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
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stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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Everyone who is both creative and brave is both generous and not strong and vice versa. If alice is either kind or patient then someone is both generous and old and vice versa. Everyone who is not creative or quiet is either strong or not creative. If mary is both quiet and not calm then lucy is generous or not quiet. Everyone who is either not rich or not kind is either not generous or quiet. If john is either not curious or wise then someone is not old or not quiet and vice versa. If someone is both not happy and not quiet then alice is not brave or quiet. Everyone who is creative is not calm or not rich. If susan is either old or not strong then someone is both not creative and not old. If someone is not humble or not creative then alice is humble or not rich. Everyone who is both not kind and curious is both not wise and rich and vice versa. Everyone who is creative or wise is both not rich and not creative. Everyone who is funny or rich is either humble or strong. Everyone who is wise or not curious is either not creative or wise. Everyone who is either kind or curious is not old or funny and vice versa. Everyone who is calm or not strong is not tall or not generous and vice versa. Mary is not wise or not calm. Mary is not patient. Paul is not brave. Susan is not rich or not kind. Someone is either not wise or not patient. Someone is not funny. Someone is either strong or rich. Someone is not quiet or not patient. | John is not generous. | entailment | (![X]:((creative(X)&brave(X))<=>(generous(X)&~strong(X))))&
(((kind(alice)<~>patient(alice)))<=>(?[X]:((generous(X)&old(X)))))&
(![X]:((~creative(X)|quiet(X))=>(strong(X)<~>~creative(X))))&
(((quiet(mary)&~calm(mary)))=>((generous(lucy)|~quiet(lucy))))&
(![X]:((~rich(X)<~>~kind(X))=>(~generous(X)<~>quiet(X))))&
(((~curious(john)<~>wise(john)))<=>(?[X]:((~old(X)|~quiet(X)))))&
((?[X]:((~happy(X)&~quiet(X))))=>((~brave(alice)|quiet(alice))))&
(![X]:(creative(X)=>(~calm(X)|~rich(X))))&
(((old(susan)<~>~strong(susan)))=>(?[X]:((~creative(X)&~old(X)))))&
((?[X]:((~humble(X)|~creative(X))))=>((humble(alice)|~rich(alice))))&
(![X]:((~kind(X)&curious(X))<=>(~wise(X)&rich(X))))&
(![X]:((creative(X)|wise(X))=>(~rich(X)&~creative(X))))&
(![X]:((funny(X)|rich(X))=>(humble(X)<~>strong(X))))&
(![X]:((wise(X)|~curious(X))=>(~creative(X)<~>wise(X))))&
(![X]:((kind(X)<~>curious(X))<=>(~old(X)|funny(X))))&
(![X]:((calm(X)|~strong(X))<=>(~tall(X)|~generous(X))))&
((~wise(mary)|~calm(mary)))&
(~patient(mary))&
(~brave(paul))&
((~rich(susan)|~kind(susan)))&
(?[X]:((~wise(X)<~>~patient(X))))&
(?[X]:(~funny(X)))&
(?[X]:((strong(X)<~>rich(X))))&
(?[X]:((~quiet(X)|~patient(X)))) | ~generous(john) | [
"p0",
"p2",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8273097463529426270112554
% SZS output start Proof for 8273097463529426270112554
1. ! [X0] : ((brave(X0) & creative(X0)) <=> (~strong(X0) & generous(X0))) [input p0]
3. ! [X0] : ((quiet(X0) | ~creative(X0)) => (strong(X0) <~> ~creative(X0))) [input p2]
12. ! [X0] : ((wise(X0) | creative(X0)) => (~creative(X0) & ~rich(X0))) [input p11]
25. generous(john) [input hypothesis]
27. ! [X0] : ((strong(X0) <~> ~creative(X0)) | (~quiet(X0) & creative(X0))) [ennf transformation 3]
36. ! [X0] : ((~creative(X0) & ~rich(X0)) | (~wise(X0) & ~creative(X0))) [ennf transformation 12]
39. ! [X0] : (((brave(X0) & creative(X0)) | (strong(X0) | ~generous(X0))) & ((~strong(X0) & generous(X0)) | (~brave(X0) | ~creative(X0)))) [nnf transformation 1]
40. ! [X0] : (((brave(X0) & creative(X0)) | strong(X0) | ~generous(X0)) & ((~strong(X0) & generous(X0)) | ~brave(X0) | ~creative(X0))) [flattening 39]
45. ! [X0] : (((creative(X0) | ~strong(X0)) & (~creative(X0) | strong(X0))) | (~quiet(X0) & creative(X0))) [nnf transformation 27]
74. ~generous(X0) | strong(X0) | creative(X0) [cnf transformation 40]
84. creative(X0) | ~strong(X0) | creative(X0) [cnf transformation 45]
110. ~creative(X0) | ~creative(X0) [cnf transformation 36]
140. generous(john) [cnf transformation 25]
142. ~creative(X0) [duplicate literal removal 110]
143. ~strong(X0) | creative(X0) [duplicate literal removal 84]
284. strong(john) | creative(john) [resolution 74,140]
286. strong(john) [subsumption resolution 284,142]
289. creative(john) [resolution 286,143]
290. $false [subsumption resolution 289,142]
% SZS output end Proof for 8273097463529426270112554
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or quiet is both old and not brave.
If someone is both strong and not humble then paul is both not creative and not old and vice versa.
Everyone who is not creative or strong is either kind or not humble.
Everyone who is both humble and brave is not creative and vice versa.
Everyone who is either brave or humble is rich.
Everyone who is not happy or not old is either not curious or brave.
Everyone who is both not generous and calm is humble and vice versa.
If someone is either patient or not patient then susan is not quiet or not old.
Everyone who is calm or rich is either not rich or not brave.
Everyone who is either not happy or not calm is either kind or calm.
Everyone who is both not creative and humble is both quiet and humble and vice versa.
If someone is either wise or not quiet then alice is both creative and humble and vice versa.
If paul is either generous or not generous then someone is both tall and creative.
If someone is not kind or not rich then mary is both not rich and patient.
Everyone who is both not strong and quiet is not generous or calm and vice versa.
If someone is both not funny and happy then john is both not happy and tall and vice versa.
Mary is both wise and creative.
Someone is not humble.
Fred is either not brave or not patient.
John is not curious or brave.
Mary is both not curious and tall.
Fred is not creative or curious.
John is both not strong and not kind. | Susan is not kind. | neutral | (![X]:((~calm(X)<~>quiet(X))=>(old(X)&~brave(X))))&
((?[X]:((strong(X)&~humble(X))))<=>((~creative(paul)&~old(paul))))&
(![X]:((~creative(X)|strong(X))=>(kind(X)<~>~humble(X))))&
(![X]:((humble(X)&brave(X))<=>~creative(X)))&
(![X]:((brave(X)<~>humble(X))=>rich(X)))&
(![X]:((~happy(X)|~old(X))=>(~curious(X)<~>brave(X))))&
(![X]:((~generous(X)&calm(X))<=>humble(X)))&
((?[X]:((patient(X)<~>~patient(X))))=>((~quiet(susan)|~old(susan))))&
(![X]:((calm(X)|rich(X))=>(~rich(X)<~>~brave(X))))&
(![X]:((~happy(X)<~>~calm(X))=>(kind(X)<~>calm(X))))&
(![X]:((~creative(X)&humble(X))<=>(quiet(X)&humble(X))))&
((?[X]:((wise(X)<~>~quiet(X))))<=>((creative(alice)&humble(alice))))&
(((generous(paul)<~>~generous(paul)))=>(?[X]:((tall(X)&creative(X)))))&
((?[X]:((~kind(X)|~rich(X))))=>((~rich(mary)&patient(mary))))&
(![X]:((~strong(X)&quiet(X))<=>(~generous(X)|calm(X))))&
((?[X]:((~funny(X)&happy(X))))<=>((~happy(john)&tall(john))))&
((wise(mary)&creative(mary)))&
(?[X]:(~humble(X)))&
((~brave(fred)<~>~patient(fred)))&
((~curious(john)|brave(john)))&
((~curious(mary)&tall(mary)))&
((~creative(fred)|curious(fred)))&
((~strong(john)&~kind(john))) | ~kind(susan) | [] | null | 0 |
Everyone who is either not wise or not strong is both not kind and funny and vice versa. If paul is curious or rich then someone is either not brave or not funny and vice versa. If alice is either brave or patient then alice is strong and vice versa. Everyone who is calm or not brave is both not humble and generous. If someone is not brave then alice is both not quiet and not strong. If someone is both not rich and brave then someone is both not generous and wise and vice versa. Everyone who is both kind and not creative is not patient or not brave. If someone is either not creative or tall then someone is not patient or calm. If mary is both not quiet and kind then fred is not tall. If someone is both strong and not tall then john is either not generous or not creative and vice versa. Everyone who is either curious or not rich is not rich and vice versa. Everyone who is either not wise or not old is either not wise or not tall and vice versa. Everyone who is happy or not quiet is both not curious and not happy and vice versa. If alice is both tall and not brave then paul is not quiet. If mary is not old then mary is both not strong and wise and vice versa. If mary is both not patient and strong then someone is both happy and generous. Someone is wise. Someone is both strong and not patient. Someone is either happy or rich. Susan is calm. Someone is not quiet. Fred is kind. | Susan is generous. | entailment | (![X]:((~wise(X)<~>~strong(X))<=>(~kind(X)&funny(X))))&
(((curious(paul)|rich(paul)))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
(((brave(alice)<~>patient(alice)))<=>(strong(alice)))&
(![X]:((calm(X)|~brave(X))=>(~humble(X)&generous(X))))&
((?[X]:(~brave(X)))=>((~quiet(alice)&~strong(alice))))&
((?[X]:((~rich(X)&brave(X))))<=>(?[X]:((~generous(X)&wise(X)))))&
(![X]:((kind(X)&~creative(X))=>(~patient(X)|~brave(X))))&
((?[X]:((~creative(X)<~>tall(X))))=>(?[X]:((~patient(X)|calm(X)))))&
(((~quiet(mary)&kind(mary)))=>(~tall(fred)))&
((?[X]:((strong(X)&~tall(X))))<=>((~generous(john)<~>~creative(john))))&
(![X]:((curious(X)<~>~rich(X))<=>~rich(X)))&
(![X]:((~wise(X)<~>~old(X))<=>(~wise(X)<~>~tall(X))))&
(![X]:((happy(X)|~quiet(X))<=>(~curious(X)&~happy(X))))&
(((tall(alice)&~brave(alice)))=>(~quiet(paul)))&
((~old(mary))<=>((~strong(mary)&wise(mary))))&
(((~patient(mary)&strong(mary)))=>(?[X]:((happy(X)&generous(X)))))&
(?[X]:(wise(X)))&
(?[X]:((strong(X)&~patient(X))))&
(?[X]:((happy(X)<~>rich(X))))&
(calm(susan))&
(?[X]:(~quiet(X)))&
(kind(fred)) | generous(susan) | [
"p3",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3205545776517562757243658
% SZS output start Proof for 3205545776517562757243658
4. ! [X0] : ((~brave(X0) | calm(X0)) => (generous(X0) & ~humble(X0))) [input p3]
20. calm(susan) [input p19]
23. ~generous(susan) [input hypothesis]
26. ! [X0] : ((~brave(X0) | calm(X0)) => generous(X0)) [pure predicate removal 4]
27. ! [X0] : (generous(X0) | (brave(X0) & ~calm(X0))) [ennf transformation 26]
92. ~calm(X0) | generous(X0) [cnf transformation 27]
138. calm(susan) [cnf transformation 20]
141. ~generous(susan) [cnf transformation 23]
325. generous(susan) [resolution 92,138]
326. $false [subsumption resolution 325,141]
% SZS output end Proof for 3205545776517562757243658
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both not strong and not patient then someone is tall or not brave and vice versa.
If someone is not patient or not humble then someone is both not creative and not brave.
If fred is both patient and kind then john is both not old and not brave.
If john is either not funny or not generous then john is not humble or not creative and vice versa.
If mary is curious then mary is not rich or not creative.
Everyone who is wise or not wise is both rich and curious.
Everyone who is not humble is both rich and not happy and vice versa.
Everyone who is both not old and not calm is either not tall or not curious and vice versa.
Everyone who is both not quiet and not kind is both rich and kind.
Everyone who is not strong is both humble and not patient and vice versa.
If susan is either not rich or not humble then someone is quiet and vice versa.
If paul is not generous or patient then someone is either kind or old.
Everyone who is wise is brave or not kind.
Everyone who is either old or humble is tall.
Everyone who is old or not curious is tall and vice versa.
Everyone who is not funny or not brave is patient.
Someone is not tall or not humble.
Someone is not old.
Mary is both not creative and not strong.
Paul is both not wise and not generous.
Alice is both not creative and humble.
Susan is not strong.
Someone is strong or not quiet. | Susan is humble. | entailment | (((~strong(alice)&~patient(alice)))<=>(?[X]:((tall(X)|~brave(X)))))&
((?[X]:((~patient(X)|~humble(X))))=>(?[X]:((~creative(X)&~brave(X)))))&
(((patient(fred)&kind(fred)))=>((~old(john)&~brave(john))))&
(((~funny(john)<~>~generous(john)))<=>((~humble(john)|~creative(john))))&
((curious(mary))=>((~rich(mary)|~creative(mary))))&
(![X]:((wise(X)|~wise(X))=>(rich(X)&curious(X))))&
(![X]:(~humble(X)<=>(rich(X)&~happy(X))))&
(![X]:((~old(X)&~calm(X))<=>(~tall(X)<~>~curious(X))))&
(![X]:((~quiet(X)&~kind(X))=>(rich(X)&kind(X))))&
(![X]:(~strong(X)<=>(humble(X)&~patient(X))))&
(((~rich(susan)<~>~humble(susan)))<=>(?[X]:(quiet(X))))&
(((~generous(paul)|patient(paul)))=>(?[X]:((kind(X)<~>old(X)))))&
(![X]:(wise(X)=>(brave(X)|~kind(X))))&
(![X]:((old(X)<~>humble(X))=>tall(X)))&
(![X]:((old(X)|~curious(X))<=>tall(X)))&
(![X]:((~funny(X)|~brave(X))=>patient(X)))&
(?[X]:((~tall(X)|~humble(X))))&
(?[X]:(~old(X)))&
((~creative(mary)&~strong(mary)))&
((~wise(paul)&~generous(paul)))&
((~creative(alice)&humble(alice)))&
(~strong(susan))&
(?[X]:((strong(X)|~quiet(X)))) | humble(susan) | [
"p9",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5449330013541301574357380
% SZS output start Proof for 5449330013541301574357380
10. ! [X0] : (~strong(X0) <=> (~patient(X0) & humble(X0))) [input p9]
22. ~strong(susan) [input p21]
24. ~humble(susan) [input hypothesis]
53. ! [X0] : ((~strong(X0) | (patient(X0) | ~humble(X0))) & ((~patient(X0) & humble(X0)) | strong(X0))) [nnf transformation 10]
54. ! [X0] : ((~strong(X0) | patient(X0) | ~humble(X0)) & ((~patient(X0) & humble(X0)) | strong(X0))) [flattening 53]
104. humble(X0) | strong(X0) [cnf transformation 54]
131. ~strong(susan) [cnf transformation 22]
133. ~humble(susan) [cnf transformation 24]
244. 23 <=> humble(susan) [avatar definition]
246. ~humble(susan) <- (~23) [avatar component clause 244]
288. ~23 [avatar split clause 133,244]
291. strong(susan) <- (~23) [resolution 104,246]
293. $false <- (~23) [subsumption resolution 291,131]
294. 23 [avatar contradiction clause 293]
295. $false [avatar sat refutation 288,294]
% SZS output end Proof for 5449330013541301574357380
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or creative is both not rich and generous and vice versa. Everyone who is either kind or happy is either not tall or not humble. Everyone who is not happy is humble or not funny. If paul is either not old or not wise then someone is not calm and vice versa. Everyone who is not tall is not rich or creative and vice versa. Everyone who is either not brave or strong is not quiet or patient and vice versa. Everyone who is not tall is either not patient or calm. If someone is both old and humble then susan is not wise or not old and vice versa. If someone is both old and not old then someone is either not humble or kind and vice versa. If someone is both not brave and not funny then susan is not brave or strong and vice versa. Everyone who is either happy or not brave is humble or not happy and vice versa. If john is both not rich and not happy then someone is not wise and vice versa. If lucy is both not happy and old then someone is happy or not creative. Everyone who is not patient is both happy and creative. Everyone who is creative or old is not humble. If fred is both not strong and not brave then lucy is both not rich and humble and vice versa. Paul is brave. Someone is brave or humble. Someone is quiet or not brave. Someone is either quiet or not quiet. Lucy is both patient and brave. Someone is brave. Fred is not quiet. Someone is either curious or generous. | Paul is not tall. | entailment | (![X]:((~patient(X)<~>creative(X))<=>(~rich(X)&generous(X))))&
(![X]:((kind(X)<~>happy(X))=>(~tall(X)<~>~humble(X))))&
(![X]:(~happy(X)=>(humble(X)|~funny(X))))&
(((~old(paul)<~>~wise(paul)))<=>(?[X]:(~calm(X))))&
(![X]:(~tall(X)<=>(~rich(X)|creative(X))))&
(![X]:((~brave(X)<~>strong(X))<=>(~quiet(X)|patient(X))))&
(![X]:(~tall(X)=>(~patient(X)<~>calm(X))))&
((?[X]:((old(X)&humble(X))))<=>((~wise(susan)|~old(susan))))&
((?[X]:((old(X)&~old(X))))<=>(?[X]:((~humble(X)<~>kind(X)))))&
((?[X]:((~brave(X)&~funny(X))))<=>((~brave(susan)|strong(susan))))&
(![X]:((happy(X)<~>~brave(X))<=>(humble(X)|~happy(X))))&
(((~rich(john)&~happy(john)))<=>(?[X]:(~wise(X))))&
(((~happy(lucy)&old(lucy)))=>(?[X]:((happy(X)|~creative(X)))))&
(![X]:(~patient(X)=>(happy(X)&creative(X))))&
(![X]:((creative(X)|old(X))=>~humble(X)))&
(((~strong(fred)&~brave(fred)))<=>((~rich(lucy)&humble(lucy))))&
(brave(paul))&
(?[X]:((brave(X)|humble(X))))&
(?[X]:((quiet(X)|~brave(X))))&
(?[X]:((quiet(X)<~>~quiet(X))))&
((patient(lucy)&brave(lucy)))&
(?[X]:(brave(X)))&
(~quiet(fred))&
(?[X]:((curious(X)<~>generous(X)))) | ~tall(paul) | [
"p1",
"p8",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8838551667776728149608073
% SZS output start Proof for 8838551667776728149608073
2. ! [X0] : ((kind(X0) <~> happy(X0)) => (~tall(X0) <~> ~humble(X0))) [input p1]
9. ? [X0] : (~old(X0) & old(X0)) <=> ? [X0] : (~humble(X0) <~> kind(X0)) [input p8]
11. ! [X0] : ((happy(X0) <~> ~brave(X0)) <=> (~happy(X0) | humble(X0))) [input p10]
17. brave(paul) [input p16]
25. tall(paul) [input hypothesis]
26. ? [X0] : (~old(X0) & old(X0)) <=> ? [X1] : (~humble(X1) <~> kind(X1)) [rectify 9]
27. ! [X0] : ((~tall(X0) <~> ~humble(X0)) | (kind(X0) <=> happy(X0))) [ennf transformation 2]
37. ! [X0] : (((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) [nnf transformation 27]
52. (? [X0] : (~old(X0) & old(X0)) | ! [X1] : ((~humble(X1) | ~kind(X1)) & (kind(X1) | humble(X1)))) & (? [X1] : ((~kind(X1) | humble(X1)) & (kind(X1) | ~humble(X1))) | ! [X0] : (old(X0) | ~old(X0))) [nnf transformation 26]
53. (? [X0] : (~old(X0) & old(X0)) | ! [X1] : ((~humble(X1) | ~kind(X1)) & (kind(X1) | humble(X1)))) & (? [X2] : ((~kind(X2) | humble(X2)) & (kind(X2) | ~humble(X2))) | ! [X3] : (old(X3) | ~old(X3))) [rectify 52]
54. ? [X0] : (~old(X0) & old(X0)) => (~old(sK2) & old(sK2)) [choice axiom]
55. ? [X2] : ((~kind(X2) | humble(X2)) & (kind(X2) | ~humble(X2))) => ((~kind(sK3) | humble(sK3)) & (kind(sK3) | ~humble(sK3))) [choice axiom]
56. ((~old(sK2) & old(sK2)) | ! [X1] : ((~humble(X1) | ~kind(X1)) & (kind(X1) | humble(X1)))) & (((~kind(sK3) | humble(sK3)) & (kind(sK3) | ~humble(sK3))) | ! [X3] : (old(X3) | ~old(X3))) [skolemisation 53,55,54]
62. ! [X0] : ((((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | (happy(X0) & ~humble(X0))) & ((~happy(X0) | humble(X0)) | ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0))))) [nnf transformation 11]
63. ! [X0] : ((((brave(X0) | ~happy(X0)) & (~brave(X0) | happy(X0))) | (happy(X0) & ~humble(X0))) & (~happy(X0) | humble(X0) | ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0))))) [flattening 62]
92. ~humble(X0) | ~tall(X0) | kind(X0) | ~happy(X0) [cnf transformation 37]
118. old(sK2) | kind(X1) | humble(X1) [cnf transformation 56]
119. old(sK2) | ~humble(X1) | ~kind(X1) [cnf transformation 56]
120. ~old(sK2) | kind(X1) | humble(X1) [cnf transformation 56]
121. ~old(sK2) | ~humble(X1) | ~kind(X1) [cnf transformation 56]
127. ~happy(X0) | humble(X0) | ~brave(X0) | ~happy(X0) [cnf transformation 63]
130. ~brave(X0) | happy(X0) | happy(X0) [cnf transformation 63]
145. brave(paul) [cnf transformation 17]
156. tall(paul) [cnf transformation 25]
157. ~happy(X0) | humble(X0) | ~brave(X0) [duplicate literal removal 127]
158. ~brave(X0) | happy(X0) [duplicate literal removal 130]
203. 10 <=> ! [X1] : (~humble(X1) | ~kind(X1)) [avatar definition]
204. ~humble(X1) | ~kind(X1) <- (10) [avatar component clause 203]
206. 11 <=> old(sK2) [avatar definition]
209. 10 | ~11 [avatar split clause 121,206,203]
211. 12 <=> ! [X1] : (kind(X1) | humble(X1)) [avatar definition]
212. humble(X1) | kind(X1) <- (12) [avatar component clause 211]
213. 12 | ~11 [avatar split clause 120,206,211]
214. 10 | 11 [avatar split clause 119,206,203]
215. 12 | 11 [avatar split clause 118,206,211]
240. ~brave(X0) | humble(X0) [subsumption resolution 157,158]
327. happy(paul) [resolution 158,145]
342. humble(paul) [resolution 240,145]
351. ~kind(paul) <- (10) [resolution 342,204]
472. ~tall(X0) | kind(X0) | ~happy(X0) | kind(X0) <- (12) [resolution 92,212]
478. ~tall(X0) | kind(X0) | ~happy(X0) <- (12) [duplicate literal removal 472]
577. kind(paul) | ~happy(paul) <- (12) [resolution 478,156]
578. ~happy(paul) <- (10, 12) [subsumption resolution 577,351]
579. $false <- (10, 12) [subsumption resolution 578,327]
580. ~10 | ~12 [avatar contradiction clause 579]
581. $false [avatar sat refutation 209,213,214,215,580]
% SZS output end Proof for 8838551667776728149608073
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not happy and not generous then someone is humble. Everyone who is not tall or old is not kind. Everyone who is both patient and not humble is both not generous and generous. If someone is either calm or quiet then mary is both kind and wise. Everyone who is either not generous or curious is both generous and rich. Everyone who is both tall and not wise is both happy and not curious and vice versa. If someone is not calm then susan is not humble. Everyone who is both not kind and not wise is patient or kind and vice versa. Everyone who is either quiet or not creative is tall or funny. If fred is not rich then alice is not kind or not tall and vice versa. Everyone who is tall is strong. If someone is tall or kind then mary is old or funny. Everyone who is either humble or quiet is both not strong and rich. Everyone who is both creative and rich is not strong or not quiet and vice versa. If mary is either brave or not creative then someone is both not kind and humble and vice versa. Everyone who is both generous and not funny is both rich and not funny. John is wise. Someone is both tall and not kind. Mary is not patient or not kind. Someone is either not humble or not kind. Someone is both not creative and brave. Someone is both not tall and not calm. Someone is both creative and not happy. | Fred is quiet. | entailment | ((?[X]:((~happy(X)&~generous(X))))=>(?[X]:(humble(X))))&
(![X]:((~tall(X)|old(X))=>~kind(X)))&
(![X]:((patient(X)&~humble(X))=>(~generous(X)&generous(X))))&
((?[X]:((calm(X)<~>quiet(X))))=>((kind(mary)&wise(mary))))&
(![X]:((~generous(X)<~>curious(X))=>(generous(X)&rich(X))))&
(![X]:((tall(X)&~wise(X))<=>(happy(X)&~curious(X))))&
((?[X]:(~calm(X)))=>(~humble(susan)))&
(![X]:((~kind(X)&~wise(X))<=>(patient(X)|kind(X))))&
(![X]:((quiet(X)<~>~creative(X))=>(tall(X)|funny(X))))&
((~rich(fred))<=>((~kind(alice)|~tall(alice))))&
(![X]:(tall(X)=>strong(X)))&
((?[X]:((tall(X)|kind(X))))=>((old(mary)|funny(mary))))&
(![X]:((humble(X)<~>quiet(X))=>(~strong(X)&rich(X))))&
(![X]:((creative(X)&rich(X))<=>(~strong(X)|~quiet(X))))&
(((brave(mary)<~>~creative(mary)))<=>(?[X]:((~kind(X)&humble(X)))))&
(![X]:((generous(X)&~funny(X))=>(rich(X)&~funny(X))))&
(wise(john))&
(?[X]:((tall(X)&~kind(X))))&
((~patient(mary)|~kind(mary)))&
(?[X]:((~humble(X)<~>~kind(X))))&
(?[X]:((~creative(X)&brave(X))))&
(?[X]:((~tall(X)&~calm(X))))&
(?[X]:((creative(X)&~happy(X)))) | quiet(fred) | [
"p7",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7569069965088979917523040
% SZS output start Proof for 7569069965088979917523040
8. ! [X0] : ((~wise(X0) & ~kind(X0)) <=> (kind(X0) | patient(X0))) [input p7]
10. ~rich(fred) <=> (~tall(alice) | ~kind(alice)) [input p9]
14. ! [X0] : ((rich(X0) & creative(X0)) <=> (~quiet(X0) | ~strong(X0))) [input p13]
24. ~quiet(fred) [input hypothesis]
48. ! [X0] : (((~wise(X0) & ~kind(X0)) | (~kind(X0) & ~patient(X0))) & ((kind(X0) | patient(X0)) | (wise(X0) | kind(X0)))) [nnf transformation 8]
49. ! [X0] : (((~wise(X0) & ~kind(X0)) | (~kind(X0) & ~patient(X0))) & (kind(X0) | patient(X0) | wise(X0) | kind(X0))) [flattening 48]
51. (~rich(fred) | (tall(alice) & kind(alice))) & ((~tall(alice) | ~kind(alice)) | rich(fred)) [nnf transformation 10]
52. (~rich(fred) | (tall(alice) & kind(alice))) & (~tall(alice) | ~kind(alice) | rich(fred)) [flattening 51]
54. ! [X0] : (((rich(X0) & creative(X0)) | (quiet(X0) & strong(X0))) & ((~quiet(X0) | ~strong(X0)) | (~rich(X0) | ~creative(X0)))) [nnf transformation 14]
55. ! [X0] : (((rich(X0) & creative(X0)) | (quiet(X0) & strong(X0))) & (~quiet(X0) | ~strong(X0) | ~rich(X0) | ~creative(X0))) [flattening 54]
91. ~kind(X0) | ~kind(X0) [cnf transformation 49]
97. ~rich(fred) | kind(alice) [cnf transformation 52]
110. rich(X0) | quiet(X0) [cnf transformation 55]
131. ~quiet(fred) [cnf transformation 24]
133. ~kind(X0) [duplicate literal removal 91]
176. 10 <=> rich(fred) [avatar definition]
178. ~rich(fred) <- (~10) [avatar component clause 176]
180. ~rich(fred) [subsumption resolution 97,133]
181. ~10 [avatar split clause 180,176]
225. quiet(fred) <- (~10) [resolution 110,178]
226. $false <- (~10) [subsumption resolution 225,131]
227. 10 [avatar contradiction clause 226]
228. $false [avatar sat refutation 181,227]
% SZS output end Proof for 7569069965088979917523040
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is both happy and not old. Everyone who is brave or not old is not strong. If paul is either not creative or old then susan is both not curious and not strong. If paul is either strong or generous then paul is both not creative and patient. If someone is funny then mary is not calm or creative. Everyone who is funny is either rich or not strong and vice versa. Everyone who is not tall is both not humble and old. If someone is not quiet or not rich then someone is patient or tall and vice versa. Everyone who is both quiet and funny is quiet and vice versa. Everyone who is either patient or not happy is wise or not brave. If someone is both strong and curious then susan is not funny. If fred is not rich or happy then fred is both humble and not kind. Everyone who is patient or not kind is either not wise or not strong and vice versa. Everyone who is both not generous and strong is not rich and vice versa. Everyone who is not tall is funny. If someone is either not creative or not wise then fred is strong or not quiet and vice versa. Someone is kind. Alice is either not creative or old. Alice is brave. Susan is both strong and calm. Someone is tall. Fred is either not curious or patient. Someone is not generous. Mary is either not brave or brave. | Alice is not happy. | contradiction | (![X]:(~funny(X)=>(happy(X)&~old(X))))&
(![X]:((brave(X)|~old(X))=>~strong(X)))&
(((~creative(paul)<~>old(paul)))=>((~curious(susan)&~strong(susan))))&
(((strong(paul)<~>generous(paul)))=>((~creative(paul)&patient(paul))))&
((?[X]:(funny(X)))=>((~calm(mary)|creative(mary))))&
(![X]:(funny(X)<=>(rich(X)<~>~strong(X))))&
(![X]:(~tall(X)=>(~humble(X)&old(X))))&
((?[X]:((~quiet(X)|~rich(X))))<=>(?[X]:((patient(X)|tall(X)))))&
(![X]:((quiet(X)&funny(X))<=>quiet(X)))&
(![X]:((patient(X)<~>~happy(X))=>(wise(X)|~brave(X))))&
((?[X]:((strong(X)&curious(X))))=>(~funny(susan)))&
(((~rich(fred)|happy(fred)))=>((humble(fred)&~kind(fred))))&
(![X]:((patient(X)|~kind(X))<=>(~wise(X)<~>~strong(X))))&
(![X]:((~generous(X)&strong(X))<=>~rich(X)))&
(![X]:(~tall(X)=>funny(X)))&
((?[X]:((~creative(X)<~>~wise(X))))<=>((strong(fred)|~quiet(fred))))&
(?[X]:(kind(X)))&
((~creative(alice)<~>old(alice)))&
(brave(alice))&
((strong(susan)&calm(susan)))&
(?[X]:(tall(X)))&
((~curious(fred)<~>patient(fred)))&
(?[X]:(~generous(X)))&
((~brave(mary)<~>brave(mary))) | ~happy(alice) | [
"p0",
"p1",
"p5",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3234006531232429672687699
% SZS output start Proof for 3234006531232429672687699
1. ! [X0] : (~funny(X0) => (~old(X0) & happy(X0))) [input p0]
2. ! [X0] : ((~old(X0) | brave(X0)) => ~strong(X0)) [input p1]
6. ! [X0] : (funny(X0) <=> (rich(X0) <~> ~strong(X0))) [input p5]
14. ! [X0] : ((strong(X0) & ~generous(X0)) <=> ~rich(X0)) [input p13]
19. brave(alice) [input p18]
25. ~happy(alice) [input hypothesis]
27. ! [X0] : ((~old(X0) & happy(X0)) | funny(X0)) [ennf transformation 1]
28. ! [X0] : (~strong(X0) | (old(X0) & ~brave(X0))) [ennf transformation 2]
41. ! [X0] : ((funny(X0) | ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0)))) & (((strong(X0) | ~rich(X0)) & (~strong(X0) | rich(X0))) | ~funny(X0))) [nnf transformation 6]
52. ! [X0] : (((strong(X0) & ~generous(X0)) | rich(X0)) & (~rich(X0) | (~strong(X0) | generous(X0)))) [nnf transformation 14]
53. ! [X0] : (((strong(X0) & ~generous(X0)) | rich(X0)) & (~rich(X0) | ~strong(X0) | generous(X0))) [flattening 52]
68. happy(X0) | funny(X0) [cnf transformation 27]
70. ~strong(X0) | ~brave(X0) [cnf transformation 28]
82. ~rich(X0) | strong(X0) | ~funny(X0) [cnf transformation 41]
109. rich(X0) | strong(X0) [cnf transformation 53]
120. brave(alice) [cnf transformation 19]
129. ~happy(alice) [cnf transformation 25]
287. funny(alice) [resolution 68,129]
305. strong(X0) | ~funny(X0) | strong(X0) [resolution 82,109]
309. ~funny(X0) | strong(X0) [duplicate literal removal 305]
310. strong(alice) [resolution 309,287]
339. ~brave(alice) [resolution 310,70]
343. $false [subsumption resolution 339,120]
% SZS output end Proof for 3234006531232429672687699
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or humble is either not humble or not calm and vice versa.
Everyone who is either calm or happy is both not curious and not tall.
Everyone who is funny or not calm is not wise.
Everyone who is either wise or brave is either not generous or brave and vice versa.
If susan is kind or not kind then someone is either brave or not brave and vice versa.
If someone is calm then someone is strong or brave and vice versa.
If someone is both brave and not generous then mary is either not creative or not patient and vice versa.
Everyone who is either rich or wise is either not strong or old and vice versa.
If someone is either not brave or not patient then lucy is not happy or kind and vice versa.
If someone is calm then someone is either not kind or not old and vice versa.
If lucy is not quiet or not kind then someone is both quiet and not patient.
Everyone who is either happy or not happy is either not old or funny and vice versa.
Everyone who is not generous is both not curious and not old.
If susan is not humble then john is both creative and quiet.
If someone is generous or rich then someone is both funny and not wise and vice versa.
Lucy is either calm or not tall.
Someone is not old.
John is funny.
Paul is either not tall or happy.
Lucy is either not rich or wise. | Mary is not generous. | contradiction | (![X]:((~calm(X)|humble(X))<=>(~humble(X)<~>~calm(X))))&
(![X]:((calm(X)<~>happy(X))=>(~curious(X)&~tall(X))))&
(![X]:((funny(X)|~calm(X))=>~wise(X)))&
(![X]:((wise(X)<~>brave(X))<=>(~generous(X)<~>brave(X))))&
(((kind(susan)|~kind(susan)))<=>(?[X]:((brave(X)<~>~brave(X)))))&
((?[X]:(calm(X)))<=>(?[X]:((strong(X)|brave(X)))))&
((?[X]:((brave(X)&~generous(X))))<=>((~creative(mary)<~>~patient(mary))))&
(![X]:((rich(X)<~>wise(X))<=>(~strong(X)<~>old(X))))&
((?[X]:((~brave(X)<~>~patient(X))))<=>((~happy(lucy)|kind(lucy))))&
((?[X]:(calm(X)))<=>(?[X]:((~kind(X)<~>~old(X)))))&
(((~quiet(lucy)|~kind(lucy)))=>(?[X]:((quiet(X)&~patient(X)))))&
(![X]:((happy(X)<~>~happy(X))<=>(~old(X)<~>funny(X))))&
(![X]:(~generous(X)=>(~curious(X)&~old(X))))&
((~humble(susan))=>((creative(john)&quiet(john))))&
((?[X]:((generous(X)|rich(X))))<=>(?[X]:((funny(X)&~wise(X)))))&
((calm(lucy)<~>~tall(lucy)))&
(?[X]:(~old(X)))&
(funny(john))&
((~tall(paul)<~>happy(paul)))&
((~rich(lucy)<~>wise(lucy))) | ~generous(mary) | [
"p0",
"p2",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 7913754215296232973770279
% SZS output start Proof for 7913754215296232973770279
1. ! [X0] : ((humble(X0) | ~calm(X0)) <=> (~humble(X0) <~> ~calm(X0))) [input p0]
3. ! [X0] : ((~calm(X0) | funny(X0)) => ~wise(X0)) [input p2]
4. ! [X0] : ((wise(X0) <~> brave(X0)) <=> (~generous(X0) <~> brave(X0))) [input p3]
21. ~generous(mary) [input hypothesis]
30. ! [X0] : (~wise(X0) | (calm(X0) & ~funny(X0))) [ennf transformation 3]
34. ! [X0] : (((humble(X0) | ~calm(X0)) | ((~humble(X0) | calm(X0)) & (~calm(X0) | humble(X0)))) & (((calm(X0) | humble(X0)) & (~calm(X0) | ~humble(X0))) | (~humble(X0) & calm(X0)))) [nnf transformation 1]
35. ! [X0] : ((humble(X0) | ~calm(X0) | ((~humble(X0) | calm(X0)) & (~calm(X0) | humble(X0)))) & (((calm(X0) | humble(X0)) & (~calm(X0) | ~humble(X0))) | (~humble(X0) & calm(X0)))) [flattening 34]
37. ! [X0] : ((((~brave(X0) | ~wise(X0)) & (brave(X0) | wise(X0))) | ((~generous(X0) | ~brave(X0)) & (brave(X0) | generous(X0)))) & (((~brave(X0) | generous(X0)) & (brave(X0) | ~generous(X0))) | ((wise(X0) | ~brave(X0)) & (brave(X0) | ~wise(X0))))) [nnf transformation 4]
77. ~calm(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 35]
78. calm(X0) | humble(X0) | calm(X0) [cnf transformation 35]
80. humble(X0) | ~calm(X0) | ~calm(X0) | humble(X0) [cnf transformation 35]
85. ~wise(X0) | calm(X0) [cnf transformation 30]
89. ~brave(X0) | generous(X0) | wise(X0) | ~brave(X0) [cnf transformation 37]
90. brave(X0) | wise(X0) | brave(X0) | generous(X0) [cnf transformation 37]
151. ~generous(mary) [cnf transformation 21]
159. ~brave(X0) | generous(X0) | wise(X0) [duplicate literal removal 89]
160. brave(X0) | wise(X0) | generous(X0) [duplicate literal removal 90]
162. ~calm(X0) | ~humble(X0) [duplicate literal removal 77]
163. calm(X0) | humble(X0) [duplicate literal removal 78]
164. humble(X0) | ~calm(X0) [duplicate literal removal 80]
165. humble(X0) [subsumption resolution 163,164]
166. ~calm(X0) [subsumption resolution 162,165]
168. ~wise(X0) [subsumption resolution 85,166]
169. brave(X0) | generous(X0) [subsumption resolution 160,168]
170. ~brave(X0) | generous(X0) [subsumption resolution 159,168]
171. generous(X0) [subsumption resolution 170,169]
238. $false [subsumption resolution 151,171]
% SZS output end Proof for 7913754215296232973770279
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or old is not strong.
Everyone who is patient is not funny or not old.
Everyone who is not happy or not curious is both curious and not quiet.
Everyone who is not happy is both not strong and happy and vice versa.
If mary is either not generous or curious then susan is both wise and not brave and vice versa.
If someone is either quiet or not wise then paul is not tall and vice versa.
Everyone who is either not creative or not rich is either not strong or not humble.
Everyone who is not curious or not rich is either happy or generous and vice versa.
If someone is both not humble and not quiet then paul is not calm or not funny and vice versa.
Everyone who is not rich is either strong or brave and vice versa.
Everyone who is either brave or not old is either tall or not humble and vice versa.
Everyone who is old is curious.
Everyone who is either kind or not generous is not rich and vice versa.
If fred is either funny or not funny then alice is brave and vice versa.
If someone is either calm or creative then someone is not calm or not kind and vice versa.
Someone is not humble or strong.
Susan is not kind.
Someone is not calm.
Lucy is not wise.
Someone is both not quiet and curious.
Fred is not calm or not creative. | Lucy is not kind. | entailment | (![X]:((funny(X)<~>old(X))=>~strong(X)))&
(![X]:(patient(X)=>(~funny(X)|~old(X))))&
(![X]:((~happy(X)|~curious(X))=>(curious(X)&~quiet(X))))&
(![X]:(~happy(X)<=>(~strong(X)&happy(X))))&
(((~generous(mary)<~>curious(mary)))<=>((wise(susan)&~brave(susan))))&
((?[X]:((quiet(X)<~>~wise(X))))<=>(~tall(paul)))&
(![X]:((~creative(X)<~>~rich(X))=>(~strong(X)<~>~humble(X))))&
(![X]:((~curious(X)|~rich(X))<=>(happy(X)<~>generous(X))))&
((?[X]:((~humble(X)&~quiet(X))))<=>((~calm(paul)|~funny(paul))))&
(![X]:(~rich(X)<=>(strong(X)<~>brave(X))))&
(![X]:((brave(X)<~>~old(X))<=>(tall(X)<~>~humble(X))))&
(![X]:(old(X)=>curious(X)))&
(![X]:((kind(X)<~>~generous(X))<=>~rich(X)))&
(((funny(fred)<~>~funny(fred)))<=>(brave(alice)))&
((?[X]:((calm(X)<~>creative(X))))<=>(?[X]:((~calm(X)|~kind(X)))))&
(?[X]:((~humble(X)|strong(X))))&
(~kind(susan))&
(?[X]:(~calm(X)))&
(~wise(lucy))&
(?[X]:((~quiet(X)&curious(X))))&
((~calm(fred)|~creative(fred))) | ~kind(lucy) | [
"p2",
"p3",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2586918666334973471907271
% SZS output start Proof for 2586918666334973471907271
3. ! [X0] : ((~curious(X0) | ~happy(X0)) => (~quiet(X0) & curious(X0))) [input p2]
4. ! [X0] : (~happy(X0) <=> (happy(X0) & ~strong(X0))) [input p3]
8. ! [X0] : ((~rich(X0) | ~curious(X0)) <=> (happy(X0) <~> generous(X0))) [input p7]
13. ! [X0] : ((kind(X0) <~> ~generous(X0)) <=> ~rich(X0)) [input p12]
22. kind(lucy) [input hypothesis]
26. ! [X0] : ((~quiet(X0) & curious(X0)) | (curious(X0) & happy(X0))) [ennf transformation 3]
30. ! [X0] : ((~happy(X0) | (~happy(X0) | strong(X0))) & ((happy(X0) & ~strong(X0)) | happy(X0))) [nnf transformation 4]
31. ! [X0] : ((~happy(X0) | ~happy(X0) | strong(X0)) & ((happy(X0) & ~strong(X0)) | happy(X0))) [flattening 30]
39. ! [X0] : (((~rich(X0) | ~curious(X0)) | ((happy(X0) | ~generous(X0)) & (generous(X0) | ~happy(X0)))) & (((~generous(X0) | ~happy(X0)) & (generous(X0) | happy(X0))) | (rich(X0) & curious(X0)))) [nnf transformation 8]
40. ! [X0] : ((~rich(X0) | ~curious(X0) | ((happy(X0) | ~generous(X0)) & (generous(X0) | ~happy(X0)))) & (((~generous(X0) | ~happy(X0)) & (generous(X0) | happy(X0))) | (rich(X0) & curious(X0)))) [flattening 39]
48. ! [X0] : ((((generous(X0) | ~kind(X0)) & (~generous(X0) | kind(X0))) | rich(X0)) & (~rich(X0) | ((kind(X0) | generous(X0)) & (~generous(X0) | ~kind(X0))))) [nnf transformation 13]
64. curious(X0) | curious(X0) [cnf transformation 26]
68. happy(X0) | happy(X0) [cnf transformation 31]
87. ~generous(X0) | ~happy(X0) | rich(X0) [cnf transformation 40]
88. ~rich(X0) | ~curious(X0) | generous(X0) | ~happy(X0) [cnf transformation 40]
108. ~rich(X0) | ~generous(X0) | ~kind(X0) [cnf transformation 48]
111. generous(X0) | ~kind(X0) | rich(X0) [cnf transformation 48]
129. kind(lucy) [cnf transformation 22]
132. happy(X0) [duplicate literal removal 68]
134. curious(X0) [duplicate literal removal 64]
175. ~rich(X0) | generous(X0) | ~happy(X0) [subsumption resolution 88,134]
176. ~rich(X0) | generous(X0) [subsumption resolution 175,132]
177. ~generous(X0) | rich(X0) [subsumption resolution 87,132]
202. ~kind(X0) | generous(X0) [subsumption resolution 111,176]
203. ~kind(X0) | ~rich(X0) [subsumption resolution 108,202]
267. generous(lucy) [resolution 202,129]
268. rich(lucy) [resolution 267,177]
269. ~rich(lucy) [resolution 203,129]
270. $false [subsumption resolution 269,268]
% SZS output end Proof for 2586918666334973471907271
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is rich or not calm is either not rich or funny.
Everyone who is creative or not happy is both quiet and not old.
If paul is patient then someone is both not patient and patient and vice versa.
Everyone who is both not rich and not humble is not patient and vice versa.
If someone is not calm then paul is both rich and calm and vice versa.
If someone is humble then someone is not happy.
If someone is not quiet then someone is rich and vice versa.
Everyone who is either not funny or strong is not generous.
Everyone who is curious is rich and vice versa.
Everyone who is creative or not brave is either not humble or rich.
Everyone who is either generous or not humble is either not creative or quiet and vice versa.
Everyone who is not calm or quiet is not strong and vice versa.
If alice is either brave or strong then someone is brave.
Everyone who is either not curious or tall is not funny and vice versa.
Everyone who is either calm or creative is strong.
Everyone who is either not rich or not strong is happy.
Someone is both tall and not creative.
Someone is kind.
Someone is not quiet.
Mary is either patient or not strong.
Someone is either strong or not humble.
Susan is not tall. | Mary is happy. | neutral | (![X]:((rich(X)|~calm(X))=>(~rich(X)<~>funny(X))))&
(![X]:((creative(X)|~happy(X))=>(quiet(X)&~old(X))))&
((patient(paul))<=>(?[X]:((~patient(X)&patient(X)))))&
(![X]:((~rich(X)&~humble(X))<=>~patient(X)))&
((?[X]:(~calm(X)))<=>((rich(paul)&calm(paul))))&
((?[X]:(humble(X)))=>(?[X]:(~happy(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:(rich(X))))&
(![X]:((~funny(X)<~>strong(X))=>~generous(X)))&
(![X]:(curious(X)<=>rich(X)))&
(![X]:((creative(X)|~brave(X))=>(~humble(X)<~>rich(X))))&
(![X]:((generous(X)<~>~humble(X))<=>(~creative(X)<~>quiet(X))))&
(![X]:((~calm(X)|quiet(X))<=>~strong(X)))&
(((brave(alice)<~>strong(alice)))=>(?[X]:(brave(X))))&
(![X]:((~curious(X)<~>tall(X))<=>~funny(X)))&
(![X]:((calm(X)<~>creative(X))=>strong(X)))&
(![X]:((~rich(X)<~>~strong(X))=>happy(X)))&
(?[X]:((tall(X)&~creative(X))))&
(?[X]:(kind(X)))&
(?[X]:(~quiet(X)))&
((patient(mary)<~>~strong(mary)))&
(?[X]:((strong(X)<~>~humble(X))))&
(~tall(susan)) | happy(mary) | [] | null | 0 |
Everyone who is both curious and wise is happy.
If john is either quiet or not rich then mary is old or happy and vice versa.
If susan is both not generous and not kind then paul is not wise and vice versa.
Everyone who is either not old or wise is both old and not funny and vice versa.
Everyone who is both not old and not wise is both generous and brave.
If alice is either not patient or kind then someone is either not brave or not happy and vice versa.
If someone is either not quiet or quiet then fred is both not patient and not funny.
Everyone who is kind or rich is quiet.
If lucy is quiet or not creative then john is wise or happy and vice versa.
If john is both not generous and not rich then someone is both not old and patient.
Everyone who is either rich or not strong is not generous.
Everyone who is not calm or rich is not brave.
If alice is both funny and happy then mary is not tall or not strong and vice versa.
If mary is creative then someone is either not funny or patient.
Everyone who is kind is either not creative or funny and vice versa.
Everyone who is generous or not humble is not generous or generous and vice versa.
Lucy is both not funny and rich.
Someone is not patient or happy.
Mary is not strong or brave.
Someone is not tall or not generous.
Susan is not wise or humble.
Susan is both rich and strong. | Paul is not humble. | neutral | (![X]:((curious(X)&wise(X))=>happy(X)))&
(((quiet(john)<~>~rich(john)))<=>((old(mary)|happy(mary))))&
(((~generous(susan)&~kind(susan)))<=>(~wise(paul)))&
(![X]:((~old(X)<~>wise(X))<=>(old(X)&~funny(X))))&
(![X]:((~old(X)&~wise(X))=>(generous(X)&brave(X))))&
(((~patient(alice)<~>kind(alice)))<=>(?[X]:((~brave(X)<~>~happy(X)))))&
((?[X]:((~quiet(X)<~>quiet(X))))=>((~patient(fred)&~funny(fred))))&
(![X]:((kind(X)|rich(X))=>quiet(X)))&
(((quiet(lucy)|~creative(lucy)))<=>((wise(john)|happy(john))))&
(((~generous(john)&~rich(john)))=>(?[X]:((~old(X)&patient(X)))))&
(![X]:((rich(X)<~>~strong(X))=>~generous(X)))&
(![X]:((~calm(X)|rich(X))=>~brave(X)))&
(((funny(alice)&happy(alice)))<=>((~tall(mary)|~strong(mary))))&
((creative(mary))=>(?[X]:((~funny(X)<~>patient(X)))))&
(![X]:(kind(X)<=>(~creative(X)<~>funny(X))))&
(![X]:((generous(X)|~humble(X))<=>(~generous(X)|generous(X))))&
((~funny(lucy)&rich(lucy)))&
(?[X]:((~patient(X)|happy(X))))&
((~strong(mary)|brave(mary)))&
(?[X]:((~tall(X)|~generous(X))))&
((~wise(susan)|humble(susan)))&
((rich(susan)&strong(susan))) | ~humble(paul) | [] | null | 0 |
If someone is rich then mary is not patient and vice versa.
If someone is calm then someone is both not tall and not humble and vice versa.
If paul is both quiet and not rich then mary is kind or generous and vice versa.
Everyone who is calm or happy is not funny.
Everyone who is old is both wise and generous.
Everyone who is both creative and not creative is happy or not happy.
If someone is either not old or not quiet then someone is quiet or rich and vice versa.
Everyone who is happy or not kind is not wise and vice versa.
Everyone who is either curious or tall is not kind and vice versa.
If mary is not patient then someone is not rich or not creative.
Everyone who is not wise is both not strong and wise and vice versa.
Everyone who is either not generous or not calm is both not kind and not tall.
Everyone who is both kind and quiet is not humble or not curious.
Everyone who is happy or not wise is not calm or patient and vice versa.
Everyone who is not quiet is either not old or rich.
If john is either not wise or generous then fred is rich.
Paul is either not curious or happy.
Someone is curious or strong.
Mary is calm.
Someone is wise or not brave.
Mary is either not humble or creative.
Someone is not calm or wise.
Mary is not old.
John is not quiet. | Paul is kind. | entailment | ((?[X]:(rich(X)))<=>(~patient(mary)))&
((?[X]:(calm(X)))<=>(?[X]:((~tall(X)&~humble(X)))))&
(((quiet(paul)&~rich(paul)))<=>((kind(mary)|generous(mary))))&
(![X]:((calm(X)|happy(X))=>~funny(X)))&
(![X]:(old(X)=>(wise(X)&generous(X))))&
(![X]:((creative(X)&~creative(X))=>(happy(X)|~happy(X))))&
((?[X]:((~old(X)<~>~quiet(X))))<=>(?[X]:((quiet(X)|rich(X)))))&
(![X]:((happy(X)|~kind(X))<=>~wise(X)))&
(![X]:((curious(X)<~>tall(X))<=>~kind(X)))&
((~patient(mary))=>(?[X]:((~rich(X)|~creative(X)))))&
(![X]:(~wise(X)<=>(~strong(X)&wise(X))))&
(![X]:((~generous(X)<~>~calm(X))=>(~kind(X)&~tall(X))))&
(![X]:((kind(X)&quiet(X))=>(~humble(X)|~curious(X))))&
(![X]:((happy(X)|~wise(X))<=>(~calm(X)|patient(X))))&
(![X]:(~quiet(X)=>(~old(X)<~>rich(X))))&
(((~wise(john)<~>generous(john)))=>(rich(fred)))&
((~curious(paul)<~>happy(paul)))&
(?[X]:((curious(X)|strong(X))))&
(calm(mary))&
(?[X]:((wise(X)|~brave(X))))&
((~humble(mary)<~>creative(mary)))&
(?[X]:((~calm(X)|wise(X))))&
(~old(mary))&
(~quiet(john)) | kind(paul) | [
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4395981593962081638339725
% SZS output start Proof for 4395981593962081638339725
8. ! [X0] : ((~kind(X0) | happy(X0)) <=> ~wise(X0)) [input p7]
11. ! [X0] : (~wise(X0) <=> (wise(X0) & ~strong(X0))) [input p10]
25. ~kind(paul) [input hypothesis]
55. ! [X0] : (((~kind(X0) | happy(X0)) | wise(X0)) & (~wise(X0) | (kind(X0) & ~happy(X0)))) [nnf transformation 8]
56. ! [X0] : ((~kind(X0) | happy(X0) | wise(X0)) & (~wise(X0) | (kind(X0) & ~happy(X0)))) [flattening 55]
60. ! [X0] : ((~wise(X0) | (~wise(X0) | strong(X0))) & ((wise(X0) & ~strong(X0)) | wise(X0))) [nnf transformation 11]
61. ! [X0] : ((~wise(X0) | ~wise(X0) | strong(X0)) & ((wise(X0) & ~strong(X0)) | wise(X0))) [flattening 60]
93. ~wise(X0) | kind(X0) [cnf transformation 56]
101. wise(X0) | wise(X0) [cnf transformation 61]
125. ~kind(paul) [cnf transformation 25]
126. wise(X0) [duplicate literal removal 101]
267. kind(X0) [resolution 93,126]
268. $false [resolution 267,125]
% SZS output end Proof for 4395981593962081638339725
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and patient is curious or not patient. Everyone who is tall or brave is brave and vice versa. Everyone who is both not quiet and calm is either patient or happy. Everyone who is not generous or not quiet is not kind. Everyone who is quiet is both not quiet and strong. Everyone who is not wise is both not wise and rich. If someone is tall or not wise then mary is either brave or curious and vice versa. Everyone who is both not wise and curious is both not curious and not rich. If fred is brave or kind then alice is both kind and old and vice versa. If someone is not humble then john is both kind and not patient and vice versa. Everyone who is not wise is strong or humble and vice versa. If someone is either creative or humble then someone is not curious or not happy. If john is not creative or kind then lucy is either humble or not old and vice versa. Everyone who is generous or humble is either not calm or happy and vice versa. Everyone who is either not curious or old is both not old and not humble and vice versa. Everyone who is not funny or creative is patient or kind and vice versa. Someone is not kind. Someone is tall. John is not creative or not wise. Susan is not tall. | Alice is not creative. | entailment | (![X]:((rich(X)&patient(X))=>(curious(X)|~patient(X))))&
(![X]:((tall(X)|brave(X))<=>brave(X)))&
(![X]:((~quiet(X)&calm(X))=>(patient(X)<~>happy(X))))&
(![X]:((~generous(X)|~quiet(X))=>~kind(X)))&
(![X]:(quiet(X)=>(~quiet(X)&strong(X))))&
(![X]:(~wise(X)=>(~wise(X)&rich(X))))&
((?[X]:((tall(X)|~wise(X))))<=>((brave(mary)<~>curious(mary))))&
(![X]:((~wise(X)&curious(X))=>(~curious(X)&~rich(X))))&
(((brave(fred)|kind(fred)))<=>((kind(alice)&old(alice))))&
((?[X]:(~humble(X)))<=>((kind(john)&~patient(john))))&
(![X]:(~wise(X)<=>(strong(X)|humble(X))))&
((?[X]:((creative(X)<~>humble(X))))=>(?[X]:((~curious(X)|~happy(X)))))&
(((~creative(john)|kind(john)))<=>((humble(lucy)<~>~old(lucy))))&
(![X]:((generous(X)|humble(X))<=>(~calm(X)<~>happy(X))))&
(![X]:((~curious(X)<~>old(X))<=>(~old(X)&~humble(X))))&
(![X]:((~funny(X)|creative(X))<=>(patient(X)|kind(X))))&
(?[X]:(~kind(X)))&
(?[X]:(tall(X)))&
((~creative(john)|~wise(john)))&
(~tall(susan)) | ~creative(alice) | [
"p0",
"p3",
"p4",
"p5",
"p7",
"p9",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8125917989797501860218020
% SZS output start Proof for 8125917989797501860218020
1. ! [X0] : ((patient(X0) & rich(X0)) => (~patient(X0) | curious(X0))) [input p0]
4. ! [X0] : ((~quiet(X0) | ~generous(X0)) => ~kind(X0)) [input p3]
5. ! [X0] : (quiet(X0) => (strong(X0) & ~quiet(X0))) [input p4]
6. ! [X0] : (~wise(X0) => (rich(X0) & ~wise(X0))) [input p5]
8. ! [X0] : ((curious(X0) & ~wise(X0)) => (~rich(X0) & ~curious(X0))) [input p7]
10. ? [X0] : ~humble(X0) <=> (~patient(john) & kind(john)) [input p9]
11. ! [X0] : (~wise(X0) <=> (humble(X0) | strong(X0))) [input p10]
16. ! [X0] : ((creative(X0) | ~funny(X0)) <=> (kind(X0) | patient(X0))) [input p15]
21. creative(alice) [input hypothesis]
23. ! [X0] : ((~patient(X0) | curious(X0)) | (~patient(X0) | ~rich(X0))) [ennf transformation 1]
24. ! [X0] : (~patient(X0) | curious(X0) | ~patient(X0) | ~rich(X0)) [flattening 23]
27. ! [X0] : (~kind(X0) | (quiet(X0) & generous(X0))) [ennf transformation 4]
28. ! [X0] : ((strong(X0) & ~quiet(X0)) | ~quiet(X0)) [ennf transformation 5]
29. ! [X0] : ((rich(X0) & ~wise(X0)) | wise(X0)) [ennf transformation 6]
30. ! [X0] : ((~rich(X0) & ~curious(X0)) | (~curious(X0) | wise(X0))) [ennf transformation 8]
31. ! [X0] : ((~rich(X0) & ~curious(X0)) | ~curious(X0) | wise(X0)) [flattening 30]
42. (? [X0] : ~humble(X0) | (patient(john) | ~kind(john))) & ((~patient(john) & kind(john)) | ! [X0] : humble(X0)) [nnf transformation 10]
43. (? [X0] : ~humble(X0) | patient(john) | ~kind(john)) & ((~patient(john) & kind(john)) | ! [X0] : humble(X0)) [flattening 42]
44. (? [X0] : ~humble(X0) | patient(john) | ~kind(john)) & ((~patient(john) & kind(john)) | ! [X1] : humble(X1)) [rectify 43]
45. ? [X0] : ~humble(X0) => ~humble(sK1) [choice axiom]
46. (~humble(sK1) | patient(john) | ~kind(john)) & ((~patient(john) & kind(john)) | ! [X1] : humble(X1)) [skolemisation 44,45]
47. ! [X0] : ((~wise(X0) | (~humble(X0) & ~strong(X0))) & ((humble(X0) | strong(X0)) | wise(X0))) [nnf transformation 11]
48. ! [X0] : ((~wise(X0) | (~humble(X0) & ~strong(X0))) & (humble(X0) | strong(X0) | wise(X0))) [flattening 47]
59. ! [X0] : (((creative(X0) | ~funny(X0)) | (~kind(X0) & ~patient(X0))) & ((kind(X0) | patient(X0)) | (~creative(X0) & funny(X0)))) [nnf transformation 16]
60. ! [X0] : ((creative(X0) | ~funny(X0) | (~kind(X0) & ~patient(X0))) & (kind(X0) | patient(X0) | (~creative(X0) & funny(X0)))) [flattening 59]
65. ~patient(X0) | curious(X0) | ~patient(X0) | ~rich(X0) [cnf transformation 24]
72. ~kind(X0) | quiet(X0) [cnf transformation 27]
73. ~quiet(X0) | ~quiet(X0) [cnf transformation 28]
76. wise(X0) | rich(X0) [cnf transformation 29]
84. ~rich(X0) | ~curious(X0) | wise(X0) [cnf transformation 31]
90. kind(john) | humble(X1) [cnf transformation 46]
95. ~humble(X0) | ~wise(X0) [cnf transformation 48]
117. ~creative(X0) | patient(X0) | kind(X0) [cnf transformation 60]
124. creative(alice) [cnf transformation 21]
128. ~quiet(X0) [duplicate literal removal 73]
129. ~patient(X0) | curious(X0) | ~rich(X0) [duplicate literal removal 65]
158. ~curious(X0) | wise(X0) [subsumption resolution 84,76]
160. 7 <=> kind(alice) [avatar definition]
161. kind(alice) <- (7) [avatar component clause 160]
162. ~kind(alice) <- (~7) [avatar component clause 160]
181. 11 <=> kind(john) [avatar definition]
182. kind(john) <- (11) [avatar component clause 181]
194. 14 <=> ! [X1] : humble(X1) [avatar definition]
195. humble(X1) <- (14) [avatar component clause 194]
197. 14 | 11 [avatar split clause 90,181,194]
239. quiet(john) <- (11) [resolution 72,182]
240. $false <- (11) [subsumption resolution 239,128]
241. ~11 [avatar contradiction clause 240]
249. ~wise(X0) <- (14) [resolution 95,195]
250. rich(X0) <- (14) [resolution 249,76]
265. patient(alice) | kind(alice) [resolution 117,124]
266. patient(alice) <- (~7) [subsumption resolution 265,162]
269. curious(alice) | ~rich(alice) <- (~7) [resolution 129,266]
270. curious(alice) <- (~7, 14) [subsumption resolution 269,250]
272. wise(alice) <- (~7, 14) [resolution 270,158]
273. $false <- (~7, 14) [subsumption resolution 272,249]
274. 7 | ~14 [avatar contradiction clause 273]
280. quiet(alice) <- (7) [resolution 161,72]
282. $false <- (7) [subsumption resolution 280,128]
283. ~7 [avatar contradiction clause 282]
284. $false [avatar sat refutation 197,241,274,283]
% SZS output end Proof for 8125917989797501860218020
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is old then someone is curious.
If someone is not tall then someone is not rich.
Everyone who is either not patient or creative is both not patient and creative.
Everyone who is both kind and not curious is not strong and vice versa.
If john is not quiet then alice is not tall or calm.
Everyone who is patient is both not creative and quiet.
If mary is not funny or not brave then alice is not funny and vice versa.
If someone is either brave or not creative then someone is both not creative and happy.
Everyone who is either not calm or not humble is not strong.
Everyone who is both not quiet and not wise is both happy and quiet and vice versa.
Everyone who is curious or quiet is both humble and rich and vice versa.
Everyone who is not quiet is not calm or not happy.
If fred is both not tall and not old then someone is not rich or brave and vice versa.
Everyone who is both not creative and funny is curious.
If someone is not rich then paul is both not old and not curious.
If alice is quiet then john is either not rich or not kind and vice versa.
Paul is both not rich and not humble.
Alice is strong.
Someone is not kind.
Someone is either not patient or not quiet.
Someone is rich or calm.
Susan is not wise.
Someone is calm.
Alice is either not kind or brave. | Paul is creative. | entailment | ((?[X]:(old(X)))=>(?[X]:(curious(X))))&
((?[X]:(~tall(X)))=>(?[X]:(~rich(X))))&
(![X]:((~patient(X)<~>creative(X))=>(~patient(X)&creative(X))))&
(![X]:((kind(X)&~curious(X))<=>~strong(X)))&
((~quiet(john))=>((~tall(alice)|calm(alice))))&
(![X]:(patient(X)=>(~creative(X)&quiet(X))))&
(((~funny(mary)|~brave(mary)))<=>(~funny(alice)))&
((?[X]:((brave(X)<~>~creative(X))))=>(?[X]:((~creative(X)&happy(X)))))&
(![X]:((~calm(X)<~>~humble(X))=>~strong(X)))&
(![X]:((~quiet(X)&~wise(X))<=>(happy(X)&quiet(X))))&
(![X]:((curious(X)|quiet(X))<=>(humble(X)&rich(X))))&
(![X]:(~quiet(X)=>(~calm(X)|~happy(X))))&
(((~tall(fred)&~old(fred)))<=>(?[X]:((~rich(X)|brave(X)))))&
(![X]:((~creative(X)&funny(X))=>curious(X)))&
((?[X]:(~rich(X)))=>((~old(paul)&~curious(paul))))&
((quiet(alice))<=>((~rich(john)<~>~kind(john))))&
((~rich(paul)&~humble(paul)))&
(strong(alice))&
(?[X]:(~kind(X)))&
(?[X]:((~patient(X)<~>~quiet(X))))&
(?[X]:((rich(X)|calm(X))))&
(~wise(susan))&
(?[X]:(calm(X)))&
((~kind(alice)<~>brave(alice))) | creative(paul) | [
"p2",
"p5",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1431136027394581806226103
% SZS output start Proof for 1431136027394581806226103
3. ! [X0] : ((~patient(X0) <~> creative(X0)) => (creative(X0) & ~patient(X0))) [input p2]
6. ! [X0] : (patient(X0) => (quiet(X0) & ~creative(X0))) [input p5]
11. ! [X0] : ((quiet(X0) | curious(X0)) <=> (rich(X0) & humble(X0))) [input p10]
17. ~humble(paul) & ~rich(paul) [input p16]
25. ~creative(paul) [input hypothesis]
31. ! [X0] : ((creative(X0) & ~patient(X0)) | (~patient(X0) <=> creative(X0))) [ennf transformation 3]
34. ! [X0] : ((quiet(X0) & ~creative(X0)) | ~patient(X0)) [ennf transformation 6]
48. ! [X0] : ((creative(X0) & ~patient(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0)))) [nnf transformation 31]
60. ! [X0] : (((quiet(X0) | curious(X0)) | (~rich(X0) | ~humble(X0))) & ((rich(X0) & humble(X0)) | (~quiet(X0) & ~curious(X0)))) [nnf transformation 11]
61. ! [X0] : ((quiet(X0) | curious(X0) | ~rich(X0) | ~humble(X0)) & ((rich(X0) & humble(X0)) | (~quiet(X0) & ~curious(X0)))) [flattening 60]
82. creative(X0) | creative(X0) | patient(X0) [cnf transformation 48]
89. ~patient(X0) | quiet(X0) [cnf transformation 34]
106. ~quiet(X0) | rich(X0) [cnf transformation 61]
121. ~rich(paul) [cnf transformation 17]
132. ~creative(paul) [cnf transformation 25]
136. creative(X0) | patient(X0) [duplicate literal removal 82]
283. patient(paul) [resolution 136,132]
286. quiet(paul) [resolution 283,89]
294. rich(paul) [resolution 286,106]
296. $false [subsumption resolution 294,121]
% SZS output end Proof for 1431136027394581806226103
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is not creative or not quiet.
Everyone who is either not generous or quiet is both not calm and creative and vice versa.
Everyone who is patient or rich is not old or generous and vice versa.
If someone is creative then someone is brave or not quiet and vice versa.
Everyone who is creative is not strong and vice versa.
If someone is rich then susan is both brave and creative and vice versa.
If someone is both not humble and happy then someone is humble.
If someone is not strong then someone is old or happy.
Everyone who is either not tall or funny is not kind or wise and vice versa.
Everyone who is either brave or not curious is either humble or not creative.
Everyone who is both not patient and strong is either not curious or not quiet.
Everyone who is brave is happy and vice versa.
Everyone who is not brave or not creative is both calm and funny and vice versa.
Everyone who is both creative and not quiet is not happy and vice versa.
If mary is both happy and wise then john is funny or not patient.
If someone is either not calm or tall then fred is creative or rich.
Lucy is strong.
Paul is both calm and not kind.
Someone is not quiet or not patient.
Someone is patient or not creative.
Paul is funny.
Someone is both not patient and tall.
Someone is kind or happy.
