premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If fred is not generous or wise then someone is not wise or creative and vice versa.
If mary is both curious and not tall then someone is not old or not patient.
Everyone who is both not kind and old is either happy or patient.
If someone is patient or quiet then paul is not creative and vice versa.
Everyone who is not patient or strong is both not generous and generous and vice versa.
If lucy is humble or strong then lucy is both rich and not brave and vice versa.
Everyone who is not wise or not funny is either happy or not happy and vice versa.
If someone is both patient and not brave then fred is either not creative or not rich.
Everyone who is either funny or kind is both humble and not happy.
Everyone who is not patient is generous.
If someone is not humble or happy then someone is happy or humble and vice versa.
Everyone who is either tall or not patient is either not happy or brave.
If someone is strong or not quiet then alice is not strong or not brave.
Everyone who is rich is wise or tall.
Everyone who is not patient or wise is not rich or generous and vice versa.
Everyone who is either not wise or not happy is happy and vice versa.
Someone is either generous or curious.
Someone is funny or not rich.
Someone is rich or tall. | Paul is tall. | entailment | (((~generous(fred)|wise(fred)))<=>(?[X]:((~wise(X)|creative(X)))))&
(((curious(mary)&~tall(mary)))=>(?[X]:((~old(X)|~patient(X)))))&
(![X]:((~kind(X)&old(X))=>(happy(X)<~>patient(X))))&
((?[X]:((patient(X)|quiet(X))))<=>(~creative(paul)))&
(![X]:((~patient(X)|strong(X))<=>(~generous(X)&generous(X))))&
(((humble(lucy)|strong(lucy)))<=>((rich(lucy)&~brave(lucy))))&
(![X]:((~wise(X)|~funny(X))<=>(happy(X)<~>~happy(X))))&
((?[X]:((patient(X)&~brave(X))))=>((~creative(fred)<~>~rich(fred))))&
(![X]:((funny(X)<~>kind(X))=>(humble(X)&~happy(X))))&
(![X]:(~patient(X)=>generous(X)))&
((?[X]:((~humble(X)|happy(X))))<=>(?[X]:((happy(X)|humble(X)))))&
(![X]:((tall(X)<~>~patient(X))=>(~happy(X)<~>brave(X))))&
((?[X]:((strong(X)|~quiet(X))))=>((~strong(alice)|~brave(alice))))&
(![X]:(rich(X)=>(wise(X)|tall(X))))&
(![X]:((~patient(X)|wise(X))<=>(~rich(X)|generous(X))))&
(![X]:((~wise(X)<~>~happy(X))<=>happy(X)))&
(?[X]:((generous(X)<~>curious(X))))&
(?[X]:((funny(X)|~rich(X))))&
(?[X]:((rich(X)|tall(X)))) | tall(paul) | [
"p4",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4481261364615678851453945
% SZS output start Proof for 4481261364615678851453945
5. ! [X0] : ((strong(X0) | ~patient(X0)) <=> (generous(X0) & ~generous(X0))) [input p4]
14. ! [X0] : (rich(X0) => (tall(X0) | wise(X0))) [input p13]
15. ! [X0] : ((wise(X0) | ~patient(X0)) <=> (generous(X0) | ~rich(X0))) [input p14]
16. ! [X0] : ((~wise(X0) <~> ~happy(X0)) <=> happy(X0)) [input p15]
20. ~tall(paul) [input hypothesis]
30. ! [X0] : ((tall(X0) | wise(X0)) | ~rich(X0)) [ennf transformation 14]
31. ! [X0] : (tall(X0) | wise(X0) | ~rich(X0)) [flattening 30]
41. ! [X0] : (((strong(X0) | ~patient(X0)) | (~generous(X0) | generous(X0))) & ((generous(X0) & ~generous(X0)) | (~strong(X0) & patient(X0)))) [nnf transformation 5]
42. ! [X0] : ((strong(X0) | ~patient(X0) | ~generous(X0) | generous(X0)) & ((generous(X0) & ~generous(X0)) | (~strong(X0) & patient(X0)))) [flattening 41]
55. ! [X0] : (((wise(X0) | ~patient(X0)) | (~generous(X0) & rich(X0))) & ((generous(X0) | ~rich(X0)) | (~wise(X0) & patient(X0)))) [nnf transformation 15]
56. ! [X0] : ((wise(X0) | ~patient(X0) | (~generous(X0) & rich(X0))) & (generous(X0) | ~rich(X0) | (~wise(X0) & patient(X0)))) [flattening 55]
57. ! [X0] : ((((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | ~happy(X0)) & (happy(X0) | ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0))))) [nnf transformation 16]
72. ~generous(X0) | patient(X0) [cnf transformation 42]
74. patient(X0) | generous(X0) [cnf transformation 42]
105. ~rich(X0) | wise(X0) | tall(X0) [cnf transformation 31]
108. wise(X0) | ~patient(X0) | rich(X0) [cnf transformation 56]
111. happy(X0) | ~wise(X0) | happy(X0) [cnf transformation 57]
112. ~happy(X0) | ~wise(X0) | ~happy(X0) [cnf transformation 57]
118. ~tall(paul) [cnf transformation 20]
119. happy(X0) | ~wise(X0) [duplicate literal removal 111]
120. ~happy(X0) | ~wise(X0) [duplicate literal removal 112]
171. patient(X0) [subsumption resolution 72,74]
236. rich(X0) | wise(X0) [subsumption resolution 108,171]
237. ~wise(X0) [subsumption resolution 119,120]
303. wise(X0) | tall(X0) | wise(X0) [resolution 105,236]
307. wise(X0) | tall(X0) [duplicate literal removal 303]
308. tall(X0) [subsumption resolution 307,237]
309. $false [resolution 308,118]
% SZS output end Proof for 4481261364615678851453945
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or kind is wise or rich and vice versa.
Everyone who is not happy is creative or not funny and vice versa.
Everyone who is happy or not generous is tall and vice versa.
If someone is both not old and not wise then fred is happy.
Everyone who is either not generous or not happy is either humble or not brave.
If someone is calm then someone is both not happy and not brave and vice versa.
Everyone who is wise is either not tall or curious and vice versa.
If alice is not patient or generous then fred is not rich.
Everyone who is happy or not tall is not quiet and vice versa.
If lucy is both not humble and kind then susan is both not curious and happy and vice versa.
If john is either not quiet or not humble then someone is strong.
Everyone who is either happy or creative is tall and vice versa.
Everyone who is funny or not rich is either old or not calm and vice versa.
If someone is both not happy and not humble then someone is not tall or not old.
Everyone who is not patient is not tall or not creative and vice versa.
Everyone who is strong is either not rich or not strong and vice versa.
Someone is both not tall and generous.
John is either old or not humble.
Mary is not quiet or not wise.
Alice is not wise or not humble.
Someone is either not wise or strong.
Alice is not patient or patient.
Someone is not strong.
Mary is both humble and happy. | Mary is not tall. | contradiction | (![X]:((~happy(X)|kind(X))<=>(wise(X)|rich(X))))&
(![X]:(~happy(X)<=>(creative(X)|~funny(X))))&
(![X]:((happy(X)|~generous(X))<=>tall(X)))&
((?[X]:((~old(X)&~wise(X))))=>(happy(fred)))&
(![X]:((~generous(X)<~>~happy(X))=>(humble(X)<~>~brave(X))))&
((?[X]:(calm(X)))<=>(?[X]:((~happy(X)&~brave(X)))))&
(![X]:(wise(X)<=>(~tall(X)<~>curious(X))))&
(((~patient(alice)|generous(alice)))=>(~rich(fred)))&
(![X]:((happy(X)|~tall(X))<=>~quiet(X)))&
(((~humble(lucy)&kind(lucy)))<=>((~curious(susan)&happy(susan))))&
(((~quiet(john)<~>~humble(john)))=>(?[X]:(strong(X))))&
(![X]:((happy(X)<~>creative(X))<=>tall(X)))&
(![X]:((funny(X)|~rich(X))<=>(old(X)<~>~calm(X))))&
((?[X]:((~happy(X)&~humble(X))))=>(?[X]:((~tall(X)|~old(X)))))&
(![X]:(~patient(X)<=>(~tall(X)|~creative(X))))&
(![X]:(strong(X)<=>(~rich(X)<~>~strong(X))))&
(?[X]:((~tall(X)&generous(X))))&
((old(john)<~>~humble(john)))&
((~quiet(mary)|~wise(mary)))&
((~wise(alice)|~humble(alice)))&
(?[X]:((~wise(X)<~>strong(X))))&
((~patient(alice)|patient(alice)))&
(?[X]:(~strong(X)))&
((humble(mary)&happy(mary))) | ~tall(mary) | [
"p2",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4942026858708453809508265
% SZS output start Proof for 4942026858708453809508265
3. ! [X0] : ((~generous(X0) | happy(X0)) <=> tall(X0)) [input p2]
24. happy(mary) & humble(mary) [input p23]
25. ~tall(mary) [input hypothesis]
37. ! [X0] : (((~generous(X0) | happy(X0)) | ~tall(X0)) & (tall(X0) | (generous(X0) & ~happy(X0)))) [nnf transformation 3]
38. ! [X0] : ((~generous(X0) | happy(X0) | ~tall(X0)) & (tall(X0) | (generous(X0) & ~happy(X0)))) [flattening 37]
77. ~happy(X0) | tall(X0) [cnf transformation 38]
132. happy(mary) [cnf transformation 24]
133. ~tall(mary) [cnf transformation 25]
264. tall(mary) [resolution 77,132]
266. $false [subsumption resolution 264,133]
% SZS output end Proof for 4942026858708453809508265
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or quiet is not tall or wise and vice versa.
Everyone who is kind is both not funny and not strong.
Everyone who is not patient is not happy or humble.
If someone is not rich or strong then someone is both not calm and brave.
If paul is kind or not rich then someone is either not strong or not tall and vice versa.
Everyone who is kind is both not quiet and not creative and vice versa.
Everyone who is not humble is either rich or not tall and vice versa.
Everyone who is both creative and not creative is not creative or not humble and vice versa.
If paul is not quiet then alice is both not brave and not strong.
If mary is both not humble and calm then someone is either not rich or brave.
Everyone who is quiet or calm is either not calm or not quiet and vice versa.
If someone is either creative or not creative then lucy is rich or wise.
Everyone who is not wise is old or curious and vice versa.
If alice is not brave then someone is both generous and not generous and vice versa.
Everyone who is either quiet or tall is either not wise or generous and vice versa.
Everyone who is old or kind is both not tall and curious.
John is wise or not generous.
Susan is not strong.
Someone is either strong or not strong.
Susan is both not old and not patient.
Someone is not happy or not creative. | Mary is creative. | entailment | (![X]:((creative(X)<~>quiet(X))<=>(~tall(X)|wise(X))))&
(![X]:(kind(X)=>(~funny(X)&~strong(X))))&
(![X]:(~patient(X)=>(~happy(X)|humble(X))))&
((?[X]:((~rich(X)|strong(X))))=>(?[X]:((~calm(X)&brave(X)))))&
(((kind(paul)|~rich(paul)))<=>(?[X]:((~strong(X)<~>~tall(X)))))&
(![X]:(kind(X)<=>(~quiet(X)&~creative(X))))&
(![X]:(~humble(X)<=>(rich(X)<~>~tall(X))))&
(![X]:((creative(X)&~creative(X))<=>(~creative(X)|~humble(X))))&
((~quiet(paul))=>((~brave(alice)&~strong(alice))))&
(((~humble(mary)&calm(mary)))=>(?[X]:((~rich(X)<~>brave(X)))))&
(![X]:((quiet(X)|calm(X))<=>(~calm(X)<~>~quiet(X))))&
((?[X]:((creative(X)<~>~creative(X))))=>((rich(lucy)|wise(lucy))))&
(![X]:(~wise(X)<=>(old(X)|curious(X))))&
((~brave(alice))<=>(?[X]:((generous(X)&~generous(X)))))&
(![X]:((quiet(X)<~>tall(X))<=>(~wise(X)<~>generous(X))))&
(![X]:((old(X)|kind(X))=>(~tall(X)&curious(X))))&
((wise(john)|~generous(john)))&
(~strong(susan))&
(?[X]:((strong(X)<~>~strong(X))))&
((~old(susan)&~patient(susan)))&
(?[X]:((~happy(X)|~creative(X)))) | creative(mary) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4190468021212122641675669
% SZS output start Proof for 4190468021212122641675669
8. ! [X0] : ((~creative(X0) & creative(X0)) <=> (~humble(X0) | ~creative(X0))) [input p7]
22. ~creative(mary) [input hypothesis]
49. ! [X0] : (((~creative(X0) & creative(X0)) | (humble(X0) & creative(X0))) & ((~humble(X0) | ~creative(X0)) | (creative(X0) | ~creative(X0)))) [nnf transformation 8]
50. ! [X0] : (((~creative(X0) & creative(X0)) | (humble(X0) & creative(X0))) & (~humble(X0) | ~creative(X0) | creative(X0) | ~creative(X0))) [flattening 49]
92. creative(X0) | creative(X0) [cnf transformation 50]
131. ~creative(mary) [cnf transformation 22]
139. creative(X0) [duplicate literal removal 92]
226. $false [subsumption resolution 131,139]
% SZS output end Proof for 4190468021212122641675669
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is both funny and not humble and vice versa.
Everyone who is quiet or not happy is not humble or not patient and vice versa.
If someone is not kind or creative then alice is quiet and vice versa.
Everyone who is funny or tall is old.
If susan is both not funny and not quiet then paul is not strong or humble.
If someone is either not patient or not curious then susan is generous or not curious and vice versa.
Everyone who is not strong or humble is both calm and not rich and vice versa.
Everyone who is not kind or patient is not humble.
Everyone who is not rich or not kind is calm or quiet.
Everyone who is either strong or curious is either not funny or not rich.
Everyone who is not tall or generous is quiet and vice versa.
Everyone who is both old and creative is funny or not old.
If someone is not old or humble then fred is both not old and brave and vice versa.
If mary is calm or quiet then susan is either happy or not tall.
Everyone who is kind or not brave is either kind or not happy and vice versa.
If john is not humble or not happy then mary is not wise.
Susan is not patient.
Paul is both not rich and creative.
Someone is both not old and not rich.
Someone is both curious and wise.
Someone is either brave or patient.
Fred is either not rich or quiet.
John is either not patient or funny.
Someone is either calm or not brave. | Fred is rich. | entailment | (![X]:(~kind(X)<=>(funny(X)&~humble(X))))&
(![X]:((quiet(X)|~happy(X))<=>(~humble(X)|~patient(X))))&
((?[X]:((~kind(X)|creative(X))))<=>(quiet(alice)))&
(![X]:((funny(X)|tall(X))=>old(X)))&
(((~funny(susan)&~quiet(susan)))=>((~strong(paul)|humble(paul))))&
((?[X]:((~patient(X)<~>~curious(X))))<=>((generous(susan)|~curious(susan))))&
(![X]:((~strong(X)|humble(X))<=>(calm(X)&~rich(X))))&
(![X]:((~kind(X)|patient(X))=>~humble(X)))&
(![X]:((~rich(X)|~kind(X))=>(calm(X)|quiet(X))))&
(![X]:((strong(X)<~>curious(X))=>(~funny(X)<~>~rich(X))))&
(![X]:((~tall(X)|generous(X))<=>quiet(X)))&
(![X]:((old(X)&creative(X))=>(funny(X)|~old(X))))&
((?[X]:((~old(X)|humble(X))))<=>((~old(fred)&brave(fred))))&
(((calm(mary)|quiet(mary)))=>((happy(susan)<~>~tall(susan))))&
(![X]:((kind(X)|~brave(X))<=>(kind(X)<~>~happy(X))))&
(((~humble(john)|~happy(john)))=>(~wise(mary)))&
(~patient(susan))&
((~rich(paul)&creative(paul)))&
(?[X]:((~old(X)&~rich(X))))&
(?[X]:((curious(X)&wise(X))))&
(?[X]:((brave(X)<~>patient(X))))&
((~rich(fred)<~>quiet(fred)))&
((~patient(john)<~>funny(john)))&
(?[X]:((calm(X)<~>~brave(X)))) | rich(fred) | [
"p3",
"p10",
"p12",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1884900915208922843778493
% SZS output start Proof for 1884900915208922843778493
4. ! [X0] : ((tall(X0) | funny(X0)) => old(X0)) [input p3]
11. ! [X0] : ((generous(X0) | ~tall(X0)) <=> quiet(X0)) [input p10]
13. ? [X0] : (humble(X0) | ~old(X0)) <=> (brave(fred) & ~old(fred)) [input p12]
19. ? [X0] : (~rich(X0) & ~old(X0)) [input p18]
22. ~rich(fred) <~> quiet(fred) [input p21]
25. ~rich(fred) [input hypothesis]
26. ! [X0] : (old(X0) | (~tall(X0) & ~funny(X0))) [ennf transformation 4]
53. ! [X0] : (((generous(X0) | ~tall(X0)) | ~quiet(X0)) & (quiet(X0) | (~generous(X0) & tall(X0)))) [nnf transformation 11]
54. ! [X0] : ((generous(X0) | ~tall(X0) | ~quiet(X0)) & (quiet(X0) | (~generous(X0) & tall(X0)))) [flattening 53]
55. (? [X0] : (humble(X0) | ~old(X0)) | (~brave(fred) | old(fred))) & ((brave(fred) & ~old(fred)) | ! [X0] : (~humble(X0) & old(X0))) [nnf transformation 13]
56. (? [X0] : (humble(X0) | ~old(X0)) | ~brave(fred) | old(fred)) & ((brave(fred) & ~old(fred)) | ! [X0] : (~humble(X0) & old(X0))) [flattening 55]
57. (? [X0] : (humble(X0) | ~old(X0)) | ~brave(fred) | old(fred)) & ((brave(fred) & ~old(fred)) | ! [X1] : (~humble(X1) & old(X1))) [rectify 56]
58. ? [X0] : (humble(X0) | ~old(X0)) => (humble(sK2) | ~old(sK2)) [choice axiom]
59. ((humble(sK2) | ~old(sK2)) | ~brave(fred) | old(fred)) & ((brave(fred) & ~old(fred)) | ! [X1] : (~humble(X1) & old(X1))) [skolemisation 57,58]
63. ? [X0] : (~rich(X0) & ~old(X0)) => (~rich(sK3) & ~old(sK3)) [choice axiom]
64. ~rich(sK3) & ~old(sK3) [skolemisation 19,63]
70. (~quiet(fred) | rich(fred)) & (quiet(fred) | ~rich(fred)) [nnf transformation 22]
86. ~tall(X0) | old(X0) [cnf transformation 26]
107. tall(X0) | quiet(X0) [cnf transformation 54]
111. ~old(fred) | old(X1) [cnf transformation 59]
131. ~old(sK3) [cnf transformation 64]
138. ~quiet(fred) | rich(fred) [cnf transformation 70]
143. ~rich(fred) [cnf transformation 25]
216. 16 <=> old(fred) [avatar definition]
217. ~old(fred) <- (~16) [avatar component clause 216]
237. 21 <=> ! [X1] : old(X1) [avatar definition]
238. old(X1) <- (21) [avatar component clause 237]
241. 21 | ~16 [avatar split clause 111,216,237]
287. 31 <=> rich(fred) [avatar definition]
291. 32 <=> quiet(fred) [avatar definition]
293. ~quiet(fred) <- (~32) [avatar component clause 291]
294. 31 | ~32 [avatar split clause 138,291,287]
316. ~31 [avatar split clause 143,287]
326. old(X0) | quiet(X0) [resolution 107,86]
531. quiet(fred) <- (~16) [resolution 326,217]
534. $false <- (~16, ~32) [subsumption resolution 531,293]
535. 16 | 32 [avatar contradiction clause 534]
540. $false <- (21) [resolution 238,131]
541. ~21 [avatar contradiction clause 540]
543. $false [avatar sat refutation 241,294,316,535,541]
% SZS output end Proof for 1884900915208922843778493
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and brave then someone is both strong and patient. Everyone who is not happy is not rich or not generous. Everyone who is both not creative and old is either not quiet or not curious. If john is both not creative and patient then someone is kind and vice versa. If someone is both rich and not funny then someone is not patient and vice versa. If mary is either wise or funny then someone is not kind and vice versa. If someone is either patient or not tall then lucy is funny or generous. Everyone who is both kind and not strong is brave and vice versa. If someone is humble then susan is quiet or happy. If someone is both rich and happy then john is both tall and not patient. Everyone who is both wise and not wise is either rich or old and vice versa. Everyone who is creative or not creative is wise or not funny and vice versa. If someone is not generous then mary is either rich or not strong. Everyone who is not tall or not strong is either not calm or quiet. Everyone who is funny or not humble is rich or tall. If mary is both old and not strong then mary is not rich or brave and vice versa. Someone is either kind or creative. Someone is either creative or brave. Someone is either not kind or curious. Someone is not funny or not kind. John is both not generous and not calm. Someone is patient or not patient. Paul is both creative and not quiet. Someone is not wise or happy. | Mary is not brave. | entailment | ((?[X]:((~tall(X)&brave(X))))=>(?[X]:((strong(X)&patient(X)))))&
(![X]:(~happy(X)=>(~rich(X)|~generous(X))))&
(![X]:((~creative(X)&old(X))=>(~quiet(X)<~>~curious(X))))&
(((~creative(john)&patient(john)))<=>(?[X]:(kind(X))))&
((?[X]:((rich(X)&~funny(X))))<=>(?[X]:(~patient(X))))&
(((wise(mary)<~>funny(mary)))<=>(?[X]:(~kind(X))))&
((?[X]:((patient(X)<~>~tall(X))))=>((funny(lucy)|generous(lucy))))&
(![X]:((kind(X)&~strong(X))<=>brave(X)))&
((?[X]:(humble(X)))=>((quiet(susan)|happy(susan))))&
((?[X]:((rich(X)&happy(X))))=>((tall(john)&~patient(john))))&
(![X]:((wise(X)&~wise(X))<=>(rich(X)<~>old(X))))&
(![X]:((creative(X)|~creative(X))<=>(wise(X)|~funny(X))))&
((?[X]:(~generous(X)))=>((rich(mary)<~>~strong(mary))))&
(![X]:((~tall(X)|~strong(X))=>(~calm(X)<~>quiet(X))))&
(![X]:((funny(X)|~humble(X))=>(rich(X)|tall(X))))&
(((old(mary)&~strong(mary)))<=>((~rich(mary)|brave(mary))))&
(?[X]:((kind(X)<~>creative(X))))&
(?[X]:((creative(X)<~>brave(X))))&
(?[X]:((~kind(X)<~>curious(X))))&
(?[X]:((~funny(X)|~kind(X))))&
((~generous(john)&~calm(john)))&
(?[X]:((patient(X)|~patient(X))))&
((creative(paul)&~quiet(paul)))&
(?[X]:((~wise(X)|happy(X)))) | ~brave(mary) | [
"p7",
"p10",
"p12",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8844856413087132717620
% SZS output start Proof for 8844856413087132717620
8. ! [X0] : ((~strong(X0) & kind(X0)) <=> brave(X0)) [input p7]
11. ! [X0] : ((~wise(X0) & wise(X0)) <=> (rich(X0) <~> old(X0))) [input p10]
13. ? [X0] : ~generous(X0) => (rich(mary) <~> ~strong(mary)) [input p12]
16. (~strong(mary) & old(mary)) <=> (brave(mary) | ~rich(mary)) [input p15]
21. ~calm(john) & ~generous(john) [input p20]
25. brave(mary) [input hypothesis]
38. (rich(mary) <~> ~strong(mary)) | ! [X0] : generous(X0) [ennf transformation 13]
61. ! [X0] : (((~strong(X0) & kind(X0)) | ~brave(X0)) & (brave(X0) | (strong(X0) | ~kind(X0)))) [nnf transformation 8]
62. ! [X0] : (((~strong(X0) & kind(X0)) | ~brave(X0)) & (brave(X0) | strong(X0) | ~kind(X0))) [flattening 61]
63. ! [X0] : (((~wise(X0) & wise(X0)) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0)))) & (((~old(X0) | ~rich(X0)) & (old(X0) | rich(X0))) | (wise(X0) | ~wise(X0)))) [nnf transformation 11]
64. ! [X0] : (((~wise(X0) & wise(X0)) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0)))) & (((~old(X0) | ~rich(X0)) & (old(X0) | rich(X0))) | wise(X0) | ~wise(X0))) [flattening 63]
67. ((strong(mary) | ~rich(mary)) & (~strong(mary) | rich(mary))) | ! [X0] : generous(X0) [nnf transformation 38]
69. ((~strong(mary) & old(mary)) | (~brave(mary) & rich(mary))) & ((brave(mary) | ~rich(mary)) | (strong(mary) | ~old(mary))) [nnf transformation 16]
70. ((~strong(mary) & old(mary)) | (~brave(mary) & rich(mary))) & (brave(mary) | ~rich(mary) | strong(mary) | ~old(mary)) [flattening 69]
105. ~strong(X0) | ~brave(X0) [cnf transformation 62]
111. wise(X0) | old(X0) | ~rich(X0) [cnf transformation 64]
112. wise(X0) | rich(X0) | ~old(X0) [cnf transformation 64]
113. ~wise(X0) | old(X0) | ~rich(X0) [cnf transformation 64]
114. ~wise(X0) | rich(X0) | ~old(X0) [cnf transformation 64]
120. strong(mary) | ~rich(mary) | generous(X0) [cnf transformation 67]
128. old(mary) | rich(mary) [cnf transformation 70]
139. ~generous(john) [cnf transformation 21]
145. brave(mary) [cnf transformation 25]
254. ~old(X0) | rich(X0) [subsumption resolution 112,114]
255. old(X0) | ~rich(X0) [subsumption resolution 111,113]
258. 26 <=> ! [X0] : generous(X0) [avatar definition]
259. generous(X0) <- (26) [avatar component clause 258]
261. 27 <=> rich(mary) [avatar definition]
265. 28 <=> strong(mary) [avatar definition]
267. strong(mary) <- (28) [avatar component clause 265]
268. 26 | ~27 | 28 [avatar split clause 120,265,261,258]
272. 29 <=> brave(mary) [avatar definition]
273. brave(mary) <- (29) [avatar component clause 272]
276. 30 <=> old(mary) [avatar definition]
278. old(mary) <- (30) [avatar component clause 276]
280. old(mary) [subsumption resolution 128,255]
281. 30 [avatar split clause 280,276]
332. 29 [avatar split clause 145,272]
346. rich(mary) <- (30) [resolution 254,278]
349. 27 | ~30 [avatar split clause 346,276,261]
350. $false <- (26) [resolution 259,139]
351. ~26 [avatar contradiction clause 350]
353. ~brave(mary) <- (28) [resolution 267,105]
354. $false <- (28, 29) [subsumption resolution 353,273]
355. ~28 | ~29 [avatar contradiction clause 354]
356. $false [avatar sat refutation 268,281,332,349,351,355]
% SZS output end Proof for 8844856413087132717620
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong then mary is either not curious or not rich.
If someone is either strong or not happy then someone is generous.
Everyone who is humble is quiet or not rich and vice versa.
If someone is not quiet or patient then fred is both humble and not old.
Everyone who is both not humble and not rich is either tall or not patient and vice versa.
Everyone who is both not generous and curious is generous.
Everyone who is both wise and not rich is humble.
Everyone who is not calm or generous is both old and wise.
Everyone who is old or not creative is both not generous and not tall.
If fred is both not curious and not creative then someone is old or not calm.
If someone is both quiet and creative then someone is either not tall or old.
If someone is funny then mary is funny.
If mary is wise or not quiet then someone is not quiet and vice versa.
Everyone who is not rich is curious and vice versa.
If someone is not creative or not calm then mary is strong and vice versa.
If alice is rich or humble then paul is either patient or not old and vice versa.
Fred is both kind and calm.
Susan is both not patient and not quiet.
Someone is either not kind or not quiet.
Paul is either curious or happy.
Someone is not wise.
John is happy. | Susan is not old. | entailment | ((?[X]:(~strong(X)))=>((~curious(mary)<~>~rich(mary))))&
((?[X]:((strong(X)<~>~happy(X))))=>(?[X]:(generous(X))))&
(![X]:(humble(X)<=>(quiet(X)|~rich(X))))&
((?[X]:((~quiet(X)|patient(X))))=>((humble(fred)&~old(fred))))&
(![X]:((~humble(X)&~rich(X))<=>(tall(X)<~>~patient(X))))&
(![X]:((~generous(X)&curious(X))=>generous(X)))&
(![X]:((wise(X)&~rich(X))=>humble(X)))&
(![X]:((~calm(X)|generous(X))=>(old(X)&wise(X))))&
(![X]:((old(X)|~creative(X))=>(~generous(X)&~tall(X))))&
(((~curious(fred)&~creative(fred)))=>(?[X]:((old(X)|~calm(X)))))&
((?[X]:((quiet(X)&creative(X))))=>(?[X]:((~tall(X)<~>old(X)))))&
((?[X]:(funny(X)))=>(funny(mary)))&
(((wise(mary)|~quiet(mary)))<=>(?[X]:(~quiet(X))))&
(![X]:(~rich(X)<=>curious(X)))&
((?[X]:((~creative(X)|~calm(X))))<=>(strong(mary)))&
(((rich(alice)|humble(alice)))<=>((patient(paul)<~>~old(paul))))&
((kind(fred)&calm(fred)))&
((~patient(susan)&~quiet(susan)))&
(?[X]:((~kind(X)<~>~quiet(X))))&
((curious(paul)<~>happy(paul)))&
(?[X]:(~wise(X)))&
(happy(john)) | ~old(susan) | [
"p2",
"p4",
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1993817869346052573817870
% SZS output start Proof for 1993817869346052573817870
3. ! [X0] : (humble(X0) <=> (~rich(X0) | quiet(X0))) [input p2]
5. ! [X0] : ((~rich(X0) & ~humble(X0)) <=> (tall(X0) <~> ~patient(X0))) [input p4]
9. ! [X0] : ((~creative(X0) | old(X0)) => (~tall(X0) & ~generous(X0))) [input p8]
18. ~quiet(susan) & ~patient(susan) [input p17]
23. old(susan) [input hypothesis]
34. ! [X0] : ((~tall(X0) & ~generous(X0)) | (creative(X0) & ~old(X0))) [ennf transformation 9]
44. ! [X0] : ((humble(X0) | (rich(X0) & ~quiet(X0))) & ((~rich(X0) | quiet(X0)) | ~humble(X0))) [nnf transformation 3]
45. ! [X0] : ((humble(X0) | (rich(X0) & ~quiet(X0))) & (~rich(X0) | quiet(X0) | ~humble(X0))) [flattening 44]
46. ! [X0] : (((~rich(X0) & ~humble(X0)) | ((tall(X0) | patient(X0)) & (~patient(X0) | ~tall(X0)))) & (((patient(X0) | ~tall(X0)) & (~patient(X0) | tall(X0))) | (rich(X0) | humble(X0)))) [nnf transformation 5]
47. ! [X0] : (((~rich(X0) & ~humble(X0)) | ((tall(X0) | patient(X0)) & (~patient(X0) | ~tall(X0)))) & (((patient(X0) | ~tall(X0)) & (~patient(X0) | tall(X0))) | rich(X0) | humble(X0))) [flattening 46]
78. humble(X0) | rich(X0) [cnf transformation 45]
86. ~humble(X0) | tall(X0) | patient(X0) [cnf transformation 47]
88. ~rich(X0) | tall(X0) | patient(X0) [cnf transformation 47]
97. ~tall(X0) | ~old(X0) [cnf transformation 34]
119. ~patient(susan) [cnf transformation 18]
127. old(susan) [cnf transformation 23]
327. tall(X0) | patient(X0) | rich(X0) [resolution 86,78]
412. tall(X0) | patient(X0) [subsumption resolution 327,88]
422. ~old(X3) | patient(X3) [resolution 412,97]
430. patient(susan) [resolution 422,127]
431. $false [subsumption resolution 430,119]
% SZS output end Proof for 1993817869346052573817870
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not strong and not creative then someone is not humble and vice versa.
Everyone who is not happy is wise.
Everyone who is not creative is both not happy and brave and vice versa.
Everyone who is generous is both funny and not old and vice versa.
Everyone who is either generous or kind is old or not tall and vice versa.
Everyone who is both creative and old is both not rich and calm and vice versa.
Everyone who is not humble or not old is either not calm or quiet.
Everyone who is both not rich and creative is either calm or not rich.
Everyone who is not old is curious and vice versa.
If someone is wise or quiet then paul is happy or not tall.
If fred is both not brave and wise then lucy is creative or funny and vice versa.
If someone is not quiet then john is both humble and strong and vice versa.
If alice is either not patient or kind then alice is either not humble or calm.
Everyone who is happy or not generous is both rich and not rich.
If someone is calm then susan is both not wise and not calm and vice versa.
Everyone who is both brave and not brave is both not kind and kind.
Someone is brave.
Someone is both creative and strong.
Someone is quiet or patient.
Someone is both humble and not tall.
Someone is not rich or patient.
Susan is both not patient and not humble.
Someone is not funny or curious. | Lucy is strong. | neutral | ((?[X]:((~strong(X)&~creative(X))))<=>(?[X]:(~humble(X))))&
(![X]:(~happy(X)=>wise(X)))&
(![X]:(~creative(X)<=>(~happy(X)&brave(X))))&
(![X]:(generous(X)<=>(funny(X)&~old(X))))&
(![X]:((generous(X)<~>kind(X))<=>(old(X)|~tall(X))))&
(![X]:((creative(X)&old(X))<=>(~rich(X)&calm(X))))&
(![X]:((~humble(X)|~old(X))=>(~calm(X)<~>quiet(X))))&
(![X]:((~rich(X)&creative(X))=>(calm(X)<~>~rich(X))))&
(![X]:(~old(X)<=>curious(X)))&
((?[X]:((wise(X)|quiet(X))))=>((happy(paul)|~tall(paul))))&
(((~brave(fred)&wise(fred)))<=>((creative(lucy)|funny(lucy))))&
((?[X]:(~quiet(X)))<=>((humble(john)&strong(john))))&
(((~patient(alice)<~>kind(alice)))=>((~humble(alice)<~>calm(alice))))&
(![X]:((happy(X)|~generous(X))=>(rich(X)&~rich(X))))&
((?[X]:(calm(X)))<=>((~wise(susan)&~calm(susan))))&
(![X]:((brave(X)&~brave(X))=>(~kind(X)&kind(X))))&
(?[X]:(brave(X)))&
(?[X]:((creative(X)&strong(X))))&
(?[X]:((quiet(X)|patient(X))))&
(?[X]:((humble(X)&~tall(X))))&
(?[X]:((~rich(X)|patient(X))))&
((~patient(susan)&~humble(susan)))&
(?[X]:((~funny(X)|curious(X)))) | strong(lucy) | [] | null | 0 |
If someone is either old or not quiet then lucy is rich or not strong and vice versa.
If susan is both not strong and not patient then paul is both not curious and not humble and vice versa.
If lucy is both calm and not generous then someone is both strong and curious.
Everyone who is either creative or not tall is not creative and vice versa.
Everyone who is both brave and humble is either not calm or quiet.
If alice is either creative or quiet then someone is not curious or generous.
Everyone who is not humble or not kind is not patient and vice versa.
Everyone who is not humble or not creative is rich or wise and vice versa.
Everyone who is calm or not wise is both not patient and not calm and vice versa.
If paul is creative or brave then someone is not humble and vice versa.
Everyone who is both brave and tall is not rich.
Everyone who is either generous or not rich is both not kind and not humble and vice versa.
If someone is both strong and not old then john is quiet and vice versa.
Everyone who is both curious and not brave is quiet or tall.
If someone is not tall then lucy is either brave or tall.
Everyone who is happy or not old is both not happy and not funny.
Mary is both generous and brave.
Someone is both not curious and not calm.
Someone is rich.
Fred is not tall or funny.
Alice is either not rich or curious.
Someone is both not rich and generous.
Susan is not old. | Paul is not strong. | neutral | ((?[X]:((old(X)<~>~quiet(X))))<=>((rich(lucy)|~strong(lucy))))&
(((~strong(susan)&~patient(susan)))<=>((~curious(paul)&~humble(paul))))&
(((calm(lucy)&~generous(lucy)))=>(?[X]:((strong(X)&curious(X)))))&
(![X]:((creative(X)<~>~tall(X))<=>~creative(X)))&
(![X]:((brave(X)&humble(X))=>(~calm(X)<~>quiet(X))))&
(((creative(alice)<~>quiet(alice)))=>(?[X]:((~curious(X)|generous(X)))))&
(![X]:((~humble(X)|~kind(X))<=>~patient(X)))&
(![X]:((~humble(X)|~creative(X))<=>(rich(X)|wise(X))))&
(![X]:((calm(X)|~wise(X))<=>(~patient(X)&~calm(X))))&
(((creative(paul)|brave(paul)))<=>(?[X]:(~humble(X))))&
(![X]:((brave(X)&tall(X))=>~rich(X)))&
(![X]:((generous(X)<~>~rich(X))<=>(~kind(X)&~humble(X))))&
((?[X]:((strong(X)&~old(X))))<=>(quiet(john)))&
(![X]:((curious(X)&~brave(X))=>(quiet(X)|tall(X))))&
((?[X]:(~tall(X)))=>((brave(lucy)<~>tall(lucy))))&
(![X]:((happy(X)|~old(X))=>(~happy(X)&~funny(X))))&
((generous(mary)&brave(mary)))&
(?[X]:((~curious(X)&~calm(X))))&
(?[X]:(rich(X)))&
((~tall(fred)|funny(fred)))&
((~rich(alice)<~>curious(alice)))&
(?[X]:((~rich(X)&generous(X))))&
(~old(susan)) | ~strong(paul) | [] | null | 0 |
Everyone who is either generous or creative is either not humble or not curious and vice versa.
Everyone who is not happy is both not generous and brave and vice versa.
If john is not strong or not generous then someone is brave or kind.
Everyone who is generous is either curious or not kind and vice versa.
Everyone who is not patient or kind is not strong.
Everyone who is not quiet or not old is humble or funny and vice versa.
Everyone who is either creative or generous is strong or funny and vice versa.
If someone is either generous or not brave then someone is either creative or rich and vice versa.
If mary is not happy or not patient then lucy is either strong or patient.
Everyone who is either not funny or not patient is not calm or not rich and vice versa.
If someone is both humble and not patient then someone is either not funny or old.
If someone is not quiet or not wise then alice is either old or not creative and vice versa.
If fred is both calm and not brave then someone is not strong or not happy and vice versa.
Everyone who is either brave or not strong is quiet or not old and vice versa.
If someone is tall then someone is both wise and old and vice versa.
Everyone who is not funny is calm or funny and vice versa.
Someone is humble or not tall.
Susan is creative.
Paul is either not strong or not funny.
Fred is either not old or not wise.
Someone is old.
Someone is not generous.
Someone is either not happy or creative.
Someone is calm or not tall. | Paul is strong. | entailment | (![X]:((generous(X)<~>creative(X))<=>(~humble(X)<~>~curious(X))))&
(![X]:(~happy(X)<=>(~generous(X)&brave(X))))&
(((~strong(john)|~generous(john)))=>(?[X]:((brave(X)|kind(X)))))&
(![X]:(generous(X)<=>(curious(X)<~>~kind(X))))&
(![X]:((~patient(X)|kind(X))=>~strong(X)))&
(![X]:((~quiet(X)|~old(X))<=>(humble(X)|funny(X))))&
(![X]:((creative(X)<~>generous(X))<=>(strong(X)|funny(X))))&
((?[X]:((generous(X)<~>~brave(X))))<=>(?[X]:((creative(X)<~>rich(X)))))&
(((~happy(mary)|~patient(mary)))=>((strong(lucy)<~>patient(lucy))))&
(![X]:((~funny(X)<~>~patient(X))<=>(~calm(X)|~rich(X))))&
((?[X]:((humble(X)&~patient(X))))=>(?[X]:((~funny(X)<~>old(X)))))&
((?[X]:((~quiet(X)|~wise(X))))<=>((old(alice)<~>~creative(alice))))&
(((calm(fred)&~brave(fred)))<=>(?[X]:((~strong(X)|~happy(X)))))&
(![X]:((brave(X)<~>~strong(X))<=>(quiet(X)|~old(X))))&
((?[X]:(tall(X)))<=>(?[X]:((wise(X)&old(X)))))&
(![X]:(~funny(X)<=>(calm(X)|funny(X))))&
(?[X]:((humble(X)|~tall(X))))&
(creative(susan))&
((~strong(paul)<~>~funny(paul)))&
((~old(fred)<~>~wise(fred)))&
(?[X]:(old(X)))&
(?[X]:(~generous(X)))&
(?[X]:((~happy(X)<~>creative(X))))&
(?[X]:((calm(X)|~tall(X)))) | strong(paul) | [
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4391940686935888860283
% SZS output start Proof for 4391940686935888860283
16. ! [X0] : (~funny(X0) <=> (funny(X0) | calm(X0))) [input p15]
19. ~strong(paul) <~> ~funny(paul) [input p18]
25. ~strong(paul) [input hypothesis]
71. ! [X0] : ((~funny(X0) | (~funny(X0) & ~calm(X0))) & ((funny(X0) | calm(X0)) | funny(X0))) [nnf transformation 16]
72. ! [X0] : ((~funny(X0) | (~funny(X0) & ~calm(X0))) & (funny(X0) | calm(X0) | funny(X0))) [flattening 71]
75. (funny(paul) | strong(paul)) & (~funny(paul) | ~strong(paul)) [nnf transformation 19]
157. ~funny(X0) | ~funny(X0) [cnf transformation 72]
161. funny(paul) | strong(paul) [cnf transformation 75]
169. ~strong(paul) [cnf transformation 25]
171. ~funny(X0) [duplicate literal removal 157]
349. strong(paul) [subsumption resolution 161,171]
370. $false [subsumption resolution 169,349]
% SZS output end Proof for 4391940686935888860283
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or humble is quiet or humble and vice versa. Everyone who is calm or not quiet is calm. If john is not calm then fred is not kind. Everyone who is either happy or calm is either not generous or generous and vice versa. Everyone who is not humble or not creative is not humble and vice versa. Everyone who is both not patient and creative is not creative or calm. If someone is either not funny or not generous then someone is old. Everyone who is both creative and funny is either not tall or not curious. If susan is both happy and not wise then someone is either generous or not quiet. If john is not patient then someone is both brave and not old and vice versa. Everyone who is both not happy and generous is calm and vice versa. If someone is either not creative or not tall then someone is not brave or not happy. Everyone who is not old is not quiet or rich. If susan is not patient then someone is tall. Everyone who is not tall or not humble is both old and not rich and vice versa. Everyone who is kind or curious is not calm or creative. Someone is not happy or not tall. Someone is either funny or not generous. Someone is old. Paul is not calm or not curious. Susan is curious. Fred is not funny or not kind. Someone is either happy or not old. | Paul is kind. | neutral | (![X]:((patient(X)<~>humble(X))<=>(quiet(X)|humble(X))))&
(![X]:((calm(X)|~quiet(X))=>calm(X)))&
((~calm(john))=>(~kind(fred)))&
(![X]:((happy(X)<~>calm(X))<=>(~generous(X)<~>generous(X))))&
(![X]:((~humble(X)|~creative(X))<=>~humble(X)))&
(![X]:((~patient(X)&creative(X))=>(~creative(X)|calm(X))))&
((?[X]:((~funny(X)<~>~generous(X))))=>(?[X]:(old(X))))&
(![X]:((creative(X)&funny(X))=>(~tall(X)<~>~curious(X))))&
(((happy(susan)&~wise(susan)))=>(?[X]:((generous(X)<~>~quiet(X)))))&
((~patient(john))<=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((~happy(X)&generous(X))<=>calm(X)))&
((?[X]:((~creative(X)<~>~tall(X))))=>(?[X]:((~brave(X)|~happy(X)))))&
(![X]:(~old(X)=>(~quiet(X)|rich(X))))&
((~patient(susan))=>(?[X]:(tall(X))))&
(![X]:((~tall(X)|~humble(X))<=>(old(X)&~rich(X))))&
(![X]:((kind(X)|curious(X))=>(~calm(X)|creative(X))))&
(?[X]:((~happy(X)|~tall(X))))&
(?[X]:((funny(X)<~>~generous(X))))&
(?[X]:(old(X)))&
((~calm(paul)|~curious(paul)))&
(curious(susan))&
((~funny(fred)|~kind(fred)))&
(?[X]:((happy(X)<~>~old(X)))) | kind(paul) | [] | null | 0 |
If alice is curious or generous then someone is humble or not wise and vice versa.
Everyone who is strong or not humble is both humble and calm.
If someone is both generous and funny then someone is either funny or quiet and vice versa.
Everyone who is both not funny and not quiet is calm and vice versa.
If lucy is not rich or strong then paul is either not creative or kind and vice versa.
If someone is either not tall or rich then someone is patient or kind and vice versa.
Everyone who is creative or not funny is both patient and not old and vice versa.
Everyone who is curious or funny is either rich or quiet.
If someone is either rich or not happy then john is not patient.
Everyone who is either brave or patient is both quiet and not old.
Everyone who is generous or not strong is either old or strong.
If someone is not curious or not quiet then fred is rich.
Everyone who is not brave or generous is either tall or curious and vice versa.
If fred is not brave or calm then someone is not funny.
Everyone who is funny is either brave or patient.
If susan is either tall or curious then someone is either strong or not funny and vice versa.
Mary is creative or not creative.
Someone is not quiet or wise.
Mary is generous.
Someone is either not humble or kind.
Alice is both tall and not old.
Alice is both not wise and not old. | Fred is not old. | entailment | (((curious(alice)|generous(alice)))<=>(?[X]:((humble(X)|~wise(X)))))&
(![X]:((strong(X)|~humble(X))=>(humble(X)&calm(X))))&
((?[X]:((generous(X)&funny(X))))<=>(?[X]:((funny(X)<~>quiet(X)))))&
(![X]:((~funny(X)&~quiet(X))<=>calm(X)))&
(((~rich(lucy)|strong(lucy)))<=>((~creative(paul)<~>kind(paul))))&
((?[X]:((~tall(X)<~>rich(X))))<=>(?[X]:((patient(X)|kind(X)))))&
(![X]:((creative(X)|~funny(X))<=>(patient(X)&~old(X))))&
(![X]:((curious(X)|funny(X))=>(rich(X)<~>quiet(X))))&
((?[X]:((rich(X)<~>~happy(X))))=>(~patient(john)))&
(![X]:((brave(X)<~>patient(X))=>(quiet(X)&~old(X))))&
(![X]:((generous(X)|~strong(X))=>(old(X)<~>strong(X))))&
((?[X]:((~curious(X)|~quiet(X))))=>(rich(fred)))&
(![X]:((~brave(X)|generous(X))<=>(tall(X)<~>curious(X))))&
(((~brave(fred)|calm(fred)))=>(?[X]:(~funny(X))))&
(![X]:(funny(X)=>(brave(X)<~>patient(X))))&
(((tall(susan)<~>curious(susan)))<=>(?[X]:((strong(X)<~>~funny(X)))))&
((creative(mary)|~creative(mary)))&
(?[X]:((~quiet(X)|wise(X))))&
(generous(mary))&
(?[X]:((~humble(X)<~>kind(X))))&
((tall(alice)&~old(alice)))&
((~wise(alice)&~old(alice))) | ~old(fred) | [
"p1",
"p3",
"p6",
"p7",
"p9",
"p10",
"p11",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 3028271012540049330969665
% SZS output start Proof for 3028271012540049330969665
2. ! [X0] : ((~humble(X0) | strong(X0)) => (calm(X0) & humble(X0))) [input p1]
4. ! [X0] : ((~quiet(X0) & ~funny(X0)) <=> calm(X0)) [input p3]
7. ! [X0] : ((~funny(X0) | creative(X0)) <=> (~old(X0) & patient(X0))) [input p6]
8. ! [X0] : ((funny(X0) | curious(X0)) => (rich(X0) <~> quiet(X0))) [input p7]
10. ! [X0] : ((brave(X0) <~> patient(X0)) => (~old(X0) & quiet(X0))) [input p9]
11. ! [X0] : ((~strong(X0) | generous(X0)) => (old(X0) <~> strong(X0))) [input p10]
12. ? [X0] : (~quiet(X0) | ~curious(X0)) => rich(fred) [input p11]
15. ! [X0] : (funny(X0) => (brave(X0) <~> patient(X0))) [input p14]
21. ~old(alice) & tall(alice) [input p20]
23. old(fred) [input hypothesis]
26. ! [X0] : ((calm(X0) & humble(X0)) | (humble(X0) & ~strong(X0))) [ennf transformation 2]
27. ! [X0] : ((rich(X0) <~> quiet(X0)) | (~funny(X0) & ~curious(X0))) [ennf transformation 8]
29. ! [X0] : ((~old(X0) & quiet(X0)) | (brave(X0) <=> patient(X0))) [ennf transformation 10]
30. ! [X0] : ((old(X0) <~> strong(X0)) | (strong(X0) & ~generous(X0))) [ennf transformation 11]
31. rich(fred) | ! [X0] : (quiet(X0) & curious(X0)) [ennf transformation 12]
33. ! [X0] : ((brave(X0) <~> patient(X0)) | ~funny(X0)) [ennf transformation 15]
44. ! [X0] : (((~quiet(X0) & ~funny(X0)) | ~calm(X0)) & (calm(X0) | (quiet(X0) | funny(X0)))) [nnf transformation 4]
45. ! [X0] : (((~quiet(X0) & ~funny(X0)) | ~calm(X0)) & (calm(X0) | quiet(X0) | funny(X0))) [flattening 44]
53. ! [X0] : (((~funny(X0) | creative(X0)) | (old(X0) | ~patient(X0))) & ((~old(X0) & patient(X0)) | (funny(X0) & ~creative(X0)))) [nnf transformation 7]
54. ! [X0] : ((~funny(X0) | creative(X0) | old(X0) | ~patient(X0)) & ((~old(X0) & patient(X0)) | (funny(X0) & ~creative(X0)))) [flattening 53]
55. ! [X0] : (((~quiet(X0) | ~rich(X0)) & (quiet(X0) | rich(X0))) | (~funny(X0) & ~curious(X0))) [nnf transformation 27]
57. ! [X0] : ((~old(X0) & quiet(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) [nnf transformation 29]
58. ! [X0] : (((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (strong(X0) & ~generous(X0))) [nnf transformation 30]
63. ! [X0] : (((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | ~funny(X0)) [nnf transformation 33]
79. ~strong(X0) | calm(X0) [cnf transformation 26]
89. ~quiet(X0) | ~calm(X0) [cnf transformation 45]
103. patient(X0) | funny(X0) [cnf transformation 54]
105. ~old(X0) | funny(X0) [cnf transformation 54]
110. ~rich(X0) | ~quiet(X0) | ~funny(X0) [cnf transformation 55]
113. ~brave(X0) | patient(X0) | quiet(X0) [cnf transformation 57]
116. ~old(X0) | brave(X0) | ~patient(X0) [cnf transformation 57]
118. strong(X0) | old(X0) | strong(X0) [cnf transformation 58]
122. rich(fred) | quiet(X0) [cnf transformation 31]
131. patient(X0) | brave(X0) | ~funny(X0) [cnf transformation 63]
132. ~brave(X0) | ~patient(X0) | ~funny(X0) [cnf transformation 63]
147. ~old(alice) [cnf transformation 21]
150. old(fred) [cnf transformation 23]
151. old(X0) | strong(X0) [duplicate literal removal 118]
279. 29 <=> ! [X0] : quiet(X0) [avatar definition]
280. quiet(X0) <- (29) [avatar component clause 279]
282. 30 <=> rich(fred) [avatar definition]
284. rich(fred) <- (30) [avatar component clause 282]
285. 29 | 30 [avatar split clause 122,282,279]
300. 34 <=> brave(fred) [avatar definition]
302. brave(fred) <- (34) [avatar component clause 300]
304. brave(X0) | patient(X0) [subsumption resolution 131,103]
348. funny(fred) [resolution 105,150]
349. strong(alice) [resolution 151,147]
356. calm(alice) [resolution 349,79]
404. 45 <=> quiet(alice) [avatar definition]
405. ~quiet(alice) <- (~45) [avatar component clause 404]
406. quiet(alice) <- (45) [avatar component clause 404]
418. ~calm(alice) <- (45) [resolution 406,89]
419. $false <- (45) [subsumption resolution 418,356]
420. ~45 [avatar contradiction clause 419]
430. $false <- (29, ~45) [resolution 280,405]
431. ~29 | 45 [avatar contradiction clause 430]
433. 47 <=> quiet(fred) [avatar definition]
434. ~quiet(fred) <- (~47) [avatar component clause 433]
466. ~quiet(fred) | ~funny(fred) <- (30) [resolution 284,110]
468. ~quiet(fred) <- (30) [subsumption resolution 466,348]
469. ~47 | ~30 [avatar split clause 468,282,433]
477. patient(X0) | quiet(X0) | patient(X0) [resolution 113,304]
478. patient(X0) | quiet(X0) [duplicate literal removal 477]
503. brave(fred) | ~patient(fred) [resolution 116,150]
505. brave(fred) [subsumption resolution 503,304]
506. 34 [avatar split clause 505,300]
541. ~patient(fred) | ~funny(fred) <- (34) [resolution 132,302]
543. ~patient(fred) <- (34) [subsumption resolution 541,348]
621. quiet(fred) <- (34) [resolution 478,543]
624. $false <- (34, ~47) [subsumption resolution 621,434]
625. ~34 | 47 [avatar contradiction clause 624]
626. $false [avatar sat refutation 285,420,431,469,506,625]
% SZS output end Proof for 3028271012540049330969665
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and not happy is tall or old and vice versa. Everyone who is kind or not wise is either not wise or not funny and vice versa. Everyone who is happy or tall is both not happy and not wise. Everyone who is not quiet is not quiet or not creative and vice versa. If someone is not brave then lucy is either generous or rich and vice versa. Everyone who is both not wise and calm is either not brave or not tall and vice versa. Everyone who is kind is either not patient or curious and vice versa. Everyone who is curious is both not wise and kind and vice versa. If someone is not curious or strong then someone is both not wise and curious. If someone is either brave or patient then someone is both not tall and calm. If someone is happy or not wise then alice is both not strong and not rich and vice versa. If alice is funny then someone is either not happy or old. If alice is both kind and not patient then someone is not tall. Everyone who is not brave or kind is old and vice versa. If someone is either not strong or not funny then alice is not tall or happy. Everyone who is both not rich and generous is both humble and not strong. Someone is brave. Someone is either not humble or happy. John is both not old and not tall. Alice is either not quiet or generous. Someone is either not rich or rich. | Lucy is tall. | neutral | (![X]:((tall(X)&~happy(X))<=>(tall(X)|old(X))))&
(![X]:((kind(X)|~wise(X))<=>(~wise(X)<~>~funny(X))))&
(![X]:((happy(X)|tall(X))=>(~happy(X)&~wise(X))))&
(![X]:(~quiet(X)<=>(~quiet(X)|~creative(X))))&
((?[X]:(~brave(X)))<=>((generous(lucy)<~>rich(lucy))))&
(![X]:((~wise(X)&calm(X))<=>(~brave(X)<~>~tall(X))))&
(![X]:(kind(X)<=>(~patient(X)<~>curious(X))))&
(![X]:(curious(X)<=>(~wise(X)&kind(X))))&
((?[X]:((~curious(X)|strong(X))))=>(?[X]:((~wise(X)&curious(X)))))&
((?[X]:((brave(X)<~>patient(X))))=>(?[X]:((~tall(X)&calm(X)))))&
((?[X]:((happy(X)|~wise(X))))<=>((~strong(alice)&~rich(alice))))&
((funny(alice))=>(?[X]:((~happy(X)<~>old(X)))))&
(((kind(alice)&~patient(alice)))=>(?[X]:(~tall(X))))&
(![X]:((~brave(X)|kind(X))<=>old(X)))&
((?[X]:((~strong(X)<~>~funny(X))))=>((~tall(alice)|happy(alice))))&
(![X]:((~rich(X)&generous(X))=>(humble(X)&~strong(X))))&
(?[X]:(brave(X)))&
(?[X]:((~humble(X)<~>happy(X))))&
((~old(john)&~tall(john)))&
((~quiet(alice)<~>generous(alice)))&
(?[X]:((~rich(X)<~>rich(X)))) | tall(lucy) | [] | null | 0 |
Everyone who is both old and not strong is either not wise or creative.
If someone is both not generous and patient then someone is both kind and not kind.
If fred is both wise and generous then paul is either funny or creative and vice versa.
If someone is both happy and patient then mary is wise or generous and vice versa.
Everyone who is both generous and not quiet is not old and vice versa.
Everyone who is not curious is not happy or not generous.
Everyone who is generous or patient is not quiet or not tall and vice versa.
If fred is either not brave or patient then someone is either brave or not rich.
Everyone who is creative or old is not quiet.
If someone is not strong then someone is not funny or not strong.
If someone is strong or not humble then alice is either not creative or not calm.
If john is curious or happy then lucy is tall or not creative.
If someone is either rich or strong then mary is either not curious or patient and vice versa.
If paul is not funny then mary is either quiet or not funny and vice versa.
Everyone who is not quiet or not rich is either quiet or not rich and vice versa.
Fred is not patient or brave.
Someone is both creative and generous.
Someone is wise or funny.
Paul is generous or not rich.
John is funny.
Someone is not patient or not generous.
Someone is humble or generous.
Someone is not rich or humble. | John is rich. | contradiction | (![X]:((old(X)&~strong(X))=>(~wise(X)<~>creative(X))))&
((?[X]:((~generous(X)&patient(X))))=>(?[X]:((kind(X)&~kind(X)))))&
(((wise(fred)&generous(fred)))<=>((funny(paul)<~>creative(paul))))&
((?[X]:((happy(X)&patient(X))))<=>((wise(mary)|generous(mary))))&
(![X]:((generous(X)&~quiet(X))<=>~old(X)))&
(![X]:(~curious(X)=>(~happy(X)|~generous(X))))&
(![X]:((generous(X)|patient(X))<=>(~quiet(X)|~tall(X))))&
(((~brave(fred)<~>patient(fred)))=>(?[X]:((brave(X)<~>~rich(X)))))&
(![X]:((creative(X)|old(X))=>~quiet(X)))&
((?[X]:(~strong(X)))=>(?[X]:((~funny(X)|~strong(X)))))&
((?[X]:((strong(X)|~humble(X))))=>((~creative(alice)<~>~calm(alice))))&
(((curious(john)|happy(john)))=>((tall(lucy)|~creative(lucy))))&
((?[X]:((rich(X)<~>strong(X))))<=>((~curious(mary)<~>patient(mary))))&
((~funny(paul))<=>((quiet(mary)<~>~funny(mary))))&
(![X]:((~quiet(X)|~rich(X))<=>(quiet(X)<~>~rich(X))))&
((~patient(fred)|brave(fred)))&
(?[X]:((creative(X)&generous(X))))&
(?[X]:((wise(X)|funny(X))))&
((generous(paul)|~rich(paul)))&
(funny(john))&
(?[X]:((~patient(X)|~generous(X))))&
(?[X]:((humble(X)|generous(X))))&
(?[X]:((~rich(X)|humble(X)))) | rich(john) | [
"p4",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3975667261792526298329248
% SZS output start Proof for 3975667261792526298329248
5. ! [X0] : ((~quiet(X0) & generous(X0)) <=> ~old(X0)) [input p4]
9. ! [X0] : ((old(X0) | creative(X0)) => ~quiet(X0)) [input p8]
15. ! [X0] : ((~rich(X0) | ~quiet(X0)) <=> (quiet(X0) <~> ~rich(X0))) [input p14]
24. rich(john) [input hypothesis]
27. ! [X0] : (~old(X0) => (~quiet(X0) & generous(X0))) [unused predicate definition removal 5]
34. ! [X0] : ((~quiet(X0) & generous(X0)) | old(X0)) [ennf transformation 27]
38. ! [X0] : (~quiet(X0) | (~old(X0) & ~creative(X0))) [ennf transformation 9]
68. ! [X0] : (((~rich(X0) | ~quiet(X0)) | ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0)))) & (((rich(X0) | ~quiet(X0)) & (~rich(X0) | quiet(X0))) | (rich(X0) & quiet(X0)))) [nnf transformation 15]
69. ! [X0] : ((~rich(X0) | ~quiet(X0) | ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0)))) & (((rich(X0) | ~quiet(X0)) & (~rich(X0) | quiet(X0))) | (rich(X0) & quiet(X0)))) [flattening 68]
92. ~quiet(X0) | old(X0) [cnf transformation 34]
103. ~quiet(X0) | ~old(X0) [cnf transformation 38]
121. ~rich(X0) | quiet(X0) | quiet(X0) [cnf transformation 69]
134. rich(john) [cnf transformation 24]
135. ~rich(X0) | quiet(X0) [duplicate literal removal 121]
213. ~quiet(X0) [subsumption resolution 103,92]
295. ~rich(X0) [subsumption resolution 135,213]
315. $false [subsumption resolution 134,295]
% SZS output end Proof for 3975667261792526298329248
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not strong and not kind then lucy is either not patient or not wise and vice versa.
Everyone who is not calm is either old or not humble and vice versa.
If john is not quiet or not creative then someone is not old or not patient.
Everyone who is not generous or not curious is brave or not old and vice versa.
Everyone who is not happy is generous and vice versa.
If someone is not strong or not brave then someone is both curious and not calm and vice versa.
Everyone who is either not brave or kind is either wise or old and vice versa.
If someone is calm then lucy is both quiet and creative.
Everyone who is either not old or humble is both quiet and curious.
Everyone who is curious is wise or not happy.
Everyone who is quiet or not patient is both old and strong.
Everyone who is rich is either tall or not curious and vice versa.
Everyone who is not humble is kind.
Everyone who is creative or rich is quiet and vice versa.
Everyone who is both old and not brave is not wise or brave and vice versa.
If someone is either funny or strong then john is either not rich or not kind and vice versa.
Fred is either patient or not tall.
Someone is funny or not generous.
Someone is calm.
John is either not old or not strong.
Someone is either kind or happy.
Someone is either not patient or quiet.
