm(X)|curious(X))=>(~happy(X)<~>quiet(X))))&
(((~generous(lucy)&happy(lucy)))=>((~quiet(susan)&~calm(susan))))&
((?[X]:((brave(X)|~calm(X))))<=>((curious(paul)&~happy(paul))))&
((?[X]:((~wise(X)<~>~curious(X))))<=>((generous(mary)|old(mary))))&
(![X]:((old(X)<~>rich(X))<=>~creative(X)))&
(![X]:(humble(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))))&
(((~calm(john)<~>quiet(john)))=>(?[X]:((~curious(X)&~generous(X)))))&
((~humble(mary)<~>happy(mary)))&
(happy(mary))&
((~old(mary)&~curious(mary)))&
(?[X]:(~wise(X)))&
((~kind(paul)|~humble(paul))) | patient(fred) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1463688659286842634731112
% SZS output start Proof for 1463688659286842634731112
12. ! [X0] : (patient(X0) <=> (~funny(X0) | ~patient(X0))) [input p11]
21. ~patient(fred) [input hypothesis]
61. ! [X0] : ((patient(X0) | (funny(X0) & patient(X0))) & ((~funny(X0) | ~patient(X0)) | ~patient(X0))) [nnf transformation 12]
62. ! [X0] : ((patient(X0) | (funny(X0) & patient(X0))) & (~funny(X0) | ~patient(X0) | ~patient(X0))) [flattening 61]
120. patient(X0) | patient(X0) [cnf transformation 62]
143. ~patient(fred) [cnf transformation 21]
145. patient(X0) [duplicate literal removal 120]
185. 9 <=> ! [X3] : patient(X3) [avatar definition]
186. patient(X3) <- (9) [avatar component clause 185]
285. 9 [avatar split clause 145,185]
386. $false <- (9) [resolution 186,143]
387. ~9 [avatar contradiction clause 386]
388. $false [avatar sat refutation 285,387]
% SZS output end Proof for 1463688659286842634731112
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either old or curious is humble. Everyone who is either humble or creative is creative and vice versa. Everyone who is not old is rich. If someone is either curious or tall then john is either rich or kind. Everyone who is not quiet or not tall is both old and wise and vice versa. Everyone who is both not brave and old is not humble and vice versa. Everyone who is both old and brave is funny or not strong. If someone is brave then susan is either strong or wise and vice versa. If mary is not brave or not happy then susan is curious. Everyone who is not kind is not creative or not patient and vice versa. If someone is both not calm and not brave then someone is kind and vice versa. If someone is either strong or not old then susan is funny or not calm and vice versa. Everyone who is either not tall or old is both funny and calm. If someone is wise then lucy is not funny or rich and vice versa. Everyone who is kind is not funny and vice versa. Everyone who is either not kind or not creative is happy or old. Mary is both kind and rich. Paul is not strong or not tall. Susan is both not generous and not strong. Someone is either not brave or not tall. Mary is happy or old. Lucy is not brave. Someone is creative or brave. John is either calm or generous. | Mary is not tall. | entailment | (![X]:((old(X)<~>curious(X))=>humble(X)))&
(![X]:((humble(X)<~>creative(X))<=>creative(X)))&
(![X]:(~old(X)=>rich(X)))&
((?[X]:((curious(X)<~>tall(X))))=>((rich(john)<~>kind(john))))&
(![X]:((~quiet(X)|~tall(X))<=>(old(X)&wise(X))))&
(![X]:((~brave(X)&old(X))<=>~humble(X)))&
(![X]:((old(X)&brave(X))=>(funny(X)|~strong(X))))&
((?[X]:(brave(X)))<=>((strong(susan)<~>wise(susan))))&
(((~brave(mary)|~happy(mary)))=>(curious(susan)))&
(![X]:(~kind(X)<=>(~creative(X)|~patient(X))))&
((?[X]:((~calm(X)&~brave(X))))<=>(?[X]:(kind(X))))&
((?[X]:((strong(X)<~>~old(X))))<=>((funny(susan)|~calm(susan))))&
(![X]:((~tall(X)<~>old(X))=>(funny(X)&calm(X))))&
((?[X]:(wise(X)))<=>((~funny(lucy)|rich(lucy))))&
(![X]:(kind(X)<=>~funny(X)))&
(![X]:((~kind(X)<~>~creative(X))=>(happy(X)|old(X))))&
((kind(mary)&rich(mary)))&
((~strong(paul)|~tall(paul)))&
((~generous(susan)&~strong(susan)))&
(?[X]:((~brave(X)<~>~tall(X))))&
((happy(mary)|old(mary)))&
(~brave(lucy))&
(?[X]:((creative(X)|brave(X))))&
((calm(john)<~>generous(john))) | ~tall(mary) | [