Mary is tall. | Lucy is not brave. | contradiction | (![X]:(~patient(X)=>(~creative(X)|~quiet(X))))&
(![X]:((~generous(X)<~>quiet(X))<=>(~calm(X)&creative(X))))&
(![X]:((patient(X)|rich(X))<=>(~old(X)|generous(X))))&
((?[X]:(creative(X)))<=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:(creative(X)<=>~strong(X)))&
((?[X]:(rich(X)))<=>((brave(susan)&creative(susan))))&
((?[X]:((~humble(X)&happy(X))))=>(?[X]:(humble(X))))&
((?[X]:(~strong(X)))=>(?[X]:((old(X)|happy(X)))))&
(![X]:((~tall(X)<~>funny(X))<=>(~kind(X)|wise(X))))&
(![X]:((brave(X)<~>~curious(X))=>(humble(X)<~>~creative(X))))&
(![X]:((~patient(X)&strong(X))=>(~curious(X)<~>~quiet(X))))&
(![X]:(brave(X)<=>happy(X)))&
(![X]:((~brave(X)|~creative(X))<=>(calm(X)&funny(X))))&
(![X]:((creative(X)&~quiet(X))<=>~happy(X)))&
(((happy(mary)&wise(mary)))=>((funny(john)|~patient(john))))&
((?[X]:((~calm(X)<~>tall(X))))=>((creative(fred)|rich(fred))))&
(strong(lucy))&
((calm(paul)&~kind(paul)))&
(?[X]:((~quiet(X)|~patient(X))))&
(?[X]:((patient(X)|~creative(X))))&
(funny(paul))&
(?[X]:((~patient(X)&tall(X))))&
(?[X]:((kind(X)|happy(X))))&
(tall(mary)) | ~brave(lucy) | [
"p4",
"p11",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3243610362954325683735012
% SZS output start Proof for 3243610362954325683735012
5. ! [X0] : (creative(X0) <=> ~strong(X0)) [input p4]
12. ! [X0] : (brave(X0) <=> happy(X0)) [input p11]
14. ! [X0] : ((~quiet(X0) & creative(X0)) <=> ~happy(X0)) [input p13]
17. strong(lucy) [input p16]
25. ~brave(lucy) [input hypothesis]
49. ! [X0] : ((creative(X0) | strong(X0)) & (~strong(X0) | ~creative(X0))) [nnf transformation 5]
65. ! [X0] : ((brave(X0) | ~happy(X0)) & (happy(X0) | ~brave(X0))) [nnf transformation 12]
68. ! [X0] : (((~quiet(X0) & creative(X0)) | happy(X0)) & (~happy(X0) | (quiet(X0) | ~creative(X0)))) [nnf transformation 14]
69. ! [X0] : (((~quiet(X0) & creative(X0)) | happy(X0)) & (~happy(X0) | quiet(X0) | ~creative(X0))) [flattening 68]
93. ~strong(X0) | ~creative(X0) [cnf transformation 49]
113. ~happy(X0) | brave(X0) [cnf transformation 65]
120. happy(X0) | creative(X0) [cnf transformation 69]
125. strong(lucy) [cnf transformation 17]
135. ~brave(lucy) [cnf transformation 25]
258. ~creative(lucy) [resolution 93,125]
272. brave(X0) | creative(X0) [resolution 120,113]
514. creative(lucy) [resolution 272,135]
517. $false [subsumption resolution 514,258]
% SZS output end Proof for 3243610362954325683735012
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or not patient is either not patient or old and vice versa.
If someone is either not old or humble then paul is brave or funny and vice versa.
If lucy is either rich or happy then alice is strong or rich and vice versa.
If susan is both not creative and quiet then paul is either not generous or kind.
If someone is strong then fred is patient.
If paul is either not patient or generous then someone is not patient or not quiet and vice versa.
If someone is curious or not old then paul is not brave.
If mary is either not strong or not old then someone is quiet or not rich and vice versa.
Everyone who is both rich and not wise is curious and vice versa.
If mary is both funny and not strong then fred is both old and patient.
Everyone who is either not calm or not strong is not kind.
If susan is either not strong or not humble then someone is not rich or happy and vice versa.
If alice is either generous or not kind then someone is either not calm or humble and vice versa.
If alice is not quiet or not funny then mary is either not patient or not kind.
Everyone who is either not creative or creative is either brave or not generous.
If susan is either happy or not funny then lucy is either creative or not curious and vice versa.
Someone is not funny or not wise.
Paul is either not creative or brave.
Paul is not humble or not patient.
Susan is both not wise and not patient.
Someone is either not rich or strong.
Someone is either happy or not patient.
Someone is not humble or not patient.
Someone is not old or not quiet. | Susan is creative. | neutral | (![X]:((~kind(X)|~patient(X))<=>(~patient(X)<~>old(X))))&
((?[X]:((~old(X)<~>humble(X))))<=>((brave(paul)|funny(paul))))&
(((rich(lucy)<~>happy(lucy)))<=>((strong(alice)|rich(alice))))&
(((~creative(susan)&quiet(susan)))=>((~generous(paul)<~>kind(paul))))&
((?[X]:(strong(X)))=>(patient(fred)))&
(((~patient(paul)<~>generous(paul)))<=>(?[X]:((~patient(X)|~quiet(X)))))&
((?[X]:((curious(X)|~old(X))))=>(~brave(paul)))&
(((~strong(mary)<~>~old(mary)))<=>(?[X]:((quiet(X)|~rich(X)))))&
(![X]:((rich(X)&~wise(X))<=>curious(X)))&
(((funny(mary)&~strong(mary)))=>((old(fred)&patient(fred))))&
(![X]:((~calm(X)<~>~strong(X))=>~kind(X)))&
(((~strong(susan)<~>~humble(susan)))<=>(?[X]:((~rich(X)|happy(X)))))&
(((generous(alice)<~>~kind(alice)))<=>(?[X]:((~calm(X)<~>humble(X)))))&
(((~quiet(alice)|~funny(alice)))=>((~patient(mary)<~>~kind(mary))))&
(![X]:((~creative(X)<~>creative(X))=>(brave(X)<~>~generous(X))))&
(((happy(susan)<~>~funny(susan)))<=>((creative(lucy)<~>~curious(lucy))))&
(?[X]:((~funny(X)|~wise(X))))&
((~creative(paul)<~>brave(paul)))&
((~humble(paul)|~patient(paul)))&
((~wise(susan)&~patient(susan)))&
(?[X]:((~rich(X)<~>strong(X))))&
(?[X]:((happy(X)<~>~patient(X))))&
(?[X]:((~humble(X)|~patient(X))))&
(?[X]:((~old(X)|~quiet(X)))) | creative(susan) | [] | null | 0 |
If someone is strong then fred is not brave and vice versa.
Everyone who is not brave is not funny or happy.
Everyone who is kind or generous is not creative and vice versa.
Everyone who is kind is curious and vice versa.
If paul is either wise or creative then fred is not tall or not brave.
If someone is both brave and not happy then someone is old.
Everyone who is not wise is both humble and creative.
If mary is both not creative and calm then someone is not funny or not creative.
If someone is quiet or calm then alice is either kind or old and vice versa.
If lucy is brave then mary is both patient and tall.
Everyone who is generous is patient and vice versa.
Everyone who is both not generous and not creative is not rich or not funny.
Everyone who is humble is calm or curious.
Everyone who is not quiet is strong or not tall and vice versa.
Everyone who is rich or not quiet is not curious.
Everyone who is kind is both tall and not happy.
Someone is either not wise or not calm.
Someone is either not patient or curious.
Someone is not calm.
John is either not tall or not generous.
Someone is quiet.
Someone is not strong.
Paul is both not quiet and funny.
Mary is creative. | Mary is patient. | contradiction | ((?[X]:(strong(X)))<=>(~brave(fred)))&
(![X]:(~brave(X)=>(~funny(X)|happy(X))))&
(![X]:((kind(X)|generous(X))<=>~creative(X)))&
(![X]:(kind(X)<=>curious(X)))&
(((wise(paul)<~>creative(paul)))=>((~tall(fred)|~brave(fred))))&
((?[X]:((brave(X)&~happy(X))))=>(?[X]:(old(X))))&
(![X]:(~wise(X)=>(humble(X)&creative(X))))&
(((~creative(mary)&calm(mary)))=>(?[X]:((~funny(X)|~creative(X)))))&
((?[X]:((quiet(X)|calm(X))))<=>((kind(alice)<~>old(alice))))&
((brave(lucy))=>((patient(mary)&tall(mary))))&
(![X]:(generous(X)<=>patient(X)))&
(![X]:((~generous(X)&~creative(X))=>(~rich(X)|~funny(X))))&
(![X]:(humble(X)=>(calm(X)|curious(X))))&
(![X]:(~quiet(X)<=>(strong(X)|~tall(X))))&
(![X]:((rich(X)|~quiet(X))=>~curious(X)))&
(![X]:(kind(X)=>(tall(X)&~happy(X))))&
(?[X]:((~wise(X)<~>~calm(X))))&
(?[X]:((~patient(X)<~>curious(X))))&
(?[X]:(~calm(X)))&
((~tall(john)<~>~generous(john)))&
(?[X]:(quiet(X)))&
(?[X]:(~strong(X)))&
((~quiet(paul)&funny(paul)))&
(creative(mary)) | patient(mary) | [
"p2",
"p10",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3940312237137544621141013
% SZS output start Proof for 3940312237137544621141013
3. ! [X0] : ((generous(X0) | kind(X0)) <=> ~creative(X0)) [input p2]
11. ! [X0] : (generous(X0) <=> patient(X0)) [input p10]
24. creative(mary) [input p23]
25. patient(mary) [input hypothesis]
46. ! [X0] : (((generous(X0) | kind(X0)) | creative(X0)) & (~creative(X0) | (~generous(X0) & ~kind(X0)))) [nnf transformation 3]
47. ! [X0] : ((generous(X0) | kind(X0) | creative(X0)) & (~creative(X0) | (~generous(X0) & ~kind(X0)))) [flattening 46]
59. ! [X0] : ((generous(X0) | ~patient(X0)) & (patient(X0) | ~generous(X0))) [nnf transformation 11]
79. ~creative(X0) | ~generous(X0) [cnf transformation 47]
98. ~patient(X0) | generous(X0) [cnf transformation 59]
117. creative(mary) [cnf transformation 24]
118. patient(mary) [cnf transformation 25]
155. 9 <=> creative(mary) [avatar definition]
157. creative(mary) <- (9) [avatar component clause 155]
209. 21 <=> patient(mary) [avatar definition]
211. patient(mary) <- (21) [avatar component clause 209]
243. 9 [avatar split clause 117,155]
244. 21 [avatar split clause 118,209]
246. ~generous(mary) <- (9) [resolution 79,157]
247. generous(mary) <- (21) [resolution 98,211]
248. $false <- (9, 21) [subsumption resolution 247,246]
249. ~9 | ~21 [avatar contradiction clause 248]
250. $false [avatar sat refutation 243,244,249]
% SZS output end Proof for 3940312237137544621141013
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is not kind and vice versa. If lucy is either not kind or funny then someone is humble or not quiet. If someone is not tall or not quiet then fred is both not patient and not happy. Everyone who is wise or not humble is funny or not strong and vice versa. If someone is curious then fred is not curious. Everyone who is either rich or patient is old or funny. If mary is not patient or not rich then john is either not creative or humble. If john is either wise or patient then someone is not old. Everyone who is creative is both kind and not patient and vice versa. Everyone who is not rich is humble. Everyone who is kind or humble is both not brave and not generous. If someone is creative or patient then john is humble or not calm. Everyone who is not tall is generous and vice versa. If someone is funny or not calm then someone is generous or not old and vice versa. Everyone who is wise is both wise and creative. Someone is not happy. Someone is not curious or not funny. Alice is both funny and not old. Someone is not brave. Someone is not wise or tall. | Alice is creative. | contradiction | (![X]:(creative(X)<=>~kind(X)))&
(((~kind(lucy)<~>funny(lucy)))=>(?[X]:((humble(X)|~quiet(X)))))&
((?[X]:((~tall(X)|~quiet(X))))=>((~patient(fred)&~happy(fred))))&
(![X]:((wise(X)|~humble(X))<=>(funny(X)|~strong(X))))&
((?[X]:(curious(X)))=>(~curious(fred)))&
(![X]:((rich(X)<~>patient(X))=>(old(X)|funny(X))))&
(((~patient(mary)|~rich(mary)))=>((~creative(john)<~>humble(john))))&
(((wise(john)<~>patient(john)))=>(?[X]:(~old(X))))&
(![X]:(creative(X)<=>(kind(X)&~patient(X))))&
(![X]:(~rich(X)=>humble(X)))&
(![X]:((kind(X)|humble(X))=>(~brave(X)&~generous(X))))&
((?[X]:((creative(X)|patient(X))))=>((humble(john)|~calm(john))))&
(![X]:(~tall(X)<=>generous(X)))&
((?[X]:((funny(X)|~calm(X))))<=>(?[X]:((generous(X)|~old(X)))))&
(![X]:(wise(X)=>(wise(X)&creative(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~curious(X)|~funny(X))))&
((funny(alice)&~old(alice)))&
(?[X]:(~brave(X)))&
(?[X]:((~wise(X)|tall(X)))) | creative(alice) | [
"p0",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2198249106873725288332553
% SZS output start Proof for 2198249106873725288332553
1. ! [X0] : (creative(X0) <=> ~kind(X0)) [input p0]
9. ! [X0] : (creative(X0) <=> (~patient(X0) & kind(X0))) [input p8]
21. creative(alice) [input hypothesis]
42. ! [X0] : ((creative(X0) | kind(X0)) & (~kind(X0) | ~creative(X0))) [nnf transformation 1]
53. ! [X0] : ((creative(X0) | (patient(X0) | ~kind(X0))) & ((~patient(X0) & kind(X0)) | ~creative(X0))) [nnf transformation 9]
54. ! [X0] : ((creative(X0) | patient(X0) | ~kind(X0)) & ((~patient(X0) & kind(X0)) | ~creative(X0))) [flattening 53]
62. ~kind(X0) | ~creative(X0) [cnf transformation 42]
80. kind(X0) | ~creative(X0) [cnf transformation 54]
98. creative(alice) [cnf transformation 21]
164. ~creative(X0) [subsumption resolution 80,62]
206. $false [subsumption resolution 98,164]
% SZS output end Proof for 2198249106873725288332553
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not quiet or not patient then mary is both not calm and not curious and vice versa.
If someone is strong then paul is either not quiet or curious and vice versa.
Everyone who is not humble or patient is both kind and funny and vice versa.
Everyone who is not kind or funny is both not generous and not rich and vice versa.
Everyone who is both happy and not strong is not generous and vice versa.
If someone is both rich and funny then someone is not funny.
Everyone who is not kind is either rich or humble and vice versa.
Everyone who is kind is not wise or not tall and vice versa.
Everyone who is humble is not rich or old.
If john is not rich then someone is either not old or patient and vice versa.
If mary is not rich or curious then alice is either not patient or not funny.
Everyone who is either funny or strong is not patient or curious and vice versa.
If fred is tall or not creative then mary is patient or strong.
Everyone who is both not generous and tall is either quiet or calm and vice versa.
Everyone who is either not funny or tall is both funny and kind.
If someone is wise or not happy then alice is both not quiet and not wise.
Someone is kind or generous.
Someone is both happy and generous.
Someone is not curious.
Someone is either not happy or not rich.
Someone is either not generous or not old.
John is not calm.
Someone is not calm or calm.
Someone is creative. | Mary is patient. | contradiction | ((?[X]:((~quiet(X)|~patient(X))))<=>((~calm(mary)&~curious(mary))))&
((?[X]:(strong(X)))<=>((~quiet(paul)<~>curious(paul))))&
(![X]:((~humble(X)|patient(X))<=>(kind(X)&funny(X))))&
(![X]:((~kind(X)|funny(X))<=>(~generous(X)&~rich(X))))&
(![X]:((happy(X)&~strong(X))<=>~generous(X)))&
((?[X]:((rich(X)&funny(X))))=>(?[X]:(~funny(X))))&
(![X]:(~kind(X)<=>(rich(X)<~>humble(X))))&
(![X]:(kind(X)<=>(~wise(X)|~tall(X))))&
(![X]:(humble(X)=>(~rich(X)|old(X))))&
((~rich(john))<=>(?[X]:((~old(X)<~>patient(X)))))&
(((~rich(mary)|curious(mary)))=>((~patient(alice)<~>~funny(alice))))&
(![X]:((funny(X)<~>strong(X))<=>(~patient(X)|curious(X))))&
(((tall(fred)|~creative(fred)))=>((patient(mary)|strong(mary))))&
(![X]:((~generous(X)&tall(X))<=>(quiet(X)<~>calm(X))))&
(![X]:((~funny(X)<~>tall(X))=>(funny(X)&kind(X))))&
((?[X]:((wise(X)|~happy(X))))=>((~quiet(alice)&~wise(alice))))&
(?[X]:((kind(X)|generous(X))))&
(?[X]:((happy(X)&generous(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~happy(X)<~>~rich(X))))&
(?[X]:((~generous(X)<~>~old(X))))&
(~calm(john))&
(?[X]:((~calm(X)|calm(X))))&
(?[X]:(creative(X))) | patient(mary) | [
"p0",
"p2",
"p3",
"p4",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7516082285887723471532538
% SZS output start Proof for 7516082285887723471532538
1. ? [X0] : (~patient(X0) | ~quiet(X0)) <=> (~curious(mary) & ~calm(mary)) [input p0]
3. ! [X0] : ((patient(X0) | ~humble(X0)) <=> (funny(X0) & kind(X0))) [input p2]
4. ! [X0] : ((funny(X0) | ~kind(X0)) <=> (~rich(X0) & ~generous(X0))) [input p3]
5. ! [X0] : ((~strong(X0) & happy(X0)) <=> ~generous(X0)) [input p4]
11. (curious(mary) | ~rich(mary)) => (~patient(alice) <~> ~funny(alice)) [input p10]
12. ! [X0] : ((funny(X0) <~> strong(X0)) <=> (curious(X0) | ~patient(X0))) [input p11]
25. patient(mary) [input hypothesis]
32. (~patient(alice) <~> ~funny(alice)) | (~curious(mary) & rich(mary)) [ennf transformation 11]
37. (? [X0] : (~patient(X0) | ~quiet(X0)) | (curious(mary) | calm(mary))) & ((~curious(mary) & ~calm(mary)) | ! [X0] : (patient(X0) & quiet(X0))) [nnf transformation 1]
38. (? [X0] : (~patient(X0) | ~quiet(X0)) | curious(mary) | calm(mary)) & ((~curious(mary) & ~calm(mary)) | ! [X0] : (patient(X0) & quiet(X0))) [flattening 37]
39. (? [X0] : (~patient(X0) | ~quiet(X0)) | curious(mary) | calm(mary)) & ((~curious(mary) & ~calm(mary)) | ! [X1] : (patient(X1) & quiet(X1))) [rectify 38]
40. ? [X0] : (~patient(X0) | ~quiet(X0)) => (~patient(sK0) | ~quiet(sK0)) [choice axiom]
41. ((~patient(sK0) | ~quiet(sK0)) | curious(mary) | calm(mary)) & ((~curious(mary) & ~calm(mary)) | ! [X1] : (patient(X1) & quiet(X1))) [skolemisation 39,40]
46. ! [X0] : (((patient(X0) | ~humble(X0)) | (~funny(X0) | ~kind(X0))) & ((funny(X0) & kind(X0)) | (~patient(X0) & humble(X0)))) [nnf transformation 3]
47. ! [X0] : ((patient(X0) | ~humble(X0) | ~funny(X0) | ~kind(X0)) & ((funny(X0) & kind(X0)) | (~patient(X0) & humble(X0)))) [flattening 46]
48. ! [X0] : (((funny(X0) | ~kind(X0)) | (rich(X0) | generous(X0))) & ((~rich(X0) & ~generous(X0)) | (~funny(X0) & kind(X0)))) [nnf transformation 4]
49. ! [X0] : ((funny(X0) | ~kind(X0) | rich(X0) | generous(X0)) & ((~rich(X0) & ~generous(X0)) | (~funny(X0) & kind(X0)))) [flattening 48]
50. ! [X0] : (((~strong(X0) & happy(X0)) | generous(X0)) & (~generous(X0) | (strong(X0) | ~happy(X0)))) [nnf transformation 5]
51. ! [X0] : (((~strong(X0) & happy(X0)) | generous(X0)) & (~generous(X0) | strong(X0) | ~happy(X0))) [flattening 50]
62. ((funny(alice) | patient(alice)) & (~funny(alice) | ~patient(alice))) | (~curious(mary) & rich(mary)) [nnf transformation 32]
63. ! [X0] : ((((~strong(X0) | ~funny(X0)) & (strong(X0) | funny(X0))) | (~curious(X0) & patient(X0))) & ((curious(X0) | ~patient(X0)) | ((funny(X0) | ~strong(X0)) & (strong(X0) | ~funny(X0))))) [nnf transformation 12]
64. ! [X0] : ((((~strong(X0) | ~funny(X0)) & (strong(X0) | funny(X0))) | (~curious(X0) & patient(X0))) & (curious(X0) | ~patient(X0) | ((funny(X0) | ~strong(X0)) & (strong(X0) | ~funny(X0))))) [flattening 63]
85. ~curious(mary) | patient(X1) [cnf transformation 41]
94. ~patient(X0) | funny(X0) [cnf transformation 47]
97. ~generous(X0) | ~funny(X0) [cnf transformation 49]
103. ~strong(X0) | generous(X0) [cnf transformation 51]
118. ~funny(alice) | ~patient(alice) | ~curious(mary) [cnf transformation 62]
121. curious(X0) | ~patient(X0) | strong(X0) | ~funny(X0) [cnf transformation 64]
123. strong(X0) | funny(X0) | patient(X0) [cnf transformation 64]
152. patient(mary) [cnf transformation 25]
159. 2 <=> curious(mary) [avatar definition]
172. 5 <=> ! [X1] : patient(X1) [avatar definition]
173. patient(X1) <- (5) [avatar component clause 172]
174. 5 | ~2 [avatar split clause 85,159,172]
236. ~patient(alice) | ~curious(mary) [subsumption resolution 118,94]
238. 18 <=> patient(alice) [avatar definition]
240. ~patient(alice) <- (~18) [avatar component clause 238]
241. ~2 | ~18 [avatar split clause 236,238,159]
244. funny(X0) | strong(X0) [subsumption resolution 123,94]
245. ~patient(X0) | curious(X0) | strong(X0) [subsumption resolution 121,244]
251. 20 <=> patient(mary) [avatar definition]
253. patient(mary) <- (20) [avatar component clause 251]
255. 21 <=> strong(mary) [avatar definition]
257. strong(mary) <- (21) [avatar component clause 255]
299. 20 [avatar split clause 152,251]
301. funny(mary) <- (20) [resolution 94,253]
421. curious(mary) | strong(mary) <- (20) [resolution 245,253]
424. 21 | 2 | ~20 [avatar split clause 421,251,159,255]
428. $false <- (5, ~18) [resolution 173,240]
432. ~5 | 18 [avatar contradiction clause 428]
445. generous(mary) <- (21) [resolution 257,103]
453. ~funny(mary) <- (21) [resolution 445,97]
456. $false <- (20, 21) [subsumption resolution 453,301]
457. ~20 | ~21 [avatar contradiction clause 456]
458. $false [avatar sat refutation 174,241,299,424,432,457]
% SZS output end Proof for 7516082285887723471532538
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not quiet and not generous then someone is not wise and vice versa.
If lucy is not happy then paul is not creative or rich and vice versa.
Everyone who is calm or not humble is patient or kind and vice versa.
If mary is either wise or humble then john is either not quiet or old.
If someone is either funny or not happy then someone is either humble or not humble.
Everyone who is both humble and patient is both wise and not generous.
Everyone who is not calm is both not tall and brave.
Everyone who is rich or not wise is not funny or not kind and vice versa.
Everyone who is curious is not calm or not rich.
Everyone who is not patient is both patient and not generous and vice versa.
Everyone who is not brave or humble is creative.
If someone is both not calm and not humble then someone is humble or not patient.
Everyone who is old is both not kind and kind and vice versa.
If someone is curious or wise then john is humble or not strong.
If someone is not happy or curious then lucy is both creative and old and vice versa.
Someone is not brave or brave.
Someone is either not quiet or not wise.
Someone is happy or wise.
John is happy.
Mary is either strong or not generous.
Someone is not curious.
Someone is happy or rich. | John is not calm. | contradiction | (((~quiet(lucy)&~generous(lucy)))<=>(?[X]:(~wise(X))))&
((~happy(lucy))<=>((~creative(paul)|rich(paul))))&
(![X]:((calm(X)|~humble(X))<=>(patient(X)|kind(X))))&
(((wise(mary)<~>humble(mary)))=>((~quiet(john)<~>old(john))))&
((?[X]:((funny(X)<~>~happy(X))))=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((humble(X)&patient(X))=>(wise(X)&~generous(X))))&
(![X]:(~calm(X)=>(~tall(X)&brave(X))))&
(![X]:((rich(X)|~wise(X))<=>(~funny(X)|~kind(X))))&
(![X]:(curious(X)=>(~calm(X)|~rich(X))))&
(![X]:(~patient(X)<=>(patient(X)&~generous(X))))&
(![X]:((~brave(X)|humble(X))=>creative(X)))&
((?[X]:((~calm(X)&~humble(X))))=>(?[X]:((humble(X)|~patient(X)))))&
(![X]:(old(X)<=>(~kind(X)&kind(X))))&
((?[X]:((curious(X)|wise(X))))=>((humble(john)|~strong(john))))&
((?[X]:((~happy(X)|curious(X))))<=>((creative(lucy)&old(lucy))))&
(?[X]:((~brave(X)|brave(X))))&
(?[X]:((~quiet(X)<~>~wise(X))))&
(?[X]:((happy(X)|wise(X))))&
(happy(john))&
((strong(mary)<~>~generous(mary)))&
(?[X]:(~curious(X)))&
(?[X]:((happy(X)|rich(X)))) | ~calm(john) | [
"p2",
"p5",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5322126278059517881860945
% SZS output start Proof for 5322126278059517881860945
3. ! [X0] : ((~humble(X0) | calm(X0)) <=> (kind(X0) | patient(X0))) [input p2]
6. ! [X0] : ((patient(X0) & humble(X0)) => (~generous(X0) & wise(X0))) [input p5]
10. ! [X0] : (~patient(X0) <=> (~generous(X0) & patient(X0))) [input p9]
12. ? [X0] : (~humble(X0) & ~calm(X0)) => ? [X0] : (~patient(X0) | humble(X0)) [input p11]
23. ~calm(john) [input hypothesis]
25. ? [X0] : (~humble(X0) & ~calm(X0)) => ? [X1] : (~patient(X1) | humble(X1)) [rectify 12]
29. ! [X0] : ((~generous(X0) & wise(X0)) | (~patient(X0) | ~humble(X0))) [ennf transformation 6]
30. ! [X0] : ((~generous(X0) & wise(X0)) | ~patient(X0) | ~humble(X0)) [flattening 29]
35. ? [X1] : (~patient(X1) | humble(X1)) | ! [X0] : (humble(X0) | calm(X0)) [ennf transformation 25]
45. ! [X0] : (((~humble(X0) | calm(X0)) | (~kind(X0) & ~patient(X0))) & ((kind(X0) | patient(X0)) | (humble(X0) & ~calm(X0)))) [nnf transformation 3]
46. ! [X0] : ((~humble(X0) | calm(X0) | (~kind(X0) & ~patient(X0))) & (kind(X0) | patient(X0) | (humble(X0) & ~calm(X0)))) [flattening 45]
54. ! [X0] : ((~patient(X0) | (generous(X0) | ~patient(X0))) & ((~generous(X0) & patient(X0)) | patient(X0))) [nnf transformation 10]
55. ! [X0] : ((~patient(X0) | generous(X0) | ~patient(X0)) & ((~generous(X0) & patient(X0)) | patient(X0))) [flattening 54]
56. ? [X0] : (~patient(X0) | humble(X0)) | ! [X1] : (humble(X1) | calm(X1)) [rectify 35]
57. ? [X0] : (~patient(X0) | humble(X0)) => (~patient(sK2) | humble(sK2)) [choice axiom]
58. (~patient(sK2) | humble(sK2)) | ! [X1] : (humble(X1) | calm(X1)) [skolemisation 56,57]
86. ~patient(X0) | calm(X0) | ~humble(X0) [cnf transformation 46]
97. ~patient(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 30]
104. patient(X0) | patient(X0) [cnf transformation 55]
106. ~patient(X0) | generous(X0) | ~patient(X0) [cnf transformation 55]
109. ~patient(sK2) | humble(sK2) | humble(X1) | calm(X1) [cnf transformation 58]
129. ~calm(john) [cnf transformation 23]
130. patient(X0) [duplicate literal removal 104]
131. ~patient(X0) | generous(X0) [duplicate literal removal 106]
185. humble(sK2) | humble(X1) | calm(X1) [subsumption resolution 109,130]
187. 12 <=> ! [X1] : (humble(X1) | calm(X1)) [avatar definition]
188. humble(X1) | calm(X1) <- (12) [avatar component clause 187]
190. 13 <=> humble(sK2) [avatar definition]
192. humble(sK2) <- (13) [avatar component clause 190]
193. 12 | 13 [avatar split clause 185,190,187]
241. generous(X0) [resolution 131,130]
258. ~humble(X0) | calm(X0) [resolution 86,130]
259. calm(X0) <- (12) [subsumption resolution 258,188]
260. $false <- (12) [resolution 259,129]
262. ~12 [avatar contradiction clause 260]
268. ~generous(X0) | ~humble(X0) [resolution 97,130]
269. ~humble(X0) [subsumption resolution 268,241]
270. $false <- (13) [resolution 269,192]
271. ~13 [avatar contradiction clause 270]
272. $false [avatar sat refutation 193,262,271]
% SZS output end Proof for 5322126278059517881860945
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous then paul is not generous or not kind and vice versa. Everyone who is wise is both not kind and kind and vice versa. If fred is calm then john is wise or generous. Everyone who is either not generous or patient is both not creative and not patient. Everyone who is brave is both not wise and not old and vice versa. If someone is both funny and not patient then mary is curious or not quiet and vice versa. If someone is not brave then alice is both not tall and not kind and vice versa. If john is both tall and generous then paul is curious or not tall. Everyone who is either not kind or not old is not strong or not quiet. If someone is quiet or not quiet then lucy is patient. Everyone who is not funny or not kind is calm or not funny. If someone is not patient then someone is not quiet. If lucy is tall or not happy then someone is not rich. Everyone who is old is not old. If john is patient or not humble then mary is both not quiet and not wise and vice versa. Everyone who is kind or old is not calm. Someone is either old or quiet. Someone is happy. Someone is not creative or old. Someone is either not tall or generous. John is both not humble and not generous. | Paul is not generous. | neutral | ((?[X]:(generous(X)))<=>((~generous(paul)|~kind(paul))))&
(![X]:(wise(X)<=>(~kind(X)&kind(X))))&
((calm(fred))=>((wise(john)|generous(john))))&
(![X]:((~generous(X)<~>patient(X))=>(~creative(X)&~patient(X))))&
(![X]:(brave(X)<=>(~wise(X)&~old(X))))&
((?[X]:((funny(X)&~patient(X))))<=>((curious(mary)|~quiet(mary))))&
((?[X]:(~brave(X)))<=>((~tall(alice)&~kind(alice))))&
(((tall(john)&generous(john)))=>((curious(paul)|~tall(paul))))&
(![X]:((~kind(X)<~>~old(X))=>(~strong(X)|~quiet(X))))&
((?[X]:((quiet(X)|~quiet(X))))=>(patient(lucy)))&
(![X]:((~funny(X)|~kind(X))=>(calm(X)|~funny(X))))&
((?[X]:(~patient(X)))=>(?[X]:(~quiet(X))))&
(((tall(lucy)|~happy(lucy)))=>(?[X]:(~rich(X))))&
(![X]:(old(X)=>~old(X)))&
(((patient(john)|~humble(john)))<=>((~quiet(mary)&~wise(mary))))&
(![X]:((kind(X)|old(X))=>~calm(X)))&
(?[X]:((old(X)<~>quiet(X))))&
(?[X]:(happy(X)))&
(?[X]:((~creative(X)|old(X))))&
(?[X]:((~tall(X)<~>generous(X))))&
((~humble(john)&~generous(john))) | ~generous(paul) | [] | null | 0 |
If someone is not rich then someone is both not wise and not calm and vice versa.
If john is both funny and wise then someone is not happy and vice versa.
Everyone who is not rich is either kind or not rich.
Everyone who is rich or not brave is not quiet and vice versa.
If someone is both not kind and not humble then someone is not humble or not happy and vice versa.
Everyone who is both old and not rich is tall or wise and vice versa.
If someone is strong or not brave then someone is both calm and humble and vice versa.
Everyone who is patient or rich is either not rich or not humble.
Everyone who is happy is not kind and vice versa.
If someone is not kind or brave then someone is both creative and not curious and vice versa.
If paul is not patient then someone is either patient or not happy.
Everyone who is calm or not generous is either calm or not generous and vice versa.
If lucy is funny or curious then someone is rich and vice versa.
Everyone who is either quiet or not funny is either quiet or strong.
If fred is not old or not wise then john is both creative and not patient and vice versa.
Everyone who is either curious or brave is not humble and vice versa.
Someone is both not humble and not funny.
Someone is both not brave and curious.
Susan is generous or funny.
Someone is both not happy and curious.
Fred is tall or not rich.
Someone is not funny.
Someone is rich or creative.
John is tall or not strong. | John is kind. | contradiction | ((?[X]:(~rich(X)))<=>(?[X]:((~wise(X)&~calm(X)))))&
(((funny(john)&wise(john)))<=>(?[X]:(~happy(X))))&
(![X]:(~rich(X)=>(kind(X)<~>~rich(X))))&
(![X]:((rich(X)|~brave(X))<=>~quiet(X)))&
((?[X]:((~kind(X)&~humble(X))))<=>(?[X]:((~humble(X)|~happy(X)))))&
(![X]:((old(X)&~rich(X))<=>(tall(X)|wise(X))))&
((?[X]:((strong(X)|~brave(X))))<=>(?[X]:((calm(X)&humble(X)))))&
(![X]:((patient(X)|rich(X))=>(~rich(X)<~>~humble(X))))&
(![X]:(happy(X)<=>~kind(X)))&
((?[X]:((~kind(X)|brave(X))))<=>(?[X]:((creative(X)&~curious(X)))))&
((~patient(paul))=>(?[X]:((patient(X)<~>~happy(X)))))&
(![X]:((calm(X)|~generous(X))<=>(calm(X)<~>~generous(X))))&
(((funny(lucy)|curious(lucy)))<=>(?[X]:(rich(X))))&
(![X]:((quiet(X)<~>~funny(X))=>(quiet(X)<~>strong(X))))&
(((~old(fred)|~wise(fred)))<=>((creative(john)&~patient(john))))&
(![X]:((curious(X)<~>brave(X))<=>~humble(X)))&
(?[X]:((~humble(X)&~funny(X))))&
(?[X]:((~brave(X)&curious(X))))&
((generous(susan)|funny(susan)))&
(?[X]:((~happy(X)&curious(X))))&
((tall(fred)|~rich(fred)))&
(?[X]:(~funny(X)))&
(?[X]:((rich(X)|creative(X))))&
((tall(john)|~strong(john))) | kind(john) | [
"p1",
"p2",
"p5",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2863811719753361474620074
% SZS output start Proof for 2863811719753361474620074
2. (wise(john) & funny(john)) <=> ? [X0] : ~happy(X0) [input p1]
3. ! [X0] : (~rich(X0) => (kind(X0) <~> ~rich(X0))) [input p2]
6. ! [X0] : ((~rich(X0) & old(X0)) <=> (wise(X0) | tall(X0))) [input p5]
20. ? [X0] : (curious(X0) & ~happy(X0)) [input p19]
25. kind(john) [input hypothesis]
30. ! [X0] : ((kind(X0) <~> ~rich(X0)) | rich(X0)) [ennf transformation 3]
39. ((wise(john) & funny(john)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | (~wise(john) | ~funny(john))) [nnf transformation 2]
40. ((wise(john) & funny(john)) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | ~wise(john) | ~funny(john)) [flattening 39]
41. ((wise(john) & funny(john)) | ! [X0] : happy(X0)) & (? [X1] : ~happy(X1) | ~wise(john) | ~funny(john)) [rectify 40]
42. ? [X1] : ~happy(X1) => ~happy(sK2) [choice axiom]
43. ((wise(john) & funny(john)) | ! [X0] : happy(X0)) & (~happy(sK2) | ~wise(john) | ~funny(john)) [skolemisation 41,42]
44. ! [X0] : (((rich(X0) | ~kind(X0)) & (~rich(X0) | kind(X0))) | rich(X0)) [nnf transformation 30]
52. ! [X0] : (((~rich(X0) & old(X0)) | (~wise(X0) & ~tall(X0))) & ((wise(X0) | tall(X0)) | (rich(X0) | ~old(X0)))) [nnf transformation 6]
53. ! [X0] : (((~rich(X0) & old(X0)) | (~wise(X0) & ~tall(X0))) & (wise(X0) | tall(X0) | rich(X0) | ~old(X0))) [flattening 52]
84. ? [X0] : (curious(X0) & ~happy(X0)) => (curious(sK13) & ~happy(sK13)) [choice axiom]
85. curious(sK13) & ~happy(sK13) [skolemisation 20,84]
95. wise(john) | happy(X0) [cnf transformation 43]
97. rich(X0) | ~kind(X0) | rich(X0) [cnf transformation 44]
110. ~wise(X0) | ~rich(X0) [cnf transformation 53]
156. ~happy(sK13) [cnf transformation 85]
162. kind(john) [cnf transformation 25]
170. ~kind(X0) | rich(X0) [duplicate literal removal 97]
193. 6 <=> ! [X0] : happy(X0) [avatar definition]
194. happy(X0) <- (6) [avatar component clause 193]
196. 7 <=> wise(john) [avatar definition]
198. wise(john) <- (7) [avatar component clause 196]
199. 6 | 7 [avatar split clause 95,196,193]
385. $false <- (6) [resolution 194,156]
386. ~6 [avatar contradiction clause 385]
394. ~rich(john) <- (7) [resolution 110,198]
401. rich(john) [resolution 170,162]
404. $false <- (7) [subsumption resolution 401,394]
405. ~7 [avatar contradiction clause 404]
406. $false [avatar sat refutation 199,386,405]
% SZS output end Proof for 2863811719753361474620074
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise is either not brave or not happy.
If fred is not patient then alice is humble or not quiet and vice versa.
Everyone who is either creative or tall is not funny or humble and vice versa.
Everyone who is not patient or humble is not humble.
If susan is both creative and not calm then someone is funny and vice versa.
Everyone who is rich is brave or not patient.
Everyone who is not humble or wise is both not curious and patient.
Everyone who is calm is either patient or wise and vice versa.
Everyone who is either humble or brave is both not funny and not calm.
Everyone who is not tall is both tall and not brave.
Everyone who is either kind or not generous is both not humble and quiet and vice versa.
If john is happy or not humble then someone is both creative and not rich.
Everyone who is not quiet or not kind is either kind or brave.
If fred is not patient then susan is not rich or not generous.
Everyone who is both patient and not patient is either kind or happy and vice versa.
Someone is wise or not curious.
Susan is either not old or rich.
Someone is not happy or not kind.
Someone is either not kind or curious.
Mary is not brave or not old.
Someone is not strong. | Alice is not curious. | entailment | (![X]:(wise(X)=>(~brave(X)<~>~happy(X))))&
((~patient(fred))<=>((humble(alice)|~quiet(alice))))&
(![X]:((creative(X)<~>tall(X))<=>(~funny(X)|humble(X))))&
(![X]:((~patient(X)|humble(X))=>~humble(X)))&
(((creative(susan)&~calm(susan)))<=>(?[X]:(funny(X))))&
(![X]:(rich(X)=>(brave(X)|~patient(X))))&
(![X]:((~humble(X)|wise(X))=>(~curious(X)&patient(X))))&
(![X]:(calm(X)<=>(patient(X)<~>wise(X))))&
(![X]:((humble(X)<~>brave(X))=>(~funny(X)&~calm(X))))&
(![X]:(~tall(X)=>(tall(X)&~brave(X))))&
(![X]:((kind(X)<~>~generous(X))<=>(~humble(X)&quiet(X))))&
(((happy(john)|~humble(john)))=>(?[X]:((creative(X)&~rich(X)))))&
(![X]:((~quiet(X)|~kind(X))=>(kind(X)<~>brave(X))))&
((~patient(fred))=>((~rich(susan)|~generous(susan))))&
(![X]:((patient(X)&~patient(X))<=>(kind(X)<~>happy(X))))&
(?[X]:((wise(X)|~curious(X))))&
((~old(susan)<~>rich(susan)))&
(?[X]:((~happy(X)|~kind(X))))&
(?[X]:((~kind(X)<~>curious(X))))&
((~brave(mary)|~old(mary)))&
(?[X]:(~strong(X))) | ~curious(alice) | [
"p3",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 1034220584212328736340564
% SZS output start Proof for 1034220584212328736340564
4. ! [X0] : ((humble(X0) | ~patient(X0)) => ~humble(X0)) [input p3]
7. ! [X0] : ((wise(X0) | ~humble(X0)) => (patient(X0) & ~curious(X0))) [input p6]
22. curious(alice) [input hypothesis]
25. ! [X0] : (~humble(X0) | (~humble(X0) & patient(X0))) [ennf transformation 4]
28. ! [X0] : ((patient(X0) & ~curious(X0)) | (~wise(X0) & humble(X0))) [ennf transformation 7]
74. ~humble(X0) | ~humble(X0) [cnf transformation 25]
79. ~curious(X0) | humble(X0) [cnf transformation 28]
121. curious(alice) [cnf transformation 22]
124. ~humble(X0) [duplicate literal removal 74]
159. ~curious(X0) [subsumption resolution 79,124]
191. $false [subsumption resolution 121,159]
% SZS output end Proof for 1034220584212328736340564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is quiet or not creative then someone is brave and vice versa. Everyone who is quiet is either not kind or humble and vice versa. Everyone who is not wise is strong or not strong. Everyone who is not quiet is either not wise or quiet. Everyone who is rich is calm or funny and vice versa. If mary is either not creative or happy then someone is happy or humble and vice versa. Everyone who is kind or creative is funny or generous. If someone is either not patient or not calm then someone is either not old or calm and vice versa. If alice is both brave and not strong then fred is either humble or kind and vice versa. If john is both not patient and not kind then someone is not calm and vice versa. If someone is kind or funny then alice is wise and vice versa. Everyone who is not creative is not humble or calm. If someone is not curious then someone is both not rich and curious and vice versa. If john is either not creative or not calm then someone is not happy and vice versa. Everyone who is both not quiet and not funny is either not creative or not strong. Everyone who is not rich is not patient and vice versa. Paul is old. Someone is wise or creative. Someone is both not generous and not rich. Someone is not old or humble. Someone is not old. Paul is both not generous and funny. Someone is either generous or creative. Someone is not strong or happy. | Paul is not generous. | entailment | ((?[X]:((quiet(X)|~creative(X))))<=>(?[X]:(brave(X))))&
(![X]:(quiet(X)<=>(~kind(X)<~>humble(X))))&
(![X]:(~wise(X)=>(strong(X)|~strong(X))))&
(![X]:(~quiet(X)=>(~wise(X)<~>quiet(X))))&
(![X]:(rich(X)<=>(calm(X)|funny(X))))&
(((~creative(mary)<~>happy(mary)))<=>(?[X]:((happy(X)|humble(X)))))&
(![X]:((kind(X)|creative(X))=>(funny(X)|generous(X))))&
((?[X]:((~patient(X)<~>~calm(X))))<=>(?[X]:((~old(X)<~>calm(X)))))&
(((brave(alice)&~strong(alice)))<=>((humble(fred)<~>kind(fred))))&
(((~patient(john)&~kind(john)))<=>(?[X]:(~calm(X))))&
((?[X]:((kind(X)|funny(X))))<=>(wise(alice)))&
(![X]:(~creative(X)=>(~humble(X)|calm(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((~rich(X)&curious(X)))))&
(((~creative(john)<~>~calm(john)))<=>(?[X]:(~happy(X))))&
(![X]:((~quiet(X)&~funny(X))=>(~creative(X)<~>~strong(X))))&
(![X]:(~rich(X)<=>~patient(X)))&
(old(paul))&
(?[X]:((wise(X)|creative(X))))&
(?[X]:((~generous(X)&~rich(X))))&
(?[X]:((~old(X)|humble(X))))&
(?[X]:(~old(X)))&
((~generous(paul)&funny(paul)))&
(?[X]:((generous(X)<~>creative(X))))&
(?[X]:((~strong(X)|happy(X)))) | ~generous(paul) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 495586559229677699195531
% SZS output start Proof for 495586559229677699195531
22. funny(paul) & ~generous(paul) [input p21]
25. generous(paul) [input hypothesis]
150. ~generous(paul) [cnf transformation 22]
155. generous(paul) [cnf transformation 25]
383. $false [subsumption resolution 155,150]
% SZS output end Proof for 495586559229677699195531
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not tall then susan is both quiet and curious and vice versa.
If john is not creative or tall then someone is either funny or not calm and vice versa.
If alice is either creative or not wise then someone is both kind and not generous.
If john is either not patient or not creative then someone is both not humble and not brave.
If susan is not kind then someone is either tall or not quiet and vice versa.
If someone is both not creative and not happy then lucy is either not funny or not creative and vice versa.
If someone is not kind then john is happy and vice versa.
Everyone who is either not patient or not happy is not generous or strong and vice versa.
Everyone who is not patient or not creative is not quiet.
Everyone who is either not calm or calm is either not quiet or not creative.
Everyone who is rich is both wise and not brave and vice versa.
Everyone who is either curious or patient is not quiet or wise and vice versa.
If susan is either rich or not curious then someone is patient or not calm.
If someone is either humble or curious then someone is both not strong and quiet and vice versa.
Everyone who is both curious and humble is both not generous and brave.
Someone is both strong and not curious.
John is both not curious and brave.
Someone is either not wise or old.
Someone is both not generous and not calm.
Someone is not curious.
Susan is either not quiet or not patient. | Alice is not calm. | entailment | ((?[X]:((calm(X)|~tall(X))))<=>((quiet(susan)&curious(susan))))&
(((~creative(john)|tall(john)))<=>(?[X]:((funny(X)<~>~calm(X)))))&
(((creative(alice)<~>~wise(alice)))=>(?[X]:((kind(X)&~generous(X)))))&
(((~patient(john)<~>~creative(john)))=>(?[X]:((~humble(X)&~brave(X)))))&
((~kind(susan))<=>(?[X]:((tall(X)<~>~quiet(X)))))&
((?[X]:((~creative(X)&~happy(X))))<=>((~funny(lucy)<~>~creative(lucy))))&
((?[X]:(~kind(X)))<=>(happy(john)))&
(![X]:((~patient(X)<~>~happy(X))<=>(~generous(X)|strong(X))))&
(![X]:((~patient(X)|~creative(X))=>~quiet(X)))&
(![X]:((~calm(X)<~>calm(X))=>(~quiet(X)<~>~creative(X))))&
(![X]:(rich(X)<=>(wise(X)&~brave(X))))&
(![X]:((curious(X)<~>patient(X))<=>(~quiet(X)|wise(X))))&
(((rich(susan)<~>~curious(susan)))=>(?[X]:((patient(X)|~calm(X)))))&
((?[X]:((humble(X)<~>curious(X))))<=>(?[X]:((~strong(X)&quiet(X)))))&
(![X]:((curious(X)&humble(X))=>(~generous(X)&brave(X))))&
(?[X]:((strong(X)&~curious(X))))&
((~curious(john)&brave(john)))&
(?[X]:((~wise(X)<~>old(X))))&
(?[X]:((~generous(X)&~calm(X))))&
(?[X]:(~curious(X)))&
((~quiet(susan)<~>~patient(susan))) | ~calm(alice) | [
"p0",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8976537686419964982592807
% SZS output start Proof for 8976537686419964982592807
1. ? [X0] : (~tall(X0) | calm(X0)) <=> (curious(susan) & quiet(susan)) [input p0]
9. ! [X0] : ((~creative(X0) | ~patient(X0)) => ~quiet(X0)) [input p8]
10. ! [X0] : ((~calm(X0) <~> calm(X0)) => (~quiet(X0) <~> ~creative(X0))) [input p9]
22. calm(alice) [input hypothesis]
26. ! [X0] : (~quiet(X0) | (creative(X0) & patient(X0))) [ennf transformation 9]
27. ! [X0] : ((~quiet(X0) <~> ~creative(X0)) | (~calm(X0) <=> calm(X0))) [ennf transformation 10]
31. (? [X0] : (~tall(X0) | calm(X0)) | (~curious(susan) | ~quiet(susan))) & ((curious(susan) & quiet(susan)) | ! [X0] : (tall(X0) & ~calm(X0))) [nnf transformation 1]
32. (? [X0] : (~tall(X0) | calm(X0)) | ~curious(susan) | ~quiet(susan)) & ((curious(susan) & quiet(susan)) | ! [X0] : (tall(X0) & ~calm(X0))) [flattening 31]
33. (? [X0] : (~tall(X0) | calm(X0)) | ~curious(susan) | ~quiet(susan)) & ((curious(susan) & quiet(susan)) | ! [X1] : (tall(X1) & ~calm(X1))) [rectify 32]
34. ? [X0] : (~tall(X0) | calm(X0)) => (~tall(sK0) | calm(sK0)) [choice axiom]
35. ((~tall(sK0) | calm(sK0)) | ~curious(susan) | ~quiet(susan)) & ((curious(susan) & quiet(susan)) | ! [X1] : (tall(X1) & ~calm(X1))) [skolemisation 33,34]
61. ! [X0] : (((creative(X0) | quiet(X0)) & (~creative(X0) | ~quiet(X0))) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0)))) [nnf transformation 27]
84. quiet(susan) | ~calm(X1) [cnf transformation 35]
122. ~quiet(X0) | creative(X0) [cnf transformation 26]
123. ~creative(X0) | ~quiet(X0) | calm(X0) | calm(X0) [cnf transformation 61]
124. ~creative(X0) | ~quiet(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 61]
125. creative(X0) | quiet(X0) | calm(X0) | calm(X0) [cnf transformation 61]
126. creative(X0) | quiet(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 61]
157. calm(alice) [cnf transformation 22]
158. ~creative(X0) | ~quiet(X0) | calm(X0) [duplicate literal removal 123]
159. ~creative(X0) | ~quiet(X0) | ~calm(X0) [duplicate literal removal 124]
160. creative(X0) | quiet(X0) | calm(X0) [duplicate literal removal 125]
161. creative(X0) | quiet(X0) | ~calm(X0) [duplicate literal removal 126]
163. 1 <=> quiet(susan) [avatar definition]
164. quiet(susan) <- (1) [avatar component clause 163]
184. 6 <=> ! [X1] : ~calm(X1) [avatar definition]
185. ~calm(X1) <- (6) [avatar component clause 184]
188. 6 | 1 [avatar split clause 84,163,184]
313. creative(X0) | ~calm(X0) [subsumption resolution 161,122]
314. creative(X0) | calm(X0) [subsumption resolution 160,122]
315. creative(X0) [subsumption resolution 314,313]
316. ~quiet(X0) | ~calm(X0) [subsumption resolution 159,315]
317. ~quiet(X0) | calm(X0) [subsumption resolution 158,315]
318. ~quiet(X0) [subsumption resolution 317,316]
357. $false <- (6) [resolution 185,157]
358. ~6 [avatar contradiction clause 357]
361. $false <- (1) [subsumption resolution 164,318]
362. ~1 [avatar contradiction clause 361]
363. $false [avatar sat refutation 188,358,362]
% SZS output end Proof for 8976537686419964982592807
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or tall is both not strong and funny. If fred is both rich and not creative then someone is not quiet or curious and vice versa. Everyone who is not strong is either not old or strong. Everyone who is not patient or creative is either not generous or not creative and vice versa. Everyone who is wise is brave or not wise and vice versa. If susan is calm then fred is not humble or not calm and vice versa. Everyone who is both generous and calm is brave or not calm and vice versa. If someone is not wise then john is not kind or not calm and vice versa. If someone is either not quiet or rich then mary is not generous and vice versa. Everyone who is both rich and kind is old. If someone is either quiet or tall then someone is either calm or not generous and vice versa. If someone is both not tall and not calm then susan is wise or not happy. Everyone who is not brave is either curious or tall. Someone is not quiet or not creative. Someone is kind or not old. Mary is not funny. Alice is not patient or not rich. Someone is either not tall or humble. Someone is brave or generous. Someone is either calm or creative. | Fred is creative. | contradiction | (![X]:((happy(X)<~>tall(X))=>(~strong(X)&funny(X))))&
(((rich(fred)&~creative(fred)))<=>(?[X]:((~quiet(X)|curious(X)))))&
(![X]:(~strong(X)=>(~old(X)<~>strong(X))))&
(![X]:((~patient(X)|creative(X))<=>(~generous(X)<~>~creative(X))))&
(![X]:(wise(X)<=>(brave(X)|~wise(X))))&
((calm(susan))<=>((~humble(fred)|~calm(fred))))&
(![X]:((generous(X)&calm(X))<=>(brave(X)|~calm(X))))&
((?[X]:(~wise(X)))<=>((~kind(john)|~calm(john))))&
((?[X]:((~quiet(X)<~>rich(X))))<=>(~generous(mary)))&
(![X]:((rich(X)&kind(X))=>old(X)))&
((?[X]:((quiet(X)<~>tall(X))))<=>(?[X]:((calm(X)<~>~generous(X)))))&
((?[X]:((~tall(X)&~calm(X))))=>((wise(susan)|~happy(susan))))&
(![X]:(~brave(X)=>(curious(X)<~>tall(X))))&
(?[X]:((~quiet(X)|~creative(X))))&
(?[X]:((kind(X)|~old(X))))&
(~funny(mary))&
((~patient(alice)|~rich(alice)))&
(?[X]:((~tall(X)<~>humble(X))))&
(?[X]:((brave(X)|generous(X))))&
(?[X]:((calm(X)<~>creative(X)))) | creative(fred) | [
"p3",
"p4",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8632421862255447534836121
% SZS output start Proof for 8632421862255447534836121
4. ! [X0] : ((creative(X0) | ~patient(X0)) <=> (~generous(X0) <~> ~creative(X0))) [input p3]
5. ! [X0] : (wise(X0) <=> (~wise(X0) | brave(X0))) [input p4]
7. ! [X0] : ((calm(X0) & generous(X0)) <=> (~calm(X0) | brave(X0))) [input p6]
21. creative(fred) [input hypothesis]
37. ! [X0] : (((creative(X0) | ~patient(X0)) | ((~generous(X0) | creative(X0)) & (~creative(X0) | generous(X0)))) & (((creative(X0) | generous(X0)) & (~creative(X0) | ~generous(X0))) | (~creative(X0) & patient(X0)))) [nnf transformation 4]
38. ! [X0] : ((creative(X0) | ~patient(X0) | ((~generous(X0) | creative(X0)) & (~creative(X0) | generous(X0)))) & (((creative(X0) | generous(X0)) & (~creative(X0) | ~generous(X0))) | (~creative(X0) & patient(X0)))) [flattening 37]
39. ! [X0] : ((wise(X0) | (wise(X0) & ~brave(X0))) & ((~wise(X0) | brave(X0)) | ~wise(X0))) [nnf transformation 5]
40. ! [X0] : ((wise(X0) | (wise(X0) & ~brave(X0))) & (~wise(X0) | brave(X0) | ~wise(X0))) [flattening 39]
43. ! [X0] : (((calm(X0) & generous(X0)) | (calm(X0) & ~brave(X0))) & ((~calm(X0) | brave(X0)) | (~calm(X0) | ~generous(X0)))) [nnf transformation 7]
44. ! [X0] : (((calm(X0) & generous(X0)) | (calm(X0) & ~brave(X0))) & (~calm(X0) | brave(X0) | ~calm(X0) | ~generous(X0))) [flattening 43]
84. ~creative(X0) | ~generous(X0) | ~creative(X0) [cnf transformation 38]
89. ~wise(X0) | brave(X0) | ~wise(X0) [cnf transformation 40]
91. wise(X0) | wise(X0) [cnf transformation 40]
96. generous(X0) | ~brave(X0) [cnf transformation 44]
128. creative(fred) [cnf transformation 21]
131. ~wise(X0) | brave(X0) [duplicate literal removal 89]
132. wise(X0) [duplicate literal removal 91]
133. ~generous(X0) | ~creative(X0) [duplicate literal removal 84]
140. 2 <=> creative(fred) [avatar definition]
141. creative(fred) <- (2) [avatar component clause 140]
163. brave(X0) [subsumption resolution 131,132]
179. generous(X0) [subsumption resolution 96,163]
235. 2 [avatar split clause 128,140]
238. ~creative(X0) [resolution 133,179]
239. $false <- (2) [resolution 238,141]
240. ~2 [avatar contradiction clause 239]
241. $false [avatar sat refutation 235,240]
% SZS output end Proof for 8632421862255447534836121
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or happy is kind and vice versa. If alice is both tall and rich then someone is brave or generous. Everyone who is both not quiet and not funny is calm. If mary is either not brave or brave then someone is either brave or not calm. If someone is both generous and not strong then someone is strong or curious and vice versa. If someone is not quiet or patient then mary is kind. Everyone who is either not generous or creative is funny and vice versa. Everyone who is either not strong or kind is both not generous and old and vice versa. Everyone who is either kind or curious is either rich or not patient and vice versa. Everyone who is tall is either not strong or happy and vice versa. If someone is wise then someone is not calm or curious. If alice is either not old or not patient then fred is old or not generous and vice versa. If john is not calm or kind then paul is old or calm. Everyone who is happy is both funny and not old. Everyone who is humble is either strong or not patient. Everyone who is either not happy or brave is not old or funny and vice versa. Fred is either tall or not old. Someone is kind. Someone is happy or patient. Someone is brave or not strong. Someone is both not humble and funny. Susan is both creative and not strong. Someone is not calm. Someone is not old. | Susan is brave. | entailment | (![X]:((~tall(X)|happy(X))<=>kind(X)))&
(((tall(alice)&rich(alice)))=>(?[X]:((brave(X)|generous(X)))))&
(![X]:((~quiet(X)&~funny(X))=>calm(X)))&
(((~brave(mary)<~>brave(mary)))=>(?[X]:((brave(X)<~>~calm(X)))))&
((?[X]:((generous(X)&~strong(X))))<=>(?[X]:((strong(X)|curious(X)))))&
((?[X]:((~quiet(X)|patient(X))))=>(kind(mary)))&
(![X]:((~generous(X)<~>creative(X))<=>funny(X)))&
(![X]:((~strong(X)<~>kind(X))<=>(~generous(X)&old(X))))&
(![X]:((kind(X)<~>curious(X))<=>(rich(X)<~>~patient(X))))&
(![X]:(tall(X)<=>(~strong(X)<~>happy(X))))&
((?[X]:(wise(X)))=>(?[X]:((~calm(X)|curious(X)))))&
(((~old(alice)<~>~patient(alice)))<=>((old(fred)|~generous(fred))))&
(((~calm(john)|kind(john)))=>((old(paul)|calm(paul))))&
(![X]:(happy(X)=>(funny(X)&~old(X))))&
(![X]:(humble(X)=>(strong(X)<~>~patient(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~old(X)|funny(X))))&
((tall(fred)<~>~old(fred)))&
(?[X]:(kind(X)))&
(?[X]:((happy(X)|patient(X))))&
(?[X]:((brave(X)|~strong(X))))&
(?[X]:((~humble(X)&funny(X))))&
((creative(susan)&~strong(susan)))&
(?[X]:(~calm(X)))&
(?[X]:(~old(X))) | brave(susan) | [
"p0",
"p6",
"p7",
"p9",
"p13",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8534252708938945710201544
% SZS output start Proof for 8534252708938945710201544
1. ! [X0] : ((happy(X0) | ~tall(X0)) <=> kind(X0)) [input p0]
7. ! [X0] : ((~generous(X0) <~> creative(X0)) <=> funny(X0)) [input p6]
8. ! [X0] : ((~strong(X0) <~> kind(X0)) <=> (old(X0) & ~generous(X0))) [input p7]
10. ! [X0] : (tall(X0) <=> (~strong(X0) <~> happy(X0))) [input p9]
14. ! [X0] : (happy(X0) => (~old(X0) & funny(X0))) [input p13]
16. ! [X0] : ((~happy(X0) <~> brave(X0)) <=> (funny(X0) | ~old(X0))) [input p15]
22. ~strong(susan) & creative(susan) [input p21]
25. ~brave(susan) [input hypothesis]
39. ! [X0] : ((~old(X0) & funny(X0)) | ~happy(X0)) [ennf transformation 14]
40. ! [X0] : (((happy(X0) | ~tall(X0)) | ~kind(X0)) & (kind(X0) | (~happy(X0) & tall(X0)))) [nnf transformation 1]
41. ! [X0] : ((happy(X0) | ~tall(X0) | ~kind(X0)) & (kind(X0) | (~happy(X0) & tall(X0)))) [flattening 40]
52. ! [X0] : ((((~creative(X0) | generous(X0)) & (creative(X0) | ~generous(X0))) | ~funny(X0)) & (funny(X0) | ((~generous(X0) | ~creative(X0)) & (creative(X0) | generous(X0))))) [nnf transformation 7]
53. ! [X0] : ((((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | (~old(X0) | generous(X0))) & ((old(X0) & ~generous(X0)) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))))) [nnf transformation 8]
54. ! [X0] : ((((~kind(X0) | strong(X0)) & (kind(X0) | ~strong(X0))) | ~old(X0) | generous(X0)) & ((old(X0) & ~generous(X0)) | ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))))) [flattening 53]
56. ! [X0] : ((tall(X0) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0)))) & (((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | ~tall(X0))) [nnf transformation 10]
59. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) & old(X0))) & ((funny(X0) | ~old(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [nnf transformation 16]
60. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) & old(X0))) & (funny(X0) | ~old(X0) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [flattening 59]
74. kind(X0) | tall(X0) [cnf transformation 41]
76. ~kind(X0) | ~tall(X0) | happy(X0) [cnf transformation 41]
91. ~creative(X0) | generous(X0) | ~funny(X0) [cnf transformation 52]
92. ~generous(X0) | kind(X0) | strong(X0) [cnf transformation 54]
93. ~strong(X0) | ~generous(X0) | ~kind(X0) [cnf transformation 54]
94. old(X0) | kind(X0) | strong(X0) [cnf transformation 54]
106. ~strong(X0) | happy(X0) | ~tall(X0) [cnf transformation 56]
108. strong(X0) | happy(X0) | tall(X0) [cnf transformation 56]
118. ~happy(X0) | funny(X0) [cnf transformation 39]
120. funny(X0) | ~old(X0) | brave(X0) | happy(X0) [cnf transformation 60]
123. brave(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 60]
132. creative(susan) [cnf transformation 22]
133. ~strong(susan) [cnf transformation 22]
136. ~brave(susan) [cnf transformation 25]
252. ~happy(X0) | brave(X0) [subsumption resolution 123,118]
253. ~old(X0) | funny(X0) | brave(X0) [subsumption resolution 120,252]
306. 32 <=> funny(susan) [avatar definition]
307. ~funny(susan) <- (~32) [avatar component clause 306]
310. 33 <=> generous(susan) [avatar definition]
311. generous(susan) <- (33) [avatar component clause 310]
334. generous(susan) | ~funny(susan) [resolution 91,132]
432. happy(X2) | tall(X2) | ~generous(X2) | ~kind(X2) [resolution 108,93]
434. happy(susan) | tall(susan) [resolution 108,133]
440. ~generous(X2) | happy(X2) | ~kind(X2) [subsumption resolution 432,76]
443. 53 <=> tall(susan) [avatar definition]
445. tall(susan) <- (53) [avatar component clause 443]
447. 54 <=> happy(susan) [avatar definition]
449. happy(susan) <- (54) [avatar component clause 447]
450. 53 | 54 [avatar split clause 434,447,443]
508. strong(X0) | brave(X0) | kind(X0) | funny(X0) [resolution 253,94]
624. brave(X1) | kind(X1) | funny(X1) | happy(X1) | ~tall(X1) [resolution 508,106]
632. brave(X1) | kind(X1) | funny(X1) | happy(X1) [subsumption resolution 624,74]
633. funny(X1) | kind(X1) | brave(X1) [subsumption resolution 632,252]
820. kind(susan) | brave(susan) <- (~32) [resolution 633,307]
821. kind(susan) <- (~32) [subsumption resolution 820,136]
845. ~tall(susan) | happy(susan) <- (~32) [resolution 821,76]
851. happy(susan) <- (~32, 53) [subsumption resolution 845,445]
852. 54 | 32 | ~53 [avatar split clause 851,443,306,447]
853. ~32 | 33 [avatar split clause 334,310,306]
856. happy(susan) | ~kind(susan) <- (33) [resolution 311,440]
857. kind(susan) | strong(susan) <- (33) [resolution 311,92]
859. 91 <=> kind(susan) [avatar definition]
862. ~91 | 54 | ~33 [avatar split clause 856,310,447,859]
863. kind(susan) <- (33) [subsumption resolution 857,133]
864. 91 | ~33 [avatar split clause 863,310,859]
866. brave(susan) <- (54) [resolution 449,252]
872. $false <- (54) [subsumption resolution 866,136]
873. ~54 [avatar contradiction clause 872]
874. $false [avatar sat refutation 450,852,853,862,864,873]
% SZS output end Proof for 8534252708938945710201544
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If mary is curious or not brave then someone is tall or old.
Everyone who is either not brave or not quiet is either not strong or not funny.
Everyone who is not strong is either not quiet or funny and vice versa.
If alice is either calm or happy then mary is both tall and strong and vice versa.
If someone is not rich or brave then alice is not patient or not humble.
Everyone who is rich is both kind and not humble and vice versa.
If paul is wise or kind then alice is both funny and not generous and vice versa.
If fred is not generous then someone is not rich or not old and vice versa.
If alice is both brave and not curious then alice is both brave and not creative.
If someone is not rich then someone is either funny or not rich.
If paul is strong then john is humble and vice versa.
If someone is patient then someone is either creative or not patient and vice versa.
Everyone who is strong or not calm is generous.
If susan is quiet or strong then someone is not strong or rich.
If john is tall or humble then someone is both brave and curious.
Everyone who is both not strong and old is either not old or not curious.
Someone is curious or not old.
Paul is both not patient and not brave.
Lucy is funny or happy.
Paul is either funny or quiet.
Paul is creative or not humble.
Someone is both humble and generous.
Someone is old. | John is rich. | contradiction | (((curious(mary)|~brave(mary)))=>(?[X]:((tall(X)|old(X)))))&
(![X]:((~brave(X)<~>~quiet(X))=>(~strong(X)<~>~funny(X))))&
(![X]:(~strong(X)<=>(~quiet(X)<~>funny(X))))&
(((calm(alice)<~>happy(alice)))<=>((tall(mary)&strong(mary))))&
((?[X]:((~rich(X)|brave(X))))=>((~patient(alice)|~humble(alice))))&
(![X]:(rich(X)<=>(kind(X)&~humble(X))))&
(((wise(paul)|kind(paul)))<=>((funny(alice)&~generous(alice))))&
((~generous(fred))<=>(?[X]:((~rich(X)|~old(X)))))&
(((brave(alice)&~curious(alice)))=>((brave(alice)&~creative(alice))))&
((?[X]:(~rich(X)))=>(?[X]:((funny(X)<~>~rich(X)))))&
((strong(paul))<=>(humble(john)))&
((?[X]:(patient(X)))<=>(?[X]:((creative(X)<~>~patient(X)))))&
(![X]:((strong(X)|~calm(X))=>generous(X)))&
(((quiet(susan)|strong(susan)))=>(?[X]:((~strong(X)|rich(X)))))&
(((tall(john)|humble(john)))=>(?[X]:((brave(X)&curious(X)))))&
(![X]:((~strong(X)&old(X))=>(~old(X)<~>~curious(X))))&
(?[X]:((curious(X)|~old(X))))&
((~patient(paul)&~brave(paul)))&
((funny(lucy)|happy(lucy)))&
((funny(paul)<~>quiet(paul)))&
((creative(paul)|~humble(paul)))&
(?[X]:((humble(X)&generous(X))))&
(?[X]:(old(X))) | rich(john) | [
"p2",
"p5",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3263378808753832983451247
% SZS output start Proof for 3263378808753832983451247
3. ! [X0] : (~strong(X0) <=> (~quiet(X0) <~> funny(X0))) [input p2]
6. ! [X0] : (rich(X0) <=> (~humble(X0) & kind(X0))) [input p5]
11. strong(paul) <=> humble(john) [input p10]
20. funny(paul) <~> quiet(paul) [input p19]
24. rich(john) [input hypothesis]
42. ! [X0] : ((~strong(X0) | ((~quiet(X0) | ~funny(X0)) & (funny(X0) | quiet(X0)))) & (((~funny(X0) | quiet(X0)) & (funny(X0) | ~quiet(X0))) | strong(X0))) [nnf transformation 3]
45. ! [X0] : ((rich(X0) | (humble(X0) | ~kind(X0))) & ((~humble(X0) & kind(X0)) | ~rich(X0))) [nnf transformation 6]
46. ! [X0] : ((rich(X0) | humble(X0) | ~kind(X0)) & ((~humble(X0) & kind(X0)) | ~rich(X0))) [flattening 45]
57. (strong(paul) | ~humble(john)) & (humble(john) | ~strong(paul)) [nnf transformation 11]
70. (~quiet(paul) | ~funny(paul)) & (quiet(paul) | funny(paul)) [nnf transformation 20]
81. ~quiet(X0) | funny(X0) | strong(X0) [cnf transformation 42]
82. ~funny(X0) | quiet(X0) | strong(X0) [cnf transformation 42]
94. ~humble(X0) | ~rich(X0) [cnf transformation 46]
108. humble(john) | ~strong(paul) [cnf transformation 57]
128. quiet(paul) | funny(paul) [cnf transformation 70]
129. ~quiet(paul) | ~funny(paul) [cnf transformation 70]
134. rich(john) [cnf transformation 24]
255. 26 <=> humble(john) [avatar definition]
256. humble(john) <- (26) [avatar component clause 255]
259. 27 <=> strong(paul) [avatar definition]
260. ~strong(paul) <- (~27) [avatar component clause 259]
263. ~27 | 26 [avatar split clause 108,255,259]
342. 45 <=> funny(paul) [avatar definition]
343. funny(paul) <- (45) [avatar component clause 342]
344. ~funny(paul) <- (~45) [avatar component clause 342]
346. 46 <=> quiet(paul) [avatar definition]
347. quiet(paul) <- (46) [avatar component clause 346]
348. ~quiet(paul) <- (~46) [avatar component clause 346]
349. ~45 | ~46 [avatar split clause 129,346,342]
350. 45 | 46 [avatar split clause 128,346,342]
369. quiet(paul) | strong(paul) <- (45) [resolution 82,343]
379. strong(paul) <- (45, ~46) [subsumption resolution 369,348]
382. 27 | ~45 | 46 [avatar split clause 379,346,342,259]
383. ~rich(john) <- (26) [resolution 256,94]
384. $false <- (26) [subsumption resolution 383,134]
385. ~26 [avatar contradiction clause 384]
386. funny(paul) | strong(paul) <- (46) [resolution 347,81]
387. strong(paul) <- (~45, 46) [subsumption resolution 386,344]
388. $false <- (~27, ~45, 46) [subsumption resolution 387,260]
389. 27 | 45 | ~46 [avatar contradiction clause 388]
390. $false [avatar sat refutation 263,349,350,382,385,389]
% SZS output end Proof for 3263378808753832983451247
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is either not patient or strong is not brave or patient.