Someone is both strong and not happy. | Lucy is happy. | contradiction | ((?[X]:((~strong(X)&~kind(X))))<=>((~patient(lucy)<~>~wise(lucy))))&
(![X]:(~calm(X)<=>(old(X)<~>~humble(X))))&
(((~quiet(john)|~creative(john)))=>(?[X]:((~old(X)|~patient(X)))))&
(![X]:((~generous(X)|~curious(X))<=>(brave(X)|~old(X))))&
(![X]:(~happy(X)<=>generous(X)))&
((?[X]:((~strong(X)|~brave(X))))<=>(?[X]:((curious(X)&~calm(X)))))&
(![X]:((~brave(X)<~>kind(X))<=>(wise(X)<~>old(X))))&
((?[X]:(calm(X)))=>((quiet(lucy)&creative(lucy))))&
(![X]:((~old(X)<~>humble(X))=>(quiet(X)&curious(X))))&
(![X]:(curious(X)=>(wise(X)|~happy(X))))&
(![X]:((quiet(X)|~patient(X))=>(old(X)&strong(X))))&
(![X]:(rich(X)<=>(tall(X)<~>~curious(X))))&
(![X]:(~humble(X)=>kind(X)))&
(![X]:((creative(X)|rich(X))<=>quiet(X)))&
(![X]:((old(X)&~brave(X))<=>(~wise(X)|brave(X))))&
((?[X]:((funny(X)<~>strong(X))))<=>((~rich(john)<~>~kind(john))))&
((patient(fred)<~>~tall(fred)))&
(?[X]:((funny(X)|~generous(X))))&
(?[X]:(calm(X)))&
((~old(john)<~>~strong(john)))&
(?[X]:((kind(X)<~>happy(X))))&
(?[X]:((~patient(X)<~>quiet(X))))&
(?[X]:((strong(X)&~happy(X)))) | happy(lucy) | [
"p3",
"p4",
"p7",
"p10",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2463055799899420333314607
% SZS output start Proof for 2463055799899420333314607
4. ! [X0] : ((~curious(X0) | ~generous(X0)) <=> (~old(X0) | brave(X0))) [input p3]
5. ! [X0] : (~happy(X0) <=> generous(X0)) [input p4]
8. ? [X0] : calm(X0) => (creative(lucy) & quiet(lucy)) [input p7]
11. ! [X0] : ((~patient(X0) | quiet(X0)) => (strong(X0) & old(X0))) [input p10]
15. ! [X0] : ((~brave(X0) & old(X0)) <=> (brave(X0) | ~wise(X0))) [input p14]
19. ? [X0] : calm(X0) [input p18]
24. happy(lucy) [input hypothesis]
27. (creative(lucy) & quiet(lucy)) | ! [X0] : ~calm(X0) [ennf transformation 8]
31. ! [X0] : ((strong(X0) & old(X0)) | (patient(X0) & ~quiet(X0))) [ennf transformation 11]
40. ! [X0] : (((~curious(X0) | ~generous(X0)) | (old(X0) & ~brave(X0))) & ((~old(X0) | brave(X0)) | (curious(X0) & generous(X0)))) [nnf transformation 4]
41. ! [X0] : ((~curious(X0) | ~generous(X0) | (old(X0) & ~brave(X0))) & (~old(X0) | brave(X0) | (curious(X0) & generous(X0)))) [flattening 40]
42. ! [X0] : ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0))) [nnf transformation 5]
53. ! [X0] : (((~brave(X0) & old(X0)) | (~brave(X0) & wise(X0))) & ((brave(X0) | ~wise(X0)) | (brave(X0) | ~old(X0)))) [nnf transformation 15]
54. ! [X0] : (((~brave(X0) & old(X0)) | (~brave(X0) & wise(X0))) & (brave(X0) | ~wise(X0) | brave(X0) | ~old(X0))) [flattening 53]
62. ? [X0] : calm(X0) => calm(sK6) [choice axiom]
63. calm(sK6) [skolemisation 19,62]
85. ~old(X0) | brave(X0) | generous(X0) [cnf transformation 41]
90. ~happy(X0) | ~generous(X0) [cnf transformation 42]
104. quiet(lucy) | ~calm(X0) [cnf transformation 27]
111. ~quiet(X0) | old(X0) [cnf transformation 31]
127. ~brave(X0) | ~brave(X0) [cnf transformation 54]
139. calm(sK6) [cnf transformation 63]
148. happy(lucy) [cnf transformation 24]
150. ~brave(X0) [duplicate literal removal 127]
225. 17 <=> ! [X0] : ~calm(X0) [avatar definition]
226. ~calm(X0) <- (17) [avatar component clause 225]
233. 19 <=> quiet(lucy) [avatar definition]
235. quiet(lucy) <- (19) [avatar component clause 233]
236. 17 | 19 [avatar split clause 104,233,225]
321. $false <- (17) [resolution 226,139]
322. ~17 [avatar contradiction clause 321]
325. ~generous(lucy) [resolution 90,148]
327. old(lucy) <- (19) [resolution 111,235]
392. brave(lucy) | generous(lucy) <- (19) [resolution 85,327]
397. generous(lucy) <- (19) [subsumption resolution 392,150]
398. $false <- (19) [subsumption resolution 397,325]
399. ~19 [avatar contradiction clause 398]
402. $false [avatar sat refutation 236,322,399]
% SZS output end Proof for 2463055799899420333314607
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not curious is both patient and old and vice versa.
Everyone who is not generous or funny is not old or not strong and vice versa.
Everyone who is either happy or not brave is strong or not creative.
If someone is both happy and curious then someone is not strong or not quiet.
If someone is either curious or creative then someone is both not patient and curious.
Everyone who is not kind or old is not wise and vice versa.
If susan is funny or not happy then john is both kind and not strong.
Everyone who is not brave or not kind is patient and vice versa.
If john is calm or old then someone is either not brave or not funny and vice versa.
If someone is both not patient and not kind then someone is not rich and vice versa.
Everyone who is both not old and strong is rich or creative.
If lucy is either not curious or not humble then paul is rich.
Everyone who is both not generous and happy is both rich and not kind and vice versa.
Everyone who is either tall or funny is kind or tall and vice versa.
Everyone who is both tall and happy is either not calm or not quiet.
Everyone who is generous or funny is both strong and patient and vice versa.
Someone is not calm.
Lucy is kind.
Fred is not tall.
Someone is not wise.
John is kind or not generous.
Someone is both creative and not funny.
Someone is creative or not tall. | Lucy is not patient. | contradiction | (![X]:((~happy(X)|~curious(X))<=>(patient(X)&old(X))))&
(![X]:((~generous(X)|funny(X))<=>(~old(X)|~strong(X))))&
(![X]:((happy(X)<~>~brave(X))=>(strong(X)|~creative(X))))&
((?[X]:((happy(X)&curious(X))))=>(?[X]:((~strong(X)|~quiet(X)))))&
((?[X]:((curious(X)<~>creative(X))))=>(?[X]:((~patient(X)&curious(X)))))&
(![X]:((~kind(X)|old(X))<=>~wise(X)))&
(((funny(susan)|~happy(susan)))=>((kind(john)&~strong(john))))&
(![X]:((~brave(X)|~kind(X))<=>patient(X)))&
(((calm(john)|old(john)))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
((?[X]:((~patient(X)&~kind(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~old(X)&strong(X))=>(rich(X)|creative(X))))&
(((~curious(lucy)<~>~humble(lucy)))=>(rich(paul)))&
(![X]:((~generous(X)&happy(X))<=>(rich(X)&~kind(X))))&
(![X]:((tall(X)<~>funny(X))<=>(kind(X)|tall(X))))&
(![X]:((tall(X)&happy(X))=>(~calm(X)<~>~quiet(X))))&
(![X]:((generous(X)|funny(X))<=>(strong(X)&patient(X))))&
(?[X]:(~calm(X)))&
(kind(lucy))&
(~tall(fred))&
(?[X]:(~wise(X)))&
((kind(john)|~generous(john)))&
(?[X]:((creative(X)&~funny(X))))&
(?[X]:((creative(X)|~tall(X)))) | ~patient(lucy) | [
"p0",
"p7",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 306620705094952276837746
% SZS output start Proof for 306620705094952276837746
1. ! [X0] : ((~curious(X0) | ~happy(X0)) <=> (old(X0) & patient(X0))) [input p0]
8. ! [X0] : ((~kind(X0) | ~brave(X0)) <=> patient(X0)) [input p7]
13. ! [X0] : ((happy(X0) & ~generous(X0)) <=> (~kind(X0) & rich(X0))) [input p12]
16. ! [X0] : ((funny(X0) | generous(X0)) <=> (patient(X0) & strong(X0))) [input p15]
24. ~patient(lucy) [input hypothesis]
41. ! [X0] : (((~curious(X0) | ~happy(X0)) | (~old(X0) | ~patient(X0))) & ((old(X0) & patient(X0)) | (curious(X0) & happy(X0)))) [nnf transformation 1]
42. ! [X0] : ((~curious(X0) | ~happy(X0) | ~old(X0) | ~patient(X0)) & ((old(X0) & patient(X0)) | (curious(X0) & happy(X0)))) [flattening 41]
53. ! [X0] : (((~kind(X0) | ~brave(X0)) | ~patient(X0)) & (patient(X0) | (kind(X0) & brave(X0)))) [nnf transformation 8]
54. ! [X0] : ((~kind(X0) | ~brave(X0) | ~patient(X0)) & (patient(X0) | (kind(X0) & brave(X0)))) [flattening 53]
66. ! [X0] : (((happy(X0) & ~generous(X0)) | (kind(X0) | ~rich(X0))) & ((~kind(X0) & rich(X0)) | (~happy(X0) | generous(X0)))) [nnf transformation 13]
67. ! [X0] : (((happy(X0) & ~generous(X0)) | kind(X0) | ~rich(X0)) & ((~kind(X0) & rich(X0)) | ~happy(X0) | generous(X0))) [flattening 66]
71. ! [X0] : (((funny(X0) | generous(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~funny(X0) & ~generous(X0)))) [nnf transformation 16]
72. ! [X0] : ((funny(X0) | generous(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~funny(X0) & ~generous(X0)))) [flattening 71]
81. patient(X0) | happy(X0) [cnf transformation 42]
103. kind(X0) | patient(X0) [cnf transformation 54]
118. ~kind(X0) | ~happy(X0) | generous(X0) [cnf transformation 67]
131. ~generous(X0) | patient(X0) [cnf transformation 72]
142. ~patient(lucy) [cnf transformation 24]
316. ~happy(X0) | generous(X0) | patient(X0) [resolution 118,103]
319. generous(X0) | patient(X0) [subsumption resolution 316,81]
320. patient(X0) [subsumption resolution 319,131]
328. $false [resolution 320,142]
% SZS output end Proof for 306620705094952276837746
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong then paul is patient and vice versa.
Everyone who is not generous or not creative is either humble or curious.
Everyone who is quiet is both strong and not patient.
If fred is brave then someone is not strong or not happy and vice versa.
Everyone who is not generous is both not curious and generous.
If someone is brave then lucy is both not curious and not humble and vice versa.
Everyone who is patient or tall is both generous and calm.
If fred is patient then someone is quiet and vice versa.
If someone is both humble and not old then someone is quiet or tall.
If lucy is either brave or not happy then someone is not generous and vice versa.
If someone is not brave then alice is either tall or not brave and vice versa.
Everyone who is either curious or humble is either humble or rich.
Everyone who is both not creative and not generous is rich or not old and vice versa.
If someone is either strong or kind then alice is happy or wise.
Everyone who is brave or strong is happy or quiet and vice versa.
If someone is not wise then john is not calm or not funny.
Fred is both strong and not tall.
Someone is not kind.
Fred is either not funny or not generous.
Someone is not quiet.
Someone is either brave or happy. | Fred is calm. | neutral | ((strong(lucy))<=>(patient(paul)))&
(![X]:((~generous(X)|~creative(X))=>(humble(X)<~>curious(X))))&
(![X]:(quiet(X)=>(strong(X)&~patient(X))))&
((brave(fred))<=>(?[X]:((~strong(X)|~happy(X)))))&
(![X]:(~generous(X)=>(~curious(X)&generous(X))))&
((?[X]:(brave(X)))<=>((~curious(lucy)&~humble(lucy))))&
(![X]:((patient(X)|tall(X))=>(generous(X)&calm(X))))&
((patient(fred))<=>(?[X]:(quiet(X))))&
((?[X]:((humble(X)&~old(X))))=>(?[X]:((quiet(X)|tall(X)))))&
(((brave(lucy)<~>~happy(lucy)))<=>(?[X]:(~generous(X))))&
((?[X]:(~brave(X)))<=>((tall(alice)<~>~brave(alice))))&
(![X]:((curious(X)<~>humble(X))=>(humble(X)<~>rich(X))))&
(![X]:((~creative(X)&~generous(X))<=>(rich(X)|~old(X))))&
((?[X]:((strong(X)<~>kind(X))))=>((happy(alice)|wise(alice))))&
(![X]:((brave(X)|strong(X))<=>(happy(X)|quiet(X))))&
((?[X]:(~wise(X)))=>((~calm(john)|~funny(john))))&
((strong(fred)&~tall(fred)))&
(?[X]:(~kind(X)))&
((~funny(fred)<~>~generous(fred)))&
(?[X]:(~quiet(X)))&
(?[X]:((brave(X)<~>happy(X)))) | calm(fred) | [] | null | 0 |
If someone is either not kind or not rich then mary is both not brave and not humble.
Everyone who is both humble and not curious is not generous or not calm and vice versa.
Everyone who is not curious is old or not kind and vice versa.
Everyone who is not humble is strong.
If john is either not creative or not kind then fred is both not quiet and old.
Everyone who is not happy or patient is generous.
Everyone who is both rich and patient is not kind or not wise and vice versa.
Everyone who is not strong or not brave is both funny and wise.
If someone is brave then susan is not wise and vice versa.
Everyone who is not curious is both not brave and not funny and vice versa.
Everyone who is quiet or funny is both not creative and happy and vice versa.
Everyone who is creative or not humble is either not patient or rich and vice versa.
Everyone who is not wise is brave and vice versa.
Everyone who is both not wise and not calm is not kind or not calm.
Someone is both patient and happy.
Fred is old or curious.
Mary is old or not creative.
Someone is either not old or humble. | Fred is brave. | neutral | ((?[X]:((~kind(X)<~>~rich(X))))=>((~brave(mary)&~humble(mary))))&
(![X]:((humble(X)&~curious(X))<=>(~generous(X)|~calm(X))))&
(![X]:(~curious(X)<=>(old(X)|~kind(X))))&
(![X]:(~humble(X)=>strong(X)))&
(((~creative(john)<~>~kind(john)))=>((~quiet(fred)&old(fred))))&
(![X]:((~happy(X)|patient(X))=>generous(X)))&
(![X]:((rich(X)&patient(X))<=>(~kind(X)|~wise(X))))&
(![X]:((~strong(X)|~brave(X))=>(funny(X)&wise(X))))&
((?[X]:(brave(X)))<=>(~wise(susan)))&
(![X]:(~curious(X)<=>(~brave(X)&~funny(X))))&
(![X]:((quiet(X)|funny(X))<=>(~creative(X)&happy(X))))&
(![X]:((creative(X)|~humble(X))<=>(~patient(X)<~>rich(X))))&
(![X]:(~wise(X)<=>brave(X)))&
(![X]:((~wise(X)&~calm(X))=>(~kind(X)|~calm(X))))&
(?[X]:((patient(X)&happy(X))))&
((old(fred)|curious(fred)))&
((old(mary)|~creative(mary)))&
(?[X]:((~old(X)<~>humble(X)))) | brave(fred) | [] | null | 0 |
If someone is both tall and not happy then someone is both brave and not strong and vice versa.
If susan is either rich or not tall then someone is either not happy or quiet.
If lucy is either funny or not strong then someone is both kind and strong and vice versa.
If someone is both wise and not brave then someone is both not brave and not wise.
If someone is not wise then someone is both tall and quiet.
If someone is tall then susan is both calm and not generous.
Everyone who is humble is not calm and vice versa.
If someone is rich or old then john is both not humble and not calm and vice versa.
Everyone who is both not strong and not tall is humble or not quiet.
Everyone who is both strong and not calm is either quiet or kind and vice versa.
If someone is both not creative and not rich then someone is both not kind and funny and vice versa.
Everyone who is humble or not tall is either not brave or not curious.
Everyone who is either not quiet or not wise is either happy or not curious and vice versa.
If someone is not happy or not strong then someone is not patient and vice versa.
If susan is either calm or wise then lucy is both patient and not rich.
If someone is both not brave and humble then susan is not curious or calm and vice versa.
Alice is either humble or wise.
Someone is not strong.
Lucy is both not strong and not kind.
Susan is both not humble and wise.
Someone is quiet or not brave.
Susan is patient or tall.
Someone is humble or not strong.
Someone is wise. | Susan is not generous. | entailment | ((?[X]:((tall(X)&~happy(X))))<=>(?[X]:((brave(X)&~strong(X)))))&
(((rich(susan)<~>~tall(susan)))=>(?[X]:((~happy(X)<~>quiet(X)))))&
(((funny(lucy)<~>~strong(lucy)))<=>(?[X]:((kind(X)&strong(X)))))&
((?[X]:((wise(X)&~brave(X))))=>(?[X]:((~brave(X)&~wise(X)))))&
((?[X]:(~wise(X)))=>(?[X]:((tall(X)&quiet(X)))))&
((?[X]:(tall(X)))=>((calm(susan)&~generous(susan))))&
(![X]:(humble(X)<=>~calm(X)))&
((?[X]:((rich(X)|old(X))))<=>((~humble(john)&~calm(john))))&
(![X]:((~strong(X)&~tall(X))=>(humble(X)|~quiet(X))))&
(![X]:((strong(X)&~calm(X))<=>(quiet(X)<~>kind(X))))&
((?[X]:((~creative(X)&~rich(X))))<=>(?[X]:((~kind(X)&funny(X)))))&
(![X]:((humble(X)|~tall(X))=>(~brave(X)<~>~curious(X))))&
(![X]:((~quiet(X)<~>~wise(X))<=>(happy(X)<~>~curious(X))))&
((?[X]:((~happy(X)|~strong(X))))<=>(?[X]:(~patient(X))))&
(((calm(susan)<~>wise(susan)))=>((patient(lucy)&~rich(lucy))))&
((?[X]:((~brave(X)&humble(X))))<=>((~curious(susan)|calm(susan))))&
((humble(alice)<~>wise(alice)))&
(?[X]:(~strong(X)))&
((~strong(lucy)&~kind(lucy)))&
((~humble(susan)&wise(susan)))&
(?[X]:((quiet(X)|~brave(X))))&
((patient(susan)|tall(susan)))&
(?[X]:((humble(X)|~strong(X))))&
(?[X]:(wise(X))) | ~generous(susan) | [
"p0",
"p3",
"p4",
"p5",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5744802931752839447208853
% SZS output start Proof for 5744802931752839447208853
1. ? [X0] : (~happy(X0) & tall(X0)) <=> ? [X0] : (~strong(X0) & brave(X0)) [input p0]
4. ? [X0] : (~brave(X0) & wise(X0)) => ? [X0] : (~wise(X0) & ~brave(X0)) [input p3]
5. ? [X0] : ~wise(X0) => ? [X0] : (quiet(X0) & tall(X0)) [input p4]
6. ? [X0] : tall(X0) => (~generous(susan) & calm(susan)) [input p5]
18. ? [X0] : ~strong(X0) [input p17]
25. generous(susan) [input hypothesis]
26. ? [X0] : (~happy(X0) & tall(X0)) <=> ? [X1] : (~strong(X1) & brave(X1)) [rectify 1]
27. ? [X0] : (~brave(X0) & wise(X0)) => ? [X1] : (~wise(X1) & ~brave(X1)) [rectify 4]
28. ? [X0] : ~wise(X0) => ? [X1] : (quiet(X1) & tall(X1)) [rectify 5]
32. ? [X1] : (~wise(X1) & ~brave(X1)) | ! [X0] : (brave(X0) | ~wise(X0)) [ennf transformation 27]
33. ? [X1] : (quiet(X1) & tall(X1)) | ! [X0] : wise(X0) [ennf transformation 28]
34. (~generous(susan) & calm(susan)) | ! [X0] : ~tall(X0) [ennf transformation 6]
39. (? [X0] : (~happy(X0) & tall(X0)) | ! [X1] : (strong(X1) | ~brave(X1))) & (? [X1] : (~strong(X1) & brave(X1)) | ! [X0] : (happy(X0) | ~tall(X0))) [nnf transformation 26]
40. (? [X0] : (~happy(X0) & tall(X0)) | ! [X1] : (strong(X1) | ~brave(X1))) & (? [X2] : (~strong(X2) & brave(X2)) | ! [X3] : (happy(X3) | ~tall(X3))) [rectify 39]
41. ? [X0] : (~happy(X0) & tall(X0)) => (~happy(sK0) & tall(sK0)) [choice axiom]
42. ? [X2] : (~strong(X2) & brave(X2)) => (~strong(sK1) & brave(sK1)) [choice axiom]
43. ((~happy(sK0) & tall(sK0)) | ! [X1] : (strong(X1) | ~brave(X1))) & ((~strong(sK1) & brave(sK1)) | ! [X3] : (happy(X3) | ~tall(X3))) [skolemisation 40,42,41]
51. ? [X0] : (~wise(X0) & ~brave(X0)) | ! [X1] : (brave(X1) | ~wise(X1)) [rectify 32]
52. ? [X0] : (~wise(X0) & ~brave(X0)) => (~wise(sK4) & ~brave(sK4)) [choice axiom]
53. (~wise(sK4) & ~brave(sK4)) | ! [X1] : (brave(X1) | ~wise(X1)) [skolemisation 51,52]
54. ? [X0] : (quiet(X0) & tall(X0)) | ! [X1] : wise(X1) [rectify 33]
55. ? [X0] : (quiet(X0) & tall(X0)) => (quiet(sK5) & tall(sK5)) [choice axiom]
56. (quiet(sK5) & tall(sK5)) | ! [X1] : wise(X1) [skolemisation 54,55]
84. ? [X0] : ~strong(X0) => ~strong(sK12) [choice axiom]
85. ~strong(sK12) [skolemisation 18,84]
94. tall(sK0) | strong(X1) | ~brave(X1) [cnf transformation 43]
107. ~wise(sK4) | brave(X1) | ~wise(X1) [cnf transformation 53]
108. tall(sK5) | wise(X1) [cnf transformation 56]
111. ~generous(susan) | ~tall(X0) [cnf transformation 34]
156. ~strong(sK12) [cnf transformation 85]
165. generous(susan) [cnf transformation 25]
167. 1 <=> ! [X1] : (strong(X1) | ~brave(X1)) [avatar definition]
168. strong(X1) | ~brave(X1) <- (1) [avatar component clause 167]
175. 3 <=> tall(sK0) [avatar definition]
177. tall(sK0) <- (3) [avatar component clause 175]
178. 1 | 3 [avatar split clause 94,175,167]
238. 16 <=> ! [X1] : (brave(X1) | ~wise(X1)) [avatar definition]
239. brave(X1) | ~wise(X1) <- (16) [avatar component clause 238]
241. 17 <=> wise(sK4) [avatar definition]
243. ~wise(sK4) <- (~17) [avatar component clause 241]
244. 16 | ~17 [avatar split clause 107,241,238]
251. 19 <=> ! [X1] : wise(X1) [avatar definition]
252. wise(X1) <- (19) [avatar component clause 251]
259. 21 <=> tall(sK5) [avatar definition]
261. tall(sK5) <- (21) [avatar component clause 259]
262. 19 | 21 [avatar split clause 108,259,251]
264. 22 <=> ! [X0] : ~tall(X0) [avatar definition]
265. ~tall(X0) <- (22) [avatar component clause 264]
267. 23 <=> generous(susan) [avatar definition]
270. 22 | ~23 [avatar split clause 111,267,264]
333. 38 <=> ! [X3] : strong(X3) [avatar definition]
334. strong(X3) <- (38) [avatar component clause 333]
415. 23 [avatar split clause 165,267]
416. $false <- (~17, 19) [subsumption resolution 243,252]
417. 17 | ~19 [avatar contradiction clause 416]
420. $false <- (3, 22) [subsumption resolution 177,265]
421. ~3 | ~22 [avatar contradiction clause 420]
422. brave(X1) <- (16, 19) [subsumption resolution 239,252]
423. strong(X1) <- (1, 16, 19) [subsumption resolution 168,422]
424. 38 | ~1 | ~16 | ~19 [avatar split clause 423,251,238,167,333]
425. $false <- (21, 22) [subsumption resolution 261,265]
426. ~21 | ~22 [avatar contradiction clause 425]
428. $false <- (38) [resolution 334,156]
431. ~38 [avatar contradiction clause 428]
432. $false [avatar sat refutation 178,244,262,270,415,417,421,424,426,431]
% SZS output end Proof for 5744802931752839447208853
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and creative is both not happy and wise and vice versa.
If susan is wise or old then mary is generous or funny and vice versa.
Everyone who is not rich or not kind is either patient or not kind and vice versa.
If paul is both funny and not happy then someone is calm and vice versa.
Everyone who is both brave and strong is brave or not happy and vice versa.
Everyone who is quiet is both not patient and not kind and vice versa.
Everyone who is either patient or rich is either curious or not rich and vice versa.
Everyone who is either not humble or not old is either patient or old and vice versa.
Everyone who is calm or humble is both strong and generous.
If someone is both old and not creative then someone is not old and vice versa.
Everyone who is either not kind or not rich is either not generous or not old.
Everyone who is old or not generous is old or humble and vice versa.
If lucy is both tall and not humble then someone is kind and vice versa.
If susan is either not generous or curious then someone is both wise and kind.
Everyone who is old or brave is either brave or not humble.
Susan is not quiet or brave.
Someone is both not old and wise.
Someone is not rich or wise.
Susan is not rich or rich. | Susan is not curious. | contradiction | (![X]:((~wise(X)&creative(X))<=>(~happy(X)&wise(X))))&
(((wise(susan)|old(susan)))<=>((generous(mary)|funny(mary))))&
(![X]:((~rich(X)|~kind(X))<=>(patient(X)<~>~kind(X))))&
(((funny(paul)&~happy(paul)))<=>(?[X]:(calm(X))))&
(![X]:((brave(X)&strong(X))<=>(brave(X)|~happy(X))))&
(![X]:(quiet(X)<=>(~patient(X)&~kind(X))))&
(![X]:((patient(X)<~>rich(X))<=>(curious(X)<~>~rich(X))))&
(![X]:((~humble(X)<~>~old(X))<=>(patient(X)<~>old(X))))&
(![X]:((calm(X)|humble(X))=>(strong(X)&generous(X))))&
((?[X]:((old(X)&~creative(X))))<=>(?[X]:(~old(X))))&
(![X]:((~kind(X)<~>~rich(X))=>(~generous(X)<~>~old(X))))&
(![X]:((old(X)|~generous(X))<=>(old(X)|humble(X))))&
(((tall(lucy)&~humble(lucy)))<=>(?[X]:(kind(X))))&
(((~generous(susan)<~>curious(susan)))=>(?[X]:((wise(X)&kind(X)))))&
(![X]:((old(X)|brave(X))=>(brave(X)<~>~humble(X))))&
((~quiet(susan)|brave(susan)))&
(?[X]:((~old(X)&wise(X))))&
(?[X]:((~rich(X)|wise(X))))&
((~rich(susan)|rich(susan))) | ~curious(susan) | [
"p2",
"p6",
"p7",
"p8",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 268407583589208436200892
% SZS output start Proof for 268407583589208436200892
3. ! [X0] : ((~kind(X0) | ~rich(X0)) <=> (patient(X0) <~> ~kind(X0))) [input p2]
7. ! [X0] : ((patient(X0) <~> rich(X0)) <=> (curious(X0) <~> ~rich(X0))) [input p6]
8. ! [X0] : ((~humble(X0) <~> ~old(X0)) <=> (patient(X0) <~> old(X0))) [input p7]
9. ! [X0] : ((humble(X0) | calm(X0)) => (generous(X0) & strong(X0))) [input p8]
11. ! [X0] : ((~kind(X0) <~> ~rich(X0)) => (~generous(X0) <~> ~old(X0))) [input p10]
12. ! [X0] : ((~generous(X0) | old(X0)) <=> (humble(X0) | old(X0))) [input p11]
20. ~curious(susan) [input hypothesis]
25. ! [X0] : ((generous(X0) & strong(X0)) | (~humble(X0) & ~calm(X0))) [ennf transformation 9]
26. ! [X0] : ((~generous(X0) <~> ~old(X0)) | (~kind(X0) <=> ~rich(X0))) [ennf transformation 11]
33. ! [X0] : (((~kind(X0) | ~rich(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | (kind(X0) & rich(X0)))) [nnf transformation 3]
34. ! [X0] : ((~kind(X0) | ~rich(X0) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) & (((kind(X0) | ~patient(X0)) & (~kind(X0) | patient(X0))) | (kind(X0) & rich(X0)))) [flattening 33]
42. ! [X0] : ((((~rich(X0) | ~patient(X0)) & (rich(X0) | patient(X0))) | ((curious(X0) | rich(X0)) & (~rich(X0) | ~curious(X0)))) & (((rich(X0) | ~curious(X0)) & (~rich(X0) | curious(X0))) | ((patient(X0) | ~rich(X0)) & (rich(X0) | ~patient(X0))))) [nnf transformation 7]
43. ! [X0] : ((((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0)))) & (((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))))) [nnf transformation 8]
49. ! [X0] : (((old(X0) | generous(X0)) & (~old(X0) | ~generous(X0))) | ((~kind(X0) | rich(X0)) & (~rich(X0) | kind(X0)))) [nnf transformation 26]
50. ! [X0] : (((~generous(X0) | old(X0)) | (~humble(X0) & ~old(X0))) & ((humble(X0) | old(X0)) | (generous(X0) & ~old(X0)))) [nnf transformation 12]
51. ! [X0] : ((~generous(X0) | old(X0) | (~humble(X0) & ~old(X0))) & (humble(X0) | old(X0) | (generous(X0) & ~old(X0)))) [flattening 50]
76. kind(X0) | ~patient(X0) | kind(X0) [cnf transformation 34]
77. ~kind(X0) | ~rich(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 34]
89. ~rich(X0) | curious(X0) | patient(X0) | ~rich(X0) [cnf transformation 42]
93. rich(X0) | patient(X0) | curious(X0) | rich(X0) [cnf transformation 42]
98. ~old(X0) | ~patient(X0) | ~old(X0) | humble(X0) [cnf transformation 43]
102. old(X0) | humble(X0) | old(X0) | ~patient(X0) [cnf transformation 43]
107. ~humble(X0) | generous(X0) [cnf transformation 25]
112. ~kind(X0) | ~generous(X0) | ~old(X0) | rich(X0) [cnf transformation 49]
118. ~generous(X0) | old(X0) | ~humble(X0) [cnf transformation 51]
135. ~curious(susan) [cnf transformation 20]
138. ~old(X0) | ~patient(X0) | humble(X0) [duplicate literal removal 98]
140. ~patient(X0) | humble(X0) | old(X0) [duplicate literal removal 102]
141. ~rich(X0) | curious(X0) | patient(X0) [duplicate literal removal 89]
143. curious(X0) | patient(X0) | rich(X0) [duplicate literal removal 93]
145. ~patient(X0) | kind(X0) [duplicate literal removal 76]
146. ~patient(X0) | ~rich(X0) | ~kind(X0) [duplicate literal removal 77]
158. 3 <=> old(susan) [avatar definition]
189. curious(X0) | patient(X0) [subsumption resolution 141,143]
190. ~patient(X0) | humble(X0) [subsumption resolution 138,140]
213. ~humble(X0) | old(X0) [subsumption resolution 118,107]
234. 18 <=> curious(susan) [avatar definition]
236. ~curious(susan) <- (~18) [avatar component clause 234]
238. 19 <=> generous(susan) [avatar definition]
272. ~18 [avatar split clause 135,234]
283. patient(susan) <- (~18) [resolution 189,236]
285. humble(susan) <- (~18) [resolution 283,190]
286. kind(susan) <- (~18) [resolution 283,145]
288. generous(susan) <- (~18) [resolution 285,107]
290. old(susan) <- (~18) [resolution 213,285]
340. ~rich(susan) | ~kind(susan) <- (~18) [resolution 146,283]
341. ~rich(susan) <- (~18) [subsumption resolution 340,286]
343. ~generous(susan) | ~old(susan) | rich(susan) <- (~18) [resolution 112,286]
351. 3 | 18 [avatar split clause 290,234,158]
352. ~generous(susan) | ~old(susan) <- (~18) [subsumption resolution 343,341]
353. ~3 | ~19 | 18 [avatar split clause 352,234,238,158]
354. 19 | 18 [avatar split clause 288,234,238]
355. $false [avatar sat refutation 272,351,353,354]
% SZS output end Proof for 268407583589208436200892
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not rich and not strong then mary is not brave.
Everyone who is not old is either tall or not patient and vice versa.
Everyone who is both not kind and not humble is either generous or not kind and vice versa.
If someone is not strong then someone is not brave.
If paul is humble or wise then someone is not curious and vice versa.
Everyone who is both quiet and calm is both strong and not old and vice versa.
If fred is both generous and not funny then someone is both not funny and quiet and vice versa.
Everyone who is not brave or funny is either not kind or not funny.
Everyone who is quiet or not humble is both rich and humble and vice versa.
Everyone who is either not calm or not tall is creative and vice versa.
If john is either funny or not generous then someone is both not rich and tall.
Everyone who is both tall and not strong is both not tall and creative and vice versa.
If someone is not old or not happy then lucy is old and vice versa.
Everyone who is not old or old is either not calm or calm and vice versa.
If mary is either not quiet or not curious then fred is either not happy or not old.
Everyone who is not humble is funny or not quiet and vice versa.
Someone is both not generous and quiet.
Alice is either not quiet or not brave.
Someone is both generous and not wise.
Fred is not funny.
Fred is calm.
Mary is either generous or happy.
Someone is either not old or not patient. | Mary is generous. | neutral | ((?[X]:((~rich(X)&~strong(X))))=>(~brave(mary)))&
(![X]:(~old(X)<=>(tall(X)<~>~patient(X))))&
(![X]:((~kind(X)&~humble(X))<=>(generous(X)<~>~kind(X))))&
((?[X]:(~strong(X)))=>(?[X]:(~brave(X))))&
(((humble(paul)|wise(paul)))<=>(?[X]:(~curious(X))))&
(![X]:((quiet(X)&calm(X))<=>(strong(X)&~old(X))))&
(((generous(fred)&~funny(fred)))<=>(?[X]:((~funny(X)&quiet(X)))))&
(![X]:((~brave(X)|funny(X))=>(~kind(X)<~>~funny(X))))&
(![X]:((quiet(X)|~humble(X))<=>(rich(X)&humble(X))))&
(![X]:((~calm(X)<~>~tall(X))<=>creative(X)))&
(((funny(john)<~>~generous(john)))=>(?[X]:((~rich(X)&tall(X)))))&
(![X]:((tall(X)&~strong(X))<=>(~tall(X)&creative(X))))&
((?[X]:((~old(X)|~happy(X))))<=>(old(lucy)))&
(![X]:((~old(X)|old(X))<=>(~calm(X)<~>calm(X))))&
(((~quiet(mary)<~>~curious(mary)))=>((~happy(fred)<~>~old(fred))))&
(![X]:(~humble(X)<=>(funny(X)|~quiet(X))))&
(?[X]:((~generous(X)&quiet(X))))&
((~quiet(alice)<~>~brave(alice)))&
(?[X]:((generous(X)&~wise(X))))&
(~funny(fred))&
(calm(fred))&
((generous(mary)<~>happy(mary)))&
(?[X]:((~old(X)<~>~patient(X)))) | generous(mary) | [] | null | 0 |
If someone is either not rich or not quiet then john is both not calm and strong.
Everyone who is both creative and quiet is happy and vice versa.
Everyone who is kind or creative is either not old or not curious.
Everyone who is patient or wise is creative or humble and vice versa.
If alice is creative or not funny then paul is calm or kind and vice versa.
Everyone who is strong is either not brave or calm and vice versa.
Everyone who is not old is both calm and not calm.
If someone is either humble or quiet then someone is not humble or not strong and vice versa.
If someone is either not patient or rich then mary is both not quiet and not strong.
Everyone who is both not curious and not old is not quiet and vice versa.
Everyone who is old is kind.
If mary is not patient or old then paul is not happy or strong.
Everyone who is not strong or happy is either not kind or not happy and vice versa.
Everyone who is both calm and not calm is either not happy or not kind.
Everyone who is not rich or creative is either not rich or not quiet.
If susan is not generous then someone is not old or creative and vice versa.
Paul is either not patient or not quiet.
Someone is either generous or not humble.
Susan is humble.
Paul is not calm.
Alice is either not humble or not strong. | John is humble. | neutral | ((?[X]:((~rich(X)<~>~quiet(X))))=>((~calm(john)&strong(john))))&
(![X]:((creative(X)&quiet(X))<=>happy(X)))&
(![X]:((kind(X)|creative(X))=>(~old(X)<~>~curious(X))))&
(![X]:((patient(X)|wise(X))<=>(creative(X)|humble(X))))&
(((creative(alice)|~funny(alice)))<=>((calm(paul)|kind(paul))))&
(![X]:(strong(X)<=>(~brave(X)<~>calm(X))))&
(![X]:(~old(X)=>(calm(X)&~calm(X))))&
((?[X]:((humble(X)<~>quiet(X))))<=>(?[X]:((~humble(X)|~strong(X)))))&
((?[X]:((~patient(X)<~>rich(X))))=>((~quiet(mary)&~strong(mary))))&
(![X]:((~curious(X)&~old(X))<=>~quiet(X)))&
(![X]:(old(X)=>kind(X)))&
(((~patient(mary)|old(mary)))=>((~happy(paul)|strong(paul))))&
(![X]:((~strong(X)|happy(X))<=>(~kind(X)<~>~happy(X))))&
(![X]:((calm(X)&~calm(X))=>(~happy(X)<~>~kind(X))))&
(![X]:((~rich(X)|creative(X))=>(~rich(X)<~>~quiet(X))))&
((~generous(susan))<=>(?[X]:((~old(X)|creative(X)))))&
((~patient(paul)<~>~quiet(paul)))&
(?[X]:((generous(X)<~>~humble(X))))&
(humble(susan))&
(~calm(paul))&
((~humble(alice)<~>~strong(alice))) | humble(john) | [] | null | 0 |
If someone is happy then someone is either curious or wise.
Everyone who is either not happy or tall is both not generous and not brave.
If alice is both not humble and not quiet then lucy is both calm and happy and vice versa.
Everyone who is not strong or rich is not old.
Everyone who is either strong or calm is either not old or happy.
Everyone who is both calm and not rich is both patient and calm.
If paul is both not strong and generous then fred is both not calm and not strong.
Everyone who is not curious or humble is both not curious and calm and vice versa.
If someone is either wise or quiet then lucy is not patient and vice versa.
Everyone who is not rich is not creative.
If someone is not funny or not old then someone is kind or tall and vice versa.
Everyone who is either not strong or not old is either not quiet or not generous.
Everyone who is both happy and humble is humble.
If mary is both not calm and not tall then alice is quiet.
If john is both not tall and calm then someone is wise.
If someone is either not rich or not patient then someone is both not strong and brave.
John is not happy or not quiet.
Someone is tall.
Fred is tall or generous.
Someone is quiet or not creative.
Lucy is either not tall or not quiet.
Susan is strong or tall.
Alice is either tall or not curious. | John is calm. | neutral | ((?[X]:(happy(X)))=>(?[X]:((curious(X)<~>wise(X)))))&
(![X]:((~happy(X)<~>tall(X))=>(~generous(X)&~brave(X))))&
(((~humble(alice)&~quiet(alice)))<=>((calm(lucy)&happy(lucy))))&
(![X]:((~strong(X)|rich(X))=>~old(X)))&
(![X]:((strong(X)<~>calm(X))=>(~old(X)<~>happy(X))))&
(![X]:((calm(X)&~rich(X))=>(patient(X)&calm(X))))&
(((~strong(paul)&generous(paul)))=>((~calm(fred)&~strong(fred))))&
(![X]:((~curious(X)|humble(X))<=>(~curious(X)&calm(X))))&
((?[X]:((wise(X)<~>quiet(X))))<=>(~patient(lucy)))&
(![X]:(~rich(X)=>~creative(X)))&
((?[X]:((~funny(X)|~old(X))))<=>(?[X]:((kind(X)|tall(X)))))&
(![X]:((~strong(X)<~>~old(X))=>(~quiet(X)<~>~generous(X))))&
(![X]:((happy(X)&humble(X))=>humble(X)))&
(((~calm(mary)&~tall(mary)))=>(quiet(alice)))&
(((~tall(john)&calm(john)))=>(?[X]:(wise(X))))&
((?[X]:((~rich(X)<~>~patient(X))))=>(?[X]:((~strong(X)&brave(X)))))&
((~happy(john)|~quiet(john)))&
(?[X]:(tall(X)))&
((tall(fred)|generous(fred)))&
(?[X]:((quiet(X)|~creative(X))))&
((~tall(lucy)<~>~quiet(lucy)))&
((strong(susan)|tall(susan)))&
((tall(alice)<~>~curious(alice))) | calm(john) | [] | null | 0 |
If susan is not old then fred is not calm or not humble and vice versa.
Everyone who is not calm is not creative.
If someone is both kind and strong then paul is not creative and vice versa.
Everyone who is brave or happy is either not kind or curious and vice versa.
If someone is either not quiet or humble then someone is not curious and vice versa.
If someone is both brave and not funny then someone is funny and vice versa.
Everyone who is either not generous or tall is either not calm or not old.
If someone is not quiet or not generous then alice is not quiet and vice versa.
Everyone who is brave is either kind or creative.
If susan is not creative or quiet then someone is either not calm or curious.
If someone is not creative then john is old and vice versa.
Everyone who is not old is not wise or old.
If someone is either not calm or not tall then someone is either not creative or creative and vice versa.
Everyone who is calm or rich is both not patient and quiet and vice versa.
Everyone who is calm is not strong and vice versa.
Everyone who is either quiet or creative is not curious and vice versa.
Someone is either not brave or not humble.
Someone is either not creative or not wise.
Someone is not generous.
Someone is either not patient or not wise.
Someone is either patient or not humble.
Susan is not strong or not curious.
Paul is either not calm or not tall. | Alice is rich. | contradiction | ((~old(susan))<=>((~calm(fred)|~humble(fred))))&
(![X]:(~calm(X)=>~creative(X)))&
((?[X]:((kind(X)&strong(X))))<=>(~creative(paul)))&
(![X]:((brave(X)|happy(X))<=>(~kind(X)<~>curious(X))))&
((?[X]:((~quiet(X)<~>humble(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((brave(X)&~funny(X))))<=>(?[X]:(funny(X))))&
(![X]:((~generous(X)<~>tall(X))=>(~calm(X)<~>~old(X))))&
((?[X]:((~quiet(X)|~generous(X))))<=>(~quiet(alice)))&
(![X]:(brave(X)=>(kind(X)<~>creative(X))))&
(((~creative(susan)|quiet(susan)))=>(?[X]:((~calm(X)<~>curious(X)))))&
((?[X]:(~creative(X)))<=>(old(john)))&
(![X]:(~old(X)=>(~wise(X)|old(X))))&
((?[X]:((~calm(X)<~>~tall(X))))<=>(?[X]:((~creative(X)<~>creative(X)))))&
(![X]:((calm(X)|rich(X))<=>(~patient(X)&quiet(X))))&
(![X]:(calm(X)<=>~strong(X)))&
(![X]:((quiet(X)<~>creative(X))<=>~curious(X)))&
(?[X]:((~brave(X)<~>~humble(X))))&
(?[X]:((~creative(X)<~>~wise(X))))&
(?[X]:(~generous(X)))&
(?[X]:((~patient(X)<~>~wise(X))))&
(?[X]:((patient(X)<~>~humble(X))))&
((~strong(susan)|~curious(susan)))&
((~calm(paul)<~>~tall(paul))) | rich(alice) | [
"p7",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 178640433384580346363143
% SZS output start Proof for 178640433384580346363143
8. ? [X0] : (~generous(X0) | ~quiet(X0)) <=> ~quiet(alice) [input p7]
14. ! [X0] : ((rich(X0) | calm(X0)) <=> (quiet(X0) & ~patient(X0))) [input p13]
19. ? [X0] : ~generous(X0) [input p18]
24. rich(alice) [input hypothesis]
53. (? [X0] : (~generous(X0) | ~quiet(X0)) | quiet(alice)) & (~quiet(alice) | ! [X0] : (generous(X0) & quiet(X0))) [nnf transformation 8]
54. (? [X0] : (~generous(X0) | ~quiet(X0)) | quiet(alice)) & (~quiet(alice) | ! [X1] : (generous(X1) & quiet(X1))) [rectify 53]
55. ? [X0] : (~generous(X0) | ~quiet(X0)) => (~generous(sK5) | ~quiet(sK5)) [choice axiom]
56. ((~generous(sK5) | ~quiet(sK5)) | quiet(alice)) & (~quiet(alice) | ! [X1] : (generous(X1) & quiet(X1))) [skolemisation 54,55]
70. ! [X0] : (((rich(X0) | calm(X0)) | (~quiet(X0) | patient(X0))) & ((quiet(X0) & ~patient(X0)) | (~rich(X0) & ~calm(X0)))) [nnf transformation 14]
71. ! [X0] : ((rich(X0) | calm(X0) | ~quiet(X0) | patient(X0)) & ((quiet(X0) & ~patient(X0)) | (~rich(X0) & ~calm(X0)))) [flattening 70]
80. ? [X0] : ~generous(X0) => ~generous(sK12) [choice axiom]
81. ~generous(sK12) [skolemisation 19,80]
114. ~quiet(alice) | generous(X1) [cnf transformation 56]
136. ~rich(X0) | quiet(X0) [cnf transformation 71]
148. ~generous(sK12) [cnf transformation 81]
156. rich(alice) [cnf transformation 24]
242. 19 <=> quiet(alice) [avatar definition]
243. ~quiet(alice) <- (~19) [avatar component clause 242]
255. 22 <=> ! [X1] : generous(X1) [avatar definition]
256. generous(X1) <- (22) [avatar component clause 255]
257. 22 | ~19 [avatar split clause 114,242,255]
394. $false <- (22) [resolution 256,148]
397. ~22 [avatar contradiction clause 394]
400. quiet(alice) [resolution 136,156]
401. $false <- (~19) [subsumption resolution 400,243]
402. 19 [avatar contradiction clause 401]
403. $false [avatar sat refutation 257,397,402]
% SZS output end Proof for 178640433384580346363143
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong or humble then someone is both not kind and brave.
If someone is either not humble or strong then someone is not kind or happy and vice versa.
If someone is not kind then fred is both humble and brave and vice versa.
Everyone who is not funny or curious is not calm and vice versa.
Everyone who is not calm is not curious and vice versa.
Everyone who is either not wise or kind is both not brave and not humble.
Everyone who is both not kind and rich is funny and vice versa.
Everyone who is both not quiet and rich is either not old or kind and vice versa.
Everyone who is both humble and brave is not tall and vice versa.
If mary is either not rich or wise then susan is happy and vice versa.
If lucy is both not strong and strong then someone is both not brave and calm and vice versa.
Everyone who is not strong or calm is either not happy or calm.
If someone is not rich or strong then paul is quiet and vice versa.
Everyone who is not wise is both not quiet and not rich and vice versa.
If susan is either not calm or not patient then someone is humble or not quiet.
Everyone who is creative is both not brave and not quiet and vice versa.
Fred is either rich or patient.
Someone is creative or wise.
John is either funny or old.
John is wise or not kind.
Someone is both not strong and generous.
Someone is not humble or kind.
Mary is either not strong or not old. | Fred is not patient. | contradiction | ((?[X]:((strong(X)|humble(X))))=>(?[X]:((~kind(X)&brave(X)))))&
((?[X]:((~humble(X)<~>strong(X))))<=>(?[X]:((~kind(X)|happy(X)))))&
((?[X]:(~kind(X)))<=>((humble(fred)&brave(fred))))&
(![X]:((~funny(X)|curious(X))<=>~calm(X)))&
(![X]:(~calm(X)<=>~curious(X)))&
(![X]:((~wise(X)<~>kind(X))=>(~brave(X)&~humble(X))))&
(![X]:((~kind(X)&rich(X))<=>funny(X)))&
(![X]:((~quiet(X)&rich(X))<=>(~old(X)<~>kind(X))))&
(![X]:((humble(X)&brave(X))<=>~tall(X)))&
(((~rich(mary)<~>wise(mary)))<=>(happy(susan)))&
(((~strong(lucy)&strong(lucy)))<=>(?[X]:((~brave(X)&calm(X)))))&
(![X]:((~strong(X)|calm(X))=>(~happy(X)<~>calm(X))))&
((?[X]:((~rich(X)|strong(X))))<=>(quiet(paul)))&
(![X]:(~wise(X)<=>(~quiet(X)&~rich(X))))&
(((~calm(susan)<~>~patient(susan)))=>(?[X]:((humble(X)|~quiet(X)))))&
(![X]:(creative(X)<=>(~brave(X)&~quiet(X))))&
((rich(fred)<~>patient(fred)))&
(?[X]:((creative(X)|wise(X))))&
((funny(john)<~>old(john)))&
((wise(john)|~kind(john)))&
(?[X]:((~strong(X)&generous(X))))&
(?[X]:((~humble(X)|kind(X))))&
((~strong(mary)<~>~old(mary))) | ~patient(fred) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p5",
"p6",
"p11",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1448156627448185214326635
% SZS output start Proof for 1448156627448185214326635
1. ? [X0] : (humble(X0) | strong(X0)) => ? [X0] : (brave(X0) & ~kind(X0)) [input p0]
2. ? [X0] : (~humble(X0) <~> strong(X0)) <=> ? [X0] : (happy(X0) | ~kind(X0)) [input p1]
3. ? [X0] : ~kind(X0) <=> (brave(fred) & humble(fred)) [input p2]
4. ! [X0] : ((curious(X0) | ~funny(X0)) <=> ~calm(X0)) [input p3]
5. ! [X0] : (~calm(X0) <=> ~curious(X0)) [input p4]
6. ! [X0] : ((~wise(X0) <~> kind(X0)) => (~humble(X0) & ~brave(X0))) [input p5]
7. ! [X0] : ((rich(X0) & ~kind(X0)) <=> funny(X0)) [input p6]
12. ! [X0] : ((calm(X0) | ~strong(X0)) => (~happy(X0) <~> calm(X0))) [input p11]
14. ! [X0] : (~wise(X0) <=> (~rich(X0) & ~quiet(X0))) [input p13]
17. rich(fred) <~> patient(fred) [input p16]
24. ~patient(fred) [input hypothesis]
25. ? [X0] : (humble(X0) | strong(X0)) => ? [X1] : (brave(X1) & ~kind(X1)) [rectify 1]
26. ? [X0] : (~humble(X0) <~> strong(X0)) <=> ? [X1] : (happy(X1) | ~kind(X1)) [rectify 2]
29. ? [X1] : (brave(X1) & ~kind(X1)) | ! [X0] : (~humble(X0) & ~strong(X0)) [ennf transformation 25]
30. ! [X0] : ((~humble(X0) & ~brave(X0)) | (~wise(X0) <=> kind(X0))) [ennf transformation 6]
31. ! [X0] : ((~happy(X0) <~> calm(X0)) | (~calm(X0) & strong(X0))) [ennf transformation 12]
34. ? [X0] : (brave(X0) & ~kind(X0)) | ! [X1] : (~humble(X1) & ~strong(X1)) [rectify 29]
35. ? [X0] : (brave(X0) & ~kind(X0)) => (brave(sK0) & ~kind(sK0)) [choice axiom]
36. (brave(sK0) & ~kind(sK0)) | ! [X1] : (~humble(X1) & ~strong(X1)) [skolemisation 34,35]
37. (? [X0] : ((~strong(X0) | humble(X0)) & (strong(X0) | ~humble(X0))) | ! [X1] : (~happy(X1) & kind(X1))) & (? [X1] : (happy(X1) | ~kind(X1)) | ! [X0] : ((~humble(X0) | ~strong(X0)) & (strong(X0) | humble(X0)))) [nnf transformation 26]
38. (? [X0] : ((~strong(X0) | humble(X0)) & (strong(X0) | ~humble(X0))) | ! [X1] : (~happy(X1) & kind(X1))) & (? [X2] : (happy(X2) | ~kind(X2)) | ! [X3] : ((~humble(X3) | ~strong(X3)) & (strong(X3) | humble(X3)))) [rectify 37]
39. ? [X0] : ((~strong(X0) | humble(X0)) & (strong(X0) | ~humble(X0))) => ((~strong(sK1) | humble(sK1)) & (strong(sK1) | ~humble(sK1))) [choice axiom]
40. ? [X2] : (happy(X2) | ~kind(X2)) => (happy(sK2) | ~kind(sK2)) [choice axiom]
41. (((~strong(sK1) | humble(sK1)) & (strong(sK1) | ~humble(sK1))) | ! [X1] : (~happy(X1) & kind(X1))) & ((happy(sK2) | ~kind(sK2)) | ! [X3] : ((~humble(X3) | ~strong(X3)) & (strong(X3) | humble(X3)))) [skolemisation 38,40,39]
42. (? [X0] : ~kind(X0) | (~brave(fred) | ~humble(fred))) & ((brave(fred) & humble(fred)) | ! [X0] : kind(X0)) [nnf transformation 3]
43. (? [X0] : ~kind(X0) | ~brave(fred) | ~humble(fred)) & ((brave(fred) & humble(fred)) | ! [X0] : kind(X0)) [flattening 42]
44. (? [X0] : ~kind(X0) | ~brave(fred) | ~humble(fred)) & ((brave(fred) & humble(fred)) | ! [X1] : kind(X1)) [rectify 43]
45. ? [X0] : ~kind(X0) => ~kind(sK3) [choice axiom]
46. (~kind(sK3) | ~brave(fred) | ~humble(fred)) & ((brave(fred) & humble(fred)) | ! [X1] : kind(X1)) [skolemisation 44,45]
47. ! [X0] : (((curious(X0) | ~funny(X0)) | calm(X0)) & (~calm(X0) | (~curious(X0) & funny(X0)))) [nnf transformation 4]
48. ! [X0] : ((curious(X0) | ~funny(X0) | calm(X0)) & (~calm(X0) | (~curious(X0) & funny(X0)))) [flattening 47]
49. ! [X0] : ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0))) [nnf transformation 5]
50. ! [X0] : ((~humble(X0) & ~brave(X0)) | ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0)))) [nnf transformation 30]
51. ! [X0] : (((rich(X0) & ~kind(X0)) | ~funny(X0)) & (funny(X0) | (~rich(X0) | kind(X0)))) [nnf transformation 7]
52. ! [X0] : (((rich(X0) & ~kind(X0)) | ~funny(X0)) & (funny(X0) | ~rich(X0) | kind(X0))) [flattening 51]
61. ! [X0] : (((~calm(X0) | happy(X0)) & (calm(X0) | ~happy(X0))) | (~calm(X0) & strong(X0))) [nnf transformation 31]
66. ! [X0] : ((~wise(X0) | (rich(X0) | quiet(X0))) & ((~rich(X0) & ~quiet(X0)) | wise(X0))) [nnf transformation 14]
67. ! [X0] : ((~wise(X0) | rich(X0) | quiet(X0)) & ((~rich(X0) & ~quiet(X0)) | wise(X0))) [flattening 66]
71. (~patient(fred) | ~rich(fred)) & (patient(fred) | rich(fred)) [nnf transformation 17]
80. ~kind(sK0) | ~strong(X1) [cnf transformation 36]
81. ~kind(sK0) | ~humble(X1) [cnf transformation 36]
84. happy(sK2) | ~kind(sK2) | strong(X3) | humble(X3) [cnf transformation 41]
91. brave(fred) | kind(X1) [cnf transformation 46]
94. ~calm(X0) | ~curious(X0) [cnf transformation 48]
95. ~funny(X0) | curious(X0) | calm(X0) [cnf transformation 48]
96. ~curious(X0) | calm(X0) [cnf transformation 49]
97. ~calm(X0) | curious(X0) [cnf transformation 49]
99. ~wise(X0) | ~brave(X0) | ~kind(X0) [cnf transformation 50]
102. ~rich(X0) | funny(X0) | kind(X0) [cnf transformation 52]
119. calm(X0) | ~happy(X0) | strong(X0) [cnf transformation 61]
127. ~rich(X0) | wise(X0) [cnf transformation 67]
133. patient(fred) | rich(fred) [cnf transformation 71]
143. ~patient(fred) [cnf transformation 24]
146. 1 <=> ! [X1] : ~humble(X1) [avatar definition]
147. ~humble(X1) <- (1) [avatar component clause 146]
154. 3 <=> ! [X1] : ~strong(X1) [avatar definition]
155. ~strong(X1) <- (3) [avatar component clause 154]
158. 4 <=> kind(sK0) [avatar definition]
160. ~kind(sK0) <- (~4) [avatar component clause 158]
161. 1 | ~4 [avatar split clause 81,158,146]
162. 3 | ~4 [avatar split clause 80,158,154]
176. 8 <=> ! [X1] : kind(X1) [avatar definition]
177. kind(X1) <- (8) [avatar component clause 176]
185. 10 <=> kind(sK2) [avatar definition]
187. ~kind(sK2) <- (~10) [avatar component clause 185]
189. 11 <=> happy(sK2) [avatar definition]
191. happy(sK2) <- (11) [avatar component clause 189]
194. 12 <=> ! [X3] : (strong(X3) | humble(X3)) [avatar definition]
195. strong(X3) | humble(X3) <- (12) [avatar component clause 194]
196. 12 | ~10 | 11 [avatar split clause 84,189,185,194]
202. 14 <=> brave(fred) [avatar definition]
203. brave(fred) <- (14) [avatar component clause 202]
210. 8 | 14 [avatar split clause 91,202,176]
212. ~calm(X0) [subsumption resolution 97,94]
213. ~curious(X0) [subsumption resolution 96,212]
230. ~happy(X0) | strong(X0) [subsumption resolution 119,212]
264. 26 <=> rich(fred) [avatar definition]
265. rich(fred) <- (26) [avatar component clause 264]
268. 27 <=> patient(fred) [avatar definition]
272. 26 | 27 [avatar split clause 133,268,264]
320. ~27 [avatar split clause 143,268]
321. $false <- (~4, 8) [subsumption resolution 160,177]
322. 4 | ~8 [avatar contradiction clause 321]
326. wise(fred) <- (26) [resolution 127,265]
336. ~brave(fred) | ~kind(fred) <- (26) [resolution 99,326]
346. ~kind(fred) <- (14, 26) [subsumption resolution 336,203]
352. funny(fred) | kind(fred) <- (26) [resolution 102,265]
353. funny(fred) <- (14, 26) [subsumption resolution 352,346]
354. curious(fred) | calm(fred) <- (14, 26) [resolution 353,95]
357. calm(fred) <- (14, 26) [subsumption resolution 354,213]
358. $false <- (14, 26) [subsumption resolution 357,212]
359. ~14 | ~26 [avatar contradiction clause 358]
383. $false <- (8, ~10) [resolution 177,187]
386. ~8 | 10 [avatar contradiction clause 383]
389. strong(sK2) <- (11) [resolution 191,230]
390. $false <- (3, 11) [subsumption resolution 389,155]
391. ~3 | ~11 [avatar contradiction clause 390]
392. humble(X3) <- (3, 12) [subsumption resolution 195,155]
393. $false <- (1, 3, 12) [subsumption resolution 392,147]
394. ~1 | ~3 | ~12 [avatar contradiction clause 393]
395. $false [avatar sat refutation 161,162,196,210,272,320,322,359,386,391,394]
% SZS output end Proof for 1448156627448185214326635
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is kind and vice versa. Everyone who is not rich or wise is generous and vice versa. Everyone who is either not curious or not wise is either not curious or not brave. If someone is not generous then paul is both strong and not patient. Everyone who is generous is either happy or not wise. Everyone who is not patient or patient is rich and vice versa. If mary is not funny then lucy is both rich and funny. Everyone who is either not humble or not patient is not curious and vice versa. If someone is happy then lucy is not calm or curious. Everyone who is either not happy or old is not curious or not creative. If lucy is either strong or curious then paul is both not generous and old. If someone is either curious or strong then alice is not wise or brave and vice versa. If someone is wise then someone is either not rich or not wise and vice versa. Everyone who is either old or generous is both not quiet and curious. Everyone who is either old or wise is old or not old and vice versa. Fred is either not rich or calm. Mary is not calm or kind. Someone is humble or generous. Someone is humble or not creative. Paul is kind. | Fred is not kind. | neutral | (![X]:(creative(X)<=>kind(X)))&
(![X]:((~rich(X)|wise(X))<=>generous(X)))&
(![X]:((~curious(X)<~>~wise(X))=>(~curious(X)<~>~brave(X))))&
((?[X]:(~generous(X)))=>((strong(paul)&~patient(paul))))&
(![X]:(generous(X)=>(happy(X)<~>~wise(X))))&
(![X]:((~patient(X)|patient(X))<=>rich(X)))&
((~funny(mary))=>((rich(lucy)&funny(lucy))))&
(![X]:((~humble(X)<~>~patient(X))<=>~curious(X)))&
((?[X]:(happy(X)))=>((~calm(lucy)|curious(lucy))))&
(![X]:((~happy(X)<~>old(X))=>(~curious(X)|~creative(X))))&
(((strong(lucy)<~>curious(lucy)))=>((~generous(paul)&old(paul))))&
((?[X]:((curious(X)<~>strong(X))))<=>((~wise(alice)|brave(alice))))&
((?[X]:(wise(X)))<=>(?[X]:((~rich(X)<~>~wise(X)))))&
(![X]:((old(X)<~>generous(X))=>(~quiet(X)&curious(X))))&
(![X]:((old(X)<~>wise(X))<=>(old(X)|~old(X))))&
((~rich(fred)<~>calm(fred)))&
((~calm(mary)|kind(mary)))&
(?[X]:((humble(X)|generous(X))))&
(?[X]:((humble(X)|~creative(X))))&
(kind(paul)) | ~kind(fred) | [] | null | 0 |
If susan is generous or old then paul is not old and vice versa. If someone is both not brave and curious then someone is not funny and vice versa. Everyone who is either not humble or not strong is both calm and patient and vice versa. Everyone who is both not creative and strong is both not calm and not humble. Everyone who is either brave or not happy is both not patient and not funny and vice versa. Everyone who is patient is both not humble and not calm. If someone is humble then lucy is not rich or not generous. Everyone who is both brave and wise is either kind or not curious and vice versa. If someone is either curious or kind then john is both calm and not creative. Everyone who is either not strong or not humble is both not calm and humble and vice versa. If someone is happy or not quiet then someone is patient or kind and vice versa. Everyone who is not rich is both not wise and humble. If john is not curious or happy then someone is both humble and generous and vice versa. Everyone who is either not kind or patient is either not kind or rich and vice versa. If john is quiet then paul is either rich or not funny. Everyone who is either not quiet or humble is either creative or calm. Alice is kind. Susan is not quiet or curious. Paul is either rich or not creative. Someone is curious or quiet. Someone is strong or not humble. Someone is both creative and kind. Someone is either calm or not curious. Someone is tall. | Susan is humble. | contradiction | (((generous(susan)|old(susan)))<=>(~old(paul)))&
((?[X]:((~brave(X)&curious(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~humble(X)<~>~strong(X))<=>(calm(X)&patient(X))))&
(![X]:((~creative(X)&strong(X))=>(~calm(X)&~humble(X))))&
(![X]:((brave(X)<~>~happy(X))<=>(~patient(X)&~funny(X))))&
(![X]:(patient(X)=>(~humble(X)&~calm(X))))&
((?[X]:(humble(X)))=>((~rich(lucy)|~generous(lucy))))&
(![X]:((brave(X)&wise(X))<=>(kind(X)<~>~curious(X))))&
((?[X]:((curious(X)<~>kind(X))))=>((calm(john)&~creative(john))))&
(![X]:((~strong(X)<~>~humble(X))<=>(~calm(X)&humble(X))))&
((?[X]:((happy(X)|~quiet(X))))<=>(?[X]:((patient(X)|kind(X)))))&
(![X]:(~rich(X)=>(~wise(X)&humble(X))))&
(((~curious(john)|happy(john)))<=>(?[X]:((humble(X)&generous(X)))))&
(![X]:((~kind(X)<~>patient(X))<=>(~kind(X)<~>rich(X))))&
((quiet(john))=>((rich(paul)<~>~funny(paul))))&
(![X]:((~quiet(X)<~>humble(X))=>(creative(X)<~>calm(X))))&
(kind(alice))&
((~quiet(susan)|curious(susan)))&
((rich(paul)<~>~creative(paul)))&
(?[X]:((curious(X)|quiet(X))))&
(?[X]:((strong(X)|~humble(X))))&
(?[X]:((creative(X)&kind(X))))&
(?[X]:((calm(X)<~>~curious(X))))&
(?[X]:(tall(X))) | humble(susan) | [
"p2",
"p3",
"p5",
"p7",
"p8",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7880045271585685623491904
% SZS output start Proof for 7880045271585685623491904
3. ! [X0] : ((~humble(X0) <~> ~strong(X0)) <=> (patient(X0) & calm(X0))) [input p2]
4. ! [X0] : ((strong(X0) & ~creative(X0)) => (~humble(X0) & ~calm(X0))) [input p3]
6. ! [X0] : (patient(X0) => (~calm(X0) & ~humble(X0))) [input p5]
8. ! [X0] : ((wise(X0) & brave(X0)) <=> (kind(X0) <~> ~curious(X0))) [input p7]
9. ? [X0] : (curious(X0) <~> kind(X0)) => (~creative(john) & calm(john)) [input p8]
10. ! [X0] : ((~strong(X0) <~> ~humble(X0)) <=> (humble(X0) & ~calm(X0))) [input p9]
12. ! [X0] : (~rich(X0) => (humble(X0) & ~wise(X0))) [input p11]
14. ! [X0] : ((~kind(X0) <~> patient(X0)) <=> (~kind(X0) <~> rich(X0))) [input p13]
25. humble(susan) [input hypothesis]
29. ! [X0] : ((~humble(X0) & ~calm(X0)) | (~strong(X0) | creative(X0))) [ennf transformation 4]
30. ! [X0] : ((~humble(X0) & ~calm(X0)) | ~strong(X0) | creative(X0)) [flattening 29]
31. ! [X0] : ((~calm(X0) & ~humble(X0)) | ~patient(X0)) [ennf transformation 6]
34. (~creative(john) & calm(john)) | ! [X0] : (curious(X0) <=> kind(X0)) [ennf transformation 9]
35. ! [X0] : ((humble(X0) & ~wise(X0)) | rich(X0)) [ennf transformation 12]
45. ! [X0] : ((((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | (~patient(X0) | ~calm(X0))) & ((patient(X0) & calm(X0)) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0))))) [nnf transformation 3]
46. ! [X0] : ((((strong(X0) | humble(X0)) & (~strong(X0) | ~humble(X0))) | ~patient(X0) | ~calm(X0)) & ((patient(X0) & calm(X0)) | ((~humble(X0) | strong(X0)) & (~strong(X0) | humble(X0))))) [flattening 45]
49. ! [X0] : (((wise(X0) & brave(X0)) | ((kind(X0) | curious(X0)) & (~curious(X0) | ~kind(X0)))) & (((curious(X0) | ~kind(X0)) & (~curious(X0) | kind(X0))) | (~wise(X0) | ~brave(X0)))) [nnf transformation 8]
50. ! [X0] : (((wise(X0) & brave(X0)) | ((kind(X0) | curious(X0)) & (~curious(X0) | ~kind(X0)))) & (((curious(X0) | ~kind(X0)) & (~curious(X0) | kind(X0))) | ~wise(X0) | ~brave(X0))) [flattening 49]
51. (~creative(john) & calm(john)) | ! [X0] : ((curious(X0) | ~kind(X0)) & (kind(X0) | ~curious(X0))) [nnf transformation 34]
52. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | (~humble(X0) | calm(X0))) & ((humble(X0) & ~calm(X0)) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [nnf transformation 10]
53. ! [X0] : ((((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | ~humble(X0) | calm(X0)) & ((humble(X0) & ~calm(X0)) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0))))) [flattening 52]
64. ! [X0] : ((((~patient(X0) | kind(X0)) & (patient(X0) | ~kind(X0))) | ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0)))) & (((~rich(X0) | kind(X0)) & (rich(X0) | ~kind(X0))) | ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0))))) [nnf transformation 14]
84. ~humble(X0) | calm(X0) | strong(X0) [cnf transformation 46]
89. ~calm(X0) | ~strong(X0) | creative(X0) [cnf transformation 30]
97. ~patient(X0) | ~humble(X0) [cnf transformation 31]
98. ~patient(X0) | ~calm(X0) [cnf transformation 31]
104. ~kind(X0) | ~curious(X0) | wise(X0) [cnf transformation 50]
105. kind(X0) | wise(X0) | curious(X0) [cnf transformation 50]
106. calm(john) | kind(X0) | ~curious(X0) [cnf transformation 51]
107. calm(john) | curious(X0) | ~kind(X0) [cnf transformation 51]
108. ~creative(john) | kind(X0) | ~curious(X0) [cnf transformation 51]
109. ~creative(john) | curious(X0) | ~kind(X0) [cnf transformation 51]
110. ~calm(X0) | ~humble(X0) | strong(X0) [cnf transformation 53]
114. ~humble(X0) | ~strong(X0) | ~humble(X0) | calm(X0) [cnf transformation 53]
120. ~wise(X0) | rich(X0) [cnf transformation 35]
121. rich(X0) | humble(X0) [cnf transformation 35]
129. ~rich(X0) | kind(X0) | patient(X0) | kind(X0) [cnf transformation 64]
132. patient(X0) | ~kind(X0) | ~kind(X0) | ~rich(X0) [cnf transformation 64]
151. humble(susan) [cnf transformation 25]
153. ~rich(X0) | kind(X0) | patient(X0) [duplicate literal removal 129]
154. ~kind(X0) | patient(X0) | ~rich(X0) [duplicate literal removal 132]
157. ~humble(X0) | ~strong(X0) | calm(X0) [duplicate literal removal 114]
207. 12 <=> ! [X0] : (curious(X0) | ~kind(X0)) [avatar definition]
208. ~kind(X0) | curious(X0) <- (12) [avatar component clause 207]
210. 13 <=> creative(john) [avatar definition]
212. ~creative(john) <- (~13) [avatar component clause 210]
213. 12 | ~13 [avatar split clause 109,210,207]
215. 14 <=> ! [X0] : (kind(X0) | ~curious(X0)) [avatar definition]
216. ~curious(X0) | kind(X0) <- (14) [avatar component clause 215]
217. 14 | ~13 [avatar split clause 108,210,215]
219. 15 <=> calm(john) [avatar definition]
221. calm(john) <- (15) [avatar component clause 219]
222. 12 | 15 [avatar split clause 107,219,207]
223. 14 | 15 [avatar split clause 106,219,215]
224. ~humble(X0) | calm(X0) [subsumption resolution 157,84]
225. ~humble(X0) | strong(X0) [subsumption resolution 110,224]
282. ~rich(X0) | patient(X0) [subsumption resolution 153,154]
305. 33 <=> curious(susan) [avatar definition]
307. curious(susan) <- (33) [avatar component clause 305]
347. calm(susan) [resolution 224,151]
363. patient(X0) | humble(X0) [resolution 282,121]
446. ~strong(john) | creative(john) <- (15) [resolution 221,89]
447. ~strong(john) <- (~13, 15) [subsumption resolution 446,212]
595. ~calm(X4) | humble(X4) [resolution 363,98]
603. humble(john) <- (15) [resolution 595,221]
608. strong(john) <- (15) [resolution 603,225]
612. $false <- (~13, 15) [subsumption resolution 608,447]
613. 13 | ~15 [avatar contradiction clause 612]
629. curious(X0) | wise(X0) | curious(X0) <- (12) [resolution 208,105]
634. wise(X0) | curious(X0) <- (12) [duplicate literal removal 629]
686. rich(X1) | curious(X1) <- (12) [resolution 634,120]
759. patient(X0) | curious(X0) <- (12) [resolution 686,282]
773. ~humble(X3) | curious(X3) <- (12) [resolution 759,97]
794. curious(susan) <- (12) [resolution 773,151]
797. 33 | ~12 [avatar split clause 794,207,305]
798. kind(susan) <- (14, 33) [resolution 307,216]
803. ~curious(susan) | wise(susan) <- (14, 33) [resolution 798,104]
805. wise(susan) <- (14, 33) [subsumption resolution 803,307]
807. rich(susan) <- (14, 33) [resolution 805,120]
808. patient(susan) <- (14, 33) [resolution 807,282]
813. ~calm(susan) <- (14, 33) [resolution 808,98]
822. $false <- (14, 33) [subsumption resolution 813,347]
823. ~14 | ~33 [avatar contradiction clause 822]
824. $false [avatar sat refutation 213,217,222,223,613,797,823]
% SZS output end Proof for 7880045271585685623491904
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not patient or not wise then someone is calm or not quiet.