"p1",
"p5",
"p12",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 9064985595087392794114725
% SZS output start Proof for 9064985595087392794114725
2. ! [X0] : ((humble(X0) <~> creative(X0)) <=> creative(X0)) [input p1]
6. ! [X0] : ((old(X0) & ~brave(X0)) <=> ~humble(X0)) [input p5]
13. ! [X0] : ((~tall(X0) <~> old(X0)) => (calm(X0) & funny(X0))) [input p12]
15. ! [X0] : (kind(X0) <=> ~funny(X0)) [input p14]
17. rich(mary) & kind(mary) [input p16]
25. tall(mary) [input hypothesis]
36. ! [X0] : ((calm(X0) & funny(X0)) | (~tall(X0) <=> old(X0))) [ennf transformation 13]
38. ! [X0] : ((((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | ~creative(X0)) & (creative(X0) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0))))) [nnf transformation 2]
42. ! [X0] : (((old(X0) & ~brave(X0)) | humble(X0)) & (~humble(X0) | (~old(X0) | brave(X0)))) [nnf transformation 6]
43. ! [X0] : (((old(X0) & ~brave(X0)) | humble(X0)) & (~humble(X0) | ~old(X0) | brave(X0))) [flattening 42]
60. ! [X0] : ((calm(X0) & funny(X0)) | ((~tall(X0) | ~old(X0)) & (old(X0) | tall(X0)))) [nnf transformation 36]
66. ! [X0] : ((kind(X0) | funny(X0)) & (~funny(X0) | ~kind(X0))) [nnf transformation 15]
75. creative(X0) | creative(X0) | ~humble(X0) [cnf transformation 38]
78. ~creative(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 38]
91. old(X0) | humble(X0) [cnf transformation 43]
111. funny(X0) | ~tall(X0) | ~old(X0) [cnf transformation 60]
117. ~funny(X0) | ~kind(X0) [cnf transformation 66]
119. kind(mary) [cnf transformation 17]
130. tall(mary) [cnf transformation 25]
131. creative(X0) | ~humble(X0) [duplicate literal removal 75]
132. ~creative(X0) | ~humble(X0) [duplicate literal removal 78]
133. ~humble(X0) [subsumption resolution 131,132]
152. old(X0) [subsumption resolution 91,133]
206. ~tall(X0) | funny(X0) [subsumption resolution 111,152]
274. funny(mary) [resolution 206,130]
279. ~kind(mary) [resolution 274,117]
280. $false [subsumption resolution 279,119]
% SZS output end Proof for 9064985595087392794114725
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not kind then alice is brave or not creative and vice versa. If someone is not creative then john is either old or curious and vice versa. Everyone who is not rich is both not quiet and not calm and vice versa. Everyone who is tall or curious is either calm or not kind. Everyone who is strong or not calm is either curious or strong. If someone is not patient then someone is generous. If john is rich or patient then someone is calm or quiet and vice versa. Everyone who is either not humble or funny is both not wise and not brave and vice versa. Everyone who is not old or not quiet is kind or generous. Everyone who is both not curious and kind is curious or patient and vice versa. If fred is both wise and rich then someone is rich and vice versa. If susan is both creative and not happy then john is both not tall and not humble and vice versa. Everyone who is not wise or not rich is not tall. Everyone who is either brave or calm is either not creative or not humble and vice versa. Everyone who is both creative and strong is both patient and rich and vice versa. Everyone who is curious is funny and vice versa. Mary is curious or patient. John is not brave. Someone is either not generous or not happy. Someone is either quiet or not old. Someone is both creative and not funny. Someone is either happy or not generous. Mary is both wise and not rich. Fred is both not generous and not patient. | John is old. | entailment | ((~kind(mary))<=>((brave(alice)|~creative(alice))))&
((?[X]:(~creative(X)))<=>((old(john)<~>curious(john))))&
(![X]:(~rich(X)<=>(~quiet(X)&~calm(X))))&
(![X]:((tall(X)|curious(X))=>(calm(X)<~>~kind(X))))&
(![X]:((strong(X)|~calm(X))=>(curious(X)<~>strong(X))))&
((?[X]:(~patient(X)))=>(?[X]:(generous(X))))&
(((rich(john)|patient(john)))<=>(?[X]:((calm(X)|quiet(X)))))&