Everyone who is calm or not kind is kind and vice versa.
Everyone who is both not kind and humble is old or happy and vice versa.
If someone is calm then john is curious or brave.
If someone is not quiet then alice is happy or not generous and vice versa.
If someone is old then alice is either not patient or not strong and vice versa.
If someone is not kind or not happy then someone is kind.
If someone is not humble or not happy then fred is calm or funny.
Everyone who is rich or kind is not wise or patient and vice versa.
Everyone who is not wise or not funny is either not old or rich.
If someone is not wise or humble then alice is not quiet.
Everyone who is generous is not curious or strong and vice versa.
If someone is both brave and curious then john is not patient and vice versa.
Everyone who is patient or funny is either not quiet or tall and vice versa.
Everyone who is wise or not curious is both funny and generous.
Mary is either not wise or not tall.
Someone is strong.
Someone is either curious or patient.
Someone is not old or patient.
Someone is either not brave or creative.
Fred is either funny or not generous. | John is old. | contradiction | (![X]:((~patient(X)<~>strong(X))=>(~brave(X)|patient(X))))&
(![X]:((calm(X)|~kind(X))<=>kind(X)))&
(![X]:((~kind(X)&humble(X))<=>(old(X)|happy(X))))&
((?[X]:(calm(X)))=>((curious(john)|brave(john))))&
((?[X]:(~quiet(X)))<=>((happy(alice)|~generous(alice))))&
((?[X]:(old(X)))<=>((~patient(alice)<~>~strong(alice))))&
((?[X]:((~kind(X)|~happy(X))))=>(?[X]:(kind(X))))&
((?[X]:((~humble(X)|~happy(X))))=>((calm(fred)|funny(fred))))&
(![X]:((rich(X)|kind(X))<=>(~wise(X)|patient(X))))&
(![X]:((~wise(X)|~funny(X))=>(~old(X)<~>rich(X))))&
((?[X]:((~wise(X)|humble(X))))=>(~quiet(alice)))&
(![X]:(generous(X)<=>(~curious(X)|strong(X))))&
((?[X]:((brave(X)&curious(X))))<=>(~patient(john)))&
(![X]:((patient(X)|funny(X))<=>(~quiet(X)<~>tall(X))))&
(![X]:((wise(X)|~curious(X))=>(funny(X)&generous(X))))&
((~wise(mary)<~>~tall(mary)))&
(?[X]:(strong(X)))&
(?[X]:((curious(X)<~>patient(X))))&
(?[X]:((~old(X)|patient(X))))&
(?[X]:((~brave(X)<~>creative(X))))&
((funny(fred)<~>~generous(fred))) | old(john) | [
"p1",
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 5729676449926802867909478
% SZS output start Proof for 5729676449926802867909478
2. ! [X0] : ((~kind(X0) | calm(X0)) <=> kind(X0)) [input p1]
3. ! [X0] : ((humble(X0) & ~kind(X0)) <=> (happy(X0) | old(X0))) [input p2]
22. old(john) [input hypothesis]
35. ! [X0] : (((~kind(X0) | calm(X0)) | ~kind(X0)) & (kind(X0) | (kind(X0) & ~calm(X0)))) [nnf transformation 2]
36. ! [X0] : ((~kind(X0) | calm(X0) | ~kind(X0)) & (kind(X0) | (kind(X0) & ~calm(X0)))) [flattening 35]
37. ! [X0] : (((humble(X0) & ~kind(X0)) | (~happy(X0) & ~old(X0))) & ((happy(X0) | old(X0)) | (~humble(X0) | kind(X0)))) [nnf transformation 3]
38. ! [X0] : (((humble(X0) & ~kind(X0)) | (~happy(X0) & ~old(X0))) & (happy(X0) | old(X0) | ~humble(X0) | kind(X0))) [flattening 37]
77. kind(X0) | kind(X0) [cnf transformation 36]
80. ~kind(X0) | ~old(X0) [cnf transformation 38]
132. old(john) [cnf transformation 22]
133. kind(X0) [duplicate literal removal 77]
137. ~old(X0) [subsumption resolution 80,133]
259. $false [subsumption resolution 132,137]
% SZS output end Proof for 5729676449926802867909478
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy then someone is either patient or not patient. If someone is both not brave and rich then susan is either not wise or strong and vice versa. Everyone who is either not brave or kind is not strong. If someone is not quiet then alice is both wise and kind. If alice is either not quiet or funny then someone is either not kind or creative. Everyone who is not brave is both not strong and not wise. If someone is tall or not tall then someone is not curious or not strong. Everyone who is not quiet or quiet is both kind and not brave and vice versa. Everyone who is both patient and not strong is both generous and not strong. If someone is either quiet or curious then someone is both curious and rich and vice versa. If someone is not curious then mary is tall and vice versa. Everyone who is generous is not happy and vice versa. If alice is patient then lucy is quiet and vice versa. If lucy is either patient or calm then paul is calm and vice versa. If alice is both not happy and quiet then lucy is both creative and calm. John is either not happy or calm. Mary is either calm or curious. Someone is both not strong and old. Someone is happy. Someone is curious or not curious. | Paul is happy. | neutral | ((?[X]:((funny(X)<~>happy(X))))=>(?[X]:((patient(X)<~>~patient(X)))))&
((?[X]:((~brave(X)&rich(X))))<=>((~wise(susan)<~>strong(susan))))&
(![X]:((~brave(X)<~>kind(X))=>~strong(X)))&
((?[X]:(~quiet(X)))=>((wise(alice)&kind(alice))))&
(((~quiet(alice)<~>funny(alice)))=>(?[X]:((~kind(X)<~>creative(X)))))&
(![X]:(~brave(X)=>(~strong(X)&~wise(X))))&
((?[X]:((tall(X)|~tall(X))))=>(?[X]:((~curious(X)|~strong(X)))))&
(![X]:((~quiet(X)|quiet(X))<=>(kind(X)&~brave(X))))&
(![X]:((patient(X)&~strong(X))=>(generous(X)&~strong(X))))&
((?[X]:((quiet(X)<~>curious(X))))<=>(?[X]:((curious(X)&rich(X)))))&
((?[X]:(~curious(X)))<=>(tall(mary)))&
(![X]:(generous(X)<=>~happy(X)))&
((patient(alice))<=>(quiet(lucy)))&
(((patient(lucy)<~>calm(lucy)))<=>(calm(paul)))&
(((~happy(alice)&quiet(alice)))=>((creative(lucy)&calm(lucy))))&
((~happy(john)<~>calm(john)))&
((calm(mary)<~>curious(mary)))&
(?[X]:((~strong(X)&old(X))))&
(?[X]:(happy(X)))&
(?[X]:((curious(X)|~curious(X)))) | happy(paul) | [] | null | 0 |
Everyone who is both funny and not creative is both not quiet and not funny and vice versa. Everyone who is not kind is either not old or not brave and vice versa. Everyone who is happy or not patient is either not kind or not quiet. Everyone who is quiet or not funny is not creative. Everyone who is happy is kind and vice versa. Everyone who is not happy is not rich and vice versa. If someone is not rich or not old then someone is creative or not happy. If someone is not old or not patient then paul is wise. Everyone who is not creative is either not kind or quiet and vice versa. If someone is funny or not old then someone is either tall or happy. If someone is either not rich or wise then someone is not patient. Everyone who is calm is curious or generous. Everyone who is quiet or rich is either not wise or happy. Everyone who is calm is either funny or not curious and vice versa. Someone is not curious. Someone is brave or strong. Lucy is curious. Fred is calm. Susan is curious or not strong. John is not humble. | John is not kind. | contradiction | (![X]:((funny(X)&~creative(X))<=>(~quiet(X)&~funny(X))))&
(![X]:(~kind(X)<=>(~old(X)<~>~brave(X))))&
(![X]:((happy(X)|~patient(X))=>(~kind(X)<~>~quiet(X))))&
(![X]:((quiet(X)|~funny(X))=>~creative(X)))&
(![X]:(happy(X)<=>kind(X)))&
(![X]:(~happy(X)<=>~rich(X)))&
((?[X]:((~rich(X)|~old(X))))=>(?[X]:((creative(X)|~happy(X)))))&
((?[X]:((~old(X)|~patient(X))))=>(wise(paul)))&
(![X]:(~creative(X)<=>(~kind(X)<~>quiet(X))))&
((?[X]:((funny(X)|~old(X))))=>(?[X]:((tall(X)<~>happy(X)))))&
((?[X]:((~rich(X)<~>wise(X))))=>(?[X]:(~patient(X))))&
(![X]:(calm(X)=>(curious(X)|generous(X))))&
(![X]:((quiet(X)|rich(X))=>(~wise(X)<~>happy(X))))&
(![X]:(calm(X)<=>(funny(X)<~>~curious(X))))&
(?[X]:(~curious(X)))&
(?[X]:((brave(X)|strong(X))))&
(curious(lucy))&
(calm(fred))&
((curious(susan)|~strong(susan)))&
(~humble(john)) | ~kind(john) | [
"p0",
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4969754429690111101809630
% SZS output start Proof for 4969754429690111101809630
1. ! [X0] : ((~creative(X0) & funny(X0)) <=> (~funny(X0) & ~quiet(X0))) [input p0]
4. ! [X0] : ((~funny(X0) | quiet(X0)) => ~creative(X0)) [input p3]
9. ! [X0] : (~creative(X0) <=> (~kind(X0) <~> quiet(X0))) [input p8]
21. ~kind(john) [input hypothesis]
29. ! [X0] : (~creative(X0) | (funny(X0) & ~quiet(X0))) [ennf transformation 4]
36. ! [X0] : (((~creative(X0) & funny(X0)) | (funny(X0) | quiet(X0))) & ((~funny(X0) & ~quiet(X0)) | (creative(X0) | ~funny(X0)))) [nnf transformation 1]
37. ! [X0] : (((~creative(X0) & funny(X0)) | funny(X0) | quiet(X0)) & ((~funny(X0) & ~quiet(X0)) | creative(X0) | ~funny(X0))) [flattening 36]
45. ! [X0] : ((~creative(X0) | ((~kind(X0) | ~quiet(X0)) & (quiet(X0) | kind(X0)))) & (((~quiet(X0) | kind(X0)) & (quiet(X0) | ~kind(X0))) | creative(X0))) [nnf transformation 9]
61. ~funny(X0) | creative(X0) | ~funny(X0) [cnf transformation 37]
62. funny(X0) | funny(X0) | quiet(X0) [cnf transformation 37]
72. ~quiet(X0) | ~creative(X0) [cnf transformation 29]
83. ~quiet(X0) | kind(X0) | creative(X0) [cnf transformation 45]
84. ~creative(X0) | quiet(X0) | kind(X0) [cnf transformation 45]
103. ~kind(john) [cnf transformation 21]
104. ~funny(X0) | creative(X0) [duplicate literal removal 61]
105. quiet(X0) | funny(X0) [duplicate literal removal 62]
131. ~creative(X0) | kind(X0) [subsumption resolution 84,72]
132. ~quiet(X0) | kind(X0) [subsumption resolution 83,131]
180. kind(X0) | funny(X0) [resolution 132,105]
181. funny(john) [resolution 180,103]
183. creative(john) [resolution 181,104]
197. kind(john) [resolution 183,131]
199. $false [subsumption resolution 197,103]
% SZS output end Proof for 4969754429690111101809630
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and not rich is both old and generous. If alice is not patient then alice is both not wise and quiet and vice versa. If someone is not rich or creative then john is patient and vice versa. Everyone who is not quiet or not creative is not patient or generous. If someone is not happy then paul is rich. Everyone who is not quiet is both not strong and not funny. Everyone who is both not funny and not kind is creative or patient. Everyone who is not brave is not generous. If susan is rich then fred is calm or creative and vice versa. If someone is not strong then someone is both not funny and not quiet. If susan is not humble or old then susan is both not kind and not patient and vice versa. If someone is both not generous and not creative then susan is generous or not funny and vice versa. Everyone who is funny is either not kind or not curious and vice versa. Everyone who is not creative is either happy or calm. If someone is not wise then someone is funny. If paul is not creative or not quiet then alice is not rich and vice versa. Fred is tall. Someone is wise or kind. Susan is either generous or quiet. Susan is funny. Fred is not funny. Alice is not brave. Someone is kind or not old. John is not humble or curious. | Susan is not quiet. | contradiction | (![X]:((~generous(X)&~rich(X))=>(old(X)&generous(X))))&
((~patient(alice))<=>((~wise(alice)&quiet(alice))))&
((?[X]:((~rich(X)|creative(X))))<=>(patient(john)))&
(![X]:((~quiet(X)|~creative(X))=>(~patient(X)|generous(X))))&
((?[X]:(~happy(X)))=>(rich(paul)))&
(![X]:(~quiet(X)=>(~strong(X)&~funny(X))))&
(![X]:((~funny(X)&~kind(X))=>(creative(X)|patient(X))))&
(![X]:(~brave(X)=>~generous(X)))&
((rich(susan))<=>((calm(fred)|creative(fred))))&
((?[X]:(~strong(X)))=>(?[X]:((~funny(X)&~quiet(X)))))&
(((~humble(susan)|old(susan)))<=>((~kind(susan)&~patient(susan))))&
((?[X]:((~generous(X)&~creative(X))))<=>((generous(susan)|~funny(susan))))&
(![X]:(funny(X)<=>(~kind(X)<~>~curious(X))))&
(![X]:(~creative(X)=>(happy(X)<~>calm(X))))&
((?[X]:(~wise(X)))=>(?[X]:(funny(X))))&
(((~creative(paul)|~quiet(paul)))<=>(~rich(alice)))&
(tall(fred))&
(?[X]:((wise(X)|kind(X))))&
((generous(susan)<~>quiet(susan)))&
(funny(susan))&
(~funny(fred))&
(~brave(alice))&
(?[X]:((kind(X)|~old(X))))&
((~humble(john)|curious(john))) | ~quiet(susan) | [
"p5",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7178163970925160253585706
% SZS output start Proof for 7178163970925160253585706
6. ! [X0] : (~quiet(X0) => (~funny(X0) & ~strong(X0))) [input p5]
20. funny(susan) [input p19]
25. ~quiet(susan) [input hypothesis]
34. ! [X0] : ((~funny(X0) & ~strong(X0)) | quiet(X0)) [ennf transformation 6]
83. ~funny(X0) | quiet(X0) [cnf transformation 34]
114. funny(susan) [cnf transformation 20]
119. ~quiet(susan) [cnf transformation 25]
215. 21 <=> funny(susan) [avatar definition]
217. funny(susan) <- (21) [avatar component clause 215]
271. 33 <=> quiet(susan) [avatar definition]
273. ~quiet(susan) <- (~33) [avatar component clause 271]
276. 21 [avatar split clause 114,215]
295. ~33 [avatar split clause 119,271]
298. quiet(susan) <- (21) [resolution 83,217]
300. $false <- (21, ~33) [subsumption resolution 298,273]
301. ~21 | 33 [avatar contradiction clause 300]
302. $false [avatar sat refutation 276,295,301]
% SZS output end Proof for 7178163970925160253585706
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not quiet or not curious then fred is both curious and not tall.
If mary is both not funny and not creative then someone is either patient or not creative and vice versa.
If someone is both not creative and curious then someone is both calm and not rich and vice versa.
Everyone who is either not tall or brave is not humble.
If fred is not happy then fred is either wise or funny.
If john is either not calm or not humble then someone is either not creative or not happy.
If lucy is either rich or strong then alice is either not generous or not old and vice versa.
Everyone who is both funny and patient is both not brave and not patient.
Everyone who is either old or rich is either calm or kind and vice versa.
If mary is either not funny or kind then john is not old.
Everyone who is not wise or humble is either wise or not funny.
Everyone who is either not old or quiet is strong.
Everyone who is brave or not tall is wise and vice versa.
Everyone who is curious is both not creative and creative.
If someone is not old or not patient then mary is both kind and tall and vice versa.
Everyone who is quiet is either creative or not happy and vice versa.
Someone is both tall and rich.
Someone is either generous or wise.
Someone is both patient and not wise.
Someone is not rich.
Someone is kind.
Paul is not wise or patient.
Alice is both creative and calm.
Someone is both old and not wise. | Lucy is quiet. | contradiction | ((?[X]:((~quiet(X)<~>~curious(X))))=>((curious(fred)&~tall(fred))))&
(((~funny(mary)&~creative(mary)))<=>(?[X]:((patient(X)<~>~creative(X)))))&
((?[X]:((~creative(X)&curious(X))))<=>(?[X]:((calm(X)&~rich(X)))))&
(![X]:((~tall(X)<~>brave(X))=>~humble(X)))&
((~happy(fred))=>((wise(fred)<~>funny(fred))))&
(((~calm(john)<~>~humble(john)))=>(?[X]:((~creative(X)<~>~happy(X)))))&
(((rich(lucy)<~>strong(lucy)))<=>((~generous(alice)<~>~old(alice))))&
(![X]:((funny(X)&patient(X))=>(~brave(X)&~patient(X))))&
(![X]:((old(X)<~>rich(X))<=>(calm(X)<~>kind(X))))&
(((~funny(mary)<~>kind(mary)))=>(~old(john)))&
(![X]:((~wise(X)|humble(X))=>(wise(X)<~>~funny(X))))&
(![X]:((~old(X)<~>quiet(X))=>strong(X)))&
(![X]:((brave(X)|~tall(X))<=>wise(X)))&
(![X]:(curious(X)=>(~creative(X)&creative(X))))&
((?[X]:((~old(X)|~patient(X))))<=>((kind(mary)&tall(mary))))&
(![X]:(quiet(X)<=>(creative(X)<~>~happy(X))))&
(?[X]:((tall(X)&rich(X))))&
(?[X]:((generous(X)<~>wise(X))))&
(?[X]:((patient(X)&~wise(X))))&
(?[X]:(~rich(X)))&
(?[X]:(kind(X)))&
((~wise(paul)|patient(paul)))&
((creative(alice)&calm(alice)))&
(?[X]:((old(X)&~wise(X)))) | quiet(lucy) | [
"p0",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2679987082869059583830593
% SZS output start Proof for 2679987082869059583830593
1. ? [X0] : (~quiet(X0) <~> ~curious(X0)) => (~tall(fred) & curious(fred)) [input p0]
14. ! [X0] : (curious(X0) => (creative(X0) & ~creative(X0))) [input p13]
25. quiet(lucy) [input hypothesis]
27. (~tall(fred) & curious(fred)) | ! [X0] : (~quiet(X0) <=> ~curious(X0)) [ennf transformation 1]
36. ! [X0] : ((creative(X0) & ~creative(X0)) | ~curious(X0)) [ennf transformation 14]
37. (~tall(fred) & curious(fred)) | ! [X0] : ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0))) [nnf transformation 27]
80. curious(fred) | ~quiet(X0) | curious(X0) [cnf transformation 37]
130. ~creative(X0) | ~curious(X0) [cnf transformation 36]
131. creative(X0) | ~curious(X0) [cnf transformation 36]
154. quiet(lucy) [cnf transformation 25]
158. 1 <=> ! [X0] : (~quiet(X0) | curious(X0)) [avatar definition]
159. ~quiet(X0) | curious(X0) <- (1) [avatar component clause 158]
170. 4 <=> curious(fred) [avatar definition]
172. curious(fred) <- (4) [avatar component clause 170]
173. 1 | 4 [avatar split clause 80,170,158]
217. 14 <=> ! [X3] : (~curious(X3) | creative(X3)) [avatar definition]
218. ~curious(X3) | creative(X3) <- (14) [avatar component clause 217]
297. 14 [avatar split clause 131,217]
340. ~curious(X3) <- (14) [subsumption resolution 218,130]
341. $false <- (4, 14) [subsumption resolution 172,340]
342. ~4 | ~14 [avatar contradiction clause 341]
343. ~quiet(X0) <- (1, 14) [subsumption resolution 159,340]
344. $false <- (1, 14) [resolution 343,154]
345. ~1 | ~14 [avatar contradiction clause 344]
346. $false [avatar sat refutation 173,297,342,345]
% SZS output end Proof for 2679987082869059583830593
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either generous or wise then someone is not calm and vice versa.
Everyone who is both strong and humble is funny or not brave and vice versa.
Everyone who is not tall or not patient is both strong and not happy.
Everyone who is either not brave or happy is either not brave or curious.
Everyone who is not quiet is not kind or not brave.
If someone is not curious or rich then lucy is not humble and vice versa.
Everyone who is both not happy and not wise is not patient.
If someone is happy or old then john is not rich or not patient.
Everyone who is calm or not generous is either quiet or not generous and vice versa.
Everyone who is humble or not funny is wise and vice versa.
If lucy is either wise or not curious then mary is both not generous and not funny.
Everyone who is either not curious or not humble is not quiet and vice versa.
Everyone who is either rich or not happy is either not patient or rich.
Everyone who is both not curious and not kind is both tall and funny.
Everyone who is either tall or calm is not strong or not creative.
Everyone who is generous or funny is not old or not tall.
Mary is either quiet or not quiet.
Someone is not strong or not humble.
Lucy is both strong and creative.
Someone is either not happy or not curious.
John is both rich and not kind.
Someone is both not quiet and not patient.
Mary is both wise and creative.
Someone is either not tall or quiet. | Mary is not generous. | neutral | ((?[X]:((generous(X)<~>wise(X))))<=>(?[X]:(~calm(X))))&
(![X]:((strong(X)&humble(X))<=>(funny(X)|~brave(X))))&
(![X]:((~tall(X)|~patient(X))=>(strong(X)&~happy(X))))&
(![X]:((~brave(X)<~>happy(X))=>(~brave(X)<~>curious(X))))&
(![X]:(~quiet(X)=>(~kind(X)|~brave(X))))&
((?[X]:((~curious(X)|rich(X))))<=>(~humble(lucy)))&
(![X]:((~happy(X)&~wise(X))=>~patient(X)))&
((?[X]:((happy(X)|old(X))))=>((~rich(john)|~patient(john))))&
(![X]:((calm(X)|~generous(X))<=>(quiet(X)<~>~generous(X))))&
(![X]:((humble(X)|~funny(X))<=>wise(X)))&
(((wise(lucy)<~>~curious(lucy)))=>((~generous(mary)&~funny(mary))))&
(![X]:((~curious(X)<~>~humble(X))<=>~quiet(X)))&
(![X]:((rich(X)<~>~happy(X))=>(~patient(X)<~>rich(X))))&
(![X]:((~curious(X)&~kind(X))=>(tall(X)&funny(X))))&
(![X]:((tall(X)<~>calm(X))=>(~strong(X)|~creative(X))))&
(![X]:((generous(X)|funny(X))=>(~old(X)|~tall(X))))&
((quiet(mary)<~>~quiet(mary)))&
(?[X]:((~strong(X)|~humble(X))))&
((strong(lucy)&creative(lucy)))&
(?[X]:((~happy(X)<~>~curious(X))))&
((rich(john)&~kind(john)))&
(?[X]:((~quiet(X)&~patient(X))))&
((wise(mary)&creative(mary)))&
(?[X]:((~tall(X)<~>quiet(X)))) | ~generous(mary) | [] | null | 0 |
If mary is both not wise and not curious then someone is either not strong or not generous.
Everyone who is funny or not curious is wise and vice versa.
Everyone who is rich is not wise or not patient.
Everyone who is humble is either not rich or not old.
Everyone who is either not creative or old is humble or funny and vice versa.
Everyone who is both not humble and not curious is both tall and not strong and vice versa.
If lucy is not quiet then someone is wise and vice versa.
Everyone who is either strong or not funny is not calm and vice versa.
If someone is either not humble or brave then someone is not creative or quiet.
If fred is patient then lucy is calm or not creative and vice versa.
Everyone who is either not generous or not old is both kind and curious.
Everyone who is not rich or old is either not tall or creative.
If susan is both not tall and funny then someone is both not curious and kind and vice versa.
Everyone who is either rich or not brave is either happy or not curious and vice versa.
Everyone who is not tall or humble is tall or calm and vice versa.
Everyone who is rich or not rich is either tall or patient and vice versa.
Susan is not funny or brave.
Fred is funny or humble.
Fred is either not creative or not patient.
Someone is quiet or brave.
Mary is either not kind or not strong.
Susan is both kind and old.
Someone is strong.
Someone is both not curious and rich. | Susan is curious. | entailment | (((~wise(mary)&~curious(mary)))=>(?[X]:((~strong(X)<~>~generous(X)))))&
(![X]:((funny(X)|~curious(X))<=>wise(X)))&
(![X]:(rich(X)=>(~wise(X)|~patient(X))))&
(![X]:(humble(X)=>(~rich(X)<~>~old(X))))&
(![X]:((~creative(X)<~>old(X))<=>(humble(X)|funny(X))))&
(![X]:((~humble(X)&~curious(X))<=>(tall(X)&~strong(X))))&
((~quiet(lucy))<=>(?[X]:(wise(X))))&
(![X]:((strong(X)<~>~funny(X))<=>~calm(X)))&
((?[X]:((~humble(X)<~>brave(X))))=>(?[X]:((~creative(X)|quiet(X)))))&
((patient(fred))<=>((calm(lucy)|~creative(lucy))))&
(![X]:((~generous(X)<~>~old(X))=>(kind(X)&curious(X))))&
(![X]:((~rich(X)|old(X))=>(~tall(X)<~>creative(X))))&
(((~tall(susan)&funny(susan)))<=>(?[X]:((~curious(X)&kind(X)))))&
(![X]:((rich(X)<~>~brave(X))<=>(happy(X)<~>~curious(X))))&
(![X]:((~tall(X)|humble(X))<=>(tall(X)|calm(X))))&
(![X]:((rich(X)|~rich(X))<=>(tall(X)<~>patient(X))))&
((~funny(susan)|brave(susan)))&
((funny(fred)|humble(fred)))&
((~creative(fred)<~>~patient(fred)))&
(?[X]:((quiet(X)|brave(X))))&
((~kind(mary)<~>~strong(mary)))&
((kind(susan)&old(susan)))&
(?[X]:(strong(X)))&
(?[X]:((~curious(X)&rich(X)))) | curious(susan) | [
"p1",
"p2",
"p4",
"p5",
"p11",
"p12",
"p14",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2186585520504782089903621
% SZS output start Proof for 2186585520504782089903621
2. ! [X0] : ((~curious(X0) | funny(X0)) <=> wise(X0)) [input p1]
3. ! [X0] : (rich(X0) => (~patient(X0) | ~wise(X0))) [input p2]
5. ! [X0] : ((~creative(X0) <~> old(X0)) <=> (funny(X0) | humble(X0))) [input p4]
6. ! [X0] : ((~curious(X0) & ~humble(X0)) <=> (~strong(X0) & tall(X0))) [input p5]
12. ! [X0] : ((old(X0) | ~rich(X0)) => (~tall(X0) <~> creative(X0))) [input p11]
13. (funny(susan) & ~tall(susan)) <=> ? [X0] : (kind(X0) & ~curious(X0)) [input p12]
15. ! [X0] : ((humble(X0) | ~tall(X0)) <=> (calm(X0) | tall(X0))) [input p14]
16. ! [X0] : ((~rich(X0) | rich(X0)) <=> (tall(X0) <~> patient(X0))) [input p15]
22. old(susan) & kind(susan) [input p21]
25. ~curious(susan) [input hypothesis]
29. ! [X0] : ((~patient(X0) | ~wise(X0)) | ~rich(X0)) [ennf transformation 3]
30. ! [X0] : (~patient(X0) | ~wise(X0) | ~rich(X0)) [flattening 29]
34. ! [X0] : ((~tall(X0) <~> creative(X0)) | (~old(X0) & rich(X0))) [ennf transformation 12]
38. ! [X0] : (((~curious(X0) | funny(X0)) | ~wise(X0)) & (wise(X0) | (curious(X0) & ~funny(X0)))) [nnf transformation 2]
39. ! [X0] : ((~curious(X0) | funny(X0) | ~wise(X0)) & (wise(X0) | (curious(X0) & ~funny(X0)))) [flattening 38]
41. ! [X0] : ((((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | (~funny(X0) & ~humble(X0))) & ((funny(X0) | humble(X0)) | ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0))))) [nnf transformation 5]
42. ! [X0] : ((((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | (~funny(X0) & ~humble(X0))) & (funny(X0) | humble(X0) | ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0))))) [flattening 41]
43. ! [X0] : (((~curious(X0) & ~humble(X0)) | (strong(X0) | ~tall(X0))) & ((~strong(X0) & tall(X0)) | (curious(X0) | humble(X0)))) [nnf transformation 6]
44. ! [X0] : (((~curious(X0) & ~humble(X0)) | strong(X0) | ~tall(X0)) & ((~strong(X0) & tall(X0)) | curious(X0) | humble(X0))) [flattening 43]
57. ! [X0] : (((~creative(X0) | tall(X0)) & (creative(X0) | ~tall(X0))) | (~old(X0) & rich(X0))) [nnf transformation 34]
58. ((funny(susan) & ~tall(susan)) | ! [X0] : (~kind(X0) | curious(X0))) & (? [X0] : (kind(X0) & ~curious(X0)) | (~funny(susan) | tall(susan))) [nnf transformation 13]
59. ((funny(susan) & ~tall(susan)) | ! [X0] : (~kind(X0) | curious(X0))) & (? [X0] : (kind(X0) & ~curious(X0)) | ~funny(susan) | tall(susan)) [flattening 58]
60. ((funny(susan) & ~tall(susan)) | ! [X0] : (~kind(X0) | curious(X0))) & (? [X1] : (kind(X1) & ~curious(X1)) | ~funny(susan) | tall(susan)) [rectify 59]
61. ? [X1] : (kind(X1) & ~curious(X1)) => (kind(sK3) & ~curious(sK3)) [choice axiom]
62. ((funny(susan) & ~tall(susan)) | ! [X0] : (~kind(X0) | curious(X0))) & ((kind(sK3) & ~curious(sK3)) | ~funny(susan) | tall(susan)) [skolemisation 60,61]
64. ! [X0] : (((humble(X0) | ~tall(X0)) | (~calm(X0) & ~tall(X0))) & ((calm(X0) | tall(X0)) | (~humble(X0) & tall(X0)))) [nnf transformation 15]
65. ! [X0] : ((humble(X0) | ~tall(X0) | (~calm(X0) & ~tall(X0))) & (calm(X0) | tall(X0) | (~humble(X0) & tall(X0)))) [flattening 64]
66. ! [X0] : (((~rich(X0) | rich(X0)) | ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0)))) & (((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) | (rich(X0) & ~rich(X0)))) [nnf transformation 16]
67. ! [X0] : ((~rich(X0) | rich(X0) | ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0)))) & (((~patient(X0) | ~tall(X0)) & (patient(X0) | tall(X0))) | (rich(X0) & ~rich(X0)))) [flattening 66]
79. curious(X0) | wise(X0) [cnf transformation 39]
81. ~patient(X0) | ~wise(X0) | ~rich(X0) [cnf transformation 30]
88. ~old(X0) | creative(X0) | ~humble(X0) [cnf transformation 42]
90. tall(X0) | curious(X0) | humble(X0) [cnf transformation 44]
111. ~creative(X0) | tall(X0) | rich(X0) [cnf transformation 57]
115. ~tall(susan) | ~kind(X0) | curious(X0) [cnf transformation 62]
127. humble(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 65]
129. patient(X0) | tall(X0) | ~rich(X0) [cnf transformation 67]
130. patient(X0) | tall(X0) | rich(X0) [cnf transformation 67]
131. ~patient(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 67]
132. ~patient(X0) | ~tall(X0) | rich(X0) [cnf transformation 67]
142. kind(susan) [cnf transformation 22]
143. old(susan) [cnf transformation 22]
147. ~curious(susan) [cnf transformation 25]
149. ~tall(X0) | humble(X0) [duplicate literal removal 127]
213. 15 <=> ! [X0] : (~kind(X0) | curious(X0)) [avatar definition]
214. ~kind(X0) | curious(X0) <- (15) [avatar component clause 213]
221. 17 <=> tall(susan) [avatar definition]
223. ~tall(susan) <- (~17) [avatar component clause 221]
224. 15 | ~17 [avatar split clause 115,221,213]
235. ~tall(X0) | ~patient(X0) [subsumption resolution 131,132]
236. tall(X0) | patient(X0) [subsumption resolution 129,130]
280. wise(susan) [resolution 79,147]
281. curious(susan) <- (15) [resolution 214,142]
283. $false <- (15) [subsumption resolution 281,147]
284. ~15 [avatar contradiction clause 283]
288. humble(X1) | patient(X1) [resolution 236,149]
289. patient(susan) <- (~17) [resolution 236,223]
298. ~wise(susan) | ~rich(susan) <- (~17) [resolution 81,289]
300. ~rich(susan) <- (~17) [subsumption resolution 298,280]
303. creative(susan) | ~humble(susan) [resolution 88,143]
305. 29 <=> humble(susan) [avatar definition]
307. ~humble(susan) <- (~29) [avatar component clause 305]
309. 30 <=> creative(susan) [avatar definition]
311. creative(susan) <- (30) [avatar component clause 309]
312. ~29 | 30 [avatar split clause 303,309,305]
319. curious(X0) | humble(X0) | ~patient(X0) [resolution 90,235]
323. humble(X0) | curious(X0) [subsumption resolution 319,288]
325. curious(susan) <- (~29) [resolution 323,307]
326. $false <- (~29) [subsumption resolution 325,147]
327. 29 [avatar contradiction clause 326]
421. tall(susan) | rich(susan) <- (30) [resolution 111,311]
422. rich(susan) <- (~17, 30) [subsumption resolution 421,223]
423. $false <- (~17, 30) [subsumption resolution 422,300]
424. 17 | ~30 [avatar contradiction clause 423]
425. $false [avatar sat refutation 224,284,312,327,424]
% SZS output end Proof for 2186585520504782089903621
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or brave is not strong or curious and vice versa.
If someone is wise or humble then someone is humble or patient.
If john is both not strong and generous then fred is not strong and vice versa.
Everyone who is tall is both not creative and not humble and vice versa.
Everyone who is both not creative and rich is either not humble or not strong and vice versa.
Everyone who is strong or kind is creative or brave and vice versa.
If mary is either old or not kind then someone is not creative.
If someone is either not curious or not brave then john is both creative and not curious and vice versa.
If fred is both not strong and not old then someone is not calm and vice versa.
If susan is both not patient and calm then someone is not wise.
Everyone who is not wise or not tall is either not generous or generous and vice versa.
If someone is kind or not strong then someone is not calm or kind and vice versa.
If lucy is both rich and not generous then someone is either generous or not rich.
Everyone who is not generous is both wise and quiet and vice versa.
Everyone who is quiet is both not rich and not calm.
Everyone who is both not tall and not strong is not creative or not calm.
Paul is both not humble and generous.
Fred is either kind or patient.
Someone is either rich or not wise.
Someone is both patient and humble.
Mary is both curious and quiet.
Paul is either funny or old.
Someone is both not curious and funny. | Paul is creative. | neutral | (![X]:((wise(X)<~>brave(X))<=>(~strong(X)|curious(X))))&
((?[X]:((wise(X)|humble(X))))=>(?[X]:((humble(X)|patient(X)))))&
(((~strong(john)&generous(john)))<=>(~strong(fred)))&
(![X]:(tall(X)<=>(~creative(X)&~humble(X))))&
(![X]:((~creative(X)&rich(X))<=>(~humble(X)<~>~strong(X))))&
(![X]:((strong(X)|kind(X))<=>(creative(X)|brave(X))))&
(((old(mary)<~>~kind(mary)))=>(?[X]:(~creative(X))))&
((?[X]:((~curious(X)<~>~brave(X))))<=>((creative(john)&~curious(john))))&
(((~strong(fred)&~old(fred)))<=>(?[X]:(~calm(X))))&
(((~patient(susan)&calm(susan)))=>(?[X]:(~wise(X))))&
(![X]:((~wise(X)|~tall(X))<=>(~generous(X)<~>generous(X))))&
((?[X]:((kind(X)|~strong(X))))<=>(?[X]:((~calm(X)|kind(X)))))&
(((rich(lucy)&~generous(lucy)))=>(?[X]:((generous(X)<~>~rich(X)))))&
(![X]:(~generous(X)<=>(wise(X)&quiet(X))))&
(![X]:(quiet(X)=>(~rich(X)&~calm(X))))&
(![X]:((~tall(X)&~strong(X))=>(~creative(X)|~calm(X))))&
((~humble(paul)&generous(paul)))&
((kind(fred)<~>patient(fred)))&
(?[X]:((rich(X)<~>~wise(X))))&
(?[X]:((patient(X)&humble(X))))&
((curious(mary)&quiet(mary)))&
((funny(paul)<~>old(paul)))&
(?[X]:((~curious(X)&funny(X)))) | creative(paul) | [] | null | 0 |
If lucy is either not curious or not humble then someone is not quiet or not kind and vice versa.
If someone is happy then someone is both curious and kind and vice versa.
Everyone who is both tall and not rich is both quiet and humble.
If someone is either happy or calm then someone is either not funny or not happy and vice versa.
If lucy is both not patient and not strong then lucy is both humble and not kind.
Everyone who is both patient and funny is not quiet and vice versa.
If someone is creative or kind then mary is funny.
Everyone who is not funny or not kind is not wise.
If lucy is tall or old then lucy is both patient and not funny and vice versa.
If someone is both rich and not curious then fred is both generous and not tall.
If fred is either old or not curious then someone is tall.
If someone is not kind then lucy is patient or old.
If someone is not brave or not funny then someone is either wise or not rich and vice versa.
Everyone who is either not quiet or rich is both rich and humble.
If paul is both not kind and not curious then susan is either not brave or not funny.
Everyone who is either not rich or not creative is not calm.
Someone is rich or not patient.
Someone is rich or old.
Someone is either generous or not quiet.
Lucy is humble or happy.
Lucy is either not wise or not happy.
Mary is either brave or creative.
Someone is not quiet.
Fred is both not strong and rich. | Mary is not funny. | contradiction | (((~curious(lucy)<~>~humble(lucy)))<=>(?[X]:((~quiet(X)|~kind(X)))))&
((?[X]:(happy(X)))<=>(?[X]:((curious(X)&kind(X)))))&
(![X]:((tall(X)&~rich(X))=>(quiet(X)&humble(X))))&
((?[X]:((happy(X)<~>calm(X))))<=>(?[X]:((~funny(X)<~>~happy(X)))))&
(((~patient(lucy)&~strong(lucy)))=>((humble(lucy)&~kind(lucy))))&
(![X]:((patient(X)&funny(X))<=>~quiet(X)))&
((?[X]:((creative(X)|kind(X))))=>(funny(mary)))&
(![X]:((~funny(X)|~kind(X))=>~wise(X)))&
(((tall(lucy)|old(lucy)))<=>((patient(lucy)&~funny(lucy))))&
((?[X]:((rich(X)&~curious(X))))=>((generous(fred)&~tall(fred))))&
(((old(fred)<~>~curious(fred)))=>(?[X]:(tall(X))))&
((?[X]:(~kind(X)))=>((patient(lucy)|old(lucy))))&
((?[X]:((~brave(X)|~funny(X))))<=>(?[X]:((wise(X)<~>~rich(X)))))&
(![X]:((~quiet(X)<~>rich(X))=>(rich(X)&humble(X))))&
(((~kind(paul)&~curious(paul)))=>((~brave(susan)<~>~funny(susan))))&
(![X]:((~rich(X)<~>~creative(X))=>~calm(X)))&
(?[X]:((rich(X)|~patient(X))))&
(?[X]:((rich(X)|old(X))))&
(?[X]:((generous(X)<~>~quiet(X))))&
((humble(lucy)|happy(lucy)))&
((~wise(lucy)<~>~happy(lucy)))&
((brave(mary)<~>creative(mary)))&
(?[X]:(~quiet(X)))&
((~strong(fred)&rich(fred))) | ~funny(mary) | [
"p1",
"p6",
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4943601784778067893258992
% SZS output start Proof for 4943601784778067893258992
2. ? [X0] : happy(X0) <=> ? [X0] : (kind(X0) & curious(X0)) [input p1]
7. ? [X0] : (kind(X0) | creative(X0)) => funny(mary) [input p6]
8. ! [X0] : ((~kind(X0) | ~funny(X0)) => ~wise(X0)) [input p7]
21. ~wise(lucy) <~> ~happy(lucy) [input p20]
25. ~funny(mary) [input hypothesis]
26. ? [X0] : happy(X0) <=> ? [X1] : (kind(X1) & curious(X1)) [rectify 2]
33. funny(mary) | ! [X0] : (~kind(X0) & ~creative(X0)) [ennf transformation 7]
34. ! [X0] : (~wise(X0) | (kind(X0) & funny(X0))) [ennf transformation 8]
47. (? [X0] : happy(X0) | ! [X1] : (~kind(X1) | ~curious(X1))) & (? [X1] : (kind(X1) & curious(X1)) | ! [X0] : ~happy(X0)) [nnf transformation 26]
48. (? [X0] : happy(X0) | ! [X1] : (~kind(X1) | ~curious(X1))) & (? [X2] : (kind(X2) & curious(X2)) | ! [X3] : ~happy(X3)) [rectify 47]
49. ? [X0] : happy(X0) => happy(sK1) [choice axiom]
50. ? [X2] : (kind(X2) & curious(X2)) => (kind(sK2) & curious(sK2)) [choice axiom]
51. (happy(sK1) | ! [X1] : (~kind(X1) | ~curious(X1))) & ((kind(sK2) & curious(sK2)) | ! [X3] : ~happy(X3)) [skolemisation 48,50,49]
79. (happy(lucy) | wise(lucy)) & (~happy(lucy) | ~wise(lucy)) [nnf transformation 21]
90. kind(sK2) | ~happy(X3) [cnf transformation 51]
108. funny(mary) | ~kind(X0) [cnf transformation 33]
110. ~wise(X0) | kind(X0) [cnf transformation 34]
141. happy(lucy) | wise(lucy) [cnf transformation 79]
147. ~funny(mary) [cnf transformation 25]
186. 9 <=> ! [X3] : ~happy(X3) [avatar definition]
187. ~happy(X3) <- (9) [avatar component clause 186]
189. 10 <=> kind(sK2) [avatar definition]
191. kind(sK2) <- (10) [avatar component clause 189]
192. 9 | 10 [avatar split clause 90,189,186]
249. 23 <=> ! [X0] : ~kind(X0) [avatar definition]
250. ~kind(X0) <- (23) [avatar component clause 249]
252. 24 <=> funny(mary) [avatar definition]
255. 23 | 24 [avatar split clause 108,252,249]
386. 53 <=> happy(lucy) [avatar definition]
388. happy(lucy) <- (53) [avatar component clause 386]
391. 54 <=> wise(lucy) [avatar definition]
393. wise(lucy) <- (54) [avatar component clause 391]
394. 54 | 53 [avatar split clause 141,386,391]
406. ~24 [avatar split clause 147,252]
409. $false <- (10, 23) [subsumption resolution 191,250]
410. ~10 | ~23 [avatar contradiction clause 409]
413. $false <- (9, 53) [resolution 388,187]
414. ~9 | ~53 [avatar contradiction clause 413]
424. kind(lucy) <- (54) [resolution 110,393]
425. $false <- (23, 54) [subsumption resolution 424,250]
426. ~23 | ~54 [avatar contradiction clause 425]
427. $false [avatar sat refutation 192,255,394,406,410,414,426]
% SZS output end Proof for 4943601784778067893258992
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not kind and not wise then paul is brave.
Everyone who is brave is both not brave and not happy and vice versa.
If someone is either kind or happy then someone is both not kind and not creative and vice versa.
Everyone who is creative is both quiet and old.
Everyone who is not wise or humble is creative or not strong and vice versa.
Everyone who is both funny and strong is either funny or curious and vice versa.
Everyone who is either strong or not strong is humble.
If someone is both rich and old then someone is quiet.
If someone is both not brave and not creative then john is both patient and strong and vice versa.
Everyone who is not kind or brave is quiet and vice versa.
Everyone who is both happy and not generous is both rich and not brave and vice versa.
Everyone who is both creative and humble is either humble or wise.
Everyone who is either generous or not humble is either not calm or humble.
Everyone who is either not old or brave is not kind.
If someone is not strong or funny then paul is strong or happy and vice versa.
Someone is either patient or wise.
Fred is both not wise and not generous.
Paul is both not rich and not funny.
Alice is calm or kind.
Fred is both kind and patient.
Fred is humble or old. | John is not quiet. | contradiction | (((~kind(fred)&~wise(fred)))=>(brave(paul)))&
(![X]:(brave(X)<=>(~brave(X)&~happy(X))))&
((?[X]:((kind(X)<~>happy(X))))<=>(?[X]:((~kind(X)&~creative(X)))))&
(![X]:(creative(X)=>(quiet(X)&old(X))))&
(![X]:((~wise(X)|humble(X))<=>(creative(X)|~strong(X))))&
(![X]:((funny(X)&strong(X))<=>(funny(X)<~>curious(X))))&
(![X]:((strong(X)<~>~strong(X))=>humble(X)))&
((?[X]:((rich(X)&old(X))))=>(?[X]:(quiet(X))))&
((?[X]:((~brave(X)&~creative(X))))<=>((patient(john)&strong(john))))&
(![X]:((~kind(X)|brave(X))<=>quiet(X)))&
(![X]:((happy(X)&~generous(X))<=>(rich(X)&~brave(X))))&
(![X]:((creative(X)&humble(X))=>(humble(X)<~>wise(X))))&
(![X]:((generous(X)<~>~humble(X))=>(~calm(X)<~>humble(X))))&
(![X]:((~old(X)<~>brave(X))=>~kind(X)))&
((?[X]:((~strong(X)|funny(X))))<=>((strong(paul)|happy(paul))))&
(?[X]:((patient(X)<~>wise(X))))&
((~wise(fred)&~generous(fred)))&
((~rich(paul)&~funny(paul)))&
((calm(alice)|kind(alice)))&
((kind(fred)&patient(fred)))&
((humble(fred)|old(fred))) | ~quiet(john) | [
"p1",
"p2",
"p3",
"p4",
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7949253155046782781526968
% SZS output start Proof for 7949253155046782781526968
2. ! [X0] : (brave(X0) <=> (~happy(X0) & ~brave(X0))) [input p1]
3. ? [X0] : (kind(X0) <~> happy(X0)) <=> ? [X0] : (~creative(X0) & ~kind(X0)) [input p2]
4. ! [X0] : (creative(X0) => (old(X0) & quiet(X0))) [input p3]
5. ! [X0] : ((humble(X0) | ~wise(X0)) <=> (~strong(X0) | creative(X0))) [input p4]
7. ! [X0] : ((strong(X0) <~> ~strong(X0)) => humble(X0)) [input p6]
9. ? [X0] : (~creative(X0) & ~brave(X0)) <=> (strong(john) & patient(john)) [input p8]
10. ! [X0] : ((brave(X0) | ~kind(X0)) <=> quiet(X0)) [input p9]
22. ~quiet(john) [input hypothesis]
23. ? [X0] : (kind(X0) <~> happy(X0)) <=> ? [X1] : (~creative(X1) & ~kind(X1)) [rectify 3]
27. ! [X0] : ((old(X0) & quiet(X0)) | ~creative(X0)) [ennf transformation 4]
28. ! [X0] : (humble(X0) | (strong(X0) <=> ~strong(X0))) [ennf transformation 7]
34. ! [X0] : ((brave(X0) | (happy(X0) | brave(X0))) & ((~happy(X0) & ~brave(X0)) | ~brave(X0))) [nnf transformation 2]
35. ! [X0] : ((brave(X0) | happy(X0) | brave(X0)) & ((~happy(X0) & ~brave(X0)) | ~brave(X0))) [flattening 34]
36. (? [X0] : ((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | ! [X1] : (creative(X1) | kind(X1))) & (? [X1] : (~creative(X1) & ~kind(X1)) | ! [X0] : ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) [nnf transformation 23]
37. (? [X0] : ((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | ! [X1] : (creative(X1) | kind(X1))) & (? [X2] : (~creative(X2) & ~kind(X2)) | ! [X3] : ((kind(X3) | ~happy(X3)) & (happy(X3) | ~kind(X3)))) [rectify 36]
38. ? [X0] : ((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) => ((~happy(sK0) | ~kind(sK0)) & (happy(sK0) | kind(sK0))) [choice axiom]
39. ? [X2] : (~creative(X2) & ~kind(X2)) => (~creative(sK1) & ~kind(sK1)) [choice axiom]
40. (((~happy(sK0) | ~kind(sK0)) & (happy(sK0) | kind(sK0))) | ! [X1] : (creative(X1) | kind(X1))) & ((~creative(sK1) & ~kind(sK1)) | ! [X3] : ((kind(X3) | ~happy(X3)) & (happy(X3) | ~kind(X3)))) [skolemisation 37,39,38]
41. ! [X0] : (((humble(X0) | ~wise(X0)) | (strong(X0) & ~creative(X0))) & ((~strong(X0) | creative(X0)) | (~humble(X0) & wise(X0)))) [nnf transformation 5]
42. ! [X0] : ((humble(X0) | ~wise(X0) | (strong(X0) & ~creative(X0))) & (~strong(X0) | creative(X0) | (~humble(X0) & wise(X0)))) [flattening 41]
45. ! [X0] : (humble(X0) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) [nnf transformation 28]
49. (? [X0] : (~creative(X0) & ~brave(X0)) | (~strong(john) | ~patient(john))) & ((strong(john) & patient(john)) | ! [X0] : (creative(X0) | brave(X0))) [nnf transformation 9]
50. (? [X0] : (~creative(X0) & ~brave(X0)) | ~strong(john) | ~patient(john)) & ((strong(john) & patient(john)) | ! [X0] : (creative(X0) | brave(X0))) [flattening 49]
51. (? [X0] : (~creative(X0) & ~brave(X0)) | ~strong(john) | ~patient(john)) & ((strong(john) & patient(john)) | ! [X1] : (creative(X1) | brave(X1))) [rectify 50]
52. ? [X0] : (~creative(X0) & ~brave(X0)) => (~creative(sK3) & ~brave(sK3)) [choice axiom]
53. ((~creative(sK3) & ~brave(sK3)) | ~strong(john) | ~patient(john)) & ((strong(john) & patient(john)) | ! [X1] : (creative(X1) | brave(X1))) [skolemisation 51,52]
54. ! [X0] : (((brave(X0) | ~kind(X0)) | ~quiet(X0)) & (quiet(X0) | (~brave(X0) & kind(X0)))) [nnf transformation 10]
55. ! [X0] : ((brave(X0) | ~kind(X0) | ~quiet(X0)) & (quiet(X0) | (~brave(X0) & kind(X0)))) [flattening 54]
70. ~brave(X0) | ~brave(X0) [cnf transformation 35]
72. brave(X0) | happy(X0) | brave(X0) [cnf transformation 35]
76. ~creative(sK1) | kind(X3) | ~happy(X3) [cnf transformation 40]
79. ~creative(X0) | quiet(X0) [cnf transformation 27]
82. ~strong(X0) | creative(X0) | ~humble(X0) [cnf transformation 42]
91. humble(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 45]
92. humble(X0) | strong(X0) | strong(X0) [cnf transformation 45]
95. strong(john) | creative(X1) | brave(X1) [cnf transformation 53]
100. brave(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 55]
127. ~quiet(john) [cnf transformation 22]
131. humble(X0) | ~strong(X0) [duplicate literal removal 91]
132. strong(X0) | humble(X0) [duplicate literal removal 92]
135. ~brave(X0) [duplicate literal removal 70]
136. happy(X0) | brave(X0) [duplicate literal removal 72]
164. 7 <=> ! [X3] : (kind(X3) | ~happy(X3)) [avatar definition]
165. ~happy(X3) | kind(X3) <- (7) [avatar component clause 164]
167. 8 <=> creative(sK1) [avatar definition]
168. creative(sK1) <- (8) [avatar component clause 167]
169. ~creative(sK1) <- (~8) [avatar component clause 167]
170. 7 | ~8 [avatar split clause 76,167,164]
182. humble(X0) [subsumption resolution 131,132]
196. 14 <=> strong(john) [avatar definition]
197. strong(john) <- (14) [avatar component clause 196]
204. strong(john) | creative(X1) [subsumption resolution 95,135]
206. 16 <=> ! [X1] : creative(X1) [avatar definition]
207. creative(X1) <- (16) [avatar component clause 206]
208. 16 | 14 [avatar split clause 204,196,206]
211. ~quiet(X0) | ~kind(X0) [subsumption resolution 100,135]
275. quiet(sK1) <- (8) [resolution 168,79]
277. kind(X0) | brave(X0) <- (7) [resolution 165,136]
278. kind(X0) <- (7) [subsumption resolution 277,135]
284. ~kind(sK1) <- (8) [resolution 211,275]
288. $false <- (7, 8) [subsumption resolution 284,278]
289. ~7 | ~8 [avatar contradiction clause 288]
312. 28 <=> creative(john) [avatar definition]
314. creative(john) <- (28) [avatar component clause 312]
316. creative(john) | ~humble(john) <- (14) [resolution 82,197]
318. creative(john) <- (14) [subsumption resolution 316,182]
319. 28 | ~14 [avatar split clause 318,196,312]
324. quiet(john) <- (28) [resolution 314,79]
327. $false <- (28) [subsumption resolution 324,127]
328. ~28 [avatar contradiction clause 327]
335. $false <- (~8, 16) [resolution 207,169]
336. 8 | ~16 [avatar contradiction clause 335]
338. $false [avatar sat refutation 170,208,289,319,328,336]
% SZS output end Proof for 7949253155046782781526968
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not old is strong or kind and vice versa.
If someone is not strong or wise then john is both brave and not wise and vice versa.
Everyone who is not rich or not patient is either not humble or not old.
If susan is not calm then john is both not tall and creative.
Everyone who is both not calm and old is not funny or not kind and vice versa.
Everyone who is not quiet is calm.
If fred is both not old and not rich then alice is old.
If someone is both happy and humble then someone is wise.
If paul is calm or brave then fred is not happy or strong.
If someone is both brave and strong then susan is either not kind or not patient.
If fred is funny then someone is either tall or curious and vice versa.
If someone is patient then someone is either not wise or not tall and vice versa.
If alice is kind or patient then alice is either not calm or not patient.
If someone is both humble and not generous then someone is not wise and vice versa.
Everyone who is either funny or not generous is both not calm and not creative and vice versa.
Everyone who is both curious and not generous is not rich and vice versa.
Someone is not patient or not strong.
Susan is calm.
Someone is not wise.
Paul is not strong.
Someone is both old and not tall.
Paul is not happy.
Lucy is not strong.
Fred is generous or not strong. | Susan is old. | contradiction | (![X]:((generous(X)|~old(X))<=>(strong(X)|kind(X))))&
((?[X]:((~strong(X)|wise(X))))<=>((brave(john)&~wise(john))))&
(![X]:((~rich(X)|~patient(X))=>(~humble(X)<~>~old(X))))&
((~calm(susan))=>((~tall(john)&creative(john))))&
(![X]:((~calm(X)&old(X))<=>(~funny(X)|~kind(X))))&
(![X]:(~quiet(X)=>calm(X)))&
(((~old(fred)&~rich(fred)))=>(old(alice)))&
((?[X]:((happy(X)&humble(X))))=>(?[X]:(wise(X))))&
(((calm(paul)|brave(paul)))=>((~happy(fred)|strong(fred))))&
((?[X]:((brave(X)&strong(X))))=>((~kind(susan)<~>~patient(susan))))&
((funny(fred))<=>(?[X]:((tall(X)<~>curious(X)))))&
((?[X]:(patient(X)))<=>(?[X]:((~wise(X)<~>~tall(X)))))&
(((kind(alice)|patient(alice)))=>((~calm(alice)<~>~patient(alice))))&
((?[X]:((humble(X)&~generous(X))))<=>(?[X]:(~wise(X))))&
(![X]:((funny(X)<~>~generous(X))<=>(~calm(X)&~creative(X))))&
(![X]:((curious(X)&~generous(X))<=>~rich(X)))&
(?[X]:((~patient(X)|~strong(X))))&
(calm(susan))&
(?[X]:(~wise(X)))&
(~strong(paul))&
(?[X]:((old(X)&~tall(X))))&
(~happy(paul))&
(~strong(lucy))&
((generous(fred)|~strong(fred))) | old(susan) | [
"p0",
"p4",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 34737025255218872735734
% SZS output start Proof for 34737025255218872735734
1. ! [X0] : ((~old(X0) | generous(X0)) <=> (kind(X0) | strong(X0))) [input p0]
5. ! [X0] : ((old(X0) & ~calm(X0)) <=> (~kind(X0) | ~funny(X0))) [input p4]
15. ! [X0] : ((funny(X0) <~> ~generous(X0)) <=> (~creative(X0) & ~calm(X0))) [input p14]
18. calm(susan) [input p17]
25. old(susan) [input hypothesis]
42. ! [X0] : (((~old(X0) | generous(X0)) | (~kind(X0) & ~strong(X0))) & ((kind(X0) | strong(X0)) | (old(X0) & ~generous(X0)))) [nnf transformation 1]
43. ! [X0] : ((~old(X0) | generous(X0) | (~kind(X0) & ~strong(X0))) & (kind(X0) | strong(X0) | (old(X0) & ~generous(X0)))) [flattening 42]
50. ! [X0] : (((old(X0) & ~calm(X0)) | (kind(X0) & funny(X0))) & ((~kind(X0) | ~funny(X0)) | (~old(X0) | calm(X0)))) [nnf transformation 5]
51. ! [X0] : (((old(X0) & ~calm(X0)) | (kind(X0) & funny(X0))) & (~kind(X0) | ~funny(X0) | ~old(X0) | calm(X0))) [flattening 50]
68. ! [X0] : ((((generous(X0) | ~funny(X0)) & (~generous(X0) | funny(X0))) | (creative(X0) | calm(X0))) & ((~creative(X0) & ~calm(X0)) | ((funny(X0) | generous(X0)) & (~generous(X0) | ~funny(X0))))) [nnf transformation 15]
69. ! [X0] : ((((generous(X0) | ~funny(X0)) & (~generous(X0) | funny(X0))) | creative(X0) | calm(X0)) & ((~creative(X0) & ~calm(X0)) | ((funny(X0) | generous(X0)) & (~generous(X0) | ~funny(X0))))) [flattening 68]
79. ~kind(X0) | generous(X0) | ~old(X0) [cnf transformation 43]
92. ~calm(X0) | funny(X0) [cnf transformation 51]
93. ~calm(X0) | kind(X0) [cnf transformation 51]
114. ~calm(X0) | ~generous(X0) | ~funny(X0) [cnf transformation 69]
122. calm(susan) [cnf transformation 18]
129. old(susan) [cnf transformation 25]
159. 7 <=> calm(susan) [avatar definition]
161. calm(susan) <- (7) [avatar component clause 159]
189. 14 <=> kind(susan) [avatar definition]
191. kind(susan) <- (14) [avatar component clause 189]
283. ~calm(X0) | ~generous(X0) [subsumption resolution 114,92]
293. 7 [avatar split clause 122,159]
315. kind(susan) <- (7) [resolution 93,161]
316. 14 | ~7 [avatar split clause 315,159,189]
321. ~generous(susan) <- (7) [resolution 283,161]
323. generous(susan) | ~old(susan) <- (14) [resolution 79,191]
326. ~old(susan) <- (7, 14) [subsumption resolution 323,321]
327. $false <- (7, 14) [subsumption resolution 326,129]
328. ~7 | ~14 [avatar contradiction clause 327]
329. $false [avatar sat refutation 293,316,328]
% SZS output end Proof for 34737025255218872735734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or quiet then alice is both brave and curious.
If someone is either not calm or not quiet then someone is not strong.
If lucy is not brave then alice is strong or tall and vice versa.
Everyone who is both brave and patient is either not strong or wise and vice versa.
Everyone who is both brave and not old is not rich or not old and vice versa.
Everyone who is both not curious and not strong is patient and vice versa.
Everyone who is generous or wise is both strong and not quiet.
Everyone who is tall is both rich and not humble and vice versa.
If someone is not funny or not tall then someone is either not creative or funny and vice versa.
If someone is calm or patient then lucy is strong or kind.
If someone is both creative and not curious then mary is either not calm or old.
Everyone who is either not brave or not tall is not old and vice versa.
If mary is not calm then john is either not patient or curious and vice versa.
Everyone who is not rich or old is not calm and vice versa.
If someone is calm or not brave then lucy is curious or wise.
John is either happy or quiet.
Mary is not tall or quiet.
Someone is not happy or not wise.
Someone is strong or rich.
Paul is both creative and kind.
Someone is both generous and rich. | Lucy is not rich. | contradiction | ((?[X]:((~curious(X)|quiet(X))))=>((brave(alice)&curious(alice))))&
((?[X]:((~calm(X)<~>~quiet(X))))=>(?[X]:(~strong(X))))&
((~brave(lucy))<=>((strong(alice)|tall(alice))))&
(![X]:((brave(X)&patient(X))<=>(~strong(X)<~>wise(X))))&
(![X]:((brave(X)&~old(X))<=>(~rich(X)|~old(X))))&
(![X]:((~curious(X)&~strong(X))<=>patient(X)))&
(![X]:((generous(X)|wise(X))=>(strong(X)&~quiet(X))))&
(![X]:(tall(X)<=>(rich(X)&~humble(X))))&
((?[X]:((~funny(X)|~tall(X))))<=>(?[X]:((~creative(X)<~>funny(X)))))&
((?[X]:((calm(X)|patient(X))))=>((strong(lucy)|kind(lucy))))&
((?[X]:((creative(X)&~curious(X))))=>((~calm(mary)<~>old(mary))))&
(![X]:((~brave(X)<~>~tall(X))<=>~old(X)))&
((~calm(mary))<=>((~patient(john)<~>curious(john))))&
(![X]:((~rich(X)|old(X))<=>~calm(X)))&
((?[X]:((calm(X)|~brave(X))))=>((curious(lucy)|wise(lucy))))&
((happy(john)<~>quiet(john)))&
((~tall(mary)|quiet(mary)))&
(?[X]:((~happy(X)|~wise(X))))&
(?[X]:((strong(X)|rich(X))))&
((creative(paul)&kind(paul)))&
(?[X]:((generous(X)&rich(X)))) | ~rich(lucy) | [
"p0",
"p2",
"p3",
"p4",
"p5",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 938417556043542188383118
% SZS output start Proof for 938417556043542188383118
1. ? [X0] : (quiet(X0) | ~curious(X0)) => (curious(alice) & brave(alice)) [input p0]
3. ~brave(lucy) <=> (tall(alice) | strong(alice)) [input p2]
4. ! [X0] : ((patient(X0) & brave(X0)) <=> (~strong(X0) <~> wise(X0))) [input p3]
5. ! [X0] : ((~old(X0) & brave(X0)) <=> (~old(X0) | ~rich(X0))) [input p4]
6. ! [X0] : ((~strong(X0) & ~curious(X0)) <=> patient(X0)) [input p5]
7. ! [X0] : ((wise(X0) | generous(X0)) => (~quiet(X0) & strong(X0))) [input p6]
22. ~rich(lucy) [input hypothesis]
27. (curious(alice) & brave(alice)) | ! [X0] : (~quiet(X0) & curious(X0)) [ennf transformation 1]
29. ! [X0] : ((~quiet(X0) & strong(X0)) | (~wise(X0) & ~generous(X0))) [ennf transformation 7]
37. (~brave(lucy) | (~tall(alice) & ~strong(alice))) & ((tall(alice) | strong(alice)) | brave(lucy)) [nnf transformation 3]
38. (~brave(lucy) | (~tall(alice) & ~strong(alice))) & (tall(alice) | strong(alice) | brave(lucy)) [flattening 37]
39. ! [X0] : (((patient(X0) & brave(X0)) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0)))) & (((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | (~patient(X0) | ~brave(X0)))) [nnf transformation 4]
40. ! [X0] : (((patient(X0) & brave(X0)) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0)))) & (((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | ~patient(X0) | ~brave(X0))) [flattening 39]
41. ! [X0] : (((~old(X0) & brave(X0)) | (old(X0) & rich(X0))) & ((~old(X0) | ~rich(X0)) | (old(X0) | ~brave(X0)))) [nnf transformation 5]
42. ! [X0] : (((~old(X0) & brave(X0)) | (old(X0) & rich(X0))) & (~old(X0) | ~rich(X0) | old(X0) | ~brave(X0))) [flattening 41]
43. ! [X0] : (((~strong(X0) & ~curious(X0)) | ~patient(X0)) & (patient(X0) | (strong(X0) | curious(X0)))) [nnf transformation 6]
44. ! [X0] : (((~strong(X0) & ~curious(X0)) | ~patient(X0)) & (patient(X0) | strong(X0) | curious(X0))) [flattening 43]
66. curious(alice) | curious(X0) [cnf transformation 27]
71. ~brave(lucy) | ~strong(alice) [cnf transformation 38]
77. wise(X0) | patient(X0) | strong(X0) [cnf transformation 40]
80. rich(X0) | brave(X0) [cnf transformation 42]
85. ~patient(X0) | ~curious(X0) [cnf transformation 44]
88. ~wise(X0) | strong(X0) [cnf transformation 29]
123. ~rich(lucy) [cnf transformation 22]
128. 2 <=> curious(alice) [avatar definition]
129. ~curious(alice) <- (~2) [avatar component clause 128]
130. curious(alice) <- (2) [avatar component clause 128]
133. 3 <=> ! [X0] : curious(X0) [avatar definition]
134. curious(X0) <- (3) [avatar component clause 133]
135. 3 | 2 [avatar split clause 66,128,133]
159. 9 <=> brave(lucy) [avatar definition]
164. 10 <=> strong(alice) [avatar definition]
166. ~strong(alice) <- (~10) [avatar component clause 164]
167. ~10 | ~9 [avatar split clause 71,159,164]
284. brave(lucy) [resolution 80,123]
287. 9 [avatar split clause 284,159]
316. patient(X2) | strong(X2) | strong(X2) [resolution 77,88]
317. patient(X2) | strong(X2) [duplicate literal removal 316]
364. ~curious(X2) | strong(X2) [resolution 317,85]
366. strong(alice) <- (2) [resolution 364,130]
368. $false <- (2, ~10) [subsumption resolution 366,166]
369. ~2 | 10 [avatar contradiction clause 368]
370. $false <- (~2, 3) [subsumption resolution 129,134]
371. 2 | ~3 [avatar contradiction clause 370]
372. $false [avatar sat refutation 135,167,287,369,371]
% SZS output end Proof for 938417556043542188383118
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both old and kind then susan is not brave or not kind and vice versa.
If paul is either old or not patient then someone is not humble or not funny.
If someone is either brave or creative then mary is wise and vice versa.
Everyone who is either not tall or strong is not quiet or not calm.
Everyone who is both kind and not rich is either humble or rich and vice versa.
Everyone who is curious is not humble and vice versa.
Everyone who is either not wise or rich is not old.
Everyone who is either not creative or not tall is both not funny and not humble and vice versa.
Everyone who is wise is both not wise and not calm and vice versa.
If someone is not strong then someone is either wise or rich.
Everyone who is both not strong and not patient is both not calm and old.
If someone is both curious and old then john is not kind and vice versa.
Everyone who is not strong is patient and vice versa.
If someone is patient then someone is not kind or happy.
Everyone who is both kind and generous is both calm and not brave and vice versa.
If mary is either strong or brave then someone is either not humble or creative.
Someone is both not wise and not quiet.
Someone is either not generous or not creative.
Paul is tall.
Someone is not quiet or not calm.
Someone is not strong.