Everyone who is not creative is tall.
If someone is wise or kind then someone is brave or strong.
Everyone who is not funny is both not funny and tall and vice versa.
If someone is tall or kind then someone is both humble and not kind and vice versa.
Everyone who is not humble is both old and not curious.
Everyone who is generous is both not curious and not kind.
Everyone who is tall or strong is both generous and not patient.
If john is either not creative or not tall then someone is not brave or patient and vice versa.
If someone is not brave then someone is not tall or calm.
Everyone who is either not humble or calm is not happy or not kind and vice versa.
If someone is wise then susan is both rich and quiet.
Everyone who is not rich or not quiet is not calm or not brave and vice versa.
Everyone who is not calm is not old or not happy and vice versa.
Everyone who is both strong and humble is old or not brave and vice versa.
If someone is both not quiet and not curious then someone is not curious.
Someone is either humble or not happy.
Someone is funny.
Fred is either creative or not creative.
Someone is either patient or calm.
Fred is happy.
Fred is both rich and not strong. | John is creative. | neutral | ((?[X]:((~patient(X)<~>~wise(X))))=>(?[X]:((calm(X)|~quiet(X)))))&
(![X]:(~creative(X)=>tall(X)))&
((?[X]:((wise(X)|kind(X))))=>(?[X]:((brave(X)|strong(X)))))&
(![X]:(~funny(X)<=>(~funny(X)&tall(X))))&
((?[X]:((tall(X)|kind(X))))<=>(?[X]:((humble(X)&~kind(X)))))&
(![X]:(~humble(X)=>(old(X)&~curious(X))))&
(![X]:(generous(X)=>(~curious(X)&~kind(X))))&
(![X]:((tall(X)|strong(X))=>(generous(X)&~patient(X))))&
(((~creative(john)<~>~tall(john)))<=>(?[X]:((~brave(X)|patient(X)))))&
((?[X]:(~brave(X)))=>(?[X]:((~tall(X)|calm(X)))))&
(![X]:((~humble(X)<~>calm(X))<=>(~happy(X)|~kind(X))))&
((?[X]:(wise(X)))=>((rich(susan)&quiet(susan))))&
(![X]:((~rich(X)|~quiet(X))<=>(~calm(X)|~brave(X))))&
(![X]:(~calm(X)<=>(~old(X)|~happy(X))))&
(![X]:((strong(X)&humble(X))<=>(old(X)|~brave(X))))&
((?[X]:((~quiet(X)&~curious(X))))=>(?[X]:(~curious(X))))&
(?[X]:((humble(X)<~>~happy(X))))&
(?[X]:(funny(X)))&
((creative(fred)<~>~creative(fred)))&
(?[X]:((patient(X)<~>calm(X))))&
(happy(fred))&
((rich(fred)&~strong(fred))) | creative(john) | [] | null | 0 |
Everyone who is either not brave or brave is not generous or strong.
Everyone who is either happy or kind is both not brave and patient and vice versa.
Everyone who is either creative or calm is not happy or brave and vice versa.
Everyone who is patient or not happy is humble.
Everyone who is either not strong or happy is not happy or brave and vice versa.
If someone is tall or quiet then someone is either quiet or generous and vice versa.
If someone is either quiet or not curious then someone is both not humble and quiet.
Everyone who is kind is curious or not old and vice versa.
If someone is either not generous or wise then someone is either not happy or not brave and vice versa.
Everyone who is both not humble and not curious is not humble.
Everyone who is both not old and strong is not kind or rich and vice versa.
If john is both humble and kind then someone is either old or brave.
Everyone who is not calm or not quiet is either not brave or not calm and vice versa.
Everyone who is either quiet or rich is either not old or not curious.
If susan is not rich or humble then fred is either curious or not curious and vice versa.
Everyone who is humble is either not rich or not brave.
Someone is not wise.
Mary is both quiet and tall.
Someone is not patient or strong.
Someone is patient or tall.
Someone is rich or not patient.
Someone is either not funny or not brave.
Someone is either not funny or not humble. | Susan is not happy. | contradiction | (![X]:((~brave(X)<~>brave(X))=>(~generous(X)|strong(X))))&
(![X]:((happy(X)<~>kind(X))<=>(~brave(X)&patient(X))))&
(![X]:((creative(X)<~>calm(X))<=>(~happy(X)|brave(X))))&
(![X]:((patient(X)|~happy(X))=>humble(X)))&
(![X]:((~strong(X)<~>happy(X))<=>(~happy(X)|brave(X))))&
((?[X]:((tall(X)|quiet(X))))<=>(?[X]:((quiet(X)<~>generous(X)))))&
((?[X]:((quiet(X)<~>~curious(X))))=>(?[X]:((~humble(X)&quiet(X)))))&
(![X]:(kind(X)<=>(curious(X)|~old(X))))&
((?[X]:((~generous(X)<~>wise(X))))<=>(?[X]:((~happy(X)<~>~brave(X)))))&
(![X]:((~humble(X)&~curious(X))=>~humble(X)))&
(![X]:((~old(X)&strong(X))<=>(~kind(X)|rich(X))))&
(((humble(john)&kind(john)))=>(?[X]:((old(X)<~>brave(X)))))&
(![X]:((~calm(X)|~quiet(X))<=>(~brave(X)<~>~calm(X))))&
(![X]:((quiet(X)<~>rich(X))=>(~old(X)<~>~curious(X))))&
(((~rich(susan)|humble(susan)))<=>((curious(fred)<~>~curious(fred))))&
(![X]:(humble(X)=>(~rich(X)<~>~brave(X))))&
(?[X]:(~wise(X)))&
((quiet(mary)&tall(mary)))&
(?[X]:((~patient(X)|strong(X))))&
(?[X]:((patient(X)|tall(X))))&
(?[X]:((rich(X)|~patient(X))))&
(?[X]:((~funny(X)<~>~brave(X))))&
(?[X]:((~funny(X)<~>~humble(X)))) | ~happy(susan) | [
"p1",
"p3",
"p4",
"p7",
"p10",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6348416562716272755361623
% SZS output start Proof for 6348416562716272755361623
2. ! [X0] : ((happy(X0) <~> kind(X0)) <=> (patient(X0) & ~brave(X0))) [input p1]
4. ! [X0] : ((~happy(X0) | patient(X0)) => humble(X0)) [input p3]
5. ! [X0] : ((~strong(X0) <~> happy(X0)) <=> (brave(X0) | ~happy(X0))) [input p4]
8. ! [X0] : (kind(X0) <=> (~old(X0) | curious(X0))) [input p7]
11. ! [X0] : ((strong(X0) & ~old(X0)) <=> (rich(X0) | ~kind(X0))) [input p10]
15. (humble(susan) | ~rich(susan)) <=> (curious(fred) <~> ~curious(fred)) [input p14]
16. ! [X0] : (humble(X0) => (~rich(X0) <~> ~brave(X0))) [input p15]
24. ~happy(susan) [input hypothesis]
30. ! [X0] : (humble(X0) | (happy(X0) & ~patient(X0))) [ennf transformation 4]
37. ! [X0] : ((~rich(X0) <~> ~brave(X0)) | ~humble(X0)) [ennf transformation 16]
39. ! [X0] : ((((~kind(X0) | ~happy(X0)) & (kind(X0) | happy(X0))) | (~patient(X0) | brave(X0))) & ((patient(X0) & ~brave(X0)) | ((happy(X0) | ~kind(X0)) & (kind(X0) | ~happy(X0))))) [nnf transformation 2]
40. ! [X0] : ((((~kind(X0) | ~happy(X0)) & (kind(X0) | happy(X0))) | ~patient(X0) | brave(X0)) & ((patient(X0) & ~brave(X0)) | ((happy(X0) | ~kind(X0)) & (kind(X0) | ~happy(X0))))) [flattening 39]
43. ! [X0] : ((((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | (~brave(X0) & happy(X0))) & ((brave(X0) | ~happy(X0)) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0))))) [nnf transformation 5]
44. ! [X0] : ((((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | (~brave(X0) & happy(X0))) & (brave(X0) | ~happy(X0) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0))))) [flattening 43]
54. ! [X0] : ((kind(X0) | (old(X0) & ~curious(X0))) & ((~old(X0) | curious(X0)) | ~kind(X0))) [nnf transformation 8]
55. ! [X0] : ((kind(X0) | (old(X0) & ~curious(X0))) & (~old(X0) | curious(X0) | ~kind(X0))) [flattening 54]
61. ! [X0] : (((strong(X0) & ~old(X0)) | (~rich(X0) & kind(X0))) & ((rich(X0) | ~kind(X0)) | (~strong(X0) | old(X0)))) [nnf transformation 11]
62. ! [X0] : (((strong(X0) & ~old(X0)) | (~rich(X0) & kind(X0))) & (rich(X0) | ~kind(X0) | ~strong(X0) | old(X0))) [flattening 61]
69. ((humble(susan) | ~rich(susan)) | ((curious(fred) | curious(fred)) & (~curious(fred) | ~curious(fred)))) & (((curious(fred) | ~curious(fred)) & (~curious(fred) | curious(fred))) | (~humble(susan) & rich(susan))) [nnf transformation 15]
70. (humble(susan) | ~rich(susan) | ((curious(fred) | curious(fred)) & (~curious(fred) | ~curious(fred)))) & (((curious(fred) | ~curious(fred)) & (~curious(fred) | curious(fred))) | (~humble(susan) & rich(susan))) [flattening 69]
71. ! [X0] : (((brave(X0) | rich(X0)) & (~brave(X0) | ~rich(X0))) | ~humble(X0)) [nnf transformation 37]
89. ~kind(X0) | happy(X0) | ~brave(X0) [cnf transformation 40]
101. humble(X0) | happy(X0) [cnf transformation 30]
103. brave(X0) | ~happy(X0) | ~strong(X0) | ~happy(X0) [cnf transformation 44]
104. happy(X0) | ~strong(X0) | happy(X0) [cnf transformation 44]
120. old(X0) | kind(X0) [cnf transformation 55]
131. ~old(X0) | kind(X0) [cnf transformation 62]
134. ~rich(X0) | strong(X0) [cnf transformation 62]
151. humble(susan) | ~rich(susan) | ~curious(fred) | ~curious(fred) [cnf transformation 70]
152. humble(susan) | ~rich(susan) | curious(fred) | curious(fred) [cnf transformation 70]
153. ~rich(X0) | ~brave(X0) | ~humble(X0) [cnf transformation 71]
154. ~humble(X0) | rich(X0) | brave(X0) [cnf transformation 71]
165. ~happy(susan) [cnf transformation 24]
166. humble(susan) | ~rich(susan) | ~curious(fred) [duplicate literal removal 151]
167. humble(susan) | ~rich(susan) | curious(fred) [duplicate literal removal 152]
170. brave(X0) | ~happy(X0) | ~strong(X0) [duplicate literal removal 103]
171. ~strong(X0) | happy(X0) [duplicate literal removal 104]
175. ~strong(X0) | brave(X0) [subsumption resolution 170,171]
241. 16 <=> ! [X1] : (~brave(X1) | happy(X1)) [avatar definition]
242. ~brave(X1) | happy(X1) <- (16) [avatar component clause 241]
264. kind(X0) [subsumption resolution 131,120]
285. 24 <=> curious(fred) [avatar definition]
289. 25 <=> rich(susan) [avatar definition]
290. rich(susan) <- (25) [avatar component clause 289]
291. ~rich(susan) <- (~25) [avatar component clause 289]
293. 26 <=> humble(susan) [avatar definition]
295. humble(susan) <- (26) [avatar component clause 293]
296. 24 | ~25 | 26 [avatar split clause 167,293,289,285]
297. ~24 | ~25 | 26 [avatar split clause 166,293,289,285]
354. happy(X1) | ~brave(X1) [resolution 89,264]
356. 16 [avatar split clause 354,241]
387. rich(X0) | brave(X0) | happy(X0) [resolution 154,101]
397. rich(X0) | happy(X0) <- (16) [subsumption resolution 387,242]
538. happy(susan) <- (16, ~25) [resolution 397,291]
543. $false <- (16, ~25) [subsumption resolution 538,165]
544. ~16 | 25 [avatar contradiction clause 543]
547. ~brave(susan) | ~humble(susan) <- (25) [resolution 290,153]
548. strong(susan) <- (25) [resolution 290,134]
550. ~brave(susan) <- (25, 26) [subsumption resolution 547,295]
554. brave(susan) <- (25) [resolution 548,175]
556. $false <- (25, 26) [subsumption resolution 554,550]
557. ~25 | ~26 [avatar contradiction clause 556]
558. $false [avatar sat refutation 296,297,356,544,557]
% SZS output end Proof for 6348416562716272755361623
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not wise or not old is both rich and not wise and vice versa.
If john is not brave or not kind then alice is either not humble or not kind.
Everyone who is humble or creative is either not humble or brave.
Everyone who is not creative or creative is funny.
If someone is patient then someone is both not curious and not generous and vice versa.
If someone is both brave and not old then someone is kind or not strong.
If someone is both old and not funny then someone is rich and vice versa.
Everyone who is both not strong and not wise is both not wise and not calm.
Everyone who is not calm is not quiet or old and vice versa.
Everyone who is patient is either not old or not wise and vice versa.
If lucy is both old and not tall then alice is either not curious or curious and vice versa.
Everyone who is rich or quiet is not generous.
Everyone who is both rich and not happy is curious and vice versa.
Everyone who is quiet is either not funny or not calm.
Everyone who is both curious and not patient is either kind or strong.
Everyone who is both patient and not old is patient or not old and vice versa.
Someone is brave.
John is both not tall and old.
Susan is not humble or not quiet.
Someone is calm or not patient.
Someone is either not patient or not kind.
Someone is both not quiet and creative. | Lucy is quiet. | contradiction | (![X]:((~wise(X)|~old(X))<=>(rich(X)&~wise(X))))&
(((~brave(john)|~kind(john)))=>((~humble(alice)<~>~kind(alice))))&
(![X]:((humble(X)|creative(X))=>(~humble(X)<~>brave(X))))&
(![X]:((~creative(X)|creative(X))=>funny(X)))&
((?[X]:(patient(X)))<=>(?[X]:((~curious(X)&~generous(X)))))&
((?[X]:((brave(X)&~old(X))))=>(?[X]:((kind(X)|~strong(X)))))&
((?[X]:((old(X)&~funny(X))))<=>(?[X]:(rich(X))))&
(![X]:((~strong(X)&~wise(X))=>(~wise(X)&~calm(X))))&
(![X]:(~calm(X)<=>(~quiet(X)|old(X))))&
(![X]:(patient(X)<=>(~old(X)<~>~wise(X))))&
(((old(lucy)&~tall(lucy)))<=>((~curious(alice)<~>curious(alice))))&
(![X]:((rich(X)|quiet(X))=>~generous(X)))&
(![X]:((rich(X)&~happy(X))<=>curious(X)))&
(![X]:(quiet(X)=>(~funny(X)<~>~calm(X))))&
(![X]:((curious(X)&~patient(X))=>(kind(X)<~>strong(X))))&
(![X]:((patient(X)&~old(X))<=>(patient(X)|~old(X))))&
(?[X]:(brave(X)))&
((~tall(john)&old(john)))&
((~humble(susan)|~quiet(susan)))&
(?[X]:((calm(X)|~patient(X))))&
(?[X]:((~patient(X)<~>~kind(X))))&
(?[X]:((~quiet(X)&creative(X)))) | quiet(lucy) | [
"p0",
"p3",
"p4",
"p6",
"p9",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1125914126648561583317783
% SZS output start Proof for 1125914126648561583317783
1. ! [X0] : ((~old(X0) | ~wise(X0)) <=> (~wise(X0) & rich(X0))) [input p0]
4. ! [X0] : ((creative(X0) | ~creative(X0)) => funny(X0)) [input p3]
5. ? [X0] : patient(X0) <=> ? [X0] : (~generous(X0) & ~curious(X0)) [input p4]
7. ? [X0] : (~funny(X0) & old(X0)) <=> ? [X0] : rich(X0) [input p6]
10. ! [X0] : (patient(X0) <=> (~old(X0) <~> ~wise(X0))) [input p9]
12. ! [X0] : ((quiet(X0) | rich(X0)) => ~generous(X0)) [input p11]
13. ! [X0] : ((~happy(X0) & rich(X0)) <=> curious(X0)) [input p12]
16. ! [X0] : ((~old(X0) & patient(X0)) <=> (~old(X0) | patient(X0))) [input p15]
23. quiet(lucy) [input hypothesis]
24. ? [X0] : patient(X0) <=> ? [X1] : (~generous(X1) & ~curious(X1)) [rectify 5]
26. ? [X0] : (~funny(X0) & old(X0)) <=> ? [X1] : rich(X1) [rectify 7]
29. ! [X0] : (funny(X0) | (~creative(X0) & creative(X0))) [ennf transformation 4]
33. ! [X0] : (~generous(X0) | (~quiet(X0) & ~rich(X0))) [ennf transformation 12]
37. ! [X0] : (((~old(X0) | ~wise(X0)) | (wise(X0) | ~rich(X0))) & ((~wise(X0) & rich(X0)) | (old(X0) & wise(X0)))) [nnf transformation 1]
38. ! [X0] : ((~old(X0) | ~wise(X0) | wise(X0) | ~rich(X0)) & ((~wise(X0) & rich(X0)) | (old(X0) & wise(X0)))) [flattening 37]
41. (? [X0] : patient(X0) | ! [X1] : (generous(X1) | curious(X1))) & (? [X1] : (~generous(X1) & ~curious(X1)) | ! [X0] : ~patient(X0)) [nnf transformation 24]
42. (? [X0] : patient(X0) | ! [X1] : (generous(X1) | curious(X1))) & (? [X2] : (~generous(X2) & ~curious(X2)) | ! [X3] : ~patient(X3)) [rectify 41]
43. ? [X0] : patient(X0) => patient(sK0) [choice axiom]
44. ? [X2] : (~generous(X2) & ~curious(X2)) => (~generous(sK1) & ~curious(sK1)) [choice axiom]
45. (patient(sK0) | ! [X1] : (generous(X1) | curious(X1))) & ((~generous(sK1) & ~curious(sK1)) | ! [X3] : ~patient(X3)) [skolemisation 42,44,43]
49. (? [X0] : (~funny(X0) & old(X0)) | ! [X1] : ~rich(X1)) & (? [X1] : rich(X1) | ! [X0] : (funny(X0) | ~old(X0))) [nnf transformation 26]
50. (? [X0] : (~funny(X0) & old(X0)) | ! [X1] : ~rich(X1)) & (? [X2] : rich(X2) | ! [X3] : (funny(X3) | ~old(X3))) [rectify 49]
51. ? [X0] : (~funny(X0) & old(X0)) => (~funny(sK3) & old(sK3)) [choice axiom]
52. ? [X2] : rich(X2) => rich(sK4) [choice axiom]
53. ((~funny(sK3) & old(sK3)) | ! [X1] : ~rich(X1)) & (rich(sK4) | ! [X3] : (funny(X3) | ~old(X3))) [skolemisation 50,52,51]
56. ! [X0] : ((patient(X0) | ((~old(X0) | wise(X0)) & (~wise(X0) | old(X0)))) & (((wise(X0) | old(X0)) & (~wise(X0) | ~old(X0))) | ~patient(X0))) [nnf transformation 10]
59. ! [X0] : (((~happy(X0) & rich(X0)) | ~curious(X0)) & (curious(X0) | (happy(X0) | ~rich(X0)))) [nnf transformation 13]
60. ! [X0] : (((~happy(X0) & rich(X0)) | ~curious(X0)) & (curious(X0) | happy(X0) | ~rich(X0))) [flattening 59]
63. ! [X0] : (((~old(X0) & patient(X0)) | (old(X0) & ~patient(X0))) & ((~old(X0) | patient(X0)) | (old(X0) | ~patient(X0)))) [nnf transformation 16]
64. ! [X0] : (((~old(X0) & patient(X0)) | (old(X0) & ~patient(X0))) & (~old(X0) | patient(X0) | old(X0) | ~patient(X0))) [flattening 63]
77. ~wise(X0) | old(X0) [cnf transformation 38]
87. funny(X0) | creative(X0) [cnf transformation 29]
88. ~creative(X0) | funny(X0) [cnf transformation 29]
91. patient(sK0) | generous(X1) | curious(X1) [cnf transformation 45]
95. ~funny(sK3) | ~rich(X1) [cnf transformation 53]
102. wise(X0) | old(X0) | ~patient(X0) [cnf transformation 56]
112. ~quiet(X0) | ~generous(X0) [cnf transformation 33]
114. rich(X0) | ~curious(X0) [cnf transformation 60]
123. ~old(X0) | ~patient(X0) [cnf transformation 64]
134. quiet(lucy) [cnf transformation 23]
160. funny(X0) [subsumption resolution 87,88]
162. 5 <=> ! [X1] : (generous(X1) | curious(X1)) [avatar definition]
163. generous(X1) | curious(X1) <- (5) [avatar component clause 162]
165. 6 <=> patient(sK0) [avatar definition]
167. patient(sK0) <- (6) [avatar component clause 165]
168. 5 | 6 [avatar split clause 91,165,162]
170. 7 <=> ! [X3] : ~patient(X3) [avatar definition]
171. ~patient(X3) <- (7) [avatar component clause 170]
194. ~rich(X1) [subsumption resolution 95,160]
195. old(X0) | ~patient(X0) [subsumption resolution 102,77]
213. ~curious(X0) [subsumption resolution 114,194]
216. ~patient(X0) [subsumption resolution 123,195]
217. 7 [avatar split clause 216,170]
239. generous(X1) <- (5) [subsumption resolution 163,213]
246. ~generous(lucy) [resolution 112,134]
247. $false <- (5) [subsumption resolution 246,239]
248. ~5 [avatar contradiction clause 247]
249. $false <- (6, 7) [subsumption resolution 167,171]
250. ~6 | ~7 [avatar contradiction clause 249]
251. $false [avatar sat refutation 168,217,248,250]
% SZS output end Proof for 1125914126648561583317783
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is both creative and humble then someone is either not calm or quiet.
Everyone who is strong is not patient or rich and vice versa.
Everyone who is both kind and not creative is both not patient and not curious and vice versa.
If someone is not brave then someone is either wise or not creative.
Everyone who is either not old or not humble is calm.
Everyone who is both not calm and wise is both funny and generous and vice versa.
If someone is not quiet then someone is not funny or not creative.
If someone is rich or curious then mary is either not old or not humble and vice versa.
If someone is generous or old then alice is both tall and kind and vice versa.
Everyone who is not funny is either not wise or wise.
If alice is brave then fred is either strong or not creative.
Everyone who is both kind and calm is not funny or humble.
If someone is either curious or creative then someone is funny and vice versa.
Everyone who is funny is not quiet or not patient.
Everyone who is both not happy and brave is not funny or tall.
Everyone who is not patient is both happy and not happy.
Someone is both not funny and not tall.
Someone is either not wise or not rich.
John is both not humble and not tall.
Someone is not kind or old.
Someone is happy.
Fred is either not happy or not brave.
Someone is either not wise or humble.
Mary is either creative or kind. | Mary is not creative. | contradiction | (((creative(susan)&humble(susan)))=>(?[X]:((~calm(X)<~>quiet(X)))))&
(![X]:(strong(X)<=>(~patient(X)|rich(X))))&
(![X]:((kind(X)&~creative(X))<=>(~patient(X)&~curious(X))))&
((?[X]:(~brave(X)))=>(?[X]:((wise(X)<~>~creative(X)))))&
(![X]:((~old(X)<~>~humble(X))=>calm(X)))&
(![X]:((~calm(X)&wise(X))<=>(funny(X)&generous(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~funny(X)|~creative(X)))))&
((?[X]:((rich(X)|curious(X))))<=>((~old(mary)<~>~humble(mary))))&
((?[X]:((generous(X)|old(X))))<=>((tall(alice)&kind(alice))))&
(![X]:(~funny(X)=>(~wise(X)<~>wise(X))))&
((brave(alice))=>((strong(fred)<~>~creative(fred))))&
(![X]:((kind(X)&calm(X))=>(~funny(X)|humble(X))))&
((?[X]:((curious(X)<~>creative(X))))<=>(?[X]:(funny(X))))&
(![X]:(funny(X)=>(~quiet(X)|~patient(X))))&
(![X]:((~happy(X)&brave(X))=>(~funny(X)|tall(X))))&
(![X]:(~patient(X)=>(happy(X)&~happy(X))))&
(?[X]:((~funny(X)&~tall(X))))&
(?[X]:((~wise(X)<~>~rich(X))))&
((~humble(john)&~tall(john)))&
(?[X]:((~kind(X)|old(X))))&
(?[X]:(happy(X)))&
((~happy(fred)<~>~brave(fred)))&
(?[X]:((~wise(X)<~>humble(X))))&
((creative(mary)<~>kind(mary))) | ~creative(mary) | [
"p2",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2883898101239335162883523
% SZS output start Proof for 2883898101239335162883523
3. ! [X0] : ((~creative(X0) & kind(X0)) <=> (~curious(X0) & ~patient(X0))) [input p2]
16. ! [X0] : (~patient(X0) => (~happy(X0) & happy(X0))) [input p15]
24. creative(mary) <~> kind(mary) [input p23]
25. ~creative(mary) [input hypothesis]
42. ! [X0] : ((~happy(X0) & happy(X0)) | patient(X0)) [ennf transformation 16]
48. ! [X0] : (((~creative(X0) & kind(X0)) | (curious(X0) | patient(X0))) & ((~curious(X0) & ~patient(X0)) | (creative(X0) | ~kind(X0)))) [nnf transformation 3]
49. ! [X0] : (((~creative(X0) & kind(X0)) | curious(X0) | patient(X0)) & ((~curious(X0) & ~patient(X0)) | creative(X0) | ~kind(X0))) [flattening 48]
89. (~kind(mary) | ~creative(mary)) & (kind(mary) | creative(mary)) [nnf transformation 24]
95. ~kind(X0) | creative(X0) | ~patient(X0) [cnf transformation 49]
130. happy(X0) | patient(X0) [cnf transformation 42]
131. ~happy(X0) | patient(X0) [cnf transformation 42]
144. kind(mary) | creative(mary) [cnf transformation 89]
146. ~creative(mary) [cnf transformation 25]
284. patient(X0) [subsumption resolution 130,131]
325. 40 <=> creative(mary) [avatar definition]
327. ~creative(mary) <- (~40) [avatar component clause 325]
329. 41 <=> kind(mary) [avatar definition]
330. kind(mary) <- (41) [avatar component clause 329]
333. 40 | 41 [avatar split clause 144,329,325]
334. ~40 [avatar split clause 146,325]
343. creative(mary) | ~patient(mary) <- (41) [resolution 95,330]
345. ~patient(mary) <- (~40, 41) [subsumption resolution 343,327]
346. $false <- (~40, 41) [subsumption resolution 345,284]
347. 40 | ~41 [avatar contradiction clause 346]
348. $false [avatar sat refutation 333,334,347]
% SZS output end Proof for 2883898101239335162883523
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and rich is both not brave and not patient.
If mary is both quiet and not old then someone is both not quiet and brave.
If susan is either not brave or not tall then paul is not happy or not brave and vice versa.
Everyone who is not kind or not curious is both not brave and not humble and vice versa.
If susan is creative or funny then alice is not old or not kind.
If someone is either not quiet or not curious then alice is either happy or not old and vice versa.
If mary is both quiet and not strong then lucy is both strong and not wise and vice versa.
Everyone who is not funny is either not curious or quiet and vice versa.
Everyone who is both funny and not tall is not curious or old.
If lucy is happy then someone is not happy and vice versa.
Everyone who is not kind is kind or not humble and vice versa.
If someone is curious or happy then john is old or not old and vice versa.
Everyone who is both old and not old is not calm.
If someone is either humble or not curious then someone is both not strong and not funny.
Everyone who is not funny or not patient is not generous or humble and vice versa.
Everyone who is calm is both creative and old.
Fred is not old.
Alice is either not quiet or funny.
John is both not calm and curious.
Fred is either kind or tall.
Susan is kind or funny.
John is both curious and not kind. | Fred is not brave. | entailment | (![X]:((strong(X)&rich(X))=>(~brave(X)&~patient(X))))&
(((quiet(mary)&~old(mary)))=>(?[X]:((~quiet(X)&brave(X)))))&
(((~brave(susan)<~>~tall(susan)))<=>((~happy(paul)|~brave(paul))))&
(![X]:((~kind(X)|~curious(X))<=>(~brave(X)&~humble(X))))&
(((creative(susan)|funny(susan)))=>((~old(alice)|~kind(alice))))&
((?[X]:((~quiet(X)<~>~curious(X))))<=>((happy(alice)<~>~old(alice))))&
(((quiet(mary)&~strong(mary)))<=>((strong(lucy)&~wise(lucy))))&
(![X]:(~funny(X)<=>(~curious(X)<~>quiet(X))))&
(![X]:((funny(X)&~tall(X))=>(~curious(X)|old(X))))&
((happy(lucy))<=>(?[X]:(~happy(X))))&
(![X]:(~kind(X)<=>(kind(X)|~humble(X))))&
((?[X]:((curious(X)|happy(X))))<=>((old(john)|~old(john))))&
(![X]:((old(X)&~old(X))=>~calm(X)))&
((?[X]:((humble(X)<~>~curious(X))))=>(?[X]:((~strong(X)&~funny(X)))))&
(![X]:((~funny(X)|~patient(X))<=>(~generous(X)|humble(X))))&
(![X]:(calm(X)=>(creative(X)&old(X))))&
(~old(fred))&
((~quiet(alice)<~>funny(alice)))&
((~calm(john)&curious(john)))&
((kind(fred)<~>tall(fred)))&
((kind(susan)|funny(susan)))&
((curious(john)&~kind(john))) | ~brave(fred) | [
"p3",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4612381738585288231314440
% SZS output start Proof for 4612381738585288231314440
4. ! [X0] : ((~curious(X0) | ~kind(X0)) <=> (~humble(X0) & ~brave(X0))) [input p3]
11. ! [X0] : (~kind(X0) <=> (~humble(X0) | kind(X0))) [input p10]
23. brave(fred) [input hypothesis]
41. ! [X0] : (((~curious(X0) | ~kind(X0)) | (humble(X0) | brave(X0))) & ((~humble(X0) & ~brave(X0)) | (curious(X0) & kind(X0)))) [nnf transformation 4]
42. ! [X0] : ((~curious(X0) | ~kind(X0) | humble(X0) | brave(X0)) & ((~humble(X0) & ~brave(X0)) | (curious(X0) & kind(X0)))) [flattening 41]
54. ! [X0] : ((~kind(X0) | (humble(X0) & ~kind(X0))) & ((~humble(X0) | kind(X0)) | kind(X0))) [nnf transformation 11]
55. ! [X0] : ((~kind(X0) | (humble(X0) & ~kind(X0))) & (~humble(X0) | kind(X0) | kind(X0))) [flattening 54]
77. ~brave(X0) | kind(X0) [cnf transformation 42]
103. ~kind(X0) | ~kind(X0) [cnf transformation 55]
126. brave(fred) [cnf transformation 23]
128. ~kind(X0) [duplicate literal removal 103]
288. kind(fred) [resolution 77,126]
290. $false [subsumption resolution 288,128]
% SZS output end Proof for 4612381738585288231314440
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or not wise is either not creative or not funny. Everyone who is either patient or tall is not brave or not strong. If someone is either kind or not happy then someone is either humble or generous. If someone is either quiet or not old then someone is both not generous and patient. If someone is either old or not rich then someone is not generous or calm. Everyone who is happy or curious is not generous or not quiet and vice versa. If someone is either brave or not creative then mary is both not strong and not brave. If susan is not tall or not brave then someone is both not wise and not patient. Everyone who is both not happy and not humble is either not funny or tall and vice versa. Everyone who is quiet is strong. Everyone who is both patient and not patient is not old. Everyone who is not wise is either curious or not funny. If someone is quiet or generous then lucy is not strong or not humble. Everyone who is either not quiet or not brave is both patient and not patient. If alice is both not kind and not funny then someone is humble or strong and vice versa. If alice is both not creative and funny then lucy is creative and vice versa. Someone is not curious or rich. Someone is either not humble or not brave. Lucy is not funny. John is either happy or not quiet. Someone is both curious and happy. Susan is either funny or not wise. | Mary is not strong. | neutral | (![X]:((~curious(X)|~wise(X))=>(~creative(X)<~>~funny(X))))&
(![X]:((patient(X)<~>tall(X))=>(~brave(X)|~strong(X))))&
((?[X]:((kind(X)<~>~happy(X))))=>(?[X]:((humble(X)<~>generous(X)))))&
((?[X]:((quiet(X)<~>~old(X))))=>(?[X]:((~generous(X)&patient(X)))))&
((?[X]:((old(X)<~>~rich(X))))=>(?[X]:((~generous(X)|calm(X)))))&
(![X]:((happy(X)|curious(X))<=>(~generous(X)|~quiet(X))))&
((?[X]:((brave(X)<~>~creative(X))))=>((~strong(mary)&~brave(mary))))&
(((~tall(susan)|~brave(susan)))=>(?[X]:((~wise(X)&~patient(X)))))&
(![X]:((~happy(X)&~humble(X))<=>(~funny(X)<~>tall(X))))&
(![X]:(quiet(X)=>strong(X)))&
(![X]:((patient(X)&~patient(X))=>~old(X)))&
(![X]:(~wise(X)=>(curious(X)<~>~funny(X))))&
((?[X]:((quiet(X)|generous(X))))=>((~strong(lucy)|~humble(lucy))))&
(![X]:((~quiet(X)<~>~brave(X))=>(patient(X)&~patient(X))))&
(((~kind(alice)&~funny(alice)))<=>(?[X]:((humble(X)|strong(X)))))&
(((~creative(alice)&funny(alice)))<=>(creative(lucy)))&
(?[X]:((~curious(X)|rich(X))))&
(?[X]:((~humble(X)<~>~brave(X))))&
(~funny(lucy))&
((happy(john)<~>~quiet(john)))&
(?[X]:((curious(X)&happy(X))))&
((funny(susan)<~>~wise(susan))) | ~strong(mary) | [] | null | 0 |
If someone is either not tall or old then someone is either curious or not tall.
Everyone who is both wise and happy is either not strong or wise and vice versa.
Everyone who is both not strong and funny is not tall or wise and vice versa.
If paul is humble or not creative then someone is wise or rich.
Everyone who is both not calm and generous is not generous or not tall.
If someone is calm then someone is either generous or creative and vice versa.
If paul is either brave or kind then someone is not tall or not generous.
Everyone who is both kind and wise is strong and vice versa.
If someone is either quiet or not quiet then someone is not creative or happy and vice versa.
Everyone who is old is not quiet or tall.
If fred is not wise then someone is not curious.
Everyone who is old is quiet.
If someone is not quiet then someone is both wise and not curious.
If someone is wise or not patient then someone is old.
If someone is humble or not humble then paul is rich.
If someone is both not old and funny then someone is generous or patient and vice versa.
Lucy is either wise or not humble.
Someone is either funny or curious.
Alice is both generous and not creative.
Someone is brave or not quiet.
Someone is not patient.
John is rich. | Alice is not kind. | entailment | ((?[X]:((~tall(X)<~>old(X))))=>(?[X]:((curious(X)<~>~tall(X)))))&
(![X]:((wise(X)&happy(X))<=>(~strong(X)<~>wise(X))))&
(![X]:((~strong(X)&funny(X))<=>(~tall(X)|wise(X))))&
(((humble(paul)|~creative(paul)))=>(?[X]:((wise(X)|rich(X)))))&
(![X]:((~calm(X)&generous(X))=>(~generous(X)|~tall(X))))&
((?[X]:(calm(X)))<=>(?[X]:((generous(X)<~>creative(X)))))&
(((brave(paul)<~>kind(paul)))=>(?[X]:((~tall(X)|~generous(X)))))&
(![X]:((kind(X)&wise(X))<=>strong(X)))&
((?[X]:((quiet(X)<~>~quiet(X))))<=>(?[X]:((~creative(X)|happy(X)))))&
(![X]:(old(X)=>(~quiet(X)|tall(X))))&
((~wise(fred))=>(?[X]:(~curious(X))))&
(![X]:(old(X)=>quiet(X)))&
((?[X]:(~quiet(X)))=>(?[X]:((wise(X)&~curious(X)))))&
((?[X]:((wise(X)|~patient(X))))=>(?[X]:(old(X))))&
((?[X]:((humble(X)|~humble(X))))=>(rich(paul)))&
((?[X]:((~old(X)&funny(X))))<=>(?[X]:((generous(X)|patient(X)))))&
((wise(lucy)<~>~humble(lucy)))&
(?[X]:((funny(X)<~>curious(X))))&
((generous(alice)&~creative(alice)))&
(?[X]:((brave(X)|~quiet(X))))&
(?[X]:(~patient(X)))&
(rich(john)) | ~kind(alice) | [
"p1",
"p2",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2629465187198920618431399
% SZS output start Proof for 2629465187198920618431399
2. ! [X0] : ((happy(X0) & wise(X0)) <=> (~strong(X0) <~> wise(X0))) [input p1]
3. ! [X0] : ((funny(X0) & ~strong(X0)) <=> (wise(X0) | ~tall(X0))) [input p2]
8. ! [X0] : ((wise(X0) & kind(X0)) <=> strong(X0)) [input p7]
23. kind(alice) [input hypothesis]
47. ! [X0] : (((happy(X0) & wise(X0)) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0)))) & (((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | (~happy(X0) | ~wise(X0)))) [nnf transformation 2]
48. ! [X0] : (((happy(X0) & wise(X0)) | ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0)))) & (((~wise(X0) | strong(X0)) & (wise(X0) | ~strong(X0))) | ~happy(X0) | ~wise(X0))) [flattening 47]
49. ! [X0] : (((funny(X0) & ~strong(X0)) | (~wise(X0) & tall(X0))) & ((wise(X0) | ~tall(X0)) | (~funny(X0) | strong(X0)))) [nnf transformation 3]
50. ! [X0] : (((funny(X0) & ~strong(X0)) | (~wise(X0) & tall(X0))) & (wise(X0) | ~tall(X0) | ~funny(X0) | strong(X0))) [flattening 49]
59. ! [X0] : (((wise(X0) & kind(X0)) | ~strong(X0)) & (strong(X0) | (~wise(X0) | ~kind(X0)))) [nnf transformation 8]
60. ! [X0] : (((wise(X0) & kind(X0)) | ~strong(X0)) & (strong(X0) | ~wise(X0) | ~kind(X0))) [flattening 59]
93. wise(X0) | wise(X0) | strong(X0) [cnf transformation 48]
99. ~strong(X0) | ~wise(X0) [cnf transformation 50]
109. strong(X0) | ~wise(X0) | ~kind(X0) [cnf transformation 60]
111. wise(X0) | ~strong(X0) [cnf transformation 60]
138. kind(alice) [cnf transformation 23]
143. strong(X0) | wise(X0) [duplicate literal removal 93]
206. ~strong(X0) [subsumption resolution 111,99]
207. ~kind(X0) | ~wise(X0) [subsumption resolution 109,206]
322. wise(X2) [resolution 143,206]
329. ~wise(alice) [resolution 207,138]
330. $false [subsumption resolution 329,322]
% SZS output end Proof for 2629465187198920618431399
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or generous is both tall and not curious and vice versa.
If susan is not happy then someone is either happy or creative.
Everyone who is strong is either not creative or not happy and vice versa.
If someone is kind then someone is calm and vice versa.
Everyone who is either quiet or old is not rich and vice versa.
If someone is both not old and happy then someone is not old or old.
If someone is not old then susan is happy or not curious and vice versa.
Everyone who is creative or old is not funny or not patient and vice versa.
If alice is not patient or curious then john is strong and vice versa.
Everyone who is either funny or generous is rich.
Everyone who is either not humble or not old is old.
Everyone who is either not generous or kind is creative and vice versa.
If someone is not kind then someone is not patient and vice versa.
Everyone who is calm is both not tall and not brave and vice versa.
If paul is both not tall and not strong then someone is not patient.
If someone is curious then alice is either not generous or creative.
Lucy is not strong or brave.
Someone is either not curious or not old.
Susan is either curious or creative.
Fred is either old or humble.
John is both rich and quiet.
Someone is either not quiet or not patient.
Susan is either not curious or calm. | Paul is not happy. | neutral | (![X]:((curious(X)|generous(X))<=>(tall(X)&~curious(X))))&
((~happy(susan))=>(?[X]:((happy(X)<~>creative(X)))))&
(![X]:(strong(X)<=>(~creative(X)<~>~happy(X))))&
((?[X]:(kind(X)))<=>(?[X]:(calm(X))))&
(![X]:((quiet(X)<~>old(X))<=>~rich(X)))&
((?[X]:((~old(X)&happy(X))))=>(?[X]:((~old(X)|old(X)))))&
((?[X]:(~old(X)))<=>((happy(susan)|~curious(susan))))&
(![X]:((creative(X)|old(X))<=>(~funny(X)|~patient(X))))&
(((~patient(alice)|curious(alice)))<=>(strong(john)))&
(![X]:((funny(X)<~>generous(X))=>rich(X)))&
(![X]:((~humble(X)<~>~old(X))=>old(X)))&
(![X]:((~generous(X)<~>kind(X))<=>creative(X)))&
((?[X]:(~kind(X)))<=>(?[X]:(~patient(X))))&
(![X]:(calm(X)<=>(~tall(X)&~brave(X))))&
(((~tall(paul)&~strong(paul)))=>(?[X]:(~patient(X))))&
((?[X]:(curious(X)))=>((~generous(alice)<~>creative(alice))))&
((~strong(lucy)|brave(lucy)))&
(?[X]:((~curious(X)<~>~old(X))))&
((curious(susan)<~>creative(susan)))&
((old(fred)<~>humble(fred)))&
((rich(john)&quiet(john)))&
(?[X]:((~quiet(X)<~>~patient(X))))&
((~curious(susan)<~>calm(susan))) | ~happy(paul) | [] | null | 0 |
Everyone who is curious or kind is both curious and not brave.
Everyone who is funny or quiet is not quiet and vice versa.
If someone is not old or not curious then someone is both not tall and not rich and vice versa.
If john is not calm then someone is not curious or not tall.
If someone is not tall or happy then someone is both quiet and funny.
Everyone who is funny is both rich and calm.
Everyone who is both humble and happy is not rich.
Everyone who is old is not strong or not happy.
Everyone who is not happy is either rich or happy and vice versa.
Everyone who is creative or humble is not old or not creative and vice versa.
Everyone who is both old and funny is both not strong and rich.
If lucy is either happy or not wise then someone is wise or not curious and vice versa.
If paul is not strong or brave then someone is humble or tall.
If susan is patient or strong then someone is not strong and vice versa.
Someone is either calm or not old.
Someone is not happy or not generous.
Lucy is not generous or creative.
John is either calm or not generous. | Paul is funny. | entailment | (![X]:((curious(X)|kind(X))=>(curious(X)&~brave(X))))&
(![X]:((funny(X)|quiet(X))<=>~quiet(X)))&
((?[X]:((~old(X)|~curious(X))))<=>(?[X]:((~tall(X)&~rich(X)))))&
((~calm(john))=>(?[X]:((~curious(X)|~tall(X)))))&
((?[X]:((~tall(X)|happy(X))))=>(?[X]:((quiet(X)&funny(X)))))&
(![X]:(funny(X)=>(rich(X)&calm(X))))&
(![X]:((humble(X)&happy(X))=>~rich(X)))&
(![X]:(old(X)=>(~strong(X)|~happy(X))))&
(![X]:(~happy(X)<=>(rich(X)<~>happy(X))))&
(![X]:((creative(X)|humble(X))<=>(~old(X)|~creative(X))))&
(![X]:((old(X)&funny(X))=>(~strong(X)&rich(X))))&
(((happy(lucy)<~>~wise(lucy)))<=>(?[X]:((wise(X)|~curious(X)))))&
(((~strong(paul)|brave(paul)))=>(?[X]:((humble(X)|tall(X)))))&
(((patient(susan)|strong(susan)))<=>(?[X]:(~strong(X))))&
(?[X]:((calm(X)<~>~old(X))))&
(?[X]:((~happy(X)|~generous(X))))&
((~generous(lucy)|creative(lucy)))&
((calm(john)<~>~generous(john))) | funny(paul) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 6992776482795651738473728
% SZS output start Proof for 6992776482795651738473728
2. ! [X0] : ((quiet(X0) | funny(X0)) <=> ~quiet(X0)) [input p1]
19. ~funny(paul) [input hypothesis]
36. ! [X0] : (((quiet(X0) | funny(X0)) | quiet(X0)) & (~quiet(X0) | (~quiet(X0) & ~funny(X0)))) [nnf transformation 2]
37. ! [X0] : ((quiet(X0) | funny(X0) | quiet(X0)) & (~quiet(X0) | (~quiet(X0) & ~funny(X0)))) [flattening 36]
70. ~quiet(X0) | ~quiet(X0) [cnf transformation 37]
71. quiet(X0) | funny(X0) | quiet(X0) [cnf transformation 37]
112. ~funny(paul) [cnf transformation 19]
117. ~quiet(X0) [duplicate literal removal 70]
118. quiet(X0) | funny(X0) [duplicate literal removal 71]
295. funny(X0) [resolution 118,117]
297. $false [resolution 295,112]
% SZS output end Proof for 6992776482795651738473728
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and not funny is not patient or not humble. If john is either wise or not kind then john is not patient. Everyone who is curious is not humble and vice versa. Everyone who is not humble is either rich or not humble. If john is wise or not brave then lucy is not humble. Everyone who is both happy and wise is either not calm or old and vice versa. If someone is not happy then mary is either tall or kind and vice versa. If fred is both happy and not happy then someone is patient or not brave. Everyone who is not patient or not funny is either not wise or not patient and vice versa. Everyone who is either not kind or tall is not generous. Everyone who is not quiet is either rich or not old and vice versa. Everyone who is both funny and calm is not wise or humble and vice versa. If paul is either strong or not old then someone is not funny. Everyone who is not tall is both not wise and not funny and vice versa. If someone is both strong and happy then paul is either happy or wise. Everyone who is curious is patient. Susan is not old. Someone is not patient or tall. Lucy is not brave. Someone is either old or rich. Someone is either kind or not patient. Someone is not patient or patient. Someone is kind. Someone is not quiet or humble. | Paul is tall. | entailment | (![X]:((happy(X)&~funny(X))=>(~patient(X)|~humble(X))))&
(((wise(john)<~>~kind(john)))=>(~patient(john)))&
(![X]:(curious(X)<=>~humble(X)))&
(![X]:(~humble(X)=>(rich(X)<~>~humble(X))))&
(((wise(john)|~brave(john)))=>(~humble(lucy)))&
(![X]:((happy(X)&wise(X))<=>(~calm(X)<~>old(X))))&
((?[X]:(~happy(X)))<=>((tall(mary)<~>kind(mary))))&
(((happy(fred)&~happy(fred)))=>(?[X]:((patient(X)|~brave(X)))))&
(![X]:((~patient(X)|~funny(X))<=>(~wise(X)<~>~patient(X))))&
(![X]:((~kind(X)<~>tall(X))=>~generous(X)))&
(![X]:(~quiet(X)<=>(rich(X)<~>~old(X))))&
(![X]:((funny(X)&calm(X))<=>(~wise(X)|humble(X))))&
(((strong(paul)<~>~old(paul)))=>(?[X]:(~funny(X))))&
(![X]:(~tall(X)<=>(~wise(X)&~funny(X))))&
((?[X]:((strong(X)&happy(X))))=>((happy(paul)<~>wise(paul))))&
(![X]:(curious(X)=>patient(X)))&
(~old(susan))&
(?[X]:((~patient(X)|tall(X))))&
(~brave(lucy))&
(?[X]:((old(X)<~>rich(X))))&
(?[X]:((kind(X)<~>~patient(X))))&
(?[X]:((~patient(X)|patient(X))))&
(?[X]:(kind(X)))&
(?[X]:((~quiet(X)|humble(X)))) | tall(paul) | [
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6298378394366750889570661
% SZS output start Proof for 6298378394366750889570661
12. ! [X0] : ((calm(X0) & funny(X0)) <=> (humble(X0) | ~wise(X0))) [input p11]
14. ! [X0] : (~tall(X0) <=> (~funny(X0) & ~wise(X0))) [input p13]
25. ~tall(paul) [input hypothesis]
54. ! [X0] : (((calm(X0) & funny(X0)) | (~humble(X0) & wise(X0))) & ((humble(X0) | ~wise(X0)) | (~calm(X0) | ~funny(X0)))) [nnf transformation 12]
55. ! [X0] : (((calm(X0) & funny(X0)) | (~humble(X0) & wise(X0))) & (humble(X0) | ~wise(X0) | ~calm(X0) | ~funny(X0))) [flattening 54]
59. ! [X0] : ((~tall(X0) | (funny(X0) | wise(X0))) & ((~funny(X0) & ~wise(X0)) | tall(X0))) [nnf transformation 14]
60. ! [X0] : ((~tall(X0) | funny(X0) | wise(X0)) & ((~funny(X0) & ~wise(X0)) | tall(X0))) [flattening 59]
104. wise(X0) | funny(X0) [cnf transformation 55]
110. ~wise(X0) | tall(X0) [cnf transformation 60]
111. ~funny(X0) | tall(X0) [cnf transformation 60]
126. ~tall(paul) [cnf transformation 25]
239. tall(X0) | funny(X0) [resolution 110,104]
240. tall(X0) [subsumption resolution 239,111]
241. $false [resolution 240,126]
% SZS output end Proof for 6298378394366750889570661
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not strong and not wise then someone is either not funny or not humble. If someone is either happy or not patient then alice is both not funny and not strong. If susan is strong then someone is not wise and vice versa. Everyone who is old is both not wise and not humble and vice versa. Everyone who is both tall and not old is both not creative and brave and vice versa. Everyone who is not happy is both not generous and not wise. If alice is not strong then susan is not brave or patient. Everyone who is either not kind or not humble is not wise. If susan is either not strong or not funny then someone is not strong or not patient and vice versa. Everyone who is either not creative or wise is both happy and not brave. If fred is generous or not creative then someone is both not quiet and not creative. Everyone who is not strong or not happy is not wise. Everyone who is either funny or not kind is both humble and not brave. Everyone who is not brave or not humble is not rich or not calm and vice versa. If john is both happy and not curious then lucy is both not humble and rich. Everyone who is both wise and tall is not humble and vice versa. Lucy is either not curious or not rich. Someone is brave or patient. Someone is either not strong or generous. John is not happy. John is both not brave and not patient. Paul is humble. Someone is either kind or not creative. Someone is either quiet or not patient. | John is tall. | contradiction | ((?[X]:((~strong(X)&~wise(X))))=>(?[X]:((~funny(X)<~>~humble(X)))))&
((?[X]:((happy(X)<~>~patient(X))))=>((~funny(alice)&~strong(alice))))&
((strong(susan))<=>(?[X]:(~wise(X))))&
(![X]:(old(X)<=>(~wise(X)&~humble(X))))&
(![X]:((tall(X)&~old(X))<=>(~creative(X)&brave(X))))&
(![X]:(~happy(X)=>(~generous(X)&~wise(X))))&
((~strong(alice))=>((~brave(susan)|patient(susan))))&
(![X]:((~kind(X)<~>~humble(X))=>~wise(X)))&
(((~strong(susan)<~>~funny(susan)))<=>(?[X]:((~strong(X)|~patient(X)))))&
(![X]:((~creative(X)<~>wise(X))=>(happy(X)&~brave(X))))&
(((generous(fred)|~creative(fred)))=>(?[X]:((~quiet(X)&~creative(X)))))&
(![X]:((~strong(X)|~happy(X))=>~wise(X)))&
(![X]:((funny(X)<~>~kind(X))=>(humble(X)&~brave(X))))&
(![X]:((~brave(X)|~humble(X))<=>(~rich(X)|~calm(X))))&
(((happy(john)&~curious(john)))=>((~humble(lucy)&rich(lucy))))&
(![X]:((wise(X)&tall(X))<=>~humble(X)))&
((~curious(lucy)<~>~rich(lucy)))&
(?[X]:((brave(X)|patient(X))))&
(?[X]:((~strong(X)<~>generous(X))))&
(~happy(john))&
((~brave(john)&~patient(john)))&
(humble(paul))&
(?[X]:((kind(X)<~>~creative(X))))&
(?[X]:((quiet(X)<~>~patient(X)))) | tall(john) | [
"p3",
"p4",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8582979424777980727662703
% SZS output start Proof for 8582979424777980727662703
4. ! [X0] : (old(X0) <=> (~humble(X0) & ~wise(X0))) [input p3]
5. ! [X0] : ((~old(X0) & tall(X0)) <=> (brave(X0) & ~creative(X0))) [input p4]
16. ! [X0] : ((tall(X0) & wise(X0)) <=> ~humble(X0)) [input p15]
21. ~patient(john) & ~brave(john) [input p20]
25. tall(john) [input hypothesis]
48. ! [X0] : ((old(X0) | (humble(X0) | wise(X0))) & ((~humble(X0) & ~wise(X0)) | ~old(X0))) [nnf transformation 4]
49. ! [X0] : ((old(X0) | humble(X0) | wise(X0)) & ((~humble(X0) & ~wise(X0)) | ~old(X0))) [flattening 48]
50. ! [X0] : (((~old(X0) & tall(X0)) | (~brave(X0) | creative(X0))) & ((brave(X0) & ~creative(X0)) | (old(X0) | ~tall(X0)))) [nnf transformation 5]
51. ! [X0] : (((~old(X0) & tall(X0)) | ~brave(X0) | creative(X0)) & ((brave(X0) & ~creative(X0)) | old(X0) | ~tall(X0))) [flattening 50]
63. ! [X0] : (((tall(X0) & wise(X0)) | humble(X0)) & (~humble(X0) | (~tall(X0) | ~wise(X0)))) [nnf transformation 16]
64. ! [X0] : (((tall(X0) & wise(X0)) | humble(X0)) & (~humble(X0) | ~tall(X0) | ~wise(X0))) [flattening 63]
85. ~old(X0) | ~wise(X0) [cnf transformation 49]
86. ~old(X0) | ~humble(X0) [cnf transformation 49]
89. ~tall(X0) | old(X0) | brave(X0) [cnf transformation 51]
124. humble(X0) | wise(X0) [cnf transformation 64]
132. ~brave(john) [cnf transformation 21]
139. tall(john) [cnf transformation 25]
310. old(john) | brave(john) [resolution 89,139]
312. old(john) [subsumption resolution 310,132]
313. ~humble(john) [resolution 312,86]
314. ~wise(john) [resolution 312,85]
325. wise(john) [resolution 313,124]
326. $false [subsumption resolution 325,314]
% SZS output end Proof for 8582979424777980727662703
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or patient is both not wise and happy.
If paul is not brave then someone is quiet or not strong and vice versa.
If john is kind then someone is rich or wise.
Everyone who is either not old or happy is tall.
If mary is not tall then someone is old or generous and vice versa.
If someone is either not funny or not happy then susan is either not happy or not humble and vice versa.
Everyone who is either not wise or humble is both strong and not curious and vice versa.
Everyone who is both wise and not generous is kind or not quiet and vice versa.
Everyone who is curious is either not humble or generous.
If fred is old or patient then someone is both creative and patient.
Everyone who is both not patient and not humble is either curious or wise.
Everyone who is either not strong or happy is not happy.
If someone is both wise and not patient then someone is quiet or not kind.
Everyone who is either tall or not old is either not funny or not creative and vice versa.
If paul is either not quiet or not wise then someone is not strong or not quiet and vice versa.
Everyone who is rich or not tall is either quiet or patient.
Lucy is not calm or funny.
Someone is either funny or strong.
Someone is both not kind and not calm.
Someone is either curious or strong.
Paul is both not wise and not old. | John is old. | neutral | (![X]:((~curious(X)|patient(X))=>(~wise(X)&happy(X))))&
((~brave(paul))<=>(?[X]:((quiet(X)|~strong(X)))))&
((kind(john))=>(?[X]:((rich(X)|wise(X)))))&
(![X]:((~old(X)<~>happy(X))=>tall(X)))&
((~tall(mary))<=>(?[X]:((old(X)|generous(X)))))&
((?[X]:((~funny(X)<~>~happy(X))))<=>((~happy(susan)<~>~humble(susan))))&
(![X]:((~wise(X)<~>humble(X))<=>(strong(X)&~curious(X))))&
(![X]:((wise(X)&~generous(X))<=>(kind(X)|~quiet(X))))&
(![X]:(curious(X)=>(~humble(X)<~>generous(X))))&
(((old(fred)|patient(fred)))=>(?[X]:((creative(X)&patient(X)))))&
(![X]:((~patient(X)&~humble(X))=>(curious(X)<~>wise(X))))&
(![X]:((~strong(X)<~>happy(X))=>~happy(X)))&
((?[X]:((wise(X)&~patient(X))))=>(?[X]:((quiet(X)|~kind(X)))))&
(![X]:((tall(X)<~>~old(X))<=>(~funny(X)<~>~creative(X))))&
(((~quiet(paul)<~>~wise(paul)))<=>(?[X]:((~strong(X)|~quiet(X)))))&
(![X]:((rich(X)|~tall(X))=>(quiet(X)<~>patient(X))))&
((~calm(lucy)|funny(lucy)))&
(?[X]:((funny(X)<~>strong(X))))&
(?[X]:((~kind(X)&~calm(X))))&
(?[X]:((curious(X)<~>strong(X))))&
((~wise(paul)&~old(paul))) | old(john) | [] | null | 0 |
Everyone who is both humble and not happy is both not wise and old.