(![X]:((~humble(X)<~>funny(X))<=>(~wise(X)&~brave(X))))&
(![X]:((~old(X)|~quiet(X))=>(kind(X)|generous(X))))&
(![X]:((~curious(X)&kind(X))<=>(curious(X)|patient(X))))&
(((wise(fred)&rich(fred)))<=>(?[X]:(rich(X))))&
(((creative(susan)&~happy(susan)))<=>((~tall(john)&~humble(john))))&
(![X]:((~wise(X)|~rich(X))=>~tall(X)))&
(![X]:((brave(X)<~>calm(X))<=>(~creative(X)<~>~humble(X))))&
(![X]:((creative(X)&strong(X))<=>(patient(X)&rich(X))))&
(![X]:(curious(X)<=>funny(X)))&
((curious(mary)|patient(mary)))&
(~brave(john))&
(?[X]:((~generous(X)<~>~happy(X))))&
(?[X]:((quiet(X)<~>~old(X))))&
(?[X]:((creative(X)&~funny(X))))&
(?[X]:((happy(X)<~>~generous(X))))&
((wise(mary)&~rich(mary)))&
((~generous(fred)&~patient(fred))) | old(john) | [
"p1",
"p2",
"p4",
"p9",
"p14",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7024917847148724303570242
% SZS output start Proof for 7024917847148724303570242
2. ? [X0] : ~creative(X0) <=> (old(john) <~> curious(john)) [input p1]
3. ! [X0] : (~rich(X0) <=> (~calm(X0) & ~quiet(X0))) [input p2]
5. ! [X0] : ((~calm(X0) | strong(X0)) => (curious(X0) <~> strong(X0))) [input p4]
10. ! [X0] : ((kind(X0) & ~curious(X0)) <=> (patient(X0) | curious(X0))) [input p9]
15. ! [X0] : ((strong(X0) & creative(X0)) <=> (rich(X0) & patient(X0))) [input p14]
23. ~rich(mary) & wise(mary) [input p22]
25. ~old(john) [input hypothesis]
28. ! [X0] : ((curious(X0) <~> strong(X0)) | (calm(X0) & ~strong(X0))) [ennf transformation 5]
35. (? [X0] : ~creative(X0) | ((old(john) | ~curious(john)) & (curious(john) | ~old(john)))) & (((~curious(john) | ~old(john)) & (curious(john) | old(john))) | ! [X0] : creative(X0)) [nnf transformation 2]
36. (? [X0] : ~creative(X0) | ((old(john) | ~curious(john)) & (curious(john) | ~old(john)))) & (((~curious(john) | ~old(john)) & (curious(john) | old(john))) | ! [X1] : creative(X1)) [rectify 35]
37. ? [X0] : ~creative(X0) => ~creative(sK0) [choice axiom]
38. (~creative(sK0) | ((old(john) | ~curious(john)) & (curious(john) | ~old(john)))) & (((~curious(john) | ~old(john)) & (curious(john) | old(john))) | ! [X1] : creative(X1)) [skolemisation 36,37]
39. ! [X0] : ((~rich(X0) | (calm(X0) | quiet(X0))) & ((~calm(X0) & ~quiet(X0)) | rich(X0))) [nnf transformation 3]
40. ! [X0] : ((~rich(X0) | calm(X0) | quiet(X0)) & ((~calm(X0) & ~quiet(X0)) | rich(X0))) [flattening 39]
42. ! [X0] : (((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | (calm(X0) & ~strong(X0))) [nnf transformation 28]
53. ! [X0] : (((kind(X0) & ~curious(X0)) | (~patient(X0) & ~curious(X0))) & ((patient(X0) | curious(X0)) | (~kind(X0) | curious(X0)))) [nnf transformation 10]
54. ! [X0] : (((kind(X0) & ~curious(X0)) | (~patient(X0) & ~curious(X0))) & (patient(X0) | curious(X0) | ~kind(X0) | curious(X0))) [flattening 53]
63. ! [X0] : (((strong(X0) & creative(X0)) | (~rich(X0) | ~patient(X0))) & ((rich(X0) & patient(X0)) | (~strong(X0) | ~creative(X0)))) [nnf transformation 15]
64. ! [X0] : (((strong(X0) & creative(X0)) | ~rich(X0) | ~patient(X0)) & ((rich(X0) & patient(X0)) | ~strong(X0) | ~creative(X0))) [flattening 63]
80. curious(john) | old(john) | creative(X1) [cnf transformation 38]
85. ~calm(X0) | rich(X0) [cnf transformation 40]
92. strong(X0) | curious(X0) | calm(X0) [cnf transformation 42]
109. ~curious(X0) | ~curious(X0) [cnf transformation 54]
131. ~strong(X0) | rich(X0) | ~creative(X0) [cnf transformation 64]
147. ~rich(mary) [cnf transformation 23]
150. ~old(john) [cnf transformation 25]
152. ~curious(X0) [duplicate literal removal 109]
170. 4 <=> curious(john) [avatar definition]
171. curious(john) <- (4) [avatar component clause 170]
174. 5 <=> old(john) [avatar definition]
184. 7 <=> ! [X1] : creative(X1) [avatar definition]
185. creative(X1) <- (7) [avatar component clause 184]
187. 7 | 5 | 4 [avatar split clause 80,170,174,184]
293. ~5 [avatar split clause 150,174]
294. $false <- (4) [subsumption resolution 171,152]
295. ~4 [avatar contradiction clause 294]