Mary is creative or funny. | Susan is patient. | neutral | (((old(susan)&kind(susan)))<=>((~brave(susan)|~kind(susan))))&
(((old(paul)<~>~patient(paul)))=>(?[X]:((~humble(X)|~funny(X)))))&
((?[X]:((brave(X)<~>creative(X))))<=>(wise(mary)))&
(![X]:((~tall(X)<~>strong(X))=>(~quiet(X)|~calm(X))))&
(![X]:((kind(X)&~rich(X))<=>(humble(X)<~>rich(X))))&
(![X]:(curious(X)<=>~humble(X)))&
(![X]:((~wise(X)<~>rich(X))=>~old(X)))&
(![X]:((~creative(X)<~>~tall(X))<=>(~funny(X)&~humble(X))))&
(![X]:(wise(X)<=>(~wise(X)&~calm(X))))&
((?[X]:(~strong(X)))=>(?[X]:((wise(X)<~>rich(X)))))&
(![X]:((~strong(X)&~patient(X))=>(~calm(X)&old(X))))&
((?[X]:((curious(X)&old(X))))<=>(~kind(john)))&
(![X]:(~strong(X)<=>patient(X)))&
((?[X]:(patient(X)))=>(?[X]:((~kind(X)|happy(X)))))&
(![X]:((kind(X)&generous(X))<=>(calm(X)&~brave(X))))&
(((strong(mary)<~>brave(mary)))=>(?[X]:((~humble(X)<~>creative(X)))))&
(?[X]:((~wise(X)&~quiet(X))))&
(?[X]:((~generous(X)<~>~creative(X))))&
(tall(paul))&
(?[X]:((~quiet(X)|~calm(X))))&
(?[X]:(~strong(X)))&
((creative(mary)|funny(mary))) | patient(susan) | [] | null | 0 |
If paul is either happy or not humble then someone is creative or happy. Everyone who is both not happy and not funny is not generous. Everyone who is either not strong or not brave is both not old and not tall and vice versa. If someone is both not curious and patient then john is either kind or not wise. Everyone who is not rich or not patient is humble or patient and vice versa. If someone is curious or not brave then someone is either kind or calm and vice versa. Everyone who is both not tall and creative is wise or strong and vice versa. Everyone who is funny or kind is quiet and vice versa. Everyone who is not generous or happy is both not rich and not brave. If someone is not calm then john is both not calm and creative and vice versa. If alice is not brave then someone is rich or not quiet and vice versa. Everyone who is both wise and curious is generous. Everyone who is either not generous or not wise is both rich and calm. If john is not creative then someone is both not patient and not brave and vice versa. Everyone who is both not tall and not happy is funny or curious and vice versa. Everyone who is both not quiet and happy is either not old or old and vice versa. Someone is brave or generous. Someone is not quiet. Alice is either strong or not old. Someone is calm. Someone is not humble. Someone is either not tall or not happy. Someone is not curious or not calm. | John is creative. | neutral | (((happy(paul)<~>~humble(paul)))=>(?[X]:((creative(X)|happy(X)))))&
(![X]:((~happy(X)&~funny(X))=>~generous(X)))&
(![X]:((~strong(X)<~>~brave(X))<=>(~old(X)&~tall(X))))&
((?[X]:((~curious(X)&patient(X))))=>((kind(john)<~>~wise(john))))&
(![X]:((~rich(X)|~patient(X))<=>(humble(X)|patient(X))))&
((?[X]:((curious(X)|~brave(X))))<=>(?[X]:((kind(X)<~>calm(X)))))&
(![X]:((~tall(X)&creative(X))<=>(wise(X)|strong(X))))&
(![X]:((funny(X)|kind(X))<=>quiet(X)))&
(![X]:((~generous(X)|happy(X))=>(~rich(X)&~brave(X))))&
((?[X]:(~calm(X)))<=>((~calm(john)&creative(john))))&
((~brave(alice))<=>(?[X]:((rich(X)|~quiet(X)))))&
(![X]:((wise(X)&curious(X))=>generous(X)))&
(![X]:((~generous(X)<~>~wise(X))=>(rich(X)&calm(X))))&
((~creative(john))<=>(?[X]:((~patient(X)&~brave(X)))))&
(![X]:((~tall(X)&~happy(X))<=>(funny(X)|curious(X))))&
(![X]:((~quiet(X)&happy(X))<=>(~old(X)<~>old(X))))&
(?[X]:((brave(X)|generous(X))))&
(?[X]:(~quiet(X)))&
((strong(alice)<~>~old(alice)))&
(?[X]:(calm(X)))&
(?[X]:(~humble(X)))&
(?[X]:((~tall(X)<~>~happy(X))))&
(?[X]:((~curious(X)|~calm(X)))) | creative(john) | [] | null | 0 |
Everyone who is not kind is both creative and wise.
Everyone who is not curious or curious is generous and vice versa.
Everyone who is not generous is either not quiet or rich.
Everyone who is not happy or not quiet is both wise and not curious.
Everyone who is both not patient and not funny is both not curious and generous and vice versa.
If paul is not humble then someone is either wise or brave and vice versa.
Everyone who is happy or not old is funny or not kind and vice versa.
If someone is quiet then paul is generous and vice versa.
If lucy is both not brave and not quiet then someone is rich and vice versa.
Everyone who is both not patient and wise is wise or not old and vice versa.
Everyone who is both not brave and funny is either not happy or kind.
Everyone who is either not quiet or not curious is not creative or wise and vice versa.
Everyone who is either not tall or funny is strong or humble and vice versa.
Everyone who is not quiet or funny is wise or not generous.
If lucy is generous then susan is not curious.
If someone is both not kind and curious then someone is kind or humble and vice versa.
Lucy is not calm.
Mary is either tall or quiet.
Someone is either brave or not curious.
Paul is either not calm or not kind.
Paul is either not wise or not kind.
Someone is not patient or brave. | Paul is not funny. | entailment | (![X]:(~kind(X)=>(creative(X)&wise(X))))&
(![X]:((~curious(X)|curious(X))<=>generous(X)))&
(![X]:(~generous(X)=>(~quiet(X)<~>rich(X))))&
(![X]:((~happy(X)|~quiet(X))=>(wise(X)&~curious(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~curious(X)&generous(X))))&
((~humble(paul))<=>(?[X]:((wise(X)<~>brave(X)))))&
(![X]:((happy(X)|~old(X))<=>(funny(X)|~kind(X))))&
((?[X]:(quiet(X)))<=>(generous(paul)))&
(((~brave(lucy)&~quiet(lucy)))<=>(?[X]:(rich(X))))&
(![X]:((~patient(X)&wise(X))<=>(wise(X)|~old(X))))&
(![X]:((~brave(X)&funny(X))=>(~happy(X)<~>kind(X))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~creative(X)|wise(X))))&
(![X]:((~tall(X)<~>funny(X))<=>(strong(X)|humble(X))))&
(![X]:((~quiet(X)|funny(X))=>(wise(X)|~generous(X))))&
((generous(lucy))=>(~curious(susan)))&
((?[X]:((~kind(X)&curious(X))))<=>(?[X]:((kind(X)|humble(X)))))&
(~calm(lucy))&
((tall(mary)<~>quiet(mary)))&
(?[X]:((brave(X)<~>~curious(X))))&
((~calm(paul)<~>~kind(paul)))&
((~wise(paul)<~>~kind(paul)))&
(?[X]:((~patient(X)|brave(X)))) | ~funny(paul) | [
"p0",
"p1",
"p3",
"p4",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1623921133821571207517463
% SZS output start Proof for 1623921133821571207517463
1. ! [X0] : (~kind(X0) => (wise(X0) & creative(X0))) [input p0]
2. ! [X0] : ((curious(X0) | ~curious(X0)) <=> generous(X0)) [input p1]
4. ! [X0] : ((~quiet(X0) | ~happy(X0)) => (~curious(X0) & wise(X0))) [input p3]
5. ! [X0] : ((~funny(X0) & ~patient(X0)) <=> (generous(X0) & ~curious(X0))) [input p4]
12. ! [X0] : ((~quiet(X0) <~> ~curious(X0)) <=> (wise(X0) | ~creative(X0))) [input p11]
16. ? [X0] : (curious(X0) & ~kind(X0)) <=> ? [X0] : (humble(X0) | kind(X0)) [input p15]
23. funny(paul) [input hypothesis]
24. ? [X0] : (curious(X0) & ~kind(X0)) <=> ? [X1] : (humble(X1) | kind(X1)) [rectify 16]
25. ! [X0] : ((wise(X0) & creative(X0)) | kind(X0)) [ennf transformation 1]
27. ! [X0] : ((~curious(X0) & wise(X0)) | (quiet(X0) & happy(X0))) [ennf transformation 4]
33. ! [X0] : (((curious(X0) | ~curious(X0)) | ~generous(X0)) & (generous(X0) | (~curious(X0) & curious(X0)))) [nnf transformation 2]
34. ! [X0] : ((curious(X0) | ~curious(X0) | ~generous(X0)) & (generous(X0) | (~curious(X0) & curious(X0)))) [flattening 33]
36. ! [X0] : (((~funny(X0) & ~patient(X0)) | (~generous(X0) | curious(X0))) & ((generous(X0) & ~curious(X0)) | (funny(X0) | patient(X0)))) [nnf transformation 5]
37. ! [X0] : (((~funny(X0) & ~patient(X0)) | ~generous(X0) | curious(X0)) & ((generous(X0) & ~curious(X0)) | funny(X0) | patient(X0))) [flattening 36]
56. ! [X0] : ((((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | (~wise(X0) & creative(X0))) & ((wise(X0) | ~creative(X0)) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0))))) [nnf transformation 12]
57. ! [X0] : ((((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | (~wise(X0) & creative(X0))) & (wise(X0) | ~creative(X0) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0))))) [flattening 56]
60. (? [X0] : (curious(X0) & ~kind(X0)) | ! [X1] : (~humble(X1) & ~kind(X1))) & (? [X1] : (humble(X1) | kind(X1)) | ! [X0] : (~curious(X0) | kind(X0))) [nnf transformation 24]
61. (? [X0] : (curious(X0) & ~kind(X0)) | ! [X1] : (~humble(X1) & ~kind(X1))) & (? [X2] : (humble(X2) | kind(X2)) | ! [X3] : (~curious(X3) | kind(X3))) [rectify 60]
62. ? [X0] : (curious(X0) & ~kind(X0)) => (curious(sK3) & ~kind(sK3)) [choice axiom]
63. ? [X2] : (humble(X2) | kind(X2)) => (humble(sK4) | kind(sK4)) [choice axiom]
64. ((curious(sK3) & ~kind(sK3)) | ! [X1] : (~humble(X1) & ~kind(X1))) & ((humble(sK4) | kind(sK4)) | ! [X3] : (~curious(X3) | kind(X3))) [skolemisation 61,63,62]
74. wise(X0) | kind(X0) [cnf transformation 25]
75. generous(X0) | curious(X0) [cnf transformation 34]
76. ~curious(X0) | generous(X0) [cnf transformation 34]
81. quiet(X0) | wise(X0) [cnf transformation 27]
83. ~curious(X0) | quiet(X0) [cnf transformation 27]
87. ~funny(X0) | ~generous(X0) | curious(X0) [cnf transformation 37]
111. ~curious(X0) | ~quiet(X0) | ~wise(X0) [cnf transformation 57]
113. curious(X0) | quiet(X0) | ~wise(X0) [cnf transformation 57]
124. ~kind(sK3) | ~kind(X1) [cnf transformation 64]
126. curious(sK3) | ~kind(X1) [cnf transformation 64]
138. funny(paul) [cnf transformation 23]
139. generous(X0) [subsumption resolution 75,76]
140. ~funny(X0) | curious(X0) [subsumption resolution 87,139]
183. quiet(X0) | ~wise(X0) [subsumption resolution 113,83]
184. quiet(X0) [subsumption resolution 183,81]
185. ~curious(X0) | ~wise(X0) [subsumption resolution 111,184]
194. 11 <=> curious(sK3) [avatar definition]
196. curious(sK3) <- (11) [avatar component clause 194]
199. 12 <=> ! [X1] : ~kind(X1) [avatar definition]
200. ~kind(X1) <- (12) [avatar component clause 199]
201. 12 | 11 [avatar split clause 126,194,199]
203. 13 <=> kind(sK3) [avatar definition]
205. ~kind(sK3) <- (~13) [avatar component clause 203]
207. 12 | ~13 [avatar split clause 124,203,199]
236. 20 <=> kind(paul) [avatar definition]
238. kind(paul) <- (20) [avatar component clause 236]
242. 21 <=> wise(paul) [avatar definition]
244. ~wise(paul) <- (~21) [avatar component clause 242]
258. curious(paul) [resolution 140,138]
262. ~wise(sK3) <- (11) [resolution 185,196]
263. ~wise(paul) [resolution 185,258]
264. ~21 [avatar split clause 263,242]
265. kind(paul) <- (~21) [resolution 244,74]
268. 20 | 21 [avatar split clause 265,242,236]
271. kind(sK3) <- (11) [resolution 262,74]
272. $false <- (11, ~13) [subsumption resolution 271,205]
273. ~11 | 13 [avatar contradiction clause 272]
274. $false <- (12, 20) [resolution 200,238]
275. ~12 | ~20 [avatar contradiction clause 274]
276. $false [avatar sat refutation 201,207,264,268,273,275]
% SZS output end Proof for 1623921133821571207517463
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not rich and old then someone is not rich or quiet. Everyone who is either not old or creative is wise and vice versa. Everyone who is not tall is both not tall and not patient. If someone is both wise and brave then someone is either not wise or curious and vice versa. If paul is either quiet or not quiet then someone is not generous and vice versa. If someone is either not generous or not old then mary is both calm and not brave and vice versa. Everyone who is both not tall and not rich is not happy or calm and vice versa. If someone is either brave or curious then mary is not rich or not tall and vice versa. If someone is both strong and not wise then john is generous or not strong. If someone is both not brave and creative then someone is either not humble or not brave and vice versa. If paul is both generous and wise then someone is curious. If mary is both not brave and rich then someone is both strong and patient. If someone is both not generous and not patient then someone is not calm or quiet. Everyone who is generous is either old or not wise and vice versa. If someone is wise then john is not strong. Susan is creative. Someone is either not funny or funny. Someone is both not happy and not creative. Someone is both not calm and not humble. Paul is both generous and not wise. Someone is both happy and funny. Fred is not brave. Someone is not brave. | Mary is not tall. | entailment | ((?[X]:((~rich(X)&old(X))))=>(?[X]:((~rich(X)|quiet(X)))))&
(![X]:((~old(X)<~>creative(X))<=>wise(X)))&
(![X]:(~tall(X)=>(~tall(X)&~patient(X))))&
((?[X]:((wise(X)&brave(X))))<=>(?[X]:((~wise(X)<~>curious(X)))))&
(((quiet(paul)<~>~quiet(paul)))<=>(?[X]:(~generous(X))))&
((?[X]:((~generous(X)<~>~old(X))))<=>((calm(mary)&~brave(mary))))&
(![X]:((~tall(X)&~rich(X))<=>(~happy(X)|calm(X))))&
((?[X]:((brave(X)<~>curious(X))))<=>((~rich(mary)|~tall(mary))))&
((?[X]:((strong(X)&~wise(X))))=>((generous(john)|~strong(john))))&
((?[X]:((~brave(X)&creative(X))))<=>(?[X]:((~humble(X)<~>~brave(X)))))&
(((generous(paul)&wise(paul)))=>(?[X]:(curious(X))))&
(((~brave(mary)&rich(mary)))=>(?[X]:((strong(X)&patient(X)))))&
((?[X]:((~generous(X)&~patient(X))))=>(?[X]:((~calm(X)|quiet(X)))))&
(![X]:(generous(X)<=>(old(X)<~>~wise(X))))&
((?[X]:(wise(X)))=>(~strong(john)))&
(creative(susan))&
(?[X]:((~funny(X)<~>funny(X))))&
(?[X]:((~happy(X)&~creative(X))))&
(?[X]:((~calm(X)&~humble(X))))&
((generous(paul)&~wise(paul)))&
(?[X]:((happy(X)&funny(X))))&
(~brave(fred))&
(?[X]:(~brave(X))) | ~tall(mary) | [
"p5",
"p6",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 9088899380856375513803039
% SZS output start Proof for 9088899380856375513803039
6. ? [X0] : (~generous(X0) <~> ~old(X0)) <=> (~brave(mary) & calm(mary)) [input p5]
7. ! [X0] : ((~rich(X0) & ~tall(X0)) <=> (calm(X0) | ~happy(X0))) [input p6]
14. ! [X0] : (generous(X0) <=> (old(X0) <~> ~wise(X0))) [input p13]
20. ~wise(paul) & generous(paul) [input p19]
24. tall(mary) [input hypothesis]
52. (? [X0] : ((old(X0) | generous(X0)) & (~old(X0) | ~generous(X0))) | (brave(mary) | ~calm(mary))) & ((~brave(mary) & calm(mary)) | ! [X0] : ((~generous(X0) | old(X0)) & (~old(X0) | generous(X0)))) [nnf transformation 6]
53. (? [X0] : ((old(X0) | generous(X0)) & (~old(X0) | ~generous(X0))) | brave(mary) | ~calm(mary)) & ((~brave(mary) & calm(mary)) | ! [X0] : ((~generous(X0) | old(X0)) & (~old(X0) | generous(X0)))) [flattening 52]
54. (? [X0] : ((old(X0) | generous(X0)) & (~old(X0) | ~generous(X0))) | brave(mary) | ~calm(mary)) & ((~brave(mary) & calm(mary)) | ! [X1] : ((~generous(X1) | old(X1)) & (~old(X1) | generous(X1)))) [rectify 53]
55. ? [X0] : ((old(X0) | generous(X0)) & (~old(X0) | ~generous(X0))) => ((old(sK4) | generous(sK4)) & (~old(sK4) | ~generous(sK4))) [choice axiom]
56. (((old(sK4) | generous(sK4)) & (~old(sK4) | ~generous(sK4))) | brave(mary) | ~calm(mary)) & ((~brave(mary) & calm(mary)) | ! [X1] : ((~generous(X1) | old(X1)) & (~old(X1) | generous(X1)))) [skolemisation 54,55]
57. ! [X0] : (((~rich(X0) & ~tall(X0)) | (~calm(X0) & happy(X0))) & ((calm(X0) | ~happy(X0)) | (rich(X0) | tall(X0)))) [nnf transformation 7]
58. ! [X0] : (((~rich(X0) & ~tall(X0)) | (~calm(X0) & happy(X0))) & (calm(X0) | ~happy(X0) | rich(X0) | tall(X0))) [flattening 57]
76. ! [X0] : ((generous(X0) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0)))) & (((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | ~generous(X0))) [nnf transformation 14]
106. calm(mary) | ~generous(X1) | old(X1) [cnf transformation 56]
113. ~calm(X0) | ~tall(X0) [cnf transformation 58]
134. ~generous(X0) | ~old(X0) | wise(X0) [cnf transformation 76]
145. generous(paul) [cnf transformation 20]
146. ~wise(paul) [cnf transformation 20]
151. tall(mary) [cnf transformation 24]
208. 13 <=> calm(mary) [avatar definition]
209. calm(mary) <- (13) [avatar component clause 208]
226. 17 <=> ! [X1] : (~generous(X1) | old(X1)) [avatar definition]
227. ~generous(X1) | old(X1) <- (17) [avatar component clause 226]
233. 17 | 13 [avatar split clause 106,208,226]
236. 19 <=> tall(mary) [avatar definition]
238. tall(mary) <- (19) [avatar component clause 236]
307. 35 <=> generous(paul) [avatar definition]
308. generous(paul) <- (35) [avatar component clause 307]
311. 36 <=> wise(paul) [avatar definition]
313. ~wise(paul) <- (~36) [avatar component clause 311]
345. ~36 [avatar split clause 146,311]
346. 35 [avatar split clause 145,307]
347. 19 [avatar split clause 151,236]
349. ~tall(mary) <- (13) [resolution 113,209]
350. $false <- (13, 19) [subsumption resolution 349,238]
351. ~13 | ~19 [avatar contradiction clause 350]
358. old(paul) <- (17, 35) [resolution 227,308]
432. ~old(paul) | wise(paul) <- (35) [resolution 134,308]
433. wise(paul) <- (17, 35) [subsumption resolution 432,358]
434. $false <- (17, 35, ~36) [subsumption resolution 433,313]
435. ~17 | ~35 | 36 [avatar contradiction clause 434]
436. $false [avatar sat refutation 233,345,346,347,351,435]
% SZS output end Proof for 9088899380856375513803039
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is both curious and not wise. If someone is both not kind and not calm then alice is both patient and not patient. If mary is both funny and not brave then lucy is either not strong or patient and vice versa. If fred is humble then susan is both not rich and curious and vice versa. If someone is either brave or generous then someone is not happy. If someone is either rich or not brave then susan is either humble or wise and vice versa. Everyone who is either not funny or creative is not funny or not kind and vice versa. Everyone who is either not wise or patient is curious or not old. Everyone who is brave or not tall is generous. Everyone who is either not rich or wise is not patient and vice versa. If someone is both not funny and not curious then lucy is not kind and vice versa. Everyone who is either quiet or generous is quiet and vice versa. If someone is not curious or funny then someone is not kind or tall and vice versa. If someone is both old and funny then someone is calm and vice versa. Everyone who is both patient and creative is either brave or patient. Everyone who is tall or not old is wise. Mary is wise or not humble. Someone is funny. Someone is not quiet. Fred is funny or not curious. Someone is either quiet or kind. Someone is either not patient or strong. | Mary is not generous. | entailment | (![X]:(~strong(X)=>(curious(X)&~wise(X))))&
((?[X]:((~kind(X)&~calm(X))))=>((patient(alice)&~patient(alice))))&
(((funny(mary)&~brave(mary)))<=>((~strong(lucy)<~>patient(lucy))))&
((humble(fred))<=>((~rich(susan)&curious(susan))))&
((?[X]:((brave(X)<~>generous(X))))=>(?[X]:(~happy(X))))&
((?[X]:((rich(X)<~>~brave(X))))<=>((humble(susan)<~>wise(susan))))&
(![X]:((~funny(X)<~>creative(X))<=>(~funny(X)|~kind(X))))&
(![X]:((~wise(X)<~>patient(X))=>(curious(X)|~old(X))))&
(![X]:((brave(X)|~tall(X))=>generous(X)))&
(![X]:((~rich(X)<~>wise(X))<=>~patient(X)))&
((?[X]:((~funny(X)&~curious(X))))<=>(~kind(lucy)))&
(![X]:((quiet(X)<~>generous(X))<=>quiet(X)))&
((?[X]:((~curious(X)|funny(X))))<=>(?[X]:((~kind(X)|tall(X)))))&
((?[X]:((old(X)&funny(X))))<=>(?[X]:(calm(X))))&
(![X]:((patient(X)&creative(X))=>(brave(X)<~>patient(X))))&
(![X]:((tall(X)|~old(X))=>wise(X)))&
((wise(mary)|~humble(mary)))&
(?[X]:(funny(X)))&
(?[X]:(~quiet(X)))&
((funny(fred)|~curious(fred)))&
(?[X]:((quiet(X)<~>kind(X))))&
(?[X]:((~patient(X)<~>strong(X)))) | ~generous(mary) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2467161273500066631901813
% SZS output start Proof for 2467161273500066631901813
12. ! [X0] : ((quiet(X0) <~> generous(X0)) <=> quiet(X0)) [input p11]
23. generous(mary) [input hypothesis]
52. ! [X0] : ((((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | ~quiet(X0)) & (quiet(X0) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))))) [nnf transformation 12]
113. quiet(X0) | quiet(X0) | ~generous(X0) [cnf transformation 52]
115. ~generous(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 52]
135. generous(mary) [cnf transformation 23]
137. quiet(X0) | ~generous(X0) [duplicate literal removal 113]
138. ~generous(X0) | ~quiet(X0) [duplicate literal removal 115]
236. ~generous(X0) [subsumption resolution 137,138]
328. $false [subsumption resolution 135,236]
% SZS output end Proof for 2467161273500066631901813
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or happy then mary is either not brave or old. If someone is not rich or not tall then mary is not old. If someone is both generous and not old then lucy is either not curious or not generous. Everyone who is either tall or kind is either kind or not kind and vice versa. Everyone who is either patient or not strong is not patient or old and vice versa. Everyone who is either calm or not strong is either kind or not brave and vice versa. Everyone who is both not patient and not funny is both old and not quiet. Everyone who is not quiet or wise is not strong or funny and vice versa. If someone is either curious or tall then someone is either not calm or rich. If lucy is creative then someone is not quiet. Everyone who is creative or not brave is not funny or patient and vice versa. Everyone who is either not calm or curious is both not tall and wise. Everyone who is kind or not creative is either not curious or not quiet and vice versa. Everyone who is wise or not humble is not creative or not calm and vice versa. Everyone who is either calm or not quiet is not quiet or kind and vice versa. Everyone who is tall or not patient is either creative or quiet. Mary is both funny and brave. Mary is either not happy or not generous. Someone is not wise. Someone is quiet. Lucy is not humble. Someone is funny. Someone is either not calm or not tall. | Lucy is patient. | entailment | ((?[X]:((~funny(X)|happy(X))))=>((~brave(mary)<~>old(mary))))&
((?[X]:((~rich(X)|~tall(X))))=>(~old(mary)))&
((?[X]:((generous(X)&~old(X))))=>((~curious(lucy)<~>~generous(lucy))))&
(![X]:((tall(X)<~>kind(X))<=>(kind(X)<~>~kind(X))))&
(![X]:((patient(X)<~>~strong(X))<=>(~patient(X)|old(X))))&
(![X]:((calm(X)<~>~strong(X))<=>(kind(X)<~>~brave(X))))&
(![X]:((~patient(X)&~funny(X))=>(old(X)&~quiet(X))))&
(![X]:((~quiet(X)|wise(X))<=>(~strong(X)|funny(X))))&
((?[X]:((curious(X)<~>tall(X))))=>(?[X]:((~calm(X)<~>rich(X)))))&
((creative(lucy))=>(?[X]:(~quiet(X))))&
(![X]:((creative(X)|~brave(X))<=>(~funny(X)|patient(X))))&
(![X]:((~calm(X)<~>curious(X))=>(~tall(X)&wise(X))))&
(![X]:((kind(X)|~creative(X))<=>(~curious(X)<~>~quiet(X))))&
(![X]:((wise(X)|~humble(X))<=>(~creative(X)|~calm(X))))&
(![X]:((calm(X)<~>~quiet(X))<=>(~quiet(X)|kind(X))))&
(![X]:((tall(X)|~patient(X))=>(creative(X)<~>quiet(X))))&
((funny(mary)&brave(mary)))&
((~happy(mary)<~>~generous(mary)))&
(?[X]:(~wise(X)))&
(?[X]:(quiet(X)))&
(~humble(lucy))&
(?[X]:(funny(X)))&
(?[X]:((~calm(X)<~>~tall(X)))) | patient(lucy) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p8",
"p10",
"p12",
"p14",
"p15",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 616139913816391678865702
% SZS output start Proof for 616139913816391678865702
1. ? [X0] : (happy(X0) | ~funny(X0)) => (~brave(mary) <~> old(mary)) [input p0]
2. ? [X0] : (~tall(X0) | ~rich(X0)) => ~old(mary) [input p1]
4. ! [X0] : ((tall(X0) <~> kind(X0)) <=> (kind(X0) <~> ~kind(X0))) [input p3]
5. ! [X0] : ((patient(X0) <~> ~strong(X0)) <=> (old(X0) | ~patient(X0))) [input p4]
6. ! [X0] : ((calm(X0) <~> ~strong(X0)) <=> (kind(X0) <~> ~brave(X0))) [input p5]
9. ? [X0] : (curious(X0) <~> tall(X0)) => ? [X0] : (~calm(X0) <~> rich(X0)) [input p8]
11. ! [X0] : ((~brave(X0) | creative(X0)) <=> (patient(X0) | ~funny(X0))) [input p10]
13. ! [X0] : ((~creative(X0) | kind(X0)) <=> (~curious(X0) <~> ~quiet(X0))) [input p12]
15. ! [X0] : ((calm(X0) <~> ~quiet(X0)) <=> (kind(X0) | ~quiet(X0))) [input p14]
16. ! [X0] : ((~patient(X0) | tall(X0)) => (creative(X0) <~> quiet(X0))) [input p15]
17. brave(mary) & funny(mary) [input p16]
20. ? [X0] : quiet(X0) [input p19]
24. ~patient(lucy) [input hypothesis]
25. ? [X0] : (curious(X0) <~> tall(X0)) => ? [X1] : (~calm(X1) <~> rich(X1)) [rectify 9]
26. (~brave(mary) <~> old(mary)) | ! [X0] : (~happy(X0) & funny(X0)) [ennf transformation 1]
27. ~old(mary) | ! [X0] : (tall(X0) & rich(X0)) [ennf transformation 2]
31. ? [X1] : (~calm(X1) <~> rich(X1)) | ! [X0] : (curious(X0) <=> tall(X0)) [ennf transformation 25]
34. ! [X0] : ((creative(X0) <~> quiet(X0)) | (patient(X0) & ~tall(X0))) [ennf transformation 16]
35. ((~old(mary) | brave(mary)) & (old(mary) | ~brave(mary))) | ! [X0] : (~happy(X0) & funny(X0)) [nnf transformation 26]
37. ! [X0] : ((((~kind(X0) | ~tall(X0)) & (kind(X0) | tall(X0))) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ((tall(X0) | ~kind(X0)) & (kind(X0) | ~tall(X0))))) [nnf transformation 4]
38. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (~old(X0) & patient(X0))) & ((old(X0) | ~patient(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [nnf transformation 5]
39. ! [X0] : ((((strong(X0) | ~patient(X0)) & (~strong(X0) | patient(X0))) | (~old(X0) & patient(X0))) & (old(X0) | ~patient(X0) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))))) [flattening 38]
40. ! [X0] : ((((strong(X0) | ~calm(X0)) & (~strong(X0) | calm(X0))) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0))))) [nnf transformation 6]
43. ? [X1] : ((~rich(X1) | calm(X1)) & (rich(X1) | ~calm(X1))) | ! [X0] : ((curious(X0) | ~tall(X0)) & (tall(X0) | ~curious(X0))) [nnf transformation 31]
44. ? [X0] : ((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | ! [X1] : ((curious(X1) | ~tall(X1)) & (tall(X1) | ~curious(X1))) [rectify 43]
45. ? [X0] : ((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) => ((~rich(sK0) | calm(sK0)) & (rich(sK0) | ~calm(sK0))) [choice axiom]
46. ((~rich(sK0) | calm(sK0)) & (rich(sK0) | ~calm(sK0))) | ! [X1] : ((curious(X1) | ~tall(X1)) & (tall(X1) | ~curious(X1))) [skolemisation 44,45]
49. ! [X0] : (((~brave(X0) | creative(X0)) | (~patient(X0) & funny(X0))) & ((patient(X0) | ~funny(X0)) | (brave(X0) & ~creative(X0)))) [nnf transformation 11]
50. ! [X0] : ((~brave(X0) | creative(X0) | (~patient(X0) & funny(X0))) & (patient(X0) | ~funny(X0) | (brave(X0) & ~creative(X0)))) [flattening 49]
52. ! [X0] : (((~creative(X0) | kind(X0)) | ((~curious(X0) | quiet(X0)) & (~quiet(X0) | curious(X0)))) & (((quiet(X0) | curious(X0)) & (~quiet(X0) | ~curious(X0))) | (creative(X0) & ~kind(X0)))) [nnf transformation 13]
53. ! [X0] : ((~creative(X0) | kind(X0) | ((~curious(X0) | quiet(X0)) & (~quiet(X0) | curious(X0)))) & (((quiet(X0) | curious(X0)) & (~quiet(X0) | ~curious(X0))) | (creative(X0) & ~kind(X0)))) [flattening 52]
56. ! [X0] : ((((quiet(X0) | ~calm(X0)) & (~quiet(X0) | calm(X0))) | (~kind(X0) & quiet(X0))) & ((kind(X0) | ~quiet(X0)) | ((calm(X0) | quiet(X0)) & (~quiet(X0) | ~calm(X0))))) [nnf transformation 15]
57. ! [X0] : ((((quiet(X0) | ~calm(X0)) & (~quiet(X0) | calm(X0))) | (~kind(X0) & quiet(X0))) & (kind(X0) | ~quiet(X0) | ((calm(X0) | quiet(X0)) & (~quiet(X0) | ~calm(X0))))) [flattening 56]
58. ! [X0] : (((~quiet(X0) | ~creative(X0)) & (quiet(X0) | creative(X0))) | (patient(X0) & ~tall(X0))) [nnf transformation 34]
62. ? [X0] : quiet(X0) => quiet(sK3) [choice axiom]
63. quiet(sK3) [skolemisation 20,62]
69. old(mary) | ~brave(mary) | funny(X0) [cnf transformation 35]
73. ~old(mary) | rich(X0) [cnf transformation 27]
74. ~old(mary) | tall(X0) [cnf transformation 27]
83. ~kind(X0) | ~tall(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 37]
87. ~strong(X0) | patient(X0) | patient(X0) [cnf transformation 39]
92. ~brave(X0) | kind(X0) | calm(X0) | strong(X0) [cnf transformation 40]
97. ~calm(X0) | strong(X0) | ~brave(X0) | ~kind(X0) [cnf transformation 40]
108. ~rich(sK0) | calm(sK0) | curious(X1) | ~tall(X1) [cnf transformation 46]
110. ~creative(X0) | ~funny(X0) | patient(X0) [cnf transformation 50]
111. ~funny(X0) | patient(X0) | brave(X0) [cnf transformation 50]
119. ~quiet(X0) | ~curious(X0) | creative(X0) [cnf transformation 53]
121. creative(X0) | curious(X0) | quiet(X0) [cnf transformation 53]
128. kind(X0) | ~quiet(X0) | ~quiet(X0) | ~calm(X0) [cnf transformation 57]
131. ~quiet(X0) | calm(X0) | ~kind(X0) [cnf transformation 57]
132. quiet(X0) | ~calm(X0) | quiet(X0) [cnf transformation 57]
135. creative(X0) | quiet(X0) | patient(X0) [cnf transformation 58]
136. ~creative(X0) | ~quiet(X0) | ~tall(X0) [cnf transformation 58]
139. brave(mary) [cnf transformation 17]
143. quiet(sK3) [cnf transformation 63]
148. ~patient(lucy) [cnf transformation 24]
149. kind(X0) | ~quiet(X0) | ~calm(X0) [duplicate literal removal 128]
150. ~calm(X0) | quiet(X0) [duplicate literal removal 132]
152. ~strong(X0) | patient(X0) [duplicate literal removal 87]
159. ~kind(X0) | ~tall(X0) [duplicate literal removal 83]
165. 2 <=> brave(mary) [avatar definition]
169. 3 <=> old(mary) [avatar definition]
174. 4 <=> ! [X0] : funny(X0) [avatar definition]
175. funny(X0) <- (4) [avatar component clause 174]
178. 4 | ~2 | 3 [avatar split clause 69,169,165,174]
180. 5 <=> ! [X0] : tall(X0) [avatar definition]
181. tall(X0) <- (5) [avatar component clause 180]
182. 5 | ~3 [avatar split clause 74,169,180]
184. 6 <=> ! [X0] : rich(X0) [avatar definition]
185. rich(X0) <- (6) [avatar component clause 184]
186. 6 | ~3 [avatar split clause 73,169,184]
191. 8 <=> curious(lucy) [avatar definition]
192. ~curious(lucy) <- (~8) [avatar component clause 191]
193. curious(lucy) <- (8) [avatar component clause 191]
202. 10 <=> ! [X1] : (curious(X1) | ~tall(X1)) [avatar definition]
203. ~tall(X1) | curious(X1) <- (10) [avatar component clause 202]
205. 11 <=> calm(sK0) [avatar definition]
207. calm(sK0) <- (11) [avatar component clause 205]
209. 12 <=> rich(sK0) [avatar definition]
211. ~rich(sK0) <- (~12) [avatar component clause 209]
212. 10 | 11 | ~12 [avatar split clause 108,209,205,202]
220. 14 <=> creative(lucy) [avatar definition]
221. creative(lucy) <- (14) [avatar component clause 220]
222. ~creative(lucy) <- (~14) [avatar component clause 220]
228. ~calm(X0) | kind(X0) [subsumption resolution 149,150]
229. 2 [avatar split clause 139,165]
250. $false <- (6, ~12) [resolution 211,185]
251. ~6 | 12 [avatar contradiction clause 250]
256. kind(sK0) <- (11) [resolution 228,207]
257. ~tall(sK0) <- (11) [resolution 256,159]
258. $false <- (5, 11) [subsumption resolution 257,181]
259. ~5 | ~11 [avatar contradiction clause 258]
260. curious(X1) <- (5, 10) [subsumption resolution 203,181]
327. 30 <=> creative(sK3) [avatar definition]
329. creative(sK3) <- (30) [avatar component clause 327]
336. ~curious(sK3) | creative(sK3) [resolution 119,143]
337. creative(sK3) <- (5, 10) [subsumption resolution 336,260]
338. 30 | ~5 | ~10 [avatar split clause 337,202,180,327]
361. patient(X0) | brave(X0) <- (4) [resolution 175,111]
368. curious(lucy) | quiet(lucy) <- (~14) [resolution 121,222]
370. quiet(lucy) <- (~8, ~14) [subsumption resolution 368,192]
393. calm(lucy) | ~kind(lucy) <- (~8, ~14) [resolution 131,370]
400. 36 <=> kind(lucy) [avatar definition]
404. 37 <=> calm(lucy) [avatar definition]
405. ~calm(lucy) <- (~37) [avatar component clause 404]
406. calm(lucy) <- (37) [avatar component clause 404]
407. ~36 | 37 | 8 | 14 [avatar split clause 393,220,191,404,400]
413. quiet(X2) | patient(X2) | ~funny(X2) | patient(X2) [resolution 135,110]
414. quiet(X2) | patient(X2) | ~funny(X2) [duplicate literal removal 413]
415. quiet(X2) | patient(X2) <- (4) [subsumption resolution 414,175]
475. ~quiet(sK3) | ~tall(sK3) <- (30) [resolution 329,136]
479. ~tall(sK3) <- (30) [subsumption resolution 475,143]
480. $false <- (5, 30) [subsumption resolution 479,181]
481. ~5 | ~30 [avatar contradiction clause 480]
549. brave(lucy) <- (4) [resolution 361,148]
580. ~curious(X1) | patient(X1) | creative(X1) <- (4) [resolution 415,119]
754. kind(lucy) | calm(lucy) | strong(lucy) <- (4) [resolution 549,92]
758. 57 <=> strong(lucy) [avatar definition]
760. strong(lucy) <- (57) [avatar component clause 758]
764. strong(lucy) | ~brave(lucy) | ~kind(lucy) <- (37) [resolution 406,97]
770. kind(lucy) <- (37) [resolution 406,228]
780. 36 | ~37 [avatar split clause 770,404,400]
782. strong(lucy) | ~kind(lucy) <- (4, 37) [subsumption resolution 764,549]
783. ~36 | 57 | ~4 | ~37 [avatar split clause 782,404,174,758,400]
797. kind(lucy) | strong(lucy) <- (4, ~37) [subsumption resolution 754,405]
798. 57 | 36 | ~4 | 37 [avatar split clause 797,404,174,400,758]
847. ~funny(lucy) | patient(lucy) <- (14) [resolution 221,110]
854. patient(lucy) <- (4, 14) [subsumption resolution 847,175]
855. $false <- (4, 14) [subsumption resolution 854,148]
856. ~4 | ~14 [avatar contradiction clause 855]
1025. patient(lucy) <- (57) [resolution 760,152]
1031. $false <- (57) [subsumption resolution 1025,148]
1032. ~57 [avatar contradiction clause 1031]
1040. patient(lucy) | creative(lucy) <- (4, 8) [resolution 193,580]
1041. creative(lucy) <- (4, 8) [subsumption resolution 1040,148]
1042. $false <- (4, 8, ~14) [subsumption resolution 1041,222]
1043. ~4 | ~8 | 14 [avatar contradiction clause 1042]
1044. $false [avatar sat refutation 178,182,186,212,229,251,259,338,407,481,780,783,798,856,1032,1043]
% SZS output end Proof for 616139913816391678865702
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy then john is calm or humble and vice versa. If someone is either not humble or quiet then someone is both tall and not funny and vice versa. Everyone who is kind is both not strong and not tall and vice versa. Everyone who is humble is not strong or not humble. If mary is either not curious or strong then fred is calm or strong and vice versa. If someone is either not funny or not quiet then someone is not kind. If paul is not strong then john is both rich and old. Everyone who is both not tall and humble is both happy and not tall. Everyone who is curious or not old is both rich and not funny. Everyone who is either not old or creative is old or not wise. If paul is both brave and not generous then someone is either not funny or not humble. If susan is rich or creative then someone is not strong or not kind. Everyone who is not strong or brave is strong and vice versa. If someone is either not patient or not generous then someone is not patient. Everyone who is not quiet or strong is both not humble and not creative and vice versa. Everyone who is both kind and wise is either not creative or not patient. Lucy is not calm or not curious. Lucy is either brave or quiet. Someone is not calm. Someone is old or brave. John is not tall or rich. | Fred is quiet. | neutral | ((?[X]:(~happy(X)))<=>((calm(john)|humble(john))))&
((?[X]:((~humble(X)<~>quiet(X))))<=>(?[X]:((tall(X)&~funny(X)))))&
(![X]:(kind(X)<=>(~strong(X)&~tall(X))))&
(![X]:(humble(X)=>(~strong(X)|~humble(X))))&
(((~curious(mary)<~>strong(mary)))<=>((calm(fred)|strong(fred))))&
((?[X]:((~funny(X)<~>~quiet(X))))=>(?[X]:(~kind(X))))&
((~strong(paul))=>((rich(john)&old(john))))&
(![X]:((~tall(X)&humble(X))=>(happy(X)&~tall(X))))&
(![X]:((curious(X)|~old(X))=>(rich(X)&~funny(X))))&
(![X]:((~old(X)<~>creative(X))=>(old(X)|~wise(X))))&
(((brave(paul)&~generous(paul)))=>(?[X]:((~funny(X)<~>~humble(X)))))&
(((rich(susan)|creative(susan)))=>(?[X]:((~strong(X)|~kind(X)))))&
(![X]:((~strong(X)|brave(X))<=>strong(X)))&
((?[X]:((~patient(X)<~>~generous(X))))=>(?[X]:(~patient(X))))&
(![X]:((~quiet(X)|strong(X))<=>(~humble(X)&~creative(X))))&
(![X]:((kind(X)&wise(X))=>(~creative(X)<~>~patient(X))))&
((~calm(lucy)|~curious(lucy)))&
((brave(lucy)<~>quiet(lucy)))&
(?[X]:(~calm(X)))&
(?[X]:((old(X)|brave(X))))&
((~tall(john)|rich(john))) | quiet(fred) | [] | null | 0 |
If someone is either quiet or not wise then someone is either happy or not brave and vice versa.
Everyone who is not kind is generous.
Everyone who is either old or funny is not generous or tall.
If someone is either not tall or kind then someone is not curious and vice versa.
Everyone who is both strong and not brave is both not happy and not patient.
If john is either not rich or creative then someone is either kind or patient.
Everyone who is not kind or not generous is humble or not quiet and vice versa.
Everyone who is either generous or creative is either not creative or not strong and vice versa.
If someone is not kind then someone is either curious or calm and vice versa.
Everyone who is both happy and not curious is either kind or not calm.
Everyone who is either not kind or not humble is either not calm or not curious and vice versa.
If someone is not strong or not kind then susan is both funny and not humble and vice versa.
If mary is not wise then lucy is tall.
Everyone who is both creative and not quiet is either rich or not strong and vice versa.
John is wise or curious.
Someone is not funny.
Someone is both not happy and creative.
Alice is brave or not old.
Susan is not generous or tall. | Mary is humble. | neutral | ((?[X]:((quiet(X)<~>~wise(X))))<=>(?[X]:((happy(X)<~>~brave(X)))))&
(![X]:(~kind(X)=>generous(X)))&
(![X]:((old(X)<~>funny(X))=>(~generous(X)|tall(X))))&
((?[X]:((~tall(X)<~>kind(X))))<=>(?[X]:(~curious(X))))&
(![X]:((strong(X)&~brave(X))=>(~happy(X)&~patient(X))))&
(((~rich(john)<~>creative(john)))=>(?[X]:((kind(X)<~>patient(X)))))&
(![X]:((~kind(X)|~generous(X))<=>(humble(X)|~quiet(X))))&
(![X]:((generous(X)<~>creative(X))<=>(~creative(X)<~>~strong(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((curious(X)<~>calm(X)))))&
(![X]:((happy(X)&~curious(X))=>(kind(X)<~>~calm(X))))&
(![X]:((~kind(X)<~>~humble(X))<=>(~calm(X)<~>~curious(X))))&
((?[X]:((~strong(X)|~kind(X))))<=>((funny(susan)&~humble(susan))))&
((~wise(mary))=>(tall(lucy)))&
(![X]:((creative(X)&~quiet(X))<=>(rich(X)<~>~strong(X))))&
((wise(john)|curious(john)))&
(?[X]:(~funny(X)))&
(?[X]:((~happy(X)&creative(X))))&
((brave(alice)|~old(alice)))&
((~generous(susan)|tall(susan))) | humble(mary) | [] | null | 0 |
Everyone who is either funny or happy is not funny or humble and vice versa. If someone is both not curious and humble then someone is either not old or patient and vice versa. Everyone who is creative or patient is not kind. If someone is not funny then someone is either kind or strong. Everyone who is either kind or calm is patient or curious and vice versa. If someone is either calm or not humble then someone is either rich or not humble. If fred is not brave or generous then john is either not strong or not old and vice versa. If someone is wise or not curious then susan is quiet. Everyone who is not quiet or quiet is both quiet and not happy and vice versa. If someone is creative then someone is not tall and vice versa. If someone is not generous or not strong then someone is either not calm or calm. If john is tall or not quiet then someone is either creative or not happy and vice versa. Everyone who is both tall and generous is rich and vice versa. Everyone who is wise or not old is generous. Everyone who is either not tall or calm is both happy and not wise and vice versa. Everyone who is not kind or not patient is both generous and rich. Someone is funny or not generous. Alice is both not happy and not old. Paul is either not happy or not strong. Someone is not happy or not wise. Someone is generous or brave. Alice is both wise and rich. Someone is both not old and not wise. | John is not patient. | entailment | (![X]:((funny(X)<~>happy(X))<=>(~funny(X)|humble(X))))&
((?[X]:((~curious(X)&humble(X))))<=>(?[X]:((~old(X)<~>patient(X)))))&
(![X]:((creative(X)|patient(X))=>~kind(X)))&
((?[X]:(~funny(X)))=>(?[X]:((kind(X)<~>strong(X)))))&
(![X]:((kind(X)<~>calm(X))<=>(patient(X)|curious(X))))&
((?[X]:((calm(X)<~>~humble(X))))=>(?[X]:((rich(X)<~>~humble(X)))))&
(((~brave(fred)|generous(fred)))<=>((~strong(john)<~>~old(john))))&
((?[X]:((wise(X)|~curious(X))))=>(quiet(susan)))&
(![X]:((~quiet(X)|quiet(X))<=>(quiet(X)&~happy(X))))&
((?[X]:(creative(X)))<=>(?[X]:(~tall(X))))&
((?[X]:((~generous(X)|~strong(X))))=>(?[X]:((~calm(X)<~>calm(X)))))&
(((tall(john)|~quiet(john)))<=>(?[X]:((creative(X)<~>~happy(X)))))&
(![X]:((tall(X)&generous(X))<=>rich(X)))&
(![X]:((wise(X)|~old(X))=>generous(X)))&
(![X]:((~tall(X)<~>calm(X))<=>(happy(X)&~wise(X))))&
(![X]:((~kind(X)|~patient(X))=>(generous(X)&rich(X))))&
(?[X]:((funny(X)|~generous(X))))&
((~happy(alice)&~old(alice)))&
((~happy(paul)<~>~strong(paul)))&
(?[X]:((~happy(X)|~wise(X))))&
(?[X]:((generous(X)|brave(X))))&
((wise(alice)&rich(alice)))&
(?[X]:((~old(X)&~wise(X)))) | ~patient(john) | [
"p2",
"p4",
"p8",
"p9",
"p11",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4961723648494893933754783
% SZS output start Proof for 4961723648494893933754783
3. ! [X0] : ((patient(X0) | creative(X0)) => ~kind(X0)) [input p2]
5. ! [X0] : ((kind(X0) <~> calm(X0)) <=> (curious(X0) | patient(X0))) [input p4]
9. ! [X0] : ((quiet(X0) | ~quiet(X0)) <=> (~happy(X0) & quiet(X0))) [input p8]
10. ? [X0] : creative(X0) <=> ? [X0] : ~tall(X0) [input p9]
12. (~quiet(john) | tall(john)) <=> ? [X0] : (creative(X0) <~> ~happy(X0)) [input p11]
13. ! [X0] : ((generous(X0) & tall(X0)) <=> rich(X0)) [input p12]
15. ! [X0] : ((~tall(X0) <~> calm(X0)) <=> (~wise(X0) & happy(X0))) [input p14]
16. ! [X0] : ((~patient(X0) | ~kind(X0)) => (rich(X0) & generous(X0))) [input p15]
24. patient(john) [input hypothesis]
28. ? [X0] : creative(X0) <=> ? [X1] : ~tall(X1) [rectify 10]
30. ! [X0] : (~kind(X0) | (~patient(X0) & ~creative(X0))) [ennf transformation 3]
36. ! [X0] : ((rich(X0) & generous(X0)) | (patient(X0) & kind(X0))) [ennf transformation 16]
48. ! [X0] : ((((~calm(X0) | ~kind(X0)) & (calm(X0) | kind(X0))) | (~curious(X0) & ~patient(X0))) & ((curious(X0) | patient(X0)) | ((kind(X0) | ~calm(X0)) & (calm(X0) | ~kind(X0))))) [nnf transformation 5]
49. ! [X0] : ((((~calm(X0) | ~kind(X0)) & (calm(X0) | kind(X0))) | (~curious(X0) & ~patient(X0))) & (curious(X0) | patient(X0) | ((kind(X0) | ~calm(X0)) & (calm(X0) | ~kind(X0))))) [flattening 48]
56. ! [X0] : (((quiet(X0) | ~quiet(X0)) | (happy(X0) | ~quiet(X0))) & ((~happy(X0) & quiet(X0)) | (~quiet(X0) & quiet(X0)))) [nnf transformation 9]
57. ! [X0] : ((quiet(X0) | ~quiet(X0) | happy(X0) | ~quiet(X0)) & ((~happy(X0) & quiet(X0)) | (~quiet(X0) & quiet(X0)))) [flattening 56]
58. (? [X0] : creative(X0) | ! [X1] : tall(X1)) & (? [X1] : ~tall(X1) | ! [X0] : ~creative(X0)) [nnf transformation 28]
59. (? [X0] : creative(X0) | ! [X1] : tall(X1)) & (? [X2] : ~tall(X2) | ! [X3] : ~creative(X3)) [rectify 58]
60. ? [X0] : creative(X0) => creative(sK4) [choice axiom]
61. ? [X2] : ~tall(X2) => ~tall(sK5) [choice axiom]
62. (creative(sK4) | ! [X1] : tall(X1)) & (~tall(sK5) | ! [X3] : ~creative(X3)) [skolemisation 59,61,60]
67. ((~quiet(john) | tall(john)) | ! [X0] : ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) & (? [X0] : ((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) | (quiet(john) & ~tall(john))) [nnf transformation 12]
68. (~quiet(john) | tall(john) | ! [X0] : ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) & (? [X0] : ((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) | (quiet(john) & ~tall(john))) [flattening 67]
69. (~quiet(john) | tall(john) | ! [X0] : ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) & (? [X1] : ((happy(X1) | ~creative(X1)) & (~happy(X1) | creative(X1))) | (quiet(john) & ~tall(john))) [rectify 68]
70. ? [X1] : ((happy(X1) | ~creative(X1)) & (~happy(X1) | creative(X1))) => ((happy(sK7) | ~creative(sK7)) & (~happy(sK7) | creative(sK7))) [choice axiom]
71. (~quiet(john) | tall(john) | ! [X0] : ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) & (((happy(sK7) | ~creative(sK7)) & (~happy(sK7) | creative(sK7))) | (quiet(john) & ~tall(john))) [skolemisation 69,70]
72. ! [X0] : (((generous(X0) & tall(X0)) | ~rich(X0)) & (rich(X0) | (~generous(X0) | ~tall(X0)))) [nnf transformation 13]
73. ! [X0] : (((generous(X0) & tall(X0)) | ~rich(X0)) & (rich(X0) | ~generous(X0) | ~tall(X0))) [flattening 72]
74. ! [X0] : ((((~calm(X0) | tall(X0)) & (calm(X0) | ~tall(X0))) | (wise(X0) | ~happy(X0))) & ((~wise(X0) & happy(X0)) | ((~tall(X0) | ~calm(X0)) & (calm(X0) | tall(X0))))) [nnf transformation 15]
75. ! [X0] : ((((~calm(X0) | tall(X0)) & (calm(X0) | ~tall(X0))) | wise(X0) | ~happy(X0)) & ((~wise(X0) & happy(X0)) | ((~tall(X0) | ~calm(X0)) & (calm(X0) | tall(X0))))) [flattening 74]
97. ~kind(X0) | ~creative(X0) [cnf transformation 30]
98. ~kind(X0) | ~patient(X0) [cnf transformation 30]
103. calm(X0) | kind(X0) | ~patient(X0) [cnf transformation 49]
119. quiet(X0) | quiet(X0) [cnf transformation 57]
121. ~happy(X0) | quiet(X0) [cnf transformation 57]
122. ~quiet(X0) | ~happy(X0) [cnf transformation 57]
124. ~tall(sK5) | ~creative(X3) [cnf transformation 62]
135. ~quiet(john) | tall(john) | creative(X0) | happy(X0) [cnf transformation 71]
137. ~rich(X0) | tall(X0) [cnf transformation 73]
142. happy(X0) | ~tall(X0) | ~calm(X0) [cnf transformation 75]
149. rich(X0) | kind(X0) [cnf transformation 36]
162. patient(john) [cnf transformation 24]
163. quiet(X0) [duplicate literal removal 119]
212. ~patient(X0) | calm(X0) [subsumption resolution 103,98]
266. ~happy(X0) [subsumption resolution 121,122]
276. 24 <=> ! [X3] : ~creative(X3) [avatar definition]
277. ~creative(X3) <- (24) [avatar component clause 276]
279. 25 <=> tall(sK5) [avatar definition]
281. ~tall(sK5) <- (~25) [avatar component clause 279]
282. 24 | ~25 [avatar split clause 124,279,276]
283. tall(john) | creative(X0) | happy(X0) [subsumption resolution 135,163]
284. tall(john) | creative(X0) [subsumption resolution 283,266]
286. 26 <=> ! [X0] : creative(X0) [avatar definition]
287. creative(X0) <- (26) [avatar component clause 286]
289. 27 <=> tall(john) [avatar definition]
291. tall(john) <- (27) [avatar component clause 289]
292. 26 | 27 [avatar split clause 284,289,286]
299. ~tall(X0) | ~calm(X0) [subsumption resolution 142,266]
337. tall(X1) | kind(X1) [resolution 149,137]
348. calm(john) [resolution 212,162]
350. ~calm(john) <- (27) [resolution 299,291]
352. $false <- (27) [subsumption resolution 350,348]
353. ~27 [avatar contradiction clause 352]
366. kind(sK5) <- (~25) [resolution 337,281]
374. ~creative(sK5) <- (~25) [resolution 366,97]
375. $false <- (~25, 26) [subsumption resolution 374,287]
376. 25 | ~26 [avatar contradiction clause 375]
377. $false <- (24, 26) [subsumption resolution 277,287]
378. ~24 | ~26 [avatar contradiction clause 377]
379. $false [avatar sat refutation 282,292,353,376,378]
% SZS output end Proof for 4961723648494893933754783
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is both quiet and happy and vice versa. If someone is both not generous and not wise then john is either humble or not wise and vice versa. If paul is strong then paul is brave. If alice is either not old or not brave then paul is both not calm and not brave. Everyone who is not tall or not kind is old or quiet and vice versa. If someone is not calm then susan is old and vice versa. Everyone who is both curious and kind is not brave or patient and vice versa. Everyone who is either curious or not curious is brave or not wise. Everyone who is not happy or quiet is either not wise or not funny. If someone is both not patient and not creative then paul is both tall and patient. If someone is either not humble or not strong then someone is either happy or not calm. If paul is not patient or curious then fred is not rich or not tall and vice versa. Everyone who is both not strong and quiet is either happy or not tall. Everyone who is either tall or brave is both not patient and not curious and vice versa. Everyone who is not brave or not humble is both not patient and not curious and vice versa. Everyone who is not curious is not strong or not funny and vice versa. Paul is quiet. Someone is both not quiet and funny. Someone is not old or not curious. John is kind or not rich. Someone is not humble or not happy. Alice is wise. | Paul is patient. | contradiction | (![X]:(~wise(X)<=>(quiet(X)&happy(X))))&
((?[X]:((~generous(X)&~wise(X))))<=>((humble(john)<~>~wise(john))))&
((strong(paul))=>(brave(paul)))&
(((~old(alice)<~>~brave(alice)))=>((~calm(paul)&~brave(paul))))&
(![X]:((~tall(X)|~kind(X))<=>(old(X)|quiet(X))))&
((?[X]:(~calm(X)))<=>(old(susan)))&
(![X]:((curious(X)&kind(X))<=>(~brave(X)|patient(X))))&
(![X]:((curious(X)<~>~curious(X))=>(brave(X)|~wise(X))))&
(![X]:((~happy(X)|quiet(X))=>(~wise(X)<~>~funny(X))))&
((?[X]:((~patient(X)&~creative(X))))=>((tall(paul)&patient(paul))))&
((?[X]:((~humble(X)<~>~strong(X))))=>(?[X]:((happy(X)<~>~calm(X)))))&
(((~patient(paul)|curious(paul)))<=>((~rich(fred)|~tall(fred))))&
(![X]:((~strong(X)&quiet(X))=>(happy(X)<~>~tall(X))))&
(![X]:((tall(X)<~>brave(X))<=>(~patient(X)&~curious(X))))&
(![X]:((~brave(X)|~humble(X))<=>(~patient(X)&~curious(X))))&
(![X]:(~curious(X)<=>(~strong(X)|~funny(X))))&
(quiet(paul))&
(?[X]:((~quiet(X)&funny(X))))&
(?[X]:((~old(X)|~curious(X))))&
((kind(john)|~rich(john)))&
(?[X]:((~humble(X)|~happy(X))))&
(wise(alice)) | patient(paul) | [
"p4",
"p6",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4833887735291361748153960
% SZS output start Proof for 4833887735291361748153960
5. ! [X0] : ((~kind(X0) | ~tall(X0)) <=> (quiet(X0) | old(X0))) [input p4]
7. ! [X0] : ((kind(X0) & curious(X0)) <=> (patient(X0) | ~brave(X0))) [input p6]
14. ! [X0] : ((tall(X0) <~> brave(X0)) <=> (~curious(X0) & ~patient(X0))) [input p13]
15. ! [X0] : ((~humble(X0) | ~brave(X0)) <=> (~curious(X0) & ~patient(X0))) [input p14]
17. quiet(paul) [input p16]
23. patient(paul) [input hypothesis]
41. ! [X0] : (((~kind(X0) | ~tall(X0)) | (~quiet(X0) & ~old(X0))) & ((quiet(X0) | old(X0)) | (kind(X0) & tall(X0)))) [nnf transformation 5]
42. ! [X0] : ((~kind(X0) | ~tall(X0) | (~quiet(X0) & ~old(X0))) & (quiet(X0) | old(X0) | (kind(X0) & tall(X0)))) [flattening 41]
47. ! [X0] : (((kind(X0) & curious(X0)) | (~patient(X0) & brave(X0))) & ((patient(X0) | ~brave(X0)) | (~kind(X0) | ~curious(X0)))) [nnf transformation 7]
48. ! [X0] : (((kind(X0) & curious(X0)) | (~patient(X0) & brave(X0))) & (patient(X0) | ~brave(X0) | ~kind(X0) | ~curious(X0))) [flattening 47]
58. ! [X0] : ((((~brave(X0) | ~tall(X0)) & (brave(X0) | tall(X0))) | (curious(X0) | patient(X0))) & ((~curious(X0) & ~patient(X0)) | ((tall(X0) | ~brave(X0)) & (brave(X0) | ~tall(X0))))) [nnf transformation 14]
59. ! [X0] : ((((~brave(X0) | ~tall(X0)) & (brave(X0) | tall(X0))) | curious(X0) | patient(X0)) & ((~curious(X0) & ~patient(X0)) | ((tall(X0) | ~brave(X0)) & (brave(X0) | ~tall(X0))))) [flattening 58]
60. ! [X0] : (((~humble(X0) | ~brave(X0)) | (curious(X0) | patient(X0))) & ((~curious(X0) & ~patient(X0)) | (humble(X0) & brave(X0)))) [nnf transformation 15]
61. ! [X0] : ((~humble(X0) | ~brave(X0) | curious(X0) | patient(X0)) & ((~curious(X0) & ~patient(X0)) | (humble(X0) & brave(X0)))) [flattening 60]
87. ~kind(X0) | ~tall(X0) | ~quiet(X0) [cnf transformation 42]
91. curious(X0) | brave(X0) [cnf transformation 48]
94. ~patient(X0) | kind(X0) [cnf transformation 48]
112. ~patient(X0) | tall(X0) | ~brave(X0) [cnf transformation 59]
119. ~curious(X0) | brave(X0) [cnf transformation 61]
125. quiet(paul) [cnf transformation 17]
132. patient(paul) [cnf transformation 23]
233. 21 <=> patient(paul) [avatar definition]
235. patient(paul) <- (21) [avatar component clause 233]
242. brave(X0) [subsumption resolution 119,91]
270. 21 [avatar split clause 132,233]
279. kind(paul) <- (21) [resolution 94,235]
327. 31 <=> tall(paul) [avatar definition]
329. ~tall(paul) <- (~31) [avatar component clause 327]
333. ~tall(paul) | ~quiet(paul) <- (21) [resolution 87,279]
334. ~tall(paul) <- (21) [subsumption resolution 333,125]
335. ~31 | ~21 [avatar split clause 334,233,327]
348. tall(paul) | ~brave(paul) <- (21) [resolution 112,235]
349. ~brave(paul) <- (21, ~31) [subsumption resolution 348,329]
350. $false <- (21, ~31) [subsumption resolution 349,242]
351. ~21 | 31 [avatar contradiction clause 350]
352. $false [avatar sat refutation 270,335,351]
% SZS output end Proof for 4833887735291361748153960
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or strong is strong and vice versa.
Everyone who is either humble or strong is curious and vice versa.
Everyone who is either not humble or rich is both calm and strong and vice versa.
If someone is wise then lucy is either not calm or not old and vice versa.
Everyone who is either not generous or not quiet is either brave or not quiet and vice versa.
If someone is not quiet or wise then mary is either kind or tall.
If alice is not patient or not happy then john is brave and vice versa.
Everyone who is not calm is both not strong and not wise and vice versa.
If someone is not patient then fred is either not quiet or wise.
Everyone who is kind or generous is not rich or wise.
If fred is either not patient or not funny then someone is wise and vice versa.
Everyone who is either not tall or not strong is both not creative and calm.
Everyone who is both tall and calm is not tall or not funny and vice versa.
Everyone who is not curious is not rich.
If someone is both not brave and not patient then lucy is kind and vice versa.
Someone is not wise.
Paul is not old.
Lucy is old or funny.
Someone is not patient or not curious.
Susan is not curious or not patient.
Someone is not tall or creative.
Someone is either not tall or quiet.
Alice is happy or kind. | Fred is patient. | contradiction | (![X]:((funny(X)<~>strong(X))<=>strong(X)))&
(![X]:((humble(X)<~>strong(X))<=>curious(X)))&
(![X]:((~humble(X)<~>rich(X))<=>(calm(X)&strong(X))))&
((?[X]:(wise(X)))<=>((~calm(lucy)<~>~old(lucy))))&
(![X]:((~generous(X)<~>~quiet(X))<=>(brave(X)<~>~quiet(X))))&
((?[X]:((~quiet(X)|wise(X))))=>((kind(mary)<~>tall(mary))))&
(((~patient(alice)|~happy(alice)))<=>(brave(john)))&
(![X]:(~calm(X)<=>(~strong(X)&~wise(X))))&
((?[X]:(~patient(X)))=>((~quiet(fred)<~>wise(fred))))&
(![X]:((kind(X)|generous(X))=>(~rich(X)|wise(X))))&
(((~patient(fred)<~>~funny(fred)))<=>(?[X]:(wise(X))))&
(![X]:((~tall(X)<~>~strong(X))=>(~creative(X)&calm(X))))&
(![X]:((tall(X)&calm(X))<=>(~tall(X)|~funny(X))))&
(![X]:(~curious(X)=>~rich(X)))&
((?[X]:((~brave(X)&~patient(X))))<=>(kind(lucy)))&
(?[X]:(~wise(X)))&
(~old(paul))&
((old(lucy)|funny(lucy)))&
(?[X]:((~patient(X)|~curious(X))))&
((~curious(susan)|~patient(susan)))&
(?[X]:((~tall(X)|creative(X))))&
(?[X]:((~tall(X)<~>quiet(X))))&
((happy(alice)|kind(alice))) | patient(fred) | [
"p0",
"p3",
"p10",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7507193659919761724311035
% SZS output start Proof for 7507193659919761724311035
1. ! [X0] : ((funny(X0) <~> strong(X0)) <=> strong(X0)) [input p0]
4. ? [X0] : wise(X0) <=> (~calm(lucy) <~> ~old(lucy)) [input p3]
11. (~patient(fred) <~> ~funny(fred)) <=> ? [X0] : wise(X0) [input p10]
13. ! [X0] : ((calm(X0) & tall(X0)) <=> (~funny(X0) | ~tall(X0))) [input p12]
18. funny(lucy) | old(lucy) [input p17]
24. patient(fred) [input hypothesis]
31. ! [X0] : ((((~strong(X0) | ~funny(X0)) & (strong(X0) | funny(X0))) | ~strong(X0)) & (strong(X0) | ((funny(X0) | ~strong(X0)) & (strong(X0) | ~funny(X0))))) [nnf transformation 1]
35. (? [X0] : wise(X0) | ((~calm(lucy) | old(lucy)) & (~old(lucy) | calm(lucy)))) & (((old(lucy) | calm(lucy)) & (~old(lucy) | ~calm(lucy))) | ! [X0] : ~wise(X0)) [nnf transformation 4]
36. (? [X0] : wise(X0) | ((~calm(lucy) | old(lucy)) & (~old(lucy) | calm(lucy)))) & (((old(lucy) | calm(lucy)) & (~old(lucy) | ~calm(lucy))) | ! [X1] : ~wise(X1)) [rectify 35]
37. ? [X0] : wise(X0) => wise(sK0) [choice axiom]
38. (wise(sK0) | ((~calm(lucy) | old(lucy)) & (~old(lucy) | calm(lucy)))) & (((old(lucy) | calm(lucy)) & (~old(lucy) | ~calm(lucy))) | ! [X1] : ~wise(X1)) [skolemisation 36,37]
46. (((funny(fred) | patient(fred)) & (~funny(fred) | ~patient(fred))) | ! [X0] : ~wise(X0)) & (? [X0] : wise(X0) | ((~patient(fred) | funny(fred)) & (~funny(fred) | patient(fred)))) [nnf transformation 11]
47. (((funny(fred) | patient(fred)) & (~funny(fred) | ~patient(fred))) | ! [X0] : ~wise(X0)) & (? [X1] : wise(X1) | ((~patient(fred) | funny(fred)) & (~funny(fred) | patient(fred)))) [rectify 46]
48. ? [X1] : wise(X1) => wise(sK1) [choice axiom]
49. (((funny(fred) | patient(fred)) & (~funny(fred) | ~patient(fred))) | ! [X0] : ~wise(X0)) & (wise(sK1) | ((~patient(fred) | funny(fred)) & (~funny(fred) | patient(fred)))) [skolemisation 47,48]
51. ! [X0] : (((calm(X0) & tall(X0)) | (funny(X0) & tall(X0))) & ((~funny(X0) | ~tall(X0)) | (~calm(X0) | ~tall(X0)))) [nnf transformation 13]
52. ! [X0] : (((calm(X0) & tall(X0)) | (funny(X0) & tall(X0))) & (~funny(X0) | ~tall(X0) | ~calm(X0) | ~tall(X0))) [flattening 51]
66. strong(X0) | strong(X0) | ~funny(X0) [cnf transformation 31]
69. ~strong(X0) | ~funny(X0) | ~strong(X0) [cnf transformation 31]
80. ~old(lucy) | ~calm(lucy) | ~wise(X1) [cnf transformation 38]
107. wise(sK1) | ~patient(fred) | funny(fred) [cnf transformation 49]
118. calm(X0) | funny(X0) [cnf transformation 52]
125. funny(lucy) | old(lucy) [cnf transformation 18]
132. patient(fred) [cnf transformation 24]
139. strong(X0) | ~funny(X0) [duplicate literal removal 66]
140. ~strong(X0) | ~funny(X0) [duplicate literal removal 69]
141. ~funny(X0) [subsumption resolution 139,140]
143. 1 <=> old(lucy) [avatar definition]
147. 2 <=> calm(lucy) [avatar definition]
149. ~calm(lucy) <- (~2) [avatar component clause 147]
157. 4 <=> ! [X1] : ~wise(X1) [avatar definition]
158. ~wise(X1) <- (4) [avatar component clause 157]
160. 4 | ~2 | ~1 [avatar split clause 80,143,147,157]
208. 14 <=> patient(fred) [avatar definition]
212. wise(sK1) | ~patient(fred) [subsumption resolution 107,141]
214. 15 <=> wise(sK1) [avatar definition]
216. wise(sK1) <- (15) [avatar component clause 214]
217. ~14 | 15 [avatar split clause 212,214,208]
219. calm(X0) [subsumption resolution 118,141]
239. old(lucy) [subsumption resolution 125,141]
240. 1 [avatar split clause 239,143]
266. 14 [avatar split clause 132,208]
269. $false <- (~2) [subsumption resolution 149,219]
270. 2 [avatar contradiction clause 269]
273. $false <- (4, 15) [resolution 216,158]
274. ~4 | ~15 [avatar contradiction clause 273]
275. $false [avatar sat refutation 160,217,240,266,270,274]
% SZS output end Proof for 7507193659919761724311035
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or quiet is both brave and not funny and vice versa.