Everyone who is either quiet or happy is not wise or not curious and vice versa.
If someone is either generous or curious then john is happy and vice versa.
If mary is either curious or brave then someone is tall or not calm.
Everyone who is either kind or not strong is humble or not strong.
Everyone who is both not patient and calm is calm.
If someone is not funny then mary is either wise or not old.
Everyone who is funny or not brave is not curious and vice versa.
Everyone who is either funny or not curious is both not creative and not calm and vice versa.
Everyone who is either not quiet or tall is either quiet or not wise and vice versa.
If mary is both creative and humble then someone is curious or quiet and vice versa.
If lucy is both not rich and strong then someone is wise.
Everyone who is either not quiet or quiet is not kind and vice versa.
Everyone who is not tall or not quiet is happy and vice versa.
If alice is curious then paul is either not happy or not tall.
If someone is humble then paul is both not rich and happy and vice versa.
Someone is not patient.
Someone is both not creative and tall.
Someone is quiet or not generous.
Fred is both calm and old.
Someone is old or not quiet.
Susan is both not creative and not curious.
Someone is strong or creative.
Someone is not happy. | Mary is humble. | entailment | (![X]:((humble(X)&~happy(X))=>(~wise(X)&old(X))))&
(![X]:((quiet(X)<~>happy(X))<=>(~wise(X)|~curious(X))))&
((?[X]:((generous(X)<~>curious(X))))<=>(happy(john)))&
(((curious(mary)<~>brave(mary)))=>(?[X]:((tall(X)|~calm(X)))))&
(![X]:((kind(X)<~>~strong(X))=>(humble(X)|~strong(X))))&
(![X]:((~patient(X)&calm(X))=>calm(X)))&
((?[X]:(~funny(X)))=>((wise(mary)<~>~old(mary))))&
(![X]:((funny(X)|~brave(X))<=>~curious(X)))&
(![X]:((funny(X)<~>~curious(X))<=>(~creative(X)&~calm(X))))&
(![X]:((~quiet(X)<~>tall(X))<=>(quiet(X)<~>~wise(X))))&
(((creative(mary)&humble(mary)))<=>(?[X]:((curious(X)|quiet(X)))))&
(((~rich(lucy)&strong(lucy)))=>(?[X]:(wise(X))))&
(![X]:((~quiet(X)<~>quiet(X))<=>~kind(X)))&
(![X]:((~tall(X)|~quiet(X))<=>happy(X)))&
((curious(alice))=>((~happy(paul)<~>~tall(paul))))&
((?[X]:(humble(X)))<=>((~rich(paul)&happy(paul))))&
(?[X]:(~patient(X)))&
(?[X]:((~creative(X)&tall(X))))&
(?[X]:((quiet(X)|~generous(X))))&
((calm(fred)&old(fred)))&
(?[X]:((old(X)|~quiet(X))))&
((~creative(susan)&~curious(susan)))&
(?[X]:((strong(X)|creative(X))))&
(?[X]:(~happy(X))) | humble(mary) | [
"p10",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4144649934754177588677581
% SZS output start Proof for 4144649934754177588677581
11. (humble(mary) & creative(mary)) <=> ? [X0] : (quiet(X0) | curious(X0)) [input p10]
14. ! [X0] : ((~quiet(X0) | ~tall(X0)) <=> happy(X0)) [input p13]
24. ? [X0] : ~happy(X0) [input p23]
25. ~humble(mary) [input hypothesis]
53. ((humble(mary) & creative(mary)) | ! [X0] : (~quiet(X0) & ~curious(X0))) & (? [X0] : (quiet(X0) | curious(X0)) | (~humble(mary) | ~creative(mary))) [nnf transformation 11]
54. ((humble(mary) & creative(mary)) | ! [X0] : (~quiet(X0) & ~curious(X0))) & (? [X0] : (quiet(X0) | curious(X0)) | ~humble(mary) | ~creative(mary)) [flattening 53]
55. ((humble(mary) & creative(mary)) | ! [X0] : (~quiet(X0) & ~curious(X0))) & (? [X1] : (quiet(X1) | curious(X1)) | ~humble(mary) | ~creative(mary)) [rectify 54]
56. ? [X1] : (quiet(X1) | curious(X1)) => (quiet(sK2) | curious(sK2)) [choice axiom]
57. ((humble(mary) & creative(mary)) | ! [X0] : (~quiet(X0) & ~curious(X0))) & ((quiet(sK2) | curious(sK2)) | ~humble(mary) | ~creative(mary)) [skolemisation 55,56]
61. ! [X0] : (((~quiet(X0) | ~tall(X0)) | ~happy(X0)) & (happy(X0) | (quiet(X0) & tall(X0)))) [nnf transformation 14]
62. ! [X0] : ((~quiet(X0) | ~tall(X0) | ~happy(X0)) & (happy(X0) | (quiet(X0) & tall(X0)))) [flattening 61]
79. ? [X0] : ~happy(X0) => ~happy(sK10) [choice axiom]
80. ~happy(sK10) [skolemisation 24,79]
121. humble(mary) | ~quiet(X0) [cnf transformation 57]
128. quiet(X0) | happy(X0) [cnf transformation 62]
145. ~happy(sK10) [cnf transformation 80]
146. ~humble(mary) [cnf transformation 25]
212. 13 <=> ! [X0] : ~quiet(X0) [avatar definition]
213. ~quiet(X0) <- (13) [avatar component clause 212]
215. 14 <=> humble(mary) [avatar definition]
218. 13 | 14 [avatar split clause 121,215,212]
306. ~14 [avatar split clause 146,215]
308. happy(X0) <- (13) [resolution 128,213]
310. $false <- (13) [resolution 308,145]
313. ~13 [avatar contradiction clause 310]
314. $false [avatar sat refutation 218,306,313]
% SZS output end Proof for 4144649934754177588677581
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong is either not kind or not generous. Everyone who is not creative or patient is funny or tall. If fred is either not strong or patient then someone is either not quiet or not creative and vice versa. If alice is wise then alice is curious and vice versa. Everyone who is not strong or generous is not patient and vice versa. If someone is not rich or curious then someone is creative or quiet and vice versa. If someone is humble or not happy then alice is both not patient and calm. If john is both wise and not old then someone is both brave and tall and vice versa. Everyone who is brave is not strong or not rich. Everyone who is not kind or happy is both quiet and not calm and vice versa. Everyone who is either not brave or rich is curious or not funny. If susan is not humble then someone is either not strong or not old. Everyone who is not old or not happy is not brave or not funny. Everyone who is kind is both not creative and quiet. Everyone who is old or humble is not rich or kind. If someone is either not creative or not generous then someone is not happy. Someone is strong. Fred is both humble and generous. Paul is wise. Someone is not generous. Lucy is not generous or funny. Fred is humble. Susan is funny. Lucy is patient. | Lucy is funny. | neutral | (![X]:(strong(X)=>(~kind(X)<~>~generous(X))))&
(![X]:((~creative(X)|patient(X))=>(funny(X)|tall(X))))&
(((~strong(fred)<~>patient(fred)))<=>(?[X]:((~quiet(X)<~>~creative(X)))))&
((wise(alice))<=>(curious(alice)))&
(![X]:((~strong(X)|generous(X))<=>~patient(X)))&
((?[X]:((~rich(X)|curious(X))))<=>(?[X]:((creative(X)|quiet(X)))))&
((?[X]:((humble(X)|~happy(X))))=>((~patient(alice)&calm(alice))))&
(((wise(john)&~old(john)))<=>(?[X]:((brave(X)&tall(X)))))&
(![X]:(brave(X)=>(~strong(X)|~rich(X))))&
(![X]:((~kind(X)|happy(X))<=>(quiet(X)&~calm(X))))&
(![X]:((~brave(X)<~>rich(X))=>(curious(X)|~funny(X))))&
((~humble(susan))=>(?[X]:((~strong(X)<~>~old(X)))))&
(![X]:((~old(X)|~happy(X))=>(~brave(X)|~funny(X))))&
(![X]:(kind(X)=>(~creative(X)&quiet(X))))&
(![X]:((old(X)|humble(X))=>(~rich(X)|kind(X))))&
((?[X]:((~creative(X)<~>~generous(X))))=>(?[X]:(~happy(X))))&
(?[X]:(strong(X)))&
((humble(fred)&generous(fred)))&
(wise(paul))&
(?[X]:(~generous(X)))&
((~generous(lucy)|funny(lucy)))&
(humble(fred))&
(funny(susan))&
(patient(lucy)) | funny(lucy) | [] | null | 0 |
Everyone who is either strong or not calm is not curious or not funny and vice versa.
If fred is either patient or not humble then someone is not happy or humble and vice versa.
Everyone who is both not happy and kind is both not curious and not wise and vice versa.
Everyone who is not strong or not kind is calm.
Everyone who is strong or calm is either humble or tall and vice versa.
Everyone who is either wise or strong is creative or brave.
Everyone who is not curious is both creative and happy.
If someone is both not old and humble then fred is not humble or not happy.
Everyone who is old or generous is not tall and vice versa.
Everyone who is both quiet and not kind is either not old or generous and vice versa.
Everyone who is curious is not happy or not quiet and vice versa.
If someone is rich or funny then john is either not old or brave.
Everyone who is creative is happy.
If someone is strong then someone is calm or not strong and vice versa.
If susan is wise or not kind then someone is not curious and vice versa.
Everyone who is humble is not old or strong and vice versa.
Alice is tall or strong.
Someone is strong.
Alice is not tall.
Lucy is both not happy and quiet.
Alice is not brave or not happy.
Someone is both not calm and rich.
Fred is quiet.
Someone is either not curious or humble. | Lucy is funny. | contradiction | (![X]:((strong(X)<~>~calm(X))<=>(~curious(X)|~funny(X))))&
(((patient(fred)<~>~humble(fred)))<=>(?[X]:((~happy(X)|humble(X)))))&
(![X]:((~happy(X)&kind(X))<=>(~curious(X)&~wise(X))))&
(![X]:((~strong(X)|~kind(X))=>calm(X)))&
(![X]:((strong(X)|calm(X))<=>(humble(X)<~>tall(X))))&
(![X]:((wise(X)<~>strong(X))=>(creative(X)|brave(X))))&
(![X]:(~curious(X)=>(creative(X)&happy(X))))&
((?[X]:((~old(X)&humble(X))))=>((~humble(fred)|~happy(fred))))&
(![X]:((old(X)|generous(X))<=>~tall(X)))&
(![X]:((quiet(X)&~kind(X))<=>(~old(X)<~>generous(X))))&
(![X]:(curious(X)<=>(~happy(X)|~quiet(X))))&
((?[X]:((rich(X)|funny(X))))=>((~old(john)<~>brave(john))))&
(![X]:(creative(X)=>happy(X)))&
((?[X]:(strong(X)))<=>(?[X]:((calm(X)|~strong(X)))))&
(((wise(susan)|~kind(susan)))<=>(?[X]:(~curious(X))))&
(![X]:(humble(X)<=>(~old(X)|strong(X))))&
((tall(alice)|strong(alice)))&
(?[X]:(strong(X)))&
(~tall(alice))&
((~happy(lucy)&quiet(lucy)))&
((~brave(alice)|~happy(alice)))&
(?[X]:((~calm(X)&rich(X))))&
(quiet(fred))&
(?[X]:((~curious(X)<~>humble(X)))) | funny(lucy) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p8",
"p9",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8547687673146415202700210
% SZS output start Proof for 8547687673146415202700210
1. ! [X0] : ((strong(X0) <~> ~calm(X0)) <=> (~funny(X0) | ~curious(X0))) [input p0]
3. ! [X0] : ((kind(X0) & ~happy(X0)) <=> (~wise(X0) & ~curious(X0))) [input p2]
4. ! [X0] : ((~kind(X0) | ~strong(X0)) => calm(X0)) [input p3]
5. ! [X0] : ((calm(X0) | strong(X0)) <=> (humble(X0) <~> tall(X0))) [input p4]
7. ! [X0] : (~curious(X0) => (happy(X0) & creative(X0))) [input p6]
9. ! [X0] : ((generous(X0) | old(X0)) <=> ~tall(X0)) [input p8]
10. ! [X0] : ((~kind(X0) & quiet(X0)) <=> (~old(X0) <~> generous(X0))) [input p9]
16. ! [X0] : (humble(X0) <=> (strong(X0) | ~old(X0))) [input p15]
20. quiet(lucy) & ~happy(lucy) [input p19]
25. funny(lucy) [input hypothesis]
27. ! [X0] : (calm(X0) | (kind(X0) & strong(X0))) [ennf transformation 4]
30. ! [X0] : ((happy(X0) & creative(X0)) | curious(X0)) [ennf transformation 7]
35. ! [X0] : ((((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | (funny(X0) & curious(X0))) & ((~funny(X0) | ~curious(X0)) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0))))) [nnf transformation 1]
36. ! [X0] : ((((calm(X0) | ~strong(X0)) & (~calm(X0) | strong(X0))) | (funny(X0) & curious(X0))) & (~funny(X0) | ~curious(X0) | ((strong(X0) | calm(X0)) & (~calm(X0) | ~strong(X0))))) [flattening 35]
41. ! [X0] : (((kind(X0) & ~happy(X0)) | (wise(X0) | curious(X0))) & ((~wise(X0) & ~curious(X0)) | (~kind(X0) | happy(X0)))) [nnf transformation 3]
42. ! [X0] : (((kind(X0) & ~happy(X0)) | wise(X0) | curious(X0)) & ((~wise(X0) & ~curious(X0)) | ~kind(X0) | happy(X0))) [flattening 41]
43. ! [X0] : (((calm(X0) | strong(X0)) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) & (((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | (~calm(X0) & ~strong(X0)))) [nnf transformation 5]
44. ! [X0] : ((calm(X0) | strong(X0) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) & (((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | (~calm(X0) & ~strong(X0)))) [flattening 43]
46. ! [X0] : (((generous(X0) | old(X0)) | tall(X0)) & (~tall(X0) | (~generous(X0) & ~old(X0)))) [nnf transformation 9]
47. ! [X0] : ((generous(X0) | old(X0) | tall(X0)) & (~tall(X0) | (~generous(X0) & ~old(X0)))) [flattening 46]
48. ! [X0] : (((~kind(X0) & quiet(X0)) | ((~old(X0) | ~generous(X0)) & (generous(X0) | old(X0)))) & (((~generous(X0) | old(X0)) & (generous(X0) | ~old(X0))) | (kind(X0) | ~quiet(X0)))) [nnf transformation 10]
49. ! [X0] : (((~kind(X0) & quiet(X0)) | ((~old(X0) | ~generous(X0)) & (generous(X0) | old(X0)))) & (((~generous(X0) | old(X0)) & (generous(X0) | ~old(X0))) | kind(X0) | ~quiet(X0))) [flattening 48]
63. ! [X0] : ((humble(X0) | (~strong(X0) & old(X0))) & ((strong(X0) | ~old(X0)) | ~humble(X0))) [nnf transformation 16]
64. ! [X0] : ((humble(X0) | (~strong(X0) & old(X0))) & (strong(X0) | ~old(X0) | ~humble(X0))) [flattening 63]
72. ~funny(X0) | ~curious(X0) | ~calm(X0) | ~strong(X0) [cnf transformation 36]
84. ~kind(X0) | ~curious(X0) | happy(X0) [cnf transformation 42]
88. calm(X0) | strong(X0) [cnf transformation 27]
89. kind(X0) | calm(X0) [cnf transformation 27]
90. ~strong(X0) | humble(X0) | tall(X0) [cnf transformation 44]
91. ~calm(X0) | humble(X0) | tall(X0) [cnf transformation 44]
93. ~tall(X0) | ~humble(X0) | ~calm(X0) [cnf transformation 44]
99. happy(X0) | curious(X0) [cnf transformation 30]
101. ~old(X0) | ~tall(X0) [cnf transformation 47]
103. generous(X0) | old(X0) | tall(X0) [cnf transformation 47]
105. ~quiet(X0) | old(X0) | kind(X0) | ~generous(X0) [cnf transformation 49]
124. ~old(X0) | strong(X0) | ~humble(X0) [cnf transformation 64]
125. old(X0) | humble(X0) [cnf transformation 64]
130. ~happy(lucy) [cnf transformation 20]
131. quiet(lucy) [cnf transformation 20]
138. funny(lucy) [cnf transformation 25]
269. curious(lucy) [resolution 99,130]
274. ~tall(X0) | humble(X0) [resolution 125,101]
348. ~curious(X0) | happy(X0) | calm(X0) [resolution 84,89]
349. happy(X0) | calm(X0) [subsumption resolution 348,99]
365. humble(X0) | tall(X0) | strong(X0) [resolution 91,88]
370. humble(X0) | tall(X0) [subsumption resolution 365,90]
371. humble(X0) [subsumption resolution 370,274]
423. ~curious(lucy) | ~calm(lucy) | ~strong(lucy) [resolution 72,138]
426. ~calm(lucy) | ~strong(lucy) [subsumption resolution 423,269]
428. 43 <=> strong(lucy) [avatar definition]
430. ~strong(lucy) <- (~43) [avatar component clause 428]
432. 44 <=> calm(lucy) [avatar definition]
435. ~43 | ~44 [avatar split clause 426,432,428]
536. 62 <=> generous(lucy) [avatar definition]
537. ~generous(lucy) <- (~62) [avatar component clause 536]
538. generous(lucy) <- (62) [avatar component clause 536]
540. 63 <=> kind(lucy) [avatar definition]
542. kind(lucy) <- (63) [avatar component clause 540]
544. 64 <=> old(lucy) [avatar definition]
545. old(lucy) <- (64) [avatar component clause 544]
546. ~old(lucy) <- (~64) [avatar component clause 544]
561. old(lucy) | kind(lucy) | ~generous(lucy) [resolution 105,131]
575. old(lucy) | tall(lucy) <- (~62) [resolution 537,103]
576. tall(lucy) <- (~62, ~64) [subsumption resolution 575,546]
617. calm(lucy) [resolution 349,130]
627. ~humble(lucy) | ~calm(lucy) <- (~62, ~64) [resolution 576,93]
629. ~calm(lucy) <- (~62, ~64) [subsumption resolution 627,371]
634. ~44 | 62 | 64 [avatar split clause 629,544,536,432]
635. 44 [avatar split clause 617,432]
643. ~curious(lucy) | happy(lucy) <- (63) [resolution 542,84]
644. happy(lucy) <- (63) [subsumption resolution 643,269]
645. $false <- (63) [subsumption resolution 644,130]
646. ~63 [avatar contradiction clause 645]
648. old(lucy) | kind(lucy) <- (62) [subsumption resolution 561,538]
649. 63 | 64 | ~62 [avatar split clause 648,536,544,540]
651. strong(lucy) | ~humble(lucy) <- (64) [resolution 545,124]
653. ~humble(lucy) <- (~43, 64) [subsumption resolution 651,430]
654. $false <- (~43, 64) [subsumption resolution 653,371]
655. 43 | ~64 [avatar contradiction clause 654]
656. $false [avatar sat refutation 435,634,635,646,649,655]
% SZS output end Proof for 8547687673146415202700210
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not happy or not generous then someone is either not rich or quiet and vice versa.
Everyone who is humble is either not rich or happy.
If someone is not rich then someone is rich or not creative.
Everyone who is not creative or rich is not quiet and vice versa.
Everyone who is tall is both not rich and patient and vice versa.
If someone is kind then someone is both not creative and strong and vice versa.
If lucy is not curious or happy then someone is happy or funny and vice versa.
Everyone who is both not tall and humble is both curious and funny.
Everyone who is either brave or wise is both creative and rich.
Everyone who is not patient or curious is old and vice versa.
Everyone who is both strong and not quiet is both creative and calm and vice versa.
If someone is not happy then lucy is either not patient or rich and vice versa.
If someone is funny then someone is either not tall or strong and vice versa.
Everyone who is either not happy or patient is both not calm and brave and vice versa.
If someone is either generous or not creative then someone is patient or not calm.
If someone is not old then someone is not patient.
Mary is not kind.
Someone is either generous or not brave.
Someone is both tall and calm.
Someone is curious or not tall.
Someone is not kind or not creative.
Someone is not wise or not quiet.
Someone is not strong or not happy.
Mary is either not generous or not curious. | Mary is not generous. | neutral | (((~happy(lucy)|~generous(lucy)))<=>(?[X]:((~rich(X)<~>quiet(X)))))&
(![X]:(humble(X)=>(~rich(X)<~>happy(X))))&
((?[X]:(~rich(X)))=>(?[X]:((rich(X)|~creative(X)))))&
(![X]:((~creative(X)|rich(X))<=>~quiet(X)))&
(![X]:(tall(X)<=>(~rich(X)&patient(X))))&
((?[X]:(kind(X)))<=>(?[X]:((~creative(X)&strong(X)))))&
(((~curious(lucy)|happy(lucy)))<=>(?[X]:((happy(X)|funny(X)))))&
(![X]:((~tall(X)&humble(X))=>(curious(X)&funny(X))))&
(![X]:((brave(X)<~>wise(X))=>(creative(X)&rich(X))))&
(![X]:((~patient(X)|curious(X))<=>old(X)))&
(![X]:((strong(X)&~quiet(X))<=>(creative(X)&calm(X))))&
((?[X]:(~happy(X)))<=>((~patient(lucy)<~>rich(lucy))))&
((?[X]:(funny(X)))<=>(?[X]:((~tall(X)<~>strong(X)))))&
(![X]:((~happy(X)<~>patient(X))<=>(~calm(X)&brave(X))))&
((?[X]:((generous(X)<~>~creative(X))))=>(?[X]:((patient(X)|~calm(X)))))&
((?[X]:(~old(X)))=>(?[X]:(~patient(X))))&
(~kind(mary))&
(?[X]:((generous(X)<~>~brave(X))))&
(?[X]:((tall(X)&calm(X))))&
(?[X]:((curious(X)|~tall(X))))&
(?[X]:((~kind(X)|~creative(X))))&
(?[X]:((~wise(X)|~quiet(X))))&
(?[X]:((~strong(X)|~happy(X))))&
((~generous(mary)<~>~curious(mary))) | ~generous(mary) | [] | null | 0 |
If someone is happy or not old then fred is not generous or quiet and vice versa. If someone is both rich and patient then someone is tall and vice versa. Everyone who is both brave and not strong is rich or patient and vice versa. Everyone who is either generous or quiet is both humble and curious and vice versa. If someone is not rich or rich then someone is generous or brave and vice versa. If alice is both not curious and not funny then susan is either not calm or wise and vice versa. Everyone who is both not old and not wise is curious and vice versa. Everyone who is not patient or not funny is both not calm and not brave. Everyone who is both patient and humble is wise or patient and vice versa. Everyone who is wise is either creative or funny. If someone is either not curious or not strong then someone is both wise and funny. Everyone who is either not tall or humble is strong and vice versa. If someone is not creative or not rich then someone is humble. If someone is tall or not creative then alice is either not wise or old and vice versa. If someone is not generous then someone is either not strong or not calm and vice versa. If someone is not old then mary is not generous and vice versa. Fred is rich. Someone is not old or not humble. Someone is either not patient or not strong. Alice is not rich. Someone is tall or not rich. Someone is funny or not creative. Someone is either funny or not humble. | Fred is not funny. | contradiction | ((?[X]:((happy(X)|~old(X))))<=>((~generous(fred)|quiet(fred))))&
((?[X]:((rich(X)&patient(X))))<=>(?[X]:(tall(X))))&
(![X]:((brave(X)&~strong(X))<=>(rich(X)|patient(X))))&
(![X]:((generous(X)<~>quiet(X))<=>(humble(X)&curious(X))))&
((?[X]:((~rich(X)|rich(X))))<=>(?[X]:((generous(X)|brave(X)))))&
(((~curious(alice)&~funny(alice)))<=>((~calm(susan)<~>wise(susan))))&
(![X]:((~old(X)&~wise(X))<=>curious(X)))&
(![X]:((~patient(X)|~funny(X))=>(~calm(X)&~brave(X))))&
(![X]:((patient(X)&humble(X))<=>(wise(X)|patient(X))))&
(![X]:(wise(X)=>(creative(X)<~>funny(X))))&
((?[X]:((~curious(X)<~>~strong(X))))=>(?[X]:((wise(X)&funny(X)))))&
(![X]:((~tall(X)<~>humble(X))<=>strong(X)))&
((?[X]:((~creative(X)|~rich(X))))=>(?[X]:(humble(X))))&
((?[X]:((tall(X)|~creative(X))))<=>((~wise(alice)<~>old(alice))))&
((?[X]:(~generous(X)))<=>(?[X]:((~strong(X)<~>~calm(X)))))&
((?[X]:(~old(X)))<=>(~generous(mary)))&
(rich(fred))&
(?[X]:((~old(X)|~humble(X))))&
(?[X]:((~patient(X)<~>~strong(X))))&
(~rich(alice))&
(?[X]:((tall(X)|~rich(X))))&
(?[X]:((funny(X)|~creative(X))))&
(?[X]:((funny(X)<~>~humble(X)))) | ~funny(fred) | [
"p2",
"p7",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 574724145343673207386547
% SZS output start Proof for 574724145343673207386547
3. ! [X0] : ((~strong(X0) & brave(X0)) <=> (patient(X0) | rich(X0))) [input p2]
8. ! [X0] : ((~funny(X0) | ~patient(X0)) => (~brave(X0) & ~calm(X0))) [input p7]
17. rich(fred) [input p16]
24. ~funny(fred) [input hypothesis]
30. ! [X0] : ((~brave(X0) & ~calm(X0)) | (funny(X0) & patient(X0))) [ennf transformation 8]
44. ! [X0] : (((~strong(X0) & brave(X0)) | (~patient(X0) & ~rich(X0))) & ((patient(X0) | rich(X0)) | (strong(X0) | ~brave(X0)))) [nnf transformation 3]
45. ! [X0] : (((~strong(X0) & brave(X0)) | (~patient(X0) & ~rich(X0))) & (patient(X0) | rich(X0) | strong(X0) | ~brave(X0))) [flattening 44]
101. ~rich(X0) | brave(X0) [cnf transformation 45]
127. ~brave(X0) | funny(X0) [cnf transformation 30]
157. rich(fred) [cnf transformation 17]
166. ~funny(fred) [cnf transformation 24]
388. brave(fred) [resolution 101,157]
394. funny(fred) [resolution 127,388]
396. $false [subsumption resolution 394,166]
% SZS output end Proof for 574724145343673207386547
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is either patient or kind.
Everyone who is not calm or not funny is either not humble or brave.
Everyone who is not calm is not brave or patient.
Everyone who is quiet or wise is patient or not strong.
Everyone who is either not humble or quiet is not strong.
Everyone who is both humble and not calm is not old and vice versa.
Everyone who is not wise is either wise or curious and vice versa.
Everyone who is both not calm and strong is not kind.
If someone is not old then mary is either not creative or not tall.
Everyone who is not strong is old or tall and vice versa.
If someone is rich or kind then someone is curious and vice versa.
Everyone who is wise is not strong and vice versa.
If paul is old or not humble then someone is not happy.
Everyone who is strong or kind is not curious and vice versa.
If alice is tall then john is both wise and not tall.
Everyone who is both not wise and brave is not calm.
Alice is either not happy or tall.
Someone is not creative.
Lucy is not generous.
Someone is rich or patient.
John is tall.
Someone is not generous.
Someone is either curious or not old.
Lucy is both tall and not rich. | Alice is old. | entailment | (![X]:(~tall(X)=>(patient(X)<~>kind(X))))&
(![X]:((~calm(X)|~funny(X))=>(~humble(X)<~>brave(X))))&
(![X]:(~calm(X)=>(~brave(X)|patient(X))))&
(![X]:((quiet(X)|wise(X))=>(patient(X)|~strong(X))))&
(![X]:((~humble(X)<~>quiet(X))=>~strong(X)))&
(![X]:((humble(X)&~calm(X))<=>~old(X)))&
(![X]:(~wise(X)<=>(wise(X)<~>curious(X))))&
(![X]:((~calm(X)&strong(X))=>~kind(X)))&
((?[X]:(~old(X)))=>((~creative(mary)<~>~tall(mary))))&
(![X]:(~strong(X)<=>(old(X)|tall(X))))&
((?[X]:((rich(X)|kind(X))))<=>(?[X]:(curious(X))))&
(![X]:(wise(X)<=>~strong(X)))&
(((old(paul)|~humble(paul)))=>(?[X]:(~happy(X))))&
(![X]:((strong(X)|kind(X))<=>~curious(X)))&
((tall(alice))=>((wise(john)&~tall(john))))&
(![X]:((~wise(X)&brave(X))=>~calm(X)))&
((~happy(alice)<~>tall(alice)))&
(?[X]:(~creative(X)))&
(~generous(lucy))&
(?[X]:((rich(X)|patient(X))))&
(tall(john))&
(?[X]:(~generous(X)))&
(?[X]:((curious(X)<~>~old(X))))&
((tall(lucy)&~rich(lucy))) | old(alice) | [
"p6",
"p9",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8895912324475858370350883
% SZS output start Proof for 8895912324475858370350883
7. ! [X0] : (~wise(X0) <=> (wise(X0) <~> curious(X0))) [input p6]
10. ! [X0] : (~strong(X0) <=> (tall(X0) | old(X0))) [input p9]
14. ! [X0] : ((kind(X0) | strong(X0)) <=> ~curious(X0)) [input p13]
15. tall(alice) => (~tall(john) & wise(john)) [input p14]
21. tall(john) [input p20]
25. ~old(alice) [input hypothesis]
41. (~tall(john) & wise(john)) | ~tall(alice) [ennf transformation 15]
49. ! [X0] : ((~wise(X0) | ((wise(X0) | ~curious(X0)) & (curious(X0) | ~wise(X0)))) & (((~curious(X0) | ~wise(X0)) & (curious(X0) | wise(X0))) | wise(X0))) [nnf transformation 7]
51. ! [X0] : ((~strong(X0) | (~tall(X0) & ~old(X0))) & ((tall(X0) | old(X0)) | strong(X0))) [nnf transformation 10]
52. ! [X0] : ((~strong(X0) | (~tall(X0) & ~old(X0))) & (tall(X0) | old(X0) | strong(X0))) [flattening 51]
61. ! [X0] : (((kind(X0) | strong(X0)) | curious(X0)) & (~curious(X0) | (~kind(X0) & ~strong(X0)))) [nnf transformation 14]
62. ! [X0] : ((kind(X0) | strong(X0) | curious(X0)) & (~curious(X0) | (~kind(X0) & ~strong(X0)))) [flattening 61]
83. curious(X0) | wise(X0) | wise(X0) [cnf transformation 49]
85. ~wise(X0) | curious(X0) | ~wise(X0) [cnf transformation 49]
90. old(X0) | tall(X0) | strong(X0) [cnf transformation 52]
100. ~curious(X0) | ~strong(X0) [cnf transformation 62]
104. ~tall(john) | ~tall(alice) [cnf transformation 41]
110. tall(john) [cnf transformation 21]
115. ~old(alice) [cnf transformation 25]
116. curious(X0) | wise(X0) [duplicate literal removal 83]
117. ~wise(X0) | curious(X0) [duplicate literal removal 85]
118. curious(X0) [subsumption resolution 116,117]
157. ~strong(X0) [subsumption resolution 100,118]
159. 9 <=> tall(alice) [avatar definition]
161. ~tall(alice) <- (~9) [avatar component clause 159]
163. 10 <=> tall(john) [avatar definition]
166. ~9 | ~10 [avatar split clause 104,163,159]
187. 10 [avatar split clause 110,163]
233. tall(alice) | strong(alice) [resolution 90,115]
236. strong(alice) <- (~9) [subsumption resolution 233,161]
237. $false <- (~9) [subsumption resolution 236,157]
238. 9 [avatar contradiction clause 237]
240. $false [avatar sat refutation 166,187,238]
% SZS output end Proof for 8895912324475858370350883
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either rich or funny then paul is both not generous and rich.
Everyone who is strong is both not rich and not old and vice versa.
If alice is both quiet and not funny then someone is brave and vice versa.
Everyone who is either old or not calm is both patient and not patient and vice versa.
Everyone who is creative is not quiet or not wise.
If lucy is both old and not strong then someone is not rich and vice versa.
If mary is not rich or not kind then john is creative.
Everyone who is rich or not wise is happy or not strong and vice versa.
Everyone who is both not tall and strong is not strong or rich.
Everyone who is quiet or not curious is both not strong and calm and vice versa.
If someone is both not old and patient then alice is humble or patient and vice versa.
Everyone who is both rich and not curious is either wise or not generous.
Everyone who is both not humble and brave is either not tall or not strong.
If susan is either funny or brave then mary is brave or kind and vice versa.
Everyone who is either not generous or not curious is both not curious and not old and vice versa.
If someone is both happy and patient then paul is curious and vice versa.
Someone is not calm.
Someone is curious.
Someone is both calm and not funny.
Fred is both not curious and generous.
John is both not strong and not curious.
Susan is kind.
Fred is not funny or creative.
John is generous. | Fred is not rich. | contradiction | ((?[X]:((rich(X)<~>funny(X))))=>((~generous(paul)&rich(paul))))&
(![X]:(strong(X)<=>(~rich(X)&~old(X))))&
(((quiet(alice)&~funny(alice)))<=>(?[X]:(brave(X))))&
(![X]:((old(X)<~>~calm(X))<=>(patient(X)&~patient(X))))&
(![X]:(creative(X)=>(~quiet(X)|~wise(X))))&
(((old(lucy)&~strong(lucy)))<=>(?[X]:(~rich(X))))&
(((~rich(mary)|~kind(mary)))=>(creative(john)))&
(![X]:((rich(X)|~wise(X))<=>(happy(X)|~strong(X))))&
(![X]:((~tall(X)&strong(X))=>(~strong(X)|rich(X))))&
(![X]:((quiet(X)|~curious(X))<=>(~strong(X)&calm(X))))&
((?[X]:((~old(X)&patient(X))))<=>((humble(alice)|patient(alice))))&
(![X]:((rich(X)&~curious(X))=>(wise(X)<~>~generous(X))))&
(![X]:((~humble(X)&brave(X))=>(~tall(X)<~>~strong(X))))&
(((funny(susan)<~>brave(susan)))<=>((brave(mary)|kind(mary))))&
(![X]:((~generous(X)<~>~curious(X))<=>(~curious(X)&~old(X))))&
((?[X]:((happy(X)&patient(X))))<=>(curious(paul)))&
(?[X]:(~calm(X)))&
(?[X]:(curious(X)))&
(?[X]:((calm(X)&~funny(X))))&
((~curious(fred)&generous(fred)))&
((~strong(john)&~curious(john)))&
(kind(susan))&
((~funny(fred)|creative(fred)))&
(generous(john)) | ~rich(fred) | [
"p1",
"p9",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 301388038344372393568386
% SZS output start Proof for 301388038344372393568386
2. ! [X0] : (strong(X0) <=> (~old(X0) & ~rich(X0))) [input p1]
10. ! [X0] : ((~curious(X0) | quiet(X0)) <=> (calm(X0) & ~strong(X0))) [input p9]
15. ! [X0] : ((~generous(X0) <~> ~curious(X0)) <=> (~old(X0) & ~curious(X0))) [input p14]
20. generous(fred) & ~curious(fred) [input p19]
25. ~rich(fred) [input hypothesis]
37. ! [X0] : ((strong(X0) | (old(X0) | rich(X0))) & ((~old(X0) & ~rich(X0)) | ~strong(X0))) [nnf transformation 2]
38. ! [X0] : ((strong(X0) | old(X0) | rich(X0)) & ((~old(X0) & ~rich(X0)) | ~strong(X0))) [flattening 37]
53. ! [X0] : (((~curious(X0) | quiet(X0)) | (~calm(X0) | strong(X0))) & ((calm(X0) & ~strong(X0)) | (curious(X0) & ~quiet(X0)))) [nnf transformation 10]
54. ! [X0] : ((~curious(X0) | quiet(X0) | ~calm(X0) | strong(X0)) & ((calm(X0) & ~strong(X0)) | (curious(X0) & ~quiet(X0)))) [flattening 53]
64. ! [X0] : ((((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | (old(X0) | curious(X0))) & ((~old(X0) & ~curious(X0)) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0))))) [nnf transformation 15]
65. ! [X0] : ((((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | old(X0) | curious(X0)) & ((~old(X0) & ~curious(X0)) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0))))) [flattening 64]
82. old(X0) | strong(X0) | rich(X0) [cnf transformation 38]
104. ~strong(X0) | curious(X0) [cnf transformation 54]
126. ~old(X0) | ~generous(X0) | curious(X0) [cnf transformation 65]
136. ~curious(fred) [cnf transformation 20]
137. generous(fred) [cnf transformation 20]
143. ~rich(fred) [cnf transformation 25]
355. ~generous(X0) | curious(X0) | strong(X0) | rich(X0) [resolution 126,82]
359. ~generous(X0) | curious(X0) | rich(X0) [subsumption resolution 355,104]
438. curious(fred) | rich(fred) [resolution 359,137]
441. rich(fred) [subsumption resolution 438,136]
442. $false [subsumption resolution 441,143]
% SZS output end Proof for 301388038344372393568386
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If john is either tall or not brave then alice is both not generous and calm and vice versa. If someone is not quiet then mary is either creative or humble and vice versa. If someone is both not quiet and not tall then john is either patient or not creative and vice versa. Everyone who is both not funny and patient is not happy. Everyone who is either not quiet or patient is humble or happy and vice versa. If lucy is both not tall and not happy then someone is not old and vice versa. Everyone who is quiet is both patient and curious and vice versa. Everyone who is either strong or wise is not wise. Everyone who is patient is humble or calm and vice versa. If someone is not strong then someone is not patient or curious. Everyone who is both old and not happy is both not funny and quiet. Everyone who is not old or not strong is both not humble and not strong. If someone is both rich and not kind then john is either happy or creative. Everyone who is rich or not generous is either not rich or not patient. Everyone who is both not quiet and brave is rich or not generous. If someone is not old then someone is either creative or not rich and vice versa. Alice is both brave and strong. Someone is both brave and funny. Someone is both not funny and not rich. Someone is either strong or not wise. Alice is both rich and strong. Paul is tall or not curious. Mary is both rich and strong. | Alice is humble. | contradiction | (((tall(john)<~>~brave(john)))<=>((~generous(alice)&calm(alice))))&
((?[X]:(~quiet(X)))<=>((creative(mary)<~>humble(mary))))&
((?[X]:((~quiet(X)&~tall(X))))<=>((patient(john)<~>~creative(john))))&
(![X]:((~funny(X)&patient(X))=>~happy(X)))&
(![X]:((~quiet(X)<~>patient(X))<=>(humble(X)|happy(X))))&
(((~tall(lucy)&~happy(lucy)))<=>(?[X]:(~old(X))))&
(![X]:(quiet(X)<=>(patient(X)&curious(X))))&
(![X]:((strong(X)<~>wise(X))=>~wise(X)))&
(![X]:(patient(X)<=>(humble(X)|calm(X))))&
((?[X]:(~strong(X)))=>(?[X]:((~patient(X)|curious(X)))))&
(![X]:((old(X)&~happy(X))=>(~funny(X)&quiet(X))))&
(![X]:((~old(X)|~strong(X))=>(~humble(X)&~strong(X))))&
((?[X]:((rich(X)&~kind(X))))=>((happy(john)<~>creative(john))))&
(![X]:((rich(X)|~generous(X))=>(~rich(X)<~>~patient(X))))&
(![X]:((~quiet(X)&brave(X))=>(rich(X)|~generous(X))))&
((?[X]:(~old(X)))<=>(?[X]:((creative(X)<~>~rich(X)))))&
((brave(alice)&strong(alice)))&
(?[X]:((brave(X)&funny(X))))&
(?[X]:((~funny(X)&~rich(X))))&
(?[X]:((strong(X)<~>~wise(X))))&
((rich(alice)&strong(alice)))&
((tall(paul)|~curious(paul)))&
((rich(mary)&strong(mary))) | humble(alice) | [
"p8",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4638929233624946825793190
% SZS output start Proof for 4638929233624946825793190
9. ! [X0] : (patient(X0) <=> (calm(X0) | humble(X0))) [input p8]
14. ! [X0] : ((~generous(X0) | rich(X0)) => (~rich(X0) <~> ~patient(X0))) [input p13]
21. strong(alice) & rich(alice) [input p20]
24. humble(alice) [input hypothesis]
35. ! [X0] : ((~rich(X0) <~> ~patient(X0)) | (generous(X0) & ~rich(X0))) [ennf transformation 14]
58. ! [X0] : ((patient(X0) | (~calm(X0) & ~humble(X0))) & ((calm(X0) | humble(X0)) | ~patient(X0))) [nnf transformation 9]
59. ! [X0] : ((patient(X0) | (~calm(X0) & ~humble(X0))) & (calm(X0) | humble(X0) | ~patient(X0))) [flattening 58]
63. ! [X0] : (((patient(X0) | rich(X0)) & (~patient(X0) | ~rich(X0))) | (generous(X0) & ~rich(X0))) [nnf transformation 35]
108. ~humble(X0) | patient(X0) [cnf transformation 59]
117. ~patient(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 63]
134. rich(alice) [cnf transformation 21]
139. humble(alice) [cnf transformation 24]
140. ~rich(X0) | ~patient(X0) [duplicate literal removal 117]
278. patient(alice) [resolution 108,139]
287. ~patient(alice) [resolution 140,134]
289. $false [subsumption resolution 287,278]
% SZS output end Proof for 4638929233624946825793190
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is not quiet then alice is not patient and vice versa.
If someone is patient then fred is both not patient and generous and vice versa.
If fred is both happy and not quiet then mary is not curious or not old.
Everyone who is both not kind and not generous is happy.
If someone is not funny then lucy is both rich and not creative.
If lucy is not creative or rich then alice is not tall and vice versa.
If someone is both not kind and wise then susan is either creative or not kind.
Everyone who is both kind and funny is generous and vice versa.
If someone is either not tall or not wise then someone is old and vice versa.
Everyone who is either calm or funny is either not old or not strong.
If john is both kind and not humble then susan is both not quiet and not calm and vice versa.
Everyone who is either curious or patient is either curious or not calm and vice versa.
Everyone who is both humble and strong is patient or kind and vice versa.
If someone is either not kind or patient then fred is patient.
If fred is old then fred is either not funny or rich.
Everyone who is both not old and quiet is both patient and not humble and vice versa.
Paul is either not strong or quiet.
Fred is old or wise.
Someone is both generous and not old.
Someone is both tall and not creative.
John is both not funny and not old.
Someone is both wise and funny.
Lucy is not kind. | Paul is old. | entailment | ((~quiet(john))<=>(~patient(alice)))&
((?[X]:(patient(X)))<=>((~patient(fred)&generous(fred))))&
(((happy(fred)&~quiet(fred)))=>((~curious(mary)|~old(mary))))&
(![X]:((~kind(X)&~generous(X))=>happy(X)))&
((?[X]:(~funny(X)))=>((rich(lucy)&~creative(lucy))))&
(((~creative(lucy)|rich(lucy)))<=>(~tall(alice)))&
((?[X]:((~kind(X)&wise(X))))=>((creative(susan)<~>~kind(susan))))&
(![X]:((kind(X)&funny(X))<=>generous(X)))&
((?[X]:((~tall(X)<~>~wise(X))))<=>(?[X]:(old(X))))&
(![X]:((calm(X)<~>funny(X))=>(~old(X)<~>~strong(X))))&
(((kind(john)&~humble(john)))<=>((~quiet(susan)&~calm(susan))))&
(![X]:((curious(X)<~>patient(X))<=>(curious(X)<~>~calm(X))))&
(![X]:((humble(X)&strong(X))<=>(patient(X)|kind(X))))&
((?[X]:((~kind(X)<~>patient(X))))=>(patient(fred)))&
((old(fred))=>((~funny(fred)<~>rich(fred))))&
(![X]:((~old(X)&quiet(X))<=>(patient(X)&~humble(X))))&
((~strong(paul)<~>quiet(paul)))&
((old(fred)|wise(fred)))&
(?[X]:((generous(X)&~old(X))))&
(?[X]:((tall(X)&~creative(X))))&
((~funny(john)&~old(john)))&
(?[X]:((wise(X)&funny(X))))&
(~kind(lucy)) | old(paul) | [
"p1",
"p12",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7618005102220709200843241
% SZS output start Proof for 7618005102220709200843241
2. ? [X0] : patient(X0) <=> (generous(fred) & ~patient(fred)) [input p1]
13. ! [X0] : ((strong(X0) & humble(X0)) <=> (kind(X0) | patient(X0))) [input p12]
14. ? [X0] : (~kind(X0) <~> patient(X0)) => patient(fred) [input p13]
16. ! [X0] : ((quiet(X0) & ~old(X0)) <=> (~humble(X0) & patient(X0))) [input p15]
17. ~strong(paul) <~> quiet(paul) [input p16]
24. ~old(paul) [input hypothesis]
33. patient(fred) | ! [X0] : (~kind(X0) <=> patient(X0)) [ennf transformation 14]
36. (? [X0] : patient(X0) | (~generous(fred) | patient(fred))) & ((generous(fred) & ~patient(fred)) | ! [X0] : ~patient(X0)) [nnf transformation 2]
37. (? [X0] : patient(X0) | ~generous(fred) | patient(fred)) & ((generous(fred) & ~patient(fred)) | ! [X0] : ~patient(X0)) [flattening 36]
38. (? [X0] : patient(X0) | ~generous(fred) | patient(fred)) & ((generous(fred) & ~patient(fred)) | ! [X1] : ~patient(X1)) [rectify 37]
39. ? [X0] : patient(X0) => patient(sK0) [choice axiom]
40. (patient(sK0) | ~generous(fred) | patient(fred)) & ((generous(fred) & ~patient(fred)) | ! [X1] : ~patient(X1)) [skolemisation 38,39]
55. ! [X0] : (((strong(X0) & humble(X0)) | (~kind(X0) & ~patient(X0))) & ((kind(X0) | patient(X0)) | (~strong(X0) | ~humble(X0)))) [nnf transformation 13]
56. ! [X0] : (((strong(X0) & humble(X0)) | (~kind(X0) & ~patient(X0))) & (kind(X0) | patient(X0) | ~strong(X0) | ~humble(X0))) [flattening 55]
57. patient(fred) | ! [X0] : ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0))) [nnf transformation 33]
59. ! [X0] : (((quiet(X0) & ~old(X0)) | (humble(X0) | ~patient(X0))) & ((~humble(X0) & patient(X0)) | (~quiet(X0) | old(X0)))) [nnf transformation 16]
60. ! [X0] : (((quiet(X0) & ~old(X0)) | humble(X0) | ~patient(X0)) & ((~humble(X0) & patient(X0)) | ~quiet(X0) | old(X0))) [flattening 59]
61. (~quiet(paul) | strong(paul)) & (quiet(paul) | ~strong(paul)) [nnf transformation 17]
70. ~patient(fred) | ~patient(X1) [cnf transformation 40]
106. ~patient(X0) | humble(X0) [cnf transformation 56]
107. ~kind(X0) | humble(X0) [cnf transformation 56]
108. ~patient(X0) | strong(X0) [cnf transformation 56]
109. ~kind(X0) | strong(X0) [cnf transformation 56]
110. patient(fred) | patient(X0) | kind(X0) [cnf transformation 57]
115. ~humble(X0) | ~quiet(X0) | old(X0) [cnf transformation 60]
118. quiet(paul) | ~strong(paul) [cnf transformation 61]
130. ~old(paul) [cnf transformation 24]
146. 3 <=> patient(fred) [avatar definition]
148. patient(fred) <- (3) [avatar component clause 146]
159. 6 <=> ! [X1] : ~patient(X1) [avatar definition]
160. ~patient(X1) <- (6) [avatar component clause 159]
162. 6 | ~3 [avatar split clause 70,146,159]
265. 29 <=> ! [X0] : (patient(X0) | kind(X0)) [avatar definition]
266. kind(X0) | patient(X0) <- (29) [avatar component clause 265]
267. 29 | 3 [avatar split clause 110,146,265]
283. 33 <=> strong(paul) [avatar definition]
284. ~strong(paul) <- (~33) [avatar component clause 283]
287. 34 <=> quiet(paul) [avatar definition]
288. quiet(paul) <- (34) [avatar component clause 287]
291. ~33 | 34 [avatar split clause 118,287,283]
297. $false <- (3, 6) [subsumption resolution 148,160]
298. ~3 | ~6 [avatar contradiction clause 297]
327. patient(X1) | strong(X1) <- (29) [resolution 266,109]
328. patient(X2) | humble(X2) <- (29) [resolution 266,107]
332. strong(X1) <- (29) [subsumption resolution 327,108]
333. humble(X2) <- (29) [subsumption resolution 328,106]
388. $false <- (29, ~33) [resolution 332,284]
389. ~29 | 33 [avatar contradiction clause 388]
394. ~quiet(X0) | old(X0) <- (29) [resolution 115,333]
475. old(paul) <- (29, 34) [resolution 394,288]
476. $false <- (29, 34) [subsumption resolution 475,130]
477. ~29 | ~34 [avatar contradiction clause 476]
478. $false [avatar sat refutation 162,267,291,298,389,477]
% SZS output end Proof for 7618005102220709200843241
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If mary is rich then someone is quiet and vice versa. If john is not patient or not old then someone is not rich. Everyone who is curious is either not humble or not creative. If someone is old then someone is both rich and not funny. Everyone who is kind is both quiet and creative and vice versa. Everyone who is both not old and wise is both calm and kind. Everyone who is not calm or brave is both not calm and not tall. Everyone who is calm is not funny and vice versa. Everyone who is both tall and quiet is brave or kind and vice versa. Everyone who is either wise or not funny is both not calm and brave. Everyone who is either rich or not rich is both creative and curious. If someone is not tall then someone is either not generous or not humble and vice versa. If alice is both generous and not humble then paul is not happy and vice versa. Everyone who is calm or not kind is happy and vice versa. If alice is both humble and not tall then someone is patient or not calm and vice versa. Everyone who is either calm or tall is both not patient and creative. Lucy is either not wise or curious. Someone is both strong and not generous. Someone is either not kind or wise. Paul is either strong or not brave. Someone is either old or funny. Someone is strong. Lucy is both curious and creative. | Mary is not wise. | contradiction | ((rich(mary))<=>(?[X]:(quiet(X))))&
(((~patient(john)|~old(john)))=>(?[X]:(~rich(X))))&
(![X]:(curious(X)=>(~humble(X)<~>~creative(X))))&
((?[X]:(old(X)))=>(?[X]:((rich(X)&~funny(X)))))&
(![X]:(kind(X)<=>(quiet(X)&creative(X))))&
(![X]:((~old(X)&wise(X))=>(calm(X)&kind(X))))&
(![X]:((~calm(X)|brave(X))=>(~calm(X)&~tall(X))))&
(![X]:(calm(X)<=>~funny(X)))&
(![X]:((tall(X)&quiet(X))<=>(brave(X)|kind(X))))&
(![X]:((wise(X)<~>~funny(X))=>(~calm(X)&brave(X))))&
(![X]:((rich(X)<~>~rich(X))=>(creative(X)&curious(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~generous(X)<~>~humble(X)))))&
(((generous(alice)&~humble(alice)))<=>(~happy(paul)))&
(![X]:((calm(X)|~kind(X))<=>happy(X)))&
(((humble(alice)&~tall(alice)))<=>(?[X]:((patient(X)|~calm(X)))))&
(![X]:((calm(X)<~>tall(X))=>(~patient(X)&creative(X))))&
((~wise(lucy)<~>curious(lucy)))&
(?[X]:((strong(X)&~generous(X))))&
(?[X]:((~kind(X)<~>wise(X))))&
((strong(paul)<~>~brave(paul)))&
(?[X]:((old(X)<~>funny(X))))&
(?[X]:(strong(X)))&
((curious(lucy)&creative(lucy))) | ~wise(mary) | [
"p2",
"p6",
"p7",
"p8",
"p9",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7028681351032597561435
% SZS output start Proof for 7028681351032597561435
3. ! [X0] : (curious(X0) => (~humble(X0) <~> ~creative(X0))) [input p2]
7. ! [X0] : ((brave(X0) | ~calm(X0)) => (~tall(X0) & ~calm(X0))) [input p6]
8. ! [X0] : (calm(X0) <=> ~funny(X0)) [input p7]
9. ! [X0] : ((quiet(X0) & tall(X0)) <=> (kind(X0) | brave(X0))) [input p8]
10. ! [X0] : ((wise(X0) <~> ~funny(X0)) => (brave(X0) & ~calm(X0))) [input p9]
11. ! [X0] : ((rich(X0) <~> ~rich(X0)) => (curious(X0) & creative(X0))) [input p10]
15. (~tall(alice) & humble(alice)) <=> ? [X0] : (~calm(X0) | patient(X0)) [input p14]
24. ~wise(mary) [input hypothesis]
28. ! [X0] : ((~humble(X0) <~> ~creative(X0)) | ~curious(X0)) [ennf transformation 3]
32. ! [X0] : ((~tall(X0) & ~calm(X0)) | (~brave(X0) & calm(X0))) [ennf transformation 7]
33. ! [X0] : ((brave(X0) & ~calm(X0)) | (wise(X0) <=> ~funny(X0))) [ennf transformation 10]
34. ! [X0] : ((curious(X0) & creative(X0)) | (rich(X0) <=> ~rich(X0))) [ennf transformation 11]
42. ! [X0] : (((creative(X0) | humble(X0)) & (~creative(X0) | ~humble(X0))) | ~curious(X0)) [nnf transformation 28]
48. ! [X0] : ((calm(X0) | funny(X0)) & (~funny(X0) | ~calm(X0))) [nnf transformation 8]
49. ! [X0] : (((quiet(X0) & tall(X0)) | (~kind(X0) & ~brave(X0))) & ((kind(X0) | brave(X0)) | (~quiet(X0) | ~tall(X0)))) [nnf transformation 9]
50. ! [X0] : (((quiet(X0) & tall(X0)) | (~kind(X0) & ~brave(X0))) & (kind(X0) | brave(X0) | ~quiet(X0) | ~tall(X0))) [flattening 49]
51. ! [X0] : ((brave(X0) & ~calm(X0)) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0)))) [nnf transformation 33]
52. ! [X0] : ((curious(X0) & creative(X0)) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0)))) [nnf transformation 34]
62. ((~tall(alice) & humble(alice)) | ! [X0] : (calm(X0) & ~patient(X0))) & (? [X0] : (~calm(X0) | patient(X0)) | (tall(alice) | ~humble(alice))) [nnf transformation 15]
63. ((~tall(alice) & humble(alice)) | ! [X0] : (calm(X0) & ~patient(X0))) & (? [X0] : (~calm(X0) | patient(X0)) | tall(alice) | ~humble(alice)) [flattening 62]
64. ((~tall(alice) & humble(alice)) | ! [X0] : (calm(X0) & ~patient(X0))) & (? [X1] : (~calm(X1) | patient(X1)) | tall(alice) | ~humble(alice)) [rectify 63]
65. ? [X1] : (~calm(X1) | patient(X1)) => (~calm(sK5) | patient(sK5)) [choice axiom]
66. ((~tall(alice) & humble(alice)) | ! [X0] : (calm(X0) & ~patient(X0))) & ((~calm(sK5) | patient(sK5)) | tall(alice) | ~humble(alice)) [skolemisation 64,65]
84. ~creative(X0) | ~humble(X0) | ~curious(X0) [cnf transformation 42]
96. ~tall(X0) | ~brave(X0) [cnf transformation 32]
97. ~calm(X0) | ~funny(X0) [cnf transformation 48]
100. tall(X0) | ~brave(X0) [cnf transformation 50]
107. brave(X0) | wise(X0) | funny(X0) [cnf transformation 51]
108. creative(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 52]
109. creative(X0) | rich(X0) | rich(X0) [cnf transformation 52]
110. curious(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 52]
111. curious(X0) | rich(X0) | rich(X0) [cnf transformation 52]
124. humble(alice) | calm(X0) [cnf transformation 66]
144. ~wise(mary) [cnf transformation 24]
145. creative(X0) | ~rich(X0) [duplicate literal removal 108]
146. creative(X0) | rich(X0) [duplicate literal removal 109]
147. curious(X0) | ~rich(X0) [duplicate literal removal 110]
148. curious(X0) | rich(X0) [duplicate literal removal 111]
189. ~brave(X0) [subsumption resolution 100,96]
191. wise(X0) | funny(X0) [subsumption resolution 107,189]
193. curious(X0) [subsumption resolution 147,148]
194. creative(X0) [subsumption resolution 145,146]
225. 17 <=> humble(alice) [avatar definition]
226. humble(alice) <- (17) [avatar component clause 225]
236. 19 <=> ! [X0] : calm(X0) [avatar definition]
237. calm(X0) <- (19) [avatar component clause 236]
247. 19 | 17 [avatar split clause 124,225,236]
293. funny(mary) [resolution 191,144]
303. ~humble(X1) | ~curious(X1) [resolution 84,194]
305. ~humble(X1) [subsumption resolution 303,193]
310. $false <- (17) [resolution 305,226]
311. ~17 [avatar contradiction clause 310]
315. ~funny(X1) <- (19) [resolution 237,97]
325. $false <- (19) [resolution 315,293]
326. ~19 [avatar contradiction clause 325]
328. $false [avatar sat refutation 247,311,326]
% SZS output end Proof for 7028681351032597561435
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and not happy is rich or not kind and vice versa. If fred is either not curious or rich then someone is both not old and not funny and vice versa. Everyone who is both happy and not tall is both brave and not wise. Everyone who is not old is creative or not funny and vice versa. If someone is not quiet then john is either not strong or not old. Everyone who is either not quiet or not funny is not strong. Everyone who is funny or strong is patient and vice versa. Everyone who is either not creative or curious is not strong. If someone is both humble and calm then someone is tall or not quiet and vice versa. If susan is either old or not old then someone is quiet or kind and vice versa. Everyone who is not old is happy and vice versa. If susan is both not quiet and not brave then someone is both not calm and not brave and vice versa. If someone is both strong and wise then someone is not curious and vice versa. If someone is either brave or old then mary is rich and vice versa. Everyone who is either not strong or not patient is happy and vice versa. Everyone who is not wise or old is either quiet or funny. Someone is patient or not curious. Lucy is funny. Someone is not happy or not old. Someone is either not strong or not patient. Someone is either generous or creative. | Fred is quiet. | entailment | (![X]:((quiet(X)&~happy(X))<=>(rich(X)|~kind(X))))&
(((~curious(fred)<~>rich(fred)))<=>(?[X]:((~old(X)&~funny(X)))))&
(![X]:((happy(X)&~tall(X))=>(brave(X)&~wise(X))))&
(![X]:(~old(X)<=>(creative(X)|~funny(X))))&
((?[X]:(~quiet(X)))=>((~strong(john)<~>~old(john))))&
(![X]:((~quiet(X)<~>~funny(X))=>~strong(X)))&
(![X]:((funny(X)|strong(X))<=>patient(X)))&
(![X]:((~creative(X)<~>curious(X))=>~strong(X)))&
((?[X]:((humble(X)&calm(X))))<=>(?[X]:((tall(X)|~quiet(X)))))&
(((old(susan)<~>~old(susan)))<=>(?[X]:((quiet(X)|kind(X)))))&
(![X]:(~old(X)<=>happy(X)))&
(((~quiet(susan)&~brave(susan)))<=>(?[X]:((~calm(X)&~brave(X)))))&
((?[X]:((strong(X)&wise(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((brave(X)<~>old(X))))<=>(rich(mary)))&
(![X]:((~strong(X)<~>~patient(X))<=>happy(X)))&
(![X]:((~wise(X)|old(X))=>(quiet(X)<~>funny(X))))&
(?[X]:((patient(X)|~curious(X))))&
(funny(lucy))&
(?[X]:((~happy(X)|~old(X))))&
(?[X]:((~strong(X)<~>~patient(X))))&
(?[X]:((generous(X)<~>creative(X)))) | quiet(fred) | [
"p3",
"p4",
"p6",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5782801566620598530998736
% SZS output start Proof for 5782801566620598530998736
4. ! [X0] : (~old(X0) <=> (~funny(X0) | creative(X0))) [input p3]
5. ? [X0] : ~quiet(X0) => (~strong(john) <~> ~old(john)) [input p4]
7. ! [X0] : ((strong(X0) | funny(X0)) <=> patient(X0)) [input p6]
11. ! [X0] : (~old(X0) <=> happy(X0)) [input p10]
15. ! [X0] : ((~strong(X0) <~> ~patient(X0)) <=> happy(X0)) [input p14]
22. ~quiet(fred) [input hypothesis]
27. (~strong(john) <~> ~old(john)) | ! [X0] : quiet(X0) [ennf transformation 5]
37. ! [X0] : ((~old(X0) | (funny(X0) & ~creative(X0))) & ((~funny(X0) | creative(X0)) | old(X0))) [nnf transformation 4]
38. ! [X0] : ((~old(X0) | (funny(X0) & ~creative(X0))) & (~funny(X0) | creative(X0) | old(X0))) [flattening 37]
39. ((old(john) | strong(john)) & (~old(john) | ~strong(john))) | ! [X0] : quiet(X0) [nnf transformation 27]
41. ! [X0] : (((strong(X0) | funny(X0)) | ~patient(X0)) & (patient(X0) | (~strong(X0) & ~funny(X0)))) [nnf transformation 7]
42. ! [X0] : ((strong(X0) | funny(X0) | ~patient(X0)) & (patient(X0) | (~strong(X0) & ~funny(X0)))) [flattening 41]
53. ! [X0] : ((~old(X0) | ~happy(X0)) & (happy(X0) | old(X0))) [nnf transformation 11]
68. ! [X0] : ((((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | ~happy(X0)) & (happy(X0) | ((~strong(X0) | patient(X0)) & (~patient(X0) | strong(X0))))) [nnf transformation 15]
95. ~old(X0) | funny(X0) [cnf transformation 38]
96. ~old(john) | ~strong(john) | quiet(X0) [cnf transformation 39]
97. old(john) | strong(john) | quiet(X0) [cnf transformation 39]
100. ~funny(X0) | patient(X0) [cnf transformation 42]
101. ~strong(X0) | patient(X0) [cnf transformation 42]
116. old(X0) | happy(X0) [cnf transformation 53]
117. ~old(X0) | ~happy(X0) [cnf transformation 53]
129. ~patient(X0) | happy(X0) | strong(X0) [cnf transformation 68]
131. ~patient(X0) | ~strong(X0) | ~happy(X0) [cnf transformation 68]
132. patient(X0) | strong(X0) | ~happy(X0) [cnf transformation 68]
144. ~quiet(fred) [cnf transformation 22]
173. 6 <=> ! [X0] : quiet(X0) [avatar definition]
174. quiet(X0) <- (6) [avatar component clause 173]
176. 7 <=> strong(john) [avatar definition]
177. ~strong(john) <- (~7) [avatar component clause 176]
178. strong(john) <- (7) [avatar component clause 176]
180. 8 <=> old(john) [avatar definition]
181. ~old(john) <- (~8) [avatar component clause 180]
182. old(john) <- (8) [avatar component clause 180]
183. 6 | 7 | 8 [avatar split clause 97,180,176,173]
184. 6 | ~7 | ~8 [avatar split clause 96,180,176,173]
278. ~happy(X0) | patient(X0) [subsumption resolution 132,101]
279. ~strong(X0) | ~happy(X0) [subsumption resolution 131,278]
304. $false <- (6) [resolution 174,144]
305. ~6 [avatar contradiction clause 304]
312. happy(john) <- (~8) [resolution 116,181]
318. ~happy(john) <- (7) [resolution 279,178]
320. $false <- (7, ~8) [subsumption resolution 318,312]
321. ~7 | 8 [avatar contradiction clause 320]
322. ~happy(john) <- (8) [resolution 182,117]
323. funny(john) <- (8) [resolution 182,95]
345. patient(john) <- (8) [resolution 323,100]
520. happy(john) | strong(john) <- (8) [resolution 345,129]
522. strong(john) <- (8) [subsumption resolution 520,322]
523. $false <- (~7, 8) [subsumption resolution 522,177]
524. 7 | ~8 [avatar contradiction clause 523]
525. $false [avatar sat refutation 183,184,305,321,524]
% SZS output end Proof for 5782801566620598530998736
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both kind and generous then someone is both not wise and tall. Everyone who is not funny or wise is both not generous and generous and vice versa. If someone is calm then someone is curious. If someone is both not brave and funny then mary is rich and vice versa. Everyone who is funny or not funny is not wise or patient. If susan is both not tall and not patient then john is quiet or not rich. Everyone who is both wise and quiet is not rich. If lucy is either not tall or not rich then someone is calm. If paul is both not rich and kind then mary is both generous and not kind and vice versa. Everyone who is both humble and funny is old. Everyone who is humble is both not wise and not generous. Everyone who is rich is tall. Everyone who is not curious is not brave or wise. If mary is either patient or wise then someone is patient and vice versa. Everyone who is both not funny and not kind is either curious or kind. Everyone who is either not kind or not happy is strong or not quiet. Lucy is both not old and not happy. Someone is either brave or funny. Someone is either not tall or old. Someone is not rich or not kind. Someone is either not happy or rich. Someone is not funny or old. Someone is generous. | Susan is not wise. | entailment | ((?[X]:((kind(X)&generous(X))))=>(?[X]:((~wise(X)&tall(X)))))&
(![X]:((~funny(X)|wise(X))<=>(~generous(X)&generous(X))))&
((?[X]:(calm(X)))=>(?[X]:(curious(X))))&
((?[X]:((~brave(X)&funny(X))))<=>(rich(mary)))&
(![X]:((funny(X)|~funny(X))=>(~wise(X)|patient(X))))&
(((~tall(susan)&~patient(susan)))=>((quiet(john)|~rich(john))))&
(![X]:((wise(X)&quiet(X))=>~rich(X)))&
(((~tall(lucy)<~>~rich(lucy)))=>(?[X]:(calm(X))))&
(((~rich(paul)&kind(paul)))<=>((generous(mary)&~kind(mary))))&
(![X]:((humble(X)&funny(X))=>old(X)))&
(![X]:(humble(X)=>(~wise(X)&~generous(X))))&
(![X]:(rich(X)=>tall(X)))&
(![X]:(~curious(X)=>(~brave(X)|wise(X))))&
(((patient(mary)<~>wise(mary)))<=>(?[X]:(patient(X))))&
(![X]:((~funny(X)&~kind(X))=>(curious(X)<~>kind(X))))&
(![X]:((~kind(X)<~>~happy(X))=>(strong(X)|~quiet(X))))&
((~old(lucy)&~happy(lucy)))&
(?[X]:((brave(X)<~>funny(X))))&
(?[X]:((~tall(X)<~>old(X))))&
(?[X]:((~rich(X)|~kind(X))))&
(?[X]:((~happy(X)<~>rich(X))))&
(?[X]:((~funny(X)|old(X))))&
(?[X]:(generous(X))) | ~wise(susan) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 374881459010096893588441
% SZS output start Proof for 374881459010096893588441
2. ! [X0] : ((wise(X0) | ~funny(X0)) <=> (generous(X0) & ~generous(X0))) [input p1]
24. wise(susan) [input hypothesis]
47. ! [X0] : (((wise(X0) | ~funny(X0)) | (~generous(X0) | generous(X0))) & ((generous(X0) & ~generous(X0)) | (~wise(X0) & funny(X0)))) [nnf transformation 2]
48. ! [X0] : ((wise(X0) | ~funny(X0) | ~generous(X0) | generous(X0)) & ((generous(X0) & ~generous(X0)) | (~wise(X0) & funny(X0)))) [flattening 47]
84. ~generous(X0) | ~wise(X0) [cnf transformation 48]
86. generous(X0) | ~wise(X0) [cnf transformation 48]
121. wise(susan) [cnf transformation 24]
136. ~wise(X0) [subsumption resolution 84,86]
258. $false [subsumption resolution 121,136]
% SZS output end Proof for 374881459010096893588441
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.043 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or wise is not quiet and vice versa.