379. rich(X0) | ~creative(X0) | curious(X0) | calm(X0) [resolution 131,92]
380. rich(X0) | curious(X0) | calm(X0) <- (7) [subsumption resolution 379,185]
381. rich(X0) | calm(X0) <- (7) [subsumption resolution 380,152]
382. rich(X0) <- (7) [subsumption resolution 381,85]
420. $false <- (7) [resolution 382,147]
424. ~7 [avatar contradiction clause 420]
425. $false [avatar sat refutation 187,293,295,424]
% SZS output end Proof for 7024917847148724303570242
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or strong is not kind or not humble. If someone is both creative and old then someone is not curious. If someone is both old and generous then someone is not wise or creative and vice versa. If mary is strong or creative then someone is generous and vice versa. If fred is both kind and not creative then someone is not curious and vice versa. If lucy is both not rich and not humble then someone is creative or not funny. Everyone who is humble or not patient is either not tall or patient. Everyone who is rich is strong and vice versa. Everyone who is generous is both not funny and old. Everyone who is not funny or funny is both not tall and not rich. If lucy is either not strong or not quiet then alice is old and vice versa. Everyone who is either not brave or calm is not strong. Everyone who is both not generous and wise is both wise and rich and vice versa. If someone is both generous and not patient then alice is happy or not patient and vice versa. If lucy is brave or not old then mary is not strong. Everyone who is both old and curious is both not rich and brave. Someone is not curious or creative. Someone is not funny. Mary is wise. Susan is both not humble and not quiet. Someone is not patient. Someone is both old and generous. Someone is either rich or old. Someone is not tall or not funny. | Fred is not strong. | entailment | (![X]:((happy(X)|strong(X))=>(~kind(X)|~humble(X))))&
((?[X]:((creative(X)&old(X))))=>(?[X]:(~curious(X))))&
((?[X]:((old(X)&generous(X))))<=>(?[X]:((~wise(X)|creative(X)))))&
(((strong(mary)|creative(mary)))<=>(?[X]:(generous(X))))&
(((kind(fred)&~creative(fred)))<=>(?[X]:(~curious(X))))&
(((~rich(lucy)&~humble(lucy)))=>(?[X]:((creative(X)|~funny(X)))))&
(![X]:((humble(X)|~patient(X))=>(~tall(X)<~>patient(X))))&
(![X]:(rich(X)<=>strong(X)))&
(![X]:(generous(X)=>(~funny(X)&old(X))))&
(![X]:((~funny(X)|funny(X))=>(~tall(X)&~rich(X))))&
(((~strong(lucy)<~>~quiet(lucy)))<=>(old(alice)))&
(![X]:((~brave(X)<~>calm(X))=>~strong(X)))&
(![X]:((~generous(X)&wise(X))<=>(wise(X)&rich(X))))&
((?[X]:((generous(X)&~patient(X))))<=>((happy(alice)|~patient(alice))))&
(((brave(lucy)|~old(lucy)))=>(~strong(mary)))&
(![X]:((old(X)&curious(X))=>(~rich(X)&brave(X))))&
(?[X]:((~curious(X)|creative(X))))&
(?[X]:(~funny(X)))&
(wise(mary))&
((~humble(susan)&~quiet(susan)))&
(?[X]:(~patient(X)))&
(?[X]:((old(X)&generous(X))))&
(?[X]:((rich(X)<~>old(X))))&
(?[X]:((~tall(X)|~funny(X)))) | ~strong(fred) | [
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6342729393425995407732233
% SZS output start Proof for 6342729393425995407732233
8. ! [X0] : (rich(X0) <=> strong(X0)) [input p7]
10. ! [X0] : ((funny(X0) | ~funny(X0)) => (~rich(X0) & ~tall(X0))) [input p9]
25. strong(fred) [input hypothesis]
35. ! [X0] : ((~rich(X0) & ~tall(X0)) | (~funny(X0) & funny(X0))) [ennf transformation 10]
61. ! [X0] : ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0))) [nnf transformation 8]
104. ~strong(X0) | rich(X0) [cnf transformation 61]
109. ~rich(X0) | funny(X0) [cnf transformation 35]
110. ~rich(X0) | ~funny(X0) [cnf transformation 35]
141. strong(fred) [cnf transformation 25]
234. ~rich(X0) [subsumption resolution 109,110]
313. rich(fred) [resolution 104,141]
314. $false [subsumption resolution 313,234]
% SZS output end Proof for 6342729393425995407732233
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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