If someone is either patient or not humble then john is both kind and humble.
If alice is either not humble or kind then someone is strong or rich.
If someone is not creative then someone is old or rich and vice versa.
Everyone who is both not calm and not wise is patient or funny and vice versa.
Everyone who is either patient or generous is funny or strong.
Everyone who is both not wise and not creative is either tall or not funny and vice versa.
If susan is quiet then paul is both wise and patient and vice versa.
Everyone who is kind is either happy or not funny and vice versa.
If someone is tall then susan is not strong or patient and vice versa.
If john is not curious then john is not calm or not old.
If someone is not calm or not quiet then lucy is old or rich and vice versa.
If lucy is not wise then someone is either wise or not rich and vice versa.
Everyone who is both humble and strong is either calm or not happy and vice versa.
Everyone who is either not kind or humble is funny or not funny and vice versa.
If mary is either patient or humble then someone is either not funny or wise and vice versa.
Someone is either not tall or not happy.
Susan is kind or not generous.
Someone is both wise and happy.
Someone is brave.
Someone is not generous or not quiet.
Someone is both creative and not humble.
Paul is both not generous and not brave.
Mary is not quiet or not wise. | John is kind. | entailment | (![X]:((~curious(X)<~>quiet(X))<=>(brave(X)&~funny(X))))&
((?[X]:((patient(X)<~>~humble(X))))=>((kind(john)&humble(john))))&
(((~humble(alice)<~>kind(alice)))=>(?[X]:((strong(X)|rich(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((old(X)|rich(X)))))&
(![X]:((~calm(X)&~wise(X))<=>(patient(X)|funny(X))))&
(![X]:((patient(X)<~>generous(X))=>(funny(X)|strong(X))))&
(![X]:((~wise(X)&~creative(X))<=>(tall(X)<~>~funny(X))))&
((quiet(susan))<=>((wise(paul)&patient(paul))))&
(![X]:(kind(X)<=>(happy(X)<~>~funny(X))))&
((?[X]:(tall(X)))<=>((~strong(susan)|patient(susan))))&
((~curious(john))=>((~calm(john)|~old(john))))&
((?[X]:((~calm(X)|~quiet(X))))<=>((old(lucy)|rich(lucy))))&
((~wise(lucy))<=>(?[X]:((wise(X)<~>~rich(X)))))&
(![X]:((humble(X)&strong(X))<=>(calm(X)<~>~happy(X))))&
(![X]:((~kind(X)<~>humble(X))<=>(funny(X)|~funny(X))))&
(((patient(mary)<~>humble(mary)))<=>(?[X]:((~funny(X)<~>wise(X)))))&
(?[X]:((~tall(X)<~>~happy(X))))&
((kind(susan)|~generous(susan)))&
(?[X]:((wise(X)&happy(X))))&
(?[X]:(brave(X)))&
(?[X]:((~generous(X)|~quiet(X))))&
(?[X]:((creative(X)&~humble(X))))&
((~generous(paul)&~brave(paul)))&
((~quiet(mary)|~wise(mary))) | kind(john) | [
"p1",
"p4",
"p8",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3344902280701351991756848
% SZS output start Proof for 3344902280701351991756848
2. ? [X0] : (patient(X0) <~> ~humble(X0)) => (humble(john) & kind(john)) [input p1]
5. ! [X0] : ((~wise(X0) & ~calm(X0)) <=> (funny(X0) | patient(X0))) [input p4]
9. ! [X0] : (kind(X0) <=> (happy(X0) <~> ~funny(X0))) [input p8]
15. ! [X0] : ((~kind(X0) <~> humble(X0)) <=> (~funny(X0) | funny(X0))) [input p14]
19. ? [X0] : (happy(X0) & wise(X0)) [input p18]
25. ~kind(john) [input hypothesis]
27. (humble(john) & kind(john)) | ! [X0] : (patient(X0) <=> ~humble(X0)) [ennf transformation 2]
35. (humble(john) & kind(john)) | ! [X0] : ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0))) [nnf transformation 27]
44. ! [X0] : (((~wise(X0) & ~calm(X0)) | (~funny(X0) & ~patient(X0))) & ((funny(X0) | patient(X0)) | (wise(X0) | calm(X0)))) [nnf transformation 5]
45. ! [X0] : (((~wise(X0) & ~calm(X0)) | (~funny(X0) & ~patient(X0))) & (funny(X0) | patient(X0) | wise(X0) | calm(X0))) [flattening 44]
51. ! [X0] : ((kind(X0) | ((happy(X0) | funny(X0)) & (~funny(X0) | ~happy(X0)))) & (((funny(X0) | ~happy(X0)) & (~funny(X0) | happy(X0))) | ~kind(X0))) [nnf transformation 9]
68. ! [X0] : ((((~humble(X0) | kind(X0)) & (humble(X0) | ~kind(X0))) | (funny(X0) & ~funny(X0))) & ((~funny(X0) | funny(X0)) | ((~kind(X0) | ~humble(X0)) & (humble(X0) | kind(X0))))) [nnf transformation 15]
69. ! [X0] : ((((~humble(X0) | kind(X0)) & (humble(X0) | ~kind(X0))) | (funny(X0) & ~funny(X0))) & (~funny(X0) | funny(X0) | ((~kind(X0) | ~humble(X0)) & (humble(X0) | kind(X0))))) [flattening 68]
77. ? [X0] : (happy(X0) & wise(X0)) => (happy(sK8) & wise(sK8)) [choice axiom]
78. happy(sK8) & wise(sK8) [skolemisation 19,77]
92. kind(john) | patient(X0) | humble(X0) [cnf transformation 35]
103. ~wise(X0) | ~patient(X0) [cnf transformation 45]
104. ~wise(X0) | ~funny(X0) [cnf transformation 45]
117. ~happy(X0) | funny(X0) | ~kind(X0) [cnf transformation 51]
142. ~humble(X0) | kind(X0) | ~funny(X0) [cnf transformation 69]
143. ~humble(X0) | kind(X0) | funny(X0) [cnf transformation 69]
155. wise(sK8) [cnf transformation 78]
156. happy(sK8) [cnf transformation 78]
164. ~kind(john) [cnf transformation 25]
166. 1 <=> ! [X0] : (patient(X0) | humble(X0)) [avatar definition]
167. humble(X0) | patient(X0) <- (1) [avatar component clause 166]
178. 4 <=> kind(john) [avatar definition]
181. 1 | 4 [avatar split clause 92,178,166]
320. ~humble(X0) | kind(X0) [subsumption resolution 142,143]
388. ~4 [avatar split clause 164,178]
395. ~patient(sK8) [resolution 103,155]
396. ~funny(sK8) [resolution 104,155]
405. kind(X0) | patient(X0) <- (1) [resolution 320,167]
480. funny(sK8) | ~kind(sK8) [resolution 117,156]
481. ~kind(sK8) [subsumption resolution 480,396]
482. patient(sK8) <- (1) [resolution 481,405]
483. $false <- (1) [subsumption resolution 482,395]
484. ~1 [avatar contradiction clause 483]
485. $false [avatar sat refutation 181,388,484]
% SZS output end Proof for 3344902280701351991756848
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is both not kind and happy then someone is happy. If someone is both kind and happy then someone is kind. If someone is old then someone is tall and vice versa. If someone is both not creative and funny then someone is not humble or not creative and vice versa. If john is not calm or patient then susan is happy. Everyone who is not wise or not tall is both not kind and not humble and vice versa. If john is both calm and wise then fred is either quiet or brave and vice versa. Everyone who is either not patient or not happy is patient and vice versa. If someone is both kind and rich then susan is humble and vice versa. Everyone who is rich is not patient and vice versa. If someone is both tall and not quiet then someone is not creative or not strong and vice versa. Everyone who is both calm and not quiet is creative. Everyone who is not quiet or not creative is not tall and vice versa. Everyone who is both tall and rich is both not generous and not happy. Everyone who is both generous and tall is patient and vice versa. If lucy is both not rich and wise then someone is both kind and quiet. Someone is either brave or not humble. Paul is either creative or funny. Susan is brave. Lucy is not generous. Someone is generous or not creative. Someone is not calm. | Susan is not wise. | contradiction | (((~kind(john)&happy(john)))=>(?[X]:(happy(X))))&
((?[X]:((kind(X)&happy(X))))=>(?[X]:(kind(X))))&
((?[X]:(old(X)))<=>(?[X]:(tall(X))))&
((?[X]:((~creative(X)&funny(X))))<=>(?[X]:((~humble(X)|~creative(X)))))&
(((~calm(john)|patient(john)))=>(happy(susan)))&
(![X]:((~wise(X)|~tall(X))<=>(~kind(X)&~humble(X))))&
(((calm(john)&wise(john)))<=>((quiet(fred)<~>brave(fred))))&
(![X]:((~patient(X)<~>~happy(X))<=>patient(X)))&
((?[X]:((kind(X)&rich(X))))<=>(humble(susan)))&
(![X]:(rich(X)<=>~patient(X)))&
((?[X]:((tall(X)&~quiet(X))))<=>(?[X]:((~creative(X)|~strong(X)))))&
(![X]:((calm(X)&~quiet(X))=>creative(X)))&
(![X]:((~quiet(X)|~creative(X))<=>~tall(X)))&
(![X]:((tall(X)&rich(X))=>(~generous(X)&~happy(X))))&
(![X]:((generous(X)&tall(X))<=>patient(X)))&
(((~rich(lucy)&wise(lucy)))=>(?[X]:((kind(X)&quiet(X)))))&
(?[X]:((brave(X)<~>~humble(X))))&
((creative(paul)<~>funny(paul)))&
(brave(susan))&
(~generous(lucy))&
(?[X]:((generous(X)|~creative(X))))&
(?[X]:(~calm(X))) | ~wise(susan) | [
"p3",
"p5",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2573917611406104100538387
% SZS output start Proof for 2573917611406104100538387
4. ? [X0] : (funny(X0) & ~creative(X0)) <=> ? [X0] : (~creative(X0) | ~humble(X0)) [input p3]
6. ! [X0] : ((~tall(X0) | ~wise(X0)) <=> (~humble(X0) & ~kind(X0))) [input p5]
11. ? [X0] : (~quiet(X0) & tall(X0)) <=> ? [X0] : (~strong(X0) | ~creative(X0)) [input p10]
13. ! [X0] : ((~creative(X0) | ~quiet(X0)) <=> ~tall(X0)) [input p12]
23. ~wise(susan) [input hypothesis]
26. ? [X0] : (funny(X0) & ~creative(X0)) <=> ? [X1] : (~creative(X1) | ~humble(X1)) [rectify 4]
27. ? [X0] : (~quiet(X0) & tall(X0)) <=> ? [X1] : (~strong(X1) | ~creative(X1)) [rectify 11]
48. (? [X0] : (funny(X0) & ~creative(X0)) | ! [X1] : (creative(X1) & humble(X1))) & (? [X1] : (~creative(X1) | ~humble(X1)) | ! [X0] : (~funny(X0) | creative(X0))) [nnf transformation 26]
49. (? [X0] : (funny(X0) & ~creative(X0)) | ! [X1] : (creative(X1) & humble(X1))) & (? [X2] : (~creative(X2) | ~humble(X2)) | ! [X3] : (~funny(X3) | creative(X3))) [rectify 48]
50. ? [X0] : (funny(X0) & ~creative(X0)) => (funny(sK4) & ~creative(sK4)) [choice axiom]
51. ? [X2] : (~creative(X2) | ~humble(X2)) => (~creative(sK5) | ~humble(sK5)) [choice axiom]
52. ((funny(sK4) & ~creative(sK4)) | ! [X1] : (creative(X1) & humble(X1))) & ((~creative(sK5) | ~humble(sK5)) | ! [X3] : (~funny(X3) | creative(X3))) [skolemisation 49,51,50]
53. ! [X0] : (((~tall(X0) | ~wise(X0)) | (humble(X0) | kind(X0))) & ((~humble(X0) & ~kind(X0)) | (tall(X0) & wise(X0)))) [nnf transformation 6]
54. ! [X0] : ((~tall(X0) | ~wise(X0) | humble(X0) | kind(X0)) & ((~humble(X0) & ~kind(X0)) | (tall(X0) & wise(X0)))) [flattening 53]
63. (? [X0] : (~quiet(X0) & tall(X0)) | ! [X1] : (strong(X1) & creative(X1))) & (? [X1] : (~strong(X1) | ~creative(X1)) | ! [X0] : (quiet(X0) | ~tall(X0))) [nnf transformation 27]
64. (? [X0] : (~quiet(X0) & tall(X0)) | ! [X1] : (strong(X1) & creative(X1))) & (? [X2] : (~strong(X2) | ~creative(X2)) | ! [X3] : (quiet(X3) | ~tall(X3))) [rectify 63]
65. ? [X0] : (~quiet(X0) & tall(X0)) => (~quiet(sK7) & tall(sK7)) [choice axiom]
66. ? [X2] : (~strong(X2) | ~creative(X2)) => (~strong(sK8) | ~creative(sK8)) [choice axiom]
67. ((~quiet(sK7) & tall(sK7)) | ! [X1] : (strong(X1) & creative(X1))) & ((~strong(sK8) | ~creative(sK8)) | ! [X3] : (quiet(X3) | ~tall(X3))) [skolemisation 64,66,65]
68. ! [X0] : (((~creative(X0) | ~quiet(X0)) | tall(X0)) & (~tall(X0) | (creative(X0) & quiet(X0)))) [nnf transformation 13]
69. ! [X0] : ((~creative(X0) | ~quiet(X0) | tall(X0)) & (~tall(X0) | (creative(X0) & quiet(X0)))) [flattening 68]
87. ~creative(sK4) | humble(X1) [cnf transformation 52]
95. ~humble(X0) | wise(X0) [cnf transformation 54]
114. tall(sK7) | creative(X1) [cnf transformation 67]
116. ~quiet(sK7) | creative(X1) [cnf transformation 67]
119. ~tall(X0) | quiet(X0) [cnf transformation 69]
137. ~wise(susan) [cnf transformation 23]
178. 10 <=> ! [X1] : creative(X1) [avatar definition]
179. creative(X1) <- (10) [avatar component clause 178]
186. 12 <=> ! [X1] : humble(X1) [avatar definition]
187. humble(X1) <- (12) [avatar component clause 186]
190. 13 <=> creative(sK4) [avatar definition]
192. ~creative(sK4) <- (~13) [avatar component clause 190]
194. 12 | ~13 [avatar split clause 87,190,186]
262. 28 <=> quiet(sK7) [avatar definition]
266. 10 | ~28 [avatar split clause 116,262,178]
268. 29 <=> tall(sK7) [avatar definition]
270. tall(sK7) <- (29) [avatar component clause 268]
272. 10 | 29 [avatar split clause 114,268,178]
274. 30 <=> ! [X3] : (quiet(X3) | ~tall(X3)) [avatar definition]
275. ~tall(X3) | quiet(X3) <- (30) [avatar component clause 274]
285. 30 [avatar split clause 119,274]
335. $false <- (10, ~13) [resolution 192,179]
336. ~10 | 13 [avatar contradiction clause 335]
371. quiet(sK7) <- (29, 30) [resolution 275,270]
376. 28 | ~29 | ~30 [avatar split clause 371,274,268,262]
378. wise(X1) <- (12) [resolution 187,95]
389. $false <- (12) [resolution 378,137]
394. ~12 [avatar contradiction clause 389]
395. $false [avatar sat refutation 194,266,272,285,336,376,394]
% SZS output end Proof for 2573917611406104100538387
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or calm is tall or not brave. If someone is both not tall and rich then john is either not kind or not creative. Everyone who is not strong or quiet is not brave and vice versa. Everyone who is not quiet or not humble is kind or creative. Everyone who is both not humble and strong is curious and vice versa. Everyone who is brave is both creative and not strong and vice versa. Everyone who is happy or not patient is either quiet or not strong. Everyone who is either wise or kind is either not funny or not brave. Everyone who is not tall is not wise. If someone is both not funny and not patient then someone is either humble or calm and vice versa. If someone is either not strong or not patient then someone is both not old and old. If susan is either kind or brave then someone is not curious and vice versa. Everyone who is either quiet or generous is both generous and creative. If mary is not creative then alice is both wise and not wise. Everyone who is not humble is either not calm or not patient. If someone is not happy or not calm then alice is not brave. Someone is either not generous or rich. Someone is not generous or curious. Someone is happy or wise. Someone is either not happy or not old. Someone is creative or curious. Someone is both not patient and kind. Alice is either not happy or creative. Someone is either rich or not patient. | John is brave. | contradiction | (![X]:((~wise(X)|calm(X))=>(tall(X)|~brave(X))))&
((?[X]:((~tall(X)&rich(X))))=>((~kind(john)<~>~creative(john))))&
(![X]:((~strong(X)|quiet(X))<=>~brave(X)))&
(![X]:((~quiet(X)|~humble(X))=>(kind(X)|creative(X))))&
(![X]:((~humble(X)&strong(X))<=>curious(X)))&
(![X]:(brave(X)<=>(creative(X)&~strong(X))))&
(![X]:((happy(X)|~patient(X))=>(quiet(X)<~>~strong(X))))&
(![X]:((wise(X)<~>kind(X))=>(~funny(X)<~>~brave(X))))&
(![X]:(~tall(X)=>~wise(X)))&
((?[X]:((~funny(X)&~patient(X))))<=>(?[X]:((humble(X)<~>calm(X)))))&
((?[X]:((~strong(X)<~>~patient(X))))=>(?[X]:((~old(X)&old(X)))))&
(((kind(susan)<~>brave(susan)))<=>(?[X]:(~curious(X))))&
(![X]:((quiet(X)<~>generous(X))=>(generous(X)&creative(X))))&
((~creative(mary))=>((wise(alice)&~wise(alice))))&
(![X]:(~humble(X)=>(~calm(X)<~>~patient(X))))&
((?[X]:((~happy(X)|~calm(X))))=>(~brave(alice)))&
(?[X]:((~generous(X)<~>rich(X))))&
(?[X]:((~generous(X)|curious(X))))&
(?[X]:((happy(X)|wise(X))))&
(?[X]:((~happy(X)<~>~old(X))))&
(?[X]:((creative(X)|curious(X))))&
(?[X]:((~patient(X)&kind(X))))&
((~happy(alice)<~>creative(alice)))&
(?[X]:((rich(X)<~>~patient(X)))) | brave(john) | [
"p2",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 8044424072120091107591546
% SZS output start Proof for 8044424072120091107591546
3. ! [X0] : ((quiet(X0) | ~strong(X0)) <=> ~brave(X0)) [input p2]
6. ! [X0] : (brave(X0) <=> (~strong(X0) & creative(X0))) [input p5]
25. brave(john) [input hypothesis]
40. ! [X0] : (((quiet(X0) | ~strong(X0)) | brave(X0)) & (~brave(X0) | (~quiet(X0) & strong(X0)))) [nnf transformation 3]
41. ! [X0] : ((quiet(X0) | ~strong(X0) | brave(X0)) & (~brave(X0) | (~quiet(X0) & strong(X0)))) [flattening 40]
44. ! [X0] : ((brave(X0) | (strong(X0) | ~creative(X0))) & ((~strong(X0) & creative(X0)) | ~brave(X0))) [nnf transformation 6]
45. ! [X0] : ((brave(X0) | strong(X0) | ~creative(X0)) & ((~strong(X0) & creative(X0)) | ~brave(X0))) [flattening 44]
81. ~brave(X0) | strong(X0) [cnf transformation 41]
90. ~strong(X0) | ~brave(X0) [cnf transformation 45]
137. brave(john) [cnf transformation 25]
140. ~brave(X0) [subsumption resolution 90,81]
280. $false [subsumption resolution 137,140]
% SZS output end Proof for 8044424072120091107591546
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or wise is rich and vice versa. Everyone who is both rich and not patient is quiet or brave and vice versa. If lucy is either not calm or not curious then paul is either not strong or kind and vice versa. If someone is not wise then paul is either strong or not old. Everyone who is rich is both calm and wise and vice versa. Everyone who is not generous or funny is patient or not strong and vice versa. Everyone who is creative or not patient is either curious or not old and vice versa. If fred is not generous or curious then alice is both not brave and not creative and vice versa. If someone is either not happy or not humble then susan is either not quiet or quiet and vice versa. Everyone who is either rich or not funny is both old and patient. Everyone who is humble is happy. If someone is not strong or not humble then john is either old or rich. If john is strong then someone is strong and vice versa. If lucy is either not kind or not strong then someone is curious. Everyone who is either not happy or not creative is either not happy or tall. If someone is happy or not kind then fred is rich and vice versa. Someone is either calm or generous. Someone is either not calm or patient. Lucy is quiet or not happy. Lucy is not humble. Lucy is tall. Fred is both not kind and not funny. Lucy is patient or tall. Someone is not humble or not calm. | Lucy is strong. | neutral | (![X]:((humble(X)<~>wise(X))<=>rich(X)))&
(![X]:((rich(X)&~patient(X))<=>(quiet(X)|brave(X))))&
(((~calm(lucy)<~>~curious(lucy)))<=>((~strong(paul)<~>kind(paul))))&
((?[X]:(~wise(X)))=>((strong(paul)<~>~old(paul))))&
(![X]:(rich(X)<=>(calm(X)&wise(X))))&
(![X]:((~generous(X)|funny(X))<=>(patient(X)|~strong(X))))&
(![X]:((creative(X)|~patient(X))<=>(curious(X)<~>~old(X))))&
(((~generous(fred)|curious(fred)))<=>((~brave(alice)&~creative(alice))))&
((?[X]:((~happy(X)<~>~humble(X))))<=>((~quiet(susan)<~>quiet(susan))))&
(![X]:((rich(X)<~>~funny(X))=>(old(X)&patient(X))))&
(![X]:(humble(X)=>happy(X)))&
((?[X]:((~strong(X)|~humble(X))))=>((old(john)<~>rich(john))))&
((strong(john))<=>(?[X]:(strong(X))))&
(((~kind(lucy)<~>~strong(lucy)))=>(?[X]:(curious(X))))&
(![X]:((~happy(X)<~>~creative(X))=>(~happy(X)<~>tall(X))))&
((?[X]:((happy(X)|~kind(X))))<=>(rich(fred)))&
(?[X]:((calm(X)<~>generous(X))))&
(?[X]:((~calm(X)<~>patient(X))))&
((quiet(lucy)|~happy(lucy)))&
(~humble(lucy))&
(tall(lucy))&
((~kind(fred)&~funny(fred)))&
((patient(lucy)|tall(lucy)))&
(?[X]:((~humble(X)|~calm(X)))) | strong(lucy) | [] | null | 0 |
If paul is both not funny and tall then someone is old or not brave and vice versa.
If someone is rich or not calm then someone is both calm and not strong and vice versa.
If lucy is either not quiet or not calm then john is either not funny or wise.
Everyone who is both happy and funny is both happy and strong and vice versa.
Everyone who is humble or generous is tall.
If someone is both not happy and curious then someone is not brave or creative and vice versa.
Everyone who is both happy and not creative is generous.
Everyone who is strong is quiet or old.
Everyone who is not strong is either kind or not generous and vice versa.
Everyone who is kind or calm is either happy or not humble and vice versa.
Everyone who is either funny or kind is either not generous or not curious and vice versa.
Everyone who is patient is tall and vice versa.
Everyone who is patient is both kind and not creative.
Everyone who is humble or not humble is either not brave or not funny.
If paul is creative then someone is either quiet or brave and vice versa.
If john is both curious and rich then someone is calm.
Lucy is both strong and not wise.
Someone is either quiet or strong.
Someone is either not rich or not calm.
Alice is humble or brave.
Someone is not kind or humble.
Susan is either rich or old.
Someone is either not old or old.
Alice is both not quiet and not patient. | Lucy is not happy. | entailment | (((~funny(paul)&tall(paul)))<=>(?[X]:((old(X)|~brave(X)))))&
((?[X]:((rich(X)|~calm(X))))<=>(?[X]:((calm(X)&~strong(X)))))&
(((~quiet(lucy)<~>~calm(lucy)))=>((~funny(john)<~>wise(john))))&
(![X]:((happy(X)&funny(X))<=>(happy(X)&strong(X))))&
(![X]:((humble(X)|generous(X))=>tall(X)))&
((?[X]:((~happy(X)&curious(X))))<=>(?[X]:((~brave(X)|creative(X)))))&
(![X]:((happy(X)&~creative(X))=>generous(X)))&
(![X]:(strong(X)=>(quiet(X)|old(X))))&
(![X]:(~strong(X)<=>(kind(X)<~>~generous(X))))&
(![X]:((kind(X)|calm(X))<=>(happy(X)<~>~humble(X))))&
(![X]:((funny(X)<~>kind(X))<=>(~generous(X)<~>~curious(X))))&
(![X]:(patient(X)<=>tall(X)))&
(![X]:(patient(X)=>(kind(X)&~creative(X))))&
(![X]:((humble(X)|~humble(X))=>(~brave(X)<~>~funny(X))))&
((creative(paul))<=>(?[X]:((quiet(X)<~>brave(X)))))&
(((curious(john)&rich(john)))=>(?[X]:(calm(X))))&
((strong(lucy)&~wise(lucy)))&
(?[X]:((quiet(X)<~>strong(X))))&
(?[X]:((~rich(X)<~>~calm(X))))&
((humble(alice)|brave(alice)))&
(?[X]:((~kind(X)|humble(X))))&
((rich(susan)<~>old(susan)))&
(?[X]:((~old(X)<~>old(X))))&
((~quiet(alice)&~patient(alice))) | ~happy(lucy) | [
"p0",
"p3",
"p4",
"p11",
"p12",
"p13",
"p14",
"p16",
"p19",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 19351231924327239997086
% SZS output start Proof for 19351231924327239997086
1. (tall(paul) & ~funny(paul)) <=> ? [X0] : (~brave(X0) | old(X0)) [input p0]
4. ! [X0] : ((funny(X0) & happy(X0)) <=> (strong(X0) & happy(X0))) [input p3]
5. ! [X0] : ((generous(X0) | humble(X0)) => tall(X0)) [input p4]
12. ! [X0] : (patient(X0) <=> tall(X0)) [input p11]
13. ! [X0] : (patient(X0) => (~creative(X0) & kind(X0))) [input p12]
14. ! [X0] : ((~humble(X0) | humble(X0)) => (~brave(X0) <~> ~funny(X0))) [input p13]
15. creative(paul) <=> ? [X0] : (quiet(X0) <~> brave(X0)) [input p14]
17. ~wise(lucy) & strong(lucy) [input p16]
20. brave(alice) | humble(alice) [input p19]
24. ~patient(alice) & ~quiet(alice) [input p23]
25. happy(lucy) [input hypothesis]
28. ! [X0] : (tall(X0) => patient(X0)) [unused predicate definition removal 12]
30. ! [X0] : (tall(X0) | (~generous(X0) & ~humble(X0))) [ennf transformation 5]
35. ! [X0] : (patient(X0) | ~tall(X0)) [ennf transformation 28]
36. ! [X0] : ((~creative(X0) & kind(X0)) | ~patient(X0)) [ennf transformation 13]
37. ! [X0] : ((~brave(X0) <~> ~funny(X0)) | (humble(X0) & ~humble(X0))) [ennf transformation 14]
40. ((tall(paul) & ~funny(paul)) | ! [X0] : (brave(X0) & ~old(X0))) & (? [X0] : (~brave(X0) | old(X0)) | (~tall(paul) | funny(paul))) [nnf transformation 1]
41. ((tall(paul) & ~funny(paul)) | ! [X0] : (brave(X0) & ~old(X0))) & (? [X0] : (~brave(X0) | old(X0)) | ~tall(paul) | funny(paul)) [flattening 40]
42. ((tall(paul) & ~funny(paul)) | ! [X0] : (brave(X0) & ~old(X0))) & (? [X1] : (~brave(X1) | old(X1)) | ~tall(paul) | funny(paul)) [rectify 41]
43. ? [X1] : (~brave(X1) | old(X1)) => (~brave(sK0) | old(sK0)) [choice axiom]
44. ((tall(paul) & ~funny(paul)) | ! [X0] : (brave(X0) & ~old(X0))) & ((~brave(sK0) | old(sK0)) | ~tall(paul) | funny(paul)) [skolemisation 42,43]
51. ! [X0] : (((funny(X0) & happy(X0)) | (~strong(X0) | ~happy(X0))) & ((strong(X0) & happy(X0)) | (~funny(X0) | ~happy(X0)))) [nnf transformation 4]
52. ! [X0] : (((funny(X0) & happy(X0)) | ~strong(X0) | ~happy(X0)) & ((strong(X0) & happy(X0)) | ~funny(X0) | ~happy(X0))) [flattening 51]
62. ! [X0] : (((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | (humble(X0) & ~humble(X0))) [nnf transformation 37]
63. (creative(paul) | ! [X0] : ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0)))) & (? [X0] : ((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | ~creative(paul)) [nnf transformation 15]
64. (creative(paul) | ! [X0] : ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0)))) & (? [X1] : ((~brave(X1) | ~quiet(X1)) & (brave(X1) | quiet(X1))) | ~creative(paul)) [rectify 63]
65. ? [X1] : ((~brave(X1) | ~quiet(X1)) & (brave(X1) | quiet(X1))) => ((~brave(sK5) | ~quiet(sK5)) & (brave(sK5) | quiet(sK5))) [choice axiom]
66. (creative(paul) | ! [X0] : ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0)))) & (((~brave(sK5) | ~quiet(sK5)) & (brave(sK5) | quiet(sK5))) | ~creative(paul)) [skolemisation 64,65]
85. tall(paul) | brave(X0) [cnf transformation 44]
98. ~happy(X0) | ~strong(X0) | funny(X0) [cnf transformation 52]
99. ~humble(X0) | tall(X0) [cnf transformation 30]
126. ~tall(X0) | patient(X0) [cnf transformation 35]
128. ~patient(X0) | ~creative(X0) [cnf transformation 36]
129. ~funny(X0) | ~brave(X0) | ~humble(X0) [cnf transformation 62]
130. ~funny(X0) | ~brave(X0) | humble(X0) [cnf transformation 62]
136. creative(paul) | quiet(X0) | ~brave(X0) [cnf transformation 66]
138. strong(lucy) [cnf transformation 17]
144. brave(alice) | humble(alice) [cnf transformation 20]
150. ~quiet(alice) [cnf transformation 24]
151. ~patient(alice) [cnf transformation 24]
152. happy(lucy) [cnf transformation 25]
154. 1 <=> ! [X0] : brave(X0) [avatar definition]
155. brave(X0) <- (1) [avatar component clause 154]
157. 2 <=> tall(paul) [avatar definition]
159. tall(paul) <- (2) [avatar component clause 157]
160. 1 | 2 [avatar split clause 85,157,154]
258. ~brave(X0) | ~funny(X0) [subsumption resolution 129,130]
260. 24 <=> ! [X0] : (quiet(X0) | ~brave(X0)) [avatar definition]
261. ~brave(X0) | quiet(X0) <- (24) [avatar component clause 260]
263. 25 <=> creative(paul) [avatar definition]
266. 24 | 25 [avatar split clause 136,263,260]
315. 36 <=> humble(alice) [avatar definition]
317. humble(alice) <- (36) [avatar component clause 315]
319. 37 <=> brave(alice) [avatar definition]
321. brave(alice) <- (37) [avatar component clause 319]
322. 36 | 37 [avatar split clause 144,319,315]
349. tall(alice) <- (36) [resolution 99,317]
350. patient(paul) <- (2) [resolution 126,159]
351. patient(alice) <- (36) [resolution 126,349]
352. $false <- (36) [subsumption resolution 351,151]
353. ~36 [avatar contradiction clause 352]
355. ~creative(paul) <- (2) [resolution 128,350]
364. quiet(alice) <- (24, 37) [resolution 261,321]
366. $false <- (24, 37) [subsumption resolution 364,150]
367. ~24 | ~37 [avatar contradiction clause 366]
368. ~25 | ~2 [avatar split clause 355,157,263]
371. ~funny(X0) <- (1) [resolution 155,258]
386. ~strong(lucy) | funny(lucy) [resolution 98,152]
387. funny(lucy) [subsumption resolution 386,138]
388. $false <- (1) [subsumption resolution 387,371]
389. ~1 [avatar contradiction clause 388]
390. $false [avatar sat refutation 160,266,322,353,367,368,389]
% SZS output end Proof for 19351231924327239997086
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is quiet then someone is not rich.
Everyone who is both wise and generous is both funny and not humble and vice versa.
If someone is either strong or not patient then someone is not patient and vice versa.
Everyone who is either not kind or not generous is humble or tall.
If alice is both not humble and not funny then someone is not wise or not creative and vice versa.
If paul is either happy or not calm then someone is not kind or strong.
If someone is either not funny or curious then someone is patient or creative and vice versa.
Everyone who is both quiet and not tall is both tall and not funny.
Everyone who is tall is both rich and funny.
Everyone who is both not creative and not humble is either rich or not funny.
Everyone who is either brave or creative is both wise and not rich and vice versa.
If someone is strong then someone is not strong.
Everyone who is both not curious and rich is both calm and wise and vice versa.
If someone is brave or not humble then someone is quiet or not creative and vice versa.
Everyone who is creative is old or not curious and vice versa.
If lucy is not patient then alice is either tall or old and vice versa.
Alice is not calm or creative.
Someone is wise or not happy.
John is not brave or funny.
Someone is not happy.
Someone is not wise.
Mary is both humble and not patient.
Lucy is either not funny or not happy.
Someone is either rich or patient. | Lucy is not funny. | neutral | ((quiet(john))=>(?[X]:(~rich(X))))&
(![X]:((wise(X)&generous(X))<=>(funny(X)&~humble(X))))&
((?[X]:((strong(X)<~>~patient(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~kind(X)<~>~generous(X))=>(humble(X)|tall(X))))&
(((~humble(alice)&~funny(alice)))<=>(?[X]:((~wise(X)|~creative(X)))))&
(((happy(paul)<~>~calm(paul)))=>(?[X]:((~kind(X)|strong(X)))))&
((?[X]:((~funny(X)<~>curious(X))))<=>(?[X]:((patient(X)|creative(X)))))&
(![X]:((quiet(X)&~tall(X))=>(tall(X)&~funny(X))))&
(![X]:(tall(X)=>(rich(X)&funny(X))))&
(![X]:((~creative(X)&~humble(X))=>(rich(X)<~>~funny(X))))&
(![X]:((brave(X)<~>creative(X))<=>(wise(X)&~rich(X))))&
((?[X]:(strong(X)))=>(?[X]:(~strong(X))))&
(![X]:((~curious(X)&rich(X))<=>(calm(X)&wise(X))))&
((?[X]:((brave(X)|~humble(X))))<=>(?[X]:((quiet(X)|~creative(X)))))&
(![X]:(creative(X)<=>(old(X)|~curious(X))))&
((~patient(lucy))<=>((tall(alice)<~>old(alice))))&
((~calm(alice)|creative(alice)))&
(?[X]:((wise(X)|~happy(X))))&
((~brave(john)|funny(john)))&
(?[X]:(~happy(X)))&
(?[X]:(~wise(X)))&
((humble(mary)&~patient(mary)))&
((~funny(lucy)<~>~happy(lucy)))&
(?[X]:((rich(X)<~>patient(X)))) | ~funny(lucy) | [] | null | 0 |
If someone is either brave or not happy then someone is wise or funny and vice versa.
If someone is not calm or strong then someone is brave and vice versa.
Everyone who is not curious or kind is not generous and vice versa.
If fred is not curious then someone is not generous and vice versa.
If someone is either wise or not patient then fred is happy or calm.
If susan is not wise then mary is kind.
Everyone who is either funny or curious is either calm or brave and vice versa.
Everyone who is both generous and creative is brave or humble and vice versa.
If someone is not calm then mary is both not kind and not quiet.
Everyone who is not wise is curious.
If mary is either kind or not patient then someone is wise or funny and vice versa.
If lucy is either not kind or not creative then someone is either old or not tall.
Everyone who is calm or not old is not funny.
Everyone who is either old or not curious is patient or old and vice versa.
If someone is either not happy or quiet then alice is rich.
If someone is humble then john is not happy or strong and vice versa.
Someone is either kind or not strong.
Someone is both funny and not rich.
Someone is either not creative or not tall.
Fred is funny.
Someone is not tall.
Someone is not brave.
Someone is both not kind and not humble.
Someone is brave or kind. | John is not curious. | contradiction | ((?[X]:((brave(X)<~>~happy(X))))<=>(?[X]:((wise(X)|funny(X)))))&
((?[X]:((~calm(X)|strong(X))))<=>(?[X]:(brave(X))))&
(![X]:((~curious(X)|kind(X))<=>~generous(X)))&
((~curious(fred))<=>(?[X]:(~generous(X))))&
((?[X]:((wise(X)<~>~patient(X))))=>((happy(fred)|calm(fred))))&
((~wise(susan))=>(kind(mary)))&
(![X]:((funny(X)<~>curious(X))<=>(calm(X)<~>brave(X))))&
(![X]:((generous(X)&creative(X))<=>(brave(X)|humble(X))))&
((?[X]:(~calm(X)))=>((~kind(mary)&~quiet(mary))))&
(![X]:(~wise(X)=>curious(X)))&
(((kind(mary)<~>~patient(mary)))<=>(?[X]:((wise(X)|funny(X)))))&
(((~kind(lucy)<~>~creative(lucy)))=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:((calm(X)|~old(X))=>~funny(X)))&
(![X]:((old(X)<~>~curious(X))<=>(patient(X)|old(X))))&
((?[X]:((~happy(X)<~>quiet(X))))=>(rich(alice)))&
((?[X]:(humble(X)))<=>((~happy(john)|strong(john))))&
(?[X]:((kind(X)<~>~strong(X))))&
(?[X]:((funny(X)&~rich(X))))&
(?[X]:((~creative(X)<~>~tall(X))))&
(funny(fred))&
(?[X]:(~tall(X)))&
(?[X]:(~brave(X)))&
(?[X]:((~kind(X)&~humble(X))))&
(?[X]:((brave(X)|kind(X)))) | ~curious(john) | [
"p2",
"p3",
"p12",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 7300706995468949903102072
% SZS output start Proof for 7300706995468949903102072
3. ! [X0] : ((kind(X0) | ~curious(X0)) <=> ~generous(X0)) [input p2]
4. ~curious(fred) <=> ? [X0] : ~generous(X0) [input p3]
13. ! [X0] : ((~old(X0) | calm(X0)) => ~funny(X0)) [input p12]
14. ! [X0] : ((old(X0) <~> ~curious(X0)) <=> (old(X0) | patient(X0))) [input p13]
20. funny(fred) [input p19]
25. ~curious(john) [input hypothesis]
34. ! [X0] : (~funny(X0) | (old(X0) & ~calm(X0))) [ennf transformation 13]
46. ! [X0] : (((kind(X0) | ~curious(X0)) | generous(X0)) & (~generous(X0) | (~kind(X0) & curious(X0)))) [nnf transformation 3]
47. ! [X0] : ((kind(X0) | ~curious(X0) | generous(X0)) & (~generous(X0) | (~kind(X0) & curious(X0)))) [flattening 46]
48. (~curious(fred) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | curious(fred)) [nnf transformation 4]
49. (~curious(fred) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | curious(fred)) [rectify 48]
50. ? [X1] : ~generous(X1) => ~generous(sK4) [choice axiom]
51. (~curious(fred) | ! [X0] : generous(X0)) & (~generous(sK4) | curious(fred)) [skolemisation 49,50]
63. ! [X0] : ((((curious(X0) | ~old(X0)) & (~curious(X0) | old(X0))) | (~old(X0) & ~patient(X0))) & ((old(X0) | patient(X0)) | ((old(X0) | curious(X0)) & (~curious(X0) | ~old(X0))))) [nnf transformation 14]
64. ! [X0] : ((((curious(X0) | ~old(X0)) & (~curious(X0) | old(X0))) | (~old(X0) & ~patient(X0))) & (old(X0) | patient(X0) | ((old(X0) | curious(X0)) & (~curious(X0) | ~old(X0))))) [flattening 63]
96. ~generous(X0) | curious(X0) [cnf transformation 47]
100. ~curious(fred) | generous(X0) [cnf transformation 51]
131. ~funny(X0) | old(X0) [cnf transformation 34]
137. curious(X0) | ~old(X0) | ~old(X0) [cnf transformation 64]
149. funny(fred) [cnf transformation 20]
155. ~curious(john) [cnf transformation 25]
157. ~old(X0) | curious(X0) [duplicate literal removal 137]
217. 15 <=> ! [X0] : generous(X0) [avatar definition]
218. generous(X0) <- (15) [avatar component clause 217]
220. 16 <=> curious(fred) [avatar definition]
223. 15 | ~16 [avatar split clause 100,220,217]
374. old(fred) [resolution 131,149]
377. curious(fred) [resolution 374,157]
380. 16 [avatar split clause 377,220]
383. curious(X1) <- (15) [resolution 218,96]
391. $false <- (15) [resolution 383,155]
393. ~15 [avatar contradiction clause 391]
394. $false [avatar sat refutation 223,380,393]
% SZS output end Proof for 7300706995468949903102072
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not kind or humble then someone is both not wise and not quiet and vice versa.
Everyone who is quiet is not wise and vice versa.
Everyone who is quiet or creative is not strong and vice versa.
If someone is not funny then someone is either not patient or calm.
If someone is either not curious or patient then someone is not quiet.
If lucy is not funny then someone is quiet and vice versa.
If someone is not calm or rich then someone is both not patient and funny.
If someone is both humble and patient then alice is either not kind or generous.
If someone is both not old and funny then someone is both not kind and calm.
Everyone who is not humble is both calm and not creative.
Everyone who is either brave or humble is not wise or humble and vice versa.
Everyone who is either calm or not creative is either strong or funny and vice versa.
Everyone who is either calm or wise is both generous and funny and vice versa.
Everyone who is old is both strong and not rich and vice versa.
Everyone who is both not brave and kind is either not rich or creative and vice versa.
Everyone who is both not old and funny is not strong and vice versa.
Mary is not wise or happy.
Someone is both not creative and kind.
Someone is both not humble and not patient.
Someone is both not patient and strong.
Fred is quiet or not brave. | Fred is generous. | contradiction | ((?[X]:((~kind(X)|humble(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
(![X]:(quiet(X)<=>~wise(X)))&
(![X]:((quiet(X)|creative(X))<=>~strong(X)))&
((?[X]:(~funny(X)))=>(?[X]:((~patient(X)<~>calm(X)))))&
((?[X]:((~curious(X)<~>patient(X))))=>(?[X]:(~quiet(X))))&
((~funny(lucy))<=>(?[X]:(quiet(X))))&
((?[X]:((~calm(X)|rich(X))))=>(?[X]:((~patient(X)&funny(X)))))&
((?[X]:((humble(X)&patient(X))))=>((~kind(alice)<~>generous(alice))))&
((?[X]:((~old(X)&funny(X))))=>(?[X]:((~kind(X)&calm(X)))))&
(![X]:(~humble(X)=>(calm(X)&~creative(X))))&
(![X]:((brave(X)<~>humble(X))<=>(~wise(X)|humble(X))))&
(![X]:((calm(X)<~>~creative(X))<=>(strong(X)<~>funny(X))))&
(![X]:((calm(X)<~>wise(X))<=>(generous(X)&funny(X))))&
(![X]:(old(X)<=>(strong(X)&~rich(X))))&
(![X]:((~brave(X)&kind(X))<=>(~rich(X)<~>creative(X))))&
(![X]:((~old(X)&funny(X))<=>~strong(X)))&
((~wise(mary)|happy(mary)))&
(?[X]:((~creative(X)&kind(X))))&
(?[X]:((~humble(X)&~patient(X))))&
(?[X]:((~patient(X)&strong(X))))&
((quiet(fred)|~brave(fred))) | generous(fred) | [
"p0",
"p1",
"p2",
"p8",
"p9",
"p11",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1454239808745544697911961
% SZS output start Proof for 1454239808745544697911961
1. ? [X0] : (humble(X0) | ~kind(X0)) <=> ? [X0] : (~quiet(X0) & ~wise(X0)) [input p0]
2. ! [X0] : (quiet(X0) <=> ~wise(X0)) [input p1]
3. ! [X0] : ((creative(X0) | quiet(X0)) <=> ~strong(X0)) [input p2]
9. ? [X0] : (funny(X0) & ~old(X0)) => ? [X0] : (calm(X0) & ~kind(X0)) [input p8]
10. ! [X0] : (~humble(X0) => (~creative(X0) & calm(X0))) [input p9]
12. ! [X0] : ((calm(X0) <~> ~creative(X0)) <=> (strong(X0) <~> funny(X0))) [input p11]
13. ! [X0] : ((calm(X0) <~> wise(X0)) <=> (funny(X0) & generous(X0))) [input p12]
14. ! [X0] : (old(X0) <=> (~rich(X0) & strong(X0))) [input p13]
16. ! [X0] : ((funny(X0) & ~old(X0)) <=> ~strong(X0)) [input p15]
22. generous(fred) [input hypothesis]
23. ? [X0] : (humble(X0) | ~kind(X0)) <=> ? [X1] : (~quiet(X1) & ~wise(X1)) [rectify 1]
27. ? [X0] : (funny(X0) & ~old(X0)) => ? [X1] : (calm(X1) & ~kind(X1)) [rectify 9]
33. ? [X1] : (calm(X1) & ~kind(X1)) | ! [X0] : (~funny(X0) | old(X0)) [ennf transformation 27]
34. ! [X0] : ((~creative(X0) & calm(X0)) | humble(X0)) [ennf transformation 10]
35. (? [X0] : (humble(X0) | ~kind(X0)) | ! [X1] : (quiet(X1) | wise(X1))) & (? [X1] : (~quiet(X1) & ~wise(X1)) | ! [X0] : (~humble(X0) & kind(X0))) [nnf transformation 23]
36. (? [X0] : (humble(X0) | ~kind(X0)) | ! [X1] : (quiet(X1) | wise(X1))) & (? [X2] : (~quiet(X2) & ~wise(X2)) | ! [X3] : (~humble(X3) & kind(X3))) [rectify 35]
37. ? [X0] : (humble(X0) | ~kind(X0)) => (humble(sK0) | ~kind(sK0)) [choice axiom]
38. ? [X2] : (~quiet(X2) & ~wise(X2)) => (~quiet(sK1) & ~wise(sK1)) [choice axiom]
39. ((humble(sK0) | ~kind(sK0)) | ! [X1] : (quiet(X1) | wise(X1))) & ((~quiet(sK1) & ~wise(sK1)) | ! [X3] : (~humble(X3) & kind(X3))) [skolemisation 36,38,37]
40. ! [X0] : ((quiet(X0) | wise(X0)) & (~wise(X0) | ~quiet(X0))) [nnf transformation 2]
41. ! [X0] : (((creative(X0) | quiet(X0)) | strong(X0)) & (~strong(X0) | (~creative(X0) & ~quiet(X0)))) [nnf transformation 3]
42. ! [X0] : ((creative(X0) | quiet(X0) | strong(X0)) & (~strong(X0) | (~creative(X0) & ~quiet(X0)))) [flattening 41]
59. ? [X0] : (calm(X0) & ~kind(X0)) | ! [X1] : (~funny(X1) | old(X1)) [rectify 33]
60. ? [X0] : (calm(X0) & ~kind(X0)) => (calm(sK6) & ~kind(sK6)) [choice axiom]
61. (calm(sK6) & ~kind(sK6)) | ! [X1] : (~funny(X1) | old(X1)) [skolemisation 59,60]
64. ! [X0] : ((((creative(X0) | ~calm(X0)) & (~creative(X0) | calm(X0))) | ((strong(X0) | ~funny(X0)) & (funny(X0) | ~strong(X0)))) & (((~funny(X0) | ~strong(X0)) & (funny(X0) | strong(X0))) | ((calm(X0) | creative(X0)) & (~creative(X0) | ~calm(X0))))) [nnf transformation 12]
65. ! [X0] : ((((~wise(X0) | ~calm(X0)) & (wise(X0) | calm(X0))) | (~funny(X0) | ~generous(X0))) & ((funny(X0) & generous(X0)) | ((calm(X0) | ~wise(X0)) & (wise(X0) | ~calm(X0))))) [nnf transformation 13]
66. ! [X0] : ((((~wise(X0) | ~calm(X0)) & (wise(X0) | calm(X0))) | ~funny(X0) | ~generous(X0)) & ((funny(X0) & generous(X0)) | ((calm(X0) | ~wise(X0)) & (wise(X0) | ~calm(X0))))) [flattening 65]
67. ! [X0] : ((old(X0) | (rich(X0) | ~strong(X0))) & ((~rich(X0) & strong(X0)) | ~old(X0))) [nnf transformation 14]
68. ! [X0] : ((old(X0) | rich(X0) | ~strong(X0)) & ((~rich(X0) & strong(X0)) | ~old(X0))) [flattening 67]
71. ! [X0] : (((funny(X0) & ~old(X0)) | strong(X0)) & (~strong(X0) | (~funny(X0) | old(X0)))) [nnf transformation 16]
72. ! [X0] : (((funny(X0) & ~old(X0)) | strong(X0)) & (~strong(X0) | ~funny(X0) | old(X0))) [flattening 71]
79. ~wise(sK1) | kind(X3) [cnf transformation 39]
80. ~wise(sK1) | ~humble(X3) [cnf transformation 39]
81. ~quiet(sK1) | kind(X3) [cnf transformation 39]
85. quiet(X0) | wise(X0) [cnf transformation 40]
86. ~strong(X0) | ~quiet(X0) [cnf transformation 42]
87. ~strong(X0) | ~creative(X0) [cnf transformation 42]
101. ~kind(sK6) | ~funny(X1) | old(X1) [cnf transformation 61]
103. calm(X0) | humble(X0) [cnf transformation 34]
114. ~funny(X0) | ~strong(X0) | calm(X0) | creative(X0) [cnf transformation 64]
116. ~creative(X0) | calm(X0) | strong(X0) | ~funny(X0) [cnf transformation 64]
117. creative(X0) | ~calm(X0) | funny(X0) | ~strong(X0) [cnf transformation 64]
124. ~generous(X0) | ~calm(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 66]
125. ~old(X0) | strong(X0) [cnf transformation 68]
136. funny(X0) | strong(X0) [cnf transformation 72]
144. generous(fred) [cnf transformation 22]
148. 1 <=> ! [X1] : (quiet(X1) | wise(X1)) [avatar definition]
149. quiet(X1) | wise(X1) <- (1) [avatar component clause 148]
160. 4 <=> ! [X3] : ~humble(X3) [avatar definition]
161. ~humble(X3) <- (4) [avatar component clause 160]
163. 5 <=> quiet(sK1) [avatar definition]
165. ~quiet(sK1) <- (~5) [avatar component clause 163]
168. 6 <=> ! [X3] : kind(X3) [avatar definition]
169. kind(X3) <- (6) [avatar component clause 168]
170. 6 | ~5 [avatar split clause 81,163,168]
172. 7 <=> wise(sK1) [avatar definition]
174. ~wise(sK1) <- (~7) [avatar component clause 172]
175. 4 | ~7 [avatar split clause 80,172,160]
176. 6 | ~7 [avatar split clause 79,172,168]
177. 1 [avatar split clause 85,148]
179. 8 <=> ! [X1] : funny(X1) [avatar definition]
180. funny(X1) <- (8) [avatar component clause 179]
204. 14 <=> ! [X0] : ~quiet(X0) [avatar definition]
205. ~quiet(X0) <- (14) [avatar component clause 204]
225. 19 <=> ! [X1] : calm(X1) [avatar definition]
226. calm(X1) <- (19) [avatar component clause 225]
248. 24 <=> ! [X1] : (~funny(X1) | old(X1)) [avatar definition]
249. ~funny(X1) | old(X1) <- (24) [avatar component clause 248]
256. 26 <=> kind(sK6) [avatar definition]
258. ~kind(sK6) <- (~26) [avatar component clause 256]
259. 24 | ~26 [avatar split clause 101,256,248]
261. ~calm(X0) | funny(X0) | ~strong(X0) [subsumption resolution 117,87]
262. ~funny(X0) | calm(X0) | ~creative(X0) [subsumption resolution 116,87]
263. ~funny(X0) | ~strong(X0) | calm(X0) [subsumption resolution 114,262]
274. wise(X1) <- (1, 14) [subsumption resolution 149,205]
275. $false <- (1, ~7, 14) [resolution 274,174]
276. ~1 | 7 | ~14 [avatar contradiction clause 275]
289. wise(sK1) <- (1, ~5) [resolution 149,165]
294. 7 | ~1 | 5 [avatar split clause 289,163,148,172]
296. old(X0) | strong(X0) <- (24) [resolution 249,136]
297. strong(X0) <- (24) [subsumption resolution 296,125]
303. ~quiet(X1) <- (24) [resolution 297,86]
304. 14 | ~24 [avatar split clause 303,248,204]
348. $false <- (6, ~26) [subsumption resolution 258,169]
349. ~6 | 26 [avatar contradiction clause 348]
355. wise(X0) <- (1, 14) [resolution 205,149]
363. old(X0) | strong(X0) <- (24) [resolution 249,136]
365. strong(X0) <- (24) [subsumption resolution 363,125]
419. funny(X0) | ~strong(X0) | humble(X0) [resolution 261,103]
423. funny(X0) | humble(X0) <- (24) [subsumption resolution 419,365]
424. funny(X0) <- (4, 24) [subsumption resolution 423,161]
425. 8 | ~4 | ~24 [avatar split clause 424,248,160,179]
439. ~strong(X0) | calm(X0) <- (8) [resolution 263,180]
444. calm(X0) <- (8, 24) [subsumption resolution 439,365]
445. 19 | ~8 | ~24 [avatar split clause 444,248,179,225]
491. ~calm(fred) | ~funny(fred) | ~wise(fred) [resolution 124,144]
494. ~funny(fred) | ~wise(fred) <- (19) [subsumption resolution 491,226]
506. ~wise(fred) <- (8, 19) [subsumption resolution 494,180]
507. $false <- (1, 8, 14, 19) [subsumption resolution 506,355]
508. ~1 | ~8 | ~14 | ~19 [avatar contradiction clause 507]
511. $false [avatar sat refutation 170,175,176,177,259,276,294,304,349,425,445,508]
% SZS output end Proof for 1454239808745544697911961
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is kind or not old. If someone is either not curious or not happy then mary is strong. If fred is both patient and not humble then someone is either not wise or kind and vice versa. Everyone who is curious or wise is not quiet. If someone is both not funny and not rich then someone is both not kind and old and vice versa. Everyone who is both not funny and not tall is rich or funny and vice versa. If mary is not generous or not rich then alice is quiet or not humble. If fred is creative or not funny then alice is not creative or strong. If someone is both brave and happy then lucy is not kind or not happy and vice versa. Everyone who is both happy and rich is either happy or generous. If alice is creative or not quiet then lucy is not quiet. If fred is both not old and not rich then someone is brave and vice versa. Everyone who is both not generous and wise is either not generous or not patient and vice versa. If someone is not strong or kind then john is not rich. Everyone who is either not wise or kind is both not funny and not wise and vice versa. Everyone who is not generous is curious or not patient. Susan is calm or funny. John is both not curious and not calm. Alice is either humble or wise. Someone is both not strong and not creative. Someone is both not creative and not kind. Alice is strong. Someone is wise or not funny. | Lucy is not quiet. | neutral | (![X]:(brave(X)=>(kind(X)|~old(X))))&
((?[X]:((~curious(X)<~>~happy(X))))=>(strong(mary)))&
(((patient(fred)&~humble(fred)))<=>(?[X]:((~wise(X)<~>kind(X)))))&
(![X]:((curious(X)|wise(X))=>~quiet(X)))&
((?[X]:((~funny(X)&~rich(X))))<=>(?[X]:((~kind(X)&old(X)))))&
(![X]:((~funny(X)&~tall(X))<=>(rich(X)|funny(X))))&
(((~generous(mary)|~rich(mary)))=>((quiet(alice)|~humble(alice))))&
(((creative(fred)|~funny(fred)))=>((~creative(alice)|strong(alice))))&
((?[X]:((brave(X)&happy(X))))<=>((~kind(lucy)|~happy(lucy))))&
(![X]:((happy(X)&rich(X))=>(happy(X)<~>generous(X))))&
(((creative(alice)|~quiet(alice)))=>(~quiet(lucy)))&
(((~old(fred)&~rich(fred)))<=>(?[X]:(brave(X))))&
(![X]:((~generous(X)&wise(X))<=>(~generous(X)<~>~patient(X))))&
((?[X]:((~strong(X)|kind(X))))=>(~rich(john)))&
(![X]:((~wise(X)<~>kind(X))<=>(~funny(X)&~wise(X))))&
(![X]:(~generous(X)=>(curious(X)|~patient(X))))&
((calm(susan)|funny(susan)))&
((~curious(john)&~calm(john)))&
((humble(alice)<~>wise(alice)))&
(?[X]:((~strong(X)&~creative(X))))&
(?[X]:((~creative(X)&~kind(X))))&
(strong(alice))&
(?[X]:((wise(X)|~funny(X)))) | ~quiet(lucy) | [] | null | 0 |
Everyone who is not generous or not rich is both not tall and calm.
Everyone who is both rich and not rich is either not creative or strong.
Everyone who is both not kind and not generous is both not curious and not happy.
If someone is not strong or funny then someone is not rich.
If lucy is not strong or curious then someone is both humble and not quiet.
If someone is either not calm or funny then susan is both creative and not generous and vice versa.
Everyone who is curious or not brave is either creative or not tall.
Everyone who is either happy or not old is either tall or old.
Everyone who is either funny or not patient is not tall.
If mary is either not patient or not happy then susan is both not patient and wise and vice versa.
Everyone who is either quiet or happy is either calm or not brave and vice versa.
If paul is patient or quiet then someone is wise.
Everyone who is either generous or brave is both not rich and rich.
Everyone who is rich or not old is both curious and patient and vice versa.
Everyone who is both strong and not humble is both not quiet and not old and vice versa.
Everyone who is both humble and rich is both happy and generous.
Someone is both not wise and calm.
Fred is both not wise and funny.
Lucy is both not curious and strong.
Fred is curious.
Someone is not wise.
Paul is either not happy or generous.
John is happy or kind.
Someone is both kind and tall. | Fred is not rich. | contradiction | (![X]:((~generous(X)|~rich(X))=>(~tall(X)&calm(X))))&
(![X]:((rich(X)&~rich(X))=>(~creative(X)<~>strong(X))))&
(![X]:((~kind(X)&~generous(X))=>(~curious(X)&~happy(X))))&
((?[X]:((~strong(X)|funny(X))))=>(?[X]:(~rich(X))))&
(((~strong(lucy)|curious(lucy)))=>(?[X]:((humble(X)&~quiet(X)))))&
((?[X]:((~calm(X)<~>funny(X))))<=>((creative(susan)&~generous(susan))))&
(![X]:((curious(X)|~brave(X))=>(creative(X)<~>~tall(X))))&
(![X]:((happy(X)<~>~old(X))=>(tall(X)<~>old(X))))&
(![X]:((funny(X)<~>~patient(X))=>~tall(X)))&
(((~patient(mary)<~>~happy(mary)))<=>((~patient(susan)&wise(susan))))&
(![X]:((quiet(X)<~>happy(X))<=>(calm(X)<~>~brave(X))))&
(((patient(paul)|quiet(paul)))=>(?[X]:(wise(X))))&
(![X]:((generous(X)<~>brave(X))=>(~rich(X)&rich(X))))&
(![X]:((rich(X)|~old(X))<=>(curious(X)&patient(X))))&
(![X]:((strong(X)&~humble(X))<=>(~quiet(X)&~old(X))))&
(![X]:((humble(X)&rich(X))=>(happy(X)&generous(X))))&
(?[X]:((~wise(X)&calm(X))))&
((~wise(fred)&funny(fred)))&
((~curious(lucy)&strong(lucy)))&
(curious(fred))&
(?[X]:(~wise(X)))&
((~happy(paul)<~>generous(paul)))&
((happy(john)|kind(john)))&
(?[X]:((kind(X)&tall(X)))) | ~rich(fred) | [
"p0",
"p5",
"p6",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5347115582192170507341444
% SZS output start Proof for 5347115582192170507341444
1. ! [X0] : ((~rich(X0) | ~generous(X0)) => (calm(X0) & ~tall(X0))) [input p0]
6. ? [X0] : (~calm(X0) <~> funny(X0)) <=> (~generous(susan) & creative(susan)) [input p5]
7. ! [X0] : ((~brave(X0) | curious(X0)) => (creative(X0) <~> ~tall(X0))) [input p6]
13. ! [X0] : ((generous(X0) <~> brave(X0)) => (rich(X0) & ~rich(X0))) [input p12]
18. funny(fred) & ~wise(fred) [input p17]
25. ~rich(fred) [input hypothesis]
30. ! [X0] : ((calm(X0) & ~tall(X0)) | (rich(X0) & generous(X0))) [ennf transformation 1]
35. ! [X0] : ((creative(X0) <~> ~tall(X0)) | (brave(X0) & ~curious(X0))) [ennf transformation 7]
39. ! [X0] : ((rich(X0) & ~rich(X0)) | (generous(X0) <=> brave(X0))) [ennf transformation 13]
48. (? [X0] : ((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | (generous(susan) | ~creative(susan))) & ((~generous(susan) & creative(susan)) | ! [X0] : ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0)))) [nnf transformation 6]
49. (? [X0] : ((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | generous(susan) | ~creative(susan)) & ((~generous(susan) & creative(susan)) | ! [X0] : ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0)))) [flattening 48]
50. (? [X0] : ((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | generous(susan) | ~creative(susan)) & ((~generous(susan) & creative(susan)) | ! [X1] : ((~calm(X1) | ~funny(X1)) & (funny(X1) | calm(X1)))) [rectify 49]
51. ? [X0] : ((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) => ((~funny(sK2) | calm(sK2)) & (funny(sK2) | ~calm(sK2))) [choice axiom]
52. (((~funny(sK2) | calm(sK2)) & (funny(sK2) | ~calm(sK2))) | generous(susan) | ~creative(susan)) & ((~generous(susan) & creative(susan)) | ! [X1] : ((~calm(X1) | ~funny(X1)) & (funny(X1) | calm(X1)))) [skolemisation 50,51]
53. ! [X0] : (((tall(X0) | ~creative(X0)) & (~tall(X0) | creative(X0))) | (brave(X0) & ~curious(X0))) [nnf transformation 35]
61. ! [X0] : ((rich(X0) & ~rich(X0)) | ((generous(X0) | ~brave(X0)) & (brave(X0) | ~generous(X0)))) [nnf transformation 39]
73. ~tall(X0) | generous(X0) [cnf transformation 30]
76. calm(X0) | rich(X0) [cnf transformation 30]
86. creative(susan) | ~calm(X1) | ~funny(X1) [cnf transformation 52]
88. ~generous(susan) | ~calm(X1) | ~funny(X1) [cnf transformation 52]
94. ~creative(X0) | tall(X0) | brave(X0) [cnf transformation 53]
118. ~rich(X0) | generous(X0) | ~brave(X0) [cnf transformation 61]
120. rich(X0) | generous(X0) | ~brave(X0) [cnf transformation 61]
135. funny(fred) [cnf transformation 18]
143. ~rich(fred) [cnf transformation 25]
179. 8 <=> creative(susan) [avatar definition]
180. creative(susan) <- (8) [avatar component clause 179]
183. 9 <=> generous(susan) [avatar definition]
184. ~generous(susan) <- (~9) [avatar component clause 183]
197. 12 <=> ! [X1] : (~calm(X1) | ~funny(X1)) [avatar definition]
198. ~funny(X1) | ~calm(X1) <- (12) [avatar component clause 197]
199. 12 | ~9 [avatar split clause 88,183,197]
204. 12 | 8 [avatar split clause 86,179,197]
242. ~brave(X0) | generous(X0) [subsumption resolution 118,120]
300. 27 <=> brave(susan) [avatar definition]
302. brave(susan) <- (27) [avatar component clause 300]
304. 28 <=> tall(susan) [avatar definition]
306. tall(susan) <- (28) [avatar component clause 304]
308. ~calm(fred) <- (12) [resolution 198,135]
309. rich(fred) <- (12) [resolution 308,76]
311. $false <- (12) [subsumption resolution 309,143]
312. ~12 [avatar contradiction clause 311]
313. tall(susan) | brave(susan) <- (8) [resolution 180,94]
314. generous(susan) <- (27) [resolution 302,242]
315. $false <- (~9, 27) [subsumption resolution 314,184]
316. 9 | ~27 [avatar contradiction clause 315]
317. 27 | 28 | ~8 [avatar split clause 313,179,304,300]
326. generous(susan) <- (28) [resolution 306,73]
327. $false <- (~9, 28) [subsumption resolution 326,184]
328. 9 | ~28 [avatar contradiction clause 327]
329. $false [avatar sat refutation 199,204,312,316,317,328]
% SZS output end Proof for 5347115582192170507341444
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is not old.
Everyone who is generous is either not calm or brave.
Everyone who is funny or patient is not tall and vice versa.
Everyone who is either old or not old is either funny or happy and vice versa.
If susan is humble then mary is not patient and vice versa.
Everyone who is not wise is not funny.
Everyone who is either curious or humble is not generous or wise and vice versa.
If someone is not rich or quiet then someone is either humble or tall.
If someone is both quiet and curious then susan is not happy and vice versa.
Everyone who is brave or rich is both not brave and happy.
If susan is not funny or strong then someone is either not wise or humble.
Everyone who is not brave or funny is both tall and curious and vice versa.
Everyone who is either curious or not happy is either not old or quiet and vice versa.
If alice is both wise and strong then paul is not curious or not tall.
Everyone who is both happy and kind is either quiet or not wise and vice versa.
Everyone who is either not calm or rich is either old or not rich and vice versa.
Fred is not generous.
Someone is both kind and generous.
Someone is both strong and not rich.
Someone is either not generous or not creative. | Susan is not tall. | contradiction | (![X]:(~curious(X)=>~old(X)))&
(![X]:(generous(X)=>(~calm(X)<~>brave(X))))&
(![X]:((funny(X)|patient(X))<=>~tall(X)))&
(![X]:((old(X)<~>~old(X))<=>(funny(X)<~>happy(X))))&
((humble(susan))<=>(~patient(mary)))&
(![X]:(~wise(X)=>~funny(X)))&
(![X]:((curious(X)<~>humble(X))<=>(~generous(X)|wise(X))))&
((?[X]:((~rich(X)|quiet(X))))=>(?[X]:((humble(X)<~>tall(X)))))&
((?[X]:((quiet(X)&curious(X))))<=>(~happy(susan)))&
(![X]:((brave(X)|rich(X))=>(~brave(X)&happy(X))))&
(((~funny(susan)|strong(susan)))=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:((~brave(X)|funny(X))<=>(tall(X)&curious(X))))&
(![X]:((curious(X)<~>~happy(X))<=>(~old(X)<~>quiet(X))))&
(((wise(alice)&strong(alice)))=>((~curious(paul)|~tall(paul))))&
(![X]:((happy(X)&kind(X))<=>(quiet(X)<~>~wise(X))))&
(![X]:((~calm(X)<~>rich(X))<=>(old(X)<~>~rich(X))))&
(~generous(fred))&
(?[X]:((kind(X)&generous(X))))&
(?[X]:((strong(X)&~rich(X))))&
(?[X]:((~generous(X)<~>~creative(X)))) | ~tall(susan) | [
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8287401096979254223285284
% SZS output start Proof for 8287401096979254223285284
10. ! [X0] : ((rich(X0) | brave(X0)) => (happy(X0) & ~brave(X0))) [input p9]
12. ! [X0] : ((funny(X0) | ~brave(X0)) <=> (curious(X0) & tall(X0))) [input p11]
21. ~tall(susan) [input hypothesis]
27. ! [X0] : ((happy(X0) & ~brave(X0)) | (~rich(X0) & ~brave(X0))) [ennf transformation 10]
49. ! [X0] : (((funny(X0) | ~brave(X0)) | (~curious(X0) | ~tall(X0))) & ((curious(X0) & tall(X0)) | (~funny(X0) & brave(X0)))) [nnf transformation 12]
50. ! [X0] : ((funny(X0) | ~brave(X0) | ~curious(X0) | ~tall(X0)) & ((curious(X0) & tall(X0)) | (~funny(X0) & brave(X0)))) [flattening 49]
92. ~brave(X0) | ~brave(X0) [cnf transformation 27]
100. tall(X0) | brave(X0) [cnf transformation 50]
135. ~tall(susan) [cnf transformation 21]
140. ~brave(X0) [duplicate literal removal 92]
215. tall(X0) [subsumption resolution 100,140]
243. $false [subsumption resolution 135,215]
% SZS output end Proof for 8287401096979254223285284
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or brave is not rich.
If someone is either not wise or kind then someone is not generous.
If someone is either generous or not patient then someone is happy or not curious and vice versa.
If john is either strong or happy then paul is either not funny or not generous and vice versa.
If lucy is strong then mary is both not humble and not quiet and vice versa.
Everyone who is both brave and not generous is both calm and funny and vice versa.
Everyone who is strong or rich is not old and vice versa.
Everyone who is wise or creative is strong and vice versa.
Everyone who is not tall is both curious and not happy.
If susan is creative then lucy is patient or not calm and vice versa.