Everyone who is generous is both not happy and not generous and vice versa.
Everyone who is not kind or quiet is creative and vice versa.
If someone is either tall or kind then someone is not brave and vice versa.
Everyone who is tall is not curious or rich.
If someone is both not humble and kind then mary is not strong or old.
If john is not brave or curious then john is both not strong and curious and vice versa.
If someone is funny then lucy is either not brave or quiet.
If alice is kind then someone is either funny or kind.
If susan is either wise or not curious then someone is either not humble or not strong and vice versa.
If mary is either happy or not wise then someone is both curious and not quiet.
If someone is both generous and not humble then someone is old or not brave and vice versa.
If someone is both quiet and not happy then someone is old or quiet and vice versa.
If paul is both not wise and tall then someone is not old.
Everyone who is either kind or not quiet is either calm or funny and vice versa.
Everyone who is not strong is both quiet and calm and vice versa.
Paul is either strong or patient.
Alice is not quiet or not happy.
John is happy.
Alice is calm or rich.
Fred is happy or not creative.
Paul is both not generous and strong. | Susan is old. | contradiction | (![X]:((~creative(X)<~>wise(X))<=>~quiet(X)))&
(![X]:(generous(X)<=>(~happy(X)&~generous(X))))&
(![X]:((~kind(X)|quiet(X))<=>creative(X)))&
((?[X]:((tall(X)<~>kind(X))))<=>(?[X]:(~brave(X))))&
(![X]:(tall(X)=>(~curious(X)|rich(X))))&
((?[X]:((~humble(X)&kind(X))))=>((~strong(mary)|old(mary))))&
(((~brave(john)|curious(john)))<=>((~strong(john)&curious(john))))&
((?[X]:(funny(X)))=>((~brave(lucy)<~>quiet(lucy))))&
((kind(alice))=>(?[X]:((funny(X)<~>kind(X)))))&
(((wise(susan)<~>~curious(susan)))<=>(?[X]:((~humble(X)<~>~strong(X)))))&
(((happy(mary)<~>~wise(mary)))=>(?[X]:((curious(X)&~quiet(X)))))&
((?[X]:((generous(X)&~humble(X))))<=>(?[X]:((old(X)|~brave(X)))))&
((?[X]:((quiet(X)&~happy(X))))<=>(?[X]:((old(X)|quiet(X)))))&
(((~wise(paul)&tall(paul)))=>(?[X]:(~old(X))))&
(![X]:((kind(X)<~>~quiet(X))<=>(calm(X)<~>funny(X))))&
(![X]:(~strong(X)<=>(quiet(X)&calm(X))))&
((strong(paul)<~>patient(paul)))&
((~quiet(alice)|~happy(alice)))&
(happy(john))&
((calm(alice)|rich(alice)))&
((happy(fred)|~creative(fred)))&
((~generous(paul)&strong(paul))) | old(susan) | [
"p1",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 16435932314211680287144
% SZS output start Proof for 16435932314211680287144
2. ! [X0] : (generous(X0) <=> (~generous(X0) & ~happy(X0))) [input p1]
12. ? [X0] : (~humble(X0) & generous(X0)) <=> ? [X0] : (~brave(X0) | old(X0)) [input p11]
23. old(susan) [input hypothesis]
25. ? [X0] : (~humble(X0) & generous(X0)) <=> ? [X1] : (~brave(X1) | old(X1)) [rectify 12]
37. ! [X0] : ((generous(X0) | (generous(X0) | happy(X0))) & ((~generous(X0) & ~happy(X0)) | ~generous(X0))) [nnf transformation 2]
38. ! [X0] : ((generous(X0) | generous(X0) | happy(X0)) & ((~generous(X0) & ~happy(X0)) | ~generous(X0))) [flattening 37]
59. (? [X0] : (~humble(X0) & generous(X0)) | ! [X1] : (brave(X1) & ~old(X1))) & (? [X1] : (~brave(X1) | old(X1)) | ! [X0] : (humble(X0) | ~generous(X0))) [nnf transformation 25]
60. (? [X0] : (~humble(X0) & generous(X0)) | ! [X1] : (brave(X1) & ~old(X1))) & (? [X2] : (~brave(X2) | old(X2)) | ! [X3] : (humble(X3) | ~generous(X3))) [rectify 59]
61. ? [X0] : (~humble(X0) & generous(X0)) => (~humble(sK5) & generous(sK5)) [choice axiom]
62. ? [X2] : (~brave(X2) | old(X2)) => (~brave(sK6) | old(sK6)) [choice axiom]
63. ((~humble(sK5) & generous(sK5)) | ! [X1] : (brave(X1) & ~old(X1))) & ((~brave(sK6) | old(sK6)) | ! [X3] : (humble(X3) | ~generous(X3))) [skolemisation 60,62,61]
80. ~generous(X0) | ~generous(X0) [cnf transformation 38]
112. generous(sK5) | ~old(X1) [cnf transformation 63]
140. old(susan) [cnf transformation 23]
141. ~generous(X0) [duplicate literal removal 80]
278. 30 <=> ! [X1] : ~old(X1) [avatar definition]
279. ~old(X1) <- (30) [avatar component clause 278]
283. ~old(X1) [subsumption resolution 112,141]
284. 30 [avatar split clause 283,278]
360. $false <- (30) [resolution 279,140]
361. ~30 [avatar contradiction clause 360]
362. $false [avatar sat refutation 284,361]
% SZS output end Proof for 16435932314211680287144
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both happy and not kind then someone is both old and curious and vice versa.
Everyone who is not strong or not generous is creative.
Everyone who is both quiet and not rich is either patient or calm and vice versa.
If paul is strong or not generous then someone is both kind and tall and vice versa.
Everyone who is not humble is both not calm and not kind and vice versa.
Everyone who is either not quiet or not happy is either creative or not quiet.
If john is both not curious and not happy then someone is either not kind or not generous and vice versa.
If someone is generous or wise then fred is either not kind or not calm and vice versa.
If someone is tall then fred is not strong and vice versa.
If someone is both not old and not humble then paul is both humble and kind and vice versa.
If someone is quiet then fred is funny or curious and vice versa.
Everyone who is both creative and brave is either not strong or calm and vice versa.
Everyone who is both not brave and quiet is funny or quiet and vice versa.
If lucy is either curious or not brave then someone is patient or curious.
Everyone who is either kind or not brave is not brave or old and vice versa.
Someone is both not funny and not tall.
Alice is funny.
John is both rich and not strong.
Someone is either old or patient.
Someone is either not creative or curious.
Susan is wise or rich.
Someone is either curious or not funny.
Someone is not calm. | Alice is humble. | neutral | (((happy(mary)&~kind(mary)))<=>(?[X]:((old(X)&curious(X)))))&
(![X]:((~strong(X)|~generous(X))=>creative(X)))&
(![X]:((quiet(X)&~rich(X))<=>(patient(X)<~>calm(X))))&
(((strong(paul)|~generous(paul)))<=>(?[X]:((kind(X)&tall(X)))))&
(![X]:(~humble(X)<=>(~calm(X)&~kind(X))))&
(![X]:((~quiet(X)<~>~happy(X))=>(creative(X)<~>~quiet(X))))&
(((~curious(john)&~happy(john)))<=>(?[X]:((~kind(X)<~>~generous(X)))))&
((?[X]:((generous(X)|wise(X))))<=>((~kind(fred)<~>~calm(fred))))&
((?[X]:(tall(X)))<=>(~strong(fred)))&
((?[X]:((~old(X)&~humble(X))))<=>((humble(paul)&kind(paul))))&
((?[X]:(quiet(X)))<=>((funny(fred)|curious(fred))))&
(![X]:((creative(X)&brave(X))<=>(~strong(X)<~>calm(X))))&
(![X]:((~brave(X)&quiet(X))<=>(funny(X)|quiet(X))))&
(((curious(lucy)<~>~brave(lucy)))=>(?[X]:((patient(X)|curious(X)))))&
(![X]:((kind(X)<~>~brave(X))<=>(~brave(X)|old(X))))&
(?[X]:((~funny(X)&~tall(X))))&
(funny(alice))&
((rich(john)&~strong(john)))&
(?[X]:((old(X)<~>patient(X))))&
(?[X]:((~creative(X)<~>curious(X))))&
((wise(susan)|rich(susan)))&
(?[X]:((curious(X)<~>~funny(X))))&
(?[X]:(~calm(X))) | humble(alice) | [] | null | 0 |
Everyone who is not tall or not humble is generous or not curious.
If lucy is not curious then alice is quiet or not rich and vice versa.
Everyone who is not old or calm is humble.
Everyone who is not brave or rich is not humble and vice versa.
Everyone who is either old or creative is both not tall and not generous.
If mary is not wise or creative then someone is not creative or patient and vice versa.
Everyone who is both not kind and happy is happy or quiet.
Everyone who is either not old or brave is either humble or tall and vice versa.
Everyone who is either creative or tall is quiet or calm and vice versa.
Everyone who is either not tall or not curious is wise or not happy and vice versa.
Everyone who is strong is not generous and vice versa.
If john is either not tall or not strong then someone is patient or tall and vice versa.
If someone is both happy and not happy then mary is not happy and vice versa.
If someone is either not rich or humble then someone is either old or funny and vice versa.
Everyone who is not funny or creative is funny.
Everyone who is not calm or kind is quiet and vice versa.
Mary is creative.
Someone is not happy.
Susan is not old.
Someone is not kind or not creative.
Someone is either not kind or not tall.
Alice is patient or strong.
Susan is either not kind or not wise.
Alice is either not curious or not creative. | Susan is not creative. | entailment | (![X]:((~tall(X)|~humble(X))=>(generous(X)|~curious(X))))&
((~curious(lucy))<=>((quiet(alice)|~rich(alice))))&
(![X]:((~old(X)|calm(X))=>humble(X)))&
(![X]:((~brave(X)|rich(X))<=>~humble(X)))&
(![X]:((old(X)<~>creative(X))=>(~tall(X)&~generous(X))))&
(((~wise(mary)|creative(mary)))<=>(?[X]:((~creative(X)|patient(X)))))&
(![X]:((~kind(X)&happy(X))=>(happy(X)|quiet(X))))&
(![X]:((~old(X)<~>brave(X))<=>(humble(X)<~>tall(X))))&
(![X]:((creative(X)<~>tall(X))<=>(quiet(X)|calm(X))))&
(![X]:((~tall(X)<~>~curious(X))<=>(wise(X)|~happy(X))))&
(![X]:(strong(X)<=>~generous(X)))&
(((~tall(john)<~>~strong(john)))<=>(?[X]:((patient(X)|tall(X)))))&
((?[X]:((happy(X)&~happy(X))))<=>(~happy(mary)))&
((?[X]:((~rich(X)<~>humble(X))))<=>(?[X]:((old(X)<~>funny(X)))))&
(![X]:((~funny(X)|creative(X))=>funny(X)))&
(![X]:((~calm(X)|kind(X))<=>quiet(X)))&
(creative(mary))&
(?[X]:(~happy(X)))&
(~old(susan))&
(?[X]:((~kind(X)|~creative(X))))&
(?[X]:((~kind(X)<~>~tall(X))))&
((patient(alice)|strong(alice)))&
((~kind(susan)<~>~wise(susan)))&
((~curious(alice)<~>~creative(alice))) | ~creative(susan) | [
"p2",
"p3",
"p4",
"p7",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2084691023153480921929
% SZS output start Proof for 2084691023153480921929
3. ! [X0] : ((calm(X0) | ~old(X0)) => humble(X0)) [input p2]
4. ! [X0] : ((rich(X0) | ~brave(X0)) <=> ~humble(X0)) [input p3]
5. ! [X0] : ((old(X0) <~> creative(X0)) => (~generous(X0) & ~tall(X0))) [input p4]
8. ! [X0] : ((~old(X0) <~> brave(X0)) <=> (humble(X0) <~> tall(X0))) [input p7]
19. ~old(susan) [input p18]
25. creative(susan) [input hypothesis]
29. ! [X0] : (humble(X0) | (~calm(X0) & old(X0))) [ennf transformation 3]
30. ! [X0] : ((~generous(X0) & ~tall(X0)) | (old(X0) <=> creative(X0))) [ennf transformation 5]
36. ! [X0] : (((rich(X0) | ~brave(X0)) | humble(X0)) & (~humble(X0) | (~rich(X0) & brave(X0)))) [nnf transformation 4]
37. ! [X0] : ((rich(X0) | ~brave(X0) | humble(X0)) & (~humble(X0) | (~rich(X0) & brave(X0)))) [flattening 36]
38. ! [X0] : ((~generous(X0) & ~tall(X0)) | ((old(X0) | ~creative(X0)) & (creative(X0) | ~old(X0)))) [nnf transformation 30]
44. ! [X0] : ((((~brave(X0) | old(X0)) & (brave(X0) | ~old(X0))) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) & (((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | ((~old(X0) | ~brave(X0)) & (brave(X0) | old(X0))))) [nnf transformation 8]
79. old(X0) | humble(X0) [cnf transformation 29]
81. ~humble(X0) | brave(X0) [cnf transformation 37]
85. ~creative(X0) | old(X0) | ~tall(X0) [cnf transformation 38]
99. ~brave(X0) | old(X0) | tall(X0) | ~humble(X0) [cnf transformation 44]
139. ~old(susan) [cnf transformation 19]
148. creative(susan) [cnf transformation 25]
191. ~brave(X0) | old(X0) | tall(X0) [subsumption resolution 99,79]
318. humble(susan) [resolution 79,139]
319. brave(susan) [resolution 81,318]
353. old(susan) | ~tall(susan) [resolution 85,148]
355. ~tall(susan) [subsumption resolution 353,139]
427. old(susan) | tall(susan) [resolution 191,319]
429. tall(susan) [subsumption resolution 427,139]
430. $false [subsumption resolution 429,355]
% SZS output end Proof for 2084691023153480921929
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or strong is either not kind or happy and vice versa. If susan is curious or tall then someone is creative or strong and vice versa. If john is both not calm and not strong then susan is not curious. Everyone who is both rich and creative is not wise. Everyone who is not generous or not kind is either wise or not strong and vice versa. Everyone who is tall or not strong is not kind or not strong. Everyone who is either not tall or strong is not creative or not brave and vice versa. Everyone who is not humble is both tall and calm and vice versa. If someone is brave or not old then someone is either wise or not brave and vice versa. Everyone who is either not patient or not brave is both not kind and not rich and vice versa. Everyone who is not wise or creative is both not calm and strong. If someone is either patient or funny then john is quiet or not generous. Everyone who is both not kind and generous is not strong or not old and vice versa. Everyone who is both curious and not kind is either not wise or not happy and vice versa. Everyone who is both generous and not curious is either brave or patient and vice versa. If fred is not tall then fred is not rich or old and vice versa. Someone is quiet. Someone is either not old or not patient. Lucy is both old and not kind. Lucy is either not kind or not calm. Susan is either not generous or not tall. Someone is kind. Someone is generous or not brave. | Susan is tall. | entailment | (![X]:((wise(X)|strong(X))<=>(~kind(X)<~>happy(X))))&
(((curious(susan)|tall(susan)))<=>(?[X]:((creative(X)|strong(X)))))&
(((~calm(john)&~strong(john)))=>(~curious(susan)))&
(![X]:((rich(X)&creative(X))=>~wise(X)))&
(![X]:((~generous(X)|~kind(X))<=>(wise(X)<~>~strong(X))))&
(![X]:((tall(X)|~strong(X))=>(~kind(X)|~strong(X))))&
(![X]:((~tall(X)<~>strong(X))<=>(~creative(X)|~brave(X))))&
(![X]:(~humble(X)<=>(tall(X)&calm(X))))&
((?[X]:((brave(X)|~old(X))))<=>(?[X]:((wise(X)<~>~brave(X)))))&
(![X]:((~patient(X)<~>~brave(X))<=>(~kind(X)&~rich(X))))&
(![X]:((~wise(X)|creative(X))=>(~calm(X)&strong(X))))&
((?[X]:((patient(X)<~>funny(X))))=>((quiet(john)|~generous(john))))&
(![X]:((~kind(X)&generous(X))<=>(~strong(X)|~old(X))))&
(![X]:((curious(X)&~kind(X))<=>(~wise(X)<~>~happy(X))))&
(![X]:((generous(X)&~curious(X))<=>(brave(X)<~>patient(X))))&
((~tall(fred))<=>((~rich(fred)|old(fred))))&
(?[X]:(quiet(X)))&
(?[X]:((~old(X)<~>~patient(X))))&
((old(lucy)&~kind(lucy)))&
((~kind(lucy)<~>~calm(lucy)))&
((~generous(susan)<~>~tall(susan)))&
(?[X]:(kind(X)))&
(?[X]:((generous(X)|~brave(X)))) | tall(susan) | [
"p0",
"p3",
"p4",
"p6",
"p9",
"p10",
"p12",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7695562945637819583730682
% SZS output start Proof for 7695562945637819583730682
1. ! [X0] : ((strong(X0) | wise(X0)) <=> (~kind(X0) <~> happy(X0))) [input p0]
4. ! [X0] : ((creative(X0) & rich(X0)) => ~wise(X0)) [input p3]
5. ! [X0] : ((~kind(X0) | ~generous(X0)) <=> (wise(X0) <~> ~strong(X0))) [input p4]
7. ! [X0] : ((~tall(X0) <~> strong(X0)) <=> (~brave(X0) | ~creative(X0))) [input p6]
10. ! [X0] : ((~patient(X0) <~> ~brave(X0)) <=> (~rich(X0) & ~kind(X0))) [input p9]
11. ! [X0] : ((creative(X0) | ~wise(X0)) => (strong(X0) & ~calm(X0))) [input p10]
13. ! [X0] : ((generous(X0) & ~kind(X0)) <=> (~old(X0) | ~strong(X0))) [input p12]
14. ! [X0] : ((~kind(X0) & curious(X0)) <=> (~wise(X0) <~> ~happy(X0))) [input p13]
15. ! [X0] : ((~curious(X0) & generous(X0)) <=> (brave(X0) <~> patient(X0))) [input p14]
21. ~generous(susan) <~> ~tall(susan) [input p20]
24. ~tall(susan) [input hypothesis]
30. ! [X0] : (~wise(X0) | (~creative(X0) | ~rich(X0))) [ennf transformation 4]
31. ! [X0] : (~wise(X0) | ~creative(X0) | ~rich(X0)) [flattening 30]
34. ! [X0] : ((strong(X0) & ~calm(X0)) | (~creative(X0) & wise(X0))) [ennf transformation 11]
35. ! [X0] : (((strong(X0) | wise(X0)) | ((~kind(X0) | ~happy(X0)) & (happy(X0) | kind(X0)))) & (((~happy(X0) | kind(X0)) & (happy(X0) | ~kind(X0))) | (~strong(X0) & ~wise(X0)))) [nnf transformation 1]
36. ! [X0] : ((strong(X0) | wise(X0) | ((~kind(X0) | ~happy(X0)) & (happy(X0) | kind(X0)))) & (((~happy(X0) | kind(X0)) & (happy(X0) | ~kind(X0))) | (~strong(X0) & ~wise(X0)))) [flattening 35]
42. ! [X0] : (((~kind(X0) | ~generous(X0)) | ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0)))) & (((strong(X0) | ~wise(X0)) & (~strong(X0) | wise(X0))) | (kind(X0) & generous(X0)))) [nnf transformation 5]
43. ! [X0] : ((~kind(X0) | ~generous(X0) | ((wise(X0) | strong(X0)) & (~strong(X0) | ~wise(X0)))) & (((strong(X0) | ~wise(X0)) & (~strong(X0) | wise(X0))) | (kind(X0) & generous(X0)))) [flattening 42]
44. ! [X0] : ((((~strong(X0) | tall(X0)) & (strong(X0) | ~tall(X0))) | (brave(X0) & creative(X0))) & ((~brave(X0) | ~creative(X0)) | ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0))))) [nnf transformation 7]
45. ! [X0] : ((((~strong(X0) | tall(X0)) & (strong(X0) | ~tall(X0))) | (brave(X0) & creative(X0))) & (~brave(X0) | ~creative(X0) | ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0))))) [flattening 44]
51. ! [X0] : ((((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | (rich(X0) | kind(X0))) & ((~rich(X0) & ~kind(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0))))) [nnf transformation 10]
52. ! [X0] : ((((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | rich(X0) | kind(X0)) & ((~rich(X0) & ~kind(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0))))) [flattening 51]
53. ! [X0] : (((generous(X0) & ~kind(X0)) | (old(X0) & strong(X0))) & ((~old(X0) | ~strong(X0)) | (~generous(X0) | kind(X0)))) [nnf transformation 13]
54. ! [X0] : (((generous(X0) & ~kind(X0)) | (old(X0) & strong(X0))) & (~old(X0) | ~strong(X0) | ~generous(X0) | kind(X0))) [flattening 53]
55. ! [X0] : (((~kind(X0) & curious(X0)) | ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0)))) & (((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | (kind(X0) | ~curious(X0)))) [nnf transformation 14]
56. ! [X0] : (((~kind(X0) & curious(X0)) | ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0)))) & (((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | kind(X0) | ~curious(X0))) [flattening 55]
57. ! [X0] : (((~curious(X0) & generous(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) & (((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | (curious(X0) | ~generous(X0)))) [nnf transformation 15]
58. ! [X0] : (((~curious(X0) & generous(X0)) | ((brave(X0) | ~patient(X0)) & (patient(X0) | ~brave(X0)))) & (((~patient(X0) | ~brave(X0)) & (patient(X0) | brave(X0))) | curious(X0) | ~generous(X0))) [flattening 57]
65. (tall(susan) | generous(susan)) & (~tall(susan) | ~generous(susan)) [nnf transformation 21]
71. ~kind(X0) | happy(X0) | ~strong(X0) [cnf transformation 36]
73. ~happy(X0) | kind(X0) | ~strong(X0) [cnf transformation 36]
81. ~rich(X0) | ~creative(X0) | ~wise(X0) [cnf transformation 31]
83. ~strong(X0) | wise(X0) | kind(X0) [cnf transformation 43]
85. ~wise(X0) | strong(X0) | kind(X0) [cnf transformation 43]
86. ~generous(X0) | ~kind(X0) | ~strong(X0) | ~wise(X0) [cnf transformation 43]
94. ~strong(X0) | tall(X0) | creative(X0) [cnf transformation 45]
95. ~strong(X0) | tall(X0) | brave(X0) [cnf transformation 45]
106. ~patient(X0) | ~brave(X0) | rich(X0) | kind(X0) [cnf transformation 52]
110. strong(X0) | wise(X0) [cnf transformation 34]
113. ~kind(X0) | strong(X0) [cnf transformation 54]
120. ~wise(X0) | curious(X0) | happy(X0) [cnf transformation 56]
121. ~happy(X0) | ~kind(X0) | wise(X0) [cnf transformation 56]
127. ~brave(X0) | patient(X0) | ~curious(X0) [cnf transformation 58]
139. tall(susan) | generous(susan) [cnf transformation 65]
142. ~tall(susan) [cnf transformation 24]
147. 2 <=> curious(susan) [avatar definition]
149. curious(susan) <- (2) [avatar component clause 147]
151. 3 <=> tall(susan) [avatar definition]
152. ~tall(susan) <- (~3) [avatar component clause 151]
239. 22 <=> generous(susan) [avatar definition]
241. generous(susan) <- (22) [avatar component clause 239]
242. 22 | 3 [avatar split clause 139,151,239]
253. ~3 [avatar split clause 142,151]
282. wise(X0) | kind(X0) | wise(X0) [resolution 83,110]
285. kind(X0) | wise(X0) [duplicate literal removal 282]
456. ~kind(susan) | ~strong(susan) | ~wise(susan) <- (22) [resolution 86,241]
460. ~kind(susan) | ~wise(susan) <- (22) [subsumption resolution 456,113]
462. 43 <=> wise(susan) [avatar definition]
463. wise(susan) <- (43) [avatar component clause 462]
464. ~wise(susan) <- (~43) [avatar component clause 462]
466. 44 <=> kind(susan) [avatar definition]
467. kind(susan) <- (44) [avatar component clause 466]
468. ~kind(susan) <- (~44) [avatar component clause 466]
469. ~43 | ~44 | ~22 [avatar split clause 460,239,466,462]
769. 70 <=> brave(susan) [avatar definition]
771. brave(susan) <- (70) [avatar component clause 769]
773. 71 <=> rich(susan) [avatar definition]
775. rich(susan) <- (71) [avatar component clause 773]
803. happy(susan) | ~strong(susan) <- (44) [resolution 467,71]
806. strong(susan) <- (44) [resolution 467,113]
808. 77 <=> strong(susan) [avatar definition]
809. strong(susan) <- (77) [avatar component clause 808]
812. 78 <=> happy(susan) [avatar definition]
813. ~happy(susan) <- (~78) [avatar component clause 812]
814. happy(susan) <- (78) [avatar component clause 812]
815. ~77 | 78 | ~44 [avatar split clause 803,466,812,808]
816. 77 | ~44 [avatar split clause 806,466,808]
861. tall(susan) | brave(susan) <- (77) [resolution 809,95]
865. brave(susan) <- (~3, 77) [subsumption resolution 861,152]
866. 70 | 3 | ~77 [avatar split clause 865,808,151,769]
870. patient(susan) | ~curious(susan) <- (70) [resolution 771,127]
874. patient(susan) <- (2, 70) [subsumption resolution 870,149]
876. ~kind(susan) | wise(susan) <- (78) [resolution 814,121]
878. kind(susan) | ~strong(susan) <- (78) [resolution 814,73]
885. ~kind(susan) <- (~43, 78) [subsumption resolution 876,464]
886. ~44 | 43 | ~78 [avatar split clause 885,812,462,466]
887. ~strong(susan) <- (~44, 78) [subsumption resolution 878,468]
888. ~77 | 44 | ~78 [avatar split clause 887,812,466,808]
889. wise(susan) <- (~44) [resolution 468,285]
892. 43 | 44 [avatar split clause 889,466,462]
893. curious(susan) | happy(susan) <- (43) [resolution 463,120]
894. strong(susan) | kind(susan) <- (43) [resolution 463,85]
896. strong(susan) <- (43, ~44) [subsumption resolution 894,468]
897. 77 | ~43 | 44 [avatar split clause 896,466,462,808]
899. tall(susan) | creative(susan) <- (77) [resolution 809,94]
902. creative(susan) <- (~3, 77) [subsumption resolution 899,152]
991. ~brave(susan) | rich(susan) | kind(susan) <- (2, 70) [resolution 874,106]
996. rich(susan) | kind(susan) <- (2, 70) [subsumption resolution 991,771]
997. rich(susan) <- (2, ~44, 70) [subsumption resolution 996,468]
998. 71 | ~2 | 44 | ~70 [avatar split clause 997,769,466,147,773]
1001. ~creative(susan) | ~wise(susan) <- (71) [resolution 775,81]
1002. ~wise(susan) <- (~3, 71, 77) [subsumption resolution 1001,902]
1003. $false <- (~3, 43, 71, 77) [subsumption resolution 1002,463]
1004. 3 | ~43 | ~71 | ~77 [avatar contradiction clause 1003]
1005. curious(susan) <- (43, ~78) [subsumption resolution 893,813]
1006. 2 | ~43 | 78 [avatar split clause 1005,812,462,147]
1013. $false [avatar sat refutation 242,253,469,815,816,866,886,888,892,897,998,1004,1006]
% SZS output end Proof for 7695562945637819583730682
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.043 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich or not curious then someone is both curious and kind. Everyone who is quiet or not happy is rich and vice versa. If john is both not funny and not creative then someone is not curious or generous. If someone is quiet or not rich then someone is both not curious and not patient and vice versa. Everyone who is either not patient or not old is wise or not happy and vice versa. Everyone who is calm or quiet is both not kind and happy. If someone is both funny and humble then paul is not funny and vice versa. Everyone who is either not calm or funny is kind and vice versa. If susan is calm or old then alice is either not quiet or not creative and vice versa. Everyone who is quiet or not generous is calm or humble and vice versa. Everyone who is calm is both tall and not humble. If john is either tall or kind then someone is either not old or not calm and vice versa. Everyone who is happy is calm and vice versa. Everyone who is not patient or not calm is both not humble and old and vice versa. Everyone who is patient is not quiet. Someone is not wise or rich. Paul is both brave and not creative. John is not wise or brave. Someone is not old. Someone is either wise or happy. Mary is either not rich or old. Someone is happy. | Paul is not old. | contradiction | ((?[X]:((~rich(X)|~curious(X))))=>(?[X]:((curious(X)&kind(X)))))&
(![X]:((quiet(X)|~happy(X))<=>rich(X)))&
(((~funny(john)&~creative(john)))=>(?[X]:((~curious(X)|generous(X)))))&
((?[X]:((quiet(X)|~rich(X))))<=>(?[X]:((~curious(X)&~patient(X)))))&
(![X]:((~patient(X)<~>~old(X))<=>(wise(X)|~happy(X))))&
(![X]:((calm(X)|quiet(X))=>(~kind(X)&happy(X))))&
((?[X]:((funny(X)&humble(X))))<=>(~funny(paul)))&
(![X]:((~calm(X)<~>funny(X))<=>kind(X)))&
(((calm(susan)|old(susan)))<=>((~quiet(alice)<~>~creative(alice))))&
(![X]:((quiet(X)|~generous(X))<=>(calm(X)|humble(X))))&
(![X]:(calm(X)=>(tall(X)&~humble(X))))&
(((tall(john)<~>kind(john)))<=>(?[X]:((~old(X)<~>~calm(X)))))&
(![X]:(happy(X)<=>calm(X)))&
(![X]:((~patient(X)|~calm(X))<=>(~humble(X)&old(X))))&
(![X]:(patient(X)=>~quiet(X)))&
(?[X]:((~wise(X)|rich(X))))&
((brave(paul)&~creative(paul)))&
((~wise(john)|brave(john)))&
(?[X]:(~old(X)))&
(?[X]:((wise(X)<~>happy(X))))&
((~rich(mary)<~>old(mary)))&
(?[X]:(happy(X))) | ~old(paul) | [
"p5",
"p6",
"p7",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 903117177451583844332837
% SZS output start Proof for 903117177451583844332837
6. ! [X0] : ((quiet(X0) | calm(X0)) => (happy(X0) & ~kind(X0))) [input p5]
7. ? [X0] : (humble(X0) & funny(X0)) <=> ~funny(paul) [input p6]
8. ! [X0] : ((~calm(X0) <~> funny(X0)) <=> kind(X0)) [input p7]
11. ! [X0] : (calm(X0) => (~humble(X0) & tall(X0))) [input p10]
14. ! [X0] : ((~calm(X0) | ~patient(X0)) <=> (old(X0) & ~humble(X0))) [input p13]
23. ~old(paul) [input hypothesis]
31. ! [X0] : ((happy(X0) & ~kind(X0)) | (~quiet(X0) & ~calm(X0))) [ennf transformation 6]
32. ! [X0] : ((~humble(X0) & tall(X0)) | ~calm(X0)) [ennf transformation 11]
48. (? [X0] : (humble(X0) & funny(X0)) | funny(paul)) & (~funny(paul) | ! [X0] : (~humble(X0) | ~funny(X0))) [nnf transformation 7]
49. (? [X0] : (humble(X0) & funny(X0)) | funny(paul)) & (~funny(paul) | ! [X1] : (~humble(X1) | ~funny(X1))) [rectify 48]
50. ? [X0] : (humble(X0) & funny(X0)) => (humble(sK4) & funny(sK4)) [choice axiom]
51. ((humble(sK4) & funny(sK4)) | funny(paul)) & (~funny(paul) | ! [X1] : (~humble(X1) | ~funny(X1))) [skolemisation 49,50]
52. ! [X0] : ((((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | ~kind(X0)) & (kind(X0) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0))))) [nnf transformation 8]
62. ! [X0] : (((~calm(X0) | ~patient(X0)) | (~old(X0) | humble(X0))) & ((old(X0) & ~humble(X0)) | (calm(X0) & patient(X0)))) [nnf transformation 14]
63. ! [X0] : ((~calm(X0) | ~patient(X0) | ~old(X0) | humble(X0)) & ((old(X0) & ~humble(X0)) | (calm(X0) & patient(X0)))) [flattening 62]
93. ~calm(X0) | ~kind(X0) [cnf transformation 31]
99. humble(sK4) | funny(paul) [cnf transformation 51]
101. kind(X0) | ~calm(X0) | ~funny(X0) [cnf transformation 52]
103. ~funny(X0) | calm(X0) | ~kind(X0) [cnf transformation 52]
115. ~humble(X0) | ~calm(X0) [cnf transformation 32]
127. ~humble(X0) | calm(X0) [cnf transformation 63]
129. calm(X0) | old(X0) [cnf transformation 63]
140. ~old(paul) [cnf transformation 23]
204. 15 <=> funny(paul) [avatar definition]
206. funny(paul) <- (15) [avatar component clause 204]
208. 16 <=> humble(sK4) [avatar definition]
210. humble(sK4) <- (16) [avatar component clause 208]
211. 15 | 16 [avatar split clause 99,208,204]
221. ~funny(X0) | ~kind(X0) [subsumption resolution 103,93]
222. ~calm(X0) | ~funny(X0) [subsumption resolution 101,221]
276. ~humble(X0) [subsumption resolution 127,115]
312. $false <- (16) [subsumption resolution 210,276]
313. ~16 [avatar contradiction clause 312]
347. ~funny(X0) | old(X0) [resolution 222,129]
510. old(paul) <- (15) [resolution 347,206]
512. $false <- (15) [subsumption resolution 510,140]
513. ~15 [avatar contradiction clause 512]
514. $false [avatar sat refutation 211,313,513]
% SZS output end Proof for 903117177451583844332837
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not tall or not humble then someone is either not tall or not calm and vice versa.
If mary is both not old and not patient then alice is both not brave and funny and vice versa.
If john is not creative or not patient then lucy is either not wise or humble and vice versa.
Everyone who is not rich is not brave and vice versa.
Everyone who is rich is both strong and old and vice versa.
Everyone who is brave or calm is wise or not humble and vice versa.
Everyone who is both quiet and not tall is curious or not patient.
Everyone who is happy or not brave is both not funny and funny.
If alice is not quiet then john is either quiet or not calm and vice versa.
Everyone who is either calm or generous is not humble.
If alice is both patient and not curious then someone is both not brave and strong.
Everyone who is generous or not quiet is both not kind and not calm.
If someone is quiet or strong then alice is happy or not generous and vice versa.
If john is not strong then someone is either not kind or happy and vice versa.
Everyone who is either quiet or not brave is either quiet or not creative and vice versa.
If mary is not calm then fred is either kind or not tall.
Fred is quiet or generous.
Someone is creative or strong.
Fred is not tall or happy.
Someone is not old or strong.
Someone is brave or not generous.
Someone is humble or creative.
Someone is brave or generous.
Someone is either not creative or wise. | Mary is not quiet. | contradiction | ((?[X]:((~tall(X)|~humble(X))))<=>(?[X]:((~tall(X)<~>~calm(X)))))&
(((~old(mary)&~patient(mary)))<=>((~brave(alice)&funny(alice))))&
(((~creative(john)|~patient(john)))<=>((~wise(lucy)<~>humble(lucy))))&
(![X]:(~rich(X)<=>~brave(X)))&
(![X]:(rich(X)<=>(strong(X)&old(X))))&
(![X]:((brave(X)|calm(X))<=>(wise(X)|~humble(X))))&
(![X]:((quiet(X)&~tall(X))=>(curious(X)|~patient(X))))&
(![X]:((happy(X)|~brave(X))=>(~funny(X)&funny(X))))&
((~quiet(alice))<=>((quiet(john)<~>~calm(john))))&
(![X]:((calm(X)<~>generous(X))=>~humble(X)))&
(((patient(alice)&~curious(alice)))=>(?[X]:((~brave(X)&strong(X)))))&
(![X]:((generous(X)|~quiet(X))=>(~kind(X)&~calm(X))))&
((?[X]:((quiet(X)|strong(X))))<=>((happy(alice)|~generous(alice))))&
((~strong(john))<=>(?[X]:((~kind(X)<~>happy(X)))))&
(![X]:((quiet(X)<~>~brave(X))<=>(quiet(X)<~>~creative(X))))&
((~calm(mary))=>((kind(fred)<~>~tall(fred))))&
((quiet(fred)|generous(fred)))&
(?[X]:((creative(X)|strong(X))))&
((~tall(fred)|happy(fred)))&
(?[X]:((~old(X)|strong(X))))&
(?[X]:((brave(X)|~generous(X))))&
(?[X]:((humble(X)|creative(X))))&
(?[X]:((brave(X)|generous(X))))&
(?[X]:((~creative(X)<~>wise(X)))) | ~quiet(mary) | [
"p3",
"p4",
"p7",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4472852837685255943485312
% SZS output start Proof for 4472852837685255943485312
4. ! [X0] : (~rich(X0) <=> ~brave(X0)) [input p3]
5. ! [X0] : (rich(X0) <=> (old(X0) & strong(X0))) [input p4]
8. ! [X0] : ((~brave(X0) | happy(X0)) => (funny(X0) & ~funny(X0))) [input p7]
12. ! [X0] : ((~quiet(X0) | generous(X0)) => (~calm(X0) & ~kind(X0))) [input p11]
14. ~strong(john) <=> ? [X0] : (~kind(X0) <~> happy(X0)) [input p13]
25. ~quiet(mary) [input hypothesis]
29. ! [X0] : ((funny(X0) & ~funny(X0)) | (brave(X0) & ~happy(X0))) [ennf transformation 8]
31. ! [X0] : ((~calm(X0) & ~kind(X0)) | (quiet(X0) & ~generous(X0))) [ennf transformation 12]
42. ! [X0] : ((~rich(X0) | brave(X0)) & (~brave(X0) | rich(X0))) [nnf transformation 4]
43. ! [X0] : ((rich(X0) | (~old(X0) | ~strong(X0))) & ((old(X0) & strong(X0)) | ~rich(X0))) [nnf transformation 5]
44. ! [X0] : ((rich(X0) | ~old(X0) | ~strong(X0)) & ((old(X0) & strong(X0)) | ~rich(X0))) [flattening 43]
54. (~strong(john) | ! [X0] : ((~kind(X0) | ~happy(X0)) & (happy(X0) | kind(X0)))) & (? [X0] : ((~happy(X0) | kind(X0)) & (happy(X0) | ~kind(X0))) | strong(john)) [nnf transformation 14]
55. (~strong(john) | ! [X0] : ((~kind(X0) | ~happy(X0)) & (happy(X0) | kind(X0)))) & (? [X1] : ((~happy(X1) | kind(X1)) & (happy(X1) | ~kind(X1))) | strong(john)) [rectify 54]
56. ? [X1] : ((~happy(X1) | kind(X1)) & (happy(X1) | ~kind(X1))) => ((~happy(sK3) | kind(sK3)) & (happy(sK3) | ~kind(sK3))) [choice axiom]
57. (~strong(john) | ! [X0] : ((~kind(X0) | ~happy(X0)) & (happy(X0) | kind(X0)))) & (((~happy(sK3) | kind(sK3)) & (happy(sK3) | ~kind(sK3))) | strong(john)) [skolemisation 55,56]
89. ~brave(X0) | rich(X0) [cnf transformation 42]
91. ~rich(X0) | strong(X0) [cnf transformation 44]
98. ~funny(X0) | ~happy(X0) [cnf transformation 29]
99. ~funny(X0) | brave(X0) [cnf transformation 29]
100. ~happy(X0) | funny(X0) [cnf transformation 29]
101. funny(X0) | brave(X0) [cnf transformation 29]
109. ~kind(X0) | quiet(X0) [cnf transformation 31]
118. ~strong(john) | happy(X0) | kind(X0) [cnf transformation 57]
139. ~quiet(mary) [cnf transformation 25]
220. brave(X0) [subsumption resolution 99,101]
221. ~happy(X0) [subsumption resolution 98,100]
261. ~strong(john) | kind(X0) [subsumption resolution 118,221]
263. 25 <=> ! [X0] : kind(X0) [avatar definition]
264. kind(X0) <- (25) [avatar component clause 263]
266. 26 <=> strong(john) [avatar definition]
268. ~strong(john) <- (~26) [avatar component clause 266]
269. 25 | ~26 [avatar split clause 261,266,263]
316. rich(X0) [resolution 89,220]
318. strong(X0) [resolution 91,316]
320. $false <- (~26) [resolution 318,268]
321. 26 [avatar contradiction clause 320]
331. quiet(X0) <- (25) [resolution 109,264]
332. $false <- (25) [resolution 331,139]
337. ~25 [avatar contradiction clause 332]
338. $false [avatar sat refutation 269,321,337]
% SZS output end Proof for 4472852837685255943485312
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not calm is kind. Everyone who is brave is either patient or calm. Everyone who is old or tall is generous or not quiet. If someone is old then fred is either not patient or kind. If fred is either not curious or generous then fred is curious or not happy. Everyone who is not brave is either not humble or not patient and vice versa. If susan is curious then someone is either not patient or creative and vice versa. Everyone who is brave is quiet. Everyone who is either not humble or happy is both not wise and not funny. Everyone who is not strong or tall is not rich or not funny. If someone is both not tall and rich then john is both brave and quiet. Everyone who is either happy or not old is either curious or quiet and vice versa. If alice is either not generous or rich then paul is generous. Everyone who is either not patient or not humble is both not calm and wise. Everyone who is both not quiet and not tall is both strong and kind. If lucy is either not patient or not creative then someone is either not generous or curious and vice versa. Someone is either not old or not funny. Paul is both not happy and rich. Susan is both curious and not patient. Alice is either not calm or strong. Someone is curious or not happy. Fred is not patient or tall. Alice is both not generous and not creative. | Alice is strong. | neutral | (![X]:((~humble(X)<~>~calm(X))=>kind(X)))&
(![X]:(brave(X)=>(patient(X)<~>calm(X))))&
(![X]:((old(X)|tall(X))=>(generous(X)|~quiet(X))))&
((?[X]:(old(X)))=>((~patient(fred)<~>kind(fred))))&
(((~curious(fred)<~>generous(fred)))=>((curious(fred)|~happy(fred))))&
(![X]:(~brave(X)<=>(~humble(X)<~>~patient(X))))&
((curious(susan))<=>(?[X]:((~patient(X)<~>creative(X)))))&
(![X]:(brave(X)=>quiet(X)))&
(![X]:((~humble(X)<~>happy(X))=>(~wise(X)&~funny(X))))&
(![X]:((~strong(X)|tall(X))=>(~rich(X)|~funny(X))))&
((?[X]:((~tall(X)&rich(X))))=>((brave(john)&quiet(john))))&
(![X]:((happy(X)<~>~old(X))<=>(curious(X)<~>quiet(X))))&
(((~generous(alice)<~>rich(alice)))=>(generous(paul)))&
(![X]:((~patient(X)<~>~humble(X))=>(~calm(X)&wise(X))))&
(![X]:((~quiet(X)&~tall(X))=>(strong(X)&kind(X))))&
(((~patient(lucy)<~>~creative(lucy)))<=>(?[X]:((~generous(X)<~>curious(X)))))&
(?[X]:((~old(X)<~>~funny(X))))&
((~happy(paul)&rich(paul)))&
((curious(susan)&~patient(susan)))&
((~calm(alice)<~>strong(alice)))&
(?[X]:((curious(X)|~happy(X))))&
((~patient(fred)|tall(fred)))&
((~generous(alice)&~creative(alice))) | strong(alice) | [] | null | 0 |
If susan is both quiet and not strong then someone is both happy and not humble and vice versa.
Everyone who is brave or not quiet is not funny and vice versa.
Everyone who is strong or curious is either not humble or brave and vice versa.
Everyone who is not happy is both not tall and wise.
If paul is not old or not funny then alice is quiet and vice versa.
Everyone who is both funny and strong is either funny or not tall.
If alice is both old and not kind then someone is both patient and not old.
Everyone who is wise or not patient is not strong and vice versa.
If someone is either not brave or brave then someone is both not patient and not old and vice versa.
Everyone who is either calm or humble is not rich or not brave and vice versa.
If susan is either not happy or funny then someone is not calm or humble and vice versa.
If someone is rich then mary is both not rich and strong and vice versa.
If someone is both tall and not funny then someone is either curious or not old.
Everyone who is both curious and not happy is not humble.
Everyone who is not patient or generous is not wise.
Everyone who is old or generous is not creative or humble.
John is rich.
Someone is both not brave and tall.
Mary is both not generous and not creative.
Someone is funny or not humble.
Someone is either not funny or calm.
Fred is either not brave or tall.
Fred is both brave and wise.
Someone is either not strong or not old. | Susan is strong. | contradiction | (((quiet(susan)&~strong(susan)))<=>(?[X]:((happy(X)&~humble(X)))))&
(![X]:((brave(X)|~quiet(X))<=>~funny(X)))&
(![X]:((strong(X)|curious(X))<=>(~humble(X)<~>brave(X))))&
(![X]:(~happy(X)=>(~tall(X)&wise(X))))&
(((~old(paul)|~funny(paul)))<=>(quiet(alice)))&
(![X]:((funny(X)&strong(X))=>(funny(X)<~>~tall(X))))&
(((old(alice)&~kind(alice)))=>(?[X]:((patient(X)&~old(X)))))&
(![X]:((wise(X)|~patient(X))<=>~strong(X)))&
((?[X]:((~brave(X)<~>brave(X))))<=>(?[X]:((~patient(X)&~old(X)))))&
(![X]:((calm(X)<~>humble(X))<=>(~rich(X)|~brave(X))))&
(((~happy(susan)<~>funny(susan)))<=>(?[X]:((~calm(X)|humble(X)))))&
((?[X]:(rich(X)))<=>((~rich(mary)&strong(mary))))&
((?[X]:((tall(X)&~funny(X))))=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:((curious(X)&~happy(X))=>~humble(X)))&
(![X]:((~patient(X)|generous(X))=>~wise(X)))&
(![X]:((old(X)|generous(X))=>(~creative(X)|humble(X))))&
(rich(john))&
(?[X]:((~brave(X)&tall(X))))&
((~generous(mary)&~creative(mary)))&
(?[X]:((funny(X)|~humble(X))))&
(?[X]:((~funny(X)<~>calm(X))))&
((~brave(fred)<~>tall(fred)))&
((brave(fred)&wise(fred)))&
(?[X]:((~strong(X)<~>~old(X)))) | strong(susan) | [
"p0",
"p1",
"p2",
"p3",
"p7",
"p10",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8547423576058314279122375
% SZS output start Proof for 8547423576058314279122375
1. (~strong(susan) & quiet(susan)) <=> ? [X0] : (~humble(X0) & happy(X0)) [input p0]
2. ! [X0] : ((~quiet(X0) | brave(X0)) <=> ~funny(X0)) [input p1]
3. ! [X0] : ((curious(X0) | strong(X0)) <=> (~humble(X0) <~> brave(X0))) [input p2]
4. ! [X0] : (~happy(X0) => (wise(X0) & ~tall(X0))) [input p3]
8. ! [X0] : ((~patient(X0) | wise(X0)) <=> ~strong(X0)) [input p7]
11. (~happy(susan) <~> funny(susan)) <=> ? [X0] : (humble(X0) | ~calm(X0)) [input p10]
18. ? [X0] : (tall(X0) & ~brave(X0)) [input p17]
25. strong(susan) [input hypothesis]
33. ! [X0] : ((wise(X0) & ~tall(X0)) | happy(X0)) [ennf transformation 4]
40. ((~strong(susan) & quiet(susan)) | ! [X0] : (humble(X0) | ~happy(X0))) & (? [X0] : (~humble(X0) & happy(X0)) | (strong(susan) | ~quiet(susan))) [nnf transformation 1]
41. ((~strong(susan) & quiet(susan)) | ! [X0] : (humble(X0) | ~happy(X0))) & (? [X0] : (~humble(X0) & happy(X0)) | strong(susan) | ~quiet(susan)) [flattening 40]
42. ((~strong(susan) & quiet(susan)) | ! [X0] : (humble(X0) | ~happy(X0))) & (? [X1] : (~humble(X1) & happy(X1)) | strong(susan) | ~quiet(susan)) [rectify 41]
43. ? [X1] : (~humble(X1) & happy(X1)) => (~humble(sK0) & happy(sK0)) [choice axiom]
44. ((~strong(susan) & quiet(susan)) | ! [X0] : (humble(X0) | ~happy(X0))) & ((~humble(sK0) & happy(sK0)) | strong(susan) | ~quiet(susan)) [skolemisation 42,43]
45. ! [X0] : (((~quiet(X0) | brave(X0)) | funny(X0)) & (~funny(X0) | (quiet(X0) & ~brave(X0)))) [nnf transformation 2]
46. ! [X0] : ((~quiet(X0) | brave(X0) | funny(X0)) & (~funny(X0) | (quiet(X0) & ~brave(X0)))) [flattening 45]
47. ! [X0] : (((curious(X0) | strong(X0)) | ((~humble(X0) | ~brave(X0)) & (brave(X0) | humble(X0)))) & (((~brave(X0) | humble(X0)) & (brave(X0) | ~humble(X0))) | (~curious(X0) & ~strong(X0)))) [nnf transformation 3]
48. ! [X0] : ((curious(X0) | strong(X0) | ((~humble(X0) | ~brave(X0)) & (brave(X0) | humble(X0)))) & (((~brave(X0) | humble(X0)) & (brave(X0) | ~humble(X0))) | (~curious(X0) & ~strong(X0)))) [flattening 47]
52. ! [X0] : (((~patient(X0) | wise(X0)) | strong(X0)) & (~strong(X0) | (patient(X0) & ~wise(X0)))) [nnf transformation 8]
53. ! [X0] : ((~patient(X0) | wise(X0) | strong(X0)) & (~strong(X0) | (patient(X0) & ~wise(X0)))) [flattening 52]
61. (((~funny(susan) | happy(susan)) & (funny(susan) | ~happy(susan))) | ! [X0] : (~humble(X0) & calm(X0))) & (? [X0] : (humble(X0) | ~calm(X0)) | ((~happy(susan) | ~funny(susan)) & (funny(susan) | happy(susan)))) [nnf transformation 11]
62. (((~funny(susan) | happy(susan)) & (funny(susan) | ~happy(susan))) | ! [X0] : (~humble(X0) & calm(X0))) & (? [X1] : (humble(X1) | ~calm(X1)) | ((~happy(susan) | ~funny(susan)) & (funny(susan) | happy(susan)))) [rectify 61]
63. ? [X1] : (humble(X1) | ~calm(X1)) => (humble(sK3) | ~calm(sK3)) [choice axiom]
64. (((~funny(susan) | happy(susan)) & (funny(susan) | ~happy(susan))) | ! [X0] : (~humble(X0) & calm(X0))) & ((humble(sK3) | ~calm(sK3)) | ((~happy(susan) | ~funny(susan)) & (funny(susan) | happy(susan)))) [skolemisation 62,63]
74. ? [X0] : (tall(X0) & ~brave(X0)) => (tall(sK6) & ~brave(sK6)) [choice axiom]
75. tall(sK6) & ~brave(sK6) [skolemisation 18,74]
88. ~strong(susan) | humble(X0) | ~happy(X0) [cnf transformation 44]
89. ~funny(X0) | ~brave(X0) [cnf transformation 46]
92. ~humble(X0) | brave(X0) | ~strong(X0) [cnf transformation 48]
98. ~tall(X0) | happy(X0) [cnf transformation 33]
99. wise(X0) | happy(X0) [cnf transformation 33]
105. ~wise(X0) | ~strong(X0) [cnf transformation 53]
123. funny(susan) | ~happy(susan) | ~humble(X0) [cnf transformation 64]
135. tall(sK6) [cnf transformation 75]
145. strong(susan) [cnf transformation 25]
152. 1 <=> ! [X0] : (humble(X0) | ~happy(X0)) [avatar definition]
153. ~happy(X0) | humble(X0) <- (1) [avatar component clause 152]
155. 2 <=> strong(susan) [avatar definition]
156. strong(susan) <- (2) [avatar component clause 155]
158. 1 | ~2 [avatar split clause 88,155,152]
208. 13 <=> ! [X0] : ~humble(X0) [avatar definition]
209. ~humble(X0) <- (13) [avatar component clause 208]
211. 14 <=> happy(susan) [avatar definition]
213. happy(susan) <- (14) [avatar component clause 211]
215. 15 <=> funny(susan) [avatar definition]
216. funny(susan) <- (15) [avatar component clause 215]
223. 13 | ~14 | 15 [avatar split clause 123,215,211,208]
306. 2 [avatar split clause 145,155]
307. happy(sK6) [resolution 98,135]
310. ~strong(X0) | happy(X0) [resolution 105,99]
316. humble(sK6) <- (1) [resolution 153,307]
374. $false <- (1, 13) [resolution 209,316]
377. ~1 | ~13 [avatar contradiction clause 374]
469. happy(susan) <- (2) [resolution 310,156]
475. 14 | ~2 [avatar split clause 469,155,211]
476. humble(susan) <- (1, 14) [resolution 213,153]
479. ~brave(susan) <- (15) [resolution 216,89]
483. brave(susan) | ~strong(susan) <- (1, 14) [resolution 476,92]
484. ~strong(susan) <- (1, 14, 15) [subsumption resolution 483,479]
485. $false <- (1, 2, 14, 15) [subsumption resolution 484,156]
486. ~1 | ~2 | ~14 | ~15 [avatar contradiction clause 485]
487. $false [avatar sat refutation 158,223,306,377,475,486]
% SZS output end Proof for 8547423576058314279122375
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both creative and not tall then paul is both not calm and calm and vice versa.
If someone is both humble and not wise then someone is not patient and vice versa.
Everyone who is not generous or not rich is both brave and not kind.
Everyone who is both rich and not wise is kind or not happy.
If alice is not curious then someone is not humble or not funny.
If someone is not funny or not creative then someone is brave or tall.
If john is both not creative and not tall then someone is not strong or happy.
Everyone who is funny or not funny is not kind.
Everyone who is both old and not creative is both curious and not generous and vice versa.
Everyone who is humble or strong is both happy and not humble.
If lucy is both not humble and not kind then someone is not generous or not quiet.
Everyone who is not humble or old is not brave or not patient and vice versa.
Everyone who is not calm is either generous or not creative.
Everyone who is either humble or not calm is not tall.
If fred is curious then someone is not rich or not generous.
Everyone who is not old is either not funny or rich and vice versa.
Someone is either curious or happy.
Someone is both happy and strong.
Someone is not kind.
Someone is either curious or rich.
Someone is not old or generous.
John is strong.
Fred is not strong. | Fred is not curious. | entailment | ((?[X]:((creative(X)&~tall(X))))<=>((~calm(paul)&calm(paul))))&
((?[X]:((humble(X)&~wise(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~generous(X)|~rich(X))=>(brave(X)&~kind(X))))&
(![X]:((rich(X)&~wise(X))=>(kind(X)|~happy(X))))&
((~curious(alice))=>(?[X]:((~humble(X)|~funny(X)))))&
((?[X]:((~funny(X)|~creative(X))))=>(?[X]:((brave(X)|tall(X)))))&
(((~creative(john)&~tall(john)))=>(?[X]:((~strong(X)|happy(X)))))&
(![X]:((funny(X)|~funny(X))=>~kind(X)))&
(![X]:((old(X)&~creative(X))<=>(curious(X)&~generous(X))))&
(![X]:((humble(X)|strong(X))=>(happy(X)&~humble(X))))&
(((~humble(lucy)&~kind(lucy)))=>(?[X]:((~generous(X)|~quiet(X)))))&
(![X]:((~humble(X)|old(X))<=>(~brave(X)|~patient(X))))&
(![X]:(~calm(X)=>(generous(X)<~>~creative(X))))&
(![X]:((humble(X)<~>~calm(X))=>~tall(X)))&
((curious(fred))=>(?[X]:((~rich(X)|~generous(X)))))&
(![X]:(~old(X)<=>(~funny(X)<~>rich(X))))&
(?[X]:((curious(X)<~>happy(X))))&
(?[X]:((happy(X)&strong(X))))&
(?[X]:(~kind(X)))&
(?[X]:((curious(X)<~>rich(X))))&
(?[X]:((~old(X)|generous(X))))&
(strong(john))&
(~strong(fred)) | ~curious(fred) | [
"p1",
"p2",
"p9",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8541742352077939754256449
% SZS output start Proof for 8541742352077939754256449
2. ? [X0] : (~wise(X0) & humble(X0)) <=> ? [X0] : ~patient(X0) [input p1]
3. ! [X0] : ((~rich(X0) | ~generous(X0)) => (~kind(X0) & brave(X0))) [input p2]
10. ! [X0] : ((strong(X0) | humble(X0)) => (~humble(X0) & happy(X0))) [input p9]
12. ! [X0] : ((old(X0) | ~humble(X0)) <=> (~patient(X0) | ~brave(X0))) [input p11]
15. curious(fred) => ? [X0] : (~generous(X0) | ~rich(X0)) [input p14]
24. curious(fred) [input hypothesis]
25. ? [X0] : (~wise(X0) & humble(X0)) <=> ? [X1] : ~patient(X1) [rectify 2]
28. ! [X0] : ((~kind(X0) & brave(X0)) | (rich(X0) & generous(X0))) [ennf transformation 3]
36. ! [X0] : ((~humble(X0) & happy(X0)) | (~strong(X0) & ~humble(X0))) [ennf transformation 10]
39. ? [X0] : (~generous(X0) | ~rich(X0)) | ~curious(fred) [ennf transformation 15]
45. (? [X0] : (~wise(X0) & humble(X0)) | ! [X1] : patient(X1)) & (? [X1] : ~patient(X1) | ! [X0] : (wise(X0) | ~humble(X0))) [nnf transformation 25]
46. (? [X0] : (~wise(X0) & humble(X0)) | ! [X1] : patient(X1)) & (? [X2] : ~patient(X2) | ! [X3] : (wise(X3) | ~humble(X3))) [rectify 45]
47. ? [X0] : (~wise(X0) & humble(X0)) => (~wise(sK1) & humble(sK1)) [choice axiom]
48. ? [X2] : ~patient(X2) => ~patient(sK2) [choice axiom]
49. ((~wise(sK1) & humble(sK1)) | ! [X1] : patient(X1)) & (~patient(sK2) | ! [X3] : (wise(X3) | ~humble(X3))) [skolemisation 46,48,47]
59. ! [X0] : (((old(X0) | ~humble(X0)) | (patient(X0) & brave(X0))) & ((~patient(X0) | ~brave(X0)) | (~old(X0) & humble(X0)))) [nnf transformation 12]
60. ! [X0] : ((old(X0) | ~humble(X0) | (patient(X0) & brave(X0))) & (~patient(X0) | ~brave(X0) | (~old(X0) & humble(X0)))) [flattening 59]
63. ? [X0] : (~generous(X0) | ~rich(X0)) => (~generous(sK6) | ~rich(sK6)) [choice axiom]
64. (~generous(sK6) | ~rich(sK6)) | ~curious(fred) [skolemisation 39,63]
83. humble(sK1) | patient(X1) [cnf transformation 49]
85. brave(X0) | generous(X0) [cnf transformation 28]
86. brave(X0) | rich(X0) [cnf transformation 28]
102. ~humble(X0) | ~humble(X0) [cnf transformation 36]
104. ~patient(X0) | ~brave(X0) | humble(X0) [cnf transformation 60]
112. ~generous(sK6) | ~rich(sK6) | ~curious(fred) [cnf transformation 64]
127. curious(fred) [cnf transformation 24]
128. ~humble(X0) [duplicate literal removal 102]
139. 3 <=> ! [X1] : patient(X1) [avatar definition]
140. patient(X1) <- (3) [avatar component clause 139]
147. 5 <=> humble(sK1) [avatar definition]
149. humble(sK1) <- (5) [avatar component clause 147]
150. 3 | 5 [avatar split clause 83,147,139]
206. ~brave(X0) | ~patient(X0) [subsumption resolution 104,128]
209. 19 <=> curious(fred) [avatar definition]
213. 20 <=> rich(sK6) [avatar definition]
215. ~rich(sK6) <- (~20) [avatar component clause 213]
217. 21 <=> generous(sK6) [avatar definition]
219. ~generous(sK6) <- (~21) [avatar component clause 217]
220. ~19 | ~20 | ~21 [avatar split clause 112,217,213,209]
250. 19 [avatar split clause 127,209]
251. $false <- (5) [subsumption resolution 149,128]
252. ~5 [avatar contradiction clause 251]
259. ~patient(X0) | rich(X0) [resolution 206,86]
260. ~patient(X1) | generous(X1) [resolution 206,85]
261. rich(X0) <- (3) [subsumption resolution 259,140]
262. generous(X1) <- (3) [subsumption resolution 260,140]
266. $false <- (3, ~21) [resolution 262,219]
267. ~3 | 21 [avatar contradiction clause 266]
268. $false <- (3, ~20) [subsumption resolution 215,261]
269. ~3 | 20 [avatar contradiction clause 268]
270. $false [avatar sat refutation 150,220,250,252,267,269]
% SZS output end Proof for 8541742352077939754256449
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and not brave is humble or not curious and vice versa.