Everyone who is either not patient or creative is humble and vice versa.
Everyone who is not calm is both humble and not curious.
Everyone who is not quiet is happy or old and vice versa.
If alice is old then someone is either creative or not tall.
Everyone who is brave or generous is both not generous and not quiet.
Everyone who is either brave or kind is either not kind or not curious and vice versa.
Someone is both brave and not creative.
Lucy is not happy.
Someone is both calm and not funny.
Someone is either tall or calm.
Lucy is curious.
Lucy is either quiet or kind.
Fred is both humble and kind.
John is both not quiet and not brave. | Lucy is not wise. | entailment | (![X]:((~tall(X)|brave(X))=>~rich(X)))&
((?[X]:((~wise(X)<~>kind(X))))=>(?[X]:(~generous(X))))&
((?[X]:((generous(X)<~>~patient(X))))<=>(?[X]:((happy(X)|~curious(X)))))&
(((strong(john)<~>happy(john)))<=>((~funny(paul)<~>~generous(paul))))&
((strong(lucy))<=>((~humble(mary)&~quiet(mary))))&
(![X]:((brave(X)&~generous(X))<=>(calm(X)&funny(X))))&
(![X]:((strong(X)|rich(X))<=>~old(X)))&
(![X]:((wise(X)|creative(X))<=>strong(X)))&
(![X]:(~tall(X)=>(curious(X)&~happy(X))))&
((creative(susan))<=>((patient(lucy)|~calm(lucy))))&
(![X]:((~patient(X)<~>creative(X))<=>humble(X)))&
(![X]:(~calm(X)=>(humble(X)&~curious(X))))&
(![X]:(~quiet(X)<=>(happy(X)|old(X))))&
((old(alice))=>(?[X]:((creative(X)<~>~tall(X)))))&
(![X]:((brave(X)|generous(X))=>(~generous(X)&~quiet(X))))&
(![X]:((brave(X)<~>kind(X))<=>(~kind(X)<~>~curious(X))))&
(?[X]:((brave(X)&~creative(X))))&
(~happy(lucy))&
(?[X]:((calm(X)&~funny(X))))&
(?[X]:((tall(X)<~>calm(X))))&
(curious(lucy))&
((quiet(lucy)<~>kind(lucy)))&
((humble(fred)&kind(fred)))&
((~quiet(john)&~brave(john))) | ~wise(lucy) | [
"p6",
"p7",
"p12",
"p14",
"p15",
"p17",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3045057950569563168685731
% SZS output start Proof for 3045057950569563168685731
7. ! [X0] : ((rich(X0) | strong(X0)) <=> ~old(X0)) [input p6]
8. ! [X0] : ((creative(X0) | wise(X0)) <=> strong(X0)) [input p7]
13. ! [X0] : (~quiet(X0) <=> (old(X0) | happy(X0))) [input p12]
15. ! [X0] : ((generous(X0) | brave(X0)) => (~quiet(X0) & ~generous(X0))) [input p14]
16. ! [X0] : ((brave(X0) <~> kind(X0)) <=> (~kind(X0) <~> ~curious(X0))) [input p15]
18. ~happy(lucy) [input p17]
21. curious(lucy) [input p20]
25. wise(lucy) [input hypothesis]
33. ! [X0] : ((~quiet(X0) & ~generous(X0)) | (~generous(X0) & ~brave(X0))) [ennf transformation 15]
48. ! [X0] : (((rich(X0) | strong(X0)) | old(X0)) & (~old(X0) | (~rich(X0) & ~strong(X0)))) [nnf transformation 7]
49. ! [X0] : ((rich(X0) | strong(X0) | old(X0)) & (~old(X0) | (~rich(X0) & ~strong(X0)))) [flattening 48]
50. ! [X0] : (((creative(X0) | wise(X0)) | ~strong(X0)) & (strong(X0) | (~creative(X0) & ~wise(X0)))) [nnf transformation 8]
51. ! [X0] : ((creative(X0) | wise(X0) | ~strong(X0)) & (strong(X0) | (~creative(X0) & ~wise(X0)))) [flattening 50]
55. ! [X0] : ((~quiet(X0) | (~old(X0) & ~happy(X0))) & ((old(X0) | happy(X0)) | quiet(X0))) [nnf transformation 13]
56. ! [X0] : ((~quiet(X0) | (~old(X0) & ~happy(X0))) & (old(X0) | happy(X0) | quiet(X0))) [flattening 55]
60. ! [X0] : ((((~kind(X0) | ~brave(X0)) & (kind(X0) | brave(X0))) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0)))) & (((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | ((brave(X0) | ~kind(X0)) & (kind(X0) | ~brave(X0))))) [nnf transformation 16]
94. ~old(X0) | ~strong(X0) [cnf transformation 49]
97. ~wise(X0) | strong(X0) [cnf transformation 51]
111. old(X0) | happy(X0) | quiet(X0) [cnf transformation 56]
118. ~quiet(X0) | ~brave(X0) [cnf transformation 33]
121. ~curious(X0) | ~kind(X0) | brave(X0) | ~kind(X0) [cnf transformation 60]
124. kind(X0) | brave(X0) | ~curious(X0) | kind(X0) [cnf transformation 60]
130. ~happy(lucy) [cnf transformation 18]
135. curious(lucy) [cnf transformation 21]
142. wise(lucy) [cnf transformation 25]
143. ~curious(X0) | ~kind(X0) | brave(X0) [duplicate literal removal 121]
145. ~curious(X0) | brave(X0) | kind(X0) [duplicate literal removal 124]
227. 18 <=> strong(lucy) [avatar definition]
229. strong(lucy) <- (18) [avatar component clause 227]
263. ~curious(X0) | brave(X0) [subsumption resolution 143,145]
275. 27 <=> quiet(lucy) [avatar definition]
276. quiet(lucy) <- (27) [avatar component clause 275]
277. ~quiet(lucy) <- (~27) [avatar component clause 275]
284. strong(lucy) [resolution 97,142]
287. 18 [avatar split clause 284,227]
293. ~brave(lucy) <- (27) [resolution 118,276]
297. brave(lucy) [resolution 263,135]
300. $false <- (27) [subsumption resolution 297,293]
301. ~27 [avatar contradiction clause 300]
413. ~strong(X2) | quiet(X2) | happy(X2) [resolution 111,94]
454. quiet(lucy) | happy(lucy) <- (18) [resolution 413,229]
457. happy(lucy) <- (18, ~27) [subsumption resolution 454,277]
458. $false <- (18, ~27) [subsumption resolution 457,130]
459. ~18 | 27 [avatar contradiction clause 458]
478. $false [avatar sat refutation 287,301,459]
% SZS output end Proof for 3045057950569563168685731
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is rich then fred is both not funny and strong and vice versa.
Everyone who is funny or not brave is tall or not humble.
Everyone who is both not tall and tall is both not patient and not happy and vice versa.
Everyone who is both kind and not strong is funny.
Everyone who is both wise and not patient is either wise or not rich and vice versa.
Everyone who is both strong and creative is both not generous and old and vice versa.
Everyone who is tall or creative is either happy or not humble.
If alice is both wise and not funny then someone is not happy or not patient and vice versa.
If paul is either old or not funny then someone is generous or funny.
Everyone who is old is not creative and vice versa.
Everyone who is calm is either not kind or patient and vice versa.
Everyone who is not happy or not tall is happy.
If someone is not brave then alice is not generous or not rich and vice versa.
If someone is both not curious and not quiet then paul is both not kind and funny and vice versa.
If john is strong then someone is either not tall or funny.
If someone is both not kind and not happy then john is not curious or curious.
Lucy is both not patient and not strong.
Paul is not humble or not tall.
Someone is either not old or rich.
Someone is either rich or not generous.
Someone is either not strong or happy.
Someone is either funny or quiet. | John is not funny. | neutral | ((?[X]:(rich(X)))<=>((~funny(fred)&strong(fred))))&
(![X]:((funny(X)|~brave(X))=>(tall(X)|~humble(X))))&
(![X]:((~tall(X)&tall(X))<=>(~patient(X)&~happy(X))))&
(![X]:((kind(X)&~strong(X))=>funny(X)))&
(![X]:((wise(X)&~patient(X))<=>(wise(X)<~>~rich(X))))&
(![X]:((strong(X)&creative(X))<=>(~generous(X)&old(X))))&
(![X]:((tall(X)|creative(X))=>(happy(X)<~>~humble(X))))&
(((wise(alice)&~funny(alice)))<=>(?[X]:((~happy(X)|~patient(X)))))&
(((old(paul)<~>~funny(paul)))=>(?[X]:((generous(X)|funny(X)))))&
(![X]:(old(X)<=>~creative(X)))&
(![X]:(calm(X)<=>(~kind(X)<~>patient(X))))&
(![X]:((~happy(X)|~tall(X))=>happy(X)))&
((?[X]:(~brave(X)))<=>((~generous(alice)|~rich(alice))))&
((?[X]:((~curious(X)&~quiet(X))))<=>((~kind(paul)&funny(paul))))&
((strong(john))=>(?[X]:((~tall(X)<~>funny(X)))))&
((?[X]:((~kind(X)&~happy(X))))=>((~curious(john)|curious(john))))&
((~patient(lucy)&~strong(lucy)))&
((~humble(paul)|~tall(paul)))&
(?[X]:((~old(X)<~>rich(X))))&
(?[X]:((rich(X)<~>~generous(X))))&
(?[X]:((~strong(X)<~>happy(X))))&
(?[X]:((funny(X)<~>quiet(X)))) | ~funny(john) | [] | null | 0 |
Everyone who is rich or humble is strong or not rich and vice versa. If someone is calm then fred is not strong. Everyone who is either funny or not patient is not brave and vice versa. Everyone who is either calm or not rich is either not quiet or not rich and vice versa. Everyone who is either patient or not rich is not kind and vice versa. Everyone who is both strong and quiet is quiet or not generous. If someone is either generous or not rich then someone is either not patient or not humble and vice versa. If someone is old then mary is either curious or kind and vice versa. Everyone who is not wise is brave or quiet and vice versa. Everyone who is either not rich or not patient is not kind or patient. Everyone who is either funny or happy is either brave or humble. Everyone who is not creative is tall and vice versa. If paul is both not old and funny then someone is tall. Everyone who is both kind and patient is not funny and vice versa. If someone is not kind or old then someone is either happy or not calm. Everyone who is humble is funny or wise. Someone is not calm or not tall. Someone is both brave and not curious. Lucy is not old. Someone is either old or not creative. Paul is creative. Mary is rich. John is either quiet or not rich. | Lucy is not funny. | contradiction | (![X]:((rich(X)|humble(X))<=>(strong(X)|~rich(X))))&
((?[X]:(calm(X)))=>(~strong(fred)))&
(![X]:((funny(X)<~>~patient(X))<=>~brave(X)))&
(![X]:((calm(X)<~>~rich(X))<=>(~quiet(X)<~>~rich(X))))&
(![X]:((patient(X)<~>~rich(X))<=>~kind(X)))&
(![X]:((strong(X)&quiet(X))=>(quiet(X)|~generous(X))))&
((?[X]:((generous(X)<~>~rich(X))))<=>(?[X]:((~patient(X)<~>~humble(X)))))&
((?[X]:(old(X)))<=>((curious(mary)<~>kind(mary))))&
(![X]:(~wise(X)<=>(brave(X)|quiet(X))))&
(![X]:((~rich(X)<~>~patient(X))=>(~kind(X)|patient(X))))&
(![X]:((funny(X)<~>happy(X))=>(brave(X)<~>humble(X))))&
(![X]:(~creative(X)<=>tall(X)))&
(((~old(paul)&funny(paul)))=>(?[X]:(tall(X))))&
(![X]:((kind(X)&patient(X))<=>~funny(X)))&
((?[X]:((~kind(X)|old(X))))=>(?[X]:((happy(X)<~>~calm(X)))))&
(![X]:(humble(X)=>(funny(X)|wise(X))))&
(?[X]:((~calm(X)|~tall(X))))&
(?[X]:((brave(X)&~curious(X))))&
(~old(lucy))&
(?[X]:((old(X)<~>~creative(X))))&
(creative(paul))&
(rich(mary))&
((quiet(john)<~>~rich(john))) | ~funny(lucy) | [
"p0",
"p2",
"p4",
"p8",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7174625079310846911672514
% SZS output start Proof for 7174625079310846911672514
1. ! [X0] : ((humble(X0) | rich(X0)) <=> (~rich(X0) | strong(X0))) [input p0]
3. ! [X0] : ((funny(X0) <~> ~patient(X0)) <=> ~brave(X0)) [input p2]
5. ! [X0] : ((patient(X0) <~> ~rich(X0)) <=> ~kind(X0)) [input p4]
9. ! [X0] : (~wise(X0) <=> (quiet(X0) | brave(X0))) [input p8]
14. ! [X0] : ((patient(X0) & kind(X0)) <=> ~funny(X0)) [input p13]
16. ! [X0] : (humble(X0) => (wise(X0) | funny(X0))) [input p15]
24. ~funny(lucy) [input hypothesis]
27. ! [X0] : ((quiet(X0) | brave(X0)) => ~wise(X0)) [unused predicate definition removal 9]
31. ! [X0] : (~wise(X0) | (~quiet(X0) & ~brave(X0))) [ennf transformation 27]
38. ! [X0] : ((wise(X0) | funny(X0)) | ~humble(X0)) [ennf transformation 16]
39. ! [X0] : (wise(X0) | funny(X0) | ~humble(X0)) [flattening 38]
40. ! [X0] : (((humble(X0) | rich(X0)) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | (~humble(X0) & ~rich(X0)))) [nnf transformation 1]
41. ! [X0] : ((humble(X0) | rich(X0) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | (~humble(X0) & ~rich(X0)))) [flattening 40]
42. ! [X0] : ((((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | brave(X0)) & (~brave(X0) | ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0))))) [nnf transformation 3]
44. ! [X0] : ((((rich(X0) | ~patient(X0)) & (~rich(X0) | patient(X0))) | kind(X0)) & (~kind(X0) | ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0))))) [nnf transformation 5]
59. ! [X0] : (((patient(X0) & kind(X0)) | funny(X0)) & (~funny(X0) | (~patient(X0) | ~kind(X0)))) [nnf transformation 14]
60. ! [X0] : (((patient(X0) & kind(X0)) | funny(X0)) & (~funny(X0) | ~patient(X0) | ~kind(X0))) [flattening 59]
76. humble(X0) | rich(X0) | rich(X0) [cnf transformation 41]
80. ~patient(X0) | funny(X0) | brave(X0) [cnf transformation 42]
90. ~kind(X0) | ~rich(X0) | ~patient(X0) [cnf transformation 44]
107. ~wise(X0) | ~brave(X0) [cnf transformation 31]
119. kind(X0) | funny(X0) [cnf transformation 60]
120. patient(X0) | funny(X0) [cnf transformation 60]
125. ~humble(X0) | funny(X0) | wise(X0) [cnf transformation 39]
136. ~funny(lucy) [cnf transformation 24]
143. humble(X0) | rich(X0) [duplicate literal removal 76]
291. funny(X0) | brave(X0) | funny(X0) [resolution 80,120]
293. brave(X0) | funny(X0) [duplicate literal removal 291]
305. ~rich(X0) | ~patient(X0) | funny(X0) [resolution 90,119]
309. ~rich(X0) | funny(X0) [subsumption resolution 305,120]
335. funny(X0) | wise(X0) | rich(X0) [resolution 125,143]
336. wise(X0) | funny(X0) [subsumption resolution 335,309]
455. funny(X1) | ~brave(X1) [resolution 336,107]
456. funny(X1) [subsumption resolution 455,293]
477. $false [resolution 456,136]
% SZS output end Proof for 7174625079310846911672514
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and wise is either happy or not kind and vice versa. If mary is not curious then alice is either kind or calm and vice versa. Everyone who is humble is creative or calm and vice versa. Everyone who is both not humble and creative is quiet. Everyone who is old or not curious is both not old and not tall. Everyone who is either creative or old is curious or happy. Everyone who is not calm or not old is both calm and curious and vice versa. Everyone who is either not happy or happy is either not tall or not calm. If someone is rich then john is both humble and not humble and vice versa. Everyone who is both funny and not patient is not calm or not brave and vice versa. If someone is patient then someone is either humble or not funny. Everyone who is not old or generous is not brave and vice versa. Everyone who is rich or not strong is curious or not tall and vice versa. If lucy is both happy and quiet then mary is either not brave or not old and vice versa. Someone is not brave. Fred is not patient or not old. Someone is either quiet or wise. Someone is happy or not happy. | Alice is strong. | contradiction | (![X]:((~generous(X)&wise(X))<=>(happy(X)<~>~kind(X))))&
((~curious(mary))<=>((kind(alice)<~>calm(alice))))&
(![X]:(humble(X)<=>(creative(X)|calm(X))))&
(![X]:((~humble(X)&creative(X))=>quiet(X)))&
(![X]:((old(X)|~curious(X))=>(~old(X)&~tall(X))))&
(![X]:((creative(X)<~>old(X))=>(curious(X)|happy(X))))&
(![X]:((~calm(X)|~old(X))<=>(calm(X)&curious(X))))&
(![X]:((~happy(X)<~>happy(X))=>(~tall(X)<~>~calm(X))))&
((?[X]:(rich(X)))<=>((humble(john)&~humble(john))))&
(![X]:((funny(X)&~patient(X))<=>(~calm(X)|~brave(X))))&
((?[X]:(patient(X)))=>(?[X]:((humble(X)<~>~funny(X)))))&
(![X]:((~old(X)|generous(X))<=>~brave(X)))&
(![X]:((rich(X)|~strong(X))<=>(curious(X)|~tall(X))))&
(((happy(lucy)&quiet(lucy)))<=>((~brave(mary)<~>~old(mary))))&
(?[X]:(~brave(X)))&
((~patient(fred)|~old(fred)))&
(?[X]:((quiet(X)<~>wise(X))))&
(?[X]:((happy(X)|~happy(X)))) | strong(alice) | [
"p4",
"p6",
"p7",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 164078520272659583402967
% SZS output start Proof for 164078520272659583402967
5. ! [X0] : ((~curious(X0) | old(X0)) => (~tall(X0) & ~old(X0))) [input p4]
7. ! [X0] : ((~old(X0) | ~calm(X0)) <=> (curious(X0) & calm(X0))) [input p6]
8. ! [X0] : ((~happy(X0) <~> happy(X0)) => (~tall(X0) <~> ~calm(X0))) [input p7]
9. ? [X0] : rich(X0) <=> (~humble(john) & humble(john)) [input p8]
13. ! [X0] : ((~strong(X0) | rich(X0)) <=> (~tall(X0) | curious(X0))) [input p12]
19. strong(alice) [input hypothesis]
23. ! [X0] : ((~tall(X0) & ~old(X0)) | (curious(X0) & ~old(X0))) [ennf transformation 5]
26. ! [X0] : ((~tall(X0) <~> ~calm(X0)) | (~happy(X0) <=> happy(X0))) [ennf transformation 8]
34. ! [X0] : (((~old(X0) | ~calm(X0)) | (~curious(X0) | ~calm(X0))) & ((curious(X0) & calm(X0)) | (old(X0) & calm(X0)))) [nnf transformation 7]
35. ! [X0] : ((~old(X0) | ~calm(X0) | ~curious(X0) | ~calm(X0)) & ((curious(X0) & calm(X0)) | (old(X0) & calm(X0)))) [flattening 34]
36. ! [X0] : (((calm(X0) | tall(X0)) & (~calm(X0) | ~tall(X0))) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) [nnf transformation 26]
37. (? [X0] : rich(X0) | (humble(john) | ~humble(john))) & ((~humble(john) & humble(john)) | ! [X0] : ~rich(X0)) [nnf transformation 9]
38. (? [X0] : rich(X0) | humble(john) | ~humble(john)) & ((~humble(john) & humble(john)) | ! [X0] : ~rich(X0)) [flattening 37]
39. (? [X0] : rich(X0) | humble(john) | ~humble(john)) & ((~humble(john) & humble(john)) | ! [X1] : ~rich(X1)) [rectify 38]
40. ? [X0] : rich(X0) => rich(sK0) [choice axiom]
41. (rich(sK0) | humble(john) | ~humble(john)) & ((~humble(john) & humble(john)) | ! [X1] : ~rich(X1)) [skolemisation 39,40]
50. ! [X0] : (((~strong(X0) | rich(X0)) | (tall(X0) & ~curious(X0))) & ((~tall(X0) | curious(X0)) | (strong(X0) & ~rich(X0)))) [nnf transformation 13]
51. ! [X0] : ((~strong(X0) | rich(X0) | (tall(X0) & ~curious(X0))) & (~tall(X0) | curious(X0) | (strong(X0) & ~rich(X0)))) [flattening 50]
75. ~old(X0) | ~old(X0) [cnf transformation 23]
82. calm(X0) | old(X0) [cnf transformation 35]
86. ~calm(X0) | ~tall(X0) | happy(X0) | happy(X0) [cnf transformation 36]
87. ~calm(X0) | ~tall(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 36]
90. humble(john) | ~rich(X1) [cnf transformation 41]
91. ~humble(john) | ~rich(X1) [cnf transformation 41]
106. ~strong(X0) | rich(X0) | tall(X0) [cnf transformation 51]
118. strong(alice) [cnf transformation 19]
119. ~calm(X0) | ~tall(X0) | happy(X0) [duplicate literal removal 86]
120. ~calm(X0) | ~tall(X0) | ~happy(X0) [duplicate literal removal 87]
125. ~old(X0) [duplicate literal removal 75]
144. calm(X0) [subsumption resolution 82,125]
145. ~tall(X0) | ~happy(X0) [subsumption resolution 120,144]
146. ~tall(X0) | happy(X0) [subsumption resolution 119,144]
147. ~tall(X0) [subsumption resolution 146,145]
149. 4 <=> ! [X1] : ~rich(X1) [avatar definition]
150. ~rich(X1) <- (4) [avatar component clause 149]
152. 5 <=> humble(john) [avatar definition]
155. 4 | ~5 [avatar split clause 91,152,149]
156. 4 | 5 [avatar split clause 90,152,149]
172. ~strong(X0) | rich(X0) [subsumption resolution 106,147]
205. rich(alice) [resolution 172,118]
206. $false <- (4) [subsumption resolution 205,150]
207. ~4 [avatar contradiction clause 206]
208. $false [avatar sat refutation 155,156,207]
% SZS output end Proof for 164078520272659583402967
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and brave is curious and vice versa.
Everyone who is either calm or not brave is brave and vice versa.
Everyone who is either happy or tall is either not quiet or not tall.
Everyone who is both not funny and not brave is calm and vice versa.
Everyone who is brave or old is both not rich and curious and vice versa.
If mary is wise or not happy then someone is curious or kind.
If someone is either not patient or quiet then someone is not calm or creative and vice versa.
Everyone who is not wise or patient is either not patient or rich.
Everyone who is either not kind or not old is either not rich or quiet.
Everyone who is both old and not tall is not humble or not quiet and vice versa.
Everyone who is both not rich and calm is both not wise and not creative and vice versa.
If susan is both not rich and wise then someone is both tall and quiet and vice versa.
Everyone who is both happy and not strong is either creative or not generous and vice versa.
If someone is both curious and funny then alice is rich.
If someone is both funny and wise then someone is not kind.
Everyone who is not brave or strong is either not creative or happy and vice versa.
Mary is both not funny and humble.
Lucy is not wise.
Someone is wise.
Someone is humble.
Paul is not calm or quiet. | Lucy is not old. | entailment | (![X]:((~happy(X)&brave(X))<=>curious(X)))&
(![X]:((calm(X)<~>~brave(X))<=>brave(X)))&
(![X]:((happy(X)<~>tall(X))=>(~quiet(X)<~>~tall(X))))&
(![X]:((~funny(X)&~brave(X))<=>calm(X)))&
(![X]:((brave(X)|old(X))<=>(~rich(X)&curious(X))))&
(((wise(mary)|~happy(mary)))=>(?[X]:((curious(X)|kind(X)))))&
((?[X]:((~patient(X)<~>quiet(X))))<=>(?[X]:((~calm(X)|creative(X)))))&
(![X]:((~wise(X)|patient(X))=>(~patient(X)<~>rich(X))))&
(![X]:((~kind(X)<~>~old(X))=>(~rich(X)<~>quiet(X))))&
(![X]:((old(X)&~tall(X))<=>(~humble(X)|~quiet(X))))&
(![X]:((~rich(X)&calm(X))<=>(~wise(X)&~creative(X))))&
(((~rich(susan)&wise(susan)))<=>(?[X]:((tall(X)&quiet(X)))))&
(![X]:((happy(X)&~strong(X))<=>(creative(X)<~>~generous(X))))&
((?[X]:((curious(X)&funny(X))))=>(rich(alice)))&
((?[X]:((funny(X)&wise(X))))=>(?[X]:(~kind(X))))&
(![X]:((~brave(X)|strong(X))<=>(~creative(X)<~>happy(X))))&
((~funny(mary)&humble(mary)))&
(~wise(lucy))&
(?[X]:(wise(X)))&
(?[X]:(humble(X)))&
((~calm(paul)|quiet(paul))) | ~old(lucy) | [
"p0",
"p1",
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 4475534697709334009606592
% SZS output start Proof for 4475534697709334009606592
1. ! [X0] : ((brave(X0) & ~happy(X0)) <=> curious(X0)) [input p0]
2. ! [X0] : ((calm(X0) <~> ~brave(X0)) <=> brave(X0)) [input p1]
4. ! [X0] : ((~brave(X0) & ~funny(X0)) <=> calm(X0)) [input p3]
5. ! [X0] : ((old(X0) | brave(X0)) <=> (curious(X0) & ~rich(X0))) [input p4]
22. old(lucy) [input hypothesis]
31. ! [X0] : (((brave(X0) & ~happy(X0)) | ~curious(X0)) & (curious(X0) | (~brave(X0) | happy(X0)))) [nnf transformation 1]
32. ! [X0] : (((brave(X0) & ~happy(X0)) | ~curious(X0)) & (curious(X0) | ~brave(X0) | happy(X0))) [flattening 31]
33. ! [X0] : ((((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | ~brave(X0)) & (brave(X0) | ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0))))) [nnf transformation 2]
35. ! [X0] : (((~brave(X0) & ~funny(X0)) | ~calm(X0)) & (calm(X0) | (brave(X0) | funny(X0)))) [nnf transformation 4]
36. ! [X0] : (((~brave(X0) & ~funny(X0)) | ~calm(X0)) & (calm(X0) | brave(X0) | funny(X0))) [flattening 35]
37. ! [X0] : (((old(X0) | brave(X0)) | (~curious(X0) | rich(X0))) & ((curious(X0) & ~rich(X0)) | (~old(X0) & ~brave(X0)))) [nnf transformation 5]
38. ! [X0] : ((old(X0) | brave(X0) | ~curious(X0) | rich(X0)) & ((curious(X0) & ~rich(X0)) | (~old(X0) & ~brave(X0)))) [flattening 37]
70. ~curious(X0) | brave(X0) [cnf transformation 32]
72. brave(X0) | calm(X0) | brave(X0) [cnf transformation 33]
73. ~brave(X0) | calm(X0) | ~brave(X0) [cnf transformation 33]
81. ~brave(X0) | ~calm(X0) [cnf transformation 36]
85. ~old(X0) | curious(X0) [cnf transformation 38]
136. old(lucy) [cnf transformation 22]
140. brave(X0) | calm(X0) [duplicate literal removal 72]
141. ~brave(X0) | calm(X0) [duplicate literal removal 73]
142. calm(X0) [subsumption resolution 140,141]
143. ~brave(X0) [subsumption resolution 81,142]
216. curious(lucy) [resolution 85,136]
217. brave(lucy) [resolution 216,70]
219. $false [subsumption resolution 217,143]
% SZS output end Proof for 4475534697709334009606592
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not humble is either strong or old.
If someone is either not happy or not humble then someone is either not funny or quiet and vice versa.
Everyone who is not old is not quiet or not calm.
Everyone who is either not quiet or not kind is calm or not kind and vice versa.
If alice is funny then alice is wise.
Everyone who is either not tall or not quiet is both old and not creative and vice versa.
If fred is patient then someone is not wise or not brave and vice versa.
Everyone who is not funny is not old or tall and vice versa.
If john is both happy and not funny then fred is both kind and not kind and vice versa.
Everyone who is not calm or wise is kind.
If someone is tall or old then fred is both calm and creative and vice versa.
Everyone who is brave is either not patient or not tall.
If john is either not generous or not strong then susan is not curious.
If someone is not curious then paul is either brave or not generous.
Everyone who is not happy is either happy or not creative and vice versa.
If fred is both not generous and creative then susan is not creative or not wise.
Someone is old or not patient.
Someone is not happy or brave.
Someone is either brave or kind.
Someone is both kind and not creative.
Someone is not patient or not strong. | Susan is kind. | entailment | (![X]:((calm(X)|~humble(X))=>(strong(X)<~>old(X))))&
((?[X]:((~happy(X)<~>~humble(X))))<=>(?[X]:((~funny(X)<~>quiet(X)))))&
(![X]:(~old(X)=>(~quiet(X)|~calm(X))))&
(![X]:((~quiet(X)<~>~kind(X))<=>(calm(X)|~kind(X))))&
((funny(alice))=>(wise(alice)))&
(![X]:((~tall(X)<~>~quiet(X))<=>(old(X)&~creative(X))))&
((patient(fred))<=>(?[X]:((~wise(X)|~brave(X)))))&
(![X]:(~funny(X)<=>(~old(X)|tall(X))))&
(((happy(john)&~funny(john)))<=>((kind(fred)&~kind(fred))))&
(![X]:((~calm(X)|wise(X))=>kind(X)))&
((?[X]:((tall(X)|old(X))))<=>((calm(fred)&creative(fred))))&
(![X]:(brave(X)=>(~patient(X)<~>~tall(X))))&
(((~generous(john)<~>~strong(john)))=>(~curious(susan)))&
((?[X]:(~curious(X)))=>((brave(paul)<~>~generous(paul))))&
(![X]:(~happy(X)<=>(happy(X)<~>~creative(X))))&
(((~generous(fred)&creative(fred)))=>((~creative(susan)|~wise(susan))))&
(?[X]:((old(X)|~patient(X))))&
(?[X]:((~happy(X)|brave(X))))&
(?[X]:((brave(X)<~>kind(X))))&
(?[X]:((kind(X)&~creative(X))))&
(?[X]:((~patient(X)|~strong(X)))) | kind(susan) | [
"p2",
"p3",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2734594955972641346384655
% SZS output start Proof for 2734594955972641346384655
3. ! [X0] : (~old(X0) => (~calm(X0) | ~quiet(X0))) [input p2]
4. ! [X0] : ((~quiet(X0) <~> ~kind(X0)) <=> (~kind(X0) | calm(X0))) [input p3]
10. ! [X0] : ((wise(X0) | ~calm(X0)) => kind(X0)) [input p9]
11. ? [X0] : (old(X0) | tall(X0)) <=> (creative(fred) & calm(fred)) [input p10]
15. ! [X0] : (~happy(X0) <=> (happy(X0) <~> ~creative(X0))) [input p14]
22. ~kind(susan) [input hypothesis]
25. ! [X0] : ((~calm(X0) | ~quiet(X0)) | old(X0)) [ennf transformation 3]
26. ! [X0] : (~calm(X0) | ~quiet(X0) | old(X0)) [flattening 25]
28. ! [X0] : (kind(X0) | (~wise(X0) & calm(X0))) [ennf transformation 10]
40. ! [X0] : ((((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | (kind(X0) & ~calm(X0))) & ((~kind(X0) | calm(X0)) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0))))) [nnf transformation 4]
41. ! [X0] : ((((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | (kind(X0) & ~calm(X0))) & (~kind(X0) | calm(X0) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0))))) [flattening 40]
52. (? [X0] : (old(X0) | tall(X0)) | (~creative(fred) | ~calm(fred))) & ((creative(fred) & calm(fred)) | ! [X0] : (~old(X0) & ~tall(X0))) [nnf transformation 11]
53. (? [X0] : (old(X0) | tall(X0)) | ~creative(fred) | ~calm(fred)) & ((creative(fred) & calm(fred)) | ! [X0] : (~old(X0) & ~tall(X0))) [flattening 52]
54. (? [X0] : (old(X0) | tall(X0)) | ~creative(fred) | ~calm(fred)) & ((creative(fred) & calm(fred)) | ! [X1] : (~old(X1) & ~tall(X1))) [rectify 53]
55. ? [X0] : (old(X0) | tall(X0)) => (old(sK3) | tall(sK3)) [choice axiom]
56. ((old(sK3) | tall(sK3)) | ~creative(fred) | ~calm(fred)) & ((creative(fred) & calm(fred)) | ! [X1] : (~old(X1) & ~tall(X1))) [skolemisation 54,55]
60. ! [X0] : ((~happy(X0) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0)))) & (((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | happy(X0))) [nnf transformation 15]
84. ~quiet(X0) | ~calm(X0) | old(X0) [cnf transformation 26]
90. kind(X0) | quiet(X0) | kind(X0) [cnf transformation 41]
108. kind(X0) | calm(X0) [cnf transformation 28]
113. creative(fred) | ~old(X1) [cnf transformation 56]
121. ~creative(X0) | happy(X0) | happy(X0) [cnf transformation 60]
123. ~happy(X0) | ~creative(X0) | ~happy(X0) [cnf transformation 60]
133. ~kind(susan) [cnf transformation 22]
134. ~creative(X0) | happy(X0) [duplicate literal removal 121]
135. ~creative(X0) | ~happy(X0) [duplicate literal removal 123]
137. kind(X0) | quiet(X0) [duplicate literal removal 90]
224. 20 <=> creative(fred) [avatar definition]
225. creative(fred) <- (20) [avatar component clause 224]
237. 23 <=> ! [X1] : ~old(X1) [avatar definition]
238. ~old(X1) <- (23) [avatar component clause 237]
239. 23 | 20 [avatar split clause 113,224,237]
273. ~creative(X0) [subsumption resolution 134,135]
311. $false <- (20) [subsumption resolution 225,273]
312. ~20 [avatar contradiction clause 311]
315. calm(susan) [resolution 108,133]
317. quiet(susan) [resolution 137,133]
333. ~calm(susan) | old(susan) [resolution 84,317]
335. old(susan) [subsumption resolution 333,315]
336. $false <- (23) [subsumption resolution 335,238]
337. ~23 [avatar contradiction clause 336]
341. $false [avatar sat refutation 239,312,337]
% SZS output end Proof for 2734594955972641346384655
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave then john is either brave or not humble and vice versa.
Everyone who is old is not old.
If someone is not creative then mary is either calm or not kind.
Everyone who is patient or not happy is both happy and not brave.
Everyone who is happy is both not funny and not old.
If someone is both not tall and patient then someone is both not curious and not old.
Everyone who is both humble and not humble is either patient or not old and vice versa.
If alice is not calm or curious then john is kind or not brave.
If fred is tall or wise then someone is both funny and wise.
If someone is either wise or generous then someone is both not creative and not old and vice versa.
If someone is either not humble or patient then lucy is not tall and vice versa.
Everyone who is not generous is either kind or creative.
If fred is either kind or not tall then someone is both old and not funny and vice versa.
If someone is both happy and calm then someone is both brave and old.
If someone is not creative or not kind then alice is patient and vice versa.
Paul is either tall or not strong.
Susan is brave or not tall.
John is either curious or generous.
Mary is both rich and not strong.
John is strong or humble. | Mary is strong. | contradiction | ((?[X]:(~brave(X)))<=>((brave(john)<~>~humble(john))))&
(![X]:(old(X)=>~old(X)))&
((?[X]:(~creative(X)))=>((calm(mary)<~>~kind(mary))))&
(![X]:((patient(X)|~happy(X))=>(happy(X)&~brave(X))))&
(![X]:(happy(X)=>(~funny(X)&~old(X))))&
((?[X]:((~tall(X)&patient(X))))=>(?[X]:((~curious(X)&~old(X)))))&
(![X]:((humble(X)&~humble(X))<=>(patient(X)<~>~old(X))))&
(((~calm(alice)|curious(alice)))=>((kind(john)|~brave(john))))&
(((tall(fred)|wise(fred)))=>(?[X]:((funny(X)&wise(X)))))&
((?[X]:((wise(X)<~>generous(X))))<=>(?[X]:((~creative(X)&~old(X)))))&
((?[X]:((~humble(X)<~>patient(X))))<=>(~tall(lucy)))&
(![X]:(~generous(X)=>(kind(X)<~>creative(X))))&
(((kind(fred)<~>~tall(fred)))<=>(?[X]:((old(X)&~funny(X)))))&
((?[X]:((happy(X)&calm(X))))=>(?[X]:((brave(X)&old(X)))))&
((?[X]:((~creative(X)|~kind(X))))<=>(patient(alice)))&
((tall(paul)<~>~strong(paul)))&
((brave(susan)|~tall(susan)))&
((curious(john)<~>generous(john)))&
((rich(mary)&~strong(mary)))&
((strong(john)|humble(john))) | strong(mary) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4619139594256263814252588
% SZS output start Proof for 4619139594256263814252588
19. ~strong(mary) & rich(mary) [input p18]
21. strong(mary) [input hypothesis]
25. ~strong(mary) [pure predicate removal 19]
126. ~strong(mary) [cnf transformation 25]
128. strong(mary) [cnf transformation 21]
300. $false [subsumption resolution 128,126]
% SZS output end Proof for 4619139594256263814252588
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both creative and not creative then someone is not creative.
If john is both not curious and curious then someone is both not curious and not quiet and vice versa.
Everyone who is not strong or creative is either not brave or happy and vice versa.
Everyone who is not brave is either not brave or not generous and vice versa.
If someone is wise then john is kind or not curious and vice versa.
Everyone who is not wise is not creative and vice versa.
Everyone who is both not humble and not strong is both tall and not patient.
Everyone who is both not kind and not wise is not humble.
Everyone who is not quiet is happy.
If mary is strong or not generous then someone is rich and vice versa.
Everyone who is both quiet and not wise is kind.
Everyone who is funny is rich and vice versa.
If paul is both not rich and not happy then someone is not tall and vice versa.
If someone is either not funny or brave then someone is either curious or not wise and vice versa.
If paul is not quiet or strong then someone is both not brave and not curious.
Everyone who is not patient is not funny or humble.
Fred is both not calm and wise.
Someone is funny.
Fred is both quiet and not kind.
Susan is both calm and patient.
Someone is brave or curious.
Paul is not funny.
Susan is curious or not patient.
Mary is both not calm and creative. | John is funny. | neutral | (((creative(fred)&~creative(fred)))=>(?[X]:(~creative(X))))&
(((~curious(john)&curious(john)))<=>(?[X]:((~curious(X)&~quiet(X)))))&
(![X]:((~strong(X)|creative(X))<=>(~brave(X)<~>happy(X))))&
(![X]:(~brave(X)<=>(~brave(X)<~>~generous(X))))&
((?[X]:(wise(X)))<=>((kind(john)|~curious(john))))&
(![X]:(~wise(X)<=>~creative(X)))&
(![X]:((~humble(X)&~strong(X))=>(tall(X)&~patient(X))))&
(![X]:((~kind(X)&~wise(X))=>~humble(X)))&
(![X]:(~quiet(X)=>happy(X)))&
(((strong(mary)|~generous(mary)))<=>(?[X]:(rich(X))))&
(![X]:((quiet(X)&~wise(X))=>kind(X)))&
(![X]:(funny(X)<=>rich(X)))&
(((~rich(paul)&~happy(paul)))<=>(?[X]:(~tall(X))))&
((?[X]:((~funny(X)<~>brave(X))))<=>(?[X]:((curious(X)<~>~wise(X)))))&
(((~quiet(paul)|strong(paul)))=>(?[X]:((~brave(X)&~curious(X)))))&
(![X]:(~patient(X)=>(~funny(X)|humble(X))))&
((~calm(fred)&wise(fred)))&
(?[X]:(funny(X)))&
((quiet(fred)&~kind(fred)))&
((calm(susan)&patient(susan)))&
(?[X]:((brave(X)|curious(X))))&
(~funny(paul))&
((curious(susan)|~patient(susan)))&
((~calm(mary)&creative(mary))) | funny(john) | [] | null | 0 |
Everyone who is not calm is strong or not humble. Everyone who is not quiet or not happy is either not brave or not curious. Everyone who is not humble or kind is both tall and brave and vice versa. Everyone who is not old or not generous is either strong or brave. Everyone who is brave or not curious is both wise and not humble. Everyone who is both not humble and not quiet is generous or not wise. Everyone who is either not creative or happy is humble or not tall and vice versa. Everyone who is creative is both brave and curious and vice versa. Everyone who is not quiet is both not wise and quiet and vice versa. Everyone who is not kind or not rich is either not kind or humble. If lucy is either not tall or tall then paul is happy and vice versa. If someone is both wise and not kind then mary is creative and vice versa. If someone is either strong or not wise then someone is both not calm and old. If paul is not old then someone is both strong and tall. Someone is either not rich or not old. Someone is either kind or generous. Someone is quiet or wise. Mary is wise. Someone is not curious or generous. | Lucy is not curious. | entailment | (![X]:(~calm(X)=>(strong(X)|~humble(X))))&
(![X]:((~quiet(X)|~happy(X))=>(~brave(X)<~>~curious(X))))&
(![X]:((~humble(X)|kind(X))<=>(tall(X)&brave(X))))&
(![X]:((~old(X)|~generous(X))=>(strong(X)<~>brave(X))))&
(![X]:((brave(X)|~curious(X))=>(wise(X)&~humble(X))))&
(![X]:((~humble(X)&~quiet(X))=>(generous(X)|~wise(X))))&
(![X]:((~creative(X)<~>happy(X))<=>(humble(X)|~tall(X))))&
(![X]:(creative(X)<=>(brave(X)&curious(X))))&
(![X]:(~quiet(X)<=>(~wise(X)&quiet(X))))&
(![X]:((~kind(X)|~rich(X))=>(~kind(X)<~>humble(X))))&
(((~tall(lucy)<~>tall(lucy)))<=>(happy(paul)))&
((?[X]:((wise(X)&~kind(X))))<=>(creative(mary)))&
((?[X]:((strong(X)<~>~wise(X))))=>(?[X]:((~calm(X)&old(X)))))&
((~old(paul))=>(?[X]:((strong(X)&tall(X)))))&
(?[X]:((~rich(X)<~>~old(X))))&
(?[X]:((kind(X)<~>generous(X))))&
(?[X]:((quiet(X)|wise(X))))&
(wise(mary))&
(?[X]:((~curious(X)|generous(X)))) | ~curious(lucy) | [
"p1",
"p2",
"p4",
"p6",
"p7",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8904525052071754469613367
% SZS output start Proof for 8904525052071754469613367
2. ! [X0] : ((~happy(X0) | ~quiet(X0)) => (~brave(X0) <~> ~curious(X0))) [input p1]
3. ! [X0] : ((kind(X0) | ~humble(X0)) <=> (brave(X0) & tall(X0))) [input p2]
5. ! [X0] : ((~curious(X0) | brave(X0)) => (~humble(X0) & wise(X0))) [input p4]
7. ! [X0] : ((~creative(X0) <~> happy(X0)) <=> (~tall(X0) | humble(X0))) [input p6]
8. ! [X0] : (creative(X0) <=> (curious(X0) & brave(X0))) [input p7]
9. ! [X0] : (~quiet(X0) <=> (quiet(X0) & ~wise(X0))) [input p8]
12. ? [X0] : (~kind(X0) & wise(X0)) <=> creative(mary) [input p11]
20. curious(lucy) [input hypothesis]
24. ! [X0] : ((~brave(X0) <~> ~curious(X0)) | (happy(X0) & quiet(X0))) [ennf transformation 2]
26. ! [X0] : ((~humble(X0) & wise(X0)) | (curious(X0) & ~brave(X0))) [ennf transformation 5]
32. ! [X0] : (((curious(X0) | brave(X0)) & (~curious(X0) | ~brave(X0))) | (happy(X0) & quiet(X0))) [nnf transformation 24]
33. ! [X0] : (((kind(X0) | ~humble(X0)) | (~brave(X0) | ~tall(X0))) & ((brave(X0) & tall(X0)) | (~kind(X0) & humble(X0)))) [nnf transformation 3]
34. ! [X0] : ((kind(X0) | ~humble(X0) | ~brave(X0) | ~tall(X0)) & ((brave(X0) & tall(X0)) | (~kind(X0) & humble(X0)))) [flattening 33]
36. ! [X0] : ((((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (tall(X0) & ~humble(X0))) & ((~tall(X0) | humble(X0)) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0))))) [nnf transformation 7]
37. ! [X0] : ((((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (tall(X0) & ~humble(X0))) & (~tall(X0) | humble(X0) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0))))) [flattening 36]
38. ! [X0] : ((creative(X0) | (~curious(X0) | ~brave(X0))) & ((curious(X0) & brave(X0)) | ~creative(X0))) [nnf transformation 8]
39. ! [X0] : ((creative(X0) | ~curious(X0) | ~brave(X0)) & ((curious(X0) & brave(X0)) | ~creative(X0))) [flattening 38]
40. ! [X0] : ((~quiet(X0) | (~quiet(X0) | wise(X0))) & ((quiet(X0) & ~wise(X0)) | quiet(X0))) [nnf transformation 9]
41. ! [X0] : ((~quiet(X0) | ~quiet(X0) | wise(X0)) & ((quiet(X0) & ~wise(X0)) | quiet(X0))) [flattening 40]
44. (? [X0] : (~kind(X0) & wise(X0)) | ~creative(mary)) & (creative(mary) | ! [X0] : (kind(X0) | ~wise(X0))) [nnf transformation 12]
45. (? [X0] : (~kind(X0) & wise(X0)) | ~creative(mary)) & (creative(mary) | ! [X1] : (kind(X1) | ~wise(X1))) [rectify 44]
46. ? [X0] : (~kind(X0) & wise(X0)) => (~kind(sK0) & wise(sK0)) [choice axiom]
47. ((~kind(sK0) & wise(sK0)) | ~creative(mary)) & (creative(mary) | ! [X1] : (kind(X1) | ~wise(X1))) [skolemisation 45,46]
66. ~curious(X0) | ~brave(X0) | happy(X0) [cnf transformation 32]
69. tall(X0) | humble(X0) [cnf transformation 34]
72. ~kind(X0) | brave(X0) [cnf transformation 34]
80. ~brave(X0) | ~humble(X0) [cnf transformation 26]
84. ~tall(X0) | humble(X0) | ~creative(X0) | ~happy(X0) [cnf transformation 37]
89. ~creative(X0) | brave(X0) [cnf transformation 39]
90. ~creative(X0) | curious(X0) [cnf transformation 39]
91. ~curious(X0) | creative(X0) | ~brave(X0) [cnf transformation 39]
93. quiet(X0) | quiet(X0) [cnf transformation 41]
94. ~quiet(X0) | ~quiet(X0) | wise(X0) [cnf transformation 41]
103. creative(mary) | kind(X1) | ~wise(X1) [cnf transformation 47]
119. curious(lucy) [cnf transformation 20]
123. quiet(X0) [duplicate literal removal 93]
124. ~quiet(X0) | wise(X0) [duplicate literal removal 94]
125. ~creative(X0) | humble(X0) | ~happy(X0) [subsumption resolution 84,69]
138. 3 <=> creative(mary) [avatar definition]
139. creative(mary) <- (3) [avatar component clause 138]
152. 6 <=> ! [X1] : (kind(X1) | ~wise(X1)) [avatar definition]
153. kind(X1) | ~wise(X1) <- (6) [avatar component clause 152]
154. 6 | 3 [avatar split clause 103,138,152]
222. brave(mary) <- (3) [resolution 89,139]
223. ~humble(mary) <- (3) [resolution 222,80]
225. curious(mary) <- (3) [resolution 90,139]
226. wise(X0) [resolution 124,123]
229. ~brave(lucy) | happy(lucy) [resolution 66,119]
230. ~brave(mary) | happy(mary) <- (3) [resolution 66,225]
232. 20 <=> happy(lucy) [avatar definition]
234. happy(lucy) <- (20) [avatar component clause 232]
236. 21 <=> brave(lucy) [avatar definition]
238. ~brave(lucy) <- (~21) [avatar component clause 236]
239. 20 | ~21 [avatar split clause 229,236,232]
240. happy(mary) <- (3) [subsumption resolution 230,222]
370. 40 <=> creative(lucy) [avatar definition]
372. creative(lucy) <- (40) [avatar component clause 370]
376. creative(lucy) | ~brave(lucy) [resolution 91,119]
385. humble(mary) | ~happy(mary) <- (3) [resolution 125,139]
387. ~happy(mary) <- (3) [subsumption resolution 385,223]
388. $false <- (3) [subsumption resolution 387,240]
389. ~3 [avatar contradiction clause 388]
395. kind(X1) <- (6) [subsumption resolution 153,226]
398. brave(X1) <- (6) [resolution 395,72]
445. ~humble(X2) <- (6) [resolution 398,80]
447. $false <- (6, ~21) [resolution 398,238]
448. ~6 | 21 [avatar contradiction clause 447]
449. creative(lucy) <- (6) [subsumption resolution 376,398]
450. 40 | ~6 [avatar split clause 449,152,370]
470. humble(lucy) | ~happy(lucy) <- (40) [resolution 372,125]
475. ~happy(lucy) <- (6, 40) [subsumption resolution 470,445]
476. $false <- (6, 20, 40) [subsumption resolution 475,234]
477. ~6 | ~20 | ~40 [avatar contradiction clause 476]
478. $false [avatar sat refutation 154,239,389,448,450,477]
% SZS output end Proof for 8904525052071754469613367
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or not humble is curious or not creative and vice versa.
Everyone who is not patient or happy is both not creative and not wise.
Everyone who is funny or brave is either strong or not calm and vice versa.
Everyone who is not funny or not kind is old or curious.
If fred is either creative or happy then john is not calm.
Everyone who is not strong or generous is both not funny and not kind.
If john is both not rich and old then fred is both wise and rich and vice versa.
Everyone who is either humble or not curious is both not strong and curious and vice versa.
Everyone who is both not calm and not happy is either not calm or not curious.
If someone is not strong or happy then alice is both old and not creative and vice versa.
If someone is not generous or not rich then someone is creative.
Everyone who is either not generous or happy is both not calm and patient and vice versa.
Everyone who is not rich or funny is not kind or not quiet and vice versa.
Everyone who is not creative or humble is not funny and vice versa.
Everyone who is old or not old is either not funny or not wise and vice versa.
Everyone who is not quiet or not brave is not kind or funny.
Someone is strong.
Mary is both not strong and not rich.
Someone is brave or funny.
Someone is curious or not tall.
Someone is either generous or quiet.
Lucy is funny or brave.
Paul is not happy or quiet. | Paul is kind. | contradiction | (![X]:((funny(X)<~>~humble(X))<=>(curious(X)|~creative(X))))&
(![X]:((~patient(X)|happy(X))=>(~creative(X)&~wise(X))))&
(![X]:((funny(X)|brave(X))<=>(strong(X)<~>~calm(X))))&
(![X]:((~funny(X)|~kind(X))=>(old(X)|curious(X))))&
(((creative(fred)<~>happy(fred)))=>(~calm(john)))&
(![X]:((~strong(X)|generous(X))=>(~funny(X)&~kind(X))))&
(((~rich(john)&old(john)))<=>((wise(fred)&rich(fred))))&
(![X]:((humble(X)<~>~curious(X))<=>(~strong(X)&curious(X))))&
(![X]:((~calm(X)&~happy(X))=>(~calm(X)<~>~curious(X))))&
((?[X]:((~strong(X)|happy(X))))<=>((old(alice)&~creative(alice))))&
((?[X]:((~generous(X)|~rich(X))))=>(?[X]:(creative(X))))&
(![X]:((~generous(X)<~>happy(X))<=>(~calm(X)&patient(X))))&
(![X]:((~rich(X)|funny(X))<=>(~kind(X)|~quiet(X))))&
(![X]:((~creative(X)|humble(X))<=>~funny(X)))&
(![X]:((old(X)|~old(X))<=>(~funny(X)<~>~wise(X))))&
(![X]:((~quiet(X)|~brave(X))=>(~kind(X)|funny(X))))&
(?[X]:(strong(X)))&
((~strong(mary)&~rich(mary)))&
(?[X]:((brave(X)|funny(X))))&
(?[X]:((curious(X)|~tall(X))))&
(?[X]:((generous(X)<~>quiet(X))))&
((funny(lucy)|brave(lucy)))&
((~happy(paul)|quiet(paul))) | kind(paul) | [
"p0",
"p1",
"p2",
"p5",
"p7",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7587922091987201773924381
% SZS output start Proof for 7587922091987201773924381
1. ! [X0] : ((funny(X0) <~> ~humble(X0)) <=> (~creative(X0) | curious(X0))) [input p0]
2. ! [X0] : ((happy(X0) | ~patient(X0)) => (~wise(X0) & ~creative(X0))) [input p1]
3. ! [X0] : ((brave(X0) | funny(X0)) <=> (strong(X0) <~> ~calm(X0))) [input p2]
6. ! [X0] : ((generous(X0) | ~strong(X0)) => (~kind(X0) & ~funny(X0))) [input p5]
8. ! [X0] : ((humble(X0) <~> ~curious(X0)) <=> (curious(X0) & ~strong(X0))) [input p7]
12. ! [X0] : ((~generous(X0) <~> happy(X0)) <=> (patient(X0) & ~calm(X0))) [input p11]
14. ! [X0] : ((humble(X0) | ~creative(X0)) <=> ~funny(X0)) [input p13]
15. ! [X0] : ((~old(X0) | old(X0)) <=> (~funny(X0) <~> ~wise(X0))) [input p14]
16. ! [X0] : ((~brave(X0) | ~quiet(X0)) => (funny(X0) | ~kind(X0))) [input p15]
24. kind(paul) [input hypothesis]
27. ! [X0] : ((~wise(X0) & ~creative(X0)) | (~happy(X0) & patient(X0))) [ennf transformation 2]
31. ! [X0] : ((~kind(X0) & ~funny(X0)) | (~generous(X0) & strong(X0))) [ennf transformation 6]
35. ! [X0] : ((funny(X0) | ~kind(X0)) | (brave(X0) & quiet(X0))) [ennf transformation 16]
36. ! [X0] : (funny(X0) | ~kind(X0) | (brave(X0) & quiet(X0))) [flattening 35]
37. ! [X0] : ((((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | (creative(X0) & ~curious(X0))) & ((~creative(X0) | curious(X0)) | ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0))))) [nnf transformation 1]
38. ! [X0] : ((((humble(X0) | ~funny(X0)) & (~humble(X0) | funny(X0))) | (creative(X0) & ~curious(X0))) & (~creative(X0) | curious(X0) | ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0))))) [flattening 37]
39. ! [X0] : (((brave(X0) | funny(X0)) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0)))) & (((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | (~brave(X0) & ~funny(X0)))) [nnf transformation 3]
40. ! [X0] : ((brave(X0) | funny(X0) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0)))) & (((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | (~brave(X0) & ~funny(X0)))) [flattening 39]
44. ! [X0] : ((((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | (~curious(X0) | strong(X0))) & ((curious(X0) & ~strong(X0)) | ((humble(X0) | curious(X0)) & (~curious(X0) | ~humble(X0))))) [nnf transformation 8]
45. ! [X0] : ((((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | ~curious(X0) | strong(X0)) & ((curious(X0) & ~strong(X0)) | ((humble(X0) | curious(X0)) & (~curious(X0) | ~humble(X0))))) [flattening 44]
55. ! [X0] : ((((~happy(X0) | generous(X0)) & (happy(X0) | ~generous(X0))) | (~patient(X0) | calm(X0))) & ((patient(X0) & ~calm(X0)) | ((~generous(X0) | ~happy(X0)) & (happy(X0) | generous(X0))))) [nnf transformation 12]
56. ! [X0] : ((((~happy(X0) | generous(X0)) & (happy(X0) | ~generous(X0))) | ~patient(X0) | calm(X0)) & ((patient(X0) & ~calm(X0)) | ((~generous(X0) | ~happy(X0)) & (happy(X0) | generous(X0))))) [flattening 55]
59. ! [X0] : (((humble(X0) | ~creative(X0)) | funny(X0)) & (~funny(X0) | (~humble(X0) & creative(X0)))) [nnf transformation 14]
60. ! [X0] : ((humble(X0) | ~creative(X0) | funny(X0)) & (~funny(X0) | (~humble(X0) & creative(X0)))) [flattening 59]
61. ! [X0] : (((~old(X0) | old(X0)) | ((~funny(X0) | wise(X0)) & (~wise(X0) | funny(X0)))) & (((wise(X0) | funny(X0)) & (~wise(X0) | ~funny(X0))) | (old(X0) & ~old(X0)))) [nnf transformation 15]
62. ! [X0] : ((~old(X0) | old(X0) | ((~funny(X0) | wise(X0)) & (~wise(X0) | funny(X0)))) & (((wise(X0) | funny(X0)) & (~wise(X0) | ~funny(X0))) | (old(X0) & ~old(X0)))) [flattening 61]
74. ~curious(X0) | ~funny(X0) | humble(X0) [cnf transformation 38]
79. ~wise(X0) | ~happy(X0) [cnf transformation 27]
83. ~strong(X0) | calm(X0) | ~brave(X0) [cnf transformation 40]
92. ~kind(X0) | strong(X0) [cnf transformation 31]
93. ~generous(X0) | ~kind(X0) [cnf transformation 31]
101. curious(X0) | humble(X0) | curious(X0) [cnf transformation 45]
113. ~calm(X0) | happy(X0) | generous(X0) [cnf transformation 56]
124. ~humble(X0) | ~funny(X0) [cnf transformation 60]
128. wise(X0) | funny(X0) | ~old(X0) [cnf transformation 62]
129. old(X0) | funny(X0) | wise(X0) [cnf transformation 62]
133. ~kind(X0) | funny(X0) | brave(X0) [cnf transformation 36]
142. kind(paul) [cnf transformation 24]
144. curious(X0) | humble(X0) [duplicate literal removal 101]
221. wise(X0) | funny(X0) [subsumption resolution 128,129]
252. 23 <=> happy(paul) [avatar definition]
253. happy(paul) <- (23) [avatar component clause 252]
254. ~happy(paul) <- (~23) [avatar component clause 252]
263. strong(paul) [resolution 92,142]
268. ~happy(X0) | funny(X0) [resolution 221,79]
276. ~funny(X0) | humble(X0) | humble(X0) [resolution 74,144]
277. ~funny(X0) | humble(X0) [duplicate literal removal 276]
278. ~funny(X0) [subsumption resolution 277,124]
289. calm(paul) | ~brave(paul) [resolution 83,263]
292. 25 <=> brave(paul) [avatar definition]
296. 26 <=> calm(paul) [avatar definition]
298. calm(paul) <- (26) [avatar component clause 296]
299. ~25 | 26 [avatar split clause 289,296,292]
375. funny(paul) | brave(paul) [resolution 133,142]
376. brave(paul) [subsumption resolution 375,278]
379. 25 [avatar split clause 376,292]
390. happy(paul) | generous(paul) <- (26) [resolution 298,113]
393. generous(paul) <- (~23, 26) [subsumption resolution 390,254]
399. ~kind(paul) <- (~23, 26) [resolution 393,93]
401. $false <- (~23, 26) [subsumption resolution 399,142]
402. 23 | ~26 [avatar contradiction clause 401]
408. funny(paul) <- (23) [resolution 253,268]
410. $false <- (23) [subsumption resolution 408,278]
411. ~23 [avatar contradiction clause 410]
412. $false [avatar sat refutation 299,379,402,411]
% SZS output end Proof for 7587922091987201773924381
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or not brave is both not creative and not quiet. Everyone who is either not tall or not funny is both humble and not generous and vice versa. Everyone who is happy is not calm or strong and vice versa. Everyone who is both brave and not curious is patient or not patient. Everyone who is not tall is old or generous. Everyone who is either not funny or old is not patient or not tall and vice versa. If paul is both wise and not quiet then alice is either not kind or not curious and vice versa. Everyone who is both not quiet and not funny is patient and vice versa. Everyone who is not wise is both wise and not calm. If someone is not creative then someone is both not funny and not calm. If someone is both wise and not funny then someone is either not curious or kind. Everyone who is tall or not humble is both not quiet and not wise. Everyone who is both not generous and funny is both not wise and patient. Everyone who is both not calm and not kind is either not calm or brave and vice versa. If someone is not patient then someone is either patient or brave. Mary is not tall. Someone is kind. Fred is either not wise or happy. Someone is not patient. Susan is funny or humble. Paul is either not creative or curious. Susan is either not strong or not happy. | Alice is tall. | contradiction | (![X]:((generous(X)<~>~brave(X))=>(~creative(X)&~quiet(X))))&
(![X]:((~tall(X)<~>~funny(X))<=>(humble(X)&~generous(X))))&
(![X]:(happy(X)<=>(~calm(X)|strong(X))))&
(![X]:((brave(X)&~curious(X))=>(patient(X)|~patient(X))))&
(![X]:(~tall(X)=>(old(X)|generous(X))))&
(![X]:((~funny(X)<~>old(X))<=>(~patient(X)|~tall(X))))&
(((wise(paul)&~quiet(paul)))<=>((~kind(alice)<~>~curious(alice))))&
(![X]:((~quiet(X)&~funny(X))<=>patient(X)))&
(![X]:(~wise(X)=>(wise(X)&~calm(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~funny(X)&~calm(X)))))&
((?[X]:((wise(X)&~funny(X))))=>(?[X]:((~curious(X)<~>kind(X)))))&
(![X]:((tall(X)|~humble(X))=>(~quiet(X)&~wise(X))))&
(![X]:((~generous(X)&funny(X))=>(~wise(X)&patient(X))))&
(![X]:((~calm(X)&~kind(X))<=>(~calm(X)<~>brave(X))))&
((?[X]:(~patient(X)))=>(?[X]:((patient(X)<~>brave(X)))))&
(~tall(mary))&
(?[X]:(kind(X)))&
((~wise(fred)<~>happy(fred)))&
(?[X]:(~patient(X)))&
((funny(susan)|humble(susan)))&
((~creative(paul)<~>curious(paul)))&
((~strong(susan)<~>~happy(susan))) | tall(alice) | [
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7367731123845054921377256
% SZS output start Proof for 7367731123845054921377256
9. ! [X0] : (~wise(X0) => (~calm(X0) & wise(X0))) [input p8]
12. ! [X0] : ((~humble(X0) | tall(X0)) => (~wise(X0) & ~quiet(X0))) [input p11]
23. tall(alice) [input hypothesis]
32. ! [X0] : ((~calm(X0) & wise(X0)) | wise(X0)) [ennf transformation 9]
35. ! [X0] : ((~wise(X0) & ~quiet(X0)) | (humble(X0) & ~tall(X0))) [ennf transformation 12]
100. wise(X0) | wise(X0) [cnf transformation 32]
108. ~wise(X0) | ~tall(X0) [cnf transformation 35]
130. tall(alice) [cnf transformation 23]
133. wise(X0) [duplicate literal removal 100]
185. ~tall(X0) [subsumption resolution 108,133]
214. $false [subsumption resolution 130,185]
% SZS output end Proof for 7367731123845054921377256
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and not brave is not strong and vice versa.
Everyone who is both generous and not kind is either tall or not creative and vice versa.
Everyone who is not brave or kind is not funny and vice versa.
Everyone who is rich is wise or not tall.
Everyone who is either not curious or not calm is curious and vice versa.
Everyone who is both tall and not generous is either wise or not happy.
Everyone who is not rich is both not calm and calm and vice versa.
If someone is humble or brave then someone is not rich.
Everyone who is either not curious or humble is both not patient and tall.
Everyone who is old is not kind.
If someone is not creative or humble then john is both quiet and not strong and vice versa.
If john is both creative and not happy then paul is not strong.
If mary is brave or not strong then someone is either strong or not patient and vice versa.
Everyone who is either quiet or calm is both not wise and funny and vice versa.
If someone is both humble and curious then someone is either humble or not creative and vice versa.
Fred is either not generous or old.
Alice is either patient or rich.
Lucy is both tall and not curious.
Someone is either not calm or generous.
Susan is either not wise or rich.
Someone is not tall. | John is brave. | contradiction | (![X]:((~old(X)&~brave(X))<=>~strong(X)))&
(![X]:((generous(X)&~kind(X))<=>(tall(X)<~>~creative(X))))&
(![X]:((~brave(X)|kind(X))<=>~funny(X)))&
(![X]:(rich(X)=>(wise(X)|~tall(X))))&
(![X]:((~curious(X)<~>~calm(X))<=>curious(X)))&
(![X]:((tall(X)&~generous(X))=>(wise(X)<~>~happy(X))))&
(![X]:(~rich(X)<=>(~calm(X)&calm(X))))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(~rich(X))))&
(![X]:((~curious(X)<~>humble(X))=>(~patient(X)&tall(X))))&
(![X]:(old(X)=>~kind(X)))&
((?[X]:((~creative(X)|humble(X))))<=>((quiet(john)&~strong(john))))&
(((creative(john)&~happy(john)))=>(~strong(paul)))&
(((brave(mary)|~strong(mary)))<=>(?[X]:((strong(X)<~>~patient(X)))))&
(![X]:((quiet(X)<~>calm(X))<=>(~wise(X)&funny(X))))&
((?[X]:((humble(X)&curious(X))))<=>(?[X]:((humble(X)<~>~creative(X)))))&
((~generous(fred)<~>old(fred)))&
((patient(alice)<~>rich(alice)))&
((tall(lucy)&~curious(lucy)))&
(?[X]:((~calm(X)<~>generous(X))))&
((~wise(susan)<~>rich(susan)))&
(?[X]:(~tall(X))) | brave(john) | [
"p4",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8084649562566769460498365
% SZS output start Proof for 8084649562566769460498365
5. ! [X0] : ((~curious(X0) <~> ~calm(X0)) <=> curious(X0)) [input p4]
7. ! [X0] : (~rich(X0) <=> (calm(X0) & ~calm(X0))) [input p6]
8. ? [X0] : (brave(X0) | humble(X0)) => ? [X0] : ~rich(X0) [input p7]
22. brave(john) [input hypothesis]
23. ? [X0] : (brave(X0) | humble(X0)) => ? [X1] : ~rich(X1) [rectify 8]
29. ? [X1] : ~rich(X1) | ! [X0] : (~brave(X0) & ~humble(X0)) [ennf transformation 23]
40. ! [X0] : ((((calm(X0) | curious(X0)) & (~calm(X0) | ~curious(X0))) | ~curious(X0)) & (curious(X0) | ((~curious(X0) | calm(X0)) & (~calm(X0) | curious(X0))))) [nnf transformation 5]
42. ! [X0] : ((~rich(X0) | (~calm(X0) | calm(X0))) & ((calm(X0) & ~calm(X0)) | rich(X0))) [nnf transformation 7]
43. ! [X0] : ((~rich(X0) | ~calm(X0) | calm(X0)) & ((calm(X0) & ~calm(X0)) | rich(X0))) [flattening 42]
44. ? [X0] : ~rich(X0) | ! [X1] : (~brave(X1) & ~humble(X1)) [rectify 29]
45. ? [X0] : ~rich(X0) => ~rich(sK0) [choice axiom]
46. ~rich(sK0) | ! [X1] : (~brave(X1) & ~humble(X1)) [skolemisation 44,45]
86. curious(X0) | ~calm(X0) | curious(X0) [cnf transformation 40]
88. ~calm(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 40]
93. calm(X0) | rich(X0) [cnf transformation 43]
96. ~rich(sK0) | ~brave(X1) [cnf transformation 46]
137. brave(john) [cnf transformation 22]
138. curious(X0) | ~calm(X0) [duplicate literal removal 86]
139. ~calm(X0) | ~curious(X0) [duplicate literal removal 88]
140. ~calm(X0) [subsumption resolution 138,139]
141. rich(X0) [subsumption resolution 93,140]
142. ~brave(X1) [subsumption resolution 96,141]
227. $false [subsumption resolution 137,142]
% SZS output end Proof for 8084649562566769460498365
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both tall and generous then someone is not creative and vice versa.
Everyone who is quiet or brave is wise.
If someone is both rich and tall then someone is either not quiet or not strong.
Everyone who is not old is kind or creative.
Everyone who is humble or patient is not tall.
If someone is not brave then someone is not tall or funny and vice versa.
Everyone who is generous or not generous is both old and patient.
If someone is calm then someone is not creative and vice versa.
If mary is either curious or not wise then susan is not humble or not funny.
If fred is tall then susan is either kind or not humble and vice versa.
If fred is not tall then lucy is not wise or not strong.
Everyone who is not humble or generous is not funny or not humble and vice versa.
Everyone who is either not humble or not curious is calm.
Everyone who is either funny or old is either calm or curious.
Everyone who is both quiet and not old is both calm and patient.
Everyone who is calm or rich is either not brave or not humble.
Someone is either curious or not kind.
John is either not funny or old.
Someone is funny or not patient.
Alice is creative or patient.
Susan is both creative and not humble.
Someone is either not kind or not tall. | Susan is not curious. | entailment | (((tall(paul)&generous(paul)))<=>(?[X]:(~creative(X))))&
(![X]:((quiet(X)|brave(X))=>wise(X)))&
((?[X]:((rich(X)&tall(X))))=>(?[X]:((~quiet(X)<~>~strong(X)))))&
(![X]:(~old(X)=>(kind(X)|creative(X))))&
(![X]:((humble(X)|patient(X))=>~tall(X)))&
((?[X]:(~brave(X)))<=>(?[X]:((~tall(X)|funny(X)))))&
(![X]:((generous(X)|~generous(X))=>(old(X)&patient(X))))&
((?[X]:(calm(X)))<=>(?[X]:(~creative(X))))&
(((curious(mary)<~>~wise(mary)))=>((~humble(susan)|~funny(susan))))&
((tall(fred))<=>((kind(susan)<~>~humble(susan))))&
((~tall(fred))=>((~wise(lucy)|~strong(lucy))))&
(![X]:((~humble(X)|generous(X))<=>(~funny(X)|~humble(X))))&
(![X]:((~humble(X)<~>~curious(X))=>calm(X)))&
(![X]:((funny(X)<~>old(X))=>(calm(X)<~>curious(X))))&
(![X]:((quiet(X)&~old(X))=>(calm(X)&patient(X))))&
(![X]:((calm(X)|rich(X))=>(~brave(X)<~>~humble(X))))&
(?[X]:((curious(X)<~>~kind(X))))&
((~funny(john)<~>old(john)))&
(?[X]:((funny(X)|~patient(X))))&
((creative(alice)|patient(alice)))&
((creative(susan)&~humble(susan)))&
(?[X]:((~kind(X)<~>~tall(X)))) | ~curious(susan) | [
"p0",
"p4",
"p6",
"p7",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3219186594620575117859033
% SZS output start Proof for 3219186594620575117859033
1. (generous(paul) & tall(paul)) <=> ? [X0] : ~creative(X0) [input p0]
5. ! [X0] : ((patient(X0) | humble(X0)) => ~tall(X0)) [input p4]
7. ! [X0] : ((~generous(X0) | generous(X0)) => (patient(X0) & old(X0))) [input p6]
8. ? [X0] : calm(X0) <=> ? [X0] : ~creative(X0) [input p7]
13. ! [X0] : ((~humble(X0) <~> ~curious(X0)) => calm(X0)) [input p12]
21. ~humble(susan) & creative(susan) [input p20]
23. curious(susan) [input hypothesis]
26. ? [X0] : calm(X0) <=> ? [X1] : ~creative(X1) [rectify 8]
35. ! [X0] : (~tall(X0) | (~patient(X0) & ~humble(X0))) [ennf transformation 5]
36. ! [X0] : ((patient(X0) & old(X0)) | (generous(X0) & ~generous(X0))) [ennf transformation 7]
39. ! [X0] : (calm(X0) | (~humble(X0) <=> ~curious(X0))) [ennf transformation 13]
42. ((generous(paul) & tall(paul)) | ! [X0] : creative(X0)) & (? [X0] : ~creative(X0) | (~generous(paul) | ~tall(paul))) [nnf transformation 1]
43. ((generous(paul) & tall(paul)) | ! [X0] : creative(X0)) & (? [X0] : ~creative(X0) | ~generous(paul) | ~tall(paul)) [flattening 42]
44. ((generous(paul) & tall(paul)) | ! [X0] : creative(X0)) & (? [X1] : ~creative(X1) | ~generous(paul) | ~tall(paul)) [rectify 43]
45. ? [X1] : ~creative(X1) => ~creative(sK0) [choice axiom]
46. ((generous(paul) & tall(paul)) | ! [X0] : creative(X0)) & (~creative(sK0) | ~generous(paul) | ~tall(paul)) [skolemisation 44,45]
52. (? [X0] : calm(X0) | ! [X1] : creative(X1)) & (? [X1] : ~creative(X1) | ! [X0] : ~calm(X0)) [nnf transformation 26]
53. (? [X0] : calm(X0) | ! [X1] : creative(X1)) & (? [X2] : ~creative(X2) | ! [X3] : ~calm(X3)) [rectify 52]
54. ? [X0] : calm(X0) => calm(sK3) [choice axiom]
55. ? [X2] : ~creative(X2) => ~creative(sK4) [choice axiom]
56. (calm(sK3) | ! [X1] : creative(X1)) & (~creative(sK4) | ! [X3] : ~calm(X3)) [skolemisation 53,55,54]
61. ! [X0] : (calm(X0) | ((~humble(X0) | curious(X0)) & (~curious(X0) | humble(X0)))) [nnf transformation 39]
74. tall(paul) | creative(X0) [cnf transformation 46]
79. ~patient(X0) | ~tall(X0) [cnf transformation 35]
85. patient(X0) | ~generous(X0) [cnf transformation 36]
86. patient(X0) | generous(X0) [cnf transformation 36]
87. ~creative(sK4) | ~calm(X3) [cnf transformation 56]
99. ~curious(X0) | calm(X0) | humble(X0) [cnf transformation 61]
114. ~humble(susan) [cnf transformation 21]
117. curious(susan) [cnf transformation 23]
119. 1 <=> ! [X0] : creative(X0) [avatar definition]
120. creative(X0) <- (1) [avatar component clause 119]
127. 3 <=> tall(paul) [avatar definition]
129. tall(paul) <- (3) [avatar component clause 127]
130. 1 | 3 [avatar split clause 74,127,119]
160. patient(X0) [subsumption resolution 85,86]
168. 12 <=> ! [X3] : ~calm(X3) [avatar definition]
169. ~calm(X3) <- (12) [avatar component clause 168]
171. 13 <=> creative(sK4) [avatar definition]
173. ~creative(sK4) <- (~13) [avatar component clause 171]
174. 12 | ~13 [avatar split clause 87,171,168]
184. 16 <=> humble(susan) [avatar definition]
186. ~humble(susan) <- (~16) [avatar component clause 184]
219. ~16 [avatar split clause 114,184]
230. ~tall(X0) [resolution 79,160]
231. $false <- (3) [resolution 230,129]
232. ~3 [avatar contradiction clause 231]
234. $false <- (1, ~13) [resolution 120,173]
235. ~1 | 13 [avatar contradiction clause 234]
261. calm(susan) | humble(susan) [resolution 99,117]
262. humble(susan) <- (12) [subsumption resolution 261,169]
263. $false <- (12, ~16) [subsumption resolution 262,186]
264. ~12 | 16 [avatar contradiction clause 263]
265. $false [avatar sat refutation 130,174,219,232,235,264]
% SZS output end Proof for 3219186594620575117859033
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is either rich or quiet then mary is not curious or not generous.
If lucy is not rich then alice is strong or not tall and vice versa.
If alice is both happy and not tall then someone is not happy and vice versa.
If john is either not happy or kind then alice is not calm or calm and vice versa.
Everyone who is both creative and not funny is not calm and vice versa.
If fred is either rich or happy then someone is not creative and vice versa.
Everyone who is funny or not humble is not calm.
Everyone who is wise or old is either not calm or rich.
Everyone who is happy or calm is not tall and vice versa.
Everyone who is wise or not strong is either wise or not happy and vice versa.
If someone is old or not quiet then paul is creative.
Everyone who is either not brave or not humble is both not brave and not patient and vice versa.
If someone is either not patient or not generous then paul is not brave or curious and vice versa.
If susan is not brave or not funny then someone is not curious or not tall and vice versa.
Everyone who is quiet is either not quiet or not calm.
If mary is not curious then someone is not kind.
Someone is not patient.
Fred is either calm or not rich.
Mary is calm or not patient.
Someone is not humble or happy.
Alice is generous or patient.
Someone is either strong or not happy. | Lucy is not old. | neutral | (((rich(fred)<~>quiet(fred)))=>((~curious(mary)|~generous(mary))))&
((~rich(lucy))<=>((strong(alice)|~tall(alice))))&
(((happy(alice)&~tall(alice)))<=>(?[X]:(~happy(X))))&
(((~happy(john)<~>kind(john)))<=>((~calm(alice)|calm(alice))))&
(![X]:((creative(X)&~funny(X))<=>~calm(X)))&
(((rich(fred)<~>happy(fred)))<=>(?[X]:(~creative(X))))&
(![X]:((funny(X)|~humble(X))=>~calm(X)))&
(![X]:((wise(X)|old(X))=>(~calm(X)<~>rich(X))))&
(![X]:((happy(X)|calm(X))<=>~tall(X)))&
(![X]:((wise(X)|~strong(X))<=>(wise(X)<~>~happy(X))))&
((?[X]:((old(X)|~quiet(X))))=>(creative(paul)))&
(![X]:((~brave(X)<~>~humble(X))<=>(~brave(X)&~patient(X))))&
((?[X]:((~patient(X)<~>~generous(X))))<=>((~brave(paul)|curious(paul))))&
(((~brave(susan)|~funny(susan)))<=>(?[X]:((~curious(X)|~tall(X)))))&
(![X]:(quiet(X)=>(~quiet(X)<~>~calm(X))))&
((~curious(mary))=>(?[X]:(~kind(X))))&
(?[X]:(~patient(X)))&
((calm(fred)<~>~rich(fred)))&
((calm(mary)|~patient(mary)))&
(?[X]:((~humble(X)|happy(X))))&
((generous(alice)|patient(alice)))&
(?[X]:((strong(X)<~>~happy(X)))) | ~old(lucy) | [] | null | 0 |
Everyone who is both brave and not happy is either generous or humble.
If someone is old then mary is not funny or not happy.
Everyone who is either creative or brave is either rich or not funny.
If lucy is either not old or not rich then someone is not old or not patient.
Everyone who is either quiet or creative is brave or not strong.
Everyone who is both not kind and generous is either not calm or brave and vice versa.
If john is not happy or not calm then someone is not curious and vice versa.
Everyone who is generous is both not calm and not quiet and vice versa.
If mary is both not old and rich then someone is not kind or not tall.
If someone is patient or creative then alice is calm and vice versa.
Everyone who is not calm or patient is either kind or funny and vice versa.
If someone is quiet then lucy is both not tall and not patient and vice versa.
Everyone who is both rich and patient is not tall.
If someone is not funny or patient then someone is generous or not funny.
If susan is both not funny and not patient then alice is brave.
Everyone who is not curious or not happy is either calm or rich.
Someone is not curious or wise.
Alice is generous.
Mary is either kind or generous.
Mary is funny or strong.
Fred is either not rich or rich.
Someone is calm. | Susan is not old. | neutral | (![X]:((brave(X)&~happy(X))=>(generous(X)<~>humble(X))))&
((?[X]:(old(X)))=>((~funny(mary)|~happy(mary))))&
(![X]:((creative(X)<~>brave(X))=>(rich(X)<~>~funny(X))))&
(((~old(lucy)<~>~rich(lucy)))=>(?[X]:((~old(X)|~patient(X)))))&
(![X]:((quiet(X)<~>creative(X))=>(brave(X)|~strong(X))))&
(![X]:((~kind(X)&generous(X))<=>(~calm(X)<~>brave(X))))&
(((~happy(john)|~calm(john)))<=>(?[X]:(~curious(X))))&
(![X]:(generous(X)<=>(~calm(X)&~quiet(X))))&
(((~old(mary)&rich(mary)))=>(?[X]:((~kind(X)|~tall(X)))))&
((?[X]:((patient(X)|creative(X))))<=>(calm(alice)))&
(![X]:((~calm(X)|patient(X))<=>(kind(X)<~>funny(X))))&
((?[X]:(quiet(X)))<=>((~tall(lucy)&~patient(lucy))))&
(![X]:((rich(X)&patient(X))=>~tall(X)))&
((?[X]:((~funny(X)|patient(X))))=>(?[X]:((generous(X)|~funny(X)))))&
(((~funny(susan)&~patient(susan)))=>(brave(alice)))&
(![X]:((~curious(X)|~happy(X))=>(calm(X)<~>rich(X))))&
(?[X]:((~curious(X)|wise(X))))&
(generous(alice))&
((kind(mary)<~>generous(mary)))&
((funny(mary)|strong(mary)))&
((~rich(fred)<~>rich(fred)))&
(?[X]:(calm(X))) | ~old(susan) | [] | null | 0 |
If mary is either humble or not calm then someone is not generous and vice versa.
If lucy is not rich then someone is either not generous or calm and vice versa.
Everyone who is both tall and not curious is either not old or not patient and vice versa.
Everyone who is wise is not kind and vice versa.
Everyone who is both not quiet and rich is not quiet.
If someone is not calm then alice is both not patient and happy.
If fred is not brave or curious then someone is not tall or not patient.
Everyone who is kind or not brave is both not funny and not creative.
Everyone who is happy or curious is not happy.
Everyone who is generous or old is not old or rich and vice versa.
Everyone who is either wise or funny is kind or patient and vice versa.
If someone is both old and not creative then alice is not old.
Everyone who is either creative or tall is not tall.
Everyone who is both tall and creative is not humble or not brave.
Everyone who is not old or not funny is both generous and not tall.
If someone is not brave then someone is not strong or curious and vice versa.
Someone is quiet.
Someone is not generous.
Mary is either not generous or not creative.
Alice is either quiet or strong.
Susan is not brave or not tall. | Mary is not creative. | entailment | (((humble(mary)<~>~calm(mary)))<=>(?[X]:(~generous(X))))&
((~rich(lucy))<=>(?[X]:((~generous(X)<~>calm(X)))))&
(![X]:((tall(X)&~curious(X))<=>(~old(X)<~>~patient(X))))&
(![X]:(wise(X)<=>~kind(X)))&
(![X]:((~quiet(X)&rich(X))=>~quiet(X)))&
((?[X]:(~calm(X)))=>((~patient(alice)&happy(alice))))&
(((~brave(fred)|curious(fred)))=>(?[X]:((~tall(X)|~patient(X)))))&
(![X]:((kind(X)|~brave(X))=>(~funny(X)&~creative(X))))&
(![X]:((happy(X)|curious(X))=>~happy(X)))&
(![X]:((generous(X)|old(X))<=>(~old(X)|rich(X))))&
(![X]:((wise(X)<~>funny(X))<=>(kind(X)|patient(X))))&
((?[X]:((old(X)&~creative(X))))=>(~old(alice)))&
(![X]:((creative(X)<~>tall(X))=>~tall(X)))&
(![X]:((tall(X)&creative(X))=>(~humble(X)|~brave(X))))&
(![X]:((~old(X)|~funny(X))=>(generous(X)&~tall(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((~strong(X)|curious(X)))))&
(?[X]:(quiet(X)))&
(?[X]:(~generous(X)))&
((~generous(mary)<~>~creative(mary)))&
((quiet(alice)<~>strong(alice)))&
((~brave(susan)|~tall(susan))) | ~creative(mary) | [
"p0",
"p2",
"p3",
"p5",
"p7",
"p8",
"p9",
"p10",
"p12",
"p13",
"p14",
"p17",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 81857982526548892469635
% SZS output start Proof for 81857982526548892469635
1. (humble(mary) <~> ~calm(mary)) <=> ? [X0] : ~generous(X0) [input p0]
3. ! [X0] : ((~curious(X0) & tall(X0)) <=> (~old(X0) <~> ~patient(X0))) [input p2]
4. ! [X0] : (wise(X0) <=> ~kind(X0)) [input p3]
6. ? [X0] : ~calm(X0) => (happy(alice) & ~patient(alice)) [input p5]
8. ! [X0] : ((~brave(X0) | kind(X0)) => (~creative(X0) & ~funny(X0))) [input p7]
9. ! [X0] : ((curious(X0) | happy(X0)) => ~happy(X0)) [input p8]
10. ! [X0] : ((old(X0) | generous(X0)) <=> (rich(X0) | ~old(X0))) [input p9]
11. ! [X0] : ((wise(X0) <~> funny(X0)) <=> (patient(X0) | kind(X0))) [input p10]
13. ! [X0] : ((creative(X0) <~> tall(X0)) => ~tall(X0)) [input p12]
14. ! [X0] : ((creative(X0) & tall(X0)) => (~brave(X0) | ~humble(X0))) [input p13]
15. ! [X0] : ((~funny(X0) | ~old(X0)) => (~tall(X0) & generous(X0))) [input p14]
18. ? [X0] : ~generous(X0) [input p17]
19. ~generous(mary) <~> ~creative(mary) [input p18]
22. creative(mary) [input hypothesis]
26. (happy(alice) & ~patient(alice)) | ! [X0] : calm(X0) [ennf transformation 6]
28. ! [X0] : ((~creative(X0) & ~funny(X0)) | (brave(X0) & ~kind(X0))) [ennf transformation 8]
29. ! [X0] : (~happy(X0) | (~curious(X0) & ~happy(X0))) [ennf transformation 9]
31. ! [X0] : (~tall(X0) | (creative(X0) <=> tall(X0))) [ennf transformation 13]
32. ! [X0] : ((~brave(X0) | ~humble(X0)) | (~creative(X0) | ~tall(X0))) [ennf transformation 14]
33. ! [X0] : (~brave(X0) | ~humble(X0) | ~creative(X0) | ~tall(X0)) [flattening 32]
34. ! [X0] : ((~tall(X0) & generous(X0)) | (funny(X0) & old(X0))) [ennf transformation 15]
35. (((calm(mary) | ~humble(mary)) & (~calm(mary) | humble(mary))) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | ((humble(mary) | calm(mary)) & (~calm(mary) | ~humble(mary)))) [nnf transformation 1]
36. (((calm(mary) | ~humble(mary)) & (~calm(mary) | humble(mary))) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | ((humble(mary) | calm(mary)) & (~calm(mary) | ~humble(mary)))) [rectify 35]
37. ? [X1] : ~generous(X1) => ~generous(sK0) [choice axiom]
38. (((calm(mary) | ~humble(mary)) & (~calm(mary) | humble(mary))) | ! [X0] : generous(X0)) & (~generous(sK0) | ((humble(mary) | calm(mary)) & (~calm(mary) | ~humble(mary)))) [skolemisation 36,37]
43. ! [X0] : (((~curious(X0) & tall(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0)))) & (((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | (curious(X0) | ~tall(X0)))) [nnf transformation 3]
44. ! [X0] : (((~curious(X0) & tall(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0)))) & (((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | curious(X0) | ~tall(X0))) [flattening 43]
45. ! [X0] : ((wise(X0) | kind(X0)) & (~kind(X0) | ~wise(X0))) [nnf transformation 4]
48. ! [X0] : (((old(X0) | generous(X0)) | (~rich(X0) & old(X0))) & ((rich(X0) | ~old(X0)) | (~old(X0) & ~generous(X0)))) [nnf transformation 10]
49. ! [X0] : ((old(X0) | generous(X0) | (~rich(X0) & old(X0))) & (rich(X0) | ~old(X0) | (~old(X0) & ~generous(X0)))) [flattening 48]
50. ! [X0] : ((((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | (~patient(X0) & ~kind(X0))) & ((patient(X0) | kind(X0)) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0))))) [nnf transformation 11]
51. ! [X0] : ((((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | (~patient(X0) & ~kind(X0))) & (patient(X0) | kind(X0) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0))))) [flattening 50]
52. ! [X0] : (~tall(X0) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) [nnf transformation 31]
60. ? [X0] : ~generous(X0) => ~generous(sK6) [choice axiom]
61. ~generous(sK6) [skolemisation 18,60]
62. (creative(mary) | generous(mary)) & (~creative(mary) | ~generous(mary)) [nnf transformation 19]
66. ~calm(mary) | humble(mary) | generous(X0) [cnf transformation 38]
75. ~old(X0) | tall(X0) | patient(X0) [cnf transformation 44]
78. ~kind(X0) | ~wise(X0) [cnf transformation 45]
79. kind(X0) | wise(X0) [cnf transformation 45]
82. happy(alice) | calm(X0) [cnf transformation 26]
85. ~funny(X0) | ~kind(X0) [cnf transformation 28]
88. ~creative(X0) | brave(X0) [cnf transformation 28]
89. ~happy(X0) | ~happy(X0) [cnf transformation 29]
93. old(X0) | generous(X0) | old(X0) [cnf transformation 49]
97. funny(X0) | wise(X0) | ~kind(X0) [cnf transformation 51]
100. ~funny(X0) | ~wise(X0) | ~patient(X0) [cnf transformation 51]
103. ~tall(X0) | creative(X0) | ~tall(X0) [cnf transformation 52]
104. ~brave(X0) | ~humble(X0) | ~creative(X0) | ~tall(X0) [cnf transformation 33]
106. funny(X0) | generous(X0) [cnf transformation 34]
113. ~generous(sK6) [cnf transformation 61]
114. ~creative(mary) | ~generous(mary) [cnf transformation 62]
119. creative(mary) [cnf transformation 22]
120. ~tall(X0) | creative(X0) [duplicate literal removal 103]
122. old(X0) | generous(X0) [duplicate literal removal 93]
123. ~happy(X0) [duplicate literal removal 89]
125. 1 <=> ! [X0] : generous(X0) [avatar definition]
126. generous(X0) <- (1) [avatar component clause 125]
128. 2 <=> humble(mary) [avatar definition]
129. humble(mary) <- (2) [avatar component clause 128]
132. 3 <=> calm(mary) [avatar definition]
133. ~calm(mary) <- (~3) [avatar component clause 132]
136. 1 | 2 | ~3 [avatar split clause 66,132,128,125]
166. 10 <=> ! [X0] : calm(X0) [avatar definition]
167. calm(X0) <- (10) [avatar component clause 166]
169. 11 <=> happy(alice) [avatar definition]
171. happy(alice) <- (11) [avatar component clause 169]
172. 10 | 11 [avatar split clause 82,169,166]
196. wise(X0) | ~kind(X0) [subsumption resolution 97,85]
197. ~kind(X0) [subsumption resolution 196,78]
207. ~humble(X0) | ~creative(X0) | ~tall(X0) [subsumption resolution 104,88]
208. ~tall(X0) | ~humble(X0) [subsumption resolution 207,120]
234. 25 <=> generous(mary) [avatar definition]
235. ~generous(mary) <- (~25) [avatar component clause 234]
238. 26 <=> creative(mary) [avatar definition]
242. ~25 | ~26 [avatar split clause 114,238,234]
262. 26 [avatar split clause 119,238]
265. $false <- (~3, 10) [subsumption resolution 133,167]
266. 3 | ~10 [avatar contradiction clause 265]
267. $false <- (11) [subsumption resolution 171,123]
268. ~11 [avatar contradiction clause 267]
271. wise(X1) [resolution 79,197]
281. patient(X0) | tall(X0) | generous(X0) [resolution 75,122]
286. ~wise(X0) | ~patient(X0) | generous(X0) [resolution 100,106]
287. ~patient(X0) | generous(X0) [subsumption resolution 286,271]
321. tall(X1) | generous(X1) | generous(X1) [resolution 281,287]
326. tall(X1) | generous(X1) [duplicate literal removal 321]
330. ~humble(X1) | generous(X1) [resolution 326,208]
334. generous(mary) <- (2) [resolution 330,129]
335. $false <- (2, ~25) [subsumption resolution 334,235]
336. ~2 | 25 [avatar contradiction clause 335]
339. $false <- (1) [resolution 126,113]
340. ~1 [avatar contradiction clause 339]
343. $false [avatar sat refutation 136,172,242,262,266,268,336,340]
% SZS output end Proof for 81857982526548892469635
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy then fred is strong. If susan is both calm and happy then mary is both old and patient. Everyone who is not generous or calm is not kind. Everyone who is not creative is patient or not curious and vice versa. If lucy is not curious or happy then someone is generous. Everyone who is either not strong or curious is not strong. If someone is either not generous or not tall then someone is not happy and vice versa. Everyone who is creative is happy or not happy. If someone is calm or wise then someone is either strong or kind and vice versa. If lucy is both not tall and not generous then someone is both rich and tall and vice versa. Everyone who is wise or not kind is both not funny and not wise and vice versa. If someone is quiet or humble then susan is creative or not generous and vice versa. Everyone who is either not kind or not wise is not curious or creative and vice versa. Everyone who is either not patient or strong is either not strong or strong and vice versa. Everyone who is either not humble or not generous is not quiet or humble and vice versa. Everyone who is not patient is creative. Someone is either not strong or old. Paul is patient. Someone is not happy. Paul is both brave and rich. John is either creative or tall. Someone is brave or tall. Paul is not humble. | John is creative. | contradiction | ((?[X]:(~happy(X)))=>(strong(fred)))&
(((calm(susan)&happy(susan)))=>((old(mary)&patient(mary))))&
(![X]:((~generous(X)|calm(X))=>~kind(X)))&
(![X]:(~creative(X)<=>(patient(X)|~curious(X))))&
(((~curious(lucy)|happy(lucy)))=>(?[X]:(generous(X))))&
(![X]:((~strong(X)<~>curious(X))=>~strong(X)))&
((?[X]:((~generous(X)<~>~tall(X))))<=>(?[X]:(~happy(X))))&
(![X]:(creative(X)=>(happy(X)|~happy(X))))&
((?[X]:((calm(X)|wise(X))))<=>(?[X]:((strong(X)<~>kind(X)))))&
(((~tall(lucy)&~generous(lucy)))<=>(?[X]:((rich(X)&tall(X)))))&
(![X]:((wise(X)|~kind(X))<=>(~funny(X)&~wise(X))))&
((?[X]:((quiet(X)|humble(X))))<=>((creative(susan)|~generous(susan))))&
(![X]:((~kind(X)<~>~wise(X))<=>(~curious(X)|creative(X))))&
(![X]:((~patient(X)<~>strong(X))<=>(~strong(X)<~>strong(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>(~quiet(X)|humble(X))))&
(![X]:(~patient(X)=>creative(X)))&
(?[X]:((~strong(X)<~>old(X))))&
(patient(paul))&
(?[X]:(~happy(X)))&
((brave(paul)&rich(paul)))&
((creative(john)<~>tall(john)))&
(?[X]:((brave(X)|tall(X))))&
(~humble(paul)) | creative(john) | [
"p2",
"p3",
"p5",
"p8",
"p10",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1746287250690906801524707
% SZS output start Proof for 1746287250690906801524707
3. ! [X0] : ((calm(X0) | ~generous(X0)) => ~kind(X0)) [input p2]
4. ! [X0] : (~creative(X0) <=> (~curious(X0) | patient(X0))) [input p3]
6. ! [X0] : ((~strong(X0) <~> curious(X0)) => ~strong(X0)) [input p5]
9. ? [X0] : (wise(X0) | calm(X0)) <=> ? [X0] : (strong(X0) <~> kind(X0)) [input p8]
11. ! [X0] : ((~kind(X0) | wise(X0)) <=> (~wise(X0) & ~funny(X0))) [input p10]
13. ! [X0] : ((~kind(X0) <~> ~wise(X0)) <=> (creative(X0) | ~curious(X0))) [input p12]
14. ! [X0] : ((~patient(X0) <~> strong(X0)) <=> (~strong(X0) <~> strong(X0))) [input p13]
16. ! [X0] : (~patient(X0) => creative(X0)) [input p15]
24. creative(john) [input hypothesis]
26. ? [X0] : (wise(X0) | calm(X0)) <=> ? [X1] : (strong(X1) <~> kind(X1)) [rectify 9]
32. ! [X0] : (~kind(X0) | (~calm(X0) & generous(X0))) [ennf transformation 3]
34. ! [X0] : (~strong(X0) | (~strong(X0) <=> curious(X0))) [ennf transformation 6]
37. ! [X0] : (creative(X0) | patient(X0)) [ennf transformation 16]
38. ! [X0] : ((~creative(X0) | (curious(X0) & ~patient(X0))) & ((~curious(X0) | patient(X0)) | creative(X0))) [nnf transformation 4]
39. ! [X0] : ((~creative(X0) | (curious(X0) & ~patient(X0))) & (~curious(X0) | patient(X0) | creative(X0))) [flattening 38]
42. ! [X0] : (~strong(X0) | ((~strong(X0) | ~curious(X0)) & (curious(X0) | strong(X0)))) [nnf transformation 34]
48. (? [X0] : (wise(X0) | calm(X0)) | ! [X1] : ((strong(X1) | ~kind(X1)) & (kind(X1) | ~strong(X1)))) & (? [X1] : ((~kind(X1) | ~strong(X1)) & (kind(X1) | strong(X1))) | ! [X0] : (~wise(X0) & ~calm(X0))) [nnf transformation 26]
49. (? [X0] : (wise(X0) | calm(X0)) | ! [X1] : ((strong(X1) | ~kind(X1)) & (kind(X1) | ~strong(X1)))) & (? [X2] : ((~kind(X2) | ~strong(X2)) & (kind(X2) | strong(X2))) | ! [X3] : (~wise(X3) & ~calm(X3))) [rectify 48]
50. ? [X0] : (wise(X0) | calm(X0)) => (wise(sK3) | calm(sK3)) [choice axiom]
51. ? [X2] : ((~kind(X2) | ~strong(X2)) & (kind(X2) | strong(X2))) => ((~kind(sK4) | ~strong(sK4)) & (kind(sK4) | strong(sK4))) [choice axiom]
52. ((wise(sK3) | calm(sK3)) | ! [X1] : ((strong(X1) | ~kind(X1)) & (kind(X1) | ~strong(X1)))) & (((~kind(sK4) | ~strong(sK4)) & (kind(sK4) | strong(sK4))) | ! [X3] : (~wise(X3) & ~calm(X3))) [skolemisation 49,51,50]
58. ! [X0] : (((~kind(X0) | wise(X0)) | (wise(X0) | funny(X0))) & ((~wise(X0) & ~funny(X0)) | (kind(X0) & ~wise(X0)))) [nnf transformation 11]
59. ! [X0] : ((~kind(X0) | wise(X0) | wise(X0) | funny(X0)) & ((~wise(X0) & ~funny(X0)) | (kind(X0) & ~wise(X0)))) [flattening 58]
65. ! [X0] : ((((wise(X0) | kind(X0)) & (~wise(X0) | ~kind(X0))) | (~creative(X0) & curious(X0))) & ((creative(X0) | ~curious(X0)) | ((~kind(X0) | wise(X0)) & (~wise(X0) | kind(X0))))) [nnf transformation 13]
66. ! [X0] : ((((wise(X0) | kind(X0)) & (~wise(X0) | ~kind(X0))) | (~creative(X0) & curious(X0))) & (creative(X0) | ~curious(X0) | ((~kind(X0) | wise(X0)) & (~wise(X0) | kind(X0))))) [flattening 65]
67. ! [X0] : ((((~strong(X0) | patient(X0)) & (strong(X0) | ~patient(X0))) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) & (((~strong(X0) | strong(X0)) & (strong(X0) | ~strong(X0))) | ((~patient(X0) | ~strong(X0)) & (strong(X0) | patient(X0))))) [nnf transformation 14]
80. ~kind(X0) | ~calm(X0) [cnf transformation 32]
83. ~creative(X0) | curious(X0) [cnf transformation 39]
87. ~strong(X0) | ~strong(X0) | ~curious(X0) [cnf transformation 42]
98. wise(sK3) | calm(sK3) | strong(X1) | ~kind(X1) [cnf transformation 52]
105. ~wise(X0) | ~wise(X0) [cnf transformation 59]
106. ~wise(X0) | kind(X0) [cnf transformation 59]
116. wise(X0) | kind(X0) | curious(X0) [cnf transformation 66]
117. wise(X0) | kind(X0) | ~creative(X0) [cnf transformation 66]
122. strong(X0) | ~patient(X0) | strong(X0) | strong(X0) [cnf transformation 67]
132. creative(X0) | patient(X0) [cnf transformation 37]
141. creative(john) [cnf transformation 24]
148. ~patient(X0) | strong(X0) [duplicate literal removal 122]
152. ~wise(X0) [duplicate literal removal 105]
154. ~curious(X0) | ~strong(X0) [duplicate literal removal 87]
218. 15 <=> ! [X1] : (strong(X1) | ~kind(X1)) [avatar definition]
219. ~kind(X1) | strong(X1) <- (15) [avatar component clause 218]
221. 16 <=> calm(sK3) [avatar definition]
223. calm(sK3) <- (16) [avatar component clause 221]
225. 17 <=> wise(sK3) [avatar definition]
227. wise(sK3) <- (17) [avatar component clause 225]
228. 15 | 16 | 17 [avatar split clause 98,225,221,218]
230. 18 <=> ! [X1] : (kind(X1) | ~strong(X1)) [avatar definition]
231. ~strong(X1) | kind(X1) <- (18) [avatar component clause 230]
234. 19 <=> ! [X3] : ~wise(X3) [avatar definition]
235. ~wise(X3) <- (19) [avatar component clause 234]
274. 19 [avatar split clause 152,234]
301. ~creative(X0) | kind(X0) [subsumption resolution 117,106]
302. curious(X0) | kind(X0) [subsumption resolution 116,106]
317. 36 <=> creative(john) [avatar definition]
318. creative(john) <- (36) [avatar component clause 317]
326. 36 [avatar split clause 141,317]
328. curious(john) <- (36) [resolution 83,318]
335. ~strong(john) <- (36) [resolution 154,328]
339. kind(john) <- (36) [resolution 301,318]
340. kind(X0) | patient(X0) [resolution 301,132]
341. kind(X0) | ~strong(X0) [resolution 302,154]
342. 18 [avatar split clause 341,230]
385. ~calm(X1) | patient(X1) [resolution 340,80]
399. patient(sK3) <- (16) [resolution 385,223]
404. strong(sK3) <- (16) [resolution 399,148]
409. kind(sK3) <- (16, 18) [resolution 404,231]
416. ~calm(sK3) <- (16, 18) [resolution 409,80]
419. $false <- (16, 18) [subsumption resolution 416,223]
420. ~16 | ~18 [avatar contradiction clause 419]
424. strong(john) <- (15, 36) [resolution 219,339]
427. $false <- (15, 36) [subsumption resolution 424,335]
428. ~15 | ~36 [avatar contradiction clause 427]
431. $false <- (17, 19) [subsumption resolution 227,235]
432. ~17 | ~19 [avatar contradiction clause 431]
433. $false [avatar sat refutation 228,274,326,342,420,428,432]
% SZS output end Proof for 1746287250690906801524707
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not curious is not rich or old and vice versa.
Everyone who is brave or happy is both not quiet and not humble and vice versa.
Everyone who is not rich is either tall or rich and vice versa.
Everyone who is either humble or not rich is not old and vice versa.
Everyone who is either rich or not wise is happy.
Everyone who is happy is either rich or not quiet.
Everyone who is patient is not quiet.
If someone is not rich then paul is patient or brave and vice versa.
Everyone who is either not quiet or not generous is both strong and patient and vice versa.
Everyone who is rich or not humble is both not brave and happy.
If someone is kind or quiet then someone is not brave and vice versa.
Everyone who is calm is either not tall or calm.
If someone is not humble then someone is strong or not quiet and vice versa.
Everyone who is not humble or curious is either not calm or curious and vice versa.
If lucy is either calm or not kind then someone is both not generous and humble.
Everyone who is both not creative and strong is not brave and vice versa.
Someone is patient or happy.
Someone is calm or not kind.
Paul is creative or strong.
Paul is either old or funny.
Someone is both not calm and not rich.
Someone is humble or not kind. | Paul is kind. | neutral | (![X]:((curious(X)|~curious(X))<=>(~rich(X)|old(X))))&
(![X]:((brave(X)|happy(X))<=>(~quiet(X)&~humble(X))))&
(![X]:(~rich(X)<=>(tall(X)<~>rich(X))))&
(![X]:((humble(X)<~>~rich(X))<=>~old(X)))&
(![X]:((rich(X)<~>~wise(X))=>happy(X)))&
(![X]:(happy(X)=>(rich(X)<~>~quiet(X))))&
(![X]:(patient(X)=>~quiet(X)))&
((?[X]:(~rich(X)))<=>((patient(paul)|brave(paul))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(strong(X)&patient(X))))&
(![X]:((rich(X)|~humble(X))=>(~brave(X)&happy(X))))&
((?[X]:((kind(X)|quiet(X))))<=>(?[X]:(~brave(X))))&
(![X]:(calm(X)=>(~tall(X)<~>calm(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((strong(X)|~quiet(X)))))&
(![X]:((~humble(X)|curious(X))<=>(~calm(X)<~>curious(X))))&
(((calm(lucy)<~>~kind(lucy)))=>(?[X]:((~generous(X)&humble(X)))))&
(![X]:((~creative(X)&strong(X))<=>~brave(X)))&
(?[X]:((patient(X)|happy(X))))&
(?[X]:((calm(X)|~kind(X))))&
((creative(paul)|strong(paul)))&
((old(paul)<~>funny(paul)))&
(?[X]:((~calm(X)&~rich(X))))&
(?[X]:((humble(X)|~kind(X)))) | kind(paul) | [] | null | 0 |
Everyone who is not old or not tall is funny or happy and vice versa.
Everyone who is both not strong and tall is rich and vice versa.
If someone is both not strong and not quiet then someone is brave or not humble.
Everyone who is both quiet and curious is either not generous or not quiet and vice versa.
Everyone who is happy or not brave is not kind.
Everyone who is not funny or kind is not happy and vice versa.
If fred is either curious or not calm then lucy is both not strong and not quiet.
If alice is either happy or calm then susan is both not quiet and quiet.
If john is either humble or not humble then someone is not generous and vice versa.
Everyone who is not old is both funny and not patient.
Everyone who is not kind or not generous is both tall and kind and vice versa.
If someone is either tall or calm then mary is creative or not strong and vice versa.
Everyone who is quiet is not generous or not kind and vice versa.
If someone is either brave or not humble then mary is creative and vice versa.
Everyone who is either old or curious is either calm or curious and vice versa.
Everyone who is rich is either not brave or wise.
Paul is not rich or not patient.
Susan is either brave or not quiet.
Alice is not humble.
Someone is either not old or old.
Fred is old or not patient.
Paul is wise.
Someone is either not quiet or not strong. | Fred is funny. | entailment | (![X]:((~old(X)|~tall(X))<=>(funny(X)|happy(X))))&
(![X]:((~strong(X)&tall(X))<=>rich(X)))&
((?[X]:((~strong(X)&~quiet(X))))=>(?[X]:((brave(X)|~humble(X)))))&
(![X]:((quiet(X)&curious(X))<=>(~generous(X)<~>~quiet(X))))&
(![X]:((happy(X)|~brave(X))=>~kind(X)))&
(![X]:((~funny(X)|kind(X))<=>~happy(X)))&
(((curious(fred)<~>~calm(fred)))=>((~strong(lucy)&~quiet(lucy))))&
(((happy(alice)<~>calm(alice)))=>((~quiet(susan)&quiet(susan))))&
(((humble(john)<~>~humble(john)))<=>(?[X]:(~generous(X))))&
(![X]:(~old(X)=>(funny(X)&~patient(X))))&
(![X]:((~kind(X)|~generous(X))<=>(tall(X)&kind(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>((creative(mary)|~strong(mary))))&
(![X]:(quiet(X)<=>(~generous(X)|~kind(X))))&
((?[X]:((brave(X)<~>~humble(X))))<=>(creative(mary)))&
(![X]:((old(X)<~>curious(X))<=>(calm(X)<~>curious(X))))&
(![X]:(rich(X)=>(~brave(X)<~>wise(X))))&
((~rich(paul)|~patient(paul)))&
((brave(susan)<~>~quiet(susan)))&
(~humble(alice))&
(?[X]:((~old(X)<~>old(X))))&
((old(fred)|~patient(fred)))&
(wise(paul))&
(?[X]:((~quiet(X)<~>~strong(X)))) | funny(fred) | [
"p3",
"p6",
"p9",
"p10",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6767408108645348455768627
% SZS output start Proof for 6767408108645348455768627
4. ! [X0] : ((curious(X0) & quiet(X0)) <=> (~generous(X0) <~> ~quiet(X0))) [input p3]
7. (curious(fred) <~> ~calm(fred)) => (~quiet(lucy) & ~strong(lucy)) [input p6]
10. ! [X0] : (~old(X0) => (~patient(X0) & funny(X0))) [input p9]
11. ! [X0] : ((~generous(X0) | ~kind(X0)) <=> (kind(X0) & tall(X0))) [input p10]
13. ! [X0] : (quiet(X0) <=> (~kind(X0) | ~generous(X0))) [input p12]
15. ! [X0] : ((old(X0) <~> curious(X0)) <=> (calm(X0) <~> curious(X0))) [input p14]
24. ~funny(fred) [input hypothesis]
28. ! [X0] : (~old(X0) => funny(X0)) [pure predicate removal 10]
34. (~quiet(lucy) & ~strong(lucy)) | (curious(fred) <=> ~calm(fred)) [ennf transformation 7]
36. ! [X0] : (funny(X0) | old(X0)) [ennf transformation 28]
43. ! [X0] : (((curious(X0) & quiet(X0)) | ((~generous(X0) | quiet(X0)) & (~quiet(X0) | generous(X0)))) & (((quiet(X0) | generous(X0)) & (~quiet(X0) | ~generous(X0))) | (~curious(X0) | ~quiet(X0)))) [nnf transformation 4]
44. ! [X0] : (((curious(X0) & quiet(X0)) | ((~generous(X0) | quiet(X0)) & (~quiet(X0) | generous(X0)))) & (((quiet(X0) | generous(X0)) & (~quiet(X0) | ~generous(X0))) | ~curious(X0) | ~quiet(X0))) [flattening 43]
47. (~quiet(lucy) & ~strong(lucy)) | ((curious(fred) | calm(fred)) & (~calm(fred) | ~curious(fred))) [nnf transformation 34]
53. ! [X0] : (((~generous(X0) | ~kind(X0)) | (~kind(X0) | ~tall(X0))) & ((kind(X0) & tall(X0)) | (generous(X0) & kind(X0)))) [nnf transformation 11]
54. ! [X0] : ((~generous(X0) | ~kind(X0) | ~kind(X0) | ~tall(X0)) & ((kind(X0) & tall(X0)) | (generous(X0) & kind(X0)))) [flattening 53]
60. ! [X0] : ((quiet(X0) | (kind(X0) & generous(X0))) & ((~kind(X0) | ~generous(X0)) | ~quiet(X0))) [nnf transformation 13]
61. ! [X0] : ((quiet(X0) | (kind(X0) & generous(X0))) & (~kind(X0) | ~generous(X0) | ~quiet(X0))) [flattening 60]
66. ! [X0] : ((((~curious(X0) | ~old(X0)) & (curious(X0) | old(X0))) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0)))) & (((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0))))) [nnf transformation 15]
84. quiet(X0) | ~generous(X0) | quiet(X0) [cnf transformation 44]
85. ~quiet(X0) | curious(X0) | generous(X0) [cnf transformation 44]
94. ~quiet(lucy) | ~calm(fred) | ~curious(fred) [cnf transformation 47]
104. funny(X0) | old(X0) [cnf transformation 36]
107. kind(X0) | kind(X0) [cnf transformation 54]
116. ~kind(X0) | ~generous(X0) | ~quiet(X0) [cnf transformation 61]
117. quiet(X0) | generous(X0) [cnf transformation 61]
123. curious(X0) | calm(X0) | curious(X0) | ~old(X0) [cnf transformation 66]
130. ~curious(X0) | ~old(X0) | calm(X0) | ~curious(X0) [cnf transformation 66]
141. ~funny(fred) [cnf transformation 24]
142. curious(X0) | calm(X0) | ~old(X0) [duplicate literal removal 123]
145. ~curious(X0) | ~old(X0) | calm(X0) [duplicate literal removal 130]
146. kind(X0) [duplicate literal removal 107]
151. ~generous(X0) | quiet(X0) [duplicate literal removal 84]
166. 4 <=> calm(fred) [avatar definition]
170. 5 <=> curious(fred) [avatar definition]
171. ~curious(fred) <- (~5) [avatar component clause 170]
174. 6 <=> quiet(lucy) [avatar definition]
176. ~quiet(lucy) <- (~6) [avatar component clause 174]
178. ~5 | ~4 | ~6 [avatar split clause 94,174,166,170]
239. quiet(X0) [subsumption resolution 117,151]
240. ~generous(X0) | ~quiet(X0) [subsumption resolution 116,146]
241. ~generous(X0) [subsumption resolution 240,239]
261. ~old(X0) | calm(X0) [subsumption resolution 142,145]
266. $false <- (~6) [subsumption resolution 176,239]
267. 6 [avatar contradiction clause 266]
272. old(fred) [resolution 104,141]
279. calm(fred) [resolution 261,272]
304. curious(X0) | generous(X0) [resolution 85,239]
305. curious(X0) [subsumption resolution 304,241]
306. $false <- (~5) [resolution 305,171]
307. 5 [avatar contradiction clause 306]
308. 4 [avatar split clause 279,166]
309. $false [avatar sat refutation 178,267,307,308]
% SZS output end Proof for 6767408108645348455768627
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not tall or generous then someone is both not strong and not tall.
If mary is either not calm or humble then someone is either not generous or tall and vice versa.
If someone is both brave and not quiet then someone is both not strong and calm and vice versa.
Everyone who is either funny or not kind is creative or strong and vice versa.
Everyone who is funny is humble.
Everyone who is either curious or patient is both not old and rich and vice versa.
Everyone who is strong is calm and vice versa.
Everyone who is patient is quiet or humble and vice versa.
If paul is tall or not generous then someone is generous or not kind.
Everyone who is not funny is both not tall and quiet and vice versa.
Everyone who is both not rich and quiet is either strong or old.
Everyone who is not quiet or kind is both rich and brave.
If susan is generous or not creative then paul is either strong or not humble.
If alice is either not curious or kind then someone is not calm or brave and vice versa.
Everyone who is either rich or creative is not humble.
Someone is not rich.
Someone is both not creative and curious.
Someone is both patient and not kind.
Mary is tall or curious.
Someone is both quiet and creative. | Susan is not old. | neutral | (((~tall(lucy)|generous(lucy)))=>(?[X]:((~strong(X)&~tall(X)))))&
(((~calm(mary)<~>humble(mary)))<=>(?[X]:((~generous(X)<~>tall(X)))))&
((?[X]:((brave(X)&~quiet(X))))<=>(?[X]:((~strong(X)&calm(X)))))&
(![X]:((funny(X)<~>~kind(X))<=>(creative(X)|strong(X))))&
(![X]:(funny(X)=>humble(X)))&
(![X]:((curious(X)<~>patient(X))<=>(~old(X)&rich(X))))&
(![X]:(strong(X)<=>calm(X)))&
(![X]:(patient(X)<=>(quiet(X)|humble(X))))&
(((tall(paul)|~generous(paul)))=>(?[X]:((generous(X)|~kind(X)))))&
(![X]:(~funny(X)<=>(~tall(X)&quiet(X))))&
(![X]:((~rich(X)&quiet(X))=>(strong(X)<~>old(X))))&
(![X]:((~quiet(X)|kind(X))=>(rich(X)&brave(X))))&
(((generous(susan)|~creative(susan)))=>((strong(paul)<~>~humble(paul))))&
(((~curious(alice)<~>kind(alice)))<=>(?[X]:((~calm(X)|brave(X)))))&
(![X]:((rich(X)<~>creative(X))=>~humble(X)))&
(?[X]:(~rich(X)))&
(?[X]:((~creative(X)&curious(X))))&
(?[X]:((patient(X)&~kind(X))))&
((tall(mary)|curious(mary)))&
(?[X]:((quiet(X)&creative(X)))) | ~old(susan) | [] | null | 0 |
Everyone who is brave or not strong is creative or not creative and vice versa. Everyone who is both not quiet and generous is either tall or strong and vice versa. Everyone who is not curious or not calm is either strong or not humble. If someone is not happy then john is either not happy or tall and vice versa. If someone is either not kind or tall then someone is not humble. Everyone who is both humble and not funny is either not strong or not happy and vice versa. Everyone who is both not kind and creative is calm. If someone is both patient and calm then lucy is brave or quiet. If someone is both not creative and wise then mary is both wise and not old and vice versa. Everyone who is not strong or not calm is curious or not strong and vice versa. If susan is not generous then someone is not funny. Everyone who is generous or not generous is both not brave and not wise and vice versa. Everyone who is funny is both not strong and not kind and vice versa. If someone is either happy or not old then paul is both not quiet and not kind. Everyone who is kind or not strong is both not funny and not humble. John is both not wise and not tall. Alice is rich or calm. Mary is happy or not creative. Someone is calm. Fred is strong or not generous. Someone is either humble or not curious. | Alice is not patient. | neutral | (![X]:((brave(X)|~strong(X))<=>(creative(X)|~creative(X))))&
(![X]:((~quiet(X)&generous(X))<=>(tall(X)<~>strong(X))))&
(![X]:((~curious(X)|~calm(X))=>(strong(X)<~>~humble(X))))&
((?[X]:(~happy(X)))<=>((~happy(john)<~>tall(john))))&
((?[X]:((~kind(X)<~>tall(X))))=>(?[X]:(~humble(X))))&
(![X]:((humble(X)&~funny(X))<=>(~strong(X)<~>~happy(X))))&
(![X]:((~kind(X)&creative(X))=>calm(X)))&
((?[X]:((patient(X)&calm(X))))=>((brave(lucy)|quiet(lucy))))&
((?[X]:((~creative(X)&wise(X))))<=>((wise(mary)&~old(mary))))&
(![X]:((~strong(X)|~calm(X))<=>(curious(X)|~strong(X))))&
((~generous(susan))=>(?[X]:(~funny(X))))&
(![X]:((generous(X)|~generous(X))<=>(~brave(X)&~wise(X))))&
(![X]:(funny(X)<=>(~strong(X)&~kind(X))))&
((?[X]:((happy(X)<~>~old(X))))=>((~quiet(paul)&~kind(paul))))&
(![X]:((kind(X)|~strong(X))=>(~funny(X)&~humble(X))))&
((~wise(john)&~tall(john)))&
((rich(alice)|calm(alice)))&
((happy(mary)|~creative(mary)))&
(?[X]:(calm(X)))&
((strong(fred)|~generous(fred)))&
(?[X]:((humble(X)<~>~curious(X)))) | ~patient(alice) | [] | null | 0 |
If someone is not curious or quiet then paul is either not happy or rich and vice versa. If paul is either not curious or quiet then someone is either happy or not wise and vice versa. Everyone who is old or quiet is tall and vice versa. If fred is calm or not tall then someone is not happy. If someone is both happy and not tall then someone is either calm or not wise. Everyone who is creative is not old or patient and vice versa. Everyone who is both not tall and happy is not old and vice versa. If someone is kind then someone is either curious or not curious. If someone is calm or not creative then mary is creative or not funny. Everyone who is not kind is not old or patient and vice versa. If john is either not humble or funny then mary is curious or calm. Everyone who is either not brave or not wise is both curious and wise and vice versa. Everyone who is both not patient and quiet is not brave. If someone is both patient and not creative then someone is generous. If john is brave then john is both rich and wise and vice versa. Everyone who is both kind and calm is calm and vice versa. John is tall or quiet. Alice is quiet or old. Someone is not generous. John is both not patient and not funny. Someone is not quiet. Alice is either brave or quiet. Fred is both funny and not quiet. Someone is either not generous or humble. | John is not humble. | neutral | ((?[X]:((~curious(X)|quiet(X))))<=>((~happy(paul)<~>rich(paul))))&
(((~curious(paul)<~>quiet(paul)))<=>(?[X]:((happy(X)<~>~wise(X)))))&
(![X]:((old(X)|quiet(X))<=>tall(X)))&
(((calm(fred)|~tall(fred)))=>(?[X]:(~happy(X))))&
((?[X]:((happy(X)&~tall(X))))=>(?[X]:((calm(X)<~>~wise(X)))))&
(![X]:(creative(X)<=>(~old(X)|patient(X))))&
(![X]:((~tall(X)&happy(X))<=>~old(X)))&
((?[X]:(kind(X)))=>(?[X]:((curious(X)<~>~curious(X)))))&
((?[X]:((calm(X)|~creative(X))))=>((creative(mary)|~funny(mary))))&
(![X]:(~kind(X)<=>(~old(X)|patient(X))))&
(((~humble(john)<~>funny(john)))=>((curious(mary)|calm(mary))))&
(![X]:((~brave(X)<~>~wise(X))<=>(curious(X)&wise(X))))&
(![X]:((~patient(X)&quiet(X))=>~brave(X)))&
((?[X]:((patient(X)&~creative(X))))=>(?[X]:(generous(X))))&
((brave(john))<=>((rich(john)&wise(john))))&
(![X]:((kind(X)&calm(X))<=>calm(X)))&
((tall(john)|quiet(john)))&
((quiet(alice)|old(alice)))&
(?[X]:(~generous(X)))&
((~patient(john)&~funny(john)))&
(?[X]:(~quiet(X)))&
((brave(alice)<~>quiet(alice)))&
((funny(fred)&~quiet(fred)))&
(?[X]:((~generous(X)<~>humble(X)))) | ~humble(john) | [] | null | 0 |
If someone is not rich or not funny then paul is not wise or not funny. If lucy is both not brave and wise then lucy is rich or funny. Everyone who is either brave or not old is rich and vice versa. If john is either patient or curious then someone is both rich and not quiet. If lucy is both not rich and not humble then paul is either not kind or not humble and vice versa. If john is both curious and not strong then someone is either not rich or old and vice versa. Everyone who is both kind and not old is either generous or patient. If someone is generous or brave then someone is old or not generous. Everyone who is both humble and brave is not kind and vice versa. Everyone who is wise is not patient and vice versa. If susan is old or not funny then john is either old or not brave and vice versa. Everyone who is both wise and patient is either not strong or not tall and vice versa. If someone is old or not brave then john is both funny and not kind and vice versa. Everyone who is kind is either kind or not generous and vice versa. If paul is creative or generous then lucy is either not happy or patient and vice versa. If someone is not funny then john is calm or not strong and vice versa. Someone is not generous or humble. Someone is not brave or not curious. Paul is not wise or humble. Fred is both not creative and not old. Paul is both not wise and not kind. Someone is not patient. Alice is not rich or not strong. Alice is both creative and strong. | John is kind. | contradiction | ((?[X]:((~rich(X)|~funny(X))))=>((~wise(paul)|~funny(paul))))&
(((~brave(lucy)&wise(lucy)))=>((rich(lucy)|funny(lucy))))&
(![X]:((brave(X)<~>~old(X))<=>rich(X)))&
(((patient(john)<~>curious(john)))=>(?[X]:((rich(X)&~quiet(X)))))&
(((~rich(lucy)&~humble(lucy)))<=>((~kind(paul)<~>~humble(paul))))&
(((curious(john)&~strong(john)))<=>(?[X]:((~rich(X)<~>old(X)))))&
(![X]:((kind(X)&~old(X))=>(generous(X)<~>patient(X))))&
((?[X]:((generous(X)|brave(X))))=>(?[X]:((old(X)|~generous(X)))))&
(![X]:((humble(X)&brave(X))<=>~kind(X)))&
(![X]:(wise(X)<=>~patient(X)))&
(((old(susan)|~funny(susan)))<=>((old(john)<~>~brave(john))))&
(![X]:((wise(X)&patient(X))<=>(~strong(X)<~>~tall(X))))&
((?[X]:((old(X)|~brave(X))))<=>((funny(john)&~kind(john))))&
(![X]:(kind(X)<=>(kind(X)<~>~generous(X))))&
(((creative(paul)|generous(paul)))<=>((~happy(lucy)<~>patient(lucy))))&
((?[X]:(~funny(X)))<=>((calm(john)|~strong(john))))&
(?[X]:((~generous(X)|humble(X))))&
(?[X]:((~brave(X)|~curious(X))))&
((~wise(paul)|humble(paul)))&
((~creative(fred)&~old(fred)))&
((~wise(paul)&~kind(paul)))&
(?[X]:(~patient(X)))&
((~rich(alice)|~strong(alice)))&
((creative(alice)&strong(alice))) | kind(john) | [
"p7",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1209175600404490272471717
% SZS output start Proof for 1209175600404490272471717
8. ? [X0] : (brave(X0) | generous(X0)) => ? [X0] : (~generous(X0) | old(X0)) [input p7]
13. ? [X0] : (~brave(X0) | old(X0)) <=> (~kind(john) & funny(john)) [input p12]
14. ! [X0] : (kind(X0) <=> (kind(X0) <~> ~generous(X0))) [input p13]
25. kind(john) [input hypothesis]
26. ? [X0] : (brave(X0) | generous(X0)) => ? [X1] : (~generous(X1) | old(X1)) [rectify 8]
35. ? [X1] : (~generous(X1) | old(X1)) | ! [X0] : (~brave(X0) & ~generous(X0)) [ennf transformation 26]
48. ? [X0] : (~generous(X0) | old(X0)) | ! [X1] : (~brave(X1) & ~generous(X1)) [rectify 35]
49. ? [X0] : (~generous(X0) | old(X0)) => (~generous(sK2) | old(sK2)) [choice axiom]
50. (~generous(sK2) | old(sK2)) | ! [X1] : (~brave(X1) & ~generous(X1)) [skolemisation 48,49]
58. (? [X0] : (~brave(X0) | old(X0)) | (kind(john) | ~funny(john))) & ((~kind(john) & funny(john)) | ! [X0] : (brave(X0) & ~old(X0))) [nnf transformation 13]
59. (? [X0] : (~brave(X0) | old(X0)) | kind(john) | ~funny(john)) & ((~kind(john) & funny(john)) | ! [X0] : (brave(X0) & ~old(X0))) [flattening 58]
60. (? [X0] : (~brave(X0) | old(X0)) | kind(john) | ~funny(john)) & ((~kind(john) & funny(john)) | ! [X1] : (brave(X1) & ~old(X1))) [rectify 59]
61. ? [X0] : (~brave(X0) | old(X0)) => (~brave(sK3) | old(sK3)) [choice axiom]
62. ((~brave(sK3) | old(sK3)) | kind(john) | ~funny(john)) & ((~kind(john) & funny(john)) | ! [X1] : (brave(X1) & ~old(X1))) [skolemisation 60,61]
63. ! [X0] : ((kind(X0) | ((kind(X0) | generous(X0)) & (~generous(X0) | ~kind(X0)))) & (((generous(X0) | ~kind(X0)) & (~generous(X0) | kind(X0))) | ~kind(X0))) [nnf transformation 14]
100. ~generous(sK2) | old(sK2) | ~generous(X1) [cnf transformation 50]
121. ~kind(john) | ~old(X1) [cnf transformation 62]
125. generous(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 63]
127. kind(X0) | kind(X0) | generous(X0) [cnf transformation 63]
148. kind(john) [cnf transformation 25]
149. generous(X0) | ~kind(X0) [duplicate literal removal 125]
150. kind(X0) | generous(X0) [duplicate literal removal 127]
244. 21 <=> old(sK2) [avatar definition]
246. old(sK2) <- (21) [avatar component clause 244]
248. 22 <=> generous(sK2) [avatar definition]
250. ~generous(sK2) <- (~22) [avatar component clause 248]
253. 23 <=> ! [X1] : ~generous(X1) [avatar definition]
254. ~generous(X1) <- (23) [avatar component clause 253]
255. 23 | 21 | ~22 [avatar split clause 100,248,244,253]
283. 29 <=> kind(john) [avatar definition]
300. 33 <=> ! [X1] : ~old(X1) [avatar definition]
301. ~old(X1) <- (33) [avatar component clause 300]
302. 33 | ~29 [avatar split clause 121,283,300]
305. generous(X0) [subsumption resolution 149,150]
358. 29 [avatar split clause 148,283]
361. $false <- (~22) [subsumption resolution 250,305]
362. 22 [avatar contradiction clause 361]
365. $false <- (21, 33) [subsumption resolution 246,301]
366. ~21 | ~33 [avatar contradiction clause 365]
367. $false <- (23) [subsumption resolution 254,305]
368. ~23 [avatar contradiction clause 367]
371. $false [avatar sat refutation 255,302,358,362,366,368]
% SZS output end Proof for 1209175600404490272471717
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is not strong and vice versa.
If someone is generous then someone is both not quiet and not humble.
Everyone who is wise is either kind or funny.
If susan is not humble then someone is either calm or curious.
Everyone who is either not tall or not brave is calm or patient.
If someone is either happy or generous then mary is strong.
If someone is wise or curious then someone is strong and vice versa.
Everyone who is creative or not wise is both rich and not wise and vice versa.
Everyone who is either not strong or not generous is either not tall or not generous.
If someone is not calm or not funny then alice is either tall or strong.
Everyone who is either calm or old is either patient or not humble and vice versa.
If someone is generous then someone is funny.
Everyone who is not funny or not quiet is either brave or not curious.
Everyone who is either not kind or not rich is not patient.
Everyone who is both not happy and calm is both patient and kind and vice versa.
Everyone who is not calm is old or not old and vice versa.
Mary is both not strong and patient.
Mary is not rich or not humble.
Someone is both not funny and wise.
Lucy is either quiet or not rich.
Susan is both not strong and not tall.
Fred is not funny or strong.
Someone is not curious.
Alice is both not quiet and wise. | Mary is not funny. | contradiction | (![X]:(curious(X)<=>~strong(X)))&
((?[X]:(generous(X)))=>(?[X]:((~quiet(X)&~humble(X)))))&
(![X]:(wise(X)=>(kind(X)<~>funny(X))))&
((~humble(susan))=>(?[X]:((calm(X)<~>curious(X)))))&
(![X]:((~tall(X)<~>~brave(X))=>(calm(X)|patient(X))))&
((?[X]:((happy(X)<~>generous(X))))=>(strong(mary)))&
((?[X]:((wise(X)|curious(X))))<=>(?[X]:(strong(X))))&
(![X]:((creative(X)|~wise(X))<=>(rich(X)&~wise(X))))&
(![X]:((~strong(X)<~>~generous(X))=>(~tall(X)<~>~generous(X))))&
((?[X]:((~calm(X)|~funny(X))))=>((tall(alice)<~>strong(alice))))&
(![X]:((calm(X)<~>old(X))<=>(patient(X)<~>~humble(X))))&
((?[X]:(generous(X)))=>(?[X]:(funny(X))))&
(![X]:((~funny(X)|~quiet(X))=>(brave(X)<~>~curious(X))))&
(![X]:((~kind(X)<~>~rich(X))=>~patient(X)))&
(![X]:((~happy(X)&calm(X))<=>(patient(X)&kind(X))))&
(![X]:(~calm(X)<=>(old(X)|~old(X))))&
((~strong(mary)&patient(mary)))&
((~rich(mary)|~humble(mary)))&
(?[X]:((~funny(X)&wise(X))))&
((quiet(lucy)<~>~rich(lucy)))&
((~strong(susan)&~tall(susan)))&
((~funny(fred)|strong(fred)))&
(?[X]:(~curious(X)))&
((~quiet(alice)&wise(alice))) | ~funny(mary) | [
"p2",
"p7",
"p13",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4849285934831392837645078
% SZS output start Proof for 4849285934831392837645078
3. ! [X0] : (wise(X0) => (kind(X0) <~> funny(X0))) [input p2]
8. ! [X0] : ((~wise(X0) | creative(X0)) <=> (~wise(X0) & rich(X0))) [input p7]
14. ! [X0] : ((~kind(X0) <~> ~rich(X0)) => ~patient(X0)) [input p13]
15. ! [X0] : ((calm(X0) & ~happy(X0)) <=> (kind(X0) & patient(X0))) [input p14]
16. ! [X0] : (~calm(X0) <=> (~old(X0) | old(X0))) [input p15]
17. patient(mary) & ~strong(mary) [input p16]
25. ~funny(mary) [input hypothesis]
30. ! [X0] : ((kind(X0) <~> funny(X0)) | ~wise(X0)) [ennf transformation 3]
39. ! [X0] : (~patient(X0) | (~kind(X0) <=> ~rich(X0))) [ennf transformation 14]
44. ! [X0] : (((~funny(X0) | ~kind(X0)) & (funny(X0) | kind(X0))) | ~wise(X0)) [nnf transformation 30]
55. ! [X0] : (((~wise(X0) | creative(X0)) | (wise(X0) | ~rich(X0))) & ((~wise(X0) & rich(X0)) | (wise(X0) & ~creative(X0)))) [nnf transformation 8]
56. ! [X0] : ((~wise(X0) | creative(X0) | wise(X0) | ~rich(X0)) & ((~wise(X0) & rich(X0)) | (wise(X0) & ~creative(X0)))) [flattening 55]
64. ! [X0] : (~patient(X0) | ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0)))) [nnf transformation 39]
65. ! [X0] : (((calm(X0) & ~happy(X0)) | (~kind(X0) | ~patient(X0))) & ((kind(X0) & patient(X0)) | (~calm(X0) | happy(X0)))) [nnf transformation 15]
66. ! [X0] : (((calm(X0) & ~happy(X0)) | ~kind(X0) | ~patient(X0)) & ((kind(X0) & patient(X0)) | ~calm(X0) | happy(X0))) [flattening 65]
67. ! [X0] : ((~calm(X0) | (old(X0) & ~old(X0))) & ((~old(X0) | old(X0)) | calm(X0))) [nnf transformation 16]
68. ! [X0] : ((~calm(X0) | (old(X0) & ~old(X0))) & (~old(X0) | old(X0) | calm(X0))) [flattening 67]
78. ~wise(X0) | kind(X0) | funny(X0) [cnf transformation 44]
90. rich(X0) | wise(X0) [cnf transformation 56]
115. ~rich(X0) | ~patient(X0) | kind(X0) [cnf transformation 64]
120. ~patient(X0) | ~kind(X0) | calm(X0) [cnf transformation 66]
122. ~calm(X0) | ~old(X0) [cnf transformation 68]
123. ~calm(X0) | old(X0) [cnf transformation 68]
125. patient(mary) [cnf transformation 17]
137. ~funny(mary) [cnf transformation 25]
226. ~calm(X0) [subsumption resolution 122,123]
341. ~patient(X0) | kind(X0) | wise(X0) [resolution 115,90]
350. 40 <=> kind(mary) [avatar definition]
352. ~kind(mary) <- (~40) [avatar component clause 350]
366. ~kind(mary) | calm(mary) [resolution 120,125]
414. kind(mary) | wise(mary) [resolution 341,125]
415. wise(mary) <- (~40) [subsumption resolution 414,352]
420. kind(mary) | funny(mary) <- (~40) [resolution 415,78]
421. funny(mary) <- (~40) [subsumption resolution 420,352]
422. $false <- (~40) [subsumption resolution 421,137]
423. 40 [avatar contradiction clause 422]
429. ~kind(mary) [subsumption resolution 366,226]
430. ~40 [avatar split clause 429,350]
431. $false [avatar sat refutation 423,430]
% SZS output end Proof for 4849285934831392837645078
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous or curious then paul is either not wise or not humble and vice versa. Everyone who is generous or not humble is wise or kind and vice versa. Everyone who is not generous or not rich is both wise and funny. Everyone who is both not old and curious is either not happy or old. Everyone who is either strong or not humble is generous or not rich. Everyone who is not patient is not curious. Everyone who is not strong is both rich and not happy and vice versa. Everyone who is both not old and not funny is calm. If someone is either strong or old then someone is either humble or patient and vice versa. Everyone who is not old is happy or rich and vice versa. If john is calm then someone is old and vice versa. Everyone who is not kind or not strong is not wise and vice versa. Everyone who is either patient or not calm is kind or not tall and vice versa. If someone is both not strong and happy then someone is not calm or not quiet and vice versa. Everyone who is happy is either not patient or not wise. If paul is either not brave or not patient then someone is calm or old and vice versa. Lucy is either generous or not quiet. Susan is creative. Someone is either not patient or funny. Someone is either not curious or old. | Lucy is quiet. | entailment | ((?[X]:((generous(X)|curious(X))))<=>((~wise(paul)<~>~humble(paul))))&
(![X]:((generous(X)|~humble(X))<=>(wise(X)|kind(X))))&
(![X]:((~generous(X)|~rich(X))=>(wise(X)&funny(X))))&
(![X]:((~old(X)&curious(X))=>(~happy(X)<~>old(X))))&
(![X]:((strong(X)<~>~humble(X))=>(generous(X)|~rich(X))))&
(![X]:(~patient(X)=>~curious(X)))&
(![X]:(~strong(X)<=>(rich(X)&~happy(X))))&
(![X]:((~old(X)&~funny(X))=>calm(X)))&
((?[X]:((strong(X)<~>old(X))))<=>(?[X]:((humble(X)<~>patient(X)))))&
(![X]:(~old(X)<=>(happy(X)|rich(X))))&
((calm(john))<=>(?[X]:(old(X))))&
(![X]:((~kind(X)|~strong(X))<=>~wise(X)))&
(![X]:((patient(X)<~>~calm(X))<=>(kind(X)|~tall(X))))&
((?[X]:((~strong(X)&happy(X))))<=>(?[X]:((~calm(X)|~quiet(X)))))&
(![X]:(happy(X)=>(~patient(X)<~>~wise(X))))&
(((~brave(paul)<~>~patient(paul)))<=>(?[X]:((calm(X)|old(X)))))&
((generous(lucy)<~>~quiet(lucy)))&
(creative(susan))&
(?[X]:((~patient(X)<~>funny(X))))&
(?[X]:((~curious(X)<~>old(X)))) | quiet(lucy) | [
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5504269728344200162351673
% SZS output start Proof for 5504269728344200162351673
7. ! [X0] : (~strong(X0) <=> (~happy(X0) & rich(X0))) [input p6]
14. ? [X0] : (happy(X0) & ~strong(X0)) <=> ? [X0] : (~quiet(X0) | ~calm(X0)) [input p13]
21. ~quiet(lucy) [input hypothesis]
23. ? [X0] : (happy(X0) & ~strong(X0)) <=> ? [X1] : (~quiet(X1) | ~calm(X1)) [rectify 14]
42. ! [X0] : ((~strong(X0) | (happy(X0) | ~rich(X0))) & ((~happy(X0) & rich(X0)) | strong(X0))) [nnf transformation 7]
43. ! [X0] : ((~strong(X0) | happy(X0) | ~rich(X0)) & ((~happy(X0) & rich(X0)) | strong(X0))) [flattening 42]
59. (? [X0] : (happy(X0) & ~strong(X0)) | ! [X1] : (quiet(X1) & calm(X1))) & (? [X1] : (~quiet(X1) | ~calm(X1)) | ! [X0] : (~happy(X0) | strong(X0))) [nnf transformation 23]
60. (? [X0] : (happy(X0) & ~strong(X0)) | ! [X1] : (quiet(X1) & calm(X1))) & (? [X2] : (~quiet(X2) | ~calm(X2)) | ! [X3] : (~happy(X3) | strong(X3))) [rectify 59]
61. ? [X0] : (happy(X0) & ~strong(X0)) => (happy(sK4) & ~strong(sK4)) [choice axiom]
62. ? [X2] : (~quiet(X2) | ~calm(X2)) => (~quiet(sK5) | ~calm(sK5)) [choice axiom]
63. ((happy(sK4) & ~strong(sK4)) | ! [X1] : (quiet(X1) & calm(X1))) & ((~quiet(sK5) | ~calm(sK5)) | ! [X3] : (~happy(X3) | strong(X3))) [skolemisation 60,62,61]
96. ~happy(X0) | strong(X0) [cnf transformation 43]
123. ~strong(sK4) | quiet(X1) [cnf transformation 63]
125. happy(sK4) | quiet(X1) [cnf transformation 63]
140. ~quiet(lucy) [cnf transformation 21]
220. 18 <=> ! [X1] : quiet(X1) [avatar definition]
221. quiet(X1) <- (18) [avatar component clause 220]
223. 19 <=> happy(sK4) [avatar definition]
225. happy(sK4) <- (19) [avatar component clause 223]
226. 18 | 19 [avatar split clause 125,223,220]
232. 21 <=> strong(sK4) [avatar definition]
235. 18 | ~21 [avatar split clause 123,232,220]
267. 28 <=> quiet(lucy) [avatar definition]
268. ~quiet(lucy) <- (~28) [avatar component clause 267]
292. ~28 [avatar split clause 140,267]
302. strong(sK4) <- (19) [resolution 96,225]
305. 21 | ~19 [avatar split clause 302,223,232]
312. $false <- (18, ~28) [resolution 221,268]
313. ~18 | 28 [avatar contradiction clause 312]
314. $false [avatar sat refutation 226,235,292,305,313]
% SZS output end Proof for 5504269728344200162351673
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or not happy is old or kind. Everyone who is humble is not rich. Everyone who is not humble or curious is not funny and vice versa. Everyone who is both tall and not curious is both not curious and quiet and vice versa. If paul is creative then paul is either quiet or not strong. If susan is both not wise and not curious then fred is either curious or not old and vice versa. Everyone who is not brave is quiet and vice versa. If lucy is either not happy or funny then alice is both not patient and quiet and vice versa. Everyone who is either not strong or not creative is either not quiet or not generous. Everyone who is both rich and happy is either not humble or calm and vice versa. If someone is not creative then someone is not patient or brave. If someone is both not quiet and curious then someone is strong and vice versa. Everyone who is not calm is both not happy and not humble and vice versa. Everyone who is both happy and quiet is not old or calm. Everyone who is tall is happy or not old and vice versa. Everyone who is creative is either not old or not patient. Alice is not kind or not wise. Someone is both patient and old. Mary is either not kind or not happy. Someone is not rich or not patient. Lucy is brave. Lucy is either not kind or patient. | Lucy is funny. | contradiction | (![X]:((wise(X)|~happy(X))=>(old(X)|kind(X))))&
(![X]:(humble(X)=>~rich(X)))&
(![X]:((~humble(X)|curious(X))<=>~funny(X)))&
(![X]:((tall(X)&~curious(X))<=>(~curious(X)&quiet(X))))&
((creative(paul))=>((quiet(paul)<~>~strong(paul))))&
(((~wise(susan)&~curious(susan)))<=>((curious(fred)<~>~old(fred))))&
(![X]:(~brave(X)<=>quiet(X)))&
(((~happy(lucy)<~>funny(lucy)))<=>((~patient(alice)&quiet(alice))))&
(![X]:((~strong(X)<~>~creative(X))=>(~quiet(X)<~>~generous(X))))&
(![X]:((rich(X)&happy(X))<=>(~humble(X)<~>calm(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~patient(X)|brave(X)))))&
((?[X]:((~quiet(X)&curious(X))))<=>(?[X]:(strong(X))))&
(![X]:(~calm(X)<=>(~happy(X)&~humble(X))))&
(![X]:((happy(X)&quiet(X))=>(~old(X)|calm(X))))&
(![X]:(tall(X)<=>(happy(X)|~old(X))))&
(![X]:(creative(X)=>(~old(X)<~>~patient(X))))&
((~kind(alice)|~wise(alice)))&
(?[X]:((patient(X)&old(X))))&
((~kind(mary)<~>~happy(mary)))&
(?[X]:((~rich(X)|~patient(X))))&
(brave(lucy))&
((~kind(lucy)<~>patient(lucy))) | funny(lucy) | [
"p1",
"p2",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5363772354342460677153620
% SZS output start Proof for 5363772354342460677153620
2. ! [X0] : (humble(X0) => ~rich(X0)) [input p1]
3. ! [X0] : ((curious(X0) | ~humble(X0)) <=> ~funny(X0)) [input p2]
10. ! [X0] : ((happy(X0) & rich(X0)) <=> (~humble(X0) <~> calm(X0))) [input p9]
13. ! [X0] : (~calm(X0) <=> (~humble(X0) & ~happy(X0))) [input p12]
23. funny(lucy) [input hypothesis]
29. ! [X0] : (~rich(X0) | ~humble(X0)) [ennf transformation 2]
37. ! [X0] : (((curious(X0) | ~humble(X0)) | funny(X0)) & (~funny(X0) | (~curious(X0) & humble(X0)))) [nnf transformation 3]
38. ! [X0] : ((curious(X0) | ~humble(X0) | funny(X0)) & (~funny(X0) | (~curious(X0) & humble(X0)))) [flattening 37]
47. ! [X0] : (((happy(X0) & rich(X0)) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0)))) & (((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | (~happy(X0) | ~rich(X0)))) [nnf transformation 10]
48. ! [X0] : (((happy(X0) & rich(X0)) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0)))) & (((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | ~happy(X0) | ~rich(X0))) [flattening 47]
57. ! [X0] : ((~calm(X0) | (humble(X0) | happy(X0))) & ((~humble(X0) & ~happy(X0)) | calm(X0))) [nnf transformation 13]
58. ! [X0] : ((~calm(X0) | humble(X0) | happy(X0)) & ((~humble(X0) & ~happy(X0)) | calm(X0))) [flattening 57]
70. ~rich(X0) | ~humble(X0) [cnf transformation 29]
71. ~funny(X0) | humble(X0) [cnf transformation 38]
100. rich(X0) | ~humble(X0) | ~calm(X0) [cnf transformation 48]
108. ~humble(X0) | calm(X0) [cnf transformation 58]
125. funny(lucy) [cnf transformation 23]
175. 11 <=> funny(lucy) [avatar definition]
176. funny(lucy) <- (11) [avatar component clause 175]
184. ~humble(X0) | ~calm(X0) [subsumption resolution 100,70]
220. ~humble(X0) [subsumption resolution 108,184]
259. 11 [avatar split clause 125,175]
260. humble(lucy) <- (11) [resolution 71,176]
261. $false <- (11) [subsumption resolution 260,220]
262. ~11 [avatar contradiction clause 261]
263. $false [avatar sat refutation 259,262]
% SZS output end Proof for 5363772354342460677153620
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If john is old then someone is both funny and not old.