If someone is not brave or wise then mary is both not tall and creative.
Everyone who is wise or humble is not strong.
Everyone who is either strong or rich is both not rich and not curious and vice versa.
If mary is both not calm and creative then susan is brave or curious and vice versa.
Everyone who is either not tall or generous is not generous or creative.
Everyone who is either not humble or funny is strong.
Everyone who is either brave or generous is both brave and quiet.
Everyone who is funny is either humble or tall.
If mary is either not kind or not creative then john is both not creative and not generous and vice versa.
Everyone who is not wise is either wise or generous and vice versa.
Everyone who is both curious and happy is strong or not brave and vice versa.
If someone is both not funny and curious then lucy is both not creative and not happy and vice versa.
Everyone who is not curious or brave is not patient or not generous.
If mary is rich then someone is not patient or happy and vice versa.
Someone is creative or kind.
Someone is not old.
Fred is either not wise or not old.
Susan is not patient or funny. | Fred is rich. | neutral | (![X]:((calm(X)&~brave(X))<=>(humble(X)|~curious(X))))&
((?[X]:((~brave(X)|wise(X))))=>((~tall(mary)&creative(mary))))&
(![X]:((wise(X)|humble(X))=>~strong(X)))&
(![X]:((strong(X)<~>rich(X))<=>(~rich(X)&~curious(X))))&
(((~calm(mary)&creative(mary)))<=>((brave(susan)|curious(susan))))&
(![X]:((~tall(X)<~>generous(X))=>(~generous(X)|creative(X))))&
(![X]:((~humble(X)<~>funny(X))=>strong(X)))&
(![X]:((brave(X)<~>generous(X))=>(brave(X)&quiet(X))))&
(![X]:(funny(X)=>(humble(X)<~>tall(X))))&
(((~kind(mary)<~>~creative(mary)))<=>((~creative(john)&~generous(john))))&
(![X]:(~wise(X)<=>(wise(X)<~>generous(X))))&
(![X]:((curious(X)&happy(X))<=>(strong(X)|~brave(X))))&
((?[X]:((~funny(X)&curious(X))))<=>((~creative(lucy)&~happy(lucy))))&
(![X]:((~curious(X)|brave(X))=>(~patient(X)|~generous(X))))&
((rich(mary))<=>(?[X]:((~patient(X)|happy(X)))))&
(?[X]:((creative(X)|kind(X))))&
(?[X]:(~old(X)))&
((~wise(fred)<~>~old(fred)))&
((~patient(susan)|funny(susan))) | rich(fred) | [] | null | 0 |
If susan is either not wise or wise then lucy is kind. Everyone who is both kind and not humble is not wise. Everyone who is both humble and not humble is not curious or not funny and vice versa. Everyone who is either not quiet or not strong is not rich. Everyone who is patient or humble is both tall and not happy and vice versa. If susan is either not wise or not rich then susan is both not funny and patient. If alice is not kind then someone is either kind or humble and vice versa. Everyone who is either strong or not generous is not kind and vice versa. If someone is not wise or quiet then someone is curious or not happy and vice versa. Everyone who is both happy and strong is either curious or not strong. Everyone who is not rich is either strong or not tall and vice versa. If someone is not generous then lucy is not quiet or funny. If paul is kind or not generous then alice is both not tall and not generous and vice versa. Everyone who is brave or not rich is either quiet or not wise and vice versa. If someone is rich then mary is not generous and vice versa. If someone is either not strong or rich then paul is either happy or funny. Susan is generous or not brave. John is either tall or not creative. Mary is both happy and rich. Someone is humble. Someone is either curious or not rich. Lucy is either not old or humble. Someone is not creative. | Mary is not humble. | entailment | (((~wise(susan)<~>wise(susan)))=>(kind(lucy)))&
(![X]:((kind(X)&~humble(X))=>~wise(X)))&
(![X]:((humble(X)&~humble(X))<=>(~curious(X)|~funny(X))))&
(![X]:((~quiet(X)<~>~strong(X))=>~rich(X)))&
(![X]:((patient(X)|humble(X))<=>(tall(X)&~happy(X))))&
(((~wise(susan)<~>~rich(susan)))=>((~funny(susan)&patient(susan))))&
((~kind(alice))<=>(?[X]:((kind(X)<~>humble(X)))))&
(![X]:((strong(X)<~>~generous(X))<=>~kind(X)))&
((?[X]:((~wise(X)|quiet(X))))<=>(?[X]:((curious(X)|~happy(X)))))&
(![X]:((happy(X)&strong(X))=>(curious(X)<~>~strong(X))))&
(![X]:(~rich(X)<=>(strong(X)<~>~tall(X))))&
((?[X]:(~generous(X)))=>((~quiet(lucy)|funny(lucy))))&
(((kind(paul)|~generous(paul)))<=>((~tall(alice)&~generous(alice))))&
(![X]:((brave(X)|~rich(X))<=>(quiet(X)<~>~wise(X))))&
((?[X]:(rich(X)))<=>(~generous(mary)))&
((?[X]:((~strong(X)<~>rich(X))))=>((happy(paul)<~>funny(paul))))&
((generous(susan)|~brave(susan)))&
((tall(john)<~>~creative(john)))&
((happy(mary)&rich(mary)))&
(?[X]:(humble(X)))&
(?[X]:((curious(X)<~>~rich(X))))&
((~old(lucy)<~>humble(lucy)))&
(?[X]:(~creative(X))) | ~humble(mary) | [
"p4",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 87843162581602231262678
% SZS output start Proof for 87843162581602231262678
5. ! [X0] : ((humble(X0) | patient(X0)) <=> (~happy(X0) & tall(X0))) [input p4]
19. rich(mary) & happy(mary) [input p18]
24. humble(mary) [input hypothesis]
40. ! [X0] : (((humble(X0) | patient(X0)) | (happy(X0) | ~tall(X0))) & ((~happy(X0) & tall(X0)) | (~humble(X0) & ~patient(X0)))) [nnf transformation 5]
41. ! [X0] : ((humble(X0) | patient(X0) | happy(X0) | ~tall(X0)) & ((~happy(X0) & tall(X0)) | (~humble(X0) & ~patient(X0)))) [flattening 40]
86. ~happy(X0) | ~humble(X0) [cnf transformation 41]
131. happy(mary) [cnf transformation 19]
139. humble(mary) [cnf transformation 24]
290. ~humble(mary) [resolution 86,131]
291. $false [subsumption resolution 290,139]
% SZS output end Proof for 87843162581602231262678
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not brave and not curious then someone is happy or calm.
Everyone who is either creative or not curious is not creative or happy.
Everyone who is either humble or not quiet is not patient or not curious and vice versa.
Everyone who is both not happy and wise is both strong and rich and vice versa.
Everyone who is not old is kind or not generous and vice versa.
If someone is old then alice is both not brave and funny and vice versa.
Everyone who is both funny and calm is either tall or not tall and vice versa.
If someone is kind or not generous then someone is both not curious and curious and vice versa.
Everyone who is generous or calm is not patient or brave and vice versa.
Everyone who is not old or strong is both not humble and not generous and vice versa.
If mary is not kind then fred is either strong or old and vice versa.
If fred is both brave and rich then someone is either not old or not humble and vice versa.
Everyone who is not humble or tall is either calm or patient.
Everyone who is strong is wise and vice versa.
If someone is both not curious and not creative then john is both old and not strong and vice versa.
John is either curious or not happy.
Someone is funny or brave.
Someone is not strong.
Someone is either not patient or not brave.
John is tall or happy.
Someone is wise or curious.
Paul is either not kind or not calm. | Alice is not happy. | neutral | (((~brave(lucy)&~curious(lucy)))=>(?[X]:((happy(X)|calm(X)))))&
(![X]:((creative(X)<~>~curious(X))=>(~creative(X)|happy(X))))&
(![X]:((humble(X)<~>~quiet(X))<=>(~patient(X)|~curious(X))))&
(![X]:((~happy(X)&wise(X))<=>(strong(X)&rich(X))))&
(![X]:(~old(X)<=>(kind(X)|~generous(X))))&
((?[X]:(old(X)))<=>((~brave(alice)&funny(alice))))&
(![X]:((funny(X)&calm(X))<=>(tall(X)<~>~tall(X))))&
((?[X]:((kind(X)|~generous(X))))<=>(?[X]:((~curious(X)&curious(X)))))&
(![X]:((generous(X)|calm(X))<=>(~patient(X)|brave(X))))&
(![X]:((~old(X)|strong(X))<=>(~humble(X)&~generous(X))))&
((~kind(mary))<=>((strong(fred)<~>old(fred))))&
(((brave(fred)&rich(fred)))<=>(?[X]:((~old(X)<~>~humble(X)))))&
(![X]:((~humble(X)|tall(X))=>(calm(X)<~>patient(X))))&
(![X]:(strong(X)<=>wise(X)))&
((?[X]:((~curious(X)&~creative(X))))<=>((old(john)&~strong(john))))&
((curious(john)<~>~happy(john)))&
(?[X]:((funny(X)|brave(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~patient(X)<~>~brave(X))))&
((tall(john)|happy(john)))&
(?[X]:((wise(X)|curious(X))))&
((~kind(paul)<~>~calm(paul))) | ~happy(alice) | [] | null | 0 |
Everyone who is both brave and strong is both not old and not strong and vice versa. Everyone who is not curious or generous is both rich and not generous and vice versa. Everyone who is either not curious or not calm is either not kind or not funny. If someone is both creative and not calm then fred is old. Everyone who is generous is both not kind and rich and vice versa. Everyone who is not quiet or not generous is both calm and not old. If someone is not humble or not strong then someone is not happy and vice versa. If alice is happy then someone is both not rich and not quiet. Everyone who is creative or brave is wise or not brave. If alice is not rich or not wise then someone is either not generous or not rich. If someone is either not old or generous then someone is both not old and not quiet and vice versa. If someone is not humble or strong then lucy is creative and vice versa. Everyone who is not generous is rich and vice versa. If someone is both rich and kind then fred is both quiet and not curious. If paul is not happy or kind then fred is either not quiet or not happy. Someone is creative or not calm. John is either old or patient. John is strong. Someone is creative. Someone is not quiet. | Lucy is strong. | entailment | (![X]:((brave(X)&strong(X))<=>(~old(X)&~strong(X))))&
(![X]:((~curious(X)|generous(X))<=>(rich(X)&~generous(X))))&
(![X]:((~curious(X)<~>~calm(X))=>(~kind(X)<~>~funny(X))))&
((?[X]:((creative(X)&~calm(X))))=>(old(fred)))&
(![X]:(generous(X)<=>(~kind(X)&rich(X))))&
(![X]:((~quiet(X)|~generous(X))=>(calm(X)&~old(X))))&
((?[X]:((~humble(X)|~strong(X))))<=>(?[X]:(~happy(X))))&
((happy(alice))=>(?[X]:((~rich(X)&~quiet(X)))))&
(![X]:((creative(X)|brave(X))=>(wise(X)|~brave(X))))&
(((~rich(alice)|~wise(alice)))=>(?[X]:((~generous(X)<~>~rich(X)))))&
((?[X]:((~old(X)<~>generous(X))))<=>(?[X]:((~old(X)&~quiet(X)))))&
((?[X]:((~humble(X)|strong(X))))<=>(creative(lucy)))&
(![X]:(~generous(X)<=>rich(X)))&
((?[X]:((rich(X)&kind(X))))=>((quiet(fred)&~curious(fred))))&
(((~happy(paul)|kind(paul)))=>((~quiet(fred)<~>~happy(fred))))&
(?[X]:((creative(X)|~calm(X))))&
((old(john)<~>patient(john)))&
(strong(john))&
(?[X]:(creative(X)))&
(?[X]:(~quiet(X))) | strong(lucy) | [
"p0",
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1411885847218022164936193
% SZS output start Proof for 1411885847218022164936193
1. ! [X0] : ((strong(X0) & brave(X0)) <=> (~strong(X0) & ~old(X0))) [input p0]
2. ! [X0] : ((generous(X0) | ~curious(X0)) <=> (~generous(X0) & rich(X0))) [input p1]
6. ! [X0] : ((~generous(X0) | ~quiet(X0)) => (~old(X0) & calm(X0))) [input p5]
21. ~strong(lucy) [input hypothesis]
28. ! [X0] : ((~old(X0) & calm(X0)) | (generous(X0) & quiet(X0))) [ennf transformation 6]
33. ! [X0] : (((strong(X0) & brave(X0)) | (strong(X0) | old(X0))) & ((~strong(X0) & ~old(X0)) | (~strong(X0) | ~brave(X0)))) [nnf transformation 1]
34. ! [X0] : (((strong(X0) & brave(X0)) | strong(X0) | old(X0)) & ((~strong(X0) & ~old(X0)) | ~strong(X0) | ~brave(X0))) [flattening 33]
35. ! [X0] : (((generous(X0) | ~curious(X0)) | (generous(X0) | ~rich(X0))) & ((~generous(X0) & rich(X0)) | (~generous(X0) & curious(X0)))) [nnf transformation 2]
36. ! [X0] : ((generous(X0) | ~curious(X0) | generous(X0) | ~rich(X0)) & ((~generous(X0) & rich(X0)) | (~generous(X0) & curious(X0)))) [flattening 35]
71. strong(X0) | strong(X0) | old(X0) [cnf transformation 34]
75. ~generous(X0) | ~generous(X0) [cnf transformation 36]
88. ~old(X0) | generous(X0) [cnf transformation 28]
119. ~strong(lucy) [cnf transformation 21]
120. ~generous(X0) [duplicate literal removal 75]
123. old(X0) | strong(X0) [duplicate literal removal 71]
133. ~old(X0) [subsumption resolution 88,120]
148. 6 <=> ! [X3] : strong(X3) [avatar definition]
149. strong(X3) <- (6) [avatar component clause 148]
240. strong(X0) [resolution 123,133]
241. 6 [avatar split clause 240,148]
242. $false <- (6) [resolution 149,119]
244. ~6 [avatar contradiction clause 242]
245. $false [avatar sat refutation 241,244]
% SZS output end Proof for 1411885847218022164936193
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not quiet then lucy is both not generous and old and vice versa. Everyone who is tall is not tall or not wise and vice versa. If alice is both quiet and not kind then lucy is not tall or not wise and vice versa. Everyone who is not wise is both not curious and not old and vice versa. Everyone who is not old is either not old or strong. Everyone who is not creative or humble is happy or not tall. If lucy is happy or not quiet then john is both not patient and happy. Everyone who is rich is either calm or curious and vice versa. If john is either not generous or not creative then lucy is both not creative and wise and vice versa. Everyone who is either not calm or not kind is curious and vice versa. If someone is either strong or calm then john is both humble and not humble and vice versa. If fred is not funny then someone is not generous. Everyone who is either not curious or funny is either brave or not tall. If john is not happy then someone is generous. Fred is either not strong or not creative. Someone is not creative or rich. Paul is either not generous or not calm. Fred is patient. Someone is either funny or not curious. | John is rich. | contradiction | ((~quiet(susan))<=>((~generous(lucy)&old(lucy))))&
(![X]:(tall(X)<=>(~tall(X)|~wise(X))))&
(((quiet(alice)&~kind(alice)))<=>((~tall(lucy)|~wise(lucy))))&
(![X]:(~wise(X)<=>(~curious(X)&~old(X))))&
(![X]:(~old(X)=>(~old(X)<~>strong(X))))&
(![X]:((~creative(X)|humble(X))=>(happy(X)|~tall(X))))&
(((happy(lucy)|~quiet(lucy)))=>((~patient(john)&happy(john))))&
(![X]:(rich(X)<=>(calm(X)<~>curious(X))))&
(((~generous(john)<~>~creative(john)))<=>((~creative(lucy)&wise(lucy))))&
(![X]:((~calm(X)<~>~kind(X))<=>curious(X)))&
((?[X]:((strong(X)<~>calm(X))))<=>((humble(john)&~humble(john))))&
((~funny(fred))=>(?[X]:(~generous(X))))&
(![X]:((~curious(X)<~>funny(X))=>(brave(X)<~>~tall(X))))&
((~happy(john))=>(?[X]:(generous(X))))&
((~strong(fred)<~>~creative(fred)))&
(?[X]:((~creative(X)|rich(X))))&
((~generous(paul)<~>~calm(paul)))&
(patient(fred))&
(?[X]:((funny(X)<~>~curious(X)))) | rich(john) | [
"p1",
"p3",
"p4",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3831004230829665573666893
% SZS output start Proof for 3831004230829665573666893
2. ! [X0] : (tall(X0) <=> (~wise(X0) | ~tall(X0))) [input p1]
4. ! [X0] : (~wise(X0) <=> (~old(X0) & ~curious(X0))) [input p3]
5. ! [X0] : (~old(X0) => (~old(X0) <~> strong(X0))) [input p4]
8. ! [X0] : (rich(X0) <=> (calm(X0) <~> curious(X0))) [input p7]
11. ? [X0] : (strong(X0) <~> calm(X0)) <=> (~humble(john) & humble(john)) [input p10]
20. rich(john) [input hypothesis]
21. ! [X0] : (rich(X0) => (calm(X0) <~> curious(X0))) [unused predicate definition removal 8]
22. ! [X0] : ((~old(X0) <~> strong(X0)) | old(X0)) [ennf transformation 5]
26. ! [X0] : ((calm(X0) <~> curious(X0)) | ~rich(X0)) [ennf transformation 21]
32. ! [X0] : ((tall(X0) | (wise(X0) & tall(X0))) & ((~wise(X0) | ~tall(X0)) | ~tall(X0))) [nnf transformation 2]
33. ! [X0] : ((tall(X0) | (wise(X0) & tall(X0))) & (~wise(X0) | ~tall(X0) | ~tall(X0))) [flattening 32]
36. ! [X0] : ((~wise(X0) | (old(X0) | curious(X0))) & ((~old(X0) & ~curious(X0)) | wise(X0))) [nnf transformation 4]
37. ! [X0] : ((~wise(X0) | old(X0) | curious(X0)) & ((~old(X0) & ~curious(X0)) | wise(X0))) [flattening 36]
38. ! [X0] : (((~strong(X0) | old(X0)) & (strong(X0) | ~old(X0))) | old(X0)) [nnf transformation 22]
39. ! [X0] : (((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | ~rich(X0)) [nnf transformation 26]
43. (? [X0] : ((~calm(X0) | ~strong(X0)) & (calm(X0) | strong(X0))) | (humble(john) | ~humble(john))) & ((~humble(john) & humble(john)) | ! [X0] : ((strong(X0) | ~calm(X0)) & (calm(X0) | ~strong(X0)))) [nnf transformation 11]
44. (? [X0] : ((~calm(X0) | ~strong(X0)) & (calm(X0) | strong(X0))) | humble(john) | ~humble(john)) & ((~humble(john) & humble(john)) | ! [X0] : ((strong(X0) | ~calm(X0)) & (calm(X0) | ~strong(X0)))) [flattening 43]
45. (? [X0] : ((~calm(X0) | ~strong(X0)) & (calm(X0) | strong(X0))) | humble(john) | ~humble(john)) & ((~humble(john) & humble(john)) | ! [X1] : ((strong(X1) | ~calm(X1)) & (calm(X1) | ~strong(X1)))) [rectify 44]
46. ? [X0] : ((~calm(X0) | ~strong(X0)) & (calm(X0) | strong(X0))) => ((~calm(sK0) | ~strong(sK0)) & (calm(sK0) | strong(sK0))) [choice axiom]
47. (((~calm(sK0) | ~strong(sK0)) & (calm(sK0) | strong(sK0))) | humble(john) | ~humble(john)) & ((~humble(john) & humble(john)) | ! [X1] : ((strong(X1) | ~calm(X1)) & (calm(X1) | ~strong(X1)))) [skolemisation 45,46]
63. ~wise(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 33]
64. tall(X0) | tall(X0) [cnf transformation 33]
71. ~curious(X0) | wise(X0) [cnf transformation 37]
72. ~old(X0) | wise(X0) [cnf transformation 37]
75. ~strong(X0) | old(X0) | old(X0) [cnf transformation 38]
82. curious(X0) | calm(X0) | ~rich(X0) [cnf transformation 39]
95. humble(john) | strong(X1) | ~calm(X1) [cnf transformation 47]
97. ~humble(john) | strong(X1) | ~calm(X1) [cnf transformation 47]
114. rich(john) [cnf transformation 20]
115. ~strong(X0) | old(X0) [duplicate literal removal 75]
116. ~wise(X0) | ~tall(X0) [duplicate literal removal 63]
117. tall(X0) [duplicate literal removal 64]
133. ~wise(X0) [subsumption resolution 116,117]
136. ~old(X0) [subsumption resolution 72,133]
137. ~curious(X0) [subsumption resolution 71,133]
138. ~strong(X0) [subsumption resolution 115,136]
161. ~rich(X0) | calm(X0) [subsumption resolution 82,137]
182. ~humble(john) | ~calm(X1) [subsumption resolution 97,138]
184. 11 <=> ! [X1] : ~calm(X1) [avatar definition]
185. ~calm(X1) <- (11) [avatar component clause 184]
187. 12 <=> humble(john) [avatar definition]
190. 11 | ~12 [avatar split clause 182,187,184]
191. humble(john) | ~calm(X1) [subsumption resolution 95,138]
192. 11 | 12 [avatar split clause 191,187,184]
233. calm(john) [resolution 161,114]
234. $false <- (11) [subsumption resolution 233,185]
235. ~11 [avatar contradiction clause 234]
236. $false [avatar sat refutation 190,192,235]
% SZS output end Proof for 3831004230829665573666893
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is happy then someone is both not happy and not patient and vice versa.
Everyone who is not old or not patient is not strong.
If susan is either not kind or quiet then alice is both not wise and patient.
If someone is wise then susan is either wise or happy and vice versa.
Everyone who is not old or not creative is not happy or not brave.
If someone is creative then lucy is not generous or not creative and vice versa.
If someone is quiet then someone is humble or not humble and vice versa.
Everyone who is both creative and generous is either quiet or kind and vice versa.
Everyone who is both not rich and not patient is either not brave or quiet and vice versa.
Everyone who is not humble is not funny.
If someone is either not happy or patient then john is both tall and generous and vice versa.
Everyone who is both tall and not happy is either brave or not funny and vice versa.
Everyone who is either not patient or creative is both happy and not humble.
If someone is both patient and kind then susan is both curious and not patient and vice versa.
If someone is humble then alice is patient or quiet.
Everyone who is not tall or not generous is not generous or funny and vice versa.
Susan is wise or brave.
Someone is either kind or not kind.
Someone is both tall and calm.
Someone is either strong or not calm.
John is strong or not generous.
Fred is both not tall and not patient.
Someone is generous or funny.
Someone is wise or brave. | John is not funny. | entailment | ((?[X]:(happy(X)))<=>(?[X]:((~happy(X)&~patient(X)))))&
(![X]:((~old(X)|~patient(X))=>~strong(X)))&
(((~kind(susan)<~>quiet(susan)))=>((~wise(alice)&patient(alice))))&
((?[X]:(wise(X)))<=>((wise(susan)<~>happy(susan))))&
(![X]:((~old(X)|~creative(X))=>(~happy(X)|~brave(X))))&
((?[X]:(creative(X)))<=>((~generous(lucy)|~creative(lucy))))&
((?[X]:(quiet(X)))<=>(?[X]:((humble(X)|~humble(X)))))&
(![X]:((creative(X)&generous(X))<=>(quiet(X)<~>kind(X))))&
(![X]:((~rich(X)&~patient(X))<=>(~brave(X)<~>quiet(X))))&
(![X]:(~humble(X)=>~funny(X)))&
((?[X]:((~happy(X)<~>patient(X))))<=>((tall(john)&generous(john))))&
(![X]:((tall(X)&~happy(X))<=>(brave(X)<~>~funny(X))))&
(![X]:((~patient(X)<~>creative(X))=>(happy(X)&~humble(X))))&
((?[X]:((patient(X)&kind(X))))<=>((curious(susan)&~patient(susan))))&
((?[X]:(humble(X)))=>((patient(alice)|quiet(alice))))&
(![X]:((~tall(X)|~generous(X))<=>(~generous(X)|funny(X))))&
((wise(susan)|brave(susan)))&
(?[X]:((kind(X)<~>~kind(X))))&
(?[X]:((tall(X)&calm(X))))&
(?[X]:((strong(X)<~>~calm(X))))&
((strong(john)|~generous(john)))&
((~tall(fred)&~patient(fred)))&
(?[X]:((generous(X)|funny(X))))&
(?[X]:((wise(X)|brave(X)))) | ~funny(john) | [
"p0",
"p5",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 806896672236124424138539
% SZS output start Proof for 806896672236124424138539
1. ? [X0] : happy(X0) <=> ? [X0] : (~patient(X0) & ~happy(X0)) [input p0]
6. ? [X0] : creative(X0) <=> (~creative(lucy) | ~generous(lucy)) [input p5]
11. ? [X0] : (~happy(X0) <~> patient(X0)) <=> (generous(john) & tall(john)) [input p10]
13. ! [X0] : ((~patient(X0) <~> creative(X0)) => (~humble(X0) & happy(X0))) [input p12]
16. ! [X0] : ((~generous(X0) | ~tall(X0)) <=> (funny(X0) | ~generous(X0))) [input p15]
25. funny(john) [input hypothesis]
26. ? [X0] : happy(X0) <=> ? [X1] : (~patient(X1) & ~happy(X1)) [rectify 1]
35. ! [X0] : ((~humble(X0) & happy(X0)) | (~patient(X0) <=> creative(X0))) [ennf transformation 13]
38. (? [X0] : happy(X0) | ! [X1] : (patient(X1) | happy(X1))) & (? [X1] : (~patient(X1) & ~happy(X1)) | ! [X0] : ~happy(X0)) [nnf transformation 26]
39. (? [X0] : happy(X0) | ! [X1] : (patient(X1) | happy(X1))) & (? [X2] : (~patient(X2) & ~happy(X2)) | ! [X3] : ~happy(X3)) [rectify 38]
40. ? [X0] : happy(X0) => happy(sK0) [choice axiom]
41. ? [X2] : (~patient(X2) & ~happy(X2)) => (~patient(sK1) & ~happy(sK1)) [choice axiom]
42. (happy(sK0) | ! [X1] : (patient(X1) | happy(X1))) & ((~patient(sK1) & ~happy(sK1)) | ! [X3] : ~happy(X3)) [skolemisation 39,41,40]
48. (? [X0] : creative(X0) | (creative(lucy) & generous(lucy))) & ((~creative(lucy) | ~generous(lucy)) | ! [X0] : ~creative(X0)) [nnf transformation 6]
49. (? [X0] : creative(X0) | (creative(lucy) & generous(lucy))) & (~creative(lucy) | ~generous(lucy) | ! [X0] : ~creative(X0)) [flattening 48]
50. (? [X0] : creative(X0) | (creative(lucy) & generous(lucy))) & (~creative(lucy) | ~generous(lucy) | ! [X1] : ~creative(X1)) [rectify 49]
51. ? [X0] : creative(X0) => creative(sK3) [choice axiom]
52. (creative(sK3) | (creative(lucy) & generous(lucy))) & (~creative(lucy) | ~generous(lucy) | ! [X1] : ~creative(X1)) [skolemisation 50,51]
62. (? [X0] : ((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) | (~generous(john) | ~tall(john))) & ((generous(john) & tall(john)) | ! [X0] : ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0)))) [nnf transformation 11]
63. (? [X0] : ((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) | ~generous(john) | ~tall(john)) & ((generous(john) & tall(john)) | ! [X0] : ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0)))) [flattening 62]
64. (? [X0] : ((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) | ~generous(john) | ~tall(john)) & ((generous(john) & tall(john)) | ! [X1] : ((~happy(X1) | ~patient(X1)) & (patient(X1) | happy(X1)))) [rectify 63]
65. ? [X0] : ((~patient(X0) | happy(X0)) & (patient(X0) | ~happy(X0))) => ((~patient(sK6) | happy(sK6)) & (patient(sK6) | ~happy(sK6))) [choice axiom]
66. (((~patient(sK6) | happy(sK6)) & (patient(sK6) | ~happy(sK6))) | ~generous(john) | ~tall(john)) & ((generous(john) & tall(john)) | ! [X1] : ((~happy(X1) | ~patient(X1)) & (patient(X1) | happy(X1)))) [skolemisation 64,65]
69. ! [X0] : ((~humble(X0) & happy(X0)) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0)))) [nnf transformation 35]
75. ! [X0] : (((~generous(X0) | ~tall(X0)) | (~funny(X0) & generous(X0))) & ((funny(X0) | ~generous(X0)) | (generous(X0) & tall(X0)))) [nnf transformation 16]
76. ! [X0] : ((~generous(X0) | ~tall(X0) | (~funny(X0) & generous(X0))) & (funny(X0) | ~generous(X0) | (generous(X0) & tall(X0)))) [flattening 75]
89. ~happy(sK1) | ~happy(X3) [cnf transformation 42]
90. ~patient(sK1) | ~happy(X3) [cnf transformation 42]
102. ~creative(lucy) | ~generous(lucy) | ~creative(X1) [cnf transformation 52]
103. creative(sK3) | generous(lucy) [cnf transformation 52]
104. creative(sK3) | creative(lucy) [cnf transformation 52]
121. tall(john) | patient(X1) | happy(X1) [cnf transformation 66]
123. generous(john) | patient(X1) | happy(X1) [cnf transformation 66]
134. ~creative(X0) | ~patient(X0) | happy(X0) [cnf transformation 69]
145. ~tall(X0) | ~generous(X0) | ~funny(X0) [cnf transformation 76]
158. funny(john) [cnf transformation 25]
160. 1 <=> ! [X1] : (patient(X1) | happy(X1)) [avatar definition]
161. patient(X1) | happy(X1) <- (1) [avatar component clause 160]
168. 3 <=> ! [X3] : ~happy(X3) [avatar definition]
169. ~happy(X3) <- (3) [avatar component clause 168]
171. 4 <=> patient(sK1) [avatar definition]
173. ~patient(sK1) <- (~4) [avatar component clause 171]
174. 3 | ~4 [avatar split clause 90,171,168]
176. 5 <=> happy(sK1) [avatar definition]
178. ~happy(sK1) <- (~5) [avatar component clause 176]
179. 3 | ~5 [avatar split clause 89,176,168]
220. 14 <=> creative(lucy) [avatar definition]
222. creative(lucy) <- (14) [avatar component clause 220]
224. 15 <=> creative(sK3) [avatar definition]
226. creative(sK3) <- (15) [avatar component clause 224]
227. 14 | 15 [avatar split clause 104,224,220]
229. 16 <=> generous(lucy) [avatar definition]
232. 16 | 15 [avatar split clause 103,224,229]
234. 17 <=> ! [X1] : ~creative(X1) [avatar definition]
235. ~creative(X1) <- (17) [avatar component clause 234]
236. 17 | ~16 | ~14 [avatar split clause 102,220,229,234]
250. 21 <=> tall(john) [avatar definition]
251. tall(john) <- (21) [avatar component clause 250]
254. 22 <=> generous(john) [avatar definition]
271. 1 | 22 [avatar split clause 123,254,160]
273. 1 | 21 [avatar split clause 121,250,160]
459. ~patient(sK3) | happy(sK3) <- (15) [resolution 134,226]
464. 58 <=> happy(sK3) [avatar definition]
466. happy(sK3) <- (58) [avatar component clause 464]
468. 59 <=> patient(sK3) [avatar definition]
470. ~patient(sK3) <- (~59) [avatar component clause 468]
471. 58 | ~59 | ~15 [avatar split clause 459,224,468,464]
487. ~generous(john) | ~funny(john) <- (21) [resolution 145,251]
504. ~generous(john) <- (21) [subsumption resolution 487,158]
505. ~22 | ~21 [avatar split clause 504,250,254]
509. happy(sK1) <- (1, ~4) [resolution 161,173]
510. happy(sK3) <- (1, ~59) [resolution 161,470]
514. $false <- (1, ~4, ~5) [subsumption resolution 509,178]
515. ~1 | 4 | 5 [avatar contradiction clause 514]
516. 58 | ~1 | 59 [avatar split clause 510,468,160,464]
582. $false <- (3, 58) [resolution 466,169]
584. ~3 | ~58 [avatar contradiction clause 582]
594. $false <- (14, 17) [subsumption resolution 222,235]
595. ~14 | ~17 [avatar contradiction clause 594]
596. $false [avatar sat refutation 174,179,227,232,236,271,273,471,505,515,516,584,595]
% SZS output end Proof for 806896672236124424138539
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is quiet.
Everyone who is not tall or not funny is humble.
Everyone who is not generous or tall is brave.
Everyone who is not humble or not old is either calm or tall.
Everyone who is either not strong or not tall is funny or not rich and vice versa.
Everyone who is either generous or patient is patient and vice versa.
Everyone who is either tall or not generous is both old and wise.
Everyone who is brave or not calm is either funny or quiet and vice versa.
If someone is funny then someone is not generous.
Everyone who is happy or rich is generous and vice versa.
If mary is both patient and generous then someone is not wise.
Everyone who is either not curious or happy is happy and vice versa.
If someone is both happy and not patient then someone is both not humble and strong and vice versa.
Everyone who is either generous or not wise is both curious and quiet.
Everyone who is both not humble and kind is either not patient or not creative and vice versa.
Someone is either not happy or wise.
John is both not kind and not quiet.
Someone is either not humble or not quiet.
Someone is not quiet.
Mary is either not humble or not kind.
Susan is either creative or strong.
Someone is wise or not rich. | Mary is not brave. | contradiction | (![X]:(~strong(X)=>quiet(X)))&
(![X]:((~tall(X)|~funny(X))=>humble(X)))&
(![X]:((~generous(X)|tall(X))=>brave(X)))&
(![X]:((~humble(X)|~old(X))=>(calm(X)<~>tall(X))))&
(![X]:((~strong(X)<~>~tall(X))<=>(funny(X)|~rich(X))))&
(![X]:((generous(X)<~>patient(X))<=>patient(X)))&
(![X]:((tall(X)<~>~generous(X))=>(old(X)&wise(X))))&
(![X]:((brave(X)|~calm(X))<=>(funny(X)<~>quiet(X))))&
((?[X]:(funny(X)))=>(?[X]:(~generous(X))))&
(![X]:((happy(X)|rich(X))<=>generous(X)))&
(((patient(mary)&generous(mary)))=>(?[X]:(~wise(X))))&
(![X]:((~curious(X)<~>happy(X))<=>happy(X)))&
((?[X]:((happy(X)&~patient(X))))<=>(?[X]:((~humble(X)&strong(X)))))&
(![X]:((generous(X)<~>~wise(X))=>(curious(X)&quiet(X))))&
(![X]:((~humble(X)&kind(X))<=>(~patient(X)<~>~creative(X))))&
(?[X]:((~happy(X)<~>wise(X))))&
((~kind(john)&~quiet(john)))&
(?[X]:((~humble(X)<~>~quiet(X))))&
(?[X]:(~quiet(X)))&
((~humble(mary)<~>~kind(mary)))&
((creative(susan)<~>strong(susan)))&
(?[X]:((wise(X)|~rich(X)))) | ~brave(mary) | [
"p2",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 7267964630473251951873430
% SZS output start Proof for 7267964630473251951873430
3. ! [X0] : ((tall(X0) | ~generous(X0)) => brave(X0)) [input p2]
6. ! [X0] : ((generous(X0) <~> patient(X0)) <=> patient(X0)) [input p5]
23. ~brave(mary) [input hypothesis]
30. ! [X0] : (brave(X0) | (~tall(X0) & generous(X0))) [ennf transformation 3]
40. ! [X0] : ((((~patient(X0) | ~generous(X0)) & (patient(X0) | generous(X0))) | ~patient(X0)) & (patient(X0) | ((generous(X0) | ~patient(X0)) & (patient(X0) | ~generous(X0))))) [nnf transformation 6]
75. brave(X0) | generous(X0) [cnf transformation 30]
85. patient(X0) | patient(X0) | ~generous(X0) [cnf transformation 40]
88. ~patient(X0) | ~generous(X0) | ~patient(X0) [cnf transformation 40]
132. ~brave(mary) [cnf transformation 23]
135. patient(X0) | ~generous(X0) [duplicate literal removal 85]
136. ~patient(X0) | ~generous(X0) [duplicate literal removal 88]
138. ~generous(X0) [subsumption resolution 135,136]
188. generous(mary) [resolution 75,132]
189. $false [subsumption resolution 188,138]
% SZS output end Proof for 7267964630473251951873430
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both creative and not creative then someone is either brave or tall and vice versa.
Everyone who is either not humble or humble is both brave and not old.
Everyone who is wise is not creative.
If someone is not funny then someone is not tall and vice versa.
Everyone who is curious is both kind and patient and vice versa.
Everyone who is not kind is rich and vice versa.
If someone is both not rich and not creative then someone is either not curious or funny and vice versa.
If someone is not wise then someone is both wise and not curious and vice versa.
Everyone who is not kind or strong is both curious and rich and vice versa.
Everyone who is either not calm or patient is either curious or not generous and vice versa.
Everyone who is either not calm or not patient is not tall and vice versa.
Everyone who is not generous or wise is not patient.
If lucy is either kind or old then someone is creative or humble.
Susan is tall.
Someone is not rich or not quiet.
Fred is either not rich or curious.
Mary is not rich or funny.
Susan is both kind and generous.
Someone is quiet or curious. | Fred is calm. | contradiction | ((?[X]:((creative(X)&~creative(X))))<=>(?[X]:((brave(X)<~>tall(X)))))&
(![X]:((~humble(X)<~>humble(X))=>(brave(X)&~old(X))))&
(![X]:(wise(X)=>~creative(X)))&
((?[X]:(~funny(X)))<=>(?[X]:(~tall(X))))&
(![X]:(curious(X)<=>(kind(X)&patient(X))))&
(![X]:(~kind(X)<=>rich(X)))&
((?[X]:((~rich(X)&~creative(X))))<=>(?[X]:((~curious(X)<~>funny(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((wise(X)&~curious(X)))))&
(![X]:((~kind(X)|strong(X))<=>(curious(X)&rich(X))))&
(![X]:((~calm(X)<~>patient(X))<=>(curious(X)<~>~generous(X))))&
(![X]:((~calm(X)<~>~patient(X))<=>~tall(X)))&
(![X]:((~generous(X)|wise(X))=>~patient(X)))&
(((kind(lucy)<~>old(lucy)))=>(?[X]:((creative(X)|humble(X)))))&
(tall(susan))&
(?[X]:((~rich(X)|~quiet(X))))&
((~rich(fred)<~>curious(fred)))&
((~rich(mary)|funny(mary)))&
((kind(susan)&generous(susan)))&
(?[X]:((quiet(X)|curious(X)))) | calm(fred) | [
"p0",
"p1",
"p4",
"p5",
"p8",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9126713106301138382215279
% SZS output start Proof for 9126713106301138382215279
1. ? [X0] : (~creative(X0) & creative(X0)) <=> ? [X0] : (brave(X0) <~> tall(X0)) [input p0]
2. ! [X0] : ((~humble(X0) <~> humble(X0)) => (~old(X0) & brave(X0))) [input p1]
5. ! [X0] : (curious(X0) <=> (patient(X0) & kind(X0))) [input p4]
6. ! [X0] : (~kind(X0) <=> rich(X0)) [input p5]
9. ! [X0] : ((strong(X0) | ~kind(X0)) <=> (rich(X0) & curious(X0))) [input p8]
11. ! [X0] : ((~calm(X0) <~> ~patient(X0)) <=> ~tall(X0)) [input p10]
16. ~rich(fred) <~> curious(fred) [input p15]
20. calm(fred) [input hypothesis]
21. ? [X0] : (~creative(X0) & creative(X0)) <=> ? [X1] : (brave(X1) <~> tall(X1)) [rectify 1]
25. ! [X0] : ((~old(X0) & brave(X0)) | (~humble(X0) <=> humble(X0))) [ennf transformation 2]
29. (? [X0] : (~creative(X0) & creative(X0)) | ! [X1] : ((brave(X1) | ~tall(X1)) & (tall(X1) | ~brave(X1)))) & (? [X1] : ((~tall(X1) | ~brave(X1)) & (tall(X1) | brave(X1))) | ! [X0] : (creative(X0) | ~creative(X0))) [nnf transformation 21]
30. (? [X0] : (~creative(X0) & creative(X0)) | ! [X1] : ((brave(X1) | ~tall(X1)) & (tall(X1) | ~brave(X1)))) & (? [X2] : ((~tall(X2) | ~brave(X2)) & (tall(X2) | brave(X2))) | ! [X3] : (creative(X3) | ~creative(X3))) [rectify 29]
31. ? [X0] : (~creative(X0) & creative(X0)) => (~creative(sK0) & creative(sK0)) [choice axiom]
32. ? [X2] : ((~tall(X2) | ~brave(X2)) & (tall(X2) | brave(X2))) => ((~tall(sK1) | ~brave(sK1)) & (tall(sK1) | brave(sK1))) [choice axiom]
33. ((~creative(sK0) & creative(sK0)) | ! [X1] : ((brave(X1) | ~tall(X1)) & (tall(X1) | ~brave(X1)))) & (((~tall(sK1) | ~brave(sK1)) & (tall(sK1) | brave(sK1))) | ! [X3] : (creative(X3) | ~creative(X3))) [skolemisation 30,32,31]
34. ! [X0] : ((~old(X0) & brave(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0)))) [nnf transformation 25]
40. ! [X0] : ((curious(X0) | (~patient(X0) | ~kind(X0))) & ((patient(X0) & kind(X0)) | ~curious(X0))) [nnf transformation 5]
41. ! [X0] : ((curious(X0) | ~patient(X0) | ~kind(X0)) & ((patient(X0) & kind(X0)) | ~curious(X0))) [flattening 40]
42. ! [X0] : ((~kind(X0) | ~rich(X0)) & (rich(X0) | kind(X0))) [nnf transformation 6]
53. ! [X0] : (((strong(X0) | ~kind(X0)) | (~rich(X0) | ~curious(X0))) & ((rich(X0) & curious(X0)) | (~strong(X0) & kind(X0)))) [nnf transformation 9]
54. ! [X0] : ((strong(X0) | ~kind(X0) | ~rich(X0) | ~curious(X0)) & ((rich(X0) & curious(X0)) | (~strong(X0) & kind(X0)))) [flattening 53]
56. ! [X0] : ((((patient(X0) | calm(X0)) & (~patient(X0) | ~calm(X0))) | tall(X0)) & (~tall(X0) | ((~calm(X0) | patient(X0)) & (~patient(X0) | calm(X0))))) [nnf transformation 11]
62. (~curious(fred) | rich(fred)) & (curious(fred) | ~rich(fred)) [nnf transformation 16]
67. creative(sK0) | tall(X1) | ~brave(X1) [cnf transformation 33]
69. ~creative(sK0) | tall(X1) | ~brave(X1) [cnf transformation 33]
71. brave(X0) | humble(X0) | humble(X0) [cnf transformation 34]
72. brave(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 34]
78. ~curious(X0) | kind(X0) [cnf transformation 41]
80. ~patient(X0) | curious(X0) | ~kind(X0) [cnf transformation 41]
82. ~rich(X0) | ~kind(X0) [cnf transformation 42]
92. curious(X0) | kind(X0) [cnf transformation 54]
106. ~calm(X0) | ~tall(X0) | patient(X0) [cnf transformation 56]
116. ~curious(fred) | rich(fred) [cnf transformation 62]
121. calm(fred) [cnf transformation 20]
122. brave(X0) | humble(X0) [duplicate literal removal 71]
123. ~humble(X0) | brave(X0) [duplicate literal removal 72]
130. 2 <=> creative(sK0) [avatar definition]
135. 3 <=> ! [X1] : (tall(X1) | ~brave(X1)) [avatar definition]
136. tall(X1) | ~brave(X1) <- (3) [avatar component clause 135]
137. 3 | ~2 [avatar split clause 69,130,135]
139. 3 | 2 [avatar split clause 67,130,135]
141. brave(X0) [subsumption resolution 122,123]
143. 4 <=> ! [X1] : tall(X1) [avatar definition]
144. tall(X1) <- (4) [avatar component clause 143]
210. kind(X0) [subsumption resolution 92,78]
236. 24 <=> rich(fred) [avatar definition]
238. rich(fred) <- (24) [avatar component clause 236]
240. 25 <=> curious(fred) [avatar definition]
243. 24 | ~25 [avatar split clause 116,240,236]
265. tall(X1) <- (3) [subsumption resolution 136,141]
266. 4 | ~3 [avatar split clause 265,135,143]
306. ~tall(fred) | patient(fred) [resolution 106,121]
307. patient(fred) <- (4) [subsumption resolution 306,144]
309. curious(fred) | ~kind(fred) <- (4) [resolution 307,80]
315. curious(fred) <- (4) [subsumption resolution 309,210]
316. 25 | ~4 [avatar split clause 315,143,240]
317. ~kind(fred) <- (24) [resolution 238,82]
318. $false <- (24) [subsumption resolution 317,210]
319. ~24 [avatar contradiction clause 318]
320. $false [avatar sat refutation 137,139,243,266,316,319]
% SZS output end Proof for 9126713106301138382215279
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not humble and kind is both curious and not tall and vice versa.
Everyone who is both happy and not humble is both rich and kind.
Everyone who is either creative or calm is both not wise and not funny and vice versa.
If susan is either calm or funny then someone is generous.
If susan is not calm then someone is either humble or not creative and vice versa.
Everyone who is not kind or curious is either creative or not happy and vice versa.
Everyone who is either calm or wise is brave or patient.
Everyone who is both brave and curious is both not humble and not generous and vice versa.
If someone is both not humble and brave then fred is not rich.
If susan is both curious and funny then someone is both brave and wise.
Everyone who is both rich and not quiet is not wise.
Everyone who is generous is not quiet and vice versa.
Everyone who is happy is both not rich and not brave and vice versa.
Everyone who is not old or not wise is not old and vice versa.
Everyone who is not quiet is rich and vice versa.
If fred is calm then someone is not curious or not funny and vice versa.
Paul is patient or calm.
John is both kind and not rich.
Mary is either strong or creative.
Lucy is not quiet or calm.
Lucy is not curious.
Someone is both wise and not generous.
Someone is both brave and funny.
Someone is not wise. | Susan is happy. | neutral | (![X]:((~humble(X)&kind(X))<=>(curious(X)&~tall(X))))&
(![X]:((happy(X)&~humble(X))=>(rich(X)&kind(X))))&
(![X]:((creative(X)<~>calm(X))<=>(~wise(X)&~funny(X))))&
(((calm(susan)<~>funny(susan)))=>(?[X]:(generous(X))))&
((~calm(susan))<=>(?[X]:((humble(X)<~>~creative(X)))))&
(![X]:((~kind(X)|curious(X))<=>(creative(X)<~>~happy(X))))&
(![X]:((calm(X)<~>wise(X))=>(brave(X)|patient(X))))&
(![X]:((brave(X)&curious(X))<=>(~humble(X)&~generous(X))))&
((?[X]:((~humble(X)&brave(X))))=>(~rich(fred)))&
(((curious(susan)&funny(susan)))=>(?[X]:((brave(X)&wise(X)))))&
(![X]:((rich(X)&~quiet(X))=>~wise(X)))&
(![X]:(generous(X)<=>~quiet(X)))&
(![X]:(happy(X)<=>(~rich(X)&~brave(X))))&
(![X]:((~old(X)|~wise(X))<=>~old(X)))&
(![X]:(~quiet(X)<=>rich(X)))&
((calm(fred))<=>(?[X]:((~curious(X)|~funny(X)))))&
((patient(paul)|calm(paul)))&
((kind(john)&~rich(john)))&
((strong(mary)<~>creative(mary)))&
((~quiet(lucy)|calm(lucy)))&
(~curious(lucy))&
(?[X]:((wise(X)&~generous(X))))&
(?[X]:((brave(X)&funny(X))))&
(?[X]:(~wise(X))) | happy(susan) | [] | null | 0 |
Everyone who is both not kind and funny is happy or not creative and vice versa.
Everyone who is both funny and creative is both not tall and generous.
If someone is creative or kind then fred is not calm.
Everyone who is both not old and not happy is strong or curious and vice versa.
If john is either humble or not funny then someone is both not happy and not brave.
Everyone who is not calm or not happy is not brave or not humble and vice versa.
Everyone who is tall is not happy.
If john is both old and brave then fred is not calm and vice versa.
If lucy is both not calm and not tall then someone is either humble or not creative and vice versa.
If alice is not funny or rich then someone is generous and vice versa.
Everyone who is either not kind or not funny is either not wise or not brave.
Everyone who is generous is both not calm and not curious and vice versa.
Everyone who is both not old and not strong is either quiet or not brave and vice versa.
Everyone who is not creative is not rich.
Everyone who is either generous or rich is both strong and not wise and vice versa.
Everyone who is rich or kind is curious or not funny.
Someone is not generous or calm.
Susan is either curious or old.
Someone is not funny.
Someone is both not brave and funny.
Someone is curious or not funny.
Mary is both creative and curious.
Someone is not kind.
Someone is not quiet or wise. | John is not quiet. | entailment | (![X]:((~kind(X)&funny(X))<=>(happy(X)|~creative(X))))&
(![X]:((funny(X)&creative(X))=>(~tall(X)&generous(X))))&
((?[X]:((creative(X)|kind(X))))=>(~calm(fred)))&
(![X]:((~old(X)&~happy(X))<=>(strong(X)|curious(X))))&
(((humble(john)<~>~funny(john)))=>(?[X]:((~happy(X)&~brave(X)))))&
(![X]:((~calm(X)|~happy(X))<=>(~brave(X)|~humble(X))))&
(![X]:(tall(X)=>~happy(X)))&
(((old(john)&brave(john)))<=>(~calm(fred)))&
(((~calm(lucy)&~tall(lucy)))<=>(?[X]:((humble(X)<~>~creative(X)))))&
(((~funny(alice)|rich(alice)))<=>(?[X]:(generous(X))))&
(![X]:((~kind(X)<~>~funny(X))=>(~wise(X)<~>~brave(X))))&
(![X]:(generous(X)<=>(~calm(X)&~curious(X))))&
(![X]:((~old(X)&~strong(X))<=>(quiet(X)<~>~brave(X))))&
(![X]:(~creative(X)=>~rich(X)))&
(![X]:((generous(X)<~>rich(X))<=>(strong(X)&~wise(X))))&
(![X]:((rich(X)|kind(X))=>(curious(X)|~funny(X))))&
(?[X]:((~generous(X)|calm(X))))&
((curious(susan)<~>old(susan)))&
(?[X]:(~funny(X)))&
(?[X]:((~brave(X)&funny(X))))&
(?[X]:((curious(X)|~funny(X))))&
((creative(mary)&curious(mary)))&
(?[X]:(~kind(X)))&
(?[X]:((~quiet(X)|wise(X)))) | ~quiet(john) | [
"p2",
"p7",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7261412963092850136855762
% SZS output start Proof for 7261412963092850136855762
3. ? [X0] : (kind(X0) | creative(X0)) => ~calm(fred) [input p2]
8. (brave(john) & old(john)) <=> ~calm(fred) [input p7]
13. ! [X0] : ((~strong(X0) & ~old(X0)) <=> (quiet(X0) <~> ~brave(X0))) [input p12]
22. curious(mary) & creative(mary) [input p21]
25. quiet(john) [input hypothesis]
28. ~calm(fred) | ! [X0] : (~kind(X0) & ~creative(X0)) [ennf transformation 3]
44. ((brave(john) & old(john)) | calm(fred)) & (~calm(fred) | (~brave(john) | ~old(john))) [nnf transformation 8]
45. ((brave(john) & old(john)) | calm(fred)) & (~calm(fred) | ~brave(john) | ~old(john)) [flattening 44]
59. ! [X0] : (((~strong(X0) & ~old(X0)) | ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | (strong(X0) | old(X0)))) [nnf transformation 13]
60. ! [X0] : (((~strong(X0) & ~old(X0)) | ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | strong(X0) | old(X0))) [flattening 59]
83. ~calm(fred) | ~creative(X0) [cnf transformation 28]
100. old(john) | calm(fred) [cnf transformation 45]
101. brave(john) | calm(fred) [cnf transformation 45]
120. ~quiet(X0) | ~brave(X0) | ~old(X0) [cnf transformation 60]
140. creative(mary) [cnf transformation 22]
144. quiet(john) [cnf transformation 25]
149. 2 <=> calm(fred) [avatar definition]
154. 3 <=> ! [X0] : ~creative(X0) [avatar definition]
155. ~creative(X0) <- (3) [avatar component clause 154]
156. 3 | ~2 [avatar split clause 83,149,154]
178. 8 <=> brave(john) [avatar definition]
180. brave(john) <- (8) [avatar component clause 178]
181. 2 | 8 [avatar split clause 101,178,149]
183. 9 <=> old(john) [avatar definition]
186. 2 | 9 [avatar split clause 100,183,149]
285. ~brave(john) | ~old(john) [resolution 120,144]
286. ~old(john) <- (8) [subsumption resolution 285,180]
289. ~9 | ~8 [avatar split clause 286,178,183]
307. $false <- (3) [resolution 155,140]
309. ~3 [avatar contradiction clause 307]
310. $false [avatar sat refutation 156,181,186,289,309]
% SZS output end Proof for 7261412963092850136855762
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both happy and not humble then someone is either not strong or not quiet and vice versa.
If someone is not generous then alice is both not patient and old.
Everyone who is calm or not happy is patient.
Everyone who is wise or not tall is both wise and not happy and vice versa.
Everyone who is wise is both happy and generous.
Everyone who is either quiet or not generous is patient or curious.
Everyone who is both not brave and generous is not rich and vice versa.
Everyone who is wise is both old and tall.
Everyone who is both quiet and not happy is either not creative or rich.
Everyone who is both generous and humble is either not wise or wise and vice versa.
If someone is both not brave and generous then fred is either not wise or not quiet and vice versa.
Everyone who is not curious or strong is both patient and not curious and vice versa.
Everyone who is not curious or not calm is both not quiet and not brave and vice versa.
If alice is not tall then lucy is not rich or not tall.
If someone is brave or not humble then john is patient.
Everyone who is not kind is not tall or happy.
Mary is both rich and not quiet.
Mary is either not rich or not happy.
Someone is not wise.
Lucy is rich or not strong. | John is not strong. | entailment | ((?[X]:((happy(X)&~humble(X))))<=>(?[X]:((~strong(X)<~>~quiet(X)))))&
((?[X]:(~generous(X)))=>((~patient(alice)&old(alice))))&
(![X]:((calm(X)|~happy(X))=>patient(X)))&
(![X]:((wise(X)|~tall(X))<=>(wise(X)&~happy(X))))&
(![X]:(wise(X)=>(happy(X)&generous(X))))&
(![X]:((quiet(X)<~>~generous(X))=>(patient(X)|curious(X))))&
(![X]:((~brave(X)&generous(X))<=>~rich(X)))&
(![X]:(wise(X)=>(old(X)&tall(X))))&
(![X]:((quiet(X)&~happy(X))=>(~creative(X)<~>rich(X))))&
(![X]:((generous(X)&humble(X))<=>(~wise(X)<~>wise(X))))&
((?[X]:((~brave(X)&generous(X))))<=>((~wise(fred)<~>~quiet(fred))))&
(![X]:((~curious(X)|strong(X))<=>(patient(X)&~curious(X))))&
(![X]:((~curious(X)|~calm(X))<=>(~quiet(X)&~brave(X))))&
((~tall(alice))=>((~rich(lucy)|~tall(lucy))))&
((?[X]:((brave(X)|~humble(X))))=>(patient(john)))&
(![X]:(~kind(X)=>(~tall(X)|happy(X))))&
((rich(mary)&~quiet(mary)))&
((~rich(mary)<~>~happy(mary)))&
(?[X]:(~wise(X)))&
((rich(lucy)|~strong(lucy))) | ~strong(john) | [
"p0",
"p3",
"p4",
"p9",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7120147589269965764276668
% SZS output start Proof for 7120147589269965764276668
1. ? [X0] : (~humble(X0) & happy(X0)) <=> ? [X0] : (~strong(X0) <~> ~quiet(X0)) [input p0]
4. ! [X0] : ((~tall(X0) | wise(X0)) <=> (~happy(X0) & wise(X0))) [input p3]
5. ! [X0] : (wise(X0) => (generous(X0) & happy(X0))) [input p4]
10. ! [X0] : ((humble(X0) & generous(X0)) <=> (~wise(X0) <~> wise(X0))) [input p9]
11. ? [X0] : (generous(X0) & ~brave(X0)) <=> (~wise(fred) <~> ~quiet(fred)) [input p10]
12. ! [X0] : ((strong(X0) | ~curious(X0)) <=> (~curious(X0) & patient(X0))) [input p11]
13. ! [X0] : ((~calm(X0) | ~curious(X0)) <=> (~brave(X0) & ~quiet(X0))) [input p12]
21. strong(john) [input hypothesis]
22. ? [X0] : (~humble(X0) & happy(X0)) <=> ? [X1] : (~strong(X1) <~> ~quiet(X1)) [rectify 1]
28. ! [X0] : ((generous(X0) & happy(X0)) | ~wise(X0)) [ennf transformation 5]
37. (? [X0] : (~humble(X0) & happy(X0)) | ! [X1] : ((~strong(X1) | quiet(X1)) & (~quiet(X1) | strong(X1)))) & (? [X1] : ((quiet(X1) | strong(X1)) & (~quiet(X1) | ~strong(X1))) | ! [X0] : (humble(X0) | ~happy(X0))) [nnf transformation 22]
38. (? [X0] : (~humble(X0) & happy(X0)) | ! [X1] : ((~strong(X1) | quiet(X1)) & (~quiet(X1) | strong(X1)))) & (? [X2] : ((quiet(X2) | strong(X2)) & (~quiet(X2) | ~strong(X2))) | ! [X3] : (humble(X3) | ~happy(X3))) [rectify 37]
39. ? [X0] : (~humble(X0) & happy(X0)) => (~humble(sK0) & happy(sK0)) [choice axiom]
40. ? [X2] : ((quiet(X2) | strong(X2)) & (~quiet(X2) | ~strong(X2))) => ((quiet(sK1) | strong(sK1)) & (~quiet(sK1) | ~strong(sK1))) [choice axiom]
41. ((~humble(sK0) & happy(sK0)) | ! [X1] : ((~strong(X1) | quiet(X1)) & (~quiet(X1) | strong(X1)))) & (((quiet(sK1) | strong(sK1)) & (~quiet(sK1) | ~strong(sK1))) | ! [X3] : (humble(X3) | ~happy(X3))) [skolemisation 38,40,39]
42. ! [X0] : (((~tall(X0) | wise(X0)) | (happy(X0) | ~wise(X0))) & ((~happy(X0) & wise(X0)) | (tall(X0) & ~wise(X0)))) [nnf transformation 4]
43. ! [X0] : ((~tall(X0) | wise(X0) | happy(X0) | ~wise(X0)) & ((~happy(X0) & wise(X0)) | (tall(X0) & ~wise(X0)))) [flattening 42]
48. ! [X0] : (((humble(X0) & generous(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | (~humble(X0) | ~generous(X0)))) [nnf transformation 10]
49. ! [X0] : (((humble(X0) & generous(X0)) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ~humble(X0) | ~generous(X0))) [flattening 48]
50. (? [X0] : (generous(X0) & ~brave(X0)) | ((~wise(fred) | quiet(fred)) & (~quiet(fred) | wise(fred)))) & (((quiet(fred) | wise(fred)) & (~quiet(fred) | ~wise(fred))) | ! [X0] : (~generous(X0) | brave(X0))) [nnf transformation 11]
51. (? [X0] : (generous(X0) & ~brave(X0)) | ((~wise(fred) | quiet(fred)) & (~quiet(fred) | wise(fred)))) & (((quiet(fred) | wise(fred)) & (~quiet(fred) | ~wise(fred))) | ! [X1] : (~generous(X1) | brave(X1))) [rectify 50]
52. ? [X0] : (generous(X0) & ~brave(X0)) => (generous(sK2) & ~brave(sK2)) [choice axiom]
53. ((generous(sK2) & ~brave(sK2)) | ((~wise(fred) | quiet(fred)) & (~quiet(fred) | wise(fred)))) & (((quiet(fred) | wise(fred)) & (~quiet(fred) | ~wise(fred))) | ! [X1] : (~generous(X1) | brave(X1))) [skolemisation 51,52]
54. ! [X0] : (((strong(X0) | ~curious(X0)) | (curious(X0) | ~patient(X0))) & ((~curious(X0) & patient(X0)) | (~strong(X0) & curious(X0)))) [nnf transformation 12]
55. ! [X0] : ((strong(X0) | ~curious(X0) | curious(X0) | ~patient(X0)) & ((~curious(X0) & patient(X0)) | (~strong(X0) & curious(X0)))) [flattening 54]
56. ! [X0] : (((~calm(X0) | ~curious(X0)) | (brave(X0) | quiet(X0))) & ((~brave(X0) & ~quiet(X0)) | (calm(X0) & curious(X0)))) [nnf transformation 13]
57. ! [X0] : ((~calm(X0) | ~curious(X0) | brave(X0) | quiet(X0)) & ((~brave(X0) & ~quiet(X0)) | (calm(X0) & curious(X0)))) [flattening 56]
65. ~humble(sK0) | ~quiet(X1) | strong(X1) [cnf transformation 41]
72. ~wise(X0) | ~happy(X0) [cnf transformation 43]
75. happy(X0) | ~wise(X0) [cnf transformation 28]
87. generous(X0) | wise(X0) | wise(X0) [cnf transformation 49]
89. humble(X0) | wise(X0) | wise(X0) [cnf transformation 49]
92. quiet(fred) | wise(fred) | ~generous(X1) | brave(X1) [cnf transformation 53]
100. ~curious(X0) | ~strong(X0) [cnf transformation 55]
102. ~quiet(X0) | curious(X0) [cnf transformation 57]
104. ~brave(X0) | curious(X0) [cnf transformation 57]
116. strong(john) [cnf transformation 21]
117. generous(X0) | wise(X0) [duplicate literal removal 87]
119. humble(X0) | wise(X0) [duplicate literal removal 89]
125. 2 <=> humble(sK0) [avatar definition]
127. ~humble(sK0) <- (~2) [avatar component clause 125]
130. 3 <=> ! [X1] : (~quiet(X1) | strong(X1)) [avatar definition]
131. ~quiet(X1) | strong(X1) <- (3) [avatar component clause 130]
132. 3 | ~2 [avatar split clause 65,125,130]
153. 8 <=> ! [X0] : generous(X0) [avatar definition]
154. generous(X0) <- (8) [avatar component clause 153]
160. ~wise(X0) [subsumption resolution 75,72]
161. humble(X0) [subsumption resolution 119,160]
162. generous(X0) [subsumption resolution 117,160]
163. 8 [avatar split clause 162,153]
166. 10 <=> quiet(fred) [avatar definition]
167. quiet(fred) <- (10) [avatar component clause 166]
180. quiet(fred) | ~generous(X1) | brave(X1) [subsumption resolution 92,160]
182. 13 <=> ! [X1] : (~generous(X1) | brave(X1)) [avatar definition]
183. ~generous(X1) | brave(X1) <- (13) [avatar component clause 182]
184. 13 | 10 [avatar split clause 180,166,182]
212. $false <- (~2) [subsumption resolution 127,161]
213. 2 [avatar contradiction clause 212]
222. curious(fred) <- (10) [resolution 102,167]
224. ~strong(fred) <- (10) [resolution 222,100]
229. strong(fred) <- (3, 10) [resolution 131,167]
231. $false <- (3, 10) [subsumption resolution 229,224]
232. ~3 | ~10 [avatar contradiction clause 231]
233. brave(X1) <- (8, 13) [subsumption resolution 183,154]
239. curious(X1) <- (8, 13) [resolution 233,104]
244. ~strong(X0) <- (8, 13) [resolution 239,100]
256. $false <- (8, 13) [resolution 244,116]
257. ~8 | ~13 [avatar contradiction clause 256]
258. $false [avatar sat refutation 132,163,184,213,232,257]
% SZS output end Proof for 7120147589269965764276668
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not creative is tall or not wise and vice versa.