Everyone who is brave or not strong is both quiet and not tall and vice versa.
Everyone who is not old is both creative and calm.
Everyone who is not patient or not wise is patient and vice versa.
If someone is either not wise or not creative then someone is either humble or not tall.
Everyone who is both strong and old is both humble and not patient and vice versa.
If mary is both not tall and not creative then john is both not humble and not rich and vice versa.
If fred is both creative and not curious then someone is both not calm and kind and vice versa.
Everyone who is both not calm and wise is kind or not happy and vice versa.
If someone is creative or humble then susan is not humble or quiet.
If someone is not kind then someone is wise or not curious and vice versa.
Everyone who is either old or happy is creative or not rich.
Everyone who is not brave is either patient or tall.
If someone is not tall or quiet then alice is either not calm or not patient.
Everyone who is either not rich or creative is both kind and brave.
If someone is not funny then lucy is either wise or curious and vice versa.
Someone is both not kind and happy.
Alice is creative.
Someone is happy or not patient.
John is rich.
Someone is not tall.
Someone is either old or tall.
Lucy is not strong.
Paul is quiet. | Mary is not happy. | contradiction | ((old(john))=>(?[X]:((funny(X)&~old(X)))))&
(![X]:((brave(X)|~strong(X))<=>(quiet(X)&~tall(X))))&
(![X]:(~old(X)=>(creative(X)&calm(X))))&
(![X]:((~patient(X)|~wise(X))<=>patient(X)))&
((?[X]:((~wise(X)<~>~creative(X))))=>(?[X]:((humble(X)<~>~tall(X)))))&
(![X]:((strong(X)&old(X))<=>(humble(X)&~patient(X))))&
(((~tall(mary)&~creative(mary)))<=>((~humble(john)&~rich(john))))&
(((creative(fred)&~curious(fred)))<=>(?[X]:((~calm(X)&kind(X)))))&
(![X]:((~calm(X)&wise(X))<=>(kind(X)|~happy(X))))&
((?[X]:((creative(X)|humble(X))))=>((~humble(susan)|quiet(susan))))&
((?[X]:(~kind(X)))<=>(?[X]:((wise(X)|~curious(X)))))&
(![X]:((old(X)<~>happy(X))=>(creative(X)|~rich(X))))&
(![X]:(~brave(X)=>(patient(X)<~>tall(X))))&
((?[X]:((~tall(X)|quiet(X))))=>((~calm(alice)<~>~patient(alice))))&
(![X]:((~rich(X)<~>creative(X))=>(kind(X)&brave(X))))&
((?[X]:(~funny(X)))<=>((wise(lucy)<~>curious(lucy))))&
(?[X]:((~kind(X)&happy(X))))&
(creative(alice))&
(?[X]:((happy(X)|~patient(X))))&
(rich(john))&
(?[X]:(~tall(X)))&
(?[X]:((old(X)<~>tall(X))))&
(~strong(lucy))&
(quiet(paul)) | ~happy(mary) | [
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4032432207939678547836270
% SZS output start Proof for 4032432207939678547836270
4. ! [X0] : ((~wise(X0) | ~patient(X0)) <=> patient(X0)) [input p3]
9. ! [X0] : ((wise(X0) & ~calm(X0)) <=> (~happy(X0) | kind(X0))) [input p8]
25. ~happy(mary) [input hypothesis]
42. ! [X0] : (((~wise(X0) | ~patient(X0)) | ~patient(X0)) & (patient(X0) | (wise(X0) & patient(X0)))) [nnf transformation 4]
43. ! [X0] : ((~wise(X0) | ~patient(X0) | ~patient(X0)) & (patient(X0) | (wise(X0) & patient(X0)))) [flattening 42]
57. ! [X0] : (((wise(X0) & ~calm(X0)) | (happy(X0) & ~kind(X0))) & ((~happy(X0) | kind(X0)) | (~wise(X0) | calm(X0)))) [nnf transformation 9]
58. ! [X0] : (((wise(X0) & ~calm(X0)) | (happy(X0) & ~kind(X0))) & (~happy(X0) | kind(X0) | ~wise(X0) | calm(X0))) [flattening 57]
90. patient(X0) | patient(X0) [cnf transformation 43]
92. ~wise(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 43]
113. happy(X0) | wise(X0) [cnf transformation 58]
145. ~happy(mary) [cnf transformation 25]
146. patient(X0) [duplicate literal removal 90]
147. ~wise(X0) | ~patient(X0) [duplicate literal removal 92]
306. wise(mary) [resolution 113,145]
308. ~patient(mary) [resolution 147,306]
309. $false [subsumption resolution 308,146]
% SZS output end Proof for 4032432207939678547836270
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either rich or not curious is not funny or not calm and vice versa. Everyone who is not tall or not generous is both tall and curious. Everyone who is either not creative or not patient is kind. Everyone who is quiet or not wise is not calm. If mary is both not kind and not creative then fred is wise or not quiet and vice versa. If someone is humble then someone is both calm and old. If susan is not creative then someone is both not quiet and not kind and vice versa. Everyone who is either not rich or brave is not old and vice versa. Everyone who is either strong or not kind is funny and vice versa. Everyone who is both tall and humble is both kind and not old. If fred is not tall or not quiet then someone is either not quiet or calm and vice versa. Everyone who is either not wise or not creative is both rich and not quiet. Everyone who is happy is not patient or not quiet and vice versa. Everyone who is not curious is either generous or humble and vice versa. Everyone who is either not strong or not humble is either humble or not funny. Someone is either not funny or funny. Someone is both not calm and patient. Someone is not old. John is either generous or not tall. Someone is happy or not generous. Someone is funny or brave. Someone is both kind and not creative. Fred is either not old or not brave. | Mary is curious. | neutral | (![X]:((rich(X)<~>~curious(X))<=>(~funny(X)|~calm(X))))&
(![X]:((~tall(X)|~generous(X))=>(tall(X)&curious(X))))&
(![X]:((~creative(X)<~>~patient(X))=>kind(X)))&
(![X]:((quiet(X)|~wise(X))=>~calm(X)))&
(((~kind(mary)&~creative(mary)))<=>((wise(fred)|~quiet(fred))))&
((?[X]:(humble(X)))=>(?[X]:((calm(X)&old(X)))))&
((~creative(susan))<=>(?[X]:((~quiet(X)&~kind(X)))))&
(![X]:((~rich(X)<~>brave(X))<=>~old(X)))&
(![X]:((strong(X)<~>~kind(X))<=>funny(X)))&
(![X]:((tall(X)&humble(X))=>(kind(X)&~old(X))))&
(((~tall(fred)|~quiet(fred)))<=>(?[X]:((~quiet(X)<~>calm(X)))))&
(![X]:((~wise(X)<~>~creative(X))=>(rich(X)&~quiet(X))))&
(![X]:(happy(X)<=>(~patient(X)|~quiet(X))))&
(![X]:(~curious(X)<=>(generous(X)<~>humble(X))))&
(![X]:((~strong(X)<~>~humble(X))=>(humble(X)<~>~funny(X))))&
(?[X]:((~funny(X)<~>funny(X))))&
(?[X]:((~calm(X)&patient(X))))&
(?[X]:(~old(X)))&
((generous(john)<~>~tall(john)))&
(?[X]:((happy(X)|~generous(X))))&
(?[X]:((funny(X)|brave(X))))&
(?[X]:((kind(X)&~creative(X))))&
((~old(fred)<~>~brave(fred))) | curious(mary) | [] | null | 0 |
Everyone who is both curious and not patient is both rich and not wise.
Everyone who is either not funny or not quiet is creative or not wise.
If alice is both not happy and tall then susan is not creative or not wise and vice versa.
If paul is both not kind and not quiet then someone is both tall and calm.
Everyone who is not kind or not quiet is not humble.
If fred is both tall and not rich then someone is calm or funny and vice versa.
Everyone who is curious is either not happy or humble.
Everyone who is tall or quiet is both not patient and not strong.
Everyone who is either not rich or funny is not happy and vice versa.
If someone is calm then someone is not creative.
Everyone who is patient or rich is old or tall and vice versa.
If someone is either not creative or not humble then someone is both not brave and old and vice versa.
Everyone who is not rich or generous is both not creative and rich.
Everyone who is either not rich or patient is either brave or strong and vice versa.
Everyone who is either patient or rich is tall or not old and vice versa.
If someone is either not patient or funny then someone is not generous and vice versa.
Someone is either creative or not patient.
Someone is not kind.
Paul is wise or quiet.
Alice is calm or not old.
Susan is generous or quiet.
Alice is generous or strong.
Lucy is both not generous and humble. | Alice is not brave. | entailment | (![X]:((curious(X)&~patient(X))=>(rich(X)&~wise(X))))&
(![X]:((~funny(X)<~>~quiet(X))=>(creative(X)|~wise(X))))&
(((~happy(alice)&tall(alice)))<=>((~creative(susan)|~wise(susan))))&
(((~kind(paul)&~quiet(paul)))=>(?[X]:((tall(X)&calm(X)))))&
(![X]:((~kind(X)|~quiet(X))=>~humble(X)))&
(((tall(fred)&~rich(fred)))<=>(?[X]:((calm(X)|funny(X)))))&
(![X]:(curious(X)=>(~happy(X)<~>humble(X))))&
(![X]:((tall(X)|quiet(X))=>(~patient(X)&~strong(X))))&
(![X]:((~rich(X)<~>funny(X))<=>~happy(X)))&
((?[X]:(calm(X)))=>(?[X]:(~creative(X))))&
(![X]:((patient(X)|rich(X))<=>(old(X)|tall(X))))&
((?[X]:((~creative(X)<~>~humble(X))))<=>(?[X]:((~brave(X)&old(X)))))&
(![X]:((~rich(X)|generous(X))=>(~creative(X)&rich(X))))&
(![X]:((~rich(X)<~>patient(X))<=>(brave(X)<~>strong(X))))&
(![X]:((patient(X)<~>rich(X))<=>(tall(X)|~old(X))))&
((?[X]:((~patient(X)<~>funny(X))))<=>(?[X]:(~generous(X))))&
(?[X]:((creative(X)<~>~patient(X))))&
(?[X]:(~kind(X)))&
((wise(paul)|quiet(paul)))&
((calm(alice)|~old(alice)))&
((generous(susan)|quiet(susan)))&
((generous(alice)|strong(alice)))&
((~generous(lucy)&humble(lucy))) | ~brave(alice) | [
"p5",
"p7",
"p10",
"p12",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 555105903899400307562411
% SZS output start Proof for 555105903899400307562411
6. (~rich(fred) & tall(fred)) <=> ? [X0] : (funny(X0) | calm(X0)) [input p5]
8. ! [X0] : ((quiet(X0) | tall(X0)) => (~strong(X0) & ~patient(X0))) [input p7]
11. ! [X0] : ((rich(X0) | patient(X0)) <=> (tall(X0) | old(X0))) [input p10]
13. ! [X0] : ((generous(X0) | ~rich(X0)) => (rich(X0) & ~creative(X0))) [input p12]
14. ! [X0] : ((~rich(X0) <~> patient(X0)) <=> (brave(X0) <~> strong(X0))) [input p13]
20. ~old(alice) | calm(alice) [input p19]
24. brave(alice) [input hypothesis]
35. ! [X0] : ((~strong(X0) & ~patient(X0)) | (~quiet(X0) & ~tall(X0))) [ennf transformation 8]
37. ! [X0] : ((rich(X0) & ~creative(X0)) | (~generous(X0) & rich(X0))) [ennf transformation 13]
43. ((~rich(fred) & tall(fred)) | ! [X0] : (~funny(X0) & ~calm(X0))) & (? [X0] : (funny(X0) | calm(X0)) | (rich(fred) | ~tall(fred))) [nnf transformation 6]
44. ((~rich(fred) & tall(fred)) | ! [X0] : (~funny(X0) & ~calm(X0))) & (? [X0] : (funny(X0) | calm(X0)) | rich(fred) | ~tall(fred)) [flattening 43]
45. ((~rich(fred) & tall(fred)) | ! [X0] : (~funny(X0) & ~calm(X0))) & (? [X1] : (funny(X1) | calm(X1)) | rich(fred) | ~tall(fred)) [rectify 44]
46. ? [X1] : (funny(X1) | calm(X1)) => (funny(sK1) | calm(sK1)) [choice axiom]
47. ((~rich(fred) & tall(fred)) | ! [X0] : (~funny(X0) & ~calm(X0))) & ((funny(sK1) | calm(sK1)) | rich(fred) | ~tall(fred)) [skolemisation 45,46]
52. ! [X0] : (((rich(X0) | patient(X0)) | (~tall(X0) & ~old(X0))) & ((tall(X0) | old(X0)) | (~rich(X0) & ~patient(X0)))) [nnf transformation 11]
53. ! [X0] : ((rich(X0) | patient(X0) | (~tall(X0) & ~old(X0))) & (tall(X0) | old(X0) | (~rich(X0) & ~patient(X0)))) [flattening 52]
59. ! [X0] : ((((~patient(X0) | rich(X0)) & (patient(X0) | ~rich(X0))) | ((brave(X0) | ~strong(X0)) & (strong(X0) | ~brave(X0)))) & (((~strong(X0) | ~brave(X0)) & (strong(X0) | brave(X0))) | ((~rich(X0) | ~patient(X0)) & (patient(X0) | rich(X0))))) [nnf transformation 14]
86. ~rich(fred) | ~calm(X0) [cnf transformation 47]
88. ~tall(X0) | ~patient(X0) [cnf transformation 35]
90. ~strong(X0) | ~tall(X0) [cnf transformation 35]
98. ~rich(X0) | old(X0) | tall(X0) [cnf transformation 53]
109. rich(X0) | rich(X0) [cnf transformation 37]
115. patient(X0) | ~rich(X0) | strong(X0) | ~brave(X0) [cnf transformation 59]
133. ~old(alice) | calm(alice) [cnf transformation 20]
138. brave(alice) [cnf transformation 24]
139. rich(X0) [duplicate literal removal 109]
145. 2 <=> tall(alice) [avatar definition]
147. tall(alice) <- (2) [avatar component clause 145]
183. 10 <=> rich(fred) [avatar definition]
185. ~rich(fred) <- (~10) [avatar component clause 183]
188. 11 <=> ! [X0] : ~calm(X0) [avatar definition]
189. ~calm(X0) <- (11) [avatar component clause 188]
190. 11 | ~10 [avatar split clause 86,183,188]
245. ~brave(X0) | strong(X0) | patient(X0) [subsumption resolution 115,139]
290. 32 <=> calm(alice) [avatar definition]
292. calm(alice) <- (32) [avatar component clause 290]
294. 33 <=> old(alice) [avatar definition]
296. ~old(alice) <- (~33) [avatar component clause 294]
297. 32 | ~33 [avatar split clause 133,294,290]
312. 37 <=> strong(alice) [avatar definition]
314. strong(alice) <- (37) [avatar component clause 312]
318. ~patient(alice) <- (2) [resolution 88,147]
338. $false <- (~10) [subsumption resolution 185,139]
339. 10 [avatar contradiction clause 338]
345. old(X0) | tall(X0) [resolution 98,139]
350. tall(alice) <- (~33) [resolution 345,296]
352. strong(alice) | patient(alice) [resolution 245,138]
353. strong(alice) <- (2) [subsumption resolution 352,318]
354. 37 | ~2 [avatar split clause 353,145,312]
357. ~tall(alice) <- (37) [resolution 314,90]
360. ~2 | ~37 [avatar split clause 357,312,145]
361. 2 | 33 [avatar split clause 350,294,145]
362. $false <- (11, 32) [subsumption resolution 292,189]
363. ~11 | ~32 [avatar contradiction clause 362]
364. $false [avatar sat refutation 190,297,339,354,360,361,363]
% SZS output end Proof for 555105903899400307562411
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both not calm and wise then someone is both not strong and not rich. Everyone who is both generous and strong is either not kind or not rich and vice versa. Everyone who is either not brave or rich is calm and vice versa. Everyone who is patient is either patient or old and vice versa. Everyone who is not patient is calm or not wise. Everyone who is not strong is either not calm or not tall. If someone is both not humble and not generous then lucy is strong. If paul is both curious and not wise then lucy is either funny or calm. Everyone who is not patient or calm is not curious and vice versa. Everyone who is either not curious or not quiet is both strong and wise. If mary is both not curious and brave then paul is generous and vice versa. If someone is either quiet or not humble then someone is not wise and vice versa. If john is wise then lucy is humble or not kind. If lucy is either not curious or generous then alice is creative or not patient. If someone is both not creative and not rich then john is humble and vice versa. If someone is either not strong or wise then someone is tall. Lucy is either not tall or patient. Someone is not brave or not creative. Someone is funny or not funny. Someone is either happy or not happy. Someone is not funny. John is not strong. Someone is both not quiet and curious. John is both not kind and wise. | Mary is old. | contradiction | (((~calm(mary)&wise(mary)))=>(?[X]:((~strong(X)&~rich(X)))))&
(![X]:((generous(X)&strong(X))<=>(~kind(X)<~>~rich(X))))&
(![X]:((~brave(X)<~>rich(X))<=>calm(X)))&
(![X]:(patient(X)<=>(patient(X)<~>old(X))))&
(![X]:(~patient(X)=>(calm(X)|~wise(X))))&
(![X]:(~strong(X)=>(~calm(X)<~>~tall(X))))&
((?[X]:((~humble(X)&~generous(X))))=>(strong(lucy)))&
(((curious(paul)&~wise(paul)))=>((funny(lucy)<~>calm(lucy))))&
(![X]:((~patient(X)|calm(X))<=>~curious(X)))&
(![X]:((~curious(X)<~>~quiet(X))=>(strong(X)&wise(X))))&
(((~curious(mary)&brave(mary)))<=>(generous(paul)))&
((?[X]:((quiet(X)<~>~humble(X))))<=>(?[X]:(~wise(X))))&
((wise(john))=>((humble(lucy)|~kind(lucy))))&
(((~curious(lucy)<~>generous(lucy)))=>((creative(alice)|~patient(alice))))&
((?[X]:((~creative(X)&~rich(X))))<=>(humble(john)))&
((?[X]:((~strong(X)<~>wise(X))))=>(?[X]:(tall(X))))&
((~tall(lucy)<~>patient(lucy)))&
(?[X]:((~brave(X)|~creative(X))))&
(?[X]:((funny(X)|~funny(X))))&
(?[X]:((happy(X)<~>~happy(X))))&
(?[X]:(~funny(X)))&
(~strong(john))&
(?[X]:((~quiet(X)&curious(X))))&
((~kind(john)&wise(john))) | old(mary) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 1514910372715445396211230
% SZS output start Proof for 1514910372715445396211230
4. ! [X0] : (patient(X0) <=> (patient(X0) <~> old(X0))) [input p3]
25. old(mary) [input hypothesis]
47. ! [X0] : ((patient(X0) | ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0)))) & (((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | ~patient(X0))) [nnf transformation 4]
94. ~old(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 47]
96. patient(X0) | patient(X0) | ~old(X0) [cnf transformation 47]
137. old(mary) [cnf transformation 25]
138. ~old(X0) | ~patient(X0) [duplicate literal removal 94]
139. patient(X0) | ~old(X0) [duplicate literal removal 96]
158. ~old(X0) [subsumption resolution 138,139]
306. $false [subsumption resolution 137,158]
% SZS output end Proof for 1514910372715445396211230
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or creative is either not creative or wise.
Everyone who is old or rich is not calm or happy.
Everyone who is not patient or not kind is old or patient and vice versa.
If alice is not strong or patient then someone is not creative or humble.
Everyone who is kind or not kind is either not patient or funny.
Everyone who is creative is both not patient and humble.
Everyone who is not wise or happy is brave.
If someone is either brave or not generous then lucy is both rich and not funny.
If someone is generous or old then mary is either not rich or strong and vice versa.
If mary is brave then john is rich and vice versa.
If susan is either happy or old then lucy is either not wise or kind and vice versa.
If someone is either not wise or tall then someone is both not curious and not strong.
If someone is both not rich and rich then someone is both happy and not old and vice versa.
Everyone who is either not brave or happy is generous.
Everyone who is both generous and funny is not generous.
Someone is old.
Someone is either patient or not rich.
Someone is either not funny or not happy.
Someone is both calm and creative.
Someone is not brave or not creative.
Susan is happy.
Mary is both not quiet and brave.
Someone is not brave or not curious. | Susan is patient. | contradiction | (![X]:((~kind(X)|creative(X))=>(~creative(X)<~>wise(X))))&
(![X]:((old(X)|rich(X))=>(~calm(X)|happy(X))))&
(![X]:((~patient(X)|~kind(X))<=>(old(X)|patient(X))))&
(((~strong(alice)|patient(alice)))=>(?[X]:((~creative(X)|humble(X)))))&
(![X]:((kind(X)|~kind(X))=>(~patient(X)<~>funny(X))))&
(![X]:(creative(X)=>(~patient(X)&humble(X))))&
(![X]:((~wise(X)|happy(X))=>brave(X)))&
((?[X]:((brave(X)<~>~generous(X))))=>((rich(lucy)&~funny(lucy))))&
((?[X]:((generous(X)|old(X))))<=>((~rich(mary)<~>strong(mary))))&
((brave(mary))<=>(rich(john)))&
(((happy(susan)<~>old(susan)))<=>((~wise(lucy)<~>kind(lucy))))&
((?[X]:((~wise(X)<~>tall(X))))=>(?[X]:((~curious(X)&~strong(X)))))&
((?[X]:((~rich(X)&rich(X))))<=>(?[X]:((happy(X)&~old(X)))))&
(![X]:((~brave(X)<~>happy(X))=>generous(X)))&
(![X]:((generous(X)&funny(X))=>~generous(X)))&
(?[X]:(old(X)))&
(?[X]:((patient(X)<~>~rich(X))))&
(?[X]:((~funny(X)<~>~happy(X))))&
(?[X]:((calm(X)&creative(X))))&
(?[X]:((~brave(X)|~creative(X))))&
(happy(susan))&
((~quiet(mary)&brave(mary)))&
(?[X]:((~brave(X)|~curious(X)))) | patient(susan) | [
"p2",
"p4",
"p6",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5270993673038304460122383
% SZS output start Proof for 5270993673038304460122383
3. ! [X0] : ((~kind(X0) | ~patient(X0)) <=> (patient(X0) | old(X0))) [input p2]
5. ! [X0] : ((~kind(X0) | kind(X0)) => (~patient(X0) <~> funny(X0))) [input p4]
7. ! [X0] : ((happy(X0) | ~wise(X0)) => brave(X0)) [input p6]
14. ! [X0] : ((~brave(X0) <~> happy(X0)) => generous(X0)) [input p13]
15. ! [X0] : ((funny(X0) & generous(X0)) => ~generous(X0)) [input p14]
21. happy(susan) [input p20]
24. patient(susan) [input hypothesis]
35. ! [X0] : ((~patient(X0) <~> funny(X0)) | (kind(X0) & ~kind(X0))) [ennf transformation 5]
37. ! [X0] : (brave(X0) | (~happy(X0) & wise(X0))) [ennf transformation 7]
40. ! [X0] : (generous(X0) | (~brave(X0) <=> happy(X0))) [ennf transformation 14]
41. ! [X0] : (~generous(X0) | (~funny(X0) | ~generous(X0))) [ennf transformation 15]
42. ! [X0] : (~generous(X0) | ~funny(X0) | ~generous(X0)) [flattening 41]
44. ! [X0] : (((~kind(X0) | ~patient(X0)) | (~patient(X0) & ~old(X0))) & ((patient(X0) | old(X0)) | (kind(X0) & patient(X0)))) [nnf transformation 3]
45. ! [X0] : ((~kind(X0) | ~patient(X0) | (~patient(X0) & ~old(X0))) & (patient(X0) | old(X0) | (kind(X0) & patient(X0)))) [flattening 44]
46. ! [X0] : (((~funny(X0) | patient(X0)) & (funny(X0) | ~patient(X0))) | (kind(X0) & ~kind(X0))) [nnf transformation 35]
63. ! [X0] : (generous(X0) | ((~brave(X0) | ~happy(X0)) & (happy(X0) | brave(X0)))) [nnf transformation 40]
85. ~kind(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 45]
87. funny(X0) | ~patient(X0) | kind(X0) [cnf transformation 46]
92. ~happy(X0) | brave(X0) [cnf transformation 37]
120. generous(X0) | ~brave(X0) | ~happy(X0) [cnf transformation 63]
121. ~generous(X0) | ~funny(X0) | ~generous(X0) [cnf transformation 42]
130. happy(susan) [cnf transformation 21]
132. patient(susan) [cnf transformation 24]
133. ~generous(X0) | ~funny(X0) [duplicate literal removal 121]
135. ~patient(X0) | ~kind(X0) [duplicate literal removal 85]
138. ~patient(X0) | funny(X0) [subsumption resolution 87,135]
204. 15 <=> happy(susan) [avatar definition]
205. happy(susan) <- (15) [avatar component clause 204]
240. ~happy(X0) | generous(X0) [subsumption resolution 120,92]
272. 15 [avatar split clause 130,204]
286. funny(susan) [resolution 138,132]
298. generous(susan) <- (15) [resolution 240,205]
300. ~funny(susan) <- (15) [resolution 298,133]
303. $false <- (15) [subsumption resolution 300,286]
304. ~15 [avatar contradiction clause 303]
305. $false [avatar sat refutation 272,304]
% SZS output end Proof for 5270993673038304460122383
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not funny or not humble is not old or not humble.
If susan is both curious and not strong then someone is humble.
Everyone who is both wise and happy is not rich or not quiet and vice versa.
If someone is old then someone is both not tall and humble.
If lucy is either old or not brave then someone is either not strong or not calm and vice versa.
Everyone who is humble is funny and vice versa.
If someone is curious then someone is either not happy or humble.
Everyone who is not wise or not tall is both not wise and humble and vice versa.
Everyone who is both tall and not strong is both calm and not creative.
Everyone who is both brave and not tall is both funny and not rich and vice versa.
Everyone who is both not wise and calm is kind or tall.
If mary is either creative or not humble then someone is kind or calm and vice versa.
Everyone who is both not creative and tall is either not rich or not creative.
Everyone who is creative or not rich is not old or creative and vice versa.
If someone is not calm or not quiet then john is not calm or not happy and vice versa.
Everyone who is quiet is not happy.
Alice is both not brave and not funny.
Mary is not rich.
Someone is not creative.
Susan is either not old or wise.
Someone is not humble or rich.
Fred is quiet.
Someone is either not funny or happy.
Lucy is both not curious and not strong. | Alice is kind. | contradiction | (![X]:((~funny(X)<~>~humble(X))=>(~old(X)|~humble(X))))&
(((curious(susan)&~strong(susan)))=>(?[X]:(humble(X))))&
(![X]:((wise(X)&happy(X))<=>(~rich(X)|~quiet(X))))&
((?[X]:(old(X)))=>(?[X]:((~tall(X)&humble(X)))))&
(((old(lucy)<~>~brave(lucy)))<=>(?[X]:((~strong(X)<~>~calm(X)))))&
(![X]:(humble(X)<=>funny(X)))&
((?[X]:(curious(X)))=>(?[X]:((~happy(X)<~>humble(X)))))&
(![X]:((~wise(X)|~tall(X))<=>(~wise(X)&humble(X))))&
(![X]:((tall(X)&~strong(X))=>(calm(X)&~creative(X))))&
(![X]:((brave(X)&~tall(X))<=>(funny(X)&~rich(X))))&
(![X]:((~wise(X)&calm(X))=>(kind(X)|tall(X))))&
(((creative(mary)<~>~humble(mary)))<=>(?[X]:((kind(X)|calm(X)))))&
(![X]:((~creative(X)&tall(X))=>(~rich(X)<~>~creative(X))))&
(![X]:((creative(X)|~rich(X))<=>(~old(X)|creative(X))))&
((?[X]:((~calm(X)|~quiet(X))))<=>((~calm(john)|~happy(john))))&
(![X]:(quiet(X)=>~happy(X)))&
((~brave(alice)&~funny(alice)))&
(~rich(mary))&
(?[X]:(~creative(X)))&
((~old(susan)<~>wise(susan)))&
(?[X]:((~humble(X)|rich(X))))&
(quiet(fred))&
(?[X]:((~funny(X)<~>happy(X))))&
((~curious(lucy)&~strong(lucy))) | kind(alice) | [
"p2",
"p5",
"p7",
"p9",
"p11",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 851092952640160265091253
% SZS output start Proof for 851092952640160265091253
3. ! [X0] : ((happy(X0) & wise(X0)) <=> (~quiet(X0) | ~rich(X0))) [input p2]
6. ! [X0] : (humble(X0) <=> funny(X0)) [input p5]
8. ! [X0] : ((~tall(X0) | ~wise(X0)) <=> (humble(X0) & ~wise(X0))) [input p7]
10. ! [X0] : ((~tall(X0) & brave(X0)) <=> (~rich(X0) & funny(X0))) [input p9]
12. (creative(mary) <~> ~humble(mary)) <=> ? [X0] : (calm(X0) | kind(X0)) [input p11]
13. ! [X0] : ((tall(X0) & ~creative(X0)) => (~rich(X0) <~> ~creative(X0))) [input p12]
18. ~rich(mary) [input p17]
25. kind(alice) [input hypothesis]
38. ! [X0] : ((~rich(X0) <~> ~creative(X0)) | (~tall(X0) | creative(X0))) [ennf transformation 13]
39. ! [X0] : ((~rich(X0) <~> ~creative(X0)) | ~tall(X0) | creative(X0)) [flattening 38]
42. ! [X0] : (((happy(X0) & wise(X0)) | (quiet(X0) & rich(X0))) & ((~quiet(X0) | ~rich(X0)) | (~happy(X0) | ~wise(X0)))) [nnf transformation 3]
43. ! [X0] : (((happy(X0) & wise(X0)) | (quiet(X0) & rich(X0))) & (~quiet(X0) | ~rich(X0) | ~happy(X0) | ~wise(X0))) [flattening 42]
51. ! [X0] : ((humble(X0) | ~funny(X0)) & (funny(X0) | ~humble(X0))) [nnf transformation 6]
52. ! [X0] : (((~tall(X0) | ~wise(X0)) | (~humble(X0) | wise(X0))) & ((humble(X0) & ~wise(X0)) | (tall(X0) & wise(X0)))) [nnf transformation 8]
53. ! [X0] : ((~tall(X0) | ~wise(X0) | ~humble(X0) | wise(X0)) & ((humble(X0) & ~wise(X0)) | (tall(X0) & wise(X0)))) [flattening 52]
54. ! [X0] : (((~tall(X0) & brave(X0)) | (rich(X0) | ~funny(X0))) & ((~rich(X0) & funny(X0)) | (tall(X0) | ~brave(X0)))) [nnf transformation 10]
55. ! [X0] : (((~tall(X0) & brave(X0)) | rich(X0) | ~funny(X0)) & ((~rich(X0) & funny(X0)) | tall(X0) | ~brave(X0))) [flattening 54]
56. (((humble(mary) | ~creative(mary)) & (~humble(mary) | creative(mary))) | ! [X0] : (~calm(X0) & ~kind(X0))) & (? [X0] : (calm(X0) | kind(X0)) | ((creative(mary) | humble(mary)) & (~humble(mary) | ~creative(mary)))) [nnf transformation 12]
57. (((humble(mary) | ~creative(mary)) & (~humble(mary) | creative(mary))) | ! [X0] : (~calm(X0) & ~kind(X0))) & (? [X1] : (calm(X1) | kind(X1)) | ((creative(mary) | humble(mary)) & (~humble(mary) | ~creative(mary)))) [rectify 56]
58. ? [X1] : (calm(X1) | kind(X1)) => (calm(sK2) | kind(sK2)) [choice axiom]
59. (((humble(mary) | ~creative(mary)) & (~humble(mary) | creative(mary))) | ! [X0] : (~calm(X0) & ~kind(X0))) & ((calm(sK2) | kind(sK2)) | ((creative(mary) | humble(mary)) & (~humble(mary) | ~creative(mary)))) [skolemisation 57,58]
60. ! [X0] : (((creative(X0) | rich(X0)) & (~creative(X0) | ~rich(X0))) | ~tall(X0) | creative(X0)) [nnf transformation 39]
79. rich(X0) | wise(X0) [cnf transformation 43]
93. ~humble(X0) | funny(X0) [cnf transformation 51]
96. ~wise(X0) | tall(X0) [cnf transformation 53]
105. ~tall(X0) | rich(X0) | ~funny(X0) [cnf transformation 55]
111. humble(mary) | ~creative(mary) | ~kind(X0) [cnf transformation 59]
114. creative(X0) | rich(X0) | ~tall(X0) | creative(X0) [cnf transformation 60]
126. ~rich(mary) [cnf transformation 18]
135. kind(alice) [cnf transformation 25]
136. ~tall(X0) | rich(X0) | creative(X0) [duplicate literal removal 114]
186. 11 <=> creative(mary) [avatar definition]
190. 12 <=> humble(mary) [avatar definition]
192. humble(mary) <- (12) [avatar component clause 190]
195. 13 <=> ! [X0] : ~kind(X0) [avatar definition]
196. ~kind(X0) <- (13) [avatar component clause 195]
197. 13 | ~11 | 12 [avatar split clause 111,190,186,195]
266. $false <- (13) [resolution 196,135]
267. ~13 [avatar contradiction clause 266]
270. wise(mary) [resolution 79,126]
274. tall(mary) [resolution 96,270]
333. rich(mary) | ~funny(mary) [resolution 105,274]
335. ~funny(mary) [subsumption resolution 333,126]
345. rich(mary) | creative(mary) [resolution 136,274]
347. creative(mary) [subsumption resolution 345,126]
350. 11 [avatar split clause 347,186]
352. funny(mary) <- (12) [resolution 192,93]
353. $false <- (12) [subsumption resolution 352,335]
354. ~12 [avatar contradiction clause 353]
355. $false [avatar sat refutation 197,267,350,354]
% SZS output end Proof for 851092952640160265091253
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or not happy is either wise or rich. Everyone who is either not creative or not rich is not humble and vice versa. If someone is not patient then susan is not patient. If fred is both generous and not strong then someone is not rich or not patient. If someone is not old then lucy is not rich and vice versa. Everyone who is not tall is curious or not generous. If someone is either patient or not rich then someone is either brave or creative. Everyone who is not calm is kind. If lucy is both tall and patient then susan is not curious or humble and vice versa. Everyone who is both not kind and strong is both curious and not patient and vice versa. Everyone who is patient or not humble is both not wise and not strong and vice versa. Everyone who is kind is both generous and rich and vice versa. If someone is generous then someone is not rich or not humble and vice versa. If alice is both not generous and not funny then lucy is tall and vice versa. If someone is not quiet or old then someone is old. If susan is either not humble or calm then someone is both not funny and happy and vice versa. Someone is either not generous or happy. Someone is tall or kind. John is both not strong and old. Someone is either not kind or tall. Mary is quiet or calm. Someone is both not curious and creative. John is either kind or not quiet. | Susan is not patient. | neutral | (![X]:((~wise(X)|~happy(X))=>(wise(X)<~>rich(X))))&
(![X]:((~creative(X)<~>~rich(X))<=>~humble(X)))&
((?[X]:(~patient(X)))=>(~patient(susan)))&
(((generous(fred)&~strong(fred)))=>(?[X]:((~rich(X)|~patient(X)))))&
((?[X]:(~old(X)))<=>(~rich(lucy)))&
(![X]:(~tall(X)=>(curious(X)|~generous(X))))&
((?[X]:((patient(X)<~>~rich(X))))=>(?[X]:((brave(X)<~>creative(X)))))&
(![X]:(~calm(X)=>kind(X)))&
(((tall(lucy)&patient(lucy)))<=>((~curious(susan)|humble(susan))))&
(![X]:((~kind(X)&strong(X))<=>(curious(X)&~patient(X))))&
(![X]:((patient(X)|~humble(X))<=>(~wise(X)&~strong(X))))&
(![X]:(kind(X)<=>(generous(X)&rich(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~rich(X)|~humble(X)))))&
(((~generous(alice)&~funny(alice)))<=>(tall(lucy)))&
((?[X]:((~quiet(X)|old(X))))=>(?[X]:(old(X))))&
(((~humble(susan)<~>calm(susan)))<=>(?[X]:((~funny(X)&happy(X)))))&
(?[X]:((~generous(X)<~>happy(X))))&
(?[X]:((tall(X)|kind(X))))&
((~strong(john)&old(john)))&
(?[X]:((~kind(X)<~>tall(X))))&
((quiet(mary)|calm(mary)))&
(?[X]:((~curious(X)&creative(X))))&
((kind(john)<~>~quiet(john))) | ~patient(susan) | [] | null | 0 |
Everyone who is both quiet and happy is either not wise or not creative and vice versa.
Everyone who is quiet is either not patient or not happy and vice versa.
Everyone who is quiet or not curious is not wise.
Everyone who is either not wise or not kind is both funny and not kind.
If someone is not curious then someone is not old and vice versa.
Everyone who is both not humble and quiet is either happy or not calm and vice versa.
Everyone who is not patient is funny or humble.
Everyone who is strong or calm is not creative.
If someone is rich or not curious then paul is either generous or not patient.
If paul is both not humble and not tall then someone is either humble or rich and vice versa.
If someone is both not rich and not generous then paul is patient or not rich and vice versa.
Everyone who is both patient and not kind is both not strong and curious and vice versa.
Everyone who is both happy and not humble is either not happy or not kind and vice versa.
If someone is not calm or calm then fred is both old and not creative and vice versa.
Everyone who is both not patient and funny is both curious and strong and vice versa.
Everyone who is not funny is both funny and not brave.
Someone is strong or patient.
Paul is not happy.
Someone is both happy and not tall.
Someone is both brave and not wise.
Someone is either not humble or not funny.
Someone is either not strong or not patient.
John is both not strong and funny.
Someone is either not humble or generous. | John is not humble. | neutral | (![X]:((quiet(X)&happy(X))<=>(~wise(X)<~>~creative(X))))&
(![X]:(quiet(X)<=>(~patient(X)<~>~happy(X))))&
(![X]:((quiet(X)|~curious(X))=>~wise(X)))&
(![X]:((~wise(X)<~>~kind(X))=>(funny(X)&~kind(X))))&
((?[X]:(~curious(X)))<=>(?[X]:(~old(X))))&
(![X]:((~humble(X)&quiet(X))<=>(happy(X)<~>~calm(X))))&
(![X]:(~patient(X)=>(funny(X)|humble(X))))&
(![X]:((strong(X)|calm(X))=>~creative(X)))&
((?[X]:((rich(X)|~curious(X))))=>((generous(paul)<~>~patient(paul))))&
(((~humble(paul)&~tall(paul)))<=>(?[X]:((humble(X)<~>rich(X)))))&
((?[X]:((~rich(X)&~generous(X))))<=>((patient(paul)|~rich(paul))))&
(![X]:((patient(X)&~kind(X))<=>(~strong(X)&curious(X))))&
(![X]:((happy(X)&~humble(X))<=>(~happy(X)<~>~kind(X))))&
((?[X]:((~calm(X)|calm(X))))<=>((old(fred)&~creative(fred))))&
(![X]:((~patient(X)&funny(X))<=>(curious(X)&strong(X))))&
(![X]:(~funny(X)=>(funny(X)&~brave(X))))&
(?[X]:((strong(X)|patient(X))))&
(~happy(paul))&
(?[X]:((happy(X)&~tall(X))))&
(?[X]:((brave(X)&~wise(X))))&
(?[X]:((~humble(X)<~>~funny(X))))&
(?[X]:((~strong(X)<~>~patient(X))))&
((~strong(john)&funny(john)))&
(?[X]:((~humble(X)<~>generous(X)))) | ~humble(john) | [] | null | 0 |
Everyone who is either wise or rich is either not rich or quiet. Everyone who is not curious or patient is both humble and not creative. If fred is not tall or not kind then lucy is curious or not strong. Everyone who is either quiet or old is not old and vice versa. If someone is strong then someone is not quiet and vice versa. If alice is not funny then someone is generous or not quiet. Everyone who is not tall or strong is either not kind or humble and vice versa. Everyone who is brave is either old or not old and vice versa. If someone is not rich then alice is either not funny or wise. If paul is both not generous and not quiet then fred is generous and vice versa. Everyone who is either not rich or wise is both not kind and not tall. If someone is either humble or creative then someone is either quiet or kind and vice versa. Everyone who is both calm and curious is both funny and strong and vice versa. Everyone who is either funny or happy is calm and vice versa. Everyone who is funny is both not quiet and humble and vice versa. If someone is happy or not patient then someone is either not happy or funny. Lucy is not wise or not strong. Someone is both not calm and generous. Lucy is brave. Alice is not creative or curious. Someone is both not calm and curious. Mary is quiet. Fred is either curious or calm. Someone is rich or tall. | Paul is not brave. | contradiction | (![X]:((wise(X)<~>rich(X))=>(~rich(X)<~>quiet(X))))&
(![X]:((~curious(X)|patient(X))=>(humble(X)&~creative(X))))&
(((~tall(fred)|~kind(fred)))=>((curious(lucy)|~strong(lucy))))&
(![X]:((quiet(X)<~>old(X))<=>~old(X)))&
((?[X]:(strong(X)))<=>(?[X]:(~quiet(X))))&
((~funny(alice))=>(?[X]:((generous(X)|~quiet(X)))))&
(![X]:((~tall(X)|strong(X))<=>(~kind(X)<~>humble(X))))&
(![X]:(brave(X)<=>(old(X)<~>~old(X))))&
((?[X]:(~rich(X)))=>((~funny(alice)<~>wise(alice))))&
(((~generous(paul)&~quiet(paul)))<=>(generous(fred)))&
(![X]:((~rich(X)<~>wise(X))=>(~kind(X)&~tall(X))))&
((?[X]:((humble(X)<~>creative(X))))<=>(?[X]:((quiet(X)<~>kind(X)))))&
(![X]:((calm(X)&curious(X))<=>(funny(X)&strong(X))))&
(![X]:((funny(X)<~>happy(X))<=>calm(X)))&
(![X]:(funny(X)<=>(~quiet(X)&humble(X))))&
((?[X]:((happy(X)|~patient(X))))=>(?[X]:((~happy(X)<~>funny(X)))))&
((~wise(lucy)|~strong(lucy)))&
(?[X]:((~calm(X)&generous(X))))&
(brave(lucy))&
((~creative(alice)|curious(alice)))&
(?[X]:((~calm(X)&curious(X))))&
(quiet(mary))&
((curious(fred)<~>calm(fred)))&
(?[X]:((rich(X)|tall(X)))) | ~brave(paul) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8972615077174028972899971
% SZS output start Proof for 8972615077174028972899971
8. ! [X0] : (brave(X0) <=> (old(X0) <~> ~old(X0))) [input p7]
25. ~brave(paul) [input hypothesis]
48. ! [X0] : ((brave(X0) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0)))) & (((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) | ~brave(X0))) [nnf transformation 8]
99. brave(X0) | ~old(X0) | ~old(X0) [cnf transformation 48]
100. brave(X0) | old(X0) | old(X0) [cnf transformation 48]
144. ~brave(paul) [cnf transformation 25]
145. brave(X0) | ~old(X0) [duplicate literal removal 99]
146. brave(X0) | old(X0) [duplicate literal removal 100]
183. brave(X0) [subsumption resolution 145,146]
257. $false [subsumption resolution 144,183]
% SZS output end Proof for 8972615077174028972899971
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is either curious or not creative.
Everyone who is not old or not tall is funny.
Everyone who is not kind is either not wise or calm and vice versa.
Everyone who is either calm or wise is not kind or kind.
Everyone who is rich or creative is not humble and vice versa.
Everyone who is either happy or brave is funny or calm.
Everyone who is either not humble or not funny is creative or not patient.
If someone is either quiet or not old then someone is not calm.
Everyone who is either not generous or quiet is either not old or funny.
If someone is calm then someone is either tall or not calm and vice versa.
Everyone who is either not strong or not calm is both old and rich and vice versa.
Everyone who is both curious and patient is not wise or calm and vice versa.
If mary is both old and creative then lucy is both not humble and not quiet and vice versa.
If someone is not patient or humble then someone is quiet and vice versa.
If alice is both not quiet and strong then alice is not old.
Everyone who is both tall and not wise is not quiet and vice versa.
Someone is either not calm or not humble.
Someone is both not tall and wise.
Someone is creative or not creative.
Someone is patient or humble.
Someone is curious or not strong.
Someone is both quiet and not happy.
Lucy is both not kind and funny.
Someone is both quiet and rich. | Lucy is not patient. | contradiction | (![X]:(tall(X)=>(curious(X)<~>~creative(X))))&
(![X]:((~old(X)|~tall(X))=>funny(X)))&
(![X]:(~kind(X)<=>(~wise(X)<~>calm(X))))&
(![X]:((calm(X)<~>wise(X))=>(~kind(X)|kind(X))))&
(![X]:((rich(X)|creative(X))<=>~humble(X)))&
(![X]:((happy(X)<~>brave(X))=>(funny(X)|calm(X))))&
(![X]:((~humble(X)<~>~funny(X))=>(creative(X)|~patient(X))))&
((?[X]:((quiet(X)<~>~old(X))))=>(?[X]:(~calm(X))))&
(![X]:((~generous(X)<~>quiet(X))=>(~old(X)<~>funny(X))))&
((?[X]:(calm(X)))<=>(?[X]:((tall(X)<~>~calm(X)))))&
(![X]:((~strong(X)<~>~calm(X))<=>(old(X)&rich(X))))&
(![X]:((curious(X)&patient(X))<=>(~wise(X)|calm(X))))&
(((old(mary)&creative(mary)))<=>((~humble(lucy)&~quiet(lucy))))&
((?[X]:((~patient(X)|humble(X))))<=>(?[X]:(quiet(X))))&
(((~quiet(alice)&strong(alice)))=>(~old(alice)))&
(![X]:((tall(X)&~wise(X))<=>~quiet(X)))&
(?[X]:((~calm(X)<~>~humble(X))))&
(?[X]:((~tall(X)&wise(X))))&
(?[X]:((creative(X)|~creative(X))))&
(?[X]:((patient(X)|humble(X))))&
(?[X]:((curious(X)|~strong(X))))&
(?[X]:((quiet(X)&~happy(X))))&
((~kind(lucy)&funny(lucy)))&
(?[X]:((quiet(X)&rich(X)))) | ~patient(lucy) | [
"p2",
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5930832776048686617387473
% SZS output start Proof for 5930832776048686617387473
3. ! [X0] : (~kind(X0) <=> (~wise(X0) <~> calm(X0))) [input p2]
12. ! [X0] : ((patient(X0) & curious(X0)) <=> (calm(X0) | ~wise(X0))) [input p11]
23. funny(lucy) & ~kind(lucy) [input p22]
25. ~patient(lucy) [input hypothesis]
42. ! [X0] : ((~kind(X0) | ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0)))) & (((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | kind(X0))) [nnf transformation 3]
60. ! [X0] : (((patient(X0) & curious(X0)) | (~calm(X0) & wise(X0))) & ((calm(X0) | ~wise(X0)) | (~patient(X0) | ~curious(X0)))) [nnf transformation 12]
61. ! [X0] : (((patient(X0) & curious(X0)) | (~calm(X0) & wise(X0))) & (calm(X0) | ~wise(X0) | ~patient(X0) | ~curious(X0))) [flattening 60]
90. ~wise(X0) | calm(X0) | kind(X0) [cnf transformation 42]
122. patient(X0) | wise(X0) [cnf transformation 61]
123. ~calm(X0) | patient(X0) [cnf transformation 61]
144. ~kind(lucy) [cnf transformation 23]
148. ~patient(lucy) [cnf transformation 25]
280. wise(lucy) [resolution 122,148]
310. calm(lucy) | kind(lucy) [resolution 90,280]
314. calm(lucy) [subsumption resolution 310,144]
592. patient(lucy) [resolution 314,123]
605. $false [subsumption resolution 592,148]
% SZS output end Proof for 5930832776048686617387473
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is quiet or not creative and vice versa.
Everyone who is not humble is both funny and rich.
If someone is either humble or not curious then alice is both not humble and not curious and vice versa.
If someone is both not humble and not kind then john is not old or rich and vice versa.
Everyone who is rich is wise or not patient.
Everyone who is either patient or not patient is not generous or not wise and vice versa.
If susan is both not generous and not calm then fred is both rich and not wise.
Everyone who is not wise is rich or old and vice versa.
If lucy is not humble or not rich then someone is not quiet and vice versa.
Everyone who is both not rich and not kind is happy or rich and vice versa.
If someone is either not patient or old then lucy is not strong or humble.
If paul is not calm or brave then someone is both not old and not rich and vice versa.
Everyone who is brave or not wise is humble and vice versa.
Everyone who is not quiet or humble is both creative and not tall.
Everyone who is either not creative or generous is humble or not generous and vice versa.
Everyone who is either not funny or not quiet is either not old or curious.
Someone is not wise or calm.
Someone is either funny or not humble.
Mary is kind.
Someone is both happy and not patient.
Someone is creative or funny. | John is generous. | entailment | (![X]:(calm(X)<=>(quiet(X)|~creative(X))))&
(![X]:(~humble(X)=>(funny(X)&rich(X))))&
((?[X]:((humble(X)<~>~curious(X))))<=>((~humble(alice)&~curious(alice))))&
((?[X]:((~humble(X)&~kind(X))))<=>((~old(john)|rich(john))))&
(![X]:(rich(X)=>(wise(X)|~patient(X))))&
(![X]:((patient(X)<~>~patient(X))<=>(~generous(X)|~wise(X))))&
(((~generous(susan)&~calm(susan)))=>((rich(fred)&~wise(fred))))&
(![X]:(~wise(X)<=>(rich(X)|old(X))))&
(((~humble(lucy)|~rich(lucy)))<=>(?[X]:(~quiet(X))))&
(![X]:((~rich(X)&~kind(X))<=>(happy(X)|rich(X))))&
((?[X]:((~patient(X)<~>old(X))))=>((~strong(lucy)|humble(lucy))))&
(((~calm(paul)|brave(paul)))<=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:((brave(X)|~wise(X))<=>humble(X)))&
(![X]:((~quiet(X)|humble(X))=>(creative(X)&~tall(X))))&
(![X]:((~creative(X)<~>generous(X))<=>(humble(X)|~generous(X))))&
(![X]:((~funny(X)<~>~quiet(X))=>(~old(X)<~>curious(X))))&
(?[X]:((~wise(X)|calm(X))))&
(?[X]:((funny(X)<~>~humble(X))))&
(kind(mary))&
(?[X]:((happy(X)&~patient(X))))&
(?[X]:((creative(X)|funny(X)))) | generous(john) | [
"p1",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5436637538859863622399039
% SZS output start Proof for 5436637538859863622399039
2. ! [X0] : (~humble(X0) => (rich(X0) & funny(X0))) [input p1]
10. ! [X0] : ((~kind(X0) & ~rich(X0)) <=> (rich(X0) | happy(X0))) [input p9]
14. ! [X0] : ((humble(X0) | ~quiet(X0)) => (~tall(X0) & creative(X0))) [input p13]
15. ! [X0] : ((~creative(X0) <~> generous(X0)) <=> (~generous(X0) | humble(X0))) [input p14]
22. ~generous(john) [input hypothesis]
23. ! [X0] : ((humble(X0) | ~quiet(X0)) => creative(X0)) [pure predicate removal 14]
25. ! [X0] : ((rich(X0) & funny(X0)) | humble(X0)) [ennf transformation 2]
30. ! [X0] : (creative(X0) | (~humble(X0) & quiet(X0))) [ennf transformation 23]
53. ! [X0] : (((~kind(X0) & ~rich(X0)) | (~rich(X0) & ~happy(X0))) & ((rich(X0) | happy(X0)) | (kind(X0) | rich(X0)))) [nnf transformation 10]
54. ! [X0] : (((~kind(X0) & ~rich(X0)) | (~rich(X0) & ~happy(X0))) & (rich(X0) | happy(X0) | kind(X0) | rich(X0))) [flattening 53]
62. ! [X0] : ((((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | (generous(X0) & ~humble(X0))) & ((~generous(X0) | humble(X0)) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0))))) [nnf transformation 15]
63. ! [X0] : ((((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | (generous(X0) & ~humble(X0))) & (~generous(X0) | humble(X0) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0))))) [flattening 62]
78. rich(X0) | humble(X0) [cnf transformation 25]
107. ~rich(X0) | ~rich(X0) [cnf transformation 54]
119. ~humble(X0) | creative(X0) [cnf transformation 30]
123. generous(X0) | ~creative(X0) | generous(X0) [cnf transformation 63]
137. ~generous(john) [cnf transformation 22]
139. ~creative(X0) | generous(X0) [duplicate literal removal 123]
141. ~rich(X0) [duplicate literal removal 107]
274. humble(X0) [resolution 78,141]
288. creative(X0) [resolution 119,274]
297. generous(X0) [resolution 288,139]
335. $false [resolution 297,137]
% SZS output end Proof for 5436637538859863622399039
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not curious is generous and vice versa.
Everyone who is not kind is not quiet or not humble and vice versa.
Everyone who is both generous and happy is both kind and not kind and vice versa.
Everyone who is happy or tall is both wise and curious and vice versa.
Everyone who is not creative or wise is either humble or wise and vice versa.
If mary is either calm or curious then someone is strong.
If mary is either not patient or wise then someone is not kind.
If someone is strong then alice is both not old and strong.
If someone is both quiet and not tall then john is either funny or rich and vice versa.
If alice is not creative or patient then fred is not strong and vice versa.
Everyone who is rich or not calm is rich or curious.
Everyone who is both patient and not creative is either rich or not funny.
Everyone who is either not creative or not quiet is happy and vice versa.
If alice is either not patient or wise then paul is not creative.
If paul is quiet or strong then mary is either not old or not funny.
If paul is either not happy or not rich then someone is rich or not patient and vice versa.
Paul is not rich.
Someone is strong.
Alice is tall or not patient.
Someone is either funny or not happy.
Someone is either not old or calm.
Lucy is either not strong or not calm.
Someone is both not old and not creative.
Mary is quiet. | Alice is not kind. | entailment | (![X]:((~kind(X)<~>~curious(X))<=>generous(X)))&
(![X]:(~kind(X)<=>(~quiet(X)|~humble(X))))&
(![X]:((generous(X)&happy(X))<=>(kind(X)&~kind(X))))&
(![X]:((happy(X)|tall(X))<=>(wise(X)&curious(X))))&
(![X]:((~creative(X)|wise(X))<=>(humble(X)<~>wise(X))))&
(((calm(mary)<~>curious(mary)))=>(?[X]:(strong(X))))&
(((~patient(mary)<~>wise(mary)))=>(?[X]:(~kind(X))))&
((?[X]:(strong(X)))=>((~old(alice)&strong(alice))))&
((?[X]:((quiet(X)&~tall(X))))<=>((funny(john)<~>rich(john))))&
(((~creative(alice)|patient(alice)))<=>(~strong(fred)))&
(![X]:((rich(X)|~calm(X))=>(rich(X)|curious(X))))&
(![X]:((patient(X)&~creative(X))=>(rich(X)<~>~funny(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>happy(X)))&
(((~patient(alice)<~>wise(alice)))=>(~creative(paul)))&
(((quiet(paul)|strong(paul)))=>((~old(mary)<~>~funny(mary))))&
(((~happy(paul)<~>~rich(paul)))<=>(?[X]:((rich(X)|~patient(X)))))&
(~rich(paul))&
(?[X]:(strong(X)))&
((tall(alice)|~patient(alice)))&
(?[X]:((funny(X)<~>~happy(X))))&
(?[X]:((~old(X)<~>calm(X))))&
((~strong(lucy)<~>~calm(lucy)))&
(?[X]:((~old(X)&~creative(X))))&
(quiet(mary)) | ~kind(alice) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p15",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8726598248392125614100242
% SZS output start Proof for 8726598248392125614100242
1. ! [X0] : ((~kind(X0) <~> ~curious(X0)) <=> generous(X0)) [input p0]
2. ! [X0] : (~kind(X0) <=> (~humble(X0) | ~quiet(X0))) [input p1]
3. ! [X0] : ((happy(X0) & generous(X0)) <=> (~kind(X0) & kind(X0))) [input p2]
4. ! [X0] : ((tall(X0) | happy(X0)) <=> (curious(X0) & wise(X0))) [input p3]
5. ! [X0] : ((wise(X0) | ~creative(X0)) <=> (humble(X0) <~> wise(X0))) [input p4]
16. (~happy(paul) <~> ~rich(paul)) <=> ? [X0] : (~patient(X0) | rich(X0)) [input p15]
17. ~rich(paul) [input p16]
19. ~patient(alice) | tall(alice) [input p18]
25. kind(alice) [input hypothesis]
35. ! [X0] : ((((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | ~generous(X0)) & (generous(X0) | ((~kind(X0) | curious(X0)) & (~curious(X0) | kind(X0))))) [nnf transformation 1]
36. ! [X0] : ((~kind(X0) | (humble(X0) & quiet(X0))) & ((~humble(X0) | ~quiet(X0)) | kind(X0))) [nnf transformation 2]
37. ! [X0] : ((~kind(X0) | (humble(X0) & quiet(X0))) & (~humble(X0) | ~quiet(X0) | kind(X0))) [flattening 36]
38. ! [X0] : (((happy(X0) & generous(X0)) | (kind(X0) | ~kind(X0))) & ((~kind(X0) & kind(X0)) | (~happy(X0) | ~generous(X0)))) [nnf transformation 3]
39. ! [X0] : (((happy(X0) & generous(X0)) | kind(X0) | ~kind(X0)) & ((~kind(X0) & kind(X0)) | ~happy(X0) | ~generous(X0))) [flattening 38]
40. ! [X0] : (((tall(X0) | happy(X0)) | (~curious(X0) | ~wise(X0))) & ((curious(X0) & wise(X0)) | (~tall(X0) & ~happy(X0)))) [nnf transformation 4]
41. ! [X0] : ((tall(X0) | happy(X0) | ~curious(X0) | ~wise(X0)) & ((curious(X0) & wise(X0)) | (~tall(X0) & ~happy(X0)))) [flattening 40]
42. ! [X0] : (((wise(X0) | ~creative(X0)) | ((humble(X0) | ~wise(X0)) & (wise(X0) | ~humble(X0)))) & (((~wise(X0) | ~humble(X0)) & (wise(X0) | humble(X0))) | (~wise(X0) & creative(X0)))) [nnf transformation 5]
43. ! [X0] : ((wise(X0) | ~creative(X0) | ((humble(X0) | ~wise(X0)) & (wise(X0) | ~humble(X0)))) & (((~wise(X0) | ~humble(X0)) & (wise(X0) | humble(X0))) | (~wise(X0) & creative(X0)))) [flattening 42]
60. (((rich(paul) | happy(paul)) & (~rich(paul) | ~happy(paul))) | ! [X0] : (patient(X0) & ~rich(X0))) & (? [X0] : (~patient(X0) | rich(X0)) | ((~happy(paul) | rich(paul)) & (~rich(paul) | happy(paul)))) [nnf transformation 16]
61. (((rich(paul) | happy(paul)) & (~rich(paul) | ~happy(paul))) | ! [X0] : (patient(X0) & ~rich(X0))) & (? [X1] : (~patient(X1) | rich(X1)) | ((~happy(paul) | rich(paul)) & (~rich(paul) | happy(paul)))) [rectify 60]
62. ? [X1] : (~patient(X1) | rich(X1)) => (~patient(sK3) | rich(sK3)) [choice axiom]
63. (((rich(paul) | happy(paul)) & (~rich(paul) | ~happy(paul))) | ! [X0] : (patient(X0) & ~rich(X0))) & ((~patient(sK3) | rich(sK3)) | ((~happy(paul) | rich(paul)) & (~rich(paul) | happy(paul)))) [skolemisation 61,62]
75. ~curious(X0) | generous(X0) | kind(X0) [cnf transformation 35]
81. ~kind(X0) | humble(X0) [cnf transformation 37]
82. kind(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 39]
83. ~kind(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 39]
86. ~happy(X0) | wise(X0) [cnf transformation 41]
87. ~tall(X0) | wise(X0) [cnf transformation 41]
88. ~happy(X0) | curious(X0) [cnf transformation 41]
94. ~wise(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 43]
131. rich(paul) | happy(paul) | patient(X0) [cnf transformation 63]
132. ~rich(paul) [cnf transformation 17]
134. ~patient(alice) | tall(alice) [cnf transformation 19]
144. kind(alice) [cnf transformation 25]
145. ~wise(X0) | ~humble(X0) [duplicate literal removal 94]
147. ~happy(X0) | ~generous(X0) [subsumption resolution 82,83]
223. 17 <=> patient(alice) [avatar definition]
224. ~patient(alice) <- (~17) [avatar component clause 223]
230. 18 <=> wise(alice) [avatar definition]
231. wise(alice) <- (18) [avatar component clause 230]
260. 24 <=> ! [X0] : patient(X0) [avatar definition]
261. patient(X0) <- (24) [avatar component clause 260]
263. 25 <=> happy(paul) [avatar definition]
265. happy(paul) <- (25) [avatar component clause 263]
267. 26 <=> rich(paul) [avatar definition]
270. 24 | 25 | 26 [avatar split clause 131,267,263,260]
287. ~26 [avatar split clause 132,267]
289. 30 <=> tall(alice) [avatar definition]
291. tall(alice) <- (30) [avatar component clause 289]
292. 30 | ~17 [avatar split clause 134,223,289]
326. humble(alice) [resolution 81,144]
327. wise(paul) <- (25) [resolution 86,265]
328. curious(paul) <- (25) [resolution 88,265]
329. ~humble(paul) <- (25) [resolution 145,327]
330. ~generous(paul) <- (25) [resolution 147,265]
331. generous(paul) | kind(paul) <- (25) [resolution 75,328]
332. kind(paul) <- (25) [subsumption resolution 331,330]
348. humble(paul) <- (25) [resolution 332,81]
350. $false <- (25) [subsumption resolution 348,329]
351. ~25 [avatar contradiction clause 350]
354. $false <- (~17, 24) [resolution 261,224]
357. 17 | ~24 [avatar contradiction clause 354]
361. wise(alice) <- (30) [resolution 291,87]
364. 18 | ~30 [avatar split clause 361,289,230]
366. ~humble(alice) <- (18) [resolution 231,145]
367. $false <- (18) [subsumption resolution 366,326]
368. ~18 [avatar contradiction clause 367]
369. $false [avatar sat refutation 270,287,292,351,357,364,368]
% SZS output end Proof for 8726598248392125614100242
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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