Everyone who is not happy is either patient or kind and vice versa.
If someone is wise then paul is both not patient and wise and vice versa.
If alice is both not kind and not funny then someone is not creative or funny and vice versa.
Everyone who is both not kind and tall is both generous and not tall and vice versa.
Everyone who is both not generous and rich is either strong or not creative.
If mary is either old or not patient then someone is both curious and not funny and vice versa.
If alice is not happy then alice is creative or humble and vice versa.
If someone is not quiet then mary is both not creative and patient and vice versa.
If someone is funny then someone is quiet or not rich.
Everyone who is both quiet and not strong is either kind or not tall and vice versa.
If someone is not creative then someone is either not brave or not tall.
If alice is not brave then paul is both not brave and not wise and vice versa.
If fred is not quiet or happy then someone is tall.
Everyone who is strong is old.
If paul is both not funny and not tall then john is not strong or not generous.
Someone is either tall or old.
Paul is both happy and not quiet.
Mary is either kind or humble.
Someone is both not quiet and old.
Someone is either not calm or not patient.
John is both not humble and not calm.
Someone is creative.
Someone is not patient or generous. | Paul is not funny. | neutral | (![X]:((brave(X)<~>~creative(X))<=>(tall(X)|~wise(X))))&
(![X]:(~happy(X)<=>(patient(X)<~>kind(X))))&
((?[X]:(wise(X)))<=>((~patient(paul)&wise(paul))))&
(((~kind(alice)&~funny(alice)))<=>(?[X]:((~creative(X)|funny(X)))))&
(![X]:((~kind(X)&tall(X))<=>(generous(X)&~tall(X))))&
(![X]:((~generous(X)&rich(X))=>(strong(X)<~>~creative(X))))&
(((old(mary)<~>~patient(mary)))<=>(?[X]:((curious(X)&~funny(X)))))&
((~happy(alice))<=>((creative(alice)|humble(alice))))&
((?[X]:(~quiet(X)))<=>((~creative(mary)&patient(mary))))&
((?[X]:(funny(X)))=>(?[X]:((quiet(X)|~rich(X)))))&
(![X]:((quiet(X)&~strong(X))<=>(kind(X)<~>~tall(X))))&
((?[X]:(~creative(X)))=>(?[X]:((~brave(X)<~>~tall(X)))))&
((~brave(alice))<=>((~brave(paul)&~wise(paul))))&
(((~quiet(fred)|happy(fred)))=>(?[X]:(tall(X))))&
(![X]:(strong(X)=>old(X)))&
(((~funny(paul)&~tall(paul)))=>((~strong(john)|~generous(john))))&
(?[X]:((tall(X)<~>old(X))))&
((happy(paul)&~quiet(paul)))&
((kind(mary)<~>humble(mary)))&
(?[X]:((~quiet(X)&old(X))))&
(?[X]:((~calm(X)<~>~patient(X))))&
((~humble(john)&~calm(john)))&
(?[X]:(creative(X)))&
(?[X]:((~patient(X)|generous(X)))) | ~funny(paul) | [] | null | 0 |
If alice is either not funny or not happy then someone is not rich and vice versa. If someone is both strong and kind then paul is wise. If fred is both not calm and strong then someone is either not curious or not calm and vice versa. If someone is both not humble and not strong then fred is strong. Everyone who is both humble and brave is not old or not generous and vice versa. If someone is generous or not old then someone is both not patient and happy. Everyone who is not rich or not calm is strong or curious and vice versa. Everyone who is both not kind and not curious is not tall. If john is either creative or brave then mary is both happy and creative and vice versa. Everyone who is either tall or rich is calm and vice versa. If someone is kind or brave then someone is either not calm or not patient and vice versa. If lucy is patient then someone is curious and vice versa. Everyone who is strong is not creative or old and vice versa. Everyone who is both not creative and humble is both old and not calm. Everyone who is not old is not old or not kind and vice versa. Everyone who is not creative or wise is calm or not generous. Someone is not humble. Fred is creative or not creative. Lucy is both wise and not brave. Someone is both not humble and strong. John is either not strong or generous. Fred is not kind or not curious. Paul is curious or not generous. Someone is not funny or not old. | Lucy is tall. | entailment | (((~funny(alice)<~>~happy(alice)))<=>(?[X]:(~rich(X))))&
((?[X]:((strong(X)&kind(X))))=>(wise(paul)))&
(((~calm(fred)&strong(fred)))<=>(?[X]:((~curious(X)<~>~calm(X)))))&
((?[X]:((~humble(X)&~strong(X))))=>(strong(fred)))&
(![X]:((humble(X)&brave(X))<=>(~old(X)|~generous(X))))&
((?[X]:((generous(X)|~old(X))))=>(?[X]:((~patient(X)&happy(X)))))&
(![X]:((~rich(X)|~calm(X))<=>(strong(X)|curious(X))))&
(![X]:((~kind(X)&~curious(X))=>~tall(X)))&
(((creative(john)<~>brave(john)))<=>((happy(mary)&creative(mary))))&
(![X]:((tall(X)<~>rich(X))<=>calm(X)))&
((?[X]:((kind(X)|brave(X))))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
((patient(lucy))<=>(?[X]:(curious(X))))&
(![X]:(strong(X)<=>(~creative(X)|old(X))))&
(![X]:((~creative(X)&humble(X))=>(old(X)&~calm(X))))&
(![X]:(~old(X)<=>(~old(X)|~kind(X))))&
(![X]:((~creative(X)|wise(X))=>(calm(X)|~generous(X))))&
(?[X]:(~humble(X)))&
((creative(fred)|~creative(fred)))&
((wise(lucy)&~brave(lucy)))&
(?[X]:((~humble(X)&strong(X))))&
((~strong(john)<~>generous(john)))&
((~kind(fred)|~curious(fred)))&
((curious(paul)|~generous(paul)))&
(?[X]:((~funny(X)|~old(X)))) | tall(lucy) | [
"p4",
"p6",
"p9",
"p12",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7559378018038776787188554
% SZS output start Proof for 7559378018038776787188554
5. ! [X0] : ((brave(X0) & humble(X0)) <=> (~generous(X0) | ~old(X0))) [input p4]
7. ! [X0] : ((~calm(X0) | ~rich(X0)) <=> (curious(X0) | strong(X0))) [input p6]
10. ! [X0] : ((tall(X0) <~> rich(X0)) <=> calm(X0)) [input p9]
13. ! [X0] : (strong(X0) <=> (old(X0) | ~creative(X0))) [input p12]
16. ! [X0] : ((wise(X0) | ~creative(X0)) => (~generous(X0) | calm(X0))) [input p15]
19. ~brave(lucy) & wise(lucy) [input p18]
25. ~tall(lucy) [input hypothesis]
35. ! [X0] : ((~generous(X0) | calm(X0)) | (~wise(X0) & creative(X0))) [ennf transformation 16]
36. ! [X0] : (~generous(X0) | calm(X0) | (~wise(X0) & creative(X0))) [flattening 35]
46. ! [X0] : (((brave(X0) & humble(X0)) | (generous(X0) & old(X0))) & ((~generous(X0) | ~old(X0)) | (~brave(X0) | ~humble(X0)))) [nnf transformation 5]
47. ! [X0] : (((brave(X0) & humble(X0)) | (generous(X0) & old(X0))) & (~generous(X0) | ~old(X0) | ~brave(X0) | ~humble(X0))) [flattening 46]
51. ! [X0] : (((~calm(X0) | ~rich(X0)) | (~curious(X0) & ~strong(X0))) & ((curious(X0) | strong(X0)) | (calm(X0) & rich(X0)))) [nnf transformation 7]
52. ! [X0] : ((~calm(X0) | ~rich(X0) | (~curious(X0) & ~strong(X0))) & (curious(X0) | strong(X0) | (calm(X0) & rich(X0)))) [flattening 51]
55. ! [X0] : ((((~rich(X0) | ~tall(X0)) & (rich(X0) | tall(X0))) | ~calm(X0)) & (calm(X0) | ((tall(X0) | ~rich(X0)) & (rich(X0) | ~tall(X0))))) [nnf transformation 10]
65. ! [X0] : ((strong(X0) | (~old(X0) & creative(X0))) & ((old(X0) | ~creative(X0)) | ~strong(X0))) [nnf transformation 13]
66. ! [X0] : ((strong(X0) | (~old(X0) & creative(X0))) & (old(X0) | ~creative(X0) | ~strong(X0))) [flattening 65]
91. old(X0) | brave(X0) [cnf transformation 47]
92. generous(X0) | brave(X0) [cnf transformation 47]
99. ~calm(X0) | ~rich(X0) | ~strong(X0) [cnf transformation 52]
110. ~calm(X0) | tall(X0) | rich(X0) [cnf transformation 55]
122. ~old(X0) | strong(X0) [cnf transformation 66]
129. ~generous(X0) | calm(X0) | ~wise(X0) [cnf transformation 36]
132. wise(lucy) [cnf transformation 19]
133. ~brave(lucy) [cnf transformation 19]
141. ~tall(lucy) [cnf transformation 25]
343. brave(X0) | strong(X0) [resolution 122,91]
352. strong(lucy) [resolution 343,133]
423. ~wise(X0) | calm(X0) | brave(X0) [resolution 129,92]
471. calm(lucy) | brave(lucy) [resolution 423,132]
473. calm(lucy) [subsumption resolution 471,133]
478. tall(lucy) | rich(lucy) [resolution 473,110]
479. ~rich(lucy) | ~strong(lucy) [resolution 473,99]
480. rich(lucy) [subsumption resolution 478,141]
481. ~strong(lucy) [subsumption resolution 479,480]
482. $false [subsumption resolution 481,352]
% SZS output end Proof for 7559378018038776787188554
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is not brave or not funny and vice versa. Everyone who is creative is both tall and not generous. If john is brave then lucy is humble. If someone is funny then john is either not rich or happy. Everyone who is strong or old is old or creative. Everyone who is not quiet or happy is both not happy and generous. Everyone who is old is either generous or quiet and vice versa. Everyone who is calm or not happy is not wise. Everyone who is either not old or humble is both not creative and calm and vice versa. If alice is rich or wise then someone is both rich and creative and vice versa. Everyone who is not calm is either tall or rich and vice versa. If fred is both brave and not calm then mary is tall. If mary is either curious or happy then someone is both not patient and not creative and vice versa. Everyone who is tall or not quiet is both quiet and not funny and vice versa. If lucy is happy then someone is not old and vice versa. Everyone who is both not brave and not rich is both not generous and not tall. Fred is either strong or tall. Someone is not curious or not wise. Someone is old or quiet. Someone is either humble or old. Someone is either old or not curious. Someone is either not strong or tall. | Alice is calm. | neutral | (![X]:((~kind(X)|~happy(X))<=>(~brave(X)|~funny(X))))&
(![X]:(creative(X)=>(tall(X)&~generous(X))))&
((brave(john))=>(humble(lucy)))&
((?[X]:(funny(X)))=>((~rich(john)<~>happy(john))))&
(![X]:((strong(X)|old(X))=>(old(X)|creative(X))))&
(![X]:((~quiet(X)|happy(X))=>(~happy(X)&generous(X))))&
(![X]:(old(X)<=>(generous(X)<~>quiet(X))))&
(![X]:((calm(X)|~happy(X))=>~wise(X)))&
(![X]:((~old(X)<~>humble(X))<=>(~creative(X)&calm(X))))&
(((rich(alice)|wise(alice)))<=>(?[X]:((rich(X)&creative(X)))))&
(![X]:(~calm(X)<=>(tall(X)<~>rich(X))))&
(((brave(fred)&~calm(fred)))=>(tall(mary)))&
(((curious(mary)<~>happy(mary)))<=>(?[X]:((~patient(X)&~creative(X)))))&
(![X]:((tall(X)|~quiet(X))<=>(quiet(X)&~funny(X))))&
((happy(lucy))<=>(?[X]:(~old(X))))&
(![X]:((~brave(X)&~rich(X))=>(~generous(X)&~tall(X))))&
((strong(fred)<~>tall(fred)))&
(?[X]:((~curious(X)|~wise(X))))&
(?[X]:((old(X)|quiet(X))))&
(?[X]:((humble(X)<~>old(X))))&
(?[X]:((old(X)<~>~curious(X))))&
(?[X]:((~strong(X)<~>tall(X)))) | calm(alice) | [] | null | 0 |
If susan is both not wise and not tall then someone is either not wise or humble. Everyone who is not calm or tall is either curious or humble and vice versa. If susan is not generous or generous then mary is both not old and not kind and vice versa. If mary is curious then paul is either not curious or not patient. If someone is either not funny or not generous then mary is not brave and vice versa. Everyone who is either happy or rich is both creative and generous and vice versa. Everyone who is kind or not happy is creative or not calm and vice versa. If someone is not quiet then mary is rich and vice versa. Everyone who is not old is either strong or not brave. Everyone who is rich is calm and vice versa. Everyone who is both wise and not creative is brave and vice versa. Everyone who is both not patient and not funny is either old or patient. Everyone who is either not tall or happy is both creative and not happy and vice versa. Everyone who is both not funny and not generous is both not rich and curious. If someone is not generous or brave then someone is not calm or happy. Everyone who is not calm is not curious and vice versa. Mary is either kind or not generous. Someone is both not creative and not funny. Someone is both quiet and curious. Fred is not calm. Paul is both not generous and curious. John is not quiet. John is not rich. Someone is either humble or generous. | Mary is strong. | contradiction | (((~wise(susan)&~tall(susan)))=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:((~calm(X)|tall(X))<=>(curious(X)<~>humble(X))))&
(((~generous(susan)|generous(susan)))<=>((~old(mary)&~kind(mary))))&
((curious(mary))=>((~curious(paul)<~>~patient(paul))))&
((?[X]:((~funny(X)<~>~generous(X))))<=>(~brave(mary)))&
(![X]:((happy(X)<~>rich(X))<=>(creative(X)&generous(X))))&
(![X]:((kind(X)|~happy(X))<=>(creative(X)|~calm(X))))&
((?[X]:(~quiet(X)))<=>(rich(mary)))&
(![X]:(~old(X)=>(strong(X)<~>~brave(X))))&
(![X]:(rich(X)<=>calm(X)))&
(![X]:((wise(X)&~creative(X))<=>brave(X)))&
(![X]:((~patient(X)&~funny(X))=>(old(X)<~>patient(X))))&
(![X]:((~tall(X)<~>happy(X))<=>(creative(X)&~happy(X))))&
(![X]:((~funny(X)&~generous(X))=>(~rich(X)&curious(X))))&
((?[X]:((~generous(X)|brave(X))))=>(?[X]:((~calm(X)|happy(X)))))&
(![X]:(~calm(X)<=>~curious(X)))&
((kind(mary)<~>~generous(mary)))&
(?[X]:((~creative(X)&~funny(X))))&
(?[X]:((quiet(X)&curious(X))))&
(~calm(fred))&
((~generous(paul)&curious(paul)))&
(~quiet(john))&
(~rich(john))&
(?[X]:((humble(X)<~>generous(X)))) | strong(mary) | [
"p2",
"p4",
"p7",
"p8",
"p13",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 170715761056998086902614
% SZS output start Proof for 170715761056998086902614
3. (generous(susan) | ~generous(susan)) <=> (~kind(mary) & ~old(mary)) [input p2]
5. ? [X0] : (~funny(X0) <~> ~generous(X0)) <=> ~brave(mary) [input p4]
8. ? [X0] : ~quiet(X0) <=> rich(mary) [input p7]
9. ! [X0] : (~old(X0) => (strong(X0) <~> ~brave(X0))) [input p8]
14. ! [X0] : ((~generous(X0) & ~funny(X0)) => (curious(X0) & ~rich(X0))) [input p13]
17. kind(mary) <~> ~generous(mary) [input p16]
22. ~quiet(john) [input p21]
25. strong(mary) [input hypothesis]
30. ! [X0] : ((strong(X0) <~> ~brave(X0)) | old(X0)) [ennf transformation 9]
33. ! [X0] : ((curious(X0) & ~rich(X0)) | (generous(X0) | funny(X0))) [ennf transformation 14]
34. ! [X0] : ((curious(X0) & ~rich(X0)) | generous(X0) | funny(X0)) [flattening 33]
41. ((generous(susan) | ~generous(susan)) | (kind(mary) | old(mary))) & ((~kind(mary) & ~old(mary)) | (~generous(susan) & generous(susan))) [nnf transformation 3]
42. (generous(susan) | ~generous(susan) | kind(mary) | old(mary)) & ((~kind(mary) & ~old(mary)) | (~generous(susan) & generous(susan))) [flattening 41]
44. (? [X0] : ((generous(X0) | funny(X0)) & (~generous(X0) | ~funny(X0))) | brave(mary)) & (~brave(mary) | ! [X0] : ((~funny(X0) | generous(X0)) & (~generous(X0) | funny(X0)))) [nnf transformation 5]
45. (? [X0] : ((generous(X0) | funny(X0)) & (~generous(X0) | ~funny(X0))) | brave(mary)) & (~brave(mary) | ! [X1] : ((~funny(X1) | generous(X1)) & (~generous(X1) | funny(X1)))) [rectify 44]
46. ? [X0] : ((generous(X0) | funny(X0)) & (~generous(X0) | ~funny(X0))) => ((generous(sK1) | funny(sK1)) & (~generous(sK1) | ~funny(sK1))) [choice axiom]
47. (((generous(sK1) | funny(sK1)) & (~generous(sK1) | ~funny(sK1))) | brave(mary)) & (~brave(mary) | ! [X1] : ((~funny(X1) | generous(X1)) & (~generous(X1) | funny(X1)))) [skolemisation 45,46]
52. (? [X0] : ~quiet(X0) | ~rich(mary)) & (rich(mary) | ! [X0] : quiet(X0)) [nnf transformation 8]
53. (? [X0] : ~quiet(X0) | ~rich(mary)) & (rich(mary) | ! [X1] : quiet(X1)) [rectify 52]
54. ? [X0] : ~quiet(X0) => ~quiet(sK2) [choice axiom]
55. (~quiet(sK2) | ~rich(mary)) & (rich(mary) | ! [X1] : quiet(X1)) [skolemisation 53,54]
56. ! [X0] : (((brave(X0) | ~strong(X0)) & (~brave(X0) | strong(X0))) | old(X0)) [nnf transformation 30]
67. (generous(mary) | ~kind(mary)) & (~generous(mary) | kind(mary)) [nnf transformation 17]
83. ~old(mary) | generous(susan) [cnf transformation 42]
84. ~old(mary) | ~generous(susan) [cnf transformation 42]
85. ~kind(mary) | generous(susan) [cnf transformation 42]
86. ~kind(mary) | ~generous(susan) [cnf transformation 42]
91. ~brave(mary) | ~funny(X1) | generous(X1) [cnf transformation 47]
104. rich(mary) | quiet(X1) [cnf transformation 55]
107. ~strong(X0) | brave(X0) | old(X0) [cnf transformation 56]
121. ~rich(X0) | generous(X0) | funny(X0) [cnf transformation 34]
127. ~generous(mary) | kind(mary) [cnf transformation 67]
136. ~quiet(john) [cnf transformation 22]
140. strong(mary) [cnf transformation 25]
163. 5 <=> generous(susan) [avatar definition]
167. 6 <=> kind(mary) [avatar definition]
170. ~5 | ~6 [avatar split clause 86,167,163]
171. 5 | ~6 [avatar split clause 85,167,163]
173. 7 <=> old(mary) [avatar definition]
175. ~old(mary) <- (~7) [avatar component clause 173]
176. ~5 | ~7 [avatar split clause 84,173,163]
177. 5 | ~7 [avatar split clause 83,173,163]
193. 11 <=> brave(mary) [avatar definition]
207. 14 <=> ! [X1] : (~funny(X1) | generous(X1)) [avatar definition]
208. ~funny(X1) | generous(X1) <- (14) [avatar component clause 207]
209. 14 | ~11 [avatar split clause 91,193,207]
215. 16 <=> rich(mary) [avatar definition]
216. rich(mary) <- (16) [avatar component clause 215]
224. 18 <=> ! [X1] : quiet(X1) [avatar definition]
225. quiet(X1) <- (18) [avatar component clause 224]
226. 18 | 16 [avatar split clause 104,215,224]
244. 23 <=> generous(mary) [avatar definition]
245. ~generous(mary) <- (~23) [avatar component clause 244]
248. 6 | ~23 [avatar split clause 127,244,167]
348. $false <- (18) [resolution 225,136]
351. ~18 [avatar contradiction clause 348]
384. brave(mary) | old(mary) [resolution 107,140]
388. brave(mary) <- (~7) [subsumption resolution 384,175]
389. 11 | 7 [avatar split clause 388,173,193]
416. generous(mary) | funny(mary) <- (16) [resolution 121,216]
419. funny(mary) <- (16, ~23) [subsumption resolution 416,245]
434. generous(mary) <- (14, 16, ~23) [resolution 419,208]
435. $false <- (14, 16, ~23) [subsumption resolution 434,245]
436. ~14 | ~16 | 23 [avatar contradiction clause 435]
437. $false [avatar sat refutation 170,171,176,177,209,226,248,351,389,436]
% SZS output end Proof for 170715761056998086902614
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and rich is not old and vice versa.
If someone is generous or tall then lucy is either old or not strong.
If someone is either tall or funny then someone is either quiet or creative and vice versa.
Everyone who is either not humble or old is either not tall or not strong and vice versa.
If fred is not wise or old then someone is not brave and vice versa.
Everyone who is wise or not funny is generous or not calm and vice versa.
If lucy is not rich or generous then lucy is kind and vice versa.
Everyone who is both not rich and not calm is not strong or tall.
If john is not wise or not brave then someone is creative or not happy and vice versa.
Everyone who is not brave is quiet or not wise.
Everyone who is quiet is either not brave or brave and vice versa.
Everyone who is either generous or not humble is either not tall or kind.
Everyone who is both tall and not kind is both not rich and calm.
Everyone who is either not calm or not brave is either quiet or not generous and vice versa.
Everyone who is rich is either not tall or not old and vice versa.
Everyone who is not old is funny or curious and vice versa.
Paul is curious or not tall.
Alice is wise or not patient.
Someone is not humble or rich.
Someone is not kind.
Mary is brave.
Someone is quiet.
Someone is both generous and not strong.
Someone is either humble or not patient. | Paul is rich. | entailment | (![X]:((tall(X)&rich(X))<=>~old(X)))&
((?[X]:((generous(X)|tall(X))))=>((old(lucy)<~>~strong(lucy))))&
((?[X]:((tall(X)<~>funny(X))))<=>(?[X]:((quiet(X)<~>creative(X)))))&
(![X]:((~humble(X)<~>old(X))<=>(~tall(X)<~>~strong(X))))&
(((~wise(fred)|old(fred)))<=>(?[X]:(~brave(X))))&
(![X]:((wise(X)|~funny(X))<=>(generous(X)|~calm(X))))&
(((~rich(lucy)|generous(lucy)))<=>(kind(lucy)))&
(![X]:((~rich(X)&~calm(X))=>(~strong(X)|tall(X))))&
(((~wise(john)|~brave(john)))<=>(?[X]:((creative(X)|~happy(X)))))&
(![X]:(~brave(X)=>(quiet(X)|~wise(X))))&
(![X]:(quiet(X)<=>(~brave(X)<~>brave(X))))&
(![X]:((generous(X)<~>~humble(X))=>(~tall(X)<~>kind(X))))&
(![X]:((tall(X)&~kind(X))=>(~rich(X)&calm(X))))&
(![X]:((~calm(X)<~>~brave(X))<=>(quiet(X)<~>~generous(X))))&
(![X]:(rich(X)<=>(~tall(X)<~>~old(X))))&
(![X]:(~old(X)<=>(funny(X)|curious(X))))&
((curious(paul)|~tall(paul)))&
((wise(alice)|~patient(alice)))&
(?[X]:((~humble(X)|rich(X))))&
(?[X]:(~kind(X)))&
(brave(mary))&
(?[X]:(quiet(X)))&
(?[X]:((generous(X)&~strong(X))))&
(?[X]:((humble(X)<~>~patient(X)))) | rich(paul) | [
"p0",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2039177920642724286129003
% SZS output start Proof for 2039177920642724286129003
1. ! [X0] : ((rich(X0) & tall(X0)) <=> ~old(X0)) [input p0]
15. ! [X0] : (rich(X0) <=> (~tall(X0) <~> ~old(X0))) [input p14]
16. ! [X0] : (~old(X0) <=> (curious(X0) | funny(X0))) [input p15]
17. ~tall(paul) | curious(paul) [input p16]
25. ~rich(paul) [input hypothesis]
35. ! [X0] : (((rich(X0) & tall(X0)) | old(X0)) & (~old(X0) | (~rich(X0) | ~tall(X0)))) [nnf transformation 1]
36. ! [X0] : (((rich(X0) & tall(X0)) | old(X0)) & (~old(X0) | ~rich(X0) | ~tall(X0))) [flattening 35]
61. ! [X0] : ((rich(X0) | ((~tall(X0) | old(X0)) & (~old(X0) | tall(X0)))) & (((old(X0) | tall(X0)) & (~old(X0) | ~tall(X0))) | ~rich(X0))) [nnf transformation 15]
62. ! [X0] : ((~old(X0) | (~curious(X0) & ~funny(X0))) & ((curious(X0) | funny(X0)) | old(X0))) [nnf transformation 16]
63. ! [X0] : ((~old(X0) | (~curious(X0) & ~funny(X0))) & (curious(X0) | funny(X0) | old(X0))) [flattening 62]
76. old(X0) | tall(X0) [cnf transformation 36]
77. old(X0) | rich(X0) [cnf transformation 36]
134. rich(X0) | ~old(X0) | tall(X0) [cnf transformation 61]
138. ~curious(X0) | ~old(X0) [cnf transformation 63]
139. ~tall(paul) | curious(paul) [cnf transformation 17]
149. ~rich(paul) [cnf transformation 25]
274. rich(X0) | tall(X0) [subsumption resolution 134,76]
276. 26 <=> curious(paul) [avatar definition]
278. curious(paul) <- (26) [avatar component clause 276]
280. 27 <=> tall(paul) [avatar definition]
283. 26 | ~27 [avatar split clause 139,280,276]
318. tall(paul) [resolution 274,149]
321. 27 [avatar split clause 318,280]
322. ~old(paul) <- (26) [resolution 278,138]
323. rich(paul) <- (26) [resolution 322,77]
325. $false <- (26) [subsumption resolution 323,149]
326. ~26 [avatar contradiction clause 325]
327. $false [avatar sat refutation 283,321,326]
% SZS output end Proof for 2039177920642724286129003
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or calm is either not calm or quiet and vice versa.
If alice is both not brave and old then john is kind.
If john is either happy or not happy then someone is both quiet and not creative.
Everyone who is both funny and creative is both wise and not calm.
If someone is rich then lucy is either humble or happy.
Everyone who is both generous and not tall is not wise or not strong.
If fred is both not tall and not creative then someone is either creative or not calm.
Everyone who is quiet is patient or calm.
If susan is not humble then someone is either brave or calm and vice versa.
Everyone who is both wise and not tall is either creative or not curious and vice versa.
If someone is kind or not kind then alice is either not quiet or kind and vice versa.
If john is both not calm and not happy then someone is curious or not generous and vice versa.
Everyone who is both not patient and not rich is either kind or creative and vice versa.
Everyone who is both kind and wise is either not happy or not brave.
If paul is either wise or old then lucy is generous or creative.
If john is both not curious and not brave then mary is either wise or not tall and vice versa.
Someone is not happy.
John is both not curious and humble.
Someone is both brave and curious.
Someone is both not creative and generous.
Someone is both not calm and not happy.
Someone is either not generous or old.
Paul is either not happy or not tall.
Someone is creative. | John is calm. | contradiction | (![X]:((brave(X)|calm(X))<=>(~calm(X)<~>quiet(X))))&
(((~brave(alice)&old(alice)))=>(kind(john)))&
(((happy(john)<~>~happy(john)))=>(?[X]:((quiet(X)&~creative(X)))))&
(![X]:((funny(X)&creative(X))=>(wise(X)&~calm(X))))&
((?[X]:(rich(X)))=>((humble(lucy)<~>happy(lucy))))&
(![X]:((generous(X)&~tall(X))=>(~wise(X)|~strong(X))))&
(((~tall(fred)&~creative(fred)))=>(?[X]:((creative(X)<~>~calm(X)))))&
(![X]:(quiet(X)=>(patient(X)|calm(X))))&
((~humble(susan))<=>(?[X]:((brave(X)<~>calm(X)))))&
(![X]:((wise(X)&~tall(X))<=>(creative(X)<~>~curious(X))))&
((?[X]:((kind(X)|~kind(X))))<=>((~quiet(alice)<~>kind(alice))))&
(((~calm(john)&~happy(john)))<=>(?[X]:((curious(X)|~generous(X)))))&
(![X]:((~patient(X)&~rich(X))<=>(kind(X)<~>creative(X))))&
(![X]:((kind(X)&wise(X))=>(~happy(X)<~>~brave(X))))&
(((wise(paul)<~>old(paul)))=>((generous(lucy)|creative(lucy))))&
(((~curious(john)&~brave(john)))<=>((wise(mary)<~>~tall(mary))))&
(?[X]:(~happy(X)))&
((~curious(john)&humble(john)))&
(?[X]:((brave(X)&curious(X))))&
(?[X]:((~creative(X)&generous(X))))&
(?[X]:((~calm(X)&~happy(X))))&
(?[X]:((~generous(X)<~>old(X))))&
((~happy(paul)<~>~tall(paul)))&
(?[X]:(creative(X))) | calm(john) | [
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1996950530337407454636139
% SZS output start Proof for 1996950530337407454636139
12. (~happy(john) & ~calm(john)) <=> ? [X0] : (~generous(X0) | curious(X0)) [input p11]
19. ? [X0] : (curious(X0) & brave(X0)) [input p18]
25. calm(john) [input hypothesis]
59. ((~happy(john) & ~calm(john)) | ! [X0] : (generous(X0) & ~curious(X0))) & (? [X0] : (~generous(X0) | curious(X0)) | (happy(john) | calm(john))) [nnf transformation 12]
60. ((~happy(john) & ~calm(john)) | ! [X0] : (generous(X0) & ~curious(X0))) & (? [X0] : (~generous(X0) | curious(X0)) | happy(john) | calm(john)) [flattening 59]
61. ((~happy(john) & ~calm(john)) | ! [X0] : (generous(X0) & ~curious(X0))) & (? [X1] : (~generous(X1) | curious(X1)) | happy(john) | calm(john)) [rectify 60]
62. ? [X1] : (~generous(X1) | curious(X1)) => (~generous(sK4) | curious(sK4)) [choice axiom]
63. ((~happy(john) & ~calm(john)) | ! [X0] : (generous(X0) & ~curious(X0))) & ((~generous(sK4) | curious(sK4)) | happy(john) | calm(john)) [skolemisation 61,62]
72. ? [X0] : (curious(X0) & brave(X0)) => (curious(sK6) & brave(sK6)) [choice axiom]
73. curious(sK6) & brave(sK6) [skolemisation 19,72]
117. ~calm(john) | ~curious(X0) [cnf transformation 63]
141. curious(sK6) [cnf transformation 73]
151. calm(john) [cnf transformation 25]
263. 24 <=> ! [X0] : ~curious(X0) [avatar definition]
264. ~curious(X0) <- (24) [avatar component clause 263]
267. 25 <=> calm(john) [avatar definition]
271. 24 | ~25 [avatar split clause 117,267,263]
342. 25 [avatar split clause 151,267]
343. $false <- (24) [resolution 264,141]
344. ~24 [avatar contradiction clause 343]
345. $false [avatar sat refutation 271,342,344]
% SZS output end Proof for 1996950530337407454636139
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is creative and vice versa.
If someone is both wise and not patient then someone is not quiet or not brave and vice versa.
If john is tall or not funny then alice is wise or not creative and vice versa.
If someone is both funny and wise then alice is either not patient or not wise.
Everyone who is not brave or not old is not calm and vice versa.
Everyone who is either not tall or curious is both strong and not creative and vice versa.
If fred is not funny then paul is not old.
If fred is either rich or humble then someone is strong or rich.
Everyone who is either quiet or calm is kind and vice versa.
Everyone who is both curious and not patient is tall.
Everyone who is both not generous and not rich is both calm and not creative and vice versa.
Everyone who is either wise or humble is both not curious and not wise and vice versa.
If paul is either not happy or not quiet then someone is patient and vice versa.
Everyone who is not calm is either not happy or not wise and vice versa.
Everyone who is not tall or not humble is both strong and generous and vice versa.
If mary is either quiet or not brave then paul is rich.
Someone is not kind or not curious.
Mary is not tall.
Lucy is either not funny or quiet.
Someone is not creative or not funny.
Someone is old or brave.
Susan is not strong or not kind.
Someone is not old or generous. | Mary is calm. | contradiction | (![X]:(~strong(X)<=>creative(X)))&
((?[X]:((wise(X)&~patient(X))))<=>(?[X]:((~quiet(X)|~brave(X)))))&
(((tall(john)|~funny(john)))<=>((wise(alice)|~creative(alice))))&
((?[X]:((funny(X)&wise(X))))=>((~patient(alice)<~>~wise(alice))))&
(![X]:((~brave(X)|~old(X))<=>~calm(X)))&
(![X]:((~tall(X)<~>curious(X))<=>(strong(X)&~creative(X))))&
((~funny(fred))=>(~old(paul)))&
(((rich(fred)<~>humble(fred)))=>(?[X]:((strong(X)|rich(X)))))&
(![X]:((quiet(X)<~>calm(X))<=>kind(X)))&
(![X]:((curious(X)&~patient(X))=>tall(X)))&
(![X]:((~generous(X)&~rich(X))<=>(calm(X)&~creative(X))))&
(![X]:((wise(X)<~>humble(X))<=>(~curious(X)&~wise(X))))&
(((~happy(paul)<~>~quiet(paul)))<=>(?[X]:(patient(X))))&
(![X]:(~calm(X)<=>(~happy(X)<~>~wise(X))))&
(![X]:((~tall(X)|~humble(X))<=>(strong(X)&generous(X))))&
(((quiet(mary)<~>~brave(mary)))=>(rich(paul)))&
(?[X]:((~kind(X)|~curious(X))))&
(~tall(mary))&
((~funny(lucy)<~>quiet(lucy)))&
(?[X]:((~creative(X)|~funny(X))))&
(?[X]:((old(X)|brave(X))))&
((~strong(susan)|~kind(susan)))&
(?[X]:((~old(X)|generous(X)))) | calm(mary) | [
"p0",
"p10",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8555815298180995207843309
% SZS output start Proof for 8555815298180995207843309
1. ! [X0] : (~strong(X0) <=> creative(X0)) [input p0]
11. ! [X0] : ((~rich(X0) & ~generous(X0)) <=> (~creative(X0) & calm(X0))) [input p10]
15. ! [X0] : ((~humble(X0) | ~tall(X0)) <=> (generous(X0) & strong(X0))) [input p14]
18. ~tall(mary) [input p17]
24. calm(mary) [input hypothesis]
34. ! [X0] : ((~strong(X0) | ~creative(X0)) & (creative(X0) | strong(X0))) [nnf transformation 1]
51. ! [X0] : (((~rich(X0) & ~generous(X0)) | (creative(X0) | ~calm(X0))) & ((~creative(X0) & calm(X0)) | (rich(X0) | generous(X0)))) [nnf transformation 11]
52. ! [X0] : (((~rich(X0) & ~generous(X0)) | creative(X0) | ~calm(X0)) & ((~creative(X0) & calm(X0)) | rich(X0) | generous(X0))) [flattening 51]
60. ! [X0] : (((~humble(X0) | ~tall(X0)) | (~generous(X0) | ~strong(X0))) & ((generous(X0) & strong(X0)) | (humble(X0) & tall(X0)))) [nnf transformation 15]
61. ! [X0] : ((~humble(X0) | ~tall(X0) | ~generous(X0) | ~strong(X0)) & ((generous(X0) & strong(X0)) | (humble(X0) & tall(X0)))) [flattening 60]
73. ~creative(X0) | ~strong(X0) [cnf transformation 34]
102. ~generous(X0) | creative(X0) | ~calm(X0) [cnf transformation 52]
118. tall(X0) | strong(X0) [cnf transformation 61]
120. generous(X0) | tall(X0) [cnf transformation 61]
126. ~tall(mary) [cnf transformation 18]
133. calm(mary) [cnf transformation 24]
315. strong(mary) [resolution 118,126]
338. ~calm(X2) | creative(X2) | tall(X2) [resolution 102,120]
418. 50 <=> creative(mary) [avatar definition]
420. creative(mary) <- (50) [avatar component clause 418]
422. creative(mary) | tall(mary) [resolution 338,133]
423. creative(mary) [subsumption resolution 422,126]
424. 50 [avatar split clause 423,418]
431. ~strong(mary) <- (50) [resolution 420,73]
444. $false <- (50) [subsumption resolution 431,315]
445. ~50 [avatar contradiction clause 444]
446. $false [avatar sat refutation 424,445]
% SZS output end Proof for 8555815298180995207843309
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is both not curious and not happy then someone is not funny and vice versa.
Everyone who is brave or not humble is either not tall or not rich and vice versa.
If someone is not funny or old then john is both patient and not old.
Everyone who is not happy or brave is not generous.
If someone is creative or strong then susan is either not wise or not generous.
Everyone who is tall is creative and vice versa.
Everyone who is not happy or not humble is not brave or strong and vice versa.
If paul is not brave or creative then susan is calm and vice versa.
Everyone who is funny or not rich is both rich and not happy.
Everyone who is wise is both not generous and 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.
Paul is either not wise or not happy.
Susan is kind.
Alice is either happy or brave.
Paul is both calm and patient.
Someone is not funny or not old.
John is humble.
Someone is both not creative and not generous. | Paul is brave. | entailment | ((?[X]:((~curious(X)&~happy(X))))<=>(?[X]:(~funny(X))))&
(![X]:((brave(X)|~humble(X))<=>(~tall(X)<~>~rich(X))))&
((?[X]:((~funny(X)|old(X))))=>((patient(john)&~old(john))))&
(![X]:((~happy(X)|brave(X))=>~generous(X)))&
((?[X]:((creative(X)|strong(X))))=>((~wise(susan)<~>~generous(susan))))&
(![X]:(tall(X)<=>creative(X)))&
(![X]:((~happy(X)|~humble(X))<=>(~brave(X)|strong(X))))&
(((~brave(paul)|creative(paul)))<=>(calm(susan)))&
(![X]:((funny(X)|~rich(X))=>(rich(X)&~happy(X))))&
(![X]:(wise(X)<=>(~generous(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)))))&
((~wise(paul)<~>~happy(paul)))&
(kind(susan))&
((happy(alice)<~>brave(alice)))&
((calm(paul)&patient(paul)))&
(?[X]:((~funny(X)|~old(X))))&
(humble(john))&
(?[X]:((~creative(X)&~generous(X)))) | brave(paul) | [
"p8",
"p9",
"p11",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2909000991425773074234184
% SZS output start Proof for 2909000991425773074234184
9. ! [X0] : ((~rich(X0) | funny(X0)) => (~happy(X0) & rich(X0))) [input p8]
10. ! [X0] : (wise(X0) <=> (~rich(X0) & ~generous(X0))) [input p9]
12. ! [X0] : ((funny(X0) <~> ~patient(X0)) <=> ~brave(X0)) [input p11]
17. ~wise(paul) <~> ~happy(paul) [input p16]
20. patient(paul) & calm(paul) [input p19]
24. ~brave(paul) [input hypothesis]
33. ! [X0] : ((~happy(X0) & rich(X0)) | (rich(X0) & ~funny(X0))) [ennf transformation 9]
51. ! [X0] : ((wise(X0) | (rich(X0) | generous(X0))) & ((~rich(X0) & ~generous(X0)) | ~wise(X0))) [nnf transformation 10]
52. ! [X0] : ((wise(X0) | rich(X0) | generous(X0)) & ((~rich(X0) & ~generous(X0)) | ~wise(X0))) [flattening 51]
53. ! [X0] : ((((patient(X0) | ~funny(X0)) & (~patient(X0) | funny(X0))) | brave(X0)) & (~brave(X0) | ((funny(X0) | patient(X0)) & (~patient(X0) | ~funny(X0))))) [nnf transformation 12]
61. (happy(paul) | wise(paul)) & (~happy(paul) | ~wise(paul)) [nnf transformation 17]
91. rich(X0) | rich(X0) [cnf transformation 33]
92. ~funny(X0) | ~happy(X0) [cnf transformation 33]
95. ~rich(X0) | ~wise(X0) [cnf transformation 52]
100. ~patient(X0) | funny(X0) | brave(X0) [cnf transformation 53]
122. happy(paul) | wise(paul) [cnf transformation 61]
127. patient(paul) [cnf transformation 20]
131. ~brave(paul) [cnf transformation 24]
136. rich(X0) [duplicate literal removal 91]
186. 12 <=> brave(paul) [avatar definition]
188. ~brave(paul) <- (~12) [avatar component clause 186]
196. ~wise(X0) [subsumption resolution 95,136]
237. happy(paul) [subsumption resolution 122,196]
248. ~12 [avatar split clause 131,186]
301. funny(paul) | brave(paul) [resolution 100,127]
304. funny(paul) <- (~12) [subsumption resolution 301,188]
329. ~happy(paul) <- (~12) [resolution 304,92]
330. $false <- (~12) [subsumption resolution 329,237]
331. 12 [avatar contradiction clause 330]
332. $false [avatar sat refutation 248,331]
% SZS output end Proof for 2909000991425773074234184
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is both quiet and not humble and vice versa.
Everyone who is both humble and patient is not patient.
Everyone who is kind is curious or not generous and vice versa.
Everyone who is not patient or not strong is either not curious or not humble.
Everyone who is old is curious and vice versa.
If susan is curious or tall then someone is either not humble or not generous and vice versa.
If someone is wise or humble then mary is both not old and funny and vice versa.
If mary is either calm or tall then john is both not strong and not kind.
If someone is kind then paul is either happy or wise and vice versa.
Everyone who is not generous is old.
Everyone who is both strong and creative is both not calm and patient and vice versa.
If someone is both not calm and not brave then someone is either not curious or generous.
If mary is quiet then someone is both not tall and not creative.
Everyone who is not humble is brave.
If mary is both not rich and not calm then someone is happy or not quiet and vice versa.
If mary is either wise or not happy then someone is either strong or not funny.
John is both old and not calm.
Alice is either not calm or curious.
Fred is not quiet.
Paul is tall.
Alice is not funny.
Paul is both not wise and not strong.
Someone is either humble or quiet.
Fred is old or not calm. | Susan is humble. | contradiction | (![X]:(generous(X)<=>(quiet(X)&~humble(X))))&
(![X]:((humble(X)&patient(X))=>~patient(X)))&
(![X]:(kind(X)<=>(curious(X)|~generous(X))))&
(![X]:((~patient(X)|~strong(X))=>(~curious(X)<~>~humble(X))))&
(![X]:(old(X)<=>curious(X)))&
(((curious(susan)|tall(susan)))<=>(?[X]:((~humble(X)<~>~generous(X)))))&
((?[X]:((wise(X)|humble(X))))<=>((~old(mary)&funny(mary))))&
(((calm(mary)<~>tall(mary)))=>((~strong(john)&~kind(john))))&
((?[X]:(kind(X)))<=>((happy(paul)<~>wise(paul))))&
(![X]:(~generous(X)=>old(X)))&
(![X]:((strong(X)&creative(X))<=>(~calm(X)&patient(X))))&
((?[X]:((~calm(X)&~brave(X))))=>(?[X]:((~curious(X)<~>generous(X)))))&
((quiet(mary))=>(?[X]:((~tall(X)&~creative(X)))))&
(![X]:(~humble(X)=>brave(X)))&
(((~rich(mary)&~calm(mary)))<=>(?[X]:((happy(X)|~quiet(X)))))&
(((wise(mary)<~>~happy(mary)))=>(?[X]:((strong(X)<~>~funny(X)))))&
((old(john)&~calm(john)))&
((~calm(alice)<~>curious(alice)))&
(~quiet(fred))&
(tall(paul))&
(~funny(alice))&
((~wise(paul)&~strong(paul)))&
(?[X]:((humble(X)<~>quiet(X))))&
((old(fred)|~calm(fred))) | humble(susan) | [
"p0",
"p1",
"p3",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8874785928049701040351731
% SZS output start Proof for 8874785928049701040351731
1. ! [X0] : (generous(X0) <=> (~humble(X0) & quiet(X0))) [input p0]
2. ! [X0] : ((patient(X0) & humble(X0)) => ~patient(X0)) [input p1]
4. ! [X0] : ((~strong(X0) | ~patient(X0)) => (~curious(X0) <~> ~humble(X0))) [input p3]
5. ! [X0] : (old(X0) <=> curious(X0)) [input p4]
10. ! [X0] : (~generous(X0) => old(X0)) [input p9]
25. humble(susan) [input hypothesis]
29. ! [X0] : (~patient(X0) | (~patient(X0) | ~humble(X0))) [ennf transformation 2]
30. ! [X0] : (~patient(X0) | ~patient(X0) | ~humble(X0)) [flattening 29]
31. ! [X0] : ((~curious(X0) <~> ~humble(X0)) | (strong(X0) & patient(X0))) [ennf transformation 4]
33. ! [X0] : (old(X0) | generous(X0)) [ennf transformation 10]
36. ! [X0] : ((generous(X0) | (humble(X0) | ~quiet(X0))) & ((~humble(X0) & quiet(X0)) | ~generous(X0))) [nnf transformation 1]
37. ! [X0] : ((generous(X0) | humble(X0) | ~quiet(X0)) & ((~humble(X0) & quiet(X0)) | ~generous(X0))) [flattening 36]
40. ! [X0] : (((humble(X0) | curious(X0)) & (~humble(X0) | ~curious(X0))) | (strong(X0) & patient(X0))) [nnf transformation 31]
41. ! [X0] : ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0))) [nnf transformation 5]
74. ~humble(X0) | ~generous(X0) [cnf transformation 37]
76. ~patient(X0) | ~patient(X0) | ~humble(X0) [cnf transformation 30]
80. ~humble(X0) | ~curious(X0) | patient(X0) [cnf transformation 40]
84. ~old(X0) | curious(X0) [cnf transformation 41]
105. old(X0) | generous(X0) [cnf transformation 33]
133. humble(susan) [cnf transformation 25]
134. ~patient(X0) | ~humble(X0) [duplicate literal removal 76]
135. ~curious(X0) | ~humble(X0) [subsumption resolution 80,134]
138. 1 <=> ! [X0] : ~humble(X0) [avatar definition]
139. ~humble(X0) <- (1) [avatar component clause 138]
323. curious(X0) | generous(X0) [resolution 105,84]
331. generous(X0) | ~humble(X0) [resolution 323,135]
334. ~humble(X0) [subsumption resolution 331,74]
335. 1 [avatar split clause 334,138]
336. $false <- (1) [resolution 139,133]
341. ~1 [avatar contradiction clause 336]
342. $false [avatar sat refutation 335,341]
% SZS output end Proof for 8874785928049701040351731
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not creative then someone is quiet or not rich. Everyone who is both not strong and creative is both not funny and not happy. If someone is not quiet or creative then john is patient and vice versa. Everyone who is not rich is wise. Everyone who is either not funny or not strong is not wise. Everyone who is not quiet is either not wise or patient. Everyone who is not rich is funny and vice versa. Everyone who is either brave or generous is not brave or not kind and vice versa. If someone is either patient or not patient then mary is kind and vice versa. If mary is not curious or not calm then paul is funny and vice versa. Everyone who is both strong and rich is either wise or brave and vice versa. Everyone who is not calm or not patient is not creative and vice versa. If someone is either patient or creative then susan is either not old or not quiet. If mary is quiet then lucy is not kind. If someone is not curious or not strong then lucy is either quiet or not curious. If john is not strong or not quiet then someone is patient and vice versa. Someone is either not brave or happy. Susan is brave or not patient. Lucy is not funny or kind. Mary is funny. Someone is either creative or funny. Someone is happy. John is brave. Someone is not old. | Lucy is calm. | neutral | ((?[X]:((~rich(X)|~creative(X))))=>(?[X]:((quiet(X)|~rich(X)))))&
(![X]:((~strong(X)&creative(X))=>(~funny(X)&~happy(X))))&
((?[X]:((~quiet(X)|creative(X))))<=>(patient(john)))&
(![X]:(~rich(X)=>wise(X)))&
(![X]:((~funny(X)<~>~strong(X))=>~wise(X)))&
(![X]:(~quiet(X)=>(~wise(X)<~>patient(X))))&
(![X]:(~rich(X)<=>funny(X)))&
(![X]:((brave(X)<~>generous(X))<=>(~brave(X)|~kind(X))))&
((?[X]:((patient(X)<~>~patient(X))))<=>(kind(mary)))&
(((~curious(mary)|~calm(mary)))<=>(funny(paul)))&
(![X]:((strong(X)&rich(X))<=>(wise(X)<~>brave(X))))&
(![X]:((~calm(X)|~patient(X))<=>~creative(X)))&
((?[X]:((patient(X)<~>creative(X))))=>((~old(susan)<~>~quiet(susan))))&
((quiet(mary))=>(~kind(lucy)))&
((?[X]:((~curious(X)|~strong(X))))=>((quiet(lucy)<~>~curious(lucy))))&
(((~strong(john)|~quiet(john)))<=>(?[X]:(patient(X))))&
(?[X]:((~brave(X)<~>happy(X))))&
((brave(susan)|~patient(susan)))&
((~funny(lucy)|kind(lucy)))&
(funny(mary))&
(?[X]:((creative(X)<~>funny(X))))&
(?[X]:(happy(X)))&
(brave(john))&
(?[X]:(~old(X))) | calm(lucy) | [] | null | 0 |
Everyone who is old or wise is not tall or happy. Everyone who is generous or not patient is both not brave and old. Everyone who is either not funny or not brave is not brave or wise and vice versa. Everyone who is funny is rich or not tall and vice versa. Everyone who is wise is not strong and vice versa. Everyone who is either strong or rich is both not rich and not curious and vice versa. If mary is both not calm and creative then susan is brave or curious and vice versa. Everyone who is either not tall or generous is not generous or creative. Everyone who is either not humble or funny is strong. Everyone who is either brave or generous is both brave and quiet. Everyone who is funny is either humble or tall. If mary is either not kind or not creative then john is both not creative and not generous and vice versa. Everyone who is both curious and happy is strong or not brave and vice versa. If someone is both not funny and curious then lucy is both not creative and not happy and vice versa. Everyone who is not curious or brave is not patient or not generous. Mary is not generous. Mary is either patient or funny. Someone is old or strong. John is both not generous and quiet. Alice is calm or not creative. Someone is both creative and strong. | Susan is not calm. | neutral | (![X]:((old(X)|wise(X))=>(~tall(X)|happy(X))))&
(![X]:((generous(X)|~patient(X))=>(~brave(X)&old(X))))&
(![X]:((~funny(X)<~>~brave(X))<=>(~brave(X)|wise(X))))&
(![X]:(funny(X)<=>(rich(X)|~tall(X))))&
(![X]:(wise(X)<=>~strong(X)))&
(![X]:((strong(X)<~>rich(X))<=>(~rich(X)&~curious(X))))&
(((~calm(mary)&creative(mary)))<=>((brave(susan)|curious(susan))))&
(![X]:((~tall(X)<~>generous(X))=>(~generous(X)|creative(X))))&
(![X]:((~humble(X)<~>funny(X))=>strong(X)))&
(![X]:((brave(X)<~>generous(X))=>(brave(X)&quiet(X))))&
(![X]:(funny(X)=>(humble(X)<~>tall(X))))&
(((~kind(mary)<~>~creative(mary)))<=>((~creative(john)&~generous(john))))&
(![X]:((curious(X)&happy(X))<=>(strong(X)|~brave(X))))&
((?[X]:((~funny(X)&curious(X))))<=>((~creative(lucy)&~happy(lucy))))&
(![X]:((~curious(X)|brave(X))=>(~patient(X)|~generous(X))))&
(~generous(mary))&
((patient(mary)<~>funny(mary)))&
(?[X]:((old(X)|strong(X))))&
((~generous(john)&quiet(john)))&
((calm(alice)|~creative(alice)))&
(?[X]:((creative(X)&strong(X)))) | ~calm(susan) | [] | null | 0 |
Everyone who is both not funny and not quiet is not curious and vice versa. Everyone who is both humble and brave is not strong or rich. Everyone who is either brave or tall is happy or not kind and vice versa. If someone is humble then alice is not kind or tall and vice versa. Everyone who is either not wise or tall is both not humble and not old. Everyone who is not creative is both humble and not strong. Everyone who is not creative or not tall is both kind and generous. Everyone who is either not kind or not creative is not happy and vice versa. Everyone who is either brave or not funny is both brave and not quiet and vice versa. Everyone who is both not tall and not funny is both not calm and not brave. If fred is kind then someone is both tall and curious. If paul is both quiet and not generous then john is not happy or not kind and vice versa. Everyone who is both old and brave is humble or not kind. Everyone who is old or not brave is not tall. Everyone who is both happy and curious is both kind and happy. If susan is patient or not calm then paul is not tall or not creative and vice versa. Paul is calm. Alice is not wise or not kind. Someone is patient. Someone is either not wise or creative. Someone is either not old or happy. John is not wise. Mary is quiet. Susan is either rich or tall. | Paul is kind. | entailment | (![X]:((~funny(X)&~quiet(X))<=>~curious(X)))&
(![X]:((humble(X)&brave(X))=>(~strong(X)|rich(X))))&
(![X]:((brave(X)<~>tall(X))<=>(happy(X)|~kind(X))))&
((?[X]:(humble(X)))<=>((~kind(alice)|tall(alice))))&
(![X]:((~wise(X)<~>tall(X))=>(~humble(X)&~old(X))))&
(![X]:(~creative(X)=>(humble(X)&~strong(X))))&
(![X]:((~creative(X)|~tall(X))=>(kind(X)&generous(X))))&
(![X]:((~kind(X)<~>~creative(X))<=>~happy(X)))&
(![X]:((brave(X)<~>~funny(X))<=>(brave(X)&~quiet(X))))&
(![X]:((~tall(X)&~funny(X))=>(~calm(X)&~brave(X))))&
((kind(fred))=>(?[X]:((tall(X)&curious(X)))))&
(((quiet(paul)&~generous(paul)))<=>((~happy(john)|~kind(john))))&
(![X]:((old(X)&brave(X))=>(humble(X)|~kind(X))))&
(![X]:((old(X)|~brave(X))=>~tall(X)))&
(![X]:((happy(X)&curious(X))=>(kind(X)&happy(X))))&
(((patient(susan)|~calm(susan)))<=>((~tall(paul)|~creative(paul))))&
(calm(paul))&
((~wise(alice)|~kind(alice)))&
(?[X]:(patient(X)))&
(?[X]:((~wise(X)<~>creative(X))))&
(?[X]:((~old(X)<~>happy(X))))&
(~wise(john))&
(quiet(mary))&
((rich(susan)<~>tall(susan))) | kind(paul) | [
"p2",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3006512660086862529998305
% SZS output start Proof for 3006512660086862529998305
3. ! [X0] : ((brave(X0) <~> tall(X0)) <=> (~kind(X0) | happy(X0))) [input p2]
7. ! [X0] : ((~tall(X0) | ~creative(X0)) => (generous(X0) & kind(X0))) [input p6]
14. ! [X0] : ((~brave(X0) | old(X0)) => ~tall(X0)) [input p13]
25. ~kind(paul) [input hypothesis]
30. ! [X0] : ((generous(X0) & kind(X0)) | (tall(X0) & creative(X0))) [ennf transformation 7]
36. ! [X0] : (~tall(X0) | (brave(X0) & ~old(X0))) [ennf transformation 14]
41. ! [X0] : ((((~tall(X0) | ~brave(X0)) & (tall(X0) | brave(X0))) | (kind(X0) & ~happy(X0))) & ((~kind(X0) | happy(X0)) | ((brave(X0) | ~tall(X0)) & (tall(X0) | ~brave(X0))))) [nnf transformation 3]
42. ! [X0] : ((((~tall(X0) | ~brave(X0)) & (tall(X0) | brave(X0))) | (kind(X0) & ~happy(X0))) & (~kind(X0) | happy(X0) | ((brave(X0) | ~tall(X0)) & (tall(X0) | ~brave(X0))))) [flattening 41]
75. ~tall(X0) | ~brave(X0) | kind(X0) [cnf transformation 42]
85. kind(X0) | tall(X0) [cnf transformation 30]
109. ~tall(X0) | brave(X0) [cnf transformation 36]
127. ~kind(paul) [cnf transformation 25]
201. 15 <=> tall(paul) [avatar definition]
203. tall(paul) <- (15) [avatar component clause 201]
249. tall(paul) [resolution 85,127]
255. 15 [avatar split clause 249,201]
257. brave(paul) <- (15) [resolution 109,203]
276. ~brave(paul) | kind(paul) <- (15) [resolution 75,203]
284. kind(paul) <- (15) [subsumption resolution 276,257]
285. $false <- (15) [subsumption resolution 284,127]
286. ~15 [avatar contradiction clause 285]
287. $false [avatar sat refutation 255,286]
% SZS output end Proof for 3006512660086862529998305
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and quiet is patient or quiet.
Everyone who is not creative or kind is patient and vice versa.
If fred is creative or not generous then john is not creative.
Everyone who is calm or curious is both not curious and not happy and vice versa.
If fred is either calm or not calm then someone is not kind or patient and vice versa.
Everyone who is rich is not brave and vice versa.
If someone is not rich or not curious then someone is not quiet and vice versa.
Everyone who is both funny and generous is happy.
If susan is wise then lucy is both kind and not patient.
Everyone who is both generous and not humble is both not happy and calm.
If lucy is creative or not rich then someone is both brave and not funny.
Everyone who is either creative or not wise is not old and vice versa.
If paul is both not kind and funny then someone is not old or not quiet and vice versa.
Everyone who is brave is creative or patient.
If susan is old then someone is both not kind and happy and vice versa.
If someone is tall then paul is not rich or not old.
Someone is either not patient or funny.
Someone is both not creative and brave.
Someone is not humble or not generous.
Someone is either not wise or humble.
Someone is not kind.
Someone is old or humble.
Lucy is old.
John is happy or kind. | Lucy is generous. | neutral | (![X]:((~humble(X)&quiet(X))=>(patient(X)|quiet(X))))&
(![X]:((~creative(X)|kind(X))<=>patient(X)))&
(((creative(fred)|~generous(fred)))=>(~creative(john)))&
(![X]:((calm(X)|curious(X))<=>(~curious(X)&~happy(X))))&
(((calm(fred)<~>~calm(fred)))<=>(?[X]:((~kind(X)|patient(X)))))&
(![X]:(rich(X)<=>~brave(X)))&
((?[X]:((~rich(X)|~curious(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((funny(X)&generous(X))=>happy(X)))&
((wise(susan))=>((kind(lucy)&~patient(lucy))))&
(![X]:((generous(X)&~humble(X))=>(~happy(X)&calm(X))))&
(((creative(lucy)|~rich(lucy)))=>(?[X]:((brave(X)&~funny(X)))))&
(![X]:((creative(X)<~>~wise(X))<=>~old(X)))&
(((~kind(paul)&funny(paul)))<=>(?[X]:((~old(X)|~quiet(X)))))&
(![X]:(brave(X)=>(creative(X)|patient(X))))&
((old(susan))<=>(?[X]:((~kind(X)&happy(X)))))&
((?[X]:(tall(X)))=>((~rich(paul)|~old(paul))))&
(?[X]:((~patient(X)<~>funny(X))))&
(?[X]:((~creative(X)&brave(X))))&
(?[X]:((~humble(X)|~generous(X))))&
(?[X]:((~wise(X)<~>humble(X))))&
(?[X]:(~kind(X)))&
(?[X]:((old(X)|humble(X))))&
(old(lucy))&
((happy(john)|kind(john))) | generous(lucy) | [] | null | 0 |
Everyone who is funny or calm is either not tall or not old.
Everyone who is curious or not wise is either calm or not quiet and vice versa.
If someone is humble then fred is both calm and rich.
Everyone who is rich or strong is either patient or quiet.
If someone is happy or calm then someone is both not wise and not calm.
Everyone who is not calm or not happy is not kind.
If someone is wise then john is both not generous and not creative.
Everyone who is not generous is happy.
Everyone who is either not humble or wise is humble.
If someone is either not calm or patient then john is not strong or not happy and vice versa.
If someone is either not quiet or not funny then someone is not brave or not quiet and vice versa.
Everyone who is both tall and kind is both not generous and not patient and vice versa.
If someone is both wise and not curious then someone is both wise and strong and vice versa.
Everyone who is patient or not funny is both not wise and generous.
If someone is not old or not humble then alice is kind or creative.
If someone is happy then alice is either not old or not creative.
Someone is both funny and not quiet.
Someone is either not wise or not tall.
Alice is funny or not creative.
Fred is old.
Someone is rich or creative.
Someone is not strong.
Someone is both not calm and tall.
Paul is curious or not patient. | Fred is happy. | neutral | (![X]:((funny(X)|calm(X))=>(~tall(X)<~>~old(X))))&
(![X]:((curious(X)|~wise(X))<=>(calm(X)<~>~quiet(X))))&
((?[X]:(humble(X)))=>((calm(fred)&rich(fred))))&
(![X]:((rich(X)|strong(X))=>(patient(X)<~>quiet(X))))&
((?[X]:((happy(X)|calm(X))))=>(?[X]:((~wise(X)&~calm(X)))))&
(![X]:((~calm(X)|~happy(X))=>~kind(X)))&
((?[X]:(wise(X)))=>((~generous(john)&~creative(john))))&
(![X]:(~generous(X)=>happy(X)))&
(![X]:((~humble(X)<~>wise(X))=>humble(X)))&
((?[X]:((~calm(X)<~>patient(X))))<=>((~strong(john)|~happy(john))))&
((?[X]:((~quiet(X)<~>~funny(X))))<=>(?[X]:((~brave(X)|~quiet(X)))))&
(![X]:((tall(X)&kind(X))<=>(~generous(X)&~patient(X))))&
((?[X]:((wise(X)&~curious(X))))<=>(?[X]:((wise(X)&strong(X)))))&
(![X]:((patient(X)|~funny(X))=>(~wise(X)&generous(X))))&
((?[X]:((~old(X)|~humble(X))))=>((kind(alice)|creative(alice))))&
((?[X]:(happy(X)))=>((~old(alice)<~>~creative(alice))))&
(?[X]:((funny(X)&~quiet(X))))&
(?[X]:((~wise(X)<~>~tall(X))))&
((funny(alice)|~creative(alice)))&
(old(fred))&
(?[X]:((rich(X)|creative(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~calm(X)&tall(X))))&
((curious(paul)|~patient(paul))) | happy(fred) | [] | null | 0 |
Everyone who is either strong or not creative is both kind and wise.
Everyone who is patient or not calm is not patient and vice versa.
Everyone who is not tall is both tall and not strong.
Everyone who is not funny is both old and patient.
Everyone who is either not calm or curious is either not strong or calm.
If paul is happy then john is not humble or funny and vice versa.
Everyone who is rich or not humble is both not quiet and curious and vice versa.
Everyone who is both not kind and not strong is curious and vice versa.
Everyone who is strong or quiet is not tall and vice versa.
If lucy is both curious and not funny then someone is generous and vice versa.
Everyone who is either creative or curious is either strong or creative.
If someone is both not tall and not quiet then lucy is either strong or not funny and vice versa.
If someone is not tall or not rich then someone is either happy or not kind and vice versa.
Everyone who is both not wise and generous is either not patient or not rich.
Everyone who is either not calm or not tall is either curious or not strong.
If someone is either not generous or not funny then someone is not happy and vice versa.
Someone is both not brave and not strong.
Someone is either not humble or humble.
Mary is happy or quiet.
Someone is either generous or not rich.
Lucy is not patient.
Someone is either not calm or curious.
Someone is not wise or not generous.
Alice is both not rich and old. | Paul is not happy. | contradiction | (![X]:((strong(X)<~>~creative(X))=>(kind(X)&wise(X))))&
(![X]:((patient(X)|~calm(X))<=>~patient(X)))&
(![X]:(~tall(X)=>(tall(X)&~strong(X))))&
(![X]:(~funny(X)=>(old(X)&patient(X))))&
(![X]:((~calm(X)<~>curious(X))=>(~strong(X)<~>calm(X))))&
((happy(paul))<=>((~humble(john)|funny(john))))&
(![X]:((rich(X)|~humble(X))<=>(~quiet(X)&curious(X))))&
(![X]:((~kind(X)&~strong(X))<=>curious(X)))&
(![X]:((strong(X)|quiet(X))<=>~tall(X)))&
(((curious(lucy)&~funny(lucy)))<=>(?[X]:(generous(X))))&
(![X]:((creative(X)<~>curious(X))=>(strong(X)<~>creative(X))))&
((?[X]:((~tall(X)&~quiet(X))))<=>((strong(lucy)<~>~funny(lucy))))&
((?[X]:((~tall(X)|~rich(X))))<=>(?[X]:((happy(X)<~>~kind(X)))))&
(![X]:((~wise(X)&generous(X))=>(~patient(X)<~>~rich(X))))&
(![X]:((~calm(X)<~>~tall(X))=>(curious(X)<~>~strong(X))))&
((?[X]:((~generous(X)<~>~funny(X))))<=>(?[X]:(~happy(X))))&
(?[X]:((~brave(X)&~strong(X))))&
(?[X]:((~humble(X)<~>humble(X))))&
((happy(mary)|quiet(mary)))&
(?[X]:((generous(X)<~>~rich(X))))&
(~patient(lucy))&
(?[X]:((~calm(X)<~>curious(X))))&
(?[X]:((~wise(X)|~generous(X))))&
((~rich(alice)&old(alice))) | ~happy(paul) | [
"p1",
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1110741998420156954609833
% SZS output start Proof for 1110741998420156954609833
2. ! [X0] : ((~calm(X0) | patient(X0)) <=> ~patient(X0)) [input p1]
4. ! [X0] : (~funny(X0) => (patient(X0) & old(X0))) [input p3]
6. happy(paul) <=> (funny(john) | ~humble(john)) [input p5]
25. ~happy(paul) [input hypothesis]
29. ! [X0] : (~funny(X0) => patient(X0)) [pure predicate removal 4]
33. ! [X0] : (patient(X0) | funny(X0)) [ennf transformation 29]
40. ! [X0] : (((~calm(X0) | patient(X0)) | patient(X0)) & (~patient(X0) | (calm(X0) & ~patient(X0)))) [nnf transformation 2]
41. ! [X0] : ((~calm(X0) | patient(X0) | patient(X0)) & (~patient(X0) | (calm(X0) & ~patient(X0)))) [flattening 40]
43. (happy(paul) | (~funny(john) & humble(john))) & ((funny(john) | ~humble(john)) | ~happy(paul)) [nnf transformation 6]
44. (happy(paul) | (~funny(john) & humble(john))) & (funny(john) | ~humble(john) | ~happy(paul)) [flattening 43]
90. ~patient(X0) | ~patient(X0) [cnf transformation 41]
95. patient(X0) | funny(X0) [cnf transformation 33]
102. happy(paul) | ~funny(john) [cnf transformation 44]
154. ~happy(paul) [cnf transformation 25]
160. ~patient(X0) [duplicate literal removal 90]
162. funny(X0) [subsumption resolution 95,160]
163. happy(paul) [subsumption resolution 102,162]
210. $false [subsumption resolution 154,163]
% SZS output end Proof for 1110741998420156954609833
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not humble and happy is not calm or not happy. If someone is both generous and not humble then alice is both not old and generous. If fred is either not creative or not rich then someone is curious and vice versa. Everyone who is either not patient or not funny is not happy or not wise and vice versa. Everyone who is creative or tall is both strong and not patient and vice versa. Everyone who is either happy or not strong is strong and vice versa. If someone is either curious or not creative then lucy is not creative and vice versa. If paul is not kind then someone is either not kind or not calm and vice versa. Everyone who is not funny is either not kind or generous and vice versa. Everyone who is not calm is either not kind or not rich and vice versa. Everyone who is humble is either humble or not humble and vice versa. Everyone who is either brave or not generous is not tall or funny. If alice is tall then paul is kind or old and vice versa. If paul is both not generous and old then susan is calm. If alice is either kind or generous then someone is both tall and not brave and vice versa. Everyone who is tall is not creative and vice versa. Susan is funny. John is either not happy or wise. Susan is not calm or not quiet. Fred is not curious or patient. Someone is either curious or not funny. Someone is both curious and not old. Alice is not tall. | Alice is creative. | entailment | (![X]:((~humble(X)&happy(X))=>(~calm(X)|~happy(X))))&
((?[X]:((generous(X)&~humble(X))))=>((~old(alice)&generous(alice))))&
(((~creative(fred)<~>~rich(fred)))<=>(?[X]:(curious(X))))&
(![X]:((~patient(X)<~>~funny(X))<=>(~happy(X)|~wise(X))))&
(![X]:((creative(X)|tall(X))<=>(strong(X)&~patient(X))))&
(![X]:((happy(X)<~>~strong(X))<=>strong(X)))&
((?[X]:((curious(X)<~>~creative(X))))<=>(~creative(lucy)))&
((~kind(paul))<=>(?[X]:((~kind(X)<~>~calm(X)))))&
(![X]:(~funny(X)<=>(~kind(X)<~>generous(X))))&
(![X]:(~calm(X)<=>(~kind(X)<~>~rich(X))))&
(![X]:(humble(X)<=>(humble(X)<~>~humble(X))))&
(![X]:((brave(X)<~>~generous(X))=>(~tall(X)|funny(X))))&
((tall(alice))<=>((kind(paul)|old(paul))))&
(((~generous(paul)&old(paul)))=>(calm(susan)))&
(((kind(alice)<~>generous(alice)))<=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:(tall(X)<=>~creative(X)))&
(funny(susan))&
((~happy(john)<~>wise(john)))&
((~calm(susan)|~quiet(susan)))&
((~curious(fred)|patient(fred)))&
(?[X]:((curious(X)<~>~funny(X))))&
(?[X]:((curious(X)&~old(X))))&
(~tall(alice)) | creative(alice) | [
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2122964155374186138425673
% SZS output start Proof for 2122964155374186138425673
16. ! [X0] : (tall(X0) <=> ~creative(X0)) [input p15]
23. ~tall(alice) [input p22]
24. ~creative(alice) [input hypothesis]
60. ! [X0] : ((tall(X0) | creative(X0)) & (~creative(X0) | ~tall(X0))) [nnf transformation 16]
122. tall(X0) | creative(X0) [cnf transformation 60]
131. ~tall(alice) [cnf transformation 23]
132. ~creative(alice) [cnf transformation 24]
222. 19 <=> tall(alice) [avatar definition]
223. ~tall(alice) <- (~19) [avatar component clause 222]
278. ~19 [avatar split clause 131,222]
282. creative(alice) <- (~19) [resolution 122,223]
286. $false <- (~19) [subsumption resolution 282,132]
287. 19 [avatar contradiction clause 286]
290. $false [avatar sat refutation 278,287]
% SZS output end Proof for 2122964155374186138425673
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and not brave is either humble or not brave. Everyone who is patient or calm is funny. Everyone who is either brave or not calm is either not kind or calm. Everyone who is not kind or not old is not funny and vice versa. Everyone who is patient is happy or creative. If someone is creative or not curious then john is either kind or funny and vice versa. If fred is either not tall or not quiet then lucy is curious and vice versa. Everyone who is either calm or not curious is either not quiet or not old. If someone is either generous or not humble then susan is both old and not tall and vice versa. If someone is either quiet or not kind then someone is both happy and not brave. Everyone who is both wise and rich is both not quiet and happy and vice versa. Everyone who is either generous or not brave is both not strong and old and vice versa. If paul is both wise and kind then someone is either calm or brave and vice versa. If someone is strong then fred is either tall or not kind. If lucy is humble then someone is both not brave and not calm and vice versa. Everyone who is brave is both curious and not creative and vice versa. Susan is both not kind and not brave. Someone is not calm or not generous. Someone is both not kind and curious. Alice is either generous or creative. Someone is both happy and funny. Lucy is either not brave or not strong. Alice is both not funny and wise. | Lucy is not patient. | neutral | (![X]:((~happy(X)&~brave(X))=>(humble(X)<~>~brave(X))))&
(![X]:((patient(X)|calm(X))=>funny(X)))&
(![X]:((brave(X)<~>~calm(X))=>(~kind(X)<~>calm(X))))&
(![X]:((~kind(X)|~old(X))<=>~funny(X)))&
(![X]:(patient(X)=>(happy(X)|creative(X))))&
((?[X]:((creative(X)|~curious(X))))<=>((kind(john)<~>funny(john))))&
(((~tall(fred)<~>~quiet(fred)))<=>(curious(lucy)))&
(![X]:((calm(X)<~>~curious(X))=>(~quiet(X)<~>~old(X))))&
((?[X]:((generous(X)<~>~humble(X))))<=>((old(susan)&~tall(susan))))&
((?[X]:((quiet(X)<~>~kind(X))))=>(?[X]:((happy(X)&~brave(X)))))&
(![X]:((wise(X)&rich(X))<=>(~quiet(X)&happy(X))))&
(![X]:((generous(X)<~>~brave(X))<=>(~strong(X)&old(X))))&
(((wise(paul)&kind(paul)))<=>(?[X]:((calm(X)<~>brave(X)))))&
((?[X]:(strong(X)))=>((tall(fred)<~>~kind(fred))))&
((humble(lucy))<=>(?[X]:((~brave(X)&~calm(X)))))&
(![X]:(brave(X)<=>(curious(X)&~creative(X))))&
((~kind(susan)&~brave(susan)))&
(?[X]:((~calm(X)|~generous(X))))&
(?[X]:((~kind(X)&curious(X))))&
((generous(alice)<~>creative(alice)))&
(?[X]:((happy(X)&funny(X))))&
((~brave(lucy)<~>~strong(lucy)))&
((~funny(alice)&wise(alice))) | ~patient(lucy) | [] | null | 0 |
If someone is either not patient or not kind then alice is kind or brave.
Everyone who is rich is not rich.
If someone is funny then someone is funny or not generous.
Everyone who is either happy or kind is not funny and vice versa.
Everyone who is quiet is both generous and wise and vice versa.
If alice is both quiet and creative then someone is not tall and vice versa.
Everyone who is not tall or humble is humble or not generous.
Everyone who is not quiet is tall or rich and vice versa.
Everyone who is not strong is not old or not calm.
If someone is old or not rich then someone is either kind or quiet.
Everyone who is humble is curious and vice versa.
If someone is not brave or old then someone is curious and vice versa.
If lucy is calm then mary is not rich and vice versa.
If someone is both happy and strong then mary is not rich.
If mary is either not old or not rich then someone is both rich and not generous and vice versa.
Everyone who is generous is quiet and vice versa.
Lucy is both wise and kind.
Someone is both brave and not quiet.
Susan is not funny or not tall.
Fred is tall or not quiet.
John is patient.
Susan is happy.
Alice is both not funny and old.
Someone is not humble or rich. | John is not creative. | neutral | ((?[X]:((~patient(X)<~>~kind(X))))=>((kind(alice)|brave(alice))))&
(![X]:(rich(X)=>~rich(X)))&
((?[X]:(funny(X)))=>(?[X]:((funny(X)|~generous(X)))))&
(![X]:((happy(X)<~>kind(X))<=>~funny(X)))&
(![X]:(quiet(X)<=>(generous(X)&wise(X))))&
(((quiet(alice)&creative(alice)))<=>(?[X]:(~tall(X))))&
(![X]:((~tall(X)|humble(X))=>(humble(X)|~generous(X))))&
(![X]:(~quiet(X)<=>(tall(X)|rich(X))))&
(![X]:(~strong(X)=>(~old(X)|~calm(X))))&
((?[X]:((old(X)|~rich(X))))=>(?[X]:((kind(X)<~>quiet(X)))))&
(![X]:(humble(X)<=>curious(X)))&
((?[X]:((~brave(X)|old(X))))<=>(?[X]:(curious(X))))&
((calm(lucy))<=>(~rich(mary)))&
((?[X]:((happy(X)&strong(X))))=>(~rich(mary)))&
(((~old(mary)<~>~rich(mary)))<=>(?[X]:((rich(X)&~generous(X)))))&
(![X]:(generous(X)<=>quiet(X)))&
((wise(lucy)&kind(lucy)))&
(?[X]:((brave(X)&~quiet(X))))&
((~funny(susan)|~tall(susan)))&
((tall(fred)|~quiet(fred)))&
(patient(john))&
(happy(susan))&
((~funny(alice)&old(alice)))&
(?[X]:((~humble(X)|rich(X)))) | ~creative(john) | [] | null | 0 |
Everyone who is either not patient or brave is not strong and vice versa.
Everyone who is either calm or not creative is either old or curious.
Everyone who is either old or tall is not funny or patient and vice versa.
If john is both brave and not old then someone is not happy or calm.
Everyone who is either curious or not generous is both creative and not humble.
Everyone who is both not curious and patient is calm or generous and vice versa.
Everyone who is not old or not humble is either curious or not tall.
Everyone who is either curious or tall is either not generous or not brave and vice versa.
If someone is either rich or not strong then someone is both brave and patient and vice versa.
If someone is either generous or not curious then someone is not patient or not funny.
If someone is not tall then someone is creative.
Everyone who is funny or generous is not curious.
If john is either rich or not tall then someone is both quiet and not quiet and vice versa.
If someone is not rich then someone is either kind or wise and vice versa.
If john is not old or tall then someone is strong or funny and vice versa.
Everyone who is generous is either not wise or creative.
Someone is creative or not wise.
Someone is not brave or not generous.
Someone is both patient and rich.
Susan is either kind or not old.
Mary is brave.
Someone is not humble.
Fred is not kind or happy.
Lucy is strong or curious. | Mary is tall. | contradiction | (![X]:((~patient(X)<~>brave(X))<=>~strong(X)))&
(![X]:((calm(X)<~>~creative(X))=>(old(X)<~>curious(X))))&
(![X]:((old(X)<~>tall(X))<=>(~funny(X)|patient(X))))&
(((brave(john)&~old(john)))=>(?[X]:((~happy(X)|calm(X)))))&
(![X]:((curious(X)<~>~generous(X))=>(creative(X)&~humble(X))))&
(![X]:((~curious(X)&patient(X))<=>(calm(X)|generous(X))))&
(![X]:((~old(X)|~humble(X))=>(curious(X)<~>~tall(X))))&
(![X]:((curious(X)<~>tall(X))<=>(~generous(X)<~>~brave(X))))&
((?[X]:((rich(X)<~>~strong(X))))<=>(?[X]:((brave(X)&patient(X)))))&
((?[X]:((generous(X)<~>~curious(X))))=>(?[X]:((~patient(X)|~funny(X)))))&
((?[X]:(~tall(X)))=>(?[X]:(creative(X))))&
(![X]:((funny(X)|generous(X))=>~curious(X)))&
(((rich(john)<~>~tall(john)))<=>(?[X]:((quiet(X)&~quiet(X)))))&
((?[X]:(~rich(X)))<=>(?[X]:((kind(X)<~>wise(X)))))&
(((~old(john)|tall(john)))<=>(?[X]:((strong(X)|funny(X)))))&
(![X]:(generous(X)=>(~wise(X)<~>creative(X))))&
(?[X]:((creative(X)|~wise(X))))&
(?[X]:((~brave(X)|~generous(X))))&
(?[X]:((patient(X)&rich(X))))&
((kind(susan)<~>~old(susan)))&
(brave(mary))&
(?[X]:(~humble(X)))&
((~kind(fred)|happy(fred)))&
((strong(lucy)|curious(lucy))) | tall(mary) | [
"p4",
"p5",
"p6",
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6024761783090573338989822
% SZS output start Proof for 6024761783090573338989822
5. ! [X0] : ((curious(X0) <~> ~generous(X0)) => (~humble(X0) & creative(X0))) [input p4]
6. ! [X0] : ((patient(X0) & ~curious(X0)) <=> (generous(X0) | calm(X0))) [input p5]
7. ! [X0] : ((~humble(X0) | ~old(X0)) => (curious(X0) <~> ~tall(X0))) [input p6]
8. ! [X0] : ((curious(X0) <~> tall(X0)) <=> (~generous(X0) <~> ~brave(X0))) [input p7]
21. brave(mary) [input p20]
25. tall(mary) [input hypothesis]
33. ! [X0] : ((~humble(X0) & creative(X0)) | (curious(X0) <=> ~generous(X0))) [ennf transformation 5]
34. ! [X0] : ((curious(X0) <~> ~tall(X0)) | (humble(X0) & old(X0))) [ennf transformation 7]
45. ! [X0] : ((~humble(X0) & creative(X0)) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0)))) [nnf transformation 33]
46. ! [X0] : (((patient(X0) & ~curious(X0)) | (~generous(X0) & ~calm(X0))) & ((generous(X0) | calm(X0)) | (~patient(X0) | curious(X0)))) [nnf transformation 6]
47. ! [X0] : (((patient(X0) & ~curious(X0)) | (~generous(X0) & ~calm(X0))) & (generous(X0) | calm(X0) | ~patient(X0) | curious(X0))) [flattening 46]
48. ! [X0] : (((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) | (humble(X0) & old(X0))) [nnf transformation 34]
49. ! [X0] : ((((~tall(X0) | ~curious(X0)) & (tall(X0) | curious(X0))) | ((~generous(X0) | brave(X0)) & (~brave(X0) | generous(X0)))) & (((brave(X0) | generous(X0)) & (~brave(X0) | ~generous(X0))) | ((curious(X0) | ~tall(X0)) & (tall(X0) | ~curious(X0))))) [nnf transformation 8]
104. ~humble(X0) | curious(X0) | generous(X0) [cnf transformation 45]
107. ~generous(X0) | ~curious(X0) [cnf transformation 47]
111. ~tall(X0) | curious(X0) | humble(X0) [cnf transformation 48]
115. ~brave(X0) | ~generous(X0) | curious(X0) | ~tall(X0) [cnf transformation 49]
120. ~tall(X0) | ~curious(X0) | ~brave(X0) | generous(X0) [cnf transformation 49]
155. brave(mary) [cnf transformation 21]
159. tall(mary) [cnf transformation 25]
177. ~tall(X0) | ~curious(X0) | ~brave(X0) [subsumption resolution 120,107]
180. ~generous(X0) | ~brave(X0) | ~tall(X0) [subsumption resolution 115,177]
525. curious(mary) | humble(mary) [resolution 111,159]
552. ~curious(mary) | ~brave(mary) [resolution 177,159]
558. ~curious(mary) [subsumption resolution 552,155]
559. humble(mary) [subsumption resolution 525,558]
590. curious(mary) | generous(mary) [resolution 559,104]
592. generous(mary) [subsumption resolution 590,558]
827. ~brave(mary) | ~tall(mary) [resolution 592,180]
833. ~tall(mary) [subsumption resolution 827,155]
834. $false [subsumption resolution 833,159]
% SZS output end Proof for 6024761783090573338989822
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise is both kind and tall. If someone is either strong or not brave then paul is both not happy and patient. Everyone who is both not old and generous is not kind or not creative and vice versa. If someone is calm or humble then paul is both funny and wise and vice versa. If someone is humble then john is either not wise or not creative and vice versa. Everyone who is patient is not patient or old and vice versa. If someone is either calm or not happy then lucy is tall. Everyone who is either humble or not old is both calm and generous and vice versa. Everyone who is humble is not creative and vice versa. Everyone who is either not brave or brave is either not calm or old. Everyone who is not wise is strong or old. If someone is funny or not generous then someone is not old or not quiet and vice versa. Everyone who is both tall and creative is either happy or not calm and vice versa. If john is not kind then fred is not creative. Everyone who is either not old or creative is both not curious and wise. Someone is either not humble or generous. Mary is kind or not kind. Someone is rich. Someone is both calm and not brave. John is wise. | Fred is not old. | contradiction | (![X]:(wise(X)=>(kind(X)&tall(X))))&
((?[X]:((strong(X)<~>~brave(X))))=>((~happy(paul)&patient(paul))))&
(![X]:((~old(X)&generous(X))<=>(~kind(X)|~creative(X))))&
((?[X]:((calm(X)|humble(X))))<=>((funny(paul)&wise(paul))))&
((?[X]:(humble(X)))<=>((~wise(john)<~>~creative(john))))&
(![X]:(patient(X)<=>(~patient(X)|old(X))))&
((?[X]:((calm(X)<~>~happy(X))))=>(tall(lucy)))&
(![X]:((humble(X)<~>~old(X))<=>(calm(X)&generous(X))))&
(![X]:(humble(X)<=>~creative(X)))&
(![X]:((~brave(X)<~>brave(X))=>(~calm(X)<~>old(X))))&
(![X]:(~wise(X)=>(strong(X)|old(X))))&
((?[X]:((funny(X)|~generous(X))))<=>(?[X]:((~old(X)|~quiet(X)))))&
(![X]:((tall(X)&creative(X))<=>(happy(X)<~>~calm(X))))&
((~kind(john))=>(~creative(fred)))&
(![X]:((~old(X)<~>creative(X))=>(~curious(X)&wise(X))))&
(?[X]:((~humble(X)<~>generous(X))))&
((kind(mary)|~kind(mary)))&
(?[X]:(rich(X)))&
(?[X]:((calm(X)&~brave(X))))&
(wise(john)) | ~old(fred) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 7289302293241944310866874
% SZS output start Proof for 7289302293241944310866874
6. ! [X0] : (patient(X0) <=> (old(X0) | ~patient(X0))) [input p5]
21. ~old(fred) [input hypothesis]
45. ! [X0] : ((patient(X0) | (~old(X0) & patient(X0))) & ((old(X0) | ~patient(X0)) | ~patient(X0))) [nnf transformation 6]
46. ! [X0] : ((patient(X0) | (~old(X0) & patient(X0))) & (old(X0) | ~patient(X0) | ~patient(X0))) [flattening 45]
85. old(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 46]
86. patient(X0) | patient(X0) [cnf transformation 46]
122. ~old(fred) [cnf transformation 21]
127. old(X0) | ~patient(X0) [duplicate literal removal 85]
128. patient(X0) [duplicate literal removal 86]
190. old(X0) [subsumption resolution 127,128]
258. $false [subsumption resolution 122,190]
% SZS output end Proof for 7289302293241944310866874
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not brave or strong then susan is both not generous and wise and vice versa.
Everyone who is either not humble or strong is happy.
If someone is funny or curious then someone is not humble or not generous and vice versa.
Everyone who is either not wise or not brave is not quiet.
Everyone who is both happy and old is not happy or quiet.
If someone is both not kind and not tall then someone is either curious or not creative.
Everyone who is both not happy and rich is rich or curious and vice versa.
If someone is either humble or old then paul is either patient or happy.
If someone is calm or generous then someone is not old.
Everyone who is quiet or funny is either not patient or not calm.
If someone is kind then paul is curious and vice versa.
If someone is both not curious and brave then someone is not old or not funny.
Everyone who is old or not humble is not humble or not patient and vice versa.
Everyone who is both humble and not calm is both happy and kind.
Everyone who is tall is either kind or not brave and vice versa.
Everyone who is not old or quiet is both brave and patient and vice versa.
Someone is both not wise and kind.
Someone is either not old or not funny.
Someone is funny.
Someone is both patient and not curious.
Someone is either calm or kind.
Someone is not brave or happy.
Someone is not strong.
Someone is funny or not creative. | Susan is generous. | neutral | (((~brave(lucy)|strong(lucy)))<=>((~generous(susan)&wise(susan))))&
(![X]:((~humble(X)<~>strong(X))=>happy(X)))&
((?[X]:((funny(X)|curious(X))))<=>(?[X]:((~humble(X)|~generous(X)))))&
(![X]:((~wise(X)<~>~brave(X))=>~quiet(X)))&
(![X]:((happy(X)&old(X))=>(~happy(X)|quiet(X))))&
((?[X]:((~kind(X)&~tall(X))))=>(?[X]:((curious(X)<~>~creative(X)))))&
(![X]:((~happy(X)&rich(X))<=>(rich(X)|curious(X))))&
((?[X]:((humble(X)<~>old(X))))=>((patient(paul)<~>happy(paul))))&
((?[X]:((calm(X)|generous(X))))=>(?[X]:(~old(X))))&
(![X]:((quiet(X)|funny(X))=>(~patient(X)<~>~calm(X))))&
((?[X]:(kind(X)))<=>(curious(paul)))&
((?[X]:((~curious(X)&brave(X))))=>(?[X]:((~old(X)|~funny(X)))))&
(![X]:((old(X)|~humble(X))<=>(~humble(X)|~patient(X))))&
(![X]:((humble(X)&~calm(X))=>(happy(X)&kind(X))))&
(![X]:(tall(X)<=>(kind(X)<~>~brave(X))))&
(![X]:((~old(X)|quiet(X))<=>(brave(X)&patient(X))))&
(?[X]:((~wise(X)&kind(X))))&
(?[X]:((~old(X)<~>~funny(X))))&
(?[X]:(funny(X)))&
(?[X]:((patient(X)&~curious(X))))&
(?[X]:((calm(X)<~>kind(X))))&
(?[X]:((~brave(X)|happy(X))))&
(?[X]:(~strong(X)))&
(?[X]:((funny(X)|~creative(X)))) | generous(susan) | [] | null | 0 |
Everyone who is either humble or not creative is not happy or not rich.
Everyone who is not humble or creative is not strong.
Everyone who is not wise is both generous and strong.
If someone is either not quiet or wise then lucy is creative and vice versa.
Everyone who is strong is either curious or calm and vice versa.
If lucy is both quiet and not kind then susan is either tall or not patient.
If someone is not rich then alice is not rich or brave.
Everyone who is either curious or tall is both tall and not happy.
Everyone who is both old and patient is either not brave or not tall and vice versa.
Everyone who is either quiet or happy is not funny or humble and vice versa.
Everyone who is not generous or not kind is not generous and vice versa.
Everyone who is both strong and tall is either not tall or creative and vice versa.
Everyone who is either not rich or not strong is not curious or calm and vice versa.
If paul is either not generous or not wise then mary is rich.
Everyone who is both curious and creative is not creative or not happy and vice versa.
If alice is either not kind or not creative then john is quiet or not happy and vice versa.
Fred is either not rich or not old.
Someone is not curious or not humble.
Someone is both quiet and not tall.
Someone is either generous or happy.
Mary is strong or generous.
Someone is not wise or old. | Paul is not curious. | entailment | (![X]:((humble(X)<~>~creative(X))=>(~happy(X)|~rich(X))))&
(![X]:((~humble(X)|creative(X))=>~strong(X)))&
(![X]:(~wise(X)=>(generous(X)&strong(X))))&
((?[X]:((~quiet(X)<~>wise(X))))<=>(creative(lucy)))&
(![X]:(strong(X)<=>(curious(X)<~>calm(X))))&
(((quiet(lucy)&~kind(lucy)))=>((tall(susan)<~>~patient(susan))))&
((?[X]:(~rich(X)))=>((~rich(alice)|brave(alice))))&
(![X]:((curious(X)<~>tall(X))=>(tall(X)&~happy(X))))&
(![X]:((old(X)&patient(X))<=>(~brave(X)<~>~tall(X))))&
(![X]:((quiet(X)<~>happy(X))<=>(~funny(X)|humble(X))))&
(![X]:((~generous(X)|~kind(X))<=>~generous(X)))&
(![X]:((strong(X)&tall(X))<=>(~tall(X)<~>creative(X))))&
(![X]:((~rich(X)<~>~strong(X))<=>(~curious(X)|calm(X))))&
(((~generous(paul)<~>~wise(paul)))=>(rich(mary)))&
(![X]:((curious(X)&creative(X))<=>(~creative(X)|~happy(X))))&
(((~kind(alice)<~>~creative(alice)))<=>((quiet(john)|~happy(john))))&
((~rich(fred)<~>~old(fred)))&
(?[X]:((~curious(X)|~humble(X))))&
(?[X]:((quiet(X)&~tall(X))))&
(?[X]:((generous(X)<~>happy(X))))&
((strong(mary)|generous(mary)))&
(?[X]:((~wise(X)|old(X)))) | ~curious(paul) | [
"p1",
"p7",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6149527410524481762941303
% SZS output start Proof for 6149527410524481762941303
2. ! [X0] : ((creative(X0) | ~humble(X0)) => ~strong(X0)) [input p1]
8. ! [X0] : ((curious(X0) <~> tall(X0)) => (~happy(X0) & tall(X0))) [input p7]
12. ! [X0] : ((tall(X0) & strong(X0)) <=> (~tall(X0) <~> creative(X0))) [input p11]
15. ! [X0] : ((creative(X0) & curious(X0)) <=> (~happy(X0) | ~creative(X0))) [input p14]
23. curious(paul) [input hypothesis]
26. ! [X0] : (~strong(X0) | (~creative(X0) & humble(X0))) [ennf transformation 2]
32. ! [X0] : ((~happy(X0) & tall(X0)) | (curious(X0) <=> tall(X0))) [ennf transformation 8]
41. ! [X0] : ((~happy(X0) & tall(X0)) | ((curious(X0) | ~tall(X0)) & (tall(X0) | ~curious(X0)))) [nnf transformation 32]
48. ! [X0] : (((tall(X0) & strong(X0)) | ((~tall(X0) | ~creative(X0)) & (creative(X0) | tall(X0)))) & (((~creative(X0) | tall(X0)) & (creative(X0) | ~tall(X0))) | (~tall(X0) | ~strong(X0)))) [nnf transformation 12]
49. ! [X0] : (((tall(X0) & strong(X0)) | ((~tall(X0) | ~creative(X0)) & (creative(X0) | tall(X0)))) & (((~creative(X0) | tall(X0)) & (creative(X0) | ~tall(X0))) | ~tall(X0) | ~strong(X0))) [flattening 48]
53. ! [X0] : (((creative(X0) & curious(X0)) | (happy(X0) & creative(X0))) & ((~happy(X0) | ~creative(X0)) | (~creative(X0) | ~curious(X0)))) [nnf transformation 15]
54. ! [X0] : (((creative(X0) & curious(X0)) | (happy(X0) & creative(X0))) & (~happy(X0) | ~creative(X0) | ~creative(X0) | ~curious(X0))) [flattening 53]
70. ~strong(X0) | ~creative(X0) [cnf transformation 26]
84. tall(X0) | tall(X0) | ~curious(X0) [cnf transformation 41]
106. strong(X0) | ~tall(X0) | ~creative(X0) [cnf transformation 49]
120. creative(X0) | creative(X0) [cnf transformation 54]
137. curious(paul) [cnf transformation 23]
139. creative(X0) [duplicate literal removal 120]
142. ~curious(X0) | tall(X0) [duplicate literal removal 84]
195. ~tall(X0) | ~creative(X0) [subsumption resolution 106,70]
302. tall(paul) [resolution 142,137]
310. ~creative(paul) [resolution 195,302]
311. $false [subsumption resolution 310,139]
% SZS output end Proof for 6149527410524481762941303
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If john is rich then john is either not calm or generous. If fred is either not generous or brave then paul is humble or rich and vice versa. Everyone who is not creative or humble is strong and vice versa. If lucy is both wise and not rich then alice is either not funny or humble. If lucy is both strong and not creative then susan is either patient or not wise and vice versa. If alice is both not generous and strong then someone is either generous or not brave. Everyone who is not tall or calm is both strong and funny and vice versa. If someone is either not generous or not kind then alice is both not old and not generous and vice versa. Everyone who is both not tall and old is both wise and not quiet. Everyone who is happy or humble is both not tall and patient. If someone is both wise and tall then someone is either quiet or not tall. Everyone who is happy is generous and vice versa. If fred is both old and quiet then someone is both not funny and not quiet and vice versa. If alice is either not happy or not patient then susan is either creative or happy and vice versa. Everyone who is either happy or strong is not patient. If someone is both not kind and tall then alice is both not tall and not strong and vice versa. Susan is both patient and not generous. Someone is not old. Paul is both not tall and not kind. Someone is curious or kind. Alice is both not funny and brave. Lucy is quiet. Someone is not funny or old. | Susan is tall. | entailment | ((rich(john))=>((~calm(john)<~>generous(john))))&
(((~generous(fred)<~>brave(fred)))<=>((humble(paul)|rich(paul))))&
(![X]:((~creative(X)|humble(X))<=>strong(X)))&
(((wise(lucy)&~rich(lucy)))=>((~funny(alice)<~>humble(alice))))&
(((strong(lucy)&~creative(lucy)))<=>((patient(susan)<~>~wise(susan))))&
(((~generous(alice)&strong(alice)))=>(?[X]:((generous(X)<~>~brave(X)))))&
(![X]:((~tall(X)|calm(X))<=>(strong(X)&funny(X))))&
((?[X]:((~generous(X)<~>~kind(X))))<=>((~old(alice)&~generous(alice))))&
(![X]:((~tall(X)&old(X))=>(wise(X)&~quiet(X))))&
(![X]:((happy(X)|humble(X))=>(~tall(X)&patient(X))))&
((?[X]:((wise(X)&tall(X))))=>(?[X]:((quiet(X)<~>~tall(X)))))&
(![X]:(happy(X)<=>generous(X)))&
(((old(fred)&quiet(fred)))<=>(?[X]:((~funny(X)&~quiet(X)))))&
(((~happy(alice)<~>~patient(alice)))<=>((creative(susan)<~>happy(susan))))&
(![X]:((happy(X)<~>strong(X))=>~patient(X)))&
((?[X]:((~kind(X)&tall(X))))<=>((~tall(alice)&~strong(alice))))&
((patient(susan)&~generous(susan)))&
(?[X]:(~old(X)))&
((~tall(paul)&~kind(paul)))&
(?[X]:((curious(X)|kind(X))))&
((~funny(alice)&brave(alice)))&
(quiet(lucy))&
(?[X]:((~funny(X)|old(X)))) | tall(susan) | [
"p6",
"p11",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5623171762149170135686519
% SZS output start Proof for 5623171762149170135686519
7. ! [X0] : ((calm(X0) | ~tall(X0)) <=> (funny(X0) & strong(X0))) [input p6]
12. ! [X0] : (happy(X0) <=> generous(X0)) [input p11]
15. ! [X0] : ((happy(X0) <~> strong(X0)) => ~patient(X0)) [input p14]
17. ~generous(susan) & patient(susan) [input p16]
24. ~tall(susan) [input hypothesis]
36. ! [X0] : (~patient(X0) | (happy(X0) <=> strong(X0))) [ennf transformation 15]
48. ! [X0] : (((calm(X0) | ~tall(X0)) | (~funny(X0) | ~strong(X0))) & ((funny(X0) & strong(X0)) | (~calm(X0) & tall(X0)))) [nnf transformation 7]
49. ! [X0] : ((calm(X0) | ~tall(X0) | ~funny(X0) | ~strong(X0)) & ((funny(X0) & strong(X0)) | (~calm(X0) & tall(X0)))) [flattening 48]
59. ! [X0] : ((happy(X0) | ~generous(X0)) & (generous(X0) | ~happy(X0))) [nnf transformation 12]
66. ! [X0] : (~patient(X0) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) [nnf transformation 36]
97. tall(X0) | strong(X0) [cnf transformation 49]
116. ~happy(X0) | generous(X0) [cnf transformation 59]
131. ~patient(X0) | happy(X0) | ~strong(X0) [cnf transformation 66]
136. patient(susan) [cnf transformation 17]
137. ~generous(susan) [cnf transformation 17]
145. ~tall(susan) [cnf transformation 24]
205. 13 <=> patient(susan) [avatar definition]
207. patient(susan) <- (13) [avatar component clause 205]
304. 33 <=> happy(susan) [avatar definition]
305. happy(susan) <- (33) [avatar component clause 304]
338. 13 [avatar split clause 136,205]
352. strong(susan) [resolution 97,145]
408. happy(susan) | ~strong(susan) <- (13) [resolution 131,207]
413. happy(susan) <- (13) [subsumption resolution 408,352]
414. 33 | ~13 [avatar split clause 413,205,304]
421. generous(susan) <- (33) [resolution 305,116]
424. $false <- (33) [subsumption resolution 421,137]
425. ~33 [avatar contradiction clause 424]
426. $false [avatar sat refutation 338,414,425]
% SZS output end Proof for 5623171762149170135686519
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If john is either tall or quiet then alice is happy or not kind.
Everyone who is either not strong or patient is either not strong or not generous.
Everyone who is not old or old is either old or not old and vice versa.
Everyone who is both not calm and quiet is not quiet and vice versa.
If alice is brave or humble then someone is not funny.
If someone is both not patient and patient then fred is not calm or not strong and vice versa.
If someone is quiet or not curious then john is not creative or patient.
Everyone who is quiet is both curious and wise.
Everyone who is either not calm or not strong is both old and not brave and vice versa.
Everyone who is either not generous or calm is both not tall and not funny.
Everyone who is quiet or generous is humble or not wise.
Everyone who is either not humble or humble is humble and vice versa.
Everyone who is not generous is not creative.
Everyone who is not humble is both quiet and not kind and vice versa.
If mary is both happy and not generous then mary is both humble and calm.
If lucy is patient or not brave then alice is old and vice versa.
Lucy is not tall.
Someone is both patient and not strong.
Someone is not creative.
Someone is generous.
Someone is wise or tall.
Someone is patient.
Alice is funny or not brave. | Alice is humble. | entailment | (((tall(john)<~>quiet(john)))=>((happy(alice)|~kind(alice))))&
(![X]:((~strong(X)<~>patient(X))=>(~strong(X)<~>~generous(X))))&
(![X]:((~old(X)|old(X))<=>(old(X)<~>~old(X))))&
(![X]:((~calm(X)&quiet(X))<=>~quiet(X)))&
(((brave(alice)|humble(alice)))=>(?[X]:(~funny(X))))&
((?[X]:((~patient(X)&patient(X))))<=>((~calm(fred)|~strong(fred))))&
((?[X]:((quiet(X)|~curious(X))))=>((~creative(john)|patient(john))))&
(![X]:(quiet(X)=>(curious(X)&wise(X))))&
(![X]:((~calm(X)<~>~strong(X))<=>(old(X)&~brave(X))))&
(![X]:((~generous(X)<~>calm(X))=>(~tall(X)&~funny(X))))&
(![X]:((quiet(X)|generous(X))=>(humble(X)|~wise(X))))&
(![X]:((~humble(X)<~>humble(X))<=>humble(X)))&
(![X]:(~generous(X)=>~creative(X)))&
(![X]:(~humble(X)<=>(quiet(X)&~kind(X))))&
(((happy(mary)&~generous(mary)))=>((humble(mary)&calm(mary))))&
(((patient(lucy)|~brave(lucy)))<=>(old(alice)))&
(~tall(lucy))&
(?[X]:((patient(X)&~strong(X))))&
(?[X]:(~creative(X)))&
(?[X]:(generous(X)))&
(?[X]:((wise(X)|tall(X))))&
(?[X]:(patient(X)))&
((funny(alice)|~brave(alice))) | humble(alice) | [
"p3",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 924989868179545347700993
% SZS output start Proof for 924989868179545347700993
4. ! [X0] : ((quiet(X0) & ~calm(X0)) <=> ~quiet(X0)) [input p3]
8. ! [X0] : (quiet(X0) => (wise(X0) & curious(X0))) [input p7]
11. ! [X0] : ((generous(X0) | quiet(X0)) => (~wise(X0) | humble(X0))) [input p10]
24. ~humble(alice) [input hypothesis]
28. ! [X0] : (quiet(X0) => wise(X0)) [pure predicate removal 8]
33. ! [X0] : (wise(X0) | ~quiet(X0)) [ennf transformation 28]
35. ! [X0] : ((~wise(X0) | humble(X0)) | (~generous(X0) & ~quiet(X0))) [ennf transformation 11]
36. ! [X0] : (~wise(X0) | humble(X0) | (~generous(X0) & ~quiet(X0))) [flattening 35]
43. ! [X0] : (((quiet(X0) & ~calm(X0)) | quiet(X0)) & (~quiet(X0) | (~quiet(X0) | calm(X0)))) [nnf transformation 4]
44. ! [X0] : (((quiet(X0) & ~calm(X0)) | quiet(X0)) & (~quiet(X0) | ~quiet(X0) | calm(X0))) [flattening 43]
82. quiet(X0) | quiet(X0) [cnf transformation 44]
90. wise(X0) | ~quiet(X0) [cnf transformation 33]
101. ~wise(X0) | humble(X0) | ~quiet(X0) [cnf transformation 36]
122. ~humble(alice) [cnf transformation 24]
128. quiet(X0) [duplicate literal removal 82]
180. wise(X0) [subsumption resolution 90,128]
187. humble(X0) | ~quiet(X0) [subsumption resolution 101,180]
188. humble(X0) [subsumption resolution 187,128]
211. $false [subsumption resolution 122,188]
% SZS output end Proof for 924989868179545347700993
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both wise and not curious is either not humble or not creative and vice versa. Everyone who is not strong or not wise is curious or not funny and vice versa. If someone is either happy or creative then someone is rich or strong and vice versa. Everyone who is strong or patient is not humble. Everyone who is patient or not old is creative or curious. If someone is funny or strong then lucy is humble. If john is either not creative or calm then someone is not funny or not generous and vice versa. Everyone who is either not strong or not tall is both not generous and rich and vice versa. Everyone who is not kind or not curious is curious and vice versa. If someone is tall then fred is not rich or not humble and vice versa. Everyone who is not creative is both not strong and generous. Everyone who is not creative or not happy is not strong. If lucy is creative then someone is both wise and happy and vice versa. Everyone who is not tall is not kind or curious. If paul is both not quiet and rich then someone is either happy or not generous. If paul is both humble and brave then someone is either brave or creative and vice versa. Someone is either not funny or rich. Lucy is either generous or not curious. John is tall or not strong. Someone is not kind or not strong. Someone is tall or not strong. Susan is not humble. Paul is not creative. Someone is patient or creative. | Susan is not tall. | entailment | (![X]:((wise(X)&~curious(X))<=>(~humble(X)<~>~creative(X))))&
(![X]:((~strong(X)|~wise(X))<=>(curious(X)|~funny(X))))&
((?[X]:((happy(X)<~>creative(X))))<=>(?[X]:((rich(X)|strong(X)))))&
(![X]:((strong(X)|patient(X))=>~humble(X)))&
(![X]:((patient(X)|~old(X))=>(creative(X)|curious(X))))&
((?[X]:((funny(X)|strong(X))))=>(humble(lucy)))&
(((~creative(john)<~>calm(john)))<=>(?[X]:((~funny(X)|~generous(X)))))&
(![X]:((~strong(X)<~>~tall(X))<=>(~generous(X)&rich(X))))&
(![X]:((~kind(X)|~curious(X))<=>curious(X)))&
((?[X]:(tall(X)))<=>((~rich(fred)|~humble(fred))))&
(![X]:(~creative(X)=>(~strong(X)&generous(X))))&
(![X]:((~creative(X)|~happy(X))=>~strong(X)))&
((creative(lucy))<=>(?[X]:((wise(X)&happy(X)))))&
(![X]:(~tall(X)=>(~kind(X)|curious(X))))&
(((~quiet(paul)&rich(paul)))=>(?[X]:((happy(X)<~>~generous(X)))))&
(((humble(paul)&brave(paul)))<=>(?[X]:((brave(X)<~>creative(X)))))&
(?[X]:((~funny(X)<~>rich(X))))&
((generous(lucy)<~>~curious(lucy)))&
((tall(john)|~strong(john)))&
(?[X]:((~kind(X)|~strong(X))))&
(?[X]:((tall(X)|~strong(X))))&
(~humble(susan))&
(~creative(paul))&
(?[X]:((patient(X)|creative(X)))) | ~tall(susan) | [
"p0",
"p7",
"p8",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7637110977302860022153947
% SZS output start Proof for 7637110977302860022153947
1. ! [X0] : ((~curious(X0) & wise(X0)) <=> (~humble(X0) <~> ~creative(X0))) [input p0]
8. ! [X0] : ((~strong(X0) <~> ~tall(X0)) <=> (rich(X0) & ~generous(X0))) [input p7]
9. ! [X0] : ((~curious(X0) | ~kind(X0)) <=> curious(X0)) [input p8]
11. ! [X0] : (~creative(X0) => (generous(X0) & ~strong(X0))) [input p10]
22. ~humble(susan) [input p21]
25. tall(susan) [input hypothesis]
33. ! [X0] : ((generous(X0) & ~strong(X0)) | creative(X0)) [ennf transformation 11]
37. ! [X0] : (((~curious(X0) & wise(X0)) | ((~humble(X0) | creative(X0)) & (~creative(X0) | humble(X0)))) & (((creative(X0) | humble(X0)) & (~creative(X0) | ~humble(X0))) | (curious(X0) | ~wise(X0)))) [nnf transformation 1]
38. ! [X0] : (((~curious(X0) & wise(X0)) | ((~humble(X0) | creative(X0)) & (~creative(X0) | humble(X0)))) & (((creative(X0) | humble(X0)) & (~creative(X0) | ~humble(X0))) | curious(X0) | ~wise(X0))) [flattening 37]
50. ! [X0] : ((((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | (~rich(X0) | generous(X0))) & ((rich(X0) & ~generous(X0)) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))))) [nnf transformation 8]
51. ! [X0] : ((((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | ~rich(X0) | generous(X0)) & ((rich(X0) & ~generous(X0)) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))))) [flattening 50]
52. ! [X0] : (((~curious(X0) | ~kind(X0)) | ~curious(X0)) & (curious(X0) | (curious(X0) & kind(X0)))) [nnf transformation 9]
53. ! [X0] : ((~curious(X0) | ~kind(X0) | ~curious(X0)) & (curious(X0) | (curious(X0) & kind(X0)))) [flattening 52]
82. ~creative(X0) | ~curious(X0) | humble(X0) [cnf transformation 38]
105. ~tall(X0) | ~generous(X0) | strong(X0) [cnf transformation 51]
112. curious(X0) | curious(X0) [cnf transformation 53]
117. ~strong(X0) | creative(X0) [cnf transformation 33]
118. generous(X0) | creative(X0) [cnf transformation 33]
138. ~humble(susan) [cnf transformation 22]
141. tall(susan) [cnf transformation 25]
142. curious(X0) [duplicate literal removal 112]
361. ~generous(susan) | strong(susan) [resolution 105,141]
364. 44 <=> strong(susan) [avatar definition]
366. strong(susan) <- (44) [avatar component clause 364]
368. 45 <=> generous(susan) [avatar definition]
370. ~generous(susan) <- (~45) [avatar component clause 368]
371. 44 | ~45 [avatar split clause 361,368,364]
381. creative(susan) <- (~45) [resolution 370,118]
427. creative(susan) <- (44) [resolution 366,117]
551. ~curious(susan) | humble(susan) <- (~45) [resolution 381,82]
554. humble(susan) <- (~45) [subsumption resolution 551,142]
555. $false <- (~45) [subsumption resolution 554,138]
556. 45 [avatar contradiction clause 555]
568. ~curious(susan) | humble(susan) <- (44) [resolution 427,82]
571. humble(susan) <- (44) [subsumption resolution 568,142]
572. $false <- (44) [subsumption resolution 571,138]
573. ~44 [avatar contradiction clause 572]
577. $false [avatar sat refutation 371,556,573]
% SZS output end Proof for 7637110977302860022153947
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not rich or calm then mary is old or not generous and vice versa.
If someone is both not humble and not tall then alice is both not happy and generous and vice versa.
Everyone who is not generous is not brave or not kind.
If susan is not happy or not creative then alice is old or curious and vice versa.
If someone is either not creative or tall then someone is both brave and not tall.
If someone is not creative or brave then someone is old and vice versa.
Everyone who is funny is both quiet and humble and vice versa.
Everyone who is curious is not patient.
Everyone who is patient or not calm is either happy or not curious.
Everyone who is old or not calm is curious or not old.
Everyone who is rich or brave is not rich.
If someone is either patient or humble then john is either old or not creative and vice versa.
Everyone who is kind or not quiet is either old or not quiet.
Everyone who is not creative is quiet.
If alice is happy then mary is old or not happy.
Everyone who is both not brave and not old is either not funny or not humble and vice versa.
Fred is not quiet or not curious.
Someone is wise.
Susan is happy or kind.
Someone is humble or not generous.
Someone is either not happy or brave.
Susan is not tall or not rich.
Someone is funny or curious. | Fred is brave. | neutral | (((~rich(alice)|calm(alice)))<=>((old(mary)|~generous(mary))))&
((?[X]:((~humble(X)&~tall(X))))<=>((~happy(alice)&generous(alice))))&
(![X]:(~generous(X)=>(~brave(X)|~kind(X))))&
(((~happy(susan)|~creative(susan)))<=>((old(alice)|curious(alice))))&
((?[X]:((~creative(X)<~>tall(X))))=>(?[X]:((brave(X)&~tall(X)))))&
((?[X]:((~creative(X)|brave(X))))<=>(?[X]:(old(X))))&
(![X]:(funny(X)<=>(quiet(X)&humble(X))))&
(![X]:(curious(X)=>~patient(X)))&
(![X]:((patient(X)|~calm(X))=>(happy(X)<~>~curious(X))))&
(![X]:((old(X)|~calm(X))=>(curious(X)|~old(X))))&
(![X]:((rich(X)|brave(X))=>~rich(X)))&
((?[X]:((patient(X)<~>humble(X))))<=>((old(john)<~>~creative(john))))&
(![X]:((kind(X)|~quiet(X))=>(old(X)<~>~quiet(X))))&
(![X]:(~creative(X)=>quiet(X)))&
((happy(alice))=>((old(mary)|~happy(mary))))&
(![X]:((~brave(X)&~old(X))<=>(~funny(X)<~>~humble(X))))&
((~quiet(fred)|~curious(fred)))&
(?[X]:(wise(X)))&
((happy(susan)|kind(susan)))&
(?[X]:((humble(X)|~generous(X))))&
(?[X]:((~happy(X)<~>brave(X))))&
((~tall(susan)|~rich(susan)))&
(?[X]:((funny(X)|curious(X)))) | brave(fred) | [] | null | 0 |
If someone is not humble then someone is not happy or happy and vice versa. Everyone who is either not old or rich is not kind or curious. If someone is not old or quiet then someone is both not quiet and rich and vice versa. If someone is not wise or strong then someone is both rich and not brave. If someone is both not humble and creative then someone is both brave and not generous. If fred is either not kind or not happy then someone is happy or creative and vice versa. If someone is not strong then someone is both strong and not old and vice versa. If paul is patient then someone is both not kind and not patient and vice versa. Everyone who is brave or not funny is not old. Everyone who is kind is not old. If someone is funny then alice is either not kind or not brave and vice versa. Everyone who is patient is not wise or patient and vice versa. If alice is not funny then fred is curious or happy and vice versa. Everyone who is wise is not strong or not patient. Lucy is both not humble and funny. Someone is humble or not happy. Someone is not kind. Someone is not calm or not patient. Susan is either happy or not funny. Susan is either not kind or happy. Fred is either creative or curious. | Paul is calm. | neutral | ((?[X]:(~humble(X)))<=>(?[X]:((~happy(X)|happy(X)))))&
(![X]:((~old(X)<~>rich(X))=>(~kind(X)|curious(X))))&
((?[X]:((~old(X)|quiet(X))))<=>(?[X]:((~quiet(X)&rich(X)))))&
((?[X]:((~wise(X)|strong(X))))=>(?[X]:((rich(X)&~brave(X)))))&
((?[X]:((~humble(X)&creative(X))))=>(?[X]:((brave(X)&~generous(X)))))&
(((~kind(fred)<~>~happy(fred)))<=>(?[X]:((happy(X)|creative(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((strong(X)&~old(X)))))&
((patient(paul))<=>(?[X]:((~kind(X)&~patient(X)))))&
(![X]:((brave(X)|~funny(X))=>~old(X)))&
(![X]:(kind(X)=>~old(X)))&
((?[X]:(funny(X)))<=>((~kind(alice)<~>~brave(alice))))&
(![X]:(patient(X)<=>(~wise(X)|patient(X))))&
((~funny(alice))<=>((curious(fred)|happy(fred))))&
(![X]:(wise(X)=>(~strong(X)|~patient(X))))&
((~humble(lucy)&funny(lucy)))&
(?[X]:((humble(X)|~happy(X))))&
(?[X]:(~kind(X)))&
(?[X]:((~calm(X)|~patient(X))))&
((happy(susan)<~>~funny(susan)))&
((~kind(susan)<~>happy(susan)))&
((creative(fred)<~>curious(fred))) | calm(paul) | [] | null | 0 |
Everyone who is funny or humble is humble and vice versa. Everyone who is not tall or not generous is not tall. If someone is either not quiet or not humble then john is not tall and vice versa. Everyone who is either not strong or not wise is both curious and not kind and vice versa. Everyone who is not generous or generous is both not funny and calm and vice versa. If someone is not humble or not kind then john is not wise. Everyone who is patient is either old or not brave. If mary is either strong or not rich then john is not quiet and vice versa. Everyone who is not generous or not patient is both not curious and strong. If someone is both not patient and patient then someone is both patient and old and vice versa. Everyone who is rich is not funny and vice versa. If someone is humble then someone is not rich or strong and vice versa. If john is rich or not funny then someone is not kind. If someone is either calm or not kind then someone is either not brave or not tall and vice versa. If fred is kind or not quiet then someone is either not humble or strong and vice versa. Everyone who is both not happy and not funny is not rich or not generous and vice versa. Susan is not generous. Someone is either not happy or not strong. Someone is not humble or calm. Paul is not creative. Someone is tall or old. John is either not strong or not calm. Mary is patient. Someone is patient or not humble. | Paul is funny. | contradiction | (![X]:((funny(X)|humble(X))<=>humble(X)))&
(![X]:((~tall(X)|~generous(X))=>~tall(X)))&
((?[X]:((~quiet(X)<~>~humble(X))))<=>(~tall(john)))&
(![X]:((~strong(X)<~>~wise(X))<=>(curious(X)&~kind(X))))&
(![X]:((~generous(X)|generous(X))<=>(~funny(X)&calm(X))))&
((?[X]:((~humble(X)|~kind(X))))=>(~wise(john)))&
(![X]:(patient(X)=>(old(X)<~>~brave(X))))&
(((strong(mary)<~>~rich(mary)))<=>(~quiet(john)))&
(![X]:((~generous(X)|~patient(X))=>(~curious(X)&strong(X))))&
((?[X]:((~patient(X)&patient(X))))<=>(?[X]:((patient(X)&old(X)))))&
(![X]:(rich(X)<=>~funny(X)))&
((?[X]:(humble(X)))<=>(?[X]:((~rich(X)|strong(X)))))&
(((rich(john)|~funny(john)))=>(?[X]:(~kind(X))))&
((?[X]:((calm(X)<~>~kind(X))))<=>(?[X]:((~brave(X)<~>~tall(X)))))&
(((kind(fred)|~quiet(fred)))<=>(?[X]:((~humble(X)<~>strong(X)))))&
(![X]:((~happy(X)&~funny(X))<=>(~rich(X)|~generous(X))))&
(~generous(susan))&
(?[X]:((~happy(X)<~>~strong(X))))&
(?[X]:((~humble(X)|calm(X))))&
(~creative(paul))&
(?[X]:((tall(X)|old(X))))&
((~strong(john)<~>~calm(john)))&
(patient(mary))&
(?[X]:((patient(X)|~humble(X)))) | funny(paul) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 6472285939252567192871207
% SZS output start Proof for 6472285939252567192871207
5. ! [X0] : ((generous(X0) | ~generous(X0)) <=> (calm(X0) & ~funny(X0))) [input p4]
25. funny(paul) [input hypothesis]
43. ! [X0] : (((generous(X0) | ~generous(X0)) | (~calm(X0) | funny(X0))) & ((calm(X0) & ~funny(X0)) | (~generous(X0) & generous(X0)))) [nnf transformation 5]
44. ! [X0] : ((generous(X0) | ~generous(X0) | ~calm(X0) | funny(X0)) & ((calm(X0) & ~funny(X0)) | (~generous(X0) & generous(X0)))) [flattening 43]
97. ~funny(X0) | generous(X0) [cnf transformation 44]
98. ~funny(X0) | ~generous(X0) [cnf transformation 44]
153. funny(paul) [cnf transformation 25]
177. ~funny(X0) [subsumption resolution 97,98]
322. $false [subsumption resolution 153,177]
% SZS output end Proof for 6472285939252567192871207
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is patient then lucy is funny. If lucy is both calm and generous then someone is kind or not creative. Everyone who is either not tall or not generous is patient and vice versa. Everyone who is not generous or brave is not patient or curious. If alice is both happy and not quiet then john is either not tall or not wise and vice versa. Everyone who is either brave or not curious is not funny or not generous. If susan is generous or not happy then someone is either not strong or wise and vice versa. Everyone who is both patient and creative is either not funny or rich. Everyone who is both old and not patient is either not wise or quiet. If john is not patient or curious then alice is both kind and not calm. Everyone who is both quiet and not generous is both wise and not humble. Everyone who is not old or not wise is either not tall or curious. Everyone who is generous is not tall. If someone is not creative then someone is calm and vice versa. Everyone who is quiet or tall is both calm and not tall and vice versa. If fred is both not curious and not calm then someone is either not tall or not rich. Someone is both happy and not funny. Someone is not calm or not tall. Someone is funny or tall. Someone is both humble and rich. Susan is both humble and not quiet. Susan is patient or not quiet. Someone is curious. | John is not kind. | neutral | ((patient(mary))=>(funny(lucy)))&
(((calm(lucy)&generous(lucy)))=>(?[X]:((kind(X)|~creative(X)))))&
(![X]:((~tall(X)<~>~generous(X))<=>patient(X)))&
(![X]:((~generous(X)|brave(X))=>(~patient(X)|curious(X))))&
(((happy(alice)&~quiet(alice)))<=>((~tall(john)<~>~wise(john))))&
(![X]:((brave(X)<~>~curious(X))=>(~funny(X)|~generous(X))))&
(((generous(susan)|~happy(susan)))<=>(?[X]:((~strong(X)<~>wise(X)))))&
(![X]:((patient(X)&creative(X))=>(~funny(X)<~>rich(X))))&
(![X]:((old(X)&~patient(X))=>(~wise(X)<~>quiet(X))))&
(((~patient(john)|curious(john)))=>((kind(alice)&~calm(alice))))&
(![X]:((quiet(X)&~generous(X))=>(wise(X)&~humble(X))))&
(![X]:((~old(X)|~wise(X))=>(~tall(X)<~>curious(X))))&
(![X]:(generous(X)=>~tall(X)))&
((?[X]:(~creative(X)))<=>(?[X]:(calm(X))))&
(![X]:((quiet(X)|tall(X))<=>(calm(X)&~tall(X))))&
(((~curious(fred)&~calm(fred)))=>(?[X]:((~tall(X)<~>~rich(X)))))&
(?[X]:((happy(X)&~funny(X))))&
(?[X]:((~calm(X)|~tall(X))))&
(?[X]:((funny(X)|tall(X))))&
(?[X]:((humble(X)&rich(X))))&
((humble(susan)&~quiet(susan)))&
((patient(susan)|~quiet(susan)))&
(?[X]:(curious(X))) | ~kind(john) | [] | null | 0 |
Everyone who is both generous and not old is wise and vice versa. If mary is not rich then alice is both humble and not humble. If someone is both not generous and not old then lucy is creative or not kind and vice versa. If someone is both rich and not patient then john is both humble and curious and vice versa. If someone is kind then susan is either not wise or not brave and vice versa. If someone is creative then someone is either old or rich. Everyone who is not old is both quiet and creative. If alice is either not calm or not tall then someone is both not patient and wise and vice versa. If someone is not curious or humble then lucy is curious or not tall. Everyone who is generous is not patient or not calm and vice versa. Everyone who is either funny or not brave is creative or not creative and vice versa. If someone is both patient and quiet then someone is both not calm and calm and vice versa. If someone is not creative or not kind then someone is not curious and vice versa. If alice is both funny and not patient then susan is humble or happy and vice versa. Everyone who is rich is both not curious and not happy and vice versa. If paul is both not generous and generous then someone is calm. Mary is either not strong or not kind. Someone is both not kind and old. John is not calm or humble. Fred is not funny. Alice is happy. John is not kind. Lucy is brave or generous. Someone is both tall and not strong. | Paul is strong. | neutral | (![X]:((generous(X)&~old(X))<=>wise(X)))&
((~rich(mary))=>((humble(alice)&~humble(alice))))&
((?[X]:((~generous(X)&~old(X))))<=>((creative(lucy)|~kind(lucy))))&
((?[X]:((rich(X)&~patient(X))))<=>((humble(john)&curious(john))))&
((?[X]:(kind(X)))<=>((~wise(susan)<~>~brave(susan))))&
((?[X]:(creative(X)))=>(?[X]:((old(X)<~>rich(X)))))&
(![X]:(~old(X)=>(quiet(X)&creative(X))))&
(((~calm(alice)<~>~tall(alice)))<=>(?[X]:((~patient(X)&wise(X)))))&
((?[X]:((~curious(X)|humble(X))))=>((curious(lucy)|~tall(lucy))))&
(![X]:(generous(X)<=>(~patient(X)|~calm(X))))&
(![X]:((funny(X)<~>~brave(X))<=>(creative(X)|~creative(X))))&
((?[X]:((patient(X)&quiet(X))))<=>(?[X]:((~calm(X)&calm(X)))))&
((?[X]:((~creative(X)|~kind(X))))<=>(?[X]:(~curious(X))))&
(((funny(alice)&~patient(alice)))<=>((humble(susan)|happy(susan))))&
(![X]:(rich(X)<=>(~curious(X)&~happy(X))))&
(((~generous(paul)&generous(paul)))=>(?[X]:(calm(X))))&
((~strong(mary)<~>~kind(mary)))&
(?[X]:((~kind(X)&old(X))))&
((~calm(john)|humble(john)))&
(~funny(fred))&
(happy(alice))&
(~kind(john))&
((brave(lucy)|generous(lucy)))&
(?[X]:((tall(X)&~strong(X)))) | strong(paul) | [] | null | 0 |
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